Properties

Label 546.2.bd.a.121.2
Level $546$
Weight $2$
Character 546.121
Analytic conductor $4.360$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(121,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bd (of order \(6\), 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: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 121.2
Root \(0.960282i\) of defining polynomial
Character \(\chi\) \(=\) 546.121
Dual form 546.2.bd.a.361.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.620092 - 0.358010i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-2.52418 + 0.792781i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.620092 - 0.358010i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-2.52418 + 0.792781i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +0.716021 q^{10} +2.57068i q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.57509 + 0.467723i) q^{13} +(1.78962 - 1.94866i) q^{14} +(0.620092 + 0.358010i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.0124180 + 0.0215086i) q^{17} +(-0.866025 + 0.500000i) q^{18} -6.91088i q^{19} +(-0.620092 + 0.358010i) q^{20} +(2.52418 - 0.792781i) q^{21} +(-1.28534 - 2.22627i) q^{22} +(-4.69938 - 8.13957i) q^{23} -1.00000i q^{24} +(-2.24366 - 3.88613i) q^{25} +(-3.32998 + 1.38248i) q^{26} -1.00000 q^{27} +(-0.575523 + 2.58240i) q^{28} +(-2.77589 + 4.80797i) q^{29} -0.716021 q^{30} +(4.92140 - 2.84137i) q^{31} +(0.866025 + 0.500000i) q^{32} -2.57068i q^{33} -0.0248360i q^{34} +(1.84905 + 0.412087i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.61229 - 2.08556i) q^{37} +(3.45544 + 5.98499i) q^{38} +(-3.57509 - 0.467723i) q^{39} +(0.358010 - 0.620092i) q^{40} +(4.54901 + 2.62637i) q^{41} +(-1.78962 + 1.94866i) q^{42} +(-6.37475 - 11.0414i) q^{43} +(2.22627 + 1.28534i) q^{44} +(-0.620092 - 0.358010i) q^{45} +(8.13957 + 4.69938i) q^{46} +(-4.32056 - 2.49448i) q^{47} +(0.500000 + 0.866025i) q^{48} +(5.74300 - 4.00225i) q^{49} +(3.88613 + 2.24366i) q^{50} +(0.0124180 - 0.0215086i) q^{51} +(2.19260 - 2.86225i) q^{52} +(-4.72462 - 8.18328i) q^{53} +(0.866025 - 0.500000i) q^{54} +(0.920330 - 1.59406i) q^{55} +(-0.792781 - 2.52418i) q^{56} +6.91088i q^{57} -5.55177i q^{58} +(1.95045 + 1.12610i) q^{59} +(0.620092 - 0.358010i) q^{60} -0.652006 q^{61} +(-2.84137 + 4.92140i) q^{62} +(-2.52418 + 0.792781i) q^{63} -1.00000 q^{64} +(-2.04943 - 1.56995i) q^{65} +(1.28534 + 2.22627i) q^{66} +1.87610i q^{67} +(0.0124180 + 0.0215086i) q^{68} +(4.69938 + 8.13957i) q^{69} +(-1.80737 + 0.567647i) q^{70} +(7.52246 - 4.34310i) q^{71} +1.00000i q^{72} +(13.7568 - 7.94250i) q^{73} +(-2.08556 + 3.61229i) q^{74} +(2.24366 + 3.88613i) q^{75} +(-5.98499 - 3.45544i) q^{76} +(-2.03798 - 6.48886i) q^{77} +(3.32998 - 1.38248i) q^{78} +(-0.194223 + 0.336404i) q^{79} +0.716021i q^{80} +1.00000 q^{81} -5.25275 q^{82} +8.85439i q^{83} +(0.575523 - 2.58240i) q^{84} +(0.0154006 - 0.00889156i) q^{85} +(11.0414 + 6.37475i) q^{86} +(2.77589 - 4.80797i) q^{87} -2.57068 q^{88} +(-12.8502 + 7.41908i) q^{89} +0.716021 q^{90} +(-9.39497 + 1.65364i) q^{91} -9.39876 q^{92} +(-4.92140 + 2.84137i) q^{93} +4.98896 q^{94} +(-2.47416 + 4.28538i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(-1.78702 + 1.03174i) q^{97} +(-2.97246 + 6.33755i) q^{98} +2.57068i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −1.00000 −0.577350
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.620092 0.358010i −0.277314 0.160107i 0.354893 0.934907i \(-0.384517\pi\)
−0.632207 + 0.774800i \(0.717851\pi\)
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) −2.52418 + 0.792781i −0.954051 + 0.299643i
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) 0.716021 0.226426
\(11\) 2.57068i 0.775089i 0.921851 + 0.387544i \(0.126677\pi\)
−0.921851 + 0.387544i \(0.873323\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) 3.57509 + 0.467723i 0.991550 + 0.129723i
\(14\) 1.78962 1.94866i 0.478295 0.520801i
\(15\) 0.620092 + 0.358010i 0.160107 + 0.0924379i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.0124180 + 0.0215086i −0.00301181 + 0.00521661i −0.867527 0.497389i \(-0.834292\pi\)
0.864516 + 0.502606i \(0.167625\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) 6.91088i 1.58546i −0.609571 0.792732i \(-0.708658\pi\)
0.609571 0.792732i \(-0.291342\pi\)
\(20\) −0.620092 + 0.358010i −0.138657 + 0.0800535i
\(21\) 2.52418 0.792781i 0.550822 0.172999i
\(22\) −1.28534 2.22627i −0.274035 0.474643i
\(23\) −4.69938 8.13957i −0.979889 1.69722i −0.662755 0.748836i \(-0.730613\pi\)
−0.317134 0.948381i \(-0.602720\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −2.24366 3.88613i −0.448731 0.777226i
\(26\) −3.32998 + 1.38248i −0.653062 + 0.271127i
\(27\) −1.00000 −0.192450
\(28\) −0.575523 + 2.58240i −0.108764 + 0.488027i
\(29\) −2.77589 + 4.80797i −0.515469 + 0.892818i 0.484370 + 0.874863i \(0.339049\pi\)
−0.999839 + 0.0179551i \(0.994284\pi\)
\(30\) −0.716021 −0.130727
\(31\) 4.92140 2.84137i 0.883909 0.510325i 0.0119639 0.999928i \(-0.496192\pi\)
0.871945 + 0.489603i \(0.162858\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 2.57068i 0.447498i
\(34\) 0.0248360i 0.00425935i
\(35\) 1.84905 + 0.412087i 0.312546 + 0.0696553i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 3.61229 2.08556i 0.593856 0.342863i −0.172764 0.984963i \(-0.555270\pi\)
0.766621 + 0.642100i \(0.221937\pi\)
\(38\) 3.45544 + 5.98499i 0.560546 + 0.970894i
\(39\) −3.57509 0.467723i −0.572472 0.0748956i
\(40\) 0.358010 0.620092i 0.0566064 0.0980452i
\(41\) 4.54901 + 2.62637i 0.710436 + 0.410171i 0.811223 0.584737i \(-0.198802\pi\)
−0.100786 + 0.994908i \(0.532136\pi\)
\(42\) −1.78962 + 1.94866i −0.276144 + 0.300685i
\(43\) −6.37475 11.0414i −0.972141 1.68380i −0.689065 0.724699i \(-0.741979\pi\)
−0.283075 0.959098i \(-0.591355\pi\)
\(44\) 2.22627 + 1.28534i 0.335623 + 0.193772i
\(45\) −0.620092 0.358010i −0.0924379 0.0533690i
\(46\) 8.13957 + 4.69938i 1.20011 + 0.692886i
\(47\) −4.32056 2.49448i −0.630219 0.363857i 0.150618 0.988592i \(-0.451874\pi\)
−0.780837 + 0.624735i \(0.785207\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 5.74300 4.00225i 0.820428 0.571749i
\(50\) 3.88613 + 2.24366i 0.549582 + 0.317301i
\(51\) 0.0124180 0.0215086i 0.00173887 0.00301181i
\(52\) 2.19260 2.86225i 0.304059 0.396923i
\(53\) −4.72462 8.18328i −0.648977 1.12406i −0.983368 0.181626i \(-0.941864\pi\)
0.334391 0.942434i \(-0.391469\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0.920330 1.59406i 0.124097 0.214943i
\(56\) −0.792781 2.52418i −0.105940 0.337308i
\(57\) 6.91088i 0.915368i
\(58\) 5.55177i 0.728983i
\(59\) 1.95045 + 1.12610i 0.253928 + 0.146605i 0.621561 0.783365i \(-0.286499\pi\)
−0.367634 + 0.929971i \(0.619832\pi\)
\(60\) 0.620092 0.358010i 0.0800535 0.0462189i
\(61\) −0.652006 −0.0834808 −0.0417404 0.999128i \(-0.513290\pi\)
−0.0417404 + 0.999128i \(0.513290\pi\)
\(62\) −2.84137 + 4.92140i −0.360854 + 0.625018i
\(63\) −2.52418 + 0.792781i −0.318017 + 0.0998810i
\(64\) −1.00000 −0.125000
\(65\) −2.04943 1.56995i −0.254201 0.194728i
\(66\) 1.28534 + 2.22627i 0.158214 + 0.274035i
\(67\) 1.87610i 0.229203i 0.993412 + 0.114601i \(0.0365591\pi\)
−0.993412 + 0.114601i \(0.963441\pi\)
\(68\) 0.0124180 + 0.0215086i 0.00150591 + 0.00260831i
\(69\) 4.69938 + 8.13957i 0.565739 + 0.979889i
\(70\) −1.80737 + 0.567647i −0.216022 + 0.0678468i
