Properties

Label 121.4.c.c.27.1
Level $121$
Weight $4$
Character 121.27
Analytic conductor $7.139$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [121,4,Mod(3,121)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(121, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("121.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 121.c (of order \(5\), degree \(4\), 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: \(7.13923111069\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.324000000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) 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 11)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 27.1
Root \(1.40126 + 1.01807i\) of defining polynomial
Character \(\chi\) \(=\) 121.27
Dual form 121.4.c.c.9.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.226216 - 0.696222i) q^{2} +(-4.79602 - 3.48451i) q^{3} +(6.03859 - 4.38729i) q^{4} +(-3.97285 + 12.2272i) q^{5} +(-1.34106 + 4.12734i) q^{6} +(-13.6952 + 9.95015i) q^{7} +(-9.15848 - 6.65403i) q^{8} +(2.51651 + 7.74502i) q^{9} +O(q^{10})\) \(q+(-0.226216 - 0.696222i) q^{2} +(-4.79602 - 3.48451i) q^{3} +(6.03859 - 4.38729i) q^{4} +(-3.97285 + 12.2272i) q^{5} +(-1.34106 + 4.12734i) q^{6} +(-13.6952 + 9.95015i) q^{7} +(-9.15848 - 6.65403i) q^{8} +(2.51651 + 7.74502i) q^{9} +9.41154 q^{10} -44.2487 q^{12} +(23.0653 + 70.9878i) q^{13} +(10.0256 + 7.28401i) q^{14} +(61.6595 - 44.7983i) q^{15} +(15.8914 - 48.9087i) q^{16} +(-25.5819 + 78.7328i) q^{17} +(4.82297 - 3.50410i) q^{18} +(54.9509 + 39.9242i) q^{19} +(29.6537 + 91.2648i) q^{20} +100.354 q^{21} +13.3538 q^{23} +(20.7382 + 63.8257i) q^{24} +(-32.5930 - 23.6802i) q^{25} +(44.2055 - 32.1172i) q^{26} +(-34.5433 + 106.313i) q^{27} +(-39.0455 + 120.170i) q^{28} +(-136.720 + 99.3327i) q^{29} +(-45.1379 - 32.7946i) q^{30} +(-20.2398 - 62.2918i) q^{31} -128.210 q^{32} +60.6025 q^{34} +(-67.2532 - 206.984i) q^{35} +(49.1758 + 35.7283i) q^{36} +(-33.0535 + 24.0148i) q^{37} +(15.3653 - 47.2895i) q^{38} +(136.736 - 420.830i) q^{39} +(117.745 - 85.5469i) q^{40} +(-222.422 - 161.599i) q^{41} +(-22.7017 - 69.8685i) q^{42} -2.28719 q^{43} -104.697 q^{45} +(-3.02085 - 9.29723i) q^{46} +(-58.1247 - 42.2301i) q^{47} +(-246.638 + 179.193i) q^{48} +(-17.4397 + 53.6738i) q^{49} +(-9.11361 + 28.0488i) q^{50} +(397.036 - 288.464i) q^{51} +(450.726 + 327.472i) q^{52} +(-46.0451 - 141.712i) q^{53} +81.8320 q^{54} +191.636 q^{56} +(-124.429 - 382.954i) q^{57} +(100.086 + 72.7166i) q^{58} +(-441.425 + 320.714i) q^{59} +(175.793 - 541.036i) q^{60} +(31.3042 - 96.3445i) q^{61} +(-38.7903 + 28.1828i) q^{62} +(-111.528 - 81.0300i) q^{63} +(-98.1279 - 302.007i) q^{64} -959.615 q^{65} +411.641 q^{67} +(190.946 + 587.670i) q^{68} +(-64.0452 - 46.5316i) q^{69} +(-128.893 + 93.6462i) q^{70} +(-145.434 + 447.601i) q^{71} +(28.4882 - 87.6775i) q^{72} +(-493.986 + 358.902i) q^{73} +(24.1969 + 17.5800i) q^{74} +(73.8027 + 227.141i) q^{75} +506.985 q^{76} -323.923 q^{78} +(-302.288 - 930.348i) q^{79} +(534.881 + 388.613i) q^{80} +(714.005 - 518.755i) q^{81} +(-62.1932 + 191.411i) q^{82} +(8.08200 - 24.8738i) q^{83} +(605.995 - 440.281i) q^{84} +(-861.047 - 625.587i) q^{85} +(0.517399 + 1.59239i) q^{86} +1001.84 q^{87} -352.887 q^{89} +(23.6842 + 72.8926i) q^{90} +(-1022.22 - 742.689i) q^{91} +(80.6382 - 58.5871i) q^{92} +(-119.986 + 369.278i) q^{93} +(-16.2527 + 50.0208i) q^{94} +(-706.471 + 513.281i) q^{95} +(614.898 + 446.750i) q^{96} +(261.918 + 806.101i) q^{97} +41.3140 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} - 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 2 q^{3} + 8 q^{4} - 2 q^{5} + 26 q^{6} - 20 q^{7} + 12 q^{8} - 44 q^{9} + 200 q^{10} - 160 q^{12} - 80 q^{13} + 4 q^{14} + 194 q^{15} + 8 q^{16} + 124 q^{17} - 92 q^{18} - 72 q^{19} - 88 q^{20} + 304 q^{21} - 392 q^{23} - 252 q^{24} - 136 q^{25} + 40 q^{26} + 182 q^{27} + 128 q^{28} - 144 q^{29} + 266 q^{30} + 34 q^{31} - 416 q^{32} - 208 q^{34} + 172 q^{35} + 80 q^{36} - 54 q^{37} - 432 q^{38} - 400 q^{39} + 492 q^{40} - 536 q^{41} + 140 q^{42} - 240 q^{43} + 1712 q^{45} + 314 q^{46} + 272 q^{47} - 776 q^{48} + 390 q^{49} - 232 q^{50} + 164 q^{51} + 560 q^{52} + 492 q^{53} - 440 q^{54} + 480 q^{56} + 1512 q^{57} + 192 q^{58} - 634 q^{59} - 632 q^{60} - 840 q^{61} - 134 q^{62} - 248 q^{63} - 224 q^{64} - 3520 q^{65} + 3016 q^{67} - 640 q^{68} - 962 q^{69} - 284 q^{70} + 678 q^{71} + 744 q^{72} + 400 q^{73} - 6 q^{74} + 520 q^{75} + 1728 q^{76} - 1760 q^{78} - 316 q^{79} + 1544 q^{80} + 1294 q^{81} - 512 q^{82} - 468 q^{83} + 736 q^{84} - 452 q^{85} + 156 q^{86} + 4800 q^{87} - 7368 q^{89} - 1532 q^{90} - 1280 q^{91} + 40 q^{92} + 638 q^{93} + 992 q^{94} - 2952 q^{95} + 952 q^{96} - 2194 q^{97} - 3480 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.226216 0.696222i −0.0799795 0.246152i 0.903070 0.429494i \(-0.141308\pi\)
−0.983049 + 0.183343i \(0.941308\pi\)
\(3\) −4.79602 3.48451i −0.922994 0.670594i 0.0212735 0.999774i \(-0.493228\pi\)
−0.944267 + 0.329179i \(0.893228\pi\)
\(4\) 6.03859 4.38729i 0.754823 0.548411i
\(5\) −3.97285 + 12.2272i −0.355342 + 1.09363i 0.600468 + 0.799648i \(0.294981\pi\)
−0.955811 + 0.293983i \(0.905019\pi\)
\(6\) −1.34106 + 4.12734i −0.0912473 + 0.280830i
\(7\) −13.6952 + 9.95015i −0.739472 + 0.537258i −0.892546 0.450957i \(-0.851083\pi\)
0.153074 + 0.988215i \(0.451083\pi\)
\(8\) −9.15848 6.65403i −0.404752 0.294069i
\(9\) 2.51651 + 7.74502i 0.0932040 + 0.286853i
\(10\) 9.41154 0.297619
\(11\) 0 0
\(12\) −44.2487 −1.06446
\(13\) 23.0653 + 70.9878i 0.492090 + 1.51450i 0.821443 + 0.570291i \(0.193170\pi\)
−0.329352 + 0.944207i \(0.606830\pi\)
\(14\) 10.0256 + 7.28401i 0.191389 + 0.139052i
\(15\) 61.6595 44.7983i 1.06136 0.771124i
