Properties

Label 93.2.f.b.64.2
Level $93$
Weight $2$
Character 93.64
Analytic conductor $0.743$
Analytic rank $0$
Dimension $16$
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] = [93,2,Mod(4,93)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(93, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("93.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 93 = 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 93.f (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.742608738798\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 13 x^{14} - 28 x^{13} + 90 x^{12} - 119 x^{11} + 382 x^{10} - 356 x^{9} + 1869 x^{8} - 2812 x^{7} + 5846 x^{6} - 4987 x^{5} + 4006 x^{4} - 1014 x^{3} + 2493 x^{2} + \cdots + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 64.2
Root \(0.968675 + 0.703784i\) of defining polynomial
Character \(\chi\) \(=\) 93.64
Dual form 93.2.f.b.16.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.968675 - 0.703784i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.175014 - 0.538638i) q^{4} -2.70381 q^{5} +1.19735 q^{6} +(-1.33552 - 4.11032i) q^{7} +(-0.949555 + 2.92243i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.968675 - 0.703784i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.175014 - 0.538638i) q^{4} -2.70381 q^{5} +1.19735 q^{6} +(-1.33552 - 4.11032i) q^{7} +(-0.949555 + 2.92243i) q^{8} +(0.309017 - 0.951057i) q^{9} +(2.61912 + 1.90290i) q^{10} +(-0.299148 - 0.920682i) q^{11} +(0.458193 + 0.332897i) q^{12} +(-2.55039 + 1.85297i) q^{13} +(-1.59909 + 4.92149i) q^{14} +(2.18743 - 1.58926i) q^{15} +(2.06018 - 1.49681i) q^{16} +(1.52318 - 4.68787i) q^{17} +(-0.968675 + 0.703784i) q^{18} +(4.82213 + 3.50348i) q^{19} +(0.473206 + 1.45638i) q^{20} +(3.49645 + 2.54032i) q^{21} +(-0.358184 + 1.10238i) q^{22} +(1.05276 - 3.24006i) q^{23} +(-0.949555 - 2.92243i) q^{24} +2.31061 q^{25} +3.77458 q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.98024 + 1.43873i) q^{28} +(-4.12478 - 2.99683i) q^{29} -3.23741 q^{30} +(5.08903 - 2.25872i) q^{31} +3.09657 q^{32} +(0.783179 + 0.569013i) q^{33} +(-4.77471 + 3.46903i) q^{34} +(3.61101 + 11.1135i) q^{35} -0.566358 q^{36} -8.13184 q^{37} +(-2.20538 - 6.78747i) q^{38} +(0.974162 - 2.99816i) q^{39} +(2.56742 - 7.90170i) q^{40} +(-2.61912 - 1.90290i) q^{41} +(-1.59909 - 4.92149i) q^{42} +(-4.94934 - 3.59590i) q^{43} +(-0.443559 + 0.322265i) q^{44} +(-0.835524 + 2.57148i) q^{45} +(-3.30008 + 2.39765i) q^{46} +(-6.41291 + 4.65925i) q^{47} +(-0.786919 + 2.42189i) q^{48} +(-9.44800 + 6.86437i) q^{49} +(-2.23823 - 1.62617i) q^{50} +(1.52318 + 4.68787i) q^{51} +(1.44443 + 1.04944i) q^{52} +(1.66138 - 5.11322i) q^{53} +(0.370001 - 1.13875i) q^{54} +(0.808840 + 2.48935i) q^{55} +13.2803 q^{56} -5.96048 q^{57} +(1.88645 + 5.80591i) q^{58} +(11.0224 - 8.00828i) q^{59} +(-1.23887 - 0.900090i) q^{60} +1.99991 q^{61} +(-6.51926 - 1.39361i) q^{62} -4.32185 q^{63} +(-7.11993 - 5.17293i) q^{64} +(6.89578 - 5.01007i) q^{65} +(-0.358184 - 1.10238i) q^{66} +7.01351 q^{67} -2.79164 q^{68} +(1.05276 + 3.24006i) q^{69} +(4.32364 - 13.3068i) q^{70} +(-1.95020 + 6.00211i) q^{71} +(2.48597 + 1.80616i) q^{72} +(0.0487339 + 0.149988i) q^{73} +(7.87711 + 5.72306i) q^{74} +(-1.86932 + 1.35814i) q^{75} +(1.04317 - 3.21054i) q^{76} +(-3.38478 + 2.45919i) q^{77} +(-3.05370 + 2.21865i) q^{78} +(5.17389 - 15.9236i) q^{79} +(-5.57035 + 4.04709i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.19784 + 3.68658i) q^{82} +(5.63973 + 4.09750i) q^{83} +(0.756384 - 2.32791i) q^{84} +(-4.11840 + 12.6751i) q^{85} +(2.26356 + 6.96652i) q^{86} +5.09851 q^{87} +2.97468 q^{88} +(2.78370 + 8.56735i) q^{89} +(2.61912 - 1.90290i) q^{90} +(11.0224 + 8.00824i) q^{91} -1.92947 q^{92} +(-2.78947 + 4.81860i) q^{93} +9.49114 q^{94} +(-13.0381 - 9.47276i) q^{95} +(-2.50518 + 1.82012i) q^{96} +(0.516238 + 1.58882i) q^{97} +13.9831 q^{98} -0.968062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 3 q^{2} - 4 q^{3} - 9 q^{4} + 6 q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} - 4 q^{9} - 3 q^{10} + 10 q^{11} - 4 q^{12} - 3 q^{13} - 4 q^{14} - 4 q^{15} - 17 q^{16} - q^{17} - 3 q^{18} - 4 q^{19} + 7 q^{20} + 8 q^{21} + 10 q^{22} + 7 q^{23} - 2 q^{24} + 30 q^{25} - 16 q^{26} - 4 q^{27} + 9 q^{28} - 2 q^{29} + 12 q^{30} - 13 q^{31} + 108 q^{32} - 5 q^{33} - 4 q^{34} - 33 q^{35} + 26 q^{36} - 28 q^{37} - 62 q^{38} + 7 q^{39} - 27 q^{40} + 3 q^{41} - 4 q^{42} - 13 q^{43} - 64 q^{44} + q^{45} - q^{46} - 20 q^{47} - 2 q^{48} + q^{49} - 44 q^{50} - q^{51} + 88 q^{52} - 4 q^{53} + 2 q^{54} - 8 q^{55} + 104 q^{56} - 14 q^{57} - 31 q^{58} + 49 q^{59} - 8 q^{60} - 13 q^{62} - 2 q^{63} - 26 q^{64} - q^{65} + 10 q^{66} + 60 q^{67} - 30 q^{68} + 7 q^{69} + 85 q^{70} + 23 q^{71} - 7 q^{72} - 17 q^{73} + 70 q^{74} - 5 q^{75} + 7 q^{76} + 2 q^{77} + 19 q^{78} - 13 q^{79} - 94 q^{80} - 4 q^{81} - 9 q^{82} - 49 q^{83} - 6 q^{84} - 4 q^{85} + 24 q^{86} - 2 q^{87} - 32 q^{88} + 3 q^{89} - 3 q^{90} - 2 q^{91} - 70 q^{92} + 17 q^{93} + 74 q^{94} - 10 q^{95} - 32 q^{96} + 3 q^{97} - 82 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/93\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(34\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.968675 0.703784i −0.684957 0.497650i 0.190042 0.981776i \(-0.439138\pi\)
−0.874998 + 0.484126i \(0.839138\pi\)
\(3\) −0.809017 + 0.587785i −0.467086 + 0.339358i
\(4\) −0.175014 0.538638i −0.0875071 0.269319i
\(5\) −2.70381 −1.20918 −0.604591 0.796536i \(-0.706663\pi\)
−0.604591 + 0.796536i \(0.706663\pi\)
\(6\) 1.19735 0.488815
\(7\) −1.33552 4.11032i −0.504781 1.55356i −0.801139 0.598479i \(-0.795772\pi\)
0.296358 0.955077i \(-0.404228\pi\)
\(8\) −0.949555 + 2.92243i −0.335718 + 1.03323i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 2.61912 + 1.90290i 0.828237 + 0.601750i
\(11\) −0.299148 0.920682i −0.0901964 0.277596i 0.895776 0.444506i \(-0.146621\pi\)
−0.985972 + 0.166910i \(0.946621\pi\)
\(12\) 0.458193 + 0.332897i 0.132269 + 0.0960990i
\(13\) −2.55039 + 1.85297i −0.707351 + 0.513920i −0.882318 0.470654i \(-0.844018\pi\)
0.174967 + 0.984574i \(0.444018\pi\)
\(14\) −1.59909 + 4.92149i −0.427374 + 1.31532i
\(15\) 2.18743 1.58926i 0.564792 0.410346i
\(16\) 2.06018 1.49681i 0.515045 0.374202i
\(17\) 1.52318 4.68787i 0.369426 1.13697i −0.577738 0.816223i \(-0.696064\pi\)
0.947163 0.320752i \(-0.103936\pi\)
\(18\) −0.968675 + 0.703784i −0.228319 + 0.165883i
\(19\) 4.82213 + 3.50348i 1.10627 + 0.803754i 0.982073 0.188503i \(-0.0603636\pi\)
0.124200 + 0.992257i \(0.460364\pi\)
\(20\) 0.473206 + 1.45638i 0.105812 + 0.325656i
\(21\) 3.49645 + 2.54032i 0.762988 + 0.554343i
\(22\) −0.358184 + 1.10238i −0.0763651 + 0.235027i
\(23\) 1.05276 3.24006i 0.219515 0.675599i −0.779287 0.626668i \(-0.784418\pi\)
0.998802 0.0489316i \(-0.0155816\pi\)
\(24\) −0.949555 2.92243i −0.193827 0.596538i
\(25\) 2.31061 0.462122
\(26\) 3.77458 0.740257
\(27\) 0.309017 + 0.951057i 0.0594703 + 0.183031i
\(28\) −1.98024 + 1.43873i −0.374230 + 0.271894i
\(29\) −4.12478 2.99683i −0.765953 0.556497i 0.134778 0.990876i \(-0.456968\pi\)
−0.900730 + 0.434379i \(0.856968\pi\)
\(30\) −3.23741 −0.591067
\(31\) 5.08903 2.25872i 0.914016 0.405678i
\(32\) 3.09657 0.547402
\(33\) 0.783179 + 0.569013i 0.136334 + 0.0990524i
\(34\) −4.77471 + 3.46903i −0.818856 + 0.594934i
\(35\) 3.61101 + 11.1135i 0.610372 + 1.87853i
\(36\) −0.566358 −0.0943929
\(37\) −8.13184 −1.33687 −0.668434 0.743772i \(-0.733035\pi\)
−0.668434 + 0.743772i \(0.733035\pi\)
\(38\) −2.20538 6.78747i −0.357760 1.10107i
\(39\) 0.974162 2.99816i 0.155991 0.480090i
\(40\) 2.56742 7.90170i 0.405945 1.24937i
\(41\) −2.61912 1.90290i −0.409037 0.297183i 0.364175 0.931331i \(-0.381351\pi\)
