Properties

Label 189.2.f.b.64.2
Level $189$
Weight $2$
Character 189.64
Analytic conductor $1.509$
Analytic rank $0$
Dimension $6$
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] = [189,2,Mod(64,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.f (of order \(3\), 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: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 64.2
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 189.64
Dual form 189.2.f.b.127.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.673648 + 1.16679i) q^{2} +(0.0923963 - 0.160035i) q^{4} +(1.26604 - 2.19285i) q^{5} +(-0.500000 - 0.866025i) q^{7} +2.94356 q^{8} +O(q^{10})\) \(q+(0.673648 + 1.16679i) q^{2} +(0.0923963 - 0.160035i) q^{4} +(1.26604 - 2.19285i) q^{5} +(-0.500000 - 0.866025i) q^{7} +2.94356 q^{8} +3.41147 q^{10} +(0.233956 + 0.405223i) q^{11} +(-2.91147 + 5.04282i) q^{13} +(0.673648 - 1.16679i) q^{14} +(1.79813 + 3.11446i) q^{16} -3.87939 q^{17} -2.18479 q^{19} +(-0.233956 - 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +(-0.0530334 + 0.0918566i) q^{23} +(-0.705737 - 1.22237i) q^{25} -7.84524 q^{26} -0.184793 q^{28} +(4.39053 + 7.60462i) q^{29} +(3.84002 - 6.65111i) q^{31} +(0.520945 - 0.902302i) q^{32} +(-2.61334 - 4.52644i) q^{34} -2.53209 q^{35} -7.68004 q^{37} +(-1.47178 - 2.54920i) q^{38} +(3.72668 - 6.45480i) q^{40} +(-1.11334 + 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +0.0864665 q^{44} -0.142903 q^{46} +(-2.66637 - 4.61830i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.950837 - 1.64690i) q^{50} +(0.538019 + 0.931876i) q^{52} +0.716881 q^{53} +1.18479 q^{55} +(-1.47178 - 2.54920i) q^{56} +(-5.91534 + 10.2457i) q^{58} +(0.368241 - 0.637812i) q^{59} +(-0.479055 - 0.829748i) q^{61} +10.3473 q^{62} +8.59627 q^{64} +(7.37211 + 12.7689i) q^{65} +(4.81908 - 8.34689i) q^{67} +(-0.358441 + 0.620838i) q^{68} +(-1.70574 - 2.95442i) q^{70} -13.2344 q^{71} -10.2686 q^{73} +(-5.17365 - 8.96102i) q^{74} +(-0.201867 + 0.349643i) q^{76} +(0.233956 - 0.405223i) q^{77} +(6.31908 + 10.9450i) q^{79} +9.10607 q^{80} -3.00000 q^{82} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(0.826352 - 1.43128i) q^{86} +(0.688663 + 1.19280i) q^{88} +8.11381 q^{89} +5.82295 q^{91} +(0.00980018 + 0.0169744i) q^{92} +(3.59240 - 6.22221i) q^{94} +(-2.76604 + 4.79093i) q^{95} +(6.80200 + 11.7814i) q^{97} -1.34730 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 3 q^{14} - 3 q^{16} - 12 q^{17} - 6 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} + 6 q^{26} + 6 q^{28} + 9 q^{29} + 3 q^{31} - 9 q^{34} - 6 q^{35} - 6 q^{37} + 6 q^{38} + 9 q^{40} + 3 q^{43} - 30 q^{44} + 3 q^{47} - 3 q^{49} - 6 q^{50} + 21 q^{52} - 12 q^{53} + 6 q^{56} + 9 q^{58} - 3 q^{59} - 6 q^{61} + 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} + 6 q^{68} - 18 q^{71} - 42 q^{73} - 30 q^{74} - 15 q^{76} + 6 q^{77} + 21 q^{79} + 30 q^{80} - 18 q^{82} - 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} - 24 q^{89} - 6 q^{91} + 3 q^{92} + 18 q^{94} - 12 q^{95} + 3 q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.673648 + 1.16679i 0.476341 + 0.825047i 0.999633 0.0271067i \(-0.00862938\pi\)
−0.523291 + 0.852154i \(0.675296\pi\)
\(3\) 0 0
\(4\) 0.0923963 0.160035i 0.0461981 0.0800175i
\(5\) 1.26604 2.19285i 0.566192 0.980674i −0.430745 0.902473i \(-0.641749\pi\)
0.996938 0.0782003i \(-0.0249174\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 2.94356 1.04071
\(9\) 0 0
\(10\) 3.41147 1.07880
\(11\) 0.233956 + 0.405223i 0.0705403 + 0.122179i 0.899138 0.437665i \(-0.144194\pi\)
−0.828598 + 0.559844i \(0.810861\pi\)
\(12\) 0 0
\(13\) −2.91147 + 5.04282i −0.807498 + 1.39863i 0.107094 + 0.994249i \(0.465845\pi\)
−0.914592 + 0.404378i \(0.867488\pi\)
\(14\) 0.673648 1.16679i 0.180040 0.311839i
\(15\) 0 0
\(16\) 1.79813 + 3.11446i 0.449533 + 0.778615i
\(17\) −3.87939 −0.940889 −0.470445 0.882430i \(-0.655906\pi\)
−0.470445 + 0.882430i \(0.655906\pi\)
\(18\) 0 0
\(19\) −2.18479 −0.501226 −0.250613 0.968087i \(-0.580632\pi\)
−0.250613 + 0.968087i \(0.580632\pi\)
\(20\) −0.233956 0.405223i −0.0523141 0.0906106i
\(21\) 0 0
\(22\) −0.315207 + 0.545955i −0.0672025 + 0.116398i
\(23\) −0.0530334 + 0.0918566i −0.0110582 + 0.0191534i −0.871502 0.490393i \(-0.836853\pi\)
0.860443 + 0.509546i \(0.170187\pi\)
\(24\) 0 0
\(25\) −0.705737 1.22237i −0.141147 0.244474i
\(26\) −7.84524 −1.53858
\(27\) 0 0
\(28\) −0.184793 −0.0349225
\(29\) 4.39053 + 7.60462i 0.815301 + 1.41214i 0.909112 + 0.416552i \(0.136762\pi\)
−0.0938108 + 0.995590i \(0.529905\pi\)
\(30\) 0 0
\(31\) 3.84002 6.65111i 0.689688 1.19458i −0.282250 0.959341i \(-0.591081\pi\)
0.971939 0.235235i \(-0.0755858\pi\)
\(32\) 0.520945 0.902302i 0.0920909 0.159506i
\(33\) 0 0
\(34\) −2.61334 4.52644i −0.448184 0.776278i
\(35\) −2.53209 −0.428001
\(36\) 0 0
\(37\) −7.68004 −1.26259 −0.631296 0.775542i \(-0.717477\pi\)
−0.631296 + 0.775542i \(0.717477\pi\)
\(38\) −1.47178 2.54920i −0.238754 0.413535i
\(39\) 0 0
\(40\) 3.72668 6.45480i 0.589240 1.02059i
\(41\) −1.11334 + 1.92836i −0.173875 + 0.301160i −0.939771 0.341804i \(-0.888962\pi\)
0.765897 + 0.642964i \(0.222295\pi\)
\(42\) 0 0
\(43\) −0.613341 1.06234i −0.0935336 0.162005i 0.815462 0.578811i \(-0.196483\pi\)
−0.908996 + 0.416806i \(0.863150\pi\)
\(44\) 0.0864665 0.0130353
\(45\) 0 0
\(46\) −0.142903 −0.0210700
\(47\) −2.66637 4.61830i −0.388931 0.673648i 0.603375 0.797457i \(-0.293822\pi\)
−0.992306 + 0.123810i \(0.960489\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0.950837 1.64690i 0.134469 0.232907i
\(51\) 0 0
\(52\) 0.538019 + 0.931876i 0.0746098 + 0.129228i
\(53\) 0.716881 0.0984712 0.0492356 0.998787i \(-0.484321\pi\)
0.0492356 + 0.998787i \(0.484321\pi\)
\(54\) 0 0
\(55\) 1.18479 0.159757
\(56\) −1.47178 2.54920i −0.196675 0.340651i
\(57\) 0 0
\(58\) −5.91534 + 10.2457i −0.776723 + 1.34532i
\(59\) 0.368241 0.637812i 0.0479409 0.0830360i −0.841059 0.540943i \(-0.818067\pi\)
0.889000 + 0.457907i \(0.151401\pi\)
\(60\) 0 0
\(61\) −0.479055 0.829748i −0.0613368 0.106238i 0.833726 0.552178i \(-0.186203\pi\)
−0.895063 + 0.445939i \(0.852870\pi\)
