Properties

Label 143.4.h.a.27.1
Level $143$
Weight $4$
Character 143.27
Analytic conductor $8.437$
Analytic rank $0$
Dimension $68$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [143,4,Mod(14,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.14");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.h (of order \(5\), degree \(4\), 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: \(68\)
Relative dimension: \(17\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 27.1
Character \(\chi\) \(=\) 143.27
Dual form 143.4.h.a.53.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.47502 - 4.53963i) q^{2} +(-3.70948 - 2.69510i) q^{3} +(-11.9604 + 8.68976i) q^{4} +(-2.80173 + 8.62283i) q^{5} +(-6.76320 + 20.8150i) q^{6} +(-9.62173 + 6.99059i) q^{7} +(26.1970 + 19.0332i) q^{8} +(-1.84675 - 5.68371i) q^{9} +O(q^{10})\) \(q+(-1.47502 - 4.53963i) q^{2} +(-3.70948 - 2.69510i) q^{3} +(-11.9604 + 8.68976i) q^{4} +(-2.80173 + 8.62283i) q^{5} +(-6.76320 + 20.8150i) q^{6} +(-9.62173 + 6.99059i) q^{7} +(26.1970 + 19.0332i) q^{8} +(-1.84675 - 5.68371i) q^{9} +43.2770 q^{10} +(35.7483 - 7.28404i) q^{11} +67.7867 q^{12} +(4.01722 + 12.3637i) q^{13} +(45.9269 + 33.3678i) q^{14} +(33.6323 - 24.4353i) q^{15} +(11.2150 - 34.5163i) q^{16} +(-4.68764 + 14.4271i) q^{17} +(-23.0780 + 16.7671i) q^{18} +(-26.6482 - 19.3610i) q^{19} +(-41.4205 - 127.479i) q^{20} +54.5319 q^{21} +(-85.7961 - 151.540i) q^{22} +77.8610 q^{23} +(-45.8809 - 141.207i) q^{24} +(34.6237 + 25.1556i) q^{25} +(50.2013 - 36.4734i) q^{26} +(-46.7238 + 143.801i) q^{27} +(54.3334 - 167.221i) q^{28} +(-73.8737 + 53.6724i) q^{29} +(-160.535 - 116.636i) q^{30} +(-15.6764 - 48.2470i) q^{31} +85.8164 q^{32} +(-152.239 - 69.3252i) q^{33} +72.4080 q^{34} +(-33.3212 - 102.552i) q^{35} +(71.4780 + 51.9318i) q^{36} +(58.6818 - 42.6349i) q^{37} +(-48.5855 + 149.531i) q^{38} +(18.4196 - 56.6898i) q^{39} +(-237.517 + 172.566i) q^{40} +(94.7024 + 68.8053i) q^{41} +(-80.4354 - 247.555i) q^{42} +324.184 q^{43} +(-364.269 + 397.765i) q^{44} +54.1837 q^{45} +(-114.846 - 353.460i) q^{46} +(269.718 + 195.962i) q^{47} +(-134.627 + 97.8121i) q^{48} +(-62.2836 + 191.689i) q^{49} +(63.1265 - 194.283i) q^{50} +(56.2711 - 40.8834i) q^{51} +(-155.486 - 112.967i) q^{52} +(151.077 + 464.969i) q^{53} +721.723 q^{54} +(-37.3480 + 328.659i) q^{55} -385.114 q^{56} +(46.6711 + 143.639i) q^{57} +(352.618 + 256.192i) q^{58} +(-199.585 + 145.007i) q^{59} +(-189.920 + 584.513i) q^{60} +(149.575 - 460.343i) q^{61} +(-195.900 + 142.330i) q^{62} +(57.5014 + 41.7772i) q^{63} +(-216.301 - 665.706i) q^{64} -117.865 q^{65} +(-90.1559 + 793.364i) q^{66} +493.429 q^{67} +(-69.3017 - 213.289i) q^{68} +(-288.824 - 209.843i) q^{69} +(-416.400 + 302.532i) q^{70} +(-272.343 + 838.186i) q^{71} +(59.8001 - 184.046i) q^{72} +(-107.137 + 77.8398i) q^{73} +(-280.103 - 203.507i) q^{74} +(-60.6392 - 186.628i) q^{75} +486.967 q^{76} +(-293.041 + 319.987i) q^{77} -284.520 q^{78} +(138.610 + 426.598i) q^{79} +(266.207 + 193.411i) q^{80} +(430.338 - 312.659i) q^{81} +(172.663 - 531.403i) q^{82} +(-300.018 + 923.362i) q^{83} +(-652.225 + 473.870i) q^{84} +(-111.269 - 80.8415i) q^{85} +(-478.177 - 1471.68i) q^{86} +418.685 q^{87} +(1075.14 + 489.586i) q^{88} -1496.56 q^{89} +(-79.9218 - 245.974i) q^{90} +(-125.082 - 90.8777i) q^{91} +(-931.252 + 676.594i) q^{92} +(-71.8789 + 221.221i) q^{93} +(491.755 - 1513.47i) q^{94} +(241.608 - 175.538i) q^{95} +(-318.334 - 231.284i) q^{96} +(195.378 + 601.311i) q^{97} +962.067 q^{98} +(-107.419 - 189.731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9} - 36 q^{10} - 51 q^{11} - 524 q^{12} - 221 q^{13} + 133 q^{14} + 178 q^{15} - 140 q^{16} + 302 q^{17} + 575 q^{18} - 59 q^{19} + 73 q^{20} - 136 q^{21} - 196 q^{22} - 1264 q^{23} + 224 q^{24} - 603 q^{25} - 13 q^{26} - 45 q^{27} + 948 q^{28} + 916 q^{29} - 90 q^{30} + 160 q^{31} + 1752 q^{32} + 713 q^{33} - 1204 q^{34} - 582 q^{35} + 373 q^{36} - 692 q^{37} + 663 q^{38} + 221 q^{39} + 1293 q^{40} - 2 q^{41} - 1782 q^{42} + 698 q^{43} + 897 q^{44} - 2048 q^{45} - 3385 q^{46} + 1754 q^{47} - 3944 q^{48} - 1579 q^{49} + 1061 q^{50} + 1103 q^{51} - 208 q^{52} + 1354 q^{53} + 6262 q^{54} + 3556 q^{55} - 3350 q^{56} + 1765 q^{57} + 819 q^{58} - 217 q^{59} + 228 q^{60} - 1632 q^{61} - 823 q^{62} + 352 q^{63} - 6388 q^{64} - 728 q^{65} + 6541 q^{66} - 6426 q^{67} + 1688 q^{68} + 486 q^{69} - 6242 q^{70} + 2988 q^{71} - 2073 q^{72} + 2116 q^{73} - 3120 q^{74} - 5631 q^{75} + 4008 q^{76} + 5450 q^{77} + 936 q^{78} + 4520 q^{79} + 2955 q^{80} - 6210 q^{81} + 6592 q^{82} - 641 q^{83} + 517 q^{84} - 1856 q^{85} - 3869 q^{86} + 1924 q^{87} + 4998 q^{88} - 7266 q^{89} + 6420 q^{90} + 104 q^{91} - 1429 q^{92} + 7114 q^{93} + 1427 q^{94} - 708 q^{95} + 8925 q^{96} - 3725 q^{97} - 2974 q^{98} + 7833 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(67\) \(79\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.47502 4.53963i −0.521497 1.60500i −0.771141 0.636664i \(-0.780314\pi\)
0.249645 0.968337i \(-0.419686\pi\)
\(3\) −3.70948 2.69510i −0.713890 0.518671i 0.170536 0.985351i \(-0.445450\pi\)
−0.884426 + 0.466680i \(0.845450\pi\)
\(4\) −11.9604 + 8.68976i −1.49505 + 1.08622i
\(5\) −2.80173 + 8.62283i −0.250594 + 0.771249i 0.744072 + 0.668100i \(0.232892\pi\)
−0.994666 + 0.103149i \(0.967108\pi\)
\(6\) −6.76320 + 20.8150i −0.460177 + 1.41628i
\(7\) −9.62173 + 6.99059i −0.519524 + 0.377457i −0.816425 0.577452i \(-0.804047\pi\)
0.296900 + 0.954908i \(0.404047\pi\)
\(8\) 26.1970 + 19.0332i 1.15775 + 0.841158i
\(9\) −1.84675 5.68371i −0.0683981 0.210508i
\(10\) 43.2770 1.36854
\(11\) 35.7483 7.28404i 0.979866 0.199656i
\(12\) 67.7867 1.63070
\(13\) 4.01722 + 12.3637i 0.0857059 + 0.263776i
\(14\) 45.9269 + 33.3678i 0.876749 + 0.636995i
\(15\) 33.6323 24.4353i 0.578921 0.420611i
\(16\) 11.2150 34.5163i 0.175235 0.539318i
\(17\) −4.68764 + 14.4271i −0.0668777 + 0.205828i −0.978911 0.204288i \(-0.934512\pi\)
0.912033 + 0.410117i \(0.134512\pi\)
\(18\) −23.0780 + 16.7671i −0.302196 + 0.219558i
\(19\) −26.6482 19.3610i −0.321764 0.233775i 0.415164 0.909747i \(-0.363724\pi\)
−0.736928 + 0.675972i \(0.763724\pi\)
\(20\) −41.4205 127.479i −0.463095 1.42526i
\(21\) 54.5319 0.566659
\(22\) −85.7961 151.540i −0.831445 1.46857i
\(23\) 77.8610 0.705876 0.352938 0.935647i \(-0.385183\pi\)
0.352938 + 0.935647i \(0.385183\pi\)
\(24\) −45.8809 141.207i −0.390225 1.20099i
\(25\) 34.6237 + 25.1556i 0.276989 + 0.201245i
\(26\) 50.2013 36.4734i 0.378665 0.275116i
\(27\) −46.7238 + 143.801i −0.333037 + 1.02498i
\(28\) 54.3334 167.221i 0.366716 1.12864i
\(29\) −73.8737 + 53.6724i −0.473034 + 0.343680i −0.798623 0.601832i \(-0.794438\pi\)
0.325588 + 0.945512i \(0.394438\pi\)
\(30\) −160.535 116.636i −0.976987 0.709822i
\(31\) −15.6764 48.2470i −0.0908246 0.279529i 0.895318 0.445427i \(-0.146948\pi\)
−0.986143 + 0.165897i \(0.946948\pi\)
\(32\) 85.8164 0.474073
\(33\) −152.239 69.3252i −0.803073 0.365696i
\(34\) 72.4080 0.365231
\(35\) −33.3212 102.552i −0.160923 0.495271i
\(36\) 71.4780 + 51.9318i 0.330917 + 0.240425i
\(37\) 58.6818 42.6349i 0.260736 0.189436i −0.449735 0.893162i \(-0.648482\pi\)
0.710471 + 0.703726i \(0.248482\pi\)
\(38\) −48.5855 + 149.531i −0.207411 + 0.638344i
\(39\) 18.4196 56.6898i 0.0756283 0.232760i
\(40\) −237.517 + 172.566i −0.938869 + 0.682128i
\(41\) 94.7024 + 68.8053i 0.360733 + 0.262088i 0.753358 0.657611i \(-0.228433\pi\)
−0.392625 + 0.919699i \(0.628433\pi\)
\(42\) −80.4354 247.555i −0.295511 0.909489i
\(43\) 324.184 1.14971 0.574857 0.818254i \(-0.305058\pi\)
0.574857 + 0.818254i \(0.305058\pi\)
\(44\) −364.269 + 397.765i −1.24808 + 1.36285i
