Properties

Label 380.2.k.d.343.7
Level $380$
Weight $2$
Character 380.343
Analytic conductor $3.034$
Analytic rank $0$
Dimension $52$
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] = [380,2,Mod(267,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.267");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.k (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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 343.7
Character \(\chi\) \(=\) 380.343
Dual form 380.2.k.d.267.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.07073 + 0.923868i) q^{2} +(-1.14885 + 1.14885i) q^{3} +(0.292934 - 1.97843i) q^{4} +(1.95382 + 1.08746i) q^{5} +(0.168724 - 2.29149i) q^{6} +(-2.70883 - 2.70883i) q^{7} +(1.51416 + 2.38900i) q^{8} +0.360306i q^{9} +O(q^{10})\) \(q+(-1.07073 + 0.923868i) q^{2} +(-1.14885 + 1.14885i) q^{3} +(0.292934 - 1.97843i) q^{4} +(1.95382 + 1.08746i) q^{5} +(0.168724 - 2.29149i) q^{6} +(-2.70883 - 2.70883i) q^{7} +(1.51416 + 2.38900i) q^{8} +0.360306i q^{9} +(-3.09669 + 0.640694i) q^{10} +4.11798i q^{11} +(1.93638 + 2.60945i) q^{12} +(-1.95079 - 1.95079i) q^{13} +(5.40302 + 0.397828i) q^{14} +(-3.49397 + 0.995314i) q^{15} +(-3.82838 - 1.15910i) q^{16} +(-4.15549 + 4.15549i) q^{17} +(-0.332875 - 0.385791i) q^{18} -1.00000 q^{19} +(2.72381 - 3.54695i) q^{20} +6.22405 q^{21} +(-3.80447 - 4.40926i) q^{22} +(-3.01995 + 3.01995i) q^{23} +(-4.48413 - 1.00506i) q^{24} +(2.63485 + 4.24942i) q^{25} +(3.89106 + 0.286501i) q^{26} +(-3.86047 - 3.86047i) q^{27} +(-6.15273 + 4.56572i) q^{28} -2.35086i q^{29} +(2.82157 - 4.29368i) q^{30} -5.48110i q^{31} +(5.17002 - 2.29583i) q^{32} +(-4.73093 - 4.73093i) q^{33} +(0.610291 - 8.28855i) q^{34} +(-2.34682 - 8.23831i) q^{35} +(0.712840 + 0.105546i) q^{36} +(3.69981 - 3.69981i) q^{37} +(1.07073 - 0.923868i) q^{38} +4.48233 q^{39} +(0.360440 + 6.31428i) q^{40} -9.82744 q^{41} +(-6.66429 + 5.75020i) q^{42} +(-8.96408 + 8.96408i) q^{43} +(8.14714 + 1.20630i) q^{44} +(-0.391819 + 0.703974i) q^{45} +(0.443521 - 6.02359i) q^{46} +(-0.482563 - 0.482563i) q^{47} +(5.72985 - 3.06659i) q^{48} +7.67547i q^{49} +(-6.74712 - 2.11574i) q^{50} -9.54804i q^{51} +(-4.43097 + 3.28806i) q^{52} +(-2.71437 - 2.71437i) q^{53} +(7.70010 + 0.566964i) q^{54} +(-4.47815 + 8.04581i) q^{55} +(2.36981 - 10.5730i) q^{56} +(1.14885 - 1.14885i) q^{57} +(2.17189 + 2.51714i) q^{58} +9.02322 q^{59} +(0.945656 + 7.20414i) q^{60} -4.23945 q^{61} +(5.06381 + 5.86878i) q^{62} +(0.976005 - 0.976005i) q^{63} +(-3.41467 + 7.23464i) q^{64} +(-1.69009 - 5.93292i) q^{65} +(9.43631 + 0.694802i) q^{66} +(6.49679 + 6.49679i) q^{67} +(7.00407 + 9.43864i) q^{68} -6.93891i q^{69} +(10.1239 + 6.65288i) q^{70} +14.9562i q^{71} +(-0.860771 + 0.545559i) q^{72} +(7.29798 + 7.29798i) q^{73} +(-0.543368 + 7.37965i) q^{74} +(-7.90896 - 1.85490i) q^{75} +(-0.292934 + 1.97843i) q^{76} +(11.1549 - 11.1549i) q^{77} +(-4.79937 + 4.14108i) q^{78} +3.64828 q^{79} +(-6.21949 - 6.42790i) q^{80} +7.78926 q^{81} +(10.5226 - 9.07926i) q^{82} +(8.32940 - 8.32940i) q^{83} +(1.82324 - 12.3138i) q^{84} +(-12.6380 + 3.60015i) q^{85} +(1.31650 - 17.8798i) q^{86} +(2.70078 + 2.70078i) q^{87} +(-9.83787 + 6.23527i) q^{88} +9.76244i q^{89} +(-0.230846 - 1.11576i) q^{90} +10.5687i q^{91} +(5.09011 + 6.85941i) q^{92} +(6.29693 + 6.29693i) q^{93} +(0.962520 + 0.0708710i) q^{94} +(-1.95382 - 1.08746i) q^{95} +(-3.30201 + 8.57712i) q^{96} +(0.208633 - 0.208633i) q^{97} +(-7.09112 - 8.21837i) q^{98} -1.48373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.07073 + 0.923868i −0.757122 + 0.653274i
\(3\) −1.14885 + 1.14885i −0.663287 + 0.663287i −0.956153 0.292867i \(-0.905391\pi\)
0.292867 + 0.956153i \(0.405391\pi\)
\(4\) 0.292934 1.97843i 0.146467 0.989216i
\(5\) 1.95382 + 1.08746i 0.873776 + 0.486328i
\(6\) 0.168724 2.29149i 0.0688812 0.935496i
\(7\) −2.70883 2.70883i −1.02384 1.02384i −0.999709 0.0241310i \(-0.992318\pi\)
−0.0241310 0.999709i \(-0.507682\pi\)
\(8\) 1.51416 + 2.38900i 0.535335 + 0.844640i
\(9\) 0.360306i 0.120102i
\(10\) −3.09669 + 0.640694i −0.979261 + 0.202605i
\(11\) 4.11798i 1.24162i 0.783962 + 0.620809i \(0.213196\pi\)
−0.783962 + 0.620809i \(0.786804\pi\)
\(12\) 1.93638 + 2.60945i 0.558984 + 0.753283i
\(13\) −1.95079 1.95079i −0.541053 0.541053i 0.382785 0.923838i \(-0.374965\pi\)
−0.923838 + 0.382785i \(0.874965\pi\)
\(14\) 5.40302 + 0.397828i 1.44402 + 0.106324i
\(15\) −3.49397 + 0.995314i −0.902139 + 0.256989i
\(16\) −3.82838 1.15910i −0.957095 0.289775i
\(17\) −4.15549 + 4.15549i −1.00786 + 1.00786i −0.00788621 + 0.999969i \(0.502510\pi\)
−0.999969 + 0.00788621i \(0.997490\pi\)
\(18\) −0.332875 0.385791i −0.0784594 0.0909318i
\(19\) −1.00000 −0.229416
\(20\) 2.72381 3.54695i 0.609063 0.793122i
\(21\) 6.22405 1.35820
\(22\) −3.80447 4.40926i −0.811117 0.940057i
\(23\) −3.01995 + 3.01995i −0.629703 + 0.629703i −0.947993 0.318291i \(-0.896891\pi\)
0.318291 + 0.947993i \(0.396891\pi\)
\(24\) −4.48413 1.00506i −0.915319 0.205158i
\(25\) 2.63485 + 4.24942i 0.526970 + 0.849884i
\(26\) 3.89106 + 0.286501i 0.763099 + 0.0561875i
\(27\) −3.86047 3.86047i −0.742949 0.742949i
\(28\) −6.15273 + 4.56572i −1.16276 + 0.862839i
\(29\) 2.35086i 0.436544i −0.975888 0.218272i \(-0.929958\pi\)
0.975888 0.218272i \(-0.0700420\pi\)
\(30\) 2.82157 4.29368i 0.515145 0.783916i
\(31\) 5.48110i 0.984434i −0.870473 0.492217i \(-0.836187\pi\)
0.870473 0.492217i \(-0.163813\pi\)
\(32\) 5.17002 2.29583i 0.913940 0.405849i
\(33\) −4.73093 4.73093i −0.823549 0.823549i
\(34\) 0.610291 8.28855i 0.104664 1.42147i
\(35\) −2.34682 8.23831i −0.396685 1.39253i
\(36\) 0.712840 + 0.105546i 0.118807 + 0.0175910i
\(37\) 3.69981 3.69981i 0.608246 0.608246i −0.334242 0.942487i \(-0.608480\pi\)
0.942487 + 0.334242i \(0.108480\pi\)
\(38\) 1.07073 0.923868i 0.173696 0.149871i
\(39\) 4.48233 0.717746
\(40\) 0.360440 + 6.31428i 0.0569905 + 0.998375i
\(41\) −9.82744 −1.53479 −0.767394 0.641176i \(-0.778447\pi\)
−0.767394 + 0.641176i \(0.778447\pi\)
\(42\) −6.66429 + 5.75020i −1.02832 + 0.887275i
\(43\) −8.96408 + 8.96408i −1.36701 + 1.36701i −0.502339 + 0.864671i \(0.667527\pi\)
−0.864671 + 0.502339i \(0.832473\pi\)
\(44\) 8.14714 + 1.20630i 1.22823 + 0.181856i
\(45\) −0.391819 + 0.703974i −0.0584090 + 0.104942i
\(46\) 0.443521 6.02359i 0.0653936 0.888130i
\(47\) −0.482563 0.482563i −0.0703891 0.0703891i 0.671036 0.741425i \(-0.265850\pi\)
−0.741425 + 0.671036i \(0.765850\pi\)
\(48\) 5.72985 3.06659i 0.827032 0.442624i
\(49\) 7.67547i 1.09650i
\(50\) −6.74712 2.11574i −0.954187 0.299211i
\(51\) 9.54804i 1.33699i
\(52\) −4.43097 + 3.28806i −0.614465 + 0.455972i
\(53\) −2.71437 2.71437i −0.372848 0.372848i 0.495666 0.868513i \(-0.334924\pi\)
−0.868513 + 0.495666i \(0.834924\pi\)
\(54\) 7.70010 + 0.566964i 1.04785 + 0.0771540i
\(55\) −4.47815 + 8.04581i −0.603834 + 1.08490i
\(56\) 2.36981 10.5730i 0.316679 1.41287i
\(57\) 1.14885 1.14885i 0.152168 0.152168i
\(58\) 2.17189 + 2.51714i 0.285183 + 0.330517i
\(59\) 9.02322 1.17472 0.587361 0.809325i \(-0.300167\pi\)
0.587361 + 0.809325i \(0.300167\pi\)
\(60\) 0.945656 + 7.20414i 0.122084 + 0.930050i
\(61\) −4.23945 −0.542806 −0.271403 0.962466i \(-0.587488\pi\)
−0.271403 + 0.962466i \(0.587488\pi\)
\(62\) 5.06381 + 5.86878i 0.643105 + 0.745336i
\(63\) 0.976005 0.976005i 0.122965 0.122965i
\(64\) −3.41467 + 7.23464i −0.426833 + 0.904330i
\(65\) −1.69009 5.93292i −0.209630 0.735889i
\(66\) 9.43631 + 0.694802i 1.16153 + 0.0855242i
