Properties

Label 52.2.f.b.47.2
Level $52$
Weight $2$
Character 52.47
Analytic conductor $0.415$
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] = [52,2,Mod(31,52)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(52, 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("52.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 52 = 2^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 52.f (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: \(0.415222090511\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.18939904.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.2
Root \(0.500000 + 2.10607i\) of defining polynomial
Character \(\chi\) \(=\) 52.47
Dual form 52.2.f.b.31.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.13567 + 0.842772i) q^{2} -2.79793i q^{3} +(0.579471 - 1.91421i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(2.35802 + 3.17751i) q^{6} +(1.97844 + 1.97844i) q^{7} +(0.955161 + 2.66227i) q^{8} -4.82843 q^{9} +O(q^{10})\) \(q+(-1.13567 + 0.842772i) q^{2} -2.79793i q^{3} +(0.579471 - 1.91421i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(2.35802 + 3.17751i) q^{6} +(1.97844 + 1.97844i) q^{7} +(0.955161 + 2.66227i) q^{8} -4.82843 q^{9} +(1.39897 + 0.207107i) q^{10} +(-1.15894 - 1.15894i) q^{11} +(-5.35584 - 1.62132i) q^{12} +(3.53553 + 0.707107i) q^{13} +(-3.91421 - 0.579471i) q^{14} +(-1.97844 + 1.97844i) q^{15} +(-3.32843 - 2.21846i) q^{16} +5.82843i q^{17} +(5.48348 - 4.06926i) q^{18} +(-1.63899 + 1.63899i) q^{19} +(-1.76330 + 0.943806i) q^{20} +(5.53553 - 5.53553i) q^{21} +(2.29289 + 0.339446i) q^{22} +3.95687 q^{23} +(7.44885 - 2.67248i) q^{24} -4.00000i q^{25} +(-4.61111 + 2.17661i) q^{26} +5.11582i q^{27} +(4.93360 - 2.64070i) q^{28} -0.585786 q^{29} +(0.579471 - 3.91421i) q^{30} +(-3.95687 + 3.95687i) q^{31} +(5.64964 - 0.285675i) q^{32} +(-3.24264 + 3.24264i) q^{33} +(-4.91203 - 6.61914i) q^{34} -2.79793i q^{35} +(-2.79793 + 9.24264i) q^{36} +(-1.87868 + 1.87868i) q^{37} +(0.480049 - 3.24264i) q^{38} +(1.97844 - 9.89219i) q^{39} +(1.20711 - 2.55791i) q^{40} +(-4.24264 - 4.24264i) q^{41} +(-1.62132 + 10.9517i) q^{42} -5.11582 q^{43} +(-2.89003 + 1.54689i) q^{44} +(3.41421 + 3.41421i) q^{45} +(-4.49368 + 3.33474i) q^{46} +(-1.97844 - 1.97844i) q^{47} +(-6.20711 + 9.31271i) q^{48} +0.828427i q^{49} +(3.37109 + 4.54266i) q^{50} +16.3075 q^{51} +(3.40229 - 6.35802i) q^{52} -0.242641 q^{53} +(-4.31147 - 5.80985i) q^{54} +1.63899i q^{55} +(-3.37740 + 7.15685i) q^{56} +(4.58579 + 4.58579i) q^{57} +(0.665257 - 0.493684i) q^{58} +(2.31788 + 2.31788i) q^{59} +(2.64070 + 4.93360i) q^{60} +0.828427 q^{61} +(1.15894 - 7.82843i) q^{62} +(-9.55274 - 9.55274i) q^{63} +(-6.17534 + 5.08579i) q^{64} +(-2.00000 - 3.00000i) q^{65} +(0.949747 - 6.41536i) q^{66} +(2.79793 - 2.79793i) q^{67} +(11.1569 + 3.37740i) q^{68} -11.0711i q^{69} +(2.35802 + 3.17751i) q^{70} +(5.25642 - 5.25642i) q^{71} +(-4.61192 - 12.8546i) q^{72} +(-9.65685 + 9.65685i) q^{73} +(0.550253 - 3.71685i) q^{74} -11.1917 q^{75} +(2.18763 + 4.08713i) q^{76} -4.58579i q^{77} +(6.09001 + 12.9016i) q^{78} +9.55274i q^{79} +(0.784864 + 3.92224i) q^{80} -0.171573 q^{81} +(8.39380 + 1.24264i) q^{82} +(-6.75481 + 6.75481i) q^{83} +(-7.38851 - 13.8039i) q^{84} +(4.12132 - 4.12132i) q^{85} +(5.80985 - 4.31147i) q^{86} +1.63899i q^{87} +(1.97844 - 4.19239i) q^{88} +(6.24264 - 6.24264i) q^{89} +(-6.75481 - 1.00000i) q^{90} +(5.59587 + 8.39380i) q^{91} +(2.29289 - 7.57430i) q^{92} +(11.0711 + 11.0711i) q^{93} +(3.91421 + 0.579471i) q^{94} +2.31788 q^{95} +(-0.799300 - 15.8073i) q^{96} +(0.414214 + 0.414214i) q^{97} +(-0.698175 - 0.940816i) q^{98} +(5.59587 + 5.59587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} + 8 q^{6} - 4 q^{8} - 16 q^{9} - 20 q^{14} - 4 q^{16} - 8 q^{20} + 16 q^{21} + 24 q^{22} + 32 q^{24} + 8 q^{26} + 12 q^{28} - 16 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{34} - 32 q^{37} + 4 q^{40} + 4 q^{42} - 28 q^{44} + 16 q^{45} - 20 q^{46} - 44 q^{48} - 16 q^{50} + 8 q^{52} + 32 q^{53} - 32 q^{54} + 48 q^{57} + 12 q^{58} - 12 q^{60} - 16 q^{61} - 16 q^{65} - 32 q^{66} + 44 q^{68} + 8 q^{70} + 16 q^{72} - 32 q^{73} + 44 q^{74} + 32 q^{76} + 40 q^{78} + 16 q^{80} - 24 q^{81} - 48 q^{84} + 16 q^{85} + 32 q^{86} + 16 q^{89} + 24 q^{92} + 32 q^{93} + 20 q^{94} - 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/52\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13567 + 0.842772i −0.803037 + 0.595930i
\(3\) 2.79793i 1.61539i −0.589602 0.807694i \(-0.700716\pi\)
0.589602 0.807694i \(-0.299284\pi\)
\(4\) 0.579471 1.91421i 0.289735 0.957107i
\(5\) −0.707107 0.707107i −0.316228 0.316228i 0.531089 0.847316i \(-0.321783\pi\)
−0.847316 + 0.531089i \(0.821783\pi\)
\(6\) 2.35802 + 3.17751i 0.962657 + 1.29721i
\(7\) 1.97844 + 1.97844i 0.747779 + 0.747779i 0.974062 0.226283i \(-0.0726573\pi\)
−0.226283 + 0.974062i \(0.572657\pi\)
\(8\) 0.955161 + 2.66227i 0.337700 + 0.941254i
\(9\) −4.82843 −1.60948
\(10\) 1.39897 + 0.207107i 0.442392 + 0.0654929i
\(11\) −1.15894 1.15894i −0.349434 0.349434i 0.510465 0.859899i \(-0.329473\pi\)
−0.859899 + 0.510465i \(0.829473\pi\)
\(12\) −5.35584 1.62132i −1.54610 0.468035i
\(13\) 3.53553 + 0.707107i 0.980581 + 0.196116i
\(14\) −3.91421 0.579471i −1.04612 0.154870i
\(15\) −1.97844 + 1.97844i −0.510830 + 0.510830i
\(16\) −3.32843 2.21846i −0.832107 0.554615i
\(17\) 5.82843i 1.41360i 0.707413 + 0.706801i \(0.249862\pi\)
−0.707413 + 0.706801i \(0.750138\pi\)
\(18\) 5.48348 4.06926i 1.29247 0.959134i
\(19\) −1.63899 + 1.63899i −0.376010 + 0.376010i −0.869661 0.493650i \(-0.835662\pi\)
0.493650 + 0.869661i \(0.335662\pi\)
\(20\) −1.76330 + 0.943806i −0.394286 + 0.211041i
\(21\) 5.53553 5.53553i 1.20795 1.20795i
\(22\) 2.29289 + 0.339446i 0.488846 + 0.0723702i
\(23\) 3.95687 0.825065 0.412533 0.910943i \(-0.364644\pi\)
0.412533 + 0.910943i \(0.364644\pi\)
\(24\) 7.44885 2.67248i 1.52049 0.545517i
\(25\) 4.00000i 0.800000i
\(26\) −4.61111 + 2.17661i −0.904314 + 0.426869i
\(27\) 5.11582i 0.984539i
\(28\) 4.93360 2.64070i 0.932362 0.499046i
\(29\) −0.585786 −0.108778 −0.0543889 0.998520i \(-0.517321\pi\)
−0.0543889 + 0.998520i \(0.517321\pi\)
\(30\) 0.579471 3.91421i 0.105796 0.714634i
\(31\) −3.95687 + 3.95687i −0.710676 + 0.710676i −0.966677 0.256001i \(-0.917595\pi\)
0.256001 + 0.966677i \(0.417595\pi\)
\(32\) 5.64964 0.285675i 0.998724 0.0505007i
\(33\) −3.24264 + 3.24264i −0.564471 + 0.564471i
\(34\) −4.91203 6.61914i −0.842407 1.13517i
\(35\) 2.79793i 0.472937i
\(36\) −2.79793 + 9.24264i −0.466322 + 1.54044i
\(37\) −1.87868 + 1.87868i −0.308853 + 0.308853i −0.844465 0.535611i \(-0.820081\pi\)
0.535611 + 0.844465i \(0.320081\pi\)
\(38\) 0.480049 3.24264i 0.0778743 0.526026i
\(39\) 1.97844 9.89219i 0.316803 1.58402i
\(40\) 1.20711 2.55791i 0.190860 0.404441i
\(41\) −4.24264 4.24264i −0.662589 0.662589i 0.293400 0.955990i \(-0.405213\pi\)
−0.955990 + 0.293400i \(0.905213\pi\)
\(42\) −1.62132 + 10.9517i −0.250175 + 1.68988i
\(43\) −5.11582 −0.780155 −0.390077 0.920782i \(-0.627552\pi\)
−0.390077 + 0.920782i \(0.627552\pi\)
\(44\) −2.89003 + 1.54689i −0.435689 + 0.233202i
\(45\) 3.41421 + 3.41421i 0.508961 + 0.508961i
\(46\) −4.49368 + 3.33474i −0.662558 + 0.491681i
\(47\) −1.97844 1.97844i −0.288585 0.288585i 0.547936 0.836520i \(-0.315414\pi\)
−0.836520 + 0.547936i \(0.815414\pi\)
\(48\) −6.20711 + 9.31271i −0.895919 + 1.34417i
\(49\) 0.828427i 0.118347i
\(50\) 3.37109 + 4.54266i 0.476744 + 0.642429i
\(51\) 16.3075 2.28351
\(52\) 3.40229 6.35802i 0.471813 0.881699i
\(53\) −0.242641 −0.0333293 −0.0166646 0.999861i \(-0.505305\pi\)
−0.0166646 + 0.999861i \(0.505305\pi\)
\(54\) −4.31147 5.80985i −0.586716 0.790621i
\(55\) 1.63899i 0.221002i
