Properties

Label 495.2.n.e.136.2
Level $495$
Weight $2$
Character 495.136
Analytic conductor $3.953$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [495,2,Mod(91,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), degree \(4\), 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: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.2
Root \(0.418926 - 1.28932i\) of defining polynomial
Character \(\chi\) \(=\) 495.136
Dual form 495.2.n.e.91.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.09676 + 0.796845i) q^{2} +(-0.0501062 - 0.154211i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-1.12773 - 3.47080i) q^{7} +(0.905781 - 2.78771i) q^{8} -1.35567 q^{10} +(-0.490303 - 3.28018i) q^{11} +(2.29029 + 1.66399i) q^{13} +(1.52884 - 4.70527i) q^{14} +(2.95244 - 2.14507i) q^{16} +(2.98685 - 2.17008i) q^{17} +(-0.0293950 + 0.0904686i) q^{19} +(0.131180 + 0.0953077i) q^{20} +(2.07605 - 3.98828i) q^{22} -1.16215 q^{23} +(0.309017 - 0.951057i) q^{25} +(1.18596 + 3.65001i) q^{26} +(-0.478730 + 0.347817i) q^{28} +(2.08707 + 6.42333i) q^{29} +(-5.48382 - 3.98423i) q^{31} -0.914918 q^{32} +5.00509 q^{34} +(2.95244 + 2.14507i) q^{35} +(3.04066 + 9.35820i) q^{37} +(-0.104329 + 0.0757994i) q^{38} +(0.905781 + 2.78771i) q^{40} +(2.57047 - 7.91110i) q^{41} -2.96862 q^{43} +(-0.481274 + 0.239968i) q^{44} +(-1.27460 - 0.926052i) q^{46} +(0.687534 - 2.11601i) q^{47} +(-5.11155 + 3.71376i) q^{49} +(1.09676 - 0.796845i) q^{50} +(0.141849 - 0.436565i) q^{52} +(2.42214 + 1.75979i) q^{53} +(2.32471 + 2.36553i) q^{55} -10.6970 q^{56} +(-2.82938 + 8.70794i) q^{58} +(2.62930 + 8.09216i) q^{59} +(6.86076 - 4.98464i) q^{61} +(-2.83964 - 8.73951i) q^{62} +(-6.90832 - 5.01919i) q^{64} -2.83095 q^{65} -13.4153 q^{67} +(-0.484310 - 0.351872i) q^{68} +(1.52884 + 4.70527i) q^{70} +(6.71734 - 4.88043i) q^{71} +(-0.407912 - 1.25542i) q^{73} +(-4.12215 + 12.6867i) q^{74} +0.0154241 q^{76} +(-10.8319 + 5.40091i) q^{77} +(11.2179 + 8.15028i) q^{79} +(-1.12773 + 3.47080i) q^{80} +(9.12312 - 6.62834i) q^{82} +(-8.61155 + 6.25666i) q^{83} +(-1.14088 + 3.51126i) q^{85} +(-3.25587 - 2.36553i) q^{86} +(-9.58829 - 1.60431i) q^{88} +12.1612 q^{89} +(3.19256 - 9.82567i) q^{91} +(0.0582308 + 0.179216i) q^{92} +(2.44020 - 1.77291i) q^{94} +(-0.0293950 - 0.0904686i) q^{95} +(3.50412 + 2.54589i) q^{97} -8.56545 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8} + 2 q^{10} - 3 q^{11} - 2 q^{13} + 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} + 3 q^{20} - 7 q^{22} - 10 q^{23} - 2 q^{25} - 10 q^{26} - 6 q^{28} + 9 q^{29}+ \cdots - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.09676 + 0.796845i 0.775529 + 0.563455i 0.903634 0.428306i \(-0.140889\pi\)
−0.128105 + 0.991761i \(0.540889\pi\)
\(3\) 0 0
\(4\) −0.0501062 0.154211i −0.0250531 0.0771056i
\(5\) −0.809017 + 0.587785i −0.361803 + 0.262866i
\(6\) 0 0
\(7\) −1.12773 3.47080i −0.426242 1.31184i −0.901800 0.432154i \(-0.857754\pi\)
0.475558 0.879685i \(-0.342246\pi\)
\(8\) 0.905781 2.78771i 0.320242 0.985603i
\(9\) 0 0
\(10\) −1.35567 −0.428702
\(11\) −0.490303 3.28018i −0.147832 0.989012i
\(12\) 0 0
\(13\) 2.29029 + 1.66399i 0.635212 + 0.461509i 0.858202 0.513312i \(-0.171582\pi\)
−0.222990 + 0.974821i \(0.571582\pi\)
\(14\) 1.52884 4.70527i 0.408599 1.25754i
\(15\) 0 0
\(16\) 2.95244 2.14507i 0.738109 0.536268i
\(17\) 2.98685 2.17008i 0.724419 0.526321i −0.163374 0.986564i \(-0.552238\pi\)
0.887793 + 0.460243i \(0.152238\pi\)
\(18\) 0 0
\(19\) −0.0293950 + 0.0904686i −0.00674368 + 0.0207549i −0.954372 0.298621i \(-0.903473\pi\)
0.947628 + 0.319376i \(0.103473\pi\)
\(20\) 0.131180 + 0.0953077i 0.0293327 + 0.0213115i
\(21\) 0 0
\(22\) 2.07605 3.98828i 0.442616 0.850304i
\(23\) −1.16215 −0.242324 −0.121162 0.992633i \(-0.538662\pi\)
−0.121162 + 0.992633i \(0.538662\pi\)
\(24\) 0 0
\(25\) 0.309017 0.951057i 0.0618034 0.190211i
\(26\) 1.18596 + 3.65001i 0.232586 + 0.715827i
\(27\) 0 0
\(28\) −0.478730 + 0.347817i −0.0904714 + 0.0657313i
\(29\) 2.08707 + 6.42333i 0.387559 + 1.19278i 0.934607 + 0.355682i \(0.115751\pi\)
−0.547049 + 0.837101i \(0.684249\pi\)
\(30\) 0 0
\(31\) −5.48382 3.98423i −0.984923 0.715588i −0.0261194 0.999659i \(-0.508315\pi\)
−0.958803 + 0.284071i \(0.908315\pi\)
\(32\) −0.914918 −0.161736
\(33\) 0 0
\(34\) 5.00509 0.858366
\(35\) 2.95244 + 2.14507i 0.499053 + 0.362583i
\(36\) 0 0
\(37\) 3.04066 + 9.35820i 0.499882 + 1.53848i 0.809208 + 0.587523i \(0.199897\pi\)
−0.309326 + 0.950956i \(0.600103\pi\)
\(38\) −0.104329 + 0.0757994i −0.0169244 + 0.0122963i
\(39\) 0 0
\(40\) 0.905781 + 2.78771i 0.143216 + 0.440775i
\(41\) 2.57047 7.91110i 0.401440 1.23551i −0.522391 0.852706i \(-0.674960\pi\)
0.923831 0.382800i \(-0.125040\pi\)
\(42\) 0 0
\(43\) −2.96862 −0.452710 −0.226355 0.974045i \(-0.572681\pi\)
−0.226355 + 0.974045i \(0.572681\pi\)
\(44\) −0.481274 + 0.239968i −0.0725547 + 0.0361765i
\(45\) 0 0
\(46\) −1.27460 0.926052i −0.187930 0.136539i
\(47\) 0.687534 2.11601i 0.100287 0.308652i −0.888308 0.459248i \(-0.848119\pi\)
0.988595 + 0.150595i \(0.0481191\pi\)
\(48\) 0 0
\(49\) −5.11155 + 3.71376i −0.730221 + 0.530537i
\(50\) 1.09676 0.796845i 0.155106 0.112691i
\(51\) 0 0
\(52\) 0.141849 0.436565i 0.0196708 0.0605407i
\(53\) 2.42214 + 1.75979i 0.332706 + 0.241725i 0.741578 0.670867i \(-0.234078\pi\)
−0.408872 + 0.912592i \(0.634078\pi\)
\(54\) 0 0
\(55\) 2.32471 + 2.36553i 0.313463 + 0.318968i
\(56\) −10.6970 −1.42945
\(57\) 0 0
\(58\) −2.82938 + 8.70794i −0.371516 + 1.14341i
\(59\) 2.62930 + 8.09216i 0.342306 + 1.05351i 0.963010 + 0.269465i \(0.0868468\pi\)
−0.620704 + 0.784045i \(0.713153\pi\)
\(60\) 0 0
\(61\) 6.86076 4.98464i 0.878431 0.638217i −0.0544052 0.998519i \(-0.517326\pi\)
0.932836 + 0.360302i \(0.117326\pi\)
\(62\) −2.83964 8.73951i −0.360634 1.10992i
\(63\) 0 0
\(64\) −6.90832 5.01919i −0.863541 0.627399i
\(65\) −2.83095 −0.351137
\(66\) 0 0
\(67\) −13.4153 −1.63894 −0.819469 0.573123i \(-0.805732\pi\)
−0.819469 + 0.573123i \(0.805732\pi\)
\(68\) −0.484310 0.351872i −0.0587312 0.0426707i
\(69\) 0 0
\(70\) 1.52884 + 4.70527i 0.182731 + 0.562388i
\(71\) 6.71734 4.88043i 0.797202 0.579201i −0.112890 0.993607i \(-0.536011\pi\)
0.910092 + 0.414406i \(0.136011\pi\)
\(72\) 0 0
\(73\) −0.407912 1.25542i −0.0477425 0.146936i 0.924343 0.381562i \(-0.124614\pi\)
