Properties

Label 336.2.u.a.139.5
Level $336$
Weight $2$
Character 336.139
Analytic conductor $2.683$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [336,2,Mod(139,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.139");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.u (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: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 139.5
Character \(\chi\) \(=\) 336.139
Dual form 336.2.u.a.307.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.20526 + 0.739825i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.905318 - 1.78337i) q^{4} +(-1.32544 + 1.32544i) q^{5} +(0.329115 - 1.37538i) q^{6} +(2.64192 + 0.142388i) q^{7} +(0.228233 + 2.81920i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-1.20526 + 0.739825i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.905318 - 1.78337i) q^{4} +(-1.32544 + 1.32544i) q^{5} +(0.329115 - 1.37538i) q^{6} +(2.64192 + 0.142388i) q^{7} +(0.228233 + 2.81920i) q^{8} -1.00000i q^{9} +(0.616912 - 2.57810i) q^{10} +(-1.18514 + 1.18514i) q^{11} +(0.620874 + 1.90119i) q^{12} +(2.02086 + 2.02086i) q^{13} +(-3.28955 + 1.78294i) q^{14} -1.87446i q^{15} +(-2.36080 - 3.22903i) q^{16} +0.276387i q^{17} +(0.739825 + 1.20526i) q^{18} +(-4.58131 + 4.58131i) q^{19} +(1.16380 + 3.56370i) q^{20} +(-1.96880 + 1.76743i) q^{21} +(0.551607 - 2.30519i) q^{22} -1.81753 q^{23} +(-2.15486 - 1.83209i) q^{24} +1.48640i q^{25} +(-3.93076 - 0.940587i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.64571 - 4.58260i) q^{28} +(-2.64137 + 2.64137i) q^{29} +(1.38677 + 2.25922i) q^{30} -7.11326 q^{31} +(5.23430 + 2.14525i) q^{32} -1.67603i q^{33} +(-0.204478 - 0.333119i) q^{34} +(-3.69044 + 3.31298i) q^{35} +(-1.78337 - 0.905318i) q^{36} +(-0.786692 - 0.786692i) q^{37} +(2.13232 - 8.91105i) q^{38} -2.85793 q^{39} +(-4.03920 - 3.43419i) q^{40} +7.33055 q^{41} +(1.06533 - 3.58679i) q^{42} +(-1.69851 + 1.69851i) q^{43} +(1.04061 + 3.18646i) q^{44} +(1.32544 + 1.32544i) q^{45} +(2.19060 - 1.34465i) q^{46} -11.5721 q^{47} +(3.95261 + 0.613933i) q^{48} +(6.95945 + 0.752353i) q^{49} +(-1.09968 - 1.79150i) q^{50} +(-0.195435 - 0.195435i) q^{51} +(5.43347 - 1.77442i) q^{52} +(3.85262 + 3.85262i) q^{53} +(-1.37538 - 0.329115i) q^{54} -3.14166i q^{55} +(0.201552 + 7.48060i) q^{56} -6.47895i q^{57} +(1.22939 - 5.13770i) q^{58} +(4.25247 + 4.25247i) q^{59} +(-3.34285 - 1.69698i) q^{60} +(1.14204 + 1.14204i) q^{61} +(8.57335 - 5.26257i) q^{62} +(0.142388 - 2.64192i) q^{63} +(-7.89582 + 1.28687i) q^{64} -5.35708 q^{65} +(1.23997 + 2.02006i) q^{66} +(-3.05161 - 3.05161i) q^{67} +(0.492900 + 0.250218i) q^{68} +(1.28519 - 1.28519i) q^{69} +(1.99692 - 6.72330i) q^{70} +8.36612 q^{71} +(2.81920 - 0.228233i) q^{72} +16.9603 q^{73} +(1.53018 + 0.366156i) q^{74} +(-1.05104 - 1.05104i) q^{75} +(4.02261 + 12.3177i) q^{76} +(-3.29978 + 2.96228i) q^{77} +(3.44456 - 2.11437i) q^{78} +13.8414i q^{79} +(7.40900 + 1.15079i) q^{80} -1.00000 q^{81} +(-8.83525 + 5.42333i) q^{82} +(9.90941 - 9.90941i) q^{83} +(1.36959 + 5.11119i) q^{84} +(-0.366336 - 0.366336i) q^{85} +(0.790551 - 3.30375i) q^{86} -3.73546i q^{87} +(-3.61163 - 3.07065i) q^{88} +7.94992 q^{89} +(-2.57810 - 0.616912i) q^{90} +(5.05121 + 5.62670i) q^{91} +(-1.64544 + 3.24132i) q^{92} +(5.02983 - 5.02983i) q^{93} +(13.9474 - 8.56132i) q^{94} -12.1445i q^{95} +(-5.21813 + 2.18428i) q^{96} -13.1657i q^{97} +(-8.94458 + 4.24199i) q^{98} +(1.18514 + 1.18514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20526 + 0.739825i −0.852250 + 0.523135i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 0.905318 1.78337i 0.452659 0.891684i
\(5\) −1.32544 + 1.32544i −0.592756 + 0.592756i −0.938375 0.345619i \(-0.887669\pi\)
0.345619 + 0.938375i \(0.387669\pi\)
\(6\) 0.329115 1.37538i 0.134360 0.561499i
\(7\) 2.64192 + 0.142388i 0.998551 + 0.0538175i
\(8\) 0.228233 + 2.81920i 0.0806925 + 0.996739i
\(9\) 1.00000i 0.333333i
\(10\) 0.616912 2.57810i 0.195085 0.815268i
\(11\) −1.18514 + 1.18514i −0.357332 + 0.357332i −0.862829 0.505497i \(-0.831309\pi\)
0.505497 + 0.862829i \(0.331309\pi\)
\(12\) 0.620874 + 1.90119i 0.179231 + 0.548826i
\(13\) 2.02086 + 2.02086i 0.560487 + 0.560487i 0.929446 0.368959i \(-0.120286\pi\)
−0.368959 + 0.929446i \(0.620286\pi\)
\(14\) −3.28955 + 1.78294i −0.879168 + 0.476511i
\(15\) 1.87446i 0.483983i
\(16\) −2.36080 3.22903i −0.590199 0.807257i
\(17\) 0.276387i 0.0670337i 0.999438 + 0.0335169i \(0.0106707\pi\)
−0.999438 + 0.0335169i \(0.989329\pi\)
\(18\) 0.739825 + 1.20526i 0.174378 + 0.284083i
\(19\) −4.58131 + 4.58131i −1.05102 + 1.05102i −0.0523978 + 0.998626i \(0.516686\pi\)
−0.998626 + 0.0523978i \(0.983314\pi\)
\(20\) 1.16380 + 3.56370i 0.260235 + 0.796868i
\(21\) −1.96880 + 1.76743i −0.429628 + 0.385686i
\(22\) 0.551607 2.30519i 0.117603 0.491469i
\(23\) −1.81753 −0.378981 −0.189491 0.981883i \(-0.560684\pi\)
−0.189491 + 0.981883i \(0.560684\pi\)
\(24\) −2.15486 1.83209i −0.439860 0.373974i
\(25\) 1.48640i 0.297280i
\(26\) −3.93076 0.940587i −0.770885 0.184464i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 2.64571 4.58260i 0.499991 0.866030i
\(29\) −2.64137 + 2.64137i −0.490490 + 0.490490i −0.908461 0.417970i \(-0.862742\pi\)
0.417970 + 0.908461i \(0.362742\pi\)
\(30\) 1.38677 + 2.25922i 0.253189 + 0.412475i
\(31\) −7.11326 −1.27758 −0.638790 0.769382i \(-0.720565\pi\)
−0.638790 + 0.769382i \(0.720565\pi\)
\(32\) 5.23430 + 2.14525i 0.925302 + 0.379231i
\(33\) 1.67603i 0.291760i
\(34\) −0.204478 0.333119i −0.0350677 0.0571295i
\(35\) −3.69044 + 3.31298i −0.623798 + 0.559997i
\(36\) −1.78337 0.905318i −0.297228 0.150886i
\(37\) −0.786692 0.786692i −0.129331 0.129331i 0.639478 0.768809i \(-0.279150\pi\)
−0.768809 + 0.639478i \(0.779150\pi\)
\(38\) 2.13232 8.91105i 0.345907 1.44556i
\(39\) −2.85793 −0.457636
\(40\) −4.03920 3.43419i −0.638654 0.542992i
\(41\) 7.33055 1.14484 0.572420 0.819961i \(-0.306005\pi\)
0.572420 + 0.819961i \(0.306005\pi\)
\(42\) 1.06533 3.58679i 0.164384 0.553454i
\(43\) −1.69851 + 1.69851i −0.259020 + 0.259020i −0.824656 0.565635i \(-0.808631\pi\)
0.565635 + 0.824656i \(0.308631\pi\)
\(44\) 1.04061 + 3.18646i 0.156877 + 0.480376i
\(45\) 1.32544 + 1.32544i 0.197585 + 0.197585i
\(46\) 2.19060 1.34465i 0.322987 0.198258i
\(47\) −11.5721 −1.68796 −0.843982 0.536372i \(-0.819795\pi\)
−0.843982 + 0.536372i \(0.819795\pi\)
\(48\) 3.95261 + 0.613933i 0.570509 + 0.0886136i
\(49\) 6.95945 + 0.752353i 0.994207 + 0.107479i
\(50\) −1.09968 1.79150i −0.155518 0.253357i
\(51\) −0.195435 0.195435i −0.0273664 0.0273664i
\(52\) 5.43347 1.77442i 0.753487 0.246067i
\(53\) 3.85262 + 3.85262i 0.529198 + 0.529198i 0.920333 0.391135i \(-0.127917\pi\)
−0.391135 + 0.920333i \(0.627917\pi\)
\(54\) −1.37538 0.329115i −0.187166 0.0447868i
\(55\) 3.14166i 0.423621i
\(56\) 0.201552 + 7.48060i 0.0269336 + 0.999637i
\(57\) 6.47895i 0.858158i
\(58\) 1.22939 5.13770i 0.161427 0.674613i
\(59\) 4.25247 + 4.25247i 0.553625 + 0.553625i 0.927485 0.373860i \(-0.121966\pi\)
−0.373860 + 0.927485i \(0.621966\pi\)
\(60\) −3.34285 1.69698i −0.431560 0.219080i
\(61\) 1.14204 + 1.14204i 0.146223 + 0.146223i 0.776428 0.630206i \(-0.217029\pi\)
−0.630206 + 0.776428i \(0.717029\pi\)
\(62\) 8.57335 5.26257i 1.08882 0.668347i
\(63\) 0.142388 2.64192i 0.0179392 0.332850i
\(64\) −7.89582 + 1.28687i −0.986977 + 0.160859i
\(65\) −5.35708 −0.664464
\(66\) 1.23997 + 2.02006i 0.152630 + 0.248653i
\(67\) −3.05161 3.05161i −0.372813 0.372813i 0.495688 0.868501i \(-0.334916\pi\)