−0.773212 + 0.634148i \(0.781351\pi\)
\(42\) −1.59909 4.92149i −0.246745 0.759402i
\(43\) −4.94934 3.59590i −0.754767 0.548370i 0.142534 0.989790i \(-0.454475\pi\)
−0.897301 + 0.441420i \(0.854475\pi\)
\(44\) −0.443559 + 0.322265i −0.0668691 + 0.0485832i
\(45\) −0.835524 + 2.57148i −0.124553 + 0.383334i
\(46\) −3.30008 + 2.39765i −0.486571 + 0.353514i
\(47\) −6.41291 + 4.65925i −0.935420 + 0.679622i −0.947314 0.320307i \(-0.896214\pi\)
0.0118942 + 0.999929i \(0.496214\pi\)
\(48\) −0.786919 + 2.42189i −0.113582 + 0.349569i
\(49\) −9.44800 + 6.86437i −1.34971 + 0.980625i
\(50\) −2.23823 1.62617i −0.316533 0.229975i
\(51\) 1.52318 + 4.68787i 0.213288 + 0.656433i
\(52\) 1.44443 + 1.04944i 0.200307 + 0.145531i
\(53\) 1.66138 5.11322i 0.228209 0.702354i −0.769741 0.638356i \(-0.779615\pi\)
0.997950 0.0639983i \(-0.0203852\pi\)
\(54\) 0.370001 1.13875i 0.0503507 0.154964i
\(55\) 0.808840 + 2.48935i 0.109064 + 0.335664i
\(56\) 13.2803 1.77465
\(57\) −5.96048 −0.789485
\(58\) 1.88645 + 5.80591i 0.247703 + 0.762353i
\(59\) 11.0224 8.00828i 1.43500 1.04259i 0.445942 0.895062i \(-0.352869\pi\)
0.989058 0.147527i \(-0.0471314\pi\)
\(60\) −1.23887 0.900090i −0.159937 0.116201i
\(61\) 1.99991 0.256062 0.128031 0.991770i \(-0.459134\pi\)
0.128031 + 0.991770i \(0.459134\pi\)
\(62\) −6.51926 1.39361i −0.827947 0.176988i
\(63\) −4.32185 −0.544502
\(64\) −7.11993 5.17293i −0.889992 0.646617i
\(65\) 6.89578 5.01007i 0.855316 0.621423i
\(66\) −0.358184 1.10238i −0.0440894 0.135693i
\(67\) 7.01351 0.856836 0.428418 0.903581i \(-0.359071\pi\)
0.428418 + 0.903581i \(0.359071\pi\)
\(68\) −2.79164 −0.338536
\(69\) 1.05276 + 3.24006i 0.126737 + 0.390057i
\(70\) 4.32364 13.3068i 0.516773 1.59046i
\(71\) −1.95020 + 6.00211i −0.231446 + 0.712319i 0.766127 + 0.642690i \(0.222182\pi\)
−0.997573 + 0.0696291i \(0.977818\pi\)
\(72\) 2.48597 + 1.80616i 0.292974 + 0.212858i
\(73\) 0.0487339 + 0.149988i 0.00570387 + 0.0175547i 0.953868 0.300226i \(-0.0970623\pi\)
−0.948164 + 0.317781i \(0.897062\pi\)
\(74\) 7.87711 + 5.72306i 0.915696 + 0.665292i
\(75\) −1.86932 + 1.35814i −0.215851 + 0.156825i
\(76\) 1.04317 3.21054i 0.119660 0.368274i
\(77\) −3.38478 + 2.45919i −0.385731 + 0.280250i
\(78\) −3.05370 + 2.21865i −0.345764 + 0.251212i
\(79\) 5.17389 15.9236i 0.582109 1.79155i −0.0284757 0.999594i \(-0.509065\pi\)
0.610584 0.791951i \(-0.290935\pi\)
\(80\) −5.57035 + 4.04709i −0.622784 + 0.452479i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 1.19784 + 3.68658i 0.132280 + 0.407115i
\(83\) 5.63973 + 4.09750i 0.619041 + 0.449759i 0.852586 0.522587i \(-0.175033\pi\)
−0.233546 + 0.972346i \(0.575033\pi\)
\(84\) 0.756384 2.32791i 0.0825283 0.253996i
\(85\) −4.11840 + 12.6751i −0.446703 + 1.37481i
\(86\) 2.26356 + 6.96652i 0.244086 + 0.751220i
\(87\) 5.09851 0.546618
\(88\) 2.97468 0.317102
\(89\) 2.78370 + 8.56735i 0.295072 + 0.908137i 0.983197 + 0.182546i \(0.0584337\pi\)
−0.688126 + 0.725591i \(0.741566\pi\)
\(90\) 2.61912 1.90290i 0.276079 0.200583i
\(91\) 11.0224 + 8.00824i 1.15546 + 0.839491i
\(92\) −1.92947 −0.201161
\(93\) −2.78947 + 4.81860i −0.289254 + 0.499665i
\(94\) 9.49114 0.978936
\(95\) −13.0381 9.47276i −1.33768 0.971885i
\(96\) −2.50518 + 1.82012i −0.255684 + 0.185765i
\(97\) 0.516238 + 1.58882i 0.0524160 + 0.161320i 0.973838 0.227244i \(-0.0729714\pi\)
−0.921422 + 0.388564i \(0.872971\pi\)
\(98\) 13.9831 1.41250
\(99\) −0.968062 −0.0972939
\(100\) −0.404389 1.24458i −0.0404389 0.124458i
\(101\) −1.17169 + 3.60608i −0.116587 + 0.358819i −0.992275 0.124060i \(-0.960409\pi\)
0.875688 + 0.482878i \(0.160409\pi\)
\(102\) 1.82378 5.61301i 0.180581 0.555771i
\(103\) 2.95477 + 2.14676i 0.291142 + 0.211527i 0.723763 0.690049i \(-0.242411\pi\)
−0.432621 + 0.901576i \(0.642411\pi\)
\(104\) −2.99343 9.21282i −0.293530 0.903391i
\(105\) −9.45375 6.86855i −0.922591 0.670302i
\(106\) −5.20794 + 3.78379i −0.505840 + 0.367514i
\(107\) 2.64239 8.13245i 0.255450 0.786194i −0.738291 0.674482i \(-0.764367\pi\)
0.993741 0.111711i \(-0.0356332\pi\)
\(108\) 0.458193 0.332897i 0.0440896 0.0320330i
\(109\) −12.0046 + 8.72185i −1.14983 + 0.835401i −0.988458 0.151492i \(-0.951592\pi\)
−0.161373 + 0.986893i \(0.551592\pi\)
\(110\) 0.968463 2.98062i 0.0923393 0.284191i
\(111\) 6.57880 4.77978i 0.624432 0.453676i
\(112\) −8.90379 6.46898i −0.841329 0.611261i
\(113\) −1.91147 5.88289i −0.179816 0.553416i 0.820005 0.572356i \(-0.193971\pi\)
−0.999821 + 0.0189408i \(0.993971\pi\)
\(114\) 5.77377 + 4.19489i 0.540763 + 0.392887i
\(115\) −2.84647 + 8.76052i −0.265434 + 0.816923i
\(116\) −0.892311 + 2.74625i −0.0828490 + 0.254983i
\(117\) 0.974162 + 2.99816i 0.0900613 + 0.277180i
\(118\) −16.3133 −1.50176
\(119\) −21.3029 −1.95283
\(120\) 2.56742 + 7.90170i 0.234372 + 0.721324i
\(121\) 8.14102 5.91480i 0.740093 0.537709i
\(122\) −1.93726 1.40750i −0.175391 0.127429i
\(123\) 3.23741 0.291907
\(124\) −2.10728 2.34584i −0.189240 0.210662i
\(125\) 7.27161 0.650393
\(126\) 4.18647 + 3.04165i 0.372960 + 0.270971i
\(127\) 0.715575 0.519896i 0.0634970 0.0461333i −0.555584 0.831460i \(-0.687505\pi\)
0.619081 + 0.785327i \(0.287505\pi\)
\(128\) 1.34249 + 4.13176i 0.118660 + 0.365199i
\(129\) 6.11772 0.538635
\(130\) −10.2058 −0.895106
\(131\) −1.30131 4.00503i −0.113696 0.349921i 0.877977 0.478703i \(-0.158893\pi\)
−0.991673 + 0.128783i \(0.958893\pi\)
\(132\) 0.169425 0.521435i 0.0147465 0.0453851i
\(133\) 7.96037 24.4995i 0.690251 2.12438i
\(134\) −6.79381 4.93599i −0.586896 0.426405i
\(135\) −0.835524 2.57148i −0.0719105 0.221318i
\(136\) 12.2536 + 8.90277i 1.05074 + 0.763406i
\(137\) −7.04271 + 5.11683i −0.601699 + 0.437160i −0.846482 0.532418i \(-0.821283\pi\)
0.244782 + 0.969578i \(0.421283\pi\)
\(138\) 1.26052 3.87948i 0.107303 0.330243i
\(139\) −11.6557 + 8.46838i −0.988626 + 0.718279i −0.959620 0.281301i \(-0.909234\pi\)
−0.0290060 + 0.999579i \(0.509234\pi\)
\(140\) 5.35420 3.89005i 0.452512 0.328770i
\(141\) 2.44951 7.53883i 0.206286 0.634884i
\(142\) 6.11330 4.44157i 0.513016 0.372728i
\(143\) 2.46893 + 1.79379i 0.206463 + 0.150004i
\(144\) −0.786919 2.42189i −0.0655766 0.201824i
\(145\) 11.1526 + 8.10287i 0.926176 + 0.672907i
\(146\) 0.0583514 0.179587i 0.00482920 0.0148628i
\(147\) 3.60881 11.1068i 0.297650 0.916073i
\(148\) 1.42319 + 4.38012i 0.116985 + 0.360044i
\(149\) 12.8277 1.05089 0.525443 0.850829i \(-0.323900\pi\)
0.525443 + 0.850829i \(0.323900\pi\)
\(150\) 2.76660 0.225892
\(151\) −1.79345 5.51967i −0.145949 0.449184i 0.851183 0.524869i \(-0.175886\pi\)
−0.997132 + 0.0756849i \(0.975886\pi\)
\(152\) −14.8176 + 10.7656i −1.20186 + 0.873204i
\(153\) −3.98774 2.89726i −0.322390 0.234230i
\(154\) 5.00949 0.403676
\(155\) −13.7598 + 6.10716i −1.10521 + 0.490539i
\(156\) −1.78542 −0.142948
\(157\) 1.11267 + 0.808402i 0.0888007 + 0.0645175i 0.631300 0.775539i \(-0.282522\pi\)
−0.542499 + 0.840056i \(0.682522\pi\)
\(158\) −16.2186 + 11.7835i −1.29028 + 0.937445i
\(159\) 1.66138 + 5.11322i 0.131756 + 0.405504i
\(160\) −8.37255 −0.661908
\(161\) −14.7237 −1.16039
\(162\) 0.370001 + 1.13875i 0.0290700 + 0.0894683i
\(163\) −0.130095 + 0.400391i −0.0101898 + 0.0313611i −0.956022 0.293294i \(-0.905248\pi\)
0.945832 + 0.324656i \(0.105248\pi\)
\(164\) −0.566592 + 1.74379i −0.0442434 + 0.136167i
\(165\) −2.11757 1.53850i −0.164853 0.119772i
\(166\) −2.57931 7.93830i −0.200193 0.616131i
\(167\) 9.30952 + 6.76376i 0.720392 + 0.523396i 0.886509 0.462710i \(-0.153123\pi\)
−0.166117 + 0.986106i \(0.553123\pi\)
\(168\) −10.7440 + 7.80595i −0.828915 + 0.602242i
\(169\) −0.946221 + 2.91217i −0.0727862 + 0.224013i
\(170\) 12.9099 9.37961i 0.990146 0.719384i
\(171\) 4.82213 3.50348i 0.368757 0.267918i
\(172\) −1.07069 + 3.29524i −0.0816391 + 0.251259i
