Properties

Label 170.2.g.e.149.2
Level $170$
Weight $2$
Character 170.149
Analytic conductor $1.357$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [170,2,Mod(89,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.g (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 149.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 170.149
Dual form 170.2.g.e.89.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.292893 + 0.292893i) q^{3} +1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(0.292893 - 0.292893i) q^{6} +(1.00000 + 1.00000i) q^{7} -1.00000 q^{8} +2.82843i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.292893 + 0.292893i) q^{3} +1.00000 q^{4} +(-2.12132 + 0.707107i) q^{5} +(0.292893 - 0.292893i) q^{6} +(1.00000 + 1.00000i) q^{7} -1.00000 q^{8} +2.82843i q^{9} +(2.12132 - 0.707107i) q^{10} +(-1.58579 + 1.58579i) q^{11} +(-0.292893 + 0.292893i) q^{12} +3.00000i q^{13} +(-1.00000 - 1.00000i) q^{14} +(0.414214 - 0.828427i) q^{15} +1.00000 q^{16} +(-2.12132 - 3.53553i) q^{17} -2.82843i q^{18} +7.24264i q^{19} +(-2.12132 + 0.707107i) q^{20} -0.585786 q^{21} +(1.58579 - 1.58579i) q^{22} +(2.82843 + 2.82843i) q^{23} +(0.292893 - 0.292893i) q^{24} +(4.00000 - 3.00000i) q^{25} -3.00000i q^{26} +(-1.70711 - 1.70711i) q^{27} +(1.00000 + 1.00000i) q^{28} +(0.707107 + 0.707107i) q^{29} +(-0.414214 + 0.828427i) q^{30} +(-5.36396 - 5.36396i) q^{31} -1.00000 q^{32} -0.928932i q^{33} +(2.12132 + 3.53553i) q^{34} +(-2.82843 - 1.41421i) q^{35} +2.82843i q^{36} +(5.24264 - 5.24264i) q^{37} -7.24264i q^{38} +(-0.878680 - 0.878680i) q^{39} +(2.12132 - 0.707107i) q^{40} +(4.41421 - 4.41421i) q^{41} +0.585786 q^{42} +3.75736 q^{43} +(-1.58579 + 1.58579i) q^{44} +(-2.00000 - 6.00000i) q^{45} +(-2.82843 - 2.82843i) q^{46} -1.58579i q^{47} +(-0.292893 + 0.292893i) q^{48} -5.00000i q^{49} +(-4.00000 + 3.00000i) q^{50} +(1.65685 + 0.414214i) q^{51} +3.00000i q^{52} -3.00000 q^{53} +(1.70711 + 1.70711i) q^{54} +(2.24264 - 4.48528i) q^{55} +(-1.00000 - 1.00000i) q^{56} +(-2.12132 - 2.12132i) q^{57} +(-0.707107 - 0.707107i) q^{58} +12.8995i q^{59} +(0.414214 - 0.828427i) q^{60} +(6.12132 - 6.12132i) q^{61} +(5.36396 + 5.36396i) q^{62} +(-2.82843 + 2.82843i) q^{63} +1.00000 q^{64} +(-2.12132 - 6.36396i) q^{65} +0.928932i q^{66} +14.4853i q^{67} +(-2.12132 - 3.53553i) q^{68} -1.65685 q^{69} +(2.82843 + 1.41421i) q^{70} +(3.70711 + 3.70711i) q^{71} -2.82843i q^{72} +(-8.36396 + 8.36396i) q^{73} +(-5.24264 + 5.24264i) q^{74} +(-0.292893 + 2.05025i) q^{75} +7.24264i q^{76} -3.17157 q^{77} +(0.878680 + 0.878680i) q^{78} +(-0.242641 + 0.242641i) q^{79} +(-2.12132 + 0.707107i) q^{80} -7.48528 q^{81} +(-4.41421 + 4.41421i) q^{82} +4.24264 q^{83} -0.585786 q^{84} +(7.00000 + 6.00000i) q^{85} -3.75736 q^{86} -0.414214 q^{87} +(1.58579 - 1.58579i) q^{88} +11.4853 q^{89} +(2.00000 + 6.00000i) q^{90} +(-3.00000 + 3.00000i) q^{91} +(2.82843 + 2.82843i) q^{92} +3.14214 q^{93} +1.58579i q^{94} +(-5.12132 - 15.3640i) q^{95} +(0.292893 - 0.292893i) q^{96} +(0.121320 - 0.121320i) q^{97} +5.00000i q^{98} +(-4.48528 - 4.48528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 12 q^{11} - 4 q^{12} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 8 q^{21} + 12 q^{22} + 4 q^{24} + 16 q^{25} - 4 q^{27} + 4 q^{28} + 4 q^{30} + 4 q^{31} - 4 q^{32} + 4 q^{37} - 12 q^{39} + 12 q^{41} + 8 q^{42} + 32 q^{43} - 12 q^{44} - 8 q^{45} - 4 q^{48} - 16 q^{50} - 16 q^{51} - 12 q^{53} + 4 q^{54} - 8 q^{55} - 4 q^{56} - 4 q^{60} + 16 q^{61} - 4 q^{62} + 4 q^{64} + 16 q^{69} + 12 q^{71} - 8 q^{73} - 4 q^{74} - 4 q^{75} - 24 q^{77} + 12 q^{78} + 16 q^{79} + 4 q^{81} - 12 q^{82} - 8 q^{84} + 28 q^{85} - 32 q^{86} + 4 q^{87} + 12 q^{88} + 12 q^{89} + 8 q^{90} - 12 q^{91} - 44 q^{93} - 12 q^{95} + 4 q^{96} - 8 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.292893 + 0.292893i −0.169102 + 0.169102i −0.786585 0.617483i \(-0.788153\pi\)
0.617483 + 0.786585i \(0.288153\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.12132 + 0.707107i −0.948683 + 0.316228i
\(6\) 0.292893 0.292893i 0.119573 0.119573i
\(7\) 1.00000 + 1.00000i 0.377964 + 0.377964i 0.870367 0.492403i \(-0.163881\pi\)
−0.492403 + 0.870367i \(0.663881\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.82843i 0.942809i
\(10\) 2.12132 0.707107i 0.670820 0.223607i
\(11\) −1.58579 + 1.58579i −0.478133 + 0.478133i −0.904534 0.426401i \(-0.859781\pi\)
0.426401 + 0.904534i \(0.359781\pi\)
\(12\) −0.292893 + 0.292893i −0.0845510 + 0.0845510i
\(13\) 3.00000i 0.832050i 0.909353 + 0.416025i \(0.136577\pi\)
−0.909353 + 0.416025i \(0.863423\pi\)
\(14\) −1.00000 1.00000i −0.267261 0.267261i
\(15\) 0.414214 0.828427i 0.106949 0.213899i
\(16\) 1.00000 0.250000
\(17\) −2.12132 3.53553i −0.514496 0.857493i
\(18\) 2.82843i 0.666667i
\(19\) 7.24264i 1.66158i 0.556589 + 0.830788i \(0.312110\pi\)
−0.556589 + 0.830788i \(0.687890\pi\)
\(20\) −2.12132 + 0.707107i −0.474342 + 0.158114i
\(21\) −0.585786 −0.127829
\(22\) 1.58579 1.58579i 0.338091 0.338091i
\(23\) 2.82843 + 2.82843i 0.589768 + 0.589768i 0.937568 0.347801i \(-0.113071\pi\)
−0.347801 + 0.937568i \(0.613071\pi\)
\(24\) 0.292893 0.292893i 0.0597866 0.0597866i
\(25\) 4.00000 3.00000i 0.800000 0.600000i
\(26\) 3.00000i 0.588348i
\(27\) −1.70711 1.70711i −0.328533 0.328533i
\(28\) 1.00000 + 1.00000i 0.188982 + 0.188982i
\(29\) 0.707107 + 0.707107i 0.131306 + 0.131306i 0.769706 0.638399i \(-0.220403\pi\)
−0.638399 + 0.769706i \(0.720403\pi\)
\(30\) −0.414214 + 0.828427i −0.0756247 + 0.151249i
\(31\) −5.36396 5.36396i −0.963396 0.963396i 0.0359575 0.999353i \(-0.488552\pi\)
−0.999353 + 0.0359575i \(0.988552\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.928932i 0.161706i
\(34\) 2.12132 + 3.53553i 0.363803 + 0.606339i
\(35\) −2.82843 1.41421i −0.478091 0.239046i
\(36\) 2.82843i 0.471405i
\(37\) 5.24264 5.24264i 0.861885 0.861885i −0.129672 0.991557i \(-0.541392\pi\)
0.991557 + 0.129672i \(0.0413925\pi\)
\(38\) 7.24264i 1.17491i
\(39\) −0.878680 0.878680i −0.140701 0.140701i
\(40\) 2.12132 0.707107i 0.335410 0.111803i
\(41\) 4.41421 4.41421i 0.689384 0.689384i −0.272712 0.962096i \(-0.587920\pi\)
0.962096 + 0.272712i \(0.0879205\pi\)
\(42\) 0.585786 0.0903888
\(43\) 3.75736 0.572992 0.286496 0.958081i \(-0.407509\pi\)
0.286496 + 0.958081i \(0.407509\pi\)
\(44\) −1.58579 + 1.58579i −0.239066 + 0.239066i
\(45\) −2.00000 6.00000i −0.298142 0.894427i
\(46\) −2.82843 2.82843i −0.417029 0.417029i
\(47\) 1.58579i 0.231311i −0.993289 0.115655i \(-0.963103\pi\)
0.993289 0.115655i \(-0.0368968\pi\)
\(48\) −0.292893 + 0.292893i −0.0422755 + 0.0422755i
\(49\) 5.00000i 0.714286i
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 1.65685 + 0.414214i 0.232006 + 0.0580015i
\(52\) 3.00000i 0.416025i
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) 1.70711 + 1.70711i 0.232308 + 0.232308i
\(55\) 2.24264 4.48528i 0.302398 0.604795i
\(56\) −1.00000 1.00000i −0.133631 0.133631i
\(57\) −2.12132 2.12132i −0.280976 0.280976i
\(58\) −0.707107 0.707107i −0.0928477 0.0928477i
