Properties

Label 891.2.k.a.404.10
Level $891$
Weight $2$
Character 891.404
Analytic conductor $7.115$
Analytic rank $0$
Dimension $80$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(161,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.161");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.k (of order \(10\), degree \(4\), 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 404.10
Character \(\chi\) \(=\) 891.404
Dual form 891.2.k.a.161.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.299321 + 0.217469i) q^{2} +(-0.575734 + 1.77193i) q^{4} +(-1.39685 + 1.92260i) q^{5} +(-1.49987 - 0.487337i) q^{7} +(-0.441671 - 1.35932i) q^{8} -0.879247i q^{10} +(1.13773 + 3.11538i) q^{11} +(-3.60270 - 4.95870i) q^{13} +(0.554923 - 0.180306i) q^{14} +(-2.58677 - 1.87940i) q^{16} +(-0.887473 - 0.644787i) q^{17} +(-0.534855 + 0.173785i) q^{19} +(-2.60249 - 3.58202i) q^{20} +(-1.01805 - 0.685076i) q^{22} +5.56398i q^{23} +(-0.200115 - 0.615892i) q^{25} +(2.15673 + 0.700764i) q^{26} +(1.72705 - 2.37708i) q^{28} +(0.229389 - 0.705986i) q^{29} +(5.11890 - 3.71910i) q^{31} +4.04154 q^{32} +0.405861 q^{34} +(3.03205 - 2.20291i) q^{35} +(1.32443 - 4.07617i) q^{37} +(0.122300 - 0.168332i) q^{38} +(3.23039 + 1.04962i) q^{40} +(-3.75539 - 11.5579i) q^{41} -8.49248i q^{43} +(-6.17525 + 0.222344i) q^{44} +(-1.20999 - 1.66541i) q^{46} +(-0.731927 + 0.237817i) q^{47} +(-3.65101 - 2.65261i) q^{49} +(0.193836 + 0.140830i) q^{50} +(10.8606 - 3.52884i) q^{52} +(2.66042 + 3.66175i) q^{53} +(-7.57886 - 2.16432i) q^{55} +2.25405i q^{56} +(0.0848695 + 0.261201i) q^{58} +(0.0106843 + 0.00347154i) q^{59} +(-3.36853 + 4.63638i) q^{61} +(-0.723404 + 2.22641i) q^{62} +(3.96382 - 2.87988i) q^{64} +14.5660 q^{65} +1.47666 q^{67} +(1.65346 - 1.20131i) q^{68} +(-0.428490 + 1.31876i) q^{70} +(-4.89992 + 6.74417i) q^{71} +(-14.9894 - 4.87035i) q^{73} +(0.490013 + 1.50811i) q^{74} -1.04778i q^{76} +(-0.188206 - 5.22712i) q^{77} +(1.86989 + 2.57368i) q^{79} +(7.22666 - 2.34809i) q^{80} +(3.63756 + 2.64284i) q^{82} +(-8.40013 - 6.10305i) q^{83} +(2.47934 - 0.805585i) q^{85} +(1.84685 + 2.54198i) q^{86} +(3.73231 - 2.92252i) q^{88} +9.01115i q^{89} +(2.98703 + 9.19313i) q^{91} +(-9.85896 - 3.20337i) q^{92} +(0.167363 - 0.230355i) q^{94} +(0.412994 - 1.27106i) q^{95} +(-4.48177 + 3.25619i) q^{97} +1.66968 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.299321 + 0.217469i −0.211652 + 0.153774i −0.688561 0.725179i \(-0.741757\pi\)
0.476909 + 0.878953i \(0.341757\pi\)
\(3\) 0 0
\(4\) −0.575734 + 1.77193i −0.287867 + 0.885963i
\(5\) −1.39685 + 1.92260i −0.624691 + 0.859813i −0.997684 0.0680209i \(-0.978332\pi\)
0.372993 + 0.927834i \(0.378332\pi\)
\(6\) 0 0
\(7\) −1.49987 0.487337i −0.566898 0.184196i 0.0115248 0.999934i \(-0.496331\pi\)
−0.578422 + 0.815737i \(0.696331\pi\)
\(8\) −0.441671 1.35932i −0.156154 0.480594i
\(9\) 0 0
\(10\) 0.879247i 0.278042i
\(11\) 1.13773 + 3.11538i 0.343038 + 0.939321i
\(12\) 0 0
\(13\) −3.60270 4.95870i −0.999210 1.37529i −0.925809 0.377992i \(-0.876615\pi\)
−0.0734014 0.997302i \(-0.523385\pi\)
\(14\) 0.554923 0.180306i 0.148310 0.0481887i
\(15\) 0 0
\(16\) −2.58677 1.87940i −0.646692 0.469849i
\(17\) −0.887473 0.644787i −0.215244 0.156384i 0.474939 0.880019i \(-0.342470\pi\)
−0.690183 + 0.723635i \(0.742470\pi\)
\(18\) 0 0
\(19\) −0.534855 + 0.173785i −0.122704 + 0.0398690i −0.369725 0.929141i \(-0.620548\pi\)
0.247021 + 0.969010i \(0.420548\pi\)
\(20\) −2.60249 3.58202i −0.581935 0.800965i
\(21\) 0 0
\(22\) −1.01805 0.685076i −0.217048 0.146059i
\(23\) 5.56398i 1.16017i 0.814556 + 0.580085i \(0.196980\pi\)
−0.814556 + 0.580085i \(0.803020\pi\)
\(24\) 0 0
\(25\) −0.200115 0.615892i −0.0400231 0.123178i
\(26\) 2.15673 + 0.700764i 0.422969 + 0.137431i
\(27\) 0 0
\(28\) 1.72705 2.37708i 0.326382 0.449227i
\(29\) 0.229389 0.705986i 0.0425964 0.131098i −0.927497 0.373831i \(-0.878044\pi\)
0.970093 + 0.242733i \(0.0780439\pi\)
\(30\) 0 0
\(31\) 5.11890 3.71910i 0.919382 0.667970i −0.0239881 0.999712i \(-0.507636\pi\)
0.943370 + 0.331742i \(0.107636\pi\)
\(32\) 4.04154 0.714451
\(33\) 0 0
\(34\) 0.405861 0.0696045
\(35\) 3.03205 2.20291i 0.512510 0.372360i
\(36\) 0 0
\(37\) 1.32443 4.07617i 0.217735 0.670118i −0.781214 0.624264i \(-0.785399\pi\)
0.998948 0.0458543i \(-0.0146010\pi\)
\(38\) 0.122300 0.168332i 0.0198397 0.0273070i
\(39\) 0 0
\(40\) 3.23039 + 1.04962i 0.510769 + 0.165959i
\(41\) −3.75539 11.5579i −0.586494 1.80504i −0.593186 0.805066i \(-0.702130\pi\)
0.00669163 0.999978i \(-0.497870\pi\)
\(42\) 0 0
\(43\) 8.49248i 1.29509i −0.762027 0.647546i \(-0.775795\pi\)
0.762027 0.647546i \(-0.224205\pi\)
\(44\) −6.17525 + 0.222344i −0.930954 + 0.0335197i
\(45\) 0 0
\(46\) −1.20999 1.66541i −0.178404 0.245552i
\(47\) −0.731927 + 0.237817i −0.106763 + 0.0346892i −0.361911 0.932213i \(-0.617876\pi\)
0.255149 + 0.966902i \(0.417876\pi\)
\(48\) 0 0
\(49\) −3.65101 2.65261i −0.521572 0.378944i
\(50\) 0.193836 + 0.140830i 0.0274126 + 0.0199164i
\(51\) 0 0
\(52\) 10.8606 3.52884i 1.50610 0.489362i
\(53\) 2.66042 + 3.66175i 0.365437 + 0.502981i 0.951653 0.307174i \(-0.0993833\pi\)
−0.586217 + 0.810154i \(0.699383\pi\)
\(54\) 0 0
\(55\) −7.57886 2.16432i −1.02193 0.291837i
\(56\) 2.25405i 0.301211i
\(57\) 0 0
\(58\) 0.0848695 + 0.261201i 0.0111439 + 0.0342974i
\(59\) 0.0106843 + 0.00347154i 0.00139098 + 0.000451956i 0.309712 0.950830i \(-0.399767\pi\)
−0.308321 + 0.951282i \(0.599767\pi\)
\(60\) 0 0
\(61\) −3.36853 + 4.63638i −0.431296 + 0.593628i −0.968250 0.249983i \(-0.919575\pi\)
0.536954 + 0.843611i \(0.319575\pi\)
\(62\) −0.723404 + 2.22641i −0.0918724 + 0.282754i
\(63\) 0 0
\(64\) 3.96382 2.87988i 0.495477 0.359985i
\(65\) 14.5660 1.80669
\(66\) 0 0
\(67\) 1.47666 0.180403 0.0902017 0.995924i \(-0.471249\pi\)
0.0902017 + 0.995924i \(0.471249\pi\)
\(68\) 1.65346 1.20131i 0.200512 0.145680i
\(69\) 0 0
\(70\) −0.428490 + 1.31876i −0.0512143 + 0.157622i
\(71\) −4.89992 + 6.74417i −0.581514 + 0.800385i −0.993860 0.110642i \(-0.964709\pi\)
0.412346 + 0.911027i \(0.364709\pi\)
\(72\) 0 0
\(73\) −14.9894 4.87035i −1.75438 0.570031i −0.757783 0.652507i \(-0.773717\pi\)
−0.996593 + 0.0824752i \(0.973717\pi\)
