Properties

Label 121.4.c.f.9.2
Level $121$
Weight $4$
Character 121.9
Analytic conductor $7.139$
Analytic rank $0$
Dimension $8$
CM no
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 9.2
Root \(-1.40126 + 1.01807i\) of defining polynomial
Character \(\chi\) \(=\) 121.9
Dual form 121.4.c.f.27.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.226216 - 0.696222i) q^{2} +(-4.79602 + 3.48451i) q^{3} +(6.03859 + 4.38729i) q^{4} +(-3.97285 - 12.2272i) q^{5} +(1.34106 + 4.12734i) q^{6} +(13.6952 + 9.95015i) q^{7} +(9.15848 - 6.65403i) q^{8} +(2.51651 - 7.74502i) q^{9} +O(q^{10})\) \(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 \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

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 \(-0.858692\pi\)
0.983049 + 0.183343i \(0.0586918\pi\)
\(3\) −4.79602 + 3.48451i −0.922994 + 0.670594i −0.944267 0.329179i \(-0.893228\pi\)
0.0212735 + 0.999774i \(0.493228\pi\)
\(4\) 6.03859 + 4.38729i 0.754823 + 0.548411i
\(5\) −3.97285 12.2272i −0.355342 1.09363i −0.955811 0.293983i \(-0.905019\pi\)
0.600468 0.799648i \(-0.294981\pi\)
\(6\) 1.34106 + 4.12734i 0.0912473 + 0.280830i
\(7\) 13.6952 + 9.95015i 0.739472 + 0.537258i 0.892546 0.450957i \(-0.148917\pi\)
−0.153074 + 0.988215i \(0.548917\pi\)
\(8\) 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 0.329352 + 0.944207i \(0.393170\pi\)
−0.821443 + 0.570291i \(0.806830\pi\)
\(14\) 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 0.949999 + 0.312253i \(0.101084\pi\)
−0.585028 + 0.811013i \(0.698916\pi\)
\(18\) −4.82297 3.50410i −0.0631548 0.0458846i
\(19\) −54.9509 + 39.9242i −0.663505 + 0.482065i −0.867845 0.496835i \(-0.834495\pi\)
0.204340 + 0.978900i \(0.434495\pi\)
\(20\) 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 \(-0.118023\pi\)
−0.0565897 + 0.998398i \(0.518023\pi\)
\(30\) 45.1379 32.7946i 0.274701 0.199582i
\(31\) −20.2398 + 62.2918i −0.117264 + 0.360901i −0.992412 0.122953i \(-0.960763\pi\)
0.875149 + 0.483854i \(0.160763\pi\)
\(32\) 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 0.511927 0.859029i \(-0.328932\pi\)
−0.658791 + 0.752326i \(0.728932\pi\)
\(38\) 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 \(-0.524582\pi\)
0.924381 + 0.381471i \(0.124582\pi\)
\(42\) −22.7017 + 69.8685i −0.0834034 + 0.256689i
\(43\) 2.28719 0.00811146 0.00405573 0.999992i \(-0.498709\pi\)
0.00405573 + 0.999992i \(0.498709\pi\)
\(44\) 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 −0.674316 0.738443i \(-0.735562\pi\)
0.493926 + 0.869504i \(0.335562\pi\)
\(48\) −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 −0.992827 0.119563i \(-0.961851\pi\)
0.873491 + 0.486840i \(0.161851\pi\)
\(54\) −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 −0.0176741 0.999844i \(-0.505626\pi\)
−0.956370 + 0.292160i \(0.905626\pi\)
\(60\) 175.793 + 541.036i 0.378247 + 1.16413i
\(61\) −31.3042 96.3445i −0.0657065 0.202224i 0.912813 0.408378i \(-0.133905\pi\)
−0.978520 + 0.206154i \(0.933905\pi\)
\(62\) 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 −0.995944 0.0899799i \(-0.971320\pi\)
0.752846 0.658196i \(-0.228680\pi\)
\(72\) −28.4882 87.6775i −0.0466300 0.143512i
\(73\) 493.986 + 358.902i 0.792009 + 0.575428i 0.908559 0.417757i \(-0.137184\pi\)
−0.116550 + 0.993185i \(0.537184\pi\)
\(74\) −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 −0.467114 0.884197i \(-0.654706\pi\)
0.897621 0.440768i \(-0.145294\pi\)
\(80\) 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 \(-0.105505\pi\)
−0.956258 + 0.292523i \(0.905505\pi\)
\(84\) −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 −0.715277 0.698841i \(-0.753700\pi\)
0.989440 0.144944i \(-0.0463003\pi\)
\(98\) −41.3140 −0.0425851
\(99\) 0 0
\(100\) −300.708 −0.300708
\(101\) −399.702 + 1230.15i −0.393780 + 1.21193i 0.536127 + 0.844137i \(0.319887\pi\)
−0.929908 + 0.367793i \(0.880113\pi\)
