Properties

Label 864.2.bt.a.11.17
Level $864$
Weight $2$
Character 864.11
Analytic conductor $6.899$
Analytic rank $0$
Dimension $3408$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [864,2,Mod(11,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(72))
 
chi = DirichletCharacter(H, H._module([36, 45, 52]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bt (of order \(72\), degree \(24\), 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: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(3408\)
Relative dimension: \(142\) over \(\Q(\zeta_{72})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{72}]$

Embedding invariants

Embedding label 11.17
Character \(\chi\) \(=\) 864.11
Dual form 864.2.bt.a.707.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.32493 + 0.494525i) q^{2} +(1.65521 + 0.510185i) q^{3} +(1.51089 - 1.31042i) q^{4} +(-1.77522 - 1.62669i) q^{5} +(-2.44534 + 0.142581i) q^{6} +(-2.52489 - 3.60592i) q^{7} +(-1.35379 + 2.48340i) q^{8} +(2.47942 + 1.68892i) q^{9} +O(q^{10})\) \(q+(-1.32493 + 0.494525i) q^{2} +(1.65521 + 0.510185i) q^{3} +(1.51089 - 1.31042i) q^{4} +(-1.77522 - 1.62669i) q^{5} +(-2.44534 + 0.142581i) q^{6} +(-2.52489 - 3.60592i) q^{7} +(-1.35379 + 2.48340i) q^{8} +(2.47942 + 1.68892i) q^{9} +(3.15648 + 1.27736i) q^{10} +(-4.87964 - 0.213050i) q^{11} +(3.16939 - 1.39819i) q^{12} +(1.16003 + 0.603872i) q^{13} +(5.12853 + 3.52898i) q^{14} +(-2.10844 - 3.59820i) q^{15} +(0.565577 - 3.95981i) q^{16} +(2.98248 + 5.16581i) q^{17} +(-4.12028 - 1.01157i) q^{18} +(-0.579709 + 4.40332i) q^{19} +(-4.81381 - 0.131457i) q^{20} +(-2.33953 - 7.25671i) q^{21} +(6.57055 - 2.13083i) q^{22} +(-4.83326 - 3.38429i) q^{23} +(-3.50779 + 3.41985i) q^{24} +(0.0695078 + 0.794478i) q^{25} +(-1.83559 - 0.226427i) q^{26} +(3.24230 + 4.06048i) q^{27} +(-8.54012 - 2.13947i) q^{28} +(-1.73049 + 5.48842i) q^{29} +(4.57294 + 3.72469i) q^{30} +(-7.05551 + 1.24408i) q^{31} +(1.20888 + 5.52618i) q^{32} +(-7.96813 - 2.84216i) q^{33} +(-6.50620 - 5.36943i) q^{34} +(-1.38347 + 10.5085i) q^{35} +(5.95934 - 0.697317i) q^{36} +(-1.08442 + 0.142766i) q^{37} +(-1.40948 - 6.12079i) q^{38} +(1.61200 + 1.59136i) q^{39} +(6.44298 - 2.20638i) q^{40} +(-8.76085 - 0.766475i) q^{41} +(6.68835 + 8.45769i) q^{42} +(0.148091 - 3.39184i) q^{43} +(-7.65179 + 6.07251i) q^{44} +(-1.65416 - 7.03145i) q^{45} +(8.07736 + 2.09378i) q^{46} +(-0.994210 - 0.175306i) q^{47} +(2.95638 - 6.26576i) q^{48} +(-4.23344 + 11.6313i) q^{49} +(-0.484983 - 1.01826i) q^{50} +(2.30111 + 10.0721i) q^{51} +(2.54400 - 0.607743i) q^{52} +(-3.87895 + 9.36461i) q^{53} +(-6.30383 - 3.77647i) q^{54} +(8.31587 + 8.31587i) q^{55} +(12.3731 - 1.38865i) q^{56} +(-3.20605 + 6.99266i) q^{57} +(-0.421377 - 8.12756i) q^{58} +(8.82988 - 9.63612i) q^{59} +(-7.90079 - 2.67352i) q^{60} +(-0.690281 - 3.11365i) q^{61} +(8.73284 - 5.13744i) q^{62} +(-0.170151 - 13.2050i) q^{63} +(-4.33451 - 6.72399i) q^{64} +(-1.07699 - 2.95900i) q^{65} +(11.9627 - 0.174766i) q^{66} +(-2.84139 - 1.47913i) q^{67} +(11.2756 + 3.89665i) q^{68} +(-6.27344 - 8.06756i) q^{69} +(-3.36372 - 14.6072i) q^{70} +(1.31286 - 4.89968i) q^{71} +(-7.55088 + 3.87094i) q^{72} +(-1.28514 - 4.79622i) q^{73} +(1.36618 - 0.725428i) q^{74} +(-0.290281 + 1.35049i) q^{75} +(4.89435 + 7.41260i) q^{76} +(11.5523 + 18.1335i) q^{77} +(-2.92276 - 1.31127i) q^{78} +(4.87418 + 4.08992i) q^{79} +(-7.44540 + 6.10952i) q^{80} +(3.29507 + 8.37511i) q^{81} +(11.9866 - 3.31693i) q^{82} +(-4.01268 + 12.7266i) q^{83} +(-13.0441 - 7.89831i) q^{84} +(3.10860 - 14.0220i) q^{85} +(1.48114 + 4.56719i) q^{86} +(-5.66443 + 8.20161i) q^{87} +(7.13509 - 11.8297i) q^{88} +(-2.74504 - 10.2446i) q^{89} +(5.66889 + 8.49817i) q^{90} +(-0.751430 - 5.70767i) q^{91} +(-11.7374 + 1.22034i) q^{92} +(-12.3130 - 1.54041i) q^{93} +(1.40395 - 0.259393i) q^{94} +(8.19194 - 6.87386i) q^{95} +(-0.818431 + 9.76372i) q^{96} +(4.29599 - 1.56361i) q^{97} +(-0.142939 - 17.5042i) q^{98} +(-11.7389 - 8.76959i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3408 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 36 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3408 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 36 q^{8} - 24 q^{9} - 12 q^{10} - 24 q^{11} - 24 q^{12} - 24 q^{13} - 24 q^{14} - 48 q^{15} - 24 q^{16} - 24 q^{18} - 12 q^{19} - 24 q^{20} - 24 q^{21} - 24 q^{22} - 24 q^{23} - 84 q^{24} - 24 q^{25} - 24 q^{27} - 48 q^{28} - 24 q^{29} - 24 q^{30} - 24 q^{32} - 48 q^{33} - 36 q^{35} - 24 q^{36} - 12 q^{37} - 24 q^{38} - 24 q^{39} - 24 q^{40} - 24 q^{41} + 96 q^{42} - 24 q^{43} - 36 q^{44} - 24 q^{45} - 12 q^{46} - 48 q^{47} - 24 q^{48} - 336 q^{50} + 12 q^{51} - 24 q^{52} - 24 q^{54} - 48 q^{55} - 24 q^{56} - 24 q^{57} - 132 q^{58} - 24 q^{59} - 24 q^{60} - 24 q^{61} - 36 q^{62} - 12 q^{64} - 48 q^{65} - 216 q^{66} - 24 q^{67} + 24 q^{68} - 24 q^{69} - 24 q^{70} - 36 q^{71} - 24 q^{72} - 12 q^{73} - 24 q^{74} - 24 q^{75} - 24 q^{76} - 24 q^{77} - 24 q^{78} - 48 q^{79} - 48 q^{82} + 96 q^{83} + 204 q^{84} + 36 q^{85} - 24 q^{86} - 24 q^{87} - 24 q^{88} - 36 q^{89} - 24 q^{90} - 12 q^{91} - 252 q^{92} - 24 q^{93} - 24 q^{94} - 24 q^{96} - 48 q^{97} - 36 q^{98} - 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{18}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32493 + 0.494525i −0.936868 + 0.349682i
\(3\) 1.65521 + 0.510185i 0.955634 + 0.294555i
\(4\) 1.51089 1.31042i 0.755445 0.655212i
\(5\) −1.77522 1.62669i −0.793902 0.727477i 0.172361 0.985034i \(-0.444860\pi\)
−0.966263 + 0.257557i \(0.917083\pi\)
\(6\) −2.44534 + 0.142581i −0.998304 + 0.0582085i
\(7\) −2.52489 3.60592i −0.954320 1.36291i −0.931725 0.363165i \(-0.881696\pi\)
−0.0225950 0.999745i \(-0.507193\pi\)
\(8\) −1.35379 + 2.48340i −0.478637 + 0.878013i
\(9\) 2.47942 + 1.68892i 0.826474 + 0.562975i
\(10\) 3.15648 + 1.27736i 0.998167 + 0.403937i
\(11\) −4.87964 0.213050i −1.47127 0.0642369i −0.706120 0.708092i \(-0.749556\pi\)
−0.765148 + 0.643855i \(0.777334\pi\)
\(12\) 3.16939 1.39819i 0.914925 0.403623i
\(13\) 1.16003 + 0.603872i 0.321733 + 0.167484i 0.614958 0.788560i \(-0.289173\pi\)
−0.293225 + 0.956044i \(0.594728\pi\)
\(14\) 5.12853 + 3.52898i 1.37066 + 0.943159i
\(15\) −2.10844 3.59820i −0.544398 0.929050i
\(16\) 0.565577 3.95981i 0.141394 0.989953i
\(17\) 2.98248 + 5.16581i 0.723357 + 1.25289i 0.959647 + 0.281209i \(0.0907354\pi\)
−0.236289 + 0.971683i \(0.575931\pi\)
\(18\) −4.12028 1.01157i −0.971160 0.238430i
\(19\) −0.579709 + 4.40332i −0.132994 + 1.01019i 0.786639 + 0.617413i \(0.211819\pi\)
−0.919633 + 0.392778i \(0.871514\pi\)
\(20\) −4.81381 0.131457i −1.07640 0.0293948i
\(21\) −2.33953 7.25671i −0.510528 1.58354i
\(22\) 6.57055 2.13083i 1.40085 0.454294i
\(23\) −4.83326 3.38429i −1.00781 0.705673i −0.0516899 0.998663i \(-0.516461\pi\)
−0.956115 + 0.292990i \(0.905350\pi\)
\(24\) −3.50779 + 3.41985i −0.716025 + 0.698074i
\(25\) 0.0695078 + 0.794478i 0.0139016 + 0.158896i
\(26\) −1.83559 0.226427i −0.359988 0.0444059i
\(27\) 3.24230 + 4.06048i 0.623980 + 0.781440i
\(28\) −8.54012 2.13947i −1.61393 0.404322i
\(29\) −1.73049 + 5.48842i −0.321344 + 1.01917i 0.645490 + 0.763769i \(0.276653\pi\)
−0.966834 + 0.255405i \(0.917791\pi\)
\(30\) 4.57294 + 3.72469i 0.834901 + 0.680032i
\(31\) −7.05551 + 1.24408i −1.26721 + 0.223443i −0.766539 0.642197i \(-0.778023\pi\)
−0.500667 + 0.865640i \(0.666912\pi\)
\(32\) 1.20888 + 5.52618i 0.213701 + 0.976899i
\(33\) −7.96813 2.84216i −1.38707 0.494757i
\(34\) −6.50620 5.36943i −1.11580 0.920850i
\(35\) −1.38347 + 10.5085i −0.233849 + 1.77626i
\(36\) 5.95934 0.697317i 0.993224 0.116220i
\(37\) −1.08442 + 0.142766i −0.178277 + 0.0234707i −0.219136 0.975694i \(-0.570324\pi\)
0.0408589 + 0.999165i \(0.486991\pi\)
\(38\) −1.40948 6.12079i −0.228648 0.992923i
\(39\) 1.61200 + 1.59136i 0.258126 + 0.254822i
\(40\) 6.44298 2.20638i 1.01872 0.348859i
\(41\) −8.76085 0.766475i −1.36821 0.119703i −0.620752 0.784007i \(-0.713173\pi\)
−0.747463 + 0.664304i \(0.768728\pi\)
\(42\) 6.68835 + 8.45769i 1.03203 + 1.30505i
\(43\) 0.148091 3.39184i 0.0225837 0.517251i −0.953700 0.300758i \(-0.902760\pi\)
0.976284 0.216493i \(-0.0694619\pi\)
