Properties

Label 300.2.j.c.43.4
Level $300$
Weight $2$
Character 300.43
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [300,2,Mod(7,300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(300, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("300.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.j (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: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.4
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 300.43
Dual form 300.2.j.c.7.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.36603 - 0.366025i) q^{6} +(1.74238 + 1.74238i) q^{7} +2.82843i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.36603 - 0.366025i) q^{6} +(1.74238 + 1.74238i) q^{7} +2.82843i q^{8} -1.00000i q^{9} -2.00000i q^{11} +(1.93185 + 0.517638i) q^{12} +(-4.05317 - 4.05317i) q^{13} +(0.901924 + 3.36603i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-4.24264 + 4.24264i) q^{17} +(0.707107 - 1.22474i) q^{18} +7.19615 q^{19} +2.46410 q^{21} +(1.41421 - 2.44949i) q^{22} +(0.378937 - 0.378937i) q^{23} +(2.00000 + 2.00000i) q^{24} +(-2.09808 - 7.83013i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.27551 + 4.76028i) q^{28} -7.46410i q^{29} -0.267949i q^{31} +(-4.89898 + 2.82843i) q^{32} +(-1.41421 - 1.41421i) q^{33} +(-8.19615 + 2.19615i) q^{34} +(1.73205 - 1.00000i) q^{36} +(-2.07055 + 2.07055i) q^{37} +(8.81345 + 5.08845i) q^{38} -5.73205 q^{39} -5.46410 q^{41} +(3.01790 + 1.74238i) q^{42} +(-1.74238 + 1.74238i) q^{43} +(3.46410 - 2.00000i) q^{44} +(0.732051 - 0.196152i) q^{46} +(-9.14162 - 9.14162i) q^{47} +(1.03528 + 3.86370i) q^{48} -0.928203i q^{49} +6.00000i q^{51} +(2.96713 - 11.0735i) q^{52} +(-1.03528 - 1.03528i) q^{53} +(-0.366025 - 1.36603i) q^{54} +(-4.92820 + 4.92820i) q^{56} +(5.08845 - 5.08845i) q^{57} +(5.27792 - 9.14162i) q^{58} -4.53590 q^{59} +3.00000 q^{61} +(0.189469 - 0.328169i) q^{62} +(1.74238 - 1.74238i) q^{63} -8.00000 q^{64} +(-0.732051 - 2.73205i) q^{66} +(8.81345 + 8.81345i) q^{67} +(-11.5911 - 3.10583i) q^{68} -0.535898i q^{69} +9.46410i q^{71} +2.82843 q^{72} +(2.82843 + 2.82843i) q^{73} +(-4.00000 + 1.07180i) q^{74} +(7.19615 + 12.4641i) q^{76} +(3.48477 - 3.48477i) q^{77} +(-7.02030 - 4.05317i) q^{78} +0.535898 q^{79} -1.00000 q^{81} +(-6.69213 - 3.86370i) q^{82} +(0.656339 - 0.656339i) q^{83} +(2.46410 + 4.26795i) q^{84} +(-3.36603 + 0.901924i) q^{86} +(-5.27792 - 5.27792i) q^{87} +5.65685 q^{88} +6.92820i q^{89} -14.1244i q^{91} +(1.03528 + 0.277401i) q^{92} +(-0.189469 - 0.189469i) q^{93} +(-4.73205 - 17.6603i) q^{94} +(-1.46410 + 5.46410i) q^{96} +(4.43211 - 4.43211i) q^{97} +(0.656339 - 1.13681i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + 4 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} + 4 q^{6} + 28 q^{14} - 16 q^{16} + 16 q^{19} - 8 q^{21} + 16 q^{24} + 4 q^{26} - 24 q^{34} - 32 q^{39} - 16 q^{41} - 8 q^{46} + 4 q^{54} + 16 q^{56} - 64 q^{59} + 24 q^{61} - 64 q^{64} + 8 q^{66} - 32 q^{74} + 16 q^{76} + 32 q^{79} - 8 q^{81} - 8 q^{84} - 20 q^{86} - 24 q^{94} + 16 q^{96} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.866025 + 0.500000i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 0 0
\(6\) 1.36603 0.366025i 0.557678 0.149429i
\(7\) 1.74238 + 1.74238i 0.658559 + 0.658559i 0.955039 0.296480i \(-0.0958129\pi\)
−0.296480 + 0.955039i \(0.595813\pi\)
\(8\) 2.82843i 1.00000i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) 1.93185 + 0.517638i 0.557678 + 0.149429i
\(13\) −4.05317 4.05317i −1.12415 1.12415i −0.991111 0.133037i \(-0.957527\pi\)
−0.133037 0.991111i \(-0.542473\pi\)
\(14\) 0.901924 + 3.36603i 0.241049 + 0.899608i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) −4.24264 + 4.24264i −1.02899 + 1.02899i −0.0294245 + 0.999567i \(0.509367\pi\)
−0.999567 + 0.0294245i \(0.990633\pi\)
\(18\) 0.707107 1.22474i 0.166667 0.288675i
\(19\) 7.19615 1.65091 0.825455 0.564467i \(-0.190918\pi\)
0.825455 + 0.564467i \(0.190918\pi\)
\(20\) 0 0
\(21\) 2.46410 0.537711
\(22\) 1.41421 2.44949i 0.301511 0.522233i
\(23\) 0.378937 0.378937i 0.0790139 0.0790139i −0.666495 0.745509i \(-0.732206\pi\)
0.745509 + 0.666495i \(0.232206\pi\)
\(24\) 2.00000 + 2.00000i 0.408248 + 0.408248i
\(25\) 0 0
\(26\) −2.09808 7.83013i −0.411467 1.53561i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −1.27551 + 4.76028i −0.241049 + 0.899608i
\(29\) 7.46410i 1.38605i −0.720914 0.693024i \(-0.756278\pi\)
0.720914 0.693024i \(-0.243722\pi\)
\(30\) 0 0
\(31\) 0.267949i 0.0481251i −0.999710 0.0240625i \(-0.992340\pi\)
0.999710 0.0240625i \(-0.00766009\pi\)
\(32\) −4.89898 + 2.82843i −0.866025 + 0.500000i
\(33\) −1.41421 1.41421i −0.246183 0.246183i
\(34\) −8.19615 + 2.19615i −1.40563 + 0.376637i
\(35\) 0 0
\(36\) 1.73205 1.00000i 0.288675 0.166667i
\(37\) −2.07055 + 2.07055i −0.340397 + 0.340397i −0.856516 0.516120i \(-0.827376\pi\)
0.516120 + 0.856516i \(0.327376\pi\)
\(38\) 8.81345 + 5.08845i 1.42973 + 0.825455i
\(39\) −5.73205 −0.917863
\(40\) 0 0
\(41\) −5.46410 −0.853349 −0.426675 0.904405i \(-0.640315\pi\)
−0.426675 + 0.904405i \(0.640315\pi\)
\(42\) 3.01790 + 1.74238i 0.465671 + 0.268856i
\(43\) −1.74238 + 1.74238i −0.265711 + 0.265711i −0.827369 0.561658i \(-0.810164\pi\)
0.561658 + 0.827369i \(0.310164\pi\)
\(44\) 3.46410 2.00000i 0.522233 0.301511i
\(45\) 0 0
\(46\) 0.732051 0.196152i 0.107935 0.0289211i
\(47\) −9.14162 9.14162i −1.33344 1.33344i −0.902269 0.431173i \(-0.858100\pi\)
−0.431173 0.902269i \(-0.641900\pi\)
\(48\) 1.03528 + 3.86370i 0.149429 + 0.557678i
\(49\) 0.928203i 0.132600i
\(50\) 0 0
\(51\) 6.00000i 0.840168i
\(52\) 2.96713 11.0735i 0.411467 1.53561i
\(53\) −1.03528 1.03528i −0.142206 0.142206i 0.632420 0.774626i \(-0.282062\pi\)
−0.774626 + 0.632420i \(0.782062\pi\)
\(54\) −0.366025 1.36603i −0.0498097 0.185893i
\(55\) 0 0
\(56\) −4.92820 + 4.92820i −0.658559 + 0.658559i
\(57\) 5.08845 5.08845i 0.673981 0.673981i
\(58\) 5.27792 9.14162i 0.693024 1.20035i
\(59\) −4.53590 −0.590524 −0.295262 0.955416i \(-0.595407\pi\)
−0.295262 + 0.955416i \(0.595407\pi\)
\(60\) 0 0
\(61\) 3.00000 0.384111 0.192055 0.981384i \(-0.438485\pi\)
0.192055 + 0.981384i \(0.438485\pi\)
\(62\) 0.189469 0.328169i 0.0240625 0.0416776i
\(63\) 1.74238 1.74238i 0.219520 0.219520i
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) −0.732051 2.73205i −0.0901092 0.336292i
\(67\) 8.81345 + 8.81345i 1.07673 + 1.07673i 0.996800 + 0.0799342i \(0.0254710\pi\)
0.0799342 + 0.996800i \(0.474529\pi\)
\(68\) −11.5911 3.10583i −1.40563 0.376637i
