Properties

Label 968.2.i.q.753.2
Level $968$
Weight $2$
Character 968.753
Analytic conductor $7.730$
Analytic rank $0$
Dimension $8$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [968,2,Mod(9,968)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(968, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("968.9");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 968 = 2^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 968.i (of order \(5\), degree \(4\), 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: \(7.72951891566\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.1305015625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 5x^{6} - 9x^{5} + 29x^{4} + 36x^{3} + 80x^{2} + 64x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 88)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 753.2
Root \(0.482546 + 1.48512i\) of defining polynomial
Character \(\chi\) \(=\) 968.753
Dual form 968.2.i.q.9.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26332 + 0.917858i) q^{3} +(1.10058 - 3.38724i) q^{5} +(2.52665 - 1.83572i) q^{7} +(-0.173529 - 0.534068i) q^{9} +O(q^{10})\) \(q+(1.26332 + 0.917858i) q^{3} +(1.10058 - 3.38724i) q^{5} +(2.52665 - 1.83572i) q^{7} +(-0.173529 - 0.534068i) q^{9} +(1.58313 + 4.87236i) q^{13} +(4.49939 - 3.26900i) q^{15} +(-0.618034 + 1.90211i) q^{17} +(-3.23607 - 2.35114i) q^{19} +4.87689 q^{21} +2.43845 q^{23} +(-6.21702 - 4.51693i) q^{25} +(1.71861 - 5.28935i) q^{27} +(-4.14468 + 3.01129i) q^{29} +(-1.71861 - 5.28935i) q^{31} +(-3.43723 - 10.5787i) q^{35} +(6.11742 - 4.44457i) q^{37} +(-2.47214 + 7.60845i) q^{39} +(-0.908612 - 0.660145i) q^{41} +7.12311 q^{43} -2.00000 q^{45} +(-6.47214 - 4.70228i) q^{47} +(0.850968 - 2.61901i) q^{49} +(-2.52665 + 1.83572i) q^{51} +(3.78429 + 11.6468i) q^{53} +(-1.93019 - 5.94050i) q^{57} +(-6.31661 + 4.58929i) q^{59} +(-0.347059 + 1.06814i) q^{61} +(-1.41884 - 1.03085i) q^{63} +18.2462 q^{65} +9.56155 q^{67} +(3.08055 + 2.23815i) q^{69} +(-2.68371 + 8.25960i) q^{71} +(4.14468 - 3.01129i) q^{73} +(-3.70820 - 11.4127i) q^{75} +(3.43723 + 10.5787i) q^{79} +(5.66312 - 4.11450i) q^{81} +(-0.270975 + 0.833976i) q^{83} +(5.76271 + 4.18686i) q^{85} -8.00000 q^{87} +2.68466 q^{89} +(12.9443 + 9.40456i) q^{91} +(2.68371 - 8.25960i) q^{93} +(-11.5254 + 8.37371i) q^{95} +(4.80878 + 14.7999i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9} - 2 q^{13} + 7 q^{15} + 4 q^{17} - 8 q^{19} + 72 q^{21} + 36 q^{23} - 3 q^{25} - 7 q^{27} - 2 q^{29} + 7 q^{31} + 14 q^{35} + 11 q^{37} + 16 q^{39} + 6 q^{41} + 24 q^{43} - 16 q^{45} - 16 q^{47} - 22 q^{49} + 2 q^{51} - 8 q^{53} - 4 q^{57} + 5 q^{59} - 6 q^{61} - 20 q^{63} + 80 q^{65} + 60 q^{67} - 13 q^{69} + 5 q^{71} + 2 q^{73} + 24 q^{75} - 14 q^{79} + 14 q^{81} + 10 q^{83} + 6 q^{85} - 64 q^{87} - 28 q^{89} + 32 q^{91} - 5 q^{93} - 12 q^{95} - 27 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/968\mathbb{Z}\right)^\times\).

\(n\) \(485\) \(727\) \(849\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\)

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 0
\(3\) 1.26332 + 0.917858i 0.729380 + 0.529925i 0.889367 0.457194i \(-0.151145\pi\)
−0.159987 + 0.987119i \(0.551145\pi\)
\(4\) 0 0
\(5\) 1.10058 3.38724i 0.492194 1.51482i −0.329089 0.944299i \(-0.606742\pi\)
0.821284 0.570520i \(-0.193258\pi\)
\(6\) 0 0
\(7\) 2.52665 1.83572i 0.954982 0.693835i 0.00300226 0.999995i \(-0.499044\pi\)
0.951980 + 0.306160i \(0.0990443\pi\)
\(8\) 0 0
\(9\) −0.173529 0.534068i −0.0578431 0.178023i
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) 1.58313 + 4.87236i 0.439080 + 1.35135i 0.888847 + 0.458204i \(0.151507\pi\)
−0.449767 + 0.893146i \(0.648493\pi\)
\(14\) 0 0
\(15\) 4.49939 3.26900i 1.16174 0.844052i
\(16\) 0 0
\(17\) −0.618034 + 1.90211i −0.149895 + 0.461330i −0.997608 0.0691254i \(-0.977979\pi\)
0.847713 + 0.530456i \(0.177979\pi\)
\(18\) 0 0
\(19\) −3.23607 2.35114i −0.742405 0.539389i 0.151058 0.988525i \(-0.451732\pi\)
−0.893463 + 0.449136i \(0.851732\pi\)
\(20\) 0 0
\(21\) 4.87689 1.06423
\(22\) 0 0
\(23\) 2.43845 0.508451 0.254226 0.967145i \(-0.418179\pi\)
0.254226 + 0.967145i \(0.418179\pi\)
\(24\) 0 0
\(25\) −6.21702 4.51693i −1.24340 0.903386i
\(26\) 0 0
\(27\) 1.71861 5.28935i 0.330747 1.01794i
