Properties

Label 196.2.d.c.195.7
Level $196$
Weight $2$
Character 196.195
Analytic conductor $1.565$
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] = [196,2,Mod(195,196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(196, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("196.195");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 196.d (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: \(1.56506787962\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.1212153856.10
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 10x^{4} - 16x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 195.7
Root \(1.07072 + 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 196.195
Dual form 196.2.d.c.195.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.207107 + 1.39897i) q^{2} -2.14144 q^{3} +(-1.91421 + 0.579471i) q^{4} -2.61313i q^{5} +(-0.443508 - 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +1.58579 q^{9} +O(q^{10})\) \(q+(0.207107 + 1.39897i) q^{2} -2.14144 q^{3} +(-1.91421 + 0.579471i) q^{4} -2.61313i q^{5} +(-0.443508 - 2.99581i) q^{6} +(-1.20711 - 2.55791i) q^{8} +1.58579 q^{9} +(3.65568 - 0.541196i) q^{10} -3.95687i q^{11} +(4.09918 - 1.24090i) q^{12} -1.08239i q^{13} +5.59587i q^{15} +(3.32843 - 2.21846i) q^{16} -0.317025i q^{17} +(0.328427 + 2.21846i) q^{18} -5.16991 q^{19} +(1.51423 + 5.00208i) q^{20} +(5.53553 - 0.819496i) q^{22} -2.31788i q^{23} +(2.58495 + 5.47762i) q^{24} -1.82843 q^{25} +(1.51423 - 0.224171i) q^{26} +3.02846 q^{27} -6.82843 q^{29} +(-7.82843 + 1.15894i) q^{30} -6.05692 q^{31} +(3.79289 + 4.19690i) q^{32} +8.47343i q^{33} +(0.443508 - 0.0656581i) q^{34} +(-3.03553 + 0.918917i) q^{36} -4.00000 q^{37} +(-1.07072 - 7.23252i) q^{38} +2.31788i q^{39} +(-6.68414 + 3.15432i) q^{40} +2.29610i q^{41} -7.23486i q^{43} +(2.29289 + 7.57430i) q^{44} -4.14386i q^{45} +(3.24264 - 0.480049i) q^{46} +4.28289 q^{47} +(-7.12764 + 4.75071i) q^{48} +(-0.378680 - 2.55791i) q^{50} +0.678892i q^{51} +(0.627215 + 2.07193i) q^{52} +10.4853 q^{53} +(0.627215 + 4.23671i) q^{54} -10.3398 q^{55} +11.0711 q^{57} +(-1.41421 - 9.55274i) q^{58} +11.2268 q^{59} +(-3.24264 - 10.7117i) q^{60} -5.41196i q^{61} +(-1.25443 - 8.47343i) q^{62} +(-5.08579 + 6.17534i) q^{64} -2.82843 q^{65} +(-11.8540 + 1.75490i) q^{66} +3.27798i q^{67} +(0.183707 + 0.606854i) q^{68} +4.96362i q^{69} +(-1.91421 - 4.05630i) q^{72} +14.0167i q^{73} +(-0.828427 - 5.59587i) q^{74} +3.91548 q^{75} +(9.89630 - 2.99581i) q^{76} +(-3.24264 + 0.480049i) q^{78} +7.91375i q^{79} +(-5.79712 - 8.69760i) q^{80} -11.2426 q^{81} +(-3.21217 + 0.475538i) q^{82} +9.45280 q^{83} -0.828427 q^{85} +(10.1213 - 1.49839i) q^{86} +14.6227 q^{87} +(-10.1213 + 4.77637i) q^{88} -5.99162i q^{89} +(5.79712 - 0.858221i) q^{90} +(1.34315 + 4.43692i) q^{92} +12.9706 q^{93} +(0.887016 + 5.99162i) q^{94} +13.5096i q^{95} +(-8.12227 - 8.98743i) q^{96} -9.23880i q^{97} -6.27476i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{8} + 24 q^{9} + 4 q^{16} - 20 q^{18} + 16 q^{22} + 8 q^{25} - 32 q^{29} - 40 q^{30} + 36 q^{32} + 4 q^{36} - 32 q^{37} + 24 q^{44} - 8 q^{46} - 20 q^{50} + 16 q^{53} + 32 q^{57} + 8 q^{60} - 52 q^{64} - 4 q^{72} + 16 q^{74} + 8 q^{78} - 56 q^{81} + 16 q^{85} + 64 q^{86} - 64 q^{88} + 56 q^{92} - 32 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).

\(n\) \(99\) \(101\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.207107 + 1.39897i 0.146447 + 0.989219i
\(3\) −2.14144 −1.23636 −0.618182 0.786035i \(-0.712130\pi\)
−0.618182 + 0.786035i \(0.712130\pi\)
\(4\) −1.91421 + 0.579471i −0.957107 + 0.289735i
\(5\) 2.61313i 1.16863i −0.811529 0.584313i \(-0.801364\pi\)
0.811529 0.584313i \(-0.198636\pi\)
\(6\) −0.443508 2.99581i −0.181061 1.22303i
\(7\) 0 0
\(8\) −1.20711 2.55791i −0.426777 0.904357i
\(9\) 1.58579 0.528595
\(10\) 3.65568 0.541196i 1.15603 0.171141i
\(11\) 3.95687i 1.19304i −0.802597 0.596521i \(-0.796549\pi\)
0.802597 0.596521i \(-0.203451\pi\)
\(12\) 4.09918 1.24090i 1.18333 0.358218i
\(13\) 1.08239i 0.300202i −0.988671 0.150101i \(-0.952040\pi\)
0.988671 0.150101i \(-0.0479598\pi\)
\(14\) 0 0
\(15\) 5.59587i 1.44485i
\(16\) 3.32843 2.21846i 0.832107 0.554615i
\(17\) 0.317025i 0.0768899i −0.999261 0.0384450i \(-0.987760\pi\)
0.999261 0.0384450i \(-0.0122404\pi\)
\(18\) 0.328427 + 2.21846i 0.0774110 + 0.522896i
\(19\) −5.16991 −1.18606 −0.593029 0.805181i \(-0.702068\pi\)
−0.593029 + 0.805181i \(0.702068\pi\)
\(20\) 1.51423 + 5.00208i 0.338592 + 1.11850i
\(21\) 0 0
\(22\) 5.53553 0.819496i 1.18018 0.174717i
\(23\) 2.31788i 0.483312i −0.970362 0.241656i \(-0.922309\pi\)
0.970362 0.241656i \(-0.0776906\pi\)
\(24\) 2.58495 + 5.47762i 0.527651 + 1.11811i
\(25\) −1.82843 −0.365685
\(26\) 1.51423 0.224171i 0.296965 0.0439635i
\(27\) 3.02846 0.582827
\(28\) 0 0
\(29\) −6.82843 −1.26801 −0.634004 0.773330i \(-0.718590\pi\)
−0.634004 + 0.773330i \(0.718590\pi\)
\(30\) −7.82843 + 1.15894i −1.42927 + 0.211593i
\(31\) −6.05692 −1.08786 −0.543928 0.839132i \(-0.683063\pi\)
−0.543928 + 0.839132i \(0.683063\pi\)
\(32\) 3.79289 + 4.19690i 0.670495 + 0.741914i
\(33\) 8.47343i 1.47503i
\(34\) 0.443508 0.0656581i 0.0760610 0.0112603i
\(35\) 0 0
\(36\) −3.03553 + 0.918917i −0.505922 + 0.153153i
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) −1.07072 7.23252i −0.173694 1.17327i
\(39\) 2.31788i 0.371158i
\(40\) −6.68414 + 3.15432i −1.05685 + 0.498742i
\(41\) 2.29610i 0.358591i 0.983795 + 0.179295i \(0.0573818\pi\)
−0.983795 + 0.179295i \(0.942618\pi\)
\(42\) 0 0
\(43\) 7.23486i 1.10331i −0.834074 0.551653i \(-0.813997\pi\)
0.834074 0.551653i \(-0.186003\pi\)
\(44\) 2.29289 + 7.57430i 0.345667 + 1.14187i
\(45\) 4.14386i 0.617730i
\(46\) 3.24264 0.480049i 0.478101 0.0707794i
\(47\) 4.28289 0.624724 0.312362 0.949963i \(-0.398880\pi\)
0.312362 + 0.949963i \(0.398880\pi\)
\(48\) −7.12764 + 4.75071i −1.02879 + 0.685706i
\(49\) 0 0
\(50\) −0.378680 2.55791i −0.0535534 0.361743i
\(51\) 0.678892i 0.0950639i
\(52\) 0.627215 + 2.07193i 0.0869790 + 0.287325i
\(53\) 10.4853 1.44026 0.720132 0.693837i \(-0.244081\pi\)
0.720132 + 0.693837i \(0.244081\pi\)
\(54\) 0.627215 + 4.23671i 0.0853531 + 0.576544i
\(55\) −10.3398 −1.39422
\(56\) 0 0
\(57\) 11.0711 1.46640
\(58\) −1.41421 9.55274i −0.185695 1.25434i
