Properties

Label 441.2.s.b.374.4
Level $441$
Weight $2$
Character 441.374
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
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] = [441,2,Mod(362,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.362");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.s (of order \(6\), degree \(2\), not 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.288778218147.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 374.4
Root \(-1.04536 - 1.81062i\) of defining polynomial
Character \(\chi\) \(=\) 441.374
Dual form 441.2.s.b.362.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.30778 + 0.755047i) q^{2} +(0.919842 - 1.46761i) q^{3} +(0.140193 + 0.242822i) q^{4} +0.775876 q^{5} +(2.31107 - 1.22479i) q^{6} -2.59678i q^{8} +(-1.30778 - 2.69995i) q^{9} +O(q^{10})\) \(q+(1.30778 + 0.755047i) q^{2} +(0.919842 - 1.46761i) q^{3} +(0.140193 + 0.242822i) q^{4} +0.775876 q^{5} +(2.31107 - 1.22479i) q^{6} -2.59678i q^{8} +(-1.30778 - 2.69995i) q^{9} +(1.01468 + 0.585823i) q^{10} +3.84319i q^{11} +(0.485324 + 0.0176082i) q^{12} +(2.54198 + 1.46761i) q^{13} +(0.713684 - 1.13869i) q^{15} +(2.24108 - 3.88166i) q^{16} +(2.69901 - 4.67482i) q^{17} +(0.328298 - 4.51837i) q^{18} +(0.376551 - 0.217402i) q^{19} +(0.108773 + 0.188400i) q^{20} +(-2.90179 + 5.02605i) q^{22} -0.0557186i q^{23} +(-3.81107 - 2.38863i) q^{24} -4.39802 q^{25} +(2.21624 + 3.83863i) q^{26} +(-5.16543 - 0.564208i) q^{27} +(-0.187994 + 0.108538i) q^{29} +(1.79310 - 0.950287i) q^{30} +(-5.67806 + 3.27823i) q^{31} +(1.36392 - 0.787461i) q^{32} +(5.64031 + 3.53513i) q^{33} +(7.05942 - 4.07576i) q^{34} +(0.472264 - 0.696071i) q^{36} +(3.14698 + 5.45073i) q^{37} +0.656595 q^{38} +(4.49211 - 2.38067i) q^{39} -2.01478i q^{40} +(-3.78757 + 6.56026i) q^{41} +(6.42703 + 11.1319i) q^{43} +(-0.933209 + 0.538789i) q^{44} +(-1.01468 - 2.09482i) q^{45} +(0.0420702 - 0.0728677i) q^{46} +(-0.482772 + 0.836186i) q^{47} +(-3.63534 - 6.85955i) q^{48} +(-5.75164 - 3.32071i) q^{50} +(-4.37817 - 8.26120i) q^{51} +0.822998i q^{52} +(-6.46438 - 3.73221i) q^{53} +(-6.32924 - 4.63800i) q^{54} +2.98184i q^{55} +(0.0273056 - 0.752608i) q^{57} -0.327806 q^{58} +(1.56219 + 2.70580i) q^{59} +(0.376551 + 0.0136618i) q^{60} +(3.01744 + 1.74212i) q^{61} -9.90087 q^{62} -6.58603 q^{64} +(1.97226 + 1.13869i) q^{65} +(4.70711 + 8.88187i) q^{66} +(2.10088 + 3.63884i) q^{67} +1.51353 q^{68} +(-0.0817733 - 0.0512523i) q^{69} -3.50812i q^{71} +(-7.01117 + 3.39602i) q^{72} +(7.05942 + 4.07576i) q^{73} +9.50448i q^{74} +(-4.04548 + 6.45459i) q^{75} +(0.105580 + 0.0609566i) q^{76} +(7.67222 + 0.278359i) q^{78} +(2.48110 - 4.29739i) q^{79} +(1.73880 - 3.01169i) q^{80} +(-5.57942 + 7.06187i) q^{81} +(-9.90662 + 5.71959i) q^{82} +(4.31033 + 7.46571i) q^{83} +(2.09410 - 3.62708i) q^{85} +19.4108i q^{86} +(-0.0136324 + 0.375740i) q^{87} +9.97991 q^{88} +(-7.82041 - 13.5453i) q^{89} +(0.254718 - 3.50570i) q^{90} +(0.0135297 - 0.00781136i) q^{92} +(-0.411745 + 11.3487i) q^{93} +(-1.26272 + 0.729031i) q^{94} +(0.292157 - 0.168677i) q^{95} +(0.0989048 - 2.72605i) q^{96} +(-1.24162 + 0.716849i) q^{97} +(10.3764 - 5.02605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{4} + 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{4} + 12 q^{6} + 15 q^{10} - 6 q^{13} - 3 q^{15} - 6 q^{16} + 12 q^{17} - 18 q^{18} - 3 q^{19} + 3 q^{20} + 5 q^{22} - 27 q^{24} - 14 q^{25} - 3 q^{26} - 27 q^{27} - 15 q^{29} + 9 q^{31} + 48 q^{32} + 9 q^{33} - 3 q^{34} - 18 q^{36} + 6 q^{37} - 36 q^{38} + 12 q^{39} + 9 q^{41} + 3 q^{43} + 24 q^{44} - 15 q^{45} - 13 q^{46} - 15 q^{47} + 15 q^{48} + 3 q^{50} - 24 q^{51} - 9 q^{53} - 27 q^{54} - 36 q^{57} - 16 q^{58} + 18 q^{59} - 3 q^{60} - 12 q^{61} - 12 q^{62} + 6 q^{64} - 3 q^{65} + 33 q^{66} - 10 q^{67} + 54 q^{68} + 3 q^{69} + 18 q^{72} - 3 q^{73} + 21 q^{75} - 9 q^{76} + 24 q^{78} + 20 q^{79} + 30 q^{80} - 48 q^{81} - 9 q^{82} + 15 q^{83} + 18 q^{85} - 30 q^{87} + 16 q^{88} - 24 q^{89} - 24 q^{90} + 39 q^{92} + 6 q^{93} + 3 q^{94} - 3 q^{96} - 6 q^{97} + 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30778 + 0.755047i 0.924740 + 0.533899i 0.885144 0.465317i \(-0.154060\pi\)
0.0395961 + 0.999216i \(0.487393\pi\)
\(3\) 0.919842 1.46761i 0.531071 0.847327i
\(4\) 0.140193 + 0.242822i 0.0700966 + 0.121411i
\(5\) 0.775876 0.346982 0.173491 0.984835i \(-0.444495\pi\)
0.173491 + 0.984835i \(0.444495\pi\)
\(6\) 2.31107 1.22479i 0.943490 0.500019i
\(7\) 0 0
\(8\) 2.59678i 0.918100i
\(9\) −1.30778 2.69995i −0.435927 0.899982i
\(10\) 1.01468 + 0.585823i 0.320869 + 0.185254i
\(11\) 3.84319i 1.15876i 0.815056 + 0.579382i \(0.196706\pi\)
−0.815056 + 0.579382i \(0.803294\pi\)
\(12\) 0.485324 + 0.0176082i 0.140101 + 0.00508306i
\(13\) 2.54198 + 1.46761i 0.705019 + 0.407043i 0.809214 0.587514i \(-0.199893\pi\)
−0.104195 + 0.994557i \(0.533227\pi\)
\(14\) 0 0
\(15\) 0.713684 1.13869i 0.184272 0.294008i
\(16\) 2.24108 3.88166i 0.560270 0.970415i
\(17\) 2.69901 4.67482i 0.654606 1.13381i −0.327387 0.944890i \(-0.606168\pi\)
0.981993 0.188920i \(-0.0604986\pi\)
\(18\) 0.328298 4.51837i 0.0773805 1.06499i
\(19\) 0.376551 0.217402i 0.0863868 0.0498755i −0.456184 0.889885i \(-0.650784\pi\)
0.542571 + 0.840010i \(0.317451\pi\)
\(20\) 0.108773 + 0.188400i 0.0243223 + 0.0421274i
\(21\) 0 0
\(22\) −2.90179 + 5.02605i −0.618663 + 1.07156i
\(23\) 0.0557186i 0.0116181i −0.999983 0.00580906i \(-0.998151\pi\)
0.999983 0.00580906i \(-0.00184909\pi\)
\(24\) −3.81107 2.38863i −0.777931 0.487577i
\(25\) −4.39802 −0.879603
\(26\) 2.21624 + 3.83863i 0.434640 + 0.752818i
\(27\) −5.16543 0.564208i −0.994088 0.108582i
\(28\) 0 0
\(29\) −0.187994 + 0.108538i −0.0349096 + 0.0201551i −0.517353 0.855772i \(-0.673083\pi\)
0.482444 + 0.875927i \(0.339749\pi\)
\(30\) 1.79310 0.950287i 0.327375 0.173498i
\(31\) −5.67806 + 3.27823i −1.01981 + 0.588787i −0.914049 0.405604i \(-0.867061\pi\)
−0.105761 + 0.994392i \(0.533728\pi\)
\(32\) 1.36392 0.787461i 0.241110 0.139205i
\(33\) 5.64031 + 3.53513i 0.981853 + 0.615386i
\(34\) 7.05942 4.07576i 1.21068 0.698987i
\(35\) 0 0
\(36\) 0.472264 0.696071i 0.0787106 0.116012i
\(37\) 3.14698 + 5.45073i 0.517361 + 0.896095i 0.999797 + 0.0201636i \(0.00641872\pi\)
−0.482436 + 0.875931i \(0.660248\pi\)
\(38\) 0.656595 0.106514
\(39\) 4.49211 2.38067i 0.719314 0.381213i
\(40\) 2.01478i 0.318565i
\(41\) −3.78757 + 6.56026i −0.591519 + 1.02454i 0.402509 + 0.915416i \(0.368138\pi\)
−0.994028 + 0.109125i \(0.965195\pi\)
\(42\) 0 0
\(43\) 6.42703 + 11.1319i 0.980112 + 1.69760i 0.661914 + 0.749580i \(0.269745\pi\)
0.318198 + 0.948024i \(0.396922\pi\)
\(44\) −0.933209 + 0.538789i −0.140687 + 0.0812254i
\(45\) −1.01468 2.09482i −0.151259 0.312278i
\(46\) 0.0420702 0.0728677i 0.00620291 0.0107437i
\(47\) −0.482772 + 0.836186i −0.0704195 + 0.121970i −0.899085 0.437774i \(-0.855767\pi\)
0.828666 + 0.559744i \(0.189100\pi\)
\(48\) −3.63534 6.85955i −0.524716 0.990091i
\(49\) 0 0
\(50\) −5.75164 3.32071i −0.813405 0.469619i
\(51\) −4.37817 8.26120i −0.613066 1.15680i
\(52\) 0.822998i 0.114129i
\(53\) −6.46438 3.73221i −0.887950 0.512658i −0.0146788 0.999892i \(-0.504673\pi\)
−0.873272 + 0.487234i \(0.838006\pi\)
\(54\) −6.32924 4.63800i −0.861301 0.631153i
\(55\) 2.98184i 0.402071i
\(56\) 0 0
