Properties

Label 273.2.t.d.4.4
Level $273$
Weight $2$
Character 273.4
Analytic conductor $2.180$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(4,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.t (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + 27166 x^{4} + 6435 x^{2} + 576 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.4
Root \(-0.915396i\) of defining polynomial
Character \(\chi\) \(=\) 273.4
Dual form 273.2.t.d.205.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.915396i q^{2} +(0.500000 + 0.866025i) q^{3} +1.16205 q^{4} +(-2.26729 + 1.30902i) q^{5} +(0.792756 - 0.457698i) q^{6} +(2.57477 - 0.608732i) q^{7} -2.89453i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q-0.915396i q^{2} +(0.500000 + 0.866025i) q^{3} +1.16205 q^{4} +(-2.26729 + 1.30902i) q^{5} +(0.792756 - 0.457698i) q^{6} +(2.57477 - 0.608732i) q^{7} -2.89453i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.19827 + 2.07547i) q^{10} +(2.20526 - 1.27321i) q^{11} +(0.581025 + 1.00636i) q^{12} +(0.523154 + 3.56740i) q^{13} +(-0.557231 - 2.35694i) q^{14} +(-2.26729 - 1.30902i) q^{15} -0.325542 q^{16} +6.19960 q^{17} +(0.792756 + 0.457698i) q^{18} +(2.36676 + 1.36645i) q^{19} +(-2.63470 + 1.52115i) q^{20} +(1.81456 + 1.92545i) q^{21} +(-1.16549 - 2.01868i) q^{22} -7.89025 q^{23} +(2.50674 - 1.44726i) q^{24} +(0.927071 - 1.60573i) q^{25} +(3.26558 - 0.478894i) q^{26} -1.00000 q^{27} +(2.99201 - 0.707377i) q^{28} +(-1.77706 + 3.07796i) q^{29} +(-1.19827 + 2.07547i) q^{30} +(-7.91220 - 4.56811i) q^{31} -5.49106i q^{32} +(2.20526 + 1.27321i) q^{33} -5.67509i q^{34} +(-5.04091 + 4.75060i) q^{35} +(-0.581025 + 1.00636i) q^{36} -8.68684i q^{37} +(1.25084 - 2.16652i) q^{38} +(-2.82788 + 2.23676i) q^{39} +(3.78900 + 6.56274i) q^{40} +(-3.98821 - 2.30259i) q^{41} +(1.76255 - 1.66104i) q^{42} +(-2.11228 - 3.65857i) q^{43} +(2.56262 - 1.47953i) q^{44} -2.61804i q^{45} +7.22271i q^{46} +(-1.53652 + 0.887113i) q^{47} +(-0.162771 - 0.281927i) q^{48} +(6.25889 - 3.13469i) q^{49} +(-1.46988 - 0.848638i) q^{50} +(3.09980 + 5.36901i) q^{51} +(0.607931 + 4.14549i) q^{52} +(-3.42283 + 5.92852i) q^{53} +0.915396i q^{54} +(-3.33331 + 5.77345i) q^{55} +(-1.76199 - 7.45275i) q^{56} +2.73290i q^{57} +(2.81755 + 1.62671i) q^{58} -2.25835i q^{59} +(-2.63470 - 1.52115i) q^{60} +(-6.18601 + 10.7145i) q^{61} +(-4.18163 + 7.24280i) q^{62} +(-0.760208 + 2.53418i) q^{63} -5.67758 q^{64} +(-5.85594 - 7.40350i) q^{65} +(1.16549 - 2.01868i) q^{66} +(0.536530 - 0.309766i) q^{67} +7.20424 q^{68} +(-3.94513 - 6.83316i) q^{69} +(4.34868 + 4.61443i) q^{70} +(6.48057 - 3.74156i) q^{71} +(2.50674 + 1.44726i) q^{72} +(-10.8250 - 6.24982i) q^{73} -7.95190 q^{74} +1.85414 q^{75} +(2.75029 + 1.58788i) q^{76} +(4.90299 - 4.62062i) q^{77} +(2.04752 + 2.58863i) q^{78} +(0.621752 + 1.07691i) q^{79} +(0.738098 - 0.426141i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.10779 + 3.65079i) q^{82} +2.10018i q^{83} +(2.10861 + 2.23747i) q^{84} +(-14.0563 + 8.11541i) q^{85} +(-3.34904 + 1.93357i) q^{86} -3.55412 q^{87} +(-3.68533 - 6.38318i) q^{88} +11.4071i q^{89} -2.39655 q^{90} +(3.51859 + 8.86677i) q^{91} -9.16886 q^{92} -9.13622i q^{93} +(0.812060 + 1.40653i) q^{94} -7.15484 q^{95} +(4.75540 - 2.74553i) q^{96} +(-1.32935 + 0.767503i) q^{97} +(-2.86948 - 5.72937i) q^{98} +2.54641i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.915396i 0.647283i −0.946180 0.323641i \(-0.895093\pi\)
0.946180 0.323641i \(-0.104907\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 1.16205 0.581025
\(5\) −2.26729 + 1.30902i −1.01396 + 0.585412i −0.912350 0.409412i \(-0.865734\pi\)
−0.101614 + 0.994824i \(0.532401\pi\)
\(6\) 0.792756 0.457698i 0.323641 0.186854i
\(7\) 2.57477 0.608732i 0.973172 0.230079i
\(8\) 2.89453i 1.02337i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.19827 + 2.07547i 0.378927 + 0.656321i
\(11\) 2.20526 1.27321i 0.664910 0.383886i −0.129235 0.991614i \(-0.541252\pi\)
0.794145 + 0.607728i \(0.207919\pi\)
\(12\) 0.581025 + 1.00636i 0.167727 + 0.290512i
\(13\) 0.523154 + 3.56740i 0.145097 + 0.989417i
\(14\) −0.557231 2.35694i −0.148926 0.629918i
\(15\) −2.26729 1.30902i −0.585412 0.337988i
\(16\) −0.325542 −0.0813854
\(17\) 6.19960 1.50362 0.751812 0.659377i \(-0.229180\pi\)
0.751812 + 0.659377i \(0.229180\pi\)
\(18\) 0.792756 + 0.457698i 0.186854 + 0.107880i
\(19\) 2.36676 + 1.36645i 0.542971 + 0.313485i 0.746282 0.665630i \(-0.231837\pi\)
−0.203311 + 0.979114i \(0.565170\pi\)
\(20\) −2.63470 + 1.52115i −0.589138 + 0.340139i
\(21\) 1.81456 + 1.92545i 0.395970 + 0.420168i
\(22\) −1.16549 2.01868i −0.248483 0.430385i
\(23\) −7.89025 −1.64523 −0.822616 0.568598i \(-0.807486\pi\)
−0.822616 + 0.568598i \(0.807486\pi\)
\(24\) 2.50674 1.44726i 0.511685 0.295422i
\(25\) 0.927071 1.60573i 0.185414 0.321147i
\(26\) 3.26558 0.478894i 0.640433 0.0939188i
\(27\) −1.00000 −0.192450
\(28\) 2.99201 0.707377i 0.565437 0.133682i
\(29\) −1.77706 + 3.07796i −0.329992 + 0.571562i −0.982510 0.186211i \(-0.940379\pi\)
0.652518 + 0.757773i \(0.273713\pi\)
\(30\) −1.19827 + 2.07547i −0.218774 + 0.378927i
\(31\) −7.91220 4.56811i −1.42107 0.820457i −0.424683 0.905342i \(-0.639614\pi\)
−0.996391 + 0.0848850i \(0.972948\pi\)
\(32\) 5.49106i 0.970691i
\(33\) 2.20526 + 1.27321i 0.383886 + 0.221637i
\(34\) 5.67509i 0.973270i
\(35\) −5.04091 + 4.75060i −0.852069 + 0.802998i
\(36\) −0.581025 + 1.00636i −0.0968375 + 0.167727i
\(37\) 8.68684i 1.42811i −0.700091 0.714054i \(-0.746857\pi\)
0.700091 0.714054i \(-0.253143\pi\)
\(38\) 1.25084 2.16652i 0.202913 0.351456i
\(39\) −2.82788 + 2.23676i −0.452823 + 0.358169i
\(40\) 3.78900 + 6.56274i 0.599093 + 1.03766i
\(41\) −3.98821 2.30259i −0.622854 0.359605i 0.155125 0.987895i \(-0.450422\pi\)
−0.777979 + 0.628290i \(0.783755\pi\)
\(42\) 1.76255 1.66104i 0.271967 0.256305i
\(43\) −2.11228 3.65857i −0.322119 0.557926i 0.658806 0.752313i \(-0.271062\pi\)
−0.980925 + 0.194386i \(0.937728\pi\)
\(44\) 2.56262 1.47953i 0.386329 0.223047i
\(45\) 2.61804i 0.390275i
\(46\) 7.22271i 1.06493i
\(47\) −1.53652 + 0.887113i −0.224125 + 0.129399i −0.607859 0.794045i \(-0.707971\pi\)
0.383734 + 0.923444i \(0.374638\pi\)
\(48\) −0.162771 0.281927i −0.0234940 0.0406927i
\(49\) 6.25889 3.13469i 0.894127 0.447813i
\(50\) −1.46988 0.848638i −0.207873 0.120015i
\(51\) 3.09980 + 5.36901i 0.434059 + 0.751812i
\(52\) 0.607931 + 4.14549i 0.0843049 + 0.574876i
\(53\) −3.42283 + 5.92852i −0.470162 + 0.814345i −0.999418 0.0341173i \(-0.989138\pi\)
0.529255 + 0.848463i \(0.322471\pi\)
\(54\) 0.915396i 0.124570i
\(55\) −3.33331 + 5.77345i −0.449463 + 0.778492i
\(56\) −1.76199 7.45275i −0.235456 0.995915i
\(57\) 2.73290i 0.361981i
\(58\) 2.81755 + 1.62671i 0.369962 + 0.213598i
\(59\) 2.25835i 0.294012i −0.989136 0.147006i \(-0.953036\pi\)
0.989136 0.147006i \(-0.0469637\pi\)
\(60\) −2.63470 1.52115i −0.340139 0.196379i
\(61\) −6.18601 + 10.7145i −0.792038 + 1.37185i 0.132666 + 0.991161i \(0.457646\pi\)
−0.924703 + 0.380688i \(0.875687\pi\)
\(62\) −4.18163 + 7.24280i −0.531068 + 0.919837i
\(63\) −0.760208 + 2.53418i −0.0957772 + 0.319277i
\(64\) −5.67758 −0.709697
\(65\) −5.85594 7.40350i −0.726340 0.918291i
\(66\) 1.16549 2.01868i 0.143462 0.248483i
\(67\) 0.536530 0.309766i 0.0655476 0.0378439i −0.466868 0.884327i \(-0.654618\pi\)
0.532416 + 0.846483i \(0.321284\pi\)
