Properties

Label 297.2.n.b.289.5
Level $297$
Weight $2$
Character 297.289
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 289.5
Character \(\chi\) \(=\) 297.289
Dual form 297.2.n.b.37.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0512706 - 0.487807i) q^{2} +(1.72097 - 0.365803i) q^{4} +(0.178553 - 1.69882i) q^{5} +(2.28209 + 2.53451i) q^{7} +(-0.569818 - 1.75372i) q^{8} -0.837851 q^{10} +(2.17733 + 2.50184i) q^{11} +(-3.65228 - 1.62610i) q^{13} +(1.11935 - 1.24316i) q^{14} +(2.38835 - 1.06336i) q^{16} +(-2.67346 - 1.94238i) q^{17} +(-1.36513 - 4.20144i) q^{19} +(-0.314149 - 2.98893i) q^{20} +(1.10878 - 1.19039i) q^{22} +(3.74601 + 6.48827i) q^{23} +(2.03663 + 0.432899i) q^{25} +(-0.605969 + 1.86498i) q^{26} +(4.85453 + 3.52702i) q^{28} +(-1.13169 - 1.25687i) q^{29} +(-3.56147 - 1.58567i) q^{31} +(-2.48514 - 4.30439i) q^{32} +(-0.810437 + 1.40372i) q^{34} +(4.71315 - 3.42431i) q^{35} +(0.947300 - 2.91549i) q^{37} +(-1.97950 + 0.881330i) q^{38} +(-3.08100 + 0.654886i) q^{40} +(-0.261546 + 0.290476i) q^{41} +(-4.80634 + 8.32483i) q^{43} +(4.66230 + 3.50912i) q^{44} +(2.97296 - 2.15999i) q^{46} +(-1.05665 - 0.224598i) q^{47} +(-0.484141 + 4.60629i) q^{49} +(0.106752 - 1.01568i) q^{50} +(-6.88030 - 1.46245i) q^{52} +(-10.1643 + 7.38480i) q^{53} +(4.63895 - 3.25218i) q^{55} +(3.14445 - 5.44635i) q^{56} +(-0.555089 + 0.616488i) q^{58} +(-3.57664 + 0.760238i) q^{59} +(-3.52005 + 1.56723i) q^{61} +(-0.590902 + 1.81861i) q^{62} +(2.25785 - 1.64043i) q^{64} +(-3.41458 + 5.91423i) q^{65} +(-1.55060 - 2.68572i) q^{67} +(-5.31146 - 2.36482i) q^{68} +(-1.91205 - 2.12354i) q^{70} +(5.67699 + 4.12458i) q^{71} +(-4.64842 + 14.3064i) q^{73} +(-1.47077 - 0.312621i) q^{74} +(-3.88624 - 6.73117i) q^{76} +(-1.37210 + 11.2279i) q^{77} +(0.418023 + 3.97722i) q^{79} +(-1.38001 - 4.24724i) q^{80} +(0.155106 + 0.112691i) q^{82} +(0.114162 - 0.0508282i) q^{83} +(-3.77711 + 4.19490i) q^{85} +(4.30733 + 1.91775i) q^{86} +(3.14685 - 5.24403i) q^{88} +7.93327 q^{89} +(-4.21345 - 12.9677i) q^{91} +(8.82019 + 9.79581i) q^{92} +(-0.0553855 + 0.526958i) q^{94} +(-7.38123 + 1.56893i) q^{95} +(-0.0358699 - 0.341280i) q^{97} +2.27180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(56\) \(244\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0512706 0.487807i −0.0362538 0.344932i −0.997580 0.0695211i \(-0.977853\pi\)
0.961327 0.275411i \(-0.0888138\pi\)
\(3\) 0 0
\(4\) 1.72097 0.365803i 0.860484 0.182902i
\(5\) 0.178553 1.69882i 0.0798514 0.759735i −0.879190 0.476471i \(-0.841916\pi\)
0.959042 0.283265i \(-0.0914175\pi\)
\(6\) 0 0
\(7\) 2.28209 + 2.53451i 0.862547 + 0.957956i 0.999468 0.0326264i \(-0.0103872\pi\)
−0.136921 + 0.990582i \(0.543720\pi\)
\(8\) −0.569818 1.75372i −0.201461 0.620034i
\(9\) 0 0
\(10\) −0.837851 −0.264952
\(11\) 2.17733 + 2.50184i 0.656490 + 0.754334i
\(12\) 0 0
\(13\) −3.65228 1.62610i −1.01296 0.451000i −0.167977 0.985791i \(-0.553724\pi\)
−0.844984 + 0.534791i \(0.820390\pi\)
\(14\) 1.11935 1.24316i 0.299159 0.332249i
\(15\) 0 0
\(16\) 2.38835 1.06336i 0.597088 0.265840i
\(17\) −2.67346 1.94238i −0.648409 0.471097i 0.214320 0.976763i \(-0.431246\pi\)
−0.862729 + 0.505667i \(0.831246\pi\)
\(18\) 0 0
\(19\) −1.36513 4.20144i −0.313182 0.963875i −0.976496 0.215534i \(-0.930851\pi\)
0.663314 0.748341i \(-0.269149\pi\)
\(20\) −0.314149 2.98893i −0.0702459 0.668345i
\(21\) 0 0
\(22\) 1.10878 1.19039i 0.236394 0.253792i
\(23\) 3.74601 + 6.48827i 0.781096 + 1.35290i 0.931304 + 0.364244i \(0.118672\pi\)
−0.150208 + 0.988654i \(0.547994\pi\)
\(24\) 0 0
\(25\) 2.03663 + 0.432899i 0.407326 + 0.0865799i
\(26\) −0.605969 + 1.86498i −0.118840 + 0.365753i
\(27\) 0 0
\(28\) 4.85453 + 3.52702i 0.917420 + 0.666544i
\(29\) −1.13169 1.25687i −0.210150 0.233395i 0.628850 0.777527i \(-0.283526\pi\)
−0.839000 + 0.544131i \(0.816859\pi\)
\(30\) 0 0
\(31\) −3.56147 1.58567i −0.639659 0.284795i 0.0611661 0.998128i \(-0.480518\pi\)
−0.700825 + 0.713333i \(0.747185\pi\)
\(32\) −2.48514 4.30439i −0.439315 0.760915i
\(33\) 0 0
\(34\) −0.810437 + 1.40372i −0.138989 + 0.240736i
\(35\) 4.71315 3.42431i 0.796668 0.578813i
\(36\) 0 0
\(37\) 0.947300 2.91549i 0.155735 0.479304i −0.842499 0.538697i \(-0.818917\pi\)
0.998235 + 0.0593935i \(0.0189167\pi\)
\(38\) −1.97950 + 0.881330i −0.321117 + 0.142971i
\(39\) 0 0
\(40\) −3.08100 + 0.654886i −0.487148 + 0.103547i
\(41\) −0.261546 + 0.290476i −0.0408467 + 0.0453648i −0.763222 0.646136i \(-0.776384\pi\)
0.722375 + 0.691501i \(0.243050\pi\)
\(42\) 0 0
\(43\) −4.80634 + 8.32483i −0.732960 + 1.26952i 0.222652 + 0.974898i \(0.428529\pi\)
−0.955613 + 0.294626i \(0.904805\pi\)
\(44\) 4.66230 + 3.50912i 0.702869 + 0.529020i
\(45\) 0 0
\(46\) 2.97296 2.15999i 0.438340 0.318472i
\(47\) −1.05665 0.224598i −0.154129 0.0327610i 0.130201 0.991488i \(-0.458438\pi\)
−0.284330 + 0.958727i \(0.591771\pi\)
\(48\) 0 0
\(49\) −0.484141 + 4.60629i −0.0691630 + 0.658042i
\(50\) 0.106752 1.01568i 0.0150970 0.143639i
\(51\) 0 0
\(52\) −6.88030 1.46245i −0.954126 0.202806i
\(53\) −10.1643 + 7.38480i −1.39618 + 1.01438i −0.401020 + 0.916069i \(0.631344\pi\)
−0.995156 + 0.0983117i \(0.968656\pi\)
\(54\) 0 0
\(55\) 4.63895 3.25218i 0.625516 0.438524i
\(56\) 3.14445 5.44635i 0.420195 0.727799i
\(57\) 0 0
\(58\) −0.555089 + 0.616488i −0.0728867 + 0.0809489i
\(59\) −3.57664 + 0.760238i −0.465639 + 0.0989746i −0.434756 0.900548i \(-0.643165\pi\)
−0.0308830 + 0.999523i \(0.509832\pi\)
\(60\) 0 0
\(61\) −3.52005 + 1.56723i −0.450696 + 0.200663i −0.619516 0.784984i \(-0.712671\pi\)
0.168820 + 0.985647i \(0.446004\pi\)
\(62\) −0.590902 + 1.81861i −0.0750446 + 0.230964i
\(63\) 0 0
\(64\) 2.25785 1.64043i 0.282232 0.205053i
\(65\) −3.41458 + 5.91423i −0.423527 + 0.733570i
\(66\) 0 0
\(67\) −1.55060 2.68572i −0.189436 0.328113i 0.755626 0.655003i \(-0.227333\pi\)
−0.945062 + 0.326890i \(0.893999\pi\)
\(68\) −5.31146 2.36482i −0.644110 0.286776i
\(69\) 0 0
\(70\) −1.91205 2.12354i −0.228533 0.253812i
\(71\) 5.67699 + 4.12458i 0.673735 + 0.489497i 0.871273 0.490798i \(-0.163295\pi\)
−0.197538 + 0.980295i \(0.563295\pi\)
\(72\) 0 0
\(73\) −4.64842 + 14.3064i −0.544057 + 1.67443i 0.179165 + 0.983819i \(0.442660\pi\)
−0.723222 + 0.690615i \(0.757340\pi\)
\(74\) −1.47077 0.312621i −0.170973 0.0363414i
\(75\) 0 0
\(76\) −3.88624 6.73117i −0.445783 0.772118i
\(77\) −1.37210 + 11.2279i −0.156365 + 1.27954i
\(78\) 0 0