\(102\) −290.651 + 211.170i −0.282144 + 0.204990i
\(103\) 1395.75 + 1014.07i 1.33522 + 0.970091i 0.999605 + 0.0280904i \(0.00894263\pi\)
0.335611 + 0.942001i \(0.391057\pi\)
\(104\) 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 \(-0.770190\pi\)
0.396600 + 0.917992i \(0.370190\pi\)
\(108\) 257.835 793.535i 0.229724 0.707018i
\(109\) 64.2563 0.0564645 0.0282323 0.999601i \(-0.491012\pi\)
0.0282323 + 0.999601i \(0.491012\pi\)
\(110\) 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 0.351440 0.936210i \(-0.385692\pi\)
0.998990 0.0449344i \(-0.0143079\pi\)
\(114\) −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 \(-0.112191\pi\)
−0.962192 + 0.272374i \(0.912191\pi\)
\(128\) 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 \(-0.626052\pi\)
−0.385734 + 0.922610i \(0.626052\pi\)
\(132\) 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 0.968346 0.249613i \(-0.0803035\pi\)
−0.930127 + 0.367238i \(0.880303\pi\)
\(138\) 17.9082 + 55.1158i 0.0110467 + 0.0339983i
\(139\) −2346.26 1704.66i −1.43171 1.04020i −0.989696 0.143186i \(-0.954265\pi\)
−0.442011 0.897010i \(-0.645735\pi\)
\(140\) 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 −0.565939 0.824447i \(-0.691486\pi\)
−0.0267432 0.999642i \(-0.508514\pi\)
\(150\) −141.445 102.766i −0.0769931 0.0559388i
\(151\) −941.148 + 683.784i −0.507216 + 0.368514i −0.811766 0.583982i \(-0.801494\pi\)
0.304551 + 0.952496i \(0.401494\pi\)
\(152\) −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 −0.655895 0.754852i \(-0.727709\pi\)
0.515224 + 0.857056i \(0.327709\pi\)
\(158\) −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 0.792490 + 0.609885i \(0.208784\pi\)
−0.999619 + 0.0275936i \(0.991216\pi\)
\(164\) 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 \(-0.935376\pi\)
0.910917 + 0.412590i \(0.135376\pi\)
\(168\) −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 \(-0.569909\pi\)
0.860888 + 0.508795i \(0.169909\pi\)
\(174\) −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 0.524703 0.851285i \(-0.324176\pi\)
0.971763 0.235960i \(-0.0758235\pi\)
\(180\) −632.224 459.338i −0.261795 0.190206i
\(181\) 1053.49 + 3242.32i 0.432627 + 1.33149i 0.895499 + 0.445064i \(0.146819\pi\)
−0.462872 + 0.886425i \(0.653181\pi\)
\(182\) 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 0.0413737 0.999144i \(-0.486827\pi\)
−0.937457 + 0.348101i \(0.886827\pi\)
\(192\) −581.722 1790.36i −0.218657 0.672958i
\(193\) 767.655 + 2362.60i 0.286306 + 0.881159i 0.986004 + 0.166720i \(0.0533177\pi\)
−0.699698 + 0.714438i \(0.746682\pi\)
\(194\) −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 \(-0.122484\pi\)
0.926876 + 0.375369i \(0.122484\pi\)
\(198\) 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 0.663161 + 0.748477i \(0.269214\pi\)
−0.976452 + 0.215734i \(0.930786\pi\)
\(212\) −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 −0.586288 0.810103i \(-0.699411\pi\)
0.589281 + 0.807928i \(0.299411\pi\)
\(224\) 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 \(-0.0642214\pi\)
0.112165 + 0.993690i \(0.464221\pi\)
\(228\) 2431.51 1766.59i 0.706274 0.513138i
\(229\) 1568.15 4826.26i 0.452516 1.39270i −0.421512 0.906823i \(-0.638500\pi\)
0.874027 0.485877i \(-0.161500\pi\)
\(230\) −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 \(-0.909474\pi\)
0.941439 + 0.337183i \(0.109474\pi\)
\(234\) 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 \(-0.501651\pi\)
0.949441 + 0.313946i \(0.101651\pi\)
\(240\) −1211.17 + 3727.59i −0.325753 + 1.00256i
\(241\) 996.584 0.266372 0.133186 0.991091i \(-0.457479\pi\)
0.133186 + 0.991091i \(0.457479\pi\)
\(242\) 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 −0.961238 0.275718i \(-0.911084\pi\)
0.939721 + 0.341941i \(0.111084\pi\)
\(252\) 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 0.858221 0.513281i \(-0.171570\pi\)
