Properties

Label 297.2.n.b.91.2
Level $297$
Weight $2$
Character 297.91
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 91.2
Character \(\chi\) \(=\) 297.91
Dual form 297.2.n.b.235.2

$q$-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 \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

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 −0.158794 0.987312i \(-0.550761\pi\)
−0.839970 + 0.542633i \(0.817427\pi\)
\(3\) 0 0
\(4\) 0.261321 + 0.290226i 0.130660 + 0.145113i
\(5\) −0.540848 + 0.240801i −0.241875 + 0.107690i −0.524094 0.851660i \(-0.675596\pi\)
0.282220 + 0.959350i \(0.408929\pi\)
\(6\) 0 0
\(7\) −0.706174 + 0.150102i −0.266909 + 0.0567332i −0.339422 0.940634i \(-0.610231\pi\)
0.0725131 + 0.997367i \(0.476898\pi\)
\(8\) 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 0.993342 + 0.115207i \(0.0367531\pi\)
−0.947682 + 0.319217i \(0.896580\pi\)
\(14\) 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 0.938728 0.344658i \(-0.112005\pi\)
−0.0377065 + 0.999289i \(0.512005\pi\)
\(18\) 0 0
\(19\) 0.775200 + 2.38582i 0.177843 + 0.547345i 0.999752 0.0222743i \(-0.00709072\pi\)
−0.821909 + 0.569619i \(0.807091\pi\)
\(20\) −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 −0.999163 0.0409092i \(-0.986975\pi\)
0.535010 + 0.844846i \(0.320308\pi\)
\(24\) 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 0.475426 0.879755i \(-0.342294\pi\)
0.792152 + 0.610323i \(0.208960\pi\)
\(30\) 0 0
\(31\) 0.954161 + 9.07824i 0.171372 + 1.63050i 0.655284 + 0.755382i \(0.272549\pi\)
−0.483912 + 0.875117i \(0.660784\pi\)
\(32\) −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 −0.850347 0.526223i \(-0.823608\pi\)
0.997251 + 0.0740981i \(0.0236078\pi\)
\(38\) 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 0.118913 0.992905i \(-0.462059\pi\)
−0.295218 + 0.955430i \(0.595392\pi\)
\(42\) 0 0
\(43\) 2.10724 + 3.64985i 0.321351 + 0.556596i 0.980767 0.195182i \(-0.0625297\pi\)
−0.659416 + 0.751778i \(0.729196\pi\)
\(44\) −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 −0.731937 0.681372i \(-0.761384\pi\)
0.754147 + 0.656705i \(0.228050\pi\)
\(48\) 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 −0.857723 0.514113i \(-0.828121\pi\)
0.223899 + 0.974612i \(0.428121\pi\)
\(54\) 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 0.347452 0.937698i \(-0.387047\pi\)
−0.968880 + 0.247532i \(0.920380\pi\)
\(60\) 0 0
\(61\) −0.476541 + 4.53398i −0.0610148 + 0.580517i 0.920715 + 0.390236i \(0.127607\pi\)
−0.981730 + 0.190281i \(0.939060\pi\)
\(62\) 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 −0.505716 0.862700i \(-0.668772\pi\)
0.999978 + 0.00661279i \(0.00210493\pi\)
\(68\) 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 −0.189478 0.981885i \(-0.560680\pi\)
−0.992380 + 0.123215i \(0.960680\pi\)
\(72\) 0 0
\(73\) 4.78461 14.7255i 0.559996 1.72349i −0.122373 0.992484i \(-0.539050\pi\)
0.682370 0.731007i \(-0.260950\pi\)
\(74\) −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 −0.519925 0.854212i \(-0.674040\pi\)
−0.982701 + 0.185200i \(0.940707\pi\)
\(80\) 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 0.879378 + 0.476124i \(0.157959\pi\)
−0.959153 + 0.282886i \(0.908708\pi\)
\(84\) 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 0.939970 0.341256i \(-0.110852\pi\)