\(16\) 15.8914 48.9087i 0.248303 0.764198i
\(17\) −25.5819 + 78.7328i −0.364971 + 1.12327i 0.585028 + 0.811013i \(0.301084\pi\)
−0.949999 + 0.312253i \(0.898916\pi\)
\(18\) 4.82297 3.50410i 0.0631548 0.0458846i
\(19\) 54.9509 + 39.9242i 0.663505 + 0.482065i 0.867845 0.496835i \(-0.165505\pi\)
−0.204340 + 0.978900i \(0.565505\pi\)
\(20\) 29.6537 + 91.2648i 0.331539 + 1.02037i
\(21\) 100.354 1.04281
\(22\) 0 0
\(23\) 13.3538 0.121064 0.0605319 0.998166i \(-0.480720\pi\)
0.0605319 + 0.998166i \(0.480720\pi\)
\(24\) 20.7382 + 63.8257i 0.176382 + 0.542848i
\(25\) −32.5930 23.6802i −0.260744 0.189442i
\(26\) 44.2055 32.1172i 0.333439 0.242258i
\(27\) −34.5433 + 106.313i −0.246217 + 0.757779i
\(28\) −39.0455 + 120.170i −0.263532 + 0.811069i
\(29\) −136.720 + 99.3327i −0.875456 + 0.636056i −0.932045 0.362342i \(-0.881977\pi\)
0.0565897 + 0.998398i \(0.481977\pi\)
\(30\) −45.1379 32.7946i −0.274701 0.199582i
\(31\) −20.2398 62.2918i −0.117264 0.360901i 0.875149 0.483854i \(-0.160763\pi\)
−0.992412 + 0.122953i \(0.960763\pi\)
\(32\) −128.210 −0.708268
\(33\) 0 0
\(34\) 60.6025 0.305684
\(35\) −67.2532 206.984i −0.324796 0.999619i
\(36\) 49.1758 + 35.7283i 0.227666 + 0.165409i
\(37\) −33.0535 + 24.0148i −0.146864 + 0.106703i −0.658791 0.752326i \(-0.728932\pi\)
0.511927 + 0.859029i \(0.328932\pi\)
\(38\) 15.3653 47.2895i 0.0655942 0.201878i
\(39\) 136.736 420.830i 0.561418 1.72787i
\(40\) 117.745 85.5469i 0.465429 0.338154i
\(41\) −222.422 161.599i −0.847230 0.615548i 0.0771511 0.997019i \(-0.475418\pi\)
−0.924381 + 0.381471i \(0.875418\pi\)
\(42\) −22.7017 69.8685i −0.0834034 0.256689i
\(43\) −2.28719 −0.00811146 −0.00405573 0.999992i \(-0.501291\pi\)
−0.00405573 + 0.999992i \(0.501291\pi\)
\(44\) 0 0
\(45\) −104.697 −0.346830
\(46\) −3.02085 9.29723i −0.00968261 0.0298000i
\(47\) −58.1247 42.2301i −0.180391 0.131061i 0.493926 0.869504i \(-0.335562\pi\)
−0.674316 + 0.738443i \(0.735562\pi\)
\(48\) −246.638 + 179.193i −0.741649 + 0.538840i
\(49\) −17.4397 + 53.6738i −0.0508445 + 0.156483i
\(50\) −9.11361 + 28.0488i −0.0257772 + 0.0793340i
\(51\) 397.036 288.464i 1.09012 0.792020i
\(52\) 450.726 + 327.472i 1.20201 + 0.873311i
\(53\) −46.0451 141.712i −0.119336 0.367277i 0.873491 0.486840i \(-0.161851\pi\)
−0.992827 + 0.119563i \(0.961851\pi\)
\(54\) 81.8320 0.206221
\(55\) 0 0
\(56\) 191.636 0.457293
\(57\) −124.429 382.954i −0.289141 0.889886i
\(58\) 100.086 + 72.7166i 0.226585 + 0.164623i
\(59\) −441.425 + 320.714i −0.974044 + 0.707684i −0.956370 0.292160i \(-0.905626\pi\)
−0.0176741 + 0.999844i \(0.505626\pi\)
\(60\) 175.793 541.036i 0.378247 1.16413i
\(61\) 31.3042 96.3445i 0.0657065 0.202224i −0.912813 0.408378i \(-0.866095\pi\)
0.978520 + 0.206154i \(0.0660947\pi\)
\(62\) −38.7903 + 28.1828i −0.0794576 + 0.0577293i
\(63\) −111.528 81.0300i −0.223035 0.162045i
\(64\) −98.1279 302.007i −0.191656 0.589857i
\(65\) −959.615 −1.83116
\(66\) 0 0
\(67\) 411.641 0.750596 0.375298 0.926904i \(-0.377540\pi\)
0.375298 + 0.926904i \(0.377540\pi\)
\(68\) 190.946 + 587.670i 0.340523 + 1.04802i
\(69\) −64.0452 46.5316i −0.111741 0.0811847i
\(70\) −128.893 + 93.6462i −0.220081 + 0.159898i
\(71\) −145.434 + 447.601i −0.243097 + 0.748176i 0.752846 + 0.658196i \(0.228680\pi\)
−0.995944 + 0.0899799i \(0.971320\pi\)
\(72\) 28.4882 87.6775i 0.0466300 0.143512i
\(73\) −493.986 + 358.902i −0.792009 + 0.575428i −0.908559 0.417757i \(-0.862816\pi\)
0.116550 + 0.993185i \(0.462816\pi\)
\(74\) 24.1969 + 17.5800i 0.0380112 + 0.0276167i
\(75\) 73.8027 + 227.141i 0.113627 + 0.349707i
\(76\) 506.985 0.765199
\(77\) 0 0
\(78\) −323.923 −0.470219
\(79\) −302.288 930.348i −0.430507 1.32497i −0.897621 0.440768i \(-0.854706\pi\)
0.467114 0.884197i \(-0.345294\pi\)
\(80\) 534.881 + 388.613i 0.747518 + 0.543104i
\(81\) 714.005 518.755i 0.979431 0.711598i
\(82\) −62.1932 + 191.411i −0.0837572 + 0.257778i
\(83\) 8.08200 24.8738i 0.0106881 0.0328947i −0.945570 0.325418i \(-0.894495\pi\)
0.956258 + 0.292523i \(0.0944950\pi\)
\(84\) 605.995 440.281i 0.787137 0.571888i
\(85\) −861.047 625.587i −1.09875 0.798288i
\(86\) 0.517399 + 1.59239i 0.000648750 + 0.00199665i
\(87\) 1001.84 1.23458
\(88\) 0 0
\(89\) −352.887 −0.420292 −0.210146 0.977670i \(-0.567394\pi\)
−0.210146 + 0.977670i \(0.567394\pi\)
\(90\) 23.6842 + 72.8926i 0.0277393 + 0.0853728i
\(91\) −1022.22 742.689i −1.17756 0.855549i
\(92\) 80.6382 58.5871i 0.0913817 0.0663927i
\(93\) −119.986 + 369.278i −0.133784 + 0.411746i
\(94\) −16.2527 + 50.0208i −0.0178334 + 0.0548857i
\(95\) −706.471 + 513.281i −0.762973 + 0.554332i
\(96\) 614.898 + 446.750i 0.653727 + 0.474961i
\(97\) 261.918 + 806.101i 0.274162 + 0.843785i 0.989440 + 0.144944i \(0.0463003\pi\)
−0.715277 + 0.698841i \(0.753700\pi\)
\(98\) 41.3140 0.0425851
\(99\) 0 0
\(100\) −300.708 −0.300708
\(101\) 399.702 + 1230.15i 0.393780 + 1.21193i 0.929908 + 0.367793i \(0.119887\pi\)
−0.536127 + 0.844137i \(0.680113\pi\)
\(102\) −290.651 211.170i −0.282144 0.204990i
\(103\) 1395.75 1014.07i 1.33522 0.970091i 0.335611 0.942001i \(-0.391057\pi\)
0.999605 0.0280904i \(-0.00894263\pi\)
\(104\) 261.111 803.618i 0.246193 0.757704i
\(105\) −398.691 + 1227.04i −0.370554 + 1.14045i
\(106\) −88.2470 + 64.1152i −0.0808614 + 0.0587493i
\(107\) 391.709 + 284.593i 0.353906 + 0.257128i 0.750506 0.660864i \(-0.229810\pi\)
−0.396600 + 0.917992i \(0.629810\pi\)
\(108\) 257.835 + 793.535i 0.229724 + 0.707018i
\(109\) −64.2563 −0.0564645 −0.0282323 0.999601i \(-0.508988\pi\)
−0.0282323 + 0.999601i \(0.508988\pi\)
\(110\) 0 0
\(111\) 242.205 0.207109
\(112\) 269.013 + 827.936i 0.226958 + 0.698505i
\(113\) 1622.15 + 1178.56i 1.35043 + 0.981145i 0.998990 + 0.0449344i \(0.0143079\pi\)
0.351440 + 0.936210i \(0.385692\pi\)
\(114\) −238.473 + 173.261i −0.195921 + 0.142345i
