Properties

Label 405.3.l.g.352.2
Level $405$
Weight $3$
Character 405.352
Analytic conductor $11.035$
Analytic rank $0$
Dimension $8$
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [405,3,Mod(28,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([4, 9]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.28");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 405.l (of order \(12\), 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: \(11.0354507066\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: 8.0.3317760000.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 25x^{4} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 352.2
Root \(-2.15988 - 0.578737i\) of defining polynomial
Character \(\chi\) \(=\) 405.352
Dual form 405.3.l.g.298.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.578737 - 2.15988i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-4.89849 - 1.00240i) q^{5} +(-1.83013 + 6.83013i) q^{7} +(4.74342 - 4.74342i) q^{8} +(-5.00000 + 10.0000i) q^{10} +(7.90569 + 13.6931i) q^{11} +(3.66025 + 13.6603i) q^{13} +(13.6931 + 7.90569i) q^{14} +(-9.50000 - 16.4545i) q^{16} +(-3.16228 - 3.16228i) q^{17} +18.0000i q^{19} +(3.74101 + 3.31735i) q^{20} +(34.1506 - 9.15064i) q^{22} +(-1.15747 - 4.31975i) q^{23} +(22.9904 + 9.82051i) q^{25} +31.6228 q^{26} +(5.00000 - 5.00000i) q^{28} +(41.0792 - 23.7171i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-15.1191 + 4.05116i) q^{32} +(-8.66025 + 5.00000i) q^{34} +(15.8114 - 31.6228i) q^{35} +(10.0000 + 10.0000i) q^{37} +(38.8778 + 10.4173i) q^{38} +(-27.9904 + 18.4808i) q^{40} +(-15.8114 + 27.3861i) q^{41} +(-13.6603 - 3.66025i) q^{43} -15.8114i q^{44} -10.0000 q^{46} +(-15.0472 + 56.1568i) q^{47} +(-0.866025 - 0.500000i) q^{49} +(34.5165 - 43.9729i) q^{50} +(3.66025 - 13.6603i) q^{52} +(25.2982 - 25.2982i) q^{53} +(-25.0000 - 75.0000i) q^{55} +(23.7171 + 41.0792i) q^{56} +(-27.4519 - 102.452i) q^{58} +(41.0792 + 23.7171i) q^{59} +(29.0000 + 50.2295i) q^{61} +(12.6491 + 12.6491i) q^{62} -41.0000i q^{64} +(-4.23665 - 70.5836i) q^{65} +(-95.6218 + 25.6218i) q^{67} +(1.15747 + 4.31975i) q^{68} +(-59.1506 - 52.4519i) q^{70} -63.2456 q^{71} +(55.0000 - 55.0000i) q^{73} +(27.3861 - 15.8114i) q^{74} +(9.00000 - 15.5885i) q^{76} +(-107.994 + 28.9368i) q^{77} +(10.3923 - 6.00000i) q^{79} +(30.0416 + 90.1249i) q^{80} +(50.0000 + 50.0000i) q^{82} +(-73.4358 - 19.6771i) q^{83} +(12.3205 + 18.6603i) q^{85} +(-15.8114 + 27.3861i) q^{86} +(102.452 + 27.4519i) q^{88} -100.000 q^{91} +(-1.15747 + 4.31975i) q^{92} +(112.583 + 65.0000i) q^{94} +(18.0432 - 88.1728i) q^{95} +(-1.83013 + 6.83013i) q^{97} +(-1.58114 + 1.58114i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 20 q^{7} - 40 q^{10} - 40 q^{13} - 76 q^{16} + 100 q^{22} + 80 q^{25} + 40 q^{28} - 32 q^{31} + 80 q^{37} - 120 q^{40} - 40 q^{43} - 80 q^{46} - 40 q^{52} - 200 q^{55} + 300 q^{58} + 232 q^{61} - 280 q^{67}+ \cdots + 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.578737 2.15988i 0.289368 1.07994i −0.656219 0.754570i \(-0.727845\pi\)
0.945588 0.325368i \(-0.105488\pi\)
\(3\) 0 0
\(4\) −0.866025 0.500000i −0.216506 0.125000i
\(5\) −4.89849 1.00240i −0.979698 0.200480i
\(6\) 0 0
\(7\) −1.83013 + 6.83013i −0.261447 + 0.975732i 0.702943 + 0.711246i \(0.251869\pi\)
−0.964390 + 0.264486i \(0.914798\pi\)
\(8\) 4.74342 4.74342i 0.592927 0.592927i
\(9\) 0 0
\(10\) −5.00000 + 10.0000i −0.500000 + 1.00000i
\(11\) 7.90569 + 13.6931i 0.718699 + 1.24482i 0.961515 + 0.274752i \(0.0885956\pi\)
−0.242816 + 0.970072i \(0.578071\pi\)
\(12\) 0 0
\(13\) 3.66025 + 13.6603i 0.281558 + 1.05079i 0.951318 + 0.308211i \(0.0997303\pi\)
−0.669760 + 0.742578i \(0.733603\pi\)
\(14\) 13.6931 + 7.90569i 0.978076 + 0.564692i
\(15\) 0 0
\(16\) −9.50000 16.4545i −0.593750 1.02841i
\(17\) −3.16228 3.16228i −0.186016 0.186016i 0.607955 0.793971i \(-0.291990\pi\)
−0.793971 + 0.607955i \(0.791990\pi\)
\(18\) 0 0
\(19\) 18.0000i 0.947368i 0.880695 + 0.473684i \(0.157076\pi\)
−0.880695 + 0.473684i \(0.842924\pi\)
\(20\) 3.74101 + 3.31735i 0.187051 + 0.165867i
\(21\) 0 0
\(22\) 34.1506 9.15064i 1.55230 0.415938i
\(23\) −1.15747 4.31975i −0.0503250 0.187815i 0.936188 0.351501i \(-0.114328\pi\)
−0.986513 + 0.163685i \(0.947662\pi\)
\(24\) 0 0
\(25\) 22.9904 + 9.82051i 0.919615 + 0.392820i
\(26\) 31.6228 1.21626
\(27\) 0 0
\(28\) 5.00000 5.00000i 0.178571 0.178571i
\(29\) 41.0792 23.7171i 1.41652 0.817830i 0.420532 0.907278i \(-0.361843\pi\)
0.995992 + 0.0894471i \(0.0285100\pi\)
\(30\) 0 0
\(31\) −4.00000 + 6.92820i −0.129032 + 0.223490i −0.923302 0.384075i \(-0.874520\pi\)
0.794270 + 0.607565i \(0.207854\pi\)
\(32\) −15.1191 + 4.05116i −0.472473 + 0.126599i
\(33\) 0 0
\(34\) −8.66025 + 5.00000i −0.254713 + 0.147059i
\(35\) 15.8114 31.6228i 0.451754 0.903508i
\(36\) 0 0
\(37\) 10.0000 + 10.0000i 0.270270 + 0.270270i 0.829209 0.558939i \(-0.188791\pi\)