\(62\) 10.3473 1.31411
\(63\) 0 0
\(64\) 8.59627 1.07453
\(65\) 7.37211 + 12.7689i 0.914398 + 1.58378i
\(66\) 0 0
\(67\) 4.81908 8.34689i 0.588744 1.01973i −0.405653 0.914027i \(-0.632956\pi\)
0.994397 0.105708i \(-0.0337107\pi\)
\(68\) −0.358441 + 0.620838i −0.0434673 + 0.0752876i
\(69\) 0 0
\(70\) −1.70574 2.95442i −0.203875 0.353121i
\(71\) −13.2344 −1.57064 −0.785318 0.619092i \(-0.787501\pi\)
−0.785318 + 0.619092i \(0.787501\pi\)
\(72\) 0 0
\(73\) −10.2686 −1.20185 −0.600923 0.799307i \(-0.705200\pi\)
−0.600923 + 0.799307i \(0.705200\pi\)
\(74\) −5.17365 8.96102i −0.601424 1.04170i
\(75\) 0 0
\(76\) −0.201867 + 0.349643i −0.0231557 + 0.0401068i
\(77\) 0.233956 0.405223i 0.0266617 0.0461794i
\(78\) 0 0
\(79\) 6.31908 + 10.9450i 0.710952 + 1.23140i 0.964500 + 0.264082i \(0.0850689\pi\)
−0.253548 + 0.967323i \(0.581598\pi\)
\(80\) 9.10607 1.01809
\(81\) 0 0
\(82\) −3.00000 −0.331295
\(83\) −1.36571 2.36549i −0.149907 0.259646i 0.781286 0.624173i \(-0.214564\pi\)
−0.931193 + 0.364527i \(0.881231\pi\)
\(84\) 0 0
\(85\) −4.91147 + 8.50692i −0.532724 + 0.922705i
\(86\) 0.826352 1.43128i 0.0891078 0.154339i
\(87\) 0 0
\(88\) 0.688663 + 1.19280i 0.0734117 + 0.127153i
\(89\) 8.11381 0.860062 0.430031 0.902814i \(-0.358503\pi\)
0.430031 + 0.902814i \(0.358503\pi\)
\(90\) 0 0
\(91\) 5.82295 0.610411
\(92\) 0.00980018 + 0.0169744i 0.00102174 + 0.00176970i
\(93\) 0 0
\(94\) 3.59240 6.22221i 0.370527 0.641772i
\(95\) −2.76604 + 4.79093i −0.283790 + 0.491539i
\(96\) 0 0
\(97\) 6.80200 + 11.7814i 0.690639 + 1.19622i 0.971629 + 0.236511i \(0.0760039\pi\)
−0.280990 + 0.959711i \(0.590663\pi\)
\(98\) −1.34730 −0.136097
\(99\) 0 0
\(100\) −0.260830 −0.0260830
\(101\) −4.78699 8.29131i −0.476323 0.825016i 0.523309 0.852143i \(-0.324697\pi\)
−0.999632 + 0.0271271i \(0.991364\pi\)
\(102\) 0 0
\(103\) −1.52094 + 2.63435i −0.149863 + 0.259571i −0.931177 0.364568i \(-0.881217\pi\)
0.781314 + 0.624139i \(0.214550\pi\)
\(104\) −8.57011 + 14.8439i −0.840368 + 1.45556i
\(105\) 0 0
\(106\) 0.482926 + 0.836452i 0.0469059 + 0.0812434i
\(107\) 6.51754 0.630074 0.315037 0.949079i \(-0.397983\pi\)
0.315037 + 0.949079i \(0.397983\pi\)
\(108\) 0 0
\(109\) 10.6382 1.01895 0.509475 0.860485i \(-0.329840\pi\)
0.509475 + 0.860485i \(0.329840\pi\)
\(110\) 0.798133 + 1.38241i 0.0760990 + 0.131807i
\(111\) 0 0
\(112\) 1.79813 3.11446i 0.169908 0.294289i
\(113\) 2.58853 4.48346i 0.243508 0.421768i −0.718203 0.695834i \(-0.755035\pi\)
0.961711 + 0.274065i \(0.0883684\pi\)
\(114\) 0 0
\(115\) 0.134285 + 0.232589i 0.0125222 + 0.0216890i
\(116\) 1.62267 0.150662
\(117\) 0 0
\(118\) 0.992259 0.0913449
\(119\) 1.93969 + 3.35965i 0.177811 + 0.307978i
\(120\) 0 0
\(121\) 5.39053 9.33667i 0.490048 0.848788i
\(122\) 0.645430 1.11792i 0.0584345 0.101211i
\(123\) 0 0
\(124\) −0.709607 1.22908i −0.0637246 0.110374i
\(125\) 9.08647 0.812718
\(126\) 0 0
\(127\) −8.88207 −0.788157 −0.394078 0.919077i \(-0.628936\pi\)
−0.394078 + 0.919077i \(0.628936\pi\)
\(128\) 4.74897 + 8.22546i 0.419754 + 0.727035i
\(129\) 0 0
\(130\) −9.93242 + 17.2035i −0.871131 + 1.50884i
\(131\) 5.68139 9.84045i 0.496385 0.859764i −0.503606 0.863933i \(-0.667994\pi\)
0.999991 + 0.00416893i \(0.00132701\pi\)
\(132\) 0 0
\(133\) 1.09240 + 1.89209i 0.0947228 + 0.164065i
\(134\) 12.9855 1.12177
\(135\) 0 0
\(136\) −11.4192 −0.979190
\(137\) −2.86231 4.95767i −0.244544 0.423562i 0.717459 0.696600i \(-0.245305\pi\)
−0.962003 + 0.273038i \(0.911972\pi\)
\(138\) 0 0
\(139\) 0.461981 0.800175i 0.0391847 0.0678700i −0.845768 0.533551i \(-0.820857\pi\)
0.884953 + 0.465681i \(0.154191\pi\)
\(140\) −0.233956 + 0.405223i −0.0197729 + 0.0342476i
\(141\) 0 0
\(142\) −8.91534 15.4418i −0.748159 1.29585i
\(143\) −2.72462 −0.227844
\(144\) 0 0
\(145\) 22.2344 1.84647
\(146\) −6.91740 11.9813i −0.572488 0.991579i
\(147\) 0 0
\(148\) −0.709607 + 1.22908i −0.0583294 + 0.101029i
\(149\) 4.36231 7.55574i 0.357374 0.618991i −0.630147 0.776476i \(-0.717005\pi\)
0.987521 + 0.157485i \(0.0503387\pi\)
\(150\) 0 0
\(151\) −9.21348 15.9582i −0.749782 1.29866i −0.947927 0.318488i \(-0.896825\pi\)
0.198145 0.980173i \(-0.436508\pi\)
\(152\) −6.43107 −0.521629
\(153\) 0 0
\(154\) 0.630415 0.0508003
\(155\) −9.72328 16.8412i −0.780992 1.35272i
\(156\) 0 0
\(157\) −2.46198 + 4.26428i −0.196488 + 0.340326i −0.947387 0.320090i \(-0.896287\pi\)
0.750900 + 0.660416i \(0.229620\pi\)
\(158\) −8.51367 + 14.7461i −0.677311 + 1.17314i
\(159\) 0 0
\(160\) −1.31908 2.28471i −0.104282 0.180622i
\(161\) 0.106067 0.00835924
\(162\) 0 0
\(163\) 7.63816 0.598267 0.299133 0.954211i \(-0.403302\pi\)
0.299133 + 0.954211i \(0.403302\pi\)
\(164\) 0.205737 + 0.356347i 0.0160654 + 0.0278260i
\(165\) 0 0
\(166\) 1.84002 3.18701i 0.142813 0.247360i
\(167\) −2.82770 + 4.89771i −0.218814 + 0.378996i −0.954446 0.298385i \(-0.903552\pi\)
0.735632 + 0.677382i \(0.236885\pi\)
\(168\) 0 0
\(169\) −10.4534 18.1058i −0.804105 1.39275i
\(170\) −13.2344 −1.01503
\(171\) 0 0
\(172\) −0.226682 −0.0172843
\(173\) 10.5346 + 18.2465i 0.800932 + 1.38725i 0.919003 + 0.394250i \(0.128995\pi\)
−0.118071 + 0.993005i \(0.537671\pi\)
\(174\) 0 0
\(175\) −0.705737 + 1.22237i −0.0533487 + 0.0924027i
\(176\) −0.841367 + 1.45729i −0.0634204 + 0.109847i
\(177\) 0 0
\(178\) 5.46585 + 9.46713i 0.409683 + 0.709592i
\(179\) 5.12061 0.382733 0.191366 0.981519i \(-0.438708\pi\)
0.191366 + 0.981519i \(0.438708\pi\)
\(180\) 0 0
\(181\) −0.319955 −0.0237821 −0.0118910 0.999929i \(-0.503785\pi\)
−0.0118910 + 0.999929i \(0.503785\pi\)
\(182\) 3.92262 + 6.79417i 0.290764 + 0.503618i
\(183\) 0 0
\(184\) −0.156107 + 0.270386i −0.0115084 + 0.0199331i
\(185\) −9.72328 + 16.8412i −0.714870 + 1.23819i
\(186\) 0 0
\(187\) −0.907604 1.57202i −0.0663706 0.114957i
\(188\) −0.985452 −0.0718715
\(189\) 0 0
\(190\) −7.45336 −0.540724
\(191\) −7.78359 13.4816i −0.563200 0.975492i −0.997215 0.0745858i \(-0.976237\pi\)
0.434014 0.900906i \(-0.357097\pi\)
\(192\) 0 0
\(193\) −3.02094 + 5.23243i −0.217452 + 0.376639i −0.954028 0.299716i \(-0.903108\pi\)
0.736576 + 0.676355i \(0.236441\pi\)
\(194\) −9.16431 + 15.8731i −0.657959 + 1.13962i
\(195\) 0 0
