Properties

Label 297.2.n.b.235.2
Level $297$
Weight $2$
Character 297.235
Analytic conductor $2.372$
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] = [297,2,Mod(37,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, 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("297.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.n (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.37155694003\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 235.2
Character \(\chi\) \(=\) 297.235
Dual form 297.2.n.b.91.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41247 + 0.628870i) q^{2} +(0.261321 - 0.290226i) q^{4} +(-0.540848 - 0.240801i) q^{5} +(-0.706174 - 0.150102i) q^{7} +(0.768973 - 2.36665i) q^{8} +0.915362 q^{10} +(-3.10382 - 1.16888i) q^{11} +(0.164629 - 1.56634i) q^{13} +(1.09184 - 0.232078i) q^{14} +(0.483816 + 4.60320i) q^{16} +(3.71501 - 2.69911i) q^{17} +(0.775200 - 2.38582i) q^{19} +(-0.211222 + 0.0940420i) q^{20} +(5.11912 - 0.300892i) q^{22} +(-2.22600 - 3.85554i) q^{23} +(-3.11112 - 3.45525i) q^{25} +(0.752490 + 2.31593i) q^{26} +(-0.228102 + 0.165726i) q^{28} +(6.82612 + 1.45094i) q^{29} +(0.954161 - 9.07824i) q^{31} +(-1.08974 - 1.88749i) q^{32} +(-3.54993 + 6.14866i) q^{34} +(0.345788 + 0.251230i) q^{35} +(0.893583 + 2.75017i) q^{37} +(0.405428 + 3.85739i) q^{38} +(-0.985790 + 1.09483i) q^{40} +(-1.12890 + 0.239955i) q^{41} +(2.10724 - 3.64985i) q^{43} +(-1.15033 + 0.595357i) q^{44} +(5.56879 + 4.04596i) q^{46} +(0.152264 + 0.169107i) q^{47} +(-5.91867 - 2.63516i) q^{49} +(6.56726 + 2.92393i) q^{50} +(-0.411571 - 0.457096i) q^{52} +(-4.61430 - 3.35249i) q^{53} +(1.39723 + 1.37959i) q^{55} +(-0.898268 + 1.55585i) q^{56} +(-10.5541 + 2.24335i) q^{58} +(-4.77328 + 5.30126i) q^{59} +(-0.476541 - 4.53398i) q^{61} +(4.36131 + 13.4227i) q^{62} +(-4.76295 - 3.46049i) q^{64} +(-0.466215 + 0.807507i) q^{65} +(4.04571 + 7.00738i) q^{67} +(0.187456 - 1.78353i) q^{68} +(-0.646405 - 0.137398i) q^{70} +(-9.95852 + 7.23528i) q^{71} +(4.78461 + 14.7255i) q^{73} +(-2.99165 - 3.32257i) q^{74} +(-0.489852 - 0.848448i) q^{76} +(2.01639 + 1.29133i) q^{77} +(-13.3556 + 5.94631i) q^{79} +(0.846785 - 2.60614i) q^{80} +(1.44363 - 1.04886i) q^{82} +(-0.726787 - 6.91491i) q^{83} +(-2.65920 + 0.565231i) q^{85} +(-0.681124 + 6.48047i) q^{86} +(-5.15310 + 6.44683i) q^{88} -12.4803 q^{89} +(-0.351367 + 1.08140i) q^{91} +(-1.70068 - 0.361491i) q^{92} +(-0.321414 - 0.143103i) q^{94} +(-0.993774 + 1.10370i) q^{95} +(12.9545 - 5.76772i) q^{97} +10.0171 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41247 + 0.628870i −0.998764 + 0.444679i −0.839970 0.542633i \(-0.817427\pi\)
−0.158794 + 0.987312i \(0.550761\pi\)
\(3\) 0 0
\(4\) 0.261321 0.290226i 0.130660 0.145113i
\(5\) −0.540848 0.240801i −0.241875 0.107690i 0.282220 0.959350i \(-0.408929\pi\)
−0.524094 + 0.851660i \(0.675596\pi\)
\(6\) 0 0
\(7\) −0.706174 0.150102i −0.266909 0.0567332i 0.0725131 0.997367i \(-0.476898\pi\)
−0.339422 + 0.940634i \(0.610231\pi\)
\(8\) 0.768973 2.36665i 0.271873 0.836739i
\(9\) 0 0
\(10\) 0.915362 0.289463
\(11\) −3.10382 1.16888i −0.935837 0.352432i
\(12\) 0 0
\(13\) 0.164629 1.56634i 0.0456598 0.434424i −0.947682 0.319217i \(-0.896580\pi\)
0.993342 0.115207i \(-0.0367531\pi\)
\(14\) 1.09184 0.232078i 0.291807 0.0620255i
\(15\) 0 0
\(16\) 0.483816 + 4.60320i 0.120954 + 1.15080i
\(17\) 3.71501 2.69911i 0.901022 0.654631i −0.0377065 0.999289i \(-0.512005\pi\)
0.938728 + 0.344658i \(0.112005\pi\)
\(18\) 0 0
\(19\) 0.775200 2.38582i 0.177843 0.547345i −0.821909 0.569619i \(-0.807091\pi\)
0.999752 + 0.0222743i \(0.00709072\pi\)
\(20\) −0.211222 + 0.0940420i −0.0472306 + 0.0210284i
\(21\) 0 0
\(22\) 5.11912 0.300892i 1.09140 0.0641503i
\(23\) −2.22600 3.85554i −0.464153 0.803937i 0.535010 0.844846i \(-0.320308\pi\)
−0.999163 + 0.0409092i \(0.986975\pi\)
\(24\) 0 0
\(25\) −3.11112 3.45525i −0.622224 0.691050i
\(26\) 0.752490 + 2.31593i 0.147576 + 0.454191i
\(27\) 0 0
\(28\) −0.228102 + 0.165726i −0.0431072 + 0.0313192i
\(29\) 6.82612 + 1.45094i 1.26758 + 0.269432i 0.792152 0.610323i \(-0.208960\pi\)
0.475426 + 0.879755i \(0.342294\pi\)
\(30\) 0 0
\(31\) 0.954161 9.07824i 0.171372 1.63050i −0.483912 0.875117i \(-0.660784\pi\)
0.655284 0.755382i \(-0.272549\pi\)
\(32\) −1.08974 1.88749i −0.192641 0.333664i
\(33\) 0 0
\(34\) −3.54993 + 6.14866i −0.608808 + 1.05449i
\(35\) 0.345788 + 0.251230i 0.0584489 + 0.0424656i
\(36\) 0 0
\(37\) 0.893583 + 2.75017i 0.146904 + 0.452125i 0.997251 0.0740981i \(-0.0236078\pi\)
−0.850347 + 0.526223i \(0.823608\pi\)
\(38\) 0.405428 + 3.85739i 0.0657691 + 0.625751i
\(39\) 0 0
\(40\) −0.985790 + 1.09483i −0.155867 + 0.173108i
\(41\) −1.12890 + 0.239955i −0.176304 + 0.0374747i −0.295218 0.955430i \(-0.595392\pi\)
0.118913 + 0.992905i \(0.462059\pi\)
\(42\) 0 0
\(43\) 2.10724 3.64985i 0.321351 0.556596i −0.659416 0.751778i \(-0.729196\pi\)
0.980767 + 0.195182i \(0.0625297\pi\)
\(44\) −1.15033 + 0.595357i −0.173419 + 0.0897534i
\(45\) 0 0
\(46\) 5.56879 + 4.04596i 0.821073 + 0.596544i
\(47\) 0.152264 + 0.169107i 0.0222100 + 0.0246667i 0.754147 0.656705i \(-0.228050\pi\)
−0.731937 + 0.681372i \(0.761384\pi\)
\(48\) 0 0
\(49\) −5.91867 2.63516i −0.845524 0.376451i
\(50\) 6.56726 + 2.92393i 0.928751 + 0.413506i
\(51\) 0 0
\(52\) −0.411571 0.457096i −0.0570747 0.0633878i
\(53\) −4.61430 3.35249i −0.633823 0.460500i 0.223899 0.974612i \(-0.428121\pi\)
−0.857723 + 0.514113i \(0.828121\pi\)
\(54\) 0 0
\(55\) 1.39723 + 1.37959i 0.188402 + 0.186024i
\(56\) −0.898268 + 1.55585i −0.120036 + 0.207909i
\(57\) 0 0
\(58\) −10.5541 + 2.24335i −1.38582 + 0.294566i
\(59\) −4.77328 + 5.30126i −0.621428 + 0.690166i −0.968880 0.247532i \(-0.920380\pi\)
0.347452 + 0.937698i \(0.387047\pi\)
\(60\) 0 0
\(61\) −0.476541 4.53398i −0.0610148 0.580517i −0.981730 0.190281i \(-0.939060\pi\)
0.920715 0.390236i \(-0.127607\pi\)
\(62\) 4.36131 + 13.4227i 0.553887 + 1.70469i
\(63\) 0 0
\(64\) −4.76295 3.46049i −0.595369 0.432561i
\(65\) −0.466215 + 0.807507i −0.0578268 + 0.100159i
\(66\) 0 0
\(67\) 4.04571 + 7.00738i 0.494262 + 0.856087i 0.999978 0.00661279i \(-0.00210493\pi\)
−0.505716 + 0.862700i \(0.668772\pi\)
\(68\) 0.187456 1.78353i 0.0227324 0.216284i
\(69\) 0 0
\(70\) −0.646405 0.137398i −0.0772602 0.0164222i
\(71\) −9.95852 + 7.23528i −1.18186 + 0.858670i −0.992380 0.123215i \(-0.960680\pi\)
−0.189478 + 0.981885i \(0.560680\pi\)
\(72\) 0 0
