Properties

Label 160.2.z.a.29.8
Level $160$
Weight $2$
Character 160.29
Analytic conductor $1.278$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [160,2,Mod(29,160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(160, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("160.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 160.z (of order \(8\), degree \(4\), 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: \(1.27760643234\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 29.8
Character \(\chi\) \(=\) 160.29
Dual form 160.2.z.a.149.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.578672 - 1.29040i) q^{2} +(-0.245584 + 0.592892i) q^{3} +(-1.33028 + 1.49344i) q^{4} +(1.89351 + 1.18938i) q^{5} +(0.907181 - 0.0261881i) q^{6} +(-0.502274 - 0.502274i) q^{7} +(2.69693 + 0.852380i) q^{8} +(1.83011 + 1.83011i) q^{9} +O(q^{10})\) \(q+(-0.578672 - 1.29040i) q^{2} +(-0.245584 + 0.592892i) q^{3} +(-1.33028 + 1.49344i) q^{4} +(1.89351 + 1.18938i) q^{5} +(0.907181 - 0.0261881i) q^{6} +(-0.502274 - 0.502274i) q^{7} +(2.69693 + 0.852380i) q^{8} +(1.83011 + 1.83011i) q^{9} +(0.439066 - 3.13165i) q^{10} +(1.67371 - 0.693272i) q^{11} +(-0.558754 - 1.15547i) q^{12} +(2.07378 + 0.858986i) q^{13} +(-0.357483 + 0.938787i) q^{14} +(-1.17019 + 0.830550i) q^{15} +(-0.460728 - 3.97338i) q^{16} -2.02880 q^{17} +(1.30255 - 3.42061i) q^{18} +(1.77255 - 4.27932i) q^{19} +(-4.29516 + 1.24563i) q^{20} +(0.421144 - 0.174444i) q^{21} +(-1.86313 - 1.75858i) q^{22} +(-2.46911 + 2.46911i) q^{23} +(-1.16769 + 1.38966i) q^{24} +(2.17073 + 4.50421i) q^{25} +(-0.0915990 - 3.17308i) q^{26} +(-3.31318 + 1.37236i) q^{27} +(1.41828 - 0.0819528i) q^{28} +(-4.73420 - 1.96097i) q^{29} +(1.74890 + 1.02940i) q^{30} -0.856835 q^{31} +(-4.86065 + 2.89381i) q^{32} +1.16258i q^{33} +(1.17401 + 2.61796i) q^{34} +(-0.353661 - 1.54846i) q^{35} +(-5.16772 + 0.298607i) q^{36} +(2.81698 - 1.16683i) q^{37} +(-6.54777 + 0.189018i) q^{38} +(-1.01857 + 1.01857i) q^{39} +(4.09285 + 4.82168i) q^{40} +(5.04215 + 5.04215i) q^{41} +(-0.468807 - 0.442500i) q^{42} +(1.70397 + 4.11374i) q^{43} +(-1.19113 + 3.42182i) q^{44} +(1.28862 + 5.64203i) q^{45} +(4.61496 + 1.75734i) q^{46} -11.0620 q^{47} +(2.46893 + 0.702636i) q^{48} -6.49544i q^{49} +(4.55611 - 5.40757i) q^{50} +(0.498239 - 1.20286i) q^{51} +(-4.04154 + 1.95437i) q^{52} +(-5.21863 - 12.5989i) q^{53} +(3.68815 + 3.48118i) q^{54} +(3.99374 + 0.677967i) q^{55} +(-0.926471 - 1.78273i) q^{56} +(2.10186 + 2.10186i) q^{57} +(0.209110 + 7.24378i) q^{58} +(-4.27763 - 10.3271i) q^{59} +(0.316301 - 2.85247i) q^{60} +(-6.75690 - 2.79880i) q^{61} +(0.495826 + 1.10566i) q^{62} -1.83843i q^{63} +(6.54690 + 4.59762i) q^{64} +(2.90504 + 4.09301i) q^{65} +(1.50020 - 0.672755i) q^{66} +(5.20997 - 12.5780i) q^{67} +(2.69886 - 3.02988i) q^{68} +(-0.857543 - 2.07029i) q^{69} +(-1.79348 + 1.35241i) q^{70} +(-10.8298 + 10.8298i) q^{71} +(3.37574 + 6.49564i) q^{72} +(5.74167 - 5.74167i) q^{73} +(-3.13580 - 2.95983i) q^{74} +(-3.20361 + 0.180844i) q^{75} +(4.03292 + 8.33988i) q^{76} +(-1.18887 - 0.492447i) q^{77} +(1.90379 + 0.724948i) q^{78} -4.77217i q^{79} +(3.85349 - 8.07160i) q^{80} +5.46312i q^{81} +(3.58865 - 9.42416i) q^{82} +(12.1041 + 5.01368i) q^{83} +(-0.299717 + 0.861012i) q^{84} +(-3.84154 - 2.41302i) q^{85} +(4.32235 - 4.57932i) q^{86} +(2.32528 - 2.32528i) q^{87} +(5.10481 - 0.443075i) q^{88} +(4.49248 - 4.49248i) q^{89} +(6.53480 - 4.92772i) q^{90} +(-0.610157 - 1.47305i) q^{91} +(-0.402869 - 6.97208i) q^{92} +(0.210425 - 0.508010i) q^{93} +(6.40127 + 14.2744i) q^{94} +(8.44609 - 5.99466i) q^{95} +(-0.522019 - 3.59251i) q^{96} +1.01543i q^{97} +(-8.38173 + 3.75873i) q^{98} +(4.33183 + 1.79430i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34} + 20 q^{35} + 72 q^{36} - 8 q^{39} - 56 q^{40} - 8 q^{41} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 44 q^{50} - 48 q^{51} + 24 q^{54} + 28 q^{55} - 56 q^{56} + 24 q^{59} + 32 q^{60} + 24 q^{61} + 64 q^{64} - 8 q^{65} - 8 q^{66} - 40 q^{69} + 80 q^{70} - 40 q^{71} + 128 q^{74} + 28 q^{75} - 8 q^{76} + 48 q^{80} + 200 q^{84} - 24 q^{85} + 24 q^{86} - 8 q^{89} + 80 q^{90} - 8 q^{91} + 120 q^{94} - 8 q^{95} - 56 q^{96} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(101\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.578672 1.29040i −0.409183 0.912452i
\(3\) −0.245584 + 0.592892i −0.141788 + 0.342306i −0.978782 0.204906i \(-0.934311\pi\)
0.836994 + 0.547212i \(0.184311\pi\)
\(4\) −1.33028 + 1.49344i −0.665138 + 0.746720i
\(5\) 1.89351 + 1.18938i 0.846801 + 0.531909i
\(6\) 0.907181 0.0261881i 0.370355 0.0106912i
\(7\) −0.502274 0.502274i −0.189842 0.189842i 0.605786 0.795628i \(-0.292859\pi\)
−0.795628 + 0.605786i \(0.792859\pi\)
\(8\) 2.69693 + 0.852380i 0.953510 + 0.301362i
\(9\) 1.83011 + 1.83011i 0.610037 + 0.610037i
\(10\) 0.439066 3.13165i 0.138845 0.990314i
\(11\) 1.67371 0.693272i 0.504642 0.209029i −0.115814 0.993271i \(-0.536948\pi\)
0.620456 + 0.784242i \(0.286948\pi\)
\(12\) −0.558754 1.15547i −0.161298 0.333557i
\(13\) 2.07378 + 0.858986i 0.575162 + 0.238240i 0.651253 0.758861i \(-0.274244\pi\)
−0.0760905 + 0.997101i \(0.524244\pi\)
\(14\) −0.357483 + 0.938787i −0.0955415 + 0.250901i
\(15\) −1.17019 + 0.830550i −0.302142 + 0.214447i
\(16\) −0.460728 3.97338i −0.115182 0.993344i
\(17\) −2.02880 −0.492055 −0.246028 0.969263i \(-0.579125\pi\)
−0.246028 + 0.969263i \(0.579125\pi\)
\(18\) 1.30255 3.42061i 0.307013 0.806247i
\(19\) 1.77255 4.27932i 0.406651 0.981743i −0.579361 0.815071i \(-0.696698\pi\)
0.986012 0.166672i \(-0.0533020\pi\)
\(20\) −4.29516 + 1.24563i −0.960427 + 0.278530i
\(21\) 0.421144 0.174444i 0.0919012 0.0380667i
\(22\) −1.86313 1.75858i −0.397220 0.374930i
\(23\) −2.46911 + 2.46911i −0.514846 + 0.514846i −0.916007 0.401162i \(-0.868607\pi\)
0.401162 + 0.916007i \(0.368607\pi\)
\(24\) −1.16769 + 1.38966i −0.238354 + 0.283663i
\(25\) 2.17073 + 4.50421i 0.434145 + 0.900843i
\(26\) −0.0915990 3.17308i −0.0179640 0.622292i
\(27\) −3.31318 + 1.37236i −0.637622 + 0.264111i
\(28\) 1.41828 0.0819528i 0.268030 0.0154876i
\(29\) −4.73420 1.96097i −0.879118 0.364143i −0.102963 0.994685i \(-0.532832\pi\)
−0.776155 + 0.630543i \(0.782832\pi\)
\(30\) 1.74890 + 1.02940i 0.319304 + 0.187942i
\(31\) −0.856835 −0.153892 −0.0769460 0.997035i \(-0.524517\pi\)
−0.0769460 + 0.997035i \(0.524517\pi\)
\(32\) −4.86065 + 2.89381i −0.859249 + 0.511558i
\(33\) 1.16258i 0.202380i
\(34\) 1.17401 + 2.61796i 0.201341 + 0.448977i
\(35\) −0.353661 1.54846i −0.0597797 0.261737i
\(36\) −5.16772 + 0.298607i −0.861286 + 0.0497679i
\(37\) 2.81698 1.16683i 0.463109 0.191826i −0.138914 0.990304i \(-0.544361\pi\)
0.602024 + 0.798478i \(0.294361\pi\)
\(38\) −6.54777 + 0.189018i −1.06219 + 0.0306628i
\(39\) −1.01857 + 1.01857i −0.163102 + 0.163102i
\(40\) 4.09285 + 4.82168i 0.647136 + 0.762374i
\(41\) 5.04215 + 5.04215i 0.787452 + 0.787452i 0.981076 0.193624i \(-0.0620240\pi\)
−0.193624 + 0.981076i \(0.562024\pi\)
\(42\) −0.468807 0.442500i −0.0723385 0.0682792i
\(43\) 1.70397 + 4.11374i 0.259853 + 0.627340i 0.998928 0.0462823i \(-0.0147374\pi\)
−0.739076 + 0.673622i \(0.764737\pi\)
\(44\) −1.19113 + 3.42182i −0.179570 + 0.515859i
\(45\) 1.28862 + 5.64203i 0.192096 + 0.841065i
\(46\) 4.61496 + 1.75734i 0.680438 + 0.259106i
\(47\) −11.0620 −1.61356 −0.806779 0.590854i \(-0.798791\pi\)
−0.806779 + 0.590854i \(0.798791\pi\)
\(48\) 2.46893 + 0.702636i 0.356359 + 0.101417i
\(49\) 6.49544i 0.927920i
\(50\) 4.55611 5.40757i 0.644331 0.764747i
\(51\) 0.498239 1.20286i 0.0697674 0.168434i
\(52\) −4.04154 + 1.95437i −0.560461 + 0.271023i
\(53\) −5.21863 12.5989i −0.716833 1.73059i −0.682174 0.731190i \(-0.738965\pi\)
−0.0346593 0.999399i \(-0.511035\pi\)
\(54\) 3.68815 + 3.48118i 0.501893 + 0.473729i
\(55\) 3.99374 + 0.677967i 0.538516 + 0.0914171i
\(56\) −0.926471 1.78273i −0.123805 0.238227i
\(57\) 2.10186 + 2.10186i 0.278398 + 0.278398i
