Properties

Label 99.2.m.b.70.8
Level $99$
Weight $2$
Character 99.70
Analytic conductor $0.791$
Analytic rank $0$
Dimension $72$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,2,Mod(4,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.m (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.790518980011\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(9\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 70.8
Character \(\chi\) \(=\) 99.70
Dual form 99.2.m.b.58.8

$q$-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} +(-0.215098 - 1.71864i) q^{3} +(0.261321 - 0.290226i) q^{4} +(0.540848 + 0.240801i) q^{5} +(-1.38462 - 2.29226i) q^{6} +(-0.706174 - 0.150102i) q^{7} +(-0.768973 + 2.36665i) q^{8} +(-2.90747 + 0.739353i) q^{9} +0.915362 q^{10} +(3.10382 + 1.16888i) q^{11} +(-0.555005 - 0.386690i) q^{12} +(0.164629 - 1.56634i) q^{13} +(-1.09184 + 0.232078i) q^{14} +(0.297516 - 0.981321i) q^{15} +(0.483816 + 4.60320i) q^{16} +(-3.71501 + 2.69911i) q^{17} +(-3.64174 + 2.87273i) q^{18} +(0.775200 - 2.38582i) q^{19} +(0.211222 - 0.0940420i) q^{20} +(-0.106075 + 1.24595i) q^{21} +(5.11912 - 0.300892i) q^{22} +(2.22600 + 3.85554i) q^{23} +(4.23284 + 0.812527i) q^{24} +(-3.11112 - 3.45525i) q^{25} +(-0.752490 - 2.31593i) q^{26} +(1.89607 + 4.83786i) q^{27} +(-0.228102 + 0.165726i) q^{28} +(-6.82612 - 1.45094i) q^{29} +(-0.196892 - 1.57318i) q^{30} +(0.954161 - 9.07824i) q^{31} +(1.08974 + 1.88749i) q^{32} +(1.34127 - 5.58579i) q^{33} +(-3.54993 + 6.14866i) q^{34} +(-0.345788 - 0.251230i) q^{35} +(-0.545202 + 1.03703i) q^{36} +(0.893583 + 2.75017i) q^{37} +(-0.405428 - 3.85739i) q^{38} +(-2.72738 + 0.0539778i) q^{39} +(-0.985790 + 1.09483i) q^{40} +(1.12890 - 0.239955i) q^{41} +(0.633712 + 1.82657i) q^{42} +(2.10724 - 3.64985i) q^{43} +(1.15033 - 0.595357i) q^{44} +(-1.75053 - 0.300244i) q^{45} +(5.56879 + 4.04596i) q^{46} +(-0.152264 - 0.169107i) q^{47} +(7.80719 - 1.82164i) q^{48} +(-5.91867 - 2.63516i) q^{49} +(-6.56726 - 2.92393i) q^{50} +(5.43790 + 5.80420i) q^{51} +(-0.411571 - 0.457096i) q^{52} +(4.61430 + 3.35249i) q^{53} +(5.72053 + 5.64093i) q^{54} +(1.39723 + 1.37959i) q^{55} +(0.898268 - 1.55585i) q^{56} +(-4.26712 - 0.819107i) q^{57} +(-10.5541 + 2.24335i) q^{58} +(4.77328 - 5.30126i) q^{59} +(-0.207058 - 0.342787i) q^{60} +(-0.476541 - 4.53398i) q^{61} +(-4.36131 - 13.4227i) q^{62} +(2.16416 - 0.0856954i) q^{63} +(-4.76295 - 3.46049i) q^{64} +(0.466215 - 0.807507i) q^{65} +(-1.61824 - 8.73322i) q^{66} +(4.04571 + 7.00738i) q^{67} +(-0.187456 + 1.78353i) q^{68} +(6.14750 - 4.65502i) q^{69} +(-0.646405 - 0.137398i) q^{70} +(9.95852 - 7.23528i) q^{71} +(0.485970 - 7.44951i) q^{72} +(4.78461 + 14.7255i) q^{73} +(2.99165 + 3.32257i) q^{74} +(-5.26915 + 6.09012i) q^{75} +(-0.489852 - 0.848448i) q^{76} +(-2.01639 - 1.29133i) q^{77} +(-3.81839 + 1.79141i) q^{78} +(-13.3556 + 5.94631i) q^{79} +(-0.846785 + 2.60614i) q^{80} +(7.90672 - 4.29928i) q^{81} +(1.44363 - 1.04886i) q^{82} +(0.726787 + 6.91491i) q^{83} +(0.333887 + 0.356378i) q^{84} +(-2.65920 + 0.565231i) q^{85} +(0.681124 - 6.48047i) q^{86} +(-1.02536 + 12.0438i) q^{87} +(-5.15310 + 6.44683i) q^{88} +12.4803 q^{89} +(-2.66138 + 0.676775i) q^{90} +(-0.351367 + 1.08140i) q^{91} +(1.70068 + 0.361491i) q^{92} +(-15.8075 + 0.312847i) q^{93} +(-0.321414 - 0.143103i) q^{94} +(0.993774 - 1.10370i) q^{95} +(3.00952 - 2.27887i) q^{96} +(12.9545 - 5.76772i) q^{97} -10.0171 q^{98} +(-9.88847 - 1.10367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - q^{2} - 12 q^{3} + 11 q^{4} - 8 q^{5} - 7 q^{6} - 2 q^{7} + 6 q^{8} - 22 q^{9} - 8 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 10 q^{14} - 20 q^{15} - 9 q^{16} - 20 q^{17} - 21 q^{18} + 8 q^{19}+ \cdots - 182 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41247 0.628870i 0.998764 0.444679i 0.158794 0.987312i \(-0.449239\pi\)
0.839970 + 0.542633i \(0.182573\pi\)
\(3\) −0.215098 1.71864i −0.124187 0.992259i
\(4\) 0.261321 0.290226i 0.130660 0.145113i
\(5\) 0.540848 + 0.240801i 0.241875 + 0.107690i 0.524094 0.851660i \(-0.324404\pi\)
−0.282220 + 0.959350i \(0.591071\pi\)
\(6\) −1.38462 2.29226i −0.565269 0.935810i
\(7\) −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
\(9\) −2.90747 + 0.739353i −0.969155 + 0.246451i
\(10\) 0.915362 0.289463
\(11\) 3.10382 + 1.16888i 0.935837 + 0.352432i
\(12\) −0.555005 0.386690i −0.160216 0.111628i
\(13\) 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
\(15\) 0.297516 0.981321i 0.0768183 0.253376i
\(16\) 0.483816 + 4.60320i 0.120954 + 1.15080i
\(17\) −3.71501 + 2.69911i −0.901022 + 0.654631i −0.938728 0.344658i \(-0.887995\pi\)
0.0377065 + 0.999289i \(0.487995\pi\)
\(18\) −3.64174 + 2.87273i −0.858366 + 0.677109i
\(19\) 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
\(21\) −0.106075 + 1.24595i −0.0231475 + 0.271888i
\(22\) 5.11912 0.300892i 1.09140 0.0641503i
\(23\) 2.22600 + 3.85554i 0.464153 + 0.803937i 0.999163 0.0409092i \(-0.0130255\pi\)
−0.535010 + 0.844846i \(0.679692\pi\)
\(24\) 4.23284 + 0.812527i 0.864024 + 0.165856i
\(25\) −3.11112 3.45525i −0.622224 0.691050i
\(26\) −0.752490 2.31593i −0.147576 0.454191i
\(27\) 1.89607 + 4.83786i 0.364899 + 0.931047i
\(28\) −0.228102 + 0.165726i −0.0431072 + 0.0313192i
\(29\) −6.82612 1.45094i −1.26758 0.269432i −0.475426 0.879755i \(-0.657706\pi\)
−0.792152 + 0.610323i \(0.791040\pi\)
\(30\) −0.196892 1.57318i −0.0359475 0.287222i
\(31\) 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
\(33\) 1.34127 5.58579i 0.233485 0.972360i
\(34\) −3.54993 + 6.14866i −0.608808 + 1.05449i
\(35\) −0.345788 0.251230i −0.0584489 0.0424656i
\(36\) −0.545202 + 1.03703i −0.0908670 + 0.172839i
\(37\) 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
\(39\) −2.72738 + 0.0539778i −0.436731 + 0.00864336i
\(40\) −0.985790 + 1.09483i −0.155867 + 0.173108i
\(41\) 1.12890 0.239955i 0.176304 0.0374747i −0.118913 0.992905i \(-0.537941\pi\)
0.295218 + 0.955430i \(0.404608\pi\)
\(42\) 0.633712 + 1.82657i 0.0977839 + 0.281845i
\(43\) 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
\(45\) −1.75053 0.300244i −0.260954 0.0447577i
\(46\) 5.56879 + 4.04596i 0.821073 + 0.596544i
\(47\) −0.152264 0.169107i −0.0222100 0.0246667i 0.731937 0.681372i \(-0.238616\pi\)
−0.754147 + 0.656705i \(0.771950\pi\)
\(48\) 7.80719 1.82164i 1.12687 0.262932i
\(49\) −5.91867 2.63516i −0.845524 0.376451i
\(50\) −6.56726 2.92393i −0.928751 0.413506i
\(51\) 5.43790 + 5.80420i 0.761458 + 0.812750i
\(52\) −0.411571 0.457096i −0.0570747 0.0633878i
\(53\) 4.61430 + 3.35249i 0.633823 + 0.460500i 0.857723 0.514113i \(-0.171879\pi\)
−0.223899 + 0.974612i \(0.571879\pi\)
\(54\) 5.72053 + 5.64093i 0.778465 + 0.767634i
\(55\) 1.39723 + 1.37959i 0.188402 + 0.186024i
\(56\) 0.898268 1.55585i 0.120036 0.207909i
\(57\) −4.26712 0.819107i −0.565193 0.108493i
\(58\) −10.5541 + 2.24335i −1.38582 + 0.294566i
\(59\) 4.77328 5.30126i 0.621428 0.690166i −0.347452 0.937698i \(-0.612953\pi\)
0.968880 + 0.247532i \(0.0796196\pi\)
\(60\) −0.207058 0.342787i −0.0267311 0.0442536i
