Properties

Label 45.2.l.a.38.3
Level $45$
Weight $2$
Character 45.38
Analytic conductor $0.359$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,2,Mod(2,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45.l (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.359326809096\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} - 102 x^{7} + 144 x^{6} - 432 x^{5} + 502 x^{4} + 288 x^{3} + 72 x^{2} + 12 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 38.3
Root \(-0.186243 - 0.0499037i\) of defining polynomial
Character \(\chi\) \(=\) 45.38
Dual form 45.2.l.a.32.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.186243 - 0.0499037i) q^{2} +(1.53295 - 0.806271i) q^{3} +(-1.69985 + 0.981412i) q^{4} +(-2.04963 - 0.893868i) q^{5} +(0.245265 - 0.226662i) q^{6} +(0.632007 + 2.35868i) q^{7} +(-0.540289 + 0.540289i) q^{8} +(1.69985 - 2.47194i) q^{9} +O(q^{10})\) \(q+(0.186243 - 0.0499037i) q^{2} +(1.53295 - 0.806271i) q^{3} +(-1.69985 + 0.981412i) q^{4} +(-2.04963 - 0.893868i) q^{5} +(0.245265 - 0.226662i) q^{6} +(0.632007 + 2.35868i) q^{7} +(-0.540289 + 0.540289i) q^{8} +(1.69985 - 2.47194i) q^{9} +(-0.426337 - 0.0641924i) q^{10} +(-2.14390 - 1.23778i) q^{11} +(-1.81450 + 2.87500i) q^{12} +(-0.422032 + 1.57505i) q^{13} +(0.235414 + 0.407749i) q^{14} +(-3.86268 + 0.282308i) q^{15} +(1.88916 - 3.27212i) q^{16} +(0.403949 + 0.403949i) q^{17} +(0.193227 - 0.545211i) q^{18} -4.28779i q^{19} +(4.36133 - 0.492089i) q^{20} +(2.87057 + 3.10617i) q^{21} +(-0.461055 - 0.123539i) q^{22} +(6.82387 + 1.82845i) q^{23} +(-0.392615 + 1.26385i) q^{24} +(3.40200 + 3.66420i) q^{25} +0.314402i q^{26} +(0.612733 - 5.15990i) q^{27} +(-3.38916 - 3.38916i) q^{28} +(-3.20524 + 5.55164i) q^{29} +(-0.705309 + 0.245340i) q^{30} +(-1.97194 - 3.41550i) q^{31} +(0.584071 - 2.17978i) q^{32} +(-4.28446 - 0.168889i) q^{33} +(0.0953913 + 0.0550742i) q^{34} +(0.812968 - 5.39937i) q^{35} +(-0.463514 + 5.87020i) q^{36} +(-0.171954 + 0.171954i) q^{37} +(-0.213977 - 0.798571i) q^{38} +(0.622960 + 2.75474i) q^{39} +(1.59034 - 0.624448i) q^{40} +(-6.52359 + 3.76639i) q^{41} +(0.689633 + 0.435250i) q^{42} +(-4.95226 + 1.32695i) q^{43} +4.85908 q^{44} +(-5.69367 + 3.54713i) q^{45} +1.36214 q^{46} +(2.91430 - 0.780885i) q^{47} +(0.257767 - 6.53917i) q^{48} +(0.898221 - 0.518588i) q^{49} +(0.816456 + 0.512660i) q^{50} +(0.944926 + 0.293541i) q^{51} +(-0.828375 - 3.09154i) q^{52} +(-6.12030 + 6.12030i) q^{53} +(-0.143381 - 0.991573i) q^{54} +(3.28779 + 4.45335i) q^{55} +(-1.61584 - 0.932904i) q^{56} +(-3.45712 - 6.57296i) q^{57} +(-0.319907 + 1.19391i) q^{58} +(-2.27234 - 3.93581i) q^{59} +(6.28894 - 4.27076i) q^{60} +(-0.235795 + 0.408408i) q^{61} +(-0.537706 - 0.537706i) q^{62} +(6.90485 + 2.44713i) q^{63} +7.12153i q^{64} +(2.27289 - 2.85103i) q^{65} +(-0.806380 + 0.182356i) q^{66} +(1.65496 + 0.443446i) q^{67} +(-1.08310 - 0.290215i) q^{68} +(11.9349 - 