Properties

Label 121.4.c.c.81.2
Level $121$
Weight $4$
Character 121.81
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 81.2
Root \(-0.535233 + 1.64728i\) of defining polynomial
Character \(\chi\) \(=\) 121.81
Dual form 121.4.c.c.3.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.592242 + 0.430289i) q^{2} +(1.83192 - 5.63806i) q^{3} +(-2.30653 - 7.09878i) q^{4} +(10.4011 - 7.55681i) q^{5} +(3.51093 - 2.55084i) q^{6} +(5.23110 + 16.0997i) q^{7} +(3.49823 - 10.7664i) q^{8} +(-6.58831 - 4.78668i) q^{9} +O(q^{10})\) \(q+(0.592242 + 0.430289i) q^{2} +(1.83192 - 5.63806i) q^{3} +(-2.30653 - 7.09878i) q^{4} +(10.4011 - 7.55681i) q^{5} +(3.51093 - 2.55084i) q^{6} +(5.23110 + 16.0997i) q^{7} +(3.49823 - 10.7664i) q^{8} +(-6.58831 - 4.78668i) q^{9} +9.41154 q^{10} -44.2487 q^{12} +(-60.3859 - 43.8729i) q^{13} +(-3.82943 + 11.7858i) q^{14} +(-23.5519 - 72.4851i) q^{15} +(-41.6042 + 30.2272i) q^{16} +(66.9742 - 48.6596i) q^{17} +(-1.84221 - 5.66975i) q^{18} +(-20.9894 + 64.5987i) q^{19} +(-77.6345 - 56.4048i) q^{20} +100.354 q^{21} +13.3538 q^{23} +(-54.2934 - 39.4464i) q^{24} +(12.4494 - 38.3154i) q^{25} +(-16.8850 - 51.9667i) q^{26} +(90.4356 - 65.7053i) q^{27} +(102.222 - 74.2689i) q^{28} +(52.2223 + 160.724i) q^{29} +(17.2412 - 53.0628i) q^{30} +(52.9885 + 38.4984i) q^{31} -128.210 q^{32} +60.6025 q^{34} +(176.071 + 127.923i) q^{35} +(-18.7835 + 57.8096i) q^{36} +(12.6253 + 38.8568i) q^{37} +(-40.2269 + 29.2265i) q^{38} +(-357.980 + 260.087i) q^{39} +(-44.9747 - 138.418i) q^{40} +(84.9575 - 261.472i) q^{41} +(59.4337 + 43.1811i) q^{42} -2.28719 q^{43} -104.697 q^{45} +(7.90869 + 5.74600i) q^{46} +(22.2017 - 68.3297i) q^{47} +(94.2074 + 289.941i) q^{48} +(45.6576 - 33.1722i) q^{49} +(23.8597 - 17.3351i) q^{50} +(-151.654 - 466.744i) q^{51} +(-172.162 + 529.860i) q^{52} +(120.548 + 87.5830i) q^{53} +81.8320 q^{54} +191.636 q^{56} +(325.760 + 236.679i) q^{57} +(-38.2294 + 117.658i) q^{58} +(168.609 + 518.926i) q^{59} +(-460.233 + 334.379i) q^{60} +(-81.9556 + 59.5442i) q^{61} +(14.8166 + 45.6007i) q^{62} +(42.6000 - 131.109i) q^{63} +(256.902 + 186.650i) q^{64} -959.615 q^{65} +411.641 q^{67} +(-499.902 - 363.200i) q^{68} +(24.4631 - 75.2896i) q^{69} +(49.2327 + 151.523i) q^{70} +(380.752 - 276.633i) q^{71} +(-74.5830 + 54.1877i) q^{72} +(188.686 + 580.715i) q^{73} +(-9.24238 + 28.4451i) q^{74} +(-193.218 - 140.381i) q^{75} +506.985 q^{76} -323.923 q^{78} +(791.401 + 574.986i) q^{79} +(-204.306 + 628.790i) q^{80} +(-272.726 - 839.363i) q^{81} +(162.824 - 118.298i) q^{82} +(-21.1590 + 15.3729i) q^{83} +(-231.470 - 712.390i) q^{84} +(328.891 - 1012.22i) q^{85} +(-1.35457 - 0.984151i) q^{86} +1001.84 q^{87} -352.887 q^{89} +(-62.0061 - 45.0501i) q^{90} +(390.455 - 1201.70i) q^{91} +(-30.8011 - 94.7959i) q^{92} +(314.127 - 228.226i) q^{93} +(42.5502 - 30.9146i) q^{94} +(269.848 + 830.507i) q^{95} +(-234.870 + 722.857i) q^{96} +(-685.710 - 498.198i) 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 \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.592242 + 0.430289i 0.209389 + 0.152130i 0.687537 0.726149i \(-0.258692\pi\)
−0.478148 + 0.878279i \(0.658692\pi\)
\(3\) 1.83192 5.63806i 0.352552 1.08504i −0.604863 0.796330i \(-0.706772\pi\)
0.957415 0.288715i \(-0.0932279\pi\)
\(4\) −2.30653 7.09878i −0.288317 0.887348i
\(5\) 10.4011 7.55681i 0.930298 0.675901i −0.0157675 0.999876i \(-0.505019\pi\)
0.946066 + 0.323974i \(0.105019\pi\)
\(6\) 3.51093 2.55084i 0.238888 0.173563i
\(7\) 5.23110 + 16.0997i 0.282453 + 0.869301i 0.987151 + 0.159793i \(0.0510827\pi\)
−0.704698 + 0.709508i \(0.748917\pi\)
\(8\) 3.49823 10.7664i 0.154601 0.475814i
\(9\) −6.58831 4.78668i −0.244011 0.177285i
\(10\) 9.41154 0.297619
\(11\) 0 0
\(12\) −44.2487 −1.06446
\(13\) −60.3859 43.8729i −1.28831 0.936012i −0.288540 0.957468i \(-0.593170\pi\)
−0.999770 + 0.0214564i \(0.993170\pi\)
\(14\) −3.82943 + 11.7858i −0.0731042 + 0.224992i
\(15\) −23.5519 72.4851i −0.405404 1.24771i
\(16\) −41.6042 + 30.2272i −0.650066 + 0.472300i
\(17\) 66.9742 48.6596i 0.955507 0.694216i 0.00340407 0.999994i \(-0.498916\pi\)
0.952103 + 0.305778i \(0.0989164\pi\)
\(18\) −1.84221 5.66975i −0.0241230 0.0742429i
\(19\) −20.9894 + 64.5987i −0.253436 + 0.779997i 0.740697 + 0.671839i \(0.234495\pi\)
−0.994134 + 0.108158i \(0.965505\pi\)
\(20\) −77.6345 56.4048i −0.867980 0.630624i
\(21\) 100.354 1.04281
\(22\) 0 0
\(23\) 13.3538 0.121064 0.0605319 0.998166i \(-0.480720\pi\)
0.0605319 + 0.998166i \(0.480720\pi\)
\(24\) −54.2934 39.4464i −0.461774 0.335499i
\(25\) 12.4494 38.3154i 0.0995954 0.306523i
\(26\) −16.8850 51.9667i −0.127362 0.391981i
\(27\) 90.4356 65.7053i 0.644606 0.468333i
\(28\) 102.222 74.2689i 0.689936 0.501268i
\(29\) 52.2223 + 160.724i 0.334394 + 1.02916i 0.967020 + 0.254702i \(0.0819773\pi\)
−0.632625 + 0.774458i \(0.718023\pi\)
\(30\) 17.2412 53.0628i 0.104926 0.322930i
\(31\) 52.9885 + 38.4984i 0.307001 + 0.223049i 0.730608 0.682797i \(-0.239237\pi\)
−0.423608 + 0.905846i \(0.639237\pi\)
\(32\) −128.210 −0.708268
\(33\) 0 0
\(34\) 60.6025 0.305684
\(35\) 176.071 + 127.923i 0.850327 + 0.617799i
\(36\) −18.7835 + 57.8096i −0.0869605 + 0.267637i
\(37\) 12.6253 + 38.8568i 0.0560970 + 0.172649i 0.975179 0.221417i \(-0.0710682\pi\)
−0.919082 + 0.394066i \(0.871068\pi\)
\(38\) −40.2269 + 29.2265i −0.171728 + 0.124768i
\(39\) −357.980 + 260.087i −1.46981 + 1.06788i
