Properties

Label 441.2.z.a.142.8
Level $441$
Weight $2$
Character 441.142
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(4,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.z (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 142.8
Character \(\chi\) \(=\) 441.142
Dual form 441.2.z.a.382.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.792223 + 2.01855i) q^{2} +(1.54796 - 0.777050i) q^{3} +(-1.98083 - 1.83794i) q^{4} +(-3.11465 + 1.49994i) q^{5} +(0.342182 + 3.74024i) q^{6} +(-0.809384 - 2.51891i) q^{7} +(1.37183 - 0.660638i) q^{8} +(1.79239 - 2.40569i) q^{9} +O(q^{10})\) \(q+(-0.792223 + 2.01855i) q^{2} +(1.54796 - 0.777050i) q^{3} +(-1.98083 - 1.83794i) q^{4} +(-3.11465 + 1.49994i) q^{5} +(0.342182 + 3.74024i) q^{6} +(-0.809384 - 2.51891i) q^{7} +(1.37183 - 0.660638i) q^{8} +(1.79239 - 2.40569i) q^{9} +(-0.560202 - 7.47538i) q^{10} +(-2.48716 - 3.11879i) q^{11} +(-4.49443 - 1.30586i) q^{12} +(1.79799 - 4.58121i) q^{13} +(5.72576 + 0.361755i) q^{14} +(-3.65585 + 4.74209i) q^{15} +(-0.157129 - 2.09674i) q^{16} +(1.04587 - 0.970429i) q^{17} +(3.43604 + 5.52387i) q^{18} +(-3.96382 + 6.86554i) q^{19} +(8.92640 + 2.75343i) q^{20} +(-3.21021 - 3.27025i) q^{21} +(8.26583 - 2.54967i) q^{22} +(-0.312124 + 1.36750i) q^{23} +(1.61019 - 2.08862i) q^{24} +(4.33380 - 5.43442i) q^{25} +(7.82299 + 7.25868i) q^{26} +(0.905211 - 5.11670i) q^{27} +(-3.02635 + 6.47713i) q^{28} +(-4.98160 - 1.53662i) q^{29} +(-6.67591 - 11.1363i) q^{30} +(2.47614 - 4.28880i) q^{31} +(7.26681 + 2.24151i) q^{32} +(-6.27349 - 2.89514i) q^{33} +(1.13030 + 2.87995i) q^{34} +(6.29916 + 6.63150i) q^{35} +(-7.97193 + 1.47096i) q^{36} +(-0.415656 - 0.128213i) q^{37} +(-10.7182 - 13.4402i) q^{38} +(-0.776599 - 8.48867i) q^{39} +(-3.28186 + 4.11532i) q^{40} +(-5.50219 - 3.75133i) q^{41} +(9.14437 - 3.88922i) q^{42} +(-3.04899 + 2.07876i) q^{43} +(-0.805530 + 10.7490i) q^{44} +(-1.97428 + 10.1814i) q^{45} +(-2.51310 - 1.71341i) q^{46} +(1.49018 - 3.79693i) q^{47} +(-1.87251 - 3.12359i) q^{48} +(-5.68980 + 4.07753i) q^{49} +(7.53631 + 13.0533i) q^{50} +(0.864904 - 2.31489i) q^{51} +(-11.9815 + 5.76999i) q^{52} +(2.33411 - 0.719976i) q^{53} +(9.61119 + 5.88078i) q^{54} +(12.4246 + 5.98338i) q^{55} +(-2.77442 - 2.92080i) q^{56} +(-0.800988 + 13.7077i) q^{57} +(7.04829 - 8.83828i) q^{58} +(1.93962 - 1.32241i) q^{59} +(15.9573 - 2.67404i) q^{60} +(2.88825 - 2.67990i) q^{61} +(6.69551 + 8.39591i) q^{62} +(-7.51044 - 2.56773i) q^{63} +(-7.65961 + 9.60485i) q^{64} +(1.27141 + 16.9657i) q^{65} +(10.8140 - 10.3698i) q^{66} +(-5.56769 + 9.64352i) q^{67} -3.85529 q^{68} +(0.579462 + 2.35938i) q^{69} +(-18.3764 + 7.46154i) q^{70} +(2.11086 - 9.24828i) q^{71} +(0.869558 - 4.48432i) q^{72} +(-2.59675 - 0.391397i) q^{73} +(0.588097 - 0.737450i) q^{74} +(2.48576 - 11.7799i) q^{75} +(20.4701 - 6.31419i) q^{76} +(-5.84289 + 8.78922i) q^{77} +(17.7501 + 5.15732i) q^{78} +(-6.24432 - 10.8155i) q^{79} +(3.63439 + 6.29495i) q^{80} +(-2.57469 - 8.62386i) q^{81} +(11.9312 - 8.13456i) q^{82} +(3.03611 + 7.73588i) q^{83} +(0.348361 + 12.3780i) q^{84} +(-1.80195 + 4.59130i) q^{85} +(-1.78061 - 7.80138i) q^{86} +(-8.90538 + 1.49232i) q^{87} +(-5.47235 - 2.63534i) q^{88} +(3.08300 + 7.85535i) q^{89} +(-18.9875 - 12.0511i) q^{90} +(-12.9949 - 0.821021i) q^{91} +(3.13165 - 2.13513i) q^{92} +(0.500366 - 8.56300i) q^{93} +(6.48373 + 6.01603i) q^{94} +(2.04805 - 27.3293i) q^{95} +(12.9905 - 2.17689i) q^{96} +(-5.57496 + 9.65612i) q^{97} +(-3.72311 - 14.7155i) q^{98} +(-11.9608 + 0.393239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.792223 + 2.01855i −0.560186 + 1.42733i 0.317575 + 0.948233i \(0.397132\pi\)
−0.877761 + 0.479098i \(0.840964\pi\)
\(3\) 1.54796 0.777050i 0.893718 0.448630i
\(4\) −1.98083 1.83794i −0.990415 0.918971i
\(5\) −3.11465 + 1.49994i −1.39292 + 0.670793i −0.971711 0.236173i \(-0.924107\pi\)
−0.421204 + 0.906966i \(0.638393\pi\)
\(6\) 0.342182 + 3.74024i 0.139695 + 1.52695i
\(7\) −0.809384 2.51891i −0.305918 0.952058i
\(8\) 1.37183 0.660638i 0.485015 0.233571i
\(9\) 1.79239 2.40569i 0.597462 0.801897i
\(10\) −0.560202 7.47538i −0.177151 2.36392i
\(11\) −2.48716 3.11879i −0.749906 0.940352i 0.249703 0.968322i \(-0.419667\pi\)
−0.999609 + 0.0279706i \(0.991096\pi\)
\(12\) −4.49443 1.30586i −1.29743 0.376971i
\(13\) 1.79799 4.58121i 0.498673 1.27060i −0.431046 0.902330i \(-0.641855\pi\)
0.929719 0.368268i \(-0.120049\pi\)
\(14\) 5.72576 + 0.361755i 1.53027 + 0.0966831i
\(15\) −3.65585 + 4.74209i −0.943935 + 1.22440i
\(16\) −0.157129 2.09674i −0.0392823 0.524186i
\(17\) 1.04587 0.970429i 0.253662 0.235364i −0.543084 0.839678i \(-0.682743\pi\)
0.796746 + 0.604315i \(0.206553\pi\)
\(18\) 3.43604 + 5.52387i 0.809882 + 1.30199i
\(19\) −3.96382 + 6.86554i −0.909363 + 1.57506i −0.0944118 + 0.995533i \(0.530097\pi\)
−0.814951 + 0.579530i \(0.803236\pi\)
\(20\) 8.92640 + 2.75343i 1.99600 + 0.615685i
\(21\) −3.21021 3.27025i −0.700526 0.713627i
\(22\) 8.26583 2.54967i 1.76228 0.543592i
\(23\) −0.312124 + 1.36750i −0.0650823 + 0.285144i −0.996988 0.0775566i \(-0.975288\pi\)
0.931906 + 0.362701i \(0.118145\pi\)
\(24\) 1.61019 2.08862i 0.328679 0.426339i
\(25\) 4.33380 5.43442i 0.866761 1.08688i
\(26\) 7.82299 + 7.25868i 1.53422 + 1.42354i
\(27\) 0.905211 5.11670i 0.174208 0.984709i
\(28\) −3.02635 + 6.47713i −0.571927 + 1.22406i
\(29\) −4.98160 1.53662i −0.925061 0.285343i −0.204605 0.978845i \(-0.565591\pi\)
−0.720455 + 0.693501i \(0.756067\pi\)
\(30\) −6.67591 11.1363i −1.21885 2.03320i
\(31\) 2.47614 4.28880i 0.444728 0.770292i −0.553305 0.832979i \(-0.686634\pi\)
0.998033 + 0.0626870i \(0.0199670\pi\)
\(32\) 7.26681 + 2.24151i 1.28460 + 0.396247i
\(33\) −6.27349 2.89514i −1.09207 0.503979i
\(34\) 1.13030 + 2.87995i 0.193844 + 0.493907i
\(35\) 6.29916 + 6.63150i 1.06475 + 1.12093i
\(36\) −7.97193 + 1.47096i −1.32866 + 0.245160i
\(37\) −0.415656 0.128213i −0.0683334 0.0210781i 0.260400 0.965501i \(-0.416146\pi\)
−0.328733 + 0.944423i \(0.606622\pi\)
\(38\) −10.7182 13.4402i −1.73872 2.18029i
\(39\) −0.776599 8.48867i −0.124355 1.35928i
\(40\) −3.28186 + 4.11532i −0.518907 + 0.650689i
\(41\) −5.50219 3.75133i −0.859297 0.585859i 0.0515186 0.998672i \(-0.483594\pi\)
−0.910816 + 0.412813i \(0.864546\pi\)
\(42\) 9.14437 3.88922i 1.41101 0.600119i
\(43\) −3.04899 + 2.07876i −0.464966 + 0.317009i −0.773044 0.634353i \(-0.781267\pi\)
0.308078 + 0.951361i \(0.400314\pi\)
\(44\) −0.805530 + 10.7490i −0.121438 + 1.62048i
\(45\) −1.97428 + 10.1814i −0.294308 + 1.51775i
\(46\) −2.51310 1.71341i −0.370537 0.252628i
\(47\) 1.49018 3.79693i 0.217366 0.553839i −0.780048 0.625720i \(-0.784805\pi\)
0.997413 + 0.0718816i \(0.0229004\pi\)
\(48\) −1.87251 3.12359i −0.270273 0.450851i
\(49\) −5.68980 + 4.07753i −0.812828 + 0.582504i
\(50\) 7.53631 + 13.0533i 1.06580 + 1.84601i
\(51\) 0.864904 2.31489i 0.121111 0.324149i
\(52\) −11.9815 + 5.76999i −1.66154 + 0.800153i
\(53\) 2.33411 0.719976i 0.320614 0.0988964i −0.130271 0.991478i \(-0.541585\pi\)
0.450885 + 0.892582i \(0.351108\pi\)
\(54\) 9.61119 + 5.88078i 1.30792 + 0.800273i
\(55\) 12.4246 + 5.98338i 1.67534 + 0.806799i
\(56\) −2.77442 2.92080i −0.370748 0.390309i
\(57\) −0.800988 + 13.7077i −0.106093 + 1.81563i
\(58\) 7.04829 8.83828i 0.925486 1.16052i
\(59\) 1.93962 1.32241i 0.252517 0.172163i −0.430446 0.902617i \(-0.641644\pi\)
0.682963 + 0.730453i \(0.260691\pi\)
\(60\) 15.9573 2.67404i 2.06008 0.345218i
\(61\) 2.88825 2.67990i 0.369802 0.343126i −0.473279 0.880912i \(-0.656930\pi\)
0.843081 + 0.537786i \(0.180739\pi\)
\(62\) 6.69551 + 8.39591i 0.850331 + 1.06628i
\(63\) −7.51044 2.56773i −0.946227 0.323504i
\(64\) −7.65961 + 9.60485i −0.957452 + 1.20061i
\(65\) 1.27141 + 16.9657i 0.157699 + 2.10434i
\(66\) 10.8140 10.3698i 1.33111 1.27643i
\(67\) −5.56769 + 9.64352i −0.680201 + 1.17814i 0.294718 + 0.955584i \(0.404774\pi\)
−0.974919 + 0.222559i \(0.928559\pi\)
