Properties

Label 966.2.f.b.461.14
Level $966$
Weight $2$
Character 966.461
Analytic conductor $7.714$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [966,2,Mod(461,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.461");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.f (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.71354883526\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.14
Character \(\chi\) \(=\) 966.461
Dual form 966.2.f.b.461.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-1.66919 + 0.462387i) q^{3} -1.00000 q^{4} -1.95027 q^{5} +(-0.462387 - 1.66919i) q^{6} +(-0.602835 - 2.57616i) q^{7} -1.00000i q^{8} +(2.57240 - 1.54363i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-1.66919 + 0.462387i) q^{3} -1.00000 q^{4} -1.95027 q^{5} +(-0.462387 - 1.66919i) q^{6} +(-0.602835 - 2.57616i) q^{7} -1.00000i q^{8} +(2.57240 - 1.54363i) q^{9} -1.95027i q^{10} +4.18593i q^{11} +(1.66919 - 0.462387i) q^{12} -7.00187i q^{13} +(2.57616 - 0.602835i) q^{14} +(3.25538 - 0.901781i) q^{15} +1.00000 q^{16} +3.56933 q^{17} +(1.54363 + 2.57240i) q^{18} +8.08958i q^{19} +1.95027 q^{20} +(2.19743 + 4.02136i) q^{21} -4.18593 q^{22} -1.00000i q^{23} +(0.462387 + 1.66919i) q^{24} -1.19644 q^{25} +7.00187 q^{26} +(-3.58007 + 3.76605i) q^{27} +(0.602835 + 2.57616i) q^{28} +2.33625i q^{29} +(0.901781 + 3.25538i) q^{30} +0.237061i q^{31} +1.00000i q^{32} +(-1.93552 - 6.98711i) q^{33} +3.56933i q^{34} +(1.17569 + 5.02421i) q^{35} +(-2.57240 + 1.54363i) q^{36} -0.324825 q^{37} -8.08958 q^{38} +(3.23757 + 11.6874i) q^{39} +1.95027i q^{40} -8.81948 q^{41} +(-4.02136 + 2.19743i) q^{42} +8.54266 q^{43} -4.18593i q^{44} +(-5.01687 + 3.01049i) q^{45} +1.00000 q^{46} +0.174840 q^{47} +(-1.66919 + 0.462387i) q^{48} +(-6.27318 + 3.10600i) q^{49} -1.19644i q^{50} +(-5.95790 + 1.65041i) q^{51} +7.00187i q^{52} +5.65184i q^{53} +(-3.76605 - 3.58007i) q^{54} -8.16370i q^{55} +(-2.57616 + 0.602835i) q^{56} +(-3.74052 - 13.5031i) q^{57} -2.33625 q^{58} +7.74076 q^{59} +(-3.25538 + 0.901781i) q^{60} +9.18309i q^{61} -0.237061 q^{62} +(-5.52735 - 5.69635i) q^{63} -1.00000 q^{64} +13.6555i q^{65} +(6.98711 - 1.93552i) q^{66} +7.68745 q^{67} -3.56933 q^{68} +(0.462387 + 1.66919i) q^{69} +(-5.02421 + 1.17569i) q^{70} +5.42350i q^{71} +(-1.54363 - 2.57240i) q^{72} +11.1709i q^{73} -0.324825i q^{74} +(1.99708 - 0.553217i) q^{75} -8.08958i q^{76} +(10.7836 - 2.52342i) q^{77} +(-11.6874 + 3.23757i) q^{78} +12.2350 q^{79} -1.95027 q^{80} +(4.23444 - 7.94163i) q^{81} -8.81948i q^{82} -17.9170 q^{83} +(-2.19743 - 4.02136i) q^{84} -6.96117 q^{85} +8.54266i q^{86} +(-1.08025 - 3.89965i) q^{87} +4.18593 q^{88} +1.21795 q^{89} +(-3.01049 - 5.01687i) q^{90} +(-18.0379 + 4.22097i) q^{91} +1.00000i q^{92} +(-0.109614 - 0.395700i) q^{93} +0.174840i q^{94} -15.7769i q^{95} +(-0.462387 - 1.66919i) q^{96} +16.7148i q^{97} +(-3.10600 - 6.27318i) q^{98} +(6.46151 + 10.7679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9} + 24 q^{16} + 16 q^{18} - 28 q^{21} + 8 q^{22} - 24 q^{25} + 4 q^{28} + 24 q^{30} - 8 q^{36} + 40 q^{37} + 72 q^{39} + 64 q^{43} + 24 q^{46} - 24 q^{51} + 16 q^{58} + 12 q^{63} - 24 q^{64} - 64 q^{67} + 16 q^{70} - 16 q^{72} - 32 q^{78} + 88 q^{79} + 48 q^{81} + 28 q^{84} + 64 q^{85} - 8 q^{88} - 56 q^{91} + 8 q^{93} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.66919 + 0.462387i −0.963708 + 0.266959i
\(4\) −1.00000 −0.500000
\(5\) −1.95027 −0.872188 −0.436094 0.899901i \(-0.643639\pi\)
−0.436094 + 0.899901i \(0.643639\pi\)
\(6\) −0.462387 1.66919i −0.188769 0.681444i
\(7\) −0.602835 2.57616i −0.227850 0.973696i
\(8\) 1.00000i 0.353553i
\(9\) 2.57240 1.54363i 0.857465 0.514542i
\(10\) 1.95027i 0.616730i
\(11\) 4.18593i 1.26210i 0.775740 + 0.631052i \(0.217377\pi\)
−0.775740 + 0.631052i \(0.782623\pi\)
\(12\) 1.66919 0.462387i 0.481854 0.133480i
\(13\) 7.00187i 1.94197i −0.239144 0.970984i \(-0.576867\pi\)
0.239144 0.970984i \(-0.423133\pi\)
\(14\) 2.57616 0.602835i 0.688507 0.161114i
\(15\) 3.25538 0.901781i 0.840535 0.232839i
\(16\) 1.00000 0.250000
\(17\) 3.56933 0.865690 0.432845 0.901468i \(-0.357510\pi\)
0.432845 + 0.901468i \(0.357510\pi\)
\(18\) 1.54363 + 2.57240i 0.363836 + 0.606320i
\(19\) 8.08958i 1.85588i 0.372732 + 0.927939i \(0.378421\pi\)
−0.372732 + 0.927939i \(0.621579\pi\)
\(20\) 1.95027 0.436094
\(21\) 2.19743 + 4.02136i 0.479518 + 0.877532i
\(22\) −4.18593 −0.892443
\(23\) 1.00000i 0.208514i
\(24\) 0.462387 + 1.66919i 0.0943844 + 0.340722i
\(25\) −1.19644 −0.239287
\(26\) 7.00187 1.37318
\(27\) −3.58007 + 3.76605i −0.688984 + 0.724776i
\(28\) 0.602835 + 2.57616i 0.113925 + 0.486848i
\(29\) 2.33625i 0.433831i 0.976190 + 0.216916i \(0.0695996\pi\)
−0.976190 + 0.216916i \(0.930400\pi\)
\(30\) 0.901781 + 3.25538i 0.164642 + 0.594348i
\(31\) 0.237061i 0.0425774i 0.999773 + 0.0212887i \(0.00677692\pi\)
−0.999773 + 0.0212887i \(0.993223\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −1.93552 6.98711i −0.336931 1.21630i
\(34\) 3.56933i 0.612135i
\(35\) 1.17569 + 5.02421i 0.198728 + 0.849246i
\(36\) −2.57240 + 1.54363i −0.428733 + 0.257271i
\(37\) −0.324825 −0.0534009 −0.0267005 0.999643i \(-0.508500\pi\)
−0.0267005 + 0.999643i \(0.508500\pi\)
\(38\) −8.08958 −1.31230
\(39\) 3.23757 + 11.6874i 0.518427 + 1.87149i
\(40\) 1.95027i 0.308365i
\(41\) −8.81948 −1.37737 −0.688686 0.725060i \(-0.741812\pi\)
−0.688686 + 0.725060i \(0.741812\pi\)
\(42\) −4.02136 + 2.19743i −0.620509 + 0.339071i
\(43\) 8.54266 1.30274 0.651372 0.758759i \(-0.274194\pi\)
0.651372 + 0.758759i \(0.274194\pi\)
\(44\) 4.18593i 0.631052i
\(45\) −5.01687 + 3.01049i −0.747871 + 0.448777i
\(46\) 1.00000 0.147442
\(47\) 0.174840 0.0255030 0.0127515 0.999919i \(-0.495941\pi\)
0.0127515 + 0.999919i \(0.495941\pi\)
\(48\) −1.66919 + 0.462387i −0.240927 + 0.0667399i
\(49\) −6.27318 + 3.10600i −0.896169 + 0.443714i
\(50\) 1.19644i 0.169202i
\(51\) −5.95790 + 1.65041i −0.834272 + 0.231104i
\(52\) 7.00187i 0.970984i
\(53\) 5.65184i 0.776340i 0.921588 + 0.388170i \(0.126893\pi\)
−0.921588 + 0.388170i \(0.873107\pi\)
\(54\) −3.76605 3.58007i −0.512494 0.487185i
\(55\) 8.16370i 1.10079i
\(56\) −2.57616 + 0.602835i −0.344254 + 0.0805572i
\(57\) −3.74052 13.5031i −0.495444 1.78852i
\(58\) −2.33625 −0.306765
\(59\) 7.74076 1.00776 0.503881 0.863773i \(-0.331905\pi\)
0.503881 + 0.863773i \(0.331905\pi\)
\(60\) −3.25538 + 0.901781i −0.420267 + 0.116419i
\(61\) 9.18309i 1.17577i 0.808943 + 0.587887i \(0.200040\pi\)
