Properties

Label 575.2.p.a.49.2
Level $575$
Weight $2$
Character 575.49
Analytic conductor $4.591$
Analytic rank $0$
Dimension $20$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [575,2,Mod(49,575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(575, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("575.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 575.p (of order \(22\), degree \(10\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.59139811622\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{22})\)
Coefficient field: \(\Q(\zeta_{44})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) 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 115)
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 49.2
Root \(-0.755750 + 0.654861i\) of defining polynomial
Character \(\chi\) \(=\) 575.49
Dual form 575.2.p.a.399.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0872586 - 0.0125459i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-1.91153 + 0.561276i) q^{4} +(0.0845850 + 0.0248364i) q^{6} +(-0.835939 - 1.30075i) q^{7} +(-0.320135 + 0.146201i) q^{8} +(-1.30972 - 1.51150i) q^{9} +(0.289532 - 2.01374i) q^{11} +(-1.97195 - 0.283524i) q^{12} +(1.15727 - 1.80075i) q^{13} +(-0.0892619 - 0.103014i) q^{14} +(3.32584 - 2.13739i) q^{16} +(1.22809 - 4.18251i) q^{17} +(-0.133248 - 0.115460i) q^{18} +(7.12381 - 2.09174i) q^{19} +(-0.220047 - 1.53046i) q^{21} -0.179348i q^{22} +(-3.89854 + 2.79310i) q^{23} -0.351939 q^{24} +(0.0783898 - 0.171650i) q^{26} +(-1.40866 - 4.79746i) q^{27} +(2.32800 + 2.01722i) q^{28} +(4.30111 + 1.26292i) q^{29} +(-0.376329 - 0.824045i) q^{31} +(0.795348 - 0.689173i) q^{32} +(1.09990 - 1.71148i) q^{33} +(0.0546886 - 0.380367i) q^{34} +(3.35194 + 2.15416i) q^{36} +(-8.38507 + 7.26571i) q^{37} +(0.595371 - 0.271897i) q^{38} +(1.80075 - 1.15727i) q^{39} +(3.95750 - 4.56720i) q^{41} +(-0.0384020 - 0.130785i) q^{42} +(-4.90745 - 2.24116i) q^{43} +(0.576814 + 4.01183i) q^{44} +(-0.305139 + 0.292633i) q^{46} -2.72825i q^{47} +(3.91319 - 0.562632i) q^{48} +(1.91476 - 4.19273i) q^{49} +(2.85459 - 3.29437i) q^{51} +(-1.20144 + 4.09173i) q^{52} +(0.148283 + 0.230732i) q^{53} +(-0.183106 - 0.400947i) q^{54} +(0.457783 + 0.294199i) q^{56} +(7.34898 + 1.05662i) q^{57} +(0.391153 + 0.0562393i) q^{58} +(-6.74757 - 4.33640i) q^{59} +(-1.33718 - 2.92802i) q^{61} +(-0.0431763 - 0.0671837i) q^{62} +(-0.871230 + 2.96714i) q^{63} +(-5.11714 + 5.90549i) q^{64} +(0.0745040 - 0.163141i) q^{66} +(-1.94473 + 0.279610i) q^{67} +8.68428i q^{68} +(-4.70653 + 0.921186i) q^{69} +(1.58700 + 11.0378i) q^{71} +(0.640269 + 0.292401i) q^{72} +(-2.92170 - 9.95039i) q^{73} +(-0.640515 + 0.739194i) q^{74} +(-12.4433 + 7.99684i) q^{76} +(-2.86139 + 1.30675i) q^{77} +(0.142612 - 0.123574i) q^{78} +(-2.70849 - 1.74064i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(0.288027 - 0.448178i) q^{82} +(3.29557 - 2.85563i) q^{83} +(1.27964 + 2.80202i) q^{84} +(-0.456334 - 0.133992i) q^{86} +(3.38779 + 2.93553i) q^{87} +(0.201720 + 0.686997i) q^{88} +(-0.266861 + 0.584343i) q^{89} -3.30972 q^{91} +(5.88446 - 7.52725i) q^{92} -0.905910i q^{93} +(-0.0342284 - 0.238063i) q^{94} +(1.00977 - 0.296494i) q^{96} +(4.18748 + 3.62848i) q^{97} +(0.114478 - 0.389875i) q^{98} +(-3.42297 + 2.19981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9} + 16 q^{11} + 6 q^{14} + 10 q^{16} + 26 q^{19} + 12 q^{21} + 12 q^{24} + 22 q^{26} - 4 q^{29} - 40 q^{31} - 32 q^{34} + 48 q^{36} - 10 q^{41} - 38 q^{44} - 32 q^{46}+ \cdots - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(277\)
\(\chi(n)\) \(e\left(\frac{8}{11}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0872586 0.0125459i 0.0617012 0.00887129i −0.111395 0.993776i \(-0.535532\pi\)
0.173096 + 0.984905i \(0.444623\pi\)
\(3\) 0.909632 + 0.415415i 0.525176 + 0.239840i 0.660318 0.750986i \(-0.270422\pi\)
−0.135141 + 0.990826i \(0.543149\pi\)
\(4\) −1.91153 + 0.561276i −0.955765 + 0.280638i
\(5\) 0 0
\(6\) 0.0845850 + 0.0248364i 0.0345317 + 0.0101394i
\(7\) −0.835939 1.30075i −0.315955 0.491636i 0.646560 0.762863i \(-0.276207\pi\)
−0.962515 + 0.271227i \(0.912571\pi\)
\(8\) −0.320135 + 0.146201i −0.113185 + 0.0516897i
\(9\) −1.30972 1.51150i −0.436574 0.503833i
\(10\) 0 0
\(11\) 0.289532 2.01374i 0.0872971 0.607165i −0.898468 0.439038i \(-0.855319\pi\)
0.985765 0.168126i \(-0.0537717\pi\)
\(12\) −1.97195 0.283524i −0.569253 0.0818462i
\(13\) 1.15727 1.80075i 0.320969 0.499437i −0.642851 0.765991i \(-0.722249\pi\)
0.963820 + 0.266554i \(0.0858850\pi\)
\(14\) −0.0892619 0.103014i −0.0238563 0.0275316i
\(15\) 0 0
\(16\) 3.32584 2.13739i 0.831460 0.534347i
\(17\) 1.22809 4.18251i 0.297857 1.01441i −0.665548 0.746355i \(-0.731802\pi\)
0.963405 0.268052i \(-0.0863798\pi\)
\(18\) −0.133248 0.115460i −0.0314068 0.0272141i
\(19\) 7.12381 2.09174i 1.63431 0.479878i 0.669499 0.742813i \(-0.266509\pi\)
0.964814 + 0.262935i \(0.0846905\pi\)
\(20\) 0 0
\(21\) −0.220047 1.53046i −0.0480182 0.333974i
\(22\) 0.179348i 0.0382372i
\(23\) −3.89854 + 2.79310i −0.812901 + 0.582402i
\(24\) −0.351939 −0.0718392
\(25\) 0 0
\(26\) 0.0783898 0.171650i 0.0153735 0.0336633i
\(27\) −1.40866 4.79746i −0.271097 0.923273i
\(28\) 2.32800 + 2.01722i 0.439951 + 0.381219i
\(29\) 4.30111 + 1.26292i 0.798695 + 0.234518i 0.655519 0.755179i \(-0.272450\pi\)
0.143177 + 0.989697i \(0.454268\pi\)
\(30\) 0 0
\(31\) −0.376329 0.824045i −0.0675906 0.148003i 0.872822 0.488039i \(-0.162288\pi\)
−0.940412 + 0.340037i \(0.889561\pi\)
\(32\) 0.795348 0.689173i 0.140599 0.121830i
\(33\) 1.09990 1.71148i 0.191469 0.297931i
\(34\) 0.0546886 0.380367i 0.00937901 0.0652325i
\(35\) 0 0
\(36\) 3.35194 + 2.15416i 0.558656 + 0.359027i
\(37\) −8.38507 + 7.26571i −1.37850 + 1.19447i −0.420641 + 0.907227i \(0.638195\pi\)
−0.957856 + 0.287248i \(0.907260\pi\)
\(38\) 0.595371 0.271897i 0.0965819 0.0441075i
\(39\) 1.80075 1.15727i 0.288350 0.185311i
\(40\) 0 0
\(41\) 3.95750 4.56720i 0.618058 0.713277i −0.357279 0.933998i \(-0.616295\pi\)
0.975337 + 0.220720i \(0.0708408\pi\)
\(42\) −0.0384020 0.130785i −0.00592556 0.0201806i
\(43\) −4.90745 2.24116i −0.748379 0.341773i 0.00444961 0.999990i \(-0.498584\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(44\) 0.576814 + 4.01183i 0.0869579 + 0.604806i
\(45\) 0 0
\(46\) −0.305139 + 0.292633i −0.0449903 + 0.0431464i
\(47\) 2.72825i 0.397956i −0.980004 0.198978i \(-0.936238\pi\)
0.980004 0.198978i \(-0.0637623\pi\)
\(48\) 3.91319 0.562632i 0.564821 0.0812089i
\(49\) 1.91476 4.19273i 0.273537 0.598962i
\(50\) 0 0
\(51\) 2.85459 3.29437i 0.399723 0.461305i
\(52\) −1.20144 + 4.09173i −0.166610 + 0.567420i
\(53\) 0.148283 + 0.230732i 0.0203682 + 0.0316935i 0.851288 0.524698i \(-0.175822\pi\)
−0.830920 + 0.556392i \(0.812185\pi\)
\(54\) −0.183106 0.400947i −0.0249176 0.0545620i
\(55\) 0 0
\(56\) 0.457783 + 0.294199i 0.0611738 + 0.0393140i
\(57\) 7.34898 + 1.05662i 0.973396 + 0.139953i
\(58\) 0.391153 + 0.0562393i 0.0513609 + 0.00738458i
\(59\) −6.74757 4.33640i −0.878458 0.564551i 0.0218707 0.999761i \(-0.493038\pi\)
−0.900329 + 0.435210i \(0.856674\pi\)
\(60\) 0 0
