Properties

Label 49.2.g.a.39.3
Level $49$
Weight $2$
Character 49.39
Analytic conductor $0.391$
Analytic rank $0$
Dimension $48$
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] = [49,2,Mod(2,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([26]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 49.g (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: \(0.391266969904\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 39.3
Character \(\chi\) \(=\) 49.39
Dual form 49.2.g.a.44.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.251257 - 0.0378709i) q^{2} +(1.64786 - 1.12349i) q^{3} +(-1.84945 - 0.570480i) q^{4} +(0.0348203 + 0.464645i) q^{5} +(-0.456585 + 0.219880i) q^{6} +(-0.363905 + 2.62061i) q^{7} +(0.900946 + 0.433873i) q^{8} +(0.357192 - 0.910110i) q^{9} +O(q^{10})\) \(q+(-0.251257 - 0.0378709i) q^{2} +(1.64786 - 1.12349i) q^{3} +(-1.84945 - 0.570480i) q^{4} +(0.0348203 + 0.464645i) q^{5} +(-0.456585 + 0.219880i) q^{6} +(-0.363905 + 2.62061i) q^{7} +(0.900946 + 0.433873i) q^{8} +(0.357192 - 0.910110i) q^{9} +(0.00884768 - 0.118064i) q^{10} +(-0.940972 - 2.39756i) q^{11} +(-3.68857 + 1.13777i) q^{12} +(-1.96169 + 2.45988i) q^{13} +(0.190678 - 0.644664i) q^{14} +(0.579406 + 0.726552i) q^{15} +(2.98833 + 2.03741i) q^{16} +(-3.94998 - 3.66505i) q^{17} +(-0.124214 + 0.215144i) q^{18} +(-0.694755 - 1.20335i) q^{19} +(0.200672 - 0.879202i) q^{20} +(2.34457 + 4.72725i) q^{21} +(0.145628 + 0.638039i) q^{22} +(6.47174 - 6.00489i) q^{23} +(1.97209 - 0.297245i) q^{24} +(4.72947 - 0.712853i) q^{25} +(0.586046 - 0.543771i) q^{26} +(0.897498 + 3.93219i) q^{27} +(2.16803 - 4.63908i) q^{28} +(-0.160206 + 0.701907i) q^{29} +(-0.118065 - 0.204494i) q^{30} +(-1.17953 + 2.04301i) q^{31} +(-2.13975 - 1.98539i) q^{32} +(-4.24424 - 2.89367i) q^{33} +(0.853662 + 1.07046i) q^{34} +(-1.23032 - 0.0778363i) q^{35} +(-1.17981 + 1.47943i) q^{36} +(-6.92798 + 2.13700i) q^{37} +(0.128990 + 0.328661i) q^{38} +(-0.468935 + 6.25750i) q^{39} +(-0.170226 + 0.433728i) q^{40} +(-7.62467 - 3.67185i) q^{41} +(-0.410065 - 1.27654i) q^{42} +(4.17155 - 2.00891i) q^{43} +(0.372523 + 4.97097i) q^{44} +(0.435316 + 0.134277i) q^{45} +(-1.85348 + 1.26368i) q^{46} +(10.3965 + 1.56702i) q^{47} +7.21337 q^{48} +(-6.73515 - 1.90730i) q^{49} -1.21531 q^{50} +(-10.6267 - 1.60172i) q^{51} +(5.03136 - 3.43032i) q^{52} +(0.496607 + 0.153183i) q^{53} +(-0.0765868 - 1.02198i) q^{54} +(1.08125 - 0.520702i) q^{55} +(-1.46487 + 2.20314i) q^{56} +(-2.49682 - 1.20241i) q^{57} +(0.0668346 - 0.170292i) q^{58} +(-0.893977 + 11.9293i) q^{59} +(-0.657099 - 1.67426i) q^{60} +(-0.819354 + 0.252737i) q^{61} +(0.373737 - 0.468651i) q^{62} +(2.25506 + 1.26725i) q^{63} +(-4.04762 - 5.07555i) q^{64} +(-1.21128 - 0.825836i) q^{65} +(0.956808 + 0.887788i) q^{66} +(0.694192 - 1.20238i) q^{67} +(5.21446 + 9.03171i) q^{68} +(3.91807 - 17.1662i) q^{69} +(0.306180 + 0.0661503i) q^{70} +(-0.714786 - 3.13168i) q^{71} +(0.716683 - 0.664984i) q^{72} +(-2.15258 + 0.324450i) q^{73} +(1.82163 - 0.274567i) q^{74} +(6.99264 - 6.48822i) q^{75} +(0.598427 + 2.62188i) q^{76} +(6.62548 - 1.59343i) q^{77} +(0.354800 - 1.55448i) q^{78} +(5.38904 + 9.33410i) q^{79} +(-0.842617 + 1.45945i) q^{80} +(8.04685 + 7.46639i) q^{81} +(1.77669 + 1.21133i) q^{82} +(-0.908423 - 1.13913i) q^{83} +(-1.63937 - 10.0803i) q^{84} +(1.56541 - 1.96296i) q^{85} +(-1.12421 + 0.346773i) q^{86} +(0.524591 + 1.33664i) q^{87} +(0.192470 - 2.56833i) q^{88} +(-3.11085 + 7.92631i) q^{89} +(-0.104291 - 0.0502239i) q^{90} +(-5.73251 - 6.03598i) q^{91} +(-15.3948 + 7.41376i) q^{92} +(0.351602 + 4.69180i) q^{93} +(-2.55284 - 0.787448i) q^{94} +(0.534940 - 0.364716i) q^{95} +(-5.75659 - 0.867666i) q^{96} +10.1608 q^{97} +(1.62002 + 0.734289i) q^{98} -2.51815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 13 q^{2} - 14 q^{3} - 9 q^{4} - 14 q^{5} - 14 q^{7} - 20 q^{8} + 6 q^{9} - 14 q^{10} - 3 q^{11} + 21 q^{12} - 14 q^{13} + 21 q^{14} - 12 q^{15} - 3 q^{16} - 7 q^{17} + 2 q^{18} + 21 q^{19} + 14 q^{20} - 14 q^{21} - 20 q^{22} + 15 q^{23} + 28 q^{24} - 4 q^{25} + 7 q^{27} + 28 q^{28} + 12 q^{29} + 11 q^{30} + 35 q^{31} + 45 q^{32} - 14 q^{33} + 70 q^{34} - 12 q^{36} + 15 q^{37} - 28 q^{38} - 7 q^{39} - 42 q^{40} - 42 q^{41} + 28 q^{42} - 30 q^{43} - 50 q^{44} + 7 q^{45} - 78 q^{46} + 21 q^{47} - 84 q^{48} - 70 q^{49} + 40 q^{50} - 52 q^{51} - 70 q^{52} + 11 q^{53} - 77 q^{54} - 7 q^{55} - 28 q^{56} - 12 q^{57} + 16 q^{58} - 28 q^{59} + 56 q^{60} + 7 q^{61} - 28 q^{62} + 35 q^{63} - 32 q^{64} + 14 q^{65} + 154 q^{66} + 11 q^{67} + 77 q^{68} + 70 q^{69} + 70 q^{70} + 19 q^{71} + 170 q^{72} + 7 q^{73} + 34 q^{74} + 112 q^{75} + 119 q^{76} + 7 q^{77} + 28 q^{78} + 15 q^{79} + 70 q^{80} + 64 q^{81} - 14 q^{82} - 84 q^{84} - 26 q^{85} - 33 q^{86} - 112 q^{87} - 77 q^{88} - 14 q^{89} - 182 q^{90} + 84 q^{91} - 38 q^{92} - 80 q^{93} + 14 q^{94} - 61 q^{95} - 70 q^{96} - 161 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{17}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.251257 0.0378709i −0.177665 0.0267788i 0.0596069 0.998222i \(-0.481015\pi\)
−0.237272 + 0.971443i \(0.576253\pi\)
\(3\) 1.64786 1.12349i 0.951395 0.648650i 0.0151076 0.999886i \(-0.495191\pi\)
0.936287 + 0.351236i \(0.114239\pi\)
\(4\) −1.84945 0.570480i −0.924725 0.285240i
\(5\) 0.0348203 + 0.464645i 0.0155721 + 0.207796i 0.999563 + 0.0295745i \(0.00941522\pi\)
−0.983990 + 0.178221i \(0.942966\pi\)
\(6\) −0.456585 + 0.219880i −0.186400 + 0.0897655i
\(7\) −0.363905 + 2.62061i −0.137543 + 0.990496i
\(8\) 0.900946 + 0.433873i 0.318532 + 0.153397i
\(9\) 0.357192 0.910110i 0.119064 0.303370i
\(10\) 0.00884768 0.118064i 0.00279788 0.0373351i
\(11\) −0.940972 2.39756i −0.283714 0.722891i −0.999693 0.0247696i \(-0.992115\pi\)
0.715979 0.698121i \(-0.245980\pi\)
\(12\) −3.68857 + 1.13777i −1.06480 + 0.328447i
\(13\) −1.96169 + 2.45988i −0.544075 + 0.682248i −0.975525 0.219888i \(-0.929431\pi\)
0.431450 + 0.902137i \(0.358002\pi\)
\(14\) 0.190678 0.644664i 0.0509609 0.172294i
\(15\) 0.579406 + 0.726552i 0.149602 + 0.187595i
\(16\) 2.98833 + 2.03741i 0.747082 + 0.509352i
\(17\) −3.94998 3.66505i −0.958012 0.888905i 0.0358699 0.999356i \(-0.488580\pi\)
−0.993882 + 0.110452i \(0.964770\pi\)
\(18\) −0.124214 + 0.215144i −0.0292774 + 0.0507100i
\(19\) −0.694755 1.20335i −0.159388 0.276068i 0.775260 0.631642i \(-0.217619\pi\)
−0.934648 + 0.355574i \(0.884285\pi\)
\(20\) 0.200672 0.879202i 0.0448717 0.196596i
\(21\) 2.34457 + 4.72725i 0.511627 + 1.03157i
\(22\) 0.145628 + 0.638039i 0.0310480 + 0.136030i
\(23\) 6.47174 6.00489i 1.34945 1.25211i 0.408845 0.912604i \(-0.365932\pi\)
0.940605 0.339503i \(-0.110259\pi\)
\(24\) 1.97209 0.297245i 0.402551 0.0606748i
\(25\) 4.72947 0.712853i 0.945894 0.142571i
\(26\) 0.586046 0.543771i 0.114933 0.106642i
\(27\) 0.897498 + 3.93219i 0.172724 + 0.756751i
\(28\) 2.16803 4.63908i 0.409718 0.876703i
\(29\) −0.160206 + 0.701907i −0.0297494 + 0.130341i −0.987622 0.156853i \(-0.949865\pi\)
0.957873 + 0.287194i \(0.0927223\pi\)
\(30\) −0.118065 0.204494i −0.0215555 0.0373353i
\(31\) −1.17953 + 2.04301i −0.211850 + 0.366936i −0.952294 0.305183i \(-0.901282\pi\)
0.740443 + 0.672119i \(0.234616\pi\)
\(32\) −2.13975 1.98539i −0.378257 0.350971i
\(33\) −4.24424 2.89367i −0.738827 0.503724i
\(34\) 0.853662 + 1.07046i 0.146402 + 0.183582i
\(35\) −1.23032 0.0778363i −0.207963 0.0131567i
\(36\) −1.17981 + 1.47943i −0.196635 + 0.246572i
\(37\) −6.92798 + 2.13700i −1.13895 + 0.351320i −0.806171 0.591683i \(-0.798464\pi\)
−0.332782 + 0.943004i \(0.607987\pi\)
\(38\) 0.128990 + 0.328661i 0.0209250 + 0.0533159i
\(39\) −0.468935 + 6.25750i −0.0750896 + 1.00200i
\(40\) −0.170226 + 0.433728i −0.0269150 + 0.0685784i
\(41\) −7.62467 3.67185i −1.19077 0.573446i −0.269741 0.962933i \(-0.586938\pi\)
−0.921032 + 0.389487i \(0.872652\pi\)
\(42\) −0.410065 1.27654i −0.0632743 0.196975i
\(43\) 4.17155 2.00891i 0.636156 0.306356i −0.0878673 0.996132i \(-0.528005\pi\)
0.724023 + 0.689776i \(0.242291\pi\)
\(44\) 0.372523 + 4.97097i 0.0561599 + 0.749402i
\(45\) 0.435316 + 0.134277i 0.0648931 + 0.0200169i
\(46\) −1.85348 + 1.26368i −0.273281 + 0.186320i
\(47\) 10.3965 + 1.56702i 1.51648 + 0.228573i 0.853908 0.520424i \(-0.174226\pi\)
0.662574 + 0.748997i \(0.269464\pi\)
\(48\) 7.21337 1.04116