\(40\) −44.9747 138.418i −0.177778 0.547144i
\(41\) 84.9575 261.472i 0.323613 0.995978i −0.648450 0.761257i \(-0.724582\pi\)
0.972063 0.234721i \(-0.0754176\pi\)
\(42\) 59.4337 + 43.1811i 0.218353 + 0.158643i
\(43\) −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
\(46\) 7.90869 + 5.74600i 0.0253494 + 0.0184174i
\(47\) 22.2017 68.3297i 0.0689031 0.212062i −0.910676 0.413121i \(-0.864438\pi\)
0.979579 + 0.201060i \(0.0644385\pi\)
\(48\) 94.2074 + 289.941i 0.283285 + 0.871861i
\(49\) 45.6576 33.1722i 0.133113 0.0967120i
\(50\) 23.8597 17.3351i 0.0674856 0.0490311i
\(51\) −151.654 466.744i −0.416390 1.28152i
\(52\) −172.162 + 529.860i −0.459127 + 1.41305i
\(53\) 120.548 + 87.5830i 0.312425 + 0.226990i 0.732936 0.680297i \(-0.238149\pi\)
−0.420512 + 0.907287i \(0.638149\pi\)
\(54\) 81.8320 0.206221
\(55\) 0 0
\(56\) 191.636 0.457293
\(57\) 325.760 + 236.679i 0.756982 + 0.549980i
\(58\) −38.2294 + 117.658i −0.0865476 + 0.266366i
\(59\) 168.609 + 518.926i 0.372052 + 1.14506i 0.945446 + 0.325778i \(0.105626\pi\)
−0.573395 + 0.819279i \(0.694374\pi\)
\(60\) −460.233 + 334.379i −0.990264 + 0.719469i
\(61\) −81.9556 + 59.5442i −0.172022 + 0.124981i −0.670465 0.741941i \(-0.733905\pi\)
0.498443 + 0.866922i \(0.333905\pi\)
\(62\) 14.8166 + 45.6007i 0.0303501 + 0.0934080i
\(63\) 42.6000 131.109i 0.0851919 0.262194i
\(64\) 256.902 + 186.650i 0.501762 + 0.364552i
\(65\) −959.615 −1.83116
\(66\) 0 0
\(67\) 411.641 0.750596 0.375298 0.926904i \(-0.377540\pi\)
0.375298 + 0.926904i \(0.377540\pi\)
\(68\) −499.902 363.200i −0.891500 0.647713i
\(69\) 24.4631 75.2896i 0.0426813 0.131360i
\(70\) 49.2327 + 151.523i 0.0840634 + 0.258721i
\(71\) 380.752 276.633i 0.636437 0.462398i −0.222188 0.975004i \(-0.571320\pi\)
0.858624 + 0.512606i \(0.171320\pi\)
\(72\) −74.5830 + 54.1877i −0.122079 + 0.0886956i
\(73\) 188.686 + 580.715i 0.302520 + 0.931062i 0.980591 + 0.196065i \(0.0628164\pi\)
−0.678070 + 0.734997i \(0.737184\pi\)
\(74\) −9.24238 + 28.4451i −0.0145190 + 0.0446848i
\(75\) −193.218 140.381i −0.297479 0.216131i
\(76\) 506.985 0.765199
\(77\) 0 0
\(78\) −323.923 −0.470219
\(79\) 791.401 + 574.986i 1.12708 + 0.818874i 0.985268 0.171019i \(-0.0547061\pi\)
0.141815 + 0.989893i \(0.454706\pi\)
\(80\) −204.306 + 628.790i −0.285527 + 0.878760i
\(81\) −272.726 839.363i −0.374109 1.15139i
\(82\) 162.824 118.298i 0.219279 0.159316i
\(83\) −21.1590 + 15.3729i −0.0279819 + 0.0203300i −0.601688 0.798731i \(-0.705505\pi\)
0.573706 + 0.819061i \(0.305505\pi\)
\(84\) −231.470 712.390i −0.300659 0.925335i
\(85\) 328.891 1012.22i 0.419685 1.29166i
\(86\) −1.35457 0.984151i −0.00169845 0.00123400i
\(87\) 1001.84 1.23458
\(88\) 0 0
\(89\) −352.887 −0.420292 −0.210146 0.977670i \(-0.567394\pi\)
−0.210146 + 0.977670i \(0.567394\pi\)
\(90\) −62.0061 45.0501i −0.0726224 0.0527633i
\(91\) 390.455 1201.70i 0.449789 1.38431i
\(92\) −30.8011 94.7959i −0.0349047 0.107426i
\(93\) 314.127 228.226i 0.350252 0.254473i
\(94\) 42.5502 30.9146i 0.0466885 0.0339212i
\(95\) 269.848 + 830.507i 0.291430 + 0.896928i
\(96\) −234.870 + 722.857i −0.249702 + 0.768502i
\(97\) −685.710 498.198i −0.717766 0.521488i 0.167903 0.985803i \(-0.446300\pi\)
−0.885670 + 0.464316i \(0.846300\pi\)
\(98\) 41.3140 0.0425851
\(99\) 0 0
\(100\) −300.708 −0.300708
\(101\) −1046.43 760.277i −1.03093 0.749014i −0.0624351 0.998049i \(-0.519887\pi\)
−0.968495 + 0.249035i \(0.919887\pi\)
\(102\) 111.019 341.681i 0.107770 0.331681i
\(103\) −533.129 1640.80i −0.510007 1.56964i −0.792187 0.610279i \(-0.791057\pi\)
0.282179 0.959362i \(-0.408943\pi\)
\(104\) −683.599 + 496.663i −0.644542 + 0.468287i
\(105\) 1043.79 758.354i 0.970124 0.704836i
\(106\) 33.7074 + 103.741i 0.0308863 + 0.0950583i
\(107\) −149.620 + 460.482i −0.135180 + 0.416042i −0.995618 0.0935137i \(-0.970190\pi\)
0.860438 + 0.509555i \(0.170190\pi\)
\(108\) −675.021 490.431i −0.601425 0.436961i
\(109\) −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
\(112\) −704.284 511.693i −0.594184 0.431700i
\(113\) −619.604 + 1906.95i −0.515818 + 1.58753i 0.265970 + 0.963981i \(0.414308\pi\)
−0.781788 + 0.623544i \(0.785692\pi\)
\(114\) 91.0886 + 280.342i 0.0748353 + 0.230319i
\(115\) 138.894 100.912i 0.112625 0.0818271i
\(116\) 1020.49 741.429i 0.816811 0.593448i
\(117\) 187.835 + 578.096i 0.148422 + 0.456795i
\(118\) −123.430 + 379.880i −0.0962940 + 0.296363i
\(119\) 1133.75 + 823.719i 0.873369 + 0.634540i
\(120\) −862.797 −0.656352
\(121\) 0 0
\(122\) −74.1587 −0.0550329
\(123\) −1318.56 957.990i −0.966590 0.702269i
\(124\) 151.072 464.952i 0.109409 0.336725i
\(125\) 336.551 + 1035.80i 0.240816 + 0.741157i
\(126\) 81.6443 59.3180i 0.0577258 0.0419403i
\(127\) −88.6723 + 64.4242i −0.0619558 + 0.0450135i −0.618332 0.785917i \(-0.712191\pi\)
0.556376 + 0.830930i \(0.312191\pi\)
\(128\) 388.788 + 1196.57i 0.268471 + 0.826269i
\(129\) −4.18993 + 12.8953i −0.00285971 + 0.00880129i
\(130\) −568.324 412.912i −0.383425 0.278575i
\(131\) 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
\(134\) 243.791 + 177.124i 0.157167 + 0.114188i
\(135\) 444.103 1366.81i 0.283128 0.871379i
\(136\) −289.600 891.296i −0.182595 0.561970i
\(137\) −160.447 + 116.571i −0.100058 + 0.0726962i −0.636689 0.771121i \(-0.719697\pi\)
0.536631 + 0.843817i \(0.319697\pi\)
\(138\) 46.8843 34.0635i 0.0289207 0.0210121i
\(139\) −896.192 2758.20i −0.546863 1.68307i −0.716518 0.697569i \(-0.754265\pi\)