\(61\) −1.33718 2.92802i −0.171208 0.374894i 0.804505 0.593946i \(-0.202431\pi\)
−0.975713 + 0.219052i \(0.929704\pi\)
\(62\) −0.0431763 0.0671837i −0.00548340 0.00853233i
\(63\) −0.871230 + 2.96714i −0.109765 + 0.373824i
\(64\) −5.11714 + 5.90549i −0.639642 + 0.738187i
\(65\) 0 0
\(66\) 0.0745040 0.163141i 0.00917081 0.0200813i
\(67\) −1.94473 + 0.279610i −0.237587 + 0.0341598i −0.260080 0.965587i \(-0.583749\pi\)
0.0224928 + 0.999747i \(0.492840\pi\)
\(68\) 8.68428i 1.05312i
\(69\) −4.70653 + 0.921186i −0.566600 + 0.110898i
\(70\) 0 0
\(71\) 1.58700 + 11.0378i 0.188342 + 1.30995i 0.836301 + 0.548271i \(0.184714\pi\)
−0.647959 + 0.761675i \(0.724377\pi\)
\(72\) 0.640269 + 0.292401i 0.0754564 + 0.0344598i
\(73\) −2.92170 9.95039i −0.341959 1.16461i −0.933574 0.358385i \(-0.883328\pi\)
0.591615 0.806221i \(-0.298491\pi\)
\(74\) −0.640515 + 0.739194i −0.0744584 + 0.0859295i
\(75\) 0 0
\(76\) −12.4433 + 7.99684i −1.42735 + 0.917300i
\(77\) −2.86139 + 1.30675i −0.326086 + 0.148919i
\(78\) 0.142612 0.123574i 0.0161476 0.0139920i
\(79\) −2.70849 1.74064i −0.304729 0.195837i 0.379335 0.925259i \(-0.376153\pi\)
−0.684064 + 0.729422i \(0.739789\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0.288027 0.448178i 0.0318072 0.0494930i
\(83\) 3.29557 2.85563i 0.361736 0.313446i −0.454963 0.890510i \(-0.650347\pi\)
0.816698 + 0.577065i \(0.195802\pi\)
\(84\) 1.27964 + 2.80202i 0.139620 + 0.305725i
\(85\) 0 0
\(86\) −0.456334 0.133992i −0.0492078 0.0144487i
\(87\) 3.38779 + 2.93553i 0.363209 + 0.314722i
\(88\) 0.201720 + 0.686997i 0.0215035 + 0.0732341i
\(89\) −0.266861 + 0.584343i −0.0282872 + 0.0619403i −0.923248 0.384204i \(-0.874476\pi\)
0.894961 + 0.446144i \(0.147203\pi\)
\(90\) 0 0
\(91\) −3.30972 −0.346953
\(92\) 5.88446 7.52725i 0.613498 0.784770i
\(93\) 0.905910i 0.0939385i
\(94\) −0.0342284 0.238063i −0.00353038 0.0245544i
\(95\) 0 0
\(96\) 1.00977 0.296494i 0.103059 0.0302608i
\(97\) 4.18748 + 3.62848i 0.425175 + 0.368416i 0.841006 0.541026i \(-0.181964\pi\)
−0.415831 + 0.909442i \(0.636509\pi\)
\(98\) 0.114478 0.389875i 0.0115640 0.0393833i
\(99\) −3.42297 + 2.19981i −0.344021 + 0.221089i
\(100\) 0 0
\(101\) −2.94535 3.39912i −0.293073 0.338225i 0.590049 0.807367i \(-0.299108\pi\)
−0.883122 + 0.469143i \(0.844563\pi\)
\(102\) 0.207757 0.323276i 0.0205710 0.0320091i
\(103\) 9.63380 + 1.38513i 0.949247 + 0.136481i 0.599510 0.800367i \(-0.295362\pi\)
0.349737 + 0.936848i \(0.386271\pi\)
\(104\) −0.107212 + 0.745675i −0.0105130 + 0.0731194i
\(105\) 0 0
\(106\) 0.0158337 + 0.0182730i 0.00153790 + 0.00177483i
\(107\) 6.72833 3.07272i 0.650452 0.297051i −0.0627299 0.998031i \(-0.519981\pi\)
0.713182 + 0.700979i \(0.247253\pi\)
\(108\) 5.38540 + 8.37985i 0.518210 + 0.806351i
\(109\) 9.99029 + 2.93341i 0.956897 + 0.280970i 0.722656 0.691208i \(-0.242921\pi\)
0.234241 + 0.972179i \(0.424740\pi\)
\(110\) 0 0
\(111\) −10.6456 + 3.12583i −1.01044 + 0.296691i
\(112\) −5.56040 2.53935i −0.525408 0.239946i
\(113\) −19.3927 + 2.78825i −1.82431 + 0.262297i −0.967417 0.253189i \(-0.918520\pi\)
−0.856898 + 0.515486i \(0.827611\pi\)
\(114\) 0.654518 0.0613012
\(115\) 0 0
\(116\) −8.93053 −0.829179
\(117\) −4.23753 + 0.609264i −0.391760 + 0.0563265i
\(118\) −0.643187 0.293734i −0.0592102 0.0270404i
\(119\) −6.46699 + 1.89888i −0.592828 + 0.174070i
\(120\) 0 0
\(121\) 6.58311 + 1.93298i 0.598465 + 0.175725i
\(122\) −0.153415 0.238719i −0.0138896 0.0216126i
\(123\) 5.49716 2.51047i 0.495662 0.226361i
\(124\) 1.18188 + 1.36396i 0.106136 + 0.122487i
\(125\) 0 0
\(126\) −0.0387969 + 0.269839i −0.00345631 + 0.0240391i
\(127\) 17.3667 + 2.49696i 1.54105 + 0.221569i 0.859856 0.510536i \(-0.170553\pi\)
0.681192 + 0.732105i \(0.261462\pi\)
\(128\) −1.51036 + 2.35017i −0.133498 + 0.207727i
\(129\) −3.53296 4.07725i −0.311060 0.358982i
\(130\) 0 0
\(131\) −10.9767 + 7.05427i −0.959035 + 0.616334i −0.923731 0.383043i \(-0.874876\pi\)
−0.0353039 + 0.999377i \(0.511240\pi\)
\(132\) −1.14188 + 3.88890i −0.0993883 + 0.338486i
\(133\) −8.67589 7.51770i −0.752295 0.651867i
\(134\) −0.166187 + 0.0487968i −0.0143563 + 0.00421540i
\(135\) 0 0
\(136\) 0.218329 + 1.51851i 0.0187216 + 0.130211i
\(137\) 21.5268i 1.83916i 0.392903 + 0.919580i \(0.371471\pi\)
−0.392903 + 0.919580i \(0.628529\pi\)
\(138\) −0.399128 + 0.139429i −0.0339760 + 0.0118690i
\(139\) 16.3719 1.38864 0.694322 0.719665i \(-0.255705\pi\)
0.694322 + 0.719665i \(0.255705\pi\)
\(140\) 0 0
\(141\) 1.13336 2.48170i 0.0954458 0.208997i
\(142\) 0.276958 + 0.943233i 0.0232418 + 0.0791544i
\(143\) −3.29117 2.85181i −0.275221 0.238480i
\(144\) −7.58658 2.22762i −0.632215 0.185635i
\(145\) 0 0
\(146\) −0.379780 0.831602i −0.0314308 0.0688239i
\(147\) 3.48345 3.01843i 0.287310 0.248956i
\(148\) 11.9502 18.5950i 0.982304 1.52850i
\(149\) 2.74972 19.1247i 0.225266 1.56676i −0.492399 0.870370i \(-0.663880\pi\)
0.717665 0.696389i \(-0.245211\pi\)
\(150\) 0 0
\(151\) 16.8366 + 10.8202i 1.37015 + 0.880539i 0.998849 0.0479750i \(-0.0152768\pi\)
0.371297 + 0.928514i \(0.378913\pi\)
\(152\) −1.97476 + 1.71114i −0.160174 + 0.138792i
\(153\) −7.93032 + 3.62165i −0.641128 + 0.292793i
\(154\) −0.233287 + 0.149924i −0.0187988 + 0.0120812i
\(155\) 0 0
\(156\) −2.79263 + 3.22287i −0.223590 + 0.258036i
\(157\) −1.62683 5.54048i −0.129835 0.442179i 0.868756 0.495241i \(-0.164920\pi\)
−0.998591 + 0.0530620i \(0.983102\pi\)
\(158\) −0.258177 0.117905i −0.0205395 0.00938006i
\(159\) 0.0390330 + 0.271480i 0.00309552 + 0.0215298i
\(160\) 0 0
\(161\) 6.89206 + 2.73614i 0.543170 + 0.215638i
\(162\) 0.0881559i 0.00692618i
\(163\) −8.71401 + 1.25289i −0.682534 + 0.0981335i −0.474856 0.880064i \(-0.657500\pi\)
−0.207678 + 0.978197i \(0.566591\pi\)
\(164\) −5.00143 + 10.9516i −0.390546 + 0.855176i
\(165\) 0 0
\(166\) 0.251740 0.290524i 0.0195388 0.0225490i
\(167\) −5.50159 + 18.7367i −0.425726 + 1.44989i 0.415692 + 0.909505i \(0.363539\pi\)
−0.841418 + 0.540384i \(0.818279\pi\)
\(168\) 0.294199 + 0.457783i 0.0226980 + 0.0353187i
\(169\) 3.49698 + 7.65732i 0.268998 + 0.589024i
\(170\) 0 0
\(171\) −12.4919 8.02803i −0.955276 0.613919i
\(172\) 10.6386 + 1.52960i 0.811188 + 0.116631i
\(173\) 21.3627 + 3.07149i 1.62417 + 0.233521i 0.893454 0.449155i \(-0.148275\pi\)
0.730721 + 0.682676i \(0.239184\pi\)
\(174\) 0.332443 + 0.213648i 0.0252024 + 0.0161966i
\(175\) 0 0
\(176\) −3.34120 7.31621i −0.251852 0.551480i
\(177\) −4.33640 6.74757i −0.325944 0.507178i
\(178\) −0.0159548 + 0.0543370i −0.00119586 + 0.00407273i
\(179\) −10.0553 + 11.6044i −0.751567 + 0.867354i −0.994719 0.102634i \(-0.967273\pi\)
0.243152 + 0.969988i \(0.421818\pi\)
\(180\) 0 0
\(181\) 0.340209 0.744955i 0.0252876 0.0553720i −0.896567 0.442909i \(-0.853947\pi\)
0.921854 + 0.387537i \(0.126674\pi\)
\(182\) −0.288802 + 0.0415234i −0.0214074 + 0.00307792i
\(183\) 3.21890i 0.237948i
\(184\) 0.839703 1.46414i 0.0619037 0.107938i
\(185\) 0 0
\(186\) −0.0113655 0.0790485i −0.000833356 0.00579612i
\(187\) −8.06690 3.68403i −0.589910 0.269403i
\(188\) 1.53130 + 5.21513i 0.111682 + 0.380353i
\(189\) −5.06273 + 5.84270i −0.368259 + 0.424994i
\(190\) 0 0
\(191\) −3.58868 + 2.30630i −0.259668 + 0.166878i −0.663997 0.747735i \(-0.731141\pi\)
