Properties

Label 525.2.t.j.26.9
Level $525$
Weight $2$
Character 525.26
Analytic conductor $4.192$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(26,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.t (of order \(6\), degree \(2\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.9
Character \(\chi\) \(=\) 525.26
Dual form 525.2.t.j.101.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.31176 + 0.757344i) q^{2} +(-1.68045 + 0.419611i) q^{3} +(0.147140 + 0.254854i) q^{4} +(-2.52214 - 0.722254i) q^{6} +(-2.64468 - 0.0753638i) q^{7} -2.58363i q^{8} +(2.64785 - 1.41027i) q^{9} +O(q^{10})\) \(q+(1.31176 + 0.757344i) q^{2} +(-1.68045 + 0.419611i) q^{3} +(0.147140 + 0.254854i) q^{4} +(-2.52214 - 0.722254i) q^{6} +(-2.64468 - 0.0753638i) q^{7} -2.58363i q^{8} +(2.64785 - 1.41027i) q^{9} +(1.86048 - 1.07415i) q^{11} +(-0.354202 - 0.366529i) q^{12} -3.48097i q^{13} +(-3.41210 - 2.10179i) q^{14} +(2.25098 - 3.89881i) q^{16} +(-1.78859 - 3.09793i) q^{17} +(4.54141 + 0.155396i) q^{18} +(1.05858 + 0.611171i) q^{19} +(4.47588 - 0.983091i) q^{21} +3.25401 q^{22} +(1.31176 + 0.757344i) q^{23} +(1.08412 + 4.34168i) q^{24} +(2.63629 - 4.56619i) q^{26} +(-3.85783 + 3.48097i) q^{27} +(-0.369932 - 0.685096i) q^{28} -5.95645i q^{29} +(2.75098 - 1.58828i) q^{31} +(1.43050 - 0.825899i) q^{32} +(-2.67573 + 2.58574i) q^{33} -5.41832i q^{34} +(0.749020 + 0.467309i) q^{36} +(3.90175 - 6.75803i) q^{37} +(0.925734 + 1.60342i) q^{38} +(1.46065 + 5.84961i) q^{39} -11.8685 q^{41} +(6.61582 + 2.10021i) q^{42} +2.99294 q^{43} +(0.547504 + 0.316101i) q^{44} +(1.14714 + 1.98691i) q^{46} +(-3.05084 + 5.28420i) q^{47} +(-2.14668 + 7.49631i) q^{48} +(6.98864 + 0.398626i) q^{49} +(4.30557 + 4.45542i) q^{51} +(0.887140 - 0.512191i) q^{52} +(-9.72202 + 5.61301i) q^{53} +(-7.69683 + 1.64449i) q^{54} +(-0.194713 + 6.83288i) q^{56} +(-2.03535 - 0.582853i) q^{57} +(4.51108 - 7.81342i) q^{58} +(1.08467 + 1.87871i) q^{59} +(-2.94338 - 1.69936i) q^{61} +4.81149 q^{62} +(-7.10900 + 3.53017i) q^{63} -6.50196 q^{64} +(-5.46821 + 1.36542i) q^{66} +(5.15882 + 8.93534i) q^{67} +(0.526347 - 0.911660i) q^{68} +(-2.52214 - 0.722254i) q^{69} -10.3968i q^{71} +(-3.64363 - 6.84108i) q^{72} +(5.93710 - 3.42779i) q^{73} +(10.2363 - 5.90993i) q^{74} +0.359711i q^{76} +(-5.00133 + 2.70057i) q^{77} +(-2.51414 + 8.77950i) q^{78} +(-0.941421 + 1.63059i) q^{79} +(5.02225 - 7.46840i) q^{81} +(-15.5686 - 8.98853i) q^{82} +9.10486 q^{83} +(0.909127 + 0.996046i) q^{84} +(3.92601 + 2.26668i) q^{86} +(2.49939 + 10.0095i) q^{87} +(-2.77521 - 4.80681i) q^{88} +(-0.889962 + 1.54146i) q^{89} +(-0.262339 + 9.20605i) q^{91} +0.445743i q^{92} +(-3.95644 + 3.82337i) q^{93} +(-8.00392 + 4.62107i) q^{94} +(-2.05733 + 1.98814i) q^{96} -1.32584i q^{97} +(8.86551 + 5.81571i) q^{98} +(3.41144 - 5.46799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84} - 96 q^{91} + 72 q^{94} - 90 q^{96} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.31176 + 0.757344i 0.927553 + 0.535523i 0.886037 0.463615i \(-0.153448\pi\)
0.0415164 + 0.999138i \(0.486781\pi\)
\(3\) −1.68045 + 0.419611i −0.970211 + 0.242263i
\(4\) 0.147140 + 0.254854i 0.0735701 + 0.127427i
\(5\) 0 0
\(6\) −2.52214 0.722254i −1.02966 0.294859i
\(7\) −2.64468 0.0753638i −0.999594 0.0284849i
\(8\) 2.58363i 0.913452i
\(9\) 2.64785 1.41027i 0.882618 0.470092i
\(10\) 0 0
\(11\) 1.86048 1.07415i 0.560957 0.323869i −0.192573 0.981283i \(-0.561683\pi\)
0.753529 + 0.657414i \(0.228350\pi\)
\(12\) −0.354202 0.366529i −0.102249 0.105808i
\(13\) 3.48097i 0.965448i −0.875773 0.482724i \(-0.839647\pi\)
0.875773 0.482724i \(-0.160353\pi\)
\(14\) −3.41210 2.10179i −0.911923 0.561727i
\(15\) 0 0
\(16\) 2.25098 3.89881i 0.562745 0.974703i
\(17\) −1.78859 3.09793i −0.433797 0.751359i 0.563399 0.826185i \(-0.309493\pi\)
−0.997197 + 0.0748259i \(0.976160\pi\)
\(18\) 4.54141 + 0.155396i 1.07042 + 0.0366272i
\(19\) 1.05858 + 0.611171i 0.242855 + 0.140212i 0.616488 0.787364i \(-0.288555\pi\)
−0.373633 + 0.927576i \(0.621888\pi\)
\(20\) 0 0
\(21\) 4.47588 0.983091i 0.976718 0.214528i
\(22\) 3.25401 0.693757
\(23\) 1.31176 + 0.757344i 0.273521 + 0.157917i 0.630486 0.776200i \(-0.282855\pi\)
−0.356966 + 0.934117i \(0.616189\pi\)
\(24\) 1.08412 + 4.34168i 0.221295 + 0.886241i
\(25\) 0 0
\(26\) 2.63629 4.56619i 0.517020 0.895504i
\(27\) −3.85783 + 3.48097i −0.742439 + 0.669913i
\(28\) −0.369932 0.685096i −0.0699105 0.129471i
\(29\) 5.95645i 1.10608i −0.833153 0.553042i \(-0.813467\pi\)
0.833153 0.553042i \(-0.186533\pi\)
\(30\) 0 0
\(31\) 2.75098 1.58828i 0.494091 0.285263i −0.232179 0.972673i \(-0.574586\pi\)
0.726270 + 0.687410i \(0.241252\pi\)
\(32\) 1.43050 0.825899i 0.252879 0.146000i
\(33\) −2.67573 + 2.58574i −0.465785 + 0.450120i
\(34\) 5.41832i 0.929234i
\(35\) 0 0
\(36\) 0.749020 + 0.467309i 0.124837 + 0.0778848i
\(37\) 3.90175 6.75803i 0.641444 1.11101i −0.343667 0.939092i \(-0.611669\pi\)
0.985111 0.171921i \(-0.0549975\pi\)
\(38\) 0.925734 + 1.60342i 0.150174 + 0.260109i
\(39\) 1.46065 + 5.84961i 0.233892 + 0.936688i
\(40\) 0 0
\(41\) −11.8685 −1.85355 −0.926773 0.375622i \(-0.877429\pi\)
−0.926773 + 0.375622i \(0.877429\pi\)
\(42\) 6.61582 + 2.10021i 1.02084 + 0.324069i
\(43\) 2.99294 0.456419 0.228209 0.973612i \(-0.426713\pi\)
0.228209 + 0.973612i \(0.426713\pi\)
\(44\) 0.547504 + 0.316101i 0.0825393 + 0.0476541i
\(45\) 0 0
\(46\) 1.14714 + 1.98691i 0.169137 + 0.292953i
\(47\) −3.05084 + 5.28420i −0.445010 + 0.770780i −0.998053 0.0623727i \(-0.980133\pi\)
0.553043 + 0.833153i \(0.313467\pi\)
\(48\) −2.14668 + 7.49631i −0.309847 + 1.08200i
\(49\) 6.98864 + 0.398626i 0.998377 + 0.0569466i
\(50\) 0 0
\(51\) 4.30557 + 4.45542i 0.602901 + 0.623883i
\(52\) 0.887140 0.512191i 0.123024 0.0710281i
\(53\) −9.72202 + 5.61301i −1.33542 + 0.771006i −0.986125 0.166006i \(-0.946913\pi\)
−0.349297 + 0.937012i \(0.613580\pi\)
\(54\) −7.69683 + 1.64449i −1.04741 + 0.223787i
\(55\) 0 0
\(56\) −0.194713 + 6.83288i −0.0260196 + 0.913082i
\(57\) −2.03535 0.582853i −0.269589 0.0772008i
\(58\) 4.51108 7.81342i 0.592334 1.02595i
\(59\) 1.08467 + 1.87871i 0.141213 + 0.244587i 0.927954 0.372696i \(-0.121567\pi\)
−0.786741 + 0.617283i \(0.788233\pi\)
\(60\) 0 0
\(61\) −2.94338 1.69936i −0.376861 0.217581i 0.299591 0.954068i \(-0.403150\pi\)
−0.676452 + 0.736487i \(0.736483\pi\)
\(62\) 4.81149 0.611060
\(63\) −7.10900 + 3.53017i −0.895650 + 0.444760i
\(64\) −6.50196 −0.812745
\(65\) 0 0
\(66\) −5.46821 + 1.36542i −0.673090 + 0.168071i
\(67\) 5.15882 + 8.93534i 0.630250 + 1.09163i 0.987500 + 0.157617i \(0.0503811\pi\)
−0.357250 + 0.934009i \(0.616286\pi\)
\(68\) 0.526347 0.911660i 0.0638290 0.110555i
\(69\) −2.52214 0.722254i −0.303630 0.0869491i
\(70\) 0 0
\(71\) 10.3968i 1.23387i −0.787013 0.616936i \(-0.788374\pi\)
0.787013 0.616936i \(-0.211626\pi\)
\(72\) −3.64363 6.84108i −0.429406 0.806229i