\(73\) 4.78461 + 14.7255i 0.559996 + 1.72349i 0.682370 + 0.731007i \(0.260950\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(74\) −2.99165 3.32257i −0.347773 0.386241i
\(75\) 0 0
\(76\) −0.489852 0.848448i −0.0561899 0.0973237i
\(77\) 2.01639 + 1.29133i 0.229789 + 0.147160i
\(78\) 0 0
\(79\) −13.3556 + 5.94631i −1.50263 + 0.669012i −0.982701 0.185200i \(-0.940707\pi\)
−0.519925 + 0.854212i \(0.674040\pi\)
\(80\) 0.846785 2.60614i 0.0946734 0.291375i
\(81\) 0 0
\(82\) 1.44363 1.04886i 0.159422 0.115827i
\(83\) −0.726787 6.91491i −0.0797752 0.759010i −0.959153 0.282886i \(-0.908708\pi\)
0.879378 0.476124i \(-0.157959\pi\)
\(84\) 0 0
\(85\) −2.65920 + 0.565231i −0.288431 + 0.0613079i
\(86\) −0.681124 + 6.48047i −0.0734475 + 0.698807i
\(87\) 0 0
\(88\) −5.15310 + 6.44683i −0.549322 + 0.687235i
\(89\) −12.4803 −1.32291 −0.661453 0.749986i \(-0.730060\pi\)
−0.661453 + 0.749986i \(0.730060\pi\)
\(90\) 0 0
\(91\) −0.351367 + 1.08140i −0.0368332 + 0.113361i
\(92\) −1.70068 0.361491i −0.177308 0.0376880i
\(93\) 0 0
\(94\) −0.321414 0.143103i −0.0331514 0.0147599i
\(95\) −0.993774 + 1.10370i −0.101959 + 0.113237i
\(96\) 0 0
\(97\) 12.9545 5.76772i 1.31533 0.585623i 0.375360 0.926879i \(-0.377519\pi\)
0.939970 + 0.341256i \(0.110852\pi\)
\(98\) 10.0171 1.01188
\(99\) 0 0
\(100\) −1.81581 −0.181581
\(101\) 13.1263 5.84421i 1.30612 0.581521i 0.368641 0.929572i \(-0.379823\pi\)
0.937476 + 0.348051i \(0.113156\pi\)
\(102\) 0 0
\(103\) −2.96348 + 3.29128i −0.292000 + 0.324299i −0.871239 0.490859i \(-0.836683\pi\)
0.579239 + 0.815158i \(0.303350\pi\)
\(104\) −3.58038 1.59409i −0.351085 0.156313i
\(105\) 0 0
\(106\) 8.62583 + 1.83348i 0.837815 + 0.178083i
\(107\) 4.86529 14.9738i 0.470345 1.44757i −0.381788 0.924250i \(-0.624692\pi\)
0.852134 0.523324i \(-0.175308\pi\)
\(108\) 0 0
\(109\) −13.6970 −1.31194 −0.655969 0.754788i \(-0.727740\pi\)
−0.655969 + 0.754788i \(0.727740\pi\)
\(110\) −2.84112 1.06995i −0.270890 0.102016i
\(111\) 0 0
\(112\) 0.349291 3.32328i 0.0330049 0.314021i
\(113\) 7.85465 1.66956i 0.738904 0.157059i 0.176941 0.984221i \(-0.443380\pi\)
0.561963 + 0.827163i \(0.310046\pi\)
\(114\) 0 0
\(115\) 0.275508 + 2.62129i 0.0256913 + 0.244436i
\(116\) 2.20491 1.60196i 0.204721 0.148738i
\(117\) 0 0
\(118\) 3.40829 10.4896i 0.313758 0.965648i
\(119\) −3.02858 + 1.34841i −0.277630 + 0.123609i
\(120\) 0 0
\(121\) 8.26742 + 7.25602i 0.751583 + 0.659638i
\(122\) 3.52438 + 6.10441i 0.319083 + 0.552668i
\(123\) 0 0
\(124\) −2.38540 2.64926i −0.214215 0.237910i
\(125\) 1.76536 + 5.43321i 0.157898 + 0.485961i
\(126\) 0 0
\(127\) 9.70522 7.05126i 0.861199 0.625698i −0.0670118 0.997752i \(-0.521347\pi\)
0.928211 + 0.372054i \(0.121347\pi\)
\(128\) 13.1674 + 2.79882i 1.16385 + 0.247383i
\(129\) 0 0
\(130\) 0.150695 1.43377i 0.0132168 0.125750i
\(131\) −3.44555 5.96786i −0.301039 0.521414i 0.675333 0.737513i \(-0.264000\pi\)
−0.976372 + 0.216099i \(0.930667\pi\)
\(132\) 0 0
\(133\) −0.905543 + 1.56845i −0.0785205 + 0.136002i
\(134\) −10.1212 7.35345i −0.874335 0.635242i
\(135\) 0 0
\(136\) −3.53112 10.8677i −0.302791 0.931896i
\(137\) 0.966528 + 9.19590i 0.0825760 + 0.785658i 0.954939 + 0.296801i \(0.0959196\pi\)
−0.872363 + 0.488858i \(0.837414\pi\)
\(138\) 0 0
\(139\) 14.4608 16.0603i 1.22655 1.36222i 0.316029 0.948749i \(-0.397650\pi\)
0.910518 0.413469i \(-0.135683\pi\)
\(140\) 0.163275 0.0347052i 0.0137993 0.00293313i
\(141\) 0 0
\(142\) 9.51601 16.4822i 0.798566 1.38316i
\(143\) −2.34184 + 4.66920i −0.195835 + 0.390458i
\(144\) 0 0
\(145\) −3.34251 2.42847i −0.277580 0.201674i
\(146\) −16.0185 17.7904i −1.32570 1.47234i
\(147\) 0 0
\(148\) 1.03168 + 0.459335i 0.0848038 + 0.0377571i
\(149\) 1.04732 + 0.466296i 0.0857996 + 0.0382005i 0.449188 0.893437i \(-0.351713\pi\)
−0.363388 + 0.931638i \(0.618380\pi\)
\(150\) 0 0
\(151\) 0.589263 + 0.654443i 0.0479536 + 0.0532578i 0.766644 0.642072i \(-0.221925\pi\)
−0.718691 + 0.695330i \(0.755258\pi\)
\(152\) −5.05031 3.66926i −0.409634 0.297616i
\(153\) 0 0
\(154\) −3.66015 0.555908i −0.294944 0.0447963i
\(155\) −2.70211 + 4.68018i −0.217038 + 0.375921i
\(156\) 0 0
\(157\) 9.57236 2.03467i 0.763958 0.162384i 0.190576 0.981672i \(-0.438965\pi\)
0.573382 + 0.819288i \(0.305631\pi\)
\(158\) 15.1249 16.7979i 1.20327 1.33637i
\(159\) 0 0
\(160\) 0.134876 + 1.28326i 0.0106629 + 0.101450i
\(161\) 0.993219 + 3.05681i 0.0782766 + 0.240911i
\(162\) 0 0
\(163\) −3.74555 2.72130i −0.293374 0.213149i 0.431355 0.902182i \(-0.358035\pi\)
−0.724730 + 0.689033i \(0.758035\pi\)
\(164\) −0.225364 + 0.390342i −0.0175980 + 0.0304806i
\(165\) 0 0
\(166\) 5.37515 + 9.31002i 0.417192 + 0.722598i
\(167\) −1.77566 + 16.8943i −0.137405 + 1.30732i 0.680831 + 0.732440i \(0.261619\pi\)
−0.818236 + 0.574882i \(0.805048\pi\)
\(168\) 0 0
\(169\) 10.2896 + 2.18712i 0.791509 + 0.168240i
\(170\) 3.40058 2.47066i 0.260812 0.189491i
\(171\) 0 0
\(172\) −0.508616 1.56536i −0.0387816 0.119357i
\(173\) 0.395493 + 0.439240i 0.0300688 + 0.0333948i 0.757992 0.652264i \(-0.226181\pi\)
−0.727923 + 0.685659i \(0.759514\pi\)
\(174\) 0 0
\(175\) 1.67835 + 2.90699i 0.126872 + 0.219748i
\(176\) 3.87893 14.8530i 0.292385 1.11959i
\(177\) 0 0
\(178\) 17.6280 7.84848i 1.32127 0.588268i
\(179\) 2.97921 9.16907i 0.222677 0.685328i −0.775842 0.630927i \(-0.782675\pi\)
0.998519 0.0544017i \(-0.0173251\pi\)
\(180\) 0 0
\(181\) 3.85243 2.79896i 0.286349 0.208045i −0.435333 0.900270i \(-0.643369\pi\)
0.721682 + 0.692225i \(0.243369\pi\)
\(182\) −0.183764 1.74840i −0.0136215 0.129600i
\(183\) 0 0
\(184\) −10.8365 + 2.30336i −0.798875 + 0.169806i
\(185\) 0.178950 1.70260i 0.0131567 0.125178i
\(186\) 0 0
\(187\) −14.6857 + 4.03514i −1.07392 + 0.295079i
\(188\) 0.0888691 0.00648144
\(189\) 0 0
\(190\) 0.709589 2.18389i 0.0514790 0.158436i
\(191\) −5.08444 1.08073i −0.367897 0.0781989i 0.0202537 0.999795i \(-0.493553\pi\)
−0.388151 + 0.921596i \(0.626886\pi\)
\(192\) 0 0
\(193\) 2.98551 + 1.32923i 0.214902 + 0.0956804i 0.511364 0.859364i \(-0.329140\pi\)
−0.296463 + 0.955044i \(0.595807\pi\)
\(194\) −14.6706 + 16.2934i −1.05329 + 1.16980i
\(195\) 0 0
\(196\) −2.31146 + 1.02913i −0.165105 + 0.0735093i
\(197\) 22.4626 1.60039 0.800197 0.599737i \(-0.204728\pi\)
0.800197 + 0.599737i \(0.204728\pi\)
\(198\) 0 0
\(199\) −20.8291 −1.47654 −0.738269 0.674507i \(-0.764356\pi\)
−0.738269 + 0.674507i \(0.764356\pi\)
\(200\) −10.5698 + 4.70596i −0.747394 + 0.332761i
\(201\) 0 0
\(202\) −14.8652 + 16.5095i −1.04591 + 1.16160i
\(203\) −4.60264 2.04923i −0.323042 0.143828i