0.404329 + 0.914613i \(0.367505\pi\)
\(192\) −7.10794 + 3.24609i −0.512972 + 0.234266i
\(193\) −3.65352 + 3.16580i −0.262986 + 0.227879i −0.776366 0.630283i \(-0.782939\pi\)
0.513379 + 0.858162i \(0.328393\pi\)
\(194\) 0.410917 + 0.264080i 0.0295021 + 0.0189598i
\(195\) 0 0
\(196\) −1.30684 + 9.08924i −0.0933454 + 0.649232i
\(197\) 0.141980 0.220925i 0.0101157 0.0157403i −0.836159 0.548487i \(-0.815204\pi\)
0.846275 + 0.532747i \(0.178840\pi\)
\(198\) −0.271085 + 0.234896i −0.0192652 + 0.0166934i
\(199\) 1.79719 + 3.93530i 0.127399 + 0.278966i 0.962574 0.271019i \(-0.0873607\pi\)
−0.835175 + 0.549985i \(0.814633\pi\)
\(200\) 0 0
\(201\) −1.88514 0.553528i −0.132968 0.0390429i
\(202\) −0.299652 0.259650i −0.0210835 0.0182689i
\(203\) −1.95273 6.65037i −0.137054 0.466765i
\(204\) −3.60758 + 7.89950i −0.252581 + 0.553076i
\(205\) 0 0
\(206\) 0.858010 0.0597804
\(207\) 9.32777 + 2.23445i 0.648325 + 0.155305i
\(208\) 8.46252i 0.586770i
\(209\) −2.14964 14.9511i −0.148694 1.03419i
\(210\) 0 0
\(211\) 6.30147 1.85028i 0.433811 0.127378i −0.0575338 0.998344i \(-0.518324\pi\)
0.491345 + 0.870965i \(0.336506\pi\)
\(212\) −0.412951 0.357824i −0.0283616 0.0245755i
\(213\) −3.14169 + 10.6996i −0.215265 + 0.733125i
\(214\) 0.548554 0.352535i 0.0374984 0.0240988i
\(215\) 0 0
\(216\) 1.15235 + 1.32989i 0.0784077 + 0.0904874i
\(217\) −0.757286 + 1.17836i −0.0514079 + 0.0799923i
\(218\) 0.908542 + 0.130629i 0.0615342 + 0.00884728i
\(219\) 1.47587 10.2649i 0.0997301 0.693638i
\(220\) 0 0
\(221\) −6.11040 7.05178i −0.411030 0.474354i
\(222\) −0.889705 + 0.406315i −0.0597131 + 0.0272701i
\(223\) 4.97783 + 7.74566i 0.333340 + 0.518688i 0.966950 0.254965i \(-0.0820639\pi\)
−0.633610 + 0.773653i \(0.718428\pi\)
\(224\) −1.56130 0.458439i −0.104319 0.0306308i
\(225\) 0 0
\(226\) −1.65720 + 0.486598i −0.110235 + 0.0323680i
\(227\) −8.06985 3.68538i −0.535615 0.244607i 0.129196 0.991619i \(-0.458760\pi\)
−0.664810 + 0.747012i \(0.731488\pi\)
\(228\) −14.6408 + 2.10504i −0.969614 + 0.139409i
\(229\) 8.38484 0.554086 0.277043 0.960858i \(-0.410646\pi\)
0.277043 + 0.960858i \(0.410646\pi\)
\(230\) 0 0
\(231\) −3.14566 −0.206969
\(232\) −1.56157 + 0.224520i −0.102522 + 0.0147405i
\(233\) 21.8435 + 9.97561i 1.43102 + 0.653524i 0.972017 0.234911i \(-0.0754799\pi\)
0.459002 + 0.888435i \(0.348207\pi\)
\(234\) −0.362117 + 0.106327i −0.0236723 + 0.00695082i
\(235\) 0 0
\(236\) 15.3321 + 4.50191i 0.998034 + 0.293049i
\(237\) −1.74064 2.70849i −0.113067 0.175935i
\(238\) −0.540478 + 0.246828i −0.0350340 + 0.0159995i
\(239\) −7.35914 8.49290i −0.476023 0.549360i 0.466054 0.884756i \(-0.345675\pi\)
−0.942077 + 0.335396i \(0.891130\pi\)
\(240\) 0 0
\(241\) 4.00004 27.8209i 0.257665 1.79210i −0.291689 0.956513i \(-0.594217\pi\)
0.549355 0.835589i \(-0.314874\pi\)
\(242\) 0.598684 + 0.0860778i 0.0384849 + 0.00553329i
\(243\) −8.65025 + 13.4601i −0.554914 + 0.863463i
\(244\) 4.19948 + 4.84646i 0.268844 + 0.310263i
\(245\) 0 0
\(246\) 0.448178 0.288027i 0.0285748 0.0183639i
\(247\) 4.47747 15.2489i 0.284895 0.970262i
\(248\) 0.240952 + 0.208786i 0.0153004 + 0.0132579i
\(249\) 4.18403 1.22854i 0.265152 0.0778556i
\(250\) 0 0
\(251\) 3.91272 + 27.2135i 0.246969 + 1.71770i 0.615541 + 0.788105i \(0.288938\pi\)
−0.368572 + 0.929599i \(0.620153\pi\)
\(252\) 6.16077i 0.388092i
\(253\) 4.49583 + 8.65932i 0.282650 + 0.544407i
\(254\) 1.54672 0.0970501
\(255\) 0 0
\(256\) 6.38987 13.9919i 0.399367 0.874492i
\(257\) −5.00435 17.0432i −0.312163 1.06313i −0.954872 0.297018i \(-0.904008\pi\)
0.642709 0.766110i \(-0.277810\pi\)
\(258\) −0.359434 0.311451i −0.0223774 0.0193901i
\(259\) 16.4603 + 4.83317i 1.02279 + 0.300318i
\(260\) 0 0
\(261\) −3.72435 8.15519i −0.230531 0.504794i
\(262\) −0.869305 + 0.753257i −0.0537059 + 0.0465364i
\(263\) −4.72561 + 7.35320i −0.291394 + 0.453417i −0.955827 0.293930i \(-0.905037\pi\)
0.664433 + 0.747348i \(0.268673\pi\)
\(264\) −0.101897 + 0.708712i −0.00627135 + 0.0436182i
\(265\) 0 0
\(266\) −0.851362 0.547137i −0.0522004 0.0335471i
\(267\) −0.485490 + 0.420680i −0.0297115 + 0.0257452i
\(268\) 3.56047 1.62601i 0.217491 0.0993246i
\(269\) −2.46553 + 1.58450i −0.150326 + 0.0966086i −0.613642 0.789585i \(-0.710296\pi\)
0.463316 + 0.886193i \(0.346660\pi\)
\(270\) 0 0
\(271\) 4.29616 4.95803i 0.260973 0.301179i −0.610108 0.792318i \(-0.708874\pi\)
0.871081 + 0.491139i \(0.163419\pi\)
\(272\) −4.85519 16.5353i −0.294389 1.00260i
\(273\) −3.01063 1.37491i −0.182212 0.0832132i
\(274\) 0.270073 + 1.87840i 0.0163157 + 0.113478i
\(275\) 0 0
\(276\) 8.47963 4.40253i 0.510414 0.265001i
\(277\) 22.7888i 1.36924i −0.728898 0.684622i \(-0.759967\pi\)
0.728898 0.684622i \(-0.240033\pi\)
\(278\) 1.42859 0.205400i 0.0856809 0.0123191i
\(279\) −0.752658 + 1.64809i −0.0450604 + 0.0986686i
\(280\) 0 0
\(281\) 9.32744 10.7644i 0.556429 0.642153i −0.405940 0.913900i \(-0.633056\pi\)
0.962369 + 0.271747i \(0.0876013\pi\)
\(282\) 0.0677599 0.230769i 0.00403504 0.0137421i
\(283\) −12.8173 19.9441i −0.761910 1.18555i −0.977882 0.209155i \(-0.932929\pi\)
0.215973 0.976399i \(-0.430708\pi\)
\(284\) −9.22884 20.2083i −0.547631 1.19914i
\(285\) 0 0
\(286\) −0.322961 0.207554i −0.0190971 0.0122730i
\(287\) −9.24901 1.32981i −0.545952 0.0784960i
\(288\) −2.08337 0.299543i −0.122764 0.0176507i
\(289\) −1.68384 1.08214i −0.0990493 0.0636551i
\(290\) 0 0
\(291\) 2.30175 + 5.04012i 0.134931 + 0.295457i
\(292\) 11.1698 + 17.3806i 0.653664 + 1.01712i
\(293\) 1.20419 4.10110i 0.0703497 0.239589i −0.916810 0.399323i \(-0.869245\pi\)
0.987160 + 0.159734i \(0.0510635\pi\)
\(294\) 0.266092 0.307087i 0.0155188 0.0179097i
\(295\) 0 0
\(296\) 1.62210 3.55191i 0.0942827 0.206450i
\(297\) −10.0687 + 1.44766i −0.584245 + 0.0840017i
\(298\) 1.70330i 0.0986692i
\(299\) 0.518014 + 10.2526i 0.0299575 + 0.592926i
\(300\) 0 0
\(301\) 1.18715 + 8.25681i 0.0684262 + 0.475915i
\(302\) 1.60489 + 0.732929i 0.0923511 + 0.0421753i
\(303\) −1.26714 4.31549i −0.0727954 0.247918i
\(304\) 19.2218 22.1831i 1.10244 1.27229i
\(305\) 0 0
\(306\) −0.646552 + 0.415514i −0.0369609 + 0.0237533i
\(307\) 8.13661 3.71586i 0.464381 0.212076i −0.169463 0.985536i \(-0.554203\pi\)
0.633844 + 0.773461i \(0.281476\pi\)
\(308\) 4.73619 4.10393i 0.269869 0.233843i
\(309\) 8.18781 + 5.26199i 0.465788 + 0.299344i
\(310\) 0 0
\(311\) 3.32224 23.1067i 0.188387 1.31026i −0.647798 0.761812i \(-0.724310\pi\)
0.836185 0.548447i \(-0.184781\pi\)
\(312\) −0.407288 + 0.633752i −0.0230581 + 0.0358792i
\(313\) 17.0127 14.7416i 0.961615 0.833244i −0.0244337 0.999701i \(-0.507778\pi\)
0.986049 + 0.166457i \(0.0532328\pi\)
\(314\) −0.211465 0.463045i −0.0119337 0.0261311i
\(315\) 0 0
\(316\) 6.15434 + 1.80708i 0.346209 + 0.101656i
\(317\) −9.63606 8.34970i −0.541215 0.468966i 0.340834 0.940124i \(-0.389291\pi\)
−0.882049 + 0.471158i \(0.843836\pi\)
\(318\) 0.00681193 + 0.0231993i 0.000381994 + 0.00130095i
\(319\) 3.78849 8.29564i 0.212115 0.464467i
\(320\) 0 0
\(321\) 7.39676 0.412847
\(322\) 0.635719 + 0.152285i 0.0354272 + 0.00848651i
\(323\) 32.3642i 1.80079i
\(324\) −0.283524 1.97195i −0.0157513 0.109553i