\(61\) −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
\(63\) 2.16416 0.0856954i 0.272658 0.0107966i
\(64\) −4.76295 3.46049i −0.595369 0.432561i
\(65\) 0.466215 0.807507i 0.0578268 0.100159i
\(66\) −1.61824 8.73322i −0.199191 1.07498i
\(67\) 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
\(69\) 6.14750 4.65502i 0.740072 0.560398i
\(70\) −0.646405 0.137398i −0.0772602 0.0164222i
\(71\) 9.95852 7.23528i 1.18186 0.858670i 0.189478 0.981885i \(-0.439320\pi\)
0.992380 + 0.123215i \(0.0393203\pi\)
\(72\) 0.485970 7.44951i 0.0572721 0.877933i
\(73\) 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
\(75\) −5.26915 + 6.09012i −0.608429 + 0.703227i
\(76\) −0.489852 0.848448i −0.0561899 0.0973237i
\(77\) −2.01639 1.29133i −0.229789 0.147160i
\(78\) −3.81839 + 1.79141i −0.432348 + 0.202838i
\(79\) −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
\(81\) 7.90672 4.29928i 0.878524 0.477698i
\(82\) 1.44363 1.04886i 0.159422 0.115827i
\(83\) 0.726787 + 6.91491i 0.0797752 + 0.759010i 0.959153 + 0.282886i \(0.0912920\pi\)
−0.879378 + 0.476124i \(0.842041\pi\)
\(84\) 0.333887 + 0.356378i 0.0364301 + 0.0388840i
\(85\) −2.65920 + 0.565231i −0.288431 + 0.0613079i
\(86\) 0.681124 6.48047i 0.0734475 0.698807i
\(87\) −1.02536 + 12.0438i −0.109930 + 1.29123i
\(88\) −5.15310 + 6.44683i −0.549322 + 0.687235i
\(89\) 12.4803 1.32291 0.661453 0.749986i \(-0.269940\pi\)
0.661453 + 0.749986i \(0.269940\pi\)
\(90\) −2.66138 + 0.676775i −0.280535 + 0.0713384i
\(91\) −0.351367 + 1.08140i −0.0368332 + 0.113361i
\(92\) 1.70068 + 0.361491i 0.177308 + 0.0376880i
\(93\) −15.8075 + 0.312847i −1.63916 + 0.0324407i
\(94\) −0.321414 0.143103i −0.0331514 0.0147599i
\(95\) 0.993774 1.10370i 0.101959 0.113237i
\(96\) 3.00952 2.27887i 0.307158 0.232586i
\(97\) 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
\(99\) −9.88847 1.10367i −0.993829 0.110923i
\(100\) −1.81581 −0.181581
\(101\) −13.1263 + 5.84421i −1.30612 + 0.581521i −0.937476 0.348051i \(-0.886844\pi\)
−0.368641 + 0.929572i \(0.620177\pi\)
\(102\) 11.3309 + 4.77850i 1.12193 + 0.473142i
\(103\) −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
\(105\) −0.357396 + 0.648325i −0.0348783 + 0.0632701i
\(106\) 8.62583 + 1.83348i 0.837815 + 0.178083i
\(107\) −4.86529 + 14.9738i −0.470345 + 1.44757i 0.381788 + 0.924250i \(0.375308\pi\)
−0.852134 + 0.523324i \(0.824692\pi\)
\(108\) 1.89956 + 0.713945i 0.182785 + 0.0686994i
\(109\) −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
\(111\) 4.53435 2.12731i 0.430381 0.201915i
\(112\) 0.349291 3.32328i 0.0330049 0.314021i
\(113\) −7.85465 + 1.66956i −0.738904 + 0.157059i −0.561963 0.827163i \(-0.689954\pi\)
−0.176941 + 0.984221i \(0.556620\pi\)
\(114\) −6.54227 + 1.52650i −0.612740 + 0.142970i
\(115\) 0.275508 + 2.62129i 0.0256913 + 0.244436i
\(116\) −2.20491 + 1.60196i −0.204721 + 0.148738i
\(117\) 0.679423 + 4.67579i 0.0628127 + 0.432277i
\(118\) 3.40829 10.4896i 0.313758 0.965648i
\(119\) 3.02858 1.34841i 0.277630 0.123609i
\(120\) 2.09367 + 1.45873i 0.191125 + 0.133163i
\(121\) 8.26742 + 7.25602i 0.751583 + 0.659638i
\(122\) −3.52438 6.10441i −0.319083 0.552668i
\(123\) −0.655221 1.88856i −0.0590792 0.170286i
\(124\) −2.38540 2.64926i −0.214215 0.237910i
\(125\) −1.76536 5.43321i −0.157898 0.485961i
\(126\) 3.00290 1.48202i 0.267520 0.132028i
\(127\) 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
\(129\) −6.72605 2.83652i −0.592195 0.249742i
\(130\) 0.150695 1.43377i 0.0132168 0.125750i
\(131\) 3.44555 + 5.96786i 0.301039 + 0.521414i 0.976372 0.216099i \(-0.0693333\pi\)
−0.675333 + 0.737513i \(0.736000\pi\)
\(132\) −1.27064 1.84895i −0.110595 0.160931i
\(133\) −0.905543 + 1.56845i −0.0785205 + 0.136002i
\(134\) 10.1212 + 7.35345i 0.874335 + 0.635242i
\(135\) −0.139475 + 3.07312i −0.0120041 + 0.264492i
\(136\) −3.53112 10.8677i −0.302791 0.931896i
\(137\) −0.966528 9.19590i −0.0825760 0.785658i −0.954939 0.296801i \(-0.904080\pi\)
0.872363 0.488858i \(-0.162586\pi\)
\(138\) 5.75573 10.4410i 0.489960 0.888800i
\(139\) 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
\(141\) −0.257882 + 0.298062i −0.0217176 + 0.0251014i
\(142\) 9.51601 16.4822i 0.798566 1.38316i
\(143\) 2.34184 4.66920i 0.195835 0.390458i
\(144\) −4.81007 13.0259i −0.400839 1.08549i
\(145\) −3.34251 2.42847i −0.277580 0.201674i
\(146\) 16.0185 + 17.7904i 1.32570 + 1.47234i
\(147\) −3.25581 + 10.7389i −0.268534 + 0.885729i
\(148\) 1.03168 + 0.459335i 0.0848038 + 0.0377571i
\(149\) −1.04732 0.466296i −0.0857996 0.0382005i 0.363388 0.931638i \(-0.381620\pi\)
−0.449188 + 0.893437i \(0.648287\pi\)
\(150\) −3.61259 + 11.9157i −0.294967 + 0.972913i
\(151\) 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
\(153\) 8.80566 10.5943i 0.711896 0.856496i
\(154\) −3.66015 0.555908i −0.294944 0.0447963i
\(155\) 2.70211 4.68018i 0.217038 0.375921i
\(156\) −0.697057 + 0.805664i −0.0558092 + 0.0645048i
\(157\) 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
\(159\) 4.76920 8.65145i 0.378222 0.686105i
\(160\) 0.134876 + 1.28326i 0.0106629 + 0.101450i
\(161\) −0.993219 3.05681i −0.0782766 0.240911i
\(162\) 8.46427 11.0449i 0.665016 0.867769i
\(163\) −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
\(165\) 2.07049 2.69808i 0.161187 0.210045i
\(166\) 5.37515 + 9.31002i 0.417192 + 0.722598i
\(167\) 1.77566 16.8943i 0.137405 1.30732i −0.680831 0.732440i \(-0.738381\pi\)
0.818236 0.574882i \(-0.194952\pi\)
\(168\) −2.86716 1.20914i −0.221206 0.0932874i
\(169\) 10.2896 + 2.18712i 0.791509 + 0.168240i
\(170\) −3.40058 + 2.47066i −0.260812 + 0.189491i
\(171\) −0.489905 + 7.50984i −0.0374640 + 0.574292i
\(172\) −0.508616 1.56536i −0.0387816 0.119357i
\(173\) −0.395493 0.439240i −0.0300688 0.0333948i 0.727923 0.685659i \(-0.240486\pi\)
−0.757992 + 0.652264i \(0.773819\pi\)
\(174\) 6.12568 + 17.6562i 0.464386 + 1.33851i
\(175\) 1.67835 + 2.90699i 0.126872 + 0.219748i
\(176\) −3.87893 + 14.8530i −0.292385 + 1.11959i
\(177\) −10.1377 7.06327i −0.761996 0.530908i
\(178\) 17.6280 7.84848i 1.32127 0.588268i
\(179\) −2.97921 + 9.16907i −0.222677 + 0.685328i 0.775842 + 0.630927i \(0.217325\pi\)
−0.998519 + 0.0544017i \(0.982675\pi\)
\(180\) −0.544590 + 0.429591i −0.0405913 + 0.0320198i
\(181\) 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
\(183\) −7.68979 + 1.79425i −0.568446 + 0.132635i
\(184\) −10.8365 + 2.30336i −0.798875 + 0.169806i
\(185\) −0.178950 + 1.70260i −0.0131567 + 0.125178i
\(186\) −22.1308 + 10.3827i −1.62271 + 0.761300i
\(187\) −14.6857 + 4.03514i −1.07392 + 0.295079i
\(188\) −0.0888691 −0.00648144
\(189\) −0.612785 3.70098i −0.0445735 0.269206i
\(190\) 0.709589 2.18389i 0.0514790 0.158436i
\(191\) 5.08444 + 1.08073i 0.367897 + 0.0781989i 0.388151 0.921596i \(-0.373114\pi\)
−0.0202537 + 0.999795i \(0.506447\pi\)
\(192\) −4.92284 + 8.93016i −0.355275 + 0.644479i
\(193\) 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
\(195\) −1.48810 0.627563i −0.106565 0.0449407i
\(196\) −2.31146 + 1.02913i −0.165105 + 0.0735093i
\(197\) −22.4626 −1.60039 −0.800197 0.599737i \(-0.795272\pi\)
