Properties

Label 162.3.f.a.35.4
Level $162$
Weight $3$
Character 162.35
Analytic conductor $4.414$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,3,Mod(17,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.f (of order \(18\), degree \(6\), 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: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 35.4
Character \(\chi\) \(=\) 162.35
Dual form 162.3.f.a.125.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.909039 - 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-2.86430 + 7.86960i) q^{5} +(-1.95208 + 11.0708i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})\) \(q+(0.909039 - 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-2.86430 + 7.86960i) q^{5} +(-1.95208 + 11.0708i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(5.92177 + 10.2568i) q^{10} +(-0.538121 - 1.47848i) q^{11} +(-6.82419 + 5.72617i) q^{13} +(10.2191 + 12.1786i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(16.9870 - 9.80744i) q^{17} +(4.86486 - 8.42619i) q^{19} +(16.4948 + 2.90849i) q^{20} +(-2.09088 - 0.761018i) q^{22} +(13.8255 - 2.43781i) q^{23} +(-34.5753 - 29.0121i) q^{25} +12.5983i q^{26} +22.4832 q^{28} +(-7.05122 + 8.40331i) q^{29} +(8.04854 + 45.6456i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(4.81694 - 27.3182i) q^{34} +(-81.5316 - 47.0723i) q^{35} +(7.89337 + 13.6717i) q^{37} +(-4.70617 - 12.9301i) q^{38} +(18.1454 - 15.2258i) q^{40} +(6.59742 + 7.86250i) q^{41} +(24.6205 - 8.96112i) q^{43} +(-2.72514 + 1.57336i) q^{44} +(9.92691 - 17.1939i) q^{46} +(42.2938 + 7.45754i) q^{47} +(-72.7075 - 26.4634i) q^{49} +(-62.8606 + 11.0840i) q^{50} +(13.6484 + 11.4523i) q^{52} -41.5395i q^{53} +13.1764 q^{55} +(20.4381 - 24.3572i) q^{56} +(2.69390 + 15.2779i) q^{58} +(-20.6989 + 56.8698i) q^{59} +(13.2934 - 75.3906i) q^{61} +(56.7666 + 32.7742i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-25.5162 - 70.1051i) q^{65} +(2.09011 - 1.75381i) q^{67} +(-25.2164 - 30.0518i) q^{68} +(-125.111 + 45.5367i) q^{70} +(-65.1324 + 37.6042i) q^{71} +(33.0777 - 57.2922i) q^{73} +(21.9866 + 3.87684i) q^{74} +(-18.2859 - 6.65552i) q^{76} +(17.4184 - 3.07133i) q^{77} +(38.8113 + 32.5666i) q^{79} -33.4986i q^{80} +14.5152 q^{82} +(-21.4712 + 25.5884i) q^{83} +(28.5248 + 161.772i) q^{85} +(12.6729 - 34.8186i) q^{86} +(-0.772758 + 4.38253i) q^{88} +(75.2876 + 43.4673i) q^{89} +(-50.0720 - 86.7273i) q^{91} +(-9.60308 - 26.3842i) q^{92} +(46.5258 - 39.0398i) q^{94} +(52.3763 + 62.4197i) q^{95} +(132.434 - 48.2019i) q^{97} +(-94.7631 + 54.7115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.909039 1.08335i 0.454519 0.541675i
\(3\) 0 0
\(4\) −0.347296 1.96962i −0.0868241 0.492404i
\(5\) −2.86430 + 7.86960i −0.572860 + 1.57392i 0.227103 + 0.973871i \(0.427075\pi\)
−0.799963 + 0.600049i \(0.795148\pi\)
\(6\) 0 0
\(7\) −1.95208 + 11.0708i −0.278869 + 1.58155i 0.447527 + 0.894270i \(0.352305\pi\)
−0.726397 + 0.687276i \(0.758806\pi\)
\(8\) −2.44949 1.41421i −0.306186 0.176777i
\(9\) 0 0
\(10\) 5.92177 + 10.2568i 0.592177 + 1.02568i
\(11\) −0.538121 1.47848i −0.0489201 0.134407i 0.912826 0.408348i \(-0.133895\pi\)
−0.961747 + 0.273941i \(0.911673\pi\)
\(12\) 0 0
\(13\) −6.82419 + 5.72617i −0.524937 + 0.440475i −0.866349 0.499439i \(-0.833539\pi\)
0.341412 + 0.939914i \(0.389095\pi\)
\(14\) 10.2191 + 12.1786i 0.729933 + 0.869900i
\(15\) 0 0
\(16\) −3.75877 + 1.36808i −0.234923 + 0.0855050i
\(17\) 16.9870 9.80744i 0.999235 0.576909i 0.0912130 0.995831i \(-0.470926\pi\)
0.908022 + 0.418923i \(0.137592\pi\)
\(18\) 0 0
\(19\) 4.86486 8.42619i 0.256045 0.443484i −0.709134 0.705074i \(-0.750914\pi\)
0.965179 + 0.261591i \(0.0842470\pi\)
\(20\) 16.4948 + 2.90849i 0.824742 + 0.145424i
\(21\) 0 0
\(22\) −2.09088 0.761018i −0.0950400 0.0345917i
\(23\) 13.8255 2.43781i 0.601108 0.105992i 0.135190 0.990820i \(-0.456835\pi\)
0.465918 + 0.884828i \(0.345724\pi\)
\(24\) 0 0
\(25\) −34.5753 29.0121i −1.38301 1.16048i
\(26\) 12.5983i 0.484550i
\(27\) 0 0
\(28\) 22.4832 0.802972
\(29\) −7.05122 + 8.40331i −0.243145 + 0.289769i −0.873791 0.486301i \(-0.838346\pi\)
0.630646 + 0.776071i \(0.282790\pi\)
\(30\) 0 0
\(31\) 8.04854 + 45.6456i 0.259630 + 1.47244i 0.783901 + 0.620886i \(0.213227\pi\)
−0.524271 + 0.851552i \(0.675662\pi\)
\(32\) −1.93476 + 5.31570i −0.0604612 + 0.166116i
\(33\) 0 0
\(34\) 4.81694 27.3182i 0.141675 0.803477i
\(35\) −81.5316 47.0723i −2.32947 1.34492i
\(36\) 0 0
\(37\) 7.89337 + 13.6717i 0.213334 + 0.369506i 0.952756 0.303737i \(-0.0982343\pi\)
−0.739422 + 0.673243i \(0.764901\pi\)
\(38\) −4.70617 12.9301i −0.123846 0.340265i
\(39\) 0 0
\(40\) 18.1454 15.2258i 0.453634 0.380644i
\(41\) 6.59742 + 7.86250i 0.160913 + 0.191768i 0.840476 0.541848i \(-0.182275\pi\)
−0.679564 + 0.733617i \(0.737831\pi\)
\(42\) 0 0
\(43\) 24.6205 8.96112i 0.572569 0.208398i −0.0394765 0.999220i \(-0.512569\pi\)
0.612046 + 0.790822i \(0.290347\pi\)
\(44\) −2.72514 + 1.57336i −0.0619350 + 0.0357582i
\(45\) 0 0
\(46\) 9.92691 17.1939i 0.215802 0.373781i
\(47\) 42.2938 + 7.45754i 0.899868 + 0.158671i 0.604399 0.796682i \(-0.293413\pi\)
0.295468 + 0.955352i \(0.404524\pi\)
\(48\) 0 0
\(49\) −72.7075 26.4634i −1.48383 0.540069i
\(50\) −62.8606 + 11.0840i −1.25721 + 0.221680i
\(51\) 0 0
\(52\) 13.6484 + 11.4523i 0.262469 + 0.220237i
\(53\) 41.5395i 0.783764i −0.920016 0.391882i \(-0.871824\pi\)
0.920016 0.391882i \(-0.128176\pi\)
\(54\) 0 0
\(55\) 13.1764 0.239570
\(56\) 20.4381 24.3572i 0.364966 0.434950i
\(57\) 0 0
\(58\) 2.69390 + 15.2779i 0.0464466 + 0.263412i
\(59\) −20.6989 + 56.8698i −0.350829 + 0.963895i 0.631275 + 0.775559i \(0.282532\pi\)
−0.982105 + 0.188336i \(0.939690\pi\)
\(60\) 0 0
\(61\) 13.2934 75.3906i 0.217924 1.23591i −0.657835 0.753162i \(-0.728527\pi\)
0.875759 0.482748i \(-0.160361\pi\)
\(62\) 56.7666 + 32.7742i 0.915590 + 0.528616i
\(63\) 0 0
\(64\) 4.00000 + 6.92820i 0.0625000 + 0.108253i
\(65\) −25.5162 70.1051i −0.392556 1.07854i
\(66\) 0 0
\(67\) 2.09011 1.75381i 0.0311956 0.0261762i −0.627057 0.778974i \(-0.715741\pi\)
0.658252 + 0.752798i \(0.271296\pi\)
\(68\) −25.2164 30.0518i −0.370830 0.441938i
\(69\) 0 0
\(70\) −125.111 + 45.5367i −1.78730 + 0.650525i