\(58\) 0.209110 + 7.24378i 0.0274575 + 0.951154i
\(59\) −4.27763 10.3271i −0.556901 1.34448i −0.912208 0.409727i \(-0.865624\pi\)
0.355307 0.934749i \(-0.384376\pi\)
\(60\) 0.316301 2.85247i 0.0408342 0.368252i
\(61\) −6.75690 2.79880i −0.865132 0.358350i −0.0944198 0.995532i \(-0.530100\pi\)
−0.770713 + 0.637183i \(0.780100\pi\)
\(62\) 0.495826 + 1.10566i 0.0629700 + 0.140419i
\(63\) 1.83843i 0.231621i
\(64\) 6.54690 + 4.59762i 0.818362 + 0.574703i
\(65\) 2.90504 + 4.09301i 0.360326 + 0.507676i
\(66\) 1.50020 0.672755i 0.184662 0.0828104i
\(67\) 5.20997 12.5780i 0.636500 1.53665i −0.194813 0.980840i \(-0.562410\pi\)
0.831312 0.555805i \(-0.187590\pi\)
\(68\) 2.69886 3.02988i 0.327285 0.367427i
\(69\) −0.857543 2.07029i −0.103236 0.249234i
\(70\) −1.79348 + 1.35241i −0.214361 + 0.161644i
\(71\) −10.8298 + 10.8298i −1.28527 + 1.28527i −0.347636 + 0.937630i \(0.613015\pi\)
−0.937630 + 0.347636i \(0.886985\pi\)
\(72\) 3.37574 + 6.49564i 0.397835 + 0.765518i
\(73\) 5.74167 5.74167i 0.672012 0.672012i −0.286168 0.958179i \(-0.592382\pi\)
0.958179 + 0.286168i \(0.0923815\pi\)
\(74\) −3.13580 2.95983i −0.364529 0.344073i
\(75\) −3.20361 + 0.180844i −0.369921 + 0.0208820i
\(76\) 4.03292 + 8.33988i 0.462608 + 0.956649i
\(77\) −1.18887 0.492447i −0.135484 0.0561195i
\(78\) 1.90379 + 0.724948i 0.215561 + 0.0820842i
\(79\) 4.77217i 0.536912i −0.963292 0.268456i \(-0.913487\pi\)
0.963292 0.268456i \(-0.0865133\pi\)
\(80\) 3.85349 8.07160i 0.430833 0.902432i
\(81\) 5.46312i 0.607013i
\(82\) 3.58865 9.42416i 0.396300 1.04072i
\(83\) 12.1041 + 5.01368i 1.32860 + 0.550323i 0.930255 0.366915i \(-0.119586\pi\)
0.398341 + 0.917237i \(0.369586\pi\)
\(84\) −0.299717 + 0.861012i −0.0327018 + 0.0939441i
\(85\) −3.84154 2.41302i −0.416673 0.261729i
\(86\) 4.32235 4.57932i 0.466091 0.493800i
\(87\) 2.32528 2.32528i 0.249297 0.249297i
\(88\) 5.10481 0.443075i 0.544174 0.0472319i
\(89\) 4.49248 4.49248i 0.476202 0.476202i −0.427713 0.903915i \(-0.640681\pi\)
0.903915 + 0.427713i \(0.140681\pi\)
\(90\) 6.53480 4.92772i 0.688829 0.519428i
\(91\) −0.610157 1.47305i −0.0639619 0.154418i
\(92\) −0.402869 6.97208i −0.0420020 0.726889i
\(93\) 0.210425 0.508010i 0.0218200 0.0526782i
\(94\) 6.40127 + 14.2744i 0.660240 + 1.47229i
\(95\) 8.44609 5.99466i 0.866551 0.615040i
\(96\) −0.522019 3.59251i −0.0532783 0.366659i
\(97\) 1.01543i 0.103101i 0.998670 + 0.0515507i \(0.0164164\pi\)
−0.998670 + 0.0515507i \(0.983584\pi\)
\(98\) −8.38173 + 3.75873i −0.846683 + 0.379689i
\(99\) 4.33183 + 1.79430i 0.435366 + 0.180334i
\(100\) −9.61444 2.75000i −0.961444 0.275000i
\(101\) −2.71336 6.55064i −0.269990 0.651813i 0.729493 0.683989i \(-0.239756\pi\)
−0.999482 + 0.0321761i \(0.989756\pi\)
\(102\) −1.84049 + 0.0531303i −0.182235 + 0.00526068i
\(103\) 8.47055 + 8.47055i 0.834628 + 0.834628i 0.988146 0.153518i \(-0.0490602\pi\)
−0.153518 + 0.988146i \(0.549060\pi\)
\(104\) 4.86065 + 4.08427i 0.476626 + 0.400496i
\(105\) 1.00492 + 0.170593i 0.0980701 + 0.0166481i
\(106\) −13.2377 + 14.0247i −1.28576 + 1.36220i
\(107\) 3.82698 + 9.23915i 0.369968 + 0.893182i 0.993755 + 0.111587i \(0.0355935\pi\)
−0.623787 + 0.781595i \(0.714407\pi\)
\(108\) 2.35790 6.77366i 0.226889 0.651795i
\(109\) −0.0151896 + 0.0366710i −0.00145490 + 0.00351245i −0.924605 0.380927i \(-0.875605\pi\)
0.923150 + 0.384439i \(0.125605\pi\)
\(110\) −1.43622 5.54585i −0.136938 0.528776i
\(111\) 1.95672i 0.185724i
\(112\) −1.76431 + 2.22713i −0.166712 + 0.210444i
\(113\) −17.8934 −1.68327 −0.841634 0.540049i \(-0.818406\pi\)
−0.841634 + 0.540049i \(0.818406\pi\)
\(114\) 1.49596 3.92854i 0.140109 0.367941i
\(115\) −7.61201 + 1.73855i −0.709823 + 0.162121i
\(116\) 9.22638 4.46161i 0.856648 0.414250i
\(117\) 2.22320 + 5.36728i 0.205535 + 0.496205i
\(118\) −10.8508 + 11.4959i −0.998897 + 1.05828i
\(119\) 1.01901 + 1.01901i 0.0934126 + 0.0934126i
\(120\) −3.86387 + 1.24249i −0.352722 + 0.113423i
\(121\) −5.45751 + 5.45751i −0.496137 + 0.496137i
\(122\) 0.298453 + 10.3387i 0.0270207 + 0.936023i
\(123\) −4.22772 + 1.75118i −0.381201 + 0.157899i
\(124\) 1.13983 1.27963i 0.102359 0.114914i
\(125\) −1.24696 + 11.1106i −0.111532 + 0.993761i
\(126\) −2.37232 + 1.06385i −0.211343 + 0.0947754i
\(127\) 9.04443i 0.802564i −0.915955 0.401282i \(-0.868565\pi\)
0.915955 0.401282i \(-0.131435\pi\)
\(128\) 2.14428 11.1086i 0.189529 0.981875i
\(129\) −2.85747 −0.251586
\(130\) 3.60057 6.11719i 0.315791 0.536513i
\(131\) 15.0828 + 6.24752i 1.31779 + 0.545848i 0.927149 0.374693i \(-0.122252\pi\)
0.390645 + 0.920541i \(0.372252\pi\)
\(132\) −1.73625 1.54656i −0.151121 0.134611i
\(133\) −3.03969 + 1.25908i −0.263575 + 0.109176i
\(134\) −19.2455 + 0.555571i −1.66256 + 0.0479941i
\(135\) −7.90579 1.34207i −0.680422 0.115507i
\(136\) −5.47153 1.72930i −0.469179 0.148287i
\(137\) −4.60247 + 4.60247i −0.393216 + 0.393216i −0.875832 0.482616i \(-0.839687\pi\)
0.482616 + 0.875832i \(0.339687\pi\)
\(138\) −2.17527 + 2.30459i −0.185171 + 0.196180i
\(139\) −8.73769 + 3.61927i −0.741122 + 0.306983i −0.721113 0.692817i \(-0.756369\pi\)
−0.0200083 + 0.999800i \(0.506369\pi\)
\(140\) 2.78299 + 1.53170i 0.235206 + 0.129452i
\(141\) 2.71665 6.55856i 0.228783 0.552331i
\(142\) 20.2418 + 7.70792i 1.69865 + 0.646834i
\(143\) 4.06641 0.340050
\(144\) 6.42854 8.11491i 0.535712 0.676242i
\(145\) −6.63188 9.34389i −0.550748 0.775967i
\(146\) −10.7316 4.08652i −0.888154 0.338203i
\(147\) 3.85109 + 1.59518i 0.317633 + 0.131568i
\(148\) −2.00477 + 5.75921i −0.164791 + 0.473404i
\(149\) 5.56412 2.30473i 0.455831 0.188811i −0.142941 0.989731i \(-0.545656\pi\)
0.598771 + 0.800920i \(0.295656\pi\)
\(150\) 2.08720 + 4.02929i 0.170419 + 0.328990i
\(151\) −0.639759 0.639759i −0.0520629 0.0520629i 0.680596 0.732659i \(-0.261721\pi\)
−0.732659 + 0.680596i \(0.761721\pi\)
\(152\) 8.42806 10.0301i 0.683606 0.813552i
\(153\) −3.71292 3.71292i −0.300172 0.300172i
\(154\) 0.0525126 + 1.81909i 0.00423159 + 0.146586i
\(155\) −1.62242 1.01911i −0.130316 0.0818566i
\(156\) −0.166194 2.87616i −0.0133062 0.230277i
\(157\) −2.76534 + 6.67612i −0.220698 + 0.532812i −0.994985 0.100022i \(-0.968109\pi\)
0.774287 + 0.632834i \(0.218109\pi\)
\(158\) −6.15803 + 2.76153i −0.489906 + 0.219695i
\(159\) 8.75138 0.694030
\(160\) −12.6455 0.301738i −0.999715 0.0238545i
\(161\) 2.48034 0.195478
\(162\) 7.04962 3.16135i 0.553870 0.248379i
\(163\) −1.26452 + 3.05283i −0.0990450 + 0.239116i −0.965633 0.259908i \(-0.916308\pi\)
0.866588 + 0.499024i \(0.166308\pi\)
\(164\) −14.2376 + 0.822696i −1.11177 + 0.0642417i
\(165\) −1.38276 + 2.20136i −0.107648 + 0.171375i
\(166\) −0.534639 18.5204i −0.0414960 1.43746i
\(167\) 16.6765 + 16.6765i 1.29047 + 1.29047i 0.934498 + 0.355967i \(0.115849\pi\)
0.355967 + 0.934498i \(0.384151\pi\)
\(168\) 1.28449 0.111488i 0.0991006 0.00860149i
\(169\) −5.62970 5.62970i −0.433054 0.433054i
\(170\) −0.890775 + 6.35347i −0.0683193 + 0.487289i
\(171\) 11.0756 4.58766i 0.846972 0.350827i
\(172\) −8.41038 2.92764i −0.641286 0.223231i
\(173\) −6.82358 2.82642i −0.518787 0.214889i 0.107897 0.994162i \(-0.465588\pi\)
−0.626684 + 0.779273i \(0.715588\pi\)
\(174\) −4.34613 1.65497i −0.329479 0.125463i
\(175\) 1.17205 3.35265i 0.0885986 0.253436i
\(176\) −3.52575 6.33086i −0.265764 0.477206i
\(177\) 7.17338 0.539185
\(178\) −8.39677 3.19743i −0.629365 0.239658i
\(179\) −7.46409 + 18.0199i −0.557892 + 1.34687i 0.353539 + 0.935420i \(0.384978\pi\)
−0.911432 + 0.411452i \(0.865022\pi\)
\(180\) −10.1403 5.58099i −0.755810 0.415982i
\(181\) 12.1376 5.02754i 0.902178 0.373694i 0.117121 0.993118i \(-0.462634\pi\)
0.785057 + 0.619424i \(0.212634\pi\)
\(182\) −1.54775 + 1.63976i −0.114727 + 0.121547i
\(183\) 3.31877 3.31877i 0.245331 0.245331i
\(184\) −8.76365 + 4.55441i −0.646065 + 0.335756i
\(185\) 6.72179 + 1.14107i 0.494196 + 0.0838934i
\(186\) −0.777304 + 0.0224389i −0.0569947 + 0.00164530i
\(187\) −3.39561 + 1.40651i −0.248311 + 0.102854i
\(188\) 14.7155 16.5204i 1.07324 1.20488i