\(115\) −53.0527 + 163.280i −0.0430191 + 0.132399i
\(116\) −389.792 + 1199.66i −0.311994 + 0.960219i
\(117\) −491.758 + 357.283i −0.388573 + 0.282315i
\(118\) 323.145 + 234.779i 0.252101 + 0.183162i
\(119\) −433.055 1332.81i −0.333597 1.02671i
\(120\) −862.797 −0.656352
\(121\) 0 0
\(122\) −74.1587 −0.0550329
\(123\) 503.645 + 1550.06i 0.369205 + 1.13629i
\(124\) −395.512 287.356i −0.286436 0.208108i
\(125\) −881.102 + 640.158i −0.630465 + 0.458060i
\(126\) −31.1853 + 95.9786i −0.0220493 + 0.0678608i
\(127\) 33.8698 104.240i 0.0236650 0.0728334i −0.938527 0.345207i \(-0.887809\pi\)
0.962192 + 0.272374i \(0.0878087\pi\)
\(128\) −1017.86 + 739.518i −0.702867 + 0.510662i
\(129\) 10.9694 + 7.96973i 0.00748683 + 0.00543950i
\(130\) 217.080 + 668.105i 0.146456 + 0.450744i
\(131\) 1156.71 0.771469 0.385734 0.922610i \(-0.373948\pi\)
0.385734 + 0.922610i \(0.373948\pi\)
\(132\) 0 0
\(133\) −1149.82 −0.749636
\(134\) −93.1198 286.593i −0.0600323 0.184760i
\(135\) −1162.68 844.735i −0.741240 0.538542i
\(136\) 758.181 550.851i 0.478041 0.347317i
\(137\) 61.2853 188.617i 0.0382186 0.117625i −0.930127 0.367238i \(-0.880303\pi\)
0.968346 + 0.249613i \(0.0803035\pi\)
\(138\) −17.9082 + 55.1158i −0.0110467 + 0.0339983i
\(139\) 2346.26 1704.66i 1.43171 1.04020i 0.442011 0.897010i \(-0.354265\pi\)
0.989696 0.143186i \(-0.0457348\pi\)
\(140\) −1314.21 954.831i −0.793366 0.576414i
\(141\) 131.616 + 405.072i 0.0786104 + 0.241938i
\(142\) 344.529 0.203607
\(143\) 0 0
\(144\) 418.789 0.242355
\(145\) −671.391 2066.33i −0.384524 1.18344i
\(146\) 361.623 + 262.734i 0.204987 + 0.148932i
\(147\) 270.668 196.652i 0.151866 0.110337i
\(148\) −94.2367 + 290.031i −0.0523393 + 0.161084i
\(149\) 1077.96 3317.61i 0.592683 1.82409i 0.0267432 0.999642i \(-0.491486\pi\)
0.565939 0.824447i \(-0.308514\pi\)
\(150\) 141.445 102.766i 0.0769931 0.0559388i
\(151\) 941.148 + 683.784i 0.507216 + 0.368514i 0.811766 0.583982i \(-0.198506\pi\)
−0.304551 + 0.952496i \(0.598506\pi\)
\(152\) −237.610 731.290i −0.126794 0.390233i
\(153\) −674.164 −0.356228
\(154\) 0 0
\(155\) 842.061 0.436361
\(156\) −1020.61 3141.12i −0.523810 1.61212i
\(157\) −276.730 201.056i −0.140672 0.102204i 0.515224 0.857056i \(-0.327709\pi\)
−0.655895 + 0.754852i \(0.727709\pi\)
\(158\) −579.346 + 420.919i −0.291711 + 0.211940i
\(159\) −272.965 + 840.099i −0.136148 + 0.419020i
\(160\) 509.360 1567.65i 0.251678 0.774584i
\(161\) −182.883 + 132.873i −0.0895232 + 0.0650424i
\(162\) −522.688 379.755i −0.253495 0.184175i
\(163\) −431.045 1326.62i −0.207129 0.637479i −0.999619 0.0275936i \(-0.991216\pi\)
0.792490 0.609885i \(-0.208784\pi\)
\(164\) −2052.09 −0.977082
\(165\) 0 0
\(166\) −19.1460 −0.00895191
\(167\) 147.927 + 455.273i 0.0685447 + 0.210959i 0.979462 0.201631i \(-0.0646242\pi\)
−0.910917 + 0.412590i \(0.864624\pi\)
\(168\) −919.089 667.757i −0.422079 0.306658i
\(169\) −2729.85 + 1983.35i −1.24254 + 0.902755i
\(170\) −240.765 + 740.998i −0.108622 + 0.334305i
\(171\) −170.929 + 526.065i −0.0764401 + 0.235259i
\(172\) −13.8114 + 10.0346i −0.00612272 + 0.00444841i
\(173\) −1463.18 1063.06i −0.643024 0.467184i 0.217864 0.975979i \(-0.430091\pi\)
−0.860888 + 0.508795i \(0.830091\pi\)
\(174\) −226.631 697.500i −0.0987407 0.303893i
\(175\) 681.990 0.294592
\(176\) 0 0
\(177\) 3234.61 1.37361
\(178\) 79.8288 + 245.688i 0.0336147 + 0.103456i
\(179\) 3583.82 + 2603.80i 1.49647 + 1.08725i 0.971763 + 0.235960i \(0.0758235\pi\)
0.524703 + 0.851285i \(0.324176\pi\)
\(180\) −632.224 + 459.338i −0.261795 + 0.190206i
\(181\) 1053.49 3242.32i 0.432627 1.33149i −0.462872 0.886425i \(-0.653181\pi\)
0.895499 0.445064i \(-0.146819\pi\)
\(182\) −285.833 + 879.703i −0.116414 + 0.358285i
\(183\) −485.849 + 352.990i −0.196257 + 0.142589i
\(184\) −122.301 88.8567i −0.0490007 0.0356011i
\(185\) −162.316 499.558i −0.0645067 0.198531i
\(186\) 284.242 0.112052
\(187\) 0 0
\(188\) −536.267 −0.208039
\(189\) −584.757 1799.70i −0.225052 0.692638i
\(190\) 517.173 + 375.748i 0.197472 + 0.143472i
\(191\) −2365.37 + 1718.54i −0.896083 + 0.651043i −0.937457 0.348101i \(-0.886827\pi\)
0.0413737 + 0.999144i \(0.486827\pi\)
\(192\) −581.722 + 1790.36i −0.218657 + 0.672958i
\(193\) −767.655 + 2362.60i −0.286306 + 0.881159i 0.699698 + 0.714438i \(0.253318\pi\)
−0.986004 + 0.166720i \(0.946682\pi\)
\(194\) 501.975 364.706i 0.185772 0.134971i
\(195\) 4602.33 + 3343.79i 1.69015 + 1.22797i
\(196\) 130.171 + 400.626i 0.0474386 + 0.146001i
\(197\) −5125.67 −1.85375 −0.926876 0.375369i \(-0.877516\pi\)
−0.926876 + 0.375369i \(0.877516\pi\)
\(198\) 0 0
\(199\) −7.69219 −0.00274013 −0.00137006 0.999999i \(-0.500436\pi\)
−0.00137006 + 0.999999i \(0.500436\pi\)
\(200\) 140.934 + 433.750i 0.0498276 + 0.153354i
\(201\) −1974.24 1434.37i −0.692796 0.503346i
\(202\) 766.042 556.562i 0.266824 0.193859i
\(203\) 884.029 2720.76i 0.305649 0.940690i
\(204\) 1131.96 3483.83i 0.388497 1.19567i
\(205\) 2859.54 2077.58i 0.974240 0.707826i
\(206\) −1021.76 742.352i −0.345579 0.251078i
\(207\) 33.6050 + 103.426i 0.0112836 + 0.0347274i
\(208\) 3838.46 1.27956
\(209\) 0 0
\(210\) 944.484 0.310360
\(211\) 960.222 + 2955.26i 0.313291 + 0.964211i 0.976452 + 0.215734i \(0.0692144\pi\)
−0.663161 + 0.748477i \(0.730786\pi\)
\(212\) −899.780 653.729i −0.291496 0.211784i
\(213\) 2257.18 1639.94i 0.726100 0.527542i
\(214\) 109.529 337.096i 0.0349872 0.107680i
\(215\) 9.08665 27.9658i 0.00288234 0.00887095i
\(216\) 1023.78 743.818i 0.322496 0.234307i
\(217\) 897.001 + 651.709i 0.280610 + 0.203875i
\(218\) 14.5358 + 44.7366i 0.00451600 + 0.0138988i
\(219\) 3619.76 1.11690
\(220\) 0 0
\(221\) −6179.13 −1.88078
\(222\) −54.7907 168.628i −0.0165645 0.0509802i
\(223\) 9.96586 + 7.24062i 0.00299266 + 0.00217430i 0.589281 0.807928i \(-0.299411\pi\)