\(49\) −6.73515 1.90730i −0.962164 0.272472i
\(50\) −1.21531 −0.171871
\(51\) −10.6267 1.60172i −1.48804 0.224285i
\(52\) 5.03136 3.43032i 0.697724 0.475700i
\(53\) 0.496607 + 0.153183i 0.0682142 + 0.0210413i 0.328674 0.944443i \(-0.393398\pi\)
−0.260460 + 0.965485i \(0.583874\pi\)
\(54\) −0.0765868 1.02198i −0.0104221 0.139074i
\(55\) 1.08125 0.520702i 0.145796 0.0702115i
\(56\) −1.46487 + 2.20314i −0.195751 + 0.294406i
\(57\) −2.49682 1.20241i −0.330712 0.159262i
\(58\) 0.0668346 0.170292i 0.00877582 0.0223604i
\(59\) −0.893977 + 11.9293i −0.116386 + 1.55306i 0.567439 + 0.823416i \(0.307934\pi\)
−0.683825 + 0.729646i \(0.739685\pi\)
\(60\) −0.657099 1.67426i −0.0848311 0.216146i
\(61\) −0.819354 + 0.252737i −0.104907 + 0.0323597i −0.346765 0.937952i \(-0.612720\pi\)
0.241857 + 0.970312i \(0.422244\pi\)
\(62\) 0.373737 0.468651i 0.0474646 0.0595187i
\(63\) 2.25506 + 1.26725i 0.284110 + 0.159659i
\(64\) −4.04762 5.07555i −0.505952 0.634444i
\(65\) −1.21128 0.825836i −0.150241 0.102432i
\(66\) 0.956808 + 0.887788i 0.117775 + 0.109279i
\(67\) 0.694192 1.20238i 0.0848090 0.146894i −0.820501 0.571645i \(-0.806305\pi\)
0.905310 + 0.424752i \(0.139639\pi\)
\(68\) 5.21446 + 9.03171i 0.632346 + 1.09526i
\(69\) 3.91807 17.1662i 0.471681 2.06657i
\(70\) 0.306180 + 0.0661503i 0.0365955 + 0.00790648i
\(71\) −0.714786 3.13168i −0.0848294 0.371662i 0.914639 0.404272i \(-0.132475\pi\)
−0.999468 + 0.0326102i \(0.989618\pi\)
\(72\) 0.716683 0.664984i 0.0844618 0.0783691i
\(73\) −2.15258 + 0.324450i −0.251941 + 0.0379739i −0.273798 0.961787i \(-0.588280\pi\)
0.0218576 + 0.999761i \(0.493042\pi\)
\(74\) 1.82163 0.274567i 0.211761 0.0319178i
\(75\) 6.99264 6.48822i 0.807440 0.749195i
\(76\) 0.598427 + 2.62188i 0.0686443 + 0.300750i
\(77\) 6.62548 1.59343i 0.755043 0.181589i
\(78\) 0.354800 1.55448i 0.0401732 0.176010i
\(79\) 5.38904 + 9.33410i 0.606315 + 1.05017i 0.991842 + 0.127472i \(0.0406862\pi\)
−0.385527 + 0.922696i \(0.625981\pi\)
\(80\) −0.842617 + 1.45945i −0.0942074 + 0.163172i
\(81\) 8.04685 + 7.46639i 0.894095 + 0.829599i
\(82\) 1.77669 + 1.21133i 0.196203 + 0.133769i
\(83\) −0.908423 1.13913i −0.0997123 0.125035i 0.729472 0.684011i \(-0.239766\pi\)
−0.829184 + 0.558976i \(0.811195\pi\)
\(84\) −1.63937 10.0803i −0.178870 1.09985i
\(85\) 1.56541 1.96296i 0.169792 0.212913i
\(86\) −1.12421 + 0.346773i −0.121227 + 0.0373935i
\(87\) 0.524591 + 1.33664i 0.0562421 + 0.143303i
\(88\) 0.192470 2.56833i 0.0205174 0.273785i
\(89\) −3.11085 + 7.92631i −0.329749 + 0.840187i 0.665816 + 0.746116i \(0.268083\pi\)
−0.995565 + 0.0940713i \(0.970012\pi\)
\(90\) −0.104291 0.0502239i −0.0109932 0.00529406i
\(91\) −5.73251 6.03598i −0.600930 0.632743i
\(92\) −15.3948 + 7.41376i −1.60502 + 0.772937i
\(93\) 0.351602 + 4.69180i 0.0364594 + 0.486518i
\(94\) −2.55284 0.787448i −0.263306 0.0812190i
\(95\) 0.534940 0.364716i 0.0548837 0.0374191i
\(96\) −5.75659 0.867666i −0.587529 0.0885558i
\(97\) 10.1608 1.03168 0.515838 0.856686i \(-0.327480\pi\)
0.515838 + 0.856686i \(0.327480\pi\)
\(98\) 1.62002 + 0.734289i 0.163647 + 0.0741744i
\(99\) −2.51815 −0.253084
\(100\) −9.15359 1.37968i −0.915359 0.137968i
\(101\) −10.8529 + 7.39940i −1.07991 + 0.736267i −0.966341 0.257263i \(-0.917179\pi\)
−0.113565 + 0.993531i \(0.536227\pi\)
\(102\) 2.60937 + 0.804885i 0.258366 + 0.0796955i
\(103\) −1.05132 14.0289i −0.103589 1.38230i −0.770630 0.637283i \(-0.780058\pi\)
0.667041 0.745021i \(-0.267561\pi\)
\(104\) −2.83465 + 1.36510i −0.277960 + 0.133859i
\(105\) −2.11485 + 1.25400i −0.206389 + 0.122378i
\(106\) −0.118975 0.0572952i −0.0115558 0.00556500i
\(107\) 4.81796 12.2760i 0.465769 1.18676i −0.484350 0.874874i \(-0.660944\pi\)
0.950119 0.311887i \(-0.100961\pi\)
\(108\) 0.583360 7.78440i 0.0561339 0.749054i
\(109\) 4.45027 + 11.3391i 0.426259 + 1.08609i 0.969190 + 0.246313i \(0.0792191\pi\)
−0.542932 + 0.839777i \(0.682686\pi\)
\(110\) −0.291391 + 0.0898822i −0.0277830 + 0.00856993i
\(111\) −9.01546 + 11.3050i −0.855710 + 1.07303i
\(112\) −6.42670 + 7.08980i −0.607267 + 0.669923i
\(113\) 3.46295 + 4.34240i 0.325766 + 0.408498i 0.917564 0.397589i \(-0.130153\pi\)
−0.591797 + 0.806087i \(0.701581\pi\)
\(114\) 0.581807 + 0.396670i 0.0544913 + 0.0371515i
\(115\) 3.01549 + 2.79797i 0.281196 + 0.260912i
\(116\) 0.696716 1.20675i 0.0646885 0.112044i
\(117\) 1.53806 + 2.66400i 0.142194 + 0.246287i
\(118\) 0.676391 2.96346i 0.0622668 0.272809i
\(119\) 11.0421 9.01762i 1.01222 0.826644i
\(120\) 0.206782 + 0.905972i 0.0188765 + 0.0827035i
\(121\) 3.20071 2.96983i 0.290974 0.269984i
\(122\) 0.215440 0.0324723i 0.0195050 0.00293990i
\(123\) −16.6897 + 2.51557i −1.50486 + 0.226821i
\(124\) 3.34699 3.10555i 0.300568 0.278886i
\(125\) 1.01432 + 4.44403i 0.0907237 + 0.397486i
\(126\) −0.518606 0.403807i −0.0462011 0.0359740i
\(127\) −1.80840 + 7.92313i −0.160470 + 0.703064i 0.829111 + 0.559084i \(0.188847\pi\)
−0.989581 + 0.143980i \(0.954010\pi\)
\(128\) 3.74373 + 6.48433i 0.330902 + 0.573140i
\(129\) 4.61715 7.99713i 0.406517 0.704108i
\(130\) 0.273067 + 0.253369i 0.0239496 + 0.0222220i
\(131\) −5.99116 4.08470i −0.523450 0.356882i 0.272586 0.962131i \(-0.412121\pi\)
−0.796036 + 0.605249i \(0.793073\pi\)
\(132\) 6.19872 + 7.77295i 0.539530 + 0.676549i
\(133\) 3.40633 1.38277i 0.295367 0.119902i
\(134\) −0.219956 + 0.275816i −0.0190013 + 0.0238268i
\(135\) −1.79582 + 0.553938i −0.154560 + 0.0476754i
\(136\) −1.96856 5.01580i −0.168802 0.430101i
\(137\) 1.12600 15.0255i 0.0962010 1.28371i −0.715074 0.699048i \(-0.753607\pi\)
0.811275 0.584664i \(-0.198774\pi\)
\(138\) −1.63454 + 4.16475i −0.139142 + 0.354527i
\(139\) −7.34377 3.53657i −0.622891 0.299968i 0.0956909 0.995411i \(-0.469494\pi\)
−0.718581 + 0.695443i \(0.755208\pi\)
\(140\) 2.23102 + 0.845829i 0.188555 + 0.0714856i
\(141\) 18.8925 9.09815i 1.59104 0.766203i
\(142\) 0.0609953 + 0.813926i 0.00511861 + 0.0683032i
\(143\) 7.74361 + 2.38859i 0.647553 + 0.199744i
\(144\) 2.92167 1.99196i 0.243473 0.165997i
\(145\) −0.331716 0.0499982i −0.0275475 0.00415212i
\(146\) 0.553138 0.0457781
\(147\) −13.2414 + 4.42393i −1.09214 + 0.364879i
\(148\) 14.0321 1.15343
\(149\) 1.08135 + 0.162988i 0.0885880 + 0.0133525i 0.193187 0.981162i \(-0.438118\pi\)
−0.104599 + 0.994515i \(0.533356\pi\)
\(150\) −2.00266 + 1.36539i −0.163517 + 0.111484i
\(151\) 0.200064 + 0.0617117i 0.0162810 + 0.00502203i 0.302885 0.953027i \(-0.402050\pi\)
−0.286604 + 0.958049i \(0.592526\pi\)
\(152\) −0.103836 1.38559i −0.00842218 0.112386i
\(153\) −4.74650 + 2.28579i −0.383732 + 0.184795i
\(154\) −1.72504 + 0.149449i −0.139008 + 0.0120429i
\(155\) −0.990348 0.476926i −0.0795466 0.0383076i
\(156\) 4.43705 11.3054i 0.355248 0.905157i
\(157\) 1.25760 16.7815i 0.100367 1.33931i −0.688720 0.725027i \(-0.741827\pi\)
0.789087 0.614281i \(-0.210554\pi\)
\(158\) −1.00054 2.54934i −0.0795990 0.202815i
\(159\) 0.990440 0.305510i 0.0785470 0.0242285i
\(160\) 0.847997 1.06335i 0.0670401 0.0840656i
\(161\) 13.3814 + 19.1451i 1.05460 + 1.50884i
\(162\) −1.73907 2.18072i −0.136634 0.171334i
\(163\) −9.73152 6.63484i −0.762231 0.519680i 0.118697 0.992931i \(-0.462128\pi\)
−0.880928 + 0.473250i \(0.843081\pi\)
\(164\) 12.0067 + 11.1406i 0.937568 + 0.869936i
\(165\) 1.19675 2.07282i 0.0931665 0.161369i
\(166\) 0.185108 + 0.320616i 0.0143672 + 0.0248846i
\(167\) 0.0476387 0.208719i 0.00368639 0.0161511i −0.973051 0.230589i \(-0.925935\pi\)
0.976738 + 0.214438i \(0.0687919\pi\)
\(168\) 0.0613080 + 5.27624i 0.00473002 + 0.407071i
\(169\) 0.689983 + 3.02301i 0.0530756 + 0.232539i
\(170\) −0.467659 + 0.433924i −0.0358678 + 0.0332804i
\(171\) −1.34334 + 0.202476i −0.102728 + 0.0154838i
\(172\) −8.86112 + 1.33560i −0.675654 + 0.101838i
\(173\) −10.5461 + 9.78537i −0.801807 + 0.743968i −0.970344 0.241727i \(-0.922286\pi\)
0.168538 + 0.985695i \(0.446096\pi\)
\(174\) −0.0811876 0.355706i −0.00615482 0.0269660i
\(175\) 0.147029 + 12.6535i 0.0111144 + 0.956514i
\(176\) 2.07287 9.08183i 0.156248 0.684569i
\(177\) 11.9293 + 20.6622i 0.896665 + 1.55307i
\(178\) 1.08180 1.87373i 0.0810842 0.140442i
\(179\) −15.8146 14.6738i −1.18204 1.09677i −0.993397 0.114728i \(-0.963400\pi\)
−0.188644 0.982046i \(-0.560409\pi\)
\(180\) −0.728492 0.496678i −0.0542986 0.0370202i
\(181\) −1.73024 2.16965i −0.128608 0.161269i 0.713358 0.700799i \(-0.247173\pi\)
