Properties

Label 825.2.bx.f.49.3
Level $825$
Weight $2$
Character 825.49
Analytic conductor $6.588$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [825,2,Mod(49,825)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(825, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("825.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bx (of order \(10\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 49.3
Root \(1.23158 - 1.69513i\) of defining polynomial
Character \(\chi\) \(=\) 825.49
Dual form 825.2.bx.f.724.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.04169 - 0.338464i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.647481 + 0.470423i) q^{4} +(0.338464 - 1.04169i) q^{6} +(-0.414410 - 0.570387i) q^{7} +(-1.80285 + 2.48141i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(1.04169 - 0.338464i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.647481 + 0.470423i) q^{4} +(0.338464 - 1.04169i) q^{6} +(-0.414410 - 0.570387i) q^{7} +(-1.80285 + 2.48141i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(3.31118 + 0.189896i) q^{11} +0.800331i q^{12} +(4.48264 - 1.45650i) q^{13} +(-0.624741 - 0.453901i) q^{14} +(-0.543502 + 1.67273i) q^{16} +(7.39971 + 2.40431i) q^{17} +(-0.643798 - 0.886111i) q^{18} +(-0.970553 - 0.705148i) q^{19} -0.705037 q^{21} +(3.51349 - 0.922906i) q^{22} -6.89318i q^{23} +(0.947813 + 2.91707i) q^{24} +(4.17653 - 3.03443i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(0.536646 + 0.174367i) q^{28} +(1.07389 - 0.780229i) q^{29} +(-2.37364 - 7.30532i) q^{31} -4.20796i q^{32} +(2.09989 - 2.56719i) q^{33} +8.52195 q^{34} +(0.647481 + 0.470423i) q^{36} +(4.95951 + 6.82618i) q^{37} +(-1.24968 - 0.406045i) q^{38} +(1.45650 - 4.48264i) q^{39} +(0.188421 + 0.136896i) q^{41} +(-0.734428 + 0.238630i) q^{42} +7.32892i q^{43} +(-2.23326 + 1.43470i) q^{44} +(-2.33310 - 7.18053i) q^{46} +(-4.89171 + 6.73287i) q^{47} +(1.03380 + 1.42291i) q^{48} +(2.00951 - 6.18465i) q^{49} +(6.29457 - 4.57327i) q^{51} +(-2.21726 + 3.05179i) q^{52} +(-6.48936 + 2.10852i) q^{53} -1.09529 q^{54} +2.16248 q^{56} +(-1.14095 + 0.370718i) q^{57} +(0.854580 - 1.17623i) q^{58} +(-2.86401 + 2.08083i) q^{59} +(-3.35959 + 10.3397i) q^{61} +(-4.94518 - 6.80645i) q^{62} +(-0.414410 + 0.570387i) q^{63} +(-2.51125 - 7.72883i) q^{64} +(1.31853 - 3.38494i) q^{66} +2.04036i q^{67} +(-5.92222 + 1.92424i) q^{68} +(-5.57670 - 4.05171i) q^{69} +(0.207204 - 0.637709i) q^{71} +(2.91707 + 0.947813i) q^{72} +(2.94147 + 4.04859i) q^{73} +(7.47668 + 5.43212i) q^{74} +0.960132 q^{76} +(-1.26387 - 1.96735i) q^{77} -5.16248i q^{78} +(-0.704642 - 2.16867i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(0.242610 + 0.0788288i) q^{82} +(-2.00672 - 0.652022i) q^{83} +(0.456498 - 0.331666i) q^{84} +(2.48058 + 7.63443i) q^{86} -1.32741i q^{87} +(-6.44077 + 7.87404i) q^{88} +3.34722 q^{89} +(-2.68842 - 1.95325i) q^{91} +(3.24271 + 4.46321i) q^{92} +(-7.30532 - 2.37364i) q^{93} +(-2.81680 + 8.66921i) q^{94} +(-3.40431 - 2.47338i) q^{96} +(3.15968 - 1.02664i) q^{97} -7.12261i q^{98} +(-0.842610 - 3.20780i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9} + 6 q^{11} + 8 q^{14} - 24 q^{16} - 4 q^{19} - 24 q^{21} - 8 q^{24} + 4 q^{26} - 20 q^{29} + 38 q^{31} + 12 q^{34} + 4 q^{36} + 8 q^{39} - 18 q^{41} - 34 q^{44} - 44 q^{46} - 2 q^{49} + 20 q^{51} + 12 q^{54} - 32 q^{56} - 26 q^{59} + 26 q^{61} - 78 q^{64} - 22 q^{66} - 18 q^{69} - 22 q^{71} + 86 q^{74} - 76 q^{76} + 44 q^{79} - 4 q^{81} - 8 q^{84} + 40 q^{86} + 40 q^{89} - 22 q^{91} + 70 q^{94} - 16 q^{96} + 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.04169 0.338464i 0.736584 0.239331i 0.0833853 0.996517i \(-0.473427\pi\)
0.653198 + 0.757187i \(0.273427\pi\)
\(3\) 0.587785 0.809017i 0.339358 0.467086i
\(4\) −0.647481 + 0.470423i −0.323741 + 0.235211i
\(5\) 0 0
\(6\) 0.338464 1.04169i 0.138178 0.425267i
\(7\) −0.414410 0.570387i −0.156632 0.215586i 0.723487 0.690337i \(-0.242538\pi\)
−0.880120 + 0.474751i \(0.842538\pi\)
\(8\) −1.80285 + 2.48141i −0.637403 + 0.877309i
\(9\) −0.309017 0.951057i −0.103006 0.317019i
\(10\) 0 0
\(11\) 3.31118 + 0.189896i 0.998360 + 0.0572559i
\(12\) 0.800331i 0.231036i
\(13\) 4.48264 1.45650i 1.24326 0.403960i 0.387760 0.921761i \(-0.373249\pi\)
0.855501 + 0.517801i \(0.173249\pi\)
\(14\) −0.624741 0.453901i −0.166969 0.121310i
\(15\) 0 0
\(16\) −0.543502 + 1.67273i −0.135875 + 0.418181i
\(17\) 7.39971 + 2.40431i 1.79469 + 0.583131i 0.999723 0.0235184i \(-0.00748682\pi\)
0.794969 + 0.606649i \(0.207487\pi\)
\(18\) −0.643798 0.886111i −0.151745 0.208858i
\(19\) −0.970553 0.705148i −0.222660 0.161772i 0.470863 0.882206i \(-0.343943\pi\)
−0.693523 + 0.720434i \(0.743943\pi\)
\(20\) 0 0
\(21\) −0.705037 −0.153852
\(22\) 3.51349 0.922906i 0.749078 0.196764i
\(23\) 6.89318i 1.43733i −0.695358 0.718664i \(-0.744754\pi\)
0.695358 0.718664i \(-0.255246\pi\)
\(24\) 0.947813 + 2.91707i 0.193471 + 0.595444i
\(25\) 0 0
\(26\) 4.17653 3.03443i 0.819086 0.595101i
\(27\) −0.951057 0.309017i −0.183031 0.0594703i
\(28\) 0.536646 + 0.174367i 0.101417 + 0.0329522i
\(29\) 1.07389 0.780229i 0.199417 0.144885i −0.483596 0.875292i \(-0.660669\pi\)
0.683013 + 0.730407i \(0.260669\pi\)
\(30\) 0 0
\(31\) −2.37364 7.30532i −0.426318 1.31207i −0.901726 0.432308i \(-0.857699\pi\)
0.475408 0.879766i \(-0.342301\pi\)
\(32\) 4.20796i 0.743869i
\(33\) 2.09989 2.56719i 0.365545 0.446890i
\(34\) 8.52195 1.46150
\(35\) 0 0
\(36\) 0.647481 + 0.470423i 0.107914 + 0.0784038i
\(37\) 4.95951 + 6.82618i 0.815339 + 1.12222i 0.990478 + 0.137674i \(0.0439625\pi\)
−0.175139 + 0.984544i \(0.556037\pi\)
\(38\) −1.24968 0.406045i −0.202725 0.0658692i
\(39\) 1.45650 4.48264i 0.233226 0.717797i
\(40\) 0 0
\(41\) 0.188421 + 0.136896i 0.0294264 + 0.0213795i 0.602401 0.798193i \(-0.294211\pi\)
−0.572975 + 0.819573i \(0.694211\pi\)
\(42\) −0.734428 + 0.238630i −0.113325 + 0.0368214i
\(43\) 7.32892i 1.11765i 0.829286 + 0.558825i \(0.188748\pi\)
−0.829286 + 0.558825i \(0.811252\pi\)
\(44\) −2.23326 + 1.43470i −0.336677 + 0.216289i
\(45\) 0 0
\(46\) −2.33310 7.18053i −0.343996 1.05871i
\(47\) −4.89171 + 6.73287i −0.713530 + 0.982090i 0.286184 + 0.958175i \(0.407613\pi\)
−0.999714 + 0.0239149i \(0.992387\pi\)
\(48\) 1.03380 + 1.42291i 0.149216 + 0.205379i
\(49\) 2.00951 6.18465i 0.287073 0.883521i
\(50\) 0 0
\(51\) 6.29457 4.57327i 0.881416 0.640386i
\(52\) −2.21726 + 3.05179i −0.307478 + 0.423207i
\(53\) −6.48936 + 2.10852i −0.891382 + 0.289628i −0.718675 0.695346i \(-0.755251\pi\)
−0.172707 + 0.984973i \(0.555251\pi\)
\(54\) −1.09529 −0.149051
\(55\) 0 0
\(56\) 2.16248 0.288974
\(57\) −1.14095 + 0.370718i −0.151123 + 0.0491028i
\(58\) 0.854580 1.17623i 0.112212 0.154446i
\(59\) −2.86401 + 2.08083i −0.372862 + 0.270900i −0.758397 0.651793i \(-0.774017\pi\)
0.385534 + 0.922693i \(0.374017\pi\)
\(60\) 0 0