−0.972086 + 0.234625i \(0.924614\pi\)
\(74\) −4.12215 + 12.6867i −0.479190 + 1.47480i
\(75\) 0 0
\(76\) 0.0154241 0.00176927
\(77\) −10.8319 + 5.40091i −1.23441 + 0.615491i
\(78\) 0 0
\(79\) 11.2179 + 8.15028i 1.26211 + 0.916978i 0.998859 0.0477484i \(-0.0152046\pi\)
0.263253 + 0.964727i \(0.415205\pi\)
\(80\) −1.12773 + 3.47080i −0.126084 + 0.388047i
\(81\) 0 0
\(82\) 9.12312 6.62834i 1.00748 0.731977i
\(83\) −8.61155 + 6.25666i −0.945240 + 0.686757i −0.949676 0.313233i \(-0.898588\pi\)
0.00443607 + 0.999990i \(0.498588\pi\)
\(84\) 0 0
\(85\) −1.14088 + 3.51126i −0.123745 + 0.380849i
\(86\) −3.25587 2.36553i −0.351090 0.255082i
\(87\) 0 0
\(88\) −9.58829 1.60431i −1.02212 0.171020i
\(89\) 12.1612 1.28908 0.644540 0.764570i \(-0.277049\pi\)
0.644540 + 0.764570i \(0.277049\pi\)
\(90\) 0 0
\(91\) 3.19256 9.82567i 0.334671 1.03001i
\(92\) 0.0582308 + 0.179216i 0.00607098 + 0.0186846i
\(93\) 0 0
\(94\) 2.44020 1.77291i 0.251687 0.182861i
\(95\) −0.0293950 0.0904686i −0.00301587 0.00928188i
\(96\) 0 0
\(97\) 3.50412 + 2.54589i 0.355789 + 0.258496i 0.751294 0.659968i \(-0.229430\pi\)
−0.395504 + 0.918464i \(0.629430\pi\)
\(98\) −8.56545 −0.865241
\(99\) 0 0
\(100\) −0.162147 −0.0162147
\(101\) 8.01388 + 5.82242i 0.797411 + 0.579353i 0.910153 0.414271i \(-0.135964\pi\)
−0.112743 + 0.993624i \(0.535964\pi\)
\(102\) 0 0
\(103\) 1.25643 + 3.86690i 0.123800 + 0.381017i 0.993681 0.112245i \(-0.0358042\pi\)
−0.869880 + 0.493263i \(0.835804\pi\)
\(104\) 6.71323 4.87744i 0.658286 0.478273i
\(105\) 0 0
\(106\) 1.25424 + 3.86014i 0.121822 + 0.374930i
\(107\) −0.599053 + 1.84369i −0.0579126 + 0.178237i −0.975828 0.218539i \(-0.929871\pi\)
0.917916 + 0.396776i \(0.129871\pi\)
\(108\) 0 0
\(109\) 6.12664 0.586825 0.293413 0.955986i \(-0.405209\pi\)
0.293413 + 0.955986i \(0.405209\pi\)
\(110\) 0.664691 + 4.44686i 0.0633758 + 0.423991i
\(111\) 0 0
\(112\) −10.7747 7.82825i −1.01811 0.739700i
\(113\) −1.78775 + 5.50212i −0.168177 + 0.517596i −0.999256 0.0385582i \(-0.987724\pi\)
0.831079 + 0.556154i \(0.187724\pi\)
\(114\) 0 0
\(115\) 0.940197 0.683093i 0.0876738 0.0636987i
\(116\) 0.885974 0.643698i 0.0822606 0.0597659i
\(117\) 0 0
\(118\) −3.56448 + 10.9703i −0.328137 + 1.00990i
\(119\) −10.9003 7.91951i −0.999226 0.725980i
\(120\) 0 0
\(121\) −10.5192 + 3.21657i −0.956291 + 0.292415i
\(122\) 11.4966 1.04085
\(123\) 0 0
\(124\) −0.339639 + 1.04530i −0.0305005 + 0.0938708i
\(125\) 0.309017 + 0.951057i 0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) −1.97224 + 1.43292i −0.175008 + 0.127151i −0.671841 0.740695i \(-0.734496\pi\)
0.496833 + 0.867846i \(0.334496\pi\)
\(128\) −3.01183 9.26945i −0.266211 0.819312i
\(129\) 0 0
\(130\) −3.10489 2.25583i −0.272317 0.197850i
\(131\) −7.04156 −0.615224 −0.307612 0.951512i \(-0.599530\pi\)
−0.307612 + 0.951512i \(0.599530\pi\)
\(132\) 0 0
\(133\) 0.347148 0.0301016
\(134\) −14.7134 10.6899i −1.27104 0.923468i
\(135\) 0 0
\(136\) −3.34410 10.2921i −0.286754 0.882539i
\(137\) −7.74461 + 5.62678i −0.661666 + 0.480729i −0.867225 0.497916i \(-0.834099\pi\)
0.205559 + 0.978645i \(0.434099\pi\)
\(138\) 0 0
\(139\) 0.159299 + 0.490271i 0.0135116 + 0.0415843i 0.957585 0.288151i \(-0.0930405\pi\)
−0.944073 + 0.329735i \(0.893041\pi\)
\(140\) 0.182858 0.562780i 0.0154544 0.0475636i
\(141\) 0 0
\(142\) 11.2563 0.944607
\(143\) 4.33527 8.32843i 0.362533 0.696459i
\(144\) 0 0
\(145\) −5.46401 3.96984i −0.453761 0.329677i
\(146\) 0.552996 1.70195i 0.0457663 0.140854i
\(147\) 0 0
\(148\) 1.29078 0.937809i 0.106102 0.0770874i
\(149\) −6.60144 + 4.79623i −0.540811 + 0.392922i −0.824386 0.566028i \(-0.808479\pi\)
0.283575 + 0.958950i \(0.408479\pi\)
\(150\) 0 0
\(151\) 0.599563 1.84526i 0.0487917 0.150165i −0.923692 0.383135i \(-0.874844\pi\)
0.972484 + 0.232970i \(0.0748443\pi\)
\(152\) 0.225574 + 0.163889i 0.0182965 + 0.0132932i
\(153\) 0 0
\(154\) −16.1838 2.70785i −1.30412 0.218205i
\(155\) 6.77837 0.544452
\(156\) 0 0
\(157\) 6.57418 20.2332i 0.524676 1.61479i −0.240279 0.970704i \(-0.577239\pi\)
0.764955 0.644084i \(-0.222761\pi\)
\(158\) 5.80887 + 17.8779i 0.462129 + 1.42229i
\(159\) 0 0
\(160\) 0.740184 0.537775i 0.0585167 0.0425149i
\(161\) 1.31059 + 4.03358i 0.103289 + 0.317891i
\(162\) 0 0
\(163\) 12.9289 + 9.39337i 1.01267 + 0.735746i 0.964767 0.263107i \(-0.0847471\pi\)
0.0479001 + 0.998852i \(0.484747\pi\)
\(164\) −1.34878 −0.105322
\(165\) 0 0
\(166\) −14.4304 −1.12002
\(167\) 14.3269 + 10.4091i 1.10865 + 0.805481i 0.982450 0.186524i \(-0.0597223\pi\)
0.126199 + 0.992005i \(0.459722\pi\)
\(168\) 0 0
\(169\) −1.54066 4.74168i −0.118513 0.364744i
\(170\) −4.04920 + 2.94192i −0.310560 + 0.225635i
\(171\) 0 0
\(172\) 0.148746 + 0.457794i 0.0113418 + 0.0349065i
\(173\) −4.90888 + 15.1080i −0.373216 + 1.14864i 0.571459 + 0.820631i \(0.306378\pi\)
−0.944675 + 0.328009i \(0.893622\pi\)
\(174\) 0 0
\(175\) −3.64941 −0.275870
\(176\) −8.48382 8.63280i −0.639492 0.650722i
\(177\) 0 0
\(178\) 13.3379 + 9.69057i 0.999719 + 0.726339i
\(179\) 5.21653 16.0548i 0.389902 1.19999i −0.542960 0.839759i \(-0.682696\pi\)
0.932862 0.360235i \(-0.117304\pi\)
\(180\) 0 0
\(181\) 19.4871 14.1582i 1.44846 1.05237i 0.462277 0.886735i \(-0.347032\pi\)
0.986187 0.165636i \(-0.0529676\pi\)
\(182\) 11.3310 8.23247i 0.839911 0.610231i
\(183\) 0 0
\(184\) −1.05265 + 3.23972i −0.0776024 + 0.238836i
\(185\) −7.96056 5.78369i −0.585272 0.425225i
\(186\) 0 0
\(187\) −8.58271 8.73343i −0.627630 0.638652i
\(188\) −0.360762 −0.0263113
\(189\) 0 0
\(190\) 0.0398501 0.122646i 0.00289103 0.00889767i
\(191\) −1.66337 5.11934i −0.120358 0.370422i 0.872669 0.488312i \(-0.162387\pi\)
−0.993027 + 0.117890i \(0.962387\pi\)
\(192\) 0 0
\(193\) −14.7921 + 10.7471i −1.06476 + 0.773593i −0.974963 0.222367i \(-0.928622\pi\)
−0.0897961 + 0.995960i \(0.528622\pi\)
\(194\) 1.81451 + 5.58448i 0.130274 + 0.400942i
\(195\) 0 0
\(196\) 0.828823 + 0.602175i 0.0592017 + 0.0430125i
\(197\) −2.64566 −0.188496 −0.0942478 0.995549i \(-0.530045\pi\)
−0.0942478 + 0.995549i \(0.530045\pi\)
\(198\) 0 0
\(199\) 6.52800 0.462757 0.231379 0.972864i \(-0.425676\pi\)
0.231379 + 0.972864i \(0.425676\pi\)
\(200\) −2.37136 1.72290i −0.167681 0.121827i
\(201\) 0 0
\(202\) 4.14976 + 12.7716i 0.291976 + 0.898610i
\(203\) 19.9404 14.4876i 1.39954 1.01683i