\(28\) 0 0
\(29\) −4.14468 + 3.01129i −0.769648 + 0.559182i −0.901854 0.432040i \(-0.857794\pi\)
0.132207 + 0.991222i \(0.457794\pi\)
\(30\) 0 0
\(31\) −1.71861 5.28935i −0.308672 0.949995i −0.978281 0.207282i \(-0.933538\pi\)
0.669609 0.742714i \(-0.266462\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.43723 10.5787i −0.580998 1.78813i
\(36\) 0 0
\(37\) 6.11742 4.44457i 1.00570 0.730683i 0.0423960 0.999101i \(-0.486501\pi\)
0.963302 + 0.268418i \(0.0865009\pi\)
\(38\) 0 0
\(39\) −2.47214 + 7.60845i −0.395859 + 1.21833i
\(40\) 0 0
\(41\) −0.908612 0.660145i −0.141901 0.103097i 0.514570 0.857448i \(-0.327952\pi\)
−0.656471 + 0.754351i \(0.727952\pi\)
\(42\) 0 0
\(43\) 7.12311 1.08626 0.543132 0.839648i \(-0.317238\pi\)
0.543132 + 0.839648i \(0.317238\pi\)
\(44\) 0 0
\(45\) −2.00000 −0.298142
\(46\) 0 0
\(47\) −6.47214 4.70228i −0.944058 0.685898i 0.00533600 0.999986i \(-0.498301\pi\)
−0.949394 + 0.314087i \(0.898301\pi\)
\(48\) 0 0
\(49\) 0.850968 2.61901i 0.121567 0.374144i
\(50\) 0 0
\(51\) −2.52665 + 1.83572i −0.353801 + 0.257052i
\(52\) 0 0
\(53\) 3.78429 + 11.6468i 0.519812 + 1.59982i 0.774353 + 0.632754i \(0.218076\pi\)
−0.254541 + 0.967062i \(0.581924\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.93019 5.94050i −0.255659 0.786838i
\(58\) 0 0
\(59\) −6.31661 + 4.58929i −0.822353 + 0.597474i −0.917386 0.398000i \(-0.869705\pi\)
0.0950325 + 0.995474i \(0.469705\pi\)
\(60\) 0 0
\(61\) −0.347059 + 1.06814i −0.0444363 + 0.136761i −0.970813 0.239837i \(-0.922906\pi\)
0.926377 + 0.376598i \(0.122906\pi\)
\(62\) 0 0
\(63\) −1.41884 1.03085i −0.178758 0.129875i
\(64\) 0 0
\(65\) 18.2462 2.26316
\(66\) 0 0
\(67\) 9.56155 1.16813 0.584065 0.811707i \(-0.301461\pi\)
0.584065 + 0.811707i \(0.301461\pi\)
\(68\) 0 0
\(69\) 3.08055 + 2.23815i 0.370854 + 0.269441i
\(70\) 0 0
\(71\) −2.68371 + 8.25960i −0.318497 + 0.980234i 0.655793 + 0.754940i \(0.272334\pi\)
−0.974291 + 0.225294i \(0.927666\pi\)
\(72\) 0 0
\(73\) 4.14468 3.01129i 0.485098 0.352444i −0.318198 0.948024i \(-0.603078\pi\)
0.803296 + 0.595580i \(0.203078\pi\)
\(74\) 0 0
\(75\) −3.70820 11.4127i −0.428187 1.31782i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 3.43723 + 10.5787i 0.386718 + 1.19020i 0.935226 + 0.354051i \(0.115196\pi\)
−0.548508 + 0.836146i \(0.684804\pi\)
\(80\) 0 0
\(81\) 5.66312 4.11450i 0.629235 0.457166i
\(82\) 0 0
\(83\) −0.270975 + 0.833976i −0.0297434 + 0.0915408i −0.964826 0.262889i \(-0.915325\pi\)
0.935083 + 0.354429i \(0.115325\pi\)
\(84\) 0 0
\(85\) 5.76271 + 4.18686i 0.625054 + 0.454128i
\(86\) 0 0
\(87\) −8.00000 −0.857690
\(88\) 0 0
\(89\) 2.68466 0.284573 0.142287 0.989825i \(-0.454555\pi\)
0.142287 + 0.989825i \(0.454555\pi\)
\(90\) 0 0
\(91\) 12.9443 + 9.40456i 1.35693 + 0.985866i
\(92\) 0 0
\(93\) 2.68371 8.25960i 0.278287 0.856481i
\(94\) 0 0
\(95\) −11.5254 + 8.37371i −1.18248 + 0.859125i
\(96\) 0 0
\(97\) 4.80878 + 14.7999i 0.488258 + 1.50270i 0.827206 + 0.561899i \(0.189929\pi\)
−0.338948 + 0.940805i \(0.610071\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0.618034 + 1.90211i 0.0614967 + 0.189267i 0.977085 0.212850i \(-0.0682745\pi\)
−0.915588 + 0.402117i \(0.868274\pi\)
\(102\) 0 0
\(103\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(104\) 0 0
\(105\) 5.36741 16.5192i 0.523806 1.61211i
\(106\) 0 0
\(107\) −10.8160 7.85829i −1.04562 0.759689i −0.0742474 0.997240i \(-0.523655\pi\)
−0.971375 + 0.237551i \(0.923655\pi\)
\(108\) 0 0
\(109\) −12.2462 −1.17297 −0.586487 0.809959i \(-0.699490\pi\)
−0.586487 + 0.809959i \(0.699490\pi\)
\(110\) 0 0
\(111\) 11.8078 1.12074
\(112\) 0 0
\(113\) 0.354711 + 0.257713i 0.0333684 + 0.0242436i 0.604344 0.796723i \(-0.293435\pi\)
−0.570976 + 0.820967i \(0.693435\pi\)
\(114\) 0 0
\(115\) 2.68371 8.25960i 0.250257 0.770212i
\(116\) 0 0
\(117\) 2.32746 1.69100i 0.215173 0.156333i
\(118\) 0 0
\(119\) 1.93019 + 5.94050i 0.176940 + 0.544565i
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) −0.541951 1.66795i −0.0488660 0.150394i
\(124\) 0 0
\(125\) −7.73546 + 5.62014i −0.691880 + 0.502681i
\(126\) 0 0
\(127\) −1.93019 + 5.94050i −0.171276 + 0.527134i −0.999444 0.0333464i \(-0.989384\pi\)
0.828168 + 0.560481i \(0.189384\pi\)
\(128\) 0 0
\(129\) 8.99878 + 6.53800i 0.792299 + 0.575639i
