Properties

Label 456.2.bk.a.253.37
Level $456$
Weight $2$
Character 456.253
Analytic conductor $3.641$
Analytic rank $0$
Dimension $240$
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] = [456,2,Mod(61,456)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(456, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 9, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("456.61");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.bk (of order \(18\), degree \(6\), 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: \(3.64117833217\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(40\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 253.37
Character \(\chi\) \(=\) 456.253
Dual form 456.2.bk.a.301.37

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36002 + 0.387744i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(1.69931 + 1.05468i) q^{4} +(2.74544 - 0.484095i) q^{5} +(-0.829515 + 1.14538i) q^{6} +(-1.04707 + 1.81357i) q^{7} +(1.90215 + 2.09328i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\) \(q+(1.36002 + 0.387744i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(1.69931 + 1.05468i) q^{4} +(2.74544 - 0.484095i) q^{5} +(-0.829515 + 1.14538i) q^{6} +(-1.04707 + 1.81357i) q^{7} +(1.90215 + 2.09328i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(3.92155 + 0.406149i) q^{10} +(-0.893712 + 0.515985i) q^{11} +(-1.57227 + 1.23611i) q^{12} +(-1.06002 - 2.91237i) q^{13} +(-2.12723 + 2.06050i) q^{14} +(-0.484095 + 2.74544i) q^{15} +(1.77530 + 3.58445i) q^{16} +(0.735497 - 0.617155i) q^{17} +(-0.792599 - 1.17123i) q^{18} +(-0.854759 - 4.27427i) q^{19} +(5.17591 + 2.07293i) q^{20} +(-1.34608 - 1.60420i) q^{21} +(-1.41554 + 0.355218i) q^{22} +(-0.402778 + 2.28427i) q^{23} +(-2.61762 + 1.07149i) q^{24} +(2.60461 - 0.948001i) q^{25} +(-0.312388 - 4.37190i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-3.69203 + 1.97750i) q^{28} +(2.18766 - 2.60715i) q^{29} +(-1.72291 + 3.54614i) q^{30} +(-2.85218 + 4.94012i) q^{31} +(1.02459 + 5.56329i) q^{32} +(-0.179200 - 1.01629i) q^{33} +(1.23959 - 0.554158i) q^{34} +(-1.99672 + 5.48593i) q^{35} +(-0.623811 - 1.90023i) q^{36} -3.92447i q^{37} +(0.494834 - 6.14452i) q^{38} +3.09928 q^{39} +(6.23557 + 4.82616i) q^{40} +(-3.19432 - 1.16264i) q^{41} +(-1.20868 - 2.70368i) q^{42} +(8.90791 - 1.57071i) q^{43} +(-2.06289 - 0.0657626i) q^{44} +(-2.41430 - 1.39389i) q^{45} +(-1.43350 + 2.95048i) q^{46} +(-7.39087 - 6.20168i) q^{47} +(-3.97547 + 0.442281i) q^{48} +(1.30730 + 2.26431i) q^{49} +(3.90991 - 0.279377i) q^{50} +(0.328381 + 0.902220i) q^{51} +(1.27032 - 6.06700i) q^{52} +(-5.34877 - 0.943132i) q^{53} +(1.37168 - 0.344214i) q^{54} +(-2.20384 + 1.84924i) q^{55} +(-5.78800 + 1.25788i) q^{56} +(4.30885 + 0.658675i) q^{57} +(3.98617 - 2.69752i) q^{58} +(1.96353 + 2.34004i) q^{59} +(-3.71818 + 4.15478i) q^{60} +(-2.24640 - 0.396101i) q^{61} +(-5.79453 + 5.61275i) q^{62} +(1.96784 - 0.716236i) q^{63} +(-0.763669 + 7.96347i) q^{64} +(-4.32007 - 7.48258i) q^{65} +(0.150346 - 1.45166i) q^{66} +(5.34298 - 6.36752i) q^{67} +(1.90074 - 0.273023i) q^{68} +(-2.00875 - 1.15975i) q^{69} +(-4.84271 + 6.68676i) q^{70} +(-0.762114 - 4.32216i) q^{71} +(-0.111593 - 2.82622i) q^{72} +(8.86487 + 3.22655i) q^{73} +(1.52169 - 5.33735i) q^{74} +2.77177i q^{75} +(3.05549 - 8.16480i) q^{76} -2.16108i q^{77} +(4.21508 + 1.20173i) q^{78} +(-5.60986 - 2.04182i) q^{79} +(6.60919 + 8.98148i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-3.89354 - 2.81979i) q^{82} +(-12.4128 - 7.16654i) q^{83} +(-0.595494 - 4.14572i) q^{84} +(1.72050 - 2.05041i) q^{85} +(12.7240 + 1.31780i) q^{86} +(1.70170 + 2.94742i) q^{87} +(-2.78007 - 0.889313i) q^{88} +(0.944390 - 0.343730i) q^{89} +(-2.74302 - 2.83185i) q^{90} +(6.39171 + 1.12703i) q^{91} +(-3.09362 + 3.45688i) q^{92} +(-3.66669 - 4.36980i) q^{93} +(-7.64707 - 11.3002i) q^{94} +(-4.41584 - 11.3210i) q^{95} +(-5.57821 - 0.939956i) q^{96} +(12.5488 - 10.5297i) q^{97} +(0.899982 + 3.58641i) q^{98} +(1.01629 + 0.179200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 6 q^{4} + 6 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48} - 120 q^{49} + 18 q^{50} + 6 q^{52} - 6 q^{54} + 72 q^{58} - 12 q^{60} + 12 q^{62} + 30 q^{64} - 48 q^{66} - 78 q^{68} - 108 q^{70} - 36 q^{72} - 24 q^{73} - 96 q^{74} - 48 q^{76} - 96 q^{78} - 114 q^{80} - 66 q^{82} - 36 q^{84} - 24 q^{86} - 24 q^{88} + 6 q^{90} - 108 q^{94} + 120 q^{95} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/456\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(343\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(-1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36002 + 0.387744i 0.961679 + 0.274177i
\(3\) −0.342020 + 0.939693i −0.197465 + 0.542532i
\(4\) 1.69931 + 1.05468i 0.849654 + 0.527340i
\(5\) 2.74544 0.484095i 1.22780 0.216494i 0.478118 0.878296i \(-0.341319\pi\)
0.749679 + 0.661802i \(0.230208\pi\)
\(6\) −0.829515 + 1.14538i −0.338648 + 0.467601i
\(7\) −1.04707 + 1.81357i −0.395754 + 0.685466i −0.993197 0.116445i \(-0.962850\pi\)
0.597443 + 0.801911i \(0.296183\pi\)
\(8\) 1.90215 + 2.09328i 0.672511 + 0.740087i
\(9\) −0.766044 0.642788i −0.255348 0.214263i
\(10\) 3.92155 + 0.406149i 1.24010 + 0.128436i
\(11\) −0.893712 + 0.515985i −0.269464 + 0.155575i −0.628644 0.777693i \(-0.716390\pi\)
0.359180 + 0.933268i \(0.383056\pi\)
\(12\) −1.57227 + 1.23611i −0.453876 + 0.356833i
\(13\) −1.06002 2.91237i −0.293996 0.807746i −0.995472 0.0950538i \(-0.969698\pi\)
0.701476 0.712693i \(-0.252525\pi\)
\(14\) −2.12723 + 2.06050i −0.568527 + 0.550692i
\(15\) −0.484095 + 2.74544i −0.124993 + 0.708869i
\(16\) 1.77530 + 3.58445i 0.443825 + 0.896113i
\(17\) 0.735497 0.617155i 0.178384 0.149682i −0.549224 0.835675i \(-0.685077\pi\)
0.727608 + 0.685993i \(0.240632\pi\)
\(18\) −0.792599 1.17123i −0.186817 0.276062i
\(19\) −0.854759 4.27427i −0.196095 0.980585i
\(20\) 5.17591 + 2.07293i 1.15737 + 0.463522i
\(21\) −1.34608 1.60420i −0.293739 0.350065i
\(22\) −1.41554 + 0.355218i −0.301793 + 0.0757327i
\(23\) −0.402778 + 2.28427i −0.0839851 + 0.476303i 0.913586 + 0.406646i \(0.133302\pi\)
−0.997571 + 0.0696573i \(0.977809\pi\)
\(24\) −2.61762 + 1.07149i −0.534319 + 0.218717i
\(25\) 2.60461 0.948001i 0.520922 0.189600i
\(26\) −0.312388 4.37190i −0.0612644 0.857400i
\(27\) 0.866025 0.500000i 0.166667 0.0962250i
\(28\) −3.69203 + 1.97750i −0.697728 + 0.373712i
\(29\) 2.18766 2.60715i 0.406238 0.484136i −0.523673 0.851919i \(-0.675439\pi\)
0.929911 + 0.367784i \(0.119883\pi\)
\(30\) −1.72291 + 3.54614i −0.314558 + 0.647434i
\(31\) −2.85218 + 4.94012i −0.512267 + 0.887273i 0.487632 + 0.873049i \(0.337861\pi\)
−0.999899 + 0.0142231i \(0.995472\pi\)
\(32\) 1.02459 + 5.56329i 0.181124 + 0.983460i
\(33\) −0.179200 1.01629i −0.0311947 0.176914i
\(34\) 1.23959 0.554158i 0.212588 0.0950374i
\(35\) −1.99672 + 5.48593i −0.337506 + 0.927291i
\(36\) −0.623811 1.90023i −0.103968 0.316704i
\(37\) 3.92447i 0.645178i −0.946539 0.322589i \(-0.895447\pi\)
0.946539 0.322589i \(-0.104553\pi\)
\(38\) 0.494834 6.14452i 0.0802727 0.996773i
\(39\) 3.09928 0.496282
\(40\) 6.23557 + 4.82616i 0.985931 + 0.763082i
\(41\) −3.19432 1.16264i −0.498870 0.181574i 0.0803159 0.996769i \(-0.474407\pi\)
−0.579185 + 0.815196i \(0.696629\pi\)
\(42\) −1.20868 2.70368i −0.186504 0.417187i
\(43\) 8.90791 1.57071i 1.35844 0.239530i 0.553484 0.832860i \(-0.313298\pi\)
0.804960 + 0.593329i \(0.202187\pi\)
\(44\) −2.06289 0.0657626i −0.310993 0.00991409i
\(45\) −2.41430 1.39389i −0.359902 0.207790i
\(46\) −1.43350 + 2.95048i −0.211358 + 0.435024i
\(47\) −7.39087 6.20168i −1.07807 0.904608i −0.0823108 0.996607i \(-0.526230\pi\)
−0.995759 + 0.0919987i \(0.970674\pi\)
\(48\) −3.97547 + 0.442281i −0.573810 + 0.0638378i
\(49\) 1.30730 + 2.26431i 0.186757 + 0.323473i
\(50\) 3.90991 0.279377i 0.552944 0.0395099i
\(51\) 0.328381 + 0.902220i 0.0459826 + 0.126336i
\(52\) 1.27032 6.06700i 0.176162 0.841341i
\(53\) −5.34877 0.943132i −0.734710 0.129549i −0.206240 0.978501i \(-0.566123\pi\)