\(59\) 11.2268 1.46161 0.730804 0.682587i \(-0.239145\pi\)
0.730804 + 0.682587i \(0.239145\pi\)
\(60\) −3.24264 10.7117i −0.418623 1.38287i
\(61\) 5.41196i 0.692931i −0.938063 0.346465i \(-0.887382\pi\)
0.938063 0.346465i \(-0.112618\pi\)
\(62\) −1.25443 8.47343i −0.159313 1.07613i
\(63\) 0 0
\(64\) −5.08579 + 6.17534i −0.635723 + 0.771917i
\(65\) −2.82843 −0.350823
\(66\) −11.8540 + 1.75490i −1.45913 + 0.216014i
\(67\) 3.27798i 0.400469i 0.979748 + 0.200235i \(0.0641704\pi\)
−0.979748 + 0.200235i \(0.935830\pi\)
\(68\) 0.183707 + 0.606854i 0.0222777 + 0.0735919i
\(69\) 4.96362i 0.597550i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −1.91421 4.05630i −0.225592 0.478039i
\(73\) 14.0167i 1.64053i 0.571983 + 0.820266i \(0.306174\pi\)
−0.571983 + 0.820266i \(0.693826\pi\)
\(74\) −0.828427 5.59587i −0.0963027 0.650506i
\(75\) 3.91548 0.452120
\(76\) 9.89630 2.99581i 1.13518 0.343643i
\(77\) 0 0
\(78\) −3.24264 + 0.480049i −0.367157 + 0.0543549i
\(79\) 7.91375i 0.890366i 0.895440 + 0.445183i \(0.146861\pi\)
−0.895440 + 0.445183i \(0.853139\pi\)
\(80\) −5.79712 8.69760i −0.648138 0.972421i
\(81\) −11.2426 −1.24918
\(82\) −3.21217 + 0.475538i −0.354725 + 0.0525144i
\(83\) 9.45280 1.03758 0.518790 0.854902i \(-0.326383\pi\)
0.518790 + 0.854902i \(0.326383\pi\)
\(84\) 0 0
\(85\) −0.828427 −0.0898555
\(86\) 10.1213 1.49839i 1.09141 0.161575i
\(87\) 14.6227 1.56772
\(88\) −10.1213 + 4.77637i −1.07894 + 0.509163i
\(89\) 5.99162i 0.635110i −0.948240 0.317555i \(-0.897138\pi\)
0.948240 0.317555i \(-0.102862\pi\)
\(90\) 5.79712 0.858221i 0.611070 0.0904645i
\(91\) 0 0
\(92\) 1.34315 + 4.43692i 0.140033 + 0.462581i
\(93\) 12.9706 1.34498
\(94\) 0.887016 + 5.99162i 0.0914887 + 0.617988i
\(95\) 13.5096i 1.38606i
\(96\) −8.12227 8.98743i −0.828976 0.917276i
\(97\) 9.23880i 0.938058i −0.883183 0.469029i \(-0.844604\pi\)
0.883183 0.469029i \(-0.155396\pi\)
\(98\) 0 0
\(99\) 6.27476i 0.630637i
\(100\) 3.50000 1.05952i 0.350000 0.105952i
\(101\) 15.2304i 1.51548i −0.652555 0.757741i \(-0.726303\pi\)
0.652555 0.757741i \(-0.273697\pi\)
\(102\) −0.949747 + 0.140603i −0.0940390 + 0.0139218i
\(103\) 12.1138 1.19361 0.596806 0.802385i \(-0.296436\pi\)
0.596806 + 0.802385i \(0.296436\pi\)
\(104\) −2.76866 + 1.30656i −0.271489 + 0.128119i
\(105\) 0 0
\(106\) 2.17157 + 14.6686i 0.210922 + 1.42474i
\(107\) 2.31788i 0.224078i −0.993704 0.112039i \(-0.964262\pi\)
0.993704 0.112039i \(-0.0357382\pi\)
\(108\) −5.79712 + 1.75490i −0.557828 + 0.168866i
\(109\) −5.65685 −0.541828 −0.270914 0.962604i \(-0.587326\pi\)
−0.270914 + 0.962604i \(0.587326\pi\)
\(110\) −2.14144 14.4650i −0.204179 1.37919i
\(111\) 8.56578 0.813028
\(112\) 0 0
\(113\) −4.24264 −0.399114 −0.199557 0.979886i \(-0.563950\pi\)
−0.199557 + 0.979886i \(0.563950\pi\)
\(114\) 2.29289 + 15.4881i 0.214749 + 1.45059i
\(115\) −6.05692 −0.564811
\(116\) 13.0711 3.95687i 1.21362 0.367387i
\(117\) 1.71644i 0.158685i
\(118\) 2.32515 + 15.7060i 0.214048 + 1.44585i
\(119\) 0 0
\(120\) 14.3137 6.75481i 1.30666 0.616627i
\(121\) −4.65685 −0.423350
\(122\) 7.57115 1.12085i 0.685460 0.101477i
\(123\) 4.91697i 0.443349i
\(124\) 11.5942 3.50981i 1.04119 0.315190i
\(125\) 8.28772i 0.741276i
\(126\) 0 0
\(127\) 10.2316i 0.907911i −0.891024 0.453955i \(-0.850013\pi\)
0.891024 0.453955i \(-0.149987\pi\)
\(128\) −9.69239 5.83589i −0.856694 0.515825i
\(129\) 15.4930i 1.36409i
\(130\) −0.585786 3.95687i −0.0513769 0.347041i
\(131\) 0.367414 0.0321011 0.0160505 0.999871i \(-0.494891\pi\)
0.0160505 + 0.999871i \(0.494891\pi\)
\(132\) −4.91010 16.2200i −0.427370 1.41177i
\(133\) 0 0
\(134\) −4.58579 + 0.678892i −0.396152 + 0.0586474i
\(135\) 7.91375i 0.681107i
\(136\) −0.810922 + 0.382683i −0.0695360 + 0.0328148i
\(137\) −8.24264 −0.704216 −0.352108 0.935959i \(-0.614535\pi\)
−0.352108 + 0.935959i \(0.614535\pi\)
\(138\) −6.94394 + 1.02800i −0.591107 + 0.0875091i
\(139\) −22.8211 −1.93566 −0.967829 0.251610i \(-0.919040\pi\)
−0.967829 + 0.251610i \(0.919040\pi\)
\(140\) 0 0
\(141\) −9.17157 −0.772386
\(142\) 0 0
\(143\) −4.28289 −0.358153
\(144\) 5.27817 3.51801i 0.439848 0.293167i
\(145\) 17.8435i 1.48183i
\(146\) −19.6089 + 2.90295i −1.62284 + 0.240250i
\(147\) 0 0
\(148\) 7.65685 2.31788i 0.629390 0.190529i
\(149\) 4.82843 0.395560 0.197780 0.980246i \(-0.436627\pi\)
0.197780 + 0.980246i \(0.436627\pi\)
\(150\) 0.810922 + 5.47762i 0.0662115 + 0.447246i
\(151\) 21.4234i 1.74341i −0.490032 0.871704i \(-0.663015\pi\)
0.490032 0.871704i \(-0.336985\pi\)
\(152\) 6.24063 + 13.2241i 0.506182 + 1.07262i
\(153\) 0.502734i 0.0406437i
\(154\) 0 0
\(155\) 15.8275i 1.27130i
\(156\) −1.34315 4.43692i −0.107538 0.355238i
\(157\) 19.1886i 1.53141i −0.643189 0.765707i \(-0.722389\pi\)
0.643189 0.765707i \(-0.277611\pi\)
\(158\) −11.0711 + 1.63899i −0.880767 + 0.130391i
\(159\) −22.4537 −1.78069
\(160\) 10.9670 9.91131i 0.867019 0.783558i
\(161\) 0 0
\(162\) −2.32843 15.7281i −0.182939 1.23571i
\(163\) 15.1486i 1.18653i 0.805007 + 0.593265i \(0.202161\pi\)
−0.805007 + 0.593265i \(0.797839\pi\)
\(164\) −1.33052 4.39523i −0.103896 0.343210i
\(165\) 22.1421 1.72376
\(166\) 1.95774 + 13.2241i 0.151950 + 1.02639i
\(167\) 7.83095 0.605977 0.302989 0.952994i \(-0.402016\pi\)
0.302989 + 0.952994i \(0.402016\pi\)
\(168\) 0 0
\(169\) 11.8284 0.909879
\(170\) −0.171573 1.15894i −0.0131590 0.0888868i
\(171\) −8.19837 −0.626945
\(172\) 4.19239 + 13.8491i 0.319667 + 1.05598i
\(173\) 6.57128i 0.499605i −0.968297 0.249802i \(-0.919634\pi\)
0.968297 0.249802i \(-0.0803657\pi\)
\(174\) 3.02846 + 20.4567i 0.229587 + 1.55082i
\(175\) 0 0
\(176\) −8.77817 13.1702i −0.661680 0.992739i
\(177\) −24.0416 −1.80708
\(178\) 8.38207 1.24090i 0.628263 0.0930098i
\(179\) 13.5096i 1.00976i 0.863191 + 0.504878i \(0.168463\pi\)
−0.863191 + 0.504878i \(0.831537\pi\)
\(180\) 2.40125 + 7.93223i 0.178978 + 0.591234i
\(181\) 21.9874i 1.63431i 0.576418 + 0.817155i \(0.304450\pi\)
−0.576418 + 0.817155i \(0.695550\pi\)
\(182\) 0 0
\(183\) 11.5894i 0.856714i
\(184\) −5.92893 + 2.79793i −0.437087 + 0.206266i
\(185\) 10.4525i 0.768483i
\(186\) 2.68629 + 18.1454i 0.196968 + 1.33048i
\(187\) −1.25443 −0.0917330
\(188\) −8.19837 + 2.48181i −0.597927 + 0.181005i
\(189\) 0 0
\(190\) −18.8995 + 2.79793i −1.37111 + 0.202983i