\(69\) 0.535898i 0.0645146i
\(70\) 0 0
\(71\) 9.46410i 1.12318i 0.827415 + 0.561591i \(0.189811\pi\)
−0.827415 + 0.561591i \(0.810189\pi\)
\(72\) 2.82843 0.333333
\(73\) 2.82843 + 2.82843i 0.331042 + 0.331042i 0.852982 0.521940i \(-0.174791\pi\)
−0.521940 + 0.852982i \(0.674791\pi\)
\(74\) −4.00000 + 1.07180i −0.464991 + 0.124594i
\(75\) 0 0
\(76\) 7.19615 + 12.4641i 0.825455 + 1.42973i
\(77\) 3.48477 3.48477i 0.397126 0.397126i
\(78\) −7.02030 4.05317i −0.794892 0.458931i
\(79\) 0.535898 0.0602933 0.0301466 0.999545i \(-0.490403\pi\)
0.0301466 + 0.999545i \(0.490403\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −6.69213 3.86370i −0.739022 0.426675i
\(83\) 0.656339 0.656339i 0.0720425 0.0720425i −0.670167 0.742210i \(-0.733778\pi\)
0.742210 + 0.670167i \(0.233778\pi\)
\(84\) 2.46410 + 4.26795i 0.268856 + 0.465671i
\(85\) 0 0
\(86\) −3.36603 + 0.901924i −0.362968 + 0.0972569i
\(87\) −5.27792 5.27792i −0.565852 0.565852i
\(88\) 5.65685 0.603023
\(89\) 6.92820i 0.734388i 0.930144 + 0.367194i \(0.119682\pi\)
−0.930144 + 0.367194i \(0.880318\pi\)
\(90\) 0 0
\(91\) 14.1244i 1.48063i
\(92\) 1.03528 + 0.277401i 0.107935 + 0.0289211i
\(93\) −0.189469 0.189469i −0.0196470 0.0196470i
\(94\) −4.73205 17.6603i −0.488074 1.82152i
\(95\) 0 0
\(96\) −1.46410 + 5.46410i −0.149429 + 0.557678i
\(97\) 4.43211 4.43211i 0.450013 0.450013i −0.445346 0.895359i \(-0.646919\pi\)
0.895359 + 0.445346i \(0.146919\pi\)
\(98\) 0.656339 1.13681i 0.0663002 0.114835i
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) −1.46410 −0.145684 −0.0728418 0.997344i \(-0.523207\pi\)
−0.0728418 + 0.997344i \(0.523207\pi\)
\(102\) −4.24264 + 7.34847i −0.420084 + 0.727607i
\(103\) 4.89898 4.89898i 0.482711 0.482711i −0.423286 0.905996i \(-0.639123\pi\)
0.905996 + 0.423286i \(0.139123\pi\)
\(104\) 11.4641 11.4641i 1.12415 1.12415i
\(105\) 0 0
\(106\) −0.535898 2.00000i −0.0520511 0.194257i
\(107\) 4.62158 + 4.62158i 0.446785 + 0.446785i 0.894284 0.447499i \(-0.147685\pi\)
−0.447499 + 0.894284i \(0.647685\pi\)
\(108\) 0.517638 1.93185i 0.0498097 0.185893i
\(109\) 7.00000i 0.670478i 0.942133 + 0.335239i \(0.108817\pi\)
−0.942133 + 0.335239i \(0.891183\pi\)
\(110\) 0 0
\(111\) 2.92820i 0.277933i
\(112\) −9.52056 + 2.55103i −0.899608 + 0.241049i
\(113\) 9.79796 + 9.79796i 0.921714 + 0.921714i 0.997151 0.0754362i \(-0.0240349\pi\)
−0.0754362 + 0.997151i \(0.524035\pi\)
\(114\) 9.83013 2.63397i 0.920676 0.246694i
\(115\) 0 0
\(116\) 12.9282 7.46410i 1.20035 0.693024i
\(117\) −4.05317 + 4.05317i −0.374716 + 0.374716i
\(118\) −5.55532 3.20736i −0.511409 0.295262i
\(119\) −14.7846 −1.35530
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 3.67423 + 2.12132i 0.332650 + 0.192055i
\(123\) −3.86370 + 3.86370i −0.348378 + 0.348378i
\(124\) 0.464102 0.267949i 0.0416776 0.0240625i
\(125\) 0 0
\(126\) 3.36603 0.901924i 0.299869 0.0803498i
\(127\) 2.07055 + 2.07055i 0.183732 + 0.183732i 0.792980 0.609248i \(-0.208529\pi\)
−0.609248 + 0.792980i \(0.708529\pi\)
\(128\) −9.79796 5.65685i −0.866025 0.500000i
\(129\) 2.46410i 0.216952i
\(130\) 0 0
\(131\) 9.46410i 0.826882i −0.910531 0.413441i \(-0.864327\pi\)
0.910531 0.413441i \(-0.135673\pi\)
\(132\) 1.03528 3.86370i 0.0901092 0.336292i
\(133\) 12.5385 + 12.5385i 1.08722 + 1.08722i
\(134\) 4.56218 + 17.0263i 0.394112 + 1.47085i
\(135\) 0 0
\(136\) −12.0000 12.0000i −1.02899 1.02899i
\(137\) 6.03579 6.03579i 0.515672 0.515672i −0.400586 0.916259i \(-0.631194\pi\)
0.916259 + 0.400586i \(0.131194\pi\)
\(138\) 0.378937 0.656339i 0.0322573 0.0558713i
\(139\) 19.4641 1.65092 0.825462 0.564458i \(-0.190915\pi\)
0.825462 + 0.564458i \(0.190915\pi\)
\(140\) 0 0
\(141\) −12.9282 −1.08875
\(142\) −6.69213 + 11.5911i −0.561591 + 0.972704i
\(143\) −8.10634 + 8.10634i −0.677887 + 0.677887i
\(144\) 3.46410 + 2.00000i 0.288675 + 0.166667i
\(145\) 0 0
\(146\) 1.46410 + 5.46410i 0.121170 + 0.452212i
\(147\) −0.656339 0.656339i −0.0541339 0.0541339i
\(148\) −5.65685 1.51575i −0.464991 0.124594i
\(149\) 15.8564i 1.29901i 0.760358 + 0.649504i \(0.225023\pi\)
−0.760358 + 0.649504i \(0.774977\pi\)
\(150\) 0 0
\(151\) 4.26795i 0.347321i −0.984806 0.173660i \(-0.944440\pi\)
0.984806 0.173660i \(-0.0555595\pi\)
\(152\) 20.3538i 1.65091i
\(153\) 4.24264 + 4.24264i 0.342997 + 0.342997i
\(154\) 6.73205 1.80385i 0.542484 0.145358i
\(155\) 0 0
\(156\) −5.73205 9.92820i −0.458931 0.794892i
\(157\) −6.88160 + 6.88160i −0.549211 + 0.549211i −0.926213 0.377001i \(-0.876955\pi\)
0.377001 + 0.926213i \(0.376955\pi\)
\(158\) 0.656339 + 0.378937i 0.0522155 + 0.0301466i
\(159\) −1.46410 −0.116111
\(160\) 0 0
\(161\) 1.32051 0.104071
\(162\) −1.22474 0.707107i −0.0962250 0.0555556i
\(163\) −10.2277 + 10.2277i −0.801092 + 0.801092i −0.983266 0.182174i \(-0.941687\pi\)
0.182174 + 0.983266i \(0.441687\pi\)
\(164\) −5.46410 9.46410i −0.426675 0.739022i
\(165\) 0 0
\(166\) 1.26795 0.339746i 0.0984119 0.0263694i
\(167\) 3.10583 + 3.10583i 0.240336 + 0.240336i 0.816989 0.576653i \(-0.195642\pi\)
−0.576653 + 0.816989i \(0.695642\pi\)
\(168\) 6.96953i 0.537711i
\(169\) 19.8564i 1.52742i
\(170\) 0 0
\(171\) 7.19615i 0.550304i
\(172\) −4.76028 1.27551i −0.362968 0.0972569i
\(173\) −6.31319 6.31319i −0.479983 0.479983i 0.425143 0.905126i \(-0.360224\pi\)
−0.905126 + 0.425143i \(0.860224\pi\)
\(174\) −2.73205 10.1962i −0.207116 0.772968i
\(175\) 0 0
\(176\) 6.92820 + 4.00000i 0.522233 + 0.301511i
\(177\) −3.20736 + 3.20736i −0.241080 + 0.241080i
\(178\) −4.89898 + 8.48528i −0.367194 + 0.635999i
\(179\) 25.3205 1.89254 0.946272 0.323372i \(-0.104817\pi\)
0.946272 + 0.323372i \(0.104817\pi\)
\(180\) 0 0
\(181\) −13.9282 −1.03528 −0.517638 0.855600i \(-0.673188\pi\)
−0.517638 + 0.855600i \(0.673188\pi\)
\(182\) 9.98743 17.2987i 0.740317 1.28227i
\(183\) 2.12132 2.12132i 0.156813 0.156813i
\(184\) 1.07180 + 1.07180i 0.0790139 + 0.0790139i
\(185\) 0 0
\(186\) −0.0980762 0.366025i −0.00719130 0.0268383i
\(187\) 8.48528 + 8.48528i 0.620505 + 0.620505i
\(188\) 6.69213 24.9754i 0.488074 1.82152i
\(189\) 2.46410i 0.179237i
\(190\) 0 0
\(191\) 16.9282i 1.22488i 0.790516 + 0.612441i \(0.209812\pi\)
−0.790516 + 0.612441i \(0.790188\pi\)
\(192\) −5.65685 + 5.65685i −0.408248 + 0.408248i
\(193\) −9.71003 9.71003i −0.698943 0.698943i 0.265240 0.964183i \(-0.414549\pi\)
−0.964183 + 0.265240i \(0.914549\pi\)
\(194\) 8.56218 2.29423i 0.614729 0.164716i
\(195\) 0 0
\(196\) 1.60770 0.928203i 0.114835 0.0663002i
\(197\) 10.1769 10.1769i 0.725074 0.725074i −0.244560 0.969634i \(-0.578644\pi\)
0.969634 + 0.244560i \(0.0786436\pi\)