\(204\) 0 0
\(205\) 0.668344 + 0.142061i 0.0466792 + 0.00992197i
\(206\) 2.11603 6.51246i 0.147431 0.453745i
\(207\) 0 0
\(208\) 7.28981 0.505457
\(209\) −5.19483 + 6.49904i −0.359334 + 0.449548i
\(210\) 0 0
\(211\) −0.354563 + 3.37344i −0.0244091 + 0.232237i 0.975515 + 0.219932i \(0.0705836\pi\)
−0.999924 + 0.0123051i \(0.996083\pi\)
\(212\) −2.17880 + 0.463117i −0.149640 + 0.0318070i
\(213\) 0 0
\(214\) 2.54454 + 24.2096i 0.173941 + 1.65494i
\(215\) −2.01858 + 1.46659i −0.137666 + 0.100020i
\(216\) 0 0
\(217\) −2.03646 + 6.26759i −0.138244 + 0.425472i
\(218\) 19.3466 8.61366i 1.31032 0.583390i
\(219\) 0 0
\(220\) 0.765519 0.0449957i 0.0516113 0.00303361i
\(221\) −3.61612 6.26330i −0.243247 0.421315i
\(222\) 0 0
\(223\) −7.37810 8.19420i −0.494074 0.548725i 0.443607 0.896221i \(-0.353698\pi\)
−0.937681 + 0.347497i \(0.887032\pi\)
\(224\) 0.486232 + 1.49647i 0.0324877 + 0.0999870i
\(225\) 0 0
\(226\) −10.0445 + 7.29775i −0.668150 + 0.485439i
\(227\) −5.83650 1.24059i −0.387382 0.0823406i 0.0101037 0.999949i \(-0.496784\pi\)
−0.397486 + 0.917608i \(0.630117\pi\)
\(228\) 0 0
\(229\) −2.58715 + 24.6151i −0.170964 + 1.62661i 0.486889 + 0.873464i \(0.338132\pi\)
−0.657852 + 0.753147i \(0.728535\pi\)
\(230\) −2.03760 3.52922i −0.134355 0.232710i
\(231\) 0 0
\(232\) 8.68297 15.0393i 0.570065 0.987381i
\(233\) 3.38850 + 2.46189i 0.221988 + 0.161284i 0.693221 0.720725i \(-0.256191\pi\)
−0.471233 + 0.882009i \(0.656191\pi\)
\(234\) 0 0
\(235\) −0.0416308 0.128126i −0.00271569 0.00835805i
\(236\) 0.291208 + 2.77066i 0.0189560 + 0.180355i
\(237\) 0 0
\(238\) 3.42980 3.80917i 0.222321 0.246912i
\(239\) −7.21173 + 1.53290i −0.466488 + 0.0991551i −0.435158 0.900354i \(-0.643308\pi\)
−0.0313298 + 0.999509i \(0.509974\pi\)
\(240\) 0 0
\(241\) 4.41462 7.64634i 0.284371 0.492544i −0.688086 0.725629i \(-0.741549\pi\)
0.972456 + 0.233085i \(0.0748821\pi\)
\(242\) −16.2405 5.04975i −1.04398 0.324610i
\(243\) 0 0
\(244\) −1.44041 1.04652i −0.0922129 0.0669966i
\(245\) 2.56655 + 2.85044i 0.163971 + 0.182108i
\(246\) 0 0
\(247\) −3.60938 1.60700i −0.229659 0.102251i
\(248\) −20.7513 9.23908i −1.31771 0.586682i
\(249\) 0 0
\(250\) −5.91029 6.56404i −0.373799 0.415146i
\(251\) 16.6439 + 12.0925i 1.05056 + 0.763274i 0.972318 0.233661i \(-0.0750704\pi\)
0.0782385 + 0.996935i \(0.475070\pi\)
\(252\) 0 0
\(253\) 2.40242 + 14.5689i 0.151039 + 0.915936i
\(254\) −9.27397 + 16.0630i −0.581901 + 1.00788i
\(255\) 0 0
\(256\) −8.84127 + 1.87927i −0.552579 + 0.117454i
\(257\) 2.26326 2.51360i 0.141178 0.156794i −0.668409 0.743794i \(-0.733024\pi\)
0.809587 + 0.587000i \(0.199691\pi\)
\(258\) 0 0
\(259\) −0.218220 2.07623i −0.0135595 0.129010i
\(260\) 0.112528 + 0.346326i 0.00697871 + 0.0214783i
\(261\) 0 0
\(262\) 8.61973 + 6.26260i 0.532528 + 0.386905i
\(263\) −7.14112 + 12.3688i −0.440341 + 0.762692i −0.997715 0.0675692i \(-0.978476\pi\)
0.557374 + 0.830262i \(0.311809\pi\)
\(264\) 0 0
\(265\) 1.68836 + 2.92432i 0.103715 + 0.179639i
\(266\) 0.292699 2.78485i 0.0179465 0.170750i
\(267\) 0 0
\(268\) 3.09095 + 0.657003i 0.188810 + 0.0401328i
\(269\) 5.43693 3.95016i 0.331495 0.240845i −0.409570 0.912279i \(-0.634321\pi\)
0.741065 + 0.671433i \(0.234321\pi\)
\(270\) 0 0
\(271\) −1.23000 3.78554i −0.0747170 0.229955i 0.906722 0.421728i \(-0.138576\pi\)
−0.981439 + 0.191773i \(0.938576\pi\)
\(272\) 14.2219 + 15.7951i 0.862331 + 0.957716i
\(273\) 0 0
\(274\) −7.14821 12.3811i −0.431839 0.747968i
\(275\) 5.61758 + 14.3610i 0.338753 + 0.866002i
\(276\) 0 0
\(277\) −11.9967 + 5.34127i −0.720811 + 0.320926i −0.734152 0.678985i \(-0.762420\pi\)
0.0133410 + 0.999911i \(0.495753\pi\)
\(278\) −10.3255 + 31.7786i −0.619282 + 1.90595i
\(279\) 0 0
\(280\) 0.860476 0.625172i 0.0514233 0.0373612i
\(281\) −0.310227 2.95161i −0.0185066 0.176078i 0.981364 0.192157i \(-0.0615484\pi\)
−0.999871 + 0.0160790i \(0.994882\pi\)
\(282\) 0 0
\(283\) −7.91593 + 1.68258i −0.470553 + 0.100019i −0.437084 0.899421i \(-0.643989\pi\)
−0.0334689 + 0.999440i \(0.510655\pi\)
\(284\) −0.502499 + 4.78096i −0.0298178 + 0.283697i
\(285\) 0 0
\(286\) 0.371456 8.06780i 0.0219646 0.477059i
\(287\) 0.833217 0.0491833
\(288\) 0 0
\(289\) 1.26279 3.88648i 0.0742820 0.228616i
\(290\) 6.24837 + 1.32813i 0.366917 + 0.0779906i
\(291\) 0 0
\(292\) 5.52405 + 2.45947i 0.323271 + 0.143929i
\(293\) 10.5158 11.6789i 0.614338 0.682292i −0.353046 0.935606i \(-0.614854\pi\)
0.967384 + 0.253314i \(0.0815207\pi\)
\(294\) 0 0
\(295\) 3.85817 1.71777i 0.224631 0.100012i
\(296\) 7.19584 0.418249
\(297\) 0 0
\(298\) −1.77254 −0.102681
\(299\) −6.40554 + 2.85193i −0.370442 + 0.164931i
\(300\) 0 0
\(301\) −2.03593 + 2.26113i −0.117349 + 0.130329i
\(302\) −1.24387 0.553809i −0.0715769 0.0318681i
\(303\) 0 0
\(304\) 11.3575 + 2.41410i 0.651395 + 0.138458i
\(305\) −0.834052 + 2.56695i −0.0477577 + 0.146983i
\(306\) 0 0
\(307\) −3.51315 −0.200506 −0.100253 0.994962i \(-0.531965\pi\)
−0.100253 + 0.994962i \(0.531965\pi\)
\(308\) 0.901701 0.247758i 0.0513792 0.0141173i
\(309\) 0 0
\(310\) 0.873403 8.30987i 0.0496060 0.471969i
\(311\) 25.7589 5.47523i 1.46066 0.310472i 0.592020 0.805923i \(-0.298331\pi\)
0.868636 + 0.495451i \(0.164997\pi\)
\(312\) 0 0
\(313\) 0.257259 + 2.44766i 0.0145412 + 0.138350i 0.999384 0.0351004i \(-0.0111751\pi\)
−0.984843 + 0.173450i \(0.944508\pi\)
\(314\) −12.2411 + 8.89367i −0.690805 + 0.501899i
\(315\) 0 0
\(316\) −1.76433 + 5.43005i −0.0992513 + 0.305464i
\(317\) 24.2155 10.7814i 1.36008 0.605545i 0.408444 0.912783i \(-0.366071\pi\)
0.951633 + 0.307238i \(0.0994048\pi\)
\(318\) 0 0
\(319\) −19.4911 12.4824i −1.09129 0.698880i
\(320\) 1.74274 + 3.01852i 0.0974224 + 0.168741i
\(321\) 0 0
\(322\) −3.32523 3.69304i −0.185308 0.205805i
\(323\) −3.55972 10.9557i −0.198068 0.609591i
\(324\) 0 0
\(325\) −5.92427 + 4.30423i −0.328619 + 0.238756i
\(326\) 7.00182 + 1.48828i 0.387795 + 0.0824283i
\(327\) 0 0
\(328\) −0.300202 + 2.85623i −0.0165759 + 0.157709i
\(329\) −0.0821419 0.142274i −0.00452863 0.00784382i
\(330\) 0 0
\(331\) −4.05198 + 7.01824i −0.222717 + 0.385757i −0.955632 0.294563i \(-0.904826\pi\)
0.732915 + 0.680320i \(0.238159\pi\)
\(332\) −2.19681 1.59608i −0.120566 0.0875962i
\(333\) 0 0
\(334\) −8.11627 24.9793i −0.444103 1.36681i
\(335\) −0.500731 4.76414i −0.0273579 0.260293i
\(336\) 0 0
\(337\) 16.5413 18.3710i 0.901064 1.00073i −0.0989203 0.995095i \(-0.531539\pi\)
0.999984 0.00563738i \(-0.00179444\pi\)
