Properties

Label 78.3.f.a.31.1
Level $78$
Weight $3$
Character 78.31
Analytic conductor $2.125$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [78,3,Mod(31,78)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(78, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("78.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 78.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: \(2.12534606201\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) 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 31.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 78.31
Dual form 78.3.f.a.73.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} -1.73205 q^{3} -2.00000i q^{4} +(4.73205 - 4.73205i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(-2.73205 - 2.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} -1.73205 q^{3} -2.00000i q^{4} +(4.73205 - 4.73205i) q^{5} +(-1.73205 + 1.73205i) q^{6} +(-2.73205 - 2.73205i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000 q^{9} -9.46410i q^{10} +(1.73205 + 1.73205i) q^{11} +3.46410i q^{12} +(9.92820 - 8.39230i) q^{13} -5.46410 q^{14} +(-8.19615 + 8.19615i) q^{15} -4.00000 q^{16} +29.3205i q^{17} +(3.00000 - 3.00000i) q^{18} +(-11.2679 + 11.2679i) q^{19} +(-9.46410 - 9.46410i) q^{20} +(4.73205 + 4.73205i) q^{21} +3.46410 q^{22} +29.3205i q^{23} +(3.46410 + 3.46410i) q^{24} -19.7846i q^{25} +(1.53590 - 18.3205i) q^{26} -5.19615 q^{27} +(-5.46410 + 5.46410i) q^{28} +31.8564 q^{29} +16.3923i q^{30} +(26.9808 - 26.9808i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-3.00000 - 3.00000i) q^{33} +(29.3205 + 29.3205i) q^{34} -25.8564 q^{35} -6.00000i q^{36} +(-30.8564 - 30.8564i) q^{37} +22.5359i q^{38} +(-17.1962 + 14.5359i) q^{39} -18.9282 q^{40} +(-14.4449 + 14.4449i) q^{41} +9.46410 q^{42} +25.1769i q^{43} +(3.46410 - 3.46410i) q^{44} +(14.1962 - 14.1962i) q^{45} +(29.3205 + 29.3205i) q^{46} +(-41.1962 - 41.1962i) q^{47} +6.92820 q^{48} -34.0718i q^{49} +(-19.7846 - 19.7846i) q^{50} -50.7846i q^{51} +(-16.7846 - 19.8564i) q^{52} +2.28719 q^{53} +(-5.19615 + 5.19615i) q^{54} +16.3923 q^{55} +10.9282i q^{56} +(19.5167 - 19.5167i) q^{57} +(31.8564 - 31.8564i) q^{58} +(54.6218 + 54.6218i) q^{59} +(16.3923 + 16.3923i) q^{60} -7.42563 q^{61} -53.9615i q^{62} +(-8.19615 - 8.19615i) q^{63} +8.00000i q^{64} +(7.26795 - 86.6936i) q^{65} -6.00000 q^{66} +(-60.6936 + 60.6936i) q^{67} +58.6410 q^{68} -50.7846i q^{69} +(-25.8564 + 25.8564i) q^{70} +(38.9090 - 38.9090i) q^{71} +(-6.00000 - 6.00000i) q^{72} +(40.3205 + 40.3205i) q^{73} -61.7128 q^{74} +34.2679i q^{75} +(22.5359 + 22.5359i) q^{76} -9.46410i q^{77} +(-2.66025 + 31.7321i) q^{78} -148.210 q^{79} +(-18.9282 + 18.9282i) q^{80} +9.00000 q^{81} +28.8897i q^{82} +(73.7987 - 73.7987i) q^{83} +(9.46410 - 9.46410i) q^{84} +(138.746 + 138.746i) q^{85} +(25.1769 + 25.1769i) q^{86} -55.1769 q^{87} -6.92820i q^{88} +(25.5167 + 25.5167i) q^{89} -28.3923i q^{90} +(-50.0526 - 4.19615i) q^{91} +58.6410 q^{92} +(-46.7321 + 46.7321i) q^{93} -82.3923 q^{94} +106.641i q^{95} +(6.92820 - 6.92820i) q^{96} +(-86.0333 + 86.0333i) q^{97} +(-34.0718 - 34.0718i) q^{98} +(5.19615 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 12 q^{5} - 4 q^{7} - 8 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 12 q^{5} - 4 q^{7} - 8 q^{8} + 12 q^{9} + 12 q^{13} - 8 q^{14} - 12 q^{15} - 16 q^{16} + 12 q^{18} - 52 q^{19} - 24 q^{20} + 12 q^{21} + 20 q^{26} - 8 q^{28} + 72 q^{29} + 4 q^{31} - 16 q^{32} - 12 q^{33} + 48 q^{34} - 48 q^{35} - 68 q^{37} - 48 q^{39} - 48 q^{40} + 60 q^{41} + 24 q^{42} + 36 q^{45} + 48 q^{46} - 144 q^{47} + 4 q^{50} + 16 q^{52} + 120 q^{53} + 24 q^{55} - 12 q^{57} + 72 q^{58} - 24 q^{59} + 24 q^{60} + 192 q^{61} - 12 q^{63} + 36 q^{65} - 24 q^{66} - 28 q^{67} + 96 q^{68} - 48 q^{70} + 24 q^{71} - 24 q^{72} + 92 q^{73} - 136 q^{74} + 104 q^{76} + 24 q^{78} - 288 q^{79} - 48 q^{80} + 36 q^{81} - 72 q^{83} + 24 q^{84} + 264 q^{85} - 24 q^{86} - 96 q^{87} + 12 q^{89} - 124 q^{91} + 96 q^{92} - 180 q^{93} - 288 q^{94} - 164 q^{97} - 164 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.500000 0.500000i
\(3\) −1.73205 −0.577350
\(4\) 2.00000i 0.500000i
\(5\) 4.73205 4.73205i 0.946410 0.946410i −0.0522252 0.998635i \(-0.516631\pi\)
0.998635 + 0.0522252i \(0.0166314\pi\)
\(6\) −1.73205 + 1.73205i −0.288675 + 0.288675i
\(7\) −2.73205 2.73205i −0.390293 0.390293i 0.484499 0.874792i \(-0.339002\pi\)
−0.874792 + 0.484499i \(0.839002\pi\)
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) 3.00000 0.333333
\(10\) 9.46410i 0.946410i
\(11\) 1.73205 + 1.73205i 0.157459 + 0.157459i 0.781440 0.623981i \(-0.214486\pi\)
−0.623981 + 0.781440i \(0.714486\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 9.92820 8.39230i 0.763708 0.645562i
\(14\) −5.46410 −0.390293
\(15\) −8.19615 + 8.19615i −0.546410 + 0.546410i
\(16\) −4.00000 −0.250000
\(17\) 29.3205i 1.72474i 0.506282 + 0.862368i \(0.331019\pi\)
−0.506282 + 0.862368i \(0.668981\pi\)
\(18\) 3.00000 3.00000i 0.166667 0.166667i
\(19\) −11.2679 + 11.2679i −0.593050 + 0.593050i −0.938454 0.345404i \(-0.887742\pi\)
0.345404 + 0.938454i \(0.387742\pi\)
\(20\) −9.46410 9.46410i −0.473205 0.473205i
\(21\) 4.73205 + 4.73205i 0.225336 + 0.225336i
\(22\) 3.46410 0.157459
\(23\) 29.3205i 1.27480i 0.770531 + 0.637402i \(0.219991\pi\)
−0.770531 + 0.637402i \(0.780009\pi\)
\(24\) 3.46410 + 3.46410i 0.144338 + 0.144338i
\(25\) 19.7846i 0.791384i
\(26\) 1.53590 18.3205i 0.0590730 0.704635i
\(27\) −5.19615 −0.192450
\(28\) −5.46410 + 5.46410i −0.195146 + 0.195146i
\(29\) 31.8564 1.09850 0.549248 0.835659i \(-0.314914\pi\)
0.549248 + 0.835659i \(0.314914\pi\)
\(30\) 16.3923i 0.546410i
\(31\) 26.9808 26.9808i 0.870347 0.870347i −0.122163 0.992510i \(-0.538983\pi\)
0.992510 + 0.122163i \(0.0389830\pi\)
\(32\) −4.00000 + 4.00000i −0.125000 + 0.125000i
\(33\) −3.00000 3.00000i −0.0909091 0.0909091i
\(34\) 29.3205 + 29.3205i 0.862368 + 0.862368i
\(35\) −25.8564 −0.738754
\(36\) 6.00000i 0.166667i
\(37\) −30.8564 30.8564i −0.833957 0.833957i 0.154099 0.988055i \(-0.450753\pi\)
−0.988055 + 0.154099i \(0.950753\pi\)
\(38\) 22.5359i 0.593050i
\(39\) −17.1962 + 14.5359i −0.440927 + 0.372715i
\(40\) −18.9282 −0.473205
\(41\) −14.4449 + 14.4449i −0.352314 + 0.352314i −0.860970 0.508656i \(-0.830142\pi\)
0.508656 + 0.860970i \(0.330142\pi\)
\(42\) 9.46410 0.225336
\(43\) 25.1769i 0.585510i 0.956188 + 0.292755i \(0.0945720\pi\)
−0.956188 + 0.292755i \(0.905428\pi\)
\(44\) 3.46410 3.46410i 0.0787296 0.0787296i
\(45\) 14.1962 14.1962i 0.315470 0.315470i
\(46\) 29.3205 + 29.3205i 0.637402 + 0.637402i
\(47\) −41.1962 41.1962i −0.876514 0.876514i 0.116658 0.993172i \(-0.462782\pi\)
−0.993172 + 0.116658i \(0.962782\pi\)
\(48\) 6.92820 0.144338
\(49\) 34.0718i 0.695343i
\(50\) −19.7846 19.7846i −0.395692 0.395692i
\(51\) 50.7846i 0.995777i
\(52\) −16.7846 19.8564i −0.322781 0.381854i