−0.800197 + 0.599737i \(0.795272\pi\)
\(198\) −14.6612 + 4.65967i −1.04193 + 0.331148i
\(199\) −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
\(201\) 11.1730 8.46040i 0.788079 0.596751i
\(202\) −14.8652 + 16.5095i −1.04591 + 1.16160i
\(203\) 4.60264 + 2.04923i 0.323042 + 0.143828i
\(204\) 3.10557 0.0614624i 0.217433 0.00430323i
\(205\) 0.668344 + 0.142061i 0.0466792 + 0.00992197i
\(206\) −2.11603 + 6.51246i −0.147431 + 0.453745i
\(207\) −9.32262 9.56406i −0.647967 0.664748i
\(208\) 7.28981 0.505457
\(209\) 5.19483 6.49904i 0.359334 0.449548i
\(210\) −0.0970972 + 1.14049i −0.00670034 + 0.0787015i
\(211\) −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
\(213\) −14.5769 15.5588i −0.998794 1.06607i
\(214\) 2.54454 + 24.2096i 0.173941 + 1.65494i
\(215\) 2.01858 1.46659i 0.137666 0.100020i
\(216\) −12.9076 + 0.767165i −0.878249 + 0.0521989i
\(217\) −2.03646 + 6.26759i −0.138244 + 0.425472i
\(218\) −19.3466 + 8.61366i −1.31032 + 0.583390i
\(219\) 24.2787 11.3905i 1.64061 0.769696i
\(220\) 0.765519 0.0449957i 0.0516113 0.00303361i
\(221\) 3.61612 + 6.26330i 0.243247 + 0.421315i
\(222\) 5.06681 5.85626i 0.340062 0.393047i
\(223\) −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
\(225\) 11.6001 + 7.74581i 0.773342 + 0.516387i
\(226\) −10.0445 + 7.29775i −0.668150 + 0.485439i
\(227\) 5.83650 + 1.24059i 0.387382 + 0.0823406i 0.397486 0.917608i \(-0.369883\pi\)
−0.0101037 + 0.999949i \(0.503216\pi\)
\(228\) −1.35281 + 1.02438i −0.0895923 + 0.0678412i
\(229\) −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
\(231\) −1.78561 + 3.74321i −0.117484 + 0.246285i
\(232\) 8.68297 15.0393i 0.570065 0.987381i
\(233\) −3.38850 2.46189i −0.221988 0.161284i 0.471233 0.882009i \(-0.343809\pi\)
−0.693221 + 0.720725i \(0.743809\pi\)
\(234\) 3.90013 + 6.17712i 0.254959 + 0.403811i
\(235\) −0.0416308 0.128126i −0.00271569 0.00835805i
\(236\) −0.291208 2.77066i −0.0189560 0.180355i
\(237\) 13.0923 + 21.6745i 0.850439 + 1.40791i
\(238\) 3.42980 3.80917i 0.222321 0.246912i
\(239\) 7.21173 1.53290i 0.466488 0.0991551i 0.0313298 0.999509i \(-0.490026\pi\)
0.435158 + 0.900354i \(0.356692\pi\)
\(240\) 4.66116 + 0.894747i 0.300876 + 0.0577556i
\(241\) 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
\(243\) −9.08965 12.6641i −0.583101 0.812399i
\(244\) −1.44041 1.04652i −0.0922129 0.0669966i
\(245\) −2.56655 2.85044i −0.163971 0.182108i
\(246\) −2.11314 2.25548i −0.134729 0.143804i
\(247\) −3.60938 1.60700i −0.229659 0.102251i
\(248\) 20.7513 + 9.23908i 1.31771 + 0.586682i
\(249\) 11.7279 2.73647i 0.743228 0.173417i
\(250\) −5.91029 6.56404i −0.373799 0.415146i
\(251\) −16.6439 12.0925i −1.05056 0.763274i −0.0782385 0.996935i \(-0.524930\pi\)
−0.972318 + 0.233661i \(0.924930\pi\)
\(252\) 0.540668 0.650489i 0.0340589 0.0409770i
\(253\) 2.40242 + 14.5689i 0.151039 + 0.915936i
\(254\) 9.27397 16.0630i 0.581901 1.00788i
\(255\) 1.54342 + 4.44864i 0.0966527 + 0.278585i
\(256\) −8.84127 + 1.87927i −0.552579 + 0.117454i
\(257\) −2.26326 + 2.51360i −0.141178 + 0.156794i −0.809587 0.587000i \(-0.800309\pi\)
0.668409 + 0.743794i \(0.266976\pi\)
\(258\) −11.2841 + 0.223324i −0.702518 + 0.0139036i
\(259\) −0.218220 2.07623i −0.0135595 0.129010i
\(260\) −0.112528 0.346326i −0.00697871 0.0214783i
\(261\) 20.9195 0.828361i 1.29488 0.0512742i
\(262\) 8.61973 + 6.26260i 0.532528 + 0.386905i
\(263\) 7.14112 12.3688i 0.440341 0.762692i −0.557374 0.830262i \(-0.688191\pi\)
0.997715 + 0.0675692i \(0.0215244\pi\)
\(264\) 12.1882 + 7.46964i 0.750133 + 0.459724i
\(265\) 1.68836 + 2.92432i 0.103715 + 0.179639i
\(266\) −0.292699 + 2.78485i −0.0179465 + 0.170750i
\(267\) −2.68448 21.4491i −0.164288 1.31267i
\(268\) 3.09095 + 0.657003i 0.188810 + 0.0401328i
\(269\) −5.43693 + 3.95016i −0.331495 + 0.240845i −0.741065 0.671433i \(-0.765679\pi\)
0.409570 + 0.912279i \(0.365679\pi\)
\(270\) 1.73559 + 4.42840i 0.105625 + 0.269504i
\(271\) −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
\(273\) 1.93411 + 0.371268i 0.117058 + 0.0224702i
\(274\) −7.14821 12.3811i −0.431839 0.747968i
\(275\) −5.61758 14.3610i −0.338753 0.866002i
\(276\) 0.255461 3.00062i 0.0153769 0.180616i
\(277\) −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
\(279\) 3.93783 + 27.1001i 0.235751 + 1.62244i
\(280\) 0.860476 0.625172i 0.0514233 0.0373612i
\(281\) 0.310227 + 2.95161i 0.0185066 + 0.176078i 0.999871 0.0160790i \(-0.00511831\pi\)
−0.981364 + 0.192157i \(0.938452\pi\)
\(282\) −0.176807 + 0.583178i −0.0105287 + 0.0347277i
\(283\) −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
\(285\) −2.11062 1.47054i −0.125022 0.0871072i
\(286\) 0.371456 8.06780i 0.0219646 0.477059i
\(287\) −0.833217 −0.0491833
\(288\) −4.56391 4.68210i −0.268931 0.275896i
\(289\) 1.26279 3.88648i 0.0742820 0.228616i
\(290\) −6.24837 1.32813i −0.366917 0.0779906i
\(291\) −12.6991 21.0235i −0.744436 1.23242i
\(292\) 5.52405 + 2.45947i 0.323271 + 0.143929i
\(293\) −10.5158 + 11.6789i −0.614338 + 0.682292i −0.967384 0.253314i \(-0.918479\pi\)
0.353046 + 0.935606i \(0.385146\pi\)
\(294\) 2.15465 + 17.2158i 0.125662 + 1.00405i
\(295\) 3.85817 1.71777i 0.224631 0.100012i
\(296\) −7.19584 −0.418249
\(297\) 0.230168 + 17.2322i 0.0133557 + 0.999911i
\(298\) −1.77254 −0.102681
\(299\) 6.40554 2.85193i 0.370442 0.164931i
\(300\) 0.390576 + 3.12072i 0.0225499 + 0.180175i
\(301\) −2.03593 + 2.26113i −0.117349 + 0.130329i
\(302\) 1.24387 + 0.553809i 0.0715769 + 0.0318681i
\(303\) 12.8676 + 21.3024i 0.739222 + 1.22379i
\(304\) 11.3575 + 2.41410i 0.651395 + 0.138458i
\(305\) 0.834052 2.56695i 0.0477577 0.146983i
\(306\) 5.77528 20.5017i 0.330151 1.17200i
\(307\) −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
\(309\) 6.29397 + 4.38522i 0.358051 + 0.249466i
\(310\) 0.873403 8.30987i 0.0496060 0.471969i
\(311\) −25.7589 + 5.47523i −1.46066 + 0.310472i −0.868636 0.495451i \(-0.835003\pi\)
−0.592020 + 0.805923i \(0.701669\pi\)
\(312\) 1.96954 6.49628i 0.111503 0.367780i
\(313\) 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
\(315\) 1.19112 + 0.474783i 0.0671117 + 0.0267510i
\(316\) −1.76433 + 5.43005i −0.0992513 + 0.305464i
\(317\) −24.2155 + 10.7814i −1.36008 + 0.605545i −0.951633 0.307238i \(-0.900595\pi\)
−0.408444 + 0.912783i \(0.633929\pi\)
\(318\) 1.29569 15.2191i 0.0726589 0.853444i
\(319\) −19.4911 12.4824i −1.09129 0.698880i
\(320\) −1.74274 3.01852i −0.0974224 0.168741i
\(321\) 26.7812 + 5.14086i 1.49478 + 0.286935i
\(322\) −3.32523 3.69304i −0.185308 0.205805i
\(323\) 3.55972 + 10.9557i 0.198068 + 0.609591i
\(324\) 0.818425 3.41823i 0.0454681 0.189902i
\(325\) −5.92427 + 4.30423i −0.328619 + 0.238756i
\(326\) −7.00182 1.48828i −0.387795 0.0824283i
\(327\) 2.94620 + 23.5403i 0.162925 + 1.30178i
\(328\) −0.300202 + 2.85623i −0.0165759 + 0.157709i
\(329\) 0.0821419 + 0.142274i 0.00452863 + 0.00784382i
\(330\) 1.22775 5.11302i 0.0675853 0.281462i
\(331\) −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
\(333\) −4.63141 7.33534i −0.253799 0.401974i
\(334\) −8.11627 24.9793i −0.444103 1.36681i