\(74\) 0.490013 + 1.50811i 0.0569629 + 0.175314i
\(75\) 0 0
\(76\) 1.04778i 0.120188i
\(77\) −0.188206 5.22712i −0.0214481 0.595685i
\(78\) 0 0
\(79\) 1.86989 + 2.57368i 0.210379 + 0.289562i 0.901146 0.433515i \(-0.142727\pi\)
−0.690767 + 0.723077i \(0.742727\pi\)
\(80\) 7.22666 2.34809i 0.807965 0.262524i
\(81\) 0 0
\(82\) 3.63756 + 2.64284i 0.401701 + 0.291853i
\(83\) −8.40013 6.10305i −0.922034 0.669897i 0.0219956 0.999758i \(-0.492998\pi\)
−0.944029 + 0.329861i \(0.892998\pi\)
\(84\) 0 0
\(85\) 2.47934 0.805585i 0.268922 0.0873779i
\(86\) 1.84685 + 2.54198i 0.199151 + 0.274108i
\(87\) 0 0
\(88\) 3.73231 2.92252i 0.397865 0.311541i
\(89\) 9.01115i 0.955180i 0.878583 + 0.477590i \(0.158489\pi\)
−0.878583 + 0.477590i \(0.841511\pi\)
\(90\) 0 0
\(91\) 2.98703 + 9.19313i 0.313126 + 0.963702i
\(92\) −9.85896 3.20337i −1.02787 0.333974i
\(93\) 0 0
\(94\) 0.167363 0.230355i 0.0172622 0.0237593i
\(95\) 0.412994 1.27106i 0.0423723 0.130408i
\(96\) 0 0
\(97\) −4.48177 + 3.25619i −0.455054 + 0.330616i −0.791588 0.611055i \(-0.790745\pi\)
0.336534 + 0.941671i \(0.390745\pi\)
\(98\) 1.66968 0.168664
\(99\) 0 0
\(100\) 1.20653 0.120653
\(101\) −7.87579 + 5.72209i −0.783670 + 0.569370i −0.906078 0.423110i \(-0.860938\pi\)
0.122408 + 0.992480i \(0.460938\pi\)
\(102\) 0 0
\(103\) 0.584954 1.80030i 0.0576372 0.177389i −0.918093 0.396365i \(-0.870272\pi\)
0.975730 + 0.218976i \(0.0702715\pi\)
\(104\) −5.14927 + 7.08736i −0.504927 + 0.694973i
\(105\) 0 0
\(106\) −1.59264 0.517480i −0.154691 0.0502621i
\(107\) −3.79203 11.6707i −0.366590 1.12825i −0.948980 0.315337i \(-0.897882\pi\)
0.582390 0.812910i \(-0.302118\pi\)
\(108\) 0 0
\(109\) 8.79322i 0.842238i 0.907005 + 0.421119i \(0.138362\pi\)
−0.907005 + 0.421119i \(0.861638\pi\)
\(110\) 2.73919 1.00034i 0.261171 0.0953791i
\(111\) 0 0
\(112\) 2.96392 + 4.07948i 0.280064 + 0.385475i
\(113\) 0.0441193 0.0143352i 0.00415039 0.00134854i −0.306941 0.951729i \(-0.599305\pi\)
0.311091 + 0.950380i \(0.399305\pi\)
\(114\) 0 0
\(115\) −10.6973 7.77205i −0.997529 0.724747i
\(116\) 1.11889 + 0.812920i 0.103886 + 0.0754777i
\(117\) 0 0
\(118\) −0.00395298 + 0.00128440i −0.000363902 + 0.000118239i
\(119\) 1.01687 + 1.39960i 0.0932159 + 0.128301i
\(120\) 0 0
\(121\) −8.41115 + 7.08891i −0.764650 + 0.644446i
\(122\) 2.12032i 0.191965i
\(123\) 0 0
\(124\) 3.64285 + 11.2115i 0.327137 + 1.00683i
\(125\) −9.83712 3.19627i −0.879859 0.285883i
\(126\) 0 0
\(127\) 3.88014 5.34055i 0.344307 0.473898i −0.601386 0.798958i \(-0.705385\pi\)
0.945693 + 0.325061i \(0.105385\pi\)
\(128\) −3.05798 + 9.41149i −0.270290 + 0.831866i
\(129\) 0 0
\(130\) −4.35992 + 3.16767i −0.382390 + 0.277823i
\(131\) −7.88337 −0.688773 −0.344387 0.938828i \(-0.611913\pi\)
−0.344387 + 0.938828i \(0.611913\pi\)
\(132\) 0 0
\(133\) 0.886904 0.0769044
\(134\) −0.441997 + 0.321129i −0.0381827 + 0.0277414i
\(135\) 0 0
\(136\) −0.484503 + 1.49115i −0.0415458 + 0.127865i
\(137\) 10.3791 14.2857i 0.886749 1.22051i −0.0877559 0.996142i \(-0.527970\pi\)
0.974505 0.224364i \(-0.0720304\pi\)
\(138\) 0 0
\(139\) −13.3927 4.35156i −1.13596 0.369094i −0.320119 0.947377i \(-0.603723\pi\)
−0.815836 + 0.578283i \(0.803723\pi\)
\(140\) 2.15775 + 6.64086i 0.182363 + 0.561255i
\(141\) 0 0
\(142\) 3.08425i 0.258825i
\(143\) 11.3493 16.8654i 0.949077 1.41036i
\(144\) 0 0
\(145\) 1.03691 + 1.42718i 0.0861105 + 0.118521i
\(146\) 5.54579 1.80194i 0.458973 0.149129i
\(147\) 0 0
\(148\) 6.46016 + 4.69358i 0.531022 + 0.385810i
\(149\) 11.5245 + 8.37303i 0.944123 + 0.685946i 0.949410 0.314040i \(-0.101683\pi\)
−0.00528647 + 0.999986i \(0.501683\pi\)
\(150\) 0 0
\(151\) −2.45014 + 0.796099i −0.199390 + 0.0647856i −0.407009 0.913424i \(-0.633428\pi\)
0.207620 + 0.978210i \(0.433428\pi\)
\(152\) 0.472460 + 0.650285i 0.0383216 + 0.0527451i
\(153\) 0 0
\(154\) 1.19307 + 1.52366i 0.0961405 + 0.122780i
\(155\) 15.0366i 1.20777i
\(156\) 0 0
\(157\) 1.75945 + 5.41504i 0.140420 + 0.432167i 0.996394 0.0848519i \(-0.0270417\pi\)
−0.855974 + 0.517019i \(0.827042\pi\)
\(158\) −1.11939 0.363713i −0.0890542 0.0289355i
\(159\) 0 0
\(160\) −5.64543 + 7.77027i −0.446311 + 0.614294i
\(161\) 2.71153 8.34524i 0.213699 0.657697i
\(162\) 0 0
\(163\) 6.92500 5.03131i 0.542408 0.394083i −0.282570 0.959247i \(-0.591187\pi\)
0.824979 + 0.565164i \(0.191187\pi\)
\(164\) 22.6419 1.76803
\(165\) 0 0
\(166\) 3.84156 0.298163
\(167\) −2.46778 + 1.79294i −0.190962 + 0.138742i −0.679158 0.733992i \(-0.737655\pi\)
0.488196 + 0.872734i \(0.337655\pi\)
\(168\) 0 0
\(169\) −7.59197 + 23.3657i −0.583998 + 1.79736i
\(170\) −0.566927 + 0.780308i −0.0434813 + 0.0598469i
\(171\) 0 0
\(172\) 15.0481 + 4.88941i 1.14740 + 0.372814i
\(173\) −3.51506 10.8183i −0.267245 0.822497i −0.991168 0.132615i \(-0.957663\pi\)
0.723922 0.689882i \(-0.242337\pi\)
\(174\) 0 0
\(175\) 1.02128i 0.0772016i
\(176\) 2.91199 10.1970i 0.219500 0.768628i
\(177\) 0 0
\(178\) −1.95965 2.69722i −0.146882 0.202166i
\(179\) −10.1952 + 3.31261i −0.762023 + 0.247596i −0.664147 0.747602i \(-0.731205\pi\)
−0.0978766 + 0.995199i \(0.531205\pi\)
\(180\) 0 0
\(181\) 14.3857 + 10.4518i 1.06928 + 0.776879i 0.975783 0.218741i \(-0.0701949\pi\)
0.0934987 + 0.995619i \(0.470195\pi\)
\(182\) −2.89330 2.10211i −0.214466 0.155819i
\(183\) 0 0
\(184\) 7.56325 2.45745i 0.557570 0.181166i
\(185\) 5.98682 + 8.24015i 0.440160 + 0.605828i
\(186\) 0 0
\(187\) 0.999050 3.49840i 0.0730578 0.255829i
\(188\) 1.43384i 0.104574i
\(189\) 0 0
\(190\) 0.152800 + 0.470269i 0.0110853 + 0.0341169i
\(191\) −19.4453 6.31817i −1.40701 0.457167i −0.495562 0.868572i \(-0.665038\pi\)
−0.911452 + 0.411406i \(0.865038\pi\)
\(192\) 0 0
\(193\) −8.98083 + 12.3610i −0.646454 + 0.889768i −0.998939 0.0460498i \(-0.985337\pi\)
0.352485 + 0.935817i \(0.385337\pi\)
\(194\) 0.633364 1.94929i 0.0454729 0.139951i
\(195\) 0 0
\(196\) 6.80224 4.94212i 0.485874 0.353008i
\(197\) 13.1024 0.933507 0.466754 0.884387i \(-0.345424\pi\)
0.466754 + 0.884387i \(0.345424\pi\)
\(198\) 0 0
\(199\) −4.72311 −0.334812 −0.167406 0.985888i \(-0.553539\pi\)
−0.167406 + 0.985888i \(0.553539\pi\)
\(200\) −0.748812 + 0.544044i −0.0529490 + 0.0384697i
\(201\) 0 0