\(57\) 0.0273056 0.752608i 0.00361672 0.0996853i
\(58\) −0.327806 −0.0430431
\(59\) 1.56219 + 2.70580i 0.203380 + 0.352265i 0.949615 0.313418i \(-0.101474\pi\)
−0.746235 + 0.665682i \(0.768141\pi\)
\(60\) 0.376551 + 0.0136618i 0.0486126 + 0.00176373i
\(61\) 3.01744 + 1.74212i 0.386343 + 0.223055i 0.680575 0.732679i \(-0.261730\pi\)
−0.294231 + 0.955734i \(0.595064\pi\)
\(62\) −9.90087 −1.25741
\(63\) 0 0
\(64\) −6.58603 −0.823254
\(65\) 1.97226 + 1.13869i 0.244629 + 0.141237i
\(66\) 4.70711 + 8.88187i 0.579405 + 1.09328i
\(67\) 2.10088 + 3.63884i 0.256664 + 0.444555i 0.965346 0.260973i \(-0.0840433\pi\)
−0.708682 + 0.705528i \(0.750710\pi\)
\(68\) 1.51353 0.183542
\(69\) −0.0817733 0.0512523i −0.00984435 0.00617005i
\(70\) 0 0
\(71\) 3.50812i 0.416337i −0.978093 0.208169i \(-0.933250\pi\)
0.978093 0.208169i \(-0.0667503\pi\)
\(72\) −7.01117 + 3.39602i −0.826274 + 0.400225i
\(73\) 7.05942 + 4.07576i 0.826243 + 0.477031i 0.852564 0.522622i \(-0.175046\pi\)
−0.0263219 + 0.999654i \(0.508379\pi\)
\(74\) 9.50448i 1.10487i
\(75\) −4.04548 + 6.45459i −0.467132 + 0.745312i
\(76\) 0.105580 + 0.0609566i 0.0121108 + 0.00699220i
\(77\) 0 0
\(78\) 7.67222 + 0.278359i 0.868708 + 0.0315179i
\(79\) 2.48110 4.29739i 0.279145 0.483494i −0.692027 0.721871i \(-0.743282\pi\)
0.971173 + 0.238377i \(0.0766155\pi\)
\(80\) 1.73880 3.01169i 0.194404 0.336717i
\(81\) −5.57942 + 7.06187i −0.619936 + 0.784653i
\(82\) −9.90662 + 5.71959i −1.09400 + 0.631623i
\(83\) 4.31033 + 7.46571i 0.473120 + 0.819469i 0.999527 0.0307645i \(-0.00979420\pi\)
−0.526406 + 0.850233i \(0.676461\pi\)
\(84\) 0 0
\(85\) 2.09410 3.62708i 0.227137 0.393412i
\(86\) 19.4108i 2.09312i
\(87\) −0.0136324 + 0.375740i −0.00146154 + 0.0402836i
\(88\) 9.97991 1.06386
\(89\) −7.82041 13.5453i −0.828962 1.43580i −0.898853 0.438249i \(-0.855599\pi\)
0.0698916 0.997555i \(-0.477735\pi\)
\(90\) 0.254718 3.50570i 0.0268497 0.369533i
\(91\) 0 0
\(92\) 0.0135297 0.00781136i 0.00141057 0.000814391i
\(93\) −0.411745 + 11.3487i −0.0426959 + 1.17680i
\(94\) −1.26272 + 0.729031i −0.130240 + 0.0751938i
\(95\) 0.292157 0.168677i 0.0299747 0.0173059i
\(96\) 0.0989048 2.72605i 0.0100944 0.278226i
\(97\) −1.24162 + 0.716849i −0.126067 + 0.0727850i −0.561708 0.827336i \(-0.689855\pi\)
0.435640 + 0.900121i \(0.356522\pi\)
\(98\) 0 0
\(99\) 10.3764 5.02605i 1.04287 0.505137i
\(100\) −0.616572 1.06793i −0.0616572 0.106793i
\(101\) −16.0219 −1.59424 −0.797120 0.603821i \(-0.793644\pi\)
−0.797120 + 0.603821i \(0.793644\pi\)
\(102\) 0.511914 14.1096i 0.0506870 1.39705i
\(103\) 16.8660i 1.66186i −0.556381 0.830928i \(-0.687810\pi\)
0.556381 0.830928i \(-0.312190\pi\)
\(104\) 3.81107 6.60097i 0.373706 0.647278i
\(105\) 0 0
\(106\) −5.63599 9.76182i −0.547416 0.948152i
\(107\) −3.36444 + 1.94246i −0.325253 + 0.187785i −0.653731 0.756727i \(-0.726797\pi\)
0.328479 + 0.944511i \(0.393464\pi\)
\(108\) −0.587156 1.33338i −0.0564991 0.128304i
\(109\) 1.28254 2.22143i 0.122845 0.212774i −0.798043 0.602600i \(-0.794131\pi\)
0.920889 + 0.389826i \(0.127465\pi\)
\(110\) −2.25143 + 3.89959i −0.214665 + 0.371811i
\(111\) 10.8943 + 0.395260i 1.03404 + 0.0375164i
\(112\) 0 0
\(113\) −9.79043 5.65251i −0.921006 0.531743i −0.0370501 0.999313i \(-0.511796\pi\)
−0.883956 + 0.467570i \(0.845129\pi\)
\(114\) 0.603964 0.963629i 0.0565664 0.0902521i
\(115\) 0.0432307i 0.00403129i
\(116\) −0.0527109 0.0304327i −0.00489408 0.00282560i
\(117\) 0.638125 8.78253i 0.0589946 0.811945i
\(118\) 4.71812i 0.434338i
\(119\) 0 0
\(120\) −2.95692 1.85328i −0.269929 0.169181i
\(121\) −3.77009 −0.342735
\(122\) 2.63076 + 4.55662i 0.238178 + 0.412537i
\(123\) 6.14397 + 11.5931i 0.553983 + 1.04531i
\(124\) −1.59205 0.919171i −0.142970 0.0825440i
\(125\) −7.29170 −0.652189
\(126\) 0 0
\(127\) 2.65660 0.235735 0.117867 0.993029i \(-0.462394\pi\)
0.117867 + 0.993029i \(0.462394\pi\)
\(128\) −11.3409 6.54769i −1.00241 0.578739i
\(129\) 22.2492 + 0.807233i 1.95894 + 0.0710729i
\(130\) 1.71953 + 2.97830i 0.150812 + 0.261215i
\(131\) 8.23623 0.719602 0.359801 0.933029i \(-0.382845\pi\)
0.359801 + 0.933029i \(0.382845\pi\)
\(132\) −0.0676717 + 1.86519i −0.00589006 + 0.162344i
\(133\) 0 0
\(134\) 6.34507i 0.548131i
\(135\) −4.00774 0.437756i −0.344931 0.0376760i
\(136\) −12.1395 7.00873i −1.04095 0.600994i
\(137\) 17.3272i 1.48036i −0.672408 0.740180i \(-0.734740\pi\)
0.672408 0.740180i \(-0.265260\pi\)
\(138\) −0.0682437 0.128769i −0.00580929 0.0109616i
\(139\) 5.47677 + 3.16201i 0.464533 + 0.268198i 0.713949 0.700198i \(-0.246905\pi\)
−0.249415 + 0.968397i \(0.580238\pi\)
\(140\) 0 0
\(141\) 0.783123 + 1.47768i 0.0659509 + 0.124443i
\(142\) 2.64880 4.58785i 0.222282 0.385004i
\(143\) −5.64031 + 9.76931i −0.471667 + 0.816951i
\(144\) −13.4111 0.974430i −1.11759 0.0812025i
\(145\) −0.145860 + 0.0842123i −0.0121130 + 0.00699345i
\(146\) 6.15478 + 10.6604i 0.509373 + 0.882260i
\(147\) 0 0
\(148\) −0.882370 + 1.52831i −0.0725304 + 0.125626i
\(149\) 12.8242i 1.05060i −0.850917 0.525300i \(-0.823953\pi\)
0.850917 0.525300i \(-0.176047\pi\)
\(150\) −10.1641 + 5.38666i −0.829897 + 0.439819i
\(151\) 5.25517 0.427660 0.213830 0.976871i \(-0.431406\pi\)
0.213830 + 0.976871i \(0.431406\pi\)
\(152\) −0.564545 0.977821i −0.0457907 0.0793118i
\(153\) −16.1515 1.17354i −1.30577 0.0948751i
\(154\) 0 0
\(155\) −4.40547 + 2.54350i −0.353856 + 0.204299i
\(156\) 1.20784 + 0.757028i 0.0967048 + 0.0606107i
\(157\) 6.91794 3.99407i 0.552111 0.318762i −0.197862 0.980230i \(-0.563400\pi\)
0.749973 + 0.661468i \(0.230066\pi\)
\(158\) 6.48946 3.74669i 0.516274 0.298071i
\(159\) −11.4236 + 6.05416i −0.905954 + 0.480126i
\(160\) 1.05823 0.610972i 0.0836608 0.0483016i
\(161\) 0 0
\(162\) −12.6287 + 5.02265i −0.992205 + 0.394617i
\(163\) 5.75231 + 9.96329i 0.450556 + 0.780385i 0.998421 0.0561817i \(-0.0178926\pi\)
−0.547865 + 0.836567i \(0.684559\pi\)
\(164\) −2.12397 −0.165854
\(165\) 4.37619 + 2.74282i 0.340686 + 0.213528i
\(166\) 13.0180i 1.01039i
\(167\) 8.38240 14.5187i 0.648650 1.12349i −0.334796 0.942291i \(-0.608667\pi\)
0.983446 0.181204i \(-0.0579994\pi\)
\(168\) 0 0
\(169\) −2.19222 3.79704i −0.168632 0.292080i
\(170\) 5.47724 3.16228i 0.420085 0.242536i
\(171\) −1.07942 0.732354i −0.0825454 0.0560045i
\(172\) −1.80205 + 3.12124i −0.137405 + 0.237992i
\(173\) −0.856396 + 1.48332i −0.0651106 + 0.112775i −0.896743 0.442552i \(-0.854073\pi\)
0.831632 + 0.555326i \(0.187407\pi\)
\(174\) −0.301530 + 0.481093i −0.0228589 + 0.0364716i
\(175\) 0 0
\(176\) 14.9180 + 8.61288i 1.12448 + 0.649220i
\(177\) 5.40804 + 0.196211i 0.406493 + 0.0147481i
\(178\) 23.6191i 1.77033i
\(179\) −12.4141 7.16731i −0.927877 0.535710i −0.0417372 0.999129i \(-0.513289\pi\)
−0.886139 + 0.463419i \(0.846623\pi\)
\(180\) 0.366418 0.540065i 0.0273112 0.0402541i
\(181\) 4.83147i 0.359121i −0.983747 0.179560i \(-0.942532\pi\)
0.983747 0.179560i \(-0.0574675\pi\)
\(182\) 0 0
\(183\) 5.33232 2.82596i 0.394177 0.208901i
\(184\) −0.144689 −0.0106666
\(185\) 2.44167 + 4.22909i 0.179515 + 0.310929i
\(186\) −9.10724 + 14.5307i −0.667775 + 1.06544i
\(187\) 17.9662 + 10.3728i 1.31382 + 0.758534i
\(188\) −0.270725 −0.0197447
\(189\) 0 0
\(190\) 0.509437 0.0369584
\(191\) −2.72114 1.57105i −0.196895 0.113677i 0.398311 0.917250i \(-0.369596\pi\)