−0.841966 + 0.539531i \(0.818602\pi\)
\(182\) 1.21175 + 1.73368i 0.0898205 + 0.128509i
\(183\) −1.06623 + 1.33702i −0.0788183 + 0.0988350i
\(184\) 8.43604 2.60217i 0.621913 0.191835i
\(185\) −1.23418 3.14464i −0.0907388 0.231199i
\(186\) 0.0893403 1.19216i 0.00655075 0.0874137i
\(187\) −5.07034 + 12.9190i −0.370780 + 0.944733i
\(188\) −18.3338 8.82910i −1.33713 0.643928i
\(189\) −10.6313 + 0.921043i −0.773316 + 0.0669960i
\(190\) −0.148219 + 0.0713787i −0.0107530 + 0.00517836i
\(191\) −0.902168 12.0386i −0.0652786 0.871082i −0.929701 0.368316i \(-0.879935\pi\)
0.864422 0.502766i \(-0.167684\pi\)
\(192\) −12.3723 3.81634i −0.892892 0.275421i
\(193\) −1.62832 + 1.11017i −0.117209 + 0.0799118i −0.620506 0.784202i \(-0.713073\pi\)
0.503297 + 0.864114i \(0.332120\pi\)
\(194\) −2.55298 0.384800i −0.183293 0.0276270i
\(195\) −2.92384 −0.209381
\(196\) 11.3682 + 7.36972i 0.812017 + 0.526409i
\(197\) −15.8352 −1.12821 −0.564105 0.825703i \(-0.690779\pi\)
−0.564105 + 0.825703i \(0.690779\pi\)
\(198\) 0.632703 + 0.0953646i 0.0449642 + 0.00677727i
\(199\) −0.930925 + 0.634694i −0.0659915 + 0.0449923i −0.595866 0.803084i \(-0.703191\pi\)
0.529875 + 0.848076i \(0.322239\pi\)
\(200\) 4.57029 + 1.40975i 0.323168 + 0.0996841i
\(201\) −0.206929 2.76127i −0.0145956 0.194765i
\(202\) 3.00709 1.44814i 0.211578 0.101891i
\(203\) −1.78112 0.675263i −0.125010 0.0473942i
\(204\) 18.7398 + 9.02461i 1.31205 + 0.631849i
\(205\) 1.44061 3.67062i 0.100617 0.256367i
\(206\) −0.267134 + 3.56466i −0.0186121 + 0.248362i
\(207\) −3.15346 8.03489i −0.219181 0.558464i
\(208\) −10.8739 + 3.35417i −0.753973 + 0.232570i
\(209\) −2.23136 + 2.79804i −0.154346 + 0.193544i
\(210\) 0.578862 0.234984i 0.0399453 0.0162155i
\(211\) 8.26561 + 10.3648i 0.569028 + 0.713539i 0.980198 0.198020i \(-0.0634510\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(212\) −0.831061 0.566608i −0.0570775 0.0389148i
\(213\) −4.69629 4.35752i −0.321785 0.298573i
\(214\) −1.67545 + 2.90196i −0.114531 + 0.198374i
\(215\) 1.07869 + 1.86834i 0.0735659 + 0.127420i
\(216\) −0.897475 + 3.93209i −0.0610654 + 0.267545i
\(217\) −4.92469 3.83455i −0.334310 0.260307i
\(218\) −0.688740 3.01757i −0.0466473 0.204375i
\(219\) −3.18264 + 2.95306i −0.215063 + 0.199549i
\(220\) −2.29677 + 0.346182i −0.154848 + 0.0233396i
\(221\) 16.7642 2.52680i 1.12768 0.169971i
\(222\) 2.69333 2.49904i 0.180764 0.167725i
\(223\) 4.67329 + 20.4750i 0.312947 + 1.37111i 0.849654 + 0.527341i \(0.176811\pi\)
−0.536707 + 0.843769i \(0.680332\pi\)
\(224\) 5.98160 4.88493i 0.399662 0.326388i
\(225\) 1.04055 4.55897i 0.0693703 0.303931i
\(226\) −0.705639 1.22220i −0.0469384 0.0812997i
\(227\) 9.50674 16.4662i 0.630985 1.09290i −0.356366 0.934346i \(-0.615984\pi\)
0.987351 0.158551i \(-0.0506823\pi\)
\(228\) 3.93180 + 3.64817i 0.260390 + 0.241606i
\(229\) −6.78737 4.62755i −0.448522 0.305797i 0.317912 0.948120i \(-0.397018\pi\)
−0.766434 + 0.642323i \(0.777971\pi\)
\(230\) −0.651702 0.817209i −0.0429720 0.0538851i
\(231\) 9.12767 10.0695i 0.600557 0.662521i
\(232\) −0.448875 + 0.562871i −0.0294701 + 0.0369543i
\(233\) 8.07563 2.49100i 0.529052 0.163191i −0.0187101 0.999825i \(-0.505956\pi\)
0.547762 + 0.836634i \(0.315480\pi\)
\(234\) −0.285561 0.727597i −0.0186677 0.0475645i
\(235\) −0.366098 + 4.88524i −0.0238816 + 0.318678i
\(236\) 8.45879 21.5526i 0.550620 1.40296i
\(237\) 19.3672 + 9.32676i 1.25804 + 0.605838i
\(238\) −3.11590 + 1.84757i −0.201974 + 0.119760i
\(239\) −10.5697 + 5.09010i −0.683697 + 0.329251i −0.743288 0.668972i \(-0.766735\pi\)
0.0595909 + 0.998223i \(0.481020\pi\)
\(240\) 0.251172 + 3.35166i 0.0162131 + 0.216349i
\(241\) 10.8791 + 3.35577i 0.700786 + 0.216164i 0.624617 0.780931i \(-0.285255\pi\)
0.0761691 + 0.997095i \(0.475731\pi\)
\(242\) −0.916671 + 0.624976i −0.0589259 + 0.0401750i
\(243\) 9.68376 + 1.45959i 0.621213 + 0.0936329i
\(244\) 1.65953 0.106241
\(245\) 0.651699 3.19587i 0.0416355 0.204176i
\(246\) 4.28867 0.273436
\(247\) 4.32300 + 0.651587i 0.275066 + 0.0414595i
\(248\) −1.94910 + 1.32888i −0.123768 + 0.0843837i
\(249\) −2.77676 0.856517i −0.175970 0.0542795i
\(250\) −0.0865559 1.15501i −0.00547427 0.0730491i
\(251\) 3.34645 1.61156i 0.211226 0.101721i −0.325280 0.945618i \(-0.605458\pi\)
0.536505 + 0.843897i \(0.319744\pi\)
\(252\) −3.44767 3.63018i −0.217183 0.228680i
\(253\) −20.4868 9.86593i −1.28799 0.620266i
\(254\) 0.754430 1.92226i 0.0473371 0.120613i
\(255\) 0.374205 4.99342i 0.0234336 0.312700i
\(256\) 4.04842 + 10.3152i 0.253027 + 0.644701i
\(257\) −0.780460 + 0.240740i −0.0486838 + 0.0150170i −0.319001 0.947754i \(-0.603347\pi\)
0.270318 + 0.962771i \(0.412871\pi\)
\(258\) −1.46295 + 1.83448i −0.0910792 + 0.114210i
\(259\) −3.07910 18.9332i −0.191326 1.17645i
\(260\) 1.76908 + 2.21835i 0.109713 + 0.137576i
\(261\) 0.581588 + 0.396520i 0.0359994 + 0.0245440i
\(262\) 1.35063 + 1.25320i 0.0834421 + 0.0774229i
\(263\) −8.05573 + 13.9529i −0.496738 + 0.860375i −0.999993 0.00376276i \(-0.998802\pi\)
0.503255 + 0.864138i \(0.332136\pi\)
\(264\) −2.56834 4.44850i −0.158071 0.273786i
\(265\) −0.0538837 + 0.236080i −0.00331005 + 0.0145023i
\(266\) −0.908232 + 0.218431i −0.0556873 + 0.0133928i
\(267\) 3.77891 + 16.5565i 0.231266 + 1.01324i
\(268\) −1.96980 + 1.82771i −0.120325 + 0.111645i
\(269\) −9.23542 + 1.39202i −0.563093 + 0.0848727i −0.424420 0.905466i \(-0.639522\pi\)
−0.138673 + 0.990338i \(0.544284\pi\)
\(270\) 0.472191 0.0711714i 0.0287367 0.00433135i
\(271\) 7.72564 7.16835i 0.469299 0.435446i −0.409735 0.912205i \(-0.634379\pi\)
0.879034 + 0.476758i \(0.158188\pi\)
\(272\) −4.33664 19.0001i −0.262948 1.15205i
\(273\) −16.2278 3.50603i −0.982150 0.212194i
\(274\) −0.851944 + 3.73261i −0.0514678 + 0.225495i
\(275\) −6.15941 10.6684i −0.371426 0.643329i
\(276\) −17.0393 + 29.5129i −1.02564 + 1.77647i
\(277\) 1.34428 + 1.24731i 0.0807698 + 0.0749435i 0.719525 0.694467i \(-0.244360\pi\)
−0.638755 + 0.769410i \(0.720550\pi\)
\(278\) 1.71124 + 1.16670i 0.102633 + 0.0699742i
\(279\) 1.43805 + 1.80325i 0.0860936 + 0.107958i
\(280\) −1.07468 0.603930i −0.0642246 0.0360917i
\(281\) 4.03145 5.05527i 0.240496 0.301572i −0.646905 0.762570i \(-0.723937\pi\)
0.887401 + 0.460998i \(0.152509\pi\)
\(282\) −5.09143 + 1.57050i −0.303190 + 0.0935218i
\(283\) 5.20083 + 13.2515i 0.309157 + 0.787720i 0.998024 + 0.0628320i \(0.0200132\pi\)
−0.688867 + 0.724888i \(0.741892\pi\)
\(284\) −0.464600 + 6.19966i −0.0275689 + 0.367882i
\(285\) 0.471752 1.20200i 0.0279442 0.0712006i
\(286\) −1.85518 0.893406i −0.109699 0.0528282i
\(287\) 12.3971 18.6450i 0.731779 1.10058i
\(288\) −2.57123 + 1.23824i −0.151511 + 0.0729639i
\(289\) 0.899373 + 12.0013i 0.0529043 + 0.705959i
\(290\) 0.0814525 + 0.0251248i 0.00478306 + 0.00147538i
\(291\) 16.7437 11.4156i 0.981532 0.669197i
\(292\) 4.16618 + 0.627951i 0.243808 + 0.0367481i
\(293\) 13.8681 0.810183 0.405091 0.914276i \(-0.367240\pi\)
0.405091 + 0.914276i \(0.367240\pi\)
\(294\) 3.49454 0.610077i 0.203806 0.0355804i
\(295\) −5.57402 −0.324532
\(296\) −7.16892 1.08054i −0.416685 0.0628052i
\(297\) 8.58315 5.85189i 0.498045 0.339561i
\(298\) −0.265525 0.0819037i −0.0153815 0.00474455i
\(299\) 2.07579 + 27.6994i 0.120046 + 1.60190i
\(300\) −16.6339 + 8.01048i −0.960360 + 0.462485i
\(301\) 3.74652 + 11.6630i 0.215946 + 0.672247i
\(302\) −0.0479305 0.0230821i −0.00275809 0.00132823i
\(303\) −9.57095 + 24.3864i −0.549837 + 1.40096i
\(304\) 0.375560 5.01151i 0.0215399 0.287430i
\(305\) −0.145963 0.371908i −0.00835783 0.0212954i
\(306\) 1.27916 0.394567i 0.0731245 0.0225559i
\(307\) 12.1790 15.2719i 0.695090 0.871616i −0.301556 0.953449i \(-0.597506\pi\)
0.996646 + 0.0818328i \(0.0260773\pi\)
\(308\) −13.1625 0.832725i −0.750004 0.0474489i
\(309\) −17.4938 21.9365i −0.995186 1.24792i
\(310\) 0.230770 + 0.157336i 0.0131069 + 0.00893611i
\(311\) −6.83433 6.34133i −0.387539 0.359584i 0.462210 0.886770i \(-0.347056\pi\)
−0.849750 + 0.527186i \(0.823247\pi\)
\(312\) −3.13744 + 5.43421i −0.177623 + 0.307651i
\(313\) −1.72284 2.98404i −0.0973805 0.168668i 0.813219 0.581958i \(-0.197713\pi\)
−0.910600 + 0.413290i \(0.864380\pi\)
\(314\) −0.951510 + 4.16884i −0.0536968 + 0.235261i
\(315\) −0.510301 + 1.09193i −0.0287522 + 0.0615231i
\(316\) −4.64185 20.3373i −0.261125 1.14406i
\(317\) −3.58662 + 3.32790i −0.201445 + 0.186913i −0.774444 0.632643i \(-0.781970\pi\)
