Properties

Label 169.4.c.a.22.1
Level $169$
Weight $4$
Character 169.22
Analytic conductor $9.971$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,4,Mod(22,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.22");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 169.22
Dual form 169.4.c.a.146.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.50000 + 4.33013i) q^{2} +(3.50000 - 6.06218i) q^{3} +(-8.50000 - 14.7224i) q^{4} +7.00000 q^{5} +(17.5000 + 30.3109i) q^{6} +(-6.50000 - 11.2583i) q^{7} +45.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +O(q^{10})\) \(q+(-2.50000 + 4.33013i) q^{2} +(3.50000 - 6.06218i) q^{3} +(-8.50000 - 14.7224i) q^{4} +7.00000 q^{5} +(17.5000 + 30.3109i) q^{6} +(-6.50000 - 11.2583i) q^{7} +45.0000 q^{8} +(-11.0000 - 19.0526i) q^{9} +(-17.5000 + 30.3109i) q^{10} +(-13.0000 + 22.5167i) q^{11} -119.000 q^{12} +65.0000 q^{14} +(24.5000 - 42.4352i) q^{15} +(-44.5000 + 77.0763i) q^{16} +(-38.5000 - 66.6840i) q^{17} +110.000 q^{18} +(-63.0000 - 109.119i) q^{19} +(-59.5000 - 103.057i) q^{20} -91.0000 q^{21} +(-65.0000 - 112.583i) q^{22} +(48.0000 - 83.1384i) q^{23} +(157.500 - 272.798i) q^{24} -76.0000 q^{25} +35.0000 q^{27} +(-110.500 + 191.392i) q^{28} +(41.0000 - 71.0141i) q^{29} +(122.500 + 212.176i) q^{30} -196.000 q^{31} +(-42.5000 - 73.6122i) q^{32} +(91.0000 + 157.617i) q^{33} +385.000 q^{34} +(-45.5000 - 78.8083i) q^{35} +(-187.000 + 323.894i) q^{36} +(-65.5000 + 113.449i) q^{37} +630.000 q^{38} +315.000 q^{40} +(168.000 - 290.985i) q^{41} +(227.500 - 394.042i) q^{42} +(100.500 + 174.071i) q^{43} +442.000 q^{44} +(-77.0000 - 133.368i) q^{45} +(240.000 + 415.692i) q^{46} +105.000 q^{47} +(311.500 + 539.534i) q^{48} +(87.0000 - 150.688i) q^{49} +(190.000 - 329.090i) q^{50} -539.000 q^{51} -432.000 q^{53} +(-87.5000 + 151.554i) q^{54} +(-91.0000 + 157.617i) q^{55} +(-292.500 - 506.625i) q^{56} -882.000 q^{57} +(205.000 + 355.070i) q^{58} +(-147.000 - 254.611i) q^{59} -833.000 q^{60} +(28.0000 + 48.4974i) q^{61} +(490.000 - 848.705i) q^{62} +(-143.000 + 247.683i) q^{63} -287.000 q^{64} -910.000 q^{66} +(239.000 - 413.960i) q^{67} +(-654.500 + 1133.63i) q^{68} +(-336.000 - 581.969i) q^{69} +455.000 q^{70} +(4.50000 + 7.79423i) q^{71} +(-495.000 - 857.365i) q^{72} -98.0000 q^{73} +(-327.500 - 567.247i) q^{74} +(-266.000 + 460.726i) q^{75} +(-1071.00 + 1855.03i) q^{76} +338.000 q^{77} +1304.00 q^{79} +(-311.500 + 539.534i) q^{80} +(419.500 - 726.595i) q^{81} +(840.000 + 1454.92i) q^{82} +308.000 q^{83} +(773.500 + 1339.74i) q^{84} +(-269.500 - 466.788i) q^{85} -1005.00 q^{86} +(-287.000 - 497.099i) q^{87} +(-585.000 + 1013.25i) q^{88} +(-595.000 + 1030.57i) q^{89} +770.000 q^{90} -1632.00 q^{92} +(-686.000 + 1188.19i) q^{93} +(-262.500 + 454.663i) q^{94} +(-441.000 - 763.834i) q^{95} -595.000 q^{96} +(35.0000 + 60.6218i) q^{97} +(435.000 + 753.442i) q^{98} +572.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 5 q^{2} + 7 q^{3} - 17 q^{4} + 14 q^{5} + 35 q^{6} - 13 q^{7} + 90 q^{8} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 5 q^{2} + 7 q^{3} - 17 q^{4} + 14 q^{5} + 35 q^{6} - 13 q^{7} + 90 q^{8} - 22 q^{9} - 35 q^{10} - 26 q^{11} - 238 q^{12} + 130 q^{14} + 49 q^{15} - 89 q^{16} - 77 q^{17} + 220 q^{18} - 126 q^{19} - 119 q^{20} - 182 q^{21} - 130 q^{22} + 96 q^{23} + 315 q^{24} - 152 q^{25} + 70 q^{27} - 221 q^{28} + 82 q^{29} + 245 q^{30} - 392 q^{31} - 85 q^{32} + 182 q^{33} + 770 q^{34} - 91 q^{35} - 374 q^{36} - 131 q^{37} + 1260 q^{38} + 630 q^{40} + 336 q^{41} + 455 q^{42} + 201 q^{43} + 884 q^{44} - 154 q^{45} + 480 q^{46} + 210 q^{47} + 623 q^{48} + 174 q^{49} + 380 q^{50} - 1078 q^{51} - 864 q^{53} - 175 q^{54} - 182 q^{55} - 585 q^{56} - 1764 q^{57} + 410 q^{58} - 294 q^{59} - 1666 q^{60} + 56 q^{61} + 980 q^{62} - 286 q^{63} - 574 q^{64} - 1820 q^{66} + 478 q^{67} - 1309 q^{68} - 672 q^{69} + 910 q^{70} + 9 q^{71} - 990 q^{72} - 196 q^{73} - 655 q^{74} - 532 q^{75} - 2142 q^{76} + 676 q^{77} + 2608 q^{79} - 623 q^{80} + 839 q^{81} + 1680 q^{82} + 616 q^{83} + 1547 q^{84} - 539 q^{85} - 2010 q^{86} - 574 q^{87} - 1170 q^{88} - 1190 q^{89} + 1540 q^{90} - 3264 q^{92} - 1372 q^{93} - 525 q^{94} - 882 q^{95} - 1190 q^{96} + 70 q^{97} + 870 q^{98} + 1144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50000 + 4.33013i −0.883883 + 1.53093i −0.0368954 + 0.999319i \(0.511747\pi\)
−0.846988 + 0.531612i \(0.821586\pi\)
\(3\) 3.50000 6.06218i 0.673575 1.16667i −0.303308 0.952893i \(-0.598091\pi\)
0.976883 0.213774i \(-0.0685756\pi\)
\(4\) −8.50000 14.7224i −1.06250 1.84030i
\(5\) 7.00000 0.626099 0.313050 0.949737i \(-0.398649\pi\)
0.313050 + 0.949737i \(0.398649\pi\)
\(6\) 17.5000 + 30.3109i 1.19072 + 2.06239i
\(7\) −6.50000 11.2583i −0.350967 0.607893i 0.635452 0.772140i \(-0.280814\pi\)
−0.986419 + 0.164248i \(0.947480\pi\)
\(8\) 45.0000 1.98874
\(9\) −11.0000 19.0526i −0.407407 0.705650i
\(10\) −17.5000 + 30.3109i −0.553399 + 0.958514i
\(11\) −13.0000 + 22.5167i −0.356332 + 0.617184i −0.987345 0.158588i \(-0.949306\pi\)
0.631013 + 0.775772i \(0.282639\pi\)
\(12\) −119.000 −2.86270
\(13\) 0 0
\(14\) 65.0000 1.24086
\(15\) 24.5000 42.4352i 0.421725 0.730449i
\(16\) −44.5000 + 77.0763i −0.695312 + 1.20432i
\(17\) −38.5000 66.6840i −0.549272 0.951367i −0.998325 0.0578615i \(-0.981572\pi\)
0.449053 0.893505i \(-0.351762\pi\)
\(18\) 110.000 1.44040
\(19\) −63.0000 109.119i −0.760694 1.31756i −0.942493 0.334225i \(-0.891525\pi\)
0.181799 0.983336i \(-0.441808\pi\)
\(20\) −59.5000 103.057i −0.665230 1.15221i
\(21\) −91.0000 −0.945611
\(22\) −65.0000 112.583i −0.629911 1.09104i
\(23\) 48.0000 83.1384i 0.435161 0.753720i −0.562148 0.827037i \(-0.690025\pi\)
0.997309 + 0.0733164i \(0.0233583\pi\)
\(24\) 157.500 272.798i 1.33956 2.32019i
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) 35.0000 0.249472
\(28\) −110.500 + 191.392i −0.745805 + 1.29177i
\(29\) 41.0000 71.0141i 0.262535 0.454724i −0.704380 0.709823i \(-0.748775\pi\)
0.966915 + 0.255099i \(0.0821082\pi\)
\(30\) 122.500 + 212.176i 0.745511 + 1.29126i
\(31\) −196.000 −1.13557 −0.567785 0.823177i \(-0.692199\pi\)
−0.567785 + 0.823177i \(0.692199\pi\)
\(32\) −42.5000 73.6122i −0.234782 0.406654i
\(33\) 91.0000 + 157.617i 0.480032 + 0.831440i
\(34\) 385.000 1.94197
\(35\) −45.5000 78.8083i −0.219740 0.380601i
\(36\) −187.000 + 323.894i −0.865741 + 1.49951i
\(37\) −65.5000 + 113.449i −0.291031 + 0.504080i −0.974054 0.226317i \(-0.927331\pi\)
0.683023 + 0.730397i \(0.260665\pi\)
\(38\) 630.000 2.68946
\(39\) 0 0
\(40\) 315.000 1.24515
\(41\) 168.000 290.985i 0.639932 1.10839i −0.345516 0.938413i \(-0.612296\pi\)
0.985447 0.169981i \(-0.0543706\pi\)
\(42\) 227.500 394.042i 0.835810 1.44767i
\(43\) 100.500 + 174.071i 0.356421 + 0.617339i 0.987360 0.158493i \(-0.0506635\pi\)
−0.630939 + 0.775832i \(0.717330\pi\)
\(44\) 442.000 1.51441
\(45\) −77.0000 133.368i −0.255077 0.441807i
\(46\) 240.000 + 415.692i 0.769262 + 1.33240i
\(47\) 105.000 0.325869 0.162934 0.986637i \(-0.447904\pi\)