\(191\) 6.55596i 0.474373i −0.971464 0.237186i \(-0.923775\pi\)
0.971464 0.237186i \(-0.0762252\pi\)
\(192\) 10.8909 13.2241i 0.785985 0.954370i
\(193\) 14.5858 1.04991 0.524954 0.851131i \(-0.324083\pi\)
0.524954 + 0.851131i \(0.324083\pi\)
\(194\) 12.9248 1.91342i 0.927944 0.137375i
\(195\) 6.05692 0.433745
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 8.77817 1.29954i 0.623838 0.0923546i
\(199\) −17.1316 −1.21442 −0.607212 0.794540i \(-0.707712\pi\)
−0.607212 + 0.794540i \(0.707712\pi\)
\(200\) 2.20711 + 4.67695i 0.156066 + 0.330710i
\(201\) 7.01962i 0.495126i
\(202\) 21.3068 3.15432i 1.49914 0.221937i
\(203\) 0 0
\(204\) −0.393398 1.29954i −0.0275434 0.0909863i
\(205\) 6.00000 0.419058
\(206\) 2.50886 + 16.9469i 0.174800 + 1.18074i
\(207\) 3.67567i 0.255477i
\(208\) −2.40125 3.60266i −0.166496 0.249800i
\(209\) 20.4567i 1.41502i
\(210\) 0 0
\(211\) 14.4697i 0.996136i 0.867138 + 0.498068i \(0.165957\pi\)
−0.867138 + 0.498068i \(0.834043\pi\)
\(212\) −20.0711 + 6.07591i −1.37849 + 0.417296i
\(213\) 0 0
\(214\) 3.24264 0.480049i 0.221662 0.0328155i
\(215\) −18.9056 −1.28935
\(216\) −3.65568 7.74652i −0.248737 0.527084i
\(217\) 0 0
\(218\) −1.17157 7.91375i −0.0793489 0.535987i
\(219\) 30.0160i 2.02829i
\(220\) 19.7926 5.99162i 1.33442 0.403955i
\(221\) −0.343146 −0.0230825
\(222\) 1.77403 + 11.9832i 0.119065 + 0.804262i
\(223\) 7.83095 0.524399 0.262200 0.965014i \(-0.415552\pi\)
0.262200 + 0.965014i \(0.415552\pi\)
\(224\) 0 0
\(225\) −2.89949 −0.193300
\(226\) −0.878680 5.93531i −0.0584489 0.394811i
\(227\) −9.97240 −0.661891 −0.330946 0.943650i \(-0.607368\pi\)
−0.330946 + 0.943650i \(0.607368\pi\)
\(228\) −21.1924 + 6.41536i −1.40350 + 0.424868i
\(229\) 1.34502i 0.0888817i 0.999012 + 0.0444409i \(0.0141506\pi\)
−0.999012 + 0.0444409i \(0.985849\pi\)
\(230\) −1.25443 8.47343i −0.0827146 0.558721i
\(231\) 0 0
\(232\) 8.24264 + 17.4665i 0.541156 + 1.14673i
\(233\) 16.2426 1.06409 0.532045 0.846716i \(-0.321424\pi\)
0.532045 + 0.846716i \(0.321424\pi\)
\(234\) 2.40125 0.355487i 0.156974 0.0232389i
\(235\) 11.1917i 0.730068i
\(236\) −21.4905 + 6.50562i −1.39892 + 0.423480i
\(237\) 16.9469i 1.10082i
\(238\) 0 0
\(239\) 10.2316i 0.661829i −0.943661 0.330915i \(-0.892643\pi\)
0.943661 0.330915i \(-0.107357\pi\)
\(240\) 12.4142 + 18.6254i 0.801334 + 1.20227i
\(241\) 5.09494i 0.328194i −0.986444 0.164097i \(-0.947529\pi\)
0.986444 0.164097i \(-0.0524710\pi\)
\(242\) −0.964466 6.51478i −0.0619982 0.418786i
\(243\) 14.9901 0.961616
\(244\) 3.13607 + 10.3596i 0.200767 + 0.663209i
\(245\) 0 0
\(246\) 6.87868 1.01834i 0.438569 0.0649269i
\(247\) 5.59587i 0.356056i
\(248\) 7.31135 + 15.4930i 0.464271 + 0.983809i
\(249\) −20.2426 −1.28283
\(250\) 11.5942 1.71644i 0.733284 0.108557i
\(251\) −3.91548 −0.247143 −0.123571 0.992336i \(-0.539435\pi\)
−0.123571 + 0.992336i \(0.539435\pi\)
\(252\) 0 0
\(253\) −9.17157 −0.576612
\(254\) 14.3137 2.11904i 0.898122 0.132960i
\(255\) 1.77403 0.111094
\(256\) 6.15685 14.7680i 0.384803 0.922999i
\(257\) 19.0572i 1.18876i 0.804185 + 0.594379i \(0.202602\pi\)
−0.804185 + 0.594379i \(0.797398\pi\)
\(258\) −21.6743 + 3.20871i −1.34938 + 0.199766i
\(259\) 0 0
\(260\) 5.41421 1.63899i 0.335775 0.101646i
\(261\) −10.8284 −0.670263
\(262\) 0.0760939 + 0.514000i 0.00470110 + 0.0317550i
\(263\) 25.6614i 1.58235i −0.611588 0.791176i \(-0.709469\pi\)
0.611588 0.791176i \(-0.290531\pi\)
\(264\) 21.6743 10.2283i 1.33396 0.629510i
\(265\) 27.3994i 1.68313i
\(266\) 0 0
\(267\) 12.8307i 0.785227i
\(268\) −1.89949 6.27476i −0.116030 0.383292i
\(269\) 5.04054i 0.307327i 0.988123 + 0.153664i \(0.0491072\pi\)
−0.988123 + 0.153664i \(0.950893\pi\)
\(270\) 11.0711 1.63899i 0.673764 0.0997458i
\(271\) 4.28289 0.260167 0.130084 0.991503i \(-0.458475\pi\)
0.130084 + 0.991503i \(0.458475\pi\)
\(272\) −0.703309 1.05520i −0.0426443 0.0639806i
\(273\) 0 0
\(274\) −1.70711 11.5312i −0.103130 0.696624i
\(275\) 7.23486i 0.436278i
\(276\) −2.87627 9.50143i −0.173131 0.571919i
\(277\) −4.14214 −0.248877 −0.124438 0.992227i \(-0.539713\pi\)
−0.124438 + 0.992227i \(0.539713\pi\)
\(278\) −4.72640 31.9259i −0.283470 1.91479i
\(279\) −9.60498 −0.575035
\(280\) 0 0
\(281\) 10.3848 0.619504 0.309752 0.950817i \(-0.399754\pi\)
0.309752 + 0.950817i \(0.399754\pi\)
\(282\) −1.89949 12.8307i −0.113113 0.764058i
\(283\) 3.39587 0.201864 0.100932 0.994893i \(-0.467818\pi\)
0.100932 + 0.994893i \(0.467818\pi\)
\(284\) 0 0
\(285\) 28.9301i 1.71367i
\(286\) −0.887016 5.99162i −0.0524503 0.354292i
\(287\) 0 0
\(288\) 6.01472 + 6.65539i 0.354421 + 0.392172i
\(289\) 16.8995 0.994088
\(290\) −24.9625 + 3.69552i −1.46585 + 0.217008i
\(291\) 19.7844i 1.15978i
\(292\) −8.12227 26.8310i −0.475320 1.57016i
\(293\) 11.7975i 0.689219i −0.938746 0.344609i \(-0.888011\pi\)
0.938746 0.344609i \(-0.111989\pi\)
\(294\) 0 0
\(295\) 29.3371i 1.70807i
\(296\) 4.82843 + 10.2316i 0.280647 + 0.594702i
\(297\) 11.9832i 0.695338i
\(298\) 1.00000 + 6.75481i 0.0579284 + 0.391295i
\(299\) −2.50886 −0.145091
\(300\) −7.49506 + 2.26890i −0.432727 + 0.130995i
\(301\) 0 0
\(302\) 29.9706 4.43692i 1.72461 0.255316i
\(303\) 32.6151i 1.87369i
\(304\) −17.2077 + 11.4692i −0.986927 + 0.657806i
\(305\) −14.1421 −0.809776
\(306\) 0.703309 0.104120i 0.0402055 0.00595213i
\(307\) −3.91548 −0.223468 −0.111734 0.993738i \(-0.535640\pi\)
−0.111734 + 0.993738i \(0.535640\pi\)
\(308\) 0 0
\(309\) −25.9411 −1.47574
\(310\) −22.1421 + 3.27798i −1.25759 + 0.186177i
\(311\) 20.6796 1.17263 0.586317 0.810082i \(-0.300577\pi\)
0.586317 + 0.810082i \(0.300577\pi\)
\(312\) 5.92893 2.79793i 0.335660 0.158402i
\(313\) 12.7486i 0.720594i −0.932838 0.360297i \(-0.882675\pi\)
0.932838 0.360297i \(-0.117325\pi\)
\(314\) 26.8442 3.97408i 1.51490 0.224270i
\(315\) 0 0
\(316\) −4.58579 15.1486i −0.257971 0.852176i
\(317\) −5.51472 −0.309737 −0.154869 0.987935i \(-0.549495\pi\)
−0.154869 + 0.987935i \(0.549495\pi\)
\(318\) −4.65030 31.4119i −0.260776 1.76149i
\(319\) 27.0192i 1.51279i
\(320\) 16.1369 + 13.2898i 0.902082 + 0.742922i
\(321\) 4.96362i 0.277042i
\(322\) 0 0
\(323\) 1.63899i 0.0911959i
\(324\) 21.5208 6.51478i 1.19560 0.361932i
\(325\) 1.97908i 0.109779i
\(326\) −21.1924 + 3.13738i −1.17374 + 0.173763i
\(327\) 12.1138 0.669897
\(328\) 5.87321 2.77164i 0.324294 0.153038i
\(329\) 0 0