−0.558939 + 0.829209i \(0.688791\pi\)
\(38\) 38.8778 + 10.4173i 1.02310 + 0.274139i
\(39\) 0 0
\(40\) −27.9904 + 18.4808i −0.699760 + 0.462019i
\(41\) −15.8114 + 27.3861i −0.385644 + 0.667954i −0.991858 0.127347i \(-0.959354\pi\)
0.606215 + 0.795301i \(0.292687\pi\)
\(42\) 0 0
\(43\) −13.6603 3.66025i −0.317680 0.0851222i 0.0964555 0.995337i \(-0.469249\pi\)
−0.414136 + 0.910215i \(0.635916\pi\)
\(44\) 15.8114i 0.359350i
\(45\) 0 0
\(46\) −10.0000 −0.217391
\(47\) −15.0472 + 56.1568i −0.320152 + 1.19482i 0.598944 + 0.800791i \(0.295587\pi\)
−0.919096 + 0.394034i \(0.871079\pi\)
\(48\) 0 0
\(49\) −0.866025 0.500000i −0.0176740 0.0102041i
\(50\) 34.5165 43.9729i 0.690329 0.879458i
\(51\) 0 0
\(52\) 3.66025 13.6603i 0.0703895 0.262697i
\(53\) 25.2982 25.2982i 0.477325 0.477325i −0.426950 0.904275i \(-0.640412\pi\)
0.904275 + 0.426950i \(0.140412\pi\)
\(54\) 0 0
\(55\) −25.0000 75.0000i −0.454545 1.36364i
\(56\) 23.7171 + 41.0792i 0.423519 + 0.733557i
\(57\) 0 0
\(58\) −27.4519 102.452i −0.473309 1.76641i
\(59\) 41.0792 + 23.7171i 0.696257 + 0.401984i 0.805952 0.591981i \(-0.201654\pi\)
−0.109695 + 0.993965i \(0.534987\pi\)
\(60\) 0 0
\(61\) 29.0000 + 50.2295i 0.475410 + 0.823434i 0.999603 0.0281652i \(-0.00896646\pi\)
−0.524193 + 0.851599i \(0.675633\pi\)
\(62\) 12.6491 + 12.6491i 0.204018 + 0.204018i
\(63\) 0 0
\(64\) 41.0000i 0.640625i
\(65\) −4.23665 70.5836i −0.0651792 1.08590i
\(66\) 0 0
\(67\) −95.6218 + 25.6218i −1.42719 + 0.382415i −0.888029 0.459788i \(-0.847926\pi\)
−0.539162 + 0.842202i \(0.681259\pi\)
\(68\) 1.15747 + 4.31975i 0.0170217 + 0.0635258i
\(69\) 0 0
\(70\) −59.1506 52.4519i −0.845009 0.749313i
\(71\) −63.2456 −0.890782 −0.445391 0.895336i \(-0.646935\pi\)
−0.445391 + 0.895336i \(0.646935\pi\)
\(72\) 0 0
\(73\) 55.0000 55.0000i 0.753425 0.753425i −0.221692 0.975117i \(-0.571158\pi\)
0.975117 + 0.221692i \(0.0711580\pi\)
\(74\) 27.3861 15.8114i 0.370083 0.213667i
\(75\) 0 0
\(76\) 9.00000 15.5885i 0.118421 0.205111i
\(77\) −107.994 + 28.9368i −1.40252 + 0.375803i
\(78\) 0 0
\(79\) 10.3923 6.00000i 0.131548 0.0759494i −0.432782 0.901499i \(-0.642468\pi\)
0.564330 + 0.825549i \(0.309135\pi\)
\(80\) 30.0416 + 90.1249i 0.375520 + 1.12656i
\(81\) 0 0
\(82\) 50.0000 + 50.0000i 0.609756 + 0.609756i
\(83\) −73.4358 19.6771i −0.884768 0.237073i −0.212305 0.977203i \(-0.568097\pi\)
−0.672463 + 0.740130i \(0.734764\pi\)
\(84\) 0 0
\(85\) 12.3205 + 18.6603i 0.144947 + 0.219532i
\(86\) −15.8114 + 27.3861i −0.183853 + 0.318443i
\(87\) 0 0
\(88\) 102.452 + 27.4519i 1.16423 + 0.311953i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −100.000 −1.09890
\(92\) −1.15747 + 4.31975i −0.0125812 + 0.0469538i
\(93\) 0 0
\(94\) 112.583 + 65.0000i 1.19769 + 0.691489i
\(95\) 18.0432 88.1728i 0.189929 0.928135i
\(96\) 0 0
\(97\) −1.83013 + 6.83013i −0.0188673 + 0.0704137i −0.974718 0.223440i \(-0.928271\pi\)
0.955850 + 0.293854i \(0.0949379\pi\)
\(98\) −1.58114 + 1.58114i −0.0161341 + 0.0161341i
\(99\) 0 0
\(100\) −15.0000 20.0000i −0.150000 0.200000i
\(101\) 7.90569 + 13.6931i 0.0782742 + 0.135575i 0.902505 0.430678i \(-0.141726\pi\)
−0.824231 + 0.566253i \(0.808392\pi\)
\(102\) 0 0
\(103\) −12.8109 47.8109i −0.124378 0.464183i 0.875439 0.483328i \(-0.160572\pi\)
−0.999817 + 0.0191450i \(0.993906\pi\)
\(104\) 82.1584 + 47.4342i 0.789984 + 0.456098i
\(105\) 0 0
\(106\) −40.0000 69.2820i −0.377358 0.653604i
\(107\) −60.0833 60.0833i −0.561526 0.561526i 0.368215 0.929741i \(-0.379969\pi\)
−0.929741 + 0.368215i \(0.879969\pi\)
\(108\) 0 0
\(109\) 162.000i 1.48624i 0.669159 + 0.743119i \(0.266655\pi\)
−0.669159 + 0.743119i \(0.733345\pi\)
\(110\) −176.459 + 10.5916i −1.60417 + 0.0962875i
\(111\) 0 0
\(112\) 129.772 34.7724i 1.15868 0.310468i
\(113\) −42.8265 159.831i −0.378996 1.41443i −0.847418 0.530927i \(-0.821844\pi\)
0.468422 0.883505i \(-0.344823\pi\)
\(114\) 0 0
\(115\) 1.33975 + 22.3205i 0.0116500 + 0.194091i
\(116\) −47.4342 −0.408915
\(117\) 0 0
\(118\) 75.0000 75.0000i 0.635593 0.635593i
\(119\) 27.3861 15.8114i 0.230136 0.132869i
\(120\) 0 0
\(121\) −64.5000 + 111.717i −0.533058 + 0.923283i
\(122\) 125.273 33.5667i 1.02683 0.275137i
\(123\) 0 0
\(124\) 6.92820 4.00000i 0.0558726 0.0322581i
\(125\) −102.774 71.1512i −0.822192 0.569210i
\(126\) 0 0
\(127\) 55.0000 + 55.0000i 0.433071 + 0.433071i 0.889672 0.456601i \(-0.150933\pi\)
−0.456601 + 0.889672i \(0.650933\pi\)
\(128\) −149.031 39.9329i −1.16431 0.311975i
\(129\) 0 0
\(130\) −154.904 31.6987i −1.19157 0.243836i
\(131\) −86.9626 + 150.624i −0.663837 + 1.14980i 0.315762 + 0.948838i \(0.397740\pi\)
−0.979599 + 0.200961i \(0.935594\pi\)
\(132\) 0 0
\(133\) −122.942 32.9423i −0.924378 0.247686i
\(134\) 221.359i 1.65194i
\(135\) 0 0
\(136\) −30.0000 −0.220588
\(137\) 5.78737 21.5988i 0.0422436 0.157655i −0.941582 0.336783i \(-0.890661\pi\)
0.983826 + 0.179128i \(0.0573277\pi\)
\(138\) 0 0