\(338\) −15.9091 + 3.38159i −0.865343 + 0.183934i
\(339\) 0 0
\(340\) −0.530861 + 0.919478i −0.0287900 + 0.0498657i
\(341\) −13.5730 + 27.0619i −0.735017 + 1.46549i
\(342\) 0 0
\(343\) 7.87256 + 5.71975i 0.425078 + 0.308837i
\(344\) −7.01752 7.79374i −0.378359 0.420210i
\(345\) 0 0
\(346\) −0.834846 0.371697i −0.0448816 0.0199826i
\(347\) 1.89071 + 0.841800i 0.101499 + 0.0451902i 0.456858 0.889540i \(-0.348975\pi\)
−0.355359 + 0.934730i \(0.615641\pi\)
\(348\) 0 0
\(349\) −3.48902 3.87495i −0.186763 0.207422i 0.642491 0.766293i \(-0.277901\pi\)
−0.829254 + 0.558872i \(0.811234\pi\)
\(350\) −4.19874 3.05056i −0.224432 0.163059i
\(351\) 0 0
\(352\) 1.17611 + 7.13221i 0.0626868 + 0.380148i
\(353\) 10.8363 18.7689i 0.576756 0.998970i −0.419093 0.907943i \(-0.637652\pi\)
0.995848 0.0910266i \(-0.0290148\pi\)
\(354\) 0 0
\(355\) 7.12831 1.51517i 0.378331 0.0804168i
\(356\) −3.26136 + 3.62211i −0.172852 + 0.191971i
\(357\) 0 0
\(358\) 1.55812 + 14.8245i 0.0823493 + 0.783501i
\(359\) −2.70478 8.32446i −0.142753 0.439348i 0.853962 0.520335i \(-0.174193\pi\)
−0.996715 + 0.0809868i \(0.974193\pi\)
\(360\) 0 0
\(361\) 10.2801 + 7.46894i 0.541059 + 0.393102i
\(362\) −3.68125 + 6.37611i −0.193482 + 0.335121i
\(363\) 0 0
\(364\) 0.222030 + 0.384567i 0.0116375 + 0.0201568i
\(365\) 0.958173 9.11641i 0.0501531 0.477175i
\(366\) 0 0
\(367\) 6.61837 + 1.40678i 0.345476 + 0.0734332i 0.377382 0.926058i \(-0.376824\pi\)
−0.0319060 + 0.999491i \(0.510158\pi\)
\(368\) 16.6709 12.1121i 0.869029 0.631387i
\(369\) 0 0
\(370\) 0.817952 + 2.51740i 0.0425233 + 0.130873i
\(371\) 2.75529 + 3.06006i 0.143047 + 0.158870i
\(372\) 0 0
\(373\) 10.9467 + 18.9602i 0.566797 + 0.981722i 0.996880 + 0.0789323i \(0.0251511\pi\)
−0.430083 + 0.902790i \(0.641516\pi\)
\(374\) 18.2054 14.9349i 0.941380 0.772265i
\(375\) 0 0
\(376\) 0.517304 0.230319i 0.0266779 0.0118778i
\(377\) 3.39643 10.4531i 0.174925 0.538364i
\(378\) 0 0
\(379\) 27.3639 19.8810i 1.40559 1.02122i 0.411642 0.911346i \(-0.364955\pi\)
0.993946 0.109873i \(-0.0350445\pi\)
\(380\) 0.0606282 + 0.576839i 0.00311016 + 0.0295912i
\(381\) 0 0
\(382\) 7.86123 1.67096i 0.402216 0.0854936i
\(383\) −1.92059 + 18.2732i −0.0981378 + 0.933719i 0.829063 + 0.559155i \(0.188874\pi\)
−0.927201 + 0.374564i \(0.877792\pi\)
\(384\) 0 0
\(385\) −0.779606 1.18396i −0.0397324 0.0603402i
\(386\) −5.05284 −0.257183
\(387\) 0 0
\(388\) 1.71134 5.26696i 0.0868801 0.267390i
\(389\) −30.1333 6.40504i −1.52782 0.324748i −0.634057 0.773286i \(-0.718612\pi\)
−0.893764 + 0.448538i \(0.851945\pi\)
\(390\) 0 0
\(391\) −18.6761 8.31516i −0.944493 0.420516i
\(392\) −10.7878 + 11.9811i −0.544867 + 0.605136i
\(393\) 0 0
\(394\) −31.7277 + 14.1261i −1.59842 + 0.711661i
\(395\) 8.65524 0.435493
\(396\) 0 0
\(397\) −8.29578 −0.416353 −0.208177 0.978091i \(-0.566753\pi\)
−0.208177 + 0.978091i \(0.566753\pi\)
\(398\) 29.4204 13.0988i 1.47471 0.656584i
\(399\) 0 0
\(400\) 14.4000 15.9928i 0.720000 0.799641i
\(401\) 3.59354 + 1.59995i 0.179453 + 0.0798976i 0.494497 0.869180i \(-0.335352\pi\)
−0.315044 + 0.949077i \(0.602019\pi\)
\(402\) 0 0
\(403\) −14.0625 2.98907i −0.700503 0.148896i
\(404\) 1.73404 5.33682i 0.0862716 0.265517i
\(405\) 0 0
\(406\) 7.78977 0.386600
\(407\) 0.441104 9.58052i 0.0218647 0.474889i
\(408\) 0 0
\(409\) 0.261766 2.49054i 0.0129435 0.123149i −0.986142 0.165902i \(-0.946946\pi\)
0.999086 + 0.0427534i \(0.0136130\pi\)
\(410\) −1.03335 + 0.219646i −0.0510336 + 0.0108475i
\(411\) 0 0
\(412\) 0.180796 + 1.72016i 0.00890719 + 0.0847462i
\(413\) 4.16650 3.02714i 0.205020 0.148956i
\(414\) 0 0
\(415\) −1.27204 + 3.91493i −0.0624419 + 0.192176i
\(416\) −3.13585 + 1.39617i −0.153747 + 0.0684528i
\(417\) 0 0
\(418\) 3.25047 12.4466i 0.158986 0.608781i
\(419\) 5.36970 + 9.30060i 0.262327 + 0.454364i 0.966860 0.255307i \(-0.0821767\pi\)
−0.704533 + 0.709672i \(0.748843\pi\)
\(420\) 0 0
\(421\) 14.8463 + 16.4885i 0.723564 + 0.803600i 0.986939 0.161094i \(-0.0515022\pi\)
−0.263375 + 0.964694i \(0.584836\pi\)
\(422\) −1.62065 4.98785i −0.0788920 0.242805i
\(423\) 0 0
\(424\) −11.4825 + 8.34249i −0.557637 + 0.405147i
\(425\) −20.8839 4.43902i −1.01302 0.215324i
\(426\) 0 0
\(427\) −0.344039 + 3.27331i −0.0166492 + 0.158407i
\(428\) −3.07440 5.32501i −0.148606 0.257394i
\(429\) 0 0
\(430\) 1.92889 3.34093i 0.0930192 0.161114i
\(431\) −14.9330 10.8495i −0.719297 0.522600i 0.166862 0.985980i \(-0.446636\pi\)
−0.886160 + 0.463380i \(0.846636\pi\)
\(432\) 0 0
\(433\) 4.67130 + 14.3768i 0.224488 + 0.690904i 0.998343 + 0.0575408i \(0.0183259\pi\)
−0.773855 + 0.633363i \(0.781674\pi\)
\(434\) −1.06507 10.1334i −0.0511249 0.486420i
\(435\) 0 0
\(436\) −3.57932 + 3.97524i −0.171418 + 0.190379i
\(437\) −10.9242 + 2.32202i −0.522577 + 0.111077i
\(438\) 0 0
\(439\) −11.9777 + 20.7459i −0.571663 + 0.990150i 0.424732 + 0.905319i \(0.360368\pi\)
−0.996395 + 0.0848306i \(0.972965\pi\)
\(440\) 4.33945 2.24589i 0.206875 0.107068i
\(441\) 0 0
\(442\) 9.04645 + 6.57263i 0.430296 + 0.312628i
\(443\) −17.0613 18.9485i −0.810607 0.900270i 0.186003 0.982549i \(-0.440447\pi\)
−0.996609 + 0.0822794i \(0.973780\pi\)
\(444\) 0 0
\(445\) 6.74993 + 3.00526i 0.319978 + 0.142463i
\(446\) 15.5744 + 6.93417i 0.737469 + 0.328342i
\(447\) 0 0
\(448\) 2.84405 + 3.15864i 0.134369 + 0.149231i
\(449\) −18.1886 13.2148i −0.858375 0.623646i 0.0690672 0.997612i \(-0.477998\pi\)
−0.927442 + 0.373966i \(0.877998\pi\)
\(450\) 0 0
\(451\) 3.78438 + 0.574776i 0.178200 + 0.0270651i
\(452\) 1.56804 2.71592i 0.0737542 0.127746i
\(453\) 0 0
\(454\) 9.02402 1.91812i 0.423518 0.0900216i
\(455\) 0.450437 0.500261i 0.0211168 0.0234526i
\(456\) 0 0
\(457\) −2.26718 21.5708i −0.106054 1.00904i −0.910077 0.414439i \(-0.863978\pi\)
0.804023 0.594598i \(-0.202689\pi\)
\(458\) −11.8254 36.3950i −0.552566 1.70062i
\(459\) 0 0
\(460\) 0.832763 + 0.605037i 0.0388278 + 0.0282100i
\(461\) −6.05182 + 10.4821i −0.281861 + 0.488198i −0.971843 0.235629i \(-0.924285\pi\)
0.689982 + 0.723827i \(0.257618\pi\)
\(462\) 0 0
\(463\) −10.0154 17.3472i −0.465455 0.806192i 0.533767 0.845632i \(-0.320776\pi\)
−0.999222 + 0.0394398i \(0.987443\pi\)
\(464\) −3.37637 + 32.1240i −0.156744 + 1.49132i
\(465\) 0 0
\(466\) −6.33435 1.34641i −0.293433 0.0623711i
\(467\) 4.90871 3.56639i 0.227148 0.165033i −0.468390 0.883522i \(-0.655166\pi\)
0.695538 + 0.718489i \(0.255166\pi\)
\(468\) 0 0
\(469\) −1.80516 5.55570i −0.0833543 0.256538i
\(470\) 0.139377 + 0.154794i 0.00642898 + 0.00714011i