0.169654 0.985504i \(-0.445735\pi\)
\(140\) 501.985 1544.95i 0.303039 0.932658i
\(141\) −344.575 250.348i −0.205805 0.149526i
\(142\) 344.529 0.203607
\(143\) 0 0
\(144\) 418.789 0.242355
\(145\) 1757.72 + 1277.06i 1.00670 + 0.731408i
\(146\) −138.128 + 425.113i −0.0782981 + 0.240977i
\(147\) −103.386 318.189i −0.0580076 0.178529i
\(148\) 246.715 179.249i 0.137026 0.0995552i
\(149\) −2822.13 + 2050.40i −1.55166 + 1.12735i −0.609211 + 0.793008i \(0.708514\pi\)
−0.942452 + 0.334341i \(0.891486\pi\)
\(150\) −54.0273 166.279i −0.0294088 0.0905109i
\(151\) −359.487 + 1106.39i −0.193739 + 0.596268i 0.806250 + 0.591575i \(0.201494\pi\)
−0.999989 + 0.00469259i \(0.998506\pi\)
\(152\) 622.072 + 451.962i 0.331952 + 0.241177i
\(153\) −674.164 −0.356228
\(154\) 0 0
\(155\) 842.061 0.436361
\(156\) 2672.00 + 1941.32i 1.37135 + 0.996345i
\(157\) 105.701 325.315i 0.0537318 0.165369i −0.920590 0.390532i \(-0.872291\pi\)
0.974321 + 0.225162i \(0.0722912\pi\)
\(158\) 221.290 + 681.062i 0.111424 + 0.342926i
\(159\) 714.631 519.210i 0.356440 0.258969i
\(160\) −1333.52 + 968.860i −0.658901 + 0.478719i
\(161\) 69.8552 + 214.992i 0.0341948 + 0.105241i
\(162\) 199.649 614.457i 0.0968266 0.298002i
\(163\) 1128.49 + 819.897i 0.542272 + 0.393983i 0.824928 0.565238i \(-0.191216\pi\)
−0.282656 + 0.959221i \(0.591216\pi\)
\(164\) −2052.09 −0.977082
\(165\) 0 0
\(166\) −19.1460 −0.00895191
\(167\) −387.279 281.374i −0.179452 0.130380i 0.494433 0.869216i \(-0.335376\pi\)
−0.673885 + 0.738836i \(0.735376\pi\)
\(168\) 351.061 1080.45i 0.161220 0.496183i
\(169\) 1042.71 + 3209.13i 0.474606 + 1.46069i
\(170\) 630.330 457.962i 0.284377 0.206612i
\(171\) 447.498 325.126i 0.200123 0.145398i
\(172\) 5.27548 + 16.2362i 0.00233867 + 0.00719769i
\(173\) 558.883 1720.07i 0.245613 0.755920i −0.749922 0.661527i \(-0.769909\pi\)
0.995535 0.0943936i \(-0.0300912\pi\)
\(174\) 593.329 + 431.079i 0.258507 + 0.187816i
\(175\) 681.990 0.294592
\(176\) 0 0
\(177\) 3234.61 1.37361
\(178\) −208.995 151.843i −0.0880045 0.0639390i
\(179\) −1368.90 + 4213.03i −0.571599 + 1.75920i 0.0758796 + 0.997117i \(0.475824\pi\)
−0.647479 + 0.762084i \(0.724176\pi\)
\(180\) 241.488 + 743.224i 0.0999970 + 0.307759i
\(181\) −2758.08 + 2003.86i −1.13263 + 0.822905i −0.986076 0.166297i \(-0.946819\pi\)
−0.146557 + 0.989202i \(0.546819\pi\)
\(182\) 748.320 543.686i 0.304776 0.221432i
\(183\) 185.578 + 571.150i 0.0749635 + 0.230714i
\(184\) 46.7148 143.773i 0.0187166 0.0576038i
\(185\) 424.950 + 308.744i 0.168881 + 0.122699i
\(186\) 284.242 0.112052
\(187\) 0 0
\(188\) −536.267 −0.208039
\(189\) 1530.91 + 1112.27i 0.589193 + 0.428074i
\(190\) −197.542 + 607.973i −0.0754275 + 0.232142i
\(191\) 903.490 + 2780.65i 0.342273 + 1.05341i 0.963027 + 0.269404i \(0.0868266\pi\)
−0.620754 + 0.784005i \(0.713173\pi\)
\(192\) 1522.97 1106.50i 0.572452 0.415911i
\(193\) 2009.75 1460.17i 0.749558 0.544586i −0.146132 0.989265i \(-0.546682\pi\)
0.895690 + 0.444679i \(0.146682\pi\)
\(194\) −191.737 590.107i −0.0709584 0.218388i
\(195\) −1757.93 + 5410.36i −0.645581 + 1.98689i
\(196\) −340.793 247.601i −0.124196 0.0902335i
\(197\) −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 \(0.500436\pi\)
\(200\) −368.970 268.072i −0.130450 0.0947778i
\(201\) 754.092 2320.86i 0.264624 0.814430i
\(202\) −292.602 900.536i −0.101918 0.313671i
\(203\) −2314.42 + 1681.52i −0.800199 + 0.581378i
\(204\) −2963.52 + 2153.12i −1.01710 + 0.738965i
\(205\) −1092.25 3361.59i −0.372126 1.14529i
\(206\) 390.277 1201.15i 0.132000 0.406253i
\(207\) −87.9791 63.9206i −0.0295409 0.0214627i
\(208\) 3838.46 1.27956
\(209\) 0 0
\(210\) 944.484 0.310360
\(211\) −2513.89 1826.45i −0.820206 0.595915i 0.0965652 0.995327i \(-0.469214\pi\)
−0.916772 + 0.399412i \(0.869214\pi\)
\(212\) 343.685 1057.76i 0.111342 0.342674i
\(213\) −862.165 2653.47i −0.277345 0.853582i
\(214\) −286.751 + 208.337i −0.0915977 + 0.0665496i
\(215\) −23.7892 + 17.2838i −0.00754608 + 0.00548255i
\(216\) −391.048 1203.52i −0.123183 0.379117i
\(217\) −342.624 + 1054.49i −0.107183 + 0.329877i
\(218\) −38.0552 27.6487i −0.0118231 0.00858995i
\(219\) 3619.76 1.11690
\(220\) 0 0
\(221\) −6179.13 −1.88078
\(222\) 143.444 + 104.218i 0.0433663 + 0.0315075i
\(223\) −3.80662 + 11.7156i −0.00114310 + 0.00351809i −0.951626 0.307257i \(-0.900589\pi\)
0.950483 + 0.310776i \(0.100589\pi\)
\(224\) −670.681 2064.14i −0.200052 0.615698i
\(225\) −265.424 + 192.842i −0.0786442 + 0.0571384i
\(226\) −1187.49 + 862.764i −0.349517 + 0.253939i
\(227\) 1426.39 + 4389.98i 0.417062 + 1.28358i 0.910394 + 0.413743i \(0.135779\pi\)
−0.493332 + 0.869841i \(0.664221\pi\)
\(228\) 928.753 2858.41i 0.269773 0.830275i
\(229\) −4105.46 2982.79i −1.18470 0.860736i −0.192007 0.981394i \(-0.561500\pi\)
−0.992694 + 0.120658i \(0.961500\pi\)
\(230\) 125.680 0.0360309
\(231\) 0 0
\(232\) 1913.11 0.541386
\(233\) −171.255 124.424i −0.0481514 0.0349840i 0.563449 0.826151i \(-0.309474\pi\)
−0.611601 + 0.791167i \(0.709474\pi\)
\(234\) −137.505 + 423.196i −0.0384143 + 0.118227i
\(235\) −285.434 878.474i −0.0792325 0.243853i
\(236\) 3294.84 2393.84i 0.908795 0.660278i
\(237\) 4691.59 3408.64i 1.28587 0.934239i
\(238\) 317.018 + 975.681i 0.0863413 + 0.265731i
\(239\) 1332.63 4101.42i 0.360673 1.11004i −0.591973 0.805958i \(-0.701651\pi\)
0.952646 0.304080i \(-0.0983490\pi\)
\(240\) 3170.88 + 2303.78i 0.852831 + 0.619618i