\(173\) −6.18435 + 4.49319i −0.470187 + 0.341611i −0.797514 0.603300i \(-0.793852\pi\)
0.327327 + 0.944911i \(0.393852\pi\)
\(174\) −4.93880 3.58825i −0.374409 0.272024i
\(175\) −3.08588 9.49735i −0.233270 0.717932i
\(176\) −1.99438 1.44900i −0.150332 0.109223i
\(177\) −4.21020 + 12.9577i −0.316458 + 0.973958i
\(178\) 3.33306 10.2581i 0.249823 0.768877i
\(179\) −3.88662 11.9618i −0.290499 0.894065i −0.984696 0.174280i \(-0.944240\pi\)
0.694197 0.719785i \(-0.255760\pi\)
\(180\) 1.53133 0.114138
\(181\) 21.6662 1.61044 0.805218 0.592979i \(-0.202048\pi\)
0.805218 + 0.592979i \(0.202048\pi\)
\(182\) −5.04105 15.5148i −0.373667 1.15003i
\(183\) −1.61796 + 1.17551i −0.119603 + 0.0868966i
\(184\) 8.46919 + 6.15323i 0.624357 + 0.453622i
\(185\) 21.9870 1.61652
\(186\) 6.09334 2.70447i 0.446785 0.198302i
\(187\) −4.77169 −0.348941
\(188\) 3.63200 + 2.63880i 0.264891 + 0.192455i
\(189\) 3.49645 2.54032i 0.254329 0.184781i
\(190\) 5.96294 + 18.3521i 0.432597 + 1.33140i
\(191\) −1.43435 −0.103786 −0.0518929 0.998653i \(-0.516525\pi\)
−0.0518929 + 0.998653i \(0.516525\pi\)
\(192\) 8.80072 0.635137
\(193\) −2.84063 8.74256i −0.204473 0.629304i −0.999735 0.0230370i \(-0.992666\pi\)
0.795261 0.606267i \(-0.207334\pi\)
\(194\) 0.618116 1.90237i 0.0443782 0.136582i
\(195\) −2.63395 + 8.10647i −0.188621 + 0.580516i
\(196\) 5.35095 + 3.88769i 0.382210 + 0.277692i
\(197\) −2.32348 7.15092i −0.165541 0.509482i 0.833535 0.552467i \(-0.186313\pi\)
−0.999076 + 0.0429846i \(0.986313\pi\)
\(198\) 0.937738 + 0.681306i 0.0666421 + 0.0484183i
\(199\) −0.714198 + 0.518895i −0.0506282 + 0.0367835i −0.612812 0.790229i \(-0.709962\pi\)
0.562183 + 0.827013i \(0.309962\pi\)
\(200\) −2.19405 + 6.75259i −0.155143 + 0.477480i
\(201\) −5.67405 + 4.12244i −0.400216 + 0.290774i
\(202\) 3.67289 2.66851i 0.258423 0.187756i
\(203\) −6.80918 + 20.9565i −0.477911 + 1.47086i
\(204\) 2.25849 1.64089i 0.158126 0.114885i
\(205\) 7.08160 + 5.14509i 0.494601 + 0.359348i
\(206\) −1.35135 4.15903i −0.0941531 0.289773i
\(207\) −2.75616 2.00247i −0.191566 0.139181i
\(208\) −2.48073 + 7.63489i −0.172007 + 0.529384i
\(209\) 1.78306 5.48771i 0.123337 0.379593i
\(210\) 4.32364 + 13.3068i 0.298359 + 0.918255i
\(211\) 2.31905 0.159650 0.0798248 0.996809i \(-0.474564\pi\)
0.0798248 + 0.996809i \(0.474564\pi\)
\(212\) −3.04494 −0.209127
\(213\) −1.95020 6.00211i −0.133626 0.411257i
\(214\) −8.28311 + 6.01803i −0.566222 + 0.411384i
\(215\) 13.3821 + 9.72266i 0.912651 + 0.663080i
\(216\) −3.07282 −0.209079
\(217\) −16.0806 17.9010i −1.09162 1.21520i
\(218\) 17.7668 1.20332
\(219\) −0.127587 0.0926974i −0.00862153 0.00626391i
\(220\) 1.19930 0.871344i 0.0808569 0.0587460i
\(221\) 4.80176 + 14.7783i 0.323001 + 0.994095i
\(222\) −9.73665 −0.653481
\(223\) −5.46955 −0.366268 −0.183134 0.983088i \(-0.558624\pi\)
−0.183134 + 0.983088i \(0.558624\pi\)
\(224\) −4.13555 12.7279i −0.276318 0.850419i
\(225\) 0.714018 2.19752i 0.0476012 0.146501i
\(226\) −2.28869 + 7.04387i −0.152241 + 0.468551i
\(227\) 20.2802 + 14.7344i 1.34604 + 0.977957i 0.999198 + 0.0400345i \(0.0127468\pi\)
0.346844 + 0.937923i \(0.387253\pi\)
\(228\) 1.04317 + 3.21054i 0.0690855 + 0.212623i
\(229\) −20.4230 14.8382i −1.34959 0.980533i −0.999032 0.0439906i \(-0.985993\pi\)
−0.350555 0.936542i \(-0.614007\pi\)
\(230\) 8.92281 6.48280i 0.588353 0.427463i
\(231\) 1.29287 3.97905i 0.0850646 0.261802i
\(232\) 12.6747 9.20873i 0.832136 0.604582i
\(233\) 18.1585 13.1929i 1.18960 0.864296i 0.196379 0.980528i \(-0.437082\pi\)
0.993222 + 0.116232i \(0.0370816\pi\)
\(234\) 1.16641 3.58984i 0.0762507 0.234675i
\(235\) 17.3393 12.5978i 1.13109 0.821787i
\(236\) −6.24265 4.53555i −0.406362 0.295239i
\(237\) 5.17389 + 15.9236i 0.336081 + 1.03435i
\(238\) 20.6356 + 14.9926i 1.33761 + 0.971827i
\(239\) 2.26408 6.96812i 0.146451 0.450730i −0.850744 0.525581i \(-0.823848\pi\)
0.997195 + 0.0748508i \(0.0238481\pi\)
\(240\) 2.12768 6.54834i 0.137341 0.422693i
\(241\) −3.79880 11.6915i −0.244702 0.753115i −0.995685 0.0927940i \(-0.970420\pi\)
0.750983 0.660321i \(-0.229580\pi\)
\(242\) −12.0487 −0.774522
\(243\) 1.00000 0.0641500
\(244\) −0.350012 1.07722i −0.0224072 0.0689623i
\(245\) 25.5456 18.5600i 1.63205 1.18575i
\(246\) −3.13599 2.27843i −0.199944 0.145268i
\(247\) −18.7901 −1.19559
\(248\) 1.76864 + 17.0171i 0.112309 + 1.08059i
\(249\) −6.97109 −0.441775
\(250\) −7.04383 5.11764i −0.445491 0.323668i
\(251\) −23.8106 + 17.2994i −1.50291 + 1.09193i −0.533708 + 0.845669i \(0.679202\pi\)
−0.969204 + 0.246260i \(0.920798\pi\)
\(252\) 0.756384 + 2.32791i 0.0476477 + 0.146645i
\(253\) −3.29799 −0.207343
\(254\) −1.05905 −0.0664510
\(255\) −4.11840 12.6751i −0.257904 0.793747i
\(256\) −3.83172 + 11.7928i −0.239482 + 0.737051i
\(257\) −3.37890 + 10.3992i −0.210770 + 0.648682i 0.788657 + 0.614833i \(0.210777\pi\)
−0.999427 + 0.0338493i \(0.989223\pi\)
\(258\) −5.92608 4.30555i −0.368942 0.268052i
\(259\) 10.8603 + 33.4245i 0.674825 + 2.07690i
\(260\) −3.90547 2.83749i −0.242207 0.175974i
\(261\) −4.12478 + 2.99683i −0.255318 + 0.185499i
\(262\) −1.55812 + 4.79541i −0.0962612 + 0.296262i
\(263\) 20.0899 14.5962i 1.23880 0.900037i 0.241278 0.970456i \(-0.422434\pi\)
0.997518 + 0.0704186i \(0.0224335\pi\)
\(264\) −2.40657 + 1.74848i −0.148114 + 0.107611i
\(265\) −4.49208 + 13.8252i −0.275946 + 0.849274i
\(266\) −24.9533 + 18.1297i −1.52999 + 1.11160i
\(267\) −7.28782 5.29491i −0.446007 0.324043i
\(268\) −1.22746 3.77774i −0.0749792 0.230762i
\(269\) −20.2113 14.6844i −1.23231 0.895324i −0.235246 0.971936i \(-0.575590\pi\)
−0.997061 + 0.0766123i \(0.975590\pi\)
\(270\) −1.00041 + 3.07896i −0.0608832 + 0.187379i
\(271\) 6.25946 19.2646i 0.380235 1.17024i −0.559644 0.828733i \(-0.689062\pi\)
0.939878 0.341509i \(-0.110938\pi\)
\(272\) −3.87882 11.9378i −0.235188 0.723834i
\(273\) −13.6244 −0.824588
\(274\) 10.4232 0.629691
\(275\) −0.691213 2.12734i −0.0416817 0.128283i
\(276\) 1.56097 1.13411i 0.0939595 0.0682655i
\(277\) −1.56206 1.13491i −0.0938553 0.0681899i 0.539868 0.841750i \(-0.318474\pi\)
−0.633723 + 0.773560i \(0.718474\pi\)
\(278\) 17.2505 1.03462
\(279\) −0.575574 5.53793i −0.0344587 0.331547i
\(280\) −35.9074 −2.14588
\(281\) −3.45068 2.50707i −0.205850 0.149559i 0.480084 0.877223i \(-0.340606\pi\)
−0.685934 + 0.727664i \(0.740606\pi\)
\(282\) −7.67849 + 5.57875i −0.457247 + 0.332210i
\(283\) −8.93251 27.4914i −0.530982 1.63420i −0.752173 0.658965i \(-0.770994\pi\)
0.221191 0.975230i \(-0.429006\pi\)
\(284\) 3.57428 0.212094
\(285\) 16.1160 0.954631
\(286\) −1.12916 3.47519i −0.0667685 0.205492i
\(287\) −4.32364 + 13.3068i −0.255216 + 0.785474i
\(288\) 0.956893 2.94501i 0.0563855 0.173537i
\(289\) −5.90274 4.28859i −0.347220 0.252270i
\(290\) −5.10062 15.6981i −0.299519 0.921824i
\(291\) −1.35153 0.981943i −0.0792280 0.0575625i
\(292\) 0.0722599 0.0524999i 0.00422869 0.00307232i
\(293\) 8.00748 24.6445i 0.467802 1.43975i −0.387623 0.921818i \(-0.626704\pi\)
0.855424 0.517928i \(-0.173296\pi\)
\(294\) −11.3125 + 8.21904i −0.659761 + 0.479344i
\(295\) −29.8026 + 21.6529i −1.73518 + 1.26068i
\(296\) 7.72163 23.7647i 0.448811 1.38130i
\(297\) 0.783179 0.569013i 0.0454446 0.0330175i
\(298\) −12.4259 9.02793i −0.719812 0.522974i
\(299\) 3.31877 + 10.2141i 0.191930 + 0.590699i
\(300\) 1.05870 + 0.769194i 0.0611243 + 0.0444094i
\(301\) −8.17036 + 25.1458i −0.470932 + 1.44938i
\(302\) −2.14738 + 6.60896i −0.123568 + 0.380303i
\(303\) −1.17169 3.60608i −0.0673117 0.207164i
\(304\) 15.1785 0.870547
\(305\) −5.40737 −0.309625
\(306\) 1.82378 + 5.61301i 0.104258 + 0.320874i
\(307\) 4.87499 3.54189i 0.278230 0.202146i −0.439915 0.898040i \(-0.644991\pi\)
0.718145 + 0.695893i \(0.244991\pi\)
\(308\) 1.91700 + 1.39278i 0.109231 + 0.0793609i
\(309\) −3.65229 −0.207772