\(56\) −3.37740 + 7.15685i −0.451325 + 0.956375i
\(57\) 4.58579 + 4.58579i 0.607402 + 0.607402i
\(58\) 0.665257 0.493684i 0.0873526 0.0648239i
\(59\) 2.31788 + 2.31788i 0.301763 + 0.301763i 0.841703 0.539940i \(-0.181553\pi\)
−0.539940 + 0.841703i \(0.681553\pi\)
\(60\) 2.64070 + 4.93360i 0.340914 + 0.636925i
\(61\) 0.828427 0.106069 0.0530346 0.998593i \(-0.483111\pi\)
0.0530346 + 0.998593i \(0.483111\pi\)
\(62\) 1.15894 7.82843i 0.147186 0.994211i
\(63\) −9.55274 9.55274i −1.20353 1.20353i
\(64\) −6.17534 + 5.08579i −0.771917 + 0.635723i
\(65\) −2.00000 3.00000i −0.248069 0.372104i
\(66\) 0.949747 6.41536i 0.116906 0.789676i
\(67\) 2.79793 2.79793i 0.341822 0.341822i −0.515230 0.857052i \(-0.672294\pi\)
0.857052 + 0.515230i \(0.172294\pi\)
\(68\) 11.1569 + 3.37740i 1.35297 + 0.409570i
\(69\) 11.0711i 1.33280i
\(70\) 2.35802 + 3.17751i 0.281837 + 0.379786i
\(71\) 5.25642 5.25642i 0.623822 0.623822i −0.322684 0.946507i \(-0.604585\pi\)
0.946507 + 0.322684i \(0.104585\pi\)
\(72\) −4.61192 12.8546i −0.543520 1.51492i
\(73\) −9.65685 + 9.65685i −1.13025 + 1.13025i −0.140114 + 0.990135i \(0.544747\pi\)
−0.990135 + 0.140114i \(0.955253\pi\)
\(74\) 0.550253 3.71685i 0.0639656 0.432075i
\(75\) −11.1917 −1.29231
\(76\) 2.18763 + 4.08713i 0.250939 + 0.468826i
\(77\) 4.58579i 0.522599i
\(78\) 6.09001 + 12.9016i 0.689558 + 1.46082i
\(79\) 9.55274i 1.07477i 0.843338 + 0.537384i \(0.180587\pi\)
−0.843338 + 0.537384i \(0.819413\pi\)
\(80\) 0.784864 + 3.92224i 0.0877505 + 0.438520i
\(81\) −0.171573 −0.0190637
\(82\) 8.39380 + 1.24264i 0.926940 + 0.137227i
\(83\) −6.75481 + 6.75481i −0.741436 + 0.741436i −0.972854 0.231418i \(-0.925663\pi\)
0.231418 + 0.972854i \(0.425663\pi\)
\(84\) −7.38851 13.8039i −0.806153 1.50613i
\(85\) 4.12132 4.12132i 0.447020 0.447020i
\(86\) 5.80985 4.31147i 0.626493 0.464917i
\(87\) 1.63899i 0.175718i
\(88\) 1.97844 4.19239i 0.210902 0.446910i
\(89\) 6.24264 6.24264i 0.661719 0.661719i −0.294066 0.955785i \(-0.595009\pi\)
0.955785 + 0.294066i \(0.0950087\pi\)
\(90\) −6.75481 1.00000i −0.712019 0.105409i
\(91\) 5.59587 + 8.39380i 0.586606 + 0.879909i
\(92\) 2.29289 7.57430i 0.239051 0.789676i
\(93\) 11.0711 + 11.0711i 1.14802 + 1.14802i
\(94\) 3.91421 + 0.579471i 0.403720 + 0.0597679i
\(95\) 2.31788 0.237810
\(96\) −0.799300 15.8073i −0.0815782 1.61333i
\(97\) 0.414214 + 0.414214i 0.0420570 + 0.0420570i 0.727823 0.685766i \(-0.240532\pi\)
−0.685766 + 0.727823i \(0.740532\pi\)
\(98\) −0.698175 0.940816i −0.0705263 0.0950368i
\(99\) 5.59587 + 5.59587i 0.562406 + 0.562406i
\(100\) −7.65685 2.31788i −0.765685 0.231788i
\(101\) 10.8284i 1.07747i 0.842476 + 0.538734i \(0.181097\pi\)
−0.842476 + 0.538734i \(0.818903\pi\)
\(102\) −18.5199 + 13.7435i −1.83374 + 1.36081i
\(103\) −4.91697 −0.484484 −0.242242 0.970216i \(-0.577883\pi\)
−0.242242 + 0.970216i \(0.577883\pi\)
\(104\) 1.49450 + 10.0879i 0.146547 + 0.989204i
\(105\) −7.82843 −0.763976
\(106\) 0.275559 0.204491i 0.0267646 0.0198619i
\(107\) 10.2316i 0.989129i −0.869141 0.494565i \(-0.835328\pi\)
0.869141 0.494565i \(-0.164672\pi\)
\(108\) 9.79276 + 2.96447i 0.942309 + 0.285256i
\(109\) −4.70711 4.70711i −0.450859 0.450859i 0.444781 0.895640i \(-0.353282\pi\)
−0.895640 + 0.444781i \(0.853282\pi\)
\(110\) −1.38130 1.86135i −0.131701 0.177472i
\(111\) 5.25642 + 5.25642i 0.498917 + 0.498917i
\(112\) −2.19600 10.9742i −0.207502 1.03696i
\(113\) 15.3137 1.44059 0.720296 0.693667i \(-0.244006\pi\)
0.720296 + 0.693667i \(0.244006\pi\)
\(114\) −9.07269 1.34315i −0.849735 0.125797i
\(115\) −2.79793 2.79793i −0.260909 0.260909i
\(116\) −0.339446 + 1.12132i −0.0315168 + 0.104112i
\(117\) −17.0711 3.41421i −1.57822 0.315644i
\(118\) −4.58579 0.678892i −0.422156 0.0624971i
\(119\) −11.5312 + 11.5312i −1.05706 + 1.05706i
\(120\) −7.15685 3.37740i −0.653328 0.308313i
\(121\) 8.31371i 0.755792i
\(122\) −0.940816 + 0.698175i −0.0851775 + 0.0632098i
\(123\) −11.8706 + 11.8706i −1.07034 + 1.07034i
\(124\) 5.28141 + 9.86720i 0.474285 + 0.886100i
\(125\) −6.36396 + 6.36396i −0.569210 + 0.569210i
\(126\) 18.8995 + 2.79793i 1.68370 + 0.249260i
\(127\) 18.4266 1.63510 0.817548 0.575861i \(-0.195333\pi\)
0.817548 + 0.575861i \(0.195333\pi\)
\(128\) 2.72696 10.9802i 0.241031 0.970517i
\(129\) 14.3137i 1.26025i
\(130\) 4.79965 + 1.72145i 0.420957 + 0.150981i
\(131\) 10.7117i 0.935884i −0.883759 0.467942i \(-0.844996\pi\)
0.883759 0.467942i \(-0.155004\pi\)
\(132\) 4.32809 + 8.08612i 0.376712 + 0.703807i
\(133\) −6.48528 −0.562345
\(134\) −0.819496 + 5.53553i −0.0707936 + 0.478197i
\(135\) 3.61743 3.61743i 0.311339 0.311339i
\(136\) −15.5168 + 5.56708i −1.33056 + 0.477374i
\(137\) 8.65685 8.65685i 0.739605 0.739605i −0.232897 0.972502i \(-0.574820\pi\)
0.972502 + 0.232897i \(0.0748204\pi\)
\(138\) 9.33039 + 12.5730i 0.794255 + 1.07029i
\(139\) 21.9034i 1.85782i −0.370302 0.928912i \(-0.620746\pi\)
0.370302 0.928912i \(-0.379254\pi\)
\(140\) −5.35584 1.62132i −0.452651 0.137027i
\(141\) −5.53553 + 5.53553i −0.466176 + 0.466176i
\(142\) −1.53957 + 10.3995i −0.129198 + 0.872706i
\(143\) −3.27798 4.91697i −0.274119 0.411178i
\(144\) 16.0711 + 10.7117i 1.33926 + 0.892640i
\(145\) 0.414214 + 0.414214i 0.0343986 + 0.0343986i
\(146\) 2.82843 19.1055i 0.234082 1.58118i
\(147\) 2.31788 0.191176
\(148\) 2.50755 + 4.68483i 0.206120 + 0.385091i
\(149\) −6.48528 6.48528i −0.531295 0.531295i 0.389663 0.920958i \(-0.372592\pi\)
−0.920958 + 0.389663i \(0.872592\pi\)
\(150\) 12.7101 9.43208i 1.03777 0.770126i
\(151\) −1.29954 1.29954i −0.105755 0.105755i 0.652249 0.758005i \(-0.273826\pi\)
−0.758005 + 0.652249i \(0.773826\pi\)
\(152\) −5.92893 2.79793i −0.480900 0.226942i
\(153\) 28.1421i 2.27516i
\(154\) 3.86477 + 5.20792i 0.311432 + 0.419666i
\(155\) 5.59587 0.449471
\(156\) −17.7893 9.51938i −1.42428 0.762161i
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) −8.05078 10.8487i −0.640486 0.863077i
\(159\) 0.678892i 0.0538397i
\(160\) −4.19690 3.79289i −0.331794 0.299855i
\(161\) 7.82843 + 7.82843i 0.616966 + 0.616966i
\(162\) 0.194849 0.144597i 0.0153088 0.0113606i
\(163\) −10.7117 10.7117i −0.839004 0.839004i 0.149724 0.988728i \(-0.452161\pi\)
−0.988728 + 0.149724i \(0.952161\pi\)
\(164\) −10.5798 + 5.66283i −0.826144 + 0.442193i
\(165\) 4.58579 0.357003
\(166\) 1.97844 13.3640i 0.153557 1.03724i
\(167\) 9.55274 + 9.55274i 0.739213 + 0.739213i 0.972426 0.233213i \(-0.0749238\pi\)
−0.233213 + 0.972426i \(0.574924\pi\)
\(168\) 20.0244 + 9.44975i 1.54492 + 0.729064i
\(169\) 12.0000 + 5.00000i 0.923077 + 0.384615i
\(170\) −1.20711 + 8.15377i −0.0925809 + 0.625366i
\(171\) 7.91375 7.91375i 0.605179 0.605179i
\(172\) −2.96447 + 9.79276i −0.226038 + 0.746691i
\(173\) 12.3848i 0.941597i 0.882241 + 0.470799i \(0.156034\pi\)
−0.882241 + 0.470799i \(0.843966\pi\)
\(174\) −1.38130 1.86135i −0.104716 0.141108i
\(175\) 7.91375 7.91375i 0.598223 0.598223i
\(176\) 1.28639 + 6.42852i 0.0969649 + 0.484568i
\(177\) 6.48528 6.48528i 0.487464 0.487464i
\(178\) −1.82843 + 12.3507i −0.137046 + 0.925722i
\(179\) −7.43370 −0.555621 −0.277810 0.960636i \(-0.589609\pi\)
−0.277810 + 0.960636i \(0.589609\pi\)
\(180\) 8.51397 4.55710i 0.634594 0.339666i
\(181\) 11.4142i 0.848412i 0.905566 + 0.424206i \(0.139447\pi\)
−0.905566 + 0.424206i \(0.860553\pi\)
\(182\) −13.4291 4.81651i −0.995430 0.357023i
\(183\) 2.31788i 0.171343i
\(184\) 3.77945 + 10.5343i 0.278625 + 0.776596i
\(185\) 2.65685 0.195336
\(186\) −21.9034 3.24264i −1.60604 0.237762i
\(187\) 6.75481 6.75481i 0.493960 0.493960i
\(188\) −4.93360 + 2.64070i −0.359820 + 0.192593i
\(189\) −10.1213 + 10.1213i −0.736218 + 0.736218i
\(190\) −2.63234 + 1.95345i −0.190970 + 0.141718i
\(191\) 24.0225i 1.73820i 0.494633 + 0.869102i \(0.335302\pi\)