0.162934 + 0.986637i \(0.447904\pi\)
\(48\) 311.500 + 539.534i 0.936691 + 1.62240i
\(49\) 87.0000 150.688i 0.253644 0.439325i
\(50\) 190.000 329.090i 0.537401 0.930806i
\(51\) −539.000 −1.47990
\(52\) 0 0
\(53\) −432.000 −1.11962 −0.559809 0.828622i \(-0.689126\pi\)
−0.559809 + 0.828622i \(0.689126\pi\)
\(54\) −87.5000 + 151.554i −0.220504 + 0.381925i
\(55\) −91.0000 + 157.617i −0.223099 + 0.386419i
\(56\) −292.500 506.625i −0.697981 1.20894i
\(57\) −882.000 −2.04954
\(58\) 205.000 + 355.070i 0.464100 + 0.803845i
\(59\) −147.000 254.611i −0.324369 0.561824i 0.657015 0.753877i \(-0.271819\pi\)
−0.981384 + 0.192054i \(0.938485\pi\)
\(60\) −833.000 −1.79233
\(61\) 28.0000 + 48.4974i 0.0587710 + 0.101794i 0.893914 0.448239i \(-0.147948\pi\)
−0.835143 + 0.550033i \(0.814615\pi\)
\(62\) 490.000 848.705i 1.00371 1.73848i
\(63\) −143.000 + 247.683i −0.285973 + 0.495320i
\(64\) −287.000 −0.560547
\(65\) 0 0
\(66\) −910.000 −1.69717
\(67\) 239.000 413.960i 0.435798 0.754825i −0.561562 0.827435i \(-0.689799\pi\)
0.997360 + 0.0726096i \(0.0231327\pi\)
\(68\) −654.500 + 1133.63i −1.16720 + 2.02165i
\(69\) −336.000 581.969i −0.586227 1.01537i
\(70\) 455.000 0.776899
\(71\) 4.50000 + 7.79423i 0.00752186 + 0.0130282i 0.869762 0.493472i \(-0.164272\pi\)
−0.862240 + 0.506500i \(0.830939\pi\)
\(72\) −495.000 857.365i −0.810227 1.40335i
\(73\) −98.0000 −0.157124 −0.0785619 0.996909i \(-0.525033\pi\)
−0.0785619 + 0.996909i \(0.525033\pi\)
\(74\) −327.500 567.247i −0.514474 0.891096i
\(75\) −266.000 + 460.726i −0.409534 + 0.709333i
\(76\) −1071.00 + 1855.03i −1.61648 + 2.79982i
\(77\) 338.000 0.500243
\(78\) 0 0
\(79\) 1304.00 1.85711 0.928554 0.371198i \(-0.121053\pi\)
0.928554 + 0.371198i \(0.121053\pi\)
\(80\) −311.500 + 539.534i −0.435334 + 0.754021i
\(81\) 419.500 726.595i 0.575446 0.996701i
\(82\) 840.000 + 1454.92i 1.13125 + 1.95938i
\(83\) 308.000 0.407318 0.203659 0.979042i \(-0.434717\pi\)
0.203659 + 0.979042i \(0.434717\pi\)
\(84\) 773.500 + 1339.74i 1.00471 + 1.74021i
\(85\) −269.500 466.788i −0.343899 0.595650i
\(86\) −1005.00 −1.26014
\(87\) −287.000 497.099i −0.353674 0.612581i
\(88\) −585.000 + 1013.25i −0.708650 + 1.22742i
\(89\) −595.000 + 1030.57i −0.708650 + 1.22742i 0.256708 + 0.966489i \(0.417362\pi\)
−0.965358 + 0.260929i \(0.915971\pi\)
\(90\) 770.000 0.901835
\(91\) 0 0
\(92\) −1632.00 −1.84943
\(93\) −686.000 + 1188.19i −0.764891 + 1.32483i
\(94\) −262.500 + 454.663i −0.288030 + 0.498882i
\(95\) −441.000 763.834i −0.476270 0.824924i
\(96\) −595.000 −0.632572
\(97\) 35.0000 + 60.6218i 0.0366362 + 0.0634558i 0.883762 0.467936i \(-0.155002\pi\)
−0.847126 + 0.531392i \(0.821669\pi\)
\(98\) 435.000 + 753.442i 0.448384 + 0.776624i
\(99\) 572.000 0.580689
\(100\) 646.000 + 1118.90i 0.646000 + 1.11890i
\(101\) −210.000 + 363.731i −0.206889 + 0.358342i −0.950733 0.310011i \(-0.899667\pi\)
0.743844 + 0.668353i \(0.233001\pi\)
\(102\) 1347.50 2333.94i 1.30806 2.26563i
\(103\) 588.000 0.562499 0.281249 0.959635i \(-0.409251\pi\)
0.281249 + 0.959635i \(0.409251\pi\)
\(104\) 0 0
\(105\) −637.000 −0.592046
\(106\) 1080.00 1870.61i 0.989612 1.71406i
\(107\) 342.000 592.361i 0.308994 0.535194i −0.669148 0.743129i \(-0.733341\pi\)
0.978143 + 0.207935i \(0.0666743\pi\)
\(108\) −297.500 515.285i −0.265064 0.459105i
\(109\) −373.000 −0.327770 −0.163885 0.986479i \(-0.552403\pi\)
−0.163885 + 0.986479i \(0.552403\pi\)
\(110\) −455.000 788.083i −0.394387 0.683098i
\(111\) 458.500 + 794.145i 0.392062 + 0.679071i
\(112\) 1157.00 0.976127
\(113\) 867.000 + 1501.69i 0.721774 + 1.25015i 0.960288 + 0.279011i \(0.0900065\pi\)
−0.238514 + 0.971139i \(0.576660\pi\)
\(114\) 2205.00 3819.17i 1.81155 3.13770i
\(115\) 336.000 581.969i 0.272454 0.471903i
\(116\) −1394.00 −1.11577
\(117\) 0 0
\(118\) 1470.00 1.14682
\(119\) −500.500 + 866.891i −0.385553 + 0.667797i
\(120\) 1102.50 1909.59i 0.838700 1.45267i
\(121\) 327.500 + 567.247i 0.246056 + 0.426181i
\(122\) −280.000 −0.207787
\(123\) −1176.00 2036.89i −0.862084 1.49317i
\(124\) 1666.00 + 2885.60i 1.20654 + 2.08979i
\(125\) −1407.00 −1.00677
\(126\) −715.000 1238.42i −0.505534 0.875610i
\(127\) −946.000 + 1638.52i −0.660976 + 1.14484i 0.319384 + 0.947625i \(0.396524\pi\)
−0.980360 + 0.197218i \(0.936809\pi\)
\(128\) 1057.50 1831.64i 0.730240 1.26481i
\(129\) 1407.00 0.960306
\(130\) 0 0
\(131\) 1435.00 0.957073 0.478536 0.878068i \(-0.341167\pi\)
0.478536 + 0.878068i \(0.341167\pi\)
\(132\) 1547.00 2679.48i 1.02007 1.76681i
\(133\) −819.000 + 1418.55i −0.533957 + 0.924841i
\(134\) 1195.00 + 2069.80i 0.770390 + 1.33435i
\(135\) 245.000 0.156194
\(136\) −1732.50 3000.78i −1.09236 1.89202i
\(137\) −888.000 1538.06i −0.553773 0.959164i −0.997998 0.0632482i \(-0.979854\pi\)
0.444224 0.895916i \(-0.353479\pi\)
\(138\) 3360.00 2.07262
\(139\) 934.500 + 1618.60i 0.570239 + 0.987683i 0.996541 + 0.0831023i \(0.0264828\pi\)
−0.426302 + 0.904581i \(0.640184\pi\)
\(140\) −773.500 + 1339.74i −0.466948 + 0.808777i
\(141\) 367.500 636.529i 0.219497 0.380180i
\(142\) −45.0000 −0.0265938
\(143\) 0 0
\(144\) 1958.00 1.13310
\(145\) 287.000 497.099i 0.164373 0.284702i
\(146\) 245.000 424.352i 0.138879 0.240546i
\(147\) −609.000 1054.82i −0.341697 0.591837i
\(148\) 2227.00 1.23688
\(149\) 1233.00 + 2135.62i 0.677928 + 1.17421i 0.975604 + 0.219539i \(0.0704553\pi\)
−0.297676 + 0.954667i \(0.596211\pi\)
\(150\) −1330.00 2303.63i −0.723960 1.25394i
\(151\) 3323.00 1.79087 0.895437 0.445189i \(-0.146863\pi\)
0.895437 + 0.445189i \(0.146863\pi\)
\(152\) −2835.00 4910.36i −1.51282 2.62028i
\(153\) −847.000 + 1467.05i −0.447555 + 0.775188i
\(154\) −845.000 + 1463.58i −0.442156 + 0.765837i
\(155\) −1372.00 −0.710979
\(156\) 0 0
\(157\) −2730.00 −1.38776 −0.693878 0.720092i \(-0.744099\pi\)
−0.693878 + 0.720092i \(0.744099\pi\)
\(158\) −3260.00 + 5646.49i −1.64147 + 2.84310i
\(159\) −1512.00 + 2618.86i −0.754147 + 1.30622i
\(160\) −297.500 515.285i −0.146997 0.254605i
\(161\) −1248.00 −0.610908
\(162\) 2097.50 + 3632.98i 1.01725 + 1.76194i
\(163\) −272.000 471.118i −0.130704 0.226385i 0.793244 0.608903i \(-0.208390\pi\)
−0.923948 + 0.382518i \(0.875057\pi\)
\(164\) −5712.00 −2.71971
\(165\) 637.000 + 1103.32i 0.300548 + 0.520564i
\(166\) −770.000 + 1333.68i −0.360022 + 0.623576i
\(167\) 812.000 1406.43i 0.376254 0.651691i −0.614260 0.789104i \(-0.710545\pi\)
0.990514 + 0.137413i \(0.0438786\pi\)
\(168\) −4095.00 −1.88057
\(169\) 0 0
\(170\) 2695.00 1.21587
\(171\) −1386.00 + 2400.62i −0.619825 + 1.07357i
\(172\) 1708.50 2959.21i 0.757395 1.31185i
\(173\) 168.000 + 290.985i 0.0738312 + 0.127879i 0.900577 0.434696i \(-0.143144\pi\)
−0.826746 + 0.562575i \(0.809811\pi\)
\(174\) 2870.00 1.25043
\(175\) 494.000 + 855.633i 0.213388 + 0.369599i
\(176\) −1157.00 2003.98i −0.495524 0.858272i
\(177\) −2058.00 −0.873948
\(178\) −2975.00 5152.85i −1.25273 2.16979i
\(179\) 1514.50 2623.19i 0.632397 1.09534i −0.354663 0.934994i \(-0.615405\pi\)
0.987060 0.160350i \(-0.0512621\pi\)
\(180\) −1309.00 + 2267.25i −0.542039 + 0.938840i