\(71\) −65.1324 + 37.6042i −0.917358 + 0.529637i −0.882791 0.469765i \(-0.844338\pi\)
−0.0345668 + 0.999402i \(0.511005\pi\)
\(72\) 0 0
\(73\) 33.0777 57.2922i 0.453119 0.784825i −0.545459 0.838138i \(-0.683645\pi\)
0.998578 + 0.0533125i \(0.0169779\pi\)
\(74\) 21.9866 + 3.87684i 0.297117 + 0.0523897i
\(75\) 0 0
\(76\) −18.2859 6.65552i −0.240604 0.0875727i
\(77\) 17.4184 3.07133i 0.226213 0.0398875i
\(78\) 0 0
\(79\) 38.8113 + 32.5666i 0.491283 + 0.412235i 0.854486 0.519475i \(-0.173872\pi\)
−0.363203 + 0.931710i \(0.618317\pi\)
\(80\) 33.4986i 0.418733i
\(81\) 0 0
\(82\) 14.5152 0.177014
\(83\) −21.4712 + 25.5884i −0.258689 + 0.308294i −0.879720 0.475492i \(-0.842270\pi\)
0.621030 + 0.783787i \(0.286714\pi\)
\(84\) 0 0
\(85\) 28.5248 + 161.772i 0.335586 + 1.90320i
\(86\) 12.6729 34.8186i 0.147360 0.404868i
\(87\) 0 0
\(88\) −0.772758 + 4.38253i −0.00878135 + 0.0498015i
\(89\) 75.2876 + 43.4673i 0.845928 + 0.488397i 0.859275 0.511514i \(-0.170915\pi\)
−0.0133471 + 0.999911i \(0.504249\pi\)
\(90\) 0 0
\(91\) −50.0720 86.7273i −0.550242 0.953047i
\(92\) −9.60308 26.3842i −0.104381 0.286785i
\(93\) 0 0
\(94\) 46.5258 39.0398i 0.494956 0.415317i
\(95\) 52.3763 + 62.4197i 0.551330 + 0.657049i
\(96\) 0 0
\(97\) 132.434 48.2019i 1.36530 0.496927i 0.447608 0.894230i \(-0.352276\pi\)
0.917688 + 0.397303i \(0.130054\pi\)
\(98\) −94.7631 + 54.7115i −0.966970 + 0.558281i
\(99\) 0 0
\(100\) −45.1348 + 78.1758i −0.451348 + 0.781758i
\(101\) 88.8791 + 15.6718i 0.879991 + 0.155166i 0.595348 0.803468i \(-0.297014\pi\)
0.284642 + 0.958634i \(0.408125\pi\)
\(102\) 0 0
\(103\) 19.7299 + 7.18111i 0.191553 + 0.0697195i 0.436015 0.899939i \(-0.356389\pi\)
−0.244463 + 0.969659i \(0.578612\pi\)
\(104\) 24.8138 4.37534i 0.238594 0.0420706i
\(105\) 0 0
\(106\) −45.0018 37.7610i −0.424545 0.356236i
\(107\) 21.8959i 0.204635i 0.994752 + 0.102317i \(0.0326257\pi\)
−0.994752 + 0.102317i \(0.967374\pi\)
\(108\) 0 0
\(109\) −92.6448 −0.849953 −0.424976 0.905204i \(-0.639718\pi\)
−0.424976 + 0.905204i \(0.639718\pi\)
\(110\) 11.9778 14.2746i 0.108889 0.129769i
\(111\) 0 0
\(112\) −7.80834 44.2833i −0.0697173 0.395387i
\(113\) 52.9813 145.565i 0.468861 1.28819i −0.449796 0.893131i \(-0.648503\pi\)
0.918657 0.395055i \(-0.129274\pi\)
\(114\) 0 0
\(115\) −20.4158 + 115.784i −0.177529 + 1.00681i
\(116\) 19.0002 + 10.9697i 0.163794 + 0.0945668i
\(117\) 0 0
\(118\) 42.7938 + 74.1211i 0.362659 + 0.628145i
\(119\) 75.4164 + 207.205i 0.633752 + 1.74122i
\(120\) 0 0
\(121\) 90.7951 76.1861i 0.750372 0.629637i
\(122\) −69.5902 82.9344i −0.570411 0.679790i
\(123\) 0 0
\(124\) 87.1090 31.7051i 0.702492 0.255686i
\(125\) 146.031 84.3111i 1.16825 0.674489i
\(126\) 0 0
\(127\) −115.693 + 200.387i −0.910971 + 1.57785i −0.0982763 + 0.995159i \(0.531333\pi\)
−0.812695 + 0.582689i \(0.802000\pi\)
\(128\) 11.1418 + 1.96460i 0.0870455 + 0.0153485i
\(129\) 0 0
\(130\) −99.1436 36.0853i −0.762643 0.277579i
\(131\) 69.0825 12.1811i 0.527347 0.0929856i 0.0963653 0.995346i \(-0.469278\pi\)
0.430982 + 0.902360i \(0.358167\pi\)
\(132\) 0 0
\(133\) 83.7882 + 70.3067i 0.629987 + 0.528621i
\(134\) 3.85860i 0.0287955i
\(135\) 0 0
\(136\) −55.4793 −0.407936
\(137\) −136.898 + 163.149i −0.999257 + 1.19087i −0.0176713 + 0.999844i \(0.505625\pi\)
−0.981585 + 0.191024i \(0.938819\pi\)
\(138\) 0 0
\(139\) 9.79795 + 55.5669i 0.0704888 + 0.399762i 0.999554 + 0.0298471i \(0.00950205\pi\)
−0.929066 + 0.369915i \(0.879387\pi\)
\(140\) −64.3987 + 176.934i −0.459991 + 1.26381i
\(141\) 0 0
\(142\) −18.4694 + 104.745i −0.130066 + 0.737640i
\(143\) 12.1382 + 7.00802i 0.0848829 + 0.0490071i
\(144\) 0 0
\(145\) −45.9339 79.5599i −0.316786 0.548689i
\(146\) −31.9987 87.9156i −0.219169 0.602162i
\(147\) 0 0
\(148\) 24.1867 20.2950i 0.163424 0.137129i
\(149\) −18.5161 22.0666i −0.124269 0.148098i 0.700323 0.713826i \(-0.253039\pi\)
−0.824592 + 0.565728i \(0.808595\pi\)
\(150\) 0 0
\(151\) −145.452 + 52.9400i −0.963255 + 0.350596i −0.775308 0.631583i \(-0.782405\pi\)
−0.187947 + 0.982179i \(0.560183\pi\)
\(152\) −23.8329 + 13.7599i −0.156795 + 0.0905257i
\(153\) 0 0
\(154\) 12.5067 21.6622i 0.0812122 0.140664i
\(155\) −382.266 67.4038i −2.46623 0.434863i
\(156\) 0 0
\(157\) −200.915 73.1270i −1.27971 0.465777i −0.389375 0.921080i \(-0.627309\pi\)
−0.890337 + 0.455303i \(0.849531\pi\)
\(158\) 70.5620 12.4420i 0.446595 0.0787467i
\(159\) 0 0
\(160\) −36.2907 30.4515i −0.226817 0.190322i
\(161\) 157.818i 0.980238i
\(162\) 0 0
\(163\) 147.201 0.903076 0.451538 0.892252i \(-0.350876\pi\)
0.451538 + 0.892252i \(0.350876\pi\)
\(164\) 13.1948 15.7250i 0.0804564 0.0958842i
\(165\) 0 0
\(166\) 8.20304 + 46.5217i 0.0494159 + 0.280251i
\(167\) 50.5448 138.871i 0.302664 0.831561i −0.691371 0.722500i \(-0.742993\pi\)
0.994035 0.109062i \(-0.0347846\pi\)
\(168\) 0 0
\(169\) −15.5661 + 88.2796i −0.0921070 + 0.522364i
\(170\) 201.186 + 116.155i 1.18345 + 0.683264i
\(171\) 0 0
\(172\) −26.2006 45.3807i −0.152329 0.263841i
\(173\) −72.2331 198.459i −0.417532 1.14716i −0.953097 0.302666i \(-0.902123\pi\)
0.535565 0.844494i \(-0.320099\pi\)
\(174\) 0 0
\(175\) 388.682 326.143i 2.22104 1.86367i
\(176\) 4.04535 + 4.82106i 0.0229849 + 0.0273924i
\(177\) 0 0
\(178\) 115.530 42.0493i 0.649043 0.236232i
\(179\) 225.133 129.980i 1.25772 0.726147i 0.285092 0.958500i \(-0.407976\pi\)
0.972632 + 0.232353i \(0.0746424\pi\)
\(180\) 0 0
\(181\) 159.698 276.606i 0.882311 1.52821i 0.0335470 0.999437i \(-0.489320\pi\)
0.848764 0.528771i \(-0.177347\pi\)
\(182\) −139.474 24.5929i −0.766338 0.135126i
\(183\) 0 0
\(184\) −37.3130 13.5808i −0.202788 0.0738087i
\(185\) −130.200 + 22.9578i −0.703783 + 0.124096i
\(186\) 0 0
\(187\) −23.6411 19.8373i −0.126423 0.106082i
\(188\) 85.8925i 0.456875i
\(189\) 0 0
\(190\) 115.234 0.606497
\(191\) 25.0422 29.8442i 0.131111 0.156252i −0.696495 0.717562i \(-0.745258\pi\)
0.827606 + 0.561310i \(0.189702\pi\)
\(192\) 0 0
\(193\) −28.3760 160.928i −0.147026 0.833825i −0.965718 0.259593i \(-0.916412\pi\)
0.818692 0.574233i \(-0.194699\pi\)
\(194\) 68.1678 187.289i 0.351380 0.965410i
\(195\) 0 0
\(196\) −26.8716 + 152.397i −0.137100 + 0.777533i
\(197\) −296.815 171.366i −1.50668 0.869880i −0.999970 0.00776089i \(-0.997530\pi\)
−0.506706 0.862119i \(-0.669137\pi\)
\(198\) 0 0