−0.595206 + 0.803573i \(0.702930\pi\)
\(192\) −6.05811 + 9.66575i −0.437206 + 0.697566i
\(193\) −3.00508 5.20496i −0.216311 0.374661i 0.737367 0.675493i \(-0.236069\pi\)
−0.953677 + 0.300832i \(0.902736\pi\)
\(194\) −2.16502 −0.155439
\(195\) 3.48532 1.84711i 0.249589 0.132274i
\(196\) 0 0
\(197\) 14.0902i 1.00388i 0.864901 + 0.501942i \(0.167381\pi\)
−0.864901 + 0.501942i \(0.832619\pi\)
\(198\) 17.3650 + 1.26171i 1.23407 + 0.0896658i
\(199\) 6.84234 + 3.95043i 0.485041 + 0.280038i 0.722515 0.691355i \(-0.242986\pi\)
−0.237474 + 0.971394i \(0.576319\pi\)
\(200\) 11.4207i 0.807564i
\(201\) 7.27289 + 0.263871i 0.512990 + 0.0186120i
\(202\) −20.9531 12.0973i −1.47426 0.851163i
\(203\) 0 0
\(204\) 1.39221 2.22128i 0.0974741 0.155520i
\(205\) −2.93869 + 5.08995i −0.205247 + 0.355498i
\(206\) 12.7346 22.0570i 0.887263 1.53678i
\(207\) −0.150437 + 0.0728677i −0.0104561 + 0.00506465i
\(208\) 11.3936 6.57807i 0.790001 0.456107i
\(209\) 0.835517 + 1.44716i 0.0577939 + 0.100102i
\(210\) 0 0
\(211\) 2.57821 4.46559i 0.177491 0.307424i −0.763529 0.645773i \(-0.776535\pi\)
0.941021 + 0.338349i \(0.109868\pi\)
\(212\) 2.09292i 0.143742i
\(213\) −5.14856 3.22692i −0.352774 0.221105i
\(214\) −5.86660 −0.401032
\(215\) 4.98658 + 8.63701i 0.340082 + 0.589039i
\(216\) −1.46512 + 13.4135i −0.0996891 + 0.912672i
\(217\) 0 0
\(218\) 3.35457 1.93676i 0.227200 0.131174i
\(219\) 12.4752 6.61145i 0.842995 0.446760i
\(220\) −0.724055 + 0.418033i −0.0488158 + 0.0281838i
\(221\) 13.7217 7.92220i 0.923019 0.532905i
\(222\) 13.9489 + 8.74262i 0.936189 + 0.586766i
\(223\) −3.79823 + 2.19291i −0.254348 + 0.146848i −0.621754 0.783213i \(-0.713580\pi\)
0.367405 + 0.930061i \(0.380246\pi\)
\(224\) 0 0
\(225\) 5.75164 + 11.8744i 0.383443 + 0.791627i
\(226\) −8.53582 14.7845i −0.567794 0.983449i
\(227\) −9.67394 −0.642082 −0.321041 0.947065i \(-0.604033\pi\)
−0.321041 + 0.947065i \(0.604033\pi\)
\(228\) 0.186578 0.0988800i 0.0123564 0.00654849i
\(229\) 8.85314i 0.585032i 0.956261 + 0.292516i \(0.0944925\pi\)
−0.956261 + 0.292516i \(0.905508\pi\)
\(230\) 0.0326412 0.0565363i 0.00215230 0.00372789i
\(231\) 0 0
\(232\) 0.281850 + 0.488179i 0.0185044 + 0.0320505i
\(233\) 11.1612 6.44391i 0.731194 0.422155i −0.0876651 0.996150i \(-0.527941\pi\)
0.818859 + 0.573995i \(0.194607\pi\)
\(234\) 7.46575 11.0038i 0.488052 0.719341i
\(235\) −0.374571 + 0.648777i −0.0244343 + 0.0423215i
\(236\) −0.438017 + 0.758668i −0.0285125 + 0.0493851i
\(237\) −4.02469 7.59421i −0.261432 0.493297i
\(238\) 0 0
\(239\) 4.18421 + 2.41575i 0.270654 + 0.156262i 0.629185 0.777256i \(-0.283389\pi\)
−0.358531 + 0.933518i \(0.616722\pi\)
\(240\) −2.82058 5.32217i −0.182067 0.343544i
\(241\) 10.0336i 0.646323i 0.946344 + 0.323161i \(0.104746\pi\)
−0.946344 + 0.323161i \(0.895254\pi\)
\(242\) −4.93045 2.84659i −0.316941 0.182986i
\(243\) 5.23192 + 14.6842i 0.335628 + 0.941995i
\(244\) 0.976932i 0.0625417i
\(245\) 0 0
\(246\) −0.718379 + 19.8002i −0.0458022 + 1.26242i
\(247\) 1.27625 0.0812058
\(248\) 8.51284 + 14.7447i 0.540566 + 0.936288i
\(249\) 14.9216 + 0.541377i 0.945619 + 0.0343083i
\(250\) −9.53594 5.50558i −0.603106 0.348203i
\(251\) 7.98203 0.503821 0.251911 0.967751i \(-0.418941\pi\)
0.251911 + 0.967751i \(0.418941\pi\)
\(252\) 0 0
\(253\) 0.214137 0.0134627
\(254\) 3.47424 + 2.00586i 0.217993 + 0.125859i
\(255\) −3.39692 6.40967i −0.212723 0.401389i
\(256\) −3.30160 5.71853i −0.206350 0.357408i
\(257\) 2.68230 0.167317 0.0836585 0.996494i \(-0.473340\pi\)
0.0836585 + 0.996494i \(0.473340\pi\)
\(258\) 28.4876 + 17.8549i 1.77356 + 1.11160i
\(259\) 0 0
\(260\) 0.638544i 0.0396008i
\(261\) 0.538902 + 0.365629i 0.0333572 + 0.0226319i
\(262\) 10.7712 + 6.21874i 0.665445 + 0.384195i
\(263\) 23.4359i 1.44512i 0.691309 + 0.722560i \(0.257034\pi\)
−0.691309 + 0.722560i \(0.742966\pi\)
\(264\) 9.17994 14.6467i 0.564986 0.901439i
\(265\) −5.01556 2.89573i −0.308103 0.177883i
\(266\) 0 0
\(267\) −27.0729 0.982241i −1.65683 0.0601122i
\(268\) −0.589059 + 1.02028i −0.0359825 + 0.0623236i
\(269\) 1.98955 3.44600i 0.121305 0.210106i −0.798978 0.601361i \(-0.794625\pi\)
0.920283 + 0.391254i \(0.127959\pi\)
\(270\) −4.91071 3.59852i −0.298856 0.218999i
\(271\) −10.8303 + 6.25288i −0.657895 + 0.379836i −0.791474 0.611202i \(-0.790686\pi\)
0.133580 + 0.991038i \(0.457353\pi\)
\(272\) −12.0974 20.9533i −0.733511 1.27048i
\(273\) 0 0
\(274\) 13.0828 22.6601i 0.790363 1.36895i
\(275\) 16.9024i 1.01925i
\(276\) 0.000981105 0.0270416i 5.90556e−5 0.00162771i
\(277\) −19.6909 −1.18311 −0.591557 0.806263i \(-0.701487\pi\)
−0.591557 + 0.806263i \(0.701487\pi\)
\(278\) 4.77494 + 8.27044i 0.286382 + 0.496028i
\(279\) 16.2767 + 11.0433i 0.974460 + 0.661142i
\(280\) 0 0
\(281\) 7.03456 4.06141i 0.419647 0.242283i −0.275279 0.961364i \(-0.588770\pi\)
0.694926 + 0.719081i \(0.255437\pi\)
\(282\) −0.0915661 + 2.52378i −0.00545268 + 0.150289i
\(283\) −1.16390 + 0.671978i −0.0691867 + 0.0399450i −0.534194 0.845362i \(-0.679385\pi\)
0.465008 + 0.885307i \(0.346052\pi\)
\(284\) 0.851847 0.491814i 0.0505478 0.0291838i
\(285\) 0.0211858 0.583931i 0.00125494 0.0345891i
\(286\) −14.7526 + 8.51741i −0.872339 + 0.503645i
\(287\) 0 0
\(288\) −3.90981 2.65269i −0.230388 0.156311i
\(289\) −6.06929 10.5123i −0.357017 0.618371i
\(290\) −0.254337 −0.0149352
\(291\) −0.0900361 + 2.48161i −0.00527801 + 0.145474i
\(292\) 2.28557i 0.133753i
\(293\) 10.6300 18.4117i 0.621012 1.07562i −0.368285 0.929713i \(-0.620055\pi\)
0.989298 0.145912i \(-0.0466116\pi\)
\(294\) 0 0
\(295\) 1.21207 + 2.09936i 0.0705693 + 0.122230i
\(296\) 14.1543 8.17202i 0.822705 0.474989i
\(297\) 2.16836 19.8517i 0.125821 1.15191i
\(298\) 9.68289 16.7713i 0.560915 0.971533i
\(299\) 0.0817733 0.141636i 0.00472907 0.00819100i
\(300\) −2.13446 0.0774412i −0.123233 0.00447107i
\(301\) 0 0
\(302\) 6.87261 + 3.96790i 0.395474 + 0.228327i
\(303\) −14.7376 + 23.5140i −0.846655 + 1.35084i
\(304\) 1.94886i 0.111775i
\(305\) 2.34116 + 1.35167i 0.134054 + 0.0773963i
\(306\) −20.2365 13.7299i −1.15684 0.784884i
\(307\) 13.2098i 0.753925i −0.926229 0.376962i \(-0.876969\pi\)
0.926229 0.376962i \(-0.123031\pi\)
\(308\) 0 0
\(309\) −24.7528 15.5140i −1.40814 0.882563i
\(310\) −7.68185 −0.436300
\(311\) −10.2687 17.7859i −0.582283 1.00854i −0.995208 0.0977785i \(-0.968826\pi\)
0.412925 0.910765i \(-0.364507\pi\)
\(312\) −6.18209 11.6650i −0.349992 0.660402i
\(313\) −14.2976 8.25471i −0.808147 0.466584i 0.0381649 0.999271i \(-0.487849\pi\)
−0.846312 + 0.532688i \(0.821182\pi\)
\(314\) 12.0629 0.680746
\(315\) 0 0
\(316\) 1.39133 0.0782685
\(317\) 8.11112 + 4.68296i 0.455566 + 0.263021i 0.710178 0.704022i \(-0.248614\pi\)
−0.254612 + 0.967043i \(0.581948\pi\)
\(318\) −19.5108 0.707879i −1.09411 0.0396959i
\(319\) −0.417133 0.722496i −0.0233550 0.0404520i
\(320\) −5.10995 −0.285655
\(321\) −0.243972 + 6.72445i −0.0136172 + 0.375322i
\(322\) 0 0
\(323\) 2.34708i 0.130595i
\(324\) −2.49697 0.364778i −0.138721 0.0202654i
\(325\) −11.1797 6.45459i −0.620137 0.358036i
\(326\) 17.3731i 0.962205i
\(327\) −2.08046 3.92564i −0.115050 0.217089i
\(328\) 17.0356 + 9.83548i 0.940631 + 0.543074i
\(329\) 0 0
\(330\) 3.65213 + 6.89124i 0.201043 + 0.379350i
\(331\) −14.4220 + 24.9796i −0.792702 + 1.37300i 0.131586 + 0.991305i \(0.457993\pi\)