−0.868501 + 0.495688i \(0.834916\pi\)
\(68\) 0.492900 + 0.250218i 0.0597729 + 0.0303434i
\(69\) 1.28519 1.28519i 0.154718 0.154718i
\(70\) 1.99692 6.72330i 0.238678 0.803588i
\(71\) 8.36612 0.992876 0.496438 0.868072i \(-0.334641\pi\)
0.496438 + 0.868072i \(0.334641\pi\)
\(72\) 2.81920 0.228233i 0.332246 0.0268975i
\(73\) 16.9603 1.98505 0.992527 0.122024i \(-0.0389386\pi\)
0.992527 + 0.122024i \(0.0389386\pi\)
\(74\) 1.53018 + 0.366156i 0.177880 + 0.0425648i
\(75\) −1.05104 1.05104i −0.121364 0.121364i
\(76\) 4.02261 + 12.3177i 0.461425 + 1.41294i
\(77\) −3.29978 + 2.96228i −0.376045 + 0.337583i
\(78\) 3.44456 2.11437i 0.390020 0.239405i
\(79\) 13.8414i 1.55728i 0.627470 + 0.778641i \(0.284091\pi\)
−0.627470 + 0.778641i \(0.715909\pi\)
\(80\) 7.40900 + 1.15079i 0.828351 + 0.128663i
\(81\) −1.00000 −0.111111
\(82\) −8.83525 + 5.42333i −0.975690 + 0.598906i
\(83\) 9.90941 9.90941i 1.08770 1.08770i 0.0919340 0.995765i \(-0.470695\pi\)
0.995765 0.0919340i \(-0.0293049\pi\)
\(84\) 1.36959 + 5.11119i 0.149435 + 0.557676i
\(85\) −0.366336 0.366336i −0.0397347 0.0397347i
\(86\) 0.790551 3.30375i 0.0852474 0.356253i
\(87\) 3.73546i 0.400484i
\(88\) −3.61163 3.07065i −0.385001 0.327333i
\(89\) 7.94992 0.842690 0.421345 0.906901i \(-0.361558\pi\)
0.421345 + 0.906901i \(0.361558\pi\)
\(90\) −2.57810 0.616912i −0.271756 0.0650282i
\(91\) 5.05121 + 5.62670i 0.529511 + 0.589839i
\(92\) −1.64544 + 3.24132i −0.171549 + 0.337931i
\(93\) 5.02983 5.02983i 0.521569 0.521569i
\(94\) 13.9474 8.56132i 1.43857 0.883033i
\(95\) 12.1445i 1.24600i
\(96\) −5.21813 + 2.18428i −0.532573 + 0.222933i
\(97\) 13.1657i 1.33678i −0.743812 0.668388i \(-0.766984\pi\)
0.743812 0.668388i \(-0.233016\pi\)
\(98\) −8.94458 + 4.24199i −0.903539 + 0.428506i
\(99\) 1.18514 + 1.18514i 0.119111 + 0.119111i
\(100\) 2.65080 + 1.34566i 0.265080 + 0.134566i
\(101\) −1.20635 + 1.20635i −0.120036 + 0.120036i −0.764573 0.644537i \(-0.777050\pi\)
0.644537 + 0.764573i \(0.277050\pi\)
\(102\) 0.380139 + 0.0909630i 0.0376393 + 0.00900668i
\(103\) 11.4220i 1.12544i −0.826647 0.562722i \(-0.809754\pi\)
0.826647 0.562722i \(-0.190246\pi\)
\(104\) −5.23600 + 6.15846i −0.513432 + 0.603886i
\(105\) 0.266900 4.95217i 0.0260468 0.483282i
\(106\) −7.49369 1.79316i −0.727852 0.174167i
\(107\) 9.18783 9.18783i 0.888221 0.888221i −0.106131 0.994352i \(-0.533846\pi\)
0.994352 + 0.106131i \(0.0338464\pi\)
\(108\) 1.90119 0.620874i 0.182942 0.0597437i
\(109\) 0.541341 0.541341i 0.0518511 0.0518511i −0.680706 0.732557i \(-0.738327\pi\)
0.732557 + 0.680706i \(0.238327\pi\)
\(110\) 2.32428 + 3.78653i 0.221611 + 0.361031i
\(111\) 1.11255 0.105599
\(112\) −5.77726 8.86698i −0.545900 0.837851i
\(113\) −11.9427 −1.12347 −0.561735 0.827317i \(-0.689866\pi\)
−0.561735 + 0.827317i \(0.689866\pi\)
\(114\) 4.79329 + 7.80884i 0.448932 + 0.731365i
\(115\) 2.40903 2.40903i 0.224644 0.224644i
\(116\) 2.31925 + 7.10182i 0.215337 + 0.659387i
\(117\) 2.02086 2.02086i 0.186829 0.186829i
\(118\) −8.27144 1.97926i −0.761447 0.182206i
\(119\) −0.0393541 + 0.730192i −0.00360759 + 0.0669366i
\(120\) 5.28448 0.427813i 0.482405 0.0390538i
\(121\) 8.19091i 0.744628i
\(122\) −2.22136 0.531547i −0.201113 0.0481240i
\(123\) −5.18348 + 5.18348i −0.467379 + 0.467379i
\(124\) −6.43976 + 12.6856i −0.578308 + 1.13920i
\(125\) −8.59736 8.59736i −0.768971 0.768971i
\(126\) 1.78294 + 3.28955i 0.158837 + 0.293056i
\(127\) 18.8618i 1.67371i 0.547422 + 0.836857i \(0.315609\pi\)
−0.547422 + 0.836857i \(0.684391\pi\)
\(128\) 8.56448 7.39254i 0.757000 0.653414i
\(129\) 2.40206i 0.211489i
\(130\) 6.45669 3.96330i 0.566289 0.347605i
\(131\) −8.80983 + 8.80983i −0.769718 + 0.769718i −0.978057 0.208339i \(-0.933194\pi\)
0.208339 + 0.978057i \(0.433194\pi\)
\(132\) −2.98899 1.51735i −0.260158 0.132068i
\(133\) −12.7558 + 11.4511i −1.10606 + 0.992937i
\(134\) 5.93565 + 1.42033i 0.512762 + 0.122698i
\(135\) −1.87446 −0.161328
\(136\) −0.779192 + 0.0630806i −0.0668151 + 0.00540912i
\(137\) 4.34380i 0.371116i 0.982633 + 0.185558i \(0.0594092\pi\)
−0.982633 + 0.185558i \(0.940591\pi\)
\(138\) −0.598176 + 2.49980i −0.0509201 + 0.212797i
\(139\) 1.64886 + 1.64886i 0.139854 + 0.139854i 0.773568 0.633714i \(-0.218470\pi\)
−0.633714 + 0.773568i \(0.718470\pi\)
\(140\) 2.56725 + 9.58071i 0.216972 + 0.809718i
\(141\) 8.18271 8.18271i 0.689108 0.689108i
\(142\) −10.0834 + 6.18946i −0.846178 + 0.519408i
\(143\) −4.79000 −0.400560
\(144\) −3.22903 + 2.36080i −0.269086 + 0.196733i
\(145\) 7.00197i 0.581482i
\(146\) −20.4416 + 12.5477i −1.69176 + 1.03845i
\(147\) −5.45307 + 4.38908i −0.449762 + 0.362005i
\(148\) −2.11517 + 0.690754i −0.173866 + 0.0567796i
\(149\) −10.1553 10.1553i −0.831955 0.831955i 0.155829 0.987784i \(-0.450195\pi\)
−0.987784 + 0.155829i \(0.950195\pi\)
\(150\) 2.04437 + 0.489196i 0.166922 + 0.0399427i
\(151\) −8.92611 −0.726397 −0.363198 0.931712i \(-0.618315\pi\)
−0.363198 + 0.931712i \(0.618315\pi\)
\(152\) −13.9612 11.8700i −1.13241 0.962787i
\(153\) 0.276387 0.0223446
\(154\) 1.78553 6.01159i 0.143882 0.484427i
\(155\) 9.42822 9.42822i 0.757293 0.757293i
\(156\) −2.58734 + 5.09675i −0.207153 + 0.408066i
\(157\) −5.83300 5.83300i −0.465524 0.465524i 0.434937 0.900461i \(-0.356771\pi\)
−0.900461 + 0.434937i \(0.856771\pi\)
\(158\) −10.2402 16.6826i −0.814669 1.32719i
\(159\) −5.44843 −0.432089
\(160\) −9.78118 + 4.09435i −0.773270 + 0.323687i
\(161\) −4.80176 0.258794i −0.378432 0.0203958i
\(162\) 1.20526 0.739825i 0.0946944 0.0581261i
\(163\) 12.4751 + 12.4751i 0.977129 + 0.977129i 0.999744 0.0226151i \(-0.00719923\pi\)
−0.0226151 + 0.999744i \(0.507199\pi\)
\(164\) 6.63648 13.0731i 0.518222 1.02084i
\(165\) 2.22149 + 2.22149i 0.172943 + 0.172943i
\(166\) −4.61222 + 19.2747i −0.357978 + 1.49600i
\(167\) 21.3378i 1.65117i −0.564280 0.825584i \(-0.690846\pi\)
0.564280 0.825584i \(-0.309154\pi\)
\(168\) −5.43210 5.14706i −0.419096 0.397105i
\(169\) 4.83221i 0.371709i
\(170\) 0.712555 + 0.170507i 0.0546505 + 0.0130773i
\(171\) 4.58131 + 4.58131i 0.350341 + 0.350341i
\(172\) 1.49138 + 4.56676i 0.113716 + 0.348212i
\(173\) 10.7377 + 10.7377i 0.816371 + 0.816371i 0.985580 0.169209i \(-0.0541213\pi\)
−0.169209 + 0.985580i \(0.554121\pi\)
\(174\) 2.76359 + 4.50221i 0.209507 + 0.341312i
\(175\) −0.211645 + 3.92695i −0.0159989 + 0.296849i
\(176\) 6.62470 + 1.02897i 0.499356 + 0.0775618i
\(177\) −6.01391 −0.452033
\(178\) −9.58174 + 5.88155i −0.718182 + 0.440841i
\(179\) 2.41822 + 2.41822i 0.180746 + 0.180746i 0.791681 0.610935i \(-0.209206\pi\)
−0.610935 + 0.791681i \(0.709206\pi\)
\(180\) 3.56370 1.16380i 0.265623 0.0867448i
\(181\) −0.318290 + 0.318290i −0.0236583 + 0.0236583i −0.718837 0.695179i \(-0.755325\pi\)
0.695179 + 0.718837i \(0.255325\pi\)
\(182\) −10.2508 3.04465i −0.759841 0.225684i
\(183\) −1.61508 −0.119390
\(184\) −0.414820 5.12399i −0.0305809 0.377745i
\(185\) 2.08543 0.153324
\(186\) −2.34108 + 9.78347i −0.171656 + 0.717359i
\(187\) −0.327556 0.327556i −0.0239533 0.0239533i
\(188\) −10.4764 + 20.6373i −0.764072 + 1.50513i
\(189\) 1.76743 + 1.96880i 0.128562 + 0.143209i
\(190\) 8.98482 + 14.6374i 0.651828 + 1.06191i
\(191\) 24.4401i 1.76842i −0.467088 0.884211i \(-0.654697\pi\)
0.467088 0.884211i \(-0.345303\pi\)
\(192\) 4.67323 6.49314i 0.337262 0.468602i
\(193\) 22.3910 1.61174 0.805871 0.592091i \(-0.201698\pi\)
0.805871 + 0.592091i \(0.201698\pi\)
\(194\) 9.74033 + 15.8682i 0.699315 + 1.13927i
\(195\) 3.78803 3.78803i 0.271266 0.271266i
