Properties

Label 546.2.e.g.545.3
Level $546$
Weight $2$
Character 546.545
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(545,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.545");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.e (of order \(2\), degree \(1\), 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: \(8\)
Coefficient field: 8.0.303595776.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 545.3
Root \(-0.396143 - 1.68614i\) of defining polynomial
Character \(\chi\) \(=\) 546.545
Dual form 546.2.e.g.545.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.396143 - 1.68614i) q^{3} +1.00000 q^{4} +2.37228i q^{5} +(-0.396143 - 1.68614i) q^{6} +(-0.792287 + 2.52434i) q^{7} +1.00000 q^{8} +(-2.68614 + 1.33591i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.396143 - 1.68614i) q^{3} +1.00000 q^{4} +2.37228i q^{5} +(-0.396143 - 1.68614i) q^{6} +(-0.792287 + 2.52434i) q^{7} +1.00000 q^{8} +(-2.68614 + 1.33591i) q^{9} +2.37228i q^{10} +5.74456 q^{11} +(-0.396143 - 1.68614i) q^{12} +(3.46410 - 1.00000i) q^{13} +(-0.792287 + 2.52434i) q^{14} +(4.00000 - 0.939764i) q^{15} +1.00000 q^{16} +2.52434 q^{17} +(-2.68614 + 1.33591i) q^{18} -7.57301 q^{19} +2.37228i q^{20} +(4.57025 + 0.335907i) q^{21} +5.74456 q^{22} +6.78073i q^{23} +(-0.396143 - 1.68614i) q^{24} -0.627719 q^{25} +(3.46410 - 1.00000i) q^{26} +(3.31662 + 4.00000i) q^{27} +(-0.792287 + 2.52434i) q^{28} -7.57301i q^{29} +(4.00000 - 0.939764i) q^{30} +5.84096 q^{31} +1.00000 q^{32} +(-2.27567 - 9.68614i) q^{33} +2.52434 q^{34} +(-5.98844 - 1.87953i) q^{35} +(-2.68614 + 1.33591i) q^{36} -4.90120i q^{37} -7.57301 q^{38} +(-3.05842 - 5.44482i) q^{39} +2.37228i q^{40} +2.62772i q^{41} +(4.57025 + 0.335907i) q^{42} -8.37228 q^{43} +5.74456 q^{44} +(-3.16915 - 6.37228i) q^{45} +6.78073i q^{46} -4.62772i q^{47} +(-0.396143 - 1.68614i) q^{48} +(-5.74456 - 4.00000i) q^{49} -0.627719 q^{50} +(-1.00000 - 4.25639i) q^{51} +(3.46410 - 1.00000i) q^{52} -3.16915i q^{53} +(3.31662 + 4.00000i) q^{54} +13.6277i q^{55} +(-0.792287 + 2.52434i) q^{56} +(3.00000 + 12.7692i) q^{57} -7.57301i q^{58} +8.74456i q^{59} +(4.00000 - 0.939764i) q^{60} -3.74456i q^{61} +5.84096 q^{62} +(-1.24409 - 7.83915i) q^{63} +1.00000 q^{64} +(2.37228 + 8.21782i) q^{65} +(-2.27567 - 9.68614i) q^{66} -2.67181i q^{67} +2.52434 q^{68} +(11.4333 - 2.68614i) q^{69} +(-5.98844 - 1.87953i) q^{70} -2.00000 q^{71} +(-2.68614 + 1.33591i) q^{72} -3.61158 q^{73} -4.90120i q^{74} +(0.248667 + 1.05842i) q^{75} -7.57301 q^{76} +(-4.55134 + 14.5012i) q^{77} +(-3.05842 - 5.44482i) q^{78} -9.37228 q^{79} +2.37228i q^{80} +(5.43070 - 7.17687i) q^{81} +2.62772i q^{82} +4.74456i q^{83} +(4.57025 + 0.335907i) q^{84} +5.98844i q^{85} -8.37228 q^{86} +(-12.7692 + 3.00000i) q^{87} +5.74456 q^{88} +10.0000i q^{89} +(-3.16915 - 6.37228i) q^{90} +(-0.220225 + 9.53685i) q^{91} +6.78073i q^{92} +(-2.31386 - 9.84868i) q^{93} -4.62772i q^{94} -17.9653i q^{95} +(-0.396143 - 1.68614i) q^{96} +7.42554 q^{97} +(-5.74456 - 4.00000i) q^{98} +(-15.4307 + 7.67420i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9} + 32 q^{15} + 8 q^{16} - 10 q^{18} + 14 q^{21} - 28 q^{25} + 32 q^{30} + 8 q^{32} - 10 q^{36} + 10 q^{39} + 14 q^{42} - 44 q^{43} - 28 q^{50} - 8 q^{51} + 24 q^{57} + 32 q^{60} - 4 q^{63} + 8 q^{64} - 4 q^{65} - 16 q^{71} - 10 q^{72} + 10 q^{78} - 52 q^{79} - 14 q^{81} + 14 q^{84} - 44 q^{86} + 24 q^{91} - 30 q^{93} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.396143 1.68614i −0.228714 0.973494i
\(4\) 1.00000 0.500000
\(5\) 2.37228i 1.06092i 0.847711 + 0.530458i \(0.177980\pi\)
−0.847711 + 0.530458i \(0.822020\pi\)
\(6\) −0.396143 1.68614i −0.161725 0.688364i
\(7\) −0.792287 + 2.52434i −0.299456 + 0.954110i
\(8\) 1.00000 0.353553
\(9\) −2.68614 + 1.33591i −0.895380 + 0.445302i
\(10\) 2.37228i 0.750181i
\(11\) 5.74456 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) −0.396143 1.68614i −0.114357 0.486747i
\(13\) 3.46410 1.00000i 0.960769 0.277350i
\(14\) −0.792287 + 2.52434i −0.211748 + 0.674658i
\(15\) 4.00000 0.939764i 1.03280 0.242646i
\(16\) 1.00000 0.250000
\(17\) 2.52434 0.612242 0.306121 0.951993i \(-0.400969\pi\)
0.306121 + 0.951993i \(0.400969\pi\)
\(18\) −2.68614 + 1.33591i −0.633129 + 0.314876i
\(19\) −7.57301 −1.73737 −0.868684 0.495366i \(-0.835034\pi\)
−0.868684 + 0.495366i \(0.835034\pi\)
\(20\) 2.37228i 0.530458i
\(21\) 4.57025 + 0.335907i 0.997310 + 0.0733010i
\(22\) 5.74456 1.22474
\(23\) 6.78073i 1.41388i 0.707274 + 0.706940i \(0.249925\pi\)
−0.707274 + 0.706940i \(0.750075\pi\)
\(24\) −0.396143 1.68614i −0.0808625 0.344182i
\(25\) −0.627719 −0.125544
\(26\) 3.46410 1.00000i 0.679366 0.196116i
\(27\) 3.31662 + 4.00000i 0.638285 + 0.769800i
\(28\) −0.792287 + 2.52434i −0.149728 + 0.477055i
\(29\) 7.57301i 1.40627i −0.711055 0.703137i \(-0.751782\pi\)
0.711055 0.703137i \(-0.248218\pi\)
\(30\) 4.00000 0.939764i 0.730297 0.171577i
\(31\) 5.84096 1.04907 0.524534 0.851390i \(-0.324240\pi\)
0.524534 + 0.851390i \(0.324240\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.27567 9.68614i −0.396143 1.68614i
\(34\) 2.52434 0.432920
\(35\) −5.98844 1.87953i −1.01223 0.317698i
\(36\) −2.68614 + 1.33591i −0.447690 + 0.222651i
\(37\) 4.90120i 0.805752i −0.915255 0.402876i \(-0.868011\pi\)
0.915255 0.402876i \(-0.131989\pi\)
\(38\) −7.57301 −1.22850
\(39\) −3.05842 5.44482i −0.489739 0.871869i
\(40\) 2.37228i 0.375091i
\(41\) 2.62772i 0.410381i 0.978722 + 0.205190i \(0.0657813\pi\)
−0.978722 + 0.205190i \(0.934219\pi\)
\(42\) 4.57025 + 0.335907i 0.705205 + 0.0518316i
\(43\) −8.37228 −1.27676 −0.638380 0.769721i \(-0.720395\pi\)
−0.638380 + 0.769721i \(0.720395\pi\)
\(44\) 5.74456 0.866025
\(45\) −3.16915 6.37228i −0.472429 0.949924i
\(46\) 6.78073i 0.999764i
\(47\) 4.62772i 0.675022i −0.941322 0.337511i \(-0.890415\pi\)
0.941322 0.337511i \(-0.109585\pi\)
\(48\) −0.396143 1.68614i −0.0571784 0.243373i
\(49\) −5.74456 4.00000i −0.820652 0.571429i
\(50\) −0.627719 −0.0887728
\(51\) −1.00000 4.25639i −0.140028 0.596014i
\(52\) 3.46410 1.00000i 0.480384 0.138675i
\(53\) 3.16915i 0.435316i −0.976025 0.217658i \(-0.930158\pi\)
0.976025 0.217658i \(-0.0698417\pi\)
\(54\) 3.31662 + 4.00000i 0.451335 + 0.544331i
\(55\) 13.6277i 1.83756i
\(56\) −0.792287 + 2.52434i −0.105874 + 0.337329i
\(57\) 3.00000 + 12.7692i 0.397360 + 1.69132i
\(58\) 7.57301i 0.994385i
\(59\) 8.74456i 1.13845i 0.822183 + 0.569223i \(0.192756\pi\)
−0.822183 + 0.569223i \(0.807244\pi\)
\(60\) 4.00000 0.939764i 0.516398 0.121323i
\(61\) 3.74456i 0.479442i −0.970842 0.239721i \(-0.922944\pi\)