\(330\) 4.58579 + 30.9761i 0.252439 + 1.70518i
\(331\) 15.1486i 0.832643i 0.909218 + 0.416321i \(0.136681\pi\)
−0.909218 + 0.416321i \(0.863319\pi\)
\(332\) −18.0947 + 5.47762i −0.993074 + 0.300623i
\(333\) −6.34315 −0.347602
\(334\) 1.62184 + 10.9552i 0.0887433 + 0.599444i
\(335\) 8.56578 0.467999
\(336\) 0 0
\(337\) 10.8284 0.589862 0.294931 0.955519i \(-0.404703\pi\)
0.294931 + 0.955519i \(0.404703\pi\)
\(338\) 2.44975 + 16.5476i 0.133249 + 0.900069i
\(339\) 9.08538 0.493450
\(340\) 1.58579 0.480049i 0.0860013 0.0260343i
\(341\) 23.9665i 1.29786i
\(342\) −1.69794 11.4692i −0.0918139 0.620185i
\(343\) 0 0
\(344\) −18.5061 + 8.73324i −0.997782 + 0.470865i
\(345\) 12.9706 0.698312
\(346\) 9.19299 1.36096i 0.494218 0.0731654i
\(347\) 3.95687i 0.212416i −0.994344 0.106208i \(-0.966129\pi\)
0.994344 0.106208i \(-0.0338710\pi\)
\(348\) −27.9910 + 8.47343i −1.50047 + 0.454223i
\(349\) 8.47343i 0.453572i 0.973945 + 0.226786i \(0.0728218\pi\)
−0.973945 + 0.226786i \(0.927178\pi\)
\(350\) 0 0
\(351\) 3.27798i 0.174966i
\(352\) 16.6066 15.0080i 0.885135 0.799929i
\(353\) 10.0586i 0.535363i 0.963507 + 0.267681i \(0.0862575\pi\)
−0.963507 + 0.267681i \(0.913743\pi\)
\(354\) −4.97918 33.6334i −0.264641 1.78760i
\(355\) 0 0
\(356\) 3.47197 + 11.4692i 0.184014 + 0.607868i
\(357\) 0 0
\(358\) −18.8995 + 2.79793i −0.998869 + 0.147875i
\(359\) 31.2573i 1.64970i −0.565353 0.824849i \(-0.691260\pi\)
0.565353 0.824849i \(-0.308740\pi\)
\(360\) −10.5996 + 5.00208i −0.558649 + 0.263633i
\(361\) 7.72792 0.406733
\(362\) −30.7596 + 4.55374i −1.61669 + 0.239339i
\(363\) 9.97240 0.523415
\(364\) 0 0
\(365\) 36.6274 1.91717
\(366\) −16.2132 + 2.40025i −0.847478 + 0.125463i
\(367\) 12.8487 0.670695 0.335348 0.942094i \(-0.391146\pi\)
0.335348 + 0.942094i \(0.391146\pi\)
\(368\) −5.14214 7.71491i −0.268052 0.402167i
\(369\) 3.64113i 0.189549i
\(370\) −14.6227 + 2.16478i −0.760198 + 0.112542i
\(371\) 0 0
\(372\) −24.8284 + 7.51606i −1.28729 + 0.389690i
\(373\) −20.1421 −1.04292 −0.521460 0.853276i \(-0.674612\pi\)
−0.521460 + 0.853276i \(0.674612\pi\)
\(374\) −0.259801 1.75490i −0.0134340 0.0907440i
\(375\) 17.7477i 0.916487i
\(376\) −5.16991 10.9552i −0.266618 0.564973i
\(377\) 7.39104i 0.380658i
\(378\) 0 0
\(379\) 21.7046i 1.11489i −0.830214 0.557444i \(-0.811782\pi\)
0.830214 0.557444i \(-0.188218\pi\)
\(380\) −7.82843 25.8603i −0.401590 1.32660i
\(381\) 21.9105i 1.12251i
\(382\) 9.17157 1.35778i 0.469258 0.0694703i
\(383\) 31.0194 1.58502 0.792509 0.609860i \(-0.208774\pi\)
0.792509 + 0.609860i \(0.208774\pi\)
\(384\) 20.7557 + 12.4972i 1.05919 + 0.637747i
\(385\) 0 0
\(386\) 3.02082 + 20.4050i 0.153755 + 1.03859i
\(387\) 11.4729i 0.583202i
\(388\) 5.35361 + 17.6850i 0.271788 + 0.897821i
\(389\) 14.1421 0.717035 0.358517 0.933523i \(-0.383282\pi\)
0.358517 + 0.933523i \(0.383282\pi\)
\(390\) 1.25443 + 8.47343i 0.0635205 + 0.429069i
\(391\) −0.734828 −0.0371618
\(392\) 0 0
\(393\) −0.786797 −0.0396886
\(394\) 0.414214 + 2.79793i 0.0208678 + 0.140958i
\(395\) 20.6796 1.04050
\(396\) 3.63604 + 12.0112i 0.182718 + 0.603587i
\(397\) 16.1271i 0.809396i −0.914450 0.404698i \(-0.867377\pi\)
0.914450 0.404698i \(-0.132623\pi\)
\(398\) −3.54806 23.9665i −0.177848 1.20133i
\(399\) 0 0
\(400\) −6.08579 + 4.05630i −0.304289 + 0.202815i
\(401\) −12.8284 −0.640621 −0.320311 0.947313i \(-0.603787\pi\)
−0.320311 + 0.947313i \(0.603787\pi\)
\(402\) 9.82021 1.45381i 0.489788 0.0725095i
\(403\) 6.55596i 0.326576i
\(404\) 8.82558 + 29.1543i 0.439089 + 1.45048i
\(405\) 29.3784i 1.45983i
\(406\) 0 0
\(407\) 15.8275i 0.784540i
\(408\) 1.73654 0.819496i 0.0859717 0.0405711i
\(409\) 13.8310i 0.683899i −0.939718 0.341949i \(-0.888913\pi\)
0.939718 0.341949i \(-0.111087\pi\)
\(410\) 1.24264 + 8.39380i 0.0613696 + 0.414540i
\(411\) 17.6512 0.870668
\(412\) −23.1885 + 7.01962i −1.14241 + 0.345832i
\(413\) 0 0
\(414\) 5.14214 0.761256i 0.252722 0.0374137i
\(415\) 24.7013i 1.21254i
\(416\) 4.54269 4.10540i 0.222724 0.201284i
\(417\) 48.8701 2.39318
\(418\) −28.6182 + 4.23671i −1.39976 + 0.207224i
\(419\) −17.2837 −0.844366 −0.422183 0.906511i \(-0.638736\pi\)
−0.422183 + 0.906511i \(0.638736\pi\)
\(420\) 0 0
\(421\) −10.4853 −0.511021 −0.255511 0.966806i \(-0.582244\pi\)
−0.255511 + 0.966806i \(0.582244\pi\)
\(422\) −20.2426 + 2.99678i −0.985396 + 0.145881i
\(423\) 6.79175 0.330226
\(424\) −12.6569 26.8204i −0.614671 1.30251i
\(425\) 0.579658i 0.0281175i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.34315 + 4.43692i 0.0649234 + 0.214467i
\(429\) 9.17157 0.442808
\(430\) −3.91548 26.4483i −0.188821 1.27545i
\(431\) 0.960099i 0.0462463i −0.999733 0.0231232i \(-0.992639\pi\)
0.999733 0.0231232i \(-0.00736099\pi\)
\(432\) 10.0800 6.71852i 0.484975 0.323245i
\(433\) 26.1857i 1.25840i 0.777243 + 0.629201i \(0.216618\pi\)
−0.777243 + 0.629201i \(0.783382\pi\)
\(434\) 0 0
\(435\) 38.2110i 1.83208i
\(436\) 10.8284 3.27798i 0.518588 0.156987i
\(437\) 11.9832i 0.573236i
\(438\) 41.9914 6.21652i 2.00643 0.297037i
\(439\) −22.4537 −1.07165 −0.535827 0.844328i \(-0.680000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(440\) 12.4813 + 26.4483i 0.595021 + 1.26087i
\(441\) 0 0
\(442\) −0.0710678 0.480049i −0.00338035 0.0228336i
\(443\) 28.3770i 1.34823i 0.738625 + 0.674116i \(0.235475\pi\)
−0.738625 + 0.674116i \(0.764525\pi\)
\(444\) −16.3967 + 4.96362i −0.778154 + 0.235563i
\(445\) −15.6569 −0.742206
\(446\) 1.62184 + 10.9552i 0.0767965 + 0.518746i
\(447\) −10.3398 −0.489056
\(448\) 0 0
\(449\) −16.2843 −0.768502 −0.384251 0.923229i \(-0.625540\pi\)
−0.384251 + 0.923229i \(0.625540\pi\)
\(450\) −0.600505 4.05630i −0.0283081 0.191216i
\(451\) 9.08538 0.427814
\(452\) 8.12132 2.45849i 0.381995 0.115637i
\(453\) 45.8770i 2.15549i
\(454\) −2.06535 13.9510i −0.0969317 0.654755i
\(455\) 0 0
\(456\) −13.3640 28.3188i −0.625825 1.32615i
\(457\) 0.727922 0.0340508 0.0170254 0.999855i \(-0.494580\pi\)
0.0170254 + 0.999855i \(0.494580\pi\)
\(458\) −1.88164 + 0.278564i −0.0879235 + 0.0130164i
\(459\) 0.960099i 0.0448136i
\(460\) 11.5942 3.50981i 0.540584 0.163646i
\(461\) 29.7499i 1.38559i −0.721135 0.692794i \(-0.756379\pi\)
0.721135 0.692794i \(-0.243621\pi\)
\(462\) 0 0
\(463\) 34.9330i 1.62347i 0.584024 + 0.811737i \(0.301477\pi\)
−0.584024 + 0.811737i \(0.698523\pi\)