\(68\) −3.85529 −0.467523
\(69\) 0.579462 + 2.35938i 0.0697590 + 0.284036i
\(70\) −18.3764 + 7.46154i −2.19640 + 0.891825i
\(71\) 2.11086 9.24828i 0.250513 1.09757i −0.680547 0.732704i \(-0.738258\pi\)
0.931060 0.364865i \(-0.118885\pi\)
\(72\) 0.869558 4.48432i 0.102478 0.528482i
\(73\) −2.59675 0.391397i −0.303926 0.0458095i −0.00469145 0.999989i \(-0.501493\pi\)
−0.299235 + 0.954179i \(0.596731\pi\)
\(74\) 0.588097 0.737450i 0.0683648 0.0857268i
\(75\) 2.48576 11.7799i 0.287031 1.36022i
\(76\) 20.4701 6.31419i 2.34808 0.724288i
\(77\) −5.84289 + 8.78922i −0.665860 + 1.00162i
\(78\) 17.7501 + 5.15732i 2.00980 + 0.583951i
\(79\) −6.24432 10.8155i −0.702540 1.21684i −0.967572 0.252596i \(-0.918716\pi\)
0.265032 0.964240i \(-0.414618\pi\)
\(80\) 3.63439 + 6.29495i 0.406337 + 0.703797i
\(81\) −2.57469 8.62386i −0.286077 0.958207i
\(82\) 11.9312 8.13456i 1.31758 0.898312i
\(83\) 3.03611 + 7.73588i 0.333256 + 0.849123i 0.995044 + 0.0994319i \(0.0317025\pi\)
−0.661788 + 0.749691i \(0.730202\pi\)
\(84\) 0.348361 + 12.3780i 0.0380093 + 1.35055i
\(85\) −1.80195 + 4.59130i −0.195449 + 0.497996i
\(86\) −1.78061 7.80138i −0.192009 0.841245i
\(87\) −8.90538 + 1.49232i −0.954757 + 0.159993i
\(88\) −5.47235 2.63534i −0.583354 0.280929i
\(89\) 3.08300 + 7.85535i 0.326797 + 0.832665i 0.995981 + 0.0895681i \(0.0285487\pi\)
−0.669184 + 0.743097i \(0.733356\pi\)
\(90\) −18.9875 12.0511i −2.00146 1.27030i
\(91\) −12.9949 0.821021i −1.36224 0.0860664i
\(92\) 3.13165 2.13513i 0.326498 0.222602i
\(93\) 0.500366 8.56300i 0.0518855 0.887942i
\(94\) 6.48373 + 6.01603i 0.668746 + 0.620506i
\(95\) 2.04805 27.3293i 0.210125 2.80392i
\(96\) 12.9905 2.17689i 1.32584 0.222178i
\(97\) −5.57496 + 9.65612i −0.566052 + 0.980430i 0.430899 + 0.902400i \(0.358196\pi\)
−0.996951 + 0.0780303i \(0.975137\pi\)
\(98\) −3.72311 14.7155i −0.376091 1.48649i
\(99\) −11.9608 + 0.393239i −1.20211 + 0.0395220i
\(100\) −18.5727 + 2.79938i −1.85727 + 0.279938i
\(101\) 6.48237 3.12175i 0.645020 0.310625i −0.0826234 0.996581i \(-0.526330\pi\)
0.727643 + 0.685956i \(0.240616\pi\)
\(102\) 3.98752 + 3.57976i 0.394823 + 0.354449i
\(103\) 11.0027 5.29862i 1.08413 0.522089i 0.195494 0.980705i \(-0.437369\pi\)
0.888634 + 0.458616i \(0.151655\pi\)
\(104\) −0.559983 7.47245i −0.0549109 0.732734i
\(105\) 14.9039 + 5.37057i 1.45447 + 0.524114i
\(106\) −0.395823 + 5.28190i −0.0384458 + 0.513023i
\(107\) −4.11674 10.4893i −0.397980 1.01404i −0.979668 0.200625i \(-0.935703\pi\)
0.581688 0.813412i \(-0.302392\pi\)
\(108\) −11.1973 + 8.47158i −1.07746 + 0.815178i
\(109\) −4.25933 + 10.8526i −0.407969 + 1.03949i 0.568279 + 0.822836i \(0.307609\pi\)
−0.976249 + 0.216653i \(0.930486\pi\)
\(110\) −21.9208 + 20.3396i −2.09007 + 1.93930i
\(111\) −0.743048 + 0.124516i −0.0705270 + 0.0118186i
\(112\) −5.15433 + 2.09286i −0.487038 + 0.197757i
\(113\) −19.7165 2.97178i −1.85477 0.279562i −0.875666 0.482917i \(-0.839577\pi\)
−0.979105 + 0.203356i \(0.934815\pi\)
\(114\) −27.0351 12.4764i −2.53207 1.16852i
\(115\) −1.07901 4.72747i −0.100619 0.440839i
\(116\) 7.04349 + 12.1997i 0.653971 + 1.13271i
\(117\) −7.79827 12.5367i −0.720950 1.15902i
\(118\) 1.13274 + 4.96287i 0.104277 + 0.456869i
\(119\) −3.29094 1.84901i −0.301680 0.169499i
\(120\) −1.88239 + 8.92053i −0.171838 + 0.814329i
\(121\) −1.09321 + 4.78964i −0.0993823 + 0.435422i
\(122\) 3.12138 + 7.95315i 0.282597 + 0.720044i
\(123\) −11.4322 1.53145i −1.03080 0.138086i
\(124\) −12.7874 + 3.94438i −1.14834 + 0.354216i
\(125\) −1.50073 + 6.57512i −0.134229 + 0.588096i
\(126\) 11.1330 13.1260i 0.991811 1.16936i
\(127\) −1.12286 4.91956i −0.0996375 0.436540i −0.999999 0.00139766i \(-0.999555\pi\)
0.900362 0.435143i \(-0.143302\pi\)
\(128\) −5.71511 9.89885i −0.505149 0.874943i
\(129\) −3.10442 + 5.58707i −0.273329 + 0.491914i
\(130\) −35.2535 10.8743i −3.09193 0.953736i
\(131\) 20.0128 + 9.63766i 1.74853 + 0.842046i 0.979119 + 0.203287i \(0.0651625\pi\)
0.769407 + 0.638759i \(0.220552\pi\)
\(132\) 7.10561 + 17.2651i 0.618464 + 1.50273i
\(133\) 20.5019 + 4.42765i 1.77774 + 0.383926i
\(134\) −15.0551 18.8785i −1.30056 1.63085i
\(135\) 4.85531 + 17.2945i 0.417879 + 1.48847i
\(136\) 0.793658 2.02221i 0.0680556 0.173403i
\(137\) −10.0212 4.82596i −0.856169 0.412309i −0.0463053 0.998927i \(-0.514745\pi\)
−0.809864 + 0.586618i \(0.800459\pi\)
\(138\) −5.22160 0.699484i −0.444492 0.0595440i
\(139\) 7.84940 + 5.35163i 0.665778 + 0.453920i 0.848465 0.529252i \(-0.177527\pi\)
−0.182687 + 0.983171i \(0.558480\pi\)
\(140\) −0.289244 24.7134i −0.0244456 2.08866i
\(141\) −0.643649 7.03545i −0.0542051 0.592492i
\(142\) 16.9959 + 11.5876i 1.42626 + 0.972409i
\(143\) −18.7597 + 5.78661i −1.56877 + 0.483901i
\(144\) −5.32575 3.38017i −0.443813 0.281681i
\(145\) 17.8208 2.68605i 1.47994 0.223065i
\(146\) 2.84726 4.93160i 0.235641 0.408142i
\(147\) −5.63916 + 10.7331i −0.465110 + 0.885253i
\(148\) 0.587696 + 1.01792i 0.0483083 + 0.0836724i
\(149\) 6.32995 + 7.93751i 0.518570 + 0.650266i 0.970305 0.241886i \(-0.0777661\pi\)
−0.451735 + 0.892152i \(0.649195\pi\)
\(150\) 21.8090 + 14.3499i 1.78070 + 1.17167i
\(151\) −0.498584 + 2.18444i −0.0405742 + 0.177767i −0.991155 0.132711i \(-0.957632\pi\)
0.950581 + 0.310478i \(0.100489\pi\)
\(152\) −0.902048 + 12.0370i −0.0731658 + 0.976329i
\(153\) −0.459941 4.25543i −0.0371840 0.344032i
\(154\) −13.1126 18.7572i −1.05664 1.51150i
\(155\) −1.27938 + 17.0722i −0.102763 + 1.37127i
\(156\) −14.0634 + 18.2420i −1.12597 + 1.46053i
\(157\) 7.23388 4.93198i 0.577327 0.393615i −0.239159 0.970980i \(-0.576872\pi\)
0.816486 + 0.577366i \(0.195919\pi\)
\(158\) 26.7785 4.03621i 2.13038 0.321103i
\(159\) 3.05366 2.92821i 0.242171 0.232223i
\(160\) −25.9957 + 3.91822i −2.05514 + 0.309763i
\(161\) 3.69724 0.320624i 0.291384 0.0252687i
\(162\) 19.4474 + 1.63487i 1.52794 + 0.128447i
\(163\) 10.9721 7.48063i 0.859399 0.585928i −0.0514464 0.998676i \(-0.516383\pi\)
0.910846 + 0.412747i \(0.135431\pi\)
\(164\) 4.00417 + 17.5434i 0.312673 + 1.36991i
\(165\) 23.8823 0.392486i 1.85923 0.0305550i
\(166\) −18.0205 −1.39867
\(167\) 12.1482 11.2719i 0.940053 0.872242i −0.0519249 0.998651i \(-0.516536\pi\)
0.991978 + 0.126409i \(0.0403452\pi\)
\(168\) −6.56432 2.36543i −0.506448 0.182497i
\(169\) −8.22501 7.63170i −0.632693 0.587054i
\(170\) −7.84022 7.27466i −0.601318 0.557941i
\(171\) 9.41166 + 21.8414i 0.719728 + 1.67026i
\(172\) 9.86017 + 1.48618i 0.751831 + 0.113320i
\(173\) −18.7992 + 5.79879i −1.42928 + 0.440874i −0.910313 0.413921i \(-0.864159\pi\)
−0.518965 + 0.854795i \(0.673683\pi\)
\(174\) 4.04272 19.1582i 0.306478 1.45238i
\(175\) −17.1965 6.51793i −1.29993 0.492709i
\(176\) −6.14851 + 5.70498i −0.463461 + 0.430029i
\(177\) 1.97488 3.55423i 0.148441 0.267152i
\(178\) −18.2988 −1.37156
\(179\) 8.54155 7.92540i 0.638425 0.592372i −0.293085 0.956086i \(-0.594682\pi\)
0.931511 + 0.363714i \(0.118491\pi\)
\(180\) 22.6235 16.5389i 1.68625 1.23274i
\(181\) 8.86996 11.1226i 0.659299 0.826734i −0.333968 0.942584i \(-0.608388\pi\)
0.993267 + 0.115850i \(0.0369592\pi\)
\(182\) 11.9521 25.5805i 0.885951 1.89615i
\(183\) 2.38849 6.39270i 0.176562 0.472562i
\(184\) 0.475244 + 2.08218i 0.0350355 + 0.153500i
\(185\) 1.48694 0.224119i 0.109322 0.0164776i
\(186\) 16.8885 + 7.79382i 1.23832 + 0.571471i
\(187\) −5.62782 0.848257i −0.411547 0.0620307i
\(188\) −9.93033 + 4.78219i −0.724244 + 0.348777i
\(189\) −13.6212 + 1.86123i −0.990793 + 0.135384i
\(190\) 53.5430 + 25.7850i 3.88442 + 1.87064i
\(191\) −1.56367 1.06609i −0.113143 0.0771398i 0.505426 0.862870i \(-0.331335\pi\)
−0.618570 + 0.785730i \(0.712288\pi\)
\(192\) −4.39336 + 20.8199i −0.317064 + 1.50254i
\(193\) −0.0803480 + 1.07217i −0.00578358 + 0.0771765i −0.999349 0.0360859i \(-0.988511\pi\)
0.993565 + 0.113262i \(0.0361301\pi\)
\(194\) −15.0748 18.9032i −1.08230 1.35717i
\(195\) 15.1513 + 25.2744i 1.08501 + 1.80994i
\(196\) 18.7648 + 2.38063i 1.34034 + 0.170045i
