Properties

Label 78.3.f.a.73.1
Level $78$
Weight $3$
Character 78.73
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 73.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 78.73
Dual form 78.3.f.a.31.1

$q$-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 \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 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 0.998635 0.0522252i \(-0.0166314\pi\)
−0.0522252 + 0.998635i \(0.516631\pi\)
\(6\) −1.73205 1.73205i −0.288675 0.288675i
\(7\) −2.73205 + 2.73205i −0.390293 + 0.390293i −0.874792 0.484499i \(-0.839002\pi\)
0.484499 + 0.874792i \(0.339002\pi\)
\(8\) −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 −0.623981 0.781440i \(-0.714486\pi\)
0.781440 + 0.623981i \(0.214486\pi\)
\(12\) 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 \(-0.668981\pi\)
0.506282 0.862368i \(-0.331019\pi\)
\(18\) 3.00000 + 3.00000i 0.166667 + 0.166667i
\(19\) −11.2679 11.2679i −0.593050 0.593050i 0.345404 0.938454i \(-0.387742\pi\)
−0.938454 + 0.345404i \(0.887742\pi\)
\(20\) −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 \(-0.780009\pi\)
0.770531 0.637402i \(-0.219991\pi\)
\(24\) 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 0.992510 0.122163i \(-0.0389830\pi\)
−0.122163 + 0.992510i \(0.538983\pi\)
\(32\) −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 −0.988055 0.154099i \(-0.950753\pi\)
0.154099 + 0.988055i \(0.450753\pi\)
\(38\) 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 0.508656 0.860970i \(-0.330142\pi\)
−0.860970 + 0.508656i \(0.830142\pi\)
\(42\) 9.46410 0.225336
\(43\) 25.1769i 0.585510i −0.956188 0.292755i \(-0.905428\pi\)
0.956188 0.292755i \(-0.0945720\pi\)
\(44\) 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 −0.993172 0.116658i \(-0.962782\pi\)
0.116658 + 0.993172i \(0.462782\pi\)
\(48\) 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 −0.0716379 0.997431i \(-0.522823\pi\)
0.997431 + 0.0716379i \(0.0228226\pi\)
\(60\) 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 0.0900619 0.995936i \(-0.471294\pi\)
−0.995936 + 0.0900619i \(0.971294\pi\)
\(68\) 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 0.925866 0.377852i \(-0.123337\pi\)
−0.377852 + 0.925866i \(0.623337\pi\)
\(72\) −6.00000 + 6.00000i −0.0833333 + 0.0833333i
\(73\) 40.3205 40.3205i 0.552336 0.552336i −0.374779 0.927114i \(-0.622281\pi\)
0.927114 + 0.374779i \(0.122281\pi\)
\(74\) −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 0.994441 0.105300i \(-0.0335802\pi\)
−0.105300 + 0.994441i \(0.533580\pi\)
\(84\) 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 −0.549071 0.835775i \(-0.685019\pi\)
0.835775 + 0.549071i \(0.185019\pi\)
\(90\) 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 0.107287 0.994228i \(-0.465784\pi\)
−0.994228 + 0.107287i \(0.965784\pi\)
\(98\) −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 \(-0.826861\pi\)
0.855681 0.517504i \(-0.173139\pi\)
\(102\) −50.7846 + 50.7846i −0.497888 + 0.497888i
\(103\) 36.6795i 0.356112i −0.984020 0.178056i \(-0.943019\pi\)
0.984020 0.178056i \(-0.0569808\pi\)
\(104\) −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 0.995027 + 0.0996097i \(0.0317594\pi\)
0.0996097 + 0.995027i \(0.468241\pi\)
\(110\) 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 \(0.240149\pi\)
−0.728648 + 0.684888i \(0.759851\pi\)
\(128\) 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 −0.998775 0.0494861i \(-0.984242\pi\)
0.0494861 + 0.998775i \(0.484242\pi\)
\(138\) −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 −0.990336 0.138686i \(-0.955712\pi\)