\(130\) 0 0
\(131\) −13.3693 −1.16808 −0.584041 0.811724i \(-0.698529\pi\)
−0.584041 + 0.811724i \(0.698529\pi\)
\(132\) 0 0
\(133\) −12.4924 −1.08323
\(134\) 0 0
\(135\) −16.0248 11.6427i −1.37920 1.00205i
\(136\) 0 0
\(137\) −2.60762 + 8.02544i −0.222784 + 0.685660i 0.775725 + 0.631072i \(0.217385\pi\)
−0.998509 + 0.0545881i \(0.982615\pi\)
\(138\) 0 0
\(139\) 12.2348 8.88914i 1.03775 0.753967i 0.0679020 0.997692i \(-0.478369\pi\)
0.969844 + 0.243725i \(0.0783695\pi\)
\(140\) 0 0
\(141\) −3.86037 11.8810i −0.325102 1.00056i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 5.63839 + 17.3532i 0.468243 + 1.44110i
\(146\) 0 0
\(147\) 3.47892 2.52759i 0.286937 0.208472i
\(148\) 0 0
\(149\) −1.31215 + 4.03839i −0.107496 + 0.330838i −0.990308 0.138888i \(-0.955647\pi\)
0.882812 + 0.469726i \(0.155647\pi\)
\(150\) 0 0
\(151\) −7.57994 5.50715i −0.616846 0.448165i 0.234972 0.972002i \(-0.424500\pi\)
−0.851819 + 0.523837i \(0.824500\pi\)
\(152\) 0 0
\(153\) 1.12311 0.0907977
\(154\) 0 0
\(155\) −19.8078 −1.59100
\(156\) 0 0
\(157\) 3.59078 + 2.60885i 0.286575 + 0.208209i 0.721780 0.692122i \(-0.243324\pi\)
−0.435205 + 0.900331i \(0.643324\pi\)
\(158\) 0 0
\(159\) −5.90936 + 18.1872i −0.468643 + 1.44234i
\(160\) 0 0
\(161\) 6.16109 4.47630i 0.485562 0.352781i
\(162\) 0 0
\(163\) −1.23607 3.80423i −0.0968163 0.297970i 0.890906 0.454187i \(-0.150070\pi\)
−0.987723 + 0.156217i \(0.950070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.47214 7.60845i −0.191300 0.588760i −1.00000 0.000538710i \(-0.999829\pi\)
0.808700 0.588221i \(-0.200171\pi\)
\(168\) 0 0
\(169\) −10.7164 + 7.78593i −0.824339 + 0.598918i
\(170\) 0 0
\(171\) −0.694117 + 2.13627i −0.0530805 + 0.163365i
\(172\) 0 0
\(173\) 9.90739 + 7.19814i 0.753245 + 0.547265i 0.896831 0.442373i \(-0.145863\pi\)
−0.143586 + 0.989638i \(0.545863\pi\)
\(174\) 0 0
\(175\) −24.0000 −1.81423
\(176\) 0 0
\(177\) −12.1922 −0.916425
\(178\) 0 0
\(179\) 5.20881 + 3.78442i 0.389325 + 0.282861i 0.765179 0.643818i \(-0.222651\pi\)
−0.375854 + 0.926679i \(0.622651\pi\)
\(180\) 0 0
\(181\) −0.406463 + 1.25096i −0.0302121 + 0.0929834i −0.965026 0.262156i \(-0.915567\pi\)
0.934813 + 0.355139i \(0.115567\pi\)
\(182\) 0 0
\(183\) −1.41884 + 1.03085i −0.104884 + 0.0762027i
\(184\) 0 0
\(185\) −8.32210 25.6128i −0.611853 1.88309i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −5.36741 16.5192i −0.390422 1.20160i
\(190\) 0 0
\(191\) 8.44488 6.13557i 0.611050 0.443954i −0.238734 0.971085i \(-0.576732\pi\)
0.849784 + 0.527131i \(0.176732\pi\)
\(192\) 0 0
\(193\) 2.81919 8.67659i 0.202930 0.624555i −0.796862 0.604161i \(-0.793508\pi\)
0.999792 0.0203931i \(-0.00649179\pi\)
\(194\) 0 0
\(195\) 23.0509 + 16.7474i 1.65071 + 1.19931i
\(196\) 0 0
\(197\) 14.4924 1.03254 0.516271 0.856425i \(-0.327320\pi\)
0.516271 + 0.856425i \(0.327320\pi\)
\(198\) 0 0
\(199\) −12.4924 −0.885564 −0.442782 0.896629i \(-0.646009\pi\)
−0.442782 + 0.896629i \(0.646009\pi\)
\(200\) 0 0
\(201\) 12.0793 + 8.77615i 0.852010 + 0.619022i
\(202\) 0 0
\(203\) −4.94427 + 15.2169i −0.347020 + 1.06802i
\(204\) 0 0
\(205\) −3.23607 + 2.35114i −0.226017 + 0.164211i
\(206\) 0 0
\(207\) −0.423142 1.30230i −0.0294104 0.0905159i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −2.62430 8.07677i −0.180664 0.556028i 0.819182 0.573533i \(-0.194428\pi\)
−0.999847 + 0.0175052i \(0.994428\pi\)
\(212\) 0 0
\(213\) −10.9715 + 7.97128i −0.751757 + 0.546183i
\(214\) 0 0
\(215\) 7.83955 24.1277i 0.534653 1.64549i
\(216\) 0 0
\(217\) −14.0521 10.2094i −0.953917 0.693061i
\(218\) 0 0
\(219\) 8.00000 0.540590
\(220\) 0 0
\(221\) −10.2462 −0.689235
\(222\) 0 0
\(223\) 9.55268 + 6.94043i 0.639695 + 0.464766i 0.859745 0.510723i \(-0.170622\pi\)
−0.220050 + 0.975488i \(0.570622\pi\)
\(224\) 0 0
\(225\) −1.33351 + 4.10413i −0.0889009 + 0.273609i
\(226\) 0 0
\(227\) 18.7070 13.5914i 1.24163 0.902094i 0.243921 0.969795i \(-0.421566\pi\)
0.997706 + 0.0677010i \(0.0215664\pi\)
\(228\) 0 0
\(229\) 4.53781 + 13.9659i 0.299867 + 0.922895i 0.981543 + 0.191241i \(0.0612513\pi\)
−0.681676 + 0.731654i \(0.738749\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.27724 + 7.00864i 0.149187 + 0.459151i 0.997526 0.0703033i \(-0.0223967\pi\)