−0.924288 + 0.381696i \(0.875340\pi\)
\(332\) −1.20856 + 2.09328i −0.0663282 + 0.114884i
\(333\) 10.6011 15.6250i 0.580938 0.856247i
\(334\) 21.9247 12.6582i 1.19967 0.692627i
\(335\) 1.63003 + 2.82329i 0.0890579 + 0.154253i
\(336\) 0 0
\(337\) −6.26205 + 10.8462i −0.341116 + 0.590829i −0.984640 0.174596i \(-0.944138\pi\)
0.643525 + 0.765425i \(0.277471\pi\)
\(338\) 6.62092i 0.360130i
\(339\) −17.3013 + 9.16915i −0.939680 + 0.498000i
\(340\) 1.17431 0.0636860
\(341\) −12.5988 21.8218i −0.682266 1.18172i
\(342\) −0.858683 1.77277i −0.0464322 0.0958606i
\(343\) 0 0
\(344\) 28.9072 16.6896i 1.55857 0.899841i
\(345\) −0.0634460 0.0397654i −0.00341582 0.00214090i
\(346\) −2.23996 + 1.29324i −0.120421 + 0.0695250i
\(347\) 24.8740 14.3610i 1.33531 0.770939i 0.349199 0.937049i \(-0.386454\pi\)
0.986107 + 0.166109i \(0.0531204\pi\)
\(348\) −0.0931491 + 0.0493660i −0.00499332 + 0.00264630i
\(349\) −11.0854 + 6.40017i −0.593389 + 0.342593i −0.766436 0.642320i \(-0.777972\pi\)
0.173048 + 0.984913i \(0.444639\pi\)
\(350\) 0 0
\(351\) −12.3024 9.01506i −0.656653 0.481188i
\(352\) 3.02636 + 5.24181i 0.161305 + 0.279389i
\(353\) 26.9982 1.43697 0.718485 0.695542i \(-0.244836\pi\)
0.718485 + 0.695542i \(0.244836\pi\)
\(354\) 6.92437 + 4.33992i 0.368026 + 0.230664i
\(355\) 2.72187i 0.144462i
\(356\) 2.19274 3.79793i 0.116215 0.201290i
\(357\) 0 0
\(358\) −10.8233 18.7465i −0.572030 0.990785i
\(359\) −24.2669 + 14.0105i −1.28076 + 0.739445i −0.976987 0.213300i \(-0.931579\pi\)
−0.303770 + 0.952745i \(0.598245\pi\)
\(360\) −5.43980 + 2.63489i −0.286703 + 0.138871i
\(361\) −9.40547 + 16.2908i −0.495025 + 0.857408i
\(362\) 3.64799 6.31851i 0.191734 0.332093i
\(363\) −3.46789 + 5.53303i −0.182017 + 0.290409i
\(364\) 0 0
\(365\) 5.47724 + 3.16228i 0.286692 + 0.165522i
\(366\) 9.10724 + 0.330423i 0.476043 + 0.0172715i
\(367\) 33.4382i 1.74546i 0.488202 + 0.872731i \(0.337653\pi\)
−0.488202 + 0.872731i \(0.662347\pi\)
\(368\) −0.216281 0.124870i −0.0112744 0.00650928i
\(369\) 22.6657 + 1.64685i 1.17993 + 0.0857316i
\(370\) 7.37430i 0.383372i
\(371\) 0 0
\(372\) −2.81342 + 1.49102i −0.145869 + 0.0773059i
\(373\) −7.96805 −0.412570 −0.206285 0.978492i \(-0.566137\pi\)
−0.206285 + 0.978492i \(0.566137\pi\)
\(374\) 15.6639 + 27.1307i 0.809961 + 1.40289i
\(375\) −6.70721 + 10.7014i −0.346359 + 0.552618i
\(376\) 2.17139 + 1.25365i 0.111981 + 0.0646522i
\(377\) −0.637169 −0.0328159
\(378\) 0 0
\(379\) 3.88714 0.199669 0.0998345 0.995004i \(-0.468169\pi\)
0.0998345 + 0.995004i \(0.468169\pi\)
\(380\) 0.0819169 + 0.0472948i 0.00420225 + 0.00242617i
\(381\) 2.44365 3.89886i 0.125192 0.199744i
\(382\) −2.37244 4.10918i −0.121384 0.210244i
\(383\) −12.6830 −0.648071 −0.324036 0.946045i \(-0.605040\pi\)
−0.324036 + 0.946045i \(0.605040\pi\)
\(384\) −20.0413 + 10.6213i −1.02273 + 0.542014i
\(385\) 0 0
\(386\) 9.07592i 0.461952i
\(387\) 21.6505 31.9108i 1.10056 1.62211i
\(388\) −0.348133 0.200995i −0.0176738 0.0102040i
\(389\) 20.5614i 1.04250i −0.853403 0.521252i \(-0.825465\pi\)
0.853403 0.521252i \(-0.174535\pi\)
\(390\) 5.95269 + 0.215972i 0.301426 + 0.0109362i
\(391\) −0.260474 0.150385i −0.0131727 0.00760529i
\(392\) 0 0
\(393\) 7.57603 12.0876i 0.382160 0.609739i
\(394\) −10.6388 + 18.4269i −0.535973 + 0.928332i
\(395\) 1.92503 3.33424i 0.0968586 0.167764i
\(396\) 2.67513 + 1.81500i 0.134430 + 0.0912070i
\(397\) −12.9646 + 7.48513i −0.650676 + 0.375668i −0.788715 0.614759i \(-0.789253\pi\)
0.138039 + 0.990427i \(0.455920\pi\)
\(398\) 5.96552 + 10.3326i 0.299025 + 0.517926i
\(399\) 0 0
\(400\) −9.85630 + 17.0716i −0.492815 + 0.853580i
\(401\) 10.3164i 0.515178i 0.966255 + 0.257589i \(0.0829280\pi\)
−0.966255 + 0.257589i \(0.917072\pi\)
\(402\) 9.31211 + 5.83646i 0.464446 + 0.291096i
\(403\) −19.2447 −0.958647
\(404\) −2.24616 3.89047i −0.111751 0.193558i
\(405\) −4.32894 + 5.47914i −0.215107 + 0.272261i
\(406\) 0 0
\(407\) −20.9482 + 12.0944i −1.03836 + 0.599499i
\(408\) −21.4525 + 11.3691i −1.06206 + 0.562856i
\(409\) 16.0387 9.25995i 0.793063 0.457875i −0.0479769 0.998848i \(-0.515277\pi\)
0.841040 + 0.540973i \(0.181944\pi\)
\(410\) −7.68631 + 4.43769i −0.379600 + 0.219162i
\(411\) −25.4296 15.9383i −1.25435 0.786177i
\(412\) 4.09543 2.36450i 0.201767 0.116490i
\(413\) 0 0
\(414\) −0.251757 0.0182923i −0.0123732 0.000899017i
\(415\) 3.34429 + 5.79247i 0.164165 + 0.284341i
\(416\) 4.62275 0.226649
\(417\) 9.67838 5.12923i 0.473952 0.251179i
\(418\) 2.52342i 0.123424i
\(419\) −6.37677 + 11.0449i −0.311526 + 0.539578i −0.978693 0.205330i \(-0.934173\pi\)
0.667167 + 0.744908i \(0.267507\pi\)
\(420\) 0 0
\(421\) 6.78793 + 11.7570i 0.330824 + 0.573003i 0.982674 0.185345i \(-0.0593402\pi\)
−0.651850 + 0.758348i \(0.726007\pi\)
\(422\) 6.74347 3.89334i 0.328267 0.189525i
\(423\) 2.88902 + 0.209911i 0.140469 + 0.0102062i
\(424\) −9.69173 + 16.7866i −0.470672 + 0.815227i
\(425\) −11.8703 + 20.5599i −0.575793 + 0.997303i
\(426\) −4.29672 8.10751i −0.208177 0.392810i
\(427\) 0 0
\(428\) −0.943342 0.544639i −0.0455982 0.0263261i
\(429\) 9.14938 + 17.2640i 0.441736 + 0.833515i
\(430\) 15.0604i 0.726277i
\(431\) 31.3069 + 18.0750i 1.50800 + 0.870643i 0.999957 + 0.00931038i \(0.00296363\pi\)
0.508041 + 0.861333i \(0.330370\pi\)
\(432\) −13.7662 + 18.7860i −0.662326 + 0.903843i
\(433\) 33.0085i 1.58629i −0.609034 0.793144i \(-0.708443\pi\)
0.609034 0.793144i \(-0.291557\pi\)
\(434\) 0 0
\(435\) −0.0105770 + 0.291528i −0.000507130 + 0.0139777i
\(436\) 0.719215 0.0344442
\(437\) −0.0121133 0.0209809i −0.000579459 0.00100365i
\(438\) 21.3068 + 0.773039i 1.01808 + 0.0369372i
\(439\) −26.4673 15.2809i −1.26321 0.729317i −0.289519 0.957172i \(-0.593495\pi\)
−0.973695 + 0.227856i \(0.926829\pi\)
\(440\) 7.74318 0.369141
\(441\) 0 0
\(442\) 23.9266 1.13807
\(443\) −17.9290 10.3513i −0.851833 0.491806i 0.00943615 0.999955i \(-0.496996\pi\)
−0.861269 + 0.508150i \(0.830330\pi\)
\(444\) 1.43133 + 2.70078i 0.0679278 + 0.128174i
\(445\) −6.06767 10.5095i −0.287635 0.498199i
\(446\) −6.62300 −0.313608
\(447\) −18.8210 11.7963i −0.890203 0.557944i
\(448\) 0 0
\(449\) 6.40243i 0.302150i −0.988522 0.151075i \(-0.951727\pi\)
0.988522 0.151075i \(-0.0482734\pi\)
\(450\) −1.44386 + 19.8719i −0.0680641 + 0.936769i
\(451\) −25.2123 14.5563i −1.18720 0.685431i
\(452\) 3.16977i 0.149093i
\(453\) 4.83393 7.71256i 0.227118 0.362368i
\(454\) −12.6514 7.30428i −0.593759 0.342807i
\(455\) 0 0
\(456\) −1.95436 0.0709067i −0.0915211 0.00332051i
\(457\) 1.57340 2.72521i 0.0736007 0.127480i −0.826876 0.562384i \(-0.809884\pi\)
0.900477 + 0.434904i \(0.143218\pi\)
\(458\) −6.68454 + 11.5780i −0.312348 + 0.541003i
\(459\) −16.5791 + 22.6246i −0.773846 + 1.05603i
\(460\) 0.0104974 0.00606065i 0.000489442 0.000282579i
\(461\) −7.44225 12.8904i −0.346620 0.600364i 0.639026 0.769185i \(-0.279337\pi\)
−0.985647 + 0.168821i \(0.946004\pi\)
\(462\) 0 0
\(463\) 13.3616 23.1429i 0.620964 1.07554i −0.368342 0.929690i \(-0.620075\pi\)
0.989307 0.145851i \(-0.0465921\pi\)
\(464\) 0.972971i 0.0451691i
\(465\) −0.319463 + 8.80515i −0.0148147 + 0.408329i
\(466\) 19.4618 0.901552
\(467\) 12.3967 + 21.4717i 0.573650 + 0.993591i 0.996187 + 0.0872454i \(0.0278064\pi\)
−0.422537 + 0.906346i \(0.638860\pi\)
\(468\) 2.22205 1.07630i 0.102714 0.0497520i
\(469\) 0 0
