Properties

Label 546.2.g.c.209.1
Level $546$
Weight $2$
Character 546.209
Analytic conductor $4.360$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(209,546)]
 
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, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.209");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.g (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: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2x^{11} + 4x^{10} - 8x^{8} + 26x^{7} - 50x^{6} + 78x^{5} - 72x^{4} + 324x^{2} - 486x + 729 \) 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 209.1
Root \(0.146987 + 1.72580i\) of defining polynomial
Character \(\chi\) \(=\) 546.209
Dual form 546.2.g.c.209.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.72580 - 0.146987i) q^{3} -1.00000 q^{4} +3.83276 q^{5} +(-0.146987 + 1.72580i) q^{6} +(-0.655092 - 2.56337i) q^{7} +1.00000i q^{8} +(2.95679 + 0.507343i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.72580 - 0.146987i) q^{3} -1.00000 q^{4} +3.83276 q^{5} +(-0.146987 + 1.72580i) q^{6} +(-0.655092 - 2.56337i) q^{7} +1.00000i q^{8} +(2.95679 + 0.507343i) q^{9} -3.83276i q^{10} +3.53879i q^{11} +(1.72580 + 0.146987i) q^{12} -1.00000i q^{13} +(-2.56337 + 0.655092i) q^{14} +(-6.61459 - 0.563368i) q^{15} +1.00000 q^{16} +6.47987 q^{17} +(0.507343 - 2.95679i) q^{18} -1.55008i q^{19} -3.83276 q^{20} +(0.753777 + 4.52016i) q^{21} +3.53879 q^{22} +3.87495i q^{23} +(0.146987 - 1.72580i) q^{24} +9.69005 q^{25} -1.00000 q^{26} +(-5.02826 - 1.31018i) q^{27} +(0.655092 + 2.56337i) q^{28} -6.70339i q^{29} +(-0.563368 + 6.61459i) q^{30} -9.76102i q^{31} -1.00000i q^{32} +(0.520157 - 6.10725i) q^{33} -6.47987i q^{34} +(-2.51081 - 9.82477i) q^{35} +(-2.95679 - 0.507343i) q^{36} -0.597183 q^{37} -1.55008 q^{38} +(-0.146987 + 1.72580i) q^{39} +3.83276i q^{40} -11.0403 q^{41} +(4.52016 - 0.753777i) q^{42} -0.604159 q^{43} -3.53879i q^{44} +(11.3327 + 1.94452i) q^{45} +3.87495 q^{46} +12.5799 q^{47} +(-1.72580 - 0.146987i) q^{48} +(-6.14171 + 3.35848i) q^{49} -9.69005i q^{50} +(-11.1830 - 0.952459i) q^{51} +1.00000i q^{52} -6.84142i q^{53} +(-1.31018 + 5.02826i) q^{54} +13.5633i q^{55} +(2.56337 - 0.655092i) q^{56} +(-0.227842 + 2.67513i) q^{57} -6.70339 q^{58} +1.74126 q^{59} +(6.61459 + 0.563368i) q^{60} -5.28005i q^{61} -9.76102 q^{62} +(-0.636464 - 7.91169i) q^{63} -1.00000 q^{64} -3.83276i q^{65} +(-6.10725 - 0.520157i) q^{66} +5.39566 q^{67} -6.47987 q^{68} +(0.569569 - 6.68740i) q^{69} +(-9.82477 + 2.51081i) q^{70} +9.18326i q^{71} +(-0.507343 + 2.95679i) q^{72} +11.6727i q^{73} +0.597183i q^{74} +(-16.7231 - 1.42432i) q^{75} +1.55008i q^{76} +(9.07121 - 2.31823i) q^{77} +(1.72580 + 0.146987i) q^{78} -3.29905 q^{79} +3.83276 q^{80} +(8.48521 + 3.00021i) q^{81} +11.0403i q^{82} +2.06179 q^{83} +(-0.753777 - 4.52016i) q^{84} +24.8358 q^{85} +0.604159i q^{86} +(-0.985315 + 11.5687i) q^{87} -3.53879 q^{88} +1.46706 q^{89} +(1.94452 - 11.3327i) q^{90} +(-2.56337 + 0.655092i) q^{91} -3.87495i q^{92} +(-1.43475 + 16.8456i) q^{93} -12.5799i q^{94} -5.94108i q^{95} +(-0.146987 + 1.72580i) q^{96} +10.3490i q^{97} +(3.35848 + 6.14171i) q^{98} +(-1.79538 + 10.4634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{3} - 12 q^{4} + 4 q^{5} - 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{3} - 12 q^{4} + 4 q^{5} - 2 q^{6} - 8 q^{7} + 4 q^{9} + 2 q^{12} - 10 q^{14} + 4 q^{15} + 12 q^{16} - 12 q^{17} + 8 q^{18} - 4 q^{20} + 2 q^{24} + 20 q^{25} - 12 q^{26} - 8 q^{27} + 8 q^{28} + 14 q^{30} - 46 q^{33} + 22 q^{35} - 4 q^{36} + 16 q^{37} + 8 q^{38} - 2 q^{39} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 24 q^{46} + 68 q^{47} - 2 q^{48} + 26 q^{49} - 50 q^{51} - 16 q^{54} + 10 q^{56} - 28 q^{57} - 24 q^{58} - 8 q^{59} - 4 q^{60} - 16 q^{62} + 2 q^{63} - 12 q^{64} + 12 q^{66} + 8 q^{67} + 12 q^{68} + 24 q^{69} - 28 q^{70} - 8 q^{72} - 92 q^{75} + 8 q^{77} + 2 q^{78} + 36 q^{79} + 4 q^{80} + 16 q^{81} + 32 q^{83} - 8 q^{87} + 48 q^{89} - 2 q^{90} - 10 q^{91} + 8 q^{93} - 2 q^{96} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.72580 0.146987i −0.996393 0.0848633i
\(4\) −1.00000 −0.500000
\(5\) 3.83276 1.71406 0.857031 0.515264i \(-0.172306\pi\)
0.857031 + 0.515264i \(0.172306\pi\)
\(6\) −0.146987 + 1.72580i −0.0600074 + 0.704556i
\(7\) −0.655092 2.56337i −0.247602 0.968862i
\(8\) 1.00000i 0.353553i
\(9\) 2.95679 + 0.507343i 0.985596 + 0.169114i
\(10\) 3.83276i 1.21203i
\(11\) 3.53879i 1.06698i 0.845805 + 0.533492i \(0.179121\pi\)
−0.845805 + 0.533492i \(0.820879\pi\)
\(12\) 1.72580 + 0.146987i 0.498196 + 0.0424316i
\(13\) 1.00000i 0.277350i
\(14\) −2.56337 + 0.655092i −0.685089 + 0.175081i
\(15\) −6.61459 0.563368i −1.70788 0.145461i
\(16\) 1.00000 0.250000
\(17\) 6.47987 1.57160 0.785799 0.618482i \(-0.212252\pi\)
0.785799 + 0.618482i \(0.212252\pi\)
\(18\) 0.507343 2.95679i 0.119582 0.696922i
\(19\) 1.55008i 0.355612i −0.984066 0.177806i \(-0.943100\pi\)
0.984066 0.177806i \(-0.0569000\pi\)
\(20\) −3.83276 −0.857031
\(21\) 0.753777 + 4.52016i 0.164488 + 0.986379i
\(22\) 3.53879 0.754472
\(23\) 3.87495i 0.807983i 0.914763 + 0.403991i \(0.132377\pi\)
−0.914763 + 0.403991i \(0.867623\pi\)
\(24\) 0.146987 1.72580i 0.0300037 0.352278i
\(25\) 9.69005 1.93801
\(26\) −1.00000 −0.196116
\(27\) −5.02826 1.31018i −0.967689 0.252145i
\(28\) 0.655092 + 2.56337i 0.123801 + 0.484431i
\(29\) 6.70339i 1.24479i −0.782704 0.622394i \(-0.786160\pi\)
0.782704 0.622394i \(-0.213840\pi\)
\(30\) −0.563368 + 6.61459i −0.102856 + 1.20765i
\(31\) 9.76102i 1.75313i −0.481282 0.876566i \(-0.659829\pi\)
0.481282 0.876566i \(-0.340171\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.520157 6.10725i 0.0905477 1.06313i
\(34\) 6.47987i 1.11129i
\(35\) −2.51081 9.82477i −0.424405 1.66069i
\(36\) −2.95679 0.507343i −0.492798 0.0845571i
\(37\) −0.597183 −0.0981763 −0.0490882 0.998794i \(-0.515632\pi\)
−0.0490882 + 0.998794i \(0.515632\pi\)
\(38\) −1.55008 −0.251456
\(39\) −0.146987 + 1.72580i −0.0235368 + 0.276350i
\(40\) 3.83276i 0.606013i
\(41\) −11.0403 −1.72421 −0.862104 0.506732i \(-0.830853\pi\)
−0.862104 + 0.506732i \(0.830853\pi\)
\(42\) 4.52016 0.753777i 0.697475 0.116310i
\(43\) −0.604159 −0.0921334 −0.0460667 0.998938i \(-0.514669\pi\)
−0.0460667 + 0.998938i \(0.514669\pi\)
\(44\) 3.53879i 0.533492i
\(45\) 11.3327 + 1.94452i 1.68937 + 0.289872i
\(46\) 3.87495 0.571330
\(47\) 12.5799 1.83496 0.917481 0.397780i \(-0.130219\pi\)
0.917481 + 0.397780i \(0.130219\pi\)
\(48\) −1.72580 0.146987i −0.249098 0.0212158i
\(49\) −6.14171 + 3.35848i −0.877387 + 0.479783i
\(50\) 9.69005i 1.37038i