0.970842 0.239721i \(-0.0770560\pi\)
\(62\) 5.84096 0.741803
\(63\) −1.24409 7.83915i −0.156740 0.987640i
\(64\) 1.00000 0.125000
\(65\) 2.37228 + 8.21782i 0.294245 + 1.01930i
\(66\) −2.27567 9.68614i −0.280116 1.19228i
\(67\) 2.67181i 0.326414i −0.986592 0.163207i \(-0.947816\pi\)
0.986592 0.163207i \(-0.0521839\pi\)
\(68\) 2.52434 0.306121
\(69\) 11.4333 2.68614i 1.37640 0.323373i
\(70\) −5.98844 1.87953i −0.715755 0.224647i
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) −2.68614 + 1.33591i −0.316565 + 0.157438i
\(73\) −3.61158 −0.422703 −0.211352 0.977410i \(-0.567787\pi\)
−0.211352 + 0.977410i \(0.567787\pi\)
\(74\) 4.90120i 0.569753i
\(75\) 0.248667 + 1.05842i 0.0287136 + 0.122216i
\(76\) −7.57301 −0.868684
\(77\) −4.55134 + 14.5012i −0.518674 + 1.65257i
\(78\) −3.05842 5.44482i −0.346298 0.616504i
\(79\) −9.37228 −1.05446 −0.527232 0.849721i \(-0.676770\pi\)
−0.527232 + 0.849721i \(0.676770\pi\)
\(80\) 2.37228i 0.265229i
\(81\) 5.43070 7.17687i 0.603411 0.797430i
\(82\) 2.62772i 0.290183i
\(83\) 4.74456i 0.520783i 0.965503 + 0.260392i \(0.0838517\pi\)
−0.965503 + 0.260392i \(0.916148\pi\)
\(84\) 4.57025 + 0.335907i 0.498655 + 0.0366505i
\(85\) 5.98844i 0.649537i
\(86\) −8.37228 −0.902806
\(87\) −12.7692 + 3.00000i −1.36900 + 0.321634i
\(88\) 5.74456 0.612372
\(89\) 10.0000i 1.06000i 0.847998 + 0.529999i \(0.177808\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(90\) −3.16915 6.37228i −0.334058 0.671697i
\(91\) −0.220225 + 9.53685i −0.0230858 + 0.999733i
\(92\) 6.78073i 0.706940i
\(93\) −2.31386 9.84868i −0.239936 1.02126i
\(94\) 4.62772i 0.477313i
\(95\) 17.9653i 1.84320i
\(96\) −0.396143 1.68614i −0.0404312 0.172091i
\(97\) 7.42554 0.753949 0.376975 0.926224i \(-0.376964\pi\)
0.376975 + 0.926224i \(0.376964\pi\)
\(98\) −5.74456 4.00000i −0.580288 0.404061i
\(99\) −15.4307 + 7.67420i −1.55084 + 0.771286i
\(100\) −0.627719 −0.0627719
\(101\) −5.54601 −0.551849 −0.275924 0.961179i \(-0.588984\pi\)
−0.275924 + 0.961179i \(0.588984\pi\)
\(102\) −1.00000 4.25639i −0.0990148 0.421445i
\(103\) 1.62772i 0.160384i −0.996779 0.0801919i \(-0.974447\pi\)
0.996779 0.0801919i \(-0.0255533\pi\)
\(104\) 3.46410 1.00000i 0.339683 0.0980581i
\(105\) −0.796867 + 10.8419i −0.0777662 + 1.05806i
\(106\) 3.16915i 0.307815i
\(107\) 3.75906i 0.363402i −0.983354 0.181701i \(-0.941840\pi\)
0.983354 0.181701i \(-0.0581602\pi\)
\(108\) 3.31662 + 4.00000i 0.319142 + 0.384900i
\(109\) 9.74749i 0.933641i −0.884352 0.466820i \(-0.845399\pi\)
0.884352 0.466820i \(-0.154601\pi\)
\(110\) 13.6277i 1.29935i
\(111\) −8.26411 + 1.94158i −0.784395 + 0.184286i
\(112\) −0.792287 + 2.52434i −0.0748641 + 0.238528i
\(113\) 10.8896i 1.02441i −0.858863 0.512205i \(-0.828829\pi\)
0.858863 0.512205i \(-0.171171\pi\)
\(114\) 3.00000 + 12.7692i 0.280976 + 1.19594i
\(115\) −16.0858 −1.50001
\(116\) 7.57301i 0.703137i
\(117\) −7.96916 + 7.31386i −0.736749 + 0.676167i
\(118\) 8.74456i 0.805002i
\(119\) −2.00000 + 6.37228i −0.183340 + 0.584146i
\(120\) 4.00000 0.939764i 0.365148 0.0857883i
\(121\) 22.0000 2.00000
\(122\) 3.74456i 0.339017i
\(123\) 4.43070 1.04095i 0.399503 0.0938596i
\(124\) 5.84096 0.524534
\(125\) 10.3723i 0.927725i
\(126\) −1.24409 7.83915i −0.110832 0.698367i
\(127\) −4.62772 −0.410644 −0.205322 0.978695i \(-0.565824\pi\)
−0.205322 + 0.978695i \(0.565824\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.31662 + 14.1168i 0.292013 + 1.24292i
\(130\) 2.37228 + 8.21782i 0.208063 + 0.720751i
\(131\) −12.6217 −1.10276 −0.551381 0.834254i \(-0.685899\pi\)
−0.551381 + 0.834254i \(0.685899\pi\)
\(132\) −2.27567 9.68614i −0.198072 0.843070i
\(133\) 6.00000 19.1168i 0.520266 1.65764i
\(134\) 2.67181i 0.230810i
\(135\) −9.48913 + 7.86797i −0.816694 + 0.677167i
\(136\) 2.52434 0.216460
\(137\) −0.883156 −0.0754531 −0.0377266 0.999288i \(-0.512012\pi\)
−0.0377266 + 0.999288i \(0.512012\pi\)
\(138\) 11.4333 2.68614i 0.973264 0.228659i
\(139\) 16.7446i 1.42026i −0.704073 0.710128i \(-0.748637\pi\)
0.704073 0.710128i \(-0.251363\pi\)
\(140\) −5.98844 1.87953i −0.506116 0.158849i
\(141\) −7.80298 + 1.83324i −0.657130 + 0.154387i
\(142\) −2.00000 −0.167836
\(143\) 19.8997 5.74456i 1.66410 0.480384i
\(144\) −2.68614 + 1.33591i −0.223845 + 0.111326i
\(145\) 17.9653 1.49194
\(146\) −3.61158 −0.298896
\(147\) −4.46889 + 11.2707i −0.368588 + 0.929593i
\(148\) 4.90120i 0.402876i
\(149\) −13.3723 −1.09550 −0.547750 0.836642i \(-0.684515\pi\)
−0.547750 + 0.836642i \(0.684515\pi\)
\(150\) 0.248667 + 1.05842i 0.0203035 + 0.0864198i
\(151\) 1.23472i 0.100480i 0.998737 + 0.0502399i \(0.0159986\pi\)
−0.998737 + 0.0502399i \(0.984001\pi\)
\(152\) −7.57301 −0.614252
\(153\) −6.78073 + 3.37228i −0.548189 + 0.272633i
\(154\) −4.55134 + 14.5012i −0.366758 + 1.16854i
\(155\) 13.8564i 1.11297i
\(156\) −3.05842 5.44482i −0.244870 0.435934i
\(157\) 19.7446i 1.57579i −0.615811 0.787894i \(-0.711172\pi\)
0.615811 0.787894i \(-0.288828\pi\)
\(158\) −9.37228 −0.745619
\(159\) −5.34363 + 1.25544i −0.423777 + 0.0995627i
\(160\) 2.37228i 0.187545i
\(161\) −17.1168 5.37228i −1.34900 0.423395i
\(162\) 5.43070 7.17687i 0.426676 0.563868i
\(163\) 11.6819i 0.914999i −0.889210 0.457499i \(-0.848745\pi\)
0.889210 0.457499i \(-0.151255\pi\)
\(164\) 2.62772i 0.205190i
\(165\) 22.9783 5.39853i 1.78885 0.420275i
\(166\) 4.74456i 0.368249i
\(167\) 18.3723i 1.42169i −0.703349 0.710845i \(-0.748313\pi\)
0.703349 0.710845i \(-0.251687\pi\)
\(168\) 4.57025 + 0.335907i 0.352602 + 0.0259158i
\(169\) 11.0000 6.92820i 0.846154 0.532939i
\(170\) 5.98844i 0.459292i
\(171\) 20.3422 10.1168i 1.55561 0.773654i
\(172\) −8.37228 −0.638380
\(173\) 23.9538 1.82117 0.910585 0.413321i \(-0.135631\pi\)
0.910585 + 0.413321i \(0.135631\pi\)
\(174\) −12.7692 + 3.00000i −0.968028 + 0.227429i
\(175\) 0.497333 1.58457i 0.0375949 0.119783i
\(176\) 5.74456 0.433013
\(177\) 14.7446 3.46410i 1.10827 0.260378i
\(178\) 10.0000i 0.749532i
\(179\) 6.33830i 0.473746i −0.971541 0.236873i \(-0.923877\pi\)
0.971541 0.236873i \(-0.0761226\pi\)
\(180\) −3.16915 6.37228i −0.236214 0.474962i
\(181\) 14.6277i 1.08727i −0.839322 0.543635i \(-0.817048\pi\)
0.839322 0.543635i \(-0.182952\pi\)
\(182\) −0.220225 + 9.53685i −0.0163242 + 0.706918i
\(183\) −6.31386 + 1.48338i −0.466734 + 0.109655i
\(184\) 6.78073i 0.499882i
\(185\) 11.6270 0.854836
\(186\) −2.31386 9.84868i −0.169660 0.722141i
\(187\) 14.5012 1.06043
\(188\) 4.62772i 0.337511i
\(189\) −12.7251 + 5.20313i −0.925613 + 0.378472i
\(190\) 17.9653i 1.30334i
\(191\) 19.5499i 1.41458i 0.706923 + 0.707290i \(0.250083\pi\)
−0.706923 + 0.707290i \(0.749917\pi\)