−0.222954 + 0.974829i \(0.571570\pi\)
\(258\) 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 \(-0.507760\pi\)
−0.0243772 + 0.999703i \(0.507760\pi\)
\(264\) 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 0.957433 + 0.288654i \(0.0932078\pi\)
−0.604913 + 0.796291i \(0.706792\pi\)
\(270\) 325.106 + 1000.57i 0.0732790 + 0.225530i
\(271\) 1203.02 + 874.043i 0.269661 + 0.195920i 0.714395 0.699742i \(-0.246702\pi\)
−0.444734 + 0.895663i \(0.646702\pi\)
\(272\) −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 \(-0.891858\pi\)
0.958649 + 0.284590i \(0.0918575\pi\)
\(278\) −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 0.972583 + 0.232555i \(0.0747084\pi\)
−0.650144 + 0.759811i \(0.725292\pi\)
\(282\) −252.246 183.268i −0.0532662 0.0387001i
\(283\) −4206.53 + 3056.22i −0.883577 + 0.641956i −0.934195 0.356762i \(-0.883881\pi\)
0.0506182 + 0.998718i \(0.483881\pi\)
\(284\) 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 −0.989532 0.144313i \(-0.953903\pi\)
−0.443032 0.896506i \(-0.646097\pi\)
\(294\) 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 \(-0.455535\pi\)
0.139237 + 0.990259i \(0.455535\pi\)
\(308\) 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 0.122340 0.992488i \(-0.460960\pi\)
0.981718 + 0.190343i \(0.0609601\pi\)
\(312\) −4052.51 2944.32i −0.735347 0.534261i
\(313\) −203.445 626.140i −0.0367393 0.113072i 0.931005 0.365007i \(-0.118933\pi\)
−0.967744 + 0.251934i \(0.918933\pi\)
\(314\) 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 −0.944455 0.328641i \(-0.893409\pi\)
0.957251 + 0.289260i \(0.0934092\pi\)
\(318\) −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 0.956861 + 0.290545i \(0.0938366\pi\)
0.572011 + 0.820246i \(0.306163\pi\)
\(338\) −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 −0.998773 0.0495148i \(-0.984232\pi\)
0.778921 0.627123i \(-0.215768\pi\)
\(348\) −6049.67 4395.34i −0.931886 0.677055i
\(349\) 5436.81 3950.08i 0.833885 0.605853i −0.0867706 0.996228i \(-0.527655\pi\)
0.920656 + 0.390375i \(0.127655\pi\)
\(350\) −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 \(-0.397821\pi\)
−0.804975 + 0.593308i \(0.797821\pi\)
\(360\) −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 −0.128948 0.991651i \(-0.541160\pi\)
−0.982964 + 0.183800i \(0.941160\pi\)
\(368\) 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 \(-0.496868\pi\)
0.00984062 + 0.999952i \(0.496868\pi\)
\(374\) 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 0.874485 0.485053i \(-0.161200\pi\)
−0.992580 + 0.121594i \(0.961200\pi\)
\(380\) 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 0.731233 + 0.682128i \(0.238945\pi\)
−0.992525 + 0.122045i \(0.961055\pi\)
\(384\) −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 0.945622 0.325269i \(-0.105455\pi\)
−0.0171360 + 0.999853i \(0.505455\pi\)
\(390\) 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 0.957775 0.287520i \(-0.0928309\pi\)
−0.943856 + 0.330357i \(0.892831\pi\)
\(402\) 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 0.617396 + 0.786652i \(0.288188\pi\)
−0.961867 + 0.273519i \(0.911812\pi\)
\(410\) −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 0.264139 0.964485i \(-0.414912\pi\)
0.998903 + 0.0468306i \(0.0149121\pi\)
\(422\) 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 \(-0.907228\pi\)
0.943795 + 0.330532i \(0.107228\pi\)
\(432\) 4650.71 3378.94i 0.517957 0.376318i
\(433\) 1429.29 + 1038.44i 0.158631 + 0.115252i 0.664269 0.747494i \(-0.268743\pi\)
−0.505638 + 0.862746i \(0.668743\pi\)
\(434\) 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 \(-0.639837\pi\)
−0.425317 + 0.905044i \(0.639837\pi\)
\(440\) 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 −0.964707 0.263325i \(-0.915181\pi\)
−0.0476744 + 0.998863i \(0.515181\pi\)
\(444\) 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 −0.154035 0.988065i \(-0.549227\pi\)