2.69897i) q^{69} +(-0.118039 - 1.04617i) q^{70} -3.50583i q^{71} +(0.417150 + 2.25397i) q^{72} +(6.88847 + 6.88847i) q^{73} +(-0.0234441 + 0.0406064i) q^{74} +(8.16943 + 2.87410i) q^{75} +(4.20809 + 7.28862i) q^{76} +(1.56457 - 5.83906i) q^{77} +(0.253493 + 0.481962i) q^{78} +(-6.50159 - 3.75369i) q^{79} +(-6.79693 + 5.01799i) q^{80} +(-3.22099 - 8.40388i) q^{81} +(-1.02702 + 1.02702i) q^{82} +(-2.85794 - 10.6660i) q^{83} +(-7.92799 - 2.46282i) q^{84} +(-0.466871 - 1.18903i) q^{85} +(-0.856104 + 0.494272i) q^{86} +(-0.437340 + 11.0947i) q^{87} +(1.82708 - 0.489565i) q^{88} +2.90124 q^{89} +(-0.883391 + 0.944763i) q^{90} -3.98176 q^{91} +(-13.3941 + 3.58893i) q^{92} +(-5.77670 - 3.64587i) q^{93} +(0.503800 - 0.290869i) q^{94} +(-3.83272 + 8.78840i) q^{95} +(-0.862145 - 3.81241i) q^{96} +(-0.379633 - 1.41681i) q^{97} +(0.141408 - 0.141408i) q^{98} +(-6.70403 + 3.19554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7} - 8 q^{10} - 6 q^{12} - 2 q^{13} - 6 q^{15} - 8 q^{16} + 36 q^{18} + 18 q^{20} - 12 q^{21} - 10 q^{22} + 18 q^{23} + 4 q^{25} + 18 q^{27} - 16 q^{28} + 30 q^{30} - 4 q^{31} + 30 q^{32} - 12 q^{33} - 48 q^{36} + 4 q^{37} - 30 q^{38} + 6 q^{40} - 24 q^{41} + 6 q^{42} - 2 q^{43} - 36 q^{45} + 32 q^{46} - 12 q^{47} - 30 q^{48} - 54 q^{50} + 36 q^{51} - 14 q^{52} - 16 q^{55} + 36 q^{56} - 6 q^{57} - 6 q^{58} + 18 q^{60} + 8 q^{61} + 36 q^{63} + 66 q^{65} + 36 q^{66} + 4 q^{67} + 42 q^{68} + 18 q^{70} + 18 q^{72} - 8 q^{73} + 42 q^{75} + 24 q^{76} - 6 q^{77} - 42 q^{78} - 48 q^{81} + 32 q^{82} - 66 q^{83} + 22 q^{85} - 48 q^{86} - 18 q^{87} + 18 q^{88} - 66 q^{90} - 40 q^{91} - 60 q^{92} - 18 q^{93} - 36 q^{95} - 24 q^{96} + 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.186243 0.0499037i 0.131694 0.0352872i −0.192370 0.981322i \(-0.561617\pi\)
0.324064 + 0.946035i \(0.394951\pi\)
\(3\) 1.53295 0.806271i 0.885048 0.465501i
\(4\) −1.69985 + 0.981412i −0.849927 + 0.490706i
\(5\) −2.04963 0.893868i −0.916624 0.399750i
\(6\) 0.245265 0.226662i 0.100129 0.0925344i
\(7\) 0.632007 + 2.35868i 0.238876 + 0.891499i 0.976363 + 0.216137i \(0.0693458\pi\)
−0.737487 + 0.675362i \(0.763988\pi\)
\(8\) −0.540289 + 0.540289i −0.191021 + 0.191021i
\(9\) 1.69985 2.47194i 0.566618 0.823980i
\(10\) −0.426337 0.0641924i −0.134820 0.0202994i
\(11\) −2.14390 1.23778i −0.646409 0.373204i 0.140670 0.990057i \(-0.455074\pi\)
−0.787079 + 0.616852i \(0.788408\pi\)
\(12\) −1.81450 + 2.87500i −0.523802 + 0.829940i
\(13\) −0.422032 + 1.57505i −0.117051 + 0.436839i −0.999432 0.0336956i \(-0.989272\pi\)
0.882381 + 0.470535i \(0.155939\pi\)
\(14\) 0.235414 + 0.407749i 0.0629170 + 0.108975i
\(15\) −3.86268 + 0.282308i −0.997340 + 0.0728916i
\(16\) 1.88916 3.27212i 0.472290 0.818031i
\(17\) 0.403949 + 0.403949i 0.0979721 + 0.0979721i 0.754394 0.656422i \(-0.227931\pi\)
−0.656422 + 0.754394i \(0.727931\pi\)
\(18\) 0.193227 0.545211i 0.0455441 0.128507i