\(73\) 5.93710 3.42779i 0.694885 0.401192i −0.110555 0.993870i \(-0.535263\pi\)
0.805439 + 0.592678i \(0.201929\pi\)
\(74\) 10.2363 5.90993i 1.18995 0.687016i
\(75\) 0 0
\(76\) 0.359711i 0.0412617i
\(77\) −5.00133 + 2.70057i −0.569955 + 0.307758i
\(78\) −2.51414 + 8.77950i −0.284671 + 0.994082i
\(79\) −0.941421 + 1.63059i −0.105918 + 0.183456i −0.914113 0.405460i \(-0.867111\pi\)
0.808195 + 0.588915i \(0.200445\pi\)
\(80\) 0 0
\(81\) 5.02225 7.46840i 0.558028 0.829822i
\(82\) −15.5686 8.98853i −1.71926 0.992617i
\(83\) 9.10486 0.999388 0.499694 0.866202i \(-0.333446\pi\)
0.499694 + 0.866202i \(0.333446\pi\)
\(84\) 0.909127 + 0.996046i 0.0991939 + 0.108678i
\(85\) 0 0
\(86\) 3.92601 + 2.26668i 0.423353 + 0.244423i
\(87\) 2.49939 + 10.0095i 0.267963 + 1.07313i
\(88\) −2.77521 4.80681i −0.295839 0.512407i
\(89\) −0.889962 + 1.54146i −0.0943358 + 0.163394i −0.909331 0.416073i \(-0.863406\pi\)
0.814995 + 0.579467i \(0.196739\pi\)
\(90\) 0 0
\(91\) −0.262339 + 9.20605i −0.0275006 + 0.965056i
\(92\) 0.445743i 0.0464719i
\(93\) −3.95644 + 3.82337i −0.410263 + 0.396465i
\(94\) −8.00392 + 4.62107i −0.825541 + 0.476626i
\(95\) 0 0
\(96\) −2.05733 + 1.98814i −0.209976 + 0.202914i
\(97\) 1.32584i 0.134618i −0.997732 0.0673092i \(-0.978559\pi\)
0.997732 0.0673092i \(-0.0214414\pi\)
\(98\) 8.86551 + 5.81571i 0.895552 + 0.587475i
\(99\) 3.41144 5.46799i 0.342863 0.549553i
\(100\) 0 0
\(101\) 6.71005 + 11.6221i 0.667675 + 1.15645i 0.978553 + 0.205997i \(0.0660438\pi\)
−0.310878 + 0.950450i \(0.600623\pi\)
\(102\) 2.27359 + 9.10523i 0.225119 + 0.901553i
\(103\) −5.01154 2.89342i −0.493802 0.285097i 0.232348 0.972633i \(-0.425359\pi\)
−0.726150 + 0.687536i \(0.758692\pi\)
\(104\) −8.99355 −0.881890
\(105\) 0 0
\(106\) −17.0039 −1.65157
\(107\) −3.36576 1.94323i −0.325381 0.187859i 0.328408 0.944536i \(-0.393488\pi\)
−0.653788 + 0.756677i \(0.726821\pi\)
\(108\) −1.45478 0.470993i −0.139986 0.0453214i
\(109\) 2.60384 + 4.50998i 0.249403 + 0.431978i 0.963360 0.268211i \(-0.0864324\pi\)
−0.713958 + 0.700189i \(0.753099\pi\)
\(110\) 0 0
\(111\) −3.72097 + 12.9938i −0.353179 + 1.23331i
\(112\) −6.24695 + 10.1415i −0.590281 + 0.958278i
\(113\) 9.36235i 0.880736i −0.897817 0.440368i \(-0.854848\pi\)
0.897817 0.440368i \(-0.145152\pi\)
\(114\) −2.22847 2.30602i −0.208715 0.215979i
\(115\) 0 0
\(116\) 1.51803 0.876432i 0.140945 0.0813747i
\(117\) −4.90913 9.21710i −0.453849 0.852121i
\(118\) 3.28589i 0.302490i
\(119\) 4.49678 + 8.32783i 0.412219 + 0.763411i
\(120\) 0 0
\(121\) −3.19240 + 5.52940i −0.290218 + 0.502673i
\(122\) −2.57400 4.45830i −0.233039 0.403636i
\(123\) 19.9444 4.98015i 1.79833 0.449045i
\(124\) 0.809559 + 0.467399i 0.0727006 + 0.0419737i
\(125\) 0 0
\(126\) −11.9988 0.753230i −1.06894 0.0671030i
\(127\) 9.57778 0.849891 0.424945 0.905219i \(-0.360293\pi\)
0.424945 + 0.905219i \(0.360293\pi\)
\(128\) −11.3900 6.57602i −1.00674 0.581243i
\(129\) −5.02950 + 1.25587i −0.442823 + 0.110573i
\(130\) 0 0
\(131\) −4.72508 + 8.18408i −0.412832 + 0.715047i −0.995198 0.0978802i \(-0.968794\pi\)
0.582366 + 0.812927i \(0.302127\pi\)
\(132\) −1.05269 0.301455i −0.0916253 0.0262383i
\(133\) −2.75354 1.69613i −0.238762 0.147073i
\(134\) 15.6280i 1.35005i
\(135\) 0 0
\(136\) −8.00392 + 4.62107i −0.686330 + 0.396253i
\(137\) 9.27125 5.35276i 0.792096 0.457317i −0.0486038 0.998818i \(-0.515477\pi\)
0.840700 + 0.541501i \(0.182144\pi\)
\(138\) −2.76144 2.85755i −0.235070 0.243251i
\(139\) 4.11136i 0.348721i 0.984682 + 0.174360i \(0.0557858\pi\)
−0.984682 + 0.174360i \(0.944214\pi\)
\(140\) 0 0
\(141\) 2.90948 10.1600i 0.245022 0.855629i
\(142\) 7.87395 13.6381i 0.660767 1.14448i
\(143\) −3.73909 6.47629i −0.312678 0.541575i
\(144\) 0.461868 13.4980i 0.0384890 1.12483i
\(145\) 0 0
\(146\) 10.3841 0.859390
\(147\) −11.9114 + 2.26264i −0.982432 + 0.186619i
\(148\) 2.29642 0.188764
\(149\) 2.20294 + 1.27187i 0.180472 + 0.104196i 0.587514 0.809214i \(-0.300107\pi\)
−0.407042 + 0.913409i \(0.633440\pi\)
\(150\) 0 0
\(151\) 2.80956 + 4.86630i 0.228639 + 0.396014i 0.957405 0.288749i \(-0.0932392\pi\)
−0.728766 + 0.684763i \(0.759906\pi\)
\(152\) 1.57904 2.73498i 0.128077 0.221836i
\(153\) −9.10486 5.68046i −0.736084 0.459238i
\(154\) −8.60580 0.245234i −0.693475 0.0197616i
\(155\) 0 0
\(156\) −1.27588 + 1.23297i −0.102152 + 0.0987164i
\(157\) 12.0584 6.96194i 0.962368 0.555623i 0.0654670 0.997855i \(-0.479146\pi\)
0.896901 + 0.442231i \(0.145813\pi\)
\(158\) −2.46983 + 1.42596i −0.196489 + 0.113443i
\(159\) 13.9821 13.5119i 1.10885 1.07156i
\(160\) 0 0
\(161\) −3.41210 2.10179i −0.268911 0.165644i
\(162\) 12.2441 5.99317i 0.961990 0.470868i
\(163\) 2.03535 3.52533i 0.159421 0.276125i −0.775239 0.631668i \(-0.782371\pi\)
0.934660 + 0.355543i \(0.115704\pi\)
\(164\) −1.74633 3.02473i −0.136366 0.236192i
\(165\) 0 0
\(166\) 11.9434 + 6.89551i 0.926986 + 0.535196i
\(167\) 13.9722 1.08120 0.540602 0.841279i \(-0.318197\pi\)
0.540602 + 0.841279i \(0.318197\pi\)
\(168\) −2.53995 11.5640i −0.195961 0.892185i
\(169\) 0.882841 0.0679109
\(170\) 0 0
\(171\) 3.66488 + 0.125403i 0.280261 + 0.00958983i
\(172\) 0.440382 + 0.762763i 0.0335788 + 0.0581602i
\(173\) 5.00133 8.66256i 0.380244 0.658602i −0.610853 0.791744i \(-0.709173\pi\)
0.991097 + 0.133142i \(0.0425066\pi\)
\(174\) −4.30206 + 15.0230i −0.326139 + 1.13889i
\(175\) 0 0
\(176\) 9.67157i 0.729022i
\(177\) −2.61107 2.70195i −0.196260 0.203091i
\(178\) −2.33483 + 1.34801i −0.175003 + 0.101038i
\(179\) −14.0378 + 8.10475i −1.04924 + 0.605777i −0.922436 0.386151i \(-0.873804\pi\)
−0.126801 + 0.991928i \(0.540471\pi\)
\(180\) 0 0
\(181\) 19.4123i 1.44290i −0.692465 0.721451i \(-0.743475\pi\)
0.692465 0.721451i \(-0.256525\pi\)
\(182\) −7.31627 + 11.8774i −0.542318 + 0.880414i
\(183\) 5.65929 + 1.62062i 0.418347 + 0.119800i
\(184\) 1.95670 3.38910i 0.144250 0.249848i
\(185\) 0 0
\(186\) −8.08550 + 2.01896i −0.592857 + 0.148037i
\(187\) −6.65529 3.84243i −0.486683 0.280987i
\(188\) −1.79560 −0.130958
\(189\) 10.4651 8.91531i 0.761221 0.648493i
\(190\) 0 0
\(191\) 11.0018 + 6.35188i 0.796061 + 0.459606i 0.842092 0.539334i \(-0.181324\pi\)
−0.0460309 + 0.998940i \(0.514657\pi\)
\(192\) 10.9262 2.72830i 0.788534 0.196898i
\(193\) 10.4098 + 18.0302i 0.749311 + 1.29785i 0.948153 + 0.317813i \(0.102949\pi\)
−0.198842 + 0.980032i \(0.563718\pi\)
\(194\) 1.00411 1.73918i 0.0720912 0.124866i
\(195\) 0 0
\(196\) 0.926718 + 1.83974i 0.0661942 + 0.131410i
\(197\) 2.23465i 0.159212i −0.996826 0.0796062i \(-0.974634\pi\)
0.996826 0.0796062i \(-0.0253663\pi\)
\(198\) 8.61613 4.58904i 0.612322 0.326129i
\(199\) 21.5831 12.4610i 1.52998 0.883337i 0.530622 0.847608i \(-0.321958\pi\)
0.999362 0.0357284i \(-0.0113751\pi\)
\(200\) 0 0
\(201\) −12.4185 12.8507i −0.875936 0.906421i
\(202\) 20.3273i 1.43022i
\(203\) −0.448901 + 15.7529i −0.0315066 + 1.10564i
\(204\) −0.501960 + 1.75286i −0.0351442 + 0.122725i
\(205\) 0 0