0.705387 0.708822i \(-0.250773\pi\)
\(450\) 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 0.788337 + 0.615244i \(0.210943\pi\)
−0.276146 + 0.961116i \(0.589057\pi\)
\(458\) −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 \(-0.642800\pi\)
−0.433722 + 0.901047i \(0.642800\pi\)
\(462\) 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 −0.860177 0.509995i \(-0.829647\pi\)
0.396130 0.918194i \(-0.370353\pi\)
\(468\) 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 −0.983289 0.182054i \(-0.941725\pi\)
0.688489 0.725247i \(-0.258275\pi\)
\(480\) 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 −0.820468 0.571693i \(-0.806287\pi\)
0.290174 + 0.956974i \(0.406287\pi\)
\(488\) −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 \(-0.509811\pi\)
−0.960128 + 0.279562i \(0.909811\pi\)
\(492\) −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 0.984237 + 0.176856i \(0.0565928\pi\)
0.472346 + 0.881413i \(0.343407\pi\)
\(500\) −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 \(-0.587903\pi\)
0.830765 + 0.556623i \(0.187903\pi\)
\(504\) 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 −0.534581 0.845117i \(-0.679530\pi\)
0.638560 + 0.769572i \(0.279530\pi\)
\(510\) 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 0.298055 0.954549i \(-0.403662\pi\)
−0.815725 + 0.578439i \(0.803662\pi\)
\(522\) −311.324 958.158i −0.0261040 0.0803399i
\(523\) −3848.16 11843.4i −0.321737 0.990204i −0.972892 0.231259i \(-0.925715\pi\)
0.651155 0.758944i \(-0.274285\pi\)
\(524\) −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 0.769212 + 0.638994i \(0.220649\pi\)
−0.997897 + 0.0648254i \(0.979351\pi\)
\(542\) 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 \(-0.841712\pi\)
0.182096 + 0.983281i \(0.441712\pi\)
\(548\) −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 \(-0.451121\pi\)
−0.892599 + 0.450851i \(0.851121\pi\)
\(558\) 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 −0.797070 0.603887i \(-0.793618\pi\)
0.999799 0.0200493i \(-0.00638233\pi\)
\(564\) 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 \(-0.823542\pi\)
0.237897 + 0.971290i \(0.423542\pi\)
\(570\) −1171.07 + 3604.19i −0.0860540 + 0.264847i
\(571\) −2602.62 −0.190747 −0.0953734 0.995442i \(-0.530404\pi\)
−0.0953734 + 0.995442i \(0.530404\pi\)
\(572\) 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 −0.888060 0.459728i \(-0.847947\pi\)
0.448235 0.893916i \(-0.352053\pi\)
\(578\) 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 0.837085 0.547073i \(-0.184258\pi\)
−0.261624 + 0.965170i \(0.584258\pi\)
\(588\) 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 \(-0.534569\pi\)
−0.108387 + 0.994109i \(0.534569\pi\)
\(594\) 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 0.999323 + 0.0367829i \(0.0117110\pi\)
−0.786849 + 0.617145i \(0.788289\pi\)
\(600\) −835.484 2571.36i −0.0568475 0.174959i
\(601\) 3864.69 + 2807.86i 0.262303 + 0.190574i 0.711162 0.703029i \(-0.248169\pi\)
−0.448859 + 0.893603i \(0.648169\pi\)
\(602\) 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 \(-0.872601\pi\)
0.974102 + 0.226110i \(0.0726010\pi\)
\(608\) −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 \(-0.562457\pi\)
0.872562 + 0.488504i \(0.162457\pi\)
\(614\) 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 −0.868318 0.496009i \(-0.834798\pi\)
0.203407 + 0.979094i \(0.434798\pi\)
\(620\) 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 0.684008 0.729474i \(-0.260235\pi\)
−0.482401 + 0.875951i \(0.660235\pi\)
\(632\) −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 −0.387908 0.921698i \(-0.626802\pi\)
0.756717 + 0.653743i \(0.226802\pi\)
\(642\) −1699.92 1235.06i −0.104502 0.0759253i
\(643\) −3860.14 11880.3i −0.236748 0.728637i −0.996885 0.0788729i \(-0.974868\pi\)
0.760136 0.649764i \(-0.225132\pi\)