\(192\) −0.396143 1.68614i −0.0285892 0.121687i
\(193\) 20.7846i 1.49611i 0.663637 + 0.748054i \(0.269012\pi\)
−0.663637 + 0.748054i \(0.730988\pi\)
\(194\) 7.42554 0.533122
\(195\) 12.9166 7.25544i 0.924980 0.519573i
\(196\) −5.74456 4.00000i −0.410326 0.285714i
\(197\) 3.88316 0.276663 0.138332 0.990386i \(-0.455826\pi\)
0.138332 + 0.990386i \(0.455826\pi\)
\(198\) −15.4307 + 7.67420i −1.09661 + 0.545382i
\(199\) 5.11684i 0.362723i −0.983416 0.181362i \(-0.941950\pi\)
0.983416 0.181362i \(-0.0580505\pi\)
\(200\) −0.627719 −0.0443864
\(201\) −4.50506 + 1.05842i −0.317762 + 0.0746553i
\(202\) −5.54601 −0.390216
\(203\) 19.1168 + 6.00000i 1.34174 + 0.421117i
\(204\) −1.00000 4.25639i −0.0700140 0.298007i
\(205\) −6.23369 −0.435380
\(206\) 1.62772i 0.113409i
\(207\) −9.05842 18.2140i −0.629604 1.26596i
\(208\) 3.46410 1.00000i 0.240192 0.0693375i
\(209\) −43.5036 −3.00921
\(210\) −0.796867 + 10.8419i −0.0549890 + 0.748163i
\(211\) 11.6277 0.800485 0.400243 0.916409i \(-0.368926\pi\)
0.400243 + 0.916409i \(0.368926\pi\)
\(212\) 3.16915i 0.217658i
\(213\) 0.792287 + 3.37228i 0.0542866 + 0.231065i
\(214\) 3.75906i 0.256964i
\(215\) 19.8614i 1.35454i
\(216\) 3.31662 + 4.00000i 0.225668 + 0.272166i
\(217\) −4.62772 + 14.7446i −0.314150 + 1.00093i
\(218\) 9.74749i 0.660184i
\(219\) 1.43070 + 6.08963i 0.0966780 + 0.411499i
\(220\) 13.6277i 0.918781i
\(221\) 8.74456 2.52434i 0.588223 0.169805i
\(222\) −8.26411 + 1.94158i −0.554651 + 0.130310i
\(223\) 9.30506 0.623113 0.311557 0.950228i \(-0.399150\pi\)
0.311557 + 0.950228i \(0.399150\pi\)
\(224\) −0.792287 + 2.52434i −0.0529369 + 0.168664i
\(225\) 1.68614 0.838574i 0.112409 0.0559049i
\(226\) 10.8896i 0.724368i
\(227\) 11.4891i 0.762560i 0.924460 + 0.381280i \(0.124517\pi\)
−0.924460 + 0.381280i \(0.875483\pi\)
\(228\) 3.00000 + 12.7692i 0.198680 + 0.845659i
\(229\) −1.58457 −0.104712 −0.0523558 0.998628i \(-0.516673\pi\)
−0.0523558 + 0.998628i \(0.516673\pi\)
\(230\) −16.0858 −1.06067
\(231\) 26.2541 + 1.92964i 1.72739 + 0.126961i
\(232\) 7.57301i 0.497193i
\(233\) 12.4742i 0.817213i 0.912711 + 0.408606i \(0.133985\pi\)
−0.912711 + 0.408606i \(0.866015\pi\)
\(234\) −7.96916 + 7.31386i −0.520960 + 0.478122i
\(235\) 10.9783 0.716142
\(236\) 8.74456i 0.569223i
\(237\) 3.71277 + 15.8030i 0.241170 + 1.02651i
\(238\) −2.00000 + 6.37228i −0.129641 + 0.413054i
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 4.00000 0.939764i 0.258199 0.0606615i
\(241\) −23.3639 −1.50500 −0.752499 0.658593i \(-0.771152\pi\)
−0.752499 + 0.658593i \(0.771152\pi\)
\(242\) 22.0000 1.41421
\(243\) −14.2525 6.31386i −0.914302 0.405034i
\(244\) 3.74456i 0.239721i
\(245\) 9.48913 13.6277i 0.606238 0.870643i
\(246\) 4.43070 1.04095i 0.282491 0.0663688i
\(247\) −26.2337 + 7.57301i −1.66921 + 0.481859i
\(248\) 5.84096 0.370901
\(249\) 8.00000 1.87953i 0.506979 0.119110i
\(250\) 10.3723i 0.656001i
\(251\) 0.147477 0.00930865 0.00465433 0.999989i \(-0.498518\pi\)
0.00465433 + 0.999989i \(0.498518\pi\)
\(252\) −1.24409 7.83915i −0.0783701 0.493820i
\(253\) 38.9523i 2.44891i
\(254\) −4.62772 −0.290369
\(255\) 10.0974 2.37228i 0.632321 0.148558i
\(256\) 1.00000 0.0625000
\(257\) 12.2718 0.765496 0.382748 0.923853i \(-0.374978\pi\)
0.382748 + 0.923853i \(0.374978\pi\)
\(258\) 3.31662 + 14.1168i 0.206484 + 0.878876i
\(259\) 12.3723 + 3.88316i 0.768776 + 0.241288i
\(260\) 2.37228 + 8.21782i 0.147123 + 0.509648i
\(261\) 10.1168 + 20.3422i 0.626217 + 1.25915i
\(262\) −12.6217 −0.779771
\(263\) 20.4897i 1.26345i −0.775194 0.631723i \(-0.782348\pi\)
0.775194 0.631723i \(-0.217652\pi\)
\(264\) −2.27567 9.68614i −0.140058 0.596141i
\(265\) 7.51811 0.461834
\(266\) 6.00000 19.1168i 0.367884 1.17213i
\(267\) 16.8614 3.96143i 1.03190 0.242436i
\(268\) 2.67181i 0.163207i
\(269\) −4.55134 −0.277500 −0.138750 0.990327i \(-0.544308\pi\)
−0.138750 + 0.990327i \(0.544308\pi\)
\(270\) −9.48913 + 7.86797i −0.577490 + 0.478829i
\(271\) −14.6487 −0.889845 −0.444922 0.895569i \(-0.646769\pi\)
−0.444922 + 0.895569i \(0.646769\pi\)
\(272\) 2.52434 0.153060
\(273\) 16.1677 3.40663i 0.978514 0.206179i
\(274\) −0.883156 −0.0533534
\(275\) −3.60597 −0.217448
\(276\) 11.4333 2.68614i 0.688201 0.161687i
\(277\) −5.48913 −0.329810 −0.164905 0.986309i \(-0.552732\pi\)
−0.164905 + 0.986309i \(0.552732\pi\)
\(278\) 16.7446i 1.00427i
\(279\) −15.6896 + 7.80298i −0.939315 + 0.467152i
\(280\) −5.98844 1.87953i −0.357878 0.112323i
\(281\) −14.0000 −0.835170 −0.417585 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) −7.80298 + 1.83324i −0.464661 + 0.109168i
\(283\) 5.37228i 0.319349i 0.987170 + 0.159674i \(0.0510445\pi\)
−0.987170 + 0.159674i \(0.948956\pi\)
\(284\) −2.00000 −0.118678
\(285\) −30.2921 + 7.11684i −1.79435 + 0.421565i
\(286\) 19.8997 5.74456i 1.17670 0.339683i
\(287\) −6.63325 2.08191i −0.391548 0.122891i
\(288\) −2.68614 + 1.33591i −0.158282 + 0.0787191i
\(289\) −10.6277 −0.625160
\(290\) 17.9653 1.05496
\(291\) −2.94158 12.5205i −0.172438 0.733965i
\(292\) −3.61158 −0.211352
\(293\) 11.4891i 0.671202i −0.942004 0.335601i \(-0.891061\pi\)
0.942004 0.335601i \(-0.108939\pi\)
\(294\) −4.46889 + 11.2707i −0.260631 + 0.657321i
\(295\) −20.7446 −1.20780
\(296\) 4.90120i 0.284876i
\(297\) 19.0526 + 22.9783i 1.10554 + 1.33333i
\(298\) −13.3723 −0.774635
\(299\) 6.78073 + 23.4891i 0.392140 + 1.35841i
\(300\) 0.248667 + 1.05842i 0.0143568 + 0.0611080i
\(301\) 6.63325 21.1345i 0.382334 1.21817i
\(302\) 1.23472i 0.0710500i
\(303\) 2.19702 + 9.35135i 0.126215 + 0.537221i
\(304\) −7.57301 −0.434342
\(305\) 8.88316 0.508648
\(306\) −6.78073 + 3.37228i −0.387628 + 0.192780i
\(307\) −14.5561 −0.830762 −0.415381 0.909648i \(-0.636352\pi\)
−0.415381 + 0.909648i \(0.636352\pi\)
\(308\) −4.55134 + 14.5012i −0.259337 + 0.826284i
\(309\) −2.74456 + 0.644810i −0.156133 + 0.0366820i
\(310\) 13.8564i 0.786991i
\(311\) −10.3923 −0.589294 −0.294647 0.955606i \(-0.595202\pi\)
−0.294647 + 0.955606i \(0.595202\pi\)
\(312\) −3.05842 5.44482i −0.173149 0.308252i
\(313\) 8.74456i 0.494272i −0.968981 0.247136i \(-0.920511\pi\)
0.968981 0.247136i \(-0.0794894\pi\)
\(314\) 19.7446i 1.11425i
\(315\) 18.5967 2.95132i 1.04780 0.166288i
\(316\) −9.37228 −0.527232
\(317\) 24.8614 1.39636 0.698178 0.715924i \(-0.253994\pi\)
0.698178 + 0.715924i \(0.253994\pi\)
\(318\) −5.34363 + 1.25544i −0.299656 + 0.0704014i
\(319\) 43.5036i 2.43574i
\(320\) 2.37228i 0.132615i
\(321\) −6.33830 + 1.48913i −0.353769 + 0.0831149i
\(322\) −17.1168 5.37228i −0.953884 0.299386i
\(323\) −19.1168 −1.06369
\(324\) 5.43070 7.17687i 0.301706 0.398715i