\(44\) −7.65179 + 6.07251i −1.15355 + 0.915465i
\(45\) −1.65416 7.03145i −0.246588 1.04819i
\(46\) 8.07736 + 2.09378i 1.19094 + 0.308711i
\(47\) −0.994210 0.175306i −0.145020 0.0255710i 0.100667 0.994920i \(-0.467902\pi\)
−0.245687 + 0.969349i \(0.579014\pi\)
\(48\) 2.95638 6.26576i 0.426717 0.904385i
\(49\) −4.23344 + 11.6313i −0.604777 + 1.66161i
\(50\) −0.484983 1.01826i −0.0685869 0.144003i
\(51\) 2.30111 + 10.0721i 0.322219 + 1.41038i
\(52\) 2.54400 0.607743i 0.352789 0.0842788i
\(53\) −3.87895 + 9.36461i −0.532815 + 1.28633i 0.396837 + 0.917889i \(0.370108\pi\)
−0.929652 + 0.368439i \(0.879892\pi\)
\(54\) −6.30383 3.77647i −0.857843 0.513912i
\(55\) 8.31587 + 8.31587i 1.12131 + 1.12131i
\(56\) 12.3731 1.38865i 1.65343 0.185567i
\(57\) −3.20605 + 6.99266i −0.424651 + 0.926200i
\(58\) −0.421377 8.12756i −0.0553295 1.06720i
\(59\) 8.82988 9.63612i 1.14955 1.25452i 0.187316 0.982300i \(-0.440021\pi\)
0.962236 0.272216i \(-0.0877567\pi\)
\(60\) −7.90079 2.67352i −1.01999 0.345150i
\(61\) −0.690281 3.11365i −0.0883814 0.398663i 0.911540 0.411212i \(-0.134894\pi\)
−0.999921 + 0.0125491i \(0.996005\pi\)
\(62\) 8.73284 5.13744i 1.10907 0.652456i
\(63\) −0.170151 13.2050i −0.0214371 1.66367i
\(64\) −4.33451 6.72399i −0.541814 0.840498i
\(65\) −1.07699 2.95900i −0.133584 0.367019i
\(66\) 11.9627 0.174766i 1.47251 0.0215122i
\(67\) −2.84139 1.47913i −0.347131 0.180705i 0.279257 0.960216i \(-0.409912\pi\)
−0.626388 + 0.779512i \(0.715467\pi\)
\(68\) 11.2756 + 3.89665i 1.36737 + 0.472538i
\(69\) −6.27344 8.06756i −0.755234 0.971220i
\(70\) −3.36372 14.6072i −0.402041 1.74590i
\(71\) 1.31286 4.89968i 0.155808 0.581485i −0.843226 0.537559i \(-0.819347\pi\)
0.999035 0.0439262i \(-0.0139866\pi\)
\(72\) −7.55088 + 3.87094i −0.889880 + 0.456195i
\(73\) −1.28514 4.79622i −0.150415 0.561355i −0.999454 0.0330260i \(-0.989486\pi\)
0.849040 0.528329i \(-0.177181\pi\)
\(74\) 1.36618 0.725428i 0.158815 0.0843293i
\(75\) −0.290281 + 1.35049i −0.0335188 + 0.155941i
\(76\) 4.89435 + 7.41260i 0.561420 + 0.850284i
\(77\) 11.5523 + 18.1335i 1.31651 + 2.06651i
\(78\) −2.92276 1.31127i −0.330937 0.148472i
\(79\) 4.87418 + 4.08992i 0.548388 + 0.460152i 0.874395 0.485215i \(-0.161259\pi\)
−0.326007 + 0.945367i \(0.605703\pi\)
\(80\) −7.44540 + 6.10952i −0.832421 + 0.683065i
\(81\) 3.29507 + 8.37511i 0.366119 + 0.930568i
\(82\) 11.9866 3.31693i 1.32370 0.366294i
\(83\) −4.01268 + 12.7266i −0.440449 + 1.39693i 0.429180 + 0.903219i \(0.358803\pi\)
−0.869629 + 0.493706i \(0.835642\pi\)
\(84\) −13.0441 7.89831i −1.42323 0.861776i
\(85\) 3.10860 14.0220i 0.337175 1.52090i
\(86\) 1.48114 + 4.56719i 0.159715 + 0.492493i
\(87\) −5.66443 + 8.20161i −0.607291 + 0.879304i
\(88\) 7.13509 11.8297i 0.760604 1.26105i
\(89\) −2.74504 10.2446i −0.290974 1.08593i −0.944362 0.328907i \(-0.893320\pi\)
0.653388 0.757023i \(-0.273347\pi\)
\(90\) 5.66889 + 8.49817i 0.597553 + 0.895786i
\(91\) −0.751430 5.70767i −0.0787712 0.598327i
\(92\) −11.7374 + 1.22034i −1.22371 + 0.127229i
\(93\) −12.3130 1.54041i −1.27680 0.159733i
\(94\) 1.40395 0.259393i 0.144807 0.0267544i
\(95\) 8.19194 6.87386i 0.840476 0.705243i
\(96\) −0.818431 + 9.76372i −0.0835308 + 0.996505i
\(97\) 4.29599 1.56361i 0.436191 0.158761i −0.114585 0.993413i \(-0.536554\pi\)
0.550777 + 0.834653i \(0.314332\pi\)
\(98\) −0.142939 17.5042i −0.0144391 1.76819i
\(99\) −11.7389 8.76959i −1.17980 0.881377i
\(100\) 1.14612 + 1.10928i 0.114612 + 0.110928i
\(101\) 2.23175 3.50314i 0.222067 0.348575i −0.714153 0.699990i \(-0.753188\pi\)
0.936220 + 0.351414i \(0.114299\pi\)
\(102\) −8.02971 12.2069i −0.795060 1.20866i
\(103\) −2.92670 + 1.36474i −0.288377 + 0.134472i −0.561424 0.827528i \(-0.689746\pi\)
0.273047 + 0.962001i \(0.411968\pi\)
\(104\) −3.07008 + 2.06329i −0.301046 + 0.202322i
\(105\) −7.65121 + 16.6879i −0.746682 + 1.62858i
\(106\) 0.508309 14.3257i 0.0493713 1.39144i
\(107\) −4.84689 2.00765i −0.468567 0.194087i 0.135891 0.990724i \(-0.456610\pi\)
−0.604458 + 0.796637i \(0.706610\pi\)
\(108\) 10.2197 + 1.88616i 0.983392 + 0.181496i
\(109\) −2.09438 5.05629i −0.200606 0.484305i 0.791278 0.611457i \(-0.209416\pi\)
−0.991883 + 0.127152i \(0.959416\pi\)
\(110\) −15.1304 6.90555i −1.44262 0.658419i
\(111\) −1.86777 0.316946i −0.177281 0.0300832i
\(112\) −15.7068 + 7.95868i −1.48415 + 0.752025i
\(113\) −11.7506 4.27686i −1.10540 0.402333i −0.276096 0.961130i \(-0.589041\pi\)
−0.829304 + 0.558797i \(0.811263\pi\)
\(114\) 0.789752 10.8503i 0.0739671 1.01622i
\(115\) 3.07492 + 13.8701i 0.286738 + 1.29339i
\(116\) 4.57758 + 10.5601i 0.425017 + 0.980479i
\(117\) 1.85630 + 3.45645i 0.171615 + 0.319549i
\(118\) −6.93369 + 17.1338i −0.638297 + 1.57729i
\(119\) 11.0970 23.7977i 1.01726 2.18153i
\(120\) 11.7901 0.364901i 1.07629 0.0333107i
\(121\) 12.8074 + 1.12050i 1.16431 + 0.101864i
\(122\) 2.45435 + 3.78402i 0.222207 + 0.342589i
\(123\) −14.1100 5.73833i −1.27225 0.517408i
\(124\) −9.02983 + 11.1254i −0.810902 + 0.999088i
\(125\) −6.15991 + 8.02775i −0.550959 + 0.718024i
\(126\) 6.75562 + 17.4115i 0.601838 + 1.55114i
\(127\) −8.69021 5.01730i −0.771132 0.445213i 0.0621465 0.998067i \(-0.480205\pi\)
−0.833278 + 0.552854i \(0.813539\pi\)
\(128\) 9.06811 + 6.76530i 0.801516 + 0.597974i
\(129\) 1.97559 5.53865i 0.173941 0.487651i
\(130\) 2.89024 + 3.38788i 0.253491 + 0.297137i
\(131\) −11.8683 18.6295i −1.03694 1.62767i −0.739793 0.672834i \(-0.765077\pi\)
−0.297144 0.954833i \(-0.596034\pi\)
\(132\) −15.7634 + 6.14743i −1.37203 + 0.535065i
\(133\) 17.3417 9.02754i 1.50372 0.782787i
\(134\) 4.49611 + 0.554613i 0.388405 + 0.0479113i
\(135\) 0.849357 12.4824i 0.0731010 1.07432i
\(136\) −16.8664 + 0.413266i −1.44628 + 0.0354373i
\(137\) 0.834562 + 9.53909i 0.0713014 + 0.814979i 0.944692 + 0.327959i \(0.106361\pi\)
−0.873391 + 0.487020i \(0.838084\pi\)
\(138\) 12.3015 + 7.58659i 1.04717 + 0.645814i
\(139\) −4.18024 0.926737i −0.354563 0.0786048i 0.0355597 0.999368i \(-0.488679\pi\)
−0.390123 + 0.920763i \(0.627567\pi\)
\(140\) 11.6803 + 17.6901i 0.987168 + 1.49509i
\(141\) −1.55618 0.797399i −0.131054 0.0671531i
\(142\) 0.683557 + 7.14098i 0.0573628 + 0.599258i
\(143\) −5.53186 3.19382i −0.462597 0.267081i
\(144\) 8.09013 8.86283i 0.674177 0.738570i
\(145\) 12.0000 6.92818i 0.996542 0.575354i
\(146\) 4.07458 + 5.71913i 0.337214 + 0.473318i
\(147\) −12.9413 + 17.0923i −1.06738 + 1.40975i
\(148\) −1.45135 + 1.63675i −0.119300 + 0.134540i
\(149\) 1.75754 + 5.57420i 0.143983 + 0.456656i 0.997973 0.0636328i \(-0.0202686\pi\)
−0.853990 + 0.520289i \(0.825824\pi\)
\(150\) −0.283248 1.93286i −0.0231271 0.157817i
\(151\) 9.35798 + 4.36370i 0.761542 + 0.355113i 0.764281 0.644883i \(-0.223094\pi\)
−0.00273906 + 0.999996i \(0.500872\pi\)
\(152\) −10.1504 7.40082i −0.823306 0.600286i
\(153\) −1.32983 + 17.8454i −0.107510 + 1.44271i
\(154\) −24.2735 18.3128i −1.95602 1.47569i
\(155\) 14.5488 + 9.26860i 1.16859 + 0.744472i
\(156\) 4.52091 + 0.291969i 0.361962 + 0.0233763i
\(157\) 1.46220 0.0638408i 0.116696 0.00509505i 0.0148030 0.999890i \(-0.495288\pi\)
0.101893 + 0.994795i \(0.467510\pi\)
\(158\) −8.48052 3.00846i −0.674674 0.239341i
\(159\) −11.1982 + 13.5214i −0.888071 + 1.07232i
\(160\) 6.84334 11.7766i 0.541014 0.931025i
\(161\) 25.9733i 2.04699i
\(162\) −8.50745 9.46696i −0.668408 0.743794i
\(163\) 4.64869 + 11.2229i 0.364113 + 0.879047i 0.994690 + 0.102920i \(0.0328186\pi\)
−0.630576 + 0.776127i \(0.717181\pi\)
\(164\) −14.2411 + 10.3224i −1.11204 + 0.806042i
\(165\) 9.52185 + 18.0071i 0.741275 + 1.40185i
\(166\) −0.977092 18.8462i −0.0758370 1.46275i
\(167\) −7.06777 15.1569i −0.546921 1.17287i −0.964463 0.264217i \(-0.914886\pi\)
0.417543 0.908657i \(-0.362891\pi\)
\(168\) 21.1885 + 4.01406i 1.63473 + 0.309692i
\(169\) −6.47549 9.24796i −0.498115 0.711382i
\(170\) 2.81554 + 20.1155i 0.215942 + 1.54279i
\(171\) −8.87422 + 9.93862i −0.678629 + 0.760025i
\(172\) −4.22100 5.31876i −0.321848 0.405552i
\(173\) 18.8525 17.2752i 1.43333 1.31341i 0.558036 0.829816i \(-0.311555\pi\)
0.875295 0.483590i \(-0.160667\pi\)
\(174\) 3.44909 13.6678i 0.261475 1.03615i
\(175\) 2.68933 2.25661i 0.203294 0.170584i
\(176\) −3.60345 + 19.2020i −0.271620 + 1.44740i
