Properties

Label 625.2.d.q.376.1
Level $625$
Weight $2$
Character 625.376
Analytic conductor $4.991$
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] = [625,2,Mod(126,625)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(625, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("625.126");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 625 = 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 625.d (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.99065012633\)
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: \( x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 376.1
Root \(-1.80544i\) of defining polynomial
Character \(\chi\) \(=\) 625.376
Dual form 625.2.d.q.251.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36191 - 0.989484i) q^{2} +(-0.219507 - 0.675574i) q^{3} +(0.257680 + 0.793058i) q^{4} +(-0.369521 + 1.13727i) q^{6} -4.59110 q^{7} +(-0.606623 + 1.86699i) q^{8} +(2.01883 - 1.46677i) q^{9} +O(q^{10})\) \(q+(-1.36191 - 0.989484i) q^{2} +(-0.219507 - 0.675574i) q^{3} +(0.257680 + 0.793058i) q^{4} +(-0.369521 + 1.13727i) q^{6} -4.59110 q^{7} +(-0.606623 + 1.86699i) q^{8} +(2.01883 - 1.46677i) q^{9} +(-3.16713 - 2.30105i) q^{11} +(0.479206 - 0.348164i) q^{12} +(0.463518 - 0.336765i) q^{13} +(6.25266 + 4.54282i) q^{14} +(4.02276 - 2.92270i) q^{16} +(-0.0718808 + 0.221226i) q^{17} -4.20081 q^{18} +(-1.71507 + 5.27846i) q^{19} +(1.00778 + 3.10163i) q^{21} +(2.03648 + 6.26765i) q^{22} +(3.99061 + 2.89935i) q^{23} +1.39445 q^{24} -0.964492 q^{26} +(-3.15809 - 2.29449i) q^{27} +(-1.18304 - 3.64101i) q^{28} +(1.27643 + 3.92845i) q^{29} +(-1.08011 + 3.32424i) q^{31} -4.44444 q^{32} +(-0.859324 + 2.64473i) q^{33} +(0.316795 - 0.230165i) q^{34} +(1.68345 + 1.22310i) q^{36} +(4.38203 - 3.18373i) q^{37} +(7.55872 - 5.49173i) q^{38} +(-0.329255 - 0.239218i) q^{39} +(-8.43214 + 6.12630i) q^{41} +(1.69651 - 5.22132i) q^{42} +1.38833 q^{43} +(1.00876 - 3.10465i) q^{44} +(-2.56598 - 7.89729i) q^{46} +(0.284425 + 0.875370i) q^{47} +(-2.85753 - 2.07611i) q^{48} +14.0782 q^{49} +0.165233 q^{51} +(0.386514 + 0.280819i) q^{52} +(0.380455 + 1.17092i) q^{53} +(2.03067 + 6.24976i) q^{54} +(2.78507 - 8.57157i) q^{56} +3.94246 q^{57} +(2.14876 - 6.61320i) q^{58} +(-3.64689 + 2.64962i) q^{59} +(9.43214 + 6.85285i) q^{61} +(4.76029 - 3.45856i) q^{62} +(-9.26868 + 6.73409i) q^{63} +(-1.99259 - 1.44770i) q^{64} +(3.78724 - 2.75159i) q^{66} +(-0.912982 + 2.80987i) q^{67} -0.193968 q^{68} +(1.08276 - 3.33238i) q^{69} +(0.990558 + 3.04862i) q^{71} +(1.51378 + 4.65893i) q^{72} +(8.32657 + 6.04961i) q^{73} -9.11816 q^{74} -4.62806 q^{76} +(14.5406 + 10.5644i) q^{77} +(0.211713 + 0.651586i) q^{78} +(-2.97123 - 9.14449i) q^{79} +(1.45651 - 4.48267i) q^{81} +17.5457 q^{82} +(-3.23955 + 9.97030i) q^{83} +(-2.20009 + 1.59846i) q^{84} +(-1.89077 - 1.37373i) q^{86} +(2.37377 - 1.72465i) q^{87} +(6.21731 - 4.51714i) q^{88} +(-5.87207 - 4.26631i) q^{89} +(-2.12806 + 1.54612i) q^{91} +(-1.27105 + 3.91189i) q^{92} +2.48286 q^{93} +(0.478804 - 1.47361i) q^{94} +(0.975587 + 3.00255i) q^{96} +(-2.57093 - 7.91252i) q^{97} +(-19.1733 - 13.9302i) q^{98} -9.76903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36191 0.989484i −0.963014 0.699671i −0.00916528 0.999958i \(-0.502917\pi\)
−0.953849 + 0.300287i \(0.902917\pi\)
\(3\) −0.219507 0.675574i −0.126733 0.390043i 0.867480 0.497472i \(-0.165738\pi\)
−0.994213 + 0.107429i \(0.965738\pi\)
\(4\) 0.257680 + 0.793058i 0.128840 + 0.396529i
\(5\) 0 0
\(6\) −0.369521 + 1.13727i −0.150856 + 0.464288i
\(7\) −4.59110 −1.73527 −0.867637 0.497198i \(-0.834362\pi\)
−0.867637 + 0.497198i \(0.834362\pi\)
\(8\) −0.606623 + 1.86699i −0.214474 + 0.660082i
\(9\) 2.01883 1.46677i 0.672945 0.488923i
\(10\) 0 0
\(11\) −3.16713 2.30105i −0.954926 0.693794i −0.00295900 0.999996i \(-0.500942\pi\)
−0.951967 + 0.306201i \(0.900942\pi\)
\(12\) 0.479206 0.348164i 0.138335 0.100506i
\(13\) 0.463518 0.336765i 0.128557 0.0934019i −0.521649 0.853160i \(-0.674683\pi\)
0.650205 + 0.759758i \(0.274683\pi\)
\(14\) 6.25266 + 4.54282i 1.67109 + 1.21412i
\(15\) 0 0
\(16\) 4.02276 2.92270i 1.00569 0.730676i
\(17\) −0.0718808 + 0.221226i −0.0174337 + 0.0536553i −0.959395 0.282066i \(-0.908980\pi\)
0.941961 + 0.335722i \(0.108980\pi\)
\(18\) −4.20081 −0.990140
\(19\) −1.71507 + 5.27846i −0.393465 + 1.21096i 0.536685 + 0.843782i \(0.319676\pi\)
−0.930151 + 0.367178i \(0.880324\pi\)
\(20\) 0 0
\(21\) 1.00778 + 3.10163i 0.219916 + 0.676831i
\(22\) 2.03648 + 6.26765i 0.434179 + 1.33627i
\(23\) 3.99061 + 2.89935i 0.832100 + 0.604556i 0.920153 0.391560i \(-0.128064\pi\)
−0.0880529 + 0.996116i \(0.528064\pi\)
\(24\) 1.39445 0.284641
\(25\) 0 0
\(26\) −0.964492 −0.189152
\(27\) −3.15809 2.29449i −0.607775 0.441574i
\(28\) −1.18304 3.64101i −0.223573 0.688086i
\(29\) 1.27643 + 3.92845i 0.237028 + 0.729496i 0.996846 + 0.0793604i \(0.0252878\pi\)
−0.759818 + 0.650135i \(0.774712\pi\)
\(30\) 0 0
\(31\) −1.08011 + 3.32424i −0.193994 + 0.597051i 0.805993 + 0.591925i \(0.201632\pi\)
−0.999987 + 0.00512633i \(0.998368\pi\)
\(32\) −4.44444 −0.785674
\(33\) −0.859324 + 2.64473i −0.149589 + 0.460388i
\(34\) 0.316795 0.230165i 0.0543299 0.0394730i
\(35\) 0 0
\(36\) 1.68345 + 1.22310i 0.280574 + 0.203849i
\(37\) 4.38203 3.18373i 0.720401 0.523402i −0.166112 0.986107i \(-0.553121\pi\)
0.886512 + 0.462705i \(0.153121\pi\)
\(38\) 7.55872 5.49173i 1.22619 0.890876i
\(39\) −0.329255 0.239218i −0.0527230 0.0383055i
\(40\) 0 0
\(41\) −8.43214 + 6.12630i −1.31688 + 0.956768i −0.316913 + 0.948455i \(0.602646\pi\)
−0.999965 + 0.00831339i \(0.997354\pi\)
\(42\) 1.69651 5.22132i 0.261777 0.805666i
\(43\) 1.38833 0.211718 0.105859 0.994381i \(-0.466241\pi\)
0.105859 + 0.994381i \(0.466241\pi\)
\(44\) 1.00876 3.10465i 0.152077 0.468044i
\(45\) 0 0
\(46\) −2.56598 7.89729i −0.378334 1.16439i
\(47\) 0.284425 + 0.875370i 0.0414876 + 0.127686i 0.969655 0.244477i \(-0.0786163\pi\)
−0.928167 + 0.372163i \(0.878616\pi\)
\(48\) −2.85753 2.07611i −0.412448 0.299661i
\(49\) 14.0782 2.01118
\(50\) 0 0
\(51\) 0.165233 0.0231373
\(52\) 0.386514 + 0.280819i 0.0535998 + 0.0389425i
\(53\) 0.380455 + 1.17092i 0.0522595 + 0.160838i 0.973780 0.227491i \(-0.0730523\pi\)
−0.921521 + 0.388329i \(0.873052\pi\)
\(54\) 2.03067 + 6.24976i 0.276339 + 0.850485i
\(55\) 0 0
\(56\) 2.78507 8.57157i 0.372171 1.14542i
\(57\) 3.94246 0.522191
\(58\) 2.14876 6.61320i 0.282146 0.868356i
\(59\) −3.64689 + 2.64962i −0.474785 + 0.344951i −0.799303 0.600928i \(-0.794798\pi\)
0.324518 + 0.945879i \(0.394798\pi\)
\(60\) 0 0
\(61\) 9.43214 + 6.85285i 1.20766 + 0.877417i 0.995016 0.0997121i \(-0.0317922\pi\)
0.212645 + 0.977129i \(0.431792\pi\)
\(62\) 4.76029 3.45856i 0.604558 0.439237i
\(63\) −9.26868 + 6.73409i −1.16774 + 0.848416i
\(64\) −1.99259 1.44770i −0.249074 0.180963i
\(65\) 0 0
\(66\) 3.78724 2.75159i 0.466177 0.338697i