\(204\) 0 0
\(205\) 2.57047 + 7.91110i 0.179530 + 0.552535i
\(206\) −1.70331 + 5.24226i −0.118676 + 0.365246i
\(207\) 0 0
\(208\) 10.3313 0.716349
\(209\) 0.311166 + 0.0520641i 0.0215238 + 0.00360135i
\(210\) 0 0
\(211\) 22.2057 + 16.1334i 1.52871 + 1.11067i 0.956953 + 0.290243i \(0.0937362\pi\)
0.571752 + 0.820426i \(0.306264\pi\)
\(212\) 0.150014 0.461697i 0.0103030 0.0317095i
\(213\) 0 0
\(214\) −2.12616 + 1.54474i −0.145341 + 0.105597i
\(215\) 2.40166 1.74491i 0.163792 0.119002i
\(216\) 0 0
\(217\) −7.64418 + 23.5264i −0.518921 + 1.59707i
\(218\) 6.71947 + 4.88198i 0.455100 + 0.330650i
\(219\) 0 0
\(220\) 0.248309 0.477024i 0.0167410 0.0321609i
\(221\) 10.4518 0.703061
\(222\) 0 0
\(223\) −1.57040 + 4.83321i −0.105162 + 0.323656i −0.989768 0.142683i \(-0.954427\pi\)
0.884606 + 0.466338i \(0.154427\pi\)
\(224\) 1.03178 + 3.17550i 0.0689388 + 0.212172i
\(225\) 0 0
\(226\) −6.34507 + 4.60997i −0.422068 + 0.306650i
\(227\) −1.15566 3.55676i −0.0767040 0.236071i 0.905351 0.424663i \(-0.139607\pi\)
−0.982055 + 0.188593i \(0.939607\pi\)
\(228\) 0 0
\(229\) −21.7821 15.8256i −1.43940 1.04578i −0.988168 0.153378i \(-0.950985\pi\)
−0.451232 0.892407i \(-0.649015\pi\)
\(230\) 1.57549 0.103885
\(231\) 0 0
\(232\) 19.7968 1.29972
\(233\) 14.8185 + 10.7663i 0.970794 + 0.705323i 0.955632 0.294562i \(-0.0951737\pi\)
0.0151615 + 0.999885i \(0.495174\pi\)
\(234\) 0 0
\(235\) 0.687534 + 2.11601i 0.0448498 + 0.138033i
\(236\) 1.11616 0.810936i 0.0726557 0.0527874i
\(237\) 0 0
\(238\) −5.64439 17.3717i −0.365872 1.12604i
\(239\) 3.38555 10.4196i 0.218993 0.673991i −0.779853 0.625963i \(-0.784706\pi\)
0.998846 0.0480283i \(-0.0152938\pi\)
\(240\) 0 0
\(241\) −9.99444 −0.643798 −0.321899 0.946774i \(-0.604321\pi\)
−0.321899 + 0.946774i \(0.604321\pi\)
\(242\) −14.1002 4.85437i −0.906394 0.312050i
\(243\) 0 0
\(244\) −1.11245 0.808245i −0.0712175 0.0517426i
\(245\) 1.95244 6.00899i 0.124737 0.383900i
\(246\) 0 0
\(247\) −0.217862 + 0.158286i −0.0138622 + 0.0100715i
\(248\) −16.0740 + 11.6784i −1.02070 + 0.741581i
\(249\) 0 0
\(250\) −0.418926 + 1.28932i −0.0264952 + 0.0815439i
\(251\) 7.81303 + 5.67650i 0.493154 + 0.358297i 0.806396 0.591376i \(-0.201415\pi\)
−0.313242 + 0.949673i \(0.601415\pi\)
\(252\) 0 0
\(253\) 0.569804 + 3.81206i 0.0358233 + 0.239662i
\(254\) −3.30490 −0.207368
\(255\) 0 0
\(256\) −1.19443 + 3.67608i −0.0746520 + 0.229755i
\(257\) −3.22230 9.91721i −0.201001 0.618618i −0.999854 0.0170916i \(-0.994559\pi\)
0.798853 0.601527i \(-0.205441\pi\)
\(258\) 0 0
\(259\) 29.0514 21.1071i 1.80517 1.31153i
\(260\) 0.141849 + 0.436565i 0.00879707 + 0.0270746i
\(261\) 0 0
\(262\) −7.72292 5.61103i −0.477124 0.346651i
\(263\) 10.9619 0.675937 0.337968 0.941157i \(-0.390260\pi\)
0.337968 + 0.941157i \(0.390260\pi\)
\(264\) 0 0
\(265\) −2.99393 −0.183915
\(266\) 0.380739 + 0.276623i 0.0233446 + 0.0169609i
\(267\) 0 0
\(268\) 0.672190 + 2.06879i 0.0410605 + 0.126371i
\(269\) −0.0722816 + 0.0525156i −0.00440708 + 0.00320193i −0.589987 0.807413i \(-0.700867\pi\)
0.585580 + 0.810615i \(0.300867\pi\)
\(270\) 0 0
\(271\) −4.14069 12.7437i −0.251529 0.774126i −0.994494 0.104796i \(-0.966581\pi\)
0.742965 0.669330i \(-0.233419\pi\)
\(272\) 4.16353 12.8140i 0.252451 0.776965i
\(273\) 0 0
\(274\) −12.9777 −0.784010
\(275\) −3.27115 0.547326i −0.197258 0.0330050i
\(276\) 0 0
\(277\) 3.16057 + 2.29629i 0.189901 + 0.137971i 0.678673 0.734440i \(-0.262555\pi\)
−0.488773 + 0.872411i \(0.662555\pi\)
\(278\) −0.215957 + 0.664648i −0.0129523 + 0.0398630i
\(279\) 0 0
\(280\) 8.65409 6.28756i 0.517181 0.375754i
\(281\) −1.24381 + 0.903680i −0.0741994 + 0.0539090i −0.624267 0.781211i \(-0.714602\pi\)
0.550067 + 0.835120i \(0.314602\pi\)
\(282\) 0 0
\(283\) −1.67231 + 5.14683i −0.0994083 + 0.305947i −0.988377 0.152020i \(-0.951422\pi\)
0.888969 + 0.457967i \(0.151422\pi\)
\(284\) −1.08920 0.791349i −0.0646320 0.0469579i
\(285\) 0 0
\(286\) 11.3912 5.67979i 0.673578 0.335853i
\(287\) −30.3566 −1.79190
\(288\) 0 0
\(289\) −1.04122 + 3.20456i −0.0612484 + 0.188503i
\(290\) −2.82938 8.70794i −0.166147 0.511348i
\(291\) 0 0
\(292\) −0.173162 + 0.125809i −0.0101335 + 0.00736243i
\(293\) −3.52789 10.8577i −0.206102 0.634315i −0.999666 0.0258295i \(-0.991777\pi\)
0.793565 0.608486i \(-0.208223\pi\)
\(294\) 0 0
\(295\) −6.88361 5.00123i −0.400779 0.291183i
\(296\) 28.8421 1.67641
\(297\) 0 0
\(298\) −11.0621 −0.640808
\(299\) −2.66165 1.93381i −0.153927 0.111835i
\(300\) 0 0
\(301\) 3.34780 + 10.3035i 0.192964 + 0.593883i
\(302\) 2.12797 1.54606i 0.122451 0.0889657i
\(303\) 0 0
\(304\) 0.107275 + 0.330157i 0.00615262 + 0.0189358i
\(305\) −2.62058 + 8.06531i −0.150054 + 0.461818i
\(306\) 0 0
\(307\) −4.25008 −0.242565 −0.121282 0.992618i \(-0.538701\pi\)
−0.121282 + 0.992618i \(0.538701\pi\)
\(308\) 1.37563 + 1.39978i 0.0783836 + 0.0797601i
\(309\) 0 0
\(310\) 7.43427 + 5.40131i 0.422238 + 0.306774i
\(311\) 5.13570 15.8061i 0.291219 0.896279i −0.693247 0.720700i \(-0.743820\pi\)
0.984465 0.175579i \(-0.0561796\pi\)
\(312\) 0 0
\(313\) 21.5012 15.6215i 1.21532 0.882982i 0.219617 0.975586i \(-0.429519\pi\)
0.995703 + 0.0926041i \(0.0295191\pi\)
\(314\) 23.3331 16.9525i 1.31676 0.956683i
\(315\) 0 0
\(316\) 0.694778 2.13831i 0.0390843 0.120289i
\(317\) 4.68982 + 3.40736i 0.263407 + 0.191376i 0.711648 0.702537i \(-0.247949\pi\)
−0.448241 + 0.893913i \(0.647949\pi\)
\(318\) 0 0
\(319\) 20.0464 9.99534i 1.12238 0.559632i
\(320\) 8.53916 0.477353
\(321\) 0 0
\(322\) −1.77673 + 5.46822i −0.0990134 + 0.304732i
\(323\) 0.108525 + 0.334006i 0.00603850 + 0.0185846i
\(324\) 0 0
\(325\) 2.29029 1.66399i 0.127042 0.0923018i
\(326\) 6.69484 + 20.6046i 0.370793 + 1.14118i
\(327\) 0 0
\(328\) −19.7255 14.3314i −1.08916 0.791321i
\(329\) −8.11961 −0.447648
\(330\) 0 0
\(331\) −12.9230 −0.710311 −0.355155 0.934807i \(-0.615572\pi\)
−0.355155 + 0.934807i \(0.615572\pi\)
\(332\) 1.39634 + 1.01450i 0.0766340 + 0.0556779i
\(333\) 0 0
\(334\) 7.41878 + 22.8327i 0.405938 + 1.24935i
\(335\) 10.8532 7.88531i 0.592974 0.430820i
\(336\) 0 0
\(337\) 4.13631 + 12.7303i 0.225319 + 0.693461i 0.998259 + 0.0589818i \(0.0187854\pi\)
−0.772940 + 0.634479i \(0.781215\pi\)
\(338\) 2.08864 6.42817i 0.113607 0.349646i
\(339\) 0 0
\(340\) 0.598640 0.0324658