\(71\) 7.52246 4.34310i 0.892752 0.515431i 0.0179106 0.999840i \(-0.494299\pi\)
0.874842 + 0.484409i \(0.160965\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 13.7568 7.94250i 1.61011 0.929600i 0.620772 0.783991i \(-0.286819\pi\)
0.989342 0.145608i \(-0.0465139\pi\)
\(74\) −2.08556 + 3.61229i −0.242441 + 0.419920i
\(75\) 2.24366 + 3.88613i 0.259075 + 0.448731i
\(76\) −5.98499 3.45544i −0.686526 0.396366i
\(77\) −2.03798 6.48886i −0.232250 0.739475i
\(78\) 3.32998 1.38248i 0.377046 0.156535i
\(79\) −0.194223 + 0.336404i −0.0218518 + 0.0378484i −0.876744 0.480956i \(-0.840290\pi\)
0.854893 + 0.518805i \(0.173623\pi\)
\(80\) 0.716021i 0.0800535i
\(81\) 1.00000 0.111111
\(82\) −5.25275 −0.580069
\(83\) 8.85439i 0.971895i 0.873988 + 0.485948i \(0.161525\pi\)
−0.873988 + 0.485948i \(0.838475\pi\)
\(84\) 0.575523 2.58240i 0.0627947 0.281763i
\(85\) 0.0154006 0.00889156i 0.00167043 0.000964425i
\(86\) 11.0414 + 6.37475i 1.19062 + 0.687407i
\(87\) 2.77589 4.80797i 0.297606 0.515469i
\(88\) −2.57068 −0.274035
\(89\) −12.8502 + 7.41908i −1.36212 + 0.786420i −0.989906 0.141726i \(-0.954735\pi\)
−0.372214 + 0.928147i \(0.621401\pi\)
\(90\) 0.716021 0.0754752
\(91\) −9.39497 + 1.65364i −0.984861 + 0.173349i
\(92\) −9.39876 −0.979889
\(93\) −4.92140 + 2.84137i −0.510325 + 0.294636i
\(94\) 4.98896 0.514572
\(95\) −2.47416 + 4.28538i −0.253844 + 0.439671i
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) −1.78702 + 1.03174i −0.181445 + 0.104757i −0.587971 0.808882i \(-0.700073\pi\)
0.406527 + 0.913639i \(0.366740\pi\)
\(98\) −2.97246 + 6.33755i −0.300264 + 0.640189i
\(99\) 2.57068i 0.258363i
\(100\) −4.48731 −0.448731
\(101\) 11.5903 1.15328 0.576638 0.817000i \(-0.304364\pi\)
0.576638 + 0.817000i \(0.304364\pi\)
\(102\) 0.0248360i 0.00245913i
\(103\) −7.89706 + 13.6781i −0.778120 + 1.34774i 0.154903 + 0.987930i \(0.450493\pi\)
−0.933024 + 0.359814i \(0.882840\pi\)
\(104\) −0.467723 + 3.57509i −0.0458640 + 0.350566i
\(105\) −1.84905 0.412087i −0.180449 0.0402155i
\(106\) 8.18328 + 4.72462i 0.794831 + 0.458896i
\(107\) 0.241343 + 0.418019i 0.0233315 + 0.0404114i 0.877455 0.479658i \(-0.159239\pi\)
−0.854124 + 0.520070i \(0.825906\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −2.77524 + 1.60228i −0.265819 + 0.153471i −0.626986 0.779030i \(-0.715712\pi\)
0.361167 + 0.932501i \(0.382378\pi\)
\(110\) 1.84066i 0.175500i
\(111\) −3.61229 + 2.08556i −0.342863 + 0.197952i
\(112\) 1.94866 + 1.78962i 0.184131 + 0.169103i
\(113\) −4.18781 7.25350i −0.393956 0.682352i 0.599011 0.800741i \(-0.295560\pi\)
−0.992967 + 0.118389i \(0.962227\pi\)
\(114\) −3.45544 5.98499i −0.323631 0.560546i
\(115\) 6.72971i 0.627548i
\(116\) 2.77589 + 4.80797i 0.257734 + 0.446409i
\(117\) 3.57509 + 0.467723i 0.330517 + 0.0432410i
\(118\) −2.25219 −0.207331
\(119\) 0.0142937 0.0641365i 0.00131030 0.00587939i
\(120\) −0.358010 + 0.620092i −0.0326817 + 0.0566064i
\(121\) 4.39161 0.399237
\(122\) 0.564654 0.326003i 0.0511214 0.0295149i
\(123\) −4.54901 2.62637i −0.410171 0.236812i
\(124\) 5.68274i 0.510325i
\(125\) 6.79311i 0.607594i
\(126\) 1.78962 1.94866i 0.159432 0.173600i
\(127\) −11.0533 + 19.1448i −0.980820 + 1.69883i −0.321610 + 0.946872i \(0.604224\pi\)
−0.659211 + 0.751958i \(0.729109\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 6.37475 + 11.0414i 0.561266 + 0.972141i
\(130\) 2.55983 + 0.334899i 0.224512 + 0.0293726i
\(131\) 5.57371 9.65394i 0.486977 0.843469i −0.512911 0.858442i \(-0.671433\pi\)
0.999888 + 0.0149731i \(0.00476625\pi\)
\(132\) −2.22627 1.28534i −0.193772 0.111874i
\(133\) 5.47881 + 17.4443i 0.475073 + 1.51261i
\(134\) −0.938052 1.62475i −0.0810354 0.140357i
\(135\) 0.620092 + 0.358010i 0.0533690 + 0.0308126i
\(136\) −0.0215086 0.0124180i −0.00184435 0.00106484i
\(137\) −14.5467 8.39853i −1.24281 0.717534i −0.273142 0.961974i \(-0.588063\pi\)
−0.969665 + 0.244439i \(0.921396\pi\)
\(138\) −8.13957 4.69938i −0.692886 0.400038i
\(139\) −9.50946 16.4709i −0.806582 1.39704i −0.915218 0.402959i \(-0.867982\pi\)
0.108636 0.994082i \(-0.465352\pi\)
\(140\) 1.28140 1.39528i 0.108298 0.117923i
\(141\) 4.32056 + 2.49448i 0.363857 + 0.210073i
\(142\) −4.34310 + 7.52246i −0.364465 + 0.631271i
\(143\) −1.20237 + 9.19040i −0.100547 + 0.768540i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 3.44261 1.98759i 0.285893 0.165060i
\(146\) −7.94250 + 13.7568i −0.657326 + 1.13852i
\(147\) −5.74300 + 4.00225i −0.473674 + 0.330100i
\(148\) 4.17111i 0.342863i
\(149\) 12.2538i 1.00387i −0.864906 0.501934i \(-0.832622\pi\)
0.864906 0.501934i \(-0.167378\pi\)
\(150\) −3.88613 2.24366i −0.317301 0.183194i
\(151\) −11.5364 + 6.66053i −0.938817 + 0.542026i −0.889589 0.456761i \(-0.849009\pi\)
−0.0492279 + 0.998788i \(0.515676\pi\)
\(152\) 6.91088 0.560546
\(153\) −0.0124180 + 0.0215086i −0.00100394 + 0.00173887i
\(154\) 5.00938 + 4.60053i 0.403667 + 0.370721i
\(155\) −4.06896 −0.326827
\(156\) −2.19260 + 2.86225i −0.175549 + 0.229164i
\(157\) −3.49931 6.06098i −0.279275 0.483719i 0.691930 0.721965i \(-0.256761\pi\)
−0.971205 + 0.238246i \(0.923427\pi\)
\(158\) 0.388445i 0.0309031i
\(159\) 4.72462 + 8.18328i 0.374687 + 0.648977i
\(160\) −0.358010 0.620092i −0.0283032 0.0490226i
\(161\) 18.3150 + 16.8202i 1.44342 + 1.32562i
\(162\) −0.866025 + 0.500000i −0.0680414 + 0.0392837i
\(163\) 10.1930i 0.798376i −0.916869 0.399188i \(-0.869292\pi\)
0.916869 0.399188i \(-0.130708\pi\)
\(164\) 4.54901 2.62637i 0.355218 0.205085i
\(165\) −0.920330 + 1.59406i −0.0716476 + 0.124097i
\(166\) −4.42719 7.66812i −0.343617 0.595162i
\(167\) −6.33732 3.65885i −0.490397 0.283131i 0.234342 0.972154i \(-0.424706\pi\)
−0.724739 + 0.689023i \(0.758040\pi\)
\(168\) 0.792781 + 2.52418i 0.0611643 + 0.194745i
\(169\) 12.5625 + 3.34430i 0.966344 + 0.257254i
\(170\) −0.00889156 + 0.0154006i −0.000681951 + 0.00118117i
\(171\) 6.91088i 0.528488i
\(172\) −12.7495 −0.972141
\(173\) 6.48507 0.493051 0.246525 0.969136i \(-0.420711\pi\)
0.246525 + 0.969136i \(0.420711\pi\)
\(174\) 5.55177i 0.420879i
\(175\) 8.74425 + 8.03057i 0.661003 + 0.607054i
\(176\) 2.22627 1.28534i 0.167812 0.0968861i
\(177\) −1.95045 1.12610i −0.146605 0.0846425i
\(178\) 7.41908 12.8502i 0.556083 0.963164i
\(179\) 23.2228 1.73576 0.867878 0.496777i \(-0.165483\pi\)
0.867878 + 0.496777i \(0.165483\pi\)
\(180\) −0.620092 + 0.358010i −0.0462189 + 0.0266845i
\(181\) −5.61910 −0.417664 −0.208832 0.977952i \(-0.566966\pi\)
−0.208832 + 0.977952i \(0.566966\pi\)
\(182\) 7.30946 6.12958i 0.541813 0.454355i
\(183\) 0.652006 0.0481977
\(184\) 8.13957 4.69938i 0.600057 0.346443i
\(185\) −2.98660 −0.219579
\(186\) 2.84137 4.92140i 0.208339 0.360854i
\(187\) −0.0552918 0.0319228i −0.00404334 0.00233442i
\(188\) −4.32056 + 2.49448i −0.315109 + 0.181929i
\(189\) 2.52418 0.792781i 0.183607 0.0576663i
\(190\) 4.94833i 0.358990i
\(191\) −23.8945 −1.72894 −0.864472 0.502681i \(-0.832347\pi\)
−0.864472 + 0.502681i \(0.832347\pi\)
\(192\) 1.00000 0.0721688
\(193\) 20.9972i 1.51141i 0.654910 + 0.755707i \(0.272707\pi\)
−0.654910 + 0.755707i \(0.727293\pi\)
\(194\) 1.03174 1.78702i 0.0740744 0.128301i
\(195\) 2.04943 + 1.56995i 0.146763 + 0.112426i
\(196\) −0.594548 6.97471i −0.0424677 0.498193i
\(197\) −4.48984 2.59221i −0.319888 0.184688i 0.331455 0.943471i \(-0.392461\pi\)
−0.651343 + 0.758784i \(0.725794\pi\)
\(198\) −1.28534 2.22627i −0.0913451 0.158214i
\(199\) 8.07086 13.9791i 0.572128 0.990955i −0.424219 0.905560i \(-0.639451\pi\)