\(335\) 0.500731 + 4.76414i 0.0273579 + 0.260293i
\(336\) −5.78667 + 0.114524i −0.315689 + 0.00624781i
\(337\) 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
\(339\) 4.55889 + 13.1402i 0.247605 + 0.713679i
\(340\) −0.530861 + 0.919478i −0.0287900 + 0.0498657i
\(341\) 13.5730 27.0619i 0.735017 1.46549i
\(342\) 4.03074 + 10.9155i 0.217957 + 0.590241i
\(343\) 7.87256 + 5.71975i 0.425078 + 0.308837i
\(344\) 7.01752 + 7.79374i 0.378359 + 0.420210i
\(345\) 4.44579 1.03733i 0.239354 0.0558482i
\(346\) −0.834846 0.371697i −0.0448816 0.0199826i
\(347\) −1.89071 0.841800i −0.101499 0.0451902i 0.355359 0.934730i \(-0.384359\pi\)
−0.456858 + 0.889540i \(0.651025\pi\)
\(348\) 3.22747 + 3.44487i 0.173010 + 0.184665i
\(349\) −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
\(351\) 7.88987 2.17344i 0.421130 0.116009i
\(352\) 1.17611 + 7.13221i 0.0626868 + 0.380148i
\(353\) −10.8363 + 18.7689i −0.576756 + 0.998970i 0.419093 + 0.907943i \(0.362348\pi\)
−0.995848 + 0.0910266i \(0.970985\pi\)
\(354\) −18.7610 3.60133i −0.997138 0.191409i
\(355\) 7.12831 1.51517i 0.378331 0.0804168i
\(356\) 3.26136 3.62211i 0.172852 0.191971i
\(357\) −2.96888 4.91501i −0.157130 0.260130i
\(358\) 1.55812 + 14.8245i 0.0823493 + 0.783501i
\(359\) 2.70478 + 8.32446i 0.142753 + 0.439348i 0.996715 0.0809868i \(-0.0258072\pi\)
−0.853962 + 0.520335i \(0.825807\pi\)
\(360\) 2.05669 3.91203i 0.108397 0.206182i
\(361\) 10.2801 + 7.46894i 0.541059 + 0.393102i
\(362\) 3.68125 6.37611i 0.193482 0.335121i
\(363\) 10.6922 15.7695i 0.561195 0.827684i
\(364\) 0.222030 + 0.384567i 0.0116375 + 0.0201568i
\(365\) −0.958173 + 9.11641i −0.0501531 + 0.477175i
\(366\) −9.73322 + 7.37020i −0.508763 + 0.385247i
\(367\) 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
\(369\) −3.10482 + 1.53232i −0.161631 + 0.0797692i
\(370\) 0.817952 + 2.51740i 0.0425233 + 0.130873i
\(371\) −2.75529 3.06006i −0.143047 0.158870i
\(372\) −4.04003 + 4.66950i −0.209466 + 0.242102i
\(373\) 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
\(375\) −8.95802 + 4.20269i −0.462590 + 0.217026i
\(376\) 0.517304 0.230319i 0.0266779 0.0118778i
\(377\) −3.39643 + 10.4531i −0.174925 + 0.538364i
\(378\) −3.19297 4.84214i −0.164229 0.249053i
\(379\) 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
\(381\) −14.2062 15.1631i −0.727804 0.776829i
\(382\) 7.86123 1.67096i 0.402216 0.0854936i
\(383\) 1.92059 18.2732i 0.0981378 0.933719i −0.829063 0.559155i \(-0.811126\pi\)
0.927201 0.374564i \(-0.122208\pi\)
\(384\) −1.97789 + 23.2321i −0.100934 + 1.18556i
\(385\) −0.779606 1.18396i −0.0397324 0.0603402i
\(386\) 5.05284 0.257183
\(387\) −3.42821 + 12.1698i −0.174265 + 0.618626i
\(388\) 1.71134 5.26696i 0.0868801 0.267390i
\(389\) 30.1333 + 6.40504i 1.52782 + 0.324748i 0.893764 0.448538i \(-0.148055\pi\)
0.634057 + 0.773286i \(0.281388\pi\)
\(390\) −2.49654 + 0.0494092i −0.126417 + 0.00250193i
\(391\) −18.6761 8.31516i −0.944493 0.420516i
\(392\) 10.7878 11.9811i 0.544867 0.605136i
\(393\) 9.51549 7.20534i 0.479993 0.363461i
\(394\) −31.7277 + 14.1261i −1.59842 + 0.711661i
\(395\) −8.65524 −0.435493
\(396\) −2.90438 + 2.58148i −0.145951 + 0.129724i
\(397\) −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
\(399\) 2.89038 + 1.21894i 0.144700 + 0.0610231i
\(400\) 14.4000 15.9928i 0.720000 0.799641i
\(401\) −3.59354 1.59995i −0.179453 0.0798976i 0.315044 0.949077i \(-0.397981\pi\)
−0.494497 + 0.869180i \(0.664648\pi\)
\(402\) 10.4609 18.9764i 0.521743 0.946455i
\(403\) −14.0625 2.98907i −0.700503 0.148896i
\(404\) −1.73404 + 5.33682i −0.0862716 + 0.265517i
\(405\) 5.31160 0.421314i 0.263936 0.0209353i
\(406\) 7.78977 0.386600
\(407\) −0.441104 + 9.58052i −0.0218647 + 0.474889i
\(408\) −17.9181 + 8.40636i −0.887080 + 0.416177i
\(409\) 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
\(411\) −15.5966 + 3.63913i −0.769322 + 0.179505i
\(412\) 0.180796 + 1.72016i 0.00890719 + 0.0847462i
\(413\) −4.16650 + 3.02714i −0.205020 + 0.148956i
\(414\) −19.1824 7.64619i −0.942766 0.375790i
\(415\) −1.27204 + 3.91493i −0.0624419 + 0.192176i
\(416\) 3.13585 1.39617i 0.153747 0.0684528i
\(417\) −30.7124 21.3984i −1.50399 1.04788i
\(418\) 3.25047 12.4466i 0.158986 0.608781i
\(419\) −5.36970 9.30060i −0.262327 0.454364i 0.704533 0.709672i \(-0.251157\pi\)
−0.966860 + 0.255307i \(0.917823\pi\)
\(420\) 0.0947660 + 0.273147i 0.00462411 + 0.0133282i
\(421\) 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
\(423\) 0.567733 + 0.379095i 0.0276041 + 0.0184322i
\(424\) −11.4825 + 8.34249i −0.557637 + 0.405147i
\(425\) 20.8839 + 4.43902i 1.01302 + 0.215324i
\(426\) −30.3739 12.8093i −1.47162 0.620614i
\(427\) −0.344039 + 3.27331i −0.0166492 + 0.158407i
\(428\) 3.07440 + 5.32501i 0.148606 + 0.257394i
\(429\) −8.52841 3.02046i −0.411755 0.145829i
\(430\) 1.92889 3.34093i 0.0930192 0.161114i
\(431\) 14.9330 + 10.8495i 0.719297 + 0.522600i 0.886160 0.463380i \(-0.153364\pi\)
−0.166862 + 0.985980i \(0.553364\pi\)
\(432\) −21.3523 + 11.0686i −1.02731 + 0.532540i
\(433\) 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
\(435\) −3.45471 + 6.26694i −0.165641 + 0.300477i
\(436\) −3.57932 + 3.97524i −0.171418 + 0.190379i
\(437\) 10.9242 2.32202i 0.522577 0.111077i
\(438\) 27.1298 31.3568i 1.29631 1.49829i
\(439\) −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
\(441\) 19.1566 + 3.28566i 0.912221 + 0.156460i
\(442\) 9.04645 + 6.57263i 0.430296 + 0.312628i
\(443\) 17.0613 + 18.9485i 0.810607 + 0.900270i 0.996609 0.0822794i \(-0.0262200\pi\)
−0.186003 + 0.982549i \(0.559553\pi\)
\(444\) 0.567520 1.87190i 0.0269333 0.0888363i
\(445\) 6.74993 + 3.00526i 0.319978 + 0.142463i
\(446\) −15.5744 6.93417i −0.737469 0.328342i
\(447\) −0.576121 + 1.90027i −0.0272496 + 0.0898795i
\(448\) 2.84405 + 3.15864i 0.134369 + 0.149231i
\(449\) 18.1886 + 13.2148i 0.858375 + 0.623646i 0.927442 0.373966i \(-0.122002\pi\)
−0.0690672 + 0.997612i \(0.522002\pi\)
\(450\) 21.2559 + 3.64571i 1.00201 + 0.171861i
\(451\) 3.78438 + 0.574776i 0.178200 + 0.0270651i
\(452\) −1.56804 + 2.71592i −0.0737542 + 0.127746i
\(453\) 0.998005 1.15350i 0.0468904 0.0541963i
\(454\) 9.02402 1.91812i 0.423518 0.0900216i
\(455\) −0.450437 + 0.500261i −0.0211168 + 0.0234526i
\(456\) 5.21984 9.46892i 0.244441 0.443423i
\(457\) −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
\(459\) −20.1019 12.8550i −0.938274 0.600019i
\(460\) 0.832763 + 0.605037i 0.0388278 + 0.0282100i
\(461\) 6.05182 10.4821i 0.281861 0.488198i −0.689982 0.723827i \(-0.742382\pi\)
0.971843 + 0.235629i \(0.0757149\pi\)
\(462\) −0.168116 + 6.41007i −0.00782146 + 0.298224i
\(463\) −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
\(465\) −8.62478 3.63726i −0.399965 0.168674i
\(466\) −6.33435 1.34641i −0.293433 0.0623711i
\(467\) −4.90871 + 3.56639i −0.227148 + 0.165033i −0.695538 0.718489i \(-0.744834\pi\)
0.468390 + 0.883522i \(0.344834\pi\)
\(468\) 1.53458 + 1.02470i 0.0709362 + 0.0473666i
\(469\) −1.80516 5.55570i −0.0833543 0.256538i
\(470\) −0.139377 0.154794i −0.00642898 0.00714011i
\(471\) −5.55586 16.0138i −0.256001 0.737878i