\(470\) −0.979714 + 0.565638i −0.0451908 + 0.0260909i
\(471\) 0.501654 13.8268i 0.0231150 0.637104i
\(472\) 7.02636 4.05667i 0.323414 0.186723i
\(473\) −42.7821 + 24.7003i −1.96712 + 1.13572i
\(474\) 0.470584 12.9704i 0.0216146 0.595750i
\(475\) −1.65608 + 0.956138i −0.0759861 + 0.0438706i
\(476\) 0 0
\(477\) −1.62278 + 22.3344i −0.0743020 + 1.02262i
\(478\) 3.64801 + 6.31855i 0.166856 + 0.289004i
\(479\) −12.5271 −0.572377 −0.286189 0.958173i \(-0.592388\pi\)
−0.286189 + 0.958173i \(0.592388\pi\)
\(480\) 0.0767379 2.11508i 0.00350259 0.0965397i
\(481\) 18.4742i 0.842352i
\(482\) −7.57587 + 13.1218i −0.345071 + 0.597681i
\(483\) 0 0
\(484\) −0.528540 0.915459i −0.0240246 0.0416118i
\(485\) −0.963343 + 0.556187i −0.0437432 + 0.0252551i
\(486\) −4.24510 + 23.1541i −0.192562 + 1.05029i
\(487\) 1.69748 2.94012i 0.0769202 0.133230i −0.824999 0.565133i \(-0.808825\pi\)
0.901920 + 0.431904i \(0.142158\pi\)
\(488\) 4.52390 7.83562i 0.204787 0.354702i
\(489\) 19.9135 + 0.722488i 0.900519 + 0.0326720i
\(490\) 0 0
\(491\) 0.780171 + 0.450432i 0.0352086 + 0.0203277i 0.517501 0.855683i \(-0.326862\pi\)
−0.482292 + 0.876010i \(0.660196\pi\)
\(492\) −1.95371 + 3.11716i −0.0880802 + 0.140532i
\(493\) 1.17178i 0.0527745i
\(494\) 1.66905 + 0.963629i 0.0750943 + 0.0433557i
\(495\) 8.05080 3.89959i 0.361857 0.175274i
\(496\) 29.3871i 1.31952i
\(497\) 0 0
\(498\) 19.1054 + 11.9745i 0.856135 + 0.536591i
\(499\) 21.8688 0.978984 0.489492 0.872008i \(-0.337182\pi\)
0.489492 + 0.872008i \(0.337182\pi\)
\(500\) −1.02225 1.77058i −0.0457162 0.0791829i
\(501\) −13.5974 25.6571i −0.607488 1.14627i
\(502\) 10.4387 + 6.02681i 0.465904 + 0.268990i
\(503\) −42.9876 −1.91672 −0.958362 0.285557i \(-0.907821\pi\)
−0.958362 + 0.285557i \(0.907821\pi\)
\(504\) 0 0
\(505\) −12.4310 −0.553173
\(506\) 0.280044 + 0.161684i 0.0124495 + 0.00718771i
\(507\) −7.58908 0.275342i −0.337043 0.0122284i
\(508\) 0.372436 + 0.645079i 0.0165242 + 0.0286207i
\(509\) 30.0832 1.33342 0.666708 0.745319i \(-0.267703\pi\)
0.666708 + 0.745319i \(0.267703\pi\)
\(510\) 0.397182 10.9473i 0.0175875 0.484753i
\(511\) 0 0
\(512\) 16.2193i 0.716799i
\(513\) −2.06771 + 0.910522i −0.0912916 + 0.0402005i
\(514\) 3.50785 + 2.02526i 0.154725 + 0.0893304i
\(515\) 13.0859i 0.576635i
\(516\) 2.92318 + 5.51576i 0.128686 + 0.242818i
\(517\) −3.21362 1.85538i −0.141335 0.0815997i
\(518\) 0 0
\(519\) 1.38919 + 2.62128i 0.0609789 + 0.115061i
\(520\) 2.95692 5.12153i 0.129669 0.224594i
\(521\) −6.00837 + 10.4068i −0.263231 + 0.455930i −0.967099 0.254401i \(-0.918122\pi\)
0.703867 + 0.710331i \(0.251455\pi\)
\(522\) 0.428699 + 0.885059i 0.0187636 + 0.0387380i
\(523\) 16.1185 9.30602i 0.704813 0.406924i −0.104325 0.994543i \(-0.533268\pi\)
0.809137 + 0.587620i \(0.199935\pi\)
\(524\) 1.15466 + 1.99993i 0.0504417 + 0.0873675i
\(525\) 0 0
\(526\) −17.6952 + 30.6490i −0.771548 + 1.33636i
\(527\) 35.3919i 1.54169i
\(528\) 26.3625 13.9713i 1.14728 0.608023i
\(529\) 22.9969 0.999865
\(530\) −4.37283 7.57397i −0.189944 0.328992i
\(531\) 5.26250 7.75642i 0.228373 0.336600i
\(532\) 0 0
\(533\) −19.2559 + 11.1174i −0.834064 + 0.481547i
\(534\) −34.6637 21.7259i −1.50005 0.940170i
\(535\) −2.61039 + 1.50711i −0.112857 + 0.0651580i
\(536\) 9.44926 5.45554i 0.408146 0.235643i
\(537\) −21.9379 + 11.6264i −0.946690 + 0.501715i
\(538\) 5.20379 3.00441i 0.224351 0.129529i
\(539\) 0 0
\(540\) −0.455560 1.03454i −0.0196042 0.0445193i
\(541\) −21.1242 36.5882i −0.908201 1.57305i −0.816562 0.577258i \(-0.804123\pi\)
−0.0916391 0.995792i \(-0.529211\pi\)
\(542\) −18.8849 −0.811176
\(543\) −7.09074 4.44419i −0.304293 0.190719i
\(544\) 8.50145i 0.364497i
\(545\) 0.995095 1.72356i 0.0426252 0.0738290i
\(546\) 0 0
\(547\) −6.92349 11.9918i −0.296027 0.512734i 0.679196 0.733957i \(-0.262329\pi\)
−0.975223 + 0.221223i \(0.928995\pi\)
\(548\) 4.20741 2.42915i 0.179732 0.103768i
\(549\) 0.757480 10.4252i 0.0323285 0.444938i
\(550\) 12.7621 22.1046i 0.544178 0.942544i
\(551\) −0.0471929 + 0.0817405i −0.00201049 + 0.00348226i
\(552\) −0.133091 + 0.212347i −0.00566473 + 0.00903810i
\(553\) 0 0
\(554\) −25.7514 14.8676i −1.09407 0.631664i
\(555\) 8.45263 + 0.306673i 0.358794 + 0.0130175i
\(556\) 1.77317i 0.0751992i
\(557\) −27.2305 15.7215i −1.15379 0.666143i −0.203985 0.978974i \(-0.565389\pi\)
−0.949809 + 0.312831i \(0.898723\pi\)
\(558\) 12.9482 + 26.7318i 0.548140 + 1.13165i
\(559\) 37.7296i 1.59579i
\(560\) 0 0
\(561\) 31.7493 16.8261i 1.34046 0.710399i
\(562\) 12.2662 0.517419
\(563\) −17.0829 29.5884i −0.719956 1.24700i −0.961017 0.276491i \(-0.910828\pi\)
0.241060 0.970510i \(-0.422505\pi\)
\(564\) −0.249025 + 0.397320i −0.0104858 + 0.0167302i
\(565\) −7.59616 4.38565i −0.319573 0.184506i
\(566\) −2.02950 −0.0853063
\(567\) 0 0
\(568\) −9.10981 −0.382239
\(569\) 19.6652 + 11.3537i 0.824407 + 0.475972i 0.851934 0.523649i \(-0.175430\pi\)
−0.0275266 + 0.999621i \(0.508763\pi\)
\(570\) 0.468602 0.747657i 0.0196276 0.0313159i
\(571\) 5.29931 + 9.17867i 0.221769 + 0.384116i 0.955345 0.295492i \(-0.0954835\pi\)
−0.733576 + 0.679607i \(0.762150\pi\)
\(572\) −3.16293 −0.132249
\(573\) −4.80872 + 2.54846i −0.200887 + 0.106464i
\(574\) 0 0
\(575\) 0.245051i 0.0102193i
\(576\) 8.61308 + 17.7819i 0.358878 + 0.740914i
\(577\) 12.6222 + 7.28745i 0.525471 + 0.303381i 0.739170 0.673519i \(-0.235218\pi\)
−0.213699 + 0.976899i \(0.568551\pi\)
\(578\) 18.3304i 0.762444i
\(579\) −10.4031 0.377438i −0.432337 0.0156858i
\(580\) −0.0408971 0.0236120i −0.00169816 0.000980434i
\(581\) 0 0
\(582\) −1.99148 + 3.17741i −0.0825494 + 0.131708i
\(583\) 14.3436 24.8438i 0.594050 1.02893i
\(584\) 10.5838 18.3318i 0.437963 0.758574i
\(585\) 0.495106 6.81416i 0.0204701 0.281731i
\(586\) 27.8035 16.0523i 1.14855 0.663116i
\(587\) 15.0927 + 26.1414i 0.622944 + 1.07897i 0.988935 + 0.148352i \(0.0473969\pi\)
−0.365991 + 0.930619i \(0.619270\pi\)
\(588\) 0 0
\(589\) −1.42539 + 2.46884i −0.0587321 + 0.101727i
\(590\) 3.66068i 0.150708i
\(591\) 20.6789 + 12.9607i 0.850618 + 0.533134i
\(592\) 28.2105 1.15945
\(593\) −15.2911 26.4850i −0.627930 1.08761i −0.987966 0.154669i \(-0.950569\pi\)
0.360036 0.932938i \(-0.382764\pi\)
\(594\) 17.8247 24.3245i 0.731357 0.998045i
\(595\) 0 0
\(596\) 3.11400 1.79787i 0.127554 0.0736435i
\(597\) 12.0916 6.40815i 0.494875 0.262268i
\(598\) 0.213883 0.123485i 0.00874633 0.00504970i
\(599\) 2.33872 1.35026i 0.0955573 0.0551701i −0.451460 0.892291i \(-0.649097\pi\)
0.547017 + 0.837121i \(0.315763\pi\)
\(600\) 16.7611 + 10.5052i 0.684271 + 0.428874i
\(601\) 21.0197 12.1357i 0.857411 0.495026i −0.00573343 0.999984i \(-0.501825\pi\)
0.863144 + 0.504957i \(0.168492\pi\)
\(602\) 0 0
\(603\) 7.07717 10.4311i 0.288205 0.424786i
\(604\) 0.736739 + 1.27607i 0.0299775 + 0.0519225i
\(605\) −2.92512 −0.118923
\(606\) −37.0278 + 19.6235i −1.50415 + 0.797151i
\(607\) 21.4181i 0.869334i 0.900591 + 0.434667i \(0.143134\pi\)
−0.900591 + 0.434667i \(0.856866\pi\)
\(608\) 0.342391 0.593039i 0.0138858 0.0240509i
\(609\) 0 0
\(610\) 2.04115 + 3.53537i 0.0826437 + 0.143143i
\(611\) −2.45439 + 1.41705i −0.0992942 + 0.0573275i
\(612\) −1.97936 4.08645i −0.0800111 0.165185i
\(613\) −2.95306 + 5.11485i −0.119273 + 0.206587i −0.919480 0.393137i \(-0.871390\pi\)
0.800207 + 0.599724i \(0.204723\pi\)