\(202\) 1.11301 3.42548i 0.0783109 0.241016i
\(203\) −0.688107 + 0.947098i −0.0482956 + 0.0664732i
\(204\) 0 0
\(205\) 27.4670 + 8.92456i 1.91838 + 0.623319i
\(206\) 0.216422 + 0.666078i 0.0150788 + 0.0464078i
\(207\) 0 0
\(208\) 19.5979i 1.35887i
\(209\) −1.14992 1.46855i −0.0795420 0.101582i
\(210\) 0 0
\(211\) 11.4835 + 15.8056i 0.790554 + 1.08810i 0.994039 + 0.109026i \(0.0347732\pi\)
−0.203485 + 0.979078i \(0.565227\pi\)
\(212\) −8.02005 + 2.60587i −0.550820 + 0.178972i
\(213\) 0 0
\(214\) 3.67305 + 2.66863i 0.251085 + 0.182424i
\(215\) 16.3277 + 11.8627i 1.11354 + 0.809032i
\(216\) 0 0
\(217\) −9.49015 + 3.08354i −0.644233 + 0.209324i
\(218\) −1.91226 2.63199i −0.129514 0.178261i
\(219\) 0 0
\(220\) 8.19842 12.1831i 0.552738 0.821386i
\(221\) 6.72368i 0.452284i
\(222\) 0 0
\(223\) −5.07706 15.6256i −0.339985 1.04637i −0.964214 0.265125i \(-0.914587\pi\)
0.624229 0.781242i \(-0.285413\pi\)
\(224\) −6.06179 1.96959i −0.405020 0.131599i
\(225\) 0 0
\(226\) −0.0100884 + 0.0138854i −0.000671067 + 0.000923645i
\(227\) −8.39445 + 25.8355i −0.557159 + 1.71476i 0.133012 + 0.991114i \(0.457535\pi\)
−0.690171 + 0.723646i \(0.742465\pi\)
\(228\) 0 0
\(229\) 3.50738 2.54826i 0.231774 0.168394i −0.465837 0.884871i \(-0.654247\pi\)
0.697611 + 0.716477i \(0.254247\pi\)
\(230\) 4.89211 0.322576
\(231\) 0 0
\(232\) −1.06098 −0.0696567
\(233\) −9.48697 + 6.89268i −0.621512 + 0.451555i −0.853449 0.521176i \(-0.825494\pi\)
0.231937 + 0.972731i \(0.425494\pi\)
\(234\) 0 0
\(235\) 0.565165 1.73940i 0.0368673 0.113466i
\(236\) −0.0123026 + 0.0169331i −0.000800832 + 0.00110225i
\(237\) 0 0
\(238\) −0.608738 0.197791i −0.0394586 0.0128209i
\(239\) −5.54433 17.0637i −0.358633 1.10376i −0.953873 0.300210i \(-0.902943\pi\)
0.595240 0.803548i \(-0.297057\pi\)
\(240\) 0 0
\(241\) 2.67184i 0.172108i −0.996290 0.0860541i \(-0.972574\pi\)
0.996290 0.0860541i \(-0.0274258\pi\)
\(242\) 0.976011 3.95102i 0.0627404 0.253982i
\(243\) 0 0
\(244\) −6.27595 8.63811i −0.401777 0.552998i
\(245\) 10.1998 3.31412i 0.651643 0.211732i
\(246\) 0 0
\(247\) 2.78867 + 2.02609i 0.177439 + 0.128917i
\(248\) −7.31634 5.31563i −0.464588 0.337543i
\(249\) 0 0
\(250\) 3.63955 1.18256i 0.230185 0.0747917i
\(251\) −7.98861 10.9954i −0.504237 0.694022i 0.478697 0.877980i \(-0.341109\pi\)
−0.982934 + 0.183958i \(0.941109\pi\)
\(252\) 0 0
\(253\) −17.3339 + 6.33030i −1.08977 + 0.397982i
\(254\) 2.44235i 0.153247i
\(255\) 0 0
\(256\) 1.89669 + 5.83743i 0.118543 + 0.364839i
\(257\) −4.52222 1.46936i −0.282088 0.0916561i 0.164556 0.986368i \(-0.447381\pi\)
−0.446644 + 0.894712i \(0.647381\pi\)
\(258\) 0 0
\(259\) −3.97294 + 5.46828i −0.246866 + 0.339783i
\(260\) −8.38616 + 25.8099i −0.520088 + 1.60066i
\(261\) 0 0
\(262\) 2.35966 1.71439i 0.145780 0.105915i
\(263\) −18.5223 −1.14213 −0.571067 0.820903i \(-0.693471\pi\)
−0.571067 + 0.820903i \(0.693471\pi\)
\(264\) 0 0
\(265\) −10.7563 −0.660754
\(266\) −0.265469 + 0.192875i −0.0162770 + 0.0118259i
\(267\) 0 0
\(268\) −0.850166 + 2.61654i −0.0519322 + 0.159831i
\(269\) −12.6954 + 17.4737i −0.774049 + 1.06539i 0.221864 + 0.975078i \(0.428786\pi\)
−0.995914 + 0.0903100i \(0.971214\pi\)
\(270\) 0 0
\(271\) −0.869236 0.282432i −0.0528023 0.0171565i 0.282497 0.959268i \(-0.408837\pi\)
−0.335299 + 0.942112i \(0.608837\pi\)
\(272\) 1.08388 + 3.33583i 0.0657197 + 0.202264i
\(273\) 0 0
\(274\) 6.53314i 0.394681i
\(275\) 1.69106 1.32415i 0.101975 0.0798494i
\(276\) 0 0
\(277\) 8.70688 + 11.9840i 0.523145 + 0.720048i 0.986067 0.166352i \(-0.0531986\pi\)
−0.462921 + 0.886400i \(0.653199\pi\)
\(278\) 4.95505 1.60999i 0.297184 0.0965610i
\(279\) 0 0
\(280\) −4.33365 3.14858i −0.258985 0.188164i
\(281\) −1.48662 1.08010i −0.0886846 0.0644331i 0.542559 0.840017i \(-0.317455\pi\)
−0.631244 + 0.775584i \(0.717455\pi\)
\(282\) 0 0
\(283\) −11.4793 + 3.72985i −0.682373 + 0.221716i −0.629634 0.776892i \(-0.716795\pi\)
−0.0527388 + 0.998608i \(0.516795\pi\)
\(284\) −9.12912 12.5652i −0.541713 0.745605i
\(285\) 0 0
\(286\) 0.270630 + 7.51630i 0.0160027 + 0.444448i
\(287\) 19.1655i 1.13130i
\(288\) 0 0
\(289\) −4.88143 15.0235i −0.287143 0.883735i
\(290\) −0.620736 0.201689i −0.0364509 0.0118436i
\(291\) 0 0
\(292\) 17.2598 23.7561i 1.01005 1.39022i
\(293\) −5.27855 + 16.2457i −0.308376 + 0.949085i 0.670019 + 0.742344i \(0.266286\pi\)
−0.978396 + 0.206741i \(0.933714\pi\)
\(294\) 0 0
\(295\) −0.0215987 + 0.0156924i −0.00125753 + 0.000913647i
\(296\) −6.12580 −0.356055
\(297\) 0 0
\(298\) −5.27040 −0.305306
\(299\) 27.5901 20.0454i 1.59557 1.15925i
\(300\) 0 0
\(301\) −4.13870 + 12.7376i −0.238551 + 0.734184i
\(302\) 0.560251 0.771119i 0.0322388 0.0443729i
\(303\) 0 0
\(304\) 1.71016 + 0.555663i 0.0980842 + 0.0318695i
\(305\) −4.20858 12.9527i −0.240983 0.741668i
\(306\) 0 0
\(307\) 16.6906i 0.952585i −0.879287 0.476293i \(-0.841980\pi\)
0.879287 0.476293i \(-0.158020\pi\)
\(308\) 9.37043 + 2.67594i 0.533930 + 0.152476i
\(309\) 0 0
\(310\) −3.27001 4.50078i −0.185724 0.255627i
\(311\) 28.0994 9.13006i 1.59337 0.517718i 0.627915 0.778282i \(-0.283908\pi\)
0.965457 + 0.260564i \(0.0839083\pi\)
\(312\) 0 0
\(313\) −13.0604 9.48891i −0.738215 0.536345i 0.153936 0.988081i \(-0.450805\pi\)
−0.892152 + 0.451736i \(0.850805\pi\)
\(314\) −1.70424 1.23821i −0.0961761 0.0698760i
\(315\) 0 0
\(316\) −5.63693 + 1.83155i −0.317102 + 0.103033i
\(317\) 4.92818 + 6.78306i 0.276794 + 0.380974i 0.924669 0.380773i \(-0.124342\pi\)
−0.647875 + 0.761747i \(0.724342\pi\)
\(318\) 0 0
\(319\) 2.46039 0.0885883i 0.137756 0.00495999i
\(320\) 11.6436i 0.650898i
\(321\) 0 0
\(322\) 1.00322 + 3.08758i 0.0559070 + 0.172064i
\(323\) 0.586723 + 0.190638i 0.0326462 + 0.0106074i
\(324\) 0 0
\(325\) −2.33306 + 3.21119i −0.129415 + 0.178125i
\(326\) −0.978643 + 3.01195i −0.0542020 + 0.166817i
\(327\) 0 0
\(328\) −14.0523 + 10.2096i −0.775909 + 0.563731i
\(329\) 1.21369 0.0669130
\(330\) 0 0
\(331\) −1.00708 −0.0553542 −0.0276771 0.999617i \(-0.508811\pi\)
−0.0276771 + 0.999617i \(0.508811\pi\)
\(332\) 15.6504 11.3707i 0.858927 0.624047i
\(333\) 0 0
\(334\) 0.348746 1.07333i 0.0190826 0.0587301i
\(335\) −2.06268 + 2.83904i −0.112696 + 0.155113i