−0.528470 + 0.848952i \(0.677234\pi\)
\(54\) 1.37168 0.344214i 0.186663 0.0468415i
\(55\) −2.20384 + 1.84924i −0.297166 + 0.249352i
\(56\) −5.78800 + 1.25788i −0.773454 + 0.168091i
\(57\) 4.30885 + 0.658675i 0.570720 + 0.0872437i
\(58\) 3.98617 2.69752i 0.523409 0.354202i
\(59\) 1.96353 + 2.34004i 0.255629 + 0.304647i 0.878562 0.477628i \(-0.158503\pi\)
−0.622933 + 0.782275i \(0.714059\pi\)
\(60\) −3.71818 + 4.15478i −0.480015 + 0.536380i
\(61\) −2.24640 0.396101i −0.287622 0.0507156i 0.0279756 0.999609i \(-0.491094\pi\)
−0.315598 + 0.948893i \(0.602205\pi\)
\(62\) −5.79453 + 5.61275i −0.735906 + 0.712820i
\(63\) 1.96784 0.716236i 0.247925 0.0902373i
\(64\) −0.763669 + 7.96347i −0.0954586 + 0.995433i
\(65\) −4.32007 7.48258i −0.535839 0.928100i
\(66\) 0.150346 1.45166i 0.0185063 0.178687i
\(67\) 5.34298 6.36752i 0.652749 0.777916i −0.333577 0.942723i \(-0.608256\pi\)
0.986326 + 0.164807i \(0.0527000\pi\)
\(68\) 1.90074 0.273023i 0.230498 0.0331089i
\(69\) −2.00875 1.15975i −0.241825 0.139618i
\(70\) −4.84271 + 6.68676i −0.578815 + 0.799221i
\(71\) −0.762114 4.32216i −0.0904462 0.512946i −0.996048 0.0888170i \(-0.971691\pi\)
0.905602 0.424129i \(-0.139420\pi\)
\(72\) −0.111593 2.82622i −0.0131514 0.333074i
\(73\) 8.86487 + 3.22655i 1.03755 + 0.377639i 0.803952 0.594694i \(-0.202727\pi\)
0.233602 + 0.972332i \(0.424949\pi\)
\(74\) 1.52169 5.33735i 0.176893 0.620455i
\(75\) 2.77177i 0.320057i
\(76\) 3.05549 8.16480i 0.350488 0.936567i
\(77\) 2.16108i 0.246278i
\(78\) 4.21508 + 1.20173i 0.477264 + 0.136069i
\(79\) −5.60986 2.04182i −0.631159 0.229723i 0.00657683 0.999978i \(-0.497907\pi\)
−0.637736 + 0.770255i \(0.720129\pi\)
\(80\) 6.60919 + 8.98148i 0.738930 + 1.00416i
\(81\) 0.173648 + 0.984808i 0.0192942 + 0.109423i
\(82\) −3.89354 2.81979i −0.429969 0.311394i
\(83\) −12.4128 7.16654i −1.36248 0.786630i −0.372530 0.928020i \(-0.621510\pi\)
−0.989954 + 0.141390i \(0.954843\pi\)
\(84\) −0.595494 4.14572i −0.0649737 0.452335i
\(85\) 1.72050 2.05041i 0.186614 0.222398i
\(86\) 12.7240 + 1.31780i 1.37206 + 0.142102i
\(87\) 1.70170 + 2.94742i 0.182441 + 0.315997i
\(88\) −2.78007 0.889313i −0.296357 0.0948011i
\(89\) 0.944390 0.343730i 0.100105 0.0364353i −0.291482 0.956576i \(-0.594148\pi\)
0.391587 + 0.920141i \(0.371926\pi\)
\(90\) −2.74302 2.83185i −0.289139 0.298504i
\(91\) 6.39171 + 1.12703i 0.670033 + 0.118145i
\(92\) −3.09362 + 3.45688i −0.322532 + 0.360404i
\(93\) −3.66669 4.36980i −0.380219 0.453127i
\(94\) −7.64707 11.3002i −0.788735 1.16552i
\(95\) −4.41584 11.3210i −0.453056 1.16151i
\(96\) −5.57821 0.939956i −0.569324 0.0959339i
\(97\) 12.5488 10.5297i 1.27414 1.06913i 0.280119 0.959965i \(-0.409626\pi\)
0.994023 0.109167i \(-0.0348182\pi\)
\(98\) 0.899982 + 3.58641i 0.0909119 + 0.362282i
\(99\) 1.01629 + 0.179200i 0.102141 + 0.0180102i
\(100\) 5.42588 + 1.13609i 0.542588 + 0.113609i
\(101\) −5.48689 15.0751i −0.545966 1.50003i −0.839111 0.543961i \(-0.816924\pi\)
0.293145 0.956068i \(-0.405298\pi\)
\(102\) 0.0967744 + 1.35437i 0.00958209 + 0.134102i
\(103\) −3.27137 5.66618i −0.322338 0.558306i 0.658632 0.752465i \(-0.271135\pi\)
−0.980970 + 0.194160i \(0.937802\pi\)
\(104\) 4.08011 7.75867i 0.400088 0.760801i
\(105\) −4.47217 3.75260i −0.436439 0.366216i
\(106\) −6.90874 3.35663i −0.671036 0.326025i
\(107\) 10.7464 + 6.20442i 1.03889 + 0.599804i 0.919519 0.393045i \(-0.128578\pi\)
0.119372 + 0.992850i \(0.461912\pi\)
\(108\) 1.99898 + 0.0637253i 0.192352 + 0.00613197i
\(109\) 1.31485 0.231843i 0.125940 0.0222066i −0.110323 0.993896i \(-0.535189\pi\)
0.236263 + 0.971689i \(0.424077\pi\)
\(110\) −3.71431 + 1.66048i −0.354145 + 0.158321i
\(111\) 3.68779 + 1.34225i 0.350030 + 0.127400i
\(112\) −8.35953 0.533527i −0.789901 0.0504135i
\(113\) −11.3673 −1.06934 −0.534672 0.845060i \(-0.679565\pi\)
−0.534672 + 0.845060i \(0.679565\pi\)
\(114\) 5.60472 + 2.56654i 0.524930 + 0.240379i
\(115\) 6.46630i 0.602986i
\(116\) 6.46722 2.12307i 0.600466 0.197122i
\(117\) −1.06002 + 2.91237i −0.0979985 + 0.269249i
\(118\) 1.76310 + 3.94385i 0.162306 + 0.363061i
\(119\) 0.349141 + 1.98008i 0.0320057 + 0.181514i
\(120\) −6.66780 + 4.20888i −0.608684 + 0.384216i
\(121\) −4.96752 + 8.60400i −0.451593 + 0.782181i
\(122\) −2.90157 1.40974i −0.262695 0.127631i
\(123\) 2.18505 2.60404i 0.197019 0.234798i
\(124\) −10.0570 + 5.38666i −0.903144 + 0.483736i
\(125\) −5.37961 + 3.10592i −0.481167 + 0.277802i
\(126\) 2.95402 0.211076i 0.263165 0.0188041i
\(127\) −10.2958 + 3.74735i −0.913602 + 0.332524i −0.755690 0.654930i \(-0.772698\pi\)
−0.157912 + 0.987453i \(0.550476\pi\)
\(128\) −4.12639 + 10.5344i −0.364725 + 0.931115i
\(129\) −1.57071 + 8.90791i −0.138293 + 0.784298i
\(130\) −2.97405 11.8515i −0.260842 1.03945i
\(131\) 7.88203 + 9.39344i 0.688657 + 0.820709i 0.991192 0.132429i \(-0.0422777\pi\)
−0.302536 + 0.953138i \(0.597833\pi\)
\(132\) 0.767347 1.91599i 0.0667890 0.166766i
\(133\) 8.64669 + 2.92528i 0.749763 + 0.253654i
\(134\) 9.73553 6.58824i 0.841022 0.569137i
\(135\) 2.13557 1.79196i 0.183801 0.154227i
\(136\) 2.69090 + 0.365683i 0.230743 + 0.0313571i
\(137\) −1.94418 + 11.0260i −0.166102 + 0.942014i 0.781818 + 0.623507i \(0.214293\pi\)
−0.947920 + 0.318507i \(0.896819\pi\)
\(138\) −2.28226 2.35617i −0.194279 0.200571i
\(139\) 4.90131 + 13.4662i 0.415724 + 1.14219i 0.954100 + 0.299488i \(0.0968157\pi\)
−0.538376 + 0.842705i \(0.680962\pi\)
\(140\) −9.17894 + 7.21639i −0.775762 + 0.609897i
\(141\) 8.35550 4.82405i 0.703660 0.406258i
\(142\) 0.639404 6.17373i 0.0536576 0.518088i
\(143\) 2.45009 + 2.05587i 0.204887 + 0.171920i
\(144\) 0.944084 3.88699i 0.0786736 0.323916i
\(145\) 4.74397 8.21680i 0.393965 0.682368i
\(146\) 10.8053 + 7.82547i 0.894255 + 0.647640i
\(147\) −2.57488 + 0.454021i −0.212373 + 0.0374470i
\(148\) 4.13906 6.66888i 0.340228 0.548179i
\(149\) −7.64081 + 20.9930i −0.625960 + 1.71981i 0.0659468 + 0.997823i \(0.478993\pi\)
−0.691907 + 0.721987i \(0.743229\pi\)
\(150\) −1.07474 + 3.76966i −0.0877520 + 0.307792i
\(151\) 8.46245 0.688665 0.344332 0.938848i \(-0.388105\pi\)
0.344332 + 0.938848i \(0.388105\pi\)
\(152\) 7.32138 9.91955i 0.593842 0.804581i
\(153\) −0.960123 −0.0776213
\(154\) 0.837948 2.93912i 0.0675237 0.236841i
\(155\) −5.43900 + 14.9435i −0.436871 + 1.20029i
\(156\) 5.26663 + 3.26875i 0.421668 + 0.261709i
\(157\) 18.9844 3.34746i 1.51512 0.267157i 0.646608 0.762823i \(-0.276187\pi\)
0.868513 + 0.495666i \(0.165076\pi\)
\(158\) −6.83782 4.95211i −0.543988 0.393969i
\(159\) 2.71564 4.70363i 0.215364 0.373022i
\(160\) 5.50611 + 14.7777i 0.435296 + 1.16828i
\(161\) −3.72095 3.12225i −0.293252 0.246068i
\(162\) −0.145689 + 1.40669i −0.0114464 + 0.110520i
\(163\) −8.96240 + 5.17444i −0.701989 + 0.405294i −0.808088 0.589062i \(-0.799497\pi\)
0.106099 + 0.994356i \(0.466164\pi\)
\(164\) −4.20193 5.34467i −0.328116 0.417349i
\(165\) −0.983963 2.70342i −0.0766014 0.210461i
\(166\) −14.1029 14.5596i −1.09460 1.13005i
\(167\) −3.31815 + 18.8182i −0.256766 + 1.45619i 0.534731 + 0.845022i \(0.320413\pi\)
−0.791498 + 0.611172i \(0.790698\pi\)
\(168\) 0.797595 5.86916i 0.0615358 0.452815i
\(169\) 2.60031 2.18192i 0.200024 0.167840i
\(170\) 3.13495 2.12149i 0.240439 0.162710i
\(171\) −2.09266 + 3.82371i −0.160030 + 0.292406i
\(172\) 16.7939 + 6.72589i 1.28052 + 0.512844i
\(173\) −11.3616 13.5402i −0.863807 1.02944i −0.999252 0.0386600i \(-0.987691\pi\)
0.135446 0.990785i \(-0.456753\pi\)
\(174\) 1.17149 + 4.66838i 0.0888107 + 0.353909i
\(175\) −1.00793 + 5.71628i −0.0761926 + 0.432110i
\(176\) −3.43613 2.28744i −0.259008 0.172422i
\(177\) −2.87048 + 1.04477i −0.215759 + 0.0785298i
\(178\) 1.41767 0.101298i 0.106259 0.00759258i
\(179\) −7.78401 + 4.49410i −0.581804 + 0.335905i −0.761850 0.647753i \(-0.775709\pi\)
0.180046 + 0.983658i \(0.442375\pi\)
\(180\) −2.63252 4.91497i −0.196217 0.366340i
\(181\) −12.9198 + 15.3972i −0.960318 + 1.14446i 0.0291307 + 0.999576i \(0.490726\pi\)
−0.989448 + 0.144886i \(0.953718\pi\)
\(182\) 8.25585 + 4.01113i 0.611964 + 0.297325i
