Properties

Label 966.2.l.c.47.5
Level $966$
Weight $2$
Character 966.47
Analytic conductor $7.714$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(47,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.l (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: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 47.5
Character \(\chi\) \(=\) 966.47
Dual form 966.2.l.c.185.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-1.13768 - 1.30602i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.890465 - 1.54233i) q^{5} +(0.332245 + 1.69989i) q^{6} +(-2.00001 - 1.73204i) q^{7} -1.00000i q^{8} +(-0.411389 + 2.97166i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-1.13768 - 1.30602i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.890465 - 1.54233i) q^{5} +(0.332245 + 1.69989i) q^{6} +(-2.00001 - 1.73204i) q^{7} -1.00000i q^{8} +(-0.411389 + 2.97166i) q^{9} +(-1.54233 + 0.890465i) q^{10} +(-0.864424 + 0.499076i) q^{11} +(0.562211 - 1.63827i) q^{12} +6.26372i q^{13} +(0.866040 + 2.50000i) q^{14} +(-3.02738 + 0.591704i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.67970 + 2.90933i) q^{17} +(1.84210 - 2.36784i) q^{18} +(-1.42779 - 0.824336i) q^{19} +1.78093 q^{20} +(0.0132797 + 4.58256i) q^{21} +0.998151 q^{22} +(0.866025 + 0.500000i) q^{23} +(-1.30602 + 1.13768i) q^{24} +(0.914144 + 1.58334i) q^{25} +(3.13186 - 5.42454i) q^{26} +(4.34908 - 2.84350i) q^{27} +(0.499985 - 2.59808i) q^{28} +1.24938i q^{29} +(2.91764 + 1.00126i) q^{30} +(-6.98992 + 4.03563i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.63524 + 0.561171i) q^{33} -3.35941i q^{34} +(-4.45232 + 1.54236i) q^{35} +(-2.77923 + 1.12956i) q^{36} +(0.235496 - 0.407891i) q^{37} +(0.824336 + 1.42779i) q^{38} +(8.18056 - 7.12608i) q^{39} +(-1.54233 - 0.890465i) q^{40} -4.34340 q^{41} +(2.27978 - 3.97525i) q^{42} +4.79063 q^{43} +(-0.864424 - 0.499076i) q^{44} +(4.21695 + 3.28066i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(4.22866 - 7.32426i) q^{47} +(1.69989 - 0.332245i) q^{48} +(1.00008 + 6.92819i) q^{49} -1.82829i q^{50} +(1.88870 - 5.50361i) q^{51} +(-5.42454 + 3.13186i) q^{52} +(-5.24099 + 3.02589i) q^{53} +(-5.18816 + 0.288003i) q^{54} +1.77764i q^{55} +(-1.73204 + 2.00001i) q^{56} +(0.547762 + 2.80256i) q^{57} +(0.624691 - 1.08200i) q^{58} +(0.600268 + 1.03970i) q^{59} +(-2.02612 - 2.32593i) q^{60} +(1.01927 + 0.588474i) q^{61} +8.07127 q^{62} +(5.96981 - 5.23081i) q^{63} -1.00000 q^{64} +(9.66073 + 5.57762i) q^{65} +(-1.13557 - 1.30361i) q^{66} +(4.81654 + 8.34250i) q^{67} +(-1.67970 + 2.90933i) q^{68} +(-0.332245 - 1.69989i) q^{69} +(4.62700 + 0.890439i) q^{70} +9.62306i q^{71} +(2.97166 + 0.411389i) q^{72} +(9.57661 - 5.52906i) q^{73} +(-0.407891 + 0.235496i) q^{74} +(1.02788 - 2.99523i) q^{75} -1.64867i q^{76} +(2.59328 + 0.499061i) q^{77} +(-10.6476 + 2.08109i) q^{78} +(0.576636 - 0.998763i) q^{79} +(0.890465 + 1.54233i) q^{80} +(-8.66152 - 2.44502i) q^{81} +(3.76149 + 2.17170i) q^{82} -7.53838 q^{83} +(-3.96197 + 2.30278i) q^{84} +5.98287 q^{85} +(-4.14881 - 2.39532i) q^{86} +(1.63172 - 1.42139i) q^{87} +(0.499076 + 0.864424i) q^{88} +(4.81612 - 8.34177i) q^{89} +(-2.01166 - 4.94961i) q^{90} +(10.8490 - 12.5275i) q^{91} +1.00000i q^{92} +(13.2229 + 4.53775i) q^{93} +(-7.32426 + 4.22866i) q^{94} +(-2.54280 + 1.46808i) q^{95} +(-1.63827 - 0.562211i) q^{96} +11.6654i q^{97} +(2.59800 - 6.50003i) q^{98} +(-1.12747 - 2.77409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −1.13768 1.30602i −0.656837 0.754032i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.890465 1.54233i 0.398228 0.689751i −0.595279 0.803519i \(-0.702959\pi\)
0.993507 + 0.113768i \(0.0362919\pi\)
\(6\) 0.332245 + 1.69989i 0.135638 + 0.693976i
\(7\) −2.00001 1.73204i −0.755933 0.654649i
\(8\) 1.00000i 0.353553i
\(9\) −0.411389 + 2.97166i −0.137130 + 0.990553i
\(10\) −1.54233 + 0.890465i −0.487728 + 0.281590i
\(11\) −0.864424 + 0.499076i −0.260634 + 0.150477i −0.624624 0.780926i \(-0.714748\pi\)
0.363990 + 0.931403i \(0.381414\pi\)
\(12\) 0.562211 1.63827i 0.162296 0.472927i
\(13\) 6.26372i 1.73724i 0.495476 + 0.868622i \(0.334994\pi\)
−0.495476 + 0.868622i \(0.665006\pi\)
\(14\) 0.866040 + 2.50000i 0.231459 + 0.668152i
\(15\) −3.02738 + 0.591704i −0.781666 + 0.152777i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.67970 + 2.90933i 0.407388 + 0.705617i 0.994596 0.103819i \(-0.0331063\pi\)
−0.587208 + 0.809436i \(0.699773\pi\)
\(18\) 1.84210 2.36784i 0.434188 0.558105i
\(19\) −1.42779 0.824336i −0.327558 0.189116i 0.327198 0.944956i \(-0.393895\pi\)
−0.654756 + 0.755840i \(0.727229\pi\)
\(20\) 1.78093 0.398228
\(21\) 0.0132797 + 4.58256i 0.00289787 + 0.999996i
\(22\) 0.998151 0.212807
\(23\) 0.866025 + 0.500000i 0.180579 + 0.104257i
\(24\) −1.30602 + 1.13768i −0.266591 + 0.232227i
\(25\) 0.914144 + 1.58334i 0.182829 + 0.316669i
\(26\) 3.13186 5.42454i 0.614208 1.06384i
\(27\) 4.34908 2.84350i 0.836981 0.547232i
\(28\) 0.499985 2.59808i 0.0944883 0.490991i
\(29\) 1.24938i 0.232004i 0.993249 + 0.116002i \(0.0370080\pi\)
−0.993249 + 0.116002i \(0.962992\pi\)
\(30\) 2.91764 + 1.00126i 0.532686 + 0.182804i
\(31\) −6.98992 + 4.03563i −1.25543 + 0.724821i −0.972182 0.234227i \(-0.924744\pi\)
−0.283245 + 0.959048i \(0.591411\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 1.63524 + 0.561171i 0.284658 + 0.0976874i
\(34\) 3.35941i 0.576134i
\(35\) −4.45232 + 1.54236i −0.752579 + 0.260706i
\(36\) −2.77923 + 1.12956i −0.463204 + 0.188259i
\(37\) 0.235496 0.407891i 0.0387153 0.0670569i −0.846018 0.533154i \(-0.821007\pi\)
0.884734 + 0.466097i \(0.154340\pi\)
\(38\) 0.824336 + 1.42779i 0.133725 + 0.231618i
\(39\) 8.18056 7.12608i 1.30994 1.14109i
\(40\) −1.54233 0.890465i −0.243864 0.140795i
\(41\) −4.34340 −0.678325 −0.339162 0.940728i \(-0.610144\pi\)
−0.339162 + 0.940728i \(0.610144\pi\)
\(42\) 2.27978 3.97525i 0.351777 0.613394i
\(43\) 4.79063 0.730565 0.365282 0.930897i \(-0.380972\pi\)
0.365282 + 0.930897i \(0.380972\pi\)
\(44\) −0.864424 0.499076i −0.130317 0.0752385i
\(45\) 4.21695 + 3.28066i 0.628626 + 0.489051i
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) 4.22866 7.32426i 0.616814 1.06835i −0.373250 0.927731i \(-0.621757\pi\)
0.990063 0.140622i \(-0.0449101\pi\)
\(48\) 1.69989 0.332245i 0.245357 0.0479554i
\(49\) 1.00008 + 6.92819i 0.142868 + 0.989742i
\(50\) 1.82829i 0.258559i
\(51\) 1.88870 5.50361i 0.264470 0.770659i
\(52\) −5.42454 + 3.13186i −0.752248 + 0.434311i
\(53\) −5.24099 + 3.02589i −0.719906 + 0.415638i −0.814718 0.579857i \(-0.803108\pi\)
0.0948123 + 0.995495i \(0.469775\pi\)
\(54\) −5.18816 + 0.288003i −0.706020 + 0.0391923i
\(55\) 1.77764i 0.239697i
\(56\) −1.73204 + 2.00001i −0.231454 + 0.267263i
\(57\) 0.547762 + 2.80256i 0.0725529 + 0.371207i
\(58\) 0.624691 1.08200i 0.0820260 0.142073i
\(59\) 0.600268 + 1.03970i 0.0781483 + 0.135357i 0.902451 0.430792i \(-0.141766\pi\)
−0.824303 + 0.566149i \(0.808433\pi\)
\(60\) −2.02612 2.32593i −0.261571 0.300277i
\(61\) 1.01927 + 0.588474i 0.130504 + 0.0753464i 0.563831 0.825890i \(-0.309327\pi\)
−0.433327 + 0.901237i \(0.642660\pi\)
\(62\) 8.07127 1.02505
\(63\) 5.96981 5.23081i 0.752126 0.659020i
\(64\) −1.00000 −0.125000
\(65\) 9.66073 + 5.57762i 1.19827 + 0.691819i
\(66\) −1.13557 1.30361i −0.139779 0.160463i
\(67\) 4.81654 + 8.34250i 0.588435 + 1.01920i 0.994438 + 0.105327i \(0.0335889\pi\)
−0.406003 + 0.913872i \(0.633078\pi\)
\(68\) −1.67970 + 2.90933i −0.203694 + 0.352809i
\(69\) −0.332245 1.69989i −0.0399976 0.204642i