0.375360 + 0.926879i \(0.377519\pi\)
\(98\) 10.0171 1.01188
\(99\) 0 0
\(100\) −1.81581 −0.181581
\(101\) 13.1263 + 5.84421i 1.30612 + 0.581521i 0.937476 0.348051i \(-0.113156\pi\)
0.368641 + 0.929572i \(0.379823\pi\)
\(102\) 0 0
\(103\) −2.96348 3.29128i −0.292000 0.324299i 0.579239 0.815158i \(-0.303350\pi\)
−0.871239 + 0.490859i \(0.836683\pi\)
\(104\) −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 0.852134 + 0.523324i \(0.175308\pi\)
−0.381788 + 0.924250i \(0.624692\pi\)
\(108\) 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 0.561963 0.827163i \(-0.310046\pi\)
0.176941 + 0.984221i \(0.443380\pi\)
\(114\) 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 0.928211 0.372054i \(-0.121347\pi\)
−0.0670118 + 0.997752i \(0.521347\pi\)
\(128\) 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 −0.976372 0.216099i \(-0.930667\pi\)
0.675333 + 0.737513i \(0.264000\pi\)
\(132\) 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 −0.872363 0.488858i \(-0.837414\pi\)
0.954939 0.296801i \(-0.0959196\pi\)
\(138\) 0 0
\(139\) 14.4608 + 16.0603i 1.22655 + 1.36222i 0.910518 + 0.413469i \(0.135683\pi\)
0.316029 + 0.948749i \(0.397650\pi\)
\(140\) 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 −0.363388 0.931638i \(-0.618380\pi\)
0.449188 + 0.893437i \(0.351713\pi\)
\(150\) 0 0
\(151\) 0.589263 0.654443i 0.0479536 0.0532578i −0.718691 0.695330i \(-0.755258\pi\)
0.766644 + 0.642072i \(0.221925\pi\)
\(152\) −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 0.573382 0.819288i \(-0.305631\pi\)
0.190576 + 0.981672i \(0.438965\pi\)
\(158\) 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 −0.724730 0.689033i \(-0.758035\pi\)
0.431355 + 0.902182i \(0.358035\pi\)
\(164\) −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 −0.818236 0.574882i \(-0.805048\pi\)
0.680831 0.732440i \(-0.261619\pi\)
\(168\) 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 −0.727923 0.685659i \(-0.759514\pi\)
0.757992 + 0.652264i \(0.226181\pi\)
\(174\) 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 0.998519 + 0.0544017i \(0.0173251\pi\)
−0.775842 + 0.630927i \(0.782675\pi\)
\(180\) 0 0
\(181\) 3.85243 + 2.79896i 0.286349 + 0.208045i 0.721682 0.692225i \(-0.243369\pi\)
−0.435333 + 0.900270i \(0.643369\pi\)
\(182\) −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 −0.388151 0.921596i \(-0.626886\pi\)
0.0202537 + 0.999795i \(0.493553\pi\)
\(192\) 0 0
\(193\) 2.98551 1.32923i 0.214902 0.0956804i −0.296463 0.955044i \(-0.595807\pi\)
0.511364 + 0.859364i \(0.329140\pi\)
\(194\) −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 −0.999924 0.0123051i \(-0.996083\pi\)
0.975515 0.219932i \(-0.0705836\pi\)
\(212\) −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 −0.937681 0.347497i \(-0.887032\pi\)
0.443607 + 0.896221i \(0.353698\pi\)
\(224\) 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 −0.397486 0.917608i \(-0.630117\pi\)
0.0101037 + 0.999949i \(0.496784\pi\)
\(228\) 0 0
\(229\) −2.58715 24.6151i −0.170964 1.62661i −0.657852 0.753147i \(-0.728535\pi\)
0.486889 0.873464i \(-0.338132\pi\)
\(230\) −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 −0.471233 0.882009i \(-0.656191\pi\)
0.693221 + 0.720725i \(0.256191\pi\)
\(234\) 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 −0.0313298 0.999509i \(-0.509974\pi\)