\(196\) 7.64224 11.7301i 0.545874 0.837867i
\(197\) 13.4527 + 13.4527i 0.958463 + 0.958463i 0.999171 0.0407083i \(-0.0129614\pi\)
−0.0407083 + 0.999171i \(0.512961\pi\)
\(198\) −2.30519 0.551607i −0.163823 0.0392010i
\(199\) 5.64437i 0.400119i 0.979784 + 0.200059i \(0.0641135\pi\)
−0.979784 + 0.200059i \(0.935886\pi\)
\(200\) −4.19046 + 0.339245i −0.296311 + 0.0239883i
\(201\) 4.31563 0.304401
\(202\) 0.561482 2.34646i 0.0395057 0.165096i
\(203\) −7.35438 + 6.60218i −0.516176 + 0.463382i
\(204\) −0.525464 + 0.171602i −0.0367898 + 0.0120145i
\(205\) −9.71623 + 9.71623i −0.678611 + 0.678611i
\(206\) 8.45028 + 13.7665i 0.588759 + 0.959159i
\(207\) 1.81753i 0.126327i
\(208\) 1.75458 11.2963i 0.121658 0.783256i
\(209\) 10.8589i 0.751129i
\(210\) 3.34205 + 6.16612i 0.230624 + 0.425503i
\(211\) −13.9095 13.9095i −0.957568 0.957568i 0.0415678 0.999136i \(-0.486765\pi\)
−0.999136 + 0.0415678i \(0.986765\pi\)
\(212\) 10.3585 3.38279i 0.711424 0.232331i
\(213\) −5.91574 + 5.91574i −0.405340 + 0.405340i
\(214\) −4.27637 + 17.8711i −0.292326 + 1.22165i
\(215\) 4.50256i 0.307072i
\(216\) −1.83209 + 2.15486i −0.124658 + 0.146620i
\(217\) −18.7926 1.01284i −1.27573 0.0687561i
\(218\) −0.251961 + 1.05296i −0.0170649 + 0.0713152i
\(219\) −11.9928 + 11.9928i −0.810395 + 0.810395i
\(220\) −5.60273 2.84420i −0.377736 0.191756i
\(221\) −0.558541 + 0.558541i −0.0375715 + 0.0375715i
\(222\) −1.34092 + 0.823092i −0.0899963 + 0.0552423i
\(223\) 15.4893 1.03724 0.518622 0.855004i \(-0.326445\pi\)
0.518622 + 0.855004i \(0.326445\pi\)
\(224\) 13.5231 + 6.41288i 0.903552 + 0.428479i
\(225\) 1.48640 0.0990933
\(226\) 14.3940 8.83548i 0.957478 0.587727i
\(227\) 4.24437 4.24437i 0.281709 0.281709i −0.552081 0.833790i \(-0.686166\pi\)
0.833790 + 0.552081i \(0.186166\pi\)
\(228\) −11.5543 5.86551i −0.765205 0.388453i
\(229\) 2.39096 2.39096i 0.157999 0.157999i −0.623680 0.781679i \(-0.714363\pi\)
0.781679 + 0.623680i \(0.214363\pi\)
\(230\) −1.12126 + 4.68578i −0.0739334 + 0.308971i
\(231\) 0.238647 4.42795i 0.0157018 0.291337i
\(232\) −8.04941 6.84371i −0.528470 0.449312i
\(233\) 2.92061i 0.191336i 0.995413 + 0.0956678i \(0.0304987\pi\)
−0.995413 + 0.0956678i \(0.969501\pi\)
\(234\) −0.940587 + 3.93076i −0.0614881 + 0.256962i
\(235\) 15.3382 15.3382i 1.00055 1.00055i
\(236\) 11.4336 3.73388i 0.744262 0.243055i
\(237\) −9.78736 9.78736i −0.635758 0.635758i
\(238\) −0.492782 0.909189i −0.0319423 0.0589339i
\(239\) 7.83859i 0.507036i −0.967331 0.253518i \(-0.918412\pi\)
0.967331 0.253518i \(-0.0815877\pi\)
\(240\) −6.05269 + 4.42522i −0.390699 + 0.285647i
\(241\) 18.3656i 1.18303i 0.806293 + 0.591516i \(0.201470\pi\)
−0.806293 + 0.591516i \(0.798530\pi\)
\(242\) −6.05984 9.87220i −0.389541 0.634609i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 3.07058 1.00276i 0.196574 0.0641954i
\(245\) −10.2216 + 8.22716i −0.653031 + 0.525614i
\(246\) 2.41259 10.0823i 0.153821 0.642826i
\(247\) −18.5164 −1.17817
\(248\) −1.62348 20.0537i −0.103091 1.27341i
\(249\) 14.0140i 0.888103i
\(250\) 16.7226 + 4.00154i 1.05763 + 0.253079i
\(251\) 16.2774 + 16.2774i 1.02742 + 1.02742i 0.999613 + 0.0278042i \(0.00885149\pi\)
0.0278042 + 0.999613i \(0.491149\pi\)
\(252\) −4.58260 2.64571i −0.288677 0.166664i
\(253\) 2.15402 2.15402i 0.135422 0.135422i
\(254\) −13.9544 22.7334i −0.875578 1.42642i
\(255\) 0.518077 0.0324432
\(256\) −4.85327 + 15.2462i −0.303329 + 0.952886i
\(257\) 13.6309i 0.850274i −0.905129 0.425137i \(-0.860226\pi\)
0.905129 0.425137i \(-0.139774\pi\)
\(258\) 1.77710 + 2.89511i 0.110637 + 0.180242i
\(259\) −1.96636 2.19039i −0.122184 0.136104i
\(260\) −4.84986 + 9.55365i −0.300776 + 0.592492i
\(261\) 2.64137 + 2.64137i 0.163497 + 0.163497i
\(262\) 4.10043 17.1359i 0.253325 1.05866i
\(263\) 5.88266 0.362740 0.181370 0.983415i \(-0.441947\pi\)
0.181370 + 0.983415i \(0.441947\pi\)
\(264\) 4.72508 0.382526i 0.290809 0.0235429i
\(265\) −10.2129 −0.627371
\(266\) 6.90222 23.2386i 0.423203 1.42485i
\(267\) −5.62144 + 5.62144i −0.344027 + 0.344027i
\(268\) −8.20481 + 2.67946i −0.501189 + 0.163674i
\(269\) −7.28207 7.28207i −0.443995 0.443995i 0.449357 0.893352i \(-0.351653\pi\)
−0.893352 + 0.449357i \(0.851653\pi\)
\(270\) 2.25922 1.38677i 0.137492 0.0843963i
\(271\) 7.65390 0.464941 0.232471 0.972603i \(-0.425319\pi\)
0.232471 + 0.972603i \(0.425319\pi\)
\(272\) 0.892462 0.652494i 0.0541135 0.0395633i
\(273\) −7.55042 0.406935i −0.456972 0.0246288i
\(274\) −3.21365 5.23542i −0.194144 0.316283i
\(275\) −1.76159 1.76159i −0.106228 0.106228i
\(276\) −1.12846 3.45547i −0.0679252 0.207995i
\(277\) −20.9351 20.9351i −1.25787 1.25787i −0.952109 0.305758i \(-0.901090\pi\)
−0.305758 0.952109i \(-0.598910\pi\)
\(278\) −3.20717 0.767440i −0.192353 0.0460280i
\(279\) 7.11326i 0.425860i
\(280\) −10.1823 9.64797i −0.608506 0.576576i
\(281\) 13.2903i 0.792835i 0.918070 + 0.396417i \(0.129747\pi\)
−0.918070 + 0.396417i \(0.870253\pi\)
\(282\) −3.80854 + 15.9161i −0.226796 + 0.947789i
\(283\) 7.97242 + 7.97242i 0.473911 + 0.473911i 0.903178 0.429267i \(-0.141228\pi\)
−0.429267 + 0.903178i \(0.641228\pi\)
\(284\) 7.57400 14.9199i 0.449434 0.885331i
\(285\) 8.58748 + 8.58748i 0.508678 + 0.508678i
\(286\) 5.77321 3.54376i 0.341377 0.209547i
\(287\) 19.3667 + 1.04378i 1.14318 + 0.0616124i
\(288\) 2.14525 5.23430i 0.126410 0.308434i
\(289\) 16.9236 0.995506
\(290\) 5.18024 + 8.43922i 0.304194 + 0.495568i
\(291\) 9.30957 + 9.30957i 0.545737 + 0.545737i
\(292\) 15.3545 30.2465i 0.898553 1.77004i
\(293\) −11.7572 + 11.7572i −0.686863 + 0.686863i −0.961537 0.274674i \(-0.911430\pi\)
0.274674 + 0.961537i \(0.411430\pi\)
\(294\) 3.32523 9.32431i 0.193931 0.543805i
\(295\) −11.2728 −0.656329
\(296\) 2.03829 2.39739i 0.118473 0.139346i
\(297\) −1.67603 −0.0972534
\(298\) 19.7530 + 4.72667i 1.14426 + 0.273808i
\(299\) −3.67298 3.67298i −0.212414 0.212414i
\(300\) −2.82593 + 0.922868i −0.163155 + 0.0532818i
\(301\) −4.72917 + 4.24548i −0.272585 + 0.244705i
\(302\) 10.7583 6.60376i 0.619071 0.380004i
\(303\) 1.70604i 0.0980093i
\(304\) 25.6087 + 3.97764i 1.46876 + 0.228133i
\(305\) −3.02741 −0.173349
\(306\) −0.333119 + 0.204478i −0.0190432 + 0.0116892i
\(307\) 20.0939 20.0939i 1.14682 1.14682i 0.159645 0.987174i \(-0.448965\pi\)
0.987174 0.159645i \(-0.0510350\pi\)
\(308\) 2.29549 + 8.56653i 0.130797 + 0.488123i
\(309\) 8.07657 + 8.07657i 0.459460 + 0.459460i
\(310\) −4.38825 + 18.3387i −0.249236 + 1.04157i
\(311\) 26.0652i 1.47802i 0.673693 + 0.739012i \(0.264707\pi\)
−0.673693 + 0.739012i \(0.735293\pi\)
\(312\) −0.652274 8.05710i −0.0369278 0.456143i
\(313\) 13.5651 0.766743 0.383372 0.923594i \(-0.374763\pi\)
0.383372 + 0.923594i \(0.374763\pi\)
\(314\) 11.3457 + 2.71490i 0.640275 + 0.153211i
\(315\) 3.31298 + 3.69044i 0.186666 + 0.207933i
\(316\) 24.6843 + 12.5309i 1.38860 + 0.704918i
\(317\) 21.5304 21.5304i 1.20927 1.20927i 0.238004 0.971264i \(-0.423507\pi\)
0.971264 0.238004i \(-0.0764931\pi\)
\(318\) 6.56679 4.03089i 0.368247 0.226041i
\(319\) 6.26077i 0.350536i
\(320\) 8.75979 12.1711i 0.489687 0.680387i
\(321\) 12.9935i 0.725229i
\(322\) 5.97885 3.24055i 0.333188 0.180589i
\(323\) −1.26621 1.26621i −0.0704541 0.0704541i
\(324\) −0.905318 + 1.78337i −0.0502955 + 0.0990760i
\(325\) −3.00381 + 3.00381i −0.166622 + 0.166622i
\(326\) −24.2653 5.80641i −1.34393 0.321587i
\(327\) 0.765572i 0.0423362i
\(328\) 1.67307 + 20.6663i 0.0923800 + 1.14111i
\(329\) −30.5725 1.64772i −1.68552 0.0908420i
\(330\) −4.32099 1.03397i −0.237863 0.0569180i