\(70\) 4.62700 + 0.890439i 0.553032 + 0.106428i
\(71\) 9.62306i 1.14205i 0.820934 + 0.571023i \(0.193453\pi\)
−0.820934 + 0.571023i \(0.806547\pi\)
\(72\) 2.97166 + 0.411389i 0.350213 + 0.0484827i
\(73\) 9.57661 5.52906i 1.12086 0.647128i 0.179238 0.983806i \(-0.442637\pi\)
0.941620 + 0.336678i \(0.109303\pi\)
\(74\) −0.407891 + 0.235496i −0.0474164 + 0.0273759i
\(75\) 1.02788 2.99523i 0.118690 0.345859i
\(76\) 1.64867i 0.189116i
\(77\) 2.59328 + 0.499061i 0.295531 + 0.0568733i
\(78\) −10.6476 + 2.08109i −1.20560 + 0.235637i
\(79\) 0.576636 0.998763i 0.0648766 0.112370i −0.831763 0.555131i \(-0.812668\pi\)
0.896639 + 0.442762i \(0.146001\pi\)
\(80\) 0.890465 + 1.54233i 0.0995570 + 0.172438i
\(81\) −8.66152 2.44502i −0.962391 0.271668i
\(82\) 3.76149 + 2.17170i 0.415387 + 0.239824i
\(83\) −7.53838 −0.827445 −0.413722 0.910403i \(-0.635772\pi\)
−0.413722 + 0.910403i \(0.635772\pi\)
\(84\) −3.96197 + 2.30278i −0.432286 + 0.251254i
\(85\) 5.98287 0.648934
\(86\) −4.14881 2.39532i −0.447378 0.258294i
\(87\) 1.63172 1.42139i 0.174939 0.152389i
\(88\) 0.499076 + 0.864424i 0.0532016 + 0.0921480i
\(89\) 4.81612 8.34177i 0.510508 0.884225i −0.489418 0.872049i \(-0.662791\pi\)
0.999926 0.0121761i \(-0.00387588\pi\)
\(90\) −2.01166 4.94961i −0.212048 0.521735i
\(91\) 10.8490 12.5275i 1.13729 1.31324i
\(92\) 1.00000i 0.104257i
\(93\) 13.2229 + 4.53775i 1.37115 + 0.470543i
\(94\) −7.32426 + 4.22866i −0.755439 + 0.436153i
\(95\) −2.54280 + 1.46808i −0.260885 + 0.150622i
\(96\) −1.63827 0.562211i −0.167205 0.0573804i
\(97\) 11.6654i 1.18444i 0.805776 + 0.592220i \(0.201748\pi\)
−0.805776 + 0.592220i \(0.798252\pi\)
\(98\) 2.59800 6.50003i 0.262438 0.656602i
\(99\) −1.12747 2.77409i −0.113315 0.278806i
\(100\) −0.914144 + 1.58334i −0.0914144 + 0.158334i
\(101\) −8.67140 15.0193i −0.862836 1.49448i −0.869180 0.494496i \(-0.835353\pi\)
0.00634380 0.999980i \(-0.497981\pi\)
\(102\) −4.38746 + 3.82192i −0.434424 + 0.378426i
\(103\) 7.08086 + 4.08814i 0.697698 + 0.402816i 0.806490 0.591248i \(-0.201365\pi\)
−0.108791 + 0.994065i \(0.534698\pi\)
\(104\) 6.26372 0.614208
\(105\) 7.07964 + 4.06012i 0.690902 + 0.396228i
\(106\) 6.05178 0.587800
\(107\) 17.0877 + 9.86556i 1.65193 + 0.953740i 0.976279 + 0.216514i \(0.0694688\pi\)
0.675647 + 0.737226i \(0.263865\pi\)
\(108\) 4.63708 + 2.34466i 0.446204 + 0.225615i
\(109\) 7.96954 + 13.8036i 0.763343 + 1.32215i 0.941118 + 0.338078i \(0.109777\pi\)
−0.177775 + 0.984071i \(0.556890\pi\)
\(110\) 0.888819 1.53948i 0.0847455 0.146784i
\(111\) −0.800633 + 0.156485i −0.0759927 + 0.0148529i
\(112\) 2.50000 0.866040i 0.236227 0.0818330i
\(113\) 6.36516i 0.598784i −0.954130 0.299392i \(-0.903216\pi\)
0.954130 0.299392i \(-0.0967839\pi\)
\(114\) 0.926901 2.70097i 0.0868123 0.252969i
\(115\) 1.54233 0.890465i 0.143823 0.0830363i
\(116\) −1.08200 + 0.624691i −0.100461 + 0.0580011i
\(117\) −18.6136 2.57683i −1.72083 0.238228i
\(118\) 1.20054i 0.110518i
\(119\) 1.67966 8.72801i 0.153974 0.800095i
\(120\) 0.591704 + 3.02738i 0.0540150 + 0.276361i
\(121\) −5.00185 + 8.66345i −0.454713 + 0.787587i
\(122\) −0.588474 1.01927i −0.0532780 0.0922802i
\(123\) 4.94138 + 5.67257i 0.445549 + 0.511479i
\(124\) −6.98992 4.03563i −0.627713 0.362411i
\(125\) 12.1607 1.08769
\(126\) −7.78541 + 1.54510i −0.693580 + 0.137649i
\(127\) −1.66680 −0.147904 −0.0739522 0.997262i \(-0.523561\pi\)
−0.0739522 + 0.997262i \(0.523561\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −5.45019 6.25668i −0.479862 0.550870i
\(130\) −5.57762 9.66073i −0.489190 0.847302i
\(131\) 0.963948 1.66961i 0.0842205 0.145874i −0.820838 0.571161i \(-0.806493\pi\)
0.905059 + 0.425286i \(0.139827\pi\)
\(132\) 0.331630 + 1.69674i 0.0288647 + 0.147683i
\(133\) 1.42782 + 4.12167i 0.123807 + 0.357394i
\(134\) 9.63309i 0.832172i
\(135\) −0.512914 9.23976i −0.0441446 0.795232i
\(136\) 2.90933 1.67970i 0.249473 0.144033i
\(137\) −7.54322 + 4.35508i −0.644461 + 0.372080i −0.786331 0.617806i \(-0.788022\pi\)
0.141870 + 0.989885i \(0.454688\pi\)
\(138\) −0.562211 + 1.63827i −0.0478586 + 0.139459i
\(139\) 0.941550i 0.0798613i 0.999202 + 0.0399306i \(0.0127137\pi\)
−0.999202 + 0.0399306i \(0.987286\pi\)
\(140\) −3.56188 3.08464i −0.301034 0.260700i
\(141\) −14.3765 + 2.80990i −1.21072 + 0.236636i
\(142\) 4.81153 8.33381i 0.403774 0.699358i
\(143\) −3.12607 5.41451i −0.261415 0.452784i
\(144\) −2.36784 1.84210i −0.197320 0.153509i
\(145\) 1.92696 + 1.11253i 0.160025 + 0.0923907i
\(146\) −11.0581 −0.915177
\(147\) 7.91061 9.18816i 0.652456 0.757827i
\(148\) 0.470992 0.0387153
\(149\) 0.753321 + 0.434930i 0.0617144 + 0.0356309i 0.530540 0.847660i \(-0.321989\pi\)
−0.468825 + 0.883291i \(0.655323\pi\)
\(150\) −2.38779 + 2.08000i −0.194962 + 0.169831i
\(151\) 3.57086 + 6.18491i 0.290593 + 0.503321i 0.973950 0.226763i \(-0.0728142\pi\)
−0.683357 + 0.730084i \(0.739481\pi\)
\(152\) −0.824336 + 1.42779i −0.0668625 + 0.115809i
\(153\) −9.33656 + 3.79464i −0.754816 + 0.306779i
\(154\) −1.99631 1.72884i −0.160867 0.139314i
\(155\) 14.3744i 1.15458i
\(156\) 10.2616 + 3.52153i 0.821589 + 0.281948i
\(157\) −11.8872 + 6.86308i −0.948702 + 0.547733i −0.892677 0.450696i \(-0.851176\pi\)
−0.0560243 + 0.998429i \(0.517842\pi\)
\(158\) −0.998763 + 0.576636i −0.0794573 + 0.0458747i
\(159\) 9.91443 + 3.40237i 0.786265 + 0.269826i
\(160\) 1.78093i 0.140795i
\(161\) −0.866040 2.50000i −0.0682535 0.197027i
\(162\) 6.27859 + 6.44821i 0.493292 + 0.506619i
\(163\) 4.67610 8.09924i 0.366260 0.634381i −0.622717 0.782447i \(-0.713971\pi\)
0.988978 + 0.148066i \(0.0473047\pi\)
\(164\) −2.17170 3.76149i −0.169581 0.293723i
\(165\) 2.32163 2.02237i 0.180739 0.157442i
\(166\) 6.52843 + 3.76919i 0.506704 + 0.292546i
\(167\) −24.8198 −1.92061 −0.960307 0.278945i \(-0.910015\pi\)
−0.960307 + 0.278945i \(0.910015\pi\)
\(168\) 4.58256 0.0132797i 0.353552 0.00102455i
\(169\) −26.2342 −2.01801
\(170\) −5.18132 2.99144i −0.397389 0.229433i
\(171\) 3.03702 3.90379i 0.232247 0.298530i
\(172\) 2.39532 + 4.14881i 0.182641 + 0.316344i
\(173\) −1.64788 + 2.85421i −0.125286 + 0.217002i −0.921845 0.387560i \(-0.873318\pi\)
0.796559 + 0.604561i \(0.206651\pi\)
\(174\) −2.12381 + 0.415101i −0.161005 + 0.0314687i
\(175\) 0.914118 4.75004i 0.0691008 0.359069i
\(176\) 0.998151i 0.0752385i
\(177\) 0.674955 1.96680i 0.0507327 0.147834i
\(178\) −8.34177 + 4.81612i −0.625242 + 0.360984i
\(179\) −19.3860 + 11.1925i −1.44897 + 0.836566i −0.998420 0.0561832i \(-0.982107\pi\)
−0.450554 + 0.892749i \(0.648774\pi\)
\(180\) −0.732655 + 5.29232i −0.0546089 + 0.394466i
\(181\) 2.62713i 0.195273i 0.995222 + 0.0976366i \(0.0311283\pi\)
−0.995222 + 0.0976366i \(0.968872\pi\)
\(182\) −15.6593 + 5.42463i −1.16074 + 0.402100i
\(183\) −0.391035 2.00068i −0.0289061 0.147894i
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −0.419402 0.726425i −0.0308350 0.0534079i
\(186\) −9.18248 10.5413i −0.673292 0.772922i
\(187\) −2.90396 1.67660i −0.212358 0.122605i
\(188\) 8.45732 0.616814
\(189\) −13.6233 1.84575i −0.990946 0.134259i
\(190\) 2.93617 0.213012
\(191\) −4.07616 2.35337i −0.294941 0.170284i 0.345227 0.938519i \(-0.387802\pi\)
−0.640168 + 0.768235i \(0.721135\pi\)
\(192\) 1.13768 + 1.30602i 0.0821047 + 0.0942540i
\(193\) 0.532666 + 0.922605i 0.0383422 + 0.0664106i 0.884560 0.466427i \(-0.154459\pi\)
−0.846218 + 0.532838i \(0.821126\pi\)
\(194\) 5.83269 10.1025i 0.418763 0.725318i
\(195\) −3.70627 18.9626i −0.265412 1.35794i
\(196\) −5.49995 + 4.33019i −0.392854 + 0.309299i
\(197\) 16.9781i 1.20964i 0.796362 + 0.604820i \(0.206755\pi\)