\(197\) −5.22824 −0.372496 −0.186248 0.982503i \(-0.559633\pi\)
−0.186248 + 0.982503i \(0.559633\pi\)
\(198\) 8.68185 24.4550i 0.616992 1.73794i
\(199\) 16.5013 + 11.2504i 1.16974 + 0.797518i 0.982767 0.184847i \(-0.0591789\pi\)
0.186976 + 0.982364i \(0.440131\pi\)
\(200\) 2.35505 10.3182i 0.166528 0.729605i
\(201\) −1.12509 + 19.2542i −0.0793577 + 1.35809i
\(202\) 1.16592 + 15.5581i 0.0820338 + 1.09467i
\(203\) 0.161420 + 13.7919i 0.0113295 + 0.968003i
\(204\) −5.96785 + 2.99575i −0.417833 + 0.209745i
\(205\) 22.7642 + 3.43115i 1.58992 + 0.239642i
\(206\) 1.97895 + 26.4072i 0.137880 + 1.83988i
\(207\) 2.73034 + 3.20197i 0.189772 + 0.222552i
\(208\) −9.88814 3.05009i −0.685619 0.211485i
\(209\) 31.2708 4.71332i 2.16305 0.326027i
\(210\) −22.6480 + 25.8296i −1.56286 + 1.78241i
\(211\) 20.2689 + 3.05504i 1.39537 + 0.210318i 0.803302 0.595572i \(-0.203074\pi\)
0.592066 + 0.805890i \(0.298313\pi\)
\(212\) −5.94674 2.86380i −0.408424 0.196687i
\(213\) −3.91884 15.9563i −0.268514 1.09330i
\(214\) 24.4345 1.67031
\(215\) 6.37852 11.0479i 0.435012 0.753462i
\(216\) −2.13849 7.61725i −0.145506 0.518288i
\(217\) −12.8072 2.76589i −0.869413 0.187761i
\(218\) −18.5322 17.1953i −1.25516 1.16462i
\(219\) −4.32381 + 1.41193i −0.292176 + 0.0954097i
\(220\) −13.6140 34.6878i −0.917853 2.33865i
\(221\) −2.56527 6.53619i −0.172558 0.439672i
\(222\) 0.337317 1.59853i 0.0226393 0.107286i
\(223\) 9.95324 + 9.23526i 0.666519 + 0.618439i 0.939080 0.343700i \(-0.111680\pi\)
−0.272561 + 0.962138i \(0.587871\pi\)
\(224\) −0.235468 20.1187i −0.0157329 1.34423i
\(225\) −5.30567 20.1664i −0.353712 1.34443i
\(226\) 21.6186 37.4444i 1.43804 2.49077i
\(227\) −18.5880 −1.23373 −0.616864 0.787070i \(-0.711597\pi\)
−0.616864 + 0.787070i \(0.711597\pi\)
\(228\) 26.7806 25.6804i 1.77359 1.70073i
\(229\) −11.3308 5.45661i −0.748758 0.360583i 0.0202729 0.999794i \(-0.493547\pi\)
−0.769031 + 0.639212i \(0.779261\pi\)
\(230\) 10.3975 + 1.56716i 0.685588 + 0.103336i
\(231\) −2.21493 + 18.1456i −0.145732 + 1.19389i
\(232\) −7.84906 + 1.18306i −0.515316 + 0.0776714i
\(233\) −3.09574 0.954908i −0.202808 0.0625581i 0.191687 0.981456i \(-0.438604\pi\)
−0.394495 + 0.918898i \(0.629080\pi\)
\(234\) 31.4840 5.80934i 2.05817 0.379768i
\(235\) 1.05375 + 14.0613i 0.0687390 + 0.917258i
\(236\) −6.27257 0.945438i −0.408310 0.0615428i
\(237\) −18.0701 11.8898i −1.17378 0.772327i
\(238\) 6.33948 5.17809i 0.410927 0.335646i
\(239\) −1.06308 14.1858i −0.0687647 0.917601i −0.919774 0.392450i \(-0.871628\pi\)
0.851009 0.525151i \(-0.175991\pi\)
\(240\) 10.5174 + 6.92025i 0.678895 + 0.446700i
\(241\) 5.95918 26.1089i 0.383865 1.68182i −0.301377 0.953505i \(-0.597446\pi\)
0.685242 0.728315i \(-0.259696\pi\)
\(242\) −8.80208 6.00116i −0.565819 0.385769i
\(243\) −10.6867 11.3488i −0.685552 0.728023i
\(244\) −10.6466 −0.681580
\(245\) 11.6057 21.2344i 0.741462 1.35662i
\(246\) 12.1481 21.8631i 0.774536 1.39394i
\(247\) 24.3255 + 30.5033i 1.54780 + 1.94088i
\(248\) 0.563496 7.51934i 0.0357821 0.477478i
\(249\) 10.7109 + 9.61565i 0.678779 + 0.609367i
\(250\) −12.0833 8.23826i −0.764215 0.521033i
\(251\) 14.6358 + 7.04825i 0.923806 + 0.444882i 0.834429 0.551116i \(-0.185798\pi\)
0.0893779 + 0.995998i \(0.471512\pi\)
\(252\) 10.1576 + 18.8900i 0.639866 + 1.18996i
\(253\) 5.04126 2.42774i 0.316941 0.152631i
\(254\) 10.8199 + 1.63084i 0.678903 + 0.102328i
\(255\) 0.778310 + 8.50737i 0.0487397 + 0.532752i
\(256\) 0.213280 0.0321468i 0.0133300 0.00200918i
\(257\) 2.74576 + 12.0299i 0.171276 + 0.750407i 0.985475 + 0.169822i \(0.0543192\pi\)
−0.814199 + 0.580586i \(0.802824\pi\)
\(258\) −8.81839 10.6926i −0.549009 0.665695i
\(259\) 0.0134686 + 1.15077i 0.000836898 + 0.0715055i
\(260\) 28.6636 35.9430i 1.77764 2.22909i
\(261\) −12.6256 + 9.22998i −0.781505 + 0.571321i
\(262\) −35.3087 + 32.7617i −2.18138 + 2.02402i
\(263\) −16.7955 −1.03566 −0.517829 0.855484i \(-0.673260\pi\)
−0.517829 + 0.855484i \(0.673260\pi\)
\(264\) −10.5188 + 0.172868i −0.647387 + 0.0106393i
\(265\) −6.19001 + 5.74349i −0.380249 + 0.352820i
\(266\) −25.1795 + 37.8765i −1.54386 + 2.32236i
\(267\) 10.8764 + 9.76416i 0.665623 + 0.597557i
\(268\) 28.7529 8.86908i 1.75636 0.541766i
\(269\) −8.11982 1.22387i −0.495074 0.0746204i −0.103240 0.994656i \(-0.532921\pi\)
−0.391834 + 0.920036i \(0.628159\pi\)
\(270\) −38.7563 3.90040i −2.35864 0.237371i
\(271\) 5.17934 + 4.80572i 0.314622 + 0.291927i 0.821638 0.570010i \(-0.193061\pi\)
−0.507015 + 0.861937i \(0.669251\pi\)
\(272\) −2.19908 2.04045i −0.133339 0.123720i
\(273\) −20.7536 + 8.82678i −1.25607 + 0.534221i
\(274\) 17.6805 16.4051i 1.06812 0.991067i
\(275\) −27.7277 −1.67204
\(276\) 3.18859 5.73855i 0.191931 0.345420i
\(277\) 3.15837 + 13.8377i 0.189768 + 0.831428i 0.976738 + 0.214437i \(0.0687916\pi\)
−0.786970 + 0.616992i \(0.788351\pi\)
\(278\) −17.0210 + 11.6047i −1.02085 + 0.696006i
\(279\) −5.87933 13.6440i −0.351986 0.816846i
\(280\) 13.0224 + 4.93582i 0.778236 + 0.294972i
\(281\) 15.5252 2.34005i 0.926156 0.139596i 0.331389 0.943494i \(-0.392483\pi\)
0.594767 + 0.803899i \(0.297245\pi\)
\(282\) 14.7113 + 4.27441i 0.876048 + 0.254537i
\(283\) 8.15710 1.22949i 0.484889 0.0730853i 0.0979517 0.995191i \(-0.468771\pi\)
0.386938 + 0.922106i \(0.373533\pi\)
\(284\) −21.1791 + 14.4396i −1.25675 + 0.856835i
\(285\) −18.0659 43.8962i −1.07013 2.60018i
\(286\) 3.18132 42.4518i 0.188115 2.51023i
\(287\) −4.99587 + 16.8958i −0.294897 + 0.997325i
\(288\) 18.4173 13.4640i 1.08525 0.793376i
\(289\) −1.11829 + 14.9226i −0.0657819 + 0.877798i
\(290\) −8.69612 + 38.1002i −0.510654 + 2.23732i
\(291\) −1.12656 + 19.2794i −0.0660401 + 1.13018i
\(292\) 4.42435 + 5.54796i 0.258916 + 0.324670i
\(293\) 12.5891 + 21.8050i 0.735465 + 1.27386i 0.954519 + 0.298149i \(0.0963694\pi\)
−0.219055 + 0.975713i \(0.570297\pi\)
\(294\) −17.1979 19.8860i −1.00300 1.15977i
\(295\) −4.05771 + 7.02816i −0.236249 + 0.409196i
\(296\) −0.654911 + 0.0987120i −0.0380659 + 0.00573752i
\(297\) −18.2093 + 9.90286i −1.05661 + 0.574622i
\(298\) −21.0370 + 6.48906i −1.21864 + 0.375901i
\(299\) 5.70362 + 3.88866i 0.329849 + 0.224887i
\(300\) −26.5746 + 18.7652i −1.53428 + 1.08341i
\(301\) 7.70402 + 5.99760i 0.444052 + 0.345696i
\(302\) −4.01442 2.73698i −0.231004 0.157496i
\(303\) 7.60873 9.86948i 0.437110 0.566987i
\(304\) 15.0181 + 7.23234i 0.861348 + 0.414803i
\(305\) −4.97620 + 12.6791i −0.284936 + 0.726006i
\(306\) 8.95419 + 2.44284i 0.511877 + 0.139648i
\(307\) −18.2211 22.8485i −1.03993 1.30403i −0.951400 0.307959i \(-0.900354\pi\)
−0.0885313 0.996073i \(-0.528217\pi\)
\(308\) 27.7278 6.67104i 1.57994 0.380118i
\(309\) 12.9145 16.7517i 0.734680 0.952972i
\(310\) −33.4475 16.1075i −1.89969 0.914844i
\(311\) 2.99066 + 0.922495i 0.169585 + 0.0523099i 0.378385 0.925648i \(-0.376480\pi\)
−0.208800 + 0.977958i \(0.566956\pi\)
\(312\) −6.67330 11.1320i −0.377801 0.630223i
\(313\) −2.72048 4.71201i −0.153771 0.266338i 0.778840 0.627222i \(-0.215808\pi\)
−0.932611 + 0.360884i \(0.882475\pi\)
\(314\) 4.22460 + 18.5092i 0.238408 + 1.04453i
\(315\) 27.2439 3.26760i 1.53502 0.184108i
\(316\) −7.50928 + 32.9003i −0.422430 + 1.85079i
\(317\) −2.29368 + 0.707506i −0.128826 + 0.0397375i −0.358498 0.933531i \(-0.616711\pi\)
0.229672 + 0.973268i \(0.426235\pi\)
\(318\) 3.49158 + 8.48376i 0.195798 + 0.475746i
\(319\) 7.59762 + 19.3584i 0.425385 + 1.08386i
\(320\) 9.45036 41.4047i 0.528291 2.31460i
\(321\) −14.5233 13.0381i −0.810609 0.727717i
\(322\) −2.28185 + 7.71708i −0.127162 + 0.430056i
\(323\) 2.51686 + 11.0271i 0.140042 + 0.613564i
\(324\) −10.7501 + 21.8145i −0.597229 + 1.21192i
\(325\) −17.1041 29.6251i −0.948762 1.64330i
\(326\) 6.40771 + 28.0740i 0.354890 + 1.55488i
\(327\) 1.83971 + 20.1091i 0.101736 + 1.11204i
\(328\) −10.0263 1.51123i −0.553611 0.0834435i
\(329\) −10.7702 0.680467i −0.593783 0.0375153i
\(330\) −18.1278 + 48.5185i −0.997904 + 2.67086i