\(614\) 9.97404 17.2756i 0.402520 0.697185i
\(615\) 4.76696 + 8.99481i 0.192222 + 0.362706i
\(616\) 0 0
\(617\) −1.19246 0.688465i −0.0480065 0.0277166i 0.475805 0.879551i \(-0.342157\pi\)
−0.523811 + 0.851834i \(0.675490\pi\)
\(618\) −20.6573 38.9785i −0.830960 1.56794i
\(619\) 33.8233i 1.35947i −0.733457 0.679736i \(-0.762094\pi\)
0.733457 0.679736i \(-0.237906\pi\)
\(620\) −1.23523 0.713163i −0.0496082 0.0286413i
\(621\) −0.0314369 + 0.287810i −0.00126152 + 0.0115494i
\(622\) 31.0133i 1.24352i
\(623\) 0 0
\(624\) 0.826204 22.7721i 0.0330746 0.911615i
\(625\) 16.3326 0.653305
\(626\) −12.4654 21.5907i −0.498218 0.862938i
\(627\) 2.89241 + 0.104941i 0.115512 + 0.00419093i
\(628\) 1.93969 + 1.11988i 0.0774022 + 0.0446882i
\(629\) 33.9749 1.35467
\(630\) 0 0
\(631\) −25.0205 −0.996049 −0.498024 0.867163i \(-0.665941\pi\)
−0.498024 + 0.867163i \(0.665941\pi\)
\(632\) −11.1594 6.44287i −0.443896 0.256283i
\(633\) −4.18222 7.89146i −0.166228 0.313657i
\(634\) 7.07171 + 12.2486i 0.280853 + 0.486452i
\(635\) 2.06119 0.0817958
\(636\) −3.07160 1.92516i −0.121797 0.0763374i
\(637\) 0 0
\(638\) 1.25982i 0.0498768i
\(639\) −9.47173 + 4.58785i −0.374696 + 0.181493i
\(640\) −8.79916 5.08020i −0.347817 0.200812i
\(641\) 10.6830i 0.421952i −0.977491 0.210976i \(-0.932336\pi\)
0.977491 0.210976i \(-0.0676642\pi\)
\(642\) −5.39634 + 8.60990i −0.212977 + 0.339805i
\(643\) 38.1128 + 22.0044i 1.50302 + 0.867771i 0.999994 + 0.00350106i \(0.00111442\pi\)
0.503029 + 0.864270i \(0.332219\pi\)
\(644\) 0 0
\(645\) 17.2627 + 0.626313i 0.679716 + 0.0246610i
\(646\) 1.77216 3.06946i 0.0697246 0.120766i
\(647\) −23.5043 + 40.7107i −0.924050 + 1.60050i −0.130968 + 0.991387i \(0.541808\pi\)
−0.793082 + 0.609115i \(0.791525\pi\)
\(648\) 18.3381 + 14.4885i 0.720390 + 0.569163i
\(649\) −10.3989 + 6.00380i −0.408192 + 0.235670i
\(650\) −9.74704 16.8824i −0.382310 0.662181i
\(651\) 0 0
\(652\) −1.61287 + 2.79357i −0.0631648 + 0.109405i
\(653\) 33.9388i 1.32813i −0.747677 0.664063i \(-0.768831\pi\)
0.747677 0.664063i \(-0.231169\pi\)
\(654\) 0.243257 6.70473i 0.00951209 0.262176i
\(655\) 6.39029 0.249689
\(656\) 16.9765 + 29.4041i 0.662820 + 1.14804i
\(657\) 1.77216 24.3903i 0.0691384 0.951554i
\(658\) 0 0
\(659\) −1.36652 + 0.788962i −0.0532322 + 0.0307336i −0.526380 0.850249i \(-0.676451\pi\)
0.473148 + 0.880983i \(0.343118\pi\)
\(660\) −0.0525049 + 1.44716i −0.00204375 + 0.0563305i
\(661\) −2.08470 + 1.20360i −0.0810854 + 0.0468147i −0.539994 0.841669i \(-0.681574\pi\)
0.458909 + 0.888483i \(0.348240\pi\)
\(662\) −37.7215 + 21.7785i −1.46609 + 0.846446i
\(663\) 0.995026 27.4253i 0.0386436 1.06511i
\(664\) 19.3868 11.1930i 0.752354 0.434372i
\(665\) 0 0
\(666\) 25.6616 12.4298i 0.994366 0.481644i
\(667\) 0.00604760 + 0.0104747i 0.000234164 + 0.000405584i
\(668\) 4.70062 0.181873
\(669\) −0.275429 + 7.59146i −0.0106487 + 0.293503i
\(670\) 4.92299i 0.190192i
\(671\) −6.69529 + 11.5966i −0.258469 + 0.447681i
\(672\) 0 0
\(673\) 12.1767 + 21.0906i 0.469377 + 0.812984i 0.999387 0.0350069i \(-0.0111453\pi\)
−0.530010 + 0.847991i \(0.677812\pi\)
\(674\) −16.3788 + 9.45629i −0.630887 + 0.364243i
\(675\) 22.7176 + 2.48140i 0.874403 + 0.0955090i
\(676\) 0.614668 1.06464i 0.0236411 0.0409476i
\(677\) 4.83847 8.38048i 0.185958 0.322088i −0.757941 0.652323i \(-0.773795\pi\)
0.943899 + 0.330235i \(0.107128\pi\)
\(678\) −29.5495 1.07210i −1.13484 0.0411736i
\(679\) 0 0
\(680\) −9.41873 5.43791i −0.361192 0.208534i
\(681\) −8.89850 + 14.1976i −0.340991 + 0.544053i
\(682\) 38.0509i 1.45704i
\(683\) 18.6341 + 10.7584i 0.713012 + 0.411658i 0.812175 0.583413i \(-0.198283\pi\)
−0.0991632 + 0.995071i \(0.531617\pi\)
\(684\) 0.0265042 0.364778i 0.00101341 0.0139476i
\(685\) 13.4437i 0.513659i
\(686\) 0 0
\(687\) 12.9930 + 8.14349i 0.495714 + 0.310694i
\(688\) 57.6139 2.19651
\(689\) −10.9549 18.9744i −0.417348 0.722868i
\(690\) −0.0529487 0.0999092i −0.00201572 0.00380348i
\(691\) 25.4980 + 14.7213i 0.969989 + 0.560023i 0.899233 0.437470i \(-0.144126\pi\)
0.0707559 + 0.997494i \(0.477459\pi\)
\(692\) −0.480244 −0.0182561
\(693\) 0 0
\(694\) 43.3730 1.64642
\(695\) 4.24929 + 2.45333i 0.161185 + 0.0930602i
\(696\) 0.975715 + 0.0354003i 0.0369844 + 0.00134184i
\(697\) 20.4454 + 35.4124i 0.774423 + 1.34134i
\(698\) −19.3297 −0.731641
\(699\) 0.809354 22.3077i 0.0306126 0.843754i
\(700\) 0 0
\(701\) 40.4325i 1.52712i −0.645740 0.763558i \(-0.723451\pi\)
0.645740 0.763558i \(-0.276549\pi\)
\(702\) −9.28202 21.0786i −0.350327 0.795561i
\(703\) 2.37000 + 1.36832i 0.0893863 + 0.0516072i
\(704\) 25.3114i 0.953958i
\(705\) 0.607607 + 1.14650i 0.0228838 + 0.0431796i
\(706\) 35.3077 + 20.3849i 1.32882 + 0.767197i
\(707\) 0 0
\(708\) 0.710525 + 1.34070i 0.0267032 + 0.0503864i
\(709\) 7.95114 13.7718i 0.298611 0.517210i −0.677207 0.735792i \(-0.736810\pi\)
0.975818 + 0.218582i \(0.0701433\pi\)
\(710\) 2.05514 3.55960i 0.0771280 0.133590i
\(711\) −14.8474 1.07879i −0.556823 0.0404579i
\(712\) −35.1743 + 20.3079i −1.31821 + 0.761070i
\(713\) 0.182658 + 0.316373i 0.00684061 + 0.0118483i
\(714\) 0 0
\(715\) −4.37619 + 7.57978i −0.163660 + 0.283468i
\(716\) 4.01923i 0.150206i
\(717\) 7.39420 3.91869i 0.276141 0.146346i
\(718\) −42.3143 −1.57916
\(719\) 13.0488 + 22.6012i 0.486638 + 0.842883i 0.999882 0.0153605i \(-0.00488959\pi\)
−0.513244 + 0.858243i \(0.671556\pi\)
\(720\) −10.4054 0.756037i −0.387785 0.0281758i
\(721\) 0 0
\(722\) −24.6006 + 14.2032i −0.915539 + 0.528587i
\(723\) 14.7255 + 9.22936i 0.547647 + 0.343243i
\(724\) 1.17319 0.677340i 0.0436011 0.0251731i
\(725\) 0.826800 0.477353i 0.0307066 0.0177285i
\(726\) −8.71294 + 4.61757i −0.323367 + 0.171374i
\(727\) −3.74533 + 2.16237i −0.138907 + 0.0801977i −0.567843 0.823137i \(-0.692222\pi\)
0.428936 + 0.903335i \(0.358889\pi\)
\(728\) 0 0
\(729\) 26.3633 + 5.82876i 0.976420 + 0.215880i
\(730\) 4.77535 + 8.27115i 0.176744 + 0.306129i
\(731\) 69.3864 2.56635
\(732\) 1.43376 + 0.898624i 0.0529933 + 0.0332141i
\(733\) 42.3174i 1.56303i −0.623886 0.781515i \(-0.714447\pi\)
0.623886 0.781515i \(-0.285553\pi\)
\(734\) −25.2475 + 43.7299i −0.931901 + 1.61410i
\(735\) 0 0
\(736\) −0.0438762 0.0759958i −0.00161730 0.00280124i
\(737\) −13.9847 + 8.07409i −0.515135 + 0.297413i
\(738\) 28.3983 + 19.2674i 1.04535 + 0.709242i
\(739\) 1.62120 2.80801i 0.0596369 0.103294i −0.834666 0.550757i \(-0.814339\pi\)
0.894302 + 0.447463i \(0.147672\pi\)
\(740\) −0.684610 + 1.18578i −0.0251668 + 0.0435901i
\(741\) 1.17395 1.87304i 0.0431261 0.0688079i
\(742\) 0 0
\(743\) 5.41770 + 3.12791i 0.198756 + 0.114752i 0.596075 0.802929i \(-0.296726\pi\)
−0.397319 + 0.917681i \(0.630059\pi\)
\(744\) 29.4700 + 1.06921i 1.08042 + 0.0391992i
\(745\) 9.95001i 0.364540i
\(746\) −10.4205 6.01626i −0.381520 0.220271i
\(747\) 14.5201 21.4012i 0.531261 0.783028i
\(748\) 5.81678i 0.212682i
\(749\) 0 0
\(750\) −16.8516 + 8.93082i −0.615334 + 0.326107i
\(751\) −18.9063 −0.689900 −0.344950 0.938621i \(-0.612104\pi\)
−0.344950 + 0.938621i \(0.612104\pi\)
\(752\) 2.16386 + 3.74791i 0.0789078 + 0.136672i
\(753\) 7.34220 11.7145i 0.267565 0.426901i
\(754\) −0.833277 0.481093i −0.0303462 0.0175204i
\(755\) 4.07736 0.148390
\(756\) 0 0
\(757\) −40.7873 −1.48244 −0.741220 0.671262i \(-0.765752\pi\)
−0.741220 + 0.671262i \(0.765752\pi\)