−0.796362 + 0.604820i \(0.793245\pi\)
\(198\) −0.410628 + 2.96617i −0.0291821 + 0.210796i
\(199\) 1.85652 1.07186i 0.131605 0.0759823i −0.432752 0.901513i \(-0.642457\pi\)
0.564357 + 0.825531i \(0.309124\pi\)
\(200\) 1.58334 0.914144i 0.111959 0.0646398i
\(201\) 5.41583 15.7816i 0.382003 1.11315i
\(202\) 17.3428i 1.22023i
\(203\) 2.16398 2.49878i 0.151882 0.175380i
\(204\) 5.71061 1.11615i 0.399823 0.0781458i
\(205\) −3.86764 + 6.69895i −0.270128 + 0.467875i
\(206\) −4.08814 7.08086i −0.284834 0.493347i
\(207\) −1.84210 + 2.36784i −0.128035 + 0.164576i
\(208\) −5.42454 3.13186i −0.376124 0.217155i
\(209\) 1.64562 0.113830
\(210\) −4.10109 7.05599i −0.283002 0.486910i
\(211\) −25.7800 −1.77477 −0.887385 0.461029i \(-0.847480\pi\)
−0.887385 + 0.461029i \(0.847480\pi\)
\(212\) −5.24099 3.02589i −0.359953 0.207819i
\(213\) 12.5679 10.9479i 0.861140 0.750139i
\(214\) −9.86556 17.0877i −0.674396 1.16809i
\(215\) 4.26589 7.38874i 0.290931 0.503908i
\(216\) −2.84350 4.34908i −0.193476 0.295917i
\(217\) 20.9698 + 4.03551i 1.42352 + 0.273949i
\(218\) 15.9391i 1.07953i
\(219\) −18.1162 6.21700i −1.22418 0.420106i
\(220\) −1.53948 + 0.888819i −0.103792 + 0.0599241i
\(221\) −18.2233 + 10.5212i −1.22583 + 0.707732i
\(222\) 0.771611 + 0.264797i 0.0517871 + 0.0177720i
\(223\) 10.0664i 0.674094i 0.941488 + 0.337047i \(0.109428\pi\)
−0.941488 + 0.337047i \(0.890572\pi\)
\(224\) −2.59808 0.499985i −0.173591 0.0334067i
\(225\) −5.08123 + 2.06516i −0.338749 + 0.137677i
\(226\) −3.18258 + 5.51239i −0.211702 + 0.366679i
\(227\) 13.1471 + 22.7715i 0.872604 + 1.51140i 0.859293 + 0.511484i \(0.170904\pi\)
0.0133113 + 0.999911i \(0.495763\pi\)
\(228\) −2.15320 + 1.87565i −0.142599 + 0.124218i
\(229\) −17.0205 9.82677i −1.12474 0.649371i −0.182136 0.983273i \(-0.558301\pi\)
−0.942608 + 0.333902i \(0.891635\pi\)
\(230\) −1.78093 −0.117431
\(231\) −2.29852 3.95465i −0.151232 0.260197i
\(232\) 1.24938 0.0820260
\(233\) 2.78352 + 1.60706i 0.182354 + 0.105282i 0.588398 0.808571i \(-0.299759\pi\)
−0.406044 + 0.913853i \(0.633092\pi\)
\(234\) 14.8315 + 11.5384i 0.969564 + 0.754290i
\(235\) −7.53095 13.0440i −0.491265 0.850896i
\(236\) −0.600268 + 1.03970i −0.0390741 + 0.0676784i
\(237\) −1.96043 + 0.383168i −0.127344 + 0.0248895i
\(238\) −5.81863 + 6.71885i −0.377166 + 0.435518i
\(239\) 8.42177i 0.544759i −0.962190 0.272380i \(-0.912189\pi\)
0.962190 0.272380i \(-0.0878106\pi\)
\(240\) 1.00126 2.91764i 0.0646309 0.188333i
\(241\) 7.66278 4.42411i 0.493603 0.284982i −0.232465 0.972605i \(-0.574679\pi\)
0.726068 + 0.687623i \(0.241346\pi\)
\(242\) 8.66345 5.00185i 0.556908 0.321531i
\(243\) 6.66075 + 14.0938i 0.427287 + 0.904116i
\(244\) 1.17695i 0.0753464i
\(245\) 11.5761 + 4.62686i 0.739570 + 0.295599i
\(246\) −1.44307 7.38328i −0.0920068 0.470741i
\(247\) 5.16341 8.94329i 0.328540 0.569048i
\(248\) 4.03563 + 6.98992i 0.256263 + 0.443860i
\(249\) 8.57623 + 9.84529i 0.543497 + 0.623920i
\(250\) −10.5315 6.08035i −0.666069 0.384555i
\(251\) −28.0228 −1.76879 −0.884393 0.466743i \(-0.845427\pi\)
−0.884393 + 0.466743i \(0.845427\pi\)
\(252\) 7.51492 + 2.55461i 0.473395 + 0.160925i
\(253\) −0.998151 −0.0627532
\(254\) 1.44349 + 0.833399i 0.0905726 + 0.0522921i
\(255\) −6.80657 7.81376i −0.426244 0.489317i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.26044 10.8434i 0.390516 0.676393i −0.602002 0.798495i \(-0.705630\pi\)
0.992518 + 0.122102i \(0.0389634\pi\)
\(258\) 1.59166 + 8.14353i 0.0990926 + 0.506994i
\(259\) −1.17748 + 0.407898i −0.0731649 + 0.0253455i
\(260\) 11.1552i 0.691819i
\(261\) −3.71274 0.513982i −0.229813 0.0318147i
\(262\) −1.66961 + 0.963948i −0.103149 + 0.0595529i
\(263\) −7.36275 + 4.25089i −0.454007 + 0.262121i −0.709521 0.704684i \(-0.751089\pi\)
0.255514 + 0.966805i \(0.417755\pi\)
\(264\) 0.561171 1.63524i 0.0345377 0.100642i
\(265\) 10.7778i 0.662074i
\(266\) 0.824312 4.28338i 0.0505418 0.262631i
\(267\) −16.3737 + 3.20026i −1.00206 + 0.195853i
\(268\) −4.81654 + 8.34250i −0.294217 + 0.509599i
\(269\) 5.33348 + 9.23785i 0.325188 + 0.563242i 0.981550 0.191204i \(-0.0612391\pi\)
−0.656363 + 0.754446i \(0.727906\pi\)
\(270\) −4.17568 + 8.25832i −0.254124 + 0.502585i
\(271\) 10.1811 + 5.87807i 0.618459 + 0.357067i 0.776269 0.630402i \(-0.217110\pi\)
−0.157810 + 0.987469i \(0.550443\pi\)
\(272\) −3.35941 −0.203694
\(273\) −28.7038 + 0.0831803i −1.73724 + 0.00503430i
\(274\) 8.71016 0.526200
\(275\) −1.58042 0.912454i −0.0953028 0.0550231i
\(276\) 1.30602 1.13768i 0.0786133 0.0684800i
\(277\) 8.89694 + 15.4099i 0.534565 + 0.925894i 0.999184 + 0.0403832i \(0.0128579\pi\)
−0.464619 + 0.885511i \(0.653809\pi\)
\(278\) 0.470775 0.815407i 0.0282352 0.0489048i
\(279\) −9.11695 22.4319i −0.545817 1.34296i
\(280\) 1.54236 + 4.45232i 0.0921734 + 0.266077i
\(281\) 1.55697i 0.0928810i −0.998921 0.0464405i \(-0.985212\pi\)
0.998921 0.0464405i \(-0.0147878\pi\)
\(282\) 13.8554 + 4.75480i 0.825074 + 0.283144i
\(283\) 24.6744 14.2458i 1.46674 0.846822i 0.467432 0.884029i \(-0.345179\pi\)
0.999308 + 0.0372070i \(0.0118461\pi\)
\(284\) −8.33381 + 4.81153i −0.494521 + 0.285512i
\(285\) 4.81023 + 1.65075i 0.284933 + 0.0977818i
\(286\) 6.25214i 0.369697i
\(287\) 8.68684 + 7.52294i 0.512768 + 0.444065i
\(288\) 1.12956 + 2.77923i 0.0665597 + 0.163768i
\(289\) 2.85719 4.94879i 0.168070 0.291105i
\(290\) −1.11253 1.92696i −0.0653301 0.113155i
\(291\) 15.2352 13.2714i 0.893106 0.777984i
\(292\) 9.57661 + 5.52906i 0.560429 + 0.323564i
\(293\) 13.8727 0.810454 0.405227 0.914216i \(-0.367193\pi\)
0.405227 + 0.914216i \(0.367193\pi\)
\(294\) −11.4449 + 4.00187i −0.667478 + 0.233394i
\(295\) 2.13807 0.124483
\(296\) −0.407891 0.235496i −0.0237082 0.0136879i
\(297\) −2.34033 + 4.62851i −0.135800 + 0.268573i
\(298\) −0.434930 0.753321i −0.0251948 0.0436387i
\(299\) −3.13186 + 5.42454i −0.181120 + 0.313709i
\(300\) 3.10788 0.607439i 0.179434 0.0350705i
\(301\) −9.58132 8.29757i −0.552258 0.478264i
\(302\) 7.14172i 0.410960i
\(303\) −9.75030 + 28.4121i −0.560140 + 1.63223i
\(304\) 1.42779 0.824336i 0.0818895 0.0472789i
\(305\) 1.81524 1.04803i 0.103941 0.0600101i
\(306\) 9.98302 + 1.38202i 0.570691 + 0.0790051i
\(307\) 26.0728i 1.48805i −0.668151 0.744025i \(-0.732914\pi\)
0.668151 0.744025i \(-0.267086\pi\)
\(308\) 0.864439 + 2.49537i 0.0492560 + 0.142187i
\(309\) −2.71652 13.8987i −0.154538 0.790672i
\(310\) 7.18718 12.4486i 0.408204 0.707031i
\(311\) −4.89012 8.46993i −0.277293 0.480286i 0.693418 0.720536i \(-0.256104\pi\)
−0.970711 + 0.240250i \(0.922771\pi\)
\(312\) −7.12608 8.18056i −0.403435 0.463133i
\(313\) −14.9080 8.60715i −0.842651 0.486505i 0.0155136 0.999880i \(-0.495062\pi\)
−0.858164 + 0.513375i \(0.828395\pi\)
\(314\) 13.7262 0.774612
\(315\) −2.75172 13.8653i −0.155042 0.781220i
\(316\) 1.15327 0.0648766
\(317\) 7.16590 + 4.13723i 0.402477 + 0.232370i 0.687552 0.726135i \(-0.258685\pi\)
−0.285075 + 0.958505i \(0.592019\pi\)
\(318\) −6.88496 7.90376i −0.386089 0.443221i
\(319\) −0.623536 1.08000i −0.0349113 0.0604682i
\(320\) −0.890465 + 1.54233i −0.0497785 + 0.0862189i
\(321\) −6.55556 33.5407i −0.365896 1.87206i
\(322\) −0.499985 + 2.59808i −0.0278631 + 0.144785i
\(323\) 5.53856i 0.308174i
\(324\) −2.21331 8.72360i −0.122962 0.484645i
\(325\) −9.91763 + 5.72594i −0.550131 + 0.317618i
\(326\) −8.09924 + 4.67610i −0.448575 + 0.258985i
\(327\) 8.96112 26.1125i 0.495551 1.44402i
\(328\) 4.34340i 0.239824i
\(329\) −21.1433 + 7.32438i −1.16567 + 0.403806i
\(330\) −3.02178 + 0.590611i −0.166344 + 0.0325120i