\(59\) 12.8995i 1.67937i 0.543073 + 0.839686i \(0.317261\pi\)
−0.543073 + 0.839686i \(0.682739\pi\)
\(60\) 0.414214 0.828427i 0.0534747 0.106949i
\(61\) 6.12132 6.12132i 0.783755 0.783755i −0.196707 0.980462i \(-0.563025\pi\)
0.980462 + 0.196707i \(0.0630249\pi\)
\(62\) 5.36396 + 5.36396i 0.681224 + 0.681224i
\(63\) −2.82843 + 2.82843i −0.356348 + 0.356348i
\(64\) 1.00000 0.125000
\(65\) −2.12132 6.36396i −0.263117 0.789352i
\(66\) 0.928932i 0.114344i
\(67\) 14.4853i 1.76966i 0.465915 + 0.884829i \(0.345725\pi\)
−0.465915 + 0.884829i \(0.654275\pi\)
\(68\) −2.12132 3.53553i −0.257248 0.428746i
\(69\) −1.65685 −0.199462
\(70\) 2.82843 + 1.41421i 0.338062 + 0.169031i
\(71\) 3.70711 + 3.70711i 0.439953 + 0.439953i 0.891996 0.452043i \(-0.149305\pi\)
−0.452043 + 0.891996i \(0.649305\pi\)
\(72\) 2.82843i 0.333333i
\(73\) −8.36396 + 8.36396i −0.978928 + 0.978928i −0.999783 0.0208549i \(-0.993361\pi\)
0.0208549 + 0.999783i \(0.493361\pi\)
\(74\) −5.24264 + 5.24264i −0.609445 + 0.609445i
\(75\) −0.292893 + 2.05025i −0.0338204 + 0.236743i
\(76\) 7.24264i 0.830788i
\(77\) −3.17157 −0.361434
\(78\) 0.878680 + 0.878680i 0.0994909 + 0.0994909i
\(79\) −0.242641 + 0.242641i −0.0272992 + 0.0272992i −0.720625 0.693325i \(-0.756145\pi\)
0.693325 + 0.720625i \(0.256145\pi\)
\(80\) −2.12132 + 0.707107i −0.237171 + 0.0790569i
\(81\) −7.48528 −0.831698
\(82\) −4.41421 + 4.41421i −0.487468 + 0.487468i
\(83\) 4.24264 0.465690 0.232845 0.972514i \(-0.425196\pi\)
0.232845 + 0.972514i \(0.425196\pi\)
\(84\) −0.585786 −0.0639145
\(85\) 7.00000 + 6.00000i 0.759257 + 0.650791i
\(86\) −3.75736 −0.405166
\(87\) −0.414214 −0.0444084
\(88\) 1.58579 1.58579i 0.169045 0.169045i
\(89\) 11.4853 1.21744 0.608719 0.793386i \(-0.291684\pi\)
0.608719 + 0.793386i \(0.291684\pi\)
\(90\) 2.00000 + 6.00000i 0.210819 + 0.632456i
\(91\) −3.00000 + 3.00000i −0.314485 + 0.314485i
\(92\) 2.82843 + 2.82843i 0.294884 + 0.294884i
\(93\) 3.14214 0.325824
\(94\) 1.58579i 0.163561i
\(95\) −5.12132 15.3640i −0.525436 1.57631i
\(96\) 0.292893 0.292893i 0.0298933 0.0298933i
\(97\) 0.121320 0.121320i 0.0123182 0.0123182i −0.700921 0.713239i \(-0.747227\pi\)
0.713239 + 0.700921i \(0.247227\pi\)
\(98\) 5.00000i 0.505076i
\(99\) −4.48528 4.48528i −0.450788 0.450788i
\(100\) 4.00000 3.00000i 0.400000 0.300000i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −1.65685 0.414214i −0.164053 0.0410133i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 3.00000i 0.294174i
\(105\) 1.24264 0.414214i 0.121269 0.0404231i
\(106\) 3.00000 0.291386
\(107\) −2.82843 + 2.82843i −0.273434 + 0.273434i −0.830481 0.557047i \(-0.811934\pi\)
0.557047 + 0.830481i \(0.311934\pi\)
\(108\) −1.70711 1.70711i −0.164266 0.164266i
\(109\) 8.60660 8.60660i 0.824363 0.824363i −0.162367 0.986730i \(-0.551913\pi\)
0.986730 + 0.162367i \(0.0519130\pi\)
\(110\) −2.24264 + 4.48528i −0.213827 + 0.427655i
\(111\) 3.07107i 0.291493i
\(112\) 1.00000 + 1.00000i 0.0944911 + 0.0944911i
\(113\) 2.46447 + 2.46447i 0.231837 + 0.231837i 0.813459 0.581622i \(-0.197582\pi\)
−0.581622 + 0.813459i \(0.697582\pi\)
\(114\) 2.12132 + 2.12132i 0.198680 + 0.198680i
\(115\) −8.00000 4.00000i −0.746004 0.373002i
\(116\) 0.707107 + 0.707107i 0.0656532 + 0.0656532i
\(117\) −8.48528 −0.784465
\(118\) 12.8995i 1.18749i
\(119\) 1.41421 5.65685i 0.129641 0.518563i
\(120\) −0.414214 + 0.828427i −0.0378124 + 0.0756247i
\(121\) 5.97056i 0.542778i
\(122\) −6.12132 + 6.12132i −0.554198 + 0.554198i
\(123\) 2.58579i 0.233153i
\(124\) −5.36396 5.36396i −0.481698 0.481698i
\(125\) −6.36396 + 9.19239i −0.569210 + 0.822192i
\(126\) 2.82843 2.82843i 0.251976 0.251976i
\(127\) 17.7279 1.57310 0.786549 0.617527i \(-0.211866\pi\)
0.786549 + 0.617527i \(0.211866\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.10051 + 1.10051i −0.0968941 + 0.0968941i
\(130\) 2.12132 + 6.36396i 0.186052 + 0.558156i
\(131\) 7.58579 + 7.58579i 0.662773 + 0.662773i 0.956033 0.293260i \(-0.0947400\pi\)
−0.293260 + 0.956033i \(0.594740\pi\)
\(132\) 0.928932i 0.0808532i
\(133\) −7.24264 + 7.24264i −0.628017 + 0.628017i
\(134\) 14.4853i 1.25134i
\(135\) 4.82843 + 2.41421i 0.415565 + 0.207782i
\(136\) 2.12132 + 3.53553i 0.181902 + 0.303170i
\(137\) 4.58579i 0.391790i −0.980625 0.195895i \(-0.937239\pi\)
0.980625 0.195895i \(-0.0627612\pi\)
\(138\) 1.65685 0.141041
\(139\) −11.0000 11.0000i −0.933008 0.933008i 0.0648849 0.997893i \(-0.479332\pi\)
−0.997893 + 0.0648849i \(0.979332\pi\)
\(140\) −2.82843 1.41421i −0.239046 0.119523i
\(141\) 0.464466 + 0.464466i 0.0391151 + 0.0391151i
\(142\) −3.70711 3.70711i −0.311093 0.311093i
\(143\) −4.75736 4.75736i −0.397830 0.397830i
\(144\) 2.82843i 0.235702i
\(145\) −2.00000 1.00000i −0.166091 0.0830455i
\(146\) 8.36396 8.36396i 0.692206 0.692206i
\(147\) 1.46447 + 1.46447i 0.120787 + 0.120787i
\(148\) 5.24264 5.24264i 0.430942 0.430942i
\(149\) −12.7279 −1.04271 −0.521356 0.853339i \(-0.674574\pi\)
−0.521356 + 0.853339i \(0.674574\pi\)
\(150\) 0.292893 2.05025i 0.0239146 0.167402i
\(151\) 12.0000i 0.976546i −0.872691 0.488273i \(-0.837627\pi\)
0.872691 0.488273i \(-0.162373\pi\)
\(152\) 7.24264i 0.587456i
\(153\) 10.0000 6.00000i 0.808452 0.485071i
\(154\) 3.17157 0.255573
\(155\) 15.1716 + 7.58579i 1.21861 + 0.609305i
\(156\) −0.878680 0.878680i −0.0703507 0.0703507i
\(157\) 12.0000i 0.957704i −0.877896 0.478852i \(-0.841053\pi\)
0.877896 0.478852i \(-0.158947\pi\)
\(158\) 0.242641 0.242641i 0.0193035 0.0193035i
\(159\) 0.878680 0.878680i 0.0696838 0.0696838i
\(160\) 2.12132 0.707107i 0.167705 0.0559017i
\(161\) 5.65685i 0.445823i
\(162\) 7.48528 0.588099
\(163\) −4.48528 4.48528i −0.351314 0.351314i 0.509284 0.860598i \(-0.329910\pi\)
−0.860598 + 0.509284i \(0.829910\pi\)
\(164\) 4.41421 4.41421i 0.344692 0.344692i
\(165\) 0.656854 + 1.97056i 0.0511360 + 0.153408i
\(166\) −4.24264 −0.329293
\(167\) −1.07107 + 1.07107i −0.0828817 + 0.0828817i −0.747332 0.664451i \(-0.768666\pi\)
0.664451 + 0.747332i \(0.268666\pi\)
\(168\) 0.585786 0.0451944
\(169\) 4.00000 0.307692
\(170\) −7.00000 6.00000i −0.536875 0.460179i
\(171\) −20.4853 −1.56655
\(172\) 3.75736 0.286496
\(173\) 17.6569 17.6569i 1.34243 1.34243i 0.448787 0.893639i \(-0.351856\pi\)
0.893639 0.448787i \(-0.148144\pi\)
\(174\) 0.414214 0.0314014
\(175\) 7.00000 + 1.00000i 0.529150 + 0.0755929i
\(176\) −1.58579 + 1.58579i −0.119533 + 0.119533i
\(177\) −3.77817 3.77817i −0.283985 0.283985i
\(178\) −11.4853 −0.860858
\(179\) 0.686292i 0.0512958i 0.999671 + 0.0256479i \(0.00816488\pi\)
−0.999671 + 0.0256479i \(0.991835\pi\)
\(180\) −2.00000 6.00000i −0.149071 0.447214i
\(181\) −14.0000 + 14.0000i −1.04061 + 1.04061i −0.0414721 + 0.999140i \(0.513205\pi\)
−0.999140 + 0.0414721i \(0.986795\pi\)
\(182\) 3.00000 3.00000i 0.222375 0.222375i
\(183\) 3.58579i 0.265069i
\(184\) −2.82843 2.82843i −0.208514 0.208514i
\(185\) −7.41421 + 14.8284i −0.545104 + 1.09021i
\(186\) −3.14214 −0.230393
\(187\) 8.97056 + 2.24264i 0.655993 + 0.163998i
\(188\) 1.58579i 0.115655i
\(189\) 3.41421i 0.248347i
\(190\) 5.12132 + 15.3640i 0.371540 + 1.11462i