\(53\) 2.28719 0.0431545 0.0215772 0.999767i \(-0.493131\pi\)
0.0215772 + 0.999767i \(0.493131\pi\)
\(54\) −5.19615 + 5.19615i −0.0962250 + 0.0962250i
\(55\) 16.3923 0.298042
\(56\) 10.9282i 0.195146i
\(57\) 19.5167 19.5167i 0.342398 0.342398i
\(58\) 31.8564 31.8564i 0.549248 0.549248i
\(59\) 54.6218 + 54.6218i 0.925793 + 0.925793i 0.997431 0.0716379i \(-0.0228226\pi\)
−0.0716379 + 0.997431i \(0.522823\pi\)
\(60\) 16.3923 + 16.3923i 0.273205 + 0.273205i
\(61\) −7.42563 −0.121732 −0.0608658 0.998146i \(-0.519386\pi\)
−0.0608658 + 0.998146i \(0.519386\pi\)
\(62\) 53.9615i 0.870347i
\(63\) −8.19615 8.19615i −0.130098 0.130098i
\(64\) 8.00000i 0.125000i
\(65\) 7.26795 86.6936i 0.111815 1.33375i
\(66\) −6.00000 −0.0909091
\(67\) −60.6936 + 60.6936i −0.905874 + 0.905874i −0.995936 0.0900619i \(-0.971294\pi\)
0.0900619 + 0.995936i \(0.471294\pi\)
\(68\) 58.6410 0.862368
\(69\) 50.7846i 0.736009i
\(70\) −25.8564 + 25.8564i −0.369377 + 0.369377i
\(71\) 38.9090 38.9090i 0.548014 0.548014i −0.377852 0.925866i \(-0.623337\pi\)
0.925866 + 0.377852i \(0.123337\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) 40.3205 + 40.3205i 0.552336 + 0.552336i 0.927114 0.374779i \(-0.122281\pi\)
−0.374779 + 0.927114i \(0.622281\pi\)
\(74\) −61.7128 −0.833957
\(75\) 34.2679i 0.456906i
\(76\) 22.5359 + 22.5359i 0.296525 + 0.296525i
\(77\) 9.46410i 0.122910i
\(78\) −2.66025 + 31.7321i −0.0341058 + 0.406821i
\(79\) −148.210 −1.87608 −0.938039 0.346528i \(-0.887360\pi\)
−0.938039 + 0.346528i \(0.887360\pi\)
\(80\) −18.9282 + 18.9282i −0.236603 + 0.236603i
\(81\) 9.00000 0.111111
\(82\) 28.8897i 0.352314i
\(83\) 73.7987 73.7987i 0.889141 0.889141i −0.105300 0.994441i \(-0.533580\pi\)
0.994441 + 0.105300i \(0.0335802\pi\)
\(84\) 9.46410 9.46410i 0.112668 0.112668i
\(85\) 138.746 + 138.746i 1.63231 + 1.63231i
\(86\) 25.1769 + 25.1769i 0.292755 + 0.292755i
\(87\) −55.1769 −0.634217
\(88\) 6.92820i 0.0787296i
\(89\) 25.5167 + 25.5167i 0.286704 + 0.286704i 0.835775 0.549071i \(-0.185019\pi\)
−0.549071 + 0.835775i \(0.685019\pi\)
\(90\) 28.3923i 0.315470i
\(91\) −50.0526 4.19615i −0.550028 0.0461116i
\(92\) 58.6410 0.637402
\(93\) −46.7321 + 46.7321i −0.502495 + 0.502495i
\(94\) −82.3923 −0.876514
\(95\) 106.641i 1.12254i
\(96\) 6.92820 6.92820i 0.0721688 0.0721688i
\(97\) −86.0333 + 86.0333i −0.886941 + 0.886941i −0.994228 0.107287i \(-0.965784\pi\)
0.107287 + 0.994228i \(0.465784\pi\)
\(98\) −34.0718 34.0718i −0.347671 0.347671i
\(99\) 5.19615 + 5.19615i 0.0524864 + 0.0524864i
\(100\) −39.5692 −0.395692
\(101\) 104.536i 1.03501i 0.855681 + 0.517504i \(0.173139\pi\)
−0.855681 + 0.517504i \(0.826861\pi\)
\(102\) −50.7846 50.7846i −0.497888 0.497888i
\(103\) 36.6795i 0.356112i 0.984020 + 0.178056i \(0.0569808\pi\)
−0.984020 + 0.178056i \(0.943019\pi\)
\(104\) −36.6410 3.07180i −0.352317 0.0295365i
\(105\) 44.7846 0.426520
\(106\) 2.28719 2.28719i 0.0215772 0.0215772i
\(107\) −123.464 −1.15387 −0.576935 0.816790i \(-0.695751\pi\)
−0.576935 + 0.816790i \(0.695751\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) 119.315 119.315i 1.09464 1.09464i 0.0996097 0.995027i \(-0.468241\pi\)
0.995027 0.0996097i \(-0.0317594\pi\)
\(110\) 16.3923 16.3923i 0.149021 0.149021i
\(111\) 53.4449 + 53.4449i 0.481485 + 0.481485i
\(112\) 10.9282 + 10.9282i 0.0975732 + 0.0975732i
\(113\) −184.277 −1.63077 −0.815384 0.578920i \(-0.803474\pi\)
−0.815384 + 0.578920i \(0.803474\pi\)
\(114\) 39.0333i 0.342398i
\(115\) 138.746 + 138.746i 1.20649 + 1.20649i
\(116\) 63.7128i 0.549248i
\(117\) 29.7846 25.1769i 0.254569 0.215187i
\(118\) 109.244 0.925793
\(119\) 80.1051 80.1051i 0.673152 0.673152i
\(120\) 32.7846 0.273205
\(121\) 115.000i 0.950413i
\(122\) −7.42563 + 7.42563i −0.0608658 + 0.0608658i
\(123\) 25.0192 25.0192i 0.203408 0.203408i
\(124\) −53.9615 53.9615i −0.435174 0.435174i
\(125\) 24.6795 + 24.6795i 0.197436 + 0.197436i
\(126\) −16.3923 −0.130098
\(127\) 173.962i 1.36978i −0.728648 0.684888i \(-0.759851\pi\)
0.728648 0.684888i \(-0.240149\pi\)
\(128\) 8.00000 + 8.00000i 0.0625000 + 0.0625000i
\(129\) 43.6077i 0.338044i
\(130\) −79.4256 93.9615i −0.610966 0.722781i
\(131\) 121.110 0.924506 0.462253 0.886748i \(-0.347041\pi\)
0.462253 + 0.886748i \(0.347041\pi\)
\(132\) −6.00000 + 6.00000i −0.0454545 + 0.0454545i
\(133\) 61.5692 0.462926
\(134\) 121.387i 0.905874i
\(135\) −24.5885 + 24.5885i −0.182137 + 0.182137i
\(136\) 58.6410 58.6410i 0.431184 0.431184i
\(137\) −130.053 130.053i −0.949289 0.949289i 0.0494861 0.998775i \(-0.484242\pi\)
−0.998775 + 0.0494861i \(0.984242\pi\)
\(138\) −50.7846 50.7846i −0.368004 0.368004i
\(139\) −27.1384 −0.195241 −0.0976203 0.995224i \(-0.531123\pi\)
−0.0976203 + 0.995224i \(0.531123\pi\)
\(140\) 51.7128i 0.369377i
\(141\) 71.3538 + 71.3538i 0.506056 + 0.506056i
\(142\) 77.8179i 0.548014i
\(143\) 31.7321 + 2.66025i 0.221902 + 0.0186032i
\(144\) −12.0000 −0.0833333
\(145\) 150.746 150.746i 1.03963 1.03963i
\(146\) 80.6410 0.552336
\(147\) 59.0141i 0.401456i
\(148\) −61.7128 + 61.7128i −0.416978 + 0.416978i
\(149\) −168.224 + 168.224i −1.12902 + 1.12902i −0.138686 + 0.990336i \(0.544288\pi\)
−0.990336 + 0.138686i \(0.955712\pi\)
\(150\) 34.2679 + 34.2679i 0.228453 + 0.228453i
\(151\) −38.4064 38.4064i −0.254347 0.254347i 0.568403 0.822750i \(-0.307561\pi\)
−0.822750 + 0.568403i \(0.807561\pi\)
\(152\) 45.0718 0.296525
\(153\) 87.9615i 0.574912i
\(154\) −9.46410 9.46410i −0.0614552 0.0614552i
\(155\) 255.349i 1.64741i
\(156\) 29.0718 + 34.3923i 0.186358 + 0.220463i
\(157\) −227.215 −1.44723 −0.723616 0.690203i \(-0.757521\pi\)
−0.723616 + 0.690203i \(0.757521\pi\)
\(158\) −148.210 + 148.210i −0.938039 + 0.938039i
\(159\) −3.96152 −0.0249152
\(160\) 37.8564i 0.236603i
\(161\) 80.1051 80.1051i 0.497547 0.497547i
\(162\) 9.00000 9.00000i 0.0555556 0.0555556i
\(163\) 12.4449 + 12.4449i 0.0763489 + 0.0763489i 0.744250 0.667901i \(-0.232807\pi\)
−0.667901 + 0.744250i \(0.732807\pi\)
\(164\) 28.8897 + 28.8897i 0.176157 + 0.176157i
\(165\) −28.3923 −0.172075
\(166\) 147.597i 0.889141i
\(167\) 119.512 + 119.512i 0.715638 + 0.715638i 0.967709 0.252071i \(-0.0811116\pi\)
−0.252071 + 0.967709i \(0.581112\pi\)
\(168\) 18.9282i 0.112668i
\(169\) 28.1384 166.641i 0.166500 0.986042i
\(170\) 277.492 1.63231
\(171\) −33.8038 + 33.8038i −0.197683 + 0.197683i
\(172\) 50.3538 0.292755
\(173\) 69.3975i 0.401141i 0.979679 + 0.200571i \(0.0642796\pi\)
−0.979679 + 0.200571i \(0.935720\pi\)
\(174\) −55.1769 + 55.1769i −0.317109 + 0.317109i
\(175\) −54.0526 + 54.0526i −0.308872 + 0.308872i
\(176\) −6.92820 6.92820i −0.0393648 0.0393648i
\(177\) −94.6077 94.6077i −0.534507 0.534507i
\(178\) 51.0333 0.286704
\(179\) 165.282i 0.923363i −0.887046 0.461682i \(-0.847246\pi\)
0.887046 0.461682i \(-0.152754\pi\)
\(180\) −28.3923 28.3923i −0.157735 0.157735i
\(181\) 283.856i 1.56827i 0.620592 + 0.784134i \(0.286892\pi\)