\(68\) 7.20424 0.873643
\(69\) −3.94513 6.83316i −0.474937 0.822616i
\(70\) 4.34868 + 4.61443i 0.519767 + 0.551530i
\(71\) 6.48057 3.74156i 0.769102 0.444041i −0.0634524 0.997985i \(-0.520211\pi\)
0.832554 + 0.553944i \(0.186878\pi\)
\(72\) 2.50674 + 1.44726i 0.295422 + 0.170562i
\(73\) −10.8250 6.24982i −1.26697 0.731486i −0.292557 0.956248i \(-0.594506\pi\)
−0.974414 + 0.224762i \(0.927840\pi\)
\(74\) −7.95190 −0.924390
\(75\) 1.85414 0.214098
\(76\) 2.75029 + 1.58788i 0.315480 + 0.182142i
\(77\) 4.90299 4.62062i 0.558748 0.526569i
\(78\) 2.04752 + 2.58863i 0.231836 + 0.293105i
\(79\) 0.621752 + 1.07691i 0.0699526 + 0.121161i 0.898880 0.438194i \(-0.144382\pi\)
−0.828928 + 0.559356i \(0.811049\pi\)
\(80\) 0.738098 0.426141i 0.0825218 0.0476440i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.10779 + 3.65079i −0.232766 + 0.403163i
\(83\) 2.10018i 0.230524i 0.993335 + 0.115262i \(0.0367708\pi\)
−0.993335 + 0.115262i \(0.963229\pi\)
\(84\) 2.10861 + 2.23747i 0.230068 + 0.244128i
\(85\) −14.0563 + 8.11541i −1.52462 + 0.880240i
\(86\) −3.34904 + 1.93357i −0.361136 + 0.208502i
\(87\) −3.55412 −0.381041
\(88\) −3.68533 6.38318i −0.392857 0.680449i
\(89\) 11.4071i 1.20915i 0.796550 + 0.604573i \(0.206656\pi\)
−0.796550 + 0.604573i \(0.793344\pi\)
\(90\) −2.39655 −0.252618
\(91\) 3.51859 + 8.86677i 0.368848 + 0.929490i
\(92\) −9.16886 −0.955920
\(93\) 9.13622i 0.947382i
\(94\) 0.812060 + 1.40653i 0.0837576 + 0.145072i
\(95\) −7.15484 −0.734071
\(96\) 4.75540 2.74553i 0.485345 0.280214i
\(97\) −1.32935 + 0.767503i −0.134975 + 0.0779281i −0.565967 0.824428i \(-0.691497\pi\)
0.430992 + 0.902356i \(0.358164\pi\)
\(98\) −2.86948 5.72937i −0.289862 0.578753i
\(99\) 2.54641i 0.255924i
\(100\) 1.07730 1.86594i 0.107730 0.186594i
\(101\) −0.252376 0.437129i −0.0251124 0.0434959i 0.853196 0.521590i \(-0.174661\pi\)
−0.878308 + 0.478094i \(0.841328\pi\)
\(102\) 4.91477 2.83755i 0.486635 0.280959i
\(103\) −2.66915 4.62310i −0.262999 0.455528i 0.704038 0.710162i \(-0.251378\pi\)
−0.967038 + 0.254634i \(0.918045\pi\)
\(104\) 10.3259 1.51429i 1.01254 0.148488i
\(105\) −6.63460 1.99026i −0.647470 0.194229i
\(106\) 5.42695 + 3.13325i 0.527112 + 0.304328i
\(107\) 17.8113 1.72189 0.860944 0.508700i \(-0.169874\pi\)
0.860944 + 0.508700i \(0.169874\pi\)
\(108\) −1.16205 −0.111818
\(109\) 16.0930 + 9.29129i 1.54143 + 0.889944i 0.998749 + 0.0500036i \(0.0159233\pi\)
0.542679 + 0.839940i \(0.317410\pi\)
\(110\) 5.28500 + 3.05130i 0.503905 + 0.290930i
\(111\) 7.52303 4.34342i 0.714054 0.412259i
\(112\) −0.838195 + 0.198168i −0.0792020 + 0.0187251i
\(113\) −3.61615 6.26336i −0.340179 0.589207i 0.644287 0.764784i \(-0.277154\pi\)
−0.984466 + 0.175577i \(0.943821\pi\)
\(114\) 2.50168 0.234304
\(115\) 17.8895 10.3285i 1.66820 0.963138i
\(116\) −2.06503 + 3.57674i −0.191733 + 0.332092i
\(117\) −3.35103 1.33063i −0.309803 0.123017i
\(118\) −2.06729 −0.190309
\(119\) 15.9626 3.77390i 1.46328 0.345952i
\(120\) −3.78900 + 6.56274i −0.345887 + 0.599093i
\(121\) −2.25790 + 3.91079i −0.205263 + 0.355526i
\(122\) 9.80800 + 5.66265i 0.887975 + 0.512672i
\(123\) 4.60519i 0.415236i
\(124\) −9.19437 5.30837i −0.825679 0.476706i
\(125\) 8.23599i 0.736649i
\(126\) 2.31978 + 0.695892i 0.206663 + 0.0619950i
\(127\) 4.21069 7.29312i 0.373638 0.647160i −0.616484 0.787367i \(-0.711444\pi\)
0.990122 + 0.140207i \(0.0447769\pi\)
\(128\) 5.78488i 0.511316i
\(129\) 2.11228 3.65857i 0.185975 0.322119i
\(130\) −6.77714 + 5.36050i −0.594394 + 0.470147i
\(131\) 8.26809 + 14.3207i 0.722386 + 1.25121i 0.960041 + 0.279860i \(0.0902879\pi\)
−0.237655 + 0.971350i \(0.576379\pi\)
\(132\) 2.56262 + 1.47953i 0.223047 + 0.128776i
\(133\) 6.92566 + 2.07757i 0.600531 + 0.180148i
\(134\) −0.283559 0.491138i −0.0244957 0.0424278i
\(135\) 2.26729 1.30902i 0.195137 0.112663i
\(136\) 17.9449i 1.53876i
\(137\) 1.91854i 0.163912i −0.996636 0.0819558i \(-0.973883\pi\)
0.996636 0.0819558i \(-0.0261166\pi\)
\(138\) −6.25505 + 3.61135i −0.532465 + 0.307419i
\(139\) −11.0300 19.1046i −0.935556 1.62043i −0.773640 0.633626i \(-0.781566\pi\)
−0.161916 0.986805i \(-0.551767\pi\)
\(140\) −5.85779 + 5.52043i −0.495073 + 0.466562i
\(141\) −1.53652 0.887113i −0.129399 0.0747084i
\(142\) −3.42501 5.93229i −0.287420 0.497826i
\(143\) 5.69572 + 7.20094i 0.476300 + 0.602173i
\(144\) 0.162771 0.281927i 0.0135642 0.0234940i
\(145\) 9.30483i 0.772724i
\(146\) −5.72106 + 9.90917i −0.473478 + 0.820089i
\(147\) 5.84417 + 3.85301i 0.482019 + 0.317791i
\(148\) 10.0945i 0.829766i
\(149\) −12.9855 7.49720i −1.06382 0.614195i −0.137331 0.990525i \(-0.543852\pi\)
−0.926485 + 0.376331i \(0.877186\pi\)
\(150\) 1.69728i 0.138582i
\(151\) 7.81993 + 4.51484i 0.636377 + 0.367413i 0.783218 0.621748i \(-0.213577\pi\)
−0.146840 + 0.989160i \(0.546910\pi\)
\(152\) 3.95522 6.85065i 0.320811 0.555661i
\(153\) −3.09980 + 5.36901i −0.250604 + 0.434059i
\(154\) −4.22970 4.48818i −0.340839 0.361668i
\(155\) 23.9190 1.92122
\(156\) −3.28613 + 2.59923i −0.263101 + 0.208105i
\(157\) 0.0998014 0.172861i 0.00796501 0.0137958i −0.862015 0.506882i \(-0.830798\pi\)
0.869980 + 0.493086i \(0.164131\pi\)
\(158\) 0.985797 0.569150i 0.0784258 0.0452791i
\(159\) −6.84567 −0.542897
\(160\) 7.18791 + 12.4498i 0.568254 + 0.984245i
\(161\) −20.3156 + 4.80305i −1.60109 + 0.378533i
\(162\) −0.792756 + 0.457698i −0.0622848 + 0.0359602i
\(163\) −6.10731 3.52606i −0.478362 0.276182i 0.241372 0.970433i \(-0.422403\pi\)
−0.719733 + 0.694250i \(0.755736\pi\)
\(164\) −4.63450 2.67573i −0.361894 0.208939i
\(165\) −6.66661 −0.518995
\(166\) 1.92249 0.149214
\(167\) −1.55981 0.900559i −0.120702 0.0696874i 0.438433 0.898764i \(-0.355534\pi\)
−0.559135 + 0.829076i \(0.688867\pi\)
\(168\) 5.57327 5.25230i 0.429987 0.405224i
\(169\) −12.4526 + 3.73260i −0.957894 + 0.287123i
\(170\) 7.42881 + 12.8671i 0.569764 + 0.986860i
\(171\) −2.36676 + 1.36645i −0.180990 + 0.104495i
\(172\) −2.45457 4.25144i −0.187159 0.324169i
\(173\) 5.96284 10.3279i 0.453346 0.785219i −0.545245 0.838277i \(-0.683563\pi\)
0.998591 + 0.0530578i \(0.0168968\pi\)
\(174\) 3.25343i 0.246642i
\(175\) 1.40953 4.69874i 0.106551 0.355191i
\(176\) −0.717903 + 0.414482i −0.0541140 + 0.0312427i
\(177\) 1.95579 1.12918i 0.147006 0.0848741i
\(178\) 10.4420 0.782659
\(179\) 8.17000 + 14.1509i 0.610655 + 1.05768i 0.991130 + 0.132894i \(0.0424269\pi\)
−0.380476 + 0.924791i \(0.624240\pi\)
\(180\) 3.04229i 0.226759i
\(181\) 16.7748 1.24686 0.623429 0.781880i \(-0.285739\pi\)
0.623429 + 0.781880i \(0.285739\pi\)
\(182\) 8.11660 3.22090i 0.601643 0.238749i
\(183\) −12.3720 −0.914566
\(184\) 22.8386i 1.68368i
\(185\) 11.3713 + 19.6956i 0.836031 + 1.44805i
\(186\) −8.36327 −0.613224
\(187\) 13.6717 7.89337i 0.999775 0.577220i
\(188\) −1.78552 + 1.03087i −0.130222 + 0.0751839i
\(189\) −2.57477 + 0.608732i −0.187287 + 0.0442787i
\(190\) 6.54951i 0.475151i
\(191\) −3.74195 + 6.48125i −0.270758 + 0.468967i −0.969056 0.246840i \(-0.920608\pi\)
0.698298 + 0.715807i \(0.253941\pi\)
\(192\) −2.83879 4.91693i −0.204872 0.354849i
\(193\) −10.1206 + 5.84311i −0.728494 + 0.420596i −0.817871 0.575402i \(-0.804846\pi\)
0.0893768 + 0.995998i \(0.471512\pi\)
\(194\) 0.702569 + 1.21689i 0.0504416 + 0.0873673i
\(195\) 3.48365 8.77314i 0.249469 0.628258i
\(196\) 7.27314 3.64267i 0.519510 0.260190i
\(197\) 0.388915 + 0.224540i 0.0277091 + 0.0159978i 0.513791 0.857916i \(-0.328241\pi\)
