Properties

Label 441.2.bd.a.437.52
Level $441$
Weight $2$
Character 441.437
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(47,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([7, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bd (of order \(42\), degree \(12\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 437.52
Character \(\chi\) \(=\) 441.437
Dual form 441.2.bd.a.110.52

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.60229 + 0.195015i) q^{2} +(-1.58818 - 0.691152i) q^{3} +(4.75622 + 0.716885i) q^{4} +(-0.564942 + 2.47517i) q^{5} +(-3.99812 - 2.10829i) q^{6} +(1.46081 + 2.20591i) q^{7} +(7.14895 + 1.63170i) q^{8} +(2.04462 + 2.19534i) q^{9} +O(q^{10})\) \(q+(2.60229 + 0.195015i) q^{2} +(-1.58818 - 0.691152i) q^{3} +(4.75622 + 0.716885i) q^{4} +(-0.564942 + 2.47517i) q^{5} +(-3.99812 - 2.10829i) q^{6} +(1.46081 + 2.20591i) q^{7} +(7.14895 + 1.63170i) q^{8} +(2.04462 + 2.19534i) q^{9} +(-1.95284 + 6.33094i) q^{10} +(-0.836003 - 1.73598i) q^{11} +(-7.05825 - 4.42581i) q^{12} +(-6.25756 - 0.468939i) q^{13} +(3.37126 + 6.02530i) q^{14} +(2.60795 - 3.54055i) q^{15} +(9.09293 + 2.80480i) q^{16} +(4.89533 - 0.737852i) q^{17} +(4.89257 + 6.11165i) q^{18} +(6.22673 - 3.59501i) q^{19} +(-4.46140 + 11.3675i) q^{20} +(-0.795401 - 4.51302i) q^{21} +(-1.83698 - 4.68055i) q^{22} +(-2.42163 - 1.93118i) q^{23} +(-10.2260 - 7.53244i) q^{24} +(-1.30247 - 0.627234i) q^{25} +(-16.1925 - 2.44063i) q^{26} +(-1.72990 - 4.89974i) q^{27} +(5.36653 + 11.5390i) q^{28} +(-4.50492 - 1.76805i) q^{29} +(7.47709 - 8.70495i) q^{30} +(1.58116 - 0.912886i) q^{31} +(9.46364 + 3.71421i) q^{32} +(0.127898 + 3.33485i) q^{33} +(12.8830 - 0.965444i) q^{34} +(-6.28528 + 2.36953i) q^{35} +(8.15085 + 11.9073i) q^{36} +(0.637384 - 1.62403i) q^{37} +(16.9048 - 8.14094i) q^{38} +(9.61400 + 5.06968i) q^{39} +(-8.07747 + 16.7730i) q^{40} +(-5.19833 - 4.82334i) q^{41} +(-1.18976 - 11.8993i) q^{42} +(2.51167 - 2.33049i) q^{43} +(-2.73172 - 8.85602i) q^{44} +(-6.58894 + 3.82054i) q^{45} +(-5.92517 - 5.49776i) q^{46} +(-0.676524 + 9.02758i) q^{47} +(-12.5026 - 10.7391i) q^{48} +(-2.73209 + 6.44482i) q^{49} +(-3.26707 - 1.88625i) q^{50} +(-8.28462 - 2.21157i) q^{51} +(-29.4261 - 6.71633i) q^{52} +(-2.80647 + 1.10146i) q^{53} +(-3.54619 - 13.0879i) q^{54} +(4.76914 - 1.08852i) q^{55} +(6.84384 + 18.1535i) q^{56} +(-12.3739 + 1.40589i) q^{57} +(-11.3783 - 5.47950i) q^{58} +(-1.03526 + 0.960578i) q^{59} +(14.9421 - 14.9701i) q^{60} +(-1.94485 - 12.9032i) q^{61} +(4.29268 - 2.06724i) q^{62} +(-1.85594 + 7.71722i) q^{63} +(6.75615 + 3.25359i) q^{64} +(4.69586 - 15.2236i) q^{65} +(-0.317517 + 8.70318i) q^{66} +(1.52929 + 2.64880i) q^{67} +23.8122 q^{68} +(2.51124 + 4.74078i) q^{69} +(-16.8182 + 4.94049i) q^{70} +(-9.12620 - 7.27790i) q^{71} +(11.0347 + 19.0306i) q^{72} +(3.85339 + 5.65188i) q^{73} +(1.97537 - 4.10189i) q^{74} +(1.63503 + 1.89636i) q^{75} +(32.1929 - 12.6348i) q^{76} +(2.60818 - 4.38008i) q^{77} +(24.0298 + 15.0676i) q^{78} +(-2.00311 + 3.46949i) q^{79} +(-12.0793 + 20.9220i) q^{80} +(-0.639065 + 8.97728i) q^{81} +(-12.5869 - 13.5655i) q^{82} +(0.241757 + 3.22602i) q^{83} +(-0.547787 - 22.0351i) q^{84} +(-0.939264 + 12.5336i) q^{85} +(6.99058 - 5.57480i) q^{86} +(5.93262 + 5.92156i) q^{87} +(-3.14395 - 13.7745i) q^{88} +(-0.423211 - 5.64736i) q^{89} +(-17.8914 + 8.65722i) q^{90} +(-8.10664 - 14.4886i) q^{91} +(-10.1334 - 10.9212i) q^{92} +(-3.14211 + 0.357001i) q^{93} +(-3.52102 + 23.3605i) q^{94} +(5.38051 + 17.4432i) q^{95} +(-12.4629 - 12.4396i) q^{96} +(2.32075 - 1.33988i) q^{97} +(-8.36653 + 16.2385i) q^{98} +(2.10176 - 5.38473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 18 q^{2} - 11 q^{3} - 60 q^{4} - 15 q^{5} - 22 q^{6} - 5 q^{7} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 18 q^{2} - 11 q^{3} - 60 q^{4} - 15 q^{5} - 22 q^{6} - 5 q^{7} + 13 q^{9} - 22 q^{10} - 21 q^{11} + 24 q^{12} - 10 q^{13} - 24 q^{14} - 10 q^{15} + 42 q^{16} + 9 q^{17} + 12 q^{18} - 36 q^{19} - 15 q^{20} - 38 q^{21} - 9 q^{22} - 84 q^{23} - 38 q^{24} - 97 q^{25} - 6 q^{26} - 20 q^{27} - 26 q^{28} - 123 q^{29} - q^{30} - 6 q^{31} - 30 q^{32} - 8 q^{33} - q^{34} + 70 q^{36} - 13 q^{37} - 75 q^{38} - 24 q^{39} - 7 q^{40} - 15 q^{41} - 133 q^{42} - 9 q^{43} - 51 q^{44} - 41 q^{45} - 108 q^{46} - 36 q^{47} + 15 q^{48} + 5 q^{49} - 45 q^{50} + 10 q^{51} - 35 q^{52} + 12 q^{53} - 50 q^{54} + 14 q^{55} + 33 q^{56} - 7 q^{57} + 33 q^{58} - 3 q^{59} + 180 q^{60} + 55 q^{61} - 66 q^{62} - 20 q^{63} + 64 q^{64} + 3 q^{65} + 285 q^{66} + 13 q^{67} + 6 q^{68} + 82 q^{69} + 11 q^{70} + 63 q^{71} - 21 q^{72} - 22 q^{73} - 21 q^{74} - 107 q^{75} + 21 q^{76} - 69 q^{77} + 63 q^{78} + q^{79} + 45 q^{80} - 211 q^{81} - 28 q^{82} + 9 q^{83} + 239 q^{84} - 10 q^{85} - 21 q^{86} - 109 q^{87} - 29 q^{88} - 132 q^{89} - 275 q^{90} - 13 q^{91} + 195 q^{92} + 19 q^{93} - 4 q^{94} - 129 q^{95} - 5 q^{96} - 3 q^{97} - 21 q^{98} - 148 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.60229 + 0.195015i 1.84010 + 0.137896i 0.948871 0.315664i \(-0.102227\pi\)
0.891226 + 0.453560i \(0.149846\pi\)
\(3\) −1.58818 0.691152i −0.916935 0.399037i
\(4\) 4.75622 + 0.716885i 2.37811 + 0.358443i
\(5\) −0.564942 + 2.47517i −0.252650 + 1.10693i 0.676272 + 0.736652i \(0.263595\pi\)
−0.928921 + 0.370278i \(0.879263\pi\)
\(6\) −3.99812 2.10829i −1.63222 0.860708i
\(7\) 1.46081 + 2.20591i 0.552133 + 0.833756i
\(8\) 7.14895 + 1.63170i 2.52753 + 0.576893i
\(9\) 2.04462 + 2.19534i 0.681540 + 0.731781i
\(10\) −1.95284 + 6.33094i −0.617541 + 2.00202i
\(11\) −0.836003 1.73598i −0.252064 0.523417i 0.736089 0.676884i \(-0.236670\pi\)
−0.988154 + 0.153467i \(0.950956\pi\)
\(12\) −7.05825 4.42581i −2.03754 1.27762i
\(13\) −6.25756 0.468939i −1.73553 0.130060i −0.830947 0.556351i \(-0.812201\pi\)
−0.904586 + 0.426291i \(0.859820\pi\)
\(14\) 3.37126 + 6.02530i 0.901006 + 1.61033i
\(15\) 2.60795 3.54055i 0.673369 0.914166i
\(16\) 9.09293 + 2.80480i 2.27323 + 0.701199i
\(17\) 4.89533 0.737852i 1.18729 0.178955i 0.474451 0.880282i \(-0.342647\pi\)
0.712840 + 0.701327i \(0.247409\pi\)
\(18\) 4.89257 + 6.11165i 1.15319 + 1.44053i
\(19\) 6.22673 3.59501i 1.42851 0.824751i 0.431507 0.902110i \(-0.357982\pi\)
0.997003 + 0.0773588i \(0.0246487\pi\)
\(20\) −4.46140 + 11.3675i −0.997599 + 2.54184i
\(21\) −0.795401 4.51302i −0.173571 0.984821i
\(22\) −1.83698 4.68055i −0.391646 0.997897i
\(23\) −2.42163 1.93118i −0.504944 0.402680i 0.337614 0.941285i \(-0.390380\pi\)
−0.842558 + 0.538605i \(0.818952\pi\)
\(24\) −10.2260 7.53244i −2.08738 1.53755i
\(25\) −1.30247 0.627234i −0.260493 0.125447i
\(26\) −16.1925 2.44063i −3.17562 0.478647i
\(27\) −1.72990 4.89974i −0.332920 0.942955i
\(28\) 5.36653 + 11.5390i 1.01418 + 2.18067i
\(29\) −4.50492 1.76805i −0.836542 0.328319i −0.0918883 0.995769i \(-0.529290\pi\)
−0.744654 + 0.667451i \(0.767386\pi\)
\(30\) 7.47709 8.70495i 1.36512 1.58930i
\(31\) 1.58116 0.912886i 0.283986 0.163959i −0.351241 0.936285i \(-0.614240\pi\)
0.635226 + 0.772326i \(0.280907\pi\)
\(32\) 9.46364 + 3.71421i 1.67295 + 0.656585i
\(33\) 0.127898 + 3.33485i 0.0222641 + 0.580523i
\(34\) 12.8830 0.965444i 2.20941 0.165572i
\(35\) −6.28528 + 2.36953i −1.06241 + 0.400524i
\(36\) 8.15085 + 11.9073i 1.35848 + 1.98455i
\(37\) 0.637384 1.62403i 0.104785 0.266988i −0.868859 0.495059i \(-0.835146\pi\)
0.973645 + 0.228071i \(0.0732417\pi\)
\(38\) 16.9048 8.14094i 2.74233 1.32064i
\(39\) 9.61400 + 5.06968i 1.53947 + 0.811798i
\(40\) −8.07747 + 16.7730i −1.27716 + 2.65205i
\(41\) −5.19833 4.82334i −0.811842 0.753279i 0.160451 0.987044i \(-0.448705\pi\)
−0.972293 + 0.233764i \(0.924896\pi\)
\(42\) −1.18976 11.8993i −0.183584 1.83610i
\(43\) 2.51167 2.33049i 0.383026 0.355396i −0.465037 0.885291i \(-0.653959\pi\)
0.848063 + 0.529895i \(0.177769\pi\)
\(44\) −2.73172 8.85602i −0.411822 1.33509i
\(45\) −6.58894 + 3.82054i −0.982221 + 0.569533i
\(46\) −5.92517 5.49776i −0.873619 0.810600i
\(47\) −0.676524 + 9.02758i −0.0986811 + 1.31681i 0.699605 + 0.714530i \(0.253359\pi\)
−0.798286 + 0.602278i \(0.794260\pi\)