\(310\) 17.6269 + 3.76806i 1.00114 + 0.214011i
\(311\) −21.4723 −1.21758 −0.608791 0.793331i \(-0.708345\pi\)
−0.608791 + 0.793331i \(0.708345\pi\)
\(312\) 7.83689 + 5.69384i 0.443677 + 0.322350i
\(313\) 1.05789 0.768601i 0.0597954 0.0434439i −0.557486 0.830186i \(-0.688234\pi\)
0.617281 + 0.786742i \(0.288234\pi\)
\(314\) −0.508875 1.56616i −0.0287175 0.0883834i
\(315\) 11.6855 0.658402
\(316\) −9.48256 −0.533436
\(317\) 6.59915 + 20.3101i 0.370645 + 1.14073i 0.946370 + 0.323085i \(0.104720\pi\)
−0.575725 + 0.817643i \(0.695280\pi\)
\(318\) 1.98926 6.12230i 0.111552 0.343322i
\(319\) −1.52521 + 4.69411i −0.0853952 + 0.262819i
\(320\) 19.2510 + 13.9867i 1.07616 + 0.781878i
\(321\) 2.64239 + 8.13245i 0.147484 + 0.453909i
\(322\) 14.2625 + 10.3623i 0.794815 + 0.577467i
\(323\) 23.7688 17.2691i 1.32253 0.960877i
\(324\) −0.175014 + 0.538638i −0.00972301 + 0.0299243i
\(325\) −5.89295 + 4.28148i −0.326882 + 0.237494i
\(326\) 0.407808 0.296290i 0.0225864 0.0164100i
\(327\) 4.58535 14.1122i 0.253570 0.780409i
\(328\) 8.04808 5.84727i 0.444381 0.322862i
\(329\) 27.7156 + 20.1366i 1.52801 + 1.11017i
\(330\) 0.968463 + 2.98062i 0.0533121 + 0.164078i
\(331\) −18.3782 13.3525i −1.01016 0.733921i −0.0459137 0.998945i \(-0.514620\pi\)
−0.964242 + 0.265025i \(0.914620\pi\)
\(332\) 1.22004 3.75489i 0.0669583 0.206076i
\(333\) −2.51288 + 7.73384i −0.137705 + 0.423812i
\(334\) −4.25767 13.1038i −0.232970 0.717007i
\(335\) −18.9632 −1.03607
\(336\) 11.0057 0.600410
\(337\) 8.01397 + 24.6645i 0.436549 + 1.34356i 0.891491 + 0.453038i \(0.149660\pi\)
−0.454943 + 0.890521i \(0.650340\pi\)
\(338\) 2.96612 2.15501i 0.161336 0.117217i
\(339\) 5.00428 + 3.63583i 0.271795 + 0.197471i
\(340\) 7.54808 0.409352
\(341\) −3.60193 4.00968i −0.195056 0.217137i
\(342\) −7.13677 −0.385912
\(343\) 16.3577 + 11.8845i 0.883231 + 0.641705i
\(344\) 15.2084 11.0496i 0.819984 0.595753i
\(345\) −2.84647 8.76052i −0.153249 0.471650i
\(346\) 9.15286 0.492061
\(347\) 3.06248 0.164402 0.0822012 0.996616i \(-0.473805\pi\)
0.0822012 + 0.996616i \(0.473805\pi\)
\(348\) −0.892311 2.74625i −0.0478329 0.147215i
\(349\) −0.706484 + 2.17434i −0.0378172 + 0.116390i −0.968183 0.250243i \(-0.919489\pi\)
0.930366 + 0.366633i \(0.119489\pi\)
\(350\) −3.69487 + 11.3716i −0.197499 + 0.607839i
\(351\) −2.55039 1.85297i −0.136130 0.0989040i
\(352\) −0.926332 2.85096i −0.0493737 0.151956i
\(353\) 10.3883 + 7.54752i 0.552911 + 0.401714i 0.828858 0.559459i \(-0.188991\pi\)
−0.275946 + 0.961173i \(0.588991\pi\)
\(354\) 13.1977 9.58870i 0.701450 0.509633i
\(355\) 5.27298 16.2286i 0.279861 0.861323i
\(356\) 4.12751 2.99881i 0.218758 0.158937i
\(357\) 17.2344 12.5215i 0.912141 0.662709i
\(358\) −4.65363 + 14.3224i −0.245952 + 0.756963i
\(359\) −7.27240 + 5.28371i −0.383823 + 0.278864i −0.762919 0.646493i \(-0.776235\pi\)
0.379097 + 0.925357i \(0.376235\pi\)
\(360\) −6.72159 4.88352i −0.354259 0.257384i
\(361\) 5.10722 + 15.7184i 0.268801 + 0.827285i
\(362\) −20.9875 15.2483i −1.10308 0.801433i
\(363\) −3.10959 + 9.57034i −0.163211 + 0.502313i
\(364\) 2.38447 7.33863i 0.124980 0.384649i
\(365\) −0.131767 0.405538i −0.00689702 0.0212268i
\(366\) 2.39458 0.125167
\(367\) 18.2920 0.954833 0.477416 0.878677i \(-0.341573\pi\)
0.477416 + 0.878677i \(0.341573\pi\)
\(368\) −2.68088 8.25089i −0.139750 0.430107i
\(369\) −2.61912 + 1.90290i −0.136346 + 0.0990610i
\(370\) −21.2983 15.4741i −1.10724 0.804459i
\(371\) −23.2358 −1.20634
\(372\) 3.08368 + 0.659191i 0.159881 + 0.0341774i
\(373\) 34.6042 1.79174 0.895868 0.444321i \(-0.146555\pi\)
0.895868 + 0.444321i \(0.146555\pi\)
\(374\) 4.62222 + 3.35824i 0.239009 + 0.173650i
\(375\) −5.88286 + 4.27415i −0.303789 + 0.220716i
\(376\) −7.52693 23.1655i −0.388172 1.19467i
\(377\) 16.0728 0.827792
\(378\) −5.17476 −0.266161
\(379\) 3.28910 + 10.1228i 0.168950 + 0.519974i 0.999306 0.0372596i \(-0.0118629\pi\)
−0.830356 + 0.557233i \(0.811863\pi\)
\(380\) −2.82053 + 8.68071i −0.144690 + 0.445311i
\(381\) −0.273325 + 0.841209i −0.0140029 + 0.0430965i
\(382\) 1.38942 + 1.00947i 0.0710888 + 0.0516490i
\(383\) 4.69200 + 14.4405i 0.239750 + 0.737874i 0.996456 + 0.0841187i \(0.0268075\pi\)
−0.756706 + 0.653755i \(0.773193\pi\)
\(384\) −3.51468 2.55357i −0.179358 0.130311i
\(385\) 9.15181 6.64918i 0.466420 0.338874i
\(386\) −3.40122 + 10.4679i −0.173118 + 0.532802i
\(387\) −4.94934 + 3.59590i −0.251589 + 0.182790i
\(388\) 0.765448 0.556131i 0.0388597 0.0282333i
\(389\) −10.5433 + 32.4488i −0.534564 + 1.64522i 0.210025 + 0.977696i \(0.432646\pi\)
−0.744589 + 0.667523i \(0.767354\pi\)
\(390\) 8.25664 5.99880i 0.418091 0.303761i
\(391\) −13.5854 9.87039i −0.687045 0.499167i
\(392\) −11.0892 34.1292i −0.560092 1.72378i
\(393\) 3.40688 + 2.47524i 0.171854 + 0.124860i
\(394\) −2.78201 + 8.56214i −0.140156 + 0.431355i
\(395\) −13.9892 + 43.0545i −0.703875 + 2.16631i
\(396\) 0.169425 + 0.521435i 0.00851390 + 0.0262031i
\(397\) 18.0947 0.908146 0.454073 0.890965i \(-0.349971\pi\)
0.454073 + 0.890965i \(0.349971\pi\)
\(398\) 1.05702 0.0529834
\(399\) 7.96037 + 24.4995i 0.398517 + 1.22651i
\(400\) 4.76027 3.45854i 0.238014 0.172927i
\(401\) −15.7130 11.4162i −0.784672 0.570097i 0.121706 0.992566i \(-0.461164\pi\)
−0.906377 + 0.422469i \(0.861164\pi\)
\(402\) 8.39761 0.418835
\(403\) −8.79367 + 15.1904i −0.438044 + 0.756688i
\(404\) 2.14743 0.106839
\(405\) 2.18743 + 1.58926i 0.108694 + 0.0789711i
\(406\) 21.3447 15.5079i 1.05932 0.769642i
\(407\) 2.43262 + 7.48684i 0.120581 + 0.371109i
\(408\) −15.1463 −0.749854
\(409\) 15.4039 0.761673 0.380836 0.924642i \(-0.375636\pi\)
0.380836 + 0.924642i \(0.375636\pi\)
\(410\) −3.23875 9.96783i −0.159950 0.492276i
\(411\) 2.69008 8.27920i 0.132692 0.408383i
\(412\) 0.639202 1.96726i 0.0314912 0.0969201i
\(413\) −47.6373 34.6106i −2.34408 1.70307i
\(414\) 1.26052 + 3.87948i 0.0619511 + 0.190666i
\(415\) −15.2488 11.0789i −0.748533 0.543841i
\(416\) −7.89746 + 5.73784i −0.387205 + 0.281321i
\(417\) 4.45209 13.7021i 0.218020 0.670996i
\(418\) −5.58937 + 4.06091i −0.273385 + 0.198626i
\(419\) −6.28375 + 4.56541i −0.306981 + 0.223035i −0.730600 0.682805i \(-0.760760\pi\)
0.423619 + 0.905841i \(0.360760\pi\)
\(420\) −2.04512 + 6.29424i −0.0997918 + 0.307127i
\(421\) −4.30613 + 3.12859i −0.209868 + 0.152478i −0.687754 0.725944i \(-0.741403\pi\)
0.477886 + 0.878422i \(0.341403\pi\)
\(422\) −2.24640 1.63211i −0.109353 0.0794497i
\(423\) 2.44951 + 7.53883i 0.119099 + 0.366551i
\(424\) 13.3654 + 9.71056i 0.649083 + 0.471586i
\(425\) 3.51948 10.8318i 0.170720 0.525421i
\(426\) −2.33507 + 7.18661i −0.113135 + 0.348192i
\(427\) −2.67092 8.22025i −0.129255 0.397806i
\(428\) −4.84290 −0.234091
\(429\) −3.05177 −0.147341
\(430\) −6.12025 18.8362i −0.295145 0.908362i
\(431\) 7.83383 5.69161i 0.377342 0.274155i −0.382907 0.923787i \(-0.625077\pi\)
0.760249 + 0.649632i \(0.225077\pi\)
\(432\) 2.06018 + 1.49681i 0.0991205 + 0.0720153i
\(433\) 11.3906 0.547398 0.273699 0.961815i \(-0.411753\pi\)
0.273699 + 0.961815i \(0.411753\pi\)
\(434\) 2.97845 + 28.6575i 0.142970 + 1.37560i
\(435\) −13.7854 −0.660960
\(436\) 6.79889 + 4.93968i 0.325608 + 0.236568i
\(437\) 16.4280 11.9357i 0.785859 0.570960i
\(438\) 0.0583514 + 0.179587i 0.00278814 + 0.00858101i
\(439\) 16.4255 0.783946 0.391973 0.919977i \(-0.371793\pi\)
0.391973 + 0.919977i \(0.371793\pi\)
\(440\) −8.04299 −0.383435
\(441\) 3.60881 + 11.1068i 0.171848 + 0.528895i
\(442\) 5.74937 17.6948i 0.273470 0.841654i
\(443\) −2.93757 + 9.04092i −0.139568 + 0.429547i −0.996273 0.0862607i \(-0.972508\pi\)
0.856704 + 0.515808i \(0.172508\pi\)
\(444\) −3.72595 2.70706i −0.176826 0.128472i
\(445\) −7.52661 23.1645i −0.356795 1.09810i
\(446\) 5.29822 + 3.84938i 0.250878 + 0.182274i