−0.486081 + 0.873913i \(0.661574\pi\)
\(198\) 2.33098 0.165655
\(199\) −9.82331 −0.696356 −0.348178 0.937428i \(-0.613200\pi\)
−0.348178 + 0.937428i \(0.613200\pi\)
\(200\) −4.64784 2.68343i −0.328652 0.189747i
\(201\) 0.536530 + 0.309766i 0.0378439 + 0.0218492i
\(202\) −0.400146 + 0.231024i −0.0281542 + 0.0162548i
\(203\) −2.70187 + 9.00678i −0.189634 + 0.632152i
\(204\) 3.60212 + 6.23906i 0.252199 + 0.436821i
\(205\) 12.0566 0.842068
\(206\) −4.23197 + 2.44333i −0.294856 + 0.170235i
\(207\) 3.94513 6.83316i 0.274205 0.474937i
\(208\) −0.170309 1.16134i −0.0118088 0.0805242i
\(209\) 6.95908 0.481369
\(210\) −1.82187 + 6.07329i −0.125721 + 0.419097i
\(211\) 1.80752 3.13072i 0.124435 0.215528i −0.797077 0.603878i \(-0.793621\pi\)
0.921512 + 0.388350i \(0.126955\pi\)
\(212\) −3.97750 + 6.88924i −0.273176 + 0.473155i
\(213\) 6.48057 + 3.74156i 0.444041 + 0.256367i
\(214\) 16.3044i 1.11455i
\(215\) 9.57828 + 5.53002i 0.653233 + 0.377145i
\(216\) 2.89453i 0.196948i
\(217\) −23.1529 6.94543i −1.57172 0.471487i
\(218\) 8.50521 14.7315i 0.576045 0.997740i
\(219\) 12.4996i 0.844647i
\(220\) −3.87347 + 6.70904i −0.261149 + 0.452323i
\(221\) 3.24335 + 22.1164i 0.218171 + 1.48771i
\(222\) −3.97595 6.88655i −0.266848 0.462195i
\(223\) 3.07998 + 1.77823i 0.206251 + 0.119079i 0.599568 0.800324i \(-0.295339\pi\)
−0.393317 + 0.919403i \(0.628672\pi\)
\(224\) −3.34258 14.1382i −0.223336 0.944649i
\(225\) 0.927071 + 1.60573i 0.0618047 + 0.107049i
\(226\) −5.73345 + 3.31021i −0.381384 + 0.220192i
\(227\) 7.79500i 0.517372i 0.965961 + 0.258686i \(0.0832895\pi\)
−0.965961 + 0.258686i \(0.916711\pi\)
\(228\) 3.17576i 0.210320i
\(229\) −14.2182 + 8.20887i −0.939563 + 0.542457i −0.889823 0.456305i \(-0.849173\pi\)
−0.0497400 + 0.998762i \(0.515839\pi\)
\(230\) −9.45467 16.3760i −0.623423 1.07980i
\(231\) 6.45307 + 1.93580i 0.424581 + 0.127366i
\(232\) 8.90923 + 5.14375i 0.584920 + 0.337704i
\(233\) −3.78863 6.56210i −0.248201 0.429898i 0.714825 0.699303i \(-0.246506\pi\)
−0.963027 + 0.269405i \(0.913173\pi\)
\(234\) −1.21806 + 3.06752i −0.0796268 + 0.200530i
\(235\) 2.32250 4.02269i 0.151503 0.262411i
\(236\) 2.62432i 0.170829i
\(237\) −0.621752 + 1.07691i −0.0403872 + 0.0699526i
\(238\) −3.45461 14.6121i −0.223929 0.947159i
\(239\) 4.68654i 0.303147i −0.988446 0.151574i \(-0.951566\pi\)
0.988446 0.151574i \(-0.0484341\pi\)
\(240\) 0.738098 + 0.426141i 0.0476440 + 0.0275073i
\(241\) 10.7233i 0.690748i 0.938465 + 0.345374i \(0.112248\pi\)
−0.938465 + 0.345374i \(0.887752\pi\)
\(242\) 3.57992 + 2.06687i 0.230126 + 0.132863i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −7.18845 + 12.4508i −0.460193 + 0.797078i
\(245\) −10.0873 + 15.3003i −0.644457 + 0.977499i
\(246\) −4.21557 −0.268775
\(247\) −3.63648 + 9.15802i −0.231384 + 0.582711i
\(248\) −13.2225 + 22.9021i −0.839632 + 1.45428i
\(249\) −1.81881 + 1.05009i −0.115262 + 0.0665466i
\(250\) −7.53919 −0.476820
\(251\) 5.93135 + 10.2734i 0.374384 + 0.648452i 0.990235 0.139411i \(-0.0445209\pi\)
−0.615851 + 0.787863i \(0.711188\pi\)
\(252\) −0.883400 + 2.94485i −0.0556489 + 0.185508i
\(253\) −17.4000 + 10.0459i −1.09393 + 0.631581i
\(254\) −6.67610 3.85445i −0.418896 0.241849i
\(255\) −14.0563 8.11541i −0.880240 0.508207i
\(256\) −16.6506 −1.04066
\(257\) 9.34756 0.583085 0.291542 0.956558i \(-0.405832\pi\)
0.291542 + 0.956558i \(0.405832\pi\)
\(258\) −3.34904 1.93357i −0.208502 0.120379i
\(259\) −5.28796 22.3666i −0.328578 1.38979i
\(260\) −6.80489 8.60324i −0.422021 0.533550i
\(261\) −1.77706 3.07796i −0.109997 0.190521i
\(262\) 13.1092 7.56858i 0.809886 0.467588i
\(263\) −0.471710 0.817026i −0.0290869 0.0503800i 0.851116 0.524978i \(-0.175927\pi\)
−0.880202 + 0.474598i \(0.842593\pi\)
\(264\) 3.68533 6.38318i 0.226816 0.392857i
\(265\) 17.9222i 1.10095i
\(266\) 1.90180 6.33972i 0.116607 0.388713i
\(267\) −9.87880 + 5.70353i −0.604573 + 0.349050i
\(268\) 0.623475 0.359963i 0.0380848 0.0219883i
\(269\) −7.58306 −0.462347 −0.231174 0.972913i \(-0.574257\pi\)
−0.231174 + 0.972913i \(0.574257\pi\)
\(270\) −1.19827 2.07547i −0.0729246 0.126309i
\(271\) 20.5902i 1.25077i 0.780317 + 0.625384i \(0.215058\pi\)
−0.780317 + 0.625384i \(0.784942\pi\)
\(272\) −2.01823 −0.122373
\(273\) −5.91955 + 7.48057i −0.358267 + 0.452745i
\(274\) −1.75622 −0.106097
\(275\) 4.72141i 0.284712i
\(276\) −4.58443 7.94047i −0.275950 0.477960i
\(277\) 20.4256 1.22726 0.613628 0.789595i \(-0.289710\pi\)
0.613628 + 0.789595i \(0.289710\pi\)
\(278\) −17.4883 + 10.0969i −1.04888 + 0.605569i
\(279\) 7.91220 4.56811i 0.473691 0.273486i
\(280\) 13.7508 + 14.5911i 0.821765 + 0.871983i
\(281\) 10.8703i 0.648466i −0.945977 0.324233i \(-0.894894\pi\)
0.945977 0.324233i \(-0.105106\pi\)
\(282\) −0.812060 + 1.40653i −0.0483575 + 0.0837576i
\(283\) −1.91077 3.30955i −0.113583 0.196732i 0.803629 0.595130i \(-0.202900\pi\)
−0.917213 + 0.398398i \(0.869566\pi\)
\(284\) 7.53074 4.34787i 0.446867 0.257999i
\(285\) −3.57742 6.19627i −0.211908 0.367035i
\(286\) 6.59171 5.21384i 0.389776 0.308301i
\(287\) −11.6704 3.50090i −0.688882 0.206652i
\(288\) 4.75540 + 2.74553i 0.280214 + 0.161782i
\(289\) 21.4351 1.26089
\(290\) −8.51760 −0.500171
\(291\) −1.32935 0.767503i −0.0779281 0.0449918i
\(292\) −12.5792 7.26260i −0.736141 0.425011i
\(293\) 15.6392 9.02929i 0.913651 0.527497i 0.0320472 0.999486i \(-0.489797\pi\)
0.881604 + 0.471989i \(0.156464\pi\)
\(294\) 3.52703 5.34973i 0.205701 0.312003i
\(295\) 2.95623 + 5.12034i 0.172118 + 0.298118i
\(296\) −25.1443 −1.46148
\(297\) −2.20526 + 1.27321i −0.127962 + 0.0738789i
\(298\) −6.86291 + 11.8869i −0.397558 + 0.688590i
\(299\) −4.12782 28.1476i −0.238718 1.62782i
\(300\) 2.15461 0.124396
\(301\) −7.66571 8.13416i −0.441844 0.468845i
\(302\) 4.13287 7.15834i 0.237820 0.411916i
\(303\) 0.252376 0.437129i 0.0144986 0.0251124i
\(304\) −0.770478 0.444836i −0.0441900 0.0255131i
\(305\) 32.3905i 1.85467i
\(306\) 4.91477 + 2.83755i 0.280959 + 0.162212i
\(307\) 8.88791i 0.507260i −0.967301 0.253630i \(-0.918375\pi\)
0.967301 0.253630i \(-0.0816246\pi\)
\(308\) 5.69752 5.36939i 0.324646 0.305950i
\(309\) 2.66915 4.62310i 0.151843 0.262999i
\(310\) 21.8954i 1.24357i
\(311\) −8.24533 + 14.2813i −0.467550 + 0.809820i −0.999313 0.0370736i \(-0.988196\pi\)
0.531763 + 0.846893i \(0.321530\pi\)
\(312\) 6.47437 + 8.18537i 0.366539 + 0.463405i
\(313\) −11.0236 19.0935i −0.623092 1.07923i −0.988907 0.148539i \(-0.952543\pi\)
0.365815 0.930688i \(-0.380790\pi\)
\(314\) −0.158236 0.0913578i −0.00892979 0.00515562i
\(315\) −1.59369 6.74086i −0.0897940 0.379804i
\(316\) 0.722507 + 1.25142i 0.0406442 + 0.0703978i
\(317\) −19.7541 + 11.4050i −1.10950 + 0.640569i −0.938699 0.344737i \(-0.887968\pi\)
−0.170799 + 0.985306i \(0.554635\pi\)
\(318\) 6.26650i 0.351408i
\(319\) 9.05024i 0.506716i
\(320\) 12.8727 7.43207i 0.719607 0.415465i
\(321\) 8.90567 + 15.4251i 0.497066 + 0.860944i
\(322\) 4.39669 + 18.5968i 0.245018 + 1.03636i
\(323\) 14.6730 + 8.47143i 0.816425 + 0.471363i
\(324\) −0.581025 1.00636i −0.0322792 0.0559091i
\(325\) 6.21329 + 2.46718i 0.344651 + 0.136855i
\(326\) −3.22774 + 5.59061i −0.178768 + 0.309635i
\(327\) 18.5826i 1.02762i
\(328\) −6.66493 + 11.5440i −0.368009 + 0.637410i
\(329\) −3.41619 + 3.21944i −0.188340 + 0.177494i
\(330\) 6.10259i 0.335937i