\(341\) −10.3803 + 19.9414i −0.562123 + 1.07989i
\(342\) 0 0
\(343\) −2.01291 1.46246i −0.108687 0.0789656i
\(344\) −2.68892 + 8.27564i −0.144977 + 0.446193i
\(345\) 0 0
\(346\) −17.4226 + 12.6583i −0.936646 + 0.680513i
\(347\) −6.83538 + 4.96619i −0.366942 + 0.266599i −0.755942 0.654639i \(-0.772821\pi\)
0.389000 + 0.921238i \(0.372821\pi\)
\(348\) 0 0
\(349\) −3.21341 + 9.88987i −0.172010 + 0.529393i −0.999484 0.0321111i \(-0.989777\pi\)
0.827474 + 0.561504i \(0.189777\pi\)
\(350\) −4.00254 2.90802i −0.213945 0.155440i
\(351\) 0 0
\(352\) 0.448587 + 3.00110i 0.0239098 + 0.159959i
\(353\) −19.1073 −1.01698 −0.508489 0.861069i \(-0.669796\pi\)
−0.508489 + 0.861069i \(0.669796\pi\)
\(354\) 0 0
\(355\) −2.56580 + 7.89671i −0.136178 + 0.419114i
\(356\) −0.609350 1.87539i −0.0322955 0.0993953i
\(357\) 0 0
\(358\) 18.5145 13.4516i 0.978522 0.710938i
\(359\) 1.36405 + 4.19813i 0.0719920 + 0.221569i 0.980578 0.196129i \(-0.0628371\pi\)
−0.908586 + 0.417698i \(0.862837\pi\)
\(360\) 0 0
\(361\) 15.3640 + 11.1626i 0.808632 + 0.587505i
\(362\) 32.6546 1.71629
\(363\) 0 0
\(364\) −1.67520 −0.0878041
\(365\) 1.06793 + 0.775895i 0.0558979 + 0.0406122i
\(366\) 0 0
\(367\) −9.07327 27.9247i −0.473621 1.45766i −0.847809 0.530302i \(-0.822078\pi\)
0.374188 0.927353i \(-0.377922\pi\)
\(368\) −3.43117 + 2.49289i −0.178862 + 0.129951i
\(369\) 0 0
\(370\) −4.12215 12.6867i −0.214300 0.659549i
\(371\) 3.37634 10.3913i 0.175291 0.539490i
\(372\) 0 0
\(373\) −4.96478 −0.257067 −0.128533 0.991705i \(-0.541027\pi\)
−0.128533 + 0.991705i \(0.541027\pi\)
\(374\) −2.45401 16.4176i −0.126894 0.848934i
\(375\) 0 0
\(376\) −5.27606 3.83329i −0.272092 0.197687i
\(377\) −5.90839 + 18.1842i −0.304298 + 0.936532i
\(378\) 0 0
\(379\) −6.40996 + 4.65711i −0.329258 + 0.239220i −0.740116 0.672480i \(-0.765229\pi\)
0.410858 + 0.911699i \(0.365229\pi\)
\(380\) −0.0124784 + 0.00906608i −0.000640128 + 0.000465080i
\(381\) 0 0
\(382\) 2.25499 6.94016i 0.115375 0.355089i
\(383\) −19.8335 14.4099i −1.01344 0.736309i −0.0485140 0.998823i \(-0.515449\pi\)
−0.964928 + 0.262514i \(0.915449\pi\)
\(384\) 0 0
\(385\) 5.58864 10.7363i 0.284823 0.547171i
\(386\) −24.7872 −1.26164
\(387\) 0 0
\(388\) 0.217026 0.667939i 0.0110179 0.0339095i
\(389\) −1.68752 5.19366i −0.0855608 0.263329i 0.899118 0.437706i \(-0.144209\pi\)
−0.984679 + 0.174377i \(0.944209\pi\)
\(390\) 0 0
\(391\) −3.47116 + 2.52195i −0.175544 + 0.127540i
\(392\) 5.72292 + 17.6133i 0.289051 + 0.889608i
\(393\) 0 0
\(394\) −2.90166 2.10818i −0.146184 0.106209i
\(395\) −13.8661 −0.697679
\(396\) 0 0
\(397\) −6.43455 −0.322941 −0.161470 0.986878i \(-0.551624\pi\)
−0.161470 + 0.986878i \(0.551624\pi\)
\(398\) 7.15967 + 5.20180i 0.358882 + 0.260743i
\(399\) 0 0
\(400\) −1.12773 3.47080i −0.0563865 0.173540i
\(401\) −11.8947 + 8.64197i −0.593991 + 0.431560i −0.843741 0.536751i \(-0.819652\pi\)
0.249750 + 0.968310i \(0.419652\pi\)
\(402\) 0 0
\(403\) −5.92981 18.2501i −0.295385 0.909101i
\(404\) 0.496337 1.52757i 0.0246937 0.0759994i
\(405\) 0 0
\(406\) 33.4143 1.65832
\(407\) 29.2058 14.5623i 1.44768 0.721826i
\(408\) 0 0
\(409\) −3.55625 2.58376i −0.175845 0.127759i 0.496381 0.868105i \(-0.334662\pi\)
−0.672226 + 0.740346i \(0.734662\pi\)
\(410\) −3.48472 + 10.7249i −0.172098 + 0.529664i
\(411\) 0 0
\(412\) 0.533365 0.387512i 0.0262770 0.0190914i
\(413\) 25.1211 18.2516i 1.23613 0.898101i
\(414\) 0 0
\(415\) 3.28932 10.1235i 0.161466 0.496942i
\(416\) −2.09543 1.52242i −0.102737 0.0746427i
\(417\) 0 0
\(418\) 0.299789 + 0.305053i 0.0146631 + 0.0149206i
\(419\) −17.8526 −0.872159 −0.436079 0.899908i \(-0.643633\pi\)
−0.436079 + 0.899908i \(0.643633\pi\)
\(420\) 0 0
\(421\) −1.49210 + 4.59221i −0.0727205 + 0.223811i −0.980810 0.194965i \(-0.937541\pi\)
0.908090 + 0.418776i \(0.137541\pi\)
\(422\) 11.4986 + 35.3891i 0.559743 + 1.72271i
\(423\) 0 0
\(424\) 7.09969 5.15823i 0.344792 0.250506i
\(425\) −1.14088 3.51126i −0.0553407 0.170321i
\(426\) 0 0
\(427\) −25.0378 18.1910i −1.21166 0.880324i
\(428\) 0.314335 0.0151939
\(429\) 0 0
\(430\) 4.02448 0.194078
\(431\) −20.1234 14.6205i −0.969312 0.704247i −0.0140175 0.999902i \(-0.504462\pi\)
−0.955295 + 0.295655i \(0.904462\pi\)
\(432\) 0 0
\(433\) −6.56669 20.2102i −0.315575 0.971240i −0.975517 0.219923i \(-0.929419\pi\)
0.659942 0.751316i \(-0.270581\pi\)
\(434\) −27.1307 + 19.7116i −1.30232 + 0.946188i
\(435\) 0 0
\(436\) −0.306983 0.944796i −0.0147018 0.0452475i
\(437\) 0.0341614 0.105138i 0.00163416 0.00502943i
\(438\) 0 0
\(439\) −15.9119 −0.759434 −0.379717 0.925103i \(-0.623979\pi\)
−0.379717 + 0.925103i \(0.623979\pi\)
\(440\) 8.70008 4.33795i 0.414760 0.206804i
\(441\) 0 0
\(442\) 11.4631 + 8.32843i 0.545244 + 0.396143i
\(443\) −8.12332 + 25.0010i −0.385951 + 1.18783i 0.549838 + 0.835272i \(0.314690\pi\)
−0.935788 + 0.352562i \(0.885310\pi\)
\(444\) 0 0
\(445\) −9.83859 + 7.14815i −0.466394 + 0.338855i
\(446\) −5.57368 + 4.04952i −0.263922 + 0.191750i
\(447\) 0 0
\(448\) −9.62987 + 29.6377i −0.454969 + 1.40025i
\(449\) −6.62554 4.81373i −0.312678 0.227174i 0.420366 0.907354i \(-0.361902\pi\)
−0.733045 + 0.680180i \(0.761902\pi\)
\(450\) 0 0
\(451\) −27.2102 4.55278i −1.28128 0.214382i
\(452\) 0.938065 0.0441229
\(453\) 0 0
\(454\) 1.56670 4.82181i 0.0735289 0.226299i
\(455\) 3.19256 + 9.82567i 0.149669 + 0.460635i
\(456\) 0 0
\(457\) −9.64056 + 7.00428i −0.450966 + 0.327646i −0.789977 0.613136i \(-0.789908\pi\)
0.339011 + 0.940782i \(0.389908\pi\)
\(458\) −11.2792 34.7139i −0.527043 1.62207i
\(459\) 0 0
\(460\) −0.152450 0.110762i −0.00710803 0.00516429i
\(461\) −6.96172 −0.324240 −0.162120 0.986771i \(-0.551833\pi\)
−0.162120 + 0.986771i \(0.551833\pi\)
\(462\) 0 0
\(463\) 12.4762 0.579817 0.289909 0.957054i \(-0.406375\pi\)
0.289909 + 0.957054i \(0.406375\pi\)
\(464\) 19.9404 + 14.4876i 0.925712 + 0.672569i
\(465\) 0 0
\(466\) 7.67335 + 23.6161i 0.355461 + 1.09400i
\(467\) −4.97235 + 3.61263i −0.230093 + 0.167172i −0.696858 0.717209i \(-0.745419\pi\)
0.466765 + 0.884381i \(0.345419\pi\)
\(468\) 0 0
\(469\) 15.1288 + 46.5618i 0.698585 + 2.15002i
\(470\) −0.932072 + 2.86862i −0.0429933 + 0.132320i
\(471\) 0 0
\(472\) 24.9401 1.14796
\(473\) 1.45552 + 9.73762i 0.0669250 + 0.447736i
\(474\) 0 0
\(475\) 0.0769572 + 0.0559127i 0.00353104 + 0.00256545i
