Properties

Label 891.2.k.a.161.11
Level $891$
Weight $2$
Character 891.161
Analytic conductor $7.115$
Analytic rank $0$
Dimension $80$
Inner twists $4$

Related objects

Downloads

Learn more

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 161.11
Character \(\chi\) \(=\) 891.161
Dual form 891.2.k.a.404.11

$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\) \(-1\)

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 \(-0.258243\pi\)
−0.476909 + 0.878953i \(0.658243\pi\)
\(3\) 0 0
\(4\) −0.575734 1.77193i −0.287867 0.885963i
\(5\) 1.39685 + 1.92260i 0.624691 + 0.859813i 0.997684 0.0680209i \(-0.0216685\pi\)
−0.372993 + 0.927834i \(0.621668\pi\)
\(6\) 0 0
\(7\) −1.49987 + 0.487337i −0.566898 + 0.184196i −0.578422 0.815737i \(-0.696331\pi\)
0.0115248 + 0.999934i \(0.496331\pi\)
\(8\) 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 −0.0734014 + 0.997302i \(0.523385\pi\)
−0.925809 + 0.377992i \(0.876615\pi\)
\(14\) −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 \(-0.657530\pi\)
0.690183 + 0.723635i \(0.257530\pi\)
\(18\) 0 0
\(19\) −0.534855 0.173785i −0.122704 0.0398690i 0.247021 0.969010i \(-0.420548\pi\)
−0.369725 + 0.929141i \(0.620548\pi\)
\(20\) 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 \(-0.121956\pi\)
−0.970093 + 0.242733i \(0.921956\pi\)
\(30\) 0 0
\(31\) 5.11890 + 3.71910i 0.919382 + 0.667970i 0.943370 0.331742i \(-0.107636\pi\)
−0.0239881 + 0.999712i \(0.507636\pi\)
\(32\) −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 0.998948 + 0.0458543i \(0.0146010\pi\)
−0.781214 + 0.624264i \(0.785399\pi\)
\(38\) −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 −0.00669163 0.999978i \(-0.502130\pi\)
0.593186 0.805066i \(-0.297870\pi\)
\(42\) 0 0
\(43\) 8.49248i 1.29509i 0.762027 + 0.647546i \(0.224205\pi\)
−0.762027 + 0.647546i \(0.775795\pi\)
\(44\) 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 \(-0.382124\pi\)
−0.255149 + 0.966902i \(0.582124\pi\)
\(48\) 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 \(-0.900617\pi\)
0.586217 + 0.810154i \(0.300617\pi\)
\(54\) 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 \(-0.600233\pi\)
0.308321 + 0.951282i \(0.400233\pi\)
\(60\) 0 0
\(61\) −3.36853 4.63638i −0.431296 0.593628i 0.536954 0.843611i \(-0.319575\pi\)
−0.968250 + 0.249983i \(0.919575\pi\)
\(62\) 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 \(-0.0352906\pi\)
−0.412346 + 0.911027i \(0.635291\pi\)
\(72\) 0 0
\(73\) −14.9894 + 4.87035i −1.75438 + 0.570031i −0.996593 0.0824752i \(-0.973717\pi\)
−0.757783 + 0.652507i \(0.773717\pi\)
\(74\) −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 −0.690767 0.723077i \(-0.742727\pi\)
0.901146 + 0.433515i \(0.142727\pi\)
\(80\) −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 \(-0.507002\pi\)
0.944029 + 0.329861i \(0.107002\pi\)
\(84\) 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 0.336534 0.941671i \(-0.390745\pi\)
−0.791588 + 0.611055i \(0.790745\pi\)
\(98\) −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 \(-0.139062\pi\)
−0.122408 + 0.992480i \(0.539062\pi\)
\(102\) 0 0
\(103\) 0.584954 + 1.80030i 0.0576372 + 0.177389i 0.975730 0.218976i \(-0.0702715\pi\)
−0.918093 + 0.396365i \(0.870272\pi\)
\(104\) 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 −0.582390 0.812910i \(-0.697882\pi\)
0.948980 0.315337i \(-0.102118\pi\)
\(108\) 0 0
\(109\) 8.79322i 0.842238i −0.907005 0.421119i \(-0.861638\pi\)