0.996347 0.0853954i \(-0.0272153\pi\)
\(200\) 3.88613 2.24366i 0.274791 0.158651i
\(201\) 1.87610i 0.132330i
\(202\) −10.0375 + 5.79514i −0.706235 + 0.407745i
\(203\) 3.19517 14.3369i 0.224257 1.00625i
\(204\) −0.0124180 0.0215086i −0.000869435 0.00150591i
\(205\) −1.88054 3.25719i −0.131342 0.227492i
\(206\) 15.7941i 1.10043i
\(207\) −4.69938 8.13957i −0.326630 0.565739i
\(208\) −1.38248 3.32998i −0.0958579 0.230892i
\(209\) 17.7656 1.22888
\(210\) 1.80737 0.567647i 0.124720 0.0391714i
\(211\) 7.68735 13.3149i 0.529219 0.916635i −0.470200 0.882560i \(-0.655818\pi\)
0.999419 0.0340747i \(-0.0108484\pi\)
\(212\) −9.44924 −0.648977
\(213\) −7.52246 + 4.34310i −0.515431 + 0.297584i
\(214\) −0.418019 0.241343i −0.0285752 0.0164979i
\(215\) 9.12891i 0.622586i
\(216\) 1.00000i 0.0680414i
\(217\) −10.1699 + 11.0737i −0.690380 + 0.751734i
\(218\) 1.60228 2.77524i 0.108520 0.187963i
\(219\) −13.7568 + 7.94250i −0.929600 + 0.536705i
\(220\) −0.920330 1.59406i −0.0620486 0.107471i
\(221\) −0.0544556 + 0.0710871i −0.00366308 + 0.00478183i
\(222\) 2.08556 3.61229i 0.139973 0.242441i
\(223\) 11.0984 + 6.40769i 0.743207 + 0.429091i 0.823234 0.567702i \(-0.192167\pi\)
−0.0800273 + 0.996793i \(0.525501\pi\)
\(224\) −2.58240 0.575523i −0.172544 0.0384538i
\(225\) −2.24366 3.88613i −0.149577 0.259075i
\(226\) 7.25350 + 4.18781i 0.482496 + 0.278569i
\(227\) 17.4536 + 10.0768i 1.15843 + 0.668823i 0.950928 0.309411i \(-0.100132\pi\)
0.207506 + 0.978234i \(0.433465\pi\)
\(228\) 5.98499 + 3.45544i 0.396366 + 0.228842i
\(229\) 8.89145 + 5.13348i 0.587564 + 0.339230i 0.764134 0.645058i \(-0.223167\pi\)
−0.176570 + 0.984288i \(0.556500\pi\)
\(230\) −3.36485 5.82810i −0.221872 0.384293i
\(231\) 2.03798 + 6.48886i 0.134090 + 0.426936i
\(232\) −4.80797 2.77589i −0.315659 0.182246i
\(233\) −1.56117 + 2.70402i −0.102276 + 0.177146i −0.912622 0.408805i \(-0.865946\pi\)
0.810346 + 0.585951i \(0.199279\pi\)
\(234\) −3.32998 + 1.38248i −0.217687 + 0.0903757i
\(235\) 1.78610 + 3.09361i 0.116512 + 0.201805i
\(236\) 1.95045 1.12610i 0.126964 0.0733026i
\(237\) 0.194223 0.336404i 0.0126161 0.0218518i
\(238\) 0.0196895 + 0.0626907i 0.00127628 + 0.00406364i
\(239\) 12.2325i 0.791253i 0.918411 + 0.395627i \(0.129473\pi\)
−0.918411 + 0.395627i \(0.870527\pi\)
\(240\) 0.716021i 0.0462189i
\(241\) −1.63586 0.944462i −0.105375 0.0608382i 0.446386 0.894840i \(-0.352711\pi\)
−0.551761 + 0.834002i \(0.686044\pi\)
\(242\) −3.80324 + 2.19580i −0.244482 + 0.141152i
\(243\) −1.00000 −0.0641500
\(244\) −0.326003 + 0.564654i −0.0208702 + 0.0361483i
\(245\) −4.99403 + 0.425708i −0.319057 + 0.0271975i
\(246\) 5.25275 0.334903
\(247\) 3.23238 24.7070i 0.205671 1.57207i
\(248\) 2.84137 + 4.92140i 0.180427 + 0.312509i
\(249\) 8.85439i 0.561124i
\(250\) −3.39656 5.88301i −0.214817 0.372074i
\(251\) −7.56052 13.0952i −0.477216 0.826562i 0.522443 0.852674i \(-0.325021\pi\)
−0.999659 + 0.0261123i \(0.991687\pi\)
\(252\) −0.575523 + 2.58240i −0.0362546 + 0.162676i
\(253\) 20.9242 12.0806i 1.31549 0.759501i
\(254\) 22.1066i 1.38709i
\(255\) −0.0154006 + 0.00889156i −0.000964425 + 0.000556811i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −2.82704 4.89658i −0.176346 0.305440i 0.764280 0.644884i \(-0.223094\pi\)
−0.940626 + 0.339444i \(0.889761\pi\)
\(258\) −11.0414 6.37475i −0.687407 0.396875i
\(259\) −7.46469 + 8.12807i −0.463833 + 0.505054i
\(260\) −2.38433 + 0.989886i −0.147870 + 0.0613901i
\(261\) −2.77589 + 4.80797i −0.171823 + 0.297606i
\(262\) 11.1474i 0.688689i
\(263\) −14.5482 −0.897083 −0.448541 0.893762i \(-0.648056\pi\)
−0.448541 + 0.893762i \(0.648056\pi\)
\(264\) 2.57068 0.158214
\(265\) 6.76585i 0.415623i
\(266\) −13.4669 12.3678i −0.825711 0.758319i
\(267\) 12.8502 7.41908i 0.786420 0.454040i
\(268\) 1.62475 + 0.938052i 0.0992477 + 0.0573007i
\(269\) −1.73031 + 2.99698i −0.105499 + 0.182729i −0.913942 0.405845i \(-0.866977\pi\)
0.808443 + 0.588574i \(0.200311\pi\)
\(270\) −0.716021 −0.0435756
\(271\) −10.0207 + 5.78543i −0.608712 + 0.351440i −0.772461 0.635062i \(-0.780975\pi\)
0.163749 + 0.986502i \(0.447641\pi\)
\(272\) 0.0248360 0.00150591
\(273\) 9.39497 1.65364i 0.568609 0.100083i
\(274\) 16.7971 1.01475
\(275\) 9.98999 5.76772i 0.602419 0.347807i
\(276\) 9.39876 0.565739
\(277\) −2.31998 + 4.01832i −0.139394 + 0.241438i −0.927267 0.374400i \(-0.877849\pi\)
0.787873 + 0.615837i \(0.211182\pi\)
\(278\) 16.4709 + 9.50946i 0.987857 + 0.570340i
\(279\) 4.92140 2.84137i 0.294636 0.170108i
\(280\) −0.412087 + 1.84905i −0.0246269 + 0.110502i
\(281\) 20.9621i 1.25049i −0.780428 0.625246i \(-0.784999\pi\)
0.780428 0.625246i \(-0.215001\pi\)
\(282\) −4.98896 −0.297088
\(283\) −4.72036 −0.280596 −0.140298 0.990109i \(-0.544806\pi\)
−0.140298 + 0.990109i \(0.544806\pi\)
\(284\) 8.68619i 0.515431i
\(285\) 2.47416 4.28538i 0.146557 0.253844i
\(286\) −3.55392 8.56030i −0.210148 0.506181i
\(287\) −13.5647 3.02308i −0.800698 0.178447i
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) 8.49969 + 14.7219i 0.499982 + 0.865994i
\(290\) −1.98759 + 3.44261i −0.116715 + 0.202157i
\(291\) 1.78702 1.03174i 0.104757 0.0604815i
\(292\) 15.8850i 0.929600i
\(293\) 29.0541 16.7744i 1.69736 0.979970i 0.749105 0.662451i \(-0.230484\pi\)
0.948252 0.317518i \(-0.102850\pi\)
\(294\) 2.97246 6.33755i 0.173357 0.369613i
\(295\) −0.806308 1.39657i −0.0469450 0.0813112i
\(296\) 2.08556 + 3.61229i 0.121220 + 0.209960i
\(297\) 2.57068i 0.149166i
\(298\) 6.12689 + 10.6121i 0.354921 + 0.614741i
\(299\) −12.9936 31.2977i −0.751441 1.80999i
\(300\) 4.48731 0.259075
\(301\) 24.8444 + 22.8167i 1.43201 + 1.31513i
\(302\) 6.66053 11.5364i 0.383271 0.663844i
\(303\) −11.5903 −0.665845
\(304\) −5.98499 + 3.45544i −0.343263 + 0.198183i
\(305\) 0.404304 + 0.233425i 0.0231504 + 0.0133659i
\(306\) 0.0248360i 0.00141978i
\(307\) 5.49245i 0.313471i 0.987641 + 0.156735i \(0.0500970\pi\)
−0.987641 + 0.156735i \(0.949903\pi\)
\(308\) −6.63851 1.47949i −0.378264 0.0843015i
\(309\) 7.89706 13.6781i 0.449248 0.778120i
\(310\) 3.52382 2.03448i 0.200140 0.115551i
\(311\) 7.45213 + 12.9075i 0.422572 + 0.731916i 0.996190 0.0872069i \(-0.0277941\pi\)
−0.573619 + 0.819123i \(0.694461\pi\)
\(312\) 0.467723 3.57509i 0.0264796 0.202399i
\(313\) 1.80173 3.12069i 0.101840 0.176392i −0.810603 0.585596i \(-0.800860\pi\)
0.912443 + 0.409205i \(0.134194\pi\)
\(314\) 6.06098 + 3.49931i 0.342041 + 0.197477i
\(315\) 1.84905 + 0.412087i 0.104182 + 0.0232184i
\(316\) 0.194223 + 0.336404i 0.0109259 + 0.0189242i
\(317\) −3.54331 2.04573i −0.199012 0.114900i 0.397183 0.917740i \(-0.369988\pi\)
−0.596194 + 0.802840i \(0.703321\pi\)
\(318\) −8.18328 4.72462i −0.458896 0.264944i
\(319\) −12.3598 7.13591i −0.692014 0.399534i
\(320\) 0.620092 + 0.358010i 0.0346642 + 0.0200134i
\(321\) −0.241343 0.418019i −0.0134705 0.0233315i
\(322\) −24.2713 5.40921i −1.35259 0.301443i
\(323\) 0.148644 + 0.0858194i 0.00827075 + 0.00477512i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −6.20363 14.9427i −0.344116 0.828869i
\(326\) 5.09649 + 8.82738i 0.282268 + 0.488903i
\(327\) 2.77524 1.60228i 0.153471 0.0886065i
\(328\) −2.62637 + 4.54901i −0.145017 + 0.251177i
\(329\) 12.8835 + 2.87126i 0.710289 + 0.158298i
\(330\) 1.84066i 0.101325i
\(331\) 19.4070i 1.06670i 0.845893 + 0.533352i \(0.179068\pi\)
−0.845893 + 0.533352i \(0.820932\pi\)
\(332\) 7.66812 + 4.42719i 0.420843 + 0.242974i