\(183\) 1.14053 1.97545i 0.0843103 0.146030i
\(184\) −5.54777 + 3.50189i −0.408987 + 0.258163i
\(185\) −1.89981 10.7744i −0.139677 0.792148i
\(186\) −3.29241 7.36475i −0.241412 0.540010i
\(187\) −0.338880 + 0.931064i −0.0247813 + 0.0680861i
\(188\) −6.01859 18.3336i −0.438951 1.33711i
\(189\) 2.09413i 0.152326i
\(190\) −1.61599 17.1089i −0.117236 1.24121i
\(191\) −20.3624 −1.47338 −0.736688 0.676233i \(-0.763611\pi\)
−0.736688 + 0.676233i \(0.763611\pi\)
\(192\) −7.22202 3.44128i −0.521204 0.248353i
\(193\) 16.1429 + 5.87554i 1.16199 + 0.422931i 0.849809 0.527091i \(-0.176717\pi\)
0.312183 + 0.950022i \(0.398940\pi\)
\(194\) 21.1495 9.45490i 1.51845 0.678822i
\(195\) 8.50888 1.50034i 0.609333 0.107442i
\(196\) −0.166616 + 5.22655i −0.0119012 + 0.373325i
\(197\) 7.74832 + 4.47350i 0.552045 + 0.318723i 0.749946 0.661499i \(-0.230079\pi\)
−0.197901 + 0.980222i \(0.563413\pi\)
\(198\) 1.31269 + 0.637776i 0.0932891 + 0.0453248i
\(199\) 17.5510 + 14.7270i 1.24416 + 1.04397i 0.997187 + 0.0749474i \(0.0238789\pi\)
0.246969 + 0.969023i \(0.420566\pi\)
\(200\) 6.93879 + 3.64895i 0.490647 + 0.258020i
\(201\) 4.15610 + 7.19858i 0.293149 + 0.507749i
\(202\) −1.61699 22.6300i −0.113771 1.59224i
\(203\) 2.43763 + 6.69734i 0.171088 + 0.470061i
\(204\) −0.393532 + 1.87949i −0.0275528 + 0.131590i
\(205\) −9.33264 1.64560i −0.651820 0.114933i
\(206\) −2.25210 8.97458i −0.156911 0.625289i
\(207\) 1.77685 1.49095i 0.123499 0.103628i
\(208\) 8.55741 8.96991i 0.593350 0.621952i
\(209\) 2.96937 + 3.37892i 0.205395 + 0.233725i
\(210\) −4.62719 6.83767i −0.319307 0.471844i
\(211\) −13.8564 16.5134i −0.953913 1.13683i −0.990502 0.137498i \(-0.956094\pi\)
0.0365893 0.999330i \(-0.488351\pi\)
\(212\) −8.09451 7.24391i −0.555933 0.497514i
\(213\) 4.32216 + 0.762114i 0.296150 + 0.0522192i
\(214\) 12.2096 + 12.6050i 0.834628 + 0.861659i
\(215\) 23.6957 8.62455i 1.61604 0.588189i
\(216\) 2.69395 + 0.861763i 0.183300 + 0.0586355i
\(217\) −5.97285 10.3453i −0.405464 0.702283i
\(218\) 1.87812 + 0.194514i 0.127202 + 0.0131741i
\(219\) −6.06393 + 7.22670i −0.409762 + 0.488335i
\(220\) −5.69537 + 0.818087i −0.383982 + 0.0551554i
\(221\) −2.57702 1.48784i −0.173349 0.100083i
\(222\) 4.49502 + 3.25540i 0.301686 + 0.218488i
\(223\) −0.762240 4.32288i −0.0510433 0.289481i 0.948591 0.316503i \(-0.102509\pi\)
−0.999635 + 0.0270218i \(0.991398\pi\)
\(224\) −11.1623 3.96697i −0.745809 0.265054i
\(225\) −2.60461 0.948001i −0.173641 0.0632001i
\(226\) −15.4597 4.40760i −1.02837 0.293189i
\(227\) 17.6130i 1.16901i −0.811389 0.584507i \(-0.801288\pi\)
0.811389 0.584507i \(-0.198712\pi\)
\(228\) 6.62737 + 5.66375i 0.438908 + 0.375091i
\(229\) 25.3331i 1.67406i 0.547158 + 0.837030i \(0.315710\pi\)
−0.547158 + 0.837030i \(0.684290\pi\)
\(230\) −2.50727 + 8.79430i −0.165325 + 0.579879i
\(231\) 2.03075 + 0.739134i 0.133614 + 0.0486314i
\(232\) 9.61875 0.379795i 0.631502 0.0249348i
\(233\) 2.41152 + 13.6764i 0.157984 + 0.895972i 0.956007 + 0.293345i \(0.0947684\pi\)
−0.798023 + 0.602628i \(0.794120\pi\)
\(234\) −2.57090 + 3.54987i −0.168065 + 0.232062i
\(235\) −23.2934 13.4484i −1.51949 0.877279i
\(236\) 0.868644 + 6.04734i 0.0565439 + 0.393648i
\(237\) 3.83737 4.57320i 0.249264 0.297061i
\(238\) −0.292925 + 2.82833i −0.0189875 + 0.183333i
\(239\) 11.2171 + 19.4286i 0.725575 + 1.25673i 0.958737 + 0.284295i \(0.0917595\pi\)
−0.233162 + 0.972438i \(0.574907\pi\)
\(240\) −10.7003 + 3.13876i −0.690702 + 0.202606i
\(241\) 21.3730 7.77913i 1.37676 0.501098i 0.455562 0.890204i \(-0.349438\pi\)
0.921193 + 0.389106i \(0.127216\pi\)
\(242\) −10.0921 + 9.77548i −0.648743 + 0.628392i
\(243\) −0.984808 0.173648i −0.0631754 0.0111395i
\(244\) −3.39957 3.04233i −0.217635 0.194765i
\(245\) 4.68526 + 5.58367i 0.299330 + 0.356728i
\(246\) 3.98141 2.69430i 0.253845 0.171782i
\(247\) −11.5422 + 7.02017i −0.734413 + 0.446683i
\(248\) −15.7664 + 3.42642i −1.00116 + 0.217578i
\(249\) 10.9798 9.21313i 0.695815 0.583858i
\(250\) −8.52067 + 2.13820i −0.538895 + 0.135231i
\(251\) 17.5350 + 3.09189i 1.10680 + 0.195158i 0.697038 0.717035i \(-0.254501\pi\)
0.409761 + 0.912193i \(0.365612\pi\)
\(252\) 4.09937 + 0.858338i 0.258236 + 0.0540702i
\(253\) −0.818681 2.24931i −0.0514700 0.141413i
\(254\) −15.4555 + 1.10435i −0.969762 + 0.0692930i
\(255\) 1.33831 + 2.31802i 0.0838082 + 0.145160i
\(256\) −9.69662 + 12.7270i −0.606039 + 0.795435i
\(257\) −14.4237 12.1029i −0.899728 0.754961i 0.0704095 0.997518i \(-0.477569\pi\)
−0.970137 + 0.242557i \(0.922014\pi\)
\(258\) −5.59018 + 11.5059i −0.348030 + 0.716327i
\(259\) 7.11731 + 4.10918i 0.442248 + 0.255332i
\(260\) 0.550596 17.2715i 0.0341465 1.07113i
\(261\) −3.35169 + 0.590993i −0.207464 + 0.0365815i
\(262\) 7.07747 + 15.8315i 0.437248 + 0.978072i
\(263\) 5.55042 + 2.02019i 0.342254 + 0.124570i 0.507428 0.861694i \(-0.330596\pi\)
−0.165174 + 0.986264i \(0.552819\pi\)
\(264\) 1.78652 2.30825i 0.109953 0.142063i
\(265\) −15.1413 −0.930121
\(266\) 10.6254 + 7.33114i 0.651486 + 0.449501i
\(267\) 1.00500i 0.0615050i
\(268\) 15.7951 5.18524i 0.964838 0.316739i
\(269\) −5.08143 + 13.9611i −0.309821 + 0.851225i 0.682870 + 0.730540i \(0.260731\pi\)
−0.992691 + 0.120685i \(0.961491\pi\)
\(270\) 3.59924 1.60904i 0.219043 0.0979231i
\(271\) −4.90947 27.8430i −0.298229 1.69134i −0.653781 0.756684i \(-0.726818\pi\)
0.355552 0.934656i \(-0.384293\pi\)
\(272\) 3.51789 + 1.54072i 0.213303 + 0.0934198i
\(273\) −3.24515 + 5.62077i −0.196406 + 0.340185i
\(274\) −6.91939 + 14.2417i −0.418015 + 0.860374i
\(275\) −1.83862 + 2.19118i −0.110873 + 0.132133i
\(276\) −2.19032 4.08937i −0.131842 0.246151i
\(277\) −12.6750 + 7.31790i −0.761566 + 0.439690i −0.829858 0.557975i \(-0.811578\pi\)
0.0682920 + 0.997665i \(0.478245\pi\)
\(278\) 1.44442 + 20.2148i 0.0866307 + 1.21240i
\(279\) 5.36035 1.95101i 0.320916 0.116804i
\(280\) −15.2817 + 6.25536i −0.913253 + 0.373829i
\(281\) 1.22075 6.92323i 0.0728239 0.413005i −0.926502 0.376290i \(-0.877200\pi\)
0.999326 0.0367149i \(-0.0116893\pi\)
\(282\) 13.2341 3.32101i 0.788082 0.197763i
\(283\) −18.7427 22.3367i −1.11414 1.32778i −0.939267 0.343186i \(-0.888494\pi\)
−0.174871 0.984591i \(-0.555951\pi\)
\(284\) 3.26343 8.14847i 0.193649 0.483523i
\(285\) 12.1485 0.277537i 0.719616 0.0164399i
\(286\) 2.53502 + 3.74603i 0.149899 + 0.221507i
\(287\) 5.45320 4.57578i 0.321892 0.270100i
\(288\) 2.79113 4.92032i 0.164469 0.289933i
\(289\) −2.79194 + 15.8339i −0.164232 + 0.931406i
\(290\) 9.63791 9.33556i 0.565958 0.548203i
\(291\) 5.60275 + 15.3934i 0.328439 + 0.902379i
\(292\) 11.6612 + 14.8325i 0.682418 + 0.868006i
\(293\) 16.9133 9.76489i 0.988085 0.570471i 0.0833836 0.996518i \(-0.473427\pi\)
0.904701 + 0.426046i \(0.140094\pi\)
\(294\) −3.67793 0.380918i −0.214501 0.0222156i
\(295\) 6.52354 + 5.47390i 0.379815 + 0.318703i
\(296\) 8.21502 7.46491i 0.477488 0.433889i
\(297\) −0.515985 + 0.893712i −0.0299405 + 0.0518584i
\(298\) −18.5316 + 25.5882i −1.07350 + 1.48228i
\(299\) 7.07959 1.24832i 0.409423 0.0721924i
\(300\) −2.92333 + 4.71009i −0.168779 + 0.271937i
\(301\) −6.47859 + 17.7998i −0.373420 + 1.02596i
\(302\) 11.5091 + 3.28127i 0.662274 + 0.188816i
\(303\) 16.0426 0.921623
\(304\) 13.8035 10.6520i 0.791683 0.610932i
\(305\) −6.35910 −0.364121
\(306\) −1.30579 0.372282i −0.0746468 0.0212820i
\(307\) 1.51249 4.15553i 0.0863223 0.237168i −0.889019 0.457870i \(-0.848612\pi\)
0.975341 + 0.220702i \(0.0708347\pi\)
\(308\) 2.27925 3.67235i 0.129872 0.209251i
\(309\) 6.44335 1.13614i 0.366549 0.0646325i
\(310\) −13.1914 + 18.2146i −0.749222 + 1.03452i
\(311\) 5.86864 10.1648i 0.332780 0.576392i −0.650276 0.759698i \(-0.725347\pi\)
0.983056 + 0.183306i \(0.0586800\pi\)
\(312\) 5.89529 + 6.48767i 0.333755 + 0.367292i
\(313\) 16.7422 + 14.0484i 0.946324 + 0.794060i 0.978675 0.205417i \(-0.0658550\pi\)
−0.0323509 + 0.999477i \(0.510299\pi\)
\(314\) 27.1171 + 2.80848i 1.53031 + 0.158492i
\(315\) 5.05586 2.91900i 0.284865 0.164467i
\(316\) −7.37942 9.38630i −0.415125 0.528020i
\(317\) 1.99541 + 5.48235i 0.112073 + 0.307919i 0.983031 0.183439i \(-0.0587229\pi\)