\(198\) −2.44949 1.41421i −0.174078 0.100504i
\(199\) −14.1244 −1.00125 −0.500625 0.865665i \(-0.666896\pi\)
−0.500625 + 0.865665i \(0.666896\pi\)
\(200\) 0 0
\(201\) 12.4641 0.879150
\(202\) −1.79315 1.03528i −0.126166 0.0728418i
\(203\) 13.0053 13.0053i 0.912795 0.912795i
\(204\) −10.3923 + 6.00000i −0.727607 + 0.420084i
\(205\) 0 0
\(206\) 9.46410 2.53590i 0.659395 0.176684i
\(207\) −0.378937 0.378937i −0.0263380 0.0263380i
\(208\) 22.1469 5.93426i 1.53561 0.411467i
\(209\) 14.3923i 0.995537i
\(210\) 0 0
\(211\) 7.19615i 0.495404i 0.968836 + 0.247702i \(0.0796753\pi\)
−0.968836 + 0.247702i \(0.920325\pi\)
\(212\) 0.757875 2.82843i 0.0520511 0.194257i
\(213\) 6.69213 + 6.69213i 0.458537 + 0.458537i
\(214\) 2.39230 + 8.92820i 0.163535 + 0.610319i
\(215\) 0 0
\(216\) 2.00000 2.00000i 0.136083 0.136083i
\(217\) 0.466870 0.466870i 0.0316932 0.0316932i
\(218\) −4.94975 + 8.57321i −0.335239 + 0.580651i
\(219\) 4.00000 0.270295
\(220\) 0 0
\(221\) 34.3923 2.31348
\(222\) −2.07055 + 3.58630i −0.138966 + 0.240697i
\(223\) −8.05558 + 8.05558i −0.539441 + 0.539441i −0.923365 0.383924i \(-0.874573\pi\)
0.383924 + 0.923365i \(0.374573\pi\)
\(224\) −13.4641 3.60770i −0.899608 0.241049i
\(225\) 0 0
\(226\) 5.07180 + 18.9282i 0.337371 + 1.25909i
\(227\) 8.76268 + 8.76268i 0.581600 + 0.581600i 0.935343 0.353743i \(-0.115091\pi\)
−0.353743 + 0.935343i \(0.615091\pi\)
\(228\) 13.9019 + 3.72500i 0.920676 + 0.246694i
\(229\) 24.8564i 1.64256i −0.570527 0.821279i \(-0.693261\pi\)
0.570527 0.821279i \(-0.306739\pi\)
\(230\) 0 0
\(231\) 4.92820i 0.324252i
\(232\) 21.1117 1.38605
\(233\) −8.76268 8.76268i −0.574062 0.574062i 0.359199 0.933261i \(-0.383050\pi\)
−0.933261 + 0.359199i \(0.883050\pi\)
\(234\) −7.83013 + 2.09808i −0.511871 + 0.137156i
\(235\) 0 0
\(236\) −4.53590 7.85641i −0.295262 0.511409i
\(237\) 0.378937 0.378937i 0.0246146 0.0246146i
\(238\) −18.1074 10.4543i −1.17373 0.677651i
\(239\) −17.4641 −1.12966 −0.564829 0.825208i \(-0.691058\pi\)
−0.564829 + 0.825208i \(0.691058\pi\)
\(240\) 0 0
\(241\) −14.8564 −0.956985 −0.478493 0.878092i \(-0.658817\pi\)
−0.478493 + 0.878092i \(0.658817\pi\)
\(242\) 8.57321 + 4.94975i 0.551107 + 0.318182i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 3.00000 + 5.19615i 0.192055 + 0.332650i
\(245\) 0 0
\(246\) −7.46410 + 2.00000i −0.475894 + 0.127515i
\(247\) −29.1672 29.1672i −1.85587 1.85587i
\(248\) 0.757875 0.0481251
\(249\) 0.928203i 0.0588225i
\(250\) 0 0
\(251\) 2.14359i 0.135302i 0.997709 + 0.0676512i \(0.0215505\pi\)
−0.997709 + 0.0676512i \(0.978449\pi\)
\(252\) 4.76028 + 1.27551i 0.299869 + 0.0803498i
\(253\) −0.757875 0.757875i −0.0476472 0.0476472i
\(254\) 1.07180 + 4.00000i 0.0672505 + 0.250982i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −9.04008 + 9.04008i −0.563905 + 0.563905i −0.930414 0.366509i \(-0.880553\pi\)
0.366509 + 0.930414i \(0.380553\pi\)
\(258\) −1.74238 + 3.01790i −0.108476 + 0.187886i
\(259\) −7.21539 −0.448343
\(260\) 0 0
\(261\) −7.46410 −0.462016
\(262\) 6.69213 11.5911i 0.413441 0.716101i
\(263\) 15.1774 15.1774i 0.935879 0.935879i −0.0621853 0.998065i \(-0.519807\pi\)
0.998065 + 0.0621853i \(0.0198070\pi\)
\(264\) 4.00000 4.00000i 0.246183 0.246183i
\(265\) 0 0
\(266\) 6.49038 + 24.2224i 0.397951 + 1.48517i
\(267\) 4.89898 + 4.89898i 0.299813 + 0.299813i
\(268\) −6.45189 + 24.0788i −0.394112 + 1.47085i
\(269\) 1.60770i 0.0980229i 0.998798 + 0.0490115i \(0.0156071\pi\)
−0.998798 + 0.0490115i \(0.984393\pi\)
\(270\) 0 0
\(271\) 24.2487i 1.47300i 0.676435 + 0.736502i \(0.263524\pi\)
−0.676435 + 0.736502i \(0.736476\pi\)
\(272\) −6.21166 23.1822i −0.376637 1.40563i
\(273\) −9.98743 9.98743i −0.604467 0.604467i
\(274\) 11.6603 3.12436i 0.704422 0.188749i
\(275\) 0 0
\(276\) 0.928203 0.535898i 0.0558713 0.0322573i
\(277\) −0.845807 + 0.845807i −0.0508196 + 0.0508196i −0.732060 0.681240i \(-0.761441\pi\)
0.681240 + 0.732060i \(0.261441\pi\)
\(278\) 23.8386 + 13.7632i 1.42974 + 0.825462i
\(279\) −0.267949 −0.0160417
\(280\) 0 0
\(281\) −14.3923 −0.858573 −0.429286 0.903168i \(-0.641235\pi\)
−0.429286 + 0.903168i \(0.641235\pi\)
\(282\) −15.8338 9.14162i −0.942886 0.544376i
\(283\) 15.1266 15.1266i 0.899186 0.899186i −0.0961785 0.995364i \(-0.530662\pi\)
0.995364 + 0.0961785i \(0.0306620\pi\)
\(284\) −16.3923 + 9.46410i −0.972704 + 0.561591i
\(285\) 0 0
\(286\) −15.6603 + 4.19615i −0.926010 + 0.248124i
\(287\) −9.52056 9.52056i −0.561981 0.561981i
\(288\) 2.82843 + 4.89898i 0.166667 + 0.288675i
\(289\) 19.0000i 1.11765i
\(290\) 0 0
\(291\) 6.26795i 0.367434i
\(292\) −2.07055 + 7.72741i −0.121170 + 0.452212i
\(293\) −8.86422 8.86422i −0.517853 0.517853i 0.399068 0.916921i \(-0.369334\pi\)
−0.916921 + 0.399068i \(0.869334\pi\)
\(294\) −0.339746 1.26795i −0.0198144 0.0739483i
\(295\) 0 0
\(296\) −5.85641 5.85641i −0.340397 0.340397i
\(297\) −1.41421 + 1.41421i −0.0820610 + 0.0820610i
\(298\) −11.2122 + 19.4201i −0.649504 + 1.12497i
\(299\) −3.07180 −0.177647
\(300\) 0 0
\(301\) −6.07180 −0.349973
\(302\) 3.01790 5.22715i 0.173660 0.300789i
\(303\) −1.03528 + 1.03528i −0.0594751 + 0.0594751i
\(304\) −14.3923 + 24.9282i −0.825455 + 1.42973i
\(305\) 0 0
\(306\) 2.19615 + 8.19615i 0.125546 + 0.468543i
\(307\) −9.46979 9.46979i −0.540469 0.540469i 0.383197 0.923667i \(-0.374823\pi\)
−0.923667 + 0.383197i \(0.874823\pi\)
\(308\) 9.52056 + 2.55103i 0.542484 + 0.145358i
\(309\) 6.92820i 0.394132i
\(310\) 0 0
\(311\) 27.4641i 1.55735i −0.627430 0.778673i \(-0.715893\pi\)
0.627430 0.778673i \(-0.284107\pi\)
\(312\) 16.2127i 0.917863i
\(313\) −5.74479 5.74479i −0.324715 0.324715i 0.525858 0.850572i \(-0.323744\pi\)
−0.850572 + 0.525858i \(0.823744\pi\)
\(314\) −13.2942 + 3.56218i −0.750237 + 0.201025i
\(315\) 0 0
\(316\) 0.535898 + 0.928203i 0.0301466 + 0.0522155i
\(317\) 4.89898 4.89898i 0.275154 0.275154i −0.556017 0.831171i \(-0.687671\pi\)
0.831171 + 0.556017i \(0.187671\pi\)
\(318\) −1.79315 1.03528i −0.100555 0.0580554i
\(319\) −14.9282 −0.835819
\(320\) 0 0
\(321\) 6.53590 0.364798
\(322\) 1.61729 + 0.933740i 0.0901278 + 0.0520353i
\(323\) −30.5307 + 30.5307i −1.69877 + 1.69877i
\(324\) −1.00000 1.73205i −0.0555556 0.0962250i
\(325\) 0 0
\(326\) −19.7583 + 5.29423i −1.09431 + 0.293220i
\(327\) 4.94975 + 4.94975i 0.273722 + 0.273722i
\(328\) 15.4548i 0.853349i
\(329\) 31.8564i 1.75630i
\(330\) 0 0
\(331\) 2.39230i 0.131493i −0.997836 0.0657465i \(-0.979057\pi\)
0.997836 0.0657465i \(-0.0209429\pi\)
\(332\) 1.79315 + 0.480473i 0.0984119 + 0.0263694i