\(325\) 0 0
\(326\) −0.744654 + 0.218650i −0.0412426 + 0.0121099i
\(327\) 7.86891 + 6.81845i 0.435151 + 0.377061i
\(328\) −0.599206 + 2.04071i −0.0330856 + 0.112679i
\(329\) −3.54876 + 2.28065i −0.195650 + 0.125736i
\(330\) 0 0
\(331\) 10.7382 + 12.3926i 0.590227 + 0.681158i 0.969771 0.244015i \(-0.0784647\pi\)
−0.379545 + 0.925173i \(0.623919\pi\)
\(332\) −4.69678 + 7.30834i −0.257769 + 0.401097i
\(333\) 21.9642 + 3.15798i 1.20363 + 0.173056i
\(334\) −0.244993 + 1.70396i −0.0134054 + 0.0932366i
\(335\) 0 0
\(336\) −4.00303 4.61974i −0.218383 0.252028i
\(337\) −24.9589 + 11.3983i −1.35960 + 0.620907i −0.955821 0.293951i \(-0.905030\pi\)
−0.403776 + 0.914858i \(0.632303\pi\)
\(338\) 0.401210 + 0.624294i 0.0218229 + 0.0339571i
\(339\) −18.7985 5.51975i −1.02100 0.299792i
\(340\) 0 0
\(341\) −1.76837 + 0.519240i −0.0957626 + 0.0281184i
\(342\) −1.19074 0.543793i −0.0643879 0.0294050i
\(343\) −17.7675 + 2.55459i −0.959357 + 0.137935i
\(344\) 1.89870 0.102371
\(345\) 0 0
\(346\) 1.90261 0.102285
\(347\) 5.97415 0.858953i 0.320709 0.0461110i 0.0199196 0.999802i \(-0.493659\pi\)
0.300789 + 0.953691i \(0.402750\pi\)
\(348\) −8.12350 3.70988i −0.435465 0.198870i
\(349\) 8.00915 2.35170i 0.428720 0.125883i −0.0602518 0.998183i \(-0.519190\pi\)
0.488972 + 0.872300i \(0.337372\pi\)
\(350\) 0 0
\(351\) −10.2692 3.01532i −0.548130 0.160946i
\(352\) −1.15753 1.80116i −0.0616968 0.0960021i
\(353\) −23.7892 + 10.8642i −1.26617 + 0.578242i −0.931380 0.364049i \(-0.881394\pi\)
−0.334794 + 0.942291i \(0.608667\pi\)
\(354\) −0.463042 0.534379i −0.0246104 0.0284019i
\(355\) 0 0
\(356\) 0.182134 1.26677i 0.00965310 0.0671388i
\(357\) −6.67141 0.959204i −0.353088 0.0507664i
\(358\) −0.731822 + 1.13874i −0.0386780 + 0.0601841i
\(359\) 3.70672 + 4.27779i 0.195633 + 0.225773i 0.845088 0.534628i \(-0.179548\pi\)
−0.649454 + 0.760401i \(0.725003\pi\)
\(360\) 0 0
\(361\) 30.3894 19.5301i 1.59944 1.02790i
\(362\) 0.0203401 0.0692719i 0.00106905 0.00364085i
\(363\) 5.18522 + 4.49302i 0.272154 + 0.235822i
\(364\) 6.32663 1.85767i 0.331605 0.0973682i
\(365\) 0 0
\(366\) −0.0403840 0.280877i −0.00211091 0.0146817i
\(367\) 12.3147i 0.642822i −0.946940 0.321411i \(-0.895843\pi\)
0.946940 0.321411i \(-0.104157\pi\)
\(368\) −6.99596 + 17.6221i −0.364690 + 0.918615i
\(369\) −12.0866 −0.629201
\(370\) 0 0
\(371\) 0.176169 0.385756i 0.00914624 0.0200275i
\(372\) 0.508465 + 1.73167i 0.0263627 + 0.0897831i
\(373\) 22.0119 + 19.0734i 1.13973 + 0.987585i 0.999997 0.00260397i \(-0.000828872\pi\)
0.139737 + 0.990189i \(0.455374\pi\)
\(374\) −0.750126 0.220257i −0.0387881 0.0113892i
\(375\) 0 0
\(376\) 0.398872 + 0.873407i 0.0205702 + 0.0450426i
\(377\) 7.25173 6.28366i 0.373483 0.323625i
\(378\) −0.368465 + 0.573343i −0.0189518 + 0.0294896i
\(379\) −4.74698 + 33.0160i −0.243836 + 1.69592i 0.388683 + 0.921372i \(0.372930\pi\)
−0.632519 + 0.774545i \(0.717979\pi\)
\(380\) 0 0
\(381\) 14.7601 + 9.48571i 0.756181 + 0.485968i
\(382\) −0.284209 + 0.246268i −0.0145414 + 0.0126002i
\(383\) 28.2775 12.9139i 1.44491 0.659870i 0.470044 0.882643i \(-0.344238\pi\)
0.974870 + 0.222773i \(0.0715108\pi\)
\(384\) −2.35017 + 1.51036i −0.119931 + 0.0770753i
\(385\) 0 0
\(386\) −0.279084 + 0.322080i −0.0142050 + 0.0163934i
\(387\) 3.03988 + 10.3529i 0.154526 + 0.526267i
\(388\) −10.0411 4.58560i −0.509758 0.232799i
\(389\) −1.80544 12.5571i −0.0915394 0.636670i −0.983005 0.183581i \(-0.941231\pi\)
0.891465 0.453089i \(-0.149678\pi\)
\(390\) 0 0
\(391\) 6.89440 + 19.7358i 0.348665 + 0.998085i
\(392\) 1.62218i 0.0819324i
\(393\) −12.9152 + 1.85692i −0.651484 + 0.0936692i
\(394\) 0.00961727 0.0210589i 0.000484511 0.00106093i
\(395\) 0 0
\(396\) 5.30841 6.12623i 0.266757 0.307855i
\(397\) 3.47123 11.8219i 0.174216 0.593325i −0.825371 0.564590i \(-0.809034\pi\)
0.999587 0.0287344i \(-0.00914770\pi\)
\(398\) 0.206192 + 0.320841i 0.0103355 + 0.0160823i
\(399\) −4.76890 10.4424i −0.238744 0.522776i
\(400\) 0 0
\(401\) −28.3895 18.2448i −1.41770 0.911102i −0.999997 0.00251937i \(-0.999198\pi\)
−0.417705 0.908583i \(-0.637166\pi\)
\(402\) −0.171440 0.0246493i −0.00855063 0.00122940i
\(403\) −1.91941 0.275970i −0.0956126 0.0137470i
\(404\) 7.53797 + 4.84436i 0.375028 + 0.241016i
\(405\) 0 0
\(406\) −0.253827 0.555804i −0.0125972 0.0275841i
\(407\) 12.2035 + 18.9890i 0.604904 + 0.941249i
\(408\) −0.432214 + 1.47199i −0.0213978 + 0.0728741i
\(409\) 10.6316 12.2695i 0.525698 0.606688i −0.429350 0.903138i \(-0.641257\pi\)
0.955048 + 0.296450i \(0.0958028\pi\)
\(410\) 0 0
\(411\) −8.94256 + 19.5815i −0.441104 + 0.965883i
\(412\) −19.1927 + 2.75950i −0.945558 + 0.135951i
\(413\) 12.4018i 0.610254i
\(414\) 0.841961 + 0.0779495i 0.0413801 + 0.00383101i
\(415\) 0 0
\(416\) −0.320594 2.22978i −0.0157184 0.109324i
\(417\) 14.8924 + 6.80112i 0.729282 + 0.333052i
\(418\) −0.375150 1.27764i −0.0183492 0.0624916i
\(419\) −8.76692 + 10.1176i −0.428292 + 0.494275i −0.928345 0.371719i \(-0.878768\pi\)
0.500053 + 0.865995i \(0.333314\pi\)
\(420\) 0 0
\(421\) −10.9478 + 7.03572i −0.533563 + 0.342900i −0.779517 0.626382i \(-0.784535\pi\)
0.245954 + 0.969282i \(0.420899\pi\)
\(422\) 0.526644 0.240510i 0.0256366 0.0117079i
\(423\) −4.12375 + 3.57325i −0.200504 + 0.173737i
\(424\) −0.0812036 0.0521864i −0.00394360 0.00253439i
\(425\) 0 0
\(426\) −0.139903 + 0.973048i −0.00677833 + 0.0471443i
\(427\) −2.69081 + 4.18698i −0.130217 + 0.202622i
\(428\) −11.1367 + 9.65005i −0.538315 + 0.466453i
\(429\) −1.80906 3.96130i −0.0873424 0.191253i
\(430\) 0 0
\(431\) −8.97982 2.63671i −0.432543 0.127006i 0.0582112 0.998304i \(-0.481460\pi\)
−0.490754 + 0.871298i \(0.663279\pi\)
\(432\) −14.9390 12.9447i −0.718754 0.622804i
\(433\) −9.56922 32.5898i −0.459867 1.56616i −0.784378 0.620283i \(-0.787018\pi\)
0.324511 0.945882i \(-0.394800\pi\)
\(434\) −0.0512961 + 0.112323i −0.00246229 + 0.00539167i
\(435\) 0 0
\(436\) −20.7432 −0.993419
\(437\) −21.9300 + 28.0522i −1.04905 + 1.34192i
\(438\) 0.914218i 0.0436830i
\(439\) 4.53831 + 31.5646i 0.216602 + 1.50650i 0.750456 + 0.660921i \(0.229834\pi\)
−0.533854 + 0.845577i \(0.679257\pi\)
\(440\) 0 0
\(441\) −8.84511 + 2.59716i −0.421196 + 0.123674i
\(442\) −0.621656 0.538668i −0.0295691 0.0256218i
\(443\) −8.62354 + 29.3691i −0.409717 + 1.39537i 0.453825 + 0.891091i \(0.350059\pi\)
−0.863542 + 0.504277i \(0.831759\pi\)
\(444\) 18.5950 11.9502i 0.882477 0.567134i
\(445\) 0 0
\(446\) 0.531535 + 0.613424i 0.0251689 + 0.0290465i
\(447\) 10.4459 16.2542i 0.494076 0.768797i
\(448\) 11.9592 + 1.71947i 0.565018 + 0.0812373i
\(449\) −2.39840 + 16.6812i −0.113187 + 0.787236i 0.851597 + 0.524196i \(0.175634\pi\)
−0.964785 + 0.263040i \(0.915275\pi\)
\(450\) 0 0
\(451\) −8.05133 9.29173i −0.379122 0.437530i
\(452\) 35.5048 16.2145i 1.67001 0.762666i
\(453\) 10.8202 + 16.8366i 0.508380 + 0.791054i
\(454\) −0.750400 0.220337i −0.0352180 0.0103409i
\(455\) 0 0
\(456\) −2.50714 + 0.736163i −0.117408 + 0.0344740i
\(457\) −2.47375 1.12972i −0.115717 0.0528463i 0.356715 0.934213i \(-0.383897\pi\)
−0.472432 + 0.881367i \(0.656624\pi\)
\(458\) 0.731650 0.105195i 0.0341877 0.00491546i