\(336\) 0 0
\(337\) 21.1314 + 6.86601i 1.15110 + 0.374015i 0.821558 0.570125i \(-0.193105\pi\)
0.329543 + 0.944141i \(0.393105\pi\)
\(338\) −2.80889 8.64486i −0.152783 0.470218i
\(339\) 0 0
\(340\) 4.85700i 0.263408i
\(341\) 17.4103 + 11.7160i 0.942822 + 0.634456i
\(342\) 0 0
\(343\) 10.6721 + 14.6889i 0.576240 + 0.793126i
\(344\) −11.5440 + 3.75089i −0.622413 + 0.202234i
\(345\) 0 0
\(346\) 3.40477 + 2.47371i 0.183042 + 0.132988i
\(347\) 9.70317 + 7.04977i 0.520894 + 0.378451i 0.816940 0.576722i \(-0.195668\pi\)
−0.296047 + 0.955173i \(0.595668\pi\)
\(348\) 0 0
\(349\) −9.66986 + 3.14193i −0.517616 + 0.168183i −0.556163 0.831073i \(-0.687727\pi\)
0.0385474 + 0.999257i \(0.487727\pi\)
\(350\) −0.222097 0.305691i −0.0118716 0.0163399i
\(351\) 0 0
\(352\) 4.59818 + 12.5909i 0.245084 + 0.671099i
\(353\) 4.61511i 0.245638i −0.992429 0.122819i \(-0.960807\pi\)
0.992429 0.122819i \(-0.0391934\pi\)
\(354\) 0 0
\(355\) −6.12188 18.8412i −0.324915 0.999987i
\(356\) −15.9671 5.18802i −0.846254 0.274965i
\(357\) 0 0
\(358\) 2.33124 3.20867i 0.123210 0.169584i
\(359\) 2.51158 7.72985i 0.132556 0.407966i −0.862646 0.505809i \(-0.831194\pi\)
0.995202 + 0.0978426i \(0.0311942\pi\)
\(360\) 0 0
\(361\) −15.1155 + 10.9820i −0.795550 + 0.578001i
\(362\) −6.57890 −0.345779
\(363\) 0 0
\(364\) −18.0093 −0.943943
\(365\) 30.3017 22.0155i 1.58606 1.15234i
\(366\) 0 0
\(367\) 11.7284 36.0963i 0.612217 1.88421i 0.175928 0.984403i \(-0.443707\pi\)
0.436289 0.899807i \(-0.356293\pi\)
\(368\) 10.4569 14.3927i 0.545105 0.750272i
\(369\) 0 0
\(370\) −3.58396 1.16450i −0.186321 0.0605394i
\(371\) −2.20578 6.78868i −0.114518 0.352451i
\(372\) 0 0
\(373\) 6.48359i 0.335707i −0.985812 0.167854i \(-0.946316\pi\)
0.985812 0.167854i \(-0.0536836\pi\)
\(374\) 0.461759 + 1.26441i 0.0238770 + 0.0653810i
\(375\) 0 0
\(376\) 0.646542 + 0.889889i 0.0333429 + 0.0458925i
\(377\) −4.32719 + 1.40599i −0.222862 + 0.0724121i
\(378\) 0 0
\(379\) −10.0492 7.30119i −0.516194 0.375037i 0.298974 0.954261i \(-0.403356\pi\)
−0.815168 + 0.579224i \(0.803356\pi\)
\(380\) 2.01446 + 1.46359i 0.103339 + 0.0750805i
\(381\) 0 0
\(382\) 7.19440 2.33760i 0.368098 0.119602i
\(383\) −8.38804 11.5452i −0.428609 0.589930i 0.539024 0.842290i \(-0.318793\pi\)
−0.967633 + 0.252361i \(0.918793\pi\)
\(384\) 0 0
\(385\) 10.3126 + 6.93966i 0.525577 + 0.353678i
\(386\) 5.65297i 0.287729i
\(387\) 0 0
\(388\) −3.18943 9.81606i −0.161919 0.498335i
\(389\) −10.2422 3.32789i −0.519300 0.168731i 0.0376278 0.999292i \(-0.488020\pi\)
−0.556927 + 0.830561i \(0.688020\pi\)
\(390\) 0 0
\(391\) 3.58758 4.93788i 0.181432 0.249719i
\(392\) −1.99322 + 6.13449i −0.100673 + 0.309838i
\(393\) 0 0
\(394\) −3.92182 + 2.84937i −0.197578 + 0.143549i
\(395\) −7.56012 −0.380391
\(396\) 0 0
\(397\) 13.8356 0.694387 0.347193 0.937794i \(-0.387135\pi\)
0.347193 + 0.937794i \(0.387135\pi\)
\(398\) 1.41373 1.02713i 0.0708637 0.0514855i
\(399\) 0 0
\(400\) −0.639853 + 1.96927i −0.0319927 + 0.0984633i
\(401\) −21.0754 + 29.0078i −1.05245 + 1.44858i −0.165792 + 0.986161i \(0.553018\pi\)
−0.886662 + 0.462418i \(0.846982\pi\)
\(402\) 0 0
\(403\) −36.8838 11.9843i −1.83731 0.596979i
\(404\) −5.60477 17.2497i −0.278848 0.858206i
\(405\) 0 0
\(406\) 0.433128i 0.0214958i
\(407\) 14.2056 0.511484i 0.704148 0.0253533i
\(408\) 0 0
\(409\) −9.23715 12.7138i −0.456748 0.628659i 0.517083 0.855935i \(-0.327018\pi\)
−0.973830 + 0.227276i \(0.927018\pi\)
\(410\) −10.1623 + 3.30192i −0.501878 + 0.163070i
\(411\) 0 0
\(412\) 2.85323 + 2.07299i 0.140568 + 0.102129i
\(413\) −0.0143332 0.0104137i −0.000705293 0.000512425i
\(414\) 0 0
\(415\) 23.4675 7.62504i 1.15197 0.374298i
\(416\) −14.5605 20.0408i −0.713886 0.982580i
\(417\) 0 0
\(418\) 0.663562 + 0.189495i 0.0324559 + 0.00926853i
\(419\) 15.2101i 0.743062i 0.928421 + 0.371531i \(0.121167\pi\)
−0.928421 + 0.371531i \(0.878833\pi\)
\(420\) 0 0
\(421\) −3.75191 11.5472i −0.182857 0.562776i 0.817048 0.576570i \(-0.195609\pi\)
−0.999905 + 0.0137940i \(0.995609\pi\)
\(422\) −6.87448 2.23365i −0.334644 0.108733i
\(423\) 0 0
\(424\) 3.80248 5.23367i 0.184665 0.254169i
\(425\) −0.219522 + 0.675619i −0.0106484 + 0.0327723i
\(426\) 0 0
\(427\) 7.31184 5.31236i 0.353845 0.257083i
\(428\) 22.8628 1.10511
\(429\) 0 0
\(430\) −7.46699 −0.360090
\(431\) 20.7468 15.0734i 0.999336 0.726060i 0.0373906 0.999301i \(-0.488095\pi\)
0.961946 + 0.273240i \(0.0880954\pi\)
\(432\) 0 0
\(433\) −0.399073 + 1.22822i −0.0191782 + 0.0590245i −0.960188 0.279356i \(-0.909879\pi\)
0.941009 + 0.338380i \(0.109879\pi\)
\(434\) 2.17002 2.98678i 0.104165 0.143370i
\(435\) 0 0
\(436\) −15.5809 5.06256i −0.746192 0.242452i
\(437\) −0.966935 2.97592i −0.0462548 0.142357i
\(438\) 0 0
\(439\) 8.98876i 0.429010i 0.976723 + 0.214505i \(0.0688138\pi\)
−0.976723 + 0.214505i \(0.931186\pi\)
\(440\) 0.405354 + 11.2581i 0.0193245 + 0.536707i
\(441\) 0 0
\(442\) −1.46220 2.01254i −0.0695495 0.0957267i
\(443\) −13.6420 + 4.43255i −0.648151 + 0.210597i −0.614599 0.788840i \(-0.710682\pi\)
−0.0335523 + 0.999437i \(0.510682\pi\)
\(444\) 0 0
\(445\) −17.3248 12.5872i −0.821276 0.596692i
\(446\) 4.91776 + 3.57296i 0.232863 + 0.169185i
\(447\) 0 0
\(448\) −7.34869 + 2.38773i −0.347193 + 0.112810i
\(449\) −8.37515 11.5274i −0.395248 0.544012i 0.564296 0.825573i \(-0.309148\pi\)
−0.959543 + 0.281561i \(0.909148\pi\)
\(450\) 0 0
\(451\) 31.7346 24.8492i 1.49433 1.17011i
\(452\) 0.0864294i 0.00406530i
\(453\) 0 0
\(454\) −3.10579 9.55863i −0.145762 0.448609i
\(455\) −21.8472 7.09857i −1.02421 0.332786i
\(456\) 0 0
\(457\) 15.2683 21.0150i 0.714220 0.983039i −0.285476 0.958386i \(-0.592152\pi\)
0.999696 0.0246533i \(-0.00784819\pi\)
\(458\) −0.495664 + 1.52550i −0.0231608 + 0.0712817i
\(459\) 0 0
\(460\) 19.9303 14.4802i 0.929255 0.675143i
\(461\) 11.6547 0.542812 0.271406 0.962465i \(-0.412511\pi\)
0.271406 + 0.962465i \(0.412511\pi\)
\(462\) 0 0
\(463\) 18.6647 0.867423 0.433712 0.901052i \(-0.357204\pi\)
0.433712 + 0.901052i \(0.357204\pi\)
\(464\) −1.92020 + 1.39511i −0.0891432 + 0.0647664i
\(465\) 0 0
\(466\) 1.34070 4.12625i 0.0621067 0.191145i
\(467\) 1.77499 2.44307i 0.0821369 0.113052i −0.765971 0.642875i \(-0.777742\pi\)