\(177\) 19.5315 11.4449i 1.46808 0.860252i
\(178\) 8.70323 + 12.2160i 0.652334 + 0.915625i
\(179\) 6.80037 8.86242i 0.508284 0.662408i −0.466770 0.884379i \(-0.654582\pi\)
0.975053 + 0.221971i \(0.0712490\pi\)
\(180\) −11.7134 8.45610i −0.873069 0.630280i
\(181\) 5.56135 4.26738i 0.413372 0.317192i −0.381054 0.924553i \(-0.624439\pi\)
0.794426 + 0.607361i \(0.207772\pi\)
\(182\) 3.81818 + 7.19068i 0.283022 + 0.533009i
\(183\) 0.445982 5.50591i 0.0329679 0.407009i
\(184\) 14.9477 7.42130i 1.10196 0.547105i
\(185\) 2.15732 + 1.51057i 0.158609 + 0.111059i
\(186\) 17.0757 4.04817i 1.25205 0.296826i
\(187\) −13.4529 25.8427i −0.983770 1.88981i
\(188\) −1.73187 + 1.03797i −0.126309 + 0.0757016i
\(189\) 6.45533 21.9437i 0.469556 1.59617i
\(190\) −7.45447 + 13.1585i −0.540804 + 0.954619i
\(191\) −0.575064 0.482536i −0.0416102 0.0349151i 0.621745 0.783219i \(-0.286424\pi\)
−0.663356 + 0.748304i \(0.730868\pi\)
\(192\) −3.74404 13.3410i −0.270203 0.962803i
\(193\) 3.90013 + 22.1187i 0.280737 + 1.59214i 0.720126 + 0.693843i \(0.244084\pi\)
−0.439389 + 0.898297i \(0.644805\pi\)
\(194\) −4.91865 + 4.19615i −0.353138 + 0.301266i
\(195\) −0.273001 5.44723i −0.0195500 0.390084i
\(196\) 8.84565 + 23.1212i 0.631832 + 1.65151i
\(197\) 7.01023 5.37914i 0.499458 0.383248i −0.328086 0.944648i \(-0.606404\pi\)
0.827545 + 0.561400i \(0.189737\pi\)
\(198\) 19.8900 + 5.81394i 1.41352 + 0.413179i
\(199\) −13.8531 3.71193i −0.982020 0.263132i −0.268125 0.963384i \(-0.586404\pi\)
−0.713895 + 0.700252i \(0.753071\pi\)
\(200\) −2.06710 0.902940i −0.146166 0.0638475i
\(201\) −3.94845 3.89790i −0.278503 0.274937i
\(202\) −1.22452 + 5.74508i −0.0861570 + 0.404222i
\(203\) 24.1601 7.61766i 1.69571 0.534655i
\(204\) 16.6754 + 12.2024i 1.16751 + 0.854339i
\(205\) 14.3056 + 15.6118i 0.999147 + 1.09038i
\(206\) 3.20278 3.25552i 0.223148 0.226823i
\(207\) −6.26790 16.5541i −0.435649 1.15059i
\(208\) 3.04730 4.25195i 0.211292 0.294820i
\(209\) 3.76690 21.3631i 0.260562 1.47772i
\(210\) 1.88474 25.8941i 0.130059 1.78686i
\(211\) 18.1341 0.791751i 1.24840 0.0545064i 0.590143 0.807298i \(-0.299071\pi\)
0.658258 + 0.752792i \(0.271293\pi\)
\(212\) 6.41095 + 19.2320i 0.440306 + 1.32086i
\(213\) 4.67281 7.44018i 0.320175 0.509793i
\(214\) 7.41463 + 0.263088i 0.506854 + 0.0179843i
\(215\) −5.78036 + 5.78036i −0.394217 + 0.394217i
\(216\) −14.4732 + 2.55487i −0.984775 + 0.173837i
\(217\) 22.3004 + 22.3004i 1.51385 + 1.51385i
\(218\) 5.27538 + 5.66352i 0.357294 + 0.383582i
\(219\) 0.319780 8.59439i 0.0216088 0.580755i
\(220\) 23.4617 + 1.66705i 1.58179 + 0.112392i
\(221\) 0.340272 + 7.79350i 0.0228892 + 0.524248i
\(222\) 2.63141 0.503729i 0.176609 0.0338081i
\(223\) −14.5067 2.55791i −0.971437 0.171291i −0.334660 0.942339i \(-0.608622\pi\)
−0.636777 + 0.771048i \(0.719733\pi\)
\(224\) 16.8747 18.3121i 1.12749 1.22353i
\(225\) −1.16947 + 2.08724i −0.0779649 + 0.139149i
\(226\) 17.6837 0.144405i 1.17630 0.00960569i
\(227\) 0.286867 0.262866i 0.0190401 0.0174470i −0.666014 0.745939i \(-0.732001\pi\)
0.685054 + 0.728492i \(0.259779\pi\)
\(228\) 4.31936 + 14.7664i 0.286057 + 0.977930i
\(229\) 3.91652 + 12.4216i 0.258811 + 0.820843i 0.990295 + 0.138984i \(0.0443837\pi\)
−0.731484 + 0.681859i \(0.761172\pi\)
\(230\) −10.9332 16.8563i −0.720911 1.11147i
\(231\) 9.87005 + 35.9086i 0.649402 + 2.36261i
\(232\) −11.2872 11.7277i −0.741041 0.769959i
\(233\) 0.857656 3.20082i 0.0561869 0.209693i −0.932125 0.362136i \(-0.882048\pi\)
0.988312 + 0.152444i \(0.0487142\pi\)
\(234\) −4.16878 3.66157i −0.272521 0.239364i
\(235\) 1.47977 + 1.92848i 0.0965296 + 0.125800i
\(236\) 0.713568 26.1300i 0.0464493 1.70092i
\(237\) 5.98116 + 9.25640i 0.388518 + 0.601268i
\(238\) −2.93428 + 37.0181i −0.190201 + 2.39953i
\(239\) 19.3252 3.40755i 1.25004 0.220416i 0.490827 0.871257i \(-0.336695\pi\)
0.759214 + 0.650841i \(0.225583\pi\)
\(240\) −15.4407 + 6.31398i −0.996691 + 0.407566i
\(241\) −1.54020 + 1.83554i −0.0992132 + 0.118238i −0.813366 0.581752i \(-0.802368\pi\)
0.714153 + 0.699989i \(0.246812\pi\)
\(242\) −17.5230 + 4.84898i −1.12642 + 0.311705i
\(243\) 1.18117 + 15.5436i 0.0757723 + 0.997125i
\(244\) −5.12315 3.79983i −0.327976 0.243259i
\(245\) 26.4357 13.7616i 1.68892 0.879195i
\(246\) 21.5325 + 0.625158i 1.37286 + 0.0398586i
\(247\) −3.33152 + 4.75790i −0.211980 + 0.302738i
\(248\) 6.46213 19.2058i 0.410346 1.21957i
\(249\) −13.1347 + 19.0179i −0.832380 + 1.20521i
\(250\) 4.19154 13.6825i 0.265096 0.865354i
\(251\) −1.17606 1.53267i −0.0742323 0.0967414i 0.754761 0.656000i \(-0.227753\pi\)
−0.828994 + 0.559258i \(0.811086\pi\)
\(252\) −17.5612 19.7283i −1.10625 1.24276i
\(253\) 22.8636 + 17.5438i 1.43742 + 1.10297i
\(254\) 13.9951 + 2.35005i 0.878132 + 0.147455i
\(255\) 12.2992 21.6233i 0.770205 1.35411i
\(256\) −15.3602 4.47916i −0.960015 0.279947i
\(257\) −13.8561 16.5130i −0.864318 1.03005i −0.999232 0.0391969i \(-0.987520\pi\)
0.134913 0.990857i \(-0.456924\pi\)
\(258\) 0.121480 + 8.31531i 0.00756302 + 0.517689i
\(259\) 3.25284 + 3.54986i 0.202122 + 0.220577i
\(260\) −5.50476 3.05942i −0.341391 0.189737i
\(261\) −13.5601 + 10.6854i −0.839352 + 0.661413i
\(262\) 24.9374 + 18.8136i 1.54064 + 1.16231i
\(263\) −3.72996 + 2.61175i −0.229999 + 0.161047i −0.682896 0.730516i \(-0.739280\pi\)
0.452896 + 0.891563i \(0.350391\pi\)
\(264\) 17.8454 15.9403i 1.09831 0.981059i
\(265\) 22.1193 10.3144i 1.35878 0.633608i
\(266\) −18.5123 + 20.5368i −1.13506 + 1.25919i
\(267\) 0.683046 18.3575i 0.0418017 1.12346i
\(268\) −6.23132 + 1.48862i −0.380638 + 0.0909317i
\(269\) −6.93173 + 2.87122i −0.422635 + 0.175061i −0.583856 0.811857i \(-0.698457\pi\)
0.161221 + 0.986918i \(0.448457\pi\)
\(270\) 5.04754 + 16.9584i 0.307184 + 1.03206i
\(271\) 3.70365 0.224980 0.112490 0.993653i \(-0.464117\pi\)
0.112490 + 0.993653i \(0.464117\pi\)
\(272\) 22.1424 8.88840i 1.34258 0.538938i
\(273\) 1.66820 9.83075i 0.100964 0.594984i
\(274\) −5.82305 12.2259i −0.351784 0.738595i
\(275\) −0.169910 3.89158i −0.0102460 0.234671i
\(276\) −20.0504 3.96832i −1.20689 0.238865i
\(277\) −16.4970 + 25.8952i −0.991211 + 1.55589i −0.169858 + 0.985469i \(0.554331\pi\)
−0.821353 + 0.570421i \(0.806780\pi\)
\(278\) 5.99683 0.839370i 0.359666 0.0503420i
\(279\) −19.5947 8.83162i −1.17311 0.528735i
\(280\) −24.2239 17.6620i −1.44765 1.05551i
\(281\) 10.9940 23.5768i 0.655850 1.40647i −0.243784 0.969829i \(-0.578389\pi\)
0.899634 0.436645i \(-0.143833\pi\)
\(282\) 2.45617 + 0.286927i 0.146263 + 0.0170862i
\(283\) −15.8106 + 4.98505i −0.939841 + 0.296331i −0.731590 0.681745i \(-0.761221\pi\)
−0.208251 + 0.978075i \(0.566777\pi\)
\(284\) −4.43706 9.12328i −0.263291 0.541367i
\(285\) 17.0663 7.19825i 1.01092 0.426388i
\(286\) 8.90876 + 1.49595i 0.526786 + 0.0884575i
\(287\) 19.3564 + 33.5262i 1.14257 + 1.97899i
\(288\) −6.33597 + 15.7434i −0.373351 + 0.927690i
\(289\) −9.29036 + 16.0914i −0.546492 + 0.946552i
\(290\) −12.4730 + 15.1136i −0.732438 + 0.887503i
\(291\) 7.90848 0.396353i 0.463603 0.0232346i
\(292\) −8.22679 5.56247i −0.481436 0.325519i
\(293\) −5.86364 + 26.4492i −0.342558 + 1.54518i 0.425597 + 0.904913i \(0.360064\pi\)
−0.768154 + 0.640265i \(0.778825\pi\)
\(294\) 8.69378 29.0460i 0.507032 1.69400i
\(295\) −31.3499 + 2.74276i −1.82526 + 0.159690i
\(296\) 1.11353 2.88632i 0.0647225 0.167764i
\(297\) −14.9562 20.5045i −0.867844 1.18979i
\(298\) −5.08520 6.51629i −0.294578 0.377479i
\(299\) −3.56304 6.84454i −0.206056 0.395830i
\(300\) 1.33113 + 2.42083i 0.0768528 + 0.139767i
\(301\) −12.6046 + 8.03003i −0.726519 + 0.462843i
\(302\) −14.5567 1.15385i −0.837641 0.0663965i
\(303\) 5.48125 4.65982i 0.314890 0.267700i
\(304\) 17.1085 + 4.78596i 0.981238 + 0.274493i
\(305\) −3.83954 + 6.65029i −0.219852 + 0.380794i
\(306\) −7.06307 24.3016i −0.403769 1.38923i
\(307\) 24.7451 + 18.9876i 1.41228 + 1.08368i 0.983629 + 0.180207i \(0.0576767\pi\)
0.428648 + 0.903471i \(0.358990\pi\)
\(308\) 41.2169 + 12.2593i 2.34855 + 0.698539i
\(309\) −5.54057 + 0.765775i −0.315192 + 0.0435634i
\(310\) −23.8597 5.08553i −1.35514 0.288838i
\(311\) −1.94414 + 22.2216i −0.110242 + 1.26007i 0.716540 + 0.697546i \(0.245725\pi\)
−0.826782 + 0.562523i \(0.809831\pi\)