\(206\) −4.38262 7.59093i −0.305352 0.528885i
\(207\) 4.54141 + 0.155396i 0.315650 + 0.0108008i
\(208\) −13.5716 7.83560i −0.941025 0.543301i
\(209\) 2.62596 0.181641
\(210\) 0 0
\(211\) −6.61520 −0.455409 −0.227705 0.973730i \(-0.573122\pi\)
−0.227705 + 0.973730i \(0.573122\pi\)
\(212\) −2.86100 1.65180i −0.196494 0.113446i
\(213\) 4.36261 + 17.4713i 0.298921 + 1.19712i
\(214\) −2.94338 5.09808i −0.201205 0.348498i
\(215\) 0 0
\(216\) 8.99355 + 9.96721i 0.611934 + 0.678183i
\(217\) −7.39515 + 3.99316i −0.502016 + 0.271073i
\(218\) 7.88801i 0.534243i
\(219\) −8.53868 + 8.25151i −0.576991 + 0.557585i
\(220\) 0 0
\(221\) −10.7838 + 6.22604i −0.725398 + 0.418808i
\(222\) −14.7218 + 14.2266i −0.988060 + 0.954830i
\(223\) 4.31027i 0.288637i −0.989531 0.144318i \(-0.953901\pi\)
0.989531 0.144318i \(-0.0460990\pi\)
\(224\) −3.84545 + 2.07643i −0.256935 + 0.138737i
\(225\) 0 0
\(226\) 7.09052 12.2811i 0.471654 0.816929i
\(227\) −5.55561 9.62260i −0.368739 0.638675i 0.620630 0.784104i \(-0.286877\pi\)
−0.989369 + 0.145429i \(0.953544\pi\)
\(228\) −0.150939 0.604478i −0.00999617 0.0400326i
\(229\) −8.63774 4.98700i −0.570798 0.329550i 0.186670 0.982423i \(-0.440230\pi\)
−0.757468 + 0.652872i \(0.773564\pi\)
\(230\) 0 0
\(231\) 7.27132 6.63680i 0.478418 0.436669i
\(232\) −15.3893 −1.01036
\(233\) 17.8650 + 10.3144i 1.17037 + 0.675716i 0.953768 0.300543i \(-0.0971678\pi\)
0.216606 + 0.976259i \(0.430501\pi\)
\(234\) 0.540929 15.8085i 0.0353616 1.03343i
\(235\) 0 0
\(236\) −0.319198 + 0.552868i −0.0207780 + 0.0359886i
\(237\) 0.897801 3.13516i 0.0583184 0.203650i
\(238\) −0.408345 + 14.3297i −0.0264691 + 0.928857i
\(239\) 2.87353i 0.185873i −0.995672 0.0929365i \(-0.970375\pi\)
0.995672 0.0929365i \(-0.0296254\pi\)
\(240\) 0 0
\(241\) 22.5792 13.0361i 1.45445 0.839728i 0.455722 0.890122i \(-0.349381\pi\)
0.998729 + 0.0503940i \(0.0160477\pi\)
\(242\) −8.37532 + 4.83549i −0.538386 + 0.310837i
\(243\) −5.30584 + 14.6577i −0.340370 + 0.940292i
\(244\) 1.00018i 0.0640298i
\(245\) 0 0
\(246\) 29.9340 + 8.57206i 1.90852 + 0.546534i
\(247\) 2.12747 3.68488i 0.135368 0.234464i
\(248\) −4.10353 7.10752i −0.260574 0.451328i
\(249\) −15.3003 + 3.82050i −0.969617 + 0.242114i
\(250\) 0 0
\(251\) 0.161120 0.0101698 0.00508489 0.999987i \(-0.498381\pi\)
0.00508489 + 0.999987i \(0.498381\pi\)
\(252\) −1.94570 1.29233i −0.122567 0.0814091i
\(253\) 3.25401 0.204578
\(254\) 12.5637 + 7.25368i 0.788319 + 0.455136i
\(255\) 0 0
\(256\) −3.45866 5.99057i −0.216166 0.374411i
\(257\) −6.56514 + 11.3712i −0.409522 + 0.709314i −0.994836 0.101493i \(-0.967638\pi\)
0.585314 + 0.810807i \(0.300971\pi\)
\(258\) −7.54861 2.16166i −0.469956 0.134579i
\(259\) −10.8282 + 17.5788i −0.672830 + 1.09229i
\(260\) 0 0
\(261\) −8.40022 15.7718i −0.519961 0.976249i
\(262\) −12.3963 + 7.15703i −0.765848 + 0.442163i
\(263\) −15.3551 + 8.86526i −0.946835 + 0.546655i −0.892096 0.451846i \(-0.850766\pi\)
−0.0547384 + 0.998501i \(0.517432\pi\)
\(264\) 6.68061 + 6.91311i 0.411163 + 0.425473i
\(265\) 0 0
\(266\) −2.32743 4.31029i −0.142704 0.264281i
\(267\) 0.848727 2.96379i 0.0519412 0.181381i
\(268\) −1.51814 + 2.62950i −0.0927352 + 0.160622i
\(269\) −2.20294 3.81561i −0.134316 0.232642i 0.791020 0.611790i \(-0.209550\pi\)
−0.925336 + 0.379148i \(0.876217\pi\)
\(270\) 0 0
\(271\) 20.4287 + 11.7945i 1.24095 + 0.716465i 0.969288 0.245927i \(-0.0790923\pi\)
0.271665 + 0.962392i \(0.412426\pi\)
\(272\) −16.1043 −0.976469
\(273\) −3.42211 15.5804i −0.207116 0.942970i
\(274\) 16.2155 0.979615
\(275\) 0 0
\(276\) −0.187039 0.749051i −0.0112584 0.0450876i
\(277\) 6.41589 + 11.1127i 0.385494 + 0.667695i 0.991838 0.127508i \(-0.0406978\pi\)
−0.606344 + 0.795203i \(0.707364\pi\)
\(278\) −3.11371 + 5.39311i −0.186748 + 0.323457i
\(279\) 5.04428 8.08517i 0.301993 0.484046i
\(280\) 0 0
\(281\) 21.2397i 1.26706i 0.773719 + 0.633528i \(0.218394\pi\)
−0.773719 + 0.633528i \(0.781606\pi\)
\(282\) 11.5112 11.1240i 0.685480 0.662426i
\(283\) −5.67603 + 3.27706i −0.337405 + 0.194801i −0.659124 0.752034i \(-0.729073\pi\)
0.321719 + 0.946835i \(0.395739\pi\)
\(284\) 2.64967 1.52979i 0.157229 0.0907761i
\(285\) 0 0
\(286\) 11.3271i 0.669786i
\(287\) 31.3883 + 0.894454i 1.85279 + 0.0527980i
\(288\) 2.62301 4.20426i 0.154562 0.247738i
\(289\) 2.10188 3.64056i 0.123640 0.214151i
\(290\) 0 0
\(291\) 0.556336 + 2.22801i 0.0326130 + 0.130608i
\(292\) 1.74717 + 1.00873i 0.102245 + 0.0590315i
\(293\) 3.71937 0.217288 0.108644 0.994081i \(-0.465349\pi\)
0.108644 + 0.994081i \(0.465349\pi\)
\(294\) −17.3384 6.05296i −1.01120 0.353016i
\(295\) 0 0
\(296\) −17.4603 10.0807i −1.01486 0.585928i
\(297\) −3.43834 + 10.6202i −0.199513 + 0.616245i
\(298\) 1.92648 + 3.33677i 0.111598 + 0.193294i
\(299\) 2.63629 4.56619i 0.152461 0.264070i
\(300\) 0 0
\(301\) −7.91536 0.225559i −0.456234 0.0130010i
\(302\) 8.51121i 0.489765i
\(303\) −16.1527 16.7149i −0.927949 0.960245i
\(304\) 4.76568 2.75147i 0.273331 0.157808i
\(305\) 0 0
\(306\) −7.64132 14.3469i −0.436825 0.820158i
\(307\) 11.2102i 0.639800i −0.947451 0.319900i \(-0.896351\pi\)
0.947451 0.319900i \(-0.103649\pi\)
\(308\) −1.42415 0.877248i −0.0811484 0.0499859i
\(309\) 9.63578 + 2.75935i 0.548160 + 0.156974i
\(310\) 0 0
\(311\) −9.46050 16.3861i −0.536456 0.929168i −0.999091 0.0426199i \(-0.986430\pi\)
0.462636 0.886548i \(-0.346904\pi\)
\(312\) 15.1133 3.77380i 0.855620 0.213649i
\(313\) 14.1859 + 8.19024i 0.801835 + 0.462940i 0.844112 0.536166i \(-0.180128\pi\)
−0.0422775 + 0.999106i \(0.513461\pi\)
\(314\) 21.0903 1.19020
\(315\) 0 0
\(316\) −0.554083 −0.0311696
\(317\) 8.76134 + 5.05836i 0.492086 + 0.284106i 0.725439 0.688286i \(-0.241637\pi\)
−0.233353 + 0.972392i \(0.574970\pi\)
\(318\) 28.5743 7.13503i 1.60237 0.400113i
\(319\) −6.39812 11.0819i −0.358226 0.620466i
\(320\) 0 0
\(321\) 6.47141 + 1.85319i 0.361199 + 0.103435i
\(322\) −2.88408 5.34118i −0.160723 0.297652i
\(323\) 4.37254i 0.243295i
\(324\) 2.64233 + 0.181040i 0.146796 + 0.0100578i
\(325\) 0 0
\(326\) 5.33977 3.08292i 0.295743 0.170747i
\(327\) −6.26807 6.48622i −0.346625 0.358689i
\(328\) 30.6638i 1.69313i
\(329\) 8.46672 13.7451i 0.466785 0.757791i
\(330\) 0 0
\(331\) −9.63774 + 16.6931i −0.529738 + 0.917533i 0.469660 + 0.882847i \(0.344376\pi\)
−0.999398 + 0.0346861i \(0.988957\pi\)
\(332\) 1.33969 + 2.32041i 0.0735251 + 0.127349i
\(333\) 0.800582 23.3968i 0.0438716 1.28214i
\(334\) 18.3282 + 10.5818i 1.00287 + 0.579009i
\(335\) 0 0
\(336\) 6.24224 19.6635i 0.340542 1.07273i
\(337\) 23.6381 1.28765 0.643824 0.765174i \(-0.277347\pi\)
0.643824 + 0.765174i \(0.277347\pi\)
\(338\) 1.15807 + 0.668614i 0.0629909 + 0.0363678i
\(339\) 3.92855 + 15.7330i 0.213369 + 0.854499i
\(340\) 0 0
\(341\) 3.41210 5.90993i 0.184776 0.320041i
\(342\) 4.71247 + 2.94008i 0.254821 + 0.158981i
\(343\) −18.4527 1.58093i −0.996350 0.0853621i
\(344\) 7.73266i 0.416917i
\(345\) 0 0