0.848108 + 0.529823i \(0.177742\pi\)
\(468\) 0 0
\(469\) −2.21481 0.719634i −0.102270 0.0332296i
\(470\) 0.209100 + 0.643544i 0.00964508 + 0.0296845i
\(471\) 0 0
\(472\) 0.0160567i 0.000739070i
\(473\) 26.4573 9.66214i 1.21651 0.444266i
\(474\) 0 0
\(475\) 0.214065 + 0.294636i 0.00982199 + 0.0135188i
\(476\) −3.06542 + 0.996017i −0.140503 + 0.0456523i
\(477\) 0 0
\(478\) 5.37036 + 3.90180i 0.245635 + 0.178464i
\(479\) 31.2962 + 22.7380i 1.42996 + 1.03893i 0.990025 + 0.140895i \(0.0449979\pi\)
0.439933 + 0.898031i \(0.355002\pi\)
\(480\) 0 0
\(481\) −24.9840 + 8.11780i −1.13917 + 0.370140i
\(482\) 0.581043 + 0.799737i 0.0264658 + 0.0364270i
\(483\) 0 0
\(484\) −7.71845 18.9853i −0.350838 0.862966i
\(485\) 13.1651i 0.597795i
\(486\) 0 0
\(487\) −3.79422 11.6774i −0.171933 0.529154i 0.827548 0.561396i \(-0.189735\pi\)
−0.999480 + 0.0322416i \(0.989735\pi\)
\(488\) 7.79013 + 2.53117i 0.352643 + 0.114581i
\(489\) 0 0
\(490\) −2.33230 + 3.21014i −0.105363 + 0.145019i
\(491\) −11.2694 + 34.6836i −0.508580 + 1.56525i 0.286087 + 0.958204i \(0.407645\pi\)
−0.794667 + 0.607045i \(0.792355\pi\)
\(492\) 0 0
\(493\) −0.658787 + 0.478637i −0.0296703 + 0.0215567i
\(494\) −1.27532 −0.0573793
\(495\) 0 0
\(496\) −20.2311 −0.908403
\(497\) 10.6359 7.72746i 0.477087 0.346624i
\(498\) 0 0
\(499\) 7.50331 23.0928i 0.335894 1.03378i −0.630386 0.776282i \(-0.717103\pi\)
0.966280 0.257494i \(-0.0828968\pi\)
\(500\) 11.3271 15.5905i 0.506564 0.697226i
\(501\) 0 0
\(502\) 4.78232 + 1.55387i 0.213445 + 0.0693526i
\(503\) 6.87821 + 21.1689i 0.306684 + 0.943876i 0.979043 + 0.203652i \(0.0652810\pi\)
−0.672359 + 0.740225i \(0.734719\pi\)
\(504\) 0 0
\(505\) 23.1349i 1.02949i
\(506\) 3.81175 5.66438i 0.169453 0.251812i
\(507\) 0 0
\(508\) 7.22914 + 9.95006i 0.320741 + 0.441463i
\(509\) −26.9514 + 8.75705i −1.19460 + 0.388150i −0.837772 0.546020i \(-0.816142\pi\)
−0.356830 + 0.934170i \(0.616142\pi\)
\(510\) 0 0
\(511\) 20.1086 + 14.6098i 0.889554 + 0.646299i
\(512\) −17.8490 12.9680i −0.788820 0.573111i
\(513\) 0 0
\(514\) 1.67314 0.543635i 0.0737989 0.0239787i
\(515\) 2.64417 + 3.63939i 0.116516 + 0.160371i
\(516\) 0 0
\(517\) −1.57363 2.00966i −0.0692080 0.0883846i
\(518\) 2.50076i 0.109877i
\(519\) 0 0
\(520\) −6.43340 19.8000i −0.282123 0.868286i
\(521\) −14.9548 4.85911i −0.655182 0.212882i −0.0374843 0.999297i \(-0.511934\pi\)
−0.617698 + 0.786416i \(0.711934\pi\)
\(522\) 0 0
\(523\) 8.59617 11.8316i 0.375884 0.517360i −0.578604 0.815609i \(-0.696402\pi\)
0.954488 + 0.298248i \(0.0964023\pi\)
\(524\) 4.53872 13.9688i 0.198275 0.610228i
\(525\) 0 0
\(526\) 5.54412 4.02804i 0.241735 0.175631i
\(527\) −6.94091 −0.302351
\(528\) 0 0
\(529\) −7.95782 −0.345992
\(530\) 3.21959 2.33917i 0.139850 0.101607i
\(531\) 0 0
\(532\) −0.510621 + 1.57153i −0.0221382 + 0.0681345i
\(533\) −43.7826 + 60.2616i −1.89644 + 2.61022i
\(534\) 0 0
\(535\) 27.7350 + 9.01164i 1.19909 + 0.389607i
\(536\) −0.652201 2.00727i −0.0281708 0.0867007i
\(537\) 0 0
\(538\) 7.99108i 0.344520i
\(539\) 4.11003 14.3922i 0.177031 0.619916i
\(540\) 0 0
\(541\) 10.4934 + 14.4429i 0.451146 + 0.620950i 0.972643 0.232303i \(-0.0746262\pi\)
−0.521497 + 0.853253i \(0.674626\pi\)
\(542\) 0.321601 0.104494i 0.0138139 0.00448842i
\(543\) 0 0
\(544\) −3.58676 2.60593i −0.153781 0.111728i
\(545\) −16.9059 12.2828i −0.724167 0.526138i
\(546\) 0 0
\(547\) 4.29253 1.39473i 0.183535 0.0596342i −0.215807 0.976436i \(-0.569238\pi\)
0.399343 + 0.916802i \(0.369238\pi\)
\(548\) 19.3375 + 26.6158i 0.826058 + 1.13697i
\(549\) 0 0
\(550\) −0.218206 + 0.764100i −0.00930435 + 0.0325813i
\(551\) 0.417464i 0.0177846i
\(552\) 0 0
\(553\) −1.55034 4.77146i −0.0659272 0.202903i
\(554\) −5.21230 1.69358i −0.221449 0.0719533i
\(555\) 0 0
\(556\) 15.4213 21.2256i 0.654008 0.900165i
\(557\) −8.48770 + 26.1225i −0.359635 + 1.10684i 0.593637 + 0.804733i \(0.297691\pi\)
−0.953273 + 0.302111i \(0.902309\pi\)
\(558\) 0 0
\(559\) −42.1116 + 30.5959i −1.78113 + 1.29407i
\(560\) −11.9834 −0.506390
\(561\) 0 0
\(562\) 0.679865 0.0286784
\(563\) 8.46897 6.15307i 0.356925 0.259321i −0.394844 0.918748i \(-0.629201\pi\)
0.751768 + 0.659427i \(0.229201\pi\)
\(564\) 0 0
\(565\) −0.0340672 + 0.104848i −0.00143322 + 0.00441099i
\(566\) 2.62486 3.61281i 0.110331 0.151858i
\(567\) 0 0
\(568\) 11.3317 + 3.68188i 0.475466 + 0.154488i
\(569\) −11.4567 35.2600i −0.480288 1.47818i −0.838690 0.544608i \(-0.816678\pi\)
0.358402 0.933567i \(-0.383322\pi\)
\(570\) 0 0
\(571\) 6.14821i 0.257295i −0.991690 0.128647i \(-0.958936\pi\)
0.991690 0.128647i \(-0.0410635\pi\)
\(572\) 23.3501 + 29.8201i 0.976318 + 1.24684i
\(573\) 0 0
\(574\) −4.16791 5.73664i −0.173965 0.239443i
\(575\) 3.42681 1.11344i 0.142908 0.0464335i
\(576\) 0 0
\(577\) −8.59300 6.24318i −0.357731 0.259907i 0.394374 0.918950i \(-0.370961\pi\)
−0.752105 + 0.659043i \(0.770961\pi\)
\(578\) 4.72826 + 3.43529i 0.196670 + 0.142889i
\(579\) 0 0
\(580\) −3.12584 + 1.01565i −0.129794 + 0.0421725i
\(581\) 9.62486 + 13.2475i 0.399306 + 0.549598i
\(582\) 0 0
\(583\) −8.38091 + 12.4543i −0.347102 + 0.515804i
\(584\) 22.5266i 0.932155i
\(585\) 0 0
\(586\) −1.95296 6.01061i −0.0806762 0.248296i
\(587\) −5.97470 1.94130i −0.246602 0.0801259i 0.183108 0.983093i \(-0.441384\pi\)
−0.429710 + 0.902967i \(0.641384\pi\)
\(588\) 0 0
\(589\) −2.09155 + 2.87877i −0.0861806 + 0.118617i
\(590\) 0.00305234 0.00939413i 0.000125663 0.000386750i
\(591\) 0 0
\(592\) −11.0867 + 8.05498i −0.455662 + 0.331058i
\(593\) 13.2967 0.546030 0.273015 0.962010i \(-0.411979\pi\)
0.273015 + 0.962010i \(0.411979\pi\)
\(594\) 0 0
\(595\) −4.11127 −0.168546
\(596\) −21.4714 + 15.5999i −0.879505 + 0.638997i
\(597\) 0 0
\(598\) −3.89903 + 12.0000i −0.159443 + 0.490716i
\(599\) 20.5665 28.3074i 0.840325 1.15661i −0.145587 0.989345i \(-0.546507\pi\)
0.985912 0.167263i \(-0.0534928\pi\)
\(600\) 0 0
\(601\) −5.01758 1.63031i −0.204671 0.0665017i 0.204887 0.978786i \(-0.434317\pi\)
−0.409558 + 0.912284i \(0.634317\pi\)
\(602\) −1.53124 4.71268i −0.0624087 0.192074i
\(603\) 0 0
\(604\) 4.79981i 0.195301i
\(605\) −1.88002 26.0734i −0.0764338 1.06004i
\(606\) 0 0