\(67\) 6.49679 + 6.49679i 0.793710 + 0.793710i 0.982095 0.188386i \(-0.0603255\pi\)
−0.188386 + 0.982095i \(0.560325\pi\)
\(68\) 7.00407 + 9.43864i 0.849368 + 1.14460i
\(69\) 6.93891i 0.835347i
\(70\) 10.1239 + 6.65288i 1.21004 + 0.795171i
\(71\) 14.9562i 1.77497i 0.460837 + 0.887485i \(0.347549\pi\)
−0.460837 + 0.887485i \(0.652451\pi\)
\(72\) −0.860771 + 0.545559i −0.101443 + 0.0642947i
\(73\) 7.29798 + 7.29798i 0.854164 + 0.854164i 0.990643 0.136479i \(-0.0435785\pi\)
−0.136479 + 0.990643i \(0.543579\pi\)
\(74\) −0.543368 + 7.37965i −0.0631653 + 0.857867i
\(75\) −7.90896 1.85490i −0.913249 0.214185i
\(76\) −0.292934 + 1.97843i −0.0336019 + 0.226942i
\(77\) 11.1549 11.1549i 1.27122 1.27122i
\(78\) −4.79937 + 4.14108i −0.543422 + 0.468885i
\(79\) 3.64828 0.410464 0.205232 0.978713i \(-0.434205\pi\)
0.205232 + 0.978713i \(0.434205\pi\)
\(80\) −6.21949 6.42790i −0.695361 0.718661i
\(81\) 7.78926 0.865474
\(82\) 10.5226 9.07926i 1.16202 1.00264i
\(83\) 8.32940 8.32940i 0.914270 0.914270i −0.0823347 0.996605i \(-0.526238\pi\)
0.996605 + 0.0823347i \(0.0262377\pi\)
\(84\) 1.82324 12.3138i 0.198932 1.34355i
\(85\) −12.6380 + 3.60015i −1.37079 + 0.390491i
\(86\) 1.31650 17.8798i 0.141962 1.92802i
\(87\) 2.70078 + 2.70078i 0.289554 + 0.289554i
\(88\) −9.83787 + 6.23527i −1.04872 + 0.664682i
\(89\) 9.76244i 1.03482i 0.855739 + 0.517408i \(0.173103\pi\)
−0.855739 + 0.517408i \(0.826897\pi\)
\(90\) −0.230846 1.11576i −0.0243333 0.117611i
\(91\) 10.5687i 1.10790i
\(92\) 5.09011 + 6.85941i 0.530681 + 0.715142i
\(93\) 6.29693 + 6.29693i 0.652962 + 0.652962i
\(94\) 0.962520 + 0.0708710i 0.0992764 + 0.00730979i
\(95\) −1.95382 1.08746i −0.200458 0.111571i
\(96\) −3.30201 + 8.57712i −0.337010 + 0.875399i
\(97\) 0.208633 0.208633i 0.0211835 0.0211835i −0.696436 0.717619i \(-0.745232\pi\)
0.717619 + 0.696436i \(0.245232\pi\)
\(98\) −7.09112 8.21837i −0.716312 0.830181i
\(99\) −1.48373 −0.149121
\(100\) 9.17902 3.96806i 0.917902 0.396806i
\(101\) −18.7952 −1.87019 −0.935096 0.354394i \(-0.884687\pi\)
−0.935096 + 0.354394i \(0.884687\pi\)
\(102\) 8.82114 + 10.2234i 0.873423 + 1.01227i
\(103\) −0.733254 + 0.733254i −0.0722496 + 0.0722496i −0.742308 0.670059i \(-0.766269\pi\)
0.670059 + 0.742308i \(0.266269\pi\)
\(104\) 1.70665 7.61426i 0.167350 0.746640i
\(105\) 12.1607 + 6.76842i 1.18676 + 0.660530i
\(106\) 5.41409 + 0.398643i 0.525863 + 0.0387196i
\(107\) 4.19542 + 4.19542i 0.405586 + 0.405586i 0.880196 0.474610i \(-0.157411\pi\)
−0.474610 + 0.880196i \(0.657411\pi\)
\(108\) −8.76855 + 6.50682i −0.843754 + 0.626119i
\(109\) 2.82743i 0.270819i −0.990790 0.135409i \(-0.956765\pi\)
0.990790 0.135409i \(-0.0432350\pi\)
\(110\) −2.63836 12.7521i −0.251558 1.21587i
\(111\) 8.50103i 0.806882i
\(112\) 7.23061 + 13.5102i 0.683228 + 1.27660i
\(113\) 1.04439 + 1.04439i 0.0982483 + 0.0982483i 0.754522 0.656274i \(-0.227869\pi\)
−0.656274 + 0.754522i \(0.727869\pi\)
\(114\) −0.168724 + 2.29149i −0.0158024 + 0.214618i
\(115\) −9.18453 + 2.61636i −0.856461 + 0.243977i
\(116\) −4.65102 0.688649i −0.431836 0.0639394i
\(117\) 0.702883 0.702883i 0.0649815 0.0649815i
\(118\) −9.66145 + 8.33627i −0.889408 + 0.767415i
\(119\) 22.5130 2.06376
\(120\) −7.66822 6.84004i −0.700010 0.624407i
\(121\) −5.95778 −0.541616
\(122\) 4.53931 3.91669i 0.410970 0.354601i
\(123\) 11.2902 11.2902i 1.01800 1.01800i
\(124\) −10.8440 1.60560i −0.973817 0.144187i
\(125\) 0.526938 + 11.1679i 0.0471308 + 0.998889i
\(126\) −0.143340 + 1.94674i −0.0127697 + 0.173429i
\(127\) 2.30575 + 2.30575i 0.204602 + 0.204602i 0.801969 0.597366i \(-0.203786\pi\)
−0.597366 + 0.801969i \(0.703786\pi\)
\(128\) −3.02767 10.9011i −0.267610 0.963527i
\(129\) 20.5967i 1.81344i
\(130\) 7.29087 + 4.79115i 0.639452 + 0.420212i
\(131\) 1.87892i 0.164162i −0.996626 0.0820810i \(-0.973843\pi\)
0.996626 0.0820810i \(-0.0261566\pi\)
\(132\) −10.7457 + 7.97396i −0.935290 + 0.694044i
\(133\) 2.70883 + 2.70883i 0.234885 + 0.234885i
\(134\) −12.9585 0.954143i −1.11944 0.0824254i
\(135\) −3.34456 11.7408i −0.287854 1.01049i
\(136\) −16.2195 3.63542i −1.39081 0.311735i
\(137\) 4.38444 4.38444i 0.374588 0.374588i −0.494557 0.869145i \(-0.664670\pi\)
0.869145 + 0.494557i \(0.164670\pi\)
\(138\) 6.41064 + 7.42971i 0.545710 + 0.632459i
\(139\) 5.70518 0.483907 0.241953 0.970288i \(-0.422212\pi\)
0.241953 + 0.970288i \(0.422212\pi\)
\(140\) −16.9864 + 2.22973i −1.43561 + 0.188447i
\(141\) 1.10878 0.0933762
\(142\) −13.8175 16.0140i −1.15954 1.34387i
\(143\) 8.03334 8.03334i 0.671781 0.671781i
\(144\) 0.417631 1.37939i 0.0348026 0.114949i
\(145\) 2.55648 4.59317i 0.212304 0.381442i
\(146\) −14.5566 1.07181i −1.20471 0.0887035i
\(147\) −8.81793 8.81793i −0.727291 0.727291i
\(148\) −6.23602 8.40363i −0.512598 0.690774i
\(149\) 3.91665i 0.320864i 0.987047 + 0.160432i \(0.0512888\pi\)
−0.987047 + 0.160432i \(0.948711\pi\)
\(150\) 10.1821 5.32075i 0.831362 0.434437i
\(151\) 4.24151i 0.345169i −0.984995 0.172584i \(-0.944788\pi\)
0.984995 0.172584i \(-0.0552118\pi\)
\(152\) −1.51416 2.38900i −0.122814 0.193774i
\(153\) −1.49725 1.49725i −0.121045 0.121045i
\(154\) −1.63825 + 22.2496i −0.132014 + 1.79292i
\(155\) 5.96049 10.7091i 0.478758 0.860175i
\(156\) 1.31303 8.86797i 0.105126 0.710006i
\(157\) −1.83855 + 1.83855i −0.146733 + 0.146733i −0.776657 0.629924i \(-0.783086\pi\)
0.629924 + 0.776657i \(0.283086\pi\)
\(158\) −3.90633 + 3.37053i −0.310771 + 0.268145i
\(159\) 6.23679 0.494610
\(160\) 12.5979 + 1.13656i 0.995955 + 0.0898532i
\(161\) 16.3610 1.28943
\(162\) −8.34021 + 7.19625i −0.655269 + 0.565391i
\(163\) 1.72096 1.72096i 0.134796 0.134796i −0.636489 0.771285i \(-0.719614\pi\)
0.771285 + 0.636489i \(0.219614\pi\)
\(164\) −2.87879 + 19.4429i −0.224796 + 1.51824i
\(165\) −4.09869 14.3881i −0.319082 1.12011i
\(166\) −1.22329 + 16.6138i −0.0949454 + 1.28948i
\(167\) 9.53008 + 9.53008i 0.737460 + 0.737460i 0.972086 0.234626i \(-0.0753866\pi\)
−0.234626 + 0.972086i \(0.575387\pi\)
\(168\) 9.42417 + 14.8693i 0.727091 + 1.14719i
\(169\) 5.38880i 0.414523i
\(170\) 10.2059 15.5307i 0.782756 1.19115i
\(171\) 0.360306i 0.0275533i
\(172\) 15.1089 + 20.3607i 1.15205 + 1.55249i
\(173\) 1.38868 + 1.38868i 0.105579 + 0.105579i 0.757923 0.652344i \(-0.226214\pi\)
−0.652344 + 0.757923i \(0.726214\pi\)
\(174\) −5.38697 0.396646i −0.408386 0.0300697i
\(175\) 4.37360 18.6483i 0.330613 1.40968i
\(176\) 4.77316 15.7652i 0.359790 1.18835i
\(177\) −10.3663 + 10.3663i −0.779178 + 0.779178i
\(178\) −9.01921 10.4530i −0.676019 0.783483i
\(179\) −20.9758 −1.56780 −0.783901 0.620886i \(-0.786773\pi\)
−0.783901 + 0.620886i \(0.786773\pi\)
\(180\) 1.27799 + 0.981405i 0.0952555 + 0.0731496i
\(181\) 15.9695 1.18701 0.593503 0.804832i \(-0.297744\pi\)
0.593503 + 0.804832i \(0.297744\pi\)
\(182\) −9.76411 11.3163i −0.723764 0.838818i
\(183\) 4.87047 4.87047i 0.360036 0.360036i
\(184\) −11.7873 2.64199i −0.868974 0.194770i
\(185\) 11.2522 3.20537i 0.827277 0.235663i
\(186\) −12.5599 0.924791i −0.920934 0.0678090i
\(187\) −17.1122 17.1122i −1.25137 1.25137i
\(188\) −1.09608 + 0.813358i −0.0799396 + 0.0593203i
\(189\) 20.9147i 1.52132i
\(190\) 3.09669 0.640694i 0.224658 0.0464808i
\(191\) 5.91787i 0.428202i −0.976811 0.214101i \(-0.931318\pi\)
0.976811 0.214101i \(-0.0686822\pi\)
\(192\) −4.38857 12.2344i −0.316717 0.882943i
\(193\) 1.66414 + 1.66414i 0.119788 + 0.119788i 0.764460 0.644672i \(-0.223006\pi\)
−0.644672 + 0.764460i \(0.723006\pi\)
\(194\) −0.0306406 + 0.416139i −0.00219987 + 0.0298771i