\(189\) 2.35343 + 0.974821i 0.171186 + 0.0709078i
\(190\) −12.6230 7.42991i −0.915772 0.539022i
\(191\) −12.8998 −0.933400 −0.466700 0.884416i \(-0.654557\pi\)
−0.466700 + 0.884416i \(0.654557\pi\)
\(192\) −4.33370 + 2.75250i −0.312758 + 0.198645i
\(193\) 5.34854i 0.384996i −0.981297 0.192498i \(-0.938341\pi\)
0.981297 0.192498i \(-0.0616589\pi\)
\(194\) 1.31031 0.587601i 0.0940751 0.0421873i
\(195\) −3.14015 + 0.717197i −0.224871 + 0.0513596i
\(196\) 9.70055 + 8.64074i 0.692897 + 0.617195i
\(197\) 1.50704 0.624236i 0.107372 0.0444749i −0.328351 0.944556i \(-0.606493\pi\)
0.435723 + 0.900081i \(0.356493\pi\)
\(198\) −0.191338 6.62812i −0.0135978 0.471040i
\(199\) 10.7252 10.7252i 0.760288 0.760288i −0.216086 0.976374i \(-0.569329\pi\)
0.976374 + 0.216086i \(0.0693292\pi\)
\(200\) 2.01500 + 13.9978i 0.142482 + 0.989797i
\(201\) 6.17790 + 6.17790i 0.435756 + 0.435756i
\(202\) −6.88281 + 7.29200i −0.484273 + 0.513063i
\(203\) 1.39292 + 3.36281i 0.0977638 + 0.236023i
\(204\) 1.13360 + 2.34422i 0.0793677 + 0.164128i
\(205\) 3.55029 + 15.5444i 0.247963 + 1.08567i
\(206\) 6.02875 15.8321i 0.420043 1.10307i
\(207\) −9.03750 −0.628150
\(208\) 2.45763 8.63566i 0.170406 0.598775i
\(209\) 8.39118i 0.580430i
\(210\) −0.361386 1.39547i −0.0249380 0.0962964i
\(211\) 3.82019 9.22276i 0.262993 0.634921i −0.736128 0.676842i \(-0.763348\pi\)
0.999121 + 0.0419214i \(0.0133479\pi\)
\(212\) 25.7579 + 8.96629i 1.76906 + 0.615807i
\(213\) −3.76129 9.08055i −0.257719 0.622189i
\(214\) 9.70765 10.2848i 0.663601 0.703053i
\(215\) −1.66635 + 9.81607i −0.113644 + 0.669451i
\(216\) −10.1052 + 0.877086i −0.687572 + 0.0596782i
\(217\) 0.430366 + 0.430366i 0.0292151 + 0.0292151i
\(218\) 0.0561102 0.00161976i 0.00380026 0.000109704i
\(219\) 1.99413 + 4.81425i 0.134751 + 0.325317i
\(220\) −6.32528 + 5.06253i −0.426451 + 0.341316i
\(221\) −4.20727 1.74271i −0.283011 0.117227i
\(222\) 2.52496 1.13230i 0.169464 0.0759951i
\(223\) 17.8672i 1.19648i 0.801318 + 0.598239i \(0.204133\pi\)
−0.801318 + 0.598239i \(0.795867\pi\)
\(224\) 3.89486 + 0.987891i 0.260236 + 0.0660063i
\(225\) −4.27054 + 12.2159i −0.284703 + 0.814392i
\(226\) 10.3544 + 23.0897i 0.688764 + 1.53590i
\(227\) 6.24074 15.0665i 0.414212 0.999997i −0.569782 0.821796i \(-0.692972\pi\)
0.983994 0.178201i \(-0.0570276\pi\)
\(228\) −5.93506 + 0.342947i −0.393059 + 0.0227122i
\(229\) 9.48118 + 22.8896i 0.626534 + 1.51259i 0.843902 + 0.536497i \(0.180253\pi\)
−0.217368 + 0.976090i \(0.569747\pi\)
\(230\) 6.64829 + 8.81650i 0.438375 + 0.581343i
\(231\) 0.583935 0.583935i 0.0384201 0.0384201i
\(232\) −11.0963 9.32393i −0.728509 0.612146i
\(233\) 7.39110 7.39110i 0.484207 0.484207i −0.422265 0.906472i \(-0.638765\pi\)
0.906472 + 0.422265i \(0.138765\pi\)
\(234\) 5.63945 5.97472i 0.368662 0.390580i
\(235\) −20.9459 13.1570i −1.36636 0.858266i
\(236\) 21.1134 + 7.34954i 1.37436 + 0.478414i
\(237\) 2.82938 + 1.17197i 0.183788 + 0.0761275i
\(238\) 0.725261 1.90461i 0.0470117 0.123457i
\(239\) 9.75748i 0.631159i 0.948899 + 0.315579i \(0.102199\pi\)
−0.948899 + 0.315579i \(0.897801\pi\)
\(240\) 3.83923 + 4.26695i 0.247821 + 0.275431i
\(241\) 2.34142i 0.150824i 0.997152 + 0.0754120i \(0.0240272\pi\)
−0.997152 + 0.0754120i \(0.975973\pi\)
\(242\) 10.2005 + 3.88427i 0.655712 + 0.249690i
\(243\) −13.1786 5.45874i −0.845406 0.350179i
\(244\) 13.1684 6.36785i 0.843020 0.407660i
\(245\) 7.72558 12.2992i 0.493569 0.785764i
\(246\) 4.70619 + 4.44210i 0.300056 + 0.283218i
\(247\) 7.35175 7.35175i 0.467781 0.467781i
\(248\) −2.31083 0.730348i −0.146738 0.0463772i
\(249\) −5.94513 + 5.94513i −0.376758 + 0.376758i
\(250\) 15.0587 4.82030i 0.952396 0.304863i
\(251\) 3.85766 + 9.31321i 0.243493 + 0.587844i 0.997625 0.0688785i \(-0.0219421\pi\)
−0.754132 + 0.656723i \(0.771942\pi\)
\(252\) 2.74559 + 2.44563i 0.172956 + 0.154060i
\(253\) −2.42080 + 5.84434i −0.152195 + 0.367430i
\(254\) −11.6710 + 5.23376i −0.732301 + 0.328395i
\(255\) 2.37408 1.68502i 0.148671 0.105520i
\(256\) −15.5755 + 3.66129i −0.973466 + 0.228831i
\(257\) 15.5892i 0.972429i −0.873839 0.486215i \(-0.838377\pi\)
0.873839 0.486215i \(-0.161623\pi\)
\(258\) 1.65354 + 3.68729i 0.102945 + 0.229561i
\(259\) −2.00097 0.828828i −0.124334 0.0515009i
\(260\) −9.97718 1.10634i −0.618759 0.0686120i
\(261\) −5.07531 12.2529i −0.314154 0.758435i
\(262\) −0.666211 23.0782i −0.0411586 1.42578i
\(263\) 0.610694 + 0.610694i 0.0376570 + 0.0376570i 0.725685 0.688028i \(-0.241523\pi\)
−0.688028 + 0.725685i \(0.741523\pi\)
\(264\) −0.990962 + 3.13541i −0.0609895 + 0.192971i
\(265\) 5.10342 30.0630i 0.313501 1.84676i
\(266\) 3.38371 + 3.19383i 0.207469 + 0.195826i
\(267\) 1.56027 + 3.76683i 0.0954871 + 0.230526i
\(268\) 11.8538 + 24.5130i 0.724084 + 1.49737i
\(269\) −2.14408 + 5.17628i −0.130727 + 0.315603i −0.975667 0.219258i \(-0.929636\pi\)
0.844940 + 0.534862i \(0.179636\pi\)
\(270\) 2.84306 + 10.9783i 0.173023 + 0.668116i
\(271\) 23.4133i 1.42226i −0.703061 0.711129i \(-0.748184\pi\)
0.703061 0.711129i \(-0.251816\pi\)
\(272\) 0.934722 + 8.06117i 0.0566758 + 0.488780i
\(273\) 1.02320 0.0619271
\(274\) 8.60236 + 3.27572i 0.519688 + 0.197893i
\(275\) 6.75581 + 6.03383i 0.407390 + 0.363854i
\(276\) 4.23262 + 1.47337i 0.254774 + 0.0886865i
\(277\) 7.93812 + 19.1643i 0.476956 + 1.15147i 0.961030 + 0.276446i \(0.0891566\pi\)
−0.484074 + 0.875027i \(0.660843\pi\)
\(278\) 9.72658 + 9.18077i 0.583361 + 0.550626i
\(279\) −1.56810 1.56810i −0.0938798 0.0938798i
\(280\) 0.366071 4.47753i 0.0218769 0.267584i
\(281\) −15.2603 + 15.2603i −0.910350 + 0.910350i −0.996300 0.0859493i \(-0.972608\pi\)
0.0859493 + 0.996300i \(0.472608\pi\)
\(282\) −10.0352 + 0.289693i −0.597589 + 0.0172509i
\(283\) 4.67729 1.93740i 0.278036 0.115166i −0.239308 0.970944i \(-0.576921\pi\)
0.517344 + 0.855777i \(0.326921\pi\)
\(284\) −1.76703 30.5804i −0.104854 1.81461i
\(285\) 1.47996 + 6.47981i 0.0876655 + 0.383831i
\(286\) −2.35312 5.24730i −0.139143 0.310279i
\(287\) 5.06508i 0.298983i
\(288\) −14.1915 3.59953i −0.836243 0.212104i
\(289\) −12.8840 −0.757882
\(290\) −8.21969 + 13.9648i −0.482677 + 0.820044i
\(291\) −0.602040 0.249373i −0.0352922 0.0146185i
\(292\) 0.936831 + 16.2129i 0.0548239 + 0.948785i
\(293\) 7.00218 2.90040i 0.409072 0.169443i −0.168651 0.985676i \(-0.553941\pi\)
0.577723 + 0.816233i \(0.303941\pi\)
\(294\) −0.170103 5.89254i −0.00992062 0.343660i
\(295\) 4.18320 24.6422i 0.243555 1.43473i
\(296\) 8.59180 0.745730i 0.499388 0.0433447i
\(297\) −4.59387 + 4.59387i −0.266563 + 0.266563i
\(298\) −6.19384 5.84627i −0.358799 0.338665i
\(299\) −7.24132 + 2.99945i −0.418777 + 0.173463i
\(300\) 3.99160 5.02497i 0.230455 0.290117i
\(301\) 1.21037 2.92209i 0.0697644 0.168426i
\(302\) −0.455336 + 1.19576i −0.0262016 + 0.0688081i
\(303\) 4.55018 0.261401
\(304\) −17.8200 5.07142i −1.02205 0.290866i
\(305\) −9.46538 13.3361i −0.541986 0.763623i
\(306\) −2.64260 + 6.93973i −0.151067 + 0.396718i
\(307\) −25.8284 10.6985i −1.47410 0.610594i −0.506313 0.862350i \(-0.668992\pi\)
−0.967791 + 0.251756i \(0.918992\pi\)
\(308\) 2.31697 1.12042i 0.132021 0.0638417i
\(309\) −7.10235 + 2.94189i −0.404039 + 0.167358i
\(310\) −0.376207 + 2.68330i −0.0213671 + 0.152401i
\(311\) −16.7678 16.7678i −0.950815 0.950815i 0.0480311 0.998846i \(-0.484705\pi\)
−0.998846 + 0.0480311i \(0.984705\pi\)
\(312\) −3.61523 + 1.87881i −0.204672 + 0.106367i
\(313\) 0.669162 + 0.669162i 0.0378233 + 0.0378233i 0.725765 0.687942i \(-0.241486\pi\)
−0.687942 + 0.725765i \(0.741486\pi\)
\(314\) 10.2151 0.294885i 0.576472 0.0166413i
\(315\) 2.18661 3.48108i 0.123201 0.196137i
\(316\) 7.12696 + 6.34831i 0.400923 + 0.357120i
\(317\) 6.17935 14.9183i 0.347067 0.837893i −0.649897 0.760023i \(-0.725188\pi\)
0.996963 0.0778707i \(-0.0248121\pi\)
\(318\) −5.06418 11.2928i −0.283985 0.633269i
\(319\) −9.28314 −0.519756
\(320\) 6.92824 + 16.4924i 0.387301 + 0.921954i
\(321\) −6.41766 −0.358199
\(322\) −1.43530 3.20064i −0.0799864 0.178365i