\(79\) 0.418023 + 3.97722i 0.0470313 + 0.447473i 0.992544 + 0.121887i \(0.0388946\pi\)
−0.945513 + 0.325585i \(0.894439\pi\)
\(80\) −1.38001 4.24724i −0.154290 0.474856i
\(81\) 0 0
\(82\) 0.155106 + 0.112691i 0.0171286 + 0.0124447i
\(83\) 0.114162 0.0508282i 0.0125309 0.00557912i −0.400462 0.916314i \(-0.631150\pi\)
0.412993 + 0.910734i \(0.364484\pi\)
\(84\) 0 0
\(85\) −3.77711 + 4.19490i −0.409685 + 0.455001i
\(86\) 4.30733 + 1.91775i 0.464472 + 0.206796i
\(87\) 0 0
\(88\) 3.14685 5.24403i 0.335455 0.559015i
\(89\) 7.93327 0.840925 0.420462 0.907310i \(-0.361868\pi\)
0.420462 + 0.907310i \(0.361868\pi\)
\(90\) 0 0
\(91\) −4.21345 12.9677i −0.441690 1.35938i
\(92\) 8.82019 + 9.79581i 0.919568 + 1.02128i
\(93\) 0 0
\(94\) −0.0553855 + 0.526958i −0.00571258 + 0.0543515i
\(95\) −7.38123 + 1.56893i −0.757298 + 0.160969i
\(96\) 0 0
\(97\) −0.0358699 0.341280i −0.00364204 0.0346517i 0.992550 0.121838i \(-0.0388790\pi\)
−0.996192 + 0.0871867i \(0.972212\pi\)
\(98\) 2.27180 0.229487
\(99\) 0 0
\(100\) 3.66333 0.366333
\(101\) 0.743781 + 7.07660i 0.0740090 + 0.704148i 0.967121 + 0.254315i \(0.0818500\pi\)
−0.893112 + 0.449833i \(0.851483\pi\)
\(102\) 0 0
\(103\) 1.61814 0.343946i 0.159440 0.0338900i −0.127500 0.991839i \(-0.540695\pi\)
0.286940 + 0.957949i \(0.407362\pi\)
\(104\) −0.770589 + 7.33167i −0.0755625 + 0.718929i
\(105\) 0 0
\(106\) 4.12349 + 4.57960i 0.400509 + 0.444810i
\(107\) −1.02187 3.14498i −0.0987876 0.304037i 0.889435 0.457062i \(-0.151098\pi\)
−0.988222 + 0.153025i \(0.951098\pi\)
\(108\) 0 0
\(109\) −5.50709 −0.527484 −0.263742 0.964593i \(-0.584957\pi\)
−0.263742 + 0.964593i \(0.584957\pi\)
\(110\) −1.82428 2.09617i −0.173938 0.199862i
\(111\) 0 0
\(112\) 8.14552 + 3.62662i 0.769680 + 0.342683i
\(113\) 10.9799 12.1944i 1.03290 1.14716i 0.0439343 0.999034i \(-0.486011\pi\)
0.988969 0.148121i \(-0.0473225\pi\)
\(114\) 0 0
\(115\) 11.6913 5.20529i 1.09022 0.485395i
\(116\) −2.40738 1.74906i −0.223519 0.162396i
\(117\) 0 0
\(118\) 0.554226 + 1.70573i 0.0510206 + 0.157025i
\(119\) −1.17807 11.2086i −0.107994 1.02749i
\(120\) 0 0
\(121\) −1.51845 + 10.8947i −0.138040 + 0.990427i
\(122\) 0.944980 + 1.63675i 0.0855545 + 0.148185i
\(123\) 0 0
\(124\) −6.70922 1.42609i −0.602506 0.128067i
\(125\) 3.73834 11.5054i 0.334368 1.02908i
\(126\) 0 0
\(127\) −8.73327 6.34509i −0.774952 0.563036i 0.128508 0.991709i \(-0.458981\pi\)
−0.903460 + 0.428673i \(0.858981\pi\)
\(128\) −7.56750 8.40456i −0.668879 0.742865i
\(129\) 0 0
\(130\) 3.06007 + 1.36243i 0.268386 + 0.119493i
\(131\) −10.5778 18.3213i −0.924189 1.60074i −0.792860 0.609404i \(-0.791409\pi\)
−0.131329 0.991339i \(-0.541925\pi\)
\(132\) 0 0
\(133\) 7.53325 13.0480i 0.653216 1.13140i
\(134\) −1.23061 + 0.894092i −0.106309 + 0.0772378i
\(135\) 0 0
\(136\) −1.88301 + 5.79530i −0.161467 + 0.496943i
\(137\) −2.92382 + 1.30177i −0.249799 + 0.111218i −0.527817 0.849358i \(-0.676989\pi\)
0.278018 + 0.960576i \(0.410323\pi\)
\(138\) 0 0
\(139\) 14.6660 3.11735i 1.24395 0.264411i 0.461512 0.887134i \(-0.347307\pi\)
0.782442 + 0.622723i \(0.213974\pi\)
\(140\) 6.85856 7.61721i 0.579654 0.643771i
\(141\) 0 0
\(142\) 1.72094 2.98075i 0.144418 0.250139i
\(143\) −3.88399 12.6780i −0.324795 1.06019i
\(144\) 0 0
\(145\) −2.33727 + 1.69812i −0.194099 + 0.141021i
\(146\) 7.21708 + 1.53404i 0.597290 + 0.126958i
\(147\) 0 0
\(148\) 0.563778 5.36399i 0.0463423 0.440917i
\(149\) 0.423458 4.02893i 0.0346910 0.330063i −0.963388 0.268111i \(-0.913601\pi\)
0.998079 0.0619522i \(-0.0197326\pi\)
\(150\) 0 0
\(151\) 7.62367 + 1.62046i 0.620405 + 0.131871i 0.507382 0.861721i \(-0.330613\pi\)
0.113023 + 0.993592i \(0.463947\pi\)
\(152\) −6.59027 + 4.78811i −0.534541 + 0.388367i
\(153\) 0 0
\(154\) 5.54740 + 0.0936570i 0.447022 + 0.00754709i
\(155\) −3.32968 + 5.76717i −0.267446 + 0.463230i
\(156\) 0 0
\(157\) 0.206863 0.229745i 0.0165095 0.0183356i −0.734834 0.678248i \(-0.762740\pi\)
0.751343 + 0.659912i \(0.229406\pi\)
\(158\) 1.91868 0.407829i 0.152642 0.0324451i
\(159\) 0 0
\(160\) −7.75610 + 3.45324i −0.613174 + 0.273003i
\(161\) −7.89590 + 24.3011i −0.622284 + 1.91519i
\(162\) 0 0
\(163\) −8.89442 + 6.46217i −0.696665 + 0.506157i −0.878844 0.477109i \(-0.841685\pi\)
0.182179 + 0.983265i \(0.441685\pi\)
\(164\) −0.343855 + 0.595575i −0.0268506 + 0.0465066i
\(165\) 0 0
\(166\) −0.0306475 0.0530830i −0.00237871 0.00412004i
\(167\) 16.0545 + 7.14793i 1.24234 + 0.553124i 0.919410 0.393300i \(-0.128667\pi\)
0.322926 + 0.946424i \(0.395333\pi\)
\(168\) 0 0
\(169\) 1.99628 + 2.21709i 0.153560 + 0.170546i
\(170\) 2.23996 + 1.62742i 0.171797 + 0.124818i
\(171\) 0 0
\(172\) −5.22631 + 16.0849i −0.398503 + 1.22646i
\(173\) 12.0955 + 2.57098i 0.919605 + 0.195468i 0.643311 0.765605i \(-0.277560\pi\)
0.276294 + 0.961073i \(0.410894\pi\)
\(174\) 0 0
\(175\) 3.55058 + 6.14978i 0.268398 + 0.464880i
\(176\) 7.86060 + 3.65999i 0.592515 + 0.275882i
\(177\) 0 0
\(178\) −0.406743 3.86990i −0.0304867 0.290061i
\(179\) −6.76200 20.8113i −0.505416 1.55551i −0.800071 0.599906i \(-0.795205\pi\)
0.294655 0.955604i \(-0.404795\pi\)
\(180\) 0 0
\(181\) 3.54364 + 2.57460i 0.263396 + 0.191369i 0.711643 0.702541i \(-0.247951\pi\)
−0.448247 + 0.893910i \(0.647951\pi\)
\(182\) −6.10969 + 2.72021i −0.452880 + 0.201635i
\(183\) 0 0
\(184\) 9.24407 10.2666i 0.681482 0.756862i
\(185\) −4.78375 2.12986i −0.351708 0.156591i
\(186\) 0 0
\(187\) −0.961474 10.9178i −0.0703099 0.798387i
\(188\) −1.90062 −0.138617
\(189\) 0 0
\(190\) 1.14377 + 3.52018i 0.0829781 + 0.255380i
\(191\) −8.37399 9.30026i −0.605921 0.672943i 0.359649 0.933088i \(-0.382896\pi\)
−0.965570 + 0.260144i \(0.916230\pi\)
\(192\) 0 0
\(193\) 1.31347 12.4969i 0.0945460 0.899545i −0.839732 0.543000i \(-0.817288\pi\)
0.934278 0.356544i \(-0.116045\pi\)
\(194\) −0.164640 + 0.0349952i −0.0118204 + 0.00251251i
\(195\) 0 0
\(196\) 0.851805 + 8.10438i 0.0608432 + 0.578885i
\(197\) 10.3453 0.737075 0.368538 0.929613i \(-0.379859\pi\)
0.368538 + 0.929613i \(0.379859\pi\)
\(198\) 0 0
\(199\) 26.4773 1.87693 0.938464 0.345376i \(-0.112249\pi\)
0.938464 + 0.345376i \(0.112249\pi\)
\(200\) −0.401325 3.81836i −0.0283780 0.269999i
\(201\) 0 0
\(202\) 3.41388 0.725643i 0.240200 0.0510561i
\(203\) 0.602939 5.73658i 0.0423180 0.402629i
\(204\) 0 0
\(205\) 0.446767 + 0.496185i 0.0312036 + 0.0346551i
\(206\) −0.250742 0.771705i −0.0174700 0.0537672i
\(207\) 0 0
\(208\) −10.4521 −0.724721