−0.138686 0.990336i \(-0.544288\pi\)
\(150\) 34.2679 34.2679i 0.228453 0.228453i
\(151\) −38.4064 + 38.4064i −0.254347 + 0.254347i −0.822750 0.568403i \(-0.807561\pi\)
0.568403 + 0.822750i \(0.307561\pi\)
\(152\) 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 −0.667901 0.744250i \(-0.732807\pi\)
0.744250 + 0.667901i \(0.232807\pi\)
\(164\) 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 −0.252071 0.967709i \(-0.581112\pi\)
0.967709 + 0.252071i \(0.0811116\pi\)
\(168\) 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 \(-0.935720\pi\)
0.979679 0.200571i \(-0.0642796\pi\)
\(174\) −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 \(0.152754\pi\)
−0.887046 + 0.461682i \(0.847246\pi\)
\(180\) −28.3923 + 28.3923i −0.157735 + 0.157735i
\(181\) 283.856i 1.56827i −0.620592 0.784134i \(-0.713108\pi\)
0.620592 0.784134i \(-0.286892\pi\)
\(182\) −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 −0.761129 0.648601i \(-0.775355\pi\)
0.648601 + 0.761129i \(0.275355\pi\)
\(194\) 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 0.360511 0.932755i \(-0.382602\pi\)
−0.932755 + 0.360511i \(0.882602\pi\)
\(198\) 10.3923 0.0524864
\(199\) 245.100i 1.23166i 0.787880 + 0.615829i \(0.211179\pi\)
−0.787880 + 0.615829i \(0.788821\pi\)
\(200\) −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 0.977216 0.212246i \(-0.0680777\pi\)
−0.212246 + 0.977216i \(0.568078\pi\)
\(224\) 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 0.973747 0.227633i \(-0.0730986\pi\)
−0.227633 + 0.973747i \(0.573099\pi\)
\(228\) −39.0333 + 39.0333i −0.171199 + 0.171199i
\(229\) 141.823 141.823i 0.619315 0.619315i −0.326041 0.945356i \(-0.605715\pi\)
0.945356 + 0.326041i \(0.105715\pi\)
\(230\) 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 \(0.0885986\pi\)
−0.961513 + 0.274761i \(0.911401\pi\)
\(234\) 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 0.866850 0.498569i \(-0.166141\pi\)
−0.498569 + 0.866850i \(0.666141\pi\)
\(240\) 32.7846 + 32.7846i 0.136603 + 0.136603i
\(241\) −147.459 + 147.459i −0.611863 + 0.611863i −0.943431 0.331568i \(-0.892422\pi\)
0.331568 + 0.943431i \(0.392422\pi\)
\(242\) −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 \(0.117670\pi\)
−0.932446 + 0.361308i \(0.882330\pi\)
\(252\) −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 \(-0.803399\pi\)
0.815247 0.579113i \(-0.196601\pi\)
\(258\) −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 −0.376696 0.926337i \(-0.622940\pi\)
0.926337 + 0.376696i \(0.122940\pi\)
\(272\) 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 \(0.0156434\pi\)
−0.998793 + 0.0491253i \(0.984357\pi\)
\(278\) −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 −0.792969 0.609262i \(-0.791466\pi\)
0.609262 + 0.792969i \(0.291466\pi\)
\(282\) 142.708 0.506056
\(283\) 93.8076i 0.331476i −0.986170 0.165738i \(-0.946999\pi\)
0.986170 0.165738i \(-0.0530006\pi\)
\(284\) −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 −0.881634 0.471934i \(-0.843556\pi\)
0.471934 + 0.881634i \(0.343556\pi\)
\(294\) 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 −0.694805 0.719198i \(-0.744509\pi\)
0.719198 + 0.694805i \(0.244509\pi\)
\(308\) −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 \(-0.845969\pi\)
0.885187 0.465236i \(-0.154031\pi\)
\(312\) 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 0.537322 0.843377i \(-0.319436\pi\)
−0.843377 + 0.537322i \(0.819436\pi\)
\(318\) −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 0.490427 0.871483i \(-0.336841\pi\)
−0.871483 + 0.490427i \(0.836841\pi\)