\(241\) −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
\(244\) 611.725 + 444.444i 0.160499 + 0.116609i
\(245\) 224.211 690.052i 0.0584667 0.179942i
\(246\) −368.694 1134.72i −0.0955572 0.294095i
\(247\) 4101.59 2979.98i 1.05659 0.767658i
\(248\) 599.857 435.822i 0.153593 0.111592i
\(249\) 47.9117 + 147.457i 0.0121939 + 0.0375290i
\(250\) −246.373 + 758.257i −0.0623279 + 0.191825i
\(251\) 224.010 + 162.753i 0.0563323 + 0.0409278i 0.615595 0.788063i \(-0.288916\pi\)
−0.559263 + 0.828990i \(0.688916\pi\)
\(252\) −1028.97 −0.257219
\(253\) 0 0
\(254\) −80.2364 −0.0198208
\(255\) −5104.46 3708.61i −1.25354 0.910753i
\(256\) 500.411 1540.11i 0.122171 0.376003i
\(257\) −999.725 3076.84i −0.242650 0.746801i −0.996014 0.0891969i \(-0.971570\pi\)
0.753364 0.657604i \(-0.228430\pi\)
\(258\) −8.03015 + 5.83425i −0.00193773 + 0.00140785i
\(259\) −559.537 + 406.527i −0.134239 + 0.0975304i
\(260\) 2213.39 + 6812.10i 0.527955 + 1.62488i
\(261\) 425.277 1308.87i 0.100858 0.310410i
\(262\) 685.053 + 497.720i 0.161537 + 0.117364i
\(263\) 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
\(266\) −680.968 494.752i −0.156966 0.114042i
\(267\) −646.460 + 1989.60i −0.148175 + 0.456035i
\(268\) −949.464 2922.15i −0.216410 0.666040i
\(269\) −4071.81 + 2958.34i −0.922910 + 0.670533i −0.944247 0.329239i \(-0.893208\pi\)
0.0213369 + 0.999772i \(0.493208\pi\)
\(270\) 851.139 618.389i 0.191847 0.139385i
\(271\) 459.512 + 1414.23i 0.103001 + 0.317005i 0.989256 0.146193i \(-0.0467019\pi\)
−0.886255 + 0.463198i \(0.846702\pi\)
\(272\) −1315.56 + 4048.89i −0.293264 + 0.902573i
\(273\) −6059.95 4402.81i −1.34346 0.976082i
\(274\) −145.183 −0.0320102
\(275\) 0 0
\(276\) −590.890 −0.128867
\(277\) 190.795 + 138.621i 0.0413855 + 0.0300683i 0.608286 0.793718i \(-0.291858\pi\)
−0.566900 + 0.823786i \(0.691858\pi\)
\(278\) 656.058 2019.14i 0.141539 0.435611i
\(279\) −164.825 507.279i −0.0353685 0.108853i
\(280\) 1993.21 1448.16i 0.425419 0.309085i
\(281\) 3976.33 2888.97i 0.844156 0.613316i −0.0793722 0.996845i \(-0.525292\pi\)
0.923529 + 0.383530i \(0.125292\pi\)
\(282\) −96.3496 296.534i −0.0203459 0.0626181i
\(283\) −1606.75 + 4945.07i −0.337496 + 1.03871i 0.627983 + 0.778227i \(0.283881\pi\)
−0.965479 + 0.260480i \(0.916119\pi\)
\(284\) −2841.97 2064.82i −0.593803 0.431423i
\(285\) 5176.78 1.07595
\(286\) 0 0
\(287\) 4654.04 0.957210
\(288\) 844.688 + 613.702i 0.172825 + 0.125565i
\(289\) 599.583 1845.33i 0.122040 0.375601i
\(290\) 491.492 + 1512.66i 0.0995221 + 0.306298i
\(291\) −4065.03 + 2953.42i −0.818888 + 0.594957i
\(292\) 3687.16 2678.88i 0.738954 0.536882i
\(293\) −2744.35 8446.25i −0.547191 1.68408i −0.715723 0.698384i \(-0.753903\pi\)
0.168533 0.985696i \(-0.446097\pi\)
\(294\) 75.6837 232.931i 0.0150135 0.0462067i
\(295\) 5675.13 + 4123.23i 1.12006 + 0.813774i
\(296\) 462.515 0.0908215
\(297\) 0 0
\(298\) −2553.64 −0.496405
\(299\) −806.382 585.871i −0.155968 0.113317i
\(300\) −550.871 + 1695.41i −0.106015 + 0.326281i
\(301\) −11.9645 36.8230i −0.00229111 0.00705130i
\(302\) −688.968 + 500.565i −0.131277 + 0.0953784i
\(303\) −6203.46 + 4507.08i −1.17617 + 0.854538i
\(304\) −1079.39 3322.03i −0.203643 0.626748i
\(305\) −402.460 + 1238.64i −0.0755567 + 0.232540i
\(306\) −399.268 290.085i −0.0745903 0.0541930i
\(307\) −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
\(310\) 498.704 + 362.330i 0.0913693 + 0.0663837i
\(311\) −2312.90 + 7118.38i −0.421713 + 1.29790i 0.484395 + 0.874850i \(0.339040\pi\)
−0.906107 + 0.423048i \(0.860960\pi\)
\(312\) 1547.92 + 4764.01i 0.280878 + 0.864452i
\(313\) 532.627 386.976i 0.0961848 0.0698824i −0.538653 0.842527i \(-0.681067\pi\)
0.634838 + 0.772645i \(0.281067\pi\)
\(314\) 202.580 147.183i 0.0364085 0.0264523i
\(315\) −547.683 1685.59i −0.0979632 0.301500i
\(316\) 2256.31 6944.21i 0.401669 1.23621i
\(317\) −189.073 137.370i −0.0334998 0.0243390i 0.570909 0.821013i \(-0.306591\pi\)
−0.604409 + 0.796674i \(0.706591\pi\)
\(318\) 646.645 0.114032
\(319\) 0 0
\(320\) 4082.53 0.713189
\(321\) 2322.13 + 1687.13i 0.403766 + 0.293353i
\(322\) −51.1376 + 157.385i −0.00885027 + 0.0272383i
\(323\) 1737.60 + 5347.77i 0.299327 + 0.921233i
\(324\) −5329.41 + 3872.04i −0.913822 + 0.663930i
\(325\) −2432.78 + 1767.52i −0.415219 + 0.301674i
\(326\) 315.547 + 971.154i 0.0536090 + 0.164992i
\(327\) −117.712 + 362.280i −0.0199067 + 0.0612665i
\(328\) −2517.93 1829.38i −0.423869 0.307959i
\(329\) 1216.23 0.203808
\(330\) 0 0
\(331\) 8532.95 1.41696 0.708480 0.705731i \(-0.249381\pi\)
0.708480 + 0.705731i \(0.249381\pi\)
\(332\) 157.933 + 114.745i 0.0261075 + 0.0189682i
\(333\) 102.816 316.434i 0.0169197 0.0520734i
\(334\) −108.290 333.283i −0.0177407 0.0546002i
\(335\) 4281.50 3110.69i 0.698278 0.507329i
\(336\) −4175.14 + 3033.42i −0.677895 + 0.492519i
\(337\) 3612.77 + 11119.0i 0.583977 + 1.79730i 0.603339 + 0.797485i \(0.293837\pi\)
−0.0193617 + 0.999813i \(0.506163\pi\)
\(338\) −763.317 + 2349.25i −0.122837 + 0.378054i
\(339\) 9616.41 + 6986.73i 1.54068 + 1.11937i
\(340\) −7944.14 −1.26715
\(341\) 0 0
\(342\) 404.925 0.0640229
\(343\) 5470.36 + 3974.45i 0.861141 + 0.625656i
\(344\) −8.00111 + 24.6249i −0.00125404 + 0.00385955i
\(345\) −314.507 967.954i −0.0490797 0.151052i
\(346\) 1071.12 778.213i 0.166427 0.120916i
\(347\) −3720.50 + 2703.10i −0.575582 + 0.418185i −0.837129 0.547006i \(-0.815768\pi\)
0.261547 + 0.965191i \(0.415768\pi\)