−0.494633 + 0.869102i \(0.664698\pi\)
\(192\) 14.2297 + 17.2782i 1.02694 + 1.24694i
\(193\) −6.07107 + 6.07107i −0.437005 + 0.437005i −0.891003 0.453998i \(-0.849997\pi\)
0.453998 + 0.891003i \(0.349997\pi\)
\(194\) −0.819496 0.121320i −0.0588363 0.00871029i
\(195\) −8.39380 + 5.59587i −0.601092 + 0.400728i
\(196\) 1.58579 + 0.480049i 0.113270 + 0.0342892i
\(197\) −18.6066 18.6066i −1.32567 1.32567i −0.909111 0.416555i \(-0.863237\pi\)
−0.416555 0.909111i \(-0.636763\pi\)
\(198\) −11.0711 1.63899i −0.786787 0.116478i
\(199\) −16.5064 −1.17011 −0.585053 0.810995i \(-0.698926\pi\)
−0.585053 + 0.810995i \(0.698926\pi\)
\(200\) 10.6491 3.82064i 0.753003 0.270160i
\(201\) −7.82843 7.82843i −0.552175 0.552175i
\(202\) −9.12589 12.2975i −0.642096 0.865247i
\(203\) −1.15894 1.15894i −0.0813418 0.0813418i
\(204\) 9.44975 31.2161i 0.661615 2.18557i
\(205\) 6.00000i 0.419058i
\(206\) 5.58404 4.14389i 0.389058 0.288718i
\(207\) −19.1055 −1.32792
\(208\) −10.1991 10.1970i −0.707179 0.707035i
\(209\) 3.79899 0.262782
\(210\) 8.89047 6.59758i 0.613501 0.455276i
\(211\) 9.75158i 0.671327i 0.941982 + 0.335663i \(0.108960\pi\)
−0.941982 + 0.335663i \(0.891040\pi\)
\(212\) −0.140603 + 0.464466i −0.00965667 + 0.0318997i
\(213\) −14.7071 14.7071i −1.00771 1.00771i
\(214\) 8.62293 + 11.6197i 0.589452 + 0.794307i
\(215\) 3.61743 + 3.61743i 0.246707 + 0.246707i
\(216\) −13.6197 + 4.88643i −0.926701 + 0.332479i
\(217\) −15.6569 −1.06286
\(218\) 9.31271 + 1.37868i 0.630737 + 0.0933760i
\(219\) 27.0192 + 27.0192i 1.82579 + 1.82579i
\(220\) 3.13738 + 0.949747i 0.211522 + 0.0640320i
\(221\) −4.12132 + 20.6066i −0.277230 + 1.38615i
\(222\) −10.3995 1.53957i −0.697968 0.103329i
\(223\) 17.8059 17.8059i 1.19237 1.19237i 0.215975 0.976399i \(-0.430707\pi\)
0.976399 0.215975i \(-0.0692928\pi\)
\(224\) 11.7426 + 10.6123i 0.784588 + 0.709061i
\(225\) 19.3137i 1.28758i
\(226\) −17.3912 + 12.9060i −1.15685 + 0.858492i
\(227\) −12.8307 + 12.8307i −0.851605 + 0.851605i −0.990331 0.138726i \(-0.955699\pi\)
0.138726 + 0.990331i \(0.455699\pi\)
\(228\) 11.4355 6.12085i 0.757335 0.405363i
\(229\) 14.7071 14.7071i 0.971873 0.971873i −0.0277421 0.999615i \(-0.508832\pi\)
0.999615 + 0.0277421i \(0.00883173\pi\)
\(230\) 5.53553 + 0.819496i 0.365002 + 0.0540359i
\(231\) −12.8307 −0.844200
\(232\) −0.559520 1.55952i −0.0367343 0.102388i
\(233\) 11.9706i 0.784218i −0.919919 0.392109i \(-0.871746\pi\)
0.919919 0.392109i \(-0.128254\pi\)
\(234\) 22.2644 10.5096i 1.45547 0.687035i
\(235\) 2.79793i 0.182517i
\(236\) 5.78007 3.09378i 0.376250 0.201388i
\(237\) 26.7279 1.73617
\(238\) 3.37740 22.8137i 0.218925 1.47879i
\(239\) 8.25319 8.25319i 0.533855 0.533855i −0.387862 0.921717i \(-0.626786\pi\)
0.921717 + 0.387862i \(0.126786\pi\)
\(240\) 10.9742 2.19600i 0.708380 0.141751i
\(241\) 13.0711 13.0711i 0.841981 0.841981i −0.147135 0.989116i \(-0.547005\pi\)
0.989116 + 0.147135i \(0.0470052\pi\)
\(242\) 7.00656 + 9.44159i 0.450399 + 0.606928i
\(243\) 15.8275i 1.01533i
\(244\) 0.480049 1.58579i 0.0307320 0.101520i
\(245\) 0.585786 0.585786i 0.0374245 0.0374245i
\(246\) 3.47682 23.4853i 0.221674 1.49737i
\(247\) −6.95365 + 4.63577i −0.442450 + 0.294967i
\(248\) −14.3137 6.75481i −0.908921 0.428931i
\(249\) 18.8995 + 18.8995i 1.19771 + 1.19771i
\(250\) 1.86396 12.5907i 0.117887 0.796306i
\(251\) 18.1454 1.14533 0.572663 0.819791i \(-0.305910\pi\)
0.572663 + 0.819791i \(0.305910\pi\)
\(252\) −23.8215 + 12.7504i −1.50061 + 0.803203i
\(253\) −4.58579 4.58579i −0.288306 0.288306i
\(254\) −20.9264 + 15.5294i −1.31304 + 0.974402i
\(255\) −11.5312 11.5312i −0.722110 0.722110i
\(256\) 6.15685 + 14.7680i 0.384803 + 0.922999i
\(257\) 0.656854i 0.0409734i 0.999790 + 0.0204867i \(0.00652158\pi\)
−0.999790 + 0.0204867i \(0.993478\pi\)
\(258\) −12.0632 16.2556i −0.751022 1.01203i
\(259\) −7.43370 −0.461908
\(260\) −6.90158 + 2.09001i −0.428018 + 0.129617i
\(261\) 2.82843 0.175075
\(262\) 9.02750 + 12.1649i 0.557721 + 0.751549i
\(263\) 8.87385i 0.547185i 0.961846 + 0.273592i \(0.0882119\pi\)
−0.961846 + 0.273592i \(0.911788\pi\)
\(264\) −11.7300 5.53553i −0.721933 0.340689i
\(265\) 0.171573 + 0.171573i 0.0105396 + 0.0105396i
\(266\) 7.36511 5.46561i 0.451584 0.335118i
\(267\) −17.4665 17.4665i −1.06893 1.06893i
\(268\) −3.73452 6.97716i −0.228122 0.426198i
\(269\) −8.14214 −0.496435 −0.248217 0.968704i \(-0.579845\pi\)
−0.248217 + 0.968704i \(0.579845\pi\)
\(270\) −1.05952 + 7.15685i −0.0644803 + 0.435552i
\(271\) −13.1702 13.1702i −0.800031 0.800031i 0.183069 0.983100i \(-0.441397\pi\)
−0.983100 + 0.183069i \(0.941397\pi\)
\(272\) 12.9301 19.3995i 0.784005 1.17627i
\(273\) 23.4853 15.6569i 1.42139 0.947596i
\(274\) −2.53553 + 17.1270i −0.153177 + 1.03468i
\(275\) −4.63577 + 4.63577i −0.279547 + 0.279547i
\(276\) −21.1924 6.41536i −1.27563 0.386159i
\(277\) 6.00000i 0.360505i 0.983620 + 0.180253i \(0.0576915\pi\)
−0.983620 + 0.180253i \(0.942309\pi\)
\(278\) 18.4596 + 24.8749i 1.10713 + 1.49190i
\(279\) 19.1055 19.1055i 1.14382 1.14382i
\(280\) 7.44885 2.67248i 0.445154 0.159711i
\(281\) −7.75736 + 7.75736i −0.462765 + 0.462765i −0.899561 0.436796i \(-0.856113\pi\)
0.436796 + 0.899561i \(0.356113\pi\)
\(282\) 1.62132 10.9517i 0.0965482 0.652165i
\(283\) 1.35778 0.0807119 0.0403560 0.999185i \(-0.487151\pi\)
0.0403560 + 0.999185i \(0.487151\pi\)
\(284\) −7.01597 13.1079i −0.416321 0.777808i
\(285\) 6.48528i 0.384155i
\(286\) 7.86658 + 2.82144i 0.465160 + 0.166835i
\(287\) 16.7876i 0.990940i
\(288\) −27.2789 + 1.37936i −1.60742 + 0.0812797i
\(289\) −16.9706 −0.998268
\(290\) −0.819496 0.121320i −0.0481224 0.00712418i
\(291\) 1.15894 1.15894i 0.0679384 0.0679384i
\(292\) 12.8894 + 24.0811i 0.754296 + 1.40924i
\(293\) −19.1924 + 19.1924i −1.12123 + 1.12123i −0.129675 + 0.991557i \(0.541393\pi\)
−0.991557 + 0.129675i \(0.958607\pi\)
\(294\) −2.63234 + 1.95345i −0.153521 + 0.113927i
\(295\) 3.27798i 0.190851i
\(296\) −6.79599 3.20711i −0.395009 0.186409i
\(297\) 5.92893 5.92893i 0.344032 0.344032i
\(298\) 12.8307 + 1.89949i 0.743264 + 0.110035i
\(299\) 13.9897 + 2.79793i 0.809043 + 0.161809i
\(300\) −6.48528 + 21.4234i −0.374428 + 1.23688i
\(301\) −10.1213 10.1213i −0.583383 0.583383i
\(302\) 2.57107 + 0.380628i 0.147948 + 0.0219027i
\(303\) 30.2972 1.74053
\(304\) 9.09130 1.81922i 0.521422 0.104340i
\(305\) −0.585786 0.585786i −0.0335420 0.0335420i
\(306\) 23.7174 + 31.9600i 1.35583 + 1.82703i
\(307\) 19.1055 + 19.1055i 1.09041 + 1.09041i 0.995485 + 0.0949226i \(0.0302604\pi\)
0.0949226 + 0.995485i \(0.469740\pi\)
\(308\) −8.77817 2.65733i −0.500183 0.151415i
\(309\) 13.7574i 0.782629i
\(310\) −6.35503 + 4.71604i −0.360941 + 0.267853i
\(311\) −22.7811 −1.29180 −0.645900 0.763422i \(-0.723518\pi\)
−0.645900 + 0.763422i \(0.723518\pi\)
\(312\) 28.2254 4.18150i 1.59795 0.236731i
\(313\) −13.4853 −0.762233 −0.381117 0.924527i \(-0.624460\pi\)
−0.381117 + 0.924527i \(0.624460\pi\)
\(314\) −13.6280 + 10.1133i −0.769072 + 0.570724i
\(315\) 13.5096i 0.761181i
\(316\) 18.2860 + 5.53553i 1.02867 + 0.311398i
\(317\) −4.34315 4.34315i −0.243935 0.243935i 0.574541 0.818476i \(-0.305181\pi\)
−0.818476 + 0.574541i \(0.805181\pi\)
\(318\) −0.572151 0.770994i −0.0320847 0.0432352i
\(319\) 0.678892 + 0.678892i 0.0380107 + 0.0380107i
\(320\) 7.96282 + 0.770428i 0.445135 + 0.0430682i
\(321\) −28.6274 −1.59783
\(322\) −15.4881 2.29289i −0.863115 0.127778i
\(323\) −9.55274 9.55274i −0.531529 0.531529i
\(324\) −0.0994215 + 0.328427i −0.00552342 + 0.0182460i
\(325\) 2.82843 14.1421i 0.156893 0.784465i
\(326\) 21.1924 + 3.13738i 1.17374 + 0.173763i
\(327\) −13.1702 + 13.1702i −0.728312 + 0.728312i
\(328\) 7.24264 15.3474i 0.399908 0.847421i