0.907005 0.421119i \(-0.138362\pi\)
\(110\) −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 \(-0.400695\pi\)
−0.311091 + 0.950380i \(0.600695\pi\)
\(114\) 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 0.945693 0.325061i \(-0.105385\pi\)
−0.601386 + 0.798958i \(0.705385\pi\)
\(128\) 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 \(-0.388087\pi\)
0.344387 + 0.938828i \(0.388087\pi\)
\(132\) 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 −0.974505 0.224364i \(-0.927970\pi\)
0.0877559 0.996142i \(-0.472030\pi\)
\(138\) 0 0
\(139\) −13.3927 + 4.35156i −1.13596 + 0.369094i −0.815836 0.578283i \(-0.803723\pi\)
−0.320119 + 0.947377i \(0.603723\pi\)
\(140\) −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 \(-0.898317\pi\)
0.00528647 + 0.999986i \(0.498317\pi\)
\(150\) 0 0
\(151\) −2.45014 0.796099i −0.199390 0.0647856i 0.207620 0.978210i \(-0.433428\pi\)
−0.407009 + 0.913424i \(0.633428\pi\)
\(152\) −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 −0.855974 0.517019i \(-0.827042\pi\)
0.996394 + 0.0848519i \(0.0270417\pi\)
\(158\) 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 0.824979 0.565164i \(-0.191187\pi\)
−0.282570 + 0.959247i \(0.591187\pi\)
\(164\) −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 \(-0.262345\pi\)
−0.488196 + 0.872734i \(0.662345\pi\)
\(168\) 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 −0.723922 0.689882i \(-0.757663\pi\)
0.991168 0.132615i \(-0.0423374\pi\)
\(174\) 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 \(-0.268795\pi\)
0.0978766 + 0.995199i \(0.468795\pi\)
\(180\) 0 0
\(181\) 14.3857 10.4518i 1.06928 0.776879i 0.0934987 0.995619i \(-0.470195\pi\)
0.975783 + 0.218741i \(0.0701949\pi\)
\(182\) 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 \(-0.334962\pi\)
0.911452 + 0.411406i \(0.134962\pi\)
\(192\) 0 0
\(193\) −8.98083 12.3610i −0.646454 0.889768i 0.352485 0.935817i \(-0.385337\pi\)
−0.998939 + 0.0460498i \(0.985337\pi\)
\(194\) −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 \(-0.654576\pi\)
−0.466754 + 0.884387i \(0.654576\pi\)
\(198\) 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 −0.203485 0.979078i \(-0.565227\pi\)
0.994039 0.109026i \(-0.0347732\pi\)
\(212\) 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 0.624229 + 0.781242i \(0.285413\pi\)
−0.964214 + 0.265125i \(0.914587\pi\)
\(224\) 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 0.690171 + 0.723646i \(0.257535\pi\)
−0.133012 + 0.991114i \(0.542465\pi\)
\(228\) 0 0
\(229\) 3.50738 + 2.54826i 0.231774 + 0.168394i 0.697611 0.716477i \(-0.254247\pi\)
−0.465837 + 0.884871i \(0.654247\pi\)
\(230\) −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 \(-0.174506\pi\)
−0.231937 + 0.972731i \(0.574506\pi\)
\(234\) 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 −0.595240 0.803548i \(-0.702943\pi\)
0.953873 0.300210i \(-0.0970569\pi\)
\(240\) 0 0
\(241\) 2.67184i 0.172108i 0.996290 + 0.0860541i \(0.0274258\pi\)
−0.996290 + 0.0860541i \(0.972574\pi\)
\(242\) −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 \(-0.658891\pi\)
0.982934 + 0.183958i \(0.0588909\pi\)
\(252\) 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 \(-0.552619\pi\)
0.446644 + 0.894712i \(0.352619\pi\)
\(258\) 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 \(-0.306529\pi\)
0.571067 + 0.820903i \(0.306529\pi\)