\(323\) −3.59614 + 8.68186i −0.200095 + 0.483072i
\(324\) −8.15884 7.26746i −0.453269 0.403748i
\(325\) 0.632543 + 11.2054i 0.0350872 + 0.621562i
\(326\) 4.67112 0.134844i 0.258709 0.00746830i
\(327\) −0.0180116 0.0180116i −0.000996045 0.000996045i
\(328\) 9.30052 + 17.8962i 0.513536 + 0.988152i
\(329\) 5.55615 + 5.55615i 0.306320 + 0.306320i
\(330\) 3.64080 + 0.510451i 0.200420 + 0.0280994i
\(331\) 3.63950 1.50753i 0.200045 0.0828614i −0.280412 0.959880i \(-0.590471\pi\)
0.480457 + 0.877018i \(0.340471\pi\)
\(332\) −23.5894 + 11.4072i −1.29464 + 0.626049i
\(333\) 7.29083 + 3.01996i 0.399535 + 0.165493i
\(334\) 11.8692 31.1696i 0.649452 1.70553i
\(335\) 24.8252 17.6198i 1.35634 0.962674i
\(336\) −0.887163 1.59299i −0.0483987 0.0869050i
\(337\) 28.7667 1.56702 0.783511 0.621378i \(-0.213427\pi\)
0.783511 + 0.621378i \(0.213427\pi\)
\(338\) −4.00682 + 10.5223i −0.217942 + 0.572339i
\(339\) 4.39432 10.6088i 0.238667 0.576193i
\(340\) 8.71400 2.52712i 0.472583 0.137052i
\(341\) −1.43409 + 0.594019i −0.0776603 + 0.0321680i
\(342\) −12.3291 11.6372i −0.666680 0.629269i
\(343\) −6.77841 + 6.77841i −0.366000 + 0.366000i
\(344\) 1.08902 + 12.5469i 0.0587159 + 0.676485i
\(345\) 0.838611 4.94006i 0.0451493 0.265964i
\(346\) 0.301398 + 10.4407i 0.0162033 + 0.561297i
\(347\) −24.0857 + 9.97664i −1.29299 + 0.535574i −0.919875 0.392211i \(-0.871710\pi\)
−0.373115 + 0.927785i \(0.621710\pi\)
\(348\) 0.379401 + 6.56594i 0.0203381 + 0.351971i
\(349\) 14.9642 + 6.19839i 0.801017 + 0.331792i 0.745364 0.666658i \(-0.232276\pi\)
0.0556535 + 0.998450i \(0.482276\pi\)
\(350\) −5.00450 + 0.427669i −0.267502 + 0.0228599i
\(351\) −8.04963 −0.429658
\(352\) −6.12910 + 8.21313i −0.326682 + 0.437762i
\(353\) 9.97151i 0.530730i −0.964148 0.265365i \(-0.914508\pi\)
0.964148 0.265365i \(-0.0854924\pi\)
\(354\) −4.15104 9.25655i −0.220625 0.491980i
\(355\) −33.3872 + 7.62551i −1.77201 + 0.404720i
\(356\) 0.733008 + 12.6855i 0.0388494 + 0.672329i
\(357\) −0.854416 + 0.353911i −0.0452205 + 0.0187309i
\(358\) 27.5722 0.795942i 1.45724 0.0420668i
\(359\) −4.65497 + 4.65497i −0.245680 + 0.245680i −0.819195 0.573515i \(-0.805579\pi\)
0.573515 + 0.819195i \(0.305579\pi\)
\(360\) −1.33384 + 16.3146i −0.0702993 + 0.859854i
\(361\) −1.73559 1.73559i −0.0913467 0.0913467i
\(362\) −13.5112 12.7530i −0.710134 0.670285i
\(363\) −1.89544 4.57599i −0.0994846 0.240177i
\(364\) 3.01159 + 1.04833i 0.157850 + 0.0549475i
\(365\) 17.7009 4.04283i 0.926510 0.211611i
\(366\) −6.20303 2.36207i −0.324238 0.123467i
\(367\) −14.2125 −0.741886 −0.370943 0.928656i \(-0.620965\pi\)
−0.370943 + 0.928656i \(0.620965\pi\)
\(368\) 10.9483 + 8.67313i 0.570720 + 0.452118i
\(369\) 18.4554i 0.960750i
\(370\) −2.41727 9.33412i −0.125668 0.485258i
\(371\) −3.70691 + 8.94927i −0.192453 + 0.464623i
\(372\) 0.478760 + 0.990051i 0.0248225 + 0.0513317i
\(373\) 5.09201 + 12.2932i 0.263655 + 0.636518i 0.999159 0.0410014i \(-0.0130548\pi\)
−0.735505 + 0.677520i \(0.763055\pi\)
\(374\) 3.77990 + 3.56779i 0.195454 + 0.184486i
\(375\) −6.28114 3.46789i −0.324357 0.179081i
\(376\) −29.8334 9.42902i −1.53854 0.486264i
\(377\) −8.13322 8.13322i −0.418882 0.418882i
\(378\) −0.103951 3.60097i −0.00534667 0.185214i
\(379\) 6.23491 + 15.0524i 0.320266 + 0.773190i 0.999238 + 0.0390263i \(0.0124256\pi\)
−0.678972 + 0.734164i \(0.737574\pi\)
\(380\) −2.28296 + 20.5883i −0.117114 + 1.05616i
\(381\) 5.36237 + 2.22117i 0.274723 + 0.113794i
\(382\) 7.46479 + 16.6460i 0.381932 + 0.851683i
\(383\) 11.4676i 0.585967i −0.956117 0.292984i \(-0.905352\pi\)
0.956117 0.292984i \(-0.0946481\pi\)
\(384\) 6.05963 + 3.99943i 0.309229 + 0.204095i
\(385\) −1.66543 2.34648i −0.0848780 0.119588i
\(386\) −6.90176 + 3.09505i −0.351291 + 0.157534i
\(387\) −4.41016 + 10.6471i −0.224181 + 0.541221i
\(388\) −1.51648 1.35080i −0.0769878 0.0685767i
\(389\) 2.64514 + 6.38594i 0.134114 + 0.323780i 0.976642 0.214872i \(-0.0689336\pi\)
−0.842528 + 0.538653i \(0.818934\pi\)
\(390\) 2.74259 + 3.63703i 0.138876 + 0.184168i
\(391\) 5.00932 5.00932i 0.253332 0.253332i
\(392\) 5.53658 17.5178i 0.279640 0.884781i
\(393\) −7.40820 + 7.40820i −0.373694 + 0.373694i
\(394\) −1.67760 1.58346i −0.0845161 0.0797734i
\(395\) 5.67595 9.03614i 0.285588 0.454657i
\(396\) −8.44222 + 4.08241i −0.424238 + 0.205149i
\(397\) −31.5582 13.0718i −1.58386 0.656056i −0.594840 0.803844i \(-0.702785\pi\)
−0.989019 + 0.147788i \(0.952785\pi\)
\(398\) −20.0462 7.63344i −1.00482 0.382630i
\(399\) 2.11142i 0.105703i
\(400\) 16.8968 10.7003i 0.844842 0.535017i
\(401\) 28.0739i 1.40195i 0.713188 + 0.700973i \(0.247251\pi\)
−0.713188 + 0.700973i \(0.752749\pi\)
\(402\) 4.39700 11.5470i 0.219302 0.575910i
\(403\) −1.77688 0.736009i −0.0885129 0.0366632i
\(404\) 13.3925 + 4.66191i 0.666302 + 0.231939i
\(405\) −6.49775 + 10.3444i −0.322876 + 0.514020i
\(406\) 3.53333 3.74339i 0.175356 0.185781i
\(407\) 3.90587 3.90587i 0.193607 0.193607i
\(408\) 2.36901 2.81933i 0.117283 0.139578i
\(409\) 5.70294 5.70294i 0.281992 0.281992i −0.551911 0.833903i \(-0.686101\pi\)
0.833903 + 0.551911i \(0.186101\pi\)
\(410\) 18.0041 13.5764i 0.889159 0.670491i
\(411\) −1.59847 3.85906i −0.0788469 0.190353i
\(412\) −23.9184 + 1.38209i −1.17838 + 0.0680904i
\(413\) −3.03850 + 7.33559i −0.149515 + 0.360961i
\(414\) 5.22975 + 11.6620i 0.257028 + 0.573157i
\(415\) 16.9560 + 23.8898i 0.832335 + 1.17271i
\(416\) −12.5656 + 1.82588i −0.616081 + 0.0895212i
\(417\) 6.06934i 0.297217i
\(418\) −10.8280 + 4.85574i −0.529615 + 0.237502i
\(419\) −8.85002 3.66580i −0.432352 0.179086i 0.155884 0.987775i \(-0.450177\pi\)
−0.588236 + 0.808689i \(0.700177\pi\)
\(420\) −1.59159 + 1.27385i −0.0776617 + 0.0621576i
\(421\) −4.55395 10.9942i −0.221946 0.535825i 0.773208 0.634152i \(-0.218651\pi\)
−0.995154 + 0.0983274i \(0.968651\pi\)
\(422\) −14.1117 + 0.407370i −0.686947 + 0.0198305i
\(423\) −20.2447 20.2447i −0.984330 0.984330i
\(424\) −3.33526 38.4266i −0.161974 1.86616i
\(425\) −4.40396 9.13813i −0.213623 0.443264i
\(426\) −9.54102 + 10.1082i −0.462264 + 0.489746i
\(427\) 1.98805 + 4.79958i 0.0962085 + 0.232268i
\(428\) −18.8891 6.57526i −0.913037 0.317827i
\(429\) −0.998643 + 2.41094i −0.0482149 + 0.116401i
\(430\) 13.6310 3.53003i 0.657343 0.170233i
\(431\) 33.7928i 1.62774i 0.581047 + 0.813870i \(0.302643\pi\)
−0.581047 + 0.813870i \(0.697357\pi\)
\(432\) 6.97939 + 12.5322i 0.335796 + 0.602957i
\(433\) 25.3512 1.21830 0.609151 0.793054i \(-0.291510\pi\)
0.609151 + 0.793054i \(0.291510\pi\)
\(434\) 0.306304 0.804385i 0.0147031 0.0386117i
\(435\) 7.16859 1.63728i 0.343708 0.0785016i
\(436\) −0.0345596 0.0714674i −0.00165510 0.00342267i
\(437\) 6.18949 + 14.9427i 0.296083 + 0.714808i
\(438\) 5.05837 5.35910i 0.241698 0.256068i
\(439\) 12.8961 + 12.8961i 0.615498 + 0.615498i 0.944373 0.328875i \(-0.106670\pi\)
−0.328875 + 0.944373i \(0.606670\pi\)
\(440\) 10.1930 + 5.23262i 0.485931 + 0.249455i
\(441\) 11.8874 11.8874i 0.566066 0.566066i
\(442\) 0.185836 + 6.43753i 0.00883930 + 0.306202i
\(443\) 7.61662 3.15491i 0.361876 0.149894i −0.194334 0.980935i \(-0.562255\pi\)
0.556211 + 0.831041i \(0.312255\pi\)
\(444\) −2.92225 2.60298i −0.138684 0.123532i
\(445\) 13.8498 3.16325i 0.656544 0.149952i
\(446\) 23.0559 10.3393i 1.09173 0.489579i
\(447\) 3.86493i 0.182805i
\(448\) −0.979070 5.59760i −0.0462567 0.264462i
\(449\) 13.9213 0.656989 0.328494 0.944506i \(-0.393459\pi\)
0.328494 + 0.944506i \(0.393459\pi\)
\(450\) 18.2346 1.55828i 0.859590 0.0734578i
\(451\) 11.9347 + 4.94350i 0.561982 + 0.232780i
\(452\) 23.8031 26.7227i 1.11961 1.25693i
\(453\) 0.536423 0.222194i 0.0252033 0.0104396i
\(454\) −23.0531 + 0.665488i −1.08194 + 0.0312329i
\(455\) 0.596687 3.51494i 0.0279731 0.164783i
\(456\) 3.87700 + 7.46017i 0.181557 + 0.349354i
\(457\) −28.8382 + 28.8382i −1.34899 + 1.34899i −0.462236 + 0.886757i \(0.652953\pi\)
−0.886757 + 0.462236i \(0.847047\pi\)
\(458\) 24.0503 25.4801i 1.12380 1.19061i