\(331\) 5.85042 5.85042i 0.321568 0.321568i −0.527800 0.849369i \(-0.676983\pi\)
0.849369 + 0.527800i \(0.176983\pi\)
\(332\) −8.70095 26.6433i −0.477527 1.46224i
\(333\) −0.786692 + 0.786692i −0.0431104 + 0.0431104i
\(334\) 15.7862 + 25.7176i 0.863784 + 1.40721i
\(335\) 8.08947 0.441975
\(336\) 10.3550 + 2.18476i 0.564914 + 0.119189i
\(337\) 11.1243 0.605980 0.302990 0.952994i \(-0.402015\pi\)
0.302990 + 0.952994i \(0.402015\pi\)
\(338\) 3.57499 + 5.82409i 0.194454 + 0.316789i
\(339\) 8.44474 8.44474i 0.458655 0.458655i
\(340\) −0.984961 + 0.321661i −0.0534170 + 0.0174445i
\(341\) 8.43018 8.43018i 0.456520 0.456520i
\(342\) −8.91105 2.13232i −0.481854 0.115302i
\(343\) 18.2792 + 2.97859i 0.986982 + 0.160829i
\(344\) −5.17610 4.40079i −0.279077 0.237275i
\(345\) 3.40689i 0.183421i
\(346\) −20.8857 4.99773i −1.12282 0.268680i
\(347\) −16.7722 + 16.7722i −0.900379 + 0.900379i −0.995469 0.0950894i \(-0.969686\pi\)
0.0950894 + 0.995469i \(0.469686\pi\)
\(348\) −6.66170 3.38178i −0.357105 0.181283i
\(349\) −11.9769 11.9769i −0.641110 0.641110i 0.309718 0.950828i \(-0.399765\pi\)
−0.950828 + 0.309718i \(0.899765\pi\)
\(350\) −2.65016 4.88958i −0.141657 0.261359i
\(351\) 2.85793i 0.152545i
\(352\) −8.74577 + 3.66094i −0.466151 + 0.195129i
\(353\) 34.7417i 1.84912i 0.381041 + 0.924558i \(0.375566\pi\)
−0.381041 + 0.924558i \(0.624434\pi\)
\(354\) 7.24834 4.44924i 0.385245 0.236474i
\(355\) −11.0888 + 11.0888i −0.588533 + 0.588533i
\(356\) 7.19721 14.1776i 0.381451 0.751413i
\(357\) −0.488496 0.544151i −0.0258540 0.0287995i
\(358\) −4.70364 1.12553i −0.248595 0.0594861i
\(359\) 22.2884 1.17634 0.588168 0.808739i \(-0.299850\pi\)
0.588168 + 0.808739i \(0.299850\pi\)
\(360\) −3.43419 + 4.03920i −0.180997 + 0.212885i
\(361\) 22.9768i 1.20930i
\(362\) 0.148144 0.619102i 0.00778629 0.0325393i
\(363\) −5.79185 5.79185i −0.303993 0.303993i
\(364\) 14.6074 3.91421i 0.765637 0.205160i
\(365\) −22.4799 + 22.4799i −1.17665 + 1.17665i
\(366\) 1.94660 1.19488i 0.101750 0.0624573i
\(367\) −35.3887 −1.84728 −0.923639 0.383264i \(-0.874800\pi\)
−0.923639 + 0.383264i \(0.874800\pi\)
\(368\) 4.29082 + 5.86886i 0.223675 + 0.305935i
\(369\) 7.33055i 0.381613i
\(370\) −2.51349 + 1.54285i −0.130670 + 0.0802091i
\(371\) 9.62974 + 10.7269i 0.499951 + 0.556912i
\(372\) −4.41644 13.5236i −0.228982 0.701168i
\(373\) 6.16397 + 6.16397i 0.319158 + 0.319158i 0.848444 0.529285i \(-0.177540\pi\)
−0.529285 + 0.848444i \(0.677540\pi\)
\(374\) 0.637126 + 0.152457i 0.0329450 + 0.00788337i
\(375\) 12.1585 0.627862
\(376\) −2.64113 32.6241i −0.136206 1.68246i
\(377\) −10.6757 −0.549827
\(378\) −3.58679 1.06533i −0.184485 0.0547947i
\(379\) 7.14409 7.14409i 0.366967 0.366967i −0.499403 0.866370i \(-0.666447\pi\)
0.866370 + 0.499403i \(0.166447\pi\)
\(380\) −21.6582 10.9947i −1.11104 0.564014i
\(381\) −13.3373 13.3373i −0.683291 0.683291i
\(382\) 18.0814 + 29.4567i 0.925123 + 1.50714i
\(383\) 15.8856 0.811718 0.405859 0.913936i \(-0.366972\pi\)
0.405859 + 0.913936i \(0.366972\pi\)
\(384\) −0.828688 + 11.2833i −0.0422888 + 0.575799i
\(385\) 0.447334 8.30001i 0.0227982 0.423007i
\(386\) −26.9871 + 16.5654i −1.37361 + 0.843159i
\(387\) 1.69851 + 1.69851i 0.0863401 + 0.0863401i
\(388\) −23.4793 11.9192i −1.19198 0.605104i
\(389\) 3.30347 + 3.30347i 0.167493 + 0.167493i 0.785876 0.618384i \(-0.212212\pi\)
−0.618384 + 0.785876i \(0.712212\pi\)
\(390\) −1.76309 + 7.36805i −0.0892777 + 0.373096i
\(391\) 0.502342i 0.0254045i
\(392\) −0.532661 + 19.7918i −0.0269034 + 0.999638i
\(393\) 12.4590i 0.628472i
\(394\) −26.1666 6.26139i −1.31826 0.315444i
\(395\) −18.3460 18.3460i −0.923088 0.923088i
\(396\) 3.18646 1.04061i 0.160125 0.0522925i
\(397\) 11.0837 + 11.0837i 0.556274 + 0.556274i 0.928244 0.371971i \(-0.121318\pi\)
−0.371971 + 0.928244i \(0.621318\pi\)
\(398\) −4.17585 6.80295i −0.209316 0.341001i
\(399\) 0.922522 17.1168i 0.0461839 0.856914i
\(400\) 4.79963 3.50909i 0.239981 0.175454i
\(401\) −12.6471 −0.631566 −0.315783 0.948831i \(-0.602267\pi\)
−0.315783 + 0.948831i \(0.602267\pi\)
\(402\) −5.20146 + 3.19281i −0.259425 + 0.159243i
\(403\) −14.3749 14.3749i −0.716066 0.716066i
\(404\) 1.05924 + 3.24350i 0.0526989 + 0.161370i
\(405\) 1.32544 1.32544i 0.0658618 0.0658618i
\(406\) 3.97950 13.3983i 0.197499 0.664948i
\(407\) 1.86467 0.0924284
\(408\) 0.506367 0.595576i 0.0250689 0.0294854i
\(409\) −6.39999 −0.316459 −0.158230 0.987402i \(-0.550579\pi\)
−0.158230 + 0.987402i \(0.550579\pi\)
\(410\) 4.52231 18.8989i 0.223341 0.933352i
\(411\) −3.07153 3.07153i −0.151507 0.151507i
\(412\) −20.3696 10.3405i −1.00354 0.509442i
\(413\) 10.6292 + 11.8402i 0.523028 + 0.582617i
\(414\) −1.34465 2.19060i −0.0660861 0.107662i
\(415\) 26.2687i 1.28948i
\(416\) 6.24254 + 14.9131i 0.306066 + 0.731174i
\(417\) −2.33183 −0.114190
\(418\) 8.03372 + 13.0879i 0.392942 + 0.640149i
\(419\) −3.92319 + 3.92319i −0.191660 + 0.191660i −0.796413 0.604753i \(-0.793272\pi\)
0.604753 + 0.796413i \(0.293272\pi\)
\(420\) −8.58990 4.95927i −0.419144 0.241988i
\(421\) −19.9120 19.9120i −0.970449 0.970449i 0.0291264 0.999576i \(-0.490727\pi\)
−0.999576 + 0.0291264i \(0.990727\pi\)
\(422\) 27.0552 + 6.47400i 1.31702 + 0.315149i
\(423\) 11.5721i 0.562655i
\(424\) −9.98203 + 11.7406i −0.484770 + 0.570175i
\(425\) −0.410822 −0.0199278
\(426\) 2.75341 11.5066i 0.133403 0.557498i
\(427\) 2.85455 + 3.17978i 0.138142 + 0.153880i
\(428\) −8.06736 24.7032i −0.389951 1.19407i
\(429\) 3.38704 3.38704i 0.163528 0.163528i
\(430\) 3.33110 + 5.42677i 0.160640 + 0.261702i
\(431\) 23.6983i 1.14151i 0.821122 + 0.570753i \(0.193349\pi\)
−0.821122 + 0.570753i \(0.806651\pi\)
\(432\) 0.613933 3.95261i 0.0295379 0.190170i
\(433\) 25.8198i 1.24082i 0.784278 + 0.620410i \(0.213034\pi\)
−0.784278 + 0.620410i \(0.786966\pi\)
\(434\) 23.3994 12.6825i 1.12321 0.608781i
\(435\) 4.95114 + 4.95114i 0.237389 + 0.237389i
\(436\) −0.475324 1.45550i −0.0227639 0.0697056i
\(437\) 8.32666 8.32666i 0.398318 0.398318i
\(438\) 5.58188 23.3270i 0.266713 1.11461i
\(439\) 13.7981i 0.658548i 0.944234 + 0.329274i \(0.106804\pi\)
−0.944234 + 0.329274i \(0.893196\pi\)
\(440\) 8.85698 0.717030i 0.422240 0.0341831i
\(441\) 0.752353 6.95945i 0.0358263 0.331402i
\(442\) 0.259966 1.08641i 0.0123653 0.0516753i
\(443\) 9.61155 9.61155i 0.456658 0.456658i −0.440898 0.897557i \(-0.645340\pi\)
0.897557 + 0.440898i \(0.145340\pi\)
\(444\) 1.00721 1.98408i 0.0478001 0.0941605i
\(445\) −10.5372 + 10.5372i −0.499510 + 0.499510i
\(446\) −18.6687 + 11.4594i −0.883990 + 0.542619i
\(447\) 14.3618 0.679288
\(448\) −21.0433 + 2.27554i −0.994204 + 0.107509i
\(449\) −27.2681 −1.28686 −0.643430 0.765505i \(-0.722489\pi\)
−0.643430 + 0.765505i \(0.722489\pi\)
\(450\) −1.79150 + 1.09968i −0.0844523 + 0.0518392i
\(451\) −8.68770 + 8.68770i −0.409088 + 0.409088i
\(452\) −10.8119 + 21.2981i −0.508549 + 1.00178i
\(453\) 6.31171 6.31171i 0.296550 0.296550i
\(454\) −1.97549 + 8.25567i −0.0927144 + 0.387458i
\(455\) −14.1530 0.762782i −0.663501 0.0357598i
\(456\) 18.2655 1.47871i 0.855359 0.0692469i
\(457\) 15.7041i 0.734607i −0.930101 0.367303i \(-0.880281\pi\)
0.930101 0.367303i \(-0.119719\pi\)
\(458\) −1.11284 + 4.65062i −0.0519997 + 0.217309i
\(459\) −0.195435 + 0.195435i −0.00912214 + 0.00912214i
\(460\) −2.11525 6.47713i −0.0986240 0.301998i
\(461\) −8.60225 8.60225i −0.400647 0.400647i 0.477814 0.878461i \(-0.341429\pi\)
−0.878461 + 0.477814i \(0.841429\pi\)
\(462\) 2.98827 + 5.51340i 0.139027 + 0.256506i