−0.435158 + 0.900354i \(0.643308\pi\)
\(240\) 0 0
\(241\) 4.41462 + 7.64634i 0.284371 + 0.492544i 0.972456 0.233085i \(-0.0748821\pi\)
−0.688086 + 0.725629i \(0.741549\pi\)
\(242\) −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 0.0782385 0.996935i \(-0.475070\pi\)
0.972318 + 0.233661i \(0.0750704\pi\)
\(252\) 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 0.809587 0.587000i \(-0.199691\pi\)
−0.668409 + 0.743794i \(0.733024\pi\)
\(258\) 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 0.557374 0.830262i \(-0.311809\pi\)
−0.997715 + 0.0675692i \(0.978476\pi\)
\(264\) 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 0.741065 0.671433i \(-0.234321\pi\)
−0.409570 + 0.912279i \(0.634321\pi\)
\(270\) 0 0
\(271\) −1.23000 + 3.78554i −0.0747170 + 0.229955i −0.981439 0.191773i \(-0.938576\pi\)
0.906722 + 0.421728i \(0.138576\pi\)
\(272\) 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 0.0133410 0.999911i \(-0.495753\pi\)
−0.734152 + 0.678985i \(0.762420\pi\)
\(278\) −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 −0.999871 0.0160790i \(-0.994882\pi\)
0.981364 + 0.192157i \(0.0615484\pi\)
\(282\) 0 0
\(283\) −7.91593 1.68258i −0.470553 0.100019i −0.0334689 0.999440i \(-0.510655\pi\)
−0.437084 + 0.899421i \(0.643989\pi\)
\(284\) −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 0.967384 0.253314i \(-0.0815207\pi\)
−0.353046 + 0.935606i \(0.614854\pi\)
\(294\) 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 0.868636 0.495451i \(-0.164997\pi\)
0.592020 + 0.805923i \(0.298331\pi\)
\(312\) 0 0
\(313\) 0.257259 2.44766i 0.0145412 0.138350i −0.984843 0.173450i \(-0.944508\pi\)
0.999384 + 0.0351004i \(0.0111751\pi\)
\(314\) −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 0.951633 0.307238i \(-0.0994048\pi\)
0.408444 + 0.912783i \(0.366071\pi\)
\(318\) 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 0.732915 0.680320i \(-0.238159\pi\)
−0.955632 + 0.294563i \(0.904826\pi\)
\(332\) −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 0.999984 + 0.00563738i \(0.00179444\pi\)
−0.0989203 + 0.995095i \(0.531539\pi\)
\(338\) −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 −0.355359 0.934730i \(-0.615641\pi\)
0.456858 + 0.889540i \(0.348975\pi\)
\(348\) 0 0
\(349\) −3.48902 + 3.87495i −0.186763 + 0.207422i −0.829254 0.558872i \(-0.811234\pi\)
0.642491 + 0.766293i \(0.277901\pi\)
\(350\) −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 0.995848 + 0.0910266i \(0.0290148\pi\)
−0.419093 + 0.907943i \(0.637652\pi\)
\(354\) 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 −0.996715 0.0809868i \(-0.974193\pi\)
0.853962 + 0.520335i \(0.174193\pi\)
\(360\) 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 −0.0319060 0.999491i \(-0.510158\pi\)
0.377382 + 0.926058i \(0.376824\pi\)
\(368\) 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 −0.430083 0.902790i \(-0.641516\pi\)
0.996880 0.0789323i \(-0.0251511\pi\)
\(374\) 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 0.993946 + 0.109873i \(0.0350445\pi\)
0.411642 + 0.911346i \(0.364955\pi\)
\(380\) 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 −0.927201 0.374564i \(-0.877792\pi\)
0.829063 0.559155i \(-0.188874\pi\)
\(384\) 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 −0.893764 0.448538i \(-0.851945\pi\)