\(181\) −28.0000 −0.0114985 −0.00574924 0.999983i \(-0.501830\pi\)
−0.00574924 + 0.999983i \(0.501830\pi\)
\(182\) 0 0
\(183\) 392.000 0.158347
\(184\) 2160.00 3741.23i 0.865420 1.49895i
\(185\) −458.500 + 794.145i −0.182214 + 0.315604i
\(186\) −3430.00 5940.93i −1.35215 2.34199i
\(187\) 2002.00 0.782892
\(188\) −892.500 1545.86i −0.346235 0.599697i
\(189\) −227.500 394.042i −0.0875566 0.151652i
\(190\) 4410.00 1.68387
\(191\) −211.000 365.463i −0.0799342 0.138450i 0.823287 0.567625i \(-0.192138\pi\)
−0.903221 + 0.429175i \(0.858804\pi\)
\(192\) −1004.50 + 1739.85i −0.377571 + 0.653971i
\(193\) 246.000 426.084i 0.0917485 0.158913i −0.816498 0.577348i \(-0.804088\pi\)
0.908247 + 0.418435i \(0.137421\pi\)
\(194\) −350.000 −0.129529
\(195\) 0 0
\(196\) −2958.00 −1.07799
\(197\) 1495.50 2590.28i 0.540863 0.936802i −0.457992 0.888956i \(-0.651431\pi\)
0.998855 0.0478455i \(-0.0152355\pi\)
\(198\) −1430.00 + 2476.83i −0.513261 + 0.888994i
\(199\) 35.0000 + 60.6218i 0.0124678 + 0.0215948i 0.872192 0.489164i \(-0.162698\pi\)
−0.859724 + 0.510759i \(0.829365\pi\)
\(200\) −3420.00 −1.20915
\(201\) −1673.00 2897.72i −0.587086 1.01686i
\(202\) −1050.00 1818.65i −0.365731 0.633465i
\(203\) −1066.00 −0.368564
\(204\) 4581.50 + 7935.39i 1.57240 + 2.72347i
\(205\) 1176.00 2036.89i 0.400661 0.693964i
\(206\) −1470.00 + 2546.11i −0.497183 + 0.861147i
\(207\) −2112.00 −0.709150
\(208\) 0 0
\(209\) 3276.00 1.08424
\(210\) 1592.50 2758.29i 0.523300 0.906382i
\(211\) −1425.50 + 2469.04i −0.465097 + 0.805572i −0.999206 0.0398440i \(-0.987314\pi\)
0.534109 + 0.845416i \(0.320647\pi\)
\(212\) 3672.00 + 6360.09i 1.18959 + 2.06044i
\(213\) 63.0000 0.0202661
\(214\) 1710.00 + 2961.81i 0.546230 + 0.946098i
\(215\) 703.500 + 1218.50i 0.223155 + 0.386516i
\(216\) 1575.00 0.496135
\(217\) 1274.00 + 2206.63i 0.398547 + 0.690304i
\(218\) 932.500 1615.14i 0.289710 0.501793i
\(219\) −343.000 + 594.093i −0.105835 + 0.183311i
\(220\) 3094.00 0.948170
\(221\) 0 0
\(222\) −4585.00 −1.38615
\(223\) 108.500 187.928i 0.0325816 0.0564330i −0.849275 0.527951i \(-0.822960\pi\)
0.881856 + 0.471518i \(0.156294\pi\)
\(224\) −552.500 + 956.958i −0.164801 + 0.285444i
\(225\) 836.000 + 1447.99i 0.247704 + 0.429035i
\(226\) −8670.00 −2.55186
\(227\) −1288.00 2230.88i −0.376597 0.652285i 0.613968 0.789331i \(-0.289573\pi\)
−0.990565 + 0.137046i \(0.956239\pi\)
\(228\) 7497.00 + 12985.2i 2.17764 + 3.77178i
\(229\) −455.000 −0.131298 −0.0656490 0.997843i \(-0.520912\pi\)
−0.0656490 + 0.997843i \(0.520912\pi\)
\(230\) 1680.00 + 2909.85i 0.481634 + 0.834215i
\(231\) 1183.00 2049.02i 0.336951 0.583616i
\(232\) 1845.00 3195.63i 0.522113 0.904326i
\(233\) 3061.00 0.860656 0.430328 0.902673i \(-0.358398\pi\)
0.430328 + 0.902673i \(0.358398\pi\)
\(234\) 0 0
\(235\) 735.000 0.204026
\(236\) −2499.00 + 4328.39i −0.689284 + 1.19388i
\(237\) 4564.00 7905.08i 1.25090 2.16662i
\(238\) −2502.50 4334.46i −0.681567 1.18051i
\(239\) 3477.00 0.941039 0.470520 0.882389i \(-0.344066\pi\)
0.470520 + 0.882389i \(0.344066\pi\)
\(240\) 2180.50 + 3776.74i 0.586461 + 1.01578i
\(241\) −805.000 1394.30i −0.215164 0.372676i 0.738159 0.674627i \(-0.235695\pi\)
−0.953323 + 0.301951i \(0.902362\pi\)
\(242\) −3275.00 −0.869938
\(243\) −2464.00 4267.77i −0.650476 1.12666i
\(244\) 476.000 824.456i 0.124888 0.216313i
\(245\) 609.000 1054.82i 0.158806 0.275061i
\(246\) 11760.0 3.04793
\(247\) 0 0
\(248\) −8820.00 −2.25835
\(249\) 1078.00 1867.15i 0.274359 0.475204i
\(250\) 3517.50 6092.49i 0.889865 1.54129i
\(251\) −504.000 872.954i −0.126742 0.219523i 0.795671 0.605730i \(-0.207119\pi\)
−0.922412 + 0.386206i \(0.873785\pi\)
\(252\) 4862.00 1.21539
\(253\) 1248.00 + 2161.60i 0.310123 + 0.537149i
\(254\) −4730.00 8192.60i −1.16845 2.02382i
\(255\) −3773.00 −0.926566
\(256\) 4139.50 + 7169.82i 1.01062 + 1.75045i
\(257\) −3020.50 + 5231.66i −0.733127 + 1.26981i 0.222413 + 0.974952i \(0.428607\pi\)
−0.955540 + 0.294861i \(0.904727\pi\)
\(258\) −3517.50 + 6092.49i −0.848798 + 1.47016i
\(259\) 1703.00 0.408569
\(260\) 0 0
\(261\) −1804.00 −0.427834
\(262\) −3587.50 + 6213.73i −0.845941 + 1.46521i
\(263\) 1854.00 3211.22i 0.434686 0.752899i −0.562584 0.826740i \(-0.690193\pi\)
0.997270 + 0.0738414i \(0.0235259\pi\)
\(264\) 4095.00 + 7092.75i 0.954658 + 1.65352i
\(265\) −3024.00 −0.700992
\(266\) −4095.00 7092.75i −0.943912 1.63490i
\(267\) 4165.00 + 7213.99i 0.954659 + 1.65352i
\(268\) −8126.00 −1.85214
\(269\) −4172.00 7226.12i −0.945618 1.63786i −0.754508 0.656290i \(-0.772125\pi\)
−0.191110 0.981569i \(-0.561209\pi\)
\(270\) −612.500 + 1060.88i −0.138058 + 0.239123i
\(271\) −808.500 + 1400.36i −0.181228 + 0.313897i −0.942299 0.334772i \(-0.891341\pi\)
0.761071 + 0.648669i \(0.224674\pi\)
\(272\) 6853.00 1.52766
\(273\) 0 0
\(274\) 8880.00 1.95788
\(275\) 988.000 1711.27i 0.216650 0.375248i
\(276\) −5712.00 + 9893.47i −1.24573 + 2.15767i
\(277\) 1910.00 + 3308.22i 0.414299 + 0.717587i 0.995355 0.0962771i \(-0.0306935\pi\)
−0.581056 + 0.813864i \(0.697360\pi\)
\(278\) −9345.00 −2.01610
\(279\) 2156.00 + 3734.30i 0.462639 + 0.801315i
\(280\) −2047.50 3546.37i −0.437005 0.756916i
\(281\) 6214.00 1.31920 0.659602 0.751615i \(-0.270725\pi\)
0.659602 + 0.751615i \(0.270725\pi\)
\(282\) 1837.50 + 3182.64i 0.388020 + 0.672070i
\(283\) 2646.00 4583.01i 0.555789 0.962655i −0.442052 0.896989i \(-0.645749\pi\)
0.997842 0.0656661i \(-0.0209172\pi\)
\(284\) 76.5000 132.502i 0.0159839 0.0276850i
\(285\) −6174.00 −1.28321
\(286\) 0 0
\(287\) −4368.00 −0.898379
\(288\) −935.000 + 1619.47i −0.191303 + 0.331347i
\(289\) −508.000 + 879.882i −0.103399 + 0.179093i
\(290\) 1435.00 + 2485.49i 0.290573 + 0.503287i
\(291\) 490.000 0.0987090
\(292\) 833.000 + 1442.80i 0.166944 + 0.289155i
\(293\) −451.500 782.021i −0.0900236 0.155925i 0.817497 0.575933i \(-0.195361\pi\)
−0.907521 + 0.420007i \(0.862028\pi\)
\(294\) 6090.00 1.20808
\(295\) −1029.00 1782.28i −0.203087 0.351757i
\(296\) −2947.50 + 5105.22i −0.578784 + 1.00248i
\(297\) −455.000 + 788.083i −0.0888949 + 0.153970i
\(298\) −12330.0 −2.39684
\(299\) 0 0
\(300\) 9044.00 1.74052
\(301\) 1306.50 2262.92i 0.250184 0.433332i
\(302\) −8307.50 + 14389.0i −1.58292 + 2.74170i
\(303\) 1470.00 + 2546.11i 0.278711 + 0.482741i
\(304\) 11214.0 2.11568
\(305\) 196.000 + 339.482i 0.0367965 + 0.0637334i
\(306\) −4235.00 7335.24i −0.791173 1.37035i
\(307\) −2114.00 −0.393004 −0.196502 0.980503i \(-0.562958\pi\)
−0.196502 + 0.980503i \(0.562958\pi\)
\(308\) −2873.00 4976.18i −0.531508 0.920598i
\(309\) 2058.00 3564.56i 0.378885 0.656248i
\(310\) 3430.00 5940.93i 0.628422 1.08846i
\(311\) 3402.00 0.620288 0.310144 0.950690i \(-0.399623\pi\)
0.310144 + 0.950690i \(0.399623\pi\)
\(312\) 0 0
\(313\) −10689.0 −1.93028 −0.965141 0.261732i \(-0.915706\pi\)
−0.965141 + 0.261732i \(0.915706\pi\)
\(314\) 6825.00 11821.2i 1.22661 2.12456i
\(315\) −1001.00 + 1733.78i −0.179047 + 0.310119i
\(316\) −11084.0 19198.1i −1.97318 3.41764i
\(317\) 7054.00 1.24982 0.624909 0.780698i \(-0.285136\pi\)
0.624909 + 0.780698i \(0.285136\pi\)