\(463\) 1.85673i 0.0862897i 0.999069 + 0.0431449i \(0.0137377\pi\)
−0.999069 + 0.0431449i \(0.986262\pi\)
\(464\) 14.7648 + 2.29332i 0.685439 + 0.106465i
\(465\) 13.3335i 0.618327i
\(466\) −2.16074 3.52011i −0.100094 0.163066i
\(467\) −12.0605 + 12.0605i −0.558093 + 0.558093i −0.928764 0.370671i \(-0.879128\pi\)
0.370671 + 0.928764i \(0.379128\pi\)
\(468\) −1.77442 5.43347i −0.0820225 0.251162i
\(469\) −7.62758 8.49661i −0.352209 0.392337i
\(470\) −7.13896 + 29.8341i −0.329296 + 1.37614i
\(471\) 8.24911 0.380099
\(472\) −11.0180 + 12.9591i −0.507146 + 0.596493i
\(473\) 4.02593i 0.185112i
\(474\) 19.0373 + 4.55541i 0.874411 + 0.209237i
\(475\) −6.80966 6.80966i −0.312448 0.312448i
\(476\) 1.26657 + 0.731239i 0.0580533 + 0.0335163i
\(477\) 3.85262 3.85262i 0.176399 0.176399i
\(478\) 5.79918 + 9.44756i 0.265248 + 0.432121i
\(479\) −14.9496 −0.683063 −0.341531 0.939870i \(-0.610946\pi\)
−0.341531 + 0.939870i \(0.610946\pi\)
\(480\) 4.02119 9.81148i 0.183541 0.447831i
\(481\) 3.17959i 0.144977i
\(482\) −13.5873 22.1354i −0.618886 1.00824i
\(483\) 3.57835 3.21236i 0.162821 0.146168i
\(484\) 14.6074 + 7.41538i 0.663973 + 0.337063i
\(485\) 17.4504 + 17.4504i 0.792383 + 0.792383i
\(486\) −0.329115 + 1.37538i −0.0149289 + 0.0623887i
\(487\) 2.67317 0.121133 0.0605664 0.998164i \(-0.480709\pi\)
0.0605664 + 0.998164i \(0.480709\pi\)
\(488\) −2.95898 + 3.48028i −0.133947 + 0.157545i
\(489\) −17.6425 −0.797823
\(490\) 6.23301 17.4781i 0.281579 0.789578i
\(491\) −7.71425 + 7.71425i −0.348139 + 0.348139i −0.859416 0.511277i \(-0.829173\pi\)
0.511277 + 0.859416i \(0.329173\pi\)
\(492\) 4.55135 + 13.9368i 0.205191 + 0.628318i
\(493\) −0.730041 0.730041i −0.0328794 0.0328794i
\(494\) 22.3171 13.6989i 1.00410 0.616342i
\(495\) −3.14166 −0.141207
\(496\) 16.7930 + 22.9689i 0.754026 + 1.03134i
\(497\) 22.1026 + 1.19123i 0.991437 + 0.0534341i
\(498\) −10.3679 16.8906i −0.464598 0.756885i
\(499\) −10.9644 10.9644i −0.490835 0.490835i 0.417734 0.908569i \(-0.362824\pi\)
−0.908569 + 0.417734i \(0.862824\pi\)
\(500\) −23.1156 + 7.54890i −1.03376 + 0.337597i
\(501\) 15.0881 + 15.0881i 0.674086 + 0.674086i
\(502\) −31.6609 7.57610i −1.41309 0.338138i
\(503\) 16.3842i 0.730533i 0.930903 + 0.365267i \(0.119022\pi\)
−0.930903 + 0.365267i \(0.880978\pi\)
\(504\) 7.48060 0.201552i 0.333212 0.00897785i
\(505\) 3.19790i 0.142305i
\(506\) −1.00256 + 4.18976i −0.0445694 + 0.186257i
\(507\) 3.41689 + 3.41689i 0.151749 + 0.151749i
\(508\) 33.6375 + 17.0759i 1.49242 + 0.757622i
\(509\) 18.7512 + 18.7512i 0.831133 + 0.831133i 0.987672 0.156539i \(-0.0500337\pi\)
−0.156539 + 0.987672i \(0.550034\pi\)
\(510\) −0.624419 + 0.383286i −0.0276497 + 0.0169722i
\(511\) 44.8077 + 2.41494i 1.98218 + 0.106831i
\(512\) −5.43003 21.9662i −0.239976 0.970779i
\(513\) −6.47895 −0.286053
\(514\) 10.0845 + 16.4288i 0.444808 + 0.724645i
\(515\) 15.1392 + 15.1392i 0.667113 + 0.667113i
\(516\) −4.28375 2.17463i −0.188581 0.0957325i
\(517\) 13.7145 13.7145i 0.603163 0.603163i
\(518\) 3.99048 + 1.18523i 0.175332 + 0.0520762i
\(519\) −15.1854 −0.666564
\(520\) −1.22266 15.1027i −0.0536173 0.662297i
\(521\) −4.36154 −0.191083 −0.0955413 0.995425i \(-0.530458\pi\)
−0.0955413 + 0.995425i \(0.530458\pi\)
\(522\) −5.13770 1.22939i −0.224871 0.0538092i
\(523\) −28.7720 28.7720i −1.25811 1.25811i −0.951994 0.306118i \(-0.900970\pi\)
−0.306118 0.951994i \(-0.599030\pi\)
\(524\) 7.73546 + 23.6869i 0.337925 + 1.03477i
\(525\) −2.62711 2.92643i −0.114657 0.127720i
\(526\) −7.09015 + 4.35214i −0.309145 + 0.189762i
\(527\) 1.96601i 0.0856409i
\(528\) −5.41197 + 3.95678i −0.235526 + 0.172197i
\(529\) −19.6966 −0.856373
\(530\) 12.3092 7.55573i 0.534677 0.328200i
\(531\) 4.25247 4.25247i 0.184542 0.184542i
\(532\) 8.87352 + 33.1151i 0.384716 + 1.43572i
\(533\) 14.8141 + 14.8141i 0.641668 + 0.641668i
\(534\) 2.61643 10.9342i 0.113224 0.473169i
\(535\) 24.3559i 1.05300i
\(536\) 7.90663 9.29958i 0.341514 0.401681i
\(537\) −3.41987 −0.147578
\(538\) 14.1643 + 3.38935i 0.610665 + 0.146125i
\(539\) −9.13953 + 7.35625i −0.393668 + 0.316856i
\(540\) −1.69698 + 3.34285i −0.0730265 + 0.143853i
\(541\) −11.4795 + 11.4795i −0.493541 + 0.493541i −0.909420 0.415879i \(-0.863474\pi\)
0.415879 + 0.909420i \(0.363474\pi\)
\(542\) −9.22496 + 5.66254i −0.396246 + 0.243227i
\(543\) 0.450130i 0.0193169i
\(544\) −0.592921 + 1.44669i −0.0254213 + 0.0620265i
\(545\) 1.43503i 0.0614701i
\(546\) 9.40131 5.09553i 0.402339 0.218068i
\(547\) −27.5701 27.5701i −1.17881 1.17881i −0.980047 0.198764i \(-0.936307\pi\)
−0.198764 0.980047i \(-0.563693\pi\)
\(548\) 7.74659 + 3.93252i 0.330918 + 0.167989i
\(549\) 1.14204 1.14204i 0.0487409 0.0487409i
\(550\) 3.42644 + 0.819909i 0.146104 + 0.0349610i
\(551\) 24.2019i 1.03103i
\(552\) 3.91653 + 3.32988i 0.166699 + 0.141729i
\(553\) −1.97085 + 36.5679i −0.0838090 + 1.55502i
\(554\) 40.7206 + 9.74399i 1.73005 + 0.413982i
\(555\) −1.47462 + 1.47462i −0.0625942 + 0.0625942i
\(556\) 4.43325 1.44778i 0.188012 0.0613994i
\(557\) 7.84102 7.84102i 0.332235 0.332235i −0.521200 0.853435i \(-0.674515\pi\)
0.853435 + 0.521200i \(0.174515\pi\)
\(558\) −5.26257 8.57335i −0.222782 0.362939i
\(559\) −6.86492 −0.290355
\(560\) 19.4101 + 4.09525i 0.820227 + 0.173056i
\(561\) 0.463235 0.0195578
\(562\) −9.83252 16.0183i −0.414760 0.675693i
\(563\) 20.5300 20.5300i 0.865238 0.865238i −0.126703 0.991941i \(-0.540439\pi\)
0.991941 + 0.126703i \(0.0404395\pi\)
\(564\) −7.18482 22.0007i −0.302535 0.926398i
\(565\) 15.8293 15.8293i 0.665944 0.665944i
\(566\) −15.5071 3.71067i −0.651810 0.155971i
\(567\) −2.64192 0.142388i −0.110950 0.00597972i
\(568\) 1.90942 + 23.5858i 0.0801176 + 0.989638i
\(569\) 8.26625i 0.346539i −0.984874 0.173270i \(-0.944567\pi\)
0.984874 0.173270i \(-0.0554332\pi\)
\(570\) −16.7034 3.99694i −0.699628 0.167413i
\(571\) 11.1033 11.1033i 0.464659 0.464659i −0.435520 0.900179i \(-0.643435\pi\)
0.900179 + 0.435520i \(0.143435\pi\)
\(572\) −4.33647 + 8.54232i −0.181317 + 0.357172i
\(573\) 17.2817 + 17.2817i 0.721955 + 0.721955i
\(574\) −24.1142 + 13.0699i −1.00651 + 0.545529i
\(575\) 2.70158i 0.112664i
\(576\) 1.28687 + 7.89582i 0.0536196 + 0.328992i
\(577\) 1.00276i 0.0417454i −0.999782 0.0208727i \(-0.993356\pi\)
0.999782 0.0208727i \(-0.00664447\pi\)
\(578\) −20.3974 + 12.5205i −0.848420 + 0.520784i
\(579\) −15.8328 + 15.8328i −0.657991 + 0.657991i
\(580\) −12.4871 6.33902i −0.518498 0.263213i
\(581\) 27.5908 24.7689i 1.14466 1.02759i
\(582\) −18.1079 4.33303i −0.750598 0.179610i
\(583\) −9.13176 −0.378199
\(584\) 3.87090 + 47.8146i 0.160179 + 1.97858i
\(585\) 5.35708i 0.221488i
\(586\) 5.47225 22.8688i 0.226057 0.944701i
\(587\) −2.42198 2.42198i −0.0999658 0.0999658i 0.655355 0.755321i \(-0.272519\pi\)
−0.755321 + 0.655355i \(0.772519\pi\)
\(588\) 2.89058 + 13.6983i 0.119206 + 0.564910i
\(589\) 32.5880 32.5880i 1.34277 1.34277i
\(590\) 13.5867 8.33992i 0.559357 0.343349i
\(591\) −19.0249 −0.782582
\(592\) −0.683031 + 4.39747i −0.0280724 + 0.180735i
\(593\) 22.2544i 0.913881i −0.889497 0.456940i \(-0.848945\pi\)
0.889497 0.456940i \(-0.151055\pi\)
\(594\) 2.02006 1.23997i 0.0828842 0.0508767i
\(595\) −0.915666 1.01999i −0.0375387 0.0418155i
\(596\) −27.3044 + 8.91686i −1.11843 + 0.365249i
\(597\) −3.99117 3.99117i −0.163348 0.163348i
\(598\) 7.14427 + 1.70955i 0.292151 + 0.0699085i
\(599\) −6.97729 −0.285085 −0.142542 0.989789i \(-0.545528\pi\)
−0.142542 + 0.989789i \(0.545528\pi\)
\(600\) 2.72322 3.20299i 0.111175 0.130761i