\(209\) 7.53900 12.5633i 0.521483 0.869019i
\(210\) 0 0
\(211\) −6.65418 2.96263i −0.458092 0.203956i 0.164699 0.986344i \(-0.447335\pi\)
−0.622791 + 0.782388i \(0.714001\pi\)
\(212\) −14.7911 + 16.4272i −1.01586 + 1.12822i
\(213\) 0 0
\(214\) −1.48175 + 0.659719i −0.101291 + 0.0450975i
\(215\) 13.2842 + 9.65153i 0.905974 + 0.658229i
\(216\) 0 0
\(217\) −4.10868 12.6452i −0.278916 0.858414i
\(218\) 0.282352 + 2.68640i 0.0191233 + 0.181946i
\(219\) 0 0
\(220\) 6.79383 7.29385i 0.458040 0.491751i
\(221\) 6.60572 + 11.4414i 0.444349 + 0.769635i
\(222\) 0 0
\(223\) −22.9963 4.88802i −1.53995 0.327326i −0.641748 0.766915i \(-0.721791\pi\)
−0.898199 + 0.439590i \(0.855124\pi\)
\(224\) 5.23822 16.1216i 0.349993 1.07717i
\(225\) 0 0
\(226\) −6.51148 4.73086i −0.433137 0.314692i
\(227\) 7.97750 + 8.85991i 0.529485 + 0.588053i 0.947247 0.320503i \(-0.103852\pi\)
−0.417762 + 0.908557i \(0.637185\pi\)
\(228\) 0 0
\(229\) 2.79323 + 1.24363i 0.184582 + 0.0821811i 0.496947 0.867781i \(-0.334454\pi\)
−0.312365 + 0.949962i \(0.601121\pi\)
\(230\) −3.13859 5.43620i −0.206953 0.358453i
\(231\) 0 0
\(232\) −1.55934 + 2.70086i −0.102376 + 0.177320i
\(233\) −19.8463 + 14.4192i −1.30017 + 0.944632i −0.999957 0.00923938i \(-0.997059\pi\)
−0.300217 + 0.953871i \(0.597059\pi\)
\(234\) 0 0
\(235\) −0.570221 + 1.75496i −0.0371971 + 0.114481i
\(236\) −5.87718 + 2.61669i −0.382572 + 0.170332i
\(237\) 0 0
\(238\) −5.40723 + 1.14934i −0.350499 + 0.0745008i
\(239\) 4.65088 5.16532i 0.300840 0.334117i −0.573704 0.819063i \(-0.694494\pi\)
0.874544 + 0.484946i \(0.161161\pi\)
\(240\) 0 0
\(241\) 3.88529 6.72952i 0.250274 0.433487i −0.713327 0.700831i \(-0.752813\pi\)
0.963601 + 0.267344i \(0.0861461\pi\)
\(242\) 5.39236 + 0.182131i 0.346634 + 0.0117078i
\(243\) 0 0
\(244\) −5.48460 + 3.98480i −0.351116 + 0.255100i
\(245\) 7.73881 + 1.64494i 0.494415 + 0.105091i
\(246\) 0 0
\(247\) −1.84612 + 17.5647i −0.117466 + 1.11761i
\(248\) −0.751429 + 7.14937i −0.0477158 + 0.453985i
\(249\) 0 0
\(250\) −5.80410 1.23370i −0.367084 0.0780260i
\(251\) 0.264684 0.192304i 0.0167067 0.0121381i −0.579401 0.815043i \(-0.696713\pi\)
0.596107 + 0.802905i \(0.296713\pi\)
\(252\) 0 0
\(253\) −8.07634 + 23.4990i −0.507755 + 1.47737i
\(254\) −2.64742 + 4.58547i −0.166114 + 0.287718i
\(255\) 0 0
\(256\) 0.0230840 0.0256374i 0.00144275 0.00160234i
\(257\) −13.4292 + 2.85445i −0.837688 + 0.178056i −0.606730 0.794908i \(-0.707519\pi\)
−0.230957 + 0.972964i \(0.574186\pi\)
\(258\) 0 0
\(259\) 9.55117 4.25245i 0.593481 0.264235i
\(260\) −3.71294 + 11.4273i −0.230267 + 0.708689i
\(261\) 0 0
\(262\) −8.39495 + 6.09928i −0.518641 + 0.376815i
\(263\) −8.42709 + 14.5961i −0.519637 + 0.900037i 0.480103 + 0.877212i \(0.340599\pi\)
−0.999739 + 0.0228249i \(0.992734\pi\)
\(264\) 0 0
\(265\) 10.7306 + 18.5859i 0.659174 + 1.14172i
\(266\) −6.75113 3.00579i −0.413938 0.184297i
\(267\) 0 0
\(268\) −3.65098 4.05482i −0.223019 0.247688i
\(269\) 10.0297 + 7.28700i 0.611522 + 0.444296i 0.849950 0.526864i \(-0.176632\pi\)
−0.238428 + 0.971160i \(0.576632\pi\)
\(270\) 0 0
\(271\) 5.95460 18.3264i 0.361716 1.11325i −0.590296 0.807187i \(-0.700989\pi\)
0.952012 0.306061i \(-0.0990112\pi\)
\(272\) −8.45061 1.79623i −0.512393 0.108913i
\(273\) 0 0
\(274\) 0.784919 + 1.35952i 0.0474187 + 0.0821316i
\(275\) 3.35138 + 6.03790i 0.202096 + 0.364099i
\(276\) 0 0
\(277\) −1.08198 10.2944i −0.0650100 0.618529i −0.977719 0.209919i \(-0.932680\pi\)
0.912709 0.408611i \(-0.133987\pi\)
\(278\) −2.27260 6.99435i −0.136302 0.419493i
\(279\) 0 0
\(280\) −8.69092 6.31432i −0.519382 0.377353i
\(281\) 15.0149 6.68504i 0.895711 0.398796i 0.0933486 0.995633i \(-0.470243\pi\)
0.802362 + 0.596837i \(0.203576\pi\)
\(282\) 0 0
\(283\) −0.846419 + 0.940044i −0.0503144 + 0.0558798i −0.767777 0.640718i \(-0.778637\pi\)
0.717462 + 0.696597i \(0.245304\pi\)
\(284\) 11.2787 + 5.02160i 0.669268 + 0.297977i
\(285\) 0 0
\(286\) −5.98529 + 2.54464i −0.353918 + 0.150468i
\(287\) −1.33309 −0.0786896
\(288\) 0 0
\(289\) −1.87876 5.78222i −0.110515 0.340130i
\(290\) 0.948189 + 1.05307i 0.0556796 + 0.0618385i
\(291\) 0 0
\(292\) −2.76647 + 26.3212i −0.161896 + 1.54033i
\(293\) −23.5610 + 5.00805i −1.37645 + 0.292574i −0.835966 0.548780i \(-0.815092\pi\)
−0.540484 + 0.841354i \(0.681759\pi\)
\(294\) 0 0
\(295\) 0.652887 + 6.21181i 0.0380126 + 0.361665i
\(296\) −5.65274 −0.328559
\(297\) 0 0
\(298\) −1.98705 −0.115107
\(299\) −3.13089 29.7884i −0.181064 1.72271i
\(300\) 0 0
\(301\) −32.0679 + 6.81623i −1.84836 + 0.392881i
\(302\) 0.399602 3.80196i 0.0229945 0.218778i
\(303\) 0 0
\(304\) −7.72805 8.58287i −0.443234 0.492262i
\(305\) 2.03392 + 6.25977i 0.116462 + 0.358433i
\(306\) 0 0
\(307\) 16.2949 0.930001 0.465001 0.885310i \(-0.346054\pi\)
0.465001 + 0.885310i \(0.346054\pi\)
\(308\) 1.74587 + 19.8248i 0.0994800 + 1.12962i
\(309\) 0 0
\(310\) 2.98398 + 1.32855i 0.169479 + 0.0754568i
\(311\) −14.3002 + 15.8819i −0.810888 + 0.900582i −0.996631 0.0820162i \(-0.973864\pi\)
0.185743 + 0.982598i \(0.440531\pi\)
\(312\) 0 0
\(313\) 2.84672 1.26744i 0.160906 0.0716401i −0.324703 0.945816i \(-0.605264\pi\)
0.485609 + 0.874176i \(0.338598\pi\)
\(314\) −0.122677 0.0891301i −0.00692307 0.00502990i
\(315\) 0 0
\(316\) 2.17428 + 6.69176i 0.122313 + 0.376441i
\(317\) −1.90920 18.1648i −0.107231 1.02024i −0.907345 0.420388i \(-0.861894\pi\)
0.800113 0.599849i \(-0.204773\pi\)
\(318\) 0 0
\(319\) 0.680426 5.56795i 0.0380966 0.311745i
\(320\) −2.38364 4.12859i −0.133250 0.230795i
\(321\) 0 0
\(322\) 12.2591 + 2.60575i 0.683171 + 0.145212i
\(323\) −4.51117 + 13.8840i −0.251008 + 0.772524i
\(324\) 0 0
\(325\) −6.73442 4.89284i −0.373558 0.271406i
\(326\) 3.60832 + 4.00744i 0.199846 + 0.221952i
\(327\) 0 0
\(328\) 0.658448 + 0.293160i 0.0363567 + 0.0161871i
\(329\) −1.84212 3.19065i −0.101560 0.175906i
\(330\) 0 0
\(331\) −1.88308 + 3.26159i −0.103503 + 0.179273i −0.913126 0.407678i \(-0.866339\pi\)
0.809622 + 0.586951i \(0.199672\pi\)
\(332\) 0.177876 0.129235i 0.00976222 0.00709267i
\(333\) 0 0
\(334\) 2.66369 8.19799i 0.145751 0.448574i
\(335\) −4.83941 + 2.15465i −0.264405 + 0.117721i
\(336\) 0 0
\(337\) −5.83580 + 1.24044i −0.317896 + 0.0675710i −0.364096 0.931361i \(-0.618622\pi\)
0.0462001 + 0.998932i \(0.485289\pi\)
\(338\) 0.979163 1.08747i 0.0532594 0.0591506i
\(339\) 0 0
\(340\) −4.96577 + 8.60097i −0.269307 + 0.466453i
\(341\) −3.78741 12.3628i −0.205100 0.669482i