\(476\) −0.675105 + 2.07776i −0.0309434 + 0.0952340i
\(477\) 0 0
\(478\) 12.0160 8.73013i 0.549599 0.399307i
\(479\) 17.9555 13.0454i 0.820406 0.596060i −0.0964228 0.995340i \(-0.530740\pi\)
0.916829 + 0.399281i \(0.130740\pi\)
\(480\) 0 0
\(481\) −8.60798 + 26.4926i −0.392490 + 1.20796i
\(482\) −10.9615 7.96402i −0.499284 0.362751i
\(483\) 0 0
\(484\) 1.02311 + 1.46101i 0.0465049 + 0.0664095i
\(485\) −4.33133 −0.196675
\(486\) 0 0
\(487\) −10.5778 + 32.5553i −0.479328 + 1.47522i 0.360702 + 0.932681i \(0.382537\pi\)
−0.840030 + 0.542539i \(0.817463\pi\)
\(488\) −7.68135 23.6408i −0.347719 1.07017i
\(489\) 0 0
\(490\) 6.92960 5.03465i 0.313047 0.227442i
\(491\) 5.25197 + 16.1639i 0.237018 + 0.729467i 0.996847 + 0.0793441i \(0.0252826\pi\)
−0.759829 + 0.650123i \(0.774717\pi\)
\(492\) 0 0
\(493\) 20.1729 + 14.6565i 0.908541 + 0.660094i
\(494\) −0.365073 −0.0164254
\(495\) 0 0
\(496\) −24.7371 −1.11073
\(497\) −24.5144 17.8107i −1.09962 0.798920i
\(498\) 0 0
\(499\) 1.61599 + 4.97352i 0.0723418 + 0.222645i 0.980690 0.195570i \(-0.0626558\pi\)
−0.908348 + 0.418215i \(0.862656\pi\)
\(500\) 0.131180 0.0953077i 0.00586654 0.00426229i
\(501\) 0 0
\(502\) 4.04575 + 12.4515i 0.180571 + 0.555740i
\(503\) −12.9617 + 39.8919i −0.577931 + 1.77869i 0.0480416 + 0.998845i \(0.484702\pi\)
−0.625973 + 0.779845i \(0.715298\pi\)
\(504\) 0 0
\(505\) −9.90570 −0.440798
\(506\) −2.41268 + 4.63497i −0.107257 + 0.206050i
\(507\) 0 0
\(508\) 0.319794 + 0.232344i 0.0141886 + 0.0103086i
\(509\) −6.29399 + 19.3709i −0.278976 + 0.858601i 0.709163 + 0.705044i \(0.249073\pi\)
−0.988140 + 0.153557i \(0.950927\pi\)
\(510\) 0 0
\(511\) −3.89731 + 2.83156i −0.172407 + 0.125261i
\(512\) −20.0094 + 14.5377i −0.884300 + 0.642481i
\(513\) 0 0
\(514\) 4.36838 13.4445i 0.192681 0.593012i
\(515\) −3.28939 2.38988i −0.144948 0.105311i
\(516\) 0 0
\(517\) −7.27801 1.21775i −0.320086 0.0535566i
\(518\) 48.6816 2.13895
\(519\) 0 0
\(520\) −2.56422 + 7.89187i −0.112449 + 0.346081i
\(521\) −4.47391 13.7693i −0.196005 0.603243i −0.999963 0.00855656i \(-0.997276\pi\)
0.803958 0.594686i \(-0.202724\pi\)
\(522\) 0 0
\(523\) −9.02873 + 6.55975i −0.394799 + 0.286838i −0.767419 0.641146i \(-0.778459\pi\)
0.372620 + 0.927984i \(0.378459\pi\)
\(524\) 0.352826 + 1.08589i 0.0154133 + 0.0474372i
\(525\) 0 0
\(526\) 12.0226 + 8.73490i 0.524209 + 0.380860i
\(527\) −25.0254 −1.09013
\(528\) 0 0
\(529\) −21.6494 −0.941279
\(530\) −3.28363 2.38570i −0.142632 0.103628i
\(531\) 0 0
\(532\) −0.0173943 0.0535341i −0.000754138 0.00232100i
\(533\) 19.0511 13.8415i 0.825197 0.599540i
\(534\) 0 0
\(535\) −0.599053 1.84369i −0.0258993 0.0797099i
\(536\) −12.1513 + 37.3979i −0.524857 + 1.61534i
\(537\) 0 0
\(538\) −0.121123 −0.00522197
\(539\) 14.6880 + 14.9459i 0.632658 + 0.643768i
\(540\) 0 0
\(541\) −8.64094 6.27801i −0.371503 0.269913i 0.386331 0.922360i \(-0.373742\pi\)
−0.757834 + 0.652447i \(0.773742\pi\)
\(542\) 5.61343 17.2763i 0.241117 0.742083i
\(543\) 0 0
\(544\) −2.73273 + 1.98544i −0.117165 + 0.0851251i
\(545\) −4.95655 + 3.60115i −0.212315 + 0.154256i
\(546\) 0 0
\(547\) 0.540038 1.66207i 0.0230904 0.0710648i −0.938847 0.344334i \(-0.888105\pi\)
0.961938 + 0.273269i \(0.0881049\pi\)
\(548\) 1.25577 + 0.912367i 0.0536437 + 0.0389744i
\(549\) 0 0
\(550\) −3.15155 3.20689i −0.134382 0.136742i
\(551\) −0.642459 −0.0273697
\(552\) 0 0
\(553\) 15.6372 48.1264i 0.664962 2.04654i
\(554\) 1.63661 + 5.03698i 0.0695331 + 0.214001i
\(555\) 0 0
\(556\) 0.0676235 0.0491313i 0.00286787 0.00208363i
\(557\) 6.02100 + 18.5307i 0.255118 + 0.785173i 0.993806 + 0.111126i \(0.0354456\pi\)
−0.738688 + 0.674047i \(0.764554\pi\)
\(558\) 0 0
\(559\) −6.79900 4.93976i −0.287567 0.208930i
\(560\) 13.3182 0.562798
\(561\) 0 0
\(562\) −2.08426 −0.0879191
\(563\) −11.8838 8.63407i −0.500842 0.363883i 0.308497 0.951225i \(-0.400174\pi\)
−0.809338 + 0.587343i \(0.800174\pi\)
\(564\) 0 0
\(565\) −1.78775 5.50212i −0.0752111 0.231476i
\(566\) −5.93535 + 4.31228i −0.249481 + 0.181259i
\(567\) 0 0
\(568\) −7.52078 23.1466i −0.315565 0.971209i
\(569\) −6.15980 + 18.9579i −0.258232 + 0.794758i 0.734943 + 0.678129i \(0.237209\pi\)
−0.993176 + 0.116629i \(0.962791\pi\)
\(570\) 0 0
\(571\) 5.24422 0.219464 0.109732 0.993961i \(-0.465001\pi\)
0.109732 + 0.993961i \(0.465001\pi\)
\(572\) −1.50156 0.251240i −0.0627834 0.0105049i
\(573\) 0 0
\(574\) −33.2940 24.1895i −1.38967 1.00965i
\(575\) −0.359123 + 1.10527i −0.0149765 + 0.0460928i
\(576\) 0 0
\(577\) −30.4194 + 22.1010i −1.26637 + 0.920075i −0.999052 0.0435320i \(-0.986139\pi\)
−0.267323 + 0.963607i \(0.586139\pi\)
\(578\) −3.69551 + 2.68495i −0.153713 + 0.111679i
\(579\) 0 0
\(580\) −0.338412 + 1.04153i −0.0140518 + 0.0432470i
\(581\) 31.4271 + 22.8331i 1.30382 + 0.947278i
\(582\) 0 0
\(583\) 4.58484 8.80789i 0.189885 0.364785i
\(584\) −3.86923 −0.160110
\(585\) 0 0
\(586\) 4.78267 14.7195i 0.197570 0.608059i
\(587\) −7.90191 24.3196i −0.326147 1.00378i −0.970920 0.239403i \(-0.923048\pi\)
0.644774 0.764373i \(-0.276952\pi\)
\(588\) 0 0
\(589\) 0.521644 0.378997i 0.0214940 0.0156163i
\(590\) −3.56448 10.9703i −0.146747 0.451642i
\(591\) 0 0
\(592\) 29.0514 + 21.1071i 1.19400 + 0.867495i
\(593\) −40.2260 −1.65188 −0.825942 0.563754i \(-0.809356\pi\)
−0.825942 + 0.563754i \(0.809356\pi\)
\(594\) 0 0
\(595\) 13.4735 0.552358
\(596\) 1.07040 + 0.777695i 0.0438455 + 0.0318556i
\(597\) 0 0
\(598\) −1.37826 4.24185i −0.0563613 0.173462i
\(599\) 3.98843 2.89776i 0.162963 0.118399i −0.503315 0.864103i \(-0.667886\pi\)
0.666278 + 0.745704i \(0.267886\pi\)
\(600\) 0 0
\(601\) 14.2425 + 43.8338i 0.580963 + 1.78802i 0.614912 + 0.788596i \(0.289191\pi\)
−0.0339497 + 0.999424i \(0.510809\pi\)
\(602\) −4.53853 + 13.9682i −0.184977 + 0.569300i
\(603\) 0 0
\(604\) −0.314602 −0.0128010
\(605\) 6.61956 8.78529i 0.269124 0.357173i
\(606\) 0 0
\(607\) 36.5162 + 26.5306i 1.48215 + 1.07684i 0.976857 + 0.213891i \(0.0686139\pi\)
0.505288 + 0.862951i \(0.331386\pi\)
\(608\) 0.0268941 0.0827714i 0.00109070 0.00335682i
\(609\) 0 0
\(610\) −9.30096 + 6.75754i −0.376585 + 0.273605i
\(611\) 5.09568 3.70223i 0.206149 0.149776i
\(612\) 0 0
\(613\) 1.46294 4.50247i 0.0590877 0.181853i −0.917156 0.398528i \(-0.869521\pi\)
0.976244 + 0.216675i \(0.0695212\pi\)
\(614\) −4.66133 3.38666i −0.188116 0.136674i