\(329\) 7.82843i 0.431595i
\(330\) −5.20792 + 3.86477i −0.286686 + 0.212749i
\(331\) 14.6686 14.6686i 0.806257 0.806257i −0.177808 0.984065i \(-0.556901\pi\)
0.984065 + 0.177808i \(0.0569007\pi\)
\(332\) 9.01593 + 16.8444i 0.494813 + 0.924454i
\(333\) 9.07107 9.07107i 0.497091 0.497091i
\(334\) −18.8995 2.79793i −1.03413 0.153096i
\(335\) −3.95687 −0.216187
\(336\) −30.7050 + 6.14425i −1.67509 + 0.335196i
\(337\) 8.17157i 0.445134i 0.974917 + 0.222567i \(0.0714436\pi\)
−0.974917 + 0.222567i \(0.928556\pi\)
\(338\) −17.8418 + 4.43494i −0.970468 + 0.241229i
\(339\) 42.8467i 2.32711i
\(340\) −5.50090 10.2773i −0.298328 0.557363i
\(341\) 9.17157 0.496669
\(342\) −2.31788 + 15.6569i −0.125337 + 0.846626i
\(343\) 12.2101 12.2101i 0.659282 0.659282i
\(344\) −4.88643 13.6197i −0.263458 0.734323i
\(345\) −7.82843 + 7.82843i −0.421468 + 0.421468i
\(346\) −10.4375 14.0650i −0.561126 0.756137i
\(347\) 9.35390i 0.502143i −0.967968 0.251072i \(-0.919217\pi\)
0.967968 0.251072i \(-0.0807830\pi\)
\(348\) 3.13738 + 0.949747i 0.168181 + 0.0509118i
\(349\) −0.464466 + 0.464466i −0.0248623 + 0.0248623i −0.719429 0.694566i \(-0.755596\pi\)
0.694566 + 0.719429i \(0.255596\pi\)
\(350\) −2.31788 + 15.6569i −0.123896 + 0.836894i
\(351\) −3.61743 + 18.0871i −0.193084 + 0.965420i
\(352\) −6.87868 6.21652i −0.366635 0.331342i
\(353\) −4.41421 4.41421i −0.234945 0.234945i 0.579808 0.814753i \(-0.303127\pi\)
−0.814753 + 0.579808i \(0.803127\pi\)
\(354\) −1.89949 + 12.8307i −0.100957 + 0.681945i
\(355\) −7.43370 −0.394540
\(356\) −8.33232 15.5672i −0.441612 0.825059i
\(357\) 32.2635 + 32.2635i 1.70756 + 1.70756i
\(358\) 8.44219 6.26491i 0.446184 0.331111i
\(359\) −3.95687 3.95687i −0.208836 0.208836i 0.594937 0.803773i \(-0.297177\pi\)
−0.803773 + 0.594937i \(0.797177\pi\)
\(360\) −5.82843 + 12.3507i −0.307185 + 0.650938i
\(361\) 13.6274i 0.717232i
\(362\) −9.61958 12.9627i −0.505594 0.681306i
\(363\) −23.2612 −1.22090
\(364\) 19.3102 5.84772i 1.01213 0.306504i
\(365\) 13.6569 0.714832
\(366\) 1.95345 + 2.63234i 0.102108 + 0.137595i
\(367\) 15.1486i 0.790751i 0.918520 + 0.395375i \(0.129385\pi\)
−0.918520 + 0.395375i \(0.870615\pi\)
\(368\) −13.1702 8.77817i −0.686542 0.457594i
\(369\) 20.4853 + 20.4853i 1.06642 + 1.06642i
\(370\) −3.01730 + 2.23912i −0.156862 + 0.116406i
\(371\) −0.480049 0.480049i −0.0249229 0.0249229i
\(372\) 27.6077 14.7770i 1.43140 0.766153i
\(373\) 30.6274 1.58583 0.792914 0.609334i \(-0.208563\pi\)
0.792914 + 0.609334i \(0.208563\pi\)
\(374\) −1.97844 + 13.3640i −0.102303 + 0.691034i
\(375\) 17.8059 + 17.8059i 0.919494 + 0.919494i
\(376\) 3.37740 7.15685i 0.174176 0.369087i
\(377\) −2.07107 0.414214i −0.106665 0.0213331i
\(378\) 2.96447 20.0244i 0.152476 1.02994i
\(379\) −13.9897 + 13.9897i −0.718601 + 0.718601i −0.968319 0.249718i \(-0.919662\pi\)
0.249718 + 0.968319i \(0.419662\pi\)
\(380\) 1.34315 4.43692i 0.0689019 0.227609i
\(381\) 51.5563i 2.64131i
\(382\) −20.2454 27.2815i −1.03585 1.39584i
\(383\) −11.5312 + 11.5312i −0.589216 + 0.589216i −0.937419 0.348203i \(-0.886792\pi\)
0.348203 + 0.937419i \(0.386792\pi\)
\(384\) −30.7217 7.62984i −1.56776 0.389359i
\(385\) −3.24264 + 3.24264i −0.165260 + 0.165260i
\(386\) 1.77817 12.0112i 0.0905067 0.611355i
\(387\) 24.7013 1.25564
\(388\) 1.03292 0.552869i 0.0524385 0.0280676i
\(389\) 22.1421i 1.12265i −0.827595 0.561325i \(-0.810292\pi\)
0.827595 0.561325i \(-0.189708\pi\)
\(390\) 4.81651 13.4291i 0.243893 0.680008i
\(391\) 23.0624i 1.16631i
\(392\) −2.20549 + 0.791281i −0.111394 + 0.0399657i
\(393\) −29.9706 −1.51181
\(394\) 36.8120 + 5.44975i 1.85456 + 0.274554i
\(395\) 6.75481 6.75481i 0.339871 0.339871i
\(396\) 13.9543 7.46904i 0.701231 0.375333i
\(397\) −1.51472 + 1.51472i −0.0760215 + 0.0760215i −0.744095 0.668074i \(-0.767119\pi\)
0.668074 + 0.744095i \(0.267119\pi\)
\(398\) 18.7457 13.9111i 0.939639 0.697302i
\(399\) 18.1454i 0.908405i
\(400\) −8.87385 + 13.3137i −0.443692 + 0.665685i
\(401\) 19.4853 19.4853i 0.973049 0.973049i −0.0265977 0.999646i \(-0.508467\pi\)
0.999646 + 0.0265977i \(0.00846731\pi\)
\(402\) 15.4881 + 2.29289i 0.772474 + 0.114359i
\(403\) −16.7876 + 11.1917i −0.836250 + 0.557500i
\(404\) 20.7279 + 6.27476i 1.03125 + 0.312181i
\(405\) 0.121320 + 0.121320i 0.00602846 + 0.00602846i
\(406\) 2.29289 + 0.339446i 0.113794 + 0.0168464i
\(407\) 4.35456 0.215848
\(408\) 15.5763 + 43.4151i 0.771143 + 2.14937i
\(409\) 5.14214 + 5.14214i 0.254262 + 0.254262i 0.822716 0.568453i \(-0.192458\pi\)
−0.568453 + 0.822716i \(0.692458\pi\)
\(410\) −5.05663 6.81399i −0.249729 0.336519i
\(411\) −24.2213 24.2213i −1.19475 1.19475i
\(412\) −2.84924 + 9.41214i −0.140372 + 0.463703i
\(413\) 9.17157i 0.451304i
\(414\) 21.6974 16.1016i 1.06637 0.791349i
\(415\) 9.55274 0.468926
\(416\) 20.1765 + 2.98488i 0.989233 + 0.146346i
\(417\) −61.2843 −3.00110
\(418\) −4.31438 + 3.20168i −0.211023 + 0.156599i
\(419\) 5.11582i 0.249924i −0.992162 0.124962i \(-0.960119\pi\)
0.992162 0.124962i \(-0.0398809\pi\)
\(420\) −4.53635 + 14.9853i −0.221351 + 0.731207i
\(421\) 0.0208153 + 0.0208153i 0.00101447 + 0.00101447i 0.707614 0.706599i \(-0.249772\pi\)
−0.706599 + 0.707614i \(0.749772\pi\)
\(422\) −8.21836 11.0745i −0.400064 0.539100i
\(423\) 9.55274 + 9.55274i 0.464470 + 0.464470i
\(424\) −0.231761 0.645974i −0.0112553 0.0313713i
\(425\) 23.3137 1.13088
\(426\) 29.0971 + 4.30761i 1.40976 + 0.208704i
\(427\) 1.63899 + 1.63899i 0.0793163 + 0.0793163i
\(428\) −19.5855 5.92893i −0.946702 0.286586i
\(429\) −13.7574 + 9.17157i −0.664212 + 0.442808i
\(430\) −7.15685 1.05952i −0.345134 0.0510946i
\(431\) 26.0009 26.0009i 1.25242 1.25242i 0.297786 0.954633i \(-0.403752\pi\)
0.954633 0.297786i \(-0.0962482\pi\)
\(432\) 11.3492 17.0276i 0.546041 0.819242i
\(433\) 9.68629i 0.465493i 0.972537 + 0.232747i \(0.0747713\pi\)
−0.972537 + 0.232747i \(0.925229\pi\)
\(434\) 17.7809 13.1952i 0.853513 0.633388i
\(435\) 1.15894 1.15894i 0.0555670 0.0555670i
\(436\) −11.7380 + 6.28278i −0.562150 + 0.300890i
\(437\) −6.48528 + 6.48528i −0.310233 + 0.310233i
\(438\) −53.4558 7.91375i −2.55422 0.378134i
\(439\) −23.7412 −1.13311 −0.566554 0.824025i \(-0.691724\pi\)
−0.566554 + 0.824025i \(0.691724\pi\)
\(440\) −4.36343 + 1.56550i −0.208018 + 0.0746323i
\(441\) 4.00000i 0.190476i
\(442\) −12.6862 26.8755i −0.603422 1.27834i
\(443\) 27.4993i 1.30653i 0.757129 + 0.653265i \(0.226601\pi\)
−0.757129 + 0.653265i \(0.773399\pi\)
\(444\) 13.1079 7.01597i 0.622071 0.332963i
\(445\) −8.82843 −0.418508
\(446\) −5.21524 + 35.2279i −0.246949 + 1.66809i
\(447\) −18.1454 + 18.1454i −0.858247 + 0.858247i
\(448\) −22.2794 2.15561i −1.05260 0.101843i
\(449\) 0.272078 0.272078i 0.0128402 0.0128402i −0.700658 0.713498i \(-0.747110\pi\)
0.713498 + 0.700658i \(0.247110\pi\)
\(450\) −16.2771 21.9339i −0.767308 1.03397i
\(451\) 9.83395i 0.463062i
\(452\) 8.87385 29.3137i 0.417391 1.37880i
\(453\) −3.63604 + 3.63604i −0.170836 + 0.170836i
\(454\) 3.75803 25.3848i 0.176373 1.19137i
\(455\) 1.97844 9.89219i 0.0927506 0.463753i
\(456\) −7.82843 + 16.5888i −0.366600 + 0.776840i
\(457\) 3.41421 + 3.41421i 0.159710 + 0.159710i 0.782438 0.622728i \(-0.213976\pi\)
−0.622728 + 0.782438i \(0.713976\pi\)
\(458\) −4.30761 + 29.0971i −0.201281 + 1.35962i
\(459\) −29.8172 −1.39175
\(460\) −6.97716 + 3.73452i −0.325312 + 0.174123i
\(461\) 13.5355 + 13.5355i 0.630413 + 0.630413i 0.948172 0.317759i \(-0.102930\pi\)
−0.317759 + 0.948172i \(0.602930\pi\)
\(462\) 14.5714 10.8134i 0.677923 0.503084i
\(463\) 16.1087 + 16.1087i 0.748635 + 0.748635i 0.974223 0.225588i \(-0.0724303\pi\)
−0.225588 + 0.974223i \(0.572430\pi\)
\(464\) 1.94975 + 1.29954i 0.0905148 + 0.0603299i
\(465\) 15.6569i 0.726069i