−0.586288 + 0.810103i \(0.699411\pi\)
\(224\) 1755.87 1275.71i 0.523744 0.380522i
\(225\) 101.383 312.025i 0.0300394 0.0924518i
\(226\) 453.582 1395.98i 0.133504 0.410882i
\(227\) −3734.34 + 2713.16i −1.09188 + 0.793298i −0.979716 0.200391i \(-0.935779\pi\)
−0.112165 + 0.993690i \(0.535779\pi\)
\(228\) −2431.51 1766.59i −0.706274 0.513138i
\(229\) 1568.15 + 4826.26i 0.452516 + 1.39270i 0.874027 + 0.485877i \(0.161500\pi\)
−0.421512 + 0.906823i \(0.638500\pi\)
\(230\) 125.680 0.0360309
\(231\) 0 0
\(232\) 1913.11 0.541386
\(233\) 65.4135 + 201.322i 0.0183922 + 0.0566054i 0.959831 0.280577i \(-0.0905260\pi\)
−0.941439 + 0.337183i \(0.890526\pi\)
\(234\) 359.992 + 261.549i 0.100570 + 0.0730684i
\(235\) 747.275 542.927i 0.207433 0.150709i
\(236\) −1258.52 + 3873.31i −0.347129 + 1.06835i
\(237\) −1792.03 + 5515.29i −0.491159 + 1.51163i
\(238\) −829.964 + 603.004i −0.226044 + 0.164231i
\(239\) −3488.88 2534.82i −0.944254 0.686041i 0.00518659 0.999987i \(-0.498349\pi\)
−0.949441 + 0.313946i \(0.898349\pi\)
\(240\) −1211.17 3727.59i −0.325753 1.00256i
\(241\) −996.584 −0.266372 −0.133186 0.991091i \(-0.542521\pi\)
−0.133186 + 0.991091i \(0.542521\pi\)
\(242\) 0 0
\(243\) −2213.80 −0.584426
\(244\) −233.658 719.125i −0.0613050 0.188677i
\(245\) −586.993 426.475i −0.153068 0.111210i
\(246\) 965.253 701.297i 0.250172 0.181761i
\(247\) −1566.67 + 4821.71i −0.403582 + 1.24210i
\(248\) −229.125 + 705.174i −0.0586671 + 0.180559i
\(249\) −125.435 + 91.1335i −0.0319241 + 0.0231942i
\(250\) 645.012 + 468.628i 0.163176 + 0.118555i
\(251\) −85.5644 263.340i −0.0215170 0.0662226i 0.939721 0.341941i \(-0.111084\pi\)
−0.961238 + 0.275718i \(0.911084\pi\)
\(252\) −1028.97 −0.257219
\(253\) 0 0
\(254\) −80.2364 −0.0198208
\(255\) 1949.73 + 6000.65i 0.478811 + 1.47363i
\(256\) −1310.09 951.838i −0.319847 0.232382i
\(257\) 2617.31 1901.59i 0.635267 0.461548i −0.222954 0.974829i \(-0.571570\pi\)
0.858221 + 0.513281i \(0.171570\pi\)
\(258\) 3.06724 9.44001i 0.000740148 0.00227794i
\(259\) 213.724 657.775i 0.0512748 0.157808i
\(260\) −5794.72 + 4210.11i −1.38220 + 1.00423i
\(261\) −1113.39 808.925i −0.264050 0.191844i
\(262\) −261.667 805.328i −0.0617017 0.189898i
\(263\) 207.944 0.0487544 0.0243772 0.999703i \(-0.492240\pi\)
0.0243772 + 0.999703i \(0.492240\pi\)
\(264\) 0 0
\(265\) 1915.67 0.444071
\(266\) 260.107 + 800.526i 0.0599555 + 0.184524i
\(267\) 1692.45 + 1229.64i 0.387927 + 0.281845i
\(268\) 2485.73 1805.99i 0.566567 0.411635i
\(269\) 1555.29 4786.70i 0.352520 1.08495i −0.604913 0.796291i \(-0.706792\pi\)
0.957433 0.288654i \(-0.0932078\pi\)
\(270\) −325.106 + 1000.57i −0.0732790 + 0.225530i
\(271\) −1203.02 + 874.043i −0.269661 + 0.195920i −0.714395 0.699742i \(-0.753298\pi\)
0.444734 + 0.895663i \(0.353298\pi\)
\(272\) 3444.19 + 2502.35i 0.767774 + 0.557821i
\(273\) 2314.70 + 7123.90i 0.513157 + 1.57933i
\(274\) −145.183 −0.0320102
\(275\) 0 0
\(276\) −590.890 −0.128867
\(277\) −72.8773 224.293i −0.0158078 0.0486515i 0.942841 0.333242i \(-0.108142\pi\)
−0.958649 + 0.284590i \(0.908142\pi\)
\(278\) −1717.58 1247.90i −0.370553 0.269223i
\(279\) 431.517 313.515i 0.0925959 0.0672748i
\(280\) −761.340 + 2343.16i −0.162496 + 0.500110i
\(281\) −1518.82 + 4674.46i −0.322439 + 0.992365i 0.650144 + 0.759811i \(0.274708\pi\)
−0.972583 + 0.232555i \(0.925292\pi\)
\(282\) 252.246 183.268i 0.0532662 0.0387001i
\(283\) 4206.53 + 3056.22i 0.883577 + 0.641956i 0.934195 0.356762i \(-0.116119\pi\)
−0.0506182 + 0.998718i \(0.516119\pi\)
\(284\) 1085.54 + 3340.94i 0.226813 + 0.698058i
\(285\) 5176.78 1.07595
\(286\) 0 0
\(287\) 4654.04 0.957210
\(288\) −322.642 992.991i −0.0660134 0.203169i
\(289\) −1569.73 1140.47i −0.319505 0.232134i
\(290\) −1286.74 + 934.874i −0.260552 + 0.189302i
\(291\) 1552.70 4778.73i 0.312787 0.962660i
\(292\) −1408.37 + 4334.52i −0.282255 + 0.868693i
\(293\) 7184.81 5220.07i 1.43256 1.04082i 0.443032 0.896506i \(-0.353903\pi\)
0.989532 0.144313i \(-0.0460971\pi\)
\(294\) −198.143 143.959i −0.0393058 0.0285573i
\(295\) −2167.71 6671.52i −0.427827 1.31671i
\(296\) 462.515 0.0908215
\(297\) 0 0
\(298\) −2553.64 −0.496405
\(299\) 308.011 + 947.959i 0.0595743 + 0.183351i
\(300\) 1442.20 + 1047.82i 0.277551 + 0.201653i
\(301\) 31.3235 22.7579i 0.00599819 0.00435794i
\(302\) 263.163 809.931i 0.0501434 0.154325i
\(303\) 2369.51 7292.61i 0.449257 1.38267i
\(304\) 2825.88 2053.13i 0.533143 0.387351i
\(305\) 1053.65 + 765.524i 0.197810 + 0.143717i
\(306\) 152.507 + 469.368i 0.0284910 + 0.0876862i
\(307\) −1497.93 −0.278474 −0.139237 0.990259i \(-0.544465\pi\)
−0.139237 + 0.990259i \(0.544465\pi\)
\(308\) 0 0
\(309\) −10227.6 −1.88293
\(310\) −190.488 586.261i −0.0349000 0.107411i
\(311\) 6055.25 + 4399.40i 1.10406 + 0.802145i 0.981718 0.190343i \(-0.0609601\pi\)
0.122340 + 0.992488i \(0.460960\pi\)
\(312\) −4052.51 + 2944.32i −0.735347 + 0.534261i
\(313\) −203.445 + 626.140i −0.0367393 + 0.113072i −0.967744 0.251934i \(-0.918933\pi\)
0.931005 + 0.365007i \(0.118933\pi\)
\(314\) −77.3787 + 238.147i −0.0139068 + 0.0428007i
\(315\) 1433.85 1041.75i 0.256471 0.186337i
\(316\) −5907.10 4291.76i −1.05158 0.764020i
\(317\) 72.2196 + 222.269i 0.0127958 + 0.0393813i 0.957251 0.289260i \(-0.0934092\pi\)
−0.944455 + 0.328641i \(0.893409\pi\)
\(318\) 646.645 0.114032
\(319\) 0 0
\(320\) 4082.53 0.713189
\(321\) −886.976 2729.83i −0.154225 0.474655i
\(322\) 133.880 + 97.2695i 0.0231703 + 0.0168342i
\(323\) −4549.09 + 3305.11i −0.783647 + 0.569353i
\(324\) 2035.65 6265.09i 0.349049 1.07426i
\(325\) 929.238 2859.90i 0.158599 0.488119i
\(326\) −826.113 + 600.206i −0.140350 + 0.101970i
\(327\) 308.174 + 223.902i 0.0521164 + 0.0378648i
\(328\) 961.762 + 2960.00i 0.161904 + 0.498288i
\(329\) 1216.23 0.203808
\(330\) 0 0