\(459\) 6.72176 2.78424i 0.313745 0.129957i
\(460\) 7.52965 13.6808i 0.351072 0.637872i
\(461\) 9.32827 22.5204i 0.434461 1.04888i −0.543371 0.839492i \(-0.682852\pi\)
0.977832 0.209389i \(-0.0671475\pi\)
\(462\) −1.09142 0.415604i −0.0507774 0.0193357i
\(463\) 17.1677 0.797853 0.398926 0.916983i \(-0.369383\pi\)
0.398926 + 0.916983i \(0.369383\pi\)
\(464\) −5.61049 + 19.7142i −0.260461 + 0.915210i
\(465\) 1.00266 0.711644i 0.0464972 0.0330017i
\(466\) −13.8145 5.26047i −0.639946 0.243687i
\(467\) 15.5078 + 6.42354i 0.717615 + 0.297246i 0.711452 0.702735i \(-0.248038\pi\)
0.00616357 + 0.999981i \(0.498038\pi\)
\(468\) −10.9732 3.81975i −0.507236 0.176568i
\(469\) −8.93443 + 3.70076i −0.412554 + 0.170885i
\(470\) −4.85694 + 34.6423i −0.224034 + 1.59793i
\(471\) −3.27909 3.27909i −0.151093 0.151093i
\(472\) −2.73386 31.4977i −0.125836 1.44980i
\(473\) 5.70389 + 5.70389i 0.262265 + 0.262265i
\(474\) −0.124974 4.32923i −0.00574025 0.198848i
\(475\) 23.1227 1.30528i 1.06094 0.0598902i
\(476\) −2.87740 + 0.166265i −0.131885 + 0.00762076i
\(477\) 13.5067 32.6080i 0.618428 1.49302i
\(478\) 12.5911 5.64638i 0.575902 0.258260i
\(479\) 23.9560 1.09458 0.547289 0.836944i \(-0.315660\pi\)
0.547289 + 0.836944i \(0.315660\pi\)
\(480\) 3.28443 7.42332i 0.149913 0.338827i
\(481\) 6.84409 0.312064
\(482\) 3.02137 1.35491i 0.137620 0.0617146i
\(483\) −0.609132 + 1.47057i −0.0277165 + 0.0669134i
\(484\) −0.890466 15.4105i −0.0404757 0.700475i
\(485\) −1.20774 + 1.92272i −0.0548405 + 0.0873064i
\(486\) 0.582099 + 20.1645i 0.0264046 + 0.914680i
\(487\) 0.772205 + 0.772205i 0.0349919 + 0.0349919i 0.724386 0.689394i \(-0.242123\pi\)
−0.689394 + 0.724386i \(0.742123\pi\)
\(488\) −15.8373 13.3076i −0.716919 0.602408i
\(489\) −1.49945 1.49945i −0.0678075 0.0678075i
\(490\) −20.3414 2.85193i −0.918933 0.128837i
\(491\) 16.8569 6.98234i 0.760740 0.315109i 0.0316245 0.999500i \(-0.489932\pi\)
0.729115 + 0.684391i \(0.239932\pi\)
\(492\) 3.00876 8.64341i 0.135645 0.389675i
\(493\) 9.60471 + 3.97840i 0.432575 + 0.179178i
\(494\) −13.7410 5.23246i −0.618236 0.235420i
\(495\) 6.06823 + 8.54974i 0.272747 + 0.384282i
\(496\) 0.394767 + 3.40453i 0.0177256 + 0.152868i
\(497\) 10.8791 0.487994
\(498\) 11.1119 + 4.23133i 0.497936 + 0.189610i
\(499\) −9.43633 + 22.7813i −0.422428 + 1.01983i 0.559201 + 0.829032i \(0.311108\pi\)
−0.981629 + 0.190800i \(0.938892\pi\)
\(500\) −14.9342 16.6424i −0.667877 0.744271i
\(501\) −13.9828 + 5.79188i −0.624707 + 0.258762i
\(502\) 9.78547 10.3672i 0.436747 0.462712i
\(503\) 0.404662 0.404662i 0.0180430 0.0180430i −0.698028 0.716071i \(-0.745939\pi\)
0.716071 + 0.698028i \(0.245939\pi\)
\(504\) 1.56704 4.95813i 0.0698017 0.220853i
\(505\) 2.65346 15.6309i 0.118077 0.695566i
\(506\) 8.94240 0.258145i 0.397538 0.0114759i
\(507\) 4.72036 1.95524i 0.209639 0.0868352i
\(508\) 13.5073 + 12.0316i 0.599290 + 0.533816i
\(509\) −2.65667 1.10043i −0.117755 0.0487756i 0.323028 0.946389i \(-0.395299\pi\)
−0.440783 + 0.897614i \(0.645299\pi\)
\(510\) −3.54816 2.08844i −0.157115 0.0924778i
\(511\) −5.76778 −0.255152
\(512\) 13.7376 + 17.9799i 0.607123 + 0.794608i
\(513\) 16.6107i 0.733381i
\(514\) −20.1164 + 9.02105i −0.887295 + 0.397902i
\(515\) 5.96429 + 26.1138i 0.262818 + 1.15071i
\(516\) 3.80123 4.26746i 0.167340 0.187865i
\(517\) −18.5145 + 7.66897i −0.814268 + 0.337281i
\(518\) 0.0883830 + 3.06167i 0.00388332 + 0.134522i
\(519\) 3.35152 3.35152i 0.147115 0.147115i
\(520\) 4.34590 + 13.5148i 0.190580 + 0.592663i
\(521\) −2.93908 2.93908i −0.128764 0.128764i 0.639788 0.768552i \(-0.279022\pi\)
−0.768552 + 0.639788i \(0.779022\pi\)
\(522\) −12.8742 + 13.6396i −0.563489 + 0.596989i
\(523\) −8.52201 20.5740i −0.372642 0.899637i −0.993301 0.115556i \(-0.963135\pi\)
0.620659 0.784080i \(-0.286865\pi\)
\(524\) −29.3946 + 14.2144i −1.28411 + 0.620959i
\(525\) 1.69992 + 1.51825i 0.0741906 + 0.0662621i
\(526\) 0.434649 1.14143i 0.0189516 0.0497688i
\(527\) 1.73834 0.0757234
\(528\) 4.61938 0.535634i 0.201033 0.0233105i
\(529\) 10.8070i 0.469868i
\(530\) −41.7466 + 10.8112i −1.81336 + 0.469607i
\(531\) 11.0712 26.7283i 0.480451 1.15991i
\(532\) 2.16327 6.21453i 0.0937897 0.269434i
\(533\) 6.12516 + 14.7874i 0.265310 + 0.640515i
\(534\) 3.95784 4.19314i 0.171273 0.181455i
\(535\) −3.74249 + 22.0461i −0.161802 + 0.953137i
\(536\) 24.7722 29.4811i 1.06999 1.27339i
\(537\) −8.85080 8.85080i −0.381940 0.381940i
\(538\) 7.92020 0.228637i 0.341464 0.00985723i
\(539\) −4.50311 10.8715i −0.193963 0.468267i
\(540\) 12.5212 10.0215i 0.538826 0.431257i
\(541\) 13.7037 + 5.67627i 0.589170 + 0.244042i 0.657293 0.753635i \(-0.271701\pi\)
−0.0681237 + 0.997677i \(0.521701\pi\)
\(542\) −30.2126 + 13.5486i −1.29774 + 0.581964i
\(543\) 8.43094i 0.361806i
\(544\) 9.86126 5.87094i 0.422798 0.251715i
\(545\) −0.0723776 + 0.0513705i −0.00310032 + 0.00220047i
\(546\) −0.592100 1.32034i −0.0253395 0.0565055i
\(547\) 12.1381 29.3041i 0.518990 1.25295i −0.419535 0.907739i \(-0.637807\pi\)
0.938524 0.345213i \(-0.112193\pi\)
\(548\) −0.750955 12.9961i −0.0320792 0.555165i
\(549\) −7.24376 17.4880i −0.309156 0.746369i
\(550\) 3.87667 12.2093i 0.165302 0.520607i
\(551\) −16.7832 + 16.7832i −0.714989 + 0.714989i
\(552\) −0.548061 6.31439i −0.0233270 0.268758i
\(553\) −2.39694 + 2.39694i −0.101928 + 0.101928i
\(554\) 20.1361 21.3332i 0.855502 0.906362i
\(555\) −2.32730 + 3.70506i −0.0987882 + 0.157271i
\(556\) 6.21839 17.8639i 0.263718 0.757596i
\(557\) −37.5187 15.5408i −1.58972 0.658484i −0.599805 0.800146i \(-0.704755\pi\)
−0.989915 + 0.141662i \(0.954755\pi\)
\(558\) −1.11607 + 2.93090i −0.0472468 + 0.124075i
\(559\) 9.99467i 0.422730i
\(560\) −5.98966 + 2.11865i −0.253109 + 0.0895291i
\(561\) 2.35864i 0.0995820i
\(562\) 28.5225 + 10.8612i 1.20315 + 0.458151i
\(563\) 7.82620 + 3.24172i 0.329835 + 0.136622i 0.541455 0.840730i \(-0.317874\pi\)
−0.211620 + 0.977352i \(0.567874\pi\)
\(564\) 6.18093 + 12.7819i 0.260264 + 0.538213i
\(565\) −33.8812 21.2821i −1.42539 0.895345i
\(566\) −5.20664 4.91447i −0.218852 0.206571i
\(567\) 2.74398 2.74398i 0.115236 0.115236i
\(568\) −38.4385 + 19.9762i −1.61284 + 0.838183i
\(569\) 12.3803 12.3803i 0.519007 0.519007i −0.398264 0.917271i \(-0.630387\pi\)
0.917271 + 0.398264i \(0.130387\pi\)
\(570\) 7.50515 5.65944i 0.314356 0.237048i
\(571\) 5.36008 + 12.9404i 0.224312 + 0.541538i 0.995467 0.0951104i \(-0.0303204\pi\)
−0.771154 + 0.636648i \(0.780320\pi\)
\(572\) −5.40944 + 6.07293i −0.226180 + 0.253922i
\(573\) 3.16799 7.64821i 0.132345 0.319509i
\(574\) −6.53600 + 2.93102i −0.272807 + 0.122339i
\(575\) −16.4812 5.76164i −0.687313 0.240277i
\(576\) 3.56739 + 20.3957i 0.148641 + 0.849821i
\(577\) 0.460727i 0.0191803i 0.999954 + 0.00959016i \(0.00305269\pi\)
−0.999954 + 0.00959016i \(0.996947\pi\)
\(578\) 7.45561 + 16.6255i 0.310112 + 0.691531i
\(579\) 3.17110 + 1.31351i 0.131787 + 0.0545878i
\(580\) 22.7768 + 2.52564i 0.945754 + 0.104871i
\(581\) −3.56133 8.59780i −0.147749 0.356697i
\(582\) 0.0265922 + 0.921180i 0.00110228 + 0.0381841i
\(583\) −17.4689 17.4689i −0.723488 0.723488i
\(584\) 20.3790 10.5908i 0.843288 0.438251i
\(585\) −2.17412 + 12.8072i −0.0898889 + 0.529513i
\(586\) −7.79465 7.35725i −0.321994 0.303925i
\(587\) 10.0340 + 24.2243i 0.414149 + 0.999844i 0.984012 + 0.178104i \(0.0569964\pi\)
−0.569863 + 0.821740i \(0.693004\pi\)
\(588\) −7.50532 + 3.62935i −0.309514 + 0.149672i
\(589\) −1.51878 + 3.66667i −0.0625804 + 0.151082i
\(590\) −34.2191 + 8.86176i −1.40878 + 0.364833i
\(591\) 1.04681i 0.0430601i
\(592\) −5.93413 10.6554i −0.243891 0.437932i
\(593\) −17.7591 −0.729279 −0.364640 0.931149i \(-0.618808\pi\)
−0.364640 + 0.931149i \(0.618808\pi\)
\(594\) 8.58628 + 3.26959i 0.352299 + 0.134153i
\(595\) 0.717506 + 3.14150i 0.0294149 + 0.128789i
\(596\) −3.95984 + 11.3756i −0.162201 + 0.465963i
\(597\) 3.72494 + 8.99280i 0.152452 + 0.368051i
\(598\) 8.06086 + 7.60852i 0.329633 + 0.311136i