−0.848338 + 0.529454i \(0.822397\pi\)
\(234\) 0 0
\(235\) −23.0509 + 16.7474i −1.50367 + 1.09248i
\(236\) 0 0
\(237\) −5.36741 + 16.5192i −0.348651 + 1.07304i
\(238\) 0 0
\(239\) −3.94549 2.86657i −0.255213 0.185423i 0.452821 0.891601i \(-0.350418\pi\)
−0.708034 + 0.706179i \(0.750418\pi\)
\(240\) 0 0
\(241\) −29.1231 −1.87598 −0.937992 0.346657i \(-0.887317\pi\)
−0.937992 + 0.346657i \(0.887317\pi\)
\(242\) 0 0
\(243\) −5.75379 −0.369106
\(244\) 0 0
\(245\) −7.93465 5.76486i −0.506926 0.368303i
\(246\) 0 0
\(247\) 6.33251 19.4895i 0.402928 1.24008i
\(248\) 0 0
\(249\) −1.10780 + 0.804864i −0.0702040 + 0.0510062i
\(250\) 0 0
\(251\) 0.482546 + 1.48512i 0.0304581 + 0.0937403i 0.965130 0.261771i \(-0.0843066\pi\)
−0.934672 + 0.355512i \(0.884307\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 3.43723 + 10.5787i 0.215248 + 0.662464i
\(256\) 0 0
\(257\) −9.50901 + 6.90870i −0.593156 + 0.430953i −0.843443 0.537219i \(-0.819475\pi\)
0.250287 + 0.968172i \(0.419475\pi\)
\(258\) 0 0
\(259\) 7.29760 22.4597i 0.453451 1.39558i
\(260\) 0 0
\(261\) 2.32746 + 1.69100i 0.144066 + 0.104670i
\(262\) 0 0
\(263\) −19.1231 −1.17918 −0.589591 0.807702i \(-0.700711\pi\)
−0.589591 + 0.807702i \(0.700711\pi\)
\(264\) 0 0
\(265\) 43.6155 2.67928
\(266\) 0 0
\(267\) 3.39159 + 2.46413i 0.207562 + 0.150803i
\(268\) 0 0
\(269\) −6.40859 + 19.7236i −0.390739 + 1.20257i 0.541492 + 0.840706i \(0.317860\pi\)
−0.932231 + 0.361864i \(0.882140\pi\)
\(270\) 0 0
\(271\) −23.0509 + 16.7474i −1.40024 + 1.01733i −0.405587 + 0.914056i \(0.632933\pi\)
−0.994653 + 0.103277i \(0.967067\pi\)
\(272\) 0 0
\(273\) 7.72074 + 23.7620i 0.467281 + 1.43814i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 5.56231 + 17.1190i 0.334207 + 1.02858i 0.967112 + 0.254353i \(0.0818624\pi\)
−0.632905 + 0.774229i \(0.718138\pi\)
\(278\) 0 0
\(279\) −2.52665 + 1.83572i −0.151266 + 0.109901i
\(280\) 0 0
\(281\) −5.02036 + 15.4511i −0.299489 + 0.921733i 0.682187 + 0.731178i \(0.261029\pi\)
−0.981676 + 0.190556i \(0.938971\pi\)
\(282\) 0 0
\(283\) 16.1803 + 11.7557i 0.961821 + 0.698804i 0.953573 0.301162i \(-0.0973744\pi\)
0.00824833 + 0.999966i \(0.497374\pi\)
\(284\) 0 0
\(285\) −22.2462 −1.31775
\(286\) 0 0
\(287\) −3.50758 −0.207046
\(288\) 0 0
\(289\) 10.5172 + 7.64121i 0.618660 + 0.449483i
\(290\) 0 0
\(291\) −7.50917 + 23.1109i −0.440195 + 1.35478i
\(292\) 0 0
\(293\) −2.72583 + 1.98043i −0.159245 + 0.115698i −0.664554 0.747240i \(-0.731378\pi\)
0.505309 + 0.862938i \(0.331378\pi\)
\(294\) 0 0
\(295\) 8.59307 + 26.4468i 0.500308 + 1.53979i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.86037 + 11.8810i 0.223251 + 0.687096i
\(300\) 0 0
\(301\) 17.9976 13.0760i 1.03736 0.753688i
\(302\) 0 0
\(303\) −0.965093 + 2.97025i −0.0554431 + 0.170636i
\(304\) 0 0
\(305\) 3.23607 + 2.35114i 0.185297 + 0.134626i
\(306\) 0 0
\(307\) 32.4924 1.85444 0.927220 0.374516i \(-0.122191\pi\)
0.927220 + 0.374516i \(0.122191\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −7.89098 5.73313i −0.447456 0.325096i 0.341134 0.940015i \(-0.389189\pi\)
−0.788591 + 0.614918i \(0.789189\pi\)
\(312\) 0 0
\(313\) −3.03077 + 9.32774i −0.171309 + 0.527235i −0.999446 0.0332913i \(-0.989401\pi\)
0.828137 + 0.560526i \(0.189401\pi\)
\(314\) 0 0
\(315\) −5.05329 + 3.67143i −0.284721 + 0.206862i
\(316\) 0 0
\(317\) −4.38564 13.4976i −0.246322 0.758102i −0.995416 0.0956380i \(-0.969511\pi\)
0.749094 0.662464i \(-0.230489\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −6.45132 19.8551i −0.360077 1.10820i
\(322\) 0 0
\(323\) 6.47214 4.70228i 0.360119 0.261642i
\(324\) 0 0
\(325\) 12.1658 37.4424i 0.674836 2.07693i
\(326\) 0 0
\(327\) −15.4709 11.2403i −0.855544 0.621589i
\(328\) 0 0
\(329\) −24.9848 −1.37746
\(330\) 0 0
\(331\) 34.9309 1.91997 0.959987 0.280044i \(-0.0903491\pi\)
0.959987 + 0.280044i \(0.0903491\pi\)
\(332\) 0 0
\(333\) −3.43526 2.49586i −0.188251 0.136772i
\(334\) 0 0
\(335\) 10.5233 32.3873i 0.574947 1.76950i
\(336\) 0 0
\(337\) −13.5418 + 9.83872i −0.737671 + 0.535949i −0.891981 0.452073i \(-0.850685\pi\)
0.154310 + 0.988023i \(0.450685\pi\)
\(338\) 0 0
\(339\) 0.211571 + 0.651149i 0.0114910 + 0.0353656i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 4.09799 + 12.6123i 0.221271 + 0.681001i
\(344\) 0 0