\(264\) 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 0.995914 + 0.0903100i \(0.0287858\pi\)
−0.221864 + 0.975078i \(0.571214\pi\)
\(270\) 0 0
\(271\) −0.869236 + 0.282432i −0.0528023 + 0.0171565i −0.335299 0.942112i \(-0.608837\pi\)
0.282497 + 0.959268i \(0.408837\pi\)
\(272\) −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 −0.462921 0.886400i \(-0.653199\pi\)
0.986067 + 0.166352i \(0.0531986\pi\)
\(278\) −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 \(-0.682545\pi\)
0.631244 + 0.775584i \(0.282545\pi\)
\(282\) 0 0
\(283\) −11.4793 3.72985i −0.682373 0.221716i −0.0527388 0.998608i \(-0.516795\pi\)
−0.629634 + 0.776892i \(0.716795\pi\)
\(284\) 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 0.978396 + 0.206741i \(0.0662858\pi\)
−0.670019 + 0.742344i \(0.733714\pi\)
\(294\) 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 \(0.158020\pi\)
−0.879287 + 0.476293i \(0.841980\pi\)
\(308\) −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 \(-0.716092\pi\)
−0.965457 + 0.260564i \(0.916092\pi\)
\(312\) 0 0
\(313\) −13.0604 + 9.48891i −0.738215 + 0.536345i −0.892152 0.451736i \(-0.850805\pi\)
0.153936 + 0.988081i \(0.450805\pi\)
\(314\) 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 \(-0.875658\pi\)
0.647875 + 0.761747i \(0.275658\pi\)
\(318\) 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 0.329543 0.944141i \(-0.393105\pi\)
0.821558 + 0.570125i \(0.193105\pi\)
\(338\) 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 \(-0.804332\pi\)
0.296047 + 0.955173i \(0.404332\pi\)
\(348\) 0 0
\(349\) −9.66986 3.14193i −0.517616 0.168183i 0.0385474 0.999257i \(-0.487727\pi\)
−0.556163 + 0.831073i \(0.687727\pi\)
\(350\) 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 \(-0.168806\pi\)
−0.995202 + 0.0978426i \(0.968806\pi\)
\(360\) 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 0.436289 + 0.899807i \(0.356293\pi\)
0.175928 + 0.984403i \(0.443707\pi\)
\(368\) −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 \(0.0536836\pi\)
−0.985812 + 0.167854i \(0.946316\pi\)
\(374\) −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 −0.815168 0.579224i \(-0.803356\pi\)
0.298974 + 0.954261i \(0.403356\pi\)
\(380\) −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 \(-0.681207\pi\)
0.967633 + 0.252361i \(0.0812069\pi\)
\(384\) 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 \(-0.511980\pi\)
0.556927 + 0.830561i \(0.311980\pi\)
\(390\) 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 0.886662 + 0.462418i \(0.153018\pi\)
0.165792 + 0.986161i \(0.446982\pi\)
\(402\) 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 −0.973830 0.227276i \(-0.927018\pi\)
0.517083 + 0.855935i \(0.327018\pi\)
\(410\) 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 −0.999905 0.0137940i \(-0.995609\pi\)
0.817048 + 0.576570i \(0.195609\pi\)
\(422\) 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 \(-0.511905\pi\)
−0.961946 + 0.273240i \(0.911905\pi\)
\(432\) 0 0
\(433\) −0.399073 1.22822i −0.0191782 0.0590245i 0.941009 0.338380i \(-0.109879\pi\)
−0.960188 + 0.279356i \(0.909879\pi\)
\(434\) −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 \(-0.931186\pi\)
0.976723 0.214505i \(-0.0688138\pi\)
\(440\) −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 \(-0.289318\pi\)
0.0335523 + 0.999437i \(0.489318\pi\)
\(444\) 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 \(-0.690852\pi\)