\(601\) −9.75706 −0.397999 −0.198999 0.980000i \(-0.563769\pi\)
−0.198999 + 0.980000i \(0.563769\pi\)
\(602\) 2.55898 8.61567i 0.104296 0.351149i
\(603\) −3.05161 + 3.05161i −0.124271 + 0.124271i
\(604\) −8.08097 + 15.9185i −0.328810 + 0.647716i
\(605\) −10.8566 10.8566i −0.441383 0.441383i
\(606\) 1.26217 + 2.05622i 0.0512721 + 0.0835284i
\(607\) −0.646351 −0.0262346 −0.0131173 0.999914i \(-0.504175\pi\)
−0.0131173 + 0.999914i \(0.504175\pi\)
\(608\) −33.8080 + 14.1519i −1.37110 + 0.573934i
\(609\) 0.531884 9.86878i 0.0215530 0.399903i
\(610\) 3.64882 2.23975i 0.147737 0.0906849i
\(611\) −23.3856 23.3856i −0.946082 0.946082i
\(612\) 0.250218 0.492900i 0.0101145 0.0199243i
\(613\) −22.8864 22.8864i −0.924372 0.924372i 0.0729627 0.997335i \(-0.476755\pi\)
−0.997335 + 0.0729627i \(0.976755\pi\)
\(614\) −9.35247 + 39.0844i −0.377435 + 1.57732i
\(615\) 13.7408i 0.554084i
\(616\) −9.10439 8.62666i −0.366826 0.347578i
\(617\) 28.2900i 1.13891i 0.822022 + 0.569456i \(0.192846\pi\)
−0.822022 + 0.569456i \(0.807154\pi\)
\(618\) −15.7096 3.75915i −0.631935 0.151215i
\(619\) −27.0007 27.0007i −1.08525 1.08525i −0.996010 0.0892388i \(-0.971557\pi\)
−0.0892388 0.996010i \(-0.528443\pi\)
\(620\) −8.27844 25.3495i −0.332470 1.01806i
\(621\) −1.28519 1.28519i −0.0515728 0.0515728i
\(622\) −19.2837 31.4155i −0.773206 1.25964i
\(623\) 21.0030 + 1.13197i 0.841468 + 0.0453514i
\(624\) 6.74700 + 9.22835i 0.270096 + 0.369430i
\(625\) 15.3586 0.614345
\(626\) −16.3495 + 10.0358i −0.653457 + 0.401110i
\(627\) 7.67843 + 7.67843i 0.306647 + 0.306647i
\(628\) −15.6831 + 5.12166i −0.625824 + 0.204376i
\(629\) 0.217431 0.217431i 0.00866956 0.00866956i
\(630\) −6.72330 1.99692i −0.267863 0.0795592i
\(631\) 31.2622 1.24453 0.622265 0.782807i \(-0.286213\pi\)
0.622265 + 0.782807i \(0.286213\pi\)
\(632\) −39.0218 + 3.15907i −1.55220 + 0.125661i
\(633\) 19.6710 0.781851
\(634\) −10.0211 + 41.8785i −0.397988 + 1.66321i
\(635\) −25.0002 25.0002i −0.992104 0.992104i
\(636\) −4.93256 + 9.71655i −0.195589 + 0.385286i
\(637\) 12.5437 + 15.5845i 0.497000 + 0.617481i
\(638\) 4.63187 + 7.54587i 0.183377 + 0.298744i
\(639\) 8.36612i 0.330959i
\(640\) −1.55334 + 21.1501i −0.0614012 + 0.836032i
\(641\) 13.0504 0.515458 0.257729 0.966217i \(-0.417026\pi\)
0.257729 + 0.966217i \(0.417026\pi\)
\(642\) −9.61295 15.6606i −0.379393 0.618076i
\(643\) 0.786696 0.786696i 0.0310242 0.0310242i −0.691424 0.722449i \(-0.743017\pi\)
0.722449 + 0.691424i \(0.243017\pi\)
\(644\) −4.80865 + 8.32902i −0.189487 + 0.328209i
\(645\) 3.18379 + 3.18379i 0.125362 + 0.125362i
\(646\) 2.46290 + 0.589345i 0.0969015 + 0.0231875i
\(647\) 22.9721i 0.903125i 0.892239 + 0.451563i \(0.149133\pi\)
−0.892239 + 0.451563i \(0.850867\pi\)
\(648\) −0.228233 2.81920i −0.00896583 0.110749i
\(649\) −10.0795 −0.395656
\(650\) 1.39809 5.84268i 0.0548376 0.229169i
\(651\) 14.0046 12.5722i 0.548883 0.492744i
\(652\) 33.5418 10.9538i 1.31360 0.428984i
\(653\) −11.7129 + 11.7129i −0.458362 + 0.458362i −0.898118 0.439756i \(-0.855065\pi\)
0.439756 + 0.898118i \(0.355065\pi\)
\(654\) −0.566389 0.922715i −0.0221476 0.0360810i
\(655\) 23.3539i 0.912511i
\(656\) −17.3060 23.6706i −0.675684 0.924181i
\(657\) 16.9603i 0.661685i
\(658\) 38.0670 20.6324i 1.48400 0.804333i
\(659\) 28.8441 + 28.8441i 1.12361 + 1.12361i 0.991195 + 0.132413i \(0.0422725\pi\)
0.132413 + 0.991195i \(0.457728\pi\)
\(660\) 5.97289 1.95058i 0.232494 0.0759261i
\(661\) 20.5775 20.5775i 0.800371 0.800371i −0.182782 0.983153i \(-0.558510\pi\)
0.983153 + 0.182782i \(0.0585103\pi\)
\(662\) −2.72301 + 11.3796i −0.105833 + 0.442280i
\(663\) 0.789896i 0.0306770i
\(664\) 30.1983 + 25.6750i 1.17192 + 0.996383i
\(665\) 1.72923 32.0848i 0.0670567 1.24420i
\(666\) 0.366156 1.53018i 0.0141883 0.0592934i
\(667\) 4.80077 4.80077i 0.185887 0.185887i
\(668\) −38.0531 19.3175i −1.47232 0.747416i
\(669\) −10.9526 + 10.9526i −0.423453 + 0.423453i
\(670\) −9.74994 + 5.98479i −0.376673 + 0.231213i
\(671\) −2.70694 −0.104500
\(672\) −14.0969 + 5.02770i −0.543799 + 0.193948i
\(673\) 19.3585 0.746215 0.373108 0.927788i \(-0.378292\pi\)
0.373108 + 0.927788i \(0.378292\pi\)
\(674\) −13.4077 + 8.23004i −0.516446 + 0.317009i
\(675\) −1.05104 + 1.05104i −0.0404547 + 0.0404547i
\(676\) −8.61761 4.37469i −0.331447 0.168257i
\(677\) 26.0458 26.0458i 1.00102 1.00102i 0.00102364 0.999999i \(-0.499674\pi\)
0.999999 0.00102364i \(-0.000325836\pi\)
\(678\) −3.93050 + 16.4258i −0.150950 + 0.630827i
\(679\) 1.87464 34.7828i 0.0719420 1.33484i
\(680\) 0.949165 1.11638i 0.0363988 0.0428114i
\(681\) 6.00245i 0.230014i
\(682\) −3.92373 + 16.3974i −0.150247 + 0.627890i
\(683\) −21.8826 + 21.8826i −0.837315 + 0.837315i −0.988505 0.151189i \(-0.951690\pi\)
0.151189 + 0.988505i \(0.451690\pi\)
\(684\) 12.3177 4.02261i 0.470979 0.153808i
\(685\) −5.75746 5.75746i −0.219981 0.219981i
\(686\) −24.2348 + 9.93339i −0.925291 + 0.379259i
\(687\) 3.38133i 0.129006i
\(688\) 9.49438 + 1.47470i 0.361970 + 0.0562225i
\(689\) 15.5713i 0.593218i
\(690\) −2.52050 4.10620i −0.0959538 0.156320i
\(691\) −12.1294 + 12.1294i −0.461424 + 0.461424i −0.899122 0.437698i \(-0.855794\pi\)
0.437698 + 0.899122i \(0.355794\pi\)
\(692\) 28.8703 9.42821i 1.09748 0.358407i
\(693\) 2.96228 + 3.29978i 0.112528 + 0.125348i
\(694\) 7.80643 32.6234i 0.296328 1.23837i
\(695\) −4.37093 −0.165799
\(696\) 10.5310 0.852555i 0.399178 0.0323160i
\(697\) 2.02607i 0.0767429i
\(698\) 23.2962 + 5.57452i 0.881774 + 0.210999i
\(699\) −2.06518 2.06518i −0.0781125 0.0781125i
\(700\) 6.81158 + 3.93258i 0.257454 + 0.148637i
\(701\) −1.76393 + 1.76393i −0.0666225 + 0.0666225i −0.739633 0.673010i \(-0.765001\pi\)
0.673010 + 0.739633i \(0.265001\pi\)
\(702\) −2.11437 3.44456i −0.0798018 0.130007i
\(703\) 7.20815 0.271861
\(704\) 7.83250 10.8827i 0.295199 0.410158i
\(705\) 21.6914i 0.816947i
\(706\) −25.7028 41.8729i −0.967338 1.57591i
\(707\) −3.35885 + 3.01531i −0.126322 + 0.113402i
\(708\) −5.44450 + 10.7250i −0.204617 + 0.403070i
\(709\) 24.0457 + 24.0457i 0.903055 + 0.903055i 0.995699 0.0926439i \(-0.0295318\pi\)
−0.0926439 + 0.995699i \(0.529532\pi\)
\(710\) 5.16116 21.5687i 0.193695 0.809460i
\(711\) 13.8414 0.519094
\(712\) 1.81443 + 22.4124i 0.0679987 + 0.839942i
\(713\) 12.9286 0.484178
\(714\) 0.991343 + 0.294444i 0.0371001 + 0.0110193i
\(715\) 6.34887 6.34887i 0.237434 0.237434i
\(716\) 6.50182 2.12331i 0.242984 0.0793519i
\(717\) 5.54272 + 5.54272i 0.206997 + 0.206997i
\(718\) −26.8633 + 16.4895i −1.00253 + 0.615382i
\(719\) −21.8470 −0.814754 −0.407377 0.913260i \(-0.633556\pi\)
−0.407377 + 0.913260i \(0.633556\pi\)
\(720\) 1.15079 7.40900i 0.0428875 0.276117i
\(721\) 1.62635 30.1760i 0.0605685 1.12381i
\(722\) 16.9988 + 27.6930i 0.632629 + 1.03063i
\(723\) −12.9864 12.9864i −0.482971 0.482971i
\(724\) 0.279474 + 0.855781i 0.0103866 + 0.0318049i
\(725\) −3.92613 3.92613i −0.145813 0.145813i
\(726\) 11.2656 + 2.69575i 0.418107 + 0.100049i
\(727\) 42.6131i 1.58043i 0.612829 + 0.790216i \(0.290031\pi\)
−0.612829 + 0.790216i \(0.709969\pi\)
\(728\) −14.7100 + 15.5246i −0.545188 + 0.575379i
\(729\) 1.00000i 0.0370370i
\(730\) 10.4630 43.7254i 0.387254 1.61835i
\(731\) −0.469446 0.469446i −0.0173631 0.0173631i
\(732\) −1.46216 + 2.88029i −0.0540432 + 0.106458i
\(733\) 27.0115 + 27.0115i 0.997693 + 0.997693i 0.999997 0.00230393i \(-0.000733364\pi\)
−0.00230393 + 0.999997i \(0.500733\pi\)
\(734\) 42.6528 26.1815i 1.57434 0.966376i
\(735\) 1.41026 13.0452i 0.0520180 0.481180i
\(736\) −9.51350 3.89906i −0.350672 0.143721i