−0.870958 + 0.491358i \(0.836501\pi\)
\(318\) 5.51713 5.34405i 0.309385 0.299680i
\(319\) −0.609887 + 3.45884i −0.0341471 + 0.193658i
\(320\) 1.75847 + 22.2329i 0.0983013 + 1.24286i
\(321\) −9.50573 + 7.97625i −0.530558 + 0.445191i
\(322\) −3.84994 5.68910i −0.214549 0.317041i
\(323\) −3.26656 2.61619i −0.181756 0.145569i
\(324\) −0.743575 + 1.85664i −0.0413097 + 0.103146i
\(325\) −5.52186 6.58070i −0.306298 0.365032i
\(326\) −14.1954 + 3.56223i −0.786211 + 0.197294i
\(327\) −0.231843 + 1.31485i −0.0128210 + 0.0727113i
\(328\) −3.64234 8.89813i −0.201115 0.491317i
\(329\) 18.9859 6.91032i 1.04673 0.380978i
\(330\) −0.289975 4.05822i −0.0159626 0.223398i
\(331\) −13.0410 + 7.52924i −0.716800 + 0.413844i −0.813574 0.581462i \(-0.802481\pi\)
0.0967739 + 0.995306i \(0.469148\pi\)
\(332\) −13.5348 25.2697i −0.742819 1.38686i
\(333\) −2.52260 + 3.00632i −0.138238 + 0.164745i
\(334\) −11.8094 + 24.3065i −0.646181 + 1.32999i
\(335\) 11.5863 20.0681i 0.633029 1.09644i
\(336\) 3.36048 7.67291i 0.183329 0.418592i
\(337\) 1.84009 + 10.4357i 0.100236 + 0.568467i 0.993017 + 0.117975i \(0.0376403\pi\)
−0.892780 + 0.450492i \(0.851249\pi\)
\(338\) 4.38250 1.95920i 0.238376 0.106566i
\(339\) 3.88784 10.6817i 0.211158 0.580153i
\(340\) 5.08618 1.66970i 0.275837 0.0905524i
\(341\) 5.88673i 0.318784i
\(342\) −4.32869 + 4.38890i −0.234069 + 0.237325i
\(343\) −20.1343 −1.08715
\(344\) 20.2321 + 15.6591i 1.09084 + 0.844281i
\(345\) −6.07633 2.21160i −0.327139 0.119069i
\(346\) −10.2019 22.8204i −0.548455 1.22683i
\(347\) 17.5477 3.09414i 0.942012 0.166102i 0.318506 0.947921i \(-0.396819\pi\)
0.623506 + 0.781819i \(0.285708\pi\)
\(348\) −0.216882 + 6.80333i −0.0116261 + 0.364697i
\(349\) 12.0948 + 6.98292i 0.647418 + 0.373787i 0.787466 0.616358i \(-0.211392\pi\)
−0.140048 + 0.990145i \(0.544726\pi\)
\(350\) −3.58726 + 7.38343i −0.191747 + 0.394661i
\(351\) −2.37419 1.99218i −0.126725 0.106335i
\(352\) −3.78626 4.44331i −0.201809 0.236829i
\(353\) 5.78632 + 10.0222i 0.307975 + 0.533428i 0.977919 0.208983i \(-0.0670154\pi\)
−0.669944 + 0.742411i \(0.733682\pi\)
\(354\) −4.30902 + 0.307895i −0.229022 + 0.0163644i
\(355\) −4.18467 11.4973i −0.222099 0.610212i
\(356\) 1.96734 + 0.411926i 0.104269 + 0.0218321i
\(357\) −1.98008 0.349141i −0.104797 0.0184785i
\(358\) −12.3290 + 3.09386i −0.651607 + 0.163516i
\(359\) 1.08064 0.906767i 0.0570342 0.0478573i −0.613825 0.789442i \(-0.710370\pi\)
0.670859 + 0.741585i \(0.265926\pi\)
\(360\) −1.67453 7.70520i −0.0882556 0.406100i
\(361\) −17.5388 + 7.30695i −0.923093 + 0.384576i
\(362\) −23.5413 + 15.9309i −1.23730 + 0.837309i
\(363\) −6.38612 7.61068i −0.335184 0.399457i
\(364\) 9.67283 + 8.65638i 0.506994 + 0.453717i
\(365\) 25.8999 + 4.56685i 1.35566 + 0.239040i
\(366\) 2.31711 2.24442i 0.121117 0.117318i
\(367\) −25.5661 + 9.30532i −1.33454 + 0.485734i −0.908089 0.418776i \(-0.862459\pi\)
−0.426453 + 0.904510i \(0.640237\pi\)
\(368\) −8.90291 + 2.61152i −0.464096 + 0.136135i
\(369\) 1.69966 + 2.94390i 0.0884810 + 0.153254i
\(370\) 1.59392 15.3900i 0.0828639 0.800088i
\(371\) 7.31096 8.71286i 0.379566 0.452349i
\(372\) −1.62211 11.2928i −0.0841024 0.585506i
\(373\) 11.2308 + 6.48409i 0.581508 + 0.335734i 0.761732 0.647892i \(-0.224349\pi\)
−0.180225 + 0.983625i \(0.557682\pi\)
\(374\) −0.821898 + 1.13487i −0.0424993 + 0.0586826i
\(375\) −1.07867 6.11746i −0.0557025 0.315904i
\(376\) −1.07666 27.2677i −0.0555246 1.40622i
\(377\) −9.91194 3.60765i −0.510491 0.185804i
\(378\) −0.811989 + 2.84806i −0.0417642 + 0.146489i
\(379\) 11.4676i 0.589050i −0.955644 0.294525i \(-0.904839\pi\)
0.955644 0.294525i \(-0.0951614\pi\)
\(380\) 4.43611 23.8951i 0.227568 1.22579i
\(381\) 10.9565i 0.561320i
\(382\) −27.6933 7.89542i −1.41691 0.403965i
\(383\) −11.9026 4.33218i −0.608193 0.221364i 0.0195196 0.999809i \(-0.493786\pi\)
−0.627712 + 0.778445i \(0.716009\pi\)
\(384\) −8.48776 7.48051i −0.433139 0.381738i
\(385\) −1.04617 5.93312i −0.0533177 0.302380i
\(386\) 19.6765 + 14.2502i 1.00151 + 0.725315i
\(387\) −7.83349 4.52267i −0.398199 0.229900i
\(388\) 32.4299 4.65825i 1.64638 0.236487i
\(389\) 0.206971 0.246659i 0.0104939 0.0125061i −0.760772 0.649019i \(-0.775179\pi\)
0.771266 + 0.636513i \(0.219624\pi\)
\(390\) 12.1540 + 1.25877i 0.615441 + 0.0637403i
\(391\) 1.11351 + 1.92865i 0.0563124 + 0.0975360i
\(392\) −2.25317 + 7.04361i −0.113802 + 0.355756i
\(393\) −11.5228 + 4.19394i −0.581247 + 0.211556i
\(394\) 8.80330 + 9.08841i 0.443504 + 0.457868i
\(395\) −16.3900 2.88999i −0.824668 0.145411i
\(396\) 1.53800 + 1.37638i 0.0772872 + 0.0691656i
\(397\) −7.87054 9.37974i −0.395011 0.470756i 0.531481 0.847070i \(-0.321636\pi\)
−0.926492 + 0.376314i \(0.877191\pi\)
\(398\) 18.1594 + 26.8343i 0.910247 + 1.34508i
\(399\) −5.70621 + 7.12473i −0.285668 + 0.356683i
\(400\) 8.02204 + 7.65313i 0.401102 + 0.382656i
\(401\) −12.3059 + 10.3259i −0.614526 + 0.515649i −0.896078 0.443897i \(-0.853596\pi\)
0.281551 + 0.959546i \(0.409151\pi\)
\(402\) 2.86117 + 11.4017i 0.142702 + 0.568666i
\(403\) 17.4108 + 3.07000i 0.867295 + 0.152928i
\(404\) 6.57549 31.4042i 0.327143 1.56242i
\(405\) 0.953480 + 2.61967i 0.0473788 + 0.130172i
\(406\) 0.718373 + 10.0537i 0.0356523 + 0.498956i
\(407\) 2.02497 + 3.50734i 0.100374 + 0.173853i
\(408\) −1.26397 + 2.40355i −0.0625760 + 0.118994i
\(409\) 17.2457 + 14.4709i 0.852745 + 0.715538i 0.960392 0.278651i \(-0.0898873\pi\)
−0.107647 + 0.994189i \(0.534332\pi\)
\(410\) −12.0545 5.85672i −0.595330 0.289243i
\(411\) −9.69609 5.59804i −0.478273 0.276131i
\(412\) 0.416939 13.0788i 0.0205411 0.644348i
\(413\) −6.29978 + 1.11082i −0.309992 + 0.0546599i
\(414\) 2.99465 1.33876i 0.147179 0.0657965i
\(415\) −37.5479 13.6663i −1.84315 0.670853i
\(416\) 15.1163 8.88117i 0.741137 0.435435i
\(417\) −14.3305 −0.701767
\(418\) 2.72824 + 5.74676i 0.133443 + 0.281083i
\(419\) 9.23590i 0.451203i −0.974220 0.225602i \(-0.927565\pi\)
0.974220 0.225602i \(-0.0724348\pi\)
\(420\) −3.64181 11.0935i −0.177702 0.541309i
\(421\) 3.22808 8.86907i 0.157327 0.432252i −0.835837 0.548977i \(-0.815017\pi\)
0.993164 + 0.116725i \(0.0372397\pi\)
\(422\) −12.4420 27.8313i −0.605666 1.35481i
\(423\) 1.67538 + 9.50153i 0.0814595 + 0.461980i
\(424\) −8.19990 12.9905i −0.398223 0.630873i
\(425\) 1.33062 2.30470i 0.0645445 0.111794i
\(426\) 5.58272 + 2.71238i 0.270484 + 0.131415i
\(427\) 3.07049 3.65927i 0.148592 0.177084i
\(428\) 11.7177 + 21.8772i 0.566398 + 1.05748i
\(429\) −2.76986 + 1.59918i −0.133730 + 0.0772092i
\(430\) 35.5708 2.54166i 1.71538 0.122570i
\(431\) 1.52770 0.556037i 0.0735867 0.0267834i −0.304965 0.952364i \(-0.598645\pi\)
0.378551 + 0.925580i \(0.376422\pi\)
\(432\) 3.32968 + 2.21658i 0.160199 + 0.106645i
\(433\) 5.49481 31.1626i 0.264064 1.49758i −0.507624 0.861578i \(-0.669476\pi\)
0.771688 0.636001i \(-0.219413\pi\)
\(434\) −4.11187 16.3857i −0.197376 0.786540i
\(435\) 6.09873 + 7.26818i 0.292412 + 0.348483i
\(436\) 2.47886 + 0.992772i 0.118716 + 0.0475451i
\(437\) 10.1079 0.230917i 0.483525 0.0110463i
\(438\) −11.0492 + 7.47721i −0.527950 + 0.357275i
\(439\) 5.70419 4.78638i 0.272246 0.228442i −0.496435 0.868074i \(-0.665358\pi\)
0.768681 + 0.639632i \(0.220913\pi\)
\(440\) −8.06303 1.09573i −0.384390 0.0522370i
\(441\) 0.454021 2.57488i 0.0216201 0.122613i
\(442\) −2.92790 3.02272i −0.139266 0.143776i
\(443\) −8.34692 22.9330i −0.396574 1.08958i −0.963942 0.266114i \(-0.914260\pi\)
0.567367 0.823465i \(-0.307962\pi\)
\(444\) 4.85106 + 6.17033i 0.230221 + 0.292831i
\(445\) 2.42637 1.40086i 0.115021 0.0664073i
\(446\) 0.639509 6.17475i 0.0302816 0.292383i
\(447\) −17.1136 14.3600i −0.809446 0.679206i
\(448\) −13.6427 9.72325i −0.644558 0.459381i
\(449\) −6.99430 + 12.1145i −0.330081 + 0.571718i −0.982528 0.186117i \(-0.940410\pi\)
0.652446 + 0.757835i \(0.273743\pi\)
\(450\) −3.17474 2.29922i −0.149659 0.108386i
\(451\) 3.45471 0.609158i 0.162676 0.0286841i
\(452\) −19.3165 11.9888i −0.908572 0.563908i
\(453\) −2.89433 + 7.95210i −0.135987 + 0.373622i