\(48\) −12.5026 10.7391i −1.80460 1.55006i
\(49\) −2.73209 + 6.44482i −0.390299 + 0.920688i
\(50\) −3.26707 1.88625i −0.462034 0.266755i
\(51\) −8.28462 2.21157i −1.16008 0.309682i
\(52\) −29.4261 6.71633i −4.08067 0.931387i
\(53\) −2.80647 + 1.10146i −0.385498 + 0.151297i −0.550172 0.835051i \(-0.685438\pi\)
0.164674 + 0.986348i \(0.447343\pi\)
\(54\) −3.54619 13.0879i −0.482576 1.78104i
\(55\) 4.76914 1.08852i 0.643070 0.146777i
\(56\) 6.84384 + 18.1535i 0.914546 + 2.42587i
\(57\) −12.3739 + 1.40589i −1.63896 + 0.186215i
\(58\) −11.3783 5.47950i −1.49405 0.719494i
\(59\) −1.03526 + 0.960578i −0.134779 + 0.125057i −0.744682 0.667419i \(-0.767399\pi\)
0.609903 + 0.792476i \(0.291208\pi\)
\(60\) 14.9421 14.9701i 1.92902 1.93263i
\(61\) −1.94485 12.9032i −0.249012 1.65209i −0.668048 0.744118i \(-0.732870\pi\)
0.419036 0.907969i \(-0.362368\pi\)
\(62\) 4.29268 2.06724i 0.545170 0.262540i
\(63\) −1.85594 + 7.71722i −0.233827 + 0.972278i
\(64\) 6.75615 + 3.25359i 0.844519 + 0.406699i
\(65\) 4.69586 15.2236i 0.582449 1.88825i
\(66\) −0.317517 + 8.70318i −0.0390837 + 1.07129i
\(67\) 1.52929 + 2.64880i 0.186832 + 0.323602i 0.944192 0.329395i \(-0.106845\pi\)
−0.757360 + 0.652997i \(0.773511\pi\)
\(68\) 23.8122 2.88765
\(69\) 2.51124 + 4.74078i 0.302317 + 0.570722i
\(70\) −16.8182 + 4.94049i −2.01016 + 0.590502i
\(71\) −9.12620 7.27790i −1.08308 0.863728i −0.0918367 0.995774i \(-0.529274\pi\)
−0.991244 + 0.132046i \(0.957845\pi\)
\(72\) 11.0347 + 19.0306i 1.30046 + 2.24278i
\(73\) 3.85339 + 5.65188i 0.451005 + 0.661503i 0.982651 0.185464i \(-0.0593788\pi\)
−0.531646 + 0.846967i \(0.678426\pi\)
\(74\) 1.97537 4.10189i 0.229632 0.476835i
\(75\) 1.63503 + 1.89636i 0.188797 + 0.218973i
\(76\) 32.1929 12.6348i 3.69278 1.44931i
\(77\) 2.60818 4.38008i 0.297229 0.499156i
\(78\) 24.0298 + 15.0676i 2.72084 + 1.70607i
\(79\) −2.00311 + 3.46949i −0.225367 + 0.390348i −0.956430 0.291963i \(-0.905692\pi\)
0.731062 + 0.682311i \(0.239025\pi\)
\(80\) −12.0793 + 20.9220i −1.35051 + 2.33915i
\(81\) −0.639065 + 8.97728i −0.0710072 + 0.997476i
\(82\) −12.5869 13.5655i −1.38999 1.49806i
\(83\) 0.241757 + 3.22602i 0.0265363 + 0.354102i 0.994629 + 0.103508i \(0.0330068\pi\)
−0.968092 + 0.250594i \(0.919374\pi\)
\(84\) −0.547787 22.0351i −0.0597685 2.40423i
\(85\) −0.939264 + 12.5336i −0.101878 + 1.35946i
\(86\) 6.99058 5.57480i 0.753813 0.601146i
\(87\) 5.93262 + 5.92156i 0.636044 + 0.634858i
\(88\) −3.14395 13.7745i −0.335146 1.46837i
\(89\) −0.423211 5.64736i −0.0448603 0.598619i −0.973655 0.228025i \(-0.926773\pi\)
0.928795 0.370594i \(-0.120846\pi\)
\(90\) −17.8914 + 8.65722i −1.88592 + 0.912551i
\(91\) −8.10664 14.4886i −0.849806 1.51882i
\(92\) −10.1334 10.9212i −1.05648 1.13861i
\(93\) −3.14211 + 0.357001i −0.325822 + 0.0370193i
\(94\) −3.52102 + 23.3605i −0.363166 + 2.40945i
\(95\) 5.38051 + 17.4432i 0.552029 + 1.78963i
\(96\) −12.4629 12.4396i −1.27199 1.26961i
\(97\) 2.32075 1.33988i 0.235636 0.136045i −0.377533 0.925996i \(-0.623228\pi\)
0.613169 + 0.789951i \(0.289894\pi\)
\(98\) −8.36653 + 16.2385i −0.845147 + 1.64033i
\(99\) 2.10176 5.38473i 0.211235 0.541186i
\(100\) −5.74516 3.91698i −0.574516 0.391698i
\(101\) 0.0177944 0.0779626i 0.00177061 0.00775756i −0.974035 0.226398i \(-0.927305\pi\)
0.975806 + 0.218640i \(0.0701622\pi\)
\(102\) −21.1277 7.37077i −2.09195 0.729815i
\(103\) 15.8948 + 3.62789i 1.56616 + 0.357467i 0.915634 0.402013i \(-0.131689\pi\)
0.650531 + 0.759480i \(0.274547\pi\)
\(104\) −43.9698 13.5629i −4.31159 1.32995i
\(105\) 11.6198 + 0.580839i 1.13398 + 0.0566841i
\(106\) −7.51804 + 2.31901i −0.730216 + 0.225242i
\(107\) 4.16091 0.311817i 0.402250 0.0301445i 0.127931 0.991783i \(-0.459167\pi\)
0.274319 + 0.961639i \(0.411547\pi\)
\(108\) −4.71526 24.5444i −0.453726 2.36178i
\(109\) 0.0553975 0.739228i 0.00530612 0.0708052i −0.993922 0.110086i \(-0.964888\pi\)
0.999228 + 0.0392804i \(0.0125066\pi\)
\(110\) 12.6230 1.90260i 1.20355 0.181406i
\(111\) −2.13473 + 2.13872i −0.202619 + 0.202998i
\(112\) 7.09587 + 24.1555i 0.670496 + 2.28248i
\(113\) 1.57333 + 2.30765i 0.148006 + 0.217085i 0.893081 0.449895i \(-0.148539\pi\)
−0.745075 + 0.666981i \(0.767586\pi\)
\(114\) −32.4745 + 1.24546i −3.04152 + 0.116648i
\(115\) 6.14809 4.90294i 0.573312 0.457201i
\(116\) −20.1589 11.6387i −1.87171 1.08063i
\(117\) −11.7648 14.6963i −1.08766 1.35867i
\(118\) −2.88137 + 2.29781i −0.265251 + 0.211531i
\(119\) 8.77876 + 9.72080i 0.804747 + 0.891104i
\(120\) 24.4212 21.0558i 2.22934 1.92213i
\(121\) 4.54367 5.69758i 0.413061 0.517962i
\(122\) −2.54474 33.9572i −0.230390 3.07434i
\(123\) 4.92221 + 11.2532i 0.443820 + 1.01466i
\(124\) 8.17480 3.20837i 0.734119 0.288120i
\(125\) −5.62633 + 7.05519i −0.503234 + 0.631035i
\(126\) −6.33467 + 19.7205i −0.564337 + 1.75684i
\(127\) 12.6039 + 15.8048i 1.11841 + 1.40245i 0.904962 + 0.425493i \(0.139899\pi\)
0.213452 + 0.976953i \(0.431529\pi\)
\(128\) −0.661767 0.382072i −0.0584925 0.0337707i
\(129\) −5.59970 + 1.96529i −0.493026 + 0.173034i
\(130\) 15.1888 38.7004i 1.33215 3.39425i
\(131\) 1.67115 + 7.32177i 0.146009 + 0.639706i 0.993970 + 0.109648i \(0.0349725\pi\)
−0.847962 + 0.530057i \(0.822170\pi\)
\(132\) −1.78239 + 15.9530i −0.155137 + 1.38853i
\(133\) 17.0263 + 8.48402i 1.47637 + 0.735657i
\(134\) 3.46309 + 7.19118i 0.299165 + 0.621223i
\(135\) 13.1050 1.51374i 1.12790 0.130282i
\(136\) 36.2004 + 2.71284i 3.10416 + 0.232624i
\(137\) −12.5079 + 2.85484i −1.06862 + 0.243905i −0.720436 0.693521i \(-0.756058\pi\)
−0.348183 + 0.937427i \(0.613201\pi\)
\(138\) 5.61045 + 12.8266i 0.477593 + 1.09187i
\(139\) −2.61503 + 2.81833i −0.221804 + 0.239048i −0.834144 0.551547i \(-0.814038\pi\)
0.612340 + 0.790594i \(0.290228\pi\)
\(140\) −31.5929 + 6.76420i −2.67008 + 0.571679i
\(141\) 7.31387 13.8698i 0.615939 1.16805i
\(142\) −22.3297 20.7189i −1.87387 1.73870i
\(143\) 4.41727 + 11.2550i 0.369391 + 0.941192i
\(144\) 12.4341 + 25.6968i 1.03617 + 2.14140i
\(145\) 6.92124 10.1516i 0.574778 0.843044i
\(146\) 8.92543 + 15.4593i 0.738674 + 1.27942i
\(147\) 8.79339 8.34723i 0.725267 0.688468i
\(148\) 4.19578 7.26730i 0.344891 0.597369i
\(149\) 4.83377 + 10.0374i 0.395998 + 0.822298i 0.999686 + 0.0250774i \(0.00798321\pi\)
−0.603687 + 0.797221i \(0.706303\pi\)
\(150\) 3.88501 + 5.25374i 0.317210 + 0.428966i
\(151\) −1.00778 + 1.26371i −0.0820116 + 0.102839i −0.821145 0.570720i \(-0.806664\pi\)
0.739133 + 0.673560i \(0.235236\pi\)
\(152\) 50.3806 15.5403i 4.08640 1.26049i
\(153\) 11.6289 + 9.23830i 0.940142 + 0.746872i
\(154\) 7.64141 10.8896i 0.615763 0.877509i
\(155\) 1.36628 + 4.42938i 0.109742 + 0.355776i
\(156\) 42.0920 + 31.0046i 3.37005 + 2.48236i
\(157\) −12.5625 13.5392i −1.00260 1.08054i −0.996750 0.0805590i \(-0.974329\pi\)
−0.00584656 0.999983i \(-0.501861\pi\)
\(158\) −5.88927 + 8.63798i −0.468525 + 0.687200i
\(159\) 5.21844 + 0.190384i 0.413849 + 0.0150984i
\(160\) −14.5397 + 21.3258i −1.14946 + 1.68595i
\(161\) 0.722493 8.16298i 0.0569404 0.643333i
\(162\) −3.41373 + 23.2369i −0.268208 + 1.82566i
\(163\) 12.1358 11.2604i 0.950551 0.881982i −0.0425679 0.999094i \(-0.513554\pi\)
0.993119 + 0.117111i \(0.0373634\pi\)
\(164\) −21.2666 26.6675i −1.66064 2.08238i
\(165\) −8.32657 1.56743i −0.648223 0.122024i
\(166\) 8.44220i 0.655242i
\(167\) −16.3533 + 2.46487i −1.26546 + 0.190737i −0.747265 0.664526i \(-0.768633\pi\)
−0.518193 + 0.855264i \(0.673395\pi\)
\(168\) 1.67762 33.5612i 0.129431 2.58930i
\(169\) 26.0823 + 3.93127i 2.00633 + 0.302406i
\(170\) −4.88848 + 32.4329i −0.374929 + 2.48749i
\(171\) 20.6236 + 6.31940i 1.57712 + 0.483256i
\(172\) 13.6168 9.28375i 1.03827 0.707879i
\(173\) −3.66684 9.34296i −0.278785 0.710332i −0.999848 0.0174622i \(-0.994441\pi\)
0.721063 0.692870i \(-0.243654\pi\)
\(174\) 14.2836 + 16.5666i 1.08284 + 1.25591i
\(175\) −0.519026 3.78939i −0.0392347 0.286451i
\(176\) −2.73265 18.1299i −0.205981 1.36660i
\(177\) 2.30808 0.810050i 0.173486 0.0608871i
\(178\) 14.7786i 1.10770i
\(179\) −0.395423 2.62346i −0.0295553 0.196087i 0.969181 0.246351i \(-0.0792317\pi\)