−0.634057 + 0.773286i \(0.718612\pi\)
\(390\) 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 −0.315044 0.949077i \(-0.602019\pi\)
0.494497 + 0.869180i \(0.335352\pi\)
\(402\) 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 0.999086 0.0427534i \(-0.0136130\pi\)
−0.986142 + 0.165902i \(0.946946\pi\)
\(410\) −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 −0.704533 0.709672i \(-0.748843\pi\)
0.966860 + 0.255307i \(0.0821767\pi\)
\(420\) 0 0
\(421\) 14.8463 16.4885i 0.723564 0.803600i −0.263375 0.964694i \(-0.584836\pi\)
0.986939 + 0.161094i \(0.0515022\pi\)
\(422\) −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 −0.886160 0.463380i \(-0.846636\pi\)
0.166862 + 0.985980i \(0.446636\pi\)
\(432\) 0 0
\(433\) 4.67130 14.3768i 0.224488 0.690904i −0.773855 0.633363i \(-0.781674\pi\)
0.998343 0.0575408i \(-0.0183259\pi\)
\(434\) −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 −0.996395 0.0848306i \(-0.972965\pi\)
0.424732 0.905319i \(-0.360368\pi\)
\(440\) 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 −0.996609 0.0822794i \(-0.973780\pi\)
0.186003 + 0.982549i \(0.440447\pi\)
\(444\) 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 −0.927442 0.373966i \(-0.877998\pi\)
0.0690672 + 0.997612i \(0.477998\pi\)
\(450\) 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 0.804023 + 0.594598i \(0.202689\pi\)
−0.910077 + 0.414439i \(0.863978\pi\)
\(458\) −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 0.689982 0.723827i \(-0.257618\pi\)
−0.971843 + 0.235629i \(0.924285\pi\)
\(462\) 0 0
\(463\) −10.0154 + 17.3472i −0.465455 + 0.806192i −0.999222 0.0394398i \(-0.987443\pi\)
0.533767 + 0.845632i \(0.320776\pi\)
\(464\) −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 0.695538 0.718489i \(-0.255166\pi\)
−0.468390 + 0.883522i \(0.655166\pi\)
\(468\) 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 −0.470046 0.882642i \(-0.655763\pi\)
0.643286 0.765626i \(-0.277571\pi\)
\(480\) 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 0.871655 0.490120i \(-0.163047\pi\)
−0.993269 + 0.115830i \(0.963047\pi\)
\(488\) −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 0.993549 + 0.113400i \(0.0361742\pi\)
0.00892472 + 0.999960i \(0.497159\pi\)
\(492\) 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 0.969695 0.244318i \(-0.0785641\pi\)
−0.344340 + 0.938845i \(0.611897\pi\)
\(500\) 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 −0.973085 0.230448i \(-0.925981\pi\)
0.651788 0.758401i \(-0.274019\pi\)
\(504\) 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 0.346254 0.938141i \(-0.387453\pi\)
−0.0652572 + 0.997868i \(0.520787\pi\)
\(510\) 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 −0.427738 0.903903i \(-0.640689\pi\)
0.877348 0.479855i \(-0.159311\pi\)
\(522\) 0 0
\(523\) 32.4728 + 23.5929i 1.41994 + 1.03164i 0.991782 + 0.127938i \(0.0408359\pi\)
0.428154 + 0.903706i \(0.359164\pi\)
\(524\) −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 −0.927158 0.374671i \(-0.877756\pi\)
0.0698260 + 0.997559i \(0.477756\pi\)
\(542\) 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 −0.252787 0.967522i \(-0.581347\pi\)
0.988645 + 0.150269i \(0.0480139\pi\)
\(548\) 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 −0.997948 0.0640357i \(-0.979603\pi\)
0.844996 + 0.534773i \(0.179603\pi\)