\(454\) 6.82932 23.9540i 0.320516 1.12422i
\(455\) 18.0936 0.848242
\(456\) 6.81727 + 10.2725i 0.319248 + 0.481055i
\(457\) −31.0992 −1.45476 −0.727380 0.686235i \(-0.759262\pi\)
−0.727380 + 0.686235i \(0.759262\pi\)
\(458\) −9.82277 + 34.4535i −0.458988 + 1.60991i
\(459\) 0.328381 0.902220i 0.0153275 0.0421120i
\(460\) −6.81988 + 10.9882i −0.317978 + 0.512329i
\(461\) −24.3494 + 4.29346i −1.13406 + 0.199966i −0.709008 0.705201i \(-0.750857\pi\)
−0.425057 + 0.905167i \(0.639746\pi\)
\(462\) 2.47527 + 1.79265i 0.115160 + 0.0834016i
\(463\) 12.7614 22.1034i 0.593072 1.02723i −0.400744 0.916190i \(-0.631248\pi\)
0.993816 0.111041i \(-0.0354185\pi\)
\(464\) 13.2290 + 3.21309i 0.614139 + 0.149164i
\(465\) −12.1821 10.2220i −0.564930 0.474033i
\(466\) −2.02324 + 19.5353i −0.0937246 + 0.904954i
\(467\) −10.3292 + 5.96357i −0.477978 + 0.275961i −0.719574 0.694416i \(-0.755663\pi\)
0.241595 + 0.970377i \(0.422329\pi\)
\(468\) −4.87291 + 3.83104i −0.225251 + 0.177090i
\(469\) 5.95350 + 16.3571i 0.274907 + 0.755301i
\(470\) −26.4649 27.3220i −1.22074 1.26027i
\(471\) −3.34746 + 18.9844i −0.154243 + 0.874756i
\(472\) −1.16345 + 8.56132i −0.0535521 + 0.394067i
\(473\) −7.15065 + 6.00011i −0.328787 + 0.275885i
\(474\) 6.99213 4.73173i 0.321159 0.217335i
\(475\) −6.27833 10.3225i −0.288070 0.473629i
\(476\) −1.49505 + 3.73300i −0.0685256 + 0.171102i
\(477\) 3.49116 + 4.16060i 0.159849 + 0.190501i
\(478\) 7.72217 + 30.7727i 0.353204 + 1.40751i
\(479\) 1.98083 11.2338i 0.0905065 0.513288i −0.905526 0.424292i \(-0.860523\pi\)
0.996032 0.0889959i \(-0.0283658\pi\)
\(480\) −15.7697 + 0.119793i −0.719783 + 0.00546779i
\(481\) −11.4295 + 4.16000i −0.521140 + 0.189680i
\(482\) 32.0840 2.29252i 1.46139 0.104421i
\(483\) 4.20660 2.42868i 0.191407 0.110509i
\(484\) −17.5158 + 9.38170i −0.796173 + 0.426441i
\(485\) 29.3547 34.9835i 1.33293 1.58852i
\(486\) −1.27203 0.618019i −0.0577003 0.0280339i
\(487\) 11.3671 19.6884i 0.515092 0.892166i −0.484755 0.874650i \(-0.661091\pi\)
0.999847 0.0175154i \(-0.00557560\pi\)
\(488\) −3.44384 5.45580i −0.155895 0.246972i
\(489\) −1.79707 10.1917i −0.0812661 0.460883i
\(490\) 4.20700 + 9.41058i 0.190053 + 0.425127i
\(491\) 4.60913 12.6635i 0.208007 0.571495i −0.791190 0.611571i \(-0.790538\pi\)
0.999197 + 0.0400763i \(0.0127601\pi\)
\(492\) 6.45949 2.12054i 0.291216 0.0956012i
\(493\) 3.26767i 0.147169i
\(494\) −18.4197 + 5.07215i −0.828740 + 0.228207i
\(495\) 2.87691 0.129308
\(496\) −22.7711 1.45331i −1.02245 0.0652556i
\(497\) 8.63654 + 3.14344i 0.387402 + 0.141003i
\(498\) 18.5051 8.27269i 0.829232 0.370708i
\(499\) −6.06861 + 1.07006i −0.271668 + 0.0479024i −0.307823 0.951444i \(-0.599600\pi\)
0.0361544 + 0.999346i \(0.488489\pi\)
\(500\) −12.4174 0.395851i −0.555321 0.0177030i
\(501\) −16.5484 9.55424i −0.739329 0.426852i
\(502\) 22.6491 + 11.0041i 1.01088 + 0.491138i
\(503\) 22.3714 + 18.7718i 0.997490 + 0.836993i 0.986635 0.162948i \(-0.0521002\pi\)
0.0108550 + 0.999941i \(0.496545\pi\)
\(504\) 5.24241 + 2.75686i 0.233516 + 0.122801i
\(505\) −22.3617 38.7316i −0.995082 1.72353i
\(506\) −0.241266 3.37654i −0.0107256 0.150106i
\(507\) 1.16097 + 3.18975i 0.0515607 + 0.141662i
\(508\) −21.4479 4.49083i −0.951599 0.199248i
\(509\) 6.46829 + 1.14053i 0.286702 + 0.0505533i 0.315150 0.949042i \(-0.397945\pi\)
−0.0284476 + 0.999595i \(0.509056\pi\)
\(510\) 0.921329 + 3.67148i 0.0407971 + 0.162576i
\(511\) −15.1337 + 12.6987i −0.669475 + 0.561756i
\(512\) −18.1224 + 13.5491i −0.800905 + 0.598792i
\(513\) −2.87738 3.27425i −0.127039 0.144562i
\(514\) −14.9237 22.0530i −0.658257 0.972715i
\(515\) −11.7243 13.9725i −0.516635 0.615702i
\(516\) −12.0641 + 13.4807i −0.531093 + 0.593455i
\(517\) 9.80529 + 1.72894i 0.431236 + 0.0760385i
\(518\) 8.08637 + 8.34826i 0.355295 + 0.366802i
\(519\) 16.6096 6.04538i 0.729078 0.265363i
\(520\) 7.44575 23.2761i 0.326518 1.02072i
\(521\) −16.9413 29.3431i −0.742210 1.28555i −0.951487 0.307689i \(-0.900444\pi\)
0.209277 0.977856i \(-0.432889\pi\)
\(522\) −4.78752 0.495835i −0.209544 0.0217021i
\(523\) 8.76581 10.4467i 0.383302 0.456802i −0.539551 0.841953i \(-0.681406\pi\)
0.922854 + 0.385151i \(0.125851\pi\)
\(524\) 3.48693 + 24.2754i 0.152327 + 1.06047i
\(525\) −5.02681 2.90223i −0.219388 0.126664i
\(526\) 6.76537 + 4.89964i 0.294984 + 0.213635i
\(527\) 0.951052 + 5.39368i 0.0414285 + 0.234953i
\(528\) 3.32472 2.44656i 0.144690 0.106473i
\(529\) 16.5573 + 6.02635i 0.719881 + 0.262015i
\(530\) −20.5924 5.87094i −0.894478 0.255017i
\(531\) 3.05470i 0.132563i
\(532\) 11.6082 + 14.0904i 0.503278 + 0.610898i
\(533\) 10.5355i 0.456342i
\(534\) −0.389683 + 1.36682i −0.0168632 + 0.0591480i
\(535\) 32.5070 + 11.8316i 1.40540 + 0.511524i
\(536\) 23.4922 0.927585i 1.01471 0.0400656i
\(537\) −1.56079 8.85165i −0.0673529 0.381977i
\(538\) −12.3242 + 17.0171i −0.531334 + 0.733660i
\(539\) −2.33670 1.34910i −0.100649 0.0581097i
\(540\) 5.51893 0.792744i 0.237497 0.0341143i
\(541\) 6.23407 7.42948i 0.268024 0.319418i −0.615199 0.788372i \(-0.710924\pi\)
0.883223 + 0.468953i \(0.155369\pi\)
\(542\) 4.11898 39.7706i 0.176925 1.70829i
\(543\) −10.0498 17.4067i −0.431277 0.746995i
\(544\) 4.18700 + 3.45945i 0.179516 + 0.148323i
\(545\) 3.49760 1.27302i 0.149821 0.0545303i
\(546\) −6.59290 + 6.38607i −0.282150 + 0.273299i
\(547\) 18.6027 + 3.28016i 0.795394 + 0.140249i 0.556556 0.830810i \(-0.312122\pi\)
0.238838 + 0.971059i \(0.423233\pi\)
\(548\) −14.9327 + 16.6861i −0.637891 + 0.712794i
\(549\) 1.46623 + 1.74739i 0.0625774 + 0.0745768i
\(550\) −3.35018 + 2.26714i −0.142852 + 0.0966710i
\(551\) −13.0136 7.12216i −0.554397 0.303414i
\(552\) −1.39325 6.41091i −0.0593007 0.272867i
\(553\) 9.57690 8.03597i 0.407251 0.341724i
\(554\) −20.0757 + 5.03784i −0.852935 + 0.214037i
\(555\) 10.7744 + 1.89981i 0.457347 + 0.0806426i
\(556\) −5.87374 + 28.0526i −0.249102 + 1.18970i
\(557\) −8.65678 23.7843i −0.366799 1.00777i −0.976571 0.215196i \(-0.930961\pi\)
0.609772 0.792577i \(-0.291261\pi\)
\(558\) 8.04667 0.574964i 0.340643 0.0243402i
\(559\) −14.0170 24.2782i −0.592856 1.02686i
\(560\) −23.2088 + 2.58204i −0.980752 + 0.109111i
\(561\) −0.759010 0.636885i −0.0320454 0.0268893i
\(562\) 4.34469 8.94239i 0.183270 0.377212i
\(563\) −9.18809 5.30474i −0.387232 0.223568i 0.293728 0.955889i \(-0.405104\pi\)
−0.680960 + 0.732321i \(0.738437\pi\)
\(564\) 19.2864 + 0.614829i 0.812104 + 0.0258890i
\(565\) −31.2081 + 5.50284i −1.31294 + 0.231506i
\(566\) −16.8295 37.6457i −0.707398 1.58237i
\(567\) −1.96784 0.716236i −0.0826416 0.0300791i
\(568\) 7.59785 9.81671i 0.318799 0.411900i
\(569\) −11.8869 −0.498326 −0.249163 0.968462i \(-0.580156\pi\)
−0.249163 + 0.968462i \(0.580156\pi\)
\(570\) 16.6298 + 4.33307i 0.696548 + 0.181492i
\(571\) 10.7383i 0.449386i 0.974430 + 0.224693i \(0.0721379\pi\)
−0.974430 + 0.224693i \(0.927862\pi\)
\(572\) 1.99517 + 6.07761i 0.0834224 + 0.254118i
\(573\) 6.96437 19.1344i 0.290941 0.799353i
\(574\) 9.19069 4.10870i 0.383612 0.171494i
\(575\) 1.11641 + 6.33147i 0.0465575 + 0.264041i
\(576\) 5.70382 5.60949i 0.237659 0.233729i
\(577\) 1.17003 2.02656i 0.0487092 0.0843667i −0.840643 0.541590i \(-0.817823\pi\)
0.889352 + 0.457223i \(0.151156\pi\)
\(578\) −9.93660 + 20.4519i −0.413308 + 0.850685i
\(579\) −11.0424 + 13.1598i −0.458907 + 0.546904i
\(580\) 16.7276 8.95951i 0.694574 0.372023i
\(581\) 25.9941 15.0077i 1.07842 0.622624i
\(582\) 1.65114 + 23.1078i 0.0684419 + 0.957850i
\(583\) 5.26690 1.91700i 0.218133 0.0793938i
\(584\) 10.1082 + 24.6940i 0.418281 + 1.02185i
\(585\) −1.50034 + 8.50888i −0.0620316 + 0.351799i
\(586\) 26.7887 6.72242i 1.10663 0.277700i
\(587\) −17.3895 20.7240i −0.717743 0.855373i 0.276667 0.960966i \(-0.410770\pi\)
−0.994409 + 0.105593i \(0.966326\pi\)
\(588\) −4.85437 1.94415i −0.200191 0.0801756i
\(589\) 23.5534 + 7.96838i 0.970499 + 0.328331i
\(590\) 6.74967 + 9.97408i 0.277879 + 0.410626i
\(591\) −6.85379 + 5.75102i −0.281927 + 0.236565i
\(592\) 14.0671 6.96711i 0.578153 0.286346i