\(51\) −11.1830 0.952459i −1.56593 0.133371i
\(52\) 1.00000i 0.138675i
\(53\) 6.84142i 0.939741i −0.882735 0.469871i \(-0.844301\pi\)
0.882735 0.469871i \(-0.155699\pi\)
\(54\) −1.31018 + 5.02826i −0.178294 + 0.684260i
\(55\) 13.5633i 1.82888i
\(56\) 2.56337 0.655092i 0.342544 0.0875404i
\(57\) −0.227842 + 2.67513i −0.0301784 + 0.354330i
\(58\) −6.70339 −0.880199
\(59\) 1.74126 0.226693 0.113347 0.993556i \(-0.463843\pi\)
0.113347 + 0.993556i \(0.463843\pi\)
\(60\) 6.61459 + 0.563368i 0.853940 + 0.0727305i
\(61\) 5.28005i 0.676041i −0.941139 0.338020i \(-0.890243\pi\)
0.941139 0.338020i \(-0.109757\pi\)
\(62\) −9.76102 −1.23965
\(63\) −0.636464 7.91169i −0.0801869 0.996780i
\(64\) −1.00000 −0.125000
\(65\) 3.83276i 0.475395i
\(66\) −6.10725 0.520157i −0.751750 0.0640269i
\(67\) 5.39566 0.659184 0.329592 0.944123i \(-0.393089\pi\)
0.329592 + 0.944123i \(0.393089\pi\)
\(68\) −6.47987 −0.785799
\(69\) 0.569569 6.68740i 0.0685680 0.805068i
\(70\) −9.82477 + 2.51081i −1.17429 + 0.300099i
\(71\) 9.18326i 1.08985i 0.838484 + 0.544926i \(0.183442\pi\)
−0.838484 + 0.544926i \(0.816558\pi\)
\(72\) −0.507343 + 2.95679i −0.0597909 + 0.348461i
\(73\) 11.6727i 1.36619i 0.730329 + 0.683095i \(0.239367\pi\)
−0.730329 + 0.683095i \(0.760633\pi\)
\(74\) 0.597183i 0.0694211i
\(75\) −16.7231 1.42432i −1.93102 0.164466i
\(76\) 1.55008i 0.177806i
\(77\) 9.07121 2.31823i 1.03376 0.264187i
\(78\) 1.72580 + 0.146987i 0.195409 + 0.0166431i
\(79\) −3.29905 −0.371172 −0.185586 0.982628i \(-0.559418\pi\)
−0.185586 + 0.982628i \(0.559418\pi\)
\(80\) 3.83276 0.428516
\(81\) 8.48521 + 3.00021i 0.942801 + 0.333357i
\(82\) 11.0403i 1.21920i
\(83\) 2.06179 0.226311 0.113155 0.993577i \(-0.463904\pi\)
0.113155 + 0.993577i \(0.463904\pi\)
\(84\) −0.753777 4.52016i −0.0822438 0.493190i
\(85\) 24.8358 2.69382
\(86\) 0.604159i 0.0651482i
\(87\) −0.985315 + 11.5687i −0.105637 + 1.24030i
\(88\) −3.53879 −0.377236
\(89\) 1.46706 0.155508 0.0777538 0.996973i \(-0.475225\pi\)
0.0777538 + 0.996973i \(0.475225\pi\)
\(90\) 1.94452 11.3327i 0.204971 1.19457i
\(91\) −2.56337 + 0.655092i −0.268714 + 0.0686723i
\(92\) 3.87495i 0.403991i
\(93\) −1.43475 + 16.8456i −0.148776 + 1.74681i
\(94\) 12.5799i 1.29751i
\(95\) 5.94108i 0.609542i
\(96\) −0.146987 + 1.72580i −0.0150018 + 0.176139i
\(97\) 10.3490i 1.05078i 0.850862 + 0.525390i \(0.176080\pi\)
−0.850862 + 0.525390i \(0.823920\pi\)
\(98\) 3.35848 + 6.14171i 0.339258 + 0.620406i
\(99\) −1.79538 + 10.4634i −0.180442 + 1.05162i
\(100\) −9.69005 −0.969005
\(101\) −10.9143 −1.08602 −0.543009 0.839727i \(-0.682715\pi\)
−0.543009 + 0.839727i \(0.682715\pi\)
\(102\) −0.952459 + 11.1830i −0.0943075 + 1.10728i
\(103\) 0.598318i 0.0589540i −0.999565 0.0294770i \(-0.990616\pi\)
0.999565 0.0294770i \(-0.00938419\pi\)
\(104\) 1.00000 0.0980581
\(105\) 2.88905 + 17.3247i 0.281942 + 1.69072i
\(106\) −6.84142 −0.664498
\(107\) 12.7010i 1.22785i 0.789364 + 0.613926i \(0.210411\pi\)
−0.789364 + 0.613926i \(0.789589\pi\)
\(108\) 5.02826 + 1.31018i 0.483845 + 0.126073i
\(109\) −5.62257 −0.538545 −0.269272 0.963064i \(-0.586783\pi\)
−0.269272 + 0.963064i \(0.586783\pi\)
\(110\) 13.5633 1.29321
\(111\) 1.03062 + 0.0877784i 0.0978221 + 0.00833156i
\(112\) −0.655092 2.56337i −0.0619004 0.242215i
\(113\) 10.6609i 1.00289i 0.865190 + 0.501445i \(0.167198\pi\)
−0.865190 + 0.501445i \(0.832802\pi\)
\(114\) 2.67513 + 0.227842i 0.250549 + 0.0213394i
\(115\) 14.8518i 1.38493i
\(116\) 6.70339i 0.622394i
\(117\) 0.507343 2.95679i 0.0469038 0.273355i
\(118\) 1.74126i 0.160296i
\(119\) −4.24491 16.6103i −0.389130 1.52266i
\(120\) 0.563368 6.61459i 0.0514282 0.603827i
\(121\) −1.52300 −0.138455
\(122\) −5.28005 −0.478033
\(123\) 19.0534 + 1.62279i 1.71799 + 0.146322i
\(124\) 9.76102i 0.876566i
\(125\) 17.9759 1.60781
\(126\) −7.91169 + 0.636464i −0.704830 + 0.0567007i
\(127\) 4.95442 0.439634 0.219817 0.975541i \(-0.429454\pi\)
0.219817 + 0.975541i \(0.429454\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.04266 + 0.0888038i 0.0918011 + 0.00781874i
\(130\) −3.83276 −0.336155
\(131\) −9.02449 −0.788474 −0.394237 0.919009i \(-0.628991\pi\)
−0.394237 + 0.919009i \(0.628991\pi\)
\(132\) −0.520157 + 6.10725i −0.0452739 + 0.531567i
\(133\) −3.97342 + 1.01544i −0.344539 + 0.0880502i
\(134\) 5.39566i 0.466114i
\(135\) −19.2721 5.02162i −1.65868 0.432192i
\(136\) 6.47987i 0.555644i
\(137\) 4.15721i 0.355174i −0.984105 0.177587i \(-0.943171\pi\)
0.984105 0.177587i \(-0.0568292\pi\)
\(138\) −6.68740 0.569569i −0.569269 0.0484849i
\(139\) 0.0159714i 0.00135467i 1.00000 0.000677337i \(0.000215603\pi\)
−1.00000 0.000677337i \(0.999784\pi\)
\(140\) 2.51081 + 9.82477i 0.212202 + 0.830345i
\(141\) −21.7104 1.84908i −1.82834 0.155721i
\(142\) 9.18326 0.770642
\(143\) 3.53879 0.295928
\(144\) 2.95679 + 0.507343i 0.246399 + 0.0422786i
\(145\) 25.6925i 2.13365i
\(146\) 11.6727 0.966042
\(147\) 11.0930 4.89333i 0.914938 0.403595i
\(148\) 0.597183 0.0490882
\(149\) 10.5043i 0.860548i 0.902698 + 0.430274i \(0.141583\pi\)
−0.902698 + 0.430274i \(0.858417\pi\)
\(150\) −1.42432 + 16.7231i −0.116295 + 1.36544i
\(151\) −7.95857 −0.647659 −0.323830 0.946115i \(-0.604970\pi\)
−0.323830 + 0.946115i \(0.604970\pi\)
\(152\) 1.55008 0.125728
\(153\) 19.1596 + 3.28751i 1.54896 + 0.265780i
\(154\) −2.31823 9.07121i −0.186808 0.730979i
\(155\) 37.4117i 3.00498i
\(156\) 0.146987 1.72580i 0.0117684 0.138175i
\(157\) 4.29431i 0.342723i −0.985208 0.171362i \(-0.945183\pi\)
0.985208 0.171362i \(-0.0548167\pi\)
\(158\) 3.29905i 0.262458i
\(159\) −1.00560 + 11.8069i −0.0797495 + 0.936351i
\(160\) 3.83276i 0.303006i
\(161\) 9.93292 2.53845i 0.782824 0.200058i
\(162\) 3.00021 8.48521i 0.235719 0.666661i
\(163\) 18.5687 1.45442 0.727208 0.686418i \(-0.240818\pi\)
0.727208 + 0.686418i \(0.240818\pi\)
\(164\) 11.0403 0.862104
\(165\) 1.99364 23.4076i 0.155204 1.82228i
\(166\) 2.06179i 0.160026i
\(167\) −10.6873 −0.827005 −0.413503 0.910503i \(-0.635695\pi\)
−0.413503 + 0.910503i \(0.635695\pi\)
\(168\) −4.52016 + 0.753777i −0.348738 + 0.0581551i
\(169\) −1.00000 −0.0769231
\(170\) 24.8358i 1.90482i
\(171\) 0.786421 4.58326i 0.0601391 0.350490i
\(172\) 0.604159 0.0460667
\(173\) −13.4395 −1.02179 −0.510894 0.859644i \(-0.670686\pi\)
−0.510894 + 0.859644i \(0.670686\pi\)
\(174\) 11.5687 + 0.985315i 0.877023 + 0.0746965i
\(175\) −6.34788 24.8392i −0.479854 1.87766i
\(176\) 3.53879i 0.266746i
\(177\) −3.00508 0.255944i −0.225875 0.0192379i
\(178\) 1.46706i 0.109960i
\(179\) 6.55533i 0.489969i 0.969527 + 0.244984i \(0.0787828\pi\)
−0.969527 + 0.244984i \(0.921217\pi\)