\(599\) −2.10331 2.10331i −0.0859389 0.0859389i 0.662831 0.748769i \(-0.269355\pi\)
−0.748769 + 0.662831i \(0.769355\pi\)
\(600\) −8.79406 2.24297i −0.359016 0.0915687i
\(601\) 15.0864 15.0864i 0.615387 0.615387i −0.328958 0.944345i \(-0.606697\pi\)
0.944345 + 0.328958i \(0.106697\pi\)
\(602\) −4.47107 + 0.129069i −0.182227 + 0.00526045i
\(603\) 32.5539 13.4843i 1.32570 0.549123i
\(604\) 1.80650 0.104385i 0.0735054 0.00424738i
\(605\) −16.8249 + 3.84274i −0.684029 + 0.156230i
\(606\) −2.63306 5.87156i −0.106961 0.238516i
\(607\) 21.4336i 0.869962i 0.900440 + 0.434981i \(0.143245\pi\)
−0.900440 + 0.434981i \(0.856755\pi\)
\(608\) 3.76778 + 25.9297i 0.152804 + 1.05159i
\(609\) −2.33586 −0.0946537
\(610\) −11.7316 + 19.9314i −0.474998 + 0.806998i
\(611\) −22.9401 9.50210i −0.928057 0.384414i
\(612\) 10.4842 0.605813i 0.423800 0.0244885i
\(613\) −26.1252 + 10.8214i −1.05519 + 0.437072i −0.841740 0.539883i \(-0.818469\pi\)
−0.213446 + 0.976955i \(0.568469\pi\)
\(614\) 1.14084 + 39.5199i 0.0460407 + 1.59489i
\(615\) −10.0880 1.71252i −0.406789 0.0690555i
\(616\) −2.78656 2.34147i −0.112274 0.0943403i
\(617\) −22.8655 + 22.8655i −0.920530 + 0.920530i −0.997067 0.0765371i \(-0.975614\pi\)
0.0765371 + 0.997067i \(0.475614\pi\)
\(618\) 7.90616 + 7.46250i 0.318032 + 0.300186i
\(619\) −4.29399 + 1.77863i −0.172590 + 0.0714891i −0.467305 0.884096i \(-0.654775\pi\)
0.294715 + 0.955585i \(0.404775\pi\)
\(620\) 3.68024 1.06730i 0.147802 0.0428636i
\(621\) 4.79209 11.5691i 0.192300 0.464253i
\(622\) −11.9341 + 31.3403i −0.478516 + 1.25663i
\(623\) −4.51291 −0.180806
\(624\) 4.51646 + 3.57789i 0.180803 + 0.143230i
\(625\) −15.5759 + 19.5548i −0.623036 + 0.782193i
\(626\) 0.476262 1.25071i 0.0190353 0.0499886i
\(627\) 4.97506 + 2.06074i 0.198685 + 0.0822980i
\(628\) −6.29172 13.0110i −0.251067 0.519194i
\(629\) −5.71508 + 2.36727i −0.227875 + 0.0943891i
\(630\) −5.75733 0.807194i −0.229377 0.0321594i
\(631\) 12.4813 + 12.4813i 0.496872 + 0.496872i 0.910463 0.413591i \(-0.135726\pi\)
−0.413591 + 0.910463i \(0.635726\pi\)
\(632\) 4.06771 12.8702i 0.161805 0.511950i
\(633\) 4.52992 + 4.52992i 0.180048 + 0.180048i
\(634\) −22.8264 + 0.658942i −0.906551 + 0.0261699i
\(635\) 10.7573 17.1257i 0.426891 0.679612i
\(636\) −11.6418 + 13.0697i −0.461626 + 0.518246i
\(637\) 5.57950 13.4701i 0.221068 0.533705i
\(638\) 5.37190 + 11.9790i 0.212675 + 0.474253i
\(639\) −39.6396 −1.56812
\(640\) 17.2727 18.4839i 0.682762 0.730641i
\(641\) 12.7423 0.503292 0.251646 0.967819i \(-0.419028\pi\)
0.251646 + 0.967819i \(0.419028\pi\)
\(642\) 3.71372 + 8.28136i 0.146569 + 0.326839i
\(643\) −10.2578 + 24.7645i −0.404529 + 0.976618i 0.582024 + 0.813172i \(0.302261\pi\)
−0.986552 + 0.163446i \(0.947739\pi\)
\(644\) −3.29954 + 3.70424i −0.130020 + 0.145968i
\(645\) −5.41064 3.39863i −0.213044 0.133821i
\(646\) 13.2841 0.383479i 0.522655 0.0150878i
\(647\) 17.9550 + 17.9550i 0.705884 + 0.705884i 0.965667 0.259783i \(-0.0836510\pi\)
−0.259783 + 0.965667i \(0.583651\pi\)
\(648\) −4.65665 + 14.7337i −0.182931 + 0.578793i
\(649\) −14.3190 14.3190i −0.562070 0.562070i
\(650\) 14.0934 7.30047i 0.552788 0.286348i
\(651\) −0.360851 + 0.149469i −0.0141429 + 0.00585817i
\(652\) −2.87705 5.94959i −0.112674 0.233004i
\(653\) 10.0446 + 4.16062i 0.393077 + 0.162818i 0.570462 0.821324i \(-0.306764\pi\)
−0.177386 + 0.984141i \(0.556764\pi\)
\(654\) −0.0128194 + 0.0336651i −0.000501279 + 0.00131641i
\(655\) 21.1287 + 29.7690i 0.825568 + 1.16317i
\(656\) 17.7113 22.3574i 0.691511 0.872912i
\(657\) 21.0158 0.819904
\(658\) 3.95448 10.3849i 0.154162 0.404844i
\(659\) 16.3572 39.4898i 0.637187 1.53830i −0.193225 0.981154i \(-0.561895\pi\)
0.830412 0.557150i \(-0.188105\pi\)
\(660\) −1.44814 4.99348i −0.0563689 0.194371i
\(661\) −6.74148 + 2.79241i −0.262213 + 0.108612i −0.509917 0.860224i \(-0.670324\pi\)
0.247704 + 0.968836i \(0.420324\pi\)
\(662\) −4.05140 3.82406i −0.157462 0.148626i
\(663\) 2.06647 2.06647i 0.0802552 0.0802552i
\(664\) 28.3704 + 23.8388i 1.10098 + 0.925126i
\(665\) −7.25321 1.23129i −0.281268 0.0477473i
\(666\) −0.322037 11.1557i −0.0124787 0.432273i
\(667\) 16.5311 6.84741i 0.640087 0.265133i
\(668\) −47.0897 + 2.72099i −1.82195 + 0.105278i
\(669\) −10.5933 4.38790i −0.409562 0.169646i
\(670\) −37.1023 21.8384i −1.43339 0.843690i
\(671\) −13.2494 −0.511487
\(672\) −1.54223 + 2.06662i −0.0594927 + 0.0797216i
\(673\) 40.4640i 1.55977i 0.625921 + 0.779886i \(0.284723\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(674\) −16.6465 37.1206i −0.641199 1.42983i
\(675\) −13.3734 11.9442i −0.514743 0.459734i
\(676\) 15.8967 0.918561i 0.611410 0.0353293i
\(677\) 43.5678 18.0464i 1.67445 0.693579i 0.675410 0.737442i \(-0.263967\pi\)
0.999038 + 0.0438631i \(0.0139665\pi\)
\(678\) −16.2325 + 0.468593i −0.623407 + 0.0179962i
\(679\) 0.510024 0.510024i 0.0195729 0.0195729i
\(680\) −8.30356 9.78220i −0.318427 0.375130i
\(681\) 7.40016 + 7.40016i 0.283575 + 0.283575i
\(682\) 1.59639 + 1.50681i 0.0611290 + 0.0576987i
\(683\) −16.4106 39.6187i −0.627934 1.51597i −0.842185 0.539188i \(-0.818731\pi\)
0.214251 0.976779i \(-0.431269\pi\)
\(684\) −7.88221 + 22.6436i −0.301384 + 0.865799i
\(685\) −14.1889 + 3.24069i −0.542130 + 0.123821i
\(686\) 12.6693 + 4.82440i 0.483718 + 0.184196i
\(687\) −15.8995 −0.606603
\(688\) 15.5604 8.66583i 0.593235 0.330382i
\(689\) 30.6100i 1.16615i
\(690\) −6.85994 + 1.77653i −0.261153 + 0.0676312i
\(691\) −3.00753 + 7.26082i −0.114412 + 0.276215i −0.970705 0.240276i \(-0.922762\pi\)
0.856293 + 0.516491i \(0.172762\pi\)
\(692\) 13.2983 6.43069i 0.505527 0.244458i
\(693\) −1.27453 3.07700i −0.0484156 0.116886i
\(694\) 26.8116 + 25.3071i 1.01776 + 0.960644i
\(695\) −20.8496 3.53937i −0.790870 0.134256i
\(696\) 8.25316 4.28911i 0.312835 0.162578i
\(697\) −10.2295 10.2295i −0.387470 0.387470i
\(698\) −0.660972 22.8967i −0.0250182 0.866654i
\(699\) 2.56699 + 6.19726i 0.0970924 + 0.234402i
\(700\) 3.44783 + 6.21034i 0.130316 + 0.234729i
\(701\) −32.8906 13.6237i −1.24226 0.514561i −0.337841 0.941203i \(-0.609696\pi\)
−0.904421 + 0.426642i \(0.859696\pi\)
\(702\) 4.65810 + 10.3873i 0.175809 + 0.392042i
\(703\) 14.1230i 0.532661i
\(704\) 14.1450 + 3.15629i 0.533109 + 0.118957i
\(705\) 12.9446 9.18754i 0.487523 0.346023i
\(706\) −12.8673 + 5.77024i −0.484266 + 0.217166i
\(707\) −1.92736 + 4.65306i −0.0724859 + 0.174996i
\(708\) −9.54258 + 10.7130i −0.358632 + 0.402620i
\(709\) −7.30178 17.6281i −0.274224 0.662035i 0.725431 0.688295i \(-0.241640\pi\)
−0.999655 + 0.0262594i \(0.991640\pi\)
\(710\) 29.1602 + 38.6703i 1.09436 + 1.45127i
\(711\) 8.73361 8.73361i 0.327536 0.327536i
\(712\) 15.9452 8.28661i 0.597572 0.310554i
\(713\) 2.11562 2.11562i 0.0792306 0.0792306i
\(714\) 0.951114 + 0.897742i 0.0355945 + 0.0335971i
\(715\) 7.69976 + 4.83652i 0.287955 + 0.180876i
\(716\) −16.9824 35.1186i −0.634660 1.31245i
\(717\) −5.78513 2.39628i −0.216050 0.0894907i
\(718\) 8.70049 + 3.31308i 0.324699 + 0.123643i
\(719\) 4.32239i 0.161198i −0.996747 0.0805990i \(-0.974317\pi\)
0.996747 0.0805990i \(-0.0256833\pi\)
\(720\) 21.8242 7.71961i 0.813341 0.287693i
\(721\) 8.50907i 0.316894i
\(722\) −1.23527 + 3.24394i −0.0459720 + 0.120727i
\(723\) −1.38821 0.575014i −0.0516280 0.0213850i
\(724\) −8.63798 + 24.8147i −0.321028 + 0.922232i
\(725\) −1.44402 25.5806i −0.0536297 0.950038i
\(726\) −4.80803 + 5.09387i −0.178443 + 0.189051i
\(727\) 27.4349 27.4349i 1.01750 1.01750i 0.0176592 0.999844i \(-0.494379\pi\)
0.999844 0.0176592i \(-0.00562138\pi\)
\(728\) −0.389955 4.49280i −0.0144527 0.166514i
\(729\) −5.11613 + 5.11613i −0.189486 + 0.189486i
\(730\) −15.4599 20.5019i −0.572197 0.758808i
\(731\) −3.45700 8.34595i −0.127862 0.308686i
\(732\) 0.541502 + 9.37127i 0.0200145 + 0.346372i
\(733\) 8.88835 21.4584i 0.328299 0.792583i −0.670420 0.741982i \(-0.733886\pi\)
0.998719 0.0506015i \(-0.0161138\pi\)
\(734\) 8.22437 + 18.3398i 0.303567 + 0.676935i
\(735\) 5.39479 + 7.60091i 0.198990 + 0.280364i