\(346\) 13.1211 7.57546i 0.705394 0.407259i
\(347\) −13.7760 + 7.95360i −0.739536 + 0.426971i −0.821901 0.569631i \(-0.807086\pi\)
0.0823644 + 0.996602i \(0.473753\pi\)
\(348\) −2.18321 + 2.10979i −0.117032 + 0.113096i
\(349\) 0.0192397i 0.00102988i 1.00000 0.000514938i \(0.000163910\pi\)
−1.00000 0.000514938i \(0.999836\pi\)
\(350\) 0 0
\(351\) 12.1172 + 13.4290i 0.646766 + 0.716786i
\(352\) 1.77428 3.07314i 0.0945695 0.163799i
\(353\) −12.7100 22.0143i −0.676484 1.17170i −0.976033 0.217624i \(-0.930170\pi\)
0.299549 0.954081i \(-0.403164\pi\)
\(354\) −1.37880 5.52178i −0.0732821 0.293479i
\(355\) 0 0
\(356\) −0.523797 −0.0277612
\(357\) −11.0511 12.1076i −0.584885 0.640804i
\(358\) −24.5523 −1.29763
\(359\) −20.9396 12.0895i −1.10515 0.638057i −0.167579 0.985859i \(-0.553595\pi\)
−0.937568 + 0.347801i \(0.886928\pi\)
\(360\) 0 0
\(361\) −8.75294 15.1605i −0.460681 0.797923i
\(362\) 14.7018 25.4642i 0.772708 1.33837i
\(363\) 3.04448 10.6315i 0.159794 0.558007i
\(364\) −2.38480 + 1.28772i −0.124998 + 0.0674949i
\(365\) 0 0
\(366\) 6.19625 + 6.41189i 0.323883 + 0.335155i
\(367\) −7.85721 + 4.53636i −0.410143 + 0.236796i −0.690851 0.722997i \(-0.742764\pi\)
0.280708 + 0.959793i \(0.409431\pi\)
\(368\) 5.90548 3.40953i 0.307845 0.177734i
\(369\) −31.4260 + 16.7378i −1.63597 + 0.871336i
\(370\) 0 0
\(371\) 26.1346 14.1119i 1.35684 0.732654i
\(372\) −1.55655 0.445743i −0.0807035 0.0231107i
\(373\) −7.78183 + 13.4785i −0.402928 + 0.697891i −0.994078 0.108670i \(-0.965341\pi\)
0.591150 + 0.806562i \(0.298674\pi\)
\(374\) −5.82009 10.0807i −0.300950 0.521260i
\(375\) 0 0
\(376\) 13.6524 + 7.88224i 0.704071 + 0.406496i
\(377\) −20.7342 −1.06787
\(378\) 20.4796 3.76908i 1.05336 0.193861i
\(379\) −34.0984 −1.75152 −0.875758 0.482751i \(-0.839638\pi\)
−0.875758 + 0.482751i \(0.839638\pi\)
\(380\) 0 0
\(381\) −16.0950 + 4.01894i −0.824573 + 0.205897i
\(382\) 9.62112 + 16.6643i 0.492259 + 0.852618i
\(383\) 5.28833 9.15965i 0.270221 0.468036i −0.698697 0.715417i \(-0.746237\pi\)
0.968918 + 0.247381i \(0.0795699\pi\)
\(384\) 21.8997 + 6.27133i 1.11757 + 0.320032i
\(385\) 0 0
\(386\) 31.5351i 1.60509i
\(387\) 7.92486 4.22087i 0.402843 0.214559i
\(388\) 0.337895 0.195084i 0.0171540 0.00990388i
\(389\) −14.6659 + 8.46736i −0.743590 + 0.429312i −0.823373 0.567500i \(-0.807911\pi\)
0.0797828 + 0.996812i \(0.474577\pi\)
\(390\) 0 0
\(391\) 5.41832i 0.274016i
\(392\) 1.02990 18.0561i 0.0520180 0.911970i
\(393\) 4.50615 15.7357i 0.227305 0.793760i
\(394\) 1.69240 2.93132i 0.0852619 0.147678i
\(395\) 0 0
\(396\) 1.89550 + 0.0648594i 0.0952524 + 0.00325931i
\(397\) −0.353188 0.203913i −0.0177260 0.0102341i 0.491111 0.871097i \(-0.336591\pi\)
−0.508837 + 0.860863i \(0.669924\pi\)
\(398\) 37.7491 1.89219
\(399\) 5.33892 + 1.69485i 0.267280 + 0.0848487i
\(400\) 0 0
\(401\) −24.2302 13.9893i −1.21000 0.698593i −0.247240 0.968954i \(-0.579524\pi\)
−0.962759 + 0.270361i \(0.912857\pi\)
\(402\) −6.55769 26.2622i −0.327068 1.30984i
\(403\) −5.52875 9.57608i −0.275407 0.477019i
\(404\) −1.97464 + 3.42017i −0.0982418 + 0.170160i
\(405\) 0 0
\(406\) −12.5192 + 20.3240i −0.621317 + 1.00866i
\(407\) 16.7643i 0.830974i
\(408\) 11.5112 11.1240i 0.569888 0.550721i
\(409\) −2.26960 + 1.31036i −0.112225 + 0.0647929i −0.555062 0.831809i \(-0.687305\pi\)
0.442837 + 0.896602i \(0.353972\pi\)
\(410\) 0 0
\(411\) −13.3338 + 12.8854i −0.657709 + 0.635589i
\(412\) 1.70295i 0.0838984i
\(413\) −2.72703 5.05033i −0.134188 0.248511i
\(414\) 5.83954 + 3.64325i 0.286998 + 0.179056i
\(415\) 0 0
\(416\) −2.87493 4.97953i −0.140955 0.244141i
\(417\) −1.72517 6.90895i −0.0844820 0.338333i
\(418\) 3.44462 + 1.98876i 0.168482 + 0.0972732i
\(419\) 8.39649 0.410195 0.205098 0.978742i \(-0.434249\pi\)
0.205098 + 0.978742i \(0.434249\pi\)
\(420\) 0 0
\(421\) −7.84952 −0.382562 −0.191281 0.981535i \(-0.561264\pi\)
−0.191281 + 0.981535i \(0.561264\pi\)
\(422\) −8.67754 5.00998i −0.422416 0.243882i
\(423\) −0.625987 + 18.2943i −0.0304365 + 0.889500i
\(424\) 14.5020 + 25.1181i 0.704277 + 1.21984i
\(425\) 0 0
\(426\) −7.50912 + 26.2222i −0.363818 + 1.27047i
\(427\) 7.65622 + 4.71609i 0.370511 + 0.228227i
\(428\) 1.14371i 0.0552831i
\(429\) 9.00089 + 9.31415i 0.434567 + 0.449691i
\(430\) 0 0
\(431\) −10.6154 + 6.12880i −0.511326 + 0.295214i −0.733378 0.679821i \(-0.762058\pi\)
0.222053 + 0.975035i \(0.428724\pi\)
\(432\) 4.88776 + 22.8765i 0.235162 + 1.10065i
\(433\) 5.13957i 0.246992i −0.992345 0.123496i \(-0.960589\pi\)
0.992345 0.123496i \(-0.0394106\pi\)
\(434\) −12.7249 0.362613i −0.610813 0.0174060i
\(435\) 0 0
\(436\) −0.766259 + 1.32720i −0.0366971 + 0.0635613i
\(437\) 0.925734 + 1.60342i 0.0442838 + 0.0767019i
\(438\) −17.4499 + 4.35726i −0.833790 + 0.208198i
\(439\) 14.4620 + 8.34964i 0.690234 + 0.398507i 0.803700 0.595035i \(-0.202862\pi\)
−0.113466 + 0.993542i \(0.536195\pi\)
\(440\) 0 0
\(441\) 19.0671 8.80040i 0.907955 0.419067i
\(442\) −18.8610 −0.897127
\(443\) −0.218429 0.126110i −0.0103779 0.00599167i 0.494802 0.869006i \(-0.335241\pi\)
−0.505180 + 0.863014i \(0.668574\pi\)
\(444\) −3.85902 + 0.963602i −0.183141 + 0.0457305i
\(445\) 0 0
\(446\) 3.26436 5.65403i 0.154572 0.267726i
\(447\) −4.23563 1.21294i −0.200339 0.0573700i
\(448\) 17.1956 + 0.490013i 0.812415 + 0.0231509i
\(449\) 28.8710i 1.36250i −0.732049 0.681252i \(-0.761436\pi\)
0.732049 0.681252i \(-0.238564\pi\)
\(450\) 0 0
\(451\) −22.0811 + 12.7485i −1.03976 + 0.600305i
\(452\) 2.38603 1.37758i 0.112230 0.0647958i
\(453\) −6.76329 6.99867i −0.317767 0.328826i
\(454\) 16.8300i 0.789873i
\(455\) 0 0
\(456\) −1.50588 + 5.25859i −0.0705193 + 0.246256i
\(457\) −12.0368 + 20.8483i −0.563056 + 0.975242i 0.434171 + 0.900830i \(0.357041\pi\)
−0.997228 + 0.0744117i \(0.976292\pi\)
\(458\) −7.55375 13.0835i −0.352964 0.611351i
\(459\) 17.6839 + 5.72525i 0.825413 + 0.267232i
\(460\) 0 0
\(461\) 39.8709 1.85697 0.928486 0.371367i \(-0.121111\pi\)
0.928486 + 0.371367i \(0.121111\pi\)
\(462\) 14.5646 3.19898i 0.677604 0.148830i
\(463\) 29.8417 1.38686 0.693430 0.720524i \(-0.256099\pi\)
0.693430 + 0.720524i \(0.256099\pi\)
\(464\) −23.2231 13.4078i −1.07810 0.622443i
\(465\) 0 0
\(466\) 15.6230 + 27.0599i 0.723723 + 1.25353i
\(467\) −2.09082 + 3.62140i −0.0967515 + 0.167579i −0.910338 0.413865i \(-0.864179\pi\)
0.813587 + 0.581444i \(0.197512\pi\)
\(468\) 1.62669 2.60732i 0.0751937 0.120523i
\(469\) −12.9700 24.0199i −0.598900 1.10914i
\(470\) 0 0
\(471\) −17.3423 + 16.7591i −0.799093 + 0.772218i
\(472\) 4.85390 2.80240i 0.223419 0.128991i
\(473\) 5.56831 3.21487i 0.256031 0.147820i
\(474\) 3.55209 3.43263i 0.163153 0.157666i
\(475\) 0 0
\(476\) −1.46073 + 2.37138i −0.0669522 + 0.108692i
\(477\) −17.8266 + 28.5731i −0.816223 + 1.30827i
\(478\) 2.17625 3.76937i 0.0995393 0.172407i
\(479\) 13.9676 + 24.1926i 0.638196 + 1.10539i 0.985828 + 0.167757i \(0.0536525\pi\)
−0.347632 + 0.937631i \(0.613014\pi\)