−0.620592 + 0.784134i \(0.713108\pi\)
\(182\) −54.2487 + 45.8564i −0.298070 + 0.251958i
\(183\) 12.8616 0.0702818
\(184\) 58.6410 58.6410i 0.318701 0.318701i
\(185\) −292.028 −1.57853
\(186\) 93.4641i 0.502495i
\(187\) −50.7846 + 50.7846i −0.271575 + 0.271575i
\(188\) −82.3923 + 82.3923i −0.438257 + 0.438257i
\(189\) 14.1962 + 14.1962i 0.0751119 + 0.0751119i
\(190\) 106.641 + 106.641i 0.561269 + 0.561269i
\(191\) 9.28203 0.0485970 0.0242985 0.999705i \(-0.492265\pi\)
0.0242985 + 0.999705i \(0.492265\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) −21.7180 21.7180i −0.112528 0.112528i 0.648601 0.761129i \(-0.275355\pi\)
−0.761129 + 0.648601i \(0.775355\pi\)
\(194\) 172.067i 0.886941i
\(195\) −12.5885 + 150.158i −0.0645562 + 0.770039i
\(196\) −68.1436 −0.347671
\(197\) −112.732 + 112.732i −0.572244 + 0.572244i −0.932755 0.360511i \(-0.882602\pi\)
0.360511 + 0.932755i \(0.382602\pi\)
\(198\) 10.3923 0.0524864
\(199\) 245.100i 1.23166i −0.787880 0.615829i \(-0.788821\pi\)
0.787880 0.615829i \(-0.211179\pi\)
\(200\) −39.5692 + 39.5692i −0.197846 + 0.197846i
\(201\) 105.124 105.124i 0.523007 0.523007i
\(202\) 104.536 + 104.536i 0.517504 + 0.517504i
\(203\) −87.0333 87.0333i −0.428736 0.428736i
\(204\) −101.569 −0.497888
\(205\) 136.708i 0.666867i
\(206\) 36.6795 + 36.6795i 0.178056 + 0.178056i
\(207\) 87.9615i 0.424935i
\(208\) −39.7128 + 33.5692i −0.190927 + 0.161390i
\(209\) −39.0333 −0.186762
\(210\) 44.7846 44.7846i 0.213260 0.213260i
\(211\) 345.282 1.63641 0.818204 0.574928i \(-0.194970\pi\)
0.818204 + 0.574928i \(0.194970\pi\)
\(212\) 4.57437i 0.0215772i
\(213\) −67.3923 + 67.3923i −0.316396 + 0.316396i
\(214\) −123.464 + 123.464i −0.576935 + 0.576935i
\(215\) 119.138 + 119.138i 0.554132 + 0.554132i
\(216\) 10.3923 + 10.3923i 0.0481125 + 0.0481125i
\(217\) −147.426 −0.679381
\(218\) 238.631i 1.09464i
\(219\) −69.8372 69.8372i −0.318891 0.318891i
\(220\) 32.7846i 0.149021i
\(221\) 246.067 + 291.100i 1.11342 + 1.31719i
\(222\) 106.890 0.481485
\(223\) 170.588 170.588i 0.764971 0.764971i −0.212246 0.977216i \(-0.568078\pi\)
0.977216 + 0.212246i \(0.0680777\pi\)
\(224\) 21.8564 0.0975732
\(225\) 59.3538i 0.263795i
\(226\) −184.277 + 184.277i −0.815384 + 0.815384i
\(227\) 169.368 169.368i 0.746114 0.746114i −0.227633 0.973747i \(-0.573099\pi\)
0.973747 + 0.227633i \(0.0730986\pi\)
\(228\) −39.0333 39.0333i −0.171199 0.171199i
\(229\) 141.823 + 141.823i 0.619315 + 0.619315i 0.945356 0.326041i \(-0.105715\pi\)
−0.326041 + 0.945356i \(0.605715\pi\)
\(230\) 277.492 1.20649
\(231\) 16.3923i 0.0709624i
\(232\) −63.7128 63.7128i −0.274624 0.274624i
\(233\) 128.038i 0.549521i −0.961513 0.274761i \(-0.911401\pi\)
0.961513 0.274761i \(-0.0885986\pi\)
\(234\) 4.60770 54.9615i 0.0196910 0.234878i
\(235\) −389.885 −1.65908
\(236\) 109.244 109.244i 0.462896 0.462896i
\(237\) 256.708 1.08315
\(238\) 160.210i 0.673152i
\(239\) 88.0192 88.0192i 0.368281 0.368281i −0.498569 0.866850i \(-0.666141\pi\)
0.866850 + 0.498569i \(0.166141\pi\)
\(240\) 32.7846 32.7846i 0.136603 0.136603i
\(241\) −147.459 147.459i −0.611863 0.611863i 0.331568 0.943431i \(-0.392422\pi\)
−0.943431 + 0.331568i \(0.892422\pi\)
\(242\) −115.000 115.000i −0.475207 0.475207i
\(243\) −15.5885 −0.0641500
\(244\) 14.8513i 0.0608658i
\(245\) −161.229 161.229i −0.658079 0.658079i
\(246\) 50.0385i 0.203408i
\(247\) −17.3064 + 206.435i −0.0700665 + 0.835767i
\(248\) −107.923 −0.435174
\(249\) −127.823 + 127.823i −0.513346 + 0.513346i
\(250\) 49.3590 0.197436
\(251\) 181.377i 0.722617i −0.932446 0.361308i \(-0.882330\pi\)
0.932446 0.361308i \(-0.117670\pi\)
\(252\) −16.3923 + 16.3923i −0.0650488 + 0.0650488i
\(253\) −50.7846 + 50.7846i −0.200730 + 0.200730i
\(254\) −173.962 173.962i −0.684888 0.684888i
\(255\) −240.315 240.315i −0.942413 0.942413i
\(256\) 16.0000 0.0625000
\(257\) 297.664i 1.15823i 0.815247 + 0.579113i \(0.196601\pi\)
−0.815247 + 0.579113i \(0.803399\pi\)
\(258\) −43.6077 43.6077i −0.169022 0.169022i
\(259\) 168.603i 0.650975i
\(260\) −173.387 14.5359i −0.666874 0.0559073i
\(261\) 95.5692 0.366166
\(262\) 121.110 121.110i 0.462253 0.462253i
\(263\) 22.8897 0.0870332 0.0435166 0.999053i \(-0.486144\pi\)
0.0435166 + 0.999053i \(0.486144\pi\)
\(264\) 12.0000i 0.0454545i
\(265\) 10.8231 10.8231i 0.0408418 0.0408418i
\(266\) 61.5692 61.5692i 0.231463 0.231463i
\(267\) −44.1962 44.1962i −0.165529 0.165529i
\(268\) 121.387 + 121.387i 0.452937 + 0.452937i
\(269\) 220.774 0.820722 0.410361 0.911923i \(-0.365403\pi\)
0.410361 + 0.911923i \(0.365403\pi\)
\(270\) 49.1769i 0.182137i
\(271\) 148.953 + 148.953i 0.549641 + 0.549641i 0.926337 0.376696i \(-0.122940\pi\)
−0.376696 + 0.926337i \(0.622940\pi\)
\(272\) 117.282i 0.431184i
\(273\) 86.6936 + 7.26795i 0.317559 + 0.0266225i
\(274\) −260.105 −0.949289
\(275\) 34.2679 34.2679i 0.124611 0.124611i
\(276\) −101.569 −0.368004
\(277\) 27.2154i 0.0982505i −0.998793 0.0491253i \(-0.984357\pi\)
0.998793 0.0491253i \(-0.0156434\pi\)
\(278\) −27.1384 + 27.1384i −0.0976203 + 0.0976203i
\(279\) 80.9423 80.9423i 0.290116 0.290116i
\(280\) 51.7128 + 51.7128i 0.184689 + 0.184689i
\(281\) −51.6218 51.6218i −0.183707 0.183707i 0.609262 0.792969i \(-0.291466\pi\)
−0.792969 + 0.609262i \(0.791466\pi\)
\(282\) 142.708 0.506056
\(283\) 93.8076i 0.331476i 0.986170 + 0.165738i \(0.0530006\pi\)
−0.986170 + 0.165738i \(0.946999\pi\)
\(284\) −77.8179 77.8179i −0.274007 0.274007i
\(285\) 184.708i 0.648097i
\(286\) 34.3923 29.0718i 0.120253 0.101650i
\(287\) 78.9282 0.275011
\(288\) −12.0000 + 12.0000i −0.0416667 + 0.0416667i
\(289\) −570.692 −1.97471
\(290\) 301.492i 1.03963i
\(291\) 149.014 149.014i 0.512076 0.512076i
\(292\) 80.6410 80.6410i 0.276168 0.276168i
\(293\) −120.042 120.042i −0.409701 0.409701i 0.471934 0.881634i \(-0.343556\pi\)
−0.881634 + 0.471934i \(0.843556\pi\)
\(294\) 59.0141 + 59.0141i 0.200728 + 0.200728i
\(295\) 516.946 1.75236
\(296\) 123.426i 0.416978i
\(297\) −9.00000 9.00000i −0.0303030 0.0303030i
\(298\) 336.449i 1.12902i
\(299\) 246.067 + 291.100i 0.822965 + 0.973578i
\(300\) 68.5359 0.228453
\(301\) 68.7846 68.7846i 0.228520 0.228520i
\(302\) −76.8128 −0.254347
\(303\) 181.061i 0.597563i
\(304\) 45.0718 45.0718i 0.148262 0.148262i
\(305\) −35.1384 + 35.1384i −0.115208 + 0.115208i
\(306\) 87.9615 + 87.9615i 0.287456 + 0.287456i
\(307\) 7.48849 + 7.48849i 0.0243925 + 0.0243925i 0.719198 0.694805i \(-0.244509\pi\)
−0.694805 + 0.719198i \(0.744509\pi\)
\(308\) −18.9282 −0.0614552
\(309\) 63.5307i 0.205601i
\(310\) −255.349 255.349i −0.823705 0.823705i
\(311\) 289.377i 0.930472i 0.885187 + 0.465236i \(0.154031\pi\)
−0.885187 + 0.465236i \(0.845969\pi\)
\(312\) 63.4641 + 5.32051i 0.203411 + 0.0170529i
\(313\) 346.841 1.10812 0.554059 0.832477i \(-0.313078\pi\)
0.554059 + 0.832477i \(0.313078\pi\)
\(314\) −227.215 + 227.215i −0.723616 + 0.723616i
\(315\) −77.5692 −0.246251
\(316\) 296.420i 0.938039i