\(67\) −0.912982 + 2.80987i −0.111539 + 0.343280i −0.991209 0.132303i \(-0.957763\pi\)
0.879671 + 0.475583i \(0.157763\pi\)
\(68\) −0.193968 −0.0235220
\(69\) 1.08276 3.33238i 0.130348 0.401171i
\(70\) 0 0
\(71\) 0.990558 + 3.04862i 0.117558 + 0.361805i 0.992472 0.122473i \(-0.0390824\pi\)
−0.874914 + 0.484278i \(0.839082\pi\)
\(72\) 1.51378 + 4.65893i 0.178400 + 0.549060i
\(73\) 8.32657 + 6.04961i 0.974551 + 0.708053i 0.956484 0.291784i \(-0.0942489\pi\)
0.0180667 + 0.999837i \(0.494249\pi\)
\(74\) −9.11816 −1.05996
\(75\) 0 0
\(76\) −4.62806 −0.530875
\(77\) 14.5406 + 10.5644i 1.65706 + 1.20392i
\(78\) 0.211713 + 0.651586i 0.0239718 + 0.0737775i
\(79\) −2.97123 9.14449i −0.334289 1.02884i −0.967071 0.254506i \(-0.918087\pi\)
0.632782 0.774330i \(-0.281913\pi\)
\(80\) 0 0
\(81\) 1.45651 4.48267i 0.161834 0.498074i
\(82\) 17.5457 1.93759
\(83\) −3.23955 + 9.97030i −0.355587 + 1.09438i 0.600082 + 0.799939i \(0.295135\pi\)
−0.955669 + 0.294445i \(0.904865\pi\)
\(84\) −2.20009 + 1.59846i −0.240049 + 0.174406i
\(85\) 0 0
\(86\) −1.89077 1.37373i −0.203887 0.148133i
\(87\) 2.37377 1.72465i 0.254495 0.184902i
\(88\) 6.21731 4.51714i 0.662768 0.481529i
\(89\) −5.87207 4.26631i −0.622438 0.452228i 0.231334 0.972874i \(-0.425691\pi\)
−0.853772 + 0.520646i \(0.825691\pi\)
\(90\) 0 0
\(91\) −2.12806 + 1.54612i −0.223081 + 0.162078i
\(92\) −1.27105 + 3.91189i −0.132516 + 0.407843i
\(93\) 2.48286 0.257461
\(94\) 0.478804 1.47361i 0.0493848 0.151991i
\(95\) 0 0
\(96\) 0.975587 + 3.00255i 0.0995704 + 0.306446i
\(97\) −2.57093 7.91252i −0.261039 0.803394i −0.992580 0.121597i \(-0.961199\pi\)
0.731541 0.681797i \(-0.238801\pi\)
\(98\) −19.1733 13.9302i −1.93679 1.40716i
\(99\) −9.76903 −0.981824
\(100\) 0 0
\(101\) −3.56513 −0.354744 −0.177372 0.984144i \(-0.556760\pi\)
−0.177372 + 0.984144i \(0.556760\pi\)
\(102\) −0.225032 0.163495i −0.0222815 0.0161885i
\(103\) −0.123398 0.379779i −0.0121587 0.0374207i 0.944793 0.327668i \(-0.106263\pi\)
−0.956952 + 0.290247i \(0.906263\pi\)
\(104\) 0.347558 + 1.06967i 0.0340809 + 0.104890i
\(105\) 0 0
\(106\) 0.640462 1.97114i 0.0622071 0.191454i
\(107\) −1.64372 −0.158904 −0.0794522 0.996839i \(-0.525317\pi\)
−0.0794522 + 0.996839i \(0.525317\pi\)
\(108\) 1.00588 3.09579i 0.0967913 0.297893i
\(109\) −0.0606078 + 0.0440342i −0.00580518 + 0.00421771i −0.590684 0.806903i \(-0.701142\pi\)
0.584879 + 0.811121i \(0.301142\pi\)
\(110\) 0 0
\(111\) −3.11273 2.26153i −0.295447 0.214655i
\(112\) −18.4689 + 13.4184i −1.74515 + 1.26792i
\(113\) −11.4337 + 8.30708i −1.07559 + 0.781464i −0.976909 0.213655i \(-0.931463\pi\)
−0.0986840 + 0.995119i \(0.531463\pi\)
\(114\) −5.36926 3.90100i −0.502878 0.365362i
\(115\) 0 0
\(116\) −2.78658 + 2.02457i −0.258728 + 0.187977i
\(117\) 0.441808 1.35975i 0.0408452 0.125709i
\(118\) 7.58848 0.698576
\(119\) 0.330012 1.01567i 0.0302522 0.0931066i
\(120\) 0 0
\(121\) 1.33667 + 4.11386i 0.121516 + 0.373987i
\(122\) −6.06492 18.6659i −0.549092 1.68993i
\(123\) 5.98969 + 4.35176i 0.540072 + 0.392385i
\(124\) −2.91464 −0.261742
\(125\) 0 0
\(126\) 19.2864 1.71817
\(127\) −9.55647 6.94318i −0.848000 0.616108i 0.0765941 0.997062i \(-0.475595\pi\)
−0.924594 + 0.380955i \(0.875595\pi\)
\(128\) 4.02807 + 12.3971i 0.356034 + 1.09576i
\(129\) −0.304748 0.937917i −0.0268315 0.0825790i
\(130\) 0 0
\(131\) −5.17210 + 15.9181i −0.451888 + 1.39077i 0.422862 + 0.906194i \(0.361026\pi\)
−0.874750 + 0.484575i \(0.838974\pi\)
\(132\) −2.31885 −0.201830
\(133\) 7.87408 24.2339i 0.682770 2.10135i
\(134\) 4.02372 2.92340i 0.347596 0.252544i
\(135\) 0 0
\(136\) −0.369424 0.268402i −0.0316778 0.0230153i
\(137\) −8.43168 + 6.12598i −0.720367 + 0.523378i −0.886502 0.462726i \(-0.846872\pi\)
0.166134 + 0.986103i \(0.446872\pi\)
\(138\) −4.77195 + 3.46702i −0.406215 + 0.295133i
\(139\) −5.38800 3.91461i −0.457004 0.332033i 0.335351 0.942093i \(-0.391145\pi\)
−0.792355 + 0.610060i \(0.791145\pi\)
\(140\) 0 0
\(141\) 0.528944 0.384300i 0.0445451 0.0323639i
\(142\) 1.66752 5.13208i 0.139935 0.430675i
\(143\) −2.24294 −0.187564
\(144\) 3.83435 11.8009i 0.319529 0.983409i
\(145\) 0 0
\(146\) −5.35403 16.4780i −0.443103 1.36373i
\(147\) −3.09027 9.51089i −0.254882 0.784445i
\(148\) 3.65404 + 2.65482i 0.300360 + 0.218225i
\(149\) −12.0316 −0.985667 −0.492834 0.870124i \(-0.664039\pi\)
−0.492834 + 0.870124i \(0.664039\pi\)
\(150\) 0 0
\(151\) −1.54218 −0.125501 −0.0627505 0.998029i \(-0.519987\pi\)
−0.0627505 + 0.998029i \(0.519987\pi\)
\(152\) −8.81445 6.40407i −0.714946 0.519439i
\(153\) 0.179373 + 0.552052i 0.0145014 + 0.0446308i
\(154\) −9.34970 28.7754i −0.753420 2.31879i
\(155\) 0 0
\(156\) 0.104871 0.322760i 0.00839641 0.0258415i
\(157\) −9.82482 −0.784106 −0.392053 0.919943i \(-0.628235\pi\)
−0.392053 + 0.919943i \(0.628235\pi\)
\(158\) −5.00179 + 15.3939i −0.397921 + 1.22468i
\(159\) 0.707530 0.514051i 0.0561108 0.0407669i
\(160\) 0 0
\(161\) −18.3213 13.3112i −1.44392 1.04907i
\(162\) −6.41915 + 4.66379i −0.504336 + 0.366422i
\(163\) 4.51518 3.28047i 0.353656 0.256946i −0.396745 0.917929i \(-0.629860\pi\)
0.750401 + 0.660982i \(0.229860\pi\)
\(164\) −7.03131 5.10854i −0.549053 0.398910i
\(165\) 0 0
\(166\) 14.2774 10.3732i 1.10814 0.805113i
\(167\) −6.75534 + 20.7908i −0.522744 + 1.60884i 0.245991 + 0.969272i \(0.420887\pi\)
−0.768735 + 0.639568i \(0.779113\pi\)
\(168\) −6.40207 −0.493930
\(169\) −3.91578 + 12.0515i −0.301214 + 0.927042i
\(170\) 0 0
\(171\) 4.27982 + 13.1719i 0.327286 + 1.00728i
\(172\) 0.357744 + 1.10102i 0.0272777 + 0.0839522i
\(173\) −18.9622 13.7768i −1.44167 1.04743i −0.987691 0.156420i \(-0.950005\pi\)
−0.453977 0.891013i \(-0.649995\pi\)
\(174\) −4.93937 −0.374453
\(175\) 0 0
\(176\) −19.4659 −1.46730
\(177\) 2.59053 + 1.88213i 0.194716 + 0.141470i
\(178\) 3.77577 + 11.6206i 0.283006 + 0.871004i
\(179\) −1.95259 6.00947i −0.145944 0.449169i 0.851187 0.524862i \(-0.175883\pi\)
−0.997131 + 0.0756932i \(0.975883\pi\)
\(180\) 0 0
\(181\) −4.12158 + 12.6849i −0.306355 + 0.942863i 0.672813 + 0.739812i \(0.265086\pi\)
−0.979168 + 0.203051i \(0.934914\pi\)
\(182\) 4.42808 0.328231
\(183\) 2.55918 7.87636i 0.189180 0.582237i
\(184\) −7.83387 + 5.69164i −0.577520 + 0.419593i
\(185\) 0 0
\(186\) −3.38143 2.45675i −0.247938 0.180138i
\(187\) 0.736710 0.535251i 0.0538736 0.0391414i
\(188\) −0.620928 + 0.451131i −0.0452859 + 0.0329021i
\(189\) 14.4991 + 10.5342i 1.05466 + 0.766253i
\(190\) 0 0
\(191\) 2.24974 1.63453i 0.162785 0.118270i −0.503410 0.864047i \(-0.667922\pi\)
0.666196 + 0.745777i \(0.267922\pi\)
\(192\) −0.540642 + 1.66393i −0.0390175 + 0.120084i
\(193\) 22.5667 1.62438 0.812192 0.583391i \(-0.198274\pi\)
0.812192 + 0.583391i \(0.198274\pi\)
\(194\) −4.32793 + 13.3200i −0.310728 + 0.956321i
\(195\) 0 0
\(196\) 3.62768 + 11.1649i 0.259120 + 0.797490i