\(199\) 98.8611 + 171.232i 0.496789 + 0.860464i 0.999993 0.00370331i \(-0.00117880\pi\)
−0.503204 + 0.864168i \(0.667845\pi\)
\(200\) 43.6625 + 119.962i 0.218312 + 0.599809i
\(201\) 0 0
\(202\) 97.7725 82.0409i 0.484022 0.406143i
\(203\) −79.2670 94.4668i −0.390478 0.465353i
\(204\) 0 0
\(205\) −80.7718 + 29.3985i −0.394009 + 0.143407i
\(206\) 25.7149 14.8465i 0.124830 0.0720705i
\(207\) 0 0
\(208\) 17.8167 30.8594i 0.0856571 0.148363i
\(209\) −15.0758 2.65827i −0.0721330 0.0127190i
\(210\) 0 0
\(211\) −214.619 78.1150i −1.01715 0.370213i −0.220977 0.975279i \(-0.570925\pi\)
−0.796176 + 0.605066i \(0.793147\pi\)
\(212\) −81.8168 + 14.4265i −0.385928 + 0.0680496i
\(213\) 0 0
\(214\) 23.7210 + 19.9042i 0.110846 + 0.0930105i
\(215\) 219.421i 1.02056i
\(216\) 0 0
\(217\) −521.045 −2.40113
\(218\) −84.2178 + 100.367i −0.386320 + 0.460398i
\(219\) 0 0
\(220\) −4.57610 25.9524i −0.0208005 0.117965i
\(221\) −59.7633 + 164.198i −0.270422 + 0.742979i
\(222\) 0 0
\(223\) 67.0596 380.314i 0.300716 1.70544i −0.342301 0.939590i \(-0.611206\pi\)
0.643016 0.765852i \(-0.277683\pi\)
\(224\) −55.0724 31.7961i −0.245859 0.141947i
\(225\) 0 0
\(226\) −109.536 189.722i −0.484672 0.839476i
\(227\) 63.6795 + 174.958i 0.280527 + 0.770740i 0.997300 + 0.0734342i \(0.0233959\pi\)
−0.716774 + 0.697306i \(0.754382\pi\)
\(228\) 0 0
\(229\) −236.706 + 198.620i −1.03365 + 0.867336i −0.991281 0.131766i \(-0.957935\pi\)
−0.0423704 + 0.999102i \(0.513491\pi\)
\(230\) 106.876 + 127.369i 0.464676 + 0.553780i
\(231\) 0 0
\(232\) 29.1560 10.6119i 0.125672 0.0457410i
\(233\) 17.8085 10.2818i 0.0764315 0.0441277i −0.461297 0.887246i \(-0.652616\pi\)
0.537729 + 0.843118i \(0.319282\pi\)
\(234\) 0 0
\(235\) −179.830 + 311.475i −0.765234 + 1.32542i
\(236\) 119.200 + 21.0182i 0.505086 + 0.0890603i
\(237\) 0 0
\(238\) 293.032 + 106.655i 1.23123 + 0.448130i
\(239\) 101.144 17.8344i 0.423197 0.0746211i 0.0420061 0.999117i \(-0.486625\pi\)
0.381191 + 0.924496i \(0.375514\pi\)
\(240\) 0 0
\(241\) 294.337 + 246.978i 1.22131 + 1.02480i 0.998755 + 0.0498853i \(0.0158856\pi\)
0.222559 + 0.974919i \(0.428559\pi\)
\(242\) 167.619i 0.692641i
\(243\) 0 0
\(244\) −153.107 −0.627488
\(245\) 416.512 496.380i 1.70005 2.02604i
\(246\) 0 0
\(247\) 15.0511 + 85.3589i 0.0609355 + 0.345583i
\(248\) 44.8377 123.191i 0.180797 0.496737i
\(249\) 0 0
\(250\) 41.4095 234.845i 0.165638 0.939380i
\(251\) −281.668 162.621i −1.12218 0.647893i −0.180227 0.983625i \(-0.557683\pi\)
−0.941958 + 0.335732i \(0.891016\pi\)
\(252\) 0 0
\(253\) −11.0440 19.1288i −0.0436523 0.0756080i
\(254\) 111.919 + 307.496i 0.440627 + 1.21061i
\(255\) 0 0
\(256\) 12.2567 10.2846i 0.0478778 0.0401742i
\(257\) 21.5034 + 25.6267i 0.0836708 + 0.0997150i 0.806256 0.591567i \(-0.201491\pi\)
−0.722585 + 0.691282i \(0.757046\pi\)
\(258\) 0 0
\(259\) −166.766 + 60.6977i −0.643883 + 0.234354i
\(260\) −129.218 + 74.6043i −0.496994 + 0.286940i
\(261\) 0 0
\(262\) 49.6023 85.9137i 0.189322 0.327915i
\(263\) 154.814 + 27.2979i 0.588646 + 0.103794i 0.460035 0.887901i \(-0.347837\pi\)
0.128611 + 0.991695i \(0.458948\pi\)
\(264\) 0 0
\(265\) 326.899 + 118.982i 1.23358 + 0.448987i
\(266\) 152.333 26.8605i 0.572682 0.100979i
\(267\) 0 0
\(268\) −4.18021 3.50762i −0.0155978 0.0130881i
\(269\) 289.194i 1.07507i 0.843241 + 0.537536i \(0.180645\pi\)
−0.843241 + 0.537536i \(0.819355\pi\)
\(270\) 0 0
\(271\) 438.046 1.61641 0.808204 0.588903i \(-0.200440\pi\)
0.808204 + 0.588903i \(0.200440\pi\)
\(272\) −50.4328 + 60.1035i −0.185415 + 0.220969i
\(273\) 0 0
\(274\) 52.3016 + 296.617i 0.190882 + 1.08255i
\(275\) −24.2880 + 66.7308i −0.0883201 + 0.242657i
\(276\) 0 0
\(277\) 2.95396 16.7527i 0.0106641 0.0604791i −0.979011 0.203806i \(-0.934669\pi\)
0.989675 + 0.143327i \(0.0457800\pi\)
\(278\) 69.1052 + 39.8979i 0.248580 + 0.143518i
\(279\) 0 0
\(280\) 133.141 + 230.606i 0.475502 + 0.823594i
\(281\) −31.3851 86.2298i −0.111691 0.306867i 0.871236 0.490864i \(-0.163319\pi\)
−0.982927 + 0.183996i \(0.941097\pi\)
\(282\) 0 0
\(283\) −335.404 + 281.438i −1.18517 + 0.994479i −0.185243 + 0.982693i \(0.559307\pi\)
−0.999931 + 0.0117863i \(0.996248\pi\)
\(284\) 96.6861 + 115.226i 0.340444 + 0.405725i
\(285\) 0 0
\(286\) 18.6263 6.77941i 0.0651269 0.0237042i
\(287\) −99.9231 + 57.6906i −0.348164 + 0.201013i
\(288\) 0 0
\(289\) 47.8719 82.9166i 0.165647 0.286909i
\(290\) −127.947 22.5605i −0.441196 0.0777948i
\(291\) 0 0
\(292\) −124.331 45.2529i −0.425793 0.154976i
\(293\) −254.746 + 44.9185i −0.869439 + 0.153305i −0.590533 0.807013i \(-0.701083\pi\)
−0.278905 + 0.960319i \(0.589972\pi\)
\(294\) 0 0
\(295\) −388.255 325.784i −1.31612 1.10435i
\(296\) 44.6516i 0.150850i
\(297\) 0 0
\(298\) −40.7377 −0.136704
\(299\) −80.3884 + 95.8031i −0.268857 + 0.320412i
\(300\) 0 0
\(301\) 51.1457 + 290.062i 0.169919 + 0.963661i
\(302\) −74.8685 + 205.700i −0.247909 + 0.681124i
\(303\) 0 0
\(304\) −6.75819 + 38.3276i −0.0222309 + 0.126078i
\(305\) 555.217 + 320.555i 1.82038 + 1.05100i
\(306\) 0 0
\(307\) 106.596 + 184.630i 0.347219 + 0.601401i 0.985754 0.168192i \(-0.0537927\pi\)
−0.638535 + 0.769592i \(0.720459\pi\)
\(308\) −12.0987 33.2409i −0.0392815 0.107925i
\(309\) 0 0
\(310\) −420.516 + 352.855i −1.35650 + 1.13824i
\(311\) −299.915 357.425i −0.964358 1.14928i −0.988750 0.149575i \(-0.952210\pi\)
0.0243925 0.999702i \(-0.492235\pi\)
\(312\) 0 0
\(313\) −88.7107 + 32.2881i −0.283421 + 0.103157i −0.479819 0.877367i \(-0.659298\pi\)
0.196398 + 0.980524i \(0.437075\pi\)
\(314\) −261.861 + 151.186i −0.833953 + 0.481483i
\(315\) 0 0
\(316\) 50.6646 87.7536i 0.160331 0.277701i
\(317\) 250.991 + 44.2565i 0.791769 + 0.139610i 0.554884 0.831927i \(-0.312762\pi\)
0.236885 + 0.971538i \(0.423874\pi\)
\(318\) 0 0
\(319\) 16.2185 + 5.90305i 0.0508417 + 0.0185049i
\(320\) −65.9794 + 11.6339i −0.206186 + 0.0363561i
\(321\) 0 0
\(322\) 170.973 + 143.463i 0.530971 + 0.445537i
\(323\) 190.847i 0.590859i
\(324\) 0 0
\(325\) 402.076 1.23716
\(326\) 133.812 159.471i 0.410466 0.489174i
\(327\) 0 0
\(328\) −5.04106 28.5893i −0.0153691 0.0871625i
\(329\) −165.122 + 453.669i −0.501891 + 1.37893i
\(330\) 0 0
\(331\) −63.9844 + 362.874i −0.193306 + 1.09629i 0.721504 + 0.692410i \(0.243451\pi\)
−0.914810 + 0.403884i \(0.867660\pi\)