\(345\) 10.9715 7.97128i 0.590687 0.429159i
\(346\) 0 0
\(347\) −7.02662 + 21.6257i −0.377209 + 1.16093i 0.564767 + 0.825250i \(0.308966\pi\)
−0.941976 + 0.335680i \(0.891034\pi\)
\(348\) 0 0
\(349\) −26.0877 18.9538i −1.39644 1.01458i −0.995123 0.0986387i \(-0.968551\pi\)
−0.401321 0.915937i \(-0.631449\pi\)
\(350\) 0 0
\(351\) 28.4924 1.52081
\(352\) 0 0
\(353\) −24.0540 −1.28026 −0.640132 0.768265i \(-0.721120\pi\)
−0.640132 + 0.768265i \(0.721120\pi\)
\(354\) 0 0
\(355\) 25.0236 + 18.1807i 1.32811 + 0.964932i
\(356\) 0 0
\(357\) −3.01409 + 9.27640i −0.159522 + 0.490959i
\(358\) 0 0
\(359\) 3.63445 2.64058i 0.191819 0.139364i −0.487731 0.872994i \(-0.662175\pi\)
0.679550 + 0.733630i \(0.262175\pi\)
\(360\) 0 0
\(361\) −0.927051 2.85317i −0.0487922 0.150167i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.63839 17.3532i −0.295127 0.908307i
\(366\) 0 0
\(367\) −18.5515 + 13.4784i −0.968379 + 0.703568i −0.955081 0.296343i \(-0.904233\pi\)
−0.0132971 + 0.999912i \(0.504233\pi\)
\(368\) 0 0
\(369\) −0.194892 + 0.599815i −0.0101457 + 0.0312251i
\(370\) 0 0
\(371\) 30.9418 + 22.4806i 1.60642 + 1.16713i
\(372\) 0 0
\(373\) 8.24621 0.426973 0.213486 0.976946i \(-0.431518\pi\)
0.213486 + 0.976946i \(0.431518\pi\)
\(374\) 0 0
\(375\) −14.9309 −0.771027
\(376\) 0 0
\(377\) −21.2336 15.4271i −1.09359 0.794538i
\(378\) 0 0
\(379\) 0.0594042 0.182827i 0.00305139 0.00939120i −0.949519 0.313709i \(-0.898428\pi\)
0.952571 + 0.304318i \(0.0984284\pi\)
\(380\) 0 0
\(381\) −7.89098 + 5.73313i −0.404267 + 0.293717i
\(382\) 0 0
\(383\) −0.634713 1.95345i −0.0324323 0.0998165i 0.933530 0.358499i \(-0.116712\pi\)
−0.965962 + 0.258683i \(0.916712\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.23607 3.80423i −0.0628329 0.193380i
\(388\) 0 0
\(389\) −2.88136 + 2.09343i −0.146091 + 0.106141i −0.658430 0.752642i \(-0.728779\pi\)
0.512339 + 0.858783i \(0.328779\pi\)
\(390\) 0 0
\(391\) −1.50704 + 4.63820i −0.0762145 + 0.234564i
\(392\) 0 0
\(393\) −16.8898 12.2711i −0.851976 0.618997i
\(394\) 0 0
\(395\) 39.6155 1.99327
\(396\) 0 0
\(397\) 10.4924 0.526600 0.263300 0.964714i \(-0.415189\pi\)
0.263300 + 0.964714i \(0.415189\pi\)
\(398\) 0 0
\(399\) −15.7820 11.4663i −0.790086 0.574031i
\(400\) 0 0
\(401\) 9.42268 29.0000i 0.470546 1.44819i −0.381325 0.924441i \(-0.624532\pi\)
0.851871 0.523751i \(-0.175468\pi\)
\(402\) 0 0
\(403\) 23.0509 16.7474i 1.14824 0.834249i
\(404\) 0 0
\(405\) −7.70406 23.7107i −0.382818 1.17819i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −6.95054 21.3916i −0.343682 1.05774i −0.962286 0.272041i \(-0.912301\pi\)
0.618603 0.785703i \(-0.287699\pi\)
\(410\) 0 0
\(411\) −10.6605 + 7.74529i −0.525843 + 0.382047i
\(412\) 0 0
\(413\) −7.53522 + 23.1910i −0.370784 + 1.14116i
\(414\) 0 0
\(415\) 2.52665 + 1.83572i 0.124028 + 0.0901117i
\(416\) 0 0
\(417\) 23.6155 1.15646
\(418\) 0 0
\(419\) −32.4924 −1.58736 −0.793679 0.608336i \(-0.791837\pi\)
−0.793679 + 0.608336i \(0.791837\pi\)
\(420\) 0 0
\(421\) −2.01641 1.46501i −0.0982739 0.0714002i 0.537563 0.843223i \(-0.319345\pi\)
−0.635837 + 0.771823i \(0.719345\pi\)
\(422\) 0 0
\(423\) −1.38823 + 4.27255i −0.0674983 + 0.207738i
\(424\) 0 0
\(425\) 12.4340 9.03386i 0.603139 0.438206i
\(426\) 0 0
\(427\) 1.08390 + 3.33590i 0.0524536 + 0.161436i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.38150 25.7956i −0.403723 1.24253i −0.921957 0.387292i \(-0.873411\pi\)
0.518234 0.855239i \(-0.326589\pi\)
\(432\) 0 0
\(433\) 18.3523 13.3337i 0.881954 0.640777i −0.0518137 0.998657i \(-0.516500\pi\)
0.933768 + 0.357880i \(0.116500\pi\)
\(434\) 0 0
\(435\) −8.80464 + 27.0979i −0.422150 + 1.29925i
\(436\) 0 0
\(437\) −7.89098 5.73313i −0.377477 0.274253i
\(438\) 0 0
\(439\) −4.49242 −0.214412 −0.107206 0.994237i \(-0.534190\pi\)
−0.107206 + 0.994237i \(0.534190\pi\)
\(440\) 0 0
\(441\) −1.54640 −0.0736380
\(442\) 0 0
\(443\) −9.15430 6.65099i −0.434934 0.315998i 0.348685 0.937240i \(-0.386628\pi\)
−0.783619 + 0.621242i \(0.786628\pi\)
\(444\) 0 0
\(445\) 2.95468 9.09358i 0.140065 0.431077i
\(446\) 0 0
\(447\) −5.36434 + 3.89742i −0.253724 + 0.184342i
\(448\) 0 0
\(449\) −11.2935 34.7577i −0.532971 1.64032i −0.747992 0.663707i \(-0.768982\pi\)