−0.808943 + 0.587887i \(0.799960\pi\)
\(62\) −0.237061 −0.0301068
\(63\) −5.52735 5.69635i −0.696381 0.717672i
\(64\) −1.00000 −0.125000
\(65\) 13.6555i 1.69376i
\(66\) 6.98711 1.93552i 0.860054 0.238246i
\(67\) 7.68745 0.939171 0.469586 0.882887i \(-0.344403\pi\)
0.469586 + 0.882887i \(0.344403\pi\)
\(68\) −3.56933 −0.432845
\(69\) 0.462387 + 1.66919i 0.0556649 + 0.200947i
\(70\) −5.02421 + 1.17569i −0.600508 + 0.140522i
\(71\) 5.42350i 0.643651i 0.946799 + 0.321826i \(0.104297\pi\)
−0.946799 + 0.321826i \(0.895703\pi\)
\(72\) −1.54363 2.57240i −0.181918 0.303160i
\(73\) 11.1709i 1.30745i 0.756732 + 0.653726i \(0.226795\pi\)
−0.756732 + 0.653726i \(0.773205\pi\)
\(74\) 0.324825i 0.0377602i
\(75\) 1.99708 0.553217i 0.230603 0.0638801i
\(76\) 8.08958i 0.927939i
\(77\) 10.7836 2.52342i 1.22891 0.287571i
\(78\) −11.6874 + 3.23757i −1.32334 + 0.366583i
\(79\) 12.2350 1.37654 0.688271 0.725454i \(-0.258370\pi\)
0.688271 + 0.725454i \(0.258370\pi\)
\(80\) −1.95027 −0.218047
\(81\) 4.23444 7.94163i 0.470493 0.882404i
\(82\) 8.81948i 0.973949i
\(83\) −17.9170 −1.96664 −0.983321 0.181880i \(-0.941782\pi\)
−0.983321 + 0.181880i \(0.941782\pi\)
\(84\) −2.19743 4.02136i −0.239759 0.438766i
\(85\) −6.96117 −0.755045
\(86\) 8.54266i 0.921178i
\(87\) −1.08025 3.89965i −0.115815 0.418086i
\(88\) 4.18593 0.446221
\(89\) 1.21795 0.129102 0.0645510 0.997914i \(-0.479438\pi\)
0.0645510 + 0.997914i \(0.479438\pi\)
\(90\) −3.01049 5.01687i −0.317334 0.528825i
\(91\) −18.0379 + 4.22097i −1.89089 + 0.442478i
\(92\) 1.00000i 0.104257i
\(93\) −0.109614 0.395700i −0.0113665 0.0410322i
\(94\) 0.174840i 0.0180334i
\(95\) 15.7769i 1.61868i
\(96\) −0.462387 1.66919i −0.0471922 0.170361i
\(97\) 16.7148i 1.69713i 0.529088 + 0.848567i \(0.322534\pi\)
−0.529088 + 0.848567i \(0.677466\pi\)
\(98\) −3.10600 6.27318i −0.313753 0.633687i
\(99\) 6.46151 + 10.7679i 0.649406 + 1.08221i
\(100\) 1.19644 0.119644
\(101\) 10.8858 1.08318 0.541591 0.840642i \(-0.317822\pi\)
0.541591 + 0.840642i \(0.317822\pi\)
\(102\) −1.65041 5.95790i −0.163415 0.589920i
\(103\) 1.91420i 0.188612i −0.995543 0.0943058i \(-0.969937\pi\)
0.995543 0.0943058i \(-0.0300631\pi\)
\(104\) −7.00187 −0.686589
\(105\) −4.28559 7.84274i −0.418230 0.765373i
\(106\) −5.65184 −0.548956
\(107\) 13.7767i 1.33185i 0.746019 + 0.665924i \(0.231963\pi\)
−0.746019 + 0.665924i \(0.768037\pi\)
\(108\) 3.58007 3.76605i 0.344492 0.362388i
\(109\) −4.26102 −0.408131 −0.204066 0.978957i \(-0.565416\pi\)
−0.204066 + 0.978957i \(0.565416\pi\)
\(110\) 8.16370 0.778378
\(111\) 0.542195 0.150195i 0.0514629 0.0142559i
\(112\) −0.602835 2.57616i −0.0569626 0.243424i
\(113\) 9.50152i 0.893828i −0.894577 0.446914i \(-0.852523\pi\)
0.894577 0.446914i \(-0.147477\pi\)
\(114\) 13.5031 3.74052i 1.26468 0.350332i
\(115\) 1.95027i 0.181864i
\(116\) 2.33625i 0.216916i
\(117\) −10.8083 18.0116i −0.999224 1.66517i
\(118\) 7.74076i 0.712595i
\(119\) −2.15172 9.19516i −0.197248 0.842919i
\(120\) −0.901781 3.25538i −0.0823210 0.297174i
\(121\) −6.52200 −0.592909
\(122\) −9.18309 −0.831398
\(123\) 14.7214 4.07802i 1.32738 0.367702i
\(124\) 0.237061i 0.0212887i
\(125\) 12.0847 1.08089
\(126\) 5.69635 5.52735i 0.507471 0.492416i
\(127\) 4.82854 0.428464 0.214232 0.976783i \(-0.431275\pi\)
0.214232 + 0.976783i \(0.431275\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −14.2593 + 3.95002i −1.25546 + 0.347780i
\(130\) −13.6555 −1.19767
\(131\) 18.7373 1.63709 0.818544 0.574444i \(-0.194782\pi\)
0.818544 + 0.574444i \(0.194782\pi\)
\(132\) 1.93552 + 6.98711i 0.168465 + 0.608150i
\(133\) 20.8400 4.87669i 1.80706 0.422862i
\(134\) 7.68745i 0.664094i
\(135\) 6.98211 7.34482i 0.600924 0.632142i
\(136\) 3.56933i 0.306068i
\(137\) 6.80806i 0.581652i −0.956776 0.290826i \(-0.906070\pi\)
0.956776 0.290826i \(-0.0939301\pi\)
\(138\) −1.66919 + 0.462387i −0.142091 + 0.0393610i
\(139\) 12.9800i 1.10095i 0.834852 + 0.550475i \(0.185553\pi\)
−0.834852 + 0.550475i \(0.814447\pi\)
\(140\) −1.17569 5.02421i −0.0993642 0.424623i
\(141\) −0.291841 + 0.0808438i −0.0245775 + 0.00680827i
\(142\) −5.42350 −0.455130
\(143\) 29.3093 2.45097
\(144\) 2.57240 1.54363i 0.214366 0.128635i
\(145\) 4.55633i 0.378382i
\(146\) −11.1709 −0.924508
\(147\) 9.03496 8.08514i 0.745191 0.666851i
\(148\) 0.324825 0.0267005
\(149\) 13.6518i 1.11840i 0.829032 + 0.559201i \(0.188892\pi\)
−0.829032 + 0.559201i \(0.811108\pi\)
\(150\) 0.553217 + 1.99708i 0.0451700 + 0.163061i
\(151\) 2.79942 0.227814 0.113907 0.993491i \(-0.463663\pi\)
0.113907 + 0.993491i \(0.463663\pi\)
\(152\) 8.08958 0.656152
\(153\) 9.18173 5.50971i 0.742299 0.445434i
\(154\) 2.52342 + 10.7836i 0.203343 + 0.868968i
\(155\) 0.462334i 0.0371355i
\(156\) −3.23757 11.6874i −0.259213 0.935745i
\(157\) 9.02729i 0.720456i 0.932864 + 0.360228i \(0.117301\pi\)
−0.932864 + 0.360228i \(0.882699\pi\)
\(158\) 12.2350i 0.973362i
\(159\) −2.61334 9.43401i −0.207251 0.748165i
\(160\) 1.95027i 0.154183i
\(161\) −2.57616 + 0.602835i −0.203030 + 0.0475101i
\(162\) 7.94163 + 4.23444i 0.623954 + 0.332689i
\(163\) 1.52485 0.119436 0.0597178 0.998215i \(-0.480980\pi\)
0.0597178 + 0.998215i \(0.480980\pi\)
\(164\) 8.81948 0.688686
\(165\) 3.77479 + 13.6268i 0.293867 + 1.06084i
\(166\) 17.9170i 1.39063i
\(167\) −7.96658 −0.616472 −0.308236 0.951310i \(-0.599739\pi\)
−0.308236 + 0.951310i \(0.599739\pi\)
\(168\) 4.02136 2.19743i 0.310254 0.169535i
\(169\) −36.0261 −2.77124
\(170\) 6.96117i 0.533897i
\(171\) 12.4873 + 20.8096i 0.954927 + 1.59135i
\(172\) −8.54266 −0.651372
\(173\) 4.99294 0.379606 0.189803 0.981822i \(-0.439215\pi\)
0.189803 + 0.981822i \(0.439215\pi\)
\(174\) 3.89965 1.08025i 0.295632 0.0818938i
\(175\) 0.721254 + 3.08221i 0.0545217 + 0.232993i
\(176\) 4.18593i 0.315526i
\(177\) −12.9208 + 3.57923i −0.971188 + 0.269031i
\(178\) 1.21795i 0.0912889i
\(179\) 9.35057i 0.698895i 0.936956 + 0.349447i \(0.113631\pi\)
−0.936956 + 0.349447i \(0.886369\pi\)
\(180\) 5.01687 3.01049i 0.373936 0.224389i
\(181\) 13.1624i 0.978355i −0.872184 0.489178i \(-0.837297\pi\)
0.872184 0.489178i \(-0.162703\pi\)
\(182\) −4.22097 18.0379i −0.312879 1.33706i
\(183\) −4.24614 15.3283i −0.313884 1.13310i
\(184\) −1.00000 −0.0737210
\(185\) 0.633498 0.0465757
\(186\) 0.395700 0.109614i 0.0290142 0.00803729i
\(187\) 14.9410i 1.09259i
\(188\) −0.174840 −0.0127515
\(189\) 11.8601 + 6.95251i 0.862697 + 0.505721i
\(190\) 15.7769 1.14458
\(191\) 20.9301i 1.51445i −0.653154 0.757225i \(-0.726555\pi\)
0.653154 0.757225i \(-0.273445\pi\)