\(615\) 0 0
\(616\) 5.24479 + 35.0883i 0.211319 + 1.41375i
\(617\) −17.8468 −0.718486 −0.359243 0.933244i \(-0.616965\pi\)
−0.359243 + 0.933244i \(0.616965\pi\)
\(618\) 0 0
\(619\) 0.110304 0.339482i 0.00443351 0.0136449i −0.948815 0.315832i \(-0.897717\pi\)
0.953249 + 0.302187i \(0.0977166\pi\)
\(620\) −0.339639 1.04530i −0.0136402 0.0419803i
\(621\) 0 0
\(622\) 18.2276 13.2431i 0.730861 0.531002i
\(623\) −13.7145 42.2089i −0.549461 1.69107i
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.0323607 0.0235114i
\(626\) 36.0297 1.44004
\(627\) 0 0
\(628\) −3.44960 −0.137654
\(629\) 29.3900 + 21.3531i 1.17186 + 0.851404i
\(630\) 0 0
\(631\) −9.88614 30.4264i −0.393561 1.21126i −0.930077 0.367366i \(-0.880260\pi\)
0.536516 0.843890i \(-0.319740\pi\)
\(632\) 32.8815 23.8898i 1.30796 0.950287i
\(633\) 0 0
\(634\) 2.42849 + 7.47413i 0.0964477 + 0.296836i
\(635\) 0.753330 2.31851i 0.0298950 0.0920073i
\(636\) 0 0
\(637\) −17.8866 −0.708693
\(638\) 29.9509 + 5.01136i 1.18577 + 0.198402i
\(639\) 0 0
\(640\) 7.88507 + 5.72884i 0.311685 + 0.226452i
\(641\) −0.312987 + 0.963274i −0.0123622 + 0.0380470i −0.957047 0.289932i \(-0.906367\pi\)
0.944685 + 0.327979i \(0.106367\pi\)
\(642\) 0 0
\(643\) 12.1130 8.80057i 0.477688 0.347061i −0.322742 0.946487i \(-0.604605\pi\)
0.800430 + 0.599426i \(0.204605\pi\)
\(644\) 0.556354 0.404215i 0.0219234 0.0159283i
\(645\) 0 0
\(646\) −0.147125 + 0.452803i −0.00578855 + 0.0178153i
\(647\) 14.4712 + 10.5139i 0.568920 + 0.413345i 0.834713 0.550686i \(-0.185634\pi\)
−0.265793 + 0.964030i \(0.585634\pi\)
\(648\) 0 0
\(649\) 25.2546 12.5922i 0.991331 0.494287i
\(650\) 3.83785 0.150533
\(651\) 0 0
\(652\) 0.800746 2.46444i 0.0313596 0.0965150i
\(653\) −14.1419 43.5244i −0.553416 1.70324i −0.700089 0.714055i \(-0.746856\pi\)
0.146673 0.989185i \(-0.453144\pi\)
\(654\) 0 0
\(655\) 5.69674 4.13892i 0.222590 0.161721i
\(656\) −9.38072 28.8709i −0.366255 1.12722i
\(657\) 0 0
\(658\) −8.90529 6.47007i −0.347164 0.252230i
\(659\) 9.54036 0.371640 0.185820 0.982584i \(-0.440506\pi\)
0.185820 + 0.982584i \(0.440506\pi\)
\(660\) 0 0
\(661\) 15.7769 0.613651 0.306825 0.951766i \(-0.400733\pi\)
0.306825 + 0.951766i \(0.400733\pi\)
\(662\) −14.1734 10.2976i −0.550866 0.400228i
\(663\) 0 0
\(664\) 9.64154 + 29.6736i 0.374164 + 1.15156i
\(665\) −0.280849 + 0.204048i −0.0108908 + 0.00791266i
\(666\) 0 0
\(667\) −2.42548 7.46486i −0.0939149 0.289040i
\(668\) 0.887333 2.73093i 0.0343319 0.105663i
\(669\) 0 0
\(670\) 18.1868 0.702616
\(671\) −19.7144 20.0606i −0.761065 0.774430i
\(672\) 0 0
\(673\) −38.2690 27.8041i −1.47516 1.07177i −0.979076 0.203494i \(-0.934770\pi\)
−0.496086 0.868273i \(-0.665230\pi\)
\(674\) −5.60749 + 17.2581i −0.215992 + 0.664756i
\(675\) 0 0
\(676\) −0.654023 + 0.475175i −0.0251547 + 0.0182760i
\(677\) 22.2828 16.1894i 0.856399 0.622210i −0.0705039 0.997512i \(-0.522461\pi\)
0.926903 + 0.375301i \(0.122461\pi\)
\(678\) 0 0
\(679\) 4.88457 15.0332i 0.187453 0.576920i
\(680\) 8.75497 + 6.36086i 0.335738 + 0.243928i
\(681\) 0 0
\(682\) −27.2749 + 13.5995i −1.04441 + 0.520753i
\(683\) 27.1617 1.03931 0.519656 0.854375i \(-0.326060\pi\)
0.519656 + 0.854375i \(0.326060\pi\)
\(684\) 0 0
\(685\) 2.95818 9.10433i 0.113026 0.347859i
\(686\) −1.04233 3.20795i −0.0397962 0.122480i
\(687\) 0 0
\(688\) −8.76467 + 6.36790i −0.334150 + 0.242774i
\(689\) 2.61913 + 8.06084i 0.0997808 + 0.307094i
\(690\) 0 0
\(691\) 6.08931 + 4.42414i 0.231648 + 0.168302i 0.697554 0.716532i \(-0.254272\pi\)
−0.465906 + 0.884834i \(0.654272\pi\)
\(692\) 2.57579 0.0979167
\(693\) 0 0
\(694\) −11.4541 −0.434791
\(695\) −0.417050 0.303004i −0.0158196 0.0114936i
\(696\) 0 0
\(697\) −9.49007 29.2074i −0.359462 1.10631i
\(698\) −11.4051 + 8.28625i −0.431688 + 0.313639i
\(699\) 0 0
\(700\) 0.182858 + 0.562780i 0.00691140 + 0.0212711i
\(701\) 9.83315 30.2633i 0.371393 1.14303i −0.574487 0.818513i \(-0.694799\pi\)
0.945880 0.324516i \(-0.105201\pi\)
\(702\) 0 0
\(703\) −0.936004 −0.0353021
\(704\) −13.0767 + 25.1215i −0.492847 + 0.946802i
\(705\) 0 0
\(706\) −20.9562 15.2255i −0.788696 0.573021i
\(707\) 11.1710 34.3807i 0.420127 1.29302i
\(708\) 0 0
\(709\) 11.6807 8.48651i 0.438677 0.318718i −0.346432 0.938075i \(-0.612607\pi\)
0.785109 + 0.619357i \(0.212607\pi\)
\(710\) −9.10653 + 6.61628i −0.341762 + 0.248305i
\(711\) 0 0
\(712\) 11.0153 33.9017i 0.412817 1.27052i
\(713\) 6.37300 + 4.63026i 0.238671 + 0.173405i
\(714\) 0 0
\(715\) 1.38803 + 9.28605i 0.0519092 + 0.347279i
\(716\) −2.73721 −0.102294
\(717\) 0 0
\(718\) −1.84921 + 5.69129i −0.0690120 + 0.212397i
\(719\) −1.67179 5.14526i −0.0623474 0.191886i 0.915031 0.403383i \(-0.132166\pi\)
−0.977378 + 0.211498i \(0.932166\pi\)
\(720\) 0 0
\(721\) 12.0043 8.72166i 0.447065 0.324811i
\(722\) 7.95581 + 24.4855i 0.296085 + 0.911255i
\(723\) 0 0
\(724\) −3.15978 2.29571i −0.117432 0.0853195i
\(725\) 6.75389 0.250833
\(726\) 0 0
\(727\) −16.7753 −0.622161 −0.311080 0.950384i \(-0.600691\pi\)
−0.311080 + 0.950384i \(0.600691\pi\)
\(728\) −24.4993 17.7998i −0.908006 0.659705i
\(729\) 0 0
\(730\) 0.552996 + 1.70195i 0.0204673 + 0.0629919i
\(731\) −8.86684 + 6.44213i −0.327952 + 0.238271i
\(732\) 0 0
\(733\) −4.35252 13.3957i −0.160764 0.494781i 0.837935 0.545770i \(-0.183763\pi\)
−0.998699 + 0.0509889i \(0.983763\pi\)
\(734\) 12.3004 37.8567i 0.454016 1.39732i
\(735\) 0 0
\(736\) 1.06327 0.0391926
\(737\) 6.57756 + 44.0046i 0.242287 + 1.62093i
\(738\) 0 0
\(739\) 29.4043 + 21.3635i 1.08165 + 0.785868i 0.977971 0.208743i \(-0.0669371\pi\)
0.103683 + 0.994610i \(0.466937\pi\)
\(740\) −0.493035 + 1.51741i −0.0181243 + 0.0557810i
\(741\) 0 0
\(742\) 11.9833 8.70640i 0.439922 0.319622i
\(743\) −1.58338 + 1.15039i −0.0580884 + 0.0422037i −0.616451 0.787394i \(-0.711430\pi\)
0.558362 + 0.829597i \(0.311430\pi\)
\(744\) 0 0
\(745\) 2.52153 7.76046i 0.0923815 0.284321i
\(746\) −5.44519 3.95617i −0.199363 0.144846i
\(747\) 0 0
\(748\) −0.916745 + 1.76115i −0.0335195 + 0.0643940i
\(749\) 7.07466 0.258503
\(750\) 0 0
\(751\) 5.78189 17.7948i 0.210984 0.649342i −0.788430 0.615124i \(-0.789106\pi\)
0.999414 0.0342181i \(-0.0108941\pi\)
\(752\) −2.50910 7.72220i −0.0914973 0.281600i
\(753\) 0 0
\(754\) −20.9701 + 15.2356i −0.763685 + 0.554850i
\(755\) 0.599563 + 1.84526i 0.0218203 + 0.0671560i