\(480\) 0 0
\(481\) −23.5245 13.5819i −1.07262 0.619280i
\(482\) 39.4912 1.79878
\(483\) 6.61582 + 2.10021i 0.301030 + 0.0955627i
\(484\) −1.87892 −0.0854055
\(485\) 0 0
\(486\) −18.0609 + 15.2090i −0.819259 + 0.689895i
\(487\) −18.6216 32.2536i −0.843826 1.46155i −0.886637 0.462466i \(-0.846965\pi\)
0.0428116 0.999083i \(-0.486368\pi\)
\(488\) −4.39053 + 7.60462i −0.198750 + 0.344245i
\(489\) −1.94104 + 6.77821i −0.0877770 + 0.306521i
\(490\) 0 0
\(491\) 5.90572i 0.266522i 0.991081 + 0.133261i \(0.0425448\pi\)
−0.991081 + 0.133261i \(0.957455\pi\)
\(492\) 4.20384 + 4.35015i 0.189524 + 0.196120i
\(493\) −18.4527 + 10.6536i −0.831066 + 0.479816i
\(494\) 5.58145 3.22245i 0.251121 0.144985i
\(495\) 0 0
\(496\) 14.3007i 0.642122i
\(497\) −0.783542 + 27.4962i −0.0351467 + 1.23337i
\(498\) −22.9637 6.57602i −1.02903 0.294678i
\(499\) −9.37010 + 16.2295i −0.419463 + 0.726532i −0.995886 0.0906204i \(-0.971115\pi\)
0.576422 + 0.817152i \(0.304448\pi\)
\(500\) 0 0
\(501\) −23.4797 + 5.86290i −1.04899 + 0.261935i
\(502\) 0.211350 + 0.122023i 0.00943301 + 0.00544615i
\(503\) −32.0398 −1.42858 −0.714291 0.699849i \(-0.753251\pi\)
−0.714291 + 0.699849i \(0.753251\pi\)
\(504\) 9.12067 + 18.3671i 0.406267 + 0.818134i
\(505\) 0 0
\(506\) 4.26847 + 2.46440i 0.189757 + 0.109556i
\(507\) −1.48357 + 0.370450i −0.0658878 + 0.0164523i
\(508\) 1.40928 + 2.44094i 0.0625265 + 0.108299i
\(509\) −9.57465 + 16.5838i −0.424389 + 0.735063i −0.996363 0.0852085i \(-0.972844\pi\)
0.571974 + 0.820272i \(0.306178\pi\)
\(510\) 0 0
\(511\) −15.9600 + 8.61794i −0.706031 + 0.381235i
\(512\) 15.8265i 0.699439i
\(513\) −6.21129 + 1.32709i −0.274235 + 0.0585925i
\(514\) −17.2238 + 9.94415i −0.759708 + 0.438617i
\(515\) 0 0
\(516\) −1.06011 1.09700i −0.0466685 0.0482927i
\(517\) 13.1082i 0.576499i
\(518\) −27.5171 + 14.8584i −1.20903 + 0.652842i
\(519\) −4.76960 + 16.6557i −0.209362 + 0.731102i
\(520\) 0 0
\(521\) 1.94104 + 3.36199i 0.0850387 + 0.147291i 0.905408 0.424543i \(-0.139565\pi\)
−0.820369 + 0.571834i \(0.806232\pi\)
\(522\) 0.925607 27.0506i 0.0405127 1.18397i
\(523\) −1.83929 1.06192i −0.0804266 0.0464343i 0.459247 0.888308i \(-0.348119\pi\)
−0.539674 + 0.841874i \(0.681452\pi\)
\(524\) −2.78100 −0.121488
\(525\) 0 0
\(526\) −26.8562 −1.17099
\(527\) −9.84076 5.68157i −0.428670 0.247493i
\(528\) 4.05830 + 16.2526i 0.176615 + 0.707305i
\(529\) −10.3529 17.9317i −0.450124 0.779638i
\(530\) 0 0
\(531\) 5.52156 + 3.44486i 0.239615 + 0.149494i
\(532\) 0.0271092 0.951321i 0.00117533 0.0412450i
\(533\) 41.3138i 1.78950i
\(534\) 3.35793 3.24500i 0.145312 0.140425i
\(535\) 0 0
\(536\) 23.0856 13.3285i 0.997148 0.575704i
\(537\) 20.1891 19.5101i 0.871224 0.841922i
\(538\) 6.67354i 0.287717i
\(539\) 13.4304 6.76522i 0.578490 0.291398i
\(540\) 0 0
\(541\) 7.59052 13.1472i 0.326342 0.565241i −0.655441 0.755246i \(-0.727517\pi\)
0.981783 + 0.190005i \(0.0608506\pi\)
\(542\) 17.8650 + 30.9431i 0.767367 + 1.32912i
\(543\) 8.14561 + 32.6214i 0.349561 + 1.39992i
\(544\) −5.11716 2.95439i −0.219396 0.126669i
\(545\) 0 0
\(546\) 7.31076 23.0295i 0.312871 0.985570i
\(547\) 11.7540 0.502566 0.251283 0.967914i \(-0.419148\pi\)
0.251283 + 0.967914i \(0.419148\pi\)
\(548\) 2.72835 + 1.57521i 0.116549 + 0.0672897i
\(549\) −10.1902 0.348684i −0.434907 0.0148815i
\(550\) 0 0
\(551\) 3.64041 6.30537i 0.155087 0.268618i
\(552\) −1.86604 + 6.51629i −0.0794239 + 0.277352i
\(553\) 2.61264 4.24143i 0.111101 0.180364i
\(554\) 19.4362i 0.825763i
\(555\) 0 0
\(556\) −1.04780 + 0.604946i −0.0444365 + 0.0256554i
\(557\) −8.14298 + 4.70135i −0.345029 + 0.199203i −0.662494 0.749068i \(-0.730502\pi\)
0.317465 + 0.948270i \(0.397169\pi\)
\(558\) 12.7401 6.78553i 0.539333 0.287254i
\(559\) 10.4183i 0.440649i
\(560\) 0 0
\(561\) 12.7962 + 3.66440i 0.540258 + 0.154711i
\(562\) −16.0858 + 27.8614i −0.678538 + 1.17526i
\(563\) 9.76331 + 16.9106i 0.411475 + 0.712695i 0.995051 0.0993632i \(-0.0316806\pi\)
−0.583577 + 0.812058i \(0.698347\pi\)
\(564\) 3.01743 0.753455i 0.127057 0.0317262i
\(565\) 0 0
\(566\) −9.92744 −0.417281
\(567\) −13.8451 + 19.3730i −0.581439 + 0.813590i
\(568\) −26.8615 −1.12708
\(569\) 11.1702 + 6.44911i 0.468279 + 0.270361i 0.715519 0.698593i \(-0.246190\pi\)
−0.247240 + 0.968954i \(0.579524\pi\)
\(570\) 0 0
\(571\) 20.8321 + 36.0823i 0.871796 + 1.51000i 0.860137 + 0.510063i \(0.170378\pi\)
0.0116595 + 0.999932i \(0.496289\pi\)
\(572\) 1.10034 1.90584i 0.0460075 0.0796874i
\(573\) −21.1533 6.05758i −0.883692 0.253059i
\(574\) 40.4965 + 24.9451i 1.69029 + 1.04119i
\(575\) 0 0
\(576\) −17.2162 + 9.16955i −0.717343 + 0.382065i
\(577\) 6.48634 3.74489i 0.270030 0.155902i −0.358871 0.933387i \(-0.616838\pi\)
0.628901 + 0.777485i \(0.283505\pi\)
\(578\) 5.51432 3.18369i 0.229365 0.132424i
\(579\) −25.0588 25.9309i −1.04141 1.07765i
\(580\) 0 0
\(581\) −24.0794 0.686177i −0.998983 0.0284674i
\(582\) −0.957590 + 3.34395i −0.0396934 + 0.138611i
\(583\) −12.0584 + 20.8858i −0.499409 + 0.865003i
\(584\) −8.85614 15.3393i −0.366470 0.634744i
\(585\) 0 0
\(586\) 4.87892 + 2.81685i 0.201546 + 0.116363i
\(587\) −22.1920 −0.915961 −0.457981 0.888962i \(-0.651427\pi\)
−0.457981 + 0.888962i \(0.651427\pi\)
\(588\) −2.32928 2.70274i −0.0960580 0.111459i
\(589\) 3.88284 0.159990
\(590\) 0 0
\(591\) 0.937685 + 3.75523i 0.0385712 + 0.154470i
\(592\) −17.5655 30.4244i −0.721938 1.25043i
\(593\) −3.15687 + 5.46787i −0.129637 + 0.224538i −0.923536 0.383512i \(-0.874715\pi\)
0.793899 + 0.608050i \(0.208048\pi\)
\(594\) −12.5534 + 11.3271i −0.515072 + 0.464757i
\(595\) 0 0
\(596\) 0.748572i 0.0306627i
\(597\) −31.0406 + 29.9966i −1.27041 + 1.22768i
\(598\) 6.91636 3.99316i 0.282831 0.163293i
\(599\) 17.8962 10.3324i 0.731219 0.422170i −0.0876487 0.996151i \(-0.527935\pi\)
0.818868 + 0.573982i \(0.194602\pi\)
\(600\) 0 0
\(601\) 12.5956i 0.513785i −0.966440 0.256892i \(-0.917301\pi\)
0.966440 0.256892i \(-0.0826986\pi\)
\(602\) −10.2122 6.29053i −0.416219 0.256383i
\(603\) 26.2611 + 16.3841i 1.06943 + 0.667213i
\(604\) −0.826798 + 1.43206i −0.0336419 + 0.0582695i
\(605\) 0 0
\(606\) −8.52955 34.1590i −0.346489 1.38762i
\(607\) 36.9590 + 21.3383i 1.50012 + 0.866095i 1.00000 0.000139312i \(4.43443e-5\pi\)
0.500121 + 0.865956i \(0.333289\pi\)
\(608\) 2.01906 0.0818838
\(609\) −5.85573 26.6604i −0.237286 1.08033i
\(610\) 0 0
\(611\) 18.3942 + 10.6199i 0.744148 + 0.429634i
\(612\) 0.107999 3.15624i 0.00436559 0.127583i
\(613\) 2.66142 + 4.60972i 0.107494 + 0.186185i 0.914754 0.404011i \(-0.132384\pi\)
−0.807261 + 0.590195i \(0.799051\pi\)
\(614\) 8.48998 14.7051i 0.342628 0.593448i
\(615\) 0 0
\(616\) 6.97728 + 12.9216i 0.281123 + 0.520626i
\(617\) 30.1002i 1.21179i −0.795545 0.605895i \(-0.792815\pi\)
0.795545 0.605895i \(-0.207185\pi\)
\(618\) 10.5500 + 10.9172i 0.424385 + 0.439154i
\(619\) −11.0265 + 6.36613i −0.443191 + 0.255876i −0.704950 0.709257i \(-0.749031\pi\)