0.959543 + 0.281561i \(0.0908522\pi\)
\(450\) 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 0.999696 + 0.0246533i \(0.00784819\pi\)
−0.285476 + 0.958386i \(0.592152\pi\)
\(458\) 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 \(-0.587489\pi\)
−0.271406 + 0.962465i \(0.587489\pi\)
\(462\) 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 \(-0.222258\pi\)
−0.848108 + 0.529823i \(0.822258\pi\)
\(468\) 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 −0.439933 + 0.898031i \(0.644998\pi\)
−0.990025 + 0.140895i \(0.955002\pi\)
\(480\) 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 −0.999480 0.0322416i \(-0.989735\pi\)
0.827548 + 0.561396i \(0.189735\pi\)
\(488\) −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 0.794667 + 0.607045i \(0.207645\pi\)
−0.286087 + 0.958204i \(0.592355\pi\)
\(492\) 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 0.966280 + 0.257494i \(0.0828968\pi\)
−0.630386 + 0.776282i \(0.717103\pi\)
\(500\) −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 0.672359 + 0.740225i \(0.265281\pi\)
−0.979043 + 0.203652i \(0.934719\pi\)
\(504\) 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 \(-0.183858\pi\)
0.356830 + 0.934170i \(0.383858\pi\)
\(510\) 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 \(-0.488066\pi\)
0.617698 + 0.786416i \(0.288066\pi\)
\(522\) 0 0
\(523\) 8.59617 + 11.8316i 0.375884 + 0.517360i 0.954488 0.298248i \(-0.0964023\pi\)
−0.578604 + 0.815609i \(0.696402\pi\)
\(524\) −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 −0.521497 0.853253i \(-0.674626\pi\)
0.972643 + 0.232303i \(0.0746262\pi\)
\(542\) −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 0.399343 0.916802i \(-0.369238\pi\)
−0.215807 + 0.976436i \(0.569238\pi\)
\(548\) −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 0.953273 + 0.302111i \(0.0976914\pi\)
−0.593637 + 0.804733i \(0.702309\pi\)
\(558\) 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 \(-0.370799\pi\)
−0.751768 + 0.659427i \(0.770799\pi\)
\(564\) 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 −0.358402 0.933567i \(-0.616678\pi\)
0.838690 0.544608i \(-0.183322\pi\)
\(570\) 0 0
\(571\) 6.14821i 0.257295i 0.991690 + 0.128647i \(0.0410635\pi\)
−0.991690 + 0.128647i \(0.958936\pi\)
\(572\) −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 −0.752105 0.659043i \(-0.770961\pi\)
0.394374 + 0.918950i \(0.370961\pi\)
\(578\) −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 \(-0.558616\pi\)
0.429710 + 0.902967i \(0.358616\pi\)
\(588\) 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 \(-0.588021\pi\)
−0.273015 + 0.962010i \(0.588021\pi\)
\(594\) 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 −0.985912 0.167263i \(-0.946507\pi\)
0.145587 0.989345i \(-0.453493\pi\)
\(600\) 0 0
\(601\) −5.01758 + 1.63031i −0.204671 + 0.0665017i −0.409558 0.912284i \(-0.634317\pi\)
0.204887 + 0.978786i \(0.434317\pi\)
\(602\) 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 −0.981518 0.191367i \(-0.938708\pi\)
0.485307 + 0.874344i \(0.338708\pi\)
\(608\) 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 −0.257652 0.966238i \(-0.582949\pi\)
−0.776385 + 0.630259i \(0.782949\pi\)
\(614\) −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 −0.397534 0.917588i \(-0.630134\pi\)
0.860956 0.508680i \(-0.169866\pi\)
\(620\) 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 −0.999328 0.0366537i \(-0.988330\pi\)