\(348\) −2310.77 7111.81i −0.355949 1.09550i
\(349\) 2076.68 6391.36i 0.318516 0.980291i −0.655767 0.754963i \(-0.727655\pi\)
0.974283 0.225328i \(-0.0723453\pi\)
\(350\) 403.903 + 293.452i 0.0616843 + 0.0448163i
\(351\) −8343.72 −1.26882
\(352\) 0 0
\(353\) 5738.70 0.865270 0.432635 0.901569i \(-0.357584\pi\)
0.432635 + 0.901569i \(0.357584\pi\)
\(354\) 1915.67 + 1391.82i 0.287618 + 0.208967i
\(355\) 1869.76 5754.54i 0.279540 0.860337i
\(356\) 813.947 + 2505.07i 0.121177 + 0.372945i
\(357\) 6721.11 4883.17i 0.996412 0.723936i
\(358\) −2623.54 + 1906.11i −0.387314 + 0.281400i
\(359\) −1271.69 3913.85i −0.186956 0.575391i 0.813021 0.582235i \(-0.197821\pi\)
−0.999977 + 0.00684400i \(0.997821\pi\)
\(360\) −366.255 + 1127.22i −0.0536204 + 0.165027i
\(361\) 1816.61 + 1319.85i 0.264851 + 0.192426i
\(362\) −2495.69 −0.362349
\(363\) 0 0
\(364\) −9431.18 −1.35804
\(365\) 6350.88 + 4614.18i 0.910740 + 0.661692i
\(366\) −135.852 + 418.111i −0.0194020 + 0.0597131i
\(367\) 2986.03 + 9190.05i 0.424712 + 1.30713i 0.903269 + 0.429074i \(0.141160\pi\)
−0.478557 + 0.878057i \(0.658840\pi\)
\(368\) −555.575 + 403.649i −0.0786994 + 0.0571784i
\(369\) −1811.31 + 1315.99i −0.255537 + 0.185658i
\(370\) 118.824 + 365.702i 0.0166956 + 0.0513836i
\(371\) −779.461 + 2398.94i −0.109077 + 0.335705i
\(372\) −2344.67 1703.51i −0.326789 0.237426i
\(373\) −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
\(376\) −658.001 478.066i −0.0902495 0.0655701i
\(377\) 3897.92 11996.6i 0.532502 1.63887i
\(378\) 428.072 + 1317.47i 0.0582477 + 0.179268i
\(379\) 2281.21 1657.40i 0.309177 0.224630i −0.422366 0.906425i \(-0.638800\pi\)
0.731543 + 0.681795i \(0.238800\pi\)
\(380\) 5273.17 3831.18i 0.711863 0.517199i
\(381\) 200.787 + 617.959i 0.0269990 + 0.0830945i
\(382\) −661.400 + 2035.58i −0.0885869 + 0.272642i
\(383\) 5127.42 + 3725.29i 0.684070 + 0.497006i 0.874705 0.484655i \(-0.161055\pi\)
−0.190636 + 0.981661i \(0.561055\pi\)
\(384\) 7458.53 0.991189
\(385\) 0 0
\(386\) 1818.55 0.239797
\(387\) 15.0687 + 10.9480i 0.00197929 + 0.00143804i
\(388\) −1954.98 + 6016.82i −0.255797 + 0.787262i
\(389\) −2720.97 8374.29i −0.354650 1.09150i −0.956212 0.292674i \(-0.905455\pi\)
0.601562 0.798826i \(-0.294545\pi\)
\(390\) −3369.14 + 2447.82i −0.437444 + 0.317821i
\(391\) 894.361 649.792i 0.115677 0.0840444i
\(392\) −197.426 607.614i −0.0254375 0.0782887i
\(393\) 2119.00 6521.61i 0.271983 0.837078i
\(394\) −3035.64 2205.52i −0.388155 0.282011i
\(395\) 12576.5 1.60200
\(396\) 0 0
\(397\) 4315.26 0.545534 0.272767 0.962080i \(-0.412061\pi\)
0.272767 + 0.962080i \(0.412061\pi\)
\(398\) −4.55564 3.30986i −0.000573752 0.000416855i
\(399\) −2106.36 + 6482.72i −0.264286 + 0.813389i
\(400\) 640.219 + 1970.39i 0.0800274 + 0.246299i
\(401\) −292.606 + 212.591i −0.0364390 + 0.0264745i −0.605856 0.795575i \(-0.707169\pi\)
0.569417 + 0.822049i \(0.307169\pi\)
\(402\) 1445.24 1050.03i 0.179309 0.130275i
\(403\) −1510.72 4649.52i −0.186735 0.574712i
\(404\) −2983.41 + 9182.00i −0.367402 + 1.13075i
\(405\) −9179.54 6669.33i −1.12626 0.818275i
\(406\) −2094.24 −0.255998
\(407\) 0 0
\(408\) −5555.70 −0.674137
\(409\) −7459.54 5419.67i −0.901835 0.655222i 0.0371015 0.999312i \(-0.488188\pi\)
−0.938937 + 0.344090i \(0.888188\pi\)
\(410\) 799.581 2460.86i 0.0963134 0.296422i
\(411\) 363.311 + 1118.16i 0.0436030 + 0.134196i
\(412\) −10418.0 + 7569.13i −1.24577 + 0.905107i
\(413\) −7472.52 + 5429.11i −0.890312 + 0.646850i
\(414\) −24.6006 75.7128i −0.00292042 0.00898812i
\(415\) −103.905 + 319.788i −0.0122904 + 0.0378260i
\(416\) 7742.08 + 5624.95i 0.912469 + 0.662947i
\(417\) −17192.6 −2.01901
\(418\) 0 0
\(419\) −14912.9 −1.73876 −0.869380 0.494144i \(-0.835481\pi\)
−0.869380 + 0.494144i \(0.835481\pi\)
\(420\) −7790.92 5660.43i −0.905138 0.657621i
\(421\) −4167.41 + 12826.0i −0.482439 + 1.48480i 0.353217 + 0.935542i \(0.385088\pi\)
−0.835656 + 0.549254i \(0.814912\pi\)
\(422\) −702.931 2163.40i −0.0810857 0.249556i
\(423\) −473.344 + 343.905i −0.0544085 + 0.0395301i
\(424\) 1364.66 991.484i 0.156306 0.113563i
\(425\) −1030.62 3171.92i −0.117629 0.362026i
\(426\) 631.149 1942.48i 0.0717823 0.220923i
\(427\) −1387.36 1007.98i −0.157234 0.114237i
\(428\) 3613.96 0.408148
\(429\) 0 0
\(430\) −21.5260 −0.00241413
\(431\) −328.731 238.837i −0.0367388 0.0266923i 0.569264 0.822155i \(-0.307228\pi\)
−0.606003 + 0.795462i \(0.707228\pi\)
\(432\) −1776.41 + 5467.24i −0.197842 + 0.608895i
\(433\) −545.938 1680.23i −0.0605915 0.186481i 0.916179 0.400769i \(-0.131257\pi\)
−0.976771 + 0.214288i \(0.931257\pi\)
\(434\) −656.650 + 477.084i −0.0726272 + 0.0527668i
\(435\) 10420.1 7570.68i 1.14852 0.834451i
\(436\) 148.209 + 456.141i 0.0162797 + 0.0501037i
\(437\) −280.289 + 862.639i −0.0306820 + 0.0944294i
\(438\) 2143.77 + 1557.54i 0.233866 + 0.169914i
\(439\) 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
\(442\) −3659.54 2658.81i −0.393815 0.286124i
\(443\) 3605.58 11096.8i 0.386695 1.19013i −0.548548 0.836119i \(-0.684819\pi\)
0.935243 0.354007i \(-0.115181\pi\)
\(444\) −558.654 1719.36i −0.0597130 0.183778i
\(445\) −3670.40 + 2666.70i −0.390997 + 0.284076i
\(446\) −7.29552 + 5.30050i −0.000774558 + 0.000562749i
\(447\) 6390.35 + 19667.5i 0.676182 + 2.08107i
\(448\) −1661.13 + 5112.43i −0.175181 + 0.539151i
\(449\) −13733.3 9977.80i −1.44346 1.04873i −0.987305 0.158833i \(-0.949227\pi\)