\(332\) −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 \(-0.784002\pi\)
0.778465 0.627688i \(-0.215998\pi\)
\(338\) −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 −0.652432 0.757847i \(-0.726251\pi\)
0.757847 + 0.652432i \(0.226251\pi\)
\(350\) 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 0.854070 0.520159i \(-0.174127\pi\)
−0.520159 + 0.854070i \(0.674127\pi\)
\(354\) −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 −0.688599 0.725143i \(-0.741774\pi\)
0.725143 + 0.688599i \(0.241774\pi\)
\(360\) −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 0.884857 0.465863i \(-0.154256\pi\)
−0.465863 + 0.884857i \(0.654256\pi\)
\(380\) 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 0.942820 0.333303i \(-0.108163\pi\)
−0.333303 + 0.942820i \(0.608163\pi\)
\(384\) −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 \(0.0113335\pi\)
−0.999366 + 0.0355976i \(0.988667\pi\)
\(390\) 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 −0.00427158 + 0.999991i \(0.501360\pi\)
−0.999991 + 0.00427158i \(0.998640\pi\)
\(398\) −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 −0.859273 0.511517i \(-0.829084\pi\)
0.511517 + 0.859273i \(0.329084\pi\)
\(402\) 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 0.999848 0.0174209i \(-0.00554553\pi\)
−0.0174209 + 0.999848i \(0.505546\pi\)
\(410\) 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 0.990826 0.135141i \(-0.0431487\pi\)
−0.135141 + 0.990826i \(0.543149\pi\)
\(422\) 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 0.910006 0.414596i \(-0.136077\pi\)
−0.414596 + 0.910006i \(0.636077\pi\)
\(432\) 20.7846 0.0481125
\(433\) 446.708i 1.03166i 0.856692 + 0.515829i \(0.172516\pi\)
−0.856692 + 0.515829i \(0.827484\pi\)
\(434\) −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 \(0.0598958\pi\)
−0.982349 + 0.187060i \(0.940104\pi\)
\(440\) −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 −0.415610 0.909543i \(-0.636432\pi\)
0.909543 + 0.415610i \(0.136432\pi\)
\(450\) −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 0.762673 0.646784i \(-0.223886\pi\)
−0.646784 + 0.762673i \(0.723886\pi\)
\(458\) 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 0.776468 0.630156i \(-0.217009\pi\)
−0.630156 + 0.776468i \(0.717009\pi\)
\(462\) 16.3923 16.3923i 0.0354812 0.0354812i
\(463\) 549.247 549.247i 1.18628 1.18628i 0.208191 0.978088i \(-0.433242\pi\)
0.978088 0.208191i \(-0.0667576\pi\)
\(464\) −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 \(-0.989712\pi\)
0.999478 0.0323148i \(-0.0102879\pi\)
\(468\) −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 −0.923658 0.383218i \(-0.874816\pi\)
0.383218 + 0.923658i \(0.374816\pi\)
\(480\) 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 0.366600 0.930379i \(-0.380522\pi\)
−0.930379 + 0.366600i \(0.880522\pi\)
\(488\) 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 \(0.0721635\pi\)
−0.974412 + 0.224771i \(0.927836\pi\)
\(492\) −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 −0.954534 0.298102i \(-0.903647\pi\)
−0.298102 0.954534i \(-0.596353\pi\)
\(500\) 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 0.981355 0.192204i \(-0.0615634\pi\)
−0.192204 + 0.981355i \(0.561563\pi\)
\(510\) −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 −0.949643 0.313333i \(-0.898554\pi\)
0.313333 + 0.949643i \(0.398554\pi\)
\(542\) 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 −0.612370 0.790571i \(-0.709784\pi\)
0.790571 + 0.612370i \(0.209784\pi\)
\(558\) 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 \(0.194903\pi\)