\(333\) 2.07055 + 2.07055i 0.113466 + 0.113466i
\(334\) 1.60770 + 6.00000i 0.0879692 + 0.328305i
\(335\) 0 0
\(336\) −4.92820 + 8.53590i −0.268856 + 0.465671i
\(337\) −8.01841 + 8.01841i −0.436791 + 0.436791i −0.890930 0.454140i \(-0.849947\pi\)
0.454140 + 0.890930i \(0.349947\pi\)
\(338\) −14.0406 + 24.3190i −0.763708 + 1.32278i
\(339\) 13.8564 0.752577
\(340\) 0 0
\(341\) −0.535898 −0.0290205
\(342\) 5.08845 8.81345i 0.275152 0.476577i
\(343\) 13.8140 13.8140i 0.745884 0.745884i
\(344\) −4.92820 4.92820i −0.265711 0.265711i
\(345\) 0 0
\(346\) −3.26795 12.1962i −0.175686 0.655669i
\(347\) 7.82894 + 7.82894i 0.420280 + 0.420280i 0.885300 0.465020i \(-0.153953\pi\)
−0.465020 + 0.885300i \(0.653953\pi\)
\(348\) 3.86370 14.4195i 0.207116 0.772968i
\(349\) 3.85641i 0.206429i 0.994659 + 0.103214i \(0.0329128\pi\)
−0.994659 + 0.103214i \(0.967087\pi\)
\(350\) 0 0
\(351\) 5.73205i 0.305954i
\(352\) 5.65685 + 9.79796i 0.301511 + 0.522233i
\(353\) 11.2122 + 11.2122i 0.596764 + 0.596764i 0.939450 0.342686i \(-0.111337\pi\)
−0.342686 + 0.939450i \(0.611337\pi\)
\(354\) −6.19615 + 1.66025i −0.329322 + 0.0882415i
\(355\) 0 0
\(356\) −12.0000 + 6.92820i −0.635999 + 0.367194i
\(357\) −10.4543 + 10.4543i −0.553300 + 0.553300i
\(358\) 31.0112 + 17.9043i 1.63899 + 0.946272i
\(359\) 24.3923 1.28738 0.643688 0.765288i \(-0.277403\pi\)
0.643688 + 0.765288i \(0.277403\pi\)
\(360\) 0 0
\(361\) 32.7846 1.72551
\(362\) −17.0585 9.84873i −0.896575 0.517638i
\(363\) 4.94975 4.94975i 0.259794 0.259794i
\(364\) 24.4641 14.1244i 1.28227 0.740317i
\(365\) 0 0
\(366\) 4.09808 1.09808i 0.214210 0.0573974i
\(367\) −7.50077 7.50077i −0.391537 0.391537i 0.483698 0.875235i \(-0.339293\pi\)
−0.875235 + 0.483698i \(0.839293\pi\)
\(368\) 0.554803 + 2.07055i 0.0289211 + 0.107935i
\(369\) 5.46410i 0.284450i
\(370\) 0 0
\(371\) 3.60770i 0.187302i
\(372\) 0.138701 0.517638i 0.00719130 0.0268383i
\(373\) −13.6753 13.6753i −0.708078 0.708078i 0.258052 0.966131i \(-0.416919\pi\)
−0.966131 + 0.258052i \(0.916919\pi\)
\(374\) 4.39230 + 16.3923i 0.227121 + 0.847626i
\(375\) 0 0
\(376\) 25.8564 25.8564i 1.33344 1.33344i
\(377\) −30.2533 + 30.2533i −1.55812 + 1.55812i
\(378\) 1.74238 3.01790i 0.0896185 0.155224i
\(379\) −15.7321 −0.808101 −0.404051 0.914737i \(-0.632398\pi\)
−0.404051 + 0.914737i \(0.632398\pi\)
\(380\) 0 0
\(381\) 2.92820 0.150016
\(382\) −11.9700 + 20.7327i −0.612441 + 1.06078i
\(383\) 11.8685 11.8685i 0.606453 0.606453i −0.335565 0.942017i \(-0.608927\pi\)
0.942017 + 0.335565i \(0.108927\pi\)
\(384\) −10.9282 + 2.92820i −0.557678 + 0.149429i
\(385\) 0 0
\(386\) −5.02628 18.7583i −0.255831 0.954774i
\(387\) 1.74238 + 1.74238i 0.0885703 + 0.0885703i
\(388\) 12.1087 + 3.24453i 0.614729 + 0.164716i
\(389\) 14.5359i 0.736999i 0.929628 + 0.368500i \(0.120128\pi\)
−0.929628 + 0.368500i \(0.879872\pi\)
\(390\) 0 0
\(391\) 3.21539i 0.162609i
\(392\) 2.62536 0.132600
\(393\) −6.69213 6.69213i −0.337573 0.337573i
\(394\) 19.6603 5.26795i 0.990469 0.265395i
\(395\) 0 0
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) 13.8511 13.8511i 0.695168 0.695168i −0.268196 0.963364i \(-0.586427\pi\)
0.963364 + 0.268196i \(0.0864275\pi\)
\(398\) −17.2987 9.98743i −0.867107 0.500625i
\(399\) 17.7321 0.887713
\(400\) 0 0
\(401\) −33.1769 −1.65678 −0.828388 0.560155i \(-0.810742\pi\)
−0.828388 + 0.560155i \(0.810742\pi\)
\(402\) 15.2653 + 8.81345i 0.761366 + 0.439575i
\(403\) −1.08604 + 1.08604i −0.0540997 + 0.0540997i
\(404\) −1.46410 2.53590i −0.0728418 0.126166i
\(405\) 0 0
\(406\) 25.1244 6.73205i 1.24690 0.334106i
\(407\) 4.14110 + 4.14110i 0.205267 + 0.205267i
\(408\) −16.9706 −0.840168
\(409\) 27.7846i 1.37386i −0.726723 0.686930i \(-0.758958\pi\)
0.726723 0.686930i \(-0.241042\pi\)
\(410\) 0 0
\(411\) 8.53590i 0.421045i
\(412\) 13.3843 + 3.58630i 0.659395 + 0.176684i
\(413\) −7.90327 7.90327i −0.388895 0.388895i
\(414\) −0.196152 0.732051i −0.00964037 0.0359783i
\(415\) 0 0
\(416\) 31.3205 + 8.39230i 1.53561 + 0.411467i
\(417\) 13.7632 13.7632i 0.673987 0.673987i
\(418\) 10.1769 17.6269i 0.497768 0.862160i
\(419\) 26.5359 1.29636 0.648182 0.761486i \(-0.275530\pi\)
0.648182 + 0.761486i \(0.275530\pi\)
\(420\) 0 0
\(421\) 6.78461 0.330662 0.165331 0.986238i \(-0.447131\pi\)
0.165331 + 0.986238i \(0.447131\pi\)
\(422\) −5.08845 + 8.81345i −0.247702 + 0.429032i
\(423\) −9.14162 + 9.14162i −0.444481 + 0.444481i
\(424\) 2.92820 2.92820i 0.142206 0.142206i
\(425\) 0 0
\(426\) 3.46410 + 12.9282i 0.167836 + 0.626373i
\(427\) 5.22715 + 5.22715i 0.252959 + 0.252959i
\(428\) −3.38323 + 12.6264i −0.163535 + 0.610319i
\(429\) 11.4641i 0.553492i
\(430\) 0 0
\(431\) 25.7128i 1.23854i 0.785177 + 0.619271i \(0.212572\pi\)
−0.785177 + 0.619271i \(0.787428\pi\)
\(432\) 3.86370 1.03528i 0.185893 0.0498097i
\(433\) 3.11943 + 3.11943i 0.149910 + 0.149910i 0.778078 0.628168i \(-0.216195\pi\)
−0.628168 + 0.778078i \(0.716195\pi\)
\(434\) 0.901924 0.241670i 0.0432937 0.0116005i
\(435\) 0 0
\(436\) −12.1244 + 7.00000i −0.580651 + 0.335239i
\(437\) 2.72689 2.72689i 0.130445 0.130445i
\(438\) 4.89898 + 2.82843i 0.234082 + 0.135147i
\(439\) −27.9808 −1.33545 −0.667724 0.744409i \(-0.732732\pi\)
−0.667724 + 0.744409i \(0.732732\pi\)
\(440\) 0 0
\(441\) −0.928203 −0.0442002
\(442\) 42.1218 + 24.3190i 2.00353 + 1.15674i
\(443\) −9.04008 + 9.04008i −0.429507 + 0.429507i −0.888460 0.458953i \(-0.848225\pi\)
0.458953 + 0.888460i \(0.348225\pi\)
\(444\) −5.07180 + 2.92820i −0.240697 + 0.138966i
\(445\) 0 0
\(446\) −15.5622 + 4.16987i −0.736890 + 0.197449i
\(447\) 11.2122 + 11.2122i 0.530318 + 0.530318i
\(448\) −13.9391 13.9391i −0.658559 0.658559i
\(449\) 33.8564i 1.59778i 0.601475 + 0.798891i \(0.294580\pi\)
−0.601475 + 0.798891i \(0.705420\pi\)
\(450\) 0 0
\(451\) 10.9282i 0.514589i
\(452\) −7.17260 + 26.7685i −0.337371 + 1.25909i
\(453\) −3.01790 3.01790i −0.141793 0.141793i
\(454\) 4.53590 + 16.9282i 0.212880 + 0.794480i
\(455\) 0 0
\(456\) 14.3923 + 14.3923i 0.673981 + 0.673981i
\(457\) 25.2528 25.2528i 1.18127 1.18127i 0.201861 0.979414i \(-0.435301\pi\)
0.979414 0.201861i \(-0.0646988\pi\)
\(458\) 17.5761 30.4428i 0.821279 1.42250i
\(459\) 6.00000 0.280056
\(460\) 0 0
\(461\) 15.6077 0.726923 0.363461 0.931609i \(-0.381595\pi\)
0.363461 + 0.931609i \(0.381595\pi\)
\(462\) 3.48477 6.03579i 0.162126 0.280810i
\(463\) −9.24316 + 9.24316i −0.429566 + 0.429566i −0.888480 0.458915i \(-0.848238\pi\)
0.458915 + 0.888480i \(0.348238\pi\)
\(464\) 25.8564 + 14.9282i 1.20035 + 0.693024i
\(465\) 0 0
\(466\) −4.53590 16.9282i −0.210121 0.784184i