\(464\) −22.7279 + 15.1486i −1.05512 + 0.703256i
\(465\) 33.8937i 1.57178i
\(466\) 3.36396 + 22.7229i 0.155832 + 1.05262i
\(467\) −24.0755 −1.11408 −0.557041 0.830485i \(-0.688063\pi\)
−0.557041 + 0.830485i \(0.688063\pi\)
\(468\) 0.994629 + 3.28564i 0.0459767 + 0.151879i
\(469\) 0 0
\(470\) 15.6569 2.31788i 0.722197 0.106916i
\(471\) 41.0913i 1.89339i
\(472\) −13.5520 28.7172i −0.623780 1.32182i
\(473\) −28.6274 −1.31629
\(474\) 23.7081 3.50981i 1.08895 0.161211i
\(475\) 9.45280 0.433724
\(476\) 0 0
\(477\) 16.6274 0.761317
\(478\) 14.3137 2.11904i 0.654694 0.0969226i
\(479\) −32.7935 −1.49837 −0.749186 0.662360i \(-0.769555\pi\)
−0.749186 + 0.662360i \(0.769555\pi\)
\(480\) −23.4853 + 21.2245i −1.07195 + 0.968762i
\(481\) 4.32957i 0.197411i
\(482\) 7.12764 1.05520i 0.324655 0.0480628i
\(483\) 0 0
\(484\) 8.91421 2.69851i 0.405192 0.122660i
\(485\) −24.1421 −1.09624
\(486\) 3.10455 + 20.9707i 0.140825 + 0.951249i
\(487\) 19.5032i 0.883773i 0.897071 + 0.441886i \(0.145691\pi\)
−0.897071 + 0.441886i \(0.854309\pi\)
\(488\) −13.8433 + 6.53281i −0.626657 + 0.295727i
\(489\) 32.4399i 1.46698i
\(490\) 0 0
\(491\) 14.4697i 0.653009i −0.945196 0.326504i \(-0.894129\pi\)
0.945196 0.326504i \(-0.105871\pi\)
\(492\) 2.84924 + 9.41214i 0.128454 + 0.424332i
\(493\) 2.16478i 0.0974970i
\(494\) −7.82843 + 1.15894i −0.352218 + 0.0521433i
\(495\) −16.3967 −0.736978
\(496\) −20.1600 + 13.4370i −0.905212 + 0.603341i
\(497\) 0 0
\(498\) −4.19239 28.3188i −0.187865 1.26899i
\(499\) 12.5495i 0.561793i −0.959738 0.280897i \(-0.909368\pi\)
0.959738 0.280897i \(-0.0906318\pi\)
\(500\) 4.80249 + 15.8645i 0.214774 + 0.709480i
\(501\) −16.7696 −0.749208
\(502\) −0.810922 5.47762i −0.0361932 0.244478i
\(503\) −7.83095 −0.349165 −0.174582 0.984643i \(-0.555858\pi\)
−0.174582 + 0.984643i \(0.555858\pi\)
\(504\) 0 0
\(505\) −39.7990 −1.77103
\(506\) −1.89949 12.8307i −0.0844428 0.570395i
\(507\) −25.3299 −1.12494
\(508\) 5.92893 + 19.5855i 0.263054 + 0.868967i
\(509\) 6.57128i 0.291267i −0.989339 0.145633i \(-0.953478\pi\)
0.989339 0.145633i \(-0.0465220\pi\)
\(510\) 0.367414 + 2.48181i 0.0162694 + 0.109896i
\(511\) 0 0
\(512\) 21.9350 + 5.55468i 0.969400 + 0.245485i
\(513\) −15.6569 −0.691267
\(514\) −26.6604 + 3.94689i −1.17594 + 0.174090i
\(515\) 31.6550i 1.39489i
\(516\) −8.97777 29.6570i −0.395224 1.30558i
\(517\) 16.9469i 0.745322i
\(518\) 0 0
\(519\) 14.0720i 0.617693i
\(520\) 3.41421 + 7.23486i 0.149723 + 0.317269i
\(521\) 12.0376i 0.527378i 0.964608 + 0.263689i \(0.0849393\pi\)
−0.964608 + 0.263689i \(0.915061\pi\)
\(522\) −2.24264 15.1486i −0.0981577 0.663036i
\(523\) −7.46354 −0.326358 −0.163179 0.986597i \(-0.552175\pi\)
−0.163179 + 0.986597i \(0.552175\pi\)
\(524\) −0.703309 + 0.212906i −0.0307242 + 0.00930083i
\(525\) 0 0
\(526\) 35.8995 5.31466i 1.56529 0.231730i
\(527\) 1.92020i 0.0836451i
\(528\) 18.7980 + 28.2032i 0.818077 + 1.22739i
\(529\) 17.6274 0.766409
\(530\) 38.3308 5.67459i 1.66498 0.246489i
\(531\) 17.8033 0.772600
\(532\) 0 0
\(533\) 2.48528 0.107649
\(534\) −17.9497 + 2.65733i −0.776762 + 0.114994i
\(535\) −6.05692 −0.261864
\(536\) 8.38478 3.95687i 0.362167 0.170911i
\(537\) 28.9301i 1.24843i
\(538\) −7.05155 + 1.04393i −0.304014 + 0.0450070i
\(539\) 0 0
\(540\) 4.58579 + 15.1486i 0.197341 + 0.651892i
\(541\) 45.3137 1.94819 0.974094 0.226142i \(-0.0726115\pi\)
0.974094 + 0.226142i \(0.0726115\pi\)
\(542\) 0.887016 + 5.99162i 0.0381006 + 0.257362i
\(543\) 47.0848i 2.02060i
\(544\) 1.33052 1.20244i 0.0570457 0.0515543i
\(545\) 14.7821i 0.633194i
\(546\) 0 0
\(547\) 27.6981i 1.18429i 0.805833 + 0.592143i \(0.201718\pi\)
−0.805833 + 0.592143i \(0.798282\pi\)
\(548\) 15.7782 4.77637i 0.674010 0.204036i
\(549\) 8.58221i 0.366280i
\(550\) −10.1213 + 1.49839i −0.431575 + 0.0638915i
\(551\) 35.3023 1.50393
\(552\) 12.6965 5.99162i 0.540398 0.255020i
\(553\) 0 0
\(554\) −0.857864 5.79471i −0.0364472 0.246194i
\(555\) 22.3835i 0.950125i
\(556\) 43.6844 13.2241i 1.85263 0.560829i
\(557\) −19.6569 −0.832888 −0.416444 0.909161i \(-0.636724\pi\)
−0.416444 + 0.909161i \(0.636724\pi\)
\(558\) −1.98926 13.4370i −0.0842120 0.568836i
\(559\) −7.83095 −0.331214
\(560\) 0 0
\(561\) 2.68629 0.113415
\(562\) 2.15076 + 14.5280i 0.0907242 + 0.612825i
\(563\) −21.0470 −0.887027 −0.443513 0.896268i \(-0.646268\pi\)
−0.443513 + 0.896268i \(0.646268\pi\)
\(564\) 17.5563 5.31466i 0.739256 0.223788i
\(565\) 11.0866i 0.466415i
\(566\) 0.703309 + 4.75071i 0.0295623 + 0.199687i
\(567\) 0 0
\(568\) 0 0
\(569\) 18.8284 0.789329 0.394664 0.918825i \(-0.370861\pi\)
0.394664 + 0.918825i \(0.370861\pi\)
\(570\) 40.4722 5.99162i 1.69520 0.250961i
\(571\) 9.95043i 0.416412i −0.978085 0.208206i \(-0.933237\pi\)
0.978085 0.208206i \(-0.0667625\pi\)
\(572\) 8.19837 2.48181i 0.342791 0.103770i
\(573\) 14.0392i 0.586497i
\(574\) 0 0
\(575\) 4.23808i 0.176740i
\(576\) −8.06497 + 9.79276i −0.336040 + 0.408032i
\(577\) 0.842290i 0.0350650i 0.999846 + 0.0175325i \(0.00558105\pi\)
−0.999846 + 0.0175325i \(0.994419\pi\)
\(578\) 3.50000 + 23.6418i 0.145581 + 0.983370i
\(579\) −31.2347 −1.29807
\(580\) −10.3398 34.1563i −0.429337 1.41827i
\(581\) 0 0
\(582\) −27.6777 + 4.09748i −1.14728 + 0.169846i
\(583\) 41.4889i 1.71830i
\(584\) 35.8534 16.9197i 1.48363 0.700141i
\(585\) −4.48528 −0.185444
\(586\) 16.5043 2.44335i 0.681788 0.100934i
\(587\) 22.8211 0.941926 0.470963 0.882153i \(-0.343906\pi\)
0.470963 + 0.882153i \(0.343906\pi\)
\(588\) 0 0
\(589\) 31.3137 1.29026
\(590\) 41.0416 6.07591i 1.68966 0.250141i
\(591\) −4.28289 −0.176175
\(592\) −13.3137 + 8.87385i −0.547190 + 0.364713i
\(593\) 37.4579i 1.53821i −0.639121 0.769106i \(-0.720702\pi\)
0.639121 0.769106i \(-0.279298\pi\)
\(594\) 16.7641 2.48181i 0.687841 0.101830i
\(595\) 0 0
\(596\) −9.24264 + 2.79793i −0.378593 + 0.114608i
\(597\) 36.6863 1.50147
\(598\) −0.519602 3.50981i −0.0212481 0.143527i
\(599\) 32.2174i 1.31637i 0.752857 + 0.658184i \(0.228675\pi\)
−0.752857 + 0.658184i \(0.771325\pi\)
\(600\) −4.72640 10.0154i −0.192954 0.408878i
\(601\) 25.5516i 1.04227i −0.853474 0.521136i \(-0.825509\pi\)
0.853474 0.521136i \(-0.174491\pi\)
\(602\) 0 0
\(603\) 5.19818i 0.211686i
\(604\) 12.4142 + 41.0089i 0.505127 + 1.66863i
\(605\) 12.1689i 0.494738i