\(331\) 11.5524 10.7190i 0.634975 0.589171i −0.295582 0.955317i \(-0.595514\pi\)
0.930557 + 0.366147i \(0.119323\pi\)
\(332\) 8.20407 20.9036i 0.450257 1.14724i
\(333\) −1.05346 + 0.770132i −0.0577291 + 0.0422030i
\(334\) 13.1288 + 33.4515i 0.718374 + 1.83039i
\(335\) 2.87674 38.3874i 0.157173 2.09733i
\(336\) −6.35246 + 7.24485i −0.346555 + 0.395239i
\(337\) −1.25316 16.7223i −0.0682642 0.910922i −0.921246 0.388981i \(-0.872827\pi\)
0.852982 0.521941i \(-0.174792\pi\)
\(338\) 21.9210 10.5566i 1.19235 0.574204i
\(339\) −32.8296 + 10.7205i −1.78306 + 0.582256i
\(340\) 12.0079 5.78270i 0.651219 0.313611i
\(341\) −19.5344 + 2.94434i −1.05785 + 0.159445i
\(342\) −51.5442 + 1.69463i −2.78719 + 0.0916354i
\(343\) 14.8761 + 11.0318i 0.803236 + 0.595661i
\(344\) −2.80938 + 4.86599i −0.151472 + 0.262356i
\(345\) −5.34375 6.47950i −0.287698 0.348845i
\(346\) 3.18802 42.5411i 0.171389 2.28703i
\(347\) −18.8887 17.5261i −1.01400 0.940852i −0.0157408 0.999876i \(-0.505011\pi\)
−0.998257 + 0.0590240i \(0.981201\pi\)
\(348\) 20.3828 + 13.4115i 1.09263 + 0.718933i
\(349\) −7.28245 + 4.96509i −0.389820 + 0.265775i −0.742332 0.670032i \(-0.766280\pi\)
0.352511 + 0.935808i \(0.385328\pi\)
\(350\) 26.7802 29.5484i 1.43146 1.57943i
\(351\) −21.8131 13.3467i −1.16430 0.712396i
\(352\) −11.0829 28.2387i −0.590718 1.50513i
\(353\) 13.3762 + 6.44163i 0.711943 + 0.342853i 0.754554 0.656238i \(-0.227853\pi\)
−0.0426112 + 0.999092i \(0.513568\pi\)
\(354\) 5.60984 + 6.80215i 0.298160 + 0.361530i
\(355\) 7.29725 + 31.9714i 0.387298 + 1.69686i
\(356\) 8.33077 21.2265i 0.441530 1.12500i
\(357\) −6.53102 0.304983i −0.345658 0.0161414i
\(358\) 9.23102 + 23.5202i 0.487874 + 1.24308i
\(359\) 20.2065 13.7766i 1.06646 0.727100i 0.102926 0.994689i \(-0.467179\pi\)
0.963533 + 0.267589i \(0.0862271\pi\)
\(360\) 4.01782 + 15.2714i 0.211758 + 0.804872i
\(361\) −21.9238 37.9731i −1.15388 1.99858i
\(362\) 15.4245 + 26.7160i 0.810694 + 1.40416i
\(363\) 2.02955 + 8.26367i 0.106524 + 0.433730i
\(364\) 24.2317 + 25.5102i 1.27009 + 1.33710i
\(365\) 8.67504 2.67590i 0.454072 0.140063i
\(366\) 11.0118 + 9.88573i 0.575595 + 0.516735i
\(367\) 12.8800 16.1510i 0.672332 0.843078i −0.322291 0.946641i \(-0.604453\pi\)
0.994623 + 0.103563i \(0.0330243\pi\)
\(368\) 2.91635 + 0.439569i 0.152025 + 0.0229141i
\(369\) −18.8866 + 6.51273i −0.983196 + 0.339039i
\(370\) −0.725588 + 3.17901i −0.0377215 + 0.165269i
\(371\) −3.70274 5.29666i −0.192237 0.274989i
\(372\) −16.7294 + 16.0422i −0.867380 + 0.831749i
\(373\) −31.9671 −1.65519 −0.827597 0.561323i \(-0.810293\pi\)
−0.827597 + 0.561323i \(0.810293\pi\)
\(374\) 6.17074 10.6880i 0.319081 0.552665i
\(375\) 2.78612 + 11.3442i 0.143875 + 0.585811i
\(376\) −0.464117 6.19321i −0.0239350 0.319390i
\(377\) −15.9965 + 20.0589i −0.823860 + 1.03309i
\(378\) 7.03401 28.9695i 0.361790 1.49003i
\(379\) −5.96511 7.48001i −0.306407 0.384222i 0.604658 0.796485i \(-0.293310\pi\)
−0.911065 + 0.412263i \(0.864738\pi\)
\(380\) −54.2864 + 50.3704i −2.78483 + 2.58395i
\(381\) −5.56088 6.74279i −0.284893 0.345443i
\(382\) 3.39074 2.31177i 0.173486 0.118280i
\(383\) 13.3468 16.7363i 0.681988 0.855186i −0.313548 0.949572i \(-0.601518\pi\)
0.995536 + 0.0943867i \(0.0300890\pi\)
\(384\) −16.5387 10.8822i −0.843986 0.555327i
\(385\) 5.01531 36.1393i 0.255604 1.84183i
\(386\) −2.10058 1.01158i −0.106917 0.0514883i
\(387\) −0.464103 + 11.0609i −0.0235917 + 0.562256i
\(388\) 28.7904 8.88067i 1.46161 0.450848i
\(389\) 10.3710 4.99441i 0.525831 0.253227i −0.152083 0.988368i \(-0.548598\pi\)
0.677914 + 0.735141i \(0.262884\pi\)
\(390\) −63.0210 + 10.5607i −3.19119 + 0.534764i
\(391\) 1.00062 + 1.73313i 0.0506037 + 0.0876482i
\(392\) −5.11166 + 9.35256i −0.258178 + 0.472376i
\(393\) 38.4680 0.632192i 1.94046 0.0318899i
\(394\) 4.14193 10.5535i 0.208667 0.531676i
\(395\) 35.6714 + 24.3204i 1.79482 + 1.22369i
\(396\) 24.4151 + 21.2043i 1.22690 + 1.06556i
\(397\) 2.03095 27.1012i 0.101931 1.36017i −0.678350 0.734739i \(-0.737304\pi\)
0.780280 0.625430i \(-0.215076\pi\)
\(398\) −35.7821 + 24.3958i −1.79360 + 1.22285i
\(399\) 35.1767 9.07717i 1.76104 0.454427i
\(400\) −12.0756 8.23297i −0.603778 0.411649i
\(401\) 15.7330 19.7285i 0.785667 0.985195i −0.214298 0.976768i \(-0.568746\pi\)
0.999964 0.00842640i \(-0.00268224\pi\)
\(402\) −37.9743 17.5247i −1.89398 0.874051i
\(403\) −15.1958 19.0549i −0.756957 0.949194i
\(404\) −18.5781 5.73057i −0.924293 0.285107i
\(405\) 20.9545 + 22.9985i 1.04124 + 1.14280i
\(406\) −27.9676 10.6004i −1.38801 0.526091i
\(407\) 0.633931 + 1.61523i 0.0314228 + 0.0800640i
\(408\) −0.342802 3.74702i −0.0169712 0.185505i
\(409\) −11.3108 3.48891i −0.559282 0.172516i 0.00221049 0.999998i \(-0.499296\pi\)
−0.561492 + 0.827482i \(0.689773\pi\)
\(410\) −24.9602 + 43.2324i −1.23270 + 2.13510i
\(411\) −19.2625 + 0.316564i −0.950148 + 0.0156149i
\(412\) −31.5330 9.72665i −1.55352 0.479198i
\(413\) −4.90093 3.81539i −0.241159 0.187743i
\(414\) −8.62638 + 2.97467i −0.423964 + 0.146197i
\(415\) −21.0598 19.5406i −1.03378 0.959210i
\(416\) 23.3345 29.2605i 1.14407 1.43462i
\(417\) 16.3091 + 2.18476i 0.798659 + 0.106988i
\(418\) −15.2594 + 66.8558i −0.746362 + 3.27002i
\(419\) 9.24523 2.85177i 0.451659 0.139318i −0.0605762 0.998164i \(-0.519294\pi\)
0.512235 + 0.858845i \(0.328818\pi\)
\(420\) −19.6512 38.0306i −0.958882 1.85570i
\(421\) 7.53505 + 2.32426i 0.367236 + 0.113277i 0.472880 0.881127i \(-0.343214\pi\)
−0.105644 + 0.994404i \(0.533691\pi\)
\(422\) −22.2242 + 38.4935i −1.08186 + 1.87384i
\(423\) −6.46324 10.3905i −0.314254 0.505203i
\(424\) 2.72635 2.52968i 0.132403 0.122852i
\(425\) −0.741106 9.88937i −0.0359489 0.479705i
\(426\) 35.3131 + 4.73054i 1.71093 + 0.229195i
\(427\) −9.08812 5.10616i −0.439805 0.247104i
\(428\) −11.1241 + 28.3438i −0.537704 + 1.37005i
\(429\) −24.5429 + 23.5347i −1.18494 + 1.13627i
\(430\) 17.2476 + 21.6278i 0.831753 + 1.04299i
\(431\) 0.191633 + 2.55716i 0.00923062 + 0.123174i 0.999915 0.0130004i \(-0.00413827\pi\)
−0.990685 + 0.136174i \(0.956519\pi\)
\(432\) −10.8706 1.09401i −0.523014 0.0526357i
\(433\) 21.9140 10.5532i 1.05312 0.507156i 0.174490 0.984659i \(-0.444172\pi\)
0.878630 + 0.477503i \(0.158458\pi\)
\(434\) 15.7293 23.6609i 0.755030 1.13576i
\(435\) 25.4988 18.0056i 1.22257 0.863301i
\(436\) 28.3834 13.6687i 1.35932 0.654614i
\(437\) −8.15145 7.56344i −0.389937 0.361808i
\(438\) 0.575359 9.84640i 0.0274917 0.470479i
\(439\) 1.58011 4.02607i 0.0754147 0.192154i −0.888195 0.459467i \(-0.848041\pi\)
0.963610 + 0.267313i \(0.0861358\pi\)
\(440\) 20.9973 1.00101
\(441\) −0.389055 + 20.9964i −0.0185264 + 0.999828i
\(442\) 15.2259 0.724222
\(443\) 4.61303 11.7538i 0.219172 0.558440i −0.778424 0.627738i \(-0.783981\pi\)
0.997596 + 0.0692983i \(0.0220760\pi\)
\(444\) 1.70071 + 1.11903i 0.0807119 + 0.0531070i
\(445\) −21.3850 19.8424i −1.01375 0.940619i
\(446\) −26.5270 + 12.7748i −1.25609 + 0.604902i
\(447\) 15.9664 + 7.36829i 0.755184 + 0.348508i
\(448\) 30.3933 + 11.5199i 1.43595 + 0.544262i
\(449\) −2.18381 + 1.05167i −0.103060 + 0.0496313i −0.484704 0.874678i \(-0.661073\pi\)
0.381643 + 0.924310i \(0.375358\pi\)
\(450\) 44.9101 + 5.26649i 2.11708 + 0.248265i
\(451\) 1.98518 + 26.4903i 0.0934782 + 1.24738i
\(452\) 33.5930 + 42.1243i 1.58008 + 1.98136i
\(453\) 0.925628 + 3.76886i 0.0434898 + 0.177077i
\(454\) 14.7258 37.5208i 0.691118 1.76094i
\(455\) 41.7061 16.9344i 1.95521 0.793895i
\(456\) 7.95701 + 19.3338i 0.372621 + 0.905387i
\(457\) 1.08510 + 14.4796i 0.0507587 + 0.677328i 0.963314 + 0.268375i \(0.0864868\pi\)
−0.912556 + 0.408952i \(0.865894\pi\)
\(458\) 19.9909 18.5489i 0.934115 0.866732i
\(459\) −4.01866 6.22986i −0.187575 0.290785i
\(460\) −6.55146 + 11.3475i −0.305464 + 0.529078i
\(461\) −30.6932 9.46761i −1.42953 0.440951i −0.519133 0.854693i \(-0.673745\pi\)
−0.910394 + 0.413743i \(0.864221\pi\)
\(462\) −34.8731 18.8463i −1.62245 0.876811i