\(195\) 8.75767 + 4.87436i 0.627150 + 0.349060i
\(196\) 15.1854 + 2.24841i 1.08467 + 0.160601i
\(197\) −7.74801 + 7.74801i −0.552023 + 0.552023i −0.927024 0.375001i \(-0.877642\pi\)
0.375001 + 0.927024i \(0.377642\pi\)
\(198\) 1.58868 1.37077i 0.112903 0.0974167i
\(199\) 18.3552 1.30117 0.650583 0.759435i \(-0.274525\pi\)
0.650583 + 0.759435i \(0.274525\pi\)
\(200\) −6.16231 + 12.7289i −0.435741 + 0.900072i
\(201\) −14.9276 −1.05291
\(202\) 20.1246 17.3643i 1.41596 1.22175i
\(203\) −6.36808 + 6.36808i −0.446951 + 0.446951i
\(204\) −18.8901 2.79695i −1.32257 0.195826i
\(205\) −19.2011 10.6870i −1.34106 0.746411i
\(206\) 0.107688 1.46255i 0.00750300 0.101901i
\(207\) −1.08810 1.08810i −0.0756285 0.0756285i
\(208\) 5.20721 + 9.72955i 0.361055 + 0.674623i
\(209\) 4.11798i 0.284847i
\(210\) −19.2740 + 3.98771i −1.33003 + 0.275178i
\(211\) 10.7675i 0.741266i 0.928779 + 0.370633i \(0.120859\pi\)
−0.928779 + 0.370633i \(0.879141\pi\)
\(212\) −6.16533 + 4.57507i −0.423437 + 0.314217i
\(213\) −17.1823 17.1823i −1.17731 1.17731i
\(214\) −8.36818 0.616155i −0.572037 0.0421195i
\(215\) −27.2623 + 7.76612i −1.85928 + 0.529645i
\(216\) 3.37732 15.0680i 0.229798 1.02525i
\(217\) −14.8473 + 14.8473i −1.00790 + 1.00790i
\(218\) 2.61217 + 3.02742i 0.176919 + 0.205043i
\(219\) −16.7685 −1.13311
\(220\) 14.6063 + 11.2166i 0.984755 + 0.756224i
\(221\) 16.2130 1.09061
\(222\) −7.85383 9.10233i −0.527115 0.610908i
\(223\) −2.60632 + 2.60632i −0.174532 + 0.174532i −0.788967 0.614435i \(-0.789384\pi\)
0.614435 + 0.788967i \(0.289384\pi\)
\(224\) −20.2237 7.78569i −1.35125 0.520203i
\(225\) −1.53109 + 0.949351i −0.102073 + 0.0632901i
\(226\) −2.08315 0.153384i −0.138569 0.0102029i
\(227\) 7.03256 + 7.03256i 0.466767 + 0.466767i 0.900866 0.434098i \(-0.142933\pi\)
−0.434098 + 0.900866i \(0.642933\pi\)
\(228\) −1.93638 2.60945i −0.128240 0.172815i
\(229\) 3.08487i 0.203854i 0.994792 + 0.101927i \(0.0325008\pi\)
−0.994792 + 0.101927i \(0.967499\pi\)
\(230\) 7.41699 11.2867i 0.489062 0.744224i
\(231\) 25.6305i 1.68636i
\(232\) 5.61622 3.55957i 0.368723 0.233697i
\(233\) 16.5824 + 16.5824i 1.08635 + 1.08635i 0.995901 + 0.0904463i \(0.0288294\pi\)
0.0904463 + 0.995901i \(0.471171\pi\)
\(234\) −0.103228 + 1.40197i −0.00674822 + 0.0916496i
\(235\) −0.418073 1.46761i −0.0272721 0.0957365i
\(236\) 2.64321 17.8518i 0.172058 1.16205i
\(237\) −4.19132 + 4.19132i −0.272255 + 0.272255i
\(238\) −24.1054 + 20.7991i −1.56252 + 1.34820i
\(239\) 9.09479 0.588293 0.294146 0.955760i \(-0.404965\pi\)
0.294146 + 0.955760i \(0.404965\pi\)
\(240\) 14.5299 + 0.239425i 0.937901 + 0.0154548i
\(241\) 0.806689 0.0519634 0.0259817 0.999662i \(-0.491729\pi\)
0.0259817 + 0.999662i \(0.491729\pi\)
\(242\) 6.37919 5.50420i 0.410070 0.353824i
\(243\) 2.63276 2.63276i 0.168892 0.168892i
\(244\) −1.24188 + 8.38745i −0.0795032 + 0.536952i
\(245\) −8.34679 + 14.9965i −0.533257 + 0.958092i
\(246\) −1.65812 + 22.5195i −0.105718 + 1.43579i
\(247\) 1.95079 + 1.95079i 0.124126 + 0.124126i
\(248\) 13.0943 8.29923i 0.831492 0.527002i
\(249\) 19.1384i 1.21285i
\(250\) −10.8819 11.4710i −0.688231 0.725491i
\(251\) 2.39055i 0.150890i −0.997150 0.0754451i \(-0.975962\pi\)
0.997150 0.0754451i \(-0.0240378\pi\)
\(252\) −1.64505 2.21687i −0.103629 0.139649i
\(253\) −12.4361 12.4361i −0.781850 0.781850i
\(254\) −4.59906 0.338631i −0.288570 0.0212476i
\(255\) 10.3831 18.6552i 0.650218 1.16823i
\(256\) 13.3130 + 8.87496i 0.832061 + 0.554685i
\(257\) 16.0798 16.0798i 1.00303 1.00303i 0.00303293 0.999995i \(-0.499035\pi\)
0.999995 0.00303293i \(-0.000965412\pi\)
\(258\) 19.0286 + 22.0535i 1.18467 + 1.37299i
\(259\) −20.0443 −1.24549
\(260\) −12.2330 + 1.60577i −0.758656 + 0.0995856i
\(261\) 0.847029 0.0524298
\(262\) 1.73587 + 2.01182i 0.107243 + 0.124291i
\(263\) −3.25350 + 3.25350i −0.200619 + 0.200619i −0.800265 0.599646i \(-0.795308\pi\)
0.599646 + 0.800265i \(0.295308\pi\)
\(264\) 4.13884 18.4656i 0.254728 1.13648i
\(265\) −2.35162 8.25518i −0.144459 0.507112i
\(266\) −5.40302 0.397828i −0.331281 0.0243924i
\(267\) −11.2155 11.2155i −0.686380 0.686380i
\(268\) 14.7566 10.9503i 0.901402 0.668897i
\(269\) 19.3588i 1.18033i −0.807284 0.590163i \(-0.799064\pi\)
0.807284 0.590163i \(-0.200936\pi\)
\(270\) 14.4281 + 9.48132i 0.878065 + 0.577015i
\(271\) 2.77454i 0.168542i −0.996443 0.0842708i \(-0.973144\pi\)
0.996443 0.0842708i \(-0.0268561\pi\)
\(272\) 20.7254 11.0922i 1.25666 0.672561i
\(273\) −12.1418 12.1418i −0.734857 0.734857i
\(274\) −0.643915 + 8.74521i −0.0389003 + 0.528317i
\(275\) −17.4990 + 10.8503i −1.05523 + 0.654295i
\(276\) −13.7282 2.03265i −0.826338 0.122351i
\(277\) 3.48594 3.48594i 0.209450 0.209450i −0.594584 0.804034i \(-0.702683\pi\)
0.804034 + 0.594584i \(0.202683\pi\)
\(278\) −6.10872 + 5.27083i −0.366377 + 0.316124i
\(279\) 1.97487 0.118232
\(280\) 16.1279 18.0806i 0.963827 1.08052i
\(281\) −27.6567 −1.64986 −0.824930 0.565235i \(-0.808786\pi\)
−0.824930 + 0.565235i \(0.808786\pi\)
\(282\) −1.18721 + 1.02437i −0.0706972 + 0.0610002i
\(283\) 6.97300 6.97300i 0.414502 0.414502i −0.468802 0.883304i \(-0.655314\pi\)
0.883304 + 0.468802i \(0.155314\pi\)
\(284\) 29.5897 + 4.38117i 1.75583 + 0.259975i
\(285\) 3.49397 0.995314i 0.206965 0.0589573i
\(286\) −1.17981 + 16.0233i −0.0697634 + 0.947478i
\(287\) 26.6208 + 26.6208i 1.57138 + 1.57138i
\(288\) 0.827201 + 1.86279i 0.0487433 + 0.109766i
\(289\) 17.5362i 1.03154i
\(290\) 1.50618 + 7.27990i 0.0884461 + 0.427491i
\(291\) 0.479374i 0.0281014i
\(292\) 16.5764 12.3007i 0.970060 0.719846i
\(293\) −4.11824 4.11824i −0.240590 0.240590i 0.576504 0.817094i \(-0.304416\pi\)
−0.817094 + 0.576504i \(0.804416\pi\)
\(294\) 17.5883 + 1.29503i 1.02577 + 0.0755279i
\(295\) 17.6298 + 9.81242i 1.02644 + 0.571301i
\(296\) 14.4410 + 3.23677i 0.839363 + 0.188133i
\(297\) 15.8974 15.8974i 0.922459 0.922459i
\(298\) −3.61847 4.19368i −0.209612 0.242933i
\(299\) 11.7826 0.681405
\(300\) −5.98659 + 15.1040i −0.345636 + 0.872029i
\(301\) 48.5643 2.79920
\(302\) 3.91859 + 4.54152i 0.225490 + 0.261335i
\(303\) 21.5928 21.5928i 1.24047 1.24047i
\(304\) 3.82838 + 1.15910i 0.219573 + 0.0664790i
\(305\) −8.28313 4.61024i −0.474291 0.263982i
\(306\) 2.98641 + 0.219891i 0.170722 + 0.0125704i
\(307\) −23.2710 23.2710i −1.32814 1.32814i −0.906989 0.421155i \(-0.861625\pi\)
−0.421155 0.906989i \(-0.638375\pi\)
\(308\) −18.8015 25.3368i −1.07132 1.44370i
\(309\) 1.68479i 0.0958444i
\(310\) 3.51170 + 16.9733i 0.199451 + 0.964017i
\(311\) 31.9359i 1.81092i 0.424434 + 0.905459i \(0.360473\pi\)
−0.424434 + 0.905459i \(0.639527\pi\)
\(312\) 6.78694 + 10.7083i 0.384235 + 0.606237i
\(313\) 3.53818 + 3.53818i 0.199990 + 0.199990i 0.799996 0.600006i \(-0.204835\pi\)
−0.600006 + 0.799996i \(0.704835\pi\)
\(314\) 0.270017 3.66718i 0.0152379 0.206951i
\(315\) 2.96831 0.845572i 0.167245 0.0476426i
\(316\) 1.06871 7.21788i 0.0601195 0.406037i
\(317\) −7.96927 + 7.96927i −0.447599 + 0.447599i −0.894556 0.446957i \(-0.852508\pi\)
0.446957 + 0.894556i \(0.352508\pi\)
\(318\) −6.67793 + 5.76197i −0.374480 + 0.323115i
\(319\) 9.68081 0.542021
\(320\) −14.5391 + 10.4219i −0.812758 + 0.582601i
\(321\) −9.63978 −0.538040
\(322\) −17.5183 + 15.1154i −0.976255 + 0.842350i
\(323\) 4.15549 4.15549i 0.231218 0.231218i
\(324\) 2.28174 15.4105i 0.126764 0.856140i
\(325\) 3.14970 13.4298i 0.174714 0.744951i
\(326\) −0.252747 + 3.43263i −0.0139983 + 0.190116i
\(327\) 3.24828 + 3.24828i 0.179630 + 0.179630i
\(328\) −14.8803 23.4778i −0.821625 1.29634i