\(19\) 4.28779i 0.983687i −0.870684 0.491843i \(-0.836323\pi\)
0.870684 0.491843i \(-0.163677\pi\)
\(20\) 4.36133 0.492089i 0.975224 0.110035i
\(21\) 2.87057 + 3.10617i 0.626410 + 0.677822i
\(22\) −0.461055 0.123539i −0.0982973 0.0263387i
\(23\) 6.82387 + 1.82845i 1.42288 + 0.381258i 0.886503 0.462723i \(-0.153128\pi\)
0.536373 + 0.843981i \(0.319794\pi\)
\(24\) −0.392615 + 1.26385i −0.0801422 + 0.257983i
\(25\) 3.40200 + 3.66420i 0.680400 + 0.732841i
\(26\) 0.314402i 0.0616594i
\(27\) 0.612733 5.15990i 0.117921 0.993023i
\(28\) −3.38916 3.38916i −0.640491 0.640491i
\(29\) −3.20524 + 5.55164i −0.595199 + 1.03091i 0.398320 + 0.917247i \(0.369593\pi\)
−0.993519 + 0.113668i \(0.963740\pi\)
\(30\) −0.705309 + 0.245340i −0.128771 + 0.0447927i
\(31\) −1.97194 3.41550i −0.354171 0.613442i 0.632805 0.774312i \(-0.281904\pi\)
−0.986976 + 0.160869i \(0.948570\pi\)
\(32\) 0.584071 2.17978i 0.103250 0.385335i
\(33\) −4.28446 0.168889i −0.745829 0.0293998i
\(34\) 0.0953913 + 0.0550742i 0.0163595 + 0.00944515i
\(35\) 0.812968 5.39937i 0.137417 0.912660i
\(36\) −0.463514 + 5.87020i −0.0772524 + 0.978366i
\(37\) −0.171954 + 0.171954i −0.0282691 + 0.0282691i −0.721100 0.692831i \(-0.756363\pi\)
0.692831 + 0.721100i \(0.256363\pi\)
\(38\) −0.213977 0.798571i −0.0347116 0.129545i
\(39\) 0.622960 + 2.75474i 0.0997535 + 0.441111i
\(40\) 1.59034 0.624448i 0.251455 0.0987338i
\(41\) −6.52359 + 3.76639i −1.01881 + 0.588212i −0.913760 0.406255i \(-0.866835\pi\)
−0.105053 + 0.994467i \(0.533501\pi\)
\(42\) 0.689633 + 0.435250i 0.106413 + 0.0671606i
\(43\) −4.95226 + 1.32695i −0.755213 + 0.202359i −0.615829 0.787880i \(-0.711179\pi\)
−0.139384 + 0.990238i \(0.544512\pi\)
\(44\) 4.85908 0.732534
\(45\) −5.69367 + 3.54713i −0.848762 + 0.528775i
\(46\) 1.36214 0.200837
\(47\) 2.91430 0.780885i 0.425095 0.113904i −0.0399279 0.999203i \(-0.512713\pi\)
0.465023 + 0.885299i \(0.346046\pi\)
\(48\) 0.257767 6.53917i 0.0372055 0.943847i
\(49\) 0.898221 0.518588i 0.128317 0.0740841i
\(50\) 0.816456 + 0.512660i 0.115464 + 0.0725011i
\(51\) 0.944926 + 0.293541i 0.132316 + 0.0411039i
\(52\) −0.828375 3.09154i −0.114875 0.428719i
\(53\) −6.12030 + 6.12030i −0.840688 + 0.840688i −0.988948 0.148260i \(-0.952633\pi\)
0.148260 + 0.988948i \(0.452633\pi\)
\(54\) −0.143381 0.991573i −0.0195116 0.134936i
\(55\) 3.28779 + 4.45335i 0.443326 + 0.600490i
\(56\) −1.61584 0.932904i −0.215925 0.124665i
\(57\) −3.45712 6.57296i −0.457907 0.870610i
\(58\) −0.319907 + 1.19391i −0.0420058 + 0.156768i
\(59\) −2.27234 3.93581i −0.295833 0.512399i 0.679345 0.733819i \(-0.262264\pi\)
−0.975178 + 0.221421i \(0.928931\pi\)
\(60\) 6.28894 4.27076i 0.811898 0.551353i
\(61\) −0.235795 + 0.408408i −0.0301904 + 0.0522913i −0.880726 0.473626i \(-0.842945\pi\)
0.850535 + 0.525918i \(0.176278\pi\)
\(62\) −0.537706 0.537706i −0.0682888 0.0682888i
\(63\) 6.90485 + 2.44713i 0.869929 + 0.308310i
