Properties

Label 143.4.e.b.133.2
Level $143$
Weight $4$
Character 143.133
Analytic conductor $8.437$
Analytic rank $0$
Dimension $34$
CM no
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [143,4,Mod(100,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, 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("143.100");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.e (of order \(3\), degree \(2\), 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: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 133.2
Character \(\chi\) \(=\) 143.133
Dual form 143.4.e.b.100.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.09541 - 3.62936i) q^{2} +(-2.35272 - 4.07503i) q^{3} +(-4.78153 + 8.28185i) q^{4} +14.4259 q^{5} +(-9.85985 + 17.0778i) q^{6} +(17.3506 - 30.0521i) q^{7} +6.55048 q^{8} +(2.42942 - 4.20788i) q^{9} +O(q^{10})\) \(q+(-2.09541 - 3.62936i) q^{2} +(-2.35272 - 4.07503i) q^{3} +(-4.78153 + 8.28185i) q^{4} +14.4259 q^{5} +(-9.85985 + 17.0778i) q^{6} +(17.3506 - 30.0521i) q^{7} +6.55048 q^{8} +(2.42942 - 4.20788i) q^{9} +(-30.2283 - 52.3570i) q^{10} +(-5.50000 - 9.52628i) q^{11} +44.9984 q^{12} +(40.3094 - 23.9197i) q^{13} -145.427 q^{14} +(-33.9402 - 58.7861i) q^{15} +(24.5262 + 42.4807i) q^{16} +(37.6196 - 65.1590i) q^{17} -20.3626 q^{18} +(-25.2778 + 43.7824i) q^{19} +(-68.9779 + 119.473i) q^{20} -163.284 q^{21} +(-23.0496 + 39.9230i) q^{22} +(85.1614 + 147.504i) q^{23} +(-15.4114 - 26.6934i) q^{24} +83.1074 q^{25} +(-171.278 - 96.1758i) q^{26} -149.910 q^{27} +(165.925 + 287.390i) q^{28} +(132.876 + 230.149i) q^{29} +(-142.237 + 246.362i) q^{30} -134.471 q^{31} +(128.987 - 223.412i) q^{32} +(-25.8799 + 44.8253i) q^{33} -315.315 q^{34} +(250.298 - 433.530i) q^{35} +(23.2327 + 40.2402i) q^{36} +(3.68075 + 6.37524i) q^{37} +211.870 q^{38} +(-192.310 - 107.986i) q^{39} +94.4968 q^{40} +(-53.3593 - 92.4211i) q^{41} +(342.148 + 592.618i) q^{42} +(-218.702 + 378.803i) q^{43} +105.194 q^{44} +(35.0467 - 60.7026i) q^{45} +(356.897 - 618.163i) q^{46} -374.024 q^{47} +(115.407 - 199.890i) q^{48} +(-430.586 - 745.797i) q^{49} +(-174.144 - 301.627i) q^{50} -354.033 q^{51} +(5.35896 + 448.209i) q^{52} +650.058 q^{53} +(314.123 + 544.078i) q^{54} +(-79.3426 - 137.425i) q^{55} +(113.655 - 196.856i) q^{56} +237.886 q^{57} +(556.862 - 964.514i) q^{58} +(-139.299 + 241.272i) q^{59} +649.143 q^{60} +(-26.2898 + 45.5353i) q^{61} +(281.773 + 488.045i) q^{62} +(-84.3038 - 146.019i) q^{63} -688.707 q^{64} +(581.500 - 345.064i) q^{65} +216.917 q^{66} +(42.5053 + 73.6213i) q^{67} +(359.758 + 623.119i) q^{68} +(400.722 - 694.070i) q^{69} -2097.92 q^{70} +(-132.378 + 229.286i) q^{71} +(15.9139 - 27.5637i) q^{72} +269.190 q^{73} +(15.4254 - 26.7176i) q^{74} +(-195.528 - 338.665i) q^{75} +(-241.733 - 418.694i) q^{76} -381.713 q^{77} +(11.0506 + 924.239i) q^{78} +214.784 q^{79} +(353.814 + 612.823i) q^{80} +(287.101 + 497.274i) q^{81} +(-223.620 + 387.321i) q^{82} +1129.86 q^{83} +(780.748 - 1352.30i) q^{84} +(542.697 - 939.980i) q^{85} +1833.08 q^{86} +(625.242 - 1082.95i) q^{87} +(-36.0277 - 62.4017i) q^{88} +(436.827 + 756.606i) q^{89} -293.749 q^{90} +(-19.4459 - 1626.40i) q^{91} -1628.81 q^{92} +(316.373 + 547.974i) q^{93} +(783.734 + 1357.47i) q^{94} +(-364.656 + 631.602i) q^{95} -1213.88 q^{96} +(260.296 - 450.847i) q^{97} +(-1804.51 + 3125.51i) q^{98} -53.4473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.09541 3.62936i −0.740841 1.28317i −0.952113 0.305747i \(-0.901094\pi\)
0.211272 0.977427i \(-0.432239\pi\)
\(3\) −2.35272 4.07503i −0.452781 0.784240i 0.545777 0.837931i \(-0.316235\pi\)
−0.998558 + 0.0536910i \(0.982901\pi\)
\(4\) −4.78153 + 8.28185i −0.597691 + 1.03523i
\(5\) 14.4259 1.29029 0.645147 0.764058i \(-0.276796\pi\)
0.645147 + 0.764058i \(0.276796\pi\)
\(6\) −9.85985 + 17.0778i −0.670878 + 1.16199i
\(7\) 17.3506 30.0521i 0.936844 1.62266i 0.165531 0.986205i \(-0.447066\pi\)
0.771312 0.636457i \(-0.219601\pi\)
\(8\) 6.55048 0.289493
\(9\) 2.42942 4.20788i 0.0899786 0.155848i
\(10\) −30.2283 52.3570i −0.955903 1.65567i
\(11\) −5.50000 9.52628i −0.150756 0.261116i
\(12\) 44.9984 1.08249
\(13\) 40.3094 23.9197i 0.859986 0.510318i
\(14\) −145.427 −2.77621
\(15\) −33.9402 58.7861i −0.584221 1.01190i
\(16\) 24.5262 + 42.4807i 0.383222 + 0.663761i
\(17\) 37.6196 65.1590i 0.536711 0.929611i −0.462367 0.886689i \(-0.653000\pi\)
0.999078 0.0429226i \(-0.0136669\pi\)
\(18\) −20.3626 −0.266639
\(19\) −25.2778 + 43.7824i −0.305217 + 0.528652i −0.977310 0.211816i \(-0.932062\pi\)
0.672093 + 0.740467i \(0.265396\pi\)
\(20\) −68.9779 + 119.473i −0.771197 + 1.33575i
\(21\) −163.284 −1.69674
\(22\) −23.0496 + 39.9230i −0.223372 + 0.386892i
\(23\) 85.1614 + 147.504i 0.772060 + 1.33725i 0.936432 + 0.350848i \(0.114107\pi\)
−0.164372 + 0.986398i \(0.552560\pi\)
\(24\) −15.4114 26.6934i −0.131077 0.227032i
\(25\) 83.1074 0.664859
\(26\) −171.278 96.1758i −1.29194 0.725447i
\(27\) −149.910 −1.06852
\(28\) 165.925 + 287.390i 1.11989 + 1.93970i
\(29\) 132.876 + 230.149i 0.850846 + 1.47371i 0.880446 + 0.474147i \(0.157243\pi\)
−0.0295999 + 0.999562i \(0.509423\pi\)
\(30\) −142.237 + 246.362i −0.865629 + 1.49931i
\(31\) −134.471 −0.779088 −0.389544 0.921008i \(-0.627367\pi\)
−0.389544 + 0.921008i \(0.627367\pi\)
\(32\) 128.987 223.412i 0.712560 1.23419i
\(33\) −25.8799 + 44.8253i −0.136519 + 0.236457i
\(34\) −315.315 −1.59047
\(35\) 250.298 433.530i 1.20880 2.09371i
\(36\) 23.2327 + 40.2402i 0.107559 + 0.186297i
\(37\) 3.68075 + 6.37524i 0.0163544 + 0.0283266i 0.874087 0.485770i \(-0.161461\pi\)
−0.857732 + 0.514096i \(0.828127\pi\)
\(38\) 211.870 0.904469
\(39\) −192.310 107.986i −0.789597 0.443373i
\(40\) 94.4968 0.373531
\(41\) −53.3593 92.4211i −0.203252 0.352043i 0.746322 0.665585i \(-0.231818\pi\)
−0.949574 + 0.313542i \(0.898484\pi\)
\(42\) 342.148 + 592.618i 1.25702 + 2.17721i
\(43\) −218.702 + 378.803i −0.775621 + 1.34342i 0.158823 + 0.987307i \(0.449230\pi\)
−0.934445 + 0.356108i \(0.884103\pi\)
\(44\) 105.194 0.360421
\(45\) 35.0467 60.7026i 0.116099 0.201089i
\(46\) 356.897 618.163i 1.14395 1.98137i
\(47\) −374.024 −1.16079 −0.580393 0.814337i \(-0.697101\pi\)
−0.580393 + 0.814337i \(0.697101\pi\)
\(48\) 115.407 199.890i 0.347032 0.601076i
\(49\) −430.586 745.797i −1.25535 2.17434i
\(50\) −174.144 301.627i −0.492555 0.853130i
\(51\) −354.033 −0.972051
\(52\) 5.35896 + 448.209i 0.0142914 + 1.19530i
\(53\) 650.058 1.68476 0.842381 0.538882i \(-0.181153\pi\)
0.842381 + 0.538882i \(0.181153\pi\)
\(54\) 314.123 + 544.078i 0.791607 + 1.37110i
\(55\) −79.3426 137.425i −0.194519 0.336917i
\(56\) 113.655 196.856i 0.271210 0.469749i
\(57\) 237.886 0.552786
\(58\) 556.862 964.514i 1.26068 2.18357i
\(59\) −139.299 + 241.272i −0.307375 + 0.532390i −0.977787 0.209599i \(-0.932784\pi\)
0.670412 + 0.741989i \(0.266117\pi\)
\(60\) 649.143 1.39673
\(61\) −26.2898 + 45.5353i −0.0551815 + 0.0955771i −0.892297 0.451450i \(-0.850907\pi\)
0.837115 + 0.547027i \(0.184240\pi\)
\(62\) 281.773 + 488.045i 0.577180 + 0.999705i
\(63\) −84.3038 146.019i −0.168592 0.292010i
\(64\) −688.707 −1.34513
\(65\) 581.500 345.064i 1.10963 0.658460i