\(331\) 8532.95 1.41696 0.708480 0.705731i \(-0.249381\pi\)
0.708480 + 0.705731i \(0.249381\pi\)
\(332\) −60.3249 185.661i −0.00997216 0.0306912i
\(333\) −269.174 195.567i −0.0442963 0.0321832i
\(334\) 283.508 205.980i 0.0464457 0.0337448i
\(335\) −1635.39 + 5033.20i −0.266719 + 0.820876i
\(336\) 1594.76 4908.17i 0.258933 0.796913i
\(337\) −9458.37 + 6871.90i −1.52887 + 1.11079i −0.572011 + 0.820246i \(0.693837\pi\)
−0.956861 + 0.290545i \(0.906163\pi\)
\(338\) 1998.39 + 1451.92i 0.321592 + 0.233650i
\(339\) −3673.14 11304.8i −0.588489 1.81118i
\(340\) −7944.14 −1.26715
\(341\) 0 0
\(342\) 404.925 0.0640229
\(343\) −2089.49 6430.79i −0.328927 1.01233i
\(344\) 20.9472 + 15.2190i 0.00328313 + 0.00238533i
\(345\) 823.391 598.229i 0.128492 0.0933552i
\(346\) −409.131 + 1259.18i −0.0635694 + 0.195647i
\(347\) 1421.11 4373.71i 0.219853 0.676637i −0.778921 0.627123i \(-0.784232\pi\)
0.998773 0.0495148i \(-0.0157675\pi\)
\(348\) 6049.67 4395.34i 0.931886 0.677055i
\(349\) −5436.81 3950.08i −0.833885 0.605853i 0.0867706 0.996228i \(-0.472345\pi\)
−0.920656 + 0.390375i \(0.872345\pi\)
\(350\) −154.277 474.816i −0.0235613 0.0725142i
\(351\) −8343.72 −1.26882
\(352\) 0 0
\(353\) 5738.70 0.865270 0.432635 0.901569i \(-0.357584\pi\)
0.432635 + 0.901569i \(0.357584\pi\)
\(354\) −731.721 2252.01i −0.109860 0.338115i
\(355\) −4895.11 3556.50i −0.731846 0.531717i
\(356\) −2130.94 + 1548.22i −0.317246 + 0.230493i
\(357\) −2567.24 + 7901.14i −0.380595 + 1.17135i
\(358\) 1002.10 3084.15i 0.147941 0.455315i
\(359\) 3329.32 2418.89i 0.489456 0.355611i −0.315519 0.948919i \(-0.602179\pi\)
0.804975 + 0.593308i \(0.202179\pi\)
\(360\) 958.869 + 696.659i 0.140380 + 0.101992i
\(361\) −693.885 2135.56i −0.101164 0.311351i
\(362\) −2495.69 −0.362349
\(363\) 0 0
\(364\) −9431.18 −1.35804
\(365\) −2425.82 7465.91i −0.347872 1.07064i
\(366\) 355.666 + 258.407i 0.0507950 + 0.0369047i
\(367\) −7817.53 + 5679.77i −1.11191 + 0.807851i −0.982964 0.183800i \(-0.941160\pi\)
−0.128948 + 0.991651i \(0.541160\pi\)
\(368\) 212.211 653.118i 0.0300605 0.0925167i
\(369\) 691.859 2129.32i 0.0976064 0.300402i
\(370\) −311.085 + 226.016i −0.0437095 + 0.0317568i
\(371\) 2040.66 + 1482.62i 0.285568 + 0.207477i
\(372\) 895.586 + 2756.33i 0.124822 + 0.384164i
\(373\) −141.780 −0.0196812 −0.00984062 0.999952i \(-0.503132\pi\)
−0.00984062 + 0.999952i \(0.503132\pi\)
\(374\) 0 0
\(375\) 6456.42 0.889088
\(376\) 251.334 + 773.527i 0.0344723 + 0.106095i
\(377\) −10204.9 7414.29i −1.39411 1.01288i
\(378\) −1120.71 + 814.241i −0.152494 + 0.110794i
\(379\) −871.345 + 2681.73i −0.118095 + 0.363459i −0.992580 0.121594i \(-0.961200\pi\)
0.874485 + 0.485053i \(0.161200\pi\)
\(380\) −2014.17 + 6198.99i −0.271908 + 0.836845i
\(381\) −525.667 + 381.920i −0.0706844 + 0.0513552i
\(382\) 1731.57 + 1258.06i 0.231923 + 0.168502i
\(383\) −1958.50 6027.64i −0.261291 0.804172i −0.992525 0.122045i \(-0.961055\pi\)
0.731233 0.682128i \(-0.238945\pi\)
\(384\) 7458.53 0.991189
\(385\) 0 0
\(386\) 1818.55 0.239797
\(387\) −5.75573 17.7143i −0.000756021 0.00232679i
\(388\) 5118.21 + 3718.60i 0.669685 + 0.486555i
\(389\) 7123.60 5175.60i 0.928486 0.674584i −0.0171360 0.999853i \(-0.505455\pi\)
0.945622 + 0.325269i \(0.105455\pi\)
\(390\) 1286.90 3960.66i 0.167089 0.514246i
\(391\) −341.616 + 1051.38i −0.0441848 + 0.135987i
\(392\) 516.868 375.526i 0.0665963 0.0483851i
\(393\) −5547.61 4030.58i −0.712061 0.517343i
\(394\) 1159.51 + 3568.60i 0.148262 + 0.456304i
\(395\) 12576.5 1.60200
\(396\) 0 0
\(397\) 4315.26 0.545534 0.272767 0.962080i \(-0.412061\pi\)
0.272767 + 0.962080i \(0.412061\pi\)
\(398\) 1.74010 + 5.35547i 0.000219154 + 0.000674486i
\(399\) 5514.53 + 4006.54i 0.691910 + 0.502702i
\(400\) −1676.12 + 1217.77i −0.209515 + 0.152221i
\(401\) 111.766 343.979i 0.0139185 0.0428367i −0.943856 0.330357i \(-0.892831\pi\)
0.957775 + 0.287520i \(0.0928309\pi\)
\(402\) −552.033 + 1698.98i −0.0684899 + 0.210790i
\(403\) 3955.12 2873.56i 0.488880 0.355192i
\(404\) 7810.68 + 5674.79i 0.961870 + 0.698840i
\(405\) 3506.27 + 10791.2i 0.430193 + 1.32400i
\(406\) −2094.24 −0.255998
\(407\) 0 0
\(408\) −5555.70 −0.674137
\(409\) 2849.29 + 8769.22i 0.344470 + 1.06017i 0.961867 + 0.273519i \(0.0881875\pi\)
−0.617396 + 0.786652i \(0.711812\pi\)
\(410\) −2093.33 1520.89i −0.252152 0.183199i
\(411\) −951.162 + 691.060i −0.114154 + 0.0829378i
\(412\) 3979.33 12247.1i 0.475843 1.46449i
\(413\) 2854.25 8784.48i 0.340069 1.04662i
\(414\) 64.4052 46.7931i 0.00764575 0.00555496i
\(415\) 272.028 + 197.640i 0.0321767 + 0.0233777i
\(416\) −2957.21 9101.37i −0.348532 1.07267i
\(417\) −17192.6 −2.01901
\(418\) 0 0
\(419\) −14912.9 −1.73876 −0.869380 0.494144i \(-0.835481\pi\)
−0.869380 + 0.494144i \(0.835481\pi\)
\(420\) 2975.87 + 9158.78i 0.345732 + 1.06405i
\(421\) 10910.4 + 7926.88i 1.26304 + 0.917654i 0.998903 0.0468306i \(-0.0149121\pi\)
0.264139 + 0.964485i \(0.414912\pi\)
\(422\) 1840.30 1337.05i 0.212285 0.154234i
\(423\) 180.801 556.449i 0.0207822 0.0639610i
\(424\) −521.254 + 1604.26i −0.0597036 + 0.183749i
\(425\) 2698.20 1960.36i 0.307958 0.223744i
\(426\) −1652.37 1200.52i −0.187928 0.136538i
\(427\) 529.925 + 1630.94i 0.0600582 + 0.184840i
\(428\) 3613.96 0.408148
\(429\) 0 0
\(430\) −21.5260 −0.00241413
\(431\) 125.564 + 386.447i 0.0140330 + 0.0431890i 0.957828 0.287343i \(-0.0927719\pi\)
−0.943795 + 0.330532i \(0.892772\pi\)
\(432\) 4650.71 + 3378.94i 0.517957 + 0.376318i
\(433\) 1429.29 1038.44i 0.158631 0.115252i −0.505638 0.862746i \(-0.668743\pi\)
0.664269 + 0.747494i \(0.268743\pi\)
\(434\) 250.818 771.938i 0.0277411 0.0853784i
\(435\) −3980.14 + 12249.6i −0.438697 + 1.35017i
\(436\) −388.017 + 281.911i −0.0426207 + 0.0309658i
\(437\) 733.805 + 533.140i 0.0803264 + 0.0583606i
\(438\) −818.848 2520.16i −0.0893289 0.274926i