\(607\) −12.2253 16.8267i −0.496211 0.682976i 0.485307 0.874344i \(-0.338708\pi\)
−0.981518 + 0.191367i \(0.938708\pi\)
\(608\) −2.16164 + 0.702359i −0.0876660 + 0.0284844i
\(609\) 0 0
\(610\) 4.07653 + 2.96177i 0.165054 + 0.119919i
\(611\) 3.81618 + 2.77262i 0.154386 + 0.112168i
\(612\) 0 0
\(613\) −25.6016 + 8.31845i −1.03404 + 0.335979i −0.776385 0.630259i \(-0.782949\pi\)
−0.257652 + 0.966238i \(0.582949\pi\)
\(614\) 3.62970 + 4.99586i 0.146483 + 0.201616i
\(615\) 0 0
\(616\) −7.02223 + 2.56450i −0.282934 + 0.103327i
\(617\) 33.5621i 1.35116i −0.737287 0.675580i \(-0.763893\pi\)
0.737287 0.675580i \(-0.236107\pi\)
\(618\) 0 0
\(619\) 11.5298 + 35.4851i 0.463422 + 1.42627i 0.860956 + 0.508680i \(0.169866\pi\)
−0.397534 + 0.917588i \(0.630134\pi\)
\(620\) −26.6438 8.65710i −1.07004 0.347678i
\(621\) 0 0
\(622\) −6.42524 + 8.84358i −0.257629 + 0.354595i
\(623\) 4.39147 13.5156i 0.175940 0.541489i
\(624\) 0 0
\(625\) 22.5057 16.3513i 0.900228 0.654054i
\(626\) 5.97279 0.238721
\(627\) 0 0
\(628\) −10.6080 −0.423306
\(629\) −3.80365 + 2.76352i −0.151662 + 0.110189i
\(630\) 0 0
\(631\) −5.33541 + 16.4207i −0.212399 + 0.653698i 0.786929 + 0.617044i \(0.211670\pi\)
−0.999328 + 0.0366537i \(0.988330\pi\)
\(632\) 2.67259 3.67851i 0.106310 0.146323i
\(633\) 0 0
\(634\) −2.95021 0.958583i −0.117168 0.0380702i
\(635\) 4.84778 + 14.9199i 0.192378 + 0.592079i
\(636\) 0 0
\(637\) 27.6608i 1.09596i
\(638\) −0.717182 + 0.561577i −0.0283935 + 0.0222330i
\(639\) 0 0
\(640\) −13.8230 19.0257i −0.546402 0.752058i
\(641\) 8.97340 2.91563i 0.354428 0.115161i −0.126391 0.991980i \(-0.540339\pi\)
0.480819 + 0.876820i \(0.340339\pi\)
\(642\) 0 0
\(643\) −6.60864 4.80146i −0.260619 0.189351i 0.449801 0.893129i \(-0.351495\pi\)
−0.710420 + 0.703778i \(0.751495\pi\)
\(644\) 13.2260 + 9.60928i 0.521179 + 0.378659i
\(645\) 0 0
\(646\) −0.217076 + 0.0705324i −0.00854076 + 0.00277506i
\(647\) 12.6621 + 17.4279i 0.497799 + 0.685162i 0.981803 0.189904i \(-0.0608178\pi\)
−0.484003 + 0.875066i \(0.660818\pi\)
\(648\) 0 0
\(649\) 0.00134068 + 0.0372353i 5.26264e−5 + 0.00146161i
\(650\) 1.46855i 0.0576011i
\(651\) 0 0
\(652\) 4.92815 + 15.1673i 0.193001 + 0.593997i
\(653\) −43.4797 14.1274i −1.70149 0.552848i −0.712610 0.701560i \(-0.752487\pi\)
−0.988880 + 0.148713i \(0.952487\pi\)
\(654\) 0 0
\(655\) 11.0119 15.1566i 0.430270 0.592216i
\(656\) −12.0076 + 36.9555i −0.468817 + 1.44287i
\(657\) 0 0
\(658\) −0.363284 + 0.263941i −0.0141623 + 0.0102895i
\(659\) −5.75272 −0.224094 −0.112047 0.993703i \(-0.535741\pi\)
−0.112047 + 0.993703i \(0.535741\pi\)
\(660\) 0 0
\(661\) 29.9259 1.16398 0.581991 0.813195i \(-0.302274\pi\)
0.581991 + 0.813195i \(0.302274\pi\)
\(662\) 0.301440 0.219009i 0.0117158 0.00851204i
\(663\) 0 0
\(664\) −4.58593 + 14.1140i −0.177969 + 0.547731i
\(665\) −1.23887 + 1.70516i −0.0480415 + 0.0661234i
\(666\) 0 0
\(667\) 3.92809 + 1.27631i 0.152096 + 0.0494190i
\(668\) −1.75618 5.40498i −0.0679488 0.209125i
\(669\) 0 0
\(670\) 1.29835i 0.0501598i
\(671\) −18.2766 5.21929i −0.705559 0.201489i
\(672\) 0 0
\(673\) −0.761268 1.04780i −0.0293447 0.0403895i 0.794093 0.607797i \(-0.207947\pi\)
−0.823437 + 0.567407i \(0.807947\pi\)
\(674\) −7.81821 + 2.54029i −0.301146 + 0.0978484i
\(675\) 0 0
\(676\) −37.0313 26.9048i −1.42428 1.03480i
\(677\) 16.9486 + 12.3139i 0.651389 + 0.473262i 0.863744 0.503931i \(-0.168113\pi\)
−0.212355 + 0.977193i \(0.568113\pi\)
\(678\) 0 0
\(679\) 8.30893 2.69974i 0.318868 0.103606i
\(680\) −2.19010 3.01442i −0.0839866 0.115598i
\(681\) 0 0
\(682\) −7.75914 + 0.279373i −0.297113 + 0.0106978i
\(683\) 12.7750i 0.488822i −0.969672 0.244411i \(-0.921405\pi\)
0.969672 0.244411i \(-0.0785945\pi\)
\(684\) 0 0
\(685\) 12.9675 + 39.9099i 0.495463 + 1.52488i
\(686\) −6.38877 2.07584i −0.243924 0.0792559i
\(687\) 0 0
\(688\) −15.9608 + 21.9681i −0.608498 + 0.837526i
\(689\) 8.57282 26.3844i 0.326598 1.00517i
\(690\) 0 0
\(691\) 23.3392 16.9569i 0.887866 0.645073i −0.0474545 0.998873i \(-0.515111\pi\)
0.935321 + 0.353801i \(0.115111\pi\)
\(692\) 21.1929 0.805633
\(693\) 0 0
\(694\) −4.43747 −0.168444
\(695\) 27.0739 19.6704i 1.02697 0.746139i
\(696\) 0 0
\(697\) −4.11958 + 12.6788i −0.156040 + 0.480242i
\(698\) 2.21112 3.04334i 0.0836920 0.115192i
\(699\) 0 0
\(700\) −1.80964 0.587986i −0.0683978 0.0222238i
\(701\) −1.64023 5.04812i −0.0619507 0.190665i 0.915291 0.402793i \(-0.131961\pi\)
−0.977242 + 0.212128i \(0.931961\pi\)
\(702\) 0 0
\(703\) 2.41032i 0.0909071i
\(704\) 13.4817 + 9.07227i 0.508110 + 0.341924i
\(705\) 0 0
\(706\) 1.00365 + 1.38140i 0.0377727 + 0.0519896i
\(707\) 14.6012 4.74423i 0.549136 0.178425i
\(708\) 0 0
\(709\) 23.3574 + 16.9701i 0.877204 + 0.637326i 0.932510 0.361143i \(-0.117613\pi\)
−0.0553060 + 0.998469i \(0.517613\pi\)
\(710\) 5.92979 + 4.30824i 0.222541 + 0.161685i
\(711\) 0 0
\(712\) 12.2491 3.97997i 0.459054 0.149156i
\(713\) 20.6930 + 28.4814i 0.774958 + 1.06664i
\(714\) 0 0
\(715\) 16.5722 + 45.3787i 0.619765 + 1.69707i
\(716\) 19.9723i 0.746400i
\(717\) 0 0
\(718\) 0.929237 + 2.85990i 0.0346788 + 0.106730i
\(719\) −35.5978 11.5664i −1.32757 0.431355i −0.442484 0.896776i \(-0.645903\pi\)
−0.885089 + 0.465422i \(0.845903\pi\)
\(720\) 0 0
\(721\) −1.75471 + 2.41515i −0.0653488 + 0.0899449i
\(722\) 2.13612 6.57430i 0.0794981 0.244670i
\(723\) 0 0
\(724\) −26.8022 + 19.4730i −0.996097 + 0.723707i
\(725\) −0.480715 −0.0178533
\(726\) 0 0
\(727\) 43.7941 1.62423 0.812116 0.583496i \(-0.198316\pi\)
0.812116 + 0.583496i \(0.198316\pi\)
\(728\) 11.1772 8.12069i 0.414253 0.300973i
\(729\) 0 0
\(730\) −4.28224 + 13.1794i −0.158493 + 0.487791i
\(731\) −5.47584 + 7.53685i −0.202531 + 0.278760i
\(732\) 0 0
\(733\) −5.05270 1.64172i −0.186626 0.0606384i 0.214213 0.976787i \(-0.431281\pi\)
−0.400839 + 0.916149i \(0.631281\pi\)
\(734\) 4.33928 + 13.3549i 0.160166 + 0.492940i
\(735\) 0 0
\(736\) 22.4870i 0.828883i
\(737\) 1.68004 + 4.60037i 0.0618852 + 0.169457i
\(738\) 0 0
\(739\) 3.62411 + 4.98816i 0.133315 + 0.183492i 0.870455 0.492247i \(-0.163824\pi\)
−0.737140 + 0.675740i \(0.763824\pi\)
\(740\) −18.0478 + 5.86407i −0.663449 + 0.215568i
\(741\) 0 0
\(742\) 2.13656 + 1.55230i 0.0784357 + 0.0569869i