\(139\) 88.3346 + 51.0000i 0.635501 + 0.366906i 0.782879 0.622174i \(-0.213750\pi\)
−0.147379 + 0.989080i \(0.547084\pi\)
\(140\) −29.5045 + 19.4804i −0.210746 + 0.139146i
\(141\) 0 0
\(142\) −36.6025 + 136.603i −0.257764 + 0.961990i
\(143\) −158.114 + 158.114i −1.10569 + 1.10569i
\(144\) 0 0
\(145\) −225.000 + 75.0000i −1.55172 + 0.517241i
\(146\) −86.9626 150.624i −0.595634 1.03167i
\(147\) 0 0
\(148\) −3.66025 13.6603i −0.0247314 0.0922990i
\(149\) 41.0792 + 23.7171i 0.275699 + 0.159175i 0.631475 0.775396i \(-0.282450\pi\)
−0.355776 + 0.934571i \(0.615783\pi\)
\(150\) 0 0
\(151\) 11.0000 + 19.0526i 0.0728477 + 0.126176i 0.900148 0.435584i \(-0.143458\pi\)
−0.827301 + 0.561759i \(0.810125\pi\)
\(152\) 85.3815 + 85.3815i 0.561720 + 0.561720i
\(153\) 0 0
\(154\) 250.000i 1.62338i
\(155\) 26.5388 29.9281i 0.171218 0.193085i
\(156\) 0 0
\(157\) 273.205 73.2051i 1.74016 0.466274i 0.757677 0.652629i \(-0.226334\pi\)
0.982482 + 0.186355i \(0.0596675\pi\)
\(158\) −6.94484 25.9185i −0.0439547 0.164041i
\(159\) 0 0
\(160\) 78.1218 4.68911i 0.488261 0.0293069i
\(161\) 31.6228 0.196415
\(162\) 0 0
\(163\) 100.000 100.000i 0.613497 0.613497i −0.330359 0.943856i \(-0.607170\pi\)
0.943856 + 0.330359i \(0.107170\pi\)
\(164\) 27.3861 15.8114i 0.166989 0.0964109i
\(165\) 0 0
\(166\) −85.0000 + 147.224i −0.512048 + 0.886893i
\(167\) −203.028 + 54.4013i −1.21574 + 0.325756i −0.809011 0.587793i \(-0.799997\pi\)
−0.406727 + 0.913550i \(0.633330\pi\)
\(168\) 0 0
\(169\) −26.8468 + 15.5000i −0.158857 + 0.0917160i
\(170\) 47.4342 15.8114i 0.279024 0.0930082i
\(171\) 0 0
\(172\) 10.0000 + 10.0000i 0.0581395 + 0.0581395i
\(173\) −151.191 40.5116i −0.873938 0.234171i −0.206148 0.978521i \(-0.566093\pi\)
−0.667790 + 0.744350i \(0.732760\pi\)
\(174\) 0 0
\(175\) −109.151 + 139.054i −0.623718 + 0.794597i
\(176\) 150.208 260.168i 0.853456 1.47823i
\(177\) 0 0
\(178\) 0 0
\(179\) 142.302i 0.794986i −0.917605 0.397493i \(-0.869880\pi\)
0.917605 0.397493i \(-0.130120\pi\)
\(180\) 0 0
\(181\) 218.000 1.20442 0.602210 0.798338i \(-0.294287\pi\)
0.602210 + 0.798338i \(0.294287\pi\)
\(182\) −57.8737 + 215.988i −0.317987 + 1.18674i
\(183\) 0 0
\(184\) −25.9808 15.0000i −0.141200 0.0815217i
\(185\) −38.9609 59.0089i −0.210599 0.318967i
\(186\) 0 0
\(187\) 18.3013 68.3013i 0.0978678 0.365247i
\(188\) 41.1096 41.1096i 0.218668 0.218668i
\(189\) 0 0
\(190\) −180.000 90.0000i −0.947368 0.473684i
\(191\) 79.0569 + 136.931i 0.413911 + 0.716914i 0.995313 0.0967016i \(-0.0308292\pi\)
−0.581403 + 0.813616i \(0.697496\pi\)
\(192\) 0 0
\(193\) −45.7532 170.753i −0.237063 0.884731i −0.977208 0.212284i \(-0.931910\pi\)
0.740145 0.672447i \(-0.234757\pi\)
\(194\) 13.6931 + 7.90569i 0.0705828 + 0.0407510i
\(195\) 0 0
\(196\) 0.500000 + 0.866025i 0.00255102 + 0.00441850i
\(197\) −145.465 145.465i −0.738400 0.738400i 0.233868 0.972268i \(-0.424862\pi\)
−0.972268 + 0.233868i \(0.924862\pi\)
\(198\) 0 0
\(199\) 18.0000i 0.0904523i −0.998977 0.0452261i \(-0.985599\pi\)
0.998977 0.0452261i \(-0.0144008\pi\)
\(200\) 155.636 62.4702i 0.778179 0.312351i
\(201\) 0 0
\(202\) 34.1506 9.15064i 0.169063 0.0453002i
\(203\) 86.8105 + 323.981i 0.427638 + 1.59597i
\(204\) 0 0
\(205\) 104.904 118.301i 0.511726 0.577079i
\(206\) −110.680 −0.537280
\(207\) 0 0
\(208\) 190.000 190.000i 0.913462 0.913462i
\(209\) −246.475 + 142.302i −1.17931 + 0.680873i
\(210\) 0 0
\(211\) 149.000 258.076i 0.706161 1.22311i −0.260110 0.965579i \(-0.583759\pi\)
0.966271 0.257528i \(-0.0829079\pi\)
\(212\) −34.5580 + 9.25979i −0.163009 + 0.0436783i
\(213\) 0 0
\(214\) −164.545 + 95.0000i −0.768901 + 0.443925i
\(215\) 63.2456 + 31.6228i 0.294165 + 0.147083i
\(216\) 0 0
\(217\) −40.0000 40.0000i −0.184332 0.184332i
\(218\) 349.900 + 93.7554i 1.60505 + 0.430071i
\(219\) 0 0
\(220\) −15.8494 + 77.4519i −0.0720426 + 0.352054i
\(221\) 31.6228 54.7723i 0.143089 0.247838i
\(222\) 0 0
\(223\) 293.695 + 78.6955i 1.31702 + 0.352894i 0.847861 0.530219i \(-0.177890\pi\)
0.469159 + 0.883114i \(0.344557\pi\)
\(224\) 110.680i 0.494106i
\(225\) 0 0
\(226\) −370.000 −1.63717
\(227\) 99.5428 371.499i 0.438514 1.63656i −0.293999 0.955806i \(-0.594986\pi\)
0.732514 0.680752i \(-0.238347\pi\)
\(228\) 0 0
\(229\) −67.5500 39.0000i −0.294978 0.170306i 0.345207 0.938527i \(-0.387809\pi\)
−0.640185 + 0.768221i \(0.721142\pi\)
\(230\) 48.9849 + 10.0240i 0.212978 + 0.0435827i
\(231\) 0 0
\(232\) 82.3557 307.356i 0.354982 1.32481i
\(233\) 110.680 110.680i 0.475020 0.475020i −0.428515 0.903535i \(-0.640963\pi\)
0.903535 + 0.428515i \(0.140963\pi\)
\(234\) 0 0
\(235\) 130.000 260.000i 0.553191 1.10638i
\(236\) −23.7171 41.0792i −0.100496 0.174064i
\(237\) 0 0
\(238\) −18.3013 68.3013i −0.0768961 0.286980i
\(239\) −328.634 189.737i −1.37504 0.793877i −0.383479 0.923550i \(-0.625274\pi\)
−0.991557 + 0.129672i \(0.958607\pi\)
\(240\) 0 0
\(241\) −106.000 183.597i −0.439834 0.761815i 0.557842 0.829947i \(-0.311629\pi\)