\(318\) −7560.00 13094.3i −1.33316 2.30909i
\(319\) 1066.00 + 1846.37i 0.187099 + 0.324065i
\(320\) −2009.00 −0.350958
\(321\) −2394.00 4146.53i −0.416262 0.720987i
\(322\) 3120.00 5404.00i 0.539971 0.935258i
\(323\) −4851.00 + 8402.18i −0.835656 + 1.44740i
\(324\) −14263.0 −2.44564
\(325\) 0 0
\(326\) 2720.00 0.462107
\(327\) −1305.50 + 2261.19i −0.220778 + 0.382398i
\(328\) 7560.00 13094.3i 1.27266 2.20430i
\(329\) −682.500 1182.12i −0.114369 0.198093i
\(330\) −6370.00 −1.06260
\(331\) 4852.00 + 8403.91i 0.805710 + 1.39553i 0.915811 + 0.401610i \(0.131549\pi\)
−0.110101 + 0.993920i \(0.535117\pi\)
\(332\) −2618.00 4534.51i −0.432775 0.749589i
\(333\) 2882.00 0.474272
\(334\) 4060.00 + 7032.13i 0.665130 + 1.15204i
\(335\) 1673.00 2897.72i 0.272853 0.472595i
\(336\) 4049.50 7013.94i 0.657495 1.13881i
\(337\) −10449.0 −1.68900 −0.844500 0.535555i \(-0.820103\pi\)
−0.844500 + 0.535555i \(0.820103\pi\)
\(338\) 0 0
\(339\) 12138.0 1.94468
\(340\) −4581.50 + 7935.39i −0.730784 + 1.26576i
\(341\) 2548.00 4413.27i 0.404639 0.700855i
\(342\) −6930.00 12003.1i −1.09571 1.89782i
\(343\) −6721.00 −1.05802
\(344\) 4522.50 + 7833.20i 0.708828 + 1.22773i
\(345\) −2352.00 4073.78i −0.367036 0.635725i
\(346\) −1680.00 −0.261033
\(347\) 310.500 + 537.802i 0.0480361 + 0.0832009i 0.889044 0.457822i \(-0.151370\pi\)
−0.841008 + 0.541023i \(0.818037\pi\)
\(348\) −4879.00 + 8450.68i −0.751557 + 1.30173i
\(349\) 6240.50 10808.9i 0.957153 1.65784i 0.227790 0.973710i \(-0.426850\pi\)
0.729363 0.684127i \(-0.239817\pi\)
\(350\) −4940.00 −0.754440
\(351\) 0 0
\(352\) 2210.00 0.334640
\(353\) −700.000 + 1212.44i −0.105545 + 0.182809i −0.913961 0.405803i \(-0.866992\pi\)
0.808416 + 0.588612i \(0.200325\pi\)
\(354\) 5145.00 8911.40i 0.772468 1.33795i
\(355\) 31.5000 + 54.5596i 0.00470943 + 0.00815697i
\(356\) 20230.0 3.01176
\(357\) 3503.50 + 6068.24i 0.519397 + 0.899623i
\(358\) 7572.50 + 13116.0i 1.11793 + 1.93631i
\(359\) 4968.00 0.730365 0.365182 0.930936i \(-0.381007\pi\)
0.365182 + 0.930936i \(0.381007\pi\)
\(360\) −3465.00 6001.56i −0.507282 0.878638i
\(361\) −4508.50 + 7808.95i −0.657312 + 1.13850i
\(362\) 70.0000 121.244i 0.0101633 0.0176034i
\(363\) 4585.00 0.662948
\(364\) 0 0
\(365\) −686.000 −0.0983750
\(366\) −980.000 + 1697.41i −0.139960 + 0.242418i
\(367\) −4361.00 + 7553.47i −0.620279 + 1.07435i 0.369155 + 0.929368i \(0.379647\pi\)
−0.989434 + 0.144987i \(0.953686\pi\)
\(368\) 4272.00 + 7399.32i 0.605145 + 1.04814i
\(369\) −7392.00 −1.04285
\(370\) −2292.50 3970.73i −0.322112 0.557914i
\(371\) 2808.00 + 4863.60i 0.392949 + 0.680608i
\(372\) 23324.0 3.25079
\(373\) −5006.00 8670.65i −0.694908 1.20362i −0.970212 0.242259i \(-0.922112\pi\)
0.275303 0.961357i \(-0.411222\pi\)
\(374\) −5005.00 + 8668.91i −0.691985 + 1.19855i
\(375\) −4924.50 + 8529.48i −0.678134 + 1.17456i
\(376\) 4725.00 0.648067
\(377\) 0 0
\(378\) 2275.00 0.309559
\(379\) −1686.00 + 2920.24i −0.228507 + 0.395785i −0.957366 0.288879i \(-0.906718\pi\)
0.728859 + 0.684664i \(0.240051\pi\)
\(380\) −7497.00 + 12985.2i −1.01207 + 1.75296i
\(381\) 6622.00 + 11469.6i 0.890434 + 1.54228i
\(382\) 2110.00 0.282610
\(383\) −423.500 733.524i −0.0565009 0.0978624i 0.836392 0.548132i \(-0.184661\pi\)
−0.892892 + 0.450270i \(0.851328\pi\)
\(384\) −7402.50 12821.5i −0.983743 1.70389i
\(385\) 2366.00 0.313201
\(386\) 1230.00 + 2130.42i 0.162190 + 0.280921i
\(387\) 2211.00 3829.56i 0.290417 0.503017i
\(388\) 595.000 1030.57i 0.0778519 0.134843i
\(389\) 11314.0 1.47466 0.737330 0.675533i \(-0.236086\pi\)
0.737330 + 0.675533i \(0.236086\pi\)
\(390\) 0 0
\(391\) −7392.00 −0.956086
\(392\) 3915.00 6780.98i 0.504432 0.873702i
\(393\) 5022.50 8699.23i 0.644661 1.11658i
\(394\) 7477.50 + 12951.4i 0.956119 + 1.65605i
\(395\) 9128.00 1.16273
\(396\) −4862.00 8421.23i −0.616982 1.06864i
\(397\) 931.000 + 1612.54i 0.117697 + 0.203856i 0.918854 0.394597i \(-0.129116\pi\)
−0.801158 + 0.598453i \(0.795782\pi\)
\(398\) −350.000 −0.0440802
\(399\) 5733.00 + 9929.85i 0.719321 + 1.24590i
\(400\) 3382.00 5857.80i 0.422750 0.732224i
\(401\) 3410.00 5906.29i 0.424657 0.735527i −0.571732 0.820441i \(-0.693728\pi\)
0.996388 + 0.0849139i \(0.0270615\pi\)
\(402\) 16730.0 2.07566
\(403\) 0 0
\(404\) 7140.00 0.879278
\(405\) 2936.50 5086.17i 0.360286 0.624034i
\(406\) 2665.00 4615.92i 0.325768 0.564246i
\(407\) −1703.00 2949.68i −0.207407 0.359239i
\(408\) −24255.0 −2.94314
\(409\) −6496.00 11251.4i −0.785346 1.36026i −0.928792 0.370601i \(-0.879152\pi\)
0.143446 0.989658i \(-0.454182\pi\)
\(410\) 5880.00 + 10184.5i 0.708274 + 1.22677i
\(411\) −12432.0 −1.49203
\(412\) −4998.00 8656.79i −0.597655 1.03517i
\(413\) −1911.00 + 3309.95i −0.227686 + 0.394363i
\(414\) 5280.00 9145.23i 0.626806 1.08566i
\(415\) 2156.00 0.255021
\(416\) 0 0
\(417\) 13083.0 1.53640
\(418\) −8190.00 + 14185.5i −0.958340 + 1.65989i
\(419\) 3671.50 6359.22i 0.428078 0.741452i −0.568625 0.822597i \(-0.692524\pi\)
0.996702 + 0.0811449i \(0.0258577\pi\)
\(420\) 5414.50 + 9378.19i 0.629049 + 1.08954i
\(421\) 5059.00 0.585655 0.292827 0.956165i \(-0.405404\pi\)
0.292827 + 0.956165i \(0.405404\pi\)
\(422\) −7127.50 12345.2i −0.822183 1.42406i
\(423\) −1155.00 2000.52i −0.132761 0.229949i
\(424\) −19440.0 −2.22663
\(425\) 2926.00 + 5067.98i 0.333957 + 0.578431i
\(426\) −157.500 + 272.798i −0.0179129 + 0.0310261i
\(427\) 364.000 630.466i 0.0412534 0.0714530i
\(428\) −11628.0 −1.31323
\(429\) 0 0
\(430\) −7035.00 −0.788972
\(431\) 1621.50 2808.52i 0.181218 0.313879i −0.761078 0.648661i \(-0.775329\pi\)
0.942296 + 0.334782i \(0.108663\pi\)
\(432\) −1557.50 + 2697.67i −0.173461 + 0.300444i
\(433\) −5799.50 10045.0i −0.643663 1.11486i −0.984609 0.174774i \(-0.944080\pi\)
0.340945 0.940083i \(-0.389253\pi\)
\(434\) −12740.0 −1.40908
\(435\) −2009.00 3479.69i −0.221435 0.383536i
\(436\) 3170.50 + 5491.47i 0.348256 + 0.603196i
\(437\) −12096.0 −1.32410
\(438\) −1715.00 2970.47i −0.187091 0.324051i
\(439\) 8687.00 15046.3i 0.944437 1.63581i 0.187563 0.982253i \(-0.439941\pi\)
0.756874 0.653560i \(-0.226725\pi\)
\(440\) −4095.00 + 7092.75i −0.443685 + 0.768485i
\(441\) −3828.00 −0.413346
\(442\) 0 0
\(443\) 989.000 0.106070 0.0530348 0.998593i \(-0.483111\pi\)
0.0530348 + 0.998593i \(0.483111\pi\)
\(444\) 7794.50 13500.5i 0.833132 1.44303i
\(445\) −4165.00 + 7213.99i −0.443685 + 0.768485i
\(446\) 542.500 + 939.638i 0.0575967 + 0.0997604i
\(447\) 17262.0 1.82654
\(448\) 1865.50 + 3231.14i 0.196733 + 0.340752i
\(449\) −7237.00 12534.9i −0.760657 1.31750i −0.942512 0.334172i \(-0.891543\pi\)
0.181855 0.983325i \(-0.441790\pi\)
\(450\) −8360.00 −0.875765
\(451\) 4368.00 + 7565.60i 0.456056 + 0.789912i
\(452\) 14739.0 25528.7i 1.53377 2.65657i
\(453\) 11630.5 20144.6i 1.20629 2.08935i
\(454\) 12880.0 1.33147
\(455\) 0 0
\(456\) −39690.0 −4.07600
\(457\) −797.000 + 1380.44i −0.0815801 + 0.141301i −0.903929 0.427683i \(-0.859330\pi\)
0.822349 + 0.568984i \(0.192663\pi\)
\(458\) 1137.50 1970.21i 0.116052 0.201008i