\(66\) 216.917 0.404554
\(67\) 42.5053 + 73.6213i 0.0775051 + 0.134243i 0.902173 0.431375i \(-0.141971\pi\)
−0.824668 + 0.565617i \(0.808638\pi\)
\(68\) 359.758 + 623.119i 0.641575 + 1.11124i
\(69\) 400.722 694.070i 0.699148 1.21096i
\(70\) −2097.92 −3.58213
\(71\) −132.378 + 229.286i −0.221273 + 0.383257i −0.955195 0.295978i \(-0.904355\pi\)
0.733921 + 0.679234i \(0.237688\pi\)
\(72\) 15.9139 27.5637i 0.0260482 0.0451168i
\(73\) 269.190 0.431593 0.215796 0.976438i \(-0.430765\pi\)
0.215796 + 0.976438i \(0.430765\pi\)
\(74\) 15.4254 26.7176i 0.0242320 0.0419710i
\(75\) −195.528 338.665i −0.301036 0.521409i
\(76\) −241.733 418.694i −0.364851 0.631940i
\(77\) −381.713 −0.564938
\(78\) 11.0506 + 924.239i 0.0160414 + 1.34166i
\(79\) 214.784 0.305887 0.152943 0.988235i \(-0.451125\pi\)
0.152943 + 0.988235i \(0.451125\pi\)
\(80\) 353.814 + 612.823i 0.494470 + 0.856446i
\(81\) 287.101 + 497.274i 0.393829 + 0.682132i
\(82\) −223.620 + 387.321i −0.301155 + 0.521615i
\(83\) 1129.86 1.49419 0.747095 0.664717i \(-0.231448\pi\)
0.747095 + 0.664717i \(0.231448\pi\)
\(84\) 780.748 1352.30i 1.01413 1.75652i
\(85\) 542.697 939.980i 0.692515 1.19947i
\(86\) 1833.08 2.29845
\(87\) 625.242 1082.95i 0.770494 1.33453i
\(88\) −36.0277 62.4017i −0.0436427 0.0755914i
\(89\) 436.827 + 756.606i 0.520264 + 0.901124i 0.999722 + 0.0235594i \(0.00749988\pi\)
−0.479458 + 0.877565i \(0.659167\pi\)
\(90\) −293.749 −0.344043
\(91\) −19.4459 1626.40i −0.0224010 1.87355i
\(92\) −1628.81 −1.84581
\(93\) 316.373 + 547.974i 0.352756 + 0.610992i
\(94\) 783.734 + 1357.47i 0.859958 + 1.48949i
\(95\) −364.656 + 631.602i −0.393820 + 0.682116i
\(96\) −1213.88 −1.29054
\(97\) 260.296 450.847i 0.272465 0.471923i −0.697027 0.717044i \(-0.745494\pi\)
0.969492 + 0.245121i \(0.0788278\pi\)
\(98\) −1804.51 + 3125.51i −1.86003 + 3.22167i
\(99\) −53.4473 −0.0542591
\(100\) −397.380 + 688.283i −0.397380 + 0.688283i
\(101\) 207.101 + 358.709i 0.204033 + 0.353395i 0.949824 0.312785i \(-0.101262\pi\)
−0.745792 + 0.666179i \(0.767928\pi\)
\(102\) 741.847 + 1284.92i 0.720135 + 1.24731i
\(103\) −1396.04 −1.33549 −0.667746 0.744389i \(-0.732741\pi\)
−0.667746 + 0.744389i \(0.732741\pi\)
\(104\) 264.046 156.686i 0.248960 0.147734i
\(105\) −2355.53 −2.18929
\(106\) −1362.14 2359.30i −1.24814 2.16184i
\(107\) −164.717 285.299i −0.148821 0.257765i 0.781971 0.623315i \(-0.214214\pi\)
−0.930792 + 0.365550i \(0.880881\pi\)
\(108\) 716.798 1241.53i 0.638647 1.10617i
\(109\) −726.701 −0.638581 −0.319290 0.947657i \(-0.603445\pi\)
−0.319290 + 0.947657i \(0.603445\pi\)
\(110\) −332.511 + 575.927i −0.288216 + 0.499204i
\(111\) 17.3195 29.9983i 0.0148099 0.0256515i
\(112\) 1702.18 1.43608
\(113\) −837.170 + 1450.02i −0.696941 + 1.20714i 0.272581 + 0.962133i \(0.412123\pi\)
−0.969522 + 0.245004i \(0.921211\pi\)
\(114\) −498.470 863.376i −0.409527 0.709321i
\(115\) 1228.53 + 2127.88i 0.996184 + 1.72544i
\(116\) −2541.41 −2.03417
\(117\) −2.72281 227.728i −0.00215149 0.179944i
\(118\) 1167.55 0.910865
\(119\) −1305.44 2261.10i −1.00563 1.74180i
\(120\) −222.324 385.077i −0.169128 0.292938i
\(121\) −60.5000 + 104.789i −0.0454545 + 0.0787296i
\(122\) 220.352 0.163523
\(123\) −251.079 + 434.882i −0.184057 + 0.318796i
\(124\) 642.977 1113.67i 0.465654 0.806536i
\(125\) −604.340 −0.432430
\(126\) −353.303 + 611.939i −0.249799 + 0.432665i
\(127\) −336.909 583.544i −0.235400 0.407726i 0.723989 0.689812i \(-0.242307\pi\)
−0.959389 + 0.282086i \(0.908973\pi\)
\(128\) 411.229 + 712.270i 0.283968 + 0.491846i
\(129\) 2058.18 1.40475
\(130\) −2470.85 1387.42i −1.66698 0.936040i
\(131\) 1455.87 0.970989 0.485495 0.874240i \(-0.338640\pi\)
0.485495 + 0.874240i \(0.338640\pi\)
\(132\) −247.491 428.667i −0.163192 0.282657i
\(133\) 877.170 + 1519.30i 0.571882 + 0.990528i
\(134\) 178.132 308.534i 0.114838 0.198905i
\(135\) −2162.59 −1.37871
\(136\) 246.426 426.823i 0.155374 0.269116i
\(137\) 1116.45 1933.75i 0.696239 1.20592i −0.273522 0.961866i \(-0.588189\pi\)
0.969761 0.244056i \(-0.0784781\pi\)
\(138\) −3358.71 −2.07183
\(139\) 652.130 1129.52i 0.397935 0.689244i −0.595536 0.803329i \(-0.703060\pi\)
0.993471 + 0.114085i \(0.0363936\pi\)
\(140\) 2393.62 + 4145.87i 1.44498 + 2.50278i
\(141\) 879.972 + 1524.16i 0.525582 + 0.910335i
\(142\) 1109.55 0.655714
\(143\) −449.568 252.440i −0.262900 0.147623i
\(144\) 238.338 0.137927
\(145\) 1916.87 + 3320.11i 1.09784 + 1.90152i
\(146\) −564.064 976.988i −0.319742 0.553809i
\(147\) −2026.10 + 3509.30i −1.13680 + 1.96900i
\(148\) −70.3984 −0.0390994
\(149\) 1135.03 1965.93i 0.624063 1.08091i −0.364659 0.931141i \(-0.618814\pi\)
0.988721 0.149767i \(-0.0478523\pi\)
\(150\) −819.426 + 1419.29i −0.446039 + 0.772562i
\(151\) 1327.17 0.715257 0.357629 0.933864i \(-0.383585\pi\)
0.357629 + 0.933864i \(0.383585\pi\)
\(152\) −165.582 + 286.796i −0.0883583 + 0.153041i
\(153\) −182.788 316.598i −0.0965851 0.167290i
\(154\) 799.847 + 1385.38i 0.418529 + 0.724914i
\(155\) −1939.87 −1.00525
\(156\) 1813.86 1076.35i 0.930928 0.552415i
\(157\) −554.004 −0.281620 −0.140810 0.990037i \(-0.544971\pi\)
−0.140810 + 0.990037i \(0.544971\pi\)
\(158\) −450.061 779.529i −0.226613 0.392506i
\(159\) −1529.41 2649.01i −0.762828 1.32126i
\(160\) 1860.76 3222.93i 0.919412 1.59247i
\(161\) 5910.40 2.89320
\(162\) 1203.19 2083.99i 0.583529 1.01070i
\(163\) 387.250 670.737i 0.186084 0.322308i −0.757857 0.652421i \(-0.773754\pi\)
0.943941 + 0.330113i \(0.107087\pi\)
\(164\) 1020.56 0.485927
\(165\) −373.342 + 646.647i −0.176149 + 0.305099i
\(166\) −2367.52 4100.66i −1.10696 1.91731i
\(167\) 325.532 + 563.839i 0.150841 + 0.261264i 0.931537 0.363647i \(-0.118468\pi\)
−0.780696 + 0.624911i \(0.785135\pi\)
\(168\) −1069.59 −0.491195
\(169\) 1052.69 1928.38i 0.479151 0.877733i
\(170\) −4548.71 −2.05218
\(171\) 122.821 + 212.732i 0.0549260 + 0.0951347i
\(172\) −2091.46 3622.51i −0.927163 1.60589i
\(173\) −1727.23 + 2991.65i −0.759069 + 1.31475i 0.184257 + 0.982878i \(0.441012\pi\)
−0.943326 + 0.331868i \(0.892321\pi\)
\(174\) −5240.56 −2.28325
\(175\) 1441.96 2497.55i 0.622869 1.07884i
\(176\) 269.789 467.287i 0.115546 0.200131i
\(177\) 1310.92 0.556695
\(178\) 1830.67 3170.81i 0.770866 1.33518i
\(179\) 944.081 + 1635.20i 0.394212 + 0.682795i 0.993000 0.118112i \(-0.0376843\pi\)
−0.598788 + 0.800907i \(0.704351\pi\)
\(180\) 335.153 + 580.502i 0.138782 + 0.240378i
\(181\) −3714.29 −1.52531 −0.762654 0.646807i \(-0.776104\pi\)
−0.762654 + 0.646807i \(0.776104\pi\)
\(182\) −5862.06 + 3478.57i −2.38750 + 1.41675i
\(183\) 247.410 0.0999405
\(184\) 557.848 + 966.221i 0.223506 + 0.387124i
\(185\) 53.0982 + 91.9688i 0.0211019 + 0.0365496i
\(186\) 1325.86 2296.46i 0.522673 0.905295i
\(187\) −827.631 −0.323649
\(188\) 1788.40 3097.61i 0.693791 1.20168i
\(189\) −2601.02 + 4505.11i −1.00104 + 1.73385i
\(190\) 3056.42 1.16703
\(191\) 472.908 819.101i 0.179154 0.310304i −0.762437 0.647063i \(-0.775997\pi\)
0.941591 + 0.336759i \(0.109331\pi\)
\(192\) 1620.33 + 2806.50i 0.609050 + 1.05490i
\(193\) 57.9300 + 100.338i 0.0216057 + 0.0374221i 0.876626 0.481172i \(-0.159789\pi\)