\(325\) −2.17448 + 0.627719i −0.120619 + 0.0348196i
\(326\) 11.6819i 0.647002i
\(327\) −16.4356 + 3.86141i −0.908893 + 0.213536i
\(328\) 2.62772i 0.145091i
\(329\) 11.6819 + 3.66648i 0.644045 + 0.202140i
\(330\) 22.9783 5.39853i 1.26491 0.297179i
\(331\) 32.6689i 1.79565i 0.440357 + 0.897823i \(0.354852\pi\)
−0.440357 + 0.897823i \(0.645148\pi\)
\(332\) 4.74456i 0.260392i
\(333\) 6.54755 + 13.1653i 0.358803 + 0.721455i
\(334\) 18.3723i 1.00529i
\(335\) 6.33830 0.346298
\(336\) 4.57025 + 0.335907i 0.249327 + 0.0183252i
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) 11.0000 6.92820i 0.598321 0.376845i
\(339\) −18.3615 + 4.31386i −0.997258 + 0.234297i
\(340\) 5.98844i 0.324769i
\(341\) 33.5538 1.81704
\(342\) 20.3422 10.1168i 1.09998 0.547056i
\(343\) 14.6487 11.3321i 0.790955 0.611874i
\(344\) −8.37228 −0.451403
\(345\) 6.37228 + 27.1229i 0.343072 + 1.46025i
\(346\) 23.9538 1.28776
\(347\) 25.8333i 1.38680i 0.720551 + 0.693402i \(0.243889\pi\)
−0.720551 + 0.693402i \(0.756111\pi\)
\(348\) −12.7692 + 3.00000i −0.684499 + 0.160817i
\(349\) 23.3639 1.25064 0.625319 0.780369i \(-0.284969\pi\)
0.625319 + 0.780369i \(0.284969\pi\)
\(350\) 0.497333 1.58457i 0.0265836 0.0846990i
\(351\) 15.4891 + 10.5398i 0.826748 + 0.562572i
\(352\) 5.74456 0.306186
\(353\) 6.11684i 0.325567i −0.986662 0.162783i \(-0.947953\pi\)
0.986662 0.162783i \(-0.0520472\pi\)
\(354\) 14.7446 3.46410i 0.783665 0.184115i
\(355\) 4.74456i 0.251815i
\(356\) 10.0000i 0.529999i
\(357\) 11.5368 + 0.847944i 0.610595 + 0.0448779i
\(358\) 6.33830i 0.334989i
\(359\) −28.2337 −1.49012 −0.745059 0.666999i \(-0.767578\pi\)
−0.745059 + 0.666999i \(0.767578\pi\)
\(360\) −3.16915 6.37228i −0.167029 0.335849i
\(361\) 38.3505 2.01845
\(362\) 14.6277i 0.768816i
\(363\) −8.71516 37.0951i −0.457427 1.94699i
\(364\) −0.220225 + 9.53685i −0.0115429 + 0.499867i
\(365\) 8.56768i 0.448453i
\(366\) −6.31386 + 1.48338i −0.330031 + 0.0775377i
\(367\) 6.74456i 0.352063i 0.984385 + 0.176032i \(0.0563261\pi\)
−0.984385 + 0.176032i \(0.943674\pi\)
\(368\) 6.78073i 0.353470i
\(369\) −3.51039 7.05842i −0.182744 0.367447i
\(370\) 11.6270 0.604460
\(371\) 8.00000 + 2.51087i 0.415339 + 0.130358i
\(372\) −2.31386 9.84868i −0.119968 0.510631i
\(373\) 22.2337 1.15122 0.575608 0.817726i \(-0.304765\pi\)
0.575608 + 0.817726i \(0.304765\pi\)
\(374\) 14.5012 0.749840
\(375\) 17.4891 4.10891i 0.903135 0.212183i
\(376\) 4.62772i 0.238656i
\(377\) −7.57301 26.2337i −0.390030 1.35110i
\(378\) −12.7251 + 5.20313i −0.654507 + 0.267620i
\(379\) 14.8511i 0.762848i 0.924400 + 0.381424i \(0.124566\pi\)
−0.924400 + 0.381424i \(0.875434\pi\)
\(380\) 17.9653i 0.921601i
\(381\) 1.83324 + 7.80298i 0.0939198 + 0.399759i
\(382\) 19.5499i 1.00026i
\(383\) 26.4891i 1.35353i −0.736199 0.676766i \(-0.763381\pi\)
0.736199 0.676766i \(-0.236619\pi\)
\(384\) −0.396143 1.68614i −0.0202156 0.0860455i
\(385\) −34.4010 10.7971i −1.75324 0.550269i
\(386\) 20.7846i 1.05791i
\(387\) 22.4891 11.1846i 1.14319 0.568545i
\(388\) 7.42554 0.376975
\(389\) 7.92287i 0.401705i 0.979621 + 0.200853i \(0.0643713\pi\)
−0.979621 + 0.200853i \(0.935629\pi\)
\(390\) 12.9166 7.25544i 0.654060 0.367393i
\(391\) 17.1168i 0.865636i
\(392\) −5.74456 4.00000i −0.290144 0.202031i
\(393\) 5.00000 + 21.2819i 0.252217 + 1.07353i
\(394\) 3.88316 0.195631
\(395\) 22.2337i 1.11870i
\(396\) −15.4307 + 7.67420i −0.775422 + 0.385643i
\(397\) 6.63325 0.332913 0.166457 0.986049i \(-0.446767\pi\)
0.166457 + 0.986049i \(0.446767\pi\)
\(398\) 5.11684i 0.256484i
\(399\) −34.6105 2.54383i −1.73269 0.127351i
\(400\) −0.627719 −0.0313859
\(401\) −16.9783 −0.847853 −0.423927 0.905697i \(-0.639349\pi\)
−0.423927 + 0.905697i \(0.639349\pi\)
\(402\) −4.50506 + 1.05842i −0.224692 + 0.0527893i
\(403\) 20.2337 5.84096i 1.00791 0.290959i
\(404\) −5.54601 −0.275924
\(405\) 17.0256 + 12.8832i 0.846007 + 0.640169i
\(406\) 19.1168 + 6.00000i 0.948753 + 0.297775i
\(407\) 28.1552i 1.39560i
\(408\) −1.00000 4.25639i −0.0495074 0.210723i
\(409\) −6.57835 −0.325278 −0.162639 0.986686i \(-0.552001\pi\)
−0.162639 + 0.986686i \(0.552001\pi\)
\(410\) −6.23369 −0.307860
\(411\) 0.349857 + 1.48913i 0.0172571 + 0.0734531i
\(412\) 1.62772i 0.0801919i
\(413\) −22.0742 6.92820i −1.08620 0.340915i
\(414\) −9.05842 18.2140i −0.445197 0.895169i
\(415\) −11.2554 −0.552508
\(416\) 3.46410 1.00000i 0.169842 0.0490290i
\(417\) −28.2337 + 6.63325i −1.38261 + 0.324832i
\(418\) −43.5036 −2.12783
\(419\) 8.36530 0.408672 0.204336 0.978901i \(-0.434497\pi\)
0.204336 + 0.978901i \(0.434497\pi\)
\(420\) −0.796867 + 10.8419i −0.0388831 + 0.529031i
\(421\) 6.43087i 0.313421i 0.987645 + 0.156711i \(0.0500890\pi\)
−0.987645 + 0.156711i \(0.949911\pi\)
\(422\) 11.6277 0.566028
\(423\) 6.18220 + 12.4307i 0.300589 + 0.604401i
\(424\) 3.16915i 0.153907i
\(425\) −1.58457 −0.0768631
\(426\) 0.792287 + 3.37228i 0.0383864 + 0.163388i
\(427\) 9.45254 + 2.96677i 0.457441 + 0.143572i
\(428\) 3.75906i 0.181701i
\(429\) −17.5693 31.2781i −0.848254 1.51012i
\(430\) 19.8614i 0.957802i
\(431\) 6.23369 0.300266 0.150133 0.988666i \(-0.452030\pi\)
0.150133 + 0.988666i \(0.452030\pi\)
\(432\) 3.31662 + 4.00000i 0.159571 + 0.192450i
\(433\) 38.4674i 1.84862i 0.381638 + 0.924312i \(0.375360\pi\)
−0.381638 + 0.924312i \(0.624640\pi\)
\(434\) −4.62772 + 14.7446i −0.222138 + 0.707762i
\(435\) −7.11684 30.2921i −0.341227 1.45239i
\(436\) 9.74749i 0.466820i
\(437\) 51.3505i 2.45643i
\(438\) 1.43070 + 6.08963i 0.0683616 + 0.290974i
\(439\) 34.6060i 1.65165i 0.563924 + 0.825826i \(0.309291\pi\)
−0.563924 + 0.825826i \(0.690709\pi\)
\(440\) 13.6277i 0.649676i
\(441\) 20.7743 + 3.07036i 0.989254 + 0.146208i
\(442\) 8.74456 2.52434i 0.415936 0.120071i
\(443\) 9.80240i 0.465726i −0.972510 0.232863i \(-0.925191\pi\)
0.972510 0.232863i \(-0.0748094\pi\)
\(444\) −8.26411 + 1.94158i −0.392197 + 0.0921432i
\(445\) −23.7228 −1.12457
\(446\) 9.30506 0.440608
\(447\) 5.29734 + 22.5475i 0.250556 + 1.06646i
\(448\) −0.792287 + 2.52434i −0.0374320 + 0.119264i
\(449\) −3.11684 −0.147093 −0.0735465 0.997292i \(-0.523432\pi\)
−0.0735465 + 0.997292i \(0.523432\pi\)
\(450\) 1.68614 0.838574i 0.0794854 0.0395308i
\(451\) 15.0951i 0.710800i
\(452\) 10.8896i 0.512205i
\(453\) 2.08191 0.489125i 0.0978165 0.0229811i
\(454\) 11.4891i 0.539211i
\(455\) −22.6241 0.522435i −1.06063 0.0244921i
\(456\) 3.00000 + 12.7692i 0.140488 + 0.597971i
\(457\) 2.87419i 0.134449i 0.997738 + 0.0672246i \(0.0214144\pi\)
−0.997738 + 0.0672246i \(0.978586\pi\)
\(458\) −1.58457 −0.0740423
\(459\) 8.37228 + 10.0974i 0.390785 + 0.471304i
\(460\) −16.0858 −0.750004