\(191\) 21.2132 1.53493 0.767467 0.641089i \(-0.221517\pi\)
0.767467 + 0.641089i \(0.221517\pi\)
\(192\) −0.292893 + 0.292893i −0.0211377 + 0.0211377i
\(193\) 18.4853 + 18.4853i 1.33060 + 1.33060i 0.904833 + 0.425767i \(0.139996\pi\)
0.425767 + 0.904833i \(0.360004\pi\)
\(194\) −0.121320 + 0.121320i −0.00871029 + 0.00871029i
\(195\) 2.48528 + 1.24264i 0.177975 + 0.0889873i
\(196\) 5.00000i 0.357143i
\(197\) 3.34315 + 3.34315i 0.238189 + 0.238189i 0.816100 0.577911i \(-0.196132\pi\)
−0.577911 + 0.816100i \(0.696132\pi\)
\(198\) 4.48528 + 4.48528i 0.318755 + 0.318755i
\(199\) −7.12132 7.12132i −0.504817 0.504817i 0.408114 0.912931i \(-0.366187\pi\)
−0.912931 + 0.408114i \(0.866187\pi\)
\(200\) −4.00000 + 3.00000i −0.282843 + 0.212132i
\(201\) −4.24264 4.24264i −0.299253 0.299253i
\(202\) 0 0
\(203\) 1.41421i 0.0992583i
\(204\) 1.65685 + 0.414214i 0.116003 + 0.0290008i
\(205\) −6.24264 + 12.4853i −0.436005 + 0.872010i
\(206\) 0 0
\(207\) −8.00000 + 8.00000i −0.556038 + 0.556038i
\(208\) 3.00000i 0.208013i
\(209\) −11.4853 11.4853i −0.794454 0.794454i
\(210\) −1.24264 + 0.414214i −0.0857504 + 0.0285835i
\(211\) −8.00000 + 8.00000i −0.550743 + 0.550743i −0.926655 0.375912i \(-0.877329\pi\)
0.375912 + 0.926655i \(0.377329\pi\)
\(212\) −3.00000 −0.206041
\(213\) −2.17157 −0.148794
\(214\) 2.82843 2.82843i 0.193347 0.193347i
\(215\) −7.97056 + 2.65685i −0.543588 + 0.181196i
\(216\) 1.70711 + 1.70711i 0.116154 + 0.116154i
\(217\) 10.7279i 0.728259i
\(218\) −8.60660 + 8.60660i −0.582913 + 0.582913i
\(219\) 4.89949i 0.331077i
\(220\) 2.24264 4.48528i 0.151199 0.302398i
\(221\) 10.6066 6.36396i 0.713477 0.428086i
\(222\) 3.07107i 0.206117i
\(223\) −23.2426 −1.55644 −0.778221 0.627990i \(-0.783878\pi\)
−0.778221 + 0.627990i \(0.783878\pi\)
\(224\) −1.00000 1.00000i −0.0668153 0.0668153i
\(225\) 8.48528 + 11.3137i 0.565685 + 0.754247i
\(226\) −2.46447 2.46447i −0.163934 0.163934i
\(227\) −4.05025 4.05025i −0.268825 0.268825i 0.559802 0.828627i \(-0.310877\pi\)
−0.828627 + 0.559802i \(0.810877\pi\)
\(228\) −2.12132 2.12132i −0.140488 0.140488i
\(229\) 7.75736i 0.512621i 0.966595 + 0.256310i \(0.0825069\pi\)
−0.966595 + 0.256310i \(0.917493\pi\)
\(230\) 8.00000 + 4.00000i 0.527504 + 0.263752i
\(231\) 0.928932 0.928932i 0.0611193 0.0611193i
\(232\) −0.707107 0.707107i −0.0464238 0.0464238i
\(233\) −10.9497 + 10.9497i −0.717342 + 0.717342i −0.968060 0.250718i \(-0.919333\pi\)
0.250718 + 0.968060i \(0.419333\pi\)
\(234\) 8.48528 0.554700
\(235\) 1.12132 + 3.36396i 0.0731469 + 0.219441i
\(236\) 12.8995i 0.839686i
\(237\) 0.142136i 0.00923270i
\(238\) −1.41421 + 5.65685i −0.0916698 + 0.366679i
\(239\) 22.2426 1.43876 0.719378 0.694618i \(-0.244427\pi\)
0.719378 + 0.694618i \(0.244427\pi\)
\(240\) 0.414214 0.828427i 0.0267374 0.0534747i
\(241\) 2.75736 + 2.75736i 0.177617 + 0.177617i 0.790316 0.612699i \(-0.209916\pi\)
−0.612699 + 0.790316i \(0.709916\pi\)
\(242\) 5.97056i 0.383802i
\(243\) 7.31371 7.31371i 0.469175 0.469175i
\(244\) 6.12132 6.12132i 0.391877 0.391877i
\(245\) 3.53553 + 10.6066i 0.225877 + 0.677631i
\(246\) 2.58579i 0.164864i
\(247\) −21.7279 −1.38251
\(248\) 5.36396 + 5.36396i 0.340612 + 0.340612i
\(249\) −1.24264 + 1.24264i −0.0787492 + 0.0787492i
\(250\) 6.36396 9.19239i 0.402492 0.581378i
\(251\) 20.4853 1.29302 0.646510 0.762906i \(-0.276228\pi\)
0.646510 + 0.762906i \(0.276228\pi\)
\(252\) −2.82843 + 2.82843i −0.178174 + 0.178174i
\(253\) −8.97056 −0.563974
\(254\) −17.7279 −1.11235
\(255\) −3.80761 + 0.292893i −0.238442 + 0.0183417i
\(256\) 1.00000 0.0625000
\(257\) 6.72792 0.419676 0.209838 0.977736i \(-0.432706\pi\)
0.209838 + 0.977736i \(0.432706\pi\)
\(258\) 1.10051 1.10051i 0.0685145 0.0685145i
\(259\) 10.4853 0.651524
\(260\) −2.12132 6.36396i −0.131559 0.394676i
\(261\) −2.00000 + 2.00000i −0.123797 + 0.123797i
\(262\) −7.58579 7.58579i −0.468651 0.468651i
\(263\) 4.75736 0.293351 0.146676 0.989185i \(-0.453143\pi\)
0.146676 + 0.989185i \(0.453143\pi\)
\(264\) 0.928932i 0.0571718i
\(265\) 6.36396 2.12132i 0.390935 0.130312i
\(266\) 7.24264 7.24264i 0.444075 0.444075i
\(267\) −3.36396 + 3.36396i −0.205871 + 0.205871i
\(268\) 14.4853i 0.884829i
\(269\) −11.2929 11.2929i −0.688540 0.688540i 0.273369 0.961909i \(-0.411862\pi\)
−0.961909 + 0.273369i \(0.911862\pi\)
\(270\) −4.82843 2.41421i −0.293849 0.146924i
\(271\) −6.48528 −0.393953 −0.196976 0.980408i \(-0.563112\pi\)
−0.196976 + 0.980408i \(0.563112\pi\)
\(272\) −2.12132 3.53553i −0.128624 0.214373i
\(273\) 1.75736i 0.106360i
\(274\) 4.58579i 0.277037i
\(275\) −1.58579 + 11.1005i −0.0956265 + 0.669386i
\(276\) −1.65685 −0.0997309
\(277\) 8.24264 8.24264i 0.495252 0.495252i −0.414704 0.909956i \(-0.636115\pi\)
0.909956 + 0.414704i \(0.136115\pi\)
\(278\) 11.0000 + 11.0000i 0.659736 + 0.659736i
\(279\) 15.1716 15.1716i 0.908298 0.908298i
\(280\) 2.82843 + 1.41421i 0.169031 + 0.0845154i
\(281\) 3.34315i 0.199435i −0.995016 0.0997177i \(-0.968206\pi\)
0.995016 0.0997177i \(-0.0317940\pi\)
\(282\) −0.464466 0.464466i −0.0276586 0.0276586i
\(283\) −19.1213 19.1213i −1.13664 1.13664i −0.989048 0.147597i \(-0.952846\pi\)
−0.147597 0.989048i \(-0.547154\pi\)
\(284\) 3.70711 + 3.70711i 0.219976 + 0.219976i
\(285\) 6.00000 + 3.00000i 0.355409 + 0.177705i
\(286\) 4.75736 + 4.75736i 0.281309 + 0.281309i
\(287\) 8.82843 0.521126
\(288\) 2.82843i 0.166667i
\(289\) −8.00000 + 15.0000i −0.470588 + 0.882353i
\(290\) 2.00000 + 1.00000i 0.117444 + 0.0587220i
\(291\) 0.0710678i 0.00416607i
\(292\) −8.36396 + 8.36396i −0.489464 + 0.489464i
\(293\) 20.6569i 1.20679i 0.797444 + 0.603393i \(0.206185\pi\)
−0.797444 + 0.603393i \(0.793815\pi\)
\(294\) −1.46447 1.46447i −0.0854094 0.0854094i
\(295\) −9.12132 27.3640i −0.531064 1.59319i
\(296\) −5.24264 + 5.24264i −0.304722 + 0.304722i
\(297\) 5.41421 0.314165
\(298\) 12.7279 0.737309
\(299\) −8.48528 + 8.48528i −0.490716 + 0.490716i
\(300\) −0.292893 + 2.05025i −0.0169102 + 0.118371i
\(301\) 3.75736 + 3.75736i 0.216571 + 0.216571i
\(302\) 12.0000i 0.690522i
\(303\) 0 0
\(304\) 7.24264i 0.415394i
\(305\) −8.65685 + 17.3137i −0.495690 + 0.991380i
\(306\) −10.0000 + 6.00000i −0.571662 + 0.342997i
\(307\) 33.2132i 1.89558i 0.318899 + 0.947789i \(0.396687\pi\)
−0.318899 + 0.947789i \(0.603313\pi\)
\(308\) −3.17157 −0.180717
\(309\) 0 0
\(310\) −15.1716 7.58579i −0.861687 0.430844i
\(311\) −1.41421 1.41421i −0.0801927 0.0801927i 0.665873 0.746065i \(-0.268059\pi\)
−0.746065 + 0.665873i \(0.768059\pi\)
\(312\) 0.878680 + 0.878680i 0.0497454 + 0.0497454i
\(313\) −22.4853 22.4853i −1.27094 1.27094i −0.945594 0.325349i \(-0.894518\pi\)
−0.325349 0.945594i \(-0.605482\pi\)
\(314\) 12.0000i 0.677199i
\(315\) 4.00000 8.00000i 0.225374 0.450749i
\(316\) −0.242641 + 0.242641i −0.0136496 + 0.0136496i
\(317\) −14.1421 14.1421i −0.794301 0.794301i 0.187889 0.982190i \(-0.439836\pi\)
−0.982190 + 0.187889i \(0.939836\pi\)
\(318\) −0.878680 + 0.878680i −0.0492739 + 0.0492739i
\(319\) −2.24264 −0.125564
\(320\) −2.12132 + 0.707107i −0.118585 + 0.0395285i