−0.855020 + 0.518594i \(0.826456\pi\)
\(194\) −2181.72 −0.807413
\(195\) −2774.25 1557.79i −1.01881 0.572081i
\(196\) 8235.43 3.00125
\(197\) 1257.50 + 2178.05i 0.454787 + 0.787715i 0.998676 0.0514425i \(-0.0163819\pi\)
−0.543889 + 0.839157i \(0.683049\pi\)
\(198\) 111.994 + 193.980i 0.0401974 + 0.0696239i
\(199\) 398.451 690.138i 0.141937 0.245842i −0.786289 0.617859i \(-0.788000\pi\)
0.928226 + 0.372017i \(0.121334\pi\)
\(200\) 544.394 0.192472
\(201\) 200.006 346.420i 0.0701857 0.121565i
\(202\) 867.924 1503.29i 0.302311 0.523619i
\(203\) 9221.94 3.18844
\(204\) 1692.82 2932.05i 0.580986 1.00630i
\(205\) −769.758 1333.26i −0.262255 0.454239i
\(206\) 2925.28 + 5066.73i 0.989388 + 1.71367i
\(207\) 827.572 0.277875
\(208\) 2004.76 + 1125.71i 0.668295 + 0.375259i
\(209\) 556.112 0.184053
\(210\) 4935.81 + 8549.07i 1.62192 + 2.80925i
\(211\) −84.7465 146.785i −0.0276502 0.0478915i 0.851869 0.523755i \(-0.175469\pi\)
−0.879519 + 0.475863i \(0.842136\pi\)
\(212\) −3108.27 + 5383.68i −1.00697 + 1.74412i
\(213\) 1245.80 0.400754
\(214\) −690.302 + 1195.64i −0.220505 + 0.381926i
\(215\) −3154.98 + 5464.58i −1.00078 + 1.73340i
\(216\) −981.982 −0.309331
\(217\) −2333.15 + 4041.14i −0.729884 + 1.26420i
\(218\) 1522.74 + 2637.46i 0.473087 + 0.819410i
\(219\) −633.328 1096.96i −0.195417 0.338472i
\(220\) 1517.51 0.465049
\(221\) −42.1627 3526.37i −0.0128333 1.07335i
\(222\) −145.166 −0.0438871
\(223\) 1428.61 + 2474.43i 0.429000 + 0.743050i 0.996785 0.0801271i \(-0.0255326\pi\)
−0.567784 + 0.823177i \(0.692199\pi\)
\(224\) −4476.01 7752.67i −1.33512 2.31249i
\(225\) 201.903 349.706i 0.0598231 0.103617i
\(226\) 7016.87 2.06529
\(227\) 147.869 256.117i 0.0432354 0.0748859i −0.843598 0.536975i \(-0.819567\pi\)
0.886833 + 0.462090i \(0.152900\pi\)
\(228\) −1137.46 + 1970.14i −0.330395 + 0.572261i
\(229\) −3805.61 −1.09817 −0.549087 0.835765i \(-0.685024\pi\)
−0.549087 + 0.835765i \(0.685024\pi\)
\(230\) 5148.57 8917.58i 1.47603 2.55656i
\(231\) 898.064 + 1555.49i 0.255793 + 0.443047i
\(232\) 870.405 + 1507.59i 0.246314 + 0.426629i
\(233\) −1773.05 −0.498526 −0.249263 0.968436i \(-0.580188\pi\)
−0.249263 + 0.968436i \(0.580188\pi\)
\(234\) −820.804 + 487.067i −0.229306 + 0.136071i
\(235\) −5395.64 −1.49776
\(236\) −1332.12 2307.30i −0.367431 0.636409i
\(237\) −505.326 875.250i −0.138500 0.239889i
\(238\) −5470.89 + 9475.87i −1.49002 + 2.58080i
\(239\) 1276.93 0.345597 0.172799 0.984957i \(-0.444719\pi\)
0.172799 + 0.984957i \(0.444719\pi\)
\(240\) 1664.85 2883.60i 0.447773 0.775565i
\(241\) −179.882 + 311.564i −0.0480797 + 0.0832765i −0.889064 0.457784i \(-0.848643\pi\)
0.840984 + 0.541060i \(0.181977\pi\)
\(242\) 507.090 0.134698
\(243\) −672.845 + 1165.40i −0.177626 + 0.307657i
\(244\) −251.411 435.457i −0.0659629 0.114251i
\(245\) −6211.60 10758.8i −1.61977 2.80553i
\(246\) 2104.46 0.545429
\(247\) 28.3305 + 2369.48i 0.00729807 + 0.610391i
\(248\) −880.851 −0.225541
\(249\) −2658.23 4604.20i −0.676541 1.17180i
\(250\) 1266.34 + 2193.37i 0.320362 + 0.554883i
\(251\) 600.203 1039.58i 0.150934 0.261426i −0.780637 0.624985i \(-0.785105\pi\)
0.931571 + 0.363559i \(0.118439\pi\)
\(252\) 1612.40 0.403063
\(253\) 936.775 1622.54i 0.232785 0.403195i
\(254\) −1411.93 + 2445.53i −0.348789 + 0.604120i
\(255\) −5107.26 −1.25423
\(256\) −1031.44 + 1786.50i −0.251816 + 0.436157i
\(257\) −2223.57 3851.33i −0.539698 0.934784i −0.998920 0.0464625i \(-0.985205\pi\)
0.459222 0.888321i \(-0.348128\pi\)
\(258\) −4312.73 7469.87i −1.04069 1.80253i
\(259\) 255.453 0.0612859
\(260\) 77.3080 + 6465.83i 0.0184402 + 1.54228i
\(261\) 1291.25 0.306232
\(262\) −3050.64 5283.87i −0.719349 1.24595i
\(263\) 1263.22 + 2187.96i 0.296173 + 0.512986i 0.975257 0.221074i \(-0.0709562\pi\)
−0.679084 + 0.734060i \(0.737623\pi\)
\(264\) −169.526 + 293.628i −0.0395212 + 0.0684528i
\(265\) 9377.70 2.17384
\(266\) 3676.07 6367.14i 0.847347 1.46765i
\(267\) 2055.46 3560.16i 0.471132 0.816024i
\(268\) −812.960 −0.185296
\(269\) −2043.23 + 3538.98i −0.463115 + 0.802138i −0.999114 0.0420799i \(-0.986602\pi\)
0.535999 + 0.844218i \(0.319935\pi\)
\(270\) 4531.52 + 7848.82i 1.02141 + 1.76913i
\(271\) −2947.04 5104.43i −0.660591 1.14418i −0.980461 0.196715i \(-0.936973\pi\)
0.319870 0.947461i \(-0.396361\pi\)
\(272\) 3690.67 0.822719
\(273\) −6581.89 + 3905.71i −1.45917 + 0.865877i
\(274\) −9357.71 −2.06321
\(275\) −457.091 791.704i −0.100231 0.173606i
\(276\) 3832.12 + 6637.43i 0.835749 + 1.44756i
\(277\) −222.600 + 385.555i −0.0482844 + 0.0836309i −0.889157 0.457601i \(-0.848709\pi\)
0.840873 + 0.541232i \(0.182042\pi\)
\(278\) −5465.93 −1.17923
\(279\) −326.687 + 565.839i −0.0701012 + 0.121419i
\(280\) 1639.58 2839.83i 0.349941 0.606115i
\(281\) 1700.06 0.360914 0.180457 0.983583i \(-0.442242\pi\)
0.180457 + 0.983583i \(0.442242\pi\)
\(282\) 3687.81 6387.48i 0.778745 1.34883i
\(283\) −4031.35 6982.51i −0.846781 1.46667i −0.884066 0.467363i \(-0.845204\pi\)
0.0372848 0.999305i \(-0.488129\pi\)
\(284\) −1265.94 2192.67i −0.264506 0.458138i
\(285\) 3431.73 0.713257
\(286\) 25.8331 + 2160.61i 0.00534107 + 0.446712i
\(287\) −3703.26 −0.761661
\(288\) −626.729 1085.53i −0.128230 0.222101i
\(289\) −373.967 647.730i −0.0761179 0.131840i
\(290\) 8033.26 13914.0i 1.62665 2.81744i
\(291\) −2449.62 −0.493468
\(292\) −1287.14 + 2229.39i −0.257959 + 0.446798i
\(293\) 1903.70 3297.31i 0.379575 0.657442i −0.611426 0.791302i \(-0.709404\pi\)
0.991000 + 0.133859i \(0.0427370\pi\)
\(294\) 16982.0 3.36875
\(295\) −2009.51 + 3480.58i −0.396605 + 0.686939i
\(296\) 24.1107 + 41.7609i 0.00473448 + 0.00820035i
\(297\) 824.504 + 1428.08i 0.161086 + 0.279009i
\(298\) −9513.44 −1.84932
\(299\) 6961.05 + 3908.75i 1.34638 + 0.756017i
\(300\) 3739.70 0.719705
\(301\) 7589.21 + 13144.9i 1.45327 + 2.51714i
\(302\) −2780.98 4816.80i −0.529892 0.917800i
\(303\) 974.499 1687.88i 0.184764 0.320021i
\(304\) −2479.88 −0.467864
\(305\) −379.255 + 656.889i −0.0712003 + 0.123323i
\(306\) −766.032 + 1326.81i −0.143108 + 0.247871i
\(307\) −7435.92 −1.38238 −0.691189 0.722674i \(-0.742913\pi\)
−0.691189 + 0.722674i \(0.742913\pi\)
\(308\) 1825.17 3161.29i 0.337658 0.584841i
\(309\) 3284.49 + 5688.90i 0.604686 + 1.04735i
\(310\) 4064.83 + 7040.50i 0.744732 + 1.28991i
\(311\) −3396.84 −0.619347 −0.309674 0.950843i \(-0.600220\pi\)
−0.309674 + 0.950843i \(0.600220\pi\)
\(312\) −1259.72 707.358i −0.228583 0.128353i
\(313\) 1123.70 0.202925 0.101462 0.994839i \(-0.467648\pi\)
0.101462 + 0.994839i \(0.467648\pi\)
\(314\) 1160.87 + 2010.68i 0.208636 + 0.361368i
\(315\) −1216.16 2106.45i −0.217533 0.376778i
\(316\) −1026.99 + 1778.81i −0.182826 + 0.316663i
\(317\) −2824.61 −0.500460 −0.250230 0.968186i \(-0.580506\pi\)
−0.250230 + 0.968186i \(0.580506\pi\)
\(318\) −6409.48 + 11101.5i −1.13027 + 1.95768i
\(319\) 1461.64 2531.64i 0.256540 0.444340i
\(320\) −9935.24 −1.73561
\(321\) −775.067 + 1342.45i −0.134766 + 0.233422i
\(322\) −12384.7 21451.0i −2.14340 3.71248i
\(323\) 1901.88 + 3294.15i 0.327627 + 0.567466i
\(324\) −5491.13 −0.941552
\(325\) 3350.01 1987.91i 0.571769 0.339290i
\(326\) −3245.80 −0.551436