\(180\) −11.3327 1.94452i −0.844687 0.144936i
\(181\) 17.1646i 1.27583i 0.770106 + 0.637916i \(0.220203\pi\)
−0.770106 + 0.637916i \(0.779797\pi\)
\(182\) 0.655092 + 2.56337i 0.0485587 + 0.190009i
\(183\) −0.776101 + 9.11232i −0.0573710 + 0.673602i
\(184\) −3.87495 −0.285665
\(185\) −2.28886 −0.168280
\(186\) 16.8456 + 1.43475i 1.23518 + 0.105201i
\(187\) 22.9309i 1.67687i
\(188\) −12.5799 −0.917481
\(189\) −0.0645093 + 13.7476i −0.00469236 + 0.999989i
\(190\) −5.94108 −0.431011
\(191\) 9.04802i 0.654692i −0.944905 0.327346i \(-0.893846\pi\)
0.944905 0.327346i \(-0.106154\pi\)
\(192\) 1.72580 + 0.146987i 0.124549 + 0.0106079i
\(193\) −6.04974 −0.435470 −0.217735 0.976008i \(-0.569867\pi\)
−0.217735 + 0.976008i \(0.569867\pi\)
\(194\) 10.3490 0.743013
\(195\) −0.563368 + 6.61459i −0.0403436 + 0.473681i
\(196\) 6.14171 3.35848i 0.438693 0.239892i
\(197\) 1.88643i 0.134402i 0.997739 + 0.0672011i \(0.0214069\pi\)
−0.997739 + 0.0672011i \(0.978593\pi\)
\(198\) 10.4634 + 1.79538i 0.743605 + 0.127592i
\(199\) 11.4529i 0.811877i −0.913900 0.405939i \(-0.866945\pi\)
0.913900 0.405939i \(-0.133055\pi\)
\(200\) 9.69005i 0.685190i
\(201\) −9.31184 0.793094i −0.656806 0.0559405i
\(202\) 10.9143i 0.767930i
\(203\) −17.1833 + 4.39134i −1.20603 + 0.308212i
\(204\) 11.1830 + 0.952459i 0.782965 + 0.0666855i
\(205\) −42.3149 −2.95540
\(206\) −0.598318 −0.0416868
\(207\) −1.96593 + 11.4574i −0.136641 + 0.796345i
\(208\) 1.00000i 0.0693375i
\(209\) 5.48540 0.379433
\(210\) 17.3247 2.88905i 1.19552 0.199363i
\(211\) 16.5318 1.13810 0.569048 0.822305i \(-0.307312\pi\)
0.569048 + 0.822305i \(0.307312\pi\)
\(212\) 6.84142i 0.469871i
\(213\) 1.34982 15.8485i 0.0924884 1.08592i
\(214\) 12.7010 0.868222
\(215\) −2.31560 −0.157922
\(216\) 1.31018 5.02826i 0.0891468 0.342130i
\(217\) −25.0211 + 6.39437i −1.69854 + 0.434078i
\(218\) 5.62257i 0.380809i
\(219\) 1.71575 20.1448i 0.115939 1.36126i
\(220\) 13.5633i 0.914439i
\(221\) 6.47987i 0.435883i
\(222\) 0.0877784 1.03062i 0.00589130 0.0691707i
\(223\) 10.9849i 0.735601i −0.929905 0.367800i \(-0.880111\pi\)
0.929905 0.367800i \(-0.119889\pi\)
\(224\) −2.56337 + 0.655092i −0.171272 + 0.0437702i
\(225\) 28.6514 + 4.91618i 1.91010 + 0.327745i
\(226\) 10.6609 0.709150
\(227\) −18.3687 −1.21918 −0.609588 0.792718i \(-0.708665\pi\)
−0.609588 + 0.792718i \(0.708665\pi\)
\(228\) 0.227842 2.67513i 0.0150892 0.177165i
\(229\) 8.77152i 0.579638i −0.957081 0.289819i \(-0.906405\pi\)
0.957081 0.289819i \(-0.0935952\pi\)
\(230\) 14.8518 0.979295
\(231\) −15.9959 + 2.66745i −1.05245 + 0.175506i
\(232\) 6.70339 0.440099
\(233\) 25.7318i 1.68574i 0.538114 + 0.842872i \(0.319137\pi\)
−0.538114 + 0.842872i \(0.680863\pi\)
\(234\) −2.95679 0.507343i −0.193291 0.0331660i
\(235\) 48.2156 3.14524
\(236\) −1.74126 −0.113347
\(237\) 5.69351 + 0.484919i 0.369833 + 0.0314989i
\(238\) −16.6103 + 4.24491i −1.07668 + 0.275157i
\(239\) 12.7421i 0.824221i 0.911134 + 0.412111i \(0.135208\pi\)
−0.911134 + 0.412111i \(0.864792\pi\)
\(240\) −6.61459 0.563368i −0.426970 0.0363652i
\(241\) 13.1363i 0.846184i 0.906087 + 0.423092i \(0.139055\pi\)
−0.906087 + 0.423092i \(0.860945\pi\)
\(242\) 1.52300i 0.0979024i
\(243\) −14.2028 6.42499i −0.911110 0.412163i
\(244\) 5.28005i 0.338020i
\(245\) −23.5397 + 12.8723i −1.50390 + 0.822379i
\(246\) 1.62279 19.0534i 0.103465 1.21480i
\(247\) −1.55008 −0.0986292
\(248\) 9.76102 0.619826
\(249\) −3.55824 0.303057i −0.225494 0.0192055i
\(250\) 17.9759i 1.13689i
\(251\) −20.8113 −1.31359 −0.656797 0.754067i \(-0.728089\pi\)
−0.656797 + 0.754067i \(0.728089\pi\)
\(252\) 0.636464 + 7.91169i 0.0400934 + 0.498390i
\(253\) −13.7126 −0.862105
\(254\) 4.95442i 0.310868i
\(255\) −42.8617 3.65055i −2.68410 0.228606i
\(256\) 1.00000 0.0625000
\(257\) 14.9960 0.935424 0.467712 0.883881i \(-0.345078\pi\)
0.467712 + 0.883881i \(0.345078\pi\)
\(258\) 0.0888038 1.04266i 0.00552869 0.0649132i
\(259\) 0.391210 + 1.53080i 0.0243086 + 0.0951193i
\(260\) 3.83276i 0.237698i
\(261\) 3.40092 19.8205i 0.210511 1.22686i
\(262\) 9.02449i 0.557535i
\(263\) 11.2324i 0.692621i −0.938120 0.346310i \(-0.887434\pi\)
0.938120 0.346310i \(-0.112566\pi\)
\(264\) 6.10725 + 0.520157i 0.375875 + 0.0320135i
\(265\) 26.2215i 1.61078i
\(266\) 1.01544 + 3.97342i 0.0622609 + 0.243626i
\(267\) −2.53185 0.215639i −0.154947 0.0131969i
\(268\) −5.39566 −0.329592
\(269\) −0.548970 −0.0334713 −0.0167356 0.999860i \(-0.505327\pi\)
−0.0167356 + 0.999860i \(0.505327\pi\)
\(270\) −5.02162 + 19.2721i −0.305606 + 1.17286i
\(271\) 17.9616i 1.09109i 0.838082 + 0.545545i \(0.183677\pi\)
−0.838082 + 0.545545i \(0.816323\pi\)
\(272\) 6.47987 0.392900
\(273\) 4.52016 0.753777i 0.273572 0.0456207i
\(274\) −4.15721 −0.251146
\(275\) 34.2910i 2.06783i
\(276\) −0.569569 + 6.68740i −0.0342840 + 0.402534i
\(277\) −9.40678 −0.565199 −0.282599 0.959238i \(-0.591197\pi\)
−0.282599 + 0.959238i \(0.591197\pi\)
\(278\) 0.0159714 0.000957899
\(279\) 4.95218 28.8613i 0.296480 1.72788i
\(280\) 9.82477 2.51081i 0.587143 0.150050i
\(281\) 28.3782i 1.69290i 0.532467 + 0.846451i \(0.321265\pi\)
−0.532467 + 0.846451i \(0.678735\pi\)
\(282\) −1.84908 + 21.7104i −0.110111 + 1.29283i
\(283\) 21.3006i 1.26619i −0.774075 0.633094i \(-0.781785\pi\)
0.774075 0.633094i \(-0.218215\pi\)
\(284\) 9.18326i 0.544926i
\(285\) −0.873264 + 10.2531i −0.0517277 + 0.607343i
\(286\) 3.53879i 0.209253i
\(287\) 7.23242 + 28.3004i 0.426916 + 1.67052i
\(288\) 0.507343 2.95679i 0.0298955 0.174230i
\(289\) 24.9887 1.46992
\(290\) −25.6925 −1.50872
\(291\) 1.52117 17.8603i 0.0891725 1.04699i
\(292\) 11.6727i 0.683095i
\(293\) −10.8691 −0.634978 −0.317489 0.948262i \(-0.602840\pi\)
−0.317489 + 0.948262i \(0.602840\pi\)
\(294\) −4.89333 11.0930i −0.285385 0.646959i
\(295\) 6.67384 0.388566
\(296\) 0.597183i 0.0347106i
\(297\) 4.63646 17.7939i 0.269035 1.03251i
\(298\) 10.5043 0.608499
\(299\) 3.87495 0.224094
\(300\) 16.7231 + 1.42432i 0.965510 + 0.0822329i
\(301\) 0.395780 + 1.54868i 0.0228124 + 0.0892646i
\(302\) 7.95857i 0.457964i
\(303\) 18.8360 + 1.60427i 1.08210 + 0.0921630i
\(304\) 1.55008i 0.0889031i
\(305\) 20.2372i 1.15878i
\(306\) 3.28751 19.1596i 0.187935 1.09528i
\(307\) 8.05501i 0.459723i 0.973223 + 0.229862i \(0.0738274\pi\)
−0.973223 + 0.229862i \(0.926173\pi\)
\(308\) −9.07121 + 2.31823i −0.516880 + 0.132093i
\(309\) −0.0879453 + 1.03258i −0.00500303 + 0.0587414i
\(310\) −37.4117 −2.12484
\(311\) 2.09862 0.119002 0.0595009 0.998228i \(-0.481049\pi\)
0.0595009 + 0.998228i \(0.481049\pi\)
\(312\) −1.72580 0.146987i −0.0977043 0.00832153i