0.215021 0.976609i \(-0.431018\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −4.52113 13.9146i −0.212421 0.653765i
\(454\) 0 0
\(455\) 46.1017 33.4949i 2.16128 1.57026i
\(456\) 0 0
\(457\) −7.37368 + 22.6939i −0.344926 + 1.06157i 0.616697 + 0.787201i \(0.288470\pi\)
−0.961623 + 0.274373i \(0.911530\pi\)
\(458\) 0 0
\(459\) 8.99878 + 6.53800i 0.420027 + 0.305168i
\(460\) 0 0
\(461\) −1.12311 −0.0523082 −0.0261541 0.999658i \(-0.508326\pi\)
−0.0261541 + 0.999658i \(0.508326\pi\)
\(462\) 0 0
\(463\) 15.3153 0.711764 0.355882 0.934531i \(-0.384180\pi\)
0.355882 + 0.934531i \(0.384180\pi\)
\(464\) 0 0
\(465\) −25.0236 18.1807i −1.16044 0.843110i
\(466\) 0 0
\(467\) 8.74524 26.9151i 0.404681 1.24548i −0.516480 0.856299i \(-0.672758\pi\)
0.921161 0.389182i \(-0.127242\pi\)
\(468\) 0 0
\(469\) 24.1587 17.5523i 1.11554 0.810489i
\(470\) 0 0
\(471\) 2.14176 + 6.59165i 0.0986869 + 0.303727i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 9.49876 + 29.2342i 0.435833 + 1.34136i
\(476\) 0 0
\(477\) 5.56352 4.04214i 0.254736 0.185077i
\(478\) 0 0
\(479\) 4.94427 15.2169i 0.225910 0.695278i −0.772288 0.635272i \(-0.780888\pi\)
0.998198 0.0600061i \(-0.0191120\pi\)
\(480\) 0 0
\(481\) 31.3402 + 22.7700i 1.42899 + 1.03822i
\(482\) 0 0
\(483\) 11.8920 0.541107
\(484\) 0 0
\(485\) 55.4233 2.51664
\(486\) 0 0
\(487\) −12.0793 8.77615i −0.547367 0.397685i 0.279447 0.960161i \(-0.409849\pi\)
−0.826814 + 0.562476i \(0.809849\pi\)
\(488\) 0 0
\(489\) 1.93019 5.94050i 0.0872860 0.268639i
\(490\) 0 0
\(491\) 11.1270 8.08427i 0.502157 0.364838i −0.307683 0.951489i \(-0.599554\pi\)
0.809840 + 0.586651i \(0.199554\pi\)
\(492\) 0 0
\(493\) −3.16625 9.74473i −0.142601 0.438880i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.38150 + 25.7956i 0.375962 + 1.15709i
\(498\) 0 0
\(499\) 23.4492 17.0369i 1.04973 0.762675i 0.0775704 0.996987i \(-0.475284\pi\)
0.972161 + 0.234312i \(0.0752838\pi\)
\(500\) 0 0
\(501\) 3.86037 11.8810i 0.172469 0.530804i
\(502\) 0 0
\(503\) −25.5775 18.5831i −1.14044 0.828581i −0.153263 0.988185i \(-0.548978\pi\)
−0.987181 + 0.159604i \(0.948978\pi\)
\(504\) 0 0
\(505\) 7.12311 0.316974
\(506\) 0 0
\(507\) −20.6847 −0.918638
\(508\) 0 0
\(509\) 14.8052 + 10.7566i 0.656227 + 0.476777i 0.865387 0.501105i \(-0.167073\pi\)
−0.209160 + 0.977882i \(0.567073\pi\)
\(510\) 0 0
\(511\) 4.94427 15.2169i 0.218722 0.673156i
\(512\) 0 0
\(513\) −17.9976 + 13.0760i −0.794612 + 0.577319i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 5.90936 + 18.1872i 0.259392 + 0.798327i
\(520\) 0 0
\(521\) −1.06413 + 0.773138i −0.0466205 + 0.0338718i −0.610851 0.791745i \(-0.709173\pi\)
0.564231 + 0.825617i \(0.309173\pi\)
\(522\) 0 0
\(523\) 3.70820 11.4127i 0.162148 0.499042i −0.836666 0.547713i \(-0.815499\pi\)
0.998815 + 0.0486712i \(0.0154987\pi\)
\(524\) 0 0
\(525\) −30.3197 22.0286i −1.32326 0.961406i
\(526\) 0 0
\(527\) 11.1231 0.484530
\(528\) 0 0
\(529\) −17.0540 −0.741477
\(530\) 0 0
\(531\) 3.54711 + 2.57713i 0.153932 + 0.111838i
\(532\) 0 0
\(533\) 1.77802 5.47218i 0.0770145 0.237026i
\(534\) 0 0
\(535\) −38.5218 + 27.9877i −1.66544 + 1.21001i
\(536\) 0 0
\(537\) 3.10685 + 9.56190i 0.134070 + 0.412626i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 7.37368 + 22.6939i 0.317019 + 0.975685i 0.974915 + 0.222576i \(0.0714467\pi\)
−0.657896 + 0.753109i \(0.728553\pi\)
\(542\) 0 0
\(543\) −1.66170 + 1.20730i −0.0713104 + 0.0518100i
\(544\) 0 0
\(545\) −13.4779 + 41.4808i −0.577331 + 1.77684i
\(546\) 0 0
\(547\) −34.1779 24.8317i −1.46134 1.06173i −0.983011 0.183547i \(-0.941242\pi\)
−0.478331 0.878180i \(-0.658758\pi\)
\(548\) 0 0
\(549\) 0.630683 0.0269169
\(550\) 0 0
\(551\) 20.4924 0.873007
\(552\) 0 0
\(553\) 28.1041 + 20.4189i 1.19511 + 0.868298i
\(554\) 0 0
\(555\) 12.9954 39.9957i 0.551624 1.69772i
\(556\) 0 0
\(557\) −3.03688 + 2.20642i −0.128677 + 0.0934891i −0.650262 0.759710i \(-0.725341\pi\)
0.521585 + 0.853199i \(0.325341\pi\)
\(558\) 0 0
\(559\) 11.2768 + 34.7064i 0.476957 + 1.46792i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.56857 23.2937i −0.318977 0.981711i −0.974086 0.226177i \(-0.927377\pi\)
0.655109 0.755535i \(-0.272623\pi\)
\(564\) 0 0
\(565\) 1.26332 0.917858i 0.0531484 0.0386146i
\(566\) 0 0
\(567\) 6.75565 20.7917i 0.283711 0.873171i