\(461\) 18.6060i 0.866566i 0.901258 + 0.433283i \(0.142645\pi\)
−0.901258 + 0.433283i \(0.857355\pi\)
\(462\) 26.2541 + 1.92964i 1.22145 + 0.0897750i
\(463\) 15.0911i 0.701344i −0.936498 0.350672i \(-0.885953\pi\)
0.936498 0.350672i \(-0.114047\pi\)
\(464\) 7.57301i 0.351568i
\(465\) 23.3639 5.48913i 1.08347 0.254552i
\(466\) 12.4742i 0.577857i
\(467\) 18.2603 0.844985 0.422492 0.906367i \(-0.361155\pi\)
0.422492 + 0.906367i \(0.361155\pi\)
\(468\) −7.96916 + 7.31386i −0.368374 + 0.338083i
\(469\) 6.74456 + 2.11684i 0.311435 + 0.0977468i
\(470\) 10.9783 0.506389
\(471\) −33.2921 + 7.82168i −1.53402 + 0.360404i
\(472\) 8.74456i 0.402501i
\(473\) −48.0951 −2.21141
\(474\) 3.71277 + 15.8030i 0.170533 + 0.725855i
\(475\) 4.75372 0.218116
\(476\) −2.00000 + 6.37228i −0.0916698 + 0.292073i
\(477\) 4.23369 + 8.51278i 0.193847 + 0.389773i
\(478\) 18.0000 0.823301
\(479\) 34.3723i 1.57051i 0.619173 + 0.785255i \(0.287468\pi\)
−0.619173 + 0.785255i \(0.712532\pi\)
\(480\) 4.00000 0.939764i 0.182574 0.0428942i
\(481\) −4.90120 16.9783i −0.223475 0.774142i
\(482\) −23.3639 −1.06419
\(483\) −2.27770 + 30.9896i −0.103639 + 1.41008i
\(484\) 22.0000 1.00000
\(485\) 17.6155i 0.799877i
\(486\) −14.2525 6.31386i −0.646509 0.286402i
\(487\) 10.9822i 0.497652i 0.968548 + 0.248826i \(0.0800447\pi\)
−0.968548 + 0.248826i \(0.919955\pi\)
\(488\) 3.74456i 0.169508i
\(489\) −19.6974 + 4.62772i −0.890746 + 0.209273i
\(490\) 9.48913 13.6277i 0.428675 0.615638i
\(491\) 8.21782i 0.370865i −0.982657 0.185433i \(-0.940631\pi\)
0.982657 0.185433i \(-0.0593686\pi\)
\(492\) 4.43070 1.04095i 0.199752 0.0469298i
\(493\) 19.1168i 0.860979i
\(494\) −26.2337 + 7.57301i −1.18031 + 0.340726i
\(495\) −18.2054 36.6060i −0.818270 1.64532i
\(496\) 5.84096 0.262267
\(497\) 1.58457 5.04868i 0.0710779 0.226464i
\(498\) 8.00000 1.87953i 0.358489 0.0842236i
\(499\) 26.0357i 1.16552i 0.812646 + 0.582758i \(0.198027\pi\)
−0.812646 + 0.582758i \(0.801973\pi\)
\(500\) 10.3723i 0.463863i
\(501\) −30.9783 + 7.27806i −1.38401 + 0.325160i
\(502\) 0.147477 0.00658221
\(503\) −14.1514 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(504\) −1.24409 7.83915i −0.0554160 0.349183i
\(505\) 13.1567i 0.585465i
\(506\) 38.9523i 1.73164i
\(507\) −16.0395 15.8030i −0.712339 0.701835i
\(508\) −4.62772 −0.205322
\(509\) 4.88316i 0.216442i 0.994127 + 0.108221i \(0.0345154\pi\)
−0.994127 + 0.108221i \(0.965485\pi\)
\(510\) 10.0974 2.37228i 0.447118 0.105046i
\(511\) 2.86141 9.11684i 0.126581 0.403305i
\(512\) 1.00000 0.0441942
\(513\) −25.1168 30.2921i −1.10894 1.33743i
\(514\) 12.2718 0.541287
\(515\) 3.86141 0.170154
\(516\) 3.31662 + 14.1168i 0.146006 + 0.621459i
\(517\) 26.5842i 1.16917i
\(518\) 12.3723 + 3.88316i 0.543607 + 0.170616i
\(519\) −9.48913 40.3894i −0.416526 1.77290i
\(520\) 2.37228 + 8.21782i 0.104031 + 0.360375i
\(521\) −35.9855 −1.57656 −0.788278 0.615320i \(-0.789027\pi\)
−0.788278 + 0.615320i \(0.789027\pi\)
\(522\) 10.1168 + 20.3422i 0.442802 + 0.890353i
\(523\) 14.3505i 0.627505i 0.949505 + 0.313752i \(0.101586\pi\)
−0.949505 + 0.313752i \(0.898414\pi\)
\(524\) −12.6217 −0.551381
\(525\) −2.86883 0.210855i −0.125206 0.00920248i
\(526\) 20.4897i 0.893391i
\(527\) 14.7446 0.642283
\(528\) −2.27567 9.68614i −0.0990359 0.421535i
\(529\) −22.9783 −0.999054
\(530\) 7.51811 0.326566
\(531\) −11.6819 23.4891i −0.506952 1.01934i
\(532\) 6.00000 19.1168i 0.260133 0.828820i
\(533\) 2.62772 + 9.10268i 0.113819 + 0.394281i
\(534\) 16.8614 3.96143i 0.729664 0.171428i
\(535\) 8.91754 0.385539
\(536\) 2.67181i 0.115405i
\(537\) −10.6873 + 2.51087i −0.461189 + 0.108352i
\(538\) −4.55134 −0.196222
\(539\) −33.0000 22.9783i −1.42141 0.989743i
\(540\) −9.48913 + 7.86797i −0.408347 + 0.338583i
\(541\) 5.39853i 0.232101i −0.993243 0.116051i \(-0.962977\pi\)
0.993243 0.116051i \(-0.0370234\pi\)
\(542\) −14.6487 −0.629215
\(543\) −24.6644 + 5.79468i −1.05845 + 0.248673i
\(544\) 2.52434 0.108230
\(545\) 23.1238 0.990515
\(546\) 16.1677 3.40663i 0.691914 0.145790i
\(547\) 17.4891 0.747781 0.373890 0.927473i \(-0.378024\pi\)
0.373890 + 0.927473i \(0.378024\pi\)
\(548\) −0.883156 −0.0377266
\(549\) 5.00239 + 10.0584i 0.213497 + 0.429283i
\(550\) −3.60597 −0.153759
\(551\) 57.3505i 2.44321i
\(552\) 11.4333 2.68614i 0.486632 0.114330i
\(553\) 7.42554 23.6588i 0.315766 1.00607i
\(554\) −5.48913 −0.233211
\(555\) −4.60597 19.6048i −0.195513 0.832177i
\(556\) 16.7446i 0.710128i
\(557\) 24.6277 1.04351 0.521755 0.853095i \(-0.325278\pi\)
0.521755 + 0.853095i \(0.325278\pi\)
\(558\) −15.6896 + 7.80298i −0.664196 + 0.330327i
\(559\) −29.0024 + 8.37228i −1.22667 + 0.354110i
\(560\) −5.98844 1.87953i −0.253058 0.0794245i
\(561\) −5.74456 24.4511i −0.242536 1.03233i
\(562\) −14.0000 −0.590554
\(563\) 35.7832 1.50808 0.754040 0.656828i \(-0.228102\pi\)
0.754040 + 0.656828i \(0.228102\pi\)
\(564\) −7.80298 + 1.83324i −0.328565 + 0.0771934i
\(565\) 25.8333 1.08681
\(566\) 5.37228i 0.225814i
\(567\) 13.8142 + 19.3951i 0.580141 + 0.814516i
\(568\) −2.00000 −0.0839181
\(569\) 39.5971i 1.66000i −0.557765 0.829999i \(-0.688341\pi\)
0.557765 0.829999i \(-0.311659\pi\)
\(570\) −30.2921 + 7.11684i −1.26879 + 0.298092i
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 19.8997 5.74456i 0.832050 0.240192i
\(573\) 32.9639 7.74456i 1.37709 0.323534i
\(574\) −6.63325 2.08191i −0.276866 0.0868971i
\(575\) 4.25639i 0.177504i
\(576\) −2.68614 + 1.33591i −0.111923 + 0.0556628i
\(577\) −6.92820 −0.288425 −0.144212 0.989547i \(-0.546065\pi\)
−0.144212 + 0.989547i \(0.546065\pi\)
\(578\) −10.6277 −0.442055
\(579\) 35.0458 8.23369i 1.45645 0.342180i
\(580\) 17.9653 0.745969
\(581\) −11.9769 3.75906i −0.496885 0.155952i
\(582\) −2.94158 12.5205i −0.121932 0.518991i
\(583\) 18.2054i 0.753989i
\(584\) −3.61158 −0.149448
\(585\) −17.3505 18.9051i −0.717356 0.781629i
\(586\) 11.4891i 0.474611i
\(587\) 5.25544i 0.216915i −0.994101 0.108458i \(-0.965409\pi\)
0.994101 0.108458i \(-0.0345912\pi\)
\(588\) −4.46889 + 11.2707i −0.184294 + 0.464796i
\(589\) −44.2337 −1.82262
\(590\) −20.7446 −0.854040
\(591\) −1.53829 6.54755i −0.0632767 0.269330i
\(592\) 4.90120i 0.201438i
\(593\) 30.7446i 1.26253i 0.775568 + 0.631264i \(0.217464\pi\)
−0.775568 + 0.631264i \(0.782536\pi\)
\(594\) 19.0526 + 22.9783i 0.781736 + 0.942809i
\(595\) −15.1168 4.74456i −0.619730 0.194508i
\(596\) −13.3723 −0.547750
\(597\) −8.62772 + 2.02700i −0.353109 + 0.0829598i
\(598\) 6.78073 + 23.4891i 0.277285 + 0.960542i
\(599\) 1.43710i 0.0587182i 0.999569 + 0.0293591i \(0.00934663\pi\)
−0.999569 + 0.0293591i \(0.990653\pi\)