\(439\) 7824.19 0.850634 0.425317 0.905044i \(-0.360163\pi\)
0.425317 + 0.905044i \(0.360163\pi\)
\(440\) 0 0
\(441\) −459.591 −0.0496265
\(442\) 1397.82 + 4302.04i 0.150424 + 0.462958i
\(443\) −9439.52 6858.21i −1.01238 0.735538i −0.0476744 0.998863i \(-0.515181\pi\)
−0.964707 + 0.263325i \(0.915181\pi\)
\(444\) 1462.58 1062.62i 0.156331 0.113581i
\(445\) 1401.97 4314.81i 0.149348 0.459644i
\(446\) 2.78664 8.57640i 0.000295855 0.000910547i
\(447\) −16730.2 + 12155.2i −1.77027 + 1.28617i
\(448\) 4348.89 + 3159.66i 0.458629 + 0.333214i
\(449\) 5245.64 + 16144.4i 0.551352 + 1.69689i 0.705387 + 0.708822i \(0.250773\pi\)
−0.154035 + 0.988065i \(0.549227\pi\)
\(450\) −240.173 −0.0251597
\(451\) 0 0
\(452\) 14966.1 1.55741
\(453\) −2131.11 6558.88i −0.221034 0.680272i
\(454\) 2733.73 + 1986.17i 0.282600 + 0.205321i
\(455\) 13142.1 9548.31i 1.35409 0.983806i
\(456\) −1408.60 + 4335.23i −0.144658 + 0.445210i
\(457\) −5003.87 + 15400.3i −0.512190 + 1.57636i 0.276146 + 0.961116i \(0.410943\pi\)
−0.788337 + 0.615244i \(0.789057\pi\)
\(458\) 3005.41 2183.56i 0.306623 0.222775i
\(459\) −7486.68 5439.39i −0.761325 0.553135i
\(460\) 395.991 + 1218.73i 0.0401373 + 0.123530i
\(461\) 8586.04 0.867444 0.433722 0.901047i \(-0.357200\pi\)
0.433722 + 0.901047i \(0.357200\pi\)
\(462\) 0 0
\(463\) −7917.20 −0.794694 −0.397347 0.917668i \(-0.630069\pi\)
−0.397347 + 0.917668i \(0.630069\pi\)
\(464\) 2685.56 + 8265.31i 0.268694 + 0.826956i
\(465\) −4038.54 2934.17i −0.402759 0.292621i
\(466\) 125.367 91.0846i 0.0124625 0.00905454i
\(467\) −4683.14 + 14413.2i −0.464047 + 1.42819i 0.396130 + 0.918194i \(0.370353\pi\)
−0.860177 + 0.509995i \(0.829647\pi\)
\(468\) −1402.02 + 4314.97i −0.138479 + 0.426195i
\(469\) −5637.51 + 4095.89i −0.555045 + 0.403264i
\(470\) −547.043 397.450i −0.0536877 0.0390064i
\(471\) 626.619 + 1928.53i 0.0613017 + 0.188667i
\(472\) 6176.82 0.602354
\(473\) 0 0
\(474\) 4245.25 0.411373
\(475\) −845.603 2602.50i −0.0816819 0.251391i
\(476\) −8462.44 6148.32i −0.814864 0.592033i
\(477\) 981.691 713.241i 0.0942318 0.0684634i
\(478\) −975.555 + 3002.45i −0.0933491 + 0.287299i
\(479\) 3090.51 9511.62i 0.294800 0.907301i −0.688489 0.725247i \(-0.741725\pi\)
0.983289 0.182054i \(-0.0582745\pi\)
\(480\) −7905.38 + 5743.60i −0.751729 + 0.546163i
\(481\) −2467.15 1792.49i −0.233872 0.169918i
\(482\) 225.443 + 693.843i 0.0213043 + 0.0655678i
\(483\) 1340.11 0.126246
\(484\) 0 0
\(485\) −10896.9 −1.02021
\(486\) 500.798 + 1541.30i 0.0467421 + 0.143857i
\(487\) −5699.15 4140.68i −0.530294 0.385281i 0.290174 0.956974i \(-0.406287\pi\)
−0.820468 + 0.571693i \(0.806287\pi\)
\(488\) −927.779 + 674.071i −0.0860626 + 0.0625282i
\(489\) −2555.33 + 7864.48i −0.236310 + 0.727289i
\(490\) −164.134 + 505.153i −0.0151323 + 0.0465724i
\(491\) 10781.3 7833.07i 0.990944 0.719963i 0.0308160 0.999525i \(-0.490189\pi\)
0.960128 + 0.279562i \(0.0901894\pi\)
\(492\) 9841.87 + 7150.54i 0.901841 + 0.655226i
\(493\) −4323.20 13305.4i −0.394944 1.21551i
\(494\) 3711.38 0.338022
\(495\) 0 0
\(496\) −3368.25 −0.304917
\(497\) −2461.94 7577.09i −0.222200 0.683861i
\(498\) 91.8245 + 66.7144i 0.00826256 + 0.00600310i
\(499\) 16236.3 11796.3i 1.45658 1.05827i 0.472346 0.881413i \(-0.343407\pi\)
0.984237 0.176856i \(-0.0565928\pi\)
\(500\) −2512.05 + 7731.30i −0.224685 + 0.691509i
\(501\) 876.943 2698.95i 0.0782015 0.240679i
\(502\) −163.987 + 119.144i −0.0145799 + 0.0105929i
\(503\) −6296.05 4574.35i −0.558106 0.405487i 0.272660 0.962111i \(-0.412097\pi\)
−0.830765 + 0.556623i \(0.812097\pi\)
\(504\) 482.253 + 1484.22i 0.0426216 + 0.131176i
\(505\) −16629.3 −1.46533
\(506\) 0 0
\(507\) 20003.4 1.75224
\(508\) −252.808 778.062i −0.0220798 0.0679545i
\(509\) 1194.05 + 867.531i 0.103979 + 0.0755455i 0.638560 0.769572i \(-0.279530\pi\)
−0.534581 + 0.845117i \(0.679530\pi\)
\(510\) 3736.73 2714.89i 0.324441 0.235720i
\(511\) 3194.11 9830.46i 0.276515 0.851025i
\(512\) −3476.63 + 10700.0i −0.300091 + 0.923586i
\(513\) −6142.66 + 4462.91i −0.528665 + 0.384098i
\(514\) −1916.01 1392.06i −0.164419 0.119458i
\(515\) 6854.12 + 21094.8i 0.586463 + 1.80495i
\(516\) 101.205 0.00863431
\(517\) 0 0
\(518\) −506.305 −0.0429455
\(519\) 3313.17 + 10196.9i 0.280216 + 0.862417i
\(520\) 8788.62 + 6385.31i 0.741166 + 0.538489i
\(521\) −6156.16 + 4472.71i −0.517670 + 0.376109i −0.815725 0.578439i \(-0.803662\pi\)
0.298055 + 0.954549i \(0.403662\pi\)
\(522\) −311.324 + 958.158i −0.0261040 + 0.0803399i
\(523\) 3848.16 11843.4i 0.321737 0.990204i −0.651155 0.758944i \(-0.725715\pi\)
0.972892 0.231259i \(-0.0742846\pi\)
\(524\) 6984.91 5074.83i 0.582323 0.423082i
\(525\) −3270.83 2376.40i −0.271906 0.197552i
\(526\) −47.0404 144.775i −0.00389935 0.0120010i
\(527\) 5422.18 0.448186
\(528\) 0 0
\(529\) −11988.7 −0.985344
\(530\) −433.356 1333.73i −0.0355165 0.109309i
\(531\) −3594.78 2611.76i −0.293786 0.213448i
\(532\) −6943.26 + 5044.57i −0.565843 + 0.411109i
\(533\) 6341.31 19516.6i 0.515334 1.58603i
\(534\) 473.241 1456.49i 0.0383505 0.118031i
\(535\) −5035.97 + 3658.85i −0.406961 + 0.295674i
\(536\) −3770.01 2739.07i −0.303805 0.220727i
\(537\) −8115.10 24975.7i −0.652128 2.00704i
\(538\) −3684.44 −0.295255
\(539\) 0 0
\(540\) −10727.0 −0.854847
\(541\) 2877.62 + 8856.40i 0.228685 + 0.703819i 0.997897 + 0.0648254i \(0.0206491\pi\)
−0.769212 + 0.638994i \(0.779351\pi\)
\(542\) 880.670 + 639.844i 0.0697933 + 0.0507078i
\(543\) −16350.5 + 11879.3i −1.29220 + 0.938839i
\(544\) 3279.86 10094.4i 0.258497 0.795573i
\(545\) 255.280 785.672i 0.0200642 0.0617514i
\(546\) 4436.19 3223.08i 0.347713 0.252629i
\(547\) 8914.20 + 6476.54i 0.696789 + 0.506247i 0.878885 0.477034i \(-0.158288\pi\)
−0.182096 + 0.983281i \(0.558288\pi\)
\(548\) −457.439 1407.85i −0.0356585 0.109745i