\(331\) 27.7264 + 16.0079i 1.52398 + 0.879871i 0.999597 + 0.0283898i \(0.00903797\pi\)
0.524385 + 0.851481i \(0.324295\pi\)
\(332\) 2.44051i 0.133940i
\(333\) 7.52303 + 4.34342i 0.412259 + 0.238018i
\(334\) −0.824369 + 1.42785i −0.0451074 + 0.0781284i
\(335\) −0.810980 + 1.40466i −0.0443086 + 0.0767447i
\(336\) −0.590716 0.626815i −0.0322262 0.0341955i
\(337\) 4.99719 0.272214 0.136107 0.990694i \(-0.456541\pi\)
0.136107 + 0.990694i \(0.456541\pi\)
\(338\) 3.41681 + 11.3991i 0.185850 + 0.620028i
\(339\) 3.61615 6.26336i 0.196402 0.340179i
\(340\) −16.3341 + 9.43051i −0.885842 + 0.511441i
\(341\) −23.2646 −1.25985
\(342\) 1.25084 + 2.16652i 0.0676378 + 0.117152i
\(343\) 14.2070 11.8811i 0.767107 0.641519i
\(344\) −10.5898 + 6.11404i −0.570965 + 0.329647i
\(345\) 17.8895 + 10.3285i 0.963138 + 0.556068i
\(346\) −9.45416 5.45836i −0.508259 0.293443i
\(347\) 34.3420 1.84358 0.921789 0.387692i \(-0.126728\pi\)
0.921789 + 0.387692i \(0.126728\pi\)
\(348\) −4.13006 −0.221394
\(349\) 8.51580 + 4.91660i 0.455841 + 0.263180i 0.710294 0.703905i \(-0.248562\pi\)
−0.254453 + 0.967085i \(0.581895\pi\)
\(350\) −4.30121 1.29028i −0.229909 0.0689685i
\(351\) −0.523154 3.56740i −0.0279239 0.190413i
\(352\) −6.99124 12.1092i −0.372635 0.645422i
\(353\) 13.2871 7.67129i 0.707199 0.408302i −0.102824 0.994700i \(-0.532788\pi\)
0.810023 + 0.586398i \(0.199454\pi\)
\(354\) −1.03364 1.79032i −0.0549375 0.0951546i
\(355\) −9.79555 + 16.9664i −0.519894 + 0.900483i
\(356\) 13.2556i 0.702544i
\(357\) 11.2496 + 11.9370i 0.595390 + 0.631775i
\(358\) 12.9536 7.47879i 0.684621 0.395266i
\(359\) 25.1701 14.5319i 1.32842 0.766966i 0.343369 0.939201i \(-0.388432\pi\)
0.985056 + 0.172235i \(0.0550987\pi\)
\(360\) −7.57800 −0.399395
\(361\) −5.76564 9.98638i −0.303455 0.525599i
\(362\) 15.3555i 0.807070i
\(363\) −4.51579 −0.237018
\(364\) 4.08878 + 10.3036i 0.214310 + 0.540056i
\(365\) 32.7246 1.71288
\(366\) 11.3253i 0.591983i
\(367\) −9.15105 15.8501i −0.477681 0.827368i 0.521992 0.852950i \(-0.325189\pi\)
−0.999673 + 0.0255830i \(0.991856\pi\)
\(368\) 2.56861 0.133898
\(369\) 3.98821 2.30259i 0.207618 0.119868i
\(370\) 18.0293 10.4092i 0.937297 0.541149i
\(371\) −5.20413 + 17.3482i −0.270185 + 0.900672i
\(372\) 10.6167i 0.550453i
\(373\) −6.43274 + 11.1418i −0.333074 + 0.576902i −0.983113 0.182999i \(-0.941419\pi\)
0.650039 + 0.759901i \(0.274753\pi\)
\(374\) −7.22556 12.5150i −0.373625 0.647137i
\(375\) 7.13257 4.11799i 0.368325 0.212652i
\(376\) 2.56777 + 4.44752i 0.132423 + 0.229363i
\(377\) −11.9100 4.72922i −0.613394 0.243567i
\(378\) 0.557231 + 2.35694i 0.0286609 + 0.121228i
\(379\) 22.8080 + 13.1682i 1.17157 + 0.676405i 0.954049 0.299651i \(-0.0968703\pi\)
0.217519 + 0.976056i \(0.430204\pi\)
\(380\) −8.31427 −0.426513
\(381\) 8.42137 0.431440
\(382\) 5.93291 + 3.42537i 0.303554 + 0.175257i
\(383\) −12.4747 7.20224i −0.637425 0.368017i 0.146197 0.989255i \(-0.453297\pi\)
−0.783622 + 0.621238i \(0.786630\pi\)
\(384\) 5.00985 2.89244i 0.255658 0.147604i
\(385\) −5.06801 + 16.8944i −0.258290 + 0.861019i
\(386\) 5.34876 + 9.26433i 0.272245 + 0.471542i
\(387\) 4.22455 0.214746
\(388\) −1.54478 + 0.891877i −0.0784241 + 0.0452782i
\(389\) 3.30891 5.73120i 0.167768 0.290584i −0.769866 0.638205i \(-0.779677\pi\)
0.937635 + 0.347621i \(0.113011\pi\)
\(390\) −8.03090 3.18892i −0.406661 0.161477i
\(391\) −48.9164 −2.47381
\(392\) −9.07345 18.1165i −0.458279 0.915023i
\(393\) −8.26809 + 14.3207i −0.417070 + 0.722386i
\(394\) 0.205543 0.356012i 0.0103551 0.0179356i
\(395\) −2.81939 1.62777i −0.141859 0.0819022i
\(396\) 2.95906i 0.148698i
\(397\) −19.6031 11.3178i −0.983851 0.568027i −0.0804203 0.996761i \(-0.525626\pi\)
−0.903431 + 0.428734i \(0.858960\pi\)
\(398\) 8.99222i 0.450739i
\(399\) 1.66360 + 7.03658i 0.0832842 + 0.352270i
\(400\) −0.301800 + 0.522734i −0.0150900 + 0.0261367i
\(401\) 0.450563i 0.0225000i 0.999937 + 0.0112500i \(0.00358107\pi\)
−0.999937 + 0.0112500i \(0.996419\pi\)
\(402\) 0.283559 0.491138i 0.0141426 0.0244957i
\(403\) 12.1570 30.6158i 0.605581 1.52508i
\(404\) −0.293274 0.507965i −0.0145909 0.0252722i
\(405\) 2.26729 + 1.30902i 0.112663 + 0.0650458i
\(406\) 8.24478 + 2.47328i 0.409181 + 0.122747i
\(407\) −11.0601 19.1567i −0.548231 0.949563i
\(408\) 15.5408 8.97246i 0.769382 0.444203i
\(409\) 34.4616i 1.70402i 0.523529 + 0.852008i \(0.324615\pi\)
−0.523529 + 0.852008i \(0.675385\pi\)
\(410\) 11.0365i 0.545056i
\(411\) 1.66150 0.959268i 0.0819558 0.0473172i
\(412\) −3.10169 5.37228i −0.152809 0.264673i
\(413\) −1.37473 5.81474i −0.0676461 0.286125i
\(414\) −6.25505 3.61135i −0.307419 0.177488i
\(415\) −2.74917 4.76171i −0.134952 0.233743i
\(416\) 19.5888 2.87267i 0.960419 0.140844i
\(417\) 11.0300 19.1046i 0.540143 0.935556i
\(418\) 6.37031i 0.311582i
\(419\) 0.195021 0.337787i 0.00952742 0.0165020i −0.861222 0.508228i \(-0.830301\pi\)
0.870750 + 0.491726i \(0.163634\pi\)
\(420\) −7.70973 2.31278i −0.376196 0.112852i
\(421\) 24.5494i 1.19646i 0.801323 + 0.598232i \(0.204130\pi\)
−0.801323 + 0.598232i \(0.795870\pi\)
\(422\) −2.86585 1.65460i −0.139507 0.0805447i
\(423\) 1.77423i 0.0862658i
\(424\) 17.1603 + 9.90749i 0.833377 + 0.481150i
\(425\) 5.74747 9.95491i 0.278793 0.482884i
\(426\) 3.42501 5.93229i 0.165942 0.287420i
\(427\) −9.40531 + 31.3530i −0.455155 + 1.51728i
\(428\) 20.6977 1.00046
\(429\) −3.38834 + 8.53311i −0.163590 + 0.411982i
\(430\) 5.06216 8.76793i 0.244119 0.422827i
\(431\) −0.983361 + 0.567744i −0.0473668 + 0.0273473i −0.523496 0.852028i \(-0.675373\pi\)
0.476130 + 0.879375i \(0.342039\pi\)
\(432\) 0.325542 0.0156626
\(433\) 10.1233 + 17.5341i 0.486495 + 0.842634i 0.999879 0.0155250i \(-0.00494195\pi\)
−0.513385 + 0.858159i \(0.671609\pi\)
\(434\) −6.35782 + 21.1940i −0.305185 + 1.01735i
\(435\) 8.05822 4.65241i 0.386362 0.223066i
\(436\) 18.7008 + 10.7969i 0.895608 + 0.517079i
\(437\) −18.6743 10.7816i −0.893313 0.515755i
\(438\) −11.4421 −0.546726
\(439\) 27.9764 1.33524 0.667621 0.744501i \(-0.267313\pi\)
0.667621 + 0.744501i \(0.267313\pi\)
\(440\) 16.7114 + 9.64835i 0.796686 + 0.459967i
\(441\) −0.414724 + 6.98770i −0.0197487 + 0.332748i
\(442\) 20.2453 2.96895i 0.962971 0.141219i
\(443\) 10.7712 + 18.6562i 0.511755 + 0.886385i 0.999907 + 0.0136266i \(0.00433761\pi\)
−0.488153 + 0.872758i \(0.662329\pi\)
\(444\) 8.74213 5.04727i 0.414883 0.239533i
\(445\) −14.9321 25.8631i −0.707848 1.22603i
\(446\) 1.62778 2.81941i 0.0770778 0.133503i
\(447\) 14.9944i 0.709211i
\(448\) −14.6185 + 3.45612i −0.690657 + 0.163286i
\(449\) −2.50177 + 1.44440i −0.118066 + 0.0681652i −0.557870 0.829928i \(-0.688381\pi\)
0.439804 + 0.898094i \(0.355048\pi\)
\(450\) 1.46988 0.848638i 0.0692910 0.0400052i
\(451\) −11.7267 −0.552189
\(452\) −4.20215 7.27833i −0.197652 0.342344i
\(453\) 9.02968i 0.424251i
\(454\) 7.13551 0.334886
\(455\) −19.5844 15.4976i −0.918133 0.726540i
\(456\) 7.91045 0.370441
\(457\) 32.6685i 1.52817i −0.645118 0.764083i \(-0.723192\pi\)
0.645118 0.764083i \(-0.276808\pi\)
\(458\) 7.51437 + 13.0153i 0.351123 + 0.608163i
\(459\) −6.19960 −0.289373
\(460\) 20.7885 12.0022i 0.969268 0.559607i
\(461\) −32.7978 + 18.9358i −1.52755 + 0.881930i −0.528084 + 0.849192i \(0.677089\pi\)
−0.999464 + 0.0327376i \(0.989577\pi\)
\(462\) 1.77203 5.90712i 0.0824421 0.274824i
\(463\) 20.8936i 0.971006i 0.874235 + 0.485503i \(0.161364\pi\)