\(196\) 0.0923963 + 0.160035i 0.00659973 + 0.0114311i
\(197\) −25.2344 −1.79788 −0.898939 0.438074i \(-0.855661\pi\)
−0.898939 + 0.438074i \(0.855661\pi\)
\(198\) 0 0
\(199\) 3.04189 0.215634 0.107817 0.994171i \(-0.465614\pi\)
0.107817 + 0.994171i \(0.465614\pi\)
\(200\) −2.07738 3.59813i −0.146893 0.254426i
\(201\) 0 0
\(202\) 6.44949 11.1708i 0.453785 0.785978i
\(203\) 4.39053 7.60462i 0.308155 0.533740i
\(204\) 0 0
\(205\) 2.81908 + 4.88279i 0.196893 + 0.341029i
\(206\) −4.09833 −0.285544
\(207\) 0 0
\(208\) −20.9409 −1.45199
\(209\) −0.511144 0.885328i −0.0353566 0.0612394i
\(210\) 0 0
\(211\) 2.72668 4.72275i 0.187713 0.325128i −0.756775 0.653676i \(-0.773226\pi\)
0.944487 + 0.328548i \(0.106559\pi\)
\(212\) 0.0662372 0.114726i 0.00454919 0.00787942i
\(213\) 0 0
\(214\) 4.39053 + 7.60462i 0.300130 + 0.519841i
\(215\) −3.10607 −0.211832
\(216\) 0 0
\(217\) −7.68004 −0.521355
\(218\) 7.16637 + 12.4125i 0.485368 + 0.840682i
\(219\) 0 0
\(220\) 0.109470 0.189608i 0.00738049 0.0127834i
\(221\) 11.2947 19.5630i 0.759766 1.31595i
\(222\) 0 0
\(223\) −7.09627 12.2911i −0.475201 0.823073i 0.524395 0.851475i \(-0.324291\pi\)
−0.999597 + 0.0284023i \(0.990958\pi\)
\(224\) −1.04189 −0.0696141
\(225\) 0 0
\(226\) 6.97502 0.463972
\(227\) −1.44697 2.50622i −0.0960385 0.166344i 0.814003 0.580861i \(-0.197284\pi\)
−0.910042 + 0.414517i \(0.863951\pi\)
\(228\) 0 0
\(229\) −4.58378 + 7.93934i −0.302905 + 0.524646i −0.976793 0.214187i \(-0.931290\pi\)
0.673888 + 0.738834i \(0.264623\pi\)
\(230\) −0.180922 + 0.313366i −0.0119297 + 0.0206628i
\(231\) 0 0
\(232\) 12.9238 + 22.3847i 0.848489 + 1.46963i
\(233\) −13.2713 −0.869429 −0.434715 0.900568i \(-0.643151\pi\)
−0.434715 + 0.900568i \(0.643151\pi\)
\(234\) 0 0
\(235\) −13.5030 −0.880838
\(236\) −0.0680482 0.117863i −0.00442956 0.00767222i
\(237\) 0 0
\(238\) −2.61334 + 4.52644i −0.169398 + 0.293405i
\(239\) 4.76857 8.25941i 0.308453 0.534257i −0.669571 0.742748i \(-0.733522\pi\)
0.978024 + 0.208491i \(0.0668553\pi\)
\(240\) 0 0
\(241\) 4.47906 + 7.75795i 0.288521 + 0.499734i 0.973457 0.228870i \(-0.0735031\pi\)
−0.684936 + 0.728604i \(0.740170\pi\)
\(242\) 14.5253 0.933720
\(243\) 0 0
\(244\) −0.177052 −0.0113346
\(245\) 1.26604 + 2.19285i 0.0808846 + 0.140096i
\(246\) 0 0
\(247\) 6.36097 11.0175i 0.404739 0.701028i
\(248\) 11.3033 19.5780i 0.717763 1.24320i
\(249\) 0 0
\(250\) 6.12108 + 10.6020i 0.387131 + 0.670531i
\(251\) 24.9982 1.57788 0.788938 0.614473i \(-0.210631\pi\)
0.788938 + 0.614473i \(0.210631\pi\)
\(252\) 0 0
\(253\) −0.0496299 −0.00312020
\(254\) −5.98339 10.3635i −0.375431 0.650266i
\(255\) 0 0
\(256\) 2.19800 3.80704i 0.137375 0.237940i
\(257\) 5.42602 9.39815i 0.338466 0.586240i −0.645678 0.763609i \(-0.723425\pi\)
0.984144 + 0.177369i \(0.0567587\pi\)
\(258\) 0 0
\(259\) 3.84002 + 6.65111i 0.238607 + 0.413280i
\(260\) 2.72462 0.168974
\(261\) 0 0
\(262\) 15.3090 0.945795
\(263\) 13.0437 + 22.5924i 0.804309 + 1.39310i 0.916757 + 0.399446i \(0.130798\pi\)
−0.112448 + 0.993658i \(0.535869\pi\)
\(264\) 0 0
\(265\) 0.907604 1.57202i 0.0557537 0.0965682i
\(266\) −1.47178 + 2.54920i −0.0902407 + 0.156302i
\(267\) 0 0
\(268\) −0.890530 1.54244i −0.0543978 0.0942197i
\(269\) 7.63310 0.465399 0.232699 0.972549i \(-0.425244\pi\)
0.232699 + 0.972549i \(0.425244\pi\)
\(270\) 0 0
\(271\) 3.40373 0.206762 0.103381 0.994642i \(-0.467034\pi\)
0.103381 + 0.994642i \(0.467034\pi\)
\(272\) −6.97565 12.0822i −0.422961 0.732590i
\(273\) 0 0
\(274\) 3.85638 6.67945i 0.232973 0.403520i
\(275\) 0.330222 0.571962i 0.0199131 0.0344906i
\(276\) 0 0
\(277\) 2.86097 + 4.95534i 0.171899 + 0.297738i 0.939084 0.343689i \(-0.111676\pi\)
−0.767185 + 0.641426i \(0.778343\pi\)
\(278\) 1.24485 0.0746612
\(279\) 0 0
\(280\) −7.45336 −0.445424
\(281\) 14.1887 + 24.5755i 0.846425 + 1.46605i 0.884378 + 0.466771i \(0.154583\pi\)
−0.0379535 + 0.999280i \(0.512084\pi\)
\(282\) 0 0
\(283\) −2.28564 + 3.95885i −0.135867 + 0.235329i −0.925929 0.377699i \(-0.876715\pi\)
0.790061 + 0.613028i \(0.210049\pi\)
\(284\) −1.22281 + 2.11797i −0.0725605 + 0.125678i
\(285\) 0 0
\(286\) −1.83544 3.17907i −0.108532 0.187982i
\(287\) 2.22668 0.131437
\(288\) 0 0
\(289\) −1.95037 −0.114728
\(290\) 14.9782 + 25.9430i 0.879549 + 1.52342i
\(291\) 0 0
\(292\) −0.948778 + 1.64333i −0.0555230 + 0.0961687i
\(293\) 2.16385 3.74789i 0.126413 0.218954i −0.795871 0.605466i \(-0.792987\pi\)
0.922285 + 0.386512i \(0.126320\pi\)
\(294\) 0 0
\(295\) −0.932419 1.61500i −0.0542875 0.0940287i
\(296\) −22.6067 −1.31399
\(297\) 0 0
\(298\) 11.7547 0.680929
\(299\) −0.308811 0.534876i −0.0178590 0.0309327i
\(300\) 0 0
\(301\) −0.613341 + 1.06234i −0.0353524 + 0.0612321i
\(302\) 12.4133 21.5004i 0.714304 1.23721i
\(303\) 0 0
\(304\) −3.92855 6.80445i −0.225318 0.390262i
\(305\) −2.42602 −0.138914
\(306\) 0 0
\(307\) 12.3773 0.706411 0.353206 0.935546i \(-0.385092\pi\)
0.353206 + 0.935546i \(0.385092\pi\)
\(308\) −0.0432332 0.0748822i −0.00246344 0.00426681i
\(309\) 0 0
\(310\) 13.1001 22.6901i 0.744038 1.28871i
\(311\) −10.9927 + 19.0400i −0.623340 + 1.07966i 0.365519 + 0.930804i \(0.380892\pi\)
−0.988859 + 0.148853i \(0.952442\pi\)
\(312\) 0 0
\(313\) 6.94491 + 12.0289i 0.392549 + 0.679915i 0.992785 0.119908i \(-0.0382599\pi\)
−0.600236 + 0.799823i \(0.704927\pi\)
\(314\) −6.63404 −0.374380
\(315\) 0 0
\(316\) 2.33544 0.131379
\(317\) −3.09105 5.35386i −0.173611 0.300703i 0.766069 0.642759i \(-0.222210\pi\)
−0.939680 + 0.342056i \(0.888877\pi\)
\(318\) 0 0
\(319\) −2.05438 + 3.55829i −0.115023 + 0.199226i
\(320\) 10.8833 18.8504i 0.608392 1.05377i
\(321\) 0 0
\(322\) 0.0714517 + 0.123758i 0.00398185 + 0.00689677i
\(323\) 8.47565 0.471598
\(324\) 0 0
\(325\) 8.21894 0.455905
\(326\) 5.14543 + 8.91215i 0.284979 + 0.493598i
\(327\) 0 0
\(328\) −3.27719 + 5.67626i −0.180952 + 0.313419i
\(329\) −2.66637 + 4.61830i −0.147002 + 0.254615i
\(330\) 0 0
\(331\) −5.36571 9.29369i −0.294926 0.510827i 0.680041 0.733174i \(-0.261962\pi\)
−0.974968 + 0.222346i \(0.928628\pi\)
\(332\) −0.504748 −0.0277016
\(333\) 0 0
\(334\) −7.61949 −0.416920
\(335\) −12.2023 21.1351i −0.666685 1.15473i