0.572999 + 0.819556i \(0.305780\pi\)
\(318\) −0.260425 + 0.0392527i −0.0146039 + 0.00220118i
\(319\) 1.83361 0.276373i 0.102663 0.0154739i
\(320\) 2.21739 2.05744i 0.123956 0.115014i
\(321\) −5.85263 25.6420i −0.326662 1.43120i
\(322\) −2.63712 5.31710i −0.146961 0.296310i
\(323\) −1.66607 + 7.29953i −0.0927026 + 0.406157i
\(324\) −10.6228 18.3993i −0.590157 1.02218i
\(325\) −7.52422 + 13.0323i −0.417369 + 0.722904i
\(326\) 2.19384 + 2.03559i 0.121506 + 0.112741i
\(327\) 20.0729 + 13.6855i 1.11003 + 0.756807i
\(328\) −5.27630 6.61627i −0.291335 0.365322i
\(329\) −7.88986 + 26.6748i −0.434982 + 1.47063i
\(330\) −0.379190 + 0.475490i −0.0208737 + 0.0261748i
\(331\) −18.1552 + 5.60012i −0.997897 + 0.307811i −0.750332 0.661061i \(-0.770107\pi\)
−0.247565 + 0.968871i \(0.579630\pi\)
\(332\) 1.03023 + 2.62499i 0.0565414 + 0.144065i
\(333\) −0.529714 + 7.06854i −0.0290282 + 0.387354i
\(334\) −0.0198739 + 0.0506379i −0.00108745 + 0.00277078i
\(335\) 0.582850 + 0.280686i 0.0318445 + 0.0153355i
\(336\) −2.62498 + 18.9034i −0.143204 + 1.03126i
\(337\) 2.75160 1.32510i 0.149889 0.0721827i −0.357436 0.933938i \(-0.616349\pi\)
0.507325 + 0.861755i \(0.330635\pi\)
\(338\) −0.0588788 0.785683i −0.00320259 0.0427355i
\(339\) 10.5851 + 3.26508i 0.574905 + 0.177335i
\(340\) −4.01497 + 2.73736i −0.217742 + 0.148454i
\(341\) 6.00815 + 0.905583i 0.325360 + 0.0490401i
\(342\) 0.345192 0.0186659
\(343\) 7.44924 16.9561i 0.402221 0.915543i
\(344\) 4.62996 0.249631
\(345\) 8.11262 + 1.22278i 0.436769 + 0.0658323i
\(346\) 3.02037 2.05925i 0.162376 0.110706i
\(347\) −6.89689 2.12741i −0.370245 0.114205i 0.104049 0.994572i \(-0.466820\pi\)
−0.474293 + 0.880367i \(0.657296\pi\)
\(348\) −0.207681 2.77131i −0.0111329 0.148558i
\(349\) 24.6510 11.8713i 1.31954 0.635455i 0.364295 0.931284i \(-0.381310\pi\)
0.955241 + 0.295829i \(0.0955958\pi\)
\(350\) 0.442257 3.18485i 0.0236396 0.170237i
\(351\) −11.4333 5.50601i −0.610267 0.293889i
\(352\) −2.74666 + 6.99837i −0.146397 + 0.373014i
\(353\) −1.73118 + 23.1010i −0.0921414 + 1.22954i 0.739087 + 0.673610i \(0.235257\pi\)
−0.831228 + 0.555931i \(0.812362\pi\)
\(354\) −2.21483 5.64330i −0.117717 0.299938i
\(355\) 1.43023 0.441168i 0.0759088 0.0234148i
\(356\) 10.2752 12.8846i 0.544582 0.682884i
\(357\) 8.06457 27.2655i 0.426823 1.44304i
\(358\) 3.41782 + 4.28582i 0.180638 + 0.226512i
\(359\) 12.5654 + 8.56694i 0.663176 + 0.452146i 0.847554 0.530710i \(-0.178075\pi\)
−0.184378 + 0.982855i \(0.559027\pi\)
\(360\) 0.333937 + 0.309848i 0.0176000 + 0.0163304i
\(361\) 8.53463 14.7824i 0.449191 0.778022i
\(362\) 0.352568 + 0.610665i 0.0185306 + 0.0320959i
\(363\) 1.93775 8.48985i 0.101706 0.445602i
\(364\) 7.15859 + 14.4335i 0.375212 + 0.756522i
\(365\) −0.225708 0.988890i −0.0118141 0.0517608i
\(366\) 0.318533 0.295555i 0.0166500 0.0154489i
\(367\) 19.7643 2.97899i 1.03169 0.155502i 0.388690 0.921369i \(-0.372928\pi\)
0.643000 + 0.765866i \(0.277690\pi\)
\(368\) 31.5741 4.75903i 1.64591 0.248081i
\(369\) −6.06525 + 5.62773i −0.315745 + 0.292968i
\(370\) 0.191006 + 0.836853i 0.00992994 + 0.0435059i
\(371\) −0.582149 + 1.24567i −0.0302237 + 0.0646718i
\(372\) 2.02631 8.87784i 0.105059 0.460295i
\(373\) −9.26435 16.0463i −0.479690 0.830847i 0.520039 0.854143i \(-0.325917\pi\)
−0.999729 + 0.0232955i \(0.992584\pi\)
\(374\) 1.76321 3.05398i 0.0911736 0.157917i
\(375\) 6.66431 + 6.18358i 0.344144 + 0.319319i
\(376\) 8.68678 + 5.92254i 0.447986 + 0.305432i
\(377\) −1.41233 1.77101i −0.0727389 0.0912117i
\(378\) 2.70608 + 0.171200i 0.139186 + 0.00880556i
\(379\) 6.64452 8.33196i 0.341306 0.427984i −0.581323 0.813673i \(-0.697465\pi\)
0.922629 + 0.385689i \(0.126036\pi\)
\(380\) −1.19741 + 0.369351i −0.0614257 + 0.0189473i
\(381\) 5.92159 + 15.0880i 0.303372 + 0.772980i
\(382\) −0.229236 + 3.05895i −0.0117287 + 0.156509i
\(383\) 6.65011 16.9442i 0.339805 0.865809i −0.654185 0.756335i \(-0.726988\pi\)
0.993990 0.109474i \(-0.0349166\pi\)
\(384\) 13.4543 + 6.47924i 0.686585 + 0.330642i
\(385\) 0.971083 + 3.02301i 0.0494910 + 0.154067i
\(386\) 0.451170 0.217272i 0.0229639 0.0110589i
\(387\) −0.338288 4.51414i −0.0171961 0.229467i
\(388\) −18.7920 5.79655i −0.954017 0.294275i
\(389\) −20.2465 + 13.8038i −1.02654 + 0.699882i −0.954711 0.297535i \(-0.903835\pi\)
−0.0718275 + 0.997417i \(0.522883\pi\)
\(390\) 0.734636 + 0.110729i 0.0371998 + 0.00560696i
\(391\) −47.5715 −2.40579
\(392\) −5.24048 4.64057i −0.264684 0.234384i
\(393\) −14.4617 −0.729499
\(394\) 3.97870 + 0.599693i 0.200444 + 0.0302121i
\(395\) −4.14940 + 2.82901i −0.208779 + 0.142343i
\(396\) 4.65719 + 1.43655i 0.234033 + 0.0721895i
\(397\) 1.12967 + 15.0744i 0.0566965 + 0.756562i 0.951018 + 0.309136i \(0.100040\pi\)
−0.894321 + 0.447425i \(0.852341\pi\)
\(398\) 0.257938 0.124216i 0.0129293 0.00622640i
\(399\) 4.05964 6.10562i 0.203236 0.305663i
\(400\) 15.5856 + 7.50562i 0.779279 + 0.375281i
\(401\) −8.51588 + 21.6981i −0.425263 + 1.08355i 0.544340 + 0.838865i \(0.316780\pi\)
−0.969602 + 0.244686i \(0.921315\pi\)
\(402\) −0.0525795 + 0.701625i −0.00262243 + 0.0349939i
\(403\) −2.71169 6.90927i −0.135079 0.344175i
\(404\) 24.2931 7.49344i 1.20863 0.372813i
\(405\) −3.18903 + 3.99892i −0.158464 + 0.198708i
\(406\) 0.421946 + 0.237117i 0.0209408 + 0.0117679i
\(407\) 11.6426 + 14.5994i 0.577103 + 0.723664i
\(408\) −8.87914 6.05369i −0.439583 0.299702i
\(409\) −24.5931 22.8191i −1.21605 1.12833i −0.987963 0.154690i \(-0.950562\pi\)
−0.228088 0.973641i \(-0.573247\pi\)
\(410\) −0.500974 + 0.867712i −0.0247413 + 0.0428532i
\(411\) −15.0255 26.0250i −0.741155 1.28372i
\(412\) −6.05882 + 26.5454i −0.298497 + 1.30780i
\(413\) −30.9367 6.68389i −1.52229 0.328893i
\(414\) 0.488041 + 2.13825i 0.0239859 + 0.105089i
\(415\) 0.497658 0.461759i 0.0244291 0.0226669i
\(416\) 9.08135 1.36879i 0.445250 0.0671106i
\(417\) −16.0749 + 2.42289i −0.787189 + 0.118650i
\(418\) 0.666609 0.618523i 0.0326049 0.0302529i
\(419\) 4.25627 + 18.6479i 0.207933 + 0.911012i 0.965940 + 0.258766i \(0.0833159\pi\)
−0.758007 + 0.652246i \(0.773827\pi\)
\(420\) 4.62670 1.11272i 0.225760 0.0542954i
\(421\) 1.09630 4.80319i 0.0534303 0.234093i −0.941161 0.337958i \(-0.890264\pi\)
0.994591 + 0.103865i \(0.0331209\pi\)
\(422\) −1.68427 2.91724i −0.0819890 0.142009i
\(423\) 5.13969 8.90221i 0.249900 0.432840i
\(424\) 0.380954 + 0.353474i 0.0185008 + 0.0171662i
\(425\) −21.2940 14.5180i −1.03291 0.704226i
\(426\) 1.01495 + 1.27271i 0.0491747 + 0.0616631i
\(427\) −0.364158 2.23918i −0.0176228 0.108361i
\(428\) −15.9138 + 19.9552i −0.769220 + 0.964572i
\(429\) 15.4440 4.76383i 0.745642 0.230000i
\(430\) −0.200272 0.510285i −0.00965797 0.0246081i
\(431\) −2.27088 + 30.3027i −0.109384 + 1.45963i 0.624855 + 0.780741i \(0.285158\pi\)
−0.734239 + 0.678891i \(0.762461\pi\)
\(432\) −5.32946 + 13.5792i −0.256414 + 0.653332i
\(433\) 24.3670 + 11.7345i 1.17101 + 0.563926i 0.915278 0.402823i \(-0.131971\pi\)
0.255727 + 0.966749i \(0.417685\pi\)
\(434\) 1.09214 + 1.14996i 0.0524246 + 0.0551999i
\(435\) −0.602796 + 0.290291i −0.0289018 + 0.0139184i
\(436\) −1.76182 23.5099i −0.0843761 1.12592i
\(437\) −11.7223 3.61584i −0.560752 0.172969i
\(438\) 0.911497 0.621448i 0.0435530 0.0296939i
\(439\) −28.0196 4.22327i −1.33730 0.201566i −0.558848 0.829270i \(-0.688757\pi\)
−0.778452 + 0.627704i \(0.783995\pi\)
\(440\) 1.20007 0.0572109
\(441\) −4.14160 + 5.44845i −0.197219 + 0.259450i
\(442\) −4.30782 −0.204902
\(443\) 17.1223 + 2.58077i 0.813506 + 0.122616i 0.542602 0.839990i \(-0.317439\pi\)
0.270904 + 0.962606i \(0.412677\pi\)
\(444\) 23.1229 15.7649i 1.09737 0.748171i
\(445\) −3.79124 1.16944i −0.179722 0.0554369i
\(446\) −0.398790 5.32148i −0.0188832 0.251979i
\(447\) 1.96504 0.946314i 0.0929432 0.0447591i
\(448\) 14.7740 8.76019i 0.698004 0.413880i
\(449\) 12.7466 + 6.13844i 0.601550 + 0.289691i 0.709767 0.704436i \(-0.248800\pi\)
−0.108218 + 0.994127i \(0.534514\pi\)
\(450\) −0.434099 + 1.10607i −0.0204636 + 0.0521404i
\(451\) −1.62886 + 21.7357i −0.0767003 + 1.02349i
\(452\) −3.92729 10.0066i −0.184724 0.470670i
\(453\) 0.399012 0.123079i 0.0187472 0.00578275i
\(454\) −3.01222 + 3.77721i −0.141371 + 0.177273i
\(455\) 2.60498 2.87376i 0.122123 0.134724i
\(456\) −1.72781 2.16660i −0.0809121 0.101461i
\(457\) 26.9539 + 18.3769i 1.26085 + 0.859633i 0.994550 0.104257i \(-0.0332466\pi\)