−0.874235 + 0.485503i \(0.838636\pi\)
\(464\) 0.578507 1.00200i 0.0268565 0.0465168i
\(465\) 11.9595 + 20.7145i 0.554609 + 0.960611i
\(466\) −6.00692 + 3.46810i −0.278265 + 0.160657i
\(467\) −10.8858 18.8548i −0.503735 0.872494i −0.999991 0.00431766i \(-0.998626\pi\)
0.496256 0.868176i \(-0.334708\pi\)
\(468\) −3.89407 1.54626i −0.180003 0.0714759i
\(469\) 1.19288 1.12418i 0.0550820 0.0519098i
\(470\) −3.68235 2.12601i −0.169854 0.0980654i
\(471\) 0.199603 0.00919721
\(472\) −6.53687 −0.300884
\(473\) −9.31622 5.37872i −0.428360 0.247314i
\(474\) 0.985797 + 0.569150i 0.0452791 + 0.0261419i
\(475\) 4.38830 2.53359i 0.201349 0.116249i
\(476\) 18.5493 4.38545i 0.850205 0.201007i
\(477\) −3.42283 5.92852i −0.156721 0.271448i
\(478\) −4.29004 −0.196222
\(479\) −9.43952 + 5.44991i −0.431303 + 0.249013i −0.699901 0.714239i \(-0.746773\pi\)
0.268599 + 0.963252i \(0.413439\pi\)
\(480\) −7.18791 + 12.4498i −0.328082 + 0.568254i
\(481\) 30.9894 4.54456i 1.41299 0.207214i
\(482\) 9.81606 0.447109
\(483\) −14.3174 15.1923i −0.651462 0.691273i
\(484\) −2.62379 + 4.54453i −0.119263 + 0.206570i
\(485\) 2.00936 3.48031i 0.0912401 0.158033i
\(486\) −0.792756 0.457698i −0.0359602 0.0207616i
\(487\) 6.15209i 0.278778i −0.990238 0.139389i \(-0.955486\pi\)
0.990238 0.139389i \(-0.0445138\pi\)
\(488\) 31.0134 + 17.9056i 1.40391 + 0.810548i
\(489\) 7.05212i 0.318908i
\(490\) 14.0058 + 9.23392i 0.632718 + 0.417146i
\(491\) 5.40015 9.35334i 0.243705 0.422110i −0.718061 0.695980i \(-0.754970\pi\)
0.961767 + 0.273869i \(0.0883036\pi\)
\(492\) 5.35146i 0.241262i
\(493\) −11.0171 + 19.0821i −0.496183 + 0.859415i
\(494\) 8.38322 + 3.32882i 0.377179 + 0.149771i
\(495\) −3.33331 5.77345i −0.149821 0.259497i
\(496\) 2.57575 + 1.48711i 0.115655 + 0.0667733i
\(497\) 14.4084 13.5786i 0.646304 0.609082i
\(498\) 0.961247 + 1.66493i 0.0430745 + 0.0746072i
\(499\) −1.85936 + 1.07350i −0.0832362 + 0.0480565i −0.541040 0.840997i \(-0.681969\pi\)
0.457804 + 0.889053i \(0.348636\pi\)
\(500\) 9.57062i 0.428011i
\(501\) 1.80112i 0.0804680i
\(502\) 9.40424 5.42954i 0.419732 0.242332i
\(503\) −3.07639 5.32846i −0.137169 0.237584i 0.789255 0.614066i \(-0.210467\pi\)
−0.926424 + 0.376482i \(0.877134\pi\)
\(504\) 7.33527 + 2.20044i 0.326739 + 0.0980156i
\(505\) 1.14442 + 0.660732i 0.0509261 + 0.0294022i
\(506\) 9.19599 + 15.9279i 0.408812 + 0.708083i
\(507\) −9.45883 8.91799i −0.420082 0.396062i
\(508\) 4.89302 8.47497i 0.217093 0.376016i
\(509\) 4.58685i 0.203309i −0.994820 0.101654i \(-0.967586\pi\)
0.994820 0.101654i \(-0.0324136\pi\)
\(510\) −7.42881 + 12.8671i −0.328953 + 0.569764i
\(511\) −31.6764 9.50233i −1.40128 0.420358i
\(512\) 3.67215i 0.162288i
\(513\) −2.36676 1.36645i −0.104495 0.0603302i
\(514\) 8.55672i 0.377421i
\(515\) 12.1035 + 6.98795i 0.533343 + 0.307926i
\(516\) 2.45457 4.25144i 0.108056 0.187159i
\(517\) −2.25895 + 3.91262i −0.0993487 + 0.172077i
\(518\) −20.4743 + 4.84058i −0.899590 + 0.212683i
\(519\) 11.9257 0.523479
\(520\) −21.4296 + 16.9502i −0.939752 + 0.743315i
\(521\) 10.7536 18.6258i 0.471123 0.816009i −0.528331 0.849038i \(-0.677182\pi\)
0.999454 + 0.0330292i \(0.0105154\pi\)
\(522\) −2.81755 + 1.62671i −0.123321 + 0.0711993i
\(523\) −12.0380 −0.526387 −0.263193 0.964743i \(-0.584776\pi\)
−0.263193 + 0.964743i \(0.584776\pi\)
\(524\) 9.60793 + 16.6414i 0.419724 + 0.726984i
\(525\) 4.77399 1.12868i 0.208354 0.0492594i
\(526\) −0.747902 + 0.431802i −0.0326101 + 0.0188274i
\(527\) −49.0525 28.3205i −2.13676 1.23366i
\(528\) −0.717903 0.414482i −0.0312427 0.0180380i
\(529\) 39.2561 1.70679
\(530\) −16.4060 −0.712629
\(531\) 1.95579 + 1.12918i 0.0848741 + 0.0490021i
\(532\) 8.04796 + 2.41424i 0.348923 + 0.104671i
\(533\) 6.12782 15.4321i 0.265425 0.668440i
\(534\) 5.22099 + 9.04302i 0.225934 + 0.391330i
\(535\) −40.3835 + 23.3154i −1.74593 + 1.00801i
\(536\) −0.896626 1.55300i −0.0387283 0.0670795i
\(537\) −8.17000 + 14.1509i −0.352562 + 0.610655i
\(538\) 6.94150i 0.299269i
\(539\) 9.81135 14.8817i 0.422605 0.640998i
\(540\) 2.63470 1.52115i 0.113380 0.0654597i
\(541\) −1.68945 + 0.975405i −0.0726352 + 0.0419360i −0.535878 0.844296i \(-0.680019\pi\)
0.463243 + 0.886232i \(0.346686\pi\)
\(542\) 18.8482 0.809601
\(543\) 8.38738 + 14.5274i 0.359937 + 0.623429i
\(544\) 34.0424i 1.45955i
\(545\) −48.6500 −2.08393
\(546\) 6.84769 + 5.41873i 0.293054 + 0.231900i
\(547\) 4.27037 0.182588 0.0912940 0.995824i \(-0.470900\pi\)
0.0912940 + 0.995824i \(0.470900\pi\)
\(548\) 2.22943i 0.0952367i
\(549\) −6.18601 10.7145i −0.264013 0.457283i
\(550\) −4.32196 −0.184289
\(551\) −8.41173 + 4.85652i −0.358352 + 0.206895i
\(552\) −19.7788 + 11.4193i −0.841840 + 0.486037i
\(553\) 2.25642 + 2.39431i 0.0959527 + 0.101816i
\(554\) 18.6975i 0.794382i
\(555\) −11.3713 + 19.6956i −0.482683 + 0.836031i
\(556\) −12.8175 22.2005i −0.543581 0.941510i
\(557\) −34.6266 + 19.9917i −1.46718 + 0.847075i −0.999325 0.0367316i \(-0.988305\pi\)
−0.467852 + 0.883807i \(0.654972\pi\)
\(558\) −4.18163 7.24280i −0.177023 0.306612i
\(559\) 11.9465 9.44932i 0.505284 0.399663i
\(560\) 1.64103 1.54652i 0.0693460 0.0653524i
\(561\) 13.6717 + 7.89337i 0.577220 + 0.333258i
\(562\) −9.95061 −0.419741
\(563\) 33.5147 1.41248 0.706239 0.707974i \(-0.250391\pi\)
0.706239 + 0.707974i \(0.250391\pi\)
\(564\) −1.78552 1.03087i −0.0751839 0.0434074i
\(565\) 16.3977 + 9.46723i 0.689858 + 0.398290i
\(566\) −3.02955 + 1.74911i −0.127342 + 0.0735207i
\(567\) −1.81456 1.92545i −0.0762045 0.0808613i
\(568\) −10.8300 18.7582i −0.454418 0.787076i
\(569\) −38.8836 −1.63009 −0.815043 0.579401i \(-0.803287\pi\)
−0.815043 + 0.579401i \(0.803287\pi\)
\(570\) −5.67204 + 3.27476i −0.237576 + 0.137164i
\(571\) 11.3324 19.6282i 0.474245 0.821417i −0.525320 0.850905i \(-0.676054\pi\)
0.999565 + 0.0294882i \(0.00938774\pi\)
\(572\) 6.61871 + 8.36785i 0.276742 + 0.349877i
\(573\) −7.48391 −0.312645
\(574\) −3.20471 + 10.6830i −0.133762 + 0.445901i
\(575\) −7.31482 + 12.6696i −0.305049 + 0.528361i
\(576\) 2.83879 4.91693i 0.118283 0.204872i
\(577\) 20.1472 + 11.6320i 0.838740 + 0.484247i 0.856836 0.515589i \(-0.172427\pi\)
−0.0180956 + 0.999836i \(0.505760\pi\)
\(578\) 19.6216i 0.816150i
\(579\) −10.1206 5.84311i −0.420596 0.242831i
\(580\) 10.8127i 0.448972i
\(581\) 1.27844 + 5.40747i 0.0530388 + 0.224340i
\(582\) −0.702569 + 1.21689i −0.0291224 + 0.0504416i
\(583\) 17.4319i 0.721955i
\(584\) −18.0903 + 31.3333i −0.748581 + 1.29658i
\(585\) 9.33959 1.36964i 0.386145 0.0566276i
\(586\) −8.26538 14.3161i −0.341440 0.591391i
\(587\) −11.6230 6.71057i −0.479734 0.276975i 0.240571 0.970631i \(-0.422665\pi\)
−0.720306 + 0.693657i \(0.755998\pi\)
\(588\) 6.79121 + 4.47739i 0.280065 + 0.184645i
\(589\) −12.4842 21.6232i −0.514402 0.890970i
\(590\) 4.68714 2.70612i 0.192967 0.111409i
\(591\) 0.449081i 0.0184727i
\(592\) 2.82793i 0.116227i
\(593\) −7.76746 + 4.48455i −0.318972 + 0.184158i −0.650934 0.759134i \(-0.725623\pi\)
0.331963 + 0.943293i \(0.392289\pi\)
\(594\) 1.16549 + 2.01868i 0.0478205 + 0.0828276i
\(595\) −31.2516 + 29.4518i −1.28119 + 1.20741i
\(596\) −15.0898 8.71212i −0.618104 0.356862i
\(597\) −4.91166 8.50724i −0.201021 0.348178i
\(598\) −25.7663 + 3.77859i −1.05366 + 0.154518i
\(599\) −17.2505 + 29.8787i −0.704836 + 1.22081i 0.261914 + 0.965091i \(0.415646\pi\)
−0.966751 + 0.255721i \(0.917687\pi\)
\(600\) 5.36687i 0.219101i