\(606\) −45.6274 + 6.75481i −1.85349 + 0.274395i
\(607\) 12.1138 0.491686 0.245843 0.969310i \(-0.420935\pi\)
0.245843 + 0.969310i \(0.420935\pi\)
\(608\) −19.6089 21.6976i −0.795246 0.879953i
\(609\) 0 0
\(610\) −2.92893 19.7844i −0.118589 0.801046i
\(611\) 4.63577i 0.187543i
\(612\) 0.291320 + 0.962341i 0.0117759 + 0.0389003i
\(613\) −8.68629 −0.350836 −0.175418 0.984494i \(-0.556128\pi\)
−0.175418 + 0.984494i \(0.556128\pi\)
\(614\) −0.810922 5.47762i −0.0327261 0.221059i
\(615\) −12.8487 −0.518108
\(616\) 0 0
\(617\) −35.4558 −1.42740 −0.713699 0.700452i \(-0.752982\pi\)
−0.713699 + 0.700452i \(0.752982\pi\)
\(618\) −5.37258 36.2908i −0.216117 1.45983i
\(619\) 13.5205 0.543433 0.271717 0.962377i \(-0.412409\pi\)
0.271717 + 0.962377i \(0.412409\pi\)
\(620\) −9.17157 30.2972i −0.368339 1.21677i
\(621\) 7.01962i 0.281688i
\(622\) 4.28289 + 28.9301i 0.171728 + 1.15999i
\(623\) 0 0
\(624\) 5.14214 + 7.71491i 0.205850 + 0.308843i
\(625\) −30.7990 −1.23196
\(626\) 17.8349 2.64032i 0.712825 0.105529i
\(627\) 43.8068i 1.74948i
\(628\) 11.1192 + 36.7310i 0.443705 + 1.46573i
\(629\) 1.26810i 0.0505625i
\(630\) 0 0
\(631\) 20.4633i 0.814630i 0.913288 + 0.407315i \(0.133535\pi\)
−0.913288 + 0.407315i \(0.866465\pi\)
\(632\) 20.2426 9.55274i 0.805209 0.379988i
\(633\) 30.9861i 1.23159i
\(634\) −1.14214 7.71491i −0.0453600 0.306398i
\(635\) −26.7365 −1.06101
\(636\) 42.9811 13.0112i 1.70431 0.515929i
\(637\) 0 0
\(638\) −37.7990 + 5.59587i −1.49648 + 0.221542i
\(639\) 0 0
\(640\) −15.2499 + 25.3274i −0.602806 + 1.00115i
\(641\) 49.4558 1.95339 0.976694 0.214636i \(-0.0688564\pi\)
0.976694 + 0.214636i \(0.0688564\pi\)
\(642\) −6.94394 + 1.02800i −0.274055 + 0.0405719i
\(643\) 41.7267 1.64554 0.822769 0.568375i \(-0.192428\pi\)
0.822769 + 0.568375i \(0.192428\pi\)
\(644\) 0 0
\(645\) 40.4853 1.59411
\(646\) −2.29289 + 0.339446i −0.0902127 + 0.0133553i
\(647\) −43.8681 −1.72463 −0.862317 0.506370i \(-0.830987\pi\)
−0.862317 + 0.506370i \(0.830987\pi\)
\(648\) 13.5711 + 28.7576i 0.533122 + 1.12971i
\(649\) 44.4231i 1.74376i
\(650\) −2.76866 + 0.409880i −0.108596 + 0.0160768i
\(651\) 0 0
\(652\) −8.77817 28.9977i −0.343780 1.13564i
\(653\) −23.7990 −0.931326 −0.465663 0.884962i \(-0.654184\pi\)
−0.465663 + 0.884962i \(0.654184\pi\)
\(654\) 2.50886 + 16.9469i 0.0981041 + 0.662675i
\(655\) 0.960099i 0.0375142i
\(656\) 5.09381 + 7.64240i 0.198880 + 0.298386i
\(657\) 22.2275i 0.867177i
\(658\) 0 0
\(659\) 13.2284i 0.515306i 0.966238 + 0.257653i \(0.0829491\pi\)
−0.966238 + 0.257653i \(0.917051\pi\)
\(660\) −42.3848 + 12.8307i −1.64983 + 0.499435i
\(661\) 37.6662i 1.46504i 0.680744 + 0.732522i \(0.261657\pi\)
−0.680744 + 0.732522i \(0.738343\pi\)
\(662\) −21.1924 + 3.13738i −0.823666 + 0.121938i
\(663\) 0.734828 0.0285383
\(664\) −11.4105 24.1794i −0.442815 0.938342i
\(665\) 0 0
\(666\) −1.31371 8.87385i −0.0509052 0.343855i
\(667\) 15.8275i 0.612843i
\(668\) −14.9901 + 4.53781i −0.579985 + 0.175573i
\(669\) −16.7696 −0.648348
\(670\) 1.77403 + 11.9832i 0.0685368 + 0.462953i
\(671\) −21.4144 −0.826696
\(672\) 0 0
\(673\) 10.3848 0.400304 0.200152 0.979765i \(-0.435856\pi\)
0.200152 + 0.979765i \(0.435856\pi\)
\(674\) 2.24264 + 15.1486i 0.0863833 + 0.583502i
\(675\) −5.53732 −0.213132
\(676\) −22.6421 + 6.85423i −0.870851 + 0.263624i
\(677\) 28.8532i 1.10892i 0.832211 + 0.554459i \(0.187075\pi\)
−0.832211 + 0.554459i \(0.812925\pi\)
\(678\) 1.88164 + 12.7101i 0.0722641 + 0.488130i
\(679\) 0 0
\(680\) 1.00000 + 2.11904i 0.0383482 + 0.0812615i
\(681\) 21.3553 0.818338
\(682\) −33.5283 + 4.96362i −1.28386 + 0.190067i
\(683\) 32.2174i 1.23276i 0.787447 + 0.616382i \(0.211402\pi\)
−0.787447 + 0.616382i \(0.788598\pi\)
\(684\) 15.6934 4.75071i 0.600053 0.181648i
\(685\) 21.5391i 0.822965i
\(686\) 0 0
\(687\) 2.88030i 0.109890i
\(688\) −16.0503 24.0807i −0.611910 0.918068i
\(689\) 11.3492i 0.432370i
\(690\) 2.68629 + 18.1454i 0.102265 + 0.690783i
\(691\) 8.19837 0.311881 0.155940 0.987766i \(-0.450159\pi\)
0.155940 + 0.987766i \(0.450159\pi\)
\(692\) 3.80786 + 12.5788i 0.144753 + 0.478175i
\(693\) 0 0
\(694\) 5.53553 0.819496i 0.210126 0.0311076i
\(695\) 59.6343i 2.26206i
\(696\) −17.6512 37.4035i −0.669066 1.41778i
\(697\) 0.727922 0.0275720
\(698\) −11.8540 + 1.75490i −0.448682 + 0.0664241i
\(699\) −34.7827 −1.31560
\(700\) 0 0
\(701\) 16.0000 0.604312 0.302156 0.953259i \(-0.402294\pi\)
0.302156 + 0.953259i \(0.402294\pi\)
\(702\) 4.58579 0.678892i 0.173079 0.0256231i
\(703\) 20.6796 0.779947
\(704\) 24.4350 + 20.1238i 0.920930 + 0.758445i
\(705\) 23.9665i 0.902630i
\(706\) −14.0716 + 2.08319i −0.529591 + 0.0784021i
\(707\) 0 0
\(708\) 46.0208 13.9314i 1.72957 0.523575i
\(709\) −46.6274 −1.75113 −0.875565 0.483101i \(-0.839510\pi\)
−0.875565 + 0.483101i \(0.839510\pi\)
\(710\) 0 0
\(711\) 12.5495i 0.470644i
\(712\) −15.3260 + 7.23252i −0.574366 + 0.271050i
\(713\) 14.0392i 0.525774i
\(714\) 0 0
\(715\) 11.1917i 0.418547i
\(716\) −7.82843 25.8603i −0.292562 0.966444i
\(717\) 21.9105i 0.818262i
\(718\) 43.7279 6.47360i 1.63191 0.241593i
\(719\) −33.5283 −1.25039 −0.625197 0.780467i \(-0.714981\pi\)
−0.625197 + 0.780467i \(0.714981\pi\)
\(720\) −9.19299 13.7925i −0.342603 0.514017i
\(721\) 0 0
\(722\) 1.60051 + 10.8111i 0.0595646 + 0.402348i
\(723\) 10.9105i 0.405767i
\(724\) −12.7411 42.0886i −0.473518 1.56421i
\(725\) 12.4853 0.463692
\(726\) 2.06535 + 13.9510i 0.0766524 + 0.517772i
\(727\) 29.9802 1.11191 0.555953 0.831214i \(-0.312354\pi\)
0.555953 + 0.831214i \(0.312354\pi\)
\(728\) 0 0
\(729\) 1.62742 0.0602747
\(730\) 7.58579 + 51.2405i 0.280763 + 1.89650i
\(731\) −2.29363 −0.0848331
\(732\) −6.71573 22.1846i −0.248220 0.819967i
\(733\) 20.4567i 0.755584i 0.925890 + 0.377792i \(0.123317\pi\)
−0.925890 + 0.377792i \(0.876683\pi\)
\(734\) 2.66105 + 17.9749i 0.0982210 + 0.663464i
\(735\) 0 0
\(736\) 9.72792 8.79148i 0.358576 0.324058i
\(737\) 12.9706 0.477777
\(738\) −5.09381 + 0.754102i −0.187506 + 0.0277589i
\(739\) 12.4330i 0.457357i −0.973502 0.228678i \(-0.926560\pi\)
0.973502 0.228678i \(-0.0734404\pi\)
\(740\) −6.05692 20.0083i −0.222657 0.735521i
\(741\) 11.9832i 0.440215i
\(742\) 0 0
\(743\) 45.1646i 1.65693i −0.560042 0.828464i \(-0.689215\pi\)
0.560042 0.828464i \(-0.310785\pi\)
\(744\) −15.6569 33.1775i −0.574008 1.21635i