\(333\) 3.61229 2.08556i 0.197952 0.114288i
\(334\) 7.31771 0.400407
\(335\) 0.671665 1.16336i 0.0366970 0.0635610i
\(336\) −1.94866 1.78962i −0.106308 0.0976316i
\(337\) −23.0545 −1.25586 −0.627929 0.778271i \(-0.716097\pi\)
−0.627929 + 0.778271i \(0.716097\pi\)
\(338\) −12.5516 + 3.38499i −0.682715 + 0.184119i
\(339\) 4.18781 + 7.25350i 0.227451 + 0.393956i
\(340\) 0.0177831i 0.000964425i
\(341\) 7.30425 + 12.6513i 0.395547 + 0.685108i
\(342\) 3.45544 + 5.98499i 0.186849 + 0.323631i
\(343\) −11.3235 + 14.6553i −0.611410 + 0.791314i
\(344\) 11.0414 6.37475i 0.595312 0.343704i
\(345\) 6.72971i 0.362315i
\(346\) −5.61624 + 3.24254i −0.301931 + 0.174320i
\(347\) 2.30078 3.98507i 0.123513 0.213930i −0.797638 0.603136i \(-0.793917\pi\)
0.921151 + 0.389207i \(0.127251\pi\)
\(348\) −2.77589 4.80797i −0.148803 0.257734i
\(349\) −3.23204 1.86602i −0.173007 0.0998858i 0.410996 0.911637i \(-0.365181\pi\)
−0.584003 + 0.811751i \(0.698514\pi\)
\(350\) −11.5880 2.58255i −0.619406 0.138043i
\(351\) −3.57509 0.467723i −0.190824 0.0249652i
\(352\) −1.28534 + 2.22627i −0.0685088 + 0.118661i
\(353\) 26.3529i 1.40262i −0.712854 0.701312i \(-0.752598\pi\)
0.712854 0.701312i \(-0.247402\pi\)
\(354\) 2.25219 0.119703
\(355\) −6.21949 −0.330096
\(356\) 14.8382i 0.786420i
\(357\) −0.0142937 + 0.0641365i −0.000756504 + 0.00339446i
\(358\) −20.1116 + 11.6114i −1.06293 + 0.613683i
\(359\) −7.11568 4.10824i −0.375551 0.216825i 0.300330 0.953835i \(-0.402903\pi\)
−0.675881 + 0.737011i \(0.736237\pi\)
\(360\) 0.358010 0.620092i 0.0188688 0.0326817i
\(361\) −28.7602 −1.51370
\(362\) 4.86628 2.80955i 0.255766 0.147667i
\(363\) −4.39161 −0.230500
\(364\) −3.26539 + 8.96310i −0.171153 + 0.469794i
\(365\) −11.3740 −0.595342
\(366\) −0.564654 + 0.326003i −0.0295149 + 0.0170405i
\(367\) 0.428797 0.0223830 0.0111915 0.999937i \(-0.496438\pi\)
0.0111915 + 0.999937i \(0.496438\pi\)
\(368\) −4.69938 + 8.13957i −0.244972 + 0.424304i
\(369\) 4.54901 + 2.62637i 0.236812 + 0.136724i
\(370\) 2.58647 1.49330i 0.134464 0.0776330i
\(371\) 18.4134 + 16.9105i 0.955974 + 0.877950i
\(372\) 5.68274i 0.294636i
\(373\) −2.01507 −0.104336 −0.0521682 0.998638i \(-0.516613\pi\)
−0.0521682 + 0.998638i \(0.516613\pi\)
\(374\) 0.0638455 0.00330137
\(375\) 6.79311i 0.350795i
\(376\) 2.49448 4.32056i 0.128643 0.222816i
\(377\) −12.1728 + 15.8906i −0.626932 + 0.818406i
\(378\) −1.78962 + 1.94866i −0.0920479 + 0.100228i
\(379\) 15.0823 + 8.70779i 0.774727 + 0.447289i 0.834558 0.550920i \(-0.185723\pi\)
−0.0598312 + 0.998209i \(0.519056\pi\)
\(380\) 2.47416 + 4.28538i 0.126922 + 0.219835i
\(381\) 11.0533 19.1448i 0.566277 0.980820i
\(382\) 20.6932 11.9472i 1.05876 0.611274i
\(383\) 0.328330i 0.0167769i −0.999965 0.00838845i \(-0.997330\pi\)
0.999965 0.00838845i \(-0.00267016\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) −1.05934 + 4.75331i −0.0539891 + 0.242251i
\(386\) −10.4986 18.1841i −0.534365 0.925548i
\(387\) −6.37475 11.0414i −0.324047 0.561266i
\(388\) 2.06347i 0.104757i
\(389\) −4.30458 7.45575i −0.218251 0.378022i 0.736022 0.676957i \(-0.236702\pi\)
−0.954273 + 0.298935i \(0.903368\pi\)
\(390\) −2.55983 0.334899i −0.129622 0.0169583i
\(391\) 0.233428 0.0118050
\(392\) 4.00225 + 5.74300i 0.202144 + 0.290065i
\(393\) −5.57371 + 9.65394i −0.281156 + 0.486977i
\(394\) 5.18443 0.261188
\(395\) 0.240872 0.139067i 0.0121196 0.00699724i
\(396\) 2.22627 + 1.28534i 0.111874 + 0.0645907i
\(397\) 1.72832i 0.0867420i 0.999059 + 0.0433710i \(0.0138097\pi\)
−0.999059 + 0.0433710i \(0.986190\pi\)
\(398\) 16.1417i 0.809111i
\(399\) −5.47881 17.4443i −0.274283 0.873308i
\(400\) −2.24366 + 3.88613i −0.112183 + 0.194306i
\(401\) −11.7488 + 6.78319i −0.586709 + 0.338737i −0.763795 0.645459i \(-0.776666\pi\)
0.177086 + 0.984195i \(0.443333\pi\)
\(402\) 0.938052 + 1.62475i 0.0467858 + 0.0810354i
\(403\) 18.9234 7.85629i 0.942641 0.391350i
\(404\) 5.79514 10.0375i 0.288319 0.499383i
\(405\) −0.620092 0.358010i −0.0308126 0.0177897i
\(406\) 4.40134 + 14.0137i 0.218435 + 0.695487i
\(407\) 5.36129 + 9.28603i 0.265749 + 0.460292i
\(408\) 0.0215086 + 0.0124180i 0.00106484 + 0.000614784i
\(409\) 1.00634 + 0.581012i 0.0497605 + 0.0287292i 0.524674 0.851303i \(-0.324187\pi\)
−0.474913 + 0.880033i \(0.657521\pi\)
\(410\) 3.25719 + 1.88054i 0.160861 + 0.0928731i
\(411\) 14.5467 + 8.39853i 0.717534 + 0.414269i
\(412\) 7.89706 + 13.6781i 0.389060 + 0.673872i
\(413\) −5.81605 1.29619i −0.286189 0.0637813i
\(414\) 8.13957 + 4.69938i 0.400038 + 0.230962i
\(415\) 3.16996 5.49053i 0.155607 0.269520i
\(416\) 2.86225 + 2.19260i 0.140334 + 0.107501i
\(417\) 9.50946 + 16.4709i 0.465680 + 0.806582i
\(418\) −15.3855 + 8.88282i −0.752529 + 0.434473i
\(419\) 16.6656 28.8657i 0.814169 1.41018i −0.0957534 0.995405i \(-0.530526\pi\)
0.909923 0.414778i \(-0.136141\pi\)
\(420\) −1.28140 + 1.39528i −0.0625260 + 0.0680827i
\(421\) 17.4686i 0.851367i 0.904872 + 0.425684i \(0.139966\pi\)
−0.904872 + 0.425684i \(0.860034\pi\)
\(422\) 15.3747i 0.748429i
\(423\) −4.32056 2.49448i −0.210073 0.121286i
\(424\) 8.18328 4.72462i 0.397415 0.229448i
\(425\) 0.111447 0.00540598
\(426\) 4.34310 7.52246i 0.210424 0.364465i
\(427\) 1.64578 0.516898i 0.0796450 0.0250144i
\(428\) 0.482687 0.0233315
\(429\) 1.20237 9.19040i 0.0580508 0.443717i
\(430\) −4.56445 7.90587i −0.220118 0.381255i
\(431\) 22.8866i 1.10241i −0.834370 0.551205i \(-0.814168\pi\)
0.834370 0.551205i \(-0.185832\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −9.81620 17.0022i −0.471736 0.817071i 0.527741 0.849405i \(-0.323039\pi\)
−0.999477 + 0.0323342i \(0.989706\pi\)
\(434\) 3.27055 14.6751i 0.156991 0.704427i
\(435\) −3.44261 + 1.98759i −0.165060 + 0.0952977i
\(436\) 3.20457i 0.153471i
\(437\) −56.2515 + 32.4768i −2.69088 + 1.55358i
\(438\) 7.94250 13.7568i 0.379507 0.657326i
\(439\) 12.7988 + 22.1682i 0.610854 + 1.05803i 0.991097 + 0.133144i \(0.0425072\pi\)
−0.380242 + 0.924887i \(0.624159\pi\)
\(440\) 1.59406 + 0.920330i 0.0759937 + 0.0438750i
\(441\) 5.74300 4.00225i 0.273476 0.190583i
\(442\) 0.0116164 0.0887910i 0.000552535 0.00422336i
\(443\) 10.9535 18.9721i 0.520418 0.901390i −0.479301 0.877651i \(-0.659110\pi\)
0.999718 0.0237390i \(-0.00755706\pi\)
\(444\) 4.17111i 0.197952i
\(445\) 10.6244 0.503646
\(446\) −12.8154 −0.606826
\(447\) 12.2538i 0.579584i
\(448\) 2.52418 0.792781i 0.119256 0.0374554i
\(449\) −23.0029 + 13.2807i −1.08557 + 0.626756i −0.932394 0.361443i \(-0.882284\pi\)
−0.153179 + 0.988198i \(0.548951\pi\)
\(450\) 3.88613 + 2.24366i 0.183194 + 0.105767i
\(451\) −6.75156 + 11.6941i −0.317919 + 0.550651i
\(452\) −8.37562 −0.393956
\(453\) 11.5364 6.66053i 0.542026 0.312939i
\(454\) −20.1537 −0.945858
\(455\) 6.41777 + 2.33809i 0.300870 + 0.109611i
\(456\) −6.91088 −0.323631
\(457\) 25.3660 14.6451i 1.18657 0.685068i 0.229046 0.973416i \(-0.426439\pi\)
0.957526 + 0.288348i \(0.0931060\pi\)
\(458\) −10.2670 −0.479744
\(459\) 0.0124180 0.0215086i 0.000579624 0.00100394i
\(460\) 5.82810 + 3.36485i 0.271736 + 0.156887i
\(461\) −1.95594 + 1.12927i −0.0910974 + 0.0525951i −0.544857 0.838529i \(-0.683416\pi\)
0.453759 + 0.891124i \(0.350083\pi\)
\(462\) −5.00938 4.60053i −0.233057 0.214036i
\(463\) 2.33300i 0.108424i −0.998529 0.0542119i \(-0.982735\pi\)
0.998529 0.0542119i \(-0.0172647\pi\)
\(464\) 5.55177 0.257734
\(465\) 4.06896 0.188694
\(466\) 3.12234i 0.144639i
