Properties

Label 99.2.m.b.25.6
Level $99$
Weight $2$
Character 99.25
Analytic conductor $0.791$
Analytic rank $0$
Dimension $72$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,2,Mod(4,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.m (of order \(15\), degree \(8\), 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: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 25.6
Character \(\chi\) \(=\) 99.25
Dual form 99.2.m.b.4.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0694404 + 0.660681i) q^{2} +(-0.106925 + 1.72875i) q^{3} +(1.52462 - 0.324067i) q^{4} +(-0.116719 + 1.11051i) q^{5} +(-1.14958 + 0.0494014i) q^{6} +(-2.61265 - 2.90164i) q^{7} +(0.730548 + 2.24840i) q^{8} +(-2.97713 - 0.369694i) q^{9} -0.741796 q^{10} +(3.27403 + 0.529836i) q^{11} +(0.397211 + 2.67033i) q^{12} +(2.44648 + 1.08924i) q^{13} +(1.73564 - 1.92762i) q^{14} +(-1.90730 - 0.320519i) q^{15} +(1.41310 - 0.629154i) q^{16} +(-4.48727 - 3.26019i) q^{17} +(0.0375162 - 1.99261i) q^{18} +(-1.58598 - 4.88115i) q^{19} +(0.181927 + 1.73092i) q^{20} +(5.29556 - 4.20635i) q^{21} +(-0.122703 + 2.19988i) q^{22} +(-1.05719 - 1.83110i) q^{23} +(-3.96502 + 1.02252i) q^{24} +(3.67114 + 0.780324i) q^{25} +(-0.549758 + 1.69198i) q^{26} +(0.957438 - 5.10718i) q^{27} +(-4.92362 - 3.57722i) q^{28} +(0.724696 + 0.804856i) q^{29} +(0.0793167 - 1.28238i) q^{30} +(-0.392973 - 0.174963i) q^{31} +(2.87790 + 4.98467i) q^{32} +(-1.26603 + 5.60332i) q^{33} +(1.84235 - 3.19104i) q^{34} +(3.52724 - 2.56269i) q^{35} +(-4.65880 + 0.401151i) q^{36} +(-2.69024 + 8.27970i) q^{37} +(3.11475 - 1.38678i) q^{38} +(-2.14462 + 4.11288i) q^{39} +(-2.58213 + 0.548848i) q^{40} +(-1.95324 + 2.16930i) q^{41} +(3.14678 + 3.20659i) q^{42} +(1.11628 - 1.93346i) q^{43} +(5.16335 - 0.253209i) q^{44} +(0.758035 - 3.26298i) q^{45} +(1.13637 - 0.825618i) q^{46} +(-12.5550 - 2.66864i) q^{47} +(0.936552 + 2.51017i) q^{48} +(-0.861884 + 8.20028i) q^{49} +(-0.260620 + 2.47964i) q^{50} +(6.11585 - 7.40876i) q^{51} +(4.08293 + 0.867854i) q^{52} +(-4.56381 + 3.31581i) q^{53} +(3.44070 + 0.277916i) q^{54} +(-0.970527 + 3.57399i) q^{55} +(4.61537 - 7.99405i) q^{56} +(8.60785 - 2.21984i) q^{57} +(-0.481430 + 0.534682i) q^{58} +(2.32346 - 0.493867i) q^{59} +(-3.01178 + 0.129427i) q^{60} +(-3.73133 + 1.66130i) q^{61} +(0.0883065 - 0.271779i) q^{62} +(6.70549 + 9.60445i) q^{63} +(-0.590604 + 0.429099i) q^{64} +(-1.49516 + 2.58969i) q^{65} +(-3.78992 - 0.447345i) q^{66} +(4.87584 + 8.44521i) q^{67} +(-7.89789 - 3.51637i) q^{68} +(3.27856 - 1.63182i) q^{69} +(1.93805 + 2.15242i) q^{70} +(-5.11062 - 3.71308i) q^{71} +(-1.34372 - 6.96385i) q^{72} +(-3.60705 + 11.1014i) q^{73} +(-5.65706 - 1.20244i) q^{74} +(-1.74152 + 6.26303i) q^{75} +(-3.99983 - 6.92792i) q^{76} +(-7.01650 - 10.8843i) q^{77} +(-2.86622 - 1.13131i) q^{78} +(-0.471916 - 4.48998i) q^{79} +(0.533744 + 1.64269i) q^{80} +(8.72665 + 2.20125i) q^{81} +(-1.56885 - 1.13983i) q^{82} +(0.440332 - 0.196049i) q^{83} +(6.71056 - 8.12919i) q^{84} +(4.14421 - 4.60261i) q^{85} +(1.35492 + 0.603248i) q^{86} +(-1.46888 + 1.16676i) q^{87} +(1.20056 + 7.74839i) q^{88} +16.0830 q^{89} +(2.20843 + 0.274237i) q^{90} +(-3.23120 - 9.94461i) q^{91} +(-2.20521 - 2.44913i) q^{92} +(0.344485 - 0.660643i) q^{93} +(0.891300 - 8.48015i) q^{94} +(5.60566 - 1.19152i) q^{95} +(-8.92495 + 4.44217i) q^{96} +(-0.837864 - 7.97174i) q^{97} -5.47762 q^{98} +(-9.55135 - 2.78778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0694404 + 0.660681i 0.0491018 + 0.467172i 0.991252 + 0.131982i \(0.0421340\pi\)
−0.942150 + 0.335191i \(0.891199\pi\)
\(3\) −0.106925 + 1.72875i −0.0617333 + 0.998093i
\(4\) 1.52462 0.324067i 0.762309 0.162034i
\(5\) −0.116719 + 1.11051i −0.0521983 + 0.496634i 0.936923 + 0.349535i \(0.113660\pi\)
−0.989122 + 0.147099i \(0.953006\pi\)
\(6\) −1.14958 + 0.0494014i −0.469312 + 0.0201680i
\(7\) −2.61265 2.90164i −0.987488 1.09672i −0.995309 0.0967475i \(-0.969156\pi\)
0.00782061 0.999969i \(-0.497511\pi\)
\(8\) 0.730548 + 2.24840i 0.258288 + 0.794928i
\(9\) −2.97713 0.369694i −0.992378 0.123231i
\(10\) −0.741796 −0.234576
\(11\) 3.27403 + 0.529836i 0.987157 + 0.159752i
\(12\) 0.397211 + 2.67033i 0.114665 + 0.770858i
\(13\) 2.44648 + 1.08924i 0.678531 + 0.302101i 0.716914 0.697162i \(-0.245554\pi\)
−0.0383829 + 0.999263i \(0.512221\pi\)
\(14\) 1.73564 1.92762i 0.463868 0.515178i
\(15\) −1.90730 0.320519i −0.492464 0.0827576i
\(16\) 1.41310 0.629154i 0.353276 0.157289i
\(17\) −4.48727 3.26019i −1.08832 0.790713i −0.109207 0.994019i \(-0.534831\pi\)
−0.979115 + 0.203306i \(0.934831\pi\)
\(18\) 0.0375162 1.99261i 0.00884266 0.469662i
\(19\) −1.58598 4.88115i −0.363849 1.11981i −0.950699 0.310116i \(-0.899632\pi\)
0.586850 0.809696i \(-0.300368\pi\)
\(20\) 0.181927 + 1.73092i 0.0406802 + 0.387046i
\(21\) 5.29556 4.20635i 1.15559 0.917901i
\(22\) −0.122703 + 2.19988i −0.0261603 + 0.469017i
\(23\) −1.05719 1.83110i −0.220439 0.381812i 0.734502 0.678606i \(-0.237416\pi\)
−0.954941 + 0.296795i \(0.904082\pi\)
\(24\) −3.96502 + 1.02252i −0.809357 + 0.208722i
\(25\) 3.67114 + 0.780324i 0.734227 + 0.156065i
\(26\) −0.549758 + 1.69198i −0.107816 + 0.331825i
\(27\) 0.957438 5.10718i 0.184259 0.982878i
\(28\) −4.92362 3.57722i −0.930476 0.676030i
\(29\) 0.724696 + 0.804856i 0.134573 + 0.149458i 0.806664 0.591010i \(-0.201271\pi\)
−0.672092 + 0.740468i \(0.734604\pi\)
\(30\) 0.0793167 1.28238i 0.0144812 0.234129i
\(31\) −0.392973 0.174963i −0.0705800 0.0314243i 0.371143 0.928576i \(-0.378966\pi\)
−0.441723 + 0.897151i \(0.645633\pi\)
\(32\) 2.87790 + 4.98467i 0.508746 + 0.881173i
\(33\) −1.26603 + 5.60332i −0.220387 + 0.975412i
\(34\) 1.84235 3.19104i 0.315960 0.547259i
\(35\) 3.52724 2.56269i 0.596212 0.433173i
\(36\) −4.65880 + 0.401151i −0.776466 + 0.0668585i
\(37\) −2.69024 + 8.27970i −0.442273 + 1.36118i 0.443175 + 0.896435i \(0.353852\pi\)
−0.885447 + 0.464740i \(0.846148\pi\)
\(38\) 3.11475 1.38678i 0.505279 0.224965i
\(39\) −2.14462 + 4.11288i −0.343413 + 0.658587i
\(40\) −2.58213 + 0.548848i −0.408270 + 0.0867805i
\(41\) −1.95324 + 2.16930i −0.305045 + 0.338787i −0.876104 0.482122i \(-0.839866\pi\)
0.571059 + 0.820909i \(0.306533\pi\)
\(42\) 3.14678 + 3.20659i 0.485559 + 0.494787i
\(43\) 1.11628 1.93346i 0.170232 0.294850i −0.768269 0.640127i \(-0.778882\pi\)
0.938501 + 0.345277i \(0.112215\pi\)
\(44\) 5.16335 0.253209i 0.778404 0.0381728i
\(45\) 0.758035 3.26298i 0.113001 0.486416i
\(46\) 1.13637 0.825618i 0.167548 0.121731i
\(47\) −12.5550 2.66864i −1.83133 0.389262i −0.842549 0.538619i \(-0.818946\pi\)
−0.988783 + 0.149357i \(0.952279\pi\)
\(48\) 0.936552 + 2.51017i 0.135180 + 0.362312i
\(49\) −0.861884 + 8.20028i −0.123126 + 1.17147i
\(50\) −0.260620 + 2.47964i −0.0368573 + 0.350674i
\(51\) 6.11585 7.40876i 0.856390 1.03743i
\(52\) 4.08293 + 0.867854i 0.566201 + 0.120350i
\(53\) −4.56381 + 3.31581i −0.626888 + 0.455461i −0.855321 0.518099i \(-0.826640\pi\)
0.228433 + 0.973560i \(0.426640\pi\)
\(54\) 3.44070 + 0.277916i 0.468221 + 0.0378196i
\(55\) −0.970527 + 3.57399i −0.130866 + 0.481917i
\(56\) 4.61537 7.99405i 0.616755 1.06825i
\(57\) 8.60785 2.21984i 1.14014 0.294025i
\(58\) −0.481430 + 0.534682i −0.0632149 + 0.0702072i
\(59\) 2.32346 0.493867i 0.302489 0.0642960i −0.0541667 0.998532i \(-0.517250\pi\)
0.356656 + 0.934236i \(0.383917\pi\)
\(60\) −3.01178 + 0.129427i −0.388819 + 0.0167089i
\(61\) −3.73133 + 1.66130i −0.477748 + 0.212707i −0.631460 0.775408i \(-0.717544\pi\)
0.153712 + 0.988116i \(0.450877\pi\)
\(62\) 0.0883065 0.271779i 0.0112149 0.0345160i
\(63\) 6.70549 + 9.60445i 0.844812 + 1.21005i
\(64\) −0.590604 + 0.429099i −0.0738255 + 0.0536374i
\(65\) −1.49516 + 2.58969i −0.185452 + 0.321212i
\(66\) −3.78992 0.447345i −0.466507 0.0550644i
\(67\) 4.87584 + 8.44521i 0.595679 + 1.03175i 0.993451 + 0.114262i \(0.0364503\pi\)
−0.397772 + 0.917484i \(0.630216\pi\)
\(68\) −7.89789 3.51637i −0.957760 0.426422i
\(69\) 3.27856 1.63182i 0.394692 0.196448i
\(70\) 1.93805 + 2.15242i 0.231641 + 0.257264i
\(71\) −5.11062 3.71308i −0.606519 0.440662i 0.241668 0.970359i \(-0.422306\pi\)