\(329\) 2.61436i 0.144134i
\(330\) 17.6813 + 11.6192i 0.973324 + 0.639614i
\(331\) 0.243939i 0.0134081i 0.999978 + 0.00670406i \(0.00213398\pi\)
−0.999978 + 0.00670406i \(0.997866\pi\)
\(332\) −14.0392 18.9191i −0.770500 1.03832i
\(333\) 1.33306 + 1.33306i 0.0730515 + 0.0730515i
\(334\) −19.0087 1.39962i −1.04011 0.0765840i
\(335\) 5.62856 + 19.7586i 0.307521 + 1.07953i
\(336\) −23.8280 7.21430i −1.29992 0.393572i
\(337\) −21.6007 + 21.6007i −1.17666 + 1.17666i −0.196075 + 0.980589i \(0.562820\pi\)
−0.980589 + 0.196075i \(0.937180\pi\)
\(338\) 4.97854 + 5.76996i 0.270797 + 0.313845i
\(339\) −2.39969 −0.130334
\(340\) 3.42053 + 26.0581i 0.185505 + 1.41320i
\(341\) 22.5711 1.22229
\(342\) 0.332875 + 0.385791i 0.0179998 + 0.0208612i
\(343\) 1.82973 1.82973i 0.0987963 0.0987963i
\(344\) −34.9882 7.84220i −1.88644 0.422823i
\(345\) 7.54581 13.5574i 0.406253 0.729906i
\(346\) −2.76985 0.203946i −0.148908 0.0109642i
\(347\) −21.4891 21.4891i −1.15360 1.15360i −0.985826 0.167770i \(-0.946343\pi\)
−0.167770 0.985826i \(-0.553657\pi\)
\(348\) 6.13446 4.55215i 0.328841 0.244021i
\(349\) 16.9878i 0.909334i 0.890661 + 0.454667i \(0.150242\pi\)
−0.890661 + 0.454667i \(0.849758\pi\)
\(350\) 12.5456 + 24.0079i 0.670591 + 1.28328i
\(351\) 15.0620i 0.803949i
\(352\) 9.45419 + 21.2901i 0.503910 + 1.13476i
\(353\) 21.9390 + 21.9390i 1.16769 + 1.16769i 0.982749 + 0.184946i \(0.0592110\pi\)
0.184946 + 0.982749i \(0.440789\pi\)
\(354\) 1.52243 20.6766i 0.0809163 1.09895i
\(355\) −16.2643 + 29.2217i −0.863218 + 1.55093i
\(356\) 19.3143 + 2.85976i 1.02366 + 0.151567i
\(357\) −25.8640 + 25.8640i −1.36887 + 1.36887i
\(358\) 22.4594 19.3788i 1.18702 1.02420i
\(359\) −9.38281 −0.495206 −0.247603 0.968862i \(-0.579643\pi\)
−0.247603 + 0.968862i \(0.579643\pi\)
\(360\) −2.27507 + 0.129869i −0.119907 + 0.00684467i
\(361\) 1.00000 0.0526316
\(362\) −17.0991 + 14.7538i −0.898709 + 0.775440i
\(363\) 6.84457 6.84457i 0.359247 0.359247i
\(364\) 20.9095 + 3.09594i 1.09596 + 0.162272i
\(365\) 6.32268 + 22.1953i 0.330944 + 1.16175i
\(366\) −0.715296 + 9.71465i −0.0373891 + 0.507793i
\(367\) −8.72035 8.72035i −0.455199 0.455199i 0.441877 0.897076i \(-0.354313\pi\)
−0.897076 + 0.441877i \(0.854313\pi\)
\(368\) 15.0619 8.06108i 0.785157 0.420213i
\(369\) 3.54088i 0.184331i
\(370\) −9.08674 + 13.8276i −0.472397 + 0.718864i
\(371\) 14.7055i 0.763473i
\(372\) 14.3026 10.6135i 0.741557 0.550282i
\(373\) 16.4931 + 16.4931i 0.853979 + 0.853979i 0.990621 0.136641i \(-0.0436308\pi\)
−0.136641 + 0.990621i \(0.543631\pi\)
\(374\) 34.1321 + 2.51317i 1.76493 + 0.129953i
\(375\) −13.4356 12.2248i −0.693811 0.631288i
\(376\) 0.422169 1.88352i 0.0217717 0.0971351i
\(377\) −4.58605 + 4.58605i −0.236194 + 0.236194i
\(378\) −19.3224 22.3940i −0.993839 1.15183i
\(379\) −29.7168 −1.52645 −0.763224 0.646133i \(-0.776385\pi\)
−0.763224 + 0.646133i \(0.776385\pi\)
\(380\) −2.72381 + 3.54695i −0.139729 + 0.181955i
\(381\) −5.29791 −0.271420
\(382\) 5.46734 + 6.33646i 0.279733 + 0.324201i
\(383\) −8.57457 + 8.57457i −0.438140 + 0.438140i −0.891386 0.453246i \(-0.850266\pi\)
0.453246 + 0.891386i \(0.350266\pi\)
\(384\) 16.0020 + 9.04532i 0.816597 + 0.461592i
\(385\) 33.9252 9.66415i 1.72899 0.492531i
\(386\) −3.31930 0.244402i −0.168948 0.0124398i
\(387\) −3.22981 3.22981i −0.164180 0.164180i
\(388\) −0.351650 0.473881i −0.0178523 0.0240577i
\(389\) 9.66869i 0.490222i −0.969495 0.245111i \(-0.921176\pi\)
0.969495 0.245111i \(-0.0788244\pi\)
\(390\) −13.8804 + 2.87180i −0.702861 + 0.145419i
\(391\) 25.0987i 1.26930i
\(392\) −18.3367 + 11.6219i −0.926144 + 0.586992i
\(393\) 2.15859 + 2.15859i 0.108886 + 0.108886i
\(394\) 1.13790 15.4542i 0.0573266 0.778570i
\(395\) 7.12810 + 3.96737i 0.358654 + 0.199620i
\(396\) −0.434636 + 2.93546i −0.0218413 + 0.147513i
\(397\) 19.0447 19.0447i 0.955827 0.955827i −0.0432378 0.999065i \(-0.513767\pi\)
0.999065 + 0.0432378i \(0.0137673\pi\)
\(398\) −19.6535 + 16.9578i −0.985141 + 0.850017i
\(399\) −6.22405 −0.311592
\(400\) −5.16169 19.3224i −0.258084 0.966122i
\(401\) −0.178250 −0.00890139 −0.00445069 0.999990i \(-0.501417\pi\)
−0.00445069 + 0.999990i \(0.501417\pi\)
\(402\) 15.9835 13.7912i 0.797184 0.687841i
\(403\) −10.6925 + 10.6925i −0.532631 + 0.532631i
\(404\) −5.50576 + 37.1850i −0.273922 + 1.85002i
\(405\) 15.2188 + 8.47054i 0.756230 + 0.420904i
\(406\) 0.935239 12.7018i 0.0464151 0.630378i
\(407\) 15.2358 + 15.2358i 0.755209 + 0.755209i
\(408\) 22.8103 14.4572i 1.12928 0.715739i
\(409\) 2.01061i 0.0994184i −0.998764 0.0497092i \(-0.984171\pi\)
0.998764 0.0497092i \(-0.0158295\pi\)
\(410\) 30.4326 6.29637i 1.50296 0.310956i
\(411\) 10.0741i 0.496918i
\(412\) 1.23590 + 1.66549i 0.0608882 + 0.0820526i
\(413\) −24.4423 24.4423i −1.20273 1.20273i
\(414\) 2.17033 + 0.159803i 0.106666 + 0.00785389i
\(415\) 25.3321 7.21625i 1.24350 0.354232i
\(416\) −14.5644 5.60696i −0.714076 0.274904i
\(417\) −6.55437 + 6.55437i −0.320969 + 0.320969i
\(418\) 3.80447 + 4.40926i 0.186083 + 0.215664i
\(419\) −13.6641 −0.667536 −0.333768 0.942655i \(-0.608320\pi\)
−0.333768 + 0.942655i \(0.608320\pi\)
\(420\) 16.9531 22.0764i 0.827228 1.07722i
\(421\) −13.8989 −0.677390 −0.338695 0.940896i \(-0.609985\pi\)
−0.338695 + 0.940896i \(0.609985\pi\)
\(422\) −9.94776 11.5291i −0.484249 0.561229i
\(423\) 0.173870 0.173870i 0.00845386 0.00845386i
\(424\) 2.37466 10.5946i 0.115324 0.514520i
\(425\) −28.6075 6.70935i −1.38767 0.325451i
\(426\) 34.2719 + 2.52346i 1.66048 + 0.122262i
\(427\) 11.4839 + 11.4839i 0.555746 + 0.555746i
\(428\) 9.52933 7.07136i 0.460618 0.341807i
\(429\) 18.4581i 0.891167i
\(430\) 22.0158 33.5022i 1.06170 1.61562i
\(431\) 20.3636i 0.980879i −0.871475 0.490440i \(-0.836836\pi\)
0.871475 0.490440i \(-0.163164\pi\)
\(432\) 10.3047 + 19.2540i 0.495784 + 0.926360i
\(433\) 5.89872 + 5.89872i 0.283475 + 0.283475i 0.834493 0.551018i \(-0.185761\pi\)
−0.551018 + 0.834493i \(0.685761\pi\)
\(434\) 2.18053 29.6145i 0.104669 1.42154i
\(435\) 2.33985 + 8.21384i 0.112187 + 0.393824i
\(436\) −5.59388 0.828252i −0.267898 0.0396661i
\(437\) 3.01995 3.01995i 0.144464 0.144464i
\(438\) 17.9546 15.4919i 0.857903 0.740232i
\(439\) −27.2435 −1.30026 −0.650131 0.759822i \(-0.725286\pi\)
−0.650131 + 0.759822i \(0.725286\pi\)
\(440\) −26.0021 + 1.48428i −1.23960 + 0.0707605i
\(441\) −2.76552 −0.131691
\(442\) −17.3598 + 14.9787i −0.825722 + 0.712464i
\(443\) 20.1874 20.1874i 0.959131 0.959131i −0.0400656 0.999197i \(-0.512757\pi\)
0.999197 + 0.0400656i \(0.0127567\pi\)
\(444\) 16.8187 + 2.49024i 0.798180 + 0.118182i
\(445\) −10.6163 + 19.0741i −0.503261 + 0.904198i
\(446\) 0.382774 5.19857i 0.0181249 0.246159i
\(447\) −4.49963 4.49963i −0.212825 0.212825i
\(448\) 28.8471 10.3477i 1.36290 0.488881i
\(449\) 4.84516i 0.228657i 0.993443 + 0.114329i \(0.0364717\pi\)
−0.993443 + 0.114329i \(0.963528\pi\)
\(450\) 0.762313 2.43103i 0.0359358 0.114600i
\(451\) 40.4692i 1.90562i
\(452\) 2.37220 1.76032i 0.111579 0.0827986i
\(453\) 4.87284 + 4.87284i 0.228946 + 0.228946i
\(454\) −14.0271 1.03283i −0.658326 0.0484730i
\(455\) −11.4931 + 20.6494i −0.538805 + 0.968060i
\(456\) 4.48413 + 1.00506i 0.209989 + 0.0470664i
\(457\) −14.6913 + 14.6913i −0.687230 + 0.687230i −0.961619 0.274389i \(-0.911524\pi\)
0.274389 + 0.961619i \(0.411524\pi\)
\(458\) −2.85002 3.30307i −0.133172 0.154342i
\(459\) 32.0843 1.49757
\(460\) 2.48583 + 18.9374i 0.115902 + 0.882960i
\(461\) 24.5016 1.14115 0.570577 0.821244i \(-0.306720\pi\)