\(736\) 4.85635 19.1466i 0.179007 0.705754i
\(737\) 24.6638i 0.908502i
\(738\) 23.8149 10.6796i 0.876639 0.393123i
\(739\) −31.6292 13.1012i −1.16350 0.481936i −0.284459 0.958688i \(-0.591814\pi\)
−0.879038 + 0.476752i \(0.841814\pi\)
\(740\) −10.6460 + 8.52065i −0.391354 + 0.313225i
\(741\) 2.55332 + 6.16426i 0.0937986 + 0.226450i
\(742\) 13.6932 0.395290i 0.502695 0.0145116i
\(743\) −28.7330 28.7330i −1.05411 1.05411i −0.998450 0.0556617i \(-0.982273\pi\)
−0.0556617 0.998450i \(-0.517727\pi\)
\(744\) 1.00052 1.19071i 0.0366808 0.0436535i
\(745\) 13.2769 + 2.25385i 0.486428 + 0.0825749i
\(746\) 12.9166 13.6845i 0.472910 0.501025i
\(747\) 12.9762 + 31.3274i 0.474776 + 1.14621i
\(748\) 2.41656 6.94218i 0.0883583 0.253831i
\(749\) 2.71839 6.56277i 0.0993278 0.239799i
\(750\) −0.840256 + 10.1120i −0.0306818 + 0.369237i
\(751\) 41.5090i 1.51469i 0.653018 + 0.757343i \(0.273503\pi\)
−0.653018 + 0.757343i \(0.726497\pi\)
\(752\) 5.09656 + 43.9535i 0.185853 + 1.60282i
\(753\) −6.46910 −0.235747
\(754\) −5.78866 + 15.2016i −0.210810 + 0.553609i
\(755\) −0.450468 1.97231i −0.0163942 0.0717796i
\(756\) −4.58654 + 2.21792i −0.166811 + 0.0806649i
\(757\) 17.0243 + 41.1003i 0.618758 + 1.49382i 0.853146 + 0.521672i \(0.174691\pi\)
−0.234388 + 0.972143i \(0.575309\pi\)
\(758\) 15.8157 16.7560i 0.574452 0.608604i
\(759\) −2.87055 2.87055i −0.104194 0.104194i
\(760\) 27.8883 8.96793i 1.01161 0.325301i
\(761\) −22.7964 + 22.7964i −0.826368 + 0.826368i −0.987012 0.160644i \(-0.948643\pi\)
0.160644 + 0.987012i \(0.448643\pi\)
\(762\) −0.236857 8.20494i −0.00858041 0.297234i
\(763\) 0.0260482 0.0107895i 0.000943010 0.000390607i
\(764\) 17.1604 19.2652i 0.620840 0.696989i
\(765\) −2.61434 11.4465i −0.0945218 0.413850i
\(766\) −14.7978 + 6.63598i −0.534667 + 0.239768i
\(767\) 25.0906i 0.905968i
\(768\) 1.65433 10.1337i 0.0596956 0.365669i
\(769\) 1.06539 0.0384188 0.0192094 0.999815i \(-0.493885\pi\)
0.0192094 + 0.999815i \(0.493885\pi\)
\(770\) −2.06416 + 3.50691i −0.0743873 + 0.126380i
\(771\) 9.24272 + 3.82846i 0.332868 + 0.137879i
\(772\) 7.98772 + 7.11503i 0.287484 + 0.256076i
\(773\) 10.9283 4.52664i 0.393062 0.162812i −0.177394 0.984140i \(-0.556767\pi\)
0.570456 + 0.821328i \(0.306767\pi\)
\(774\) 16.2910 0.470282i 0.585569 0.0169039i
\(775\) −1.85995 3.85937i −0.0668115 0.138633i
\(776\) −0.865532 + 2.73855i −0.0310708 + 0.0983081i
\(777\) 0.982810 0.982810i 0.0352581 0.0352581i
\(778\) 6.70976 7.10867i 0.240557 0.254858i
\(779\) 30.5145 12.6395i 1.09329 0.452857i
\(780\) 3.10617 5.64369i 0.111219 0.202077i
\(781\) −10.6179 + 25.6340i −0.379940 + 0.917256i
\(782\) −9.36280 3.56529i −0.334813 0.127494i
\(783\) 18.3764 0.656719
\(784\) −25.8088 + 2.99263i −0.921744 + 0.106880i
\(785\) −13.1767 + 9.35222i −0.470295 + 0.333795i
\(786\) 13.8465 + 5.27264i 0.493888 + 0.188069i
\(787\) −3.42688 1.41946i −0.122155 0.0505982i 0.320769 0.947158i \(-0.396059\pi\)
−0.442924 + 0.896559i \(0.646059\pi\)
\(788\) −1.07252 + 3.08108i −0.0382069 + 0.109759i
\(789\) −0.512052 + 0.212099i −0.0182295 + 0.00755091i
\(790\) −14.9448 2.09530i −0.531711 0.0745474i
\(791\) 8.98737 + 8.98737i 0.319554 + 0.319554i
\(792\) 10.1532 + 8.53149i 0.360780 + 0.303153i
\(793\) −11.6082 11.6082i −0.412218 0.412218i
\(794\) 1.39393 + 48.2870i 0.0494687 + 1.71364i
\(795\) 16.5708 + 10.4088i 0.587705 + 0.369161i
\(796\) 1.74996 + 30.2849i 0.0620256 + 1.07342i
\(797\) 3.69486 8.92018i 0.130879 0.315969i −0.844832 0.535031i \(-0.820300\pi\)
0.975711 + 0.219062i \(0.0702998\pi\)
\(798\) −2.72458 + 1.22182i −0.0964491 + 0.0432520i
\(799\) 22.4425 0.793959
\(800\) −23.5855 15.6117i −0.833872 0.551958i
\(801\) 16.4435 0.581001
\(802\) 36.2267 16.2456i 1.27921 0.573652i
\(803\) 5.62933 13.5904i 0.198655 0.479595i
\(804\) −17.4446 + 1.00801i −0.615225 + 0.0355497i
\(805\) 4.69654 + 2.95008i 0.165531 + 0.103977i
\(806\) 0.0784852 + 2.71880i 0.00276452 + 0.0957658i
\(807\) −2.54242 2.54242i −0.0894974 0.0894974i
\(808\) −1.73413 19.9794i −0.0610064 0.702874i
\(809\) −2.20420 2.20420i −0.0774956 0.0774956i 0.667297 0.744792i \(-0.267451\pi\)
−0.744792 + 0.667297i \(0.767451\pi\)
\(810\) 17.1086 + 2.39867i 0.601134 + 0.0842807i
\(811\) 0.921897 0.381862i 0.0323722 0.0134090i −0.366439 0.930442i \(-0.619423\pi\)
0.398811 + 0.917033i \(0.369423\pi\)
\(812\) −6.87512 2.39322i −0.241269 0.0839855i
\(813\) 13.8816 + 5.74994i 0.486848 + 0.201659i
\(814\) −7.30037 2.77993i −0.255878 0.0974364i
\(815\) −6.02537 + 4.27654i −0.211059 + 0.149801i
\(816\) −5.00895 1.42550i −0.175348 0.0499026i
\(817\) 20.6244 0.721556
\(818\) −10.6592 4.05895i −0.372691 0.141918i
\(819\) 1.57919 3.81250i 0.0551814 0.133220i
\(820\) −27.9375 15.3762i −0.975620 0.536961i
\(821\) −1.40597 + 0.582371i −0.0490686 + 0.0203249i −0.407083 0.913391i \(-0.633454\pi\)
0.358014 + 0.933716i \(0.383454\pi\)
\(822\) −4.05474 + 4.29580i −0.141425 + 0.149833i
\(823\) −24.8286 + 24.8286i −0.865471 + 0.865471i −0.991967 0.126496i \(-0.959627\pi\)
0.126496 + 0.991967i \(0.459627\pi\)
\(824\) 15.6244 + 30.0646i 0.544301 + 1.04735i
\(825\) −5.23652 + 2.52365i −0.182312 + 0.0878622i
\(826\) 11.2242 0.324014i 0.390538 0.0112739i
\(827\) −17.9629 + 7.44048i −0.624631 + 0.258731i −0.672470 0.740124i \(-0.734767\pi\)
0.0478387 + 0.998855i \(0.484767\pi\)
\(828\) 12.0224 13.4970i 0.417807 0.469052i
\(829\) 14.5454 + 6.02491i 0.505183 + 0.209254i 0.620694 0.784053i \(-0.286851\pi\)
−0.115512 + 0.993306i \(0.536851\pi\)
\(830\) 21.0156 35.7044i 0.729461 1.23932i
\(831\) −13.3118 −0.461783
\(832\) 9.62751 + 15.1581i 0.333774 + 0.525514i
\(833\) 13.1779i 0.456588i
\(834\) −7.83189 + 3.51216i −0.271196 + 0.121616i
\(835\) 11.7423 + 51.4118i 0.406358 + 1.77918i
\(836\) 12.5317 + 11.1626i 0.433419 + 0.386066i
\(837\) 2.83885 1.17589i 0.0981249 0.0406447i
\(838\) 0.390906 + 13.5414i 0.0135036 + 0.467779i
\(839\) 6.61405 6.61405i 0.228342 0.228342i −0.583658 0.812000i \(-0.698379\pi\)
0.812000 + 0.583658i \(0.198379\pi\)
\(840\) 2.56479 + 1.31665i 0.0884937 + 0.0454287i
\(841\) −1.93888 1.93888i −0.0668581 0.0668581i
\(842\) −11.5517 + 12.2385i −0.398098 + 0.421766i
\(843\) −5.30001 12.7953i −0.182542 0.440695i
\(844\) 8.69173 + 17.9741i 0.299182 + 0.618692i
\(845\) −3.96398 17.3557i −0.136365 0.597055i
\(846\) −14.4087 + 37.8388i −0.495383 + 1.30092i
\(847\) 5.48233 0.188375
\(848\) −47.6557 + 26.5402i −1.63650 + 0.911395i
\(849\) 3.24892i 0.111503i
\(850\) −9.24341 + 10.9709i −0.317046 + 0.376297i
\(851\) −4.07441 + 9.83650i −0.139669 + 0.337191i
\(852\) 18.5648 + 6.46239i 0.636020 + 0.221398i
\(853\) −0.496943 1.19973i −0.0170150 0.0410779i 0.915144 0.403128i \(-0.132077\pi\)
−0.932159 + 0.362050i \(0.882077\pi\)
\(854\) 5.04296 5.34277i 0.172566 0.182826i
\(855\) 26.4282 + 4.48638i 0.903825 + 0.153431i
\(856\) 2.44585 + 28.1794i 0.0835973 + 0.963152i
\(857\) 23.4719 + 23.4719i 0.801783 + 0.801783i 0.983374 0.181591i \(-0.0581246\pi\)
−0.181591 + 0.983374i \(0.558125\pi\)
\(858\) 3.68897 0.106491i 0.125939 0.00363556i
\(859\) 2.99136 + 7.22178i 0.102064 + 0.246404i 0.966660 0.256064i \(-0.0824257\pi\)
−0.864596 + 0.502467i \(0.832426\pi\)
\(860\) −12.4430 15.5467i −0.424303 0.530138i
\(861\) 3.00305 + 1.24390i 0.102344 + 0.0423921i
\(862\) 43.6063 19.5549i 1.48524 0.666044i
\(863\) 19.4200i 0.661065i −0.943795 0.330532i \(-0.892772\pi\)
0.943795 0.330532i \(-0.107228\pi\)
\(864\) 12.1328 16.2583i 0.412767 0.553118i
\(865\) −9.55879 13.4677i −0.325009 0.457916i
\(866\) −14.6701 32.7133i −0.498509 1.11164i
\(867\) 3.16410 7.63881i 0.107458 0.259428i
\(868\) −1.21523 + 0.0702200i −0.0412476 + 0.00238342i
\(869\) −3.30841 7.98722i −0.112230 0.270948i
\(870\) −6.26102 8.30292i −0.212268 0.281495i
\(871\) 21.6086 21.6086i 0.732181 0.732181i
\(872\) −0.0722231 + 0.0859519i −0.00244578 + 0.00291070i
\(873\) −1.85835 + 1.85835i −0.0628956 + 0.0628956i
\(874\) 15.7005 16.6339i 0.531076 0.562650i
\(875\) 6.20687 4.95424i 0.209831 0.167484i