\(758\) 5.08353 + 2.93498i 0.184642 + 0.106603i
\(759\) 0.196972 0.314270i 0.00714964 0.0114073i
\(760\) −0.438017 0.758668i −0.0158886 0.0275198i
\(761\) 42.6212 1.54502 0.772508 0.635005i \(-0.219002\pi\)
0.772508 + 0.635005i \(0.219002\pi\)
\(762\) 6.13958 3.25378i 0.222413 0.117872i
\(763\) 0 0
\(764\) 0.881003i 0.0318736i
\(765\) −12.5315 0.910522i −0.453079 0.0329200i
\(766\) −16.5866 9.57627i −0.599298 0.346005i
\(767\) 9.17078i 0.331138i
\(768\) −11.4295 0.414680i −0.412428 0.0149635i
\(769\) 0.932209 + 0.538211i 0.0336163 + 0.0194084i 0.516714 0.856158i \(-0.327155\pi\)
−0.483098 + 0.875566i \(0.660488\pi\)
\(770\) 0 0
\(771\) 2.46729 3.93658i 0.0888573 0.141772i
\(772\) 0.842584 1.45940i 0.0303253 0.0525249i
\(773\) −2.96855 + 5.14169i −0.106771 + 0.184934i −0.914461 0.404675i \(-0.867385\pi\)
0.807689 + 0.589609i \(0.200718\pi\)
\(774\) 52.4082 25.3851i 1.88377 0.912449i
\(775\) 24.9722 14.4177i 0.897028 0.517899i
\(776\) 1.86150 + 3.22421i 0.0668240 + 0.115742i
\(777\) 0 0
\(778\) 15.5248 26.8898i 0.556592 0.964046i
\(779\) 3.29370i 0.118009i
\(780\) 0.937137 + 0.587360i 0.0335549 + 0.0210309i
\(781\) 13.4824 0.482437
\(782\) −0.227095 0.393341i −0.00812091 0.0140658i
\(783\) 1.03231 0.454579i 0.0368917 0.0162453i
\(784\) 0 0
\(785\) 5.36746 3.09891i 0.191573 0.110605i
\(786\) 19.0345 10.0877i 0.678938 0.359815i
\(787\) 7.65434 4.41923i 0.272848 0.157529i −0.357333 0.933977i \(-0.616314\pi\)
0.630181 + 0.776448i \(0.282981\pi\)
\(788\) −3.42140 + 1.97535i −0.121882 + 0.0703688i
\(789\) 34.3948 + 21.5573i 1.22449 + 0.767461i
\(790\) 5.03502 2.90697i 0.179138 0.103425i
\(791\) 0 0
\(792\) −13.0515 26.9452i −0.463766 0.957457i
\(793\) 5.11351 + 8.85687i 0.181586 + 0.314517i
\(794\) −22.6065 −0.802275
\(795\) −8.86334 + 4.69728i −0.314350 + 0.166595i
\(796\) 2.21529i 0.0785190i
\(797\) −19.0123 + 32.9303i −0.673450 + 1.16645i 0.303469 + 0.952841i \(0.401855\pi\)
−0.976919 + 0.213609i \(0.931478\pi\)
\(798\) 0 0
\(799\) 2.60601 + 4.51374i 0.0921940 + 0.159685i
\(800\) −5.99855 + 3.46326i −0.212081 + 0.122445i
\(801\) −26.3443 + 38.8290i −0.930831 + 1.37196i
\(802\) −7.78939 + 13.4916i −0.275053 + 0.476406i
\(803\) −15.6639 + 27.1307i −0.552767 + 0.957421i
\(804\) 0.955536 + 1.80301i 0.0336992 + 0.0635872i
\(805\) 0 0
\(806\) −25.1678 14.5307i −0.886499 0.511821i
\(807\) −3.22733 6.08967i −0.113607 0.214366i
\(808\) 41.6054i 1.46367i
\(809\) 14.6570 + 8.46222i 0.515312 + 0.297516i 0.735015 0.678051i \(-0.237175\pi\)
−0.219702 + 0.975567i \(0.570509\pi\)
\(810\) −9.79832 + 3.89696i −0.344278 + 0.136925i
\(811\) 26.9840i 0.947536i −0.880650 0.473768i \(-0.842894\pi\)
0.880650 0.473768i \(-0.157106\pi\)
\(812\) 0 0
\(813\) −0.785360 + 21.6464i −0.0275438 + 0.759172i
\(814\) −36.5275 −1.28029
\(815\) 4.46308 + 7.73028i 0.156335 + 0.270780i
\(816\) −41.8790 1.51943i −1.46606 0.0531906i
\(817\) 4.84021 + 2.79450i 0.169338 + 0.0977671i
\(818\) 27.9668 0.977836
\(819\) 0 0
\(820\) −1.64793 −0.0575484
\(821\) 27.7572 + 16.0256i 0.968732 + 0.559297i 0.898849 0.438258i \(-0.144404\pi\)
0.0698823 + 0.997555i \(0.477738\pi\)
\(822\) −21.2222 40.0443i −0.740209 1.39671i
\(823\) −10.3974 18.0089i −0.362431 0.627749i 0.625929 0.779880i \(-0.284720\pi\)
−0.988360 + 0.152131i \(0.951387\pi\)
\(824\) −43.7973 −1.52575
\(825\) −24.8062 15.5475i −0.863641 0.541296i
\(826\) 0 0
\(827\) 34.0792i 1.18505i 0.805552 + 0.592525i \(0.201869\pi\)
−0.805552 + 0.592525i \(0.798131\pi\)
\(828\) −0.0387841 0.0263139i −0.00134784 0.000914470i
\(829\) 29.3229 + 16.9296i 1.01843 + 0.587988i 0.913648 0.406507i \(-0.133253\pi\)
0.104778 + 0.994496i \(0.466587\pi\)
\(830\) 10.1004i 0.350589i
\(831\) −18.1126 + 28.8987i −0.628318 + 1.00248i
\(832\) −16.7416 9.66575i −0.580410 0.335100i
\(833\) 0 0
\(834\) 16.5300 + 0.599731i 0.572387 + 0.0207670i
\(835\) 6.50371 11.2648i 0.225070 0.389833i
\(836\) −0.234267 + 0.405763i −0.00810231 + 0.0140336i
\(837\) 31.1792 13.7299i 1.07771 0.474573i
\(838\) −16.6788 + 9.62953i −0.576161 + 0.332647i
\(839\) −11.7633 20.3747i −0.406115 0.703412i 0.588335 0.808617i \(-0.299784\pi\)
−0.994451 + 0.105205i \(0.966450\pi\)
\(840\) 0 0
\(841\) −14.4764 + 25.0739i −0.499188 + 0.864618i
\(842\) 20.5008i 0.706506i
\(843\) 0.510112 14.0599i 0.0175692 0.484248i
\(844\) 1.44579 0.0497661
\(845\) −1.70089 2.94603i −0.0585124 0.101347i
\(846\) 3.61971 + 2.45586i 0.124448 + 0.0844343i
\(847\) 0 0
\(848\) −28.9743 + 16.7283i −0.994983 + 0.574454i
\(849\) −0.0844003 + 2.32627i −0.00289661 + 0.0798374i
\(850\) −31.0474 + 17.9252i −1.06492 + 0.614831i
\(851\) 0.303707 0.175345i 0.0104109 0.00601076i
\(852\) 0.0617717 1.70257i 0.00211627 0.0583292i
\(853\) −39.7270 + 22.9364i −1.36023 + 0.785328i −0.989654 0.143475i \(-0.954172\pi\)
−0.370574 + 0.928803i \(0.620839\pi\)
\(854\) 0 0
\(855\) −0.837497 0.568217i −0.0286418 0.0194326i
\(856\) 5.04414 + 8.73670i 0.172405 + 0.298614i
\(857\) −18.2455 −0.623253 −0.311627 0.950205i \(-0.600874\pi\)
−0.311627 + 0.950205i \(0.600874\pi\)
\(858\) −1.06978 + 29.4858i −0.0365218 + 1.00663i
\(859\) 5.81666i 0.198462i −0.995064 0.0992309i \(-0.968362\pi\)
0.995064 0.0992309i \(-0.0316382\pi\)
\(860\) −1.39817 + 2.42170i −0.0476771 + 0.0825792i
\(861\) 0 0
\(862\) 27.2950 + 47.2763i 0.929671 + 1.61024i
\(863\) −27.7060 + 15.9961i −0.943123 + 0.544513i −0.890938 0.454125i \(-0.849952\pi\)
−0.0521854 + 0.998637i \(0.516619\pi\)
\(864\) −7.48953 + 3.29804i −0.254799 + 0.112202i
\(865\) −0.664458 + 1.15087i −0.0225922 + 0.0391309i
\(866\) 24.9230 43.1679i 0.846918 1.46690i
\(867\) −21.0108 0.762301i −0.713564 0.0258891i
\(868\) 0 0
\(869\) 16.5157 + 9.53533i 0.560256 + 0.323464i
\(870\) −0.233950 + 0.373269i −0.00793165 + 0.0126550i
\(871\) 12.3332i 0.417893i
\(872\) −5.76857 3.33048i −0.195348 0.112784i
\(873\) 3.55922 + 2.41482i 0.120461 + 0.0817294i
\(874\) 0.0365846i 0.00123749i
\(875\) 0 0
\(876\) 3.35434 + 2.10237i 0.113333 + 0.0710324i
\(877\) −48.3898 −1.63401 −0.817004 0.576632i \(-0.804367\pi\)
−0.817004 + 0.576632i \(0.804367\pi\)
\(878\) −23.0756 39.9681i −0.778763 1.34886i
\(879\) −17.2434 32.5366i −0.581604 1.09743i
\(880\) 11.5745 + 6.68253i 0.390176 + 0.225268i
\(881\) −26.6822 −0.898946 −0.449473 0.893294i \(-0.648388\pi\)
−0.449473 + 0.893294i \(0.648388\pi\)
\(882\) 0 0
\(883\) 35.0484 1.17947 0.589737 0.807595i \(-0.299231\pi\)
0.589737 + 0.807595i \(0.299231\pi\)
\(884\) 3.84736 + 2.22128i 0.129401 + 0.0747096i
\(885\) 4.19597 + 0.152235i 0.141046 + 0.00511734i
\(886\) −15.6315 27.0745i −0.525149 0.909585i
\(887\) −12.9676 −0.435410 −0.217705 0.976015i \(-0.569857\pi\)
−0.217705 + 0.976015i \(0.569857\pi\)
\(888\) 1.02640 28.2901i 0.0344438 0.949353i
\(889\) 0 0
\(890\) 18.3255i 0.614273i
\(891\) −27.1401 21.4428i −0.909228 0.718359i
\(892\) −1.06497 0.614862i −0.0356579 0.0205871i
\(893\) 0.419822i 0.0140488i
\(894\) −15.7070 29.6377i −0.525321 0.991231i
\(895\) −9.63184 5.56095i −0.321957 0.185882i
\(896\) 0 0
\(897\) −0.132648 0.250294i −0.00442898 0.00835708i
\(898\) 4.83414 8.37298i 0.161317 0.279410i
\(899\) 0.711627 1.23257i 0.0237341 0.0411086i
\(900\) −2.07702 + 3.06133i −0.0692341 + 0.102044i
\(901\) −34.8948 + 20.1465i −1.16251 + 0.671178i
\(902\) −21.9815 38.0730i −0.731902 1.26769i
\(903\) 0 0