\(317\) −97.0192 + 97.0192i −0.306054 + 0.306054i −0.843377 0.537322i \(-0.819436\pi\)
0.537322 + 0.843377i \(0.319436\pi\)
\(318\) −3.96152 + 3.96152i −0.0124576 + 0.0124576i
\(319\) 55.1769 + 55.1769i 0.172968 + 0.172968i
\(320\) 37.8564 + 37.8564i 0.118301 + 0.118301i
\(321\) 213.846 0.666187
\(322\) 160.210i 0.497547i
\(323\) −330.382 330.382i −1.02285 1.02285i
\(324\) 18.0000i 0.0555556i
\(325\) −166.038 196.426i −0.510888 0.604387i
\(326\) 24.8897 0.0763489
\(327\) −206.660 + 206.660i −0.631989 + 0.631989i
\(328\) 57.7795 0.176157
\(329\) 225.100i 0.684194i
\(330\) −28.3923 + 28.3923i −0.0860373 + 0.0860373i
\(331\) −126.130 + 126.130i −0.381056 + 0.381056i −0.871483 0.490427i \(-0.836841\pi\)
0.490427 + 0.871483i \(0.336841\pi\)
\(332\) −147.597 147.597i −0.444570 0.444570i
\(333\) −92.5692 92.5692i −0.277986 0.277986i
\(334\) 239.023 0.715638
\(335\) 574.410i 1.71466i
\(336\) −18.9282 18.9282i −0.0563339 0.0563339i
\(337\) 423.061i 1.25538i 0.778465 + 0.627688i \(0.215998\pi\)
−0.778465 + 0.627688i \(0.784002\pi\)
\(338\) −138.503 194.779i −0.409771 0.576271i
\(339\) 319.177 0.941525
\(340\) 277.492 277.492i 0.816154 0.816154i
\(341\) 93.4641 0.274088
\(342\) 67.6077i 0.197683i
\(343\) −226.956 + 226.956i −0.661680 + 0.661680i
\(344\) 50.3538 50.3538i 0.146377 0.146377i
\(345\) −240.315 240.315i −0.696566 0.696566i
\(346\) 69.3975 + 69.3975i 0.200571 + 0.200571i
\(347\) −191.867 −0.552930 −0.276465 0.961024i \(-0.589163\pi\)
−0.276465 + 0.961024i \(0.589163\pi\)
\(348\) 110.354i 0.317109i
\(349\) 36.7898 + 36.7898i 0.105415 + 0.105415i 0.757847 0.652432i \(-0.226251\pi\)
−0.652432 + 0.757847i \(0.726251\pi\)
\(350\) 108.105i 0.308872i
\(351\) −51.5885 + 43.6077i −0.146976 + 0.124238i
\(352\) −13.8564 −0.0393648
\(353\) 117.870 117.870i 0.333911 0.333911i −0.520159 0.854070i \(-0.674127\pi\)
0.854070 + 0.520159i \(0.174127\pi\)
\(354\) −189.215 −0.534507
\(355\) 368.238i 1.03729i
\(356\) 51.0333 51.0333i 0.143352 0.143352i
\(357\) −138.746 + 138.746i −0.388645 + 0.388645i
\(358\) −165.282 165.282i −0.461682 0.461682i
\(359\) 13.1192 + 13.1192i 0.0365437 + 0.0365437i 0.725143 0.688599i \(-0.241774\pi\)
−0.688599 + 0.725143i \(0.741774\pi\)
\(360\) −56.7846 −0.157735
\(361\) 107.067i 0.296583i
\(362\) 283.856 + 283.856i 0.784134 + 0.784134i
\(363\) 199.186i 0.548721i
\(364\) −8.39230 + 100.105i −0.0230558 + 0.275014i
\(365\) 381.597 1.04547
\(366\) 12.8616 12.8616i 0.0351409 0.0351409i
\(367\) −600.708 −1.63681 −0.818403 0.574645i \(-0.805140\pi\)
−0.818403 + 0.574645i \(0.805140\pi\)
\(368\) 117.282i 0.318701i
\(369\) −43.3346 + 43.3346i −0.117438 + 0.117438i
\(370\) −292.028 + 292.028i −0.789265 + 0.789265i
\(371\) −6.24871 6.24871i −0.0168429 0.0168429i
\(372\) 93.4641 + 93.4641i 0.251248 + 0.251248i
\(373\) 671.836 1.80117 0.900584 0.434682i \(-0.143139\pi\)
0.900584 + 0.434682i \(0.143139\pi\)
\(374\) 101.569i 0.271575i
\(375\) −42.7461 42.7461i −0.113990 0.113990i
\(376\) 164.785i 0.438257i
\(377\) 316.277 267.349i 0.838931 0.709148i
\(378\) 28.3923 0.0751119
\(379\) 158.799 158.799i 0.418994 0.418994i −0.465863 0.884857i \(-0.654256\pi\)
0.884857 + 0.465863i \(0.154256\pi\)
\(380\) 213.282 0.561269
\(381\) 301.310i 0.790840i
\(382\) 9.28203 9.28203i 0.0242985 0.0242985i
\(383\) 233.445 233.445i 0.609517 0.609517i −0.333303 0.942820i \(-0.608163\pi\)
0.942820 + 0.333303i \(0.108163\pi\)
\(384\) −13.8564 13.8564i −0.0360844 0.0360844i
\(385\) −44.7846 44.7846i −0.116324 0.116324i
\(386\) −43.4359 −0.112528
\(387\) 75.5307i 0.195170i
\(388\) 172.067 + 172.067i 0.443471 + 0.443471i
\(389\) 27.6950i 0.0711953i −0.999366 0.0355976i \(-0.988667\pi\)
0.999366 0.0355976i \(-0.0113335\pi\)
\(390\) 137.569 + 162.746i 0.352742 + 0.417298i
\(391\) −859.692 −2.19870
\(392\) −68.1436 + 68.1436i −0.173836 + 0.173836i
\(393\) −209.769 −0.533764
\(394\) 225.464i 0.572244i
\(395\) −701.338 + 701.338i −1.77554 + 1.77554i
\(396\) 10.3923 10.3923i 0.0262432 0.0262432i
\(397\) −398.692 398.692i −1.00426 1.00426i −0.999991 0.00427158i \(-0.998640\pi\)
−0.00427158 0.999991i \(-0.501360\pi\)
\(398\) −245.100 245.100i −0.615829 0.615829i
\(399\) −106.641 −0.267271
\(400\) 79.1384i 0.197846i
\(401\) −139.450 139.450i −0.347756 0.347756i 0.511517 0.859273i \(-0.329084\pi\)
−0.859273 + 0.511517i \(0.829084\pi\)
\(402\) 210.249i 0.523007i
\(403\) 41.4397 494.301i 0.102828 1.22655i
\(404\) 209.072 0.517504
\(405\) 42.5885 42.5885i 0.105157 0.105157i
\(406\) −174.067 −0.428736
\(407\) 106.890i 0.262628i
\(408\) −101.569 + 101.569i −0.248944 + 0.248944i
\(409\) 401.813 401.813i 0.982427 0.982427i −0.0174209 0.999848i \(-0.505546\pi\)
0.999848 + 0.0174209i \(0.00554553\pi\)
\(410\) 136.708 + 136.708i 0.333433 + 0.333433i
\(411\) 225.258 + 225.258i 0.548072 + 0.548072i
\(412\) 73.3590 0.178056
\(413\) 298.459i 0.722661i
\(414\) 87.9615 + 87.9615i 0.212467 + 0.212467i
\(415\) 698.438i 1.68298i
\(416\) −6.14359 + 73.2820i −0.0147683 + 0.176159i
\(417\) 47.0052 0.112722
\(418\) −39.0333 + 39.0333i −0.0933812 + 0.0933812i
\(419\) 139.177 0.332164 0.166082 0.986112i \(-0.446888\pi\)
0.166082 + 0.986112i \(0.446888\pi\)
\(420\) 89.5692i 0.213260i
\(421\) 360.244 360.244i 0.855685 0.855685i −0.135141 0.990826i \(-0.543149\pi\)
0.990826 + 0.135141i \(0.0431487\pi\)
\(422\) 345.282 345.282i 0.818204 0.818204i
\(423\) −123.588 123.588i −0.292171 0.292171i
\(424\) −4.57437 4.57437i −0.0107886 0.0107886i
\(425\) 580.095 1.36493
\(426\) 134.785i 0.316396i
\(427\) 20.2872 + 20.2872i 0.0475110 + 0.0475110i
\(428\) 246.928i 0.576935i
\(429\) −54.9615 4.60770i −0.128115 0.0107405i
\(430\) 238.277 0.554132
\(431\) 213.522 213.522i 0.495410 0.495410i −0.414596 0.910006i \(-0.636077\pi\)
0.910006 + 0.414596i \(0.136077\pi\)
\(432\) 20.7846 0.0481125
\(433\) 446.708i 1.03166i −0.856692 0.515829i \(-0.827484\pi\)
0.856692 0.515829i \(-0.172516\pi\)
\(434\) −147.426 + 147.426i −0.339690 + 0.339690i
\(435\) −261.100 + 261.100i −0.600230 + 0.600230i
\(436\) −238.631 238.631i −0.547318 0.547318i
\(437\) −330.382 330.382i −0.756023 0.756023i
\(438\) −139.674 −0.318891
\(439\) 164.238i 0.374119i −0.982349 0.187060i \(-0.940104\pi\)
0.982349 0.187060i \(-0.0598958\pi\)
\(440\) −32.7846 32.7846i −0.0745105 0.0745105i
\(441\) 102.215i 0.231781i
\(442\) 537.167 + 45.0333i 1.21531 + 0.101885i
\(443\) −458.736 −1.03552 −0.517761 0.855526i \(-0.673234\pi\)
−0.517761 + 0.855526i \(0.673234\pi\)
\(444\) 106.890 106.890i 0.240743 0.240743i
\(445\) 241.492 0.542679
\(446\) 341.177i 0.764971i
\(447\) 291.373 291.373i 0.651841 0.651841i
\(448\) 21.8564 21.8564i 0.0487866 0.0487866i
\(449\) 221.776 + 221.776i 0.493932 + 0.493932i 0.909543 0.415610i \(-0.136432\pi\)
−0.415610 + 0.909543i \(0.636432\pi\)
\(450\) −59.3538 59.3538i −0.131897 0.131897i
\(451\) −50.0385 −0.110950
\(452\) 368.554i 0.815384i
\(453\) 66.5218 + 66.5218i 0.146847 + 0.146847i