\(61\) −3.35959 + 10.3397i −0.430151 + 1.32387i 0.467824 + 0.883822i \(0.345038\pi\)
−0.897975 + 0.440047i \(0.854962\pi\)
\(62\) −4.94518 6.80645i −0.628038 0.864421i
\(63\) −0.414410 + 0.570387i −0.0522108 + 0.0718620i
\(64\) −2.51125 7.72883i −0.313906 0.966103i
\(65\) 0 0
\(66\) 1.31853 3.38494i 0.162300 0.416658i
\(67\) 2.04036i 0.249269i 0.992203 + 0.124635i \(0.0397759\pi\)
−0.992203 + 0.124635i \(0.960224\pi\)
\(68\) −5.92222 + 1.92424i −0.718174 + 0.233349i
\(69\) −5.57670 4.05171i −0.671356 0.487768i
\(70\) 0 0
\(71\) 0.207204 0.637709i 0.0245906 0.0756821i −0.938008 0.346613i \(-0.887332\pi\)
0.962599 + 0.270931i \(0.0873316\pi\)
\(72\) 2.91707 + 0.947813i 0.343780 + 0.111701i
\(73\) 2.94147 + 4.04859i 0.344273 + 0.473852i 0.945684 0.325089i \(-0.105394\pi\)
−0.601410 + 0.798941i \(0.705394\pi\)
\(74\) 7.47668 + 5.43212i 0.869146 + 0.631472i
\(75\) 0 0
\(76\) 0.960132 0.110135
\(77\) −1.26387 1.96735i −0.144032 0.224200i
\(78\) 5.16248i 0.584536i
\(79\) −0.704642 2.16867i −0.0792784 0.243994i 0.903560 0.428461i \(-0.140944\pi\)
−0.982839 + 0.184467i \(0.940944\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0.242610 + 0.0788288i 0.0267918 + 0.00870518i
\(83\) −2.00672 0.652022i −0.220266 0.0715687i 0.196805 0.980443i \(-0.436943\pi\)
−0.417071 + 0.908874i \(0.636943\pi\)
\(84\) 0.456498 0.331666i 0.0498081 0.0361877i
\(85\) 0 0
\(86\) 2.48058 + 7.63443i 0.267488 + 0.823242i
\(87\) 1.32741i 0.142313i
\(88\) −6.44077 + 7.87404i −0.686588 + 0.839375i
\(89\) 3.34722 0.354805 0.177402 0.984138i \(-0.443231\pi\)
0.177402 + 0.984138i \(0.443231\pi\)
\(90\) 0 0
\(91\) −2.68842 1.95325i −0.281823 0.204756i
\(92\) 3.24271 + 4.46321i 0.338076 + 0.465321i
\(93\) −7.30532 2.37364i −0.757526 0.246135i
\(94\) −2.81680 + 8.66921i −0.290530 + 0.894160i
\(95\) 0 0
\(96\) −3.40431 2.47338i −0.347451 0.252438i
\(97\) 3.15968 1.02664i 0.320817 0.104240i −0.144182 0.989551i \(-0.546055\pi\)
0.464998 + 0.885312i \(0.346055\pi\)
\(98\) 7.12261i 0.719492i
\(99\) −0.842610 3.20780i −0.0846855 0.322396i
\(100\) 0 0
\(101\) −5.84715 17.9957i −0.581813 1.79064i −0.611708 0.791084i \(-0.709517\pi\)
0.0298945 0.999553i \(-0.490483\pi\)
\(102\) 5.00908 6.89440i 0.495972 0.682648i
\(103\) 10.6368 + 14.6403i 1.04807 + 1.44255i 0.890467 + 0.455049i \(0.150378\pi\)
0.157608 + 0.987502i \(0.449622\pi\)
\(104\) −4.46735 + 13.7491i −0.438060 + 1.34821i
\(105\) 0 0
\(106\) −6.04622 + 4.39283i −0.587261 + 0.426670i
\(107\) 3.59692 4.95074i 0.347727 0.478606i −0.598951 0.800786i \(-0.704416\pi\)
0.946678 + 0.322180i \(0.104416\pi\)
\(108\) 0.761160 0.247316i 0.0732427 0.0237980i
\(109\) −9.03128 −0.865039 −0.432520 0.901625i \(-0.642375\pi\)
−0.432520 + 0.901625i \(0.642375\pi\)
\(110\) 0 0
\(111\) 8.43763 0.800864
\(112\) 1.17933 0.383189i 0.111437 0.0362079i
\(113\) 2.30226 3.16879i 0.216579 0.298095i −0.686879 0.726771i \(-0.741020\pi\)
0.903458 + 0.428676i \(0.141020\pi\)
\(114\) −1.06304 + 0.772344i −0.0995629 + 0.0723366i
\(115\) 0 0
\(116\) −0.328288 + 1.01037i −0.0304808 + 0.0938103i
\(117\) −2.77042 3.81316i −0.256126 0.352527i
\(118\) −2.27912 + 3.13693i −0.209810 + 0.288778i
\(119\) −1.69513 5.21707i −0.155392 0.478248i
\(120\) 0 0
\(121\) 10.9279 + 1.25756i 0.993444 + 0.114324i
\(122\) 11.9079i 1.07809i
\(123\) 0.221502 0.0719704i 0.0199722 0.00648935i
\(124\) 4.97348 + 3.61344i 0.446631 + 0.324497i
\(125\) 0 0
\(126\) −0.238630 + 0.734428i −0.0212588 + 0.0654280i
\(127\) −10.3356 3.35825i −0.917138 0.297996i −0.187846 0.982199i \(-0.560151\pi\)
−0.729292 + 0.684202i \(0.760151\pi\)
\(128\) −0.285113 0.392424i −0.0252006 0.0346857i
\(129\) 5.92922 + 4.30783i 0.522039 + 0.379283i
\(130\) 0 0
\(131\) −11.7094 −1.02305 −0.511526 0.859268i \(-0.670920\pi\)
−0.511526 + 0.859268i \(0.670920\pi\)
\(132\) −0.151980 + 2.65004i −0.0132282 + 0.230657i
\(133\) 0.845811i 0.0733411i
\(134\) 0.690588 + 2.12541i 0.0596577 + 0.183608i
\(135\) 0 0
\(136\) −19.3066 + 14.0271i −1.65553 + 1.20281i
\(137\) −19.4303 6.31328i −1.66004 0.539380i −0.679160 0.733990i \(-0.737656\pi\)
−0.980881 + 0.194611i \(0.937656\pi\)
\(138\) −7.18053 2.33310i −0.611247 0.198606i
\(139\) −6.61048 + 4.80280i −0.560694 + 0.407368i −0.831713 0.555206i \(-0.812639\pi\)
0.271019 + 0.962574i \(0.412639\pi\)
\(140\) 0 0
\(141\) 2.57173 + 7.91496i 0.216578 + 0.666560i
\(142\) 0.734424i 0.0616315i
\(143\) 15.1194 3.97150i 1.26435 0.332113i
\(144\) 1.75881 0.146567
\(145\) 0 0
\(146\) 4.43440 + 3.22178i 0.366993 + 0.266636i
\(147\) −3.82232 5.26097i −0.315260 0.433918i
\(148\) −6.42238 2.08676i −0.527917 0.171531i
\(149\) 2.96723 9.13221i 0.243085 0.748140i −0.752860 0.658181i \(-0.771326\pi\)
0.995945 0.0899592i \(-0.0286737\pi\)
\(150\) 0 0
\(151\) −5.58850 4.06028i −0.454785 0.330421i 0.336697 0.941613i \(-0.390690\pi\)
−0.791482 + 0.611192i \(0.790690\pi\)
\(152\) 3.49951 1.13706i 0.283848 0.0922278i
\(153\) 7.78051i 0.629017i
\(154\) −1.98244 1.62159i −0.159750 0.130671i
\(155\) 0 0
\(156\) 1.16568 + 3.58760i 0.0933292 + 0.287238i
\(157\) −6.67248 + 9.18388i −0.532522 + 0.732953i −0.987512 0.157543i \(-0.949643\pi\)
0.454990 + 0.890496i \(0.349643\pi\)
\(158\) −1.46803 2.02057i −0.116790 0.160748i
\(159\) −2.10852 + 6.48936i −0.167217 + 0.514640i
\(160\) 0 0
\(161\) −3.93178 + 2.85661i −0.309868 + 0.225132i
\(162\) −0.643798 + 0.886111i −0.0505815 + 0.0696195i
\(163\) 1.70480 0.553922i 0.133530 0.0433865i −0.241490 0.970403i \(-0.577636\pi\)
0.375020 + 0.927017i \(0.377636\pi\)
\(164\) −0.186398 −0.0145552
\(165\) 0 0
\(166\) −2.31106 −0.179373
\(167\) 5.72964 1.86167i 0.443373 0.144060i −0.0788186 0.996889i \(-0.525115\pi\)
0.522191 + 0.852829i \(0.325115\pi\)
\(168\) 1.27107 1.74948i 0.0980655 0.134976i
\(169\) 7.45546 5.41671i 0.573497 0.416670i
\(170\) 0 0
\(171\) −0.370718 + 1.14095i −0.0283495 + 0.0872509i
\(172\) −3.44769 4.74534i −0.262884 0.361829i
\(173\) 2.46091 3.38715i 0.187099 0.257520i −0.705155 0.709053i \(-0.749123\pi\)
0.892254 + 0.451533i \(0.149123\pi\)
\(174\) −0.449279 1.38274i −0.0340598 0.104825i
\(175\) 0 0
\(176\) −2.11728 + 5.43549i −0.159596 + 0.409716i
\(177\) 3.54011i 0.266091i
\(178\) 3.48676 1.13292i 0.261343 0.0849156i
\(179\) 3.92507 + 2.85173i 0.293374 + 0.213148i 0.724730 0.689033i \(-0.241965\pi\)
−0.431356 + 0.902182i \(0.641965\pi\)
\(180\) 0 0
\(181\) −7.13450 + 21.9577i −0.530303 + 1.63211i 0.223281 + 0.974754i \(0.428323\pi\)
−0.753584 + 0.657351i \(0.771677\pi\)
\(182\) −3.46160 1.12474i −0.256591 0.0833714i
\(183\) 6.39031 + 8.79551i 0.472386 + 0.650183i
\(184\) 17.1048 + 12.4273i 1.26098 + 0.916156i
\(185\) 0 0
\(186\) −8.41324 −0.616889
\(187\) 24.0452 + 9.36629i 1.75836 + 0.684931i
\(188\) 6.66058i 0.485773i
\(189\) 0.217868 + 0.670530i 0.0158476 + 0.0487739i
\(190\) 0 0
\(191\) −5.03670 + 3.65938i −0.364443 + 0.264783i −0.754903 0.655837i \(-0.772316\pi\)
0.390460 + 0.920620i \(0.372316\pi\)