\(313\) 16.8977i 0.955117i −0.878600 0.477559i \(-0.841522\pi\)
0.878600 0.477559i \(-0.158478\pi\)
\(314\) −4.29431 −0.242342
\(315\) −2.43941 30.3236i −0.137445 1.70854i
\(316\) 3.29905 0.185586
\(317\) 32.7364i 1.83866i −0.393491 0.919328i \(-0.628733\pi\)
0.393491 0.919328i \(-0.371267\pi\)
\(318\) 11.8069 + 1.00560i 0.662100 + 0.0563914i
\(319\) 23.7219 1.32817
\(320\) −3.83276 −0.214258
\(321\) 1.86689 21.9194i 0.104199 1.22342i
\(322\) −2.53845 9.93292i −0.141462 0.553540i
\(323\) 10.0443i 0.558880i
\(324\) −8.48521 3.00021i −0.471400 0.166678i
\(325\) 9.69005i 0.537507i
\(326\) 18.5687i 1.02843i
\(327\) 9.70345 + 0.826448i 0.536602 + 0.0457027i
\(328\) 11.0403i 0.609599i
\(329\) −8.24097 32.2468i −0.454339 1.77782i
\(330\) −23.4076 1.99364i −1.28855 0.109746i
\(331\) −13.6138 −0.748283 −0.374142 0.927372i \(-0.622063\pi\)
−0.374142 + 0.927372i \(0.622063\pi\)
\(332\) −2.06179 −0.113155
\(333\) −1.76574 0.302977i −0.0967622 0.0166030i
\(334\) 10.6873i 0.584781i
\(335\) 20.6803 1.12988
\(336\) 0.753777 + 4.52016i 0.0411219 + 0.246595i
\(337\) −0.276737 −0.0150748 −0.00753740 0.999972i \(-0.502399\pi\)
−0.00753740 + 0.999972i \(0.502399\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 1.56701 18.3986i 0.0851085 0.999272i
\(340\) −24.8358 −1.34691
\(341\) 34.5422 1.87056
\(342\) −4.58326 0.786421i −0.247834 0.0425248i
\(343\) 12.6324 + 13.5433i 0.682086 + 0.731272i
\(344\) 0.604159i 0.0325741i
\(345\) 2.18302 25.6312i 0.117530 1.37994i
\(346\) 13.4395i 0.722513i
\(347\) 2.85298i 0.153156i 0.997064 + 0.0765780i \(0.0243994\pi\)
−0.997064 + 0.0765780i \(0.975601\pi\)
\(348\) 0.985315 11.5687i 0.0528184 0.620149i
\(349\) 9.55389i 0.511408i −0.966755 0.255704i \(-0.917693\pi\)
0.966755 0.255704i \(-0.0823073\pi\)
\(350\) −24.8392 + 6.34788i −1.32771 + 0.339308i
\(351\) −1.31018 + 5.02826i −0.0699325 + 0.268389i
\(352\) 3.53879 0.188618
\(353\) 10.7608 0.572742 0.286371 0.958119i \(-0.407551\pi\)
0.286371 + 0.958119i \(0.407551\pi\)
\(354\) −0.255944 + 3.00508i −0.0136033 + 0.159718i
\(355\) 35.1972i 1.86808i
\(356\) −1.46706 −0.0777538
\(357\) 4.88437 + 29.2900i 0.258508 + 1.55019i
\(358\) 6.55533 0.346460
\(359\) 24.5118i 1.29368i −0.762624 0.646842i \(-0.776089\pi\)
0.762624 0.646842i \(-0.223911\pi\)
\(360\) −1.94452 + 11.3327i −0.102485 + 0.597284i
\(361\) 16.5973 0.873540
\(362\) 17.1646 0.902150
\(363\) 2.62840 + 0.223862i 0.137955 + 0.0117497i
\(364\) 2.56337 0.655092i 0.134357 0.0343362i
\(365\) 44.7388i 2.34174i
\(366\) 9.11232 + 0.776101i 0.476309 + 0.0405674i
\(367\) 18.6513i 0.973588i 0.873517 + 0.486794i \(0.161834\pi\)
−0.873517 + 0.486794i \(0.838166\pi\)
\(368\) 3.87495i 0.201996i
\(369\) −32.6439 5.60122i −1.69937 0.291588i
\(370\) 2.28886i 0.118992i
\(371\) −17.5371 + 4.48176i −0.910480 + 0.232681i
\(372\) 1.43475 16.8456i 0.0743882 0.873404i
\(373\) 4.55264 0.235727 0.117863 0.993030i \(-0.462396\pi\)
0.117863 + 0.993030i \(0.462396\pi\)
\(374\) 22.9309 1.18573
\(375\) −31.0228 2.64223i −1.60201 0.136444i
\(376\) 12.5799i 0.648757i
\(377\) −6.70339 −0.345242
\(378\) 13.7476 + 0.0645093i 0.707099 + 0.00331800i
\(379\) −14.4380 −0.741629 −0.370815 0.928707i \(-0.620922\pi\)
−0.370815 + 0.928707i \(0.620922\pi\)
\(380\) 5.94108i 0.304771i
\(381\) −8.55035 0.728238i −0.438048 0.0373087i
\(382\) −9.04802 −0.462937
\(383\) 19.0301 0.972391 0.486196 0.873850i \(-0.338384\pi\)
0.486196 + 0.873850i \(0.338384\pi\)
\(384\) 0.146987 1.72580i 0.00750092 0.0880695i
\(385\) 34.7678 8.88522i 1.77193 0.452833i
\(386\) 6.04974i 0.307924i
\(387\) −1.78637 0.306516i −0.0908064 0.0155811i
\(388\) 10.3490i 0.525390i
\(389\) 1.06894i 0.0541973i 0.999633 + 0.0270986i \(0.00862682\pi\)
−0.999633 + 0.0270986i \(0.991373\pi\)
\(390\) 6.61459 + 0.563368i 0.334943 + 0.0285272i
\(391\) 25.1092i 1.26982i
\(392\) −3.35848 6.14171i −0.169629 0.310203i
\(393\) 15.5745 + 1.32649i 0.785629 + 0.0669124i
\(394\) 1.88643 0.0950368
\(395\) −12.6445 −0.636213
\(396\) 1.79538 10.4634i 0.0902211 0.525808i
\(397\) 5.70472i 0.286312i 0.989700 + 0.143156i \(0.0457250\pi\)
−0.989700 + 0.143156i \(0.954275\pi\)
\(398\) −11.4529 −0.574084
\(399\) 7.00660 1.16841i 0.350769 0.0584938i
\(400\) 9.69005 0.484503
\(401\) 25.1273i 1.25480i 0.778698 + 0.627399i \(0.215880\pi\)
−0.778698 + 0.627399i \(0.784120\pi\)
\(402\) −0.793094 + 9.31184i −0.0395559 + 0.464432i
\(403\) −9.76102 −0.486231
\(404\) 10.9143 0.543009
\(405\) 32.5218 + 11.4991i 1.61602 + 0.571394i
\(406\) 4.39134 + 17.1833i 0.217939 + 0.852791i
\(407\) 2.11330i 0.104753i
\(408\) 0.952459 11.1830i 0.0471538 0.553640i
\(409\) 10.6907i 0.528619i 0.964438 + 0.264310i \(0.0851441\pi\)
−0.964438 + 0.264310i \(0.914856\pi\)
\(410\) 42.3149i 2.08978i
\(411\) −0.611058 + 7.17452i −0.0301412 + 0.353893i
\(412\) 0.598318i 0.0294770i
\(413\) −1.14069 4.46350i −0.0561296 0.219634i
\(414\) 11.4574 + 1.96593i 0.563101 + 0.0966200i
\(415\) 7.90235 0.387911
\(416\) −1.00000 −0.0490290
\(417\) 0.00234759 0.0275634i 0.000114962 0.00134979i
\(418\) 5.48540i 0.268300i
\(419\) −11.5531 −0.564406 −0.282203 0.959355i \(-0.591065\pi\)
−0.282203 + 0.959355i \(0.591065\pi\)
\(420\) −2.88905 17.3247i −0.140971 0.845358i
\(421\) −4.18647 −0.204036 −0.102018 0.994783i \(-0.532530\pi\)
−0.102018 + 0.994783i \(0.532530\pi\)
\(422\) 16.5318i 0.804755i
\(423\) 37.1960 + 6.38230i 1.80853 + 0.310318i
\(424\) 6.84142 0.332249
\(425\) 62.7903 3.04577
\(426\) −15.8485 1.34982i −0.767862 0.0653992i
\(427\) −13.5347 + 3.45892i −0.654990 + 0.167389i
\(428\) 12.7010i 0.613926i
\(429\) −6.10725 0.520157i −0.294861 0.0251134i
\(430\) 2.31560i 0.111668i
\(431\) 30.3437i 1.46160i 0.682590 + 0.730802i \(0.260854\pi\)
−0.682590 + 0.730802i \(0.739146\pi\)
\(432\) −5.02826 1.31018i −0.241922 0.0630363i
\(433\) 7.90187i 0.379740i 0.981809 + 0.189870i \(0.0608066\pi\)
−0.981809 + 0.189870i \(0.939193\pi\)
\(434\) 6.39437 + 25.0211i 0.306940 + 1.20105i
\(435\) −3.77647 + 44.3402i −0.181068 + 2.12595i
\(436\) 5.62257 0.269272
\(437\) 6.00648 0.287329
\(438\) −20.1448 1.71575i −0.962558 0.0819815i
\(439\) 38.0804i 1.81748i −0.417364 0.908739i \(-0.637046\pi\)
0.417364 0.908739i \(-0.362954\pi\)
\(440\) −13.5633 −0.646606
\(441\) −19.8636 + 6.81438i −0.945888 + 0.324494i
\(442\) −6.47987 −0.308216
\(443\) 4.75228i 0.225788i −0.993607 0.112894i \(-0.963988\pi\)
0.993607 0.112894i \(-0.0360120\pi\)
\(444\) −1.03062 0.0877784i −0.0489111 0.00416578i
\(445\) 5.62287 0.266550
\(446\) −10.9849 −0.520148
\(447\) 1.54400 18.1284i 0.0730289 0.857443i
\(448\) 0.655092 + 2.56337i 0.0309502 + 0.121108i
\(449\) 18.2285i 0.860257i −0.902768 0.430129i \(-0.858468\pi\)