\(331\) 8.69571 15.0614i 0.477959 0.827850i −0.521721 0.853116i \(-0.674710\pi\)
0.999681 + 0.0252659i \(0.00804325\pi\)
\(332\) −3.76919 6.52843i −0.206861 0.358294i
\(333\) 1.11523 + 0.867616i 0.0611144 + 0.0475451i
\(334\) 21.4946 + 12.4099i 1.17613 + 0.679040i
\(335\) 17.1559 0.937325
\(336\) −3.97525 2.27978i −0.216868 0.124372i
\(337\) 24.0061 1.30770 0.653848 0.756626i \(-0.273153\pi\)
0.653848 + 0.756626i \(0.273153\pi\)
\(338\) 22.7195 + 13.1171i 1.23578 + 0.713476i
\(339\) −8.31305 + 7.24149i −0.451503 + 0.393304i
\(340\) 2.99144 + 5.18132i 0.162233 + 0.280996i
\(341\) 4.02817 6.97700i 0.218138 0.377826i
\(342\) −4.58203 + 1.86227i −0.247768 + 0.100700i
\(343\) 9.99974 15.5886i 0.539935 0.841707i
\(344\) 4.79063i 0.258294i
\(345\) −2.91764 1.00126i −0.157080 0.0539059i
\(346\) 2.85421 1.64788i 0.153443 0.0885905i
\(347\) −20.7550 + 11.9829i −1.11419 + 0.643276i −0.939911 0.341420i \(-0.889092\pi\)
−0.174277 + 0.984697i \(0.555759\pi\)
\(348\) 2.04682 + 0.702416i 0.109721 + 0.0376535i
\(349\) 25.6100i 1.37087i 0.728132 + 0.685437i \(0.240389\pi\)
−0.728132 + 0.685437i \(0.759611\pi\)
\(350\) −3.16667 + 3.65660i −0.169266 + 0.195453i
\(351\) 17.8109 + 27.2414i 0.950675 + 1.45404i
\(352\) −0.499076 + 0.864424i −0.0266008 + 0.0460740i
\(353\) 3.17800 + 5.50445i 0.169148 + 0.292972i 0.938120 0.346309i \(-0.112565\pi\)
−0.768973 + 0.639281i \(0.779232\pi\)
\(354\) −1.56793 + 1.36582i −0.0833344 + 0.0725926i
\(355\) 14.8419 + 8.56899i 0.787728 + 0.454795i
\(356\) 9.63224 0.510508
\(357\) −13.3099 + 7.73598i −0.704434 + 0.409431i
\(358\) 22.3850 1.18308
\(359\) 21.2047 + 12.2425i 1.11914 + 0.646136i 0.941181 0.337902i \(-0.109717\pi\)
0.177959 + 0.984038i \(0.443051\pi\)
\(360\) 3.28066 4.21695i 0.172906 0.222253i
\(361\) −8.14094 14.1005i −0.428471 0.742133i
\(362\) 1.31357 2.27516i 0.0690395 0.119580i
\(363\) 17.0051 3.32367i 0.892539 0.174448i
\(364\) 16.2736 + 3.13177i 0.852970 + 0.164149i
\(365\) 19.6937i 1.03082i
\(366\) −0.661693 + 1.92816i −0.0345873 + 0.100786i
\(367\) −25.7670 + 14.8766i −1.34503 + 0.776552i −0.987540 0.157365i \(-0.949700\pi\)
−0.357488 + 0.933918i \(0.616367\pi\)
\(368\) −0.866025 + 0.500000i −0.0451447 + 0.0260643i
\(369\) 1.78683 12.9071i 0.0930184 0.671917i
\(370\) 0.838804i 0.0436073i
\(371\) 15.7230 + 3.02580i 0.816297 + 0.157092i
\(372\) 2.68163 + 13.7202i 0.139036 + 0.711361i
\(373\) −4.84352 + 8.38922i −0.250788 + 0.434377i −0.963743 0.266832i \(-0.914023\pi\)
0.712955 + 0.701210i \(0.247356\pi\)
\(374\) 1.67660 + 2.90396i 0.0866949 + 0.150160i
\(375\) −13.8349 15.8822i −0.714433 0.820151i
\(376\) −7.32426 4.22866i −0.377720 0.218077i
\(377\) −7.82578 −0.403048
\(378\) 10.8752 + 8.41010i 0.559361 + 0.432569i
\(379\) −20.7752 −1.06715 −0.533576 0.845752i \(-0.679152\pi\)
−0.533576 + 0.845752i \(0.679152\pi\)
\(380\) −2.54280 1.46808i −0.130443 0.0753112i
\(381\) 1.89628 + 2.17688i 0.0971491 + 0.111525i
\(382\) 2.35337 + 4.07616i 0.120409 + 0.208555i
\(383\) 4.36899 7.56732i 0.223245 0.386672i −0.732546 0.680717i \(-0.761668\pi\)
0.955791 + 0.294045i \(0.0950016\pi\)
\(384\) −0.332245 1.69989i −0.0169548 0.0867470i
\(385\) 3.07894 3.55529i 0.156917 0.181194i
\(386\) 1.06533i 0.0542240i
\(387\) −1.97081 + 14.2361i −0.100182 + 0.723663i
\(388\) −10.1025 + 5.83269i −0.512878 + 0.296110i
\(389\) −20.6982 + 11.9501i −1.04944 + 0.605895i −0.922493 0.386015i \(-0.873851\pi\)
−0.126948 + 0.991909i \(0.540518\pi\)
\(390\) −6.27160 + 18.2753i −0.317575 + 0.925404i
\(391\) 3.35941i 0.169893i
\(392\) 6.92819 1.00008i 0.349927 0.0505116i
\(393\) −3.27720 + 0.640533i −0.165313 + 0.0323106i
\(394\) 8.48905 14.7035i 0.427672 0.740750i
\(395\) −1.02695 1.77873i −0.0516714 0.0894974i
\(396\) 1.83870 2.36346i 0.0923980 0.118768i
\(397\) 26.7399 + 15.4383i 1.34204 + 0.774825i 0.987106 0.160067i \(-0.0511711\pi\)
0.354931 + 0.934893i \(0.384504\pi\)
\(398\) −2.14372 −0.107455
\(399\) 3.75861 6.55388i 0.188166 0.328105i
\(400\) −1.82829 −0.0914144
\(401\) 28.6452 + 16.5383i 1.43047 + 0.825883i 0.997156 0.0753598i \(-0.0240105\pi\)
0.433315 + 0.901243i \(0.357344\pi\)
\(402\) −12.5810 + 10.9593i −0.627485 + 0.546602i
\(403\) −25.2781 43.7829i −1.25919 2.18098i
\(404\) 8.67140 15.0193i 0.431418 0.747238i
\(405\) −11.4838 + 11.1817i −0.570635 + 0.555624i
\(406\) −3.12345 + 1.08201i −0.155014 + 0.0536995i
\(407\) 0.470121i 0.0233031i
\(408\) −5.50361 1.88870i −0.272469 0.0935044i
\(409\) 30.8832 17.8304i 1.52707 0.881657i 0.527591 0.849498i \(-0.323095\pi\)
0.999483 0.0321581i \(-0.0102380\pi\)
\(410\) 6.69895 3.86764i 0.330838 0.191009i
\(411\) 14.2696 + 4.89695i 0.703866 + 0.241549i
\(412\) 8.17628i 0.402816i
\(413\) 0.600251 3.11909i 0.0295364 0.153480i
\(414\) 2.77923 1.12956i 0.136592 0.0555147i
\(415\) −6.71266 + 11.6267i −0.329512 + 0.570731i
\(416\) 3.13186 + 5.42454i 0.153552 + 0.265960i
\(417\) 1.22969 1.07118i 0.0602180 0.0524559i
\(418\) −1.42515 0.822812i −0.0697065 0.0402451i
\(419\) −22.3712 −1.09291 −0.546454 0.837489i \(-0.684022\pi\)
−0.546454 + 0.837489i \(0.684022\pi\)
\(420\) 0.0236502 + 8.16121i 0.00115401 + 0.398226i
\(421\) −7.17807 −0.349838 −0.174919 0.984583i \(-0.555966\pi\)
−0.174919 + 0.984583i \(0.555966\pi\)
\(422\) 22.3262 + 12.8900i 1.08682 + 0.627476i
\(423\) 20.0256 + 15.5793i 0.973677 + 0.757490i
\(424\) 3.02589 + 5.24099i 0.146950 + 0.254525i
\(425\) −3.07099 + 5.31910i −0.148965 + 0.258014i
\(426\) −16.3581 + 3.19721i −0.792553 + 0.154905i
\(427\) −1.01928 2.94237i −0.0493266 0.142391i
\(428\) 19.7311i 0.953740i
\(429\) −3.51502 + 10.2427i −0.169707 + 0.494521i
\(430\) −7.38874 + 4.26589i −0.356317 + 0.205720i
\(431\) 12.9486 7.47587i 0.623712 0.360100i −0.154601 0.987977i \(-0.549409\pi\)
0.778313 + 0.627877i \(0.216076\pi\)
\(432\) 0.288003 + 5.18816i 0.0138566 + 0.249616i
\(433\) 15.7882i 0.758735i 0.925246 + 0.379367i \(0.123858\pi\)
−0.925246 + 0.379367i \(0.876142\pi\)
\(434\) −16.1426 13.9798i −0.774870 0.671050i
\(435\) −0.739265 3.78235i −0.0354450 0.181350i
\(436\) −7.96954 + 13.8036i −0.381672 + 0.661075i
\(437\) −0.824336 1.42779i −0.0394333 0.0683005i
\(438\) 12.5806 + 14.4422i 0.601122 + 0.690073i
\(439\) −35.6172 20.5636i −1.69992 0.981448i −0.945824 0.324681i \(-0.894743\pi\)
−0.754094 0.656767i \(-0.771924\pi\)
\(440\) 1.77764 0.0847455
\(441\) −20.9996 + 0.121710i −0.999983 + 0.00579571i
\(442\) 21.0424 1.00088
\(443\) −12.6002 7.27471i −0.598652 0.345632i 0.169859 0.985468i \(-0.445669\pi\)
−0.768511 + 0.639837i \(0.779002\pi\)
\(444\) −0.535836 0.615126i −0.0254297 0.0291926i
\(445\) −8.57717 14.8561i −0.406597 0.704247i
\(446\) 5.03319 8.71774i 0.238328 0.412797i
\(447\) −0.289006 1.47866i −0.0136695 0.0699384i
\(448\) 2.00001 + 1.73204i 0.0944916 + 0.0818312i
\(449\) 5.90954i 0.278889i 0.990230 + 0.139444i \(0.0445316\pi\)
−0.990230 + 0.139444i \(0.955468\pi\)
\(450\) 5.43305 + 0.752138i 0.256117 + 0.0354561i
\(451\) 3.75454 2.16768i 0.176794 0.102072i
\(452\) 5.51239 3.18258i 0.259281 0.149696i
\(453\) 4.01515 11.7001i 0.188648 0.549716i
\(454\) 26.2942i 1.23405i
\(455\) −9.66088 27.8881i −0.452909 1.30741i
\(456\) 2.80256 0.547762i 0.131242 0.0256513i
\(457\) 3.47842 6.02479i 0.162713 0.281828i −0.773127 0.634251i \(-0.781309\pi\)
0.935841 + 0.352423i \(0.114642\pi\)
\(458\) 9.82677 + 17.0205i 0.459175 + 0.795314i
\(459\) 15.5779 + 7.87669i 0.727112 + 0.367652i
\(460\) 1.54233 + 0.890465i 0.0719115 + 0.0415181i
\(461\) 18.8889 0.879742 0.439871 0.898061i \(-0.355024\pi\)
0.439871 + 0.898061i \(0.355024\pi\)