0.570577 + 0.821244i \(0.306720\pi\)
\(462\) −23.6792 27.4434i −1.10166 1.27678i
\(463\) −25.8168 + 25.8168i −1.19981 + 1.19981i −0.225586 + 0.974223i \(0.572430\pi\)
−0.974223 + 0.225586i \(0.927570\pi\)
\(464\) −2.72489 + 8.99999i −0.126500 + 0.417814i
\(465\) 5.45541 + 19.1508i 0.252989 + 0.888096i
\(466\) −33.0752 2.43535i −1.53218 0.112815i
\(467\) −6.04830 6.04830i −0.279882 0.279882i 0.553180 0.833062i \(-0.313414\pi\)
−0.833062 + 0.553180i \(0.813414\pi\)
\(468\) −1.18471 1.59650i −0.0547631 0.0737984i
\(469\) 35.1974i 1.62526i
\(470\) 1.80352 + 1.18517i 0.0831904 + 0.0546680i
\(471\) 4.22443i 0.194651i
\(472\) 13.6626 + 21.5565i 0.628870 + 0.992218i
\(473\) −36.9139 36.9139i −1.69730 1.69730i
\(474\) 0.615552 8.36000i 0.0282733 0.383988i
\(475\) −2.63485 4.24942i −0.120895 0.194977i
\(476\) 6.59484 44.5404i 0.302274 2.04151i
\(477\) 0.978004 0.978004i 0.0447797 0.0447797i
\(478\) −9.73808 + 8.40239i −0.445409 + 0.384316i
\(479\) −22.0969 −1.00963 −0.504816 0.863227i \(-0.668440\pi\)
−0.504816 + 0.863227i \(0.668440\pi\)
\(480\) −15.7788 + 13.1674i −0.720202 + 0.601005i
\(481\) −14.4352 −0.658186
\(482\) −0.863748 + 0.745275i −0.0393427 + 0.0339463i
\(483\) −18.7963 + 18.7963i −0.855261 + 0.855261i
\(484\) −1.74524 + 11.7871i −0.0793290 + 0.535775i
\(485\) 0.634512 0.180751i 0.0288117 0.00820748i
\(486\) −0.386657 + 5.25130i −0.0175391 + 0.238204i
\(487\) −21.8223 21.8223i −0.988864 0.988864i 0.0110744 0.999939i \(-0.496475\pi\)
−0.999939 + 0.0110744i \(0.996475\pi\)
\(488\) −6.41918 10.1280i −0.290583 0.458475i
\(489\) 3.95424i 0.178817i
\(490\) −4.91762 23.7686i −0.222156 1.07376i
\(491\) 29.1044i 1.31346i 0.754124 + 0.656732i \(0.228062\pi\)
−0.754124 + 0.656732i \(0.771938\pi\)
\(492\) −19.0296 25.6442i −0.857921 1.15613i
\(493\) 9.76899 + 9.76899i 0.439973 + 0.439973i
\(494\) −3.89106 0.286501i −0.175067 0.0128903i
\(495\) −2.89895 1.61350i −0.130298 0.0725216i
\(496\) −6.35314 + 20.9837i −0.285265 + 0.942196i
\(497\) 40.5136 40.5136i 1.81728 1.81728i
\(498\) −17.6814 20.4921i −0.792320 0.918272i
\(499\) 25.5652 1.14446 0.572228 0.820094i \(-0.306079\pi\)
0.572228 + 0.820094i \(0.306079\pi\)
\(500\) 22.2493 + 2.22896i 0.995019 + 0.0996820i
\(501\) −21.8972 −0.978294
\(502\) 2.20855 + 2.55964i 0.0985726 + 0.114242i
\(503\) −23.8295 + 23.8295i −1.06250 + 1.06250i −0.0645931 + 0.997912i \(0.520575\pi\)
−0.997912 + 0.0645931i \(0.979425\pi\)
\(504\) 3.80950 + 0.853855i 0.169689 + 0.0380337i
\(505\) −36.7225 20.4391i −1.63413 0.909527i
\(506\) 24.8050 + 1.82641i 1.10272 + 0.0811939i
\(507\) 6.19090 + 6.19090i 0.274948 + 0.274948i
\(508\) 5.23721 3.88634i 0.232363 0.172428i
\(509\) 0.373579i 0.0165586i −0.999966 0.00827931i \(-0.997365\pi\)
0.999966 0.00827931i \(-0.00263542\pi\)
\(510\) 6.11737 + 29.5674i 0.270882 + 1.30926i
\(511\) 39.5379i 1.74905i
\(512\) −22.4539 + 2.79673i −0.992332 + 0.123599i
\(513\) 3.86047 + 3.86047i 0.170444 + 0.170444i
\(514\) −2.36153 + 32.0727i −0.104163 + 1.41467i
\(515\) −2.23003 + 0.635261i −0.0982670 + 0.0279930i
\(516\) −40.7491 6.03348i −1.79388 0.265609i
\(517\) 1.98719 1.98719i 0.0873963 0.0873963i
\(518\) 21.4621 18.5183i 0.942989 0.813647i
\(519\) −3.19075 −0.140058
\(520\) 11.6147 13.0210i 0.509339 0.571009i
\(521\) −21.9839 −0.963131 −0.481566 0.876410i \(-0.659932\pi\)
−0.481566 + 0.876410i \(0.659932\pi\)
\(522\) −0.906942 + 0.782544i −0.0396958 + 0.0342510i
\(523\) 25.4734 25.4734i 1.11388 1.11388i 0.121255 0.992621i \(-0.461308\pi\)
0.992621 0.121255i \(-0.0386918\pi\)
\(524\) −3.71731 0.550400i −0.162392 0.0240443i
\(525\) 16.3994 + 26.4486i 0.715729 + 1.15431i
\(526\) 0.477821 6.48943i 0.0208340 0.282953i
\(527\) 22.7767 + 22.7767i 0.992167 + 0.992167i
\(528\) 12.6282 + 23.5954i 0.549570 + 1.02686i
\(529\) 4.75983i 0.206949i
\(530\) 10.1447 + 6.66650i 0.440656 + 0.289574i
\(531\) 3.25112i 0.141086i
\(532\) 6.15273 4.56572i 0.266755 0.197949i
\(533\) 19.1713 + 19.1713i 0.830402 + 0.830402i
\(534\) 22.3705 + 1.64716i 0.968067 + 0.0712794i
\(535\) 3.63474 + 12.7595i 0.157144 + 0.551640i
\(536\) −5.68370 + 25.3580i −0.245498 + 1.09530i
\(537\) 24.0979 24.0979i 1.03990 1.03990i
\(538\) 17.8850 + 20.7281i 0.771075 + 0.893650i
\(539\) −31.6075 −1.36143
\(540\) −24.2081 + 3.17769i −1.04175 + 0.136746i
\(541\) −11.3955 −0.489932 −0.244966 0.969532i \(-0.578777\pi\)
−0.244966 + 0.969532i \(0.578777\pi\)
\(542\) 2.56331 + 2.97079i 0.110104 + 0.127606i
\(543\) −18.3465 + 18.3465i −0.787326 + 0.787326i
\(544\) −11.9437 + 31.0243i −0.512082 + 1.33016i
\(545\) 3.07473 5.52430i 0.131707 0.236635i
\(546\) 24.2181 + 1.78320i 1.03644 + 0.0763137i
\(547\) −20.7225 20.7225i −0.886032 0.886032i 0.108107 0.994139i \(-0.465521\pi\)
−0.994139 + 0.108107i \(0.965521\pi\)
\(548\) −7.38996 9.95867i −0.315683 0.425413i
\(549\) 1.52750i 0.0651920i
\(550\) 8.71257 27.7845i 0.371505 1.18474i
\(551\) 2.35086i 0.100150i
\(552\) 16.5771 10.5066i 0.705567 0.447190i
\(553\) −9.88257 9.88257i −0.420249 0.420249i
\(554\) −0.511958 + 6.95306i −0.0217510 + 0.295407i
\(555\) −9.24456 + 16.6095i −0.392410 + 0.705034i
\(556\) 1.67124 11.2873i 0.0708765 0.478688i
\(557\) 12.2789 12.2789i 0.520272 0.520272i −0.397382 0.917653i \(-0.630081\pi\)
0.917653 + 0.397382i \(0.130081\pi\)
\(558\) −2.11456 + 1.82452i −0.0895163 + 0.0772381i
\(559\) 34.9742 1.47925
\(560\) −0.564532 + 34.2596i −0.0238558 + 1.44773i
\(561\) 39.3187 1.66004
\(562\) 29.6129 25.5512i 1.24915 1.07781i
\(563\) 13.3587 13.3587i 0.563001 0.563001i −0.367158 0.930159i \(-0.619669\pi\)
0.930159 + 0.367158i \(0.119669\pi\)
\(564\) 0.324800 2.19365i 0.0136766 0.0923692i
\(565\) 0.904821 + 3.17630i 0.0380661 + 0.133628i
\(566\) −1.02408 + 13.9084i −0.0430453 + 0.584612i
\(567\) −21.0998 21.0998i −0.886106 0.886106i
\(568\) −35.7303 + 22.6459i −1.49921 + 0.950203i
\(569\) 17.3531i 0.727478i −0.931501 0.363739i \(-0.881500\pi\)
0.931501 0.363739i \(-0.118500\pi\)
\(570\) −2.82157 + 4.29368i −0.118182 + 0.179843i
\(571\) 19.3548i 0.809972i 0.914323 + 0.404986i \(0.132724\pi\)
−0.914323 + 0.404986i \(0.867276\pi\)
\(572\) −13.5402 18.2466i −0.566143 0.762931i
\(573\) 6.79873 + 6.79873i 0.284021 + 0.284021i
\(574\) −53.0979 3.90963i −2.21626 0.163185i
\(575\) −20.7901 4.87593i −0.867008 0.203340i
\(576\) −2.60668 1.23032i −0.108612 0.0512635i
\(577\) 3.22845 3.22845i 0.134402 0.134402i −0.636705 0.771107i \(-0.719703\pi\)
0.771107 + 0.636705i \(0.219703\pi\)
\(578\) 16.2012 + 18.7766i 0.673880 + 0.781004i
\(579\) −3.82369 −0.158907
\(580\) −8.33839 6.40331i −0.346233 0.265883i
\(581\) −45.1258 −1.87213
\(582\) −0.442878 0.513281i −0.0183579 0.0212762i
\(583\) 11.1777 11.1777i 0.462935 0.462935i
\(584\) −6.38462 + 28.4852i −0.264197 + 1.17873i
\(585\) 2.13767 0.608949i 0.0883817 0.0251770i
\(586\) 8.21425 + 0.604820i 0.339327 + 0.0249849i
\(587\) −19.7717 19.7717i −0.816064 0.816064i 0.169471 0.985535i \(-0.445794\pi\)
−0.985535 + 0.169471i \(0.945794\pi\)
\(588\) −20.0288 + 14.8626i −0.825972 + 0.612923i
\(589\) 5.48110i 0.225845i
\(590\) −27.9421 + 5.78112i −1.15036 + 0.238005i
\(591\) 17.8025i 0.732298i
\(592\) −18.4527 + 9.87583i −0.758403 + 0.405894i
\(593\) 0.671001 + 0.671001i 0.0275547 + 0.0275547i 0.720750 0.693195i \(-0.243798\pi\)
−0.693195 + 0.720750i \(0.743798\pi\)
\(594\) −2.33475 + 31.7089i −0.0957958 + 1.30103i
\(595\) 43.9864 + 24.4821i 1.80327 + 1.00367i
\(596\) 7.74882 + 1.14732i 0.317404 + 0.0469961i
\(597\) −21.0873 + 21.0873i −0.863046 + 0.863046i