\(454\) 338.736i 0.746114i
\(455\) −256.708 + 216.995i −0.564193 + 0.476912i
\(456\) −78.0666 −0.171199
\(457\) 52.9615 52.9615i 0.115890 0.115890i −0.646784 0.762673i \(-0.723886\pi\)
0.762673 + 0.646784i \(0.223886\pi\)
\(458\) 283.646 0.619315
\(459\) 152.354i 0.331926i
\(460\) 277.492 277.492i 0.603244 0.603244i
\(461\) 67.4500 67.4500i 0.146312 0.146312i −0.630156 0.776468i \(-0.717009\pi\)
0.776468 + 0.630156i \(0.217009\pi\)
\(462\) 16.3923 + 16.3923i 0.0354812 + 0.0354812i
\(463\) 549.247 + 549.247i 1.18628 + 1.18628i 0.978088 + 0.208191i \(0.0667576\pi\)
0.208191 + 0.978088i \(0.433242\pi\)
\(464\) −127.426 −0.274624
\(465\) 442.277i 0.951133i
\(466\) −128.038 128.038i −0.274761 0.274761i
\(467\) 30.1821i 0.0646297i 0.999478 + 0.0323148i \(0.0102879\pi\)
−0.999478 + 0.0323148i \(0.989712\pi\)
\(468\) −50.3538 59.5692i −0.107594 0.127285i
\(469\) 331.636 0.707113
\(470\) −389.885 + 389.885i −0.829542 + 0.829542i
\(471\) 393.549 0.835560
\(472\) 218.487i 0.462896i
\(473\) −43.6077 + 43.6077i −0.0921939 + 0.0921939i
\(474\) 256.708 256.708i 0.541577 0.541577i
\(475\) 222.932 + 222.932i 0.469330 + 0.469330i
\(476\) −160.210 160.210i −0.336576 0.336576i
\(477\) 6.86156 0.0143848
\(478\) 176.038i 0.368281i
\(479\) −258.870 258.870i −0.540439 0.540439i 0.383218 0.923658i \(-0.374816\pi\)
−0.923658 + 0.383218i \(0.874816\pi\)
\(480\) 65.5692i 0.136603i
\(481\) −565.305 47.3923i −1.17527 0.0985287i
\(482\) −294.918 −0.611863
\(483\) −138.746 + 138.746i −0.287259 + 0.287259i
\(484\) −230.000 −0.475207
\(485\) 814.228i 1.67882i
\(486\) −15.5885 + 15.5885i −0.0320750 + 0.0320750i
\(487\) −274.560 + 274.560i −0.563779 + 0.563779i −0.930379 0.366600i \(-0.880522\pi\)
0.366600 + 0.930379i \(0.380522\pi\)
\(488\) 14.8513 + 14.8513i 0.0304329 + 0.0304329i
\(489\) −21.5551 21.5551i −0.0440800 0.0440800i
\(490\) −322.459 −0.658079
\(491\) 220.726i 0.449543i −0.974412 0.224771i \(-0.927836\pi\)
0.974412 0.224771i \(-0.0721635\pi\)
\(492\) −50.0385 50.0385i −0.101704 0.101704i
\(493\) 934.046i 1.89462i
\(494\) 189.128 + 223.741i 0.382850 + 0.452917i
\(495\) 49.1769 0.0993473
\(496\) −107.923 + 107.923i −0.217587 + 0.217587i
\(497\) −212.603 −0.427772
\(498\) 255.646i 0.513346i
\(499\) −625.065 + 625.065i −1.25264 + 1.25264i −0.298102 + 0.954534i \(0.596353\pi\)
−0.954534 + 0.298102i \(0.903647\pi\)
\(500\) 49.3590 49.3590i 0.0987180 0.0987180i
\(501\) −207.000 207.000i −0.413174 0.413174i
\(502\) −181.377 181.377i −0.361308 0.361308i
\(503\) −696.018 −1.38373 −0.691867 0.722025i \(-0.743211\pi\)
−0.691867 + 0.722025i \(0.743211\pi\)
\(504\) 32.7846i 0.0650488i
\(505\) 494.669 + 494.669i 0.979543 + 0.979543i
\(506\) 101.569i 0.200730i
\(507\) −48.7372 + 288.631i −0.0961286 + 0.569291i
\(508\) −347.923 −0.684888
\(509\) 401.678 401.678i 0.789151 0.789151i −0.192204 0.981355i \(-0.561563\pi\)
0.981355 + 0.192204i \(0.0615634\pi\)
\(510\) −480.631 −0.942413
\(511\) 220.315i 0.431146i
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 58.5500 58.5500i 0.114133 0.114133i
\(514\) 297.664 + 297.664i 0.579113 + 0.579113i
\(515\) 173.569 + 173.569i 0.337028 + 0.337028i
\(516\) −87.2154 −0.169022
\(517\) 142.708i 0.276030i
\(518\) 168.603 + 168.603i 0.325488 + 0.325488i
\(519\) 120.200i 0.231599i
\(520\) −187.923 + 158.851i −0.361390 + 0.305483i
\(521\) −602.651 −1.15672 −0.578360 0.815782i \(-0.696307\pi\)
−0.578360 + 0.815782i \(0.696307\pi\)
\(522\) 95.5692 95.5692i 0.183083 0.183083i
\(523\) 854.677 1.63418 0.817091 0.576509i \(-0.195586\pi\)
0.817091 + 0.576509i \(0.195586\pi\)
\(524\) 242.221i 0.462253i
\(525\) 93.6218 93.6218i 0.178327 0.178327i
\(526\) 22.8897 22.8897i 0.0435166 0.0435166i
\(527\) 791.090 + 791.090i 1.50112 + 1.50112i
\(528\) 12.0000 + 12.0000i 0.0227273 + 0.0227273i
\(529\) −330.692 −0.625127
\(530\) 21.6462i 0.0408418i
\(531\) 163.865 + 163.865i 0.308598 + 0.308598i
\(532\) 123.138i 0.231463i
\(533\) −22.1858 + 264.637i −0.0416245 + 0.496505i
\(534\) −88.3923 −0.165529
\(535\) −584.238 + 584.238i −1.09203 + 1.09203i
\(536\) 242.774 0.452937
\(537\) 286.277i 0.533104i
\(538\) 220.774 220.774i 0.410361 0.410361i
\(539\) 59.0141 59.0141i 0.109488 0.109488i
\(540\) 49.1769 + 49.1769i 0.0910684 + 0.0910684i
\(541\) −344.244 344.244i −0.636310 0.636310i 0.313333 0.949643i \(-0.398554\pi\)
−0.949643 + 0.313333i \(0.898554\pi\)
\(542\) 297.905 0.549641
\(543\) 491.654i 0.905440i
\(544\) −117.282 117.282i −0.215592 0.215592i
\(545\) 1129.21i 2.07195i
\(546\) 93.9615 79.4256i 0.172091 0.145468i
\(547\) 842.200 1.53967 0.769835 0.638242i \(-0.220338\pi\)
0.769835 + 0.638242i \(0.220338\pi\)
\(548\) −260.105 + 260.105i −0.474644 + 0.474644i
\(549\) −22.2769 −0.0405772
\(550\) 68.5359i 0.124611i
\(551\) −358.956 + 358.956i −0.651463 + 0.651463i
\(552\) −101.569 + 101.569i −0.184002 + 0.184002i
\(553\) 404.918 + 404.918i 0.732220 + 0.732220i
\(554\) −27.2154 27.2154i −0.0491253 0.0491253i
\(555\) 505.808 0.911365
\(556\) 54.2769i 0.0976203i
\(557\) 99.2576 + 99.2576i 0.178200 + 0.178200i 0.790571 0.612370i \(-0.209784\pi\)
−0.612370 + 0.790571i \(0.709784\pi\)
\(558\) 161.885i 0.290116i
\(559\) 211.292 + 249.962i 0.377983 + 0.447158i
\(560\) 103.426 0.184689
\(561\) 87.9615 87.9615i 0.156794 0.156794i
\(562\) −103.244 −0.183707
\(563\) 647.174i 1.14951i −0.818326 0.574755i \(-0.805097\pi\)
0.818326 0.574755i \(-0.194903\pi\)
\(564\) 142.708 142.708i 0.253028 0.253028i
\(565\) −872.008 + 872.008i −1.54338 + 1.54338i
\(566\) 93.8076 + 93.8076i 0.165738 + 0.165738i
\(567\) −24.5885 24.5885i −0.0433659 0.0433659i
\(568\) −155.636 −0.274007
\(569\) 701.223i 1.23238i −0.787598 0.616189i \(-0.788676\pi\)
0.787598 0.616189i \(-0.211324\pi\)
\(570\) −184.708 184.708i −0.324049 0.324049i
\(571\) 218.746i 0.383093i −0.981484 0.191547i \(-0.938650\pi\)
0.981484 0.191547i \(-0.0613503\pi\)
\(572\) 5.32051 63.4641i 0.00930159 0.110951i
\(573\) −16.0770 −0.0280575
\(574\) 78.9282 78.9282i 0.137506 0.137506i
\(575\) 580.095 1.00886
\(576\) 24.0000i 0.0416667i
\(577\) −12.3590 + 12.3590i −0.0214194 + 0.0214194i −0.717735 0.696316i \(-0.754821\pi\)
0.696316 + 0.717735i \(0.254821\pi\)
\(578\) −570.692 + 570.692i −0.987357 + 0.987357i
\(579\) 37.6166 + 37.6166i 0.0649683 + 0.0649683i
\(580\) −301.492 301.492i −0.519814 0.519814i
\(581\) −403.244 −0.694051
\(582\) 298.028i 0.512076i
\(583\) 3.96152 + 3.96152i 0.00679507 + 0.00679507i
\(584\) 161.282i 0.276168i
\(585\) 21.8038 260.081i 0.0372715 0.444582i
\(586\) −240.084 −0.409701
\(587\) −106.219 + 106.219i −0.180953 + 0.180953i −0.791771 0.610818i \(-0.790841\pi\)
0.610818 + 0.791771i \(0.290841\pi\)
\(588\) 118.028 0.200728
\(589\) 608.036i 1.03232i
\(590\) 516.946 516.946i 0.876180 0.876180i
\(591\) 195.258 195.258i 0.330385 0.330385i
\(592\) 123.426 + 123.426i 0.208489 + 0.208489i
\(593\) 770.645 + 770.645i 1.29957 + 1.29957i 0.928675 + 0.370895i \(0.120949\pi\)