\(332\) 57.8562 + 33.4033i 0.174266 + 0.100612i
\(333\) 0 0
\(334\) −104.498 180.997i −0.312870 0.541906i
\(335\) 7.81507 + 21.4717i 0.0233286 + 0.0640947i
\(336\) 0 0
\(337\) 150.868 126.593i 0.447679 0.375647i −0.390895 0.920435i \(-0.627834\pi\)
0.838574 + 0.544788i \(0.183390\pi\)
\(338\) 81.4876 + 97.1131i 0.241087 + 0.287317i
\(339\) 0 0
\(340\) 308.723 112.366i 0.908008 0.330488i
\(341\) 63.1548 36.4624i 0.185205 0.106928i
\(342\) 0 0
\(343\) 159.483 276.233i 0.464966 0.805344i
\(344\) −72.9805 12.8684i −0.212153 0.0374083i
\(345\) 0 0
\(346\) −280.663 102.153i −0.811165 0.295240i
\(347\) 263.673 46.4927i 0.759864 0.133985i 0.219727 0.975561i \(-0.429483\pi\)
0.540137 + 0.841577i \(0.318372\pi\)
\(348\) 0 0
\(349\) −395.788 332.105i −1.13406 0.951591i −0.134834 0.990868i \(-0.543050\pi\)
−0.999228 + 0.0392770i \(0.987495\pi\)
\(350\) 717.555i 2.05016i
\(351\) 0 0
\(352\) 8.90028 0.0252849
\(353\) 186.396 222.139i 0.528035 0.629288i −0.434426 0.900708i \(-0.643049\pi\)
0.962461 + 0.271420i \(0.0874932\pi\)
\(354\) 0 0
\(355\) −109.371 620.276i −0.308088 1.74726i
\(356\) 59.4668 163.384i 0.167041 0.458943i
\(357\) 0 0
\(358\) 63.8400 362.055i 0.178324 1.01133i
\(359\) −35.8110 20.6755i −0.0997520 0.0575918i 0.449294 0.893384i \(-0.351676\pi\)
−0.549046 + 0.835792i \(0.685009\pi\)
\(360\) 0 0
\(361\) 133.166 + 230.651i 0.368882 + 0.638922i
\(362\) −154.489 424.455i −0.426765 1.17253i
\(363\) 0 0
\(364\) −153.430 + 128.743i −0.421510 + 0.353689i
\(365\) 356.123 + 424.410i 0.975678 + 1.16277i
\(366\) 0 0
\(367\) 152.544 55.5215i 0.415651 0.151285i −0.125725 0.992065i \(-0.540126\pi\)
0.541376 + 0.840780i \(0.317903\pi\)
\(368\) −48.6317 + 28.0775i −0.132151 + 0.0762976i
\(369\) 0 0
\(370\) −93.4855 + 161.922i −0.252663 + 0.437626i
\(371\) 459.876 + 81.0886i 1.23956 + 0.218568i
\(372\) 0 0
\(373\) 63.6401 + 23.1631i 0.170617 + 0.0620995i 0.425916 0.904763i \(-0.359952\pi\)
−0.255299 + 0.966862i \(0.582174\pi\)
\(374\) −42.9814 + 7.57879i −0.114924 + 0.0202641i
\(375\) 0 0
\(376\) −93.0516 78.0796i −0.247478 0.207659i
\(377\) 97.7223i 0.259210i
\(378\) 0 0
\(379\) 122.431 0.323038 0.161519 0.986870i \(-0.448361\pi\)
0.161519 + 0.986870i \(0.448361\pi\)
\(380\) 104.753 124.839i 0.275665 0.328524i
\(381\) 0 0
\(382\) −9.56733 54.2590i −0.0250454 0.142039i
\(383\) 20.6906 56.8471i 0.0540226 0.148426i −0.909746 0.415165i \(-0.863724\pi\)
0.963769 + 0.266739i \(0.0859462\pi\)
\(384\) 0 0
\(385\) −25.7214 + 145.873i −0.0668087 + 0.378891i
\(386\) −200.137 115.549i −0.518489 0.299350i
\(387\) 0 0
\(388\) −140.933 244.103i −0.363229 0.629132i
\(389\) 82.3102 + 226.145i 0.211594 + 0.581350i 0.999402 0.0345705i \(-0.0110063\pi\)
−0.787808 + 0.615921i \(0.788784\pi\)
\(390\) 0 0
\(391\) 210.945 177.004i 0.539501 0.452695i
\(392\) 140.672 + 167.646i 0.358856 + 0.427668i
\(393\) 0 0
\(394\) −455.466 + 165.776i −1.15601 + 0.420752i
\(395\) −367.453 + 212.149i −0.930261 + 0.537087i
\(396\) 0 0
\(397\) 14.3451 24.8464i 0.0361337 0.0625854i −0.847393 0.530966i \(-0.821829\pi\)
0.883527 + 0.468381i \(0.155162\pi\)
\(398\) 275.373 + 48.5557i 0.691893 + 0.121999i
\(399\) 0 0
\(400\) 169.651 + 61.7481i 0.424129 + 0.154370i
\(401\) −697.035 + 122.906i −1.73824 + 0.306499i −0.950780 0.309866i \(-0.899716\pi\)
−0.787461 + 0.616365i \(0.788605\pi\)
\(402\) 0 0
\(403\) −316.299 265.406i −0.784861 0.658577i
\(404\) 180.500i 0.446783i
\(405\) 0 0
\(406\) −174.397 −0.429550
\(407\) 15.9657 19.0272i 0.0392278 0.0467499i
\(408\) 0 0
\(409\) −13.6664 77.5062i −0.0334143 0.189502i 0.963532 0.267593i \(-0.0862284\pi\)
−0.996946 + 0.0780917i \(0.975117\pi\)
\(410\) −41.5758 + 114.229i −0.101404 + 0.278606i
\(411\) 0 0
\(412\) 7.29189 41.3543i 0.0176988 0.100375i
\(413\) −589.190 340.169i −1.42661 0.823653i
\(414\) 0 0
\(415\) −139.871 242.263i −0.337037 0.583766i
\(416\) −17.2355 47.3541i −0.0414315 0.113832i
\(417\) 0 0
\(418\) −16.5843 + 13.9159i −0.0396754 + 0.0332916i
\(419\) −33.8949 40.3944i −0.0808948 0.0964067i 0.724079 0.689717i \(-0.242265\pi\)
−0.804974 + 0.593310i \(0.797821\pi\)
\(420\) 0 0
\(421\) 664.624 241.903i 1.57868 0.574592i 0.603763 0.797164i \(-0.293667\pi\)
0.974916 + 0.222572i \(0.0714452\pi\)
\(422\) −279.723 + 161.498i −0.662851 + 0.382697i
\(423\) 0 0
\(424\) −58.7457 + 101.751i −0.138551 + 0.239978i
\(425\) −871.865 153.733i −2.05145 0.361725i
\(426\) 0 0
\(427\) 808.686 + 294.338i 1.89388 + 0.689315i
\(428\) 43.1265 7.60437i 0.100763 0.0177672i
\(429\) 0 0
\(430\) 237.709 + 199.462i 0.552813 + 0.463865i
\(431\) 279.279i 0.647978i −0.946061 0.323989i \(-0.894976\pi\)
0.946061 0.323989i \(-0.105024\pi\)
\(432\) 0 0
\(433\) 100.836 0.232877 0.116439 0.993198i \(-0.462852\pi\)
0.116439 + 0.993198i \(0.462852\pi\)
\(434\) −473.650 + 564.475i −1.09136 + 1.30063i
\(435\) 0 0
\(436\) 32.1752 + 182.475i 0.0737964 + 0.418520i
\(437\) 46.7177 128.356i 0.106905 0.293720i
\(438\) 0 0
\(439\) 17.2883 98.0470i 0.0393812 0.223342i −0.958765 0.284199i \(-0.908272\pi\)
0.998146 + 0.0608574i \(0.0193835\pi\)
\(440\) −32.2754 18.6342i −0.0733531 0.0423504i
\(441\) 0 0
\(442\) 123.557 + 214.007i 0.279541 + 0.484179i
\(443\) −117.281 322.226i −0.264742 0.727373i −0.998832 0.0483203i \(-0.984613\pi\)
0.734090 0.679052i \(-0.237609\pi\)
\(444\) 0 0
\(445\) −557.716 + 467.980i −1.25330 + 1.05164i
\(446\) −351.053 418.369i −0.787115 0.938047i
\(447\) 0 0
\(448\) −84.5092 + 30.7589i −0.188637 + 0.0686581i
\(449\) 433.309 250.171i 0.965053 0.557174i 0.0673285 0.997731i \(-0.478552\pi\)
0.897725 + 0.440557i \(0.145219\pi\)
\(450\) 0 0
\(451\) 8.07431 13.9851i 0.0179031 0.0310091i
\(452\) −305.107 53.7987i −0.675016 0.119024i
\(453\) 0 0
\(454\) 247.428 + 90.0564i 0.544996 + 0.198362i
\(455\) 825.931 145.634i 1.81523 0.320074i
\(456\) 0 0
\(457\) 88.1631 + 73.9776i 0.192917 + 0.161877i 0.734130 0.679009i \(-0.237590\pi\)
−0.541213 + 0.840886i \(0.682035\pi\)
\(458\) 436.989i 0.954125i
\(459\) 0 0
\(460\) 235.140 0.511173
\(461\) −371.972 + 443.299i −0.806880 + 0.961602i −0.999808 0.0196109i \(-0.993757\pi\)
0.192928 + 0.981213i \(0.438202\pi\)
\(462\) 0 0
\(463\) −138.386 784.826i −0.298890 1.69509i −0.650957 0.759114i \(-0.725632\pi\)
0.352067 0.935975i \(-0.385479\pi\)