\(197\) 0.393014 + 1.20957i 0.0280011 + 0.0861786i 0.964080 0.265610i \(-0.0855735\pi\)
−0.936079 + 0.351789i \(0.885573\pi\)
\(198\) 13.3045 + 9.66629i 0.945511 + 0.686954i
\(199\) −8.62648 −0.611515 −0.305757 0.952109i \(-0.598910\pi\)
−0.305757 + 0.952109i \(0.598910\pi\)
\(200\) 0 0
\(201\) 2.09868 0.148030
\(202\) 4.85538 + 3.52764i 0.341623 + 0.248204i
\(203\) −5.86023 18.0359i −0.411308 1.26588i
\(204\) 0.0425773 + 0.131039i 0.00298101 + 0.00917459i
\(205\) 0 0
\(206\) −0.207729 + 0.639324i −0.0144732 + 0.0445438i
\(207\) 12.3091 0.855538
\(208\) 0.880354 2.70945i 0.0610415 0.187867i
\(209\) 17.5779 12.7711i 1.21589 0.883394i
\(210\) 0 0
\(211\) 17.0149 + 12.3621i 1.17136 + 0.851039i 0.991171 0.132593i \(-0.0423305\pi\)
0.180185 + 0.983633i \(0.442330\pi\)
\(212\) −0.830571 + 0.603445i −0.0570439 + 0.0414448i
\(213\) 1.84214 1.33839i 0.126221 0.0917050i
\(214\) 2.23859 + 1.62643i 0.153027 + 0.111181i
\(215\) 0 0
\(216\) 6.19957 4.50425i 0.421827 0.306475i
\(217\) 4.95890 15.2619i 0.336632 1.03605i
\(218\) 0.126113 0.00854148
\(219\) 2.25921 6.95314i 0.152663 0.469850i
\(220\) 0 0
\(221\) 0.0411833 + 0.126749i 0.00277029 + 0.00852608i
\(222\) 2.00150 + 6.15999i 0.134332 + 0.413432i
\(223\) 5.12542 + 3.72384i 0.343224 + 0.249367i 0.746021 0.665923i \(-0.231962\pi\)
−0.402797 + 0.915289i \(0.631962\pi\)
\(224\) 20.4049 1.36336
\(225\) 0 0
\(226\) 23.7914 1.58258
\(227\) 9.11148 + 6.61988i 0.604750 + 0.439377i 0.847562 0.530697i \(-0.178070\pi\)
−0.242812 + 0.970073i \(0.578070\pi\)
\(228\) 1.01589 + 3.12660i 0.0672792 + 0.207064i
\(229\) 4.64788 + 14.3047i 0.307140 + 0.945281i 0.978870 + 0.204484i \(0.0655518\pi\)
−0.671729 + 0.740797i \(0.734448\pi\)
\(230\) 0 0
\(231\) 3.94525 12.1422i 0.259578 0.798900i
\(232\) −8.10872 −0.532363
\(233\) −2.41883 + 7.44438i −0.158463 + 0.487698i −0.998495 0.0548381i \(-0.982536\pi\)
0.840033 + 0.542536i \(0.182536\pi\)
\(234\) −1.94715 + 1.41469i −0.127289 + 0.0924810i
\(235\) 0 0
\(236\) −3.04103 2.20944i −0.197954 0.143822i
\(237\) −5.52557 + 4.01456i −0.358925 + 0.260774i
\(238\) −1.45444 + 1.05671i −0.0942772 + 0.0684964i
\(239\) −7.06988 5.13657i −0.457313 0.332257i 0.335163 0.942160i \(-0.391208\pi\)
−0.792476 + 0.609903i \(0.791208\pi\)
\(240\) 0 0
\(241\) 0.486132 0.353195i 0.0313145 0.0227513i −0.572018 0.820241i \(-0.693839\pi\)
0.603332 + 0.797490i \(0.293839\pi\)
\(242\) 2.25017 6.92531i 0.144646 0.445176i
\(243\) −15.0589 −0.966031
\(244\) −3.00423 + 9.24607i −0.192326 + 0.591919i
\(245\) 0 0
\(246\) −3.85140 11.8534i −0.245556 0.755745i
\(247\) 0.982634 + 3.02423i 0.0625235 + 0.192427i
\(248\) −5.55112 4.03312i −0.352496 0.256104i
\(249\) 7.44678 0.471921
\(250\) 0 0
\(251\) −14.1908 −0.895712 −0.447856 0.894106i \(-0.647812\pi\)
−0.447856 + 0.894106i \(0.647812\pi\)
\(252\) −7.72888 5.61536i −0.486873 0.353734i
\(253\) −5.96722 18.3652i −0.375156 1.15461i
\(254\) 6.14486 + 18.9119i 0.385563 + 1.18664i
\(255\) 0 0
\(256\) 5.25868 16.1846i 0.328668 1.01153i
\(257\) −17.6859 −1.10322 −0.551609 0.834103i \(-0.685986\pi\)
−0.551609 + 0.834103i \(0.685986\pi\)
\(258\) −0.513015 + 1.57890i −0.0319389 + 0.0982980i
\(259\) −20.1183 + 14.6168i −1.25009 + 0.908245i
\(260\) 0 0
\(261\) 8.33904 + 6.05867i 0.516174 + 0.375022i
\(262\) 22.7946 16.5612i 1.40825 1.02316i
\(263\) 19.6873 14.3036i 1.21397 0.882000i 0.218384 0.975863i \(-0.429922\pi\)
0.995585 + 0.0938630i \(0.0299216\pi\)
\(264\) −4.41641 3.20871i −0.271811 0.197482i
\(265\) 0 0
\(266\) −34.7029 + 25.2131i −2.12777 + 1.54591i
\(267\) −1.59324 + 4.90350i −0.0975050 + 0.300090i
\(268\) −2.46365 −0.150491
\(269\) 9.26490 28.5144i 0.564891 1.73856i −0.103384 0.994642i \(-0.532967\pi\)
0.668275 0.743915i \(-0.267033\pi\)
\(270\) 0 0
\(271\) −8.55920 26.3425i −0.519934 1.60019i −0.774121 0.633038i \(-0.781808\pi\)
0.254187 0.967155i \(-0.418192\pi\)
\(272\) 0.357420 + 1.10003i 0.0216718 + 0.0666989i
\(273\) 1.51165 + 1.09827i 0.0914889 + 0.0664706i
\(274\) 17.5447 1.05992
\(275\) 0 0
\(276\) 2.92177 0.175870
\(277\) −1.85594 1.34842i −0.111513 0.0810189i 0.530631 0.847603i \(-0.321955\pi\)
−0.642144 + 0.766584i \(0.721955\pi\)
\(278\) 3.46451 + 10.6627i 0.207788 + 0.639505i
\(279\) 2.69533 + 8.29536i 0.161365 + 0.496630i
\(280\) 0 0
\(281\) −0.500078 + 1.53908i −0.0298321 + 0.0918139i −0.964864 0.262750i \(-0.915371\pi\)
0.935032 + 0.354564i \(0.115371\pi\)
\(282\) −1.10063 −0.0655416
\(283\) −4.01481 + 12.3563i −0.238656 + 0.734506i 0.757960 + 0.652301i \(0.226196\pi\)
−0.996615 + 0.0822051i \(0.973804\pi\)
\(284\) −2.16249 + 1.57114i −0.128320 + 0.0932300i
\(285\) 0 0
\(286\) 3.05467 + 2.21935i 0.180627 + 0.131233i
\(287\) 38.7128 28.1265i 2.28514 1.66025i
\(288\) −8.97259 + 6.51897i −0.528715 + 0.384134i
\(289\) 13.7095 + 9.96055i 0.806442 + 0.585914i
\(290\) 0 0
\(291\) −4.78115 + 3.47371i −0.280276 + 0.203632i
\(292\) −2.65210 + 8.16231i −0.155202 + 0.477663i
\(293\) −11.7009 −0.683572 −0.341786 0.939778i \(-0.611032\pi\)
−0.341786 + 0.939778i \(0.611032\pi\)
\(294\) −5.20220 + 16.0107i −0.303398 + 0.933765i
\(295\) 0 0
\(296\) 3.28576 + 10.1125i 0.190981 + 0.587780i
\(297\) 4.72235 + 14.5339i 0.274018 + 0.843342i
\(298\) 16.3859 + 11.9051i 0.949211 + 0.689642i
\(299\) 2.82612 0.163439
\(300\) 0 0
\(301\) −6.37395 −0.367388
\(302\) 2.10031 + 1.52596i 0.120859 + 0.0878094i
\(303\) 0.782572 + 2.40851i 0.0449576 + 0.138365i
\(304\) 8.52804 + 26.2466i 0.489116 + 1.50535i
\(305\) 0 0
\(306\) 0.301958 0.929330i 0.0172618 0.0531263i
\(307\) 26.5673 1.51628 0.758138 0.652094i \(-0.226109\pi\)
0.758138 + 0.652094i \(0.226109\pi\)
\(308\) −4.63134 + 14.2538i −0.263895 + 0.812185i
\(309\) −0.229482 + 0.166728i −0.0130548 + 0.00948485i
\(310\) 0 0
\(311\) 10.9145 + 7.92981i 0.618902 + 0.449658i 0.852538 0.522666i \(-0.175062\pi\)
−0.233636 + 0.972324i \(0.575062\pi\)
\(312\) 0.646353 0.469603i 0.0365925 0.0265860i
\(313\) −13.7487 + 9.98904i −0.777124 + 0.564614i −0.904115 0.427290i \(-0.859468\pi\)
0.126990 + 0.991904i \(0.459468\pi\)
\(314\) 13.3805 + 9.72150i 0.755105 + 0.548616i
\(315\) 0 0
\(316\) 6.48649 4.71271i 0.364893 0.265111i
\(317\) 5.19021 15.9738i 0.291511 0.897180i −0.692860 0.721072i \(-0.743649\pi\)
0.984371 0.176107i \(-0.0563505\pi\)
\(318\) −1.47224 −0.0825588
\(319\) 4.99696 15.3791i 0.279776 0.861063i
\(320\) 0 0
\(321\) 0.360808 + 1.11045i 0.0201384 + 0.0619795i
\(322\) 11.7807 + 36.2573i 0.656513 + 2.02054i
\(323\) −1.04445 0.758839i −0.0581149 0.0422230i
\(324\) 3.93033 0.218351
\(325\) 0 0
\(326\) −9.39524 −0.520354
\(327\) 0.0430522 + 0.0312793i 0.00238079 + 0.00172975i
\(328\) −6.32265 19.4591i −0.349110 1.07445i
\(329\) −1.30582 4.01891i −0.0719924 0.221570i
\(330\) 0 0
\(331\) 3.96604 12.2062i 0.217994 0.670915i −0.780934 0.624614i \(-0.785257\pi\)
0.998928 0.0463015i \(-0.0147435\pi\)
\(332\) −8.74180 −0.479768
\(333\) 4.17679 12.8548i 0.228887 0.704441i