−0.998736 + 0.0502645i \(0.983994\pi\)
\(180\) −34.0773 + 13.4478i −2.53998 + 1.00234i
\(181\) −3.17461 + 6.59214i −0.235967 + 0.489990i −0.985003 0.172540i \(-0.944803\pi\)
0.749036 + 0.662529i \(0.230517\pi\)
\(182\) −18.2703 39.2846i −1.35429 2.91197i
\(183\) −5.82931 + 21.8368i −0.430915 + 1.61422i
\(184\) −14.1610 17.7573i −1.04396 1.30909i
\(185\) 3.65966 + 2.49511i 0.269064 + 0.183444i
\(186\) −8.24631 + 0.316262i −0.604649 + 0.0231894i
\(187\) −5.37340 7.88133i −0.392942 0.576340i
\(188\) −9.68944 + 42.4522i −0.706675 + 3.09614i
\(189\) 8.28133 10.9736i 0.602378 0.798211i
\(190\) 10.6000 + 46.4415i 0.769003 + 3.36922i
\(191\) −6.43747 + 6.93795i −0.465799 + 0.502012i −0.921638 0.388050i \(-0.873149\pi\)
0.455839 + 0.890062i \(0.349339\pi\)
\(192\) −8.48125 9.83680i −0.612081 0.709910i
\(193\) −21.5151 + 6.63652i −1.54869 + 0.477707i −0.947057 0.321067i \(-0.895959\pi\)
−0.601632 + 0.798774i \(0.705482\pi\)
\(194\) 6.30055 3.03419i 0.452353 0.217842i
\(195\) −17.9797 + 20.9322i −1.28755 + 1.49899i
\(196\) −17.6146 + 28.6944i −1.25819 + 2.04960i
\(197\) 8.53046i 0.607770i 0.952709 + 0.303885i \(0.0982839\pi\)
−0.952709 + 0.303885i \(0.901716\pi\)
\(198\) 6.51949 13.6028i 0.463320 0.966706i
\(199\) 3.95037 4.25749i 0.280034 0.301805i −0.577334 0.816508i \(-0.695907\pi\)
0.857369 + 0.514702i \(0.172098\pi\)
\(200\) −8.28780 6.60930i −0.586036 0.467348i
\(201\) −0.598055 5.26373i −0.0421836 0.371275i
\(202\) 0.0615102 0.199411i 0.00432784 0.0140305i
\(203\) −2.68065 12.5202i −0.188145 0.878748i
\(204\) −37.8180 16.4578i −2.64779 1.15228i
\(205\) 14.8753 10.1418i 1.03894 0.708337i
\(206\) 40.6555 + 12.5406i 2.83260 + 0.873742i
\(207\) −0.711696 9.26484i −0.0494663 0.643951i
\(208\) −55.5842 21.8152i −3.85407 1.51261i
\(209\) −11.4464 7.80404i −0.791765 0.539817i
\(210\) 30.1249 + 3.77755i 2.07882 + 0.260676i
\(211\) 4.89376 3.33651i 0.336900 0.229695i −0.383038 0.923732i \(-0.625122\pi\)
0.719939 + 0.694038i \(0.244170\pi\)
\(212\) −14.1378 + 3.22686i −0.970987 + 0.221622i
\(213\) 9.46389 + 17.8662i 0.648455 + 1.22417i
\(214\) 10.8887 0.744336
\(215\) 4.34941 + 7.53340i 0.296627 + 0.513774i
\(216\) −4.37209 37.8507i −0.297483 2.57541i
\(217\) 4.32352 + 2.15436i 0.293500 + 0.146248i
\(218\) 0.288321 1.91288i 0.0195275 0.129557i
\(219\) −2.21356 11.6395i −0.149578 0.786522i
\(220\) 23.4634 1.75834i 1.58190 0.118547i
\(221\) −30.9788 + 2.32154i −2.08386 + 0.156164i
\(222\) −5.97226 + 5.14926i −0.400832 + 0.345595i
\(223\) 3.60753 23.9344i 0.241578 1.60277i −0.458495 0.888697i \(-0.651611\pi\)
0.700074 0.714071i \(-0.253151\pi\)
\(224\) 5.63133 + 26.3017i 0.376259 + 1.75736i
\(225\) −1.28605 4.14182i −0.0857368 0.276121i
\(226\) 3.64423 + 6.31199i 0.242411 + 0.419867i
\(227\) 20.2341 1.34299 0.671494 0.741010i \(-0.265653\pi\)
0.671494 + 0.741010i \(0.265653\pi\)
\(228\) −59.8607 2.18389i −3.96437 0.144632i
\(229\) −6.54663 + 1.49423i −0.432614 + 0.0987413i −0.433282 0.901259i \(-0.642644\pi\)
0.000668047 1.00000i \(0.499787\pi\)
\(230\) 16.9553 11.5599i 1.11800 0.762237i
\(231\) −7.16955 + 5.15370i −0.471721 + 0.339088i
\(232\) −29.3205 19.9904i −1.92498 1.31243i
\(233\) −18.8575 7.40103i −1.23540 0.484857i −0.344381 0.938830i \(-0.611911\pi\)
−0.891016 + 0.453973i \(0.850006\pi\)
\(234\) −27.7495 40.5383i −1.81404 2.65007i
\(235\) −21.9626 6.77457i −1.43268 0.441924i
\(236\) −5.61254 + 3.82656i −0.365345 + 0.249088i
\(237\) 5.57923 4.12571i 0.362410 0.267994i
\(238\) 20.9492 + 27.0083i 1.35793 + 1.75069i
\(239\) 2.88637 9.35737i 0.186704 0.605278i −0.813031 0.582221i \(-0.802184\pi\)
0.999734 0.0230572i \(-0.00733997\pi\)
\(240\) 33.6444 24.8792i 2.17174 1.60595i
\(241\) 5.04070 + 4.01982i 0.324700 + 0.258940i 0.772249 0.635320i \(-0.219132\pi\)
−0.447549 + 0.894259i \(0.647703\pi\)
\(242\) 12.9351 13.9407i 0.831497 0.896140i
\(243\) 7.21961 13.8158i 0.463138 0.886286i
\(244\) 62.7648i 4.01810i
\(245\) −14.4086 10.4033i −0.920528 0.664645i
\(246\) 10.6145 + 30.2439i 0.676755 + 1.92828i
\(247\) −40.6500 + 19.5760i −2.58649 + 1.24559i
\(248\) 12.7932 3.94619i 0.812370 0.250583i
\(249\) 1.84572 5.29059i 0.116968 0.335278i
\(250\) −16.0172 + 17.2624i −1.01302 + 1.09177i
\(251\) 2.93205 + 12.8461i 0.185069 + 0.810842i 0.979168 + 0.203053i \(0.0650862\pi\)
−0.794099 + 0.607789i \(0.792057\pi\)
\(252\) −14.3596 + 35.3743i −0.904572 + 2.22837i
\(253\) −1.32801 + 5.81837i −0.0834910 + 0.365798i
\(254\) 29.7168 + 43.5865i 1.86460 + 2.73486i
\(255\) 10.1543 19.2564i 0.635890 1.20588i
\(256\) −14.0391 9.57172i −0.877446 0.598233i
\(257\) 4.96157 + 6.22161i 0.309494 + 0.388093i 0.912115 0.409934i \(-0.134448\pi\)
−0.602621 + 0.798028i \(0.705877\pi\)
\(258\) −14.9553 + 4.02223i −0.931077 + 0.250413i
\(259\) 4.51356 0.966377i 0.280459 0.0600477i
\(260\) 33.2481 69.0404i 2.06196 4.28170i
\(261\) −5.32937 13.5048i −0.329879 0.835928i
\(262\) 2.92095 + 19.3793i 0.180457 + 1.19726i
\(263\) 3.83489i 0.236469i 0.992986 + 0.118235i \(0.0377235\pi\)
−0.992986 + 0.118235i \(0.962277\pi\)
\(264\) −4.52714 + 24.0493i −0.278626 + 1.48013i
\(265\) −1.14080 7.56874i −0.0700790 0.464944i
\(266\) 42.6529 + 25.3983i 2.61522 + 1.55727i
\(267\) −3.23105 + 9.26152i −0.197737 + 0.566796i
\(268\) 5.37474 + 13.6946i 0.328314 + 0.836531i
\(269\) −23.6310 + 16.1113i −1.44081 + 0.982325i −0.444560 + 0.895749i \(0.646640\pi\)
−0.996245 + 0.0865755i \(0.972408\pi\)
\(270\) 34.3982 1.38354i 2.09341 0.0841993i
\(271\) −3.77216 + 25.0266i −0.229142 + 1.52026i 0.517876 + 0.855456i \(0.326723\pi\)
−0.747018 + 0.664804i \(0.768515\pi\)
\(272\) 46.5824 + 7.02116i 2.82447 + 0.425720i
\(273\) 2.86093 + 28.6135i 0.173152 + 1.73177i
\(274\) −33.1058 + 4.98990i −2.00000 + 0.301451i
\(275\) 2.78542i 0.167967i
\(276\) 8.54541 + 24.3485i 0.514373 + 1.46560i
\(277\) 4.75139 + 5.95805i 0.285483 + 0.357985i 0.903808 0.427938i \(-0.140760\pi\)
−0.618325 + 0.785923i \(0.712188\pi\)
\(278\) −7.35468 + 6.82415i −0.441105 + 0.409285i
\(279\) 5.23698 + 1.60470i 0.313530 + 0.0960706i
\(280\) −48.7995 + 6.68397i −2.91633 + 0.399444i
\(281\) 1.61755 2.37252i 0.0964952 0.141532i −0.774955 0.632016i \(-0.782228\pi\)
0.871450 + 0.490484i \(0.163180\pi\)
\(282\) 21.7376 34.6670i 1.29446 2.06439i
\(283\) −14.5730 + 21.3747i −0.866277 + 1.27060i 0.0951294 + 0.995465i \(0.469674\pi\)
−0.961407 + 0.275131i \(0.911279\pi\)
\(284\) −38.1888 41.1577i −2.26609 2.44226i
\(285\) 3.51068 31.4216i 0.207955 1.86126i
\(286\) 9.30012 + 30.1503i 0.549928 + 1.78282i
\(287\) 3.04612 18.5130i 0.179807 1.09279i
\(288\) 11.1956 + 28.3701i 0.659706 + 1.67172i
\(289\) 7.17505 2.21321i 0.422062 0.130189i
\(290\) 19.9908 25.0677i 1.17390 1.47202i
\(291\) −4.61182 + 0.523986i −0.270350 + 0.0307166i
\(292\) 14.2758 + 29.6440i 0.835429 + 1.73479i
\(293\) 9.64356 16.7031i 0.563383 0.975807i −0.433815 0.901002i \(-0.642833\pi\)
0.997198 0.0748057i \(-0.0238337\pi\)
\(294\) 24.5108 20.0071i 1.42950 1.16684i
\(295\) −1.79273 3.10511i −0.104377 0.180786i
\(296\) 7.20655 10.5701i 0.418872 0.614373i
\(297\) −7.05963 + 7.09927i −0.409642 + 0.411942i
\(298\) 10.6214 + 27.0630i 0.615283 + 1.56772i
\(299\) 14.2479 + 13.2201i 0.823975 + 0.764538i
\(300\) 6.41711 + 10.1916i 0.370492 + 0.588415i
\(301\) 8.80992 + 2.13613i 0.507795 + 0.123124i
\(302\) −2.86897 + 3.09201i −0.165090 + 0.177925i
\(303\) −0.0821447 + 0.111520i −0.00471909 + 0.00640664i
\(304\) 66.7025 15.2244i 3.82565 0.873179i
\(305\) 33.0364 + 2.47573i 1.89166 + 0.141760i
\(306\) 28.4602 + 26.3085i 1.62696 + 1.50396i
\(307\) 7.55153 + 15.6809i 0.430988 + 0.894957i 0.997484 + 0.0708920i \(0.0225846\pi\)
−0.566496 + 0.824065i \(0.691701\pi\)
\(308\) 15.5451 18.9629i 0.885763 1.08051i
\(309\) −22.7364 16.7475i −1.29343 0.952731i
\(310\) 2.69167 + 11.7930i 0.152877 + 0.669796i
\(311\) −1.85046 + 4.71490i −0.104930 + 0.267357i −0.973690 0.227876i \(-0.926822\pi\)
0.868760 + 0.495233i \(0.164917\pi\)
\(312\) 60.4578 + 51.9300i 3.42275 + 2.93996i
\(313\) −4.36156 2.51815i −0.246530 0.142334i 0.371644 0.928375i \(-0.378794\pi\)
−0.618174 + 0.786041i \(0.712127\pi\)