\(321\) 1.65685i 0.0924766i
\(322\) 5.65685i 0.315244i
\(323\) 25.6066 15.3640i 1.42479 0.854874i
\(324\) −7.48528 −0.415849
\(325\) 9.00000 + 12.0000i 0.499230 + 0.665640i
\(326\) 4.48528 + 4.48528i 0.248417 + 0.248417i
\(327\) 5.04163i 0.278803i
\(328\) −4.41421 + 4.41421i −0.243734 + 0.243734i
\(329\) 1.58579 1.58579i 0.0874272 0.0874272i
\(330\) −0.656854 1.97056i −0.0361586 0.108476i
\(331\) 15.7279i 0.864485i −0.901757 0.432242i \(-0.857722\pi\)
0.901757 0.432242i \(-0.142278\pi\)
\(332\) 4.24264 0.232845
\(333\) 14.8284 + 14.8284i 0.812593 + 0.812593i
\(334\) 1.07107 1.07107i 0.0586062 0.0586062i
\(335\) −10.2426 30.7279i −0.559615 1.67885i
\(336\) −0.585786 −0.0319573
\(337\) 12.8492 12.8492i 0.699943 0.699943i −0.264455 0.964398i \(-0.585192\pi\)
0.964398 + 0.264455i \(0.0851921\pi\)
\(338\) −4.00000 −0.217571
\(339\) −1.44365 −0.0784083
\(340\) 7.00000 + 6.00000i 0.379628 + 0.325396i
\(341\) 17.0122 0.921262
\(342\) 20.4853 1.10772
\(343\) 12.0000 12.0000i 0.647939 0.647939i
\(344\) −3.75736 −0.202583
\(345\) 3.51472 1.17157i 0.189226 0.0630754i
\(346\) −17.6569 + 17.6569i −0.949238 + 0.949238i
\(347\) 15.7071 + 15.7071i 0.843202 + 0.843202i 0.989274 0.146072i \(-0.0466632\pi\)
−0.146072 + 0.989274i \(0.546663\pi\)
\(348\) −0.414214 −0.0222042
\(349\) 10.9706i 0.587241i 0.955922 + 0.293620i \(0.0948602\pi\)
−0.955922 + 0.293620i \(0.905140\pi\)
\(350\) −7.00000 1.00000i −0.374166 0.0534522i
\(351\) 5.12132 5.12132i 0.273356 0.273356i
\(352\) 1.58579 1.58579i 0.0845227 0.0845227i
\(353\) 11.3137i 0.602168i −0.953598 0.301084i \(-0.902652\pi\)
0.953598 0.301084i \(-0.0973484\pi\)
\(354\) 3.77817 + 3.77817i 0.200808 + 0.200808i
\(355\) −10.4853 5.24264i −0.556501 0.278250i
\(356\) 11.4853 0.608719
\(357\) 1.24264 + 2.07107i 0.0657675 + 0.109613i
\(358\) 0.686292i 0.0362716i
\(359\) 7.07107i 0.373197i −0.982436 0.186598i \(-0.940254\pi\)
0.982436 0.186598i \(-0.0597463\pi\)
\(360\) 2.00000 + 6.00000i 0.105409 + 0.316228i
\(361\) −33.4558 −1.76083
\(362\) 14.0000 14.0000i 0.735824 0.735824i
\(363\) −1.74874 1.74874i −0.0917849 0.0917849i
\(364\) −3.00000 + 3.00000i −0.157243 + 0.157243i
\(365\) 11.8284 23.6569i 0.619128 1.23826i
\(366\) 3.58579i 0.187432i
\(367\) −18.2426 18.2426i −0.952258 0.952258i 0.0466531 0.998911i \(-0.485144\pi\)
−0.998911 + 0.0466531i \(0.985144\pi\)
\(368\) 2.82843 + 2.82843i 0.147442 + 0.147442i
\(369\) 12.4853 + 12.4853i 0.649958 + 0.649958i
\(370\) 7.41421 14.8284i 0.385447 0.770893i
\(371\) −3.00000 3.00000i −0.155752 0.155752i
\(372\) 3.14214 0.162912
\(373\) 32.4853i 1.68202i −0.541016 0.841012i \(-0.681960\pi\)
0.541016 0.841012i \(-0.318040\pi\)
\(374\) −8.97056 2.24264i −0.463857 0.115964i
\(375\) −0.828427 4.55635i −0.0427798 0.235289i
\(376\) 1.58579i 0.0817807i
\(377\) −2.12132 + 2.12132i −0.109254 + 0.109254i
\(378\) 3.41421i 0.175608i
\(379\) 0.485281 + 0.485281i 0.0249272 + 0.0249272i 0.719461 0.694533i \(-0.244389\pi\)
−0.694533 + 0.719461i \(0.744389\pi\)
\(380\) −5.12132 15.3640i −0.262718 0.788155i
\(381\) −5.19239 + 5.19239i −0.266014 + 0.266014i
\(382\) −21.2132 −1.08536
\(383\) −13.2426 −0.676667 −0.338334 0.941026i \(-0.609863\pi\)
−0.338334 + 0.941026i \(0.609863\pi\)
\(384\) 0.292893 0.292893i 0.0149466 0.0149466i
\(385\) 6.72792 2.24264i 0.342887 0.114296i
\(386\) −18.4853 18.4853i −0.940876 0.940876i
\(387\) 10.6274i 0.540222i
\(388\) 0.121320 0.121320i 0.00615911 0.00615911i
\(389\) 16.6274i 0.843044i 0.906818 + 0.421522i \(0.138504\pi\)
−0.906818 + 0.421522i \(0.861496\pi\)
\(390\) −2.48528 1.24264i −0.125847 0.0629236i
\(391\) 4.00000 16.0000i 0.202289 0.809155i
\(392\) 5.00000i 0.252538i
\(393\) −4.44365 −0.224153
\(394\) −3.34315 3.34315i −0.168425 0.168425i
\(395\) 0.343146 0.686292i 0.0172655 0.0345311i
\(396\) −4.48528 4.48528i −0.225394 0.225394i
\(397\) 4.72792 + 4.72792i 0.237288 + 0.237288i 0.815726 0.578438i \(-0.196338\pi\)
−0.578438 + 0.815726i \(0.696338\pi\)
\(398\) 7.12132 + 7.12132i 0.356960 + 0.356960i
\(399\) 4.24264i 0.212398i
\(400\) 4.00000 3.00000i 0.200000 0.150000i
\(401\) −2.10051 + 2.10051i −0.104894 + 0.104894i −0.757606 0.652712i \(-0.773631\pi\)
0.652712 + 0.757606i \(0.273631\pi\)
\(402\) 4.24264 + 4.24264i 0.211604 + 0.211604i
\(403\) 16.0919 16.0919i 0.801594 0.801594i
\(404\) 0 0
\(405\) 15.8787 5.29289i 0.789018 0.263006i
\(406\) 1.41421i 0.0701862i
\(407\) 16.6274i 0.824190i
\(408\) −1.65685 0.414214i −0.0820265 0.0205066i
\(409\) 25.4853 1.26017 0.630083 0.776528i \(-0.283021\pi\)
0.630083 + 0.776528i \(0.283021\pi\)
\(410\) 6.24264 12.4853i 0.308302 0.616604i
\(411\) 1.34315 + 1.34315i 0.0662525 + 0.0662525i
\(412\) 0 0
\(413\) −12.8995 + 12.8995i −0.634743 + 0.634743i
\(414\) 8.00000 8.00000i 0.393179 0.393179i
\(415\) −9.00000 + 3.00000i −0.441793 + 0.147264i
\(416\) 3.00000i 0.147087i
\(417\) 6.44365 0.315547
\(418\) 11.4853 + 11.4853i 0.561763 + 0.561763i
\(419\) −11.3137 + 11.3137i −0.552711 + 0.552711i −0.927222 0.374511i \(-0.877810\pi\)
0.374511 + 0.927222i \(0.377810\pi\)
\(420\) 1.24264 0.414214i 0.0606347 0.0202116i
\(421\) −19.2132 −0.936394 −0.468197 0.883624i \(-0.655096\pi\)
−0.468197 + 0.883624i \(0.655096\pi\)
\(422\) 8.00000 8.00000i 0.389434 0.389434i
\(423\) 4.48528 0.218082
\(424\) 3.00000 0.145693
\(425\) −19.0919 7.77817i −0.926092 0.377297i
\(426\) 2.17157 0.105213
\(427\) 12.2426 0.592463
\(428\) −2.82843 + 2.82843i −0.136717 + 0.136717i
\(429\) 2.78680 0.134548
\(430\) 7.97056 2.65685i 0.384375 0.128125i
\(431\) 17.6569 17.6569i 0.850501 0.850501i −0.139694 0.990195i \(-0.544612\pi\)
0.990195 + 0.139694i \(0.0446119\pi\)
\(432\) −1.70711 1.70711i −0.0821332 0.0821332i
\(433\) −5.75736 −0.276681 −0.138341 0.990385i \(-0.544177\pi\)
−0.138341 + 0.990385i \(0.544177\pi\)
\(434\) 10.7279i 0.514957i
\(435\) 0.878680 0.292893i 0.0421295 0.0140432i
\(436\) 8.60660 8.60660i 0.412181 0.412181i
\(437\) −20.4853 + 20.4853i −0.979944 + 0.979944i
\(438\) 4.89949i 0.234107i
\(439\) 20.9706 + 20.9706i 1.00087 + 1.00087i 1.00000 0.000870732i \(0.000277162\pi\)
0.000870732 1.00000i \(0.499723\pi\)
\(440\) −2.24264 + 4.48528i −0.106914 + 0.213827i
\(441\) 14.1421 0.673435
\(442\) −10.6066 + 6.36396i −0.504505 + 0.302703i
\(443\) 37.7990i 1.79588i −0.440114 0.897942i \(-0.645062\pi\)
0.440114 0.897942i \(-0.354938\pi\)
\(444\) 3.07107i 0.145746i
\(445\) −24.3640 + 8.12132i −1.15496 + 0.384988i
\(446\) 23.2426 1.10057
\(447\) 3.72792 3.72792i 0.176325 0.176325i
\(448\) 1.00000 + 1.00000i 0.0472456 + 0.0472456i
\(449\) −28.7990 + 28.7990i −1.35911 + 1.35911i −0.484090 + 0.875018i \(0.660849\pi\)
−0.875018 + 0.484090i \(0.839151\pi\)
\(450\) −8.48528 11.3137i −0.400000 0.533333i
\(451\) 14.0000i 0.659234i
\(452\) 2.46447 + 2.46447i 0.115919 + 0.115919i
\(453\) 3.51472 + 3.51472i 0.165136 + 0.165136i
\(454\) 4.05025 + 4.05025i 0.190088 + 0.190088i
\(455\) 4.24264 8.48528i 0.198898 0.397796i
\(456\) 2.12132 + 2.12132i 0.0993399 + 0.0993399i
\(457\) −2.24264 −0.104906 −0.0524532 0.998623i \(-0.516704\pi\)
−0.0524532 + 0.998623i \(0.516704\pi\)