0.370895 + 0.928675i \(0.379051\pi\)
\(594\) −18.0000 −0.0303030
\(595\) 758.123i 1.27416i
\(596\) 336.449 + 336.449i 0.564511 + 0.564511i
\(597\) 424.526i 0.711098i
\(598\) 537.167 + 45.0333i 0.898272 + 0.0753066i
\(599\) −130.392 −0.217683 −0.108842 0.994059i \(-0.534714\pi\)
−0.108842 + 0.994059i \(0.534714\pi\)
\(600\) 68.5359 68.5359i 0.114226 0.114226i
\(601\) −551.108 −0.916984 −0.458492 0.888698i \(-0.651610\pi\)
−0.458492 + 0.888698i \(0.651610\pi\)
\(602\) 137.569i 0.228520i
\(603\) −182.081 + 182.081i −0.301958 + 0.301958i
\(604\) −76.8128 + 76.8128i −0.127173 + 0.127173i
\(605\) −544.186 544.186i −0.899481 0.899481i
\(606\) −181.061 181.061i −0.298781 0.298781i
\(607\) 63.6001 0.104778 0.0523889 0.998627i \(-0.483316\pi\)
0.0523889 + 0.998627i \(0.483316\pi\)
\(608\) 90.1436i 0.148262i
\(609\) 150.746 + 150.746i 0.247531 + 0.247531i
\(610\) 70.2769i 0.115208i
\(611\) −754.734 63.2731i −1.23524 0.103557i
\(612\) 175.923 0.287456
\(613\) −26.3487 + 26.3487i −0.0429832 + 0.0429832i −0.728272 0.685289i \(-0.759676\pi\)
0.685289 + 0.728272i \(0.259676\pi\)
\(614\) 14.9770 0.0243925
\(615\) 236.785i 0.385016i
\(616\) −18.9282 + 18.9282i −0.0307276 + 0.0307276i
\(617\) 375.391 375.391i 0.608413 0.608413i −0.334118 0.942531i \(-0.608438\pi\)
0.942531 + 0.334118i \(0.108438\pi\)
\(618\) −63.5307 63.5307i −0.102801 0.102801i
\(619\) 264.070 + 264.070i 0.426608 + 0.426608i 0.887471 0.460863i \(-0.152460\pi\)
−0.460863 + 0.887471i \(0.652460\pi\)
\(620\) −510.697 −0.823705
\(621\) 152.354i 0.245336i
\(622\) 289.377 + 289.377i 0.465236 + 0.465236i
\(623\) 139.426i 0.223797i
\(624\) 68.7846 58.1436i 0.110232 0.0931788i
\(625\) 728.184 1.16510
\(626\) 346.841 346.841i 0.554059 0.554059i
\(627\) 67.6077 0.107827
\(628\) 454.431i 0.723616i
\(629\) 904.726 904.726i 1.43836 1.43836i
\(630\) −77.5692 + 77.5692i −0.123126 + 0.123126i
\(631\) −441.594 441.594i −0.699831 0.699831i 0.264543 0.964374i \(-0.414779\pi\)
−0.964374 + 0.264543i \(0.914779\pi\)
\(632\) 296.420 + 296.420i 0.469020 + 0.469020i
\(633\) −598.046 −0.944780
\(634\) 194.038i 0.306054i
\(635\) −823.195 823.195i −1.29637 1.29637i
\(636\) 7.92305i 0.0124576i
\(637\) −285.941 338.272i −0.448887 0.531039i
\(638\) 110.354 0.172968
\(639\) 116.727 116.727i 0.182671 0.182671i
\(640\) 75.7128 0.118301
\(641\) 829.910i 1.29471i 0.762188 + 0.647356i \(0.224125\pi\)
−0.762188 + 0.647356i \(0.775875\pi\)
\(642\) 213.846 213.846i 0.333094 0.333094i
\(643\) 424.196 424.196i 0.659714 0.659714i −0.295598 0.955312i \(-0.595519\pi\)
0.955312 + 0.295598i \(0.0955190\pi\)
\(644\) −160.210 160.210i −0.248774 0.248774i
\(645\) −206.354 206.354i −0.319928 0.319928i
\(646\) −660.764 −1.02285
\(647\) 477.913i 0.738660i −0.929298 0.369330i \(-0.879587\pi\)
0.929298 0.369330i \(-0.120413\pi\)
\(648\) −18.0000 18.0000i −0.0277778 0.0277778i
\(649\) 189.215i 0.291549i
\(650\) −362.464 30.3872i −0.557637 0.0467495i
\(651\) 255.349 0.392241
\(652\) 24.8897 24.8897i 0.0381744 0.0381744i
\(653\) −243.380 −0.372710 −0.186355 0.982482i \(-0.559667\pi\)
−0.186355 + 0.982482i \(0.559667\pi\)
\(654\) 413.321i 0.631989i
\(655\) 573.100 573.100i 0.874962 0.874962i
\(656\) 57.7795 57.7795i 0.0880784 0.0880784i
\(657\) 120.962 + 120.962i 0.184112 + 0.184112i
\(658\) 225.100 + 225.100i 0.342097 + 0.342097i
\(659\) −190.677 −0.289343 −0.144671 0.989480i \(-0.546212\pi\)
−0.144671 + 0.989480i \(0.546212\pi\)
\(660\) 56.7846i 0.0860373i
\(661\) −446.149 446.149i −0.674960 0.674960i 0.283895 0.958855i \(-0.408373\pi\)
−0.958855 + 0.283895i \(0.908373\pi\)
\(662\) 252.259i 0.381056i
\(663\) −426.200 504.200i −0.642835 0.760483i
\(664\) −295.195 −0.444570
\(665\) 291.349 291.349i 0.438118 0.438118i
\(666\) −185.138 −0.277986
\(667\) 934.046i 1.40037i
\(668\) 239.023 239.023i 0.357819 0.357819i
\(669\) −295.468 + 295.468i −0.441656 + 0.441656i
\(670\) 574.410 + 574.410i 0.857329 + 0.857329i
\(671\) −12.8616 12.8616i −0.0191678 0.0191678i
\(672\) −37.8564 −0.0563339
\(673\) 176.221i 0.261843i 0.991393 + 0.130922i \(0.0417936\pi\)
−0.991393 + 0.130922i \(0.958206\pi\)
\(674\) 423.061 + 423.061i 0.627688 + 0.627688i
\(675\) 102.804i 0.152302i
\(676\) −333.282 56.2769i −0.493021 0.0832498i
\(677\) 672.600 0.993500 0.496750 0.867894i \(-0.334527\pi\)
0.496750 + 0.867894i \(0.334527\pi\)
\(678\) 319.177 319.177i 0.470762 0.470762i
\(679\) 470.095 0.692334
\(680\) 554.985i 0.816154i
\(681\) −293.354 + 293.354i −0.430769 + 0.430769i
\(682\) 93.4641 93.4641i 0.137044 0.137044i
\(683\) 306.191 + 306.191i 0.448303 + 0.448303i 0.894790 0.446487i \(-0.147325\pi\)
−0.446487 + 0.894790i \(0.647325\pi\)
\(684\) 67.6077 + 67.6077i 0.0988417 + 0.0988417i
\(685\) −1230.83 −1.79683
\(686\) 453.913i 0.661680i
\(687\) −245.645 245.645i −0.357562 0.357562i
\(688\) 100.708i 0.146377i
\(689\) 22.7077 19.1948i 0.0329574 0.0278589i
\(690\) −480.631 −0.696566
\(691\) −474.865 + 474.865i −0.687215 + 0.687215i −0.961615 0.274401i \(-0.911521\pi\)
0.274401 + 0.961615i \(0.411521\pi\)
\(692\) 138.795 0.200571
\(693\) 28.3923i 0.0409701i
\(694\) −191.867 + 191.867i −0.276465 + 0.276465i
\(695\) −128.420 + 128.420i −0.184778 + 0.184778i
\(696\) 110.354 + 110.354i 0.158554 + 0.158554i
\(697\) −423.531 423.531i −0.607648 0.607648i
\(698\) 73.5795 0.105415
\(699\) 221.769i 0.317266i
\(700\) 108.105 + 108.105i 0.154436 + 0.154436i
\(701\) 204.480i 0.291697i −0.989307 0.145848i \(-0.953409\pi\)
0.989307 0.145848i \(-0.0465912\pi\)
\(702\) −7.98076 + 95.1962i −0.0113686 + 0.135607i
\(703\) 695.377 0.989156
\(704\) −13.8564 + 13.8564i −0.0196824 + 0.0196824i
\(705\) 675.300 0.957872
\(706\) 235.741i 0.333911i
\(707\) 285.597 285.597i 0.403957 0.403957i
\(708\) −189.215 + 189.215i −0.267253 + 0.267253i
\(709\) −629.018 629.018i −0.887190 0.887190i 0.107062 0.994252i \(-0.465856\pi\)
−0.994252 + 0.107062i \(0.965856\pi\)
\(710\) −368.238 368.238i −0.518646 0.518646i
\(711\) −444.631 −0.625360
\(712\) 102.067i 0.143352i
\(713\) 791.090 + 791.090i 1.10952 + 1.10952i
\(714\) 277.492i 0.388645i
\(715\) 162.746 137.569i 0.227617 0.192405i
\(716\) −330.564 −0.461682
\(717\) −152.454 + 152.454i −0.212627 + 0.212627i
\(718\) 26.2384 0.0365437
\(719\) 863.290i 1.20068i 0.799745 + 0.600340i \(0.204968\pi\)
−0.799745 + 0.600340i \(0.795032\pi\)
\(720\) −56.7846 + 56.7846i −0.0788675 + 0.0788675i
\(721\) 100.210 100.210i 0.138988 0.138988i
\(722\) 107.067 + 107.067i 0.148292 + 0.148292i
\(723\) 255.406 + 255.406i 0.353259 + 0.353259i
\(724\) 567.713 0.784134
\(725\) 630.267i 0.869333i
\(726\) 199.186 + 199.186i 0.274361 + 0.274361i
\(727\) 605.577i 0.832980i −0.909140 0.416490i \(-0.863260\pi\)
0.909140 0.416490i \(-0.136740\pi\)
\(728\) 91.7128 + 108.497i 0.125979 + 0.149035i
\(729\) 27.0000 0.0370370
\(730\) 381.597 381.597i 0.522736 0.522736i
\(731\) −738.200 −1.00985
\(732\) 25.7231i 0.0351409i