\(334\) 29.7723 21.6308i 1.62907 1.18359i
\(335\) 0 0
\(336\) 13.1192 + 9.53166i 0.715711 + 0.519995i
\(337\) −17.1815 + 12.4831i −0.935935 + 0.679997i −0.947439 0.319937i \(-0.896338\pi\)
0.0115037 + 0.999934i \(0.496338\pi\)
\(338\) 17.2577 12.5385i 0.938697 0.682003i
\(339\) 8.12183 + 5.90085i 0.441117 + 0.320490i
\(340\) 0 0
\(341\) 11.0701 8.04291i 0.599480 0.435548i
\(342\) 7.20470 22.1738i 0.389586 1.19902i
\(343\) −32.4969 −1.75467
\(344\) −0.842191 + 2.59200i −0.0454079 + 0.139751i
\(345\) 0 0
\(346\) 12.1928 + 37.5255i 0.655488 + 2.01739i
\(347\) 8.84658 + 27.2270i 0.474909 + 1.46162i 0.846080 + 0.533056i \(0.178956\pi\)
−0.371171 + 0.928565i \(0.621044\pi\)
\(348\) 1.97942 + 1.43813i 0.106108 + 0.0770920i
\(349\) 19.9124 1.06588 0.532942 0.846152i \(-0.321086\pi\)
0.532942 + 0.846152i \(0.321086\pi\)
\(350\) 0 0
\(351\) −2.23654 −0.119377
\(352\) 14.0761 + 10.2269i 0.750260 + 0.545096i
\(353\) 7.63011 + 23.4831i 0.406110 + 1.24988i 0.919965 + 0.392000i \(0.128217\pi\)
−0.513855 + 0.857877i \(0.671783\pi\)
\(354\) −1.66573 5.12658i −0.0885324 0.272475i
\(355\) 0 0
\(356\) 1.87031 5.75624i 0.0991265 0.305080i
\(357\) −0.758602 −0.0401495
\(358\) −3.28702 + 10.1164i −0.173724 + 0.534668i
\(359\) −17.3947 + 12.6380i −0.918058 + 0.667008i −0.943040 0.332679i \(-0.892047\pi\)
0.0249816 + 0.999688i \(0.492047\pi\)
\(360\) 0 0
\(361\) −9.54930 6.93797i −0.502595 0.365156i
\(362\) 18.1647 13.1975i 0.954718 0.693643i
\(363\) 2.48581 1.80604i 0.130471 0.0947927i
\(364\) −1.77452 1.28927i −0.0930103 0.0675760i
\(365\) 0 0
\(366\) −11.2789 + 8.19460i −0.589557 + 0.428338i
\(367\) −0.353463 + 1.08785i −0.0184506 + 0.0567852i −0.959858 0.280487i \(-0.909504\pi\)
0.941407 + 0.337272i \(0.109504\pi\)
\(368\) 24.5272 1.27857
\(369\) −8.03721 + 24.7360i −0.418400 + 1.28770i
\(370\) 0 0
\(371\) −1.74671 5.37581i −0.0906845 0.279098i
\(372\) 0.639784 + 1.96905i 0.0331713 + 0.102091i
\(373\) −9.33566 6.78275i −0.483382 0.351198i 0.319251 0.947670i \(-0.396569\pi\)
−0.802634 + 0.596472i \(0.796569\pi\)
\(374\) −1.53295 −0.0792671
\(375\) 0 0
\(376\) −1.80685 −0.0931812
\(377\) 1.91462 + 1.39105i 0.0986077 + 0.0716427i
\(378\) −9.32302 28.6933i −0.479524 1.47582i
\(379\) 6.52188 + 20.0723i 0.335007 + 1.03104i 0.966719 + 0.255841i \(0.0823525\pi\)
−0.631712 + 0.775203i \(0.717648\pi\)
\(380\) 0 0
\(381\) −2.59292 + 7.98018i −0.132839 + 0.408837i
\(382\) −4.68127 −0.239515
\(383\) −0.265176 + 0.816129i −0.0135499 + 0.0417022i −0.957603 0.288092i \(-0.906979\pi\)
0.944053 + 0.329794i \(0.106979\pi\)
\(384\) 7.49097 5.44251i 0.382272 0.277737i
\(385\) 0 0
\(386\) −30.7337 22.3293i −1.56430 1.13653i
\(387\) 2.80280 2.03635i 0.142474 0.103514i
\(388\) 5.61260 4.07780i 0.284937 0.207019i
\(389\) 27.4537 + 19.9463i 1.39196 + 1.01132i 0.995647 + 0.0931998i \(0.0297095\pi\)
0.396310 + 0.918117i \(0.370290\pi\)
\(390\) 0 0
\(391\) −0.928260 + 0.674421i −0.0469442 + 0.0341069i
\(392\) −8.54019 + 26.2840i −0.431345 + 1.32754i
\(393\) 11.8891 0.599728
\(394\) 0.661604 2.03621i 0.0333311 0.102583i
\(395\) 0 0
\(396\) −2.51728 7.74740i −0.126498 0.389322i
\(397\) −8.29049 25.5155i −0.416088 1.28059i −0.911274 0.411800i \(-0.864900\pi\)
0.495186 0.868787i \(-0.335100\pi\)
\(398\) 11.7485 + 8.53576i 0.588897 + 0.427859i
\(399\) −18.1002 −0.906145
\(400\) 0 0
\(401\) 3.79757 0.189642 0.0948208 0.995494i \(-0.469772\pi\)
0.0948208 + 0.995494i \(0.469772\pi\)
\(402\) −2.85821 2.07661i −0.142555 0.103572i
\(403\) 0.618838 + 1.90459i 0.0308265 + 0.0948743i
\(404\) −0.918663 2.82736i −0.0457052 0.140666i
\(405\) 0 0
\(406\) −9.86518 + 30.3619i −0.489601 + 1.50684i
\(407\) −21.2044 −1.05106
\(408\) −0.100234 + 0.308489i −0.00496234 + 0.0152725i
\(409\) 11.4681 8.33207i 0.567062 0.411994i −0.266975 0.963703i \(-0.586024\pi\)
0.834037 + 0.551709i \(0.186024\pi\)
\(410\) 0 0
\(411\) 5.98936 + 4.35153i 0.295434 + 0.214645i
\(412\) 0.269389 0.195723i 0.0132719 0.00964257i
\(413\) 16.7432 12.1647i 0.823881 0.598585i
\(414\) −16.7638 12.1796i −0.823896 0.598595i
\(415\) 0 0
\(416\) −2.06008 + 1.49673i −0.101004 + 0.0733834i
\(417\) −1.46190 + 4.49928i −0.0715897 + 0.220331i
\(418\) −36.5762 −1.78900
\(419\) −6.05576 + 18.6377i −0.295843 + 0.910512i 0.687094 + 0.726569i \(0.258886\pi\)
−0.982937 + 0.183943i \(0.941114\pi\)
\(420\) 0 0
\(421\) −7.96770 24.5221i −0.388322 1.19513i −0.934042 0.357164i \(-0.883744\pi\)
0.545720 0.837968i \(-0.316256\pi\)
\(422\) −10.9407 33.6720i −0.532584 1.63913i
\(423\) 1.85817 + 1.35004i 0.0903474 + 0.0656412i
\(424\) −2.41689 −0.117375
\(425\) 0 0
\(426\) −3.83313 −0.185716
\(427\) −43.3039 31.4621i −2.09562 1.52256i
\(428\) −0.423554 1.30356i −0.0204732 0.0630102i
\(429\) 0.492341 + 1.51527i 0.0237704 + 0.0731579i
\(430\) 0 0
\(431\) 2.91259 8.96402i 0.140294 0.431782i −0.856081 0.516841i \(-0.827108\pi\)
0.996376 + 0.0850590i \(0.0271079\pi\)
\(432\) −19.4103 −0.933881
\(433\) −0.541277 + 1.66588i −0.0260121 + 0.0800571i −0.963220 0.268715i \(-0.913401\pi\)
0.937208 + 0.348772i \(0.113401\pi\)
\(434\) −21.8550 + 15.8786i −1.04907 + 0.762197i
\(435\) 0 0
\(436\) −0.0505391 0.0367188i −0.00242038 0.00175851i
\(437\) −22.1483 + 16.0917i −1.05950 + 0.769769i
\(438\) −9.95686 + 7.23408i −0.475757 + 0.345658i
\(439\) −22.7197 16.5068i −1.08435 0.787827i −0.105914 0.994375i \(-0.533777\pi\)
−0.978436 + 0.206549i \(0.933777\pi\)
\(440\) 0 0
\(441\) 28.4216 20.6495i 1.35341 0.983311i
\(442\) 0.0693285 0.213371i 0.00329762 0.0101490i
\(443\) 29.9110 1.42111 0.710557 0.703640i \(-0.248443\pi\)
0.710557 + 0.703640i \(0.248443\pi\)
\(444\) 0.991436 3.05133i 0.0470515 0.144810i
\(445\) 0 0
\(446\) −3.29568 10.1430i −0.156055 0.480287i
\(447\) 2.64102 + 8.12823i 0.124916 + 0.384452i
\(448\) 9.14821 + 6.64656i 0.432212 + 0.314021i
\(449\) 6.29974 0.297303 0.148652 0.988890i \(-0.452507\pi\)
0.148652 + 0.988890i \(0.452507\pi\)
\(450\) 0 0
\(451\) 40.8026 1.92132
\(452\) −9.53424 6.92703i −0.448453 0.325820i
\(453\) 0.338520 + 1.04186i 0.0159051 + 0.0489508i
\(454\) −5.85873 18.0313i −0.274964 0.846252i
\(455\) 0 0
\(456\) −2.39159 + 7.36055i −0.111996 + 0.344689i
\(457\) −19.1809 −0.897243 −0.448622 0.893722i \(-0.648085\pi\)
−0.448622 + 0.893722i \(0.648085\pi\)
\(458\) 7.82429 24.0807i 0.365605 1.12522i
\(459\) 0.734607 0.533724i 0.0342885 0.0249121i
\(460\) 0 0
\(461\) −5.72064 4.15629i −0.266437 0.193578i 0.446543 0.894762i \(-0.352655\pi\)
−0.712980 + 0.701184i \(0.752655\pi\)
\(462\) −17.3876 + 12.6328i −0.808944 + 0.587732i
\(463\) −7.78146 + 5.65356i −0.361635 + 0.262743i −0.753734 0.657180i \(-0.771749\pi\)
0.392099 + 0.919923i \(0.371749\pi\)
\(464\) 16.6165 + 12.0726i 0.771401 + 0.560456i
\(465\) 0 0
\(466\) 10.6603 7.74517i 0.493830 0.358788i
\(467\) 5.93992 18.2812i 0.274867 0.845953i −0.714388 0.699750i \(-0.753295\pi\)
0.989255 0.146203i \(-0.0467053\pi\)