−0.997676 + 0.0681321i \(0.978296\pi\)
\(242\) 203.967 + 203.967i 0.842838 + 0.842838i
\(243\) 0 0
\(244\) 58.0000i 0.237705i
\(245\) 3.74101 + 3.31735i 0.0152694 + 0.0135402i
\(246\) 0 0
\(247\) −245.885 + 65.8846i −0.995484 + 0.266739i
\(248\) 13.8897 + 51.8370i 0.0560068 + 0.209020i
\(249\) 0 0
\(250\) −213.157 + 180.801i −0.852628 + 0.723205i
\(251\) 363.662 1.44885 0.724426 0.689352i \(-0.242105\pi\)
0.724426 + 0.689352i \(0.242105\pi\)
\(252\) 0 0
\(253\) 50.0000 50.0000i 0.197628 0.197628i
\(254\) 150.624 86.9626i 0.593007 0.342373i
\(255\) 0 0
\(256\) −90.5000 + 156.751i −0.353516 + 0.612307i
\(257\) 419.016 112.275i 1.63041 0.436868i 0.676375 0.736557i \(-0.263550\pi\)
0.954037 + 0.299690i \(0.0968831\pi\)
\(258\) 0 0
\(259\) −86.6025 + 50.0000i −0.334373 + 0.193050i
\(260\) −31.6228 + 63.2456i −0.121626 + 0.243252i
\(261\) 0 0
\(262\) 275.000 + 275.000i 1.04962 + 1.04962i
\(263\) 393.097 + 105.330i 1.49467 + 0.400495i 0.911310 0.411721i \(-0.135072\pi\)
0.583357 + 0.812216i \(0.301739\pi\)
\(264\) 0 0
\(265\) −149.282 + 98.5641i −0.563328 + 0.371940i
\(266\) −142.302 + 246.475i −0.534972 + 0.926598i
\(267\) 0 0
\(268\) 95.6218 + 25.6218i 0.356798 + 0.0956037i
\(269\) 142.302i 0.529006i 0.964385 + 0.264503i \(0.0852078\pi\)
−0.964385 + 0.264503i \(0.914792\pi\)
\(270\) 0 0
\(271\) −178.000 −0.656827 −0.328413 0.944534i \(-0.606514\pi\)
−0.328413 + 0.944534i \(0.606514\pi\)
\(272\) −21.9920 + 82.0753i −0.0808530 + 0.301747i
\(273\) 0 0
\(274\) −43.3013 25.0000i −0.158034 0.0912409i
\(275\) 47.2821 + 392.447i 0.171935 + 1.42708i
\(276\) 0 0
\(277\) −84.1858 + 314.186i −0.303920 + 1.13424i 0.629951 + 0.776635i \(0.283075\pi\)
−0.933871 + 0.357610i \(0.883592\pi\)
\(278\) 161.276 161.276i 0.580130 0.580130i
\(279\) 0 0
\(280\) −75.0000 225.000i −0.267857 0.803571i
\(281\) 79.0569 + 136.931i 0.281341 + 0.487298i 0.971715 0.236155i \(-0.0758873\pi\)
−0.690374 + 0.723453i \(0.742554\pi\)
\(282\) 0 0
\(283\) −128.109 478.109i −0.452682 1.68943i −0.694816 0.719188i \(-0.744514\pi\)
0.242134 0.970243i \(-0.422153\pi\)
\(284\) 54.7723 + 31.6228i 0.192860 + 0.111348i
\(285\) 0 0
\(286\) 250.000 + 433.013i 0.874126 + 1.51403i
\(287\) −158.114 158.114i −0.550919 0.550919i
\(288\) 0 0
\(289\) 269.000i 0.930796i
\(290\) 31.7749 + 529.377i 0.109569 + 1.82544i
\(291\) 0 0
\(292\) −75.1314 + 20.1314i −0.257299 + 0.0689431i
\(293\) −74.0783 276.464i −0.252827 0.943563i −0.969286 0.245935i \(-0.920905\pi\)
0.716459 0.697629i \(-0.245762\pi\)
\(294\) 0 0
\(295\) −177.452 157.356i −0.601532 0.533409i
\(296\) 94.8683 0.320501
\(297\) 0 0
\(298\) 75.0000 75.0000i 0.251678 0.251678i
\(299\) 54.7723 31.6228i 0.183185 0.105762i
\(300\) 0 0
\(301\) 50.0000 86.6025i 0.166113 0.287716i
\(302\) 47.5173 12.7322i 0.157342 0.0421596i
\(303\) 0 0
\(304\) 296.181 171.000i 0.974279 0.562500i
\(305\) −91.7061 275.118i −0.300676 0.902027i
\(306\) 0 0
\(307\) 190.000 + 190.000i 0.618893 + 0.618893i 0.945247 0.326355i \(-0.105820\pi\)
−0.326355 + 0.945247i \(0.605820\pi\)
\(308\) 107.994 + 28.9368i 0.350629 + 0.0939508i
\(309\) 0 0
\(310\) −49.2820 74.6410i −0.158974 0.240777i
\(311\) 126.491 219.089i 0.406724 0.704466i −0.587797 0.809009i \(-0.700004\pi\)
0.994520 + 0.104542i \(0.0333378\pi\)
\(312\) 0 0
\(313\) −198.074 53.0737i −0.632823 0.169564i −0.0718727 0.997414i \(-0.522898\pi\)
−0.560951 + 0.827849i \(0.689564\pi\)
\(314\) 632.456i 2.01419i
\(315\) 0 0
\(316\) −12.0000 −0.0379747
\(317\) 5.78737 21.5988i 0.0182567 0.0681349i −0.956197 0.292725i \(-0.905438\pi\)
0.974453 + 0.224591i \(0.0721045\pi\)
\(318\) 0 0
\(319\) 649.519 + 375.000i 2.03611 + 1.17555i
\(320\) −41.0985 + 200.838i −0.128433 + 0.627619i
\(321\) 0 0
\(322\) 18.3013 68.3013i 0.0568362 0.212116i
\(323\) 56.9210 56.9210i 0.176226 0.176226i
\(324\) 0 0
\(325\) −50.0000 + 350.000i −0.153846 + 1.07692i
\(326\) −158.114 273.861i −0.485012 0.840065i
\(327\) 0 0
\(328\) 54.9038 + 204.904i 0.167390 + 0.624707i
\(329\) −356.020 205.548i −1.08213 0.624766i
\(330\) 0 0
\(331\) −241.000 417.424i −0.728097 1.26110i −0.957687 0.287813i \(-0.907072\pi\)
0.229590 0.973287i \(-0.426261\pi\)
\(332\) 53.7587 + 53.7587i 0.161924 + 0.161924i
\(333\) 0 0
\(334\) 470.000i 1.40719i
\(335\) 494.086 29.6565i 1.47488 0.0885270i
\(336\) 0 0
\(337\) 211.734 56.7339i 0.628291 0.168350i 0.0693967 0.997589i \(-0.477893\pi\)
0.558894 + 0.829239i \(0.311226\pi\)
\(338\) 17.9408 + 66.9562i 0.0530794 + 0.198095i
\(339\) 0 0
\(340\) −1.33975 22.3205i −0.00394043 0.0656486i
\(341\) −126.491 −0.370942
\(342\) 0 0
\(343\) −240.000 + 240.000i −0.699708 + 0.699708i
\(344\) −82.1584 + 47.4342i −0.238833 + 0.137890i
\(345\) 0 0
\(346\) −175.000 + 303.109i −0.505780 + 0.876037i
\(347\) 224.627 60.1886i 0.647340 0.173454i 0.0798143 0.996810i \(-0.474567\pi\)
0.567526 + 0.823355i \(0.307901\pi\)
\(348\) 0 0
\(349\) 275.396 159.000i 0.789101 0.455587i −0.0505453 0.998722i \(-0.516096\pi\)