0.261759 + 0.965133i \(0.415697\pi\)
\(620\) 0 0
\(621\) −7.69683 + 1.64449i −0.308863 + 0.0659911i
\(622\) 28.6594i 1.14914i
\(623\) 2.46983 4.00959i 0.0989518 0.160641i
\(624\) 26.0944 + 7.47254i 1.04461 + 0.299141i
\(625\) 0 0
\(626\) 12.4057 + 21.4872i 0.495830 + 0.858802i
\(627\) −4.41281 + 1.10188i −0.176230 + 0.0440049i
\(628\) 3.54856 + 2.04876i 0.141603 + 0.0817545i
\(629\) −27.9145 −1.11303
\(630\) 0 0
\(631\) −17.4114 −0.693138 −0.346569 0.938024i \(-0.612653\pi\)
−0.346569 + 0.938024i \(0.612653\pi\)
\(632\) 4.21284 + 2.43229i 0.167578 + 0.0967511i
\(633\) 11.1165 2.77581i 0.441843 0.110329i
\(634\) 7.66184 + 13.2707i 0.304291 + 0.527047i
\(635\) 0 0
\(636\) 5.50089 + 1.57526i 0.218125 + 0.0624633i
\(637\) 1.38761 24.3273i 0.0549789 0.963881i
\(638\) 19.3823i 0.767353i
\(639\) −14.6623 27.5292i −0.580033 1.08904i
\(640\) 0 0
\(641\) −1.13893 + 0.657564i −0.0449852 + 0.0259722i −0.522324 0.852747i \(-0.674935\pi\)
0.477339 + 0.878719i \(0.341601\pi\)
\(642\) 7.08543 + 7.33202i 0.279640 + 0.289372i
\(643\) 39.2223i 1.54678i −0.633932 0.773389i \(-0.718560\pi\)
0.633932 0.773389i \(-0.281440\pi\)
\(644\) 0.0335929 1.17885i 0.00132375 0.0464531i
\(645\) 0 0
\(646\) 3.31152 5.73572i 0.130290 0.225669i
\(647\) −3.11558 5.39634i −0.122486 0.212152i 0.798261 0.602311i \(-0.205753\pi\)
−0.920747 + 0.390159i \(0.872420\pi\)
\(648\) −19.2956 12.9757i −0.758003 0.509732i
\(649\) 4.03604 + 2.33021i 0.158428 + 0.0914687i
\(650\) 0 0
\(651\) 10.7516 9.81341i 0.421390 0.384618i
\(652\) 1.19793 0.0469144
\(653\) 16.3348 + 9.43091i 0.639230 + 0.369060i 0.784318 0.620359i \(-0.213013\pi\)
−0.145088 + 0.989419i \(0.546346\pi\)
\(654\) −3.30990 13.2554i −0.129427 0.518329i
\(655\) 0 0
\(656\) −26.7157 + 46.2730i −1.04307 + 1.80666i
\(657\) 10.8864 17.4492i 0.424721 0.680759i
\(658\) 21.5160 11.6180i 0.838783 0.452918i
\(659\) 41.6170i 1.62117i 0.585622 + 0.810584i \(0.300850\pi\)
−0.585622 + 0.810584i \(0.699150\pi\)
\(660\) 0 0
\(661\) 3.27232 1.88927i 0.127278 0.0734842i −0.435009 0.900426i \(-0.643255\pi\)
0.562287 + 0.826942i \(0.309921\pi\)
\(662\) −25.2848 + 14.5982i −0.982721 + 0.567374i
\(663\) 15.5092 14.9876i 0.602327 0.582069i
\(664\) 23.5236i 0.912894i
\(665\) 0 0
\(666\) 18.7696 30.0846i 0.727307 1.16576i
\(667\) 4.51108 7.81342i 0.174670 0.302537i
\(668\) 2.05588 + 3.56088i 0.0795442 + 0.137775i
\(669\) 1.80864 + 7.24321i 0.0699259 + 0.280039i
\(670\) 0 0
\(671\) −7.30148 −0.281871
\(672\) 5.59081 5.10294i 0.215670 0.196850i
\(673\) 31.2573 1.20488 0.602441 0.798163i \(-0.294195\pi\)
0.602441 + 0.798163i \(0.294195\pi\)
\(674\) 31.0075 + 17.9022i 1.19436 + 0.689565i
\(675\) 0 0
\(676\) 0.129901 + 0.224996i 0.00499621 + 0.00865369i
\(677\) 4.36895 7.56724i 0.167912 0.290832i −0.769773 0.638317i \(-0.779631\pi\)
0.937686 + 0.347485i \(0.112964\pi\)
\(678\) −6.76199 + 23.6132i −0.259693 + 0.906858i
\(679\) −0.0999201 + 3.50641i −0.00383458 + 0.134564i
\(680\) 0 0
\(681\) 13.3737 + 13.8391i 0.512481 + 0.530317i
\(682\) 8.95171 5.16827i 0.342779 0.197903i
\(683\) 18.9393 10.9346i 0.724691 0.418401i −0.0917858 0.995779i \(-0.529257\pi\)
0.816477 + 0.577378i \(0.195924\pi\)
\(684\) 0.507292 + 0.952463i 0.0193968 + 0.0364183i
\(685\) 0 0
\(686\) −23.0081 16.0488i −0.878454 0.612746i
\(687\) 16.6079 + 4.75594i 0.633632 + 0.181450i
\(688\) 6.73705 11.6689i 0.256847 0.444873i
\(689\) 19.5387 + 33.8421i 0.744366 + 1.28928i
\(690\) 0 0
\(691\) 19.5167 + 11.2680i 0.742449 + 0.428653i 0.822959 0.568101i \(-0.192322\pi\)
−0.0805102 + 0.996754i \(0.525655\pi\)
\(692\) 2.94359 0.111898
\(693\) −9.43425 + 14.2040i −0.358377 + 0.539564i
\(694\) −24.0944 −0.914612
\(695\) 0 0
\(696\) 25.8610 6.45751i 0.980257 0.244771i
\(697\) 21.2279 + 36.7678i 0.804063 + 1.39268i
\(698\) −0.0145711 + 0.0252378i −0.000551523 + 0.000955266i
\(699\) −34.3493 9.83646i −1.29921 0.372049i
\(700\) 0 0
\(701\) 35.5019i 1.34089i −0.741960 0.670444i \(-0.766104\pi\)
0.741960 0.670444i \(-0.233896\pi\)
\(702\) 5.72442 + 26.7924i 0.216054 + 1.01122i
\(703\) 8.26062 4.76927i 0.311555 0.179877i
\(704\) −12.0968 + 6.98408i −0.455915 + 0.263223i
\(705\) 0 0
\(706\) 38.5033i 1.44909i
\(707\) −16.8700 31.2425i −0.634463 1.17500i
\(708\) 0.304409 1.06301i 0.0114404 0.0399503i
\(709\) 2.03390 3.52282i 0.0763847 0.132302i −0.825303 0.564690i \(-0.808996\pi\)
0.901688 + 0.432388i \(0.142329\pi\)
\(710\) 0 0
\(711\) −0.193166 + 5.64522i −0.00724428 + 0.211712i
\(712\) 3.98257 + 2.29934i 0.149253 + 0.0861712i
\(713\) 4.81149 0.180192
\(714\) −5.32670 24.2518i −0.199347 0.907599i
\(715\) 0 0
\(716\) −4.13106 2.38507i −0.154385 0.0891342i
\(717\) 1.20576 + 4.82883i 0.0450301 + 0.180336i
\(718\) −18.3118 31.7169i −0.683389 1.18366i
\(719\) 15.2703 26.4489i 0.569484 0.986376i −0.427133 0.904189i \(-0.640476\pi\)
0.996617 0.0821868i \(-0.0261904\pi\)
\(720\) 0 0
\(721\) 13.0359 + 8.02984i 0.485481 + 0.299047i
\(722\) 26.5159i 0.986821i
\(723\) −32.4732 + 31.3810i −1.20769 + 1.16707i
\(724\) 4.94730 2.85632i 0.183865 0.106154i
\(725\) 0 0
\(726\) 12.0453 11.6402i 0.447043 0.432008i
\(727\) 23.4181i 0.868528i −0.900786 0.434264i \(-0.857008\pi\)
0.900786 0.434264i \(-0.142992\pi\)
\(728\) 23.7850 + 0.677789i 0.881533 + 0.0251205i
\(729\) 2.76568 26.8580i 0.102433 0.994740i
\(730\) 0 0
\(731\) −5.35315 9.27192i −0.197993 0.342934i
\(732\) 0.419686 + 1.68075i 0.0155120 + 0.0621224i
\(733\) 14.6277 + 8.44533i 0.540288 + 0.311935i 0.745196 0.666846i \(-0.232356\pi\)
−0.204908 + 0.978781i \(0.565689\pi\)
\(734\) −13.7423 −0.507239
\(735\) 0 0
\(736\) 2.50196 0.0922235
\(737\) 19.1958 + 11.0827i 0.707087 + 0.408237i
\(738\) −53.8996 1.84431i −1.98407 0.0678901i
\(739\) 13.8321 + 23.9579i 0.508822 + 0.881306i 0.999948 + 0.0102170i \(0.00325222\pi\)
−0.491126 + 0.871089i \(0.663414\pi\)
\(740\) 0 0
\(741\) −2.02890 + 7.08499i −0.0745333 + 0.260274i
\(742\) 44.9699 + 1.28148i 1.65090 + 0.0470446i
\(743\) 40.1701i 1.47370i −0.676056 0.736850i \(-0.736312\pi\)
0.676056 0.736850i \(-0.263688\pi\)
\(744\) 9.87819 + 10.2220i 0.362152 + 0.374756i
\(745\) 0 0
\(746\) −20.4158 + 11.7870i −0.747474 + 0.431554i
\(747\) 24.1083 12.8404i 0.882078 0.469804i
\(748\) 2.26151i 0.0826888i
\(749\) 8.75491 + 5.39286i 0.319898 + 0.197051i
\(750\) 0 0
\(751\) 24.8188 42.9874i 0.905650 1.56863i 0.0856082 0.996329i \(-0.472717\pi\)
0.820042 0.572303i \(-0.193950\pi\)
\(752\) 13.7347 + 23.7893i 0.500854 + 0.867505i
\(753\) −0.270754 + 0.0676076i −0.00986683 + 0.00246376i
\(754\) −27.1983 15.7029i −0.990503 0.571867i
\(755\) 0 0
\(756\) 3.81193 + 1.35526i 0.138639 + 0.0492905i
\(757\) −47.7116 −1.73411 −0.867054 0.498214i \(-0.833989\pi\)
−0.867054 + 0.498214i \(0.833989\pi\)
\(758\) −44.7288 25.8242i −1.62462 0.937977i
\(759\) −5.46821 + 1.36542i −0.198483 + 0.0495615i
\(760\) 0 0
\(761\) 9.91711 17.1769i 0.359495 0.622663i −0.628382 0.777905i \(-0.716282\pi\)