\(192\) 1.66919 0.462387i 0.120463 0.0333699i
\(193\) −2.02912 −0.146059 −0.0730296 0.997330i \(-0.523267\pi\)
−0.0730296 + 0.997330i \(0.523267\pi\)
\(194\) −16.7148 −1.20005
\(195\) −6.31415 22.7937i −0.452166 1.63229i
\(196\) 6.27318 3.10600i 0.448084 0.221857i
\(197\) 17.2251i 1.22724i −0.789602 0.613620i \(-0.789713\pi\)
0.789602 0.613620i \(-0.210287\pi\)
\(198\) −10.7679 + 6.46151i −0.765239 + 0.459199i
\(199\) 10.9423i 0.775682i 0.921726 + 0.387841i \(0.126779\pi\)
−0.921726 + 0.387841i \(0.873221\pi\)
\(200\) 1.19644i 0.0846009i
\(201\) −12.8318 + 3.55458i −0.905087 + 0.250721i
\(202\) 10.8858i 0.765925i
\(203\) 6.01855 1.40837i 0.422420 0.0988485i
\(204\) 5.95790 1.65041i 0.417136 0.115552i
\(205\) 17.2004 1.20133
\(206\) 1.91420 0.133368
\(207\) −1.54363 2.57240i −0.107289 0.178794i
\(208\) 7.00187i 0.485492i
\(209\) −33.8624 −2.34231
\(210\) 7.84274 4.28559i 0.541200 0.295734i
\(211\) 16.5236 1.13753 0.568765 0.822500i \(-0.307422\pi\)
0.568765 + 0.822500i \(0.307422\pi\)
\(212\) 5.65184i 0.388170i
\(213\) −2.50776 9.05286i −0.171829 0.620292i
\(214\) −13.7767 −0.941759
\(215\) −16.6605 −1.13624
\(216\) 3.76605 + 3.58007i 0.256247 + 0.243593i
\(217\) 0.610707 0.142909i 0.0414575 0.00970128i
\(218\) 4.26102i 0.288593i
\(219\) −5.16527 18.6463i −0.349037 1.26000i
\(220\) 8.16370i 0.550397i
\(221\) 24.9920i 1.68114i
\(222\) 0.150195 + 0.542195i 0.0100804 + 0.0363898i
\(223\) 6.83216i 0.457515i 0.973483 + 0.228758i \(0.0734663\pi\)
−0.973483 + 0.228758i \(0.926534\pi\)
\(224\) 2.57616 0.602835i 0.172127 0.0402786i
\(225\) −3.07771 + 1.84685i −0.205181 + 0.123123i
\(226\) 9.50152 0.632032
\(227\) −6.00651 −0.398666 −0.199333 0.979932i \(-0.563878\pi\)
−0.199333 + 0.979932i \(0.563878\pi\)
\(228\) 3.74052 + 13.5031i 0.247722 + 0.894262i
\(229\) 10.3531i 0.684150i −0.939673 0.342075i \(-0.888870\pi\)
0.939673 0.342075i \(-0.111130\pi\)
\(230\) −1.95027 −0.128597
\(231\) −16.8331 + 9.19828i −1.10754 + 0.605203i
\(232\) 2.33625 0.153382
\(233\) 9.24182i 0.605451i 0.953078 + 0.302726i \(0.0978966\pi\)
−0.953078 + 0.302726i \(0.902103\pi\)
\(234\) 18.0116 10.8083i 1.17745 0.706558i
\(235\) −0.340985 −0.0222434
\(236\) −7.74076 −0.503881
\(237\) −20.4225 + 5.65730i −1.32658 + 0.367481i
\(238\) 9.19516 2.15172i 0.596034 0.139475i
\(239\) 11.2399i 0.727047i −0.931585 0.363524i \(-0.881574\pi\)
0.931585 0.363524i \(-0.118426\pi\)
\(240\) 3.25538 0.901781i 0.210134 0.0582097i
\(241\) 3.48754i 0.224652i −0.993671 0.112326i \(-0.964170\pi\)
0.993671 0.112326i \(-0.0358301\pi\)
\(242\) 6.52200i 0.419250i
\(243\) −3.39598 + 15.2141i −0.217852 + 0.975982i
\(244\) 9.18309i 0.587887i
\(245\) 12.2344 6.05754i 0.781628 0.387002i
\(246\) 4.07802 + 14.7214i 0.260005 + 0.938602i
\(247\) 56.6422 3.60406
\(248\) 0.237061 0.0150534
\(249\) 29.9068 8.28458i 1.89527 0.525014i
\(250\) 12.0847i 0.764306i
\(251\) −0.529091 −0.0333959 −0.0166979 0.999861i \(-0.505315\pi\)
−0.0166979 + 0.999861i \(0.505315\pi\)
\(252\) 5.52735 + 5.69635i 0.348191 + 0.358836i
\(253\) 4.18593 0.263167
\(254\) 4.82854i 0.302970i
\(255\) 11.6195 3.21876i 0.727643 0.201566i
\(256\) 1.00000 0.0625000
\(257\) 8.82434 0.550447 0.275224 0.961380i \(-0.411248\pi\)
0.275224 + 0.961380i \(0.411248\pi\)
\(258\) −3.95002 14.2593i −0.245917 0.887747i
\(259\) 0.195816 + 0.836801i 0.0121674 + 0.0519963i
\(260\) 13.6555i 0.846881i
\(261\) 3.60630 + 6.00976i 0.223224 + 0.371995i
\(262\) 18.7373i 1.15760i
\(263\) 23.8672i 1.47171i 0.677137 + 0.735857i \(0.263220\pi\)
−0.677137 + 0.735857i \(0.736780\pi\)
\(264\) −6.98711 + 1.93552i −0.430027 + 0.119123i
\(265\) 11.0226i 0.677115i
\(266\) 4.87669 + 20.8400i 0.299009 + 1.27779i
\(267\) −2.03298 + 0.563163i −0.124417 + 0.0344650i
\(268\) −7.68745 −0.469586
\(269\) 0.592775 0.0361421 0.0180711 0.999837i \(-0.494247\pi\)
0.0180711 + 0.999837i \(0.494247\pi\)
\(270\) 7.34482 + 6.98211i 0.446992 + 0.424917i
\(271\) 2.86434i 0.173996i 0.996208 + 0.0869980i \(0.0277274\pi\)
−0.996208 + 0.0869980i \(0.972273\pi\)
\(272\) 3.56933 0.216423
\(273\) 28.1570 15.3861i 1.70414 0.931210i
\(274\) 6.80806 0.411290
\(275\) 5.00820i 0.302006i
\(276\) −0.462387 1.66919i −0.0278324 0.100473i
\(277\) −13.9675 −0.839224 −0.419612 0.907704i \(-0.637834\pi\)
−0.419612 + 0.907704i \(0.637834\pi\)
\(278\) −12.9800 −0.778489
\(279\) 0.365934 + 0.609815i 0.0219079 + 0.0365087i
\(280\) 5.02421 1.17569i 0.300254 0.0702611i
\(281\) 16.7970i 1.00202i −0.865440 0.501012i \(-0.832961\pi\)
0.865440 0.501012i \(-0.167039\pi\)
\(282\) −0.0808438 0.291841i −0.00481418 0.0173789i
\(283\) 17.3411i 1.03082i 0.856943 + 0.515411i \(0.172361\pi\)
−0.856943 + 0.515411i \(0.827639\pi\)
\(284\) 5.42350i 0.321826i
\(285\) 7.29504 + 26.3346i 0.432121 + 1.55993i
\(286\) 29.3093i 1.73310i
\(287\) 5.31669 + 22.7204i 0.313835 + 1.34114i
\(288\) 1.54363 + 2.57240i 0.0909590 + 0.151580i
\(289\) −4.25987 −0.250581
\(290\) 4.55633 0.267557
\(291\) −7.72873 27.9002i −0.453066 1.63554i
\(292\) 11.1709i 0.653726i
\(293\) 9.55084 0.557966 0.278983 0.960296i \(-0.410003\pi\)
0.278983 + 0.960296i \(0.410003\pi\)
\(294\) 8.08514 + 9.03496i 0.471535 + 0.526930i
\(295\) −15.0966 −0.878958
\(296\) 0.324825i 0.0188801i
\(297\) −15.7644 14.9859i −0.914744 0.869570i
\(298\) −13.6518 −0.790830
\(299\) −7.00187 −0.404928
\(300\) −1.99708 + 0.553217i −0.115302 + 0.0319400i
\(301\) −5.14981 22.0072i −0.296830 1.26848i
\(302\) 2.79942i 0.161088i
\(303\) −18.1705 + 5.03347i −1.04387 + 0.289166i
\(304\) 8.08958i 0.463969i
\(305\) 17.9095i 1.02550i
\(306\) 5.50971 + 9.18173i 0.314969 + 0.524885i
\(307\) 19.5248i 1.11434i −0.830399 0.557169i \(-0.811888\pi\)
0.830399 0.557169i \(-0.188112\pi\)
\(308\) −10.7836 + 2.52342i −0.614453 + 0.143785i
\(309\) 0.885101 + 3.19516i 0.0503516 + 0.181766i
\(310\) 0.462334 0.0262588
\(311\) −20.0679 −1.13795 −0.568973 0.822356i \(-0.692659\pi\)
−0.568973 + 0.822356i \(0.692659\pi\)
\(312\) 11.6874 3.23757i 0.661672 0.183292i
\(313\) 16.3669i 0.925114i −0.886590 0.462557i \(-0.846932\pi\)
0.886590 0.462557i \(-0.153068\pi\)
\(314\) −9.02729 −0.509439
\(315\) 10.7798 + 11.1094i 0.607376 + 0.625945i
\(316\) −12.2350 −0.688271
\(317\) 8.14630i 0.457542i 0.973480 + 0.228771i \(0.0734707\pi\)
−0.973480 + 0.228771i \(0.926529\pi\)
\(318\) 9.43401 2.61334i 0.529033 0.146549i
\(319\) −9.77938 −0.547540
\(320\) 1.95027 0.109024
\(321\) −6.37019 22.9960i −0.355550 1.28351i
\(322\) −0.602835 2.57616i −0.0335947 0.143564i
\(323\) 28.8744i 1.60662i