\(463\) −18.5687 + 5.72770i −0.862963 + 0.266189i −0.694477 0.719515i \(-0.744364\pi\)
−0.168486 + 0.985704i \(0.553888\pi\)
\(464\) −2.43915 + 10.6866i −0.113235 + 0.496113i
\(465\) 11.2855 + 27.4213i 0.523353 + 1.27163i
\(466\) 4.38004 5.49240i 0.202902 0.254431i
\(467\) 22.0761 + 20.4836i 1.02156 + 0.947870i 0.998654 0.0518679i \(-0.0165175\pi\)
0.0229066 + 0.999738i \(0.492708\pi\)
\(468\) −7.59469 + 39.1658i −0.351065 + 1.81044i
\(469\) 28.7975 + 6.21919i 1.32975 + 0.287176i
\(470\) −29.2183 9.01264i −1.34774 0.415722i
\(471\) 7.36540 13.2556i 0.339380 0.610786i
\(472\) 1.78719 3.09551i 0.0822622 0.142482i
\(473\) 14.0665 + 4.33895i 0.646780 + 0.199505i
\(474\) 38.3158 27.0561i 1.75990 1.24273i
\(475\) 20.1318 + 51.2950i 0.923710 + 2.35357i
\(476\) 3.12041 + 9.71112i 0.143024 + 0.445109i
\(477\) 2.45158 6.90561i 0.112250 0.316186i
\(478\) 29.4769 + 9.09242i 1.34824 + 0.415877i
\(479\) 1.12862 + 1.41524i 0.0515679 + 0.0646641i 0.806947 0.590624i \(-0.201118\pi\)
−0.755379 + 0.655288i \(0.772547\pi\)
\(480\) −37.1958 + 26.2652i −1.69775 + 1.19884i
\(481\) −1.33472 + 1.67368i −0.0608578 + 0.0763132i
\(482\) 47.9811 + 32.7130i 2.18548 + 1.49003i
\(483\) 5.47406 3.36926i 0.249078 0.153306i
\(484\) 10.9685 7.47822i 0.498570 0.339919i
\(485\) 2.88050 38.4376i 0.130797 1.74536i
\(486\) 31.3743 12.5809i 1.42317 0.570682i
\(487\) 12.3283 + 8.40530i 0.558649 + 0.380880i 0.809477 0.587151i \(-0.199751\pi\)
−0.250828 + 0.968032i \(0.580703\pi\)
\(488\) 2.19173 5.58445i 0.0992152 0.252796i
\(489\) 11.1716 20.1056i 0.505195 0.909207i
\(490\) 33.6685 + 40.2491i 1.52099 + 1.81827i
\(491\) −5.48645 9.50282i −0.247600 0.428856i 0.715259 0.698859i \(-0.246309\pi\)
−0.962859 + 0.270003i \(0.912975\pi\)
\(492\) 19.8304 + 24.0452i 0.894025 + 1.08404i
\(493\) −6.70131 + 3.22718i −0.301812 + 0.145345i
\(494\) −80.8437 + 24.9370i −3.63733 + 1.12197i
\(495\) 36.6639 19.1653i 1.64792 0.861415i
\(496\) −9.38160 4.51794i −0.421246 0.202861i
\(497\) −25.0041 + 2.16834i −1.12159 + 0.0972636i
\(498\) −27.8952 + 14.0029i −1.25001 + 0.627483i
\(499\) 4.31758 5.41407i 0.193281 0.242367i −0.675742 0.737138i \(-0.736177\pi\)
0.869023 + 0.494771i \(0.164748\pi\)
\(500\) 15.0574 10.2659i 0.673386 0.459107i
\(501\) 10.0461 26.8882i 0.448828 1.20127i
\(502\) −25.8221 + 23.9594i −1.15250 + 1.06936i
\(503\) −17.9430 22.4999i −0.800041 1.00322i −0.999727 0.0233594i \(-0.992564\pi\)
0.199687 0.979860i \(-0.436008\pi\)
\(504\) −11.9994 + 1.43919i −0.534495 + 0.0641068i
\(505\) −15.5079 + 19.4463i −0.690093 + 0.865350i
\(506\) 0.906722 + 12.0994i 0.0403087 + 0.537882i
\(507\) −18.6622 5.42235i −0.828819 0.240815i
\(508\) −6.81767 + 11.8086i −0.302485 + 0.523920i
\(509\) −9.26906 −0.410844 −0.205422 0.978674i \(-0.565857\pi\)
−0.205422 + 0.978674i \(0.565857\pi\)
\(510\) −17.7892 5.16868i −0.787717 0.228873i
\(511\) 1.11587 + 6.85776i 0.0493633 + 0.303369i
\(512\) 4.98285 21.8313i 0.220213 0.964815i
\(513\) 31.5408 + 26.4964i 1.39256 + 1.16985i
\(514\) −26.4583 3.98795i −1.16703 0.175901i
\(515\) −26.3220 + 33.0067i −1.15989 + 1.45445i
\(516\) 16.4180 5.36129i 0.722763 0.236018i
\(517\) −15.5482 + 4.79597i −0.683807 + 0.210927i
\(518\) −2.33356 0.884481i −0.102531 0.0388619i
\(519\) −24.5946 + 23.5842i −1.07958 + 1.03523i
\(520\) 12.9524 + 22.4342i 0.567999 + 0.983803i
\(521\) −2.26439 3.92204i −0.0992047 0.171828i 0.812151 0.583447i \(-0.198297\pi\)
−0.911356 + 0.411620i \(0.864963\pi\)
\(522\) −8.62889 32.7976i −0.377676 1.43551i
\(523\) −15.0828 + 10.2833i −0.659526 + 0.449657i −0.846272 0.532751i \(-0.821158\pi\)
0.186746 + 0.982408i \(0.440206\pi\)
\(524\) −21.9285 55.8729i −0.957951 2.44082i
\(525\) −31.6843 + 3.27303i −1.38282 + 0.142847i
\(526\) 13.3058 33.9027i 0.580161 1.47823i
\(527\) −1.57225 6.88847i −0.0684882 0.300066i
\(528\) −5.08462 + 13.6088i −0.221280 + 0.592247i
\(529\) 18.9496 + 9.12567i 0.823897 + 0.396768i
\(530\) −6.68966 17.0450i −0.290580 0.740387i
\(531\) 0.295240 7.03640i 0.0128123 0.305354i
\(532\) −32.4730 46.4517i −1.40788 2.01394i
\(533\) −27.0785 + 18.4618i −1.17290 + 0.799669i
\(534\) −28.3260 + 14.2191i −1.22578 + 0.615321i
\(535\) 28.5555 + 26.4956i 1.23456 + 1.14551i
\(536\) −1.26704 + 16.9075i −0.0547278 + 0.730292i
\(537\) 7.06359 18.9054i 0.304816 0.815830i
\(538\) 8.90315 15.4207i 0.383842 0.664834i
\(539\) 26.8684 + 7.60387i 1.15730 + 0.327522i
\(540\) 22.1687 43.1812i 0.953990 1.85822i
\(541\) −11.9566 + 1.80217i −0.514054 + 0.0774812i −0.400946 0.916102i \(-0.631319\pi\)
−0.113108 + 0.993583i \(0.536081\pi\)
\(542\) −13.8038 + 6.64756i −0.592924 + 0.285537i
\(543\) 5.08758 24.1097i 0.218329 1.03465i
\(544\) 9.77540 4.70758i 0.419117 0.201836i
\(545\) −3.01188 40.1908i −0.129015 1.72158i
\(546\) −1.37580 48.8850i −0.0588788 2.09209i
\(547\) −3.03845 + 40.5453i −0.129915 + 1.73359i 0.428075 + 0.903743i \(0.359192\pi\)
−0.557990 + 0.829848i \(0.688427\pi\)
\(548\) 10.9805 + 27.9778i 0.469062 + 1.19515i
\(549\) −1.27016 11.7516i −0.0542089 0.501548i
\(550\) 21.9665 55.9698i 0.936655 2.38656i
\(551\) 30.2959 28.1105i 1.29065 1.19755i
\(552\) 2.35362 + 2.85385i 0.100177 + 0.121468i
\(553\) −22.1891 + 24.4827i −0.943578 + 1.04111i
\(554\) −30.4343 4.58723i −1.29303 0.194893i
\(555\) 2.12757 1.50235i 0.0903104 0.0637713i
\(556\) −5.71234 25.0274i −0.242257 1.06140i
\(557\) 2.60485 + 4.51174i 0.110371 + 0.191169i 0.915920 0.401361i \(-0.131463\pi\)
−0.805549 + 0.592529i \(0.798129\pi\)
\(558\) 32.1989 1.05861i 1.36309 0.0448147i
\(559\) 4.04120 + 17.7056i 0.170924 + 0.748869i
\(560\) 12.9148 14.2497i 0.545749 0.602161i
\(561\) −9.37080 + 3.06002i −0.395636 + 0.129194i
\(562\) −7.57592 + 33.1923i −0.319571 + 1.40013i
\(563\) 2.27876 + 5.80619i 0.0960384 + 0.244702i 0.970817 0.239821i \(-0.0770886\pi\)
−0.874779 + 0.484522i \(0.838993\pi\)
\(564\) −11.6558 + 15.1190i −0.490797 + 0.636626i
\(565\) 65.8675 20.3174i 2.77107 0.854761i
\(566\) −3.98047 + 17.4396i −0.167311 + 0.733039i
\(567\) −19.6388 + 13.4654i −0.824752 + 0.565495i
\(568\) −3.21403 14.0816i −0.134858 0.590850i
\(569\) −4.40656 7.63239i −0.184733 0.319966i 0.758754 0.651378i \(-0.225809\pi\)
−0.943486 + 0.331411i \(0.892475\pi\)
\(570\) 102.919 1.69139i 4.31080 0.0708446i
\(571\) −0.912447 0.281453i −0.0381847 0.0117784i 0.275604 0.961271i \(-0.411122\pi\)
−0.313789 + 0.949493i \(0.601598\pi\)
\(572\) 47.7953 + 23.0170i 1.99842 + 0.962389i
\(573\) −3.24892 0.435224i −0.135725 0.0181817i
\(574\) −30.1471 23.4696i −1.25832 0.979604i
\(575\) 6.07890 + 7.62270i 0.253508 + 0.317889i
\(576\) 9.37731 + 35.6423i 0.390721 + 1.48510i
\(577\) −10.6369 + 27.1025i −0.442822 + 1.12829i 0.519039 + 0.854751i \(0.326290\pi\)
−0.961860 + 0.273540i \(0.911805\pi\)
\(578\) −29.2360 14.0793i −1.21606 0.585623i
\(579\) 0.708753 + 1.72212i 0.0294548 + 0.0715687i
\(580\) −40.2368 27.4330i −1.67074 1.13909i
\(581\) 17.0286 13.9090i 0.706465 0.577041i
\(582\) −38.0239 17.5476i −1.57614 0.727370i
\(583\) −8.05074 5.48890i −0.333428 0.227327i
\(584\) −3.82087 + 1.17858i −0.158109 + 0.0487700i
\(585\) 43.0932 + 27.3506i 1.78168 + 1.13081i
\(586\) −53.9879 + 8.13737i −2.23022 + 0.336152i
\(587\) −11.6292 + 20.1423i −0.479987 + 0.831362i −0.999736 0.0229569i \(-0.992692\pi\)
0.519750 + 0.854319i \(0.326025\pi\)
\(588\) 30.8971 10.8960i 1.27417 0.449345i
\(589\) 19.6300 + 34.0001i 0.808838 + 1.40095i
\(590\) −10.9721 13.7586i −0.451714 0.566432i
\(591\) −8.09312 + 4.06260i −0.332907 + 0.167113i
\(592\) −0.203518 + 0.891670i −0.00836453 + 0.0366474i
\(593\) 0.240225 3.20558i 0.00986487 0.131637i −0.990097 0.140386i \(-0.955166\pi\)
0.999962 + 0.00874840i \(0.00278474\pi\)
\(594\) −5.56358 44.6017i −0.228276 1.83003i
\(595\) 13.0235 + 0.822830i 0.533913 + 0.0337327i
\(596\) 2.05012 27.3569i 0.0839761 1.12058i
\(597\) 34.2855 + 4.59287i 1.40321 + 0.187974i
\(598\) −12.3680 + 8.43236i −0.505765 + 0.344825i