\(462\) 0.0132551 + 4.57408i 0.000616685 + 0.212806i
\(463\) 17.2700 0.802607 0.401304 0.915945i \(-0.368557\pi\)
0.401304 + 0.915945i \(0.368557\pi\)
\(464\) −1.08200 0.624691i −0.0502304 0.0290006i
\(465\) 18.7732 16.3534i 0.870588 0.758369i
\(466\) −1.60706 2.78352i −0.0744458 0.128944i
\(467\) −9.47185 + 16.4057i −0.438305 + 0.759166i −0.997559 0.0698300i \(-0.977754\pi\)
0.559254 + 0.828996i \(0.311088\pi\)
\(468\) −7.07522 17.4083i −0.327052 0.804699i
\(469\) 4.81640 25.0275i 0.222401 1.15566i
\(470\) 15.0619i 0.694754i
\(471\) 22.4871 + 7.71699i 1.03615 + 0.355580i
\(472\) 1.03970 0.600268i 0.0478558 0.0276296i
\(473\) −4.14114 + 2.39089i −0.190410 + 0.109933i
\(474\) 1.88937 + 0.648382i 0.0867815 + 0.0297812i
\(475\) 3.01425i 0.138303i
\(476\) 8.39851 2.90938i 0.384945 0.133351i
\(477\) −6.83582 16.8193i −0.312991 0.770101i
\(478\) −4.21089 + 7.29347i −0.192601 + 0.333595i
\(479\) −0.290036 0.502357i −0.0132521 0.0229533i 0.859323 0.511433i \(-0.170885\pi\)
−0.872575 + 0.488479i \(0.837552\pi\)
\(480\) −2.32593 + 2.02612i −0.106164 + 0.0924793i
\(481\) 2.55492 + 1.47508i 0.116494 + 0.0672579i
\(482\) −8.84821 −0.403025
\(483\) −2.27978 + 3.97525i −0.103733 + 0.180880i
\(484\) −10.0037 −0.454713
\(485\) 17.9919 + 10.3876i 0.816969 + 0.471677i
\(486\) 1.27851 15.5359i 0.0579942 0.704725i
\(487\) −7.33055 12.6969i −0.332179 0.575351i 0.650760 0.759284i \(-0.274450\pi\)
−0.982939 + 0.183933i \(0.941117\pi\)
\(488\) 0.588474 1.01927i 0.0266390 0.0461401i
\(489\) −15.8977 + 3.10722i −0.718917 + 0.140513i
\(490\) −7.71176 9.79503i −0.348382 0.442494i
\(491\) 21.9498i 0.990579i 0.868728 + 0.495290i \(0.164938\pi\)
−0.868728 + 0.495290i \(0.835062\pi\)
\(492\) −2.44191 + 7.11564i −0.110090 + 0.320798i
\(493\) −3.63487 + 2.09859i −0.163706 + 0.0945159i
\(494\) −8.94329 + 5.16341i −0.402378 + 0.232313i
\(495\) −5.28253 0.731301i −0.237432 0.0328695i
\(496\) 8.07127i 0.362411i
\(497\) 16.6675 19.2462i 0.747640 0.863310i
\(498\) −2.50459 12.8144i −0.112233 0.574227i
\(499\) −16.6874 + 28.9034i −0.747029 + 1.29389i 0.202212 + 0.979342i \(0.435187\pi\)
−0.949241 + 0.314550i \(0.898146\pi\)
\(500\) 6.08035 + 10.5315i 0.271922 + 0.470982i
\(501\) 28.2369 + 32.4152i 1.26153 + 1.44821i
\(502\) 24.2685 + 14.0114i 1.08316 + 0.625360i
\(503\) 13.0707 0.582793 0.291396 0.956602i \(-0.405880\pi\)
0.291396 + 0.956602i \(0.405880\pi\)
\(504\) −5.23081 5.96981i −0.232999 0.265917i
\(505\) −30.8863 −1.37442
\(506\) 0.864424 + 0.499076i 0.0384284 + 0.0221866i
\(507\) 29.8460 + 34.2624i 1.32551 + 1.52165i
\(508\) −0.833399 1.44349i −0.0369761 0.0640445i
\(509\) 7.51025 13.0081i 0.332886 0.576575i −0.650190 0.759771i \(-0.725311\pi\)
0.983076 + 0.183196i \(0.0586442\pi\)
\(510\) 1.98778 + 10.1702i 0.0880203 + 0.450344i
\(511\) −28.7299 5.52890i −1.27093 0.244584i
\(512\) 1.00000i 0.0441942i
\(513\) −8.55358 + 0.474823i −0.377650 + 0.0209640i
\(514\) −10.8434 + 6.26044i −0.478282 + 0.276136i
\(515\) 12.6105 7.28069i 0.555686 0.320825i
\(516\) 2.69335 7.84834i 0.118568 0.345504i
\(517\) 8.44169i 0.371265i
\(518\) 1.22367 + 0.235489i 0.0537652 + 0.0103468i
\(519\) 5.60241 1.09500i 0.245919 0.0480651i
\(520\) 5.57762 9.66073i 0.244595 0.423651i
\(521\) −1.62224 2.80981i −0.0710718 0.123100i 0.828300 0.560286i \(-0.189309\pi\)
−0.899371 + 0.437186i \(0.855975\pi\)
\(522\) 2.95833 + 2.30149i 0.129483 + 0.100734i
\(523\) 15.4763 + 8.93522i 0.676730 + 0.390710i 0.798622 0.601833i \(-0.205563\pi\)
−0.121892 + 0.992543i \(0.538896\pi\)
\(524\) 1.92790 0.0842205
\(525\) −7.24363 + 4.21014i −0.316138 + 0.183746i
\(526\) 8.50177 0.370695
\(527\) −23.4820 13.5573i −1.02289 0.590567i
\(528\) −1.30361 + 1.13557i −0.0567323 + 0.0494194i
\(529\) 0.500000 + 0.866025i 0.0217391 + 0.0376533i
\(530\) 5.38889 9.33384i 0.234079 0.405436i
\(531\) −3.33656 + 1.35607i −0.144795 + 0.0588486i
\(532\) −2.85557 + 3.29736i −0.123804 + 0.142959i
\(533\) 27.2058i 1.17841i
\(534\) 15.7802 + 5.41535i 0.682875 + 0.234345i
\(535\) 30.4319 17.5699i 1.31569 0.759612i
\(536\) 8.34250 4.81654i 0.360341 0.208043i
\(537\) 36.6726 + 12.5851i 1.58254 + 0.543086i
\(538\) 10.6670i 0.459885i
\(539\) −4.32218 5.48978i −0.186170 0.236462i
\(540\) 7.74541 5.06408i 0.333309 0.217923i
\(541\) −14.0263 + 24.2942i −0.603037 + 1.04449i 0.389321 + 0.921102i \(0.372710\pi\)
−0.992358 + 0.123389i \(0.960624\pi\)
\(542\) −5.87807 10.1811i −0.252485 0.437316i
\(543\) 3.43109 2.98882i 0.147242 0.128263i
\(544\) 2.90933 + 1.67970i 0.124737 + 0.0720167i
\(545\) 28.3864 1.21594
\(546\) 24.8999 + 14.2799i 1.06562 + 0.611123i
\(547\) 1.55799 0.0666150 0.0333075 0.999445i \(-0.489396\pi\)
0.0333075 + 0.999445i \(0.489396\pi\)
\(548\) −7.54322 4.35508i −0.322230 0.186040i
\(549\) −2.16806 + 2.78682i −0.0925306 + 0.118939i
\(550\) 0.912454 + 1.58042i 0.0389072 + 0.0673892i
\(551\) 1.02991 1.78386i 0.0438757 0.0759949i
\(552\) −1.69989 + 0.332245i −0.0723520 + 0.0141413i
\(553\) −2.88317 + 0.998779i −0.122605 + 0.0424724i
\(554\) 17.7939i 0.755989i
\(555\) −0.471585 + 1.37418i −0.0200177 + 0.0583309i
\(556\) −0.815407 + 0.470775i −0.0345809 + 0.0199653i
\(557\) 2.17616 1.25641i 0.0922068 0.0532356i −0.453188 0.891415i \(-0.649713\pi\)
0.545394 + 0.838180i \(0.316380\pi\)
\(558\) −3.32043 + 23.9851i −0.140565 + 1.01537i
\(559\) 30.0072i 1.26917i
\(560\) 0.890439 4.62700i 0.0376279 0.195526i
\(561\) 1.11408 + 5.70006i 0.0470366 + 0.240657i
\(562\) −0.778484 + 1.34837i −0.0328384 + 0.0568778i
\(563\) 8.48717 + 14.7002i 0.357691 + 0.619540i 0.987575 0.157150i \(-0.0502306\pi\)
−0.629883 + 0.776690i \(0.716897\pi\)
\(564\) −9.62169 11.0455i −0.405146 0.465098i
\(565\) −9.81719 5.66795i −0.413012 0.238453i
\(566\) −28.4915 −1.19759
\(567\) 13.0883 + 19.8921i 0.549655 + 0.835392i
\(568\) 9.62306 0.403774
\(569\) −11.0775 6.39562i −0.464395 0.268118i 0.249496 0.968376i \(-0.419735\pi\)
−0.713890 + 0.700258i \(0.753068\pi\)
\(570\) −3.34041 3.83470i −0.139914 0.160618i
\(571\) 18.6681 + 32.3341i 0.781236 + 1.35314i 0.931222 + 0.364452i \(0.118744\pi\)
−0.149986 + 0.988688i \(0.547923\pi\)
\(572\) 3.12607 5.41451i 0.130708 0.226392i
\(573\) 1.56379 + 8.00093i 0.0653283 + 0.334244i
\(574\) −3.76155 10.8585i −0.157004 0.453224i
\(575\) 1.82829i 0.0762449i
\(576\) 0.411389 2.97166i 0.0171412 0.123819i
\(577\) 1.30824 0.755315i 0.0544629 0.0314442i −0.472521 0.881319i \(-0.656656\pi\)
0.526984 + 0.849875i \(0.323323\pi\)
\(578\) −4.94879 + 2.85719i −0.205843 + 0.118843i
\(579\) 0.598941 1.74530i 0.0248912 0.0725322i
\(580\) 2.22506i 0.0923907i
\(581\) 15.0768 + 13.0568i 0.625493 + 0.541686i
\(582\) −19.8298 + 3.87576i −0.821973 + 0.160655i
\(583\) 3.02029 5.23130i 0.125088 0.216658i
\(584\) −5.52906 9.57661i −0.228794 0.396283i
\(585\) −20.5491 + 26.4138i −0.849601 + 1.09208i
\(586\) −12.0141 6.93637i −0.496299 0.286539i
\(587\) 19.3744 0.799666 0.399833 0.916588i \(-0.369068\pi\)
0.399833 + 0.916588i \(0.369068\pi\)
\(588\) 11.9125 + 2.25671i 0.491263 + 0.0930651i
\(589\) 13.3069 0.548300
\(590\) −1.85162 1.06904i −0.0762302 0.0440115i
\(591\) 22.1738 19.3156i 0.912108 0.794537i
\(592\) 0.235496 + 0.407891i 0.00967883 + 0.0167642i
\(593\) 13.3874 23.1877i 0.549756 0.952204i −0.448535 0.893765i \(-0.648054\pi\)
0.998291 0.0584394i \(-0.0186125\pi\)
\(594\) 4.34104 2.83824i 0.178115 0.116455i
\(595\) −11.9658 10.3626i −0.490550 0.424824i
\(596\) 0.869860i 0.0356309i
\(597\) −3.51199 1.20523i −0.143736 0.0493266i
\(598\) 5.42454 3.13186i 0.221826 0.128071i
\(599\) 17.3871 10.0384i 0.710417 0.410159i −0.100799 0.994907i \(-0.532140\pi\)