\(45\) 54.1837 0.179494
\(46\) −114.846 353.460i −0.368112 1.13293i
\(47\) 269.718 + 195.962i 0.837073 + 0.608169i 0.921552 0.388256i \(-0.126922\pi\)
−0.0844783 + 0.996425i \(0.526922\pi\)
\(48\) −134.627 + 97.8121i −0.404827 + 0.294124i
\(49\) −62.2836 + 191.689i −0.181585 + 0.558861i
\(50\) 63.1265 194.283i 0.178549 0.549517i
\(51\) 56.2711 40.8834i 0.154501 0.112251i
\(52\) −155.486 112.967i −0.414653 0.301263i
\(53\) 151.077 + 464.969i 0.391549 + 1.20506i 0.931617 + 0.363442i \(0.118398\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(54\) 721.723 1.81878
\(55\) −37.3480 + 328.659i −0.0915638 + 0.805753i
\(56\) −385.114 −0.918982
\(57\) 46.6711 + 143.639i 0.108452 + 0.333779i
\(58\) 352.618 + 256.192i 0.798292 + 0.579993i
\(59\) −199.585 + 145.007i −0.440403 + 0.319971i −0.785795 0.618487i \(-0.787746\pi\)
0.345392 + 0.938458i \(0.387746\pi\)
\(60\) −189.920 + 584.513i −0.408642 + 1.25767i
\(61\) 149.575 460.343i 0.313952 0.966245i −0.662232 0.749299i \(-0.730391\pi\)
0.976184 0.216946i \(-0.0696094\pi\)
\(62\) −195.900 + 142.330i −0.401280 + 0.291547i
\(63\) 57.5014 + 41.7772i 0.114992 + 0.0835466i
\(64\) −216.301 665.706i −0.422463 1.30021i
\(65\) −117.865 −0.224914
\(66\) −90.1559 + 793.364i −0.168143 + 1.47964i
\(67\) 493.429 0.899731 0.449865 0.893096i \(-0.351472\pi\)
0.449865 + 0.893096i \(0.351472\pi\)
\(68\) −69.3017 213.289i −0.123589 0.380368i
\(69\) −288.824 209.843i −0.503918 0.366118i
\(70\) −416.400 + 302.532i −0.710990 + 0.516564i
\(71\) −272.343 + 838.186i −0.455228 + 1.40105i 0.415639 + 0.909530i \(0.363558\pi\)
−0.870867 + 0.491518i \(0.836442\pi\)
\(72\) 59.8001 184.046i 0.0978821 0.301250i
\(73\) −107.137 + 77.8398i −0.171774 + 0.124801i −0.670350 0.742045i \(-0.733856\pi\)
0.498577 + 0.866846i \(0.333856\pi\)
\(74\) −280.103 203.507i −0.440018 0.319692i
\(75\) −60.6392 186.628i −0.0933601 0.287333i
\(76\) 486.967 0.734986
\(77\) −293.041 + 319.987i −0.433703 + 0.473583i
\(78\) −284.520 −0.413020
\(79\) 138.610 + 426.598i 0.197403 + 0.607545i 0.999940 + 0.0109422i \(0.00348307\pi\)
−0.802537 + 0.596602i \(0.796517\pi\)
\(80\) 266.207 + 193.411i 0.372035 + 0.270300i
\(81\) 430.338 312.659i 0.590313 0.428888i
\(82\) 172.663 531.403i 0.232530 0.715654i
\(83\) −300.018 + 923.362i −0.396763 + 1.22111i 0.530818 + 0.847486i \(0.321885\pi\)
−0.927580 + 0.373624i \(0.878115\pi\)
\(84\) −652.225 + 473.870i −0.847186 + 0.615517i
\(85\) −111.269 80.8415i −0.141986 0.103159i
\(86\) −478.177 1471.68i −0.599571 1.84529i
\(87\) 418.685 0.515951
\(88\) 1075.14 + 489.586i 1.30239 + 0.593069i
\(89\) −1496.56 −1.78242 −0.891209 0.453593i \(-0.850142\pi\)
−0.891209 + 0.453593i \(0.850142\pi\)
\(90\) −79.9218 245.974i −0.0936056 0.288088i
\(91\) −125.082 90.8777i −0.144090 0.104688i
\(92\) −931.252 + 676.594i −1.05532 + 0.766737i
\(93\) −71.8789 + 221.221i −0.0801451 + 0.246661i
\(94\) 491.755 1513.47i 0.539582 1.66066i
\(95\) 241.608 175.538i 0.260931 0.189577i
\(96\) −318.334 231.284i −0.338436 0.245888i
\(97\) 195.378 + 601.311i 0.204511 + 0.629421i 0.999733 + 0.0231026i \(0.00735442\pi\)
−0.795222 + 0.606319i \(0.792646\pi\)
\(98\) 962.067 0.991668
\(99\) −107.419 189.731i −0.109050 0.192613i
\(100\) −632.710 −0.632710
\(101\) −411.847 1267.53i −0.405745 1.24876i −0.920271 0.391281i \(-0.872032\pi\)
0.514526 0.857475i \(-0.327968\pi\)
\(102\) −268.596 195.146i −0.260735 0.189435i
\(103\) 658.980 478.777i 0.630400 0.458012i −0.226139 0.974095i \(-0.572610\pi\)
0.856539 + 0.516083i \(0.172610\pi\)
\(104\) −130.083 + 400.353i −0.122651 + 0.377480i
\(105\) −152.784 + 470.219i −0.142001 + 0.437035i
\(106\) 1887.94 1371.67i 1.72994 1.25687i
\(107\) 1386.33 + 1007.23i 1.25254 + 0.910020i 0.998366 0.0571394i \(-0.0181979\pi\)
0.254169 + 0.967160i \(0.418198\pi\)
\(108\) −690.761 2125.94i −0.615449 1.89416i
\(109\) −219.748 −0.193101 −0.0965507 0.995328i \(-0.530781\pi\)
−0.0965507 + 0.995328i \(0.530781\pi\)
\(110\) 1547.08 315.231i 1.34099 0.273238i
\(111\) −332.584 −0.284392
\(112\) 133.382 + 410.507i 0.112530 + 0.346332i
\(113\) −873.134 634.369i −0.726881 0.528110i 0.161694 0.986841i \(-0.448304\pi\)
−0.888575 + 0.458731i \(0.848304\pi\)
\(114\) 583.226 423.739i 0.479159 0.348130i
\(115\) −218.145 + 671.382i −0.176888 + 0.544406i
\(116\) 417.161 1283.89i 0.333900 1.02764i
\(117\) 62.8531 45.6654i 0.0496647 0.0360835i
\(118\) 952.669 + 692.155i 0.743223 + 0.539983i
\(119\) −55.7507 171.583i −0.0429467 0.132176i
\(120\) 1346.15 1.02405
\(121\) 1224.89 520.784i 0.920275 0.391273i
\(122\) −2310.41 −1.71455
\(123\) −165.860 510.464i −0.121586 0.374203i
\(124\) 606.751 + 440.830i 0.439418 + 0.319256i
\(125\) −1230.79 + 894.225i −0.880685 + 0.639855i
\(126\) 104.838 322.657i 0.0741245 0.228132i
\(127\) 218.148 671.389i 0.152421 0.469103i −0.845469 0.534024i \(-0.820679\pi\)
0.997890 + 0.0649202i \(0.0206793\pi\)
\(128\) −2147.59 + 1560.32i −1.48299 + 1.07745i
\(129\) −1202.56 873.708i −0.820769 0.596323i
\(130\) 173.853 + 535.066i 0.117292 + 0.360987i
\(131\) 941.040 0.627626 0.313813 0.949485i \(-0.398393\pi\)
0.313813 + 0.949485i \(0.398393\pi\)
\(132\) 2423.26 493.761i 1.59786 0.325579i
\(133\) 391.747 0.255404
\(134\) −727.816 2239.99i −0.469207 1.44407i
\(135\) −1109.07 805.783i −0.707060 0.513709i
\(136\) −397.396 + 288.725i −0.250562 + 0.182044i
\(137\) −725.077 + 2231.56i −0.452171 + 1.39164i 0.422253 + 0.906478i \(0.361239\pi\)
−0.874424 + 0.485162i \(0.838761\pi\)
\(138\) −526.589 + 1620.68i −0.324828 + 0.999718i
\(139\) −1666.90 + 1211.07i −1.01715 + 0.739006i −0.965697 0.259670i \(-0.916386\pi\)
−0.0514563 + 0.998675i \(0.516386\pi\)
\(140\) 1289.69 + 937.015i 0.778562 + 0.565659i
\(141\) −472.379 1453.83i −0.282138 0.868332i
\(142\) 4206.77 2.48608
\(143\) 233.667 + 412.721i 0.136645 + 0.241353i
\(144\) −216.892 −0.125516
\(145\) −255.834 787.375i −0.146523 0.450951i
\(146\) 511.393 + 371.549i 0.289885 + 0.210614i
\(147\) 747.661 543.207i 0.419497 0.304782i
\(148\) −331.373 + 1019.86i −0.184045 + 0.566434i
\(149\) −123.352 + 379.638i −0.0678214 + 0.208733i −0.979223 0.202784i \(-0.935001\pi\)
0.911402 + 0.411517i \(0.135001\pi\)
\(150\) −757.779 + 550.559i −0.412483 + 0.299686i
\(151\) 405.961 + 294.948i 0.218786 + 0.158957i 0.691780 0.722108i \(-0.256827\pi\)
−0.472994 + 0.881066i \(0.656827\pi\)
\(152\) −329.599 1014.40i −0.175882 0.541308i
\(153\) 90.6563 0.0479028
\(154\) 1884.86 + 858.311i 0.986276 + 0.449121i
\(155\) 459.946 0.238347
\(156\) 272.314 + 838.097i 0.139760 + 0.430138i
\(157\) −2287.24 1661.78i −1.16268 0.844740i −0.172570 0.984997i \(-0.555207\pi\)
−0.990115 + 0.140258i \(0.955207\pi\)
\(158\) 1732.14 1258.48i 0.872165 0.633665i
\(159\) 692.716 2131.96i 0.345509 1.06337i
\(160\) −240.434 + 739.980i −0.118800 + 0.365629i
\(161\) −749.158 + 544.295i −0.366720 + 0.266438i
\(162\) −2054.11 1492.40i −0.996211 0.723790i
\(163\) 1127.35 + 3469.61i 0.541721 + 1.66725i 0.728661 + 0.684875i \(0.240143\pi\)
−0.186940 + 0.982371i \(0.559857\pi\)
\(164\) −1730.58 −0.823999
\(165\) 1024.31 1118.50i 0.483288 0.527728i
\(166\) 4634.25 2.16679
\(167\) −451.697 1390.18i −0.209301 0.644163i −0.999509 0.0313245i \(-0.990027\pi\)
0.790208 0.612839i \(-0.209973\pi\)
\(168\) 1428.57 + 1037.92i 0.656052 + 0.476650i
\(169\) −136.724 + 99.3357i −0.0622321 + 0.0452143i
\(170\) −202.867 + 624.361i −0.0915248 + 0.281684i
\(171\) −60.8300 + 187.216i −0.0272034 + 0.0837236i
\(172\) −3877.39 + 2817.09i −1.71888 + 1.24884i
\(173\) 2628.55 + 1909.76i 1.15518 + 0.839284i 0.989160 0.146839i \(-0.0469100\pi\)
0.166015 + 0.986123i \(0.446910\pi\)
\(174\) −617.567 1900.68i −0.269067 0.828103i
\(175\) −508.992 −0.219864
\(176\) 149.501 1315.59i 0.0640286 0.563446i