\(466\) 10.0885 + 13.5946i 0.467339 + 0.629755i
\(467\) 6.95365 0.321777 0.160888 0.986973i \(-0.448564\pi\)
0.160888 + 0.986973i \(0.448564\pi\)
\(468\) −16.4277 + 30.6992i −0.759372 + 1.41907i
\(469\) 11.0711 0.511214
\(470\) −2.35802 3.17751i −0.108767 0.146568i
\(471\) 33.5752i 1.54706i
\(472\) −3.95687 + 8.38478i −0.182130 + 0.385941i
\(473\) 5.92893 + 5.92893i 0.272613 + 0.272613i
\(474\) −30.3540 + 22.5255i −1.39420 + 1.03463i
\(475\) 6.55596 + 6.55596i 0.300808 + 0.300808i
\(476\) 15.3912 + 28.7551i 0.705452 + 1.31799i
\(477\) 1.17157 0.0536426
\(478\) −2.41730 + 16.3284i −0.110565 + 0.746845i
\(479\) 7.57430 + 7.57430i 0.346079 + 0.346079i 0.858647 0.512568i \(-0.171306\pi\)
−0.512568 + 0.858647i \(0.671306\pi\)
\(480\) −10.6123 + 11.7426i −0.484381 + 0.535976i
\(481\) −7.97056 + 5.31371i −0.363426 + 0.242284i
\(482\) −3.82843 + 25.8603i −0.174380 + 1.17790i
\(483\) 21.9034 21.9034i 0.996640 0.996640i
\(484\) −15.9142 4.81755i −0.723373 0.218980i
\(485\) 0.585786i 0.0265992i
\(486\) −13.3390 17.9747i −0.605068 0.815351i
\(487\) 6.27476 6.27476i 0.284336 0.284336i −0.550499 0.834836i \(-0.685563\pi\)
0.834836 + 0.550499i \(0.185563\pi\)
\(488\) 0.791281 + 2.20549i 0.0358196 + 0.0998380i
\(489\) −29.9706 + 29.9706i −1.35532 + 1.35532i
\(490\) −0.171573 + 1.15894i −0.00775087 + 0.0523556i
\(491\) −2.79793 −0.126269 −0.0631345 0.998005i \(-0.520110\pi\)
−0.0631345 + 0.998005i \(0.520110\pi\)
\(492\) 15.8442 + 29.6016i 0.714313 + 1.33454i
\(493\) 3.41421i 0.153768i
\(494\) 3.99012 11.1250i 0.179524 0.500538i
\(495\) 7.91375i 0.355697i
\(496\) 21.9483 4.39199i 0.985510 0.197206i
\(497\) 20.7990 0.932962
\(498\) −37.3915 5.53553i −1.67555 0.248053i
\(499\) 3.95687 3.95687i 0.177134 0.177134i −0.612971 0.790105i \(-0.710026\pi\)
0.790105 + 0.612971i \(0.210026\pi\)
\(500\) 8.49425 + 15.8697i 0.379874 + 0.709715i
\(501\) 26.7279 26.7279i 1.19412 1.19412i
\(502\) −20.6071 + 15.2924i −0.919739 + 0.682534i
\(503\) 23.3436i 1.04084i −0.853911 0.520419i \(-0.825776\pi\)
0.853911 0.520419i \(-0.174224\pi\)
\(504\) 16.3075 34.5563i 0.726396 1.53926i
\(505\) 7.65685 7.65685i 0.340726 0.340726i
\(506\) 9.07269 + 1.34315i 0.403330 + 0.0597101i
\(507\) 13.9897 33.5752i 0.621303 1.49113i
\(508\) 10.6777 35.2724i 0.473745 1.56496i
\(509\) 8.34315 + 8.34315i 0.369803 + 0.369803i 0.867405 0.497602i \(-0.165786\pi\)
−0.497602 + 0.867405i \(0.665786\pi\)
\(510\) 22.8137 + 3.37740i 1.01021 + 0.149554i
\(511\) −38.2110 −1.69035
\(512\) −19.4382 11.5827i −0.859054 0.511886i
\(513\) −8.38478 8.38478i −0.370197 0.370197i
\(514\) −0.553578 0.745967i −0.0244173 0.0329032i
\(515\) 3.47682 + 3.47682i 0.153207 + 0.153207i
\(516\) 27.3995 + 8.29438i 1.20620 + 0.365140i
\(517\) 4.58579i 0.201683i
\(518\) 8.44219 6.26491i 0.370929 0.275264i
\(519\) 34.6518 1.52104
\(520\) 6.07648 8.19002i 0.266471 0.359156i
\(521\) 11.0000 0.481919 0.240959 0.970535i \(-0.422538\pi\)
0.240959 + 0.970535i \(0.422538\pi\)
\(522\) −3.21215 + 2.38372i −0.140592 + 0.104333i
\(523\) 14.8674i 0.650106i 0.945696 + 0.325053i \(0.105382\pi\)
−0.945696 + 0.325053i \(0.894618\pi\)
\(524\) −20.5044 6.20711i −0.895741 0.271159i
\(525\) −22.1421 22.1421i −0.966362 0.966362i
\(526\) −7.47863 10.0777i −0.326084 0.439409i
\(527\) −23.0624 23.0624i −1.00461 1.00461i
\(528\) 17.9866 3.59922i 0.782765 0.156636i
\(529\) −7.34315 −0.319267
\(530\) −0.339446 0.0502525i −0.0147446 0.00218283i
\(531\) −11.1917 11.1917i −0.485680 0.485680i
\(532\) −3.75803 + 12.4142i −0.162931 + 0.538224i
\(533\) −12.0000 18.0000i −0.519778 0.779667i
\(534\) 34.5563 + 5.11582i 1.49540 + 0.221383i
\(535\) −7.23486 + 7.23486i −0.312790 + 0.312790i
\(536\) 10.1213 + 4.77637i 0.437174 + 0.206308i
\(537\) 20.7990i 0.897543i
\(538\) 9.24674 6.86196i 0.398655 0.295840i
\(539\) 0.960099 0.960099i 0.0413544 0.0413544i
\(540\) −4.82834 9.02072i −0.207778 0.388190i
\(541\) 16.1213 16.1213i 0.693110 0.693110i −0.269805 0.962915i \(-0.586959\pi\)
0.962915 + 0.269805i \(0.0869593\pi\)
\(542\) 26.0563 + 3.85745i 1.11922 + 0.165692i
\(543\) 31.9362 1.37051
\(544\) 1.66504 + 32.9285i 0.0713879 + 1.41180i
\(545\) 6.65685i 0.285148i
\(546\) −13.4763 + 37.5737i −0.576731 + 1.60801i
\(547\) 14.3873i 0.615159i 0.951522 + 0.307579i \(0.0995189\pi\)
−0.951522 + 0.307579i \(0.900481\pi\)
\(548\) −11.5547 21.5875i −0.493591 0.922171i
\(549\) −4.00000 −0.170716
\(550\) 1.35778 9.17157i 0.0578961 0.391077i
\(551\) 0.960099 0.960099i 0.0409016 0.0409016i
\(552\) 29.4741 10.5746i 1.25450 0.450087i
\(553\) −18.8995 + 18.8995i −0.803688 + 0.803688i
\(554\) −5.05663 6.81399i −0.214836 0.289499i
\(555\) 7.43370i 0.315543i
\(556\) −41.9278 12.6924i −1.77814 0.538277i
\(557\) −8.36396 + 8.36396i −0.354392 + 0.354392i −0.861741 0.507349i \(-0.830626\pi\)
0.507349 + 0.861741i \(0.330626\pi\)
\(558\) −5.59587 + 37.7990i −0.236892 + 1.60016i
\(559\) −18.0871 3.61743i −0.765005 0.153001i
\(560\) −6.20711 + 9.31271i −0.262298 + 0.393534i
\(561\) −18.8995 18.8995i −0.797937 0.797937i
\(562\) 2.27208 15.3474i 0.0958418 0.647393i
\(563\) 28.4594 1.19942 0.599710 0.800218i \(-0.295283\pi\)
0.599710 + 0.800218i \(0.295283\pi\)
\(564\) 7.38851 + 13.8039i 0.311113 + 0.581248i
\(565\) −10.8284 10.8284i −0.455555 0.455555i
\(566\) −1.54199 + 1.14430i −0.0648146 + 0.0480986i
\(567\) −0.339446 0.339446i −0.0142554 0.0142554i
\(568\) 19.0147 + 8.97327i 0.797840 + 0.376510i
\(569\) 29.4853i 1.23609i −0.786144 0.618044i \(-0.787925\pi\)
0.786144 0.618044i \(-0.212075\pi\)
\(570\) 5.46561 + 7.36511i 0.228929 + 0.308490i
\(571\) −11.6718 −0.488449 −0.244224 0.969719i \(-0.578533\pi\)
−0.244224 + 0.969719i \(0.578533\pi\)
\(572\) −11.3116 + 3.42552i −0.472963 + 0.143228i
\(573\) 67.2132 2.80787
\(574\) 14.1481 + 19.0651i 0.590531 + 0.795761i
\(575\) 15.8275i 0.660052i
\(576\) 29.8172 24.5563i 1.24238 1.02318i
\(577\) −0.485281 0.485281i −0.0202025 0.0202025i 0.696933 0.717136i \(-0.254547\pi\)
−0.717136 + 0.696933i \(0.754547\pi\)
\(578\) 19.2729 14.3023i 0.801646 0.594898i
\(579\) 16.9864 + 16.9864i 0.705932 + 0.705932i
\(580\) 1.03292 0.552869i 0.0428896 0.0229566i
\(581\) −26.7279 −1.10886
\(582\) −0.339446 + 2.29289i −0.0140705 + 0.0950435i
\(583\) 0.281206 + 0.281206i 0.0116464 + 0.0116464i
\(584\) −34.9330 16.4853i −1.44554 0.682166i
\(585\) 9.65685 + 14.4853i 0.399262 + 0.598893i
\(586\) 5.62132 37.9709i 0.232215 1.56856i
\(587\) −25.1814 + 25.1814i −1.03935 + 1.03935i −0.0401538 + 0.999194i \(0.512785\pi\)
−0.999194 + 0.0401538i \(0.987215\pi\)
\(588\) 1.34315 4.43692i 0.0553904 0.182976i
\(589\) 12.9706i 0.534443i
\(590\) 2.76259 + 3.72269i 0.113734 + 0.153261i
\(591\) −52.0600 + 52.0600i −2.14146 + 2.14146i
\(592\) 10.4208 2.08527i 0.428293 0.0857040i
\(593\) −1.44365 + 1.44365i −0.0592836 + 0.0592836i −0.736127 0.676843i \(-0.763347\pi\)
0.676843 + 0.736127i \(0.263347\pi\)
\(594\) −1.73654 + 11.7300i −0.0712513 + 0.481289i
\(595\) 16.3075 0.668544
\(596\) −16.1722 + 8.65618i −0.662441 + 0.354571i
\(597\) 46.1838i 1.89018i
\(598\) −18.2456 + 8.61258i −0.746118 + 0.352195i
\(599\) 13.9073i 0.568237i −0.958789 0.284118i \(-0.908299\pi\)
0.958789 0.284118i \(-0.0917009\pi\)
\(600\) −10.6899 29.7954i −0.436413 1.21639i
\(601\) 15.9706 0.651453 0.325726 0.945464i \(-0.394391\pi\)
0.325726 + 0.945464i \(0.394391\pi\)
\(602\) 20.0244 + 2.96447i 0.816133 + 0.120823i
\(603\) −13.5096 + 13.5096i −0.550154 + 0.550154i
\(604\) −3.24065 + 1.73456i −0.131860 + 0.0705782i
\(605\) −5.87868 + 5.87868i −0.239002 + 0.239002i
\(606\) −34.4075 + 25.5336i −1.39771 + 1.03723i
\(607\) 25.0990i 1.01874i −0.860548 0.509369i \(-0.829879\pi\)
0.860548 0.509369i \(-0.170121\pi\)
\(608\) −8.79148 + 9.72792i −0.356542 + 0.394519i
\(609\) −3.24264 + 3.24264i −0.131398 + 0.131398i