\(549\) 824.968 0.0641325
\(550\) 0 0
\(551\) −11478.6 −0.887490
\(552\) 276.935 + 852.317i 0.0213535 + 0.0657192i
\(553\) 13397.0 + 9733.49i 1.03020 + 0.748481i
\(554\) −139.672 + 101.477i −0.0107113 + 0.00778225i
\(555\) −962.244 + 2961.48i −0.0735946 + 0.226501i
\(556\) 6689.27 20587.4i 0.510230 1.57033i
\(557\) 9723.11 7064.25i 0.739643 0.537382i −0.152956 0.988233i \(-0.548879\pi\)
0.892599 + 0.450851i \(0.148879\pi\)
\(558\) −315.892 229.509i −0.0239656 0.0174120i
\(559\) −52.7548 162.362i −0.00399157 0.0122848i
\(560\) −11192.1 −0.844555
\(561\) 0 0
\(562\) 3598.04 0.270061
\(563\) −2708.19 8334.95i −0.202729 0.623937i −0.999799 0.0200493i \(-0.993618\pi\)
0.797070 0.603887i \(-0.206382\pi\)
\(564\) 2571.94 + 1868.63i 0.192018 + 0.139510i
\(565\) −20855.0 + 15152.0i −1.55288 + 1.12823i
\(566\) 1176.22 3620.05i 0.0873505 0.268837i
\(567\) −4616.76 + 14208.9i −0.341950 + 1.05241i
\(568\) 4310.31 3131.62i 0.318410 0.231338i
\(569\) 8311.16 + 6038.41i 0.612341 + 0.444892i 0.850238 0.526399i \(-0.176458\pi\)
−0.237897 + 0.971290i \(0.576458\pi\)
\(570\) −1171.07 3604.19i −0.0860540 0.264847i
\(571\) 2602.62 0.190747 0.0953734 0.995442i \(-0.469596\pi\)
0.0953734 + 0.995442i \(0.469596\pi\)
\(572\) 0 0
\(573\) 17332.6 1.26366
\(574\) −1052.82 3240.24i −0.0765572 0.235619i
\(575\) −435.242 316.222i −0.0315667 0.0229345i
\(576\) 2092.11 1520.00i 0.151339 0.109954i
\(577\) −6095.99 + 18761.5i −0.439825 + 1.35364i 0.448235 + 0.893916i \(0.352053\pi\)
−0.888060 + 0.459728i \(0.847947\pi\)
\(578\) −438.925 + 1350.87i −0.0315863 + 0.0972127i
\(579\) 11914.2 8656.17i 0.855159 0.621309i
\(580\) −13119.8 9532.12i −0.939261 0.682413i
\(581\) 136.814 + 421.069i 0.00976935 + 0.0300670i
\(582\) −3678.30 −0.261977
\(583\) 0 0
\(584\) 6912.30 0.489783
\(585\) −2414.88 7432.24i −0.170672 0.525274i
\(586\) −5259.65 3821.36i −0.370775 0.269384i
\(587\) 8184.14 5946.12i 0.575461 0.418097i −0.261624 0.965170i \(-0.584258\pi\)
0.837085 + 0.547073i \(0.184258\pi\)
\(588\) 771.683 2374.99i 0.0541219 0.166570i
\(589\) 1374.75 4231.05i 0.0961725 0.295988i
\(590\) −4154.49 + 3018.41i −0.289894 + 0.210620i
\(591\) 24582.8 + 17860.5i 1.71100 + 1.24312i
\(592\) 649.265 + 1998.23i 0.0450754 + 0.138728i
\(593\) 3130.32 0.216774 0.108387 0.994109i \(-0.465431\pi\)
0.108387 + 0.994109i \(0.465431\pi\)
\(594\) 0 0
\(595\) 18016.9 1.24138
\(596\) −8045.98 24763.0i −0.552980 1.70190i
\(597\) 36.8919 + 26.8035i 0.00252912 + 0.00183751i
\(598\) 590.313 428.887i 0.0403674 0.0293286i
\(599\) 3114.92 9586.73i 0.212474 0.653928i −0.786849 0.617145i \(-0.788289\pi\)
0.999323 0.0367829i \(-0.0117110\pi\)
\(600\) 835.484 2571.36i 0.0568475 0.174959i
\(601\) −3864.69 + 2807.86i −0.262303 + 0.190574i −0.711162 0.703029i \(-0.751831\pi\)
0.448859 + 0.893603i \(0.351831\pi\)
\(602\) −22.9304 16.6599i −0.00155245 0.00112792i
\(603\) 1035.90 + 3188.17i 0.0699586 + 0.215310i
\(604\) 8683.16 0.584955
\(605\) 0 0
\(606\) −5613.29 −0.376278
\(607\) −794.591 2445.50i −0.0531325 0.163525i 0.920969 0.389635i \(-0.127399\pi\)
−0.974102 + 0.226110i \(0.927399\pi\)
\(608\) −7045.27 5118.69i −0.469940 0.341431i
\(609\) −13720.3 + 9968.41i −0.912933 + 0.663285i
\(610\) 294.621 906.751i 0.0195555 0.0601857i
\(611\) 1657.15 5100.20i 0.109724 0.337695i
\(612\) −4071.00 + 2957.75i −0.268889 + 0.195360i
\(613\) −10284.1 7471.84i −0.677604 0.492308i 0.194958 0.980812i \(-0.437543\pi\)
−0.872562 + 0.488504i \(0.837543\pi\)
\(614\) 338.857 + 1042.89i 0.0222722 + 0.0685468i
\(615\) −20953.8 −1.37388
\(616\) 0 0
\(617\) 16236.1 1.05939 0.529693 0.848189i \(-0.322307\pi\)
0.529693 + 0.848189i \(0.322307\pi\)
\(618\) 2313.64 + 7120.66i 0.150596 + 0.463487i
\(619\) −10240.0 7439.78i −0.664910 0.483086i 0.203407 0.979094i \(-0.434798\pi\)
−0.868318 + 0.496009i \(0.834798\pi\)
\(620\) 5084.86 3694.37i 0.329376 0.239305i
\(621\) −461.286 + 1419.69i −0.0298080 + 0.0917396i
\(622\) 1693.16 5211.01i 0.109147 0.335921i
\(623\) 4832.86 3511.28i 0.310794 0.225805i
\(624\) −18409.3 13375.2i −1.18103 0.858069i
\(625\) −5883.02 18106.1i −0.376513 1.15879i
\(626\) 481.955 0.0307713
\(627\) 0 0
\(628\) −2553.15 −0.162232
\(629\) −1045.18 3216.74i −0.0662546 0.203911i
\(630\) −1049.65 762.617i −0.0663796 0.0482276i
\(631\) 3195.59 2321.73i 0.201608 0.146477i −0.482401 0.875951i \(-0.660235\pi\)
0.684008 + 0.729474i \(0.260235\pi\)
\(632\) −3422.06 + 10532.0i −0.215383 + 0.662881i
\(633\) 5692.39 17519.4i 0.357428 1.10005i
\(634\) 138.411 100.562i 0.00867038 0.00629940i
\(635\) 1140.01 + 828.263i 0.0712437 + 0.0517616i
\(636\) 2037.44 + 6270.59i 0.127028 + 0.390951i
\(637\) −4212.44 −0.262014
\(638\) 0 0
\(639\) −3832.67 −0.237274
\(640\) −4998.41 15383.5i −0.308718 0.950137i
\(641\) 5985.32 + 4348.59i 0.368808 + 0.267955i 0.756717 0.653743i \(-0.226802\pi\)
−0.387908 + 0.921698i \(0.626802\pi\)
\(642\) −1699.92 + 1235.06i −0.104502 + 0.0759253i
\(643\) −3860.14 + 11880.3i −0.236748 + 0.728637i 0.760136 + 0.649764i \(0.225132\pi\)
−0.996885 + 0.0788729i \(0.974868\pi\)
\(644\) −521.407 + 1604.72i −0.0319042 + 0.0981910i
\(645\) −141.027 + 102.462i −0.00860919 + 0.00625494i
\(646\) 3330.16 + 2419.51i 0.202823 + 0.147359i
\(647\) −3236.02 9959.44i −0.196632 0.605172i −0.999954 0.00962607i \(-0.996936\pi\)
0.803321 0.595546i \(-0.203064\pi\)
\(648\) −9991.02 −0.605685
\(649\) 0 0
\(650\) −2201.33 −0.132836
\(651\) −2031.14 6251.22i −0.122284 0.376351i
\(652\) −8423.18 6119.80i −0.505946 0.367592i
\(653\) −5127.50 + 3725.34i −0.307281 + 0.223253i −0.730729 0.682668i \(-0.760820\pi\)
0.423448 + 0.905920i \(0.360820\pi\)
\(654\) 86.1712 265.208i 0.00515223 0.0158569i
\(655\) −4595.44 + 14143.3i −0.274136 + 0.843703i
\(656\) −11438.2 + 8310.32i −0.680771 + 0.494609i