0.839646 + 0.543134i \(0.182763\pi\)
\(350\) 237.171 + 316.228i 0.677631 + 0.903508i
\(351\) 0 0
\(352\) −175.000 175.000i −0.497159 0.497159i
\(353\) −306.702 82.1807i −0.868845 0.232806i −0.203257 0.979125i \(-0.565153\pi\)
−0.665588 + 0.746319i \(0.731819\pi\)
\(354\) 0 0
\(355\) 309.808 + 63.3975i 0.872698 + 0.178584i
\(356\) 0 0
\(357\) 0 0
\(358\) −307.356 82.3557i −0.858536 0.230044i
\(359\) 284.605i 0.792772i 0.918084 + 0.396386i \(0.129736\pi\)
−0.918084 + 0.396386i \(0.870264\pi\)
\(360\) 0 0
\(361\) 37.0000 0.102493
\(362\) 126.165 470.853i 0.348521 1.30070i
\(363\) 0 0
\(364\) 86.6025 + 50.0000i 0.237919 + 0.137363i
\(365\) −324.549 + 214.285i −0.889175 + 0.587082i
\(366\) 0 0
\(367\) −67.7147 + 252.715i −0.184509 + 0.688596i 0.810226 + 0.586117i \(0.199344\pi\)
−0.994735 + 0.102479i \(0.967323\pi\)
\(368\) −60.0833 + 60.0833i −0.163270 + 0.163270i
\(369\) 0 0
\(370\) −150.000 + 50.0000i −0.405405 + 0.135135i
\(371\) 126.491 + 219.089i 0.340946 + 0.590536i
\(372\) 0 0
\(373\) 36.6025 + 136.603i 0.0981301 + 0.366227i 0.997475 0.0710125i \(-0.0226230\pi\)
−0.899345 + 0.437239i \(0.855956\pi\)
\(374\) −136.931 79.0569i −0.366125 0.211382i
\(375\) 0 0
\(376\) 195.000 + 337.750i 0.518617 + 0.898271i
\(377\) 474.342 + 474.342i 1.25820 + 1.25820i
\(378\) 0 0
\(379\) 558.000i 1.47230i 0.676821 + 0.736148i \(0.263357\pi\)
−0.676821 + 0.736148i \(0.736643\pi\)
\(380\) −59.7123 + 67.3383i −0.157138 + 0.177206i
\(381\) 0 0
\(382\) 341.506 91.5064i 0.893996 0.239545i
\(383\) 103.015 + 384.458i 0.268969 + 1.00381i 0.959776 + 0.280767i \(0.0905889\pi\)
−0.690807 + 0.723039i \(0.742744\pi\)
\(384\) 0 0
\(385\) 558.013 33.4936i 1.44938 0.0869965i
\(386\) −395.285 −1.02405
\(387\) 0 0
\(388\) 5.00000 5.00000i 0.0128866 0.0128866i
\(389\) −451.871 + 260.888i −1.16162 + 0.670663i −0.951692 0.307053i \(-0.900657\pi\)
−0.209930 + 0.977716i \(0.567324\pi\)
\(390\) 0 0
\(391\) −10.0000 + 17.3205i −0.0255754 + 0.0442980i
\(392\) −6.47963 + 1.73621i −0.0165297 + 0.00442911i
\(393\) 0 0
\(394\) −398.372 + 230.000i −1.01110 + 0.583756i
\(395\) −56.9210 + 18.9737i −0.144104 + 0.0480346i
\(396\) 0 0
\(397\) −260.000 260.000i −0.654912 0.654912i 0.299260 0.954172i \(-0.403260\pi\)
−0.954172 + 0.299260i \(0.903260\pi\)
\(398\) −38.8778 10.4173i −0.0976828 0.0261740i
\(399\) 0 0
\(400\) −56.8172 471.590i −0.142043 1.17897i
\(401\) 126.491 219.089i 0.315439 0.546357i −0.664092 0.747651i \(-0.731182\pi\)
0.979531 + 0.201295i \(0.0645148\pi\)
\(402\) 0 0
\(403\) −109.282 29.2820i −0.271171 0.0726601i
\(404\) 15.8114i 0.0391371i
\(405\) 0 0
\(406\) 750.000 1.84729
\(407\) −57.8737 + 215.988i −0.142196 + 0.530682i
\(408\) 0 0
\(409\) −301.377 174.000i −0.736863 0.425428i 0.0840648 0.996460i \(-0.473210\pi\)
−0.820928 + 0.571032i \(0.806543\pi\)
\(410\) −194.804 295.045i −0.475133 0.719621i
\(411\) 0 0
\(412\) −12.8109 + 47.8109i −0.0310944 + 0.116046i
\(413\) −237.171 + 237.171i −0.574263 + 0.574263i
\(414\) 0 0
\(415\) 340.000 + 170.000i 0.819277 + 0.409639i
\(416\) −110.680 191.703i −0.266057 0.460824i
\(417\) 0 0
\(418\) 164.711 + 614.711i 0.394046 + 1.47060i
\(419\) 534.029 + 308.322i 1.27453 + 0.735852i 0.975838 0.218496i \(-0.0701151\pi\)
0.298696 + 0.954348i \(0.403448\pi\)
\(420\) 0 0
\(421\) −169.000 292.717i −0.401425 0.695289i 0.592473 0.805590i \(-0.298152\pi\)
−0.993898 + 0.110302i \(0.964818\pi\)
\(422\) −471.179 471.179i −1.11654 1.11654i
\(423\) 0 0
\(424\) 240.000i 0.566038i
\(425\) −41.6468 103.757i −0.0979925 0.244134i
\(426\) 0 0
\(427\) −396.147 + 106.147i −0.927746 + 0.248589i
\(428\) 21.9920 + 82.0753i 0.0513832 + 0.191765i
\(429\) 0 0
\(430\) 104.904 118.301i 0.243962 0.275119i
\(431\) 221.359 0.513595 0.256797 0.966465i \(-0.417333\pi\)
0.256797 + 0.966465i \(0.417333\pi\)
\(432\) 0 0
\(433\) 145.000 145.000i 0.334873 0.334873i −0.519561 0.854434i \(-0.673904\pi\)
0.854434 + 0.519561i \(0.173904\pi\)
\(434\) −109.545 + 63.2456i −0.252407 + 0.145727i
\(435\) 0 0
\(436\) 81.0000 140.296i 0.185780 0.321780i
\(437\) 77.7555 20.8345i 0.177930 0.0476763i
\(438\) 0 0
\(439\) −67.5500 + 39.0000i −0.153872 + 0.0888383i −0.574959 0.818182i \(-0.694982\pi\)
0.421087 + 0.907020i \(0.361649\pi\)
\(440\) −474.342 237.171i −1.07805 0.539025i
\(441\) 0 0
\(442\) −100.000 100.000i −0.226244 0.226244i
\(443\) −267.825 71.7634i −0.604570 0.161994i −0.0564665 0.998404i \(-0.517983\pi\)
−0.548104 + 0.836410i \(0.684650\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 339.945 588.802i 0.762208 1.32018i
\(447\) 0 0
\(448\) 280.035 + 75.0352i 0.625079 + 0.167489i
\(449\) 284.605i 0.633864i 0.948448 + 0.316932i \(0.102653\pi\)
−0.948448 + 0.316932i \(0.897347\pi\)
\(450\) 0 0
\(451\) −500.000 −1.10865
\(452\) −42.8265 + 159.831i −0.0947490 + 0.353608i
\(453\) 0 0
\(454\) −744.782 430.000i −1.64049 0.947137i
\(455\) 489.849 + 100.240i 1.07659 + 0.220308i
\(456\) 0 0