0.266300 + 0.963890i \(0.414199\pi\)
\(458\) 1.53012 + 1.41975i 0.0714980 + 0.0663405i
\(459\) 10.8666 18.8215i 0.507209 0.878511i
\(460\) −3.98082 6.89498i −0.185607 0.321480i
\(461\) −7.14027 + 31.2836i −0.332556 + 1.45702i 0.481608 + 0.876387i \(0.340053\pi\)
−0.814164 + 0.580635i \(0.802804\pi\)
\(462\) −2.67473 + 2.18435i −0.124440 + 0.101625i
\(463\) 2.30364 + 10.0929i 0.107059 + 0.469057i 0.999828 + 0.0185420i \(0.00590244\pi\)
−0.892769 + 0.450515i \(0.851240\pi\)
\(464\) −1.90882 + 1.77112i −0.0886146 + 0.0822223i
\(465\) −2.16778 + 0.326741i −0.100528 + 0.0151522i
\(466\) −2.12340 + 0.320050i −0.0983644 + 0.0148260i
\(467\) −21.7568 + 20.1873i −1.00678 + 0.934158i −0.997833 0.0658016i \(-0.979040\pi\)
−0.00895052 + 0.999960i \(0.502849\pi\)
\(468\) −1.32481 5.80438i −0.0612394 0.268307i
\(469\) 2.89833 + 2.25675i 0.133833 + 0.104207i
\(470\) 0.276993 1.21359i 0.0127767 0.0559785i
\(471\) −16.7816 29.0665i −0.773253 1.33931i
\(472\) −5.98122 + 10.3598i −0.275308 + 0.476847i
\(473\) −8.74180 8.11121i −0.401949 0.372954i
\(474\) −4.51293 3.07687i −0.207286 0.141325i
\(475\) −4.14364 5.19596i −0.190123 0.238407i
\(476\) −25.5661 + 10.3784i −1.17182 + 0.475691i
\(477\) 0.316797 0.397251i 0.0145051 0.0181889i
\(478\) 2.84848 0.878639i 0.130286 0.0401880i
\(479\) −13.5283 34.4695i −0.618123 1.57495i −0.805456 0.592655i \(-0.798080\pi\)
0.187333 0.982296i \(-0.440016\pi\)
\(480\) 0.202711 2.70498i 0.00925243 0.123465i
\(481\) 8.33379 21.2341i 0.379988 0.968193i
\(482\) −2.60637 1.25516i −0.118717 0.0571711i
\(483\) 43.5600 + 16.5146i 1.98205 + 0.751440i
\(484\) −7.61378 + 3.66660i −0.346081 + 0.166664i
\(485\) 0.353804 + 4.72119i 0.0160654 + 0.214378i
\(486\) −2.37784 0.733465i −0.107861 0.0332707i
\(487\) −5.73226 + 3.90819i −0.259753 + 0.177097i −0.686194 0.727419i \(-0.740720\pi\)
0.426440 + 0.904516i \(0.359767\pi\)
\(488\) −0.847849 0.127793i −0.0383803 0.00578490i
\(489\) −23.4904 −1.06227
\(490\) −0.284774 + 0.778303i −0.0128648 + 0.0351602i
\(491\) 32.9745 1.48812 0.744058 0.668115i \(-0.232898\pi\)
0.744058 + 0.668115i \(0.232898\pi\)
\(492\) 32.3019 + 4.86872i 1.45628 + 0.219499i
\(493\) 3.20533 2.18536i 0.144361 0.0984236i
\(494\) −1.06151 0.327431i −0.0477594 0.0147318i
\(495\) −0.0876829 1.17005i −0.00394105 0.0525897i
\(496\) −7.68728 + 3.70200i −0.345169 + 0.166225i
\(497\) 8.46701 0.733537i 0.379797 0.0329036i
\(498\) 0.665243 + 0.320364i 0.0298102 + 0.0143559i
\(499\) 2.97245 7.57367i 0.133065 0.339044i −0.848775 0.528754i \(-0.822659\pi\)
0.981840 + 0.189710i \(0.0607547\pi\)
\(500\) 0.659294 8.79767i 0.0294845 0.393444i
\(501\) −0.155992 0.397462i −0.00696922 0.0177573i
\(502\) −0.901849 + 0.278184i −0.0402515 + 0.0124159i
\(503\) 8.78267 11.0131i 0.391600 0.491050i −0.546479 0.837473i \(-0.684032\pi\)
0.938079 + 0.346422i \(0.112604\pi\)
\(504\) 1.48186 + 2.12013i 0.0660072 + 0.0944382i
\(505\) −3.81600 4.78511i −0.169810 0.212935i
\(506\) 4.77382 + 3.25474i 0.212222 + 0.144691i
\(507\) 4.53334 + 4.20632i 0.201332 + 0.186809i
\(508\) 7.86454 13.6218i 0.348932 0.604369i
\(509\) 13.3985 + 23.2068i 0.593877 + 1.02862i 0.993704 + 0.112034i \(0.0357366\pi\)
−0.399828 + 0.916590i \(0.630930\pi\)
\(510\) −0.283127 + 1.24046i −0.0125371 + 0.0549284i
\(511\) −0.0669191 5.75914i −0.00296033 0.254769i
\(512\) −3.95878 17.3446i −0.174955 0.766529i
\(513\) 4.10827 3.81192i 0.181385 0.168300i
\(514\) 0.205213 0.0309309i 0.00905156 0.00136430i
\(515\) 6.48183 0.976979i 0.285624 0.0430508i
\(516\) −13.1014 + 12.1563i −0.576756 + 0.535152i
\(517\) −6.02578 26.4007i −0.265014 1.16110i
\(518\) 0.0566306 + 4.87370i 0.00248821 + 0.214138i
\(519\) −6.38476 + 27.9735i −0.280260 + 1.22790i
\(520\) −0.732989 1.26957i −0.0321437 0.0556745i
\(521\) 14.6399 25.3570i 0.641386 1.11091i −0.343738 0.939066i \(-0.611693\pi\)
0.985124 0.171847i \(-0.0549734\pi\)
\(522\) −0.131112 0.121654i −0.00573860 0.00532464i
\(523\) 34.5847 + 23.5795i 1.51228 + 1.03106i 0.983209 + 0.182482i \(0.0584131\pi\)
0.529074 + 0.848576i \(0.322539\pi\)
\(524\) 8.75010 + 10.9723i 0.382250 + 0.479326i
\(525\) 14.4584 + 20.6860i 0.631017 + 0.902813i
\(526\) 2.55247 3.20070i 0.111293 0.139557i
\(527\) 12.1469 3.74682i 0.529126 0.163214i
\(528\) −6.78758 17.2945i −0.295392 0.752645i
\(529\) 4.10583 54.7885i 0.178514 2.38211i
\(530\) 0.0224792 0.0572761i 0.000976434 0.00248791i
\(531\) 10.5377 + 5.07467i 0.457295 + 0.220222i
\(532\) −7.08869 + 0.614127i −0.307334 + 0.0266258i
\(533\) 23.9895 11.5528i 1.03910 0.500405i
\(534\) −0.322469 4.30304i −0.0139546 0.186211i
\(535\) 5.87173 + 1.81119i 0.253857 + 0.0783045i
\(536\) 1.14711 0.782084i 0.0495475 0.0337809i
\(537\) −42.5463 6.41283i −1.83601 0.276734i
\(538\) 2.37318 0.102315
\(539\) 1.76472 + 17.9426i 0.0760118 + 0.772844i
\(540\) 3.63730 0.156524
\(541\) 9.35335 + 1.40979i 0.402132 + 0.0606116i 0.346995 0.937867i \(-0.387202\pi\)
0.0551374 + 0.998479i \(0.482440\pi\)
\(542\) −2.21259 + 1.50852i −0.0950390 + 0.0647965i
\(543\) −5.28879 1.63137i −0.226964 0.0700090i
\(544\) 1.17539 + 15.6845i 0.0503946 + 0.672469i
\(545\) −5.11370 + 2.46263i −0.219047 + 0.105487i
\(546\) 3.94457 + 1.49547i 0.168812 + 0.0640004i
\(547\) −14.3027 6.88782i −0.611540 0.294502i 0.102363 0.994747i \(-0.467360\pi\)
−0.713902 + 0.700245i \(0.753074\pi\)
\(548\) −10.6542 + 27.1465i −0.455125 + 1.15964i
\(549\) −0.0626479 + 0.835978i −0.00267375 + 0.0356787i
\(550\) 1.14357 + 2.91377i 0.0487621 + 0.124244i
\(551\) 0.955944 0.294870i 0.0407246 0.0125619i
\(552\) 10.9779 13.7659i 0.467251 0.585915i
\(553\) −26.4221 + 10.7258i −1.12358 + 0.456109i
\(554\) −0.290523 0.364304i −0.0123431 0.0154778i
\(555\) −5.56675 3.79535i −0.236295 0.161103i
\(556\) 11.5644 + 10.7302i 0.490439 + 0.455061i
\(557\) −12.5872 + 21.8017i −0.533338 + 0.923768i 0.465904 + 0.884835i \(0.345729\pi\)
−0.999242 + 0.0389329i \(0.987604\pi\)
\(558\) −0.293028 0.507540i −0.0124049 0.0214859i
\(559\) −3.24160 + 14.2024i −0.137105 + 0.600697i
\(560\) −3.51802 2.73927i −0.148664 0.115755i
\(561\) 6.15922 + 26.9853i 0.260042 + 1.13932i
\(562\) −1.20438 + 1.11750i −0.0508035 + 0.0471388i
\(563\) 14.9955 2.26021i 0.631986 0.0952566i 0.174766 0.984610i \(-0.444083\pi\)
0.457220 + 0.889353i \(0.348845\pi\)
\(564\) −40.1311 + 6.04878i −1.68982 + 0.254700i
\(565\) −1.89709 + 1.76024i −0.0798113 + 0.0740541i
\(566\) −0.804899 3.52649i −0.0338324 0.148229i
\(567\) −22.4948 + 18.3706i −0.944691 + 0.771492i
\(568\) 0.714767 3.13160i 0.0299910 0.131399i
\(569\) −14.6471 25.3696i −0.614040 1.06355i −0.990552 0.137136i \(-0.956210\pi\)
0.376512 0.926412i \(-0.377123\pi\)
\(570\) −0.164052 + 0.284146i −0.00687138 + 0.0119016i
\(571\) 7.97189 + 7.39683i 0.333613 + 0.309548i 0.829136 0.559047i \(-0.188833\pi\)
−0.495523 + 0.868595i \(0.665023\pi\)
\(572\) −12.9588 8.83514i −0.541833 0.369416i
\(573\) −15.0119 18.8244i −0.627133 0.786400i
\(574\) −3.82097 + 4.21521i −0.159484 + 0.175939i
\(575\) 26.3273 33.0134i 1.09792 1.37675i
\(576\) −6.06509 + 1.87083i −0.252712 + 0.0779513i
\(577\) 4.27582 + 10.8946i 0.178005 + 0.453548i 0.991831 0.127560i \(-0.0407145\pi\)
−0.813826 + 0.581108i \(0.802619\pi\)
\(578\) 0.228526 3.04947i 0.00950543 0.126841i
\(579\) −1.43598 + 3.65882i −0.0596773 + 0.152055i
\(580\) 0.584969 + 0.281706i 0.0242895 + 0.0116972i
\(581\) 3.31578 1.96608i 0.137562 0.0815669i
\(582\) −4.63929 + 2.23416i −0.192305 + 0.0926090i
\(583\) −0.100028 1.33478i −0.00414275 0.0552811i
\(584\) −2.08013 0.641635i −0.0860764 0.0265510i
\(585\) −1.18426 + 0.807415i −0.0489632 + 0.0333825i
\(586\) −3.48446 0.525197i −0.143942 0.0216957i
\(587\) −16.4484 −0.678898 −0.339449 0.940624i \(-0.610241\pi\)
−0.339449 + 0.940624i \(0.610241\pi\)
\(588\) 27.0132 0.627851i 1.11400 0.0258921i
\(589\) 3.27795 0.135066
\(590\) 1.40051 + 0.211093i 0.0576581 + 0.00869057i
\(591\) −26.0942 + 17.7907i −1.07337 + 0.731814i
\(592\) −25.0570 7.72906i −1.02984 0.317662i
\(593\) −2.31118 30.8406i −0.0949089 1.26647i −0.817797 0.575506i \(-0.804805\pi\)
0.722888 0.690965i \(-0.242814\pi\)
\(594\) −2.37819 + 1.14528i −0.0975784 + 0.0469913i
\(595\) 4.57448 + 4.81665i 0.187535 + 0.197463i
\(596\) −1.90693 0.918329i −0.0781108 0.0376162i
\(597\) −0.820962 + 2.09178i −0.0335997 + 0.0856108i
\(598\) 0.527447 7.03829i 0.0215689 0.287817i