\(459\) −1347.50 2333.94i −0.137028 0.237340i
\(460\) −11424.0 −1.15793
\(461\) −2957.50 5122.54i −0.298795 0.517528i 0.677066 0.735923i \(-0.263251\pi\)
−0.975861 + 0.218395i \(0.929918\pi\)
\(462\) 5915.00 + 10245.1i 0.595651 + 1.03170i
\(463\) 11072.0 1.11136 0.555680 0.831396i \(-0.312458\pi\)
0.555680 + 0.831396i \(0.312458\pi\)
\(464\) 3649.00 + 6320.25i 0.365087 + 0.632350i
\(465\) −4802.00 + 8317.31i −0.478898 + 0.829475i
\(466\) −7652.50 + 13254.5i −0.760719 + 1.31760i
\(467\) 1260.00 0.124852 0.0624260 0.998050i \(-0.480116\pi\)
0.0624260 + 0.998050i \(0.480116\pi\)
\(468\) 0 0
\(469\) −6214.00 −0.611804
\(470\) −1837.50 + 3182.64i −0.180335 + 0.312350i
\(471\) −9555.00 + 16549.7i −0.934758 + 1.61905i
\(472\) −6615.00 11457.5i −0.645085 1.11732i
\(473\) −5226.00 −0.508016
\(474\) 22820.0 + 39525.4i 2.21130 + 3.83009i
\(475\) 4788.00 + 8293.06i 0.462502 + 0.801077i
\(476\) 17017.0 1.63860
\(477\) 4752.00 + 8230.71i 0.456141 + 0.790059i
\(478\) −8692.50 + 15055.9i −0.831769 + 1.44067i
\(479\) −6016.50 + 10420.9i −0.573906 + 0.994034i 0.422254 + 0.906478i \(0.361239\pi\)
−0.996160 + 0.0875564i \(0.972094\pi\)
\(480\) −4165.00 −0.396053
\(481\) 0 0
\(482\) 8050.00 0.760721
\(483\) −4368.00 + 7565.60i −0.411493 + 0.712726i
\(484\) 5567.50 9643.19i 0.522868 0.905634i
\(485\) 245.000 + 424.352i 0.0229379 + 0.0397296i
\(486\) 24640.0 2.29978
\(487\) −1140.00 1974.54i −0.106075 0.183727i 0.808102 0.589042i \(-0.200495\pi\)
−0.914177 + 0.405316i \(0.867162\pi\)
\(488\) 1260.00 + 2182.38i 0.116880 + 0.202442i
\(489\) −3808.00 −0.352155
\(490\) 3045.00 + 5274.09i 0.280733 + 0.486243i
\(491\) −8383.50 + 14520.6i −0.770554 + 1.33464i 0.166706 + 0.986007i \(0.446687\pi\)
−0.937260 + 0.348632i \(0.886646\pi\)
\(492\) −19992.0 + 34627.2i −1.83193 + 3.17299i
\(493\) −6314.00 −0.576812
\(494\) 0 0
\(495\) 4004.00 0.363569
\(496\) 8722.00 15106.9i 0.789575 1.36758i
\(497\) 58.5000 101.325i 0.00527985 0.00914496i
\(498\) 5390.00 + 9335.75i 0.485003 + 0.840050i
\(499\) −12840.0 −1.15190 −0.575949 0.817485i \(-0.695367\pi\)
−0.575949 + 0.817485i \(0.695367\pi\)
\(500\) 11959.5 + 20714.5i 1.06969 + 1.85276i
\(501\) −5684.00 9844.98i −0.506871 0.877926i
\(502\) 5040.00 0.448100
\(503\) 1099.00 + 1903.52i 0.0974195 + 0.168735i 0.910616 0.413254i \(-0.135608\pi\)
−0.813196 + 0.581989i \(0.802274\pi\)
\(504\) −6435.00 + 11145.7i −0.568726 + 0.985062i
\(505\) −1470.00 + 2546.11i −0.129533 + 0.224358i
\(506\) −12480.0 −1.09645
\(507\) 0 0
\(508\) 32164.0 2.80915
\(509\) −8533.00 + 14779.6i −0.743062 + 1.28702i 0.208033 + 0.978122i \(0.433294\pi\)
−0.951095 + 0.308899i \(0.900039\pi\)
\(510\) 9432.50 16337.6i 0.818977 1.41851i
\(511\) 637.000 + 1103.32i 0.0551452 + 0.0955144i
\(512\) −24475.0 −2.11260
\(513\) −2205.00 3819.17i −0.189772 0.328695i
\(514\) −15102.5 26158.3i −1.29600 2.24473i
\(515\) 4116.00 0.352180
\(516\) −11959.5 20714.5i −1.02032 1.76725i
\(517\) −1365.00 + 2364.25i −0.116117 + 0.201121i
\(518\) −4257.50 + 7374.21i −0.361127 + 0.625490i
\(519\) 2352.00 0.198924
\(520\) 0 0
\(521\) 2583.00 0.217204 0.108602 0.994085i \(-0.465363\pi\)
0.108602 + 0.994085i \(0.465363\pi\)
\(522\) 4510.00 7811.55i 0.378156 0.654985i
\(523\) −9310.00 + 16125.4i −0.778390 + 1.34821i 0.154480 + 0.987996i \(0.450630\pi\)
−0.932869 + 0.360215i \(0.882703\pi\)
\(524\) −12197.5 21126.7i −1.01689 1.76130i
\(525\) 6916.00 0.574931
\(526\) 9270.00 + 16056.1i 0.768424 + 1.33095i
\(527\) 7546.00 + 13070.1i 0.623736 + 1.08034i
\(528\) −16198.0 −1.33509
\(529\) 1475.50 + 2555.64i 0.121271 + 0.210047i
\(530\) 7560.00 13094.3i 0.619595 1.07317i
\(531\) −3234.00 + 5601.45i −0.264301 + 0.457782i
\(532\) 27846.0 2.26932
\(533\) 0 0
\(534\) −41650.0 −3.37523
\(535\) 2394.00 4146.53i 0.193461 0.335084i
\(536\) 10755.0 18628.2i 0.866689 1.50115i
\(537\) −10601.5 18362.3i −0.851934 1.47559i
\(538\) 41720.0 3.34327
\(539\) 2262.00 + 3917.90i 0.180763 + 0.313091i
\(540\) −2082.50 3607.00i −0.165957 0.287445i
\(541\) 16833.0 1.33772 0.668861 0.743388i \(-0.266782\pi\)
0.668861 + 0.743388i \(0.266782\pi\)
\(542\) −4042.50 7001.82i −0.320369 0.554896i
\(543\) −98.0000 + 169.741i −0.00774509 + 0.0134149i
\(544\) −3272.50 + 5668.14i −0.257918 + 0.446727i
\(545\) −2611.00 −0.205216
\(546\) 0 0
\(547\) −8615.00 −0.673402 −0.336701 0.941612i \(-0.609311\pi\)
−0.336701 + 0.941612i \(0.609311\pi\)
\(548\) −15096.0 + 26147.0i −1.17677 + 2.03822i
\(549\) 616.000 1066.94i 0.0478875 0.0829436i
\(550\) 4940.00 + 8556.33i 0.382986 + 0.663351i
\(551\) −10332.0 −0.798835
\(552\) −15120.0 26188.6i −1.16585 2.01931i
\(553\) −8476.00 14680.9i −0.651783 1.12892i
\(554\) −19100.0 −1.46477
\(555\) 3209.50 + 5559.02i 0.245470 + 0.425166i
\(556\) 15886.5 27516.2i 1.21176 2.09883i
\(557\) 4267.50 7391.53i 0.324632 0.562278i −0.656806 0.754059i \(-0.728093\pi\)
0.981438 + 0.191781i \(0.0614264\pi\)
\(558\) −21560.0 −1.63568
\(559\) 0 0
\(560\) 8099.00 0.611152
\(561\) 7007.00 12136.5i 0.527336 0.913374i
\(562\) −15535.0 + 26907.4i −1.16602 + 2.01961i
\(563\) 2320.50 + 4019.22i 0.173708 + 0.300871i 0.939713 0.341963i \(-0.111092\pi\)
−0.766006 + 0.642834i \(0.777759\pi\)
\(564\) −12495.0 −0.932862
\(565\) 6069.00 + 10511.8i 0.451902 + 0.782718i
\(566\) 13230.0 + 22915.0i 0.982506 + 1.70175i
\(567\) −10907.0 −0.807850
\(568\) 202.500 + 350.740i 0.0149590 + 0.0259097i
\(569\) 2396.50 4150.86i 0.176567 0.305823i −0.764136 0.645056i \(-0.776834\pi\)
0.940702 + 0.339233i \(0.110168\pi\)
\(570\) 15435.0 26734.2i 1.13421 1.96451i
\(571\) −5563.00 −0.407713 −0.203857 0.979001i \(-0.565348\pi\)
−0.203857 + 0.979001i \(0.565348\pi\)
\(572\) 0 0
\(573\) −2954.00 −0.215367
\(574\) 10920.0 18914.0i 0.794063 1.37536i
\(575\) −3648.00 + 6318.52i −0.264578 + 0.458262i
\(576\) 3157.00 + 5468.08i 0.228371 + 0.395550i
\(577\) −24038.0 −1.73434 −0.867171 0.498011i \(-0.834064\pi\)
−0.867171 + 0.498011i \(0.834064\pi\)
\(578\) −2540.00 4399.41i −0.182786 0.316594i
\(579\) −1722.00 2982.59i −0.123599 0.214080i
\(580\) −9758.00 −0.698584
\(581\) −2002.00 3467.57i −0.142955 0.247606i
\(582\) −1225.00 + 2121.76i −0.0872472 + 0.151117i
\(583\) 5616.00 9727.20i 0.398955 0.691011i
\(584\) −4410.00 −0.312478
\(585\) 0 0
\(586\) 4515.00 0.318281
\(587\) −10612.0 + 18380.5i −0.746174 + 1.29241i 0.203470 + 0.979081i \(0.434778\pi\)
−0.949644 + 0.313330i \(0.898555\pi\)
\(588\) −10353.0 + 17931.9i −0.726106 + 1.25765i
\(589\) 12348.0 + 21387.4i 0.863821 + 1.49618i
\(590\) 10290.0 0.718021
\(591\) −10468.5 18132.0i −0.728624 1.26201i
\(592\) −5829.50 10097.0i −0.404714 0.700986i
\(593\) −4354.00 −0.301513 −0.150757 0.988571i \(-0.548171\pi\)
−0.150757 + 0.988571i \(0.548171\pi\)
\(594\) −2275.00 3940.42i −0.157145 0.272184i
\(595\) −3503.50 + 6068.24i −0.241394 + 0.418107i
\(596\) 20961.0 36305.5i 1.44060 2.49519i
\(597\) 490.000 0.0335919
\(598\) 0 0
\(599\) 7310.00 0.498629 0.249314 0.968423i \(-0.419795\pi\)
0.249314 + 0.968423i \(0.419795\pi\)
\(600\) −11970.0 + 20732.6i −0.814455 + 1.41068i