\(336\) 0 0
\(337\) 9.29726 16.1033i 0.506454 0.877204i −0.493518 0.869735i \(-0.664289\pi\)
0.999972 0.00746831i \(-0.00237726\pi\)
\(338\) 14.0838 24.3938i 0.766057 1.32685i
\(339\) 0 0
\(340\) 0.907604 + 1.57202i 0.0492217 + 0.0852545i
\(341\) 3.59358 0.194603
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −1.80541 3.12706i −0.0973410 0.168600i
\(345\) 0 0
\(346\) −14.1932 + 24.5834i −0.763034 + 1.32161i
\(347\) −10.2062 + 17.6777i −0.547898 + 0.948987i 0.450521 + 0.892766i \(0.351238\pi\)
−0.998418 + 0.0562207i \(0.982095\pi\)
\(348\) 0 0
\(349\) 1.78106 + 3.08489i 0.0953379 + 0.165130i 0.909750 0.415157i \(-0.136274\pi\)
−0.814412 + 0.580288i \(0.802940\pi\)
\(350\) −1.90167 −0.101649
\(351\) 0 0
\(352\) 0.487511 0.0259844
\(353\) 5.01114 + 8.67956i 0.266716 + 0.461966i 0.968012 0.250904i \(-0.0807280\pi\)
−0.701296 + 0.712871i \(0.747395\pi\)
\(354\) 0 0
\(355\) −16.7554 + 29.0211i −0.889283 + 1.54028i
\(356\) 0.749686 1.29849i 0.0397333 0.0688200i
\(357\) 0 0
\(358\) 3.44949 + 5.97470i 0.182311 + 0.315773i
\(359\) −9.48070 −0.500372 −0.250186 0.968198i \(-0.580492\pi\)
−0.250186 + 0.968198i \(0.580492\pi\)
\(360\) 0 0
\(361\) −14.2267 −0.748773
\(362\) −0.215537 0.373321i −0.0113284 0.0196213i
\(363\) 0 0
\(364\) 0.538019 0.931876i 0.0281998 0.0488436i
\(365\) −13.0005 + 22.5175i −0.680476 + 1.17862i
\(366\) 0 0
\(367\) −8.06670 13.9719i −0.421079 0.729329i 0.574967 0.818177i \(-0.305015\pi\)
−0.996045 + 0.0888474i \(0.971682\pi\)
\(368\) −0.381445 −0.0198842
\(369\) 0 0
\(370\) −26.2003 −1.36209
\(371\) −0.358441 0.620838i −0.0186093 0.0322323i
\(372\) 0 0
\(373\) −7.02481 + 12.1673i −0.363731 + 0.630001i −0.988572 0.150752i \(-0.951831\pi\)
0.624841 + 0.780752i \(0.285164\pi\)
\(374\) 1.22281 2.11797i 0.0632301 0.109518i
\(375\) 0 0
\(376\) −7.84864 13.5942i −0.404763 0.701070i
\(377\) −51.1317 −2.63341
\(378\) 0 0
\(379\) 16.0574 0.824812 0.412406 0.911000i \(-0.364689\pi\)
0.412406 + 0.911000i \(0.364689\pi\)
\(380\) 0.511144 + 0.885328i 0.0262212 + 0.0454164i
\(381\) 0 0
\(382\) 10.4868 18.1637i 0.536551 0.929334i
\(383\) −16.0103 + 27.7306i −0.818086 + 1.41697i 0.0890039 + 0.996031i \(0.471632\pi\)
−0.907090 + 0.420936i \(0.861702\pi\)
\(384\) 0 0
\(385\) −0.592396 1.02606i −0.0301913 0.0522929i
\(386\) −8.14022 −0.414326
\(387\) 0 0
\(388\) 2.51392 0.127625
\(389\) −15.0214 26.0178i −0.761616 1.31916i −0.942017 0.335564i \(-0.891073\pi\)
0.180402 0.983593i \(-0.442260\pi\)
\(390\) 0 0
\(391\) 0.205737 0.356347i 0.0104046 0.0180212i
\(392\) −1.47178 + 2.54920i −0.0743362 + 0.128754i
\(393\) 0 0
\(394\) −16.9991 29.4433i −0.856403 1.48333i
\(395\) 32.0009 1.61014
\(396\) 0 0
\(397\) −12.3200 −0.618321 −0.309160 0.951010i \(-0.600048\pi\)
−0.309160 + 0.951010i \(0.600048\pi\)
\(398\) 2.04916 + 3.54925i 0.102715 + 0.177908i
\(399\) 0 0
\(400\) 2.53802 4.39598i 0.126901 0.219799i
\(401\) 10.4880 18.1657i 0.523745 0.907152i −0.475873 0.879514i \(-0.657868\pi\)
0.999618 0.0276385i \(-0.00879873\pi\)
\(402\) 0 0
\(403\) 22.3603 + 38.7291i 1.11384 + 1.92923i
\(404\) −1.76920 −0.0880210
\(405\) 0 0
\(406\) 11.8307 0.587147
\(407\) −1.79679 3.11213i −0.0890635 0.154263i
\(408\) 0 0
\(409\) −12.8307 + 22.2234i −0.634437 + 1.09888i 0.352197 + 0.935926i \(0.385435\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(410\) −3.79813 + 6.57856i −0.187576 + 0.324892i
\(411\) 0 0
\(412\) 0.281059 + 0.486809i 0.0138468 + 0.0239833i
\(413\) −0.736482 −0.0362399
\(414\) 0 0
\(415\) −6.91622 −0.339504
\(416\) 3.03343 + 5.25406i 0.148726 + 0.257601i
\(417\) 0 0
\(418\) 0.688663 1.19280i 0.0336836 0.0583417i
\(419\) −0.739885 + 1.28152i −0.0361458 + 0.0626063i −0.883532 0.468370i \(-0.844841\pi\)
0.847387 + 0.530976i \(0.178175\pi\)
\(420\) 0 0
\(421\) −6.55350 11.3510i −0.319398 0.553214i 0.660965 0.750417i \(-0.270147\pi\)
−0.980363 + 0.197203i \(0.936814\pi\)
\(422\) 7.34730 0.357661
\(423\) 0 0
\(424\) 2.11019 0.102480
\(425\) 2.73783 + 4.74205i 0.132804 + 0.230023i
\(426\) 0 0
\(427\) −0.479055 + 0.829748i −0.0231831 + 0.0401543i
\(428\) 0.602196 1.04303i 0.0291083 0.0504170i
\(429\) 0 0
\(430\) −2.09240 3.62414i −0.100904 0.174771i
\(431\) −17.7270 −0.853879 −0.426939 0.904280i \(-0.640408\pi\)
−0.426939 + 0.904280i \(0.640408\pi\)
\(432\) 0 0
\(433\) −5.83843 −0.280577 −0.140289 0.990111i \(-0.544803\pi\)
−0.140289 + 0.990111i \(0.544803\pi\)
\(434\) −5.17365 8.96102i −0.248343 0.430143i
\(435\) 0 0
\(436\) 0.982926 1.70248i 0.0470736 0.0815339i
\(437\) 0.115867 0.200688i 0.00554267 0.00960019i
\(438\) 0 0
\(439\) −14.9277 25.8555i −0.712459 1.23401i −0.963931 0.266151i \(-0.914248\pi\)
0.251473 0.967864i \(-0.419085\pi\)
\(440\) 3.48751 0.166261
\(441\) 0 0
\(442\) 30.4347 1.44763
\(443\) 5.33275 + 9.23659i 0.253367 + 0.438844i 0.964451 0.264263i \(-0.0851288\pi\)
−0.711084 + 0.703107i \(0.751795\pi\)
\(444\) 0 0
\(445\) 10.2724 17.7924i 0.486960 0.843440i
\(446\) 9.56077 16.5597i 0.452716 0.784127i
\(447\) 0 0
\(448\) −4.29813 7.44459i −0.203068 0.351724i
\(449\) −3.55438 −0.167741 −0.0838707 0.996477i \(-0.526728\pi\)
−0.0838707 + 0.996477i \(0.526728\pi\)
\(450\) 0 0
\(451\) −1.04189 −0.0490606
\(452\) −0.478340 0.828510i −0.0224992 0.0389698i
\(453\) 0 0
\(454\) 1.94949 3.37662i 0.0914942 0.158473i
\(455\) 7.37211 12.7689i 0.345610 0.598614i
\(456\) 0 0
\(457\) −2.51161 4.35024i −0.117488 0.203496i 0.801283 0.598285i \(-0.204151\pi\)
−0.918772 + 0.394789i \(0.870818\pi\)
\(458\) −12.3514 −0.577144
\(459\) 0 0
\(460\) 0.0496299 0.00231400
\(461\) 9.23055 + 15.9878i 0.429910 + 0.744625i 0.996865 0.0791233i \(-0.0252121\pi\)
−0.566955 + 0.823749i \(0.691879\pi\)
\(462\) 0 0
\(463\) 7.11721 12.3274i 0.330765 0.572902i −0.651897 0.758307i \(-0.726027\pi\)
0.982662 + 0.185406i \(0.0593600\pi\)
\(464\) −15.7895 + 27.3482i −0.733010 + 1.26961i
\(465\) 0 0
\(466\) −8.94016 15.4848i −0.414145 0.717320i
\(467\) 3.36865 0.155883 0.0779413 0.996958i \(-0.475165\pi\)
0.0779413 + 0.996958i \(0.475165\pi\)
\(468\) 0 0
\(469\) −9.63816 −0.445049
\(470\) −9.09627 15.7552i −0.419579 0.726733i
\(471\) 0 0
\(472\) 1.08394 1.87744i 0.0498924 0.0864162i