\(743\) −5.40513 3.92705i −0.198295 0.144070i 0.484207 0.874953i \(-0.339108\pi\)
−0.682502 + 0.730884i \(0.739108\pi\)
\(744\) 0 0
\(745\) −32.1960 + 10.4611i −1.17957 + 0.383266i
\(746\) 1.40998 + 1.94067i 0.0516231 + 0.0710531i
\(747\) 0 0
\(748\) 5.62373 + 3.78439i 0.205624 + 0.138371i
\(749\) 19.3525i 0.707125i
\(750\) 0 0
\(751\) −8.75807 26.9546i −0.319587 0.983586i −0.973825 0.227298i \(-0.927011\pi\)
0.654239 0.756288i \(-0.272989\pi\)
\(752\) 2.34028 + 0.760403i 0.0853412 + 0.0277290i
\(753\) 0 0
\(754\) 0.989459 1.36187i 0.0360340 0.0495965i
\(755\) 1.89190 5.82267i 0.0688533 0.211909i
\(756\) 0 0
\(757\) 10.7918 7.84073i 0.392236 0.284976i −0.374135 0.927374i \(-0.622060\pi\)
0.766371 + 0.642398i \(0.222060\pi\)
\(758\) 4.59573 0.166924
\(759\) 0 0
\(760\) −1.91020 −0.0692901
\(761\) −0.449868 + 0.326848i −0.0163077 + 0.0118482i −0.595909 0.803052i \(-0.703208\pi\)
0.579602 + 0.814900i \(0.303208\pi\)
\(762\) 0 0
\(763\) 4.28526 13.1887i 0.155137 0.477463i
\(764\) 22.3907 30.8181i 0.810066 1.11496i
\(765\) 0 0
\(766\) 5.02143 + 1.63156i 0.181432 + 0.0589507i
\(767\) −0.0212780 0.0654871i −0.000768305 0.00236460i
\(768\) 0 0
\(769\) 32.6962i 1.17906i 0.807748 + 0.589528i \(0.200686\pi\)
−0.807748 + 0.589528i \(0.799314\pi\)
\(770\) −4.59593 + 0.165480i −0.165626 + 0.00596347i
\(771\) 0 0
\(772\) −16.7323 23.0300i −0.602209 0.828869i
\(773\) 1.30242 0.423182i 0.0468448 0.0152208i −0.285501 0.958378i \(-0.592160\pi\)
0.332346 + 0.943158i \(0.392160\pi\)
\(774\) 0 0
\(775\) −3.31493 2.40844i −0.119076 0.0865138i
\(776\) 6.40569 + 4.65401i 0.229951 + 0.167069i
\(777\) 0 0
\(778\) 3.78942 1.23126i 0.135857 0.0441427i
\(779\) 4.01718 + 5.52918i 0.143930 + 0.198103i
\(780\) 0 0
\(781\) −26.5854 7.59208i −0.951301 0.271666i
\(782\) 2.25820i 0.0807530i
\(783\) 0 0
\(784\) 4.45900 + 13.7234i 0.159250 + 0.490121i
\(785\) −12.8686 4.18128i −0.459302 0.149236i
\(786\) 0 0
\(787\) 5.09353 7.01064i 0.181565 0.249902i −0.708527 0.705684i \(-0.750640\pi\)
0.890092 + 0.455781i \(0.150640\pi\)
\(788\) −7.54349 + 23.2165i −0.268726 + 0.827053i
\(789\) 0 0
\(790\) 2.26290 1.64409i 0.0805104 0.0584943i
\(791\) −0.0731593 −0.00260125
\(792\) 0 0
\(793\) 35.1262 1.24737
\(794\) −4.14127 + 3.00881i −0.146968 + 0.106779i
\(795\) 0 0
\(796\) 2.71926 8.36901i 0.0963815 0.296632i
\(797\) −7.92940 + 10.9139i −0.280874 + 0.386590i −0.926023 0.377467i \(-0.876795\pi\)
0.645149 + 0.764057i \(0.276795\pi\)
\(798\) 0 0
\(799\) 0.802907 + 0.260880i 0.0284048 + 0.00922928i
\(800\) −0.808775 2.48915i −0.0285945 0.0880049i
\(801\) 0 0
\(802\) 13.2659i 0.468435i
\(803\) −1.88089 52.2388i −0.0663753 1.84347i
\(804\) 0 0
\(805\) 12.2570 + 16.8703i 0.432001 + 0.594598i
\(806\) 13.6463 4.43395i 0.480670 0.156179i
\(807\) 0 0
\(808\) 11.2567 + 8.17847i 0.396009 + 0.287717i
\(809\) 35.6994 + 25.9371i 1.25512 + 0.911900i 0.998508 0.0546139i \(-0.0173928\pi\)
0.256615 + 0.966514i \(0.417393\pi\)
\(810\) 0 0
\(811\) 39.0505 12.6883i 1.37125 0.445546i 0.471466 0.881884i \(-0.343725\pi\)
0.899782 + 0.436339i \(0.143725\pi\)
\(812\) −1.28202 1.76455i −0.0449901 0.0619236i
\(813\) 0 0
\(814\) −4.14081 + 3.24239i −0.145135 + 0.113646i
\(815\) 20.3420i 0.712550i
\(816\) 0 0
\(817\) 1.47586 + 4.54224i 0.0516340 + 0.158913i
\(818\) 5.52974 + 1.79672i 0.193343 + 0.0628209i
\(819\) 0 0
\(820\) −31.6274 + 43.5313i −1.10447 + 1.52018i
\(821\) −4.85689 + 14.9480i −0.169507 + 0.521688i −0.999340 0.0363233i \(-0.988435\pi\)
0.829833 + 0.558011i \(0.188435\pi\)
\(822\) 0 0
\(823\) 4.59885 3.34126i 0.160306 0.116469i −0.504740 0.863271i \(-0.668412\pi\)
0.665046 + 0.746802i \(0.268412\pi\)
\(824\) −2.70555 −0.0942525
\(825\) 0 0
\(826\) 0.00655490 0.000228074
\(827\) −11.5227 + 8.37170i −0.400682 + 0.291113i −0.769819 0.638263i \(-0.779653\pi\)
0.369137 + 0.929375i \(0.379653\pi\)
\(828\) 0 0
\(829\) −1.17567 + 3.61833i −0.0408326 + 0.125670i −0.969395 0.245507i \(-0.921046\pi\)
0.928562 + 0.371177i \(0.121046\pi\)
\(830\) −5.36609 + 7.38579i −0.186260 + 0.256364i
\(831\) 0 0
\(832\) −28.5609 9.28001i −0.990172 0.321726i
\(833\) 1.52980 + 4.70824i 0.0530044 + 0.163131i
\(834\) 0 0
\(835\) 7.24902i 0.250863i
\(836\) 3.26422 1.19209i 0.112895 0.0412292i
\(837\) 0 0
\(838\) −3.30773 4.55270i −0.114264 0.157270i
\(839\) 3.70686 1.20443i 0.127975 0.0415816i −0.244329 0.969692i \(-0.578568\pi\)
0.372304 + 0.928111i \(0.378568\pi\)
\(840\) 0 0
\(841\) 23.0157 + 16.7219i 0.793645 + 0.576617i
\(842\) 3.63419 + 2.64039i 0.125242 + 0.0909939i
\(843\) 0 0
\(844\) −34.6178 + 11.2480i −1.19159 + 0.387173i
\(845\) −34.3180 47.2347i −1.18058 1.62492i
\(846\) 0 0
\(847\) 16.0703 6.53338i 0.552183 0.224489i
\(848\) 14.4721i 0.496974i
\(849\) 0 0
\(850\) −0.0812189 0.249966i −0.00278579 0.00857377i
\(851\) 22.6797 + 7.36908i 0.777450 + 0.252609i
\(852\) 0 0
\(853\) −18.6366 + 25.6510i −0.638104 + 0.878275i −0.998513 0.0545195i \(-0.982637\pi\)
0.360409 + 0.932795i \(0.382637\pi\)
\(854\) −1.03331 + 3.18020i −0.0353592 + 0.108824i
\(855\) 0 0
\(856\) −14.1894 + 10.3092i −0.484984 + 0.352362i
\(857\) −39.5636 −1.35147 −0.675733 0.737147i \(-0.736173\pi\)
−0.675733 + 0.737147i \(0.736173\pi\)
\(858\) 0 0
\(859\) −38.3183 −1.30740 −0.653701 0.756753i \(-0.726785\pi\)
−0.653701 + 0.756753i \(0.726785\pi\)
\(860\) −30.4203 + 22.1016i −1.03732 + 0.753659i
\(861\) 0 0
\(862\) −2.93194 + 9.02357i −0.0998621 + 0.307344i
\(863\) −27.4819 + 37.8256i −0.935495 + 1.28760i 0.0221825 + 0.999754i \(0.492939\pi\)
−0.957677 + 0.287844i \(0.907061\pi\)
\(864\) 0 0
\(865\) 25.7092 + 8.35343i 0.874139 + 0.284025i
\(866\) −0.147649 0.454418i −0.00501733 0.0154417i
\(867\) 0 0
\(868\) 18.5911i 0.631024i
\(869\) −5.89056 + 8.75356i −0.199824 + 0.296944i
\(870\) 0 0
\(871\) −5.31999 7.32233i −0.180261 0.248108i
\(872\) 11.9528 3.88371i 0.404774 0.131519i
\(873\) 0 0
\(874\) 0.936595 + 0.680476i 0.0316808 + 0.0230174i
\(875\) 13.1967 + 9.58799i 0.446131 + 0.324133i
\(876\) 0 0
\(877\) 29.9762 9.73986i 1.01222 0.328892i 0.244484 0.969653i \(-0.421381\pi\)
0.767740 + 0.640762i \(0.221381\pi\)
\(878\) −1.95478 2.69052i −0.0659706 0.0908008i
\(879\) 0 0
\(880\) 15.5372 + 19.8423i 0.523757 + 0.668884i