\(177\) 1131.17 0.480359
\(178\) 2207.45 + 6793.84i 0.929525 + 2.86078i
\(179\) −938.463 681.833i −0.391866 0.284707i 0.374354 0.927286i \(-0.377865\pi\)
−0.766220 + 0.642579i \(0.777865\pi\)
\(180\) −648.061 + 470.844i −0.268353 + 0.194970i
\(181\) 392.968 1209.43i 0.161376 0.496665i −0.837375 0.546629i \(-0.815911\pi\)
0.998751 + 0.0499642i \(0.0159107\pi\)
\(182\) −228.053 + 701.874i −0.0928813 + 0.285859i
\(183\) −1795.51 + 1304.52i −0.725291 + 0.526955i
\(184\) 2039.73 + 1481.95i 0.817231 + 0.593753i
\(185\) 203.222 + 625.454i 0.0807633 + 0.248564i
\(186\) 1110.28 0.437687
\(187\) −62.4880 + 549.889i −0.0244362 + 0.215037i
\(188\) −4928.81 −1.91208
\(189\) −555.692 1710.24i −0.213866 0.658211i
\(190\) −1153.25 837.888i −0.440347 0.319930i
\(191\) 1897.45 1378.58i 0.718820 0.522253i −0.167187 0.985925i \(-0.553468\pi\)
0.886007 + 0.463672i \(0.153468\pi\)
\(192\) −991.776 + 3052.37i −0.372788 + 1.14732i
\(193\) 557.296 1715.18i 0.207850 0.639696i −0.791734 0.610865i \(-0.790822\pi\)
0.999584 0.0288307i \(-0.00917837\pi\)
\(194\) 2441.54 1773.89i 0.903570 0.656482i
\(195\) 437.220 + 317.659i 0.160564 + 0.116656i
\(196\) −920.795 2833.92i −0.335567 1.03277i
\(197\) −1652.94 −0.597802 −0.298901 0.954284i \(-0.596620\pi\)
−0.298901 + 0.954284i \(0.596620\pi\)
\(198\) −702.866 + 767.497i −0.252275 + 0.275473i
\(199\) −3746.42 −1.33456 −0.667278 0.744809i \(-0.732541\pi\)
−0.667278 + 0.744809i \(0.732541\pi\)
\(200\) 428.244 + 1318.00i 0.151407 + 0.465984i
\(201\) −1830.37 1329.84i −0.642309 0.466665i
\(202\) −5146.65 + 3739.26i −1.79266 + 1.30244i
\(203\) 335.591 1032.84i 0.116029 0.357100i
\(204\) −317.760 + 977.965i −0.109057 + 0.335643i
\(205\) −858.627 + 623.829i −0.292532 + 0.212537i
\(206\) −3145.47 2285.32i −1.06386 0.772941i
\(207\) −143.790 442.540i −0.0482806 0.148592i
\(208\) 471.804 0.157278
\(209\) −1093.65 498.018i −0.361960 0.164826i
\(210\) 2359.98 0.775496
\(211\) −69.5810 214.148i −0.0227021 0.0698700i 0.939064 0.343743i \(-0.111695\pi\)
−0.961766 + 0.273873i \(0.911695\pi\)
\(212\) −5847.42 4248.40i −1.89435 1.37633i
\(213\) 3269.24 2375.25i 1.05167 0.764080i
\(214\) 2527.58 7779.08i 0.807391 2.48489i
\(215\) −908.276 + 2795.39i −0.288111 + 0.886715i
\(216\) −3961.03 + 2877.85i −1.24775 + 0.906543i
\(217\) 488.109 + 354.632i 0.152696 + 0.110940i
\(218\) 324.132 + 997.575i 0.100702 + 0.309928i
\(219\) 607.210 0.187358
\(220\) −2409.27 4255.45i −0.738333 1.30410i
\(221\) −197.204 −0.0600243
\(222\) 490.567 + 1509.81i 0.148309 + 0.456449i
\(223\) 764.872 + 555.712i 0.229684 + 0.166875i 0.696675 0.717387i \(-0.254662\pi\)
−0.466991 + 0.884262i \(0.654662\pi\)
\(224\) −825.702 + 599.908i −0.246293 + 0.178942i
\(225\) 79.0357 243.247i 0.0234180 0.0720732i
\(226\) −1591.91 + 4899.41i −0.468551 + 1.44205i
\(227\) −998.279 + 725.292i −0.291886 + 0.212067i −0.724085 0.689711i \(-0.757738\pi\)
0.432199 + 0.901778i \(0.357738\pi\)
\(228\) −1806.39 1312.42i −0.524699 0.381216i
\(229\) −1440.94 4434.75i −0.415807 1.27972i −0.911527 0.411241i \(-0.865096\pi\)
0.495719 0.868483i \(-0.334904\pi\)
\(230\) 3369.59 0.966019
\(231\) 1949.43 397.213i 0.555250 0.113137i
\(232\) −2956.83 −0.836747
\(233\) 755.615 + 2325.55i 0.212455 + 0.653869i 0.999324 + 0.0367498i \(0.0117005\pi\)
−0.786869 + 0.617119i \(0.788300\pi\)
\(234\) −300.013 217.973i −0.0838141 0.0608945i
\(235\) −2445.42 + 1776.70i −0.678815 + 0.493188i
\(236\) 1127.05 3468.69i 0.310867 0.956749i
\(237\) 635.551 1956.02i 0.174192 0.536107i
\(238\) −696.690 + 506.175i −0.189747 + 0.137859i
\(239\) 4632.04 + 3365.37i 1.25365 + 0.910828i 0.998428 0.0560547i \(-0.0178521\pi\)
0.255220 + 0.966883i \(0.417852\pi\)
\(240\) −466.229 1434.91i −0.125396 0.385928i
\(241\) 2786.65 0.744830 0.372415 0.928066i \(-0.378530\pi\)
0.372415 + 0.928066i \(0.378530\pi\)
\(242\) −4170.89 4792.36i −1.10791 1.27299i
\(243\) 1643.46 0.433861
\(244\) 2211.30 + 6805.67i 0.580179 + 1.78561i
\(245\) −1478.40 1074.12i −0.385517 0.280094i
\(246\) −2072.67 + 1505.88i −0.537190 + 0.390292i
\(247\) 132.323 407.249i 0.0340871 0.104909i
\(248\) 507.621 1562.30i 0.129976 0.400024i
\(249\) 3601.46 2616.61i 0.916600 0.665949i
\(250\) 5874.89 + 4268.36i 1.48624 + 1.07982i
\(251\) 1419.11 + 4367.58i 0.356867 + 1.09832i 0.954919 + 0.296867i \(0.0959418\pi\)
−0.598052 + 0.801458i \(0.704058\pi\)
\(252\) −1050.78 −0.262669
\(253\) 2783.40 567.143i 0.691664 0.140933i
\(254\) −3369.63 −0.832399
\(255\) 194.874 + 599.760i 0.0478568 + 0.147288i
\(256\) 5720.74 + 4156.36i 1.39666 + 1.01474i
\(257\) 2758.27 2004.00i 0.669480 0.486406i −0.200371 0.979720i \(-0.564215\pi\)
0.869851 + 0.493315i \(0.164215\pi\)
\(258\) −2192.52 + 6747.89i −0.529072 + 1.62832i
\(259\) −266.578 + 820.442i −0.0639549 + 0.196833i
\(260\) 1409.72 1024.22i 0.336259 0.244306i
\(261\) 441.485 + 320.757i 0.104702 + 0.0760704i
\(262\) −1388.05 4271.97i −0.327305 1.00734i
\(263\) 882.728 0.206963 0.103482 0.994631i \(-0.467002\pi\)
0.103482 + 0.994631i \(0.467002\pi\)
\(264\) −2668.72 4713.71i −0.622153 1.09890i
\(265\) −4432.62 −1.02752
\(266\) −577.832 1778.38i −0.133192 0.409924i
\(267\) 5551.47 + 4033.38i 1.27245 + 0.924490i
\(268\) −5901.63 + 4287.78i −1.34515 + 0.977306i
\(269\) 867.049 2668.50i 0.196524 0.604838i −0.803432 0.595397i \(-0.796995\pi\)
0.999955 0.00944125i \(-0.00300529\pi\)
\(270\) −2022.07 + 6223.29i −0.455775 + 1.40273i
\(271\) 5279.63 3835.88i 1.18345 0.859827i 0.190893 0.981611i \(-0.438862\pi\)
0.992557 + 0.121784i \(0.0388615\pi\)
\(272\) 445.398 + 323.601i 0.0992876 + 0.0721367i
\(273\) 219.067 + 674.218i 0.0485660 + 0.149471i
\(274\) 11199.9 2.46939
\(275\) 1420.97 + 647.069i 0.311592 + 0.141890i
\(276\) 5277.95 1.15107
\(277\) −3.17145 9.76073i −0.000687921 0.00211720i 0.950712 0.310075i \(-0.100354\pi\)
−0.951400 + 0.307958i \(0.900354\pi\)
\(278\) 7956.52 + 5780.75i 1.71655 + 1.24714i
\(279\) −245.271 + 178.200i −0.0526309 + 0.0382386i
\(280\) 1078.98 3320.77i 0.230291 0.708764i
\(281\) −515.358 + 1586.11i −0.109408 + 0.336724i −0.990740 0.135775i \(-0.956648\pi\)
0.881332 + 0.472498i \(0.156648\pi\)
\(282\) −5903.10 + 4288.85i −1.24654 + 0.905664i
\(283\) −1194.50 867.857i −0.250904 0.182292i 0.455223 0.890377i \(-0.349559\pi\)
−0.706127 + 0.708085i \(0.749559\pi\)
\(284\) −4026.30 12391.7i −0.841256 2.58912i
\(285\) −1369.33 −0.284604
\(286\) 1528.94 1669.53i 0.316112 0.345180i
\(287\) −1392.19 −0.286336
\(288\) −158.482 487.756i −0.0324257 0.0997962i
\(289\) 3788.53 + 2752.53i 0.771124 + 0.560255i
\(290\) −3197.03 + 2322.78i −0.647366 + 0.470339i
\(291\) 895.840 2757.11i 0.180464 0.555412i
\(292\) 604.999 1862.00i 0.121250 0.373168i
\(293\) 7754.97 5634.31i 1.54625 1.12341i 0.599984 0.800012i \(-0.295174\pi\)
0.946262 0.323401i \(-0.104826\pi\)
\(294\) −3568.77 2592.86i −0.707942 0.514350i
\(295\) −691.188 2127.26i −0.136415 0.419843i
\(296\) 2348.77 0.461214
\(297\) −622.846 + 5480.99i −0.121688 + 1.07084i
\(298\) 1905.36 0.370385
\(299\) 312.785 + 962.653i 0.0604977 + 0.186193i
\(300\) 2347.03 + 1705.21i 0.451685 + 0.328169i
\(301\) −3119.21 + 2266.24i −0.597304 + 0.433967i
\(302\) 740.156 2277.96i 0.141030 0.434047i
\(303\) −1888.39 + 5811.86i −0.358036 + 1.10192i
\(304\) −967.132 + 702.663i −0.182463 + 0.132567i
\(305\) 3550.39 + 2579.51i 0.666541 + 0.484270i
\(306\) −133.719 411.546i −0.0249811 0.0768841i
\(307\) −6758.47 −1.25644 −0.628219 0.778037i \(-0.716216\pi\)
−0.628219 + 0.778037i \(0.716216\pi\)
\(308\) 724.284 6373.64i 0.133993 1.17913i
\(309\) −3734.82 −0.687594
\(310\) −678.427 2087.98i −0.124297 0.382547i
\(311\) 5269.36 + 3828.41i 0.960765 + 0.698037i 0.953328 0.301936i \(-0.0976328\pi\)