\(327\) 1709.72 + 2961.33i 0.289137 + 0.500801i
\(328\) −349.529 605.403i −0.0588400 0.101914i
\(329\) −6489.53 + 11240.2i −1.08748 + 1.88356i
\(330\) 3129.22 0.521994
\(331\) 816.053 1413.45i 0.135512 0.234713i −0.790281 0.612744i \(-0.790066\pi\)
0.925793 + 0.378031i \(0.123399\pi\)
\(332\) −5402.44 + 9357.29i −0.893064 + 1.54683i
\(333\) 35.7684 0.00588617
\(334\) 1364.25 2362.95i 0.223498 0.387111i
\(335\) 613.178 + 1062.06i 0.100004 + 0.173213i
\(336\) −4004.75 6936.43i −0.650229 1.12623i
\(337\) 3066.09 0.495609 0.247805 0.968810i \(-0.420291\pi\)
0.247805 + 0.968810i \(0.420291\pi\)
\(338\) −9204.62 + 220.140i −1.48126 + 0.0354261i
\(339\) 7878.50 1.26225
\(340\) 5189.84 + 8989.07i 0.827820 + 1.43383i
\(341\) 739.591 + 1281.01i 0.117452 + 0.203433i
\(342\) 514.722 891.524i 0.0813829 0.140959i
\(343\) −17981.2 −2.83059
\(344\) −1432.60 + 2481.34i −0.224537 + 0.388910i
\(345\) 5780.78 10012.6i 0.902107 1.56249i
\(346\) 14477.1 2.24940
\(347\) 2926.59 5069.00i 0.452759 0.784202i −0.545797 0.837917i \(-0.683773\pi\)
0.998556 + 0.0537154i \(0.0171064\pi\)
\(348\) 5979.22 + 10356.3i 0.921034 + 1.59528i
\(349\) 1252.10 + 2168.70i 0.192044 + 0.332631i 0.945928 0.324378i \(-0.105155\pi\)
−0.753883 + 0.657008i \(0.771822\pi\)
\(350\) −12086.0 −1.84579
\(351\) −6042.78 + 3585.80i −0.918916 + 0.545287i
\(352\) −2837.72 −0.429690
\(353\) 497.326 + 861.393i 0.0749857 + 0.129879i 0.901080 0.433653i \(-0.142776\pi\)
−0.826094 + 0.563532i \(0.809442\pi\)
\(354\) −2746.93 4757.82i −0.412422 0.714337i
\(355\) −1909.68 + 3307.66i −0.285508 + 0.494514i
\(356\) −8354.79 −1.24383
\(357\) −6142.69 + 10639.4i −0.910660 + 1.57731i
\(358\) 3956.48 6852.83i 0.584097 1.01168i
\(359\) −8022.18 −1.17937 −0.589686 0.807633i \(-0.700749\pi\)
−0.589686 + 0.807633i \(0.700749\pi\)
\(360\) 229.573 397.632i 0.0336098 0.0582139i
\(361\) 2151.57 + 3726.62i 0.313685 + 0.543318i
\(362\) 7782.97 + 13480.5i 1.13001 + 1.95724i
\(363\) 569.358 0.0823238
\(364\) 13562.6 + 7615.64i 1.95295 + 1.09662i
\(365\) 3883.31 0.556882
\(366\) −518.427 897.943i −0.0740400 0.128241i
\(367\) 2336.69 + 4047.27i 0.332355 + 0.575656i 0.982973 0.183749i \(-0.0588234\pi\)
−0.650618 + 0.759405i \(0.725490\pi\)
\(368\) −4177.37 + 7235.43i −0.591741 + 1.02493i
\(369\) −518.530 −0.0731533
\(370\) 222.526 385.426i 0.0312664 0.0541549i
\(371\) 11278.9 19535.6i 1.57836 2.73380i
\(372\) −6050.98 −0.843356
\(373\) 2483.97 4302.36i 0.344812 0.597232i −0.640507 0.767952i \(-0.721276\pi\)
0.985320 + 0.170720i \(0.0546092\pi\)
\(374\) 1734.23 + 3003.77i 0.239772 + 0.415298i
\(375\) 1421.84 + 2462.70i 0.195796 + 0.339129i
\(376\) −2450.04 −0.336040
\(377\) 10861.3 + 6098.79i 1.48378 + 0.833166i
\(378\) 21800.9 2.96645
\(379\) −1599.33 2770.11i −0.216759 0.375438i 0.737056 0.675832i \(-0.236215\pi\)
−0.953815 + 0.300393i \(0.902882\pi\)
\(380\) −3487.22 6040.05i −0.470765 0.815389i
\(381\) −1585.31 + 2745.83i −0.213170 + 0.369221i
\(382\) −3963.75 −0.530899
\(383\) −180.575 + 312.766i −0.0240913 + 0.0417273i −0.877820 0.478991i \(-0.841003\pi\)
0.853728 + 0.520719i \(0.174336\pi\)
\(384\) 1935.01 3351.54i 0.257150 0.445397i
\(385\) −5506.56 −0.728936
\(386\) 242.775 420.498i 0.0320127 0.0554476i
\(387\) 1062.64 + 1840.54i 0.139579 + 0.241757i
\(388\) 2489.23 + 4311.47i 0.325700 + 0.564128i
\(389\) −7648.28 −0.996872 −0.498436 0.866927i \(-0.666092\pi\)
−0.498436 + 0.866927i \(0.666092\pi\)
\(390\) 159.415 + 13333.0i 0.0206981 + 1.73114i
\(391\) 12814.9 1.65749
\(392\) −2820.55 4885.33i −0.363416 0.629455i
\(393\) −3425.24 5932.70i −0.439646 0.761488i
\(394\) 5269.97 9127.85i 0.673850 1.16714i
\(395\) 3098.45 0.394684
\(396\) 255.560 442.642i 0.0324302 0.0561707i
\(397\) 6417.23 11115.0i 0.811264 1.40515i −0.100717 0.994915i \(-0.532114\pi\)
0.911980 0.410235i \(-0.134553\pi\)
\(398\) −3339.68 −0.420611
\(399\) 4127.47 7148.98i 0.517874 0.896985i
\(400\) 2038.31 + 3530.46i 0.254789 + 0.441307i
\(401\) 74.5201 + 129.073i 0.00928020 + 0.0160738i 0.870628 0.491942i \(-0.163713\pi\)
−0.861348 + 0.508015i \(0.830379\pi\)
\(402\) −1676.38 −0.207986
\(403\) −5420.45 + 3216.51i −0.670004 + 0.397583i
\(404\) −3961.03 −0.487793
\(405\) 4141.70 + 7173.64i 0.508155 + 0.880151i
\(406\) −19323.8 33469.8i −2.36213 4.09132i
\(407\) 40.4882 70.1277i 0.00493103 0.00854079i
\(408\) −2319.09 −0.281402
\(409\) 877.721 1520.26i 0.106114 0.183794i −0.808079 0.589074i \(-0.799493\pi\)
0.914193 + 0.405280i \(0.132826\pi\)
\(410\) −3225.92 + 5587.47i −0.388578 + 0.673037i
\(411\) −10506.8 −1.26098
\(412\) 6675.19 11561.8i 0.798211 1.38254i
\(413\) 4833.83 + 8372.44i 0.575925 + 0.997532i
\(414\) −1734.11 3003.56i −0.205862 0.356563i
\(415\) 16299.2 1.92795
\(416\) −144.564 12091.0i −0.0170381 1.42502i
\(417\) −6137.12 −0.720710
\(418\) −1165.28 2018.33i −0.136354 0.236172i
\(419\) 3454.05 + 5982.59i 0.402724 + 0.697538i 0.994054 0.108892i \(-0.0347302\pi\)
−0.591330 + 0.806430i \(0.701397\pi\)
\(420\) 11263.0 19508.1i 1.30852 2.26643i
\(421\) 12297.9 1.42366 0.711831 0.702350i \(-0.247866\pi\)
0.711831 + 0.702350i \(0.247866\pi\)
\(422\) −355.158 + 615.152i −0.0409688 + 0.0709600i
\(423\) −908.661 + 1573.85i −0.104446 + 0.180906i
\(424\) 4258.20 0.487727
\(425\) 3126.47 5415.20i 0.356837 0.618060i
\(426\) −2610.46 4521.45i −0.296895 0.514237i
\(427\) 912.288 + 1580.13i 0.103393 + 0.179082i
\(428\) 3150.40 0.355795
\(429\) 29.0053 + 2425.92i 0.00326431 + 0.273018i
\(430\) 26443.9 2.96567
\(431\) −744.496 1289.50i −0.0832044 0.144114i 0.821420 0.570323i \(-0.193182\pi\)
−0.904625 + 0.426209i \(0.859849\pi\)
\(432\) −3676.72 6368.27i −0.409482 0.709244i
\(433\) −5674.97 + 9829.34i −0.629842 + 1.09092i 0.357741 + 0.933821i \(0.383547\pi\)
−0.987583 + 0.157098i \(0.949786\pi\)
\(434\) 19555.7 2.16291
\(435\) 9019.69 15622.6i 0.994164 1.72194i
\(436\) 3474.74 6018.42i 0.381674 0.661079i
\(437\) −8610.77 −0.942584
\(438\) −2654.17 + 4597.16i −0.289546 + 0.501508i
\(439\) 1619.30 + 2804.70i 0.176047 + 0.304923i 0.940523 0.339729i \(-0.110335\pi\)
−0.764476 + 0.644652i \(0.777002\pi\)
\(440\) −519.732 900.203i −0.0563120 0.0975352i
\(441\) −4184.30 −0.451820
\(442\) −12710.1 + 7542.23i −1.36778 + 0.811646i
\(443\) 10922.8 1.17146 0.585730 0.810506i \(-0.300808\pi\)
0.585730 + 0.810506i \(0.300808\pi\)
\(444\) 165.628 + 286.876i 0.0177035 + 0.0306633i
\(445\) 6301.63 + 10914.7i 0.671294 + 1.16272i
\(446\) 5987.08 10369.9i 0.635642 1.10096i
\(447\) −10681.6 −1.13025
\(448\) −11949.5 + 20697.1i −1.26018 + 2.18269i
\(449\) −6850.47 + 11865.4i −0.720030 + 1.24713i 0.240957 + 0.970536i \(0.422539\pi\)
−0.960987 + 0.276593i \(0.910795\pi\)
\(450\) −1692.28 −0.177278
\(451\) −586.953 + 1016.63i −0.0612828 + 0.106145i
\(452\) −8005.90 13866.6i −0.833110 1.44299i
\(453\) −3122.47 5408.27i −0.323855 0.560933i
\(454\) −1239.39 −0.128122
\(455\) −280.526 23462.4i −0.0289038 2.41744i
\(456\) 1558.27 0.160028
\(457\) −402.806 697.681i −0.0412308 0.0714138i 0.844674 0.535282i \(-0.179795\pi\)
−0.885904 + 0.463868i \(0.846461\pi\)
\(458\) 7974.33 + 13811.9i 0.813572 + 1.40915i
\(459\) −5639.55 + 9767.98i −0.573489 + 0.993312i
\(460\) −23497.0 −2.38164