−0.456153 0.889901i \(-0.650773\pi\)
\(450\) −240.173 −0.0251597
\(451\) 0 0
\(452\) 14966.1 1.55741
\(453\) 5579.32 + 4053.61i 0.578674 + 0.420431i
\(454\) −1044.19 + 3213.69i −0.107943 + 0.332216i
\(455\) −5019.85 15449.5i −0.517218 1.59183i
\(456\) 3687.77 2679.32i 0.378719 0.275155i
\(457\) 13100.3 9517.92i 1.34093 0.974244i 0.341523 0.939874i \(-0.389057\pi\)
0.999409 0.0343703i \(-0.0109426\pi\)
\(458\) −1147.96 3533.07i −0.117120 0.360457i
\(459\) 2859.66 8801.12i 0.290800 0.894992i
\(460\) −1036.72 753.220i −0.105081 0.0763458i
\(461\) 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 \(0.630069\pi\)
\(464\) −7030.90 5108.25i −0.703451 0.511087i
\(465\) 1542.59 4747.59i 0.153840 0.473471i
\(466\) −47.8860 147.378i −0.00476025 0.0146505i
\(467\) 12260.6 8907.86i 1.21489 0.882670i 0.219225 0.975674i \(-0.429647\pi\)
0.995666 + 0.0930047i \(0.0296472\pi\)
\(468\) 3670.53 2666.80i 0.362543 0.263403i
\(469\) 2153.34 + 6627.29i 0.212008 + 0.652494i
\(470\) 208.952 643.088i 0.0205069 0.0631137i
\(471\) −1640.51 1191.90i −0.160490 0.116603i
\(472\) 6176.82 0.602354
\(473\) 0 0
\(474\) 4245.25 0.411373
\(475\) 2213.82 + 1608.43i 0.213846 + 0.155368i
\(476\) 3232.36 9948.20i 0.311250 0.957930i
\(477\) −374.973 1154.05i −0.0359933 0.110776i
\(478\) 2554.04 1855.62i 0.244391 0.177560i
\(479\) −8091.07 + 5878.51i −0.771796 + 0.560743i −0.902506 0.430678i \(-0.858275\pi\)
0.130709 + 0.991421i \(0.458275\pi\)
\(480\) 3019.59 + 9293.34i 0.287135 + 0.883710i
\(481\) 942.367 2900.31i 0.0893311 0.274933i
\(482\) −590.218 428.819i −0.0557753 0.0405232i
\(483\) 1340.11 0.126246
\(484\) 0 0
\(485\) −10896.9 −1.02021
\(486\) −1311.11 952.575i −0.122372 0.0889088i
\(487\) 2176.88 6699.76i 0.202554 0.623398i −0.797251 0.603648i \(-0.793713\pi\)
0.999805 0.0197497i \(-0.00628694\pi\)
\(488\) 354.380 + 1090.67i 0.0328730 + 0.101173i
\(489\) 6689.93 4860.52i 0.618669 0.449489i
\(490\) 429.709 312.202i 0.0396169 0.0287833i
\(491\) −4118.09 12674.2i −0.378507 1.16492i −0.941082 0.338178i \(-0.890189\pi\)
0.562575 0.826746i \(-0.309811\pi\)
\(492\) −3759.26 + 11569.8i −0.344473 + 1.06018i
\(493\) 11318.3 + 8223.22i 1.03398 + 0.751227i
\(494\) 3711.38 0.338022
\(495\) 0 0
\(496\) −3368.25 −0.304917
\(497\) 6445.45 + 4682.90i 0.581727 + 0.422649i
\(498\) −35.0738 + 107.946i −0.00315602 + 0.00971322i
\(499\) −6201.70 19086.9i −0.556365 1.71232i −0.692311 0.721600i \(-0.743407\pi\)
0.135945 0.990716i \(-0.456593\pi\)
\(500\) 6576.64 4778.21i 0.588232 0.427376i
\(501\) −2295.87 + 1668.05i −0.204734 + 0.148748i
\(502\) 62.6375 + 192.778i 0.00556902 + 0.0171397i
\(503\) 2404.88 7401.45i 0.213177 0.656092i −0.786101 0.618099i \(-0.787903\pi\)
0.999278 0.0379939i \(-0.0120967\pi\)
\(504\) −1262.56 917.300i −0.111585 0.0810710i
\(505\) −16629.3 −1.46533
\(506\) 0 0
\(507\) 20003.4 1.75224
\(508\) 661.859 + 480.868i 0.0578056 + 0.0419982i
\(509\) −456.088 + 1403.69i −0.0397166 + 0.122235i −0.968949 0.247261i \(-0.920470\pi\)
0.929232 + 0.369496i \(0.120470\pi\)
\(510\) −1427.30 4392.78i −0.123925 0.381403i
\(511\) −8362.29 + 6075.56i −0.723925 + 0.525963i
\(512\) 9101.93 6612.94i 0.785649 0.570807i
\(513\) 2346.29 + 7221.14i 0.201932 + 0.621483i
\(514\) 731.850 2252.40i 0.0628025 0.193286i
\(515\) −17944.3 13037.3i −1.53538 1.11552i
\(516\) 101.205 0.00863431
\(517\) 0 0
\(518\) −506.305 −0.0429455
\(519\) −8674.00 6302.03i −0.733616 0.533003i
\(520\) −3356.95 + 10331.6i −0.283100 + 0.871293i
\(521\) 2351.44 + 7237.00i 0.197732 + 0.608558i 0.999934 + 0.0115042i \(0.00366198\pi\)
−0.802201 + 0.597053i \(0.796338\pi\)
\(522\) 815.058 592.174i 0.0683412 0.0496528i
\(523\) −10074.6 + 7319.63i −0.842318 + 0.611980i −0.923017 0.384759i \(-0.874285\pi\)
0.0806995 + 0.996738i \(0.474285\pi\)
\(524\) −2668.00 8211.25i −0.222427 0.684561i
\(525\) 1249.35 3845.10i 0.103859 0.319645i
\(526\) 123.153 + 89.4761i 0.0102086 + 0.00741700i
\(527\) 5422.18 0.448186
\(528\) 0 0
\(529\) −11988.7 −0.985344
\(530\) 1134.54 + 824.291i 0.0929835 + 0.0675565i
\(531\) 1373.08 4225.92i 0.112216 0.345366i
\(532\) 2652.09 + 8162.29i 0.216133 + 0.665188i
\(533\) −16601.8 + 12061.9i −1.34916 + 0.980223i
\(534\) −1238.96 + 900.159i −0.100403 + 0.0729470i
\(535\) 1923.57 + 5920.14i 0.155445 + 0.478411i
\(536\) 1440.01 4431.91i 0.116043 0.357144i
\(537\) 21245.6 + 15435.8i 1.70729 + 1.24042i
\(538\) −3684.44 −0.295255
\(539\) 0 0
\(540\) −10727.0 −0.854847
\(541\) −7533.70 5473.55i −0.598704 0.434984i 0.246714 0.969088i \(-0.420649\pi\)
−0.845419 + 0.534104i \(0.820649\pi\)
\(542\) −336.386 + 1035.29i −0.0266587 + 0.0820470i
\(543\) 6245.32 + 19221.1i 0.493577 + 1.51907i
\(544\) −8586.77 + 6238.66i −0.676755 + 0.491691i
\(545\) −668.333 + 485.572i −0.0525289 + 0.0381644i
\(546\) −1694.47 5215.06i −0.132815 0.408762i
\(547\) −3404.92 + 10479.3i −0.266150 + 0.819124i 0.725277 + 0.688458i \(0.241712\pi\)
−0.991426 + 0.130667i \(0.958288\pi\)
\(548\) 1197.59 + 870.101i 0.0933551 + 0.0678264i
\(549\) 824.968 0.0641325
\(550\) 0 0
\(551\) −11478.6 −0.887490
\(552\) −725.024 526.761i −0.0559041 0.0406167i
\(553\) −5117.20 + 15749.1i −0.393500 + 1.21107i
\(554\) 53.3499 + 164.194i 0.00409137 + 0.0125919i
\(555\) 2519.19 1830.30i 0.192673 0.139985i
\(556\) −17512.7 + 12723.7i −1.33580 + 0.970516i
\(557\) −3713.90 11430.2i −0.282519 0.869503i −0.987131 0.159911i \(-0.948879\pi\)
0.704613 0.709592i \(-0.251121\pi\)