\(599\) −2.42381 6.17576i −0.0990340 0.252335i 0.872767 0.488137i \(-0.162323\pi\)
−0.971801 + 0.235803i \(0.924228\pi\)
\(600\) 9.11505 2.81162i 0.372120 0.114784i
\(601\) −13.7703 + 17.2674i −0.561703 + 0.704353i −0.978872 0.204476i \(-0.934451\pi\)
0.417169 + 0.908829i \(0.363022\pi\)
\(602\) −0.499650 3.07231i −0.0203642 0.125218i
\(603\) −0.846335 1.06127i −0.0344654 0.0432183i
\(604\) −0.334804 0.228265i −0.0136230 0.00928799i
\(605\) 1.49137 + 1.38379i 0.0606327 + 0.0562589i
\(606\) 3.32830 5.76479i 0.135203 0.234179i
\(607\) −2.01882 3.49669i −0.0819413 0.141926i 0.822142 0.569282i \(-0.192779\pi\)
−0.904084 + 0.427355i \(0.859445\pi\)
\(608\) −0.902527 + 3.95423i −0.0366023 + 0.160365i
\(609\) −3.69370 + 0.888338i −0.149676 + 0.0359973i
\(610\) 0.0225898 + 0.0989723i 0.000914634 + 0.00400727i
\(611\) −24.2493 + 22.5001i −0.981023 + 0.910256i
\(612\) 10.0824 1.51968i 0.407557 0.0614294i
\(613\) −8.49034 + 1.27971i −0.342922 + 0.0516871i −0.318245 0.948008i \(-0.603094\pi\)
−0.0246762 + 0.999695i \(0.507855\pi\)
\(614\) −3.63841 + 3.37595i −0.146834 + 0.136242i
\(615\) −1.74999 7.66720i −0.0705664 0.309171i
\(616\) 6.66055 + 1.43902i 0.268361 + 0.0579796i
\(617\) 4.13292 18.1075i 0.166385 0.728980i −0.821037 0.570875i \(-0.806604\pi\)
0.987422 0.158106i \(-0.0505387\pi\)
\(618\) 3.56468 + 6.17420i 0.143392 + 0.248363i
\(619\) 8.01633 13.8847i 0.322204 0.558073i −0.658739 0.752372i \(-0.728910\pi\)
0.980942 + 0.194299i \(0.0622431\pi\)
\(620\) 1.55952 + 1.44702i 0.0626319 + 0.0581139i
\(621\) 29.4208 + 20.0587i 1.18062 + 0.804930i
\(622\) 1.47702 + 1.85213i 0.0592231 + 0.0742635i
\(623\) −19.6397 11.0367i −0.786847 0.442177i
\(624\) −14.1504 + 17.7440i −0.566469 + 0.710330i
\(625\) 20.8224 6.42287i 0.832897 0.256915i
\(626\) 0.319867 + 0.815007i 0.0127844 + 0.0325742i
\(627\) −0.533398 + 7.11770i −0.0213019 + 0.284254i
\(628\) −11.8994 + 30.3191i −0.474836 + 1.20986i
\(629\) 35.1976 + 16.9503i 1.40342 + 0.675852i
\(630\) 0.169569 0.255029i 0.00675579 0.0101606i
\(631\) −5.42888 + 2.61441i −0.216120 + 0.104078i −0.538812 0.842426i \(-0.681127\pi\)
0.322691 + 0.946504i \(0.395412\pi\)
\(632\) 0.805427 + 10.7477i 0.0320382 + 0.427520i
\(633\) 25.2653 + 7.79333i 1.00421 + 0.309757i
\(634\) 1.02719 0.700329i 0.0407951 0.0278136i
\(635\) −3.74441 0.564380i −0.148593 0.0223967i
\(636\) −2.00606 −0.0795453
\(637\) 17.9040 12.8261i 0.709383 0.508190i
\(638\) −0.471174 −0.0186540
\(639\) −3.10549 0.468077i −0.122851 0.0185169i
\(640\) −2.88256 + 1.96529i −0.113943 + 0.0776851i
\(641\) 27.1800 + 8.38390i 1.07354 + 0.331144i 0.780629 0.624994i \(-0.214899\pi\)
0.292914 + 0.956139i \(0.405375\pi\)
\(642\) 0.499427 + 6.66439i 0.0197108 + 0.263022i
\(643\) −3.68820 + 1.77614i −0.145448 + 0.0700443i −0.505192 0.863007i \(-0.668578\pi\)
0.359744 + 0.933051i \(0.382864\pi\)
\(644\) −13.8263 43.0417i −0.544832 1.69608i
\(645\) 3.87660 + 1.86687i 0.152641 + 0.0735080i
\(646\) 0.695051 1.77096i 0.0273464 0.0696776i
\(647\) 0.284912 3.80189i 0.0112010 0.149468i −0.988799 0.149254i \(-0.952313\pi\)
1.00000 0.000213846i \(-6.80692e-5\pi\)
\(648\) 4.01032 + 10.2181i 0.157540 + 0.401406i
\(649\) 29.4424 9.08178i 1.15572 0.356491i
\(650\) 2.38406 2.98952i 0.0935105 0.117258i
\(651\) −12.4233 0.785960i −0.486908 0.0308042i
\(652\) 14.2129 + 17.8224i 0.556621 + 0.697980i
\(653\) −34.9996 23.8623i −1.36964 0.933806i −0.999989 0.00463549i \(-0.998524\pi\)
−0.369652 0.929170i \(-0.620523\pi\)
\(654\) −4.52517 4.19874i −0.176948 0.164184i
\(655\) 1.68932 2.92599i 0.0660073 0.114328i
\(656\) −15.3040 26.5072i −0.597519 1.03493i
\(657\) −0.473600 + 2.07498i −0.0184769 + 0.0809526i
\(658\) 2.99258 6.40344i 0.116663 0.249632i
\(659\) −0.383444 1.67998i −0.0149368 0.0654426i 0.966910 0.255117i \(-0.0821139\pi\)
−0.981847 + 0.189674i \(0.939257\pi\)
\(660\) −3.39582 + 3.15086i −0.132182 + 0.122647i
\(661\) −44.0838 + 6.64456i −1.71466 + 0.258443i −0.931596 0.363497i \(-0.881583\pi\)
−0.783065 + 0.621940i \(0.786345\pi\)
\(662\) 4.77369 0.719518i 0.185535 0.0279649i
\(663\) 24.7863 22.9983i 0.962621 0.893182i
\(664\) −0.324204 1.42043i −0.0125816 0.0551234i
\(665\) 0.761109 + 1.53459i 0.0295145 + 0.0595088i
\(666\) 0.400786 1.75596i 0.0155302 0.0680421i
\(667\) 3.17807 + 5.50457i 0.123055 + 0.213138i
\(668\) −0.207175 + 0.358838i −0.00801585 + 0.0138839i
\(669\) 30.7045 + 28.4897i 1.18711 + 1.10147i
\(670\) −0.135815 0.0925973i −0.00524700 0.00357735i
\(671\) 1.37694 + 1.72663i 0.0531562 + 0.0666558i
\(672\) 4.36866 14.7700i 0.168525 0.569765i
\(673\) −17.9044 + 22.4514i −0.690164 + 0.865438i −0.996246 0.0865667i \(-0.972410\pi\)
0.306082 + 0.952005i \(0.400982\pi\)
\(674\) −0.741540 + 0.228735i −0.0285631 + 0.00881054i
\(675\) 7.04777 + 17.9574i 0.271269 + 0.691181i
\(676\) 0.448479 5.98453i 0.0172492 0.230174i
\(677\) 15.4185 39.2857i 0.592582 1.50987i −0.248316 0.968679i \(-0.579877\pi\)
0.840898 0.541194i \(-0.182028\pi\)
\(678\) −2.53593 1.22124i −0.0973919 0.0469015i
\(679\) −3.69758 + 26.6275i −0.141900 + 1.02187i
\(680\) 2.26202 1.08933i 0.0867446 0.0417740i
\(681\) −2.83382 37.8148i −0.108592 1.44906i
\(682\) −1.47529 0.455068i −0.0564919 0.0174255i
\(683\) 18.6328 12.7036i 0.712965 0.486092i −0.151708 0.988425i \(-0.548477\pi\)
0.864674 + 0.502334i \(0.167525\pi\)
\(684\) 2.59995 + 0.391880i 0.0994118 + 0.0149839i
\(685\) 7.02072 0.268248
\(686\) −2.51382 + 3.97823i −0.0959779 + 0.151889i
\(687\) −16.3837 −0.625077
\(688\) 16.5589 + 2.49586i 0.631303 + 0.0951537i
\(689\) −1.35100 + 0.921096i −0.0514690 + 0.0350910i
\(690\) −1.99205 0.614465i −0.0758359 0.0233923i
\(691\) −0.314792 4.20061i −0.0119753 0.159799i −0.999985 0.00540955i \(-0.998278\pi\)
0.988010 0.154389i \(-0.0493410\pi\)
\(692\) 25.0869 12.0812i 0.953660 0.459258i
\(693\) 0.916367 6.59908i 0.0348099 0.250678i
\(694\) 1.65233 + 0.795718i 0.0627214 + 0.0302050i
\(695\) 1.38754 3.53539i 0.0526324 0.134105i
\(696\) −0.107302 + 1.43184i −0.00406727 + 0.0542739i
\(697\) 16.6598 + 42.4485i 0.631035 + 1.60785i
\(698\) −6.64330 + 2.04919i −0.251453 + 0.0775629i
\(699\) 10.5089 13.1778i 0.397484 0.498429i
\(700\) 6.94664 23.4859i 0.262558 0.887682i
\(701\) −10.8255 13.5748i −0.408875 0.512713i 0.534170 0.845377i \(-0.320624\pi\)
−0.943046 + 0.332664i \(0.892053\pi\)
\(702\) 2.66419 + 1.81641i 0.100553 + 0.0685561i
\(703\) 7.38481 + 6.85210i 0.278523 + 0.258432i
\(704\) −8.36024 + 14.4804i −0.315088 + 0.545749i
\(705\) 4.88526 + 8.46151i 0.183989 + 0.318679i
\(706\) 1.30983 5.73872i 0.0492960 0.215980i
\(707\) −15.4415 31.1339i −0.580736 1.17091i
\(708\) −10.2753 45.0192i −0.386171 1.69193i
\(709\) −30.1977 + 28.0194i −1.13410 + 1.05229i −0.135997 + 0.990709i \(0.543424\pi\)
−0.998102 + 0.0615808i \(0.980386\pi\)
\(710\) −0.376063 + 0.0566824i −0.0141134 + 0.00212725i
\(711\) 10.4200 1.57056i 0.390780 0.0589006i
\(712\) −6.24171 + 5.79146i −0.233918 + 0.217044i
\(713\) 4.63444 + 20.3048i 0.173561 + 0.760421i
\(714\) −3.05885 + 6.54524i −0.114475 + 0.244949i
\(715\) −0.840210 + 3.68120i −0.0314221 + 0.137669i
\(716\) 20.8772 + 36.1604i 0.780219 + 1.35138i
\(717\) −11.6987 + 20.2628i −0.436897 + 0.756727i
\(718\) −2.83270 2.62837i −0.105716 0.0980897i
\(719\) −21.5481 14.6912i −0.803607 0.547890i 0.0904196 0.995904i \(-0.471179\pi\)
−0.894027 + 0.448014i \(0.852132\pi\)
\(720\) 1.02729 + 1.28818i 0.0382848 + 0.0480076i
\(721\) 37.1467 + 2.35008i 1.38341 + 0.0875216i
\(722\) −2.70421 + 3.39097i −0.100640 + 0.126199i
\(723\) 21.6975 6.69280i 0.806939 0.248908i
\(724\) 1.96225 + 4.99973i 0.0729264 + 0.185813i
\(725\) −0.257332 + 3.43385i −0.00955706 + 0.127530i
\(726\) −0.808392 + 2.05975i −0.0300023 + 0.0764445i
\(727\) −17.6548 8.50211i −0.654781 0.315326i 0.0768342 0.997044i \(-0.475519\pi\)
−0.731615 + 0.681718i \(0.761233\pi\)
\(728\) −2.54584 7.92527i −0.0943549 0.293730i
\(729\) −12.0730 + 5.81404i −0.447147 + 0.215335i
\(730\) 0.0192605 + 0.257013i 0.000712862 + 0.00951248i
\(731\) −23.8403 7.35377i −0.881766 0.271989i
\(732\) 2.73469 1.86448i 0.101077 0.0689131i
\(733\) 29.6540 + 4.46962i 1.09530 + 0.165089i 0.671745 0.740783i \(-0.265545\pi\)
0.423552 + 0.905872i \(0.360783\pi\)
\(734\) −5.07874 −0.187460
\(735\) −2.51663 5.99853i −0.0928272 0.221259i
\(736\) −25.7699 −0.949893
\(737\) −3.53598 0.532963i −0.130250 0.0196320i