\(461\) 2587.56 4481.79i 0.261420 0.452793i −0.705199 0.709009i \(-0.749142\pi\)
0.966620 + 0.256216i \(0.0824758\pi\)
\(462\) 3763.63 6518.80i 0.379004 0.656455i
\(463\) 2642.44 0.265237 0.132618 0.991167i \(-0.457662\pi\)
0.132618 + 0.991167i \(0.457662\pi\)
\(464\) −6517.92 + 11289.4i −0.652126 + 1.12952i
\(465\) 4563.97 + 7905.03i 0.455159 + 0.788359i
\(466\) 3715.28 + 6435.06i 0.369329 + 0.639696i
\(467\) 6618.54 0.655823 0.327912 0.944708i \(-0.393655\pi\)
0.327912 + 0.944708i \(0.393655\pi\)
\(468\) 1899.03 + 1066.34i 0.187570 + 0.105324i
\(469\) 2949.97 0.290441
\(470\) 11306.1 + 19582.7i 1.10960 + 1.92188i
\(471\) 1303.42 + 2257.58i 0.127512 + 0.220858i
\(472\) −912.474 + 1580.45i −0.0889831 + 0.154123i
\(473\) 4811.44 0.467717
\(474\) −2117.73 + 3668.02i −0.205213 + 0.355439i
\(475\) −2100.77 + 3638.64i −0.202926 + 0.351479i
\(476\) 24968.1 2.40422
\(477\) 1579.27 2735.37i 0.151593 0.262566i
\(478\) −2675.70 4634.44i −0.256032 0.443461i
\(479\) −7485.77 12965.7i −0.714057 1.23678i −0.963322 0.268348i \(-0.913522\pi\)
0.249265 0.968435i \(-0.419811\pi\)
\(480\) −17511.4 −1.66517
\(481\) 300.863 + 168.940i 0.0285201 + 0.0160145i
\(482\) 1507.71 0.142478
\(483\) −13905.5 24085.1i −1.30999 2.26896i
\(484\) −578.565 1002.10i −0.0543355 0.0941119i
\(485\) 3755.02 6503.88i 0.351560 0.608920i
\(486\) 5639.56 0.526369
\(487\) 43.8445 75.9409i 0.00407964 0.00706614i −0.863978 0.503529i \(-0.832035\pi\)
0.868058 + 0.496463i \(0.165368\pi\)
\(488\) −172.211 + 298.278i −0.0159747 + 0.0276689i
\(489\) −3644.36 −0.337022
\(490\) −26031.8 + 45088.3i −2.39999 + 4.15691i
\(491\) −8543.16 14797.2i −0.785229 1.36006i −0.928862 0.370426i \(-0.879212\pi\)
0.143633 0.989631i \(-0.454122\pi\)
\(492\) −2401.08 4158.80i −0.220019 0.381083i
\(493\) 19995.0 1.82663
\(494\) 8540.35 5067.87i 0.777831 0.461567i
\(495\) −771.027 −0.0700103
\(496\) −3298.07 5712.42i −0.298564 0.517128i
\(497\) 4593.68 + 7956.49i 0.414597 + 0.718104i
\(498\) −11140.2 + 19295.4i −1.00242 + 1.73624i
\(499\) −1104.76 −0.0991099 −0.0495550 0.998771i \(-0.515780\pi\)
−0.0495550 + 0.998771i \(0.515780\pi\)
\(500\) 2889.67 5005.05i 0.258460 0.447665i
\(501\) 1531.77 2653.11i 0.136596 0.236591i
\(502\) −5030.70 −0.447273
\(503\) 2760.02 4780.50i 0.244659 0.423761i −0.717377 0.696685i \(-0.754657\pi\)
0.962036 + 0.272924i \(0.0879908\pi\)
\(504\) −552.231 956.492i −0.0488062 0.0845348i
\(505\) 2987.62 + 5174.71i 0.263262 + 0.455983i
\(506\) −7851.73 −0.689826
\(507\) −10334.9 + 247.172i −0.905303 + 0.0216514i
\(508\) 6443.76 0.562787
\(509\) −4321.09 7484.35i −0.376285 0.651745i 0.614233 0.789124i \(-0.289465\pi\)
−0.990518 + 0.137380i \(0.956132\pi\)
\(510\) 10701.8 + 18536.1i 0.929186 + 1.60940i
\(511\) 4670.60 8089.72i 0.404335 0.700329i
\(512\) 15224.8 1.31416
\(513\) 3789.39 6563.42i 0.326132 0.564877i
\(514\) −9318.59 + 16140.3i −0.799660 + 1.38505i
\(515\) −20139.1 −1.72318
\(516\) −9841.22 + 17045.5i −0.839604 + 1.45424i
\(517\) 2057.13 + 3563.05i 0.174995 + 0.303100i
\(518\) −535.279 927.131i −0.0454031 0.0786405i
\(519\) 16254.8 1.37477
\(520\) 3809.11 2260.34i 0.321232 0.190620i
\(521\) 1763.72 0.148311 0.0741553 0.997247i \(-0.476374\pi\)
0.0741553 + 0.997247i \(0.476374\pi\)
\(522\) −2705.71 4686.42i −0.226869 0.392949i
\(523\) −10607.1 18372.1i −0.886839 1.53605i −0.843591 0.536986i \(-0.819563\pi\)
−0.0432477 0.999064i \(-0.513770\pi\)
\(524\) −6961.26 + 12057.3i −0.580351 + 1.00520i
\(525\) −13570.1 −1.12809
\(526\) 5293.94 9169.37i 0.438834 0.760083i
\(527\) −5058.75 + 8762.01i −0.418145 + 0.724249i
\(528\) −2538.95 −0.209268
\(529\) −8421.42 + 14586.3i −0.692153 + 1.19884i
\(530\) −19650.2 34035.1i −1.61047 2.78941i
\(531\) 676.831 + 1172.31i 0.0553144 + 0.0958074i
\(532\) −16776.8 −1.36723
\(533\) −4361.57 2449.10i −0.354447 0.199029i
\(534\) −17228.2 −1.39613
\(535\) −2376.20 4115.70i −0.192022 0.332593i
\(536\) 278.430 + 482.255i 0.0224372 + 0.0388624i
\(537\) 4442.32 7694.32i 0.356983 0.618313i
\(538\) 17125.7 1.37238
\(539\) −4736.45 + 8203.77i −0.378503 + 0.655587i
\(540\) 10340.5 17910.2i 0.824043 1.42728i
\(541\) −7949.82 −0.631773 −0.315887 0.948797i \(-0.602302\pi\)
−0.315887 + 0.948797i \(0.602302\pi\)
\(542\) −12350.6 + 21391.8i −0.978785 + 1.69531i
\(543\) 8738.67 + 15135.8i 0.690630 + 1.19621i
\(544\) −9704.89 16809.4i −0.764878 1.32481i
\(545\) −10483.3 −0.823957
\(546\) 27967.1 + 15704.0i 2.19209 + 1.23090i
\(547\) −2367.88 −0.185089 −0.0925443 0.995709i \(-0.529500\pi\)
−0.0925443 + 0.995709i \(0.529500\pi\)
\(548\) 10676.7 + 18492.5i 0.832272 + 1.44154i
\(549\) 127.738 + 221.249i 0.00993030 + 0.0171998i
\(550\) −1915.59 + 3317.90i −0.148511 + 0.257228i
\(551\) −13435.3 −1.03877
\(552\) 2624.92 4546.50i 0.202399 0.350565i
\(553\) 3726.62 6454.70i 0.286568 0.496351i
\(554\) 1865.76 0.143084
\(555\) 249.850 432.754i 0.0191091 0.0330980i
\(556\) 6236.36 + 10801.7i 0.475684 + 0.823909i
\(557\) 6926.22 + 11996.6i 0.526882 + 0.912587i 0.999509 + 0.0313241i \(0.00997240\pi\)
−0.472627 + 0.881262i \(0.656694\pi\)
\(558\) 2738.18 0.207735
\(559\) 245.113 + 20500.6i 0.0185459 + 1.55113i
\(560\) 24555.5 1.85296
\(561\) 1947.18 + 3372.62i 0.146542 + 0.253818i
\(562\) −3562.32 6170.13i −0.267380 0.463116i
\(563\) −914.505 + 1583.97i −0.0684579 + 0.118572i −0.898223 0.439541i \(-0.855141\pi\)
0.829765 + 0.558113i \(0.188475\pi\)
\(564\) −16830.4 −1.25654
\(565\) −12076.9 + 20917.9i −0.899259 + 1.55756i
\(566\) −16894.7 + 29262.5i −1.25466 + 2.17313i
\(567\) 19925.5 1.47583
\(568\) −867.142 + 1501.93i −0.0640571 + 0.110950i
\(569\) 669.855 + 1160.22i 0.0493528 + 0.0854816i 0.889646 0.456650i \(-0.150951\pi\)
−0.840294 + 0.542132i \(0.817617\pi\)
\(570\) −7190.90 12455.0i −0.528410 0.915233i
\(571\) 11875.5 0.870360 0.435180 0.900344i \(-0.356685\pi\)
0.435180 + 0.900344i \(0.356685\pi\)
\(572\) 4240.29 2516.20i 0.309957 0.183929i
\(573\) −4450.48 −0.324470
\(574\) 7759.87 + 13440.5i 0.564270 + 0.977344i
\(575\) 7077.54 + 12258.7i 0.513311 + 0.889081i
\(576\) −1673.16 + 2898.00i −0.121033 + 0.209635i
\(577\) 18998.0 1.37070 0.685352 0.728212i \(-0.259648\pi\)
0.685352 + 0.728212i \(0.259648\pi\)
\(578\) −1567.23 + 2714.53i −0.112782 + 0.195345i
\(579\) 272.586 472.133i 0.0195653 0.0338880i
\(580\) −36662.2 −2.62468
\(581\) 19603.7 33954.6i 1.39982 2.42457i
\(582\) 5132.97 + 8890.56i 0.365581 + 0.633205i
\(583\) −3575.32 6192.64i −0.253987 0.439919i
\(584\) 1763.32 0.124943
\(585\) −39.2791 3285.19i −0.00277605 0.232181i
\(586\) −15956.2 −1.12482
\(587\) 10599.3 + 18358.6i 0.745284 + 1.29087i 0.950062 + 0.312062i \(0.101020\pi\)
−0.204778 + 0.978809i \(0.565647\pi\)
\(588\) −19375.7 33559.6i −1.35891 2.35370i
\(589\) 3399.13 5887.47i 0.237791 0.411866i
\(590\) 16843.1 1.17528
\(591\) 5917.09 10248.7i 0.411838 0.713325i
\(592\) −180.550 + 312.721i −0.0125347 + 0.0217108i
\(593\) −17808.4 −1.23323 −0.616613 0.787266i \(-0.711496\pi\)
−0.616613 + 0.787266i \(0.711496\pi\)
\(594\) 3455.36 5984.85i 0.238678 0.413403i
\(595\) −18832.2 32618.4i −1.29756 2.24744i
\(596\) 10854.4 + 18800.3i 0.745993 + 1.29210i
\(597\) −3749.78 −0.257066