\(473\) 0.286989 0.497079i 0.0131958 0.0228557i
\(474\) 0 0
\(475\) 1.54189 + 2.67063i 0.0707467 + 0.122537i
\(476\) 0.716881 0.0328582
\(477\) 0 0
\(478\) 12.8494 0.587716
\(479\) −18.3833 31.8407i −0.839952 1.45484i −0.889934 0.456090i \(-0.849249\pi\)
0.0499812 0.998750i \(-0.484084\pi\)
\(480\) 0 0
\(481\) 22.3603 38.7291i 1.01954 1.76589i
\(482\) −6.03462 + 10.4523i −0.274869 + 0.476087i
\(483\) 0 0
\(484\) −0.996130 1.72535i −0.0452786 0.0784249i
\(485\) 34.4466 1.56414
\(486\) 0 0
\(487\) −37.4175 −1.69555 −0.847773 0.530358i \(-0.822057\pi\)
−0.847773 + 0.530358i \(0.822057\pi\)
\(488\) −1.41013 2.44242i −0.0638336 0.110563i
\(489\) 0 0
\(490\) −1.70574 + 2.95442i −0.0770573 + 0.133467i
\(491\) −13.3353 + 23.0974i −0.601813 + 1.04237i 0.390734 + 0.920504i \(0.372221\pi\)
−0.992547 + 0.121866i \(0.961112\pi\)
\(492\) 0 0
\(493\) −17.0326 29.5013i −0.767108 1.32867i
\(494\) 17.1402 0.771175
\(495\) 0 0
\(496\) 27.6195 1.24015
\(497\) 6.61721 + 11.4613i 0.296822 + 0.514112i
\(498\) 0 0
\(499\) −16.8726 + 29.2242i −0.755320 + 1.30825i 0.189895 + 0.981804i \(0.439185\pi\)
−0.945215 + 0.326449i \(0.894148\pi\)
\(500\) 0.839556 1.45415i 0.0375461 0.0650317i
\(501\) 0 0
\(502\) 16.8400 + 29.1678i 0.751607 + 1.30182i
\(503\) 32.0401 1.42860 0.714299 0.699840i \(-0.246745\pi\)
0.714299 + 0.699840i \(0.246745\pi\)
\(504\) 0 0
\(505\) −24.2422 −1.07876
\(506\) −0.0334331 0.0579078i −0.00148628 0.00257431i
\(507\) 0 0
\(508\) −0.820670 + 1.42144i −0.0364114 + 0.0630663i
\(509\) −3.96926 + 6.87495i −0.175934 + 0.304727i −0.940484 0.339838i \(-0.889628\pi\)
0.764550 + 0.644564i \(0.222961\pi\)
\(510\) 0 0
\(511\) 5.13429 + 8.89284i 0.227127 + 0.393396i
\(512\) 24.9186 1.10126
\(513\) 0 0
\(514\) 14.6209 0.644901
\(515\) 3.85117 + 6.67042i 0.169703 + 0.293934i
\(516\) 0 0
\(517\) 1.24763 2.16095i 0.0548705 0.0950386i
\(518\) −5.17365 + 8.96102i −0.227317 + 0.393725i
\(519\) 0 0
\(520\) 21.7003 + 37.5860i 0.951620 + 1.64825i
\(521\) 14.6750 0.642923 0.321462 0.946923i \(-0.395826\pi\)
0.321462 + 0.946923i \(0.395826\pi\)
\(522\) 0 0
\(523\) 28.3432 1.23936 0.619680 0.784854i \(-0.287262\pi\)
0.619680 + 0.784854i \(0.287262\pi\)
\(524\) −1.04988 1.81844i −0.0458641 0.0794390i
\(525\) 0 0
\(526\) −17.5737 + 30.4386i −0.766251 + 1.32719i
\(527\) −14.8969 + 25.8022i −0.648920 + 1.12396i
\(528\) 0 0
\(529\) 11.4944 + 19.9088i 0.499755 + 0.865602i
\(530\) 2.44562 0.106231
\(531\) 0 0
\(532\) 0.403733 0.0175041
\(533\) −6.48293 11.2288i −0.280807 0.486371i
\(534\) 0 0
\(535\) 8.25150 14.2920i 0.356743 0.617898i
\(536\) 14.1853 24.5696i 0.612710 1.06124i
\(537\) 0 0
\(538\) 5.14203 + 8.90625i 0.221688 + 0.383976i
\(539\) −0.467911 −0.0201544
\(540\) 0 0
\(541\) 11.2858 0.485215 0.242607 0.970125i \(-0.421997\pi\)
0.242607 + 0.970125i \(0.421997\pi\)
\(542\) 2.29292 + 3.97145i 0.0984893 + 0.170588i
\(543\) 0 0
\(544\) −2.02094 + 3.50038i −0.0866473 + 0.150077i
\(545\) 13.4684 23.3279i 0.576922 0.999258i
\(546\) 0 0
\(547\) 14.6202 + 25.3229i 0.625115 + 1.08273i 0.988519 + 0.151099i \(0.0482812\pi\)
−0.363404 + 0.931632i \(0.618385\pi\)
\(548\) −1.05787 −0.0451899
\(549\) 0 0
\(550\) 0.889814 0.0379418
\(551\) −9.59240 16.6145i −0.408650 0.707802i
\(552\) 0 0
\(553\) 6.31908 10.9450i 0.268715 0.465427i
\(554\) −3.85457 + 6.67631i −0.163765 + 0.283649i
\(555\) 0 0
\(556\) −0.0853707 0.147866i −0.00362052 0.00627093i
\(557\) 0.775682 0.0328667 0.0164334 0.999865i \(-0.494769\pi\)
0.0164334 + 0.999865i \(0.494769\pi\)
\(558\) 0 0
\(559\) 7.14290 0.302113
\(560\) −4.55303 7.88609i −0.192401 0.333248i
\(561\) 0 0
\(562\) −19.1163 + 33.1105i −0.806374 + 1.39668i
\(563\) 12.4761 21.6093i 0.525806 0.910722i −0.473742 0.880663i \(-0.657097\pi\)
0.999548 0.0300588i \(-0.00956944\pi\)
\(564\) 0 0
\(565\) −6.55438 11.3525i −0.275745 0.477604i
\(566\) −6.15888 −0.258877
\(567\) 0 0
\(568\) −38.9564 −1.63457
\(569\) −12.4017 21.4803i −0.519905 0.900502i −0.999732 0.0231391i \(-0.992634\pi\)
0.479827 0.877363i \(-0.340699\pi\)
\(570\) 0 0
\(571\) −4.39827 + 7.61803i −0.184062 + 0.318805i −0.943260 0.332055i \(-0.892258\pi\)
0.759198 + 0.650860i \(0.225591\pi\)
\(572\) −0.251745 + 0.436035i −0.0105260 + 0.0182315i
\(573\) 0 0
\(574\) 1.50000 + 2.59808i 0.0626088 + 0.108442i
\(575\) 0.149711 0.00624336
\(576\) 0 0
\(577\) −12.8743 −0.535965 −0.267983 0.963424i \(-0.586357\pi\)
−0.267983 + 0.963424i \(0.586357\pi\)
\(578\) −1.31386 2.27568i −0.0546495 0.0946557i
\(579\) 0 0
\(580\) 2.05438 3.55829i 0.0853034 0.147750i
\(581\) −1.36571 + 2.36549i −0.0566594 + 0.0981369i
\(582\) 0 0
\(583\) 0.167718 + 0.290497i 0.00694619 + 0.0120311i
\(584\) −30.2262 −1.25077
\(585\) 0 0
\(586\) 5.83069 0.240864
\(587\) 22.4315 + 38.8526i 0.925849 + 1.60362i 0.790190 + 0.612861i \(0.209982\pi\)
0.135658 + 0.990756i \(0.456685\pi\)
\(588\) 0 0
\(589\) −8.38965 + 14.5313i −0.345690 + 0.598752i
\(590\) 1.25624 2.17588i 0.0517188 0.0895795i
\(591\) 0 0
\(592\) −13.8097 23.9192i −0.567577 0.983072i
\(593\) −3.76053 −0.154426 −0.0772131 0.997015i \(-0.524602\pi\)
−0.0772131 + 0.997015i \(0.524602\pi\)
\(594\) 0 0
\(595\) 9.82295 0.402702
\(596\) −0.806123 1.39625i −0.0330201 0.0571924i
\(597\) 0 0
\(598\) 0.416060 0.720637i 0.0170139 0.0294690i
\(599\) −1.84524 + 3.19604i −0.0753943 + 0.130587i −0.901258 0.433283i \(-0.857355\pi\)
0.825863 + 0.563870i \(0.190688\pi\)
\(600\) 0 0
\(601\) 10.9285 + 18.9288i 0.445785 + 0.772122i 0.998107 0.0615091i \(-0.0195913\pi\)
−0.552322 + 0.833631i \(0.686258\pi\)
\(602\) −1.65270 −0.0673592
\(603\) 0 0
\(604\) −3.40516 −0.138554
\(605\) −13.6493 23.6413i −0.554923 0.961155i
\(606\) 0 0
\(607\) −12.1973 + 21.1263i −0.495072 + 0.857490i −0.999984 0.00568063i \(-0.998192\pi\)
0.504911 + 0.863171i \(0.331525\pi\)
\(608\) −1.13816 + 1.97134i −0.0461583 + 0.0799485i
\(609\) 0 0
\(610\) −1.63429 2.83067i −0.0661703 0.114610i
\(611\) 31.0523 1.25624
\(612\) 0 0
\(613\) 42.0215 1.69723 0.848616 0.529010i \(-0.177437\pi\)
0.848616 + 0.529010i \(0.177437\pi\)
\(614\) 8.33796 + 14.4418i 0.336493 + 0.582823i
\(615\) 0 0
\(616\) 0.688663 1.19280i 0.0277470 0.0480592i