\(314\) −30.0509 37.6827i −1.69587 2.12656i
\(315\) −18.0529 8.95355i −1.01717 0.504475i
\(316\) −12.0145 + 15.0656i −0.675866 + 0.847509i
\(317\) −1.90370 + 0.747146i −0.106922 + 0.0419639i −0.418199 0.908355i \(-0.637339\pi\)
0.311277 + 0.950319i \(0.399243\pi\)
\(318\) 13.5428 + 1.51311i 0.759441 + 0.0848508i
\(319\) 0.696829 + 9.29854i 0.0390149 + 0.520618i
\(320\) −11.8700 + 14.8845i −0.663554 + 0.832071i
\(321\) −6.82377 2.38060i −0.380866 0.132872i
\(322\) 3.47204 21.1016i 0.193489 1.17594i
\(323\) 27.8293 22.1931i 1.54846 1.23486i
\(324\) −9.47521 + 42.2398i −0.526401 + 2.34666i
\(325\) 7.85612 + 4.53573i 0.435779 + 0.251597i
\(326\) 33.7769 26.9362i 1.87073 1.49186i
\(327\) −0.598900 + 1.13574i −0.0331192 + 0.0628064i
\(328\) −29.2923 42.9639i −1.61740 2.37229i
\(329\) −20.9023 + 11.6952i −1.15238 + 0.644777i
\(330\) −21.3625 5.70270i −1.17597 0.313923i
\(331\) −15.7580 + 2.37514i −0.866139 + 0.130549i −0.567058 0.823678i \(-0.691918\pi\)
−0.299082 + 0.954228i \(0.596680\pi\)
\(332\) −1.16284 + 15.5170i −0.0638190 + 0.851606i
\(333\) 4.86851 1.92124i 0.266792 0.105283i
\(334\) −43.0368 + 3.22516i −2.35487 + 0.176473i
\(335\) −7.42019 + 2.28882i −0.405408 + 0.125052i
\(336\) 5.42558 43.2675i 0.295989 2.36043i
\(337\) 16.8520 + 5.19817i 0.917989 + 0.283162i 0.717520 0.696538i \(-0.245277\pi\)
0.200469 + 0.979700i \(0.435753\pi\)
\(338\) 67.1071 + 15.3167i 3.65014 + 0.833121i
\(339\) −0.903790 4.75236i −0.0490871 0.258113i
\(340\) −13.4525 + 58.9393i −0.729565 + 3.19643i
\(341\) −2.90661 1.98169i −0.157402 0.107315i
\(342\) 52.4361 + 20.4668i 2.83542 + 1.10672i
\(343\) −18.2078 + 3.38787i −0.983126 + 0.182928i
\(344\) 21.7585 12.5623i 1.17314 0.677311i
\(345\) −13.1529 + 3.53748i −0.708130 + 0.190451i
\(346\) −7.72017 25.0282i −0.415039 1.34552i
\(347\) −2.86101 + 18.9815i −0.153587 + 1.01898i 0.770677 + 0.637227i \(0.219918\pi\)
−0.924263 + 0.381755i \(0.875320\pi\)
\(348\) 23.9718 + 32.4173i 1.28502 + 1.73775i
\(349\) −12.5457 13.5210i −0.671555 0.723764i 0.301723 0.953396i \(-0.402438\pi\)
−0.973278 + 0.229632i \(0.926248\pi\)
\(350\) −0.611669 9.96232i −0.0326951 0.532508i
\(351\) 8.52730 + 31.4716i 0.455153 + 1.67983i
\(352\) −1.46385 19.5338i −0.0780236 1.04115i
\(353\) 3.96929 + 17.3906i 0.211264 + 0.925608i 0.963709 + 0.266954i \(0.0860170\pi\)
−0.752445 + 0.658655i \(0.771126\pi\)
\(354\) 6.16426 1.65788i 0.327627 0.0881151i
\(355\) 23.1698 18.4773i 1.22973 0.980674i
\(356\) 2.03562 27.1635i 0.107888 1.43966i
\(357\) −7.22368 21.5058i −0.382318 1.13821i
\(358\) −0.517392 6.90412i −0.0273450 0.364894i
\(359\) −16.0461 17.2936i −0.846881 0.912720i 0.150232 0.988651i \(-0.451998\pi\)
−0.997113 + 0.0759303i \(0.975807\pi\)
\(360\) −53.3380 + 16.5617i −2.81116 + 0.872877i
\(361\) 16.3481 28.3158i 0.860428 1.49030i
\(362\) −9.54681 + 16.5356i −0.501769 + 0.869089i
\(363\) −11.1540 + 5.90841i −0.585435 + 0.310111i
\(364\) −28.1703 74.7227i −1.47652 3.91654i
\(365\) −16.1663 + 6.34481i −0.846183 + 0.332102i
\(366\) −19.4281 + 55.6888i −1.01552 + 2.91090i
\(367\) 4.37602 9.08691i 0.228427 0.474333i −0.754980 0.655748i \(-0.772353\pi\)
0.983407 + 0.181415i \(0.0580677\pi\)
\(368\) −16.6031 24.3523i −0.865497 1.26945i
\(369\) −0.0397063 21.2740i −0.00206703 1.10748i
\(370\) 9.03692 + 7.20670i 0.469807 + 0.374658i
\(371\) −6.52942 4.58180i −0.338990 0.237875i
\(372\) −15.2005 0.554559i −0.788110 0.0287525i
\(373\) −6.72804 −0.348364 −0.174182 0.984713i \(-0.555728\pi\)
−0.174182 + 0.984713i \(0.555728\pi\)
\(374\) −12.4462 21.5574i −0.643577 1.11471i
\(375\) 13.8118 7.31625i 0.713239 0.377810i
\(376\) −19.5667 + 63.4338i −1.00908 + 3.27135i
\(377\) 27.3607 + 13.1762i 1.40915 + 0.678609i
\(378\) 23.6904 26.9415i 1.21850 1.38572i
\(379\) 11.6685 5.61925i 0.599370 0.288641i −0.109493 0.993988i \(-0.534923\pi\)
0.708863 + 0.705346i \(0.249208\pi\)
\(380\) 13.0861 + 86.8209i 0.671305 + 4.45382i
\(381\) −9.09372 33.8120i −0.465885 1.73224i
\(382\) −18.1052 + 16.7991i −0.926341 + 0.859519i
\(383\) 7.55460 + 3.63810i 0.386022 + 0.185898i 0.616822 0.787103i \(-0.288420\pi\)
−0.230800 + 0.973001i \(0.574134\pi\)
\(384\) 0.786935 + 1.06418i 0.0401581 + 0.0543062i
\(385\) 9.36797 + 8.93017i 0.477436 + 0.455124i
\(386\) −57.2827 + 13.0744i −2.91561 + 0.665469i
\(387\) 10.2516 + 0.749015i 0.521120 + 0.0380746i
\(388\) 11.9985 4.70907i 0.609133 0.239067i
\(389\) −29.9679 6.83997i −1.51943 0.346800i −0.620260 0.784396i \(-0.712973\pi\)
−0.899172 + 0.437596i \(0.855830\pi\)
\(390\) −50.8704 + 50.9654i −2.57592 + 2.58074i
\(391\) −13.2796 7.66697i −0.671578 0.387736i
\(392\) −30.0476 + 41.6157i −1.51763 + 2.10191i
\(393\) 2.40637 12.7833i 0.121386 0.644832i
\(394\) −1.66356 + 22.1987i −0.0838092 + 1.11836i
\(395\) −7.45593 6.91809i −0.375149 0.348087i
\(396\) 13.8567 24.1042i 0.696324 1.21128i
\(397\) 5.41575 + 17.5574i 0.271809 + 0.881182i 0.983842 + 0.179037i \(0.0572982\pi\)
−0.712034 + 0.702145i \(0.752226\pi\)
\(398\) 11.1103 10.3088i 0.556908 0.516735i
\(399\) −21.1771 25.2419i −1.06018 1.26367i
\(400\) −10.0840 9.35655i −0.504198 0.467827i
\(401\) −3.34482 + 6.94559i −0.167032 + 0.346846i −0.967637 0.252347i \(-0.918798\pi\)
0.800605 + 0.599193i \(0.204512\pi\)
\(402\) −0.529808 13.8144i −0.0264244 0.688999i
\(403\) −10.3223 + 4.97096i −0.514191 + 0.247621i
\(404\) 0.140525 0.358051i 0.00699136 0.0178137i
\(405\) −21.8593 6.65343i −1.08620 0.330612i
\(406\) −4.53420 33.1040i −0.225028 1.64293i
\(407\) −3.35213 + 0.251208i −0.166159 + 0.0124519i
\(408\) −55.6177 29.3284i −2.75348 1.45197i
\(409\) −5.48470 2.15259i −0.271201 0.106439i 0.225844 0.974164i \(-0.427486\pi\)
−0.497045 + 0.867725i \(0.665581\pi\)
\(410\) 40.6878 23.4911i 2.00943 1.16014i
\(411\) 21.8379 + 4.11084i 1.07718 + 0.202773i
\(412\) 72.9986 + 28.6498i 3.59638 + 1.41148i
\(413\) −3.63126 0.880467i −0.178683 0.0433250i
\(414\) −0.0452582 24.2486i −0.00222432 1.19175i
\(415\) −8.12154 1.22413i −0.398671 0.0600899i
\(416\) −57.4775 27.6797i −2.81807 1.35711i
\(417\) 6.10103 2.66863i 0.298769 0.130683i
\(418\) −28.2650 22.5406i −1.38249 1.10250i
\(419\) −2.42991 6.19131i −0.118709 0.302465i 0.859152 0.511720i \(-0.170991\pi\)
−0.977861 + 0.209255i \(0.932896\pi\)
\(420\) 54.8502 + 11.0927i 2.67641 + 0.541268i
\(421\) 3.08741 7.86658i 0.150471 0.383394i −0.835686 0.549207i \(-0.814930\pi\)
0.986157 + 0.165813i \(0.0530250\pi\)
\(422\) 13.3857 7.72821i 0.651603 0.376203i
\(423\) −21.2019 + 16.9728i −1.03087 + 0.825244i
\(424\) −21.8605 + 3.29494i −1.06164 + 0.160017i
\(425\) −6.83880 2.10949i −0.331731 0.102325i
\(426\) 21.1436 + 48.3386i 1.02441 + 2.34201i
\(427\) 25.6223 23.1392i 1.23995 1.11979i
\(428\) 20.0137 + 1.49982i 0.967400 + 0.0724966i
\(429\) 0.763513 20.9280i 0.0368627 1.01041i
\(430\) 9.84931 + 20.4523i 0.474976 + 0.986298i
\(431\) 2.92172 9.47197i 0.140734 0.456249i −0.857576 0.514357i \(-0.828031\pi\)
0.998310 + 0.0581082i \(0.0185068\pi\)
\(432\) −1.98713 49.4050i −0.0956058 2.37700i
\(433\) 8.54110 + 1.94945i 0.410459 + 0.0936846i 0.422764 0.906240i \(-0.361060\pi\)
−0.0123052 + 0.999924i \(0.503917\pi\)
\(434\) 10.8309 + 6.44942i 0.519901 + 0.309582i
\(435\) −18.0085 + 11.3389i −0.863439 + 0.543659i
\(436\) 0.793424 3.47622i 0.0379981 0.166481i
\(437\) −22.0215 3.31920i −1.05343 0.158779i
\(438\) −3.49046 30.7210i −0.166780 1.46790i
\(439\) −17.0074 1.27453i −0.811719 0.0608299i −0.337599 0.941290i \(-0.609615\pi\)
−0.474120 + 0.880460i \(0.657234\pi\)
\(440\) 35.8704 1.71006
\(441\) −19.7347 + 7.17932i −0.939746 + 0.341872i
\(442\) −81.0685 −3.85604
\(443\) 25.7693 + 1.93114i 1.22434 + 0.0917513i 0.671159 0.741313i \(-0.265797\pi\)
0.553176 + 0.833064i \(0.313416\pi\)
\(444\) −11.6865 + 8.64185i −0.554615 + 0.410124i
\(445\) 14.2173 + 2.14291i 0.673964 + 0.101584i
\(446\) 14.0554 61.5808i 0.665543 2.91594i
\(447\) −0.739505 19.2821i −0.0349774 0.912012i
\(448\) 2.69229 + 19.6563i 0.127199 + 0.928674i
\(449\) 24.0033 + 5.47861i 1.13279 + 0.258551i 0.747511 0.664250i \(-0.231249\pi\)
0.385277 + 0.922801i \(0.374106\pi\)