\(467\) −21.1203 + 36.5814i −0.977329 + 1.69278i −0.305305 + 0.952255i \(0.598758\pi\)
−0.672025 + 0.740529i \(0.734575\pi\)
\(468\) 2.19260 2.86225i 0.101353 0.132308i
\(469\) −1.48734 4.73563i −0.0686789 0.218671i
\(470\) −3.09361 1.78610i −0.142698 0.0823866i
\(471\) 3.49931 + 6.06098i 0.161240 + 0.279275i
\(472\) −1.12610 + 1.95045i −0.0518328 + 0.0897770i
\(473\) 28.3839 16.3874i 1.30509 0.753495i
\(474\) 0.388445i 0.0178419i
\(475\) −26.8566 + 15.5056i −1.23226 + 0.711447i
\(476\) −0.0483970 0.0444470i −0.00221827 0.00203722i
\(477\) −4.72462 8.18328i −0.216326 0.374687i
\(478\) −6.11624 10.5936i −0.279750 0.484542i
\(479\) 19.3019i 0.881925i 0.897526 + 0.440962i \(0.145363\pi\)
−0.897526 + 0.440962i \(0.854637\pi\)
\(480\) 0.358010 + 0.620092i 0.0163409 + 0.0283032i
\(481\) 13.8897 5.76649i 0.633316 0.262929i
\(482\) 1.88892 0.0860382
\(483\) −18.3150 16.8202i −0.833361 0.765345i
\(484\) 2.19580 3.80324i 0.0998093 0.172875i
\(485\) 1.47749 0.0670894
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) −12.9928 7.50142i −0.588762 0.339922i 0.175846 0.984418i \(-0.443734\pi\)
−0.764608 + 0.644496i \(0.777067\pi\)
\(488\) 0.652006i 0.0295149i
\(489\) 10.1930i 0.460942i
\(490\) 4.11210 2.86569i 0.185766 0.129459i
\(491\) 14.2048 24.6034i 0.641052 1.11033i −0.344147 0.938916i \(-0.611832\pi\)
0.985198 0.171418i \(-0.0548350\pi\)
\(492\) −4.54901 + 2.62637i −0.205085 + 0.118406i
\(493\) −0.0689420 0.119411i −0.00310499 0.00537800i
\(494\) 9.55417 + 23.0131i 0.429862 + 1.03541i
\(495\) 0.920330 1.59406i 0.0413657 0.0716476i
\(496\) −4.92140 2.84137i −0.220977 0.127581i
\(497\) −15.5450 + 16.9264i −0.697286 + 0.759254i
\(498\) 4.42719 + 7.66812i 0.198387 + 0.343617i
\(499\) 3.33919 + 1.92788i 0.149482 + 0.0863038i 0.572876 0.819642i \(-0.305828\pi\)
−0.423393 + 0.905946i \(0.639161\pi\)
\(500\) 5.88301 + 3.39656i 0.263096 + 0.151899i
\(501\) 6.33732 + 3.65885i 0.283131 + 0.163466i
\(502\) 13.0952 + 7.56052i 0.584467 + 0.337442i
\(503\) 16.3872 + 28.3835i 0.730670 + 1.26556i 0.956597 + 0.291413i \(0.0941254\pi\)
−0.225927 + 0.974144i \(0.572541\pi\)
\(504\) −0.792781 2.52418i −0.0353133 0.112436i
\(505\) −7.18704 4.14944i −0.319819 0.184648i
\(506\) −12.0806 + 20.9242i −0.537048 + 0.930195i
\(507\) −12.5625 3.34430i −0.557919 0.148526i
\(508\) 11.0533 + 19.1448i 0.490410 + 0.849415i
\(509\) −30.9031 + 17.8419i −1.36976 + 0.790829i −0.990897 0.134625i \(-0.957017\pi\)
−0.378859 + 0.925454i \(0.623684\pi\)
\(510\) 0.00889156 0.0154006i 0.000393725 0.000681951i
\(511\) −28.4281 + 30.9545i −1.25758 + 1.36935i
\(512\) 1.00000i 0.0441942i
\(513\) 6.91088i 0.305123i
\(514\) 4.89658 + 2.82704i 0.215979 + 0.124695i
\(515\) 9.79381 5.65446i 0.431567 0.249165i
\(516\) 12.7495 0.561266
\(517\) 6.41250 11.1068i 0.282022 0.488476i
\(518\) 2.40057 10.7715i 0.105475 0.473271i
\(519\) −6.48507 −0.284663
\(520\) 1.56995 2.04943i 0.0688468 0.0898735i
\(521\) −0.555626 0.962372i −0.0243424 0.0421623i 0.853598 0.520933i \(-0.174416\pi\)
−0.877940 + 0.478771i \(0.841083\pi\)
\(522\) 5.55177i 0.242994i
\(523\) −0.368072 0.637520i −0.0160947 0.0278768i 0.857866 0.513874i \(-0.171790\pi\)
−0.873961 + 0.485997i \(0.838457\pi\)
\(524\) −5.57371 9.65394i −0.243488 0.421734i
\(525\) −8.74425 8.03057i −0.381630 0.350483i
\(526\) 12.5991 7.27412i 0.549349 0.317167i
\(527\) 0.141137i 0.00614802i
\(528\) −2.22627 + 1.28534i −0.0968861 + 0.0559372i
\(529\) −32.6684 + 56.5833i −1.42036 + 2.46014i
\(530\) −3.38293 5.85940i −0.146945 0.254516i
\(531\) 1.95045 + 1.12610i 0.0846425 + 0.0488684i
\(532\) 17.8466 + 3.97737i 0.773749 + 0.172441i
\(533\) 15.0347 + 11.5172i 0.651225 + 0.498865i
\(534\) −7.41908 + 12.8502i −0.321055 + 0.556083i
\(535\) 0.345613i 0.0149422i
\(536\) −1.87610 −0.0810354
\(537\) −23.2228 −1.00214
\(538\) 3.46062i 0.149198i
\(539\) 10.2885 + 14.7634i 0.443157 + 0.635905i
\(540\) 0.620092 0.358010i 0.0266845 0.0154063i
\(541\) 3.31356 + 1.91309i 0.142461 + 0.0822500i 0.569536 0.821966i \(-0.307123\pi\)
−0.427075 + 0.904216i \(0.640456\pi\)
\(542\) 5.78543 10.0207i 0.248506 0.430424i
\(543\) 5.61910 0.241139
\(544\) −0.0215086 + 0.0124180i −0.000922176 + 0.000532418i
\(545\) 2.29454 0.0982871
\(546\) −7.30946 + 6.12958i −0.312816 + 0.262322i
\(547\) −5.24598 −0.224302 −0.112151 0.993691i \(-0.535774\pi\)
−0.112151 + 0.993691i \(0.535774\pi\)
\(548\) −14.5467 + 8.39853i −0.621403 + 0.358767i
\(549\) −0.652006 −0.0278269
\(550\) −5.76772 + 9.98999i −0.245937 + 0.425975i
\(551\) 33.2273 + 19.1838i 1.41553 + 0.817257i
\(552\) −8.13957 + 4.69938i −0.346443 + 0.200019i
\(553\) 0.223559 1.00312i 0.00950671 0.0426570i
\(554\) 4.63996i 0.197133i
\(555\) 2.98660 0.126774
\(556\) −19.0189 −0.806582
\(557\) 19.4339i 0.823440i −0.911310 0.411720i \(-0.864928\pi\)
0.911310 0.411720i \(-0.135072\pi\)
\(558\) −2.84137 + 4.92140i −0.120285 + 0.208339i
\(559\) −17.6260 42.4555i −0.745499 1.79568i
\(560\) −0.567647 1.80737i −0.0239875 0.0763752i
\(561\) 0.0552918 + 0.0319228i 0.00233442 + 0.00134778i
\(562\) 10.4810 + 18.1537i 0.442116 + 0.765767i
\(563\) −2.06339 + 3.57390i −0.0869616 + 0.150622i −0.906225 0.422795i \(-0.861049\pi\)
0.819264 + 0.573417i \(0.194382\pi\)
\(564\) 4.32056 2.49448i 0.181929 0.105036i
\(565\) 5.99712i 0.252301i
\(566\) 4.08795 2.36018i 0.171829 0.0992057i
\(567\) −2.52418 + 0.792781i −0.106006 + 0.0332937i
\(568\) 4.34310 + 7.52246i 0.182232 + 0.315636i
\(569\) 12.5267 + 21.6969i 0.525147 + 0.909581i 0.999571 + 0.0292850i \(0.00932303\pi\)
−0.474424 + 0.880296i \(0.657344\pi\)
\(570\) 4.94833i 0.207263i
\(571\) −15.9460 27.6192i −0.667318 1.15583i −0.978651 0.205528i \(-0.934109\pi\)
0.311333 0.950301i \(-0.399224\pi\)
\(572\) 7.35793 + 5.63648i 0.307651 + 0.235673i
\(573\) 23.8945 0.998206
\(574\) 13.2589 4.16428i 0.553416 0.173814i
\(575\) −21.0876 + 36.5248i −0.879414 + 1.52319i
\(576\) −1.00000 −0.0416667
\(577\) 19.6398 11.3390i 0.817614 0.472050i −0.0319788 0.999489i \(-0.510181\pi\)
0.849593 + 0.527439i \(0.176848\pi\)
\(578\) −14.7219 8.49969i −0.612350 0.353541i
\(579\) 20.9972i 0.872615i
\(580\) 3.97518i 0.165060i
\(581\) −7.01959 22.3501i −0.291221 0.927238i
\(582\) −1.03174 + 1.78702i −0.0427669 + 0.0740744i
\(583\) 21.0366 12.1455i 0.871247 0.503015i
\(584\) 7.94250 + 13.7568i 0.328663 + 0.569261i
\(585\) −2.04943 1.56995i −0.0847336 0.0649094i
\(586\) −16.7744 + 29.0541i −0.692943 + 1.20021i
\(587\) −2.99085 1.72677i −0.123446 0.0712714i 0.437006 0.899459i \(-0.356039\pi\)
−0.560451 + 0.828187i \(0.689372\pi\)
\(588\) 0.594548 + 6.97471i 0.0245187 + 0.287632i
\(589\) −19.6364 34.0112i −0.809102 1.40141i
\(590\) 1.39657 + 0.806308i 0.0574957 + 0.0331952i
\(591\) 4.48984 + 2.59221i 0.184688 + 0.106629i
\(592\) −3.61229 2.08556i −0.148464 0.0857158i
\(593\) 12.0235 + 6.94179i 0.493747 + 0.285065i 0.726128 0.687560i \(-0.241318\pi\)
−0.232380 + 0.972625i \(0.574651\pi\)
\(594\) 1.28534 + 2.22627i 0.0527381 + 0.0913451i
\(595\) −0.0318250 + 0.0346532i −0.00130470 + 0.00142064i
\(596\) −10.6121 6.12689i −0.434688 0.250967i
\(597\) −8.07086 + 13.9791i −0.330318 + 0.572128i
\(598\) 26.9016 + 20.6078i 1.10009 + 0.842714i
\(599\) −1.37576 2.38289i −0.0562122 0.0973624i 0.836550 0.547891i \(-0.184569\pi\)
−0.892762 + 0.450528i \(0.851236\pi\)
\(600\) −3.88613 + 2.24366i −0.158651 + 0.0915969i
\(601\) 17.0005 29.4457i 0.693464 1.20112i −0.277231 0.960803i \(-0.589417\pi\)