\(472\) 8.87574 + 15.3732i 0.408539 + 0.707610i
\(473\) 10.8067 8.86535i 0.496895 0.407629i
\(474\) 32.1230 + 22.3811i 1.47546 + 1.02800i
\(475\) −10.6553 + 4.74407i −0.488901 + 0.217673i
\(476\) 0.400088 1.23134i 0.0183380 0.0564385i
\(477\) −15.8946 6.33565i −0.727764 0.290089i
\(478\) 9.22233 6.70041i 0.421819 0.306470i
\(479\) −3.79154 36.0741i −0.173240 1.64827i −0.643286 0.765626i \(-0.722429\pi\)
0.470046 0.882642i \(-0.344237\pi\)
\(480\) 2.17645 0.507828i 0.0993407 0.0231791i
\(481\) 4.45480 0.946896i 0.203121 0.0431747i
\(482\) 1.42694 13.5764i 0.0649953 0.618389i
\(483\) −5.03993 + 2.36450i −0.229325 + 0.107589i
\(484\) 4.26634 0.503273i 0.193924 0.0228760i
\(485\) 8.39529 0.381211
\(486\) −20.8029 12.1713i −0.943637 0.552103i
\(487\) −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
\(489\) −3.87129 + 7.02262i −0.175066 + 0.317574i
\(490\) −5.41772 2.41213i −0.244748 0.108969i
\(491\) −22.2133 + 24.6704i −1.00247 + 1.11336i −0.00892472 + 0.999960i \(0.502841\pi\)
−0.993549 + 0.113400i \(0.963826\pi\)
\(492\) −0.719333 0.303358i −0.0324300 0.0136764i
\(493\) 29.2753 13.0342i 1.31849 0.587032i
\(494\) −6.10872 −0.274844
\(495\) −5.08240 2.97808i −0.228437 0.133855i
\(496\) 42.2506 1.89711
\(497\) −8.11848 + 3.61458i −0.364163 + 0.162136i
\(498\) 14.8444 11.2405i 0.665195 0.503700i
\(499\) 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
\(501\) −29.4172 + 0.582198i −1.31427 + 0.0260107i
\(502\) −31.1136 6.61341i −1.38867 0.295171i
\(503\) 7.20593 22.1776i 0.321297 0.988850i −0.651788 0.758401i \(-0.725981\pi\)
0.973085 0.230448i \(-0.0740193\pi\)
\(504\) −1.46137 + 5.18771i −0.0650944 + 0.231079i
\(505\) −8.50663 −0.378540
\(506\) 12.5553 + 19.0672i 0.558149 + 0.847641i
\(507\) 1.54561 18.1546i 0.0686431 0.806275i
\(508\) 0.489718 4.65935i 0.0217277 0.206725i
\(509\) −6.33958 + 1.34752i −0.280997 + 0.0597278i −0.346254 0.938141i \(-0.612547\pi\)
0.0652572 + 0.997868i \(0.479213\pi\)
\(510\) 4.97765 + 5.31294i 0.220414 + 0.235261i
\(511\) −1.16844 11.1170i −0.0516887 0.491785i
\(512\) 10.4751 7.61063i 0.462940 0.336346i
\(513\) 13.0121 0.773377i 0.574499 0.0341454i
\(514\) −1.61605 + 4.97368i −0.0712807 + 0.219379i
\(515\) −2.39534 + 1.06647i −0.105551 + 0.0469944i
\(516\) −2.58089 + 1.21083i −0.113617 + 0.0533040i
\(517\) −0.274935 0.702856i −0.0120916 0.0309116i
\(518\) −1.61390 2.79537i −0.0709109 0.122821i
\(519\) −0.669827 + 0.774192i −0.0294021 + 0.0339832i
\(520\) 1.55258 + 1.72432i 0.0680854 + 0.0756164i
\(521\) −10.2625 31.5848i −0.449610 1.38376i −0.877348 0.479855i \(-0.840689\pi\)
0.427738 0.903903i \(-0.359311\pi\)
\(522\) 29.0271 14.3257i 1.27048 0.627017i
\(523\) 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
\(525\) 4.63507 3.50978i 0.202291 0.153179i
\(526\) 2.30823 21.9613i 0.100644 0.957560i
\(527\) 20.9585 + 36.3011i 0.912965 + 1.58130i
\(528\) 26.3614 + 3.47164i 1.14723 + 0.151084i
\(529\) 1.58985 2.75370i 0.0691240 0.119726i
\(530\) 4.22376 + 3.06874i 0.183468 + 0.133298i
\(531\) −9.95864 + 18.9424i −0.432168 + 0.822029i
\(532\) 0.218567 + 0.672680i 0.00947608 + 0.0291644i
\(533\) −0.190001 1.80774i −0.00822986 0.0783019i
\(534\) −17.2805 28.6080i −0.747799 1.23799i
\(535\) −6.23710 + 6.92700i −0.269653 + 0.299480i
\(536\) −19.6951 + 4.18632i −0.850698 + 0.180821i
\(537\) 16.3992 + 3.14795i 0.707677 + 0.135844i
\(538\) −5.19534 + 8.99859i −0.223987 + 0.387957i
\(539\) −15.2903 15.0973i −0.658599 0.650287i
\(540\) 0.855454 + 0.843551i 0.0368129 + 0.0363007i
\(541\) −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
\(543\) −5.63906 6.01891i −0.241995 0.258296i
\(544\) −9.14294 4.07070i −0.392000 0.174530i
\(545\) −7.40801 3.29826i −0.317324 0.141282i
\(546\) 2.96534 0.691901i 0.126905 0.0296106i
\(547\) 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
\(549\) 4.73774 + 12.8301i 0.202202 + 0.547574i
\(550\) −16.9659 16.7517i −0.723427 0.714296i
\(551\) −8.75329 + 15.1611i −0.372902 + 0.645886i
\(552\) 6.28956 + 18.1286i 0.267701 + 0.771604i
\(553\) 10.3240 2.19442i 0.439019 0.0933164i
\(554\) −13.5859 + 15.0887i −0.577211 + 0.641058i
\(555\) 2.96465 0.0586735i 0.125842 0.00249055i
\(556\) −0.882224 8.39380i −0.0374146 0.355976i
\(557\) 3.60979 + 11.1098i 0.152952 + 0.470737i 0.997948 0.0640357i \(-0.0203972\pi\)
−0.844996 + 0.534773i \(0.820397\pi\)
\(558\) 22.6045 + 35.8016i 0.956925 + 1.51560i
\(559\) −5.36998 3.90152i −0.227126 0.165017i
\(560\) 0.989164 1.71328i 0.0417998 0.0723994i
\(561\) 10.0938 + 24.3715i 0.426162 + 1.02896i
\(562\) 2.29436 + 3.97396i 0.0967819 + 0.167631i
\(563\) −0.848991 + 8.07761i −0.0357807 + 0.340431i 0.961957 + 0.273201i \(0.0880825\pi\)
−0.997738 + 0.0672292i \(0.978584\pi\)
\(564\) 0.0191155 + 0.152734i 0.000804910 + 0.00643127i
\(565\) −4.65021 0.988432i −0.195636 0.0415836i
\(566\) −10.1229 + 7.35468i −0.425495 + 0.309140i
\(567\) −6.22885 + 1.84923i −0.261587 + 0.0776604i
\(568\) 9.46559 + 29.1321i 0.397167 + 1.22236i
\(569\) −12.0488 13.3815i −0.505111 0.560983i 0.435622 0.900129i \(-0.356528\pi\)
−0.940733 + 0.339147i \(0.889862\pi\)
\(570\) −3.90596 0.749780i −0.163603 0.0314048i
\(571\) 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
\(573\) 0.763738 8.97079i 0.0319056 0.374760i
\(574\) −1.17689 + 0.523986i −0.0491225 + 0.0218707i
\(575\) 6.39652 19.6865i 0.266753 0.820982i
\(576\) 16.4066 + 6.53975i 0.683610 + 0.272489i
\(577\) −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
\(579\) 1.64230 5.41694i 0.0682517 0.225120i
\(580\) −1.57827 + 0.335473i −0.0655343 + 0.0139297i
\(581\) 0.524704 4.99223i 0.0217684 0.207112i
\(582\) −31.1582 21.7089i −1.29155 0.899864i
\(583\) 10.4033 + 15.7991i 0.430861 + 0.654333i
\(584\) −38.5294 −1.59436
\(585\) −0.758471 + 2.69250i −0.0313589 + 0.111321i
\(586\) −7.50863 + 23.1092i −0.310179 + 0.954631i
\(587\) −23.0377 4.89682i −0.950869 0.202113i −0.293735 0.955887i \(-0.594898\pi\)
−0.657134 + 0.753774i \(0.728232\pi\)
\(588\) 2.26590 + 3.75122i 0.0934441 + 0.154698i
\(589\) −20.9194 9.31391i −0.861968 0.383773i
\(590\) 4.36928 4.85258i 0.179880 0.199777i
\(591\) 4.83166 + 38.6052i 0.198748 + 1.58801i
\(592\) −12.2272 + 5.44392i −0.502536 + 0.223744i
\(593\) 13.1828 0.541354 0.270677 0.962670i \(-0.412752\pi\)
0.270677 + 0.962670i \(0.412752\pi\)
\(594\) 11.1619 + 24.1951i 0.457978 + 0.992736i
\(595\) 1.96270 0.0804630
\(596\) −0.409018 + 0.182106i −0.0167540 + 0.00745937i
\(597\) 4.48030 + 35.7978i 0.183366 + 1.46511i
\(598\) 7.25412 8.05651i 0.296643 0.329455i
\(599\) 31.2582 + 13.9171i 1.27718 + 0.568636i 0.929446 0.368958i \(-0.120285\pi\)
0.347731 + 0.937594i \(0.386952\pi\)
\(600\) −10.3614 17.1534i −0.423002 0.700284i
\(601\) −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
\(603\) −16.9437 17.3825i −0.690000 0.707870i
\(604\) 0.343924 0.0139941
\(605\) 2.72416 + 5.91521i 0.110753 + 0.240487i
\(606\) 31.5714 + 21.9968i 1.28250 + 0.893561i
\(607\) 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
\(609\) 2.53187 8.35108i 0.102597 0.338403i
\(610\) −0.436207 4.15024i −0.0176615 0.168038i