\(568\) 0 0
\(569\) −21.7439 15.7978i −0.911550 0.662280i 0.0298562 0.999554i \(-0.490495\pi\)
−0.941406 + 0.337274i \(0.890495\pi\)
\(570\) 0 0
\(571\) −16.4924 −0.690186 −0.345093 0.938568i \(-0.612153\pi\)
−0.345093 + 0.938568i \(0.612153\pi\)
\(572\) 0 0
\(573\) 16.3002 0.680950
\(574\) 0 0
\(575\) −15.1599 11.0143i −0.632210 0.459328i
\(576\) 0 0
\(577\) 4.80878 14.7999i 0.200192 0.616129i −0.799684 0.600421i \(-0.795000\pi\)
0.999877 0.0157079i \(-0.00500018\pi\)
\(578\) 0 0
\(579\) 11.5254 8.37371i 0.478980 0.348000i
\(580\) 0 0
\(581\) 0.846284 + 2.60460i 0.0351098 + 0.108057i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −3.16625 9.74473i −0.130908 0.402895i
\(586\) 0 0
\(587\) 19.8148 14.3963i 0.817844 0.594198i −0.0982503 0.995162i \(-0.531325\pi\)
0.916094 + 0.400963i \(0.131325\pi\)
\(588\) 0 0
\(589\) −6.87446 + 21.1574i −0.283257 + 0.871776i
\(590\) 0 0
\(591\) 18.3086 + 13.3020i 0.753115 + 0.547170i
\(592\) 0 0
\(593\) −3.36932 −0.138361 −0.0691806 0.997604i \(-0.522038\pi\)
−0.0691806 + 0.997604i \(0.522038\pi\)
\(594\) 0 0
\(595\) 22.2462 0.912006
\(596\) 0 0
\(597\) −15.7820 11.4663i −0.645913 0.469283i
\(598\) 0 0
\(599\) −4.94427 + 15.2169i −0.202017 + 0.621746i 0.797805 + 0.602915i \(0.205994\pi\)
−0.999823 + 0.0188306i \(0.994006\pi\)
\(600\) 0 0
\(601\) 3.03688 2.20642i 0.123877 0.0900018i −0.524122 0.851643i \(-0.675606\pi\)
0.647999 + 0.761642i \(0.275606\pi\)
\(602\) 0 0
\(603\) −1.65921 5.10652i −0.0675683 0.207954i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 14.1721 + 43.6171i 0.575226 + 1.77036i 0.635408 + 0.772176i \(0.280832\pi\)
−0.0601823 + 0.998187i \(0.519168\pi\)
\(608\) 0 0
\(609\) −20.2132 + 14.6857i −0.819079 + 0.595096i
\(610\) 0 0
\(611\) 12.6650 38.9789i 0.512372 1.57692i
\(612\) 0 0
\(613\) 9.59635 + 6.97216i 0.387593 + 0.281603i 0.764468 0.644661i \(-0.223002\pi\)
−0.376876 + 0.926264i \(0.623002\pi\)
\(614\) 0 0
\(615\) −6.24621 −0.251872
\(616\) 0 0
\(617\) −2.49242 −0.100341 −0.0501706 0.998741i \(-0.515976\pi\)
−0.0501706 + 0.998741i \(0.515976\pi\)
\(618\) 0 0
\(619\) −15.3154 11.1273i −0.615578 0.447243i 0.235796 0.971802i \(-0.424230\pi\)
−0.851374 + 0.524559i \(0.824230\pi\)
\(620\) 0 0
\(621\) 4.19075 12.8978i 0.168169 0.517571i
\(622\) 0 0
\(623\) 6.78318 4.92827i 0.271762 0.197447i
\(624\) 0 0
\(625\) −1.35019 4.15547i −0.0540077 0.166219i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.67330 + 14.3829i 0.186337 + 0.573485i
\(630\) 0 0
\(631\) 34.0224 24.7187i 1.35441 0.984036i 0.355631 0.934626i \(-0.384266\pi\)
0.998779 0.0494097i \(-0.0157340\pi\)
\(632\) 0 0
\(633\) 4.09799 12.6123i 0.162880 0.501294i
\(634\) 0 0
\(635\) 17.9976 + 13.0760i 0.714212 + 0.518905i
\(636\) 0 0
\(637\) 14.1080 0.558977
\(638\) 0 0
\(639\) 4.87689 0.192927
\(640\) 0 0
\(641\) 37.4576 + 27.2146i 1.47949 + 1.07491i 0.977721 + 0.209908i \(0.0673163\pi\)
0.501767 + 0.865003i \(0.332684\pi\)
\(642\) 0 0
\(643\) −2.83587 + 8.72792i −0.111836 + 0.344196i −0.991274 0.131818i \(-0.957919\pi\)
0.879438 + 0.476013i \(0.157919\pi\)
\(644\) 0 0
\(645\) 32.0496 23.2854i 1.26195 0.916863i
\(646\) 0 0
\(647\) 4.19075 + 12.8978i 0.164755 + 0.507065i 0.999018 0.0443021i \(-0.0141064\pi\)
−0.834263 + 0.551367i \(0.814106\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −8.38150 25.7956i −0.328497 1.01101i
\(652\) 0 0
\(653\) −28.4589 + 20.6766i −1.11368 + 0.809137i −0.983239 0.182319i \(-0.941640\pi\)
−0.130442 + 0.991456i \(0.541640\pi\)
\(654\) 0 0
\(655\) −14.7140 + 45.2851i −0.574924 + 1.76943i
\(656\) 0 0
\(657\) −2.32746 1.69100i −0.0908027 0.0659720i
\(658\) 0 0
\(659\) 11.6155 0.452477 0.226238 0.974072i \(-0.427357\pi\)
0.226238 + 0.974072i \(0.427357\pi\)
\(660\) 0 0
\(661\) 41.8078 1.62613 0.813067 0.582170i \(-0.197796\pi\)
0.813067 + 0.582170i \(0.197796\pi\)
\(662\) 0 0
\(663\) −12.9443 9.40456i −0.502714 0.365243i
\(664\) 0 0
\(665\) −13.7489 + 42.3148i −0.533160 + 1.64090i
\(666\) 0 0
\(667\) −10.1066 + 7.34286i −0.391328 + 0.284317i
\(668\) 0 0
\(669\) 5.69779 + 17.5360i 0.220289 + 0.677981i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −10.2690 31.6046i −0.395839 1.21827i −0.928306 0.371817i \(-0.878735\pi\)
0.532467 0.846451i \(-0.321265\pi\)
\(674\) 0 0