\(324\) −4.23444 + 7.94163i −0.235247 + 0.441202i
\(325\) 8.37729i 0.464689i
\(326\) 1.52485i 0.0844537i
\(327\) 7.11245 1.97024i 0.393319 0.108955i
\(328\) 8.81948i 0.486975i
\(329\) −0.105400 0.450415i −0.00581087 0.0248322i
\(330\) −13.6268 + 3.77479i −0.750129 + 0.207795i
\(331\) −26.4631 −1.45454 −0.727271 0.686351i \(-0.759212\pi\)
−0.727271 + 0.686351i \(0.759212\pi\)
\(332\) 17.9170 0.983321
\(333\) −0.835579 + 0.501408i −0.0457894 + 0.0274770i
\(334\) 7.96658i 0.435912i
\(335\) −14.9926 −0.819134
\(336\) 2.19743 + 4.02136i 0.119880 + 0.219383i
\(337\) 27.8741 1.51840 0.759201 0.650857i \(-0.225590\pi\)
0.759201 + 0.650857i \(0.225590\pi\)
\(338\) 36.0261i 1.95956i
\(339\) 4.39338 + 15.8599i 0.238616 + 0.861389i
\(340\) 6.96117 0.377522
\(341\) −0.992321 −0.0537372
\(342\) −20.8096 + 12.4873i −1.12526 + 0.675235i
\(343\) 11.7832 + 14.2883i 0.636235 + 0.771496i
\(344\) 8.54266i 0.460589i
\(345\) −0.901781 3.25538i −0.0485503 0.175264i
\(346\) 4.99294i 0.268422i
\(347\) 10.8116i 0.580398i −0.956966 0.290199i \(-0.906278\pi\)
0.956966 0.290199i \(-0.0937215\pi\)
\(348\) 1.08025 + 3.89965i 0.0579077 + 0.209043i
\(349\) 2.76386i 0.147946i −0.997260 0.0739731i \(-0.976432\pi\)
0.997260 0.0739731i \(-0.0235679\pi\)
\(350\) −3.08221 + 0.721254i −0.164751 + 0.0385527i
\(351\) 26.3694 + 25.0671i 1.40749 + 1.33799i
\(352\) −4.18593 −0.223111
\(353\) 23.4616 1.24873 0.624367 0.781131i \(-0.285357\pi\)
0.624367 + 0.781131i \(0.285357\pi\)
\(354\) −3.57923 12.9208i −0.190234 0.686733i
\(355\) 10.5773i 0.561385i
\(356\) −1.21795 −0.0645510
\(357\) 7.84336 + 14.3536i 0.415114 + 0.759671i
\(358\) −9.35057 −0.494193
\(359\) 11.5092i 0.607435i 0.952762 + 0.303717i \(0.0982279\pi\)
−0.952762 + 0.303717i \(0.901772\pi\)
\(360\) 3.01049 + 5.01687i 0.158667 + 0.264412i
\(361\) −46.4414 −2.44428
\(362\) 13.1624 0.691802
\(363\) 10.8865 3.01569i 0.571391 0.158283i
\(364\) 18.0379 4.22097i 0.945443 0.221239i
\(365\) 21.7862i 1.14034i
\(366\) 15.3283 4.24614i 0.801224 0.221949i
\(367\) 8.53645i 0.445599i −0.974864 0.222800i \(-0.928480\pi\)
0.974864 0.222800i \(-0.0715196\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) −22.6872 + 13.6140i −1.18105 + 0.708715i
\(370\) 0.633498i 0.0329340i
\(371\) 14.5600 3.40713i 0.755920 0.176889i
\(372\) 0.109614 + 0.395700i 0.00568323 + 0.0205161i
\(373\) −31.5142 −1.63174 −0.815871 0.578234i \(-0.803742\pi\)
−0.815871 + 0.578234i \(0.803742\pi\)
\(374\) −14.9410 −0.772579
\(375\) −20.1717 + 5.58783i −1.04166 + 0.288554i
\(376\) 0.174840i 0.00901668i
\(377\) 16.3581 0.842486
\(378\) −6.95251 + 11.8601i −0.357599 + 0.610019i
\(379\) −15.0834 −0.774780 −0.387390 0.921916i \(-0.626623\pi\)
−0.387390 + 0.921916i \(0.626623\pi\)
\(380\) 15.7769i 0.809338i
\(381\) −8.05975 + 2.23266i −0.412914 + 0.114382i
\(382\) 20.9301 1.07088
\(383\) −5.99148 −0.306150 −0.153075 0.988215i \(-0.548918\pi\)
−0.153075 + 0.988215i \(0.548918\pi\)
\(384\) 0.462387 + 1.66919i 0.0235961 + 0.0851805i
\(385\) −21.0310 + 4.92137i −1.07184 + 0.250816i
\(386\) 2.02912i 0.103280i
\(387\) 21.9751 13.1867i 1.11706 0.670316i
\(388\) 16.7148i 0.848567i
\(389\) 1.08008i 0.0547622i −0.999625 0.0273811i \(-0.991283\pi\)
0.999625 0.0273811i \(-0.00871677\pi\)
\(390\) 22.7937 6.31415i 1.15420 0.319730i
\(391\) 3.56933i 0.180509i
\(392\) 3.10600 + 6.27318i 0.156877 + 0.316843i
\(393\) −31.2762 + 8.66390i −1.57767 + 0.437036i
\(394\) 17.2251 0.867789
\(395\) −23.8615 −1.20060
\(396\) −6.46151 10.7679i −0.324703 0.541106i
\(397\) 19.0645i 0.956818i 0.878137 + 0.478409i \(0.158786\pi\)
−0.878137 + 0.478409i \(0.841214\pi\)
\(398\) −10.9423 −0.548490
\(399\) −32.5311 + 17.7763i −1.62859 + 0.889928i
\(400\) −1.19644 −0.0598219
\(401\) 3.58379i 0.178966i −0.995988 0.0894831i \(-0.971479\pi\)
0.995988 0.0894831i \(-0.0285215\pi\)
\(402\) −3.55458 12.8318i −0.177286 0.639993i
\(403\) 1.65987 0.0826840
\(404\) −10.8858 −0.541591
\(405\) −8.25831 + 15.4883i −0.410359 + 0.769622i
\(406\) 1.40837 + 6.01855i 0.0698965 + 0.298696i
\(407\) 1.35969i 0.0673976i
\(408\) 1.65041 + 5.95790i 0.0817077 + 0.294960i
\(409\) 3.95955i 0.195787i 0.995197 + 0.0978936i \(0.0312105\pi\)
−0.995197 + 0.0978936i \(0.968790\pi\)
\(410\) 17.2004i 0.849467i
\(411\) 3.14796 + 11.3640i 0.155278 + 0.560543i
\(412\) 1.91420i 0.0943058i
\(413\) −4.66640 19.9414i −0.229619 0.981253i
\(414\) 2.57240 1.54363i 0.126426 0.0758651i
\(415\) 34.9429 1.71528
\(416\) 7.00187 0.343295
\(417\) −6.00179 21.6661i −0.293909 1.06099i
\(418\) 33.8624i 1.65627i
\(419\) 13.2658 0.648078 0.324039 0.946044i \(-0.394959\pi\)
0.324039 + 0.946044i \(0.394959\pi\)
\(420\) 4.28559 + 7.84274i 0.209115 + 0.382687i
\(421\) 21.2102 1.03372 0.516861 0.856069i \(-0.327100\pi\)
0.516861 + 0.856069i \(0.327100\pi\)
\(422\) 16.5236i 0.804355i
\(423\) 0.449757 0.269887i 0.0218680 0.0131224i
\(424\) 5.65184 0.274478
\(425\) −4.27048 −0.207149
\(426\) 9.05286 2.50776i 0.438613 0.121501i
\(427\) 23.6571 5.53589i 1.14485 0.267900i
\(428\) 13.7767i 0.665924i
\(429\) −48.9228 + 13.5523i −2.36202 + 0.654309i
\(430\) 16.6605i 0.803441i
\(431\) 8.01994i 0.386307i −0.981169 0.193153i \(-0.938128\pi\)
0.981169 0.193153i \(-0.0618715\pi\)
\(432\) −3.58007 + 3.76605i −0.172246 + 0.181194i
\(433\) 20.1632i 0.968981i −0.874796 0.484491i \(-0.839005\pi\)
0.874796 0.484491i \(-0.160995\pi\)
\(434\) 0.142909 + 0.610707i 0.00685984 + 0.0293149i
\(435\) 2.10679 + 7.60538i 0.101013 + 0.364650i
\(436\) 4.26102 0.204066
\(437\) 8.08958 0.386977
\(438\) 18.6463 5.16527i 0.890955 0.246806i
\(439\) 39.5350i 1.88690i 0.331508 + 0.943452i \(0.392442\pi\)
−0.331508 + 0.943452i \(0.607558\pi\)
\(440\) −8.16370 −0.389189
\(441\) −11.3426 + 17.6733i −0.540124 + 0.841585i
\(442\) 24.9920 1.18875
\(443\) 18.1483i 0.862254i 0.902291 + 0.431127i \(0.141884\pi\)
−0.902291 + 0.431127i \(0.858116\pi\)
\(444\) −0.542195 + 0.150195i −0.0257314 + 0.00712794i
\(445\) −2.37533 −0.112601
\(446\) −6.83216 −0.323512
\(447\) −6.31244 22.7875i −0.298568 1.07781i
\(448\) 0.602835 + 2.57616i 0.0284813 + 0.121712i
\(449\) 23.0015i 1.08551i 0.839892 + 0.542754i \(0.182619\pi\)
−0.839892 + 0.542754i \(0.817381\pi\)
\(450\) −1.84685 3.07771i −0.0870614 0.145085i
\(451\) 36.9177i 1.73839i
\(452\) 9.50152i 0.446914i
\(453\) −4.67276 + 1.29442i −0.219546 + 0.0608170i
\(454\) 6.00651i 0.281899i
\(455\) 35.1788 8.23204i 1.64921 0.385924i
\(456\) −13.5031 + 3.74052i −0.632339 + 0.175166i
\(457\) −5.70940 −0.267074 −0.133537 0.991044i \(-0.542634\pi\)