\(467\) 2.44949 + 2.44949i 0.113349 + 0.113349i 0.761506 0.648157i \(-0.224460\pi\)
−0.648157 + 0.761506i \(0.724460\pi\)
\(468\) −11.0735 2.96713i −0.511871 0.137156i
\(469\) 30.7128i 1.41819i
\(470\) 0 0
\(471\) 9.73205i 0.448429i
\(472\) 12.8295i 0.590524i
\(473\) 3.48477 + 3.48477i 0.160230 + 0.160230i
\(474\) 0.732051 0.196152i 0.0336242 0.00900958i
\(475\) 0 0
\(476\) −14.7846 25.6077i −0.677651 1.17373i
\(477\) −1.03528 + 1.03528i −0.0474020 + 0.0474020i
\(478\) −21.3891 12.3490i −0.978313 0.564829i
\(479\) 13.3205 0.608630 0.304315 0.952572i \(-0.401573\pi\)
0.304315 + 0.952572i \(0.401573\pi\)
\(480\) 0 0
\(481\) 16.7846 0.765312
\(482\) −18.1953 10.5051i −0.828774 0.478493i
\(483\) 0.933740 0.933740i 0.0424867 0.0424867i
\(484\) 7.00000 + 12.1244i 0.318182 + 0.551107i
\(485\) 0 0
\(486\) −1.36603 + 0.366025i −0.0619642 + 0.0166032i
\(487\) 15.2282 + 15.2282i 0.690055 + 0.690055i 0.962244 0.272189i \(-0.0877476\pi\)
−0.272189 + 0.962244i \(0.587748\pi\)
\(488\) 8.48528i 0.384111i
\(489\) 14.4641i 0.654089i
\(490\) 0 0
\(491\) 34.6410i 1.56333i −0.623700 0.781664i \(-0.714371\pi\)
0.623700 0.781664i \(-0.285629\pi\)
\(492\) −10.5558 2.82843i −0.475894 0.127515i
\(493\) 31.6675 + 31.6675i 1.42623 + 1.42623i
\(494\) −15.0981 56.3468i −0.679295 2.53516i
\(495\) 0 0
\(496\) 0.928203 + 0.535898i 0.0416776 + 0.0240625i
\(497\) −16.4901 + 16.4901i −0.739682 + 0.739682i
\(498\) 0.656339 1.13681i 0.0294112 0.0509418i
\(499\) 5.87564 0.263030 0.131515 0.991314i \(-0.458016\pi\)
0.131515 + 0.991314i \(0.458016\pi\)
\(500\) 0 0
\(501\) 4.39230 0.196234
\(502\) −1.51575 + 2.62536i −0.0676512 + 0.117175i
\(503\) −14.4195 + 14.4195i −0.642935 + 0.642935i −0.951276 0.308341i \(-0.900226\pi\)
0.308341 + 0.951276i \(0.400226\pi\)
\(504\) 4.92820 + 4.92820i 0.219520 + 0.219520i
\(505\) 0 0
\(506\) −0.392305 1.46410i −0.0174401 0.0650873i
\(507\) 14.0406 + 14.0406i 0.623565 + 0.623565i
\(508\) −1.51575 + 5.65685i −0.0672505 + 0.250982i
\(509\) 11.0718i 0.490749i −0.969428 0.245374i \(-0.921089\pi\)
0.969428 0.245374i \(-0.0789109\pi\)
\(510\) 0 0
\(511\) 9.85641i 0.436022i
\(512\) 22.6274i 1.00000i
\(513\) −5.08845 5.08845i −0.224660 0.224660i
\(514\) −17.4641 + 4.67949i −0.770309 + 0.206404i
\(515\) 0 0
\(516\) −4.26795 + 2.46410i −0.187886 + 0.108476i
\(517\) −18.2832 + 18.2832i −0.804096 + 0.804096i
\(518\) −8.83701 5.10205i −0.388276 0.224171i
\(519\) −8.92820 −0.391905
\(520\) 0 0
\(521\) −17.6077 −0.771407 −0.385704 0.922623i \(-0.626041\pi\)
−0.385704 + 0.922623i \(0.626041\pi\)
\(522\) −9.14162 5.27792i −0.400118 0.231008i
\(523\) 13.7124 13.7124i 0.599603 0.599603i −0.340604 0.940207i \(-0.610632\pi\)
0.940207 + 0.340604i \(0.110632\pi\)
\(524\) 16.3923 9.46410i 0.716101 0.413441i
\(525\) 0 0
\(526\) 29.3205 7.85641i 1.27843 0.342556i
\(527\) 1.13681 + 1.13681i 0.0495203 + 0.0495203i
\(528\) 7.72741 2.07055i 0.336292 0.0901092i
\(529\) 22.7128i 0.987514i
\(530\) 0 0
\(531\) 4.53590i 0.196841i
\(532\) −9.17878 + 34.2557i −0.397951 + 1.48517i
\(533\) 22.1469 + 22.1469i 0.959291 + 0.959291i
\(534\) 2.53590 + 9.46410i 0.109739 + 0.409552i
\(535\) 0 0
\(536\) −24.9282 + 24.9282i −1.07673 + 1.07673i
\(537\) 17.9043 17.9043i 0.772628 0.772628i
\(538\) −1.13681 + 1.96902i −0.0490115 + 0.0848903i
\(539\) −1.85641 −0.0799611
\(540\) 0 0
\(541\) −33.7846 −1.45251 −0.726257 0.687423i \(-0.758742\pi\)
−0.726257 + 0.687423i \(0.758742\pi\)
\(542\) −17.1464 + 29.6985i −0.736502 + 1.27566i
\(543\) −9.84873 + 9.84873i −0.422649 + 0.422649i
\(544\) 8.78461 32.7846i 0.376637 1.40563i
\(545\) 0 0
\(546\) −5.16987 19.2942i −0.221250 0.825717i
\(547\) −17.5254 17.5254i −0.749331 0.749331i 0.225023 0.974353i \(-0.427754\pi\)
−0.974353 + 0.225023i \(0.927754\pi\)
\(548\) 16.4901 + 4.41851i 0.704422 + 0.188749i
\(549\) 3.00000i 0.128037i
\(550\) 0 0
\(551\) 53.7128i 2.28824i
\(552\) 1.51575 0.0645146
\(553\) 0.933740 + 0.933740i 0.0397067 + 0.0397067i
\(554\) −1.63397 + 0.437822i −0.0694209 + 0.0186013i
\(555\) 0 0
\(556\) 19.4641 + 33.7128i 0.825462 + 1.42974i
\(557\) 25.6317 25.6317i 1.08605 1.08605i 0.0901194 0.995931i \(-0.471275\pi\)
0.995931 0.0901194i \(-0.0287249\pi\)
\(558\) −0.328169 0.189469i −0.0138925 0.00802085i
\(559\) 14.1244 0.597397
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) −17.6269 10.1769i −0.743546 0.429286i
\(563\) 16.3886 16.3886i 0.690695 0.690695i −0.271690 0.962385i \(-0.587582\pi\)
0.962385 + 0.271690i \(0.0875824\pi\)
\(564\) −12.9282 22.3923i −0.544376 0.942886i
\(565\) 0 0
\(566\) 29.2224 7.83013i 1.22831 0.329125i
\(567\) −1.74238 1.74238i −0.0731732 0.0731732i
\(568\) −26.7685 −1.12318
\(569\) 17.3205i 0.726113i 0.931767 + 0.363057i \(0.118267\pi\)
−0.931767 + 0.363057i \(0.881733\pi\)
\(570\) 0 0
\(571\) 16.8038i 0.703219i −0.936147 0.351610i \(-0.885634\pi\)
0.936147 0.351610i \(-0.114366\pi\)
\(572\) −22.1469 5.93426i −0.926010 0.248124i
\(573\) 11.9700 + 11.9700i 0.500056 + 0.500056i
\(574\) −4.92820 18.3923i −0.205699 0.767680i
\(575\) 0 0
\(576\) 8.00000i 0.333333i
\(577\) 10.8468 10.8468i 0.451560 0.451560i −0.444312 0.895872i \(-0.646552\pi\)
0.895872 + 0.444312i \(0.146552\pi\)
\(578\) 13.4350 23.2702i 0.558824 0.967911i
\(579\) −13.7321 −0.570685
\(580\) 0 0
\(581\) 2.28719 0.0948885
\(582\) 4.43211 7.67664i 0.183717 0.318207i
\(583\) −2.07055 + 2.07055i −0.0857535 + 0.0857535i
\(584\) −8.00000 + 8.00000i −0.331042 + 0.331042i
\(585\) 0 0
\(586\) −4.58846 17.1244i −0.189547 0.707401i
\(587\) −13.6617 13.6617i −0.563877 0.563877i 0.366529 0.930406i \(-0.380546\pi\)
−0.930406 + 0.366529i \(0.880546\pi\)
\(588\) 0.480473 1.79315i 0.0198144 0.0739483i
\(589\) 1.92820i 0.0794502i
\(590\) 0 0
\(591\) 14.3923i 0.592020i
\(592\) −3.03150 11.3137i −0.124594 0.464991i
\(593\) 22.9048 + 22.9048i 0.940588 + 0.940588i 0.998331 0.0577433i \(-0.0183905\pi\)
−0.0577433 + 0.998331i \(0.518390\pi\)
\(594\) −2.73205 + 0.732051i −0.112097 + 0.0300364i
\(595\) 0 0
\(596\) −27.4641 + 15.8564i −1.12497 + 0.649504i
\(597\) −9.98743 + 9.98743i −0.408758 + 0.408758i
\(598\) −3.76217 2.17209i −0.153846 0.0888233i
\(599\) −46.6410 −1.90570 −0.952850 0.303441i \(-0.901864\pi\)
−0.952850 + 0.303441i \(0.901864\pi\)
\(600\) 0 0
\(601\) −19.7846 −0.807031 −0.403516 0.914973i \(-0.632212\pi\)
−0.403516 + 0.914973i \(0.632212\pi\)
\(602\) −7.43640 4.29341i −0.303085 0.174986i
\(603\) 8.81345 8.81345i 0.358911 0.358911i
\(604\) 7.39230 4.26795i 0.300789 0.173660i
\(605\) 0 0
\(606\) −2.00000 + 0.535898i −0.0812444 + 0.0217694i