\(593\) −5.47915 + 31.0738i −0.225002 + 1.27605i 0.637680 + 0.770302i \(0.279894\pi\)
−0.862682 + 0.505747i \(0.831217\pi\)
\(594\) −1.04828 + 1.01540i −0.0430115 + 0.0416622i
\(595\) 1.91709 + 5.26717i 0.0785931 + 0.215933i
\(596\) −35.1250 + 27.6149i −1.43877 + 1.13115i
\(597\) −19.8417 + 11.4556i −0.812065 + 0.468846i
\(598\) 10.1124 + 1.04733i 0.413527 + 0.0428284i
\(599\) 16.3714 + 13.7372i 0.668916 + 0.561287i 0.912744 0.408531i \(-0.133959\pi\)
−0.243828 + 0.969818i \(0.578403\pi\)
\(600\) −5.80210 + 5.27232i −0.236870 + 0.215241i
\(601\) 5.98104 10.3595i 0.243972 0.422571i −0.717870 0.696177i \(-0.754883\pi\)
0.961842 + 0.273606i \(0.0882163\pi\)
\(602\) −15.7128 + 21.6960i −0.640405 + 0.884264i
\(603\) −8.18593 + 1.44340i −0.333357 + 0.0587798i
\(604\) 14.3803 + 8.92518i 0.585127 + 0.363160i
\(605\) −9.47286 + 26.0265i −0.385127 + 1.05813i
\(606\) 21.8182 + 6.22042i 0.886306 + 0.252687i
\(607\) 29.8314 1.21082 0.605409 0.795915i \(-0.293010\pi\)
0.605409 + 0.795915i \(0.293010\pi\)
\(608\) 22.9032 9.13466i 0.928849 0.370459i
\(609\) −7.12716 −0.288807
\(610\) −8.64851 2.46571i −0.350168 0.0998335i
\(611\) −10.2271 + 28.0989i −0.413746 + 1.13676i
\(612\) −1.63154 1.01262i −0.0659513 0.0409328i
\(613\) 5.67036 0.999838i 0.229024 0.0403831i −0.0579584 0.998319i \(-0.518459\pi\)
0.286982 + 0.957936i \(0.407348\pi\)
\(614\) 3.66830 5.06514i 0.148040 0.204412i
\(615\) 4.73831 8.20699i 0.191067 0.330938i
\(616\) 4.52376 4.11070i 0.182267 0.165625i
\(617\) 35.9381 + 30.1556i 1.44681 + 1.21402i 0.934864 + 0.355005i \(0.115521\pi\)
0.511949 + 0.859016i \(0.328924\pi\)
\(618\) 9.20361 + 0.953203i 0.370223 + 0.0383435i
\(619\) 10.2047 5.89167i 0.410161 0.236806i −0.280698 0.959796i \(-0.590566\pi\)
0.690859 + 0.722990i \(0.257233\pi\)
\(620\) −25.0032 + 19.6573i −1.00415 + 0.789455i
\(621\) 0.793318 + 2.17962i 0.0318348 + 0.0874653i
\(622\) 11.9228 11.5488i 0.478061 0.463064i
\(623\) −0.365460 + 2.07263i −0.0146419 + 0.0830381i
\(624\) 5.50215 + 11.1092i 0.220262 + 0.444725i
\(625\) −23.8823 + 20.0396i −0.955292 + 0.801585i
\(626\) 17.3225 + 25.5977i 0.692347 + 1.02309i
\(627\) −4.19073 + 1.63463i −0.167362 + 0.0652809i
\(628\) 35.7909 + 14.3341i 1.42821 + 0.571993i
\(629\) −2.42200 2.88643i −0.0965716 0.115090i
\(630\) 8.00790 2.00952i 0.319042 0.0800612i
\(631\) −1.91609 + 10.8667i −0.0762782 + 0.432595i 0.922622 + 0.385706i \(0.126042\pi\)
−0.998900 + 0.0468895i \(0.985069\pi\)
\(632\) −6.39667 15.6269i −0.254446 0.621604i
\(633\) 20.2567 7.37283i 0.805131 0.293044i
\(634\) 0.588050 + 8.22981i 0.0233545 + 0.326848i
\(635\) −26.4523 + 15.2722i −1.04973 + 0.606061i
\(636\) 9.57554 5.12878i 0.379695 0.203370i
\(637\) 5.20876 6.20756i 0.206378 0.245952i
\(638\) −2.17060 + 4.46761i −0.0859350 + 0.176874i
\(639\) −2.19442 + 3.80084i −0.0868099 + 0.150359i
\(640\) −6.22912 + 30.9190i −0.246228 + 1.22218i
\(641\) 7.57684 + 42.9704i 0.299267 + 1.69723i 0.649334 + 0.760504i \(0.275048\pi\)
−0.350066 + 0.936725i \(0.613841\pi\)
\(642\) −16.0207 + 7.16207i −0.632288 + 0.282664i
\(643\) 8.33026 22.8872i 0.328513 0.902583i −0.659975 0.751287i \(-0.729433\pi\)
0.988489 0.151296i \(-0.0483445\pi\)
\(644\) −3.03007 9.23008i −0.119402 0.363716i
\(645\) 25.2165i 0.992898i
\(646\) −3.42817 4.82466i −0.134880 0.189824i
\(647\) −23.0062 −0.904467 −0.452234 0.891899i \(-0.649373\pi\)
−0.452234 + 0.891899i \(0.649373\pi\)
\(648\) −1.73118 + 2.23674i −0.0680071 + 0.0878676i
\(649\) −2.96225 1.07817i −0.116279 0.0423219i
\(650\) −4.95822 11.0910i −0.194477 0.435023i
\(651\) 11.7642 2.07435i 0.461076 0.0813002i
\(652\) −20.6873 0.659487i −0.810176 0.0258275i
\(653\) 10.3956 + 6.00193i 0.406813 + 0.234874i 0.689419 0.724362i \(-0.257866\pi\)
−0.282606 + 0.959236i \(0.591199\pi\)
\(654\) −0.825137 + 1.69833i −0.0322654 + 0.0664098i
\(655\) 26.1869 + 21.9735i 1.02321 + 0.858574i
\(656\) −1.50346 13.5139i −0.0587002 0.527631i
\(657\) −4.71690 8.16990i −0.184024 0.318738i
\(658\) 28.5007 2.03648i 1.11107 0.0793902i
\(659\) 10.8725 + 29.8720i 0.423533 + 1.16365i 0.949671 + 0.313249i \(0.101417\pi\)
−0.526138 + 0.850399i \(0.676360\pi\)
\(660\) 1.17918 5.63170i 0.0458996 0.219214i
\(661\) −18.1081 3.19295i −0.704325 0.124192i −0.189997 0.981785i \(-0.560848\pi\)
−0.514329 + 0.857593i \(0.671959\pi\)
\(662\) −20.6555 + 5.18333i −0.802798 + 0.201456i
\(663\) 2.27951 1.91274i 0.0885288 0.0742845i
\(664\) −8.60941 39.6154i −0.334110 1.53737i
\(665\) 25.1551 + 3.84535i 0.975471 + 0.149116i
\(666\) −4.59647 + 3.11053i −0.178109 + 0.120530i
\(667\) 5.07429 + 6.04730i 0.196477 + 0.234153i
\(668\) −25.4857 + 28.4783i −0.986072 + 1.10186i
\(669\) 4.32288 + 0.762240i 0.167132 + 0.0294699i
\(670\) 23.5390 22.8005i 0.909389 0.880861i
\(671\) 2.21202 0.805109i 0.0853940 0.0310809i
\(672\) 7.54544 9.13230i 0.291072 0.352286i
\(673\) −10.8644 18.8177i −0.418791 0.725367i 0.577027 0.816725i \(-0.304213\pi\)
−0.995818 + 0.0913576i \(0.970879\pi\)
\(674\) −1.54381 + 14.9062i −0.0594654 + 0.574166i
\(675\) 1.78166 2.12330i 0.0685761 0.0817258i
\(676\) 6.71995 0.965258i 0.258460 0.0371253i
\(677\) −22.6174 13.0582i −0.869257 0.501866i −0.00215585 0.999998i \(-0.500686\pi\)
−0.867101 + 0.498132i \(0.834020\pi\)
\(678\) 9.42932 13.0199i 0.362131 0.500026i
\(679\) 5.95696 + 33.7836i 0.228607 + 1.29649i
\(680\) 7.56473 0.298692i 0.290094 0.0114543i
\(681\) 16.5508 + 6.02399i 0.634227 + 0.230840i
\(682\) 2.28255 8.00607i 0.0874032 0.306568i
\(683\) 31.3001i 1.19767i −0.800874 0.598833i \(-0.795631\pi\)
0.800874 0.598833i \(-0.204369\pi\)
\(684\) −7.58887 + 4.29057i −0.290168 + 0.164054i
\(685\) 31.2123i 1.19256i
\(686\) −27.3830 7.80695i −1.04549 0.298071i
\(687\) −23.8053 8.66443i −0.908230 0.330569i
\(688\) 21.4443 + 29.1415i 0.817558 + 1.11101i
\(689\) 2.92303 + 16.5773i 0.111359 + 0.631546i
\(690\) −7.40640 5.36389i −0.281957 0.204200i
\(691\) 7.30963 + 4.22022i 0.278071 + 0.160545i 0.632550 0.774519i \(-0.282008\pi\)
−0.354479 + 0.935064i \(0.615342\pi\)
\(692\) −5.02626 34.9919i −0.191070 1.33019i
\(693\) −1.38912 + 1.65549i −0.0527682 + 0.0628867i
\(694\) 25.0650 + 2.59594i 0.951455 + 0.0985407i
\(695\) 19.9752 + 34.5980i 0.757702 + 1.31238i
\(696\) −2.93292 + 9.16857i −0.111172 + 0.347534i
\(697\) −3.06694 + 1.11628i −0.116169 + 0.0422820i
\(698\) 13.7415 + 14.1866i 0.520125 + 0.536970i
\(699\) −13.6764 2.41152i −0.517290 0.0912122i
\(700\) −7.74163 + 8.65067i −0.292606 + 0.326965i
\(701\) −9.79934 11.6784i −0.370116 0.441087i 0.548553 0.836116i \(-0.315179\pi\)
−0.918669 + 0.395029i \(0.870735\pi\)
\(702\) −2.45649 3.62998i −0.0927141 0.137005i
\(703\) −16.7742 + 3.35447i −0.632652 + 0.126516i
\(704\) −3.42653 7.51109i −0.129142 0.283085i
\(705\) 20.6042 17.2890i 0.775999 0.651141i
\(706\) 3.98346 + 15.8740i 0.149919 + 0.597426i
\(707\) 33.0849 + 5.83377i 1.24429 + 0.219401i
\(708\) −5.97974 1.25205i −0.224732 0.0470551i
\(709\) −4.39632 12.0788i −0.165107 0.453628i 0.829355 0.558722i \(-0.188708\pi\)
−0.994462 + 0.105094i \(0.966486\pi\)
\(710\) −1.23323 17.2591i −0.0462822 0.647723i
\(711\) 2.98494 + 5.17008i 0.111944 + 0.193893i
\(712\) 2.51589 + 1.32305i 0.0942871 + 0.0495834i
\(713\) −10.1358 8.50493i −0.379588 0.318512i
\(714\) −2.55757 1.24260i −0.0957147 0.0465033i
\(715\) 7.72180 + 4.45818i 0.288779 + 0.166727i
\(716\) −17.9673 0.572776i −0.671469 0.0214057i
\(717\) −22.0934 + 3.89566i −0.825094 + 0.145486i
\(718\) 1.82129 0.814208i 0.0679699 0.0303860i
\(719\) −15.6338 5.69024i −0.583043 0.212210i 0.0336239 0.999435i \(-0.489295\pi\)
−0.616667 + 0.787224i \(0.711517\pi\)
\(720\) 0.710251 11.1285i 0.0264695 0.414735i
\(721\) 13.7014 0.510266
\(722\) −26.6863 + 3.13703i −0.993162 + 0.116748i
\(723\) 22.7447i 0.845883i
\(724\) −38.1937 + 12.5383i −1.41946 + 0.465983i
\(725\) 3.22642 8.86452i 0.119826 0.329220i
\(726\) −5.73425 12.8269i −0.212818 0.476049i
\(727\) 0.217213 + 1.23188i 0.00805598 + 0.0456878i 0.988571 0.150758i \(-0.0481713\pi\)
−0.980515 + 0.196445i \(0.937060\pi\)
\(728\) 9.79877 + 15.5234i 0.363167 + 0.575337i