\(558\) 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 0.997738 + 0.0672292i \(0.0214159\pi\)
−0.961957 + 0.273201i \(0.911917\pi\)
\(564\) 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 −0.435622 0.900129i \(-0.643472\pi\)
0.940733 + 0.339147i \(0.110138\pi\)
\(570\) 0 0
\(571\) 1.30322 2.25725i 0.0545382 0.0944629i −0.837467 0.546487i \(-0.815965\pi\)
0.892006 + 0.452024i \(0.149298\pi\)
\(572\) 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 −0.192409 0.981315i \(-0.561630\pi\)
−0.992744 + 0.120251i \(0.961630\pi\)
\(578\) 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 0.293735 0.955887i \(-0.405102\pi\)
0.657134 + 0.753774i \(0.271768\pi\)
\(588\) 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 −0.929446 0.368958i \(-0.879715\pi\)
−0.347731 + 0.937594i \(0.613048\pi\)
\(600\) 0 0
\(601\) −28.3942 + 6.03537i −1.15822 + 0.246188i −0.746668 0.665197i \(-0.768347\pi\)
−0.411555 + 0.911385i \(0.635014\pi\)
\(602\) 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 0.999175 0.0406085i \(-0.0129296\pi\)
−0.985784 + 0.168019i \(0.946263\pi\)
\(608\) −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 0.904309 + 0.426878i \(0.140387\pi\)
−0.480689 + 0.876891i \(0.659613\pi\)
\(614\) 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 −0.997291 0.0735523i \(-0.976566\pi\)
0.562344 + 0.826904i \(0.309900\pi\)
\(618\) 0 0
\(619\) 13.7256 15.2438i 0.551679 0.612701i −0.401223 0.915980i \(-0.631415\pi\)
0.952902 + 0.303279i \(0.0980815\pi\)
\(620\) 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 −0.581087 0.813841i \(-0.697372\pi\)
0.948473 0.316857i \(-0.102628\pi\)
\(632\) 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 0.0145863 0.999894i \(-0.495357\pi\)
0.992891 0.119024i \(-0.0379764\pi\)
\(642\) 0 0
\(643\) −15.3705 + 6.84340i −0.606154 + 0.269877i −0.686778 0.726867i \(-0.740976\pi\)
0.0806235 + 0.996745i \(0.474309\pi\)
\(644\) 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 −0.869056 0.494713i \(-0.835273\pi\)
0.201947 + 0.979396i \(0.435273\pi\)
\(648\) 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 0.426520 0.904478i \(-0.359739\pi\)
−0.944107 + 0.329639i \(0.893073\pi\)
\(654\) 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 0.727851 0.685736i \(-0.240519\pi\)
−0.957790 + 0.287469i \(0.907186\pi\)
\(660\) 0 0
\(661\) −8.90382 + 15.4219i −0.346318 + 0.599841i −0.985592 0.169138i \(-0.945902\pi\)
0.639274 + 0.768979i \(0.279235\pi\)
\(662\) 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 0.723217 0.690620i \(-0.242662\pi\)
−0.0293041 + 0.999571i \(0.509329\pi\)
\(674\) −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 0.940874 + 0.338757i \(0.110006\pi\)
−0.990745 + 0.135735i \(0.956660\pi\)
\(678\) 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 0.447043 0.894512i \(-0.352477\pi\)
−0.365622 + 0.930764i \(0.619144\pi\)
\(692\) 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 0.973591 0.228301i \(-0.0733170\pi\)
−0.921843 + 0.387563i \(0.873317\pi\)
\(702\) 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 0.764538 + 0.644578i \(0.222967\pi\)
−0.881847 + 0.471536i \(0.843700\pi\)
\(710\) −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 −0.745603 0.666390i \(-0.767838\pi\)
0.994900 0.100867i \(-0.0321616\pi\)