0.902768 0.430129i \(-0.141532\pi\)
\(450\) 4.91618 28.6514i 0.231751 1.35064i
\(451\) 39.0693i 1.83970i
\(452\) 10.6609i 0.501445i
\(453\) 13.7349 + 1.16981i 0.645323 + 0.0549625i
\(454\) 18.3687i 0.862088i
\(455\) −9.82477 + 2.51081i −0.460593 + 0.117709i
\(456\) −2.67513 0.227842i −0.125274 0.0106697i
\(457\) −20.6866 −0.967677 −0.483838 0.875157i \(-0.660758\pi\)
−0.483838 + 0.875157i \(0.660758\pi\)
\(458\) −8.77152 −0.409866
\(459\) −32.5825 8.48982i −1.52082 0.396271i
\(460\) 14.8518i 0.692466i
\(461\) −39.2144 −1.82640 −0.913198 0.407516i \(-0.866395\pi\)
−0.913198 + 0.407516i \(0.866395\pi\)
\(462\) 2.66745 + 15.9959i 0.124101 + 0.744195i
\(463\) −8.05138 −0.374179 −0.187090 0.982343i \(-0.559906\pi\)
−0.187090 + 0.982343i \(0.559906\pi\)
\(464\) 6.70339i 0.311197i
\(465\) −5.49905 + 64.5652i −0.255012 + 2.99414i
\(466\) 25.7318 1.19200
\(467\) 5.39494 0.249648 0.124824 0.992179i \(-0.460163\pi\)
0.124824 + 0.992179i \(0.460163\pi\)
\(468\) −0.507343 + 2.95679i −0.0234519 + 0.136678i
\(469\) −3.53465 13.8311i −0.163215 0.638659i
\(470\) 48.2156i 2.22402i
\(471\) −0.631210 + 7.41114i −0.0290846 + 0.341487i
\(472\) 1.74126i 0.0801481i
\(473\) 2.13799i 0.0983049i
\(474\) 0.484919 5.69351i 0.0222731 0.261512i
\(475\) 15.0203i 0.689181i
\(476\) 4.24491 + 16.6103i 0.194565 + 0.761331i
\(477\) 3.47094 20.2286i 0.158924 0.926206i
\(478\) 12.7421 0.582812
\(479\) 20.6008 0.941275 0.470638 0.882327i \(-0.344024\pi\)
0.470638 + 0.882327i \(0.344024\pi\)
\(480\) −0.563368 + 6.61459i −0.0257141 + 0.301913i
\(481\) 0.597183i 0.0272292i
\(482\) 13.1363 0.598343
\(483\) −17.5154 + 2.92085i −0.796977 + 0.132903i
\(484\) 1.52300 0.0692275
\(485\) 39.6651i 1.80110i
\(486\) −6.42499 + 14.2028i −0.291444 + 0.644252i
\(487\) −15.7925 −0.715625 −0.357813 0.933793i \(-0.616477\pi\)
−0.357813 + 0.933793i \(0.616477\pi\)
\(488\) 5.28005 0.239017
\(489\) −32.0460 2.72937i −1.44917 0.123426i
\(490\) 12.8723 + 23.5397i 0.581510 + 1.06342i
\(491\) 20.4861i 0.924524i 0.886743 + 0.462262i \(0.152962\pi\)
−0.886743 + 0.462262i \(0.847038\pi\)
\(492\) −19.0534 1.62279i −0.858994 0.0731609i
\(493\) 43.4371i 1.95631i
\(494\) 1.55008i 0.0697413i
\(495\) −6.88125 + 40.1039i −0.309289 + 1.80254i
\(496\) 9.76102i 0.438283i
\(497\) 23.5401 6.01588i 1.05592 0.269849i
\(498\) −0.303057 + 3.55824i −0.0135803 + 0.159449i
\(499\) −31.3034 −1.40133 −0.700667 0.713488i \(-0.747114\pi\)
−0.700667 + 0.713488i \(0.747114\pi\)
\(500\) −17.9759 −0.803905
\(501\) 18.4441 + 1.57089i 0.824022 + 0.0701823i
\(502\) 20.8113i 0.928852i
\(503\) −12.1873 −0.543404 −0.271702 0.962381i \(-0.587586\pi\)
−0.271702 + 0.962381i \(0.587586\pi\)
\(504\) 7.91169 0.636464i 0.352415 0.0283503i
\(505\) −41.8320 −1.86150
\(506\) 13.7126i 0.609600i
\(507\) 1.72580 + 0.146987i 0.0766456 + 0.00652794i
\(508\) −4.95442 −0.219817
\(509\) −32.4560 −1.43859 −0.719293 0.694706i \(-0.755534\pi\)
−0.719293 + 0.694706i \(0.755534\pi\)
\(510\) −3.65055 + 42.8617i −0.161649 + 1.89795i
\(511\) 29.9215 7.64672i 1.32365 0.338271i
\(512\) 1.00000i 0.0441942i
\(513\) −2.03089 + 7.79420i −0.0896659 + 0.344122i
\(514\) 14.9960i 0.661445i
\(515\) 2.29321i 0.101051i
\(516\) −1.04266 0.0888038i −0.0459005 0.00390937i
\(517\) 44.5174i 1.95787i
\(518\) 1.53080 0.391210i 0.0672595 0.0171888i
\(519\) 23.1940 + 1.97544i 1.01810 + 0.0867123i
\(520\) 3.83276 0.168078
\(521\) 23.3355 1.02235 0.511174 0.859477i \(-0.329211\pi\)
0.511174 + 0.859477i \(0.329211\pi\)
\(522\) −19.8205 3.40092i −0.867521 0.148854i
\(523\) 5.32316i 0.232765i 0.993204 + 0.116383i \(0.0371299\pi\)
−0.993204 + 0.116383i \(0.962870\pi\)
\(524\) 9.02449 0.394237
\(525\) 7.30414 + 43.8006i 0.318779 + 1.91161i
\(526\) −11.2324 −0.489757
\(527\) 63.2501i 2.75522i
\(528\) 0.520157 6.10725i 0.0226369 0.265784i
\(529\) 7.98477 0.347164
\(530\) −26.2215 −1.13899
\(531\) 5.14855 + 0.883417i 0.223428 + 0.0383370i
\(532\) 3.97342 1.01544i 0.172270 0.0440251i
\(533\) 11.0403i 0.478209i
\(534\) −0.215639 + 2.53185i −0.00933160 + 0.109564i
\(535\) 48.6799i 2.10461i
\(536\) 5.39566i 0.233057i
\(537\) 0.963552 11.3132i 0.0415803 0.488201i
\(538\) 0.548970i 0.0236678i
\(539\) −11.8850 21.7342i −0.511921 0.936158i
\(540\) 19.2721 + 5.02162i 0.829340 + 0.216096i
\(541\) 2.28504 0.0982415 0.0491207 0.998793i \(-0.484358\pi\)
0.0491207 + 0.998793i \(0.484358\pi\)
\(542\) 17.9616 0.771517
\(543\) 2.52298 29.6227i 0.108271 1.27123i
\(544\) 6.47987i 0.277822i
\(545\) −21.5500 −0.923100
\(546\) −0.753777 4.52016i −0.0322587 0.193445i
\(547\) −3.40027 −0.145385 −0.0726925 0.997354i \(-0.523159\pi\)
−0.0726925 + 0.997354i \(0.523159\pi\)
\(548\) 4.15721i 0.177587i
\(549\) 2.67879 15.6120i 0.114328 0.666304i
\(550\) 34.2910 1.46217
\(551\) −10.3908 −0.442662
\(552\) 6.68740 + 0.569569i 0.284634 + 0.0242425i
\(553\) 2.16118 + 8.45668i 0.0919028 + 0.359615i
\(554\) 9.40678i 0.399656i
\(555\) 3.95012 + 0.336434i 0.167673 + 0.0142808i
\(556\) 0.0159714i 0.000677337i
\(557\) 26.1294i 1.10714i 0.832804 + 0.553568i \(0.186734\pi\)
−0.832804 + 0.553568i \(0.813266\pi\)
\(558\) −28.8613 4.95218i −1.22180 0.209643i
\(559\) 0.604159i 0.0255532i
\(560\) −2.51081 9.82477i −0.106101 0.415173i
\(561\) 3.37055 39.5741i 0.142305 1.67082i
\(562\) 28.3782 1.19706
\(563\) 33.5979 1.41598 0.707992 0.706220i \(-0.249601\pi\)
0.707992 + 0.706220i \(0.249601\pi\)
\(564\) 21.7104 + 1.84908i 0.914171 + 0.0778604i
\(565\) 40.8606i 1.71902i
\(566\) −21.3006 −0.895330
\(567\) 2.13205 23.7161i 0.0895378 0.995983i
\(568\) −9.18326 −0.385321
\(569\) 20.2598i 0.849336i −0.905349 0.424668i \(-0.860391\pi\)
0.905349 0.424668i \(-0.139609\pi\)
\(570\) 10.2531 + 0.873264i 0.429457 + 0.0365770i
\(571\) −2.55199 −0.106797 −0.0533987 0.998573i \(-0.517005\pi\)
−0.0533987 + 0.998573i \(0.517005\pi\)
\(572\) −3.53879 −0.147964
\(573\) −1.32995 + 15.6151i −0.0555593 + 0.652330i
\(574\) 28.3004 7.23242i 1.18124 0.301876i
\(575\) 37.5485i 1.56588i
\(576\) −2.95679 0.507343i −0.123200 0.0211393i
\(577\) 29.0022i 1.20738i 0.797220 + 0.603689i \(0.206303\pi\)
−0.797220 + 0.603689i \(0.793697\pi\)
\(578\) 24.9887i 1.03939i
\(579\) 10.4407 + 0.889236i 0.433899 + 0.0369554i
\(580\) 25.6925i 1.06682i
\(581\) −1.35066 5.28512i −0.0560349 0.219264i
\(582\) −17.8603 1.52117i −0.740333 0.0630545i
\(583\) 24.2103 1.00269
\(584\) −11.6727 −0.483021
\(585\) 1.94452 11.3327i 0.0803961 0.468548i
\(586\) 10.8691i 0.448997i
\(587\) −4.97590 −0.205378 −0.102689 0.994714i \(-0.532745\pi\)
−0.102689 + 0.994714i \(0.532745\pi\)
\(588\) −11.0930 + 4.89333i −0.457469 + 0.201797i