\(312\) −6.13428 + 1.84886i −0.347285 + 0.104671i
\(313\) −24.6288 11.4846i −1.39210 0.649148i −0.425389 0.905011i \(-0.639863\pi\)
−0.966713 + 0.255863i \(0.917640\pi\)
\(314\) −1.90574 + 0.807677i −0.107547 + 0.0455798i
\(315\) −21.1783 + 23.7185i −1.19326 + 1.33638i
\(316\) 12.7239 0.207820i 0.715774 0.0116908i
\(317\) −19.5979 + 4.34475i −1.10073 + 0.244025i −0.729135 0.684370i \(-0.760077\pi\)
−0.371593 + 0.928396i \(0.621188\pi\)
\(318\) 8.15012 23.4527i 0.457036 1.31516i
\(319\) 9.61349 26.4129i 0.538252 1.47884i
\(320\) −3.24313 + 18.9874i −0.181296 + 1.06143i
\(321\) −6.99834 5.79588i −0.390609 0.323495i
\(322\) −12.8445 34.4129i −0.715794 1.91776i
\(323\) −24.4757 + 10.1382i −1.36186 + 0.564102i
\(324\) 15.9534 + 8.33593i 0.886302 + 0.463107i
\(325\) −0.399132 + 0.963590i −0.0221399 + 0.0534503i
\(326\) −11.7092 12.5707i −0.648513 0.696228i
\(327\) −0.886997 9.43774i −0.0490510 0.521908i
\(328\) 13.7638 20.7190i 0.759979 1.14402i
\(329\) 1.87813 + 4.02767i 0.103545 + 0.222053i
\(330\) −21.5208 19.1494i −1.18468 1.05414i
\(331\) −12.2674 7.81517i −0.674275 0.429561i 0.155366 0.987857i \(-0.450344\pi\)
−0.829642 + 0.558296i \(0.811455\pi\)
\(332\) 10.6145 + 24.4868i 0.582548 + 1.34389i
\(333\) −2.92985 1.47752i −0.160555 0.0809677i
\(334\) 16.8598 + 16.5867i 0.922526 + 0.907581i
\(335\) 2.63800 + 7.24783i 0.144129 + 0.395992i
\(336\) −30.0584 + 5.15989i −1.63982 + 0.281495i
\(337\) −3.72483 4.43908i −0.202905 0.241812i 0.654991 0.755637i \(-0.272673\pi\)
−0.857895 + 0.513825i \(0.828228\pi\)
\(338\) 13.1529 + 9.05063i 0.715425 + 0.492289i
\(339\) −17.2676 13.0740i −0.937849 0.710084i
\(340\) −13.6780 25.2593i −0.741794 1.36988i
\(341\) 34.6934 4.56747i 1.87875 0.247343i
\(342\) 6.84285 17.5565i 0.370019 0.949348i
\(343\) 22.8663 6.12701i 1.23466 0.330827i
\(344\) 8.22280 + 4.95961i 0.443344 + 0.267404i
\(345\) −1.98667 + 24.5266i −0.106959 + 1.32047i
\(346\) −16.4353 + 32.2115i −0.883568 + 1.73170i
\(347\) −4.56266 1.01152i −0.244937 0.0543012i 0.0922616 0.995735i \(-0.470590\pi\)
−0.337198 + 0.941434i \(0.609479\pi\)
\(348\) 2.18924 + 19.8145i 0.117356 + 1.06217i
\(349\) 9.64209 + 3.04014i 0.516129 + 0.162735i 0.547553 0.836771i \(-0.315560\pi\)
−0.0314233 + 0.999506i \(0.510004\pi\)
\(350\) −2.44722 + 4.31980i −0.130810 + 0.230903i
\(351\) 1.30914 + 6.66820i 0.0698766 + 0.355922i
\(352\) −4.72153 27.2233i −0.251659 1.45101i
\(353\) 2.51557 2.99793i 0.133890 0.159564i −0.694934 0.719074i \(-0.744566\pi\)
0.828824 + 0.559510i \(0.189011\pi\)
\(354\) −20.2181 + 24.8225i −1.07458 + 1.31930i
\(355\) −10.3009 + 6.56238i −0.546713 + 0.348295i
\(356\) −17.5723 11.8814i −0.931329 0.629710i
\(357\) 30.5091 33.7286i 1.61471 1.78510i
\(358\) −4.62734 + 15.1051i −0.244563 + 0.798327i
\(359\) −0.225976 + 0.0605501i −0.0119266 + 0.00319571i −0.264777 0.964310i \(-0.585298\pi\)
0.252851 + 0.967505i \(0.418632\pi\)
\(360\) 19.7013 + 5.41116i 1.03835 + 0.285193i
\(361\) −0.700615 0.187729i −0.0368745 0.00988048i
\(362\) −5.25809 + 8.40421i −0.276359 + 0.441716i
\(363\) 20.6272 + 8.38880i 1.08265 + 0.440298i
\(364\) −8.61480 7.63898i −0.451538 0.400391i
\(365\) −5.52054 + 10.6049i −0.288958 + 0.555084i
\(366\) 2.13192 + 7.51551i 0.111437 + 0.392842i
\(367\) −21.5854 + 7.85644i −1.12675 + 0.410103i −0.837111 0.547033i \(-0.815757\pi\)
−0.289638 + 0.957136i \(0.593535\pi\)
\(368\) −16.1347 + 17.2248i −0.841081 + 0.897902i
\(369\) −20.4273 16.6968i −1.06340 0.869202i
\(370\) −3.60531 0.934554i −0.187431 0.0485852i
\(371\) 43.5620 9.65746i 2.26163 0.501390i
\(372\) −20.6222 + 13.8079i −1.06921 + 0.715907i
\(373\) −1.73907 1.59356i −0.0900456 0.0825116i 0.629307 0.777157i \(-0.283339\pi\)
−0.719352 + 0.694646i \(0.755561\pi\)
\(374\) 30.6040 + 27.5870i 1.58249 + 1.42649i
\(375\) −14.2916 + 10.1449i −0.738013 + 0.523880i
\(376\) 1.78130 2.23169i 0.0918637 0.115091i
\(377\) −5.32172 + 5.32172i −0.274083 + 0.274083i
\(378\) 2.29885 + 32.2663i 0.118240 + 1.65960i
\(379\) −7.09675 2.93957i −0.364536 0.150996i 0.192894 0.981220i \(-0.438213\pi\)
−0.557430 + 0.830224i \(0.688213\pi\)
\(380\) 3.36946 21.1206i 0.172849 1.08346i
\(381\) −11.8244 12.7383i −0.605780 0.652602i
\(382\) 1.00055 + 0.354944i 0.0511924 + 0.0181605i
\(383\) −27.8935 10.1524i −1.42529 0.518763i −0.489712 0.871884i \(-0.662898\pi\)
−0.935577 + 0.353122i \(0.885120\pi\)
\(384\) 11.5581 + 15.8244i 0.589819 + 0.807535i
\(385\) 8.98968 50.9830i 0.458157 2.59834i
\(386\) −16.1057 27.3771i −0.819757 1.39346i
\(387\) 6.09574 8.15970i 0.309864 0.414781i
\(388\) 4.44177 7.99201i 0.225497 0.405733i
\(389\) 26.3522 + 1.15056i 1.33611 + 0.0583358i 0.700488 0.713665i \(-0.252966\pi\)
0.635622 + 0.772000i \(0.280744\pi\)
\(390\) 3.05550 + 7.08220i 0.154721 + 0.358621i
\(391\) 3.06746 35.0613i 0.155128 1.77312i
\(392\) −23.1539 26.2596i −1.16945 1.32631i
\(393\) −10.1400 36.8907i −0.511496 1.86089i
\(394\) −6.62796 + 10.5937i −0.333912 + 0.533705i
\(395\) −1.99971 15.1893i −0.100616 0.764255i
\(396\) −29.2280 + 2.13302i −1.46876 + 0.107188i
\(397\) −1.65828 0.218317i −0.0832269 0.0109570i 0.0887977 0.996050i \(-0.471698\pi\)
−0.172025 + 0.985093i \(0.555031\pi\)
\(398\) 20.1901 1.93265i 1.01204 0.0968752i
\(399\) 33.3099 6.09495i 1.66758 0.305129i
\(400\) 3.18530 + 0.174100i 0.159265 + 0.00870502i
\(401\) −0.00121463 0.00688853i −6.06560e−5 0.000343997i 0.984777 0.173820i \(-0.0556111\pi\)
−0.984838 + 0.173476i \(0.944500\pi\)
\(402\) 7.15905 + 3.21185i 0.357061 + 0.160192i
\(403\) −8.93584 2.81746i −0.445126 0.140348i
\(404\) −1.21868 8.21739i −0.0606314 0.408831i
\(405\) 7.77422 20.2277i 0.386304 1.00512i
\(406\) −28.2434 + 22.0407i −1.40170 + 1.09386i
\(407\) 5.32199 0.465614i 0.263801 0.0230796i
\(408\) −28.1282 7.92094i −1.39255 0.392145i
\(409\) −19.9312 + 28.4647i −0.985536 + 1.40749i −0.0735393 + 0.997292i \(0.523429\pi\)
−0.911996 + 0.410198i \(0.865459\pi\)
\(410\) −26.6744 13.6101i −1.31735 0.672157i
\(411\) −3.48533 + 16.2149i −0.171918 + 0.799824i
\(412\) −2.63353 + 5.89720i −0.129745 + 0.290534i
\(413\) −57.0416 7.50967i −2.80683 0.369527i
\(414\) 16.4910 + 18.8334i 0.810486 + 0.925612i
\(415\) 27.8256 16.0651i 1.36590 0.788605i
\(416\) −1.93477 + 7.14052i −0.0948600 + 0.350093i
\(417\) −6.44635 3.66664i −0.315679 0.179556i
\(418\) 5.57373 + 30.1675i 0.272620 + 1.47554i
\(419\) 12.0957 23.2357i 0.590916 1.13514i −0.386197 0.922416i \(-0.626212\pi\)
0.977113 0.212722i \(-0.0682329\pi\)
\(420\) 10.3081 + 35.2400i 0.502985 + 1.71953i
\(421\) 0.150443 3.44571i 0.00733214 0.167934i −0.991847 0.127432i \(-0.959327\pi\)
0.999179 0.0405018i \(-0.0128957\pi\)
\(422\) −23.6349 + 10.0168i −1.15053 + 0.487609i
\(423\) −2.16899 2.11380i −0.105460 0.102777i
\(424\) −18.0048 22.3107i −0.874389 1.08350i
\(425\) −3.89681 + 2.72858i −0.189023 + 0.132356i
\(426\) −2.51179 + 12.1686i −0.121697 + 0.589568i
\(427\) −9.48471 + 10.3507i −0.458997 + 0.500907i
\(428\) −9.95399 + 3.31815i −0.481144 + 0.160389i
\(429\) −7.52694 8.10871i −0.363404 0.391492i
\(430\) 4.80005 10.5171i 0.231479 0.507181i
\(431\) 13.1247i 0.632197i −0.948726 0.316098i \(-0.897627\pi\)
0.948726 0.316098i \(-0.102373\pi\)
\(432\) 17.9125 10.5424i 0.861817 0.507220i
\(433\) 3.89901i 0.187375i 0.995602 + 0.0936873i \(0.0298654\pi\)
−0.995602 + 0.0936873i \(0.970135\pi\)
\(434\) −40.5747 18.5184i −1.94765 0.888914i
\(435\) 23.3971 5.34537i 1.12180 0.256291i
\(436\) −9.79027 4.89497i −0.468869 0.234426i
\(437\) 17.7040 19.3205i 0.846897 0.924226i
\(438\) 3.82646 + 11.5451i 0.182835 + 0.551647i
\(439\) −2.23924 + 1.56794i −0.106873 + 0.0748335i −0.625791 0.779991i \(-0.715224\pi\)
0.518918 + 0.854824i \(0.326335\pi\)
\(440\) −31.9095 + 9.39366i −1.52123 + 0.447825i
\(441\) −30.1408 + 21.6889i −1.43528 + 1.03280i
\(442\) −4.30492 10.1576i −0.204764 0.483147i
\(443\) −0.398933 + 9.13706i −0.0189539 + 0.434115i 0.965707 + 0.259635i \(0.0836022\pi\)
−0.984661 + 0.174480i \(0.944176\pi\)
\(444\) −3.23734 + 1.96871i −0.153637 + 0.0934307i
\(445\) −11.7918 + 22.6518i −0.558984 + 1.07380i
\(446\) 20.4853 3.78484i 0.970006 0.179217i
\(447\) 0.0652177 + 10.1231i 0.00308469 + 0.478808i
\(448\) −13.3020 + 32.6073i −0.628460 + 1.54055i