0.786929 0.617044i \(-0.211670\pi\)
\(632\) −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 \(-0.459661\pi\)
−0.480819 + 0.876820i \(0.659661\pi\)
\(642\) 0 0
\(643\) −6.60864 + 4.80146i −0.260619 + 0.189351i −0.710420 0.703778i \(-0.751495\pi\)
0.449801 + 0.893129i \(0.351495\pi\)
\(644\) −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 \(-0.939182\pi\)
0.484003 + 0.875066i \(0.339182\pi\)
\(648\) 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 \(-0.247513\pi\)
0.988880 + 0.148713i \(0.0475129\pi\)
\(654\) 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 \(-0.464259\pi\)
0.112047 + 0.993703i \(0.464259\pi\)
\(660\) 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 −0.823437 0.567407i \(-0.807947\pi\)
0.794093 + 0.607797i \(0.207947\pi\)
\(674\) 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 \(-0.831887\pi\)
0.212355 + 0.977193i \(0.431887\pi\)
\(678\) 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 0.935321 0.353801i \(-0.115111\pi\)
−0.0474545 + 0.998873i \(0.515111\pi\)
\(692\) −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 \(-0.868039\pi\)
0.977242 + 0.212128i \(0.0680395\pi\)
\(702\) 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 −0.0553060 0.998469i \(-0.517613\pi\)
0.932510 + 0.361143i \(0.117613\pi\)
\(710\) −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 \(-0.354097\pi\)
0.885089 + 0.465422i \(0.154097\pi\)
\(720\) 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 −0.400839 0.916149i \(-0.631281\pi\)
0.214213 + 0.976787i \(0.431281\pi\)
\(734\) −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 −0.737140 0.675740i \(-0.763824\pi\)
0.870455 + 0.492247i \(0.163824\pi\)
\(740\) 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 \(-0.660892\pi\)
0.682502 + 0.730884i \(0.260892\pi\)
\(744\) 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 0.654239 + 0.756288i \(0.272989\pi\)
−0.973825 + 0.227298i \(0.927011\pi\)
\(752\) −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 0.766371 0.642398i \(-0.222060\pi\)
−0.374135 + 0.927374i \(0.622060\pi\)
\(758\) −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 \(-0.296792\pi\)
−0.579602 + 0.814900i \(0.696792\pi\)
\(762\) 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 \(-0.799314\pi\)
0.807748 0.589528i \(-0.200686\pi\)
\(770\) 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 \(-0.407840\pi\)
−0.332346 + 0.943158i \(0.607840\pi\)
\(774\) 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 0.890092 0.455781i \(-0.150640\pi\)
−0.708527 + 0.705684i \(0.750640\pi\)
\(788\) 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 \(-0.123205\pi\)
−0.645149 + 0.764057i \(0.723205\pi\)
\(798\) 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 \(-0.982607\pi\)
−0.256615 + 0.966514i \(0.582607\pi\)
\(810\) 0 0
\(811\) 39.0505 + 12.6883i 1.37125 + 0.445546i 0.899782 0.436339i \(-0.143725\pi\)
0.471466 + 0.881884i \(0.343725\pi\)
\(812\) 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 \(-0.0115646\pi\)
−0.829833 + 0.558011i \(0.811565\pi\)
\(822\) 0 0
\(823\) 4.59885 + 3.34126i 0.160306 + 0.116469i 0.665046 0.746802i \(-0.268412\pi\)
−0.504740 + 0.863271i \(0.668412\pi\)
\(824\) 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 \(-0.220347\pi\)
−0.369137 + 0.929375i \(0.620347\pi\)
\(828\) 0 0