\(601\) 3797.50 6577.46i 0.257743 0.446423i −0.707894 0.706318i \(-0.750355\pi\)
0.965637 + 0.259895i \(0.0836880\pi\)
\(602\) 6532.50 + 11314.6i 0.442267 + 0.766029i
\(603\) −10516.0 −0.710190
\(604\) −28245.5 48922.6i −1.90280 3.29575i
\(605\) 2292.50 + 3970.73i 0.154055 + 0.266831i
\(606\) −14700.0 −0.985391
\(607\) 413.000 + 715.337i 0.0276164 + 0.0478330i 0.879503 0.475893i \(-0.157875\pi\)
−0.851887 + 0.523726i \(0.824542\pi\)
\(608\) −5355.00 + 9275.13i −0.357194 + 0.618678i
\(609\) −3731.00 + 6462.28i −0.248256 + 0.429992i
\(610\) −1960.00 −0.130095
\(611\) 0 0
\(612\) 28798.0 1.90211
\(613\) 7295.00 12635.3i 0.480656 0.832521i −0.519097 0.854715i \(-0.673732\pi\)
0.999754 + 0.0221940i \(0.00706516\pi\)
\(614\) 5285.00 9153.89i 0.347370 0.601663i
\(615\) −8232.00 14258.2i −0.539750 0.934875i
\(616\) 15210.0 0.994851
\(617\) 2444.00 + 4233.13i 0.159468 + 0.276207i 0.934677 0.355498i \(-0.115689\pi\)
−0.775209 + 0.631705i \(0.782355\pi\)
\(618\) 10290.0 + 17822.8i 0.669781 + 1.16009i
\(619\) 11004.0 0.714520 0.357260 0.934005i \(-0.383711\pi\)
0.357260 + 0.934005i \(0.383711\pi\)
\(620\) 11662.0 + 20199.2i 0.755415 + 1.30842i
\(621\) 1680.00 2909.85i 0.108561 0.188032i
\(622\) −8505.00 + 14731.1i −0.548263 + 0.949619i
\(623\) 15470.0 0.994851
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 26722.5 46284.7i 1.70614 2.95513i
\(627\) 11466.0 19859.7i 0.730316 1.26494i
\(628\) 23205.0 + 40192.2i 1.47449 + 2.55389i
\(629\) 10087.0 0.639420
\(630\) −5005.00 8668.91i −0.316514 0.548219i
\(631\) −2487.50 4308.48i −0.156935 0.271819i 0.776827 0.629714i \(-0.216828\pi\)
−0.933762 + 0.357895i \(0.883495\pi\)
\(632\) 58680.0 3.69330
\(633\) 9978.50 + 17283.3i 0.626556 + 1.08523i
\(634\) −17635.0 + 30544.7i −1.10469 + 1.91338i
\(635\) −6622.00 + 11469.6i −0.413836 + 0.716786i
\(636\) 51408.0 3.20513
\(637\) 0 0
\(638\) −10660.0 −0.661494
\(639\) 99.0000 171.473i 0.00612892 0.0106156i
\(640\) 7402.50 12821.5i 0.457202 0.791898i
\(641\) −1975.00 3420.80i −0.121697 0.210785i 0.798740 0.601676i \(-0.205500\pi\)
−0.920437 + 0.390891i \(0.872167\pi\)
\(642\) 23940.0 1.47171
\(643\) −1841.00 3188.71i −0.112911 0.195568i 0.804032 0.594587i \(-0.202684\pi\)
−0.916943 + 0.399019i \(0.869351\pi\)
\(644\) 10608.0 + 18373.6i 0.649090 + 1.12426i
\(645\) 9849.00 0.601247
\(646\) −24255.0 42010.9i −1.47724 2.55866i
\(647\) −5201.00 + 9008.40i −0.316032 + 0.547383i −0.979656 0.200683i \(-0.935684\pi\)
0.663625 + 0.748066i \(0.269017\pi\)
\(648\) 18877.5 32696.8i 1.14441 1.98218i
\(649\) 7644.00 0.462332
\(650\) 0 0
\(651\) 17836.0 1.07381
\(652\) −4624.00 + 8009.00i −0.277745 + 0.481069i
\(653\) 15840.0 27435.7i 0.949260 1.64417i 0.202273 0.979329i \(-0.435167\pi\)
0.746987 0.664838i \(-0.231500\pi\)
\(654\) −6527.50 11306.0i −0.390284 0.675991i
\(655\) 10045.0 0.599222
\(656\) 14952.0 + 25897.6i 0.889905 + 1.54136i
\(657\) 1078.00 + 1867.15i 0.0640134 + 0.110874i
\(658\) 6825.00 0.404356
\(659\) −10970.0 19000.6i −0.648453 1.12315i −0.983492 0.180949i \(-0.942083\pi\)
0.335039 0.942204i \(-0.391250\pi\)
\(660\) 10829.0 18756.4i 0.638664 1.10620i
\(661\) −15687.0 + 27170.7i −0.923077 + 1.59882i −0.128451 + 0.991716i \(0.541000\pi\)
−0.794626 + 0.607100i \(0.792333\pi\)
\(662\) −48520.0 −2.84862
\(663\) 0 0
\(664\) 13860.0 0.810049
\(665\) −5733.00 + 9929.85i −0.334310 + 0.579042i
\(666\) −7205.00 + 12479.4i −0.419201 + 0.726078i
\(667\) −3936.00 6817.35i −0.228490 0.395756i
\(668\) −27608.0 −1.59908
\(669\) −759.500 1315.49i −0.0438923 0.0760237i
\(670\) 8365.00 + 14488.6i 0.482341 + 0.835438i
\(671\) −1456.00 −0.0837679
\(672\) 3867.50 + 6698.71i 0.222012 + 0.384536i
\(673\) −9006.50 + 15599.7i −0.515862 + 0.893499i 0.483969 + 0.875085i \(0.339195\pi\)
−0.999830 + 0.0184136i \(0.994138\pi\)
\(674\) 26122.5 45245.5i 1.49288 2.58574i
\(675\) −2660.00 −0.151679
\(676\) 0 0
\(677\) −10640.0 −0.604030 −0.302015 0.953303i \(-0.597659\pi\)
−0.302015 + 0.953303i \(0.597659\pi\)
\(678\) −30345.0 + 52559.1i −1.71887 + 2.97717i
\(679\) 455.000 788.083i 0.0257162 0.0445418i
\(680\) −12127.5 21005.4i −0.683924 1.18459i
\(681\) −18032.0 −1.01467
\(682\) 12740.0 + 22066.3i 0.715308 + 1.23895i
\(683\) −4668.00 8085.21i −0.261517 0.452961i 0.705128 0.709080i \(-0.250889\pi\)
−0.966645 + 0.256119i \(0.917556\pi\)
\(684\) 47124.0 2.63426
\(685\) −6216.00 10766.4i −0.346717 0.600531i
\(686\) 16802.5 29102.8i 0.935164 1.61975i
\(687\) −1592.50 + 2758.29i −0.0884391 + 0.153181i
\(688\) −17889.0 −0.991296
\(689\) 0 0
\(690\) 23520.0 1.29767
\(691\) 2100.00 3637.31i 0.115612 0.200246i −0.802412 0.596770i \(-0.796450\pi\)
0.918024 + 0.396524i \(0.129784\pi\)
\(692\) 2856.00 4946.74i 0.156891 0.271744i
\(693\) −3718.00 6439.76i −0.203803 0.352996i
\(694\) −3105.00 −0.169833
\(695\) 6541.50 + 11330.2i 0.357026 + 0.618388i
\(696\) −12915.0 22369.4i −0.703365 1.21826i
\(697\) −25872.0 −1.40599
\(698\) 31202.5 + 54044.3i 1.69202 + 2.93067i
\(699\) 10713.5 18556.3i 0.579716 1.00410i
\(700\) 8398.00 14545.8i 0.453449 0.785397i
\(701\) 9872.00 0.531898 0.265949 0.963987i \(-0.414315\pi\)
0.265949 + 0.963987i \(0.414315\pi\)
\(702\) 0 0
\(703\) 16506.0 0.885541
\(704\) 3731.00 6462.28i 0.199741 0.345961i
\(705\) 2572.50 4455.70i 0.137427 0.238030i
\(706\) −3500.00 6062.18i −0.186578 0.323163i
\(707\) 5460.00 0.290445
\(708\) 17493.0 + 30298.8i 0.928569 + 1.60833i
\(709\) 14225.0 + 24638.4i 0.753499 + 1.30510i 0.946117 + 0.323825i \(0.104969\pi\)
−0.192617 + 0.981274i \(0.561698\pi\)
\(710\) −315.000 −0.0166503
\(711\) −14344.0 24844.5i −0.756599 1.31047i
\(712\) −26775.0 + 46375.7i −1.40932 + 2.44101i
\(713\) −9408.00 + 16295.1i −0.494155 + 0.855901i
\(714\) −35035.0 −1.83635
\(715\) 0 0
\(716\) −51493.0 −2.68769
\(717\) 12169.5 21078.2i 0.633861 1.09788i
\(718\) −12420.0 + 21512.1i −0.645557 + 1.11814i
\(719\) −16359.0 28334.6i −0.848523 1.46968i −0.882527 0.470263i \(-0.844159\pi\)
0.0340039 0.999422i \(-0.489174\pi\)
\(720\) 13706.0 0.709434
\(721\) −3822.00 6619.90i −0.197418 0.341939i
\(722\) −22542.5 39044.8i −1.16197 2.01260i
\(723\) −11270.0 −0.579718
\(724\) 238.000 + 412.228i 0.0122171 + 0.0211607i
\(725\) −3116.00 + 5397.07i −0.159621 + 0.276472i
\(726\) −11462.5 + 19853.6i −0.585969 + 1.01493i
\(727\) −22834.0 −1.16488 −0.582439 0.812874i \(-0.697901\pi\)
−0.582439 + 0.812874i \(0.697901\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) 1715.00 2970.47i 0.0869521 0.150605i
\(731\) 7738.50 13403.5i 0.391544 0.678174i
\(732\) −3332.00 5771.19i −0.168244 0.291406i
\(733\) −7875.00 −0.396821 −0.198410 0.980119i \(-0.563578\pi\)
−0.198410 + 0.980119i \(0.563578\pi\)
\(734\) −21805.0 37767.4i −1.09651 1.89921i
\(735\) −4263.00 7383.73i −0.213936 0.370548i
\(736\) −8160.00 −0.408671
\(737\) 6214.00 + 10763.0i 0.310578 + 0.537936i
\(738\) 18480.0 32008.3i 0.921759 1.59653i
\(739\) −1070.00 + 1853.29i −0.0532620 + 0.0922524i −0.891427 0.453164i \(-0.850295\pi\)
0.838165 + 0.545416i \(0.183629\pi\)
\(740\) 15589.0 0.774410
\(741\) 0 0
\(742\) −28080.0 −1.38928