\(342\) 0 0
\(343\) 6.53464 4.74769i 0.352837 0.256351i
\(344\) 17.3382 + 3.68534i 0.934811 + 0.198700i
\(345\) 0 0
\(346\) 0.633999 6.03209i 0.0340840 0.324287i
\(347\) 2.54520 24.2159i 0.136633 1.29998i −0.684403 0.729104i \(-0.739937\pi\)
0.821036 0.570876i \(-0.193396\pi\)
\(348\) 0 0
\(349\) −16.3759 3.48081i −0.876583 0.186323i −0.252420 0.967618i \(-0.581227\pi\)
−0.624163 + 0.781294i \(0.714560\pi\)
\(350\) 2.81787 2.04730i 0.150621 0.109433i
\(351\) 0 0
\(352\) 5.35793 15.5895i 0.285579 0.830924i
\(353\) −4.01566 + 6.95533i −0.213732 + 0.370195i −0.952880 0.303349i \(-0.901895\pi\)
0.739148 + 0.673544i \(0.235229\pi\)
\(354\) 0 0
\(355\) 8.02056 8.90773i 0.425687 0.472773i
\(356\) 13.6529 2.90201i 0.723602 0.153806i
\(357\) 0 0
\(358\) −9.80521 + 4.36556i −0.518221 + 0.230727i
\(359\) 8.90742 27.4142i 0.470116 1.44687i −0.382317 0.924031i \(-0.624874\pi\)
0.852433 0.522836i \(-0.175126\pi\)
\(360\) 0 0
\(361\) −0.417162 + 0.303086i −0.0219559 + 0.0159519i
\(362\) 1.07422 1.86061i 0.0564600 0.0977916i
\(363\) 0 0
\(364\) −11.9948 20.7756i −0.628700 1.08894i
\(365\) 23.4740 + 10.4513i 1.22868 + 0.547045i
\(366\) 0 0
\(367\) 14.9506 + 16.6044i 0.780417 + 0.866741i 0.993909 0.110204i \(-0.0351503\pi\)
−0.213492 + 0.976945i \(0.568484\pi\)
\(368\) 15.8462 + 11.5129i 0.826038 + 0.600152i
\(369\) 0 0
\(370\) −0.793696 + 2.44275i −0.0412623 + 0.126992i
\(371\) −41.9127 8.90882i −2.17600 0.462523i
\(372\) 0 0
\(373\) −3.53936 6.13036i −0.183261 0.317418i 0.759728 0.650241i \(-0.225332\pi\)
−0.942989 + 0.332823i \(0.891999\pi\)
\(374\) −5.27648 + 1.02877i −0.272840 + 0.0531967i
\(375\) 0 0
\(376\) 0.208217 + 1.98105i 0.0107380 + 0.102165i
\(377\) 2.08946 + 6.43070i 0.107613 + 0.331198i
\(378\) 0 0
\(379\) 19.6964 + 14.3103i 1.01174 + 0.735070i 0.964573 0.263818i \(-0.0849817\pi\)
0.0471638 + 0.998887i \(0.484982\pi\)
\(380\) −12.1289 + 5.40015i −0.622202 + 0.277022i
\(381\) 0 0
\(382\) −4.10739 + 4.56172i −0.210153 + 0.233398i
\(383\) 16.1130 + 7.17398i 0.823337 + 0.366573i 0.774767 0.632247i \(-0.217867\pi\)
0.0485695 + 0.998820i \(0.484534\pi\)
\(384\) 0 0
\(385\) 18.8292 + 4.33572i 0.959624 + 0.220969i
\(386\) −6.16341 −0.313709
\(387\) 0 0
\(388\) −0.186572 0.574210i −0.00947177 0.0291511i
\(389\) 11.9661 + 13.2897i 0.606703 + 0.673812i 0.965740 0.259511i \(-0.0835615\pi\)
−0.359037 + 0.933323i \(0.616895\pi\)
\(390\) 0 0
\(391\) 2.58791 24.6223i 0.130876 1.24520i
\(392\) 8.35402 1.77570i 0.421942 0.0896865i
\(393\) 0 0
\(394\) −0.530412 5.04653i −0.0267218 0.254241i
\(395\) 6.83122 0.343716
\(396\) 0 0
\(397\) −21.9395 −1.10111 −0.550556 0.834798i \(-0.685584\pi\)
−0.550556 + 0.834798i \(0.685584\pi\)
\(398\) −1.35751 12.9158i −0.0680458 0.647412i
\(399\) 0 0
\(400\) 5.32452 1.13176i 0.266226 0.0565881i
\(401\) 0.565244 5.37793i 0.0282269 0.268561i −0.971301 0.237852i \(-0.923557\pi\)
0.999528 0.0307093i \(-0.00977662\pi\)
\(402\) 0 0
\(403\) 10.4290 + 11.5826i 0.519508 + 0.576972i
\(404\) 3.86867 + 11.9065i 0.192473 + 0.592372i
\(405\) 0 0
\(406\) −2.82926 −0.140414
\(407\) 9.35669 3.97800i 0.463794 0.197182i
\(408\) 0 0
\(409\) 21.5781 + 9.60718i 1.06697 + 0.475044i 0.863662 0.504071i \(-0.168165\pi\)
0.203305 + 0.979115i \(0.434832\pi\)
\(410\) 0.219137 0.243376i 0.0108224 0.0120195i
\(411\) 0 0
\(412\) 2.65895 1.18384i 0.130997 0.0583236i
\(413\) −10.0890 7.33011i −0.496449 0.360691i
\(414\) 0 0
\(415\) −0.0659639 0.203016i −0.00323804 0.00996567i
\(416\) 2.07706 + 19.7619i 0.101836 + 0.968908i
\(417\) 0 0
\(418\) −6.51498 3.03345i −0.318658 0.148371i
\(419\) −9.06566 15.7022i −0.442886 0.767102i 0.555016 0.831840i \(-0.312712\pi\)
−0.997902 + 0.0647380i \(0.979379\pi\)
\(420\) 0 0
\(421\) 12.5322 + 2.66381i 0.610783 + 0.129826i 0.502910 0.864339i \(-0.332263\pi\)
0.107873 + 0.994165i \(0.465596\pi\)
\(422\) −1.10403 + 3.39785i −0.0537432 + 0.165405i
\(423\) 0 0
\(424\) 18.7427 + 13.6174i 0.910226 + 0.661318i
\(425\) −4.60399 5.11325i −0.223326 0.248029i
\(426\) 0 0
\(427\) −12.0052 5.34507i −0.580973 0.258666i
\(428\) −2.90904 5.03861i −0.140614 0.243551i
\(429\) 0 0
\(430\) 4.02700 6.97496i 0.194199 0.336362i
\(431\) −5.32265 + 3.86713i −0.256383 + 0.186273i −0.708551 0.705660i \(-0.750651\pi\)
0.452168 + 0.891933i \(0.350651\pi\)
\(432\) 0 0
\(433\) 4.32555 13.3127i 0.207873 0.639767i −0.791710 0.610897i \(-0.790809\pi\)
0.999583 0.0288700i \(-0.00919089\pi\)
\(434\) −5.95778 + 2.65257i −0.285982 + 0.127328i
\(435\) 0 0
\(436\) −9.47753 + 2.01451i −0.453892 + 0.0964776i
\(437\) 22.1463 24.5959i 1.05940 1.17658i
\(438\) 0 0
\(439\) −12.5891 + 21.8050i −0.600846 + 1.04070i 0.391848 + 0.920030i \(0.371836\pi\)
−0.992693 + 0.120665i \(0.961497\pi\)
\(440\) −8.34678 6.28227i −0.397917 0.299495i
\(441\) 0 0
\(442\) 5.24254 3.80893i 0.249362 0.181172i
\(443\) 26.2363 + 5.57671i 1.24653 + 0.264957i 0.783502 0.621389i \(-0.213431\pi\)
0.463024 + 0.886346i \(0.346765\pi\)
\(444\) 0 0
\(445\) 1.41651 13.4772i 0.0671490 0.638880i
\(446\) −1.20537 + 11.4684i −0.0570761 + 0.543043i
\(447\) 0 0
\(448\) 9.31029 + 1.97896i 0.439870 + 0.0934972i
\(449\) 11.4685 8.33234i 0.541231 0.393228i −0.283311 0.959028i \(-0.591433\pi\)
0.824542 + 0.565801i \(0.191433\pi\)
\(450\) 0 0
\(451\) −1.29620 0.0218838i −0.0610357 0.00103047i
\(452\) 14.4353 25.0027i 0.678981 1.17603i
\(453\) 0 0
\(454\) 3.91292 4.34573i 0.183642 0.203955i
\(455\) −22.7820 + 4.84247i −1.06804 + 0.227019i
\(456\) 0 0
\(457\) 22.5109 10.0225i 1.05302 0.468833i 0.194118 0.980978i \(-0.437816\pi\)
0.858899 + 0.512145i \(0.171149\pi\)
\(458\) 0.463439 1.42632i 0.0216551 0.0666475i
\(459\) 0 0
\(460\) 18.2162 13.2348i 0.849334 0.617077i
\(461\) −13.1227 + 22.7292i −0.611185 + 1.05860i 0.379856 + 0.925046i \(0.375973\pi\)
−0.991041 + 0.133558i \(0.957360\pi\)
\(462\) 0 0
\(463\) −6.34609 10.9917i −0.294928 0.510830i 0.680040 0.733175i \(-0.261962\pi\)
−0.974968 + 0.222345i \(0.928629\pi\)
\(464\) −4.03939 1.79845i −0.187524 0.0834910i
\(465\) 0 0
\(466\) 8.05131 + 8.94188i 0.372970 + 0.414225i
\(467\) −22.4130 16.2840i −1.03715 0.753534i −0.0674235 0.997724i \(-0.521478\pi\)
−0.969727 + 0.244190i \(0.921478\pi\)
\(468\) 0 0
\(469\) 3.26838 10.0591i 0.150920 0.464484i
\(470\) 0.885317 + 0.188180i 0.0408366 + 0.00868009i
\(471\) 0 0
\(472\) 3.37128 + 5.83923i 0.155176 + 0.268772i
\(473\) −31.2924 + 6.10120i −1.43883 + 0.280534i
\(474\) 0 0
\(475\) −0.961466 9.14774i −0.0441151 0.419727i