\(459\) −21.7954 −1.01732
\(460\) 0 0
\(461\) −35.7457 −1.66484 −0.832421 0.554143i \(-0.813046\pi\)
−0.832421 + 0.554143i \(0.813046\pi\)
\(462\) −0.274486 + 0.0394651i −0.0127702 + 0.00183608i
\(463\) 37.8860 + 17.3020i 1.76071 + 0.804091i 0.984899 + 0.173130i \(0.0553880\pi\)
0.775814 + 0.630961i \(0.217339\pi\)
\(464\) 17.0041 4.99286i 0.789397 0.231788i
\(465\) 0 0
\(466\) 2.03119 + 0.596411i 0.0940931 + 0.0276282i
\(467\) 9.55519 + 14.8682i 0.442161 + 0.688017i 0.988782 0.149364i \(-0.0477225\pi\)
−0.546621 + 0.837380i \(0.684086\pi\)
\(468\) 7.75819 3.54305i 0.358623 0.163777i
\(469\) 1.98938 + 2.29587i 0.0918610 + 0.106013i
\(470\) 0 0
\(471\) 0.821781 5.71561i 0.0378657 0.263361i
\(472\) 2.79411 + 0.401733i 0.128609 + 0.0184913i
\(473\) −5.93396 + 9.23343i −0.272844 + 0.424553i
\(474\) −0.185866 0.214501i −0.00853712 0.00985237i
\(475\) 0 0
\(476\) 11.2961 7.25953i 0.517754 0.332740i
\(477\) 0.154543 0.526324i 0.00707602 0.0240987i
\(478\) −0.748699 0.648752i −0.0342447 0.0296732i
\(479\) −11.4723 + 3.36858i −0.524184 + 0.153914i −0.533110 0.846046i \(-0.678977\pi\)
0.00892633 + 0.999960i \(0.497159\pi\)
\(480\) 0 0
\(481\) 3.37991 + 23.5078i 0.154111 + 1.07186i
\(482\) 2.47780i 0.112861i
\(483\) 5.13260 + 5.35195i 0.233541 + 0.243522i
\(484\) −13.6687 −0.621306
\(485\) 0 0
\(486\) −0.585941 + 1.28303i −0.0265788 + 0.0581995i
\(487\) 5.31536 + 18.1024i 0.240862 + 0.820300i 0.987843 + 0.155455i \(0.0496843\pi\)
−0.746981 + 0.664845i \(0.768497\pi\)
\(488\) 0.856156 + 0.741863i 0.0387563 + 0.0335826i
\(489\) −8.44701 2.48026i −0.381987 0.112161i
\(490\) 0 0
\(491\) 9.10363 + 19.9342i 0.410841 + 0.899616i 0.996055 + 0.0887373i \(0.0282832\pi\)
−0.585214 + 0.810879i \(0.698990\pi\)
\(492\) −9.09891 + 7.88425i −0.410211 + 0.355450i
\(493\) 10.5643 16.4384i 0.475794 0.740349i
\(494\) 0.199387 1.38677i 0.00897086 0.0623937i
\(495\) 0 0
\(496\) −3.01291 1.93628i −0.135284 0.0869416i
\(497\) 13.0308 11.2912i 0.584509 0.506480i
\(498\) 0.349679 0.159693i 0.0156695 0.00715602i
\(499\) −8.48768 + 5.45470i −0.379961 + 0.244186i −0.716655 0.697428i \(-0.754328\pi\)
0.336694 + 0.941614i \(0.390691\pi\)
\(500\) 0 0
\(501\) −12.7879 + 14.7581i −0.571323 + 0.659341i
\(502\) 0.682837 + 2.32553i 0.0304765 + 0.103793i
\(503\) −12.1941 5.56885i −0.543707 0.248303i 0.124576 0.992210i \(-0.460243\pi\)
−0.668283 + 0.743907i \(0.732970\pi\)
\(504\) −0.154886 1.07726i −0.00689918 0.0479849i
\(505\) 0 0
\(506\) 0.500939 + 0.699196i 0.0222694 + 0.0310831i
\(507\) 8.41804i 0.373858i
\(508\) −34.5985 + 4.97451i −1.53506 + 0.220708i
\(509\) −8.03460 + 17.5933i −0.356127 + 0.779810i 0.643766 + 0.765222i \(0.277371\pi\)
−0.999894 + 0.0145879i \(0.995356\pi\)
\(510\) 0 0
\(511\) −10.5006 + 12.1183i −0.464518 + 0.536082i
\(512\) 1.95615 6.66205i 0.0864506 0.294424i
\(513\) −20.0701 31.2297i −0.886116 1.37882i
\(514\) −0.650495 1.42439i −0.0286921 0.0628270i
\(515\) 0 0
\(516\) 9.04182 + 5.81083i 0.398044 + 0.255807i
\(517\) −5.49398 0.789915i −0.241625 0.0347404i
\(518\) 1.49694 + 0.215227i 0.0657716 + 0.00945652i
\(519\) 18.1562 + 11.6683i 0.796970 + 0.512182i
\(520\) 0 0
\(521\) −4.67119 10.2285i −0.204648 0.448117i 0.779281 0.626674i \(-0.215584\pi\)
−0.983930 + 0.178557i \(0.942857\pi\)
\(522\) −0.427296 0.664885i −0.0187022 0.0291012i
\(523\) 5.09404 17.3487i 0.222747 0.758605i −0.769964 0.638087i \(-0.779726\pi\)
0.992711 0.120519i \(-0.0384558\pi\)
\(524\) 17.0228 19.6454i 0.743645 0.858212i
\(525\) 0 0
\(526\) −0.320098 + 0.700917i −0.0139569 + 0.0305614i
\(527\) −3.90874 + 0.561992i −0.170267 + 0.0244808i
\(528\) 8.04304i 0.350028i
\(529\) 7.39715 21.7780i 0.321615 0.946870i
\(530\) 0 0
\(531\) 2.28297 + 15.8784i 0.0990725 + 0.689064i
\(532\) 20.8037 + 9.50074i 0.901955 + 0.411909i
\(533\) −3.64448 12.4119i −0.157860 0.537621i
\(534\) −0.0370854 + 0.0427988i −0.00160484 + 0.00185209i
\(535\) 0 0
\(536\) 0.581697 0.373834i 0.0251255 0.0161472i
\(537\) −13.9672 + 6.37863i −0.602731 + 0.275258i
\(538\) −0.195260 + 0.169194i −0.00841825 + 0.00729445i
\(539\) −7.88869 5.06975i −0.339790 0.218370i
\(540\) 0 0
\(541\) 1.97456 13.7333i 0.0848928 0.590442i −0.902324 0.431059i \(-0.858140\pi\)
0.987217 0.159384i \(-0.0509507\pi\)
\(542\) 0.312674 0.486530i 0.0134305 0.0208983i
\(543\) 0.618931 0.536306i 0.0265609 0.0230151i
\(544\) −1.90571 4.17292i −0.0817065 0.178912i
\(545\) 0 0
\(546\) −0.279953 0.0822015i −0.0119809 0.00351790i
\(547\) 22.7793 + 19.7384i 0.973973 + 0.843952i 0.987764 0.155953i \(-0.0498448\pi\)
−0.0137919 + 0.999905i \(0.504390\pi\)
\(548\) −12.0825 41.1491i −0.516138 1.75780i
\(549\) −2.67436 + 5.85603i −0.114139 + 0.249929i
\(550\) 0 0
\(551\) 33.2819 1.41786
\(552\) 1.37204 0.983001i 0.0583981 0.0418393i
\(553\) 4.97813i 0.211692i
\(554\) −0.285906 1.98852i −0.0121470 0.0844840i
\(555\) 0 0
\(556\) −31.2953 + 9.18913i −1.32722 + 0.389706i
\(557\) −16.3440 14.1622i −0.692519 0.600071i 0.235824 0.971796i \(-0.424221\pi\)
−0.928343 + 0.371724i \(0.878767\pi\)
\(558\) −0.0449991 + 0.153253i −0.00190496 + 0.00648771i
\(559\) −9.71499 + 6.24345i −0.410900 + 0.264070i
\(560\) 0 0
\(561\) −5.80751 6.70222i −0.245193 0.282968i
\(562\) 0.678850 1.05631i 0.0286356 0.0445578i
\(563\) 0.283349 + 0.0407395i 0.0119418 + 0.00171696i 0.148283 0.988945i \(-0.452625\pi\)
−0.136341 + 0.990662i \(0.543534\pi\)
\(564\) −0.773524 + 5.37998i −0.0325712 + 0.226538i
\(565\) 0 0
\(566\) −1.36864 1.57949i −0.0575281 0.0663910i
\(567\) 1.40647 0.642315i 0.0590663 0.0269747i
\(568\) −2.12179 3.30156i −0.0890282 0.138531i
\(569\) −1.66147 0.487852i −0.0696525 0.0204518i 0.246721 0.969087i \(-0.420647\pi\)
−0.316373 + 0.948635i \(0.602465\pi\)
\(570\) 0 0
\(571\) −19.8922 + 5.84086i −0.832461 + 0.244433i −0.670074 0.742295i \(-0.733738\pi\)
−0.162387 + 0.986727i \(0.551919\pi\)
\(572\) 7.89181 + 3.60407i 0.329973 + 0.150694i
\(573\) −4.22245 + 0.607097i −0.176395 + 0.0253618i
\(574\) −0.823739 −0.0343822
\(575\) 0 0
\(576\) 15.6282 0.651174
\(577\) 23.8763 3.43290i 0.993985 0.142913i 0.373917 0.927462i \(-0.378014\pi\)
0.620067 + 0.784549i \(0.287105\pi\)
\(578\) −0.160506 0.0733005i −0.00667616 0.00304890i
\(579\) −4.63848 + 1.36198i −0.192769 + 0.0566020i
\(580\) 0 0
\(581\) −6.46934 1.89957i −0.268394 0.0788074i
\(582\) 0.264080 + 0.410917i 0.0109465 + 0.0170330i
\(583\) 0.507567 0.231798i 0.0210213 0.00960009i
\(584\) 2.39009 + 2.75831i 0.0989026 + 0.114140i
\(585\) 0 0
\(586\) 0.0536241 0.372964i 0.00221519 0.0154070i
\(587\) 33.2423 + 4.77952i 1.37206 + 0.197272i 0.788617 0.614885i \(-0.210798\pi\)
0.583439 + 0.812157i \(0.301707\pi\)
\(588\) −4.96455 + 7.72499i −0.204734 + 0.318573i
\(589\) −4.40458 5.08316i −0.181488 0.209448i
\(590\) 0 0
\(591\) 0.220925 0.141980i 0.00908764 0.00584027i
\(592\) −12.3578 + 42.0867i −0.507901 + 1.72975i
\(593\) 22.5585 + 19.5470i 0.926365 + 0.802700i 0.980639 0.195827i \(-0.0627389\pi\)
−0.0542739 + 0.998526i \(0.517284\pi\)
\(594\) −0.860418 + 0.252641i −0.0353034 + 0.0103660i
\(595\) 0 0
\(596\) 5.47807 + 38.1008i 0.224391 + 1.56067i
\(597\) 4.32625i 0.177062i
\(598\) 0.173830 + 0.888133i 0.00710843 + 0.0363185i