\(558\) 120.660 371.354i 0.00915404 0.0281732i
\(559\) 138.114 + 100.346i 0.0104501 + 0.00759242i
\(560\) −11192.1 −0.844555
\(561\) 0 0
\(562\) 3598.04 0.270061
\(563\) 7090.13 + 5151.28i 0.530752 + 0.385614i 0.820639 0.571447i \(-0.193618\pi\)
−0.289887 + 0.957061i \(0.593618\pi\)
\(564\) −982.395 + 3023.50i −0.0733445 + 0.225731i
\(565\) 7965.89 + 24516.5i 0.593146 + 1.82551i
\(566\) −3079.39 + 2237.31i −0.228687 + 0.166151i
\(567\) 12086.8 8781.59i 0.895236 0.650427i
\(568\) −1646.39 5067.07i −0.121622 0.374313i
\(569\) −3174.58 + 9770.35i −0.233893 + 0.719850i 0.763373 + 0.645958i \(0.223542\pi\)
−0.997266 + 0.0738917i \(0.976458\pi\)
\(570\) 3065.91 + 2227.51i 0.225292 + 0.163684i
\(571\) 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
\(574\) 2756.32 + 2002.58i 0.200429 + 0.145620i
\(575\) 166.247 511.657i 0.0120574 0.0371088i
\(576\) −799.114 2459.42i −0.0578063 0.177909i
\(577\) 15959.5 11595.3i 1.15148 0.836598i 0.162801 0.986659i \(-0.447947\pi\)
0.988677 + 0.150061i \(0.0479471\pi\)
\(578\) 1149.12 834.885i 0.0826940 0.0600807i
\(579\) −4550.82 14006.0i −0.326642 1.00530i
\(580\) 5011.33 15423.3i 0.358766 1.10417i
\(581\) −358.183 260.235i −0.0255765 0.0185824i
\(582\) −3678.30 −0.261977
\(583\) 0 0
\(584\) 6912.30 0.489783
\(585\) 6322.24 + 4593.38i 0.446825 + 0.324637i
\(586\) 2009.01 6183.09i 0.141623 0.435872i
\(587\) −3126.06 9621.03i −0.219806 0.676495i −0.998777 0.0494347i \(-0.984258\pi\)
0.778971 0.627060i \(-0.215742\pi\)
\(588\) −2020.29 + 1467.83i −0.141693 + 0.102946i
\(589\) −3599.14 + 2614.93i −0.251783 + 0.182931i
\(590\) 1586.87 + 4883.89i 0.110730 + 0.340791i
\(591\) −9389.80 + 28898.8i −0.653544 + 2.01140i
\(592\) −1699.80 1234.98i −0.118009 0.0857385i
\(593\) 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
\(596\) 21064.7 + 15304.4i 1.44772 + 1.05183i
\(597\) −14.0914 + 43.3690i −0.000966038 + 0.00297316i
\(598\) −225.479 693.954i −0.0154190 0.0474547i
\(599\) −8154.96 + 5924.92i −0.556265 + 0.404150i −0.830090 0.557629i \(-0.811711\pi\)
0.273825 + 0.961779i \(0.411711\pi\)
\(600\) −2187.33 + 1589.19i −0.148829 + 0.108130i
\(601\) 1476.18 + 4543.21i 0.100191 + 0.308355i 0.988572 0.150752i \(-0.0481694\pi\)
−0.888381 + 0.459107i \(0.848169\pi\)
\(602\) 8.75863 26.9563i 0.000592982 0.00182501i
\(603\) −2712.02 1970.40i −0.183154 0.133069i
\(604\) 8683.16 0.584955
\(605\) 0 0
\(606\) −5613.29 −0.376278
\(607\) 2080.27 + 1511.40i 0.139103 + 0.101064i 0.655160 0.755490i \(-0.272601\pi\)
−0.516058 + 0.856554i \(0.672601\pi\)
\(608\) 2691.05 8282.21i 0.179501 0.552447i
\(609\) 5240.71 + 16129.2i 0.348710 + 1.07322i
\(610\) −771.328 + 560.403i −0.0511970 + 0.0371968i
\(611\) −4338.49 + 3152.10i −0.287261 + 0.208707i
\(612\) 1554.98 + 4785.75i 0.102707 + 0.316098i
\(613\) 3928.18 12089.7i 0.258822 0.796571i −0.734231 0.678900i \(-0.762457\pi\)
0.993053 0.117671i \(-0.0375429\pi\)
\(614\) −887.138 644.544i −0.0583094 0.0423643i
\(615\) −20953.8 −1.37388
\(616\) 0 0
\(617\) 16236.1 1.05939 0.529693 0.848189i \(-0.322307\pi\)
0.529693 + 0.848189i \(0.322307\pi\)
\(618\) −6057.20 4400.81i −0.394266 0.286451i
\(619\) 3911.32 12037.8i 0.253973 0.781649i −0.740057 0.672544i \(-0.765202\pi\)
0.994030 0.109105i \(-0.0347984\pi\)
\(620\) −1942.24 5977.61i −0.125810 0.387204i
\(621\) 1207.66 877.418i 0.0780383 0.0566982i
\(622\) −4432.75 + 3220.58i −0.285751 + 0.207610i
\(623\) −1845.99 5681.37i −0.118713 0.365360i
\(624\) 7031.74 21641.5i 0.451113 1.38838i
\(625\) 15401.9 + 11190.2i 0.985724 + 0.716170i
\(626\) 481.955 0.0307713
\(627\) 0 0
\(628\) −2553.15 −0.162232
\(629\) 2736.32 + 1988.06i 0.173457 + 0.126024i
\(630\) 400.931 1233.94i 0.0253547 0.0780339i
\(631\) −1220.61 3756.64i −0.0770073 0.237004i 0.905141 0.425111i \(-0.139765\pi\)
−0.982149 + 0.188107i \(0.939765\pi\)
\(632\) 8959.06 6509.14i 0.563880 0.409683i
\(633\) −14902.9 + 10827.6i −0.935760 + 0.679869i
\(634\) −52.8684 162.712i −0.00331179 0.0101926i
\(635\) −435.444 + 1340.16i −0.0272127 + 0.0837520i
\(636\) −5334.08 3875.44i −0.332563 0.241621i
\(637\) −4212.44 −0.262014
\(638\) 0 0
\(639\) −3832.67 −0.237274
\(640\) 13086.0 + 9507.55i 0.808235 + 0.587217i
\(641\) −2286.19 + 7036.17i −0.140872 + 0.433560i −0.996457 0.0841024i \(-0.973198\pi\)
0.855585 + 0.517663i \(0.173198\pi\)
\(642\) 649.311 + 1998.37i 0.0399163 + 0.122850i
\(643\) 10106.0 7342.43i 0.619815 0.450322i −0.233042 0.972467i \(-0.574868\pi\)
0.852857 + 0.522145i \(0.174868\pi\)
\(644\) 1365.06 991.774i 0.0835263 0.0606854i
\(645\) 53.8675 + 165.787i 0.00328842 + 0.0101207i
\(646\) −1272.01 + 3914.84i −0.0774714 + 0.238433i
\(647\) 8472.01 + 6155.27i 0.514790 + 0.374017i 0.814638 0.579970i \(-0.196936\pi\)
−0.299848 + 0.953987i \(0.596936\pi\)
\(648\) −9991.02 −0.605685
\(649\) 0 0
\(650\) −2201.33 −0.132836
\(651\) 5317.60 + 3863.46i 0.320143 + 0.232598i
\(652\) 3217.37 9902.04i 0.193254 0.594776i
\(653\) 1958.53 + 6027.73i 0.117371 + 0.361230i 0.992434 0.122778i \(-0.0391804\pi\)
−0.875063 + 0.484009i \(0.839180\pi\)
\(654\) −225.599 + 163.907i −0.0134887 + 0.00980013i
\(655\) 12031.0 8741.05i 0.717696 0.521437i
\(656\) 4368.99 + 13446.4i 0.260031 + 0.800294i
\(657\) 1536.58 4729.11i 0.0912446 0.280822i
\(658\) 720.299 + 523.328i 0.0426751 + 0.0310052i
\(659\) 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 \(0.478461\pi\)
\(662\) 5053.57 + 3671.63i 0.296696 + 0.215562i