\(733\) 205.946 205.946i 0.280963 0.280963i −0.552530 0.833493i \(-0.686337\pi\)
0.833493 + 0.552530i \(0.186337\pi\)
\(734\) −600.708 + 600.708i −0.818403 + 0.818403i
\(735\) 279.258 + 279.258i 0.379942 + 0.379942i
\(736\) −117.282 117.282i −0.159351 0.159351i
\(737\) −210.249 −0.285276
\(738\) 86.6692i 0.117438i
\(739\) −58.7884 58.7884i −0.0795513 0.0795513i 0.666212 0.745763i \(-0.267915\pi\)
−0.745763 + 0.666212i \(0.767915\pi\)
\(740\) 584.056i 0.789265i
\(741\) 29.9756 357.555i 0.0404529 0.482531i
\(742\) −12.4974 −0.0168429
\(743\) −885.509 + 885.509i −1.19180 + 1.19180i −0.215241 + 0.976561i \(0.569054\pi\)
−0.976561 + 0.215241i \(0.930946\pi\)
\(744\) 186.928 0.251248
\(745\) 1592.09i 2.13704i
\(746\) 671.836 671.836i 0.900584 0.900584i
\(747\) 221.396 221.396i 0.296380 0.296380i
\(748\) 101.569 + 101.569i 0.135788 + 0.135788i
\(749\) 337.310 + 337.310i 0.450347 + 0.450347i
\(750\) −85.4923 −0.113990
\(751\) 19.5720i 0.0260612i 0.999915 + 0.0130306i \(0.00414789\pi\)
−0.999915 + 0.0130306i \(0.995852\pi\)
\(752\) 164.785 + 164.785i 0.219128 + 0.219128i
\(753\) 314.154i 0.417203i
\(754\) 48.9282 583.626i 0.0648915 0.774039i
\(755\) −363.482 −0.481433
\(756\) 28.3923 28.3923i 0.0375560 0.0375560i
\(757\) 677.836 0.895424 0.447712 0.894178i \(-0.352239\pi\)
0.447712 + 0.894178i \(0.352239\pi\)
\(758\) 317.597i 0.418994i
\(759\) 87.9615 87.9615i 0.115891 0.115891i
\(760\) 213.282 213.282i 0.280634 0.280634i
\(761\) −62.4449 62.4449i −0.0820563 0.0820563i 0.664887 0.746944i \(-0.268480\pi\)
−0.746944 + 0.664887i \(0.768480\pi\)
\(762\) 301.310 + 301.310i 0.395420 + 0.395420i
\(763\) −651.951 −0.854458
\(764\) 18.5641i 0.0242985i
\(765\) 416.238 + 416.238i 0.544102 + 0.544102i
\(766\) 466.890i 0.609517i
\(767\) 1000.70 + 83.8935i 1.30469 + 0.109379i
\(768\) −27.7128 −0.0360844
\(769\) −71.5950 + 71.5950i −0.0931014 + 0.0931014i −0.752124 0.659022i \(-0.770970\pi\)
0.659022 + 0.752124i \(0.270970\pi\)
\(770\) −89.5692 −0.116324
\(771\) 515.569i 0.668702i
\(772\) −43.4359 + 43.4359i −0.0562642 + 0.0562642i
\(773\) −778.817 + 778.817i −1.00752 + 1.00752i −0.00755317 + 0.999971i \(0.502404\pi\)
−0.999971 + 0.00755317i \(0.997596\pi\)
\(774\) 75.5307 + 75.5307i 0.0975849 + 0.0975849i
\(775\) −533.804 533.804i −0.688779 0.688779i
\(776\) 344.133 0.443471
\(777\) 292.028i 0.375841i
\(778\) −27.6950 27.6950i −0.0355976 0.0355976i
\(779\) 325.528i 0.417879i
\(780\) 300.315 + 25.1769i 0.385020 + 0.0322781i
\(781\) 134.785 0.172580
\(782\) −859.692 + 859.692i −1.09935 + 1.09935i
\(783\) −165.531 −0.211406
\(784\) 136.287i 0.173836i
\(785\) −1075.19 + 1075.19i −1.36967 + 1.36967i
\(786\) −209.769 + 209.769i −0.266882 + 0.266882i
\(787\) 548.883 + 548.883i 0.697437 + 0.697437i 0.963857 0.266420i \(-0.0858407\pi\)
−0.266420 + 0.963857i \(0.585841\pi\)
\(788\) 225.464 + 225.464i 0.286122 + 0.286122i
\(789\) −39.6462 −0.0502486
\(790\) 1402.68i 1.77554i
\(791\) 503.454 + 503.454i 0.636478 + 0.636478i
\(792\) 20.7846i 0.0262432i
\(793\) −73.7231 + 62.3181i −0.0929674 + 0.0785853i
\(794\) −797.384 −1.00426
\(795\) −18.7461 + 18.7461i −0.0235800 + 0.0235800i
\(796\) −490.200 −0.615829
\(797\) 41.5871i 0.0521795i 0.999660 + 0.0260898i \(0.00830557\pi\)
−0.999660 + 0.0260898i \(0.991694\pi\)
\(798\) −106.641 + 106.641i −0.133635 + 0.133635i
\(799\) 1207.89 1207.89i 1.51175 1.51175i
\(800\) 79.1384 + 79.1384i 0.0989230 + 0.0989230i
\(801\) 76.5500 + 76.5500i 0.0955680 + 0.0955680i
\(802\) −278.900 −0.347756
\(803\) 139.674i 0.173941i
\(804\) −210.249 210.249i −0.261503 0.261503i
\(805\) 758.123i 0.941768i
\(806\) −452.862 535.741i −0.561863 0.664691i
\(807\) −382.392 −0.473844
\(808\) 209.072 209.072i 0.258752 0.258752i
\(809\) −1338.40 −1.65439 −0.827194 0.561916i \(-0.810064\pi\)
−0.827194 + 0.561916i \(0.810064\pi\)
\(810\) 85.1769i 0.105157i
\(811\) 257.258 257.258i 0.317210 0.317210i −0.530484 0.847695i \(-0.677990\pi\)
0.847695 + 0.530484i \(0.177990\pi\)
\(812\) −174.067 + 174.067i −0.214368 + 0.214368i
\(813\) −257.993 257.993i −0.317335 0.317335i
\(814\) −106.890 106.890i −0.131314 0.131314i
\(815\) 117.779 0.144515
\(816\) 203.138i 0.248944i
\(817\) −283.692 283.692i −0.347236 0.347236i
\(818\) 803.626i 0.982427i
\(819\) −150.158 12.5885i −0.183343 0.0153705i
\(820\) 273.415 0.333433
\(821\) −306.873 + 306.873i −0.373779 + 0.373779i −0.868852 0.495072i \(-0.835142\pi\)
0.495072 + 0.868852i \(0.335142\pi\)
\(822\) 450.515 0.548072
\(823\) 1037.92i 1.26114i −0.776131 0.630571i \(-0.782821\pi\)
0.776131 0.630571i \(-0.217179\pi\)
\(824\) 73.3590 73.3590i 0.0890279 0.0890279i
\(825\) −59.3538 + 59.3538i −0.0719440 + 0.0719440i
\(826\) −298.459 298.459i −0.361330 0.361330i
\(827\) 658.153 + 658.153i 0.795831 + 0.795831i 0.982435 0.186604i \(-0.0597481\pi\)
−0.186604 + 0.982435i \(0.559748\pi\)
\(828\) 175.923 0.212467
\(829\) 372.354i 0.449160i −0.974456 0.224580i \(-0.927899\pi\)
0.974456 0.224580i \(-0.0721010\pi\)
\(830\) −698.438 698.438i −0.841492 0.841492i
\(831\) 47.1384i 0.0567250i
\(832\) 67.1384 + 79.4256i 0.0806952 + 0.0954635i
\(833\) 999.002 1.19928
\(834\) 47.0052 47.0052i 0.0563611 0.0563611i
\(835\) 1131.07 1.35457
\(836\) 78.0666i 0.0933812i
\(837\) −140.196 + 140.196i −0.167498 + 0.167498i
\(838\) 139.177 139.177i 0.166082 0.166082i
\(839\) 1018.87 + 1018.87i 1.21438 + 1.21438i 0.969570 + 0.244813i \(0.0787266\pi\)
0.244813 + 0.969570i \(0.421273\pi\)
\(840\) −89.5692 89.5692i −0.106630 0.106630i
\(841\) 173.831 0.206695
\(842\) 720.487i 0.855685i
\(843\) 89.4115 + 89.4115i 0.106064 + 0.106064i
\(844\) 690.564i 0.818204i
\(845\) −655.401 921.706i −0.775623 1.09078i
\(846\) −247.177 −0.292171
\(847\) −314.186 + 314.186i −0.370940 + 0.370940i
\(848\) −9.14875 −0.0107886
\(849\) 162.480i 0.191378i
\(850\) 580.095 580.095i 0.682464 0.682464i
\(851\) 904.726 904.726i 1.06313 1.06313i
\(852\) 134.785 + 134.785i 0.158198 + 0.158198i
\(853\) −366.790 366.790i −0.430000 0.430000i 0.458628 0.888628i \(-0.348341\pi\)
−0.888628 + 0.458628i \(0.848341\pi\)
\(854\) 40.5744 0.0475110
\(855\) 319.923i 0.374179i
\(856\) 246.928 + 246.928i 0.288468 + 0.288468i
\(857\) 469.244i 0.547542i 0.961795 + 0.273771i \(0.0882711\pi\)
−0.961795 + 0.273771i \(0.911729\pi\)
\(858\) −59.5692 + 50.3538i −0.0694280 + 0.0586874i
\(859\) −1238.66 −1.44197 −0.720987 0.692948i \(-0.756311\pi\)
−0.720987 + 0.692948i \(0.756311\pi\)
\(860\) 238.277 238.277i 0.277066 0.277066i
\(861\) −136.708 −0.158778
\(862\) 427.044i 0.495410i
\(863\) −5.71143 + 5.71143i −0.00661811 + 0.00661811i −0.710408 0.703790i \(-0.751490\pi\)
0.703790 + 0.710408i \(0.251490\pi\)
\(864\) 20.7846 20.7846i 0.0240563 0.0240563i
\(865\) 328.392 + 328.392i 0.379644 + 0.379644i
\(866\) −446.708 446.708i −0.515829 0.515829i
\(867\) 988.468 1.14010
\(868\) 294.851i 0.339690i
\(869\) −256.708 256.708i −0.295406 0.295406i
\(870\) 522.200i 0.600230i