\(449\) 4.79013 2.76558i 0.226060 0.130516i −0.382693 0.923876i \(-0.625003\pi\)
0.608753 + 0.793360i \(0.291670\pi\)
\(450\) 0.517281 3.34379i 0.0243848 0.157628i
\(451\) 42.5865 + 5.60662i 2.00532 + 0.264006i
\(452\) −23.3583 + 8.93636i −1.09868 + 0.420331i
\(453\) 13.2631 + 11.9971i 0.623155 + 0.563674i
\(454\) −0.250086 + 0.490142i −0.0117371 + 0.0230035i
\(455\) −7.95065 + 11.3547i −0.372732 + 0.532317i
\(456\) −13.0252 17.4285i −0.609962 0.816163i
\(457\) 25.6433 2.24349i 1.19954 0.104946i 0.530181 0.847884i \(-0.322124\pi\)
0.669360 + 0.742938i \(0.266568\pi\)
\(458\) −11.3319 14.5210i −0.529506 0.678521i
\(459\) −11.3056 + 28.8594i −0.527700 + 1.34704i
\(460\) 22.8215 + 16.9267i 1.06406 + 0.789211i
\(461\) 1.16486 + 0.367280i 0.0542531 + 0.0171060i 0.327711 0.944778i \(-0.393723\pi\)
−0.273458 + 0.961884i \(0.588167\pi\)
\(462\) −30.8348 42.6954i −1.43457 1.98637i
\(463\) −2.55023 14.4631i −0.118519 0.672155i −0.984947 0.172854i \(-0.944701\pi\)
0.866428 0.499301i \(-0.166410\pi\)
\(464\) 20.7544 + 9.95655i 0.963499 + 0.462221i
\(465\) 19.3526 + 22.7640i 0.897453 + 1.05566i
\(466\) 0.446548 + 4.66500i 0.0206859 + 0.216102i
\(467\) 36.9571 + 4.86549i 1.71017 + 0.225148i 0.921147 0.389216i \(-0.127254\pi\)
0.789023 + 0.614364i \(0.210587\pi\)
\(468\) 7.33408 + 2.78977i 0.339018 + 0.128957i
\(469\) 1.84056 + 13.9805i 0.0849893 + 0.645558i
\(470\) −2.91428 1.82331i −0.134425 0.0841032i
\(471\) 2.45281 + 0.640320i 0.113019 + 0.0295044i
\(472\) 11.9765 + 34.9734i 0.551264 + 1.60978i
\(473\) −1.44526 + 16.5194i −0.0664532 + 0.759564i
\(474\) −12.5022 9.30627i −0.574243 0.427451i
\(475\) −3.53864 0.154500i −0.162364 0.00708896i
\(476\) −14.4187 50.4975i −0.660878 2.31455i
\(477\) −25.4337 + 16.6676i −1.16453 + 0.763156i
\(478\) −23.9194 + 14.0716i −1.09405 + 0.643618i
\(479\) 5.20502 29.5191i 0.237823 1.34876i −0.598762 0.800927i \(-0.704340\pi\)
0.836585 0.547836i \(-0.184548\pi\)
\(480\) 17.3354 16.0014i 0.791250 0.730360i
\(481\) −1.34417 0.489237i −0.0612887 0.0223073i
\(482\) 1.13294 3.19364i 0.0516041 0.145466i
\(483\) −13.2512 + 42.9913i −0.602951 + 1.95617i
\(484\) 20.8189 15.0902i 0.946313 0.685916i
\(485\) −10.1698 4.21248i −0.461788 0.191279i
\(486\) −9.25170 20.0102i −0.419665 0.907679i
\(487\) −26.6113 + 26.6113i −1.20587 + 1.20587i −0.233520 + 0.972352i \(0.575024\pi\)
−0.972352 + 0.233520i \(0.924976\pi\)
\(488\) 8.66693 + 2.50099i 0.392334 + 0.113215i
\(489\) 1.96877 + 20.9480i 0.0890311 + 0.947299i
\(490\) −28.2201 + 31.3063i −1.27485 + 1.41427i
\(491\) 19.0401 + 17.4471i 0.859269 + 0.787375i 0.978663 0.205472i \(-0.0658730\pi\)
−0.119394 + 0.992847i \(0.538095\pi\)
\(492\) −28.8383 + 9.82008i −1.30013 + 0.442723i
\(493\) −33.5133 + 7.42971i −1.50936 + 0.334618i
\(494\) 2.06114 7.95142i 0.0927349 0.357751i
\(495\) 6.57368 + 34.6634i 0.295465 + 1.55800i
\(496\) 0.935878 + 28.6421i 0.0420222 + 1.28607i
\(497\) −20.9827 + 7.63708i −0.941202 + 0.342570i
\(498\) 7.99778 31.6929i 0.358389 1.42019i
\(499\) 6.90107 13.2568i 0.308934 0.593457i −0.681440 0.731874i \(-0.738646\pi\)
0.990374 + 0.138417i \(0.0442015\pi\)
\(500\) 1.21281 + 20.2011i 0.0542386 + 0.903423i
\(501\) −3.96581 28.6937i −0.177179 1.28194i
\(502\) 2.31614 + 1.44909i 0.103375 + 0.0646762i
\(503\) −8.09049 2.16784i −0.360737 0.0966592i 0.0738981 0.997266i \(-0.476456\pi\)
−0.434635 + 0.900607i \(0.643123\pi\)
\(504\) 33.0235 + 17.4542i 1.47098 + 0.777470i
\(505\) −9.66035 + 2.58848i −0.429880 + 0.115186i
\(506\) −38.9686 11.9378i −1.73236 0.530699i
\(507\) −6.00011 18.6110i −0.266474 0.826543i
\(508\) −19.7047 + 3.80728i −0.874256 + 0.168921i
\(509\) 11.9009 7.58173i 0.527499 0.336054i −0.246601 0.969117i \(-0.579314\pi\)
0.774100 + 0.633063i \(0.218203\pi\)
\(510\) −5.60230 + 34.7317i −0.248074 + 1.53795i
\(511\) −14.0499 + 16.7441i −0.621532 + 0.740713i
\(512\) 22.5663 1.66145i 0.997301 0.0734263i
\(513\) −19.7592 + 11.9230i −0.872391 + 0.526412i
\(514\) 26.5245 + 15.0265i 1.16994 + 0.662789i
\(515\) 7.41555 + 2.33811i 0.326768 + 0.103030i
\(516\) −4.27308 10.9571i −0.188112 0.482361i
\(517\) 4.81404 + 1.06725i 0.211721 + 0.0469375i
\(518\) −6.06529 3.09471i −0.266494 0.135974i
\(519\) 40.0184 18.9757i 1.75661 0.832941i
\(520\) 8.80640 + 1.33128i 0.386186 + 0.0583803i
\(521\) −22.3705 + 5.99416i −0.980070 + 0.262609i −0.713074 0.701089i \(-0.752698\pi\)
−0.266996 + 0.963698i \(0.586031\pi\)
\(522\) 12.6821 20.8633i 0.555078 0.913163i
\(523\) 5.24623 0.690680i 0.229402 0.0302013i −0.0149488 0.999888i \(-0.504759\pi\)
0.244351 + 0.969687i \(0.421425\pi\)
\(524\) −42.3442 12.5946i −1.84982 0.550198i
\(525\) 5.60268 2.36311i 0.244521 0.103134i
\(526\) 3.65037 5.30494i 0.159164 0.231307i
\(527\) −27.4696 32.7369i −1.19659 1.42604i
\(528\) −15.7610 + 29.9448i −0.685910 + 1.30318i
\(529\) 4.04058 + 11.1014i 0.175677 + 0.482669i
\(530\) −24.2058 + 24.6044i −1.05143 + 1.06875i
\(531\) 38.1677 8.97903i 1.65634 0.389657i
\(532\) 14.3716 36.3647i 0.623086 1.57661i
\(533\) −9.69997 6.17956i −0.420152 0.267666i
\(534\) 8.17324 + 24.6602i 0.353691 + 1.06715i
\(535\) 5.33847 + 11.4484i 0.230802 + 0.494957i
\(536\) 7.51991 5.05386i 0.324811 0.218293i
\(537\) 15.7775 11.1997i 0.680849 0.483302i
\(538\) 7.76419 7.23209i 0.334738 0.311797i
\(539\) 23.1357 55.8546i 0.996526 2.40583i
\(540\) −15.0740 19.9726i −0.648682 0.859485i
\(541\) 24.1150 9.98876i 1.03678 0.429450i 0.201628 0.979462i \(-0.435377\pi\)
0.835157 + 0.550012i \(0.185377\pi\)
\(542\) −4.90708 + 1.83155i −0.210777 + 0.0786716i
\(543\) 11.3823 4.22607i 0.488463 0.181358i
\(544\) −24.9417 + 22.7265i −1.06937 + 0.974392i
\(545\) −4.50702 + 12.3829i −0.193059 + 0.530427i
\(546\) 2.65130 + 13.8500i 0.113465 + 0.592727i
\(547\) 32.1056 7.11765i 1.37274 0.304329i 0.532446 0.846464i \(-0.321273\pi\)
0.840291 + 0.542135i \(0.182384\pi\)
\(548\) 13.7612 + 13.3189i 0.587848 + 0.568954i
\(549\) 3.54723 8.88590i 0.151392 0.379241i
\(550\) 2.14960 + 5.07205i 0.0916594 + 0.216273i
\(551\) −23.1641 10.8016i −0.986825 0.460164i
\(552\) 28.5279 4.65767i 1.21423 0.198244i
\(553\) 2.44115 27.9025i 0.103808 1.18654i
\(554\) 9.05165 42.4675i 0.384568 1.80427i
\(555\) 2.80014 + 3.60093i 0.118859 + 0.152851i
\(556\) −7.53030 + 4.07769i −0.319356 + 0.172933i
\(557\) −14.9614 11.4803i −0.633937 0.486437i 0.241095 0.970501i \(-0.422493\pi\)
−0.875032 + 0.484065i \(0.839160\pi\)
\(558\) 30.3291 + 2.01121i 1.28394 + 0.0851414i
\(559\) 2.22003 3.84520i 0.0938971 0.162635i
\(560\) 40.8293 + 11.4217i 1.72535 + 0.482653i
\(561\) −9.08271 49.6385i −0.383472 2.09574i
\(562\) −2.90704 + 36.6745i −0.122626 + 1.54702i
\(563\) −14.2868 + 9.10169i −0.602117 + 0.383591i −0.802960 0.596033i \(-0.796743\pi\)
0.200843 + 0.979623i \(0.435632\pi\)
\(564\) −3.39615 + 0.834481i −0.143004 + 0.0351380i
\(565\) 13.9027 + 26.7068i 0.584891 + 1.12357i
\(566\) 18.4827 14.4236i 0.776886 0.606268i
\(567\) 21.8803 33.0280i 0.918885 1.38705i
\(568\) 10.3905 + 9.89349i 0.435976 + 0.415122i
\(569\) −13.3809 + 1.17068i −0.560958 + 0.0490775i −0.364109 0.931356i \(-0.618626\pi\)
−0.196849 + 0.980434i \(0.563071\pi\)
\(570\) −19.0520 + 17.9769i −0.798000 + 0.752970i
\(571\) −7.40718 + 33.4116i −0.309981 + 1.39823i 0.526471 + 0.850193i \(0.323515\pi\)
−0.836452 + 0.548040i \(0.815374\pi\)
\(572\) −12.5433 + 2.42357i −0.524461 + 0.101335i
\(573\) −0.705668 1.09209i −0.0294797 0.0456226i
\(574\) −42.2254 34.8477i −1.76245 1.45452i
\(575\) 2.35279 4.07516i 0.0981183 0.169946i
\(576\) 0.609218 23.9923i 0.0253841 0.999678i
\(577\) 11.9477 + 20.6941i 0.497390 + 0.861506i 0.999995 0.00301061i \(-0.000958307\pi\)
−0.502605 + 0.864516i \(0.667625\pi\)
\(578\) 4.35151 25.9143i 0.180999 1.07789i
\(579\) −4.82912 + 38.6009i −0.200691 + 1.60420i
\(580\) 9.05176 26.1927i 0.375854 1.08759i
\(581\) 56.0227 17.6639i 2.32421 0.732822i
\(582\) −10.2822 + 4.43608i −0.426211 + 0.183882i
\(583\) 20.9230 44.8696i 0.866543 1.85831i
\(584\) 13.6507 + 3.30155i 0.564871 + 0.136619i
\(585\) 2.32722 9.15558i 0.0962187 0.378537i
\(586\) −5.31085 37.9431i −0.219389 1.56741i
\(587\) 2.49803 3.92113i 0.103105 0.161842i −0.787948 0.615742i \(-0.788856\pi\)
0.891053 + 0.453900i \(0.149968\pi\)