\(601\) 10.6843 18.5058i 0.435824 0.754869i −0.561539 0.827450i \(-0.689791\pi\)
0.997362 + 0.0725818i \(0.0231238\pi\)
\(602\) −7.44598 + 7.01716i −0.303476 + 0.285998i
\(603\) 0.619532i 0.0252293i
\(604\) 9.08715 + 5.24647i 0.369751 + 0.213476i
\(605\) 11.8225i 0.480654i
\(606\) −0.400146 0.231024i −0.0162548 0.00938472i
\(607\) 0.563082 0.975286i 0.0228548 0.0395857i −0.854372 0.519662i \(-0.826058\pi\)
0.877227 + 0.480077i \(0.159391\pi\)
\(608\) 7.50324 12.9960i 0.304297 0.527057i
\(609\) −9.15104 + 2.16350i −0.370819 + 0.0876696i
\(610\) −29.6501 −1.20050
\(611\) −3.96852 5.01729i −0.160549 0.202978i
\(612\) −3.60212 + 6.23906i −0.145607 + 0.252199i
\(613\) −25.0649 + 14.4712i −1.01236 + 0.584486i −0.911882 0.410453i \(-0.865371\pi\)
−0.100478 + 0.994939i \(0.532037\pi\)
\(614\) −8.13596 −0.328341
\(615\) 6.02829 + 10.4413i 0.243084 + 0.421034i
\(616\) −13.3745 14.1918i −0.538875 0.571806i
\(617\) −3.55424 + 2.05204i −0.143088 + 0.0826120i −0.569835 0.821759i \(-0.692993\pi\)
0.426747 + 0.904371i \(0.359660\pi\)
\(618\) −4.23197 2.44333i −0.170235 0.0982852i
\(619\) 9.06150 + 5.23166i 0.364212 + 0.210278i 0.670927 0.741523i \(-0.265896\pi\)
−0.306715 + 0.951802i \(0.599230\pi\)
\(620\) 27.7951 1.11628
\(621\) 7.89025 0.316625
\(622\) 13.0731 + 7.54774i 0.524182 + 0.302637i
\(623\) 6.94384 + 29.3706i 0.278199 + 1.17671i
\(624\) 0.920592 0.728160i 0.0368532 0.0291497i
\(625\) 15.4164 + 26.7020i 0.616657 + 1.06808i
\(626\) −17.4781 + 10.0910i −0.698565 + 0.403317i
\(627\) 3.47954 + 6.02674i 0.138959 + 0.240685i
\(628\) 0.115974 0.200873i 0.00462787 0.00801571i
\(629\) 53.8550i 2.14734i
\(630\) −6.17056 + 1.45885i −0.245841 + 0.0581221i
\(631\) 24.3336 14.0490i 0.968704 0.559281i 0.0698630 0.997557i \(-0.477744\pi\)
0.898841 + 0.438275i \(0.144410\pi\)
\(632\) 3.11714 1.79968i 0.123993 0.0715874i
\(633\) 3.61505 0.143685
\(634\) 10.4401 + 18.0828i 0.414629 + 0.718159i
\(635\) 22.0475i 0.874928i
\(636\) −7.95501 −0.315437
\(637\) 14.4570 + 20.6880i 0.572809 + 0.819689i
\(638\) 8.28456 0.327989
\(639\) 7.48311i 0.296027i
\(640\) 7.57253 + 13.1160i 0.299331 + 0.518456i
\(641\) −28.6276 −1.13072 −0.565362 0.824843i \(-0.691263\pi\)
−0.565362 + 0.824843i \(0.691263\pi\)
\(642\) 14.1201 8.15222i 0.557274 0.321742i
\(643\) −7.81711 + 4.51321i −0.308277 + 0.177984i −0.646155 0.763206i \(-0.723624\pi\)
0.337878 + 0.941190i \(0.390291\pi\)
\(644\) −23.6077 + 5.58138i −0.930275 + 0.219937i
\(645\) 11.0600i 0.435489i
\(646\) 7.75472 13.4316i 0.305105 0.528458i
\(647\) 13.1024 + 22.6940i 0.515109 + 0.892195i 0.999846 + 0.0175353i \(0.00558194\pi\)
−0.484737 + 0.874660i \(0.661085\pi\)
\(648\) −2.50674 + 1.44726i −0.0984739 + 0.0568539i
\(649\) −2.87535 4.98025i −0.112867 0.195492i
\(650\) 2.25845 5.68762i 0.0885837 0.223087i
\(651\) −5.56151 23.5237i −0.217973 0.921966i
\(652\) −7.09700 4.09745i −0.277940 0.160469i
\(653\) 45.4789 1.77973 0.889864 0.456226i \(-0.150799\pi\)
0.889864 + 0.456226i \(0.150799\pi\)
\(654\) 17.0104 0.665160
\(655\) −37.4923 21.6462i −1.46495 0.845787i
\(656\) 1.29833 + 0.749591i 0.0506912 + 0.0292666i
\(657\) 10.8250 6.24982i 0.422324 0.243829i
\(658\) 2.94707 + 3.12716i 0.114889 + 0.121910i
\(659\) 10.1806 + 17.6334i 0.396581 + 0.686899i 0.993302 0.115550i \(-0.0368632\pi\)
−0.596720 + 0.802449i \(0.703530\pi\)
\(660\) −7.74693 −0.301549
\(661\) 34.7308 20.0518i 1.35087 0.779926i 0.362501 0.931984i \(-0.381923\pi\)
0.988372 + 0.152057i \(0.0485898\pi\)
\(662\) 14.6535 25.3807i 0.569526 0.986447i
\(663\) −17.5317 + 13.8670i −0.680875 + 0.538551i
\(664\) 6.07902 0.235912
\(665\) −18.4221 + 4.35538i −0.714377 + 0.168894i
\(666\) 3.97595 6.88655i 0.154065 0.266848i
\(667\) 14.0214 24.2858i 0.542912 0.940352i
\(668\) −1.81258 1.04649i −0.0701309 0.0404901i
\(669\) 3.55646i 0.137501i
\(670\) 1.28582 + 0.742368i 0.0496755 + 0.0286802i
\(671\) 31.5043i 1.21621i
\(672\) 10.5728 9.96387i 0.407853 0.384365i
\(673\) 10.2385 17.7336i 0.394666 0.683581i −0.598393 0.801203i \(-0.704194\pi\)
0.993058 + 0.117622i \(0.0375270\pi\)
\(674\) 4.57441i 0.176200i
\(675\) −0.927071 + 1.60573i −0.0356830 + 0.0618047i
\(676\) −14.4706 + 4.33746i −0.556560 + 0.166825i
\(677\) 18.6224 + 32.2549i 0.715717 + 1.23966i 0.962682 + 0.270634i \(0.0872332\pi\)
−0.246966 + 0.969024i \(0.579433\pi\)
\(678\) −5.73345 3.31021i −0.220192 0.127128i
\(679\) −2.95558 + 2.78537i −0.113425 + 0.106893i
\(680\) 23.4903 + 40.6864i 0.900811 + 1.56025i
\(681\) −6.75066 + 3.89750i −0.258686 + 0.149352i
\(682\) 21.2963i 0.815478i
\(683\) 5.92465i 0.226700i −0.993555 0.113350i \(-0.963842\pi\)
0.993555 0.113350i \(-0.0361582\pi\)
\(684\) −2.75029 + 1.58788i −0.105160 + 0.0607141i
\(685\) 2.51140 + 4.34988i 0.0959558 + 0.166200i
\(686\) −10.8759 13.0051i −0.415244 0.496535i
\(687\) −14.2182 8.20887i −0.542457 0.313188i
\(688\) 0.687634 + 1.19102i 0.0262158 + 0.0454071i
\(689\) −22.9401 9.10907i −0.873946 0.347028i
\(690\) 9.45467 16.3760i 0.359933 0.623423i
\(691\) 3.05713i 0.116299i −0.998308 0.0581493i \(-0.981480\pi\)
0.998308 0.0581493i \(-0.0185199\pi\)
\(692\) 6.92912 12.0016i 0.263405 0.456232i
\(693\) 1.55008 + 6.55643i 0.0588827 + 0.249058i
\(694\) 31.4366i 1.19332i
\(695\) 50.0166 + 28.8771i 1.89724 + 1.09537i
\(696\) 10.2875i 0.389946i
\(697\) −24.7253 14.2752i −0.936538 0.540711i
\(698\) 4.50064 7.79534i 0.170352 0.295058i
\(699\) 3.78863 6.56210i 0.143299 0.248201i
\(700\) 1.63795 5.46016i 0.0619086 0.206375i
\(701\) −2.81064 −0.106156 −0.0530782 0.998590i \(-0.516903\pi\)
−0.0530782 + 0.998590i \(0.516903\pi\)
\(702\) −3.26558 + 0.478894i −0.123251 + 0.0180747i
\(703\) 11.8701 20.5596i 0.447690 0.775422i
\(704\) −12.5205 + 7.22872i −0.471885 + 0.272443i
\(705\) 4.64500 0.174941
\(706\) −7.02227 12.1629i −0.264287 0.457758i
\(707\) −0.915906 0.971877i −0.0344462 0.0365512i
\(708\) 2.27273 1.31216i 0.0854143 0.0493139i
\(709\) −33.2799 19.2141i −1.24985 0.721602i −0.278772 0.960357i \(-0.589927\pi\)
−0.971080 + 0.238755i \(0.923261\pi\)
\(710\) 15.5310 + 8.96681i 0.582867 + 0.336518i
\(711\) −1.24350 −0.0466351
\(712\) 33.0181 1.23740
\(713\) 62.4293 + 36.0436i 2.33799 + 1.34984i
\(714\) 10.9271 10.2978i 0.408937 0.385386i
\(715\) −22.3400 8.87081i −0.835470 0.331749i
\(716\) 9.49395 + 16.4440i 0.354805 + 0.614541i
\(717\) 4.05866 2.34327i 0.151574 0.0875111i
\(718\) −13.3025 23.0406i −0.496444 0.859867i
\(719\) 13.2943 23.0263i 0.495792 0.858737i −0.504196 0.863589i \(-0.668211\pi\)
0.999988 + 0.00485212i \(0.00154448\pi\)
\(720\) 0.852282i 0.0317627i
\(721\) −9.68668 10.2786i −0.360751 0.382797i
\(722\) −9.14150 + 5.27785i −0.340211 + 0.196421i
\(723\) −9.28664 + 5.36164i −0.345374 + 0.199402i
\(724\) 19.4931 0.724455
\(725\) 3.29492 + 5.70697i 0.122370 + 0.211951i
\(726\) 4.13374i 0.153417i
\(727\) −26.5203 −0.983583 −0.491792 0.870713i \(-0.663658\pi\)
−0.491792 + 0.870713i \(0.663658\pi\)
\(728\) 25.6651 10.1847i 0.951212 0.377469i
\(729\) 1.00000 0.0370370
\(730\) 29.9560i 1.10872i
\(731\) −13.0953 22.6817i −0.484346 0.838912i
\(732\) −14.3769 −0.531386
\(733\) −22.0215 + 12.7141i −0.813384 + 0.469607i −0.848130 0.529789i \(-0.822271\pi\)
0.0347458 + 0.999396i \(0.488938\pi\)
\(734\) −14.5091 + 8.37684i −0.535541 + 0.309195i
\(735\) −18.2941 1.08576i −0.674788 0.0400490i
\(736\) 43.3258i 1.59701i
\(737\) 0.788791 1.36623i 0.0290555 0.0503256i