\(464\) 15.0075 41.2328i 0.0323437 0.0888637i
\(465\) 0 0
\(466\) 5.04990 28.6394i 0.0108367 0.0614579i
\(467\) −234.565 135.426i −0.502281 0.289992i 0.227374 0.973807i \(-0.426986\pi\)
−0.729655 + 0.683816i \(0.760319\pi\)
\(468\) 0 0
\(469\) 15.3360 + 26.5628i 0.0326994 + 0.0566371i
\(470\) 173.964 + 477.961i 0.370136 + 1.01694i
\(471\) 0 0
\(472\) 131.128 110.029i 0.277813 0.233113i
\(473\) −26.4976 31.5786i −0.0560203 0.0667624i
\(474\) 0 0
\(475\) −412.665 + 150.198i −0.868769 + 0.316206i
\(476\) 381.922 220.503i 0.802358 0.463241i
\(477\) 0 0
\(478\) 72.6230 125.787i 0.151931 0.263152i
\(479\) 785.792 + 138.556i 1.64048 + 0.289262i 0.916344 0.400391i \(-0.131126\pi\)
0.724140 + 0.689653i \(0.242237\pi\)
\(480\) 0 0
\(481\) −132.152 48.0995i −0.274745 0.0999990i
\(482\) 535.127 94.3574i 1.11022 0.195762i
\(483\) 0 0
\(484\) −181.590 152.372i −0.375186 0.314819i
\(485\) 1180.26i 2.43354i
\(486\) 0 0
\(487\) −139.213 −0.285859 −0.142929 0.989733i \(-0.545652\pi\)
−0.142929 + 0.989733i \(0.545652\pi\)
\(488\) −139.180 + 165.869i −0.285206 + 0.339895i
\(489\) 0 0
\(490\) −159.128 902.458i −0.324750 1.84175i
\(491\) 73.6069 202.233i 0.149912 0.411881i −0.841892 0.539646i \(-0.818558\pi\)
0.991804 + 0.127765i \(0.0407804\pi\)
\(492\) 0 0
\(493\) −37.3639 + 211.901i −0.0757889 + 0.429820i
\(494\) 106.156 + 61.2890i 0.214890 + 0.124067i
\(495\) 0 0
\(496\) −92.6994 160.560i −0.186894 0.323710i
\(497\) −289.166 794.476i −0.581822 1.59854i
\(498\) 0 0
\(499\) −363.724 + 305.201i −0.728906 + 0.611624i −0.929833 0.367982i \(-0.880049\pi\)
0.200927 + 0.979606i \(0.435604\pi\)
\(500\) −216.777 258.344i −0.433553 0.516689i
\(501\) 0 0
\(502\) −432.223 + 157.316i −0.861002 + 0.313379i
\(503\) 696.911 402.362i 1.38551 0.799924i 0.392704 0.919665i \(-0.371540\pi\)
0.992805 + 0.119740i \(0.0382063\pi\)
\(504\) 0 0
\(505\) −377.907 + 654.554i −0.748331 + 1.29615i
\(506\) −30.7627 5.42429i −0.0607958 0.0107199i
\(507\) 0 0
\(508\) 434.865 + 158.278i 0.856033 + 0.311571i
\(509\) −924.707 + 163.051i −1.81671 + 0.320336i −0.975439 0.220272i \(-0.929306\pi\)
−0.841275 + 0.540607i \(0.818194\pi\)
\(510\) 0 0
\(511\) 569.702 + 478.036i 1.11488 + 0.935492i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 47.3102 0.0920431
\(515\) −113.025 + 134.698i −0.219466 + 0.261549i
\(516\) 0 0
\(517\) −11.7334 66.5434i −0.0226952 0.128711i
\(518\) −85.8396 + 235.842i −0.165713 + 0.455294i
\(519\) 0 0
\(520\) −36.6420 + 207.807i −0.0704654 + 0.399629i
\(521\) 832.809 + 480.823i 1.59848 + 0.922884i 0.991780 + 0.127955i \(0.0408414\pi\)
0.606703 + 0.794929i \(0.292492\pi\)
\(522\) 0 0
\(523\) −19.2517 33.3450i −0.0368102 0.0637572i 0.847033 0.531540i \(-0.178386\pi\)
−0.883844 + 0.467783i \(0.845053\pi\)
\(524\) −47.9842 131.836i −0.0915729 0.251595i
\(525\) 0 0
\(526\) 170.305 142.903i 0.323774 0.271679i
\(527\) 584.387 + 696.445i 1.10889 + 1.32153i
\(528\) 0 0
\(529\) −311.896 + 113.521i −0.589596 + 0.214595i
\(530\) 426.063 245.987i 0.803892 0.464127i
\(531\) 0 0
\(532\) 109.378 189.448i 0.205597 0.356105i
\(533\) −90.0441 15.8772i −0.168938 0.0297884i
\(534\) 0 0
\(535\) −172.312 62.7165i −0.322079 0.117227i
\(536\) −7.59995 + 1.34008i −0.0141790 + 0.00250014i
\(537\) 0 0
\(538\) 313.299 + 262.889i 0.582340 + 0.488641i
\(539\) 121.737i 0.225857i
\(540\) 0 0
\(541\) −16.4860 −0.0304731 −0.0152366 0.999884i \(-0.504850\pi\)
−0.0152366 + 0.999884i \(0.504850\pi\)
\(542\) 398.201 474.558i 0.734689 0.875568i
\(543\) 0 0
\(544\) 19.2678 + 109.273i 0.0354187 + 0.200869i
\(545\) 265.363 729.078i 0.486904 1.33776i
\(546\) 0 0
\(547\) 8.02809 45.5295i 0.0146766 0.0832350i −0.976590 0.215111i \(-0.930989\pi\)
0.991266 + 0.131876i \(0.0420999\pi\)
\(548\) 368.885 + 212.976i 0.673147 + 0.388642i
\(549\) 0 0
\(550\) 50.2141 + 86.9733i 0.0912983 + 0.158133i
\(551\) 36.5047 + 100.296i 0.0662517 + 0.182025i
\(552\) 0 0
\(553\) −436.302 + 366.101i −0.788972 + 0.662026i
\(554\) −15.4638 18.4290i −0.0279130 0.0332654i
\(555\) 0 0
\(556\) 106.043 38.5964i 0.190724 0.0694179i
\(557\) −62.2086 + 35.9161i −0.111685 + 0.0644814i −0.554802 0.831982i \(-0.687206\pi\)
0.443117 + 0.896464i \(0.353873\pi\)
\(558\) 0 0
\(559\) −116.702 + 202.133i −0.208769 + 0.361598i
\(560\) 370.857 + 65.3921i 0.662245 + 0.116772i
\(561\) 0 0
\(562\) −121.947 44.3852i −0.216988 0.0789772i
\(563\) 342.983 60.4772i 0.609206 0.107420i 0.139470 0.990226i \(-0.455460\pi\)
0.469736 + 0.882807i \(0.344349\pi\)
\(564\) 0 0
\(565\) 993.784 + 833.884i 1.75891 + 1.47590i
\(566\) 619.198i 1.09399i
\(567\) 0 0
\(568\) 212.722 0.374510
\(569\) −218.985 + 260.976i −0.384859 + 0.458657i −0.923342 0.383980i \(-0.874553\pi\)
0.538483 + 0.842637i \(0.318998\pi\)
\(570\) 0 0
\(571\) −93.4096 529.752i −0.163589 0.927762i −0.950507 0.310704i \(-0.899435\pi\)
0.786917 0.617058i \(-0.211676\pi\)
\(572\) 9.58754 26.3415i 0.0167614 0.0460516i
\(573\) 0 0
\(574\) −28.3348 + 160.695i −0.0493638 + 0.279956i
\(575\) −548.746 316.819i −0.954341 0.550989i
\(576\) 0 0
\(577\) −146.659 254.021i −0.254175 0.440244i 0.710496 0.703701i \(-0.248471\pi\)
−0.964671 + 0.263457i \(0.915137\pi\)
\(578\) −46.3103 127.237i −0.0801216 0.220132i
\(579\) 0 0
\(580\) −140.750 + 118.103i −0.242672 + 0.203626i
\(581\) −241.371 287.655i −0.415441 0.495103i
\(582\) 0 0
\(583\) −61.4151 + 22.3533i −0.105343 + 0.0383418i
\(584\) −162.047 + 93.5578i −0.277478 + 0.160202i
\(585\) 0 0
\(586\) −182.911 + 316.811i −0.312135 + 0.540634i
\(587\) −462.413 81.5359i −0.787757 0.138903i −0.234724 0.972062i \(-0.575419\pi\)
−0.553033 + 0.833159i \(0.686530\pi\)
\(588\) 0 0
\(589\) 423.773 + 154.241i 0.719479 + 0.261869i
\(590\) −705.877 + 124.465i −1.19640 + 0.210958i
\(591\) 0 0
\(592\) −48.3734 40.5901i −0.0817118 0.0685643i
\(593\) 880.585i 1.48497i −0.669864 0.742483i \(-0.733648\pi\)
0.669864 0.742483i \(-0.266352\pi\)
\(594\) 0 0
\(595\) −1846.64 −3.10359
\(596\) −37.0322 + 44.1332i −0.0621345 + 0.0740490i
\(597\) 0 0
\(598\) 30.7122 + 174.178i 0.0513582 + 0.291267i
\(599\) −117.916 + 323.972i −0.196855 + 0.540855i −0.998367 0.0571238i \(-0.981807\pi\)
0.801512 + 0.597979i \(0.204029\pi\)
\(600\) 0 0
\(601\) 108.241 613.865i 0.180102 1.02141i −0.751987 0.659177i \(-0.770905\pi\)