\(599\) −4.70186 −0.192113 −0.0960564 0.995376i \(-0.530623\pi\)
−0.0960564 + 0.995376i \(0.530623\pi\)
\(600\) 0 0
\(601\) 8.89729 19.4823i 0.362928 0.794701i −0.636792 0.771036i \(-0.719739\pi\)
0.999720 0.0236658i \(-0.00753375\pi\)
\(602\) 0.207178 + 0.705584i 0.00844395 + 0.0287575i
\(603\) 2.96969 + 2.57325i 0.120935 + 0.104791i
\(604\) −38.2569 11.2332i −1.55665 0.457073i
\(605\) 0 0
\(606\) −0.164711 0.360666i −0.00669091 0.0146511i
\(607\) −29.1696 + 25.2756i −1.18396 + 1.02591i −0.184891 + 0.982759i \(0.559193\pi\)
−0.999069 + 0.0431477i \(0.986261\pi\)
\(608\) 4.22433 6.57319i 0.171319 0.266578i
\(609\) 0.986403 6.86058i 0.0399711 0.278005i
\(610\) 0 0
\(611\) −4.91289 3.15732i −0.198754 0.127732i
\(612\) 13.1263 11.3740i 0.530599 0.459766i
\(613\) 17.1155 7.81638i 0.691288 0.315700i −0.0386125 0.999254i \(-0.512294\pi\)
0.729900 + 0.683554i \(0.239567\pi\)
\(614\) 0.663370 0.426322i 0.0267714 0.0172050i
\(615\) 0 0
\(616\) 0.724983 0.836675i 0.0292104 0.0337106i
\(617\) −4.46602 15.2099i −0.179795 0.612326i −0.999233 0.0391580i \(-0.987532\pi\)
0.819438 0.573168i \(-0.194286\pi\)
\(618\) 0.780473 + 0.356430i 0.0313952 + 0.0143377i
\(619\) −4.22984 29.4192i −0.170012 1.18246i −0.878854 0.477091i \(-0.841691\pi\)
0.708842 0.705367i \(-0.249218\pi\)
\(620\) 0 0
\(621\) 18.8915 + 14.7685i 0.758091 + 0.592641i
\(622\) 2.05794i 0.0825158i
\(623\) 0.983162 0.141357i 0.0393896 0.00566336i
\(624\) 3.51546 7.69778i 0.140731 0.308158i
\(625\) 0 0
\(626\) 1.29956 1.49977i 0.0519408 0.0599429i
\(627\) 4.25553 14.4930i 0.169949 0.578794i
\(628\) 6.21947 + 9.67769i 0.248184 + 0.386182i
\(629\) 20.0912 + 43.9936i 0.801089 + 1.75414i
\(630\) 0 0
\(631\) −14.0318 9.01768i −0.558597 0.358988i 0.230677 0.973030i \(-0.425906\pi\)
−0.789273 + 0.614042i \(0.789542\pi\)
\(632\) 1.12156 + 0.161257i 0.0446134 + 0.00641444i
\(633\) 6.50065 + 0.934652i 0.258378 + 0.0371491i
\(634\) −0.945584 0.607690i −0.0375539 0.0241345i
\(635\) 0 0
\(636\) −0.226988 0.497034i −0.00900066 0.0197087i
\(637\) −5.33416 8.30012i −0.211347 0.328863i
\(638\) 0.226502 0.771397i 0.00896732 0.0305399i
\(639\) 14.6051 16.8552i 0.577769 0.666781i
\(640\) 0 0
\(641\) −12.5542 + 27.4898i −0.495859 + 1.08578i 0.481934 + 0.876208i \(0.339935\pi\)
−0.977793 + 0.209573i \(0.932793\pi\)
\(642\) 0.645431 0.0927990i 0.0254731 0.00366248i
\(643\) 7.45857i 0.294137i 0.989126 + 0.147069i \(0.0469838\pi\)
−0.989126 + 0.147069i \(0.953016\pi\)
\(644\) −14.7101 1.36187i −0.579659 0.0536653i
\(645\) 0 0
\(646\) −0.406038 2.82406i −0.0159754 0.111111i
\(647\) 6.94356 + 3.17102i 0.272980 + 0.124666i 0.547202 0.837001i \(-0.315693\pi\)
−0.274222 + 0.961666i \(0.588420\pi\)
\(648\) −0.0991526 0.337683i −0.00389508 0.0132654i
\(649\) −10.6860 + 12.3323i −0.419462 + 0.484085i
\(650\) 0 0
\(651\) −1.17836 + 0.757286i −0.0461836 + 0.0296804i
\(652\) 15.9539 7.28589i 0.624802 0.285337i
\(653\) −29.3782 + 25.4564i −1.14966 + 0.996185i −0.149686 + 0.988734i \(0.547826\pi\)
−0.999972 + 0.00745135i \(0.997628\pi\)
\(654\) 0.772173 + 0.496246i 0.0301944 + 0.0194047i
\(655\) 0 0
\(656\) 3.40014 23.6485i 0.132753 0.923319i
\(657\) −11.2134 + 17.4484i −0.437476 + 0.680726i
\(658\) −0.281047 + 0.243529i −0.0109564 + 0.00949374i
\(659\) 5.38310 + 11.7873i 0.209696 + 0.459170i 0.985030 0.172381i \(-0.0551460\pi\)
−0.775335 + 0.631551i \(0.782419\pi\)
\(660\) 0 0
\(661\) 28.9778 + 8.50866i 1.12711 + 0.330949i 0.791570 0.611078i \(-0.209264\pi\)
0.335537 + 0.942027i \(0.391082\pi\)
\(662\) 1.09248 + 0.946639i 0.0424604 + 0.0367922i
\(663\) −2.62880 8.95287i −0.102094 0.347701i
\(664\) −0.637531 + 1.39600i −0.0247410 + 0.0541753i
\(665\) 0 0
\(666\) 1.95619 0.0758007
\(667\) −20.2955 + 7.08990i −0.785844 + 0.274522i
\(668\) 38.9037i 1.50523i
\(669\) 1.31033 + 9.11356i 0.0506604 + 0.352351i
\(670\) 0 0
\(671\) −6.28342 + 1.84498i −0.242569 + 0.0712246i
\(672\) −1.22977 1.06560i −0.0474393 0.0411064i
\(673\) 0.667173 2.27218i 0.0257176 0.0875862i −0.945634 0.325232i \(-0.894558\pi\)
0.971352 + 0.237646i \(0.0763758\pi\)
\(674\) −2.03488 + 1.30773i −0.0783805 + 0.0503721i
\(675\) 0 0
\(676\) −10.9824 12.6744i −0.422402 0.487478i
\(677\) 18.7600 29.1912i 0.721006 1.12191i −0.266425 0.963856i \(-0.585842\pi\)
0.987431 0.158052i \(-0.0505213\pi\)
\(678\) −1.70958 0.245801i −0.0656562 0.00943993i
\(679\) 1.21925 8.48004i 0.0467904 0.325434i
\(680\) 0 0
\(681\) −5.80963 6.70467i −0.222626 0.256924i
\(682\) −0.147791 + 0.0674940i −0.00565922 + 0.00258448i
\(683\) 12.5776 + 19.5711i 0.481269 + 0.748869i 0.993965 0.109702i \(-0.0349895\pi\)
−0.512696 + 0.858570i \(0.671353\pi\)
\(684\) 28.3845 + 8.33444i 1.08531 + 0.318675i
\(685\) 0 0
\(686\) −1.51832 + 0.445819i −0.0579698 + 0.0170215i
\(687\) 7.62712 + 3.48319i 0.290993 + 0.132892i
\(688\) −21.1116 + 3.03539i −0.804872 + 0.115723i
\(689\) 0.587093 0.0223665
\(690\) 0 0
\(691\) −45.0096 −1.71225 −0.856123 0.516772i \(-0.827133\pi\)
−0.856123 + 0.516772i \(0.827133\pi\)
\(692\) −42.5593 + 6.11911i −1.61786 + 0.232614i
\(693\) 5.72279 + 2.61351i 0.217391 + 0.0992790i
\(694\) 0.510520 0.149902i 0.0193791 0.00569020i
\(695\) 0 0
\(696\) −1.51372 0.444470i −0.0573776 0.0168476i
\(697\) −14.2422 22.1612i −0.539461 0.839417i
\(698\) 0.669363 0.305688i 0.0253358 0.0115705i
\(699\) 15.7256 + 18.1483i 0.594796 + 0.686431i
\(700\) 0 0
\(701\) −3.34738 + 23.2815i −0.126429 + 0.879332i 0.823600 + 0.567171i \(0.191962\pi\)
−0.950029 + 0.312161i \(0.898947\pi\)
\(702\) −0.933908 0.134276i −0.0352481 0.00506791i
\(703\) −44.5357 + 69.2989i −1.67969 + 2.61366i
\(704\) 10.4105 + 12.0144i 0.392362 + 0.452810i
\(705\) 0 0
\(706\) −1.93952 + 1.24645i −0.0729946 + 0.0469108i
\(707\) −1.95925 + 6.67261i −0.0736854 + 0.250949i
\(708\) 12.0764 + 10.4643i 0.453859 + 0.393271i
\(709\) −32.8793 + 9.65422i −1.23481 + 0.362572i −0.833062 0.553180i \(-0.813414\pi\)
−0.401745 + 0.915752i \(0.631596\pi\)
\(710\) 0 0
\(711\) 0.916390 + 6.37363i 0.0343673 + 0.239030i
\(712\) 0.226084i 0.00847285i
\(713\) 3.76877 + 2.16144i 0.141142 + 0.0809467i
\(714\) −0.594172 −0.0222363
\(715\) 0 0
\(716\) 12.7077 27.8260i 0.474909 1.03990i
\(717\) −3.16603 10.7825i −0.118238 0.402680i
\(718\) 0.377112 + 0.326770i 0.0140737 + 0.0121949i
\(719\) 22.3827 + 6.57217i 0.834735 + 0.245100i 0.671050 0.741412i \(-0.265844\pi\)
0.163685 + 0.986513i \(0.447662\pi\)
\(720\) 0 0
\(721\) −6.25157 13.6890i −0.232821 0.509806i
\(722\) 2.40672 2.08543i 0.0895687 0.0776117i
\(723\) 15.1958 23.6451i 0.565138 0.879371i
\(724\) −0.232195 + 1.61495i −0.00862947 + 0.0600193i
\(725\) 0 0
\(726\) 0.508824 + 0.327001i 0.0188842 + 0.0121362i
\(727\) 30.4481 26.3834i 1.12926 0.978507i 0.129343 0.991600i \(-0.458713\pi\)
0.999914 + 0.0130932i \(0.00416783\pi\)
\(728\) 1.05956 0.483883i 0.0392698 0.0179339i
\(729\) −10.9363 + 7.02833i −0.405048 + 0.260309i
\(730\) 0 0
\(731\) −15.4005 + 17.7731i −0.569607 + 0.657361i
\(732\) 1.80669 + 6.15303i 0.0667773 + 0.227422i
\(733\) 20.6659 + 9.43781i 0.763313 + 0.348594i 0.758738 0.651396i \(-0.225816\pi\)
0.00457542 + 0.999990i \(0.498544\pi\)
\(734\) −0.154499 1.07456i −0.00570266 0.0396629i