−0.848187 + 0.529697i \(0.822306\pi\)
\(72\) −1.34372 6.96385i −0.158359 0.820698i
\(73\) −3.60705 + 11.1014i −0.422174 + 1.29932i 0.483501 + 0.875344i \(0.339365\pi\)
−0.905675 + 0.423973i \(0.860635\pi\)
\(74\) −5.65706 1.20244i −0.657620 0.139781i
\(75\) −1.74152 + 6.26303i −0.201093 + 0.723193i
\(76\) −3.99983 6.92792i −0.458812 0.794686i
\(77\) −7.01650 10.8843i −0.799604 1.24038i
\(78\) −2.86622 1.13131i −0.324536 0.128095i
\(79\) −0.471916 4.48998i −0.0530946 0.505162i −0.988460 0.151480i \(-0.951596\pi\)
0.935366 0.353682i \(-0.115071\pi\)
\(80\) 0.533744 + 1.64269i 0.0596744 + 0.183659i
\(81\) 8.72665 + 2.20125i 0.969628 + 0.244584i
\(82\) −1.56885 1.13983i −0.173250 0.125874i
\(83\) 0.440332 0.196049i 0.0483327 0.0215191i −0.382428 0.923985i \(-0.624912\pi\)
0.430761 + 0.902466i \(0.358245\pi\)
\(84\) 6.71056 8.12919i 0.732182 0.886968i
\(85\) 4.14421 4.60261i 0.449503 0.499224i
\(86\) 1.35492 + 0.603248i 0.146104 + 0.0650499i
\(87\) −1.46888 + 1.16676i −0.157481 + 0.125089i
\(88\) 1.20056 + 7.74839i 0.127980 + 0.825981i
\(89\) 16.0830 1.70480 0.852399 0.522891i \(-0.175147\pi\)
0.852399 + 0.522891i \(0.175147\pi\)
\(90\) 2.20843 + 0.274237i 0.232788 + 0.0289071i
\(91\) −3.23120 9.94461i −0.338722 1.04248i
\(92\) −2.20521 2.44913i −0.229909 0.255340i
\(93\) 0.344485 0.660643i 0.0357215 0.0685055i
\(94\) 0.891300 8.48015i 0.0919306 0.874661i
\(95\) 5.60566 1.19152i 0.575128 0.122247i
\(96\) −8.92495 + 4.44217i −0.910899 + 0.453378i
\(97\) −0.837864 7.97174i −0.0850722 0.809408i −0.950990 0.309222i \(-0.899932\pi\)
0.865918 0.500186i \(-0.166735\pi\)
\(98\) −5.47762 −0.553323
\(99\) −9.55135 2.78778i −0.959947 0.280182i
\(100\) 5.84996 0.584996
\(101\) −0.184108 1.75167i −0.0183194 0.174297i 0.981536 0.191275i \(-0.0612622\pi\)
−0.999856 + 0.0169777i \(0.994596\pi\)
\(102\) 5.31951 + 3.52616i 0.526710 + 0.349142i
\(103\) −2.62893 + 0.558797i −0.259036 + 0.0550599i −0.335599 0.942005i \(-0.608939\pi\)
0.0765627 + 0.997065i \(0.475605\pi\)
\(104\) −0.661778 + 6.29640i −0.0648927 + 0.617412i
\(105\) 4.05309 + 6.37171i 0.395541 + 0.621816i
\(106\) −2.50760 2.78498i −0.243560 0.270501i
\(107\) −3.17558 9.77342i −0.306995 0.944833i −0.978925 0.204219i \(-0.934535\pi\)
0.671931 0.740614i \(-0.265465\pi\)
\(108\) −0.195346 8.09677i −0.0187971 0.779112i
\(109\) 2.36284 0.226319 0.113160 0.993577i \(-0.463903\pi\)
0.113160 + 0.993577i \(0.463903\pi\)
\(110\) −2.42866 0.393030i −0.231564 0.0374739i
\(111\) −14.0259 5.53605i −1.33128 0.525459i
\(112\) −5.51752 2.45656i −0.521357 0.232123i
\(113\) 1.02540 1.13882i 0.0964613 0.107131i −0.692981 0.720956i \(-0.743703\pi\)
0.789442 + 0.613825i \(0.210370\pi\)
\(114\) 2.06434 + 5.53290i 0.193343 + 0.518203i
\(115\) 2.15685 0.960290i 0.201127 0.0895475i
\(116\) 1.36571 + 0.992247i 0.126803 + 0.0921279i
\(117\) −6.88081 4.14727i −0.636131 0.383415i
\(118\) 0.487631 + 1.50077i 0.0448901 + 0.138157i
\(119\) 2.26375 + 21.5382i 0.207518 + 1.97440i
\(120\) −0.672725 4.52253i −0.0614111 0.412849i
\(121\) 10.4385 + 3.46940i 0.948959 + 0.315400i
\(122\) −1.35669 2.34986i −0.122829 0.212746i
\(123\) −3.54131 3.60862i −0.319310 0.325378i
\(124\) −0.655833 0.139402i −0.0588956 0.0125186i
\(125\) −3.02032 + 9.29560i −0.270146 + 0.831424i
\(126\) −5.87985 + 5.09713i −0.523819 + 0.454088i
\(127\) 6.19006 + 4.49734i 0.549279 + 0.399074i 0.827519 0.561437i \(-0.189751\pi\)
−0.278241 + 0.960511i \(0.589751\pi\)
\(128\) 7.37825 + 8.19438i 0.652152 + 0.724288i
\(129\) 3.22311 + 2.13651i 0.283779 + 0.188109i
\(130\) −1.81479 0.807995i −0.159167 0.0708659i
\(131\) 2.67956 + 4.64113i 0.234114 + 0.405498i 0.959015 0.283356i \(-0.0914477\pi\)
−0.724901 + 0.688853i \(0.758114\pi\)
\(132\) −0.114357 + 8.95319i −0.00995350 + 0.779276i
\(133\) −10.0197 + 17.3547i −0.868820 + 1.50484i
\(134\) −5.24101 + 3.80782i −0.452754 + 0.328945i
\(135\) 5.55981 + 1.65935i 0.478512 + 0.142814i
\(136\) 4.05203 12.4709i 0.347459 1.06937i
\(137\) 15.2847 6.80519i 1.30586 0.581407i 0.368455 0.929646i \(-0.379887\pi\)
0.937406 + 0.348239i \(0.113220\pi\)
\(138\) 1.30578 + 2.05277i 0.111155 + 0.174743i
\(139\) −13.4399 + 2.85673i −1.13995 + 0.242305i −0.738943 0.673768i \(-0.764675\pi\)
−0.401011 + 0.916073i \(0.631341\pi\)
\(140\) 4.54720 5.05018i 0.384309 0.426818i
\(141\) 5.95586 21.4190i 0.501574 1.80381i
\(142\) 2.09828 3.63433i 0.176084 0.304986i
\(143\) 7.43273 + 4.86244i 0.621556 + 0.406618i
\(144\) −4.43959 + 1.35066i −0.369966 + 0.112555i
\(145\) −0.978384 + 0.710837i −0.0812503 + 0.0590318i
\(146\) −7.58494 1.61223i −0.627734 0.133429i
\(147\) −14.0841 2.36680i −1.16163 0.195210i
\(148\) −1.41840 + 13.4952i −0.116592 + 1.10930i
\(149\) −0.581142 + 5.52920i −0.0476090 + 0.452970i 0.944585 + 0.328267i \(0.106464\pi\)
−0.992194 + 0.124703i \(0.960202\pi\)
\(150\) −4.25880 0.715683i −0.347730 0.0584353i
\(151\) 0.160326 + 0.0340783i 0.0130471 + 0.00277325i 0.214431 0.976739i \(-0.431210\pi\)
−0.201384 + 0.979512i \(0.564544\pi\)
\(152\) 9.81611 7.13182i 0.796192 0.578467i
\(153\) 12.1539 + 11.3649i 0.982587 + 0.918801i
\(154\) 6.70385 5.39148i 0.540211 0.434458i
\(155\) 0.240165 0.415978i 0.0192905 0.0334121i
\(156\) −1.93687 + 6.96556i −0.155074 + 0.557691i
\(157\) 15.9608 17.7262i 1.27381 1.41471i 0.409058 0.912509i \(-0.365858\pi\)
0.864752 0.502200i \(-0.167476\pi\)
\(158\) 2.93367 0.623572i 0.233391 0.0496087i
\(159\) −5.24420 8.24422i −0.415892 0.653810i
\(160\) −5.87141 + 2.61412i −0.464176 + 0.206664i
\(161\) −2.55114 + 7.85161i −0.201058 + 0.618794i
\(162\) −0.848345 + 5.91839i −0.0666523 + 0.464993i
\(163\) 3.39466 2.46636i 0.265890 0.193180i −0.446850 0.894609i \(-0.647454\pi\)
0.712740 + 0.701429i \(0.247454\pi\)
\(164\) −2.27495 + 3.94033i −0.177644 + 0.307688i
\(165\) −6.07475 2.05995i −0.472919 0.160367i
\(166\) 0.160102 + 0.277306i 0.0124264 + 0.0215231i
\(167\) 14.4709 + 6.44287i 1.11979 + 0.498564i 0.881289 0.472577i \(-0.156676\pi\)
0.238504 + 0.971141i \(0.423343\pi\)
\(168\) 13.3262 + 8.83357i 1.02814 + 0.681525i
\(169\) −3.89989 4.33127i −0.299992 0.333174i
\(170\) 3.32864 + 2.41840i 0.255295 + 0.185482i
\(171\) 2.91715 + 15.1182i 0.223080 + 1.15611i
\(172\) 1.07533 3.30954i 0.0819935 0.252350i
\(173\) 2.54601 + 0.541171i 0.193569 + 0.0411445i 0.303676 0.952775i \(-0.401786\pi\)
−0.110107 + 0.993920i \(0.535119\pi\)
\(174\) −0.872854 0.889442i −0.0661709 0.0674284i
\(175\) −7.32717 12.6910i −0.553882 0.959352i
\(176\) 4.95989 1.31116i 0.373866 0.0988322i
\(177\) 0.605335 + 4.06949i 0.0454997 + 0.305881i
\(178\) 1.11681 + 10.6258i 0.0837087 + 0.796435i
\(179\) 2.34483 + 7.21663i 0.175261 + 0.539396i 0.999645 0.0266334i \(-0.00847867\pi\)
−0.824385 + 0.566030i \(0.808479\pi\)
\(180\) 0.0982890 5.22044i 0.00732603 0.389109i
\(181\) 1.94179 + 1.41080i 0.144332 + 0.104864i 0.657608 0.753360i \(-0.271568\pi\)
−0.513276 + 0.858224i \(0.671568\pi\)
\(182\) 6.34584 2.82535i 0.470385 0.209429i
\(183\) −2.47299 6.62817i −0.182809 0.489968i
\(184\) 3.34472 3.71469i 0.246576 0.273850i
\(185\) −8.88066 3.95393i −0.652919 0.290698i
\(186\) 0.460396 + 0.181720i 0.0337579 + 0.0133243i
\(187\) −12.9641 13.0515i −0.948028 0.954419i
\(188\) −20.0064 −1.45911
\(189\) −17.3207 + 10.5651i −1.25989 + 0.768500i
\(190\) 1.17647 + 3.62081i 0.0853504 + 0.262681i
\(191\) −11.0529 12.2754i −0.799757 0.888220i 0.195966 0.980611i \(-0.437216\pi\)
−0.995723 + 0.0923909i \(0.970549\pi\)
\(192\) −0.678653 1.06689i −0.0489776 0.0769959i
\(193\) 0.850335 8.09040i 0.0612085 0.582360i −0.920336 0.391128i \(-0.872085\pi\)
0.981545 0.191232i \(-0.0612482\pi\)
\(194\) 5.20860 1.10712i 0.373956 0.0794867i
\(195\) −4.31706 2.86166i −0.309151 0.204928i
\(196\) 1.34340 + 12.7816i 0.0959571 + 0.912971i
\(197\) −22.9072 −1.63207 −0.816035 0.578003i \(-0.803832\pi\)
−0.816035 + 0.578003i \(0.803832\pi\)
\(198\) 1.17858 6.50398i 0.0837584 0.462218i
\(199\) 9.27177 0.657259 0.328629 0.944459i \(-0.393413\pi\)
0.328629 + 0.944459i \(0.393413\pi\)
\(200\) 0.927464 + 8.82423i 0.0655816 + 0.623967i