\(447\) −10.3778 + 7.53993i −0.490854 + 0.356627i
\(448\) −11.7536 + 36.1738i −0.555304 + 1.70905i
\(449\) 3.57166 2.59496i 0.168557 0.122464i −0.500309 0.865847i \(-0.666780\pi\)
0.668866 + 0.743383i \(0.266780\pi\)
\(450\) −2.23823 + 1.62617i −0.105511 + 0.0766583i
\(451\) −0.968463 + 2.98062i −0.0456031 + 0.140352i
\(452\) −2.83421 + 2.05918i −0.133310 + 0.0968555i
\(453\) 4.69531 + 3.41134i 0.220605 + 0.160279i
\(454\) −9.27506 28.5457i −0.435300 1.33972i
\(455\) −29.8025 21.6528i −1.39716 1.01510i
\(456\) 5.65980 17.4191i 0.265044 0.815723i
\(457\) −8.19600 + 25.2247i −0.383393 + 1.17996i 0.554247 + 0.832353i \(0.313006\pi\)
−0.937639 + 0.347609i \(0.886994\pi\)
\(458\) 9.34037 + 28.7467i 0.436447 + 1.34324i
\(459\) 4.92912 0.230071
\(460\) 5.21692 0.243240
\(461\) −6.60062 20.3146i −0.307422 0.946146i −0.978762 0.204998i \(-0.934281\pi\)
0.671341 0.741149i \(-0.265719\pi\)
\(462\) −4.05276 + 2.94450i −0.188551 + 0.136991i
\(463\) −12.1130 8.80062i −0.562940 0.409000i 0.269594 0.962974i \(-0.413111\pi\)
−0.832534 + 0.553974i \(0.813111\pi\)
\(464\) −12.9835 −0.602743
\(465\) 7.54220 13.0286i 0.349761 0.604186i
\(466\) −26.8746 −1.24494
\(467\) −6.89119 5.00674i −0.318886 0.231684i 0.416814 0.908992i \(-0.363147\pi\)
−0.735700 + 0.677307i \(0.763147\pi\)
\(468\) 1.44443 1.04944i 0.0667689 0.0485104i
\(469\) −9.36671 28.8278i −0.432514 1.33114i
\(470\) −25.6623 −1.18371
\(471\) −1.37534 −0.0633721
\(472\) 12.9372 + 39.8166i 0.595483 + 1.83271i
\(473\) −1.83010 + 5.63247i −0.0841481 + 0.258981i
\(474\) 6.19495 19.0661i 0.284544 0.875735i
\(475\) 11.1421 + 8.09518i 0.511233 + 0.371432i
\(476\) 3.72831 + 11.4745i 0.170887 + 0.525935i
\(477\) −4.34956 3.16014i −0.199153 0.144693i
\(478\) −7.09720 + 5.15642i −0.324618 + 0.235849i
\(479\) 4.44665 13.6854i 0.203173 0.625301i −0.796611 0.604492i \(-0.793376\pi\)
0.999783 0.0208085i \(-0.00662403\pi\)
\(480\) 6.77354 4.92126i 0.309168 0.224624i
\(481\) 20.7394 15.0680i 0.945634 0.687043i
\(482\) −4.54848 + 13.9988i −0.207178 + 0.637627i
\(483\) 11.9117 8.65436i 0.542001 0.393787i
\(484\) −4.61073 3.34989i −0.209579 0.152268i
\(485\) −1.39581 4.29586i −0.0633805 0.195065i
\(486\) −0.968675 0.703784i −0.0439400 0.0319243i
\(487\) 8.07893 24.8644i 0.366091 1.12671i −0.583203 0.812326i \(-0.698201\pi\)
0.949295 0.314387i \(-0.101799\pi\)
\(488\) −1.89902 + 5.84458i −0.0859646 + 0.264572i
\(489\) −0.130095 0.400391i −0.00588310 0.0181063i
\(490\) −37.8076 −1.70797
\(491\) 16.3293 0.736931 0.368466 0.929641i \(-0.379883\pi\)
0.368466 + 0.929641i \(0.379883\pi\)
\(492\) −0.566592 1.74379i −0.0255439 0.0786161i
\(493\) −20.3315 + 14.7717i −0.915686 + 0.665285i
\(494\) 18.2015 + 13.2242i 0.818926 + 0.594984i
\(495\) 2.61746 0.117646
\(496\) 7.10345 12.2707i 0.318954 0.550969i
\(497\) 27.2751 1.22346
\(498\) 6.75272 + 4.90614i 0.302597 + 0.219849i
\(499\) −18.8884 + 13.7232i −0.845559 + 0.614335i −0.923918 0.382590i \(-0.875032\pi\)
0.0783587 + 0.996925i \(0.475032\pi\)
\(500\) −1.27263 3.91677i −0.0569139 0.175163i
\(501\) −11.5072 −0.514104
\(502\) 35.2398 1.57283
\(503\) 0.402009 + 1.23726i 0.0179247 + 0.0551665i 0.959619 0.281304i \(-0.0907668\pi\)
−0.941694 + 0.336470i \(0.890767\pi\)
\(504\) 4.10383 12.6303i 0.182799 0.562598i
\(505\) 3.16802 9.75018i 0.140975 0.433877i
\(506\) 3.19469 + 2.32107i 0.142021 + 0.103184i
\(507\) −0.946221 2.91217i −0.0420232 0.129334i
\(508\) −0.405271 0.294447i −0.0179810 0.0130640i
\(509\) −22.9756 + 16.6927i −1.01838 + 0.739893i −0.965949 0.258732i \(-0.916695\pi\)
−0.0524261 + 0.998625i \(0.516695\pi\)
\(510\) −4.93115 + 15.1765i −0.218355 + 0.672028i
\(511\) 0.551412 0.400624i 0.0243930 0.0177226i
\(512\) 19.0406 13.8338i 0.841485 0.611375i
\(513\) −1.84189 + 5.66875i −0.0813214 + 0.250282i
\(514\) 10.5918 7.69541i 0.467185 0.339430i
\(515\) −7.98914 5.80445i −0.352043 0.255774i
\(516\) −1.07069 3.29524i −0.0471344 0.145065i
\(517\) 6.20810 + 4.51045i 0.273032 + 0.198369i
\(518\) 13.0035 40.0208i 0.571342 1.75841i
\(519\) 2.36221 7.27014i 0.103690 0.319124i
\(520\) 8.09367 + 24.9098i 0.354931 + 1.09236i
\(521\) 31.4473 1.37773 0.688866 0.724889i \(-0.258109\pi\)
0.688866 + 0.724889i \(0.258109\pi\)
\(522\) 6.10469 0.267195
\(523\) −0.397623 1.22376i −0.0173868 0.0535112i 0.941987 0.335650i \(-0.108956\pi\)
−0.959374 + 0.282139i \(0.908956\pi\)
\(524\) −1.92951 + 1.40187i −0.0842911 + 0.0612411i
\(525\) 8.07893 + 5.86968i 0.352593 + 0.256174i
\(526\) −29.7331 −1.29642
\(527\) −2.83707 27.2971i −0.123585 1.18908i
\(528\) 2.46519 0.107284
\(529\) 9.21770 + 6.69705i 0.400770 + 0.291176i
\(530\) 14.0813 10.2307i 0.611653 0.444392i
\(531\) −4.21020 12.9577i −0.182707 0.562315i
\(532\) −14.5895 −0.632536
\(533\) 10.2058 0.442061
\(534\) 3.33306 + 10.2581i 0.144236 + 0.443911i
\(535\) −7.14454 + 21.9886i −0.308885 + 0.950652i
\(536\) −6.65971 + 20.4965i −0.287656 + 0.885313i
\(537\) 10.1753 + 7.39279i 0.439096 + 0.319022i
\(538\) 9.24358 + 28.4488i 0.398519 + 1.22652i
\(539\) 9.14625 + 6.64514i 0.393957 + 0.286226i
\(540\) −1.23887 + 0.900090i −0.0533124 + 0.0387337i
\(541\) −4.18567 + 12.8822i −0.179956 + 0.553848i −0.999825 0.0187031i \(-0.994046\pi\)
0.819869 + 0.572551i \(0.194046\pi\)
\(542\) −19.6215 + 14.2559i −0.842816 + 0.612341i
\(543\) −17.5283 + 12.7351i −0.752212 + 0.546514i
\(544\) 4.71664 14.5163i 0.202224 0.622382i
\(545\) 32.4582 23.5823i 1.39036 1.01015i
\(546\) 13.1976 + 9.58865i 0.564807 + 0.410356i
\(547\) 4.89483 + 15.0648i 0.209288 + 0.644122i 0.999510 + 0.0313015i \(0.00996521\pi\)
−0.790222 + 0.612821i \(0.790035\pi\)
\(548\) 3.98869 + 2.89795i 0.170388 + 0.123794i
\(549\) 0.618005 1.90202i 0.0263758 0.0811764i
\(550\) −0.827623 + 2.54716i −0.0352900 + 0.108611i
\(551\) −9.39089 28.9022i −0.400065 1.23127i
\(552\) −10.4685 −0.445569
\(553\) −72.3610 −3.07710
\(554\) 0.714404 + 2.19871i 0.0303521 + 0.0934142i
\(555\) −17.7879 + 12.9236i −0.755052 + 0.548578i
\(556\) 6.60131 + 4.79613i 0.279958 + 0.203401i
\(557\) −10.3809 −0.439855 −0.219927 0.975516i \(-0.570582\pi\)
−0.219927 + 0.975516i \(0.570582\pi\)
\(558\) −3.33996 + 5.76954i −0.141392 + 0.244244i
\(559\) 19.2858 0.815703
\(560\) 24.0742 + 17.4909i 1.01732 + 0.739126i
\(561\) 3.86038 2.80473i 0.162985 0.118416i
\(562\) 1.57816 + 4.85707i 0.0665705 + 0.204883i
\(563\) −11.0602 −0.466133 −0.233067 0.972461i \(-0.574876\pi\)
−0.233067 + 0.972461i \(0.574876\pi\)
\(564\) −4.48940 −0.189038
\(565\) 5.16825 + 15.9062i 0.217430 + 0.669180i
\(566\) −10.6953 + 32.9168i −0.449558 + 1.38360i
\(567\) −1.33552 + 4.11032i −0.0560868 + 0.172617i
\(568\) −15.6889 11.3987i −0.658292 0.478277i
\(569\) −0.408127 1.25609i −0.0171096 0.0526579i 0.942137 0.335227i \(-0.108813\pi\)
−0.959247 + 0.282570i \(0.908813\pi\)
\(570\) −15.6112 11.3422i −0.653881 0.475072i
\(571\) 24.1749 17.5641i 1.01169 0.735035i 0.0471262 0.998889i \(-0.484994\pi\)
0.964563 + 0.263854i \(0.0849937\pi\)
\(572\) 0.534103 1.64380i 0.0223320 0.0687307i
\(573\) 1.16041 0.843089i 0.0484769 0.0352205i
\(574\) 13.5533 9.84704i 0.565703 0.411008i
\(575\) 2.43252 7.48651i 0.101443 0.312209i
\(576\) −7.11993 + 5.17293i −0.296664 + 0.215539i
\(577\) −7.60522 5.52552i −0.316610 0.230030i 0.418118 0.908393i \(-0.362690\pi\)
−0.734727 + 0.678362i \(0.762690\pi\)
\(578\) 2.69959 + 8.30850i 0.112288 + 0.345588i
\(579\) 7.43687 + 5.40320i 0.309066 + 0.224549i
\(580\) 2.41264 7.42535i 0.100180 0.308321i
\(581\) 9.31006 28.6534i 0.386246 1.18874i
\(582\) 0.618116 + 1.90237i 0.0256217 + 0.0788556i
\(583\) −5.20465 −0.215554
\(584\) −0.484603 −0.0200530
\(585\) −2.63395 8.10647i −0.108901 0.335161i
\(586\) −25.1010 + 18.2370i −1.03691 + 0.753362i
\(587\) 16.0801 + 11.6828i 0.663695 + 0.482202i 0.867909 0.496724i \(-0.165464\pi\)