\(450\) −2.53896 11.0290i −0.119688 0.519912i
\(451\) −4.02740 + 13.0565i −0.189643 + 0.614807i
\(452\) 5.82878 + 12.1036i 0.274163 + 0.569304i
\(453\) 2.47394 1.31047i 0.116236 0.0615713i
\(454\) 52.6551 + 3.94596i 2.47123 + 0.185193i
\(455\) 40.4416 11.8801i 1.89593 0.556946i
\(456\) −90.7540 10.1398i −4.24995 0.474838i
\(457\) 19.4901 + 6.01189i 0.911708 + 0.281225i 0.714908 0.699219i \(-0.246469\pi\)
0.196800 + 0.980444i \(0.436945\pi\)
\(458\) −17.3276 + 2.61172i −0.809667 + 0.122038i
\(459\) −12.0837 22.7094i −0.564020 1.05998i
\(460\) 32.7565 18.9120i 1.52728 0.881776i
\(461\) 2.55187 6.50207i 0.118853 0.302832i −0.859050 0.511891i \(-0.828945\pi\)
0.977903 + 0.209060i \(0.0670403\pi\)
\(462\) −19.6623 + 12.0132i −0.914772 + 0.558907i
\(463\) 3.59416 + 9.15777i 0.167035 + 0.425598i 0.989742 0.142868i \(-0.0456324\pi\)
−0.822707 + 0.568466i \(0.807537\pi\)
\(464\) −36.0039 28.7121i −1.67144 1.33293i
\(465\) 0.891472 7.97895i 0.0413410 0.370015i
\(466\) −47.6294 22.9371i −2.20639 1.06254i
\(467\) −18.0951 2.72739i −0.837340 0.126209i −0.283646 0.958929i \(-0.591544\pi\)
−0.553694 + 0.832720i \(0.686782\pi\)
\(468\) −45.4206 78.3328i −2.09957 3.62094i
\(469\) −3.60903 + 7.24285i −0.166649 + 0.334444i
\(470\) −55.8319 21.9124i −2.57534 1.01074i
\(471\) 10.5939 + 30.1852i 0.488140 + 1.39086i
\(472\) −8.96837 + 5.17789i −0.412803 + 0.238332i
\(473\) −6.14545 2.41191i −0.282568 0.110900i
\(474\) 15.3234 9.64826i 0.703825 0.443159i
\(475\) −10.3650 + 0.776751i −0.475580 + 0.0356398i
\(476\) 34.7850 + 52.5276i 1.59437 + 2.40760i
\(477\) −8.15623 3.90910i −0.373448 0.178985i
\(478\) 9.33599 23.7877i 0.427018 1.08802i
\(479\) 2.58514 1.24494i 0.118118 0.0568826i −0.373892 0.927472i \(-0.621977\pi\)
0.492010 + 0.870590i \(0.336263\pi\)
\(480\) 37.8310 23.8201i 1.72674 1.08723i
\(481\) −4.75003 + 9.86355i −0.216583 + 0.449739i
\(482\) 12.3334 + 11.4438i 0.561773 + 0.521249i
\(483\) −6.78931 + 12.4649i −0.308924 + 0.567174i
\(484\) 25.6952 23.8417i 1.16796 1.08371i
\(485\) 2.00535 + 6.50120i 0.0910584 + 0.295204i
\(486\) 21.4818 34.5449i 0.974435 1.56699i
\(487\) −2.19510 2.03676i −0.0994695 0.0922942i 0.628871 0.777510i \(-0.283517\pi\)
−0.728340 + 0.685216i \(0.759708\pi\)
\(488\) 7.15058 95.4178i 0.323691 4.31936i
\(489\) −27.0565 + 9.49582i −1.22354 + 0.429416i
\(490\) −35.4664 29.8824i −1.60221 1.34995i
\(491\) 16.2166 + 9.36267i 0.731846 + 0.422531i 0.819097 0.573655i \(-0.194475\pi\)
−0.0872514 + 0.996186i \(0.527808\pi\)
\(492\) 15.3439 + 57.0512i 0.691756 + 2.57206i
\(493\) −23.3576 5.33122i −1.05197 0.240106i
\(494\) −109.601 + 43.0151i −4.93116 + 1.93534i
\(495\) 12.1408 + 8.24427i 0.545686 + 0.370553i
\(496\) 16.9379 3.86596i 0.760533 0.173587i
\(497\) 2.72280 30.7632i 0.122134 1.37992i
\(498\) 5.83484 13.4077i 0.261465 0.600814i
\(499\) −16.5739 7.98155i −0.741948 0.357303i 0.0244230 0.999702i \(-0.492225\pi\)
−0.766371 + 0.642399i \(0.777939\pi\)
\(500\) −31.8178 + 29.5226i −1.42294 + 1.32029i
\(501\) 27.6756 + 7.38798i 1.23645 + 0.330070i
\(502\) 5.12486 + 34.0012i 0.228734 + 1.51755i
\(503\) −8.58591 + 4.13476i −0.382827 + 0.184360i −0.615392 0.788221i \(-0.711002\pi\)
0.232565 + 0.972581i \(0.425288\pi\)
\(504\) −25.8602 + 52.1417i −1.15191 + 2.32257i
\(505\) 0.182918 + 0.0880886i 0.00813974 + 0.00391989i
\(506\) −4.59052 + 14.8821i −0.204074 + 0.661591i
\(507\) −38.7062 24.2704i −1.71900 1.07789i
\(508\) 48.6167 + 84.2065i 2.15702 + 3.73606i
\(509\) 2.31623 0.102665 0.0513326 0.998682i \(-0.483653\pi\)
0.0513326 + 0.998682i \(0.483653\pi\)
\(510\) 30.1798 48.1306i 1.33639 2.13126i
\(511\) −6.83850 + 16.7565i −0.302517 + 0.741265i
\(512\) −33.4724 26.6934i −1.47929 1.17969i
\(513\) −28.3862 24.2903i −1.25328 1.07244i
\(514\) 11.6981 + 17.1580i 0.515983 + 0.756808i
\(515\) −17.9593 + 37.2929i −0.791381 + 1.64332i
\(516\) −28.0423 + 5.33300i −1.23449 + 0.234772i
\(517\) 16.2373 6.37266i 0.714114 0.280269i
\(518\) 11.9340 1.63458i 0.524352 0.0718195i
\(519\) −0.633803 + 17.3726i −0.0278209 + 0.762573i
\(520\) 58.4108 101.170i 2.56148 4.43662i
\(521\) 20.7646 35.9653i 0.909712 1.57567i 0.0952479 0.995454i \(-0.469636\pi\)
0.814464 0.580214i \(-0.197031\pi\)
\(522\) −11.2349 36.1828i −0.491739 1.58368i
\(523\) 4.19846 + 4.52486i 0.183586 + 0.197858i 0.818139 0.575021i \(-0.195006\pi\)
−0.634553 + 0.772879i \(0.718816\pi\)
\(524\) 2.69947 + 36.0220i 0.117927 + 1.57363i
\(525\) −1.79474 + 6.37696i −0.0783288 + 0.278313i
\(526\) −0.747859 + 9.97949i −0.0326082 + 0.435126i
\(527\) 7.06674 5.63554i 0.307832 0.245488i
\(528\) −8.19060 + 30.6823i −0.356450 + 1.33527i
\(529\) −2.98317 13.0701i −0.129703 0.568266i
\(530\) −1.49269 19.9185i −0.0648382 0.865206i
\(531\) −4.22550 0.308728i −0.183371 0.0133977i
\(532\) 74.8988 + 52.5578i 3.24728 + 2.27867i
\(533\) 30.2670 + 32.6200i 1.31101 + 1.41293i
\(534\) −10.2143 + 23.4711i −0.442014 + 1.01569i
\(535\) −1.57887 + 10.4751i −0.0682604 + 0.452878i
\(536\) 6.61073 + 21.4315i 0.285540 + 0.925698i
\(537\) −1.18521 + 4.43982i −0.0511454 + 0.191592i
\(538\) −64.6366 + 37.3179i −2.78668 + 1.60889i
\(539\) 13.4721 0.645035i 0.580285 0.0277836i
\(540\) 63.4154 + 2.19507i 2.72896 + 0.0944606i
\(541\) 11.9961 + 8.17879i 0.515752 + 0.351634i 0.793056 0.609148i \(-0.208489\pi\)
−0.277304 + 0.960782i \(0.589441\pi\)
\(542\) −14.6968 + 64.3909i −0.631282 + 2.76583i
\(543\) 9.59800 8.27535i 0.411890 0.355129i
\(544\) 49.0681 + 11.1995i 2.10378 + 0.480174i
\(545\) 1.79842 + 0.554739i 0.0770358 + 0.0237624i
\(546\) 1.86494 + 75.0184i 0.0798119 + 3.21049i
\(547\) 12.8735 3.97096i 0.550432 0.169786i −0.00704945 0.999975i \(-0.502244\pi\)
0.557482 + 0.830189i \(0.311768\pi\)
\(548\) −61.5368 + 4.61155i −2.62872 + 0.196995i
\(549\) 24.3505 30.6518i 1.03925 1.30819i
\(550\) −0.543198 + 7.24848i −0.0231621 + 0.309076i
\(551\) −34.4071 + 5.18603i −1.46579 + 0.220932i
\(552\) 10.2172 + 37.9892i 0.434872 + 1.61693i
\(553\) −10.5795 + 0.649565i −0.449888 + 0.0276223i
\(554\) 11.2026 + 16.4312i 0.475952 + 0.698093i
\(555\) −4.08769 6.49207i −0.173513 0.275573i
\(556\) −14.4581 + 11.5299i −0.613159 + 0.488978i
\(557\) 38.8710 + 22.4422i 1.64702 + 0.950905i 0.978249 + 0.207434i \(0.0665111\pi\)
0.668767 + 0.743472i \(0.266822\pi\)
\(558\) 13.3152 + 5.19717i 0.563677 + 0.220014i
\(559\) −16.8098 + 13.4053i −0.710978 + 0.566986i
\(560\) −63.7976 + 3.91706i −2.69594 + 0.165526i
\(561\) 3.08672 + 16.2308i 0.130322 + 0.685265i
\(562\) 4.67202 5.85853i 0.197077 0.247127i
\(563\) 0.629185 + 8.39589i 0.0265170 + 0.353845i 0.994642 + 0.103378i \(0.0329651\pi\)
−0.968125 + 0.250467i \(0.919416\pi\)
\(564\) 44.7294 60.7248i 1.88345 2.55697i
\(565\) −6.60066 + 2.59057i −0.277692 + 0.108986i
\(566\) −42.0917 + 52.7813i −1.76924 + 2.21856i
\(567\) −20.7366 + 11.7043i −0.870857 + 0.491536i
\(568\) −53.3673 66.9205i −2.23924 2.80792i
\(569\) 9.51803 + 5.49524i 0.399017 + 0.230372i 0.686060 0.727545i \(-0.259339\pi\)
−0.287043 + 0.957918i \(0.592672\pi\)
\(570\) 15.2635 81.0836i 0.639317 3.39622i
\(571\) 14.9276 38.0349i 0.624700 1.59171i −0.170497 0.985358i \(-0.554537\pi\)
0.795197 0.606351i \(-0.207368\pi\)
\(572\) 12.9410 + 56.6980i 0.541089 + 2.37066i
\(573\) 15.0190 6.56942i 0.627429 0.274442i
\(574\) 11.5372 47.5822i 0.481553 1.98604i
\(575\) 1.94278 + 4.03423i 0.0810197 + 0.168239i
\(576\) 6.67101 + 21.4844i 0.277959 + 0.895184i
\(577\) −11.0216 0.825957i −0.458836 0.0343850i −0.156693 0.987647i \(-0.550083\pi\)
−0.302144 + 0.953262i \(0.597702\pi\)
\(578\) 19.1032 4.36018i 0.794587 0.181359i
\(579\) 38.7566 + 4.33020i 1.61067 + 0.179957i
\(580\) 40.1965 43.3215i 1.66907 1.79883i
\(581\) −6.76316 + 5.24589i −0.280583 + 0.217636i
\(582\) −12.1035 + 0.464192i −0.501705 + 0.0192414i
\(583\) 4.25832 + 3.95114i 0.176362 + 0.163640i
\(584\) 18.3255 + 46.6926i 0.758314 + 1.93215i
\(585\) 43.0223 20.8174i 1.77875 0.860695i
\(586\) 28.3527 41.5858i 1.17124 1.71789i
\(587\) −13.0540 22.6102i −0.538796 0.933222i −0.998969 0.0453928i \(-0.985546\pi\)
0.460173 0.887829i \(-0.347787\pi\)
\(588\) 47.8073 33.3974i 1.97154 1.37729i