\(607\) −13.9391 13.9391i −0.565769 0.565769i 0.365171 0.930940i \(-0.381010\pi\)
−0.930940 + 0.365171i \(0.881010\pi\)
\(608\) −35.2538 + 20.3538i −1.42973 + 0.825455i
\(609\) 18.3923i 0.745294i
\(610\) 0 0
\(611\) 74.1051i 2.99797i
\(612\) −3.10583 + 11.5911i −0.125546 + 0.468543i
\(613\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(614\) −4.90192 18.2942i −0.197826 0.738295i
\(615\) 0 0
\(616\) 9.85641 + 9.85641i 0.397126 + 0.397126i
\(617\) −10.0754 + 10.0754i −0.405619 + 0.405619i −0.880208 0.474589i \(-0.842597\pi\)
0.474589 + 0.880208i \(0.342597\pi\)
\(618\) 4.89898 8.48528i 0.197066 0.341328i
\(619\) −35.9808 −1.44619 −0.723094 0.690749i \(-0.757281\pi\)
−0.723094 + 0.690749i \(0.757281\pi\)
\(620\) 0 0
\(621\) −0.535898 −0.0215049
\(622\) 19.4201 33.6365i 0.778673 1.34870i
\(623\) −12.0716 + 12.0716i −0.483638 + 0.483638i
\(624\) 11.4641 19.8564i 0.458931 0.794892i
\(625\) 0 0
\(626\) −2.97372 11.0981i −0.118854 0.443568i
\(627\) −10.1769 10.1769i −0.406426 0.406426i
\(628\) −18.8009 5.03768i −0.750237 0.201025i
\(629\) 17.5692i 0.700531i
\(630\) 0 0
\(631\) 1.58846i 0.0632355i −0.999500 0.0316177i \(-0.989934\pi\)
0.999500 0.0316177i \(-0.0100659\pi\)
\(632\) 1.51575i 0.0602933i
\(633\) 5.08845 + 5.08845i 0.202248 + 0.202248i
\(634\) 9.46410 2.53590i 0.375867 0.100713i
\(635\) 0 0
\(636\) −1.46410 2.53590i −0.0580554 0.100555i
\(637\) −3.76217 + 3.76217i −0.149062 + 0.149062i
\(638\) −18.2832 10.5558i −0.723840 0.417909i
\(639\) 9.46410 0.374394
\(640\) 0 0
\(641\) −3.21539 −0.127000 −0.0635001 0.997982i \(-0.520226\pi\)
−0.0635001 + 0.997982i \(0.520226\pi\)
\(642\) 8.00481 + 4.62158i 0.315925 + 0.182399i
\(643\) −12.0716 + 12.0716i −0.476057 + 0.476057i −0.903868 0.427811i \(-0.859285\pi\)
0.427811 + 0.903868i \(0.359285\pi\)
\(644\) 1.32051 + 2.28719i 0.0520353 + 0.0901278i
\(645\) 0 0
\(646\) −58.9808 + 15.8038i −2.32057 + 0.621794i
\(647\) 3.58630 + 3.58630i 0.140992 + 0.140992i 0.774080 0.633088i \(-0.218213\pi\)
−0.633088 + 0.774080i \(0.718213\pi\)
\(648\) 2.82843i 0.111111i
\(649\) 9.07180i 0.356099i
\(650\) 0 0
\(651\) 0.660254i 0.0258774i
\(652\) −27.9425 7.48717i −1.09431 0.293220i
\(653\) −7.34847 7.34847i −0.287568 0.287568i 0.548550 0.836118i \(-0.315180\pi\)
−0.836118 + 0.548550i \(0.815180\pi\)
\(654\) 2.56218 + 9.56218i 0.100189 + 0.373911i
\(655\) 0 0
\(656\) 10.9282 18.9282i 0.426675 0.739022i
\(657\) 2.82843 2.82843i 0.110347 0.110347i
\(658\) 22.5259 39.0160i 0.878150 1.52100i
\(659\) −14.5359 −0.566238 −0.283119 0.959085i \(-0.591369\pi\)
−0.283119 + 0.959085i \(0.591369\pi\)
\(660\) 0 0
\(661\) −7.85641 −0.305579 −0.152789 0.988259i \(-0.548826\pi\)
−0.152789 + 0.988259i \(0.548826\pi\)
\(662\) 1.69161 2.92996i 0.0657465 0.113876i
\(663\) 24.3190 24.3190i 0.944473 0.944473i
\(664\) 1.85641 + 1.85641i 0.0720425 + 0.0720425i
\(665\) 0 0
\(666\) 1.07180 + 4.00000i 0.0415313 + 0.154997i
\(667\) −2.82843 2.82843i −0.109517 0.109517i
\(668\) −2.27362 + 8.48528i −0.0879692 + 0.328305i
\(669\) 11.3923i 0.440452i
\(670\) 0 0
\(671\) 6.00000i 0.231627i
\(672\) −12.0716 + 6.96953i −0.465671 + 0.268856i
\(673\) −2.82843 2.82843i −0.109028 0.109028i 0.650488 0.759516i \(-0.274564\pi\)
−0.759516 + 0.650488i \(0.774564\pi\)
\(674\) −15.4904 + 4.15064i −0.596667 + 0.159876i
\(675\) 0 0
\(676\) −34.3923 + 19.8564i −1.32278 + 0.763708i
\(677\) 25.9091 25.9091i 0.995768 0.995768i −0.00422306 0.999991i \(-0.501344\pi\)
0.999991 + 0.00422306i \(0.00134424\pi\)
\(678\) 16.9706 + 9.79796i 0.651751 + 0.376288i
\(679\) 15.4449 0.592719
\(680\) 0 0
\(681\) 12.3923 0.474874
\(682\) −0.656339 0.378937i −0.0251325 0.0145103i
\(683\) 3.58630 3.58630i 0.137226 0.137226i −0.635157 0.772383i \(-0.719065\pi\)
0.772383 + 0.635157i \(0.219065\pi\)
\(684\) 12.4641 7.19615i 0.476577 0.275152i
\(685\) 0 0
\(686\) 26.6865 7.15064i 1.01890 0.273013i
\(687\) −17.5761 17.5761i −0.670571 0.670571i
\(688\) −2.55103 9.52056i −0.0972569 0.362968i
\(689\) 8.39230i 0.319721i
\(690\) 0 0
\(691\) 25.3205i 0.963238i 0.876381 + 0.481619i \(0.159951\pi\)
−0.876381 + 0.481619i \(0.840049\pi\)
\(692\) 4.62158 17.2480i 0.175686 0.655669i
\(693\) −3.48477 3.48477i −0.132375 0.132375i
\(694\) 4.05256 + 15.1244i 0.153833 + 0.574113i
\(695\) 0 0
\(696\) 14.9282 14.9282i 0.565852 0.565852i
\(697\) 23.1822 23.1822i 0.878089 0.878089i
\(698\) −2.72689 + 4.72311i −0.103214 + 0.178773i
\(699\) −12.3923 −0.468720
\(700\) 0 0
\(701\) −15.4641 −0.584071 −0.292036 0.956407i \(-0.594333\pi\)
−0.292036 + 0.956407i \(0.594333\pi\)
\(702\) −4.05317 + 7.02030i −0.152977 + 0.264964i
\(703\) −14.9000 + 14.9000i −0.561965 + 0.561965i
\(704\) 16.0000i 0.603023i
\(705\) 0 0
\(706\) 5.80385 + 21.6603i 0.218431 + 0.815194i
\(707\) −2.55103 2.55103i −0.0959412 0.0959412i
\(708\) −8.76268 2.34795i −0.329322 0.0882415i
\(709\) 24.8564i 0.933502i −0.884389 0.466751i \(-0.845424\pi\)
0.884389 0.466751i \(-0.154576\pi\)
\(710\) 0 0
\(711\) 0.535898i 0.0200978i
\(712\) −19.5959 −0.734388
\(713\) −0.101536 0.101536i −0.00380255 0.00380255i
\(714\) −20.1962 + 5.41154i −0.755822 + 0.202522i
\(715\) 0 0
\(716\) 25.3205 + 43.8564i 0.946272 + 1.63899i
\(717\) −12.3490 + 12.3490i −0.461181 + 0.461181i
\(718\) 29.8744 + 17.2480i 1.11490 + 0.643688i
\(719\) 12.9282 0.482141 0.241070 0.970508i \(-0.422502\pi\)
0.241070 + 0.970508i \(0.422502\pi\)
\(720\) 0 0
\(721\) 17.0718 0.635787
\(722\) 40.1528 + 23.1822i 1.49433 + 0.862753i
\(723\) −10.5051 + 10.5051i −0.390688 + 0.390688i
\(724\) −13.9282 24.1244i −0.517638 0.896575i
\(725\) 0 0
\(726\) 9.56218 2.56218i 0.354886 0.0950913i
\(727\) 33.3083 + 33.3083i 1.23534 + 1.23534i 0.961885 + 0.273453i \(0.0881658\pi\)
0.273453 + 0.961885i \(0.411834\pi\)
\(728\) 39.9497 1.48063
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 14.7846i 0.546829i
\(732\) 5.79555 + 1.55291i 0.214210 + 0.0573974i
\(733\) −13.9391 13.9391i −0.514851 0.514851i 0.401158 0.916009i \(-0.368608\pi\)
−0.916009 + 0.401158i \(0.868608\pi\)
\(734\) −3.88269 14.4904i −0.143313 0.534850i
\(735\) 0 0
\(736\) −0.784610 + 2.92820i −0.0289211 + 0.107935i
\(737\) 17.6269 17.6269i 0.649295 0.649295i
\(738\) −3.86370 + 6.69213i −0.142225 + 0.246341i
\(739\) 14.3923 0.529429 0.264715 0.964327i \(-0.414722\pi\)
0.264715 + 0.964327i \(0.414722\pi\)
\(740\) 0 0
\(741\) −41.2487 −1.51531
\(742\) 2.55103 4.41851i 0.0936511 0.162208i
\(743\) 21.8695 21.8695i 0.802316 0.802316i −0.181141 0.983457i \(-0.557979\pi\)
0.983457 + 0.181141i \(0.0579792\pi\)
\(744\) 0.535898 0.535898i 0.0196470 0.0196470i