\(644\) 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 0.803321 + 0.595546i \(0.203064\pi\)
−0.999954 + 0.00962607i \(0.996936\pi\)
\(648\) 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 0.423448 0.905920i \(-0.360820\pi\)
−0.730729 + 0.682668i \(0.760820\pi\)
\(654\) 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 \(-0.648274\pi\)
−0.449151 + 0.893456i \(0.648274\pi\)
\(660\) 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 0.505489 + 0.862833i \(0.331312\pi\)
−0.916110 + 0.400928i \(0.868688\pi\)
\(674\) 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 \(-0.0806041\pi\)
−0.930473 + 0.366359i \(0.880604\pi\)
\(678\) 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 −0.375644 0.926764i \(-0.622578\pi\)
0.848641 0.528970i \(-0.177422\pi\)
\(692\) 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 \(-0.878053\pi\)
0.0688945 + 0.997624i \(0.478053\pi\)
\(702\) 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 0.976566 + 0.215218i \(0.0690464\pi\)
−0.663556 + 0.748126i \(0.730954\pi\)
\(710\) 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 0.548565 0.836108i \(-0.315174\pi\)
−0.625670 + 0.780088i \(0.715174\pi\)
\(720\) −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 \(-0.202362\pi\)
−0.316065 + 0.948738i \(0.602362\pi\)
\(734\) −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 −0.492479 0.870324i \(-0.663909\pi\)
0.909988 0.414635i \(-0.136091\pi\)
\(740\) −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 0.881515 + 0.472156i \(0.156524\pi\)
−0.435634 + 0.900124i \(0.643476\pi\)
\(744\) −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 −0.399880 0.916568i \(-0.630948\pi\)
0.748138 + 0.663543i \(0.230948\pi\)
\(752\) −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 −0.223653 0.974669i \(-0.571798\pi\)
0.753835 0.657064i \(-0.228202\pi\)
\(758\) −2064.19 −0.0989112
\(759\) 0 0
\(760\) 9885.59 0.471826
\(761\) −10628.5 + 32711.3i −0.506287 + 1.55819i 0.292310 + 0.956324i \(0.405576\pi\)
−0.798597 + 0.601867i \(0.794424\pi\)
\(762\) 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 9130.06i 0.139382 0.428975i
\(769\) 11602.7 0.544091 0.272045 0.962284i \(-0.412300\pi\)
0.272045 + 0.962284i \(0.412300\pi\)
\(770\) 0 0
\(771\) −19178.8 −0.895859
\(772\) −5729.86 + 17634.7i −0.267127 + 0.822132i
\(773\) 10258.8 7453.47i 0.477341 0.346808i −0.322955 0.946414i \(-0.604676\pi\)
0.800295 + 0.599606i \(0.204676\pi\)
\(774\) −11.0310 8.01452i −0.000512277 0.000372191i
\(775\) −815.405 2509.56i −0.0377938 0.116317i
\(776\) −2965.05 9125.47i −0.137164 0.422146i
\(777\) 3317.05 + 2409.98i 0.153151 + 0.111271i
\(778\) 5214.84 3788.80i 0.240310 0.174595i
\(779\) −5770.57 + 17760.0i −0.265407 + 0.816839i
\(780\) −42461.7 −1.94920
\(781\) 0 0
\(782\) 809.276 0.0370072
\(783\) 5837.65 17966.4i 0.266437 0.820010i
\(784\) 2347.97 1705.90i 0.106959 0.0777105i
\(785\) 3557.75 + 2584.86i 0.161760 + 0.117525i
\(786\) −1551.22 4774.15i −0.0703944 0.216652i
\(787\) 1365.12 + 4201.39i 0.0618312 + 0.190297i 0.977201 0.212318i \(-0.0681013\pi\)
−0.915369 + 0.402615i \(0.868101\pi\)
\(788\) 30951.8 + 22487.8i 1.39925 + 1.01662i
\(789\) 997.305 724.584i 0.0450000 0.0326944i
\(790\) −2845.00 + 8756.01i −0.128127 + 0.394335i
\(791\) 33942.4 1.52573
\(792\) 0 0
\(793\) 7561.33 0.338601
\(794\) 976.182 3004.38i 0.0436315 0.134284i
\(795\) −9187.59 + 6675.18i −0.409875 + 0.297791i
\(796\) −46.4500 33.7479i −0.00206831 0.00150272i
\(797\) −8352.75 25707.1i −0.371229 1.14253i −0.945988 0.324203i \(-0.894904\pi\)
0.574758 0.818323i \(-0.305096\pi\)
\(798\) −1541.97 4745.68i −0.0684022 0.210520i
\(799\) −4811.83 3496.00i −0.213054 0.154793i
\(800\) −4178.76 + 3036.05i −0.184677 + 0.134176i
\(801\) −888.044 + 2733.12i −0.0391729 + 0.120562i
\(802\) 264.769 0.0116575
\(803\) 0 0
\(804\) −18214.6 −0.798979
\(805\) 898.087 2764.03i 0.0393210 0.121018i