\(735\) 0 0
\(736\) −1.17576 + 4.90825i −0.0433391 + 0.180921i
\(737\) 3.99714i 0.147236i
\(738\) −1.05466 + 0.151637i −0.0388224 + 0.00558182i
\(739\) 7.47356 16.3648i 0.274919 0.601989i −0.720930 0.693008i \(-0.756285\pi\)
0.995849 + 0.0910188i \(0.0290123\pi\)
\(740\) 0 0
\(741\) 10.4075 12.0109i 0.382328 0.441230i
\(742\) 0.0105326 0.0358708i 0.000386664 0.00131686i
\(743\) 3.14797 + 4.89833i 0.115488 + 0.179702i 0.894185 0.447697i \(-0.147756\pi\)
−0.778698 + 0.627399i \(0.784119\pi\)
\(744\) 0.132445 + 0.290013i 0.00485566 + 0.0106324i
\(745\) 0 0
\(746\) 2.16002 + 1.38816i 0.0790840 + 0.0508242i
\(747\) −8.63256 1.24117i −0.315849 0.0454122i
\(748\) 17.4879 + 2.51438i 0.639420 + 0.0919347i
\(749\) −9.62131 6.18324i −0.351555 0.225931i
\(750\) 0 0
\(751\) 3.84740 + 8.42462i 0.140393 + 0.307419i 0.966748 0.255732i \(-0.0823164\pi\)
−0.826354 + 0.563151i \(0.809589\pi\)
\(752\) −5.83133 9.07372i −0.212647 0.330885i
\(753\) −7.74578 + 26.3797i −0.282272 + 0.961330i
\(754\) 0.553942 0.639283i 0.0201734 0.0232813i
\(755\) 0 0
\(756\) 6.39819 14.0101i 0.232700 0.509542i
\(757\) −8.04064 + 1.15607i −0.292242 + 0.0420180i −0.286877 0.957968i \(-0.592617\pi\)
−0.00536536 + 0.999986i \(0.501708\pi\)
\(758\) 2.94048i 0.106803i
\(759\) 0.492336 + 9.74443i 0.0178707 + 0.353700i
\(760\) 0 0
\(761\) −4.15984 28.9323i −0.150794 1.04880i −0.914893 0.403697i \(-0.867725\pi\)
0.764099 0.645099i \(-0.223184\pi\)
\(762\) 1.40695 + 0.642532i 0.0509684 + 0.0232765i
\(763\) −4.53565 15.4470i −0.164201 0.559219i
\(764\) 5.56539 6.42281i 0.201349 0.232369i
\(765\) 0 0
\(766\) 2.30544 1.48162i 0.0832990 0.0535330i
\(767\) −15.6175 + 7.13228i −0.563915 + 0.257532i
\(768\) 11.6249 10.0730i 0.419476 0.363478i
\(769\) −12.2803 7.89208i −0.442840 0.284596i 0.300158 0.953889i \(-0.402960\pi\)
−0.742998 + 0.669294i \(0.766597\pi\)
\(770\) 0 0
\(771\) 2.52790 17.5820i 0.0910403 0.633199i
\(772\) 5.20693 8.10215i 0.187402 0.291603i
\(773\) 13.0471 11.3054i 0.469271 0.406625i −0.387865 0.921716i \(-0.626787\pi\)
0.857136 + 0.515091i \(0.172242\pi\)
\(774\) 0.395142 + 0.865241i 0.0142031 + 0.0311004i
\(775\) 0 0
\(776\) −1.87104 0.549388i −0.0671666 0.0197219i
\(777\) 12.9650 + 11.2342i 0.465117 + 0.403026i
\(778\) −0.315080 1.07306i −0.0112962 0.0384712i
\(779\) 18.6391 40.8139i 0.667815 1.46231i
\(780\) 0 0
\(781\) 22.6867 0.811795
\(782\) 0.849200 + 1.63563i 0.0303673 + 0.0584899i
\(783\) 22.4134i 0.800991i
\(784\) −2.59332 18.0369i −0.0926186 0.644176i
\(785\) 0 0
\(786\) −1.10366 + 0.324065i −0.0393663 + 0.0115590i
\(787\) −11.5950 10.0471i −0.413318 0.358142i 0.423243 0.906016i \(-0.360892\pi\)
−0.836561 + 0.547875i \(0.815437\pi\)
\(788\) −0.147399 + 0.501995i −0.00525087 + 0.0178828i
\(789\) −7.35320 + 4.72561i −0.261781 + 0.168236i
\(790\) 0 0
\(791\) 19.8380 + 22.8942i 0.705356 + 0.814025i
\(792\) 0.774198 1.20467i 0.0275099 0.0428063i
\(793\) −6.82010 0.980582i −0.242189 0.0348215i
\(794\) 0.154578 1.07511i 0.00548577 0.0381544i
\(795\) 0 0
\(796\) −5.64417 6.51371i −0.200052 0.230872i
\(797\) −22.8517 + 10.4360i −0.809448 + 0.369663i −0.776755 0.629803i \(-0.783136\pi\)
−0.0326932 + 0.999465i \(0.510408\pi\)
\(798\) −0.547137 0.851362i −0.0193685 0.0301379i
\(799\) −11.4109 3.35055i −0.403690 0.118534i
\(800\) 0 0
\(801\) 1.23275 0.361967i 0.0435570 0.0127895i
\(802\) −2.70612 1.23584i −0.0955565 0.0436392i
\(803\) −20.8834 + 3.00258i −0.736959 + 0.105959i
\(804\) 3.91419 0.138043
\(805\) 0 0
\(806\) −0.170947 −0.00602136
\(807\) −2.90095 + 0.417094i −0.102118 + 0.0146824i
\(808\) 1.43986 + 0.657563i 0.0506542 + 0.0231330i
\(809\) 21.8919 6.42804i 0.769678 0.225998i 0.126761 0.991933i \(-0.459542\pi\)
0.642917 + 0.765935i \(0.277724\pi\)
\(810\) 0 0
\(811\) 41.7803 + 12.2678i 1.46711 + 0.430781i 0.915157 0.403097i \(-0.132066\pi\)
0.551949 + 0.833878i \(0.313884\pi\)
\(812\) 7.46538 + 11.6164i 0.261984 + 0.407654i
\(813\) 5.96757 2.72530i 0.209292 0.0955803i
\(814\) 1.30309 + 1.50385i 0.0456734 + 0.0527099i
\(815\) 0 0
\(816\) 2.45256 17.0579i 0.0858567 0.597147i
\(817\) −39.6476 5.70046i −1.38709 0.199434i
\(818\) 0.773766 1.20400i 0.0270541 0.0420970i
\(819\) 4.33481 + 5.00264i 0.151471 + 0.174806i
\(820\) 0 0
\(821\) 40.9122 26.2927i 1.42785 0.917621i 0.427942 0.903806i \(-0.359239\pi\)
0.999905 0.0138148i \(-0.00439753\pi\)
\(822\) −0.534648 + 1.82085i −0.0186480 + 0.0635093i
\(823\) 0.868528 + 0.752583i 0.0302750 + 0.0262334i 0.669867 0.742481i \(-0.266351\pi\)
−0.639592 + 0.768715i \(0.720897\pi\)
\(824\) −3.28662 + 0.965039i −0.114495 + 0.0336187i
\(825\) 0 0
\(826\) 0.155592 + 1.08217i 0.00541374 + 0.0376534i
\(827\) 15.3873i 0.535069i −0.963548 0.267534i \(-0.913791\pi\)
0.963548 0.267534i \(-0.0862089\pi\)
\(828\) −19.0844 + 0.964240i −0.663230 + 0.0335096i
\(829\) 43.7168 1.51835 0.759174 0.650888i \(-0.225603\pi\)
0.759174 + 0.650888i \(0.225603\pi\)
\(830\) 0 0
\(831\) 9.46680 20.7294i 0.328400 0.719095i
\(832\) 4.71239 + 16.0489i 0.163373 + 0.556396i
\(833\) −15.1846 13.1576i −0.526117 0.455883i
\(834\) 1.38481 + 0.406618i 0.0479522 + 0.0140800i
\(835\) 0 0
\(836\) 12.5008 + 27.3729i 0.432349 + 0.946712i
\(837\) −3.42321 + 2.96623i −0.118323 + 0.102528i
\(838\) −0.638055 + 0.992833i −0.0220413 + 0.0342969i
\(839\) −1.60650 + 11.1735i −0.0554627 + 0.385751i 0.943116 + 0.332462i \(0.107879\pi\)
−0.998579 + 0.0532888i \(0.983030\pi\)
\(840\) 0 0
\(841\) −7.49181 4.81469i −0.258338 0.166024i
\(842\) −0.867020 + 0.751277i −0.0298795 + 0.0258907i
\(843\) 12.9563 5.91692i 0.446237 0.203790i
\(844\) −11.0069 + 7.07372i −0.378874 + 0.243488i
\(845\) 0 0
\(846\) −0.315003 + 0.363533i −0.0108300 + 0.0124985i
\(847\) −2.98877 10.1788i −0.102695 0.349748i
\(848\) 0.986328 + 0.450441i 0.0338707 + 0.0154682i
\(849\) −3.37394 23.4663i −0.115793 0.805361i
\(850\) 0 0
\(851\) 12.3956 51.7460i 0.424917 1.77383i
\(852\) 22.2160i 0.761106i
\(853\) −16.5522 + 2.37985i −0.566737 + 0.0814845i −0.419727 0.907651i \(-0.637874\pi\)
−0.147010 + 0.989135i \(0.546965\pi\)
\(854\) −0.182267 + 0.399108i −0.00623704 + 0.0136572i
\(855\) 0 0
\(856\) −1.70474 + 1.96737i −0.0582667 + 0.0672433i
\(857\) 1.74302 5.93618i 0.0595405 0.202776i −0.924351 0.381543i \(-0.875393\pi\)
0.983891 + 0.178767i \(0.0572109\pi\)
\(858\) −0.207554 0.322961i −0.00708579 0.0110257i
\(859\) 3.60612 + 7.89631i 0.123039 + 0.269419i 0.961122 0.276125i \(-0.0890504\pi\)
−0.838082 + 0.545544i \(0.816323\pi\)
\(860\) 0 0
\(861\) −7.86077 5.05181i −0.267894 0.172165i
\(862\) −0.816646 0.117416i −0.0278151 0.00399921i
\(863\) 11.1982 + 1.61006i 0.381192 + 0.0548072i 0.330248 0.943894i \(-0.392868\pi\)
0.0509446 + 0.998701i \(0.483777\pi\)
\(864\) −4.42666 2.84484i −0.150598 0.0967834i
\(865\) 0 0
\(866\) −1.24386 2.72368i −0.0422682 0.0925546i
\(867\) −1.08214 1.68384i −0.0367513 0.0571861i
\(868\) 0.786189 2.67752i 0.0266850 0.0908808i
\(869\) −4.28939 + 4.95022i −0.145508 + 0.167925i
\(870\) 0 0
\(871\) −1.74707 + 3.82555i −0.0591973 + 0.129624i
\(872\) −3.62711 + 0.521499i −0.122829 + 0.0176602i
\(873\) 11.0817i 0.375058i
\(874\) −1.56164 + 2.72293i −0.0528232 + 0.0921045i