\(476\) −6.12756 18.8587i −0.280856 0.864386i
\(477\) 0 0
\(478\) −2.75813 2.00390i −0.126154 0.0916563i
\(479\) 14.2716 6.35412i 0.652086 0.290327i −0.0539074 0.998546i \(-0.517168\pi\)
0.705993 + 0.708219i \(0.250501\pi\)
\(480\) 0 0
\(481\) −8.20070 + 9.10780i −0.373920 + 0.415280i
\(482\) −3.48191 1.55025i −0.158597 0.0706118i
\(483\) 0 0
\(484\) 1.37212 + 19.3049i 0.0623689 + 0.877494i
\(485\) −0.586177 −0.0266169
\(486\) 0 0
\(487\) 8.32090 + 25.6091i 0.377056 + 1.16046i 0.942081 + 0.335386i \(0.108867\pi\)
−0.565025 + 0.825074i \(0.691133\pi\)
\(488\) 4.75427 + 5.28015i 0.215216 + 0.239021i
\(489\) 0 0
\(490\) 0.405638 3.85938i 0.0183248 0.174349i
\(491\) 38.1475 8.10850i 1.72157 0.365932i 0.762040 0.647529i \(-0.224198\pi\)
0.959533 + 0.281598i \(0.0908644\pi\)
\(492\) 0 0
\(493\) 0.584209 + 5.55837i 0.0263114 + 0.250337i
\(494\) 8.66283 0.389759
\(495\) 0 0
\(496\) −10.1922 −0.457642
\(497\) 2.50159 + 23.8010i 0.112212 + 1.06762i
\(498\) 0 0
\(499\) 23.5099 4.99718i 1.05245 0.223705i 0.350963 0.936389i \(-0.385854\pi\)
0.701485 + 0.712685i \(0.252521\pi\)
\(500\) 2.22485 21.1680i 0.0994981 0.946661i
\(501\) 0 0
\(502\) −0.107378 0.119255i −0.00479251 0.00532262i
\(503\) 7.41223 + 22.8125i 0.330495 + 1.01716i 0.968899 + 0.247457i \(0.0795949\pi\)
−0.638404 + 0.769701i \(0.720405\pi\)
\(504\) 0 0
\(505\) 12.1547 0.540876
\(506\) 11.8771 + 2.73489i 0.528001 + 0.121581i
\(507\) 0 0
\(508\) −17.3507 7.72504i −0.769814 0.342743i
\(509\) −2.47502 + 2.74879i −0.109703 + 0.121838i −0.795495 0.605960i \(-0.792789\pi\)
0.685792 + 0.727798i \(0.259456\pi\)
\(510\) 0 0
\(511\) −46.8678 + 20.8669i −2.07331 + 0.923096i
\(512\) −18.3128 13.3050i −0.809318 0.588004i
\(513\) 0 0
\(514\) 2.08094 + 6.40449i 0.0917865 + 0.282490i
\(515\) −0.295378 2.81034i −0.0130159 0.123838i
\(516\) 0 0
\(517\) −1.73877 3.13260i −0.0764712 0.137772i
\(518\) −2.56407 4.44110i −0.112659 0.195131i
\(519\) 0 0
\(520\) 12.3176 + 2.61818i 0.540162 + 0.114815i
\(521\) 1.98178 6.09929i 0.0868234 0.267215i −0.898213 0.439560i \(-0.855134\pi\)
0.985037 + 0.172345i \(0.0551344\pi\)
\(522\) 0 0
\(523\) 2.21554 + 1.60969i 0.0968790 + 0.0703867i 0.635170 0.772372i \(-0.280930\pi\)
−0.538291 + 0.842759i \(0.680930\pi\)
\(524\) −24.9061 27.6610i −1.08803 1.20838i
\(525\) 0 0
\(526\) 7.55217 + 3.36244i 0.329290 + 0.146609i
\(527\) 6.44147 + 11.1570i 0.280595 + 0.486005i
\(528\) 0 0
\(529\) −16.5651 + 28.6916i −0.720222 + 1.24746i
\(530\) 8.51617 6.18736i 0.369919 0.268762i
\(531\) 0 0
\(532\) 8.19149 25.2108i 0.355146 1.09303i
\(533\) 1.42759 0.635602i 0.0618356 0.0275310i
\(534\) 0 0
\(535\) −5.52522 + 1.17442i −0.238876 + 0.0507746i
\(536\) −3.82644 + 4.24969i −0.165277 + 0.183559i
\(537\) 0 0
\(538\) 3.04042 5.26617i 0.131082 0.227041i
\(539\) −12.5784 + 8.81819i −0.541788 + 0.379826i
\(540\) 0 0
\(541\) −16.9114 + 12.2869i −0.727079 + 0.528254i −0.888638 0.458609i \(-0.848348\pi\)
0.161559 + 0.986863i \(0.448348\pi\)
\(542\) −9.24503 1.96509i −0.397108 0.0844080i
\(543\) 0 0
\(544\) −1.71684 + 16.3347i −0.0736091 + 0.700344i
\(545\) −0.983309 + 9.35556i −0.0421203 + 0.400748i
\(546\) 0 0
\(547\) 40.9613 + 8.70658i 1.75138 + 0.372267i 0.968326 0.249690i \(-0.0803288\pi\)
0.783051 + 0.621957i \(0.213662\pi\)
\(548\) −4.55562 + 3.30985i −0.194606 + 0.141390i
\(549\) 0 0
\(550\) 2.77350 1.94439i 0.118263 0.0829092i
\(551\) −3.73576 + 6.47053i −0.159149 + 0.275654i
\(552\) 0 0
\(553\) −9.12636 + 10.1358i −0.388092 + 0.431020i
\(554\) −4.96620 + 1.05560i −0.210993 + 0.0448480i
\(555\) 0 0
\(556\) 24.0994 10.7297i 1.02204 0.455042i
\(557\) 3.87025 11.9114i 0.163988 0.504702i −0.834973 0.550291i \(-0.814517\pi\)
0.998960 + 0.0455895i \(0.0145166\pi\)
\(558\) 0 0
\(559\) 31.0911 22.5890i 1.31502 0.955415i
\(560\) 7.61538 13.1902i 0.321809 0.557389i
\(561\) 0 0
\(562\) −4.03083 6.98160i −0.170030 0.294501i
\(563\) 13.2544 + 5.90124i 0.558606 + 0.248707i 0.666564 0.745448i \(-0.267764\pi\)
−0.107958 + 0.994155i \(0.534431\pi\)
\(564\) 0 0
\(565\) −18.7556 20.8302i −0.789056 0.876335i
\(566\) 0.501956 + 0.364693i 0.0210988 + 0.0153292i
\(567\) 0 0
\(568\) 3.99850 12.3061i 0.167773 0.516353i
\(569\) −27.3612 5.81579i −1.14704 0.243811i −0.405096 0.914274i \(-0.632762\pi\)
−0.741943 + 0.670463i \(0.766095\pi\)
\(570\) 0 0
\(571\) −4.52443 7.83654i −0.189341 0.327949i 0.755689 0.654930i \(-0.227302\pi\)
−0.945031 + 0.326981i \(0.893969\pi\)
\(572\) −11.3219 20.3977i −0.473391 0.852870i
\(573\) 0 0
\(574\) 0.0683481 + 0.650289i 0.00285280 + 0.0271425i
\(575\) 4.82046 + 14.8359i 0.201027 + 0.618698i
\(576\) 0 0
\(577\) −31.0234 22.5398i −1.29152 0.938346i −0.291687 0.956514i \(-0.594217\pi\)
−0.999835 + 0.0181683i \(0.994217\pi\)
\(578\) −2.72428 + 1.21293i −0.113315 + 0.0504511i
\(579\) 0 0
\(580\) −3.40118 + 3.77740i −0.141226 + 0.156848i
\(581\) 0.389352 + 0.173351i 0.0161530 + 0.00719180i
\(582\) 0 0
\(583\) −40.6067 9.35034i −1.68176 0.387252i
\(584\) 27.7381 1.14781
\(585\) 0 0
\(586\) 3.65095 + 11.2365i 0.150819 + 0.464175i
\(587\) 0.483525 + 0.537009i 0.0199572 + 0.0221647i 0.753041 0.657974i \(-0.228586\pi\)
−0.733084 + 0.680139i \(0.761920\pi\)
\(588\) 0 0
\(589\) −1.80022 + 17.1279i −0.0741767 + 0.705744i
\(590\) 2.99669 0.636966i 0.123372 0.0262235i
\(591\) 0 0
\(592\) −0.837737 7.97054i −0.0344308 0.327587i
\(593\) 39.6596 1.62863 0.814313 0.580426i \(-0.197114\pi\)
0.814313 + 0.580426i \(0.197114\pi\)
\(594\) 0 0
\(595\) −19.2517 −0.789244
\(596\) −0.745038 7.08856i −0.0305179 0.290359i
\(597\) 0 0
\(598\) −14.3705 + 3.05454i −0.587652 + 0.124909i
\(599\) −2.12996 + 20.2652i −0.0870276 + 0.828013i 0.860739 + 0.509047i \(0.170002\pi\)
−0.947766 + 0.318965i \(0.896665\pi\)
\(600\) 0 0
\(601\) −32.3670 35.9472i −1.32028 1.46632i −0.781560 0.623830i \(-0.785576\pi\)
−0.538717 0.842487i \(-0.681091\pi\)
\(602\) 4.96914 + 15.2935i 0.202527 + 0.623315i
\(603\) 0 0
\(604\) 13.7129 0.557968
\(605\) 18.2370 + 4.52485i 0.741439 + 0.183961i
\(606\) 0 0
\(607\) −17.9989 8.01364i −0.730554 0.325264i 0.00753068 0.999972i \(-0.497603\pi\)
−0.738085 + 0.674708i \(0.764270\pi\)
\(608\) −14.6921 + 16.3172i −0.595842 + 0.661750i
\(609\) 0 0
\(610\) 2.94928 1.31310i 0.119413 0.0531660i
\(611\) 3.49397 + 2.53852i 0.141351 + 0.102698i
\(612\) 0 0
\(613\) 1.76690 + 5.43796i 0.0713644 + 0.219637i 0.980377 0.197131i \(-0.0631626\pi\)
−0.909013 + 0.416768i \(0.863163\pi\)