−0.133537 + 0.991044i \(0.542634\pi\)
\(458\) 10.3531 0.483767
\(459\) −12.7784 + 13.4423i −0.596447 + 0.627432i
\(460\) 1.95027i 0.0909319i
\(461\) −21.1482 −0.984969 −0.492485 0.870321i \(-0.663911\pi\)
−0.492485 + 0.870321i \(0.663911\pi\)
\(462\) −9.19828 16.8331i −0.427943 0.783147i
\(463\) −3.64251 −0.169282 −0.0846410 0.996412i \(-0.526974\pi\)
−0.0846410 + 0.996412i \(0.526974\pi\)
\(464\) 2.33625i 0.108458i
\(465\) 0.213777 + 0.771723i 0.00991369 + 0.0357878i
\(466\) −9.24182 −0.428119
\(467\) −7.13820 −0.330317 −0.165158 0.986267i \(-0.552814\pi\)
−0.165158 + 0.986267i \(0.552814\pi\)
\(468\) 10.8083 + 18.0116i 0.499612 + 0.832585i
\(469\) −4.63426 19.8041i −0.213990 0.914468i
\(470\) 0.340985i 0.0157285i
\(471\) −4.17411 15.0683i −0.192333 0.694309i
\(472\) 7.74076i 0.356297i
\(473\) 35.7590i 1.64420i
\(474\) −5.65730 20.4225i −0.259848 0.938037i
\(475\) 9.67868i 0.444088i
\(476\) 2.15172 + 9.19516i 0.0986239 + 0.421460i
\(477\) 8.72433 + 14.5388i 0.399460 + 0.665685i
\(478\) 11.2399 0.514100
\(479\) −25.8976 −1.18329 −0.591646 0.806198i \(-0.701522\pi\)
−0.591646 + 0.806198i \(0.701522\pi\)
\(480\) 0.901781 + 3.25538i 0.0411605 + 0.148587i
\(481\) 2.27438i 0.103703i
\(482\) 3.48754 0.158853
\(483\) 4.02136 2.19743i 0.182978 0.0999865i
\(484\) 6.52200 0.296454
\(485\) 32.5985i 1.48022i
\(486\) −15.2141 3.39598i −0.690123 0.154045i
\(487\) −19.2742 −0.873395 −0.436698 0.899608i \(-0.643852\pi\)
−0.436698 + 0.899608i \(0.643852\pi\)
\(488\) 9.18309 0.415699
\(489\) −2.54527 + 0.705072i −0.115101 + 0.0318845i
\(490\) 6.05754 + 12.2344i 0.273652 + 0.552694i
\(491\) 31.9607i 1.44237i 0.692744 + 0.721184i \(0.256402\pi\)
−0.692744 + 0.721184i \(0.743598\pi\)
\(492\) −14.7214 + 4.07802i −0.663692 + 0.183851i
\(493\) 8.33886i 0.375563i
\(494\) 56.6422i 2.54845i
\(495\) −12.6017 21.0003i −0.566404 0.943892i
\(496\) 0.237061i 0.0106444i
\(497\) 13.9718 3.26948i 0.626721 0.146656i
\(498\) 8.28458 + 29.9068i 0.371241 + 1.34016i
\(499\) −36.6266 −1.63963 −0.819815 0.572628i \(-0.805924\pi\)
−0.819815 + 0.572628i \(0.805924\pi\)
\(500\) −12.0847 −0.540446
\(501\) 13.2977 3.68364i 0.594099 0.164573i
\(502\) 0.529091i 0.0236145i
\(503\) −12.8526 −0.573070 −0.286535 0.958070i \(-0.592503\pi\)
−0.286535 + 0.958070i \(0.592503\pi\)
\(504\) −5.69635 + 5.52735i −0.253735 + 0.246208i
\(505\) −21.2304 −0.944738
\(506\) 4.18593i 0.186087i
\(507\) 60.1345 16.6580i 2.67067 0.739809i
\(508\) −4.82854 −0.214232
\(509\) −6.44339 −0.285598 −0.142799 0.989752i \(-0.545610\pi\)
−0.142799 + 0.989752i \(0.545610\pi\)
\(510\) 3.21876 + 11.6195i 0.142529 + 0.514521i
\(511\) 28.7779 6.73419i 1.27306 0.297903i
\(512\) 1.00000i 0.0441942i
\(513\) −30.4658 28.9613i −1.34510 1.27867i
\(514\) 8.82434i 0.389225i
\(515\) 3.73321i 0.164505i
\(516\) 14.2593 3.95002i 0.627732 0.173890i
\(517\) 0.731867i 0.0321875i
\(518\) −0.836801 + 0.195816i −0.0367669 + 0.00860366i
\(519\) −8.33417 + 2.30867i −0.365829 + 0.101339i
\(520\) 13.6555 0.598835
\(521\) 32.2374 1.41235 0.706174 0.708039i \(-0.250420\pi\)
0.706174 + 0.708039i \(0.250420\pi\)
\(522\) −6.00976 + 3.60630i −0.263040 + 0.157843i
\(523\) 2.19484i 0.0959735i 0.998848 + 0.0479867i \(0.0152805\pi\)
−0.998848 + 0.0479867i \(0.984719\pi\)
\(524\) −18.7373 −0.818544
\(525\) −2.62909 4.81130i −0.114743 0.209982i
\(526\) −23.8672 −1.04066
\(527\) 0.846150i 0.0368589i
\(528\) −1.93552 6.98711i −0.0842327 0.304075i
\(529\) −1.00000 −0.0434783
\(530\) 11.0226 0.478793
\(531\) 19.9123 11.9488i 0.864120 0.518535i
\(532\) −20.8400 + 4.87669i −0.903531 + 0.211431i
\(533\) 61.7528i 2.67481i
\(534\) −0.563163 2.03298i −0.0243704 0.0879758i
\(535\) 26.8684i 1.16162i
\(536\) 7.68745i 0.332047i
\(537\) −4.32359 15.6079i −0.186577 0.673530i
\(538\) 0.592775i 0.0255563i
\(539\) −13.0015 26.2591i −0.560013 1.13106i
\(540\) −6.98211 + 7.34482i −0.300462 + 0.316071i
\(541\) −42.5880 −1.83100 −0.915502 0.402314i \(-0.868206\pi\)
−0.915502 + 0.402314i \(0.868206\pi\)
\(542\) −2.86434 −0.123034
\(543\) 6.08614 + 21.9706i 0.261181 + 0.942849i
\(544\) 3.56933i 0.153034i
\(545\) 8.31014 0.355968
\(546\) 15.3861 + 28.1570i 0.658465 + 1.20501i
\(547\) 7.98052 0.341222 0.170611 0.985338i \(-0.445426\pi\)
0.170611 + 0.985338i \(0.445426\pi\)
\(548\) 6.80806i 0.290826i
\(549\) 14.1752 + 23.6225i 0.604985 + 1.00819i
\(550\) 5.00820 0.213550
\(551\) −18.8993 −0.805137
\(552\) 1.66919 0.462387i 0.0710455 0.0196805i
\(553\) −7.37567 31.5192i −0.313645 1.34033i
\(554\) 13.9675i 0.593421i
\(555\) −1.05743 + 0.292921i −0.0448853 + 0.0124338i
\(556\) 12.9800i 0.550475i
\(557\) 15.3471i 0.650278i −0.945666 0.325139i \(-0.894589\pi\)
0.945666 0.325139i \(-0.105411\pi\)
\(558\) −0.609815 + 0.365934i −0.0258155 + 0.0154912i
\(559\) 59.8145i 2.52989i
\(560\) 1.17569 + 5.02421i 0.0496821 + 0.212312i
\(561\) −6.90851 24.9393i −0.291678 1.05294i
\(562\) 16.7970 0.708539
\(563\) −33.4328 −1.40902 −0.704512 0.709692i \(-0.748834\pi\)
−0.704512 + 0.709692i \(0.748834\pi\)
\(564\) 0.291841 0.0808438i 0.0122887 0.00340414i
\(565\) 18.5306i 0.779586i
\(566\) −17.3411 −0.728902
\(567\) −23.0116 6.12109i −0.966395 0.257062i
\(568\) 5.42350 0.227565
\(569\) 29.4280i 1.23369i 0.787087 + 0.616843i \(0.211589\pi\)
−0.787087 + 0.616843i \(0.788411\pi\)
\(570\) −26.3346 + 7.29504i −1.10304 + 0.305555i
\(571\) 25.1047 1.05060 0.525299 0.850918i \(-0.323953\pi\)
0.525299 + 0.850918i \(0.323953\pi\)
\(572\) −29.3093 −1.22548
\(573\) 9.67782 + 34.9364i 0.404297 + 1.45949i
\(574\) −22.7204 + 5.31669i −0.948330 + 0.221915i
\(575\) 1.19644i 0.0498949i
\(576\) −2.57240 + 1.54363i −0.107183 + 0.0643177i
\(577\) 20.8099i 0.866329i −0.901315 0.433165i \(-0.857397\pi\)
0.901315 0.433165i \(-0.142603\pi\)
\(578\) 4.25987i 0.177187i
\(579\) 3.38699 0.938240i 0.140758 0.0389919i
\(580\) 4.55633i 0.189191i
\(581\) 10.8010 + 46.1569i 0.448100 + 1.91491i
\(582\) 27.9002 7.72873i 1.15650 0.320366i
\(583\) −23.6582 −0.979823
\(584\) 11.1709 0.462254
\(585\) 21.0790 + 35.1275i 0.871511 + 1.45234i
\(586\) 9.55084i 0.394541i
\(587\) 33.0545 1.36431 0.682153 0.731209i \(-0.261044\pi\)
0.682153 + 0.731209i \(0.261044\pi\)
\(588\) −9.03496 + 8.08514i −0.372595 + 0.333426i
\(589\) −1.91773 −0.0790185
\(590\) 15.0966i 0.621517i
\(591\) 7.96468 + 28.7520i 0.327623 + 1.18270i
\(592\) −0.324825 −0.0133502
\(593\) 15.1171 0.620786 0.310393 0.950608i \(-0.399539\pi\)
0.310393 + 0.950608i \(0.399539\pi\)
\(594\) 14.9859 15.7644i 0.614879 0.646822i