\(738\) 1.73706 1.18431i 0.0639422 0.0435951i
\(739\) 21.8874 + 6.75138i 0.805142 + 0.248353i 0.669893 0.742458i \(-0.266340\pi\)
0.135250 + 0.990812i \(0.456816\pi\)
\(740\) 0.488601 + 6.51993i 0.0179613 + 0.239677i
\(741\) 7.85576 3.78314i 0.288589 0.138977i
\(742\) 0.193444 0.290936i 0.00710154 0.0106806i
\(743\) −17.3846 8.37199i −0.637780 0.307138i 0.0869077 0.996216i \(-0.472301\pi\)
−0.724687 + 0.689078i \(0.758016\pi\)
\(744\) −1.71887 + 4.37961i −0.0630169 + 0.160564i
\(745\) −0.0380784 + 0.508121i −0.00139509 + 0.0186161i
\(746\) 1.72004 + 4.38260i 0.0629753 + 0.160458i
\(747\) −1.36121 + 0.419878i −0.0498041 + 0.0153625i
\(748\) 16.7474 21.0006i 0.612345 0.767857i
\(749\) 30.4172 + 17.0932i 1.11142 + 0.624574i
\(750\) −1.44028 1.80605i −0.0525915 0.0659476i
\(751\) −22.6255 15.4258i −0.825616 0.562895i 0.0751641 0.997171i \(-0.476052\pi\)
−0.900780 + 0.434276i \(0.857004\pi\)
\(752\) 27.8754 + 25.8646i 1.01651 + 0.943185i
\(753\) 3.70390 6.41535i 0.134978 0.233788i
\(754\) 0.287789 + 0.498465i 0.0104807 + 0.0181530i
\(755\) −0.0217077 + 0.0951078i −0.000790025 + 0.00346133i
\(756\) 20.1876 + 4.36154i 0.734214 + 0.158628i
\(757\) 3.78057 + 16.5638i 0.137407 + 0.602021i 0.995999 + 0.0893611i \(0.0284825\pi\)
−0.858592 + 0.512659i \(0.828660\pi\)
\(758\) −1.98502 + 1.84183i −0.0720992 + 0.0668983i
\(759\) −44.8438 + 6.75911i −1.62773 + 0.245340i
\(760\) 0.640192 0.0964934i 0.0232222 0.00350018i
\(761\) −15.6208 + 14.4939i −0.566252 + 0.525405i −0.910519 0.413467i \(-0.864318\pi\)
0.344267 + 0.938872i \(0.388127\pi\)
\(762\) −0.916446 4.01521i −0.0331994 0.145456i
\(763\) −31.3348 + 7.53605i −1.13440 + 0.272823i
\(764\) −5.19926 + 22.7794i −0.188103 + 0.824131i
\(765\) −1.22736 2.12585i −0.0443752 0.0768601i
\(766\) −2.31258 + 4.00550i −0.0835569 + 0.144725i
\(767\) −27.5910 25.6007i −0.996251 0.924386i
\(768\) 18.2603 + 12.4497i 0.658913 + 0.449240i
\(769\) −24.0195 30.1195i −0.866167 1.08614i −0.995521 0.0945402i \(-0.969862\pi\)
0.129354 0.991598i \(-0.458710\pi\)
\(770\) −0.129507 0.796329i −0.00466711 0.0286977i
\(771\) −1.01562 + 1.27355i −0.0365767 + 0.0458658i
\(772\) 3.64483 1.12428i 0.131180 0.0404637i
\(773\) −4.77022 12.1543i −0.171573 0.437161i 0.819061 0.573707i \(-0.194495\pi\)
−0.990634 + 0.136546i \(0.956400\pi\)
\(774\) −0.0859573 + 1.14702i −0.00308967 + 0.0412288i
\(775\) −4.12220 + 10.5032i −0.148074 + 0.377286i
\(776\) 9.15437 + 4.40851i 0.328623 + 0.158256i
\(777\) −26.3453 27.7399i −0.945131 0.995164i
\(778\) 5.60984 2.70156i 0.201122 0.0968555i
\(779\) 0.878756 + 11.7262i 0.0314847 + 0.420134i
\(780\) 5.40750 + 1.66799i 0.193620 + 0.0597238i
\(781\) −6.83579 + 4.66057i −0.244604 + 0.166768i
\(782\) 11.9527 + 1.80157i 0.427426 + 0.0644242i
\(783\) −2.90382 −0.103774
\(784\) −16.2409 19.4219i −0.580031 0.693638i
\(785\) 7.84123 0.279865
\(786\) 3.63361 + 0.547679i 0.129607 + 0.0195351i
\(787\) −22.9432 + 15.6424i −0.817838 + 0.557593i −0.898411 0.439156i \(-0.855278\pi\)
0.0805725 + 0.996749i \(0.474325\pi\)
\(788\) 29.2864 + 9.03365i 1.04328 + 0.321811i
\(789\) 2.40130 + 32.0431i 0.0854885 + 1.14077i
\(790\) 1.14970 0.553667i 0.0409045 0.0196986i
\(791\) −12.6399 + 7.49479i −0.449423 + 0.266484i
\(792\) −2.26872 1.09256i −0.0806153 0.0388223i
\(793\) 0.985615 2.51131i 0.0350002 0.0891791i
\(794\) 0.287043 3.83033i 0.0101868 0.135933i
\(795\) 0.176441 + 0.449565i 0.00625773 + 0.0159444i
\(796\) 2.08378 0.642761i 0.0738576 0.0227820i
\(797\) −5.26584 + 6.60315i −0.186526 + 0.233896i −0.866298 0.499527i \(-0.833507\pi\)
0.679773 + 0.733423i \(0.262078\pi\)
\(798\) −1.25124 + 1.38034i −0.0442933 + 0.0488634i
\(799\) −35.3227 44.2933i −1.24963 1.56698i
\(800\) −11.5352 7.86454i −0.407830 0.278053i
\(801\) 6.10264 + 5.66243i 0.215626 + 0.200072i
\(802\) 2.96140 5.12929i 0.104571 0.181122i
\(803\) 2.80341 + 4.85564i 0.0989301 + 0.171352i
\(804\) −1.19255 + 5.22488i −0.0420578 + 0.184267i
\(805\) −8.42973 + 6.88422i −0.297109 + 0.242637i
\(806\) 0.419670 + 1.83870i 0.0147823 + 0.0647653i
\(807\) −13.6548 + 12.6698i −0.480671 + 0.445998i
\(808\) −12.9883 + 1.95767i −0.456926 + 0.0688706i
\(809\) 16.9869 2.56037i 0.597229 0.0900178i 0.156531 0.987673i \(-0.449969\pi\)
0.440698 + 0.897655i \(0.354731\pi\)
\(810\) 0.952708 0.883984i 0.0334747 0.0310600i
\(811\) −2.51908 11.0368i −0.0884568 0.387555i 0.911248 0.411858i \(-0.135120\pi\)
−0.999705 + 0.0243039i \(0.992263\pi\)
\(812\) 2.90887 + 2.26496i 0.102081 + 0.0794845i
\(813\) 4.67721 20.4922i 0.164037 0.718692i
\(814\) −2.37240 4.10911i −0.0831525 0.144024i
\(815\) 2.74399 4.75273i 0.0961178 0.166481i
\(816\) −28.4927 26.4373i −0.997444 0.925492i
\(817\) −5.31564 3.62414i −0.185971 0.126793i
\(818\) 5.31501 + 6.66481i 0.185835 + 0.233030i
\(819\) −7.54101 + 3.06121i −0.263504 + 0.106967i
\(820\) −4.75835 + 5.96679i −0.166169 + 0.208369i
\(821\) −41.3718 + 12.7615i −1.44389 + 0.445380i −0.915049 0.403343i \(-0.867848\pi\)
−0.528837 + 0.848723i \(0.677372\pi\)
\(822\) 2.78968 + 7.10799i 0.0973013 + 0.247920i
\(823\) −1.73660 + 23.1733i −0.0605340 + 0.807771i 0.881485 + 0.472212i \(0.156544\pi\)
−0.942019 + 0.335559i \(0.891075\pi\)
\(824\) 5.13956 13.0954i 0.179045 0.456199i
\(825\) −22.1358 10.6600i −0.770668 0.371134i
\(826\) 7.51993 + 2.85097i 0.261652 + 0.0991980i
\(827\) 7.08100 3.41003i 0.246230 0.118578i −0.306699 0.951807i \(-0.599224\pi\)
0.552929 + 0.833228i \(0.313510\pi\)
\(828\) 1.24843 + 16.6591i 0.0433859 + 0.578944i
\(829\) 48.3146 + 14.9031i 1.67804 + 0.517605i 0.980091 0.198547i \(-0.0636221\pi\)
0.697944 + 0.716152i \(0.254098\pi\)
\(830\) −0.142527 + 0.0971734i −0.00494719 + 0.00337294i
\(831\) 3.61653 + 0.545104i 0.125456 + 0.0189095i
\(832\) 20.4254 0.708124
\(833\) 19.6134 + 32.2185i 0.679563 + 1.11630i
\(834\) 4.13068 0.143034
\(835\) 0.0986390 + 0.0148674i 0.00341354 + 0.000514509i
\(836\) 5.72301 3.90188i 0.197934 0.134949i
\(837\) −9.09215 2.80456i −0.314271 0.0969397i
\(838\) −0.363204 4.84662i −0.0125467 0.167424i
\(839\) 27.7575 13.3673i 0.958296 0.461491i 0.111709 0.993741i \(-0.464368\pi\)
0.846587 + 0.532250i \(0.178653\pi\)
\(840\) −2.44944 + 0.212207i −0.0845138 + 0.00732183i
\(841\) 25.6611 + 12.3577i 0.884865 + 0.426129i
\(842\) −0.457354 + 1.16532i −0.0157614 + 0.0401595i
\(843\) 0.963702 12.8597i 0.0331917 0.442912i
\(844\) −9.37396 23.8845i −0.322665 0.822137i
\(845\) −1.38060 + 0.425860i −0.0474942 + 0.0146500i
\(846\) −1.62852 + 2.04210i −0.0559896 + 0.0702088i
\(847\) 6.61799 + 9.46854i 0.227397 + 0.325343i
\(848\) 1.17193 + 1.46955i 0.0402441 + 0.0504645i
\(849\) 23.4582 + 15.9936i 0.805085 + 0.548898i
\(850\) 4.80045 + 4.45417i 0.164654 + 0.152777i
\(851\) −32.0036 + 55.4319i −1.09707 + 1.90018i
\(852\) 6.19968 + 10.7382i 0.212398 + 0.367883i
\(853\) 6.16659 27.0176i 0.211140 0.925064i −0.752654 0.658416i \(-0.771227\pi\)
0.963794 0.266648i \(-0.0859161\pi\)
\(854\) 0.00669755 + 0.576399i 0.000229186 + 0.0197240i
\(855\) −0.140855 0.617128i −0.00481715 0.0211053i
\(856\) 9.66692 8.96959i 0.330409 0.306574i
\(857\) 49.4309 7.45051i 1.68853 0.254505i 0.766672 0.642039i \(-0.221911\pi\)
0.921855 + 0.387534i \(0.126673\pi\)
\(858\) −4.06082 + 0.612070i −0.138634 + 0.0208957i
\(859\) 40.9265 37.9742i 1.39639 1.29566i 0.490956 0.871184i \(-0.336648\pi\)
0.905437 0.424480i \(-0.139543\pi\)
\(860\) −0.929127 4.07077i −0.0316830 0.138812i
\(861\) −0.518847 44.6526i −0.0176823 1.52176i
\(862\) 1.71816 7.52777i 0.0585209 0.256397i
\(863\) 4.90861 + 8.50196i 0.167091 + 0.289410i 0.937396 0.348266i \(-0.113229\pi\)
−0.770305 + 0.637676i \(0.779896\pi\)
\(864\) 5.88654 10.1958i 0.200264 0.346868i
\(865\) −4.91394 4.55947i −0.167079 0.155027i
\(866\) −5.67799 3.87119i −0.192946 0.131548i
\(867\) 14.9654 + 18.7661i 0.508253 + 0.637329i
\(868\) 6.92043 + 9.90125i 0.234895 + 0.336070i
\(869\) 17.3081 21.7037i 0.587137 0.736247i
\(870\) 0.162450 0.0501092i 0.00550758 0.00169886i
\(871\) 1.59591 + 4.06632i 0.0540754 + 0.137782i
\(872\) −0.910275 + 12.1468i −0.0308258 + 0.411342i
\(873\) 3.62937 9.24748i 0.122836 0.312980i
\(874\) 2.80837 + 1.35244i 0.0949944 + 0.0457469i
\(875\) −12.0152 + 1.04093i −0.406187 + 0.0351899i
\(876\) 7.57080 3.64591i 0.255794 0.123184i
\(877\) −0.749469 10.0010i −0.0253078 0.337709i −0.995458 0.0952033i \(-0.969650\pi\)
0.970150 0.242505i \(-0.0779692\pi\)