\(468\) 1.19220 0.0551096
\(469\) 4.19160 12.9004i 0.193550 0.595686i
\(470\) 0 0
\(471\) 2.15662 + 6.63739i 0.0993717 + 0.305835i
\(472\) −2.73454 8.41605i −0.125867 0.387380i
\(473\) −4.39701 3.19462i −0.202175 0.146889i
\(474\) 11.4977 0.528105
\(475\) 0 0
\(476\) 0.890525 0.0408172
\(477\) 2.48554 + 1.80585i 0.113805 + 0.0826843i
\(478\) 4.54598 + 13.9911i 0.207928 + 0.639937i
\(479\) −11.7425 36.1398i −0.536529 1.65127i −0.740321 0.672253i \(-0.765327\pi\)
0.203792 0.979014i \(-0.434673\pi\)
\(480\) 0 0
\(481\) 0.958977 2.95143i 0.0437256 0.134574i
\(482\) −1.01155 −0.0460747
\(483\) −4.97104 + 15.2993i −0.226190 + 0.696142i
\(484\) −2.91809 + 2.12012i −0.132641 + 0.0963691i
\(485\) 0 0
\(486\) 20.5089 + 14.9006i 0.930302 + 0.675904i
\(487\) −13.5502 + 9.84481i −0.614019 + 0.446111i −0.850827 0.525445i \(-0.823899\pi\)
0.236808 + 0.971556i \(0.423899\pi\)
\(488\) −18.5160 + 13.4527i −0.838180 + 0.608973i
\(489\) −3.20732 2.33025i −0.145040 0.105378i
\(490\) 0 0
\(491\) 7.24115 5.26100i 0.326789 0.237426i −0.412278 0.911058i \(-0.635267\pi\)
0.739067 + 0.673632i \(0.235267\pi\)
\(492\) −1.90778 + 5.87153i −0.0860092 + 0.264709i
\(493\) −0.960829 −0.0432736
\(494\) 1.65418 5.09103i 0.0744249 0.229056i
\(495\) 0 0
\(496\) 5.37075 + 16.5295i 0.241154 + 0.742194i
\(497\) −4.54775 13.9965i −0.203995 0.627831i
\(498\) −10.1418 7.36847i −0.454466 0.330189i
\(499\) −36.3310 −1.62640 −0.813200 0.581985i \(-0.802276\pi\)
−0.813200 + 0.581985i \(0.802276\pi\)
\(500\) 0 0
\(501\) 15.5286 0.693765
\(502\) 19.3265 + 14.0415i 0.862583 + 0.626704i
\(503\) −3.79921 11.6928i −0.169398 0.521354i 0.829935 0.557860i \(-0.188377\pi\)
−0.999333 + 0.0365056i \(0.988377\pi\)
\(504\) −6.94991 21.3896i −0.309574 0.952770i
\(505\) 0 0
\(506\) −10.0453 + 30.9162i −0.446567 + 1.37439i
\(507\) 9.00125 0.399759
\(508\) 3.04383 9.36795i 0.135048 0.415636i
\(509\) 25.1841 18.2973i 1.11626 0.811013i 0.132625 0.991166i \(-0.457659\pi\)
0.983639 + 0.180153i \(0.0576594\pi\)
\(510\) 0 0
\(511\) −38.2281 27.7744i −1.69111 1.22867i
\(512\) −2.08496 + 1.51482i −0.0921433 + 0.0669460i
\(513\) 17.5277 12.7346i 0.773868 0.562248i
\(514\) 24.0866 + 17.4999i 1.06241 + 0.771889i
\(515\) 0 0
\(516\) 0.665295 0.483365i 0.0292880 0.0212790i
\(517\) 1.11346 3.42689i 0.0489701 0.150714i
\(518\) 41.8624 1.83933
\(519\) −5.14493 + 15.8345i −0.225837 + 0.695056i
\(520\) 0 0
\(521\) 5.01130 + 15.4232i 0.219549 + 0.675702i 0.998799 + 0.0489896i \(0.0156001\pi\)
−0.779250 + 0.626713i \(0.784400\pi\)
\(522\) −5.36205 16.5027i −0.234691 0.722303i
\(523\) −24.7504 17.9822i −1.08226 0.786307i −0.104183 0.994558i \(-0.533223\pi\)
−0.978075 + 0.208251i \(0.933223\pi\)
\(524\) −13.9567 −0.609701
\(525\) 0 0
\(526\) −40.9655 −1.78618
\(527\) −0.657770 0.477898i −0.0286529 0.0208176i
\(528\) 4.27291 + 13.1507i 0.185954 + 0.572309i
\(529\) 0.411359 + 1.26603i 0.0178852 + 0.0550449i
\(530\) 0 0
\(531\) −3.47608 + 10.6983i −0.150849 + 0.464266i
\(532\) 21.2479 0.921214
\(533\) −1.84532 + 5.67930i −0.0799295 + 0.245998i
\(534\) 7.02179 5.10163i 0.303863 0.220769i
\(535\) 0 0
\(536\) −4.69218 3.40907i −0.202671 0.147249i
\(537\) −3.63123 + 2.63824i −0.156699 + 0.113849i
\(538\) −40.8325 + 29.6666i −1.76041 + 1.27902i
\(539\) −44.5876 32.3948i −1.92052 1.39534i
\(540\) 0 0
\(541\) −14.8062 + 10.7573i −0.636567 + 0.462493i −0.858669 0.512530i \(-0.828708\pi\)
0.222102 + 0.975023i \(0.428708\pi\)
\(542\) −14.4086 + 44.3452i −0.618904 + 1.90479i
\(543\) 9.47432 0.406582
\(544\) 0.319470 0.983228i 0.0136972 0.0421555i
\(545\) 0 0
\(546\) −0.971996 2.99150i −0.0415976 0.128024i
\(547\) 2.02592 + 6.23515i 0.0866223 + 0.266596i 0.984980 0.172669i \(-0.0552390\pi\)
−0.898358 + 0.439265i \(0.855239\pi\)
\(548\) −7.03093 5.10827i −0.300346 0.218214i
\(549\) 29.0935 1.24168
\(550\) 0 0
\(551\) −22.9254 −0.976653
\(552\) 5.56471 + 4.04300i 0.236850 + 0.172081i
\(553\) 13.6412 + 41.9833i 0.580083 + 1.78531i
\(554\) 1.19338 + 3.67285i 0.0507020 + 0.156045i
\(555\) 0 0
\(556\) 1.71613 5.28171i 0.0727802 0.223994i
\(557\) 35.5383 1.50581 0.752904 0.658131i \(-0.228653\pi\)
0.752904 + 0.658131i \(0.228653\pi\)
\(558\) 4.53734 13.9645i 0.192081 0.591164i
\(559\) 0.643514 0.467540i 0.0272177 0.0197748i
\(560\) 0 0
\(561\) −0.523315 0.380210i −0.0220944 0.0160525i
\(562\) 2.20396 1.60127i 0.0929682 0.0675454i
\(563\) 30.9432 22.4816i 1.30410 0.947486i 0.304115 0.952635i \(-0.401639\pi\)
0.999987 + 0.00514973i \(0.00163922\pi\)
\(564\) 0.441070 + 0.320456i 0.0185724 + 0.0134936i
\(565\) 0 0
\(566\) 17.6942 12.8556i 0.743741 0.540360i
\(567\) −6.68697 + 20.5804i −0.280826 + 0.864295i
\(568\) −6.29266 −0.264034
\(569\) 2.33585 7.18901i 0.0979240 0.301379i −0.890081 0.455803i \(-0.849352\pi\)
0.988005 + 0.154424i \(0.0493522\pi\)
\(570\) 0 0
\(571\) 7.11549 + 21.8992i 0.297774 + 0.916454i 0.982276 + 0.187443i \(0.0600199\pi\)
−0.684501 + 0.729011i \(0.739980\pi\)
\(572\) −0.577960 1.77878i −0.0241657 0.0743745i
\(573\) −1.59808 1.16107i −0.0667607 0.0485045i
\(574\) −80.5540 −3.36226
\(575\) 0 0
\(576\) −6.14617 −0.256090
\(577\) 18.0546 + 13.1175i 0.751624 + 0.546087i 0.896330 0.443388i \(-0.146223\pi\)
−0.144706 + 0.989475i \(0.546223\pi\)
\(578\) −8.81529 27.1307i −0.366668 1.12849i
\(579\) −4.95354 15.2454i −0.205862 0.633579i
\(580\) 0 0
\(581\) 14.8731 45.7747i 0.617040 1.89905i
\(582\) 9.94866 0.412385
\(583\) 1.48940 4.58390i 0.0616846 0.189846i
\(584\) −16.3457 + 11.8758i −0.676389 + 0.491425i
\(585\) 0 0
\(586\) 15.9355 + 11.5778i 0.658290 + 0.478276i
\(587\) −17.0530 + 12.3897i −0.703851 + 0.511378i −0.881184 0.472773i \(-0.843253\pi\)
0.177333 + 0.984151i \(0.443253\pi\)
\(588\) 6.74638 4.90153i 0.278216 0.202136i
\(589\) −15.6944 11.4026i −0.646676 0.469838i
\(590\) 0 0
\(591\) 0.730887 0.531020i 0.0300647 0.0218433i
\(592\) 8.32273 25.6147i 0.342062 1.05276i
\(593\) −34.3547 −1.41078 −0.705390 0.708819i \(-0.749228\pi\)
−0.705390 + 0.708819i \(0.749228\pi\)
\(594\) 7.94965 24.4665i 0.326178 1.00387i
\(595\) 0 0
\(596\) −3.10030 9.54175i −0.126993 0.390846i
\(597\) 1.89357 + 5.82782i 0.0774988 + 0.238517i
\(598\) −3.84891 2.79640i −0.157394 0.114353i
\(599\) 0.498231 0.0203572 0.0101786 0.999948i \(-0.496760\pi\)
0.0101786 + 0.999948i \(0.496760\pi\)
\(600\) 0 0
\(601\) 27.8635 1.13657 0.568287 0.822830i \(-0.307606\pi\)
0.568287 + 0.822830i \(0.307606\pi\)
\(602\) 8.68073 + 6.30692i 0.353800 + 0.257051i
\(603\) 2.27827 + 7.01180i 0.0927784 + 0.285543i
\(604\) −0.397390 1.22304i −0.0161696 0.0497648i
\(605\) 0 0
\(606\) 1.31739 4.05451i 0.0535153 0.164703i
\(607\) 14.1000 0.572303 0.286152 0.958184i \(-0.407624\pi\)
0.286152 + 0.958184i \(0.407624\pi\)
\(608\) 7.62255 23.4598i 0.309135 0.951420i
\(609\) −10.8982 + 7.91804i −0.441619 + 0.320855i
\(610\) 0 0
\(611\) 0.426630 + 0.309965i 0.0172596 + 0.0125398i