−0.818326 + 0.574755i \(0.805097\pi\)
\(564\) 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 \(0.211324\pi\)
−0.787598 + 0.616189i \(0.788676\pi\)
\(570\) −184.708 + 184.708i −0.324049 + 0.324049i
\(571\) 218.746i 0.383093i 0.981484 + 0.191547i \(0.0613503\pi\)
−0.981484 + 0.191547i \(0.938650\pi\)
\(572\) 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 0.696316 0.717735i \(-0.254821\pi\)
−0.717735 + 0.696316i \(0.754821\pi\)
\(578\) −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 0.610818 0.791771i \(-0.290841\pi\)
−0.791771 + 0.610818i \(0.790841\pi\)
\(588\) 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 0.370895 0.928675i \(-0.379051\pi\)
0.928675 0.370895i \(-0.120949\pi\)
\(594\) −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 0.685289 0.728272i \(-0.259676\pi\)
−0.728272 + 0.685289i \(0.759676\pi\)
\(614\) 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 0.942531 0.334118i \(-0.108438\pi\)
−0.334118 + 0.942531i \(0.608438\pi\)
\(618\) −63.5307 + 63.5307i −0.102801 + 0.102801i
\(619\) 264.070 264.070i 0.426608 0.426608i −0.460863 0.887471i \(-0.652460\pi\)
0.887471 + 0.460863i \(0.152460\pi\)
\(620\) −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 −0.964374 0.264543i \(-0.914779\pi\)
0.264543 + 0.964374i \(0.414779\pi\)
\(632\) 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 \(-0.775875\pi\)
0.762188 0.647356i \(-0.224125\pi\)
\(642\) 213.846 + 213.846i 0.333094 + 0.333094i
\(643\) 424.196 + 424.196i 0.659714 + 0.659714i 0.955312 0.295598i \(-0.0955190\pi\)
−0.295598 + 0.955312i \(0.595519\pi\)
\(644\) −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 \(0.120413\pi\)
−0.929298 + 0.369330i \(0.879587\pi\)
\(648\) −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 −0.958855 0.283895i \(-0.908373\pi\)
0.283895 + 0.958855i \(0.408373\pi\)
\(662\) 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 \(-0.958206\pi\)
0.991393 0.130922i \(-0.0417936\pi\)
\(674\) 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 −0.446487 0.894790i \(-0.647325\pi\)
0.894790 + 0.446487i \(0.147325\pi\)
\(684\) 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 0.274401 0.961615i \(-0.411521\pi\)
−0.961615 + 0.274401i \(0.911521\pi\)
\(692\) 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 \(0.0465912\pi\)
−0.989307 + 0.145848i \(0.953409\pi\)
\(702\) −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 −0.994252 0.107062i \(-0.965856\pi\)
0.107062 + 0.994252i \(0.465856\pi\)
\(710\) −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 \(-0.795032\pi\)
0.799745 0.600340i \(-0.204968\pi\)
\(720\) −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 \(0.136740\pi\)
−0.909140 + 0.416490i \(0.863260\pi\)
\(728\) 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 0.833493 0.552530i \(-0.186337\pi\)
−0.552530 + 0.833493i \(0.686337\pi\)
\(734\) −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 −0.745763 0.666212i \(-0.767915\pi\)
0.666212 + 0.745763i \(0.267915\pi\)
\(740\) 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 −0.976561 0.215241i \(-0.930946\pi\)
−0.215241 0.976561i \(-0.569054\pi\)
\(744\) 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 \(-0.995852\pi\)
0.999915 0.0130306i \(-0.00414789\pi\)
\(752\) 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 −0.746944 0.664887i \(-0.768480\pi\)
0.664887 + 0.746944i \(0.268480\pi\)
\(762\) 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 0.659022 0.752124i \(-0.270970\pi\)
−0.752124 + 0.659022i \(0.770970\pi\)
\(770\) −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 −0.999971 0.00755317i \(-0.997596\pi\)