\(737\) 7.23314 0.266436
\(738\) 5.42333 + 8.83525i 0.199635 + 0.325230i
\(739\) −1.43265 1.43265i −0.0527008 0.0527008i 0.680265 0.732966i \(-0.261865\pi\)
−0.732966 + 0.680265i \(0.761865\pi\)
\(740\) 1.88798 3.71909i 0.0694034 0.136716i
\(741\) 13.0931 13.0931i 0.480986 0.480986i
\(742\) −19.5424 5.80438i −0.717424 0.213086i
\(743\) −21.5309 −0.789892 −0.394946 0.918704i \(-0.629237\pi\)
−0.394946 + 0.918704i \(0.629237\pi\)
\(744\) 15.3281 + 13.0322i 0.561955 + 0.477782i
\(745\) 26.9206 0.986293
\(746\) −11.9895 2.86895i −0.438966 0.105040i
\(747\) −9.90941 9.90941i −0.362566 0.362566i
\(748\) −0.880696 + 0.287610i −0.0322014 + 0.0105161i
\(749\) 25.5817 22.9652i 0.934735 0.839132i
\(750\) −14.6542 + 8.99516i −0.535095 + 0.328457i
\(751\) 4.47866i 0.163429i −0.996656 0.0817143i \(-0.973960\pi\)
0.996656 0.0817143i \(-0.0260395\pi\)
\(752\) 27.3194 + 37.3666i 0.996235 + 1.36262i
\(753\) −23.0197 −0.838883
\(754\) 12.8670 7.89815i 0.468590 0.287634i
\(755\) 11.8311 11.8311i 0.430576 0.430576i
\(756\) 5.11119 1.36959i 0.185892 0.0498116i
\(757\) −13.9860 13.9860i −0.508329 0.508329i 0.405684 0.914013i \(-0.367033\pi\)
−0.914013 + 0.405684i \(0.867033\pi\)
\(758\) −3.32513 + 13.8959i −0.120774 + 0.504721i
\(759\) 3.04624i 0.110572i
\(760\) 34.2379 2.77178i 1.24194 0.100543i
\(761\) 26.8043 0.971653 0.485827 0.874055i \(-0.338519\pi\)
0.485827 + 0.874055i \(0.338519\pi\)
\(762\) 25.9422 + 6.20769i 0.939788 + 0.224881i
\(763\) 1.50726 1.35310i 0.0545664 0.0489854i
\(764\) −43.5856 22.1260i −1.57687 0.800492i
\(765\) −0.366336 + 0.366336i −0.0132449 + 0.0132449i
\(766\) −19.1464 + 11.7526i −0.691787 + 0.424638i
\(767\) 17.1873i 0.620599i
\(768\) −7.34889 14.2125i −0.265180 0.512848i
\(769\) 31.2390i 1.12651i 0.826285 + 0.563253i \(0.190450\pi\)
−0.826285 + 0.563253i \(0.809550\pi\)
\(770\) 5.60140 + 10.3346i 0.201860 + 0.372435i
\(771\) 9.63852 + 9.63852i 0.347123 + 0.347123i
\(772\) 20.2710 39.9314i 0.729570 1.43716i
\(773\) 21.9282 21.9282i 0.788703 0.788703i −0.192578 0.981282i \(-0.561685\pi\)
0.981282 + 0.192578i \(0.0616850\pi\)
\(774\) −3.30375 0.790551i −0.118751 0.0284158i
\(775\) 10.5731i 0.379799i
\(776\) 37.1169 3.00485i 1.33242 0.107868i
\(777\) 2.93926 + 0.158413i 0.105446 + 0.00568305i
\(778\) −6.42554 1.53756i −0.230367 0.0551242i
\(779\) −33.5835 + 33.5835i −1.20325 + 1.20325i
\(780\) −3.32608 10.1848i −0.119093 0.364675i
\(781\) −9.91499 + 9.91499i −0.354786 + 0.354786i
\(782\) 0.371645 + 0.605454i 0.0132900 + 0.0216510i
\(783\) −3.73546 −0.133495
\(784\) −14.0005 24.2484i −0.500017 0.866015i
\(785\) 15.4626 0.551885
\(786\) 9.21746 + 15.0163i 0.328776 + 0.535615i
\(787\) 33.9965 33.9965i 1.21184 1.21184i 0.241424 0.970420i \(-0.422385\pi\)
0.970420 0.241424i \(-0.0776145\pi\)
\(788\) 36.1700 11.8121i 1.28850 0.420789i
\(789\) −4.15967 + 4.15967i −0.148088 + 0.148088i
\(790\) 35.6846 + 8.53894i 1.26960 + 0.303802i
\(791\) −31.5515 1.70049i −1.12184 0.0604624i
\(792\) −3.07065 + 3.61163i −0.109111 + 0.128334i
\(793\) 4.61580i 0.163912i
\(794\) −21.5587 5.15877i −0.765091 0.183078i
\(795\) 7.22159 7.22159i 0.256123 0.256123i
\(796\) 10.0660 + 5.10995i 0.356780 + 0.181117i
\(797\) 4.75244 + 4.75244i 0.168340 + 0.168340i 0.786249 0.617909i \(-0.212020\pi\)
−0.617909 + 0.786249i \(0.712020\pi\)
\(798\) 11.5516 + 21.3128i 0.408922 + 0.754465i
\(799\) 3.19838i 0.113151i
\(800\) −3.18870 + 7.78026i −0.112738 + 0.275074i
\(801\) 7.94992i 0.280897i
\(802\) 15.2431 9.35664i 0.538252 0.330395i
\(803\) −20.1003 + 20.1003i −0.709323 + 0.709323i
\(804\) 3.90701 7.69634i 0.137790 0.271429i
\(805\) 6.70748 6.02145i 0.236408 0.212228i
\(806\) 27.9605 + 6.69064i 0.984867 + 0.235668i
\(807\) 10.2984 0.362521
\(808\) −3.67628 3.12562i −0.129331 0.109959i
\(809\) 32.4123i 1.13956i −0.821798 0.569778i \(-0.807029\pi\)
0.821798 0.569778i \(-0.192971\pi\)
\(810\) −0.616912 + 2.57810i −0.0216761 + 0.0905853i
\(811\) −0.225151 0.225151i −0.00790612 0.00790612i 0.703143 0.711049i \(-0.251780\pi\)
−0.711049 + 0.703143i \(0.751780\pi\)
\(812\) 5.11606 + 19.0926i 0.179539 + 0.670020i
\(813\) −5.41212 + 5.41212i −0.189811 + 0.189811i
\(814\) −2.24742 + 1.37953i −0.0787721 + 0.0483525i
\(815\) −33.0702 −1.15840
\(816\) −0.169683 + 1.09245i −0.00594010 + 0.0382434i
\(817\) 15.5628i 0.544473i
\(818\) 7.71367 4.73487i 0.269702 0.165551i
\(819\) 5.62670 5.05121i 0.196613 0.176504i
\(820\) 8.53133 + 26.1239i 0.297927 + 0.912286i
\(821\) −37.0047 37.0047i −1.29147 1.29147i −0.933875 0.357599i \(-0.883595\pi\)
−0.357599 0.933875i \(-0.616405\pi\)
\(822\) 5.97440 + 1.42961i 0.208381 + 0.0498633i
\(823\) −1.21299 −0.0422821 −0.0211411 0.999777i \(-0.506730\pi\)
−0.0211411 + 0.999777i \(0.506730\pi\)
\(824\) 32.2009 2.60688i 1.12177 0.0908148i
\(825\) 2.49126 0.0867345
\(826\) −21.5706 6.40680i −0.750538 0.222921i
\(827\) 22.1226 22.1226i 0.769278 0.769278i −0.208701 0.977979i \(-0.566924\pi\)
0.977979 + 0.208701i \(0.0669236\pi\)
\(828\) 3.24132 + 1.64544i 0.112644 + 0.0571831i
\(829\) −27.0435 27.0435i −0.939258 0.939258i 0.0589998 0.998258i \(-0.481209\pi\)
−0.998258 + 0.0589998i \(0.981209\pi\)
\(830\) −19.4343 31.6607i −0.674573 1.09896i
\(831\) 29.6067 1.02704
\(832\) −18.5570 13.3558i −0.643347 0.463029i
\(833\) −0.207941 + 1.92350i −0.00720472 + 0.0666454i
\(834\) 2.81047 1.72515i 0.0973187 0.0597370i
\(835\) 28.2820 + 28.2820i 0.978740 + 0.978740i
\(836\) −19.3655 9.83080i −0.669769 0.340005i
\(837\) −5.02983 5.02983i −0.173856 0.173856i
\(838\) 1.82600 7.63095i 0.0630783 0.263607i
\(839\) 18.8066i 0.649277i 0.945838 + 0.324639i \(0.105243\pi\)
−0.945838 + 0.324639i \(0.894757\pi\)
\(840\) 14.0221 0.377802i 0.483808 0.0130354i
\(841\) 15.0463i 0.518839i
\(842\) 38.7305 + 9.26778i 1.33474 + 0.319389i
\(843\) −9.39768 9.39768i −0.323673 0.323673i
\(844\) −37.3982 + 12.2132i −1.28730 + 0.420396i
\(845\) 6.40483 + 6.40483i 0.220333 + 0.220333i
\(846\) −8.56132 13.9474i −0.294344 0.479522i
\(847\) −1.16628 + 21.6397i −0.0400740 + 0.743549i
\(848\) 3.34497 21.5355i 0.114867 0.739532i
\(849\) −11.2747 −0.386947
\(850\) 0.495148 0.303936i 0.0169835 0.0104249i
\(851\) 1.42984 + 1.42984i 0.0490141 + 0.0490141i
\(852\) 5.19431 + 15.9056i 0.177954 + 0.544916i
\(853\) −13.4226 + 13.4226i −0.459581 + 0.459581i −0.898518 0.438937i \(-0.855355\pi\)
0.438937 + 0.898518i \(0.355355\pi\)
\(854\) −5.79297 1.72060i −0.198231 0.0588777i
\(855\) −12.1445 −0.415334
\(856\) 27.9993 + 23.8054i 0.956997 + 0.813652i
\(857\) 14.2069 0.485297 0.242649 0.970114i \(-0.421984\pi\)
0.242649 + 0.970114i \(0.421984\pi\)
\(858\) −1.57646 + 6.58809i −0.0538194 + 0.224914i
\(859\) 12.7166 + 12.7166i 0.433886 + 0.433886i 0.889948 0.456062i \(-0.150741\pi\)
−0.456062 + 0.889948i \(0.650741\pi\)
\(860\) −8.02971 4.07625i −0.273811 0.138999i
\(861\) −14.4324 + 12.9563i −0.491855 + 0.441549i
\(862\) −17.5326 28.5627i −0.597162 0.972849i
\(863\) 0.417666i 0.0142175i 0.999975 + 0.00710875i \(0.00226281\pi\)
−0.999975 + 0.00710875i \(0.997737\pi\)
\(864\) 2.18428 + 5.21813i 0.0743109 + 0.177524i
\(865\) −28.4644 −0.967818
\(866\) −19.1021 31.1196i −0.649116 1.05749i
\(867\) −11.9668 + 11.9668i −0.406414 + 0.406414i
\(868\) −18.8196 + 32.5972i −0.638778 + 1.10642i
\(869\) −16.4040 16.4040i −0.556466 0.556466i
\(870\) −9.63041 2.30445i −0.326501 0.0781282i
\(871\) 12.3338i 0.417914i
\(872\) 1.64970 + 1.40260i 0.0558660 + 0.0474980i
\(873\) −13.1657 −0.445592
\(874\) −3.87555 + 16.1961i −0.131092 + 0.547841i