\(663\) −11319.6 + 34838.3i −0.663074 + 2.04073i
\(664\) 91.4924 + 281.585i 0.00534728 + 0.0164572i
\(665\) −11959.3 + 8688.93i −0.697385 + 0.506680i
\(666\) 197.049 143.165i 0.0114647 0.00832961i
\(667\) 697.367 + 2146.28i 0.0404830 + 0.124594i
\(668\) −1104.14 + 3398.21i −0.0639530 + 0.196827i
\(669\) 59.0797 + 42.9239i 0.00341428 + 0.00248062i
\(670\) 3874.18 0.223392
\(671\) 0 0
\(672\) −12866.4 −0.738589
\(673\) −18768.9 13636.4i −1.07502 0.781047i −0.0982115 0.995166i \(-0.531312\pi\)
−0.976808 + 0.214118i \(0.931312\pi\)
\(674\) −2644.73 + 8139.66i −0.151144 + 0.465175i
\(675\) −1391.65 4283.07i −0.0793553 0.244230i
\(676\) 20375.9 14803.9i 1.15930 0.842282i
\(677\) 1735.65 1261.02i 0.0985322 0.0715879i −0.537428 0.843309i \(-0.680604\pi\)
0.635960 + 0.771722i \(0.280604\pi\)
\(678\) 2688.93 + 8275.66i 0.152312 + 0.468768i
\(679\) 4433.80 13645.8i 0.250595 0.771251i
\(680\) −9747.49 7081.97i −0.549705 0.399384i
\(681\) 27364.0 1.53978
\(682\) 0 0
\(683\) −29544.6 −1.65519 −0.827593 0.561329i \(-0.810290\pi\)
−0.827593 + 0.561329i \(0.810290\pi\)
\(684\) −3340.17 2426.77i −0.186717 0.135658i
\(685\) −787.908 + 2424.93i −0.0439481 + 0.135258i
\(686\) 1529.61 + 4707.66i 0.0851325 + 0.262011i
\(687\) −24338.0 + 17682.6i −1.35161 + 0.981999i
\(688\) 95.1566 69.1353i 0.00527298 0.00383105i
\(689\) −3436.85 10577.6i −0.190034 0.584866i
\(690\) 230.235 708.592i 0.0127028 0.0390951i
\(691\) −22493.2 16342.2i −1.23832 0.899693i −0.240836 0.970566i \(-0.577422\pi\)
−0.997485 + 0.0708727i \(0.977422\pi\)
\(692\) −13499.5 −0.741579
\(693\) 0 0
\(694\) −3366.55 −0.184139
\(695\) −30164.5 21915.8i −1.64634 1.19613i
\(696\) 3504.65 10786.2i 0.190867 0.587428i
\(697\) −7033.17 21645.9i −0.382210 1.17632i
\(698\) 3980.02 2891.66i 0.215825 0.156806i
\(699\) −1015.23 + 737.610i −0.0549351 + 0.0399127i
\(700\) −1573.03 4841.30i −0.0849358 0.261405i
\(701\) −6086.94 + 18733.7i −0.327961 + 1.00936i 0.642125 + 0.766600i \(0.278053\pi\)
−0.970086 + 0.242760i \(0.921947\pi\)
\(702\) −4941.50 3590.21i −0.265676 0.193025i
\(703\) −2775.09 −0.148883
\(704\) 0 0
\(705\) −5475.78 −0.292524
\(706\) 3398.70 + 2469.30i 0.181178 + 0.131633i
\(707\) 6766.23 20824.3i 0.359930 1.10775i
\(708\) −7460.74 22961.8i −0.396033 1.21887i
\(709\) −15470.4 + 11239.9i −0.819470 + 0.595380i −0.916561 0.399896i \(-0.869046\pi\)
0.0970906 + 0.995276i \(0.469046\pi\)
\(710\) 3583.47 2603.54i 0.189416 0.137619i
\(711\) −2461.71 7576.37i −0.129847 0.399629i
\(712\) −1234.48 + 3799.34i −0.0649777 + 0.199981i
\(713\) 707.600 + 514.101i 0.0371666 + 0.0270031i
\(714\) 6081.70 0.318770
\(715\) 0 0
\(716\) 33064.8 1.72582
\(717\) −20682.8 15026.9i −1.07728 0.782693i
\(718\) 930.940 2865.14i 0.0483877 0.148922i
\(719\) 567.801 + 1747.51i 0.0294512 + 0.0906414i 0.964702 0.263345i \(-0.0848258\pi\)
−0.935250 + 0.353987i \(0.884826\pi\)
\(720\) 4355.85 3164.71i 0.225462 0.163808i
\(721\) 23627.5 17166.4i 1.22044 0.886699i
\(722\) 507.959 + 1563.34i 0.0261832 + 0.0805837i
\(723\) −1825.66 + 5618.80i −0.0939100 + 0.289025i
\(724\) 20586.6 + 14957.0i 1.05676 + 0.767781i
\(725\) 6808.33 0.348765
\(726\) 0 0
\(727\) −7555.46 −0.385442 −0.192721 0.981254i \(-0.561731\pi\)
−0.192721 + 0.981254i \(0.561731\pi\)
\(728\) −11572.1 8407.62i −0.589135 0.428032i
\(729\) 3308.09 10181.3i 0.168068 0.517262i
\(730\) 1775.82 + 5465.42i 0.0900359 + 0.277102i
\(731\) −153.182 + 111.294i −0.00775056 + 0.00563111i
\(732\) 3626.43 2634.75i 0.183110 0.133037i
\(733\) 3703.45 + 11398.1i 0.186617 + 0.574348i 0.999972 0.00741920i \(-0.00236163\pi\)
−0.813356 + 0.581767i \(0.802362\pi\)
\(734\) −2185.93 + 6727.59i −0.109924 + 0.338310i
\(735\) −3479.81 2528.23i −0.174632 0.126878i
\(736\) −1712.10 −0.0857456
\(737\) 0 0
\(738\) −1638.99 −0.0817508
\(739\) 21958.7 + 15953.9i 1.09305 + 0.794148i 0.979912 0.199431i \(-0.0639093\pi\)
0.113139 + 0.993579i \(0.463909\pi\)
\(740\) 1211.55 3728.75i 0.0601855 0.185232i
\(741\) −9287.53 28584.1i −0.460440 1.41709i
\(742\) −1493.86 + 1085.36i −0.0739103 + 0.0536990i
\(743\) 23641.6 17176.6i 1.16733 0.848115i 0.176644 0.984275i \(-0.443476\pi\)
0.990687 + 0.136160i \(0.0434760\pi\)
\(744\) −1358.30 4180.42i −0.0669324 0.205997i
\(745\) −13858.7 + 42652.6i −0.681533 + 2.09754i
\(746\) −83.9681 61.0064i −0.00412103 0.00299411i
\(747\) 212.987 0.0104321
\(748\) 0 0
\(749\) −8196.29 −0.399847
\(750\) 3823.76 + 2778.12i 0.186165 + 0.135257i
\(751\) −2737.70 + 8425.78i −0.133023 + 0.409402i −0.995277 0.0970731i \(-0.969052\pi\)
0.862254 + 0.506475i \(0.169052\pi\)
\(752\) 1141.73 + 3513.90i 0.0553654 + 0.170397i
\(753\) 1327.98 964.833i 0.0642686 0.0466939i
\(754\) 7470.50 5427.64i 0.360822 0.262152i
\(755\) 4621.71 + 14224.2i 0.222783 + 0.685655i
\(756\) 4364.68 13433.1i 0.209976 0.646240i
\(757\) −28909.7 21004.2i −1.38803 1.00847i −0.996078 0.0884828i \(-0.971798\pi\)
−0.391957 0.919984i \(-0.628202\pi\)
\(758\) 2064.19 0.0989112
\(759\) 0 0
\(760\) 9885.59 0.471826
\(761\) −27825.9 20216.7i −1.32548 0.963014i −0.999847 0.0175169i \(-0.994424\pi\)
−0.325629 0.945498i \(-0.605576\pi\)
\(762\) −146.986 + 452.377i −0.00698786 + 0.0215064i
\(763\) −336.131 1034.51i −0.0159486 0.0490847i
\(764\) 17655.3 12827.4i 0.836057 0.607431i
\(765\) −7012.02 + 5094.53i −0.331399 + 0.240775i
\(766\) 1433.72 + 4412.54i 0.0676272 + 0.208135i
\(767\) 12585.2 38733.1i 0.592469 1.82343i
\(768\)