\(611\) −0.289945 + 0.210657i −0.0117299 + 0.00852229i
\(612\) −0.773633 5.32414i −0.0312723 0.215216i
\(613\) 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
\(615\) 0.100393 1.17920i 0.00404822 0.0475500i
\(616\) 4.60667 3.77910i 0.185608 0.152264i
\(617\) 10.8039 + 18.7129i 0.434948 + 0.753351i 0.997291 0.0735523i \(-0.0234336\pi\)
−0.562344 + 0.826904i \(0.690100\pi\)
\(618\) 11.6478 + 2.23588i 0.468541 + 0.0899403i
\(619\) 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
\(621\) −14.4319 + 18.0795i −0.579134 + 0.725504i
\(622\) −32.9404 + 23.9326i −1.32079 + 0.959611i
\(623\) −8.81325 1.87331i −0.353095 0.0750527i
\(624\) −1.56802 12.5286i −0.0627711 0.501545i
\(625\) −2.07649 + 19.7565i −0.0830597 + 0.790260i
\(626\) 1.90263 + 3.29545i 0.0760444 + 0.131713i
\(627\) −12.2869 7.53013i −0.490693 0.300724i
\(628\) 1.91094 3.30985i 0.0762550 0.132078i
\(629\) −10.7427 7.80501i −0.428339 0.311206i
\(630\) 1.98099 0.0784423i 0.0789244 0.00312522i
\(631\) 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
\(633\) 5.87401 0.116253i 0.233471 0.00462063i
\(634\) −27.4234 + 30.4568i −1.08912 + 1.20959i
\(635\) 6.94700 1.47663i 0.275683 0.0585983i
\(636\) −1.26459 3.64495i −0.0501441 0.144532i
\(637\) −5.10193 + 8.83680i −0.202146 + 0.350127i
\(638\) −35.3803 5.37360i −1.40072 0.212743i
\(639\) −23.6046 + 28.3992i −0.933784 + 1.12345i
\(640\) −6.44762 4.68447i −0.254864 0.185170i
\(641\) −25.5073 28.3287i −1.00748 1.11892i −0.992891 0.119024i \(-0.962024\pi\)
−0.0145863 0.999894i \(-0.504643\pi\)
\(642\) 41.0604 9.58059i 1.62053 0.378116i
\(643\) −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
\(645\) −2.95473 3.15377i −0.116342 0.124179i
\(646\) 11.9177 + 13.2359i 0.468895 + 0.520761i
\(647\) 16.9687 + 12.3285i 0.667109 + 0.484683i 0.869056 0.494713i \(-0.164727\pi\)
−0.201947 + 0.979396i \(0.564727\pi\)
\(648\) 4.09487 + 22.0185i 0.160862 + 0.864968i
\(649\) 21.0120 10.8748i 0.824792 0.426872i
\(650\) −5.66102 + 9.80517i −0.222043 + 0.384591i
\(651\) 11.2098 + 2.15181i 0.439346 + 0.0843361i
\(652\) −1.76859 + 0.375925i −0.0692632 + 0.0147223i
\(653\) 13.2264 14.6894i 0.517587 0.574839i −0.426520 0.904478i \(-0.640261\pi\)
0.944107 + 0.329639i \(0.106927\pi\)
\(654\) 18.9652 + 31.3971i 0.741598 + 1.22772i
\(655\) 0.426450 + 4.05740i 0.0166628 + 0.158536i
\(656\) 1.65074 + 5.08046i 0.0644506 + 0.198358i
\(657\) −24.7984 39.2764i −0.967479 1.53232i
\(658\) 0.205494 + 0.149300i 0.00801101 + 0.00582034i
\(659\) 5.90277 10.2239i 0.229939 0.398267i −0.727851 0.685736i \(-0.759481\pi\)
0.957790 + 0.287469i \(0.0928139\pi\)
\(660\) −0.241993 1.30598i −0.00941956 0.0508350i
\(661\) −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
\(663\) 9.98656 7.56204i 0.387846 0.293685i
\(664\) −16.9241 3.59733i −0.656782 0.139603i
\(665\) −0.867445 + 0.630235i −0.0336381 + 0.0244395i
\(666\) −11.1547 7.44837i −0.432235 0.288618i
\(667\) −9.60079 29.5482i −0.371744 1.14411i
\(668\) −4.43916 4.93019i −0.171756 0.190755i
\(669\) −12.4959 + 14.4429i −0.483119 + 0.558393i
\(670\) 3.70329 + 6.41429i 0.143071 + 0.247806i
\(671\) 3.82060 14.6297i 0.147493 0.564773i
\(672\) −2.46731 + 1.15755i −0.0951784 + 0.0446533i
\(673\) 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
\(675\) 10.8171 21.6026i 0.416351 0.831484i
\(676\) 3.32365 2.41477i 0.127833 0.0928760i
\(677\) 1.29761 + 12.3459i 0.0498711 + 0.474492i 0.990745 + 0.135735i \(0.0433396\pi\)
−0.940874 + 0.338757i \(0.889994\pi\)
\(678\) 14.7028 + 15.6932i 0.564657 + 0.602693i
\(679\) −10.0139 + 2.12852i −0.384297 + 0.0816850i
\(680\) 0.707148 6.72806i 0.0271179 0.258010i
\(681\) 0.876706 10.2977i 0.0335955 0.394609i
\(682\) 2.15290 46.7597i 0.0824387 1.79052i
\(683\) 2.02837 0.0776135 0.0388068 0.999247i \(-0.487644\pi\)
0.0388068 + 0.999247i \(0.487644\pi\)
\(684\) 2.05153 + 2.10466i 0.0784422 + 0.0804738i
\(685\) 1.69164 5.20632i 0.0646341 0.198923i
\(686\) 14.7167 + 3.12813i 0.561886 + 0.119433i
\(687\) 42.8610 0.848265i 1.63525 0.0323633i
\(688\) 17.8205 + 7.93420i 0.679400 + 0.302488i
\(689\) 6.01077 6.67564i 0.228992 0.254322i
\(690\) 5.62719 4.26103i 0.214223 0.162215i
\(691\) 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
\(693\) 6.81732 + 2.26366i 0.258969 + 0.0859895i
\(694\) −3.19995 −0.121469
\(695\) 11.6884 5.20402i 0.443367 0.197400i
\(696\) −27.7149 11.6880i −1.05053 0.443032i
\(697\) −3.54620 + 3.93846i −0.134322 + 0.149180i
\(698\) −7.36497 3.27910i −0.278768 0.124116i
\(699\) −3.50225 + 6.35317i −0.132467 + 0.240299i
\(700\) 1.28228 + 0.272556i 0.0484655 + 0.0103016i
\(701\) −1.37008 + 4.21668i −0.0517473 + 0.159262i −0.973591 0.228301i \(-0.926683\pi\)
0.921843 + 0.387563i \(0.126683\pi\)
\(702\) 9.77736 8.03161i 0.369023 0.303134i
\(703\) 7.25411 0.273594
\(704\) −10.7384 16.3081i −0.404720 0.614634i
\(705\) −0.211249 + 0.0991082i −0.00795609 + 0.00373263i
\(706\) −3.50261 + 33.3251i −0.131822 + 1.25421i
\(707\) 10.1467 2.15675i 0.381606 0.0811128i
\(708\) −4.69914 + 1.09645i −0.176605 + 0.0412070i
\(709\) −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
\(711\) 34.4346 27.1632i 1.29140 1.01870i
\(712\) −9.59699 + 29.5365i −0.359662 + 1.10693i
\(713\) 37.1255 16.5293i 1.39036 0.619029i
\(714\) −7.28435 5.07525i −0.272610 0.189936i
\(715\) 2.39093 1.96141i 0.0894157 0.0733525i
\(716\) 1.88258 + 3.26072i 0.0703551 + 0.121859i
\(717\) −4.18574 12.0647i −0.156319 0.450563i
\(718\) 9.05541 + 10.0571i 0.337945 + 0.375326i
\(719\) −6.68469 20.5734i −0.249297 0.767257i −0.994900 0.100867i \(-0.967838\pi\)
0.745603 0.666390i \(-0.232162\pi\)
\(720\) 0.535145 8.20332i 0.0199437 0.305720i
\(721\) 2.58676 1.87939i 0.0963360 0.0699922i
\(722\) 19.2173 + 4.08477i 0.715194 + 0.152019i
\(723\) −14.0909 5.94244i −0.524046 0.221002i
\(724\) 0.194391 1.84950i 0.00722447 0.0687363i
\(725\) 16.2235 + 28.1000i 0.602527 + 1.04361i
\(726\) 5.18540 28.9979i 0.192448 1.07621i
\(727\) 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
\(729\) −19.8098 + 18.3459i −0.733697 + 0.679477i
\(730\) 4.37965 + 13.4792i 0.162098 + 0.498887i
\(731\) 2.02293 + 19.2469i 0.0748207 + 0.711872i
\(732\) −1.48876 + 2.70066i −0.0550263 + 0.0998191i
\(733\) −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
\(735\) −4.34683 + 5.02411i −0.160335 + 0.185317i
\(736\) −4.85153 + 8.40310i −0.178830 + 0.309742i
\(737\) 4.36635 + 26.4786i 0.160837 + 0.975352i
\(738\) −3.42183 + 4.11688i −0.125959 + 0.151544i
\(739\) 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
\(741\) −1.98549 + 6.54889i −0.0729387 + 0.240580i
\(742\) −5.81613 2.58951i −0.213517 0.0950638i
\(743\) −19.9810 8.89609i −0.733030 0.326366i 0.00605180 0.999982i \(-0.498074\pi\)
−0.739082 + 0.673616i \(0.764740\pi\)
\(744\) 11.4151 37.6514i 0.418499 1.38037i
\(745\) −0.454155 0.504391i −0.0166390 0.0184794i
\(746\) 27.3853 + 19.8966i 1.00265 + 0.728466i
\(747\) −7.22567 19.5675i −0.264373 0.715938i
\(748\) −2.66657 + 5.31664i −0.0974994 + 0.194395i
\(749\) 5.68334 9.84384i 0.207665 0.359686i
\(750\) −10.0099 + 11.5696i −0.365512 + 0.422461i