0.932089 0.362229i \(-0.117984\pi\)
\(602\) 360.732 + 208.269i 0.599223 + 0.345961i
\(603\) 0 0
\(604\) 154.786 + 268.098i 0.256269 + 0.443870i
\(605\) 339.490 + 932.741i 0.561140 + 1.54172i
\(606\) 0 0
\(607\) 725.795 609.015i 1.19571 1.00332i 0.195967 0.980610i \(-0.437215\pi\)
0.999742 0.0227086i \(-0.00722899\pi\)
\(608\) 35.3788 + 42.1628i 0.0581888 + 0.0693467i
\(609\) 0 0
\(610\) 851.987 310.098i 1.39670 0.508358i
\(611\) −331.324 + 191.290i −0.542265 + 0.313077i
\(612\) 0 0
\(613\) 352.677 610.854i 0.575329 0.996499i −0.420677 0.907211i \(-0.638207\pi\)
0.996006 0.0892887i \(-0.0284594\pi\)
\(614\) 296.919 + 52.3549i 0.483582 + 0.0852685i
\(615\) 0 0
\(616\) −47.0097 17.1101i −0.0763145 0.0277762i
\(617\) 876.465 154.544i 1.42053 0.250477i 0.589976 0.807421i \(-0.299137\pi\)
0.830550 + 0.556943i \(0.188026\pi\)
\(618\) 0 0
\(619\) −376.539 315.954i −0.608303 0.510426i 0.285800 0.958289i \(-0.407741\pi\)
−0.894102 + 0.447863i \(0.852185\pi\)
\(620\) 776.326i 1.25214i
\(621\) 0 0
\(622\) −659.851 −1.06085
\(623\) −628.186 + 748.643i −1.00832 + 1.20167i
\(624\) 0 0
\(625\) 49.2783 + 279.471i 0.0788452 + 0.447154i
\(626\) −45.6622 + 125.456i −0.0729428 + 0.200409i
\(627\) 0 0
\(628\) −74.2551 + 421.121i −0.118241 + 0.670575i
\(629\) 268.169 + 154.828i 0.426342 + 0.246149i
\(630\) 0 0
\(631\) 14.7611 + 25.5670i 0.0233932 + 0.0405183i 0.877485 0.479604i \(-0.159220\pi\)
−0.854092 + 0.520122i \(0.825886\pi\)
\(632\) −49.0119 134.659i −0.0775504 0.213068i
\(633\) 0 0
\(634\) 276.106 231.680i 0.435498 0.365426i
\(635\) −1245.58 1484.43i −1.96155 2.33768i
\(636\) 0 0
\(637\) 647.704 235.745i 1.01680 0.370086i
\(638\) 21.1383 12.2042i 0.0331322 0.0191289i
\(639\) 0 0
\(640\) −47.3742 + 82.0545i −0.0740222 + 0.128210i
\(641\) 94.3541 + 16.6372i 0.147198 + 0.0259550i 0.246762 0.969076i \(-0.420634\pi\)
−0.0995634 + 0.995031i \(0.531745\pi\)
\(642\) 0 0
\(643\) 537.766 + 195.731i 0.836339 + 0.304402i 0.724458 0.689319i \(-0.242090\pi\)
0.111881 + 0.993722i \(0.464313\pi\)
\(644\) 310.841 54.8097i 0.482673 0.0851083i
\(645\) 0 0
\(646\) −206.755 173.488i −0.320054 0.268557i
\(647\) 419.943i 0.649061i 0.945875 + 0.324531i \(0.105206\pi\)
−0.945875 + 0.324531i \(0.894794\pi\)
\(648\) 0 0
\(649\) 95.2192 0.146717
\(650\) 365.503 435.590i 0.562313 0.670138i
\(651\) 0 0
\(652\) −51.1225 289.930i −0.0784087 0.444678i
\(653\) 425.980 1170.37i 0.652343 1.79230i 0.0434334 0.999056i \(-0.486170\pi\)
0.608909 0.793240i \(-0.291607\pi\)
\(654\) 0 0
\(655\) −102.013 + 578.542i −0.155744 + 0.883270i
\(656\) −35.5547 20.5275i −0.0541993 0.0312920i
\(657\) 0 0
\(658\) 341.380 + 591.288i 0.518815 + 0.898614i
\(659\) −159.051 436.990i −0.241353 0.663111i −0.999934 0.0115322i \(-0.996329\pi\)
0.758581 0.651579i \(-0.225893\pi\)
\(660\) 0 0
\(661\) −250.507 + 210.201i −0.378982 + 0.318004i −0.812303 0.583236i \(-0.801786\pi\)
0.433320 + 0.901240i \(0.357342\pi\)
\(662\) 334.955 + 399.184i 0.505974 + 0.602996i
\(663\) 0 0
\(664\) 88.7810 32.3137i 0.133706 0.0486651i
\(665\) −793.280 + 458.000i −1.19290 + 0.688722i
\(666\) 0 0
\(667\) −77.0009 + 133.369i −0.115444 + 0.199954i
\(668\) −291.076 51.3245i −0.435742 0.0768332i
\(669\) 0 0
\(670\) 30.3656 + 11.0522i 0.0453218 + 0.0164958i
\(671\) −118.617 + 20.9153i −0.176776 + 0.0311704i
\(672\) 0 0
\(673\) −221.219 185.625i −0.328706 0.275817i 0.463466 0.886115i \(-0.346605\pi\)
−0.792172 + 0.610297i \(0.791050\pi\)
\(674\) 278.521i 0.413235i
\(675\) 0 0
\(676\) 179.283 0.265211
\(677\) −110.656 + 131.875i −0.163450 + 0.194793i −0.841553 0.540175i \(-0.818358\pi\)
0.678102 + 0.734967i \(0.262803\pi\)
\(678\) 0 0
\(679\) 275.113 + 1560.24i 0.405174 + 2.29786i
\(680\) 158.909 436.600i 0.233690 0.642059i
\(681\) 0 0
\(682\) 17.9086 101.565i 0.0262589 0.148922i
\(683\) 113.042 + 65.2651i 0.165509 + 0.0955565i 0.580466 0.814284i \(-0.302870\pi\)
−0.414958 + 0.909841i \(0.636204\pi\)
\(684\) 0 0
\(685\) −891.799 1544.64i −1.30190 2.25495i
\(686\) −154.281 423.883i −0.224899 0.617905i
\(687\) 0 0
\(688\) −80.2832 + 67.3656i −0.116691 + 0.0979151i
\(689\) 237.862 + 283.473i 0.345228 + 0.411427i
\(690\) 0 0
\(691\) −259.558 + 94.4713i −0.375626 + 0.136717i −0.522932 0.852374i \(-0.675162\pi\)
0.147306 + 0.989091i \(0.452940\pi\)
\(692\) −365.801 + 211.195i −0.528614 + 0.305196i
\(693\) 0 0
\(694\) 189.321 327.914i 0.272797 0.472498i
\(695\) −465.354 82.0544i −0.669574 0.118064i
\(696\) 0 0
\(697\) 189.181 + 68.8564i 0.271422 + 0.0987897i
\(698\) −719.573 + 126.880i −1.03091 + 0.181777i
\(699\) 0 0
\(700\) −777.364 652.286i −1.11052 0.931837i
\(701\) 865.652i 1.23488i −0.786617 0.617441i \(-0.788170\pi\)
0.786617 0.617441i \(-0.211830\pi\)
\(702\) 0 0
\(703\) 153.601 0.218493
\(704\) 8.09070 9.64212i 0.0114925 0.0136962i
\(705\) 0 0
\(706\) −71.2123 403.865i −0.100867 0.572047i
\(707\) −346.999 + 953.372i −0.490805 + 1.34847i
\(708\) 0 0
\(709\) −19.7944 + 112.259i −0.0279187 + 0.158335i −0.995580 0.0939188i \(-0.970061\pi\)
0.967661 + 0.252254i \(0.0811717\pi\)
\(710\) −771.399 445.367i −1.08648 0.627278i
\(711\) 0 0
\(712\) −122.944 212.945i −0.172674 0.299081i
\(713\) 222.550 + 611.451i 0.312132 + 0.857575i
\(714\) 0 0
\(715\) −89.9179 + 75.4501i −0.125759 + 0.105525i
\(716\) −334.199 398.283i −0.466758 0.556261i
\(717\) 0 0
\(718\) −54.9523 + 20.0010i −0.0765353 + 0.0278566i
\(719\) 117.571 67.8798i 0.163521 0.0944086i −0.416006 0.909362i \(-0.636571\pi\)
0.579527 + 0.814953i \(0.303237\pi\)
\(720\) 0 0
\(721\) −118.015 + 204.408i −0.163683 + 0.283507i
\(722\) 370.929 + 65.4048i 0.513752 + 0.0905883i
\(723\) 0 0
\(724\) −600.270 218.480i −0.829102 0.301768i
\(725\) 487.596 85.9763i 0.672546 0.118588i
\(726\) 0 0
\(727\) 76.0522 + 63.8154i 0.104611 + 0.0877790i 0.693593 0.720367i \(-0.256027\pi\)
−0.588982 + 0.808146i \(0.700471\pi\)
\(728\) 283.250i 0.389080i
\(729\) 0 0
\(730\) 783.514 1.07331
\(731\) 330.342 393.686i 0.451904 0.538559i
\(732\) 0 0
\(733\) −132.435 751.078i −0.180676 1.02466i −0.931387 0.364032i \(-0.881400\pi\)
0.750711 0.660631i \(-0.229711\pi\)
\(734\) 78.5192 215.730i 0.106974 0.293910i
\(735\) 0 0
\(736\) −13.7903 + 78.2088i −0.0187368 + 0.106262i
\(737\) −3.71769 2.14641i −0.00504436 0.00291236i