\(610\) 1.15894 + 0.171573i 0.0469242 + 0.00694678i
\(611\) −5.59587 8.39380i −0.226384 0.339577i
\(612\) −53.8701 16.3075i −2.17757 0.659193i
\(613\) 30.8701 + 30.8701i 1.24683 + 1.24683i 0.957112 + 0.289718i \(0.0935614\pi\)
0.289718 + 0.957112i \(0.406439\pi\)
\(614\) −37.7990 5.59587i −1.52544 0.225831i
\(615\) 16.7876 0.676941
\(616\) 12.2086 4.38016i 0.491898 0.176482i
\(617\) −24.4853 24.4853i −0.985740 0.985740i 0.0141594 0.999900i \(-0.495493\pi\)
−0.999900 + 0.0141594i \(0.995493\pi\)
\(618\) −11.5943 15.6238i −0.466392 0.628480i
\(619\) 21.1422 + 21.1422i 0.849775 + 0.849775i 0.990105 0.140330i \(-0.0448163\pi\)
−0.140330 + 0.990105i \(0.544816\pi\)
\(620\) 3.24264 10.7117i 0.130228 0.430191i
\(621\) 20.2426i 0.812309i
\(622\) 25.8718 19.1993i 1.03736 0.769822i
\(623\) 24.7013 0.989638
\(624\) −28.5305 + 28.5363i −1.14213 + 1.14237i
\(625\) −11.0000 −0.440000
\(626\) 15.3148 11.3650i 0.612101 0.454237i
\(627\) 10.6293i 0.424494i
\(628\) 6.95365 22.9706i 0.277481 0.916625i
\(629\) −10.9497 10.9497i −0.436595 0.436595i
\(630\) −11.3855 15.3424i −0.453610 0.611256i
\(631\) −1.97844 1.97844i −0.0787603 0.0787603i 0.666629 0.745390i \(-0.267736\pi\)
−0.745390 + 0.666629i \(0.767736\pi\)
\(632\) −25.4319 + 9.12440i −1.01163 + 0.362949i
\(633\) 27.2843 1.08445
\(634\) 8.59264 + 1.27208i 0.341257 + 0.0505207i
\(635\) −13.0296 13.0296i −0.517062 0.517062i
\(636\) 1.29954 + 0.393398i 0.0515303 + 0.0155993i
\(637\) −0.585786 + 2.92893i −0.0232097 + 0.116049i
\(638\) −1.34315 0.198843i −0.0531756 0.00787227i
\(639\) −25.3802 + 25.3802i −1.00403 + 1.00403i
\(640\) −9.69239 + 5.83589i −0.383125 + 0.230684i
\(641\) 38.1421i 1.50652i 0.657721 + 0.753262i \(0.271521\pi\)
−0.657721 + 0.753262i \(0.728479\pi\)
\(642\) 32.5112 24.1264i 1.28311 0.952192i
\(643\) 17.2676 17.2676i 0.680969 0.680969i −0.279249 0.960219i \(-0.590086\pi\)
0.960219 + 0.279249i \(0.0900856\pi\)
\(644\) 19.5216 10.4489i 0.769260 0.411746i
\(645\) 10.1213 10.1213i 0.398527 0.398527i
\(646\) 18.8995 + 2.79793i 0.743591 + 0.110083i
\(647\) −33.5752 −1.31998 −0.659988 0.751276i \(-0.729439\pi\)
−0.659988 + 0.751276i \(0.729439\pi\)
\(648\) −0.163880 0.456773i −0.00643780 0.0179437i
\(649\) 5.37258i 0.210892i
\(650\) 8.70645 + 18.4445i 0.341495 + 0.723451i
\(651\) 43.8068i 1.71692i
\(652\) −26.7116 + 14.2973i −1.04611 + 0.559927i
\(653\) −14.8284 −0.580281 −0.290141 0.956984i \(-0.593702\pi\)
−0.290141 + 0.956984i \(0.593702\pi\)
\(654\) 3.85745 26.0563i 0.150838 1.01888i
\(655\) −7.57430 + 7.57430i −0.295952 + 0.295952i
\(656\) 4.70918 + 23.5335i 0.183863 + 0.918827i
\(657\) 46.6274 46.6274i 1.81911 1.81911i
\(658\) 6.59758 + 8.89047i 0.257200 + 0.346587i
\(659\) 34.5353i 1.34530i 0.739959 + 0.672652i \(0.234845\pi\)
−0.739959 + 0.672652i \(0.765155\pi\)
\(660\) 2.65733 8.77817i 0.103436 0.341690i
\(661\) −31.0711 + 31.0711i −1.20852 + 1.20852i −0.237020 + 0.971505i \(0.576171\pi\)
−0.971505 + 0.237020i \(0.923829\pi\)
\(662\) −4.29632 + 29.0208i −0.166981 + 1.12793i
\(663\) 57.6559 + 11.5312i 2.23917 + 0.447834i
\(664\) −24.4350 11.5312i −0.948263 0.447496i
\(665\) 4.58579 + 4.58579i 0.177829 + 0.177829i
\(666\) −2.65685 + 17.9465i −0.102951 + 0.695414i
\(667\) −2.31788 −0.0897488
\(668\) 23.8215 12.7504i 0.921682 0.493330i
\(669\) −49.8198 49.8198i −1.92614 1.92614i
\(670\) 4.49368 3.33474i 0.173606 0.128832i
\(671\) −0.960099 0.960099i −0.0370642 0.0370642i
\(672\) 29.6924 32.8551i 1.14541 1.26741i
\(673\) 42.7990i 1.64978i −0.565293 0.824890i \(-0.691237\pi\)
0.565293 0.824890i \(-0.308763\pi\)
\(674\) −6.88677 9.28017i −0.265269 0.357459i
\(675\) 20.4633 0.787631
\(676\) 16.5247 20.0732i 0.635566 0.772046i
\(677\) −31.2132 −1.19962 −0.599810 0.800142i \(-0.704757\pi\)
−0.599810 + 0.800142i \(0.704757\pi\)
\(678\) 36.1100 + 48.6595i 1.38680 + 1.86876i
\(679\) 1.63899i 0.0628987i
\(680\) 14.9086 + 7.03553i 0.571718 + 0.269800i
\(681\) 35.8995 + 35.8995i 1.37567 + 1.37567i
\(682\) −10.4158 + 7.72954i −0.398843 + 0.295980i
\(683\) 31.4562 + 31.4562i 1.20364 + 1.20364i 0.973052 + 0.230584i \(0.0740635\pi\)
0.230584 + 0.973052i \(0.425936\pi\)
\(684\) −10.5628 19.7344i −0.403879 0.754563i
\(685\) −12.2426 −0.467767
\(686\) −3.57625 + 24.1569i −0.136542 + 0.922313i
\(687\) −41.1495 41.1495i −1.56995 1.56995i
\(688\) 17.0276 + 11.3492i 0.649172 + 0.432686i
\(689\) −0.857864 0.171573i −0.0326820 0.00653641i
\(690\) 2.29289 15.4881i 0.0872890 0.589620i
\(691\) 2.31788 2.31788i 0.0881764 0.0881764i −0.661643 0.749819i \(-0.730140\pi\)
0.749819 + 0.661643i \(0.230140\pi\)
\(692\) 23.7071 + 7.17662i 0.901209 + 0.272814i
\(693\) 22.1421i 0.841110i
\(694\) 7.88320 + 10.6229i 0.299242 + 0.403240i
\(695\) −15.4881 + 15.4881i −0.587495 + 0.587495i
\(696\) −4.36343 + 1.56550i −0.165395 + 0.0593401i
\(697\) 24.7279 24.7279i 0.936637 0.936637i
\(698\) 0.136039 0.918917i 0.00514915 0.0347815i
\(699\) −33.4928 −1.26682
\(700\) −10.5628 19.7344i −0.399237 0.745890i
\(701\) 31.3553i 1.18427i 0.805837 + 0.592137i \(0.201716\pi\)
−0.805837 + 0.592137i \(0.798284\pi\)
\(702\) −11.1351 23.5896i −0.420269 0.890332i
\(703\) 6.15828i 0.232264i
\(704\) 13.0510 + 1.26272i 0.491877 + 0.0475907i
\(705\) 7.82843 0.294836
\(706\) 8.73324 + 1.29289i 0.328680 + 0.0486587i
\(707\) −21.4234 + 21.4234i −0.805708 + 0.805708i
\(708\) −8.65618 16.1722i −0.325319 0.607790i
\(709\) −2.97056 + 2.97056i −0.111562 + 0.111562i −0.760684 0.649122i \(-0.775136\pi\)
0.649122 + 0.760684i \(0.275136\pi\)
\(710\) 8.44219 6.26491i 0.316830 0.235118i
\(711\) 46.1247i 1.72981i
\(712\) 22.5823 + 10.6569i 0.846308 + 0.399382i
\(713\) −15.6569 + 15.6569i −0.586354 + 0.586354i
\(714\) −63.8312 9.44975i −2.38882 0.353648i
\(715\) −1.15894 + 5.79471i −0.0433420 + 0.216710i
\(716\) −4.30761 + 14.2297i −0.160983 + 0.531788i
\(717\) −23.0919 23.0919i −0.862382 0.862382i
\(718\) 7.82843 + 1.15894i 0.292154 + 0.0432513i
\(719\) 17.0688 0.636559 0.318279 0.947997i \(-0.396895\pi\)
0.318279 + 0.947997i \(0.396895\pi\)
\(720\) −3.78966 18.9383i −0.141232 0.705787i
\(721\) −9.72792 9.72792i −0.362287 0.362287i
\(722\) −11.4848 15.4762i −0.427420 0.575964i
\(723\) −36.5720 36.5720i −1.36013 1.36013i
\(724\) 21.8492 + 6.61420i 0.812021 + 0.245815i
\(725\) 2.34315i 0.0870222i
\(726\) 26.4169 19.6039i 0.980424 0.727568i
\(727\) 43.1279 1.59953 0.799763 0.600316i \(-0.204958\pi\)
0.799763 + 0.600316i \(0.204958\pi\)
\(728\) −17.0016 + 22.9151i −0.630121 + 0.849291i
\(729\) 43.7696 1.62109
\(730\) −15.5096 + 11.5096i −0.574037 + 0.425990i
\(731\) 29.8172i 1.10283i
\(732\) −4.43692 1.34315i −0.163993 0.0496441i
\(733\) −14.8492 14.8492i −0.548469 0.548469i 0.377529 0.925998i \(-0.376774\pi\)
−0.925998 + 0.377529i \(0.876774\pi\)
\(734\) −12.7668 17.2037i −0.471232 0.635002i
\(735\) −1.63899 1.63899i −0.0604551 0.0604551i
\(736\) 22.3549 1.13038i 0.824013 0.0416664i
\(737\) −6.48528 −0.238888
\(738\) −40.5288 6.00000i −1.49189 0.220863i
\(739\) −37.5321 37.5321i −1.38064 1.38064i −0.843482 0.537157i \(-0.819498\pi\)
−0.537157 0.843482i \(-0.680502\pi\)
\(740\) 1.53957 5.08579i 0.0565957 0.186957i
\(741\) 12.9706 + 19.4558i 0.476486 + 0.714728i
\(742\) 0.949747 + 0.140603i 0.0348663 + 0.00516171i
\(743\) 9.21329 9.21329i 0.338003 0.338003i −0.517612 0.855615i \(-0.673179\pi\)
0.855615 + 0.517612i \(0.173179\pi\)
\(744\) −18.8995 + 40.0488i −0.692889 + 1.46826i
\(745\) 9.17157i 0.336020i
\(746\) −34.7825 + 25.8119i −1.27348 + 0.945042i
\(747\) 32.6151 32.6151i 1.19332 1.19332i
\(748\) −9.01593 16.8444i −0.329655 0.615891i
\(749\) 20.2426 20.2426i 0.739650 0.739650i
\(750\) −35.2279 5.21524i −1.28634 0.190434i
\(751\) 8.31143 0.303289 0.151644 0.988435i \(-0.451543\pi\)