\(201\) −15.1210 + 7.52609i −1.06655 + 0.530850i
\(202\) 1.14451 0.243273i 0.0805273 0.0171166i
\(203\) 0.442028 4.20561i 0.0310243 0.295176i
\(204\) 6.92339 13.2775i 0.484734 0.929609i
\(205\) −2.18104 2.42229i −0.152330 0.169180i
\(206\) −0.551741 1.69808i −0.0384416 0.118311i
\(207\) 2.47045 + 5.84228i 0.171708 + 0.406067i
\(208\) 4.14243 0.287226
\(209\) −2.60634 16.8213i −0.180284 1.16356i
\(210\) −3.92822 + 3.12025i −0.271073 + 0.215318i
\(211\) 3.84655 + 1.71260i 0.264808 + 0.117900i 0.534846 0.844950i \(-0.320370\pi\)
−0.270038 + 0.962850i \(0.587036\pi\)
\(212\) −5.88353 + 6.53432i −0.404082 + 0.448779i
\(213\) 6.96543 8.43795i 0.477264 0.578159i
\(214\) 6.23661 2.77672i 0.426326 0.189812i
\(215\) 2.01683 + 1.46531i 0.137547 + 0.0999334i
\(216\) 12.1824 1.57834i 0.828909 0.107393i
\(217\) 0.519021 + 1.59738i 0.0352335 + 0.108437i
\(218\) 0.164077 + 1.56109i 0.0111127 + 0.105730i
\(219\) −18.8058 7.42270i −1.27078 0.501580i
\(220\) −0.321469 + 5.76348i −0.0216735 + 0.388574i
\(221\) −7.42687 12.8637i −0.499585 0.865307i
\(222\) 2.68361 9.65105i 0.180112 0.647736i
\(223\) 6.70917 + 1.42608i 0.449280 + 0.0954973i 0.426994 0.904254i \(-0.359572\pi\)
0.0222853 + 0.999752i \(0.492906\pi\)
\(224\) 6.94477 21.3738i 0.464017 1.42810i
\(225\) −10.6410 3.68033i −0.709399 0.245355i
\(226\) 0.823601 + 0.598381i 0.0547851 + 0.0398037i
\(227\) 18.8226 + 20.9046i 1.24930 + 1.38749i 0.891078 + 0.453850i \(0.149950\pi\)
0.358221 + 0.933637i \(0.383383\pi\)
\(228\) 12.4043 6.17393i 0.821495 0.408879i
\(229\) −12.8213 5.70843i −0.847258 0.377223i −0.0632674 0.997997i \(-0.520152\pi\)
−0.783990 + 0.620773i \(0.786819\pi\)
\(230\) 0.784218 + 1.35831i 0.0517098 + 0.0895640i
\(231\) 19.5665 10.9659i 1.28738 0.721506i
\(232\) −1.28021 + 2.21739i −0.0840499 + 0.145579i
\(233\) 11.7385 8.52854i 0.769017 0.558723i −0.132646 0.991163i \(-0.542347\pi\)
0.901663 + 0.432440i \(0.142347\pi\)
\(234\) 2.26222 4.83401i 0.147886 0.316009i
\(235\) 4.42895 13.6309i 0.288913 0.889182i
\(236\) 3.38235 1.50592i 0.220172 0.0980269i
\(237\) 7.81249 0.335731i 0.507476 0.0218081i
\(238\) −14.0727 + 2.99124i −0.912196 + 0.193893i
\(239\) −16.8274 + 18.6887i −1.08847 + 1.20887i −0.111892 + 0.993720i \(0.535691\pi\)
−0.976581 + 0.215151i \(0.930976\pi\)
\(240\) −2.89687 + 0.747063i −0.186992 + 0.0482227i
\(241\) −8.87110 + 15.3652i −0.571438 + 0.989759i 0.424981 + 0.905202i \(0.360281\pi\)
−0.996419 + 0.0845570i \(0.973053\pi\)
\(242\) −1.56731 + 7.13747i −0.100750 + 0.458814i
\(243\) −4.73851 + 14.8508i −0.303976 + 0.952680i
\(244\) −5.15048 + 3.74205i −0.329726 + 0.239560i
\(245\) −9.00586 1.91426i −0.575364 0.122297i
\(246\) 2.13824 2.59026i 0.136329 0.165149i
\(247\) 1.43668 13.6691i 0.0914140 0.869746i
\(248\) 0.106300 1.01138i 0.00675006 0.0642225i
\(249\) 0.291836 + 0.782186i 0.0184943 + 0.0495690i
\(250\) −6.35116 1.34998i −0.401683 0.0853803i
\(251\) 17.6993 12.8593i 1.11717 0.811670i 0.133390 0.991064i \(-0.457414\pi\)
0.983777 + 0.179394i \(0.0574136\pi\)
\(252\) 13.3358 + 12.4701i 0.840076 + 0.785541i
\(253\) −2.49108 6.55523i −0.156613 0.412124i
\(254\) −2.54147 + 4.40195i −0.159466 + 0.276203i
\(255\) 7.51363 + 7.65643i 0.470522 + 0.479464i
\(256\) −5.87849 + 6.52873i −0.367406 + 0.408045i
\(257\) −5.05088 + 1.07360i −0.315065 + 0.0669691i −0.362730 0.931894i \(-0.618155\pi\)
0.0476651 + 0.998863i \(0.484822\pi\)
\(258\) −1.18774 + 2.27781i −0.0739453 + 0.141810i
\(259\) 31.0534 13.8259i 1.92956 0.859097i
\(260\) −1.44031 + 4.43283i −0.0893244 + 0.274912i
\(261\) −1.85997 2.66408i −0.115129 0.164902i
\(262\) −2.88024 + 2.09262i −0.177942 + 0.129282i
\(263\) 13.9491 24.1605i 0.860135 1.48980i −0.0116625 0.999932i \(-0.503712\pi\)
0.871798 0.489866i \(-0.162954\pi\)
\(264\) −13.5234 + 1.24696i −0.832306 + 0.0767450i
\(265\) −3.14954 5.45516i −0.193475 0.335108i
\(266\) −12.1617 5.41473i −0.745680 0.331998i
\(267\) −1.71968 + 27.8035i −0.105243 + 1.70155i
\(268\) 10.1706 + 11.2956i 0.621269 + 0.689989i
\(269\) −2.44290 1.77487i −0.148946 0.108216i 0.510816 0.859690i \(-0.329343\pi\)
−0.659763 + 0.751474i \(0.729343\pi\)
\(270\) −0.710223 + 3.78849i −0.0432228 + 0.230560i
\(271\) −7.84125 + 24.1329i −0.476322 + 1.46597i 0.367845 + 0.929887i \(0.380096\pi\)
−0.844167 + 0.536081i \(0.819904\pi\)
\(272\) −8.39214 1.78380i −0.508848 0.108159i
\(273\) 17.5372 4.52260i 1.06140 0.273720i
\(274\) 5.55744 + 9.62577i 0.335737 + 0.581514i
\(275\) 11.6060 + 4.49991i 0.699866 + 0.271355i
\(276\) 4.46973 3.55038i 0.269046 0.213708i
\(277\) 1.10428 + 10.5065i 0.0663497 + 0.631275i 0.976280 + 0.216513i \(0.0694684\pi\)
−0.909930 + 0.414762i \(0.863865\pi\)
\(278\) −2.82066 8.68109i −0.169172 0.520657i
\(279\) 1.10525 + 0.666167i 0.0661696 + 0.0398824i
\(280\) 8.33875 + 6.05845i 0.498335 + 0.362062i
\(281\) −20.6192 + 9.18026i −1.23004 + 0.547648i −0.915776 0.401688i \(-0.868424\pi\)
−0.314261 + 0.949336i \(0.601757\pi\)
\(282\) 14.5647 + 2.44758i 0.867318 + 0.145751i
\(283\) −3.93264 + 4.36763i −0.233771 + 0.259629i −0.848604 0.529028i \(-0.822557\pi\)
0.614833 + 0.788657i \(0.289223\pi\)
\(284\) −8.99503 4.00484i −0.533757 0.237644i
\(285\) 1.46045 + 9.81817i 0.0865095 + 0.581578i
\(286\) −2.69639 + 5.24831i −0.159441 + 0.310339i
\(287\) 11.3977 0.672782
\(288\) −6.72509 15.9040i −0.396280 0.937150i
\(289\) 4.25344 + 13.0907i 0.250202 + 0.770044i
\(290\) −0.537576 0.597039i −0.0315676 0.0350593i
\(291\) 13.8707 0.596074i 0.813116 0.0349425i
\(292\) −1.90178 + 18.0943i −0.111294 + 1.05889i
\(293\) −6.93909 + 1.47495i −0.405386 + 0.0861674i −0.406092 0.913832i \(-0.633109\pi\)
0.000705925 1.00000i \(0.499775\pi\)
\(294\) 0.585696 9.46942i 0.0341585 0.552268i
\(295\) 0.277251 + 2.63786i 0.0161422 + 0.153582i
\(296\) −20.5814 −1.19627
\(297\) 5.84065 16.2138i 0.338909 0.940819i
\(298\) −3.69339 −0.213953
\(299\) −0.591873 5.63129i −0.0342289 0.325666i
\(300\) −0.625508 + 10.1131i −0.0361137 + 0.583880i
\(301\) −8.52666 + 1.81240i −0.491469 + 0.104465i
\(302\) −0.0113818 + 0.108291i −0.000654949 + 0.00623143i
\(303\) 3.04787 0.130978i 0.175096 0.00752449i
\(304\) −5.31215 5.89974i −0.304673 0.338373i
\(305\) −1.40936 4.33757i −0.0806999 0.248369i
\(306\) −6.66463 + 8.81906i −0.380992 + 0.504152i
\(307\) −18.5370 −1.05796 −0.528981 0.848633i \(-0.677426\pi\)
−0.528981 + 0.848633i \(0.677426\pi\)
\(308\) −14.2247 14.3206i −0.810529 0.815993i
\(309\) −0.684919 4.60451i −0.0389637 0.261941i
\(310\) 0.291506 + 0.129787i 0.0165564 + 0.00737139i
\(311\) 4.60110 5.11004i 0.260905 0.289764i −0.598433 0.801173i \(-0.704210\pi\)
0.859337 + 0.511409i \(0.170876\pi\)
\(312\) −10.8141 1.81729i −0.612229 0.102884i
\(313\) −23.1363 + 10.3009i −1.30774 + 0.582243i −0.937917 0.346860i \(-0.887248\pi\)
−0.369822 + 0.929103i \(0.620581\pi\)
\(314\) 12.8197 + 9.31407i 0.723459 + 0.525624i
\(315\) −11.4485 + 6.32546i −0.645048 + 0.356400i
\(316\) −2.17455 6.69256i −0.122328 0.376486i
\(317\) −1.14765 10.9191i −0.0644582 0.613279i −0.978298 0.207204i \(-0.933564\pi\)
0.913840 0.406075i \(-0.133103\pi\)
\(318\) 5.08265 4.03723i 0.285021 0.226397i
\(319\) 1.94623 + 3.01909i 0.108968 + 0.169037i
\(320\) −0.407582 0.705953i −0.0227845 0.0394640i
\(321\) 17.2353 4.44475i 0.961982 0.248082i
\(322\) −5.36457 1.14027i −0.298956 0.0635450i
\(323\) −8.79675 + 27.0736i −0.489464 + 1.50642i
\(324\) 14.0182 + 0.528047i 0.778787 + 0.0293359i
\(325\) 8.13140 + 5.90780i 0.451049 + 0.327706i
\(326\) 1.86520 + 2.07152i 0.103304 + 0.114731i
\(327\) −0.252648 + 4.08476i −0.0139714 + 0.225888i
\(328\) −6.30437 2.80689i −0.348101 0.154984i
\(329\) 25.0583 + 43.4023i 1.38151 + 2.39284i
\(330\) 0.939135 4.15652i 0.0516977 0.228809i
\(331\) 1.85513 3.21317i 0.101967 0.176612i −0.810528 0.585700i \(-0.800820\pi\)
0.912495 + 0.409088i \(0.134153\pi\)
\(332\) 0.607805 0.441596i 0.0333576 0.0242357i
\(333\) 11.0702 23.6552i 0.606641 1.29630i
\(334\) −3.25182 + 10.0081i −0.177931 + 0.547617i
\(335\) −9.94756 + 4.42894i −0.543493 + 0.241979i
\(336\) 4.83673 9.27573i 0.263865 0.506033i