\(738\) 0 0
\(739\) 436.285 + 755.668i 0.590373 + 1.02256i 0.994182 + 0.107712i \(0.0343525\pi\)
−0.403810 + 0.914843i \(0.632314\pi\)
\(740\) 90.4359 + 248.471i 0.122211 + 0.335771i
\(741\) 0 0
\(742\) 505.893 424.494i 0.681796 0.572095i
\(743\) 515.245 + 614.045i 0.693466 + 0.826441i 0.991770 0.128030i \(-0.0408654\pi\)
−0.298304 + 0.954471i \(0.596421\pi\)
\(744\) 0 0
\(745\) 226.691 82.5088i 0.304283 0.110750i
\(746\) 82.9451 47.8884i 0.111186 0.0641935i
\(747\) 0 0
\(748\) −30.8613 + 53.4534i −0.0412584 + 0.0714617i
\(749\) −242.406 42.7427i −0.323639 0.0570663i
\(750\) 0 0
\(751\) −814.474 296.444i −1.08452 0.394733i −0.262931 0.964815i \(-0.584689\pi\)
−0.821588 + 0.570082i \(0.806911\pi\)
\(752\) −169.175 + 29.8301i −0.224967 + 0.0396677i
\(753\) 0 0
\(754\) −105.867 88.8333i −0.140408 0.117816i
\(755\) 1296.28i 1.71693i
\(756\) 0 0
\(757\) −305.290 −0.403289 −0.201644 0.979459i \(-0.564629\pi\)
−0.201644 + 0.979459i \(0.564629\pi\)
\(758\) 111.295 132.636i 0.146827 0.174981i
\(759\) 0 0
\(760\) −40.0205 226.968i −0.0526586 0.298642i
\(761\) −210.316 + 577.838i −0.276367 + 0.759313i 0.721399 + 0.692519i \(0.243499\pi\)
−0.997767 + 0.0667941i \(0.978723\pi\)
\(762\) 0 0
\(763\) 180.851 1025.65i 0.237026 1.34424i
\(764\) −67.4786 38.9588i −0.0883228 0.0509932i
\(765\) 0 0
\(766\) −42.7767 74.0914i −0.0558443 0.0967251i
\(767\) −184.393 506.616i −0.240408 0.660516i
\(768\) 0 0
\(769\) 105.505 88.5291i 0.137198 0.115122i −0.571606 0.820528i \(-0.693680\pi\)
0.708804 + 0.705406i \(0.249235\pi\)
\(770\) 134.650 + 160.470i 0.174870 + 0.208402i
\(771\) 0 0
\(772\) −307.112 + 111.780i −0.397813 + 0.144792i
\(773\) 154.674 89.3010i 0.200096 0.115525i −0.396604 0.917990i \(-0.629812\pi\)
0.596700 + 0.802464i \(0.296478\pi\)
\(774\) 0 0
\(775\) 1045.99 1811.71i 1.34967 2.33769i
\(776\) −392.563 69.2194i −0.505880 0.0892003i
\(777\) 0 0
\(778\) 319.818 + 116.404i 0.411077 + 0.149620i
\(779\) 98.3465 17.3411i 0.126247 0.0222608i
\(780\) 0 0
\(781\) 90.6461 + 76.0611i 0.116064 + 0.0973894i
\(782\) 389.430i 0.497993i
\(783\) 0 0
\(784\) 309.495 0.394764
\(785\) 1150.96 1371.66i 1.46619 1.74734i
\(786\) 0 0
\(787\) −108.344 614.451i −0.137668 0.780752i −0.972965 0.230953i \(-0.925816\pi\)
0.835297 0.549798i \(-0.185295\pi\)
\(788\) −234.443 + 644.127i −0.297516 + 0.817420i
\(789\) 0 0
\(790\) −104.197 + 590.932i −0.131895 + 0.748016i
\(791\) 1508.10 + 870.702i 1.90658 + 1.10076i
\(792\) 0 0
\(793\) 340.983 + 590.599i 0.429991 + 0.744766i
\(794\) −13.8771 38.1271i −0.0174775 0.0480190i
\(795\) 0 0
\(796\) 302.928 254.187i 0.380563 0.319330i
\(797\) 487.894 + 581.449i 0.612163 + 0.729547i 0.979702 0.200461i \(-0.0642440\pi\)
−0.367539 + 0.930008i \(0.619800\pi\)
\(798\) 0 0
\(799\) 791.584 288.113i 0.990718 0.360592i
\(800\) 221.115 127.661i 0.276393 0.159576i
\(801\) 0 0
\(802\) −500.481 + 866.859i −0.624042 + 1.08087i
\(803\) −102.505 18.0744i −0.127653 0.0225086i
\(804\) 0 0
\(805\) −1241.97 452.039i −1.54282 0.561539i
\(806\) −575.056 + 101.398i −0.713469 + 0.125804i
\(807\) 0 0
\(808\) −195.545 164.082i −0.242011 0.203072i
\(809\) 1035.21i 1.27961i −0.768537 0.639805i \(-0.779015\pi\)
0.768537 0.639805i \(-0.220985\pi\)
\(810\) 0 0
\(811\) 1435.70 1.77029 0.885144 0.465318i \(-0.154060\pi\)
0.885144 + 0.465318i \(0.154060\pi\)
\(812\) −158.534 + 188.934i −0.195239 + 0.232677i
\(813\) 0 0
\(814\) −6.09967 34.5929i −0.00749345 0.0424975i
\(815\) −421.629 + 1158.42i −0.517336 + 1.42137i
\(816\) 0 0
\(817\) 44.2671 251.051i 0.0541825 0.307284i
\(818\) −96.3897 55.6506i −0.117836 0.0680325i
\(819\) 0 0
\(820\) 85.9555 + 148.879i 0.104824 + 0.181560i
\(821\) 2.84183 + 7.80786i 0.00346142 + 0.00951018i 0.941411 0.337261i \(-0.109500\pi\)
−0.937950 + 0.346771i \(0.887278\pi\)
\(822\) 0 0
\(823\) −518.097 + 434.735i −0.629522 + 0.528232i −0.900781 0.434275i \(-0.857005\pi\)
0.271258 + 0.962507i \(0.412560\pi\)
\(824\) −38.1726 45.4924i −0.0463260 0.0552092i
\(825\) 0 0
\(826\) −904.118 + 329.072i −1.09457 + 0.398392i
\(827\) −1123.27 + 648.518i −1.35824 + 0.784181i −0.989387 0.145305i \(-0.953584\pi\)
−0.368855 + 0.929487i \(0.620250\pi\)
\(828\) 0 0
\(829\) −367.050 + 635.750i −0.442763 + 0.766888i −0.997893 0.0648754i \(-0.979335\pi\)
0.555130 + 0.831763i \(0.312668\pi\)
\(830\) −389.603 68.6976i −0.469402 0.0827682i
\(831\) 0 0
\(832\) −66.9688 24.3747i −0.0804914 0.0292965i
\(833\) −1494.62 + 263.542i −1.79426 + 0.316377i
\(834\) 0 0
\(835\) 948.082 + 795.535i 1.13543 + 0.952737i
\(836\) 30.6167i 0.0366229i
\(837\) 0 0
\(838\) −74.5731 −0.0889894
\(839\) −447.625 + 533.458i −0.533522 + 0.635826i −0.963722 0.266907i \(-0.913998\pi\)
0.430201 + 0.902733i \(0.358443\pi\)
\(840\) 0 0
\(841\) 125.142 + 709.716i 0.148802 + 0.843896i
\(842\) 342.103 939.920i 0.406298 1.11629i
\(843\) 0 0
\(844\) −79.3201 + 449.846i −0.0939811 + 0.532993i
\(845\) −650.139 375.358i −0.769396 0.444211i
\(846\) 0 0
\(847\) 666.203 + 1153.90i 0.786544 + 1.36233i
\(848\) 56.8293 + 156.137i 0.0670157 + 0.184124i
\(849\) 0 0
\(850\) −959.106 + 804.786i −1.12836 + 0.946807i
\(851\) 142.459 + 169.776i 0.167401 + 0.199501i
\(852\) 0 0
\(853\) −1214.78 + 442.144i −1.42413 + 0.518340i −0.935242 0.354009i \(-0.884818\pi\)
−0.488885 + 0.872348i \(0.662596\pi\)
\(854\) 1054.00 608.526i 1.23419 0.712559i
\(855\) 0 0
\(856\) 30.9655 53.6338i 0.0361747 0.0626564i
\(857\) 169.817 + 29.9433i 0.198153 + 0.0349397i 0.271844 0.962341i \(-0.412367\pi\)
−0.0736908 + 0.997281i \(0.523478\pi\)
\(858\) 0 0
\(859\) 602.703 + 219.366i 0.701633 + 0.255373i 0.668108 0.744064i \(-0.267104\pi\)
0.0335249 + 0.999438i \(0.489327\pi\)
\(860\) 432.174 76.2040i 0.502528 0.0886093i
\(861\) 0 0
\(862\) −302.557 253.875i −0.350994 0.294519i
\(863\) 222.895i 0.258280i −0.991626 0.129140i \(-0.958778\pi\)
0.991626 0.129140i \(-0.0412216\pi\)
\(864\) 0 0
\(865\) 1768.69 2.04473
\(866\) 91.6638 109.241i 0.105847 0.126144i
\(867\) 0 0
\(868\) 180.957 + 1026.26i 0.208476 + 1.18233i
\(869\) 27.2637 74.9064i 0.0313736 0.0861984i
\(870\) 0 0
\(871\) −4.22067 + 23.9366i −0.00484578 + 0.0274818i
\(872\) 226.933 + 131.020i 0.260244 + 0.150252i
\(873\) 0 0
\(874\) −96.5861 167.292i −0.110510 0.191410i