\(192\) −7.72883 2.51125i −0.557780 0.181234i
\(193\) 18.1526 + 5.89815i 1.30666 + 0.424558i 0.877892 0.478858i \(-0.158949\pi\)
0.428764 + 0.903417i \(0.358949\pi\)
\(194\) 2.94391 2.13888i 0.211361 0.153562i
\(195\) 0 0
\(196\) 1.60828 + 4.94977i 0.114877 + 0.353555i
\(197\) 6.80056i 0.484520i −0.970211 0.242260i \(-0.922111\pi\)
0.970211 0.242260i \(-0.0778887\pi\)
\(198\) −1.96346 3.05633i −0.139537 0.217204i
\(199\) −21.2972 −1.50972 −0.754860 0.655886i \(-0.772295\pi\)
−0.754860 + 0.655886i \(0.772295\pi\)
\(200\) 0 0
\(201\) 1.65068 + 1.19929i 0.116430 + 0.0845915i
\(202\) −12.1818 16.7668i −0.857108 1.17971i
\(203\) −0.890065 0.289200i −0.0624703 0.0202978i
\(204\) −1.92424 + 5.92222i −0.134724 + 0.414638i
\(205\) 0 0
\(206\) 16.0354 + 11.6504i 1.11724 + 0.811723i
\(207\) −6.55580 + 2.13011i −0.455660 + 0.148053i
\(208\) 8.28984i 0.574797i
\(209\) −3.07977 2.51918i −0.213032 0.174255i
\(210\) 0 0
\(211\) −2.74739 8.45559i −0.189138 0.582107i 0.810857 0.585244i \(-0.199001\pi\)
−0.999995 + 0.00313734i \(0.999001\pi\)
\(212\) 3.20984 4.41797i 0.220453 0.303427i
\(213\) −0.394126 0.542467i −0.0270050 0.0371692i
\(214\) 2.07121 6.37454i 0.141585 0.435755i
\(215\) 0 0
\(216\) 2.48141 1.80285i 0.168838 0.122668i
\(217\) −3.18320 + 4.38129i −0.216089 + 0.297422i
\(218\) −9.40776 + 3.05677i −0.637174 + 0.207030i
\(219\) 5.00433 0.338162
\(220\) 0 0
\(221\) 36.6721 2.46683
\(222\) 8.78936 2.85584i 0.589903 0.191671i
\(223\) 3.18415 4.38261i 0.213226 0.293481i −0.688985 0.724776i \(-0.741943\pi\)
0.902211 + 0.431295i \(0.141943\pi\)
\(224\) −2.40017 + 1.74382i −0.160368 + 0.116514i
\(225\) 0 0
\(226\) 1.32571 4.08012i 0.0881850 0.271406i
\(227\) −4.95998 6.82682i −0.329205 0.453112i 0.612045 0.790823i \(-0.290347\pi\)
−0.941250 + 0.337711i \(0.890347\pi\)
\(228\) 0.564352 0.776763i 0.0373751 0.0514424i
\(229\) 3.46262 + 10.6569i 0.228817 + 0.704225i 0.997882 + 0.0650545i \(0.0207221\pi\)
−0.769065 + 0.639170i \(0.779278\pi\)
\(230\) 0 0
\(231\) −2.33451 0.133884i −0.153599 0.00880892i
\(232\) 4.07140i 0.267300i
\(233\) −5.55397 + 1.80459i −0.363852 + 0.118223i −0.485237 0.874383i \(-0.661267\pi\)
0.121384 + 0.992606i \(0.461267\pi\)
\(234\) −4.17653 3.03443i −0.273029 0.198367i
\(235\) 0 0
\(236\) 0.875526 2.69459i 0.0569919 0.175403i
\(237\) −2.16867 0.704642i −0.140870 0.0457714i
\(238\) −3.53158 4.86081i −0.228919 0.315079i
\(239\) −13.3699 9.71382i −0.864829 0.628335i 0.0643656 0.997926i \(-0.479498\pi\)
−0.929194 + 0.369592i \(0.879498\pi\)
\(240\) 0 0
\(241\) −3.29180 −0.212043 −0.106022 0.994364i \(-0.533811\pi\)
−0.106022 + 0.994364i \(0.533811\pi\)
\(242\) 11.8091 2.38871i 0.759115 0.153552i
\(243\) 1.00000i 0.0641500i
\(244\) −2.68878 8.27522i −0.172132 0.529767i
\(245\) 0 0
\(246\) 0.206376 0.149941i 0.0131581 0.00955990i
\(247\) −5.37769 1.74732i −0.342174 0.111179i
\(248\) 22.4068 + 7.28040i 1.42283 + 0.462306i
\(249\) −1.70702 + 1.24022i −0.108178 + 0.0785957i
\(250\) 0 0
\(251\) −2.28652 7.03719i −0.144324 0.444183i 0.852600 0.522565i \(-0.175025\pi\)
−0.996923 + 0.0783815i \(0.975025\pi\)
\(252\) 0.564263i 0.0355452i
\(253\) 1.30899 22.8246i 0.0822955 1.43497i
\(254\) −11.9031 −0.746869
\(255\) 0 0
\(256\) 12.7192 + 9.24107i 0.794953 + 0.577567i
\(257\) −10.9911 15.1279i −0.685604 0.943653i 0.314380 0.949297i \(-0.398203\pi\)
−0.999984 + 0.00564422i \(0.998203\pi\)
\(258\) 7.63443 + 2.48058i 0.475299 + 0.154434i
\(259\) 1.83829 5.65768i 0.114226 0.351551i
\(260\) 0 0
\(261\) −1.07389 0.780229i −0.0664723 0.0482950i
\(262\) −12.1975 + 3.96321i −0.753564 + 0.244848i
\(263\) 3.99020i 0.246046i 0.992404 + 0.123023i \(0.0392589\pi\)
−0.992404 + 0.123023i \(0.960741\pi\)
\(264\) 2.58444 + 9.83893i 0.159061 + 0.605544i
\(265\) 0 0
\(266\) 0.286277 + 0.881070i 0.0175528 + 0.0540219i
\(267\) 1.96745 2.70796i 0.120406 0.165724i
\(268\) −0.959830 1.32109i −0.0586309 0.0806986i
\(269\) 3.92915 12.0927i 0.239564 0.737303i −0.756919 0.653509i \(-0.773296\pi\)
0.996483 0.0837941i \(-0.0267038\pi\)
\(270\) 0 0
\(271\) −19.2773 + 14.0057i −1.17101 + 0.850788i −0.991129 0.132900i \(-0.957571\pi\)
−0.179880 + 0.983689i \(0.557571\pi\)
\(272\) −8.04351 + 11.0709i −0.487709 + 0.671274i
\(273\) −3.16043 + 1.02689i −0.191278 + 0.0621499i
\(274\) −22.3771 −1.35185
\(275\) 0 0
\(276\) 5.51683 0.332074
\(277\) 7.04973 2.29059i 0.423577 0.137628i −0.0894691 0.995990i \(-0.528517\pi\)
0.513046 + 0.858361i \(0.328517\pi\)
\(278\) −5.26047 + 7.24042i −0.315502 + 0.434252i
\(279\) −6.21427 + 4.51493i −0.372039 + 0.270302i
\(280\) 0 0
\(281\) −8.98667 + 27.6581i −0.536100 + 1.64994i 0.205161 + 0.978728i \(0.434228\pi\)
−0.741261 + 0.671217i \(0.765772\pi\)
\(282\) 5.35786 + 7.37447i 0.319056 + 0.439143i
\(283\) −12.7390 + 17.5337i −0.757256 + 1.04227i 0.240182 + 0.970728i \(0.422793\pi\)
−0.997437 + 0.0715451i \(0.977207\pi\)
\(284\) 0.165832 + 0.510378i 0.00984031 + 0.0302854i
\(285\) 0 0
\(286\) 14.4055 9.25445i 0.851815 0.547227i
\(287\) 0.164204i 0.00969265i
\(288\) −4.00201 + 1.30033i −0.235821 + 0.0766227i
\(289\) 35.2217 + 25.5901i 2.07186 + 1.50530i
\(290\) 0 0
\(291\) 1.02664 3.15968i 0.0601828 0.185224i
\(292\) −3.80910 1.23765i −0.222911 0.0724281i
\(293\) 4.94456 + 6.80561i 0.288865 + 0.397588i 0.928645 0.370970i \(-0.120975\pi\)
−0.639780 + 0.768558i \(0.720975\pi\)
\(294\) −5.76231 4.18657i −0.336065 0.244166i
\(295\) 0 0
\(296\) −25.8798 −1.50423
\(297\) −3.09044 1.20381i −0.179326 0.0698524i
\(298\) 10.5172i 0.609245i
\(299\) −10.0399 30.8997i −0.580623 1.78697i
\(300\) 0 0
\(301\) 4.18032 3.03718i 0.240950 0.175060i
\(302\) −7.19572 2.33803i −0.414067 0.134539i
\(303\) −17.9957 5.84715i −1.03382 0.335910i
\(304\) 1.70702 1.24022i 0.0979041 0.0711315i
\(305\) 0 0
\(306\) −2.63343 8.10486i −0.150543 0.463324i
\(307\) 23.7431i 1.35509i −0.735481 0.677545i \(-0.763044\pi\)
0.735481 0.677545i \(-0.236956\pi\)
\(308\) 1.74382 + 0.679268i 0.0993635 + 0.0387049i
\(309\) 18.0964 1.02947
\(310\) 0 0
\(311\) −18.6455 13.5467i −1.05729 0.768164i −0.0837029 0.996491i \(-0.526675\pi\)
−0.973585 + 0.228326i \(0.926675\pi\)
\(312\) 8.49741 + 11.6957i 0.481071 + 0.662137i
\(313\) −16.5140 5.36571i −0.933424 0.303288i −0.197462 0.980311i \(-0.563270\pi\)
−0.735962 + 0.677023i \(0.763270\pi\)
\(314\) −3.84221 + 11.8251i −0.216829 + 0.667330i
\(315\) 0 0
\(316\) 1.47643 + 1.07269i 0.0830558 + 0.0603436i
\(317\) −5.84990 + 1.90075i −0.328563 + 0.106757i −0.468654 0.883382i \(-0.655261\pi\)
0.140090 + 0.990139i \(0.455261\pi\)
\(318\) 7.47354i 0.419095i
\(319\) 3.70402 2.37955i 0.207385 0.133229i
\(320\) 0 0
\(321\) −1.89101 5.81994i −0.105546 0.324837i
\(322\) −3.12882 + 4.30645i −0.174362 + 0.239989i
\(323\) −5.48641 7.55140i −0.305272 0.420171i
\(324\) 0.247316 0.761160i 0.0137398 0.0422867i
\(325\) 0 0
\(326\) 1.58838 1.15403i 0.0879722 0.0639156i
\(327\) −5.30845 + 7.30645i −0.293558 + 0.404048i