\(337\) 31.4916 6.69375i 1.71546 0.364632i 0.757788 0.652501i \(-0.226280\pi\)
0.957670 + 0.287869i \(0.0929469\pi\)
\(338\) 2.59078 2.87735i 0.140920 0.156507i
\(339\) 1.85909 + 1.89442i 0.100972 + 0.102891i
\(340\) 4.82678 8.36023i 0.261769 0.453397i
\(341\) −1.19390 0.781045i −0.0646535 0.0422960i
\(342\) −9.78571 + 2.97712i −0.529151 + 0.160984i
\(343\) 3.93417 2.85834i 0.212425 0.154336i
\(344\) 5.16268 + 1.09736i 0.278353 + 0.0591658i
\(345\) 1.42948 + 3.83132i 0.0769605 + 0.206272i
\(346\) −0.180746 + 1.71968i −0.00971694 + 0.0924505i
\(347\) 2.24971 21.4046i 0.120771 1.14906i −0.751397 0.659851i \(-0.770619\pi\)
0.872167 0.489207i \(-0.162714\pi\)
\(348\) −1.86137 + 2.25487i −0.0997801 + 0.120874i
\(349\) 16.4524 + 3.49707i 0.880677 + 0.187194i 0.625991 0.779830i \(-0.284695\pi\)
0.254686 + 0.967024i \(0.418028\pi\)
\(350\) 7.87593 5.72219i 0.420986 0.305864i
\(351\) 7.90531 11.4517i 0.421954 0.611248i
\(352\) 6.78127 + 17.8448i 0.361443 + 0.951129i
\(353\) −1.56543 + 2.71140i −0.0833193 + 0.144313i −0.904674 0.426105i \(-0.859885\pi\)
0.821355 + 0.570418i \(0.193219\pi\)
\(354\) −2.64660 + 0.682520i −0.140665 + 0.0362755i
\(355\) 4.71991 5.24199i 0.250507 0.278216i
\(356\) 24.5205 5.21199i 1.29958 0.276235i
\(357\) −37.4761 + 1.61048i −1.98345 + 0.0852357i
\(358\) −4.60507 + 2.05031i −0.243385 + 0.108362i
\(359\) 2.62315 8.07323i 0.138445 0.426089i −0.857665 0.514208i \(-0.828086\pi\)
0.996110 + 0.0881197i \(0.0280858\pi\)
\(360\) 7.89024 0.679398i 0.415852 0.0358074i
\(361\) −5.93893 + 4.31489i −0.312575 + 0.227099i
\(362\) −0.797247 + 1.38087i −0.0419024 + 0.0725770i
\(363\) −7.11386 + 17.6746i −0.373381 + 0.927678i
\(364\) −8.14907 14.1146i −0.427127 0.739806i
\(365\) −11.9071 5.30140i −0.623248 0.277488i
\(366\) 4.20738 2.09412i 0.219923 0.109461i
\(367\) −7.36777 8.18274i −0.384595 0.427136i 0.519498 0.854471i \(-0.326119\pi\)
−0.904093 + 0.427336i \(0.859452\pi\)
\(368\) −2.64596 1.92241i −0.137930 0.100212i
\(369\) 6.61704 5.73618i 0.344469 0.298614i
\(370\) 1.99561 6.14185i 0.103747 0.319300i
\(371\) 21.5449 + 4.57951i 1.11856 + 0.237756i
\(372\) 0.311115 1.11886i 0.0161306 0.0580104i
\(373\) −5.50342 9.53220i −0.284956 0.493558i 0.687642 0.726050i \(-0.258646\pi\)
−0.972599 + 0.232491i \(0.925312\pi\)
\(374\) 7.72264 9.47143i 0.399328 0.489756i
\(375\) −15.7468 6.21531i −0.813161 0.320957i
\(376\) −3.17185 30.1781i −0.163576 1.55632i
\(377\) 0.896269 + 2.75843i 0.0461602 + 0.142067i
\(378\) −8.18294 10.7098i −0.420885 0.550852i
\(379\) −20.5384 14.9220i −1.05499 0.766492i −0.0818315 0.996646i \(-0.526077\pi\)
−0.973154 + 0.230154i \(0.926077\pi\)
\(380\) 8.16035 3.63322i 0.418617 0.186380i
\(381\) −8.43664 + 10.2202i −0.432222 + 0.523595i
\(382\) 7.34264 8.15483i 0.375682 0.417237i
\(383\) −11.0674 4.92751i −0.565516 0.251784i 0.104006 0.994577i \(-0.466834\pi\)
−0.669521 + 0.742793i \(0.733501\pi\)
\(384\) −14.9549 + 11.8789i −0.763166 + 0.606195i
\(385\) 12.9061 6.52146i 0.657755 0.332364i
\(386\) 5.40422 0.275068
\(387\) −4.03811 + 5.34349i −0.205269 + 0.271625i
\(388\) −3.86080 11.8823i −0.196003 0.603234i
\(389\) 9.60275 + 10.6649i 0.486879 + 0.540734i 0.935658 0.352909i \(-0.114808\pi\)
−0.448779 + 0.893643i \(0.648141\pi\)
\(390\) 1.59087 3.05091i 0.0805567 0.154489i
\(391\) −1.22586 + 11.6633i −0.0619945 + 0.589838i
\(392\) −19.0671 + 4.05284i −0.963035 + 0.204699i
\(393\) −8.30986 + 4.13603i −0.419177 + 0.208635i
\(394\) −1.59068 15.1344i −0.0801375 0.762458i
\(395\) 5.04123 0.253652
\(396\) −15.4656 1.15502i −0.777175 0.0580418i
\(397\) −5.03882 −0.252891 −0.126446 0.991974i \(-0.540357\pi\)
−0.126446 + 0.991974i \(0.540357\pi\)
\(398\) 0.643836 + 6.12569i 0.0322726 + 0.307053i
\(399\) −28.9305 19.1772i −1.44833 0.960062i
\(400\) 5.67864 1.20703i 0.283932 0.0603516i
\(401\) 1.90244 18.1005i 0.0950032 0.903895i −0.838398 0.545059i \(-0.816507\pi\)
0.933401 0.358836i \(-0.116826\pi\)
\(402\) −6.02236 9.46753i −0.300368 0.472198i
\(403\) −0.770823 0.856086i −0.0383974 0.0426447i
\(404\) −0.848352 2.61096i −0.0422071 0.129900i
\(405\) −3.46307 + 9.43408i −0.172081 + 0.468783i
\(406\) 2.80926 0.139421
\(407\) −13.1948 + 25.6826i −0.654042 + 1.27304i
\(408\) 21.1257 + 8.33840i 1.04588 + 0.412812i
\(409\) 15.0100 + 6.68287i 0.742195 + 0.330447i 0.742764 0.669553i \(-0.233514\pi\)
−0.000568948 1.00000i \(0.500181\pi\)
\(410\) 1.44891 1.60917i 0.0715564 0.0794715i
\(411\) 10.1301 + 27.1510i 0.499683 + 1.33926i
\(412\) −3.82703 + 1.70390i −0.188544 + 0.0839453i
\(413\) −7.50342 5.45155i −0.369219 0.268253i
\(414\) −3.68834 + 2.03787i −0.181272 + 0.100156i
\(415\) 0.166318 + 0.511874i 0.00816423 + 0.0251269i
\(416\) 1.61121 + 15.3296i 0.0789960 + 0.751596i
\(417\) −3.50150 23.5396i −0.171469 1.15274i
\(418\) 10.9326 2.89004i 0.534729 0.141357i
\(419\) 8.70324 + 15.0745i 0.425181 + 0.736435i 0.996437 0.0843365i \(-0.0268771\pi\)
−0.571256 + 0.820772i \(0.693544\pi\)
\(420\) 8.24427 + 8.40095i 0.402279 + 0.409925i
\(421\) −4.44925 0.945717i −0.216843 0.0460914i 0.0982090 0.995166i \(-0.468689\pi\)
−0.315052 + 0.949074i \(0.602022\pi\)
\(422\) −0.864374 + 2.66027i −0.0420771 + 0.129500i
\(423\) 36.3913 + 12.5864i 1.76940 + 0.611972i
\(424\) −10.7893 7.83890i −0.523976 0.380691i
\(425\) −13.9294 15.4701i −0.675674 0.750412i
\(426\) 6.05848 + 4.01600i 0.293534 + 0.194576i
\(427\) 14.5692 + 6.48660i 0.705051 + 0.313909i
\(428\) −8.00879 13.8716i −0.387120 0.670511i
\(429\) −9.20068 + 12.3294i −0.444213 + 0.595268i
\(430\) −0.828055 + 1.43423i −0.0399323 + 0.0691648i
\(431\) −10.1004 + 7.33838i −0.486520 + 0.353477i −0.803844 0.594840i \(-0.797216\pi\)
0.317325 + 0.948317i \(0.397216\pi\)
\(432\) −1.86025 7.81935i −0.0895012 0.376209i
\(433\) 8.86451 27.2822i 0.426001 1.31110i −0.476031 0.879428i \(-0.657925\pi\)
0.902032 0.431668i \(-0.142075\pi\)
\(434\) −1.01932 + 0.453830i −0.0489289 + 0.0217846i
\(435\) −1.12424 1.76738i −0.0539034 0.0847396i
\(436\) 3.60243 0.765720i 0.172525 0.0366713i
\(437\) −7.26121 + 8.06439i −0.347351 + 0.385772i
\(438\) 3.59816 12.9401i 0.171927 0.618300i
\(439\) 2.05404 3.55769i 0.0980338 0.169799i −0.812837 0.582491i \(-0.802078\pi\)
0.910871 + 0.412692i \(0.135411\pi\)
\(440\) −8.74476 + 0.428841i −0.416890 + 0.0204442i
\(441\) 5.59753 24.0947i 0.266549 1.14737i
\(442\) 7.98309 5.80005i 0.379717 0.275880i
\(443\) 20.7658 + 4.41390i 0.986612 + 0.209711i 0.672840 0.739788i \(-0.265074\pi\)
0.313772 + 0.949498i \(0.398407\pi\)
\(444\) −23.1781 3.89504i −1.09999 0.184850i
\(445\) −1.87720 + 17.8603i −0.0889876 + 0.846660i
\(446\) −0.476296 + 4.53165i −0.0225533 + 0.214580i
\(447\) −9.49645 1.59586i −0.449167 0.0754816i
\(448\) 2.78813 + 0.592635i 0.131727 + 0.0279994i
\(449\) −20.9494 + 15.2206i −0.988663 + 0.718306i −0.959628 0.281273i \(-0.909243\pi\)
−0.0290350 + 0.999578i \(0.509243\pi\)
\(450\) 1.69261 7.28586i 0.0797903 0.343459i
\(451\) −7.54435 + 6.06744i −0.355249 + 0.285705i
\(452\) 1.19428 2.06856i 0.0561744 0.0972970i
\(453\) −0.0760556 + 0.273519i −0.00357340 + 0.0128510i
\(454\) −12.5042 + 13.8874i −0.586853 + 0.651766i
\(455\) 11.4207 2.42754i 0.535410 0.113805i
\(456\) 11.2795 + 17.7321i 0.528212 + 0.830384i
\(457\) −9.41304 + 4.19096i −0.440323 + 0.196045i −0.614910 0.788597i \(-0.710808\pi\)
0.174587 + 0.984642i \(0.444141\pi\)
\(458\) 2.88113 8.86721i 0.134626 0.414338i
\(459\) −20.9467 + 19.7959i −0.977707 + 0.923992i
\(460\) 2.97717 2.16304i 0.138811 0.100852i
\(461\) 12.7266 22.0432i 0.592738 1.02665i −0.401124 0.916024i \(-0.631380\pi\)
0.993862 0.110628i \(-0.0352863\pi\)
\(462\) 8.60370 + 12.1657i 0.400280 + 0.566002i
\(463\) 19.9277 + 34.5158i 0.926119 + 1.60409i 0.789751 + 0.613427i \(0.210210\pi\)
0.136368 + 0.990658i \(0.456457\pi\)
\(464\) 1.53045 + 0.681400i 0.0710493 + 0.0316332i
\(465\) 0.693440 + 0.459663i 0.0321575 + 0.0213163i
\(466\) 6.44977 + 7.16320i 0.298780 + 0.331829i
\(467\) 14.0582 + 10.2139i 0.650537 + 0.472643i 0.863454 0.504427i \(-0.168296\pi\)
−0.212917 + 0.977070i \(0.568296\pi\)
\(468\) −11.8346 4.09315i −0.547054 0.189206i
\(469\) 11.7661 36.2123i 0.543308 1.67213i