\(64\) 7.12153i 0.890191i
\(65\) 2.27289 2.85103i 0.281918 0.353626i
\(66\) −0.806380 + 0.182356i −0.0992585 + 0.0224465i
\(67\) 1.65496 + 0.443446i 0.202186 + 0.0541756i 0.358491 0.933533i \(-0.383291\pi\)
−0.156305 + 0.987709i \(0.549958\pi\)
\(68\) −1.08310 0.290215i −0.131345 0.0351937i
\(69\) 11.9349 2.69897i 1.43679 0.324918i
\(70\) −0.118039 1.04617i −0.0141083 0.125041i
\(71\) 3.50583i 0.416065i −0.978122 0.208032i \(-0.933294\pi\)
0.978122 0.208032i \(-0.0667060\pi\)
\(72\) 0.417150 + 2.25397i 0.0491616 + 0.265633i
\(73\) 6.88847 + 6.88847i 0.806234 + 0.806234i 0.984062 0.177827i \(-0.0569069\pi\)
−0.177827 + 0.984062i \(0.556907\pi\)
\(74\) −0.0234441 + 0.0406064i −0.00272533 + 0.00472040i
\(75\) 8.16943 + 2.87410i 0.943324 + 0.331872i
\(76\) 4.20809 + 7.28862i 0.482701 + 0.836062i
\(77\) 1.56457 5.83906i 0.178299 0.665422i
\(78\) 0.253493 + 0.481962i 0.0287025 + 0.0545715i
\(79\) −6.50159 3.75369i −0.731485 0.422323i 0.0874799 0.996166i \(-0.472119\pi\)
−0.818965 + 0.573843i \(0.805452\pi\)
\(80\) −6.79693 + 5.01799i −0.759920 + 0.561029i
\(81\) −3.22099 8.40388i −0.357888 0.933765i
\(82\) −1.02702 + 1.02702i −0.113415 + 0.113415i
\(83\) −2.85794 10.6660i −0.313700 1.17074i −0.925194 0.379495i \(-0.876098\pi\)
0.611493 0.791249i \(-0.290569\pi\)
\(84\) −7.92799 2.46282i −0.865014 0.268716i
\(85\) −0.466871 1.18903i −0.0506393 0.128968i
\(86\) −0.856104 + 0.494272i −0.0923161 + 0.0532987i
\(87\) −0.437340 + 11.0947i −0.0468878 + 1.18947i
\(88\) 1.82708 0.489565i 0.194767 0.0521878i
\(89\) 2.90124 0.307531 0.153765 0.988107i \(-0.450860\pi\)
0.153765 + 0.988107i \(0.450860\pi\)
\(90\) −0.883391 + 0.944763i −0.0931176 + 0.0995868i
\(91\) −3.98176 −0.417402
\(92\) −13.3941 + 3.58893i −1.39643 + 0.374171i
\(93\) −5.77670 3.64587i −0.599016 0.378059i
\(94\) 0.503800 0.290869i 0.0519630 0.0300008i
\(95\) −3.83272 + 8.78840i −0.393229 + 0.901671i
\(96\) −0.862145 3.81241i −0.0879923 0.389103i
\(97\) −0.379633 1.41681i −0.0385459 0.143855i 0.943971 0.330028i \(-0.107058\pi\)
−0.982517 + 0.186173i \(0.940392\pi\)
\(98\) 0.141408 0.141408i 0.0142844 0.0142844i
\(99\) −6.70403 + 3.19554i −0.673780 + 0.321164i
\(100\) −9.37900 2.88985i −0.937900 0.288985i
\(101\) 15.3563 + 8.86596i 1.52801 + 0.882196i 0.999445 + 0.0333015i \(0.0106022\pi\)
0.528563 + 0.848894i \(0.322731\pi\)
\(102\) 0.190635 + 0.00751461i 0.0188756 + 0.000744058i
\(103\) 2.74330 10.2381i 0.270305 1.00879i −0.688617 0.725125i \(-0.741782\pi\)
0.958922 0.283668i \(-0.0915515\pi\)
\(104\) −0.622960 1.07900i −0.0610863 0.105805i
\(105\) −3.10712 8.93242i −0.303224 0.871715i
\(106\) −0.834438 + 1.44529i −0.0810478 + 0.140379i
\(107\) 10.4591 + 10.4591i 1.01112 + 1.01112i 0.999937 + 0.0111806i \(0.00355898\pi\)
0.0111806 + 0.999937i \(0.496441\pi\)
\(108\) 4.02243 + 9.37242i 0.387058 + 0.901862i
\(109\) 0.343204i 0.0328730i −0.999865 0.0164365i \(-0.994768\pi\)