\(878\) 6.88017 + 2.12225i 0.232194 + 0.0716225i
\(879\) 22.8527 15.5807i 0.770804 0.525525i
\(880\) 4.29201 + 0.646916i 0.144684 + 0.0218075i
\(881\) −9.32967 −0.314325 −0.157162 0.987573i \(-0.550235\pi\)
−0.157162 + 0.987573i \(0.550235\pi\)
\(882\) 1.24694 1.21212i 0.0419867 0.0408141i
\(883\) 24.8689 0.836904 0.418452 0.908239i \(-0.362573\pi\)
0.418452 + 0.908239i \(0.362573\pi\)
\(884\) −32.4461 4.89046i −1.09128 0.164484i
\(885\) −9.18522 + 6.26238i −0.308758 + 0.210508i
\(886\) −4.20436 1.29687i −0.141248 0.0435694i
\(887\) 0.841239 + 11.2256i 0.0282460 + 0.376917i 0.993357 + 0.115075i \(0.0367109\pi\)
−0.965111 + 0.261842i \(0.915670\pi\)
\(888\) −13.0274 + 6.27366i −0.437170 + 0.210530i
\(889\) −20.1053 7.62238i −0.674311 0.255646i
\(890\) 0.908288 + 0.437408i 0.0304459 + 0.0146620i
\(891\) 10.3292 26.3185i 0.346043 0.881702i
\(892\) 3.03757 40.5336i 0.101705 1.35716i
\(893\) −5.33733 13.5993i −0.178607 0.455083i
\(894\) −0.529568 + 0.163350i −0.0177114 + 0.00546324i
\(895\) 6.26746 7.85914i 0.209498 0.262702i
\(896\) −18.3552 + 7.45116i −0.613206 + 0.248926i
\(897\) 34.5408 + 43.3128i 1.15328 + 1.44617i
\(898\) −2.97021 2.02505i −0.0991170 0.0675769i
\(899\) −1.24504 1.15522i −0.0415243 0.0385289i
\(900\) −4.52525 + 7.83796i −0.150842 + 0.261265i
\(901\) −1.40017 2.42516i −0.0466463 0.0807937i
\(902\) 1.23241 5.39956i 0.0410349 0.179786i
\(903\) 19.2771 + 15.0099i 0.641503 + 0.499499i
\(904\) 1.23588 + 5.41474i 0.0411047 + 0.180092i
\(905\) 0.947870 0.879495i 0.0315083 0.0292354i
\(906\) −0.104916 + 0.0158135i −0.00348559 + 0.000525368i
\(907\) −8.27810 + 1.24772i −0.274870 + 0.0414299i −0.285031 0.958518i \(-0.592004\pi\)
0.0101609 + 0.999948i \(0.496766\pi\)
\(908\) −26.9759 + 25.0299i −0.895225 + 0.830648i
\(909\) 2.85769 + 12.5204i 0.0947836 + 0.415274i
\(910\) −0.763351 + 0.623399i −0.0253049 + 0.0206655i
\(911\) 1.27518 5.58691i 0.0422485 0.185103i −0.949401 0.314067i \(-0.898308\pi\)
0.991649 + 0.128965i \(0.0411654\pi\)
\(912\) −5.01153 8.68022i −0.165948 0.287431i
\(913\) −1.87632 + 3.24988i −0.0620972 + 0.107555i
\(914\) −6.07641 5.63808i −0.200990 0.186491i
\(915\) −0.658365 0.448865i −0.0217649 0.0148390i
\(916\) 9.91298 + 12.4305i 0.327534 + 0.410715i
\(917\) 12.8846 14.2140i 0.425487 0.469388i
\(918\) −3.44309 + 4.31750i −0.113639 + 0.142499i
\(919\) 19.2287 5.93127i 0.634296 0.195655i 0.0391006 0.999235i \(-0.487551\pi\)
0.595196 + 0.803581i \(0.297075\pi\)
\(920\) 1.50283 + 3.82916i 0.0495470 + 0.126244i
\(921\) 2.91134 38.8491i 0.0959318 1.28012i
\(922\) 2.97878 7.58981i 0.0981009 0.249957i
\(923\) 9.10575 + 4.38510i 0.299719 + 0.144337i
\(924\) −22.6256 + 13.4158i −0.744327 + 0.441347i
\(925\) −31.2423 + 15.0455i −1.02724 + 0.494693i
\(926\) −0.196578 2.62315i −0.00645996 0.0862021i
\(927\) −13.1433 4.05418i −0.431683 0.133157i
\(928\) 1.73636 1.18383i 0.0569988 0.0388612i
\(929\) 12.5330 + 1.88904i 0.411193 + 0.0619774i 0.351382 0.936232i \(-0.385712\pi\)
0.0598116 + 0.998210i \(0.480950\pi\)
\(930\) 0.557044 0.0182662
\(931\) 2.38412 + 9.42986i 0.0781365 + 0.309051i
\(932\) −16.3565 −0.535777
\(933\) −18.3865 2.77132i −0.601947 0.0907289i
\(934\) 6.23105 4.24826i 0.203886 0.139007i
\(935\) −6.17931 1.90607i −0.202085 0.0623350i
\(936\) 0.229873 + 3.06745i 0.00751365 + 0.100263i
\(937\) −47.9701 + 23.1012i −1.56712 + 0.754683i −0.997727 0.0673852i \(-0.978534\pi\)
−0.569389 + 0.822068i \(0.692820\pi\)
\(938\) −0.642761 0.676787i −0.0209869 0.0220979i
\(939\) −6.19156 2.98170i −0.202054 0.0973040i
\(940\) 3.46401 8.82615i 0.112983 0.287877i
\(941\) 1.37957 18.4090i 0.0449725 0.600117i −0.928503 0.371325i \(-0.878903\pi\)
0.973475 0.228792i \(-0.0734775\pi\)
\(942\) 3.11571 + 7.93869i 0.101515 + 0.258657i
\(943\) −71.3939 + 22.0221i −2.32490 + 0.717138i
\(944\) −26.9763 + 33.8272i −0.878004 + 1.10098i
\(945\) −0.798145 4.90773i −0.0259637 0.159648i
\(946\) 1.88926 + 2.36906i 0.0614252 + 0.0770247i
\(947\) 19.1735 + 13.0723i 0.623055 + 0.424792i 0.833272 0.552863i \(-0.186465\pi\)
−0.210217 + 0.977655i \(0.567417\pi\)
\(948\) −30.4980 28.2980i −0.990528 0.919076i
\(949\) 3.42459 5.93157i 0.111167 0.192547i
\(950\) 0.844342 + 1.46244i 0.0273941 + 0.0474479i
\(951\) −2.17139 + 9.51347i −0.0704120 + 0.308495i
\(952\) 13.8608 3.33354i 0.449231 0.108041i
\(953\) 7.82231 + 34.2718i 0.253389 + 1.11017i 0.928171 + 0.372154i \(0.121381\pi\)
−0.674782 + 0.738017i \(0.735762\pi\)
\(954\) −0.0946417 + 0.0878147i −0.00306414 + 0.00284311i
\(955\) 5.56226 0.838376i 0.179991 0.0271292i
\(956\) 22.4519 3.38408i 0.726147 0.109449i
\(957\) 2.71104 2.51548i 0.0876355 0.0813138i
\(958\) 2.09368 + 9.17303i 0.0676439 + 0.296367i
\(959\) 38.9661 + 8.41865i 1.25828 + 0.271853i
\(960\) 1.34244 5.88161i 0.0433270 0.189828i
\(961\) 12.7174 + 22.0272i 0.410239 + 0.710554i
\(962\) −2.89808 + 5.01962i −0.0934378 + 0.161839i
\(963\) −9.45154 8.76974i −0.304571 0.282601i
\(964\) −18.2060 12.4126i −0.586376 0.399784i
\(965\) −0.572534 0.717935i −0.0184305 0.0231111i
\(966\) −10.3193 5.79906i −0.332019 0.186582i
\(967\) 19.9485 25.0147i 0.641502 0.804417i −0.349688 0.936866i \(-0.613713\pi\)
0.991190 + 0.132449i \(0.0422839\pi\)
\(968\) 4.17220 1.28695i 0.134099 0.0413642i
\(969\) 5.45552 + 13.9005i 0.175257 + 0.446547i
\(970\) 0.0898998 1.19963i 0.00288651 0.0385178i
\(971\) 0.482563 1.22955i 0.0154862 0.0394582i −0.922922 0.384988i \(-0.874206\pi\)
0.938408 + 0.345530i \(0.112301\pi\)
\(972\) −17.0770 8.22383i −0.547744 0.263779i
\(973\) 11.9404 17.9582i 0.382792 0.575712i
\(974\) 1.58828 0.764873i 0.0508916 0.0245081i
\(975\) 2.24286 + 29.9289i 0.0718291 + 0.958493i
\(976\) −2.96342 0.914095i −0.0948569 0.0292595i
\(977\) −8.16187 + 5.56467i −0.261121 + 0.178029i −0.686803 0.726843i \(-0.740987\pi\)
0.425682 + 0.904873i \(0.360034\pi\)
\(978\) 5.90213 + 0.889603i 0.188729 + 0.0284464i
\(979\) 21.9310 0.700918
\(980\) −3.02846 + 5.53881i −0.0967406 + 0.176931i
\(981\) 11.9094 0.380239
\(982\) −8.28506 1.24877i −0.264387 0.0398499i
\(983\) 2.92646 1.99523i 0.0933396 0.0636378i −0.515751 0.856739i \(-0.672487\pi\)
0.609090 + 0.793101i \(0.291535\pi\)
\(984\) −16.1280 4.97482i −0.514141 0.158591i
\(985\) −0.551387 7.35775i −0.0175686 0.234437i
\(986\) −0.888124 + 0.427698i −0.0282836 + 0.0136207i
\(987\) 16.9676 + 52.8207i 0.540084 + 1.68130i
\(988\) −7.62345 3.67126i −0.242534 0.116798i
\(989\) 14.9339 38.0509i 0.474870 1.20995i
\(990\) −0.0222798 + 0.297303i −0.000708098 + 0.00944891i
\(991\) −6.98732 17.8034i −0.221960 0.565544i 0.775906 0.630849i \(-0.217293\pi\)
−0.997865 + 0.0653050i \(0.979198\pi\)
\(992\) 6.58009 2.02969i 0.208918 0.0644426i
\(993\) −23.6255 + 29.6255i −0.749733 + 0.940135i
\(994\) −2.15518 0.136347i −0.0683580 0.00432466i
\(995\) −0.327323 0.410450i −0.0103768 0.0130121i
\(996\) 4.64685 + 3.16817i 0.147241 + 0.100387i
\(997\) −19.4944 18.0881i −0.617393 0.572857i 0.308227 0.951313i \(-0.400265\pi\)
−0.925619 + 0.378456i \(0.876455\pi\)
\(998\) −1.03367 + 1.79037i −0.0327203 + 0.0566731i
\(999\) −14.6209 25.3242i −0.462586 0.801223i
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 49.2.g.a.39.3 48
3.2 odd 2 441.2.bb.d.235.2 48
4.3 odd 2 784.2.bg.c.529.1 48
7.2 even 3 343.2.g.i.226.2 48
7.3 odd 6 343.2.e.c.295.5 48
7.4 even 3 343.2.e.d.295.5 48
7.5 odd 6 343.2.g.h.226.2 48
7.6 odd 2 343.2.g.g.165.3 48
49.3 odd 42 343.2.e.c.50.5 48
49.5 odd 42 343.2.g.g.79.3 48
49.8 even 7 343.2.g.i.214.2 48
49.17 odd 42 2401.2.a.i.1.14 24
49.32 even 21 2401.2.a.h.1.14 24
49.41 odd 14 343.2.g.h.214.2 48
49.44 even 21 inner 49.2.g.a.44.3 yes 48
49.46 even 21 343.2.e.d.50.5 48
147.44 odd 42 441.2.bb.d.289.2 48
196.191 odd 42 784.2.bg.c.289.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.2.g.a.39.3 48 1.1 even 1 trivial
49.2.g.a.44.3 yes 48 49.44 even 21 inner
343.2.e.c.50.5 48 49.3 odd 42
343.2.e.c.295.5 48 7.3 odd 6
343.2.e.d.50.5 48 49.46 even 21
343.2.e.d.295.5 48 7.4 even 3
343.2.g.g.79.3 48 49.5 odd 42
343.2.g.g.165.3 48 7.6 odd 2
343.2.g.h.214.2 48 49.41 odd 14
343.2.g.h.226.2 48 7.5 odd 6
343.2.g.i.214.2 48 49.8 even 7
343.2.g.i.226.2 48 7.2 even 3
441.2.bb.d.235.2 48 3.2 odd 2
441.2.bb.d.289.2 48 147.44 odd 42
784.2.bg.c.289.1 48 196.191 odd 42
784.2.bg.c.529.1 48 4.3 odd 2
2401.2.a.h.1.14 24 49.32 even 21
2401.2.a.i.1.14 24 49.17 odd 42