\(729\) 0.500000 0.866025i 0.0185185 0.0320750i
\(730\) 33.4536 + 16.2535i 1.23817 + 0.601570i
\(731\) 5.58237 6.65281i 0.206472 0.246063i
\(732\) 4.02158 2.15401i 0.148642 0.0796146i
\(733\) 36.5021 21.0745i 1.34824 0.778405i 0.360237 0.932861i \(-0.382696\pi\)
0.988000 + 0.154456i \(0.0493625\pi\)
\(734\) −38.3786 + 2.74229i −1.41658 + 0.101220i
\(735\) −6.84939 + 2.49297i −0.252643 + 0.0919547i
\(736\) −13.1207 + 0.0996709i −0.483637 + 0.00367392i
\(737\) −1.48954 + 8.44763i −0.0548681 + 0.311172i
\(738\) 1.17009 + 4.66280i 0.0430718 + 0.171640i
\(739\) 20.4734 + 24.3992i 0.753126 + 0.897540i 0.997393 0.0721679i \(-0.0229917\pi\)
−0.244267 + 0.969708i \(0.578547\pi\)
\(740\) 8.13515 20.3127i 0.299054 0.746709i
\(741\) −2.64914 13.2472i −0.0973186 0.486647i
\(742\) 13.3214 9.01488i 0.489044 0.330947i
\(743\) 16.4767 13.8256i 0.604470 0.507210i −0.288409 0.957507i \(-0.593126\pi\)
0.892879 + 0.450297i \(0.148682\pi\)
\(744\) 2.17263 15.9874i 0.0796524 0.586128i
\(745\) −10.8148 + 61.3337i −0.396223 + 2.24709i
\(746\) 12.7599 + 13.1732i 0.467174 + 0.482304i
\(747\) 4.90220 + 13.4687i 0.179362 + 0.492794i
\(748\) −1.55784 + 1.22476i −0.0569601 + 0.0447815i
\(749\) −22.5044 + 12.9929i −0.822291 + 0.474750i
\(750\) 0.904994 8.73812i 0.0330457 0.319071i
\(751\) −11.5356 9.67948i −0.420938 0.353209i 0.407582 0.913169i \(-0.366372\pi\)
−0.828520 + 0.559960i \(0.810817\pi\)
\(752\) 9.10862 37.5021i 0.332157 1.36756i
\(753\) −8.90275 + 15.4200i −0.324434 + 0.561936i
\(754\) −12.0816 8.74978i −0.439986 0.318648i
\(755\) 23.2331 4.09663i 0.845540 0.149092i
\(756\) −2.20864 + 3.55858i −0.0803275 + 0.129424i
\(757\) 9.52178 26.1609i 0.346075 0.950833i −0.637519 0.770435i \(-0.720039\pi\)
0.983594 0.180398i \(-0.0577387\pi\)
\(758\) 4.44649 15.5961i 0.161504 0.566477i
\(759\) 2.39366 0.0868844
\(760\) 15.2984 30.7777i 0.554931 1.11643i
\(761\) 39.1433 1.41894 0.709471 0.704734i \(-0.248934\pi\)
0.709471 + 0.704734i \(0.248934\pi\)
\(762\) 4.24833 14.9011i 0.153901 0.539810i
\(763\) −0.956270 + 2.62733i −0.0346193 + 0.0951158i
\(764\) −34.6021 21.4759i −1.25186 0.776970i
\(765\) −2.63596 + 0.464790i −0.0953032 + 0.0168045i
\(766\) −14.5079 10.5070i −0.524194 0.379633i
\(767\) 4.73369 8.19900i 0.170924 0.296049i
\(768\) −8.64299 13.4647i −0.311877 0.485866i
\(769\) 18.6611 + 15.6586i 0.672938 + 0.564662i 0.913933 0.405864i \(-0.133029\pi\)
−0.240995 + 0.970526i \(0.577474\pi\)
\(770\) 0.877722 8.47480i 0.0316309 0.305411i
\(771\) 16.3063 9.41442i 0.587256 0.339052i
\(772\) 21.2350 + 27.0100i 0.764263 + 0.972110i
\(773\) 7.58524 + 20.8403i 0.272822 + 0.749572i 0.998129 + 0.0611466i \(0.0194757\pi\)
−0.725307 + 0.688426i \(0.758302\pi\)
\(774\) −8.90006 9.18831i −0.319906 0.330267i
\(775\) −2.74558 + 15.5710i −0.0986243 + 0.559326i
\(776\) 45.9115 + 6.23918i 1.64813 + 0.223974i
\(777\) −6.29563 + 5.28266i −0.225854 + 0.189514i
\(778\) 0.377125 0.255209i 0.0135206 0.00914968i
\(779\) −2.23905 + 14.6472i −0.0802224 + 0.524790i
\(780\) 16.0416 + 6.42460i 0.574381 + 0.230037i
\(781\) 2.91128 + 3.46953i 0.104174 + 0.124149i
\(782\) 0.766568 + 3.05476i 0.0274124 + 0.109238i
\(783\) 0.590993 3.35169i 0.0211204 0.119780i
\(784\) −5.79547 + 8.70580i −0.206981 + 0.310921i
\(785\) 50.5000 18.3805i 1.80242 0.656028i
\(786\) −17.2974 + 1.23596i −0.616977 + 0.0440852i
\(787\) −34.4068 + 19.8648i −1.22647 + 0.708103i −0.966290 0.257456i \(-0.917116\pi\)
−0.260181 + 0.965560i \(0.583782\pi\)
\(788\) 8.44868 + 15.7739i 0.300972 + 0.561920i
\(789\) −3.79671 + 4.52475i −0.135167 + 0.161085i
\(790\) −21.1701 10.2856i −0.753198 0.365944i
\(791\) 11.9023 20.6154i 0.423197 0.732999i
\(792\) 1.55802 + 2.46825i 0.0553619 + 0.0877055i
\(793\) 1.22763 + 6.96223i 0.0435944 + 0.247236i
\(794\) −7.06715 15.8084i −0.250804 0.561019i
\(795\) 5.17862 14.2281i 0.183667 0.504620i
\(796\) 14.2922 + 43.5364i 0.506575 + 1.54311i
\(797\) 12.6266i 0.447257i 0.974675 + 0.223628i \(0.0717902\pi\)
−0.974675 + 0.223628i \(0.928210\pi\)
\(798\) −10.5231 + 7.47722i −0.372515 + 0.264691i
\(799\) −9.26336 −0.327714
\(800\) 7.94267 + 13.5189i 0.280816 + 0.477965i
\(801\) −0.944390 0.343730i −0.0333684 0.0121451i
\(802\) −20.7400 + 9.27184i −0.732356 + 0.327400i
\(803\) −9.58749 + 1.69053i −0.338335 + 0.0596576i
\(804\) −0.529698 + 16.6160i −0.0186810 + 0.586000i
\(805\) −11.7271 6.77065i −0.413326 0.238634i
\(806\) 22.4887 + 10.9262i 0.792131 + 0.384859i
\(807\) −11.3812 9.54997i −0.400638 0.336175i
\(808\) 21.1196 40.1607i 0.742985 1.41285i
\(809\) −13.5158 23.4101i −0.475191 0.823055i 0.524405 0.851469i \(-0.324288\pi\)
−0.999596 + 0.0284141i \(0.990954\pi\)
\(810\) 0.280992 + 3.93250i 0.00987305 + 0.138174i
\(811\) 4.31964 + 11.8681i 0.151683 + 0.416746i 0.992140 0.125132i \(-0.0399355\pi\)
−0.840457 + 0.541878i \(0.817713\pi\)
\(812\) −2.92126 + 13.9518i −0.102516 + 0.489611i
\(813\) 27.8430 + 4.90947i 0.976496 + 0.172183i
\(814\) 1.39404 + 5.55522i 0.0488611 + 0.194711i
\(815\) −22.1008 + 18.5448i −0.774157 + 0.649595i
\(816\) −2.65099 + 2.77878i −0.0928033 + 0.0972767i
\(817\) −14.3277 36.7323i −0.501264 1.28510i
\(818\) 17.8435 + 26.3676i 0.623883 + 0.921921i
\(819\) −4.17189 4.97186i −0.145778 0.173731i
\(820\) −14.1235 12.6393i −0.493213 0.441384i
\(821\) −20.7600 3.66055i −0.724530 0.127754i −0.200792 0.979634i \(-0.564352\pi\)
−0.523738 + 0.851880i \(0.675463\pi\)
\(822\) −11.0163 11.3731i −0.384237 0.396681i
\(823\) 6.83501 2.48774i 0.238254 0.0867172i −0.220134 0.975470i \(-0.570649\pi\)
0.458387 + 0.888752i \(0.348427\pi\)
\(824\) 5.63829 17.6258i 0.196419 0.614025i
\(825\) −1.43019 2.47716i −0.0497929 0.0862438i
\(826\) −8.99854 0.931964i −0.313099 0.0324272i
\(827\) −27.7840 + 33.1117i −0.966144 + 1.15141i 0.0222897 + 0.999752i \(0.492904\pi\)
−0.988434 + 0.151654i \(0.951540\pi\)
\(828\) 4.59189 0.659582i 0.159579 0.0229221i
\(829\) −43.3631 25.0357i −1.50606 0.869525i −0.999975 0.00704309i \(-0.997758\pi\)
−0.506087 0.862482i \(-0.668909\pi\)
\(830\) −45.7668 33.1454i −1.58859 1.15049i
\(831\) −2.54148 14.4135i −0.0881630 0.499997i
\(832\) 24.0021 6.21732i 0.832122 0.215547i
\(833\) 2.35895 + 0.858587i 0.0817327 + 0.0297483i
\(834\) −19.4897 5.55656i −0.674874 0.192408i
\(835\) 53.2704i 1.84350i
\(836\) 1.48219 + 8.87357i 0.0512626 + 0.306899i
\(837\) 5.70436i 0.197172i
\(838\) 3.58117 12.5610i 0.123709 0.433913i
\(839\) 3.88712 + 1.41480i 0.134198 + 0.0488442i 0.408246 0.912872i \(-0.366140\pi\)
−0.274048 + 0.961716i \(0.588363\pi\)
\(840\) −0.651481 16.4995i −0.0224782 0.569287i
\(841\) 3.02442 + 17.1523i 0.104290 + 0.591459i
\(842\) 7.82918 10.8104i 0.269811 0.372552i
\(843\) 6.08818 + 3.51501i 0.209688 + 0.121064i
\(844\) −6.12992 42.6754i −0.211001 1.46895i
\(845\) 6.08273 7.24911i 0.209252 0.249377i
\(846\) −1.40562 + 13.5719i −0.0483262 + 0.466611i
\(847\) −10.4027 18.0179i −0.357439 0.619103i
\(848\) −6.11506 20.8468i −0.209992 0.715881i
\(849\) 27.4000 9.97278i 0.940365 0.342265i
\(850\) 2.70330 2.61850i 0.0927226 0.0898138i
\(851\) 8.96454 + 1.58069i 0.307300 + 0.0541854i
\(852\) 6.54090 + 5.85356i 0.224088 + 0.200540i
\(853\) 5.78741 + 6.89717i 0.198157 + 0.236155i 0.855968 0.517028i \(-0.172962\pi\)
−0.657811 + 0.753183i \(0.728517\pi\)
\(854\) 5.59479 3.78611i 0.191450 0.129558i
\(855\) −3.89424 + 11.5108i −0.133180 + 0.393661i
\(856\) 7.45358 + 34.2969i 0.254758 + 1.17225i
\(857\) 41.2490 34.6120i 1.40904 1.18233i 0.452126 0.891954i \(-0.350666\pi\)
0.956914 0.290371i \(-0.0937787\pi\)
\(858\) −4.38714 + 1.10092i −0.149775 + 0.0375848i
\(859\) 27.5318 + 4.85460i 0.939373 + 0.165637i 0.622313 0.782769i \(-0.286193\pi\)
0.317060 + 0.948405i \(0.397304\pi\)
\(860\) 49.3625 + 10.3357i 1.68325 + 0.352443i
\(861\) 2.43472 + 6.68934i 0.0829751 + 0.227972i
\(862\) 2.29330 0.163865i 0.0781102 0.00558126i
\(863\) −3.89150 6.74028i −0.132468 0.229442i 0.792159 0.610315i \(-0.208957\pi\)
−0.924627 + 0.380873i \(0.875624\pi\)
\(864\) 3.66897 + 4.30566i 0.124821 + 0.146481i
\(865\) −37.7473 31.6738i −1.28345 1.07694i
\(866\) 19.5562 40.2512i 0.664546 1.36779i