\(470\) 9.31323 + 1.97959i 0.429587 + 0.0913116i
\(471\) 28.9376 + 29.4875i 1.33337 + 1.35871i
\(472\) 2.80781 + 4.86327i 0.129240 + 0.223850i
\(473\) 4.67916 5.73876i 0.215148 0.263868i
\(474\) 0.764314 + 5.13826i 0.0351061 + 0.236008i
\(475\) −2.01348 19.1569i −0.0923846 0.878980i
\(476\) 10.4312 + 32.1039i 0.478112 + 1.47148i
\(477\) 14.8129 8.18438i 0.678237 0.374737i
\(478\) −13.5158 9.81979i −0.618197 0.449147i
\(479\) −20.0030 + 8.90589i −0.913959 + 0.406921i −0.809170 0.587574i \(-0.800083\pi\)
−0.104788 + 0.994495i \(0.533416\pi\)
\(480\) −3.89135 10.4297i −0.177615 0.476049i
\(481\) −15.6002 + 17.3258i −0.711309 + 0.789988i
\(482\) −10.7675 4.79400i −0.490447 0.218361i
\(483\) −13.3007 5.24982i −0.605202 0.238875i
\(484\) 17.0391 + 1.90671i 0.774505 + 0.0866687i
\(485\) 8.95046 0.406420
\(486\) −10.1407 2.09940i −0.459991 0.0952307i
\(487\) 1.01084 + 3.11106i 0.0458057 + 0.140975i 0.971344 0.237679i \(-0.0763867\pi\)
−0.925538 + 0.378655i \(0.876387\pi\)
\(488\) −6.46117 7.17586i −0.292483 0.324836i
\(489\) 3.90074 + 6.13222i 0.176398 + 0.277308i
\(490\) 0.639342 6.08293i 0.0288825 0.274799i
\(491\) 7.06604 1.50193i 0.318886 0.0677813i −0.0456879 0.998956i \(-0.514548\pi\)
0.364574 + 0.931174i \(0.381215\pi\)
\(492\) −6.56858 4.35413i −0.296135 0.196300i
\(493\) −0.627919 5.97425i −0.0282801 0.269067i
\(494\) 9.13071 0.410810
\(495\) 4.21067 10.2814i 0.189256 0.462117i
\(496\) −0.665390 −0.0298769
\(497\) 2.57822 + 24.5302i 0.115649 + 1.10033i
\(498\) −0.496510 + 0.247126i −0.0222492 + 0.0110740i
\(499\) −14.5103 + 3.08427i −0.649572 + 0.138071i −0.520902 0.853617i \(-0.674404\pi\)
−0.128670 + 0.991687i \(0.541071\pi\)
\(500\) −1.59244 + 15.1510i −0.0712159 + 0.677574i
\(501\) −12.6854 + 24.3277i −0.566742 + 1.08688i
\(502\) 9.72492 + 10.8006i 0.434044 + 0.482055i
\(503\) −10.1918 31.3671i −0.454430 1.39859i −0.871803 0.489856i \(-0.837049\pi\)
0.417374 0.908735i \(-0.362951\pi\)
\(504\) −16.6959 + 22.0931i −0.743696 + 0.984105i
\(505\) 1.96673 0.0875181
\(506\) 4.15794 2.10101i 0.184843 0.0934013i
\(507\) 7.90466 6.27880i 0.351058 0.278851i
\(508\) 10.8949 + 4.85073i 0.483383 + 0.215216i
\(509\) 25.8749 28.7370i 1.14688 1.27374i 0.190481 0.981691i \(-0.438995\pi\)
0.956402 0.292052i \(-0.0943380\pi\)
\(510\) −4.53671 + 5.49578i −0.200889 + 0.243357i
\(511\) 41.6361 18.5376i 1.84187 0.820055i
\(512\) 13.1198 + 9.53213i 0.579821 + 0.421264i
\(513\) −26.4474 + 3.42650i −1.16768 + 0.151284i
\(514\) −1.06004 3.26247i −0.0467564 0.143901i
\(515\) −0.313701 2.98467i −0.0138233 0.131520i
\(516\) 5.60638 + 2.21285i 0.246807 + 0.0974155i
\(517\) −39.6915 15.3893i −1.74563 0.676821i
\(518\) 11.2908 + 19.5563i 0.496091 + 0.859255i
\(519\) −1.20778 + 4.34354i −0.0530157 + 0.190660i
\(520\) −6.91494 1.46982i −0.303240 0.0644557i
\(521\) −5.40297 + 16.6286i −0.236708 + 0.728514i 0.760182 + 0.649710i \(0.225110\pi\)
−0.996890 + 0.0788032i \(0.974890\pi\)
\(522\) 1.63095 1.41384i 0.0713848 0.0618821i
\(523\) −11.7211 8.51591i −0.512530 0.372375i 0.301253 0.953544i \(-0.402595\pi\)
−0.813782 + 0.581170i \(0.802595\pi\)
\(524\) 5.58934 + 6.20760i 0.244172 + 0.271180i
\(525\) 22.7230 11.3098i 0.991715 0.493602i
\(526\) 16.9310 + 7.53816i 0.738226 + 0.328680i
\(527\) 1.19296 + 2.06627i 0.0519663 + 0.0900082i
\(528\) 1.73632 + 8.71460i 0.0755637 + 0.379254i
\(529\) 9.26470 16.0469i 0.402813 0.697693i
\(530\) 3.38542 2.45965i 0.147053 0.106840i
\(531\) −7.09984 + 0.611340i −0.308107 + 0.0265299i
\(532\) −9.65216 + 29.7063i −0.418474 + 1.28793i
\(533\) −7.14146 + 3.17958i −0.309331 + 0.137723i
\(534\) −18.4887 + 0.794524i −0.800083 + 0.0343824i
\(535\) 11.2241 2.38576i 0.485260 0.103145i
\(536\) −15.4261 + 17.1325i −0.666307 + 0.740009i
\(537\) −12.7265 + 3.28197i −0.549187 + 0.141628i
\(538\) 1.00299 1.73722i 0.0432418 0.0748971i
\(539\) −7.16664 + 26.3913i −0.308689 + 1.13675i
\(540\) 9.01432 + 0.728114i 0.387915 + 0.0313330i
\(541\) −26.7771 + 19.4547i −1.15124 + 0.836422i −0.988645 0.150272i \(-0.951985\pi\)
−0.162591 + 0.986694i \(0.551985\pi\)
\(542\) −16.4886 3.50477i −0.708248 0.150543i
\(543\) −2.64654 + 3.20602i −0.113574 + 0.137583i
\(544\) 3.33706 31.7500i 0.143075 1.36127i
\(545\) −0.275788 + 2.62395i −0.0118135 + 0.112398i
\(546\) 4.20579 + 11.2725i 0.179991 + 0.482417i
\(547\) −9.01278 1.91573i −0.385359 0.0819105i 0.0111586 0.999938i \(-0.496448\pi\)
−0.396517 + 0.918027i \(0.629781\pi\)
\(548\) 21.0980 15.3286i 0.901262 0.654805i
\(549\) 11.7229 3.56645i 0.500319 0.152213i
\(550\) −2.16708 + 7.98032i −0.0924046 + 0.340282i
\(551\) 2.77927 4.81383i 0.118401 0.205076i
\(552\) 6.06412 + 6.17937i 0.258106 + 0.263011i
\(553\) −11.7953 + 13.1001i −0.501589 + 0.557071i
\(554\) −6.86477 + 1.45915i −0.291656 + 0.0619935i
\(555\) 7.78491 14.9296i 0.330451 0.633728i
\(556\) −19.5649 + 8.71084i −0.829735 + 0.369422i
\(557\) 11.4496 35.2384i 0.485137 1.49310i −0.346645 0.937996i \(-0.612679\pi\)
0.831782 0.555102i \(-0.187321\pi\)
\(558\) −0.363375 + 0.776477i −0.0153829 + 0.0328709i
\(559\) 4.83697 3.51427i 0.204582 0.148638i
\(560\) 3.37202 5.84052i 0.142494 0.246807i
\(561\) 23.9489 21.0161i 1.01112 0.887300i
\(562\) −7.49703 12.9852i −0.316243 0.547749i
\(563\) −24.6603 10.9795i −1.03931 0.462730i −0.185132 0.982714i \(-0.559271\pi\)
−0.854176 + 0.519984i \(0.825938\pi\)
\(564\) 2.13919 34.5860i 0.0900760 1.45633i
\(565\) 1.14498 + 1.27163i 0.0481698 + 0.0534980i
\(566\) −3.15870 2.29493i −0.132770 0.0964630i
\(567\) −16.4124 31.0727i −0.689257 1.30493i
\(568\) 4.61492 14.2033i 0.193638 0.595956i
\(569\) 26.8753 + 5.71252i 1.12667 + 0.239481i 0.733305 0.679900i \(-0.237977\pi\)
0.393367 + 0.919382i \(0.371310\pi\)
\(570\) −6.38527 + 1.64667i −0.267449 + 0.0689714i
\(571\) 19.5052 + 33.7840i 0.816266 + 1.41381i 0.908415 + 0.418069i \(0.137293\pi\)
−0.0921492 + 0.995745i \(0.529374\pi\)
\(572\) 12.9078 + 5.00466i 0.539703 + 0.209256i
\(573\) 22.4030 17.7950i 0.935897 0.743398i
\(574\) 0.791458 + 7.53022i 0.0330348 + 0.314305i
\(575\) −2.45223 7.54719i −0.102265 0.314739i
\(576\) 1.91694 1.05914i 0.0798726 0.0441309i
\(577\) 23.5957 + 17.1433i 0.982302 + 0.713684i 0.958222 0.286026i \(-0.0923344\pi\)
0.0240800 + 0.999710i \(0.492334\pi\)
\(578\) −8.35345 + 3.71920i −0.347458 + 0.154698i
\(579\) 13.8953 + 2.33508i 0.577470 + 0.0970427i
\(580\) −1.26130 + 1.40082i −0.0523727 + 0.0581658i
\(581\) −1.71930 0.765480i −0.0713284 0.0317575i
\(582\) 1.35700 + 9.12273i 0.0562496 + 0.378149i
\(583\) −16.6989 + 8.43797i −0.691598 + 0.349465i
\(584\) −27.5954 −1.14191
\(585\) 5.40869 7.15712i 0.223622 0.295910i
\(586\) −1.45632 4.48210i −0.0601602 0.185154i
\(587\) −3.40449 3.78107i −0.140518 0.156062i 0.668778 0.743463i \(-0.266818\pi\)
−0.809296 + 0.587401i \(0.800151\pi\)
\(588\) −22.2398 + 0.955723i −0.917154 + 0.0394134i
\(589\) −0.230772 + 2.19565i −0.00950878 + 0.0904700i
\(590\) −1.72353 + 0.366349i −0.0709568 + 0.0150823i
\(591\) 2.44936 39.6007i 0.100753 1.62896i
\(592\) 1.40762 + 13.3927i 0.0578530 + 0.550435i
\(593\) 3.46422 0.142258 0.0711292 0.997467i \(-0.477340\pi\)
0.0711292 + 0.997467i \(0.477340\pi\)
\(594\) 11.1177 + 2.73292i 0.456166 + 0.112133i
\(595\) −24.1825 −0.991386
\(596\) 0.905814 + 8.61825i 0.0371036 + 0.353017i
\(597\) −0.991387 + 16.0286i −0.0405748 + 0.656005i
\(598\) 3.67939 0.782079i 0.150461 0.0319816i
\(599\) −2.60013 + 24.7386i −0.106238 + 1.01079i 0.803414 + 0.595421i \(0.203015\pi\)
−0.909653 + 0.415370i \(0.863652\pi\)
\(600\) −15.3540 + 0.659818i −0.626826 + 0.0269369i
\(601\) 7.40602 + 8.22522i 0.302098 + 0.335514i 0.875012 0.484102i \(-0.160854\pi\)
−0.572914 + 0.819616i \(0.694187\pi\)
\(602\) −1.78951 5.50755i −0.0729351 0.224471i
\(603\) −11.3939 26.9451i −0.463995 1.09729i
\(604\) 0.255479 0.0103953
\(605\) −5.07116 + 11.1871i −0.206172 + 0.454821i
\(606\) 0.298180 + 2.00458i 0.0121127 + 0.0814304i
\(607\) −25.5436 11.3728i −1.03678 0.461606i −0.183483 0.983023i \(-0.558737\pi\)
−0.853302 + 0.521417i \(0.825404\pi\)
\(608\) 19.7666 21.9530i 0.801642 0.890313i