\(598\) −12.6160 + 10.8856i −0.515907 + 0.445144i
\(599\) 6.84669 0.279748 0.139874 0.990169i \(-0.455330\pi\)
0.139874 + 0.990169i \(0.455330\pi\)
\(600\) −7.54405 21.7031i −0.307985 0.886027i
\(601\) −28.9163 −1.17952 −0.589761 0.807578i \(-0.700778\pi\)
−0.589761 + 0.807578i \(0.700778\pi\)
\(602\) −51.9993 + 44.8670i −2.11933 + 1.82864i
\(603\) −2.34083 + 2.34083i −0.0953261 + 0.0953261i
\(604\) −8.39153 1.24248i −0.341446 0.0505559i
\(605\) −11.6404 6.47887i −0.473251 0.263403i
\(606\) −3.17120 + 43.0690i −0.128821 + 1.74956i
\(607\) 5.48920 + 5.48920i 0.222800 + 0.222800i 0.809676 0.586877i \(-0.199643\pi\)
−0.586877 + 0.809676i \(0.699643\pi\)
\(608\) −5.17002 + 2.29583i −0.209672 + 0.0931083i
\(609\) 14.6319i 0.592914i
\(610\) 13.1283 2.71619i 0.531548 0.109975i
\(611\) 1.88276i 0.0761684i
\(612\) −3.40080 + 2.52361i −0.137469 + 0.102011i
\(613\) 8.13079 + 8.13079i 0.328399 + 0.328399i 0.851978 0.523578i \(-0.175403\pi\)
−0.523578 + 0.851978i \(0.675403\pi\)
\(614\) 46.4163 + 3.41766i 1.87321 + 0.137925i
\(615\) 34.3368 9.78138i 1.38459 0.394423i
\(616\) 43.5393 + 9.75883i 1.75425 + 0.393194i
\(617\) −10.8891 + 10.8891i −0.438379 + 0.438379i −0.891466 0.453087i \(-0.850323\pi\)
0.453087 + 0.891466i \(0.350323\pi\)
\(618\) 1.55652 + 1.80396i 0.0626126 + 0.0725659i
\(619\) −1.24466 −0.0500273 −0.0250136 0.999687i \(-0.507963\pi\)
−0.0250136 + 0.999687i \(0.507963\pi\)
\(620\) −19.4412 14.9295i −0.780776 0.599582i
\(621\) 23.3169 0.935673
\(622\) −29.5046 34.1948i −1.18302 1.37109i
\(623\) 26.4448 26.4448i 1.05949 1.05949i
\(624\) −17.1600 5.19547i −0.686951 0.207985i
\(625\) −11.1152 + 22.3932i −0.444606 + 0.895726i
\(626\) −7.05725 0.519630i −0.282064 0.0207686i
\(627\) 4.73093 + 4.73093i 0.188935 + 0.188935i
\(628\) 3.09888 + 4.17603i 0.123659 + 0.166642i
\(629\) 30.7491i 1.22605i
\(630\) −2.39707 + 3.64771i −0.0955015 + 0.145328i
\(631\) 5.70526i 0.227123i 0.993531 + 0.113561i \(0.0362259\pi\)
−0.993531 + 0.113561i \(0.963774\pi\)
\(632\) 5.52407 + 8.71576i 0.219736 + 0.346694i
\(633\) −12.3702 12.3702i −0.491672 0.491672i
\(634\) 1.17040 15.8955i 0.0464824 0.631291i
\(635\) 1.99761 + 7.01245i 0.0792728 + 0.278281i
\(636\) 1.82697 12.3391i 0.0724441 0.489276i
\(637\) 14.9733 14.9733i 0.593262 0.593262i
\(638\) −10.3656 + 8.94379i −0.410376 + 0.354088i
\(639\) −5.38879 −0.213177
\(640\) 5.93898 24.5912i 0.234759 0.972054i
\(641\) −0.458904 −0.0181256 −0.00906280 0.999959i \(-0.502885\pi\)
−0.00906280 + 0.999959i \(0.502885\pi\)
\(642\) 10.3216 8.90589i 0.407362 0.351487i
\(643\) 2.89559 2.89559i 0.114191 0.114191i −0.647702 0.761893i \(-0.724270\pi\)
0.761893 + 0.647702i \(0.224270\pi\)
\(644\) 4.79271 32.3692i 0.188859 1.27552i
\(645\) 22.3981 40.2423i 0.881926 1.58454i
\(646\) −0.610291 + 8.28855i −0.0240116 + 0.326109i
\(647\) 26.0239 + 26.0239i 1.02311 + 1.02311i 0.999727 + 0.0233789i \(0.00744243\pi\)
0.0233789 + 0.999727i \(0.492558\pi\)
\(648\) 11.7942 + 18.6086i 0.463318 + 0.731014i
\(649\) 37.1575i 1.45856i
\(650\) 9.03488 + 17.2896i 0.354377 + 0.678155i
\(651\) 34.1146i 1.33706i
\(652\) −2.90067 3.90893i −0.113599 0.153086i
\(653\) −19.7494 19.7494i −0.772852 0.772852i 0.205752 0.978604i \(-0.434036\pi\)
−0.978604 + 0.205752i \(0.934036\pi\)
\(654\) −6.47903 0.477055i −0.253350 0.0186543i
\(655\) 2.04326 3.67108i 0.0798366 0.143441i
\(656\) 37.6231 + 11.3910i 1.46894 + 0.444744i
\(657\) −2.62951 + 2.62951i −0.102587 + 0.102587i
\(658\) −2.41532 2.79928i −0.0941591 0.109127i
\(659\) −7.33213 −0.285619 −0.142810 0.989750i \(-0.545614\pi\)
−0.142810 + 0.989750i \(0.545614\pi\)
\(660\) −29.6665 + 3.89420i −1.15477 + 0.151581i
\(661\) −32.0891 −1.24812 −0.624061 0.781376i \(-0.714518\pi\)
−0.624061 + 0.781376i \(0.714518\pi\)
\(662\) −0.225368 0.261194i −0.00875917 0.0101516i
\(663\) −18.6263 + 18.6263i −0.723384 + 0.723384i
\(664\) 32.5110 + 7.28695i 1.26167 + 0.282788i
\(665\) 2.34682 + 8.23831i 0.0910057 + 0.319468i
\(666\) −2.65893 0.195779i −0.103031 0.00758627i
\(667\) 7.09948 + 7.09948i 0.274893 + 0.274893i
\(668\) 21.6463 16.0629i 0.837520 0.621493i
\(669\) 5.98852i 0.231530i
\(670\) −24.2810 15.9561i −0.938058 0.616439i
\(671\) 17.4580i 0.673957i
\(672\) 32.1785 14.2894i 1.24131 0.551224i
\(673\) 24.8279 + 24.8279i 0.957047 + 0.957047i 0.999115 0.0420678i \(-0.0133945\pi\)
−0.0420678 + 0.999115i \(0.513395\pi\)
\(674\) 3.17236 43.0847i 0.122195 1.65956i
\(675\) 6.23302 26.5765i 0.239909 1.02293i
\(676\) −10.6614 1.57857i −0.410053 0.0607140i
\(677\) −28.6500 + 28.6500i −1.10111 + 1.10111i −0.106832 + 0.994277i \(0.534071\pi\)
−0.994277 + 0.106832i \(0.965929\pi\)
\(678\) 2.56943 2.21700i 0.0986784 0.0851434i
\(679\) −1.13030 −0.0433769
\(680\) −27.7367 24.7411i −1.06366 0.948779i
\(681\) −16.1587 −0.619201
\(682\) −24.1676 + 20.8527i −0.925423 + 0.798490i
\(683\) 10.3844 10.3844i 0.397349 0.397349i −0.479948 0.877297i \(-0.659345\pi\)
0.877297 + 0.479948i \(0.159345\pi\)
\(684\) −0.712840 0.105546i −0.0272561 0.00403565i
\(685\) 13.3343 3.79850i 0.509479 0.145133i
\(686\) −0.268721 + 3.64959i −0.0102598 + 0.139342i
\(687\) −3.54404 3.54404i −0.135214 0.135214i
\(688\) 44.7082 23.9276i 1.70448 0.912232i
\(689\) 10.5904i 0.403461i
\(690\) 4.44571 + 21.4877i 0.169245 + 0.818022i
\(691\) 4.95589i 0.188531i −0.995547 0.0942654i \(-0.969950\pi\)
0.995547 0.0942654i \(-0.0300502\pi\)
\(692\) 3.15419 2.34061i 0.119904 0.0889766i
\(693\) 4.01917 + 4.01917i 0.152676 + 0.152676i
\(694\) 42.8622 + 3.15597i 1.62703 + 0.119799i
\(695\) 11.1469 + 6.20417i 0.422826 + 0.235338i
\(696\) −2.36277 + 10.5416i −0.0895605 + 0.399577i
\(697\) 40.8378 40.8378i 1.54684 1.54684i
\(698\) −15.6945 18.1893i −0.594044 0.688477i
\(699\) −38.1012 −1.44112
\(700\) −35.6132 14.1156i −1.34605 0.533519i
\(701\) 50.5194 1.90809 0.954045 0.299662i \(-0.0968739\pi\)
0.954045 + 0.299662i \(0.0968739\pi\)
\(702\) −13.9153 16.1273i −0.525199 0.608688i
\(703\) −3.69981 + 3.69981i −0.139541 + 0.139541i
\(704\) −29.7921 14.0615i −1.12283 0.529964i
\(705\) 2.16636 + 1.20576i 0.0815899 + 0.0454115i
\(706\) −43.7595 3.22204i −1.64691 0.121263i
\(707\) 50.9129 + 50.9129i 1.91478 + 1.91478i
\(708\) 17.4723 + 23.5456i 0.656651 + 0.884899i
\(709\) 28.2010i 1.05911i 0.848276 + 0.529555i \(0.177641\pi\)
−0.848276 + 0.529555i \(0.822359\pi\)
\(710\) −9.58231 46.3146i −0.359618 1.73816i
\(711\) 1.31450i 0.0492975i
\(712\) −23.3225 + 14.7819i −0.874048 + 0.553974i
\(713\) 16.5526 + 16.5526i 0.619901 + 0.619901i
\(714\) 3.79848 51.5883i 0.142155 1.93064i
\(715\) 24.4317 6.95976i 0.913693 0.260280i
\(716\) −6.14452 + 41.4991i −0.229632 + 1.55089i
\(717\) −10.4485 + 10.4485i −0.390207 + 0.390207i
\(718\) 10.0465 8.66848i 0.374931 0.323505i
\(719\) 7.39857 0.275920 0.137960 0.990438i \(-0.455945\pi\)
0.137960 + 0.990438i \(0.455945\pi\)
\(720\) 2.31601 2.24092i 0.0863126 0.0835142i
\(721\) 3.97251 0.147944
\(722\) −1.07073 + 0.923868i −0.0398485 + 0.0343828i
\(723\) −0.926762 + 0.926762i −0.0344666 + 0.0344666i
\(724\) 4.67803 31.5946i 0.173858 1.17421i
\(725\) 9.98980 6.19417i 0.371012 0.230046i
\(726\) −1.00522 + 13.6522i −0.0373072 + 0.506680i
\(727\) −4.97602 4.97602i −0.184550 0.184550i 0.608785 0.793335i \(-0.291657\pi\)
−0.793335 + 0.608785i \(0.791657\pi\)
\(728\) −25.2487 + 16.0027i −0.935779 + 0.593099i
\(729\) 29.4171i 1.08952i
\(730\) −27.2754 17.9238i −1.00951 0.663391i
\(731\) 74.5004i 2.75550i
\(732\) −8.20916 11.0626i −0.303419 0.408886i