−0.204214 + 0.978926i \(0.565464\pi\)
\(588\) −6.61413 −0.272762
\(589\) 32.4533 + 6.93748i 1.33722 + 0.285854i
\(590\) 44.1080 1.81590
\(591\) 6.08294 + 4.41951i 0.250219 + 0.181794i
\(592\) −16.7531 + 12.1718i −0.688547 + 0.500259i
\(593\) 4.56842 + 14.0602i 0.187603 + 0.577382i 0.999983 0.00574559i \(-0.00182889\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(594\) −1.15911 −0.0475588
\(595\) 57.5990 2.36133
\(596\) −2.24503 6.90949i −0.0919600 0.283024i
\(597\) 0.272799 0.839591i 0.0111649 0.0343622i
\(598\) 3.97373 12.2299i 0.162498 0.500117i
\(599\) −6.91709 5.02556i −0.282624 0.205339i 0.437437 0.899249i \(-0.355886\pi\)
−0.720061 + 0.693910i \(0.755886\pi\)
\(600\) −2.19405 6.75259i −0.0895717 0.275673i
\(601\) −16.7106 12.1409i −0.681638 0.495239i 0.192262 0.981344i \(-0.438418\pi\)
−0.873901 + 0.486104i \(0.838418\pi\)
\(602\) 25.6116 18.6079i 1.04385 0.758403i
\(603\) 2.16729 6.67024i 0.0882590 0.271633i
\(604\) −2.65922 + 1.93204i −0.108202 + 0.0786136i
\(605\) −22.0118 + 15.9925i −0.894907 + 0.650188i
\(606\) −1.40292 + 4.31774i −0.0569896 + 0.175396i
\(607\) −1.13379 + 0.823745i −0.0460190 + 0.0334348i −0.610557 0.791972i \(-0.709054\pi\)
0.564538 + 0.825407i \(0.309054\pi\)
\(608\) 14.9321 + 10.8488i 0.605575 + 0.439976i
\(609\) −6.80918 20.9565i −0.275922 0.849201i
\(610\) 5.23799 + 3.80562i 0.212080 + 0.154085i
\(611\) 7.72198 23.7658i 0.312398 0.961462i
\(612\) −0.862665 + 2.65501i −0.0348712 + 0.107322i
\(613\) 3.44465 + 10.6015i 0.139128 + 0.428192i 0.996209 0.0869891i \(-0.0277245\pi\)
−0.857081 + 0.515181i \(0.827725\pi\)
\(614\) −7.21500 −0.291174
\(615\) −8.75334 −0.352969
\(616\) −3.97276 12.2269i −0.160067 0.492636i
\(617\) −34.5460 + 25.0992i −1.39077 + 1.01045i −0.394990 + 0.918685i \(0.629252\pi\)
−0.995780 + 0.0917689i \(0.970748\pi\)
\(618\) 3.53788 + 2.57042i 0.142315 + 0.103398i
\(619\) 0.248366 0.00998268 0.00499134 0.999988i \(-0.498411\pi\)
0.00499134 + 0.999988i \(0.498411\pi\)
\(620\) 5.69770 + 6.34270i 0.228825 + 0.254729i
\(621\) 3.40680 0.136710
\(622\) 20.7997 + 15.1118i 0.833991 + 0.605930i
\(623\) 31.4969 22.8838i 1.26189 0.916820i
\(624\) −2.48073 7.63489i −0.0993085 0.305640i
\(625\) −31.2141 −1.24857
\(626\) −1.56568 −0.0625771
\(627\) 1.78306 + 5.48771i 0.0712087 + 0.219158i
\(628\) 0.240703 0.740808i 0.00960510 0.0295615i
\(629\) −12.3863 + 38.1210i −0.493873 + 1.51998i
\(630\) −11.3194 8.22404i −0.450977 0.327654i
\(631\) 3.21031 + 9.88032i 0.127800 + 0.393329i 0.994401 0.105673i \(-0.0336998\pi\)
−0.866601 + 0.499003i \(0.833700\pi\)
\(632\) 41.6227 + 30.2407i 1.65566 + 1.20291i
\(633\) −1.87615 + 1.36310i −0.0745702 + 0.0541784i
\(634\) 7.90148 24.3182i 0.313808 0.965801i
\(635\) −1.93478 + 1.40570i −0.0767795 + 0.0557836i
\(636\) 2.46341 1.78977i 0.0976805 0.0709690i
\(637\) 11.3766 35.0136i 0.450758 1.38729i
\(638\) 4.78106 3.47365i 0.189284 0.137523i
\(639\) 5.10570 + 3.70951i 0.201978 + 0.146746i
\(640\) −3.62984 11.1715i −0.143482 0.441592i
\(641\) −13.7387 9.98175i −0.542646 0.394256i 0.282421 0.959291i \(-0.408863\pi\)
−0.825067 + 0.565035i \(0.808863\pi\)
\(642\) 3.16387 9.73738i 0.124868 0.384304i
\(643\) 0.544835 1.67683i 0.0214862 0.0661278i −0.939738 0.341894i \(-0.888932\pi\)
0.961225 + 0.275766i \(0.0889316\pi\)
\(644\) 2.57685 + 7.93073i 0.101542 + 0.312515i
\(645\) −16.5412 −0.651308
\(646\) −35.1780 −1.38406
\(647\) −9.45832 29.1097i −0.371845 1.14442i −0.945583 0.325382i \(-0.894507\pi\)
0.573738 0.819039i \(-0.305493\pi\)
\(648\) 2.48597 1.80616i 0.0976580 0.0709527i
\(649\) −10.6704 7.75251i −0.418850 0.304313i
\(650\) 8.72159 0.342089
\(651\) 23.5314 + 5.03025i 0.922268 + 0.197151i
\(652\) 0.238434 0.00933781
\(653\) −32.0256 23.2680i −1.25326 0.910546i −0.254853 0.966980i \(-0.582027\pi\)
−0.998406 + 0.0564338i \(0.982027\pi\)
\(654\) −14.3737 + 10.4431i −0.562055 + 0.408357i
\(655\) 3.51851 + 10.8288i 0.137479 + 0.423118i
\(656\) −8.24413 −0.321879
\(657\) 0.157706 0.00615271
\(658\) −12.6756 39.0116i −0.494148 1.52083i
\(659\) 13.5645 41.7473i 0.528399 1.62624i −0.229096 0.973404i \(-0.573577\pi\)
0.757495 0.652841i \(-0.226423\pi\)
\(660\) −0.458092 + 1.40986i −0.0178312 + 0.0548789i
\(661\) 20.4550 + 14.8615i 0.795609 + 0.578044i 0.909623 0.415436i \(-0.136371\pi\)
−0.114014 + 0.993479i \(0.536371\pi\)
\(662\) 8.40519 + 25.8685i 0.326677 + 1.00541i
\(663\) −12.5712 9.13348i −0.488223 0.354715i
\(664\) −17.3299 + 12.5909i −0.672530 + 0.488622i
\(665\) −21.5233 + 66.2421i −0.834640 + 2.56876i
\(666\) 7.87711 5.72306i 0.305232 0.221764i
\(667\) −14.0523 + 10.2096i −0.544108 + 0.395317i
\(668\) 2.01392 6.19821i 0.0779210 0.239816i
\(669\) 4.42496 3.21492i 0.171079 0.124296i
\(670\) 18.3692 + 13.3460i 0.709664 + 0.515601i
\(671\) −0.598267 1.84128i −0.0230958 0.0710817i
\(672\) 10.8270 + 7.86628i 0.417661 + 0.303448i
\(673\) −0.0484325 + 0.149060i −0.00186693 + 0.00574583i −0.951986 0.306143i \(-0.900962\pi\)
0.950119 + 0.311889i \(0.100962\pi\)
\(674\) 9.59551 29.5319i 0.369605 1.13753i
\(675\) 0.714018 + 2.19752i 0.0274826 + 0.0845826i
\(676\) 1.73421 0.0667003
\(677\) −18.7088 −0.719037 −0.359519 0.933138i \(-0.617059\pi\)
−0.359519 + 0.933138i \(0.617059\pi\)
\(678\) −2.28869 7.04387i −0.0878966 0.270518i
\(679\) 5.84110 4.24381i 0.224161 0.162862i
\(680\) −33.1315 24.0714i −1.27053 0.923098i
\(681\) −25.0677 −0.960596
\(682\) 0.667152 + 6.41906i 0.0255466 + 0.245799i
\(683\) 3.94761 0.151051 0.0755256 0.997144i \(-0.475937\pi\)
0.0755256 + 0.997144i \(0.475937\pi\)
\(684\) −2.73105 1.98422i −0.104424 0.0758687i
\(685\) 19.0422 13.8350i 0.727564 0.528606i
\(686\) −7.48112 23.0245i −0.285631 0.879080i
\(687\) 25.2442 0.963125
\(688\) −15.5789 −0.593941
\(689\) 5.23744 + 16.1192i 0.199531 + 0.614092i
\(690\) −3.40821 + 10.4894i −0.129748 + 0.399324i
\(691\) −5.76359 + 17.7385i −0.219257 + 0.674805i 0.779567 + 0.626319i \(0.215439\pi\)
−0.998824 + 0.0484853i \(0.984561\pi\)
\(692\) 3.50255 + 2.54475i 0.133147 + 0.0967370i
\(693\) 1.29287 + 3.97905i 0.0491121 + 0.151151i
\(694\) −2.96654 2.15532i −0.112608 0.0818148i
\(695\) 31.5149 22.8969i 1.19543 0.868530i
\(696\) −4.84131 + 14.9000i −0.183510 + 0.564784i
\(697\) −12.9099 + 9.37961i −0.488998 + 0.355278i
\(698\) 2.21462 1.60901i 0.0838244 0.0609020i
\(699\) −6.93592 + 21.3466i −0.262341 + 0.807401i
\(700\) −4.57556 + 3.32434i −0.172940 + 0.125648i
\(701\) 25.0433 + 18.1950i 0.945873 + 0.687217i 0.949827 0.312776i \(-0.101259\pi\)
−0.00395455 + 0.999992i \(0.501259\pi\)
\(702\) 1.16641 + 3.58984i 0.0440233 + 0.135490i
\(703\) −39.2128 28.4898i −1.47894 1.07451i
\(704\) −2.63272 + 8.10266i −0.0992242 + 0.305381i
\(705\) −6.62303 + 20.3836i −0.249438 + 0.767691i
\(706\) −4.75103 14.6222i −0.178808 0.550313i
\(707\) 16.3870 0.616296
\(708\) 7.71634 0.289998
\(709\) −2.34524 7.21791i −0.0880773 0.271074i 0.897310 0.441400i \(-0.145518\pi\)
−0.985388 + 0.170326i \(0.945518\pi\)
\(710\) −16.5292 + 12.0092i −0.620330 + 0.450696i
\(711\) −13.5454 9.84133i −0.507993 0.369079i
\(712\) −27.6807 −1.03738
\(713\) −1.96086 18.8666i −0.0734350 0.706561i
\(714\) −25.5070 −0.954575
\(715\) −6.67554 4.85006i −0.249651 0.181382i
\(716\) −5.76286 + 4.18696i −0.215368 + 0.156474i
\(717\) 2.26408 + 6.96812i 0.0845535 + 0.260229i
\(718\) 10.7632 0.401678
\(719\) 17.5841 0.655777 0.327888 0.944716i \(-0.393663\pi\)
0.327888 + 0.944716i \(0.393663\pi\)
\(720\) 2.12768 + 6.54834i 0.0792941 + 0.244042i
\(721\) 4.87772 15.0121i 0.181656 0.559079i
\(722\) 6.11512 18.8204i 0.227581 0.700423i
\(723\) 9.94537 + 7.22574i 0.369872 + 0.268728i
\(724\) −3.79189 11.6702i −0.140924 0.433721i
\(725\) −9.53076 6.92450i −0.353963 0.257170i
\(726\) 9.74764 7.08207i 0.361769 0.262840i