\(609\) 7.22318 + 1.21384i 0.292698 + 0.0491873i
\(610\) 2.76789 1.23234i 0.112068 0.0498961i
\(611\) −27.8087 20.2042i −1.12502 0.817375i
\(612\) 22.2131 + 13.3885i 0.897911 + 0.541198i
\(613\) 3.39680 + 10.4543i 0.137196 + 0.422245i 0.995925 0.0901845i \(-0.0287457\pi\)
−0.858729 + 0.512429i \(0.828746\pi\)
\(614\) −1.28722 12.2471i −0.0519479 0.494251i
\(615\) 4.42073 3.51146i 0.178261 0.141596i
\(616\) 19.3464 23.7274i 0.779489 0.956004i
\(617\) −9.31311 16.1308i −0.374932 0.649401i 0.615385 0.788227i \(-0.289001\pi\)
−0.990317 + 0.138826i \(0.955667\pi\)
\(618\) 2.99455 0.772252i 0.120459 0.0310645i
\(619\) −2.62973 0.558967i −0.105698 0.0224668i 0.154759 0.987952i \(-0.450540\pi\)
−0.260457 + 0.965485i \(0.583873\pi\)
\(620\) 0.231355 0.712036i 0.00929142 0.0285961i
\(621\) −10.3640 + 3.64609i −0.415892 + 0.146312i
\(622\) 3.69561 + 2.68502i 0.148180 + 0.107659i
\(623\) −42.0193 46.6672i −1.68347 1.86968i
\(624\) −0.442930 + 7.16121i −0.0177314 + 0.286678i
\(625\) 7.17308 + 3.19366i 0.286923 + 0.127746i
\(626\) −8.41222 14.5704i −0.336220 0.582350i
\(627\) 29.3585 2.70708i 1.17247 0.108110i
\(628\) 18.5896 32.1981i 0.741805 1.28484i
\(629\) 39.0652 28.3826i 1.55763 1.13169i
\(630\) −4.97410 7.12454i −0.198173 0.283848i
\(631\) −12.1224 + 37.3089i −0.482585 + 1.48524i 0.352863 + 0.935675i \(0.385208\pi\)
−0.835448 + 0.549569i \(0.814792\pi\)
\(632\) 9.75049 4.34120i 0.387853 0.172683i
\(633\) −3.37194 + 6.46660i −0.134023 + 0.257024i
\(634\) 7.13437 1.51646i 0.283342 0.0602262i
\(635\) −5.71682 + 6.34917i −0.226865 + 0.251959i
\(636\) −10.6671 10.8698i −0.422977 0.431016i
\(637\) −11.0407 + 19.1230i −0.437447 + 0.757681i
\(638\) −1.85951 + 1.49549i −0.0736187 + 0.0592069i
\(639\) 13.8423 + 12.9437i 0.547593 + 0.512045i
\(640\) −9.96109 + 7.23716i −0.393747 + 0.286074i
\(641\) −25.1863 5.35351i −0.994799 0.211451i −0.318376 0.947965i \(-0.603137\pi\)
−0.676423 + 0.736514i \(0.736471\pi\)
\(642\) 4.13339 + 11.0784i 0.163132 + 0.437230i
\(643\) 1.39358 13.2590i 0.0549574 0.522885i −0.932064 0.362294i \(-0.881993\pi\)
0.987021 0.160590i \(-0.0513398\pi\)
\(644\) −1.34507 + 12.7975i −0.0530030 + 0.504290i
\(645\) −2.74880 + 3.32991i −0.108234 + 0.131115i
\(646\) −18.4979 3.93185i −0.727789 0.154696i
\(647\) −19.2955 + 14.0190i −0.758585 + 0.551145i −0.898476 0.439022i \(-0.855325\pi\)
0.139891 + 0.990167i \(0.455325\pi\)
\(648\) 1.42595 + 21.2291i 0.0560165 + 0.833957i
\(649\) 7.86876 0.385882i 0.308876 0.0151472i
\(650\) −3.33853 + 5.78250i −0.130948 + 0.226808i
\(651\) −2.81697 + 0.726456i −0.110406 + 0.0284720i
\(652\) 4.37628 4.86035i 0.171388 0.190346i
\(653\) −12.4469 + 2.64566i −0.487083 + 0.103533i −0.444906 0.895577i \(-0.646763\pi\)
−0.0421776 + 0.999110i \(0.513430\pi\)
\(654\) −2.71627 + 0.116728i −0.106214 + 0.00456441i
\(655\) −5.46676 + 2.43396i −0.213604 + 0.0951027i
\(656\) −1.39531 + 4.29433i −0.0544778 + 0.167666i
\(657\) 14.8428 31.7168i 0.579072 1.23739i
\(658\) −26.9350 + 19.5694i −1.05004 + 0.762896i
\(659\) 13.6263 23.6015i 0.530806 0.919383i −0.468547 0.883438i \(-0.655223\pi\)
0.999354 0.0359452i \(-0.0114442\pi\)
\(660\) −9.92923 1.17200i −0.386495 0.0456201i
\(661\) −21.8220 37.7968i −0.848777 1.47012i −0.882300 0.470687i \(-0.844006\pi\)
0.0335234 0.999438i \(-0.489327\pi\)
\(662\) 2.25170 + 1.00252i 0.0875150 + 0.0389642i
\(663\) 23.0322 11.4637i 0.894497 0.445214i
\(664\) 0.762478 + 0.846818i 0.0295899 + 0.0328629i
\(665\) −18.1030 13.1526i −0.702003 0.510035i
\(666\) 16.3973 + 5.67122i 0.635382 + 0.219755i
\(667\) 0.707636 2.17788i 0.0273998 0.0843278i
\(668\) 24.1505 + 5.13336i 0.934413 + 0.198616i
\(669\) −3.18271 + 11.4460i −0.123051 + 0.442527i
\(670\) −3.61688 6.26462i −0.139732 0.242023i
\(671\) −13.0967 + 3.46214i −0.505593 + 0.133654i
\(672\) 36.2074 + 14.2912i 1.39673 + 0.551294i
\(673\) 2.78952 + 26.5405i 0.107528 + 1.02306i 0.906648 + 0.421889i \(0.138633\pi\)
−0.799120 + 0.601172i \(0.794701\pi\)
\(674\) 6.60922 + 20.3411i 0.254578 + 0.783510i
\(675\) 7.50014 18.0021i 0.288681 0.692899i
\(676\) −7.34946 5.33970i −0.282672 0.205373i
\(677\) 24.7416 11.0157i 0.950897 0.423367i 0.128138 0.991756i \(-0.459100\pi\)
0.822759 + 0.568390i \(0.192433\pi\)
\(678\) −1.12251 + 1.35982i −0.0431098 + 0.0522234i
\(679\) −20.9421 + 23.2585i −0.803683 + 0.892581i
\(680\) 13.3760 + 5.95540i 0.512948 + 0.228379i
\(681\) −38.1514 + 30.3043i −1.46196 + 1.16126i
\(682\) 0.433117 0.843026i 0.0165849 0.0322811i
\(683\) −16.7343 −0.640322 −0.320161 0.947363i \(-0.603737\pi\)
−0.320161 + 0.947363i \(0.603737\pi\)
\(684\) 9.34684 + 22.1040i 0.357385 + 0.845169i
\(685\) 5.77319 + 17.7681i 0.220582 + 0.678883i
\(686\) 2.16165 + 2.40075i 0.0825320 + 0.0916611i
\(687\) 11.2393 21.5545i 0.428808 0.822354i
\(688\) 0.360980 3.43449i 0.0137622 0.130939i
\(689\) −14.7770 + 3.14095i −0.562958 + 0.119661i
\(690\) −2.43202 + 1.21048i −0.0925854 + 0.0460821i
\(691\) 3.92186 + 37.3140i 0.149195 + 1.41949i 0.771256 + 0.636525i \(0.219629\pi\)
−0.622062 + 0.782968i \(0.713705\pi\)
\(692\) 4.05707 0.154226
\(693\) 16.8652 + 34.9981i 0.640655 + 1.32947i
\(694\) 14.2978 0.542738
\(695\) −1.60373 15.2585i −0.0608330 0.578787i
\(696\) −3.69642 2.45025i −0.140112 0.0928767i
\(697\) 15.8370 3.36627i 0.599871 0.127507i
\(698\) −1.16798 + 11.1126i −0.0442089 + 0.420619i
\(699\) 13.4885 + 21.2049i 0.510184 + 0.802042i
\(700\) −15.2839 16.9745i −0.577676 0.641575i
\(701\) 3.15219 + 9.70143i 0.119056 + 0.366418i 0.992771 0.120020i \(-0.0382959\pi\)
−0.873715 + 0.486438i \(0.838296\pi\)
\(702\) 8.11489 + 4.42768i 0.306277 + 0.167112i
\(703\) 44.6811 1.68518
\(704\) −2.16101 + 1.09196i −0.0814460 + 0.0411548i
\(705\) 23.0908 + 9.11402i 0.869651 + 0.343254i
\(706\) −1.90007 0.845967i −0.0715102 0.0318384i
\(707\) −4.60170 + 5.11070i −0.173065 + 0.192208i
\(708\) 2.24169 + 6.00824i 0.0842479 + 0.225804i
\(709\) −13.2443 + 5.89673i −0.497399 + 0.221457i −0.640074 0.768313i \(-0.721096\pi\)
0.142675 + 0.989770i \(0.454430\pi\)
\(710\) 3.79104 + 2.75435i 0.142275 + 0.103369i
\(711\) −0.254960 + 13.5417i −0.00956173 + 0.507854i
\(712\) 11.7494 + 36.1610i 0.440329 + 1.35519i
\(713\) 0.0950714 + 0.904544i 0.00356045 + 0.0338754i
\(714\) −3.66637 24.6479i −0.137210 0.922426i
\(715\) −6.26732 + 7.68655i −0.234384 + 0.287461i
\(716\) 5.91364 + 10.2427i 0.221003 + 0.382789i
\(717\) −30.5088 31.0886i −1.13937 1.16102i
\(718\) 5.51598 + 1.17246i 0.205855 + 0.0437558i
\(719\) 5.94135 18.2856i 0.221575 0.681938i −0.777046 0.629444i \(-0.783283\pi\)
0.998621 0.0524943i \(-0.0167171\pi\)
\(720\) −0.981733 5.08784i −0.0365870 0.189613i
\(721\) 8.48991 + 6.16828i 0.316181 + 0.229719i
\(722\) −3.26317 3.62411i −0.121442 0.134876i
\(723\) −25.6140 16.9788i −0.952595 0.631449i
\(724\) 3.41768 + 1.52165i 0.127017 + 0.0565517i
\(725\) 2.03241 + 3.52023i 0.0754818 + 0.130738i
\(726\) −12.1713 3.47266i −0.451719 0.128882i
\(727\) −0.363414 + 0.629451i −0.0134783 + 0.0233450i −0.872686 0.488282i \(-0.837624\pi\)
0.859208 + 0.511627i \(0.170957\pi\)
\(728\) 19.9989 14.5300i 0.741207 0.538519i
\(729\) −25.1666 9.77962i −0.932097 0.362208i
\(730\) 2.67570 8.23495i 0.0990320 0.304789i
\(731\) −11.3125 + 5.03666i −0.418408 + 0.186287i
\(732\) −5.91833 9.30401i −0.218748 0.343886i
\(733\) 1.83490 0.390019i 0.0677734 0.0144057i −0.173900 0.984763i \(-0.555637\pi\)
0.241674 + 0.970358i \(0.422304\pi\)
\(734\) 4.89456 5.43596i 0.180662 0.200645i
\(735\) 4.27222 15.3642i 0.157583 0.566716i
\(736\) 6.08497 10.5395i 0.224295 0.388490i
\(737\) 11.4891 + 30.2333i 0.423206 + 1.11366i
\(738\) 4.24928 + 3.97343i 0.156418 + 0.146264i
\(739\) 42.5402 30.9073i 1.56487 1.13694i 0.632993 0.774157i \(-0.281826\pi\)
0.931873 0.362784i \(-0.118174\pi\)
\(740\) −14.8210 3.15029i −0.544829 0.115807i
\(741\) 23.4769 + 3.94524i 0.862444 + 0.144932i
\(742\) −1.52951 + 14.5523i −0.0561501 + 0.534233i
\(743\) 3.48423 33.1502i 0.127824 1.21616i −0.723051 0.690795i \(-0.757261\pi\)
0.850875 0.525368i \(-0.176072\pi\)
\(744\) 1.73705 + 0.291908i 0.0636833 + 0.0107019i
\(745\) −6.07238 1.29072i −0.222475 0.0472885i