\(745\) 0 0
\(746\) −7.07884 26.4186i −0.259175 0.967253i
\(747\) −0.656339 0.656339i −0.0240142 0.0240142i
\(748\) −6.21166 + 23.1822i −0.227121 + 0.847626i
\(749\) 16.1051i 0.588468i
\(750\) 0 0
\(751\) 11.4641i 0.418331i 0.977880 + 0.209166i \(0.0670747\pi\)
−0.977880 + 0.209166i \(0.932925\pi\)
\(752\) 49.9507 13.3843i 1.82152 0.488074i
\(753\) 1.51575 + 1.51575i 0.0552370 + 0.0552370i
\(754\) −58.4449 + 15.6603i −2.12844 + 0.570313i
\(755\) 0 0
\(756\) 4.26795 2.46410i 0.155224 0.0896185i
\(757\) −20.6448 + 20.6448i −0.750348 + 0.750348i −0.974544 0.224196i \(-0.928024\pi\)
0.224196 + 0.974544i \(0.428024\pi\)
\(758\) −19.2677 11.1242i −0.699836 0.404051i
\(759\) −1.07180 −0.0389038
\(760\) 0 0
\(761\) 46.6410 1.69074 0.845368 0.534185i \(-0.179381\pi\)
0.845368 + 0.534185i \(0.179381\pi\)
\(762\) 3.58630 + 2.07055i 0.129918 + 0.0750082i
\(763\) −12.1967 + 12.1967i −0.441549 + 0.441549i
\(764\) −29.3205 + 16.9282i −1.06078 + 0.612441i
\(765\) 0 0
\(766\) 22.9282 6.14359i 0.828430 0.221977i
\(767\) 18.3848 + 18.3848i 0.663836 + 0.663836i
\(768\) −15.4548 4.14110i −0.557678 0.149429i
\(769\) 29.9282i 1.07924i 0.841909 + 0.539619i \(0.181432\pi\)
−0.841909 + 0.539619i \(0.818568\pi\)
\(770\) 0 0
\(771\) 12.7846i 0.460426i
\(772\) 7.10823 26.5283i 0.255831 0.954774i
\(773\) −23.4596 23.4596i −0.843784 0.843784i 0.145565 0.989349i \(-0.453500\pi\)
−0.989349 + 0.145565i \(0.953500\pi\)
\(774\) 0.901924 + 3.36603i 0.0324190 + 0.120989i
\(775\) 0 0
\(776\) 12.5359 + 12.5359i 0.450013 + 0.450013i
\(777\) −5.10205 + 5.10205i −0.183035 + 0.183035i
\(778\) −10.2784 + 17.8028i −0.368500 + 0.638260i
\(779\) −39.3205 −1.40880
\(780\) 0 0
\(781\) 18.9282 0.677304
\(782\) −2.27362 + 3.93803i −0.0813046 + 0.140824i
\(783\) −5.27792 + 5.27792i −0.188617 + 0.188617i
\(784\) 3.21539 + 1.85641i 0.114835 + 0.0663002i
\(785\) 0 0
\(786\) −3.46410 12.9282i −0.123560 0.461134i
\(787\) 10.0246 + 10.0246i 0.357338 + 0.357338i 0.862831 0.505493i \(-0.168689\pi\)
−0.505493 + 0.862831i \(0.668689\pi\)
\(788\) 27.8038 + 7.45001i 0.990469 + 0.265395i
\(789\) 21.4641i 0.764142i
\(790\) 0 0
\(791\) 34.1436i 1.21401i
\(792\) 5.65685i 0.201008i
\(793\) −12.1595 12.1595i −0.431797 0.431797i
\(794\) 26.7583 7.16987i 0.949618 0.254449i
\(795\) 0 0
\(796\) −14.1244 24.4641i −0.500625 0.867107i
\(797\) −9.79796 + 9.79796i −0.347062 + 0.347062i −0.859014 0.511952i \(-0.828922\pi\)
0.511952 + 0.859014i \(0.328922\pi\)
\(798\) 21.7172 + 12.5385i 0.768782 + 0.443856i
\(799\) 77.5692 2.74420
\(800\) 0 0
\(801\) 6.92820 0.244796
\(802\) −40.6333 23.4596i −1.43481 0.828388i
\(803\) 5.65685 5.65685i 0.199626 0.199626i
\(804\) 12.4641 + 21.5885i 0.439575 + 0.761366i
\(805\) 0 0
\(806\) −2.09808 + 0.562178i −0.0739016 + 0.0198019i
\(807\) 1.13681 + 1.13681i 0.0400177 + 0.0400177i
\(808\) 4.14110i 0.145684i
\(809\) 49.1769i 1.72897i −0.502660 0.864484i \(-0.667645\pi\)
0.502660 0.864484i \(-0.332355\pi\)
\(810\) 0 0
\(811\) 26.1244i 0.917350i −0.888604 0.458675i \(-0.848324\pi\)
0.888604 0.458675i \(-0.151676\pi\)
\(812\) 35.5312 + 9.52056i 1.24690 + 0.334106i
\(813\) 17.1464 + 17.1464i 0.601351 + 0.601351i
\(814\) 2.14359 + 8.00000i 0.0751329 + 0.280400i
\(815\) 0 0
\(816\) −20.7846 12.0000i −0.727607 0.420084i
\(817\) −12.5385 + 12.5385i −0.438665 + 0.438665i
\(818\) 19.6467 34.0291i 0.686930 1.18980i
\(819\) −14.1244 −0.493545
\(820\) 0 0
\(821\) 55.5692 1.93938 0.969690 0.244340i \(-0.0785714\pi\)
0.969690 + 0.244340i \(0.0785714\pi\)
\(822\) 6.03579 10.4543i 0.210522 0.364636i
\(823\) 33.5114 33.5114i 1.16813 1.16813i 0.185488 0.982646i \(-0.440613\pi\)
0.982646 0.185488i \(-0.0593866\pi\)
\(824\) 13.8564 + 13.8564i 0.482711 + 0.482711i
\(825\) 0 0
\(826\) −4.09103 15.2679i −0.142345 0.531240i
\(827\) −30.0774 30.0774i −1.04589 1.04589i −0.998895 0.0469995i \(-0.985034\pi\)
−0.0469995 0.998895i \(-0.514966\pi\)
\(828\) 0.277401 1.03528i 0.00964037 0.0359783i
\(829\) 17.7128i 0.615191i −0.951517 0.307596i \(-0.900476\pi\)
0.951517 0.307596i \(-0.0995244\pi\)
\(830\) 0 0
\(831\) 1.19615i 0.0414941i
\(832\) 32.4254 + 32.4254i 1.12415 + 1.12415i
\(833\) 3.93803 + 3.93803i 0.136445 + 0.136445i
\(834\) 26.5885 7.12436i 0.920683 0.246696i
\(835\) 0 0
\(836\) 24.9282 14.3923i 0.862160 0.497768i
\(837\) −0.189469 + 0.189469i −0.00654900 + 0.00654900i
\(838\) 32.4997 + 18.7637i 1.12268 + 0.648182i
\(839\) 40.6410 1.40308 0.701542 0.712628i \(-0.252495\pi\)
0.701542 + 0.712628i \(0.252495\pi\)
\(840\) 0 0
\(841\) −26.7128 −0.921131
\(842\) 8.30942 + 4.79744i 0.286361 + 0.165331i
\(843\) −10.1769 + 10.1769i −0.350511 + 0.350511i
\(844\) −12.4641 + 7.19615i −0.429032 + 0.247702i
\(845\) 0 0
\(846\) −17.6603 + 4.73205i −0.607172 + 0.162691i
\(847\) 12.1967 + 12.1967i 0.419083 + 0.419083i
\(848\) 5.65685 1.51575i 0.194257 0.0520511i
\(849\) 21.3923i 0.734182i
\(850\) 0 0
\(851\) 1.56922i 0.0537921i
\(852\) −4.89898 + 18.2832i −0.167836 + 0.626373i
\(853\) −11.0227 11.0227i −0.377410 0.377410i 0.492757 0.870167i \(-0.335989\pi\)
−0.870167 + 0.492757i \(0.835989\pi\)
\(854\) 2.70577 + 10.0981i 0.0925896 + 0.345549i
\(855\) 0 0
\(856\) −13.0718 + 13.0718i −0.446785 + 0.446785i
\(857\) −33.7381 + 33.7381i −1.15247 + 1.15247i −0.166414 + 0.986056i \(0.553219\pi\)
−0.986056 + 0.166414i \(0.946781\pi\)
\(858\) −8.10634 + 14.0406i −0.276746 + 0.479338i
\(859\) 21.6077 0.737245 0.368623 0.929579i \(-0.379830\pi\)
0.368623 + 0.929579i \(0.379830\pi\)
\(860\) 0 0
\(861\) −13.4641 −0.458855
\(862\) −18.1817 + 31.4916i −0.619271 + 1.07261i
\(863\) −27.3233 + 27.3233i −0.930097 + 0.930097i −0.997712 0.0676147i \(-0.978461\pi\)
0.0676147 + 0.997712i \(0.478461\pi\)
\(864\) 5.46410 + 1.46410i 0.185893 + 0.0498097i
\(865\) 0 0
\(866\) 1.61474 + 6.02628i 0.0548710 + 0.204781i
\(867\) −13.4350 13.4350i −0.456278 0.456278i
\(868\) 1.27551 + 0.341773i 0.0432937 + 0.0116005i
\(869\) 1.07180i 0.0363582i
\(870\) 0 0
\(871\) 71.4449i 2.42082i
\(872\) −19.7990 −0.670478
\(873\) −4.43211 4.43211i −0.150004 0.150004i
\(874\) 5.26795 1.41154i 0.178191 0.0477461i
\(875\) 0 0
\(876\) 4.00000 + 6.92820i 0.135147 + 0.234082i
\(877\) −22.5123 + 22.5123i −0.760186 + 0.760186i −0.976356 0.216170i \(-0.930643\pi\)
0.216170 + 0.976356i \(0.430643\pi\)
\(878\) −34.2693 19.7854i −1.15653 0.667724i
\(879\) −12.5359 −0.422825
\(880\) 0 0
\(881\) −50.9282 −1.71581 −0.857907 0.513804i \(-0.828236\pi\)
−0.857907 + 0.513804i \(0.828236\pi\)
\(882\) −1.13681 0.656339i −0.0382785 0.0221001i