\(458\) 7.75736i 0.362478i
\(459\) −2.41421 + 9.65685i −0.112686 + 0.450743i
\(460\) −8.00000 4.00000i −0.373002 0.186501i
\(461\) 40.2843i 1.87623i −0.346330 0.938113i \(-0.612572\pi\)
0.346330 0.938113i \(-0.387428\pi\)
\(462\) −0.928932 + 0.928932i −0.0432178 + 0.0432178i
\(463\) 25.2426i 1.17312i 0.809904 + 0.586562i \(0.199519\pi\)
−0.809904 + 0.586562i \(0.800481\pi\)
\(464\) 0.707107 + 0.707107i 0.0328266 + 0.0328266i
\(465\) −6.66548 + 2.22183i −0.309104 + 0.103035i
\(466\) 10.9497 10.9497i 0.507237 0.507237i
\(467\) −18.7279 −0.866625 −0.433312 0.901244i \(-0.642655\pi\)
−0.433312 + 0.901244i \(0.642655\pi\)
\(468\) −8.48528 −0.392232
\(469\) −14.4853 + 14.4853i −0.668868 + 0.668868i
\(470\) −1.12132 3.36396i −0.0517227 0.155168i
\(471\) 3.51472 + 3.51472i 0.161950 + 0.161950i
\(472\) 12.8995i 0.593747i
\(473\) −5.95837 + 5.95837i −0.273966 + 0.273966i
\(474\) 0.142136i 0.00652851i
\(475\) 21.7279 + 28.9706i 0.996945 + 1.32926i
\(476\) 1.41421 5.65685i 0.0648204 0.259281i
\(477\) 8.48528i 0.388514i
\(478\) −22.2426 −1.01735
\(479\) −10.0503 10.0503i −0.459208 0.459208i 0.439188 0.898395i \(-0.355266\pi\)
−0.898395 + 0.439188i \(0.855266\pi\)
\(480\) −0.414214 + 0.828427i −0.0189062 + 0.0378124i
\(481\) 15.7279 + 15.7279i 0.717132 + 0.717132i
\(482\) −2.75736 2.75736i −0.125594 0.125594i
\(483\) −1.65685 1.65685i −0.0753895 0.0753895i
\(484\) 5.97056i 0.271389i
\(485\) −0.171573 + 0.343146i −0.00779072 + 0.0155814i
\(486\) −7.31371 + 7.31371i −0.331757 + 0.331757i
\(487\) 11.2426 + 11.2426i 0.509453 + 0.509453i 0.914358 0.404906i \(-0.132696\pi\)
−0.404906 + 0.914358i \(0.632696\pi\)
\(488\) −6.12132 + 6.12132i −0.277099 + 0.277099i
\(489\) 2.62742 0.118816
\(490\) −3.53553 10.6066i −0.159719 0.479157i
\(491\) 6.89949i 0.311370i 0.987807 + 0.155685i \(0.0497585\pi\)
−0.987807 + 0.155685i \(0.950242\pi\)
\(492\) 2.58579i 0.116576i
\(493\) 1.00000 4.00000i 0.0450377 0.180151i
\(494\) 21.7279 0.977585
\(495\) 12.6863 + 6.34315i 0.570206 + 0.285103i
\(496\) −5.36396 5.36396i −0.240849 0.240849i
\(497\) 7.41421i 0.332573i
\(498\) 1.24264 1.24264i 0.0556841 0.0556841i
\(499\) −8.51472 + 8.51472i −0.381171 + 0.381171i −0.871524 0.490353i \(-0.836868\pi\)
0.490353 + 0.871524i \(0.336868\pi\)
\(500\) −6.36396 + 9.19239i −0.284605 + 0.411096i
\(501\) 0.627417i 0.0280309i
\(502\) −20.4853 −0.914303
\(503\) 13.0711 + 13.0711i 0.582810 + 0.582810i 0.935674 0.352864i \(-0.114792\pi\)
−0.352864 + 0.935674i \(0.614792\pi\)
\(504\) 2.82843 2.82843i 0.125988 0.125988i
\(505\) 0 0
\(506\) 8.97056 0.398790
\(507\) −1.17157 + 1.17157i −0.0520314 + 0.0520314i
\(508\) 17.7279 0.786549
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 3.80761 0.292893i 0.168604 0.0129695i
\(511\) −16.7279 −0.740000
\(512\) −1.00000 −0.0441942
\(513\) 12.3640 12.3640i 0.545882 0.545882i
\(514\) −6.72792 −0.296756
\(515\) 0 0
\(516\) −1.10051 + 1.10051i −0.0484470 + 0.0484470i
\(517\) 2.51472 + 2.51472i 0.110597 + 0.110597i
\(518\) −10.4853 −0.460697
\(519\) 10.3431i 0.454014i
\(520\) 2.12132 + 6.36396i 0.0930261 + 0.279078i
\(521\) −11.3137 + 11.3137i −0.495663 + 0.495663i −0.910085 0.414422i \(-0.863984\pi\)
0.414422 + 0.910085i \(0.363984\pi\)
\(522\) 2.00000 2.00000i 0.0875376 0.0875376i
\(523\) 26.4853i 1.15812i 0.815285 + 0.579060i \(0.196580\pi\)
−0.815285 + 0.579060i \(0.803420\pi\)
\(524\) 7.58579 + 7.58579i 0.331387 + 0.331387i
\(525\) −2.34315 + 1.75736i −0.102263 + 0.0766974i
\(526\) −4.75736 −0.207431
\(527\) −7.58579 + 30.3431i −0.330442 + 1.32177i
\(528\) 0.928932i 0.0404266i
\(529\) 7.00000i 0.304348i
\(530\) −6.36396 + 2.12132i −0.276433 + 0.0921443i
\(531\) −36.4853 −1.58333
\(532\) −7.24264 + 7.24264i −0.314008 + 0.314008i
\(533\) 13.2426 + 13.2426i 0.573602 + 0.573602i
\(534\) 3.36396 3.36396i 0.145573 0.145573i
\(535\) 4.00000 8.00000i 0.172935 0.345870i
\(536\) 14.4853i 0.625669i
\(537\) −0.201010 0.201010i −0.00867423 0.00867423i
\(538\) 11.2929 + 11.2929i 0.486871 + 0.486871i
\(539\) 7.92893 + 7.92893i 0.341523 + 0.341523i
\(540\) 4.82843 + 2.41421i 0.207782 + 0.103891i
\(541\) 20.9706 + 20.9706i 0.901595 + 0.901595i 0.995574 0.0939792i \(-0.0299587\pi\)
−0.0939792 + 0.995574i \(0.529959\pi\)
\(542\) 6.48528 0.278567
\(543\) 8.20101i 0.351939i
\(544\) 2.12132 + 3.53553i 0.0909509 + 0.151585i
\(545\) −12.1716 + 24.3431i −0.521373 + 1.04275i
\(546\) 1.75736i 0.0752080i
\(547\) 2.39340 2.39340i 0.102334 0.102334i −0.654086 0.756420i \(-0.726947\pi\)
0.756420 + 0.654086i \(0.226947\pi\)
\(548\) 4.58579i 0.195895i
\(549\) 17.3137 + 17.3137i 0.738931 + 0.738931i
\(550\) 1.58579 11.1005i 0.0676182 0.473327i
\(551\) −5.12132 + 5.12132i −0.218176 + 0.218176i
\(552\) 1.65685 0.0705204
\(553\) −0.485281 −0.0206363
\(554\) −8.24264 + 8.24264i −0.350196 + 0.350196i
\(555\) −2.17157 6.51472i −0.0921781 0.276534i
\(556\) −11.0000 11.0000i −0.466504 0.466504i
\(557\) 34.7990i 1.47448i −0.675631 0.737240i \(-0.736129\pi\)
0.675631 0.737240i \(-0.263871\pi\)
\(558\) −15.1716 + 15.1716i −0.642264 + 0.642264i
\(559\) 11.2721i 0.476758i
\(560\) −2.82843 1.41421i −0.119523 0.0597614i
\(561\) −3.28427 + 1.97056i −0.138662 + 0.0831972i
\(562\) 3.34315i 0.141022i
\(563\) −45.9411 −1.93619 −0.968094 0.250588i \(-0.919376\pi\)
−0.968094 + 0.250588i \(0.919376\pi\)
\(564\) 0.464466 + 0.464466i 0.0195576 + 0.0195576i
\(565\) −6.97056 3.48528i −0.293254 0.146627i
\(566\) 19.1213 + 19.1213i 0.803729 + 0.803729i
\(567\) −7.48528 7.48528i −0.314352 0.314352i
\(568\) −3.70711 3.70711i −0.155547 0.155547i
\(569\) 20.3137i 0.851595i −0.904818 0.425797i \(-0.859994\pi\)
0.904818 0.425797i \(-0.140006\pi\)
\(570\) −6.00000 3.00000i −0.251312 0.125656i
\(571\) −20.2132 + 20.2132i −0.845896 + 0.845896i −0.989618 0.143722i \(-0.954093\pi\)
0.143722 + 0.989618i \(0.454093\pi\)
\(572\) −4.75736 4.75736i −0.198915 0.198915i
\(573\) −6.21320 + 6.21320i −0.259560 + 0.259560i
\(574\) −8.82843 −0.368491
\(575\) 19.7990 + 2.82843i 0.825675 + 0.117954i
\(576\) 2.82843i 0.117851i
\(577\) 4.97056i 0.206927i −0.994633 0.103464i \(-0.967007\pi\)
0.994633 0.103464i \(-0.0329925\pi\)
\(578\) 8.00000 15.0000i 0.332756 0.623918i
\(579\) −10.8284 −0.450014
\(580\) −2.00000 1.00000i −0.0830455 0.0415227i
\(581\) 4.24264 + 4.24264i 0.176014 + 0.176014i
\(582\) 0.0710678i 0.00294586i
\(583\) 4.75736 4.75736i 0.197030 0.197030i
\(584\) 8.36396 8.36396i 0.346103 0.346103i
\(585\) 18.0000 6.00000i 0.744208 0.248069i
\(586\) 20.6569i 0.853327i
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 1.46447 + 1.46447i 0.0603936 + 0.0603936i
\(589\) 38.8492 38.8492i 1.60076 1.60076i
\(590\) 9.12132 + 27.3640i 0.375519 + 1.12656i
\(591\) −1.95837 −0.0805566
\(592\) 5.24264 5.24264i 0.215471 0.215471i
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) −5.41421 −0.222148
\(595\) 1.00000 + 13.0000i 0.0409960 + 0.532948i
\(596\) −12.7279 −0.521356
\(597\) 4.17157 0.170731
\(598\) 8.48528 8.48528i 0.346989 0.346989i
\(599\) −12.0000 −0.490307 −0.245153 0.969484i \(-0.578838\pi\)
−0.245153 + 0.969484i \(0.578838\pi\)