0.987876 + 0.155242i \(0.0496157\pi\)
\(762\) −24.1565 6.91759i −0.875098 0.250598i
\(763\) −6.54643 12.1237i −0.236997 0.438907i
\(764\) 3.73847i 0.135253i
\(765\) 0 0
\(766\) 13.8740 8.01017i 0.501289 0.289419i
\(767\) 6.53974 3.77572i 0.236136 0.136333i
\(768\) 8.32583 + 8.61559i 0.300433 + 0.310888i
\(769\) 10.6337i 0.383461i 0.981448 + 0.191731i \(0.0614100\pi\)
−0.981448 + 0.191731i \(0.938590\pi\)
\(770\) 0 0
\(771\) 6.26096 21.8635i 0.225483 0.787396i
\(772\) −3.06339 + 5.30595i −0.110254 + 0.190965i
\(773\) −7.16138 12.4039i −0.257577 0.446136i 0.708015 0.706197i \(-0.249591\pi\)
−0.965592 + 0.260061i \(0.916257\pi\)
\(774\) 13.5922 + 0.465090i 0.488560 + 0.0167173i
\(775\) 0 0
\(776\) −3.42548 −0.122967
\(777\) 10.8200 34.0839i 0.388166 1.22275i
\(778\) −25.6508 −0.919626
\(779\) −12.5637 7.25368i −0.450142 0.259890i
\(780\) 0 0
\(781\) −11.1677 19.3431i −0.399613 0.692149i
\(782\) 4.10353 7.10752i 0.146742 0.254165i
\(783\) 20.7342 + 22.9789i 0.740980 + 0.821200i
\(784\) 17.2855 26.3501i 0.617338 0.941075i
\(785\) 0 0
\(786\) 17.8283 17.2287i 0.635914 0.614527i
\(787\) −31.9859 + 18.4671i −1.14017 + 0.658280i −0.946474 0.322781i \(-0.895382\pi\)
−0.193700 + 0.981061i \(0.562049\pi\)
\(788\) 0.569511 0.328807i 0.0202880 0.0117133i
\(789\) 22.0835 21.3408i 0.786195 0.759753i
\(790\) 0 0
\(791\) −0.705583 + 24.7604i −0.0250876 + 0.880378i
\(792\) −14.1273 8.81391i −0.501991 0.313189i
\(793\) −5.91543 + 10.2458i −0.210063 + 0.363840i
\(794\) −0.308865 0.534970i −0.0109612 0.0189854i
\(795\) 0 0
\(796\) 6.35148 + 3.66703i 0.225122 + 0.129974i
\(797\) 37.4862 1.32783 0.663914 0.747809i \(-0.268894\pi\)
0.663914 + 0.747809i \(0.268894\pi\)
\(798\) 5.71978 + 6.26663i 0.202478 + 0.221836i
\(799\) 21.8268 0.772177
\(800\) 0 0
\(801\) −0.182607 + 5.33665i −0.00645210 + 0.188561i
\(802\) −21.1895 36.7012i −0.748226 1.29597i
\(803\) 7.36392 12.7547i 0.259867 0.450103i
\(804\) 1.44780 5.05578i 0.0510599 0.178303i
\(805\) 0 0
\(806\) 16.7487i 0.589947i
\(807\) 5.30301 + 5.48757i 0.186675 + 0.193172i
\(808\) 30.0274 17.3363i 1.05636 0.609889i
\(809\) 22.1518 12.7893i 0.778814 0.449649i −0.0571956 0.998363i \(-0.518216\pi\)
0.836010 + 0.548714i \(0.184883\pi\)
\(810\) 0 0
\(811\) 7.28791i 0.255913i 0.991780 + 0.127957i \(0.0408418\pi\)
−0.991780 + 0.127957i \(0.959158\pi\)
\(812\) −4.08074 + 2.20348i −0.143206 + 0.0773269i
\(813\) −39.2786 11.2480i −1.37756 0.394485i
\(814\) 12.6963 21.9907i 0.445006 0.770773i
\(815\) 0 0
\(816\) 27.0626 6.75756i 0.947380 0.236562i
\(817\) 3.16826 + 1.82920i 0.110844 + 0.0639955i
\(818\) −3.96956 −0.138792
\(819\) 12.2884 + 24.7462i 0.429392 + 0.864703i
\(820\) 0 0
\(821\) −0.00729231 0.00421022i −0.000254504 0.000146938i 0.499873 0.866099i \(-0.333380\pi\)
−0.500127 + 0.865952i \(0.666713\pi\)
\(822\) −27.2494 + 6.80421i −0.950433 + 0.237324i
\(823\) −15.6119 27.0406i −0.544198 0.942578i −0.998657 0.0518103i \(-0.983501\pi\)
0.454459 0.890767i \(-0.349832\pi\)
\(824\) −7.47553 + 12.9480i −0.260422 + 0.451065i
\(825\) 0 0
\(826\) 0.247637 8.69011i 0.00861639 0.302368i
\(827\) 38.3189i 1.33248i 0.745738 + 0.666239i \(0.232097\pi\)
−0.745738 + 0.666239i \(0.767903\pi\)
\(828\) 0.628620 + 1.18026i 0.0218461 + 0.0410169i
\(829\) 1.94142 1.12088i 0.0674283 0.0389298i −0.465907 0.884834i \(-0.654272\pi\)
0.533335 + 0.845904i \(0.320938\pi\)
\(830\) 0 0
\(831\) −15.4446 15.9821i −0.535768 0.554414i
\(832\) 22.6331i 0.784663i
\(833\) −11.2649 22.3633i −0.390306 0.774843i
\(834\) 2.96944 10.3694i 0.102823 0.359064i
\(835\) 0 0
\(836\) 0.386384 + 0.669237i 0.0133634 + 0.0231460i
\(837\) −5.08406 + 15.7034i −0.175731 + 0.542789i
\(838\) 11.0142 + 6.35903i 0.380478 + 0.219669i
\(839\) −20.6544 −0.713069 −0.356535 0.934282i \(-0.616042\pi\)
−0.356535 + 0.934282i \(0.616042\pi\)
\(840\) 0 0
\(841\) −6.47924 −0.223422
\(842\) −10.2967 5.94479i −0.354847 0.204871i
\(843\) −8.91243 35.6924i −0.306961 1.22931i
\(844\) −0.973362 1.68591i −0.0335045 0.0580315i
\(845\) 0 0
\(846\) −14.6762 + 23.5236i −0.504579 + 0.808759i
\(847\) 8.85959 14.3829i 0.304419 0.494202i
\(848\) 50.5391i 1.73552i
\(849\) 8.16322 7.88867i 0.280161 0.270738i
\(850\) 0 0
\(851\) 10.2363 5.90993i 0.350896 0.202590i
\(852\) −3.81073 + 3.68257i −0.130553 + 0.126163i
\(853\) 7.06831i 0.242014i 0.992652 + 0.121007i \(0.0386124\pi\)
−0.992652 + 0.121007i \(0.961388\pi\)
\(854\) 6.47141 + 11.9848i 0.221447 + 0.410110i
\(855\) 0 0
\(856\) −5.02058 + 8.69590i −0.171600 + 0.297220i
\(857\) −8.41661 14.5780i −0.287506 0.497975i 0.685708 0.727877i \(-0.259493\pi\)
−0.973214 + 0.229902i \(0.926159\pi\)
\(858\) 4.75298 + 19.0347i 0.162264 + 0.649833i
\(859\) 30.4698 + 17.5918i 1.03962 + 0.600223i 0.919725 0.392563i \(-0.128412\pi\)
0.119893 + 0.992787i \(0.461745\pi\)
\(860\) 0 0
\(861\) −53.1220 + 11.6678i −1.81039 + 0.397638i
\(862\) −18.5665 −0.632376
\(863\) 32.8880 + 18.9879i 1.11952 + 0.646356i 0.941279 0.337630i \(-0.109625\pi\)
0.178243 + 0.983986i \(0.442959\pi\)
\(864\) −2.64369 + 8.16571i −0.0899402 + 0.277803i
\(865\) 0 0
\(866\) 3.89242 6.74187i 0.132270 0.229098i
\(867\) −2.00449 + 6.99977i −0.0680761 + 0.237725i
\(868\) −2.10580 1.29713i −0.0714755 0.0440275i
\(869\) 4.04491i 0.137214i
\(870\) 0 0
\(871\) 31.1037 17.9577i 1.05391 0.608474i
\(872\) 11.6521 6.72737i 0.394591 0.227817i
\(873\) −1.86979 3.51062i −0.0632829 0.118817i
\(874\) 2.80440i 0.0948601i
\(875\) 0 0
\(876\) −3.35932 0.961992i −0.113501 0.0325027i
\(877\) −5.72481 + 9.91566i −0.193313 + 0.334828i −0.946346 0.323155i \(-0.895257\pi\)
0.753033 + 0.657983i \(0.228590\pi\)
\(878\) 12.6471 + 21.9054i 0.426819 + 0.739272i
\(879\) −6.25024 + 1.56069i −0.210815 + 0.0526408i
\(880\) 0 0
\(881\) −23.6698 −0.797455 −0.398728 0.917069i \(-0.630548\pi\)
−0.398728 + 0.917069i \(0.630548\pi\)
\(882\) 31.6763 + 2.89633i 1.06660 + 0.0975245i
\(883\) −16.8355 −0.566560 −0.283280 0.959037i \(-0.591423\pi\)
−0.283280 + 0.959037i \(0.591423\pi\)
\(884\) −3.17346 1.83220i −0.106735 0.0616236i
\(885\) 0 0
\(886\) −0.191017 0.330852i −0.00641735 0.0111152i
\(887\) −26.2917 + 45.5385i −0.882789 + 1.52903i −0.0345613 + 0.999403i \(0.511003\pi\)
−0.848227 + 0.529632i \(0.822330\pi\)
\(888\) 33.5712 + 9.61362i 1.12657 + 0.322612i
\(889\) −25.3301 0.721818i −0.849546 0.0242090i
\(890\) 0 0
\(891\) 1.32163 19.2895i 0.0442761 0.646222i
\(892\) 1.09849 0.634214i 0.0367802 0.0212350i
\(893\) −6.45910 + 3.72917i −0.216146 + 0.124792i
\(894\) −4.63752 4.79891i −0.155102 0.160500i
\(895\) 0 0
\(896\) 29.6273 + 18.2498i 0.989778 + 0.609685i
\(897\) −2.51414 + 8.77950i −0.0839448 + 0.293139i
\(898\) 21.8652 37.8717i 0.729653 1.26380i
\(899\) −9.46050 16.3861i −0.315525 0.546506i
\(900\) 0 0
\(901\) 34.7774 + 20.0788i 1.15860 + 0.668921i
\(902\) −38.6201 −1.28591
\(903\) 13.3960 2.94233i 0.445792 0.0979146i
\(904\) −24.1889 −0.804510
\(905\) 0 0
\(906\) −3.57140 14.3027i −0.118652 0.475176i