\(871\) −93.2192 + 1111.94i −0.107025 + 1.27662i
\(872\) −477.261 −0.547318
\(873\) −258.100 + 258.100i −0.295647 + 0.295647i
\(874\) −660.764 −0.756023
\(875\) 134.851i 0.154116i
\(876\) −139.674 + 139.674i −0.159446 + 0.159446i
\(877\) 591.287 591.287i 0.674216 0.674216i −0.284469 0.958685i \(-0.591817\pi\)
0.958685 + 0.284469i \(0.0918174\pi\)
\(878\) −164.238 164.238i −0.187060 0.187060i
\(879\) 207.919 + 207.919i 0.236541 + 0.236541i
\(880\) −65.5692 −0.0745105
\(881\) 663.997i 0.753686i 0.926277 + 0.376843i \(0.122990\pi\)
−0.926277 + 0.376843i \(0.877010\pi\)
\(882\) −102.215 102.215i −0.115890 0.115890i
\(883\) 570.192i 0.645744i −0.946443 0.322872i \(-0.895352\pi\)
0.946443 0.322872i \(-0.104648\pi\)
\(884\) 582.200 492.133i 0.658597 0.556712i
\(885\) −895.377 −1.01173
\(886\) −458.736 + 458.736i −0.517761 + 0.517761i
\(887\) 481.031 0.542312 0.271156 0.962535i \(-0.412594\pi\)
0.271156 + 0.962535i \(0.412594\pi\)
\(888\) 213.779i 0.240743i
\(889\) −475.272 + 475.272i −0.534614 + 0.534614i
\(890\) 241.492 241.492i 0.271340 0.271340i
\(891\) 15.5885 + 15.5885i 0.0174955 + 0.0174955i
\(892\) −341.177 341.177i −0.382485 0.382485i
\(893\) 928.392 1.03963
\(894\) 582.746i 0.651841i
\(895\) −782.123 782.123i −0.873880 0.873880i
\(896\) 43.7128i 0.0487866i
\(897\) −426.200 504.200i −0.475139 0.562096i
\(898\) 443.551 0.493932
\(899\) 859.510 859.510i 0.956074 0.956074i
\(900\) −118.708 −0.131897
\(901\) 67.0615i 0.0744301i
\(902\) −50.0385 + 50.0385i −0.0554750 + 0.0554750i
\(903\) −119.138 + 119.138i −0.131936 + 0.131936i
\(904\) 368.554 + 368.554i 0.407692 + 0.407692i
\(905\) 1343.22 + 1343.22i 1.48422 + 1.48422i
\(906\) 133.044 0.146847
\(907\) 193.331i 0.213154i 0.994304 + 0.106577i \(0.0339891\pi\)
−0.994304 + 0.106577i \(0.966011\pi\)
\(908\) −338.736 338.736i −0.373057 0.373057i
\(909\) 313.608i 0.345003i
\(910\) −39.7128 + 473.703i −0.0436405 + 0.520552i
\(911\) −868.743 −0.953615 −0.476808 0.879008i \(-0.658206\pi\)
−0.476808 + 0.879008i \(0.658206\pi\)
\(912\) −78.0666 + 78.0666i −0.0855994 + 0.0855994i
\(913\) 255.646 0.280007
\(914\) 105.923i 0.115890i
\(915\) 60.8616 60.8616i 0.0665154 0.0665154i
\(916\) 283.646 283.646i 0.309657 0.309657i
\(917\) −330.879 330.879i −0.360828 0.360828i
\(918\) −152.354 152.354i −0.165963 0.165963i
\(919\) 389.108 0.423403 0.211702 0.977334i \(-0.432100\pi\)
0.211702 + 0.977334i \(0.432100\pi\)
\(920\) 554.985i 0.603244i
\(921\) −12.9705 12.9705i −0.0140830 0.0140830i
\(922\) 134.900i 0.146312i
\(923\) 59.7602 712.832i 0.0647456 0.772299i
\(924\) 32.7846 0.0354812
\(925\) −610.482 + 610.482i −0.659980 + 0.659980i
\(926\) 1098.49 1.18628
\(927\) 110.038i 0.118704i
\(928\) −127.426 + 127.426i −0.137312 + 0.137312i
\(929\) −429.870 + 429.870i −0.462724 + 0.462724i −0.899547 0.436823i \(-0.856103\pi\)
0.436823 + 0.899547i \(0.356103\pi\)
\(930\) 442.277 + 442.277i 0.475567 + 0.475567i
\(931\) 383.919 + 383.919i 0.412373 + 0.412373i
\(932\) −256.077 −0.274761
\(933\) 501.215i 0.537208i
\(934\) 30.1821 + 30.1821i 0.0323148 + 0.0323148i
\(935\) 480.631i 0.514044i
\(936\) −109.923 9.21539i −0.117439 0.00984550i
\(937\) 916.441 0.978059 0.489029 0.872267i \(-0.337351\pi\)
0.489029 + 0.872267i \(0.337351\pi\)
\(938\) 331.636 331.636i 0.353556 0.353556i
\(939\) −600.746 −0.639772
\(940\) 779.769i 0.829542i
\(941\) 835.601 835.601i 0.887993 0.887993i −0.106337 0.994330i \(-0.533912\pi\)
0.994330 + 0.106337i \(0.0339124\pi\)
\(942\) 393.549 393.549i 0.417780 0.417780i
\(943\) −423.531 423.531i −0.449131 0.449131i
\(944\) −218.487 218.487i −0.231448 0.231448i
\(945\) 134.354 0.142173
\(946\) 87.2154i 0.0921939i
\(947\) −378.506 378.506i −0.399690 0.399690i 0.478434 0.878124i \(-0.341205\pi\)
−0.878124 + 0.478434i \(0.841205\pi\)
\(948\) 513.415i 0.541577i
\(949\) 738.692 + 61.9282i 0.778390 + 0.0652563i
\(950\) 445.864 0.469330
\(951\) 168.042 168.042i 0.176701 0.176701i
\(952\) −320.420 −0.336576
\(953\) 839.556i 0.880961i −0.897762 0.440481i \(-0.854808\pi\)
0.897762 0.440481i \(-0.145192\pi\)
\(954\) 6.86156 6.86156i 0.00719241 0.00719241i
\(955\) 43.9230 43.9230i 0.0459927 0.0459927i
\(956\) −176.038 176.038i −0.184141 0.184141i
\(957\) −95.5692 95.5692i −0.0998633 0.0998633i
\(958\) −517.741 −0.540439
\(959\) 710.620i 0.741001i
\(960\) −65.5692 65.5692i −0.0683013 0.0683013i
\(961\) 494.923i 0.515008i
\(962\) −612.697 + 517.913i −0.636900 + 0.538371i
\(963\) −370.392 −0.384623
\(964\) −294.918 + 294.918i −0.305931 + 0.305931i
\(965\) −205.541 −0.212996
\(966\) 277.492i 0.287259i
\(967\) −375.745 + 375.745i −0.388567 + 0.388567i −0.874176 0.485609i \(-0.838598\pi\)
0.485609 + 0.874176i \(0.338598\pi\)
\(968\) −230.000 + 230.000i −0.237603 + 0.237603i
\(969\) 572.238 + 572.238i 0.590545 + 0.590545i
\(970\) 814.228 + 814.228i 0.839410 + 0.839410i
\(971\) 134.523 0.138541 0.0692703 0.997598i \(-0.477933\pi\)
0.0692703 + 0.997598i \(0.477933\pi\)
\(972\) 31.1769i 0.0320750i
\(973\) 74.1436 + 74.1436i 0.0762010 + 0.0762010i
\(974\) 549.121i 0.563779i
\(975\) 287.587 + 340.219i 0.294961 + 0.348943i
\(976\) 29.7025 0.0304329
\(977\) 708.060 708.060i 0.724729 0.724729i −0.244836 0.969565i \(-0.578734\pi\)
0.969565 + 0.244836i \(0.0787340\pi\)
\(978\) −43.1103 −0.0440800
\(979\) 88.3923i 0.0902884i
\(980\) −322.459 + 322.459i −0.329040 + 0.329040i
\(981\) 357.946 357.946i 0.364879 0.364879i
\(982\) −220.726 220.726i −0.224771 0.224771i
\(983\) −904.881 904.881i −0.920530 0.920530i 0.0765369 0.997067i \(-0.475614\pi\)
−0.997067 + 0.0765369i \(0.975614\pi\)
\(984\) −100.077 −0.101704
\(985\) 1066.91i 1.08315i
\(986\) 934.046 + 934.046i 0.947308 + 0.947308i
\(987\) 389.885i 0.395020i
\(988\) 412.869 + 34.6128i 0.417884 + 0.0350332i
\(989\) −738.200 −0.746410
\(990\) 49.1769 49.1769i 0.0496737 0.0496737i
\(991\) 29.0155 0.0292790 0.0146395 0.999893i \(-0.495340\pi\)
0.0146395 + 0.999893i \(0.495340\pi\)
\(992\) 215.846i 0.217587i
\(993\) 218.463 218.463i 0.220003 0.220003i
\(994\) −212.603 + 212.603i −0.213886 + 0.213886i
\(995\) −1159.83 1159.83i −1.16565 1.16565i
\(996\) 255.646 + 255.646i 0.256673 + 0.256673i
\(997\) 336.123 0.337134 0.168567 0.985690i \(-0.446086\pi\)
0.168567 + 0.985690i \(0.446086\pi\)
\(998\) 1250.13i 1.25264i
\(999\) 160.335 + 160.335i 0.160495 + 0.160495i
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 78.3.f.a.31.1 4
3.2 odd 2 234.3.i.b.109.1 4
4.3 odd 2 624.3.ba.a.577.2 4
13.5 odd 4 1014.3.f.a.775.1 4
13.8 odd 4 inner 78.3.f.a.73.1 yes 4
13.12 even 2 1014.3.f.a.577.1 4
39.8 even 4 234.3.i.b.73.1 4
52.47 even 4 624.3.ba.a.385.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.3.f.a.31.1 4 1.1 even 1 trivial
78.3.f.a.73.1 yes 4 13.8 odd 4 inner
234.3.i.b.73.1 4 39.8 even 4
234.3.i.b.109.1 4 3.2 odd 2
624.3.ba.a.385.2 4 52.47 even 4
624.3.ba.a.577.2 4 4.3 odd 2
1014.3.f.a.577.1 4 13.12 even 2
1014.3.f.a.775.1 4 13.5 odd 4