0.999865 0.0164365i \(-0.00523214\pi\)
\(110\) 0.834567 + 0.665333i 0.0795728 + 0.0634370i
\(111\) −0.124955 + 0.402239i −0.0118602 + 0.0381788i
\(112\) 8.91187 + 2.38793i 0.842092 + 0.225638i
\(113\) 5.19250 + 1.39133i 0.488469 + 0.130885i 0.494643 0.869096i \(-0.335299\pi\)
−0.00617426 + 0.999981i \(0.501965\pi\)
\(114\) −0.971879 1.05164i −0.0910248 0.0984955i
\(115\) −12.3520 9.84729i −1.15183 0.918265i
\(116\) 12.5827i 1.16827i
\(117\) 3.17603 + 3.72059i 0.293624 + 0.343969i
\(118\) −0.619619 0.619619i −0.0570405 0.0570405i
\(119\) −0.697490 + 1.20809i −0.0639388 + 0.110745i
\(120\) 1.93444 2.23949i 0.176589 0.204437i
\(121\) −2.43581 4.21894i −0.221437 0.383540i
\(122\) −0.0235340 + 0.0878302i −0.00213067 + 0.00795177i
\(123\) −6.96358 + 11.0335i −0.627885 + 0.994854i
\(124\) 6.70403 + 3.87057i 0.602039 + 0.347588i
\(125\) −3.69754 10.5512i −0.330718 0.943730i
\(126\) 1.40810 + 0.111184i 0.125444 + 0.00990510i
\(127\) −3.59190 + 3.59190i −0.318729 + 0.318729i −0.848279 0.529550i \(-0.822361\pi\)
0.529550 + 0.848279i \(0.322361\pi\)
\(128\) 1.52353 + 5.68590i 0.134662 + 0.502567i
\(129\) −6.52167 + 6.02702i −0.574201 + 0.530649i
\(130\) 0.281034 0.644410i 0.0246483 0.0565185i
\(131\) 14.5188 8.38241i 1.26851 0.732375i 0.293804 0.955866i \(-0.405079\pi\)
0.974706 + 0.223491i \(0.0717453\pi\)
\(132\) 7.44872 3.91774i 0.648327 0.340995i
\(133\) 10.1135 2.70992i 0.876956 0.234980i
\(134\) 0.330355 0.0285383
\(135\) −5.86815 + 10.0282i −0.505050 + 0.863090i
\(136\) −0.436499 −0.0374295
\(137\) −6.17718 + 1.65517i −0.527752 + 0.141411i −0.512850 0.858478i \(-0.671410\pi\)
−0.0149021 + 0.999889i \(0.504744\pi\)
\(138\) 2.08810 1.09826i 0.177751 0.0934899i
\(139\) 9.09433 5.25061i 0.771371 0.445351i −0.0619924 0.998077i \(-0.519745\pi\)
0.833364 + 0.552725i \(0.186412\pi\)
\(140\) 3.91708 + 9.97600i 0.331054 + 0.843126i
\(141\) 3.83787 3.54677i 0.323207 0.298692i
\(142\) −0.174954 0.652936i −0.0146818 0.0547931i
\(143\) 2.85435 2.85435i 0.238693 0.238693i
\(144\) −4.87720 10.2320i −0.406433 0.852669i
\(145\) 11.5320 8.51378i 0.957682 0.707031i
\(146\) 1.62669 + 0.939170i 0.134626 + 0.0777262i
\(147\) 0.958803 1.51918i 0.0790808 0.125300i
\(148\) 0.123539 0.461055i 0.0101549 0.0378985i
\(149\) −4.96581 8.60103i −0.406815 0.704624i 0.587716 0.809067i \(-0.300027\pi\)
−0.994531 + 0.104443i \(0.966694\pi\)
\(150\) 1.66493 + 0.127596i 0.135941 + 0.0104182i
\(151\) −6.95939 + 12.0540i −0.566347 + 0.980942i 0.430576 + 0.902555i \(0.358311\pi\)
−0.996923 + 0.0783879i \(0.975023\pi\)
\(152\) 2.31665 + 2.31665i 0.187905 + 0.187905i
\(153\) 1.68519 0.311884i 0.136240 0.0252143i
\(154\) 1.16556i 0.0939236i
\(155\) 0.988751 + 8.76319i 0.0794184 + 0.703876i
\(156\) −3.76247 4.07127i −0.301239 0.325962i
\(157\) −20.2365 5.42234i −1.61505 0.432750i −0.665504 0.746394i \(-0.731784\pi\)
−0.949541 + 0.313644i \(0.898450\pi\)
\(158\) −1.39820 0.374646i −0.111235 0.0298052i