\(720\) 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 0.958022 0.286694i \(-0.0925561\pi\)
−0.727295 + 0.686325i \(0.759223\pi\)
\(728\) 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 −0.836736 0.547606i \(-0.815539\pi\)
−0.457143 0.889393i \(-0.651127\pi\)
\(734\) −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 0.393122 0.919486i \(-0.371395\pi\)
0.995965 0.0897445i \(-0.0286051\pi\)
\(740\) −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 −0.00605180 0.999982i \(-0.501926\pi\)
0.739082 + 0.673616i \(0.235260\pi\)
\(744\) 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 −0.562810 0.826586i \(-0.690280\pi\)
−0.850356 + 0.526208i \(0.823613\pi\)
\(752\) −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 −0.873551 0.486733i \(-0.838189\pi\)
0.192968 + 0.981205i \(0.438189\pi\)
\(758\) −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 −0.985820 0.167806i \(-0.946332\pi\)
0.929389 0.369102i \(-0.120335\pi\)
\(762\) 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 −0.992433 0.122788i \(-0.960816\pi\)
0.602554 + 0.798078i \(0.294150\pi\)
\(770\) 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 0.979117 0.203300i \(-0.0651666\pi\)
−0.911619 + 0.411037i \(0.865167\pi\)
\(774\) 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 0.665853 0.746083i \(-0.268068\pi\)
0.999990 + 0.00440228i \(0.00140129\pi\)
\(788\) 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 0.0449609 0.998989i \(-0.485684\pi\)
0.772478 + 0.635041i \(0.219017\pi\)
\(798\) 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 0.983380 + 0.181561i \(0.0581150\pi\)
0.476556 + 0.879144i \(0.341885\pi\)
\(810\) 0 0
\(811\) 1.40476 + 4.32339i 0.0493276 + 0.151815i 0.972686 0.232124i \(-0.0745674\pi\)
−0.923359 + 0.383939i \(0.874567\pi\)
\(812\) −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 −0.0185320 0.999828i \(-0.505899\pi\)
0.389737 + 0.920926i \(0.372566\pi\)
\(822\) 0 0
\(823\) 2.46856 + 23.4868i 0.0860486 + 0.818697i 0.949395 + 0.314085i \(0.101698\pi\)
−0.863346 + 0.504612i \(0.831636\pi\)
\(824\) 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 −0.903946 0.427647i \(-0.859343\pi\)
0.127382 + 0.991854i \(0.459343\pi\)
\(828\) 0 0
\(829\) −4.97546 + 15.3129i −0.172805 + 0.531839i −0.999526 0.0307727i \(-0.990203\pi\)
0.826722 + 0.562611i \(0.190203\pi\)
\(830\) −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 −0.475642 0.879639i \(-0.657784\pi\)
0.924538 + 0.381089i \(0.124451\pi\)
\(840\) 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 −0.900326 0.435215i \(-0.856672\pi\)
0.971138 0.238517i \(-0.0766611\pi\)
\(854\) −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 0.826574 0.562828i \(-0.190287\pi\)
−0.900711 + 0.434420i \(0.856953\pi\)
\(858\) 0 0
\(859\) 2.58967 4.48545i 0.0883586 0.153042i −0.818459 0.574565i \(-0.805171\pi\)
0.906817 + 0.421524i \(0.138505\pi\)
\(860\) −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 0.550073 0.835117i \(-0.314600\pi\)
−0.624261 + 0.781216i \(0.714600\pi\)
\(864\) 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 0.538858 0.842396i \(-0.318856\pi\)
0.149638 + 0.988741i \(0.452189\pi\)
\(878\) 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 0.998644 0.0520667i \(-0.0165808\pi\)
−0.838524 + 0.544865i \(0.816581\pi\)