\(600\) 0.248667 + 1.05842i 0.0101518 + 0.0432099i
\(601\) 26.0000i 1.06056i −0.847822 0.530281i \(-0.822086\pi\)
0.847822 0.530281i \(-0.177914\pi\)
\(602\) 6.63325 21.1345i 0.270351 0.861377i
\(603\) 3.56930 + 7.17687i 0.145353 + 0.292265i
\(604\) 1.23472i 0.0502399i
\(605\) 52.1902i 2.12183i
\(606\) 2.19702 + 9.35135i 0.0892476 + 0.379873i
\(607\) 0.883156i 0.0358462i 0.999839 + 0.0179231i \(0.00570541\pi\)
−0.999839 + 0.0179231i \(0.994295\pi\)
\(608\) −7.57301 −0.307126
\(609\) 2.54383 34.6105i 0.103081 1.40249i
\(610\) 8.88316 0.359668
\(611\) −4.62772 16.0309i −0.187217 0.648540i
\(612\) −6.78073 + 3.37228i −0.274095 + 0.136316i
\(613\) 3.02167i 0.122044i −0.998136 0.0610221i \(-0.980564\pi\)
0.998136 0.0610221i \(-0.0194360\pi\)
\(614\) −14.5561 −0.587437
\(615\) 2.46943 + 10.5109i 0.0995772 + 0.423839i
\(616\) −4.55134 + 14.5012i −0.183379 + 0.584271i
\(617\) 22.6060 0.910082 0.455041 0.890470i \(-0.349625\pi\)
0.455041 + 0.890470i \(0.349625\pi\)
\(618\) −2.74456 + 0.644810i −0.110403 + 0.0259381i
\(619\) −16.3807 −0.658398 −0.329199 0.944261i \(-0.606779\pi\)
−0.329199 + 0.944261i \(0.606779\pi\)
\(620\) 13.8564i 0.556487i
\(621\) −27.1229 + 22.4891i −1.08840 + 0.902458i
\(622\) −10.3923 −0.416693
\(623\) −25.2434 7.92287i −1.01135 0.317423i
\(624\) −3.05842 5.44482i −0.122435 0.217967i
\(625\) −27.7446 −1.10978
\(626\) 8.74456i 0.349503i
\(627\) 17.2337 + 73.3533i 0.688247 + 2.92945i
\(628\) 19.7446i 0.787894i
\(629\) 12.3723i 0.493315i
\(630\) 18.5967 2.95132i 0.740909 0.117584i
\(631\) 24.3036i 0.967512i 0.875203 + 0.483756i \(0.160728\pi\)
−0.875203 + 0.483756i \(0.839272\pi\)
\(632\) −9.37228 −0.372809
\(633\) −4.60625 19.6060i −0.183082 0.779267i
\(634\) 24.8614 0.987373
\(635\) 10.9783i 0.435659i
\(636\) −5.34363 + 1.25544i −0.211889 + 0.0497813i
\(637\) −23.8997 8.11184i −0.946943 0.321403i
\(638\) 43.5036i 1.72233i
\(639\) 5.37228 2.67181i 0.212524 0.105695i
\(640\) 2.37228i 0.0937727i
\(641\) 20.9870i 0.828936i 0.910064 + 0.414468i \(0.136032\pi\)
−0.910064 + 0.414468i \(0.863968\pi\)
\(642\) −6.33830 + 1.48913i −0.250153 + 0.0587711i
\(643\) −28.3576 −1.11832 −0.559158 0.829061i \(-0.688875\pi\)
−0.559158 + 0.829061i \(0.688875\pi\)
\(644\) −17.1168 5.37228i −0.674498 0.211698i
\(645\) −33.4891 + 7.86797i −1.31863 + 0.309801i
\(646\) −19.1168 −0.752142
\(647\) −32.7615 −1.28799 −0.643994 0.765031i \(-0.722724\pi\)
−0.643994 + 0.765031i \(0.722724\pi\)
\(648\) 5.43070 7.17687i 0.213338 0.281934i
\(649\) 50.2337i 1.97184i
\(650\) −2.17448 + 0.627719i −0.0852902 + 0.0246212i
\(651\) 26.6946 + 1.96202i 1.04625 + 0.0768977i
\(652\) 11.6819i 0.457499i
\(653\) 11.3321i 0.443458i −0.975108 0.221729i \(-0.928830\pi\)
0.975108 0.221729i \(-0.0711701\pi\)
\(654\) −16.4356 + 3.86141i −0.642685 + 0.150993i
\(655\) 29.9422i 1.16994i
\(656\) 2.62772i 0.102595i
\(657\) 9.70121 4.82473i 0.378480 0.188231i
\(658\) 11.6819 + 3.66648i 0.455409 + 0.142934i
\(659\) 48.3123i 1.88198i 0.338436 + 0.940990i \(0.390102\pi\)
−0.338436 + 0.940990i \(0.609898\pi\)
\(660\) 22.9783 5.39853i 0.894427 0.210138i
\(661\) −4.16381 −0.161954 −0.0809768 0.996716i \(-0.525804\pi\)
−0.0809768 + 0.996716i \(0.525804\pi\)
\(662\) 32.6689i 1.26971i
\(663\) −7.72049 13.7446i −0.299839 0.533795i
\(664\) 4.74456i 0.184125i
\(665\) 45.3505 + 14.2337i 1.75862 + 0.551959i
\(666\) 6.54755 + 13.1653i 0.253712 + 0.510145i
\(667\) 51.3505 1.98830
\(668\) 18.3723i 0.710845i
\(669\) −3.68614 15.6896i −0.142514 0.606597i
\(670\) 6.33830 0.244870
\(671\) 21.5109i 0.830418i
\(672\) 4.57025 + 0.335907i 0.176301 + 0.0129579i
\(673\) −10.7663 −0.415011 −0.207505 0.978234i \(-0.566534\pi\)
−0.207505 + 0.978234i \(0.566534\pi\)
\(674\) 5.00000 0.192593
\(675\) −2.08191 2.51087i −0.0801327 0.0966436i
\(676\) 11.0000 6.92820i 0.423077 0.266469i
\(677\) 29.2048 1.12243 0.561216 0.827669i \(-0.310334\pi\)
0.561216 + 0.827669i \(0.310334\pi\)
\(678\) −18.3615 + 4.31386i −0.705168 + 0.165673i
\(679\) −5.88316 + 18.7446i −0.225775 + 0.719350i
\(680\) 5.98844i 0.229646i
\(681\) 19.3723 4.55134i 0.742347 0.174408i
\(682\) 33.5538 1.28484
\(683\) −19.0000 −0.727015 −0.363507 0.931591i \(-0.618421\pi\)
−0.363507 + 0.931591i \(0.618421\pi\)
\(684\) 20.3422 10.1168i 0.777803 0.386827i
\(685\) 2.09509i 0.0800494i
\(686\) 14.6487 11.3321i 0.559290 0.432660i
\(687\) 0.627719 + 2.67181i 0.0239490 + 0.101936i
\(688\) −8.37228 −0.319190
\(689\) −3.16915 10.9783i −0.120735 0.418238i
\(690\) 6.37228 + 27.1229i 0.242589 + 1.03255i
\(691\) 31.1769 1.18603 0.593013 0.805193i \(-0.297938\pi\)
0.593013 + 0.805193i \(0.297938\pi\)
\(692\) 23.9538 0.910585
\(693\) −7.14674 45.0325i −0.271482 1.71064i
\(694\) 25.8333i 0.980618i
\(695\) 39.7228 1.50677
\(696\) −12.7692 + 3.00000i −0.484014 + 0.113715i
\(697\) 6.63325i 0.251252i
\(698\) 23.3639 0.884335
\(699\) 21.0333 4.94158i 0.795552 0.186908i
\(700\) 0.497333 1.58457i 0.0187974 0.0598913i
\(701\) 13.2665i 0.501069i 0.968108 + 0.250534i \(0.0806063\pi\)
−0.968108 + 0.250534i \(0.919394\pi\)
\(702\) 15.4891 + 10.5398i 0.584599 + 0.397798i
\(703\) 37.1168i 1.39989i
\(704\) 5.74456 0.216506
\(705\) −4.34896 18.5109i −0.163791 0.697160i
\(706\) 6.11684i 0.230210i
\(707\) 4.39403 14.0000i 0.165255 0.526524i
\(708\) 14.7446 3.46410i 0.554135 0.130189i
\(709\) 30.3846i 1.14112i 0.821256 + 0.570559i \(0.193274\pi\)
−0.821256 + 0.570559i \(0.806726\pi\)
\(710\) 4.74456i 0.178060i
\(711\) 25.1753 12.5205i 0.944146 0.469555i
\(712\) 10.0000i 0.374766i
\(713\) 39.6060i 1.48326i
\(714\) 11.5368 + 0.847944i 0.431756 + 0.0317335i
\(715\) 13.6277 + 47.2078i 0.509648 + 1.76547i
\(716\) 6.33830i 0.236873i
\(717\) −7.13058 30.3505i −0.266296 1.13346i
\(718\) −28.2337 −1.05367
\(719\) 23.3639 0.871325 0.435662 0.900110i \(-0.356514\pi\)
0.435662 + 0.900110i \(0.356514\pi\)
\(720\) −3.16915 6.37228i −0.118107 0.237481i
\(721\) 4.10891 + 1.28962i 0.153024 + 0.0480280i
\(722\) 38.3505 1.42726
\(723\) 9.25544 + 39.3947i 0.344213 + 1.46511i
\(724\) 14.6277i 0.543635i
\(725\) 4.75372i 0.176549i
\(726\) −8.71516 37.0951i −0.323450 1.37673i
\(727\) 29.8614i 1.10750i 0.832684 + 0.553749i \(0.186803\pi\)
−0.832684 + 0.553749i \(0.813197\pi\)
\(728\) −0.220225 + 9.53685i −0.00816208 + 0.353459i
\(729\) −5.00000 + 26.5330i −0.185185 + 0.982704i
\(730\) 8.56768i 0.317104i
\(731\) −21.1345 −0.781686
\(732\) −6.31386 + 1.48338i −0.233367 + 0.0548275i
\(733\) −1.28962 −0.0476332 −0.0238166 0.999716i \(-0.507582\pi\)
−0.0238166 + 0.999716i \(0.507582\pi\)
\(734\) 6.74456i 0.248946i
\(735\) −26.7373 10.6015i −0.986220 0.391041i
\(736\) 6.78073i 0.249941i