\(612\) −0.391588 + 0.284506i −0.0158290 + 0.0115005i
\(613\) −25.7475 + 18.7067i −1.03993 + 0.755556i −0.970272 0.242015i \(-0.922192\pi\)
−0.0696606 + 0.997571i \(0.522192\pi\)
\(614\) −36.1822 26.2879i −1.46020 1.06089i
\(615\) 0 0
\(616\) −28.5443 + 20.7387i −1.15008 + 0.835585i
\(617\) 10.4961 32.3038i 0.422559 1.30050i −0.482753 0.875756i \(-0.660363\pi\)
0.905312 0.424746i \(-0.139637\pi\)
\(618\) 0.477508 0.0192082
\(619\) 0.348700 1.07319i 0.0140155 0.0431351i −0.943804 0.330505i \(-0.892781\pi\)
0.957820 + 0.287370i \(0.0927809\pi\)
\(620\) 0 0
\(621\) −5.95019 18.3128i −0.238773 0.734868i
\(622\) −7.01805 21.5993i −0.281398 0.866055i
\(623\) 26.9593 + 19.5871i 1.08010 + 0.784739i
\(624\) −2.02368 −0.0810119
\(625\) 0 0
\(626\) 28.6085 1.14343
\(627\) −12.4863 9.07181i −0.498654 0.362293i
\(628\) −2.53166 7.79165i −0.101024 0.310921i
\(629\) 0.389341 + 1.19827i 0.0155240 + 0.0477781i
\(630\) 0 0
\(631\) 10.1296 31.1758i 0.403254 1.24109i −0.519091 0.854719i \(-0.673729\pi\)
0.922345 0.386368i \(-0.126271\pi\)
\(632\) 18.8751 0.750813
\(633\) 4.61659 14.2084i 0.183493 0.564733i
\(634\) −22.8744 + 16.6193i −0.908460 + 0.660035i
\(635\) 0 0
\(636\) 0.589988 + 0.428652i 0.0233946 + 0.0169971i
\(637\) 6.52551 4.74106i 0.258550 0.187848i
\(638\) −22.0227 + 16.0005i −0.871889 + 0.633464i
\(639\) 6.47140 + 4.70175i 0.256005 + 0.185998i
\(640\) 0 0
\(641\) −24.6043 + 17.8761i −0.971812 + 0.706063i −0.955864 0.293810i \(-0.905077\pi\)
−0.0159485 + 0.999873i \(0.505077\pi\)
\(642\) 0.607388 1.86935i 0.0239717 0.0737773i
\(643\) −1.06932 −0.0421700 −0.0210850 0.999778i \(-0.506712\pi\)
−0.0210850 + 0.999778i \(0.506712\pi\)
\(644\) 5.83552 17.9599i 0.229952 0.707719i
\(645\) 0 0
\(646\) 0.671589 + 2.06694i 0.0264233 + 0.0813226i
\(647\) −9.44602 29.0719i −0.371362 1.14293i −0.945901 0.324456i \(-0.894819\pi\)
0.574539 0.818477i \(-0.305181\pi\)
\(648\) 7.48556 + 5.43858i 0.294061 + 0.213648i
\(649\) 17.6471 0.692709
\(650\) 0 0
\(651\) −11.3991 −0.446765
\(652\) 3.76508 + 2.73549i 0.147452 + 0.107130i
\(653\) 10.3058 + 31.7179i 0.403296 + 1.24122i 0.922310 + 0.386451i \(0.126299\pi\)
−0.519014 + 0.854766i \(0.673701\pi\)
\(654\) −0.0276828 0.0851989i −0.00108248 0.00333154i
\(655\) 0 0
\(656\) −16.0151 + 49.2893i −0.625283 + 1.92442i
\(657\) 25.6833 1.00200
\(658\) −2.19824 + 6.76548i −0.0856962 + 0.263746i
\(659\) 8.18325 5.94548i 0.318774 0.231603i −0.416878 0.908962i \(-0.636876\pi\)
0.735652 + 0.677360i \(0.236876\pi\)
\(660\) 0 0
\(661\) 24.9487 + 18.1263i 0.970392 + 0.705031i 0.955541 0.294859i \(-0.0952726\pi\)
0.0148510 + 0.999890i \(0.495273\pi\)
\(662\) −17.4793 + 12.6994i −0.679350 + 0.493577i
\(663\) 0.0765885 0.0556448i 0.00297445 0.00216106i
\(664\) −16.6493 12.0964i −0.646119 0.469433i
\(665\) 0 0
\(666\) −18.4081 + 13.3742i −0.713298 + 0.518241i
\(667\) −6.29621 + 19.3778i −0.243790 + 0.750310i
\(668\) −18.2290 −0.705302
\(669\) 1.39066 4.28001i 0.0537660 0.165475i
\(670\) 0 0
\(671\) −14.1040 43.4077i −0.544480 1.67574i
\(672\) −4.47902 13.7850i −0.172782 0.531768i
\(673\) −24.9379 18.1185i −0.961286 0.698415i −0.00783693 0.999969i \(-0.502495\pi\)
−0.953449 + 0.301554i \(0.902495\pi\)
\(674\) 35.7514 1.37709
\(675\) 0 0
\(676\) −10.5666 −0.406407
\(677\) 33.3736 + 24.2474i 1.28265 + 0.931902i 0.999630 0.0272110i \(-0.00866262\pi\)
0.283023 + 0.959113i \(0.408663\pi\)
\(678\) −5.22238 16.0728i −0.200564 0.617273i
\(679\) 11.8034 + 36.3272i 0.452974 + 1.39411i
\(680\) 0 0
\(681\) 2.47218 7.60859i 0.0947342 0.291562i
\(682\) −23.0348 −0.882048
\(683\) −6.90698 + 21.2575i −0.264288 + 0.813395i 0.727568 + 0.686035i \(0.240650\pi\)
−0.991857 + 0.127360i \(0.959350\pi\)
\(684\) −9.34329 + 6.78830i −0.357250 + 0.259557i
\(685\) 0 0
\(686\) 44.2578 + 32.1552i 1.68977 + 1.22769i
\(687\) 8.64364 6.27997i 0.329775 0.239596i
\(688\) 5.58490 4.05767i 0.212922 0.154697i
\(689\) 0.570673 + 0.414618i 0.0217409 + 0.0157957i
\(690\) 0 0
\(691\) −7.43406 + 5.40116i −0.282805 + 0.205470i −0.720140 0.693829i \(-0.755922\pi\)
0.437335 + 0.899299i \(0.355922\pi\)
\(692\) 6.03965 18.5881i 0.229593 0.706614i
\(693\) 44.8506 1.70373
\(694\) 14.8924 45.8342i 0.565309 1.73984i
\(695\) 0 0
\(696\) 1.77992 + 5.47804i 0.0674678 + 0.207644i
\(697\) −0.749192 2.30577i −0.0283777 0.0873374i
\(698\) −27.1188 19.7030i −1.02646 0.745768i
\(699\) 5.56018 0.210305
\(700\) 0 0
\(701\) −35.9929 −1.35943 −0.679717 0.733475i \(-0.737897\pi\)
−0.679717 + 0.733475i \(0.737897\pi\)
\(702\) 3.04595 + 2.21302i 0.114962 + 0.0835249i
\(703\) 9.28967 + 28.5907i 0.350366 + 1.07832i
\(704\) 2.97956 + 9.17014i 0.112296 + 0.345613i
\(705\) 0 0
\(706\) 12.8446 39.5316i 0.483413 1.48779i
\(707\) 16.3679 0.615578
\(708\) −0.825111 + 2.53943i −0.0310096 + 0.0954376i
\(709\) −16.3795 + 11.9004i −0.615144 + 0.446928i −0.851222 0.524806i \(-0.824138\pi\)
0.236078 + 0.971734i \(0.424138\pi\)
\(710\) 0 0
\(711\) −19.4113 14.1031i −0.727980 0.528908i
\(712\) 11.5273 8.37508i 0.432004 0.313870i
\(713\) −13.9484 + 10.1341i −0.522373 + 0.379526i
\(714\) 1.03315 + 0.750625i 0.0386645 + 0.0280914i
\(715\) 0 0
\(716\) 4.26271 3.09704i 0.159305 0.115742i
\(717\) −1.91824 + 5.90374i −0.0716381 + 0.220479i
\(718\) 36.1951 1.35079
\(719\) −11.4418 + 35.2143i −0.426708 + 1.31327i 0.474641 + 0.880180i \(0.342578\pi\)
−0.901349 + 0.433093i \(0.857422\pi\)
\(720\) 0 0
\(721\) 0.566531 + 1.74360i 0.0210987 + 0.0649352i
\(722\) 6.14025 + 18.8977i 0.228516 + 0.703301i
\(723\) −0.345319 0.250889i −0.0128425 0.00933066i
\(724\) −11.1219 −0.413343
\(725\) 0 0
\(726\) −5.17249 −0.191969
\(727\) −9.77211 7.09986i −0.362428 0.263319i 0.391636 0.920120i \(-0.371909\pi\)
−0.754064 + 0.656801i \(0.771909\pi\)
\(728\) −1.59568 4.91099i −0.0591397 0.182013i
\(729\) −1.06397 3.27458i −0.0394065 0.121281i
\(730\) 0 0
\(731\) −0.0997940 + 0.307134i −0.00369102 + 0.0113598i
\(732\) 6.90586 0.255248
\(733\) −13.7858 + 42.4282i −0.509188 + 1.56712i 0.284425 + 0.958698i \(0.408197\pi\)
−0.793614 + 0.608422i \(0.791803\pi\)
\(734\) 1.55779 1.13180i 0.0574992 0.0417756i
\(735\) 0 0
\(736\) −17.7360 12.8860i −0.653759 0.474984i
\(737\) 9.35720 6.79840i 0.344677 0.250422i
\(738\) 35.4218 25.7354i 1.30389 0.947335i
\(739\) 11.8491 + 8.60890i 0.435877 + 0.316683i 0.783995 0.620768i \(-0.213179\pi\)
−0.348117 + 0.937451i \(0.613179\pi\)
\(740\) 0 0
\(741\) 1.82740 1.32768i 0.0671312 0.0487737i
\(742\) −2.94043 + 9.04970i −0.107946 + 0.332225i
\(743\) −24.4397 −0.896604 −0.448302 0.893882i \(-0.647971\pi\)
−0.448302 + 0.893882i \(0.647971\pi\)
\(744\) −1.50616 + 4.63549i −0.0552186 + 0.169945i
\(745\) 0 0
\(746\) 6.00288 + 18.4750i 0.219781 + 0.676417i
\(747\) 8.08402 + 24.8801i 0.295779 + 0.910314i
\(748\) 0.614321 + 0.446330i 0.0224618 + 0.0163194i
\(749\) 7.54648 0.275743
\(750\) 0 0
\(751\) 31.2863 1.14165 0.570826 0.821071i \(-0.306623\pi\)