\(328\) −0.679388 + 0.220747i −0.0375129 + 0.0121887i
\(329\) 5.86752 0.323487
\(330\) 0 0
\(331\) 19.4191 1.06737 0.533685 0.845683i \(-0.320807\pi\)
0.533685 + 0.845683i \(0.320807\pi\)
\(332\) 1.60604 0.521833i 0.0881428 0.0286393i
\(333\) 4.95951 6.82618i 0.271780 0.374072i
\(334\) 5.33837 3.87856i 0.292103 0.212225i
\(335\) 0 0
\(336\) 0.383189 1.17933i 0.0209047 0.0643379i
\(337\) 18.6250 + 25.6352i 1.01457 + 1.39644i 0.915941 + 0.401312i \(0.131446\pi\)
0.0986291 + 0.995124i \(0.468554\pi\)
\(338\) 5.93289 8.16593i 0.322707 0.444168i
\(339\) −1.21037 3.72514i −0.0657383 0.202322i
\(340\) 0 0
\(341\) −6.47231 24.6400i −0.350495 1.33433i
\(342\) 1.31399i 0.0710524i
\(343\) −9.05412 + 2.94186i −0.488876 + 0.158846i
\(344\) −18.1860 13.2129i −0.980524 0.712392i
\(345\) 0 0
\(346\) 1.41706 4.36127i 0.0761818 0.234463i
\(347\) 26.5758 + 8.63499i 1.42666 + 0.463551i 0.917712 0.397246i \(-0.130034\pi\)
0.508950 + 0.860796i \(0.330034\pi\)
\(348\) 0.624442 + 0.859470i 0.0334736 + 0.0460724i
\(349\) −0.552827 0.401652i −0.0295921 0.0214999i 0.572891 0.819632i \(-0.305822\pi\)
−0.602483 + 0.798132i \(0.705822\pi\)
\(350\) 0 0
\(351\) −4.71333 −0.251579
\(352\) 0.799077 13.9333i 0.0425909 0.742649i
\(353\) 1.55900i 0.0829769i 0.999139 + 0.0414885i \(0.0132100\pi\)
−0.999139 + 0.0414885i \(0.986790\pi\)
\(354\) 1.19820 + 3.68769i 0.0636837 + 0.195998i
\(355\) 0 0
\(356\) −2.16726 + 1.57461i −0.114865 + 0.0834542i
\(357\) −5.21707 1.69513i −0.276117 0.0897157i
\(358\) 5.05390 + 1.64211i 0.267107 + 0.0867884i
\(359\) 12.8151 9.31073i 0.676356 0.491402i −0.195791 0.980646i \(-0.562727\pi\)
0.872147 + 0.489244i \(0.162727\pi\)
\(360\) 0 0
\(361\) −5.42658 16.7013i −0.285610 0.879016i
\(362\) 25.2878i 1.32910i
\(363\) 7.44064 8.10166i 0.390532 0.425227i
\(364\) 2.65956 0.139399
\(365\) 0 0
\(366\) 9.63367 + 6.99927i 0.503560 + 0.365858i
\(367\) 9.24947 + 12.7308i 0.482818 + 0.664542i 0.979043 0.203652i \(-0.0652810\pi\)
−0.496225 + 0.868194i \(0.665281\pi\)
\(368\) 11.5304 + 3.74645i 0.601064 + 0.195297i
\(369\) 0.0719704 0.221502i 0.00374663 0.0115309i
\(370\) 0 0
\(371\) 3.89193 + 2.82765i 0.202059 + 0.146804i
\(372\) 5.84667 1.89970i 0.303136 0.0984948i
\(373\) 5.27703i 0.273234i −0.990624 0.136617i \(-0.956377\pi\)
0.990624 0.136617i \(-0.0436230\pi\)
\(374\) 28.2177 + 1.61829i 1.45910 + 0.0836797i
\(375\) 0 0
\(376\) −7.88796 24.2767i −0.406791 1.25197i
\(377\) 3.67748 5.06161i 0.189400 0.260686i
\(378\) 0.453901 + 0.624741i 0.0233462 + 0.0321332i
\(379\) −10.3549 + 31.8692i −0.531897 + 1.63701i 0.218363 + 0.975868i \(0.429928\pi\)
−0.750260 + 0.661143i \(0.770072\pi\)
\(380\) 0 0
\(381\) −8.79201 + 6.38777i −0.450428 + 0.327255i
\(382\) −4.00810 + 5.51667i −0.205072 + 0.282257i
\(383\) 19.2420 6.25212i 0.983222 0.319468i 0.227080 0.973876i \(-0.427082\pi\)
0.756142 + 0.654408i \(0.227082\pi\)
\(384\) −0.485063 −0.0247532
\(385\) 0 0
\(386\) 20.9057 1.06407
\(387\) 6.97021 2.26476i 0.354316 0.115124i
\(388\) −1.56288 + 2.15112i −0.0793430 + 0.109206i
\(389\) −22.3069 + 16.2069i −1.13101 + 0.821724i −0.985841 0.167684i \(-0.946371\pi\)
−0.145165 + 0.989408i \(0.546371\pi\)
\(390\) 0 0
\(391\) 16.5733 51.0075i 0.838150 2.57956i
\(392\) 11.7238 + 16.1364i 0.592140 + 0.815011i
\(393\) −6.88260 + 9.47308i −0.347181 + 0.477854i
\(394\) −2.30175 7.08406i −0.115960 0.356890i
\(395\) 0 0
\(396\) 2.05460 + 1.68061i 0.103247 + 0.0844539i
\(397\) 11.7601i 0.590222i −0.955463 0.295111i \(-0.904643\pi\)
0.955463 0.295111i \(-0.0953566\pi\)
\(398\) −22.1850 + 7.20835i −1.11204 + 0.361322i
\(399\) 0.684276 + 0.497155i 0.0342566 + 0.0248889i
\(400\) 0 0
\(401\) −2.38687 + 7.34602i −0.119194 + 0.366843i −0.992799 0.119794i \(-0.961777\pi\)
0.873604 + 0.486637i \(0.161777\pi\)
\(402\) 2.12541 + 0.690588i 0.106006 + 0.0344434i
\(403\) −21.2804 29.2899i −1.06005 1.45903i
\(404\) 12.2515 + 8.90124i 0.609535 + 0.442853i
\(405\) 0 0
\(406\) −1.02505 −0.0508725
\(407\) 15.1256 + 23.5445i 0.749748 + 1.16706i
\(408\) 23.8643i 1.18146i
\(409\) −5.17322 15.9215i −0.255799 0.787269i −0.993671 0.112328i \(-0.964169\pi\)
0.737872 0.674941i \(-0.235831\pi\)
\(410\) 0 0
\(411\) −16.5284 + 12.0086i −0.815285 + 0.592339i
\(412\) −13.7743 4.47553i −0.678609 0.220493i
\(413\) 2.37375 + 0.771279i 0.116805 + 0.0379521i
\(414\) −6.10813 + 4.43781i −0.300198 + 0.218107i
\(415\) 0 0
\(416\) −6.12889 18.8628i −0.300493 0.924824i
\(417\) 8.17100i 0.400136i
\(418\) −4.06081 1.58180i −0.198621 0.0773684i
\(419\) 38.0968 1.86115 0.930576 0.366100i \(-0.119307\pi\)
0.930576 + 0.366100i \(0.119307\pi\)
\(420\) 0 0
\(421\) 18.3350 + 13.3212i 0.893594 + 0.649234i 0.936813 0.349831i \(-0.113761\pi\)
−0.0432184 + 0.999066i \(0.513761\pi\)
\(422\) −5.72383 7.87818i −0.278632 0.383504i
\(423\) 7.91496 + 2.57173i 0.384839 + 0.125042i
\(424\) 6.46722 19.9041i 0.314076 0.966627i
\(425\) 0 0
\(426\) −0.594161 0.431683i −0.0287872 0.0209151i
\(427\) 7.28990 2.36863i 0.352783 0.114626i
\(428\) 4.89758i 0.236734i
\(429\) 5.67397 14.5663i 0.273942 0.703266i
\(430\) 0 0
\(431\) −10.4994 32.3137i −0.505736 1.55650i −0.799529 0.600627i \(-0.794918\pi\)
0.293793 0.955869i \(-0.405082\pi\)
\(432\) 1.03380 1.42291i 0.0497388 0.0684596i
\(433\) 21.5572 + 29.6709i 1.03597 + 1.42589i 0.900367 + 0.435131i \(0.143298\pi\)
0.135605 + 0.990763i \(0.456702\pi\)
\(434\) −1.83298 + 5.64133i −0.0879858 + 0.270793i
\(435\) 0 0
\(436\) 5.84758 4.24852i 0.280048 0.203467i
\(437\) −4.86071 + 6.69019i −0.232519 + 0.320035i
\(438\) 5.21295 1.69379i 0.249084 0.0809324i
\(439\) −1.05012 −0.0501193 −0.0250596 0.999686i \(-0.507978\pi\)
−0.0250596 + 0.999686i \(0.507978\pi\)
\(440\) 0 0
\(441\) −6.50292 −0.309663
\(442\) 38.2008 12.4122i 1.81703 0.590388i
\(443\) −17.9396 + 24.6917i −0.852334 + 1.17314i 0.131009 + 0.991381i \(0.458178\pi\)
−0.983344 + 0.181756i \(0.941822\pi\)
\(444\) −5.46321 + 3.96925i −0.259272 + 0.188372i
\(445\) 0 0
\(446\) 1.83353 5.64302i 0.0868201 0.267205i
\(447\) −5.64402 7.76832i −0.266953 0.367429i
\(448\) −3.36773 + 4.63529i −0.159111 + 0.218997i
\(449\) 11.3006 + 34.7796i 0.533308 + 1.64135i 0.747277 + 0.664513i \(0.231361\pi\)
−0.213969 + 0.976840i \(0.568639\pi\)
\(450\) 0 0
\(451\) 0.597901 + 0.489068i 0.0281540 + 0.0230293i
\(452\) 3.13477i 0.147447i
\(453\) −6.56967 + 2.13462i −0.308670 + 0.100293i
\(454\) −7.47738 5.43263i −0.350931 0.254966i
\(455\) 0 0
\(456\) 1.13706 3.49951i 0.0532478 0.163880i
\(457\) 2.26740 + 0.736724i 0.106065 + 0.0344625i 0.361568 0.932346i \(-0.382241\pi\)
−0.255504 + 0.966808i \(0.582241\pi\)
\(458\) 7.21393 + 9.92913i 0.337085 + 0.463958i
\(459\) −6.29457 4.57327i −0.293805 0.213462i
\(460\) 0 0
\(461\) 28.5962 1.33186 0.665929 0.746015i \(-0.268035\pi\)
0.665929 + 0.746015i \(0.268035\pi\)
\(462\) −2.47714 + 0.650683i −0.115247 + 0.0302725i
\(463\) 30.5806i 1.42120i −0.703596 0.710600i \(-0.748423\pi\)