0.00743680 + 0.999972i \(0.497633\pi\)
\(312\) 1561.53 1134.52i 0.283347 0.205864i
\(313\) 17.3670 53.4500i 0.00313623 0.00965231i −0.949476 0.313839i \(-0.898385\pi\)
0.952612 + 0.304187i \(0.0983847\pi\)
\(314\) −4170.14 + 12834.4i −0.749473 + 2.30664i
\(315\) −521.341 + 378.777i −0.0932516 + 0.0677512i
\(316\) −5364.87 3897.81i −0.955056 0.693889i
\(317\) −402.630 1239.17i −0.0713374 0.219554i 0.909031 0.416729i \(-0.136823\pi\)
−0.980368 + 0.197175i \(0.936823\pi\)
\(318\) −10700.1 −1.88689
\(319\) −2249.91 + 2456.80i −0.394893 + 0.431204i
\(320\) 6346.28 1.10865
\(321\) −2427.98 7472.57i −0.422171 1.29931i
\(322\) 3575.92 + 2598.06i 0.618876 + 0.449640i
\(323\) 404.241 293.698i 0.0696364 0.0505938i
\(324\) −2430.10 + 7479.07i −0.416684 + 1.28242i
\(325\) −171.926 + 529.133i −0.0293438 + 0.0903109i
\(326\) 14087.9 10235.5i 2.39343 1.73893i
\(327\) 815.151 + 592.242i 0.137853 + 0.100156i
\(328\) 1171.33 + 3604.99i 0.197183 + 0.606866i
\(329\) −3965.04 −0.664438
\(330\) −6588.45 3000.19i −1.09904 0.500469i
\(331\) −5832.34 −0.968503 −0.484252 0.874929i \(-0.660908\pi\)
−0.484252 + 0.874929i \(0.660908\pi\)
\(332\) −4435.44 13650.9i −0.733213 2.25660i
\(333\) −350.695 254.795i −0.0577116 0.0419299i
\(334\) −5644.64 + 4101.07i −0.924733 + 0.671858i
\(335\) −1382.45 + 4254.75i −0.225467 + 0.693917i
\(336\) 611.578 1882.24i 0.0992985 0.305609i
\(337\) 8165.62 5932.67i 1.31991 0.958971i 0.319977 0.947425i \(-0.396325\pi\)
0.999933 0.0115453i \(-0.00367506\pi\)
\(338\) 652.617 + 474.154i 0.105023 + 0.0763035i
\(339\) 1529.19 + 4706.36i 0.244998 + 0.754025i
\(340\) 2033.32 0.324329
\(341\) −911.837 1610.56i −0.144806 0.255768i
\(342\) 939.615 0.148563
\(343\) −2001.33 6159.46i −0.315049 0.969620i
\(344\) 8492.66 + 6170.28i 1.33109 + 0.967090i
\(345\) 2618.65 1902.56i 0.408647 0.296899i
\(346\) 4792.43 14749.6i 0.744632 2.29174i
\(347\) 3604.53 11093.6i 0.557641 1.71624i −0.131224 0.991353i \(-0.541891\pi\)
0.688865 0.724890i \(-0.258109\pi\)
\(348\) −5007.66 + 3638.28i −0.771375 + 0.560437i
\(349\) −7712.73 5603.62i −1.18296 0.859470i −0.190457 0.981696i \(-0.560997\pi\)
−0.992502 + 0.122225i \(0.960997\pi\)
\(350\) 750.771 + 2310.63i 0.114658 + 0.352882i
\(351\) −1965.62 −0.298909
\(352\) 3067.79 625.090i 0.464528 0.0946517i
\(353\) −10578.4 −1.59500 −0.797499 0.603321i \(-0.793844\pi\)
−0.797499 + 0.603321i \(0.793844\pi\)
\(354\) −1668.49 5135.07i −0.250506 0.770977i
\(355\) −6464.50 4696.74i −0.966479 0.702188i
\(356\) 17899.5 13004.8i 2.66481 1.93610i
\(357\) −255.626 + 786.737i −0.0378969 + 0.116635i
\(358\) −1711.02 + 5265.99i −0.252599 + 0.777419i
\(359\) 6366.82 4625.77i 0.936011 0.680052i −0.0114459 0.999934i \(-0.503643\pi\)
0.947457 + 0.319882i \(0.103643\pi\)
\(360\) 1419.45 + 1031.29i 0.207810 + 0.150983i
\(361\) −1784.27 5491.42i −0.260136 0.800616i
\(362\) −6070.01 −0.881305
\(363\) −5947.25 1369.35i −0.859917 0.197994i
\(364\) 2285.75 0.329136
\(365\) −371.030 1141.91i −0.0532071 0.163755i
\(366\) 8570.43 + 6226.78i 1.22400 + 0.889288i
\(367\) 5856.68 4255.12i 0.833014 0.605220i −0.0873968 0.996174i \(-0.527855\pi\)
0.920410 + 0.390954i \(0.127855\pi\)
\(368\) 873.214 2687.48i 0.123694 0.380691i
\(369\) 216.178 665.328i 0.0304980 0.0938633i
\(370\) 2539.58 1845.11i 0.356828 0.259250i
\(371\) −4704.03 3417.68i −0.658278 0.478267i
\(372\) −1062.65 3270.50i −0.148107 0.455827i
\(373\) −1489.27 −0.206733 −0.103366 0.994643i \(-0.532961\pi\)
−0.103366 + 0.994643i \(0.532961\pi\)
\(374\) 2588.46 527.422i 0.357878 0.0729207i
\(375\) 6975.63 0.960587
\(376\) 3336.02 + 10267.2i 0.457559 + 1.40822i
\(377\) −960.358 697.741i −0.131196 0.0953196i
\(378\) −6944.22 + 5045.27i −0.944900 + 0.686510i
\(379\) −3252.72 + 10010.8i −0.440847 + 1.35679i 0.446127 + 0.894969i \(0.352803\pi\)
−0.886974 + 0.461818i \(0.847197\pi\)
\(380\) −1364.35 + 4199.03i −0.184183 + 0.566857i
\(381\) −2618.67 + 1902.58i −0.352122 + 0.255832i
\(382\) −9057.00 6580.29i −1.21308 0.881354i
\(383\) 4292.46 + 13210.8i 0.572675 + 1.76251i 0.643964 + 0.765056i \(0.277289\pi\)
−0.0712891 + 0.997456i \(0.522711\pi\)
\(384\) 12171.7 1.61753
\(385\) −1938.17 3423.36i −0.256567 0.453170i
\(386\) −8608.30 −1.13511
\(387\) −598.688 1842.57i −0.0786382 0.242024i
\(388\) −7562.05 5494.15i −0.989446 0.718874i
\(389\) −2517.20 + 1828.86i −0.328091 + 0.238372i −0.739620 0.673025i \(-0.764995\pi\)
0.411529 + 0.911397i \(0.364995\pi\)
\(390\) 797.147 2453.37i 0.103500 0.318541i
\(391\) −364.985 + 1123.31i −0.0472074 + 0.145289i
\(392\) −5280.11 + 3836.22i −0.680321 + 0.494282i
\(393\) −3490.77 2536.19i −0.448056 0.325532i
\(394\) 2438.11 + 7503.73i 0.311752 + 0.959474i
\(395\) −4066.83 −0.518036
\(396\) 2933.49 + 1335.83i 0.372256 + 0.169515i
\(397\) −7136.13 −0.902147 −0.451073 0.892487i \(-0.648959\pi\)
−0.451073 + 0.892487i \(0.648959\pi\)
\(398\) 5526.03 + 17007.4i 0.695966 + 2.14196i
\(399\) −1453.18 1055.79i −0.182330 0.132471i
\(400\) 1256.58 912.962i 0.157073 0.114120i
\(401\) −4531.89 + 13947.7i −0.564368 + 1.73695i 0.105454 + 0.994424i \(0.466371\pi\)
−0.669822 + 0.742522i \(0.733629\pi\)
\(402\) −3337.16 + 10270.7i −0.414036 + 1.27427i
\(403\) 533.537 387.637i 0.0659488 0.0479146i
\(404\) 15940.4 + 11581.4i 1.96303 + 1.42623i
\(405\) 1490.31 + 4586.72i 0.182850 + 0.562755i
\(406\) −5183.72 −0.633655
\(407\) 1787.22 1951.57i 0.217664 0.237679i
\(408\) 2252.28 0.273295
\(409\) 1771.89 + 5453.33i 0.214216 + 0.659290i 0.999208 + 0.0397844i \(0.0126671\pi\)
−0.784992 + 0.619506i \(0.787333\pi\)
\(410\) 4098.44 + 2977.69i 0.493677 + 0.358677i
\(411\) 8703.92 6323.76i 1.04460 0.758950i
\(412\) −3721.22 + 11452.8i −0.444980 + 1.36951i
\(413\) 906.668 2790.44i 0.108025 0.332466i
\(414\) −1796.87 + 1305.51i −0.213313 + 0.154981i
\(415\) −7121.42 5174.01i −0.842353 0.612005i
\(416\) 344.744 + 1061.01i 0.0406309 + 0.125049i
\(417\) 9447.28 1.10944
\(418\) −647.662 + 5699.37i −0.0757852 + 0.666903i
\(419\) −14210.7 −1.65690 −0.828448 0.560066i \(-0.810776\pi\)
−0.828448 + 0.560066i \(0.810776\pi\)
\(420\) −2258.74 6951.68i −0.262417 0.807636i
\(421\) 11180.9 + 8123.43i 1.29436 + 0.940408i 0.999884 0.0152502i \(-0.00485447\pi\)
0.294477 + 0.955658i \(0.404854\pi\)
\(422\) −869.521 + 631.744i −0.100302 + 0.0728739i
\(423\) 615.688 1894.89i 0.0707702 0.217808i
\(424\) −4892.08 + 15056.3i −0.560331 + 1.72452i
\(425\) −525.225 + 381.598i −0.0599463 + 0.0435535i
\(426\) −15604.9 11337.6i −1.77479 1.28946i
\(427\) 1778.91 + 5474.91i 0.201610 + 0.620491i
\(428\) −25333.6 −2.86109
\(429\) 245.541 2160.74i 0.0276336 0.243173i
\(430\) 14029.7 1.57343
\(431\) 1568.60 + 4827.64i 0.175305 + 0.539535i 0.999647 0.0265576i \(-0.00845455\pi\)
−0.824342 + 0.566092i \(0.808455\pi\)
\(432\) 4439.48 + 3225.47i 0.494432 + 0.359226i
\(433\) −5502.76 + 3997.99i −0.610730 + 0.443721i −0.849671 0.527313i \(-0.823200\pi\)
0.238942 + 0.971034i \(0.423200\pi\)
\(434\) 889.929 2738.92i 0.0984285 0.302932i
\(435\) −1173.04 + 3610.25i −0.129294 + 0.397927i
\(436\) 2628.28 1909.56i 0.288697 0.209751i
\(437\) −2074.86 1507.47i −0.227125 0.165016i
\(438\) −895.643 2756.51i −0.0977066 0.300710i
\(439\) 10759.7 1.16978 0.584890 0.811113i \(-0.301138\pi\)
0.584890 + 0.811113i \(0.301138\pi\)
\(440\) −7233.86 + 7899.04i −0.783774 + 0.855845i
\(441\) 1204.53 0.130065
\(442\) 290.879 + 895.233i 0.0313025 + 0.0963391i
\(443\) −7703.77 5597.12i −0.826224 0.600287i 0.0922646 0.995735i \(-0.470589\pi\)
−0.918488 + 0.395448i \(0.870589\pi\)
\(444\) 3977.85 2890.08i 0.425181 0.308912i
\(445\) 4192.96 12904.6i 0.446663 1.37469i
\(446\) 1394.53 4291.92i 0.148056 0.455669i
\(447\) 1480.73 1075.82i 0.156681 0.113835i