\(595\) 4.19644 + 17.9331i 0.172037 + 0.735184i
\(596\) 13.6518i 0.559201i
\(597\) −5.05960 18.2649i −0.207076 0.747531i
\(598\) 7.00187i 0.286328i
\(599\) 29.2716i 1.19601i 0.801494 + 0.598003i \(0.204039\pi\)
−0.801494 + 0.598003i \(0.795961\pi\)
\(600\) −0.553217 1.99708i −0.0225850 0.0815305i
\(601\) 8.67668i 0.353929i −0.984217 0.176965i \(-0.943372\pi\)
0.984217 0.176965i \(-0.0566278\pi\)
\(602\) 22.0072 5.14981i 0.896948 0.209891i
\(603\) 19.7752 11.8665i 0.805307 0.483243i
\(604\) −2.79942 −0.113907
\(605\) 12.7197 0.517128
\(606\) −5.03347 18.1705i −0.204471 0.738128i
\(607\) 44.4740i 1.80515i −0.430538 0.902573i \(-0.641676\pi\)
0.430538 0.902573i \(-0.358324\pi\)
\(608\) −8.08958 −0.328076
\(609\) −9.39490 + 5.13375i −0.380701 + 0.208030i
\(610\) 17.9095 0.725135
\(611\) 1.22421i 0.0495260i
\(612\) −9.18173 + 5.50971i −0.371150 + 0.222717i
\(613\) 9.37475 0.378643 0.189321 0.981915i \(-0.439371\pi\)
0.189321 + 0.981915i \(0.439371\pi\)
\(614\) 19.5248 0.787956
\(615\) −28.7107 + 7.95325i −1.15773 + 0.320706i
\(616\) −2.52342 10.7836i −0.101672 0.434484i
\(617\) 19.2861i 0.776428i −0.921569 0.388214i \(-0.873092\pi\)
0.921569 0.388214i \(-0.126908\pi\)
\(618\) −3.19516 + 0.885101i −0.128528 + 0.0356040i
\(619\) 38.4993i 1.54742i 0.633542 + 0.773709i \(0.281601\pi\)
−0.633542 + 0.773709i \(0.718399\pi\)
\(620\) 0.462334i 0.0185678i
\(621\) 3.76605 + 3.58007i 0.151126 + 0.143663i
\(622\) 20.0679i 0.804649i
\(623\) −0.734221 3.13762i −0.0294159 0.125706i
\(624\) 3.23757 + 11.6874i 0.129607 + 0.467872i
\(625\) −17.5864 −0.703454
\(626\) 16.3669 0.654154
\(627\) 56.5228 15.6576i 2.25730 0.625303i
\(628\) 9.02729i 0.360228i
\(629\) −1.15941 −0.0462287
\(630\) −11.1094 + 10.7798i −0.442610 + 0.429479i
\(631\) 6.71012 0.267126 0.133563 0.991040i \(-0.457358\pi\)
0.133563 + 0.991040i \(0.457358\pi\)
\(632\) 12.2350i 0.486681i
\(633\) −27.5810 + 7.64029i −1.09625 + 0.303674i
\(634\) −8.14630 −0.323531
\(635\) −9.41697 −0.373701
\(636\) 2.61334 + 9.43401i 0.103626 + 0.374083i
\(637\) 21.7478 + 43.9240i 0.861678 + 1.74033i
\(638\) 9.77938i 0.387169i
\(639\) 8.37186 + 13.9514i 0.331186 + 0.551909i
\(640\) 1.95027i 0.0770913i
\(641\) 14.0351i 0.554354i 0.960819 + 0.277177i \(0.0893988\pi\)
−0.960819 + 0.277177i \(0.910601\pi\)
\(642\) 22.9960 6.37019i 0.907581 0.251412i
\(643\) 14.3748i 0.566887i 0.958989 + 0.283443i \(0.0914768\pi\)
−0.958989 + 0.283443i \(0.908523\pi\)
\(644\) 2.57616 0.602835i 0.101515 0.0237550i
\(645\) 27.8096 7.70361i 1.09500 0.303329i
\(646\) −28.8744 −1.13605
\(647\) 18.7105 0.735587 0.367793 0.929908i \(-0.380113\pi\)
0.367793 + 0.929908i \(0.380113\pi\)
\(648\) −7.94163 4.23444i −0.311977 0.166345i
\(649\) 32.4023i 1.27190i
\(650\) −8.37729 −0.328584
\(651\) −0.953307 + 0.520925i −0.0373631 + 0.0204167i
\(652\) −1.52485 −0.0597178
\(653\) 21.3030i 0.833650i 0.908987 + 0.416825i \(0.136857\pi\)
−0.908987 + 0.416825i \(0.863143\pi\)
\(654\) 1.97024 + 7.11245i 0.0770425 + 0.278119i
\(655\) −36.5429 −1.42785
\(656\) −8.81948 −0.344343
\(657\) 17.2436 + 28.7359i 0.672738 + 1.12109i
\(658\) 0.450415 0.105400i 0.0175590 0.00410891i
\(659\) 20.9096i 0.814524i −0.913311 0.407262i \(-0.866484\pi\)
0.913311 0.407262i \(-0.133516\pi\)
\(660\) −3.77479 13.6268i −0.146934 0.530422i
\(661\) 42.4302i 1.65035i −0.564881 0.825173i \(-0.691078\pi\)
0.564881 0.825173i \(-0.308922\pi\)
\(662\) 26.4631i 1.02852i
\(663\) 11.5560 + 41.7164i 0.448797 + 1.62013i
\(664\) 17.9170i 0.695313i
\(665\) −40.6438 + 9.51087i −1.57610 + 0.368816i
\(666\) −0.501408 0.835579i −0.0194292 0.0323780i
\(667\) 2.33625 0.0904600
\(668\) 7.96658 0.308236
\(669\) −3.15911 11.4042i −0.122138 0.440911i
\(670\) 14.9926i 0.579215i
\(671\) −38.4397 −1.48395
\(672\) −4.02136 + 2.19743i −0.155127 + 0.0847677i
\(673\) 42.5206 1.63905 0.819523 0.573046i \(-0.194238\pi\)
0.819523 + 0.573046i \(0.194238\pi\)
\(674\) 27.8741i 1.07367i
\(675\) 4.28332 4.50584i 0.164865 0.173430i
\(676\) 36.0261 1.38562
\(677\) −19.5004 −0.749460 −0.374730 0.927134i \(-0.622265\pi\)
−0.374730 + 0.927134i \(0.622265\pi\)
\(678\) −15.8599 + 4.39338i −0.609094 + 0.168727i
\(679\) 43.0600 10.0763i 1.65249 0.386692i
\(680\) 6.96117i 0.266949i
\(681\) 10.0260 2.77733i 0.384197 0.106428i
\(682\) 0.992321i 0.0379979i
\(683\) 24.8146i 0.949505i 0.880119 + 0.474753i \(0.157462\pi\)
−0.880119 + 0.474753i \(0.842538\pi\)
\(684\) −12.4873 20.8096i −0.477463 0.795675i
\(685\) 13.2776i 0.507310i
\(686\) −14.2883 + 11.7832i −0.545530 + 0.449886i
\(687\) 4.78713 + 17.2812i 0.182640 + 0.659320i
\(688\) 8.54266 0.325686
\(689\) 39.5735 1.50763
\(690\) 3.25538 0.901781i 0.123930 0.0343302i
\(691\) 2.77055i 0.105397i 0.998610 + 0.0526983i \(0.0167822\pi\)
−0.998610 + 0.0526983i \(0.983218\pi\)
\(692\) −4.99294 −0.189803
\(693\) 23.8445 23.1371i 0.905778 0.878906i
\(694\) 10.8116 0.410403
\(695\) 25.3146i 0.960236i
\(696\) −3.89965 + 1.08025i −0.147816 + 0.0409469i
\(697\) −31.4797 −1.19238
\(698\) 2.76386 0.104614
\(699\) −4.27330 15.4264i −0.161631 0.583478i
\(700\) −0.721254 3.08221i −0.0272609 0.116497i
\(701\) 21.9857i 0.830388i −0.909733 0.415194i \(-0.863714\pi\)
0.909733 0.415194i \(-0.136286\pi\)
\(702\) −25.0671 + 26.3694i −0.946098 + 0.995248i
\(703\) 2.62770i 0.0991056i
\(704\) 4.18593i 0.157763i
\(705\) 0.569170 0.157667i 0.0214362 0.00593810i
\(706\) 23.4616i 0.882988i
\(707\) −6.56237 28.0436i −0.246803 1.05469i
\(708\) 12.9208 3.57923i 0.485594 0.134516i
\(709\) 21.8317 0.819908 0.409954 0.912106i \(-0.365545\pi\)
0.409954 + 0.912106i \(0.365545\pi\)
\(710\) 10.5773 0.396959
\(711\) 31.4732 18.8862i 1.18034 0.708288i
\(712\) 1.21795i 0.0456445i
\(713\) 0.237061 0.00887801
\(714\) −14.3536 + 7.84336i −0.537168 + 0.293530i
\(715\) −57.1611 −2.13771
\(716\) 9.35057i 0.349447i
\(717\) 5.19718 + 18.7615i 0.194092 + 0.700661i
\(718\) −11.5092 −0.429521
\(719\) 19.3398 0.721253 0.360627 0.932710i \(-0.382563\pi\)
0.360627 + 0.932710i \(0.382563\pi\)
\(720\) −5.01687 + 3.01049i −0.186968 + 0.112194i
\(721\) −4.93128 + 1.15395i −0.183650 + 0.0429752i
\(722\) 46.4414i 1.72837i
\(723\) 1.61259 + 5.82136i 0.0599730 + 0.216499i
\(724\) 13.1624i 0.489178i
\(725\) 2.79518i 0.103810i
\(726\) 3.01569 + 10.8865i 0.111923 + 0.404034i
\(727\) 44.0259i 1.63283i 0.577465 + 0.816415i \(0.304042\pi\)
−0.577465 + 0.816415i \(0.695958\pi\)
\(728\) 4.22097 + 18.0379i 0.156440 + 0.668529i
\(729\) −1.36625 26.9654i −0.0506018 0.998719i
\(730\) 21.7862 0.806345