\(589\) 6.56366 11.3686i 0.270451 0.468435i
\(590\) −4.05967 8.43000i −0.167134 0.347058i
\(591\) 5.89584 13.5479i 0.242522 0.557286i
\(592\) 10.3508 12.9794i 0.425413 0.533451i
\(593\) 12.0679 3.72247i 0.495571 0.152863i −0.0368876 0.999319i \(-0.511744\pi\)
0.532459 + 0.846456i \(0.321268\pi\)
\(594\) −19.7557 + 17.0976i −0.810585 + 0.701525i
\(595\) −29.0201 + 16.2372i −1.18971 + 0.665662i
\(596\) 15.7948 + 51.2055i 0.646981 + 2.09746i
\(597\) −9.21646 + 4.03134i −0.377205 + 0.164992i
\(598\) 34.4990 + 37.1811i 1.41077 + 1.52045i
\(599\) 14.0041 20.5403i 0.572193 0.839253i −0.425651 0.904888i \(-0.639955\pi\)
0.997844 + 0.0656346i \(0.0209072\pi\)
\(600\) 8.59448 + 16.2249i 0.350868 + 0.662378i
\(601\) −20.7212 + 30.3924i −0.845233 + 1.23973i 0.123678 + 0.992322i \(0.460531\pi\)
−0.968912 + 0.247407i \(0.920421\pi\)
\(602\) 22.5094 + 7.27689i 0.917414 + 0.296584i
\(603\) −2.68822 + 8.77309i −0.109473 + 0.357268i
\(604\) −5.69914 + 5.28803i −0.231895 + 0.215167i
\(605\) 11.5356 + 14.4652i 0.468988 + 0.588092i
\(606\) −0.235512 + 0.274187i −0.00956703 + 0.0111381i
\(607\) 24.9894i 1.01429i −0.861861 0.507145i \(-0.830701\pi\)
0.861861 0.507145i \(-0.169299\pi\)
\(608\) 72.2801 10.8945i 2.93135 0.441829i
\(609\) −4.39603 + 21.7371i −0.178136 + 0.880831i
\(610\) 85.4874 + 12.8852i 3.46129 + 0.521705i
\(611\) 8.46677 56.1733i 0.342529 2.27253i
\(612\) 48.6869 + 52.2760i 1.96805 + 2.11313i
\(613\) −28.3602 + 19.3357i −1.14546 + 0.780960i −0.978752 0.205047i \(-0.934265\pi\)
−0.166705 + 0.986007i \(0.553313\pi\)
\(614\) 16.5933 + 42.2789i 0.669649 + 1.70624i
\(615\) −30.6342 + 5.82593i −1.23529 + 0.234924i
\(616\) 25.7927 27.0572i 1.03922 1.09016i
\(617\) −1.06172 7.04408i −0.0427434 0.283584i 0.957240 0.289294i \(-0.0934205\pi\)
−0.999984 + 0.00571008i \(0.998182\pi\)
\(618\) −55.9007 48.0157i −2.24866 1.93148i
\(619\) 43.0913i 1.73198i 0.500057 + 0.865992i \(0.333312\pi\)
−0.500057 + 0.865992i \(0.666688\pi\)
\(620\) 3.32299 + 22.0466i 0.133454 + 0.885412i
\(621\) −5.27311 + 15.2061i −0.211603 + 0.610200i
\(622\) −5.73491 + 11.9087i −0.229949 + 0.477494i
\(623\) 11.8394 9.18327i 0.474334 0.367920i
\(624\) 73.2000 + 73.0635i 2.93035 + 2.92488i
\(625\) −18.7909 23.5631i −0.751637 0.942523i
\(626\) −10.8590 7.40352i −0.434012 0.295904i
\(627\) 12.7852 + 20.3054i 0.510591 + 0.810920i
\(628\) −50.0440 73.4011i −1.99697 2.92902i
\(629\) 1.92191 8.42044i 0.0766316 0.335745i
\(630\) −45.2329 26.8203i −1.80212 1.06855i
\(631\) −5.59865 24.5293i −0.222879 0.976495i −0.955299 0.295642i \(-0.904466\pi\)
0.732420 0.680853i \(-0.238391\pi\)
\(632\) −19.9813 + 21.5347i −0.794813 + 0.856605i
\(633\) −10.0782 + 1.91664i −0.400572 + 0.0761797i
\(634\) −5.09968 + 1.57304i −0.202534 + 0.0624735i
\(635\) −46.2400 + 22.2680i −1.83498 + 0.883678i
\(636\) 24.6836 + 4.64653i 0.978767 + 0.184247i
\(637\) 20.1184 39.0476i 0.797122 1.54712i
\(638\) 24.3334i 0.963368i
\(639\) −2.68211 34.9157i −0.106103 1.38124i
\(640\) 1.31955 1.42214i 0.0521599 0.0562150i
\(641\) −27.2679 21.7454i −1.07702 0.858893i −0.0864960 0.996252i \(-0.527567\pi\)
−0.990521 + 0.137360i \(0.956138\pi\)
\(642\) −17.2932 7.52574i −0.682508 0.297017i
\(643\) −8.66628 + 28.0954i −0.341765 + 1.10797i 0.607717 + 0.794153i \(0.292085\pi\)
−0.949482 + 0.313821i \(0.898391\pi\)
\(644\) 9.28826 38.3070i 0.366009 1.50951i
\(645\) −1.70092 14.9705i −0.0669736 0.589462i
\(646\) 76.7479 52.3258i 3.01961 2.05873i
\(647\) 7.69887 + 2.37479i 0.302674 + 0.0933625i 0.442372 0.896832i \(-0.354137\pi\)
−0.139698 + 0.990194i \(0.544613\pi\)
\(648\) −19.2169 + 63.1354i −0.754910 + 2.48019i
\(649\) 2.53302 + 0.994137i 0.0994298 + 0.0390233i
\(650\) 19.5594 + 13.3353i 0.767181 + 0.523055i
\(651\) −5.37753 6.40972i −0.210762 0.251217i
\(652\) 65.7931 44.8570i 2.57666 1.75673i
\(653\) 19.5665 4.46594i 0.765698 0.174766i 0.178204 0.983994i \(-0.442971\pi\)
0.587495 + 0.809228i \(0.300114\pi\)
\(654\) −1.78000 + 2.83872i −0.0696033 + 0.111003i
\(655\) −19.0667 −0.744999
\(656\) −33.7395 58.4385i −1.31731 2.28164i
\(657\) −4.52911 + 20.0155i −0.176697 + 0.780877i
\(658\) −56.6746 + 26.3580i −2.20941 + 1.02754i
\(659\) 6.02711 39.9873i 0.234783 1.55768i −0.491864 0.870672i \(-0.663684\pi\)
0.726647 0.687011i \(-0.241078\pi\)
\(660\) −38.4794 13.4242i −1.49781 0.522537i
\(661\) 32.3873 2.42709i 1.25972 0.0944030i 0.571924 0.820306i \(-0.306197\pi\)
0.687797 + 0.725903i \(0.258578\pi\)
\(662\) −41.4701 + 3.10776i −1.61178 + 0.120786i
\(663\) 50.8044 + 17.7240i 1.97308 + 0.688344i
\(664\) −3.53560 + 23.4572i −0.137208 + 0.910314i
\(665\) −30.6183 + 37.3501i −1.18732 + 1.44837i
\(666\) 13.0439 4.05020i 0.505442 0.156942i
\(667\) 7.49481 + 12.9814i 0.290200 + 0.502641i
\(668\) −79.5470 −3.07777
\(669\) −22.2717 + 35.5188i −0.861074 + 1.37324i
\(670\) −19.7558 + 4.50914i −0.763235 + 0.174203i
\(671\) −20.7738 + 14.1633i −0.801964 + 0.546770i
\(672\) 9.23489 45.6639i 0.356244 1.76152i
\(673\) −14.3555 9.78743i −0.553365 0.377278i 0.254114 0.967174i \(-0.418216\pi\)
−0.807479 + 0.589897i \(0.799168\pi\)
\(674\) 42.8402 + 16.8135i 1.65014 + 0.647633i
\(675\) −0.820143 + 7.46680i −0.0315673 + 0.287397i
\(676\) 121.235 + 37.3960i 4.66288 + 1.43831i
\(677\) −34.1635 + 23.2923i −1.31301 + 0.895196i −0.998537 0.0540699i \(-0.982781\pi\)
−0.314474 + 0.949266i \(0.601828\pi\)
\(678\) −1.42514 12.5433i −0.0547323 0.481722i
\(679\) 6.34582 + 3.16205i 0.243530 + 0.121348i
\(680\) −27.1658 + 88.0695i −1.04176 + 3.37731i
\(681\) −32.1354 13.9849i −1.23143 0.535901i
\(682\) −7.17738 5.72377i −0.274836 0.219174i
\(683\) 30.4604 32.8285i 1.16553 1.25615i 0.204761 0.978812i \(-0.434358\pi\)
0.960773 0.277335i \(-0.0894513\pi\)
\(684\) 93.5600 + 44.8412i 3.57736 + 1.71455i
\(685\) 32.5719i 1.24451i
\(686\) −48.0425 + 5.26545i −1.83427 + 0.201036i
\(687\) 11.4300 + 2.15162i 0.436080 + 0.0820893i
\(688\) 29.3750 14.1462i 1.11991 0.539321i
\(689\) 18.0781 5.57636i 0.688722 0.212443i
\(690\) −34.9176 + 6.64053i −1.32929 + 0.252801i
\(691\) 30.5853 32.9631i 1.16352 1.25398i 0.201957 0.979394i \(-0.435270\pi\)
0.961564 0.274582i \(-0.0885395\pi\)
\(692\) −10.7425 47.0659i −0.408368 1.78918i
\(693\) 14.9485 3.22975i 0.567847 0.122688i
\(694\) −11.1468 + 48.8375i −0.423128 + 1.85385i
\(695\) −5.49851 8.06484i −0.208571 0.305917i
\(696\) 32.7498 + 52.0132i 1.24138 + 1.97155i
\(697\) −29.0064 19.7762i −1.09870 0.749078i
\(698\) −30.0107 37.6322i −1.13592 1.42440i
\(699\) 24.8339 + 24.7875i 0.939303 + 0.937551i
\(700\) 0.247956 18.3953i 0.00937187 0.695276i
\(701\) −21.7087 + 45.0786i −0.819927 + 1.70260i −0.114944 + 0.993372i \(0.536669\pi\)
−0.704983 + 0.709224i \(0.749045\pi\)
\(702\) 16.0531 + 83.5612i 0.605884 + 3.15381i
\(703\) −1.86957 12.4038i −0.0705121 0.467818i
\(704\) 14.4485i 0.544550i
\(705\) 30.1983 + 25.9387i 1.13733 + 0.976908i
\(706\) 6.93782 + 46.0295i 0.261108 + 1.73234i
\(707\) 0.197973 0.0746352i 0.00744553 0.00280695i
\(708\) 11.5584 2.19815i 0.434393 0.0826115i
\(709\) 4.72525 + 12.0397i 0.177460 + 0.452162i 0.991733 0.128322i \(-0.0409590\pi\)
−0.814272 + 0.580483i \(0.802864\pi\)
\(710\) 63.8979 43.5649i 2.39805 1.63496i
\(711\) −11.7123 + 2.69627i −0.439246 + 0.101118i
\(712\) 6.18929 41.0633i 0.231954 1.53891i
\(713\) −5.59194 0.842850i −0.209420 0.0315650i
\(714\) −14.6042 57.3731i −0.546548 2.14713i
\(715\) −30.3536 + 4.57507i −1.13516 + 0.171098i
\(716\) 12.7612i 0.476910i
\(717\) −11.0514 + 12.8663i −0.412723 + 0.480499i
\(718\) −38.3841 48.1321i −1.43248 1.79628i
\(719\) 28.5095 26.4529i 1.06322 0.986528i 0.0632902 0.997995i \(-0.479841\pi\)
0.999934 + 0.0114670i \(0.00365014\pi\)
\(720\) −70.6286 + 16.2593i −2.63217 + 0.605947i
\(721\) 15.2165 + 40.3622i 0.566691 + 1.50317i
\(722\) 48.0646 70.4978i 1.78878 2.62366i
\(723\) −5.22722 9.86809i −0.194403 0.366998i
\(724\) −19.8249 + 29.0778i −0.736788 + 1.08067i
\(725\) 4.75852 + 5.12846i 0.176727 + 0.190466i
\(726\) −30.1783 + 13.2002i −1.12002 + 0.489905i
\(727\) −0.957609 3.10449i −0.0355157 0.115139i 0.936079 0.351789i \(-0.114427\pi\)