\(159\) −4.44748 + 14.3167i −0.352708 + 1.13539i
\(160\) −3.14557 + 3.94567i −0.248679 + 0.311933i
\(161\) 17.2510i 1.35957i
\(162\) −1.01927 1.40443i −0.0800815 0.110342i
\(163\) −2.42872 2.42872i −0.190232 0.190232i 0.605564 0.795796i \(-0.292948\pi\)
−0.795796 + 0.605564i \(0.792948\pi\)
\(164\) 7.39277 12.8046i 0.577278 0.999875i
\(165\) 8.63062 + 4.17591i 0.671893 + 0.325094i
\(166\) −1.06454 1.84385i −0.0826247 0.143110i
\(167\) −2.20590 + 8.23252i −0.170697 + 0.637052i 0.826547 + 0.562868i \(0.190302\pi\)
−0.997245 + 0.0741841i \(0.976365\pi\)
\(168\) −3.22917 0.127290i −0.249136 0.00982066i
\(169\) 8.95567 + 5.17056i 0.688898 + 0.397735i
\(170\) −0.146288 0.198149i −0.0112198 0.0151974i
\(171\) −10.5992 7.28862i −0.810539 0.557375i
\(172\) 7.11584 7.11584i 0.542577 0.542577i
\(173\) −4.57458 17.0726i −0.347799 1.29800i −0.889308 0.457308i \(-0.848814\pi\)
0.541509 0.840695i \(-0.317853\pi\)
\(174\) 0.472213 + 2.08813i 0.0357984 + 0.158301i
\(175\) −6.49261 + 10.3400i −0.490795 + 0.781634i
\(176\) −8.10033 + 4.67673i −0.610585 + 0.352521i
\(177\) −6.65670 4.20126i −0.500348 0.315786i
\(178\) 0.540336 0.144783i 0.0404999 0.0108519i
\(179\) −8.30788 −0.620960 −0.310480 0.950580i \(-0.600490\pi\)
−0.310480 + 0.950580i \(0.600490\pi\)
\(180\) 6.19722 11.6174i 0.461913 0.865913i
\(181\) −4.73429 −0.351897 −0.175948 0.984399i \(-0.556299\pi\)
−0.175948 + 0.984399i \(0.556299\pi\)
\(182\) −0.741576 + 0.198705i −0.0549693 + 0.0147290i
\(183\) −0.0321731 + 0.816183i −0.00237830 + 0.0603340i
\(184\) −4.67475 + 2.69897i −0.344627 + 0.198971i
\(185\) 0.506148 0.198739i 0.0372127 0.0146116i
\(186\) −1.25781 0.390739i −0.0922273 0.0286503i
\(187\) −0.366025 1.36603i −0.0267664 0.0998937i
\(188\) −4.18752 + 4.18752i −0.305406 + 0.305406i
\(189\) 12.5578 1.81585i 0.913447 0.132084i
\(190\) −0.275244 + 1.82805i −0.0199683 + 0.132620i
\(191\) −3.34902 1.93356i −0.242327 0.139907i 0.373919 0.927461i \(-0.378014\pi\)
−0.616246 + 0.787554i \(0.711347\pi\)
\(192\) 5.74188 + 10.9169i 0.414384 + 0.787861i
\(193\) −4.44530 + 16.5901i −0.319979 + 1.19418i 0.599284 + 0.800536i \(0.295452\pi\)
−0.919263 + 0.393643i \(0.871215\pi\)
\(194\) −0.141408 0.244926i −0.0101525 0.0175847i
\(195\) 1.18553 6.20304i 0.0848974 0.444209i
\(196\) −1.01790 + 1.76305i −0.0727070 + 0.125932i
\(197\) −11.0386 11.0386i −0.786469 0.786469i 0.194445 0.980913i \(-0.437709\pi\)
−0.980913 + 0.194445i \(0.937709\pi\)
\(198\) −1.08911 + 0.929703i −0.0773996 + 0.0660711i
\(199\) 3.60138i 0.255295i 0.991820 + 0.127648i \(0.0407427\pi\)
−0.991820 + 0.127648i \(0.959257\pi\)
\(200\) −3.81779 0.141666i −0.269959 0.0100173i
\(201\) 2.89451 0.654569i 0.204163 0.0461698i
\(202\) 3.30245 + 0.884888i 0.232359 + 0.0622605i
\(203\) −15.1203 4.05148i −1.06124 0.284358i
\(204\) −1.89432 + 0.428385i −0.132629 + 0.0299929i
\(205\) 16.7376 1.88851i 1.16901 0.131899i