\(731\) 30.4916 1.12777
\(732\) 4.24614 + 15.3283i 0.156942 + 0.566551i
\(733\) 7.09779i 0.262163i −0.991372 0.131082i \(-0.958155\pi\)
0.991372 0.131082i \(-0.0418450\pi\)
\(734\) 8.53645 0.315086
\(735\) −17.6206 + 15.7682i −0.649947 + 0.581620i
\(736\) 1.00000 0.0368605
\(737\) 32.1791i 1.18533i
\(738\) −13.6140 22.6872i −0.501138 0.835127i
\(739\) −2.54034 −0.0934479 −0.0467239 0.998908i \(-0.514878\pi\)
−0.0467239 + 0.998908i \(0.514878\pi\)
\(740\) −0.633498 −0.0232878
\(741\) −94.5466 + 26.1906i −3.47326 + 0.962137i
\(742\) 3.40713 + 14.5600i 0.125080 + 0.534516i
\(743\) 24.3821i 0.894493i 0.894411 + 0.447247i \(0.147595\pi\)
−0.894411 + 0.447247i \(0.852405\pi\)
\(744\) −0.395700 + 0.109614i −0.0145071 + 0.00401865i
\(745\) 26.6248i 0.975458i
\(746\) 31.5142i 1.15382i
\(747\) −46.0895 + 27.6571i −1.68633 + 1.01192i
\(748\) 14.9410i 0.546296i
\(749\) 35.4911 8.30511i 1.29682 0.303462i
\(750\) −5.58783 20.1717i −0.204039 0.736568i
\(751\) 20.8040 0.759147 0.379574 0.925162i \(-0.376071\pi\)
0.379574 + 0.925162i \(0.376071\pi\)
\(752\) 0.174840 0.00637575
\(753\) 0.883153 0.244645i 0.0321839 0.00891535i
\(754\) 16.3581i 0.595728i
\(755\) −5.45963 −0.198696
\(756\) −11.8601 6.95251i −0.431349 0.252860i
\(757\) 32.9030 1.19588 0.597941 0.801540i \(-0.295986\pi\)
0.597941 + 0.801540i \(0.295986\pi\)
\(758\) 15.0834i 0.547852i
\(759\) −6.98711 + 1.93552i −0.253616 + 0.0702549i
\(760\) −15.7769 −0.572288
\(761\) 1.08183 0.0392163 0.0196081 0.999808i \(-0.493758\pi\)
0.0196081 + 0.999808i \(0.493758\pi\)
\(762\) −2.23266 8.05975i −0.0808806 0.291974i
\(763\) 2.56869 + 10.9771i 0.0929929 + 0.397396i
\(764\) 20.9301i 0.757225i
\(765\) −17.9069 + 10.7454i −0.647425 + 0.388502i
\(766\) 5.99148i 0.216481i
\(767\) 54.1998i 1.95704i
\(768\) −1.66919 + 0.462387i −0.0602317 + 0.0166850i
\(769\) 7.09476i 0.255844i −0.991784 0.127922i \(-0.959169\pi\)
0.991784 0.127922i \(-0.0408307\pi\)
\(770\) −4.92137 21.0310i −0.177354 0.757904i
\(771\) −14.7295 + 4.08026i −0.530470 + 0.146947i
\(772\) 2.02912 0.0730296
\(773\) −4.10143 −0.147518 −0.0737590 0.997276i \(-0.523500\pi\)
−0.0737590 + 0.997276i \(0.523500\pi\)
\(774\) 13.1867 + 21.9751i 0.473985 + 0.789879i
\(775\) 0.283629i 0.0101882i
\(776\) 16.7148 0.600027
\(777\) −0.713781 1.30624i −0.0256067 0.0468610i
\(778\) 1.08008 0.0387228
\(779\) 71.3460i 2.55623i
\(780\) 6.31415 + 22.7937i 0.226083 + 0.816146i
\(781\) −22.7024 −0.812356
\(782\) 3.56933 0.127639
\(783\) −8.79844 8.36394i −0.314431 0.298903i
\(784\) −6.27318 + 3.10600i −0.224042 + 0.110928i
\(785\) 17.6057i 0.628374i
\(786\) −8.66390 31.2762i −0.309031 1.11558i
\(787\) 6.51757i 0.232326i 0.993230 + 0.116163i \(0.0370595\pi\)
−0.993230 + 0.116163i \(0.962940\pi\)
\(788\) 17.2251i 0.613620i
\(789\) −11.0359 39.8389i −0.392888 1.41830i
\(790\) 23.8615i 0.848955i
\(791\) −24.4774 + 5.72785i −0.870317 + 0.203659i
\(792\) 10.7679 6.46151i 0.382619 0.229600i
\(793\) 64.2987 2.28332
\(794\) −19.0645 −0.676573
\(795\) 5.09673 + 18.3989i 0.180762 + 0.652541i
\(796\) 10.9423i 0.387841i
\(797\) 18.9228 0.670280 0.335140 0.942168i \(-0.391216\pi\)
0.335140 + 0.942168i \(0.391216\pi\)
\(798\) −17.7763 32.5311i −0.629274 1.15159i
\(799\) 0.624062 0.0220777
\(800\) 1.19644i 0.0423004i
\(801\) 3.13304 1.88005i 0.110700 0.0664284i
\(802\) 3.58379 0.126548
\(803\) −46.7605 −1.65014
\(804\) 12.8318 3.55458i 0.452543 0.125360i
\(805\) 5.02421 1.17569i 0.177080 0.0414377i
\(806\) 1.65987i 0.0584664i
\(807\) −0.989455 + 0.274092i −0.0348304 + 0.00964848i
\(808\) 10.8858i 0.382962i
\(809\) 13.4432i 0.472638i −0.971676 0.236319i \(-0.924059\pi\)
0.971676 0.236319i \(-0.0759411\pi\)
\(810\) −15.4883 8.25831i −0.544205 0.290168i
\(811\) 47.7213i 1.67572i −0.545883 0.837861i \(-0.683806\pi\)
0.545883 0.837861i \(-0.316194\pi\)
\(812\) −6.01855 + 1.40837i −0.211210 + 0.0494243i
\(813\) −1.32443 4.78112i −0.0464499 0.167681i
\(814\) 1.35969 0.0476573
\(815\) −2.97388 −0.104170
\(816\) −5.95790 + 1.65041i −0.208568 + 0.0577760i
\(817\) 69.1065i 2.41773i
\(818\) −3.95955 −0.138443
\(819\) −39.8850 + 38.7018i −1.39370 + 1.35235i
\(820\) −17.2004 −0.600664
\(821\) 48.4833i 1.69208i 0.533119 + 0.846040i \(0.321020\pi\)
−0.533119 + 0.846040i \(0.678980\pi\)
\(822\) −11.3640 + 3.14796i −0.396363 + 0.109798i
\(823\) 2.23643 0.0779570 0.0389785 0.999240i \(-0.487590\pi\)
0.0389785 + 0.999240i \(0.487590\pi\)
\(824\) −1.91420 −0.0666842
\(825\) 2.31573 + 8.35964i 0.0806233 + 0.291045i
\(826\) 19.9414 4.66640i 0.693851 0.162365i
\(827\) 33.5211i 1.16564i −0.812600 0.582822i \(-0.801949\pi\)
0.812600 0.582822i \(-0.198051\pi\)
\(828\) 1.54363 + 2.57240i 0.0536447 + 0.0893969i
\(829\) 34.7676i 1.20753i 0.797163 + 0.603764i \(0.206333\pi\)
−0.797163 + 0.603764i \(0.793667\pi\)
\(830\) 34.9429i 1.21289i
\(831\) 23.3144 6.45838i 0.808767 0.224039i
\(832\) 7.00187i 0.242746i
\(833\) −22.3911 + 11.0863i −0.775804 + 0.384119i
\(834\) 21.6661 6.00179i 0.750236 0.207825i
\(835\) 15.5370 0.537680
\(836\) 33.8624 1.17116
\(837\) −0.892784 0.848695i −0.0308591 0.0293352i
\(838\) 13.2658i 0.458260i
\(839\) 48.1415 1.66203 0.831015 0.556249i \(-0.187760\pi\)
0.831015 + 0.556249i \(0.187760\pi\)
\(840\) −7.84274 + 4.28559i −0.270600 + 0.147867i
\(841\) 23.5419 0.811791
\(842\) 21.2102i 0.730952i
\(843\) 7.76672 + 28.0374i 0.267500 + 0.965659i
\(844\) −16.5236 −0.568765
\(845\) 70.2607 2.41704
\(846\) 0.269887 + 0.449757i 0.00927892 + 0.0154630i
\(847\) 3.93169 + 16.8017i 0.135094 + 0.577313i
\(848\) 5.65184i 0.194085i
\(849\) −8.01831 28.9456i −0.275188 0.993412i
\(850\) 4.27048i 0.146476i
\(851\) 0.324825i 0.0111349i
\(852\) 2.50776 + 9.05286i 0.0859144 + 0.310146i
\(853\) 8.65410i 0.296311i −0.988964 0.148155i \(-0.952666\pi\)
0.988964 0.148155i \(-0.0473336\pi\)
\(854\) 5.53589 + 23.6571i 0.189434 + 0.809529i
\(855\) −24.3536 40.5844i −0.832876 1.38796i
\(856\) 13.7767 0.470880
\(857\) −46.3184 −1.58221 −0.791103 0.611682i \(-0.790493\pi\)
−0.791103 + 0.611682i \(0.790493\pi\)
\(858\) −13.5523 48.9228i −0.462666 1.67020i
\(859\) 6.15224i 0.209912i 0.994477 + 0.104956i \(0.0334701\pi\)
−0.994477 + 0.104956i \(0.966530\pi\)
\(860\) 16.6605 0.568119
\(861\) −19.3802 35.4663i −0.660475 1.20869i
\(862\) 8.01994 0.273160
\(863\) 56.0948i 1.90949i −0.297427 0.954745i \(-0.596128\pi\)
0.297427 0.954745i \(-0.403872\pi\)
\(864\) −3.76605 3.58007i −0.128124 0.121796i
\(865\) −9.73759 −0.331088
\(866\) 20.1632 0.685173
\(867\) 7.11054 1.96971i 0.241487 0.0668949i