\(471\) 0 0
\(472\) 8.87574 + 15.3732i 0.408539 + 0.707610i
\(473\) −10.8067 + 8.86535i −0.496895 + 0.407629i
\(474\) 0 0
\(475\) −10.6553 + 4.74407i −0.488901 + 0.217673i
\(476\) −0.400088 + 1.23134i −0.0183380 + 0.0564385i
\(477\) 0 0
\(478\) 9.22233 6.70041i 0.421819 0.306470i
\(479\) 3.79154 + 36.0741i 0.173240 + 1.64827i 0.643286 + 0.765626i \(0.277571\pi\)
−0.470046 + 0.882642i \(0.655763\pi\)
\(480\) 0 0
\(481\) 4.45480 0.946896i 0.203121 0.0431747i
\(482\) −1.42694 + 13.5764i −0.0649953 + 0.618389i
\(483\) 0 0
\(484\) 4.26634 0.503273i 0.193924 0.0228760i
\(485\) −8.39529 −0.381211
\(486\) 0 0
\(487\) −2.68379 + 8.25986i −0.121614 + 0.374290i −0.993269 0.115830i \(-0.963047\pi\)
0.871655 + 0.490120i \(0.163047\pi\)
\(488\) −11.0968 2.35870i −0.502329 0.106773i
\(489\) 0 0
\(490\) −5.41772 2.41213i −0.244748 0.108969i
\(491\) 22.2133 24.6704i 1.00247 1.11336i 0.00892472 0.999960i \(-0.497159\pi\)
0.993549 0.113400i \(-0.0361742\pi\)
\(492\) 0 0
\(493\) 29.2753 13.0342i 1.31849 0.587032i
\(494\) 6.10872 0.274844
\(495\) 0 0
\(496\) 42.2506 1.89711
\(497\) 8.11848 3.61458i 0.364163 0.162136i
\(498\) 0 0
\(499\) 13.9694 15.5146i 0.625355 0.694527i −0.344340 0.938845i \(-0.611897\pi\)
0.969695 + 0.244318i \(0.0785641\pi\)
\(500\) 2.03818 + 0.907458i 0.0911504 + 0.0405828i
\(501\) 0 0
\(502\) −31.1136 6.61341i −1.38867 0.295171i
\(503\) −7.20593 + 22.1776i −0.321297 + 0.988850i 0.651788 + 0.758401i \(0.274019\pi\)
−0.973085 + 0.230448i \(0.925981\pi\)
\(504\) 0 0
\(505\) −8.50663 −0.378540
\(506\) −12.5553 19.0672i −0.558149 0.847641i
\(507\) 0 0
\(508\) 0.489718 4.65935i 0.0217277 0.206725i
\(509\) 6.33958 1.34752i 0.280997 0.0597278i −0.0652572 0.997868i \(-0.520787\pi\)
0.346254 + 0.938141i \(0.387453\pi\)
\(510\) 0 0
\(511\) −1.16844 11.1170i −0.0516887 0.491785i
\(512\) −10.4751 + 7.61063i −0.462940 + 0.336346i
\(513\) 0 0
\(514\) −1.61605 + 4.97368i −0.0712807 + 0.219379i
\(515\) 2.39534 1.06647i 0.105551 0.0469944i
\(516\) 0 0
\(517\) −0.274935 0.702856i −0.0120916 0.0309116i
\(518\) 1.61390 + 2.79537i 0.0709109 + 0.122821i
\(519\) 0 0
\(520\) 1.55258 + 1.72432i 0.0680854 + 0.0756164i
\(521\) 10.2625 + 31.5848i 0.449610 + 1.38376i 0.877348 + 0.479855i \(0.159311\pi\)
−0.427738 + 0.903903i \(0.640689\pi\)
\(522\) 0 0
\(523\) 32.4728 23.5929i 1.41994 1.03164i 0.428154 0.903706i \(-0.359164\pi\)
0.991782 0.127938i \(-0.0408359\pi\)
\(524\) −2.63242 0.559539i −0.114998 0.0244436i
\(525\) 0 0
\(526\) 2.30823 21.9613i 0.100644 0.957560i
\(527\) −20.9585 36.3011i −0.912965 1.58130i
\(528\) 0 0
\(529\) 1.58985 2.75370i 0.0691240 0.119726i
\(530\) −4.22376 3.06874i −0.183468 0.133298i
\(531\) 0 0
\(532\) 0.218567 + 0.672680i 0.00947608 + 0.0291644i
\(533\) 0.190001 + 1.80774i 0.00822986 + 0.0783019i
\(534\) 0 0
\(535\) −6.23710 + 6.92700i −0.269653 + 0.299480i
\(536\) 19.6951 4.18632i 0.850698 0.180821i
\(537\) 0 0
\(538\) −5.19534 + 8.99859i −0.223987 + 0.387957i
\(539\) 15.2903 + 15.0973i 0.658599 + 0.650287i
\(540\) 0 0
\(541\) −19.9410 14.4880i −0.857332 0.622888i 0.0698260 0.997559i \(-0.477756\pi\)
−0.927158 + 0.374671i \(0.877756\pi\)
\(542\) 4.11794 + 4.57344i 0.176881 + 0.196446i
\(543\) 0 0
\(544\) −9.14294 4.07070i −0.392000 0.174530i
\(545\) 7.40801 + 3.29826i 0.317324 + 0.141282i
\(546\) 0 0
\(547\) 17.2103 + 19.1139i 0.735858 + 0.817253i 0.988645 0.150269i \(-0.0480139\pi\)
−0.252787 + 0.967522i \(0.581347\pi\)
\(548\) 2.92147 + 2.12257i 0.124799 + 0.0906716i
\(549\) 0 0
\(550\) −16.9659 16.7517i −0.723427 0.714296i
\(551\) 8.75329 15.1611i 0.372902 0.645886i
\(552\) 0 0
\(553\) 10.3240 2.19442i 0.439019 0.0933164i
\(554\) 13.5859 15.0887i 0.577211 0.641058i
\(555\) 0 0
\(556\) −0.882224 8.39380i −0.0374146 0.355976i
\(557\) −3.60979 11.1098i −0.152952 0.470737i 0.844996 0.534773i \(-0.179603\pi\)
−0.997948 + 0.0640357i \(0.979603\pi\)
\(558\) 0 0
\(559\) −5.36998 3.90152i −0.227126 0.165017i
\(560\) −0.989164 + 1.71328i −0.0417998 + 0.0723994i
\(561\) 0 0
\(562\) 2.29436 + 3.97396i 0.0967819 + 0.167631i
\(563\) 0.848991 8.07761i 0.0357807 0.340431i −0.961957 0.273201i \(-0.911917\pi\)
0.997738 0.0672292i \(-0.0214159\pi\)
\(564\) 0 0
\(565\) −4.65021 0.988432i −0.195636 0.0415836i
\(566\) 10.1229 7.35468i 0.425495 0.309140i
\(567\) 0 0
\(568\) 9.46559 + 29.1321i 0.397167 + 1.22236i
\(569\) 12.0488 + 13.3815i 0.505111 + 0.560983i 0.940733 0.339147i \(-0.110138\pi\)
−0.435622 + 0.900129i \(0.643472\pi\)
\(570\) 0 0
\(571\) 1.30322 + 2.25725i 0.0545382 + 0.0944629i 0.892006 0.452024i \(-0.149298\pi\)
−0.837467 + 0.546487i \(0.815965\pi\)
\(572\) 0.743151 + 1.89982i 0.0310727 + 0.0794356i
\(573\) 0 0
\(574\) −1.17689 + 0.523986i −0.0491225 + 0.0218707i
\(575\) −6.39652 + 19.6865i −0.266753 + 0.820982i
\(576\) 0 0
\(577\) −28.4684 + 20.6835i −1.18515 + 0.861064i −0.992744 0.120251i \(-0.961630\pi\)
−0.192409 + 0.981315i \(0.561630\pi\)
\(578\) 0.660439 + 6.28365i 0.0274706 + 0.261366i
\(579\) 0 0
\(580\) −1.57827 + 0.335473i −0.0655343 + 0.0139297i
\(581\) −0.524704 + 4.99223i −0.0217684 + 0.207112i
\(582\) 0 0
\(583\) 10.4033 + 15.7991i 0.430861 + 0.654333i
\(584\) 38.5294 1.59436
\(585\) 0 0
\(586\) −7.50863 + 23.1092i −0.310179 + 0.954631i
\(587\) 23.0377 + 4.89682i 0.950869 + 0.202113i 0.657134 0.753774i \(-0.271768\pi\)
0.293735 + 0.955887i \(0.405102\pi\)
\(588\) 0 0
\(589\) −20.9194 9.31391i −0.861968 0.383773i
\(590\) −4.36928 + 4.85258i −0.179880 + 0.199777i
\(591\) 0 0
\(592\) −12.2272 + 5.44392i −0.502536 + 0.223744i
\(593\) −13.1828 −0.541354 −0.270677 0.962670i \(-0.587248\pi\)
−0.270677 + 0.962670i \(0.587248\pi\)
\(594\) 0 0
\(595\) 1.96270 0.0804630
\(596\) 0.409018 0.182106i 0.0167540 0.00745937i
\(597\) 0 0
\(598\) 7.25412 8.05651i 0.296643 0.329455i
\(599\) −31.2582 13.9171i −1.27718 0.568636i −0.347731 0.937594i \(-0.613048\pi\)
−0.929446 + 0.368958i \(0.879715\pi\)
\(600\) 0 0
\(601\) −28.3942 6.03537i −1.15822 0.246188i −0.411555 0.911385i \(-0.635014\pi\)
−0.746668 + 0.665197i \(0.768347\pi\)
\(602\) 1.45372 4.47410i 0.0592493 0.182351i
\(603\) 0 0
\(604\) 0.343924 0.0139941
\(605\) −2.72416 5.91521i −0.110753 0.240487i
\(606\) 0 0
\(607\) 0.329929 3.13906i 0.0133914 0.127411i −0.985784 0.168019i \(-0.946263\pi\)
0.999175 + 0.0406085i \(0.0129296\pi\)
\(608\) −5.34798 + 1.13675i −0.216889 + 0.0461012i
\(609\) 0 0
\(610\) −0.436207 4.15024i −0.0176615 0.168038i
\(611\) 0.289945 0.210657i 0.0117299 0.00852229i
\(612\) 0 0