\(617\) 23.2049 40.1920i 0.934192 1.61807i 0.158125 0.987419i \(-0.449455\pi\)
0.776068 0.630650i \(-0.217212\pi\)
\(618\) 0 0
\(619\) 13.6047 + 23.5641i 0.546820 + 0.947120i 0.998490 + 0.0549349i \(0.0174951\pi\)
−0.451670 + 0.892185i \(0.649172\pi\)
\(620\) −3.59358 −0.144322
\(621\) 0 0
\(622\) −29.6209 −1.18769
\(623\) −4.05690 7.02676i −0.162536 0.281521i
\(624\) 0 0
\(625\) 15.0326 26.0372i 0.601302 1.04149i
\(626\) −9.35685 + 16.2065i −0.373975 + 0.647743i
\(627\) 0 0
\(628\) 0.454956 + 0.788006i 0.0181547 + 0.0314449i
\(629\) 29.7939 1.18796
\(630\) 0 0
\(631\) −29.6023 −1.17845 −0.589224 0.807970i \(-0.700566\pi\)
−0.589224 + 0.807970i \(0.700566\pi\)
\(632\) 18.6006 + 32.2172i 0.739892 + 1.28153i
\(633\) 0 0
\(634\) 4.16456 7.21324i 0.165396 0.286474i
\(635\) −11.2451 + 19.4771i −0.446248 + 0.772925i
\(636\) 0 0
\(637\) −2.91147 5.04282i −0.115357 0.199804i
\(638\) −5.53571 −0.219161
\(639\) 0 0
\(640\) 24.0496 0.950645
\(641\) −0.139500 0.241621i −0.00550991 0.00954345i 0.863257 0.504764i \(-0.168421\pi\)
−0.868767 + 0.495221i \(0.835087\pi\)
\(642\) 0 0
\(643\) 9.12196 15.7997i 0.359735 0.623079i −0.628181 0.778067i \(-0.716200\pi\)
0.987916 + 0.154988i \(0.0495338\pi\)
\(644\) 0.00980018 0.0169744i 0.000386181 0.000668885i
\(645\) 0 0
\(646\) 5.70961 + 9.88933i 0.224642 + 0.389090i
\(647\) −22.4570 −0.882875 −0.441438 0.897292i \(-0.645531\pi\)
−0.441438 + 0.897292i \(0.645531\pi\)
\(648\) 0 0
\(649\) 0.344608 0.0135270
\(650\) 5.53667 + 9.58980i 0.217166 + 0.376143i
\(651\) 0 0
\(652\) 0.705737 1.22237i 0.0276388 0.0478718i
\(653\) −25.2656 + 43.7614i −0.988721 + 1.71251i −0.364655 + 0.931143i \(0.618813\pi\)
−0.624066 + 0.781372i \(0.714520\pi\)
\(654\) 0 0
\(655\) −14.3858 24.9169i −0.562099 0.973584i
\(656\) −8.00774 −0.312650
\(657\) 0 0
\(658\) −7.18479 −0.280092
\(659\) −1.33631 2.31456i −0.0520554 0.0901626i 0.838824 0.544403i \(-0.183244\pi\)
−0.890879 + 0.454241i \(0.849911\pi\)
\(660\) 0 0
\(661\) 17.3050 29.9731i 0.673086 1.16582i −0.303938 0.952692i \(-0.598302\pi\)
0.977024 0.213128i \(-0.0683651\pi\)
\(662\) 7.22921 12.5214i 0.280971 0.486656i
\(663\) 0 0
\(664\) −4.02007 6.96296i −0.156009 0.270215i
\(665\) 5.53209 0.214525
\(666\) 0 0
\(667\) −0.931379 −0.0360631
\(668\) 0.522537 + 0.905061i 0.0202176 + 0.0350179i
\(669\) 0 0
\(670\) 16.4402 28.4752i 0.635139 1.10009i
\(671\) 0.224155 0.388249i 0.00865342 0.0149882i
\(672\) 0 0
\(673\) −8.25624 14.3002i −0.318255 0.551234i 0.661869 0.749619i \(-0.269763\pi\)
−0.980124 + 0.198386i \(0.936430\pi\)
\(674\) 25.0523 0.964979
\(675\) 0 0
\(676\) −3.86341 −0.148593
\(677\) −21.8790 37.8955i −0.840877 1.45644i −0.889154 0.457608i \(-0.848706\pi\)
0.0482766 0.998834i \(-0.484627\pi\)
\(678\) 0 0
\(679\) 6.80200 11.7814i 0.261037 0.452129i
\(680\) −14.4572 + 25.0407i −0.554410 + 0.960266i
\(681\) 0 0
\(682\) 2.42081 + 4.19296i 0.0926975 + 0.160557i
\(683\) −28.2412 −1.08062 −0.540310 0.841466i \(-0.681693\pi\)
−0.540310 + 0.841466i \(0.681693\pi\)
\(684\) 0 0
\(685\) −14.4953 −0.553835
\(686\) 0.673648 + 1.16679i 0.0257200 + 0.0445484i
\(687\) 0 0
\(688\) 2.20574 3.82045i 0.0840929 0.145653i
\(689\) −2.08718 + 3.61510i −0.0795153 + 0.137725i
\(690\) 0 0
\(691\) 14.5326 + 25.1711i 0.552844 + 0.957555i 0.998068 + 0.0621351i \(0.0197910\pi\)
−0.445223 + 0.895420i \(0.646876\pi\)
\(692\) 3.89344 0.148006
\(693\) 0 0
\(694\) −27.5016 −1.04395
\(695\) −1.16978 2.02611i −0.0443722 0.0768549i
\(696\) 0 0
\(697\) 4.31908 7.48086i 0.163597 0.283358i
\(698\) −2.39961 + 4.15625i −0.0908268 + 0.157317i
\(699\) 0 0
\(700\) 0.130415 + 0.225885i 0.00492922 + 0.00853766i
\(701\) 1.10876 0.0418771 0.0209386 0.999781i \(-0.493335\pi\)
0.0209386 + 0.999781i \(0.493335\pi\)
\(702\) 0 0
\(703\) 16.7793 0.632843
\(704\) 2.01114 + 3.48340i 0.0757979 + 0.131286i
\(705\) 0 0
\(706\) −6.75150 + 11.6939i −0.254096 + 0.440107i
\(707\) −4.78699 + 8.29131i −0.180033 + 0.311827i
\(708\) 0 0
\(709\) 9.23442 + 15.9945i 0.346806 + 0.600686i 0.985680 0.168626i \(-0.0539329\pi\)
−0.638874 + 0.769311i \(0.720600\pi\)
\(710\) −45.1489 −1.69441
\(711\) 0 0
\(712\) 23.8835 0.895072
\(713\) 0.407299 + 0.705463i 0.0152535 + 0.0264198i
\(714\) 0 0
\(715\) −3.44949 + 5.97470i −0.129004 + 0.223441i
\(716\) 0.473126 0.819478i 0.0176815 0.0306253i
\(717\) 0 0
\(718\) −6.38666 11.0620i −0.238348 0.412831i
\(719\) 33.7769 1.25967 0.629834 0.776730i \(-0.283123\pi\)
0.629834 + 0.776730i \(0.283123\pi\)
\(720\) 0 0
\(721\) 3.04189 0.113286
\(722\) −9.58378 16.5996i −0.356671 0.617773i
\(723\) 0 0
\(724\) −0.0295627 + 0.0512040i −0.00109869 + 0.00190298i
\(725\) 6.19712 10.7337i 0.230155 0.398641i
\(726\) 0 0
\(727\) −8.40214 14.5529i −0.311618 0.539738i 0.667095 0.744973i \(-0.267538\pi\)
−0.978713 + 0.205234i \(0.934204\pi\)
\(728\) 17.1402 0.635259
\(729\) 0 0
\(730\) −35.0310 −1.29655
\(731\) 2.37939 + 4.12122i 0.0880047 + 0.152429i
\(732\) 0 0
\(733\) 6.81820 11.8095i 0.251836 0.436193i −0.712195 0.701981i \(-0.752299\pi\)
0.964031 + 0.265789i \(0.0856323\pi\)
\(734\) 10.8682 18.8243i 0.401154 0.694819i
\(735\) 0 0
\(736\) 0.0552549 + 0.0957044i 0.00203672 + 0.00352771i
\(737\) 4.50980 0.166121
\(738\) 0 0
\(739\) −32.0419 −1.17868 −0.589340 0.807885i \(-0.700612\pi\)
−0.589340 + 0.807885i \(0.700612\pi\)
\(740\) 1.79679 + 3.11213i 0.0660513 + 0.114404i
\(741\) 0 0
\(742\) 0.482926 0.836452i 0.0177288 0.0307071i
\(743\) 16.8764 29.2309i 0.619137 1.07238i −0.370507 0.928830i \(-0.620816\pi\)
0.989644 0.143547i \(-0.0458507\pi\)
\(744\) 0 0
\(745\) −11.0458 19.1318i −0.404685 0.700936i
\(746\) −18.9290 −0.693040
\(747\) 0 0
\(748\) −0.335437 −0.0122648
\(749\) −3.25877 5.64436i −0.119073 0.206240i
\(750\) 0 0
\(751\) −13.0582 + 22.6175i −0.476502 + 0.825326i −0.999637 0.0269236i \(-0.991429\pi\)
0.523135 + 0.852250i \(0.324762\pi\)
\(752\) 9.58899 16.6086i 0.349675 0.605654i
\(753\) 0 0
\(754\) −34.4447 59.6600i −1.25440 2.17269i
\(755\) −46.6587 −1.69808
\(756\) 0 0
\(757\) 35.6536 1.29585 0.647927 0.761703i \(-0.275636\pi\)
0.647927 + 0.761703i \(0.275636\pi\)
\(758\) 10.8170 + 18.7356i 0.392892 + 0.680509i
\(759\) 0 0