\(806\) −2895.35 + 2103.59i −0.126531 + 0.0919304i
\(807\) −24138.5 17537.7i −1.05293 0.765000i
\(808\) 4524.82 + 13926.0i 0.197008 + 0.606329i
\(809\) −7307.33 22489.7i −0.317568 0.977372i −0.974685 0.223584i \(-0.928224\pi\)
0.657117 0.753789i \(-0.271776\pi\)
\(810\) −6719.89 4882.29i −0.291497 0.211785i
\(811\) 27090.8 19682.6i 1.17298 0.852219i 0.181617 0.983369i \(-0.441867\pi\)
0.991363 + 0.131150i \(0.0418669\pi\)
\(812\) −6598.48 + 20308.0i −0.285174 + 0.877676i
\(813\) −8815.30 −0.380278
\(814\) 0 0
\(815\) 17933.3 0.770768
\(816\) 7798.92 24002.6i 0.334580 1.02973i
\(817\) −125.683 + 91.3140i −0.00538200 + 0.00391025i
\(818\) 5460.76 + 3967.48i 0.233412 + 0.169584i
\(819\) 3179.71 + 9786.13i 0.135663 + 0.417527i
\(820\) −8152.65 25091.3i −0.347199 1.06857i
\(821\) 2108.05 + 1531.59i 0.0896119 + 0.0651068i 0.631689 0.775222i \(-0.282362\pi\)
−0.542077 + 0.840329i \(0.682362\pi\)
\(822\) −696.299 + 505.891i −0.0295453 + 0.0214659i
\(823\) 9881.19 30411.2i 0.418513 1.28805i −0.490557 0.871409i \(-0.663207\pi\)
0.909070 0.416642i \(-0.136793\pi\)
\(824\) 19530.6 0.825705
\(825\) 0 0
\(826\) −6761.62 −0.284827
\(827\) 11668.2 35911.0i 0.490620 1.50997i −0.333054 0.942908i \(-0.608079\pi\)
0.823674 0.567064i \(-0.191921\pi\)
\(828\) 656.685 477.110i 0.0275621 0.0200250i
\(829\) 920.300 + 668.637i 0.0385565 + 0.0280129i 0.606897 0.794781i \(-0.292414\pi\)
−0.568340 + 0.822794i \(0.692414\pi\)
\(830\) 76.0641 + 234.101i 0.00318099 + 0.00979009i
\(831\) 432.031 + 1329.66i 0.0180349 + 0.0555057i
\(832\) −19175.4 13931.8i −0.799025 0.580526i
\(833\) 3779.75 2746.15i 0.157216 0.114224i
\(834\) 3889.25 11969.9i 0.161479 0.496982i
\(835\) 6154.40 0.255068
\(836\) 0 0
\(837\) 7321.60 0.302356
\(838\) −3373.53 + 10382.6i −0.139065 + 0.427998i
\(839\) 30234.8 21966.8i 1.24412 0.903909i 0.246258 0.969204i \(-0.420799\pi\)
0.997866 + 0.0652950i \(0.0207988\pi\)
\(840\) 11816.2 + 8584.96i 0.485354 + 0.352630i
\(841\) 1288.68 + 3966.15i 0.0528386 + 0.162620i
\(842\) −3050.75 9389.25i −0.124864 0.384293i
\(843\) −23572.5 17126.4i −0.963084 0.699721i
\(844\) −18764.0 + 13632.8i −0.765263 + 0.555996i
\(845\) −13405.5 + 41257.9i −0.545756 + 1.67966i
\(846\) 428.312 0.0174062
\(847\) 0 0
\(848\) −7662.68 −0.310304
\(849\) 9525.15 29315.4i 0.385044 1.18504i
\(850\) −1975.22 + 1435.08i −0.0797053 + 0.0579093i
\(851\) −441.391 320.689i −0.0177799 0.0129179i
\(852\) 6435.29 + 19805.8i 0.258767 + 0.796402i
\(853\) 6950.05 + 21390.1i 0.278974 + 0.858595i 0.988140 + 0.153553i \(0.0490717\pi\)
−0.709166 + 0.705042i \(0.750928\pi\)
\(854\) −1015.62 737.890i −0.0406953 0.0295668i
\(855\) 5753.21 4179.95i 0.230124 0.167195i
\(856\) −1693.77 + 5212.89i −0.0676307 + 0.208146i
\(857\) −43409.5 −1.73027 −0.865135 0.501539i \(-0.832767\pi\)
−0.865135 + 0.501539i \(0.832767\pi\)
\(858\) 0 0
\(859\) 29533.2 1.17306 0.586532 0.809926i \(-0.300493\pi\)
0.586532 + 0.809926i \(0.300493\pi\)
\(860\) 67.8237 208.740i 0.00268926 0.00827670i
\(861\) −22320.9 + 16217.1i −0.883499 + 0.641900i
\(862\) 240.648 + 174.841i 0.00950870 + 0.00690847i
\(863\) 4434.90 + 13649.2i 0.174931 + 0.538384i 0.999630 0.0271884i \(-0.00865540\pi\)
−0.824699 + 0.565572i \(0.808655\pi\)
\(864\) −4428.81 13630.5i −0.174388 0.536711i
\(865\) −18811.2 13667.1i −0.739421 0.537221i
\(866\) 1046.31 760.188i 0.0410566 0.0298294i
\(867\) 3554.45 10939.5i 0.139234 0.428517i
\(868\) −8275.85 −0.323618
\(869\) 0 0
\(870\) 9428.82 0.367433
\(871\) −9494.64 + 29221.5i −0.369361 + 1.13678i
\(872\) 588.490 427.563i 0.0228541 0.0166045i
\(873\) −5584.15 4057.12i −0.216489 0.157288i
\(874\) 205.185 + 631.496i 0.00794108 + 0.0244401i
\(875\) −5697.21 17534.2i −0.220115 0.677445i
\(876\) −21858.2 15880.9i −0.843061 0.612519i
\(877\) −34988.9 + 25420.9i −1.34720 + 0.978796i −0.348051 + 0.937476i \(0.613156\pi\)
−0.999146 + 0.0413205i \(0.986844\pi\)