\(589\) −15.1304 −0.623436
\(590\) 6.67384i 0.274758i
\(591\) 0.277281 3.25560i 0.0114058 0.133917i
\(592\) −0.597183 −0.0245441
\(593\) 2.09710 0.0861176 0.0430588 0.999073i \(-0.486290\pi\)
0.0430588 + 0.999073i \(0.486290\pi\)
\(594\) −17.7939 4.63646i −0.730094 0.190236i
\(595\) −16.2697 63.6632i −0.666994 2.60994i
\(596\) 10.5043i 0.430274i
\(597\) −1.68344 + 19.7655i −0.0688986 + 0.808949i
\(598\) 3.87495i 0.158458i
\(599\) 18.5175i 0.756606i 0.925682 + 0.378303i \(0.123492\pi\)
−0.925682 + 0.378303i \(0.876508\pi\)
\(600\) 1.42432 16.7231i 0.0581475 0.682719i
\(601\) 37.7166i 1.53849i −0.638953 0.769246i \(-0.720632\pi\)
0.638953 0.769246i \(-0.279368\pi\)
\(602\) 1.54868 0.395780i 0.0631196 0.0161308i
\(603\) 15.9538 + 2.73745i 0.649690 + 0.111477i
\(604\) 7.95857 0.323830
\(605\) −5.83731 −0.237320
\(606\) 1.60427 18.8360i 0.0651690 0.765160i
\(607\) 14.2872i 0.579899i 0.957042 + 0.289950i \(0.0936386\pi\)
−0.957042 + 0.289950i \(0.906361\pi\)
\(608\) −1.55008 −0.0628640
\(609\) 30.3004 5.05286i 1.22783 0.204752i
\(610\) −20.2372 −0.819379
\(611\) 12.5799i 0.508927i
\(612\) −19.1596 3.28751i −0.774481 0.132890i
\(613\) 19.1299 0.772651 0.386325 0.922363i \(-0.373744\pi\)
0.386325 + 0.922363i \(0.373744\pi\)
\(614\) 8.05501 0.325074
\(615\) 73.0271 + 6.21976i 2.94474 + 0.250805i
\(616\) 2.31823 + 9.07121i 0.0934042 + 0.365489i
\(617\) 32.8876i 1.32400i 0.749502 + 0.662002i \(0.230293\pi\)
−0.749502 + 0.662002i \(0.769707\pi\)
\(618\) 1.03258 + 0.0879453i 0.0415364 + 0.00353768i
\(619\) 33.2924i 1.33814i 0.743201 + 0.669068i \(0.233307\pi\)
−0.743201 + 0.669068i \(0.766693\pi\)
\(620\) 37.4117i 1.50249i
\(621\) 5.07690 19.4843i 0.203729 0.781876i
\(622\) 2.09862i 0.0841470i
\(623\) −0.961057 3.76060i −0.0385039 0.150665i
\(624\) −0.146987 + 1.72580i −0.00588421 + 0.0690874i
\(625\) 20.4469 0.817875
\(626\) −16.8977 −0.675370
\(627\) −9.46671 0.806285i −0.378064 0.0321999i
\(628\) 4.29431i 0.171362i
\(629\) −3.86967 −0.154294
\(630\) −30.3236 + 2.43941i −1.20812 + 0.0971885i
\(631\) −20.4297 −0.813292 −0.406646 0.913586i \(-0.633302\pi\)
−0.406646 + 0.913586i \(0.633302\pi\)
\(632\) 3.29905i 0.131229i
\(633\) −28.5306 2.42997i −1.13399 0.0965824i
\(634\) −32.7364 −1.30013
\(635\) 18.9891 0.753560
\(636\) 1.00560 11.8069i 0.0398748 0.468176i
\(637\) 3.35848 + 6.14171i 0.133068 + 0.243343i
\(638\) 23.7219i 0.939158i
\(639\) −4.65906 + 27.1530i −0.184310 + 1.07415i
\(640\) 3.83276i 0.151503i
\(641\) 22.3785i 0.883898i −0.897040 0.441949i \(-0.854287\pi\)
0.897040 0.441949i \(-0.145713\pi\)
\(642\) −21.9194 1.86689i −0.865090 0.0736802i
\(643\) 41.9210i 1.65320i 0.562788 + 0.826602i \(0.309729\pi\)
−0.562788 + 0.826602i \(0.690271\pi\)
\(644\) −9.93292 + 2.53845i −0.391412 + 0.100029i
\(645\) 3.99626 + 0.340364i 0.157353 + 0.0134018i
\(646\) −10.0443 −0.395188
\(647\) 0.0109042 0.000428690 0.000214345 1.00000i \(-0.499932\pi\)
0.000214345 1.00000i \(0.499932\pi\)
\(648\) −3.00021 + 8.48521i −0.117859 + 0.333330i
\(649\) 6.16196i 0.241878i
\(650\) −9.69005 −0.380075
\(651\) 44.1214 7.35763i 1.72925 0.288368i
\(652\) −18.5687 −0.727208
\(653\) 10.1915i 0.398824i −0.979916 0.199412i \(-0.936097\pi\)
0.979916 0.199412i \(-0.0639033\pi\)
\(654\) 0.826448 9.70345i 0.0323167 0.379435i
\(655\) −34.5887 −1.35149
\(656\) −11.0403 −0.431052
\(657\) −5.92208 + 34.5138i −0.231042 + 1.34651i
\(658\) −32.2468 + 8.24097i −1.25711 + 0.321266i
\(659\) 7.10895i 0.276925i 0.990368 + 0.138463i \(0.0442161\pi\)
−0.990368 + 0.138463i \(0.955784\pi\)
\(660\) −1.99364 + 23.4076i −0.0776022 + 0.911140i
\(661\) 20.4994i 0.797334i −0.917096 0.398667i \(-0.869473\pi\)
0.917096 0.398667i \(-0.130527\pi\)
\(662\) 13.6138i 0.529116i
\(663\) −0.952459 + 11.1830i −0.0369905 + 0.434311i
\(664\) 2.06179i 0.0800130i
\(665\) −15.2292 + 3.89196i −0.590562 + 0.150924i
\(666\) −0.302977 + 1.76574i −0.0117401 + 0.0684212i
\(667\) 25.9753 1.00577
\(668\) 10.6873 0.413503
\(669\) −1.61464 + 18.9577i −0.0624255 + 0.732947i
\(670\) 20.6803i 0.798948i
\(671\) 18.6850 0.721325
\(672\) 4.52016 0.753777i 0.174369 0.0290776i
\(673\) −26.9039 −1.03707 −0.518534 0.855057i \(-0.673522\pi\)
−0.518534 + 0.855057i \(0.673522\pi\)
\(674\) 0.276737i 0.0106595i
\(675\) −48.7241 12.6958i −1.87539 0.488660i
\(676\) 1.00000 0.0384615
\(677\) −28.4525 −1.09352 −0.546759 0.837290i \(-0.684139\pi\)
−0.546759 + 0.837290i \(0.684139\pi\)
\(678\) −18.3986 1.56701i −0.706592 0.0601808i
\(679\) 26.5282 6.77953i 1.01806 0.260175i
\(680\) 24.8358i 0.952409i
\(681\) 31.7008 + 2.69997i 1.21478 + 0.103463i
\(682\) 34.5422i 1.32269i
\(683\) 0.283408i 0.0108443i −0.999985 0.00542215i \(-0.998274\pi\)
0.999985 0.00542215i \(-0.00172593\pi\)
\(684\) −0.786421 + 4.58326i −0.0300696 + 0.175245i
\(685\) 15.9336i 0.608791i
\(686\) 13.5433 12.6324i 0.517087 0.482308i
\(687\) −1.28930 + 15.1379i −0.0491900 + 0.577547i
\(688\) −0.604159 −0.0230334
\(689\) −6.84142 −0.260637
\(690\) −25.6312 2.18302i −0.975763 0.0831062i
\(691\) 3.14189i 0.119523i −0.998213 0.0597615i \(-0.980966\pi\)
0.998213 0.0597615i \(-0.0190340\pi\)
\(692\) 13.4395 0.510894
\(693\) 27.9978 2.25231i 1.06355 0.0855581i
\(694\) 2.85298 0.108298
\(695\) 0.0612144i 0.00232199i
\(696\) −11.5687 0.985315i −0.438512 0.0373483i
\(697\) −71.5398 −2.70976
\(698\) −9.55389 −0.361620
\(699\) 3.78225 44.4080i 0.143058 1.67966i
\(700\) 6.34788 + 24.8392i 0.239927 + 0.938832i
\(701\) 41.4916i 1.56712i −0.621318 0.783559i \(-0.713402\pi\)
0.621318 0.783559i \(-0.286598\pi\)
\(702\) 5.02826 + 1.31018i 0.189780 + 0.0494497i
\(703\) 0.925681i 0.0349127i
\(704\) 3.53879i 0.133373i
\(705\) −83.2106 7.08709i −3.13389 0.266915i
\(706\) 10.7608i 0.404990i
\(707\) 7.14990 + 27.9775i 0.268900 + 1.05220i
\(708\) 3.00508 + 0.255944i 0.112938 + 0.00961896i
\(709\) −1.50518 −0.0565282 −0.0282641 0.999600i \(-0.508998\pi\)
−0.0282641 + 0.999600i \(0.508998\pi\)
\(710\) 35.1972 1.32093
\(711\) −9.75460 1.67375i −0.365826 0.0627705i
\(712\) 1.46706i 0.0549802i
\(713\) 37.8235 1.41650
\(714\) 29.2900 4.88437i 1.09615 0.182793i
\(715\) 13.5633 0.507239
\(716\) 6.55533i 0.244984i
\(717\) 1.87294 21.9904i 0.0699461 0.821248i
\(718\) −24.5118 −0.914773
\(719\) −27.9526 −1.04245 −0.521227 0.853418i \(-0.674526\pi\)
−0.521227 + 0.853418i \(0.674526\pi\)
\(720\) 11.3327 + 1.94452i 0.422344 + 0.0724681i
\(721\) −1.53371 + 0.391954i −0.0571183 + 0.0145971i
\(722\) 16.5973i 0.617686i
\(723\) 1.93087 22.6707i 0.0718100 0.843132i
\(724\) 17.1646i 0.637916i
\(725\) 64.9562i 2.41241i
\(726\) 0.223862 2.62840i 0.00830832 0.0975492i