\(457\) −133.599 + 498.599i −0.292340 + 1.09103i 0.650967 + 0.759106i \(0.274363\pi\)
−0.943307 + 0.331921i \(0.892303\pi\)
\(458\) −123.329 + 123.329i −0.269277 + 0.269277i
\(459\) 0 0
\(460\) 10.0000 20.0000i 0.0217391 0.0434783i
\(461\) −419.002 725.732i −0.908898 1.57426i −0.815598 0.578619i \(-0.803592\pi\)
−0.0932994 0.995638i \(-0.529741\pi\)
\(462\) 0 0
\(463\) −12.8109 47.8109i −0.0276693 0.103263i 0.950710 0.310081i \(-0.100356\pi\)
−0.978380 + 0.206817i \(0.933689\pi\)
\(464\) −780.505 450.625i −1.68212 0.971174i
\(465\) 0 0
\(466\) −175.000 303.109i −0.375536 0.650448i
\(467\) −117.004 117.004i −0.250544 0.250544i 0.570649 0.821194i \(-0.306692\pi\)
−0.821194 + 0.570649i \(0.806692\pi\)
\(468\) 0 0
\(469\) 700.000i 1.49254i
\(470\) −486.332 431.255i −1.03475 0.917565i
\(471\) 0 0
\(472\) 307.356 82.3557i 0.651177 0.174482i
\(473\) −57.8737 215.988i −0.122355 0.456633i
\(474\) 0 0
\(475\) −176.769 + 413.827i −0.372146 + 0.871214i
\(476\) −31.6228 −0.0664344
\(477\) 0 0
\(478\) −600.000 + 600.000i −1.25523 + 1.25523i
\(479\) −328.634 + 189.737i −0.686083 + 0.396110i −0.802143 0.597132i \(-0.796307\pi\)
0.116060 + 0.993242i \(0.462973\pi\)
\(480\) 0 0
\(481\) −100.000 + 173.205i −0.207900 + 0.360094i
\(482\) −457.894 + 122.692i −0.949987 + 0.254548i
\(483\) 0 0
\(484\) 111.717 64.5000i 0.230821 0.133264i
\(485\) 15.8114 31.6228i 0.0326008 0.0652016i
\(486\) 0 0
\(487\) −125.000 125.000i −0.256674 0.256674i 0.567026 0.823700i \(-0.308094\pi\)
−0.823700 + 0.567026i \(0.808094\pi\)
\(488\) 375.818 + 100.700i 0.770120 + 0.206353i
\(489\) 0 0
\(490\) 9.33013 6.16025i 0.0190411 0.0125719i
\(491\) −229.265 + 397.099i −0.466935 + 0.808755i −0.999287 0.0377681i \(-0.987975\pi\)
0.532351 + 0.846523i \(0.321308\pi\)
\(492\) 0 0
\(493\) −204.904 54.9038i −0.415626 0.111367i
\(494\) 569.210i 1.15225i
\(495\) 0 0
\(496\) 152.000 0.306452
\(497\) 115.747 431.975i 0.232892 0.869165i
\(498\) 0 0
\(499\) −192.258 111.000i −0.385286 0.222445i 0.294830 0.955550i \(-0.404737\pi\)
−0.680116 + 0.733105i \(0.738070\pi\)
\(500\) 53.4293 + 113.006i 0.106859 + 0.226012i
\(501\) 0 0
\(502\) 210.465 785.465i 0.419252 1.56467i
\(503\) −458.530 + 458.530i −0.911591 + 0.911591i −0.996397 0.0848065i \(-0.972973\pi\)
0.0848065 + 0.996397i \(0.472973\pi\)
\(504\) 0 0
\(505\) −25.0000 75.0000i −0.0495050 0.148515i
\(506\) −79.0569 136.931i −0.156239 0.270614i
\(507\) 0 0
\(508\) −20.1314 75.1314i −0.0396287 0.147896i
\(509\) −205.396 118.585i −0.403528 0.232977i 0.284477 0.958683i \(-0.408180\pi\)
−0.688005 + 0.725706i \(0.741513\pi\)
\(510\) 0 0
\(511\) 275.000 + 476.314i 0.538160 + 0.932121i
\(512\) −150.208 150.208i −0.293375 0.293375i
\(513\) 0 0
\(514\) 970.000i 1.88716i
\(515\) 14.8283 + 247.043i 0.0287928 + 0.479695i
\(516\) 0 0
\(517\) −887.917 + 237.917i −1.71744 + 0.460187i
\(518\) 57.8737 + 215.988i 0.111725 + 0.416964i
\(519\) 0 0
\(520\) −354.904 314.711i −0.682507 0.605214i
\(521\) 790.569 1.51741 0.758704 0.651436i \(-0.225833\pi\)
0.758704 + 0.651436i \(0.225833\pi\)
\(522\) 0 0
\(523\) 370.000 370.000i 0.707457 0.707457i −0.258543 0.966000i \(-0.583242\pi\)
0.966000 + 0.258543i \(0.0832423\pi\)
\(524\) 150.624 86.9626i 0.287450 0.165959i
\(525\) 0 0
\(526\) 455.000 788.083i 0.865019 1.49826i
\(527\) 34.5580 9.25979i 0.0655750 0.0175708i
\(528\) 0 0
\(529\) 440.807 254.500i 0.833283 0.481096i
\(530\) 126.491 + 379.473i 0.238662 + 0.715987i
\(531\) 0 0
\(532\) 90.0000 + 90.0000i 0.169173 + 0.169173i
\(533\) −431.975 115.747i −0.810460 0.217162i
\(534\) 0 0
\(535\) 234.090 + 354.545i 0.437551 + 0.662701i
\(536\) −332.039 + 575.109i −0.619476 + 1.07296i
\(537\) 0 0
\(538\) 307.356 + 82.3557i 0.571293 + 0.153078i
\(539\) 15.8114i 0.0293347i
\(540\) 0 0
\(541\) 362.000 0.669131 0.334566 0.942372i \(-0.391410\pi\)
0.334566 + 0.942372i \(0.391410\pi\)
\(542\) −103.015 + 384.458i −0.190065 + 0.709332i
\(543\) 0 0
\(544\) 60.6218 + 35.0000i 0.111437 + 0.0643382i
\(545\) 162.389 793.555i 0.297962 1.45606i
\(546\) 0 0
\(547\) 179.352 669.352i 0.327884 1.22368i −0.583497 0.812115i \(-0.698316\pi\)
0.911381 0.411564i \(-0.135017\pi\)
\(548\) −15.8114 + 15.8114i −0.0288529 + 0.0288529i
\(549\) 0 0
\(550\) 875.000 + 125.000i 1.59091 + 0.227273i
\(551\) 426.907 + 739.425i 0.774787 + 1.34197i
\(552\) 0 0
\(553\) 21.9615 + 81.9615i 0.0397134 + 0.148213i
\(554\) 629.881 + 363.662i 1.13697 + 0.656429i
\(555\) 0 0
\(556\) −51.0000 88.3346i −0.0917266 0.158875i
\(557\) 252.982 + 252.982i 0.454187 + 0.454187i 0.896742 0.442555i \(-0.145928\pi\)
−0.442555 + 0.896742i \(0.645928\pi\)
\(558\) 0 0
\(559\) 200.000i 0.357782i
\(560\) −670.545 + 40.2482i −1.19740 + 0.0718717i
\(561\) 0 0
\(562\) 341.506 91.5064i 0.607663 0.162823i
\(563\) −74.0783 276.464i −0.131578 0.491055i 0.868411 0.495846i \(-0.165142\pi\)
−0.999989 + 0.00479040i \(0.998475\pi\)
\(564\) 0 0
\(565\) 49.5706 + 825.859i 0.0877356 + 1.46170i