\(733\) −34.5680 34.5680i −1.27680 1.27680i −0.942450 0.334348i \(-0.891484\pi\)
−0.334348 0.942450i \(-0.608516\pi\)
\(734\) 17.3936 + 1.28070i 0.642010 + 0.0472716i
\(735\) −7.63950 26.8179i −0.281787 0.989192i
\(736\) −8.67991 + 22.5465i −0.319946 + 0.831075i
\(737\) −26.7537 + 26.7537i −0.985484 + 0.985484i
\(738\) 3.27131 + 3.79134i 0.120419 + 0.139561i
\(739\) 32.5879 1.19877 0.599383 0.800462i \(-0.295413\pi\)
0.599383 + 0.800462i \(0.295413\pi\)
\(740\) −3.04545 23.2006i −0.111953 0.852873i
\(741\) −4.48233 −0.164662
\(742\) −13.5860 15.7457i −0.498756 0.578042i
\(743\) −2.79042 + 2.79042i −0.102371 + 0.102371i −0.756437 0.654066i \(-0.773062\pi\)
0.654066 + 0.756437i \(0.273062\pi\)
\(744\) −5.50885 + 24.5779i −0.201964 + 0.901071i
\(745\) −4.25921 + 7.65244i −0.156045 + 0.280364i
\(746\) −32.8971 2.42224i −1.20445 0.0886843i
\(747\) 3.00113 + 3.00113i 0.109806 + 0.109806i
\(748\) −38.8682 + 28.8426i −1.42116 + 1.05459i
\(749\) 22.7293i 0.830511i
\(750\) 25.6801 + 0.676820i 0.937703 + 0.0247140i
\(751\) 10.9120i 0.398186i 0.979981 + 0.199093i \(0.0637996\pi\)
−0.979981 + 0.199093i \(0.936200\pi\)
\(752\) 1.28809 + 2.40677i 0.0469720 + 0.0877660i
\(753\) 2.74637 + 2.74637i 0.100083 + 0.100083i
\(754\) 0.673524 9.14734i 0.0245283 0.333126i
\(755\) 4.61248 8.28715i 0.167865 0.301600i
\(756\) 41.3783 + 6.12664i 1.50491 + 0.222824i
\(757\) 27.9482 27.9482i 1.01579 1.01579i 0.0159213 0.999873i \(-0.494932\pi\)
0.999873 0.0159213i \(-0.00506814\pi\)
\(758\) 31.8187 27.4544i 1.15571 0.997189i
\(759\) 28.5743 1.03718
\(760\) −0.360440 6.31428i −0.0130745 0.229043i
\(761\) 32.7705 1.18793 0.593964 0.804491i \(-0.297562\pi\)
0.593964 + 0.804491i \(0.297562\pi\)
\(762\) 5.67264 4.89457i 0.205498 0.177312i
\(763\) −7.65902 + 7.65902i −0.277275 + 0.277275i
\(764\) −11.7081 1.73355i −0.423584 0.0627176i
\(765\) −1.29716 4.55356i −0.0468988 0.164634i
\(766\) 1.25929 17.1028i 0.0455001 0.617951i
\(767\) −17.6024 17.6024i −0.635587 0.635587i
\(768\) −25.4905 + 5.09859i −0.919810 + 0.183980i
\(769\) 48.5580i 1.75104i −0.483178 0.875522i \(-0.660518\pi\)
0.483178 0.875522i \(-0.339482\pi\)
\(770\) −27.3964 + 41.6902i −0.987299 + 1.50241i
\(771\) 36.9464i 1.33059i
\(772\) 3.77988 2.80491i 0.136041 0.100951i
\(773\) 12.6933 + 12.6933i 0.456545 + 0.456545i 0.897519 0.440975i \(-0.145367\pi\)
−0.440975 + 0.897519i \(0.645367\pi\)
\(774\) 6.44218 + 0.474342i 0.231559 + 0.0170499i
\(775\) 23.2915 14.4419i 0.836655 0.518767i
\(776\) 0.814327 + 0.182522i 0.0292326 + 0.00655215i
\(777\) 23.0278 23.0278i 0.826118 0.826118i
\(778\) 8.93260 + 10.3526i 0.320249 + 0.371158i
\(779\) 9.82744 0.352104
\(780\) 12.2090 15.8986i 0.437153 0.569260i
\(781\) −61.5892 −2.20383
\(782\) 23.1879 + 26.8740i 0.829199 + 0.961013i
\(783\) −9.07544 + 9.07544i −0.324330 + 0.324330i
\(784\) 8.89665 29.3846i 0.317737 1.04945i
\(785\) −5.59157 + 1.59285i −0.199572 + 0.0568512i
\(786\) −4.30552 0.317018i −0.153573 0.0113077i
\(787\) −5.38808 5.38808i −0.192064 0.192064i 0.604523 0.796587i \(-0.293364\pi\)
−0.796587 + 0.604523i \(0.793364\pi\)
\(788\) 13.0592 + 17.5986i 0.465216 + 0.626923i
\(789\) 7.47554i 0.266136i
\(790\) −11.2976 + 2.33743i −0.401951 + 0.0831621i
\(791\) 5.65816i 0.201181i
\(792\) −2.24660 3.54464i −0.0798295 0.125953i
\(793\) 8.27029 + 8.27029i 0.293687 + 0.293687i
\(794\) −2.79698 + 37.9866i −0.0992610 + 1.34809i
\(795\) 12.1856 + 6.78228i 0.432178 + 0.240543i
\(796\) 5.37687 36.3145i 0.190578 1.28713i
\(797\) −3.86906 + 3.86906i −0.137049 + 0.137049i −0.772303 0.635254i \(-0.780895\pi\)
0.635254 + 0.772303i \(0.280895\pi\)
\(798\) 6.66429 5.75020i 0.235913 0.203555i
\(799\) 4.01057 0.141884
\(800\) 23.3782 + 15.9204i 0.826544 + 0.562873i
\(801\) −3.51746 −0.124284
\(802\) 0.190858 0.164680i 0.00673944 0.00581504i
\(803\) −30.0530 + 30.0530i −1.06055 + 1.06055i
\(804\) −4.37282 + 29.5333i −0.154217 + 1.04156i
\(805\) 31.9665 + 17.7920i 1.12667 + 0.627086i
\(806\) 1.57034 21.3272i 0.0553128 0.751220i
\(807\) 22.2402 + 22.2402i 0.782894 + 0.782894i
\(808\) −28.4589 44.9018i −1.00118 1.57964i
\(809\) 22.3427i 0.785529i 0.919639 + 0.392764i \(0.128481\pi\)
−0.919639 + 0.392764i \(0.871519\pi\)
\(810\) −24.1210 + 4.99053i −0.847524 + 0.175349i
\(811\) 2.96304i 0.104046i −0.998646 0.0520232i \(-0.983433\pi\)
0.998646 0.0520232i \(-0.0165670\pi\)
\(812\) 10.7334 + 14.4642i 0.376667 + 0.507595i
\(813\) 3.18752 + 3.18752i 0.111791 + 0.111791i
\(814\) −30.3893 2.23758i −1.06514 0.0784272i
\(815\) 5.23393 1.49097i 0.183337 0.0522264i
\(816\) −11.0671 + 36.5535i −0.387428 + 1.27963i
\(817\) 8.96408 8.96408i 0.313614 0.313614i
\(818\) 1.85754 + 2.15283i 0.0649474 + 0.0752719i
\(819\) −3.80797 −0.133061
\(820\) −26.7681 + 34.8574i −0.934782 + 1.21727i
\(821\) 37.0186 1.29196 0.645979 0.763355i \(-0.276449\pi\)
0.645979 + 0.763355i \(0.276449\pi\)
\(822\) −9.30714 10.7867i −0.324624 0.376228i
\(823\) −26.4232 + 26.4232i −0.921055 + 0.921055i −0.997104 0.0760490i \(-0.975769\pi\)
0.0760490 + 0.997104i \(0.475769\pi\)
\(824\) −2.86200 0.641485i −0.0997026 0.0223472i
\(825\) 7.63843 32.5690i 0.265936 1.13391i
\(826\) 48.7527 + 3.58969i 1.69632 + 0.124901i
\(827\) −17.2236 17.2236i −0.598925 0.598925i 0.341101 0.940026i \(-0.389200\pi\)
−0.940026 + 0.341101i \(0.889200\pi\)
\(828\) −2.47148 + 1.83400i −0.0858900 + 0.0637358i
\(829\) 20.0047i 0.694792i −0.937718 0.347396i \(-0.887066\pi\)
0.937718 0.347396i \(-0.112934\pi\)
\(830\) −20.4570 + 31.1302i −0.710073 + 1.08054i
\(831\) 8.00962i 0.277851i
\(832\) 20.7746 7.45199i 0.720230 0.258351i
\(833\) −31.8954 31.8954i −1.10511 1.10511i
\(834\) 0.962599 13.0734i 0.0333321 0.452693i
\(835\) 8.25648 + 28.9837i 0.285727 + 1.00302i
\(836\) −8.14714 1.20630i −0.281775 0.0417207i
\(837\) −21.1596 + 21.1596i −0.731384 + 0.731384i
\(838\) 14.6306 12.6239i 0.505406 0.436084i
\(839\) −25.6540 −0.885675 −0.442838 0.896602i \(-0.646028\pi\)
−0.442838 + 0.896602i \(0.646028\pi\)
\(840\) 2.24339 + 39.3003i 0.0774045 + 1.35599i
\(841\) 23.4734 0.809429
\(842\) 14.8820 12.8407i 0.512867 0.442521i
\(843\) 31.7733 31.7733i 1.09433 1.09433i
\(844\) 21.3028 + 3.15417i 0.733272 + 0.108571i
\(845\) 5.86012 10.5288i 0.201594 0.362200i
\(846\) −0.0255352 + 0.346802i −0.000877919 + 0.0119233i
\(847\) 16.1386 + 16.1386i 0.554528 + 0.554528i
\(848\) 7.24541 + 13.5379i 0.248809 + 0.464893i
\(849\) 16.0218i 0.549867i
\(850\) 36.8296 19.2457i 1.26324 0.660121i
\(851\) 22.3465i 0.766028i
\(852\) −39.0273 + 28.9607i −1.33705 + 0.992179i
\(853\) −23.8080 23.8080i −0.815170 0.815170i 0.170234 0.985404i \(-0.445548\pi\)
−0.985404 + 0.170234i \(0.945548\pi\)
\(854\) −22.9058 1.68657i −0.783822 0.0577133i
\(855\) 0.391819 0.703974i 0.0133999 0.0240754i
\(856\) −3.67035 + 16.3754i −0.125450 + 0.559699i
\(857\) 38.1592 38.1592i 1.30349 1.30349i 0.377471 0.926021i \(-0.376794\pi\)
0.926021 0.377471i \(-0.123206\pi\)
\(858\) −17.0529 19.7637i −0.582176 0.674722i
\(859\) 44.6170 1.52231 0.761157 0.648568i \(-0.224632\pi\)
0.761157 + 0.648568i \(0.224632\pi\)
\(860\) 7.37866 + 56.2116i 0.251610 + 1.91680i
\(861\) −61.1664 −2.08455
\(862\) 18.8133 + 21.8039i 0.640783 + 0.742645i
\(863\) 9.40276 9.40276i 0.320074 0.320074i −0.528722 0.848795i \(-0.677328\pi\)
0.848795 + 0.528722i \(0.177328\pi\)
\(864\) −28.8217 11.0957i −0.980536 0.377485i
\(865\) 1.20309 + 4.22336i 0.0409064 + 0.143599i
\(866\) −11.7656 0.866308i −0.399811 0.0294384i
\(867\) 20.1464 + 20.1464i 0.684209 + 0.684209i
\(868\) 25.0251 + 33.7237i 0.849408 + 1.14466i