\(448\) 6734.86 + 4893.17i 0.710251 + 0.516028i
\(449\) 367.852 + 1132.13i 0.0386638 + 0.118995i 0.968526 0.248914i \(-0.0800738\pi\)
−0.929862 + 0.367909i \(0.880074\pi\)
\(450\) −1220.83 −0.127890
\(451\) 3886.63 + 1769.86i 0.405797 + 0.184788i
\(452\) 15955.6 1.66037
\(453\) −710.992 2188.21i −0.0737424 0.226956i
\(454\) 4765.03 + 3462.00i 0.492586 + 0.357885i
\(455\) 1134.07 823.950i 0.116848 0.0848953i
\(456\) −1511.27 + 4651.21i −0.155201 + 0.477660i
\(457\) −5325.93 + 16391.5i −0.545157 + 1.67782i 0.175461 + 0.984486i \(0.443858\pi\)
−0.720617 + 0.693333i \(0.756142\pi\)
\(458\) −18006.7 + 13082.7i −1.83712 + 1.33474i
\(459\) −1855.61 1348.18i −0.188698 0.137097i
\(460\) −3225.04 9925.65i −0.326887 1.00606i
\(461\) −16519.2 −1.66893 −0.834463 0.551064i \(-0.814222\pi\)
−0.834463 + 0.551064i \(0.814222\pi\)
\(462\) −4678.63 8263.77i −0.471146 0.832177i
\(463\) −8199.50 −0.823030 −0.411515 0.911403i \(-0.635000\pi\)
−0.411515 + 0.911403i \(0.635000\pi\)
\(464\) 1024.08 + 3151.79i 0.102460 + 0.315341i
\(465\) −1706.16 1239.60i −0.170153 0.123624i
\(466\) 9442.57 6860.43i 0.938667 0.681981i
\(467\) −4761.65 + 14654.9i −0.471826 + 1.45213i 0.378364 + 0.925657i \(0.376487\pi\)
−0.850190 + 0.526476i \(0.823513\pi\)
\(468\) −354.928 + 1092.36i −0.0350568 + 0.107894i
\(469\) −4747.64 + 3449.36i −0.467432 + 0.339609i
\(470\) 11672.6 + 8480.64i 1.14557 + 0.832304i
\(471\) 4005.82 + 12328.7i 0.391886 + 1.20610i
\(472\) −7988.48 −0.779025
\(473\) 11589.1 2361.37i 1.12656 0.229547i
\(474\) −9817.07 −0.951294
\(475\) −435.620 1340.70i −0.0420792 0.129506i
\(476\) 2157.82 + 1567.75i 0.207780 + 0.150961i
\(477\) 2363.74 1717.36i 0.226894 0.164848i
\(478\) 8445.22 25991.7i 0.808108 2.48710i
\(479\) 4185.88 12882.8i 0.399285 1.22887i −0.526288 0.850306i \(-0.676417\pi\)
0.925574 0.378568i \(-0.123583\pi\)
\(480\) 2886.20 2096.95i 0.274451 0.199400i
\(481\) 762.864 + 554.253i 0.0723152 + 0.0525400i
\(482\) −4110.35 12650.4i −0.388426 1.19545i
\(483\) 4245.91 0.399991
\(484\) −10124.7 + 16872.8i −0.950852 + 1.58459i
\(485\) −5732.39 −0.536690
\(486\) −2424.13 7460.72i −0.226257 0.696348i
\(487\) 10874.9 + 7901.04i 1.01188 + 0.735175i 0.964603 0.263706i \(-0.0849450\pi\)
0.0472791 + 0.998882i \(0.484945\pi\)
\(488\) 12680.2 9212.73i 1.17624 0.854591i
\(489\) 5169.07 15908.8i 0.478024 1.47121i
\(490\) −2695.45 + 8295.74i −0.248506 + 0.764823i
\(491\) 2358.39 1713.47i 0.216767 0.157490i −0.474103 0.880469i \(-0.657228\pi\)
0.690870 + 0.722979i \(0.257228\pi\)
\(492\) 6419.57 + 4664.09i 0.588245 + 0.427385i
\(493\) −428.042 1317.38i −0.0391036 0.120348i
\(494\) −2043.94 −0.186156
\(495\) 1936.98 394.676i 0.175880 0.0358371i
\(496\) −1841.12 −0.166671
\(497\) −3239.01 9968.64i −0.292333 0.899708i
\(498\) −17190.7 12489.8i −1.54685 1.12385i
\(499\) 2692.01 1955.86i 0.241504 0.175463i −0.460449 0.887686i \(-0.652312\pi\)
0.701953 + 0.712223i \(0.252312\pi\)
\(500\) 6950.24 21390.6i 0.621648 1.91324i
\(501\) −2071.11 + 6374.21i −0.184691 + 0.568420i
\(502\) 17734.0 12884.5i 1.57671 1.14555i
\(503\) 4922.34 + 3576.29i 0.436335 + 0.317016i 0.784177 0.620537i \(-0.213085\pi\)
−0.347842 + 0.937553i \(0.613085\pi\)
\(504\) 711.209 + 2188.88i 0.0628567 + 0.193453i
\(505\) 12083.6 1.06478
\(506\) −6680.18 11799.1i −0.586897 1.03663i
\(507\) 774.894 0.0678782
\(508\) 3225.07 + 9925.75i 0.281672 + 0.866898i
\(509\) 1902.84 + 1382.49i 0.165701 + 0.120389i 0.667545 0.744569i \(-0.267345\pi\)
−0.501844 + 0.864958i \(0.667345\pi\)
\(510\) 2435.25 1769.31i 0.211440 0.153620i
\(511\) 486.699 1497.91i 0.0421337 0.129674i
\(512\) 3867.69 11903.5i 0.333847 1.02747i
\(513\) 4029.25 2927.42i 0.346775 0.251947i
\(514\) −13165.9 9565.60i −1.12981 0.820857i
\(515\) 2282.13 + 7023.67i 0.195267 + 0.600970i
\(516\) 21975.4 1.87483
\(517\) 11069.4 + 5040.67i 0.941644 + 0.428798i
\(518\) 4117.71 0.349270
\(519\) −4603.60 14168.4i −0.389355 1.19831i
\(520\) −3087.72 2243.36i −0.260395 0.189188i
\(521\) −6206.20 + 4509.07i −0.521878 + 0.379167i −0.817311 0.576197i \(-0.804536\pi\)
0.295433 + 0.955363i \(0.404536\pi\)
\(522\) 804.923 2477.30i 0.0674914 0.207717i
\(523\) 3934.95 12110.5i 0.328993 1.01254i −0.640613 0.767864i \(-0.721320\pi\)
0.969606 0.244672i \(-0.0786802\pi\)
\(524\) −11255.2 + 8177.41i −0.938335 + 0.681740i
\(525\) 1888.10 + 1371.78i 0.156959 + 0.114037i
\(526\) −1302.04 4007.26i −0.107931 0.332176i
\(527\) 769.548 0.0636092
\(528\) −4100.22 + 4477.24i −0.337953 + 0.369029i
\(529\) −6104.66 −0.501739
\(530\) 6538.18 + 20122.5i 0.535850 + 1.64918i
\(531\) 1192.76 + 866.592i 0.0974792 + 0.0708228i
\(532\) −4685.46 + 3404.19i −0.381843 + 0.277425i
\(533\) −470.250 + 1447.28i −0.0382154 + 0.117615i
\(534\) 10121.5 31150.9i 0.820228 2.52440i
\(535\) −12569.2 + 9132.09i −1.01573 + 0.737971i
\(536\) 12926.4 + 9391.55i 1.04167 + 0.756816i
\(537\) 1643.60 + 5058.50i 0.132080 + 0.406499i
\(538\) −13392.9 −1.07325
\(539\) −830.264 + 7306.24i −0.0663488 + 0.583863i
\(540\) 20267.0 1.61509
\(541\) −1851.64 5698.75i −0.147150 0.452881i 0.850131 0.526571i \(-0.176522\pi\)
−0.997281 + 0.0736900i \(0.976522\pi\)
\(542\) −25201.0 18309.6i −1.99719 1.45104i
\(543\) −4717.24 + 3427.28i −0.372811 + 0.270863i
\(544\) −402.277 + 1238.08i −0.0317049 + 0.0975778i
\(545\) 615.674 1894.85i 0.0483900 0.148929i
\(546\) 2737.57 1988.96i 0.214574 0.155897i
\(547\) 3104.23 + 2255.35i 0.242646 + 0.176292i 0.702461 0.711722i \(-0.252084\pi\)
−0.459815 + 0.888014i \(0.652084\pi\)
\(548\) −10719.5 32991.1i −0.835607 2.57173i
\(549\) −2892.69 −0.224876
\(550\) 841.500 7405.13i 0.0652394 0.574101i
\(551\) 3007.75 0.232549
\(552\) −3572.33 10994.5i −0.275450 0.847749i
\(553\) −4315.84 3135.64i −0.331877 0.241123i
\(554\) −39.6322 + 28.7945i −0.00303937 + 0.00220823i
\(555\) 931.810 2867.82i 0.0712669 0.219337i
\(556\) 9412.88 28969.9i 0.717977 2.20971i
\(557\) −18238.1 + 13250.8i −1.38739 + 1.00800i −0.391241 + 0.920288i \(0.627954\pi\)
−0.996146 + 0.0877076i \(0.972046\pi\)
\(558\) 1170.74 + 850.594i 0.0888198 + 0.0645314i
\(559\) 1302.32 + 4008.13i 0.0985372 + 0.303266i
\(560\) −3913.42 −0.295308
\(561\) 1713.80 1871.39i 0.128978 0.140838i
\(562\) 7960.51 0.597498
\(563\) 5390.47 + 16590.2i 0.403519 + 1.24190i 0.922126 + 0.386890i \(0.126451\pi\)
−0.518607 + 0.855013i \(0.673549\pi\)
\(564\) 18283.3 + 13283.6i 1.36501 + 0.991739i
\(565\) 7916.34 5751.56i 0.589456 0.428265i
\(566\) −2177.84 + 6702.70i −0.161734 + 0.497766i
\(567\) −1954.92 + 6016.64i −0.144796 + 0.445635i
\(568\) −23088.0 + 16774.4i −1.70555 + 1.23915i
\(569\) 9882.48 + 7180.04i 0.728111 + 0.529004i 0.888965 0.457975i \(-0.151425\pi\)
−0.160854 + 0.986978i \(0.551425\pi\)
\(570\) 2019.79 + 6216.26i 0.148420 + 0.456790i
\(571\) −15055.4 −1.10341 −0.551706 0.834039i \(-0.686023\pi\)
−0.551706 + 0.834039i \(0.686023\pi\)
\(572\) −6381.20 2905.82i −0.466454 0.212409i
\(573\) −10753.9 −0.784036
\(574\) 2053.50 + 6320.03i 0.149323 + 0.459570i
\(575\) 2695.84 + 1958.64i 0.195520 + 0.142054i
\(576\) −3384.22 + 2458.78i −0.244808 + 0.177863i
\(577\) −2355.29 + 7248.84i −0.169934 + 0.523004i −0.999366 0.0356042i \(-0.988664\pi\)
0.829432 + 0.558608i \(0.188664\pi\)
\(578\) 6907.33 21258.6i 0.497071 1.52983i
\(579\) −6689.85 + 4860.46i −0.480174 + 0.348867i
\(580\) 9901.98 + 7194.21i 0.708892 + 0.515040i
\(581\) −3568.15 10981.6i −0.254788 0.784157i
\(582\) −13837.6 −0.985548
\(583\) 8787.61 + 15521.4i 0.624264 + 1.10263i
\(584\) −4288.22 −0.303849
\(585\) 217.668 + 669.913i 0.0153837 + 0.0473462i
\(586\) −37016.4 26894.0i −2.60944 1.89587i
\(587\) −5810.77 + 4221.77i −0.408580 + 0.296850i −0.773026 0.634374i \(-0.781258\pi\)