−0.971595 + 0.236650i \(0.923950\pi\)
\(728\) −34.3128 116.806i −1.27172 4.32912i
\(729\) −21.0149 + 16.9522i −0.778328 + 0.627858i
\(730\) −43.3068 + 13.3584i −1.60285 + 0.494415i
\(731\) 10.5759 13.2617i 0.391163 0.490503i
\(732\) −43.3800 + 99.6816i −1.60337 + 3.68434i
\(733\) −2.08497 4.32949i −0.0770102 0.159913i 0.858909 0.512128i \(-0.171143\pi\)
−0.935919 + 0.352215i \(0.885429\pi\)
\(734\) 13.1598 22.7934i 0.485736 0.841319i
\(735\) 15.6931 + 26.4808i 0.578847 + 0.976761i
\(736\) −15.7446 27.2705i −0.580354 1.00520i
\(737\) 3.31977 4.86921i 0.122285 0.179360i
\(738\) 4.04542 55.3689i 0.148914 2.03816i
\(739\) 8.19839 + 20.8892i 0.301583 + 0.768420i 0.998676 + 0.0514400i \(0.0163811\pi\)
−0.697093 + 0.716980i \(0.745524\pi\)
\(740\) 15.6174 + 14.4909i 0.574109 + 0.532695i
\(741\) 78.0893 2.99488i 2.86868 0.110020i
\(742\) −16.0979 13.1965i −0.590973 0.484459i
\(743\) 32.8656 35.4207i 1.20572 1.29946i 0.263428 0.964679i \(-0.415147\pi\)
0.942296 0.334782i \(-0.108663\pi\)
\(744\) −23.0453 2.57481i −0.844883 0.0943970i
\(745\) −27.5752 + 6.29385i −1.01028 + 0.230589i
\(746\) −17.5083 1.31207i −0.641024 0.0480381i
\(747\) −6.58793 + 7.12673i −0.241040 + 0.260753i
\(748\) −19.9071 41.3375i −0.727875 1.51145i
\(749\) 6.76612 + 8.72309i 0.247229 + 0.318735i
\(750\) 37.3691 16.3455i 1.36453 0.596854i
\(751\) 11.3573 + 49.7595i 0.414433 + 1.81575i 0.562528 + 0.826778i \(0.309829\pi\)
−0.148095 + 0.988973i \(0.547314\pi\)
\(752\) −31.4721 + 80.1896i −1.14767 + 2.92421i
\(753\) 4.22202 22.4285i 0.153859 0.817339i
\(754\) 68.6308 + 39.6240i 2.49939 + 1.44302i
\(755\) −2.55857 3.20834i −0.0931157 0.116763i
\(756\) 47.2547 46.2560i 1.71864 1.68232i
\(757\) 0.135287 0.169644i 0.00491709 0.00616583i −0.779367 0.626568i \(-0.784459\pi\)
0.784284 + 0.620402i \(0.213031\pi\)
\(758\) 31.4606 12.3474i 1.14270 0.448477i
\(759\) 6.13049 8.32276i 0.222523 0.302097i
\(760\) 10.0029 + 133.480i 0.362844 + 4.84182i
\(761\) 26.9801 33.8320i 0.978027 1.22641i 0.00399655 0.999992i \(-0.498728\pi\)
0.974031 0.226416i \(-0.0727007\pi\)
\(762\) −17.0707 89.7620i −0.618405 3.25173i
\(763\) 1.71160 0.957667i 0.0619639 0.0346699i
\(764\) −35.5918 + 28.3835i −1.28766 + 1.02688i
\(765\) −29.4360 + 23.5645i −1.06426 + 0.851975i
\(766\) 18.9498 + 10.9407i 0.684683 + 0.395302i
\(767\) 6.92863 5.52540i 0.250178 0.199511i
\(768\) 15.6811 + 24.9048i 0.565844 + 0.898673i
\(769\) 6.23106 + 9.13929i 0.224698 + 0.329571i 0.921988 0.387217i \(-0.126564\pi\)
−0.697291 + 0.716789i \(0.745611\pi\)
\(770\) 22.6367 + 25.0658i 0.815769 + 0.903308i
\(771\) −3.57978 13.3102i −0.128923 0.479356i
\(772\) −107.088 + 16.1409i −3.85418 + 0.580925i
\(773\) −3.95425 + 52.7658i −0.142225 + 1.89785i 0.235405 + 0.971897i \(0.424358\pi\)
−0.377629 + 0.925957i \(0.623261\pi\)
\(774\) 26.5317 + 3.94837i 0.953661 + 0.141921i
\(775\) −2.63201 + 0.197242i −0.0945445 + 0.00708513i
\(776\) 18.7772 5.79199i 0.674062 0.207920i
\(777\) −7.83624 1.58477i −0.281124 0.0568534i
\(778\) −76.6512 23.6438i −2.74808 0.847670i
\(779\) −49.7085 11.3456i −1.78099 0.406500i
\(780\) −100.521 + 86.6690i −3.59924 + 3.10325i
\(781\) −5.00475 + 21.9272i −0.179084 + 0.784618i
\(782\) −33.0622 22.5414i −1.18230 0.806079i
\(783\) −0.869903 + 25.1315i −0.0310878 + 0.898126i
\(784\) −42.9191 + 50.9393i −1.53283 + 1.81926i
\(785\) 40.6088 23.4455i 1.44939 0.836806i
\(786\) 8.75501 32.7965i 0.312281 1.16981i
\(787\) 4.79139 + 15.5333i 0.170795 + 0.553702i 0.999986 0.00526205i \(-0.00167497\pi\)
−0.829192 + 0.558965i \(0.811199\pi\)
\(788\) −6.11536 + 40.5728i −0.217851 + 1.44534i
\(789\) 2.65049 6.09048i 0.0943598 0.216827i
\(790\) −18.0534 19.4569i −0.642310 0.692246i
\(791\) −2.79214 + 6.84165i −0.0992771 + 0.243261i
\(792\) 23.8116 35.0657i 0.846110 1.24601i
\(793\) 6.11917 + 81.6546i 0.217298 + 2.89964i
\(794\) 10.6694 + 46.7457i 0.378643 + 1.65894i
\(795\) −3.41935 + 12.8090i −0.121272 + 0.454287i
\(796\) 21.8410 17.4176i 0.774133 0.617350i
\(797\) 2.67552 35.7023i 0.0947716 1.26464i −0.723709 0.690105i \(-0.757564\pi\)
0.818481 0.574534i \(-0.194817\pi\)
\(798\) −50.1864 69.8166i −1.77658 2.47148i
\(799\) 3.34921 + 44.6921i 0.118487 + 1.58109i
\(800\) −9.99639 10.7735i −0.353426 0.380902i
\(801\) 11.5326 12.4758i 0.407484 0.440811i
\(802\) −10.0587 + 17.4221i −0.355184 + 0.615197i
\(803\) 6.59010 11.4144i 0.232560 0.402805i
\(804\) 0.929008 25.4642i 0.0327636 0.898054i
\(805\) 19.7966 + 6.39990i 0.697739 + 0.225567i
\(806\) −27.8311 + 10.9229i −0.980307 + 0.384742i
\(807\) 48.6655 9.25507i 1.71311 0.325794i
\(808\) 0.254423 0.528315i 0.00895057 0.0185861i
\(809\) 23.7964 + 34.9029i 0.836636 + 1.22712i 0.971685 + 0.236281i \(0.0759286\pi\)
−0.135048 + 0.990839i \(0.543119\pi\)
\(810\) −55.5866 21.5770i −1.95312 0.758140i
\(811\) −38.2334 30.4901i −1.34256 1.07065i −0.990911 0.134519i \(-0.957051\pi\)
−0.351645 0.936133i \(-0.614378\pi\)
\(812\) −3.77420 61.4707i −0.132448 2.15720i
\(813\) 23.2881 37.1396i 0.816748 1.30254i
\(814\) −8.77221 −0.307466
\(815\) 21.0154 + 36.3997i 0.736136 + 1.27503i
\(816\) −69.1284 43.3463i −2.41998 1.51742i
\(817\) 7.26138 23.5408i 0.254043 0.823589i
\(818\) −13.8530 6.67125i −0.484359 0.233255i
\(819\) 15.2326 47.4206i 0.532269 1.65701i
\(820\) 78.0210 37.5729i 2.72461 1.31210i
\(821\) −3.99321 26.4932i −0.139364 0.924619i −0.943785 0.330560i \(-0.892762\pi\)
0.804421 0.594060i \(-0.202476\pi\)
\(822\) 56.0268 + 14.9563i 1.95416 + 0.521661i
\(823\) −11.1469 + 10.3429i −0.388558 + 0.360529i −0.850129 0.526574i \(-0.823476\pi\)
0.461571 + 0.887103i \(0.347286\pi\)
\(824\) 107.712 + 51.8712i 3.75232 + 1.80702i
\(825\) 1.92515 4.42375i 0.0670251 0.154015i
\(826\) −9.27789 2.99938i −0.322819 0.104362i
\(827\) −2.32444 + 0.530538i −0.0808286 + 0.0184486i −0.262744 0.964866i \(-0.584627\pi\)
0.181915 + 0.983314i \(0.441770\pi\)
\(828\) 3.25685 44.5759i 0.113183 1.54912i
\(829\) 19.5116 7.65774i 0.677666 0.265964i −0.00144623 0.999999i \(-0.500460\pi\)
0.679112 + 0.734035i \(0.262365\pi\)
\(830\) −20.8959 4.76935i −0.725307 0.165546i
\(831\) −3.42813 12.7464i −0.118921 0.442167i
\(832\) −40.7512 23.5277i −1.41280 0.815678i
\(833\) −8.61916 + 33.5654i −0.298636 + 1.16297i
\(834\) 16.3971 5.75476i 0.567784 0.199271i
\(835\) 3.13770 41.8698i 0.108585 1.44896i
\(836\) −48.8471 45.3235i −1.68941 1.56755i
\(837\) −7.20816 6.16809i −0.249151 0.213200i
\(838\) −5.11593 16.5854i −0.176727 0.572935i
\(839\) −11.2422 + 10.4312i −0.388124 + 0.360127i −0.849968 0.526835i \(-0.823379\pi\)
0.461844 + 0.886961i \(0.347188\pi\)
\(840\) 82.1219 + 23.1125i 2.83348 + 0.797457i
\(841\) −4.09022 3.79517i −0.141042 0.130868i
\(842\) 9.56843 19.8690i 0.329750 0.684732i
\(843\) −4.20873 + 2.65000i −0.144956 + 0.0912709i
\(844\) 25.6677 12.3609i 0.883519 0.425480i
\(845\) −24.4655 + 62.3372i −0.841640 + 2.14446i
\(846\) −58.4834 + 40.0334i −2.01070 + 1.37638i
\(847\) 19.2058 + 1.69987i 0.659918 + 0.0584083i
\(848\) −28.6083 + 2.14390i −0.982414 + 0.0736218i
\(849\) 37.9178 23.8747i 1.30133 0.819377i
\(850\) −17.3852 6.82317i −0.596306 0.234033i
\(851\) −4.67980 + 2.70189i −0.160422 + 0.0926195i
\(852\) 32.2044 + 91.7601i 1.10330 + 3.14365i
\(853\) 3.55748 + 1.39621i 0.121806 + 0.0478052i 0.425461 0.904977i \(-0.360112\pi\)
−0.303655 + 0.952782i \(0.598207\pi\)
\(854\) 71.1892 55.2183i 2.43604 1.88953i
\(855\) −27.2927 + 47.4768i −0.933390 + 1.62367i
\(856\) 30.2549 + 4.56019i 1.03409 + 0.155864i
\(857\) −22.6445 10.9050i −0.773522 0.372509i 0.00511205 0.999987i \(-0.498373\pi\)
−0.778634 + 0.627478i \(0.784087\pi\)
\(858\) 6.06814 54.3118i 0.207163 1.85417i
\(859\) −13.9319 11.1103i −0.475349 0.379079i 0.356307 0.934369i \(-0.384036\pi\)
−0.831657 + 0.555290i \(0.812607\pi\)
\(860\) 15.2862 + 38.9486i 0.521255 + 1.32814i
\(861\) −17.6331 + 27.2966i −0.600934 + 0.930267i
\(862\) 9.45033 24.0790i 0.321879 0.820135i
\(863\) 11.3877 6.57469i 0.387641 0.223805i −0.293496 0.955960i \(-0.594819\pi\)
0.681138 + 0.732155i \(0.261485\pi\)
\(864\) 1.82744 52.7946i 0.0621707 1.79611i
\(865\) 25.1970 3.79783i 0.856722 0.129130i