\(743\) 15985.5 27687.7i 0.789302 1.36711i −0.137094 0.990558i \(-0.543776\pi\)
0.926395 0.376552i \(-0.122891\pi\)
\(744\) −30870.0 + 53468.4i −1.52117 + 2.63474i
\(745\) 8631.00 + 14949.3i 0.424450 + 0.735169i
\(746\) 50060.0 2.45687
\(747\) −3388.00 5868.19i −0.165944 0.287424i
\(748\) −17017.0 29474.3i −0.831822 1.44076i
\(749\) −8892.00 −0.433787
\(750\) −24622.5 42647.4i −1.19878 2.07635i
\(751\) 3716.00 6436.30i 0.180558 0.312735i −0.761513 0.648150i \(-0.775543\pi\)
0.942071 + 0.335415i \(0.108876\pi\)
\(752\) −4672.50 + 8093.01i −0.226581 + 0.392449i
\(753\) −7056.00 −0.341481
\(754\) 0 0
\(755\) 23261.0 1.12126
\(756\) −3867.50 + 6698.71i −0.186058 + 0.322261i
\(757\) −10088.0 + 17472.9i −0.484352 + 0.838923i −0.999838 0.0179753i \(-0.994278\pi\)
0.515486 + 0.856898i \(0.327611\pi\)
\(758\) −8430.00 14601.2i −0.403946 0.699656i
\(759\) 17472.0 0.835564
\(760\) −19845.0 34372.5i −0.947176 1.64056i
\(761\) −4739.00 8208.19i −0.225741 0.390994i 0.730801 0.682591i \(-0.239147\pi\)
−0.956541 + 0.291597i \(0.905814\pi\)
\(762\) −66220.0 −3.14816
\(763\) 2424.50 + 4199.36i 0.115036 + 0.199249i
\(764\) −3587.00 + 6212.87i −0.169860 + 0.294206i
\(765\) −5929.00 + 10269.3i −0.280214 + 0.485344i
\(766\) 4235.00 0.199761
\(767\) 0 0
\(768\) 57953.0 2.72292
\(769\) −6048.00 + 10475.4i −0.283610 + 0.491228i −0.972271 0.233856i \(-0.924866\pi\)
0.688661 + 0.725084i \(0.258199\pi\)
\(770\) −5915.00 + 10245.1i −0.276834 + 0.479490i
\(771\) 21143.5 + 36621.6i 0.987632 + 1.71063i
\(772\) −8364.00 −0.389931
\(773\) 8970.50 + 15537.4i 0.417395 + 0.722950i 0.995677 0.0928877i \(-0.0296098\pi\)
−0.578281 + 0.815837i \(0.696276\pi\)
\(774\) 11055.0 + 19147.8i 0.513390 + 0.889217i
\(775\) 14896.0 0.690426
\(776\) 1575.00 + 2727.98i 0.0728598 + 0.126197i
\(777\) 5960.50 10323.9i 0.275202 0.476663i
\(778\) −28285.0 + 48991.1i −1.30343 + 2.25760i
\(779\) −42336.0 −1.94717
\(780\) 0 0
\(781\) −234.000 −0.0107211
\(782\) 18480.0 32008.3i 0.845068 1.46370i
\(783\) 1435.00 2485.49i 0.0654952 0.113441i
\(784\) 7743.00 + 13411.3i 0.352724 + 0.610936i
\(785\) −19110.0 −0.868873
\(786\) 25112.5 + 43496.1i 1.13961 + 1.97386i
\(787\) 3332.00 + 5771.19i 0.150919 + 0.261399i 0.931565 0.363574i \(-0.118444\pi\)
−0.780647 + 0.624972i \(0.785110\pi\)
\(788\) −50847.0 −2.29867
\(789\) −12978.0 22478.6i −0.585588 1.01427i
\(790\) −22820.0 + 39525.4i −1.02772 + 1.78006i
\(791\) 11271.0 19521.9i 0.506638 0.877523i
\(792\) 25740.0 1.15484
\(793\) 0 0
\(794\) −9310.00 −0.416120
\(795\) −10584.0 + 18332.0i −0.472171 + 0.817824i
\(796\) 595.000 1030.57i 0.0264940 0.0458889i
\(797\) 721.000 + 1248.81i 0.0320441 + 0.0555020i 0.881603 0.471992i \(-0.156465\pi\)
−0.849559 + 0.527494i \(0.823132\pi\)
\(798\) −57330.0 −2.54318
\(799\) −4042.50 7001.82i −0.178990 0.310021i
\(800\) 3230.00 + 5594.52i 0.142747 + 0.247245i
\(801\) 26180.0 1.15484
\(802\) 17050.0 + 29531.5i 0.750694 + 1.30024i
\(803\) 1274.00 2206.63i 0.0559881 0.0969743i
\(804\) −28441.0 + 49261.3i −1.24756 + 2.16083i
\(805\) −8736.00 −0.382489
\(806\) 0 0
\(807\) −58408.0 −2.54778
\(808\) −9450.00 + 16367.9i −0.411448 + 0.712649i
\(809\) −15103.5 + 26160.0i −0.656379 + 1.13688i 0.325167 + 0.945657i \(0.394580\pi\)
−0.981546 + 0.191226i \(0.938754\pi\)
\(810\) 14682.5 + 25430.8i 0.636902 + 1.10315i
\(811\) −21140.0 −0.915322 −0.457661 0.889127i \(-0.651313\pi\)
−0.457661 + 0.889127i \(0.651313\pi\)
\(812\) 9061.00 + 15694.1i 0.391599 + 0.678270i
\(813\) 5659.50 + 9802.54i 0.244142 + 0.422866i
\(814\) 17030.0 0.733294
\(815\) −1904.00 3297.82i −0.0818334 0.141740i
\(816\) 23985.5 41544.1i 1.02900 1.78227i
\(817\) 12663.0 21933.0i 0.542255 0.939213i
\(818\) 64960.0 2.77662
\(819\) 0 0
\(820\) −39984.0 −1.70281
\(821\) 284.500 492.768i 0.0120939 0.0209473i −0.859915 0.510437i \(-0.829484\pi\)
0.872009 + 0.489490i \(0.162817\pi\)
\(822\) 31080.0 53832.1i 1.31878 2.28420i
\(823\) 4269.00 + 7394.12i 0.180812 + 0.313175i 0.942157 0.335171i \(-0.108794\pi\)
−0.761346 + 0.648346i \(0.775461\pi\)
\(824\) 26460.0 1.11866
\(825\) −6916.00 11978.9i −0.291860 0.505516i
\(826\) −9555.00 16549.7i −0.402495 0.697142i
\(827\) 32702.0 1.37504 0.687521 0.726164i \(-0.258699\pi\)
0.687521 + 0.726164i \(0.258699\pi\)
\(828\) 17952.0 + 31093.8i 0.753472 + 1.30505i
\(829\) 10577.0 18319.9i 0.443130 0.767523i −0.554790 0.831990i \(-0.687202\pi\)
0.997920 + 0.0644673i \(0.0205348\pi\)
\(830\) −5390.00 + 9335.75i −0.225409 + 0.390420i
\(831\) 26740.0 1.11625
\(832\) 0 0
\(833\) −13398.0 −0.557279
\(834\) −32707.5 + 56651.1i −1.35800 + 2.35212i
\(835\) 5684.00 9844.98i 0.235572 0.408023i
\(836\) −27846.0 48230.7i −1.15200 1.99533i
\(837\) −6860.00 −0.283293
\(838\) 18357.5 + 31796.1i 0.756741 + 1.31071i
\(839\) −1092.00 1891.40i −0.0449345 0.0778288i 0.842683 0.538409i \(-0.180975\pi\)
−0.887618 + 0.460581i \(0.847641\pi\)
\(840\) −28665.0 −1.17742
\(841\) 8832.50 + 15298.3i 0.362151 + 0.627264i
\(842\) −12647.5 + 21906.1i −0.517650 + 0.896597i
\(843\) 21749.0 37670.4i 0.888583 1.53907i
\(844\) 48467.0 1.97666
\(845\) 0 0
\(846\) 11550.0 0.469382
\(847\) 4257.50 7374.21i 0.172715 0.299151i
\(848\) 19224.0 33296.9i 0.778485 1.34837i
\(849\) −18522.0 32081.0i −0.748732 1.29684i
\(850\) −29260.0 −1.18072
\(851\) 6288.00 + 10891.1i 0.253290 + 0.438711i
\(852\) −535.500 927.513i −0.0215328 0.0372959i
\(853\) −36687.0 −1.47261 −0.736307 0.676648i \(-0.763432\pi\)
−0.736307 + 0.676648i \(0.763432\pi\)
\(854\) 1820.00 + 3152.33i 0.0729264 + 0.126312i
\(855\) −9702.00 + 16804.4i −0.388072 + 0.672160i
\(856\) 15390.0 26656.3i 0.614509 1.06436i
\(857\) 36806.0 1.46706 0.733529 0.679658i \(-0.237872\pi\)
0.733529 + 0.679658i \(0.237872\pi\)
\(858\) 0 0
\(859\) 4900.00 0.194628 0.0973142 0.995254i \(-0.468975\pi\)
0.0973142 + 0.995254i \(0.468975\pi\)
\(860\) 11959.5 20714.5i 0.474204 0.821346i
\(861\) −15288.0 + 26479.6i −0.605126 + 1.04811i
\(862\) 8107.50 + 14042.6i 0.320351 + 0.554864i
\(863\) 13697.0 0.540268 0.270134 0.962823i \(-0.412932\pi\)
0.270134 + 0.962823i \(0.412932\pi\)
\(864\) −1487.50 2576.43i −0.0585715 0.101449i
\(865\) 1176.00 + 2036.89i 0.0462257 + 0.0800652i
\(866\) 57995.0 2.27569
\(867\) 3556.00 + 6159.17i 0.139294 + 0.241265i
\(868\) 21658.0 37512.8i 0.846913 1.46690i
\(869\) −16952.0 + 29361.7i −0.661746 + 1.14618i
\(870\) 20090.0 0.782891
\(871\) 0 0
\(872\) −16785.0 −0.651848
\(873\) 770.000 1333.68i 0.0298517 0.0517047i
\(874\) 30240.0 52377.2i 1.17035 2.02710i
\(875\) 9145.50 + 15840.5i 0.353342 + 0.612006i
\(876\) 11662.0 0.449797
\(877\) 3119.50 + 5403.13i 0.120112 + 0.208040i 0.919812 0.392360i \(-0.128341\pi\)
−0.799700 + 0.600400i \(0.795008\pi\)
\(878\) 43435.0 + 75231.6i 1.66954 + 2.89174i
\(879\) −6321.00 −0.242551
\(880\) −8099.00 14027.9i −0.310247 0.537363i
\(881\) −66.5000 + 115.181i −0.00254307 + 0.00440472i −0.867294 0.497796i \(-0.834143\pi\)
0.864751 + 0.502201i \(0.167476\pi\)
\(882\) 9570.00 16575.7i 0.365350 0.632805i
\(883\) −26003.0 −0.991020 −0.495510 0.868602i \(-0.665019\pi\)
−0.495510 + 0.868602i \(0.665019\pi\)