\(566\) −1106.80 −1.95547
\(567\) 0 0
\(568\) −300.000 + 300.000i −0.528169 + 0.528169i
\(569\) 164.317 94.8683i 0.288782 0.166728i −0.348611 0.937268i \(-0.613346\pi\)
0.637392 + 0.770539i \(0.280013\pi\)
\(570\) 0 0
\(571\) 329.000 569.845i 0.576182 0.997977i −0.419730 0.907649i \(-0.637875\pi\)
0.995912 0.0903277i \(-0.0287914\pi\)
\(572\) 215.988 57.8737i 0.377601 0.101178i
\(573\) 0 0
\(574\) −433.013 + 250.000i −0.754378 + 0.435540i
\(575\) 15.8114 110.680i 0.0274981 0.192486i
\(576\) 0 0
\(577\) −35.0000 35.0000i −0.0606586 0.0606586i 0.676127 0.736785i \(-0.263657\pi\)
−0.736785 + 0.676127i \(0.763657\pi\)
\(578\) −581.007 155.680i −1.00520 0.269343i
\(579\) 0 0
\(580\) 232.356 + 47.5481i 0.400613 + 0.0819795i
\(581\) 268.794 465.564i 0.462640 0.801315i
\(582\) 0 0
\(583\) 546.410 + 146.410i 0.937239 + 0.251132i
\(584\) 521.776i 0.893452i
\(585\) 0 0
\(586\) −640.000 −1.09215
\(587\) −56.7162 + 211.668i −0.0966205 + 0.360593i −0.997260 0.0739741i \(-0.976432\pi\)
0.900640 + 0.434567i \(0.143098\pi\)
\(588\) 0 0
\(589\) −124.708 72.0000i −0.211728 0.122241i
\(590\) −442.567 + 292.207i −0.750113 + 0.495265i
\(591\) 0 0
\(592\) 69.5448 259.545i 0.117474 0.438420i
\(593\) 167.601 167.601i 0.282632 0.282632i −0.551526 0.834158i \(-0.685954\pi\)
0.834158 + 0.551526i \(0.185954\pi\)
\(594\) 0 0
\(595\) −150.000 + 50.0000i −0.252101 + 0.0840336i
\(596\) −23.7171 41.0792i −0.0397938 0.0689248i
\(597\) 0 0
\(598\) −36.6025 136.603i −0.0612083 0.228432i
\(599\) 903.742 + 521.776i 1.50875 + 0.871078i 0.999948 + 0.0101955i \(0.00324539\pi\)
0.508804 + 0.860883i \(0.330088\pi\)
\(600\) 0 0
\(601\) 191.000 + 330.822i 0.317804 + 0.550452i 0.980029 0.198852i \(-0.0637214\pi\)
−0.662226 + 0.749304i \(0.730388\pi\)
\(602\) −158.114 158.114i −0.262648 0.262648i
\(603\) 0 0
\(604\) 22.0000i 0.0364238i
\(605\) 427.938 482.591i 0.707336 0.797671i
\(606\) 0 0
\(607\) −894.747 + 239.747i −1.47405 + 0.394970i −0.904317 0.426862i \(-0.859619\pi\)
−0.569730 + 0.821832i \(0.692952\pi\)
\(608\) −72.9209 272.144i −0.119936 0.447606i
\(609\) 0 0
\(610\) −647.295 + 38.8526i −1.06114 + 0.0636928i
\(611\) −822.192 −1.34565
\(612\) 0 0
\(613\) −620.000 + 620.000i −1.01142 + 1.01142i −0.0114852 + 0.999934i \(0.503656\pi\)
−0.999934 + 0.0114852i \(0.996344\pi\)
\(614\) 520.336 300.416i 0.847453 0.489277i
\(615\) 0 0
\(616\) −375.000 + 649.519i −0.608766 + 1.05441i
\(617\) −47.5173 + 12.7322i −0.0770134 + 0.0206357i −0.297120 0.954840i \(-0.596026\pi\)
0.220107 + 0.975476i \(0.429359\pi\)
\(618\) 0 0
\(619\) −223.435 + 129.000i −0.360961 + 0.208401i −0.669502 0.742810i \(-0.733492\pi\)
0.308542 + 0.951211i \(0.400159\pi\)
\(620\) −37.9473 + 12.6491i −0.0612054 + 0.0204018i
\(621\) 0 0
\(622\) −400.000 400.000i −0.643087 0.643087i
\(623\) 0 0
\(624\) 0 0
\(625\) 432.115 + 451.554i 0.691384 + 0.722487i
\(626\) −229.265 + 397.099i −0.366238 + 0.634343i
\(627\) 0 0
\(628\) −273.205 73.2051i −0.435040 0.116569i
\(629\) 63.2456i 0.100549i
\(630\) 0 0
\(631\) 812.000 1.28685 0.643423 0.765511i \(-0.277514\pi\)
0.643423 + 0.765511i \(0.277514\pi\)
\(632\) 20.8345 77.7555i 0.0329660 0.123031i
\(633\) 0 0
\(634\) −43.3013 25.0000i −0.0682985 0.0394322i
\(635\) −214.285 324.549i −0.337456 0.511101i
\(636\) 0 0
\(637\) 3.66025 13.6603i 0.00574608 0.0214447i
\(638\) 1185.85 1185.85i 1.85871 1.85871i
\(639\) 0 0
\(640\) 690.000 + 345.000i 1.07812 + 0.539062i
\(641\) 221.359 + 383.406i 0.345335 + 0.598137i 0.985414 0.170171i \(-0.0544321\pi\)
−0.640080 + 0.768308i \(0.721099\pi\)
\(642\) 0 0
\(643\) 300.141 + 1120.14i 0.466782 + 1.74205i 0.650913 + 0.759152i \(0.274386\pi\)
−0.184131 + 0.982902i \(0.558947\pi\)
\(644\) −27.3861 15.8114i −0.0425250 0.0245518i
\(645\) 0 0
\(646\) −90.0000 155.885i −0.139319 0.241307i
\(647\) 679.890 + 679.890i 1.05083 + 1.05083i 0.998637 + 0.0521974i \(0.0166225\pi\)
0.0521974 + 0.998637i \(0.483378\pi\)
\(648\) 0 0
\(649\) 750.000i 1.15562i
\(650\) 727.020 + 310.552i 1.11849 + 0.477772i
\(651\) 0 0
\(652\) −136.603 + 36.6025i −0.209513 + 0.0561389i
\(653\) −188.668 704.120i −0.288925 1.07828i −0.945923 0.324391i \(-0.894841\pi\)
0.656998 0.753893i \(-0.271826\pi\)
\(654\) 0 0
\(655\) 576.971 650.657i 0.880872 0.993369i
\(656\) 600.833 0.915904
\(657\) 0 0
\(658\) −650.000 + 650.000i −0.987842 + 0.987842i
\(659\) 780.505 450.625i 1.18438 0.683801i 0.227354 0.973812i \(-0.426992\pi\)
0.957023 + 0.290012i \(0.0936592\pi\)
\(660\) 0 0
\(661\) 401.000 694.552i 0.606657 1.05076i −0.385131 0.922862i \(-0.625844\pi\)
0.991787 0.127898i \(-0.0408230\pi\)
\(662\) −1041.06 + 278.951i −1.57260 + 0.421376i
\(663\) 0 0
\(664\) −441.673 + 255.000i −0.665170 + 0.384036i
\(665\) 569.210 + 284.605i 0.855955 + 0.427977i
\(666\) 0 0
\(667\) −150.000 150.000i −0.224888 0.224888i
\(668\) 203.028 + 54.4013i 0.303935 + 0.0814390i
\(669\) 0 0
\(670\) 221.891 1084.33i 0.331181 1.61840i