\(598\) −399.997 33454.7i −0.0273530 2.28773i
\(599\) −3515.70 −0.239812 −0.119906 0.992785i \(-0.538259\pi\)
−0.119906 + 0.992785i \(0.538259\pi\)
\(600\) −1280.81 2218.42i −0.0871478 0.150944i
\(601\) −4574.71 7923.63i −0.310493 0.537790i 0.667976 0.744183i \(-0.267161\pi\)
−0.978469 + 0.206393i \(0.933827\pi\)
\(602\) 31805.1 55088.0i 2.15329 3.72960i
\(603\) 413.053 0.0278952
\(604\) −6345.91 + 10991.4i −0.427503 + 0.740456i
\(605\) −872.769 + 1511.68i −0.0586497 + 0.101584i
\(606\) −8167.92 −0.547523
\(607\) −12335.0 + 21364.8i −0.824812 + 1.42862i 0.0772508 + 0.997012i \(0.475386\pi\)
−0.902063 + 0.431605i \(0.857948\pi\)
\(608\) 6521.02 + 11294.7i 0.434971 + 0.753392i
\(609\) −21696.6 37579.7i −1.44367 2.50050i
\(610\) 3178.79 0.210992
\(611\) −15076.7 + 8946.54i −0.998259 + 0.592370i
\(612\) 3496.02 0.230912
\(613\) 7739.26 + 13404.8i 0.509928 + 0.883221i 0.999934 + 0.0115017i \(0.00366120\pi\)
−0.490006 + 0.871719i \(0.663005\pi\)
\(614\) 15581.3 + 26987.7i 1.02412 + 1.77383i
\(615\) −3622.05 + 6273.57i −0.237488 + 0.411341i
\(616\) −2500.40 −0.163546
\(617\) 7183.69 12442.5i 0.468727 0.811859i −0.530634 0.847601i \(-0.678046\pi\)
0.999361 + 0.0357422i \(0.0113795\pi\)
\(618\) 13764.7 23841.2i 0.895952 1.55183i
\(619\) −16902.2 −1.09751 −0.548755 0.835983i \(-0.684898\pi\)
−0.548755 + 0.835983i \(0.684898\pi\)
\(620\) 9275.54 16065.7i 0.600830 1.04067i
\(621\) −12766.5 22112.3i −0.824965 1.42888i
\(622\) 7117.78 + 12328.4i 0.458838 + 0.794730i
\(623\) 30316.8 1.94963
\(624\) −129.344 10817.9i −0.00829790 0.694014i
\(625\) −19106.6 −1.22282
\(626\) −2354.62 4078.32i −0.150335 0.260388i
\(627\) −1308.37 2266.17i −0.0833356 0.144342i
\(628\) 2648.99 4588.18i 0.168322 0.291542i
\(629\) 553.873 0.0351103
\(630\) −5096.72 + 8827.78i −0.322315 + 0.558266i
\(631\) −12917.2 + 22373.2i −0.814935 + 1.41151i 0.0944398 + 0.995531i \(0.469894\pi\)
−0.909375 + 0.415978i \(0.863439\pi\)
\(632\) 1406.94 0.0885522
\(633\) −398.769 + 690.689i −0.0250390 + 0.0433687i
\(634\) 5918.72 + 10251.5i 0.370761 + 0.642177i
\(635\) −4860.23 8418.16i −0.303736 0.526086i
\(636\) 29251.6 1.82374
\(637\) −35195.9 19763.1i −2.18919 1.22927i
\(638\) −12251.0 −0.760221
\(639\) 643.206 + 1114.06i 0.0398198 + 0.0689698i
\(640\) 5932.36 + 10275.2i 0.366402 + 0.634627i
\(641\) 8436.96 14613.2i 0.519875 0.900450i −0.479858 0.877346i \(-0.659312\pi\)
0.999733 0.0231040i \(-0.00735489\pi\)
\(642\) 6496.34 0.399362
\(643\) 6957.80 12051.3i 0.426732 0.739121i −0.569848 0.821750i \(-0.692998\pi\)
0.996580 + 0.0826284i \(0.0263314\pi\)
\(644\) −28260.7 + 48949.0i −1.72924 + 2.99513i
\(645\) 29691.1 1.81254
\(646\) 7970.46 13805.2i 0.485439 0.840805i
\(647\) −8628.35 14944.7i −0.524290 0.908097i −0.999600 0.0282783i \(-0.990998\pi\)
0.475310 0.879818i \(-0.342336\pi\)
\(648\) 1880.65 + 3257.39i 0.114011 + 0.197473i
\(649\) 3064.57 0.185354
\(650\) −14234.5 7992.92i −0.858958 0.482320i
\(651\) 21957.0 1.32191
\(652\) 3703.29 + 6414.29i 0.222442 + 0.385281i
\(653\) −3336.57 5779.10i −0.199954 0.346330i 0.748559 0.663068i \(-0.230746\pi\)
−0.948513 + 0.316737i \(0.897413\pi\)
\(654\) 7165.16 12410.4i 0.428410 0.742027i
\(655\) 21002.2 1.25286
\(656\) 2617.41 4533.48i 0.155781 0.269821i
\(657\) 653.976 1132.72i 0.0388341 0.0672627i
\(658\) 54393.0 3.22259
\(659\) 10975.5 19010.1i 0.648779 1.12372i −0.334636 0.942347i \(-0.608613\pi\)
0.983415 0.181370i \(-0.0580533\pi\)
\(660\) −3570.29 6183.92i −0.210565 0.364710i
\(661\) 10695.8 + 18525.7i 0.629380 + 1.09012i 0.987676 + 0.156510i \(0.0500243\pi\)
−0.358297 + 0.933608i \(0.616642\pi\)
\(662\) −6839.88 −0.401570
\(663\) −14270.9 + 8468.38i −0.835950 + 0.496055i
\(664\) 7401.10 0.432558
\(665\) 12654.0 + 21917.3i 0.737896 + 1.27807i
\(666\) −74.9496 129.817i −0.00436072 0.00755298i
\(667\) −22631.9 + 39199.6i −1.31381 + 2.27558i
\(668\) −6226.17 −0.360625
\(669\) 6722.25 11643.3i 0.388486 0.672878i
\(670\) 2569.72 4450.89i 0.148175 0.256646i
\(671\) 578.376 0.0332757
\(672\) −21061.6 + 36479.7i −1.20903 + 2.09410i
\(673\) −1108.72 1920.37i −0.0635040 0.109992i 0.832525 0.553987i \(-0.186894\pi\)
−0.896029 + 0.443995i \(0.853561\pi\)
\(674\) −6424.72 11127.9i −0.367168 0.635953i
\(675\) −12458.6 −0.710418
\(676\) 10937.0 + 17938.8i 0.622272 + 1.02064i
\(677\) −4300.30 −0.244127 −0.122063 0.992522i \(-0.538951\pi\)
−0.122063 + 0.992522i \(0.538951\pi\)
\(678\) −16508.7 28594.0i −0.935124 1.61968i
\(679\) −9032.60 15644.9i −0.510514 0.884237i
\(680\) 3554.93 6157.32i 0.200478 0.347239i
\(681\) −1391.58 −0.0783046
\(682\) 3099.50 5368.49i 0.174026 0.301423i
\(683\) 6030.07 10444.4i 0.337825 0.585130i −0.646198 0.763169i \(-0.723642\pi\)
0.984023 + 0.178040i \(0.0569755\pi\)
\(684\) −2349.09 −0.131315
\(685\) 16105.8 27896.1i 0.898354 1.55599i
\(686\) 37678.0 + 65260.3i 2.09702 + 3.63214i
\(687\) 8953.53 + 15508.0i 0.497232 + 0.861231i
\(688\) −21455.7 −1.18894
\(689\) 26203.5 15549.2i 1.44887 0.859765i
\(690\) −48452.5 −2.67327
\(691\) 1145.11 + 1983.39i 0.0630420 + 0.109192i 0.895824 0.444409i \(-0.146586\pi\)
−0.832782 + 0.553601i \(0.813253\pi\)
\(692\) −16517.6 28609.3i −0.907377 1.57162i
\(693\) −927.342 + 1606.20i −0.0508324 + 0.0880442i
\(694\) −24529.7 −1.34169
\(695\) 9407.58 16294.4i 0.513453 0.889327i
\(696\) 4095.64 7093.85i 0.223053 0.386339i
\(697\) −8029.43 −0.436350
\(698\) 5247.35 9088.67i 0.284549 0.492853i
\(699\) 4171.50 + 7225.24i 0.225723 + 0.390964i
\(700\) 13789.6 + 23884.2i 0.744566 + 1.28963i
\(701\) −25045.0 −1.34941 −0.674705 0.738087i \(-0.735729\pi\)
−0.674705 + 0.738087i \(0.735729\pi\)
\(702\) 25676.3 + 14417.7i 1.38047 + 0.775158i
\(703\) −372.165 −0.0199665
\(704\) 3787.89 + 6560.81i 0.202786 + 0.351236i
\(705\) 12694.4 + 21987.4i 0.678155 + 1.17460i
\(706\) 2084.21 3609.95i 0.111105 0.192440i
\(707\) 14373.3 0.764587
\(708\) −6268.21 + 10856.9i −0.332731 + 0.576308i
\(709\) 2723.41 4717.09i 0.144260 0.249865i −0.784837 0.619702i \(-0.787253\pi\)
0.929096 + 0.369838i \(0.120587\pi\)
\(710\) 16006.3 0.846064
\(711\) 521.800 903.785i 0.0275233 0.0476717i
\(712\) 2861.42 + 4956.13i 0.150613 + 0.260869i
\(713\) −11451.7 19835.0i −0.601502 1.04183i
\(714\) 51485.9 2.69862
\(715\) −6485.43 3641.68i −0.339219 0.190477i
\(716\) −18056.6 −0.942467
\(717\) −3004.26 5203.52i −0.156480 0.271031i
\(718\) 16809.8 + 29115.4i 0.873727 + 1.51334i
\(719\) −14265.7 + 24709.0i −0.739947 + 1.28163i 0.212571 + 0.977146i \(0.431816\pi\)
−0.952519 + 0.304481i \(0.901517\pi\)
\(720\) 3438.25 0.177967
\(721\) −24222.1 + 41953.9i −1.25115 + 2.16705i
\(722\) 9016.84 15617.6i 0.464781 0.805025i
\(723\) 1692.85 0.0870783
\(724\) 17760.0 30761.1i 0.911662 1.57905i
\(725\) 11043.0 + 19127.1i 0.565693 + 0.979809i
\(726\) −1193.04 2066.41i −0.0609889 0.105636i
\(727\) 863.427 0.0440478 0.0220239 0.999757i \(-0.492989\pi\)
0.0220239 + 0.999757i \(0.492989\pi\)
\(728\) −127.380 10653.7i −0.00648492 0.542381i
\(729\) 21835.5 1.10936
\(730\) −8137.15 14094.0i −0.412561 0.714576i
\(731\) 16454.9 + 28500.8i 0.832569 + 1.44205i
\(732\) −1183.00 + 2049.01i −0.0597335 + 0.103461i