\(600\) 0.292893 2.05025i 0.0119573 0.0837012i
\(601\) 28.7279 28.7279i 1.17184 1.17184i 0.190065 0.981772i \(-0.439130\pi\)
0.981772 0.190065i \(-0.0608698\pi\)
\(602\) −3.75736 3.75736i −0.153139 0.153139i
\(603\) −40.9706 −1.66845
\(604\) 12.0000i 0.488273i
\(605\) −4.22183 12.6655i −0.171642 0.514925i
\(606\) 0 0
\(607\) 26.4558 26.4558i 1.07381 1.07381i 0.0767600 0.997050i \(-0.475542\pi\)
0.997050 0.0767600i \(-0.0244575\pi\)
\(608\) 7.24264i 0.293728i
\(609\) −0.414214 0.414214i −0.0167848 0.0167848i
\(610\) 8.65685 17.3137i 0.350506 0.701012i
\(611\) 4.75736 0.192462
\(612\) 10.0000 6.00000i 0.404226 0.242536i
\(613\) 4.02944i 0.162747i −0.996684 0.0813737i \(-0.974069\pi\)
0.996684 0.0813737i \(-0.0259307\pi\)
\(614\) 33.2132i 1.34038i
\(615\) −1.82843 5.48528i −0.0737293 0.221188i
\(616\) 3.17157 0.127786
\(617\) −19.4350 + 19.4350i −0.782425 + 0.782425i −0.980239 0.197815i \(-0.936616\pi\)
0.197815 + 0.980239i \(0.436616\pi\)
\(618\) 0 0
\(619\) 5.75736 5.75736i 0.231408 0.231408i −0.581872 0.813280i \(-0.697680\pi\)
0.813280 + 0.581872i \(0.197680\pi\)
\(620\) 15.1716 + 7.58579i 0.609305 + 0.304653i
\(621\) 9.65685i 0.387516i
\(622\) 1.41421 + 1.41421i 0.0567048 + 0.0567048i
\(623\) 11.4853 + 11.4853i 0.460148 + 0.460148i
\(624\) −0.878680 0.878680i −0.0351753 0.0351753i
\(625\) 7.00000 24.0000i 0.280000 0.960000i
\(626\) 22.4853 + 22.4853i 0.898693 + 0.898693i
\(627\) 6.72792 0.268687
\(628\) 12.0000i 0.478852i
\(629\) −29.6569 7.41421i −1.18250 0.295624i
\(630\) −4.00000 + 8.00000i −0.159364 + 0.318728i
\(631\) 2.48528i 0.0989375i −0.998776 0.0494687i \(-0.984247\pi\)
0.998776 0.0494687i \(-0.0157528\pi\)
\(632\) 0.242641 0.242641i 0.00965173 0.00965173i
\(633\) 4.68629i 0.186263i
\(634\) 14.1421 + 14.1421i 0.561656 + 0.561656i
\(635\) −37.6066 + 12.5355i −1.49237 + 0.497457i
\(636\) 0.878680 0.878680i 0.0348419 0.0348419i
\(637\) 15.0000 0.594322
\(638\) 2.24264 0.0887870
\(639\) −10.4853 + 10.4853i −0.414791 + 0.414791i
\(640\) 2.12132 0.707107i 0.0838525 0.0279508i
\(641\) 3.55635 + 3.55635i 0.140467 + 0.140467i 0.773844 0.633376i \(-0.218332\pi\)
−0.633376 + 0.773844i \(0.718332\pi\)
\(642\) 1.65685i 0.0653908i
\(643\) −3.75736 + 3.75736i −0.148176 + 0.148176i −0.777303 0.629127i \(-0.783413\pi\)
0.629127 + 0.777303i \(0.283413\pi\)
\(644\) 5.65685i 0.222911i
\(645\) 1.55635 3.11270i 0.0612812 0.122562i
\(646\) −25.6066 + 15.3640i −1.00748 + 0.604487i
\(647\) 47.5269i 1.86848i −0.356651 0.934238i \(-0.616081\pi\)
0.356651 0.934238i \(-0.383919\pi\)
\(648\) 7.48528 0.294050
\(649\) −20.4558 20.4558i −0.802962 0.802962i
\(650\) −9.00000 12.0000i −0.353009 0.470679i
\(651\) 3.14214 + 3.14214i 0.123150 + 0.123150i
\(652\) −4.48528 4.48528i −0.175657 0.175657i
\(653\) 4.79899 + 4.79899i 0.187799 + 0.187799i 0.794744 0.606945i \(-0.207605\pi\)
−0.606945 + 0.794744i \(0.707605\pi\)
\(654\) 5.04163i 0.197143i
\(655\) −21.4558 10.7279i −0.838349 0.419175i
\(656\) 4.41421 4.41421i 0.172346 0.172346i
\(657\) −23.6569 23.6569i −0.922942 0.922942i
\(658\) −1.58579 + 1.58579i −0.0618204 + 0.0618204i
\(659\) 30.2132 1.17694 0.588470 0.808519i \(-0.299731\pi\)
0.588470 + 0.808519i \(0.299731\pi\)
\(660\) 0.656854 + 1.97056i 0.0255680 + 0.0767041i
\(661\) 12.0000i 0.466746i −0.972387 0.233373i \(-0.925024\pi\)
0.972387 0.233373i \(-0.0749763\pi\)
\(662\) 15.7279i 0.611283i
\(663\) −1.24264 + 4.97056i −0.0482602 + 0.193041i
\(664\) −4.24264 −0.164646
\(665\) 10.2426 20.4853i 0.397193 0.794385i
\(666\) −14.8284 14.8284i −0.574590 0.574590i
\(667\) 4.00000i 0.154881i
\(668\) −1.07107 + 1.07107i −0.0414409 + 0.0414409i
\(669\) 6.80761 6.80761i 0.263197 0.263197i
\(670\) 10.2426 + 30.7279i 0.395708 + 1.18712i
\(671\) 19.4142i 0.749477i
\(672\) 0.585786 0.0225972
\(673\) 25.8787 + 25.8787i 0.997550 + 0.997550i 0.999997 0.00244721i \(-0.000778973\pi\)
−0.00244721 + 0.999997i \(0.500779\pi\)
\(674\) −12.8492 + 12.8492i −0.494934 + 0.494934i
\(675\) −11.9497 1.70711i −0.459946 0.0657066i
\(676\) 4.00000 0.153846
\(677\) 22.4142 22.4142i 0.861448 0.861448i −0.130058 0.991506i \(-0.541516\pi\)
0.991506 + 0.130058i \(0.0415164\pi\)
\(678\) 1.44365 0.0554431
\(679\) 0.242641 0.00931169
\(680\) −7.00000 6.00000i −0.268438 0.230089i
\(681\) 2.37258 0.0909176
\(682\) −17.0122 −0.651431
\(683\) 24.5355 24.5355i 0.938826 0.938826i −0.0594077 0.998234i \(-0.518921\pi\)
0.998234 + 0.0594077i \(0.0189212\pi\)
\(684\) −20.4853 −0.783274
\(685\) 3.24264 + 9.72792i 0.123895 + 0.371685i
\(686\) −12.0000 + 12.0000i −0.458162 + 0.458162i
\(687\) −2.27208 2.27208i −0.0866852 0.0866852i
\(688\) 3.75736 0.143248
\(689\) 9.00000i 0.342873i
\(690\) −3.51472 + 1.17157i −0.133803 + 0.0446010i
\(691\) 9.48528 9.48528i 0.360837 0.360837i −0.503284 0.864121i \(-0.667875\pi\)
0.864121 + 0.503284i \(0.167875\pi\)
\(692\) 17.6569 17.6569i 0.671213 0.671213i
\(693\) 8.97056i 0.340764i
\(694\) −15.7071 15.7071i −0.596234 0.596234i
\(695\) 31.1127 + 15.5563i 1.18017 + 0.590086i
\(696\) 0.414214 0.0157007
\(697\) −24.9706 6.24264i −0.945828 0.236457i
\(698\) 10.9706i 0.415242i
\(699\) 6.41421i 0.242608i
\(700\) 7.00000 + 1.00000i 0.264575 + 0.0377964i
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) −5.12132 + 5.12132i −0.193292 + 0.193292i
\(703\) 37.9706 + 37.9706i 1.43209 + 1.43209i
\(704\) −1.58579 + 1.58579i −0.0597666 + 0.0597666i
\(705\) −1.31371 0.656854i −0.0494771 0.0247386i
\(706\) 11.3137i 0.425797i
\(707\) 0 0
\(708\) −3.77817 3.77817i −0.141992 0.141992i
\(709\) 2.60660 + 2.60660i 0.0978930 + 0.0978930i 0.754357 0.656464i \(-0.227949\pi\)
−0.656464 + 0.754357i \(0.727949\pi\)
\(710\) 10.4853 + 5.24264i 0.393506 + 0.196753i
\(711\) −0.686292 0.686292i −0.0257379 0.0257379i
\(712\) −11.4853 −0.430429
\(713\) 30.3431i 1.13636i
\(714\) −1.24264 2.07107i −0.0465047 0.0775078i
\(715\) 13.4558 + 6.72792i 0.503220 + 0.251610i
\(716\) 0.686292i 0.0256479i
\(717\) −6.51472 + 6.51472i −0.243297 + 0.243297i
\(718\) 7.07107i 0.263890i
\(719\) −27.7487 27.7487i −1.03485 1.03485i −0.999370 0.0354830i \(-0.988703\pi\)
−0.0354830 0.999370i \(-0.511297\pi\)
\(720\) −2.00000 6.00000i −0.0745356 0.223607i
\(721\) 0 0
\(722\) 33.4558 1.24510
\(723\) −1.61522 −0.0600708
\(724\) −14.0000 + 14.0000i −0.520306 + 0.520306i
\(725\) 4.94975 + 0.707107i 0.183829 + 0.0262613i
\(726\) 1.74874 + 1.74874i 0.0649017 + 0.0649017i
\(727\) 16.7574i 0.621496i 0.950492 + 0.310748i \(0.100580\pi\)
−0.950492 + 0.310748i \(0.899420\pi\)
\(728\) 3.00000 3.00000i 0.111187 0.111187i
\(729\) 18.1716i 0.673021i
\(730\) −11.8284 + 23.6569i −0.437790 + 0.875579i
\(731\) −7.97056 13.2843i −0.294802 0.491337i
\(732\) 3.58579i 0.132534i
\(733\) −32.9706 −1.21780 −0.608898 0.793249i \(-0.708388\pi\)
−0.608898 + 0.793249i \(0.708388\pi\)
\(734\) 18.2426 + 18.2426i 0.673348 + 0.673348i
\(735\) −4.14214 2.07107i −0.152785 0.0763925i
\(736\) −2.82843 2.82843i −0.104257 0.104257i
\(737\) −22.9706 22.9706i −0.846132 0.846132i
\(738\) −12.4853 12.4853i −0.459590 0.459590i
\(739\) 35.1838i 1.29426i −0.762381 0.647128i \(-0.775970\pi\)