\(727\) 5.84819 17.9989i 0.216897 0.667541i −0.782116 0.623133i \(-0.785860\pi\)
0.999013 0.0444085i \(-0.0141403\pi\)
\(728\) −33.8699 + 24.6079i −1.25530 + 0.912029i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) −0.157771 + 0.485571i −0.00583938 + 0.0179718i
\(731\) −24.3959 + 17.7246i −0.902313 + 0.655569i
\(732\) 0.916342 + 0.665762i 0.0338690 + 0.0246073i
\(733\) 11.1233 + 34.2339i 0.410847 + 1.26446i 0.915913 + 0.401377i \(0.131468\pi\)
−0.505066 + 0.863081i \(0.668532\pi\)
\(734\) −17.7190 12.8736i −0.654019 0.475173i
\(735\) −9.75756 + 30.0307i −0.359913 + 1.10770i
\(736\) 3.25994 10.0331i 0.120163 0.369824i
\(737\) −2.09807 6.45721i −0.0772835 0.237854i
\(738\) 3.87630 0.142689
\(739\) 15.7132 0.578021 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(740\) −3.84803 11.8430i −0.141457 0.435358i
\(741\) 15.2015 11.0446i 0.558443 0.405732i
\(742\) 22.5079 + 16.3530i 0.826292 + 0.600336i
\(743\) 39.6677 1.45527 0.727634 0.685965i \(-0.240620\pi\)
0.727634 + 0.685965i \(0.240620\pi\)
\(744\) −11.4333 12.7275i −0.419163 0.466614i
\(745\) −34.6837 −1.27071
\(746\) −33.5202 24.3538i −1.22726 0.891657i
\(747\) 5.63973 4.09750i 0.206347 0.149920i
\(748\) 0.835113 + 2.57021i 0.0305348 + 0.0939763i
\(749\) −36.9560 −1.35034
\(750\) 8.70665 0.317922
\(751\) 14.7071 + 45.2637i 0.536668 + 1.65169i 0.740017 + 0.672588i \(0.234817\pi\)
−0.203349 + 0.979106i \(0.565183\pi\)
\(752\) −6.23775 + 19.1978i −0.227467 + 0.700072i
\(753\) 9.09484 27.9910i 0.331434 1.02005i
\(754\) −15.5693 11.3118i −0.567002 0.411951i
\(755\) 4.84915 + 14.9242i 0.176479 + 0.543145i
\(756\) −1.98024 1.43873i −0.0720206 0.0523260i
\(757\) 1.10661 0.804001i 0.0402205 0.0292219i −0.567493 0.823378i \(-0.692087\pi\)
0.607714 + 0.794156i \(0.292087\pi\)
\(758\) 3.93820 12.1205i 0.143042 0.440237i
\(759\) 2.66813 1.93851i 0.0968471 0.0703636i
\(760\) 40.0639 29.1081i 1.45327 1.05586i
\(761\) −9.74431 + 29.9899i −0.353231 + 1.08713i 0.603797 + 0.797138i \(0.293654\pi\)
−0.957028 + 0.289995i \(0.906346\pi\)
\(762\) 0.856793 0.622496i 0.0310383 0.0225507i
\(763\) 51.8820 + 37.6945i 1.87826 + 1.36463i
\(764\) 0.251031 + 0.772595i 0.00908199 + 0.0279515i
\(765\) 10.7821 + 7.83366i 0.389828 + 0.283226i
\(766\) 5.61795 17.2903i 0.202985 0.624723i
\(767\) −13.2725 + 40.8484i −0.479241 + 1.47495i
\(768\) −3.83172 11.7928i −0.138265 0.425537i
\(769\) −12.7303 −0.459065 −0.229533 0.973301i \(-0.573720\pi\)
−0.229533 + 0.973301i \(0.573720\pi\)
\(770\) −13.5447 −0.488118
\(771\) −3.37890 10.3992i −0.121688 0.374517i
\(772\) −4.21193 + 3.06014i −0.151591 + 0.110137i
\(773\) −27.5626 20.0254i −0.991358 0.720264i −0.0311401 0.999515i \(-0.509914\pi\)
−0.960218 + 0.279251i \(0.909914\pi\)
\(774\) 7.32504 0.263293
\(775\) 11.7588 5.21902i 0.422387 0.187473i
\(776\) −5.13340 −0.184278
\(777\) −28.4326 20.6575i −1.02001 0.741083i
\(778\) 33.0499 24.0122i 1.18490 0.860878i
\(779\) −5.96294 18.3521i −0.213645 0.657531i
\(780\) 4.82743 0.172850
\(781\) 6.10943 0.218613
\(782\) 6.21325 + 19.1224i 0.222185 + 0.683816i
\(783\) 1.57553 4.84897i 0.0563047 0.173288i
\(784\) −9.18993 + 28.2837i −0.328212 + 1.01013i
\(785\) −3.00845 2.18577i −0.107376 0.0780134i
\(786\) −1.55812 4.79541i −0.0555764 0.171047i
\(787\) −34.1974 24.8459i −1.21901 0.885660i −0.222989 0.974821i \(-0.571581\pi\)
−0.996017 + 0.0891609i \(0.971581\pi\)
\(788\) −3.44512 + 2.50302i −0.122727 + 0.0891666i
\(789\) −7.67365 + 23.6171i −0.273189 + 0.840790i
\(790\) 43.8521 31.8604i 1.56019 1.13354i
\(791\) −21.6278 + 15.7135i −0.768994 + 0.558707i
\(792\) 0.919228 2.82909i 0.0326633 0.100527i
\(793\) −5.10054 + 3.70576i −0.181125 + 0.131595i
\(794\) −17.5279 12.7347i −0.622041 0.451939i
\(795\) −4.49208 13.8252i −0.159318 0.490329i
\(796\) 0.404492 + 0.293880i 0.0143368 + 0.0104163i
\(797\) −2.29403 + 7.06029i −0.0812586 + 0.250088i −0.983430 0.181290i \(-0.941973\pi\)
0.902171 + 0.431379i \(0.141973\pi\)
\(798\) 9.53133 29.3344i 0.337405 1.03843i
\(799\) 12.0739 + 37.1598i 0.427145 + 1.31462i
\(800\) 7.15497 0.252966
\(801\) 9.00824 0.318291
\(802\) 7.18630 + 22.1172i 0.253757 + 0.780984i
\(803\) 0.123512 0.0897368i 0.00435865 0.00316674i
\(804\) 3.21354 + 2.33477i 0.113333 + 0.0823411i
\(805\) 39.8101 1.40312
\(806\) 19.2090 8.52573i 0.676607 0.300306i
\(807\) 24.9826 0.879429
\(808\) −9.42594 6.84834i −0.331603 0.240924i
\(809\) 39.4021 28.6273i 1.38530 1.00648i 0.388943 0.921262i \(-0.372840\pi\)
0.996362 0.0852207i \(-0.0271595\pi\)
\(810\) −1.00041 3.07896i −0.0351510 0.108184i
\(811\) −10.2486 −0.359875 −0.179938 0.983678i \(-0.557590\pi\)
−0.179938 + 0.983678i \(0.557590\pi\)
\(812\) 12.4797 0.437951
\(813\) 6.25946 + 19.2646i 0.219529 + 0.675640i
\(814\) 2.91270 8.96436i 0.102090 0.314201i
\(815\) 0.351753 1.08258i 0.0123214 0.0379212i
\(816\) 10.1549 + 7.37795i 0.355492 + 0.258280i
\(817\) −11.2682 34.6798i −0.394223 1.21329i
\(818\) −14.9213 10.8410i −0.521713 0.379047i
\(819\) 11.0224 8.00824i 0.385154 0.279830i
\(820\) 1.53196 4.71488i 0.0534983 0.164651i
\(821\) 24.2631 17.6281i 0.846786 0.615226i −0.0774717 0.996995i \(-0.524685\pi\)
0.924258 + 0.381768i \(0.124685\pi\)
\(822\) −8.43258 + 6.12662i −0.294120 + 0.213691i
\(823\) −7.97269 + 24.5374i −0.277911 + 0.855321i 0.710524 + 0.703673i \(0.248458\pi\)
−0.988435 + 0.151648i \(0.951542\pi\)
\(824\) −9.07947 + 6.59662i −0.316298 + 0.229804i
\(825\) 1.80962 + 1.31477i 0.0630029 + 0.0457743i
\(826\) 21.7868 + 67.0528i 0.758058 + 2.33306i
\(827\) 31.3230 + 22.7575i 1.08921 + 0.791355i 0.979265 0.202583i \(-0.0649337\pi\)
0.109941 + 0.993938i \(0.464934\pi\)
\(828\) −0.596238 + 1.83503i −0.0207207 + 0.0637718i
\(829\) −1.11055 + 3.41793i −0.0385711 + 0.118710i −0.968488 0.249060i \(-0.919878\pi\)
0.929917 + 0.367769i \(0.119878\pi\)
\(830\) 6.97397 + 21.4637i 0.242070 + 0.745015i
\(831\) 1.93082 0.0669793
\(832\) 27.7439 0.961846
\(833\) 17.7883 + 54.7467i 0.616327 + 1.89686i
\(834\) −13.9560 + 10.1396i −0.483255 + 0.351106i
\(835\) −25.1712 18.2880i −0.871085 0.632881i
\(836\) −3.26795 −0.113024
\(837\) 3.72076 + 4.14197i 0.128608 + 0.143167i
\(838\) 9.29998 0.321262
\(839\) 40.7291 + 29.5914i 1.40612 + 1.02161i 0.993872 + 0.110540i \(0.0352579\pi\)
0.412253 + 0.911070i \(0.364742\pi\)
\(840\) 29.0497 21.1058i 1.00231 0.728220i
\(841\) −0.928656 2.85811i −0.0320226 0.0985555i
\(842\) 6.37309 0.219631
\(843\) 4.26528 0.146904
\(844\) −0.405866 1.24913i −0.0139705 0.0429967i
\(845\) 2.55841 7.87396i 0.0880118 0.270873i
\(846\) 2.93292 9.02661i 0.100836 0.310341i
\(847\) −35.1843 25.5629i −1.20895 0.878350i
\(848\) −4.23076 13.0209i −0.145285 0.447141i
\(849\) 23.3856 + 16.9906i 0.802592 + 0.583117i
\(850\) −11.0325 + 8.01558i −0.378411 + 0.274932i
\(851\) −8.56088 + 26.3477i −0.293463 + 0.903186i
\(852\) −2.89165 + 2.10091i −0.0990663 + 0.0719759i
\(853\) 6.60658 4.79996i 0.226205 0.164348i −0.468910 0.883246i \(-0.655353\pi\)
0.695115 + 0.718898i \(0.255353\pi\)
\(854\) −3.19802 + 9.84250i −0.109434 + 0.336804i
\(855\) −13.0381 + 9.47276i −0.445895 + 0.323962i
\(856\) 21.2574 + 15.4444i 0.726563 + 0.527879i
\(857\) 9.86493 + 30.3611i 0.336980 + 1.03712i 0.965739 + 0.259517i \(0.0835633\pi\)
−0.628759 + 0.777600i \(0.716437\pi\)
\(858\) 2.95617 + 2.14779i 0.100922 + 0.0733242i
\(859\) 2.99613 9.22115i 0.102227 0.314622i −0.886843 0.462071i \(-0.847106\pi\)
0.989070 + 0.147450i \(0.0471064\pi\)
\(860\) 2.89494 8.90970i 0.0987166 0.303818i
\(861\) −4.32364 13.3068i −0.147349 0.453494i
\(862\) −11.5941 −0.394896
\(863\) 18.2464 0.621115 0.310558 0.950555i \(-0.399484\pi\)
0.310558 + 0.950555i \(0.399484\pi\)
\(864\) 0.956893 + 2.94501i 0.0325542 + 0.100191i
\(865\) 16.7213 12.1488i 0.568542 0.413070i
\(866\) −11.0338 8.01653i −0.374944 0.272413i