0.703596 0.710600i \(-0.251577\pi\)
\(464\) 0.721447 + 2.22038i 0.0334923 + 0.103079i
\(465\) 0 0
\(466\) −5.17470 + 3.75964i −0.239713 + 0.174162i
\(467\) 3.55903 + 1.15640i 0.164692 + 0.0535118i 0.390203 0.920729i \(-0.372405\pi\)
−0.225510 + 0.974241i \(0.572405\pi\)
\(468\) 3.58760 + 1.16568i 0.165837 + 0.0538836i
\(469\) 1.16379 0.845545i 0.0537389 0.0390436i
\(470\) 0 0
\(471\) 3.50793 + 10.7963i 0.161637 + 0.497467i
\(472\) 10.8582i 0.499788i
\(473\) −1.39174 + 24.2674i −0.0639920 + 1.11582i
\(474\) −2.49757 −0.114717
\(475\) 0 0
\(476\) 3.55179 + 2.58053i 0.162796 + 0.118278i
\(477\) 4.01064 + 5.52018i 0.183635 + 0.252752i
\(478\) −17.2151 5.59351i −0.787398 0.255841i
\(479\) 0.292006 0.898702i 0.0133421 0.0410627i −0.944164 0.329476i \(-0.893128\pi\)
0.957506 + 0.288414i \(0.0931278\pi\)
\(480\) 0 0
\(481\) 32.1740 + 23.3758i 1.46701 + 1.06584i
\(482\) −3.42902 + 1.11416i −0.156188 + 0.0507484i
\(483\) 4.85995i 0.221135i
\(484\) −7.66719 + 4.32647i −0.348508 + 0.196658i
\(485\) 0 0
\(486\) 0.338464 + 1.04169i 0.0153531 + 0.0472519i
\(487\) 7.86887 10.8306i 0.356573 0.490780i −0.592617 0.805484i \(-0.701905\pi\)
0.949190 + 0.314704i \(0.101905\pi\)
\(488\) −19.6003 26.9775i −0.887263 1.22121i
\(489\) 0.553922 1.70480i 0.0250492 0.0770935i
\(490\) 0 0
\(491\) 2.25625 1.63926i 0.101823 0.0739787i −0.535709 0.844403i \(-0.679955\pi\)
0.637532 + 0.770424i \(0.279955\pi\)
\(492\) −0.109562 + 0.150799i −0.00493944 + 0.00679855i
\(493\) 9.82241 3.19149i 0.442379 0.143738i
\(494\) −6.19327 −0.278648
\(495\) 0 0
\(496\) 13.5099 0.606611
\(497\) −0.449608 + 0.146087i −0.0201677 + 0.00655288i
\(498\) −1.35840 + 1.86968i −0.0608716 + 0.0837825i
\(499\) 14.3835 10.4503i 0.643896 0.467818i −0.217290 0.976107i \(-0.569722\pi\)
0.861187 + 0.508289i \(0.169722\pi\)
\(500\) 0 0
\(501\) 1.86167 5.72964i 0.0831733 0.255981i
\(502\) −4.76368 6.55664i −0.212613 0.292637i
\(503\) 15.1554 20.8596i 0.675744 0.930081i −0.324129 0.946013i \(-0.605071\pi\)
0.999873 + 0.0159313i \(0.00507131\pi\)
\(504\) −0.668243 2.05664i −0.0297659 0.0916100i
\(505\) 0 0
\(506\) −6.36175 24.2191i −0.282814 1.07667i
\(507\) 9.21546i 0.409273i
\(508\) 8.27192 2.68771i 0.367007 0.119248i
\(509\) −22.8386 16.5932i −1.01231 0.735483i −0.0476138 0.998866i \(-0.515162\pi\)
−0.964691 + 0.263383i \(0.915162\pi\)
\(510\) 0 0
\(511\) 1.09029 3.35556i 0.0482314 0.148441i
\(512\) 17.2999 + 5.62107i 0.764554 + 0.248419i
\(513\) 0.705148 + 0.970553i 0.0311330 + 0.0428509i
\(514\) −16.5695 12.0385i −0.730850 0.530993i
\(515\) 0 0
\(516\) −5.86556 −0.258217
\(517\) −17.4759 + 21.3648i −0.768590 + 0.939625i
\(518\) 6.51573i 0.286285i
\(519\) −1.29377 3.98183i −0.0567904 0.174783i
\(520\) 0 0
\(521\) −9.46183 + 6.87442i −0.414530 + 0.301174i −0.775433 0.631429i \(-0.782469\pi\)
0.360903 + 0.932603i \(0.382469\pi\)
\(522\) −1.38274 0.449279i −0.0605209 0.0196644i
\(523\) −18.7236 6.08365i −0.818724 0.266019i −0.130436 0.991457i \(-0.541638\pi\)
−0.688288 + 0.725437i \(0.741638\pi\)
\(524\) 7.58160 5.50836i 0.331204 0.240634i
\(525\) 0 0
\(526\) 1.35054 + 4.15654i 0.0588863 + 0.181234i
\(527\) 59.7642i 2.60337i
\(528\) 3.15290 + 4.90782i 0.137212 + 0.213585i
\(529\) −24.5159 −1.06591
\(530\) 0 0
\(531\) 2.86401 + 2.08083i 0.124287 + 0.0903001i
\(532\) −0.397889 0.547647i −0.0172507 0.0237435i
\(533\) 1.04401 + 0.339220i 0.0452212 + 0.0146933i
\(534\) 1.13292 3.48676i 0.0490261 0.150887i
\(535\) 0 0
\(536\) −5.06295 3.67845i −0.218686 0.158885i
\(537\) 4.61420 1.49924i 0.199117 0.0646972i
\(538\) 13.9266i 0.600420i
\(539\) 7.82831 20.0969i 0.337189 0.865635i
\(540\) 0 0
\(541\) −1.68443 5.18413i −0.0724191 0.222883i 0.908295 0.418330i \(-0.137384\pi\)
−0.980714 + 0.195447i \(0.937384\pi\)
\(542\) −15.3404 + 21.1143i −0.658927 + 0.906935i
\(543\) 13.5706 + 18.6784i 0.582371 + 0.801565i
\(544\) 10.1172 31.1377i 0.433773 1.33502i
\(545\) 0 0
\(546\) −2.94461 + 2.13939i −0.126018 + 0.0915572i
\(547\) −7.51731 + 10.3467i −0.321417 + 0.442393i −0.938899 0.344192i \(-0.888153\pi\)
0.617482 + 0.786585i \(0.288153\pi\)
\(548\) 15.5507 5.05271i 0.664291 0.215841i
\(549\) 10.8719 0.463999
\(550\) 0 0
\(551\) −1.59245 −0.0678405
\(552\) 20.1079 6.53344i 0.855848 0.278082i
\(553\) −0.944967 + 1.30064i −0.0401841 + 0.0553087i
\(554\) 6.56832 4.77216i 0.279061 0.202750i
\(555\) 0 0
\(556\) 2.02082 6.21944i 0.0857018 0.263763i
\(557\) −0.208351 0.286771i −0.00882812 0.0121509i 0.804580 0.593844i \(-0.202390\pi\)
−0.813408 + 0.581693i \(0.802390\pi\)
\(558\) −4.94518 + 6.80645i −0.209346 + 0.288140i
\(559\) 10.6746 + 32.8529i 0.451486 + 1.38953i
\(560\) 0 0
\(561\) 21.7109 13.9476i 0.916636 0.588869i
\(562\) 31.8528i 1.34363i
\(563\) −33.3648 + 10.8409i −1.40616 + 0.456888i −0.911177 0.412015i \(-0.864825\pi\)
−0.494981 + 0.868904i \(0.664825\pi\)
\(564\) −5.38852 3.91499i −0.226898 0.164851i
\(565\) 0 0
\(566\) −7.33551 + 22.5764i −0.308334 + 0.948956i
\(567\) 0.670530 + 0.217868i 0.0281596 + 0.00914961i
\(568\) 1.20886 + 1.66385i 0.0507225 + 0.0698135i
\(569\) −13.2015 9.59145i −0.553436 0.402094i 0.275615 0.961268i \(-0.411119\pi\)
−0.829051 + 0.559174i \(0.811119\pi\)
\(570\) 0 0
\(571\) −14.4160 −0.603291 −0.301645 0.953420i \(-0.597536\pi\)
−0.301645 + 0.953420i \(0.597536\pi\)
\(572\) −7.92127 + 9.68400i −0.331205 + 0.404908i
\(573\) 6.22571i 0.260083i
\(574\) −0.0555772 0.171049i −0.00231975 0.00713945i
\(575\) 0 0
\(576\) −6.57453 + 4.77668i −0.273939 + 0.199028i
\(577\) −8.47261 2.75292i −0.352719 0.114605i 0.127298 0.991865i \(-0.459370\pi\)
−0.480017 + 0.877259i \(0.659370\pi\)
\(578\) 45.3513 + 14.7355i 1.88636 + 0.612917i
\(579\) 15.4416 11.2190i 0.641730 0.466244i
\(580\) 0 0
\(581\) 0.459700 + 1.41481i 0.0190716 + 0.0586962i
\(582\) 3.63887i 0.150836i
\(583\) −21.8879 + 5.74939i −0.906503 + 0.238116i
\(584\) −15.3492 −0.635155
\(585\) 0 0
\(586\) 7.45414 + 5.41575i 0.307928 + 0.223723i
\(587\) −8.11225 11.1655i −0.334828 0.460851i 0.608094 0.793865i \(-0.291934\pi\)
−0.942922 + 0.333014i \(0.891934\pi\)
\(588\) 4.94977 + 1.60828i 0.204125 + 0.0663242i
\(589\) −2.84758 + 8.76396i −0.117333 + 0.361113i
\(590\) 0 0
\(591\) −5.50177 3.99727i −0.226313 0.164426i
\(592\) −14.1138 + 4.58586i −0.580075 + 0.188478i
\(593\) 16.4676i 0.676242i −0.941103 0.338121i \(-0.890209\pi\)
0.941103 0.338121i \(-0.109791\pi\)
\(594\) −3.62672 0.207992i −0.148806 0.00853403i
\(595\) 0 0
\(596\) 2.37477 + 7.30879i 0.0972744 + 0.299380i
\(597\) −12.5182 + 17.2298i −0.512336 + 0.705170i
\(598\) −20.9169 28.7896i −0.855354 1.17729i
\(599\) −11.6994 + 36.0069i −0.478023 + 1.47120i 0.363814 + 0.931472i \(0.381475\pi\)
−0.841837 + 0.539732i \(0.818525\pi\)
\(600\) 0 0
\(601\) −1.26563 + 0.919535i −0.0516262 + 0.0375086i −0.613299 0.789851i \(-0.710158\pi\)
0.561673 + 0.827359i \(0.310158\pi\)
\(602\) 3.32660 4.57868i 0.135582 0.186613i