\(588\) 2.84530 + 42.7833i 0.117338 + 1.76435i
\(589\) −1.38793 31.7889i −0.0571888 1.30984i
\(590\) 40.1802 19.1373i 1.65419 0.787870i
\(591\) 14.3477 5.32708i 0.590187 0.219127i
\(592\) −0.0479937 + 4.37484i −0.00197253 + 0.179805i
\(593\) 14.1608 0.581514 0.290757 0.956797i \(-0.406093\pi\)
0.290757 + 0.956797i \(0.406093\pi\)
\(594\) 29.9559 + 19.7708i 1.22910 + 0.811208i
\(595\) −58.4111 + 24.1947i −2.39462 + 0.991884i
\(596\) 9.96002 + 6.11888i 0.407978 + 0.250639i
\(597\) −21.0360 13.2117i −0.860946 0.540717i
\(598\) 8.10558 + 7.30653i 0.331462 + 0.298786i
\(599\) −32.7266 + 15.2607i −1.33717 + 0.623535i −0.953907 0.300103i \(-0.902979\pi\)
−0.383268 + 0.923637i \(0.625201\pi\)
\(600\) −2.96082 2.54916i −0.120875 0.104069i
\(601\) 22.4386 15.7117i 0.915292 0.640894i −0.0180680 0.999837i \(-0.505752\pi\)
0.933360 + 0.358943i \(0.116863\pi\)
\(602\) 12.7292 16.8726i 0.518804 0.687674i
\(603\) −4.54686 8.46628i −0.185162 0.344774i
\(604\) 19.8572 5.66986i 0.807977 0.230703i
\(605\) −20.9132 22.8228i −0.850242 0.927877i
\(606\) −4.95789 + 8.88456i −0.201400 + 0.360911i
\(607\) 3.77619 + 4.50029i 0.153271 + 0.182661i 0.837216 0.546872i \(-0.184182\pi\)
−0.683945 + 0.729533i \(0.739737\pi\)
\(608\) −25.0343 + 2.11950i −1.01528 + 0.0859571i
\(609\) 43.8764 0.282671i 1.77796 0.0114544i
\(610\) 1.79840 10.7099i 0.0728152 0.433632i
\(611\) −1.04745 0.803735i −0.0423752 0.0325156i
\(612\) 21.3758 + 28.7051i 0.864066 + 1.16033i
\(613\) 10.9447 + 14.2633i 0.442050 + 0.576091i 0.960240 0.279174i \(-0.0900607\pi\)
−0.518190 + 0.855265i \(0.673394\pi\)
\(614\) −42.1754 12.9202i −1.70206 0.521416i
\(615\) 15.7138 + 33.1393i 0.633643 + 1.33631i
\(616\) −60.6722 + 4.14004i −2.44455 + 0.166807i
\(617\) 24.5917 35.1205i 0.990023 1.41390i 0.0812089 0.996697i \(-0.474122\pi\)
0.908814 0.417202i \(-0.136989\pi\)
\(618\) 6.96219 3.75455i 0.280060 0.151030i
\(619\) −30.3335 + 15.7906i −1.21921 + 0.634679i −0.945025 0.326998i \(-0.893963\pi\)
−0.274183 + 0.961678i \(0.588407\pi\)
\(620\) 34.1274 5.06125i 1.37059 0.203265i
\(621\) −1.92902 30.5983i −0.0774091 1.22787i
\(622\) −8.41327 30.4035i −0.337342 1.21907i
\(623\) −30.0104 + 35.7650i −1.20234 + 1.43290i
\(624\) 7.21320 5.48318i 0.288759 0.219503i
\(625\) 27.9208 4.92319i 1.11683 0.196928i
\(626\) 38.3109 + 3.03675i 1.53121 + 0.121373i
\(627\) 17.1342 33.4386i 0.684272 1.33541i
\(628\) 2.12556 2.01255i 0.0848190 0.0803096i
\(629\) −3.97176 5.17610i −0.158364 0.206384i
\(630\) 16.3304 41.8985i 0.650619 1.66928i
\(631\) 0.503283 1.87828i 0.0200354 0.0747730i −0.955184 0.296012i \(-0.904343\pi\)
0.975220 + 0.221239i \(0.0710100\pi\)
\(632\) −16.7555 + 6.56763i −0.666498 + 0.261246i
\(633\) 30.4196 + 7.94122i 1.20907 + 0.315635i
\(634\) 23.8173 15.4481i 0.945905 0.613524i
\(635\) 7.26545 + 23.0431i 0.288321 + 0.914436i
\(636\) 0.799589 + 35.1037i 0.0317058 + 1.39195i
\(637\) −11.9347 + 10.9361i −0.472870 + 0.433306i
\(638\) 0.324593 + 39.7494i 0.0128508 + 1.57369i
\(639\) 11.5303 9.93104i 0.456133 0.392866i
\(640\) −5.09284 26.7609i −0.201312 1.05782i
\(641\) −22.2808 3.92870i −0.880038 0.155175i −0.284668 0.958626i \(-0.591883\pi\)
−0.595370 + 0.803452i \(0.702995\pi\)
\(642\) 12.1385 + 4.21830i 0.479070 + 0.166483i
\(643\) 1.44322 + 33.0552i 0.0569151 + 1.30357i 0.785606 + 0.618727i \(0.212351\pi\)
−0.728691 + 0.684843i \(0.759871\pi\)
\(644\) 34.0361 + 39.2429i 1.34121 + 1.54638i
\(645\) −12.5168 + 6.61864i −0.492847 + 0.260609i
\(646\) 27.4150 25.5362i 1.07863 1.00471i
\(647\) −10.6613 10.6613i −0.419139 0.419139i 0.465768 0.884907i \(-0.345778\pi\)
−0.884907 + 0.465768i \(0.845778\pi\)
\(648\) −25.2596 3.15516i −0.992289 0.123946i
\(649\) −45.1396 + 45.1396i −1.77189 + 1.77189i
\(650\) 0.0523034 1.47407i 0.00205151 0.0578178i
\(651\) 25.5345 + 48.2892i 1.00078 + 1.89260i
\(652\) 21.7304 + 10.8649i 0.851030 + 0.425500i
\(653\) 3.49644 0.152658i 0.136826 0.00597397i 0.0248962 0.999690i \(-0.492074\pi\)
0.111930 + 0.993716i \(0.464297\pi\)
\(654\) 5.84241 + 12.0657i 0.228456 + 0.471807i
\(655\) −9.23555 + 52.3774i −0.360863 + 2.04656i
\(656\) −7.99003 + 34.2578i −0.311958 + 1.33754i
\(657\) 4.91403 14.0624i 0.191715 0.548625i
\(658\) −4.48018 4.40761i −0.174656 0.171826i
\(659\) −24.4560 26.6890i −0.952671 1.03966i −0.999170 0.0407393i \(-0.987029\pi\)
0.0464991 0.998918i \(-0.485194\pi\)
\(660\) 37.9834 + 14.7291i 1.47850 + 0.573329i
\(661\) 7.97612 2.51486i 0.310235 0.0978167i −0.141584 0.989926i \(-0.545220\pi\)
0.451819 + 0.892109i \(0.350775\pi\)
\(662\) 20.1182 + 4.28805i 0.781917 + 0.166660i
\(663\) −3.41291 + 13.0735i −0.132546 + 0.507731i
\(664\) −26.1729 27.1942i −1.01570 1.05534i
\(665\) −45.4704 12.1837i −1.76327 0.472465i
\(666\) 4.61253 + 0.508730i 0.178732 + 0.0197129i
\(667\) 26.9383 20.6705i 1.04306 0.800365i
\(668\) −30.5406 13.6386i −1.18165 0.527693i
\(669\) −22.7065 11.6350i −0.877884 0.449833i
\(670\) −7.07940 8.29833i −0.273501 0.320593i
\(671\) 2.70496 + 15.3406i 0.104424 + 0.592217i
\(672\) 37.2736 21.7011i 1.43786 0.837140i
\(673\) −13.0418 10.9434i −0.502725 0.421837i 0.355835 0.934549i \(-0.384196\pi\)
−0.858561 + 0.512712i \(0.828641\pi\)
\(674\) 7.13039 + 4.03946i 0.274652 + 0.155594i
\(675\) −3.00060 + 2.85817i −0.115493 + 0.110011i
\(676\) −21.9025 5.48701i −0.842404 0.211039i
\(677\) 13.9547 + 26.8067i 0.536323 + 1.03027i 0.990260 + 0.139233i \(0.0444636\pi\)
−0.453937 + 0.891034i \(0.649981\pi\)
\(678\) 29.3439 + 8.78294i 1.12694 + 0.337307i
\(679\) −16.4852 11.5430i −0.632643 0.442981i
\(680\) 30.6138 + 26.7027i 1.17398 + 1.02400i
\(681\) 0.608935 0.288742i 0.0233344 0.0110646i
\(682\) −43.7077 + 23.2083i −1.67365 + 0.888694i
\(683\) −20.2869 + 15.5667i −0.776258 + 0.595644i −0.919065 0.394107i \(-0.871054\pi\)
0.142806 + 0.989751i \(0.454387\pi\)
\(684\) −0.384167 + 26.6452i −0.0146890 + 1.01880i
\(685\) 14.0356 18.2915i 0.536272 0.698883i
\(686\) −27.2663 + 19.4258i −1.04103 + 0.741681i
\(687\) 0.145332 + 22.5585i 0.00554475 + 0.860660i
\(688\) −13.3473 2.50476i −0.508861 0.0954931i
\(689\) −10.1547 + 8.52081i −0.386864 + 0.324617i
\(690\) −9.49682 33.4785i −0.361538 1.27451i
\(691\) −25.1264 + 23.0241i −0.955852 + 0.875877i −0.992350 0.123457i \(-0.960602\pi\)
0.0364981 + 0.999334i \(0.488380\pi\)
\(692\) 5.84631 50.8057i 0.222243 1.93134i
\(693\) −1.98303 + 64.4717i −0.0753293 + 2.44908i
\(694\) 6.54544 0.916159i 0.248462 0.0347769i
\(695\) 5.91332 + 8.44510i 0.224305 + 0.320341i
\(696\) −12.6994 25.1703i −0.481369 0.954077i
\(697\) −22.1696 47.5428i −0.839733 1.80081i
\(698\) −14.2785 + 0.740277i −0.540451 + 0.0280199i
\(699\) 3.05261 4.86045i 0.115460 0.183839i
\(700\) 1.10616 6.93365i 0.0418088 0.262067i
\(701\) −11.4284 27.5907i −0.431646 1.04208i −0.978757 0.205025i \(-0.934273\pi\)
0.547111 0.837060i \(-0.315727\pi\)
\(702\) −5.03211 8.18751i −0.189925 0.309018i
\(703\) 4.85781i 0.183216i
\(704\) 19.7183 + 33.7341i 0.743162 + 1.27140i
\(705\) 1.46545 + 3.94698i 0.0551920 + 0.148652i
\(706\) −1.85040 + 5.21607i −0.0696407 + 0.196309i
\(707\) −18.2670 + 0.797553i −0.687000 + 0.0299951i
\(708\) 14.5122 42.8865i 0.545403 1.61177i
\(709\) −12.2470 7.80220i −0.459946 0.293018i 0.286966 0.957941i \(-0.407353\pi\)
−0.746912 + 0.664923i \(0.768464\pi\)
\(710\) 10.4027 13.7887i 0.390406 0.517482i
\(711\) 5.17758 + 18.3728i 0.194175 + 0.689032i
\(712\) 29.1577 + 7.05205i 1.09273 + 0.264287i
\(713\) 38.3114 + 17.8649i 1.43477 + 0.669046i
\(714\) −23.7429 + 59.7756i −0.888556 + 2.23704i
\(715\) 4.62491 + 14.6683i 0.172962 + 0.548565i
\(716\) −1.33891 22.3015i −0.0500375 0.833446i
\(717\) 33.7256 + 4.21921i 1.25951 + 0.157569i
\(718\) 0.269459 0.191975i 0.0100561 0.00716446i
\(719\) 41.5723 24.0018i 1.55038 0.895115i 0.552274 0.833663i \(-0.313760\pi\)
0.998110 0.0614519i \(-0.0195731\pi\)
\(720\) −28.7788 + 2.57336i −1.07252 + 0.0959033i
\(721\) 12.3108 + 7.10763i 0.458477 + 0.264702i
\(722\) 1.02110 0.0977432i 0.0380015 0.00363762i
\(723\) −3.48582 + 2.25241i −0.129639 + 0.0837682i
\(724\) 2.81052 13.7353i 0.104452 0.510467i
\(725\) −4.48071 0.993351i −0.166410 0.0368921i
\(726\) −31.4781 0.913911i −1.16826 0.0339184i
\(727\) −2.59458 29.6562i −0.0962276 1.09989i −0.878756 0.477271i \(-0.841626\pi\)