\(878\) −1769.96 + 5447.37i −0.0680333 + 0.209385i
\(879\) 52647.9 2.02021
\(880\) 0 0
\(881\) 3816.13 0.145935 0.0729675 0.997334i \(-0.476753\pi\)
0.0729675 + 0.997334i \(0.476753\pi\)
\(882\) −103.967 + 319.977i −0.00396910 + 0.0122156i
\(883\) −39470.0 + 28676.6i −1.50427 + 1.09292i −0.535629 + 0.844454i \(0.679925\pi\)
−0.968641 + 0.248463i \(0.920075\pi\)
\(884\) −37313.2 27109.6i −1.41966 1.03144i
\(885\) −12850.6 39550.1i −0.488100 1.50222i
\(886\) 2639.46 + 8123.44i 0.100084 + 0.308027i
\(887\) 33570.3 + 24390.2i 1.27078 + 0.923274i 0.999233 0.0391521i \(-0.0124657\pi\)
0.271544 + 0.962426i \(0.412466\pi\)
\(888\) 2218.23 1611.64i 0.0838277 0.0609044i
\(889\) 573.355 1764.60i 0.0216307 0.0665725i
\(890\) 3321.21 0.125087
\(891\) 0 0
\(892\) 91.9464 0.00345134
\(893\) 1508.00 4641.16i 0.0565100 0.173920i
\(894\) 12247.3 8898.20i 0.458179 0.332886i
\(895\) −46075.1 33475.5i −1.72080 1.25024i
\(896\) 6581.48 + 20255.7i 0.245393 + 0.755241i
\(897\) −1825.95 5619.70i −0.0679673 0.209182i
\(898\) −10053.5 7304.26i −0.373595 0.271432i
\(899\) −8954.79 + 6506.03i −0.332212 + 0.241366i
\(900\) −756.733 + 2328.99i −0.0280272 + 0.0862587i
\(901\) −12335.3 −0.456104
\(902\) 0 0
\(903\) −229.528 −0.00845871
\(904\) 7014.24 21587.6i 0.258064 0.794240i
\(905\) 35459.0 25762.5i 1.30243 0.946269i
\(906\) −4084.34 2967.45i −0.149772 0.108816i
\(907\) 6679.49 + 20557.4i 0.244530 + 0.752586i 0.995713 + 0.0924926i \(0.0294835\pi\)
−0.751183 + 0.660094i \(0.770517\pi\)
\(908\) 10646.7 + 32767.3i 0.389124 + 1.19760i
\(909\) 8521.72 + 6191.39i 0.310943 + 0.225914i
\(910\) 9620.70 6989.85i 0.350465 0.254628i
\(911\) 1126.78 3467.89i 0.0409792 0.126121i −0.928474 0.371397i \(-0.878879\pi\)
0.969453 + 0.245276i \(0.0788787\pi\)
\(912\) 20707.1 0.751844
\(913\) 0 0
\(914\) 11854.0 0.428988
\(915\) 2385.86 7342.94i 0.0862014 0.265301i
\(916\) 30643.6 22263.9i 1.10534 0.803077i
\(917\) −15841.4 11509.5i −0.570479 0.414477i
\(918\) −2093.41 6442.87i −0.0752647 0.231641i
\(919\) −9666.05 29749.0i −0.346957 1.06782i −0.960528 0.278184i \(-0.910267\pi\)
0.613571 0.789640i \(-0.289733\pi\)
\(920\) −1572.35 1142.38i −0.0563465 0.0409382i
\(921\) −7184.11 + 5219.56i −0.257030 + 0.186743i
\(922\) −1942.30 + 5977.79i −0.0693777 + 0.213523i
\(923\) 35128.7 1.25274
\(924\) 0 0
\(925\) 1645.99 0.0585079
\(926\) −1791.00 + 5512.13i −0.0635592 + 0.195615i
\(927\) 11366.4 8258.18i 0.402721 0.292594i
\(928\) 17528.9 + 12735.5i 0.620057 + 0.450498i
\(929\) 2026.51 + 6236.96i 0.0715690 + 0.220267i 0.980443 0.196805i \(-0.0630565\pi\)
−0.908874 + 0.417071i \(0.863056\pi\)
\(930\) 1129.25 + 3475.48i 0.0398168 + 0.122543i
\(931\) 3101.21 + 2253.16i 0.109171 + 0.0793171i
\(932\) −1278.26 + 928.713i −0.0449259 + 0.0326406i
\(933\) −13711.3 + 42199.2i −0.481125 + 1.48075i
\(934\) −11094.2 −0.388665
\(935\) 0 0
\(936\) 6881.13 0.240296
\(937\) 7562.68 23275.5i 0.263673 0.811503i −0.728323 0.685234i \(-0.759700\pi\)
0.991996 0.126269i \(-0.0403002\pi\)
\(938\) 4126.94 2998.40i 0.143656 0.104372i
\(939\) 3157.52 + 2294.07i 0.109736 + 0.0797276i
\(940\) 2130.51 + 6557.02i 0.0739249 + 0.227518i
\(941\) −4765.30 14666.1i −0.165084 0.508078i 0.833958 0.551828i \(-0.186069\pi\)
−0.999043 + 0.0437502i \(0.986069\pi\)
\(942\) −1200.94 872.531i −0.0415378 0.0301790i
\(943\) 2970.18 2157.96i 0.102569 0.0745206i
\(944\) 8670.83 26686.1i 0.298953 0.920082i
\(945\) −24328.3 −0.837461
\(946\) 0 0
\(947\) −33141.2 −1.13722 −0.568608 0.822609i \(-0.692518\pi\)
−0.568608 + 0.822609i \(0.692518\pi\)
\(948\) −13375.9 + 41166.7i −0.458257 + 1.41037i
\(949\) −36871.6 + 26788.8i −1.26122 + 0.916333i
\(950\) −1620.63 1177.45i −0.0553474 0.0402123i
\(951\) 428.133 + 1317.66i 0.0145985 + 0.0449295i
\(952\) 4902.40 + 15088.0i 0.166899 + 0.513662i
\(953\) −16775.3 12188.0i −0.570205 0.414279i 0.264974 0.964255i \(-0.414637\pi\)