0.811215 + 0.584748i \(0.198806\pi\)
\(600\) −2.99523 1.02788i −0.122280 0.0419632i
\(601\) 1.39900i 0.0570663i 0.999593 + 0.0285331i \(0.00908361\pi\)
−0.999593 + 0.0285331i \(0.990916\pi\)
\(602\) 4.14888 + 11.9766i 0.169096 + 0.488128i
\(603\) −26.7725 + 10.8811i −1.09026 + 0.443113i
\(604\) −3.57086 + 6.18491i −0.145296 + 0.251661i
\(605\) 8.90794 + 15.4290i 0.362159 + 0.627278i
\(606\) 22.6501 19.7305i 0.920096 0.801495i
\(607\) −21.5959 12.4684i −0.876553 0.506078i −0.00703239 0.999975i \(-0.502238\pi\)
−0.869520 + 0.493897i \(0.835572\pi\)
\(608\) −1.64867 −0.0668625
\(609\) −5.72537 + 0.0165914i −0.232004 + 0.000672318i
\(610\) −2.09606 −0.0848671
\(611\) 45.8771 + 26.4872i 1.85599 + 1.07156i
\(612\) −7.95454 6.18838i −0.321543 0.250150i
\(613\) −21.9558 38.0285i −0.886785 1.53596i −0.843654 0.536887i \(-0.819600\pi\)
−0.0431305 0.999069i \(-0.513733\pi\)
\(614\) −13.0364 + 22.5797i −0.526105 + 0.911241i
\(615\) 13.1491 2.57001i 0.530223 0.103633i
\(616\) 0.499061 2.59328i 0.0201077 0.104486i
\(617\) 39.3657i 1.58480i 0.609999 + 0.792402i \(0.291170\pi\)
−0.609999 + 0.792402i \(0.708830\pi\)
\(618\) −4.59679 + 13.3949i −0.184910 + 0.538823i
\(619\) −3.83941 + 2.21668i −0.154319 + 0.0890960i −0.575171 0.818033i \(-0.695064\pi\)
0.420852 + 0.907129i \(0.361731\pi\)
\(620\) −12.4486 + 7.18718i −0.499946 + 0.288644i
\(621\) 5.18816 0.288003i 0.208194 0.0115572i
\(622\) 9.78023i 0.392152i
\(623\) −24.0806 + 8.34190i −0.964767 + 0.334211i
\(624\) 2.08109 + 10.6476i 0.0833102 + 0.426246i
\(625\) 6.25796 10.8391i 0.250318 0.433564i
\(626\) 8.60715 + 14.9080i 0.344011 + 0.595844i
\(627\) −1.87219 2.14922i −0.0747679 0.0858317i
\(628\) −11.8872 6.86308i −0.474351 0.273867i
\(629\) 1.58226 0.0630886
\(630\) −4.54958 + 13.3835i −0.181259 + 0.533213i
\(631\) 26.8091 1.06725 0.533626 0.845721i \(-0.320829\pi\)
0.533626 + 0.845721i \(0.320829\pi\)
\(632\) −0.998763 0.576636i −0.0397286 0.0229373i
\(633\) 29.3293 + 33.6693i 1.16573 + 1.33823i
\(634\) −4.13723 7.16590i −0.164310 0.284594i
\(635\) −1.48423 + 2.57075i −0.0588997 + 0.102017i
\(636\) 2.01067 + 10.2873i 0.0797283 + 0.407919i
\(637\) −43.3963 + 6.26421i −1.71942 + 0.248197i
\(638\) 1.24707i 0.0493721i
\(639\) −28.5964 3.95882i −1.13126 0.156608i
\(640\) 1.54233 0.890465i 0.0609660 0.0351987i
\(641\) −13.7645 + 7.94693i −0.543664 + 0.313885i −0.746563 0.665315i \(-0.768297\pi\)
0.202898 + 0.979200i \(0.434964\pi\)
\(642\) −11.0931 + 32.3249i −0.437808 + 1.27576i
\(643\) 35.5512i 1.40200i −0.713161 0.701001i \(-0.752737\pi\)
0.713161 0.701001i \(-0.247263\pi\)
\(644\) 1.73204 2.00001i 0.0682519 0.0788114i
\(645\) −14.5031 + 2.83464i −0.571058 + 0.111614i
\(646\) −2.76928 + 4.79654i −0.108956 + 0.188717i
\(647\) −0.832081 1.44121i −0.0327125 0.0566596i 0.849206 0.528062i \(-0.177081\pi\)
−0.881918 + 0.471403i \(0.843748\pi\)
\(648\) −2.44502 + 8.66152i −0.0960493 + 0.340257i
\(649\) −1.03777 0.599159i −0.0407362 0.0235190i
\(650\) 11.4519 0.449180
\(651\) −18.5863 31.9781i −0.728456 1.25332i
\(652\) 9.35219 0.366260
\(653\) −29.9085 17.2677i −1.17041 0.675737i −0.216634 0.976253i \(-0.569508\pi\)
−0.953777 + 0.300516i \(0.902841\pi\)
\(654\) −20.8168 + 18.1335i −0.814001 + 0.709076i
\(655\) −1.71672 2.97345i −0.0670780 0.116182i
\(656\) 2.17170 3.76149i 0.0847906 0.146862i
\(657\) 12.4908 + 30.7330i 0.487311 + 1.19901i
\(658\) 21.9728 + 4.22854i 0.856589 + 0.164846i
\(659\) 9.87817i 0.384799i 0.981317 + 0.192399i \(0.0616269\pi\)
−0.981317 + 0.192399i \(0.938373\pi\)
\(660\) 2.91224 + 0.999407i 0.113359 + 0.0389019i
\(661\) −33.4283 + 19.2999i −1.30021 + 0.750678i −0.980440 0.196817i \(-0.936940\pi\)
−0.319772 + 0.947495i \(0.603606\pi\)
\(662\) −15.0614 + 8.69571i −0.585378 + 0.337968i
\(663\) 34.4731 + 11.8303i 1.33882 + 0.459449i
\(664\) 7.53838i 0.292546i
\(665\) 7.62840 + 1.46804i 0.295817 + 0.0569282i
\(666\) −0.532012 1.30899i −0.0206150 0.0507225i
\(667\) −0.624691 + 1.08200i −0.0241881 + 0.0418951i
\(668\) −12.4099 21.4946i −0.480154 0.831650i
\(669\) 13.1469 11.4523i 0.508289 0.442770i
\(670\) −14.8574 8.57793i −0.573992 0.331394i
\(671\) −1.17477 −0.0453516
\(672\) 2.30278 + 3.96197i 0.0888316 + 0.152836i
\(673\) 31.5214 1.21506 0.607531 0.794296i \(-0.292160\pi\)
0.607531 + 0.794296i \(0.292160\pi\)
\(674\) −20.7899 12.0031i −0.800797 0.462341i
\(675\) 8.47793 + 4.28672i 0.326316 + 0.164996i
\(676\) −13.1171 22.7195i −0.504504 0.873826i
\(677\) −25.3117 + 43.8411i −0.972807 + 1.68495i −0.285817 + 0.958284i \(0.592265\pi\)
−0.686990 + 0.726667i \(0.741068\pi\)
\(678\) 10.8201 2.11479i 0.415542 0.0812181i
\(679\) 20.2049 23.3309i 0.775393 0.895357i
\(680\) 5.98287i 0.229433i
\(681\) 14.7829 43.0770i 0.566482 1.65071i
\(682\) −6.97700 + 4.02817i −0.267163 + 0.154247i
\(683\) 31.2495 18.0419i 1.19573 0.690355i 0.236130 0.971722i \(-0.424121\pi\)
0.959600 + 0.281367i \(0.0907877\pi\)
\(684\) 4.89929 + 0.678246i 0.187329 + 0.0259334i
\(685\) 15.5122i 0.592690i
\(686\) −16.4543 + 8.50028i −0.628230 + 0.324542i
\(687\) 6.52978 + 33.4088i 0.249127 + 1.27462i
\(688\) −2.39532 + 4.14881i −0.0913206 + 0.158172i
\(689\) −18.9533 32.8281i −0.722064 1.25065i
\(690\) 2.02612 + 2.32593i 0.0771331 + 0.0885468i
\(691\) −19.7530 11.4044i −0.751441 0.433845i 0.0747732 0.997201i \(-0.476177\pi\)
−0.826214 + 0.563356i \(0.809510\pi\)
\(692\) −3.29576 −0.125286
\(693\) −2.54988 + 7.50102i −0.0968621 + 0.284940i
\(694\) 23.9658 0.909730
\(695\) 1.45218 + 0.838418i 0.0550844 + 0.0318030i
\(696\) −1.42139 1.63172i −0.0538777 0.0618502i
\(697\) −7.29562 12.6364i −0.276341 0.478637i
\(698\) 12.8050 22.1789i 0.484677 0.839485i
\(699\) −1.06788 5.46365i −0.0403908 0.206654i
\(700\) 4.57071 1.58337i 0.172757 0.0598458i
\(701\) 9.21264i 0.347956i −0.984749 0.173978i \(-0.944338\pi\)
0.984749 0.173978i \(-0.0556622\pi\)
\(702\) −1.80397 32.4972i −0.0680866 1.22653i
\(703\) −0.672479 + 0.388256i −0.0253630 + 0.0146433i
\(704\) 0.864424 0.499076i 0.0325792 0.0188096i
\(705\) −8.46796 + 24.6754i −0.318922 + 0.929330i
\(706\) 6.35599i 0.239211i
\(707\) −8.67114 + 45.0579i −0.326112 + 1.69458i
\(708\) 2.04078 0.398872i 0.0766970 0.0149905i
\(709\) 4.44249 7.69463i 0.166841 0.288978i −0.770466 0.637481i \(-0.779977\pi\)
0.937308 + 0.348503i \(0.113310\pi\)
\(710\) −8.56899 14.8419i −0.321589 0.557008i
\(711\) 2.73076 + 2.12445i 0.102412 + 0.0796729i
\(712\) −8.34177 4.81612i −0.312621 0.180492i
\(713\) −8.07127 −0.302271
\(714\) 15.3947 0.0446119i 0.576131 0.00166956i
\(715\) −11.1346 −0.416411
\(716\) −19.3860 11.1925i −0.724487 0.418283i
\(717\) −10.9990 + 9.58124i −0.410766 + 0.357818i
\(718\) −12.2425 21.2047i −0.456887 0.791352i
\(719\) 16.2393 28.1273i 0.605624 1.04897i −0.386329 0.922361i \(-0.626257\pi\)
0.991953 0.126610i \(-0.0404096\pi\)
\(720\) −4.94961 + 2.01166i −0.184461 + 0.0749702i
\(721\) −7.08098 20.4406i −0.263709 0.761250i
\(722\) 16.2819i 0.605949i
\(723\) −14.4957 4.97456i −0.539102 0.185006i
\(724\) −2.27516 + 1.31357i −0.0845558 + 0.0488183i
\(725\) −1.97820 + 1.14212i −0.0734686 + 0.0424171i
\(726\) −16.3887 5.62419i −0.608243 0.208733i
\(727\) 45.2760i 1.67919i −0.543210 0.839597i \(-0.682791\pi\)
0.543210 0.839597i \(-0.317209\pi\)
\(728\) −12.5275 10.8490i −0.464300 0.402091i
\(729\) 10.8290 24.7332i 0.401074 0.916045i
\(730\) −9.84687 + 17.0553i −0.364449 + 0.631244i
\(731\) 8.04685 + 13.9376i 0.297624 + 0.515499i
\(732\) 1.53712 1.33899i 0.0568136 0.0494903i
\(733\) −36.8605 21.2814i −1.36147 0.786048i −0.371654 0.928371i \(-0.621209\pi\)