0.364447 + 0.931224i \(0.381258\pi\)
\(588\) −4222.00 + 12994.0i −0.296110 + 0.911332i
\(589\) −516.364 + 1589.20i −0.0361229 + 0.111175i
\(590\) −8637.45 + 6275.47i −0.602709 + 0.437894i
\(591\) 6131.55 + 4454.83i 0.426765 + 0.310063i
\(592\) −813.480 2503.63i −0.0564760 0.173815i
\(593\) −6280.73 −0.434939 −0.217470 0.976067i \(-0.569780\pi\)
−0.217470 + 0.976067i \(0.569780\pi\)
\(594\) 25800.4 5257.05i 1.78216 0.363130i
\(595\) 1635.73 0.112703
\(596\) −1823.62 5612.53i −0.125333 0.385736i
\(597\) 13897.3 + 10097.0i 0.952726 + 0.692196i
\(598\) 3908.73 2839.86i 0.267291 0.194198i
\(599\) −3149.71 + 9693.81i −0.214848 + 0.661233i 0.784317 + 0.620360i \(0.213014\pi\)
−0.999164 + 0.0408722i \(0.986986\pi\)
\(600\) 1963.57 6043.26i 0.133604 0.411192i
\(601\) 13250.7 9627.16i 0.899343 0.653411i −0.0389539 0.999241i \(-0.512403\pi\)
0.938297 + 0.345830i \(0.112403\pi\)
\(602\) 14888.8 + 10817.3i 1.00801 + 0.732362i
\(603\) −911.240 2804.51i −0.0615399 0.189400i
\(604\) −7418.49 −0.499759
\(605\) 1058.84 + 12021.1i 0.0711535 + 0.807812i
\(606\) 29169.1 1.95530
\(607\) 765.795 + 2356.88i 0.0512070 + 0.157599i 0.973390 0.229155i \(-0.0735963\pi\)
−0.922183 + 0.386754i \(0.873596\pi\)
\(608\) −2286.85 1661.50i −0.152540 0.110827i
\(609\) −4028.48 + 2926.86i −0.268049 + 0.194749i
\(610\) 6473.14 19922.3i 0.429656 1.32234i
\(611\) −1339.30 + 4121.95i −0.0886781 + 0.272923i
\(612\) −1084.29 + 787.782i −0.0716173 + 0.0520330i
\(613\) −6917.19 5025.63i −0.455763 0.331131i 0.336104 0.941825i \(-0.390891\pi\)
−0.791867 + 0.610694i \(0.790891\pi\)
\(614\) 9968.85 + 30681.0i 0.655228 + 2.01658i
\(615\) 4866.34 0.319073
\(616\) −13767.2 + 2805.18i −0.900480 + 0.183481i
\(617\) −4958.66 −0.323547 −0.161773 0.986828i \(-0.551721\pi\)
−0.161773 + 0.986828i \(0.551721\pi\)
\(618\) 5508.92 + 16954.7i 0.358578 + 1.10359i
\(619\) −13659.0 9923.83i −0.886915 0.644382i 0.0481565 0.998840i \(-0.484665\pi\)
−0.935072 + 0.354458i \(0.884665\pi\)
\(620\) −5501.15 + 3996.82i −0.356341 + 0.258897i
\(621\) −3637.97 + 11196.5i −0.235083 + 0.723511i
\(622\) 9607.20 29567.9i 0.619314 1.90605i
\(623\) 14399.5 10461.9i 0.926010 0.672786i
\(624\) −1750.15 1271.56i −0.112279 0.0815754i
\(625\) −2609.26 8030.48i −0.166993 0.513951i
\(626\) −268.260 −0.0171275
\(627\) 2714.68 + 4794.89i 0.172909 + 0.305406i
\(628\) 41796.8 2.65585
\(629\) 340.017 + 1046.47i 0.0215538 + 0.0663359i
\(630\) 2488.49 + 1807.99i 0.157371 + 0.114337i
\(631\) 383.020 278.280i 0.0241645 0.0175565i −0.575637 0.817705i \(-0.695246\pi\)
0.599802 + 0.800149i \(0.295246\pi\)
\(632\) −4488.37 + 13813.8i −0.282497 + 0.869435i
\(633\) −319.041 + 981.906i −0.0200327 + 0.0616545i
\(634\) −5031.48 + 3655.58i −0.315182 + 0.228993i
\(635\) 5178.08 + 3762.10i 0.323600 + 0.235109i
\(636\) 10241.0 + 31518.7i 0.638497 + 1.96509i
\(637\) −2620.20 −0.162977
\(638\) 14471.6 + 6589.94i 0.898019 + 0.408932i
\(639\) 5266.96 0.326068
\(640\) −7437.38 22889.9i −0.459357 1.41375i
\(641\) 25153.1 + 18274.8i 1.54990 + 1.12607i 0.943720 + 0.330745i \(0.107300\pi\)
0.606183 + 0.795325i \(0.292700\pi\)
\(642\) −30341.4 + 22044.3i −1.86523 + 1.35517i
\(643\) 6058.25 18645.4i 0.371562 1.14355i −0.574208 0.818710i \(-0.694690\pi\)
0.945769 0.324839i \(-0.105310\pi\)
\(644\) 4230.46 13020.0i 0.258856 0.796677i
\(645\) 10903.1 7921.54i 0.665593 0.483582i
\(646\) −1929.54 1401.89i −0.117518 0.0853820i
\(647\) 9409.54 + 28959.6i 0.571758 + 1.75969i 0.646964 + 0.762521i \(0.276039\pi\)
−0.0752061 + 0.997168i \(0.523961\pi\)
\(648\) 17224.5 1.04420
\(649\) −6078.60 + 6637.55i −0.367651 + 0.401458i
\(650\) 2655.66 0.160252
\(651\) −854.864 2631.00i −0.0514666 0.158398i
\(652\) −43633.7 31701.7i −2.62090 1.90419i
\(653\) 25029.2 18184.8i 1.49995 1.08978i 0.529549 0.848280i \(-0.322361\pi\)
0.970401 0.241498i \(-0.0776387\pi\)
\(654\) 1486.20 4574.05i 0.0888608 0.273486i
\(655\) −2636.53 + 8114.42i −0.157279 + 0.484056i
\(656\) 3437.00 2497.13i 0.204561 0.148623i
\(657\) 640.275 + 465.187i 0.0380206 + 0.0276235i
\(658\) 5848.50 + 17999.8i 0.346502 + 1.06642i
\(659\) 31012.0 1.83317 0.916584 0.399842i \(-0.130935\pi\)
0.916584 + 0.399842i \(0.130935\pi\)
\(660\) −2531.70 + 22278.8i −0.149313 + 1.31394i
\(661\) 6859.42 0.403632 0.201816 0.979423i \(-0.435316\pi\)
0.201816 + 0.979423i \(0.435316\pi\)
\(662\) 8602.79 + 26476.7i 0.505071 + 1.55445i
\(663\) 731.524 + 531.484i 0.0428508 + 0.0311329i
\(664\) −25434.1 + 18479.0i −1.48650 + 1.08001i
\(665\) −1097.57 + 3377.96i −0.0640027 + 0.196980i
\(666\) −639.393 + 1967.85i −0.0372012 + 0.114493i
\(667\) −5751.88 + 4178.99i −0.333904 + 0.242595i
\(668\) 17482.8 + 12702.0i 1.01262 + 0.735712i
\(669\) −1339.58 4122.81i −0.0774158 0.238261i
\(670\) 21354.1 1.23132
\(671\) 1993.89 17546.0i 0.114714 1.00947i
\(672\) 4679.74 0.268638
\(673\) −4318.02 13289.5i −0.247321 0.761177i −0.995246 0.0973934i \(-0.968950\pi\)
0.747925 0.663784i \(-0.231050\pi\)
\(674\) −38976.5 28318.1i −2.22748 1.61836i
\(675\) −5235.15 + 3803.56i −0.298520 + 0.216888i
\(676\) 772.073 2376.20i 0.0439277 0.135195i
\(677\) 5256.08 16176.5i 0.298386 0.918338i −0.683677 0.729785i \(-0.739620\pi\)
0.982063 0.188553i \(-0.0603798\pi\)
\(678\) 19109.6 13883.9i 1.08245 0.786443i
\(679\) −6083.39 4419.84i −0.343828 0.249806i
\(680\) −1376.23 4235.61i −0.0776119 0.238865i
\(681\) 5657.83 0.318368
\(682\) −5966.37 + 6515.00i −0.334992 + 0.365795i
\(683\) 11464.8 0.642298 0.321149 0.947029i \(-0.395931\pi\)
0.321149 + 0.947029i \(0.395931\pi\)
\(684\) −899.305 2767.78i −0.0502716 0.154720i
\(685\) −17210.9 12504.4i −0.959990 0.697473i
\(686\) −25009.7 + 18170.6i −1.39194 + 1.01131i
\(687\) −6606.95 + 20334.1i −0.366915 + 1.12925i
\(688\) 3635.74 11189.7i 0.201470 0.620061i
\(689\) −5141.84 + 3735.76i −0.284308 + 0.206562i
\(690\) −12499.4 9081.38i −0.689632 0.501047i
\(691\) 1565.81 + 4819.06i 0.0862028 + 0.265305i 0.984861 0.173344i \(-0.0554572\pi\)
−0.898659 + 0.438649i \(0.855457\pi\)
\(692\) −48034.0 −2.63870
\(693\) 2359.89 + 1074.62i 0.129357 + 0.0589056i
\(694\) −55677.6 −3.04538
\(695\) −5772.67 17766.5i −0.315065 0.969669i
\(696\) 10968.3 + 7968.93i 0.597345 + 0.433997i
\(697\) −1436.59 + 1043.75i −0.0780700 + 0.0567212i
\(698\) −14062.0 + 43278.4i −0.762542 + 2.34686i
\(699\) 3464.63 10663.0i 0.187474 0.576985i
\(700\) 6087.76 4423.02i 0.328708 0.238821i
\(701\) −28061.0 20387.5i −1.51191 1.09847i −0.965320 0.261070i \(-0.915925\pi\)
−0.546592 0.837399i \(-0.684075\pi\)
\(702\) 2899.32 + 8923.19i 0.155880 + 0.479749i
\(703\) −2389.22 −0.128181
\(704\) −12581.4 22222.3i −0.673551 1.18968i
\(705\) 13859.6 0.740402
\(706\) 15603.4 + 48022.2i 0.831785 + 2.55997i
\(707\) 12823.5 + 9316.81i 0.682145 + 0.495608i
\(708\) −13529.2 + 9829.56i −0.718163 + 0.521776i
\(709\) 3646.31 11222.2i 0.193145 0.594440i −0.806848 0.590759i \(-0.798828\pi\)
0.999993 0.00368076i \(-0.00117162\pi\)
\(710\) −11786.2 + 36274.2i −0.622998 + 1.91739i
\(711\) 2168.68 1575.64i 0.114391 0.0831098i
\(712\) −39205.4 28484.4i −2.06360 1.49930i
\(713\) −1220.58 3756.56i −0.0641109 0.197313i
\(714\) 3948.55 0.206962
\(715\) −4213.49 + 858.536i −0.220386 + 0.0449055i
\(716\) 17149.4 0.895116
\(717\) −8112.46 24967.6i −0.422546 1.30046i
\(718\) −30390.4 22079.9i −1.57961 1.14765i
\(719\) 575.018 417.775i 0.0298255 0.0216695i −0.572773 0.819714i \(-0.694132\pi\)
0.602598 + 0.798045i \(0.294132\pi\)
\(720\) 607.673 1870.22i 0.0314536 0.0968044i
\(721\) −2993.59 + 9213.32i −0.154628 + 0.475897i
\(722\) −22297.2 + 16199.9i −1.14933 + 0.835037i
\(723\) −10337.0 7510.29i −0.531727 0.386322i
\(724\) 5809.61 + 17880.1i 0.298221 + 0.917831i
\(725\) −3907.94 −0.200189