\(907\) −25.3858 43.9694i −0.842920 1.45998i −0.887415 0.460971i \(-0.847501\pi\)
0.0444946 0.999010i \(-0.485832\pi\)
\(908\) 1.63491 2.83174i 0.0542563 0.0939747i
\(909\) 34.1577 + 21.3107i 1.13294 + 0.706832i
\(910\) 0 0
\(911\) 16.1165i 0.533963i −0.963702 0.266981i \(-0.913974\pi\)
0.963702 0.266981i \(-0.0860262\pi\)
\(912\) −6.85396 + 6.62345i −0.226957 + 0.219324i
\(913\) 16.9394 9.77999i 0.560614 0.323671i
\(914\) −31.5787 + 18.2319i −1.04453 + 0.603059i
\(915\) 0 0
\(916\) 2.93515i 0.0969802i
\(917\) 13.1131 21.2882i 0.433033 0.702997i
\(918\) 18.8610 + 20.9029i 0.622506 + 0.689900i
\(919\) 19.8721 34.4194i 0.655519 1.13539i −0.326245 0.945285i \(-0.605783\pi\)
0.981763 0.190106i \(-0.0608833\pi\)
\(920\) 0 0
\(921\) 4.70392 + 18.8382i 0.155000 + 0.620740i
\(922\) 52.3010 + 30.1960i 1.72244 + 0.994452i
\(923\) −36.1909 −1.19124
\(924\) 2.76132 + 0.876587i 0.0908407 + 0.0288376i
\(925\) 0 0
\(926\) 39.1451 + 22.6004i 1.28639 + 0.742696i
\(927\) −17.3503 0.593686i −0.569860 0.0194992i
\(928\) −4.91942 8.52069i −0.161488 0.279705i
\(929\) −18.2593 + 31.6261i −0.599069 + 1.03762i 0.393889 + 0.919158i \(0.371129\pi\)
−0.992959 + 0.118461i \(0.962204\pi\)
\(930\) 0 0
\(931\) 7.15440 + 4.69323i 0.234476 + 0.153814i
\(932\) 6.07063i 0.198850i
\(933\) 22.7737 + 23.5663i 0.745578 + 0.771526i
\(934\) −5.48530 + 3.16694i −0.179484 + 0.103625i
\(935\) 0 0
\(936\) −23.8136 + 12.6834i −0.778372 + 0.414569i
\(937\) 7.60980i 0.248601i −0.992245 0.124301i \(-0.960331\pi\)
0.992245 0.124301i \(-0.0396687\pi\)
\(938\) 1.17779 41.3311i 0.0384561 1.34951i
\(939\) −27.2755 7.81075i −0.890102 0.254894i
\(940\) 0 0
\(941\) 11.0121 + 19.0735i 0.358985 + 0.621780i 0.987791 0.155782i \(-0.0497897\pi\)
−0.628807 + 0.777562i \(0.716456\pi\)
\(942\) −35.4414 + 8.84974i −1.15474 + 0.288340i
\(943\) −15.5686 8.98853i −0.506983 0.292707i
\(944\) 9.76632 0.317867
\(945\) 0 0
\(946\) 9.73904 0.316644
\(947\) 42.6589 + 24.6291i 1.38623 + 0.800339i 0.992888 0.119053i \(-0.0379860\pi\)
0.393341 + 0.919393i \(0.371319\pi\)
\(948\) 0.931111 0.232499i 0.0302411 0.00755123i
\(949\) −11.9320 20.6669i −0.387330 0.670875i
\(950\) 0 0
\(951\) −16.8456 4.82399i −0.546255 0.156429i
\(952\) 21.5160 11.6180i 0.697339 0.376542i
\(953\) 10.2538i 0.332154i 0.986113 + 0.166077i \(0.0531101\pi\)
−0.986113 + 0.166077i \(0.946890\pi\)
\(954\) −45.0239 + 23.9802i −1.45770 + 0.776388i
\(955\) 0 0
\(956\) 0.732331 0.422811i 0.0236853 0.0136747i
\(957\) 15.4018 + 15.9379i 0.497870 + 0.515198i
\(958\) 42.3131i 1.36708i
\(959\) −24.9229 + 13.4576i −0.804801 + 0.434569i
\(960\) 0 0
\(961\) −10.4547 + 18.1081i −0.337250 + 0.584134i
\(962\) −20.5723 35.6323i −0.663278 1.14883i
\(963\) −11.6525 0.398721i −0.375498 0.0128486i
\(964\) 6.64460 + 3.83626i 0.214008 + 0.123558i
\(965\) 0 0
\(966\) 7.08777 + 7.76541i 0.228045 + 0.249848i
\(967\) −4.62632 −0.148772 −0.0743862 0.997230i \(-0.523700\pi\)
−0.0743862 + 0.997230i \(0.523700\pi\)
\(968\) 14.2859 + 8.24799i 0.459168 + 0.265101i
\(969\) 1.83477 + 7.34786i 0.0589412 + 0.236047i
\(970\) 0 0
\(971\) 12.6443 21.9006i 0.405775 0.702822i −0.588637 0.808398i \(-0.700335\pi\)
0.994411 + 0.105575i \(0.0336684\pi\)
\(972\) −4.51628 + 0.804521i −0.144860 + 0.0258050i
\(973\) 0.309848 10.8732i 0.00993326 0.348579i
\(974\) 56.4119i 1.80755i
\(975\) 0 0
\(976\) −13.2510 + 7.65046i −0.424154 + 0.244885i
\(977\) 20.8797 12.0549i 0.668000 0.385670i −0.127318 0.991862i \(-0.540637\pi\)
0.795318 + 0.606192i \(0.207304\pi\)
\(978\) −7.67961 + 7.42133i −0.245567 + 0.237308i
\(979\) 3.82381i 0.122210i
\(980\) 0 0
\(981\) 13.2549 + 8.26964i 0.423196 + 0.264029i
\(982\) −4.47267 + 7.74688i −0.142728 + 0.247213i
\(983\) 24.0441 + 41.6456i 0.766888 + 1.32829i 0.939243 + 0.343254i \(0.111529\pi\)
−0.172354 + 0.985035i \(0.555137\pi\)
\(984\) −12.8669 51.5291i −0.410181 1.64269i
\(985\) 0 0
\(986\) −32.2739 −1.02781
\(987\) −8.46033 + 26.6507i −0.269295 + 0.848302i
\(988\) 1.25214 0.0398360
\(989\) 3.92601 + 2.26668i 0.124840 + 0.0720764i
\(990\) 0 0
\(991\) −14.8587 25.7361i −0.472003 0.817534i 0.527483 0.849565i \(-0.323136\pi\)
−0.999487 + 0.0320314i \(0.989802\pi\)
\(992\) 2.62352 4.54406i 0.0832967 0.144274i
\(993\) 9.19119 32.0960i 0.291674 1.01854i
\(994\) −21.8519 + 35.4749i −0.693099 + 1.12520i
\(995\) 0 0
\(996\) −3.22496 3.33720i −0.102187 0.105743i
\(997\) 23.1647 13.3742i 0.733634 0.423564i −0.0861161 0.996285i \(-0.527446\pi\)
0.819750 + 0.572721i \(0.194112\pi\)
\(998\) −24.5826 + 14.1928i −0.778149 + 0.449265i
\(999\) 8.47222 + 39.6532i 0.268049 + 1.25457i
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 525.2.t.j.26.9 24
3.2 odd 2 inner 525.2.t.j.26.3 24
5.2 odd 4 105.2.p.a.89.4 yes 24
5.3 odd 4 105.2.p.a.89.9 yes 24
5.4 even 2 inner 525.2.t.j.26.4 24
7.3 odd 6 inner 525.2.t.j.101.3 24
15.2 even 4 105.2.p.a.89.10 yes 24
15.8 even 4 105.2.p.a.89.3 yes 24
15.14 odd 2 inner 525.2.t.j.26.10 24
21.17 even 6 inner 525.2.t.j.101.9 24
35.2 odd 12 735.2.g.b.734.17 24
35.3 even 12 105.2.p.a.59.10 yes 24
35.12 even 12 735.2.g.b.734.20 24
35.13 even 4 735.2.p.f.509.10 24
35.17 even 12 105.2.p.a.59.3 24
35.18 odd 12 735.2.p.f.374.9 24
35.23 odd 12 735.2.g.b.734.8 24
35.24 odd 6 inner 525.2.t.j.101.10 24
35.27 even 4 735.2.p.f.509.3 24
35.32 odd 12 735.2.p.f.374.4 24
35.33 even 12 735.2.g.b.734.5 24
105.2 even 12 735.2.g.b.734.6 24
105.17 odd 12 105.2.p.a.59.9 yes 24
105.23 even 12 735.2.g.b.734.19 24
105.32 even 12 735.2.p.f.374.10 24
105.38 odd 12 105.2.p.a.59.4 yes 24
105.47 odd 12 735.2.g.b.734.7 24
105.53 even 12 735.2.p.f.374.3 24
105.59 even 6 inner 525.2.t.j.101.4 24
105.62 odd 4 735.2.p.f.509.9 24
105.68 odd 12 735.2.g.b.734.18 24
105.83 odd 4 735.2.p.f.509.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.p.a.59.3 24 35.17 even 12
105.2.p.a.59.4 yes 24 105.38 odd 12
105.2.p.a.59.9 yes 24 105.17 odd 12
105.2.p.a.59.10 yes 24 35.3 even 12
105.2.p.a.89.3 yes 24 15.8 even 4
105.2.p.a.89.4 yes 24 5.2 odd 4
105.2.p.a.89.9 yes 24 5.3 odd 4
105.2.p.a.89.10 yes 24 15.2 even 4
525.2.t.j.26.3 24 3.2 odd 2 inner
525.2.t.j.26.4 24 5.4 even 2 inner
525.2.t.j.26.9 24 1.1 even 1 trivial
525.2.t.j.26.10 24 15.14 odd 2 inner
525.2.t.j.101.3 24 7.3 odd 6 inner
525.2.t.j.101.4 24 105.59 even 6 inner
525.2.t.j.101.9 24 21.17 even 6 inner
525.2.t.j.101.10 24 35.24 odd 6 inner
735.2.g.b.734.5 24 35.33 even 12
735.2.g.b.734.6 24 105.2 even 12
735.2.g.b.734.7 24 105.47 odd 12
735.2.g.b.734.8 24 35.23 odd 12
735.2.g.b.734.17 24 35.2 odd 12
735.2.g.b.734.18 24 105.68 odd 12
735.2.g.b.734.19 24 105.23 even 12
735.2.g.b.734.20 24 35.12 even 12
735.2.p.f.374.3 24 105.53 even 12
735.2.p.f.374.4 24 35.32 odd 12
735.2.p.f.374.9 24 35.18 odd 12
735.2.p.f.374.10 24 105.32 even 12
735.2.p.f.509.3 24 35.27 even 4
735.2.p.f.509.4 24 105.83 odd 4
735.2.p.f.509.9 24 105.62 odd 4
735.2.p.f.509.10 24 35.13 even 4