\(869\) 15.0236i 0.509640i
\(870\) −10.0939 6.63311i −0.342214 0.224884i
\(871\) 25.3478i 0.858878i
\(872\) 6.75474 4.28117i 0.228744 0.144979i
\(873\) 0.0751716 + 0.0751716i 0.00254417 + 0.00254417i
\(874\) −0.443521 + 6.02359i −0.0150023 + 0.203751i
\(875\) 28.8246 31.6793i 0.974448 1.07096i
\(876\) −4.91208 + 33.1754i −0.165964 + 1.12089i
\(877\) −2.40711 + 2.40711i −0.0812823 + 0.0812823i −0.746579 0.665297i \(-0.768305\pi\)
0.665297 + 0.746579i \(0.268305\pi\)
\(878\) 29.1705 25.1694i 0.984458 0.849427i
\(879\) 9.46245 0.319160
\(880\) 26.4700 25.6118i 0.892303 0.863373i
\(881\) −39.5208 −1.33149 −0.665744 0.746180i \(-0.731886\pi\)
−0.665744 + 0.746180i \(0.731886\pi\)
\(882\) 2.96113 2.55497i 0.0997063 0.0860304i
\(883\) −19.8634 + 19.8634i −0.668457 + 0.668457i −0.957359 0.288901i \(-0.906710\pi\)
0.288901 + 0.957359i \(0.406710\pi\)
\(884\) 4.74935 32.0764i 0.159738 1.07884i
\(885\) −31.5268 + 8.98093i −1.05976 + 0.301891i
\(886\) −2.96479 + 40.2658i −0.0996042 + 1.35275i
\(887\) 12.1860 + 12.1860i 0.409164 + 0.409164i 0.881447 0.472283i \(-0.156570\pi\)
−0.472283 + 0.881447i \(0.656570\pi\)
\(888\) −20.3090 + 12.8719i −0.681525 + 0.431952i
\(889\) 12.4918i 0.418960i
\(890\) −6.25473 30.2313i −0.209659 1.01336i
\(891\) 32.0760i 1.07459i
\(892\) 4.39294 + 5.91991i 0.147087 + 0.198213i
\(893\) 0.482563 + 0.482563i 0.0161484 + 0.0161484i
\(894\) 8.97495 + 0.660832i 0.300167 + 0.0221015i
\(895\) −40.9829 22.8104i −1.36991 0.762466i
\(896\) −21.3277 + 37.7305i −0.712507 + 1.26049i
\(897\) −13.5364 + 13.5364i −0.451967 + 0.451967i
\(898\) −4.47629 5.18787i −0.149376 0.173122i
\(899\) −12.8853 −0.429749
\(900\) 1.42972 + 3.30726i 0.0476572 + 0.110242i
\(901\) 22.5591 0.751553
\(902\) 37.3882 + 43.3317i 1.24489 + 1.44279i
\(903\) −55.7929 + 55.7929i −1.85667 + 1.85667i
\(904\) −0.913684 + 4.07643i −0.0303887 + 0.135580i
\(905\) 31.2017 + 17.3663i 1.03718 + 0.577275i
\(906\) −9.71936 0.715643i −0.322904 0.0237756i
\(907\) 25.8877 + 25.8877i 0.859586 + 0.859586i 0.991289 0.131704i \(-0.0420447\pi\)
−0.131704 + 0.991289i \(0.542045\pi\)
\(908\) 15.9735 11.8534i 0.530099 0.393367i
\(909\) 6.77202i 0.224614i
\(910\) −6.77131 32.7281i −0.224467 1.08493i
\(911\) 18.5615i 0.614971i −0.951553 0.307485i \(-0.900513\pi\)
0.951553 0.307485i \(-0.0994875\pi\)
\(912\) −5.72985 + 3.06659i −0.189734 + 0.101545i
\(913\) 34.3003 + 34.3003i 1.13517 + 1.13517i
\(914\) 2.15762 29.3033i 0.0713677 0.969266i
\(915\) 14.8125 4.21958i 0.489686 0.139495i
\(916\) 6.10321 + 0.903665i 0.201656 + 0.0298579i
\(917\) −5.08966 + 5.08966i −0.168076 + 0.168076i
\(918\) −34.3537 + 29.6417i −1.13384 + 0.978322i
\(919\) 21.3400 0.703943 0.351971 0.936011i \(-0.385511\pi\)
0.351971 + 0.936011i \(0.385511\pi\)
\(920\) −20.1573 17.9803i −0.664566 0.592792i
\(921\) 53.4695 1.76188
\(922\) −26.2347 + 22.6363i −0.863993 + 0.745486i
\(923\) 29.1764 29.1764i 0.960352 0.960352i
\(924\) 50.7082 + 7.50806i 1.66818 + 0.246997i
\(925\) 25.4705 + 5.97362i 0.837465 + 0.196411i
\(926\) 3.79155 51.4942i 0.124598 1.69221i
\(927\) −0.264195 0.264195i −0.00867732 0.00867732i
\(928\) −5.39718 12.1540i −0.177171 0.398975i
\(929\) 23.7510i 0.779244i 0.920975 + 0.389622i \(0.127394\pi\)
−0.920975 + 0.389622i \(0.872606\pi\)
\(930\) −23.5341 15.4653i −0.771713 0.507126i
\(931\) 7.67547i 0.251553i
\(932\) 37.6646 27.9495i 1.23375 0.915518i
\(933\) −36.6894 36.6894i −1.20116 1.20116i
\(934\) 12.0639 + 0.888276i 0.394744 + 0.0290653i
\(935\) −14.8254 52.0432i −0.484841 1.70200i
\(936\) 2.74346 + 0.614915i 0.0896729 + 0.0200991i
\(937\) −20.1997 + 20.1997i −0.659895 + 0.659895i −0.955355 0.295460i \(-0.904527\pi\)
0.295460 + 0.955355i \(0.404527\pi\)
\(938\) 32.5177 + 37.6869i 1.06174 + 1.23052i
\(939\) −8.12964 −0.265301
\(940\) −3.02604 + 0.397215i −0.0986985 + 0.0129557i
\(941\) 56.6392 1.84639 0.923193 0.384337i \(-0.125570\pi\)
0.923193 + 0.384337i \(0.125570\pi\)
\(942\) 3.90282 + 4.52323i 0.127161 + 0.147375i
\(943\) 29.6783 29.6783i 0.966460 0.966460i
\(944\) −34.5443 10.4588i −1.12432 0.340406i
\(945\) −22.7440 + 40.8636i −0.739861 + 1.32929i
\(946\) 73.6285 + 5.42132i 2.39387 + 0.176262i
\(947\) 40.2926 + 40.2926i 1.30933 + 1.30933i 0.921896 + 0.387437i \(0.126639\pi\)
0.387437 + 0.921896i \(0.373361\pi\)
\(948\) 7.06445 + 9.52001i 0.229443 + 0.309196i
\(949\) 28.4737i 0.924296i
\(950\) 6.74712 + 2.11574i 0.218906 + 0.0686436i
\(951\) 18.3109i 0.593773i
\(952\) 34.0882 + 53.7836i 1.10480 + 1.74314i
\(953\) 4.11215 + 4.11215i 0.133206 + 0.133206i 0.770566 0.637360i \(-0.219974\pi\)
−0.637360 + 0.770566i \(0.719974\pi\)
\(954\) −0.143633 + 1.95073i −0.00465030 + 0.0631571i
\(955\) 6.43547 11.5625i 0.208247 0.374153i
\(956\) 2.66418 17.9934i 0.0861656 0.581948i
\(957\) −11.1218 + 11.1218i −0.359515 + 0.359515i
\(958\) 23.6598 20.4146i 0.764414 0.659565i
\(959\) −23.7534 −0.767036
\(960\) 4.73000 28.6763i 0.152660 0.925523i
\(961\) 0.957597 0.0308902
\(962\) 15.4562 13.3362i 0.498327 0.429976i
\(963\) −1.51163 + 1.51163i −0.0487117 + 0.0487117i
\(964\) 0.236307 1.59598i 0.00761094 0.0514030i
\(965\) 1.44175 + 5.06114i 0.0464115 + 0.162924i
\(966\) 2.76049 37.4911i 0.0888174 1.20626i
\(967\) 37.1217 + 37.1217i 1.19375 + 1.19375i 0.976005 + 0.217747i \(0.0698707\pi\)
0.217747 + 0.976005i \(0.430129\pi\)
\(968\) −9.02100 14.2331i −0.289946 0.457471i
\(969\) 9.54804i 0.306727i
\(970\) −0.512402 + 0.779742i −0.0164522 + 0.0250360i
\(971\) 5.78287i 0.185581i −0.995686 0.0927905i \(-0.970421\pi\)
0.995686 0.0927905i \(-0.0295787\pi\)
\(972\) −4.43751 5.97996i −0.142333 0.191807i
\(973\) −15.4543 15.4543i −0.495443 0.495443i
\(974\) 43.5268 + 3.20491i 1.39469 + 0.102692i
\(975\) 11.8102 + 19.0473i 0.378231 + 0.610001i
\(976\) 16.2302 + 4.91395i 0.519516 + 0.157292i
\(977\) −42.5957 + 42.5957i −1.36276 + 1.36276i −0.492373 + 0.870384i \(0.663870\pi\)
−0.870384 + 0.492373i \(0.836130\pi\)
\(978\) −3.65319 4.23393i −0.116816 0.135386i
\(979\) −40.2016 −1.28485
\(980\) 27.2245 + 20.9065i 0.869655 + 0.667835i
\(981\) 1.01874 0.0325259
\(982\) −26.8886 31.1630i −0.858051 0.994452i
\(983\) −19.1593 + 19.1593i −0.611085 + 0.611085i −0.943229 0.332143i \(-0.892228\pi\)
0.332143 + 0.943229i \(0.392228\pi\)
\(984\) 44.0675 + 9.87720i 1.40482 + 0.314874i
\(985\) −23.5639 + 6.71256i −0.750809 + 0.213880i
\(986\) −19.4852 1.43471i −0.620536 0.0456905i
\(987\) −3.00349 3.00349i −0.0956023 0.0956023i
\(988\) 4.43097 3.28806i 0.140968 0.104607i
\(989\) 54.1421i 1.72162i
\(990\) 4.59467 0.950618i 0.146028 0.0302126i
\(991\) 29.9003i 0.949815i −0.880036 0.474908i \(-0.842481\pi\)
0.880036 0.474908i \(-0.157519\pi\)
\(992\) −12.5837 28.3374i −0.399532 0.899713i
\(993\) −0.280249 0.280249i −0.00889342 0.00889342i
\(994\) −5.94998 + 80.8085i −0.188722 + 2.56309i
\(995\) 35.8628 + 19.9606i 1.13693 + 0.632794i
\(996\) 37.8640 + 5.60629i 1.19977 + 0.177642i
\(997\) −26.0472 + 26.0472i −0.824923 + 0.824923i −0.986809 0.161886i \(-0.948242\pi\)
0.161886 + 0.986809i \(0.448242\pi\)
\(998\) −27.3735 + 23.6189i −0.866493 + 0.747643i
\(999\) −28.5661 −0.903790
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 380.2.k.d.343.7 yes 52
4.3 odd 2 380.2.k.c.343.7 yes 52
5.2 odd 4 380.2.k.c.267.7 52
20.7 even 4 inner 380.2.k.d.267.7 yes 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.k.c.267.7 52 5.2 odd 4
380.2.k.c.343.7 yes 52 4.3 odd 2
380.2.k.d.267.7 yes 52 20.7 even 4 inner
380.2.k.d.343.7 yes 52 1.1 even 1 trivial