0.762381 0.647128i \(-0.224030\pi\)
\(740\) −7.41421 + 14.8284i −0.272552 + 0.545104i
\(741\) 6.36396 6.36396i 0.233786 0.233786i
\(742\) 3.00000 + 3.00000i 0.110133 + 0.110133i
\(743\) −17.8284 + 17.8284i −0.654062 + 0.654062i −0.953968 0.299907i \(-0.903044\pi\)
0.299907 + 0.953968i \(0.403044\pi\)
\(744\) −3.14214 −0.115196
\(745\) 27.0000 9.00000i 0.989203 0.329734i
\(746\) 32.4853i 1.18937i
\(747\) 12.0000i 0.439057i
\(748\) 8.97056 + 2.24264i 0.327996 + 0.0819991i
\(749\) −5.65685 −0.206697
\(750\) 0.828427 + 4.55635i 0.0302499 + 0.166374i
\(751\) 19.3640 + 19.3640i 0.706601 + 0.706601i 0.965819 0.259218i \(-0.0834648\pi\)
−0.259218 + 0.965819i \(0.583465\pi\)
\(752\) 1.58579i 0.0578277i
\(753\) −6.00000 + 6.00000i −0.218652 + 0.218652i
\(754\) 2.12132 2.12132i 0.0772539 0.0772539i
\(755\) 8.48528 + 25.4558i 0.308811 + 0.926433i
\(756\) 3.41421i 0.124174i
\(757\) 32.9411 1.19727 0.598633 0.801024i \(-0.295711\pi\)
0.598633 + 0.801024i \(0.295711\pi\)
\(758\) −0.485281 0.485281i −0.0176262 0.0176262i
\(759\) 2.62742 2.62742i 0.0953692 0.0953692i
\(760\) 5.12132 + 15.3640i 0.185770 + 0.557309i
\(761\) 20.4853 0.742591 0.371295 0.928515i \(-0.378914\pi\)
0.371295 + 0.928515i \(0.378914\pi\)
\(762\) 5.19239 5.19239i 0.188100 0.188100i
\(763\) 17.2132 0.623160
\(764\) 21.2132 0.767467
\(765\) −16.9706 + 19.7990i −0.613572 + 0.715834i
\(766\) 13.2426 0.478476
\(767\) −38.6985 −1.39732
\(768\) −0.292893 + 0.292893i −0.0105689 + 0.0105689i
\(769\) −14.4558 −0.521291 −0.260646 0.965435i \(-0.583935\pi\)
−0.260646 + 0.965435i \(0.583935\pi\)
\(770\) −6.72792 + 2.24264i −0.242457 + 0.0808192i
\(771\) −1.97056 + 1.97056i −0.0709681 + 0.0709681i
\(772\) 18.4853 + 18.4853i 0.665300 + 0.665300i
\(773\) −32.4853 −1.16841 −0.584207 0.811605i \(-0.698594\pi\)
−0.584207 + 0.811605i \(0.698594\pi\)
\(774\) 10.6274i 0.381995i
\(775\) −37.5477 5.36396i −1.34875 0.192679i
\(776\) −0.121320 + 0.121320i −0.00435515 + 0.00435515i
\(777\) −3.07107 + 3.07107i −0.110174 + 0.110174i
\(778\) 16.6274i 0.596122i
\(779\) 31.9706 + 31.9706i 1.14546 + 1.14546i
\(780\) 2.48528 + 1.24264i 0.0889873 + 0.0444937i
\(781\) −11.7574 −0.420711
\(782\) −4.00000 + 16.0000i −0.143040 + 0.572159i
\(783\) 2.41421i 0.0862770i
\(784\) 5.00000i 0.178571i
\(785\) 8.48528 + 25.4558i 0.302853 + 0.908558i
\(786\) 4.44365 0.158500
\(787\) 1.36396 1.36396i 0.0486200 0.0486200i −0.682379 0.730999i \(-0.739055\pi\)
0.730999 + 0.682379i \(0.239055\pi\)
\(788\) 3.34315 + 3.34315i 0.119095 + 0.119095i
\(789\) −1.39340 + 1.39340i −0.0496063 + 0.0496063i
\(790\) −0.343146 + 0.686292i −0.0122086 + 0.0244172i
\(791\) 4.92893i 0.175253i
\(792\) 4.48528 + 4.48528i 0.159378 + 0.159378i
\(793\) 18.3640 + 18.3640i 0.652123 + 0.652123i
\(794\) −4.72792 4.72792i −0.167788 0.167788i
\(795\) −1.24264 + 2.48528i −0.0440719 + 0.0881438i
\(796\) −7.12132 7.12132i −0.252409 0.252409i
\(797\) −28.9706 −1.02619 −0.513095 0.858332i \(-0.671501\pi\)
−0.513095 + 0.858332i \(0.671501\pi\)
\(798\) 4.24264i 0.150188i
\(799\) −5.60660 + 3.36396i −0.198347 + 0.119008i
\(800\) −4.00000 + 3.00000i −0.141421 + 0.106066i
\(801\) 32.4853i 1.14781i
\(802\) 2.10051 2.10051i 0.0741714 0.0741714i
\(803\) 26.5269i 0.936114i
\(804\) −4.24264 4.24264i −0.149626 0.149626i
\(805\) −4.00000 12.0000i −0.140981 0.422944i
\(806\) −16.0919 + 16.0919i −0.566812 + 0.566812i
\(807\) 6.61522 0.232867
\(808\) 0 0
\(809\) 35.1421 35.1421i 1.23553 1.23553i 0.273723 0.961809i \(-0.411745\pi\)
0.961809 0.273723i \(-0.0882552\pi\)
\(810\) −15.8787 + 5.29289i −0.557920 + 0.185973i
\(811\) 9.48528 + 9.48528i 0.333073 + 0.333073i 0.853752 0.520679i \(-0.174321\pi\)
−0.520679 + 0.853752i \(0.674321\pi\)
\(812\) 1.41421i 0.0496292i
\(813\) 1.89949 1.89949i 0.0666182 0.0666182i
\(814\) 16.6274i 0.582791i
\(815\) 12.6863 + 6.34315i 0.444381 + 0.222191i
\(816\) 1.65685 + 0.414214i 0.0580015 + 0.0145004i
\(817\) 27.2132i 0.952069i
\(818\) −25.4853 −0.891072
\(819\) −8.48528 8.48528i −0.296500 0.296500i
\(820\) −6.24264 + 12.4853i −0.218002 + 0.436005i
\(821\) −18.0208 18.0208i −0.628931 0.628931i 0.318868 0.947799i \(-0.396697\pi\)
−0.947799 + 0.318868i \(0.896697\pi\)
\(822\) −1.34315 1.34315i −0.0468476 0.0468476i
\(823\) 10.7279 + 10.7279i 0.373952 + 0.373952i 0.868914 0.494962i \(-0.164818\pi\)
−0.494962 + 0.868914i \(0.664818\pi\)
\(824\) 0 0
\(825\) −2.78680 3.71573i −0.0970238 0.129365i
\(826\) 12.8995 12.8995i 0.448831 0.448831i
\(827\) 5.31371 + 5.31371i 0.184776 + 0.184776i 0.793433 0.608657i \(-0.208292\pi\)
−0.608657 + 0.793433i \(0.708292\pi\)
\(828\) −8.00000 + 8.00000i −0.278019 + 0.278019i
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) 9.00000 3.00000i 0.312395 0.104132i
\(831\) 4.82843i 0.167496i
\(832\) 3.00000i 0.104006i
\(833\) −17.6777 + 10.6066i −0.612495 + 0.367497i
\(834\) −6.44365 −0.223125
\(835\) 1.51472 3.02944i 0.0524190 0.104838i
\(836\) −11.4853 11.4853i −0.397227 0.397227i
\(837\) 18.3137i 0.633014i
\(838\) 11.3137 11.3137i 0.390826 0.390826i
\(839\) −2.97918 + 2.97918i −0.102853 + 0.102853i −0.756661 0.653808i \(-0.773170\pi\)
0.653808 + 0.756661i \(0.273170\pi\)
\(840\) −1.24264 + 0.414214i −0.0428752 + 0.0142917i
\(841\) 28.0000i 0.965517i
\(842\) 19.2132 0.662131
\(843\) 0.979185 + 0.979185i 0.0337249 + 0.0337249i
\(844\) −8.00000 + 8.00000i −0.275371 + 0.275371i
\(845\) −8.48528 + 2.82843i −0.291903 + 0.0973009i
\(846\) −4.48528 −0.154207
\(847\) −5.97056 + 5.97056i −0.205151 + 0.205151i
\(848\) −3.00000 −0.103020
\(849\) 11.2010 0.384418
\(850\) 19.0919 + 7.77817i 0.654846 + 0.266789i
\(851\) 29.6569 1.01662
\(852\) −2.17157 −0.0743969
\(853\) −8.51472 + 8.51472i −0.291538 + 0.291538i −0.837688 0.546149i \(-0.816093\pi\)
0.546149 + 0.837688i \(0.316093\pi\)
\(854\) −12.2426 −0.418935
\(855\) 43.4558 14.4853i 1.48616 0.495386i
\(856\) 2.82843 2.82843i 0.0966736 0.0966736i
\(857\) 25.4350 + 25.4350i 0.868844 + 0.868844i 0.992345 0.123500i \(-0.0394120\pi\)
−0.123500 + 0.992345i \(0.539412\pi\)
\(858\) −2.78680 −0.0951397
\(859\) 45.7279i 1.56022i −0.625645 0.780108i \(-0.715164\pi\)
0.625645 0.780108i \(-0.284836\pi\)
\(860\) −7.97056 + 2.65685i −0.271794 + 0.0905980i
\(861\) −2.58579 + 2.58579i −0.0881234 + 0.0881234i
\(862\) −17.6569 + 17.6569i −0.601395 + 0.601395i
\(863\) 55.1127i 1.87606i 0.346557 + 0.938029i \(0.387351\pi\)
−0.346557 + 0.938029i \(0.612649\pi\)
\(864\) 1.70711 + 1.70711i 0.0580770 + 0.0580770i
\(865\) −24.9706 + 49.9411i −0.849025 + 1.69805i
\(866\) 5.75736 0.195643
\(867\) −2.05025 6.73654i −0.0696302 0.228785i
\(868\) 10.7279i 0.364129i
\(869\) 0.769553i 0.0261053i
\(870\) −0.878680 + 0.292893i −0.0297900 + 0.00993001i
\(871\) −43.4558 −1.47245
\(872\) −8.60660 + 8.60660i −0.291456 + 0.291456i
\(873\) 0.343146 + 0.343146i 0.0116137 + 0.0116137i
\(874\) 20.4853 20.4853i 0.692925 0.692925i
\(875\) −15.5563 + 2.82843i −0.525901 + 0.0956183i
\(876\) 4.89949i 0.165539i
\(877\) −8.51472 8.51472i −0.287522 0.287522i 0.548578 0.836099i \(-0.315169\pi\)