\(760\) −8.14203 + 14.1024i −0.295342 + 0.511548i
\(761\) 20.3824 35.3033i 0.738861 1.27974i −0.214148 0.976801i \(-0.568698\pi\)
0.953009 0.302943i \(-0.0979692\pi\)
\(762\) 0 0
\(763\) −5.31908 9.21291i −0.192564 0.333530i
\(764\) −2.87670 −0.104075
\(765\) 0 0
\(766\) −43.1411 −1.55875
\(767\) 2.14425 + 3.71395i 0.0774243 + 0.134103i
\(768\) 0 0
\(769\) −19.7135 + 34.1447i −0.710886 + 1.23129i 0.253639 + 0.967299i \(0.418373\pi\)
−0.964525 + 0.263992i \(0.914961\pi\)
\(770\) 0.798133 1.38241i 0.0287627 0.0498185i
\(771\) 0 0
\(772\) 0.558248 + 0.966914i 0.0200918 + 0.0348000i
\(773\) −24.9026 −0.895685 −0.447842 0.894113i \(-0.647807\pi\)
−0.447842 + 0.894113i \(0.647807\pi\)
\(774\) 0 0
\(775\) −10.8402 −0.389391
\(776\) 20.0221 + 34.6793i 0.718752 + 1.24492i
\(777\) 0 0
\(778\) 20.2383 35.0538i 0.725578 1.25674i
\(779\) 2.43242 4.21307i 0.0871504 0.150949i
\(780\) 0 0
\(781\) −3.09627 5.36289i −0.110793 0.191899i
\(782\) 0.554378 0.0198245
\(783\) 0 0
\(784\) −3.59627 −0.128438
\(785\) 6.23396 + 10.7975i 0.222499 + 0.385380i
\(786\) 0 0
\(787\) 15.3525 26.5913i 0.547258 0.947879i −0.451203 0.892421i \(-0.649005\pi\)
0.998461 0.0554572i \(-0.0176616\pi\)
\(788\) −2.33157 + 4.03839i −0.0830586 + 0.143862i
\(789\) 0 0
\(790\) 21.5574 + 37.3385i 0.766977 + 1.32844i
\(791\) −5.17705 −0.184075
\(792\) 0 0
\(793\) 5.57903 0.198117
\(794\) −8.29932 14.3748i −0.294532 0.510144i
\(795\) 0 0
\(796\) 0.281059 0.486809i 0.00996188 0.0172545i
\(797\) −5.50686 + 9.53817i −0.195063 + 0.337859i −0.946921 0.321466i \(-0.895825\pi\)
0.751858 + 0.659325i \(0.229158\pi\)
\(798\) 0 0
\(799\) 10.3439 + 17.9161i 0.365941 + 0.633828i
\(800\) −1.47060 −0.0519935
\(801\) 0 0
\(802\) 28.2608 0.997925
\(803\) −2.40239 4.16106i −0.0847785 0.146841i
\(804\) 0 0
\(805\) 0.134285 0.232589i 0.00473294 0.00819769i
\(806\) −30.1259 + 52.1796i −1.06114 + 1.83795i
\(807\) 0 0
\(808\) −14.0908 24.4060i −0.495713 0.858600i
\(809\) −16.9881 −0.597271 −0.298636 0.954367i \(-0.596532\pi\)
−0.298636 + 0.954367i \(0.596532\pi\)
\(810\) 0 0
\(811\) 37.9796 1.33364 0.666822 0.745217i \(-0.267654\pi\)
0.666822 + 0.745217i \(0.267654\pi\)
\(812\) −0.811337 1.40528i −0.0284723 0.0493156i
\(813\) 0 0
\(814\) 2.42081 4.19296i 0.0848493 0.146963i
\(815\) 9.67024 16.7494i 0.338734 0.586704i
\(816\) 0 0
\(817\) 1.34002 + 2.32099i 0.0468814 + 0.0812011i
\(818\) −34.5735 −1.20883
\(819\) 0 0
\(820\) 1.04189 0.0363843
\(821\) 4.13934 + 7.16954i 0.144464 + 0.250219i 0.929173 0.369646i \(-0.120521\pi\)
−0.784709 + 0.619864i \(0.787188\pi\)
\(822\) 0 0
\(823\) −27.2763 + 47.2440i −0.950792 + 1.64682i −0.207077 + 0.978325i \(0.566395\pi\)
−0.743716 + 0.668496i \(0.766938\pi\)
\(824\) −4.47700 + 7.75438i −0.155964 + 0.270137i
\(825\) 0 0
\(826\) −0.496130 0.859322i −0.0172626 0.0298996i
\(827\) 31.8708 1.10826 0.554129 0.832431i \(-0.313052\pi\)
0.554129 + 0.832431i \(0.313052\pi\)
\(828\) 0 0
\(829\) −0.352349 −0.0122376 −0.00611879 0.999981i \(-0.501948\pi\)
−0.00611879 + 0.999981i \(0.501948\pi\)
\(830\) −4.65910 8.06980i −0.161720 0.280107i
\(831\) 0 0
\(832\) −25.0278 + 43.3494i −0.867683 + 1.50287i
\(833\) 1.93969 3.35965i 0.0672064 0.116405i
\(834\) 0 0
\(835\) 7.15998 + 12.4014i 0.247781 + 0.429170i
\(836\) −0.188911 −0.00653363
\(837\) 0 0
\(838\) −1.99369 −0.0688709
\(839\) 12.5077 + 21.6640i 0.431815 + 0.747926i 0.997030 0.0770182i \(-0.0245399\pi\)
−0.565215 + 0.824944i \(0.691207\pi\)
\(840\) 0 0
\(841\) −24.0535 + 41.6619i −0.829431 + 1.43662i
\(842\) 8.82951 15.2932i 0.304285 0.527037i
\(843\) 0 0
\(844\) −0.503870 0.872729i −0.0173439 0.0300406i
\(845\) −52.9377 −1.82111
\(846\) 0 0
\(847\) −10.7811 −0.370442
\(848\) 1.28905 + 2.23270i 0.0442661 + 0.0766711i
\(849\) 0 0
\(850\) −3.68866 + 6.38895i −0.126520 + 0.219139i
\(851\) 0.407299 0.705463i 0.0139620 0.0241829i
\(852\) 0 0
\(853\) −19.5954 33.9402i −0.670933 1.16209i −0.977640 0.210286i \(-0.932560\pi\)
0.306706 0.951804i \(-0.400773\pi\)
\(854\) −1.29086 −0.0441723
\(855\) 0 0
\(856\) 19.1848 0.655723
\(857\) 8.20368 + 14.2092i 0.280232 + 0.485377i 0.971442 0.237278i \(-0.0762552\pi\)
−0.691210 + 0.722654i \(0.742922\pi\)
\(858\) 0 0
\(859\) 13.4162 23.2376i 0.457756 0.792856i −0.541086 0.840967i \(-0.681987\pi\)
0.998842 + 0.0481111i \(0.0153201\pi\)
\(860\) −0.286989 + 0.497079i −0.00978624 + 0.0169503i
\(861\) 0 0
\(862\) −11.9418 20.6837i −0.406738 0.704490i
\(863\) −14.5057 −0.493779 −0.246890 0.969044i \(-0.579408\pi\)
−0.246890 + 0.969044i \(0.579408\pi\)
\(864\) 0 0
\(865\) 53.3492 1.81393
\(866\) −3.93305 6.81224i −0.133650 0.231489i
\(867\) 0 0
\(868\) −0.709607 + 1.22908i −0.0240856 + 0.0417176i
\(869\) −2.95677 + 5.12127i −0.100301 + 0.173727i
\(870\) 0 0
\(871\) 28.0612 + 48.6035i 0.950819 + 1.64687i
\(872\) 31.3141 1.06043
\(873\) 0 0
\(874\) 0.312214 0.0105608
\(875\) −4.54323 7.86911i −0.153589 0.266024i
\(876\) 0 0
\(877\) −9.45723 + 16.3804i −0.319348 + 0.553127i −0.980352 0.197255i \(-0.936797\pi\)
0.661004 + 0.750382i \(0.270131\pi\)
\(878\) 20.1120 34.8350i 0.678747 1.17562i
\(879\) 0 0
\(880\) 2.13041 + 3.68999i 0.0718163 + 0.124389i
\(881\) −53.8976 −1.81585 −0.907927 0.419128i \(-0.862336\pi\)
−0.907927 + 0.419128i \(0.862336\pi\)
\(882\) 0 0
\(883\) 43.4252 1.46137 0.730687 0.682712i \(-0.239200\pi\)
0.730687 + 0.682712i \(0.239200\pi\)
\(884\) −2.08718 3.61510i −0.0701995 0.121589i
\(885\) 0 0
\(886\) −7.18479 + 12.4444i −0.241378 + 0.418079i
\(887\) −19.4800 + 33.7403i −0.654074 + 1.13289i 0.328051 + 0.944660i \(0.393608\pi\)
−0.982125 + 0.188229i \(0.939725\pi\)
\(888\) 0 0
\(889\) 4.44104 + 7.69210i 0.148948 + 0.257985i
\(890\) 27.6800 0.927837
\(891\) 0 0
\(892\) −2.62267 −0.0878136
\(893\) 5.82547 + 10.0900i 0.194942 + 0.337650i
\(894\) 0 0
\(895\) 6.48293 11.2288i 0.216700 0.375336i
\(896\) 4.74897 8.22546i 0.158652 0.274793i
\(897\) 0 0
\(898\) −2.39440 4.14722i −0.0799022 0.138395i
\(899\) 67.4389 2.24921
\(900\) 0 0
\(901\) −2.78106 −0.0926505
\(902\) −0.701867 1.21567i −0.0233696 0.0404773i
\(903\) 0 0
\(904\) 7.61949 13.1973i 0.253420 0.438937i
\(905\) −0.405078 + 0.701615i −0.0134652 + 0.0233225i