\(756\) 0 0
\(757\) 11.7688 + 8.55054i 0.427744 + 0.310775i 0.780746 0.624848i \(-0.214839\pi\)
−0.353002 + 0.935623i \(0.614839\pi\)
\(758\) −10.7412 −0.390138
\(759\) 0 0
\(760\) −0.278825 −0.0101141
\(761\) 10.6309 + 7.72383i 0.385371 + 0.279989i 0.763556 0.645741i \(-0.223452\pi\)
−0.378185 + 0.925730i \(0.623452\pi\)
\(762\) 0 0
\(763\) −6.90920 21.2643i −0.250130 0.769820i
\(764\) −0.706114 + 0.513022i −0.0255463 + 0.0185605i
\(765\) 0 0
\(766\) −10.2702 31.6084i −0.371077 1.14206i
\(767\) −7.44344 + 22.9085i −0.268767 + 0.827180i
\(768\) 0 0
\(769\) 38.9767 1.40554 0.702768 0.711419i \(-0.251947\pi\)
0.702768 + 0.711419i \(0.251947\pi\)
\(770\) 14.6846 7.32187i 0.529195 0.263862i
\(771\) 0 0
\(772\) 2.39850 + 1.74261i 0.0863239 + 0.0627179i
\(773\) 11.9756 36.8571i 0.430733 1.32566i −0.466664 0.884435i \(-0.654544\pi\)
0.897397 0.441225i \(-0.145456\pi\)
\(774\) 0 0
\(775\) −5.48382 + 3.98423i −0.196985 + 0.143118i
\(776\) 10.2712 7.46243i 0.368713 0.267886i
\(777\) 0 0
\(778\) 2.28773 7.04091i 0.0820192 0.252429i
\(779\) 0.640147 + 0.465094i 0.0229356 + 0.0166637i
\(780\) 0 0
\(781\) −19.3023 19.6412i −0.690689 0.702818i
\(782\) −5.81665 −0.208003
\(783\) 0 0
\(784\) −7.12525 + 21.9293i −0.254473 + 0.783188i
\(785\) 6.57418 + 20.2332i 0.234642 + 0.722155i
\(786\) 0 0
\(787\) 17.3002 12.5693i 0.616685 0.448048i −0.235077 0.971977i \(-0.575534\pi\)
0.851762 + 0.523929i \(0.175534\pi\)
\(788\) 0.132564 + 0.407990i 0.00472240 + 0.0145341i
\(789\) 0 0
\(790\) −15.2078 11.0491i −0.541070 0.393110i
\(791\) 21.1128 0.750686
\(792\) 0 0
\(793\) 24.0075 0.852533
\(794\) −7.05718 5.12734i −0.250450 0.181963i
\(795\) 0 0
\(796\) −0.327093 1.00669i −0.0115935 0.0356812i
\(797\) −1.79970 + 1.30756i −0.0637488 + 0.0463162i −0.619203 0.785231i \(-0.712544\pi\)
0.555454 + 0.831547i \(0.312544\pi\)
\(798\) 0 0
\(799\) −2.53834 7.81222i −0.0898002 0.276377i
\(800\) −0.282725 + 0.870139i −0.00999585 + 0.0307641i
\(801\) 0 0
\(802\) −19.9319 −0.703821
\(803\) −3.91802 + 1.95356i −0.138264 + 0.0689398i
\(804\) 0 0
\(805\) −3.43117 2.49289i −0.120933 0.0878628i
\(806\) 8.03889 24.7412i 0.283158 0.871470i
\(807\) 0 0
\(808\) 23.4900 17.0665i 0.826376 0.600397i
\(809\) 17.1254 12.4424i 0.602098 0.437450i −0.244525 0.969643i \(-0.578632\pi\)
0.846623 + 0.532193i \(0.178632\pi\)
\(810\) 0 0
\(811\) −11.3462 + 34.9201i −0.398420 + 1.22621i 0.527845 + 0.849341i \(0.323000\pi\)
−0.926266 + 0.376871i \(0.877000\pi\)
\(812\) −3.23329 2.34912i −0.113466 0.0824380i
\(813\) 0 0
\(814\) 43.6357 + 7.30109i 1.52943 + 0.255903i
\(815\) −15.9810 −0.559788
\(816\) 0 0
\(817\) 0.0872627 0.268567i 0.00305294 0.00939597i
\(818\) −1.84150 5.66756i −0.0643866 0.198161i
\(819\) 0 0
\(820\) 1.09118 0.792791i 0.0381058 0.0276855i
\(821\) 12.2585 + 37.7278i 0.427825 + 1.31671i 0.900264 + 0.435345i \(0.143374\pi\)
−0.472439 + 0.881363i \(0.656626\pi\)
\(822\) 0 0
\(823\) 37.1568 + 26.9960i 1.29520 + 0.941021i 0.999897 0.0143810i \(-0.00457777\pi\)
0.295308 + 0.955402i \(0.404578\pi\)
\(824\) 11.9178 0.415178
\(825\) 0 0
\(826\) 42.0956 1.46469
\(827\) −32.1139 23.3321i −1.11671 0.811337i −0.133002 0.991116i \(-0.542462\pi\)
−0.983707 + 0.179779i \(0.942462\pi\)
\(828\) 0 0
\(829\) 2.36578 + 7.28113i 0.0821671 + 0.252884i 0.983697 0.179832i \(-0.0575553\pi\)
−0.901530 + 0.432716i \(0.857555\pi\)
\(830\) 11.6745 8.48199i 0.405226 0.294414i
\(831\) 0 0
\(832\) −7.47017 22.9908i −0.258982 0.797063i
\(833\) −7.20831 + 22.1849i −0.249753 + 0.768661i
\(834\) 0 0
\(835\) −17.7090 −0.612846
\(836\) −0.00756251 0.0505940i −0.000261555 0.00174983i
\(837\) 0 0
\(838\) −19.5801 14.2258i −0.676384 0.491422i
\(839\) −8.52536 + 26.2383i −0.294328 + 0.905848i 0.689118 + 0.724649i \(0.257998\pi\)
−0.983446 + 0.181200i \(0.942002\pi\)
\(840\) 0 0
\(841\) −13.4418 + 9.76607i −0.463512 + 0.336761i
\(842\) −5.29576 + 3.84760i −0.182504 + 0.132597i
\(843\) 0 0
\(844\) 1.37531 4.23276i 0.0473400 0.145697i
\(845\) 4.03351 + 2.93052i 0.138757 + 0.100813i
\(846\) 0 0
\(847\) 23.0269 + 32.8826i 0.791213 + 1.12986i
\(848\) 10.9261 0.375203
\(849\) 0 0
\(850\) 1.54666 4.76012i 0.0530499 0.163271i
\(851\) −3.53370 10.8756i −0.121134 0.372811i
\(852\) 0 0
\(853\) −34.0998 + 24.7749i −1.16755 + 0.848277i −0.990714 0.135962i \(-0.956587\pi\)
−0.176840 + 0.984240i \(0.556587\pi\)
\(854\) −12.9651 39.9024i −0.443656 1.36543i
\(855\) 0 0
\(856\) 4.59707 + 3.33997i 0.157125 + 0.114158i
\(857\) 45.0850 1.54008 0.770038 0.637998i \(-0.220237\pi\)
0.770038 + 0.637998i \(0.220237\pi\)
\(858\) 0 0
\(859\) −11.8257 −0.403488 −0.201744 0.979438i \(-0.564661\pi\)
−0.201744 + 0.979438i \(0.564661\pi\)
\(860\) −0.389423 0.282932i −0.0132792 0.00964792i
\(861\) 0 0
\(862\) −10.4204 32.0705i −0.354919 1.09233i
\(863\) 22.5484 16.3823i 0.767555 0.557662i −0.133663 0.991027i \(-0.542674\pi\)
0.901218 + 0.433365i \(0.142674\pi\)
\(864\) 0 0
\(865\) −4.90888 15.1080i −0.166907 0.513687i
\(866\) 8.90229 27.3984i 0.302512 0.931037i
\(867\) 0 0
\(868\) 4.01105 0.136144
\(869\) 21.2342 40.7929i 0.720323 1.38380i
\(870\) 0 0
\(871\) −30.7249 22.3230i −1.04107 0.756384i
\(872\) 5.54939 17.0793i 0.187926 0.578377i
\(873\) 0 0
\(874\) 0.121246 0.0880900i 0.00410119 0.00297969i
\(875\) 2.95244 2.14507i 0.0998106 0.0725167i
\(876\) 0 0
\(877\) −3.53736 + 10.8869i −0.119448 + 0.367624i −0.992849 0.119379i \(-0.961910\pi\)
0.873401 + 0.487003i \(0.161910\pi\)
\(878\) −17.4516 12.6793i −0.588963 0.427907i
\(879\) 0 0
\(880\) 11.9378 + 1.99742i 0.402423 + 0.0673330i
\(881\) −47.0037 −1.58360 −0.791798 0.610783i \(-0.790855\pi\)
−0.791798 + 0.610783i \(0.790855\pi\)
\(882\) 0 0
\(883\) −14.4974 + 44.6185i −0.487877 + 1.50153i 0.339894 + 0.940464i \(0.389609\pi\)
−0.827770 + 0.561067i \(0.810391\pi\)
\(884\) −0.523698 1.61178i −0.0176139 0.0542099i
\(885\) 0 0
\(886\) −28.8313 + 20.9472i −0.968607 + 0.703734i
\(887\) 8.60386 + 26.4800i 0.288889 + 0.889110i 0.985206 + 0.171375i \(0.0548210\pi\)
−0.696316 + 0.717735i \(0.745179\pi\)
\(888\) 0 0
\(889\) 7.19754 + 5.22932i 0.241398 + 0.175386i
\(890\) −16.4866 −0.552631
\(891\) 0 0
\(892\) 0.824022 0.0275903
\(893\) 0.171223 + 0.124401i 0.00572975 + 0.00416290i
\(894\) 0 0
\(895\) 5.21653 + 16.0548i 0.174369 + 0.536653i
\(896\) −28.7759 + 20.9069i −0.961335 + 0.698451i