\(745\) 12.6173i 0.462262i
\(746\) −4.17157 28.1782i −0.152732 1.03168i
\(747\) 14.9901 0.548460
\(748\) 2.40125 0.726905i 0.0877982 0.0265783i
\(749\) 0 0
\(750\) −24.8284 + 3.67567i −0.906606 + 0.134216i
\(751\) 37.2509i 1.35930i −0.733535 0.679652i \(-0.762131\pi\)
0.733535 0.679652i \(-0.237869\pi\)
\(752\) 14.2553 9.50143i 0.519837 0.346481i
\(753\) 8.38478 0.305558
\(754\) −10.3398 + 1.53073i −0.376554 + 0.0557460i
\(755\) −55.9819 −2.03739
\(756\) 0 0
\(757\) −44.2843 −1.60954 −0.804770 0.593587i \(-0.797711\pi\)
−0.804770 + 0.593587i \(0.797711\pi\)
\(758\) 30.3640 4.49516i 1.10287 0.163272i
\(759\) 19.6404 0.712902
\(760\) 34.5563 16.3075i 1.25349 0.591537i
\(761\) 0.0543929i 0.00197174i −1.00000 0.000985871i \(-0.999686\pi\)
1.00000 0.000985871i \(-0.000313813\pi\)
\(762\) −30.6520 + 4.53781i −1.11041 + 0.164387i
\(763\) 0 0
\(764\) 3.79899 + 12.5495i 0.137443 + 0.454026i
\(765\) −1.31371 −0.0474972
\(766\) 6.42433 + 43.3951i 0.232121 + 1.56793i
\(767\) 12.1518i 0.438777i
\(768\) −13.1846 + 31.6248i −0.475757 + 1.14116i
\(769\) 19.1342i 0.689996i −0.938603 0.344998i \(-0.887880\pi\)
0.938603 0.344998i \(-0.112120\pi\)
\(770\) 0 0
\(771\) 40.8100i 1.46974i
\(772\) −27.9203 + 8.45204i −1.00487 + 0.304195i
\(773\) 49.4955i 1.78023i −0.455735 0.890116i \(-0.650624\pi\)
0.455735 0.890116i \(-0.349376\pi\)
\(774\) 16.0503 2.37612i 0.576914 0.0854080i
\(775\) 11.0746 0.397813
\(776\) −23.6320 + 11.1522i −0.848339 + 0.400341i
\(777\) 0 0
\(778\) 2.92893 + 19.7844i 0.105007 + 0.709304i
\(779\) 11.8706i 0.425309i
\(780\) −11.5942 + 3.50981i −0.415140 + 0.125671i
\(781\) 0 0
\(782\) −0.152188 1.02800i −0.00544222 0.0367612i
\(783\) −20.6796 −0.739029
\(784\) 0 0
\(785\) −50.1421 −1.78965
\(786\) −0.162951 1.10070i −0.00581227 0.0392607i
\(787\) 41.2071 1.46887 0.734436 0.678677i \(-0.237447\pi\)
0.734436 + 0.678677i \(0.237447\pi\)
\(788\) −3.82843 + 1.15894i −0.136382 + 0.0412856i
\(789\) 54.9526i 1.95636i
\(790\) 4.28289 + 28.9301i 0.152378 + 1.02929i
\(791\) 0 0
\(792\) −16.0503 + 7.57430i −0.570321 + 0.269141i
\(793\) −5.85786 −0.208019
\(794\) 22.5613 3.34003i 0.800669 0.118533i
\(795\) 58.6742i 2.08096i
\(796\) 32.7935 9.92724i 1.16233 0.351862i
\(797\) 20.1940i 0.715309i −0.933854 0.357655i \(-0.883576\pi\)
0.933854 0.357655i \(-0.116424\pi\)
\(798\) 0 0
\(799\) 1.35778i 0.0480350i
\(800\) −6.93503 7.67372i −0.245190 0.271307i
\(801\) 9.50143i 0.335716i
\(802\) −2.65685 17.9465i −0.0938168 0.633714i
\(803\) 55.4623 1.95722
\(804\) 4.06766 + 13.4370i 0.143455 + 0.473888i
\(805\) 0 0
\(806\) −9.17157 + 1.35778i −0.323055 + 0.0478259i
\(807\) 10.7940i 0.379968i
\(808\) −38.9580 + 18.3847i −1.37054 + 0.646773i
\(809\) −0.0416306 −0.00146365 −0.000731826 1.00000i \(-0.500233\pi\)
−0.000731826 1.00000i \(0.500233\pi\)
\(810\) −41.0994 + 6.08447i −1.44409 + 0.213787i
\(811\) 39.4330 1.38468 0.692340 0.721571i \(-0.256580\pi\)
0.692340 + 0.721571i \(0.256580\pi\)
\(812\) 0 0
\(813\) −9.17157 −0.321661
\(814\) −22.1421 + 3.27798i −0.776081 + 0.114893i
\(815\) 39.5852 1.38661
\(816\) 1.50610 + 2.25964i 0.0527239 + 0.0791033i
\(817\) 37.4035i 1.30858i
\(818\) 19.3491 2.86449i 0.676525 0.100155i
\(819\) 0 0
\(820\) −11.4853 + 3.47682i −0.401083 + 0.121416i
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 3.65568 + 24.6934i 0.127506 + 0.861281i
\(823\) 17.1853i 0.599041i −0.954090 0.299521i \(-0.903173\pi\)
0.954090 0.299521i \(-0.0968267\pi\)
\(824\) −14.6227 30.9861i −0.509406 1.07945i
\(825\) 15.4930i 0.539399i
\(826\) 0 0
\(827\) 45.1646i 1.57053i −0.619162 0.785264i \(-0.712527\pi\)
0.619162 0.785264i \(-0.287473\pi\)
\(828\) 2.12994 + 7.03601i 0.0740206 + 0.244518i
\(829\) 47.2220i 1.64009i 0.572301 + 0.820044i \(0.306051\pi\)
−0.572301 + 0.820044i \(0.693949\pi\)
\(830\) 34.5563 5.11582i 1.19947 0.177573i
\(831\) 8.87016 0.307702
\(832\) 6.68414 + 5.50482i 0.231731 + 0.190845i
\(833\) 0 0
\(834\) 10.1213 + 68.3676i 0.350473 + 2.36738i
\(835\) 20.4633i 0.708160i
\(836\) −11.8540 39.1584i −0.409981 1.35432i
\(837\) −18.3431 −0.634032
\(838\) −3.57958 24.1794i −0.123655 0.835263i
\(839\) 42.3984 1.46376 0.731878 0.681435i \(-0.238644\pi\)
0.731878 + 0.681435i \(0.238644\pi\)
\(840\) 0 0
\(841\) 17.6274 0.607842
\(842\) −2.17157 14.6686i −0.0748373 0.505512i
\(843\) −22.2384 −0.765932
\(844\) −8.38478 27.6981i −0.288616 0.953409i
\(845\) 30.9092i 1.06331i
\(846\) 1.40662 + 9.50143i 0.0483605 + 0.326666i
\(847\) 0 0
\(848\) 34.8995 23.2612i 1.19845 0.798793i
\(849\) −7.27208 −0.249577
\(850\) −0.810922 + 0.120051i −0.0278144 + 0.00411772i
\(851\) 9.27153i 0.317824i
\(852\) 0 0
\(853\) 38.3002i 1.31137i 0.755033 + 0.655687i \(0.227621\pi\)
−0.755033 + 0.655687i \(0.772379\pi\)
\(854\) 0 0
\(855\) 21.4234i 0.732664i
\(856\) −5.92893 + 2.79793i −0.202647 + 0.0956314i
\(857\) 3.45542i 0.118035i −0.998257 0.0590174i \(-0.981203\pi\)
0.998257 0.0590174i \(-0.0187967\pi\)
\(858\) 1.89949 + 12.8307i 0.0648477 + 0.438034i
\(859\) 2.66105 0.0907937 0.0453969 0.998969i \(-0.485545\pi\)
0.0453969 + 0.998969i \(0.485545\pi\)
\(860\) 36.1893 10.9552i 1.23405 0.373571i
\(861\) 0 0
\(862\) 1.34315 0.198843i 0.0457477 0.00677262i
\(863\) 12.5495i 0.427190i −0.976922 0.213595i \(-0.931483\pi\)
0.976922 0.213595i \(-0.0685174\pi\)
\(864\) 11.4866 + 12.7101i 0.390783 + 0.432408i
\(865\) −17.1716 −0.583851
\(866\) −36.6328 + 5.42323i −1.24483 + 0.184289i
\(867\) −36.1893 −1.22905
\(868\) 0 0
\(869\) 31.3137 1.06224
\(870\) 53.4558 7.91375i 1.81232 0.268301i
\(871\) 3.54806 0.120221
\(872\) 6.82843 + 14.4697i 0.231240 + 0.490006i
\(873\) 14.6508i 0.495853i
\(874\) −16.7641 + 2.48181i −0.567056 + 0.0839485i
\(875\) 0 0
\(876\) 17.3934 + 57.4570i 0.587668 + 1.94129i
\(877\) 30.4264 1.02743 0.513713 0.857962i \(-0.328269\pi\)
0.513713 + 0.857962i \(0.328269\pi\)
\(878\) −4.65030 31.4119i −0.156940 1.06010i
\(879\) 25.2638i 0.852125i
\(880\) −34.4153 + 22.9385i −1.16014 + 0.773256i
\(881\) 26.1857i 0.882217i 0.897454 + 0.441109i \(0.145415\pi\)
−0.897454 + 0.441109i \(0.854585\pi\)
\(882\) 0 0
\(883\) 24.7013i 0.831266i 0.909532 + 0.415633i \(0.136440\pi\)
−0.909532 + 0.415633i \(0.863560\pi\)
\(884\) 0.656854 0.198843i 0.0220924 0.00668781i
\(885\) 62.8238i 2.11180i
\(886\) −39.6985 + 5.87707i −1.33370 + 0.197444i