\(614\) −0.835451 7.94879i −0.0337161 0.320787i
\(615\) 0 0
\(616\) 20.4724 3.99159i 0.824858 0.160826i
\(617\) 3.05346 + 5.28875i 0.122928 + 0.212917i 0.920921 0.389749i \(-0.127438\pi\)
−0.797993 + 0.602666i \(0.794105\pi\)
\(618\) 0 0
\(619\) 1.74084 + 0.370027i 0.0699704 + 0.0148727i 0.242764 0.970085i \(-0.421946\pi\)
−0.172793 + 0.984958i \(0.555279\pi\)
\(620\) −3.62062 + 11.1431i −0.145408 + 0.447519i
\(621\) 0 0
\(622\) 8.48050 + 6.16144i 0.340037 + 0.247051i
\(623\) 18.1044 + 20.1070i 0.725337 + 0.805568i
\(624\) 0 0
\(625\) −9.36756 4.17071i −0.374702 0.166828i
\(626\) −0.764220 1.32367i −0.0305444 0.0529044i
\(627\) 0 0
\(628\) 0.271963 0.471055i 0.0108525 0.0187971i
\(629\) −8.19556 + 5.95442i −0.326778 + 0.237418i
\(630\) 0 0
\(631\) −13.8566 + 42.6461i −0.551621 + 1.69771i 0.153084 + 0.988213i \(0.451079\pi\)
−0.704705 + 0.709501i \(0.748921\pi\)
\(632\) 6.73674 2.99939i 0.267973 0.119309i
\(633\) 0 0
\(634\) −8.76303 + 1.86264i −0.348024 + 0.0739748i
\(635\) −12.3385 + 13.7033i −0.489639 + 0.543799i
\(636\) 0 0
\(637\) 9.25852 16.0362i 0.366836 0.635379i
\(638\) −2.75097 0.0464448i −0.108912 0.00183877i
\(639\) 0 0
\(640\) −15.6290 + 11.3552i −0.617792 + 0.448852i
\(641\) −26.4193 5.61560i −1.04350 0.221803i −0.345887 0.938276i \(-0.612422\pi\)
−0.697614 + 0.716473i \(0.745755\pi\)
\(642\) 0 0
\(643\) 3.40317 32.3790i 0.134208 1.27690i −0.695426 0.718597i \(-0.744784\pi\)
0.829634 0.558307i \(-0.188549\pi\)
\(644\) −4.69918 + 44.7097i −0.185174 + 1.76181i
\(645\) 0 0
\(646\) 7.00398 + 1.48874i 0.275568 + 0.0585738i
\(647\) −25.4705 + 18.5054i −1.00135 + 0.727523i −0.962377 0.271717i \(-0.912408\pi\)
−0.0389724 + 0.999240i \(0.512408\pi\)
\(648\) 0 0
\(649\) −9.68953 7.29290i −0.380347 0.286271i
\(650\) −2.04149 + 3.53596i −0.0800736 + 0.138692i
\(651\) 0 0
\(652\) −12.9431 + 14.3748i −0.506892 + 0.562961i
\(653\) −4.55794 + 0.968821i −0.178366 + 0.0379129i −0.296229 0.955117i \(-0.595729\pi\)
0.117863 + 0.993030i \(0.462396\pi\)
\(654\) 0 0
\(655\) −33.0133 + 14.6985i −1.28994 + 0.574318i
\(656\) −0.315782 + 0.971878i −0.0123292 + 0.0379455i
\(657\) 0 0
\(658\) −1.46197 + 1.06219i −0.0569937 + 0.0414084i
\(659\) −16.0209 + 27.7490i −0.624086 + 1.08095i 0.364631 + 0.931152i \(0.381195\pi\)
−0.988717 + 0.149797i \(0.952138\pi\)
\(660\) 0 0
\(661\) 20.3527 + 35.2519i 0.791627 + 1.37114i 0.924959 + 0.380067i \(0.124099\pi\)
−0.133331 + 0.991072i \(0.542567\pi\)
\(662\) 1.68757 + 0.751356i 0.0655894 + 0.0292023i
\(663\) 0 0
\(664\) −0.154190 0.171245i −0.00598373 0.00664561i
\(665\) −20.8211 15.1274i −0.807406 0.586615i
\(666\) 0 0
\(667\) 3.91560 12.0510i 0.151613 0.466616i
\(668\) 30.2441 + 6.42857i 1.17018 + 0.248729i
\(669\) 0 0
\(670\) 1.29917 + 2.25023i 0.0501914 + 0.0869340i
\(671\) −11.5853 5.39424i −0.447245 0.208242i
\(672\) 0 0
\(673\) 3.94736 + 37.5567i 0.152160 + 1.44770i 0.758072 + 0.652171i \(0.226142\pi\)
−0.605912 + 0.795532i \(0.707192\pi\)
\(674\) 0.904299 + 2.78315i 0.0348323 + 0.107203i
\(675\) 0 0
\(676\) 4.24655 + 3.08530i 0.163329 + 0.118665i
\(677\) −17.2666 + 7.68759i −0.663610 + 0.295458i −0.710765 0.703429i \(-0.751651\pi\)
0.0471552 + 0.998888i \(0.484984\pi\)
\(678\) 0 0
\(679\) 0.783119 0.869742i 0.0300534 0.0333776i
\(680\) 9.50895 + 4.23366i 0.364652 + 0.162353i
\(681\) 0 0
\(682\) −5.83647 + 2.48137i −0.223490 + 0.0950167i
\(683\) −31.1053 −1.19021 −0.595105 0.803648i \(-0.702890\pi\)
−0.595105 + 0.803648i \(0.702890\pi\)
\(684\) 0 0
\(685\) 1.68941 + 5.19948i 0.0645492 + 0.198662i
\(686\) −2.65099 2.94423i −0.101215 0.112411i
\(687\) 0 0
\(688\) −2.62692 + 24.9935i −0.100150 + 0.952868i
\(689\) 49.1314 10.4432i 1.87176 0.397854i
\(690\) 0 0
\(691\) −2.32172 22.0897i −0.0883225 0.840333i −0.945568 0.325425i \(-0.894493\pi\)
0.857245 0.514908i \(-0.172174\pi\)
\(692\) 21.7565 0.827057
\(693\) 0 0
\(694\) −11.9432 −0.453358
\(695\) −2.67716 25.4715i −0.101551 0.966189i
\(696\) 0 0
\(697\) 1.26345 0.268554i 0.0478565 0.0101722i
\(698\) −0.858360 + 8.16675i −0.0324894 + 0.309116i
\(699\) 0 0
\(700\) 8.36004 + 9.28477i 0.315980 + 0.350931i
\(701\) 9.25374 + 28.4801i 0.349509 + 1.07568i 0.959125 + 0.282981i \(0.0913235\pi\)
−0.609616 + 0.792697i \(0.708677\pi\)
\(702\) 0 0
\(703\) −13.5424 −0.510763
\(704\) 9.02018 + 2.07704i 0.339961 + 0.0782814i
\(705\) 0 0
\(706\) 3.59874 + 1.60226i 0.135440 + 0.0603020i
\(707\) −16.2384 + 18.0345i −0.610707 + 0.678258i
\(708\) 0 0
\(709\) 15.7182 6.99820i 0.590310 0.262823i −0.0897681 0.995963i \(-0.528613\pi\)
0.680078 + 0.733140i \(0.261946\pi\)
\(710\) −4.75647 3.45578i −0.178507 0.129693i
\(711\) 0 0
\(712\) −4.52052 13.9127i −0.169414 0.521402i
\(713\) −3.05304 29.0477i −0.114337 1.08785i
\(714\) 0 0
\(715\) −22.2311 + 4.33449i −0.831398 + 0.162101i
\(716\) −19.2500 33.3420i −0.719407 1.24605i
\(717\) 0 0
\(718\) −13.8295 2.93956i −0.516114 0.109703i
\(719\) −1.46013 + 4.49382i −0.0544537 + 0.167591i −0.974585 0.224020i \(-0.928082\pi\)
0.920131 + 0.391611i \(0.128082\pi\)
\(720\) 0 0
\(721\) 4.56446 + 3.31628i 0.169989 + 0.123505i
\(722\) 0.169236 + 0.187955i 0.00629829 + 0.00699496i
\(723\) 0 0
\(724\) 7.04028 + 3.13454i 0.261650 + 0.116494i
\(725\) −1.76074 3.04969i −0.0653923 0.113263i
\(726\) 0 0
\(727\) −2.60044 + 4.50410i −0.0964450 + 0.167048i −0.910211 0.414145i \(-0.864081\pi\)
0.813766 + 0.581193i \(0.197414\pi\)
\(728\) −20.3408 + 14.7784i −0.753879 + 0.547725i
\(729\) 0 0
\(730\) 3.89468 11.9866i 0.144149 0.443644i
\(731\) 29.0195 12.9203i 1.07333 0.477876i
\(732\) 0 0
\(733\) 47.9910 10.2008i 1.77259 0.376775i 0.798332 0.602217i \(-0.205716\pi\)
0.974257 + 0.225442i \(0.0723826\pi\)
\(734\) 7.33320 8.14435i 0.270673 0.300613i
\(735\) 0 0
\(736\) 18.6187 32.2485i 0.686294 1.18870i
\(737\) 3.34308 9.72706i 0.123144 0.358301i
\(738\) 0 0
\(739\) 12.6160 9.16603i 0.464086 0.337178i −0.331046 0.943615i \(-0.607402\pi\)
0.795132 + 0.606437i \(0.207402\pi\)
\(740\) −9.01179 1.91552i −0.331280 0.0704157i
\(741\) 0 0
\(742\) −2.19690 + 20.9021i −0.0806506 + 0.767339i
\(743\) 1.16387 11.0734i 0.0426981 0.406245i −0.952209 0.305448i \(-0.901194\pi\)
0.994907 0.100798i \(-0.0321395\pi\)
\(744\) 0 0
\(745\) −6.76882 1.43876i −0.247990 0.0527119i
\(746\) −2.80897 + 2.04083i −0.102844 + 0.0747202i
\(747\) 0 0
\(748\) −5.64842 18.4374i −0.206527 0.674140i
\(749\) 5.63901 9.76705i 0.206045 0.356880i
\(750\) 0 0