\(867\) −13.9241 8.03908i −0.472887 0.273022i
\(868\) 0.761244 23.8793i 0.0258383 0.810515i
\(869\) 6.06715 1.06980i 0.205814 0.0362906i
\(870\) 5.47620 + 12.2496i 0.185661 + 0.415301i
\(871\) −24.2082 8.81108i −0.820265 0.298552i
\(872\) 2.98635 + 2.31135i 0.101131 + 0.0782722i
\(873\) −16.3814 −0.554425
\(874\) 13.8364 + 3.60521i 0.468024 + 0.121948i
\(875\) 13.0084i 0.439765i
\(876\) −17.9263 + 5.88490i −0.605675 + 0.198832i
\(877\) 7.84447 21.5525i 0.264889 0.727777i −0.733931 0.679223i \(-0.762317\pi\)
0.998821 0.0485533i \(-0.0154611\pi\)
\(878\) 9.61371 4.29781i 0.324447 0.145044i
\(879\) 3.39131 + 19.2331i 0.114386 + 0.648716i
\(880\) −10.5410 4.61661i −0.355338 0.155626i
\(881\) 20.9027 36.2045i 0.704230 1.21976i −0.262739 0.964867i \(-0.584626\pi\)
0.966969 0.254895i \(-0.0820409\pi\)
\(882\) 1.61587 3.32585i 0.0544093 0.111987i
\(883\) −14.4098 + 17.1729i −0.484929 + 0.577915i −0.951920 0.306346i \(-0.900893\pi\)
0.466992 + 0.884262i \(0.345338\pi\)
\(884\) −2.80996 5.24624i −0.0945091 0.176450i
\(885\) −7.37496 + 4.25794i −0.247907 + 0.143129i
\(886\) −2.45985 34.4258i −0.0826402 1.15656i
\(887\) 13.7991 5.02246i 0.463328 0.168638i −0.0997995 0.995008i \(-0.531820\pi\)
0.563128 + 0.826370i \(0.309598\pi\)
\(888\) 4.20502 + 10.2727i 0.141111 + 0.344731i
\(889\) 3.98426 22.5959i 0.133628 0.757841i
\(890\) 3.84308 0.964392i 0.128820 0.0323265i
\(891\) −0.663337 0.790535i −0.0222226 0.0264839i
\(892\) 3.26397 8.14982i 0.109286 0.272876i
\(893\) −20.1902 + 36.8915i −0.675641 + 1.23453i
\(894\) −17.7068 26.1656i −0.592205 0.875110i
\(895\) −19.1949 + 16.1065i −0.641616 + 0.538380i
\(896\) −14.7842 18.5137i −0.493907 0.618499i
\(897\) −1.24832 + 7.07959i −0.0416803 + 0.236381i
\(898\) −14.2097 + 13.7639i −0.474184 + 0.459309i
\(899\) 6.64004 + 18.2434i 0.221458 + 0.608450i
\(900\) −3.42620 4.35798i −0.114207 0.145266i
\(901\) −4.51606 + 2.60735i −0.150452 + 0.0868634i
\(902\) 4.93467 + 0.511076i 0.164307 + 0.0170170i
\(903\) −14.5105 12.1758i −0.482880 0.405184i
\(904\) −21.6222 23.7949i −0.719145 0.791407i
\(905\) −28.0167 + 48.5263i −0.931306 + 1.61307i
\(906\) −7.01973 + 9.69276i −0.233215 + 0.322020i
\(907\) 2.60569 0.459453i 0.0865204 0.0152559i −0.130220 0.991485i \(-0.541568\pi\)
0.216741 + 0.976229i \(0.430457\pi\)
\(908\) 18.5760 29.9299i 0.616467 0.993257i
\(909\) −5.48689 + 15.0751i −0.181989 + 0.500010i
\(910\) 24.6077 + 7.01570i 0.815737 + 0.232568i
\(911\) −47.4044 −1.57058 −0.785289 0.619129i \(-0.787486\pi\)
−0.785289 + 0.619129i \(0.787486\pi\)
\(912\) 5.28850 + 16.6142i 0.175120 + 0.550151i
\(913\) 14.7913 0.489521
\(914\) −42.2955 12.0585i −1.39901 0.398861i
\(915\) 2.17494 5.97560i 0.0719014 0.197547i
\(916\) −26.7183 + 43.0488i −0.882798 + 1.42237i
\(917\) −25.2887 + 4.45908i −0.835107 + 0.147252i
\(918\) 0.796436 1.09971i 0.0262863 0.0362958i
\(919\) 20.6457 35.7593i 0.681037 1.17959i −0.293627 0.955920i \(-0.594863\pi\)
0.974665 0.223671i \(-0.0718042\pi\)
\(920\) −13.5358 + 12.2999i −0.446262 + 0.405514i
\(921\) 3.38762 + 2.84255i 0.111626 + 0.0936651i
\(922\) −34.7804 3.60216i −1.14543 0.118631i
\(923\) −11.7799 + 6.80112i −0.387740 + 0.223862i
\(924\) 2.67133 + 3.39781i 0.0878802 + 0.111780i
\(925\) −3.72040 10.2217i −0.122326 0.336088i
\(926\) 25.9262 25.1129i 0.851988 0.825261i
\(927\) −1.13614 + 6.44335i −0.0373156 + 0.211627i
\(928\) 16.7458 + 9.49932i 0.549708 + 0.311830i
\(929\) 31.3665 26.3196i 1.02910 0.863517i 0.0383565 0.999264i \(-0.487788\pi\)
0.990744 + 0.135747i \(0.0433433\pi\)
\(930\) −12.6044 18.6256i −0.413313 0.610758i
\(931\) 8.56086 7.52320i 0.280571 0.246563i
\(932\) −10.3263 + 25.7839i −0.338250 + 0.844578i
\(933\) 7.54458 + 8.99128i 0.246998 + 0.294361i
\(934\) −16.3603 + 4.10548i −0.535324 + 0.134335i
\(935\) −0.479649 + 2.72023i −0.0156862 + 0.0889609i
\(936\) −8.11272 + 3.32085i −0.265173 + 0.108545i
\(937\) −10.0588 + 3.66109i −0.328605 + 0.119603i −0.501054 0.865416i \(-0.667054\pi\)
0.172449 + 0.985018i \(0.444832\pi\)
\(938\) 1.75450 + 24.5544i 0.0572866 + 0.801731i
\(939\) −18.9273 + 10.9277i −0.617669 + 0.356611i
\(940\) −25.3988 47.4201i −0.828419 1.54667i
\(941\) −18.5931 + 22.1584i −0.606119 + 0.722345i −0.978618 0.205688i \(-0.934057\pi\)
0.372499 + 0.928033i \(0.378501\pi\)
\(942\) −11.9137 + 24.5212i −0.388170 + 0.798945i
\(943\) 3.94238 6.82841i 0.128382 0.222364i
\(944\) −4.90192 + 11.1924i −0.159544 + 0.364283i
\(945\) 1.01376 + 5.74931i 0.0329776 + 0.187025i
\(946\) −12.0515 + 5.38764i −0.391829 + 0.175167i
\(947\) 5.93940 16.3184i 0.193005 0.530276i −0.805010 0.593261i \(-0.797840\pi\)
0.998014 + 0.0629857i \(0.0200622\pi\)
\(948\) 11.3441 3.72408i 0.368441 0.120953i
\(949\) 29.2380i 0.949105i
\(950\) −4.53616 16.4732i −0.147173 0.534461i
\(951\) −5.83419 −0.189187
\(952\) −3.48075 + 4.49726i −0.112812 + 0.145757i
\(953\) −36.2901 13.2085i −1.17555 0.427865i −0.320922 0.947106i \(-0.603993\pi\)
−0.854628 + 0.519240i \(0.826215\pi\)
\(954\) 3.13480 + 7.01218i 0.101493 + 0.227028i
\(955\) −55.9038 + 9.85735i −1.80900 + 0.318976i
\(956\) −1.42963 + 44.8457i −0.0462375 + 1.45041i
\(957\) −3.04165 1.75610i −0.0983227 0.0567666i
\(958\) 7.04983 14.5102i 0.227770 0.468803i
\(959\) −17.9608 15.0709i −0.579983 0.486663i
\(960\) −21.4935 5.95168i −0.693700 0.192090i
\(961\) −0.769885 1.33348i −0.0248350 0.0430155i
\(962\) −17.1574 + 1.22596i −0.553176 + 0.0395264i
\(963\) −4.24408 11.6605i −0.136763 0.375754i
\(964\) 44.5238 + 9.32252i 1.43402 + 0.300258i
\(965\) 47.1637 + 8.31623i 1.51825 + 0.267709i
\(966\) 6.66276 1.67197i 0.214371 0.0537947i
\(967\) −4.53497 + 3.80529i −0.145835 + 0.122370i −0.712786 0.701381i \(-0.752567\pi\)
0.566952 + 0.823751i \(0.308123\pi\)
\(968\) −27.4596 + 5.96765i −0.882584 + 0.191807i
\(969\) 3.57565 2.17477i 0.114866 0.0698637i
\(970\) 53.4876 36.1962i 1.71738 1.16219i
\(971\) 12.2450 + 14.5931i 0.392962 + 0.468314i 0.925861 0.377865i \(-0.123342\pi\)
−0.532898 + 0.846179i \(0.678897\pi\)
\(972\) −1.49035 1.33374i −0.0478030 0.0427797i
\(973\) −29.5540 5.21117i −0.947459 0.167062i
\(974\) 23.0935 22.3691i 0.739964 0.716751i
\(975\) 8.07242 2.93812i 0.258524 0.0940952i
\(976\) −2.56823 8.75532i −0.0822071 0.280251i
\(977\) −29.4877 51.0742i −0.943394 1.63401i −0.758935 0.651167i \(-0.774280\pi\)
−0.184460 0.982840i \(-0.559054\pi\)
\(978\) 1.50772 14.5577i 0.0482114 0.465503i
\(979\) −0.666654 + 0.794487i −0.0213063 + 0.0253919i
\(980\) 2.07271 + 14.4298i 0.0662103 + 0.460944i
\(981\) −1.15626 0.667566i −0.0369165 0.0213138i
\(982\) 11.1787 15.4354i 0.356727 0.492564i
\(983\) 0.394039 + 2.23471i 0.0125679 + 0.0712761i 0.990447 0.137896i \(-0.0440341\pi\)
−0.977879 + 0.209172i \(0.932923\pi\)
\(984\) 9.60727 0.379342i 0.306268 0.0120930i
\(985\) 23.4381 + 8.53078i 0.746801 + 0.271813i
\(986\) 1.26702 4.44410i 0.0403502 0.141529i
\(987\) 20.2044i 0.643114i
\(988\) −27.0178 0.243889i −0.859551 0.00775915i
\(989\) 20.9807i 0.667148i
\(990\) 3.91266 + 1.11551i 0.124353 + 0.0354531i
\(991\) 32.4454 + 11.8092i 1.03066 + 0.375130i 0.801333 0.598219i \(-0.204125\pi\)
0.229329 + 0.973349i \(0.426347\pi\)
\(992\) −30.4057 10.8059i −0.965381 0.343088i
\(993\) −2.61488 14.8297i −0.0829806 0.470607i
\(994\) 10.5270 + 7.62391i 0.333897 + 0.241816i
\(995\) 55.3144 + 31.9358i 1.75358 + 1.01243i
\(996\) 28.3749 4.07580i 0.899094 0.129147i
\(997\) −4.29391 + 5.11729i −0.135990 + 0.162066i −0.829741 0.558148i \(-0.811512\pi\)
0.693752 + 0.720214i \(0.255957\pi\)
\(998\) −8.66833 0.897766i −0.274391 0.0284183i
\(999\) −1.96223 3.39869i −0.0620823 0.107530i
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 456.2.bk.a.253.37 yes 240
8.5 even 2 inner 456.2.bk.a.253.19 240
19.16 even 9 inner 456.2.bk.a.301.19 yes 240
152.149 even 18 inner 456.2.bk.a.301.37 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
456.2.bk.a.253.19 240 8.5 even 2 inner
456.2.bk.a.253.37 yes 240 1.1 even 1 trivial
456.2.bk.a.301.19 yes 240 19.16 even 9 inner
456.2.bk.a.301.37 yes 240 152.149 even 18 inner