0.570826 + 0.821071i \(0.306623\pi\)
\(752\) 3.70262 + 2.69011i 0.135021 + 0.0980982i
\(753\) 3.11497 + 9.58690i 0.113516 + 0.349366i
\(754\) −1.23111 3.78896i −0.0448343 0.137986i
\(755\) 0 0
\(756\) −4.61812 + 14.2131i −0.167959 + 0.516926i
\(757\) 11.3251 0.411617 0.205808 0.978592i \(-0.434018\pi\)
0.205808 + 0.978592i \(0.434018\pi\)
\(758\) 10.9790 33.7899i 0.398775 1.22730i
\(759\) −11.0972 + 8.06260i −0.402803 + 0.292654i
\(760\) 0 0
\(761\) 33.4397 + 24.2954i 1.21219 + 0.880707i 0.995428 0.0955176i \(-0.0304506\pi\)
0.216761 + 0.976225i \(0.430451\pi\)
\(762\) 11.4276 8.30262i 0.413977 0.300772i
\(763\) 0.278257 0.202165i 0.0100736 0.00731888i
\(764\) 1.87599 + 1.36299i 0.0678709 + 0.0493111i
\(765\) 0 0
\(766\) 1.16869 0.849104i 0.0422266 0.0306794i
\(767\) −0.798097 + 2.45629i −0.0288176 + 0.0886915i
\(768\) −12.0882 −0.436195
\(769\) 6.99895 21.5406i 0.252389 0.776773i −0.741944 0.670462i \(-0.766096\pi\)
0.994333 0.106311i \(-0.0339039\pi\)
\(770\) 0 0
\(771\) 3.88219 + 11.9481i 0.139814 + 0.430302i
\(772\) 5.81498 + 17.8967i 0.209286 + 0.644115i
\(773\) 13.6353 + 9.90659i 0.490426 + 0.356315i 0.805348 0.592802i \(-0.201978\pi\)
−0.314922 + 0.949118i \(0.601978\pi\)
\(774\) −5.83210 −0.209630
\(775\) 0 0
\(776\) 16.3322 0.586292
\(777\) 14.2909 + 10.3829i 0.512682 + 0.372485i
\(778\) −17.6529 54.3300i −0.632886 1.94782i
\(779\) −17.8757 55.0157i −0.640463 1.97114i
\(780\) 0 0
\(781\) 3.87782 11.9347i 0.138759 0.427058i
\(782\) 1.93153 0.0690715
\(783\) 4.98270 15.3352i 0.178067 0.548035i
\(784\) 56.6333 41.1465i 2.02262 1.46952i
\(785\) 0 0
\(786\) −16.1919 11.7641i −0.577547 0.419612i
\(787\) 16.2683 11.8196i 0.579902 0.421323i −0.258787 0.965934i \(-0.583323\pi\)
0.838689 + 0.544611i \(0.183323\pi\)
\(788\) −0.857990 + 0.623366i −0.0305646 + 0.0222065i
\(789\) −13.9847 10.1605i −0.497867 0.361722i
\(790\) 0 0
\(791\) 52.4934 38.1387i 1.86645 1.35605i
\(792\) 5.92612 18.2387i 0.210576 0.648085i
\(793\) 6.67976 0.237205
\(794\) −13.9563 + 42.9531i −0.495291 + 1.52435i
\(795\) 0 0
\(796\) −2.22287 6.84130i −0.0787876 0.242483i
\(797\) 16.7403 + 51.5213i 0.592971 + 1.82498i 0.564576 + 0.825381i \(0.309040\pi\)
0.0283955 + 0.999597i \(0.490960\pi\)
\(798\) 24.6508 + 17.9099i 0.872631 + 0.634003i
\(799\) −0.214100 −0.00757430
\(800\) 0 0
\(801\) −18.1124 −0.639971
\(802\) −5.17194 3.75763i −0.182627 0.132687i
\(803\) −12.4508 38.3198i −0.439381 1.35228i
\(804\) 0.540788 + 1.66438i 0.0190721 + 0.0586980i
\(805\) 0 0
\(806\) 1.04176 3.20620i 0.0366944 0.112934i
\(807\) −21.2973 −0.749701
\(808\) 2.16269 6.65608i 0.0760832 0.234160i
\(809\) −12.4076 + 9.01462i −0.436227 + 0.316937i −0.784134 0.620592i \(-0.786892\pi\)
0.347907 + 0.937529i \(0.386892\pi\)
\(810\) 0 0
\(811\) −9.35757 6.79868i −0.328589 0.238734i 0.411243 0.911526i \(-0.365095\pi\)
−0.739832 + 0.672792i \(0.765095\pi\)
\(812\) 12.7935 9.29501i 0.448963 0.326191i
\(813\) −15.9175 + 11.5647i −0.558251 + 0.405593i
\(814\) 28.8784 + 20.9814i 1.01219 + 0.735397i
\(815\) 0 0
\(816\) 0.664693 0.482927i 0.0232689 0.0169058i
\(817\) −2.38108 + 7.32822i −0.0833036 + 0.256382i
\(818\) −23.8630 −0.834349
\(819\) −2.02839 + 6.24274i −0.0708776 + 0.218139i
\(820\) 0 0
\(821\) 10.3111 + 31.7344i 0.359861 + 1.10754i 0.953137 + 0.302539i \(0.0978343\pi\)
−0.593276 + 0.804999i \(0.702166\pi\)
\(822\) −3.85119 11.8528i −0.134326 0.413412i
\(823\) 24.2560 + 17.6230i 0.845511 + 0.614300i 0.923905 0.382623i \(-0.124979\pi\)
−0.0783937 + 0.996922i \(0.524979\pi\)
\(824\) 0.783901 0.0273085
\(825\) 0 0
\(826\) −34.8395 −1.21222
\(827\) −20.0013 14.5318i −0.695514 0.505320i 0.182954 0.983121i \(-0.441434\pi\)
−0.878468 + 0.477801i \(0.841434\pi\)
\(828\) 3.17180 + 9.76179i 0.110228 + 0.339246i
\(829\) −0.0653280 0.201059i −0.00226893 0.00698306i 0.949916 0.312506i \(-0.101169\pi\)
−0.952185 + 0.305523i \(0.901169\pi\)
\(830\) 0 0
\(831\) −0.503566 + 1.54982i −0.0174685 + 0.0537625i
\(832\) −1.41114 −0.0489225
\(833\) −1.01195 + 3.11448i −0.0350622 + 0.107910i
\(834\) 6.44294 4.68107i 0.223101 0.162092i
\(835\) 0 0
\(836\) 14.6577 + 10.6494i 0.506946 + 0.368318i
\(837\) 11.0385 8.01995i 0.381547 0.277210i
\(838\) 26.6891 19.3908i 0.921960 0.669843i
\(839\) 4.46346 + 3.24290i 0.154096 + 0.111957i 0.662162 0.749361i \(-0.269639\pi\)
−0.508066 + 0.861318i \(0.669639\pi\)
\(840\) 0 0
\(841\) 9.65802 7.01696i 0.333035 0.241964i
\(842\) −13.4129 + 41.2807i −0.462239 + 1.42263i
\(843\) 1.14953 0.0395920
\(844\) −5.41942 + 16.6793i −0.186544 + 0.574124i
\(845\) 0 0
\(846\) −1.19482 3.67726i −0.0410786 0.126427i
\(847\) −6.13681 18.8872i −0.210863 0.648970i
\(848\) 4.95273 + 3.59837i 0.170077 + 0.123568i
\(849\) 9.22888 0.316734
\(850\) 0 0
\(851\) 26.7177 0.915871
\(852\) 1.53610 + 1.11604i 0.0526260 + 0.0382350i
\(853\) −0.475718 1.46411i −0.0162883 0.0501302i 0.942582 0.333975i \(-0.108390\pi\)
−0.958870 + 0.283845i \(0.908390\pi\)
\(854\) 27.8447 + 85.6971i 0.952825 + 2.93249i
\(855\) 0 0
\(856\) 0.997118 3.06881i 0.0340808 0.104890i
\(857\) −45.3407 −1.54881 −0.774404 0.632691i \(-0.781950\pi\)
−0.774404 + 0.632691i \(0.781950\pi\)
\(858\) 0.828811 2.55082i 0.0282952 0.0870835i
\(859\) 17.6337 12.8116i 0.601654 0.437127i −0.244812 0.969571i \(-0.578726\pi\)
0.846465 + 0.532444i \(0.178726\pi\)
\(860\) 0 0
\(861\) −27.4993 19.9794i −0.937173 0.680896i
\(862\) −12.8364 + 9.32621i −0.437211 + 0.317652i
\(863\) 10.3458 7.51669i 0.352176 0.255871i −0.397605 0.917557i \(-0.630159\pi\)
0.749782 + 0.661685i \(0.230159\pi\)
\(864\) 14.0360 + 10.1977i 0.477513 + 0.346933i
\(865\) 0 0
\(866\) 2.38553 1.73319i 0.0810637 0.0588962i
\(867\) 3.71975 11.4482i 0.126329 0.388801i
\(868\) 13.3814 0.454194
\(869\) −11.6317 + 35.7988i −0.394579 + 1.21439i
\(870\) 0 0
\(871\) 0.523084 + 1.60989i 0.0177240 + 0.0545489i
\(872\) −0.0454454 0.139867i −0.00153898 0.00473648i
\(873\) −16.7961 12.2031i −0.568463 0.413012i
\(874\) 46.0863 1.55889
\(875\) 0 0
\(876\) 6.09640 0.205978
\(877\) −7.72887 5.61535i −0.260985 0.189617i 0.449596 0.893232i \(-0.351568\pi\)
−0.710581 + 0.703615i \(0.751568\pi\)
\(878\) 14.6089 + 44.9615i 0.493025 + 1.51738i
\(879\) 2.56843 + 7.90481i 0.0866309 + 0.266622i
\(880\) 0 0
\(881\) −12.0929 + 37.2180i −0.407419 + 1.25391i 0.511440 + 0.859319i \(0.329112\pi\)
−0.918859 + 0.394587i \(0.870888\pi\)
\(882\) −59.1400 −1.99135
\(883\) −10.8234 + 33.3111i −0.364238 + 1.12101i 0.586220 + 0.810152i \(0.300616\pi\)
−0.950457 + 0.310856i \(0.899384\pi\)
\(884\) −0.0899074 + 0.0653215i −0.00302391 + 0.00219700i
\(885\) 0 0
\(886\) −40.7360 29.5964i −1.36855 0.994312i
\(887\) −29.3219 + 21.3036i −0.984531 + 0.715304i −0.958717 0.284363i \(-0.908218\pi\)
−0.0258147 + 0.999667i \(0.508218\pi\)
\(888\) 6.11052 4.43955i 0.205056 0.148982i
\(889\) 43.8747 + 31.8769i 1.47151 + 1.06912i