\(884\) 0 0
\(885\) −14406.0 −0.547178
\(886\) −2472.50 + 4282.50i −0.0937531 + 0.162385i
\(887\) 15624.0 27061.6i 0.591435 1.02439i −0.402605 0.915374i \(-0.631895\pi\)
0.994039 0.109021i \(-0.0347716\pi\)
\(888\) 20632.5 + 35736.5i 0.779709 + 1.35050i
\(889\) 24596.0 0.927923
\(890\) −20825.0 36070.0i −0.784332 1.35850i
\(891\) 10907.0 + 18891.5i 0.410099 + 0.710312i
\(892\) −3689.00 −0.138472
\(893\) −6615.00 11457.5i −0.247886 0.429352i
\(894\) −43155.0 + 74746.7i −1.61445 + 2.79631i
\(895\) 10601.5 18362.3i 0.395943 0.685794i
\(896\) −27495.0 −1.02516
\(897\) 0 0
\(898\) 72370.0 2.68933
\(899\) −8036.00 + 13918.8i −0.298126 + 0.516370i
\(900\) 14212.0 24615.9i 0.526370 0.911700i
\(901\) 16632.0 + 28807.5i 0.614975 + 1.06517i
\(902\) −43680.0 −1.61240
\(903\) −9145.50 15840.5i −0.337036 0.583763i
\(904\) 39015.0 + 67576.0i 1.43542 + 2.48622i
\(905\) −196.000 −0.00719918
\(906\) 58152.5 + 100723.i 2.13244 + 3.69349i
\(907\) 19126.5 33128.1i 0.700204 1.21279i −0.268191 0.963366i \(-0.586426\pi\)
0.968395 0.249423i \(-0.0802410\pi\)
\(908\) −21896.0 + 37925.0i −0.800269 + 1.38611i
\(909\) 9240.00 0.337152
\(910\) 0 0
\(911\) 36374.0 1.32286 0.661429 0.750007i \(-0.269950\pi\)
0.661429 + 0.750007i \(0.269950\pi\)
\(912\) 39249.0 67981.3i 1.42507 2.46829i
\(913\) −4004.00 + 6935.13i −0.145140 + 0.251390i
\(914\) −3985.00 6902.22i −0.144215 0.249787i
\(915\) 2744.00 0.0991408
\(916\) 3867.50 + 6698.71i 0.139504 + 0.241628i
\(917\) −9327.50 16155.7i −0.335901 0.581798i
\(918\) 13475.0 0.484468
\(919\) 13824.0 + 23943.9i 0.496204 + 0.859451i 0.999990 0.00437745i \(-0.00139339\pi\)
−0.503786 + 0.863828i \(0.668060\pi\)
\(920\) 15120.0 26188.6i 0.541839 0.938492i
\(921\) −7399.00 + 12815.4i −0.264718 + 0.458505i
\(922\) 29575.0 1.05640
\(923\) 0 0
\(924\) −40222.0 −1.43204
\(925\) 4978.00 8622.15i 0.176947 0.306481i
\(926\) −27680.0 + 47943.2i −0.982312 + 1.70141i
\(927\) −6468.00 11202.9i −0.229166 0.396927i
\(928\) −6970.00 −0.246553
\(929\) 378.000 + 654.715i 0.0133496 + 0.0231222i 0.872623 0.488394i \(-0.162417\pi\)
−0.859273 + 0.511517i \(0.829084\pi\)
\(930\) −24010.0 41586.5i −0.846579 1.46632i
\(931\) −21924.0 −0.771783
\(932\) −26018.5 45065.4i −0.914447 1.58387i
\(933\) 11907.0 20623.5i 0.417811 0.723670i
\(934\) −3150.00 + 5455.96i −0.110355 + 0.191140i
\(935\) 14014.0 0.490168
\(936\) 0 0
\(937\) 20846.0 0.726797 0.363399 0.931634i \(-0.381616\pi\)
0.363399 + 0.931634i \(0.381616\pi\)
\(938\) 15535.0 26907.4i 0.540763 0.936629i
\(939\) −37411.5 + 64798.6i −1.30019 + 2.25199i
\(940\) −6247.50 10821.0i −0.216778 0.375470i
\(941\) 41321.0 1.43148 0.715742 0.698365i \(-0.246089\pi\)
0.715742 + 0.698365i \(0.246089\pi\)
\(942\) −47775.0 82748.7i −1.65243 2.86210i
\(943\) −16128.0 27934.5i −0.556946 0.964659i
\(944\) 26166.0 0.902151
\(945\) −1592.50 2758.29i −0.0548191 0.0949494i
\(946\) 13065.0 22629.2i 0.449027 0.777738i
\(947\) 27483.0 47602.0i 0.943060 1.63343i 0.183469 0.983025i \(-0.441267\pi\)
0.759590 0.650402i \(-0.225399\pi\)
\(948\) −155176. −5.31633
\(949\) 0 0
\(950\) −47880.0 −1.63519
\(951\) 24689.0 42762.6i 0.841846 1.45812i
\(952\) −22522.5 + 39010.1i −0.766763 + 1.32807i
\(953\) 22276.5 + 38584.0i 0.757195 + 1.31150i 0.944276 + 0.329155i \(0.106764\pi\)
−0.187081 + 0.982344i \(0.559903\pi\)
\(954\) −47520.0 −1.61270
\(955\) −1477.00 2558.24i −0.0500467 0.0866834i
\(956\) −29554.5 51189.9i −0.999854 1.73180i
\(957\) 14924.0 0.504101
\(958\) −30082.5 52104.4i −1.01453 1.75722i
\(959\) −11544.0 + 19994.8i −0.388712 + 0.673270i
\(960\) −7031.50 + 12178.9i −0.236397 + 0.409451i
\(961\) 8625.00 0.289517
\(962\) 0 0
\(963\) −15048.0 −0.503546
\(964\) −13685.0 + 23703.1i −0.457224 + 0.791936i
\(965\) 1722.00 2982.59i 0.0574437 0.0994954i
\(966\) −21840.0 37828.0i −0.727423 1.25993i
\(967\) 27907.0 0.928054 0.464027 0.885821i \(-0.346404\pi\)
0.464027 + 0.885821i \(0.346404\pi\)
\(968\) 14737.5 + 25526.1i 0.489340 + 0.847562i
\(969\) 33957.0 + 58815.2i 1.12575 + 1.94986i
\(970\) −2450.00 −0.0810977
\(971\) 8221.50 + 14240.1i 0.271720 + 0.470634i 0.969302 0.245871i \(-0.0790741\pi\)
−0.697582 + 0.716505i \(0.745741\pi\)
\(972\) −41888.0 + 72552.1i −1.38226 + 2.39415i
\(973\) 12148.5 21041.8i 0.400270 0.693289i
\(974\) 11400.0 0.375030
\(975\) 0 0
\(976\) −4984.00 −0.163457
\(977\) −22707.0 + 39329.7i −0.743563 + 1.28789i 0.207300 + 0.978277i \(0.433532\pi\)
−0.950863 + 0.309612i \(0.899801\pi\)
\(978\) 9520.00 16489.1i 0.311264 0.539125i
\(979\) −15470.0 26794.8i −0.505029 0.874736i
\(980\) −20706.0 −0.674927
\(981\) 4103.00 + 7106.60i 0.133536 + 0.231291i
\(982\) −41917.5 72603.2i −1.36216 2.35933i
\(983\) 8981.00 0.291403 0.145702 0.989329i \(-0.453456\pi\)
0.145702 + 0.989329i \(0.453456\pi\)
\(984\) −52920.0 91660.1i −1.71446 2.96953i
\(985\) 10468.5 18132.0i 0.338634 0.586531i
\(986\) 15785.0 27340.4i 0.509834 0.883059i
\(987\) −9555.00 −0.308145
\(988\) 0 0
\(989\) 19296.0 0.620402
\(990\) −10010.0 + 17337.8i −0.321352 + 0.556598i
\(991\) 8707.00 15081.0i 0.279099 0.483413i −0.692062 0.721838i \(-0.743298\pi\)
0.971161 + 0.238424i \(0.0766309\pi\)
\(992\) 8330.00 + 14428.0i 0.266611 + 0.461783i
\(993\) 67928.0 2.17083
\(994\) 292.500 + 506.625i 0.00933354 + 0.0161662i
\(995\) 245.000 + 424.352i 0.00780605 + 0.0135205i
\(996\) −36652.0 −1.16603
\(997\) 11851.0 + 20526.5i 0.376454 + 0.652038i 0.990544 0.137199i \(-0.0438099\pi\)
−0.614089 + 0.789237i \(0.710477\pi\)
\(998\) 32100.0 55598.8i 1.01814 1.76348i
\(999\) −2292.50 + 3970.73i −0.0726041 + 0.125754i
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 169.4.c.a.22.1 2
13.2 odd 12 169.4.e.e.23.1 4
13.3 even 3 inner 169.4.c.a.146.1 2
13.4 even 6 13.4.a.a.1.1 1
13.5 odd 4 169.4.e.e.147.2 4
13.6 odd 12 169.4.b.a.168.1 2
13.7 odd 12 169.4.b.a.168.2 2
13.8 odd 4 169.4.e.e.147.1 4
13.9 even 3 169.4.a.e.1.1 1
13.10 even 6 169.4.c.e.146.1 2
13.11 odd 12 169.4.e.e.23.2 4
13.12 even 2 169.4.c.e.22.1 2
39.17 odd 6 117.4.a.b.1.1 1
39.35 odd 6 1521.4.a.a.1.1 1
52.43 odd 6 208.4.a.g.1.1 1
65.4 even 6 325.4.a.d.1.1 1
65.17 odd 12 325.4.b.b.274.1 2
65.43 odd 12 325.4.b.b.274.2 2
91.69 odd 6 637.4.a.a.1.1 1
104.43 odd 6 832.4.a.a.1.1 1
104.69 even 6 832.4.a.r.1.1 1
143.43 odd 6 1573.4.a.a.1.1 1
156.95 even 6 1872.4.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.a.a.1.1 1 13.4 even 6
117.4.a.b.1.1 1 39.17 odd 6
169.4.a.e.1.1 1 13.9 even 3
169.4.b.a.168.1 2 13.6 odd 12
169.4.b.a.168.2 2 13.7 odd 12
169.4.c.a.22.1 2 1.1 even 1 trivial
169.4.c.a.146.1 2 13.3 even 3 inner
169.4.c.e.22.1 2 13.12 even 2
169.4.c.e.146.1 2 13.10 even 6
169.4.e.e.23.1 4 13.2 odd 12
169.4.e.e.23.2 4 13.11 odd 12
169.4.e.e.147.1 4 13.8 odd 4
169.4.e.e.147.2 4 13.5 odd 4
208.4.a.g.1.1 1 52.43 odd 6
325.4.a.d.1.1 1 65.4 even 6
325.4.b.b.274.1 2 65.17 odd 12
325.4.b.b.274.2 2 65.43 odd 12
637.4.a.a.1.1 1 91.69 odd 6
832.4.a.a.1.1 1 104.43 odd 6
832.4.a.r.1.1 1 104.69 even 6
1521.4.a.a.1.1 1 39.35 odd 6
1573.4.a.a.1.1 1 143.43 odd 6
1872.4.a.k.1.1 1 156.95 even 6