\(675\) −34.5763 + 25.1211i −1.33084 + 0.966913i
\(676\) 0 0
\(677\) 6.40859 19.7236i 0.246302 0.758040i −0.749117 0.662437i \(-0.769522\pi\)
0.995420 0.0956028i \(-0.0304779\pi\)
\(678\) 0 0
\(679\) 39.3185 + 28.5666i 1.50891 + 1.09628i
\(680\) 0 0
\(681\) 36.1080 1.38366
\(682\) 0 0
\(683\) 6.73863 0.257847 0.128923 0.991655i \(-0.458848\pi\)
0.128923 + 0.991655i \(0.458848\pi\)
\(684\) 0 0
\(685\) 24.3142 + 17.6653i 0.928997 + 0.674956i
\(686\) 0 0
\(687\) −7.08603 + 21.8086i −0.270349 + 0.832048i
\(688\) 0 0
\(689\) −50.7566 + 36.8768i −1.93367 + 1.40490i
\(690\) 0 0
\(691\) −3.07349 9.45923i −0.116921 0.359846i 0.875422 0.483360i \(-0.160584\pi\)
−0.992343 + 0.123514i \(0.960584\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −16.6442 51.2256i −0.631350 1.94310i
\(696\) 0 0
\(697\) 1.81722 1.32029i 0.0688322 0.0500095i
\(698\) 0 0
\(699\) −3.55604 + 10.9444i −0.134502 + 0.413954i
\(700\) 0 0
\(701\) 40.8492 + 29.6787i 1.54285 + 1.12095i 0.948514 + 0.316735i \(0.102587\pi\)
0.594340 + 0.804214i \(0.297413\pi\)
\(702\) 0 0
\(703\) −30.2462 −1.14076
\(704\) 0 0
\(705\) −44.4924 −1.67568
\(706\) 0 0
\(707\) 5.05329 + 3.67143i 0.190049 + 0.138078i
\(708\) 0 0
\(709\) 0.677438 2.08494i 0.0254417 0.0783016i −0.937529 0.347906i \(-0.886893\pi\)
0.962971 + 0.269604i \(0.0868929\pi\)
\(710\) 0 0
\(711\) 5.05329 3.67143i 0.189513 0.137689i
\(712\) 0 0
\(713\) −4.19075 12.8978i −0.156945 0.483027i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −2.35333 7.24280i −0.0878866 0.270487i
\(718\) 0 0
\(719\) −28.6580 + 20.8213i −1.06876 + 0.776503i −0.975690 0.219156i \(-0.929670\pi\)
−0.0930749 + 0.995659i \(0.529670\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −36.7919 26.7309i −1.36830 0.994132i
\(724\) 0 0
\(725\) 39.3693 1.46214
\(726\) 0 0
\(727\) −23.3153 −0.864718 −0.432359 0.901702i \(-0.642319\pi\)
−0.432359 + 0.901702i \(0.642319\pi\)
\(728\) 0 0
\(729\) −24.2582 17.6246i −0.898454 0.652765i
\(730\) 0 0
\(731\) −4.40232 + 13.5490i −0.162826 + 0.501126i
\(732\) 0 0
\(733\) 0.908612 0.660145i 0.0335603 0.0243830i −0.570879 0.821034i \(-0.693397\pi\)
0.604439 + 0.796651i \(0.293397\pi\)
\(734\) 0 0
\(735\) −4.73270 14.5658i −0.174568 0.537266i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.812926 + 2.50193i 0.0299040 + 0.0920349i 0.964895 0.262638i \(-0.0845924\pi\)
−0.934991 + 0.354673i \(0.884592\pi\)
\(740\) 0 0
\(741\) 25.8885 18.8091i 0.951039 0.690971i
\(742\) 0 0
\(743\) −3.31842 + 10.2130i −0.121741 + 0.374680i −0.993293 0.115622i \(-0.963114\pi\)
0.871552 + 0.490303i \(0.163114\pi\)
\(744\) 0 0
\(745\) 12.2348 + 8.88914i 0.448250 + 0.325673i
\(746\) 0 0
\(747\) 0.492423 0.0180168
\(748\) 0 0
\(749\) −41.7538 −1.52565
\(750\) 0 0
\(751\) −4.49939 3.26900i −0.164185 0.119287i 0.502659 0.864485i \(-0.332355\pi\)
−0.666844 + 0.745197i \(0.732355\pi\)
\(752\) 0 0
\(753\) −0.753522 + 2.31910i −0.0274599 + 0.0845127i
\(754\) 0 0
\(755\) −26.9963 + 19.6140i −0.982498 + 0.713826i
\(756\) 0 0
\(757\) 4.86819 + 14.9827i 0.176937 + 0.544557i 0.999717 0.0238039i \(-0.00757773\pi\)
−0.822779 + 0.568361i \(0.807578\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.58313 4.87236i −0.0573883 0.176623i 0.918253 0.395993i \(-0.129600\pi\)
−0.975642 + 0.219370i \(0.929600\pi\)
\(762\) 0 0
\(763\) −30.9418 + 22.4806i −1.12017 + 0.813851i
\(764\) 0 0
\(765\) 1.23607 3.80423i 0.0446901 0.137542i
\(766\) 0 0
\(767\) −32.3607 23.5114i −1.16848 0.848948i
\(768\) 0 0
\(769\) −25.6155 −0.923720 −0.461860 0.886953i \(-0.652818\pi\)
−0.461860 + 0.886953i \(0.652818\pi\)
\(770\) 0 0
\(771\) −18.3542 −0.661009
\(772\) 0 0
\(773\) −32.9582 23.9456i −1.18543 0.861262i −0.192652 0.981267i \(-0.561709\pi\)
−0.992773 + 0.120005i \(0.961709\pi\)
\(774\) 0 0
\(775\) −13.2070 + 40.6469i −0.474408 + 1.46008i
\(776\) 0 0
\(777\) 29.8340 21.6757i 1.07029 0.777611i
\(778\) 0 0
\(779\) 1.38823 + 4.27255i 0.0497387 + 0.153080i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 8.80464 + 27.0979i 0.314652 + 0.968400i
\(784\) 0 0
\(785\) 12.7887 9.29157i 0.456450 0.331630i
\(786\) 0 0
\(787\) 9.19443 28.2975i 0.327746 1.00870i −0.642440 0.766336i \(-0.722078\pi\)
0.970186 0.242362i \(-0.0779222\pi\)
\(788\) 0 0
\(789\) −24.1587 17.5523i −0.860071 0.624878i