0.151644 + 0.988435i \(0.451543\pi\)
\(752\) 2.19600 + 10.9742i 0.0800798 + 0.400187i
\(753\) 50.7696i 1.85015i
\(754\) 2.70113 1.27503i 0.0983693 0.0464339i
\(755\) 1.83783i 0.0668856i
\(756\) 13.5094 + 25.2394i 0.491331 + 0.917947i
\(757\) 44.7279 1.62566 0.812832 0.582498i \(-0.197925\pi\)
0.812832 + 0.582498i \(0.197925\pi\)
\(758\) 4.09748 27.6777i 0.148827 1.00530i
\(759\) −12.8307 + 12.8307i −0.465726 + 0.465726i
\(760\) 2.21395 + 6.17083i 0.0803084 + 0.223839i
\(761\) −0.343146 + 0.343146i −0.0124390 + 0.0124390i −0.713299 0.700860i \(-0.752800\pi\)
0.700860 + 0.713299i \(0.252800\pi\)
\(762\) 43.4502 + 58.5508i 1.57404 + 2.12107i
\(763\) 18.6254i 0.674286i
\(764\) 45.9841 + 13.9203i 1.66365 + 0.503619i
\(765\) −19.8995 + 19.8995i −0.719468 + 0.719468i
\(766\) 3.37740 22.8137i 0.122031 0.824293i
\(767\) 6.55596 + 9.83395i 0.236722 + 0.355083i
\(768\) 41.3198 17.2265i 1.49100 0.621606i
\(769\) −1.65685 1.65685i −0.0597477 0.0597477i 0.676602 0.736349i \(-0.263452\pi\)
−0.736349 + 0.676602i \(0.763452\pi\)
\(770\) 0.949747 6.41536i 0.0342265 0.231194i
\(771\) 1.83783 0.0661880
\(772\) 8.10331 + 15.1393i 0.291645 + 0.544876i
\(773\) 32.1213 + 32.1213i 1.15532 + 1.15532i 0.985469 + 0.169854i \(0.0543298\pi\)
0.169854 + 0.985469i \(0.445670\pi\)
\(774\) −28.0525 + 20.8176i −1.00832 + 0.748273i
\(775\) 15.8275 + 15.8275i 0.568540 + 0.568540i
\(776\) −0.707107 + 1.49839i −0.0253837 + 0.0537890i
\(777\) 20.7990i 0.746160i
\(778\) 18.6608 + 25.1461i 0.669021 + 0.901530i
\(779\) 13.9073 0.498281
\(780\) 5.84772 + 19.3102i 0.209382 + 0.691415i
\(781\) −12.1838 −0.435969
\(782\) −19.4363 26.1911i −0.695041 0.936592i
\(783\) 2.99678i 0.107096i
\(784\) 1.83783 2.75736i 0.0656369 0.0984771i
\(785\) −8.48528 8.48528i −0.302853 0.302853i
\(786\) 34.0365 25.2584i 1.21404 0.900936i
\(787\) 18.4266 + 18.4266i 0.656837 + 0.656837i 0.954630 0.297793i \(-0.0962507\pi\)
−0.297793 + 0.954630i \(0.596251\pi\)
\(788\) −46.3990 + 24.8350i −1.65290 + 0.884711i
\(789\) 24.8284 0.883915
\(790\) −1.97844 + 13.3640i −0.0703896 + 0.475468i
\(791\) 30.2972 + 30.2972i 1.07724 + 1.07724i
\(792\) −9.55274 + 20.2426i −0.339442 + 0.719291i
\(793\) 2.92893 + 0.585786i 0.104009 + 0.0208019i
\(794\) 0.443651 2.99678i 0.0157446 0.106352i
\(795\) 0.480049 0.480049i 0.0170256 0.0170256i
\(796\) −9.56497 + 31.5968i −0.339021 + 1.11992i
\(797\) 31.1716i 1.10415i −0.833793 0.552077i \(-0.813835\pi\)
0.833793 0.552077i \(-0.186165\pi\)
\(798\) −15.2924 20.6071i −0.541346 0.729483i
\(799\) 11.5312 11.5312i 0.407944 0.407944i
\(800\) −1.14270 22.5985i −0.0404006 0.798979i
\(801\) −30.1421 + 30.1421i −1.06502 + 1.06502i
\(802\) −5.70711 + 38.5504i −0.201525 + 1.36126i
\(803\) 22.3835 0.789895
\(804\) −19.5216 + 10.4489i −0.688475 + 0.368506i
\(805\) 11.0711i 0.390204i
\(806\) 9.63301 26.8582i 0.339308 0.946039i
\(807\) 22.7811i 0.801934i
\(808\) −28.8282 + 10.3429i −1.01417 + 0.363862i
\(809\) −6.85786 −0.241110 −0.120555 0.992707i \(-0.538467\pi\)
−0.120555 + 0.992707i \(0.538467\pi\)
\(810\) −0.240025 0.0355339i −0.00843361 0.00124853i
\(811\) 6.55596 6.55596i 0.230211 0.230211i −0.582570 0.812781i \(-0.697953\pi\)
0.812781 + 0.582570i \(0.197953\pi\)
\(812\) −2.89003 + 1.54689i −0.101420 + 0.0542852i
\(813\) −36.8492 + 36.8492i −1.29236 + 1.29236i
\(814\) −4.94532 + 3.66990i −0.173333 + 0.128630i
\(815\) 15.1486i 0.530632i
\(816\) −54.2785 36.1777i −1.90013 1.26647i
\(817\) 8.38478 8.38478i 0.293346 0.293346i
\(818\) −10.1734 1.50610i −0.355704 0.0526594i
\(819\) −27.0192 40.5288i −0.944128 1.41619i
\(820\) 11.4853 + 3.47682i 0.401083 + 0.121416i
\(821\) −2.22183 2.22183i −0.0775422 0.0775422i 0.667272 0.744814i \(-0.267462\pi\)
−0.744814 + 0.667272i \(0.767462\pi\)
\(822\) 47.9203 + 7.09425i 1.67141 + 0.247440i
\(823\) −54.0385 −1.88366 −0.941831 0.336087i \(-0.890897\pi\)
−0.941831 + 0.336087i \(0.890897\pi\)
\(824\) −4.69650 13.0903i −0.163610 0.456022i
\(825\) 12.9706 + 12.9706i 0.451577 + 0.451577i
\(826\) −7.72954 10.4158i −0.268945 0.362413i
\(827\) −32.3339 32.3339i −1.12436 1.12436i −0.991078 0.133281i \(-0.957449\pi\)
−0.133281 0.991078i \(-0.542551\pi\)
\(828\) −11.0711 + 36.5720i −0.384746 + 1.27096i
\(829\) 22.3848i 0.777455i −0.921353 0.388728i \(-0.872915\pi\)
0.921353 0.388728i \(-0.127085\pi\)
\(830\) −10.8487 + 8.05078i −0.376564 + 0.279447i
\(831\) 16.7876 0.582355
\(832\) −25.4293 + 13.6143i −0.881603 + 0.471993i
\(833\) −4.82843 −0.167295
\(834\) 69.5984 51.6487i 2.41000 1.78845i
\(835\) 13.5096i 0.467519i
\(836\) 2.20140 7.27208i 0.0761371 0.251510i
\(837\) −20.2426 20.2426i −0.699688 0.699688i
\(838\) 4.31147 + 5.80985i 0.148937 + 0.200698i
\(839\) −24.0225 24.0225i −0.829347 0.829347i 0.158079 0.987426i \(-0.449470\pi\)
−0.987426 + 0.158079i \(0.949470\pi\)
\(840\) −7.47741 20.8414i −0.257995 0.719095i
\(841\) −28.6569 −0.988167
\(842\) −0.0411817 0.00609665i −0.00141922 0.000210105i
\(843\) 21.7046 + 21.7046i 0.747545 + 0.747545i
\(844\) 18.6666 + 5.65076i 0.642531 + 0.194507i
\(845\) −4.94975 12.0208i −0.170276 0.413529i
\(846\) −18.8995 2.79793i −0.649778 0.0961949i
\(847\) 16.4481 16.4481i 0.565165 0.565165i
\(848\) 0.807612 + 0.538289i 0.0277335 + 0.0184849i
\(849\) 3.79899i 0.130381i
\(850\) −26.4766 + 19.6481i −0.908139 + 0.673926i
\(851\) −7.43370 + 7.43370i −0.254824 + 0.254824i
\(852\) −36.6749 + 19.6302i −1.25646 + 0.672520i
\(853\) −39.5772 + 39.5772i −1.35510 + 1.35510i −0.475240 + 0.879856i \(0.657639\pi\)
−0.879856 + 0.475240i \(0.842361\pi\)
\(854\) −3.24264 0.480049i −0.110961 0.0164270i
\(855\) −11.1917 −0.382749
\(856\) 27.2393 9.77285i 0.931022 0.334029i
\(857\) 30.1421i 1.02964i 0.857300 + 0.514818i \(0.172140\pi\)
−0.857300 + 0.514818i \(0.827860\pi\)
\(858\) 7.89421 22.0102i 0.269504 0.751414i
\(859\) 35.3307i 1.20547i −0.797943 0.602733i \(-0.794078\pi\)
0.797943 0.602733i \(-0.205922\pi\)
\(860\) 9.02072 4.82834i 0.307604 0.164645i
\(861\) −46.9706 −1.60075
\(862\) −7.61548 + 51.4411i −0.259384 + 1.75209i
\(863\) −25.3220 + 25.3220i −0.861971 + 0.861971i −0.991567 0.129596i \(-0.958632\pi\)
0.129596 + 0.991567i \(0.458632\pi\)
\(864\) 1.46146 + 28.9025i 0.0497199 + 0.983283i
\(865\) 8.75736 8.75736i 0.297759 0.297759i
\(866\) −8.16333 11.0004i −0.277401 0.373808i
\(867\) 47.4825i 1.61259i
\(868\) −9.07269 + 29.9706i −0.307947 + 1.01727i
\(869\) 11.0711 11.0711i 0.375560 0.375560i
\(870\) −0.339446 + 2.29289i −0.0115083 + 0.0777364i
\(871\) 11.8706 7.91375i 0.402221 0.268147i
\(872\) 8.03553 17.0276i 0.272118 0.576628i
\(873\) −2.00000 2.00000i −0.0676897 0.0676897i
\(874\) 1.89949 12.8307i 0.0642514 0.434006i
\(875\) −25.1814 −0.851286
\(876\) 67.3774 36.0637i 2.27647 1.21848i
\(877\) 14.2635 + 14.2635i 0.481643 + 0.481643i 0.905656 0.424013i \(-0.139379\pi\)
−0.424013 + 0.905656i \(0.639379\pi\)
\(878\) 26.9621 20.0085i 0.909927 0.675253i
\(879\) 53.6990 + 53.6990i 1.81122 + 1.81122i
\(880\) 3.63604 5.45526i 0.122571 0.183897i
\(881\) 12.3137i 0.414859i −0.978250 0.207430i \(-0.933490\pi\)
0.978250 0.207430i \(-0.0665098\pi\)
\(882\) 3.37109 + 4.54266i 0.113510 + 0.152959i
\(883\) −34.4529 −1.15943 −0.579717 0.814818i \(-0.696837\pi\)
−0.579717 + 0.814818i \(0.696837\pi\)
\(884\) 37.0573 + 19.8300i 1.24637 + 0.666955i
\(885\) −9.17157 −0.308299
\(886\) −23.1756 31.2300i −0.778600 1.04919i
\(887\) 46.5224i 1.56207i 0.624488 + 0.781035i \(0.285308\pi\)
−0.624488 + 0.781035i \(0.714692\pi\)
\(888\) −8.97327 + 19.0147i −0.301123 + 0.638092i
\(889\) 36.4558 + 36.4558i 1.22269 + 1.22269i
\(890\) 10.0261 7.44035i 0.336077 0.249401i
\(891\) 0.198843 + 0.198843i 0.00666149 + 0.00666149i
\(892\) −23.7663 44.4024i −0.795756 1.48670i
\(893\) 6.48528 0.217022