\(613\) 10.4884 32.2798i 0.423620 1.30377i −0.480689 0.876891i \(-0.659613\pi\)
0.904309 0.426878i \(-0.140387\pi\)
\(614\) 4.96221 2.20932i 0.200258 0.0891608i
\(615\) 0 0
\(616\) 4.60667 3.77910i 0.185608 0.152264i
\(617\) −10.8039 18.7129i −0.434948 0.753351i 0.562344 0.826904i \(-0.309900\pi\)
−0.997291 + 0.0735523i \(0.976566\pi\)
\(618\) 0 0
\(619\) 13.7256 + 15.2438i 0.551679 + 0.612701i 0.952902 0.303279i \(-0.0980815\pi\)
−0.401223 + 0.915980i \(0.631415\pi\)
\(620\) 0.652196 + 2.00725i 0.0261928 + 0.0806132i
\(621\) 0 0
\(622\) −32.9404 + 23.9326i −1.32079 + 0.959611i
\(623\) 8.81325 + 1.87331i 0.353095 + 0.0750527i
\(624\) 0 0
\(625\) −2.07649 + 19.7565i −0.0830597 + 0.790260i
\(626\) −1.90263 3.29545i −0.0760444 0.131713i
\(627\) 0 0
\(628\) 1.91094 3.30985i 0.0762550 0.132078i
\(629\) 10.7427 + 7.80501i 0.428339 + 0.311206i
\(630\) 0 0
\(631\) 9.22863 + 28.4028i 0.367386 + 1.13070i 0.948473 + 0.316857i \(0.102628\pi\)
−0.581087 + 0.813841i \(0.697372\pi\)
\(632\) 3.80275 + 36.1807i 0.151265 + 1.43919i
\(633\) 0 0
\(634\) −27.4234 + 30.4568i −1.08912 + 1.20959i
\(635\) −6.94700 + 1.47663i −0.275683 + 0.0585983i
\(636\) 0 0
\(637\) −5.10193 + 8.83680i −0.202146 + 0.350127i
\(638\) 35.3803 + 5.37360i 1.40072 + 0.212743i
\(639\) 0 0
\(640\) −6.44762 4.68447i −0.254864 0.185170i
\(641\) 25.5073 + 28.3287i 1.00748 + 1.11892i 0.992891 + 0.119024i \(0.0379764\pi\)
0.0145863 + 0.999894i \(0.495357\pi\)
\(642\) 0 0
\(643\) −15.3705 6.84340i −0.606154 0.269877i 0.0806235 0.996745i \(-0.474309\pi\)
−0.686778 + 0.726867i \(0.740976\pi\)
\(644\) 1.14672 + 0.510551i 0.0451870 + 0.0201185i
\(645\) 0 0
\(646\) 11.9177 + 13.2359i 0.468895 + 0.520761i
\(647\) −16.9687 12.3285i −0.667109 0.484683i 0.201947 0.979396i \(-0.435273\pi\)
−0.869056 + 0.494713i \(0.835273\pi\)
\(648\) 0 0
\(649\) 21.0120 10.8748i 0.824792 0.426872i
\(650\) 5.66102 9.80517i 0.222043 0.384591i
\(651\) 0 0
\(652\) −1.76859 + 0.375925i −0.0692632 + 0.0147223i
\(653\) −13.2264 + 14.6894i −0.517587 + 0.574839i −0.944107 0.329639i \(-0.893073\pi\)
0.426520 + 0.904478i \(0.359739\pi\)
\(654\) 0 0
\(655\) 0.426450 + 4.05740i 0.0166628 + 0.158536i
\(656\) −1.65074 5.08046i −0.0644506 0.198358i
\(657\) 0 0
\(658\) 0.205494 + 0.149300i 0.00801101 + 0.00582034i
\(659\) −5.90277 + 10.2239i −0.229939 + 0.398267i −0.957790 0.287469i \(-0.907186\pi\)
0.727851 + 0.685736i \(0.240519\pi\)
\(660\) 0 0
\(661\) −8.90382 15.4219i −0.346318 0.599841i 0.639274 0.768979i \(-0.279235\pi\)
−0.985592 + 0.169138i \(0.945902\pi\)
\(662\) 1.30972 12.4612i 0.0509039 0.484318i
\(663\) 0 0
\(664\) −16.9241 3.59733i −0.656782 0.139603i
\(665\) 0.867445 0.630235i 0.0336381 0.0244395i
\(666\) 0 0
\(667\) −9.60079 29.5482i −0.371744 1.14411i
\(668\) 4.43916 + 4.93019i 0.171756 + 0.190755i
\(669\) 0 0
\(670\) 3.70329 + 6.41429i 0.143071 + 0.247806i
\(671\) −3.82060 + 14.6297i −0.147493 + 0.564773i
\(672\) 0 0
\(673\) 18.0017 8.01486i 0.693913 0.308950i −0.0293041 0.999571i \(-0.509329\pi\)
0.723217 + 0.690620i \(0.242662\pi\)
\(674\) −11.8111 + 36.3508i −0.454946 + 1.40018i
\(675\) 0 0
\(676\) 3.32365 2.41477i 0.127833 0.0928760i
\(677\) −1.29761 12.3459i −0.0498711 0.474492i −0.990745 0.135735i \(-0.956660\pi\)
0.940874 0.338757i \(-0.110006\pi\)
\(678\) 0 0
\(679\) −10.0139 + 2.12852i −0.384297 + 0.0816850i
\(680\) −0.707148 + 6.72806i −0.0271179 + 0.258010i
\(681\) 0 0
\(682\) 2.15290 46.7597i 0.0824387 1.79052i
\(683\) −2.02837 −0.0776135 −0.0388068 0.999247i \(-0.512356\pi\)
−0.0388068 + 0.999247i \(0.512356\pi\)
\(684\) 0 0
\(685\) 1.69164 5.20632i 0.0646341 0.198923i
\(686\) −14.7167 3.12813i −0.561886 0.119433i
\(687\) 0 0
\(688\) 17.8205 + 7.93420i 0.679400 + 0.302488i
\(689\) −6.01077 + 6.67564i −0.228992 + 0.254322i
\(690\) 0 0
\(691\) 2.14032 0.952931i 0.0814215 0.0362512i −0.365622 0.930764i \(-0.619144\pi\)
0.447043 + 0.894512i \(0.352477\pi\)
\(692\) 0.230830 0.00877483
\(693\) 0 0
\(694\) −3.19995 −0.121469
\(695\) −11.6884 + 5.20402i −0.443367 + 0.197400i
\(696\) 0 0
\(697\) −3.54620 + 3.93846i −0.134322 + 0.149180i
\(698\) 7.36497 + 3.27910i 0.278768 + 0.124116i
\(699\) 0 0
\(700\) 1.28228 + 0.272556i 0.0484655 + 0.0103016i
\(701\) 1.37008 4.21668i 0.0517473 0.159262i −0.921843 0.387563i \(-0.873317\pi\)
0.973591 + 0.228301i \(0.0733170\pi\)
\(702\) 0 0
\(703\) 7.25411 0.273594
\(704\) 10.7384 + 16.3081i 0.404720 + 0.614634i
\(705\) 0 0
\(706\) −3.50261 + 33.3251i −0.131822 + 1.25421i
\(707\) −10.1467 + 2.15675i −0.381606 + 0.0811128i
\(708\) 0 0
\(709\) −3.12357 29.7188i −0.117308 1.11611i −0.881847 0.471536i \(-0.843700\pi\)
0.764538 0.644578i \(-0.222967\pi\)
\(710\) −9.11565 + 6.62291i −0.342104 + 0.248553i
\(711\) 0 0
\(712\) −9.59699 + 29.5365i −0.359662 + 1.10693i
\(713\) −37.1255 + 16.5293i −1.39036 + 0.619029i
\(714\) 0 0
\(715\) 2.39093 1.96141i 0.0894157 0.0733525i
\(716\) −1.88258 3.26072i −0.0703551 0.121859i
\(717\) 0 0
\(718\) 9.05541 + 10.0571i 0.337945 + 0.375326i
\(719\) 6.68469 + 20.5734i 0.249297 + 0.767257i 0.994900 + 0.100867i \(0.0321616\pi\)
−0.745603 + 0.666390i \(0.767838\pi\)
\(720\) 0 0
\(721\) 2.58676 1.87939i 0.0963360 0.0699922i
\(722\) −19.2173 4.08477i −0.715194 0.152019i
\(723\) 0 0
\(724\) 0.194391 1.84950i 0.00722447 0.0687363i
\(725\) −16.2235 28.1000i −0.602527 1.04361i
\(726\) 0 0
\(727\) 6.22109 10.7752i 0.230727 0.399631i −0.727295 0.686325i \(-0.759223\pi\)
0.958022 + 0.286694i \(0.0925561\pi\)
\(728\) 2.28910 + 1.66313i 0.0848396 + 0.0616396i
\(729\) 0 0
\(730\) 4.37965 + 13.4792i 0.162098 + 0.498887i
\(731\) −2.02293 19.2469i −0.0748207 0.711872i
\(732\) 0 0
\(733\) −35.0305 + 38.9053i −1.29388 + 1.43700i −0.457143 + 0.889393i \(0.651127\pi\)
−0.836736 + 0.547606i \(0.815539\pi\)
\(734\) −10.2329 + 2.17507i −0.377703 + 0.0802833i
\(735\) 0 0
\(736\) −4.85153 + 8.40310i −0.178830 + 0.309742i
\(737\) −4.36635 26.4786i −0.160837 0.975352i
\(738\) 0 0
\(739\) 37.7617 + 27.4355i 1.38909 + 1.00923i 0.995965 + 0.0897445i \(0.0286051\pi\)
0.393122 + 0.919486i \(0.371395\pi\)
\(740\) −0.447375 0.496861i −0.0164458 0.0182650i
\(741\) 0 0
\(742\) −5.81613 2.58951i −0.213517 0.0950638i
\(743\) 19.9810 + 8.89609i 0.733030 + 0.326366i 0.739082 0.673616i \(-0.235260\pi\)
−0.00605180 + 0.999982i \(0.501926\pi\)
\(744\) 0 0
\(745\) −0.454155 0.504391i −0.0166390 0.0184794i
\(746\) −27.3853 19.8966i −1.00265 0.728466i
\(747\) 0 0
\(748\) −2.66657 + 5.31664i −0.0974994 + 0.194395i
\(749\) −5.68334 + 9.84384i −0.207665 + 0.359686i