\(751\) −5.41006 + 6.00848i −0.197416 + 0.219252i −0.833722 0.552184i \(-0.813795\pi\)
0.636307 + 0.771436i \(0.280461\pi\)
\(752\) −2.76248 + 0.587184i −0.100737 + 0.0214124i
\(753\) 0 0
\(754\) 3.02981 1.34896i 0.110339 0.0491262i
\(755\) 4.11410 12.6619i 0.149727 0.460814i
\(756\) 0 0
\(757\) −24.1585 + 17.5522i −0.878056 + 0.637945i −0.932737 0.360559i \(-0.882586\pi\)
0.0546803 + 0.998504i \(0.482586\pi\)
\(758\) 5.97081 10.3417i 0.216869 0.375629i
\(759\) 0 0
\(760\) 6.95742 + 12.0506i 0.252372 + 0.437121i
\(761\) −31.8760 14.1921i −1.15550 0.514463i −0.262685 0.964882i \(-0.584608\pi\)
−0.892817 + 0.450419i \(0.851275\pi\)
\(762\) 0 0
\(763\) −12.5677 13.9578i −0.454980 0.505306i
\(764\) −17.8134 12.9422i −0.644468 0.468233i
\(765\) 0 0
\(766\) 2.67339 8.22786i 0.0965936 0.297284i
\(767\) 14.2991 + 3.03937i 0.516312 + 0.109745i
\(768\) 0 0
\(769\) 2.80362 + 4.85600i 0.101101 + 0.175112i 0.912139 0.409882i \(-0.134430\pi\)
−0.811038 + 0.584994i \(0.801097\pi\)
\(770\) 1.14961 9.40730i 0.0414291 0.339016i
\(771\) 0 0
\(772\) −2.31095 21.9872i −0.0831728 0.791337i
\(773\) 3.34979 + 10.3096i 0.120483 + 0.370810i 0.993051 0.117683i \(-0.0375467\pi\)
−0.872568 + 0.488493i \(0.837547\pi\)
\(774\) 0 0
\(775\) −6.56697 4.77118i −0.235893 0.171386i
\(776\) −0.578070 + 0.257373i −0.0207515 + 0.00923916i
\(777\) 0 0
\(778\) 5.86928 6.51849i 0.210424 0.233699i
\(779\) 1.57746 + 0.702332i 0.0565185 + 0.0251636i
\(780\) 0 0
\(781\) 2.04166 + 23.1835i 0.0730562 + 0.829572i
\(782\) −12.1436 −0.434255
\(783\) 0 0
\(784\) 3.74186 + 11.5163i 0.133638 + 0.411295i
\(785\) −0.353359 0.392445i −0.0126119 0.0140070i
\(786\) 0 0
\(787\) 0.258858 2.46286i 0.00922727 0.0877916i −0.988939 0.148322i \(-0.952613\pi\)
0.998166 + 0.0605308i \(0.0192793\pi\)
\(788\) 17.8040 3.78436i 0.634242 0.134812i
\(789\) 0 0
\(790\) −0.350241 3.33232i −0.0124610 0.118559i
\(791\) 55.9640 1.98985
\(792\) 0 0
\(793\) 15.4047 0.547037
\(794\) 1.12485 + 10.7022i 0.0399195 + 0.379808i
\(795\) 0 0
\(796\) 45.5667 9.68549i 1.61507 0.343293i
\(797\) −1.01180 + 9.62666i −0.0358399 + 0.340994i 0.961878 + 0.273478i \(0.0881740\pi\)
−0.997718 + 0.0675160i \(0.978493\pi\)
\(798\) 0 0
\(799\) 2.38866 + 2.65287i 0.0845047 + 0.0938520i
\(800\) −3.19795 9.84226i −0.113064 0.347977i
\(801\) 0 0
\(802\) −2.65237 −0.0936586
\(803\) −45.9135 + 19.5201i −1.62025 + 0.688850i
\(804\) 0 0
\(805\) 39.8733 + 17.7527i 1.40535 + 0.625702i
\(806\) 5.11539 5.68121i 0.180182 0.200112i
\(807\) 0 0
\(808\) 11.9866 5.33676i 0.421686 0.187747i
\(809\) −6.36318 4.62312i −0.223717 0.162540i 0.470281 0.882517i \(-0.344153\pi\)
−0.693998 + 0.719976i \(0.744153\pi\)
\(810\) 0 0
\(811\) 12.2076 + 37.5712i 0.428668 + 1.31930i 0.899438 + 0.437048i \(0.143976\pi\)
−0.470770 + 0.882256i \(0.656024\pi\)
\(812\) −1.06082 10.0930i −0.0372275 0.354196i
\(813\) 0 0
\(814\) −2.42022 4.36030i −0.0848286 0.152829i
\(815\) 9.38994 + 16.2639i 0.328915 + 0.569698i
\(816\) 0 0
\(817\) 41.5375 + 8.82907i 1.45321 + 0.308890i
\(818\) 3.58013 11.0185i 0.125176 0.385253i
\(819\) 0 0
\(820\) 0.950378 + 0.690490i 0.0331886 + 0.0241130i
\(821\) 2.24401 + 2.49222i 0.0783165 + 0.0869792i 0.781029 0.624494i \(-0.214695\pi\)
−0.702713 + 0.711473i \(0.748028\pi\)
\(822\) 0 0
\(823\) 14.7097 + 6.54920i 0.512749 + 0.228291i 0.646766 0.762688i \(-0.276121\pi\)
−0.134017 + 0.990979i \(0.542788\pi\)
\(824\) −1.52523 2.64177i −0.0531339 0.0920306i
\(825\) 0 0
\(826\) −3.05841 + 5.29732i −0.106416 + 0.184317i
\(827\) 12.3703 8.98751i 0.430156 0.312526i −0.351555 0.936167i \(-0.614347\pi\)
0.781711 + 0.623641i \(0.214347\pi\)
\(828\) 0 0
\(829\) −13.0239 + 40.0835i −0.452340 + 1.39216i 0.421890 + 0.906647i \(0.361367\pi\)
−0.874230 + 0.485512i \(0.838633\pi\)
\(830\) −0.0956507 + 0.0425864i −0.00332008 + 0.00147820i
\(831\) 0 0
\(832\) −10.9138 + 2.31980i −0.378369 + 0.0804247i
\(833\) 10.2415 11.3743i 0.354847 0.394098i
\(834\) 0 0
\(835\) 15.0096 25.9975i 0.519430 0.899679i
\(836\) 8.37869 24.3788i 0.289783 0.843157i
\(837\) 0 0
\(838\) −7.19483 + 5.22735i −0.248541 + 0.180576i
\(839\) 2.58954 + 0.550423i 0.0894008 + 0.0190027i 0.252395 0.967624i \(-0.418782\pi\)
−0.162994 + 0.986627i \(0.552115\pi\)
\(840\) 0 0
\(841\) 2.73233 25.9963i 0.0942181 0.896426i
\(842\) 0.656889 6.24988i 0.0226379 0.215385i
\(843\) 0 0
\(844\) −12.5354 2.66447i −0.431485 0.0917150i
\(845\) 4.12288 2.99545i 0.141831 0.103047i
\(846\) 0 0
\(847\) −31.0780 + 21.0141i −1.06785 + 0.722053i
\(848\) −16.4232 + 28.4458i −0.563976 + 0.976834i
\(849\) 0 0
\(850\) −2.25823 + 2.50802i −0.0774567 + 0.0860244i
\(851\) 22.4651 4.77510i 0.770093 0.163688i
\(852\) 0 0
\(853\) 8.46891 3.77060i 0.289970 0.129103i −0.256597 0.966519i \(-0.582601\pi\)
0.546567 + 0.837416i \(0.315935\pi\)
\(854\) −1.99185 + 6.13027i −0.0681596 + 0.209774i
\(855\) 0 0
\(856\) −4.93314 + 3.58414i −0.168611 + 0.122503i
\(857\) −10.2678 + 17.7844i −0.350742 + 0.607502i −0.986380 0.164485i \(-0.947404\pi\)
0.635638 + 0.771987i \(0.280737\pi\)
\(858\) 0 0
\(859\) −18.0139 31.2010i −0.614626 1.06456i −0.990450 0.137872i \(-0.955974\pi\)
0.375824 0.926691i \(-0.377360\pi\)
\(860\) 26.3922 + 11.7506i 0.899968 + 0.400691i
\(861\) 0 0
\(862\) 2.15931 + 2.39816i 0.0735464 + 0.0816815i
\(863\) 3.49209 + 2.53715i 0.118872 + 0.0863656i 0.645633 0.763648i \(-0.276594\pi\)
−0.526761 + 0.850014i \(0.676594\pi\)
\(864\) 0 0
\(865\) 6.52733 20.0890i 0.221936 0.683048i
\(866\) −6.71579 1.42749i −0.228212 0.0485079i
\(867\) 0 0
\(868\) −11.6966 20.2591i −0.397008 0.687637i
\(869\) −9.04022 + 9.70557i −0.306668 + 0.329239i
\(870\) 0 0
\(871\) 1.29598 + 12.3304i 0.0439127 + 0.417801i
\(872\) 3.13804 + 9.65790i 0.106268 + 0.327058i
\(873\) 0 0
\(874\) −13.1335 9.54206i −0.444248 0.322765i
\(875\) 37.6919 16.7815i 1.27422 0.567319i
\(876\) 0 0
\(877\) 20.8207 23.1237i 0.703064 0.780832i −0.280797 0.959767i \(-0.590599\pi\)
0.983861 + 0.178935i \(0.0572653\pi\)
\(878\) 11.2821 + 5.02310i 0.380752 + 0.169522i
\(879\) 0 0
\(880\) 7.62119 12.7002i 0.256910 0.428125i
\(881\) −43.9267 −1.47993 −0.739964 0.672647i \(-0.765157\pi\)
−0.739964 + 0.672647i \(0.765157\pi\)
\(882\) 0 0
\(883\) −1.81685 5.59170i −0.0611420 0.188176i 0.915820 0.401589i \(-0.131542\pi\)
−0.976962 + 0.213413i \(0.931542\pi\)
\(884\) 15.5535 + 17.2740i 0.523122 + 0.580986i
\(885\) 0 0
\(886\) 1.37520 13.0842i 0.0462009 0.439572i
\(887\) −7.52695 + 1.59990i −0.252730 + 0.0537195i −0.332534 0.943091i \(-0.607904\pi\)