\(746\) 5.91558 4.29792i 0.216585 0.157358i
\(747\) −1.38341 + 0.420875i −0.0506162 + 0.0153990i
\(748\) −23.9948 15.6973i −0.877338 0.573949i
\(749\) −20.0623 + 34.7489i −0.733060 + 1.26970i
\(750\) 3.01288 10.8352i 0.110015 0.395646i
\(751\) −15.6336 + 17.3629i −0.570479 + 0.633581i −0.957480 0.288498i \(-0.906844\pi\)
0.387002 + 0.922079i \(0.373511\pi\)
\(752\) −19.4205 + 4.12795i −0.708192 + 0.150531i
\(753\) 20.3379 + 31.9725i 0.741155 + 1.16514i
\(754\) −1.76021 + 0.783695i −0.0641030 + 0.0285405i
\(755\) −0.0565572 + 0.174065i −0.00205833 + 0.00633488i
\(756\) −22.9836 + 21.7208i −0.835904 + 0.789980i
\(757\) 27.3472 19.8689i 0.993952 0.722148i 0.0331687 0.999450i \(-0.489440\pi\)
0.960783 + 0.277302i \(0.0894401\pi\)
\(758\) 8.43250 14.6055i 0.306282 0.530496i
\(759\) 11.5987 3.60553i 0.421006 0.130873i
\(760\) 6.77421 + 11.7333i 0.245726 + 0.425611i
\(761\) 18.3731 + 8.18025i 0.666026 + 0.296534i 0.711763 0.702420i \(-0.247897\pi\)
−0.0457371 + 0.998954i \(0.514564\pi\)
\(762\) −7.33811 4.86424i −0.265832 0.176213i
\(763\) −6.17328 6.85612i −0.223488 0.248208i
\(764\) −20.8294 15.1335i −0.753583 0.547510i
\(765\) −14.0394 + 12.1705i −0.507597 + 0.440026i
\(766\) 2.48699 7.65417i 0.0898586 0.276556i
\(767\) 6.22224 + 1.32258i 0.224672 + 0.0477555i
\(768\) −10.6580 10.8605i −0.384586 0.391895i
\(769\) −0.313500 0.542997i −0.0113051 0.0195810i 0.860318 0.509759i \(-0.170265\pi\)
−0.871623 + 0.490178i \(0.836932\pi\)
\(770\) 5.20481 + 8.07395i 0.187568 + 0.290965i
\(771\) −1.31591 8.84649i −0.0473914 0.318598i
\(772\) −1.32540 12.6103i −0.0477021 0.453856i
\(773\) 8.88046 + 27.3313i 0.319408 + 0.983037i 0.973902 + 0.226970i \(0.0728818\pi\)
−0.654494 + 0.756067i \(0.727118\pi\)
\(774\) −3.81075 2.29685i −0.136975 0.0825587i
\(775\) −1.30613 0.948959i −0.0469176 0.0340876i
\(776\) 17.3115 7.70759i 0.621448 0.276686i
\(777\) 20.5810 + 55.1618i 0.738340 + 1.97892i
\(778\) −6.37930 + 7.08493i −0.228709 + 0.254007i
\(779\) 13.6865 + 6.09360i 0.490368 + 0.218326i
\(780\) −7.50923 2.96392i −0.268874 0.106125i
\(781\) −14.7650 14.8645i −0.528333 0.531895i
\(782\) −7.79085 −0.278600
\(783\) 4.80440 2.93055i 0.171695 0.104729i
\(784\) 3.94131 + 12.1301i 0.140761 + 0.433218i
\(785\) 17.8222 + 19.7935i 0.636101 + 0.706462i
\(786\) −3.30964 5.20296i −0.118051 0.185584i
\(787\) 1.47416 14.0257i 0.0525481 0.499962i −0.936318 0.351153i \(-0.885790\pi\)
0.988866 0.148808i \(-0.0475437\pi\)
\(788\) −34.9247 + 7.42347i −1.24414 + 0.264450i
\(789\) 40.2758 + 26.6977i 1.43386 + 0.950465i
\(790\) 0.350065 + 3.33065i 0.0124548 + 0.118499i
\(791\) −5.98345 −0.212747
\(792\) −0.709686 23.5118i −0.0252176 0.835456i
\(793\) −10.9382 −0.388426
\(794\) −0.349898 3.32906i −0.0124174 0.118144i
\(795\) 9.76736 4.86146i 0.346413 0.172418i
\(796\) 14.1359 3.00468i 0.501034 0.106498i
\(797\) −2.73391 + 26.0114i −0.0968400 + 0.921371i 0.832967 + 0.553323i \(0.186641\pi\)
−0.929807 + 0.368048i \(0.880026\pi\)
\(798\) 10.6611 20.4455i 0.377398 0.723763i
\(799\) 47.6373 + 52.9066i 1.68529 + 1.87170i
\(800\) 6.67551 + 20.5451i 0.236015 + 0.726379i
\(801\) −47.8814 5.94580i −1.69180 0.210084i
\(802\) 12.0908 0.426939
\(803\) −17.6915 + 34.4351i −0.624320 + 1.21519i
\(804\) −20.6148 + 16.3746i −0.727026 + 0.577489i
\(805\) −8.42150 3.74949i −0.296819 0.132152i
\(806\) 0.512074 0.568715i 0.0180370 0.0200321i
\(807\) 3.32951 4.03338i 0.117204 0.141982i
\(808\) 3.80394 1.69362i 0.133822 0.0595814i
\(809\) −12.8256 9.31836i −0.450925 0.327616i 0.339036 0.940773i \(-0.389899\pi\)
−0.789961 + 0.613157i \(0.789899\pi\)
\(810\) −6.47339 1.63288i −0.227452 0.0573736i
\(811\) −11.2255 34.5484i −0.394179 1.21316i −0.929599 0.368573i \(-0.879846\pi\)
0.535420 0.844586i \(-0.320154\pi\)
\(812\) −0.688979 6.55520i −0.0241784 0.230042i
\(813\) −40.8812 16.1360i −1.43377 0.565913i
\(814\) −17.8843 6.93415i −0.626844 0.243042i
\(815\) 2.34269 + 4.05766i 0.0820608 + 0.142134i
\(816\) 3.98108 14.3172i 0.139366 0.501201i
\(817\) −11.2079 2.38231i −0.392115 0.0833466i
\(818\) −3.37295 + 10.3809i −0.117932 + 0.362958i
\(819\) 5.94326 + 30.8010i 0.207674 + 1.07627i
\(820\) −4.11023 2.98626i −0.143535 0.104285i
\(821\) −10.9448 12.1554i −0.381976 0.424227i 0.521242 0.853409i \(-0.325469\pi\)
−0.903218 + 0.429181i \(0.858802\pi\)
\(822\) −17.2347 + 8.57817i −0.601131 + 0.299198i
\(823\) −23.9116 10.6461i −0.833506 0.371101i −0.0548060 0.998497i \(-0.517454\pi\)
−0.778700 + 0.627396i \(0.784121\pi\)
\(824\) −3.17696 5.50265i −0.110675 0.191694i
\(825\) −9.02017 + 19.5826i −0.314042 + 0.681780i
\(826\) 3.08070 5.33592i 0.107191 0.185661i
\(827\) −4.48139 + 3.25592i −0.155833 + 0.113219i −0.662969 0.748647i \(-0.730704\pi\)
0.507136 + 0.861866i \(0.330704\pi\)
\(828\) 5.65978 + 8.10665i 0.196691 + 0.281726i
\(829\) 5.71784 17.5977i 0.198589 0.611194i −0.801327 0.598227i \(-0.795872\pi\)
0.999916 0.0129672i \(-0.00412771\pi\)
\(830\) −0.326637 + 0.145428i −0.0113377 + 0.00504788i
\(831\) −18.2812 + 0.785607i −0.634167 + 0.0272524i
\(832\) −1.91229 + 0.406470i −0.0662968 + 0.0140918i
\(833\) 30.6020 33.9869i 1.06030 1.17758i
\(834\) 15.3090 3.94798i 0.530108 0.136707i
\(835\) −8.84388 + 15.3180i −0.306055 + 0.530103i
\(836\) −9.42492 24.8015i −0.325968 0.857776i
\(837\) −1.26981 + 1.83947i −0.0438912 + 0.0635813i
\(838\) −9.35505 + 6.79684i −0.323165 + 0.234793i
\(839\) 17.5727 + 3.73519i 0.606677 + 0.128953i 0.501000 0.865447i \(-0.332966\pi\)
0.105677 + 0.994400i \(0.466299\pi\)
\(840\) −11.3652 + 13.7678i −0.392135 + 0.475034i
\(841\) 2.90872 27.6746i 0.100301 0.954296i
\(842\) 0.315860 3.00520i 0.0108852 0.103566i
\(843\) −13.6656 36.6270i −0.470669 1.26150i
\(844\) 6.41952 + 1.36451i 0.220969 + 0.0469684i
\(845\) 5.26509 3.82531i 0.181125 0.131595i
\(846\) −5.78858 + 24.9170i −0.199015 + 0.856666i
\(847\) −17.2053 39.3532i −0.591182 1.35219i
\(848\) −4.36299 + 7.55692i −0.149826 + 0.259506i
\(849\) −7.13004 7.26554i −0.244702 0.249353i
\(850\) 9.25357 10.2771i 0.317395 0.352503i
\(851\) 18.0051 3.82710i 0.617207 0.131191i
\(852\) 7.88516 15.1219i 0.270141 0.518068i
\(853\) 25.4999 11.3533i 0.873099 0.388729i 0.0792581 0.996854i \(-0.474745\pi\)
0.793841 + 0.608125i \(0.208078\pi\)
\(854\) −3.27389 + 10.0760i −0.112030 + 0.344794i
\(855\) −17.1293 + 1.47494i −0.585809 + 0.0504418i
\(856\) 19.6546 14.2799i 0.671781 0.488077i
\(857\) 4.24983 7.36093i 0.145172 0.251445i −0.784265 0.620426i \(-0.786960\pi\)
0.929437 + 0.368981i \(0.120293\pi\)
\(858\) −8.78469 5.22256i −0.299904 0.178295i
\(859\) −13.9259 24.1203i −0.475145 0.822974i 0.524450 0.851441i \(-0.324271\pi\)
−0.999595 + 0.0284667i \(0.990938\pi\)
\(860\) 3.54975 + 1.58045i 0.121046 + 0.0538929i
\(861\) −1.21870 + 19.7037i −0.0415331 + 0.671499i
\(862\) −5.54971 6.16357i −0.189024 0.209932i
\(863\) −10.9978 7.99035i −0.374368 0.271995i 0.384652 0.923062i \(-0.374322\pi\)
−0.759020 + 0.651067i \(0.774322\pi\)
\(864\) 28.2130 9.92545i 0.959827 0.337671i
\(865\) −0.898141 + 2.76419i −0.0305377 + 0.0939854i
\(866\) 18.6404 + 3.96213i 0.633425 + 0.134639i
\(867\) −23.0854 + 5.95339i −0.784021 + 0.202188i
\(868\) 1.30897 + 2.26720i 0.0444293 + 0.0769538i
\(869\) 0.833885 14.9504i 0.0282876 0.507156i
\(870\) 1.08961 0.865495i 0.0369412 0.0293430i
\(871\) 2.72977 + 25.9720i 0.0924946 + 0.880028i
\(872\) 1.72617 + 5.31260i 0.0584555 + 0.179907i
\(873\) −0.452669 + 24.0427i −0.0153205 + 0.813722i
\(874\) −5.83221 4.23735i −0.197278 0.143331i
\(875\) 34.8635 15.5222i 1.17860 0.524748i
\(876\) −31.0771 5.22244i −1.05000 0.176450i
\(877\) 24.2078 26.8855i 0.817439 0.907858i −0.179679 0.983725i \(-0.557506\pi\)
0.997118 + 0.0758674i \(0.0241726\pi\)
\(878\) 2.49314 + 1.11002i 0.0841392 + 0.0374612i
\(879\) −1.80785 12.1536i −0.0609772 0.409932i
\(880\) 0.877135 + 5.66103i 0.0295682 + 0.190833i
\(881\) 26.6423 0.897601 0.448800 0.893632i \(-0.351851\pi\)
0.448800 + 0.893632i \(0.351851\pi\)
\(882\) 16.3076 + 2.02504i 0.549106 + 0.0681867i
\(883\) −6.32757 19.4743i −0.212940 0.655361i −0.999293 0.0375844i \(-0.988034\pi\)