\(875\) 0 0
\(876\) 2.94027 + 20.4500i 0.0993426 + 0.690943i
\(877\) 22.5349 + 10.2913i 0.760950 + 0.347514i 0.757805 0.652481i \(-0.226272\pi\)
0.00314460 + 0.999995i \(0.498999\pi\)
\(878\) 0.792013 + 2.69735i 0.0267291 + 0.0910311i
\(879\) 2.79903 3.23025i 0.0944090 0.108954i
\(880\) 0 0
\(881\) 28.0492 18.0261i 0.945000 0.607315i 0.0251917 0.999683i \(-0.491980\pi\)
0.919808 + 0.392368i \(0.128344\pi\)
\(882\) −0.739229 + 0.337594i −0.0248911 + 0.0113674i
\(883\) 9.88198 8.56278i 0.332555 0.288161i −0.472537 0.881311i \(-0.656662\pi\)
0.805092 + 0.593150i \(0.202116\pi\)
\(884\) 15.6382 + 10.0501i 0.525969 + 0.338020i
\(885\) 0 0
\(886\) −0.384017 + 2.67090i −0.0129013 + 0.0897305i
\(887\) −11.9964 + 18.6668i −0.402800 + 0.626770i −0.982103 0.188343i \(-0.939688\pi\)
0.579303 + 0.815112i \(0.303325\pi\)
\(888\) 2.95103 2.55708i 0.0990301 0.0858101i
\(889\) −11.2696 24.6770i −0.377971 0.827641i
\(890\) 0 0
\(891\) 1.95204 + 0.573170i 0.0653957 + 0.0192019i
\(892\) −13.8627 12.0121i −0.464158 0.402195i
\(893\) −5.70679 19.4355i −0.190970 0.650385i
\(894\) 0.707574 1.54937i 0.0236648 0.0518187i
\(895\) 0 0
\(896\) 4.31954 0.144306
\(897\) −3.78790 + 9.54133i −0.126474 + 0.318576i
\(898\) 1.48567i 0.0495775i
\(899\) −0.577928 4.01958i −0.0192750 0.134060i
\(900\) 0 0
\(901\) 1.14714 0.336832i 0.0382169 0.0112215i
\(902\) −0.819121 0.709772i −0.0272737 0.0236328i
\(903\) −2.35013 + 8.00382i −0.0782076 + 0.266351i
\(904\) 5.80064 3.72784i 0.192926 0.123986i
\(905\) 0 0
\(906\) 1.15539 + 1.33339i 0.0383853 + 0.0442990i
\(907\) 11.5834 18.0240i 0.384619 0.598479i −0.593924 0.804521i \(-0.702422\pi\)
0.978543 + 0.206042i \(0.0660585\pi\)
\(908\) 17.4943 + 2.51530i 0.580568 + 0.0834730i
\(909\) −1.28017 + 8.90379i −0.0424606 + 0.295320i
\(910\) 0 0
\(911\) 25.5067 + 29.4363i 0.845076 + 0.975269i 0.999920 0.0126696i \(-0.00403297\pi\)
−0.154844 + 0.987939i \(0.549488\pi\)
\(912\) 26.6999 12.1935i 0.884123 0.403766i
\(913\) −4.79631 7.46321i −0.158735 0.246996i
\(914\) −0.230030 0.0675428i −0.00760870 0.00223412i
\(915\) 0 0
\(916\) −16.0279 + 4.70621i −0.529576 + 0.155497i
\(917\) 18.3516 + 8.38091i 0.606024 + 0.276762i
\(918\) −1.90184 + 0.273443i −0.0627700 + 0.00902496i
\(919\) −29.9408 −0.987657 −0.493829 0.869559i \(-0.664403\pi\)
−0.493829 + 0.869559i \(0.664403\pi\)
\(920\) 0 0
\(921\) 8.94494 0.294746
\(922\) −3.11912 + 0.448462i −0.102723 + 0.0147693i
\(923\) 21.7129 + 9.91594i 0.714688 + 0.326387i
\(924\) 6.01302 1.76558i 0.197814 0.0580834i
\(925\) 0 0
\(926\) 3.52295 + 1.03443i 0.115771 + 0.0339935i
\(927\) −10.5240 16.3756i −0.345653 0.537846i
\(928\) 4.29124 1.95974i 0.140867 0.0643318i
\(929\) −8.14358 9.39819i −0.267182 0.308345i 0.606266 0.795262i \(-0.292667\pi\)
−0.873448 + 0.486917i \(0.838121\pi\)
\(930\) 0 0
\(931\) 4.87026 33.8734i 0.159616 1.11016i
\(932\) −47.3537 6.80843i −1.55112 0.223017i
\(933\) 12.6209 19.6385i 0.413189 0.642934i
\(934\) 1.02031 + 1.17750i 0.0333855 + 0.0385289i
\(935\) 0 0
\(936\) 1.26750 0.814576i 0.0414297 0.0266252i
\(937\) 2.68807 9.15473i 0.0878155 0.299072i −0.903861 0.427826i \(-0.859280\pi\)
0.991677 + 0.128754i \(0.0410978\pi\)
\(938\) 0.202394 + 0.175376i 0.00660840 + 0.00572621i
\(939\) 21.5992 6.34209i 0.704863 0.206966i
\(940\) 0 0
\(941\) 0.484266 + 3.36814i 0.0157866 + 0.109798i 0.996191 0.0871966i \(-0.0277908\pi\)
−0.980405 + 0.196995i \(0.936882\pi\)
\(942\) 0.509046i 0.0165856i
\(943\) −2.67180 + 28.8591i −0.0870058 + 0.939782i
\(944\) −31.7099 −1.03207
\(945\) 0 0
\(946\) −0.401948 + 0.880143i −0.0130684 + 0.0286159i
\(947\) −3.50424 11.9343i −0.113872 0.387814i 0.882759 0.469826i \(-0.155683\pi\)
−0.996631 + 0.0820124i \(0.973865\pi\)
\(948\) 4.84750 + 4.20038i 0.157439 + 0.136422i
\(949\) −21.2993 6.25405i −0.691405 0.203015i
\(950\) 0 0
\(951\) −5.29668 11.5981i −0.171757 0.376095i
\(952\) 1.79269 1.55338i 0.0581015 0.0503452i
\(953\) 7.23572 11.2590i 0.234388 0.364715i −0.704057 0.710143i \(-0.748630\pi\)
0.938445 + 0.345429i \(0.112266\pi\)
\(954\) 0.00688198 0.0478652i 0.000222812 0.00154969i
\(955\) 0 0
\(956\) 18.8341 + 12.1039i 0.609137 + 0.391469i
\(957\) 6.89227 5.97219i 0.222795 0.193053i
\(958\) −0.958797 + 0.437868i −0.0309773 + 0.0141469i
\(959\) 28.0009 17.9951i 0.904197 0.581092i
\(960\) 0 0
\(961\) 19.7633 22.8080i 0.637524 0.735742i
\(962\) 0.589852 + 2.00885i 0.0190176 + 0.0647680i
\(963\) −13.4567 6.14545i −0.433635 0.198034i
\(964\) 7.96900 + 55.4256i 0.256664 + 1.78514i
\(965\) 0 0
\(966\) 0.515009 + 0.402610i 0.0165701 + 0.0129538i
\(967\) 24.7635i 0.796341i −0.917311 0.398170i \(-0.869645\pi\)
0.917311 0.398170i \(-0.130355\pi\)
\(968\) −2.39008 + 0.343642i −0.0768202 + 0.0110451i
\(969\) 13.4446 29.4395i 0.431902 0.945734i
\(970\) 0 0
\(971\) −11.6629 + 13.4597i −0.374281 + 0.431944i −0.911374 0.411580i \(-0.864977\pi\)
0.537092 + 0.843523i \(0.319523\pi\)
\(972\) 8.98041 30.5845i 0.288047 0.980997i
\(973\) −13.6859 21.2956i −0.438749 0.682707i
\(974\) 0.690922 + 1.51291i 0.0221386 + 0.0484767i
\(975\) 0 0
\(976\) −10.7056 6.88004i −0.342676 0.220225i
\(977\) −7.20015 1.03522i −0.230353 0.0331198i 0.0261716 0.999657i \(-0.491668\pi\)
−0.256525 + 0.966538i \(0.582577\pi\)
\(978\) −0.768191 0.110449i −0.0245640 0.00353178i
\(979\) 1.09945 + 0.706574i 0.0351386 + 0.0225822i
\(980\) 0 0
\(981\) −8.65065 18.9423i −0.276194 0.604780i
\(982\) 1.04446 + 1.62521i 0.0333301 + 0.0518627i
\(983\) 9.07613 30.9104i 0.289483 0.985890i −0.678442 0.734654i \(-0.737345\pi\)
0.967926 0.251236i \(-0.0808372\pi\)
\(984\) −1.39280 + 1.60738i −0.0444008 + 0.0512412i
\(985\) 0 0
\(986\) 0.715594 1.56693i 0.0227892 0.0499013i
\(987\) −4.17548 + 0.600344i −0.132907 + 0.0191092i
\(988\) 31.6618i 1.00729i
\(989\) 25.3916 4.96978i 0.807407 0.158030i
\(990\) 0 0
\(991\) −1.54572 10.7507i −0.0491013 0.341507i −0.999533 0.0305723i \(-0.990267\pi\)
0.950431 0.310935i \(-0.100642\pi\)
\(992\) −0.867221 0.396047i −0.0275343 0.0125745i
\(993\) 4.61978 + 15.7335i 0.146604 + 0.499288i
\(994\) 0.995387 1.14874i 0.0315718 0.0364358i
\(995\) 0 0
\(996\) −7.30834 + 4.69678i −0.231574 + 0.148823i
\(997\) 19.1851 8.76152i 0.607597 0.277480i −0.0877636 0.996141i \(-0.527972\pi\)
0.695360 + 0.718661i \(0.255245\pi\)
\(998\) −0.672189 + 0.582455i −0.0212778 + 0.0184373i
\(999\) 46.6687 + 29.9922i 1.47653 + 0.948910i
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 575.2.p.a.49.2 20
5.2 odd 4 575.2.k.a.26.1 10
5.3 odd 4 115.2.g.a.26.1 10
5.4 even 2 inner 575.2.p.a.49.1 20
23.8 even 11 inner 575.2.p.a.399.1 20
115.8 odd 44 115.2.g.a.31.1 yes 10
115.13 odd 44 2645.2.a.n.1.4 5
115.33 even 44 2645.2.a.o.1.4 5
115.54 even 22 inner 575.2.p.a.399.2 20
115.77 odd 44 575.2.k.a.376.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.2.g.a.26.1 10 5.3 odd 4
115.2.g.a.31.1 yes 10 115.8 odd 44
575.2.k.a.26.1 10 5.2 odd 4
575.2.k.a.376.1 10 115.77 odd 44
575.2.p.a.49.1 20 5.4 even 2 inner
575.2.p.a.49.2 20 1.1 even 1 trivial
575.2.p.a.399.1 20 23.8 even 11 inner
575.2.p.a.399.2 20 115.54 even 22 inner
2645.2.a.n.1.4 5 115.13 odd 44
2645.2.a.o.1.4 5 115.33 even 44