\(868\) −0.610707 + 0.142909i −0.0207287 + 0.00485064i
\(869\) 51.2147i 1.73734i
\(870\) −7.60538 + 2.10679i −0.257847 + 0.0714268i
\(871\) 53.8265i 1.82384i
\(872\) 4.26102i 0.144296i
\(873\) 25.8014 + 42.9972i 0.873246 + 1.45523i
\(874\) 8.08958i 0.273634i
\(875\) −7.28511 31.1322i −0.246282 1.05246i
\(876\) 5.16527 + 18.6463i 0.174518 + 0.630001i
\(877\) 9.97333 0.336775 0.168388 0.985721i \(-0.446144\pi\)
0.168388 + 0.985721i \(0.446144\pi\)
\(878\) −39.5350 −1.33424
\(879\) −15.9422 + 4.41619i −0.537716 + 0.148954i
\(880\) 8.16370i 0.275198i
\(881\) 51.3620 1.73043 0.865215 0.501401i \(-0.167182\pi\)
0.865215 + 0.501401i \(0.167182\pi\)
\(882\) −17.6733 11.3426i −0.595091 0.381925i
\(883\) −10.5576 −0.355292 −0.177646 0.984094i \(-0.556848\pi\)
−0.177646 + 0.984094i \(0.556848\pi\)
\(884\) 24.9920i 0.840571i
\(885\) 25.1991 6.98048i 0.847058 0.234646i
\(886\) −18.1483 −0.609705
\(887\) 39.3772 1.32216 0.661078 0.750317i \(-0.270099\pi\)
0.661078 + 0.750317i \(0.270099\pi\)
\(888\) −0.150195 0.542195i −0.00504022 0.0181949i
\(889\) −2.91081 12.4391i −0.0976255 0.417193i
\(890\) 2.37533i 0.0796211i
\(891\) 33.2431 + 17.7251i 1.11369 + 0.593812i
\(892\) 6.83216i 0.228758i
\(893\) 1.41438i 0.0473305i
\(894\) 22.7875 6.31244i 0.762129 0.211120i
\(895\) 18.2362i 0.609568i
\(896\) −2.57616 + 0.602835i −0.0860634 + 0.0201393i
\(897\) 11.6874 3.23757i 0.390233 0.108099i
\(898\) −23.0015 −0.767570
\(899\) −0.553835 −0.0184714
\(900\) 3.07771 1.84685i 0.102590 0.0615617i
\(901\) 20.1733i 0.672070i
\(902\) 36.9177 1.22923
\(903\) 18.7719 + 34.3531i 0.624689 + 1.14320i
\(904\) −9.50152 −0.316016
\(905\) 25.6703i 0.853310i
\(906\) −1.29442 4.67276i −0.0430041 0.155242i
\(907\) 39.3728 1.30735 0.653677 0.756774i \(-0.273226\pi\)
0.653677 + 0.756774i \(0.273226\pi\)
\(908\) 6.00651 0.199333
\(909\) 28.0027 16.8037i 0.928790 0.557342i
\(910\) 8.23204 + 35.1788i 0.272890 + 1.16617i
\(911\) 18.5776i 0.615505i −0.951467 0.307752i \(-0.900423\pi\)
0.951467 0.307752i \(-0.0995768\pi\)
\(912\) −3.74052 13.5031i −0.123861 0.447131i
\(913\) 74.9991i 2.48211i
\(914\) 5.70940i 0.188850i
\(915\) 8.28114 + 29.8944i 0.273766 + 0.988279i
\(916\) 10.3531i 0.342075i
\(917\) −11.2955 48.2703i −0.373011 1.59403i
\(918\) −13.4423 12.7784i −0.443661 0.421751i
\(919\) 19.5243 0.644047 0.322024 0.946732i \(-0.395637\pi\)
0.322024 + 0.946732i \(0.395637\pi\)
\(920\) 1.95027 0.0642986
\(921\) 9.02801 + 32.5906i 0.297483 + 1.07390i
\(922\) 21.1482i 0.696478i
\(923\) 37.9746 1.24995
\(924\) 16.8331 9.19828i 0.553769 0.302601i
\(925\) 0.388633 0.0127782
\(926\) 3.64251i 0.119700i
\(927\) −2.95480 4.92407i −0.0970485 0.161728i
\(928\) −2.33625 −0.0766912
\(929\) −3.45050 −0.113207 −0.0566036 0.998397i \(-0.518027\pi\)
−0.0566036 + 0.998397i \(0.518027\pi\)
\(930\) −0.771723 + 0.213777i −0.0253058 + 0.00701003i
\(931\) −25.1262 50.7474i −0.823479 1.66318i
\(932\) 9.24182i 0.302726i
\(933\) 33.4971 9.27914i 1.09665 0.303785i
\(934\) 7.13820i 0.233569i
\(935\) 29.1390i 0.952946i
\(936\) −18.0116 + 10.8083i −0.588727 + 0.353279i
\(937\) 9.13499i 0.298427i 0.988805 + 0.149214i \(0.0476742\pi\)
−0.988805 + 0.149214i \(0.952326\pi\)
\(938\) 19.8041 4.63426i 0.646626 0.151314i
\(939\) 7.56787 + 27.3195i 0.246968 + 0.891540i
\(940\) 0.340985 0.0111217
\(941\) 48.2892 1.57418 0.787091 0.616837i \(-0.211586\pi\)
0.787091 + 0.616837i \(0.211586\pi\)
\(942\) 15.0683 4.17411i 0.490951 0.136000i
\(943\) 8.81948i 0.287202i
\(944\) 7.74076 0.251940
\(945\) −23.1305 13.5593i −0.752435 0.441084i
\(946\) −35.7590 −1.16262
\(947\) 28.3766i 0.922117i 0.887370 + 0.461058i \(0.152530\pi\)
−0.887370 + 0.461058i \(0.847470\pi\)
\(948\) 20.4225 5.65730i 0.663292 0.183740i
\(949\) 78.2169 2.53903
\(950\) 9.67868 0.314018
\(951\) −3.76675 13.5977i −0.122145 0.440937i
\(952\) −9.19516 + 2.15172i −0.298017 + 0.0697376i
\(953\) 53.1134i 1.72051i −0.509862 0.860256i \(-0.670304\pi\)
0.509862 0.860256i \(-0.329696\pi\)
\(954\) −14.5388 + 8.72433i −0.470710 + 0.282461i
\(955\) 40.8194i 1.32089i
\(956\) 11.2399i 0.363524i
\(957\) 16.3237 4.52186i 0.527669 0.146171i
\(958\) 25.8976i 0.836713i
\(959\) −17.5386 + 4.10414i −0.566352 + 0.132530i
\(960\) −3.25538 + 0.901781i −0.105067 + 0.0291049i
\(961\) 30.9438 0.998187
\(962\) −2.27438 −0.0733290
\(963\) 21.2661 + 35.4392i 0.685292 + 1.14201i
\(964\) 3.48754i 0.112326i
\(965\) 3.95734 0.127391
\(966\) 2.19743 + 4.02136i 0.0707011 + 0.129385i
\(967\) −58.3617 −1.87679 −0.938393 0.345569i \(-0.887686\pi\)
−0.938393 + 0.345569i \(0.887686\pi\)
\(968\) 6.52200i 0.209625i
\(969\) −13.3512 48.1969i −0.428901 1.54831i
\(970\) 32.5985 1.04667
\(971\) −28.5530 −0.916311 −0.458155 0.888872i \(-0.651490\pi\)
−0.458155 + 0.888872i \(0.651490\pi\)
\(972\) 3.39598 15.2141i 0.108926 0.487991i
\(973\) 33.4386 7.82481i 1.07199 0.250852i
\(974\) 19.2742i 0.617584i
\(975\) −3.87355 13.9833i −0.124053 0.447824i
\(976\) 9.18309i 0.293943i
\(977\) 34.3488i 1.09891i −0.835522 0.549457i \(-0.814835\pi\)
0.835522 0.549457i \(-0.185165\pi\)
\(978\) −0.705072 2.54527i −0.0225457 0.0813887i
\(979\) 5.09823i 0.162940i
\(980\) −12.2344 + 6.05754i −0.390814 + 0.193501i
\(981\) −10.9610 + 6.57742i −0.349959 + 0.210001i
\(982\) −31.9607 −1.01991
\(983\) −40.2620 −1.28416 −0.642080 0.766638i \(-0.721928\pi\)
−0.642080 + 0.766638i \(0.721928\pi\)
\(984\) −4.07802 14.7214i −0.130002 0.469301i
\(985\) 33.5937i 1.07038i
\(986\) −8.33886 −0.265563
\(987\) 0.384198 + 0.703093i 0.0122292 + 0.0223797i
\(988\) −56.6422 −1.80203
\(989\) 8.54266i 0.271641i
\(990\) 21.0003 12.6017i 0.667432 0.400508i
\(991\) −13.7559 −0.436972 −0.218486 0.975840i \(-0.570112\pi\)
−0.218486 + 0.975840i \(0.570112\pi\)
\(992\) −0.237061 −0.00752670
\(993\) 44.1719 12.2362i 1.40175 0.388304i
\(994\) 3.26948 + 13.9718i 0.103702 + 0.443159i
\(995\) 21.3406i 0.676541i
\(996\) −29.9068 + 8.28458i −0.947634 + 0.262507i
\(997\) 36.9900i 1.17148i −0.810497 0.585742i \(-0.800803\pi\)
0.810497 0.585742i \(-0.199197\pi\)
\(998\) 36.6266i 1.15939i
\(999\) 1.16290 1.22331i 0.0367924 0.0387037i
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 966.2.f.b.461.14 yes 24
3.2 odd 2 inner 966.2.f.b.461.11 yes 24
7.6 odd 2 inner 966.2.f.b.461.23 yes 24
21.20 even 2 inner 966.2.f.b.461.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.2.f.b.461.2 24 21.20 even 2 inner
966.2.f.b.461.11 yes 24 3.2 odd 2 inner
966.2.f.b.461.14 yes 24 1.1 even 1 trivial
966.2.f.b.461.23 yes 24 7.6 odd 2 inner