0.970696 0.240312i \(-0.0772499\pi\)
\(602\) −32.9243 7.33764i −1.34189 0.299060i
\(603\) 1.87610i 0.0764009i
\(604\) 13.3211i 0.542026i
\(605\) −2.72320 1.57224i −0.110714 0.0639207i
\(606\) 10.0375 5.79514i 0.407745 0.235412i
\(607\) 30.9167 1.25487 0.627434 0.778669i \(-0.284105\pi\)
0.627434 + 0.778669i \(0.284105\pi\)
\(608\) 3.45544 5.98499i 0.140137 0.242724i
\(609\) −3.19517 + 14.3369i −0.129475 + 0.580959i
\(610\) −0.466850 −0.0189022
\(611\) −14.2797 10.9388i −0.577693 0.442537i
\(612\) 0.0124180 + 0.0215086i 0.000501969 + 0.000869435i
\(613\) 6.52803i 0.263665i −0.991272 0.131832i \(-0.957914\pi\)
0.991272 0.131832i \(-0.0420860\pi\)
\(614\) −2.74622 4.75660i −0.110829 0.191961i
\(615\) 1.88054 + 3.25719i 0.0758306 + 0.131342i
\(616\) 6.48886 2.03798i 0.261444 0.0821127i
\(617\) −10.8491 + 6.26373i −0.436768 + 0.252168i −0.702226 0.711954i \(-0.747810\pi\)
0.265458 + 0.964123i \(0.414477\pi\)
\(618\) 15.7941i 0.635333i
\(619\) 3.04630 1.75878i 0.122441 0.0706914i −0.437529 0.899205i \(-0.644146\pi\)
0.559970 + 0.828513i \(0.310813\pi\)
\(620\) −2.03448 + 3.52382i −0.0817067 + 0.141520i
\(621\) 4.69938 + 8.13957i 0.188580 + 0.326630i
\(622\) −12.9075 7.45213i −0.517543 0.298803i
\(623\) 26.5546 28.9145i 1.06389 1.15844i
\(624\) 1.38248 + 3.32998i 0.0553436 + 0.133306i
\(625\) −8.78628 + 15.2183i −0.351451 + 0.608731i
\(626\) 3.60346i 0.144023i
\(627\) −17.7656 −0.709492
\(628\) −6.99861 −0.279275
\(629\) 0.103594i 0.00413056i
\(630\) −1.80737 + 0.567647i −0.0720072 + 0.0226156i
\(631\) −17.1805 + 9.91915i −0.683944 + 0.394875i −0.801339 0.598210i \(-0.795879\pi\)
0.117395 + 0.993085i \(0.462545\pi\)
\(632\) −0.336404 0.194223i −0.0133814 0.00772577i
\(633\) −7.68735 + 13.3149i −0.305545 + 0.529219i
\(634\) 4.09146 0.162493
\(635\) 13.7081 7.91438i 0.543990 0.314073i
\(636\) 9.44924 0.374687
\(637\) 22.4037 11.6222i 0.887665 0.460490i
\(638\) 14.2718 0.565027
\(639\) 7.52246 4.34310i 0.297584 0.171810i
\(640\) −0.716021 −0.0283032
\(641\) −1.57697 + 2.73139i −0.0622865 + 0.107883i −0.895487 0.445088i \(-0.853173\pi\)
0.833201 + 0.552971i \(0.186506\pi\)
\(642\) 0.418019 + 0.241343i 0.0164979 + 0.00952506i
\(643\) 29.0975 16.7994i 1.14749 0.662505i 0.199217 0.979955i \(-0.436160\pi\)
0.948275 + 0.317451i \(0.102827\pi\)
\(644\) 23.7242 7.45116i 0.934864 0.293617i
\(645\) 9.12891i 0.359450i
\(646\) −0.171639 −0.00675304
\(647\) −22.3012 −0.876750 −0.438375 0.898792i \(-0.644446\pi\)
−0.438375 + 0.898792i \(0.644446\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −2.89483 + 5.01399i −0.113632 + 0.196816i
\(650\) 12.8438 + 9.83890i 0.503776 + 0.385913i
\(651\) 10.1699 11.0737i 0.398591 0.434014i
\(652\) −8.82738 5.09649i −0.345707 0.199594i
\(653\) 3.74174 + 6.48088i 0.146426 + 0.253616i 0.929904 0.367803i \(-0.119890\pi\)
−0.783478 + 0.621419i \(0.786556\pi\)
\(654\) −1.60228 + 2.77524i −0.0626542 + 0.108520i
\(655\) −6.91242 + 3.99089i −0.270091 + 0.155937i
\(656\) 5.25275i 0.205085i
\(657\) 13.7568 7.94250i 0.536705 0.309867i
\(658\) −12.5930 + 3.95515i −0.490928 + 0.154188i
\(659\) 4.51922 + 7.82751i 0.176044 + 0.304917i 0.940522 0.339733i \(-0.110337\pi\)
−0.764478 + 0.644650i \(0.777003\pi\)
\(660\) 0.920330 + 1.59406i 0.0358238 + 0.0620486i
\(661\) 11.6240i 0.452120i −0.974113 0.226060i \(-0.927415\pi\)
0.974113 0.226060i \(-0.0725846\pi\)
\(662\) −9.70350 16.8069i −0.377137 0.653221i
\(663\) 0.0544556 0.0710871i 0.00211488 0.00276079i
\(664\) −8.85439 −0.343617
\(665\) 2.84788 12.7785i 0.110436 0.495531i
\(666\) −2.08556 + 3.61229i −0.0808136 + 0.139973i
\(667\) 52.1798 2.02041
\(668\) −6.33732 + 3.65885i −0.245198 + 0.141565i
\(669\) −11.0984 6.40769i −0.429091 0.247736i
\(670\) 1.34333i 0.0518973i
\(671\) 1.67610i 0.0647051i
\(672\) 2.58240 + 0.575523i 0.0996181 + 0.0222013i
\(673\) 5.44014 9.42260i 0.209702 0.363214i −0.741919 0.670490i \(-0.766084\pi\)
0.951621 + 0.307275i \(0.0994173\pi\)
\(674\) 19.9658 11.5272i 0.769053 0.444013i
\(675\) 2.24366 + 3.88613i 0.0863584 + 0.149577i
\(676\) 9.17748 9.20727i 0.352980 0.354126i
\(677\) 8.71040 15.0869i 0.334768 0.579835i −0.648672 0.761068i \(-0.724675\pi\)
0.983440 + 0.181233i \(0.0580087\pi\)
\(678\) −7.25350 4.18781i −0.278569 0.160832i
\(679\) 3.69283 4.02101i 0.141718 0.154312i
\(680\) 0.00889156 + 0.0154006i 0.000340976 + 0.000590587i
\(681\) −17.4536 10.0768i −0.668823 0.386145i
\(682\) −12.6513 7.30425i −0.484445 0.279694i
\(683\) 30.8882 + 17.8333i 1.18190 + 0.682372i 0.956454 0.291883i \(-0.0942819\pi\)
0.225449 + 0.974255i \(0.427615\pi\)
\(684\) −5.98499 3.45544i −0.228842 0.132122i
\(685\) 6.01352 + 10.4157i 0.229765 + 0.397964i
\(686\) 2.47875 18.3536i 0.0946390 0.700745i
\(687\) −8.89145 5.13348i −0.339230 0.195855i
\(688\) −6.37475 + 11.0414i −0.243035 + 0.420949i
\(689\) −13.0634 31.4658i −0.497676 1.19875i
\(690\) 3.36485 + 5.82810i 0.128098 + 0.221872i
\(691\) −2.62439 + 1.51519i −0.0998365 + 0.0576406i −0.549087 0.835765i \(-0.685024\pi\)
0.449250 + 0.893406i \(0.351691\pi\)
\(692\) 3.24254 5.61624i 0.123263 0.213497i
\(693\) −2.03798 6.48886i −0.0774166 0.246492i
\(694\) 4.60157i 0.174673i
\(695\) 13.6179i 0.516558i
\(696\) 4.80797 + 2.77589i 0.182246 + 0.105220i
\(697\) −0.112979 + 0.0652287i −0.00427940 + 0.00247071i
\(698\) 3.73204 0.141260
\(699\) 1.56117 2.70402i 0.0590488 0.102276i
\(700\) 11.3268 3.55746i 0.428113 0.134459i
\(701\) −27.7372 −1.04762 −0.523810 0.851835i \(-0.675490\pi\)
−0.523810 + 0.851835i \(0.675490\pi\)
\(702\) 3.32998 1.38248i 0.125682 0.0521784i
\(703\) −14.4130 24.9641i −0.543597 0.941538i
\(704\) 2.57068i 0.0968861i
\(705\) −1.78610 3.09361i −0.0672683 0.116512i
\(706\) 13.1765 + 22.8223i 0.495903 + 0.858928i
\(707\) −29.2560 + 9.18855i −1.10029 + 0.345571i
\(708\) −1.95045 + 1.12610i −0.0733026 + 0.0423213i
\(709\) 16.3014i 0.612214i −0.951997 0.306107i \(-0.900974\pi\)
0.951997 0.306107i \(-0.0990265\pi\)
\(710\) 5.38624 3.10975i 0.202142 0.116707i
\(711\) −0.194223 + 0.336404i −0.00728392 + 0.0126161i
\(712\) −7.41908 12.8502i −0.278042 0.481582i
\(713\) −46.2551 26.7054i −1.73227 1.00012i
\(714\) −0.0196895 0.0626907i −0.000736862 0.00234614i
\(715\) 4.03583 5.26843i 0.150932 0.197028i
\(716\) 11.6114 20.1116i 0.433939 0.751605i
\(717\) 12.2325i 0.456830i
\(718\) 8.21648 0.306636
\(719\) 6.89552 0.257159 0.128580 0.991699i \(-0.458958\pi\)
0.128580 + 0.991699i \(0.458958\pi\)
\(720\) 0.716021i 0.0266845i
\(721\) 9.08988 40.7867i 0.338525 1.51898i
\(722\) 24.9071 14.3801i 0.926945 0.535172i
\(723\) 1.63586 + 0.944462i 0.0608382 + 0.0351249i
\(724\) −2.80955 + 4.86628i −0.104416 + 0.180854i
\(725\) 24.9125 0.925229
\(726\) 3.80324 2.19580i 0.141152 0.0814939i
\(727\) −26.6965 −0.990119 −0.495059 0.868859i \(-0.664854\pi\)
−0.495059 + 0.868859i \(0.664854\pi\)
\(728\) −1.65364 9.39497i −0.0612880 0.348201i
\(729\) 1.00000 0.0370370
\(730\) 9.85017 5.68700i 0.364571 0.210485i
\(731\) 0.316647 0.0117116
\(732\) 0.326003 0.564654i 0.0120494 0.0208702i
\(733\) −27.0290 15.6052i −0.998337 0.576390i −0.0905813 0.995889i \(-0.528872\pi\)
−0.907756 + 0.419499i \(0.862206\pi\)
\(734\) −0.371350 + 0.214399i −0.0137068 + 0.00791360i
\(735\) 4.99403 0.425708i 0.184208 0.0157025i
\(736\) 9.39876i 0.346443i
\(737\) −4.82286 −0.177652
\(738\) −5.25275 −0.193356
\(739\) 21.7423i 0.799804i 0.916558 + 0.399902i \(0.130956\pi\)