\(727\) 18.3871i 0.681938i −0.940075 0.340969i \(-0.889245\pi\)
0.940075 0.340969i \(-0.110755\pi\)
\(728\) −0.655092 2.56337i −0.0242793 0.0950047i
\(729\) 23.5668 + 13.1759i 0.872846 + 0.487996i
\(730\) 44.7388 1.65586
\(731\) −3.91487 −0.144797
\(732\) 0.776101 9.11232i 0.0286855 0.336801i
\(733\) 5.48224i 0.202491i −0.994861 0.101246i \(-0.967717\pi\)
0.994861 0.101246i \(-0.0322828\pi\)
\(734\) 18.6513 0.688430
\(735\) 42.5169 18.7550i 1.56826 0.691787i
\(736\) 3.87495 0.142833
\(737\) 19.0941i 0.703339i
\(738\) −5.60122 + 32.6439i −0.206184 + 1.20164i
\(739\) −49.9723 −1.83826 −0.919130 0.393955i \(-0.871106\pi\)
−0.919130 + 0.393955i \(0.871106\pi\)
\(740\) 2.28886 0.0841402
\(741\) 2.67513 + 0.227842i 0.0982734 + 0.00836999i
\(742\) 4.48176 + 17.5371i 0.164531 + 0.643806i
\(743\) 13.7626i 0.504900i −0.967610 0.252450i \(-0.918764\pi\)
0.967610 0.252450i \(-0.0812363\pi\)
\(744\) −16.8456 1.43475i −0.617590 0.0526004i
\(745\) 40.2606i 1.47503i
\(746\) 4.55264i 0.166684i
\(747\) 6.09628 + 1.04603i 0.223051 + 0.0382724i
\(748\) 22.9309i 0.838435i
\(749\) 32.5573 8.32032i 1.18962 0.304018i
\(750\) −2.64223 + 31.0228i −0.0964804 + 1.13279i
\(751\) 19.3636 0.706587 0.353294 0.935512i \(-0.385062\pi\)
0.353294 + 0.935512i \(0.385062\pi\)
\(752\) 12.5799 0.458740
\(753\) 35.9161 + 3.05899i 1.30886 + 0.111476i
\(754\) 6.70339i 0.244123i
\(755\) −30.5033 −1.11013
\(756\) 0.0645093 13.7476i 0.00234618 0.499994i
\(757\) −11.2207 −0.407822 −0.203911 0.978989i \(-0.565365\pi\)
−0.203911 + 0.978989i \(0.565365\pi\)
\(758\) 14.4380i 0.524411i
\(759\) 23.6653 + 2.01558i 0.858995 + 0.0731610i
\(760\) 5.94108 0.215506
\(761\) 6.07389 0.220178 0.110089 0.993922i \(-0.464886\pi\)
0.110089 + 0.993922i \(0.464886\pi\)
\(762\) −0.728238 + 8.55035i −0.0263813 + 0.309747i
\(763\) 3.68330 + 14.4127i 0.133345 + 0.521776i
\(764\) 9.04802i 0.327346i
\(765\) 73.4342 + 12.6003i 2.65502 + 0.455563i
\(766\) 19.0301i 0.687584i
\(767\) 1.74126i 0.0628734i
\(768\) −1.72580 0.146987i −0.0622745 0.00530395i
\(769\) 53.3703i 1.92458i −0.272022 0.962291i \(-0.587692\pi\)
0.272022 0.962291i \(-0.412308\pi\)
\(770\) −8.88522 34.7678i −0.320201 1.25294i
\(771\) −25.8801 2.20422i −0.932050 0.0793831i
\(772\) 6.04974 0.217735
\(773\) 26.8657 0.966291 0.483145 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(774\) −0.306516 + 1.78637i −0.0110175 + 0.0642098i
\(775\) 94.5849i 3.39759i
\(776\) −10.3490 −0.371507
\(777\) −0.450143 2.69936i −0.0161488 0.0968391i
\(778\) 1.06894 0.0383232
\(779\) 17.1134i 0.613150i
\(780\) 0.563368 6.61459i 0.0201718 0.236840i
\(781\) −32.4976 −1.16286
\(782\) 25.1092 0.897901
\(783\) −8.78268 + 33.7064i −0.313867 + 1.20457i
\(784\) −6.14171 + 3.35848i −0.219347 + 0.119946i
\(785\) 16.4591i 0.587449i
\(786\) 1.32649 15.5745i 0.0473142 0.555524i
\(787\) 34.2164i 1.21968i 0.792524 + 0.609841i \(0.208767\pi\)
−0.792524 + 0.609841i \(0.791233\pi\)
\(788\) 1.88643i 0.0672011i
\(789\) −1.65103 + 19.3849i −0.0587781 + 0.690122i
\(790\) 12.6445i 0.449870i
\(791\) 27.3277 6.98385i 0.971662 0.248317i
\(792\) −10.4634 1.79538i −0.371802 0.0637959i
\(793\) −5.28005 −0.187500
\(794\) 5.70472 0.202453
\(795\) −3.85424 + 45.2532i −0.136696 + 1.60496i
\(796\) 11.4529i 0.405939i
\(797\) 3.09513 0.109635 0.0548175 0.998496i \(-0.482542\pi\)
0.0548175 + 0.998496i \(0.482542\pi\)
\(798\) −1.16841 7.00660i −0.0413614 0.248031i
\(799\) 81.5159 2.88382
\(800\) 9.69005i 0.342595i
\(801\) 4.33777 + 0.744300i 0.153268 + 0.0262985i
\(802\) 25.1273 0.887276
\(803\) −41.3073 −1.45770
\(804\) 9.31184 + 0.793094i 0.328403 + 0.0279703i
\(805\) 38.0705 9.72927i 1.34181 0.342912i
\(806\) 9.76102i 0.343817i
\(807\) 0.947414 + 0.0806917i 0.0333505 + 0.00284048i
\(808\) 10.9143i 0.383965i
\(809\) 34.5753i 1.21560i −0.794089 0.607802i \(-0.792051\pi\)
0.794089 0.607802i \(-0.207949\pi\)
\(810\) 11.4991 32.5218i 0.404037 1.14270i
\(811\) 18.2511i 0.640884i 0.947268 + 0.320442i \(0.103831\pi\)
−0.947268 + 0.320442i \(0.896169\pi\)
\(812\) 17.1833 4.39134i 0.603014 0.154106i
\(813\) 2.64013 30.9982i 0.0925934 1.08715i
\(814\) −2.11330 −0.0740712
\(815\) 71.1695 2.49296
\(816\) −11.1830 0.952459i −0.391482 0.0333427i
\(817\) 0.936495i 0.0327638i
\(818\) 10.6907 0.373790
\(819\) −7.91169 + 0.636464i −0.276457 + 0.0222398i
\(820\) 42.3149 1.47770
\(821\) 12.4344i 0.433964i −0.976176 0.216982i \(-0.930379\pi\)
0.976176 0.216982i \(-0.0696214\pi\)
\(822\) 7.17452 + 0.611058i 0.250240 + 0.0213131i
\(823\) −1.74146 −0.0607034 −0.0303517 0.999539i \(-0.509663\pi\)
−0.0303517 + 0.999539i \(0.509663\pi\)
\(824\) 0.598318 0.0208434
\(825\) 5.04035 59.1795i 0.175482 2.06037i
\(826\) −4.46350 + 1.14069i −0.155305 + 0.0396896i
\(827\) 39.4093i 1.37039i −0.728358 0.685197i \(-0.759716\pi\)
0.728358 0.685197i \(-0.240284\pi\)
\(828\) 1.96593 11.4574i 0.0683207 0.398172i
\(829\) 43.3524i 1.50569i 0.658198 + 0.752845i \(0.271319\pi\)
−0.658198 + 0.752845i \(0.728681\pi\)
\(830\) 7.90235i 0.274294i
\(831\) 16.2343 + 1.38268i 0.563160 + 0.0479646i
\(832\) 1.00000i 0.0346688i
\(833\) −39.7975 + 21.7625i −1.37890 + 0.754027i
\(834\) −0.0275634 0.00234759i −0.000954443 8.12904e-5i
\(835\) −40.9617 −1.41754
\(836\) −5.48540 −0.189716
\(837\) −12.7887 + 49.0810i −0.442044 + 1.69649i
\(838\) 11.5531i 0.399095i
\(839\) −12.9744 −0.447927 −0.223964 0.974598i \(-0.571900\pi\)
−0.223964 + 0.974598i \(0.571900\pi\)
\(840\) −17.3247 + 2.88905i −0.597758 + 0.0996816i
\(841\) −15.9355 −0.549499
\(842\) 4.18647i 0.144275i
\(843\) 4.17124 48.9752i 0.143665 1.68679i
\(844\) −16.5318 −0.569048
\(845\) −3.83276 −0.131851
\(846\) 6.38230 37.1960i 0.219428 1.27883i
\(847\) 0.997708 + 3.90402i 0.0342817 + 0.134144i
\(848\) 6.84142i 0.234935i
\(849\) −3.13092 + 36.7606i −0.107453 + 1.26162i
\(850\) 62.7903i 2.15369i
\(851\) 2.31405i 0.0793247i
\(852\) −1.34982 + 15.8485i −0.0462442 + 0.542960i
\(853\) 24.7116i 0.846110i −0.906104 0.423055i \(-0.860958\pi\)
0.906104 0.423055i \(-0.139042\pi\)
\(854\) 3.45892 + 13.5347i 0.118362 + 0.463148i
\(855\) 3.01416 17.5665i 0.103082 0.600763i
\(856\) −12.7010 −0.434111
\(857\) 38.6969 1.32186 0.660930 0.750447i \(-0.270162\pi\)
0.660930 + 0.750447i \(0.270162\pi\)
\(858\) −0.520157 + 6.10725i −0.0177579 + 0.208498i
\(859\) 26.6914i 0.910699i −0.890313 0.455350i \(-0.849514\pi\)
0.890313 0.455350i \(-0.150486\pi\)
\(860\) 2.31560 0.0789612
\(861\) −8.32193 49.9040i −0.283611 1.70072i
\(862\) 30.3437 1.03351
\(863\) 16.4748i 0.560808i −0.959882 0.280404i \(-0.909532\pi\)
0.959882 0.280404i \(-0.0904684\pi\)
\(864\) −1.31018 + 5.02826i −0.0445734 + 0.171065i