\(726\) 2555.97 + 29018.1i 0.130662 + 1.48342i
\(727\) 10823.4 0.552159 0.276079 0.961135i \(-0.410965\pi\)
0.276079 + 0.961135i \(0.410965\pi\)
\(728\) −1547.09 4761.45i −0.0787622 0.242405i
\(729\) −17715.5 12871.1i −0.900042 0.653919i
\(730\) −4636.58 + 3368.68i −0.235079 + 0.170795i
\(731\) −1519.66 + 4677.04i −0.0768902 + 0.236644i
\(732\) 10139.2 31205.2i 0.511960 1.57565i
\(733\) −11093.6 + 8060.00i −0.559008 + 0.406143i −0.831096 0.556129i \(-0.812286\pi\)
0.272088 + 0.962272i \(0.412286\pi\)
\(734\) −27955.4 20310.8i −1.40579 1.02137i
\(735\) 2589.24 + 7968.87i 0.129940 + 0.399913i
\(736\) 6681.76 0.334637
\(737\) 17639.3 3594.16i 0.881616 0.179637i
\(738\) −3339.21 −0.166555
\(739\) −8871.73 27304.4i −0.441613 1.35914i −0.886156 0.463387i \(-0.846634\pi\)
0.444543 0.895757i \(-0.353366\pi\)
\(740\) −7865.68 5714.75i −0.390741 0.283890i
\(741\) −1588.42 + 1154.06i −0.0787479 + 0.0572137i
\(742\) −8576.48 + 26395.7i −0.424330 + 1.30595i
\(743\) 8106.28 24948.6i 0.400257 1.23186i −0.524535 0.851389i \(-0.675761\pi\)
0.924791 0.380474i \(-0.124239\pi\)
\(744\) −6093.55 + 4427.23i −0.300270 + 0.218159i
\(745\) −2927.96 2127.28i −0.143989 0.104614i
\(746\) 2196.69 + 6760.72i 0.107810 + 0.331807i
\(747\) 5802.18 0.284191
\(748\) −4031.02 7119.92i −0.197044 0.348035i
\(749\) −20380.0 −0.994216
\(750\) −10289.2 31666.8i −0.500943 1.54174i
\(751\) −17442.7 12672.9i −0.847528 0.615765i 0.0769353 0.997036i \(-0.475487\pi\)
−0.924463 + 0.381271i \(0.875487\pi\)
\(752\) 9788.78 7111.97i 0.474681 0.344876i
\(753\) 6506.88 20026.1i 0.314906 0.969180i
\(754\) −1750.94 + 5388.85i −0.0845697 + 0.260279i
\(755\) −3680.68 + 2674.17i −0.177422 + 0.128905i
\(756\) 21507.9 + 15626.4i 1.03470 + 0.751756i
\(757\) −4906.09 15099.4i −0.235555 0.724962i −0.997047 0.0767891i \(-0.975533\pi\)
0.761493 0.648173i \(-0.224467\pi\)
\(758\) 50243.3 2.40755
\(759\) −11853.5 5397.73i −0.566870 0.258136i
\(760\) 9670.46 0.461559
\(761\) 4799.68 + 14771.9i 0.228631 + 0.703654i 0.997903 + 0.0647319i \(0.0206192\pi\)
−0.769272 + 0.638922i \(0.779381\pi\)
\(762\) 12499.6 + 9081.47i 0.594241 + 0.431741i
\(763\) 2114.36 1536.17i 0.100321 0.0728874i
\(764\) −10714.8 + 32976.8i −0.507392 + 1.56159i
\(765\) −253.994 + 781.714i −0.0120042 + 0.0369450i
\(766\) 53640.8 38972.3i 2.53019 1.83829i
\(767\) −2594.61 1885.09i −0.122146 0.0887441i
\(768\) −10019.2 30835.9i −0.470750 1.44882i
\(769\) 31012.1 1.45426 0.727130 0.686500i \(-0.240854\pi\)
0.727130 + 0.686500i \(0.240854\pi\)
\(770\) −12681.9 + 13848.1i −0.593539 + 0.648117i
\(771\) −15632.7 −0.730220
\(772\) 8239.01 + 25357.1i 0.384104 + 1.18215i
\(773\) 9404.13 + 6832.50i 0.437572 + 0.317915i 0.784669 0.619914i \(-0.212833\pi\)
−0.347097 + 0.937829i \(0.612833\pi\)
\(774\) −7481.52 + 5435.64i −0.347439 + 0.252429i
\(775\) 670.906 2064.84i 0.0310963 0.0957046i
\(776\) −6326.58 + 19471.2i −0.292669 + 0.900742i
\(777\) 3200.03 2324.96i 0.147748 0.107346i
\(778\) 12015.2 + 8729.59i 0.553686 + 0.402276i
\(779\) −1191.50 3667.07i −0.0548011 0.168661i
\(780\) −7989.72 −0.366766
\(781\) −3630.44 + 31947.5i −0.166334 + 1.46373i
\(782\) 5637.76 0.257808
\(783\) −4266.49 13130.9i −0.194728 0.599311i
\(784\) 5917.90 + 4299.60i 0.269583 + 0.195864i
\(785\) 20737.4 15066.6i 0.942866 0.685033i
\(786\) −6364.43 + 19587.7i −0.288819 + 0.888894i
\(787\) −9571.94 + 29459.4i −0.433549 + 1.33433i 0.461018 + 0.887391i \(0.347484\pi\)
−0.894567 + 0.446934i \(0.852516\pi\)
\(788\) 19769.9 14363.6i 0.893747 0.649345i
\(789\) −3274.46 2379.04i −0.147749 0.107346i
\(790\) 5998.63 + 18461.9i 0.270154 + 0.831449i
\(791\) 12835.7 0.576971
\(792\) 797.158 7014.92i 0.0357648 0.314727i
\(793\) 6292.44 0.281779
\(794\) 10525.9 + 32395.4i 0.470467 + 1.44795i
\(795\) 16442.7 + 11946.3i 0.733539 + 0.532947i
\(796\) 44808.8 32555.5i 1.99523 1.44962i
\(797\) −11696.9 + 35999.2i −0.519855 + 1.59995i 0.254417 + 0.967095i \(0.418116\pi\)
−0.774272 + 0.632853i \(0.781884\pi\)
\(798\) −2649.46 + 8154.20i −0.117531 + 0.361724i
\(799\) −4091.50 + 2972.65i −0.181160 + 0.131620i
\(800\) 2971.28 + 2158.76i 0.131313 + 0.0954047i
\(801\) 2763.78 + 8506.03i 0.121914 + 0.375213i
\(802\) 70002.0 3.08212
\(803\) −3262.99 + 3563.04i −0.143398 + 0.156584i
\(804\) 33448.0 1.46719
\(805\) −2594.43 7984.82i −0.113592 0.349600i
\(806\) −2546.71 1850.29i −0.111295 0.0808606i
\(807\) −10408.2 + 7561.98i −0.454009 + 0.329857i
\(808\) 13336.1 41044.3i 0.580647 1.78705i
\(809\) 6116.04 18823.2i 0.265795 0.818034i −0.725714 0.687997i \(-0.758490\pi\)
0.991509 0.130037i \(-0.0415097\pi\)
\(810\) 18623.8 13531.0i 0.807867 0.586950i
\(811\) −2178.81 1583.00i −0.0943381 0.0685407i 0.539616 0.841911i \(-0.318569\pi\)
−0.633954 + 0.773370i \(0.718569\pi\)
\(812\) 4961.34 + 15269.4i 0.214420 + 0.659917i
\(813\) −29922.8 −1.29082
\(814\) −11495.6 5234.75i −0.494987 0.225403i
\(815\) −33076.4 −1.42161
\(816\) −780.061 2400.78i −0.0334652 0.102995i
\(817\) −8638.93 6276.55i −0.369936 0.268774i
\(818\) 22142.5 16087.5i 0.946449 0.687635i
\(819\) −285.527 + 878.761i −0.0121821 + 0.0374925i
\(820\) 4848.62 14922.5i 0.206489 0.635509i
\(821\) 2512.36 1825.34i 0.106799 0.0775941i −0.533104 0.846050i \(-0.678975\pi\)
0.639903 + 0.768456i \(0.278975\pi\)
\(822\) −41546.0 30184.9i −1.76287 1.28080i
\(823\) −13040.1 40133.4i −0.552309 1.69983i −0.702947 0.711242i \(-0.748133\pi\)
0.150638 0.988589i \(-0.451867\pi\)
\(824\) 26376.0 1.11511
\(825\) −3527.16 6229.95i −0.148848 0.262908i
\(826\) −14004.9 −0.589943
\(827\) −11188.1 34433.4i −0.470432 1.44784i −0.852020 0.523509i \(-0.824623\pi\)
0.381588 0.924333i \(-0.375377\pi\)
\(828\) 5565.35 + 4043.47i 0.233586 + 0.169710i
\(829\) −9698.64 + 7046.47i −0.406330 + 0.295216i −0.772114 0.635484i \(-0.780801\pi\)
0.365784 + 0.930700i \(0.380801\pi\)
\(830\) −12983.9 + 39960.3i −0.542985 + 1.67114i
\(831\) −14.5417 + 44.7546i −0.000607033 + 0.00186826i
\(832\) 7361.68 5348.57i 0.306755 0.222871i
\(833\) −2473.55 1797.14i −0.102885 0.0747506i
\(834\) −13934.9 42887.1i −0.578568 1.78065i
\(835\) 13252.8 0.549260
\(836\) 17408.2 3547.08i 0.720187 0.146744i
\(837\) 7670.43 0.316761
\(838\) 20961.0 + 64511.4i 0.864065 + 2.65932i
\(839\) −8917.59 6479.01i −0.366948 0.266603i 0.388996 0.921239i \(-0.372822\pi\)
−0.755944 + 0.654636i \(0.772822\pi\)
\(840\) −12952.3 + 9410.37i −0.532019 + 0.386534i
\(841\) −4960.02 + 15265.4i −0.203371 + 0.625912i
\(842\) 20385.3 62739.5i 0.834352 2.56787i
\(843\) 6186.43 4494.70i 0.252754 0.183637i
\(844\) 2693.12 + 1956.66i 0.109835 + 0.0797999i
\(845\) −473.492 1457.26i −0.0192765 0.0593268i
\(846\) −9510.26 −0.386489
\(847\) −8144.92 + 13573.5i −0.330417 + 0.550640i
\(848\) 17743.3 0.718525
\(849\) 2092.03 + 6438.60i 0.0845679 + 0.260273i
\(850\) 2507.03 + 1821.46i 0.101165 + 0.0735008i
\(851\) 4569.03 3319.59i 0.184047 0.133718i
\(852\) −18461.3 + 56817.9i −0.742338 + 2.28468i
\(853\) −8585.93 + 26424.8i −0.344639 + 1.06069i 0.617138 + 0.786855i \(0.288292\pi\)
−0.961777 + 0.273834i \(0.911708\pi\)
\(854\) 22230.2 16151.2i 0.890750 0.647168i
\(855\) −1443.90 1049.05i −0.0577547 0.0419613i
\(856\) 17146.8 + 52772.6i 0.684658 + 2.10716i
\(857\) −29633.9 −1.18118 −0.590592 0.806970i \(-0.701106\pi\)
−0.590592 + 0.806970i \(0.701106\pi\)
\(858\) −10171.1 + 2072.45i −0.404704 + 0.0824620i
\(859\) −24852.1 −0.987126 −0.493563 0.869710i \(-0.664306\pi\)
−0.493563 + 0.869710i \(0.664306\pi\)
\(860\) −13427.9 41326.7i −0.532426 1.63864i
\(861\) 5164.31 + 3752.09i 0.204412 + 0.148514i
\(862\) 19602.0 14241.7i 0.774533 0.562731i
\(863\) 13437.0 41354.8i 0.530012 1.63121i −0.224176 0.974549i \(-0.571969\pi\)
0.754187 0.656659i \(-0.228031\pi\)