\(883\) −21.3383 + 21.3383i −0.718091 + 0.718091i −0.968214 0.250123i \(-0.919529\pi\)
0.250123 + 0.968214i \(0.419529\pi\)
\(884\) 34.3923 + 59.5692i 1.15674 + 2.00353i
\(885\) 0 0
\(886\) −17.4641 + 4.67949i −0.586718 + 0.157211i
\(887\) 5.55532 + 5.55532i 0.186529 + 0.186529i 0.794194 0.607665i \(-0.207893\pi\)
−0.607665 + 0.794194i \(0.707893\pi\)
\(888\) −8.28221 −0.277933
\(889\) 7.21539i 0.241996i
\(890\) 0 0
\(891\) 2.00000i 0.0670025i
\(892\) −22.0082 5.89709i −0.736890 0.197449i
\(893\) −65.7845 65.7845i −2.20139 2.20139i
\(894\) 5.80385 + 21.6603i 0.194110 + 0.724427i
\(895\) 0 0
\(896\) −7.21539 26.9282i −0.241049 0.899608i
\(897\) −2.17209 + 2.17209i −0.0725239 + 0.0725239i
\(898\) −23.9401 + 41.4655i −0.798891 + 1.38372i
\(899\) −2.00000 −0.0667037
\(900\) 0 0
\(901\) 8.78461 0.292658
\(902\) −7.72741 + 13.3843i −0.257294 + 0.445647i
\(903\) −4.29341 + 4.29341i −0.142876 + 0.142876i
\(904\) −27.7128 + 27.7128i −0.921714 + 0.921714i
\(905\) 0 0
\(906\) −1.56218 5.83013i −0.0518999 0.193693i
\(907\) −6.96953 6.96953i −0.231420 0.231420i 0.581866 0.813285i \(-0.302323\pi\)
−0.813285 + 0.581866i \(0.802323\pi\)
\(908\) −6.41473 + 23.9401i −0.212880 + 0.794480i
\(909\) 1.46410i 0.0485612i
\(910\) 0 0
\(911\) 26.3923i 0.874416i 0.899360 + 0.437208i \(0.144033\pi\)
−0.899360 + 0.437208i \(0.855967\pi\)
\(912\) 7.45001 + 27.8038i 0.246694 + 0.920676i
\(913\) −1.31268 1.31268i −0.0434433 0.0434433i
\(914\) 48.7846 13.0718i 1.61365 0.432377i
\(915\) 0 0
\(916\) 43.0526 24.8564i 1.42250 0.821279i
\(917\) 16.4901 16.4901i 0.544551 0.544551i
\(918\) 7.34847 + 4.24264i 0.242536 + 0.140028i
\(919\) 9.33975 0.308090 0.154045 0.988064i \(-0.450770\pi\)
0.154045 + 0.988064i \(0.450770\pi\)
\(920\) 0 0
\(921\) −13.3923 −0.441291
\(922\) 19.1154 + 11.0363i 0.629534 + 0.363461i
\(923\) 38.3596 38.3596i 1.26262 1.26262i
\(924\) 8.53590 4.92820i 0.280810 0.162126i
\(925\) 0 0
\(926\) −17.8564 + 4.78461i −0.586798 + 0.157232i
\(927\) −4.89898 4.89898i −0.160904 0.160904i
\(928\) 21.1117 + 36.5665i 0.693024 + 1.20035i
\(929\) 7.46410i 0.244889i −0.992475 0.122445i \(-0.960927\pi\)
0.992475 0.122445i \(-0.0390734\pi\)
\(930\) 0 0
\(931\) 6.67949i 0.218912i
\(932\) 6.41473 23.9401i 0.210121 0.784184i
\(933\) −19.4201 19.4201i −0.635784 0.635784i
\(934\) 1.26795 + 4.73205i 0.0414886 + 0.154837i
\(935\) 0 0
\(936\) −11.4641 11.4641i −0.374716 0.374716i
\(937\) −37.4123 + 37.4123i −1.22221 + 1.22221i −0.255360 + 0.966846i \(0.582194\pi\)
−0.966846 + 0.255360i \(0.917806\pi\)
\(938\) −21.7172 + 37.6154i −0.709093 + 1.22819i
\(939\) −8.12436 −0.265128
\(940\) 0 0
\(941\) 24.9282 0.812636 0.406318 0.913732i \(-0.366812\pi\)
0.406318 + 0.913732i \(0.366812\pi\)
\(942\) −6.88160 + 11.9193i −0.224215 + 0.388351i
\(943\) −2.07055 + 2.07055i −0.0674265 + 0.0674265i
\(944\) 9.07180 15.7128i 0.295262 0.511409i
\(945\) 0 0
\(946\) 1.80385 + 6.73205i 0.0586481 + 0.218878i
\(947\) 11.4896 + 11.4896i 0.373361 + 0.373361i 0.868700 0.495339i \(-0.164956\pi\)
−0.495339 + 0.868700i \(0.664956\pi\)
\(948\) 1.03528 + 0.277401i 0.0336242 + 0.00900958i
\(949\) 22.9282i 0.744281i
\(950\) 0 0
\(951\) 6.92820i 0.224662i
\(952\) 41.8172i 1.35530i
\(953\) −11.1106 11.1106i −0.359909 0.359909i 0.503870 0.863779i \(-0.331909\pi\)
−0.863779 + 0.503870i \(0.831909\pi\)
\(954\) −2.00000 + 0.535898i −0.0647524 + 0.0173504i
\(955\) 0 0
\(956\) −17.4641 30.2487i −0.564829 0.978313i
\(957\) −10.5558 + 10.5558i −0.341222 + 0.341222i
\(958\) 16.3142 + 9.41902i 0.527089 + 0.304315i
\(959\) 21.0333 0.679201
\(960\) 0 0
\(961\) 30.9282 0.997684
\(962\) 20.5569 + 11.8685i 0.662780 + 0.382656i
\(963\) 4.62158 4.62158i 0.148928 0.148928i
\(964\) −14.8564 25.7321i −0.478493 0.828774i
\(965\) 0 0
\(966\) 1.80385 0.483340i 0.0580378 0.0155512i
\(967\) 33.9411 + 33.9411i 1.09147 + 1.09147i 0.995372 + 0.0961015i \(0.0306373\pi\)
0.0961015 + 0.995372i \(0.469363\pi\)
\(968\) 19.7990i 0.636364i
\(969\) 43.1769i 1.38704i
\(970\) 0 0
\(971\) 19.1769i 0.615416i 0.951481 + 0.307708i \(0.0995621\pi\)
−0.951481 + 0.307708i \(0.900438\pi\)
\(972\) −1.93185 0.517638i −0.0619642 0.0166032i
\(973\) 33.9139 + 33.9139i 1.08723 + 1.08723i
\(974\) 7.88269 + 29.4186i 0.252578 + 0.942632i
\(975\) 0 0
\(976\) −6.00000 + 10.3923i −0.192055 + 0.332650i
\(977\) 27.7023 27.7023i 0.886274 0.886274i −0.107889 0.994163i \(-0.534409\pi\)
0.994163 + 0.107889i \(0.0344091\pi\)
\(978\) −10.2277 + 17.7148i −0.327045 + 0.566458i
\(979\) 13.8564 0.442853
\(980\) 0 0
\(981\) 7.00000 0.223493
\(982\) 24.4949 42.4264i 0.781664 1.35388i
\(983\) 18.2832 18.2832i 0.583145 0.583145i −0.352621 0.935766i \(-0.614710\pi\)
0.935766 + 0.352621i \(0.114710\pi\)
\(984\) −10.9282 10.9282i −0.348378 0.348378i
\(985\) 0 0
\(986\) 16.3923 + 61.1769i 0.522037 + 1.94827i
\(987\) −22.5259 22.5259i −0.717007 0.717007i
\(988\) 21.3519 79.6864i 0.679295 2.53516i
\(989\) 1.32051i 0.0419897i
\(990\) 0 0
\(991\) 57.5885i 1.82936i −0.404181 0.914679i \(-0.632444\pi\)
0.404181 0.914679i \(-0.367556\pi\)
\(992\) 0.757875 + 1.31268i 0.0240625 + 0.0416776i
\(993\) −1.69161 1.69161i −0.0536818 0.0536818i
\(994\) −31.8564 + 8.53590i −1.01042 + 0.270742i
\(995\) 0 0
\(996\) 1.60770 0.928203i 0.0509418 0.0294112i
\(997\) −19.5959 + 19.5959i −0.620609 + 0.620609i −0.945687 0.325078i \(-0.894609\pi\)
0.325078 + 0.945687i \(0.394609\pi\)
\(998\) 7.19617 + 4.15471i 0.227791 + 0.131515i
\(999\) 2.92820 0.0926443
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 300.2.j.c.43.4 yes 8
3.2 odd 2 900.2.k.l.343.1 8
4.3 odd 2 300.2.j.a.43.1 yes 8
5.2 odd 4 300.2.j.a.7.2 8
5.3 odd 4 300.2.j.a.7.3 yes 8
5.4 even 2 inner 300.2.j.c.43.1 yes 8
12.11 even 2 900.2.k.g.343.4 8
15.2 even 4 900.2.k.g.307.3 8
15.8 even 4 900.2.k.g.307.2 8
15.14 odd 2 900.2.k.l.343.4 8
20.3 even 4 inner 300.2.j.c.7.2 yes 8
20.7 even 4 inner 300.2.j.c.7.3 yes 8
20.19 odd 2 300.2.j.a.43.4 yes 8
60.23 odd 4 900.2.k.l.307.3 8
60.47 odd 4 900.2.k.l.307.2 8
60.59 even 2 900.2.k.g.343.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
300.2.j.a.7.2 8 5.2 odd 4
300.2.j.a.7.3 yes 8 5.3 odd 4
300.2.j.a.43.1 yes 8 4.3 odd 2
300.2.j.a.43.4 yes 8 20.19 odd 2
300.2.j.c.7.2 yes 8 20.3 even 4 inner
300.2.j.c.7.3 yes 8 20.7 even 4 inner
300.2.j.c.43.1 yes 8 5.4 even 2 inner
300.2.j.c.43.4 yes 8 1.1 even 1 trivial
900.2.k.g.307.2 8 15.8 even 4
900.2.k.g.307.3 8 15.2 even 4
900.2.k.g.343.1 8 60.59 even 2
900.2.k.g.343.4 8 12.11 even 2
900.2.k.l.307.2 8 60.47 odd 4
900.2.k.l.307.3 8 60.23 odd 4
900.2.k.l.343.1 8 3.2 odd 2
900.2.k.l.343.4 8 15.14 odd 2