−0.00755317 0.999971i \(-0.502404\pi\)
\(774\) 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 −0.266420 0.963857i \(-0.585841\pi\)
0.963857 + 0.266420i \(0.0858407\pi\)
\(788\) 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 \(-0.991694\pi\)
0.999660 0.0260898i \(-0.00830557\pi\)
\(798\) −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 0.847695 0.530484i \(-0.177990\pi\)
−0.530484 + 0.847695i \(0.677990\pi\)
\(812\) −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 0.495072 0.868852i \(-0.335142\pi\)
−0.868852 + 0.495072i \(0.835142\pi\)
\(822\) 450.515 0.548072
\(823\) 1037.92i 1.26114i 0.776131 + 0.630571i \(0.217179\pi\)
−0.776131 + 0.630571i \(0.782821\pi\)
\(824\) 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 −0.186604 0.982435i \(-0.559748\pi\)
0.982435 + 0.186604i \(0.0597481\pi\)
\(828\) 175.923 0.212467
\(829\) 372.354i 0.449160i 0.974456 + 0.224580i \(0.0721010\pi\)
−0.974456 + 0.224580i \(0.927899\pi\)
\(830\) −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 0.244813 0.969570i \(-0.421273\pi\)
0.969570 0.244813i \(-0.0787266\pi\)
\(840\) −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 −0.888628 0.458628i \(-0.848341\pi\)
0.458628 + 0.888628i \(0.348341\pi\)
\(854\) 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 \(-0.911729\pi\)
0.961795 0.273771i \(-0.0882711\pi\)
\(858\) −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 0.703790 0.710408i \(-0.251490\pi\)
−0.710408 + 0.703790i \(0.751490\pi\)
\(864\) 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 0.958685 0.284469i \(-0.0918174\pi\)
−0.284469 + 0.958685i \(0.591817\pi\)
\(878\) −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 \(-0.877010\pi\)
0.926277 0.376843i \(-0.122990\pi\)
\(882\) −102.215 + 102.215i −0.115890 + 0.115890i
\(883\) 570.192i 0.645744i 0.946443 + 0.322872i \(0.104648\pi\)
−0.946443 + 0.322872i \(0.895352\pi\)
\(884\) 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 \(-0.966011\pi\)
0.994304 0.106577i \(-0.0339891\pi\)
\(908\) −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 0.436823 0.899547i \(-0.356103\pi\)
−0.899547 + 0.436823i \(0.856103\pi\)
\(930\) 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 0.994330 0.106337i \(-0.0339124\pi\)
−0.106337 + 0.994330i \(0.533912\pi\)
\(942\) 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 −0.878124 0.478434i \(-0.841205\pi\)
0.478434 + 0.878124i \(0.341205\pi\)
\(948\) 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 \(0.145192\pi\)
−0.897762 + 0.440481i \(0.854808\pi\)
\(954\) 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 0.485609 0.874176i \(-0.338598\pi\)
−0.874176 + 0.485609i \(0.838598\pi\)
\(968\) −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 0.969565 0.244836i \(-0.0787340\pi\)
−0.244836 + 0.969565i \(0.578734\pi\)
\(978\) −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 −0.997067 0.0765369i \(-0.975614\pi\)
0.0765369 + 0.997067i \(0.475614\pi\)
\(984\) −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.73.1 yes 4
3.2 odd 2 234.3.i.b.73.1 4
4.3 odd 2 624.3.ba.a.385.2 4
13.5 odd 4 inner 78.3.f.a.31.1 4
13.8 odd 4 1014.3.f.a.577.1 4
13.12 even 2 1014.3.f.a.775.1 4
39.5 even 4 234.3.i.b.109.1 4
52.31 even 4 624.3.ba.a.577.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.3.f.a.31.1 4 13.5 odd 4 inner
78.3.f.a.73.1 yes 4 1.1 even 1 trivial
234.3.i.b.73.1 4 3.2 odd 2
234.3.i.b.109.1 4 39.5 even 4
624.3.ba.a.385.2 4 4.3 odd 2
624.3.ba.a.577.2 4 52.31 even 4
1014.3.f.a.577.1 4 13.8 odd 4
1014.3.f.a.775.1 4 13.12 even 2