\(737\) 15.3484i 0.565366i
\(738\) −3.51039 7.05842i −0.129219 0.259824i
\(739\) 41.3841i 1.52234i −0.648554 0.761169i \(-0.724626\pi\)
0.648554 0.761169i \(-0.275374\pi\)
\(740\) 11.6270 0.427418
\(741\) 23.1615 + 41.2337i 0.850858 + 1.51476i
\(742\) 8.00000 + 2.51087i 0.293689 + 0.0921771i
\(743\) −44.9783 −1.65009 −0.825046 0.565066i \(-0.808851\pi\)
−0.825046 + 0.565066i \(0.808851\pi\)
\(744\) −2.31386 9.84868i −0.0848302 0.361070i
\(745\) 31.7228i 1.16223i
\(746\) 22.2337 0.814033
\(747\) −6.33830 12.7446i −0.231906 0.466299i
\(748\) 14.5012 0.530217
\(749\) 9.48913 + 2.97825i 0.346725 + 0.108823i
\(750\) 17.4891 4.10891i 0.638613 0.150036i
\(751\) −21.6060 −0.788413 −0.394207 0.919022i \(-0.628981\pi\)
−0.394207 + 0.919022i \(0.628981\pi\)
\(752\) 4.62772i 0.168756i
\(753\) −0.0584220 0.248667i −0.00212902 0.00906192i
\(754\) −7.57301 26.2337i −0.275793 0.955375i
\(755\) −2.92910 −0.106601
\(756\) −12.7251 + 5.20313i −0.462806 + 0.189236i
\(757\) −18.4674 −0.671208 −0.335604 0.942003i \(-0.608940\pi\)
−0.335604 + 0.942003i \(0.608940\pi\)
\(758\) 14.8511i 0.539415i
\(759\) 65.6791 15.4307i 2.38400 0.560099i
\(760\) 17.9653i 0.651671i
\(761\) 30.8614i 1.11873i −0.828923 0.559363i \(-0.811046\pi\)
0.828923 0.559363i \(-0.188954\pi\)
\(762\) 1.83324 + 7.80298i 0.0664113 + 0.282672i
\(763\) 24.6060 + 7.72281i 0.890796 + 0.279585i
\(764\) 19.5499i 0.707290i
\(765\) −8.00000 16.0858i −0.289241 0.581583i
\(766\) 26.4891i 0.957091i
\(767\) 8.74456 + 30.2921i 0.315748 + 1.09378i
\(768\) −0.396143 1.68614i −0.0142946 0.0608434i
\(769\) −14.2988 −0.515629 −0.257815 0.966194i \(-0.583002\pi\)
−0.257815 + 0.966194i \(0.583002\pi\)
\(770\) −34.4010 10.7971i −1.23972 0.389099i
\(771\) −4.86141 20.6920i −0.175079 0.745205i
\(772\) 20.7846i 0.748054i
\(773\) 9.86141i 0.354690i 0.984149 + 0.177345i \(0.0567509\pi\)
−0.984149 + 0.177345i \(0.943249\pi\)
\(774\) 22.4891 11.1846i 0.808355 0.402022i
\(775\) −3.66648 −0.131704
\(776\) 7.42554 0.266561
\(777\) 1.64635 22.3997i 0.0590624 0.803585i
\(778\) 7.92287i 0.284049i
\(779\) 19.8997i 0.712982i
\(780\) 12.9166 7.25544i 0.462490 0.259786i
\(781\) −11.4891 −0.411113
\(782\) 17.1168i 0.612097i
\(783\) 30.2921 25.1168i 1.08255 0.897603i
\(784\) −5.74456 4.00000i −0.205163 0.142857i
\(785\) 46.8397 1.67178
\(786\) 5.00000 + 21.2819i 0.178344 + 0.759102i
\(787\) 13.5065 0.481457 0.240728 0.970593i \(-0.422614\pi\)
0.240728 + 0.970593i \(0.422614\pi\)
\(788\) 3.88316 0.138332
\(789\) −34.5484 + 8.11684i −1.22996 + 0.288967i
\(790\) 22.2337i 0.791039i
\(791\) 27.4891 + 8.62772i 0.977401 + 0.306766i
\(792\) −15.4307 + 7.67420i −0.548306 + 0.272691i
\(793\) −3.74456 12.9715i −0.132973 0.460633i
\(794\) 6.63325 0.235405
\(795\) −2.97825 12.6766i −0.105628 0.449592i
\(796\) 5.11684i 0.181362i
\(797\) −9.01011 −0.319154 −0.159577 0.987185i \(-0.551013\pi\)
−0.159577 + 0.987185i \(0.551013\pi\)
\(798\) −34.6105 2.54383i −1.22520 0.0900506i
\(799\) 11.6819i 0.413277i
\(800\) −0.627719 −0.0221932
\(801\) −13.3591 26.8614i −0.472020 0.949101i
\(802\) −16.9783 −0.599523
\(803\) −20.7469 −0.732144
\(804\) −4.50506 + 1.05842i −0.158881 + 0.0373277i
\(805\) 12.7446 40.6060i 0.449187 1.43117i
\(806\) 20.2337 5.84096i 0.712701 0.205739i
\(807\) 1.80298 + 7.67420i 0.0634681 + 0.270145i
\(808\) −5.54601 −0.195108
\(809\) 5.04868i 0.177502i −0.996054 0.0887510i \(-0.971712\pi\)
0.996054 0.0887510i \(-0.0282875\pi\)
\(810\) 17.0256 + 12.8832i 0.598217 + 0.452668i
\(811\) −12.9166 −0.453565 −0.226782 0.973945i \(-0.572821\pi\)
−0.226782 + 0.973945i \(0.572821\pi\)
\(812\) 19.1168 + 6.00000i 0.670870 + 0.210559i
\(813\) 5.80298 + 24.6998i 0.203520 + 0.866258i
\(814\) 28.1552i 0.986841i
\(815\) 27.7128 0.970737
\(816\) −1.00000 4.25639i −0.0350070 0.149003i
\(817\) 63.4034 2.21820
\(818\) −6.57835 −0.230006
\(819\) −12.1488 25.9115i −0.424513 0.905422i
\(820\) −6.23369 −0.217690
\(821\) 13.7228 0.478929 0.239465 0.970905i \(-0.423028\pi\)
0.239465 + 0.970905i \(0.423028\pi\)
\(822\) 0.349857 + 1.48913i 0.0122026 + 0.0519392i
\(823\) 7.13859 0.248836 0.124418 0.992230i \(-0.460294\pi\)
0.124418 + 0.992230i \(0.460294\pi\)
\(824\) 1.62772i 0.0567043i
\(825\) 1.42848 + 6.08017i 0.0497333 + 0.211684i
\(826\) −22.0742 6.92820i −0.768061 0.241063i
\(827\) 4.88316 0.169804 0.0849020 0.996389i \(-0.472942\pi\)
0.0849020 + 0.996389i \(0.472942\pi\)
\(828\) −9.05842 18.2140i −0.314802 0.632980i
\(829\) 6.60597i 0.229435i 0.993398 + 0.114717i \(0.0365963\pi\)
−0.993398 + 0.114717i \(0.963404\pi\)
\(830\) −11.2554 −0.390682
\(831\) 2.17448 + 9.25544i 0.0754319 + 0.321068i
\(832\) 3.46410 1.00000i 0.120096 0.0346688i
\(833\) −14.5012 10.0974i −0.502437 0.349852i
\(834\) −28.2337 + 6.63325i −0.977653 + 0.229691i
\(835\) 43.5842 1.50829
\(836\) −43.5036 −1.50461
\(837\) 19.3723 + 23.3639i 0.669604 + 0.807573i
\(838\) 8.36530 0.288975
\(839\) 11.3723i 0.392615i 0.980542 + 0.196307i \(0.0628950\pi\)
−0.980542 + 0.196307i \(0.937105\pi\)
\(840\) −0.796867 + 10.8419i −0.0274945 + 0.374082i
\(841\) −28.3505 −0.977605
\(842\) 6.43087i 0.221622i
\(843\) 5.54601 + 23.6060i 0.191015 + 0.813033i
\(844\) 11.6277 0.400243
\(845\) 16.4356 + 26.0951i 0.565403 + 0.897699i
\(846\) 6.18220 + 12.4307i 0.212549 + 0.427376i
\(847\) −17.4303 + 55.5354i −0.598913 + 1.90822i
\(848\) 3.16915i 0.108829i
\(849\) 9.05842 2.12819i 0.310884 0.0730394i
\(850\) −1.58457 −0.0543504
\(851\) 33.2337 1.13924
\(852\) 0.792287 + 3.37228i 0.0271433 + 0.115532i
\(853\) −36.8155 −1.26054 −0.630269 0.776377i \(-0.717056\pi\)
−0.630269 + 0.776377i \(0.717056\pi\)
\(854\) 9.45254 + 2.96677i 0.323459 + 0.101521i
\(855\) 24.0000 + 48.2574i 0.820783 + 1.65037i
\(856\) 3.75906i 0.128482i
\(857\) 35.0458 1.19714 0.598570 0.801070i \(-0.295736\pi\)
0.598570 + 0.801070i \(0.295736\pi\)
\(858\) −17.5693 31.2781i −0.599806 1.06782i
\(859\) 53.0951i 1.81158i −0.423726 0.905791i \(-0.639278\pi\)
0.423726 0.905791i \(-0.360722\pi\)
\(860\) 19.8614i 0.677268i
\(861\) −0.882670 + 12.0093i −0.0300813 + 0.409277i
\(862\) 6.23369 0.212320
\(863\) −11.4891 −0.391094 −0.195547 0.980694i \(-0.562648\pi\)
−0.195547 + 0.980694i \(0.562648\pi\)
\(864\) 3.31662 + 4.00000i 0.112834 + 0.136083i
\(865\) 56.8251i 1.93211i
\(866\) 38.4674i 1.30717i
\(867\) 4.21010 + 17.9198i 0.142983 + 0.608589i
\(868\) −4.62772 + 14.7446i −0.157075 + 0.500463i
\(869\) −53.8397 −1.82639
\(870\) −7.11684 30.2921i −0.241284 1.02700i
\(871\) −2.67181 9.25544i −0.0905310 0.313609i
\(872\) 9.74749i 0.330092i
\(873\) −19.9460 + 9.91983i −0.675071 + 0.335735i
\(874\) 51.3505i 1.73696i