\(864\) −4009.67 + 12340.5i −0.157884 + 0.485917i
\(865\) −23832.0 + 17315.0i −0.936777 + 0.680608i
\(866\) 26266.1 + 19083.4i 1.03067 + 0.748823i
\(867\) −6635.16 20420.9i −0.259910 0.799920i
\(868\) −8919.66 −0.348794
\(869\) 8062.43 + 14240.5i 0.314729 + 0.555900i
\(870\) 18119.5 0.706100
\(871\) 1982.21 + 6100.63i 0.0771122 + 0.237327i
\(872\) −5756.74 4182.52i −0.223564 0.162429i
\(873\) 3056.86 2220.94i 0.118510 0.0861025i
\(874\) −3782.92 + 11642.6i −0.146406 + 0.450592i
\(875\) 5591.21 17208.0i 0.216020 0.664841i
\(876\) −7262.49 + 5276.51i −0.280110 + 0.203512i
\(877\) 14957.8 + 10867.5i 0.575928 + 0.418437i 0.837254 0.546814i \(-0.184160\pi\)
−0.261326 + 0.965251i \(0.584160\pi\)
\(878\) −15870.7 48845.1i −0.610036 1.87750i
\(879\) −43951.9 −1.68653
\(880\) 10925.3 + 4975.05i 0.418512 + 0.190578i
\(881\) 14831.7 0.567189 0.283594 0.958944i \(-0.408473\pi\)
0.283594 + 0.958944i \(0.408473\pi\)
\(882\) −1776.70 5468.11i −0.0678283 0.208754i
\(883\) −3371.26 2449.36i −0.128485 0.0933495i 0.521687 0.853137i \(-0.325303\pi\)
−0.650171 + 0.759788i \(0.725303\pi\)
\(884\) 2358.64 1713.66i 0.0897396 0.0651996i
\(885\) −3169.21 + 9753.84i −0.120375 + 0.370477i
\(886\) −14045.7 + 43228.1i −0.532588 + 1.63914i
\(887\) 27259.9 19805.5i 1.03190 0.749722i 0.0632153 0.998000i \(-0.479865\pi\)
0.968689 + 0.248278i \(0.0798645\pi\)
\(888\) −8712.71 6330.15i −0.329256 0.239218i
\(889\) 2594.45 + 7984.90i 0.0978798 + 0.301243i
\(890\) −64766.7 −2.43931
\(891\) 13106.5 14311.6i 0.492798 0.538112i
\(892\) −13977.2 −0.524654
\(893\) −3393.48 10444.0i −0.127165 0.391374i
\(894\) −7067.91 5135.13i −0.264414 0.192108i
\(895\) 8508.65 6181.89i 0.317779 0.230880i
\(896\) 9756.01 30025.9i 0.363756 1.11953i
\(897\) 1434.17 4413.93i 0.0533842 0.164300i
\(898\) 4596.88 3339.83i 0.170824 0.124111i
\(899\) 3747.60 + 2722.79i 0.139032 + 0.101012i
\(900\) 1168.46 + 3596.14i 0.0432762 + 0.133190i
\(901\) −7416.34 −0.274222
\(902\) 2301.67 20254.4i 0.0849635 0.747671i
\(903\) 17678.4 0.651496
\(904\) −10799.4 33237.1i −0.397326 1.22284i
\(905\) 9327.73 + 6776.99i 0.342612 + 0.248923i
\(906\) −8884.93 + 6455.28i −0.325808 + 0.236713i
\(907\) −1484.93 + 4570.16i −0.0543621 + 0.167309i −0.974551 0.224165i \(-0.928035\pi\)
0.920189 + 0.391474i \(0.128035\pi\)
\(908\) 5637.23 17349.6i 0.206033 0.634104i
\(909\) −6443.72 + 4681.63i −0.235121 + 0.170825i
\(910\) −5413.20 3932.92i −0.197193 0.143269i
\(911\) −9.69861 29.8493i −0.000352722 0.00108557i 0.950880 0.309560i \(-0.100182\pi\)
−0.951233 + 0.308474i \(0.900182\pi\)
\(912\) 5481.30 0.199018
\(913\) −3999.36 + 35194.0i −0.144972 + 1.27574i
\(914\) 82267.3 2.97720
\(915\) −6218.09 19137.3i −0.224660 0.691431i
\(916\) 55771.2 + 40520.1i 2.01172 + 1.46160i
\(917\) −9054.43 + 6578.42i −0.326067 + 0.236902i
\(918\) −3383.18 + 10412.4i −0.121636 + 0.374356i
\(919\) −723.403 + 2226.40i −0.0259661 + 0.0799155i −0.963200 0.268786i \(-0.913377\pi\)
0.937234 + 0.348702i \(0.113377\pi\)
\(920\) −18493.3 + 13436.2i −0.662725 + 0.481498i
\(921\) 25070.4 + 18214.7i 0.896958 + 0.651678i
\(922\) 24366.0 + 74991.0i 0.870339 + 2.67863i
\(923\) −11457.2 −0.408578
\(924\) −19864.3 + 21690.9i −0.707237 + 0.772270i
\(925\) 3104.28 0.110344
\(926\) 12094.4 + 37222.7i 0.429208 + 1.32097i
\(927\) −3938.20 2861.27i −0.139533 0.101377i
\(928\) −6339.58 + 4605.97i −0.224253 + 0.162929i
\(929\) −720.206 + 2216.57i −0.0254351 + 0.0782811i −0.962968 0.269615i \(-0.913104\pi\)
0.937533 + 0.347896i \(0.113104\pi\)
\(930\) −3110.71 + 9573.77i −0.109682 + 0.337566i
\(931\) 5371.05 3902.29i 0.189075 0.137371i
\(932\) −29245.9 21248.4i −1.02788 0.746797i
\(933\) −9228.65 28402.9i −0.323829 0.996643i
\(934\) 73551.1 2.57673
\(935\) −4566.52 2079.46i −0.159723 0.0727334i
\(936\) 2515.72 0.0878515
\(937\) 5036.56 + 15501.0i 0.175600 + 0.540442i 0.999660 0.0260604i \(-0.00829623\pi\)
−0.824060 + 0.566502i \(0.808296\pi\)
\(938\) 22661.7 + 16464.7i 0.788838 + 0.573124i
\(939\) −208.475 + 151.466i −0.00724530 + 0.00526402i
\(940\) 13809.2 42500.2i 0.479155 1.47469i
\(941\) −7515.64 + 23130.8i −0.260364 + 0.801319i 0.732361 + 0.680917i \(0.238418\pi\)
−0.992725 + 0.120402i \(0.961582\pi\)
\(942\) 50058.9 36369.9i 1.73143 1.25796i
\(943\) 7373.63 + 5357.26i 0.254632 + 0.185001i
\(944\) 2766.76 + 8515.21i 0.0953923 + 0.293587i
\(945\) 16304.0 0.561238
\(946\) −27813.8 49126.9i −0.955924 1.68843i
\(947\) 39588.2 1.35844 0.679221 0.733934i \(-0.262318\pi\)
0.679221 + 0.733934i \(0.262318\pi\)
\(948\) 9395.93 + 28917.7i 0.321905 + 0.990720i
\(949\) −1392.79 1011.92i −0.0476414 0.0346135i
\(950\) −5443.74 + 3955.11i −0.185914 + 0.135074i
\(951\) −1846.13 + 5681.80i −0.0629493 + 0.193738i
\(952\) 1805.28 5556.07i 0.0614594 0.189153i
\(953\) 20291.1 14742.3i 0.689708 0.501102i −0.186856 0.982387i \(-0.559830\pi\)
0.876564 + 0.481285i \(0.159830\pi\)
\(954\) −11282.7 8197.39i −0.382906 0.278197i
\(955\) 6571.10 + 20223.8i 0.222655 + 0.685262i
\(956\) −84645.5 −2.86363
\(957\) 14967.3 3049.72i 0.505563 0.103013i
\(958\) −64657.4 −2.18057
\(959\) −8623.41 26540.1i −0.290370 0.893666i
\(960\) −23541.4 17103.8i −0.791454 0.575025i
\(961\) 22019.4 15998.0i 0.739129 0.537009i
\(962\) 1390.87 4280.65i 0.0466147 0.143465i
\(963\) 3164.58 9739.58i 0.105895 0.325912i
\(964\) −33329.6 + 24215.3i −1.11356 + 0.809049i
\(965\) 13228.3 + 9610.93i 0.441279 + 0.320608i
\(966\) −6262.79 19274.9i −0.208594 0.641986i
\(967\) −14890.4 −0.495185 −0.247593 0.968864i \(-0.579639\pi\)
−0.247593 + 0.968864i \(0.579639\pi\)
\(968\) 42000.5 + 9670.55i 1.39457 + 0.321099i
\(969\) −2291.07 −0.0759543
\(970\) 8455.37 + 26022.9i 0.279882 + 0.861388i
\(971\) 9411.82 + 6838.08i 0.311060 + 0.225999i 0.732351 0.680927i \(-0.238423\pi\)
−0.421291 + 0.906926i \(0.638423\pi\)
\(972\) −19656.5 + 14281.3i −0.648646 + 0.471269i
\(973\) 7572.32 23305.2i 0.249494 0.767863i
\(974\) 19827.2 61022.0i 0.652264 2.00746i
\(975\) 2063.82 1499.45i 0.0677899 0.0492523i
\(976\) −14211.9 10325.5i −0.466098 0.338640i
\(977\) −10247.2 31537.5i −0.335553 1.03273i −0.966449 0.256859i \(-0.917312\pi\)
0.630896 0.775868i \(-0.282688\pi\)
\(978\) −79844.4 −2.61057
\(979\) −53499.6 + 10901.0i −1.74653 + 0.355871i
\(980\) 27016.2 0.880612
\(981\) 405.820 + 1248.98i 0.0132078 + 0.0406493i
\(982\) −11257.2 8178.82i −0.365816 0.265781i
\(983\) 7269.76 5281.79i 0.235879 0.171376i −0.463566 0.886062i \(-0.653430\pi\)
0.699445 + 0.714686i \(0.253430\pi\)
\(984\) 5370.75 16529.5i 0.173997 0.535509i
\(985\) 4631.08 14253.0i 0.149806 0.461054i
\(986\) −5349.04 + 3886.31i −0.172767 + 0.125523i
\(987\) 14708.3 + 10686.2i 0.474335 + 0.344625i
\(988\) 1956.25 + 6020.73i 0.0629926 + 0.193871i
\(989\) 25241.3 0.811555
\(990\) −4648.76 8211.01i −0.149240 0.263599i
\(991\) 22624.0 0.725202 0.362601 0.931944i \(-0.381889\pi\)
0.362601 + 0.931944i \(0.381889\pi\)
\(992\) −1345.29 4140.38i −0.0430575 0.132517i
\(993\) 21635.0 + 15718.7i 0.691405 + 0.502335i
\(994\) −40476.4 + 29407.8i −1.29158 + 0.938389i
\(995\) 10496.4 32304.7i 0.334432 1.02928i
\(996\) −20337.3 + 62591.7i −0.646999 + 1.99126i
\(997\) −22496.1 + 16344.4i −0.714604 + 0.519190i −0.884656 0.466245i \(-0.845606\pi\)
0.170052 + 0.985435i \(0.445606\pi\)
\(998\) −12849.6 9335.79i −0.407563 0.296111i
\(999\) 3389.10 + 10430.6i 0.107334 + 0.330339i
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.h.a.27.1 68
11.3 even 5 1573.4.a.o.1.2 34
11.8 odd 10 1573.4.a.p.1.33 34
11.9 even 5 inner 143.4.h.a.53.1 yes 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.h.a.27.1 68 1.1 even 1 trivial
143.4.h.a.53.1 yes 68 11.9 even 5 inner
1573.4.a.o.1.2 34 11.3 even 5
1573.4.a.p.1.33 34 11.8 odd 10