0.786354 0.617776i \(-0.211966\pi\)
\(884\) −15.4918 17.2054i −0.521047 0.578681i
\(885\) −4.58984 + 0.197242i −0.154286 + 0.00663022i
\(886\) −1.47420 + 14.0261i −0.0495267 + 0.471215i
\(887\) 31.3019 6.65342i 1.05101 0.223400i 0.350149 0.936694i \(-0.386131\pi\)
0.700865 + 0.713294i \(0.252798\pi\)
\(888\) 2.20067 35.5800i 0.0738497 1.19399i
\(889\) −3.12278 29.7113i −0.104735 0.996484i
\(890\) −11.9303 −0.399906
\(891\) 27.4050 + 11.8307i 0.918103 + 0.396342i
\(892\) 10.6911 0.357963
\(893\) 6.88592 + 65.5151i 0.230428 + 2.19238i
\(894\) 0.394917 6.38495i 0.0132080 0.213545i
\(895\) −8.28780 + 1.76163i −0.277031 + 0.0588847i
\(896\) 4.50036 42.8181i 0.150347 1.43045i
\(897\) 9.79837 0.421071i 0.327158 0.0140591i
\(898\) −11.5107 12.7839i −0.384118 0.426606i
\(899\) −0.143966 0.443082i −0.00480153 0.0147776i
\(900\) −17.4161 2.16269i −0.580537 0.0720897i
\(901\) 31.2892 1.04239
\(902\) −4.53253 4.56308i −0.150917 0.151934i
\(903\) −2.22146 14.9342i −0.0739256 0.496980i
\(904\) 3.30962 + 1.47354i 0.110076 + 0.0490091i
\(905\) −1.79334 + 1.99171i −0.0596127 + 0.0662066i
\(906\) −0.185990 0.0312553i −0.00617911 0.00103839i
\(907\) −44.8096 + 19.9505i −1.48788 + 0.662447i −0.980003 0.198983i \(-0.936236\pi\)
−0.507877 + 0.861430i \(0.669569\pi\)
\(908\) 35.4717 + 25.7717i 1.17717 + 0.855265i
\(909\) −0.0994669 + 5.28301i −0.00329911 + 0.175226i
\(910\) 2.39689 + 7.37687i 0.0794561 + 0.244541i
\(911\) 2.44401 + 23.2532i 0.0809736 + 0.770413i 0.957378 + 0.288837i \(0.0932686\pi\)
−0.876405 + 0.481576i \(0.840065\pi\)
\(912\) 10.7672 8.55253i 0.356536 0.283203i
\(913\) 1.54553 0.408565i 0.0511497 0.0135215i
\(914\) −3.42253 5.92800i −0.113207 0.196081i
\(915\) 7.64927 1.97264i 0.252877 0.0652134i
\(916\) −21.3975 4.54819i −0.706995 0.150276i
\(917\) 6.46615 19.9008i 0.213531 0.657181i
\(918\) −14.5333 12.4644i −0.479671 0.411388i
\(919\) 6.14797 + 4.46676i 0.202803 + 0.147345i 0.684551 0.728965i \(-0.259998\pi\)
−0.481749 + 0.876309i \(0.659998\pi\)
\(920\) 3.73479 + 4.14791i 0.123132 + 0.136752i
\(921\) 1.98207 32.0458i 0.0653116 1.05594i
\(922\) 15.4472 + 6.87755i 0.508728 + 0.226500i
\(923\) −8.45857 14.6507i −0.278417 0.482233i
\(924\) 26.2777 23.0597i 0.864474 0.758609i
\(925\) −16.3371 + 28.2967i −0.537160 + 0.930389i
\(926\) −21.4202 + 15.5627i −0.703910 + 0.511421i
\(927\) 8.03327 0.691714i 0.263847 0.0227189i
\(928\) −1.92634 + 5.92866i −0.0632352 + 0.194618i
\(929\) −13.5906 + 6.05092i −0.445893 + 0.198524i −0.617385 0.786661i \(-0.711808\pi\)
0.171492 + 0.985185i \(0.445141\pi\)
\(930\) −0.255538 + 0.490062i −0.00837941 + 0.0160698i
\(931\) 41.3937 8.79850i 1.35662 0.288359i
\(932\) 15.1329 16.8068i 0.495696 0.550526i
\(933\) 8.34199 + 8.50053i 0.273105 + 0.278295i
\(934\) −5.77192 + 9.99727i −0.188863 + 0.327121i
\(935\) 16.0069 12.8733i 0.523482 0.421003i
\(936\) 4.29794 18.5006i 0.140482 0.604710i
\(937\) −14.4192 + 10.4762i −0.471056 + 0.342242i −0.797853 0.602853i \(-0.794031\pi\)
0.326797 + 0.945095i \(0.394031\pi\)
\(938\) 24.7418 + 5.25904i 0.807850 + 0.171714i
\(939\) −15.3339 41.0982i −0.500401 1.34119i
\(940\) 2.33512 22.2172i 0.0761633 0.724645i
\(941\) −4.45909 + 42.4254i −0.145362 + 1.38303i 0.642078 + 0.766639i \(0.278072\pi\)
−0.787441 + 0.616391i \(0.788594\pi\)
\(942\) −17.4724 + 21.1661i −0.569283 + 0.689630i
\(943\) 6.03716 + 1.28324i 0.196597 + 0.0417879i
\(944\) 2.97257 2.15970i 0.0967491 0.0702923i
\(945\) −9.71100 20.4678i −0.315899 0.665819i
\(946\) 4.11641 + 2.69293i 0.133836 + 0.0875548i
\(947\) −3.44670 + 5.96986i −0.112003 + 0.193994i −0.916578 0.399857i \(-0.869060\pi\)
0.804575 + 0.593851i \(0.202393\pi\)
\(948\) 11.8023 3.04364i 0.383320 0.0988527i
\(949\) −20.9167 + 23.2303i −0.678984 + 0.754088i
\(950\) 12.5168 2.66053i 0.406099 0.0863190i
\(951\) 18.9991 0.816459i 0.616088 0.0264755i
\(952\) −46.7725 + 20.8245i −1.51591 + 0.674925i
\(953\) −7.31766 + 22.5214i −0.237042 + 0.729541i 0.759802 + 0.650155i \(0.225296\pi\)
−0.996844 + 0.0793863i \(0.974704\pi\)
\(954\) 6.43588 + 9.21829i 0.208369 + 0.298453i
\(955\) 14.9220 10.8415i 0.482866 0.350822i
\(956\) −19.5989 + 33.9463i −0.633874 + 1.09790i
\(957\) −5.42735 + 3.04173i −0.175441 + 0.0983251i
\(958\) −7.27297 12.5972i −0.234979 0.406996i
\(959\) −59.6798 26.5712i −1.92716 0.858027i
\(960\) 1.26400 0.629123i 0.0407953 0.0203048i
\(961\) −20.6192 22.9000i −0.665137 0.738709i
\(962\) −12.5301 9.10366i −0.403987 0.293514i
\(963\) 5.84095 + 30.2708i 0.188222 + 0.975462i
\(964\) −8.54567 + 26.3009i −0.275238 + 0.847094i
\(965\) 8.88519 + 1.88860i 0.286024 + 0.0607963i
\(966\) 2.54485 9.15206i 0.0818793 0.294463i
\(967\) 15.5700 + 26.9680i 0.500696 + 0.867231i 1.00000 0.000804082i \(0.000255947\pi\)
−0.499303 + 0.866427i \(0.666411\pi\)
\(968\) −0.174718 + 26.0045i −0.00561565 + 0.835818i
\(969\) −45.8628 18.1022i −1.47333 0.581527i
\(970\) 0.621524 + 5.91340i 0.0199559 + 0.189868i
\(971\) 4.12687 + 12.7012i 0.132438 + 0.407601i 0.995183 0.0980383i \(-0.0312568\pi\)
−0.862745 + 0.505639i \(0.831257\pi\)
\(972\) −2.41176 + 24.1774i −0.0773571 + 0.775490i
\(973\) 43.4028 + 31.5340i 1.39143 + 1.01093i
\(974\) −1.98522 + 0.883879i −0.0636107 + 0.0283213i
\(975\) −11.0826 + 13.4254i −0.354926 + 0.429958i
\(976\) −4.22755 + 4.69517i −0.135321 + 0.150289i
\(977\) −8.14511 3.62644i −0.260585 0.116020i 0.272286 0.962216i \(-0.412220\pi\)
−0.532871 + 0.846196i \(0.678887\pi\)
\(978\) −3.78057 + 3.00297i −0.120889 + 0.0960244i
\(979\) 52.6564 + 8.52137i 1.68290 + 0.272344i
\(980\) −14.3508 −0.458421
\(981\) −7.03450 0.873527i −0.224594 0.0278896i
\(982\) 1.48297 + 4.56411i 0.0473234 + 0.145647i
\(983\) −11.2806 12.5283i −0.359794 0.399592i 0.535886 0.844290i \(-0.319978\pi\)
−0.895680 + 0.444698i \(0.853311\pi\)
\(984\) 5.52650 10.5985i 0.176178 0.337869i
\(985\) 2.67370 25.4386i 0.0851912 0.810541i
\(986\) 3.90347 0.829709i 0.124312 0.0264233i
\(987\) −77.7109 + 38.6787i −2.47357 + 1.23116i
\(988\) −2.23933 21.3058i −0.0712425 0.677827i
\(989\) −4.72049 −0.150103
\(990\) 7.08515 + 2.06796i 0.225181 + 0.0657242i
\(991\) −33.5356 −1.06529 −0.532647 0.846338i \(-0.678803\pi\)
−0.532647 + 0.846338i \(0.678803\pi\)
\(992\) −0.258805 2.46237i −0.00821707 0.0781802i
\(993\) 5.35640 + 3.55061i 0.169980 + 0.112675i
\(994\) −16.0276 + 3.40677i −0.508364 + 0.108056i
\(995\) −1.08219 + 10.2964i −0.0343078 + 0.326417i
\(996\) 0.698419 + 1.09796i 0.0221302 + 0.0347902i
\(997\) −2.17044 2.41052i −0.0687385 0.0763419i 0.707795 0.706418i \(-0.249690\pi\)
−0.776533 + 0.630076i \(0.783024\pi\)
\(998\) −3.04532 9.37254i −0.0963980 0.296682i
\(999\) 39.7102 + 21.6668i 1.25638 + 0.685509i
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 99.2.m.b.25.6 yes 72
3.2 odd 2 297.2.n.b.289.4 72
9.2 odd 6 891.2.f.e.487.4 36
9.4 even 3 inner 99.2.m.b.58.4 yes 72
9.5 odd 6 297.2.n.b.91.6 72
9.7 even 3 891.2.f.f.487.6 36
11.2 odd 10 1089.2.e.o.727.8 36
11.4 even 5 inner 99.2.m.b.70.4 yes 72
11.9 even 5 1089.2.e.p.727.11 36
33.26 odd 10 297.2.n.b.235.6 72
99.2 even 30 9801.2.a.cn.1.8 18
99.4 even 15 inner 99.2.m.b.4.6 72
99.13 odd 30 1089.2.e.o.364.8 36
99.20 odd 30 9801.2.a.cp.1.11 18
99.31 even 15 1089.2.e.p.364.11 36
99.59 odd 30 297.2.n.b.37.4 72
99.70 even 15 891.2.f.f.730.6 36
99.79 odd 30 9801.2.a.co.1.11 18
99.92 odd 30 891.2.f.e.730.4 36
99.97 even 15 9801.2.a.cm.1.8 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.6 72 99.4 even 15 inner
99.2.m.b.25.6 yes 72 1.1 even 1 trivial
99.2.m.b.58.4 yes 72 9.4 even 3 inner
99.2.m.b.70.4 yes 72 11.4 even 5 inner
297.2.n.b.37.4 72 99.59 odd 30
297.2.n.b.91.6 72 9.5 odd 6
297.2.n.b.235.6 72 33.26 odd 10
297.2.n.b.289.4 72 3.2 odd 2
891.2.f.e.487.4 36 9.2 odd 6
891.2.f.e.730.4 36 99.92 odd 30
891.2.f.f.487.6 36 9.7 even 3
891.2.f.f.730.6 36 99.70 even 15
1089.2.e.o.364.8 36 99.13 odd 30
1089.2.e.o.727.8 36 11.2 odd 10
1089.2.e.p.364.11 36 99.31 even 15
1089.2.e.p.727.11 36 11.9 even 5
9801.2.a.cm.1.8 18 99.97 even 15
9801.2.a.cn.1.8 18 99.2 even 30
9801.2.a.co.1.11 18 99.79 odd 30
9801.2.a.cp.1.11 18 99.20 odd 30