\(599\) −17.3914 + 2.62133i −0.710593 + 0.107105i −0.494386 0.869243i \(-0.664607\pi\)
−0.216208 + 0.976347i \(0.569369\pi\)
\(600\) −4.37219 17.8022i −0.178494 0.726770i
\(601\) −30.5182 + 4.59987i −1.24486 + 0.187633i −0.738241 0.674537i \(-0.764343\pi\)
−0.506620 + 0.862169i \(0.669105\pi\)
\(602\) −18.2098 + 10.7995i −0.742175 + 0.440155i
\(603\) 13.2199 + 30.6791i 0.538355 + 1.24935i
\(604\) 5.00248 3.41064i 0.203548 0.138777i
\(605\) −3.77922 16.5578i −0.153647 0.673171i
\(606\) 13.8942 + 23.1774i 0.564415 + 0.941519i
\(607\) −22.6708 −0.920180 −0.460090 0.887872i \(-0.652183\pi\)
−0.460090 + 0.887872i \(0.652183\pi\)
\(608\) −44.1935 + 41.0056i −1.79228 + 1.66300i
\(609\) 10.9669 + 21.2240i 0.444400 + 0.860038i
\(610\) −21.6513 20.0894i −0.876634 0.813397i
\(611\) −14.7152 13.6537i −0.595312 0.552369i
\(612\) −6.91017 + 9.27464i −0.279327 + 0.374905i
\(613\) −20.9836 3.16277i −0.847521 0.127743i −0.289098 0.957299i \(-0.593355\pi\)
−0.558423 + 0.829556i \(0.688593\pi\)
\(614\) 60.5560 18.6791i 2.44384 0.753825i
\(615\) 37.9043 12.3776i 1.52845 0.499113i
\(616\) −2.20896 + 15.9173i −0.0890015 + 0.641328i
\(617\) 11.5088 10.6786i 0.463326 0.429904i −0.413651 0.910435i \(-0.635747\pi\)
0.876978 + 0.480531i \(0.159556\pi\)
\(618\) 23.5831 + 39.3397i 0.948649 + 1.58247i
\(619\) −39.3542 −1.58178 −0.790889 0.611960i \(-0.790381\pi\)
−0.790889 + 0.611960i \(0.790381\pi\)
\(620\) 33.9119 31.4657i 1.36194 1.26369i
\(621\) 6.71456 + 2.83492i 0.269446 + 0.113761i
\(622\) −4.23137 + 5.30597i −0.169663 + 0.212750i
\(623\) 17.2916 14.1238i 0.692772 0.565857i
\(624\) −17.6766 + 2.96215i −0.707628 + 0.118581i
\(625\) 2.54556 + 11.1528i 0.101822 + 0.446113i
\(626\) 11.6667 1.75847i 0.466293 0.0702824i
\(627\) 44.7437 31.5951i 1.78689 1.26178i
\(628\) −23.3938 3.52604i −0.933513 0.140704i
\(629\) −0.559145 + 0.269270i −0.0222946 + 0.0107365i
\(630\) −14.9874 + 57.5818i −0.597112 + 2.29411i
\(631\) −40.1055 19.3138i −1.59658 0.768871i −0.597130 0.802144i \(-0.703692\pi\)
−0.999446 + 0.0332738i \(0.989407\pi\)
\(632\) −15.7112 10.7117i −0.624960 0.426090i
\(633\) 33.7494 11.0208i 1.34142 0.438039i
\(634\) 0.388968 5.19041i 0.0154479 0.206138i
\(635\) 10.8763 + 13.6385i 0.431615 + 0.541228i
\(636\) −11.4307 + 0.187854i −0.453255 + 0.00744889i
\(637\) 8.44978 + 33.3975i 0.334793 + 1.32326i
\(638\) −45.0950 −1.78533
\(639\) −18.4650 21.6546i −0.730465 0.856642i
\(640\) 32.6482 + 22.2592i 1.29054 + 0.879872i
\(641\) 4.85902 21.2888i 0.191920 0.840856i −0.783656 0.621195i \(-0.786648\pi\)
0.975576 0.219661i \(-0.0704952\pi\)
\(642\) 37.8238 18.9868i 1.49278 0.749351i
\(643\) 0.326436 + 4.35599i 0.0128734 + 0.171783i 0.999935 + 0.0114393i \(0.00364132\pi\)
−0.987061 + 0.160344i \(0.948740\pi\)
\(644\) −7.91290 6.16022i −0.311812 0.242746i
\(645\) 1.28894 22.0582i 0.0507519 0.868542i
\(646\) −24.2527 3.65550i −0.954209 0.143824i
\(647\) 1.60515 + 21.4192i 0.0631049 + 0.842077i 0.935512 + 0.353296i \(0.114939\pi\)
−0.872407 + 0.488781i \(0.837442\pi\)
\(648\) −9.22929 10.1295i −0.362561 0.397925i
\(649\) −8.94847 2.76024i −0.351258 0.108349i
\(650\) 73.3500 11.0557i 2.87702 0.433642i
\(651\) −21.9744 + 5.67037i −0.861244 + 0.222239i
\(652\) −35.4828 5.34817i −1.38961 0.209450i
\(653\) −23.6520 11.3902i −0.925576 0.445734i −0.0905173 0.995895i \(-0.528852\pi\)
−0.835059 + 0.550161i \(0.814566\pi\)
\(654\) −42.0488 12.2174i −1.64424 0.477736i
\(655\) −76.7888 −3.00039
\(656\) −7.00102 + 12.1261i −0.273344 + 0.473445i
\(657\) −5.59596 + 5.54544i −0.218319 + 0.216348i
\(658\) 9.90599 21.2012i 0.386176 0.826509i
\(659\) 22.2748 + 20.6680i 0.867705 + 0.805112i 0.982107 0.188322i \(-0.0603049\pi\)
−0.114403 + 0.993434i \(0.536495\pi\)
\(660\) −48.0281 43.1168i −1.86949 1.67832i
\(661\) −13.1866 33.5988i −0.512898 1.30684i −0.919447 0.393214i \(-0.871363\pi\)
0.406549 0.913629i \(-0.366732\pi\)
\(662\) 12.4849 + 31.8109i 0.485238 + 1.23637i
\(663\) −9.04988 8.12445i −0.351468 0.315527i
\(664\) 9.27563 + 8.60653i 0.359964 + 0.333998i
\(665\) −70.4976 + 16.9610i −2.73378 + 0.657720i
\(666\) −0.719979 2.73657i −0.0278986 0.106040i
\(667\) 3.65621 6.33274i 0.141569 0.245205i
\(668\) −44.7804 −1.73261
\(669\) 22.5835 + 6.56169i 0.873130 + 0.253690i
\(670\) 75.2080 + 36.2182i 2.90554 + 1.39923i
\(671\) −15.5416 2.34251i −0.599976 0.0904318i
\(672\) −15.9977 30.9600i −0.617125 1.19431i
\(673\) −11.8594 + 1.78752i −0.457148 + 0.0689040i −0.373580 0.927598i \(-0.621870\pi\)
−0.0835682 + 0.996502i \(0.526632\pi\)
\(674\) 34.7476 + 10.7182i 1.33843 + 0.412850i
\(675\) −23.8833 27.0941i −0.919268 1.04285i
\(676\) 2.26574 + 30.2342i 0.0871438 + 1.16285i
\(677\) 31.7711 + 4.78872i 1.22106 + 0.184045i 0.727771 0.685820i \(-0.240556\pi\)
0.493290 + 0.869865i \(0.335794\pi\)
\(678\) 4.36856 74.7613i 0.167774 2.87119i
\(679\) 28.8352 + 6.22732i 1.10659 + 0.238982i
\(680\) 0.561216 + 7.48891i 0.0215217 + 0.287187i
\(681\) −28.7735 + 14.4438i −1.10260 + 0.553487i
\(682\) 9.53233 41.7639i 0.365012 1.59922i
\(683\) −9.13252 6.22644i −0.349446 0.238248i 0.375858 0.926677i \(-0.377348\pi\)
−0.725304 + 0.688429i \(0.758301\pi\)
\(684\) 21.5004 60.5622i 0.822087 2.31565i
\(685\) 38.4512 1.46915
\(686\) −34.0535 + 21.2886i −1.30017 + 0.812803i
\(687\) −21.7797 + 0.357932i −0.830946 + 0.0136560i
\(688\) 4.83772 + 6.06631i 0.184436 + 0.231276i
\(689\) 0.898342 11.9875i 0.0342241 0.456689i
\(690\) 17.3127 5.65342i 0.659081 0.215222i
\(691\) 14.4794 + 9.87186i 0.550821 + 0.375543i 0.806514 0.591215i \(-0.201351\pi\)
−0.255693 + 0.966758i \(0.582304\pi\)
\(692\) 47.8959 + 23.0654i 1.82073 + 0.876816i
\(693\) 10.6714 + 29.8099i 0.405373 + 1.13238i
\(694\) 50.3414 24.2432i 1.91094 0.920258i
\(695\) −32.4753 4.89486i −1.23186 0.185673i
\(696\) −11.2308 + 7.93044i −0.425701 + 0.300602i
\(697\) −9.39499 + 1.41607i −0.355861 + 0.0536374i
\(698\) −4.25296 18.6335i −0.160977 0.705287i
\(699\) −5.53410 + 0.927377i −0.209319 + 0.0350766i
\(700\) 22.0838 + 44.5171i 0.834689 + 1.68259i
\(701\) 13.3756 16.7724i 0.505188 0.633486i −0.462202 0.886774i \(-0.652941\pi\)
0.967391 + 0.253288i \(0.0815121\pi\)
\(702\) 44.2219 33.4573i 1.66905 1.26276i
\(703\) 2.52784 2.34549i 0.0953392 0.0884618i
\(704\) 49.0062 1.84699
\(705\) 12.5575 + 20.9476i 0.472942 + 0.788931i
\(706\) −23.5997 + 21.8973i −0.888186 + 0.824116i
\(707\) −13.1101 13.8018i −0.493057 0.519070i
\(708\) −10.4444 + 3.41060i −0.392523 + 0.128178i
\(709\) 5.44256 1.67881i 0.204400 0.0630489i −0.190865 0.981616i \(-0.561129\pi\)
0.395264 + 0.918567i \(0.370653\pi\)
\(710\) −70.3169 10.5986i −2.63895 0.397757i
\(711\) −37.2109 4.36362i −1.39552 0.163649i
\(712\) 9.41889 + 8.73945i 0.352988 + 0.327525i
\(713\) 5.09209 + 4.72477i 0.190700 + 0.176944i
\(714\) 5.78965 12.9416i 0.216672 0.484327i
\(715\) 49.7505 46.1617i 1.86056 1.72635i
\(716\) −31.4858 −1.17668
\(717\) −12.6686 21.1330i −0.473119 0.789226i
\(718\) 11.8006 + 51.7020i 0.440396 + 1.92950i
\(719\) 39.9505 27.2378i 1.48990 1.01580i 0.501295 0.865276i \(-0.332857\pi\)
0.988607 0.150521i \(-0.0480952\pi\)
\(720\) 21.6579 + 2.53977i 0.807143 + 0.0946516i
\(721\) −22.2521 23.4262i −0.828713 0.872436i
\(722\) 94.0191 14.1711i 3.49903 0.527394i
\(723\) −11.0633 45.0462i −0.411448 1.67529i
\(724\) −38.0125 + 5.72946i −1.41272 + 0.212934i
\(725\) −29.9399 + 20.4127i −1.11194 + 0.758109i
\(726\) −18.2885 2.44992i −0.678750 0.0909252i
\(727\) −0.279770 + 3.73327i −0.0103761 + 0.138459i −0.999986 0.00532021i \(-0.998307\pi\)
0.989610 + 0.143779i \(0.0459256\pi\)
\(728\) −18.3692 + 7.45863i −0.680807 + 0.276435i
\(729\) −25.3612 9.26338i −0.939303 0.343088i
\(730\) −1.47113 + 19.6309i −0.0544491 + 0.726573i
\(731\) −1.17156 + 5.13295i −0.0433318 + 0.189849i
\(732\) −16.4806 + 8.27295i −0.609140 + 0.305777i
\(733\) −12.6925 15.9159i −0.468810 0.587869i 0.490070 0.871683i \(-0.336971\pi\)
−0.958879 + 0.283815i \(0.908400\pi\)