\(206\) 2.04368i 0.142390i
\(207\) 16.1194 13.7601i 1.12038 0.956394i
\(208\) 4.35646 + 4.35646i 0.302066 + 0.302066i
\(209\) −5.30734 + 9.19258i −0.367116 + 0.635864i
\(210\) −1.02444 1.50854i −0.0706931 0.104099i
\(211\) 9.56007 + 16.5585i 0.658142 + 1.13994i 0.981096 + 0.193521i \(0.0619909\pi\)
−0.322954 + 0.946415i \(0.604676\pi\)
\(212\) 4.39709 16.4102i 0.301993 1.12705i
\(213\) −2.82664 5.37425i −0.193678 0.368237i
\(214\) 2.46988 + 1.42599i 0.168837 + 0.0974783i
\(215\) 11.3364 + 1.70690i 0.773139 + 0.116409i
\(216\) 2.45678 + 3.11889i 0.167163 + 0.212213i
\(217\) 6.80981 6.80981i 0.462280 0.462280i
\(218\) −0.0171272 0.0639194i −0.00116000 0.00432917i
\(219\) 16.1136 + 5.00569i 1.08886 + 0.338253i
\(220\) −9.95934 4.34338i −0.671459 0.292830i
\(221\) −0.806719 + 0.465759i −0.0542658 + 0.0313304i
\(222\) −0.00319884 + 0.0811499i −0.000214692 + 0.00544642i
\(223\) 4.03530 1.08126i 0.270224 0.0724062i −0.121163 0.992633i \(-0.538662\pi\)
0.391386 + 0.920226i \(0.371996\pi\)
\(224\) 5.51055 0.368189
\(225\) 14.8406 2.18093i 0.989374 0.145395i
\(226\) 1.03650 0.0689469
\(227\) 13.2857 3.55990i 0.881803 0.236279i 0.210618 0.977568i \(-0.432452\pi\)
0.671185 + 0.741290i \(0.265786\pi\)
\(228\) 12.3274 + 7.78022i 0.816401 + 0.515257i
\(229\) −13.2694 + 7.66109i −0.876866 + 0.506259i −0.869624 0.493715i \(-0.835639\pi\)
−0.00724242 + 0.999974i \(0.502305\pi\)
\(230\) −2.79190 1.21758i −0.184092 0.0802847i
\(231\) −2.30946 10.2124i −0.151951 0.671929i
\(232\) −1.26773 4.73125i −0.0832308 0.310622i
\(233\) −2.98562 + 2.98562i −0.195595 + 0.195595i −0.798108 0.602514i \(-0.794166\pi\)
0.602514 + 0.798108i \(0.294166\pi\)
\(234\) 0.777184 + 0.534438i 0.0508061 + 0.0349373i
\(235\) −6.67126 1.00447i −0.435185 0.0655246i
\(236\) 7.72529 + 4.46020i 0.502874 + 0.290334i
\(237\) −12.9931 0.512173i −0.843991 0.0332692i
\(238\) −0.0696146 + 0.259805i −0.00451245 + 0.0168407i
\(239\) 2.59439 + 4.49362i 0.167817 + 0.290668i 0.937652 0.347575i \(-0.112995\pi\)
−0.769835 + 0.638243i \(0.779661\pi\)
\(240\) −6.37348 + 13.1725i −0.411406 + 0.850280i
\(241\) 1.85872 3.21939i 0.119730 0.207379i −0.799930 0.600093i \(-0.795130\pi\)
0.919661 + 0.392714i \(0.128464\pi\)
\(242\) −0.664193 0.664193i −0.0426959 0.0426959i
\(243\) −11.7134 10.2857i −0.751416 0.659829i
\(244\) 0.925646i 0.0592584i
\(245\) −2.30457 + 0.260025i −0.147234 + 0.0166124i
\(246\) −0.746308 + 2.40241i −0.0475829 + 0.153172i
\(247\) 6.75347 + 1.80959i 0.429713 + 0.115141i
\(248\) 2.91078 + 0.779940i 0.184834 + 0.0495262i
\(249\) −12.9808 14.0461i −0.822622 0.890137i
\(250\) −1.21519 1.78057i −0.0768551 0.112613i
\(251\) 3.97271i 0.250755i −0.992109 0.125378i \(-0.959986\pi\)
0.992109 0.125378i \(-0.0400142\pi\)
\(252\) −14.1389 + 2.61673i −0.890666 + 0.164838i
\(253\) −12.3665 12.3665i −0.777472 0.777472i
\(254\) −0.489717 + 0.848215i −0.0307276 + 0.0532217i
\(255\) −1.67437 1.44629i −0.104853 0.0905702i