\(906\) 0 0
\(907\) −17.2638 29.9018i −0.573236 0.992874i −0.996231 0.0867416i \(-0.972355\pi\)
0.422995 0.906132i \(-0.360979\pi\)
\(908\) −0.534777 −0.0177472
\(909\) 0 0
\(910\) 19.8648 0.658513
\(911\) 23.2631 + 40.2929i 0.770741 + 1.33496i 0.937157 + 0.348907i \(0.113447\pi\)
−0.166416 + 0.986056i \(0.553220\pi\)
\(912\) 0 0
\(913\) 0.639033 1.10684i 0.0211489 0.0366310i
\(914\) 3.38388 5.86106i 0.111929 0.193867i
\(915\) 0 0
\(916\) 0.847048 + 1.46713i 0.0279873 + 0.0484753i
\(917\) −11.3628 −0.375232
\(918\) 0 0
\(919\) −9.95636 −0.328430 −0.164215 0.986425i \(-0.552509\pi\)
−0.164215 + 0.986425i \(0.552509\pi\)
\(920\) 0.395277 + 0.684640i 0.0130319 + 0.0225719i
\(921\) 0 0
\(922\) −12.4363 + 21.5403i −0.409567 + 0.709391i
\(923\) 38.5317 66.7388i 1.26829 2.19674i
\(924\) 0 0
\(925\) 5.42009 + 9.38788i 0.178212 + 0.308671i
\(926\) 19.1780 0.630228
\(927\) 0 0
\(928\) 9.14889 0.300327
\(929\) 4.52300 + 7.83407i 0.148395 + 0.257028i 0.930634 0.365950i \(-0.119256\pi\)
−0.782239 + 0.622978i \(0.785923\pi\)
\(930\) 0 0
\(931\) 1.09240 1.89209i 0.0358018 0.0620106i
\(932\) −1.22621 + 2.12387i −0.0401660 + 0.0695696i
\(933\) 0 0
\(934\) 2.26929 + 3.93052i 0.0742533 + 0.128610i
\(935\) −4.59627 −0.150314
\(936\) 0 0
\(937\) −24.3928 −0.796878 −0.398439 0.917195i \(-0.630448\pi\)
−0.398439 + 0.917195i \(0.630448\pi\)
\(938\) −6.49273 11.2457i −0.211995 0.367186i
\(939\) 0 0
\(940\) −1.24763 + 2.16095i −0.0406931 + 0.0704825i
\(941\) −29.7690 + 51.5615i −0.970443 + 1.68086i −0.276223 + 0.961094i \(0.589083\pi\)
−0.694220 + 0.719763i \(0.744251\pi\)
\(942\) 0 0
\(943\) −0.118089 0.204535i −0.00384549 0.00666059i
\(944\) 2.64858 0.0862041
\(945\) 0 0
\(946\) 0.773318 0.0251428
\(947\) 4.32429 + 7.48989i 0.140521 + 0.243389i 0.927693 0.373344i \(-0.121789\pi\)
−0.787172 + 0.616733i \(0.788456\pi\)
\(948\) 0 0
\(949\) 29.8967 51.7826i 0.970487 1.68093i
\(950\) −2.07738 + 3.59813i −0.0673992 + 0.116739i
\(951\) 0 0
\(952\) 5.70961 + 9.88933i 0.185049 + 0.320515i
\(953\) −3.78249 −0.122527 −0.0612634 0.998122i \(-0.519513\pi\)
−0.0612634 + 0.998122i \(0.519513\pi\)
\(954\) 0 0
\(955\) −39.4175 −1.27552
\(956\) −0.881196 1.52628i −0.0284999 0.0493633i
\(957\) 0 0
\(958\) 24.7677 42.8989i 0.800208 1.38600i
\(959\) −2.86231 + 4.95767i −0.0924288 + 0.160091i
\(960\) 0 0
\(961\) −13.9915 24.2341i −0.451340 0.781744i
\(962\) 60.2518 1.94260
\(963\) 0 0
\(964\) 1.65539 0.0533166
\(965\) 7.64930 + 13.2490i 0.246240 + 0.426500i
\(966\) 0 0
\(967\) 16.4745 28.5346i 0.529783 0.917611i −0.469613 0.882872i \(-0.655607\pi\)
0.999396 0.0347392i \(-0.0110601\pi\)
\(968\) 15.8674 27.4831i 0.509996 0.883340i
\(969\) 0 0
\(970\) 23.2049 + 40.1920i 0.745063 + 1.29049i
\(971\) 55.4570 1.77970 0.889850 0.456254i \(-0.150809\pi\)
0.889850 + 0.456254i \(0.150809\pi\)
\(972\) 0 0
\(973\) −0.923963 −0.0296209
\(974\) −25.2062 43.6584i −0.807659 1.39891i
\(975\) 0 0
\(976\) 1.72281 2.98400i 0.0551458 0.0955154i
\(977\) 28.2743 48.9724i 0.904573 1.56677i 0.0830847 0.996542i \(-0.473523\pi\)
0.821489 0.570225i \(-0.193144\pi\)
\(978\) 0 0
\(979\) 1.89827 + 3.28790i 0.0606690 + 0.105082i
\(980\) 0.467911 0.0149469
\(981\) 0 0
\(982\) −35.9331 −1.14667
\(983\) 14.4987 + 25.1124i 0.462435 + 0.800961i 0.999082 0.0428458i \(-0.0136424\pi\)
−0.536646 + 0.843807i \(0.680309\pi\)
\(984\) 0 0
\(985\) −31.9479 + 55.3354i −1.01794 + 1.76313i
\(986\) 22.9479 39.7469i 0.730810 1.26580i
\(987\) 0 0
\(988\) −1.17546 2.03596i −0.0373963 0.0647724i
\(989\) 0.130110 0.00413726
\(990\) 0 0
\(991\) 6.80922 0.216302 0.108151 0.994134i \(-0.465507\pi\)
0.108151 + 0.994134i \(0.465507\pi\)
\(992\) −4.00088 6.92972i −0.127028 0.220019i
\(993\) 0 0
\(994\) −8.91534 + 15.4418i −0.282778 + 0.489785i
\(995\) 3.85117 6.67042i 0.122090 0.211466i
\(996\) 0 0
\(997\) 19.4688 + 33.7210i 0.616585 + 1.06796i 0.990104 + 0.140333i \(0.0448175\pi\)
−0.373520 + 0.927622i \(0.621849\pi\)
\(998\) −45.4647 −1.43916
\(999\) 0 0
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 189.2.f.b.64.2 6
3.2 odd 2 63.2.f.a.22.2 6
4.3 odd 2 3024.2.r.k.1009.3 6
7.2 even 3 1323.2.g.d.361.2 6
7.3 odd 6 1323.2.h.b.226.2 6
7.4 even 3 1323.2.h.c.226.2 6
7.5 odd 6 1323.2.g.e.361.2 6
7.6 odd 2 1323.2.f.d.442.2 6
9.2 odd 6 63.2.f.a.43.2 yes 6
9.4 even 3 567.2.a.c.1.2 3
9.5 odd 6 567.2.a.h.1.2 3
9.7 even 3 inner 189.2.f.b.127.2 6
12.11 even 2 1008.2.r.h.337.1 6
21.2 odd 6 441.2.g.c.67.2 6
21.5 even 6 441.2.g.b.67.2 6
21.11 odd 6 441.2.h.d.373.2 6
21.17 even 6 441.2.h.e.373.2 6
21.20 even 2 441.2.f.c.148.2 6
36.7 odd 6 3024.2.r.k.2017.3 6
36.11 even 6 1008.2.r.h.673.1 6
36.23 even 6 9072.2.a.ca.1.3 3
36.31 odd 6 9072.2.a.bs.1.1 3
63.2 odd 6 441.2.h.d.214.2 6
63.11 odd 6 441.2.g.c.79.2 6
63.13 odd 6 3969.2.a.l.1.2 3
63.16 even 3 1323.2.h.c.802.2 6
63.20 even 6 441.2.f.c.295.2 6
63.25 even 3 1323.2.g.d.667.2 6
63.34 odd 6 1323.2.f.d.883.2 6
63.38 even 6 441.2.g.b.79.2 6
63.41 even 6 3969.2.a.q.1.2 3
63.47 even 6 441.2.h.e.214.2 6
63.52 odd 6 1323.2.g.e.667.2 6
63.61 odd 6 1323.2.h.b.802.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.f.a.22.2 6 3.2 odd 2
63.2.f.a.43.2 yes 6 9.2 odd 6
189.2.f.b.64.2 6 1.1 even 1 trivial
189.2.f.b.127.2 6 9.7 even 3 inner
441.2.f.c.148.2 6 21.20 even 2
441.2.f.c.295.2 6 63.20 even 6
441.2.g.b.67.2 6 21.5 even 6
441.2.g.b.79.2 6 63.38 even 6
441.2.g.c.67.2 6 21.2 odd 6
441.2.g.c.79.2 6 63.11 odd 6
441.2.h.d.214.2 6 63.2 odd 6
441.2.h.d.373.2 6 21.11 odd 6
441.2.h.e.214.2 6 63.47 even 6
441.2.h.e.373.2 6 21.17 even 6
567.2.a.c.1.2 3 9.4 even 3
567.2.a.h.1.2 3 9.5 odd 6
1008.2.r.h.337.1 6 12.11 even 2
1008.2.r.h.673.1 6 36.11 even 6
1323.2.f.d.442.2 6 7.6 odd 2
1323.2.f.d.883.2 6 63.34 odd 6
1323.2.g.d.361.2 6 7.2 even 3
1323.2.g.d.667.2 6 63.25 even 3
1323.2.g.e.361.2 6 7.5 odd 6
1323.2.g.e.667.2 6 63.52 odd 6
1323.2.h.b.226.2 6 7.3 odd 6
1323.2.h.b.802.2 6 63.61 odd 6
1323.2.h.c.226.2 6 7.4 even 3
1323.2.h.c.802.2 6 63.16 even 3
3024.2.r.k.1009.3 6 4.3 odd 2
3024.2.r.k.2017.3 6 36.7 odd 6
3969.2.a.l.1.2 3 63.13 odd 6
3969.2.a.q.1.2 3 63.41 even 6
9072.2.a.bs.1.1 3 36.31 odd 6
9072.2.a.ca.1.3 3 36.23 even 6