0.782528 0.622615i \(-0.213930\pi\)
\(728\) 15.1917 + 5.86089i 0.563042 + 0.217219i
\(729\) −5.97505 + 26.3306i −0.221298 + 0.975206i
\(730\) 2.06997 16.7808i 0.0766131 0.621084i
\(731\) 17.9633 9.35109i 0.664396 0.345862i
\(732\) −6.54125 8.90326i −0.241772 0.329074i
\(733\) −13.1299 20.6099i −0.484966 0.761244i 0.510137 0.860093i \(-0.329595\pi\)
−0.995102 + 0.0988497i \(0.968484\pi\)
\(734\) 24.7140 21.0838i 0.912210 0.778216i
\(735\) 50.7776 9.29114i 1.87296 0.342709i
\(736\) 12.8594 30.8007i 0.474002 1.13533i
\(737\) 13.5498 + 7.82300i 0.499114 + 0.288164i
\(738\) 35.3218 + 12.0203i 1.30021 + 0.442474i
\(739\) 19.4495 25.3471i 0.715463 0.932409i −0.284190 0.958768i \(-0.591725\pi\)
0.999653 + 0.0263589i \(0.00839126\pi\)
\(740\) 5.23895 0.544696i 0.192588 0.0200234i
\(741\) −7.94177 + 6.17563i −0.291748 + 0.226867i
\(742\) −52.9408 + 34.3380i −1.94352 + 1.26059i
\(743\) −30.1129 2.63454i −1.10474 0.0966519i −0.479837 0.877358i \(-0.659304\pi\)
−0.624899 + 0.780706i \(0.714860\pi\)
\(744\) 20.4947 28.4928i 0.751372 1.04459i
\(745\) 5.94747 12.7544i 0.217898 0.467285i
\(746\) 3.09221 + 1.25135i 0.113214 + 0.0458152i
\(747\) −31.4434 + 24.7775i −1.15045 + 0.906561i
\(748\) −54.1907 21.4165i −1.98141 0.783066i
\(749\) 4.99846 + 22.5466i 0.182640 + 0.823835i
\(750\) 13.9184 20.5088i 0.508230 0.748877i
\(751\) −44.3067 16.1263i −1.61678 0.588458i −0.634012 0.773323i \(-0.718593\pi\)
−0.982764 + 0.184865i \(0.940815\pi\)
\(752\) −1.25648 + 3.83774i −0.0458191 + 0.139948i
\(753\) −1.16468 3.13690i −0.0424432 0.114315i
\(754\) 4.41919 9.68264i 0.160938 0.352621i
\(755\) −9.51409 22.9690i −0.346253 0.835929i
\(756\) −19.0023 41.6138i −0.691108 1.51348i
\(757\) −0.102334 0.0423881i −0.00371939 0.00154062i 0.380823 0.924648i \(-0.375641\pi\)
−0.384542 + 0.923107i \(0.625641\pi\)
\(758\) 10.8564 + 0.385210i 0.394322 + 0.0139915i
\(759\) 28.8934 + 40.7034i 1.04876 + 1.47744i
\(760\) 5.98035 + 29.6496i 0.216930 + 1.07550i
\(761\) −42.6263 + 19.8770i −1.54520 + 0.720540i −0.993535 0.113524i \(-0.963786\pi\)
−0.551668 + 0.834064i \(0.686008\pi\)
\(762\) 21.9659 + 11.0299i 0.795739 + 0.399572i
\(763\) −12.9445 + 20.3188i −0.468622 + 0.735589i
\(764\) −1.50119 + 0.0245190i −0.0543110 + 0.000887067i
\(765\) 31.3896 29.5163i 1.13489 1.06716i
\(766\) 41.9775 0.342789i 1.51671 0.0123855i
\(767\) 16.0619 5.84604i 0.579961 0.211088i
\(768\) −23.1392 15.2505i −0.834964 0.550305i
\(769\) 26.3951 22.1481i 0.951833 0.798683i −0.0277725 0.999614i \(-0.508841\pi\)
0.979605 + 0.200932i \(0.0643969\pi\)
\(770\) 13.3017 + 71.9947i 0.479359 + 2.59451i
\(771\) −14.5100 34.4016i −0.522564 1.23894i
\(772\) 34.8776 + 28.3081i 1.25527 + 1.01883i
\(773\) 1.08339 + 8.22920i 0.0389670 + 0.295984i 0.999821 + 0.0189280i \(0.00602534\pi\)
−0.960854 + 0.277056i \(0.910641\pi\)
\(774\) −4.04127 + 13.8255i −0.145260 + 0.496949i
\(775\) −1.47880 5.51897i −0.0531202 0.198247i
\(776\) −1.93279 + 12.7854i −0.0693832 + 0.458970i
\(777\) 3.57305 + 7.53530i 0.128182 + 0.270327i
\(778\) −35.4839 + 11.5074i −1.27216 + 0.412561i
\(779\) 8.45378 38.1325i 0.302888 1.36624i
\(780\) −7.55066 7.87242i −0.270357 0.281878i
\(781\) −7.45019 + 23.6290i −0.266589 + 0.845511i
\(782\) 13.2745 + 47.9707i 0.474695 + 1.71543i
\(783\) −27.8964 + 10.7684i −0.996937 + 0.384833i
\(784\) 43.6634 + 23.3420i 1.55941 + 0.833643i
\(785\) −2.69956 2.26520i −0.0963516 0.0808486i
\(786\) 31.6782 + 43.8632i 1.12992 + 1.56455i
\(787\) 22.0517 + 34.6142i 0.786058 + 1.23386i 0.968098 + 0.250572i \(0.0806187\pi\)
−0.182040 + 0.983291i \(0.558270\pi\)
\(788\) 3.54273 17.3137i 0.126205 0.616774i
\(789\) −7.50633 + 2.42001i −0.267232 + 0.0861547i
\(790\) 10.1609 + 19.1358i 0.361510 + 0.680823i
\(791\) 14.2469 + 53.1702i 0.506562 + 1.89051i
\(792\) 37.6703 17.2801i 1.33856 0.614022i
\(793\) 1.07950 4.02876i 0.0383343 0.143066i
\(794\) 2.30508 0.530808i 0.0818042 0.0188377i
\(795\) 41.8742 5.78753i 1.48513 0.205263i
\(796\) −25.7947 + 12.5451i −0.914269 + 0.444650i
\(797\) 5.96239 + 3.10383i 0.211199 + 0.109943i 0.564064 0.825731i \(-0.309237\pi\)
−0.352865 + 0.935674i \(0.614793\pi\)
\(798\) −41.1192 + 24.5480i −1.45561 + 0.868989i
\(799\) −2.05961 5.65874i −0.0728639 0.200192i
\(800\) −4.30640 + 1.34454i −0.152254 + 0.0475366i
\(801\) 10.4963 30.0370i 0.370868 1.06130i
\(802\) 0.00501586 + 0.00852617i 0.000177116 + 0.000301070i
\(803\) 5.24920 + 23.6776i 0.185240 + 0.835565i
\(804\) −11.0736 0.715155i −0.390535 0.0252216i
\(805\) 42.2505 46.1083i 1.48913 1.62511i
\(806\) 13.2327 0.686054i 0.466101 0.0241652i
\(807\) −12.9383 + 1.21600i −0.455450 + 0.0428051i
\(808\) 5.67837 + 10.2848i 0.199764 + 0.361819i
\(809\) 9.08565 + 9.08565i 0.319434 + 0.319434i 0.848550 0.529115i \(-0.177476\pi\)
−0.529115 + 0.848550i \(0.677476\pi\)
\(810\) −0.297203 + 30.6449i −0.0104427 + 1.07675i
\(811\) 7.02378 16.9569i 0.246638 0.595438i −0.751276 0.659988i \(-0.770561\pi\)
0.997914 + 0.0645504i \(0.0205613\pi\)
\(812\) 26.5209 43.1695i 0.930702 1.51495i
\(813\) 6.13030 + 1.88954i 0.214999 + 0.0662692i
\(814\) −6.82102 + 3.24876i −0.239077 + 0.113869i
\(815\) 10.0038 27.4851i 0.350416 0.962761i
\(816\) 41.1851 3.41540i 1.44177 0.119563i
\(817\) 14.8495 + 2.61837i 0.519519 + 0.0916053i
\(818\) 12.3310 47.5703i 0.431143 1.66326i
\(819\) 7.77672 15.4208i 0.271740 0.538848i
\(820\) 42.0723 + 4.84134i 1.46923 + 0.169067i
\(821\) −1.93969 + 44.4263i −0.0676957 + 1.55049i 0.596307 + 0.802757i \(0.296634\pi\)
−0.664003 + 0.747730i \(0.731144\pi\)
\(822\) −3.40088 23.2073i −0.118619 0.809447i
\(823\) 45.7788 + 4.00513i 1.59575 + 0.139610i 0.850061 0.526684i \(-0.176565\pi\)
0.745689 + 0.666294i \(0.232120\pi\)
\(824\) 0.572938 9.11574i 0.0199593 0.317562i
\(825\) 1.70419 6.52806i 0.0593322 0.227278i
\(826\) 79.2899 18.2587i 2.75885 0.635301i
\(827\) −33.3630 + 4.39232i −1.16015 + 0.152736i −0.685927 0.727671i \(-0.740603\pi\)
−0.474219 + 0.880407i \(0.657270\pi\)
\(828\) −31.1630 16.7978i −1.08299 0.583764i
\(829\) 6.10341 46.3600i 0.211980 1.61015i −0.472644 0.881253i \(-0.656700\pi\)
0.684624 0.728896i \(-0.259966\pi\)
\(830\) −28.9224 + 35.0456i −1.00391 + 1.21645i
\(831\) −40.5173 + 34.4453i −1.40553 + 1.19489i
\(832\) −0.967722 10.4175i −0.0335497 0.361162i
\(833\) −72.7111 + 12.8209i −2.51929 + 0.444219i
\(834\) 10.3542 + 1.67016i 0.358537 + 0.0578329i
\(835\) −12.1087 + 38.4038i −0.419038 + 1.32902i
\(836\) −22.3034 37.2136i −0.771380 1.28706i
\(837\) −27.9276 24.6151i −0.965318 0.850822i
\(838\) −4.53540 + 36.7674i −0.156673 + 1.27011i
\(839\) 3.74535 + 42.8095i 0.129304 + 1.47795i 0.732724 + 0.680526i \(0.238248\pi\)
−0.603421 + 0.797423i \(0.706196\pi\)
\(840\) −31.0846 41.5929i −1.07252 1.43509i
\(841\) −3.37276 2.36163i −0.116302 0.0814357i
\(842\) 1.50466 + 4.63973i 0.0518541 + 0.159896i
\(843\) 30.2260 33.4155i 1.04104 1.15089i
\(844\) 26.3611 24.9596i 0.907386 0.859145i
\(845\) −3.54813 + 26.9508i −0.122060 + 0.927134i
\(846\) 3.91909 + 1.72803i 0.134741 + 0.0594107i
\(847\) −28.2968 49.0116i −0.972291 1.68406i
\(848\) 34.8883 + 20.6563i 1.19807 + 0.709341i
\(849\) −28.7131 + 0.184982i −0.985430 + 0.00634858i
\(850\) 3.81366 5.54225i 0.130808 0.190098i
\(851\) 5.72444 + 2.97996i 0.196231 + 0.102152i
\(852\) −2.68970 17.3646i −0.0921475 0.594903i
\(853\) 7.07259 + 0.308796i 0.242161 + 0.0105730i 0.164378 0.986397i \(-0.447438\pi\)
0.0777826 + 0.996970i \(0.475216\pi\)
\(854\) 7.44789 18.4045i 0.254862 0.629787i
\(855\) 31.9207 3.20763i 1.09167 0.109699i
\(856\) 11.5475 9.31882i 0.394684 0.318511i
\(857\) −6.09481 8.70429i −0.208195 0.297333i 0.701451 0.712718i \(-0.252536\pi\)
−0.909646 + 0.415385i \(0.863647\pi\)
\(858\) 13.9826 + 7.02123i 0.477359 + 0.239701i
\(859\) 5.46424 + 5.00706i 0.186438 + 0.170839i 0.763387 0.645941i \(-0.223535\pi\)
−0.576950 + 0.816780i \(0.695757\pi\)
\(860\) −1.15876 + 16.3082i −0.0395135 + 0.556106i
\(861\) 14.9342 + 65.3681i 0.508957 + 2.22774i
\(862\) 6.49052 + 17.3894i 0.221068 + 0.592285i
\(863\) 30.1955 1.02787 0.513933 0.857830i \(-0.328188\pi\)
0.513933 + 0.857830i \(0.328188\pi\)
\(864\) −18.5194 + 22.8261i −0.630043 + 0.776560i
\(865\) −61.5686 −2.09340