\(657\) −4022.82 2922.75i −0.238881 0.173557i
\(658\) −275.130 846.762i −0.0163004 0.0501675i
\(659\) 15196.7 0.898302 0.449151 0.893456i \(-0.351726\pi\)
0.449151 + 0.893456i \(0.351726\pi\)
\(660\) 0 0
\(661\) 2298.17 0.135232 0.0676161 0.997711i \(-0.478461\pi\)
0.0676161 + 0.997711i \(0.478461\pi\)
\(662\) −1930.29 5940.83i −0.113328 0.348787i
\(663\) 29635.2 + 21531.2i 1.73595 + 1.26124i
\(664\) −239.530 + 174.029i −0.0139994 + 0.0101711i
\(665\) 4568.04 14059.0i 0.266377 0.819826i
\(666\) −75.2662 + 231.645i −0.00437914 + 0.0134776i
\(667\) −1825.73 + 1326.47i −0.105986 + 0.0770033i
\(668\) 2890.69 + 2100.21i 0.167431 + 0.121646i
\(669\) −22.5664 69.4523i −0.00130414 0.00401372i
\(670\) 3874.18 0.223392
\(671\) 0 0
\(672\) −12866.4 −0.738589
\(673\) 7169.08 + 22064.2i 0.410621 + 1.26376i 0.916110 + 0.400928i \(0.131312\pi\)
−0.505489 + 0.862833i \(0.668688\pi\)
\(674\) 6924.00 + 5030.58i 0.395701 + 0.287494i
\(675\) 3643.40 2647.08i 0.207755 0.150943i
\(676\) −7782.90 + 23953.3i −0.442814 + 1.36284i
\(677\) −662.958 + 2040.38i −0.0376360 + 0.115832i −0.968109 0.250528i \(-0.919396\pi\)
0.930473 + 0.366359i \(0.119396\pi\)
\(678\) −7039.70 + 5114.64i −0.398758 + 0.289715i
\(679\) −11607.8 8433.59i −0.656065 0.476659i
\(680\) 3723.21 + 11458.9i 0.209968 + 0.646217i
\(681\) 27364.0 1.53978
\(682\) 0 0
\(683\) −29544.6 −1.65519 −0.827593 0.561329i \(-0.810290\pi\)
−0.827593 + 0.561329i \(0.810290\pi\)
\(684\) 1275.83 + 3926.60i 0.0713196 + 0.219499i
\(685\) 2062.77 + 1498.69i 0.115058 + 0.0835942i
\(686\) −4004.58 + 2909.50i −0.222880 + 0.161932i
\(687\) 9296.29 28611.1i 0.516267 1.58891i
\(688\) −36.3466 + 111.863i −0.00201410 + 0.00619876i
\(689\) 8997.80 6537.29i 0.497517 0.361467i
\(690\) −602.764 437.934i −0.0332563 0.0241621i
\(691\) 8591.62 + 26442.3i 0.472997 + 1.45573i 0.848641 + 0.528970i \(0.177422\pi\)
−0.375644 + 0.926764i \(0.622578\pi\)
\(692\) −13499.5 −0.741579
\(693\) 0 0
\(694\) −3366.55 −0.184139
\(695\) 11521.8 + 35460.5i 0.628845 + 1.93539i
\(696\) −9175.30 6666.24i −0.499696 0.363051i
\(697\) 18413.1 13377.9i 1.00064 0.727007i
\(698\) −1520.23 + 4678.80i −0.0824380 + 0.253718i
\(699\) 387.785 1193.48i 0.0209834 0.0645801i
\(700\) 4118.25 2992.09i 0.222365 0.161557i
\(701\) 15935.8 + 11578.0i 0.858613 + 0.623819i 0.927507 0.373805i \(-0.121947\pi\)
−0.0688945 + 0.997624i \(0.521947\pi\)
\(702\) 1887.48 + 5809.08i 0.101479 + 0.312321i
\(703\) −2775.09 −0.148883
\(704\) 0 0
\(705\) −5475.78 −0.292524
\(706\) −1298.19 3995.41i −0.0692038 0.212987i
\(707\) −17714.2 12870.1i −0.942308 0.684627i
\(708\) 19532.5 14191.2i 1.03683 0.753300i
\(709\) 5909.18 18186.6i 0.313010 0.963345i −0.663556 0.748126i \(-0.730954\pi\)
0.976566 0.215218i \(-0.0690464\pi\)
\(710\) −1368.76 + 4212.62i −0.0723504 + 0.222672i
\(711\) 6444.85 4682.46i 0.339945 0.246984i
\(712\) 3231.91 + 2348.12i 0.170114 + 0.123595i
\(713\) −270.279 831.833i −0.0141964 0.0436920i
\(714\) 6081.70 0.318770
\(715\) 0 0
\(716\) 33064.8 1.72582
\(717\) 7900.12 + 24314.1i 0.411486 + 1.26642i
\(718\) −2437.23 1770.75i −0.126681 0.0920389i
\(719\) −1486.52 + 1080.02i −0.0771042 + 0.0560195i −0.625670 0.780088i \(-0.715174\pi\)
0.548565 + 0.836108i \(0.315174\pi\)
\(720\) −1663.79 + 5120.61i −0.0861190 + 0.265047i
\(721\) −9024.91 + 27775.8i −0.466165 + 1.43471i
\(722\) −1329.85 + 966.196i −0.0685486 + 0.0498034i
\(723\) 4779.63 + 3472.61i 0.245860 + 0.178627i
\(724\) −7863.38 24201.0i −0.403647 1.24230i
\(725\) 6808.33 0.348765
\(726\) 0 0
\(727\) −7555.46 −0.385442 −0.192721 0.981254i \(-0.561731\pi\)
−0.192721 + 0.981254i \(0.561731\pi\)
\(728\) 4420.15 + 13603.8i 0.225030 + 0.692570i
\(729\) −8660.70 6292.36i −0.440009 0.319685i
\(730\) −4649.17 + 3377.82i −0.235717 + 0.171258i
\(731\) 58.5105 180.077i 0.00296045 0.00911133i
\(732\) −1385.17 + 4263.12i −0.0699419 + 0.215259i
\(733\) −9695.77 + 7044.39i −0.488569 + 0.354966i −0.804634 0.593771i \(-0.797638\pi\)
0.316065 + 0.948738i \(0.397638\pi\)
\(734\) 5722.83 + 4157.88i 0.287784 + 0.209087i
\(735\) 1329.17 + 4090.77i 0.0667037 + 0.205293i
\(736\) −1712.10 −0.0857456
\(737\) 0 0
\(738\) −1638.99 −0.0817508
\(739\) −8387.49 25814.0i −0.417508 1.28496i −0.909988 0.414635i \(-0.863909\pi\)
0.492479 0.870324i \(-0.336091\pi\)
\(740\) −3171.87 2304.50i −0.157568 0.114480i
\(741\) 24315.1 17665.9i 1.20545 0.875809i
\(742\) 570.605 1756.14i 0.0282312 0.0868868i
\(743\) −9030.29 + 27792.4i −0.445881 + 1.37228i 0.435634 + 0.900124i \(0.356524\pi\)
−0.881515 + 0.472156i \(0.843476\pi\)
\(744\) 3556.07 2583.64i 0.175231 0.127313i
\(745\) 36282.4 + 26360.7i 1.78428 + 1.29635i
\(746\) 32.0730 + 98.7104i 0.00157409 + 0.00484457i
\(747\) 212.987 0.0104321
\(748\) 0 0
\(749\) −8196.29 −0.399847
\(750\) −1460.55 4495.10i −0.0711088 0.218850i
\(751\) 7167.40 + 5207.42i 0.348258 + 0.253025i 0.748138 0.663543i \(-0.230948\pi\)
−0.399880 + 0.916568i \(0.630948\pi\)
\(752\) −2989.10 + 2171.71i −0.144948 + 0.105311i
\(753\) −507.243 + 1561.13i −0.0245484 + 0.0755523i
\(754\) −2853.48 + 8782.10i −0.137822 + 0.424172i
\(755\) −12099.8 + 8791.01i −0.583253 + 0.423758i
\(756\) −11426.9 8302.12i −0.549725 0.399398i
\(757\) 11042.5 + 33985.4i 0.530182 + 1.63173i 0.753835 + 0.657064i \(0.228202\pi\)
−0.223653 + 0.974669i \(0.571798\pi\)
\(758\) 2064.19 0.0989112
\(759\) 0 0
\(760\) 9885.59 0.471826
\(761\) 10628.5 + 32711.3i 0.506287 + 1.55819i 0.798597 + 0.601867i \(0.205576\pi\)
−0.292310 + 0.956324i \(0.594424\pi\)
\(762\) 384.815 + 279.585i 0.0182945 + 0.0132917i
\(763\) 880.003 639.359i 0.0417539 0.0303360i
\(764\) −6743.74 + 20755.1i −0.319345 + 0.982844i
\(765\) 2678.35 8243.12i 0.126583 0.389583i
\(766\) −3753.53 + 2727.10i −0.177050 + 0.128635i
\(767\) −32948.4 23938.4i −1.55110 1.12694i
\(768\) 2966.54 +