\(738\) −2.10779 3.65079i −0.0775887 0.134388i
\(739\) −25.3568 + 14.6397i −0.932763 + 0.538531i −0.887684 0.460452i \(-0.847687\pi\)
−0.0450789 + 0.998983i \(0.514354\pi\)
\(740\) 13.2140 + 22.8873i 0.485755 + 0.841352i
\(741\) −9.74932 + 1.42973i −0.358150 + 0.0525223i
\(742\) 15.8805 + 4.76384i 0.582990 + 0.174886i
\(743\) 11.9142 + 6.87868i 0.437090 + 0.252354i 0.702363 0.711819i \(-0.252129\pi\)
−0.265272 + 0.964174i \(0.585462\pi\)
\(744\) −26.4451 −0.969523
\(745\) 39.2560 1.43823
\(746\) 10.1992 + 5.88850i 0.373419 + 0.215593i
\(747\) −1.81881 1.05009i −0.0665466 0.0384207i
\(748\) 15.8872 9.17248i 0.580894 0.335379i
\(749\) 45.8601 10.8423i 1.67569 0.396170i
\(750\) −3.76960 6.52913i −0.137646 0.238410i
\(751\) 31.4688 1.14831 0.574156 0.818746i \(-0.305330\pi\)
0.574156 + 0.818746i \(0.305330\pi\)
\(752\) 0.500203 0.288792i 0.0182405 0.0105312i
\(753\) −5.93135 + 10.2734i −0.216151 + 0.374384i
\(754\) −4.32911 + 10.9023i −0.157657 + 0.397040i
\(755\) −23.6401 −0.860351
\(756\) −2.99201 + 0.707377i −0.108818 + 0.0257270i
\(757\) −20.2956 + 35.1531i −0.737657 + 1.27766i 0.215890 + 0.976418i \(0.430735\pi\)
−0.953548 + 0.301243i \(0.902599\pi\)
\(758\) 12.0541 20.8784i 0.437825 0.758336i
\(759\) −17.4000 10.0459i −0.631581 0.364644i
\(760\) 20.7099i 0.751226i
\(761\) −35.0760 20.2511i −1.27150 0.734103i −0.296232 0.955116i \(-0.595730\pi\)
−0.975271 + 0.221013i \(0.929064\pi\)
\(762\) 7.70889i 0.279264i
\(763\) 47.0916 + 14.1266i 1.70483 + 0.511418i
\(764\) −4.34833 + 7.53154i −0.157317 + 0.272481i
\(765\) 16.2308i 0.586826i
\(766\) −6.59291 + 11.4193i −0.238211 + 0.412594i
\(767\) 8.05644 1.18147i 0.290901 0.0426603i
\(768\) −8.32531 14.4199i −0.300414 0.520332i
\(769\) 25.2026 + 14.5507i 0.908828 + 0.524712i 0.880054 0.474874i \(-0.157506\pi\)
0.0287743 + 0.999586i \(0.490840\pi\)
\(770\) 15.4651 + 4.63924i 0.557323 + 0.167187i
\(771\) 4.67378 + 8.09523i 0.168322 + 0.291542i
\(772\) −11.7606 + 6.78998i −0.423273 + 0.244377i
\(773\) 10.3478i 0.372186i −0.982532 0.186093i \(-0.940417\pi\)
0.982532 0.186093i \(-0.0595825\pi\)
\(774\) 3.86714i 0.139001i
\(775\) −14.6704 + 8.46993i −0.526975 + 0.304249i
\(776\) 2.22156 + 3.84785i 0.0797493 + 0.138130i
\(777\) 16.7261 15.7628i 0.600045 0.565488i
\(778\) −5.24632 3.02897i −0.188090 0.108594i
\(779\) −6.29275 10.8994i −0.225461 0.390510i
\(780\) 4.04818 10.1948i 0.144948 0.365033i
\(781\) 9.52754 16.5022i 0.340922 0.590495i
\(782\) 44.7779i 1.60125i
\(783\) 1.77706 3.07796i 0.0635069 0.109997i
\(784\) −2.03753 + 1.02047i −0.0727689 + 0.0364455i
\(785\) 0.522568i 0.0186513i
\(786\) 13.1092 + 7.56858i 0.467588 + 0.269962i
\(787\) 29.1016i 1.03736i −0.854968 0.518680i \(-0.826423\pi\)
0.854968 0.518680i \(-0.173577\pi\)
\(788\) 0.451939 + 0.260927i 0.0160997 + 0.00929514i
\(789\) 0.471710 0.817026i 0.0167933 0.0290869i
\(790\) −1.49006 + 2.58086i −0.0530139 + 0.0918228i
\(791\) −13.1235 13.9254i −0.466617 0.495132i
\(792\) 7.37066 0.261905
\(793\) −41.4590 16.4626i −1.47225 0.584605i
\(794\) −10.3603 + 17.9446i −0.367674 + 0.636830i
\(795\) 15.5211 8.96112i 0.550477 0.317818i
\(796\) −11.4152 −0.404600
\(797\) −14.9812 25.9482i −0.530661 0.919131i −0.999360 0.0357733i \(-0.988611\pi\)
0.468699 0.883358i \(-0.344723\pi\)
\(798\) 6.44126 1.52285i 0.228018 0.0539085i
\(799\) −9.52584 + 5.49975i −0.337000 + 0.194567i
\(800\) −8.81718 5.09060i −0.311734 0.179980i
\(801\) −9.87880 5.70353i −0.349050 0.201524i
\(802\) 0.412443 0.0145639
\(803\) −31.8292 −1.12323
\(804\) 0.623475 + 0.359963i 0.0219883 + 0.0126949i
\(805\) 39.7741 37.4834i 1.40185 1.32112i
\(806\) −28.0256 11.1284i −0.987159 0.391982i
\(807\) −3.79153 6.56712i −0.133468 0.231174i
\(808\) −1.26528 + 0.730511i −0.0445124 + 0.0256993i
\(809\) 8.03836 + 13.9228i 0.282614 + 0.489501i 0.972028 0.234866i \(-0.0754653\pi\)
−0.689414 + 0.724367i \(0.742132\pi\)
\(810\) 1.19827 2.07547i 0.0421030 0.0729246i
\(811\) 41.5793i 1.46005i 0.683423 + 0.730023i \(0.260491\pi\)
−0.683423 + 0.730023i \(0.739509\pi\)
\(812\) −3.13971 + 10.4663i −0.110182 + 0.367296i
\(813\) −17.8317 + 10.2951i −0.625384 + 0.361066i
\(814\) −17.5360 + 10.1244i −0.614636 + 0.354860i
\(815\) 18.4627 0.646721
\(816\) −1.00911 1.74784i −0.0353261 0.0611866i
\(817\) 11.5453i 0.403917i
\(818\) 31.5460 1.10298
\(819\) −9.43814 1.38619i −0.329795 0.0484375i
\(820\) 14.0103 0.489262
\(821\) 4.07383i 0.142178i −0.997470 0.0710888i \(-0.977353\pi\)
0.997470 0.0710888i \(-0.0226474\pi\)
\(822\) −0.878110 1.52093i −0.0306276 0.0530486i
\(823\) 42.6371 1.48624 0.743118 0.669160i \(-0.233346\pi\)
0.743118 + 0.669160i \(0.233346\pi\)
\(824\) −13.3817 + 7.72593i −0.466174 + 0.269146i
\(825\) 4.08886 2.36070i 0.142356 0.0821892i
\(826\) −5.32279 + 1.25842i −0.185204 + 0.0437862i
\(827\) 21.7244i 0.755431i 0.925922 + 0.377716i \(0.123290\pi\)
−0.925922 + 0.377716i \(0.876710\pi\)
\(828\) 4.58443 7.94047i 0.159320 0.275950i
\(829\) −0.461472 0.799293i −0.0160276 0.0277606i 0.857900 0.513816i \(-0.171769\pi\)
−0.873928 + 0.486055i \(0.838435\pi\)
\(830\) −4.35885 + 2.51658i −0.151298 + 0.0873519i
\(831\) 10.2128 + 17.6891i 0.354278 + 0.613628i
\(832\) −2.97025 20.2542i −0.102975 0.702187i
\(833\) 38.8026 19.4338i 1.34443 0.673342i
\(834\) −17.4883 10.0969i −0.605569 0.349626i
\(835\) 4.71540 0.163183
\(836\) 8.08679 0.279688
\(837\) 7.91220 + 4.56811i 0.273486 + 0.157897i
\(838\) −0.309209 0.178522i −0.0106814 0.00616693i
\(839\) 10.4845 6.05325i 0.361966 0.208981i −0.307977 0.951394i \(-0.599652\pi\)
0.669943 + 0.742413i \(0.266319\pi\)
\(840\) −5.76085 + 19.2040i −0.198768 + 0.662602i
\(841\) 8.18413 + 14.1753i 0.282211 + 0.488804i
\(842\) 22.4724 0.774451
\(843\) 9.41393 5.43514i 0.324233 0.187196i
\(844\) 2.10043 3.63805i 0.0722998 0.125227i
\(845\) 23.3477 24.7636i 0.803184 0.851894i
\(846\) −1.62412 −0.0558384
\(847\) −3.43294 + 11.4438i −0.117957 + 0.393215i
\(848\) 1.11428 1.92998i 0.0382644 0.0662758i
\(849\) 1.91077 3.30955i 0.0655775 0.113583i
\(850\) −9.11269 5.26121i −0.312563 0.180458i
\(851\) 68.5414i 2.34957i
\(852\) 7.53074 + 4.34787i 0.257999 + 0.148956i
\(853\) 25.9127i 0.887233i −0.896217 0.443616i \(-0.853695\pi\)
0.896217 0.443616i \(-0.146305\pi\)
\(854\) 28.7004 + 8.60959i 0.982107 + 0.294614i
\(855\) 3.57742 6.19627i 0.122345 0.211908i
\(856\) 51.5554i 1.76213i
\(857\) −7.12117 + 12.3342i −0.243255 + 0.421329i −0.961639 0.274317i \(-0.911548\pi\)
0.718385 + 0.695646i \(0.244882\pi\)
\(858\) 7.81117 + 3.10167i 0.266669 + 0.105889i
\(859\) −7.79426 13.5001i −0.265937 0.460616i 0.701872 0.712303i \(-0.252348\pi\)
−0.967809 + 0.251687i \(0.919015\pi\)
\(860\) 11.1304 + 6.42616i 0.379545 + 0.219130i
\(861\) −2.80333 11.8573i −0.0955371 0.404096i
\(862\) 0.519711 + 0.900165i 0.0177014 + 0.0306597i
\(863\) 18.3943 10.6200i 0.626150 0.361508i −0.153109 0.988209i \(-0.548929\pi\)
0.779260 + 0.626701i \(0.215595\pi\)
\(864\) 5.49106i 0.186810i
\(865\) 31.2219i 1.06158i
\(866\) 16.0506 9.26683i 0.545422 0.314900i
\(867\) 10.7175 + 18.5633i 0.363986 + 0.630443i
\(868\) −26.9048 8.07094i −0.913208 0.273945i
\(869\) 2.74225 + 1.58324i 0.0930244 + 0.0537077i
\(870\) −4.25880 7.37646i −0.144387 0.250085i
\(871\) 1.38575 + 1.75196i 0.0469542 + 0.0593629i
\(872\) 26.8939 46.5816i 0.910742 1.57745i
\(873\) 1.53501i 0.0519521i