−0.835180 + 0.549977i \(0.814637\pi\)
\(954\) 718.648 522.128i 0.0243890 0.0177196i
\(955\) −11615.6 + 35749.2i −0.393584 + 1.21133i
\(956\) 32188.9 1.08898
\(957\) 0 0
\(958\) −7321.32 −0.246911
\(959\) −1037.45 + 3192.94i −0.0349333 + 0.107513i
\(960\) −19579.9 + 14225.6i −0.658269 + 0.478261i
\(961\) 20630.8 + 14989.2i 0.692518 + 0.503144i
\(962\) −689.861 2123.17i −0.0231206 0.0711578i
\(963\) 1218.44 + 3749.98i 0.0407723 + 0.125484i
\(964\) 6017.96 + 4372.30i 0.201064 + 0.146081i
\(965\) 25838.1 18772.5i 0.861926 0.626226i
\(966\) −303.154 + 933.012i −0.0100971 + 0.0310758i
\(967\) 8178.87 0.271990 0.135995 0.990710i \(-0.456577\pi\)
0.135995 + 0.990710i \(0.456577\pi\)
\(968\) 0 0
\(969\) 33334.2 1.10511
\(970\) −2465.05 + 7586.65i −0.0815960 + 0.251127i
\(971\) 16646.4 12094.3i 0.550163 0.399717i −0.277682 0.960673i \(-0.589566\pi\)
0.827846 + 0.560956i \(0.189566\pi\)
\(972\) −13368.2 9712.60i −0.441139 0.320506i
\(973\) −15170.9 46691.3i −0.499853 1.53839i
\(974\) 1593.59 + 4904.56i 0.0524249 + 0.161347i
\(975\) 14422.0 + 10478.2i 0.473716 + 0.344175i
\(976\) 4214.62 3062.10i 0.138224 0.100426i
\(977\) 4493.69 13830.1i 0.147150 0.452882i −0.850131 0.526571i \(-0.823477\pi\)
0.997281 + 0.0736895i \(0.0234774\pi\)
\(978\) −6053.48 −0.197923
\(979\) 0 0
\(980\) −5415.68 −0.176528
\(981\) 161.701 497.666i 0.00526272 0.0161970i
\(982\) −7892.46 + 5734.21i −0.256475 + 0.186340i
\(983\) 23692.6 + 17213.7i 0.768746 + 0.558527i 0.901580 0.432611i \(-0.142408\pi\)
−0.132834 + 0.991138i \(0.542408\pi\)
\(984\) 5701.52 + 17547.5i 0.184713 + 0.568489i
\(985\) −20363.5 62672.5i −0.658716 2.02732i
\(986\) 8285.56 + 6019.81i 0.267613 + 0.194432i
\(987\) 5833.04 4237.95i 0.188113 0.136672i
\(988\) 11693.8 35989.7i 0.376547 1.15889i
\(989\) 30.5427 0.000982004
\(990\) 0 0
\(991\) −38085.9 −1.22083 −0.610413 0.792083i \(-0.708997\pi\)
−0.610413 + 0.792083i \(0.708997\pi\)
\(992\) −2594.95 + 7986.44i −0.0830542 + 0.255615i
\(993\) −40924.2 + 29733.2i −1.30784 + 0.950205i
\(994\) −4718.40 3428.12i −0.150562 0.109390i
\(995\) 30.5599 + 94.0538i 0.000973683 + 0.00299669i
\(996\) 357.618 + 1100.64i 0.0113771 + 0.0350150i
\(997\) −21684.6 15754.8i −0.688825 0.500460i 0.187449 0.982274i \(-0.439978\pi\)
−0.876274 + 0.481814i \(0.839978\pi\)
\(998\) 11885.8 8635.52i 0.376991 0.273900i
\(999\) −1411.32 + 4343.59i −0.0446968 + 0.137563i
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 121.4.c.f.9.2 8
11.2 odd 10 121.4.c.c.3.2 8
11.3 even 5 inner 121.4.c.f.81.1 8
11.4 even 5 121.4.a.c.1.2 2
11.5 even 5 inner 121.4.c.f.27.2 8
11.6 odd 10 121.4.c.c.27.1 8
11.7 odd 10 11.4.a.a.1.1 2
11.8 odd 10 121.4.c.c.81.2 8
11.9 even 5 inner 121.4.c.f.3.1 8
11.10 odd 2 121.4.c.c.9.1 8
33.26 odd 10 1089.4.a.v.1.1 2
33.29 even 10 99.4.a.c.1.2 2
44.7 even 10 176.4.a.i.1.1 2
44.15 odd 10 1936.4.a.w.1.1 2
55.7 even 20 275.4.b.c.199.2 4
55.18 even 20 275.4.b.c.199.3 4
55.29 odd 10 275.4.a.b.1.2 2
77.62 even 10 539.4.a.e.1.1 2
88.29 odd 10 704.4.a.p.1.1 2
88.51 even 10 704.4.a.n.1.2 2
132.95 odd 10 1584.4.a.bc.1.2 2
143.51 odd 10 1859.4.a.a.1.2 2
165.29 even 10 2475.4.a.q.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.4.a.a.1.1 2 11.7 odd 10
99.4.a.c.1.2 2 33.29 even 10
121.4.a.c.1.2 2 11.4 even 5
121.4.c.c.3.2 8 11.2 odd 10
121.4.c.c.9.1 8 11.10 odd 2
121.4.c.c.27.1 8 11.6 odd 10
121.4.c.c.81.2 8 11.8 odd 10
121.4.c.f.3.1 8 11.9 even 5 inner
121.4.c.f.9.2 8 1.1 even 1 trivial
121.4.c.f.27.2 8 11.5 even 5 inner
121.4.c.f.81.1 8 11.3 even 5 inner
176.4.a.i.1.1 2 44.7 even 10
275.4.a.b.1.2 2 55.29 odd 10
275.4.b.c.199.2 4 55.7 even 20
275.4.b.c.199.3 4 55.18 even 20
539.4.a.e.1.1 2 77.62 even 10
704.4.a.n.1.2 2 88.51 even 10
704.4.a.p.1.1 2 88.29 odd 10
1089.4.a.v.1.1 2 33.26 odd 10
1584.4.a.bc.1.2 2 132.95 odd 10
1859.4.a.a.1.2 2 143.51 odd 10
1936.4.a.w.1.1 2 44.15 odd 10
2475.4.a.q.1.1 2 165.29 even 10