\(671\) −458.530 + 794.198i −0.683354 + 1.18360i
\(672\) 0 0
\(673\) −1058.67 283.670i −1.57306 0.421500i −0.636291 0.771449i \(-0.719532\pi\)
−0.936769 + 0.349948i \(0.886199\pi\)
\(674\) 490.153i 0.727230i
\(675\) 0 0
\(676\) 31.0000 0.0458580
\(677\) −181.723 + 678.201i −0.268425 + 1.00177i 0.691696 + 0.722189i \(0.256864\pi\)
−0.960121 + 0.279585i \(0.909803\pi\)
\(678\) 0 0
\(679\) −43.3013 25.0000i −0.0637721 0.0368189i
\(680\) 146.955 + 30.0721i 0.216110 + 0.0442236i
\(681\) 0 0
\(682\) −73.2051 + 273.205i −0.107339 + 0.400594i
\(683\) −60.0833 + 60.0833i −0.0879697 + 0.0879697i −0.749722 0.661753i \(-0.769813\pi\)
0.661753 + 0.749722i \(0.269813\pi\)
\(684\) 0 0
\(685\) −50.0000 + 100.000i −0.0729927 + 0.145985i
\(686\) 379.473 + 657.267i 0.553168 + 0.958115i
\(687\) 0 0
\(688\) 69.5448 + 259.545i 0.101083 + 0.377245i
\(689\) 438.178 + 252.982i 0.635962 + 0.367173i
\(690\) 0 0
\(691\) 281.000 + 486.706i 0.406657 + 0.704351i 0.994513 0.104615i \(-0.0333611\pi\)
−0.587856 + 0.808966i \(0.700028\pi\)
\(692\) 110.680 + 110.680i 0.159942 + 0.159942i
\(693\) 0 0
\(694\) 520.000i 0.749280i
\(695\) −381.583 338.370i −0.549041 0.486863i
\(696\) 0 0
\(697\) 136.603 36.6025i 0.195986 0.0525144i
\(698\) −184.038 686.841i −0.263665 0.984012i
\(699\) 0 0
\(700\) 164.054 65.8494i 0.234363 0.0940705i
\(701\) 363.662 0.518776 0.259388 0.965773i \(-0.416479\pi\)
0.259388 + 0.965773i \(0.416479\pi\)
\(702\) 0 0
\(703\) −180.000 + 180.000i −0.256046 + 0.256046i
\(704\) 561.416 324.133i 0.797465 0.460417i
\(705\) 0 0
\(706\) −355.000 + 614.878i −0.502833 + 0.870932i
\(707\) −107.994 + 28.9368i −0.152749 + 0.0409291i
\(708\) 0 0
\(709\) 431.281 249.000i 0.608294 0.351199i −0.164003 0.986460i \(-0.552441\pi\)
0.772298 + 0.635261i \(0.219107\pi\)
\(710\) 316.228 632.456i 0.445391 0.890782i
\(711\) 0 0
\(712\) 0 0
\(713\) 34.5580 + 9.25979i 0.0484685 + 0.0129871i
\(714\) 0 0
\(715\) 933.013 616.025i 1.30491 0.861574i
\(716\) −71.1512 + 123.238i −0.0993733 + 0.172120i
\(717\) 0 0
\(718\) 614.711 + 164.711i 0.856144 + 0.229403i
\(719\) 569.210i 0.791669i 0.918322 + 0.395834i \(0.129545\pi\)
−0.918322 + 0.395834i \(0.870455\pi\)
\(720\) 0 0
\(721\) 350.000 0.485437
\(722\) 21.4133 79.9154i 0.0296583 0.110686i
\(723\) 0 0
\(724\) −188.794 109.000i −0.260765 0.150552i
\(725\) 1177.34 141.846i 1.62392 0.195650i
\(726\) 0 0
\(727\) −331.253 + 1236.25i −0.455644 + 1.70049i 0.230545 + 0.973062i \(0.425949\pi\)
−0.686188 + 0.727424i \(0.740717\pi\)
\(728\) −474.342 + 474.342i −0.651568 + 0.651568i
\(729\) 0 0
\(730\) 275.000 + 825.000i 0.376712 + 1.13014i
\(731\) 31.6228 + 54.7723i 0.0432596 + 0.0749278i
\(732\) 0 0
\(733\) 201.314 + 751.314i 0.274644 + 1.02498i 0.956080 + 0.293107i \(0.0946892\pi\)
−0.681436 + 0.731878i \(0.738644\pi\)
\(734\) 506.643 + 292.511i 0.690250 + 0.398516i
\(735\) 0 0
\(736\) 35.0000 + 60.6218i 0.0475543 + 0.0823665i
\(737\) −1106.80 1106.80i −1.50176 1.50176i
\(738\) 0 0
\(739\) 198.000i 0.267930i 0.990986 + 0.133965i \(0.0427709\pi\)
−0.990986 + 0.133965i \(0.957229\pi\)
\(740\) 4.23665 + 70.5836i 0.00572520 + 0.0953833i
\(741\) 0 0
\(742\) 546.410 146.410i 0.736402 0.197318i
\(743\) 353.030 + 1317.52i 0.475141 + 1.77325i 0.620858 + 0.783923i \(0.286784\pi\)
−0.145717 + 0.989326i \(0.546549\pi\)
\(744\) 0 0
\(745\) −177.452 157.356i −0.238190 0.211216i
\(746\) 316.228 0.423898
\(747\) 0 0
\(748\) −50.0000 + 50.0000i −0.0668449 + 0.0668449i
\(749\) 520.336 300.416i 0.694708 0.401090i
\(750\) 0 0
\(751\) −364.000 + 630.466i −0.484687 + 0.839503i −0.999845 0.0175925i \(-0.994400\pi\)
0.515158 + 0.857095i \(0.327733\pi\)
\(752\) 1066.98 285.896i 1.41885 0.380181i
\(753\) 0 0
\(754\) 1299.04 750.000i 1.72286 0.994695i
\(755\) −34.7851 104.355i −0.0460729 0.138219i
\(756\) 0 0
\(757\) −170.000 170.000i −0.224571 0.224571i 0.585849 0.810420i \(-0.300761\pi\)
−0.810420 + 0.585849i \(0.800761\pi\)
\(758\) 1205.21 + 322.935i 1.58999 + 0.426036i
\(759\) 0 0
\(760\) −332.654 503.827i −0.437702 0.662930i
\(761\) −15.8114 + 27.3861i −0.0207771 + 0.0359870i −0.876227 0.481899i \(-0.839947\pi\)
0.855450 + 0.517886i \(0.173281\pi\)
\(762\) 0 0
\(763\) −1106.48 296.481i −1.45017 0.388572i
\(764\) 158.114i 0.206955i
\(765\) 0 0
\(766\) 890.000 1.16188
\(767\) −173.621 + 647.963i −0.226364 + 0.844801i
\(768\) 0 0
\(769\) 275.396 + 159.000i 0.358122 + 0.206762i 0.668257 0.743931i \(-0.267041\pi\)
−0.310134 + 0.950693i \(0.600374\pi\)
\(770\) 250.600 1224.62i 0.325455 1.59042i
\(771\) 0 0
\(772\) −45.7532 + 170.753i −0.0592658 + 0.221183i
\(773\) 452.206 452.206i 0.585001 0.585001i −0.351272 0.936273i \(-0.614251\pi\)
0.936273 + 0.351272i \(0.114251\pi\)
\(774\) 0 0
\(775\) −160.000 + 120.000i −0.206452 + 0.154839i
\(776\) 23.7171 + 41.0792i 0.0305633 + 0.0529371i
\(777\) 0 0
\(778\) 301.971 + 1126.97i 0.388137 + 1.44855i
\(779\) −492.950 284.605i −0.632799 0.365347i
\(780\) 0 0