−0.916558 + 0.399902i \(0.869044\pi\)
\(740\) −1.49330 + 2.58647i −0.0548948 + 0.0950806i
\(741\) −3.23238 + 24.7070i −0.118744 + 0.907633i
\(742\) −24.4017 5.43826i −0.895814 0.199645i
\(743\) 8.60858 + 4.97016i 0.315818 + 0.182338i 0.649527 0.760339i \(-0.274967\pi\)
−0.333709 + 0.942676i \(0.608300\pi\)
\(744\) −2.84137 4.92140i −0.104170 0.180427i
\(745\) −4.38698 + 7.59847i −0.160726 + 0.278386i
\(746\) 1.74510 1.00753i 0.0638927 0.0368885i
\(747\) 8.85439i 0.323965i
\(748\) −0.0552918 + 0.0319228i −0.00202167 + 0.00116721i
\(749\) −0.940592 0.863824i −0.0343685 0.0315634i
\(750\) 3.39656 + 5.88301i 0.124025 + 0.214817i
\(751\) 4.27457 + 7.40378i 0.155981 + 0.270168i 0.933416 0.358796i \(-0.116813\pi\)
−0.777435 + 0.628964i \(0.783479\pi\)
\(752\) 4.98896i 0.181929i
\(753\) 7.56052 + 13.0952i 0.275521 + 0.477216i
\(754\) 2.59669 19.8481i 0.0945659 0.722823i
\(755\) 9.53816 0.347129
\(756\) 0.575523 2.58240i 0.0209316 0.0939209i
\(757\) 3.50974 6.07905i 0.127564 0.220947i −0.795168 0.606389i \(-0.792618\pi\)
0.922732 + 0.385442i \(0.125951\pi\)
\(758\) −17.4156 −0.632562
\(759\) −20.9242 + 12.0806i −0.759501 + 0.438498i
\(760\) −4.28538 2.47416i −0.155447 0.0897474i
\(761\) 16.1732i 0.586279i −0.956070 0.293139i \(-0.905300\pi\)
0.956070 0.293139i \(-0.0947000\pi\)
\(762\) 22.1066i 0.800836i
\(763\) 5.73494 6.24461i 0.207619 0.226070i
\(764\) −11.9472 + 20.6932i −0.432236 + 0.748655i
\(765\) 0.0154006 0.00889156i 0.000556811 0.000321475i
\(766\) 0.164165 + 0.284342i 0.00593153 + 0.0102737i
\(767\) 6.44634 + 4.93816i 0.232764 + 0.178307i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 22.6397 + 13.0710i 0.816409 + 0.471354i 0.849176 0.528109i \(-0.177099\pi\)
−0.0327678 + 0.999463i \(0.510432\pi\)
\(770\) −1.45924 4.64616i −0.0525873 0.167436i
\(771\) 2.82704 + 4.89658i 0.101813 + 0.176346i
\(772\) 18.1841 + 10.4986i 0.654461 + 0.377853i
\(773\) 3.03108 + 1.74999i 0.109020 + 0.0629429i 0.553519 0.832837i \(-0.313285\pi\)
−0.444498 + 0.895780i \(0.646618\pi\)
\(774\) 11.0414 + 6.37475i 0.396875 + 0.229136i
\(775\) −22.0839 12.7501i −0.793276 0.457998i
\(776\) −1.03174 1.78702i −0.0370372 0.0641503i
\(777\) 7.46469 8.12807i 0.267794 0.291593i
\(778\) 7.45575 + 4.30458i 0.267302 + 0.154327i
\(779\) 18.1505 31.4377i 0.650311 1.12637i
\(780\) 2.38433 0.989886i 0.0853728 0.0354436i
\(781\) 11.1647 + 19.3378i 0.399505 + 0.691962i
\(782\) −0.202155 + 0.116714i −0.00722904 + 0.00417369i
\(783\) 2.77589 4.80797i 0.0992020 0.171823i
\(784\) −6.33755 2.97246i −0.226341 0.106159i
\(785\) 5.01115i 0.178856i
\(786\) 11.1474i 0.397615i
\(787\) −10.6680 6.15919i −0.380274 0.219551i 0.297664 0.954671i \(-0.403793\pi\)
−0.677937 + 0.735120i \(0.737126\pi\)
\(788\) −4.48984 + 2.59221i −0.159944 + 0.0923438i
\(789\) 14.5482 0.517931
\(790\) −0.139067 + 0.240872i −0.00494780 + 0.00856984i
\(791\) 16.3212 + 14.9892i 0.580316 + 0.532953i
\(792\) −2.57068 −0.0913451
\(793\) −2.33098 0.304958i −0.0827754 0.0108294i
\(794\) −0.864161 1.49677i −0.0306679 0.0531184i
\(795\) 6.76585i 0.239960i
\(796\) −8.07086 13.9791i −0.286064 0.495478i
\(797\) 18.9472 + 32.8176i 0.671145 + 1.16246i 0.977580 + 0.210566i \(0.0675306\pi\)
−0.306435 + 0.951892i \(0.599136\pi\)
\(798\) 13.4669 + 12.3678i 0.476725 + 0.437816i
\(799\) 0.107306 0.0619530i 0.00379620 0.00219174i
\(800\) 4.48731i 0.158651i
\(801\) −12.8502 + 7.41908i −0.454040 + 0.262140i
\(802\) 6.78319 11.7488i 0.239523 0.414866i
\(803\) 20.4176 + 35.3644i 0.720522 + 1.24798i
\(804\) −1.62475 0.938052i −0.0573007 0.0330826i
\(805\) −5.33518 16.9870i −0.188040 0.598713i
\(806\) −12.4600 + 16.2654i −0.438885 + 0.572926i
\(807\) 1.73031 2.99698i 0.0609098 0.105499i
\(808\) 11.5903i 0.407745i
\(809\) 21.0649 0.740603 0.370301 0.928912i \(-0.379254\pi\)
0.370301 + 0.928912i \(0.379254\pi\)
\(810\) 0.716021 0.0251584
\(811\) 46.4549i 1.63125i −0.578578 0.815627i \(-0.696392\pi\)
0.578578 0.815627i \(-0.303608\pi\)
\(812\) −10.8185 9.93554i −0.379655 0.348669i
\(813\) 10.0207 5.78543i 0.351440 0.202904i
\(814\) −9.28603 5.36129i −0.325475 0.187913i
\(815\) −3.64919 + 6.32059i −0.127826 + 0.221400i
\(816\) −0.0248360 −0.000869435
\(817\) −76.3057 + 44.0551i −2.66960 + 1.54129i
\(818\) −1.16202 −0.0406292
\(819\) −9.39497 + 1.65364i −0.328287 + 0.0577828i
\(820\) −3.76108 −0.131342
\(821\) −5.65583 + 3.26539i −0.197390 + 0.113963i −0.595437 0.803402i \(-0.703021\pi\)
0.398048 + 0.917365i \(0.369688\pi\)
\(822\) −16.7971 −0.585864
\(823\) 3.71035 6.42651i 0.129335 0.224014i −0.794084 0.607808i \(-0.792049\pi\)
0.923419 + 0.383793i \(0.125383\pi\)
\(824\) −13.6781 7.89706i −0.476499 0.275107i
\(825\) −9.98999 + 5.76772i −0.347807 + 0.200806i
\(826\) 5.68494 1.78549i 0.197804 0.0621253i
\(827\) 38.3288i 1.33282i 0.745584 + 0.666411i \(0.232170\pi\)
−0.745584 + 0.666411i \(0.767830\pi\)
\(828\) −9.39876 −0.326630
\(829\) −10.9300 −0.379616 −0.189808 0.981821i \(-0.560787\pi\)
−0.189808 + 0.981821i \(0.560787\pi\)
\(830\) 6.33992i 0.220062i
\(831\) 2.31998 4.01832i 0.0804792 0.139394i
\(832\) −3.57509 0.467723i −0.123944 0.0162154i
\(833\) 0.0147662 + 0.173224i 0.000511619 + 0.00600186i
\(834\) −16.4709 9.50946i −0.570340 0.329286i
\(835\) 2.61982 + 4.53765i 0.0906624 + 0.157032i
\(836\) 8.88282 15.3855i 0.307219 0.532119i
\(837\) −4.92140 + 2.84137i −0.170108 + 0.0982121i
\(838\) 33.3313i 1.15141i
\(839\) −1.82881 + 1.05586i −0.0631375 + 0.0364525i −0.531236 0.847224i \(-0.678272\pi\)
0.468099 + 0.883676i \(0.344939\pi\)
\(840\) 0.412087 1.84905i 0.0142183 0.0637983i
\(841\) −0.911078 1.57803i −0.0314165 0.0544150i
\(842\) −8.73430 15.1282i −0.301004 0.521354i
\(843\) 20.9621i 0.721972i
\(844\) −7.68735 13.3149i −0.264610 0.458317i
\(845\) −6.59259 6.57127i −0.226792 0.226058i
\(846\) 4.98896 0.171524
\(847\) −11.0852 + 3.48158i −0.380893 + 0.119629i
\(848\) −4.72462 + 8.18328i −0.162244 + 0.281015i
\(849\) 4.72036 0.162002
\(850\) −0.0965161 + 0.0557236i −0.00331047 + 0.00191130i
\(851\) −33.9510 19.6016i −1.16383 0.671935i
\(852\) 8.68619i 0.297584i
\(853\) 1.58650i 0.0543207i 0.999631 + 0.0271604i \(0.00864647\pi\)
−0.999631 + 0.0271604i \(0.991354\pi\)
\(854\) −1.16684 + 1.27054i −0.0399285 + 0.0434769i
\(855\) −2.47416 + 4.28538i −0.0846146 + 0.146557i
\(856\) −0.418019 + 0.241343i −0.0142876 + 0.00824894i
\(857\) −15.0692 26.1007i −0.514756 0.891583i −0.999853 0.0171229i \(-0.994549\pi\)
0.485098 0.874460i \(-0.338784\pi\)
\(858\) 3.55392 + 8.56030i 0.121329 + 0.292244i
\(859\) 7.96343 13.7931i 0.271709 0.470614i −0.697591 0.716497i \(-0.745745\pi\)
0.969300 + 0.245883i \(0.0790779\pi\)
\(860\) 7.90587 + 4.56445i 0.269588 + 0.155647i
\(861\) 13.5647 + 3.02308i 0.462283 + 0.103026i
\(862\) 11.4433 + 19.8204i 0.389761 + 0.675085i
\(863\) 19.4948 + 11.2553i 0.663609 + 0.383135i 0.793651 0.608373i \(-0.208178\pi\)
−0.130041 + 0.991509i \(0.541511\pi\)
\(864\) −0.866025 0.500000i −0.0294628 0.0170103i
\(865\) −4.02134 2.32172i −0.136730 0.0789409i
\(866\) 17.0022 + 9.81620i 0.577757 + 0.333568i
\(867\) −8.49969 14.7219i −0.288665 0.499982i
\(868\) 4.50517 + 14.3443i 0.152915 + 0.486877i
\(869\) −0.864786 0.499284i −0.0293359 0.0169371i
\(870\) 1.98759 3.44261i 0.0673856 0.116715i
\(871\) −0.877497 + 6.70723i −0.0297329 + 0.227266i
\(872\) −1.60228 2.77524i −0.0542601 0.0939813i
\(873\) −1.78702 + 1.03174i −0.0604815 + 0.0349190i
\(874\) 32.4768 56.2515i 1.09855 1.90274i