\(904\) −14.6783 + 25.4236i −0.488193 + 0.845576i
\(905\) 3.74863i 0.124609i
\(906\) 12.1451 6.43649i 0.403493 0.213838i
\(907\) −9.12613 −0.303028 −0.151514 0.988455i \(-0.548415\pi\)
−0.151514 + 0.988455i \(0.548415\pi\)
\(908\) −1.35622 2.34904i −0.0450077 0.0779557i
\(909\) 20.9531 + 43.2583i 0.694972 + 1.43479i
\(910\) 0 0
\(911\) 41.5720 24.0016i 1.37734 0.795209i 0.385503 0.922707i \(-0.374028\pi\)
0.991839 + 0.127498i \(0.0406947\pi\)
\(912\) −2.86017 1.79264i −0.0947098 0.0593604i
\(913\) −28.6921 + 16.5654i −0.949571 + 0.548235i
\(914\) 4.11533 2.37599i 0.136123 0.0785906i
\(915\) 4.13722 2.19260i 0.136772 0.0724850i
\(916\) −2.14973 + 1.24115i −0.0710292 + 0.0410087i
\(917\) 0 0
\(918\) −38.7645 + 17.0701i −1.27942 + 0.563396i
\(919\) 19.8096 + 34.3113i 0.653459 + 1.13182i 0.982278 + 0.187432i \(0.0600163\pi\)
−0.328818 + 0.944393i \(0.606650\pi\)
\(920\) −0.112261 −0.00370112
\(921\) −19.3869 12.1510i −0.638821 0.400388i
\(922\) 22.4770i 0.740241i
\(923\) 5.14856 8.91757i 0.169467 0.293526i
\(924\) 0 0
\(925\) −13.8405 23.9724i −0.455072 0.788208i
\(926\) 34.9480 20.1772i 1.14846 0.663065i
\(927\) −45.5373 + 22.0570i −1.49564 + 0.724447i
\(928\) −0.170939 + 0.296076i −0.00561136 + 0.00971915i
\(929\) 11.7897 20.4204i 0.386809 0.669973i −0.605209 0.796066i \(-0.706911\pi\)
0.992018 + 0.126093i \(0.0402439\pi\)
\(930\) −7.06609 + 11.2740i −0.231706 + 0.369689i
\(931\) 0 0
\(932\) 3.12944 + 1.80679i 0.102508 + 0.0591832i
\(933\) −35.5483 1.28974i −1.16380 0.0422243i
\(934\) 37.4403i 1.22509i
\(935\) 13.9396 + 8.04801i 0.455872 + 0.263198i
\(936\) −22.8063 1.65707i −0.745447 0.0541630i
\(937\) 52.5144i 1.71557i 0.514007 + 0.857786i \(0.328160\pi\)
−0.514007 + 0.857786i \(0.671840\pi\)
\(938\) 0 0
\(939\) −25.2662 + 13.3903i −0.824533 + 0.436976i
\(940\) −0.210049 −0.00685105
\(941\) 24.5713 + 42.5587i 0.801000 + 1.38737i 0.918958 + 0.394354i \(0.129032\pi\)
−0.117958 + 0.993019i \(0.537635\pi\)
\(942\) 11.0959 17.7036i 0.361525 0.576815i
\(943\) 0.365528 + 0.211038i 0.0119032 + 0.00687234i
\(944\) 14.0040 0.455791
\(945\) 0 0
\(946\) −74.5995 −2.42544
\(947\) 8.04907 + 4.64713i 0.261560 + 0.151012i 0.625046 0.780588i \(-0.285080\pi\)
−0.363486 + 0.931600i \(0.618414\pi\)
\(948\) 1.27981 2.04194i 0.0415662 0.0663191i
\(949\) 11.9633 + 20.7210i 0.388344 + 0.672632i
\(950\) −2.88772 −0.0936899
\(951\) 14.3337 7.59641i 0.464803 0.246330i
\(952\) 0 0
\(953\) 40.3761i 1.30791i −0.756534 0.653955i \(-0.773109\pi\)
0.756534 0.653955i \(-0.226891\pi\)
\(954\) −18.9858 + 27.9832i −0.614686 + 0.905989i
\(955\) −2.11127 1.21894i −0.0683191 0.0394440i
\(956\) 1.35469i 0.0438137i
\(957\) −1.44404 0.0523918i −0.0466792 0.00169359i
\(958\) −16.3827 9.45854i −0.529300 0.305592i
\(959\) 0 0
\(960\) −4.70034 + 7.49943i −0.151703 + 0.242043i
\(961\) 5.99358 10.3812i 0.193341 0.334877i
\(962\) −13.9489 + 24.1602i −0.449731 + 0.778957i
\(963\) 9.64448 + 6.54349i 0.310789 + 0.210861i
\(964\) −2.43638 + 1.40665i −0.0784706 + 0.0453050i
\(965\) −2.33157 4.03840i −0.0750560 0.130001i
\(966\) 0 0
\(967\) 8.78620 15.2181i 0.282545 0.489383i −0.689466 0.724318i \(-0.742155\pi\)
0.972011 + 0.234936i \(0.0754879\pi\)
\(968\) 9.79009i 0.314665i
\(969\) −3.44461 2.15894i −0.110657 0.0693552i
\(970\) −1.67979 −0.0539348
\(971\) 20.1321 + 34.8697i 0.646068 + 1.11902i 0.984054 + 0.177872i \(0.0569212\pi\)
−0.337985 + 0.941151i \(0.609745\pi\)
\(972\) −2.83217 + 3.32905i −0.0908420 + 0.106779i
\(973\) 0 0
\(974\) 4.43986 2.56336i 0.142262 0.0821353i
\(975\) −19.7564 + 10.4702i −0.632711 + 0.335316i
\(976\) 13.5246 7.80845i 0.432913 0.249942i
\(977\) −22.9591 + 13.2555i −0.734527 + 0.424080i −0.820076 0.572254i \(-0.806069\pi\)
0.0855487 + 0.996334i \(0.472736\pi\)
\(978\) 25.4969 + 15.9805i 0.815302 + 0.510999i
\(979\) 52.0573 30.0553i 1.66376 0.960572i
\(980\) 0 0
\(981\) −7.67503 0.557655i −0.245045 0.0178046i
\(982\) 0.680195 + 1.17813i 0.0217059 + 0.0375957i
\(983\) 38.2714 1.22067 0.610334 0.792144i \(-0.291035\pi\)
0.610334 + 0.792144i \(0.291035\pi\)
\(984\) 30.1047 15.9545i 0.959703 0.508612i
\(985\) 10.9322i 0.348330i
\(986\) −0.884752 + 1.53243i −0.0281762 + 0.0488027i
\(987\) 0 0
\(988\) 0.178921 + 0.309901i 0.00569225 + 0.00985926i
\(989\) 0.620255 0.358105i 0.0197230 0.0113871i
\(990\) 13.4731 + 0.978931i 0.428202 + 0.0311125i
\(991\) 30.4509 52.7425i 0.967305 1.67542i 0.264016 0.964518i \(-0.414953\pi\)
0.703289 0.710904i \(-0.251714\pi\)
\(992\) −5.16295 + 8.94250i −0.163924 + 0.283925i
\(993\) 23.3944 + 44.1431i 0.742399 + 1.40084i
\(994\) 0 0
\(995\) 5.30881 + 3.06504i 0.168301 + 0.0971684i
\(996\) 1.96045 + 3.69919i 0.0621192 + 0.117213i
\(997\) 14.4115i 0.456415i −0.973612 0.228208i \(-0.926713\pi\)
0.973612 0.228208i \(-0.0732865\pi\)
\(998\) 28.5996 + 16.5120i 0.905306 + 0.522679i
\(999\) −13.1802 29.9309i −0.417002 0.946973i
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 441.2.s.b.374.4 10
3.2 odd 2 1323.2.s.b.962.2 10
7.2 even 3 63.2.i.b.5.2 10
7.3 odd 6 441.2.o.c.293.2 10
7.4 even 3 441.2.o.d.293.2 10
7.5 odd 6 441.2.i.b.68.2 10
7.6 odd 2 63.2.s.b.59.4 yes 10
9.2 odd 6 441.2.i.b.227.4 10
9.7 even 3 1323.2.i.b.521.2 10
21.2 odd 6 189.2.i.b.152.4 10
21.5 even 6 1323.2.i.b.1097.4 10
21.11 odd 6 1323.2.o.c.881.4 10
21.17 even 6 1323.2.o.d.881.4 10
21.20 even 2 189.2.s.b.17.2 10
28.23 odd 6 1008.2.ca.b.257.2 10
28.27 even 2 1008.2.df.b.689.4 10
63.2 odd 6 63.2.s.b.47.4 yes 10
63.11 odd 6 441.2.o.c.146.2 10
63.13 odd 6 567.2.p.c.80.2 10
63.16 even 3 189.2.s.b.89.2 10
63.20 even 6 63.2.i.b.38.4 yes 10
63.23 odd 6 567.2.p.c.404.2 10
63.25 even 3 1323.2.o.d.440.4 10
63.34 odd 6 189.2.i.b.143.2 10
63.38 even 6 441.2.o.d.146.2 10
63.41 even 6 567.2.p.d.80.4 10
63.47 even 6 inner 441.2.s.b.362.4 10
63.52 odd 6 1323.2.o.c.440.4 10
63.58 even 3 567.2.p.d.404.4 10
63.61 odd 6 1323.2.s.b.656.2 10
84.23 even 6 3024.2.ca.b.2609.3 10
84.83 odd 2 3024.2.df.b.17.3 10
252.79 odd 6 3024.2.df.b.1601.3 10
252.83 odd 6 1008.2.ca.b.353.2 10
252.191 even 6 1008.2.df.b.929.4 10
252.223 even 6 3024.2.ca.b.2033.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.i.b.5.2 10 7.2 even 3
63.2.i.b.38.4 yes 10 63.20 even 6
63.2.s.b.47.4 yes 10 63.2 odd 6
63.2.s.b.59.4 yes 10 7.6 odd 2
189.2.i.b.143.2 10 63.34 odd 6
189.2.i.b.152.4 10 21.2 odd 6
189.2.s.b.17.2 10 21.20 even 2
189.2.s.b.89.2 10 63.16 even 3
441.2.i.b.68.2 10 7.5 odd 6
441.2.i.b.227.4 10 9.2 odd 6
441.2.o.c.146.2 10 63.11 odd 6
441.2.o.c.293.2 10 7.3 odd 6
441.2.o.d.146.2 10 63.38 even 6
441.2.o.d.293.2 10 7.4 even 3
441.2.s.b.362.4 10 63.47 even 6 inner
441.2.s.b.374.4 10 1.1 even 1 trivial
567.2.p.c.80.2 10 63.13 odd 6
567.2.p.c.404.2 10 63.23 odd 6
567.2.p.d.80.4 10 63.41 even 6
567.2.p.d.404.4 10 63.58 even 3
1008.2.ca.b.257.2 10 28.23 odd 6
1008.2.ca.b.353.2 10 252.83 odd 6
1008.2.df.b.689.4 10 28.27 even 2
1008.2.df.b.929.4 10 252.191 even 6
1323.2.i.b.521.2 10 9.7 even 3
1323.2.i.b.1097.4 10 21.5 even 6
1323.2.o.c.440.4 10 63.52 odd 6
1323.2.o.c.881.4 10 21.11 odd 6
1323.2.o.d.440.4 10 63.25 even 3
1323.2.o.d.881.4 10 21.17 even 6
1323.2.s.b.656.2 10 63.61 odd 6
1323.2.s.b.962.2 10 3.2 odd 2
3024.2.ca.b.2033.3 10 252.223 even 6
3024.2.ca.b.2609.3 10 84.23 even 6
3024.2.df.b.17.3 10 84.83 odd 2
3024.2.df.b.1601.3 10 252.79 odd 6