\(603\) 1.94049 0.630505i 0.0790230 0.0256761i
\(604\) 5.52850 0.224951
\(605\) 0 0
\(606\) −20.7249 −0.841892
\(607\) 17.9296 5.82568i 0.727740 0.236457i 0.0783641 0.996925i \(-0.475030\pi\)
0.649376 + 0.760468i \(0.275030\pi\)
\(608\) −2.96723 + 4.08405i −0.120337 + 0.165630i
\(609\) −0.757135 + 0.550090i −0.0306806 + 0.0222908i
\(610\) 0 0
\(611\) −12.1214 + 37.3058i −0.490379 + 1.50923i
\(612\) 3.66013 + 5.03774i 0.147952 + 0.203639i
\(613\) 19.2030 26.4306i 0.775601 1.06752i −0.220153 0.975465i \(-0.570656\pi\)
0.995754 0.0920574i \(-0.0293443\pi\)
\(614\) −8.03619 24.7329i −0.324314 0.998137i
\(615\) 0 0
\(616\) 7.16037 + 0.410647i 0.288499 + 0.0165454i
\(617\) 33.6559i 1.35493i 0.735553 + 0.677467i \(0.236922\pi\)
−0.735553 + 0.677467i \(0.763078\pi\)
\(618\) 18.8508 6.12499i 0.758289 0.246383i
\(619\) −7.23262 5.25480i −0.290703 0.211208i 0.432869 0.901457i \(-0.357501\pi\)
−0.723572 + 0.690248i \(0.757501\pi\)
\(620\) 0 0
\(621\) −2.13011 + 6.55580i −0.0854784 + 0.263075i
\(622\) −24.0078 7.80061i −0.962626 0.312776i
\(623\) −1.38712 1.90921i −0.0555739 0.0764910i
\(624\) 6.70662 + 4.87265i 0.268480 + 0.195062i
\(625\) 0 0
\(626\) −19.0185 −0.760131
\(627\) −3.84830 + 1.01085i −0.153686 + 0.0403696i
\(628\) 9.08528i 0.362542i
\(629\) 20.2867 + 62.4360i 0.808883 + 2.48949i
\(630\) 0 0
\(631\) 15.5798 11.3194i 0.620224 0.450619i −0.232776 0.972530i \(-0.574781\pi\)
0.853000 + 0.521912i \(0.174781\pi\)
\(632\) 6.65170 + 2.16127i 0.264590 + 0.0859706i
\(633\) −8.45559 2.74739i −0.336080 0.109199i
\(634\) −5.45043 + 3.95997i −0.216464 + 0.157270i
\(635\) 0 0
\(636\) −1.68751 5.19364i −0.0669143 0.205941i
\(637\) 30.6504i 1.21441i
\(638\) 3.05303 3.73243i 0.120871 0.147768i
\(639\) −0.670527 −0.0265256
\(640\) 0 0
\(641\) 12.0485 + 8.75375i 0.475887 + 0.345752i 0.799731 0.600358i \(-0.204975\pi\)
−0.323844 + 0.946110i \(0.604975\pi\)
\(642\) −3.93968 5.42251i −0.155487 0.214009i
\(643\) 33.5907 + 10.9143i 1.32469 + 0.430417i 0.884102 0.467295i \(-0.154771\pi\)
0.440584 + 0.897711i \(0.354771\pi\)
\(644\) 1.20194 3.69920i 0.0473632 0.145769i
\(645\) 0 0
\(646\) −8.27100 6.00923i −0.325418 0.236430i
\(647\) 29.6186 9.62366i 1.16443 0.378345i 0.337867 0.941194i \(-0.390295\pi\)
0.826560 + 0.562849i \(0.190295\pi\)
\(648\) 3.06719i 0.120490i
\(649\) −9.87841 + 6.34613i −0.387761 + 0.249107i
\(650\) 0 0
\(651\) 1.67350 + 5.15052i 0.0655898 + 0.201865i
\(652\) −0.843246 + 1.16063i −0.0330241 + 0.0454537i
\(653\) −2.97122 4.08953i −0.116273 0.160036i 0.746914 0.664921i \(-0.231535\pi\)
−0.863186 + 0.504885i \(0.831535\pi\)
\(654\) −3.05677 + 9.40776i −0.119529 + 0.367872i
\(655\) 0 0
\(656\) −0.331396 + 0.240774i −0.0129389 + 0.00940063i
\(657\) 2.94147 4.04859i 0.114758 0.157951i
\(658\) 6.11211 1.98595i 0.238275 0.0774202i
\(659\) 14.4486 0.562837 0.281419 0.959585i \(-0.409195\pi\)
0.281419 + 0.959585i \(0.409195\pi\)
\(660\) 0 0
\(661\) 14.8696 0.578361 0.289181 0.957275i \(-0.406617\pi\)
0.289181 + 0.957275i \(0.406617\pi\)
\(662\) 20.2286 6.57267i 0.786207 0.255454i
\(663\) 21.5553 29.6684i 0.837140 1.15222i
\(664\) 5.23573 3.80398i 0.203186 0.147623i
\(665\) 0 0
\(666\) 2.85584 8.78936i 0.110661 0.340581i
\(667\) −5.37826 7.40254i −0.208247 0.286627i
\(668\) −2.83406 + 3.90075i −0.109653 + 0.150925i
\(669\) −1.67401 5.15206i −0.0647208 0.199190i
\(670\) 0 0
\(671\) −13.0877 + 33.5988i −0.505245 + 1.29707i
\(672\) 2.96677i 0.114446i
\(673\) 39.5785 12.8598i 1.52564 0.495710i 0.578267 0.815848i \(-0.303729\pi\)
0.947371 + 0.320138i \(0.103729\pi\)
\(674\) 28.0780 + 20.3999i 1.08153 + 0.785774i
\(675\) 0 0
\(676\) −2.27913 + 7.01444i −0.0876588 + 0.269786i
\(677\) −42.0715 13.6699i −1.61694 0.525376i −0.645724 0.763571i \(-0.723444\pi\)
−0.971217 + 0.238195i \(0.923444\pi\)
\(678\) −2.52165 3.47076i −0.0968435 0.133294i
\(679\) −1.89499 1.37679i −0.0727229 0.0528363i
\(680\) 0 0
\(681\) −8.43842 −0.323361
\(682\) −15.0819 23.4765i −0.577515 0.898962i
\(683\) 24.5318i 0.938683i 0.883017 + 0.469342i \(0.155509\pi\)
−0.883017 + 0.469342i \(0.844491\pi\)
\(684\) −0.296697 0.913140i −0.0113445 0.0349148i
\(685\) 0 0
\(686\) −8.43584 + 6.12899i −0.322082 + 0.234006i
\(687\) 10.6569 + 3.46262i 0.406584 + 0.132107i
\(688\) −12.2593 3.98328i −0.467380 0.151861i
\(689\) −26.0184 + 18.9035i −0.991222 + 0.720165i
\(690\) 0 0
\(691\) 7.34440 + 22.6037i 0.279394 + 0.859887i 0.988023 + 0.154306i \(0.0493141\pi\)
−0.708629 + 0.705581i \(0.750686\pi\)
\(692\) 3.35078i 0.127378i
\(693\) −1.48050 + 1.80996i −0.0562397 + 0.0687547i
\(694\) 30.6063 1.16180
\(695\) 0 0
\(696\) 3.29383 + 2.39311i 0.124852 + 0.0907105i
\(697\) 1.06512 + 1.46601i 0.0403443 + 0.0555292i
\(698\) −0.711817 0.231283i −0.0269427 0.00875420i
\(699\) −1.80459 + 5.55397i −0.0682560 + 0.210070i
\(700\) 0 0
\(701\) 26.4499 + 19.2170i 0.998999 + 0.725816i 0.961873 0.273495i \(-0.0881797\pi\)
0.0371259 + 0.999311i \(0.488180\pi\)
\(702\) −4.90981 + 1.59529i −0.185309 + 0.0602105i
\(703\) 10.1224i 0.381772i
\(704\) −6.84753 26.0684i −0.258076 0.982491i
\(705\) 0 0
\(706\) 0.527664 + 1.62398i 0.0198589 + 0.0611194i
\(707\) −7.84138 + 10.7927i −0.294905 + 0.405903i
\(708\) −1.66535 2.29216i −0.0625877 0.0861445i
\(709\) −7.36278 + 22.6603i −0.276515 + 0.851025i 0.712300 + 0.701875i \(0.247654\pi\)
−0.988815 + 0.149150i \(0.952346\pi\)
\(710\) 0 0
\(711\) −1.84478 + 1.34031i −0.0691845 + 0.0502655i
\(712\) −6.03453 + 8.30582i −0.226154 + 0.311274i
\(713\) −50.3568 + 16.3619i −1.88588 + 0.612759i
\(714\) −6.00829 −0.224855
\(715\) 0 0
\(716\) −3.88293 −0.145112
\(717\) −15.7173 + 5.10686i −0.586973 + 0.190719i
\(718\) 10.1980 14.0363i 0.380586 0.523831i
\(719\) −2.30311 + 1.67331i −0.0858914 + 0.0624038i −0.629902 0.776674i \(-0.716905\pi\)
0.544011 + 0.839078i \(0.316905\pi\)
\(720\) 0 0
\(721\) 3.94263 12.1342i 0.146831 0.451900i
\(722\) −11.3056 15.5608i −0.420751 0.579114i
\(723\) −1.93487 + 2.66312i −0.0719586 + 0.0990425i
\(724\) −5.70996 17.5735i −0.212209 0.653112i
\(725\) 0 0
\(726\) 5.00869 10.9578i 0.185890 0.406681i
\(727\) 13.5192i 0.501399i 0.968065 + 0.250700i \(0.0806606\pi\)
−0.968065 + 0.250700i \(0.919339\pi\)
\(728\) 9.69362 3.14965i 0.359270 0.116734i
\(729\) 0.809017 + 0.587785i 0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) −17.6210 + 54.2318i −0.651736 + 2.00584i
\(732\) −8.27522 2.68878i −0.305861 0.0993802i
\(733\) −19.3001 26.5643i −0.712864 0.981174i −0.999731 0.0232030i \(-0.992614\pi\)
0.286866 0.957971i \(-0.407386\pi\)
\(734\) 13.9440 + 10.1309i 0.514681 + 0.373938i
\(735\) 0 0
\(736\) −29.0062 −1.06918
\(737\) −0.387456 + 6.75599i −0.0142721 + 0.248860i
\(738\) 0.255095i 0.00939018i
\(739\) −15.7267 48.4018i −0.578516 1.78049i −0.623882 0.781519i \(-0.714445\pi\)
0.0453660 0.998970i \(-0.485555\pi\)
\(740\) 0 0
\(741\) −4.57453 + 3.32359i −0.168050 + 0.122095i