\(875\) 648.328 + 1781.27i 0.740947 + 2.03573i
\(876\) 0 0
\(877\) 685.259 575.001i 0.781368 0.655645i −0.162225 0.986754i \(-0.551867\pi\)
0.943593 + 0.331108i \(0.107423\pi\)
\(878\) −90.5035 107.858i −0.103079 0.122845i
\(879\) 0 0
\(880\) −49.5269 + 18.0263i −0.0562806 + 0.0204845i
\(881\) −600.708 + 346.819i −0.681847 + 0.393665i −0.800551 0.599265i \(-0.795460\pi\)
0.118703 + 0.992930i \(0.462126\pi\)
\(882\) 0 0
\(883\) −357.452 + 619.125i −0.404815 + 0.701161i −0.994300 0.106619i \(-0.965998\pi\)
0.589485 + 0.807780i \(0.299331\pi\)
\(884\) 344.163 + 60.6852i 0.389325 + 0.0686484i
\(885\) 0 0
\(886\) −455.696 165.860i −0.514330 0.187201i
\(887\) 1637.53 288.740i 1.84614 0.325524i 0.862553 0.505966i \(-0.168864\pi\)
0.983586 + 0.180442i \(0.0577529\pi\)
\(888\) 0 0
\(889\) −1992.60 1671.99i −2.24140 1.88076i
\(890\) 1029.61i 1.15687i
\(891\) 0 0
\(892\) −772.361 −0.865876
\(893\) 268.592 320.095i 0.300775 0.358450i
\(894\) 0 0
\(895\) 378.046 + 2144.01i 0.422398 + 2.39554i
\(896\) −43.4996 + 119.514i −0.0485486 + 0.133386i
\(897\) 0 0
\(898\) 122.872 696.840i 0.136828 0.775992i
\(899\) −440.326 254.222i −0.489795 0.282783i
\(900\) 0 0
\(901\) −407.396 705.631i −0.452160 0.783164i
\(902\) −7.81092 21.4603i −0.00865955 0.0237919i
\(903\) 0 0
\(904\) −335.637 + 281.633i −0.371280 + 0.311541i
\(905\) 1719.35 + 2049.04i 1.89984 + 2.26414i
\(906\) 0 0
\(907\) 22.6374 8.23933i 0.0249585 0.00908416i −0.329511 0.944152i \(-0.606884\pi\)
0.354469 + 0.935068i \(0.384662\pi\)
\(908\) 322.484 186.186i 0.355159 0.205051i
\(909\) 0 0
\(910\) 593.031 1027.16i 0.651682 1.12875i
\(911\) 324.675 + 57.2490i 0.356394 + 0.0628419i 0.348979 0.937131i \(-0.386528\pi\)
0.00741541 + 0.999973i \(0.497640\pi\)
\(912\) 0 0
\(913\) 49.3860 + 17.9750i 0.0540920 + 0.0196879i
\(914\) 160.287 28.2630i 0.175369 0.0309223i
\(915\) 0 0
\(916\) 473.412 + 397.240i 0.516826 + 0.433668i
\(917\) 788.579i 0.859955i
\(918\) 0 0
\(919\) −174.813 −0.190220 −0.0951102 0.995467i \(-0.530320\pi\)
−0.0951102 + 0.995467i \(0.530320\pi\)
\(920\) 213.751 254.739i 0.232338 0.276890i
\(921\) 0 0
\(922\) 142.111 + 805.951i 0.154133 + 0.874134i
\(923\) 229.148 629.578i 0.248264 0.682099i
\(924\) 0 0
\(925\) 123.730 701.707i 0.133762 0.758602i
\(926\) −976.040 563.517i −1.05404 0.608550i
\(927\) 0 0
\(928\) −31.0271 53.7406i −0.0334344 0.0579101i
\(929\) 46.7382 + 128.412i 0.0503102 + 0.138226i 0.962303 0.271981i \(-0.0876787\pi\)
−0.911992 + 0.410207i \(0.865456\pi\)
\(930\) 0 0
\(931\) −576.698 + 483.907i −0.619439 + 0.519771i
\(932\) −26.4360 31.5051i −0.0283648 0.0338038i
\(933\) 0 0
\(934\) −359.943 + 131.008i −0.385378 + 0.140266i
\(935\) 223.827 129.226i 0.239387 0.138210i
\(936\) 0 0
\(937\) −288.732 + 500.099i −0.308145 + 0.533723i −0.977957 0.208808i \(-0.933042\pi\)
0.669811 + 0.742531i \(0.266375\pi\)
\(938\) 42.7179 + 7.53231i 0.0455414 + 0.00803018i
\(939\) 0 0
\(940\) 675.939 + 246.022i 0.719085 + 0.261725i
\(941\) 1294.60 228.273i 1.37577 0.242585i 0.563620 0.826034i \(-0.309408\pi\)
0.812150 + 0.583449i \(0.198297\pi\)
\(942\) 0 0
\(943\) 110.380 + 92.6197i 0.117052 + 0.0982181i
\(944\) 242.078i 0.256439i
\(945\) 0 0
\(946\) −58.2981 −0.0616259
\(947\) 395.028 470.776i 0.417136 0.497123i −0.516029 0.856571i \(-0.672590\pi\)
0.933165 + 0.359448i \(0.117035\pi\)
\(948\) 0 0
\(949\) 102.337 + 580.381i 0.107837 + 0.611571i
\(950\) −212.412 + 583.597i −0.223592 + 0.614313i
\(951\) 0 0
\(952\) 108.300 614.201i 0.113761 0.645169i
\(953\) −684.011 394.914i −0.717745 0.414391i 0.0961768 0.995364i \(-0.469339\pi\)
−0.813922 + 0.580974i \(0.802672\pi\)
\(954\) 0 0
\(955\) 163.133 + 282.555i 0.170820 + 0.295869i
\(956\) −70.2540 193.021i −0.0734874 0.201905i
\(957\) 0 0
\(958\) 864.421 725.335i 0.902318 0.757135i
\(959\) −1538.96 1834.06i −1.60475 1.91247i
\(960\) 0 0
\(961\) −1115.69 + 406.079i −1.16097 + 0.422559i
\(962\) −172.240 + 99.4430i −0.179044 + 0.103371i
\(963\) 0 0
\(964\) 384.229 665.505i 0.398578 0.690358i
\(965\) 1347.72 + 237.639i 1.39660 + 0.246258i
\(966\) 0 0
\(967\) −1642.98 597.996i −1.69905 0.618403i −0.703333 0.710861i \(-0.748305\pi\)
−0.995717 + 0.0924577i \(0.970528\pi\)
\(968\) −330.145 + 58.2135i −0.341059 + 0.0601379i
\(969\) 0 0
\(970\) 1278.64 + 1072.91i 1.31819 + 1.10609i
\(971\) 1254.82i 1.29230i 0.763211 + 0.646149i \(0.223622\pi\)
−0.763211 + 0.646149i \(0.776378\pi\)
\(972\) 0 0
\(973\) −634.298 −0.651899
\(974\) −126.550 + 150.817i −0.129928 + 0.154843i
\(975\) 0 0
\(976\) 53.1736 + 301.562i 0.0544811 + 0.308978i
\(977\) −239.287 + 657.435i −0.244920 + 0.672912i 0.754934 + 0.655801i \(0.227669\pi\)
−0.999854 + 0.0171106i \(0.994553\pi\)
\(978\) 0 0
\(979\) 23.7515 134.702i 0.0242610 0.137591i
\(980\) −1122.33 647.978i −1.14524 0.661202i
\(981\) 0 0
\(982\) −152.178 263.580i −0.154968 0.268412i
\(983\) −129.688 356.315i −0.131931 0.362477i 0.856084 0.516837i \(-0.172891\pi\)
−0.988015 + 0.154360i \(0.950668\pi\)
\(984\) 0 0
\(985\) 2198.75 1844.97i 2.23224 1.87307i
\(986\) 195.598 + 233.105i 0.198376 + 0.236415i
\(987\) 0 0
\(988\) 162.897 59.2897i 0.164876 0.0600098i
\(989\) 318.545 183.912i 0.322088 0.185957i
\(990\) 0 0
\(991\) −298.374 + 516.798i −0.301083 + 0.521492i −0.976382 0.216053i \(-0.930682\pi\)
0.675298 + 0.737545i \(0.264015\pi\)
\(992\) −258.210 45.5294i −0.260293 0.0458966i
\(993\) 0 0
\(994\) −1123.56 408.942i −1.13034 0.411410i
\(995\) −1630.70 + 287.536i −1.63889 + 0.288981i
\(996\) 0 0
\(997\) 865.580 + 726.308i 0.868185 + 0.728494i 0.963715 0.266933i \(-0.0860102\pi\)
−0.0955301 + 0.995427i \(0.530455\pi\)
\(998\) 671.480i 0.672825i
\(999\) 0 0
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 162.3.f.a.35.4 36
3.2 odd 2 54.3.f.a.11.3 yes 36
12.11 even 2 432.3.bc.c.65.1 36
27.5 odd 18 inner 162.3.f.a.125.4 36
27.7 even 9 1458.3.b.c.1457.1 36
27.20 odd 18 1458.3.b.c.1457.36 36
27.22 even 9 54.3.f.a.5.3 36
108.103 odd 18 432.3.bc.c.113.1 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.f.a.5.3 36 27.22 even 9
54.3.f.a.11.3 yes 36 3.2 odd 2
162.3.f.a.35.4 36 1.1 even 1 trivial
162.3.f.a.125.4 36 27.5 odd 18 inner
432.3.bc.c.65.1 36 12.11 even 2
432.3.bc.c.113.1 36 108.103 odd 18
1458.3.b.c.1457.1 36 27.7 even 9
1458.3.b.c.1457.36 36 27.20 odd 18