\(733\) −1088.81 −0.0548653 −0.0274327 0.999624i \(-0.508733\pi\)
−0.0274327 + 0.999624i \(0.508733\pi\)
\(734\) 9792.68 16961.4i 0.492445 0.852939i
\(735\) −29228.3 + 50624.9i −1.46681 + 2.54058i
\(736\) 43938.9 2.20056
\(737\) 467.558 809.834i 0.0233687 0.0404757i
\(738\) 1086.53 + 1881.93i 0.0541950 + 0.0938684i
\(739\) 4947.45 + 8569.24i 0.246272 + 0.426556i 0.962488 0.271322i \(-0.0874610\pi\)
−0.716216 + 0.697878i \(0.754128\pi\)
\(740\) −1015.56 −0.0504497
\(741\) 9589.05 5690.17i 0.475388 0.282097i
\(742\) −94535.9 −4.67725
\(743\) 1104.56 + 1913.16i 0.0545391 + 0.0944645i 0.892006 0.452024i \(-0.149298\pi\)
−0.837467 + 0.546488i \(0.815964\pi\)
\(744\) 2072.39 + 3589.49i 0.102121 + 0.176878i
\(745\) 16373.9 28360.4i 0.805224 1.39469i
\(746\) −20819.8 −1.02180
\(747\) 2744.90 4754.30i 0.134445 0.232866i
\(748\) 3957.34 6854.31i 0.193442 0.335051i
\(749\) −11431.8 −0.557687
\(750\) 5958.70 10320.8i 0.290108 0.502481i
\(751\) 9392.24 + 16267.8i 0.456362 + 0.790442i 0.998765 0.0496764i \(-0.0158190\pi\)
−0.542404 + 0.840118i \(0.682486\pi\)
\(752\) −9173.39 15888.8i −0.444839 0.770484i
\(753\) −5648.44 −0.273361
\(754\) −624.112 52199.0i −0.0301443 2.52119i
\(755\) 19145.7 0.922892
\(756\) −24873.7 43082.6i −1.19663 2.07262i
\(757\) 19194.6 + 33246.1i 0.921586 + 1.59623i 0.796961 + 0.604030i \(0.206439\pi\)
0.124625 + 0.992204i \(0.460227\pi\)
\(758\) −6702.50 + 11609.1i −0.321169 + 0.556280i
\(759\) −8815.88 −0.421602
\(760\) −2388.67 + 4137.30i −0.114008 + 0.197468i
\(761\) −16669.8 + 28873.0i −0.794062 + 1.37536i 0.129372 + 0.991596i \(0.458704\pi\)
−0.923433 + 0.383759i \(0.874629\pi\)
\(762\) 13287.5 0.631700
\(763\) −12608.7 + 21838.9i −0.598251 + 1.03620i
\(764\) 4522.45 + 7833.10i 0.214157 + 0.370932i
\(765\) −2636.88 4567.22i −0.124623 0.215854i
\(766\) 1513.52 0.0713913
\(767\) 156.121 + 13057.5i 0.00734968 + 0.614707i
\(768\) 9706.72 0.456069
\(769\) −7795.91 13502.9i −0.365576 0.633195i 0.623293 0.781989i \(-0.285794\pi\)
−0.988868 + 0.148793i \(0.952461\pi\)
\(770\) 11538.5 + 19985.3i 0.540026 + 0.935352i
\(771\) −10462.9 + 18122.2i −0.488730 + 0.846505i
\(772\) −1107.97 −0.0516540
\(773\) 8616.89 14924.9i 0.400942 0.694451i −0.592898 0.805277i \(-0.702016\pi\)
0.993840 + 0.110826i \(0.0353497\pi\)
\(774\) 4453.34 7713.40i 0.206811 0.358207i
\(775\) −11175.5 −0.517984
\(776\) 1705.07 2953.26i 0.0788768 0.136619i
\(777\) −601.009 1040.98i −0.0277491 0.0480629i
\(778\) 16026.3 + 27758.4i 0.738523 + 1.27916i
\(779\) 5395.23 0.248144
\(780\) 26166.6 15527.3i 1.20117 0.712778i
\(781\) 2912.32 0.133433
\(782\) −26852.6 46510.1i −1.22794 2.12685i
\(783\) −19919.5 34501.6i −0.909150 1.57469i
\(784\) 21121.3 36583.2i 0.962158 1.66651i
\(785\) −7992.02 −0.363373
\(786\) −14354.6 + 24862.9i −0.651415 + 1.12828i
\(787\) 19837.4 34359.4i 0.898510 1.55627i 0.0691108 0.997609i \(-0.477984\pi\)
0.829399 0.558656i \(-0.188683\pi\)
\(788\) −24051.1 −1.08729
\(789\) 5944.00 10295.3i 0.268203 0.464541i
\(790\) −6492.55 11245.4i −0.292398 0.506448i
\(791\) 29050.8 + 50317.4i 1.30585 + 2.26180i
\(792\) −350.106 −0.0157077
\(793\) 29.4647 + 2464.35i 0.00131945 + 0.110355i
\(794\) −53787.0 −2.40407
\(795\) −22063.1 38214.4i −0.984273 1.70481i
\(796\) 3810.41 + 6599.83i 0.169669 + 0.293875i
\(797\) −14182.8 + 24565.4i −0.630340 + 1.09178i 0.357142 + 0.934050i \(0.383751\pi\)
−0.987482 + 0.157731i \(0.949582\pi\)
\(798\) −34595.0 −1.53465
\(799\) −14070.6 + 24371.0i −0.623007 + 1.07908i
\(800\) 10719.8 18567.2i 0.473752 0.820563i
\(801\) 4244.94 0.187251
\(802\) 312.301 540.922i 0.0137503 0.0238162i
\(803\) −1480.54 2564.38i −0.0650651 0.112696i
\(804\) 1912.67 + 3312.84i 0.0838987 + 0.145317i
\(805\) 85263.0 3.73308
\(806\) 23032.0 + 12932.9i 1.00653 + 0.565187i
\(807\) 19228.6 0.838759
\(808\) 1356.61 + 2349.72i 0.0590660 + 0.102305i
\(809\) −4922.61 8526.21i −0.213930 0.370538i 0.739011 0.673694i \(-0.235293\pi\)
−0.952941 + 0.303155i \(0.901960\pi\)
\(810\) 17357.2 30063.5i 0.752925 1.30410i
\(811\) 30581.9 1.32414 0.662070 0.749442i \(-0.269678\pi\)
0.662070 + 0.749442i \(0.269678\pi\)
\(812\) −44094.9 + 76374.7i −1.90570 + 3.30077i
\(813\) −13867.1 + 24018.6i −0.598206 + 1.03612i
\(814\) −339.359 −0.0146124
\(815\) 5586.44 9676.00i 0.240104 0.415872i
\(816\) −8683.10 15039.6i −0.372512 0.645209i
\(817\) −11056.6 19150.6i −0.473466 0.820067i
\(818\) −7356.76 −0.314454
\(819\) −6890.96 3869.40i −0.294004 0.165089i
\(820\) 14722.5 0.626989
\(821\) −12271.3 21254.6i −0.521647 0.903519i −0.999683 0.0251790i \(-0.991984\pi\)
0.478036 0.878340i \(-0.341349\pi\)
\(822\) 22016.1 + 38132.9i 0.934183 + 1.61805i
\(823\) 14348.8 24852.9i 0.607739 1.05263i −0.383874 0.923386i \(-0.625410\pi\)
0.991612 0.129248i \(-0.0412565\pi\)
\(824\) −9144.72 −0.386616
\(825\) −2150.81 + 3725.32i −0.0907657 + 0.157211i
\(826\) 20257.8 35087.5i 0.853338 1.47803i
\(827\) 43827.0 1.84282 0.921412 0.388587i \(-0.127037\pi\)
0.921412 + 0.388587i \(0.127037\pi\)
\(828\) −3957.06 + 6853.82i −0.166084 + 0.287665i
\(829\) 6467.26 + 11201.6i 0.270949 + 0.469298i 0.969105 0.246648i \(-0.0793290\pi\)
−0.698156 + 0.715946i \(0.745996\pi\)
\(830\) −34153.6 59155.8i −1.42830 2.47389i
\(831\) 2094.87 0.0874490
\(832\) −27761.4 + 16473.7i −1.15679 + 0.686444i
\(833\) −64793.9 −2.69505
\(834\) 12859.8 + 22273.8i 0.533931 + 0.924796i
\(835\) 4696.11 + 8133.90i 0.194629 + 0.337108i
\(836\) −2659.06 + 4605.63i −0.110007 + 0.190537i
\(837\) 20158.5 0.832474
\(838\) 14475.3 25072.0i 0.596709 1.03353i
\(839\) −9617.52 + 16658.0i −0.395749 + 0.685458i −0.993197 0.116450i \(-0.962848\pi\)
0.597447 + 0.801908i \(0.296182\pi\)
\(840\) −15429.8 −0.633786
\(841\) −23117.8 + 40041.2i −0.947878 + 1.64177i
\(842\) −25769.2 44633.5i −1.05471 1.82681i
\(843\) −3999.76 6927.78i −0.163415 0.283043i
\(844\) 1620.87 0.0661050
\(845\) 15186.1 27818.6i 0.618246 1.13253i
\(846\) 7616.09 0.309511
\(847\) 2099.42 + 3636.30i 0.0851676 + 0.147515i
\(848\) 15943.5 + 27614.9i 0.645638 + 1.11828i
\(849\) −18969.3 + 32855.8i −0.766813 + 1.32816i
\(850\) −26205.0 −1.05744
\(851\) −626.915 + 1085.85i −0.0252531 + 0.0437396i
\(852\) −5956.81 + 10317.5i −0.239527 + 0.414872i
\(853\) 12364.7 0.496317 0.248159 0.968719i \(-0.420175\pi\)
0.248159 + 0.968719i \(0.420175\pi\)
\(854\) 3823.25 6622.05i 0.153195 0.265342i
\(855\) 1771.81 + 3068.86i 0.0708707 + 0.122752i
\(856\) −1078.98 1868.84i −0.0430826 0.0746212i
\(857\) −14924.8 −0.594893 −0.297446 0.954739i \(-0.596135\pi\)
−0.297446 + 0.954739i \(0.596135\pi\)
\(858\) 8743.78 5188.58i 0.347911 0.206451i
\(859\) −43335.2 −1.72128 −0.860639 0.509215i \(-0.829936\pi\)
−0.860639 + 0.509215i \(0.829936\pi\)
\(860\) −30171.2 52258.1i −1.19631 2.07208i
\(861\) 8712.74 + 15090.9i 0.344866 + 0.597325i
\(862\) −3120.06 + 5404.09i −0.123283 + 0.213532i
\(863\) −6338.71 −0.250026 −0.125013 0.992155i \(-0.539897\pi\)
−0.125013 + 0.992155i \(0.539897\pi\)
\(864\) −19336.4 + 33491.7i −0.761388 + 1.31876i
\(865\) −24916.9 + 43157.4i −0.979423 + 1.69641i
\(866\) 47565.7 1.86645
\(867\) −1759.68 + 3047.85i −0.0689295 + 0.119389i
\(868\) −22312.1 38645.6i −0.872489 1.51120i