\(750\) 0 0
\(751\) −38.7269 + 8.23167i −1.41317 + 0.300378i −0.850356 0.526208i \(-0.823613\pi\)
−0.562810 + 0.826586i \(0.690280\pi\)
\(752\) −0.704764 + 0.782720i −0.0257001 + 0.0285429i
\(753\) 0 0
\(754\) 1.77633 + 16.9006i 0.0646900 + 0.615484i
\(755\) −0.161111 0.495850i −0.00586344 0.0180458i
\(756\) 0 0
\(757\) −18.7253 13.6047i −0.680583 0.494472i 0.192968 0.981205i \(-0.438189\pi\)
−0.873551 + 0.486733i \(0.838189\pi\)
\(758\) −26.1480 + 45.2896i −0.949736 + 1.64499i
\(759\) 0 0
\(760\) 1.84789 + 3.20063i 0.0670299 + 0.116099i
\(761\) −1.55673 + 14.8113i −0.0564313 + 0.536908i 0.929389 + 0.369102i \(0.120335\pi\)
−0.985820 + 0.167806i \(0.946332\pi\)
\(762\) 0 0
\(763\) 9.67249 + 2.05595i 0.350168 + 0.0744304i
\(764\) −1.64233 + 1.19322i −0.0594173 + 0.0431692i
\(765\) 0 0
\(766\) −8.77872 27.0181i −0.317188 0.976204i
\(767\) 7.51774 + 8.34930i 0.271450 + 0.301476i
\(768\) 0 0
\(769\) −10.8117 18.7264i −0.389879 0.675290i 0.602554 0.798078i \(-0.294150\pi\)
−0.992433 + 0.122788i \(0.960816\pi\)
\(770\) 1.84572 + 1.18203i 0.0665153 + 0.0425974i
\(771\) 0 0
\(772\) 1.16595 0.519116i 0.0419636 0.0186834i
\(773\) 1.87664 5.77569i 0.0674979 0.207737i −0.911619 0.411037i \(-0.865167\pi\)
0.979117 + 0.203300i \(0.0651666\pi\)
\(774\) 0 0
\(775\) −34.3361 + 24.9466i −1.23339 + 0.896109i
\(776\) −3.68853 35.0941i −0.132411 1.25980i
\(777\) 0 0
\(778\) 46.5903 9.90307i 1.67034 0.355042i
\(779\) −0.302633 + 2.87936i −0.0108430 + 0.103164i
\(780\) 0 0
\(781\) 39.3667 10.8167i 1.40865 0.387051i
\(782\) 31.6086 1.13032
\(783\) 0 0
\(784\) 9.26663 28.5197i 0.330951 1.01856i
\(785\) −5.66714 1.20459i −0.202269 0.0429936i
\(786\) 0 0
\(787\) 46.7328 + 20.8068i 1.66584 + 0.741681i 0.999990 0.00440228i \(-0.00140129\pi\)
0.665853 + 0.746083i \(0.268068\pi\)
\(788\) 5.86995 6.51924i 0.209108 0.232238i
\(789\) 0 0
\(790\) −12.2252 + 5.44303i −0.434954 + 0.193654i
\(791\) −5.79736 −0.206130
\(792\) 0 0
\(793\) −7.18019 −0.254976
\(794\) 11.7175 5.21697i 0.415839 0.185143i
\(795\) 0 0
\(796\) −5.44309 + 6.04516i −0.192925 + 0.214265i
\(797\) 23.0773 + 10.2747i 0.817439 + 0.363947i 0.772478 0.635041i \(-0.219017\pi\)
0.0449609 + 0.998989i \(0.485684\pi\)
\(798\) 0 0
\(799\) 1.02210 + 0.217254i 0.0361593 + 0.00768590i
\(800\) −3.13143 + 9.63754i −0.110713 + 0.340738i
\(801\) 0 0
\(802\) −6.08192 −0.214760
\(803\) 2.36185 51.2980i 0.0833480 1.81027i
\(804\) 0 0
\(805\) 0.198903 1.89244i 0.00701042 0.0666997i
\(806\) 21.7425 4.62152i 0.765848 0.162786i
\(807\) 0 0
\(808\) −3.73745 35.5595i −0.131483 1.25098i
\(809\) 41.5248 30.1696i 1.45994 1.06071i 0.476556 0.879144i \(-0.341885\pi\)
0.983380 0.181561i \(-0.0581150\pi\)
\(810\) 0 0
\(811\) 1.40476 4.32339i 0.0493276 0.151815i −0.923359 0.383939i \(-0.874567\pi\)
0.972686 + 0.232124i \(0.0745674\pi\)
\(812\) −1.79751 + 0.800302i −0.0630801 + 0.0280851i
\(813\) 0 0
\(814\) 5.40186 + 13.8096i 0.189335 + 0.484025i
\(815\) 1.37048 + 2.37375i 0.0480059 + 0.0831487i
\(816\) 0 0
\(817\) −7.07435 7.85686i −0.247500 0.274877i
\(818\) 1.19649 + 3.68241i 0.0418342 + 0.128753i
\(819\) 0 0
\(820\) 0.215882 0.156848i 0.00753894 0.00547736i
\(821\) 10.6362 + 2.26079i 0.371205 + 0.0789021i 0.389737 0.920926i \(-0.372566\pi\)
−0.0185320 + 0.999828i \(0.505899\pi\)
\(822\) 0 0
\(823\) 2.46856 23.4868i 0.0860486 0.818697i −0.863346 0.504612i \(-0.831636\pi\)
0.949395 0.314085i \(-0.101698\pi\)
\(824\) 5.51048 + 9.54444i 0.191967 + 0.332496i
\(825\) 0 0
\(826\) −3.98136 + 6.89591i −0.138529 + 0.239940i
\(827\) −22.3321 16.2252i −0.776564 0.564207i 0.127382 0.991854i \(-0.459343\pi\)
−0.903946 + 0.427647i \(0.859343\pi\)
\(828\) 0 0
\(829\) −4.97546 15.3129i −0.172805 0.531839i 0.826722 0.562611i \(-0.190203\pi\)
−0.999526 + 0.0307727i \(0.990203\pi\)
\(830\) −0.665273 6.32965i −0.0230920 0.219705i
\(831\) 0 0
\(832\) −6.20441 + 6.89069i −0.215099 + 0.238892i
\(833\) −29.1005 + 6.18550i −1.00827 + 0.214315i
\(834\) 0 0
\(835\) 5.02854 8.70968i 0.174020 0.301411i
\(836\) 0.528675 + 3.20601i 0.0182846 + 0.110882i
\(837\) 0 0
\(838\) −13.4334 9.75993i −0.464049 0.337151i
\(839\) 13.0025 + 14.4407i 0.448896 + 0.498549i 0.924538 0.381089i \(-0.124451\pi\)
−0.475642 + 0.879639i \(0.657784\pi\)
\(840\) 0 0
\(841\) 17.9979 + 8.01318i 0.620617 + 0.276317i
\(842\) −31.3390 13.9530i −1.08001 0.480853i
\(843\) 0 0
\(844\) 0.886407 + 0.984455i 0.0305114 + 0.0338863i
\(845\) −5.03845 3.66065i −0.173328 0.125930i
\(846\) 0 0
\(847\) −4.74909 6.36497i −0.163181 0.218703i
\(848\) 13.1997 22.8626i 0.453280 0.785103i
\(849\) 0 0
\(850\) 32.2894 6.86333i 1.10752 0.235410i
\(851\) 8.61427 9.56712i 0.295293 0.327957i
\(852\) 0 0
\(853\) 2.06815 + 19.6771i 0.0708121 + 0.673732i 0.971138 + 0.238517i \(0.0766611\pi\)
−0.900326 + 0.435215i \(0.856672\pi\)
\(854\) −1.57255 4.83980i −0.0538114 0.165614i
\(855\) 0 0
\(856\) −31.6966 23.0289i −1.08337 0.787112i
\(857\) −2.17032 + 3.75911i −0.0741369 + 0.128409i −0.900711 0.434420i \(-0.856953\pi\)
0.826574 + 0.562828i \(0.190287\pi\)
\(858\) 0 0
\(859\) 2.58967 + 4.48545i 0.0883586 + 0.153042i 0.906817 0.421524i \(-0.138505\pi\)
−0.818459 + 0.574565i \(0.805171\pi\)
\(860\) −0.101856 + 0.969096i −0.00347327 + 0.0330459i
\(861\) 0 0
\(862\) 27.9153 + 5.93357i 0.950797 + 0.202098i
\(863\) −2.17943 + 1.58345i −0.0741886 + 0.0539011i −0.624261 0.781216i \(-0.714600\pi\)
0.550073 + 0.835117i \(0.314600\pi\)
\(864\) 0 0
\(865\) −0.108132 0.332797i −0.00367661 0.0113155i
\(866\) −15.6392 17.3691i −0.531441 0.590225i
\(867\) 0 0
\(868\) 1.28685 + 2.22889i 0.0436785 + 0.0756534i
\(869\) 48.4040 2.84509i 1.64199 0.0965132i
\(870\) 0 0
\(871\) 11.6420 5.18333i 0.394472 0.175630i
\(872\) −10.5326 + 32.4161i −0.356680 + 1.09775i
\(873\) 0 0
\(874\) 13.9699 10.1497i 0.472538 0.343319i
\(875\) −0.431114 4.10177i −0.0145743 0.138665i
\(876\) 0 0
\(877\) 20.3893 4.33387i 0.688497 0.146344i 0.149638 0.988741i \(-0.452189\pi\)
0.538858 + 0.842396i \(0.318856\pi\)
\(878\) 3.87155 36.8353i 0.130658 1.24313i
\(879\) 0 0
\(880\) −5.67454 + 7.09919i −0.191289 + 0.239314i
\(881\) −11.5843 −0.390286 −0.195143 0.980775i \(-0.562517\pi\)
−0.195143 + 0.980775i \(0.562517\pi\)
\(882\) 0 0
\(883\) 4.75801 14.6437i 0.160120 0.492798i −0.838524 0.544865i \(-0.816581\pi\)
0.998644 + 0.0520667i \(0.0165808\pi\)
\(884\) −2.76274 0.587239i −0.0929211 0.0197510i
\(885\) 0 0
\(886\) 36.0146 + 16.0348i 1.20994 + 0.538698i