\(866\) −1.92816 5.16592i −0.0655215 0.175545i
\(867\) −23.5871 + 21.8948i −0.801058 + 0.743585i
\(868\) 62.9165 + 4.47047i 2.13553 + 0.151738i
\(869\) −22.9129 20.9958i −0.777267 0.712234i
\(870\) −28.3561 + 18.6527i −0.961362 + 0.632385i
\(871\) −2.40288 3.43167i −0.0814184 0.116278i
\(872\) 15.3921 + 1.64397i 0.521243 + 0.0556717i
\(873\) 13.2924 + 3.37874i 0.449879 + 0.114353i
\(874\) −13.9021 + 34.3535i −0.470246 + 1.16202i
\(875\) 44.5005 + 1.94294i 1.50439 + 0.0656832i
\(876\) −10.7791 13.4042i −0.364194 0.452887i
\(877\) −40.7338 21.2047i −1.37548 0.716031i −0.396131 0.918194i \(-0.629647\pi\)
−0.979352 + 0.202163i \(0.935203\pi\)
\(878\) 2.19146 3.18477i 0.0739583 0.107481i
\(879\) −23.1995 + 40.7873i −0.782500 + 1.37572i
\(880\) 37.6325 28.2260i 1.26859 0.951499i
\(881\) 1.46617 + 2.53949i 0.0493966 + 0.0855575i 0.889667 0.456611i \(-0.150937\pi\)
−0.840270 + 0.542168i \(0.817604\pi\)
\(882\) 29.2088 43.6417i 0.983513 1.46949i
\(883\) 0.911248 6.92162i 0.0306659 0.232931i −0.969248 0.246088i \(-0.920855\pi\)
0.999913 + 0.0131570i \(0.00418813\pi\)
\(884\) 10.7269 + 11.3292i 0.360785 + 0.381043i
\(885\) −53.2899 11.4544i −1.79132 0.385036i
\(886\) −3.98995 12.3033i −0.134045 0.413336i
\(887\) 38.1182 + 26.6906i 1.27988 + 0.896183i 0.997997 0.0632648i \(-0.0201513\pi\)
0.281885 + 0.959448i \(0.409040\pi\)
\(888\) 3.31567 4.20935i 0.111267 0.141256i
\(889\) 3.84988 + 44.0044i 0.129121 + 1.47586i
\(890\) 4.42143 35.8434i 0.148207 1.20147i
\(891\) −14.2945 41.5696i −0.478883 1.39263i
\(892\) −25.2699 + 15.1451i −0.846099 + 0.507097i
\(893\) 1.34828 4.27620i 0.0451185 0.143098i
\(894\) −5.09255 13.3802i −0.170320 0.447501i
\(895\) −26.4885 + 4.67064i −0.885414 + 0.156122i
\(896\) 1.49913 49.7806i 0.0500825 1.66305i
\(897\) −2.40559 13.1469i −0.0803203 0.438963i
\(898\) −4.97894 + 6.03305i −0.166150 + 0.201325i
\(899\) 5.38149 40.8765i 0.179483 1.36331i
\(900\) 0.968225 + 4.68610i 0.0322742 + 0.156203i
\(901\) −59.9446 + 7.89186i −1.99705 + 0.262916i
\(902\) −59.1969 + 13.6317i −1.97104 + 0.453886i
\(903\) −24.9601 + 6.86068i −0.830619 + 0.228309i
\(904\) 26.5289 23.3913i 0.882338 0.777984i
\(905\) −16.8143 1.47106i −0.558926 0.0488997i
\(906\) −23.5056 9.33644i −0.780921 0.310182i
\(907\) 1.30232 29.8281i 0.0432429 0.990425i −0.846055 0.533096i \(-0.821028\pi\)
0.889298 0.457329i \(-0.151194\pi\)
\(908\) 0.0889597 0.773079i 0.00295223 0.0256555i
\(909\) 11.4500 4.91651i 0.379772 0.163070i
\(910\) 4.91889 18.9760i 0.163060 0.629049i
\(911\) 4.99752 + 0.881197i 0.165575 + 0.0291954i 0.255821 0.966724i \(-0.417654\pi\)
−0.0902459 + 0.995920i \(0.528765\pi\)
\(912\) 25.8763 + 16.6502i 0.856852 + 0.551344i
\(913\) 22.2918 61.2464i 0.737753 2.02696i
\(914\) −32.8661 + 15.6537i −1.08711 + 0.517779i
\(915\) −9.74812 + 9.04873i −0.322263 + 0.299142i
\(916\) 22.1950 + 13.6354i 0.733344 + 0.450526i
\(917\) −37.2103 + 89.8336i −1.22879 + 2.96657i
\(918\) 0.707454 43.8276i 0.0233495 1.44653i
\(919\) −25.5326 25.5326i −0.842243 0.842243i 0.146907 0.989150i \(-0.453068\pi\)
−0.989150 + 0.146907i \(0.953068\pi\)
\(920\) −38.6077 11.1409i −1.27286 0.367304i
\(921\) 31.2711 + 44.0529i 1.03042 + 1.45159i
\(922\) −1.72500 + 0.0894331i −0.0568097 + 0.00294532i
\(923\) 4.48173 4.89095i 0.147518 0.160988i
\(924\) 61.9680 + 41.3200i 2.03860 + 1.35933i
\(925\) −0.188800 0.851623i −0.00620772 0.0280012i
\(926\) 10.5312 + 17.9014i 0.346077 + 0.588277i
\(927\) −9.56148 1.55920i −0.314040 0.0512109i
\(928\) −32.4219 2.92819i −1.06430 0.0961224i
\(929\) −15.0193 41.2653i −0.492769 1.35387i −0.898136 0.439717i \(-0.855079\pi\)
0.405368 0.914154i \(-0.367144\pi\)
\(930\) −36.8982 20.5905i −1.20994 0.675188i
\(931\) −48.7621 25.3840i −1.59811 0.831926i
\(932\) −2.89860 5.95998i −0.0949469 0.195226i
\(933\) −14.5551 + 35.7894i −0.476511 + 1.17169i
\(934\) −51.3717 + 11.8298i −1.68093 + 0.387081i
\(935\) −18.1562 + 67.7600i −0.593773 + 2.21599i
\(936\) −11.0968 0.0693675i −0.362709 0.00226735i
\(937\) 4.61286 + 17.2154i 0.150696 + 0.562403i 0.999436 + 0.0335931i \(0.0106950\pi\)
−0.848740 + 0.528810i \(0.822638\pi\)
\(938\) −9.35232 17.6130i −0.305364 0.575084i
\(939\) −34.9065 31.5746i −1.13913 1.03040i
\(940\) 4.76289 + 0.974586i 0.155348 + 0.0317875i
\(941\) 22.1497 + 34.7681i 0.722060 + 1.13341i 0.985655 + 0.168774i \(0.0539808\pi\)
−0.263595 + 0.964634i \(0.584908\pi\)
\(942\) −3.56646 + 0.364594i −0.116201 + 0.0118791i
\(943\) 39.7495 + 33.3538i 1.29442 + 1.08615i
\(944\) −33.1633 40.4146i −1.07937 1.31538i
\(945\) −47.1552 + 28.4541i −1.53396 + 0.925613i
\(946\) −6.25440 22.6018i −0.203348 0.734849i
\(947\) −4.63372 + 14.6963i −0.150576 + 0.477565i −0.998629 0.0523457i \(-0.983330\pi\)
0.848053 + 0.529911i \(0.177775\pi\)
\(948\) 21.1667 + 6.14755i 0.687462 + 0.199663i
\(949\) 1.40550 6.33980i 0.0456244 0.205799i
\(950\) 4.76486 1.54524i 0.154593 0.0501343i
\(951\) −34.6552 2.80709i −1.12377 0.0910262i
\(952\) 44.0760 + 59.7754i 1.42851 + 1.93733i
\(953\) −4.95872 18.5062i −0.160629 0.599474i −0.998557 0.0536945i \(-0.982900\pi\)
0.837929 0.545779i \(-0.183766\pi\)
\(954\) 25.4554 34.6610i 0.824147 1.12219i
\(955\) 0.235929 + 1.79206i 0.00763448 + 0.0579896i
\(956\) 24.7329 30.4726i 0.799918 0.985554i
\(957\) 29.3878 38.8141i 0.949972 1.25468i
\(958\) 7.70165 + 41.6849i 0.248829 + 1.34678i
\(959\) 32.2900 27.0945i 1.04270 0.874928i
\(960\) −15.0552 + 29.7736i −0.485903 + 0.960937i
\(961\) 19.1020 6.95255i 0.616193 0.224276i
\(962\) 2.02287 0.0165188i 0.0652199 0.000532586i
\(963\) −8.62673 13.1638i −0.277992 0.424199i
\(964\) 0.0782620 + 4.79162i 0.00252065 + 0.154328i
\(965\) 29.0567 45.6098i 0.935367 1.46823i
\(966\) −3.70331 63.5135i −0.119152 2.04351i
\(967\) −35.0633 + 16.3503i −1.12756 + 0.525789i −0.894676 0.446716i \(-0.852594\pi\)
−0.232882 + 0.972505i \(0.574816\pi\)
\(968\) −20.1211 + 30.2889i −0.646718 + 0.973522i
\(969\) −45.6847 + 4.29363i −1.46760 + 0.137931i
\(970\) 15.5575 + 0.552016i 0.499521 + 0.0177242i
\(971\) 3.64680 + 1.51055i 0.117031 + 0.0484760i 0.440431 0.897787i \(-0.354826\pi\)
−0.323399 + 0.946263i \(0.604826\pi\)
\(972\) 22.1534 + 21.9369i 0.710570 + 0.703626i
\(973\) 7.21292 + 17.4135i 0.231235 + 0.558252i
\(974\) 22.0982 48.4181i 0.708071 1.55141i
\(975\) −1.15225 + 1.39131i −0.0369017 + 0.0445576i
\(976\) −12.7199 + 0.972371i −0.407154 + 0.0311248i
\(977\) 9.80488 + 3.56868i 0.313686 + 0.114172i 0.494065 0.869425i \(-0.335510\pi\)
−0.180379 + 0.983597i \(0.557733\pi\)
\(978\) −12.9678 26.7810i −0.414664 0.856362i
\(979\) 11.2122 + 50.5750i 0.358344 + 1.61638i
\(980\) 21.9080 55.4343i 0.699825 1.77078i
\(981\) 3.34683 16.0739i 0.106856 0.513201i
\(982\) −33.8549 13.7003i −1.08035 0.437196i
\(983\) −12.1487 + 26.0530i −0.387484 + 0.830961i 0.611721 + 0.791074i \(0.290478\pi\)
−0.999204 + 0.0398874i \(0.987300\pi\)
\(984\) 33.3525 27.2722i 1.06324 0.869405i
\(985\) −21.1949 1.85431i −0.675325 0.0590833i
\(986\) 40.7286 26.4170i 1.29706 0.841289i
\(987\) 1.05384 + 7.62482i 0.0335442 + 0.242701i
\(988\) 1.20131 + 11.5544i 0.0382188 + 0.367594i
\(989\) −12.1947 + 15.8925i −0.387770 + 0.505352i
\(990\) −25.8516 42.6758i −0.821618 1.35633i
\(991\) −13.9756 8.06881i −0.443949 0.256314i 0.261322 0.965252i \(-0.415842\pi\)
−0.705271 + 0.708937i \(0.749175\pi\)
\(992\) −15.4042 37.4860i −0.489084 1.19018i
\(993\) −16.3178 19.1944i −0.517831 0.609114i
\(994\) 24.0239 20.4951i 0.761992 0.650064i
\(995\) 18.5541 + 29.1242i 0.588206 + 0.923298i
\(996\) 5.07644 + 45.9461i 0.160853 + 1.45586i
\(997\) 10.0932 5.25418i 0.319654 0.166401i −0.294364 0.955693i \(-0.595108\pi\)
0.614018 + 0.789292i \(0.289552\pi\)
\(998\) −2.58761 + 20.9771i −0.0819094 + 0.664020i
\(999\) −4.09570 3.94037i −0.129582 0.124668i
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 864.2.bt.a.11.17 3408
27.5 odd 18 inner 864.2.bt.a.491.63 yes 3408
32.3 odd 8 inner 864.2.bt.a.227.63 yes 3408
864.707 even 72 inner 864.2.bt.a.707.17 yes 3408
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
864.2.bt.a.11.17 3408 1.1 even 1 trivial
864.2.bt.a.227.63 yes 3408 32.3 odd 8 inner
864.2.bt.a.491.63 yes 3408 27.5 odd 18 inner
864.2.bt.a.707.17 yes 3408 864.707 even 72 inner