\(742\) 5.01123 + 1.62825i 0.183968 + 0.0597749i
\(743\) −14.7276 4.78528i −0.540302 0.175555i 0.0261370 0.999658i \(-0.491679\pi\)
−0.566439 + 0.824104i \(0.691679\pi\)
\(744\) 19.0603 13.8481i 0.698786 0.507697i
\(745\) 0 0
\(746\) −1.78609 5.49702i −0.0653933 0.201260i
\(747\) 2.10999i 0.0772004i
\(748\) −19.9750 + 5.24692i −0.730357 + 0.191846i
\(749\) −4.31444 −0.157646
\(750\) 0 0
\(751\) −8.94571 6.49944i −0.326434 0.237168i 0.412482 0.910966i \(-0.364662\pi\)
−0.738916 + 0.673798i \(0.764662\pi\)
\(752\) −8.60359 11.8418i −0.313740 0.431827i
\(753\) −7.03719 2.28652i −0.256449 0.0833255i
\(754\) 2.11760 6.51731i 0.0771185 0.237346i
\(755\) 0 0
\(756\) −0.456498 0.331666i −0.0166027 0.0120626i
\(757\) 8.56219 2.78203i 0.311198 0.101114i −0.149254 0.988799i \(-0.547687\pi\)
0.460452 + 0.887684i \(0.347687\pi\)
\(758\) 36.7025i 1.33309i
\(759\) −17.6961 14.4750i −0.642327 0.525407i
\(760\) 0 0
\(761\) 2.56374 + 7.89038i 0.0929355 + 0.286026i 0.986710 0.162490i \(-0.0519526\pi\)
−0.893775 + 0.448516i \(0.851953\pi\)
\(762\) −6.99648 + 9.62983i −0.253456 + 0.348852i
\(763\) 3.74265 + 5.15132i 0.135493 + 0.186490i
\(764\) 1.53972 4.73876i 0.0557050 0.171442i
\(765\) 0 0
\(766\) 17.9281 13.0255i 0.647767 0.470630i
\(767\) −9.80761 + 13.4990i −0.354132 + 0.487421i
\(768\) 14.9524 4.85832i 0.539547 0.175310i
\(769\) −2.89088 −0.104248 −0.0521239 0.998641i \(-0.516599\pi\)
−0.0521239 + 0.998641i \(0.516599\pi\)
\(770\) 0 0
\(771\) −18.6991 −0.673432
\(772\) −14.5281 + 4.72047i −0.522879 + 0.169894i
\(773\) −16.3685 + 22.5293i −0.588734 + 0.810322i −0.994619 0.103602i \(-0.966963\pi\)
0.405885 + 0.913924i \(0.366963\pi\)
\(774\) 6.49424 4.71834i 0.233431 0.169597i
\(775\) 0 0
\(776\) −3.14890 + 9.69132i −0.113039 + 0.347898i
\(777\) −3.49664 4.81271i −0.125441 0.172655i
\(778\) −17.7513 + 24.4326i −0.636417 + 0.875952i
\(779\) −0.0863407 0.265729i −0.00309348 0.00952074i
\(780\) 0 0
\(781\) 0.807189 2.07222i 0.0288835 0.0741500i
\(782\) 58.7433i 2.10066i
\(783\) −1.26244 + 0.410191i −0.0451158 + 0.0146590i
\(784\) 9.25304 + 6.72273i 0.330466 + 0.240098i
\(785\) 0 0
\(786\) −3.96321 + 12.1975i −0.141363 + 0.435070i
\(787\) 23.6200 + 7.67461i 0.841963 + 0.273570i 0.698076 0.716024i \(-0.254040\pi\)
0.143887 + 0.989594i \(0.454040\pi\)
\(788\) 3.19914 + 4.40324i 0.113965 + 0.156859i
\(789\) 3.22814 + 2.34538i 0.114925 + 0.0834977i
\(790\) 0 0
\(791\) −2.76152 −0.0981883
\(792\) 9.47896 + 3.69232i 0.336820 + 0.131201i
\(793\) 51.2426i 1.81968i
\(794\) −3.98037 12.2503i −0.141258 0.434748i
\(795\) 0 0
\(796\) 13.7896 10.0187i 0.488758 0.355103i
\(797\) 2.67348 + 0.868668i 0.0946997 + 0.0307698i 0.355984 0.934492i \(-0.384146\pi\)
−0.261284 + 0.965262i \(0.584146\pi\)
\(798\) 0.881070 + 0.286277i 0.0311895 + 0.0101341i
\(799\) −52.3852 + 38.0600i −1.85325 + 1.34647i
\(800\) 0 0
\(801\) −1.03435 3.18340i −0.0365469 0.112480i
\(802\) 8.46012i 0.298737i
\(803\) 8.97095 + 13.9642i 0.316578 + 0.492786i
\(804\) −1.63296 −0.0575901
\(805\) 0 0
\(806\) −32.0811 23.3083i −1.13001 0.820998i
\(807\) −7.47368 10.2866i −0.263086 0.362107i
\(808\) 55.1961 + 17.9343i 1.94179 + 0.630926i
\(809\) −3.60825 + 11.1051i −0.126859 + 0.390433i −0.994235 0.107220i \(-0.965805\pi\)
0.867376 + 0.497654i \(0.165805\pi\)
\(810\) 0 0
\(811\) −19.4722 14.1474i −0.683761 0.496782i 0.190842 0.981621i \(-0.438878\pi\)
−0.874603 + 0.484839i \(0.838878\pi\)
\(812\) 0.712347 0.231455i 0.0249985 0.00812250i
\(813\) 23.8280i 0.835684i
\(814\) 23.7251 + 19.4066i 0.831565 + 0.680199i
\(815\) 0 0
\(816\) 4.22872 + 13.0147i 0.148035 + 0.455604i
\(817\) 5.16797 7.11310i 0.180804 0.248856i
\(818\) −10.7777 14.8343i −0.376835 0.518669i
\(819\) −1.02689 + 3.16043i −0.0358823 + 0.110434i
\(820\) 0 0
\(821\) −3.92827 + 2.85406i −0.137098 + 0.0996073i −0.654220 0.756304i \(-0.727003\pi\)
0.517123 + 0.855911i \(0.327003\pi\)
\(822\) −13.1529 + 18.1034i −0.458761 + 0.631430i
\(823\) −24.7846 + 8.05300i −0.863937 + 0.280710i −0.707272 0.706942i \(-0.750074\pi\)
−0.156665 + 0.987652i \(0.550074\pi\)
\(824\) −55.5050 −1.93361
\(825\) 0 0
\(826\) 2.73376 0.0951195
\(827\) −15.4873 + 5.03212i −0.538546 + 0.174984i −0.565645 0.824649i \(-0.691373\pi\)
0.0270996 + 0.999633i \(0.491373\pi\)
\(828\) 3.24271 4.46321i 0.112692 0.155107i
\(829\) −8.10161 + 5.88616i −0.281380 + 0.204435i −0.719519 0.694472i \(-0.755638\pi\)
0.438139 + 0.898907i \(0.355638\pi\)
\(830\) 0 0
\(831\) 2.29059 7.04973i 0.0794598 0.244552i
\(832\) −22.5140 30.9879i −0.780534 1.07431i
\(833\) 29.7396 40.9331i 1.03042 1.41825i
\(834\) 2.76559 + 8.51162i 0.0957647 + 0.294733i
\(835\) 0 0
\(836\) 3.17917 + 0.182326i 0.109954 + 0.00630587i
\(837\) 7.68126i 0.265503i
\(838\) 39.6849 12.8944i 1.37089 0.445430i
\(839\) 9.50855 + 6.90837i 0.328272 + 0.238503i 0.739697 0.672940i \(-0.234969\pi\)
−0.411425 + 0.911444i \(0.634969\pi\)
\(840\) 0 0
\(841\) −8.41700 + 25.9049i −0.290242 + 0.893271i
\(842\) 23.6081 + 7.67073i 0.813588 + 0.264351i
\(843\) 17.0937 + 23.5274i 0.588737 + 0.810327i
\(844\) 5.75659 + 4.18240i 0.198150 + 0.143964i
\(845\) 0 0
\(846\) 9.11534 0.313392
\(847\) −3.81133 6.75427i −0.130959 0.232079i
\(848\) 12.0009i 0.412113i
\(849\) 6.69730 + 20.6122i 0.229851 + 0.707407i
\(850\) 0 0
\(851\) 47.0541 34.1868i 1.61299 1.17191i
\(852\) 0.510378 + 0.165832i 0.0174853 + 0.00568131i
\(853\) −43.4018 14.1021i −1.48605 0.482847i −0.550135 0.835076i \(-0.685424\pi\)
−0.935914 + 0.352229i \(0.885424\pi\)
\(854\) 6.79210 4.93475i 0.232421 0.168864i
\(855\) 0 0
\(856\) 5.80009 + 17.8508i 0.198243 + 0.610129i
\(857\) 8.41558i 0.287471i 0.989616 + 0.143735i \(0.0459114\pi\)
−0.989616 + 0.143735i \(0.954089\pi\)
\(858\) 0.980336 17.0939i 0.0334681 0.583577i
\(859\) 45.3009 1.54565 0.772823 0.634622i \(-0.218844\pi\)
0.772823 + 0.634622i \(0.218844\pi\)
\(860\) 0 0
\(861\) −0.132844 0.0965167i −0.00452730 0.00328928i
\(862\) −21.8741 30.1071i −0.745034 1.02545i
\(863\) −11.4688 3.72644i −0.390402 0.126849i 0.107237 0.994233i \(-0.465800\pi\)
−0.497639 + 0.867384i \(0.665800\pi\)
\(864\) −1.30033 + 4.00201i −0.0442382 + 0.136151i
\(865\) 0 0
\(866\) 32.4984 + 23.6115i 1.10434 + 0.802350i
\(867\) 41.4056 13.4535i 1.40621 0.456904i
\(868\) 4.33425i 0.147114i
\(869\) −1.92138 7.31466i −0.0651783 0.248133i
\(870\) 0 0
\(871\) 2.97178 + 9.14618i 0.100695 + 0.309907i
\(872\) 16.2820 22.4103i 0.551378 0.758907i
\(873\) −1.95279 2.68778i −0.0660919 0.0909676i
\(874\) −2.79894 + 8.61426i −0.0946757 + 0.291382i
\(875\) 0 0
\(876\) −3.24021 + 2.35415i −0.109477 + 0.0795395i
\(877\) 12.4281 17.1058i 0.419666 0.577621i −0.545876 0.837866i \(-0.683803\pi\)
0.965543 + 0.260245i \(0.0838032\pi\)
\(878\) −1.09389 + 0.355427i −0.0369170 + 0.0119951i
\(879\) 8.41220 0.283736
\(880\) 0 0
\(881\) −13.1669 −0.443605 −0.221803 0.975092i \(-0.571194\pi\)
−0.221803 + 0.975092i \(0.571194\pi\)