\(894\) 5.31466 35.8995i 0.177749 1.20066i
\(895\) 5.25642 + 5.25642i 0.175703 + 0.175703i
\(896\) 27.1186 16.3284i 0.905970 0.545494i
\(897\) 7.82843 39.1421i 0.261384 1.30692i
\(898\) −0.0796898 + 0.538289i −0.00265928 + 0.0179629i
\(899\) 2.31788 2.31788i 0.0773057 0.0773057i
\(900\) 36.9706 + 11.1917i 1.23235 + 0.373058i
\(901\) 1.41421i 0.0471143i
\(902\) −8.28777 11.1681i −0.275953 0.371856i
\(903\) −28.3188 + 28.3188i −0.942390 + 0.942390i
\(904\) 14.6271 + 40.7692i 0.486489 + 1.35596i
\(905\) 8.07107 8.07107i 0.268291 0.268291i
\(906\) 1.06497 7.19367i 0.0353813 0.238994i
\(907\) 16.3075 0.541483 0.270742 0.962652i \(-0.412731\pi\)
0.270742 + 0.962652i \(0.412731\pi\)
\(908\) 17.1257 + 31.9958i 0.568337 + 1.06182i
\(909\) 52.2843i 1.73416i
\(910\) 6.09001 + 12.9016i 0.201882 + 0.427683i
\(911\) 4.91697i 0.162907i 0.996677 + 0.0814533i \(0.0259561\pi\)
−0.996677 + 0.0814533i \(0.974044\pi\)
\(912\) −5.09006 25.4368i −0.168549 0.842298i
\(913\) 15.6569 0.518166
\(914\) −6.75481 1.00000i −0.223429 0.0330771i
\(915\) −1.63899 + 1.63899i −0.0541834 + 0.0541834i
\(916\) −19.6302 36.6749i −0.648600 1.21177i
\(917\) 21.1924 21.1924i 0.699834 0.699834i
\(918\) 33.8623 25.1291i 1.11762 0.829383i
\(919\) 25.6614i 0.846493i −0.906015 0.423246i \(-0.860890\pi\)
0.906015 0.423246i \(-0.139110\pi\)
\(920\) 4.77637 10.1213i 0.157472 0.333690i
\(921\) 53.4558 53.4558i 1.76143 1.76143i
\(922\) −26.7792 3.96447i −0.881926 0.130563i
\(923\) 22.3011 14.8674i 0.734050 0.489366i
\(924\) −7.43503 + 24.5607i −0.244594 + 0.807989i
\(925\) 7.51472 + 7.51472i 0.247082 + 0.247082i
\(926\) −31.8701 4.71813i −1.04732 0.155047i
\(927\) 23.7412 0.779765
\(928\) −3.30948 + 0.167345i −0.108639 + 0.00549336i
\(929\) 20.6274 + 20.6274i 0.676764 + 0.676764i 0.959266 0.282503i \(-0.0911647\pi\)
−0.282503 + 0.959266i \(0.591165\pi\)
\(930\) 13.1952 + 17.7809i 0.432686 + 0.583060i
\(931\) −1.35778 1.35778i −0.0444996 0.0444996i
\(932\) −22.9142 6.93659i −0.750580 0.227216i
\(933\) 63.7401i 2.08676i
\(934\) −7.89702 + 5.86034i −0.258398 + 0.191756i
\(935\) −9.55274 −0.312408
\(936\) −7.21606 48.7089i −0.235864 1.59210i
\(937\) −8.97056 −0.293056 −0.146528 0.989207i \(-0.546810\pi\)
−0.146528 + 0.989207i \(0.546810\pi\)
\(938\) −12.5730 + 9.33039i −0.410524 + 0.304648i
\(939\) 37.7309i 1.23130i
\(940\) 5.35584 + 1.62132i 0.174688 + 0.0528816i
\(941\) 34.2635 + 34.2635i 1.11696 + 1.11696i 0.992186 + 0.124771i \(0.0398197\pi\)
0.124771 + 0.992186i \(0.460180\pi\)
\(942\) 28.2962 + 38.1302i 0.921941 + 1.24235i
\(943\) −16.7876 16.7876i −0.546679 0.546679i
\(944\) −2.57277 12.8570i −0.0837365 0.418461i
\(945\) 14.3137 0.465625
\(946\) −11.7300 1.73654i −0.381376 0.0564599i
\(947\) −3.07914 3.07914i −0.100059 0.100059i 0.655305 0.755364i \(-0.272540\pi\)
−0.755364 + 0.655305i \(0.772540\pi\)
\(948\) 15.4881 51.1630i 0.503029 1.66170i
\(949\) −40.9706 + 27.3137i −1.32996 + 0.886640i
\(950\) −12.9706 1.92020i −0.420821 0.0622994i
\(951\) −12.1518 + 12.1518i −0.394050 + 0.394050i
\(952\) −41.7132 19.6850i −1.35193 0.637993i
\(953\) 51.1421i 1.65666i −0.560243 0.828328i \(-0.689292\pi\)
0.560243 0.828328i \(-0.310708\pi\)
\(954\) −1.33051 + 0.987369i −0.0430770 + 0.0319672i
\(955\) 16.9864 16.9864i 0.549668 0.549668i
\(956\) −11.0159 20.5809i −0.356279 0.665633i
\(957\) 1.89949 1.89949i 0.0614020 0.0614020i
\(958\) −14.9853 2.21846i −0.484152 0.0716752i
\(959\) 34.2541 1.10612
\(960\) 2.15561 22.2794i 0.0695719 0.719065i
\(961\) 0.313708i 0.0101196i
\(962\) 4.57365 12.7520i 0.147460 0.411140i
\(963\) 49.4027i 1.59198i
\(964\) −17.4465 32.5951i −0.561914 1.04982i
\(965\) 8.58579 0.276386
\(966\) −6.41536 + 43.3345i −0.206411 + 1.39427i
\(967\) 7.85551 7.85551i 0.252616 0.252616i −0.569426 0.822042i \(-0.692835\pi\)
0.822042 + 0.569426i \(0.192835\pi\)
\(968\) 22.1333 7.94093i 0.711392 0.255231i
\(969\) −26.7279 + 26.7279i −0.858625 + 0.858625i
\(970\) 0.493684 + 0.665257i 0.0158513 + 0.0213601i
\(971\) 0.877735i 0.0281679i 0.999901 + 0.0140839i \(0.00448320\pi\)
−0.999901 + 0.0140839i \(0.995517\pi\)
\(972\) 30.2972 + 9.17157i 0.971783 + 0.294178i
\(973\) 43.3345 43.3345i 1.38924 1.38924i
\(974\) −1.83783 + 12.4142i −0.0588880 + 0.397777i
\(975\) −39.5687 7.91375i −1.26721 0.253443i
\(976\) −2.75736 1.83783i −0.0882609 0.0588276i
\(977\) 35.6274 + 35.6274i 1.13982 + 1.13982i 0.988482 + 0.151340i \(0.0483589\pi\)
0.151340 + 0.988482i \(0.451641\pi\)
\(978\) 8.77817 59.2949i 0.280695 1.89604i
\(979\) −14.4697 −0.462454
\(980\) −0.781874 1.46077i −0.0249761 0.0466625i
\(981\) 22.7279 + 22.7279i 0.725647 + 0.725647i
\(982\) 3.17751 2.35802i 0.101399 0.0752474i
\(983\) −31.3155 31.3155i −0.998811 0.998811i 0.00118842 0.999999i \(-0.499622\pi\)
−0.999999 + 0.00118842i \(0.999622\pi\)
\(984\) −42.9411 20.2644i −1.36891 0.646006i
\(985\) 26.3137i 0.838424i
\(986\) 2.87740 + 3.87740i 0.0916352 + 0.123482i
\(987\) −21.9034 −0.697193
\(988\) 4.84441 + 15.9971i 0.154121 + 0.508934i
\(989\) −20.2426 −0.643679
\(990\) 6.66949 + 8.98737i 0.211970 + 0.285637i
\(991\) 21.4234i 0.680536i −0.940329 0.340268i \(-0.889482\pi\)
0.940329 0.340268i \(-0.110518\pi\)
\(992\) −21.2245 + 23.4853i −0.673879 + 0.745658i
\(993\) −41.0416 41.0416i −1.30242 1.30242i
\(994\) −23.6207 + 17.5288i −0.749203 + 0.555980i
\(995\) 11.6718 + 11.6718i 0.370020 + 0.370020i
\(996\) 47.1294 25.2260i 1.49335 0.799315i
\(997\) −17.0711 −0.540646 −0.270323 0.962770i \(-0.587131\pi\)
−0.270323 + 0.962770i \(0.587131\pi\)
\(998\) −1.15894 + 7.82843i −0.0366857 + 0.247805i
\(999\) −9.61098 9.61098i −0.304078 0.304078i
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 52.2.f.b.47.2 yes 8
3.2 odd 2 468.2.n.i.307.3 8
4.3 odd 2 inner 52.2.f.b.47.4 yes 8
8.3 odd 2 832.2.k.h.255.1 8
8.5 even 2 832.2.k.h.255.4 8
12.11 even 2 468.2.n.i.307.1 8
13.2 odd 12 676.2.l.l.19.1 16
13.3 even 3 676.2.l.l.319.1 16
13.4 even 6 676.2.l.h.427.1 16
13.5 odd 4 inner 52.2.f.b.31.4 yes 8
13.6 odd 12 676.2.l.l.587.2 16
13.7 odd 12 676.2.l.h.587.3 16
13.8 odd 4 676.2.f.g.239.1 8
13.9 even 3 676.2.l.l.427.4 16
13.10 even 6 676.2.l.h.319.4 16
13.11 odd 12 676.2.l.h.19.4 16
13.12 even 2 676.2.f.g.99.3 8
39.5 even 4 468.2.n.i.343.1 8
52.3 odd 6 676.2.l.l.319.2 16
52.7 even 12 676.2.l.h.587.4 16
52.11 even 12 676.2.l.h.19.1 16
52.15 even 12 676.2.l.l.19.4 16
52.19 even 12 676.2.l.l.587.1 16
52.23 odd 6 676.2.l.h.319.3 16
52.31 even 4 inner 52.2.f.b.31.2 8
52.35 odd 6 676.2.l.l.427.1 16
52.43 odd 6 676.2.l.h.427.4 16
52.47 even 4 676.2.f.g.239.3 8
52.51 odd 2 676.2.f.g.99.1 8
104.5 odd 4 832.2.k.h.447.4 8
104.83 even 4 832.2.k.h.447.1 8
156.83 odd 4 468.2.n.i.343.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
52.2.f.b.31.2 8 52.31 even 4 inner
52.2.f.b.31.4 yes 8 13.5 odd 4 inner
52.2.f.b.47.2 yes 8 1.1 even 1 trivial
52.2.f.b.47.4 yes 8 4.3 odd 2 inner
468.2.n.i.307.1 8 12.11 even 2
468.2.n.i.307.3 8 3.2 odd 2
468.2.n.i.343.1 8 39.5 even 4
468.2.n.i.343.3 8 156.83 odd 4
676.2.f.g.99.1 8 52.51 odd 2
676.2.f.g.99.3 8 13.12 even 2
676.2.f.g.239.1 8 13.8 odd 4
676.2.f.g.239.3 8 52.47 even 4
676.2.l.h.19.1 16 52.11 even 12
676.2.l.h.19.4 16 13.11 odd 12
676.2.l.h.319.3 16 52.23 odd 6
676.2.l.h.319.4 16 13.10 even 6
676.2.l.h.427.1 16 13.4 even 6
676.2.l.h.427.4 16 52.43 odd 6
676.2.l.h.587.3 16 13.7 odd 12
676.2.l.h.587.4 16 52.7 even 12
676.2.l.l.19.1 16 13.2 odd 12
676.2.l.l.19.4 16 52.15 even 12
676.2.l.l.319.1 16 13.3 even 3
676.2.l.l.319.2 16 52.3 odd 6
676.2.l.l.427.1 16 52.35 odd 6
676.2.l.l.427.4 16 13.9 even 3
676.2.l.l.587.1 16 52.19 even 12
676.2.l.l.587.2 16 13.6 odd 12
832.2.k.h.255.1 8 8.3 odd 2
832.2.k.h.255.4 8 8.5 even 2
832.2.k.h.447.1 8 104.83 even 4
832.2.k.h.447.4 8 104.5 odd 4