\(881\) 42.0051i 1.41519i −0.706619 0.707595i \(-0.749780\pi\)
0.706619 0.707595i \(-0.250220\pi\)
\(882\) 0 0
\(883\) 0.787007 + 2.42216i 0.0264849 + 0.0815122i 0.963425 0.267977i \(-0.0863551\pi\)
−0.936940 + 0.349489i \(0.886355\pi\)
\(884\) −11.9139 3.87105i −0.400707 0.130198i
\(885\) 0 0
\(886\) 3.11939 4.29347i 0.104798 0.144242i
\(887\) −4.30244 + 13.2415i −0.144462 + 0.444607i −0.996941 0.0781530i \(-0.975098\pi\)
0.852480 + 0.522760i \(0.175098\pi\)
\(888\) 0 0
\(889\) −8.42236 + 6.11920i −0.282477 + 0.205231i
\(890\) 7.92302 0.265580
\(891\) 0 0
\(892\) 30.6104 1.02491
\(893\) 0.350145 0.254396i 0.0117172 0.00851302i
\(894\) 0 0
\(895\) 7.87231 24.2285i 0.263142 0.809869i
\(896\) 9.17314 12.6257i 0.306453 0.421797i
\(897\) 0 0
\(898\) 5.01372 + 1.62905i 0.167310 + 0.0543623i
\(899\) −1.45141 4.46699i −0.0484074 0.148983i
\(900\) 0 0
\(901\) 4.96511i 0.165412i
\(902\) −4.09489 + 14.3392i −0.136345 + 0.477443i
\(903\) 0 0
\(904\) −0.0389725 0.0536410i −0.00129620 0.00178407i
\(905\) −40.1894 + 13.0583i −1.33594 + 0.434074i
\(906\) 0 0
\(907\) 26.9528 + 19.5824i 0.894953 + 0.650222i 0.937165 0.348887i \(-0.113440\pi\)
−0.0422115 + 0.999109i \(0.513440\pi\)
\(908\) −40.9456 29.7487i −1.35883 0.987246i
\(909\) 0 0
\(910\) 8.08303 2.62634i 0.267950 0.0870622i
\(911\) 3.87278 + 5.33042i 0.128311 + 0.176605i 0.868339 0.495971i \(-0.165188\pi\)
−0.740028 + 0.672576i \(0.765188\pi\)
\(912\) 0 0
\(913\) 9.45623 33.1132i 0.312956 1.09589i
\(914\) 9.61060i 0.317890i
\(915\) 0 0
\(916\) 2.49601 + 7.68194i 0.0824706 + 0.253819i
\(917\) 11.8240 + 3.84186i 0.390464 + 0.126869i
\(918\) 0 0
\(919\) −19.1361 + 26.3386i −0.631241 + 0.868829i −0.998111 0.0614433i \(-0.980430\pi\)
0.366869 + 0.930273i \(0.380430\pi\)
\(920\) −5.84004 + 17.9738i −0.192540 + 0.592579i
\(921\) 0 0
\(922\) −3.48848 + 2.53453i −0.114887 + 0.0834703i
\(923\) 51.0952 1.68182
\(924\) 0 0
\(925\) −2.77552 −0.0912585
\(926\) −5.58674 + 4.05901i −0.183592 + 0.133387i
\(927\) 0 0
\(928\) 0.927084 2.85327i 0.0304330 0.0936633i
\(929\) −8.24635 + 11.3501i −0.270554 + 0.372386i −0.922577 0.385814i \(-0.873921\pi\)
0.652023 + 0.758199i \(0.273921\pi\)
\(930\) 0 0
\(931\) 2.41374 + 0.784272i 0.0791072 + 0.0257035i
\(932\) −6.75136 20.7786i −0.221148 0.680624i
\(933\) 0 0
\(934\) 1.11727i 0.0365581i
\(935\) 5.33051 + 6.80753i 0.174326 + 0.222630i
\(936\) 0 0
\(937\) 31.0358 + 42.7172i 1.01390 + 1.39551i 0.916396 + 0.400273i \(0.131085\pi\)
0.0975008 + 0.995235i \(0.468915\pi\)
\(938\) 0.819436 0.266251i 0.0267555 0.00869340i
\(939\) 0 0
\(940\) 2.75670 + 2.00286i 0.0899137 + 0.0653262i
\(941\) 1.79920 + 1.30719i 0.0586522 + 0.0426133i 0.616725 0.787179i \(-0.288459\pi\)
−0.558073 + 0.829792i \(0.688459\pi\)
\(942\) 0 0
\(943\) 64.3080 20.8949i 2.09416 0.680432i
\(944\) −0.0211134 0.0290601i −0.000687183 0.000945826i
\(945\) 0 0
\(946\) −5.81800 + 8.64573i −0.189159 + 0.281097i
\(947\) 21.9181i 0.712241i −0.934440 0.356121i \(-0.884099\pi\)
0.934440 0.356121i \(-0.115901\pi\)
\(948\) 0 0
\(949\) 29.8518 + 91.8743i 0.969029 + 2.98237i
\(950\) −0.128148 0.0416380i −0.00415768 0.00135091i
\(951\) 0 0
\(952\) 1.45338 2.00041i 0.0471044 0.0648337i
\(953\) 6.64425 20.4489i 0.215228 0.662404i −0.783909 0.620876i \(-0.786777\pi\)
0.999137 0.0415288i \(-0.0132228\pi\)
\(954\) 0 0
\(955\) 39.3095 28.5601i 1.27203 0.924182i
\(956\) 33.4277 1.08113
\(957\) 0 0
\(958\) −14.3124 −0.462413
\(959\) −22.5293 + 16.3685i −0.727509 + 0.528566i
\(960\) 0 0
\(961\) 2.79193 8.59267i 0.0900622 0.277183i
\(962\) 5.71286 7.86308i 0.184190 0.253516i
\(963\) 0 0
\(964\) 4.73430 + 1.53827i 0.152482 + 0.0495443i
\(965\) −11.2205 34.5331i −0.361200 1.11166i
\(966\) 0 0
\(967\) 15.7910i 0.507803i 0.967230 + 0.253901i \(0.0817139\pi\)
−0.967230 + 0.253901i \(0.918286\pi\)
\(968\) 13.3511 + 8.30251i 0.429120 + 0.266853i
\(969\) 0 0
\(970\) 2.86300 + 3.94058i 0.0919253 + 0.126524i
\(971\) 7.29530 2.37039i 0.234117 0.0760693i −0.189609 0.981860i \(-0.560722\pi\)
0.423726 + 0.905790i \(0.360722\pi\)
\(972\) 0 0
\(973\) 17.9667 + 13.0535i 0.575984 + 0.418477i
\(974\) 3.67517 + 2.67017i 0.117760 + 0.0855577i
\(975\) 0 0
\(976\) 17.4272 5.66245i 0.557832 0.181250i
\(977\) 4.39314 + 6.04664i 0.140549 + 0.193449i 0.873489 0.486845i \(-0.161852\pi\)
−0.732940 + 0.680294i \(0.761852\pi\)
\(978\) 0 0
\(979\) −28.0731 + 10.2522i −0.897221 + 0.327663i
\(980\) 19.9814i 0.638282i
\(981\) 0 0
\(982\) −4.16946 12.8323i −0.133053 0.409494i
\(983\) 47.5184 + 15.4397i 1.51560 + 0.492449i 0.944523 0.328446i \(-0.106525\pi\)
0.571079 + 0.820895i \(0.306525\pi\)
\(984\) 0 0
\(985\) −18.3021 + 25.1907i −0.583153 + 0.802642i
\(986\) 0.0930998 0.286532i 0.00296490 0.00912503i
\(987\) 0 0
\(988\) −5.19561 + 3.77483i −0.165294 + 0.120093i
\(989\) 47.2520 1.50252
\(990\) 0 0
\(991\) −32.0166 −1.01704 −0.508520 0.861050i \(-0.669807\pi\)
−0.508520 + 0.861050i \(0.669807\pi\)
\(992\) 20.6883 15.0309i 0.656853 0.477232i
\(993\) 0 0
\(994\) −1.50307 + 4.62598i −0.0476745 + 0.146727i
\(995\) 6.59748 9.08066i 0.209154 0.287876i
\(996\) 0 0
\(997\) −18.0018 5.84914i −0.570123 0.185244i 0.00974795 0.999952i \(-0.496897\pi\)
−0.579871 + 0.814708i \(0.696897\pi\)
\(998\) 2.77608 + 8.54390i 0.0878753 + 0.270452i
\(999\) 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 891.2.k.a.404.10 80
3.2 odd 2 inner 891.2.k.a.404.11 80
9.2 odd 6 297.2.t.a.206.5 80
9.4 even 3 297.2.t.a.8.5 80
9.5 odd 6 99.2.p.a.74.6 yes 80
9.7 even 3 99.2.p.a.41.6 yes 80
11.7 odd 10 inner 891.2.k.a.161.11 80
33.29 even 10 inner 891.2.k.a.161.10 80
99.7 odd 30 99.2.p.a.95.6 yes 80
99.29 even 30 297.2.t.a.260.5 80
99.40 odd 30 297.2.t.a.62.5 80
99.95 even 30 99.2.p.a.29.6 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.p.a.29.6 80 99.95 even 30
99.2.p.a.41.6 yes 80 9.7 even 3
99.2.p.a.74.6 yes 80 9.5 odd 6
99.2.p.a.95.6 yes 80 99.7 odd 30
297.2.t.a.8.5 80 9.4 even 3
297.2.t.a.62.5 80 99.40 odd 30
297.2.t.a.206.5 80 9.2 odd 6
297.2.t.a.260.5 80 99.29 even 30
891.2.k.a.161.10 80 33.29 even 10 inner
891.2.k.a.161.11 80 11.7 odd 10 inner
891.2.k.a.404.10 80 1.1 even 1 trivial
891.2.k.a.404.11 80 3.2 odd 2 inner