\(887\) 3.95453 4.39196i 0.132780 0.147467i −0.673088 0.739563i \(-0.735032\pi\)
0.805868 + 0.592095i \(0.201699\pi\)
\(888\) 0 0
\(889\) −7.91198 + 3.52264i −0.265359 + 0.118146i
\(890\) −11.4240 −0.382932
\(891\) 0 0
\(892\) −4.30623 −0.144183
\(893\) 0.521493 0.232184i 0.0174511 0.00776974i
\(894\) 0 0
\(895\) −3.81922 + 4.24168i −0.127663 + 0.141784i
\(896\) −8.87838 3.95291i −0.296606 0.132057i
\(897\) 0 0
\(898\) 34.0013 + 7.22719i 1.13464 + 0.241174i
\(899\) 19.6852 60.5847i 0.656537 2.02061i
\(900\) 0 0
\(901\) −26.1909 −0.872546
\(902\) −5.70677 + 1.56803i −0.190015 + 0.0522098i
\(903\) 0 0
\(904\) 2.08875 19.8731i 0.0694707 0.660969i
\(905\) −2.75757 + 0.586140i −0.0916648 + 0.0194840i
\(906\) 0 0
\(907\) 0.772812 + 7.35282i 0.0256608 + 0.244146i 0.999832 + 0.0183351i \(0.00583657\pi\)
−0.974171 + 0.225811i \(0.927497\pi\)
\(908\) −1.88525 + 1.36971i −0.0625642 + 0.0454556i
\(909\) 0 0
\(910\) −0.321628 + 0.989869i −0.0106619 + 0.0328138i
\(911\) 12.9713 5.77517i 0.429757 0.191340i −0.180447 0.983585i \(-0.557754\pi\)
0.610203 + 0.792245i \(0.291088\pi\)
\(912\) 0 0
\(913\) −5.82692 + 22.3122i −0.192843 + 0.738426i
\(914\) 16.7675 + 29.0422i 0.554620 + 0.960631i
\(915\) 0 0
\(916\) 6.46787 + 7.18330i 0.213704 + 0.237343i
\(917\) 1.53737 + 4.73153i 0.0507684 + 0.156249i
\(918\) 0 0
\(919\) 33.6895 24.4769i 1.11132 0.807418i 0.128445 0.991717i \(-0.459001\pi\)
0.982870 + 0.184299i \(0.0590013\pi\)
\(920\) 6.41554 + 1.36366i 0.211514 + 0.0449587i
\(921\) 0 0
\(922\) 1.95613 18.6114i 0.0644218 0.612932i
\(923\) 9.69344 + 16.7895i 0.319063 + 0.552634i
\(924\) 0 0
\(925\) 6.72247 11.6437i 0.221033 0.382841i
\(926\) 25.0555 + 18.2039i 0.823376 + 0.598218i
\(927\) 0 0
\(928\) −4.70008 14.4654i −0.154288 0.474849i
\(929\) −3.56785 33.9458i −0.117057 1.11373i −0.882530 0.470257i \(-0.844161\pi\)
0.765473 0.643469i \(-0.222505\pi\)
\(930\) 0 0
\(931\) −10.8752 + 12.0781i −0.356419 + 0.395844i
\(932\) 1.59999 0.340089i 0.0524094 0.0111400i
\(933\) 0 0
\(934\) −4.69059 + 8.12434i −0.153481 + 0.265837i
\(935\) 8.91439 + 1.35393i 0.291532 + 0.0442781i
\(936\) 0 0
\(937\) −41.8118 30.3780i −1.36593 0.992407i −0.998043 0.0625376i \(-0.980081\pi\)
−0.367889 0.929870i \(-0.619919\pi\)
\(938\) 6.04353 + 6.71202i 0.197328 + 0.219155i
\(939\) 0 0
\(940\) −0.0480647 0.0213998i −0.00156770 0.000697984i
\(941\) −16.4495 7.32378i −0.536237 0.238748i 0.120706 0.992688i \(-0.461484\pi\)
−0.656943 + 0.753940i \(0.728151\pi\)
\(942\) 0 0
\(943\) 3.43809 + 3.81838i 0.111959 + 0.124344i
\(944\) −26.7122 19.4075i −0.869407 0.631661i
\(945\) 0 0
\(946\) 9.68901 19.3181i 0.315017 0.628084i
\(947\) 14.3151 24.7946i 0.465180 0.805715i −0.534030 0.845466i \(-0.679323\pi\)
0.999210 + 0.0397506i \(0.0126563\pi\)
\(948\) 0 0
\(949\) 23.8528 5.07007i 0.774295 0.164581i
\(950\) 12.0669 13.4017i 0.391502 0.434808i
\(951\) 0 0
\(952\) 0.862328 + 8.20451i 0.0279482 + 0.265910i
\(953\) −5.15728 15.8725i −0.167061 0.514160i 0.832121 0.554594i \(-0.187126\pi\)
−0.999182 + 0.0404331i \(0.987126\pi\)
\(954\) 0 0
\(955\) 2.48967 + 1.80885i 0.0805637 + 0.0585330i
\(956\) −1.43969 + 2.49361i −0.0465628 + 0.0806492i
\(957\) 0 0
\(958\) −28.0414 48.5690i −0.905975 1.56919i
\(959\) 0.697785 6.63898i 0.0225327 0.214384i
\(960\) 0 0
\(961\) −51.1814 10.8789i −1.65101 0.350933i
\(962\) −5.69677 + 4.13895i −0.183671 + 0.133445i
\(963\) 0 0
\(964\) −1.06554 3.27939i −0.0343187 0.105622i
\(965\) −1.29463 1.43783i −0.0416755 0.0462853i
\(966\) 0 0
\(967\) −12.1597 21.0612i −0.391029 0.677281i 0.601557 0.798830i \(-0.294547\pi\)
−0.992585 + 0.121549i \(0.961214\pi\)
\(968\) 23.5299 13.9864i 0.756280 0.449541i
\(969\) 0 0
\(970\) 11.8581 5.27955i 0.380739 0.169516i
\(971\) −2.33367 + 7.18229i −0.0748910 + 0.230491i −0.981494 0.191495i \(-0.938667\pi\)
0.906603 + 0.421985i \(0.138667\pi\)
\(972\) 0 0
\(973\) −12.6225 + 9.17079i −0.404659 + 0.294002i
\(974\) −1.40362 13.3545i −0.0449748 0.427907i
\(975\) 0 0
\(976\) 20.6403 4.38723i 0.660679 0.140432i
\(977\) 0.212432 2.02115i 0.00679629 0.0646624i −0.990598 0.136804i \(-0.956317\pi\)
0.997394 + 0.0721420i \(0.0229835\pi\)
\(978\) 0 0
\(979\) 38.7366 + 14.5880i 1.23803 + 0.466235i
\(980\) 1.49797 0.0478508
\(981\) 0 0
\(982\) −15.8611 + 48.8154i −0.506148 + 1.55776i
\(983\) 32.7089 + 6.95248i 1.04325 + 0.221750i 0.697506 0.716579i \(-0.254293\pi\)
0.345745 + 0.938329i \(0.387626\pi\)
\(984\) 0 0
\(985\) −12.1489 5.40902i −0.387095 0.172346i
\(986\) −33.1536 + 36.8208i −1.05583 + 1.17261i
\(987\) 0 0
\(988\) −1.40960 + 0.627594i −0.0448453 + 0.0199664i
\(989\) −18.7629 −0.596624
\(990\) 0 0
\(991\) 40.1009 1.27385 0.636923 0.770927i \(-0.280207\pi\)
0.636923 + 0.770927i \(0.280207\pi\)
\(992\) −18.1749 + 8.09197i −0.577052 + 0.256920i
\(993\) 0 0
\(994\) −9.19397 + 10.2109i −0.291615 + 0.323871i
\(995\) 11.2654 + 5.01568i 0.357137 + 0.159008i
\(996\) 0 0
\(997\) −15.7776 3.35364i −0.499682 0.106211i −0.0488260 0.998807i \(-0.515548\pi\)
−0.450856 + 0.892597i \(0.648881\pi\)
\(998\) −9.97461 + 30.6987i −0.315741 + 0.971750i
\(999\) 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 297.2.n.b.235.2 72
3.2 odd 2 99.2.m.b.70.8 yes 72
9.2 odd 6 891.2.f.f.730.2 36
9.4 even 3 inner 297.2.n.b.37.8 72
9.5 odd 6 99.2.m.b.4.2 72
9.7 even 3 891.2.f.e.730.8 36
11.3 even 5 inner 297.2.n.b.289.8 72
33.5 odd 10 1089.2.e.p.727.4 36
33.14 odd 10 99.2.m.b.25.2 yes 72
33.17 even 10 1089.2.e.o.727.15 36
99.5 odd 30 1089.2.e.p.364.4 36
99.14 odd 30 99.2.m.b.58.8 yes 72
99.16 even 15 9801.2.a.cp.1.4 18
99.25 even 15 891.2.f.e.487.8 36
99.38 odd 30 9801.2.a.cm.1.15 18
99.47 odd 30 891.2.f.f.487.2 36
99.50 even 30 1089.2.e.o.364.15 36
99.58 even 15 inner 297.2.n.b.91.2 72
99.61 odd 30 9801.2.a.cn.1.15 18
99.83 even 30 9801.2.a.co.1.4 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.2 72 9.5 odd 6
99.2.m.b.25.2 yes 72 33.14 odd 10
99.2.m.b.58.8 yes 72 99.14 odd 30
99.2.m.b.70.8 yes 72 3.2 odd 2
297.2.n.b.37.8 72 9.4 even 3 inner
297.2.n.b.91.2 72 99.58 even 15 inner
297.2.n.b.235.2 72 1.1 even 1 trivial
297.2.n.b.289.8 72 11.3 even 5 inner
891.2.f.e.487.8 36 99.25 even 15
891.2.f.e.730.8 36 9.7 even 3
891.2.f.f.487.2 36 99.47 odd 30
891.2.f.f.730.2 36 9.2 odd 6
1089.2.e.o.364.15 36 99.50 even 30
1089.2.e.o.727.15 36 33.17 even 10
1089.2.e.p.364.4 36 99.5 odd 30
1089.2.e.p.727.4 36 33.5 odd 10
9801.2.a.cm.1.15 18 99.38 odd 30
9801.2.a.cn.1.15 18 99.61 odd 30
9801.2.a.co.1.4 18 99.83 even 30
9801.2.a.cp.1.4 18 99.16 even 15