0.0798043 + 0.996811i \(0.474570\pi\)
\(888\) 0 0
\(889\) −3.84835 36.6146i −0.129070 1.22801i
\(890\) −6.64689 −0.222804
\(891\) 0 0
\(892\) −41.3640 −1.38497
\(893\) 0.498831 + 4.74606i 0.0166927 + 0.158821i
\(894\) 0 0
\(895\) −36.5620 + 7.77150i −1.22213 + 0.259773i
\(896\) 4.03178 38.3598i 0.134692 1.28151i
\(897\) 0 0
\(898\) −4.65257 5.16720i −0.155258 0.172432i
\(899\) 2.03751 + 6.27081i 0.0679547 + 0.209143i
\(900\) 0 0
\(901\) 41.5180 1.38316
\(902\) 0.0557818 + 0.633417i 0.00185733 + 0.0210905i
\(903\) 0 0
\(904\) −27.6422 12.3071i −0.919365 0.409328i
\(905\) 5.00651 5.56030i 0.166422 0.184830i
\(906\) 0 0
\(907\) −17.3487 + 7.72415i −0.576055 + 0.256476i −0.674019 0.738714i \(-0.735434\pi\)
0.0979642 + 0.995190i \(0.468767\pi\)
\(908\) 16.9700 + 12.3294i 0.563170 + 0.409167i
\(909\) 0 0
\(910\) 3.53024 + 10.8650i 0.117026 + 0.360170i
\(911\) 5.23011 + 49.7612i 0.173281 + 1.64866i 0.643015 + 0.765853i \(0.277683\pi\)
−0.469734 + 0.882808i \(0.655650\pi\)
\(912\) 0 0
\(913\) 0.375733 + 0.174946i 0.0124349 + 0.00578985i
\(914\) −6.04320 10.4671i −0.199891 0.346222i
\(915\) 0 0
\(916\) 5.26198 + 1.11847i 0.173861 + 0.0369552i
\(917\) 22.2961 68.6205i 0.736284 2.26605i
\(918\) 0 0
\(919\) −2.48708 1.80697i −0.0820411 0.0596063i 0.546009 0.837780i \(-0.316147\pi\)
−0.628050 + 0.778173i \(0.716147\pi\)
\(920\) −15.7905 17.5371i −0.520598 0.578182i
\(921\) 0 0
\(922\) 11.7603 + 5.23600i 0.387303 + 0.172439i
\(923\) −14.0270 24.2955i −0.461705 0.799696i
\(924\) 0 0
\(925\) 3.19142 5.52769i 0.104933 0.181749i
\(926\) −5.03648 + 3.65922i −0.165509 + 0.120249i
\(927\) 0 0
\(928\) −2.59765 + 7.99474i −0.0852720 + 0.262440i
\(929\) 0.827283 0.368330i 0.0271423 0.0120845i −0.393121 0.919487i \(-0.628605\pi\)
0.420263 + 0.907402i \(0.361938\pi\)
\(930\) 0 0
\(931\) 20.0140 4.25410i 0.655931 0.139422i
\(932\) −28.8803 + 32.0748i −0.946004 + 1.05064i
\(933\) 0 0
\(934\) −6.79433 + 11.7681i −0.222317 + 0.385065i
\(935\) −18.7190 0.316034i −0.612177 0.0103354i
\(936\) 0 0
\(937\) 17.8423 12.9632i 0.582881 0.423488i −0.256881 0.966443i \(-0.582695\pi\)
0.839762 + 0.542955i \(0.182695\pi\)
\(938\) −5.07445 1.07861i −0.165687 0.0352178i
\(939\) 0 0
\(940\) −0.339362 + 3.22882i −0.0110688 + 0.105312i
\(941\) 0.570822 5.43101i 0.0186083 0.177046i −0.981270 0.192636i \(-0.938296\pi\)
0.999878 + 0.0155906i \(0.00496286\pi\)
\(942\) 0 0
\(943\) −2.86444 0.608856i −0.0932791 0.0198271i
\(944\) −7.73386 + 5.61898i −0.251716 + 0.182882i
\(945\) 0 0
\(946\) 4.58059 + 14.9519i 0.148928 + 0.486127i
\(947\) 16.2203 28.0944i 0.527089 0.912945i −0.472412 0.881378i \(-0.656617\pi\)
0.999502 0.0315677i \(-0.0100500\pi\)
\(948\) 0 0
\(949\) 40.2410 44.6921i 1.30628 1.45077i
\(950\) −4.41304 + 0.938020i −0.143178 + 0.0304334i
\(951\) 0 0
\(952\) −18.9854 + 8.45287i −0.615322 + 0.273959i
\(953\) 16.6278 51.1752i 0.538628 1.65773i −0.197049 0.980394i \(-0.563136\pi\)
0.735677 0.677333i \(-0.236864\pi\)
\(954\) 0 0
\(955\) −17.2947 + 12.5653i −0.559642 + 0.406604i
\(956\) 6.11452 10.5907i 0.197758 0.342527i
\(957\) 0 0
\(958\) −3.83130 6.63600i −0.123784 0.214400i
\(959\) −9.97177 4.43972i −0.322005 0.143366i
\(960\) 0 0
\(961\) −10.5733 11.7429i −0.341075 0.378802i
\(962\) 4.86330 + 3.53339i 0.156799 + 0.113921i
\(963\) 0 0
\(964\) 4.22478 13.0025i 0.136071 0.418784i
\(965\) −20.9954 4.46271i −0.675866 0.143660i
\(966\) 0 0
\(967\) 14.4075 + 24.9546i 0.463315 + 0.802486i 0.999124 0.0418540i \(-0.0133264\pi\)
−0.535809 + 0.844340i \(0.679993\pi\)
\(968\) 19.9715 3.54507i 0.641908 0.113943i
\(969\) 0 0
\(970\) 0.0300537 + 0.285941i 0.000964965 + 0.00918102i
\(971\) −1.66685 5.13005i −0.0534919 0.164631i 0.920742 0.390173i \(-0.127585\pi\)
−0.974233 + 0.225542i \(0.927585\pi\)
\(972\) 0 0
\(973\) 41.3700 + 30.0571i 1.32626 + 0.963586i
\(974\) 12.0657 5.37199i 0.386609 0.172130i
\(975\) 0 0
\(976\) −6.74058 + 7.48618i −0.215761 + 0.239627i
\(977\) 3.02599 + 1.34726i 0.0968100 + 0.0431026i 0.454570 0.890711i \(-0.349793\pi\)
−0.357760 + 0.933813i \(0.616460\pi\)
\(978\) 0 0
\(979\) 17.2734 + 19.8478i 0.552059 + 0.634338i
\(980\) 13.9200 0.444657
\(981\) 0 0
\(982\) −5.91123 18.1929i −0.188635 0.580559i
\(983\) −22.6649 25.1719i −0.722897 0.802859i 0.263946 0.964537i \(-0.414976\pi\)
−0.986843 + 0.161679i \(0.948309\pi\)
\(984\) 0 0
\(985\) 1.84719 17.5749i 0.0588565 0.559982i
\(986\) 2.68146 0.569962i 0.0853951 0.0181513i
\(987\) 0 0
\(988\) 3.24810 + 30.9036i 0.103336 + 0.983174i
\(989\) −72.0183 −2.29005
\(990\) 0 0
\(991\) 8.66640 0.275297 0.137649 0.990481i \(-0.456046\pi\)
0.137649 + 0.990481i \(0.456046\pi\)
\(992\) 2.02542 + 19.2706i 0.0643071 + 0.611841i
\(993\) 0 0
\(994\) 11.4821 2.44059i 0.364189 0.0774107i
\(995\) 4.72761 44.9802i 0.149875 1.42597i
\(996\) 0 0
\(997\) −20.2515 22.4916i −0.641372 0.712316i 0.331553 0.943437i \(-0.392427\pi\)
−0.972925 + 0.231121i \(0.925761\pi\)
\(998\) −3.64303 11.2121i −0.115318 0.354912i
\(999\) 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.289.5 72
3.2 odd 2 99.2.m.b.25.5 yes 72
9.2 odd 6 891.2.f.f.487.5 36
9.4 even 3 inner 297.2.n.b.91.5 72
9.5 odd 6 99.2.m.b.58.5 yes 72
9.7 even 3 891.2.f.e.487.5 36
11.4 even 5 inner 297.2.n.b.235.5 72
33.2 even 10 1089.2.e.o.727.9 36
33.20 odd 10 1089.2.e.p.727.10 36
33.26 odd 10 99.2.m.b.70.5 yes 72
99.2 even 30 9801.2.a.co.1.10 18
99.4 even 15 inner 297.2.n.b.37.5 72
99.20 odd 30 9801.2.a.cm.1.9 18
99.59 odd 30 99.2.m.b.4.5 72
99.68 even 30 1089.2.e.o.364.9 36
99.70 even 15 891.2.f.e.730.5 36
99.79 odd 30 9801.2.a.cn.1.9 18
99.86 odd 30 1089.2.e.p.364.10 36
99.92 odd 30 891.2.f.f.730.5 36
99.97 even 15 9801.2.a.cp.1.10 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.m.b.4.5 72 99.59 odd 30
99.2.m.b.25.5 yes 72 3.2 odd 2
99.2.m.b.58.5 yes 72 9.5 odd 6
99.2.m.b.70.5 yes 72 33.26 odd 10
297.2.n.b.37.5 72 99.4 even 15 inner
297.2.n.b.91.5 72 9.4 even 3 inner
297.2.n.b.235.5 72 11.4 even 5 inner
297.2.n.b.289.5 72 1.1 even 1 trivial
891.2.f.e.487.5 36 9.7 even 3
891.2.f.e.730.5 36 99.70 even 15
891.2.f.f.487.5 36 9.2 odd 6
891.2.f.f.730.5 36 99.92 odd 30
1089.2.e.o.364.9 36 99.68 even 30
1089.2.e.o.727.9 36 33.2 even 10
1089.2.e.p.364.10 36 99.86 odd 30
1089.2.e.p.727.10 36 33.20 odd 10
9801.2.a.cm.1.9 18 99.20 odd 30
9801.2.a.cn.1.9 18 99.79 odd 30
9801.2.a.co.1.10 18 99.2 even 30
9801.2.a.cp.1.10 18 99.97 even 15