−0.989820 + 0.142324i \(0.954543\pi\)
\(734\) 29.7532 1.09821
\(735\) −7.12706 20.3825i −0.262885 0.751820i
\(736\) 1.00000 0.0368605
\(737\) −8.32708 4.80764i −0.306732 0.177092i
\(738\) −8.00099 + 10.2845i −0.294520 + 0.378576i
\(739\) 15.0275 + 26.0284i 0.552795 + 0.957469i 0.998071 + 0.0620755i \(0.0197720\pi\)
−0.445277 + 0.895393i \(0.646895\pi\)
\(740\) 0.419402 0.726425i 0.0154175 0.0267039i
\(741\) −17.5544 + 3.43103i −0.644878 + 0.126042i
\(742\) −12.1036 10.4819i −0.444338 0.384803i
\(743\) 21.1026i 0.774179i −0.922042 0.387090i \(-0.873480\pi\)
0.922042 0.387090i \(-0.126520\pi\)
\(744\) 4.53775 13.2229i 0.166362 0.484775i
\(745\) 1.34161 0.774580i 0.0491528 0.0283784i
\(746\) 8.38922 4.84352i 0.307151 0.177334i
\(747\) 3.10121 22.4015i 0.113467 0.819628i
\(748\) 3.35320i 0.122605i
\(749\) −17.0879 49.3277i −0.624380 1.80240i
\(750\) 4.04033 + 20.6718i 0.147532 + 0.754828i
\(751\) 3.69047 6.39208i 0.134667 0.233250i −0.790803 0.612071i \(-0.790337\pi\)
0.925470 + 0.378820i \(0.123670\pi\)
\(752\) 4.22866 + 7.32426i 0.154203 + 0.267088i
\(753\) 31.8809 + 36.5984i 1.16180 + 1.33372i
\(754\) 6.77732 + 3.91289i 0.246816 + 0.142499i
\(755\) 12.7189 0.462889
\(756\) −5.21316 12.7210i −0.189601 0.462657i
\(757\) 39.1757 1.42386 0.711932 0.702248i \(-0.247820\pi\)
0.711932 + 0.702248i \(0.247820\pi\)
\(758\) 17.9919 + 10.3876i 0.653494 + 0.377295i
\(759\) 1.13557 + 1.30361i 0.0412187 + 0.0473180i
\(760\) 1.46808 + 2.54280i 0.0532530 + 0.0922369i
\(761\) 24.8222 42.9934i 0.899805 1.55851i 0.0720632 0.997400i \(-0.477042\pi\)
0.827742 0.561109i \(-0.189625\pi\)
\(762\) −0.553785 2.83337i −0.0200615 0.102642i
\(763\) 7.96930 41.4110i 0.288508 1.49918i
\(764\) 4.70674i 0.170284i
\(765\) −2.46129 + 17.7791i −0.0889880 + 0.642803i
\(766\) −7.56732 + 4.36899i −0.273418 + 0.157858i
\(767\) −6.51236 + 3.75991i −0.235148 + 0.135763i
\(768\) −0.562211 + 1.63827i −0.0202870 + 0.0591159i
\(769\) 26.5055i 0.955814i 0.878411 + 0.477907i \(0.158604\pi\)
−0.878411 + 0.477907i \(0.841396\pi\)
\(770\) −4.44408 + 1.53950i −0.160154 + 0.0554799i
\(771\) −21.2841 + 4.16000i −0.766528 + 0.149819i
\(772\) −0.532666 + 0.922605i −0.0191711 + 0.0332053i
\(773\) −20.2511 35.0760i −0.728382 1.26160i −0.957567 0.288212i \(-0.906939\pi\)
0.229184 0.973383i \(-0.426394\pi\)
\(774\) 8.82484 11.3434i 0.317202 0.407732i
\(775\) −12.7796 7.37830i −0.459057 0.265036i
\(776\) 11.6654 0.418763
\(777\) 1.87231 + 1.07376i 0.0671688 + 0.0385208i
\(778\) 23.9002 0.856864
\(779\) 6.20147 + 3.58042i 0.222191 + 0.128282i
\(780\) 14.5690 12.6910i 0.521654 0.454412i
\(781\) −4.80263 8.31840i −0.171852 0.297656i
\(782\) 1.67970 2.90933i 0.0600661 0.104038i
\(783\) 3.55262 + 5.43366i 0.126960 + 0.194183i
\(784\) −6.50003 2.59800i −0.232144 0.0927858i
\(785\) 24.4453i 0.872491i
\(786\) 3.15841 + 1.08388i 0.112657 + 0.0386609i
\(787\) 23.1463 13.3636i 0.825078 0.476359i −0.0270863 0.999633i \(-0.508623\pi\)
0.852165 + 0.523274i \(0.175290\pi\)
\(788\) −14.7035 + 8.48905i −0.523790 + 0.302410i
\(789\) 13.9282 + 4.77979i 0.495856 + 0.170165i
\(790\) 2.05390i 0.0730743i
\(791\) −11.0247 + 12.7304i −0.391994 + 0.452641i
\(792\) −2.77409 + 1.12747i −0.0985730 + 0.0400628i
\(793\) −3.68604 + 6.38441i −0.130895 + 0.226717i
\(794\) −15.4383 26.7399i −0.547884 0.948963i
\(795\) 14.0760 12.2616i 0.499225 0.434875i
\(796\) 1.85652 + 1.07186i 0.0658026 + 0.0379912i
\(797\) −30.0145 −1.06317 −0.531584 0.847006i \(-0.678403\pi\)
−0.531584 + 0.847006i \(0.678403\pi\)
\(798\) −6.53199 + 3.79653i −0.231230 + 0.134396i
\(799\) 28.4116 1.00513
\(800\) 1.58334 + 0.914144i 0.0559797 + 0.0323199i
\(801\) 22.8076 + 17.7436i 0.805866 + 0.626939i
\(802\) −16.5383 28.6452i −0.583987 1.01150i
\(803\) −5.51884 + 9.55891i −0.194756 + 0.337327i
\(804\) 16.3752 3.20054i 0.577507 0.112874i
\(805\) −4.62700 0.890439i −0.163080 0.0313838i
\(806\) 50.5561i 1.78076i
\(807\) 5.99708 17.4753i 0.211107 0.615160i
\(808\) −15.0193 + 8.67140i −0.528377 + 0.305059i
\(809\) 24.3548 14.0613i 0.856271 0.494368i −0.00649108 0.999979i \(-0.502066\pi\)
0.862762 + 0.505611i \(0.168733\pi\)
\(810\) 15.5361 3.94176i 0.545884 0.138499i
\(811\) 32.9090i 1.15559i 0.816182 + 0.577795i \(0.196087\pi\)
−0.816182 + 0.577795i \(0.803913\pi\)
\(812\) 3.24599 + 0.624673i 0.113912 + 0.0219217i
\(813\) −3.90591 19.9841i −0.136986 0.700873i
\(814\) 0.235061 0.407137i 0.00823887 0.0142701i
\(815\) −8.32780 14.4242i −0.291710 0.505257i
\(816\) 3.82192 + 4.38746i 0.133794 + 0.153592i
\(817\) −6.84003 3.94909i −0.239302 0.138161i
\(818\) −35.6608 −1.24685
\(819\) 32.7643 + 37.3932i 1.14488 + 1.30663i
\(820\) −7.73529 −0.270128
\(821\) −13.1079 7.56785i −0.457469 0.264120i 0.253510 0.967333i \(-0.418415\pi\)
−0.710979 + 0.703213i \(0.751748\pi\)
\(822\) −9.90934 11.3757i −0.345628 0.396772i
\(823\) 15.9647 + 27.6517i 0.556494 + 0.963876i 0.997786 + 0.0665125i \(0.0211872\pi\)
−0.441291 + 0.897364i \(0.645479\pi\)
\(824\) 4.08814 7.08086i 0.142417 0.246674i
\(825\) 0.606316 + 3.10214i 0.0211092 + 0.108003i
\(826\) −2.07938 + 2.40108i −0.0723508 + 0.0835444i
\(827\) 47.2478i 1.64297i −0.570233 0.821483i \(-0.693147\pi\)
0.570233 0.821483i \(-0.306853\pi\)
\(828\) −2.97166 0.411389i −0.103272 0.0142968i
\(829\) −8.53322 + 4.92666i −0.296371 + 0.171110i −0.640811 0.767698i \(-0.721402\pi\)
0.344440 + 0.938808i \(0.388069\pi\)
\(830\) 11.6267 6.71266i 0.403568 0.233000i
\(831\) 10.0039 29.1511i 0.347032 1.01124i
\(832\) 6.26372i 0.217155i
\(833\) −18.4766 + 14.5469i −0.640176 + 0.504019i
\(834\) −1.60053 + 0.312825i −0.0554218 + 0.0108322i
\(835\) −22.1012 + 38.2803i −0.764842 + 1.32475i
\(836\) 0.822812 + 1.42515i 0.0284576 + 0.0492899i
\(837\) −18.9244 + 37.4271i −0.654123 + 1.29367i
\(838\) 19.3741 + 11.1856i 0.669266 + 0.386401i
\(839\) −8.06261 −0.278352 −0.139176 0.990268i \(-0.544445\pi\)
−0.139176 + 0.990268i \(0.544445\pi\)
\(840\) 4.06012 7.07964i 0.140088 0.244271i
\(841\) 27.4390 0.946174
\(842\) 6.21639 + 3.58904i 0.214231 + 0.123686i
\(843\) −2.03344 + 1.77133i −0.0700353 + 0.0610077i
\(844\) −12.8900 22.3262i −0.443692 0.768498i
\(845\) −23.3606 + 40.4618i −0.803630 + 1.39193i
\(846\) −9.55302 23.5048i −0.328440 0.808112i
\(847\) 25.0092 8.66359i 0.859326 0.297685i
\(848\) 6.05178i 0.207819i
\(849\) −46.6767 16.0182i −1.60194 0.549744i
\(850\) 5.31910 3.07099i 0.182444 0.105334i
\(851\) 0.407891 0.235496i 0.0139823 0.00807270i
\(852\) 15.7651 + 5.41019i 0.540105 + 0.185350i
\(853\) 28.1001i 0.962128i −0.876686 0.481064i \(-0.840251\pi\)
0.876686 0.481064i \(-0.159749\pi\)
\(854\) −0.588457 + 3.05781i −0.0201366 + 0.104636i
\(855\) −3.31657 8.16028i −0.113424 0.279076i
\(856\) 9.86556 17.0877i 0.337198 0.584044i
\(857\) −8.71262 15.0907i −0.297618 0.515489i 0.677973 0.735087i \(-0.262859\pi\)
−0.975590 + 0.219598i \(0.929525\pi\)
\(858\) 8.16543 7.11291i 0.278763 0.242831i
\(859\) −15.1009 8.71853i −0.515237 0.297472i 0.219747 0.975557i \(-0.429477\pi\)
−0.734984 + 0.678085i \(0.762810\pi\)
\(860\) 8.53178 0.290931
\(861\) −0.0576790 19.9039i −0.00196570 0.678322i
\(862\) −14.9517 −0.509258
\(863\) −33.8050 19.5173i −1.15074 0.664378i −0.201669 0.979454i \(-0.564637\pi\)
−0.949066 + 0.315076i \(0.897970\pi\)
\(864\) 2.34466 4.63708i 0.0797671 0.157757i
\(865\) 2.93476 + 5.08315i 0.0997847 + 0.172832i
\(866\) 7.89412 13.6730i 0.268253 0.464628i
\(867\) −9.71378 + 1.89857i −0.329897 + 0.0644788i
\(868\) 6.99004 + 20.1781i 0.237257 + 0.684890i
\(869\) 1.15114i 0.0390497i