\(867\) 7.29618 0.247791
\(868\) −6.82781 + 11.7945i −0.231751 + 0.400333i
\(869\) −16.2083 −0.549830
\(870\) 13.3536 + 9.70195i 0.452729 + 0.328927i
\(871\) −17.8872 + 12.9958i −0.606083 + 0.440345i
\(872\) −14.0900 43.3644i −0.477146 1.46851i
\(873\) 1.67058 0.0565406
\(874\) −24.3135 −0.822418
\(875\) −9.71141 29.8887i −0.328306 1.01042i
\(876\) −0.0276008 + 0.0849466i −0.000932545 + 0.00287008i
\(877\) −1.37370 + 4.22780i −0.0463864 + 0.142763i −0.971567 0.236764i \(-0.923913\pi\)
0.925181 + 0.379527i \(0.123913\pi\)
\(878\) −15.9110 11.5600i −0.536969 0.390131i
\(879\) 8.00748 + 24.6445i 0.270086 + 0.831238i
\(880\) 5.39244 + 3.91784i 0.181779 + 0.132070i
\(881\) 44.9353 32.6474i 1.51391 1.09992i 0.549503 0.835492i \(-0.314817\pi\)
0.964406 0.264427i \(-0.0851829\pi\)
\(882\) 4.32101 13.2987i 0.145496 0.447790i
\(883\) −17.4061 + 12.6463i −0.585762 + 0.425581i −0.840797 0.541351i \(-0.817913\pi\)
0.255035 + 0.966932i \(0.417913\pi\)
\(884\) 7.11977 5.17282i 0.239464 0.173981i
\(885\) 11.3836 35.0351i 0.382655 1.17769i
\(886\) 9.20841 6.69030i 0.309362 0.224765i
\(887\) −7.23033 5.25314i −0.242771 0.176383i 0.459746 0.888050i \(-0.347940\pi\)
−0.702517 + 0.711667i \(0.747940\pi\)
\(888\) 7.72163 + 23.7647i 0.259121 + 0.797492i
\(889\) −3.09261 2.24691i −0.103723 0.0753590i
\(890\) −9.01197 + 27.7360i −0.302082 + 0.929712i
\(891\) −0.299148 + 0.920682i −0.0100218 + 0.0308440i
\(892\) 0.957249 + 2.94611i 0.0320511 + 0.0986430i
\(893\) −47.2475 −1.58108
\(894\) 15.3592 0.513689
\(895\) 10.5087 + 32.3424i 0.351267 + 1.08109i
\(896\) 15.1899 11.0361i 0.507460 0.368691i
\(897\) −8.68867 6.31268i −0.290106 0.210774i
\(898\) −5.28606 −0.176398
\(899\) −27.7601 5.93422i −0.925852 0.197917i
\(900\) −1.30863 −0.0436210
\(901\) −21.4395 15.5767i −0.714253 0.518935i
\(902\) 3.03584 2.20567i 0.101082 0.0734406i
\(903\) −8.17036 25.1458i −0.271893 0.836799i
\(904\) 19.0074 0.632176
\(905\) −58.5813 −1.94731
\(906\) −2.14738 6.60896i −0.0713420 0.219568i
\(907\) 9.92049 30.5321i 0.329404 1.01380i −0.640009 0.768368i \(-0.721069\pi\)
0.969413 0.245435i \(-0.0789307\pi\)
\(908\) 4.38720 13.5024i 0.145594 0.448093i
\(909\) 3.06752 + 2.22868i 0.101743 + 0.0739207i
\(910\) 13.6301 + 41.9490i 0.451832 + 1.39060i
\(911\) 15.5663 + 11.3095i 0.515733 + 0.374702i 0.814994 0.579469i \(-0.196740\pi\)
−0.299261 + 0.954171i \(0.596740\pi\)
\(912\) −12.2797 + 8.92170i −0.406620 + 0.295427i
\(913\) 2.08538 6.41815i 0.0690162 0.212410i
\(914\) 25.6920 18.6663i 0.849816 0.617427i
\(915\) 4.37466 3.17837i 0.144622 0.105074i
\(916\) −4.41809 + 13.5975i −0.145978 + 0.449273i
\(917\) −14.7240 + 10.6976i −0.486230 + 0.353267i
\(918\) −4.77471 3.46903i −0.157589 0.114495i
\(919\) −2.20906 6.79877i −0.0728700 0.224271i 0.907988 0.418997i \(-0.137618\pi\)
−0.980858 + 0.194726i \(0.937618\pi\)
\(920\) −22.8991 16.6372i −0.754962 0.548512i
\(921\) −1.86208 + 5.73089i −0.0613576 + 0.188839i
\(922\) −7.90324 + 24.3237i −0.260279 + 0.801057i
\(923\) −6.14792 18.9214i −0.202361 0.622804i
\(924\) −2.36954 −0.0779520
\(925\) −18.7895 −0.617796
\(926\) 5.53984 + 17.0499i 0.182051 + 0.560294i
\(927\) 2.95477 2.14676i 0.0970472 0.0705089i
\(928\) −12.7727 9.27989i −0.419284 0.304627i
\(929\) −38.1829 −1.25274 −0.626369 0.779526i \(-0.715460\pi\)
−0.626369 + 0.779526i \(0.715460\pi\)
\(930\) −16.4752 + 7.31239i −0.540245 + 0.239783i
\(931\) −69.6087 −2.28133
\(932\) −10.2842 7.47190i −0.336870 0.244750i
\(933\) 17.3714 12.6211i 0.568715 0.413196i
\(934\) 3.15166 + 9.69981i 0.103125 + 0.317388i
\(935\) 12.9018 0.421933
\(936\) −9.68693 −0.316627
\(937\) −6.72531 20.6984i −0.219706 0.676186i −0.998786 0.0492613i \(-0.984313\pi\)
0.779080 0.626925i \(-0.215687\pi\)
\(938\) −11.2152 + 34.5169i −0.366190 + 1.12702i
\(939\) −0.404077 + 1.24362i −0.0131866 + 0.0405841i
\(940\) −9.82026 7.13483i −0.320301 0.232713i
\(941\) −13.1981 40.6195i −0.430245 1.32416i −0.897882 0.440237i \(-0.854894\pi\)
0.467637 0.883921i \(-0.345106\pi\)
\(942\) 1.33225 + 0.967938i 0.0434071 + 0.0315371i
\(943\) −8.92281 + 6.48280i −0.290567 + 0.211109i
\(944\) 10.7214 32.9970i 0.348951 1.07396i
\(945\) −9.45375 + 6.86855i −0.307530 + 0.223434i
\(946\) 5.73681 4.16804i 0.186520 0.135515i
\(947\) 10.2862 31.6577i 0.334257 1.02874i −0.632830 0.774291i \(-0.718107\pi\)
0.967087 0.254447i \(-0.0818933\pi\)
\(948\) 7.67156 5.57371i 0.249161 0.181026i
\(949\) −0.402212 0.292224i −0.0130564 0.00948600i
\(950\) −5.09578 15.6832i −0.165329 0.508830i
\(951\) −17.2768 12.5523i −0.560238 0.407037i
\(952\) 20.2283 62.2562i 0.655602 2.01773i
\(953\) −9.10198 + 28.0130i −0.294842 + 0.907431i 0.688432 + 0.725301i \(0.258299\pi\)
−0.983274 + 0.182130i \(0.941701\pi\)
\(954\) 1.98926 + 6.12230i 0.0644045 + 0.198217i
\(955\) 3.87821 0.125496
\(956\) −4.14954 −0.134206
\(957\) −1.52521 4.69411i −0.0493030 0.151739i
\(958\) −13.9389 + 10.1272i −0.450345 + 0.327195i
\(959\) 30.4375 + 22.1142i 0.982879 + 0.714103i
\(960\) −23.7955 −0.767997
\(961\) 20.7964 22.9894i 0.670851 0.741592i
\(962\) −30.6943 −0.989625
\(963\) −6.91788 5.02613i −0.222925 0.161965i
\(964\) −5.63264 + 4.09235i −0.181415 + 0.131806i
\(965\) 7.68054 + 23.6383i 0.247245 + 0.760943i
\(966\) −17.6294 −0.567215
\(967\) −11.9582 −0.384548 −0.192274 0.981341i \(-0.561586\pi\)
−0.192274 + 0.981341i \(0.561586\pi\)
\(968\) 9.55523 + 29.4080i 0.307117 + 0.945208i
\(969\) −9.07889 + 27.9419i −0.291656 + 0.897624i
\(970\) −1.67127 + 5.14364i −0.0536613 + 0.165152i
\(971\) 33.5237 + 24.3564i 1.07583 + 0.781633i 0.976950 0.213467i \(-0.0684756\pi\)
0.0988750 + 0.995100i \(0.468476\pi\)
\(972\) −0.175014 0.538638i −0.00561358 0.0172768i
\(973\) 50.3743 + 36.5991i 1.61493 + 1.17331i
\(974\) −25.3250 + 18.3997i −0.811466 + 0.589564i
\(975\) 2.25091 6.92758i 0.0720867 0.221860i
\(976\) 4.12017 2.99348i 0.131883 0.0958189i
\(977\) −18.0922 + 13.1447i −0.578820 + 0.420537i −0.838299 0.545212i \(-0.816449\pi\)
0.259478 + 0.965749i \(0.416449\pi\)
\(978\) −0.155769 + 0.479408i −0.00498094 + 0.0153298i
\(979\) 7.05506 5.12580i 0.225481 0.163821i
\(980\) −14.4680 10.5116i −0.462162 0.335780i
\(981\) 4.58535 + 14.1122i 0.146399 + 0.450569i
\(982\) −15.8178 11.4923i −0.504766 0.366734i
\(983\) −12.8655 + 39.5959i −0.410346 + 1.26291i 0.506003 + 0.862532i \(0.331123\pi\)
−0.916348 + 0.400382i \(0.868877\pi\)
\(984\) −3.07409 + 9.46109i −0.0979985 + 0.301609i
\(985\) 6.28225 + 19.3348i 0.200169 + 0.616057i
\(986\) 30.0907 0.958284
\(987\) −34.2584 −1.09046
\(988\) 3.28854 + 10.1211i 0.104622 + 0.321995i
\(989\) −16.8614 + 12.2505i −0.536162 + 0.389544i
\(990\) −2.53547 1.84213i −0.0805825 0.0585466i
\(991\) 14.9553 0.475071 0.237535 0.971379i \(-0.423660\pi\)
0.237535 + 0.971379i \(0.423660\pi\)
\(992\) 15.7585 6.99428i 0.500334 0.222069i
\(993\) 22.7167 0.720891
\(994\) −26.4207 19.1958i −0.838015 0.608853i
\(995\) 1.93106 1.40300i 0.0612187 0.0444780i
\(996\) 1.22004 + 3.75489i 0.0386584 + 0.118978i
\(997\) −14.1531 −0.448235 −0.224117 0.974562i \(-0.571950\pi\)
−0.224117 + 0.974562i \(0.571950\pi\)
\(998\) 27.9548 0.884895
\(999\) −2.51288 7.73384i −0.0795040 0.244688i
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 93.2.f.b.64.2 yes 16
3.2 odd 2 279.2.i.c.64.3 16
31.4 even 5 2883.2.a.p.1.6 8
31.16 even 5 inner 93.2.f.b.16.2 16
31.27 odd 10 2883.2.a.o.1.6 8
93.35 odd 10 8649.2.a.bh.1.3 8
93.47 odd 10 279.2.i.c.109.3 16
93.89 even 10 8649.2.a.bg.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
93.2.f.b.16.2 16 31.16 even 5 inner
93.2.f.b.64.2 yes 16 1.1 even 1 trivial
279.2.i.c.64.3 16 3.2 odd 2
279.2.i.c.109.3 16 93.47 odd 10
2883.2.a.o.1.6 8 31.27 odd 10
2883.2.a.p.1.6 8 31.4 even 5
8649.2.a.bg.1.3 8 93.89 even 10
8649.2.a.bh.1.3 8 93.35 odd 10