\(734\) 22.3979 + 38.7942i 0.826720 + 1.43192i
\(735\) 1.46502 41.8883i 0.0540382 1.54507i
\(736\) −5.33342 + 9.23776i −0.196592 + 0.340508i
\(737\) 43.9239 6.62046i 1.61796 0.243868i
\(738\) 1.81611 43.2831i 0.0668520 1.59327i
\(739\) 7.99699 2.46675i 0.294174 0.0907407i −0.144155 0.989555i \(-0.546046\pi\)
0.438330 + 0.898814i \(0.355570\pi\)
\(740\) −3.35728 2.28896i −0.123416 0.0841438i
\(741\) 61.3576 + 28.3158i 2.25403 + 1.04021i
\(742\) 13.6250 3.27804i 0.500189 0.120341i
\(743\) −15.4538 10.5362i −0.566944 0.386536i 0.245656 0.969357i \(-0.420996\pi\)
−0.812601 + 0.582821i \(0.801949\pi\)
\(744\) −4.97063 12.0775i −0.182232 0.442784i
\(745\) −31.6214 15.2281i −1.15852 0.557913i
\(746\) 25.3251 64.5273i 0.927217 2.36251i
\(747\) 24.0520 + 6.56175i 0.880017 + 0.240082i
\(748\) 9.58871 + 12.0239i 0.350598 + 0.439636i
\(749\) −23.0895 + 18.8595i −0.843672 + 0.689112i
\(750\) −25.1061 3.36320i −0.916744 0.122807i
\(751\) −3.58116 1.72460i −0.130679 0.0629315i 0.367402 0.930062i \(-0.380247\pi\)
−0.498081 + 0.867131i \(0.665962\pi\)
\(752\) −8.19534 2.52793i −0.298853 0.0921840i
\(753\) 28.1326 0.462337i 1.02521 0.0168485i
\(754\) −27.8172 48.1808i −1.01304 1.75464i
\(755\) −1.72361 7.55162i −0.0627285 0.274832i
\(756\) 30.4020 + 21.3481i 1.10571 + 0.776423i
\(757\) −0.734581 + 3.21841i −0.0266988 + 0.116975i −0.986521 0.163633i \(-0.947679\pi\)
0.959823 + 0.280608i \(0.0905360\pi\)
\(758\) 19.8245 6.11504i 0.720058 0.222108i
\(759\) 5.91722 7.67537i 0.214781 0.278598i
\(760\) −15.2452 38.8441i −0.553001 1.40902i
\(761\) 0.401040 1.75707i 0.0145377 0.0636937i −0.967139 0.254249i \(-0.918172\pi\)
0.981676 + 0.190555i \(0.0610289\pi\)
\(762\) 18.0161 5.88314i 0.652655 0.213124i
\(763\) 30.7841 + 1.94495i 1.11446 + 0.0704118i
\(764\) 1.13795 + 4.98569i 0.0411696 + 0.180376i
\(765\) 7.81545 + 12.5643i 0.282568 + 0.454264i
\(766\) 23.2095 + 40.2000i 0.838593 + 1.45249i
\(767\) −2.57082 11.2635i −0.0928268 0.406701i
\(768\) 0.305170 0.215491i 0.0110119 0.00777588i
\(769\) −44.5761 6.71877i −1.60746 0.242285i −0.716906 0.697170i \(-0.754442\pi\)
−0.890550 + 0.454885i \(0.849680\pi\)
\(770\) 68.9759 + 38.7541i 2.48572 + 1.39660i
\(771\) 13.5982 + 16.4883i 0.489727 + 0.593813i
\(772\) 2.12974 1.97611i 0.0766510 0.0711218i
\(773\) 8.99201 22.9113i 0.323420 0.824061i −0.673010 0.739634i \(-0.734999\pi\)
0.996430 0.0844270i \(-0.0269060\pi\)
\(774\) −21.9593 9.69949i −0.789310 0.348641i
\(775\) −12.5760 32.0432i −0.451745 1.15103i
\(776\) −1.26870 + 16.9296i −0.0455435 + 0.607736i
\(777\) 0.915056 + 1.77089i 0.0328275 + 0.0635303i
\(778\) 1.86533 + 24.8911i 0.0668753 + 0.892389i
\(779\) 47.5646 22.9059i 1.70418 0.820689i
\(780\) 16.4407 77.9116i 0.588672 2.78968i
\(781\) −34.0935 + 16.4186i −1.21996 + 0.587503i
\(782\) −4.29113 + 0.646784i −0.153451 + 0.0231289i
\(783\) −12.3718 + 24.0984i −0.442133 + 0.861206i
\(784\) 9.44356 + 11.2893i 0.337270 + 0.403191i
\(785\) −15.1334 + 26.2118i −0.540133 + 0.935538i
\(786\) −29.1992 + 78.1506i −1.04150 + 2.78754i
\(787\) −0.166635 + 2.22359i −0.00593989 + 0.0792624i −0.999386 0.0350399i \(-0.988844\pi\)
0.993446 + 0.114302i \(0.0364632\pi\)
\(788\) 10.3562 + 9.60919i 0.368926 + 0.342313i
\(789\) −25.9989 + 13.0510i −0.925585 + 0.464627i
\(790\) −77.3516 + 52.7374i −2.75205 + 1.87631i
\(791\) 8.47255 + 52.0693i 0.301249 + 1.85137i
\(792\) −16.1484 + 8.44122i −0.573808 + 0.299946i
\(793\) −7.08414 18.0501i −0.251565 0.640977i
\(794\) 53.0962 + 25.5698i 1.88431 + 0.907437i
\(795\) −5.11894 + 13.7007i −0.181550 + 0.485913i
\(796\) −12.0087 52.6134i −0.425636 1.86483i
\(797\) −2.84304 + 7.24395i −0.100706 + 0.256594i −0.972343 0.233558i \(-0.924963\pi\)
0.871637 + 0.490151i \(0.163059\pi\)
\(798\) −9.54509 + 78.1972i −0.337893 + 2.76815i
\(799\) −2.12610 5.41723i −0.0752162 0.191648i
\(800\) 43.6742 29.7766i 1.54412 1.05276i
\(801\) 24.4235 + 6.66309i 0.862960 + 0.235429i
\(802\) 27.3590 + 47.3872i 0.966080 + 1.67330i
\(803\) 5.23783 + 9.07219i 0.184839 + 0.320151i
\(804\) 37.6167 36.0714i 1.32664 1.27214i
\(805\) −11.0347 + 6.54427i −0.388923 + 0.230655i
\(806\) 50.5019 15.5778i 1.77885 0.548703i
\(807\) −13.5202 + 4.41500i −0.475934 + 0.155415i
\(808\) 6.83036 8.56500i 0.240291 0.301316i
\(809\) 5.85083 + 0.881871i 0.205704 + 0.0310049i 0.251086 0.967965i \(-0.419212\pi\)
−0.0453817 + 0.998970i \(0.514450\pi\)
\(810\) −63.0242 + 24.0779i −2.21445 + 0.846012i
\(811\) −4.69715 + 20.5796i −0.164939 + 0.722647i 0.823030 + 0.567998i \(0.192282\pi\)
−0.987970 + 0.154649i \(0.950575\pi\)
\(812\) 25.0290 27.6161i 0.878345 0.969136i
\(813\) 11.7517 + 3.41449i 0.412151 + 0.119751i
\(814\) −3.76264 −0.131881
\(815\) −22.9537 + 39.7570i −0.804034 + 1.39263i
\(816\) −4.98963 1.44975i −0.174672 0.0507513i
\(817\) −2.18620 29.1728i −0.0764854 1.02063i
\(818\) 16.0032 20.0674i 0.559539 0.701640i
\(819\) −25.2670 + 29.7901i −0.882901 + 1.04095i
\(820\) −38.7857 48.6357i −1.35445 1.69843i
\(821\) −33.1534 + 30.7619i −1.15706 + 1.07360i −0.160820 + 0.986984i \(0.551414\pi\)
−0.996242 + 0.0866128i \(0.972396\pi\)
\(822\) 14.6212 39.1331i 0.509972 1.36492i
\(823\) −13.5829 + 9.26065i −0.473469 + 0.322806i −0.776437 0.630195i \(-0.782975\pi\)
0.302968 + 0.953001i \(0.402023\pi\)
\(824\) 11.5934 14.5376i 0.403874 0.506441i
\(825\) −42.9215 + 21.5458i −1.49433 + 0.750128i
\(826\) 11.5842 6.87014i 0.403065 0.239043i
\(827\) 2.90186 + 1.39746i 0.100907 + 0.0485944i 0.483657 0.875258i \(-0.339308\pi\)
−0.382749 + 0.923852i \(0.625023\pi\)
\(828\) 0.476686 11.3608i 0.0165660 0.394814i
\(829\) 15.0792 4.65131i 0.523722 0.161547i −0.0216110 0.999766i \(-0.506880\pi\)
0.545333 + 0.838220i \(0.316403\pi\)
\(830\) 56.1277 27.0297i 1.94822 0.938214i
\(831\) 15.6416 + 18.9661i 0.542603 + 0.657927i
\(832\) 30.2299 + 52.3597i 1.04803 + 1.81525i
\(833\) −1.99386 + 9.78612i −0.0690832 + 0.339069i
\(834\) −17.3305 + 31.1899i −0.600106 + 1.08002i
\(835\) −20.9303 + 53.3294i −0.724321 + 1.84554i
\(836\) −70.6050 48.1377i −2.44193 1.66488i
\(837\) −19.7031 16.5519i −0.681038 0.572119i
\(838\) −1.56783 + 20.9212i −0.0541597 + 0.722711i
\(839\) 5.56193 3.79206i 0.192019 0.130916i −0.463494 0.886100i \(-0.653405\pi\)
0.655514 + 0.755183i \(0.272452\pi\)
\(840\) 23.9936 2.47856i 0.827857 0.0855185i
\(841\) −1.50576 1.02661i −0.0519226 0.0354002i
\(842\) −10.6611 + 13.3686i −0.367405 + 0.460711i
\(843\) 22.2141 15.6862i 0.765095 0.540260i
\(844\) −34.5342 43.3045i −1.18872 1.49060i
\(845\) 37.0651 + 11.4331i 1.27508 + 0.393310i
\(846\) 26.0941 4.81481i 0.897132 0.165537i
\(847\) 12.9495 1.12298i 0.444950 0.0385859i
\(848\) −1.87636 4.78089i −0.0644346 0.164177i
\(849\) 11.6715 8.24168i 0.400566 0.282854i
\(850\) 20.5493 + 6.33863i 0.704836 + 0.217413i
\(851\) 0.305068 0.528393i 0.0104576 0.0181131i
\(852\) −21.5641 + 38.8092i −0.738774 + 1.32958i
\(853\) 51.4129 + 15.8588i 1.76034 + 0.542994i 0.994932 0.100546i \(-0.0320588\pi\)
0.765412 + 0.643540i \(0.222535\pi\)
\(854\) 17.5069 14.2996i 0.599072 0.489323i
\(855\) −62.0749 53.9116i −2.12292 1.84374i
\(856\) −12.5771 11.6698i −0.429876 0.398866i
\(857\) −14.6987 + 18.4315i −0.502097 + 0.629609i −0.966701 0.255909i \(-0.917625\pi\)
0.464604 + 0.885518i \(0.346197\pi\)
\(858\) −28.0626 68.1859i −0.958040 2.32783i
\(859\) 9.36571 41.0339i 0.319554 1.40006i −0.518783 0.854906i \(-0.673615\pi\)
0.838337 0.545152i \(-0.183528\pi\)
\(860\) −32.9402 + 10.1607i −1.12325 + 0.346477i
\(861\) 5.39542 + 30.0361i 0.183875 + 1.02363i
\(862\) −5.31358 1.63902i −0.180981 0.0558253i
\(863\) −5.46029 + 9.45750i −0.185870 + 0.321937i −0.943869 0.330319i \(-0.892844\pi\)
0.757999 + 0.652256i \(0.226177\pi\)
\(864\) 18.0471 35.1530i 0.613976 1.19593i
\(865\) 49.8552 46.2589i 1.69513 1.57285i
\(866\) 3.94145 + 52.5950i 0.133936 + 1.78725i
\(867\) 9.86450 + 23.9686i 0.335016 + 0.814016i
\(868\) 20.2854 + 29.0177i 0.688533 + 0.984925i