\(875\) −5.38545 17.1471i −0.182061 0.579676i
\(876\) 15.8850i 0.536705i
\(877\) 24.9627i 0.842930i 0.906845 + 0.421465i \(0.138484\pi\)
−0.906845 + 0.421465i \(0.861516\pi\)
\(878\) −22.1682 12.7988i −0.748141 0.431939i
\(879\) −29.0541 + 16.7744i −0.979970 + 0.565786i
\(880\) −1.84066 −0.0620486
\(881\) 21.0029 36.3780i 0.707605 1.22561i −0.258138 0.966108i \(-0.583109\pi\)
0.965743 0.259500i \(-0.0835576\pi\)
\(882\) −2.97246 + 6.33755i −0.100088 + 0.213396i
\(883\) 19.4571 0.654782 0.327391 0.944889i \(-0.393831\pi\)
0.327391 + 0.944889i \(0.393831\pi\)
\(884\) 0.0343354 + 0.0827034i 0.00115482 + 0.00278162i
\(885\) 0.806308 + 1.39657i 0.0271037 + 0.0469450i
\(886\) 21.9070i 0.735982i
\(887\) −24.0070 41.5813i −0.806075 1.39616i −0.915563 0.402175i \(-0.868254\pi\)
0.109488 0.993988i \(-0.465079\pi\)
\(888\) −2.08556 3.61229i −0.0699866 0.121220i
\(889\) 12.7228 57.0879i 0.426711 1.91467i
\(890\) −9.20102 + 5.31221i −0.308419 + 0.178066i
\(891\) 2.57068i 0.0861210i
\(892\) 11.0984 6.40769i 0.371603 0.214545i
\(893\) −17.2390 + 29.8589i −0.576882 + 0.999189i
\(894\) −6.12689 10.6121i −0.204914 0.354921i
\(895\) −14.4003 8.31401i −0.481349 0.277907i
\(896\) −1.78962 + 1.94866i −0.0597869 + 0.0651001i
\(897\) 12.9936 + 31.2977i 0.433845 + 1.04500i
\(898\) 13.2807 23.0029i 0.443183 0.767616i
\(899\) 31.5493i 1.05223i
\(900\) −4.48731 −0.149577
\(901\) 0.234682 0.00781838
\(902\) 13.5031i 0.449605i
\(903\) −24.8444 22.8167i −0.826771 0.759293i
\(904\) 7.25350 4.18781i 0.241248 0.139285i
\(905\) 3.48436 + 2.01169i 0.115824 + 0.0668710i
\(906\) −6.66053 + 11.5364i −0.221281 + 0.383271i
\(907\) 32.9344 1.09357 0.546785 0.837273i \(-0.315852\pi\)
0.546785 + 0.837273i \(0.315852\pi\)
\(908\) 17.4536 10.0768i 0.579217 0.334411i
\(909\) 11.5903 0.384426
\(910\) −6.72699 + 1.18404i −0.222998 + 0.0392505i
\(911\) 36.6136 1.21306 0.606532 0.795059i \(-0.292560\pi\)
0.606532 + 0.795059i \(0.292560\pi\)
\(912\) 5.98499 3.45544i 0.198183 0.114421i
\(913\) −22.7618 −0.753305
\(914\) −14.6451 + 25.3660i −0.484416 + 0.839033i
\(915\) −0.404304 0.233425i −0.0133659 0.00771679i
\(916\) 8.89145 5.13348i 0.293782 0.169615i
\(917\) −6.41560 + 28.7870i −0.211862 + 0.950632i
\(918\) 0.0248360i 0.000819712i
\(919\) 19.9240 0.657231 0.328615 0.944464i \(-0.393418\pi\)
0.328615 + 0.944464i \(0.393418\pi\)
\(920\) −6.72971 −0.221872
\(921\) 5.49245i 0.180982i
\(922\) 1.12927 1.95594i 0.0371904 0.0644156i
\(923\) 28.9248 12.0085i 0.952072 0.395265i
\(924\) 6.63851 + 1.47949i 0.218391 + 0.0486715i
\(925\) −16.2095 9.35854i −0.532964 0.307707i
\(926\) 1.16650 + 2.02044i 0.0383336 + 0.0663958i
\(927\) −7.89706 + 13.6781i −0.259373 + 0.449248i
\(928\) −4.80797 + 2.77589i −0.157829 + 0.0911229i
\(929\) 4.48490i 0.147145i 0.997290 + 0.0735724i \(0.0234400\pi\)
−0.997290 + 0.0735724i \(0.976560\pi\)
\(930\) −3.52382 + 2.03448i −0.115551 + 0.0667132i
\(931\) −27.6590 39.6891i −0.906488 1.30076i
\(932\) 1.56117 + 2.70402i 0.0511378 + 0.0885732i
\(933\) −7.45213 12.9075i −0.243972 0.422572i
\(934\) 42.2405i 1.38215i
\(935\) 0.0228573 + 0.0395901i 0.000747515 + 0.00129473i
\(936\) −0.467723 + 3.57509i −0.0152880 + 0.116855i
\(937\) −1.54887 −0.0505995 −0.0252997 0.999680i \(-0.508054\pi\)
−0.0252997 + 0.999680i \(0.508054\pi\)
\(938\) 3.65589 + 3.35751i 0.119369 + 0.109626i
\(939\) −1.80173 + 3.12069i −0.0587972 + 0.101840i
\(940\) 3.57220 0.116512
\(941\) 0.0220362 0.0127226i 0.000718359 0.000414745i −0.499641 0.866233i \(-0.666535\pi\)
0.500359 + 0.865818i \(0.333201\pi\)
\(942\) −6.06098 3.49931i −0.197477 0.114014i
\(943\) 49.3693i 1.60769i
\(944\) 2.25219i 0.0733026i
\(945\) −1.84905 0.412087i −0.0601496 0.0134052i
\(946\) −16.3874 + 28.3839i −0.532802 + 0.922840i
\(947\) 5.91870 3.41716i 0.192332 0.111043i −0.400742 0.916191i \(-0.631248\pi\)
0.593074 + 0.805148i \(0.297914\pi\)
\(948\) −0.194223 0.336404i −0.00630806 0.0109259i
\(949\) 52.8967 21.9607i 1.71710 0.712876i
\(950\) 15.5056 26.8566i 0.503069 0.871342i
\(951\) 3.54331 + 2.04573i 0.114900 + 0.0663373i
\(952\) 0.0641365 + 0.0142937i 0.00207868 + 0.000463262i
\(953\) 23.9163 + 41.4242i 0.774724 + 1.34186i 0.934949 + 0.354782i \(0.115445\pi\)
−0.160225 + 0.987081i \(0.551222\pi\)
\(954\) 8.18328 + 4.72462i 0.264944 + 0.152965i
\(955\) 14.8168 + 8.55447i 0.479460 + 0.276816i
\(956\) 10.5936 + 6.11624i 0.342623 + 0.197813i
\(957\) 12.3598 + 7.13591i 0.399534 + 0.230671i
\(958\) −9.65093 16.7159i −0.311807 0.540066i
\(959\) 43.3766 + 9.66709i 1.40070 + 0.312167i
\(960\) −0.620092 0.358010i −0.0200134 0.0115547i
\(961\) 0.646777 1.12025i 0.0208638 0.0361371i
\(962\) −9.14559 + 11.9388i −0.294866 + 0.384921i
\(963\) 0.241343 + 0.418019i 0.00777718 + 0.0134705i
\(964\) −1.63586 + 0.944462i −0.0526874 + 0.0304191i
\(965\) 7.51722 13.0202i 0.241988 0.419136i
\(966\) 24.2713 + 5.40921i 0.780917 + 0.174038i
\(967\) 14.3721i 0.462175i 0.972933 + 0.231088i \(0.0742284\pi\)
−0.972933 + 0.231088i \(0.925772\pi\)
\(968\) 4.39161i 0.141152i
\(969\) −0.148644 0.0858194i −0.00477512 0.00275692i
\(970\) −1.27954 + 0.738745i −0.0410837 + 0.0237197i
\(971\) −8.15870 −0.261825 −0.130913 0.991394i \(-0.541791\pi\)
−0.130913 + 0.991394i \(0.541791\pi\)
\(972\) −0.500000 + 0.866025i −0.0160375 + 0.0277778i
\(973\) 37.0614 + 34.0366i 1.18813 + 1.09116i
\(974\) 15.0028 0.480722
\(975\) 6.20363 + 14.9427i 0.198675 + 0.478548i
\(976\) 0.326003 + 0.564654i 0.0104351 + 0.0180741i
\(977\) 14.2110i 0.454650i −0.973819 0.227325i \(-0.927002\pi\)
0.973819 0.227325i \(-0.0729979\pi\)
\(978\) −5.09649 8.82738i −0.162968 0.282268i
\(979\) −19.0721 33.0338i −0.609546 1.05576i
\(980\) −2.12834 + 4.53781i −0.0679874 + 0.144955i
\(981\) −2.77524 + 1.60228i −0.0886065 + 0.0511570i
\(982\) 28.4095i 0.906584i
\(983\) −3.80375 + 2.19610i −0.121321 + 0.0700447i −0.559432 0.828876i \(-0.688981\pi\)
0.438111 + 0.898921i \(0.355648\pi\)
\(984\) 2.62637 4.54901i 0.0837257 0.145017i
\(985\) 1.85608 + 3.21482i 0.0591396 + 0.102433i
\(986\) 0.119411 + 0.0689420i 0.00380282 + 0.00219556i
\(987\) −12.8835 2.87126i −0.410085 0.0913933i
\(988\) −19.7807 15.1528i −0.629307 0.482075i
\(989\) −59.9148 + 103.775i −1.90518 + 3.29987i
\(990\) 1.84066i 0.0585000i
\(991\) −13.4728 −0.427978 −0.213989 0.976836i \(-0.568646\pi\)
−0.213989 + 0.976836i \(0.568646\pi\)
\(992\) 5.68274 0.180427
\(993\) 19.4070i 0.615862i
\(994\) 4.99911 22.4312i 0.158562 0.711474i
\(995\) −10.0094 + 5.77890i −0.317318 + 0.183204i
\(996\) −7.66812 4.42719i −0.242974 0.140281i
\(997\) 8.41844 14.5812i 0.266615 0.461790i −0.701371 0.712797i \(-0.747428\pi\)
0.967985 + 0.251007i \(0.0807616\pi\)
\(998\) −3.85576 −0.122052
\(999\) −3.61229 + 2.08556i −0.114288 + 0.0659840i
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 546.2.bd.a.121.2 16
3.2 odd 2 1638.2.cr.a.667.7 16
7.4 even 3 546.2.bm.a.277.3 yes 16
13.10 even 6 546.2.bm.a.205.7 yes 16
21.11 odd 6 1638.2.dt.a.1369.6 16
39.23 odd 6 1638.2.dt.a.1297.2 16
91.88 even 6 inner 546.2.bd.a.361.2 yes 16
273.179 odd 6 1638.2.cr.a.361.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bd.a.121.2 16 1.1 even 1 trivial
546.2.bd.a.361.2 yes 16 91.88 even 6 inner
546.2.bm.a.205.7 yes 16 13.10 even 6
546.2.bm.a.277.3 yes 16 7.4 even 3
1638.2.cr.a.361.7 16 273.179 odd 6
1638.2.cr.a.667.7 16 3.2 odd 2
1638.2.dt.a.1297.2 16 39.23 odd 6
1638.2.dt.a.1369.6 16 21.11 odd 6