\(869\) −1181.31 2046.09i −0.0461142 0.0798721i
\(870\) −75600.0 −2.94607
\(871\) 3474.36 + 1950.92i 0.135160 + 0.0758947i
\(872\) −4760.24 −0.184865
\(873\) −1264.74 2190.59i −0.0490320 0.0849260i
\(874\) 18043.1 + 31251.6i 0.698305 + 1.20950i
\(875\) −10485.7 + 18161.7i −0.405120 + 0.701688i
\(876\) 12113.1 0.467196
\(877\) −16958.3 + 29372.7i −0.652956 + 1.13095i 0.329446 + 0.944174i \(0.393138\pi\)
−0.982402 + 0.186778i \(0.940195\pi\)
\(878\) 6786.19 11754.0i 0.260846 0.451799i
\(879\) −17915.5 −0.687457
\(880\) 3891.95 6741.05i 0.149088 0.258228i
\(881\) 8917.77 + 15446.0i 0.341030 + 0.590681i 0.984624 0.174686i \(-0.0558909\pi\)
−0.643594 + 0.765367i \(0.722558\pi\)
\(882\) 8767.85 + 15186.4i 0.334727 + 0.579763i
\(883\) −6224.35 −0.237221 −0.118610 0.992941i \(-0.537844\pi\)
−0.118610 + 0.992941i \(0.537844\pi\)
\(884\) 29406.5 + 16512.3i 1.11883 + 0.628243i
\(885\) 18911.3 0.718300
\(886\) −22887.8 39642.8i −0.867866 1.50319i
\(887\) 3253.95 + 5636.01i 0.123176 + 0.213347i 0.921018 0.389519i \(-0.127359\pi\)
−0.797843 + 0.602866i \(0.794025\pi\)
\(888\) 113.451 196.504i 0.00428736 0.00742593i
\(889\) −23382.3 −0.882134
\(890\) 26409.0 45741.8i 0.994644 1.72277i
\(891\) 3158.12 5470.02i 0.118744 0.205671i
\(892\) −27323.8 −1.02564
\(893\) 9454.49 16375.7i 0.354292 0.613651i
\(894\) 22382.5 + 38767.5i 0.837339 + 1.45031i
\(895\) 13619.2 + 23589.2i 0.508649 + 0.881006i
\(896\) 28540.3 1.06413
\(897\) −449.115 37562.7i −0.0167174 1.39820i
\(898\) 57418.3 2.13371
\(899\) −17868.0 30948.4i −0.662884 1.14815i
\(900\) 1930.81 + 3344.26i 0.0715114 + 0.123861i
\(901\) 24454.9 42357.2i 0.904231 1.56617i
\(902\) 4919.64 0.181603
\(903\) 35710.6 61852.5i 1.31603 2.27943i
\(904\) −5483.87 + 9498.33i −0.201760 + 0.349458i
\(905\) −53582.0 −1.96810
\(906\) −13085.7 + 22665.1i −0.479850 + 0.831125i
\(907\) 20958.5 + 36301.1i 0.767271 + 1.32895i 0.939038 + 0.343814i \(0.111719\pi\)
−0.171767 + 0.985138i \(0.554948\pi\)
\(908\) 1414.08 + 2449.26i 0.0516828 + 0.0895172i
\(909\) 2012.54 0.0734343
\(910\) −84565.7 + 50181.5i −3.08058 + 1.82802i
\(911\) −16133.7 −0.586753 −0.293377 0.955997i \(-0.594779\pi\)
−0.293377 + 0.955997i \(0.594779\pi\)
\(912\) 5834.45 + 10105.6i 0.211840 + 0.366918i
\(913\) −6214.21 10763.3i −0.225258 0.390158i
\(914\) −1688.09 + 2923.86i −0.0610909 + 0.105813i
\(915\) 3569.12 0.128953
\(916\) 18196.6 31517.5i 0.656368 1.13686i
\(917\) 25260.1 43751.8i 0.909665 1.57559i
\(918\) 47268.8 1.69946
\(919\) −8288.34 + 14355.8i −0.297505 + 0.515294i −0.975565 0.219713i \(-0.929488\pi\)
0.678059 + 0.735007i \(0.262821\pi\)
\(920\) 8047.48 + 13938.6i 0.288389 + 0.499504i
\(921\) 17494.6 + 30301.6i 0.625915 + 1.08412i
\(922\) −21688.1 −0.774683
\(923\) 148.365 + 12408.8i 0.00529089 + 0.442515i
\(924\) −17176.5 −0.611541
\(925\) 305.897 + 529.830i 0.0108733 + 0.0188332i
\(926\) −5537.01 9590.38i −0.196498 0.340345i
\(927\) −3391.57 + 5874.37i −0.120166 + 0.208133i
\(928\) 68557.4 2.42512
\(929\) 25201.6 43650.5i 0.890030 1.54158i 0.0501933 0.998740i \(-0.484016\pi\)
0.839837 0.542838i \(-0.182650\pi\)
\(930\) 19126.8 33128.6i 0.674401 1.16810i
\(931\) 43537.1 1.53262
\(932\) 8477.90 14684.2i 0.297964 0.516089i
\(933\) 7991.80 + 13842.2i 0.280429 + 0.485717i
\(934\) −13868.6 24021.1i −0.485861 0.841535i
\(935\) −11939.3 −0.417602
\(936\) −17.8357 1491.73i −0.000622841 0.0520927i
\(937\) −29253.1 −1.01991 −0.509956 0.860201i \(-0.670338\pi\)
−0.509956 + 0.860201i \(0.670338\pi\)
\(938\) −6181.40 10706.5i −0.215170 0.372686i
\(939\) −2643.76 4579.12i −0.0918804 0.159142i
\(940\) 25799.4 44685.8i 0.895195 1.55052i
\(941\) 27097.4 0.938736 0.469368 0.883003i \(-0.344482\pi\)
0.469368 + 0.883003i \(0.344482\pi\)
\(942\) 5462.40 9461.15i 0.188933 0.327241i
\(943\) 9088.31 15741.4i 0.313845 0.543596i
\(944\) −13665.9 −0.471172
\(945\) −37522.2 + 64990.3i −1.29164 + 2.23718i
\(946\) −10082.0 17462.5i −0.346504 0.600163i
\(947\) 14328.4 + 24817.4i 0.491668 + 0.851593i 0.999954 0.00959491i \(-0.00305420\pi\)
−0.508286 + 0.861188i \(0.669721\pi\)
\(948\) 9664.92 0.331120
\(949\) 10850.9 6438.94i 0.371164 0.220250i
\(950\) 17608.0 0.601345
\(951\) 6645.51 + 11510.4i 0.226599 + 0.392481i
\(952\) −8551.29 14811.3i −0.291123 0.504240i
\(953\) −27408.8 + 47473.4i −0.931644 + 1.61365i −0.151132 + 0.988514i \(0.548292\pi\)
−0.780512 + 0.625141i \(0.785041\pi\)
\(954\) −13236.9 −0.449224
\(955\) 6822.14 11816.3i 0.231161 0.400383i
\(956\) −6105.67 + 10575.3i −0.206560 + 0.357773i
\(957\) −13755.3 −0.464625
\(958\) −31371.6 + 54337.1i −1.05801 + 1.83252i
\(959\) −38742.1 67103.4i −1.30454 2.25952i
\(960\) 23374.8 + 40486.4i 0.785853 + 1.36114i
\(961\) −11708.5 −0.393022
\(962\) −17.2882 1445.94i −0.000579413 0.0484605i
\(963\) −1600.67 −0.0535627
\(964\) −1720.22 2979.51i −0.0574736 0.0995472i
\(965\) 835.694 + 1447.46i 0.0278777 + 0.0482855i
\(966\) −58275.6 + 100936.i −1.94098 + 3.36188i
\(967\) −14806.3 −0.492388 −0.246194 0.969221i \(-0.579180\pi\)
−0.246194 + 0.969221i \(0.579180\pi\)
\(968\) −396.304 + 686.419i −0.0131588 + 0.0227917i
\(969\) 8949.19 15500.4i 0.296687 0.513876i
\(970\) −31473.3 −1.04180
\(971\) −27308.6 + 47299.9i −0.902549 + 1.56326i −0.0783760 + 0.996924i \(0.524973\pi\)
−0.824173 + 0.566338i \(0.808360\pi\)
\(972\) −6434.45 11144.8i −0.212330 0.367767i
\(973\) −22629.7 39195.8i −0.745606 1.29143i
\(974\) −367.489 −0.0120894
\(975\) −15982.4 8974.40i −0.524971 0.294780i
\(976\) −2579.16 −0.0845871
\(977\) −475.229 823.121i −0.0155618 0.0269539i 0.858140 0.513416i \(-0.171620\pi\)
−0.873701 + 0.486463i \(0.838287\pi\)
\(978\) 7636.45 + 13226.7i 0.249680 + 0.432458i
\(979\) 4805.09 8322.66i 0.156866 0.271699i
\(980\) 118804. 3.87250
\(981\) −1765.46 + 3057.87i −0.0574586 + 0.0995213i
\(982\) −35802.9 + 62012.5i −1.16346 + 2.01517i
\(983\) −627.901 −0.0203733 −0.0101866 0.999948i \(-0.503243\pi\)
−0.0101866 + 0.999948i \(0.503243\pi\)
\(984\) −1644.69 + 2848.69i −0.0532833 + 0.0922894i
\(985\) 18140.6 + 31420.4i 0.586810 + 1.01638i
\(986\) −41897.9 72569.2i −1.35325 2.34389i
\(987\) 61072.2 1.96955
\(988\) −19759.1 11095.1i −0.636257 0.357270i
\(989\) −74499.8 −2.39530
\(990\) 1615.62 + 2798.34i 0.0518665 + 0.0898354i
\(991\) −14478.4 25077.3i −0.464098 0.803841i 0.535062 0.844813i \(-0.320288\pi\)
−0.999160 + 0.0409713i \(0.986955\pi\)
\(992\) −17345.0 + 30042.5i −0.555147 + 0.961543i
\(993\) −7679.78 −0.245428
\(994\) 19251.3 33344.3i 0.614301 1.06400i
\(995\) 5748.03 9955.88i 0.183141 0.317209i
\(996\) 50841.7 1.61745
\(997\) 20006.3 34651.9i 0.635512 1.10074i −0.350895 0.936415i \(-0.614122\pi\)
0.986406 0.164324i \(-0.0525442\pi\)
\(998\) 2314.93 + 4009.58i 0.0734247 + 0.127175i
\(999\) −551.781 955.712i −0.0174750 0.0302677i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 143.4.e.b.133.2 yes 34
13.3 even 3 1859.4.a.g.1.16 17
13.9 even 3 inner 143.4.e.b.100.2 34
13.10 even 6 1859.4.a.h.1.2 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.e.b.100.2 34 13.9 even 3 inner
143.4.e.b.133.2 yes 34 1.1 even 1 trivial
1859.4.a.g.1.16 17 13.3 even 3
1859.4.a.h.1.2 17 13.10 even 6