\(884\) −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 0.805868 0.592095i \(-0.201699\pi\)
−0.673088 + 0.739563i \(0.735032\pi\)
\(888\) 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 −0.974171 0.225811i \(-0.927497\pi\)
0.999832 0.0183351i \(-0.00583657\pi\)
\(908\) −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 0.610203 0.792245i \(-0.291088\pi\)
−0.180447 + 0.983585i \(0.557754\pi\)
\(912\) 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 0.982870 0.184299i \(-0.0590013\pi\)
0.128445 + 0.991717i \(0.459001\pi\)
\(920\) 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 0.765473 + 0.643469i \(0.222505\pi\)
−0.882530 + 0.470257i \(0.844161\pi\)
\(930\) 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 −0.367889 + 0.929870i \(0.619919\pi\)
−0.998043 + 0.0625376i \(0.980081\pi\)
\(938\) 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 −0.656943 0.753940i \(-0.728151\pi\)
0.120706 + 0.992688i \(0.461484\pi\)
\(942\) 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 0.999210 0.0397506i \(-0.0126563\pi\)
−0.534030 + 0.845466i \(0.679323\pi\)
\(948\) 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 −0.999182 0.0404331i \(-0.987126\pi\)
0.832121 + 0.554594i \(0.187126\pi\)
\(954\) 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 −0.992585 0.121549i \(-0.961214\pi\)
0.601557 + 0.798830i \(0.294547\pi\)
\(968\) 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 0.906603 0.421985i \(-0.138667\pi\)
−0.981494 + 0.191495i \(0.938667\pi\)
\(972\) 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 0.997394 0.0721420i \(-0.0229835\pi\)
−0.990598 + 0.136804i \(0.956317\pi\)
\(978\) 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 0.345745 0.938329i \(-0.387626\pi\)
0.697506 + 0.716579i \(0.254293\pi\)
\(984\) 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 −0.450856 0.892597i \(-0.648881\pi\)
−0.0488260 + 0.998807i \(0.515548\pi\)
\(998\) −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.91.2 72
3.2 odd 2 99.2.m.b.58.8 yes 72
9.2 odd 6 99.2.m.b.25.2 yes 72
9.4 even 3 891.2.f.e.487.8 36
9.5 odd 6 891.2.f.f.487.2 36
9.7 even 3 inner 297.2.n.b.289.8 72
11.4 even 5 inner 297.2.n.b.37.8 72
33.2 even 10 1089.2.e.o.364.15 36
33.20 odd 10 1089.2.e.p.364.4 36
33.26 odd 10 99.2.m.b.4.2 72
99.2 even 30 1089.2.e.o.727.15 36
99.4 even 15 891.2.f.e.730.8 36
99.13 odd 30 9801.2.a.cn.1.15 18
99.20 odd 30 1089.2.e.p.727.4 36
99.31 even 15 9801.2.a.cp.1.4 18
99.59 odd 30 891.2.f.f.730.2 36
99.68 even 30 9801.2.a.co.1.4 18
99.70 even 15 inner 297.2.n.b.235.2 72
99.86 odd 30 9801.2.a.cm.1.15 18
99.92 odd 30 99.2.m.b.70.8 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.2 72 33.26 odd 10
99.2.m.b.25.2 yes 72 9.2 odd 6
99.2.m.b.58.8 yes 72 3.2 odd 2
99.2.m.b.70.8 yes 72 99.92 odd 30
297.2.n.b.37.8 72 11.4 even 5 inner
297.2.n.b.91.2 72 1.1 even 1 trivial
297.2.n.b.235.2 72 99.70 even 15 inner
297.2.n.b.289.8 72 9.7 even 3 inner
891.2.f.e.487.8 36 9.4 even 3
891.2.f.e.730.8 36 99.4 even 15
891.2.f.f.487.2 36 9.5 odd 6
891.2.f.f.730.2 36 99.59 odd 30
1089.2.e.o.364.15 36 33.2 even 10
1089.2.e.o.727.15 36 99.2 even 30
1089.2.e.p.364.4 36 33.20 odd 10
1089.2.e.p.727.4 36 99.20 odd 30
9801.2.a.cm.1.15 18 99.86 odd 30
9801.2.a.cn.1.15 18 99.13 odd 30
9801.2.a.co.1.4 18 99.68 even 30
9801.2.a.cp.1.4 18 99.31 even 15