\(751\) −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
\(753\) −17.2027 + 31.2061i −0.626900 + 1.13721i
\(754\) 1.77633 + 16.9006i 0.0646900 + 0.615484i
\(755\) 0.161111 + 0.495850i 0.00586344 + 0.0180458i
\(756\) −1.23425 0.789297i −0.0448894 0.0287064i
\(757\) −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
\(759\) 24.5219 7.26263i 0.890089 0.263617i
\(760\) 1.84789 + 3.20063i 0.0670299 + 0.116099i
\(761\) 1.55673 14.8113i 0.0564313 0.536908i −0.929389 0.369102i \(-0.879665\pi\)
0.985820 0.167806i \(-0.0536682\pi\)
\(762\) −29.6013 12.4835i −1.07234 0.452230i
\(763\) 9.67249 + 2.05595i 0.350168 + 0.0744304i
\(764\) 1.64233 1.19322i 0.0594173 0.0431692i
\(765\) 7.31364 3.60948i 0.264425 0.130501i
\(766\) −8.77872 27.0181i −0.317188 0.976204i
\(767\) −7.51774 8.34930i −0.271450 0.301476i
\(768\) 5.13153 + 14.7908i 0.185168 + 0.533715i
\(769\) −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
\(771\) 4.80681 + 3.34906i 0.173113 + 0.120614i
\(772\) 1.16595 0.519116i 0.0419636 0.0186834i
\(773\) −1.87664 + 5.77569i −0.0674979 + 0.207737i −0.979117 0.203300i \(-0.934833\pi\)
0.911619 + 0.411037i \(0.134833\pi\)
\(774\) 2.81100 + 19.3453i 0.101039 + 0.695353i
\(775\) −34.3361 + 24.9466i −1.23339 + 0.896109i
\(776\) 3.68853 + 35.0941i 0.132411 + 1.25980i
\(777\) −3.52135 + 0.821634i −0.126328 + 0.0294759i
\(778\) 46.5903 9.90307i 1.67034 0.355042i
\(779\) 0.302633 2.87936i 0.0108430 0.103164i
\(780\) −0.571007 + 0.267890i −0.0204453 + 0.00959200i
\(781\) 39.3667 10.8167i 1.40865 0.387051i
\(782\) −31.6086 −1.13032
\(783\) −5.92339 35.7749i −0.211685 1.27849i
\(784\) 9.26663 28.5197i 0.330951 1.01856i
\(785\) 5.66714 + 1.20459i 0.202269 + 0.0429936i
\(786\) 8.90908 16.1613i 0.317777 0.576455i
\(787\) 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
\(789\) −22.7936 9.61254i −0.811473 0.342216i
\(790\) −12.2252 + 5.44303i −0.434954 + 0.193654i
\(791\) 5.79736 0.206130
\(792\) 10.2160 22.5539i 0.363009 0.801418i
\(793\) −7.18019 −0.254976
\(794\) −11.7175 + 5.21697i −0.415839 + 0.185143i
\(795\) 4.66269 3.53069i 0.165369 0.125221i
\(796\) −5.44309 + 6.04516i −0.192925 + 0.214265i
\(797\) −23.0773 10.2747i −0.817439 0.363947i −0.0449609 0.998989i \(-0.514316\pi\)
−0.772478 + 0.635041i \(0.780983\pi\)
\(798\) 4.84911 0.0959690i 0.171657 0.00339727i
\(799\) 1.02210 + 0.217254i 0.0361593 + 0.00768590i
\(800\) 3.13143 9.63754i 0.110713 0.340738i
\(801\) −36.2860 + 9.22732i −1.28210 + 0.326031i
\(802\) −6.08192 −0.214760
\(803\) −2.36185 + 51.2980i −0.0833480 + 1.81027i
\(804\) 0.464295 5.45357i 0.0163744 0.192332i
\(805\) 0.198903 1.89244i 0.00701042 0.0666997i
\(806\) −21.7425 + 4.62152i −0.765848 + 0.162786i
\(807\) 7.95838 + 8.49446i 0.280148 + 0.299019i
\(808\) −3.73745 35.5595i −0.131483 1.25098i
\(809\) −41.5248 + 30.1696i −1.45994 + 1.06071i −0.476556 + 0.879144i \(0.658115\pi\)
−0.983380 + 0.181561i \(0.941885\pi\)
\(810\) 7.23751 3.93540i 0.254300 0.138276i
\(811\) 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
\(813\) −6.24142 + 2.92819i −0.218896 + 0.102696i
\(814\) 5.40186 + 13.8096i 0.189335 + 0.484025i
\(815\) −1.37048 2.37375i −0.0480059 0.0831487i
\(816\) −24.0869 + 27.8399i −0.843212 + 0.974591i
\(817\) −7.07435 7.85686i −0.247500 0.274877i
\(818\) −1.19649 3.68241i −0.0418342 0.128753i
\(819\) 0.222054 3.40390i 0.00775920 0.118942i
\(820\) 0.215882 0.156848i 0.00753894 0.00547736i
\(821\) −10.6362 2.26079i −0.371205 0.0789021i 0.0185320 0.999828i \(-0.494101\pi\)
−0.389737 + 0.920926i \(0.627434\pi\)
\(822\) −19.7411 + 14.9484i −0.688549 + 0.521384i
\(823\) 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
\(825\) −23.4731 + 12.7436i −0.817230 + 0.443676i
\(826\) −3.98136 + 6.89591i −0.138529 + 0.239940i
\(827\) 22.3321 + 16.2252i 0.776564 + 0.564207i 0.903946 0.427647i \(-0.140657\pi\)
−0.127382 + 0.991854i \(0.540657\pi\)
\(828\) −5.21194 + 0.206380i −0.181127 + 0.00717221i
\(829\) −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
\(831\) 11.7602 + 19.4691i 0.407956 + 0.675376i
\(832\) −6.20441 + 6.89069i −0.215099 + 0.238892i
\(833\) 29.1005 6.18550i 1.00827 0.214315i
\(834\) −56.8371 10.9103i −1.96811 0.377794i
\(835\) 5.02854 8.70968i 0.174020 0.301411i
\(836\) −0.528675 3.20601i −0.0182846 0.110882i
\(837\) 45.7284 12.5969i 1.58061 0.435412i
\(838\) −13.4334 9.75993i −0.464049 0.337151i
\(839\) −13.0025 14.4407i −0.448896 0.498549i 0.475642 0.879639i \(-0.342216\pi\)
−0.924538 + 0.381089i \(0.875549\pi\)
\(840\) −1.25953 1.34438i −0.0434581 0.0463854i
\(841\) 17.9979 + 8.01318i 0.620617 + 0.276317i
\(842\) 31.3390 + 13.9530i 1.08001 + 0.480853i
\(843\) 5.00603 1.16805i 0.172417 0.0402299i
\(844\) 0.886407 + 0.984455i 0.0305114 + 0.0338863i
\(845\) 5.03845 + 3.66065i 0.173328 + 0.125930i
\(846\) 1.04030 + 0.178428i 0.0357664 + 0.00613449i
\(847\) −4.74909 6.36497i −0.163181 0.218703i
\(848\) −13.1997 + 22.8626i −0.453280 + 0.785103i
\(849\) 4.59446 + 13.2427i 0.157681 + 0.454489i
\(850\) 32.2894 6.86333i 1.10752 0.235410i
\(851\) −8.61427 + 9.56712i −0.295293 + 0.327957i
\(852\) −8.32484 + 0.164757i −0.285204 + 0.00564449i
\(853\) 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
\(855\) −2.07334 + 3.94371i −0.0709068 + 0.134872i
\(856\) −31.6966 23.0289i −1.08337 0.787112i
\(857\) 2.17032 3.75911i 0.0741369 0.128409i −0.826574 0.562828i \(-0.809713\pi\)
0.900711 + 0.434420i \(0.143047\pi\)
\(858\) −13.9456 + 1.09697i −0.476094 + 0.0374498i
\(859\) 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
\(861\) 0.179223 + 1.43200i 0.00610791 + 0.0488025i
\(862\) 27.9153 + 5.93357i 0.950797 + 0.202098i
\(863\) 2.17943 1.58345i 0.0741886 0.0539011i −0.550073 0.835117i \(-0.685400\pi\)
0.624261 + 0.781216i \(0.285400\pi\)
\(864\) −7.06518 + 8.85084i −0.240362 + 0.301112i
\(865\) −0.108132 0.332797i −0.00367661 0.0113155i
\(866\) 15.6392 + 17.3691i 0.531441 + 0.590225i
\(867\) −6.95109 1.33432i −0.236072 0.0453158i
\(868\) 1.28685 + 2.22889i 0.0436785 + 0.0756534i
\(869\) −48.4040 + 2.84509i −1.64199 + 0.0965132i
\(870\) −0.938574 + 11.0244i −0.0318207 + 0.373762i
\(871\) 11.6420 5.18333i 0.394472 0.175630i
\(872\) 10.5326 32.4161i 0.356680 1.09775i
\(873\) −33.4004 + 26.3474i −1.13043 + 0.891724i
\(874\) 13.9699 10.1497i 0.472538 0.343319i
\(875\) 0.431114 + 4.10177i 0.0145743 + 0.138665i
\(876\) 3.03873 10.0229i 0.102669 0.338642i
\(877\) 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
\(879\) 22.3339 + 15.5607i 0.753302 + 0.524851i
\(880\) −5.67454 + 7.09919i −0.191289 + 0.239314i
\(881\) 11.5843 0.390286 0.195143 0.980775i \(-0.437483\pi\)
0.195143 + 0.980775i \(0.437483\pi\)
\(882\) 29.1243 7.40616i 0.980668 0.249378i
\(883\) 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
\(885\) −3.78211 6.26133i −0.127134 0.210472i
\(886\) 36.0146 + 16.0348i 1.20994 + 0.538698i
\(887\) −3.95453 + 4.39196i −0.132780 + 0.147467i −0.805868 0.592095i \(-0.798301\pi\)
0.673088 + 0.739563i \(0.264968\pi\)
\(888\) 1.54781 + 12.3671i 0.0519410 + 0.415012i