\(869\) −18.2006 + 46.3745i −0.617415 + 1.57315i
\(870\) 16.1445 + 65.7350i 0.547348 + 2.22863i
\(871\) 34.1683 + 42.8457i 1.15775 + 1.45177i
\(872\) 1.32656 + 17.7018i 0.0449231 + 0.599457i
\(873\) 13.2371 + 30.7191i 0.448009 + 1.03969i
\(874\) 21.7250 10.4622i 0.734858 0.353889i
\(875\) 17.7768 1.54160i 0.600965 0.0521155i
\(876\) 11.1598 + 5.15010i 0.377054 + 0.174006i
\(877\) 3.34969 1.61312i 0.113111 0.0544713i −0.376473 0.926428i \(-0.622863\pi\)
0.489584 + 0.871956i \(0.337149\pi\)
\(878\) 6.87502 + 6.37908i 0.232021 + 0.215284i
\(879\) 36.4311 + 23.9710i 1.22879 + 0.808522i
\(880\) 10.5934 26.9914i 0.357102 0.909881i
\(881\) −29.6338 −0.998389 −0.499194 0.866490i \(-0.666371\pi\)
−0.499194 + 0.866490i \(0.666371\pi\)
\(882\) −42.0741 17.4192i −1.41671 0.586534i
\(883\) −31.3263 −1.05421 −0.527107 0.849799i \(-0.676723\pi\)
−0.527107 + 0.849799i \(0.676723\pi\)
\(884\) −6.93178 + 17.6619i −0.233141 + 0.594033i
\(885\) −0.819961 + 14.0324i −0.0275627 + 0.471694i
\(886\) 20.0711 + 18.6233i 0.674302 + 0.625661i
\(887\) −18.5566 + 8.93639i −0.623070 + 0.300055i −0.718655 0.695367i \(-0.755242\pi\)
0.0955853 + 0.995421i \(0.469528\pi\)
\(888\) −0.937075 + 0.661701i −0.0314462 + 0.0222052i
\(889\) −11.4831 + 6.81018i −0.385131 + 0.228406i
\(890\) 56.9946 27.4471i 1.91046 0.920030i
\(891\) −20.4924 + 29.4788i −0.686520 + 0.987578i
\(892\) −2.74181 36.5870i −0.0918027 1.22502i
\(893\) 20.1611 + 25.2813i 0.674666 + 0.846005i
\(894\) −27.5222 + 26.3916i −0.920481 + 0.882668i
\(895\) −14.7164 + 37.4967i −0.491914 + 1.25338i
\(896\) −20.3086 + 22.4078i −0.678462 + 0.748592i
\(897\) 11.8507 + 1.58751i 0.395683 + 0.0530056i
\(898\) −0.392781 5.24130i −0.0131073 0.174904i
\(899\) −18.9254 + 17.5602i −0.631198 + 0.585666i
\(900\) −26.5550 + 49.6977i −0.885166 + 1.65659i
\(901\) 1.74249 3.01809i 0.0580509 0.100547i
\(902\) −55.0448 16.9791i −1.83279 0.565341i
\(903\) 16.5860 + 3.29767i 0.551947 + 0.109740i
\(904\) −29.0109 + 8.94868i −0.964889 + 0.297629i
\(905\) −10.9437 + 47.9474i −0.363780 + 1.59382i
\(906\) −8.34094 1.11735i −0.277109 0.0371215i
\(907\) 27.8410 34.9115i 0.924444 1.15922i −0.0624830 0.998046i \(-0.519902\pi\)
0.986927 0.161170i \(-0.0515267\pi\)
\(908\) 36.8196 + 34.1636i 1.22190 + 1.13376i
\(909\) 4.10897 21.1900i 0.136286 0.702827i
\(910\) 1.14233 + 97.6017i 0.0378678 + 3.23547i
\(911\) 2.85876 + 0.881811i 0.0947149 + 0.0292157i 0.341750 0.939791i \(-0.388980\pi\)
−0.247036 + 0.969006i \(0.579456\pi\)
\(912\) 28.8674 0.474413i 0.955895 0.0157094i
\(913\) 16.5753 28.7093i 0.548563 0.950140i
\(914\) −30.0875 9.28076i −0.995206 0.306980i
\(915\) 2.14935 + 23.4936i 0.0710553 + 0.776675i
\(916\) 12.4154 + 31.6339i 0.410216 + 1.04521i
\(917\) 8.07834 58.2110i 0.266770 1.92230i
\(918\) 15.7590 3.17642i 0.520124 0.104838i
\(919\) −33.6712 10.3862i −1.11071 0.342609i −0.315489 0.948929i \(-0.602169\pi\)
−0.795220 + 0.606321i \(0.792645\pi\)
\(920\) −4.60337 5.77244i −0.151768 0.190312i
\(921\) −45.9600 21.2100i −1.51443 0.698892i
\(922\) 43.4268 54.4554i 1.43018 1.79339i
\(923\) −38.5730 26.2986i −1.26965 0.865630i
\(924\) 37.7380 31.8724i 1.24149 1.04853i
\(925\) −2.49813 + 1.70320i −0.0821381 + 0.0560008i
\(926\) 3.14893 42.0196i 0.103480 1.38085i
\(927\) 6.97426 35.9663i 0.229065 1.18129i
\(928\) −32.7560 22.3327i −1.07527 0.733106i
\(929\) −0.474899 + 1.21002i −0.0155809 + 0.0396996i −0.938453 0.345408i \(-0.887740\pi\)
0.922872 + 0.385108i \(0.125836\pi\)
\(930\) −64.2919 + 1.05659i −2.10822 + 0.0346469i
\(931\) −5.44108 55.2261i −0.178324 1.80996i
\(932\) 4.37706 + 7.58129i 0.143375 + 0.248333i
\(933\) 5.34625 0.895899i 0.175028 0.0293304i
\(934\) −58.8365 + 28.3342i −1.92519 + 0.927122i
\(935\) 18.8010 5.79935i 0.614860 0.189659i
\(936\) −18.9801 12.0464i −0.620385 0.393748i
\(937\) 17.9146 + 8.62719i 0.585243 + 0.281838i 0.702983 0.711206i \(-0.251851\pi\)
−0.117740 + 0.993044i \(0.537565\pi\)
\(938\) −35.3678 + 53.2023i −1.15480 + 1.73712i
\(939\) −7.87267 5.18007i −0.256915 0.169045i
\(940\) 23.7565 29.7898i 0.774853 0.971635i
\(941\) 0.710672 0.484528i 0.0231672 0.0157952i −0.551681 0.834055i \(-0.686013\pi\)
0.574848 + 0.818260i \(0.305061\pi\)
\(942\) 20.9221 + 25.3688i 0.681679 + 0.826562i
\(943\) 6.84732 6.35338i 0.222979 0.206895i
\(944\) −3.07753 3.85910i −0.100165 0.125603i
\(945\) 39.6334 26.2280i 1.28928 0.853196i
\(946\) −19.9022 + 24.9566i −0.647078 + 0.811410i
\(947\) −1.69587 22.6299i −0.0551085 0.735372i −0.954497 0.298221i \(-0.903607\pi\)
0.899388 0.437151i \(-0.144012\pi\)
\(948\) 13.9411 + 56.7636i 0.452785 + 1.84359i
\(949\) −6.46200 + 11.1925i −0.209765 + 0.363324i
\(950\) −119.490 −3.87678
\(951\) −3.00077 + 2.87750i −0.0973065 + 0.0933093i
\(952\) −5.73613 0.362410i −0.185909 0.0117458i
\(953\) −3.47218 + 15.2126i −0.112475 + 0.492784i 0.887042 + 0.461689i \(0.152757\pi\)
−0.999516 + 0.0310948i \(0.990101\pi\)
\(954\) 11.9971 + 10.4194i 0.388422 + 0.337342i
\(955\) 6.46937 + 0.975101i 0.209344 + 0.0315535i
\(956\) −23.9668 + 30.0535i −0.775143 + 0.971998i
\(957\) 26.8033 + 24.0624i 0.866427 + 0.777827i
\(958\) −3.75086 + 1.15699i −0.121185 + 0.0373805i
\(959\) −4.04515 + 29.1485i −0.130625 + 0.941255i
\(960\) −17.5447 71.4365i −0.566253 2.30560i
\(961\) 3.23745 + 5.60743i 0.104434 + 0.180885i
\(962\) −2.32102 4.02012i −0.0748326 0.129614i
\(963\) −32.6127 8.89725i −1.05093 0.286710i
\(964\) −59.7907 + 40.7646i −1.92573 + 1.31294i
\(965\) −1.35793 3.45995i −0.0437134 0.111380i
\(966\) 2.46434 + 13.7189i 0.0792888 + 0.441398i
\(967\) 5.27969 13.4524i 0.169783 0.432601i −0.820503 0.571642i \(-0.806307\pi\)
0.990287 + 0.139041i \(0.0444020\pi\)
\(968\) 1.66453 + 7.29279i 0.0535000 + 0.234399i
\(969\) 12.4646 + 15.1138i 0.400421 + 0.485526i
\(970\) 75.3062 + 36.2656i 2.41794 + 1.16442i
\(971\) 4.63593 + 11.8121i 0.148774 + 0.379070i 0.985761 0.168153i \(-0.0537803\pi\)
−0.836987 + 0.547223i \(0.815685\pi\)
\(972\) 0.310183 + 42.1215i 0.00994912 + 1.35105i
\(973\) 7.12709 24.1034i 0.228484 0.772721i
\(974\) −26.7333 + 18.2265i −0.856590 + 0.584013i
\(975\) −49.4966 32.5679i −1.58516 1.04301i
\(976\) −6.07289 5.63482i −0.194389 0.180366i
\(977\) 2.37822 31.7351i 0.0760860 1.01530i −0.820274 0.571970i \(-0.806179\pi\)
0.896360 0.443326i \(-0.146202\pi\)
\(978\) 31.7338 + 38.4785i 1.01474 + 1.23041i
\(979\) 16.8313 29.1527i 0.537931 0.931724i
\(980\) −62.0166 + 20.7312i −1.98105 + 0.662233i
\(981\) 18.4736 + 29.6987i 0.589817 + 0.948205i
\(982\) 23.5284 3.54634i 0.750822 0.113168i
\(983\) −11.8124 + 5.68857i −0.376758 + 0.181437i −0.612673 0.790337i \(-0.709906\pi\)
0.235915 + 0.971774i \(0.424191\pi\)
\(984\) −16.6947 + 5.45163i −0.532207 + 0.173792i
\(985\) 16.2841 7.84203i 0.518856 0.249868i
\(986\) −1.20530 16.0836i −0.0383845 0.512206i
\(987\) −17.2007 + 7.31567i −0.547504 + 0.232860i
\(988\) 7.87846 105.131i 0.250647 3.34465i
\(989\) −1.89106 4.81833i −0.0601321 0.153214i
\(990\) 9.64007 + 89.1912i 0.306382 + 2.83468i
\(991\) 22.4111 57.1026i 0.711913 1.81392i 0.146323 0.989237i \(-0.453256\pi\)
0.565590 0.824687i \(-0.308649\pi\)
\(992\) 27.6070 25.6156i 0.876525 0.813296i
\(993\) 9.55343 25.5694i 0.303169 0.811421i
\(994\) 15.4319 52.1898i 0.489470 1.65536i
\(995\) −68.2706 10.2901i −2.16432 0.326219i
\(996\) −3.54355 38.7331i −0.112282 1.22730i
\(997\) −3.90293 17.0998i −0.123607 0.541557i −0.998373 0.0570126i \(-0.981842\pi\)
0.874767 0.484545i \(-0.161015\pi\)
\(998\) 7.50810 + 13.0044i 0.237665 + 0.411647i
\(999\) −1.03228 + 2.01073i −0.0326600 + 0.0636166i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 441.2.z.a.142.8 yes 648
9.4 even 3 441.2.y.a.436.8 yes 648
49.39 even 21 441.2.y.a.88.8 648
441.382 even 21 inner 441.2.z.a.382.8 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.y.a.88.8 648 49.39 even 21
441.2.y.a.436.8 yes 648 9.4 even 3
441.2.z.a.142.8 yes 648 1.1 even 1 trivial
441.2.z.a.382.8 yes 648 441.382 even 21 inner