\(865\) −51.5105 −1.75141
\(866\) 7.90187 0.268516
\(867\) −43.1255 3.67302i −1.46462 0.124742i
\(868\) 25.0211 6.39437i 0.849271 0.217039i
\(869\) 11.6746i 0.396035i
\(870\) 44.3402 + 3.77647i 1.50327 + 0.128034i
\(871\) 5.39566i 0.182825i
\(872\) 5.62257i 0.190404i
\(873\) −5.25048 + 30.5997i −0.177702 + 1.03564i
\(874\) 6.00648i 0.203172i
\(875\) −11.7758 46.0787i −0.398096 1.55775i
\(876\) −1.71575 + 20.1448i −0.0579697 + 0.680631i
\(877\) 34.4149 1.16211 0.581055 0.813864i \(-0.302640\pi\)
0.581055 + 0.813864i \(0.302640\pi\)
\(878\) −38.0804 −1.28515
\(879\) 18.7579 + 1.59762i 0.632687 + 0.0538863i
\(880\) 13.5633i 0.457219i
\(881\) 10.6765 0.359699 0.179850 0.983694i \(-0.442439\pi\)
0.179850 + 0.983694i \(0.442439\pi\)
\(882\) 6.81438 + 19.8636i 0.229452 + 0.668844i
\(883\) −38.0731 −1.28126 −0.640630 0.767850i \(-0.721327\pi\)
−0.640630 + 0.767850i \(0.721327\pi\)
\(884\) 6.47987i 0.217942i
\(885\) −11.5177 0.980971i −0.387165 0.0329750i
\(886\) −4.75228 −0.159656
\(887\) 22.9996 0.772251 0.386126 0.922446i \(-0.373813\pi\)
0.386126 + 0.922446i \(0.373813\pi\)
\(888\) −0.0877784 + 1.03062i −0.00294565 + 0.0345853i
\(889\) −3.24560 12.7000i −0.108854 0.425944i
\(890\) 5.62287i 0.188479i
\(891\) −10.6171 + 30.0273i −0.355686 + 1.00595i
\(892\) 10.9849i 0.367800i
\(893\) 19.4998i 0.652535i
\(894\) −18.1284 1.54400i −0.606304 0.0516392i
\(895\) 25.1250i 0.839837i
\(896\) 2.56337 0.655092i 0.0856361 0.0218851i
\(897\) −6.68740 0.569569i −0.223286 0.0190174i
\(898\) −18.2285 −0.608294
\(899\) −65.4320 −2.18228
\(900\) −28.6514 4.91618i −0.955048 0.163873i
\(901\) 44.3315i 1.47690i
\(902\) −39.0693 −1.30087
\(903\) −0.455401 2.73089i −0.0151548 0.0908785i
\(904\) −10.6609 −0.354575
\(905\) 65.7877i 2.18686i
\(906\) 1.16981 13.7349i 0.0388643 0.456312i
\(907\) 30.9557 1.02787 0.513934 0.857830i \(-0.328188\pi\)
0.513934 + 0.857830i \(0.328188\pi\)
\(908\) 18.3687 0.609588
\(909\) −32.2714 5.53731i −1.07037 0.183661i
\(910\) 2.51081 + 9.82477i 0.0832326 + 0.325688i
\(911\) 40.8374i 1.35300i 0.736440 + 0.676502i \(0.236505\pi\)
−0.736440 + 0.676502i \(0.763495\pi\)
\(912\) −0.227842 + 2.67513i −0.00754461 + 0.0885824i
\(913\) 7.29623i 0.241470i
\(914\) 20.6866i 0.684251i
\(915\) −2.97461 + 34.9253i −0.0983375 + 1.15460i
\(916\) 8.77152i 0.289819i
\(917\) 5.91188 + 23.1331i 0.195227 + 0.763922i
\(918\) −8.48982 + 32.5825i −0.280206 + 1.07538i
\(919\) 29.3642 0.968636 0.484318 0.874892i \(-0.339068\pi\)
0.484318 + 0.874892i \(0.339068\pi\)
\(920\) −14.8518 −0.489648
\(921\) 1.18398 13.9013i 0.0390136 0.458065i
\(922\) 39.2144i 1.29146i
\(923\) 9.18326 0.302271
\(924\) 15.9959 2.66745i 0.526225 0.0877528i
\(925\) −5.78674 −0.190267
\(926\) 8.05138i 0.264585i
\(927\) 0.303552 1.76910i 0.00996997 0.0581049i
\(928\) −6.70339 −0.220050
\(929\) 49.5474 1.62560 0.812799 0.582544i \(-0.197943\pi\)
0.812799 + 0.582544i \(0.197943\pi\)
\(930\) 64.5652 + 5.49905i 2.11717 + 0.180321i
\(931\) 5.20592 + 9.52013i 0.170617 + 0.312010i
\(932\) 25.7318i 0.842872i
\(933\) −3.62180 0.308471i −0.118572 0.0100989i
\(934\) 5.39494i 0.176528i
\(935\) 87.8885i 2.87426i
\(936\) 2.95679 + 0.507343i 0.0966457 + 0.0165830i
\(937\) 56.8532i 1.85731i −0.370939 0.928657i \(-0.620964\pi\)
0.370939 0.928657i \(-0.379036\pi\)
\(938\) −13.8311 + 3.53465i −0.451600 + 0.115410i
\(939\) −2.48376 + 29.1622i −0.0810543 + 0.951672i
\(940\) −48.2156 −1.57262
\(941\) −48.8828 −1.59353 −0.796766 0.604287i \(-0.793458\pi\)
−0.796766 + 0.604287i \(0.793458\pi\)
\(942\) 7.41114 + 0.631210i 0.241468 + 0.0205659i
\(943\) 42.7807i 1.39313i
\(944\) 1.74126 0.0566733
\(945\) −0.247249 + 52.6912i −0.00804301 + 1.71404i
\(946\) −2.13799 −0.0695121
\(947\) 48.7459i 1.58403i −0.610501 0.792015i \(-0.709032\pi\)
0.610501 0.792015i \(-0.290968\pi\)
\(948\) −5.69351 0.484919i −0.184917 0.0157494i
\(949\) 11.6727 0.378913
\(950\) −15.0203 −0.487324
\(951\) −4.81183 + 56.4965i −0.156034 + 1.83202i
\(952\) 16.6103 4.24491i 0.538342 0.137578i
\(953\) 2.16214i 0.0700385i −0.999387 0.0350192i \(-0.988851\pi\)
0.999387 0.0350192i \(-0.0111493\pi\)
\(954\) −20.2286 3.47094i −0.654926 0.112376i
\(955\) 34.6789i 1.12218i
\(956\) 12.7421i 0.412111i
\(957\) −40.9393 3.48682i −1.32338 0.112713i
\(958\) 20.6008i 0.665582i
\(959\) −10.6565 + 2.72335i −0.344115 + 0.0879417i
\(960\) 6.61459 + 0.563368i 0.213485 + 0.0181826i
\(961\) −64.2776 −2.07347
\(962\) 0.597183 0.0192540
\(963\) −6.44376 + 37.5542i −0.207647 + 1.21017i
\(964\) 13.1363i 0.423092i
\(965\) −23.1872 −0.746422
\(966\) 2.92085 + 17.5154i 0.0939767 + 0.563548i
\(967\) 8.43003 0.271091 0.135546 0.990771i \(-0.456721\pi\)
0.135546 + 0.990771i \(0.456721\pi\)
\(968\) 1.52300i 0.0489512i
\(969\) −1.47639 + 17.3345i −0.0474284 + 0.556864i
\(970\) 39.6651 1.27357
\(971\) 30.8086 0.988695 0.494348 0.869264i \(-0.335407\pi\)
0.494348 + 0.869264i \(0.335407\pi\)
\(972\) 14.2028 + 6.42499i 0.455555 + 0.206082i
\(973\) 0.0409405 0.0104627i 0.00131249 0.000335419i
\(974\) 15.7925i 0.506023i
\(975\) −1.42432 + 16.7231i −0.0456146 + 0.535568i
\(976\) 5.28005i 0.169010i
\(977\) 60.6092i 1.93906i −0.244970 0.969531i \(-0.578778\pi\)
0.244970 0.969531i \(-0.421222\pi\)
\(978\) −2.72937 + 32.0460i −0.0872757 + 1.02472i
\(979\) 5.19159i 0.165924i
\(980\) 23.5397 12.8723i 0.751948 0.411189i
\(981\) −16.6248 2.85257i −0.530788 0.0910756i
\(982\) 20.4861 0.653737
\(983\) 57.7943 1.84335 0.921676 0.387960i \(-0.126820\pi\)
0.921676 + 0.387960i \(0.126820\pi\)
\(984\) −1.62279 + 19.0534i −0.0517326 + 0.607400i
\(985\) 7.23022i 0.230374i
\(986\) −43.4371 −1.38332
\(987\) 9.48241 + 56.8630i 0.301828 + 1.80997i
\(988\) 1.55008 0.0493146
\(989\) 2.34109i 0.0744422i
\(990\) 40.1039 + 6.88125i 1.27458 + 0.218700i
\(991\) 35.9463 1.14187 0.570935 0.820995i \(-0.306581\pi\)
0.570935 + 0.820995i \(0.306581\pi\)
\(992\) −9.76102 −0.309913
\(993\) 23.4948 + 2.00106i 0.745584 + 0.0635017i
\(994\) −6.01588 23.5401i −0.190812 0.746646i
\(995\) 43.8964i 1.39161i
\(996\) 3.55824 + 0.303057i 0.112747 + 0.00960274i
\(997\) 9.91463i 0.313999i −0.987599 0.157000i \(-0.949818\pi\)
0.987599 0.157000i \(-0.0501822\pi\)
\(998\) 31.3034i 0.990893i
\(999\) 3.00279 + 0.782420i 0.0950042 + 0.0247547i
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.g.c.209.1 12
3.2 odd 2 546.2.g.d.209.12 yes 12
7.6 odd 2 546.2.g.d.209.6 yes 12
21.20 even 2 inner 546.2.g.c.209.7 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.g.c.209.1 12 1.1 even 1 trivial
546.2.g.c.209.7 yes 12 21.20 even 2 inner
546.2.g.d.209.6 yes 12 7.6 odd 2
546.2.g.d.209.12 yes 12 3.2 odd 2