\(889\) −7.91198 + 3.52264i −0.265359 + 0.118146i
\(890\) 11.4240 0.382932
\(891\) 29.5664 4.10217i 0.990512 0.137428i
\(892\) −4.30623 −0.144183
\(893\) −0.521493 + 0.232184i −0.0174511 + 0.00776974i
\(894\) 0.381270 + 3.04636i 0.0127516 + 0.101886i
\(895\) −3.81922 + 4.24168i −0.127663 + 0.141784i
\(896\) 8.87838 + 3.95291i 0.296606 + 0.132057i
\(897\) −6.27927 10.3954i −0.209659 0.347092i
\(898\) 34.0013 + 7.22719i 1.13464 + 0.241174i
\(899\) −19.6852 + 60.5847i −0.656537 + 2.02061i
\(900\) 5.27939 1.34252i 0.175980 0.0447507i
\(901\) −26.1909 −0.872546
\(902\) 5.70677 1.56803i 0.190015 0.0522098i
\(903\) 4.32399 + 3.01267i 0.143893 + 0.100255i
\(904\) 2.08875 19.8731i 0.0694707 0.660969i
\(905\) 2.75757 0.586140i 0.0916648 0.0194840i
\(906\) 0.684245 2.25690i 0.0227325 0.0749804i
\(907\) 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
\(909\) 33.8434 26.6968i 1.12251 0.885478i
\(910\) −0.321628 + 0.989869i −0.0106619 + 0.0328138i
\(911\) −12.9713 + 5.77517i −0.429757 + 0.191340i −0.610203 0.792245i \(-0.708912\pi\)
0.180447 + 0.983585i \(0.442246\pi\)
\(912\) 1.70602 20.0387i 0.0564918 0.663547i
\(913\) −5.82692 + 22.3122i −0.192843 + 0.738426i
\(914\) −16.7675 29.0422i −0.554620 0.960631i
\(915\) −4.59107 0.881292i −0.151776 0.0291346i
\(916\) 6.46787 + 7.18330i 0.213704 + 0.237343i
\(917\) −1.53737 4.73153i −0.0507684 0.156249i
\(918\) −36.4773 5.51577i −1.20393 0.182048i
\(919\) 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
\(921\) 0.755671 + 6.03785i 0.0249002 + 0.198954i
\(922\) 1.95613 18.6114i 0.0644218 0.612932i
\(923\) −9.69344 16.7895i −0.319063 0.552634i
\(924\) 0.619761 + 1.49641i 0.0203887 + 0.0492283i
\(925\) 6.72247 11.6437i 0.221033 0.382841i
\(926\) −25.0555 18.2039i −0.823376 0.598218i
\(927\) 6.18280 11.7603i 0.203070 0.386260i
\(928\) −4.70008 14.4654i −0.154288 0.474849i
\(929\) 3.56785 + 33.9458i 0.117057 + 1.11373i 0.882530 + 0.470257i \(0.155839\pi\)
−0.765473 + 0.643469i \(0.777495\pi\)
\(930\) −14.4696 + 0.286368i −0.474476 + 0.00939037i
\(931\) −10.8752 + 12.0781i −0.356419 + 0.395844i
\(932\) −1.59999 + 0.340089i −0.0524094 + 0.0111400i
\(933\) 14.9507 + 43.0927i 0.489463 + 1.41079i
\(934\) −4.69059 + 8.12434i −0.153481 + 0.265837i
\(935\) −8.91439 1.35393i −0.291532 0.0442781i
\(936\) −11.5884 1.98759i −0.378780 0.0649666i
\(937\) −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
\(939\) 4.15132 0.968623i 0.135473 0.0316098i
\(940\) −0.0480647 0.0213998i −0.00156770 0.000697984i
\(941\) 16.4495 + 7.32378i 0.536237 + 0.238748i 0.656943 0.753940i \(-0.271849\pi\)
−0.120706 + 0.992688i \(0.538516\pi\)
\(942\) −17.9181 19.1251i −0.583803 0.623128i
\(943\) 3.43809 + 3.81838i 0.111959 + 0.124344i
\(944\) 26.7122 + 19.4075i 0.869407 + 0.631661i
\(945\) 0.559776 2.14923i 0.0182095 0.0699143i
\(946\) 9.68901 19.3181i 0.315017 0.628084i
\(947\) −14.3151 + 24.7946i −0.465180 + 0.805715i −0.999210 0.0397506i \(-0.987344\pi\)
0.534030 + 0.845466i \(0.320677\pi\)
\(948\) 9.71182 + 1.86426i 0.315425 + 0.0605484i
\(949\) 23.8528 5.07007i 0.774295 0.164581i
\(950\) −12.0669 + 13.4017i −0.391502 + 0.434808i
\(951\) 23.7381 + 39.2987i 0.769761 + 1.27435i
\(952\) 0.862328 + 8.20451i 0.0279482 + 0.265910i
\(953\) 5.15728 + 15.8725i 0.167061 + 0.514160i 0.999182 0.0404331i \(-0.0128738\pi\)
−0.832121 + 0.554594i \(0.812874\pi\)
\(954\) −26.4349 + 1.04676i −0.855861 + 0.0338900i
\(955\) 2.48967 + 1.80885i 0.0805637 + 0.0585330i
\(956\) 1.43969 2.49361i 0.0465628 0.0806492i
\(957\) −17.2603 + 36.1832i −0.557946 + 1.16964i
\(958\) −28.0414 48.5690i −0.905975 1.56919i
\(959\) −0.697785 + 6.63898i −0.0225327 + 0.214384i
\(960\) −4.81290 + 3.64443i −0.155336 + 0.117624i
\(961\) −51.1814 10.8789i −1.65101 0.350933i
\(962\) 5.69677 4.13895i 0.183671 0.133445i
\(963\) 3.07473 47.1330i 0.0990818 1.51884i
\(964\) −1.06554 3.27939i −0.0343187 0.105622i
\(965\) 1.29463 + 1.43783i 0.0416755 + 0.0462853i
\(966\) −5.63176 + 6.50924i −0.181199 + 0.209431i
\(967\) −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
\(969\) 18.0632 8.47443i 0.580275 0.272238i
\(970\) 11.8581 5.27955i 0.380739 0.169516i
\(971\) 2.33367 7.18229i 0.0748910 0.230491i −0.906603 0.421985i \(-0.861333\pi\)
0.981494 + 0.191495i \(0.0613334\pi\)
\(972\) −6.05076 0.671326i −0.194078 0.0215328i
\(973\) −12.6225 + 9.17079i −0.404659 + 0.294002i
\(974\) 1.40362 + 13.3545i 0.0449748 + 0.427907i
\(975\) 8.67173 + 9.25586i 0.277718 + 0.296425i
\(976\) 20.6403 4.38723i 0.660679 0.140432i
\(977\) −0.212432 + 2.02115i −0.00679629 + 0.0646624i −0.997394 0.0721420i \(-0.977017\pi\)
0.990598 + 0.136804i \(0.0436832\pi\)
\(978\) −1.05175 + 12.3537i −0.0336313 + 0.395029i
\(979\) 38.7366 + 14.5880i 1.23803 + 0.466235i
\(980\) −1.49797 −0.0478508
\(981\) 39.8236 10.1269i 1.27147 0.323328i
\(982\) −15.8611 + 48.8154i −0.506148 + 1.55776i
\(983\) −32.7089 6.95248i −1.04325 0.221750i −0.345745 0.938329i \(-0.612374\pi\)
−0.697506 + 0.716579i \(0.745707\pi\)
\(984\) 4.97342 0.0984291i 0.158547 0.00313781i
\(985\) −12.1489 5.40902i −0.387095 0.172346i
\(986\) 33.1536 36.8208i 1.05583 1.17261i
\(987\) 0.226850 0.171775i 0.00722070 0.00546767i
\(988\) −1.40960 + 0.627594i −0.0448453 + 0.0199664i
\(989\) 18.7629 0.596624
\(990\) −9.05154 1.01026i −0.287677 0.0321082i
\(991\) 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
\(993\) 12.9334 + 5.45430i 0.410430 + 0.173087i
\(994\) −9.19397 + 10.2109i −0.291615 + 0.323871i
\(995\) −11.2654 5.01568i −0.357137 0.159008i
\(996\) 2.27056 4.11885i 0.0719454 0.130511i
\(997\) −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
\(999\) −11.6106 + 9.53755i −0.367344 + 0.301755i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 99.2.m.b.70.8 yes 72
3.2 odd 2 297.2.n.b.235.2 72
9.2 odd 6 891.2.f.e.730.8 36
9.4 even 3 inner 99.2.m.b.4.2 72
9.5 odd 6 297.2.n.b.37.8 72
9.7 even 3 891.2.f.f.730.2 36
11.3 even 5 inner 99.2.m.b.25.2 yes 72
11.5 even 5 1089.2.e.p.727.4 36
11.6 odd 10 1089.2.e.o.727.15 36
33.14 odd 10 297.2.n.b.289.8 72
99.14 odd 30 297.2.n.b.91.2 72
99.16 even 15 9801.2.a.cm.1.15 18
99.25 even 15 891.2.f.f.487.2 36
99.38 odd 30 9801.2.a.cp.1.4 18
99.47 odd 30 891.2.f.e.487.8 36
99.49 even 15 1089.2.e.p.364.4 36
99.58 even 15 inner 99.2.m.b.58.8 yes 72
99.61 odd 30 9801.2.a.co.1.4 18
99.83 even 30 9801.2.a.cn.1.15 18
99.94 odd 30 1089.2.e.o.364.15 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.2 72 9.4 even 3 inner
99.2.m.b.25.2 yes 72 11.3 even 5 inner
99.2.m.b.58.8 yes 72 99.58 even 15 inner
99.2.m.b.70.8 yes 72 1.1 even 1 trivial
297.2.n.b.37.8 72 9.5 odd 6
297.2.n.b.91.2 72 99.14 odd 30
297.2.n.b.235.2 72 3.2 odd 2
297.2.n.b.289.8 72 33.14 odd 10
891.2.f.e.487.8 36 99.47 odd 30
891.2.f.e.730.8 36 9.2 odd 6
891.2.f.f.487.2 36 99.25 even 15
891.2.f.f.730.2 36 9.7 even 3
1089.2.e.o.364.15 36 99.94 odd 30
1089.2.e.o.727.15 36 11.6 odd 10
1089.2.e.p.364.4 36 99.49 even 15
1089.2.e.p.727.4 36 11.5 even 5
9801.2.a.cm.1.15 18 99.16 even 15
9801.2.a.cn.1.15 18 99.83 even 30
9801.2.a.co.1.4 18 99.61 odd 30
9801.2.a.cp.1.4 18 99.38 odd 30