\(870\) −1.25095 + 3.64525i −0.0424113 + 0.123585i
\(871\) −52.2551 + 30.1695i −1.77060 + 1.02225i
\(872\) 13.8036 7.96954i 0.467450 0.269883i
\(873\) −34.6655 4.79901i −1.17325 0.162422i
\(874\) 1.64867i 0.0557672i
\(875\) −24.3215 21.0628i −0.822218 0.712053i
\(876\) −3.67400 18.7975i −0.124133 0.635110i
\(877\) 0.839003 1.45320i 0.0283311 0.0490710i −0.851512 0.524335i \(-0.824314\pi\)
0.879843 + 0.475264i \(0.157647\pi\)
\(878\) 20.5636 + 35.6172i 0.693988 + 1.20202i
\(879\) −15.7827 18.1181i −0.532336 0.611108i
\(880\) −1.53948 0.888819i −0.0518958 0.0299621i
\(881\) 41.0614 1.38339 0.691696 0.722189i \(-0.256864\pi\)
0.691696 + 0.722189i \(0.256864\pi\)
\(882\) 18.2471 + 10.3944i 0.614411 + 0.349998i
\(883\) −51.3510 −1.72810 −0.864049 0.503408i \(-0.832079\pi\)
−0.864049 + 0.503408i \(0.832079\pi\)
\(884\) −18.2233 10.5212i −0.612914 0.353866i
\(885\) −2.43243 2.79237i −0.0817653 0.0938645i
\(886\) 7.27471 + 12.6002i 0.244399 + 0.423311i
\(887\) −21.8703 + 37.8805i −0.734334 + 1.27190i 0.220681 + 0.975346i \(0.429172\pi\)
−0.955015 + 0.296558i \(0.904161\pi\)
\(888\) 0.156485 + 0.800633i 0.00525128 + 0.0268675i
\(889\) 3.33361 + 2.88696i 0.111806 + 0.0968256i
\(890\) 17.1543i 0.575015i
\(891\) 8.70748 2.20922i 0.291711 0.0740117i
\(892\) −8.71774 + 5.03319i −0.291891 + 0.168524i
\(893\) −12.0753 + 6.97168i −0.404084 + 0.233298i
\(894\) −0.489045 + 1.42506i −0.0163561 + 0.0476612i
\(895\) 39.8661i 1.33258i
\(896\) −0.866040 2.50000i −0.0289324 0.0835190i
\(897\) 10.6476 2.08109i 0.355513 0.0694855i
\(898\) 2.95477 5.11782i 0.0986020 0.170784i
\(899\) −5.04205 8.73308i −0.168162 0.291265i
\(900\) −4.32909 3.36790i −0.144303 0.112263i
\(901\) −17.6066 10.1652i −0.586562 0.338652i
\(902\) −4.33537 −0.144352
\(903\) 0.0636182 + 21.9534i 0.00211708 + 0.730562i
\(904\) −6.36516 −0.211702
\(905\) 4.05191 + 2.33937i 0.134690 + 0.0777633i
\(906\) −9.32725 + 8.12496i −0.309877 + 0.269934i
\(907\) 24.9311 + 43.1819i 0.827824 + 1.43383i 0.899742 + 0.436422i \(0.143755\pi\)
−0.0719181 + 0.997411i \(0.522912\pi\)
\(908\) −13.1471 + 22.7715i −0.436302 + 0.755698i
\(909\) 48.1996 19.5897i 1.59868 0.649748i
\(910\) −5.57746 + 28.9822i −0.184891 + 0.960751i
\(911\) 35.8440i 1.18757i 0.804625 + 0.593783i \(0.202366\pi\)
−0.804625 + 0.593783i \(0.797634\pi\)
\(912\) −2.70097 0.926901i −0.0894379 0.0306928i
\(913\) 6.51636 3.76222i 0.215660 0.124511i
\(914\) −6.02479 + 3.47842i −0.199282 + 0.115056i
\(915\) −3.43391 1.17843i −0.113522 0.0389577i
\(916\) 19.6535i 0.649371i
\(917\) −4.81973 + 1.66963i −0.159162 + 0.0551362i
\(918\) −9.55248 14.6103i −0.315279 0.482213i
\(919\) −13.3474 + 23.1183i −0.440289 + 0.762603i −0.997711 0.0676268i \(-0.978457\pi\)
0.557422 + 0.830229i \(0.311791\pi\)
\(920\) −0.890465 1.54233i −0.0293578 0.0508491i
\(921\) −34.0516 + 29.6623i −1.12204 + 0.977407i
\(922\) −16.3582 9.44443i −0.538729 0.311036i
\(923\) −60.2761 −1.98401
\(924\) 2.27556 3.96790i 0.0748605 0.130534i
\(925\) 0.861110 0.0283131
\(926\) −14.9563 8.63502i −0.491495 0.283764i
\(927\) −15.0615 + 19.3601i −0.494686 + 0.635869i
\(928\) 0.624691 + 1.08200i 0.0205065 + 0.0355183i
\(929\) −11.2304 + 19.4516i −0.368457 + 0.638186i −0.989325 0.145729i \(-0.953447\pi\)
0.620867 + 0.783916i \(0.286781\pi\)
\(930\) −24.4348 + 4.77580i −0.801248 + 0.156605i
\(931\) 4.28325 10.7164i 0.140378 0.351216i
\(932\) 3.21413i 0.105282i
\(933\) −5.49855 + 16.0226i −0.180015 + 0.524558i
\(934\) 16.4057 9.47185i 0.536812 0.309928i
\(935\) −5.17174 + 2.98591i −0.169134 + 0.0976496i
\(936\) −2.57683 + 18.6136i −0.0842262 + 0.608406i
\(937\) 36.9477i 1.20703i −0.797353 0.603514i \(-0.793767\pi\)
0.797353 0.603514i \(-0.206233\pi\)
\(938\) −16.6849 + 19.2663i −0.544781 + 0.629066i
\(939\) 5.71936 + 29.2623i 0.186644 + 0.954940i
\(940\) 7.53095 13.0440i 0.245633 0.425448i
\(941\) −25.9527 44.9514i −0.846034 1.46537i −0.884720 0.466122i \(-0.845651\pi\)
0.0386864 0.999251i \(-0.487683\pi\)
\(942\) −15.6159 17.9267i −0.508794 0.584082i
\(943\) −3.76149 2.17170i −0.122491 0.0707202i
\(944\) −1.20054 −0.0390741
\(945\) −14.9778 + 19.3680i −0.487228 + 0.630041i
\(946\) 4.78178 0.155469
\(947\) −3.70407 2.13855i −0.120366 0.0694934i 0.438608 0.898678i \(-0.355472\pi\)
−0.558974 + 0.829185i \(0.688805\pi\)
\(948\) −1.31205 1.50620i −0.0426134 0.0489191i
\(949\) 34.6325 + 59.9852i 1.12422 + 1.94720i
\(950\) −1.50712 + 2.61042i −0.0488976 + 0.0846931i
\(951\) −2.74915 14.0656i −0.0891472 0.456110i
\(952\) −8.72801 1.67966i −0.282876 0.0544379i
\(953\) 28.0861i 0.909798i −0.890543 0.454899i \(-0.849675\pi\)
0.890543 0.454899i \(-0.150325\pi\)
\(954\) −2.48963 + 17.9838i −0.0806049 + 0.582248i
\(955\) −7.25936 + 4.19119i −0.234907 + 0.135624i
\(956\) 7.29347 4.21089i 0.235888 0.136190i
\(957\) −0.701118 + 2.04304i −0.0226639 + 0.0660420i
\(958\) 0.580072i 0.0187413i
\(959\) 22.6297 + 4.35495i 0.730751 + 0.140629i
\(960\) 3.02738 0.591704i 0.0977082 0.0190972i
\(961\) 17.0727 29.5707i 0.550731 0.953894i
\(962\) −1.47508 2.55492i −0.0475585 0.0823738i
\(963\) −36.3468 + 46.7201i −1.17126 + 1.50553i
\(964\) 7.66278 + 4.42411i 0.246801 + 0.142491i
\(965\) 1.89728 0.0610757
\(966\) 3.96197 2.30278i 0.127474 0.0740907i
\(967\) 41.1377 1.32290 0.661450 0.749989i \(-0.269941\pi\)
0.661450 + 0.749989i \(0.269941\pi\)
\(968\) 8.66345 + 5.00185i 0.278454 + 0.160765i
\(969\) −7.23349 + 6.30109i −0.232373 + 0.202420i
\(970\) −10.3876 17.9919i −0.333526 0.577684i
\(971\) −10.4551 + 18.1087i −0.335519 + 0.581135i −0.983584 0.180449i \(-0.942245\pi\)
0.648066 + 0.761584i \(0.275578\pi\)
\(972\) −8.87519 + 12.8153i −0.284672 + 0.411050i
\(973\) 1.63080 1.88311i 0.0522811 0.0603697i
\(974\) 14.6611i 0.469772i
\(975\) 18.7613 + 6.43838i 0.600841 + 0.206193i
\(976\) −1.01927 + 0.588474i −0.0326260 + 0.0188366i
\(977\) −24.0409 + 13.8800i −0.769137 + 0.444062i −0.832567 0.553925i \(-0.813130\pi\)
0.0634294 + 0.997986i \(0.479796\pi\)
\(978\) 15.3214 + 5.25791i 0.489924 + 0.168129i
\(979\) 9.61443i 0.307279i
\(980\) 1.78107 + 12.3386i 0.0568942 + 0.394143i
\(981\) −44.2983 + 18.0041i −1.41434 + 0.574826i
\(982\) 10.9749 19.0091i 0.350223 0.606604i
\(983\) −9.28941 16.0897i −0.296286 0.513183i 0.678997 0.734141i \(-0.262415\pi\)
−0.975283 + 0.220958i \(0.929082\pi\)
\(984\) 5.67257 4.94138i 0.180835 0.157525i
\(985\) 26.1859 + 15.1184i 0.834351 + 0.481713i
\(986\) 4.19719 0.133666
\(987\) 33.6200 + 19.2808i 1.07014 + 0.613715i
\(988\) 10.3268 0.328540
\(989\) 4.14881 + 2.39532i 0.131925 + 0.0761667i
\(990\) 4.20916 + 3.27459i 0.133776 + 0.104073i
\(991\) 4.39574 + 7.61365i 0.139635 + 0.241856i 0.927359 0.374174i \(-0.122074\pi\)
−0.787723 + 0.616029i \(0.788740\pi\)
\(992\) −4.03563 + 6.98992i −0.128131 + 0.221930i
\(993\) −29.5634 + 5.77821i −0.938167 + 0.183366i
\(994\) −24.0576 + 8.33395i −0.763061 + 0.264337i
\(995\) 3.81782i 0.121033i
\(996\) −4.23816 + 12.3499i −0.134291 + 0.391321i
\(997\) 3.42951 1.98003i 0.108614 0.0627081i −0.444709 0.895675i \(-0.646693\pi\)
0.553323 + 0.832967i \(0.313360\pi\)
\(998\) 28.9034 16.6874i 0.914920 0.528229i
\(999\) −0.135647 2.44358i −0.00429169 0.0773116i
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 966.2.l.c.47.5 56
3.2 odd 2 inner 966.2.l.c.47.24 yes 56
7.3 odd 6 inner 966.2.l.c.185.24 yes 56
21.17 even 6 inner 966.2.l.c.185.5 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.l.c.47.5 56 1.1 even 1 trivial
966.2.l.c.47.24 yes 56 3.2 odd 2 inner
966.2.l.c.185.5 yes 56 21.17 even 6 inner
966.2.l.c.185.24 yes 56 7.3 odd 6 inner