\(875\) −21.4893 23.9377i −0.726472 0.809241i
\(876\) 10.5302 + 32.2447i 0.355783 + 1.08945i
\(877\) −37.3450 + 37.3450i −1.26105 + 1.26105i −0.310468 + 0.950584i \(0.600486\pi\)
−0.950584 + 0.310468i \(0.899514\pi\)
\(878\) −10.2082 16.6303i −0.344509 0.561247i
\(879\) 16.6272i 0.560821i
\(880\) −10.1445 + 7.41682i −0.341972 + 0.250021i
\(881\) 40.8076i 1.37484i 0.726259 + 0.687421i \(0.241257\pi\)
−0.726259 + 0.687421i \(0.758743\pi\)
\(882\) 4.24199 + 8.94458i 0.142835 + 0.301180i
\(883\) 38.1593 + 38.1593i 1.28416 + 1.28416i 0.938277 + 0.345886i \(0.112421\pi\)
0.345886 + 0.938277i \(0.387579\pi\)
\(884\) 0.490426 + 1.50174i 0.0164948 + 0.0505090i
\(885\) 7.97109 7.97109i 0.267945 0.267945i
\(886\) −4.47358 + 18.6953i −0.150293 + 0.628081i
\(887\) 34.0533i 1.14340i 0.820464 + 0.571698i \(0.193715\pi\)
−0.820464 + 0.571698i \(0.806285\pi\)
\(888\) 0.253920 + 3.13650i 0.00852101 + 0.105254i
\(889\) −2.68569 + 49.8313i −0.0900750 + 1.67129i
\(890\) 4.90440 20.4957i 0.164396 0.687018i
\(891\) 1.18514 1.18514i 0.0397035 0.0397035i
\(892\) 14.0228 27.6232i 0.469518 0.924893i
\(893\) 53.0153 53.0153i 1.77409 1.77409i
\(894\) −17.3097 + 10.6252i −0.578923 + 0.355360i
\(895\) −6.41042 −0.214277
\(896\) 23.6793 18.3110i 0.791068 0.611728i
\(897\) 5.19438 0.173435
\(898\) 32.8652 20.1736i 1.09673 0.673201i
\(899\) 18.7888 18.7888i 0.626640 0.626640i
\(900\) 1.34566 2.65080i 0.0448555 0.0883599i
\(901\) −1.06482 + 1.06482i −0.0354741 + 0.0354741i
\(902\) 4.04359 16.8983i 0.134637 0.562653i
\(903\) 0.342023 6.34603i 0.0113818 0.211183i
\(904\) −2.72571 33.6688i −0.0906557 1.11981i
\(905\) 0.843750i 0.0280472i
\(906\) −2.93771 + 12.2768i −0.0975990 + 0.407871i
\(907\) −1.29406 + 1.29406i −0.0429685 + 0.0429685i −0.728265 0.685296i \(-0.759673\pi\)
0.685296 + 0.728265i \(0.259673\pi\)
\(908\) −3.72677 11.4118i −0.123677 0.378713i
\(909\) 1.20635 + 1.20635i 0.0400121 + 0.0400121i
\(910\) 17.6224 9.55136i 0.584176 0.316625i
\(911\) 21.1193i 0.699715i −0.936803 0.349857i \(-0.886230\pi\)
0.936803 0.349857i \(-0.113770\pi\)
\(912\) −20.9207 + 15.2955i −0.692754 + 0.506484i
\(913\) 23.4880i 0.777339i
\(914\) 11.6183 + 18.9276i 0.384299 + 0.626068i
\(915\) 2.14070 2.14070i 0.0707694 0.0707694i
\(916\) −2.09938 6.42853i −0.0693654 0.212405i
\(917\) −24.5292 + 22.0204i −0.810027 + 0.727178i
\(918\) 0.0909630 0.380139i 0.00300223 0.0125464i
\(919\) 0.462843 0.0152678 0.00763389 0.999971i \(-0.497570\pi\)
0.00763389 + 0.999971i \(0.497570\pi\)
\(920\) 7.34138 + 6.24173i 0.242038 + 0.205784i
\(921\) 28.4171i 0.936374i
\(922\) 16.7321 + 4.00382i 0.551044 + 0.131859i
\(923\) 16.9068 + 16.9068i 0.556494 + 0.556494i
\(924\) −7.68060 4.43429i −0.252673 0.145878i
\(925\) 1.16934 1.16934i 0.0384476 0.0384476i
\(926\) −1.37366 2.23785i −0.0451412 0.0735404i
\(927\) −11.4220 −0.375148
\(928\) −19.4921 + 8.15931i −0.639861 + 0.267843i
\(929\) 7.13095i 0.233959i 0.993134 + 0.116980i \(0.0373212\pi\)
−0.993134 + 0.116980i \(0.962679\pi\)
\(930\) −9.86447 16.0704i −0.323469 0.526969i
\(931\) −35.3301 + 28.4366i −1.15790 + 0.931973i
\(932\) 5.20852 + 2.64408i 0.170611 + 0.0866098i
\(933\) −18.4309 18.4309i −0.603400 0.603400i
\(934\) 5.61342 23.4587i 0.183677 0.767593i
\(935\) 0.868315 0.0283969
\(936\) 6.15846 + 5.23600i 0.201295 + 0.171144i
\(937\) −5.02900 −0.164290 −0.0821452 0.996620i \(-0.526177\pi\)
−0.0821452 + 0.996620i \(0.526177\pi\)
\(938\) 15.4792 + 4.59757i 0.505415 + 0.150116i
\(939\) −9.59195 + 9.59195i −0.313022 + 0.313022i
\(940\) −13.4677 41.2395i −0.439266 1.34508i
\(941\) −38.2671 38.2671i −1.24747 1.24747i −0.956833 0.290639i \(-0.906132\pi\)
−0.290639 0.956833i \(-0.593868\pi\)
\(942\) −9.94235 + 6.10290i −0.323939 + 0.198843i
\(943\) −13.3235 −0.433873
\(944\) 3.69214 23.7706i 0.120169 0.773667i
\(945\) −4.95217 0.266900i −0.161094 0.00868226i
\(946\) 2.97848 + 4.85230i 0.0968388 + 0.157762i
\(947\) −4.42949 4.42949i −0.143939 0.143939i 0.631465 0.775404i \(-0.282454\pi\)
−0.775404 + 0.631465i \(0.782454\pi\)
\(948\) −26.3151 + 8.59378i −0.854676 + 0.279113i
\(949\) 34.2745 + 34.2745i 1.11260 + 1.11260i
\(950\) 13.2454 + 3.16947i 0.429737 + 0.102831i
\(951\) 30.4486i 0.987363i
\(952\) −2.06754 + 0.0557065i −0.0670094 + 0.00180546i
\(953\) 40.8007i 1.32166i −0.750534 0.660832i \(-0.770204\pi\)
0.750534 0.660832i \(-0.229796\pi\)
\(954\) −1.79316 + 7.49369i −0.0580556 + 0.242617i
\(955\) 32.3939 + 32.3939i 1.04824 + 1.04824i
\(956\) −13.9791 7.09642i −0.452116 0.229514i
\(957\) 4.42703 + 4.42703i 0.143106 + 0.143106i
\(958\) 18.0181 11.0601i 0.582140 0.357334i
\(959\) −0.618504 + 11.4760i −0.0199725 + 0.370578i
\(960\) 2.41219 + 14.8004i 0.0778530 + 0.477681i
\(961\) 19.5985 0.632208
\(962\) 2.35234 + 3.83225i 0.0758426 + 0.123557i
\(963\) −9.18783 9.18783i −0.296074 0.296074i
\(964\) 32.7526 + 16.6267i 1.05489 + 0.535510i
\(965\) −29.6780 + 29.6780i −0.955370 + 0.955370i
\(966\) −1.93627 + 6.51910i −0.0622985 + 0.209749i
\(967\) −2.09367 −0.0673278 −0.0336639 0.999433i \(-0.510718\pi\)
−0.0336639 + 0.999433i \(0.510718\pi\)
\(968\) −23.0918 + 1.86943i −0.742200 + 0.0600859i
\(969\) 1.79070 0.0575255
\(970\) −33.9426 8.12209i −1.08983 0.260785i
\(971\) 12.1592 + 12.1592i 0.390208 + 0.390208i 0.874762 0.484554i \(-0.161018\pi\)
−0.484554 + 0.874762i \(0.661018\pi\)
\(972\) −0.620874 1.90119i −0.0199146 0.0609806i
\(973\) 4.12136 + 4.59092i 0.132125 + 0.147178i
\(974\) −3.22187 + 1.97768i −0.103235 + 0.0633689i
\(975\) 4.24803i 0.136046i
\(976\) 0.991553 6.38379i 0.0317388 0.204340i
\(977\) 45.8415 1.46660 0.733300 0.679906i \(-0.237979\pi\)
0.733300 + 0.679906i \(0.237979\pi\)
\(978\) 21.2639 13.0524i 0.679944 0.417369i
\(979\) −9.42173 + 9.42173i −0.301120 + 0.301120i
\(980\) 5.41828 + 25.6770i 0.173081 + 0.820221i
\(981\) −0.541341 0.541341i −0.0172837 0.0172837i
\(982\) 3.59051 15.0049i 0.114578 0.478825i
\(983\) 7.70439i 0.245732i −0.992423 0.122866i \(-0.960791\pi\)
0.992423 0.122866i \(-0.0392085\pi\)
\(984\) −15.7963 13.4303i −0.503569 0.428141i
\(985\) −35.6615 −1.13627
\(986\) 1.41999 + 0.339789i 0.0452218 + 0.0108211i
\(987\) 22.7832 20.4529i 0.725196 0.651024i
\(988\) −16.7632 + 33.0215i −0.533310 + 1.05056i
\(989\) 3.08709 3.08709i 0.0981639 0.0981639i
\(990\) 3.78653 2.32428i 0.120344 0.0738704i
\(991\) 6.61965i 0.210280i −0.994457 0.105140i \(-0.966471\pi\)
0.994457 0.105140i \(-0.0335291\pi\)
\(992\) −37.2329 15.2597i −1.18215 0.484497i
\(993\) 8.27375i 0.262559i
\(994\) −27.5207 + 14.9163i −0.872905 + 0.473116i
\(995\) −7.48130 7.48130i −0.237173 0.237173i
\(996\) 24.9922 + 12.6872i 0.791907 + 0.402008i
\(997\) −20.8831 + 20.8831i −0.661376 + 0.661376i −0.955704 0.294329i \(-0.904904\pi\)
0.294329 + 0.955704i \(0.404904\pi\)
\(998\) 21.3268 + 5.10326i 0.675087 + 0.161541i
\(999\) 1.11255i 0.0351995i
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 336.2.u.a.139.5 64
4.3 odd 2 1344.2.u.a.1231.21 64
7.6 odd 2 inner 336.2.u.a.139.6 yes 64
16.3 odd 4 inner 336.2.u.a.307.6 yes 64
16.13 even 4 1344.2.u.a.559.12 64
28.27 even 2 1344.2.u.a.1231.12 64
112.13 odd 4 1344.2.u.a.559.21 64
112.83 even 4 inner 336.2.u.a.307.5 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
336.2.u.a.139.5 64 1.1 even 1 trivial
336.2.u.a.139.6 yes 64 7.6 odd 2 inner
336.2.u.a.307.5 yes 64 112.83 even 4 inner
336.2.u.a.307.6 yes 64 16.3 odd 4 inner
1344.2.u.a.559.12 64 16.13 even 4
1344.2.u.a.559.21 64 112.13 odd 4
1344.2.u.a.1231.12 64 28.27 even 2
1344.2.u.a.1231.21 64 4.3 odd 2