\(829\) −1.17567 3.61833i −0.0408326 0.125670i 0.928562 0.371177i \(-0.121046\pi\)
−0.969395 + 0.245507i \(0.921046\pi\)
\(830\) 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 \(-0.421432\pi\)
−0.372304 + 0.928111i \(0.621432\pi\)
\(840\) 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 0.360409 0.932795i \(-0.382637\pi\)
−0.998513 + 0.0545195i \(0.982637\pi\)
\(854\) 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 \(-0.263827\pi\)
0.675733 + 0.737147i \(0.263827\pi\)
\(858\) 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 0.957677 + 0.287844i \(0.0929385\pi\)
−0.0221825 + 0.999754i \(0.507061\pi\)
\(864\) 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 0.767740 0.640762i \(-0.221381\pi\)
0.244484 + 0.969653i \(0.421381\pi\)
\(878\) 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 −0.936940 0.349489i \(-0.886355\pi\)
0.963425 + 0.267977i \(0.0863551\pi\)
\(884\) 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 \(-0.0249023\pi\)
−0.852480 + 0.522760i \(0.824902\pi\)
\(888\) 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 −0.0422115 0.999109i \(-0.513440\pi\)
0.937165 + 0.348887i \(0.113440\pi\)
\(908\) 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 \(-0.834812\pi\)
0.740028 + 0.672576i \(0.234812\pi\)
\(912\) 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 0.366869 0.930273i \(-0.380430\pi\)
−0.998111 + 0.0614433i \(0.980430\pi\)
\(920\) 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 \(-0.126079\pi\)
−0.652023 + 0.758199i \(0.726079\pi\)
\(930\) 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 0.0975008 0.995235i \(-0.468915\pi\)
0.916396 0.400273i \(-0.131085\pi\)
\(938\) −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 \(-0.711541\pi\)
0.558073 + 0.829792i \(0.311541\pi\)
\(942\) 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 −0.999137 0.0415288i \(-0.986777\pi\)
0.783909 0.620876i \(-0.213223\pi\)
\(954\) 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 \(-0.918286\pi\)
0.967230 0.253901i \(-0.0817139\pi\)
\(968\) −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 \(-0.439278\pi\)
−0.423726 + 0.905790i \(0.639278\pi\)
\(972\) 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 \(-0.838148\pi\)
0.732940 + 0.680294i \(0.238148\pi\)
\(978\) 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 \(-0.893475\pi\)
−0.571079 + 0.820895i \(0.693475\pi\)
\(984\) 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 −0.579871 0.814708i \(-0.696897\pi\)
0.00974795 + 0.999952i \(0.496897\pi\)
\(998\) −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.161.11 80
3.2 odd 2 inner 891.2.k.a.161.10 80
9.2 odd 6 297.2.t.a.260.5 80
9.4 even 3 297.2.t.a.62.5 80
9.5 odd 6 99.2.p.a.29.6 80
9.7 even 3 99.2.p.a.95.6 yes 80
11.8 odd 10 inner 891.2.k.a.404.10 80
33.8 even 10 inner 891.2.k.a.404.11 80
99.41 even 30 99.2.p.a.74.6 yes 80
99.52 odd 30 99.2.p.a.41.6 yes 80
99.74 even 30 297.2.t.a.206.5 80
99.85 odd 30 297.2.t.a.8.5 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.p.a.29.6 80 9.5 odd 6
99.2.p.a.41.6 yes 80 99.52 odd 30
99.2.p.a.74.6 yes 80 99.41 even 30
99.2.p.a.95.6 yes 80 9.7 even 3
297.2.t.a.8.5 80 99.85 odd 30
297.2.t.a.62.5 80 9.4 even 3
297.2.t.a.206.5 80 99.74 even 30
297.2.t.a.260.5 80 9.2 odd 6
891.2.k.a.161.10 80 3.2 odd 2 inner
891.2.k.a.161.11 80 1.1 even 1 trivial
891.2.k.a.404.10 80 11.8 odd 10 inner
891.2.k.a.404.11 80 33.8 even 10 inner