\(874\) −9.86945 + 17.0944i −0.333839 + 0.578227i
\(875\) −5.01351 21.2058i −0.169488 0.716886i
\(876\) 14.5252i 0.490761i
\(877\) 26.0572 + 15.0441i 0.879889 + 0.508004i 0.870622 0.491953i \(-0.163717\pi\)
0.00926688 + 0.999957i \(0.497050\pi\)
\(878\) 25.6095i 0.864280i
\(879\) 15.6392 + 9.02929i 0.527497 + 0.304550i
\(880\) 1.08513 1.87950i 0.0365797 0.0633579i
\(881\) 22.2785 38.5876i 0.750583 1.30005i −0.196957 0.980412i \(-0.563106\pi\)
0.947540 0.319636i \(-0.103561\pi\)
\(882\) 6.39652 + 0.379636i 0.215382 + 0.0127830i
\(883\) −1.96438 −0.0661066 −0.0330533 0.999454i \(-0.510523\pi\)
−0.0330533 + 0.999454i \(0.510523\pi\)
\(884\) 3.76893 + 25.7004i 0.126763 + 0.864398i
\(885\) −2.95623 + 5.12034i −0.0993726 + 0.172118i
\(886\) 17.0779 9.85991i 0.573742 0.331250i
\(887\) 4.61734 0.155035 0.0775175 0.996991i \(-0.475301\pi\)
0.0775175 + 0.996991i \(0.475301\pi\)
\(888\) −12.5722 21.7756i −0.421894 0.730742i
\(889\) 6.40199 21.3413i 0.214716 0.715764i
\(890\) −23.6750 + 13.6688i −0.793588 + 0.458178i
\(891\) −2.20526 1.27321i −0.0738789 0.0426540i
\(892\) 3.57909 + 2.06639i 0.119837 + 0.0691879i
\(893\) −4.84878 −0.162258
\(894\) −13.7258 −0.459060
\(895\) −37.0475 21.3894i −1.23836 0.714969i
\(896\) −3.52144 14.8947i −0.117643 0.497598i
\(897\) 22.3127 17.6486i 0.744998 0.589270i
\(898\) 1.32219 + 2.29011i 0.0441222 + 0.0764219i
\(899\) 28.1209 16.2356i 0.937884 0.541488i
\(900\) 1.07730 + 1.86594i 0.0359101 + 0.0621981i
\(901\) −21.2202 + 36.7545i −0.706948 + 1.22447i
\(902\) 10.7346i 0.357423i
\(903\) 3.21154 10.7058i 0.106873 0.356266i
\(904\) −18.1295 + 10.4671i −0.602977 + 0.348129i
\(905\) −38.0332 + 21.9585i −1.26427 + 0.729925i
\(906\) 8.26574 0.274611
\(907\) 10.3823 + 17.9827i 0.344740 + 0.597107i 0.985306 0.170796i \(-0.0546338\pi\)
−0.640567 + 0.767903i \(0.721300\pi\)
\(908\) 9.05817i 0.300606i
\(909\) 0.504753 0.0167416
\(910\) −14.1865 + 17.9275i −0.470277 + 0.594292i
\(911\) −49.6547 −1.64513 −0.822567 0.568669i \(-0.807459\pi\)
−0.822567 + 0.568669i \(0.807459\pi\)
\(912\) 0.889672i 0.0294600i
\(913\) 2.67396 + 4.63143i 0.0884950 + 0.153278i
\(914\) −29.9046 −0.989156
\(915\) 28.0510 16.1952i 0.927336 0.535398i
\(916\) −16.5222 + 9.53911i −0.545910 + 0.315181i
\(917\) 30.0059 + 31.8396i 0.990883 + 1.05144i
\(918\) 5.67509i 0.187306i
\(919\) −27.5731 + 47.7580i −0.909553 + 1.57539i −0.0948669 + 0.995490i \(0.530243\pi\)
−0.814686 + 0.579902i \(0.803091\pi\)
\(920\) −29.8961 51.7817i −0.985647 1.70719i
\(921\) 7.69716 4.44396i 0.253630 0.146433i
\(922\) 17.3338 + 30.0230i 0.570858 + 0.988756i
\(923\) 16.7379 + 21.1613i 0.550936 + 0.696534i
\(924\) 7.49879 + 2.24950i 0.246692 + 0.0740031i
\(925\) −13.9488 8.05332i −0.458632 0.264792i
\(926\) 19.1259 0.628516
\(927\) 5.33830 0.175333
\(928\) 16.9012 + 9.75793i 0.554810 + 0.320320i
\(929\) −3.77027 2.17677i −0.123699 0.0714174i 0.436874 0.899523i \(-0.356086\pi\)
−0.560573 + 0.828105i \(0.689419\pi\)
\(930\) 18.9620 10.9477i 0.621787 0.358989i
\(931\) 19.0967 + 1.13340i 0.625868 + 0.0371456i
\(932\) −4.40258 7.62549i −0.144211 0.249781i
\(933\) −16.4907 −0.539880
\(934\) −17.2596 + 9.96482i −0.564750 + 0.326059i
\(935\) −20.6652 + 35.7931i −0.675823 + 1.17056i
\(936\) −3.85155 + 9.69966i −0.125892 + 0.317043i
\(937\) 0.712633 0.0232807 0.0116404 0.999932i \(-0.496295\pi\)
0.0116404 + 0.999932i \(0.496295\pi\)
\(938\) −1.02907 1.09196i −0.0336003 0.0356536i
\(939\) 11.0236 19.0935i 0.359742 0.623092i
\(940\) 2.69886 4.67456i 0.0880271 0.152467i
\(941\) −10.1930 5.88493i −0.332282 0.191843i 0.324572 0.945861i \(-0.394780\pi\)
−0.656854 + 0.754018i \(0.728113\pi\)
\(942\) 0.182716i 0.00595320i
\(943\) 31.4680 + 18.1681i 1.02474 + 0.591633i
\(944\) 0.735188i 0.0239283i
\(945\) 5.04091 4.75060i 0.163981 0.154537i
\(946\) −4.92366 + 8.52803i −0.160082 + 0.277270i
\(947\) 30.7176i 0.998187i −0.866548 0.499093i \(-0.833666\pi\)
0.866548 0.499093i \(-0.166334\pi\)
\(948\) −0.722507 + 1.25142i −0.0234659 + 0.0406442i
\(949\) 16.6324 41.8867i 0.539911 1.35970i
\(950\) −2.31924 4.01704i −0.0752460 0.130330i
\(951\) −19.7541 11.4050i −0.640569 0.369833i
\(952\) −10.9236 46.2041i −0.354037 1.49748i
\(953\) −13.0794 22.6542i −0.423684 0.733843i 0.572612 0.819826i \(-0.305930\pi\)
−0.996297 + 0.0859835i \(0.972597\pi\)
\(954\) −5.42695 + 3.13325i −0.175704 + 0.101443i
\(955\) 19.5932i 0.634020i
\(956\) 5.44599i 0.176136i
\(957\) −7.83774 + 4.52512i −0.253358 + 0.146276i
\(958\) 4.98883 + 8.64090i 0.161182 + 0.279175i
\(959\) −1.16787 4.93979i −0.0377126 0.159514i
\(960\) 12.8727 + 7.43207i 0.415465 + 0.239869i
\(961\) 26.2353 + 45.4409i 0.846300 + 1.46583i
\(962\) −4.16007 28.3676i −0.134126 0.914608i
\(963\) −8.90567 + 15.4251i −0.286981 + 0.497066i
\(964\) 12.4610i 0.401342i
\(965\) 15.2975 26.4961i 0.492444 0.852938i
\(966\) −13.9070 + 13.1061i −0.447449 + 0.421680i
\(967\) 2.99020i 0.0961582i −0.998844 0.0480791i \(-0.984690\pi\)
0.998844 0.0480791i \(-0.0153100\pi\)
\(968\) 11.3199 + 6.53554i 0.363835 + 0.210060i
\(969\) 16.9429i 0.544283i
\(970\) −3.18586 1.83936i −0.102292 0.0590582i
\(971\) 9.27532 16.0653i 0.297659 0.515561i −0.677941 0.735116i \(-0.737127\pi\)
0.975600 + 0.219556i \(0.0704608\pi\)
\(972\) 0.581025 1.00636i 0.0186364 0.0322792i
\(973\) −40.0294 42.4756i −1.28328 1.36171i
\(974\) −5.63160 −0.180448
\(975\) 0.970003 + 6.61446i 0.0310649 + 0.211832i
\(976\) 2.01380 3.48801i 0.0644603 0.111649i
\(977\) 3.31539 1.91414i 0.106069 0.0612387i −0.446027 0.895019i \(-0.647162\pi\)
0.552096 + 0.833781i \(0.313828\pi\)
\(978\) −6.45548 −0.206424
\(979\) 14.5235 + 25.1555i 0.464174 + 0.803973i
\(980\) −11.7220 + 17.7797i −0.374446 + 0.567951i
\(981\) −16.0930 + 9.29129i −0.513809 + 0.296648i
\(982\) −8.56201 4.94328i −0.273225 0.157746i
\(983\) −27.0572 15.6215i −0.862992 0.498248i 0.00202132 0.999998i \(-0.499357\pi\)
−0.865013 + 0.501749i \(0.832690\pi\)
\(984\) −13.3299 −0.424940
\(985\) −1.17571 −0.0374613
\(986\) 17.4677 + 10.0850i 0.556284 + 0.321171i
\(987\) −4.49621 1.34878i −0.143116 0.0429322i
\(988\) −4.22577 + 10.6421i −0.134440 + 0.338570i
\(989\) 16.6664 + 28.8670i 0.529960 + 0.917918i
\(990\) −5.28500 + 3.05130i −0.167968 + 0.0969765i
\(991\) −2.96796 5.14066i −0.0942805 0.163299i 0.815028 0.579422i \(-0.196722\pi\)
−0.909308 + 0.416124i \(0.863388\pi\)
\(992\) −25.0838 + 43.4464i −0.796410 + 1.37942i
\(993\) 32.0157i 1.01599i
\(994\) −12.4298 13.1894i −0.394249 0.418341i
\(995\) 22.2723 12.8589i 0.706079 0.407655i
\(996\) −2.11354 + 1.22025i −0.0669702 + 0.0386652i
\(997\) −7.84640 −0.248498 −0.124249 0.992251i \(-0.539652\pi\)
−0.124249 + 0.992251i \(0.539652\pi\)
\(998\) 0.982678 + 1.70205i 0.0311061 + 0.0538774i
\(999\) 8.68684i 0.274840i
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 273.2.t.d.4.4 20
3.2 odd 2 819.2.bm.g.550.7 20
7.2 even 3 273.2.bl.d.121.4 yes 20
13.10 even 6 273.2.bl.d.88.4 yes 20
21.2 odd 6 819.2.do.g.667.7 20
39.23 odd 6 819.2.do.g.361.7 20
91.23 even 6 inner 273.2.t.d.205.7 yes 20
273.23 odd 6 819.2.bm.g.478.4 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.t.d.4.4 20 1.1 even 1 trivial
273.2.t.d.205.7 yes 20 91.23 even 6 inner
273.2.bl.d.88.4 yes 20 13.10 even 6
273.2.bl.d.121.4 yes 20 7.2 even 3
819.2.bm.g.478.4 20 273.23 odd 6
819.2.bm.g.550.7 20 3.2 odd 2
819.2.do.g.361.7 20 39.23 odd 6
819.2.do.g.667.7 20 21.2 odd 6