−0.836099 + 0.548578i \(0.815169\pi\)
\(878\) −20.9706 20.9706i −0.707722 0.707722i
\(879\) −6.05025 6.05025i −0.204070 0.204070i
\(880\) 2.24264 4.48528i 0.0755994 0.151199i
\(881\) −8.44365 8.44365i −0.284474 0.284474i 0.550416 0.834890i \(-0.314469\pi\)
−0.834890 + 0.550416i \(0.814469\pi\)
\(882\) −14.1421 −0.476190
\(883\) 18.7279i 0.630245i −0.949051 0.315122i \(-0.897954\pi\)
0.949051 0.315122i \(-0.102046\pi\)
\(884\) 10.6066 6.36396i 0.356739 0.214043i
\(885\) 10.6863 + 5.34315i 0.359216 + 0.179608i
\(886\) 37.7990i 1.26988i
\(887\) −19.5858 + 19.5858i −0.657626 + 0.657626i −0.954818 0.297192i \(-0.903950\pi\)
0.297192 + 0.954818i \(0.403950\pi\)
\(888\) 3.07107i 0.103058i
\(889\) 17.7279 + 17.7279i 0.594575 + 0.594575i
\(890\) 24.3640 8.12132i 0.816682 0.272227i
\(891\) 11.8701 11.8701i 0.397662 0.397662i
\(892\) −23.2426 −0.778221
\(893\) 11.4853 0.384340
\(894\) −3.72792 + 3.72792i −0.124680 + 0.124680i
\(895\) −0.485281 1.45584i −0.0162212 0.0486635i
\(896\) −1.00000 1.00000i −0.0334077 0.0334077i
\(897\) 4.97056i 0.165962i
\(898\) 28.7990 28.7990i 0.961035 0.961035i
\(899\) 7.58579i 0.253000i
\(900\) 8.48528 + 11.3137i 0.282843 + 0.377124i
\(901\) 6.36396 + 10.6066i 0.212014 + 0.353357i
\(902\) 14.0000i 0.466149i
\(903\) −2.20101 −0.0732450
\(904\) −2.46447 2.46447i −0.0819669 0.0819669i
\(905\) 19.7990 39.5980i 0.658141 1.31628i
\(906\) −3.51472 3.51472i −0.116769 0.116769i
\(907\) −7.84924 7.84924i −0.260630 0.260630i 0.564680 0.825310i \(-0.309000\pi\)
−0.825310 + 0.564680i \(0.809000\pi\)
\(908\) −4.05025 4.05025i −0.134412 0.134412i
\(909\) 0 0
\(910\) −4.24264 + 8.48528i −0.140642 + 0.281284i
\(911\) −35.3137 + 35.3137i −1.17000 + 1.17000i −0.187785 + 0.982210i \(0.560131\pi\)
−0.982210 + 0.187785i \(0.939869\pi\)
\(912\) −2.12132 2.12132i −0.0702439 0.0702439i
\(913\) −6.72792 + 6.72792i −0.222662 + 0.222662i
\(914\) 2.24264 0.0741800
\(915\) −2.53553 7.60660i −0.0838222 0.251466i
\(916\) 7.75736i 0.256310i
\(917\) 15.1716i 0.501009i
\(918\) 2.41421 9.65685i 0.0796809 0.318724i
\(919\) −31.2132 −1.02963 −0.514814 0.857302i \(-0.672139\pi\)
−0.514814 + 0.857302i \(0.672139\pi\)
\(920\) 8.00000 + 4.00000i 0.263752 + 0.131876i
\(921\) −9.72792 9.72792i −0.320546 0.320546i
\(922\) 40.2843i 1.32669i
\(923\) −11.1213 + 11.1213i −0.366063 + 0.366063i
\(924\) 0.928932 0.928932i 0.0305596 0.0305596i
\(925\) 5.24264 36.6985i 0.172377 1.20664i
\(926\) 25.2426i 0.829525i
\(927\) 0 0
\(928\) −0.707107 0.707107i −0.0232119 0.0232119i
\(929\) −15.3431 + 15.3431i −0.503392 + 0.503392i −0.912490 0.409098i \(-0.865843\pi\)
0.409098 + 0.912490i \(0.365843\pi\)
\(930\) 6.66548 2.22183i 0.218570 0.0728565i
\(931\) 36.2132 1.18684
\(932\) −10.9497 + 10.9497i −0.358671 + 0.358671i
\(933\) 0.828427 0.0271215
\(934\) 18.7279 0.612796
\(935\) −20.6152 + 1.58579i −0.674190 + 0.0518608i
\(936\) 8.48528 0.277350
\(937\) 47.2132 1.54239 0.771194 0.636600i \(-0.219660\pi\)
0.771194 + 0.636600i \(0.219660\pi\)
\(938\) 14.4853 14.4853i 0.472961 0.472961i
\(939\) 13.1716 0.429838
\(940\) 1.12132 + 3.36396i 0.0365734 + 0.109720i
\(941\) 14.8076 14.8076i 0.482714 0.482714i −0.423283 0.905997i \(-0.639122\pi\)
0.905997 + 0.423283i \(0.139122\pi\)
\(942\) −3.51472 3.51472i −0.114516 0.114516i
\(943\) 24.9706 0.813153
\(944\) 12.8995i 0.419843i
\(945\) 2.41421 + 7.24264i 0.0785344 + 0.235603i
\(946\) 5.95837 5.95837i 0.193723 0.193723i
\(947\) 26.2929 26.2929i 0.854404 0.854404i −0.136268 0.990672i \(-0.543511\pi\)
0.990672 + 0.136268i \(0.0435108\pi\)
\(948\) 0.142136i 0.00461635i
\(949\) −25.0919 25.0919i −0.814517 0.814517i
\(950\) −21.7279 28.9706i −0.704947 0.939929i
\(951\) 8.28427 0.268636
\(952\) −1.41421 + 5.65685i −0.0458349 + 0.183340i
\(953\) 4.58579i 0.148548i −0.997238 0.0742741i \(-0.976336\pi\)
0.997238 0.0742741i \(-0.0236640\pi\)
\(954\) 8.48528i 0.274721i
\(955\) −45.0000 + 15.0000i −1.45617 + 0.485389i
\(956\) 22.2426 0.719378
\(957\) 0.656854 0.656854i 0.0212331 0.0212331i
\(958\) 10.0503 + 10.0503i 0.324709 + 0.324709i
\(959\) 4.58579 4.58579i 0.148083 0.148083i
\(960\) 0.414214 0.828427i 0.0133687 0.0267374i
\(961\) 26.5442i 0.856263i
\(962\) −15.7279 15.7279i −0.507089 0.507089i
\(963\) −8.00000 8.00000i −0.257796 0.257796i
\(964\) 2.75736 + 2.75736i 0.0888086 + 0.0888086i
\(965\) −52.2843 26.1421i −1.68309 0.841545i
\(966\) 1.65685 + 1.65685i 0.0533084 + 0.0533084i
\(967\) 30.9706 0.995946 0.497973 0.867192i \(-0.334078\pi\)
0.497973 + 0.867192i \(0.334078\pi\)
\(968\) 5.97056i 0.191901i
\(969\) −3.00000 + 12.0000i −0.0963739 + 0.385496i
\(970\) 0.171573 0.343146i 0.00550887 0.0110177i
\(971\) 30.5563i 0.980600i −0.871554 0.490300i \(-0.836887\pi\)
0.871554 0.490300i \(-0.163113\pi\)
\(972\) 7.31371 7.31371i 0.234587 0.234587i
\(973\) 22.0000i 0.705288i
\(974\) −11.2426 11.2426i −0.360237 0.360237i
\(975\) −6.15076 0.878680i −0.196982 0.0281403i
\(976\) 6.12132 6.12132i 0.195939 0.195939i
\(977\) 0.727922 0.0232883 0.0116441 0.999932i \(-0.496293\pi\)
0.0116441 + 0.999932i \(0.496293\pi\)
\(978\) −2.62742 −0.0840155
\(979\) −18.2132 + 18.2132i −0.582097 + 0.582097i
\(980\) 3.53553 + 10.6066i 0.112938 + 0.338815i
\(981\) 24.3431 + 24.3431i 0.777217 + 0.777217i
\(982\) 6.89949i 0.220172i
\(983\) −44.0122 + 44.0122i −1.40377 + 1.40377i −0.616114 + 0.787657i \(0.711294\pi\)
−0.787657 + 0.616114i \(0.788706\pi\)
\(984\) 2.58579i 0.0824319i
\(985\) −9.45584 4.72792i −0.301288 0.150644i
\(986\) −1.00000 + 4.00000i −0.0318465 + 0.127386i
\(987\) 0.928932i 0.0295682i
\(988\) −21.7279 −0.691257
\(989\) 10.6274 + 10.6274i 0.337932 + 0.337932i
\(990\) −12.6863 6.34315i −0.403197 0.201598i
\(991\) 21.1213 + 21.1213i 0.670941 + 0.670941i 0.957933 0.286992i \(-0.0926553\pi\)
−0.286992 + 0.957933i \(0.592655\pi\)
\(992\) 5.36396 + 5.36396i 0.170306 + 0.170306i
\(993\) 4.60660 + 4.60660i 0.146186 + 0.146186i
\(994\) 7.41421i 0.235165i
\(995\) 20.1421 + 10.0711i 0.638549 + 0.319274i
\(996\) −1.24264 + 1.24264i −0.0393746 + 0.0393746i
\(997\) 30.6985 + 30.6985i 0.972231 + 0.972231i 0.999625 0.0273939i \(-0.00872086\pi\)
−0.0273939 + 0.999625i \(0.508721\pi\)
\(998\) 8.51472 8.51472i 0.269529 0.269529i
\(999\) −17.8995 −0.566315
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 170.2.g.e.149.2 yes 4
3.2 odd 2 1530.2.n.o.829.2 4
5.2 odd 4 850.2.h.k.251.1 4
5.3 odd 4 850.2.h.h.251.2 4
5.4 even 2 170.2.g.f.149.1 yes 4
15.14 odd 2 1530.2.n.j.829.1 4
17.4 even 4 170.2.g.f.89.1 yes 4
51.38 odd 4 1530.2.n.j.1279.1 4
85.4 even 4 inner 170.2.g.e.89.2 4
85.38 odd 4 850.2.h.h.701.2 4
85.72 odd 4 850.2.h.k.701.1 4
255.89 odd 4 1530.2.n.o.1279.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.g.e.89.2 4 85.4 even 4 inner
170.2.g.e.149.2 yes 4 1.1 even 1 trivial
170.2.g.f.89.1 yes 4 17.4 even 4
170.2.g.f.149.1 yes 4 5.4 even 2
850.2.h.h.251.2 4 5.3 odd 4
850.2.h.h.701.2 4 85.38 odd 4
850.2.h.k.251.1 4 5.2 odd 4
850.2.h.k.701.1 4 85.72 odd 4
1530.2.n.j.829.1 4 15.14 odd 2
1530.2.n.j.1279.1 4 51.38 odd 4
1530.2.n.o.829.2 4 3.2 odd 2
1530.2.n.o.1279.2 4 255.89 odd 4