\(876\) −9.84254 3.42617i −0.332548 0.115760i
\(877\) −1.29866 0.537922i −0.0438526 0.0181643i 0.360649 0.932701i \(-0.382555\pi\)
−0.404502 + 0.914537i \(0.632555\pi\)
\(878\) 9.17856 24.1038i 0.309761 0.813464i
\(879\) 4.86383i 0.164053i
\(880\) 0.853794 16.1810i 0.0287814 0.545461i
\(881\) 15.5569i 0.524127i 0.965051 + 0.262063i \(0.0844030\pi\)
−0.965051 + 0.262063i \(0.915597\pi\)
\(882\) −22.2184 8.46061i −0.748133 0.284883i
\(883\) −17.6991 7.33121i −0.595623 0.246715i 0.0644449 0.997921i \(-0.479472\pi\)
−0.660067 + 0.751206i \(0.729472\pi\)
\(884\) 8.19946 3.96502i 0.275778 0.133358i
\(885\) 13.5828 + 8.53191i 0.456582 + 0.286797i
\(886\) −8.47862 8.00284i −0.284845 0.268861i
\(887\) −21.6904 + 21.6904i −0.728291 + 0.728291i −0.970279 0.241988i \(-0.922200\pi\)
0.241988 + 0.970279i \(0.422200\pi\)
\(888\) −1.66787 + 5.27715i −0.0559701 + 0.177090i
\(889\) −4.54278 + 4.54278i −0.152360 + 0.152360i
\(890\) −12.0964 16.0414i −0.405471 0.537707i
\(891\) 3.78743 + 9.14366i 0.126884 + 0.306324i
\(892\) −26.6836 23.7684i −0.893434 0.795824i
\(893\) −19.6079 + 47.3378i −0.656155 + 1.58410i
\(894\) 4.98731 2.23653i 0.166801 0.0748006i
\(895\) −35.5659 + 25.2431i −1.18884 + 0.843785i
\(896\) −6.65660 + 4.50257i −0.222381 + 0.150420i
\(897\) 5.02994i 0.167945i
\(898\) −8.05589 17.9641i −0.268829 0.599471i
\(899\) 4.05642 + 1.68023i 0.135289 + 0.0560386i
\(900\) −12.5627 22.6283i −0.418756 0.754277i
\(901\) 10.5875 + 25.5605i 0.352722 + 0.851545i
\(902\) −0.527156 18.2612i −0.0175524 0.608031i
\(903\) 1.43523 + 1.43523i 0.0477616 + 0.0477616i
\(904\) −48.2572 15.2520i −1.60501 0.507272i
\(905\) 28.9622 + 4.91655i 0.962737 + 0.163432i
\(906\) −0.597132 0.563624i −0.0198384 0.0187251i
\(907\) −2.25625 5.44706i −0.0749175 0.180867i 0.881984 0.471279i \(-0.156208\pi\)
−0.956902 + 0.290412i \(0.906208\pi\)
\(908\) 14.1990 + 29.3627i 0.471209 + 0.974437i
\(909\) 7.02264 16.9541i 0.232926 0.562334i
\(910\) −4.88097 + 1.26403i −0.161803 + 0.0419022i
\(911\) 56.3865i 1.86817i −0.357054 0.934084i \(-0.616219\pi\)
0.357054 0.934084i \(-0.383781\pi\)
\(912\) 7.38311 9.31988i 0.244479 0.308612i
\(913\) 23.7345 0.785498
\(914\) 53.9007 + 20.5250i 1.78288 + 0.678907i
\(915\) 10.2314 2.33681i 0.338240 0.0772527i
\(916\) −46.7968 16.2899i −1.54621 0.538234i
\(917\) −4.43775 10.7137i −0.146547 0.353797i
\(918\) −7.48249 7.06261i −0.246959 0.233101i
\(919\) −31.7925 31.7925i −1.04874 1.04874i −0.998750 0.0499863i \(-0.984082\pi\)
−0.0499863 0.998750i \(-0.515918\pi\)
\(920\) −22.0110 1.79956i −0.725680 0.0593297i
\(921\) 12.6861 12.6861i 0.418020 0.418020i
\(922\) −34.4584 + 0.994731i −1.13483 + 0.0327597i
\(923\) −31.7613 + 13.1560i −1.04544 + 0.433034i
\(924\) 0.0952769 + 1.64887i 0.00313438 + 0.0542438i
\(925\) 11.3706 + 10.1554i 0.373862 + 0.333908i
\(926\) −9.93450 22.1533i −0.326468 0.728003i
\(927\) 31.0041i 1.01831i
\(928\) 28.6859 4.16828i 0.941661 0.136830i
\(929\) 51.7288 1.69717 0.848584 0.529060i \(-0.177456\pi\)
0.848584 + 0.529060i \(0.177456\pi\)
\(930\) −1.49852 0.882026i −0.0491384 0.0289228i
\(931\) −27.7961 11.5135i −0.910979 0.377340i
\(932\) 1.20596 + 20.8704i 0.0395025 + 0.683632i
\(933\) 14.0594 5.82359i 0.460284 0.190656i
\(934\) −0.684981 23.7284i −0.0224133 0.776418i
\(935\) −8.10248 1.37546i −0.264979 0.0449822i
\(936\) 1.42086 + 16.3702i 0.0464423 + 0.535077i
\(937\) 3.14648 3.14648i 0.102791 0.102791i −0.653841 0.756632i \(-0.726843\pi\)
0.756632 + 0.653841i \(0.226843\pi\)
\(938\) 9.94558 + 9.38748i 0.324735 + 0.306512i
\(939\) −0.561076 + 0.232405i −0.0183100 + 0.00758426i
\(940\) 47.5130 13.7791i 1.54970 0.449425i
\(941\) −14.6438 + 35.3534i −0.477376 + 1.15249i 0.483460 + 0.875367i \(0.339380\pi\)
−0.960835 + 0.277120i \(0.910620\pi\)
\(942\) −2.33383 + 6.12887i −0.0760403 + 0.199689i
\(943\) −24.8993 −0.810833
\(944\) −39.0627 + 21.7546i −1.27138 + 0.708053i
\(945\) 3.29679 + 4.64496i 0.107244 + 0.151100i
\(946\) 4.05963 10.6610i 0.131990 0.346619i
\(947\) 8.87565 + 3.67642i 0.288420 + 0.119467i 0.522203 0.852821i \(-0.325110\pi\)
−0.233783 + 0.972289i \(0.575110\pi\)
\(948\) −5.51413 + 2.66647i −0.179091 + 0.0866030i
\(949\) 16.8390 6.97492i 0.546616 0.226416i
\(950\) −15.0648 29.0822i −0.488766 0.943552i
\(951\) 7.32737 + 7.32737i 0.237606 + 0.237606i
\(952\) 1.87962 + 3.61679i 0.0609188 + 0.117221i
\(953\) 39.7727 + 39.7727i 1.28836 + 1.28836i 0.935781 + 0.352582i \(0.114696\pi\)
0.352582 + 0.935781i \(0.385304\pi\)
\(954\) −49.8934 + 1.44030i −1.61536 + 0.0466314i
\(955\) −24.4259 15.3429i −0.790405 0.496484i
\(956\) −14.5722 12.9801i −0.471299 0.419808i
\(957\) 2.27979 5.50390i 0.0736951 0.177916i
\(958\) −13.8627 30.9129i −0.447883 0.998750i
\(959\) 4.62340 0.149297
\(960\) −11.4797 + 0.0574303i −0.370505 + 0.00185356i
\(961\) −30.2658 −0.976317
\(962\) −3.96049 8.83163i −0.127691 0.284743i
\(963\) −9.90487 + 23.9125i −0.319180 + 0.770568i
\(964\) −3.49677 3.11473i −0.112623 0.100319i
\(965\) 6.36147 10.1275i 0.204783 0.326015i
\(966\) 2.25012 0.0649554i 0.0723964 0.00208991i
\(967\) 17.4988 + 17.4988i 0.562723 + 0.562723i 0.930080 0.367357i \(-0.119737\pi\)
−0.367357 + 0.930080i \(0.619737\pi\)
\(968\) −19.3704 + 10.0667i −0.622588 + 0.323555i
\(969\) −4.26425 4.26425i −0.136987 0.136987i
\(970\) 3.17997 + 0.445841i 0.102103 + 0.0143151i
\(971\) −45.0976 + 18.6800i −1.44725 + 0.599471i −0.961544 0.274650i \(-0.911438\pi\)
−0.485707 + 0.874122i \(0.661438\pi\)
\(972\) 25.6835 12.4198i 0.823797 0.398364i
\(973\) 6.20658 + 2.57085i 0.198974 + 0.0824177i
\(974\) 0.549601 1.44331i 0.0176104 0.0462466i
\(975\) −6.79891 2.37682i −0.217739 0.0761193i
\(976\) −8.00760 + 28.1372i −0.256317 + 0.900650i
\(977\) −1.94663 −0.0622781 −0.0311390 0.999515i \(-0.509913\pi\)
−0.0311390 + 0.999515i \(0.509913\pi\)
\(978\) −1.06720 + 2.80258i −0.0341254 + 0.0896167i
\(979\) 4.40458 10.6336i 0.140771 0.339851i
\(980\) 8.09089 + 27.8990i 0.258454 + 0.891200i
\(981\) −0.0949108 + 0.0393133i −0.00303027 + 0.00125518i
\(982\) −18.7646 17.7116i −0.598803 0.565201i
\(983\) 3.46555 3.46555i 0.110534 0.110534i −0.649677 0.760211i \(-0.725096\pi\)
0.760211 + 0.649677i \(0.225096\pi\)
\(984\) −12.8946 + 1.11919i −0.411064 + 0.0356785i
\(985\) 3.59604 + 0.610455i 0.114579 + 0.0194507i
\(986\) −0.424241 14.6961i −0.0135106 0.468020i
\(987\) −4.65869 + 1.92969i −0.148288 + 0.0614228i
\(988\) 1.19954 + 20.7593i 0.0381624 + 0.660440i
\(989\) −14.3646 5.95001i −0.456767 0.189199i
\(990\) 7.52109 12.7780i 0.239036 0.406110i
\(991\) 55.6865 1.76894 0.884470 0.466596i \(-0.154520\pi\)
0.884470 + 0.466596i \(0.154520\pi\)
\(992\) 4.16477 2.47951i 0.132232 0.0787247i
\(993\) 2.52806i 0.0802254i
\(994\) −6.29543 14.0384i −0.199679 0.445271i
\(995\) 33.0646 7.55182i 1.04822 0.239409i
\(996\) −0.970029 16.7874i −0.0307365 0.531928i
\(997\) −33.5549 + 13.8989i −1.06270 + 0.440183i −0.844407 0.535702i \(-0.820047\pi\)
−0.218288 + 0.975884i \(0.570047\pi\)
\(998\) 34.8576 1.00625i 1.10340 0.0318524i
\(999\) −7.73185 + 7.73185i −0.244625 + 0.244625i
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 160.2.z.a.29.8 88
4.3 odd 2 640.2.z.a.209.14 88
5.2 odd 4 800.2.y.f.701.19 88
5.3 odd 4 800.2.y.f.701.4 88
5.4 even 2 inner 160.2.z.a.29.15 yes 88
20.19 odd 2 640.2.z.a.209.9 88
32.11 odd 8 640.2.z.a.49.9 88
32.21 even 8 inner 160.2.z.a.149.15 yes 88
160.53 odd 8 800.2.y.f.501.4 88
160.117 odd 8 800.2.y.f.501.19 88
160.139 odd 8 640.2.z.a.49.14 88
160.149 even 8 inner 160.2.z.a.149.8 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.2.z.a.29.8 88 1.1 even 1 trivial
160.2.z.a.29.15 yes 88 5.4 even 2 inner
160.2.z.a.149.8 yes 88 160.149 even 8 inner
160.2.z.a.149.15 yes 88 32.21 even 8 inner
640.2.z.a.49.9 88 32.11 odd 8
640.2.z.a.49.14 88 160.139 odd 8
640.2.z.a.209.9 88 20.19 odd 2
640.2.z.a.209.14 88 4.3 odd 2
800.2.y.f.501.4 88 160.53 odd 8
800.2.y.f.501.19 88 160.117 odd 8
800.2.y.f.701.4 88 5.3 odd 4
800.2.y.f.701.19 88 5.2 odd 4