\(897\) 0 0
\(898\) −3.43085 10.5591i −0.114489 0.352360i
\(899\) 14.1469 43.5397i 0.471826 1.45213i
\(900\) 0 0
\(901\) 11.0534 0.368244
\(902\) −26.2153 26.6756i −0.872872 0.888201i
\(903\) 0 0
\(904\) 13.7190 + 9.96742i 0.456287 + 0.331512i
\(905\) −7.44341 + 22.9085i −0.247427 + 0.761503i
\(906\) 0 0
\(907\) 23.1567 16.8243i 0.768907 0.558643i −0.132723 0.991153i \(-0.542372\pi\)
0.901629 + 0.432510i \(0.142372\pi\)
\(908\) −0.490586 + 0.356432i −0.0162807 + 0.0118286i
\(909\) 0 0
\(910\) −4.32807 + 13.3204i −0.143474 + 0.441567i
\(911\) 4.14883 + 3.01430i 0.137457 + 0.0998682i 0.654389 0.756158i \(-0.272926\pi\)
−0.516932 + 0.856026i \(0.672926\pi\)
\(912\) 0 0
\(913\) 24.7452 + 25.1798i 0.818948 + 0.833330i
\(914\) −16.1547 −0.534351
\(915\) 0 0
\(916\) −1.34907 + 4.15200i −0.0445744 + 0.137186i
\(917\) 7.94098 + 24.4398i 0.262234 + 0.807074i
\(918\) 0 0
\(919\) −28.5429 + 20.7376i −0.941544 + 0.684072i −0.948792 0.315902i \(-0.897693\pi\)
0.00724799 + 0.999974i \(0.497693\pi\)
\(920\) −1.05265 3.23972i −0.0347049 0.106811i
\(921\) 0 0
\(922\) −7.63536 5.54742i −0.251457 0.182694i
\(923\) 23.5057 0.773699
\(924\) 0 0
\(925\) 9.83980 0.323531
\(926\) 13.6834 + 9.94159i 0.449665 + 0.326701i
\(927\) 0 0
\(928\) −1.90950 5.87682i −0.0626823 0.192916i
\(929\) −47.8474 + 34.7632i −1.56982 + 1.14054i −0.642498 + 0.766287i \(0.722102\pi\)
−0.927325 + 0.374256i \(0.877898\pi\)
\(930\) 0 0
\(931\) −0.185724 0.571601i −0.00608687 0.0187335i
\(932\) 0.917781 2.82464i 0.0300629 0.0925242i
\(933\) 0 0
\(934\) −8.33220 −0.272638
\(935\) 12.0769 + 2.02070i 0.394958 + 0.0660841i
\(936\) 0 0
\(937\) −11.6843 8.48911i −0.381708 0.277327i 0.380341 0.924846i \(-0.375807\pi\)
−0.762049 + 0.647519i \(0.775807\pi\)
\(938\) −20.5098 + 63.1226i −0.669668 + 2.06103i
\(939\) 0 0
\(940\) 0.291863 0.212051i 0.00951952 0.00691634i
\(941\) −15.0955 + 10.9675i −0.492100 + 0.357532i −0.805991 0.591927i \(-0.798367\pi\)
0.313891 + 0.949459i \(0.398367\pi\)
\(942\) 0 0
\(943\) −2.98727 + 9.19386i −0.0972788 + 0.299393i
\(944\) 25.1211 + 18.2516i 0.817623 + 0.594038i
\(945\) 0 0
\(946\) −6.16301 + 11.8397i −0.200377 + 0.384942i
\(947\) 0.991391 0.0322159 0.0161079 0.999870i \(-0.494872\pi\)
0.0161079 + 0.999870i \(0.494872\pi\)
\(948\) 0 0
\(949\) 1.15478 3.55405i 0.0374858 0.115369i
\(950\) 0.0398501 + 0.122646i 0.00129291 + 0.00397916i
\(951\) 0 0
\(952\) −31.9505 + 23.2134i −1.03552 + 0.752351i
\(953\) 2.55373 + 7.85957i 0.0827234 + 0.254597i 0.983860 0.178938i \(-0.0572662\pi\)
−0.901137 + 0.433535i \(0.857266\pi\)
\(954\) 0 0
\(955\) 4.35477 + 3.16393i 0.140917 + 0.102382i
\(956\) −1.77646 −0.0574549
\(957\) 0 0
\(958\) 30.0881 0.972101
\(959\) 28.2633 + 20.5345i 0.912669 + 0.663093i
\(960\) 0 0
\(961\) 4.61867 + 14.2148i 0.148989 + 0.458542i
\(962\) −30.5515 + 22.1969i −0.985019 + 0.715658i
\(963\) 0 0
\(964\) 0.500784 + 1.54125i 0.0161292 + 0.0496404i
\(965\) 5.65008 17.3892i 0.181883 0.559777i
\(966\) 0 0
\(967\) 7.36029 0.236691 0.118345 0.992972i \(-0.462241\pi\)
0.118345 + 0.992972i \(0.462241\pi\)
\(968\) −0.561246 + 32.2380i −0.0180391 + 1.03617i
\(969\) 0 0
\(970\) −4.75044 3.45140i −0.152527 0.110818i
\(971\) 1.53808 4.73372i 0.0493593 0.151912i −0.923339 0.383986i \(-0.874551\pi\)
0.972698 + 0.232074i \(0.0745511\pi\)
\(972\) 0 0
\(973\) 1.52199 1.10579i 0.0487927 0.0354500i
\(974\) −37.5429 + 27.2765i −1.20295 + 0.873996i
\(975\) 0 0
\(976\) 9.56357 29.4337i 0.306123 0.942148i
\(977\) 8.36266 + 6.07583i 0.267545 + 0.194383i 0.713467 0.700689i \(-0.247124\pi\)
−0.445922 + 0.895072i \(0.647124\pi\)
\(978\) 0 0
\(979\) −5.96266 39.8908i −0.190567 1.27492i
\(980\) −1.02448 −0.0327259
\(981\) 0 0
\(982\) −7.11996 + 21.9130i −0.227207 + 0.699272i
\(983\) 8.98045 + 27.6390i 0.286432 + 0.881547i 0.985966 + 0.166947i \(0.0533910\pi\)
−0.699534 + 0.714599i \(0.746609\pi\)
\(984\) 0 0
\(985\) 2.14038 1.55508i 0.0681983 0.0495490i
\(986\) 10.4460 + 32.1493i 0.332667 + 1.02384i
\(987\) 0 0
\(988\) 0.0353258 + 0.0256657i 0.00112386 + 0.000816534i
\(989\) 3.44997 0.109703
\(990\) 0 0
\(991\) 7.70381 0.244719 0.122360 0.992486i \(-0.460954\pi\)
0.122360 + 0.992486i \(0.460954\pi\)
\(992\) 5.01724 + 3.64524i 0.159298 + 0.115737i
\(993\) 0 0
\(994\) −12.6941 39.0683i −0.402631 1.23917i
\(995\) −5.28126 + 3.83706i −0.167427 + 0.121643i
\(996\) 0 0
\(997\) −0.885080 2.72400i −0.0280308 0.0862698i 0.936062 0.351834i \(-0.114442\pi\)
−0.964093 + 0.265564i \(0.914442\pi\)
\(998\) −2.19076 + 6.74247i −0.0693473 + 0.213429i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 495.2.n.e.136.2 8
3.2 odd 2 55.2.g.b.26.1 8
11.3 even 5 inner 495.2.n.e.91.2 8
11.5 even 5 5445.2.a.bp.1.1 4
11.6 odd 10 5445.2.a.bi.1.4 4
12.11 even 2 880.2.bo.h.81.1 8
15.2 even 4 275.2.z.a.224.4 16
15.8 even 4 275.2.z.a.224.1 16
15.14 odd 2 275.2.h.a.26.2 8
33.2 even 10 605.2.g.e.511.1 8
33.5 odd 10 605.2.a.j.1.4 4
33.8 even 10 605.2.g.k.366.2 8
33.14 odd 10 55.2.g.b.36.1 yes 8
33.17 even 10 605.2.a.k.1.1 4
33.20 odd 10 605.2.g.m.511.2 8
33.26 odd 10 605.2.g.m.251.2 8
33.29 even 10 605.2.g.e.251.1 8
33.32 even 2 605.2.g.k.81.2 8
132.47 even 10 880.2.bo.h.641.1 8
132.71 even 10 9680.2.a.cn.1.2 4
132.83 odd 10 9680.2.a.cm.1.2 4
165.14 odd 10 275.2.h.a.201.2 8
165.47 even 20 275.2.z.a.124.1 16
165.104 odd 10 3025.2.a.bd.1.1 4
165.113 even 20 275.2.z.a.124.4 16
165.149 even 10 3025.2.a.w.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.g.b.26.1 8 3.2 odd 2
55.2.g.b.36.1 yes 8 33.14 odd 10
275.2.h.a.26.2 8 15.14 odd 2
275.2.h.a.201.2 8 165.14 odd 10
275.2.z.a.124.1 16 165.47 even 20
275.2.z.a.124.4 16 165.113 even 20
275.2.z.a.224.1 16 15.8 even 4
275.2.z.a.224.4 16 15.2 even 4
495.2.n.e.91.2 8 11.3 even 5 inner
495.2.n.e.136.2 8 1.1 even 1 trivial
605.2.a.j.1.4 4 33.5 odd 10
605.2.a.k.1.1 4 33.17 even 10
605.2.g.e.251.1 8 33.29 even 10
605.2.g.e.511.1 8 33.2 even 10
605.2.g.k.81.2 8 33.32 even 2
605.2.g.k.366.2 8 33.8 even 10
605.2.g.m.251.2 8 33.26 odd 10
605.2.g.m.511.2 8 33.20 odd 10
880.2.bo.h.81.1 8 12.11 even 2
880.2.bo.h.641.1 8 132.47 even 10
3025.2.a.w.1.4 4 165.149 even 10
3025.2.a.bd.1.1 4 165.104 odd 10
5445.2.a.bi.1.4 4 11.6 odd 10
5445.2.a.bp.1.1 4 11.5 even 5
9680.2.a.cm.1.2 4 132.83 odd 10
9680.2.a.cn.1.2 4 132.71 even 10