\(875\) −26.1831 8.21782i −0.885152 0.277813i
\(876\) 1.43070 + 6.08963i 0.0483390 + 0.205750i
\(877\) 36.7229i 1.24005i −0.784584 0.620023i \(-0.787123\pi\)
0.784584 0.620023i \(-0.212877\pi\)
\(878\) 34.6060i 1.16789i
\(879\) −19.3723 + 4.55134i −0.653411 + 0.153513i
\(880\) 13.6277i 0.459390i
\(881\) 7.27806 0.245204 0.122602 0.992456i \(-0.460876\pi\)
0.122602 + 0.992456i \(0.460876\pi\)
\(882\) 20.7743 + 3.07036i 0.699508 + 0.103384i
\(883\) 54.0951 1.82044 0.910222 0.414120i \(-0.135911\pi\)
0.910222 + 0.414120i \(0.135911\pi\)
\(884\) 8.74456 2.52434i 0.294111 0.0849027i
\(885\) 8.21782 + 34.9783i 0.276239 + 1.17578i
\(886\) 9.80240i 0.329318i
\(887\) −24.3585 −0.817879 −0.408939 0.912562i \(-0.634101\pi\)
−0.408939 + 0.912562i \(0.634101\pi\)
\(888\) −8.26411 + 1.94158i −0.277325 + 0.0651551i
\(889\) 3.66648 11.6819i 0.122970 0.391799i
\(890\) −23.7228 −0.795191
\(891\) 31.1970 41.2280i 1.04514 1.38119i
\(892\) 9.30506 0.311557
\(893\) 35.0458i 1.17276i
\(894\) 5.29734 + 22.5475i 0.177170 + 0.754103i
\(895\) 15.0362 0.502605
\(896\) −0.792287 + 2.52434i −0.0264685 + 0.0843322i
\(897\) 36.9198 20.7383i 1.23272 0.692432i
\(898\) −3.11684 −0.104010
\(899\) 44.2337i 1.47528i
\(900\) 1.68614 0.838574i 0.0562047 0.0279525i
\(901\) 8.00000i 0.266519i
\(902\) 15.0951i 0.502612i
\(903\) −38.2634 2.81231i −1.27333 0.0935878i
\(904\) 10.8896i 0.362184i
\(905\) 34.7011 1.15350
\(906\) 2.08191 0.489125i 0.0691667 0.0162501i
\(907\) 20.0000 0.664089 0.332045 0.943264i \(-0.392262\pi\)
0.332045 + 0.943264i \(0.392262\pi\)
\(908\) 11.4891i 0.381280i
\(909\) 14.8974 7.40895i 0.494114 0.245739i
\(910\) −22.6241 0.522435i −0.749981 0.0173186i
\(911\) 18.9600i 0.628172i 0.949394 + 0.314086i \(0.101698\pi\)
−0.949394 + 0.314086i \(0.898302\pi\)
\(912\) 3.00000 + 12.7692i 0.0993399 + 0.422829i
\(913\) 27.2554i 0.902023i
\(914\) 2.87419i 0.0950699i
\(915\) −3.51900 14.9783i −0.116335 0.495166i
\(916\) −1.58457 −0.0523558
\(917\) 10.0000 31.8614i 0.330229 1.05216i
\(918\) 8.37228 + 10.0974i 0.276326 + 0.333262i
\(919\) 40.5842 1.33875 0.669375 0.742925i \(-0.266562\pi\)
0.669375 + 0.742925i \(0.266562\pi\)
\(920\) −16.0858 −0.530333
\(921\) 5.76631 + 24.5437i 0.190006 + 0.808741i
\(922\) 18.6060i 0.612755i
\(923\) −6.92820 + 2.00000i −0.228045 + 0.0658308i
\(924\) 26.2541 + 1.92964i 0.863696 + 0.0634805i
\(925\) 3.07657i 0.101157i
\(926\) 15.0911i 0.495925i
\(927\) 2.17448 + 4.37228i 0.0714193 + 0.143605i
\(928\) 7.57301i 0.248596i
\(929\) 15.6060i 0.512015i −0.966675 0.256008i \(-0.917593\pi\)
0.966675 0.256008i \(-0.0824072\pi\)
\(930\) 23.3639 5.48913i 0.766131 0.179996i
\(931\) 43.5036 + 30.2921i 1.42577 + 0.992782i
\(932\) 12.4742i 0.408606i
\(933\) 4.11684 + 17.5229i 0.134779 + 0.573674i
\(934\) 18.2603 0.597494
\(935\) 34.4010i 1.12503i
\(936\) −7.96916 + 7.31386i −0.260480 + 0.239061i
\(937\) 20.5109i 0.670061i −0.942207 0.335031i \(-0.891253\pi\)
0.942207 0.335031i \(-0.108747\pi\)
\(938\) 6.74456 + 2.11684i 0.220218 + 0.0691174i
\(939\) −14.7446 + 3.46410i −0.481171 + 0.113047i
\(940\) 10.9783 0.358071
\(941\) 28.5109i 0.929428i 0.885461 + 0.464714i \(0.153843\pi\)
−0.885461 + 0.464714i \(0.846157\pi\)
\(942\) −33.2921 + 7.82168i −1.08472 + 0.254844i
\(943\) −17.8178 −0.580229
\(944\) 8.74456i 0.284611i
\(945\) −12.3433 30.1874i −0.401527 0.981998i
\(946\) −48.0951 −1.56371
\(947\) −4.88316 −0.158681 −0.0793406 0.996848i \(-0.525281\pi\)
−0.0793406 + 0.996848i \(0.525281\pi\)
\(948\) 3.71277 + 15.8030i 0.120585 + 0.513257i
\(949\) −12.5109 + 3.61158i −0.406120 + 0.117237i
\(950\) 4.75372 0.154231
\(951\) −9.84868 41.9198i −0.319365 1.35934i
\(952\) −2.00000 + 6.37228i −0.0648204 + 0.206527i
\(953\) 52.9562i 1.71542i 0.514134 + 0.857710i \(0.328113\pi\)
−0.514134 + 0.857710i \(0.671887\pi\)
\(954\) 4.23369 + 8.51278i 0.137071 + 0.275611i
\(955\) −46.3778 −1.50075
\(956\) 18.0000 0.582162
\(957\) −73.3533 + 17.2337i −2.37117 + 0.557086i
\(958\) 34.3723i 1.11052i
\(959\) 0.699713 2.22938i 0.0225949 0.0719906i
\(960\) 4.00000 0.939764i 0.129099 0.0303307i
\(961\) 3.11684 0.100543
\(962\) −4.90120 16.9783i −0.158021 0.547401i
\(963\) 5.02175 + 10.0974i 0.161824 + 0.325383i
\(964\) −23.3639 −0.752499
\(965\) −49.3069 −1.58725
\(966\) −2.27770 + 30.9896i −0.0732837 + 0.997074i
\(967\) 20.5446i 0.660668i −0.943864 0.330334i \(-0.892839\pi\)
0.943864 0.330334i \(-0.107161\pi\)
\(968\) 22.0000 0.707107
\(969\) 7.57301 + 32.2337i 0.243280 + 1.03550i
\(970\) 17.6155i 0.565598i
\(971\) 46.5253 1.49307 0.746534 0.665347i \(-0.231716\pi\)
0.746534 + 0.665347i \(0.231716\pi\)
\(972\) −14.2525 6.31386i −0.457151 0.202517i
\(973\) 42.2689 + 13.2665i 1.35508 + 0.425304i
\(974\) 10.9822i 0.351893i
\(975\) 1.91983 + 3.41781i 0.0614837 + 0.109458i
\(976\) 3.74456i 0.119861i
\(977\) −11.3505 −0.363136 −0.181568 0.983378i \(-0.558117\pi\)
−0.181568 + 0.983378i \(0.558117\pi\)
\(978\) −19.6974 + 4.62772i −0.629852 + 0.147978i
\(979\) 57.4456i 1.83597i
\(980\) 9.48913 13.6277i 0.303119 0.435322i
\(981\) 13.0217 + 26.1831i 0.415752 + 0.835963i
\(982\) 8.21782i 0.262241i
\(983\) 36.8832i 1.17639i 0.808719 + 0.588195i \(0.200161\pi\)
−0.808719 + 0.588195i \(0.799839\pi\)
\(984\) 4.43070 1.04095i 0.141246 0.0331844i
\(985\) 9.21194i 0.293517i
\(986\) 19.1168i 0.608804i
\(987\) 1.55448 21.1498i 0.0494798 0.673206i
\(988\) −26.2337 + 7.57301i −0.834605 + 0.240930i
\(989\) 56.7701i 1.80519i
\(990\) −18.2054 36.6060i −0.578605 1.16341i
\(991\) 2.11684 0.0672438 0.0336219 0.999435i \(-0.489296\pi\)
0.0336219 + 0.999435i \(0.489296\pi\)
\(992\) 5.84096 0.185451
\(993\) 55.0844 12.9416i 1.74805 0.410689i
\(994\) 1.58457 5.04868i 0.0502596 0.160134i
\(995\) 12.1386 0.384819
\(996\) 8.00000 1.87953i 0.253490 0.0595551i
\(997\) 2.62772i 0.0832207i −0.999134 0.0416103i \(-0.986751\pi\)
0.999134 0.0416103i \(-0.0132488\pi\)
\(998\) 26.0357i 0.824145i
\(999\) 19.6048 16.2554i 0.620268 0.514299i
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.e.g.545.3 yes 8
3.2 odd 2 546.2.e.e.545.5 yes 8
7.6 odd 2 inner 546.2.e.g.545.6 yes 8
13.12 even 2 546.2.e.e.545.3 8
21.20 even 2 546.2.e.e.545.4 yes 8
39.38 odd 2 inner 546.2.e.g.545.5 yes 8
91.90 odd 2 546.2.e.e.545.6 yes 8
273.272 even 2 inner 546.2.e.g.545.4 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.e.e.545.3 8 13.12 even 2
546.2.e.e.545.4 yes 8 21.20 even 2
546.2.e.e.545.5 yes 8 3.2 odd 2
546.2.e.e.545.6 yes 8 91.90 odd 2
546.2.e.g.545.3 yes 8 1.1 even 1 trivial
546.2.e.g.545.4 yes 8 273.272 even 2 inner
546.2.e.g.545.5 yes 8 39.38 odd 2 inner
546.2.e.g.545.6 yes 8 7.6 odd 2 inner