\(866\) 21.8463 + 6.73868i 0.742366 + 0.228990i
\(867\) −12.9249 1.44408i −0.438953 0.0490434i
\(868\) 19.0192 + 13.3461i 0.645553 + 0.452996i
\(869\) 7.69756 + 0.576852i 0.261122 + 0.0195684i
\(870\) −49.0745 + 25.9952i −1.66378 + 0.881321i
\(871\) −8.32746 17.2922i −0.282165 0.585922i
\(872\) 1.60223 5.19431i 0.0542584 0.175902i
\(873\) 7.68655 + 2.35528i 0.260150 + 0.0797143i
\(874\) −56.6589 12.9320i −1.91652 0.437432i
\(875\) −23.7821 2.10491i −0.803981 0.0711591i
\(876\) −2.18402 56.9468i −0.0737911 1.92405i
\(877\) −11.8694 + 52.0031i −0.400800 + 1.75602i 0.223370 + 0.974734i \(0.428294\pi\)
−0.624171 + 0.781288i \(0.714563\pi\)
\(878\) −44.0096 6.63339i −1.48525 0.223866i
\(879\) −26.8601 + 19.8624i −0.905968 + 0.669942i
\(880\) 46.4185 + 3.47858i 1.56477 + 0.117263i
\(881\) 20.5627 0.692776 0.346388 0.938091i \(-0.387408\pi\)
0.346388 + 0.938091i \(0.387408\pi\)
\(882\) −52.7554 + 14.8341i −1.77637 + 0.499491i
\(883\) −12.4858 −0.420181 −0.210091 0.977682i \(-0.567376\pi\)
−0.210091 + 0.977682i \(0.567376\pi\)
\(884\) −149.006 11.1665i −5.01162 0.375569i
\(885\) 0.701082 + 6.17051i 0.0235666 + 0.207420i
\(886\) 66.6826 + 10.0508i 2.24024 + 0.337663i
\(887\) −1.17303 + 5.13939i −0.0393865 + 0.172564i −0.990796 0.135366i \(-0.956779\pi\)
0.951409 + 0.307930i \(0.0996361\pi\)
\(888\) −18.7508 + 11.8063i −0.629236 + 0.396195i
\(889\) −16.4521 + 50.8908i −0.551786 + 1.70682i
\(890\) 36.5796 + 8.34905i 1.22615 + 0.279861i
\(891\) 16.1186 6.39563i 0.539994 0.214262i
\(892\) 34.3165 111.251i 1.14900 3.72497i
\(893\) 28.2417 + 58.6444i 0.945072 + 1.96246i
\(894\) 1.83589 50.3218i 0.0614012 1.68301i
\(895\) 6.71690 + 0.503362i 0.224521 + 0.0168255i
\(896\) −0.123898 2.01793i −0.00413913 0.0674144i
\(897\) −13.4911 30.8433i −0.450454 1.02983i
\(898\) 61.3952 + 18.9379i 2.04879 + 0.631967i
\(899\) −8.73704 + 1.31690i −0.291397 + 0.0439210i
\(900\) −3.14754 20.6213i −0.104918 0.687378i
\(901\) −12.9258 + 7.46274i −0.430622 + 0.248620i
\(902\) −13.0267 + 33.1914i −0.433741 + 1.10515i
\(903\) −12.5153 9.48154i −0.416484 0.315526i
\(904\) 7.48225 + 19.0644i 0.248856 + 0.634074i
\(905\) −14.5232 11.5819i −0.482767 0.384994i
\(906\) 6.69348 2.92777i 0.222376 0.0972688i
\(907\) 46.8844 + 22.5783i 1.55677 + 0.749701i 0.996885 0.0788692i \(-0.0251309\pi\)
0.559885 + 0.828570i \(0.310845\pi\)
\(908\) 96.2381 + 14.5056i 3.19377 + 0.481384i
\(909\) 0.207537 0.120339i 0.00688358 0.00399139i
\(910\) 107.558 23.0287i 3.56550 0.763393i
\(911\) 29.5333 + 11.5910i 0.978483 + 0.384026i 0.800055 0.599927i \(-0.204804\pi\)
0.178428 + 0.983953i \(0.442899\pi\)
\(912\) −116.458 21.9224i −3.85630 0.725925i
\(913\) 5.39820 3.11665i 0.178654 0.103146i
\(914\) 49.5464 + 19.4455i 1.63885 + 0.643202i
\(915\) −50.7565 26.7650i −1.67796 0.884825i
\(916\) −32.2084 + 2.41369i −1.06420 + 0.0797505i
\(917\) −13.7100 + 14.3821i −0.452743 + 0.474938i
\(918\) −27.0167 61.4530i −0.891684 2.02825i
\(919\) 3.98363 10.1501i 0.131408 0.334822i −0.849992 0.526795i \(-0.823393\pi\)
0.981400 + 0.191973i \(0.0614887\pi\)
\(920\) 51.9525 25.0190i 1.71282 0.824852i
\(921\) −1.15529 30.1233i −0.0380680 0.992597i
\(922\) 7.90872 16.4226i 0.260460 0.540850i
\(923\) 53.6948 + 49.8215i 1.76739 + 1.63989i
\(924\) −37.7946 + 19.3724i −1.24335 + 0.637305i
\(925\) −1.84882 + 1.71545i −0.0607887 + 0.0564037i
\(926\) 7.56715 + 24.5321i 0.248672 + 0.806175i
\(927\) 24.5344 + 42.3123i 0.805816 + 1.38972i
\(928\) −36.0660 33.4644i −1.18393 1.09852i
\(929\) 1.00854 13.4580i 0.0330890 0.441543i −0.955914 0.293647i \(-0.905131\pi\)
0.989003 0.147896i \(-0.0472500\pi\)
\(930\) 3.87588 20.5897i 0.127095 0.675163i
\(931\) 6.15715 + 49.9520i 0.201792 + 1.63711i
\(932\) −84.3848 48.7196i −2.76412 1.59586i
\(933\) 6.19757 6.20915i 0.202899 0.203278i
\(934\) −46.5567 10.6263i −1.52338 0.347702i
\(935\) 22.5433 8.84760i 0.737245 0.289347i
\(936\) −60.1263 124.260i −1.96529 4.06155i
\(937\) 32.2165 7.35321i 1.05247 0.240219i 0.338913 0.940818i \(-0.389941\pi\)
0.713555 + 0.700599i \(0.247084\pi\)
\(938\) −10.8042 + 18.1442i −0.352770 + 0.592429i
\(939\) 5.18651 + 7.01376i 0.169255 + 0.228886i
\(940\) −99.6024 47.9660i −3.24867 1.56448i
\(941\) −18.1894 + 16.8773i −0.592958 + 0.550185i −0.918540 0.395329i \(-0.870631\pi\)
0.325581 + 0.945514i \(0.394440\pi\)
\(942\) 21.6818 + 80.6165i 0.706431 + 2.62663i
\(943\) 3.27365 + 21.7193i 0.106605 + 0.707277i
\(944\) −12.1077 + 5.83078i −0.394073 + 0.189776i
\(945\) 22.4830 + 26.6971i 0.731373 + 0.868458i
\(946\) −15.5219 7.47494i −0.504660 0.243031i
\(947\) 11.0381 35.7845i 0.358689 1.16284i −0.578989 0.815335i \(-0.696553\pi\)
0.937678 0.347506i \(-0.112971\pi\)
\(948\) 29.4937 15.6231i 0.957912 0.507416i
\(949\) −21.4624 37.1740i −0.696699 1.20672i
\(950\) −27.1243 −0.880027
\(951\) 3.53980 + 0.129142i 0.114786 + 0.00418772i
\(952\) 46.8974 + 83.8178i 1.51995 + 2.71655i
\(953\) 4.08484 + 3.25755i 0.132321 + 0.105522i 0.687414 0.726266i \(-0.258746\pi\)
−0.555093 + 0.831788i \(0.687317\pi\)
\(954\) −20.4625 11.7632i −0.662499 0.380847i
\(955\) −13.5358 19.8534i −0.438008 0.642440i
\(956\) 20.4364 42.4366i 0.660959 1.37250i
\(957\) 5.32001 15.2493i 0.171971 0.492941i
\(958\) 6.97006 2.73555i 0.225192 0.0883815i
\(959\) −24.5691 23.4209i −0.793378 0.756300i
\(960\) 29.1392 15.4353i 0.940463 0.498172i
\(961\) −13.8333 + 23.9599i −0.446235 + 0.772901i
\(962\) −14.2845 + 24.7415i −0.460551 + 0.797698i
\(963\) 9.19201 + 8.49707i 0.296208 + 0.273814i
\(964\) 21.0929 + 22.7328i 0.679358 + 0.732174i
\(965\) −4.27176 57.0027i −0.137513 1.83498i
\(966\) −20.0986 + 31.1133i −0.646661 + 1.00105i
\(967\) 1.32086 17.6256i 0.0424758 0.566801i −0.934848 0.355049i \(-0.884464\pi\)
0.977324 0.211752i \(-0.0679168\pi\)
\(968\) 41.7792 33.3178i 1.34283 1.07087i
\(969\) −59.5367 + 16.0124i −1.91259 + 0.514392i
\(970\) 3.95068 + 17.3091i 0.126849 + 0.555761i
\(971\) −1.65033 22.0221i −0.0529615 0.706722i −0.958978 0.283480i \(-0.908511\pi\)
0.906017 0.423242i \(-0.139108\pi\)
\(972\) 44.2424 60.5355i 1.41908 1.94168i
\(973\) −10.0370 1.65149i −0.321773 0.0529443i
\(974\) −5.31509 5.72831i −0.170307 0.183547i
\(975\) −9.34204 12.6333i −0.299185 0.404590i
\(976\) 18.5065 122.783i 0.592380 3.93018i
\(977\) 8.76120 + 28.4031i 0.280296 + 0.908696i 0.980795 + 0.195043i \(0.0624845\pi\)
−0.700499 + 0.713653i \(0.747039\pi\)
\(978\) −72.2607 + 19.4345i −2.31064 + 0.621446i
\(979\) −9.44990 + 5.45590i −0.302020 + 0.174371i
\(980\) −61.0723 59.8099i −1.95088 1.91056i
\(981\) 1.73613 1.38982i 0.0554302 0.0443736i
\(982\) 40.3745 + 27.5269i 1.28840 + 0.878417i
\(983\) −7.66645 + 33.5889i −0.244522 + 1.07132i 0.692326 + 0.721585i \(0.256586\pi\)
−0.936848 + 0.349736i \(0.886271\pi\)
\(984\) 16.8268 + 88.4798i 0.536419 + 2.82063i
\(985\) −21.1143 4.81921i −0.672759 0.153553i
\(986\) −59.7436 18.4285i −1.90262 0.586882i
\(987\) 41.2798 4.12738i 1.31395 0.131376i
\(988\) −207.374 + 63.9664i −6.59744 + 2.03504i
\(989\) −10.5829 + 0.793082i −0.336518 + 0.0252185i
\(990\) 29.9860 + 23.8216i 0.953018 + 0.757101i
\(991\) 1.94428 25.9446i 0.0617621 0.824158i −0.877197 0.480130i \(-0.840589\pi\)
0.938959 0.344028i \(-0.111791\pi\)
\(992\) 18.3542 2.76645i 0.582747 0.0878350i
\(993\) 26.6681 + 7.11904i 0.846287 + 0.225916i
\(994\) 13.0848 79.5237i 0.415024 2.52234i
\(995\) 8.30628 + 12.1831i 0.263327 + 0.386229i
\(996\) 12.5714 23.8401i 0.398340 0.755401i
\(997\) −16.3799 + 13.0626i −0.518758 + 0.413695i −0.847557 0.530704i \(-0.821927\pi\)
0.328799 + 0.944400i \(0.393356\pi\)
\(998\) −41.5735 24.0025i −1.31599 0.759784i
\(999\) −9.05992 0.313601i −0.286643 0.00992190i
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 441.2.bd.a.437.52 yes 648
9.2 odd 6 441.2.bn.a.290.52 yes 648
49.12 odd 42 441.2.bn.a.257.52 yes 648
441.110 even 42 inner 441.2.bd.a.110.52 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.bd.a.110.52 648 441.110 even 42 inner
441.2.bd.a.437.52 yes 648 1.1 even 1 trivial
441.2.bn.a.257.52 yes 648 49.12 odd 42
441.2.bn.a.290.52 yes 648 9.2 odd 6