\(890\) 0 0
\(891\) −14.9278 + 10.8457i −0.500100 + 0.363344i
\(892\) −1.63250 + 5.02432i −0.0546601 + 0.168227i
\(893\) −5.10841 −0.170946
\(894\) 4.44593 13.6832i 0.148694 0.457633i
\(895\) 0 0
\(896\) −18.4933 56.9164i −0.617817 1.90144i
\(897\) −0.620353 1.90925i −0.0207130 0.0637480i
\(898\) −8.57967 6.23349i −0.286307 0.208014i
\(899\) −14.4378 −0.481528
\(900\) 0 0
\(901\) −0.286386 −0.00954089
\(902\) −55.5694 40.3735i −1.85026 1.34429i
\(903\) 1.39913 + 4.30607i 0.0465601 + 0.143297i
\(904\) −8.57332 26.3860i −0.285144 0.877584i
\(905\) 0 0
\(906\) 0.569869 1.75388i 0.0189326 0.0582686i
\(907\) −40.8532 −1.35651 −0.678255 0.734827i \(-0.737263\pi\)
−0.678255 + 0.734827i \(0.737263\pi\)
\(908\) −2.90210 + 8.93174i −0.0963095 + 0.296410i
\(909\) −7.19741 + 5.22922i −0.238723 + 0.173442i
\(910\) 0 0
\(911\) −10.3124 7.49237i −0.341664 0.248233i 0.403700 0.914892i \(-0.367724\pi\)
−0.745364 + 0.666658i \(0.767724\pi\)
\(912\) 15.8595 11.5226i 0.525162 0.381553i
\(913\) 33.2023 24.1229i 1.09884 0.798351i
\(914\) 26.1226 + 18.9792i 0.864058 + 0.627775i
\(915\) 0 0
\(916\) −10.1468 + 7.37207i −0.335259 + 0.243580i
\(917\) 23.7456 73.0815i 0.784150 2.41337i
\(918\) −1.52858 −0.0504506
\(919\) 2.98883 9.19868i 0.0985924 0.303436i −0.889581 0.456778i \(-0.849003\pi\)
0.988173 + 0.153341i \(0.0490034\pi\)
\(920\) 0 0
\(921\) −5.83172 17.9482i −0.192162 0.591413i
\(922\) 3.67840 + 11.3210i 0.121142 + 0.372836i
\(923\) 1.48581 + 1.07951i 0.0489061 + 0.0355323i
\(924\) 10.6461 0.350231
\(925\) 0 0
\(926\) 16.1917 0.532094
\(927\) −0.806167 0.585715i −0.0264780 0.0192374i
\(928\) −5.67303 17.4598i −0.186226 0.573146i
\(929\) 3.37431 + 10.3850i 0.110707 + 0.340722i 0.991028 0.133658i \(-0.0426723\pi\)
−0.880320 + 0.474380i \(0.842672\pi\)
\(930\) 0 0
\(931\) −24.1452 + 74.3113i −0.791328 + 2.43546i
\(932\) −6.52711 −0.213803
\(933\) 2.96137 9.11417i 0.0969510 0.298384i
\(934\) −26.1786 + 19.0199i −0.856589 + 0.622349i
\(935\) 0 0
\(936\) 2.27063 + 1.64971i 0.0742178 + 0.0539224i
\(937\) −12.9011 + 9.37319i −0.421460 + 0.306209i −0.778225 0.627985i \(-0.783880\pi\)
0.356765 + 0.934194i \(0.383880\pi\)
\(938\) −18.4733 + 13.4216i −0.603175 + 0.438232i
\(939\) 9.76628 + 7.09562i 0.318710 + 0.231557i
\(940\) 0 0
\(941\) −4.79505 + 3.48381i −0.156314 + 0.113569i −0.663193 0.748448i \(-0.730799\pi\)
0.506879 + 0.862017i \(0.330799\pi\)
\(942\) 3.63047 11.1734i 0.118287 0.364051i
\(943\) −51.4117 −1.67419
\(944\) −6.92649 + 21.3176i −0.225438 + 0.693827i
\(945\) 0 0
\(946\) 2.82730 + 8.70154i 0.0919235 + 0.282912i
\(947\) −0.306045 0.941910i −0.00994513 0.0306080i 0.945961 0.324281i \(-0.105122\pi\)
−0.955906 + 0.293673i \(0.905122\pi\)
\(948\) −4.60761 3.34763i −0.149648 0.108726i
\(949\) 5.89681 0.191418
\(950\) 0 0
\(951\) −11.9308 −0.386882
\(952\) 1.69606 + 1.23226i 0.0549697 + 0.0399379i
\(953\) −16.5631 50.9759i −0.536531 1.65127i −0.740318 0.672257i \(-0.765325\pi\)
0.203787 0.979015i \(-0.434675\pi\)
\(954\) −1.59822 4.91881i −0.0517442 0.159252i
\(955\) 0 0
\(956\) 2.25183 6.93042i 0.0728294 0.224146i
\(957\) −11.4866 −0.371308
\(958\) −19.7675 + 60.8380i −0.638658 + 1.96559i
\(959\) 38.7107 28.1250i 1.25003 0.908203i
\(960\) 0 0
\(961\) 15.1956 + 11.0402i 0.490180 + 0.356137i
\(962\) −4.22643 + 3.07068i −0.136266 + 0.0990027i
\(963\) −3.31840 + 2.41096i −0.106934 + 0.0776920i
\(964\) 0.405371 + 0.294519i 0.0130561 + 0.00948582i
\(965\) 0 0
\(966\) 21.9085 15.9175i 0.704895 0.512136i
\(967\) −9.18861 + 28.2796i −0.295486 + 0.909412i 0.687572 + 0.726116i \(0.258677\pi\)
−0.983058 + 0.183296i \(0.941323\pi\)
\(968\) −8.49141 −0.272924
\(969\) −0.283387 + 0.872176i −0.00910370 + 0.0280183i
\(970\) 0 0
\(971\) 18.7316 + 57.6498i 0.601125 + 1.85007i 0.521509 + 0.853246i \(0.325369\pi\)
0.0796154 + 0.996826i \(0.474631\pi\)
\(972\) −3.88039 11.9426i −0.124463 0.383059i
\(973\) 24.7369 + 17.9724i 0.793027 + 0.576168i
\(974\) 28.1954 0.903440
\(975\) 0 0
\(976\) 57.9720 1.85564
\(977\) −36.0117 26.1641i −1.15212 0.837062i −0.163356 0.986567i \(-0.552232\pi\)
−0.988761 + 0.149505i \(0.952232\pi\)
\(978\) 2.06232 + 6.34718i 0.0659458 + 0.202960i
\(979\) 8.78060 + 27.0239i 0.280629 + 0.863688i
\(980\) 0 0
\(981\) −0.0577692 + 0.177795i −0.00184443 + 0.00567657i
\(982\) −15.0675 −0.480822
\(983\) 11.8168 36.3685i 0.376898 1.15997i −0.565291 0.824892i \(-0.691236\pi\)
0.942189 0.335082i \(-0.108764\pi\)
\(984\) −11.7582 + 8.54283i −0.374838 + 0.272336i
\(985\) 0 0
\(986\) 1.30856 + 0.950724i 0.0416730 + 0.0302772i
\(987\) −2.42844 + 1.76436i −0.0772979 + 0.0561602i
\(988\) −2.14519 + 1.55857i −0.0682475 + 0.0495847i
\(989\) 5.54027 + 4.02524i 0.176170 + 0.127995i
\(990\) 0 0
\(991\) −18.3713 + 13.3475i −0.583584 + 0.423998i −0.840014 0.542564i \(-0.817453\pi\)
0.256431 + 0.966563i \(0.417453\pi\)
\(992\) 4.80049 14.7744i 0.152416 0.469087i
\(993\) −9.11678 −0.289312
\(994\) −7.65574 + 23.5619i −0.242825 + 0.747339i
\(995\) 0 0
\(996\) 1.91889 + 5.90573i 0.0608023 + 0.187130i
\(997\) 6.37453 + 19.6188i 0.201883 + 0.621333i 0.999827 + 0.0186012i \(0.00592127\pi\)
−0.797944 + 0.602732i \(0.794079\pi\)
\(998\) 49.4795 + 35.9490i 1.56625 + 1.13794i
\(999\) −21.1439 −0.668962
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 625.2.d.q.376.1 16
5.2 odd 4 625.2.e.j.249.6 32
5.3 odd 4 625.2.e.j.249.3 32
5.4 even 2 625.2.d.m.376.4 16
25.2 odd 20 625.2.e.j.374.3 32
25.3 odd 20 625.2.e.k.499.6 32
25.4 even 10 625.2.d.n.126.1 16
25.6 even 5 625.2.a.e.1.7 8
25.8 odd 20 625.2.b.d.624.5 16
25.9 even 10 625.2.d.n.501.1 16
25.11 even 5 inner 625.2.d.q.251.1 16
25.12 odd 20 625.2.e.k.124.6 32
25.13 odd 20 625.2.e.k.124.3 32
25.14 even 10 625.2.d.m.251.4 16
25.16 even 5 625.2.d.p.501.4 16
25.17 odd 20 625.2.b.d.624.12 16
25.19 even 10 625.2.a.g.1.2 yes 8
25.21 even 5 625.2.d.p.126.4 16
25.22 odd 20 625.2.e.k.499.3 32
25.23 odd 20 625.2.e.j.374.6 32
75.44 odd 10 5625.2.a.s.1.7 8
75.56 odd 10 5625.2.a.be.1.2 8
100.19 odd 10 10000.2.a.be.1.5 8
100.31 odd 10 10000.2.a.bn.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
625.2.a.e.1.7 8 25.6 even 5
625.2.a.g.1.2 yes 8 25.19 even 10
625.2.b.d.624.5 16 25.8 odd 20
625.2.b.d.624.12 16 25.17 odd 20
625.2.d.m.251.4 16 25.14 even 10
625.2.d.m.376.4 16 5.4 even 2
625.2.d.n.126.1 16 25.4 even 10
625.2.d.n.501.1 16 25.9 even 10
625.2.d.p.126.4 16 25.21 even 5
625.2.d.p.501.4 16 25.16 even 5
625.2.d.q.251.1 16 25.11 even 5 inner
625.2.d.q.376.1 16 1.1 even 1 trivial
625.2.e.j.249.3 32 5.3 odd 4
625.2.e.j.249.6 32 5.2 odd 4
625.2.e.j.374.3 32 25.2 odd 20
625.2.e.j.374.6 32 25.23 odd 20
625.2.e.k.124.3 32 25.13 odd 20
625.2.e.k.124.6 32 25.12 odd 20
625.2.e.k.499.3 32 25.22 odd 20
625.2.e.k.499.6 32 25.3 odd 20
5625.2.a.s.1.7 8 75.44 odd 10
5625.2.a.be.1.2 8 75.56 odd 10
10000.2.a.be.1.5 8 100.19 odd 10
10000.2.a.bn.1.4 8 100.31 odd 10