\(887\) −22.4537 −0.753920 −0.376960 0.926230i \(-0.623031\pi\)
−0.376960 + 0.926230i \(0.623031\pi\)
\(888\) −10.3398 21.9105i −0.346981 0.735267i
\(889\) 0 0
\(890\) −3.24264 21.9034i −0.108694 0.734204i
\(891\) 44.4857i 1.49033i
\(892\) −14.9901 + 4.53781i −0.501906 + 0.151937i
\(893\) −22.1421 −0.740958
\(894\) −2.14144 14.4650i −0.0716206 0.483784i
\(895\) 35.3023 1.18003
\(896\) 0 0
\(897\) 5.37258 0.179385
\(898\) −3.37258 22.7811i −0.112545 0.760217i
\(899\) 41.3592 1.37941
\(900\) 5.55025 1.68017i 0.185008 0.0560058i
\(901\) 3.32410i 0.110742i
\(902\) 1.88164 + 12.7101i 0.0626519 + 0.423201i
\(903\) 0 0
\(904\) 5.12132 + 10.8523i 0.170333 + 0.360942i
\(905\) 57.4558 1.90990
\(906\) −64.1803 + 9.50143i −2.13225 + 0.315664i
\(907\) 33.9729i 1.12805i 0.825757 + 0.564025i \(0.190748\pi\)
−0.825757 + 0.564025i \(0.809252\pi\)
\(908\) 19.0893 5.77871i 0.633501 0.191773i
\(909\) 24.1522i 0.801077i
\(910\) 0 0
\(911\) 18.7078i 0.619817i −0.950766 0.309908i \(-0.899702\pi\)
0.950766 0.309908i \(-0.100298\pi\)
\(912\) 36.8492 24.5607i 1.22020 0.813287i
\(913\) 37.4035i 1.23788i
\(914\) 0.150758 + 1.01834i 0.00498662 + 0.0336836i
\(915\) 30.2846 1.00118
\(916\) −0.779403 2.57466i −0.0257522 0.0850693i
\(917\) 0 0
\(918\) 1.34315 0.198843i 0.0443304 0.00656280i
\(919\) 48.8403i 1.61109i 0.592533 + 0.805546i \(0.298128\pi\)
−0.592533 + 0.805546i \(0.701872\pi\)
\(920\) 7.31135 + 15.4930i 0.241048 + 0.510791i
\(921\) 8.38478 0.276288
\(922\) 41.6190 6.16140i 1.37065 0.202915i
\(923\) 0 0
\(924\) 0 0
\(925\) 7.31371 0.240473
\(926\) −48.8701 + 7.23486i −1.60597 + 0.237752i
\(927\) 19.2100 0.630938
\(928\) −25.8995 28.6582i −0.850193 0.940752i
\(929\) 29.8812i 0.980369i −0.871619 0.490185i \(-0.836929\pi\)
0.871619 0.490185i \(-0.163071\pi\)
\(930\) 47.4162 7.01962i 1.55484 0.230182i
\(931\) 0 0
\(932\) −31.0919 + 9.41214i −1.01845 + 0.308305i
\(933\) −44.2843 −1.44980
\(934\) −4.98620 33.6808i −0.163153 1.10207i
\(935\) 3.27798i 0.107201i
\(936\) −4.39050 + 2.07193i −0.143508 + 0.0677231i
\(937\) 29.8042i 0.973662i 0.873496 + 0.486831i \(0.161847\pi\)
−0.873496 + 0.486831i \(0.838153\pi\)
\(938\) 0 0
\(939\) 27.3004i 0.890916i
\(940\) 6.48528 + 21.4234i 0.211527 + 0.698753i
\(941\) 24.7862i 0.808008i −0.914757 0.404004i \(-0.867618\pi\)
0.914757 0.404004i \(-0.132382\pi\)
\(942\) −57.4853 + 8.51028i −1.87297 + 0.277280i
\(943\) 5.32209 0.173311
\(944\) 37.3677 24.9063i 1.21621 0.810631i
\(945\) 0 0
\(946\) −5.92893 40.0488i −0.192766 1.30210i
\(947\) 9.15505i 0.297499i 0.988875 + 0.148750i \(0.0475249\pi\)
−0.988875 + 0.148750i \(0.952475\pi\)
\(948\) 9.82021 + 32.4399i 0.318946 + 1.05360i
\(949\) 15.1716 0.492490
\(950\) 1.95774 + 13.2241i 0.0635174 + 0.429048i
\(951\) 11.8095 0.382948
\(952\) 0 0
\(953\) 26.3431 0.853338 0.426669 0.904408i \(-0.359687\pi\)
0.426669 + 0.904408i \(0.359687\pi\)
\(954\) 3.44365 + 23.2612i 0.111492 + 0.753109i
\(955\) −17.1316 −0.554364
\(956\) 5.92893 + 19.5855i 0.191755 + 0.633441i
\(957\) 57.8602i 1.87035i
\(958\) −6.79175 45.8770i −0.219431 1.48222i
\(959\) 0 0
\(960\) −34.5563 28.4594i −1.11530 0.918522i
\(961\) 5.68629 0.183429
\(962\) −6.05692 + 0.896683i −0.195283 + 0.0289102i
\(963\) 3.67567i 0.118447i
\(964\) 2.95237 + 9.75279i 0.0950893 + 0.314116i
\(965\) 38.1145i 1.22695i
\(966\) 0 0
\(967\) 45.1646i 1.45240i −0.687486 0.726198i \(-0.741286\pi\)
0.687486 0.726198i \(-0.258714\pi\)
\(968\) 5.62132 + 11.9118i 0.180676 + 0.382860i
\(969\) 3.50981i 0.112751i
\(970\) −5.00000 33.7740i −0.160540 1.08442i
\(971\) −13.0009 −0.417217 −0.208609 0.977999i \(-0.566894\pi\)
−0.208609 + 0.977999i \(0.566894\pi\)
\(972\) −28.6943 + 8.68633i −0.920369 + 0.278614i
\(973\) 0 0
\(974\) −27.2843 + 4.03924i −0.874244 + 0.129426i
\(975\) 4.23808i 0.135727i
\(976\) −12.0062 18.0133i −0.384310 0.576592i
\(977\) 17.6152 0.563561 0.281780 0.959479i \(-0.409075\pi\)
0.281780 + 0.959479i \(0.409075\pi\)
\(978\) 45.3823 6.71852i 1.45117 0.214835i
\(979\) −23.7081 −0.757714
\(980\) 0 0
\(981\) −8.97056 −0.286408
\(982\) 20.2426 2.99678i 0.645969 0.0956310i
\(983\) 9.60498 0.306351 0.153176 0.988199i \(-0.451050\pi\)
0.153176 + 0.988199i \(0.451050\pi\)
\(984\) −12.5772 + 5.93531i −0.400945 + 0.189211i
\(985\) 5.22625i 0.166522i
\(986\) −3.02846 + 0.448342i −0.0964458 + 0.0142781i
\(987\) 0 0
\(988\) −3.24264 10.7117i −0.103162 0.340784i
\(989\) −16.7696 −0.533241
\(990\) −3.39587 22.9385i −0.107928 0.729033i
\(991\) 25.6614i 0.815163i −0.913169 0.407581i \(-0.866372\pi\)
0.913169 0.407581i \(-0.133628\pi\)
\(992\) −22.9733 25.4203i −0.729402 0.807095i
\(993\) 32.4399i 1.02945i
\(994\) 0 0
\(995\) 44.7669i 1.41921i
\(996\) 38.7487 11.7300i 1.22780 0.371680i
\(997\) 30.9092i 0.978903i 0.872030 + 0.489452i \(0.162803\pi\)
−0.872030 + 0.489452i \(0.837197\pi\)
\(998\) 17.5563 2.59909i 0.555737 0.0822727i
\(999\) −12.1138 −0.383265
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 196.2.d.c.195.7 yes 8
3.2 odd 2 1764.2.b.k.1567.2 8
4.3 odd 2 inner 196.2.d.c.195.6 yes 8
7.2 even 3 196.2.f.d.31.6 16
7.3 odd 6 196.2.f.d.19.1 16
7.4 even 3 196.2.f.d.19.2 16
7.5 odd 6 196.2.f.d.31.5 16
7.6 odd 2 inner 196.2.d.c.195.8 yes 8
8.3 odd 2 3136.2.f.i.3135.4 8
8.5 even 2 3136.2.f.i.3135.6 8
12.11 even 2 1764.2.b.k.1567.4 8
21.20 even 2 1764.2.b.k.1567.1 8
28.3 even 6 196.2.f.d.19.6 16
28.11 odd 6 196.2.f.d.19.5 16
28.19 even 6 196.2.f.d.31.2 16
28.23 odd 6 196.2.f.d.31.1 16
28.27 even 2 inner 196.2.d.c.195.5 8
56.13 odd 2 3136.2.f.i.3135.3 8
56.27 even 2 3136.2.f.i.3135.5 8
84.83 odd 2 1764.2.b.k.1567.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
196.2.d.c.195.5 8 28.27 even 2 inner
196.2.d.c.195.6 yes 8 4.3 odd 2 inner
196.2.d.c.195.7 yes 8 1.1 even 1 trivial
196.2.d.c.195.8 yes 8 7.6 odd 2 inner
196.2.f.d.19.1 16 7.3 odd 6
196.2.f.d.19.2 16 7.4 even 3
196.2.f.d.19.5 16 28.11 odd 6
196.2.f.d.19.6 16 28.3 even 6
196.2.f.d.31.1 16 28.23 odd 6
196.2.f.d.31.2 16 28.19 even 6
196.2.f.d.31.5 16 7.5 odd 6
196.2.f.d.31.6 16 7.2 even 3
1764.2.b.k.1567.1 8 21.20 even 2
1764.2.b.k.1567.2 8 3.2 odd 2
1764.2.b.k.1567.3 8 84.83 odd 2
1764.2.b.k.1567.4 8 12.11 even 2
3136.2.f.i.3135.3 8 56.13 odd 2
3136.2.f.i.3135.4 8 8.3 odd 2
3136.2.f.i.3135.5 8 56.27 even 2
3136.2.f.i.3135.6 8 8.5 even 2