\(882\) −6.77401 + 2.20101i −0.228093 + 0.0741118i
\(883\) −20.4371 + 28.1293i −0.687765 + 0.946627i −0.999994 0.00337992i \(-0.998924\pi\)
0.312230 + 0.950007i \(0.398924\pi\)
\(884\) −23.7445 + 17.2514i −0.798614 + 0.580227i
\(885\) 0 0
\(886\) −10.3301 + 31.7929i −0.347048 + 1.06810i
\(887\) −12.3179 16.9542i −0.413596 0.569266i 0.550495 0.834838i \(-0.314439\pi\)
−0.964091 + 0.265573i \(0.914439\pi\)
\(888\) −15.2117 + 20.9372i −0.510473 + 0.702605i
\(889\) 2.36769 + 7.28700i 0.0794097 + 0.244398i
\(890\) 0 0
\(891\) −2.79042 + 1.79264i −0.0934827 + 0.0600556i
\(892\) 4.33555i 0.145165i
\(893\) 9.49533 3.08522i 0.317749 0.103243i
\(894\) −8.50860 6.18186i −0.284570 0.206752i
\(895\) 0 0
\(896\) −0.105680 + 0.325249i −0.00353052 + 0.0108658i
\(897\) −30.8997 10.0399i −1.03171 0.335223i
\(898\) 23.5433 + 32.4046i 0.785652 + 1.08136i
\(899\) −8.24886 5.99314i −0.275115 0.199883i
\(900\) 0 0
\(901\) −53.0889 −1.76865
\(902\) 0.788357 + 0.307087i 0.0262494 + 0.0102249i
\(903\) 5.16716i 0.171952i
\(904\) 3.71243 + 11.4257i 0.123474 + 0.380013i
\(905\) 0 0
\(906\) −6.12105 + 4.44720i −0.203358 + 0.147748i
\(907\) −24.9565 8.10886i −0.828667 0.269250i −0.136183 0.990684i \(-0.543484\pi\)
−0.692484 + 0.721433i \(0.743484\pi\)
\(908\) 6.42299 + 2.08695i 0.213154 + 0.0692580i
\(909\) −15.3080 + 11.1219i −0.507736 + 0.368891i
\(910\) 0 0
\(911\) −12.2556 37.7188i −0.406045 1.24968i −0.920019 0.391873i \(-0.871827\pi\)
0.513974 0.857806i \(-0.328173\pi\)
\(912\) 2.10999i 0.0698687i
\(913\) −6.52079 2.54003i −0.215807 0.0840628i
\(914\) 2.61128 0.0863734
\(915\) 0 0
\(916\) −7.25521 5.27122i −0.239719 0.174166i
\(917\) 4.85249 + 6.67887i 0.160243 + 0.220556i
\(918\) −8.10486 2.63343i −0.267500 0.0869161i
\(919\) −4.62777 + 14.2428i −0.152656 + 0.469827i −0.997916 0.0645285i \(-0.979446\pi\)
0.845260 + 0.534356i \(0.179446\pi\)
\(920\) 0 0
\(921\) −19.2086 13.9558i −0.632944 0.459861i
\(922\) 29.7883 9.67881i 0.981025 0.318754i
\(923\) 3.16041i 0.104026i
\(924\) 1.57453 1.01152i 0.0517983 0.0332765i
\(925\) 0 0
\(926\) −10.3504 31.8554i −0.340137 1.04683i
\(927\) 10.6368 14.6403i 0.349358 0.480850i
\(928\) −3.28317 4.51890i −0.107775 0.148340i
\(929\) 15.3415 47.2162i 0.503338 1.54911i −0.300210 0.953873i \(-0.597057\pi\)
0.803547 0.595241i \(-0.202943\pi\)
\(930\) 0 0
\(931\) −6.31143 + 4.58552i −0.206849 + 0.150284i
\(932\) 2.74717 3.78115i 0.0899865 0.123856i
\(933\) −21.9191 + 7.12194i −0.717598 + 0.233162i
\(934\) 4.09880 0.134117
\(935\) 0 0
\(936\) 14.4567 0.472530
\(937\) −51.6342 + 16.7770i −1.68682 + 0.548079i −0.986214 0.165474i \(-0.947085\pi\)
−0.700601 + 0.713553i \(0.747085\pi\)
\(938\) 0.926120 1.27469i 0.0302389 0.0416203i
\(939\) −14.0476 + 10.2062i −0.458427 + 0.333066i
\(940\) 0 0
\(941\) 2.05826 6.33466i 0.0670972 0.206504i −0.911886 0.410442i \(-0.865374\pi\)
0.978984 + 0.203938i \(0.0653743\pi\)
\(942\) 7.30833 + 10.0590i 0.238118 + 0.327742i
\(943\) 0.943648 1.29882i 0.0307294 0.0422954i
\(944\) −1.92406 5.92164i −0.0626227 0.192733i
\(945\) 0 0
\(946\) 6.76390 + 25.7501i 0.219913 + 0.837207i
\(947\) 42.6250i 1.38513i 0.721358 + 0.692563i \(0.243518\pi\)
−0.721358 + 0.692563i \(0.756482\pi\)
\(948\) 1.73565 0.563947i 0.0563713 0.0183161i
\(949\) 19.0823 + 13.8641i 0.619439 + 0.450049i
\(950\) 0 0
\(951\) −1.90075 + 5.84990i −0.0616360 + 0.189696i
\(952\) 16.0017 + 5.19927i 0.518619 + 0.168509i
\(953\) 9.84772 + 13.5542i 0.318999 + 0.439064i 0.938161 0.346199i \(-0.112528\pi\)
−0.619162 + 0.785263i \(0.712528\pi\)
\(954\) 6.04622 + 4.39283i 0.195754 + 0.142223i
\(955\) 0 0
\(956\) 13.2264 0.427772
\(957\) 0.252069 4.39528i 0.00814825 0.142079i
\(958\) 1.03500i 0.0334393i
\(959\) 4.45110 + 13.6991i 0.143733 + 0.442366i
\(960\) 0 0
\(961\) −22.6539 + 16.4590i −0.730772 + 0.530937i
\(962\) 41.4271 + 13.4605i 1.33566 + 0.433984i
\(963\) −5.81994 1.89101i −0.187545 0.0609370i
\(964\) 2.13138 1.54854i 0.0686470 0.0498750i
\(965\) 0 0
\(966\) 1.64492 + 5.06254i 0.0529244 + 0.162885i
\(967\) 50.1233i 1.61186i 0.592014 + 0.805928i \(0.298333\pi\)
−0.592014 + 0.805928i \(0.701667\pi\)
\(968\) −22.8218 + 24.8493i −0.733521 + 0.798687i
\(969\) −9.33404 −0.299853
\(970\) 0 0
\(971\) −32.4602 23.5837i −1.04170 0.756837i −0.0710811 0.997471i \(-0.522645\pi\)
−0.970616 + 0.240633i \(0.922645\pi\)
\(972\) −0.470423 0.647481i −0.0150888 0.0207680i
\(973\) 5.47890 + 1.78020i 0.175646 + 0.0570707i
\(974\) 4.53113 13.9454i 0.145187 0.446839i
\(975\) 0 0
\(976\) −15.4696 11.2393i −0.495170 0.359762i
\(977\) −22.9853 + 7.46838i −0.735365 + 0.238935i −0.652672 0.757640i \(-0.726352\pi\)
−0.0826930 + 0.996575i \(0.526352\pi\)
\(978\) 1.96335i 0.0627809i
\(979\) 11.0833 + 0.635626i 0.354223 + 0.0203147i
\(980\) 0 0
\(981\) 2.79082 + 8.58925i 0.0891039 + 0.274234i
\(982\) 1.79547 2.47125i 0.0572958 0.0788608i
\(983\) −13.6966 18.8518i −0.436854 0.601278i 0.532656 0.846332i \(-0.321194\pi\)
−0.969509 + 0.245055i \(0.921194\pi\)
\(984\) −0.220747 + 0.679388i −0.00703715 + 0.0216581i
\(985\) 0 0
\(986\) 9.15166 6.64907i 0.291448 0.211750i
\(987\) 3.44884 4.74692i 0.109778 0.151096i
\(988\) 4.30393 1.39843i 0.136926 0.0444900i
\(989\) 50.5195 1.60643
\(990\) 0 0
\(991\) −54.0689 −1.71756 −0.858778 0.512348i \(-0.828776\pi\)
−0.858778 + 0.512348i \(0.828776\pi\)
\(992\) −30.7405 + 9.98818i −0.976011 + 0.317125i
\(993\) 11.4143 15.7104i 0.362220 0.498554i
\(994\) −0.418906 + 0.304353i −0.0132869 + 0.00965348i
\(995\) 0 0
\(996\) 0.521833 1.60604i 0.0165349 0.0508893i
\(997\) 29.8071 + 41.0260i 0.944001 + 1.29931i 0.954141 + 0.299357i \(0.0967721\pi\)
−0.0101405 + 0.999949i \(0.503228\pi\)
\(998\) 11.4461 15.7542i 0.362320 0.498691i
\(999\) −2.60737 8.02466i −0.0824935 0.253889i
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 825.2.bx.f.49.3 16
5.2 odd 4 165.2.m.d.16.2 8
5.3 odd 4 825.2.n.g.676.1 8
5.4 even 2 inner 825.2.bx.f.49.2 16
11.9 even 5 inner 825.2.bx.f.724.2 16
15.2 even 4 495.2.n.a.181.1 8
55.3 odd 20 9075.2.a.di.1.1 4
55.8 even 20 9075.2.a.cm.1.4 4
55.9 even 10 inner 825.2.bx.f.724.3 16
55.42 odd 20 165.2.m.d.31.2 yes 8
55.47 odd 20 1815.2.a.p.1.4 4
55.52 even 20 1815.2.a.w.1.1 4
55.53 odd 20 825.2.n.g.526.1 8
165.47 even 20 5445.2.a.bt.1.1 4
165.107 odd 20 5445.2.a.bf.1.4 4
165.152 even 20 495.2.n.a.361.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.d.16.2 8 5.2 odd 4
165.2.m.d.31.2 yes 8 55.42 odd 20
495.2.n.a.181.1 8 15.2 even 4
495.2.n.a.361.1 8 165.152 even 20
825.2.n.g.526.1 8 55.53 odd 20
825.2.n.g.676.1 8 5.3 odd 4
825.2.bx.f.49.2 16 5.4 even 2 inner
825.2.bx.f.49.3 16 1.1 even 1 trivial
825.2.bx.f.724.2 16 11.9 even 5 inner
825.2.bx.f.724.3 16 55.9 even 10 inner
1815.2.a.p.1.4 4 55.47 odd 20
1815.2.a.w.1.1 4 55.52 even 20
5445.2.a.bf.1.4 4 165.107 odd 20
5445.2.a.bt.1.1 4 165.47 even 20
9075.2.a.cm.1.4 4 55.8 even 20
9075.2.a.di.1.1 4 55.3 odd 20