\(256\) −6.55403 11.3519i −0.409627 0.709495i
\(257\) −4.42437 + 16.5120i −0.275985 + 1.02999i 0.679194 + 0.733959i \(0.262329\pi\)
−0.955179 + 0.296030i \(0.904337\pi\)
\(258\) −0.913846 + 1.44794i −0.0568935 + 0.0901451i
\(259\) −0.514262 0.296909i −0.0319547 0.0184491i
\(260\) −1.06556 + 7.07698i −0.0660832 + 0.438896i
\(261\) 8.27489 + 17.3602i 0.512203 + 1.07457i
\(262\) 2.28571 2.28571i 0.141211 0.141211i
\(263\) 2.77155 + 10.3436i 0.170901 + 0.637812i 0.997214 + 0.0746001i \(0.0237680\pi\)
−0.826312 + 0.563212i \(0.809565\pi\)
\(264\) 2.40610 2.22360i 0.148085 0.136853i
\(265\) 18.0151 7.07364i 1.10666 0.434530i
\(266\) 1.74834 1.00941i 0.107198 0.0618907i
\(267\) 4.44745 2.33919i 0.272179 0.143156i
\(268\) −3.24840 + 0.870407i −0.198428 + 0.0531685i
\(269\) 15.8925 0.968985 0.484492 0.874796i \(-0.339004\pi\)
0.484492 + 0.874796i \(0.339004\pi\)
\(270\) −0.592457 + 2.16052i −0.0360558 + 0.131485i
\(271\) 0.974200 0.0591785 0.0295892 0.999562i \(-0.490580\pi\)
0.0295892 + 0.999562i \(0.490580\pi\)
\(272\) 2.08490 0.558646i 0.126415 0.0338729i
\(273\) −6.10383 + 3.21038i −0.369421 + 0.194301i
\(274\) −1.06786 + 0.616528i −0.0645117 + 0.0372458i
\(275\) −2.75806 12.0666i −0.166317 0.727643i
\(276\) −17.6387 + 16.3009i −1.06173 + 0.981197i
\(277\) 6.18395 + 23.0788i 0.371557 + 1.38667i 0.858310 + 0.513131i \(0.171515\pi\)
−0.486753 + 0.873540i \(0.661819\pi\)
\(278\) 1.43173 1.43173i 0.0858695 0.0858695i
\(279\) −11.7949 0.931335i −0.706144 0.0557576i
\(280\) 2.47798 + 3.35646i 0.148088 + 0.200587i
\(281\) −23.9241 13.8126i −1.42720 0.823991i −0.430296 0.902688i \(-0.641591\pi\)
−0.996899 + 0.0786961i \(0.974924\pi\)
\(282\) 0.537779 0.852086i 0.0320243 0.0507410i
\(283\) 4.40870 16.4535i 0.262070 0.978058i −0.701950 0.712227i \(-0.747687\pi\)
0.964020 0.265831i \(-0.0856465\pi\)
\(284\) 3.44066 + 5.95939i 0.204165 + 0.353625i
\(285\) 1.21048 + 16.5624i 0.0717025 + 0.981070i
\(286\) 0.389161 0.674046i 0.0230115 0.0398572i
\(287\) −13.0067 13.0067i −0.767761 0.767761i
\(288\) −4.39546 5.14910i −0.259005 0.303414i
\(289\) 16.6736i 0.980803i
\(290\) 1.72289 2.16112i 0.101171 0.126905i
\(291\) −1.72429 1.86581i −0.101080 0.109376i
\(292\) −18.4698 4.94897i −1.08086 0.289617i
\(293\) 25.7566 + 6.90146i 1.50472 + 0.403188i 0.914677 0.404186i \(-0.132445\pi\)
0.590041 + 0.807374i \(0.299112\pi\)
\(294\) 0.102758 0.330784i 0.00599296 0.0192917i
\(295\) 1.13937 + 10.0981i 0.0663369 + 0.587936i
\(296\) 0.185810i 0.0108000i
\(297\) −7.70045 + 10.3039i −0.446825 + 0.597890i
\(298\) −1.35407 1.35407i −0.0784392 0.0784392i
\(299\) −5.75979 + 9.97625i −0.333097 + 0.576941i
\(300\) −16.7075 + 3.13202i −0.964609 + 0.180827i
\(301\) −6.25973 10.8422i −0.360805 0.624933i
\(302\) −0.694599 + 2.59228i −0.0399697 + 0.149169i
\(303\) 30.6887 + 1.20972i 1.76302 + 0.0694965i
\(304\) −14.0302 8.10033i −0.804686 0.464586i
\(305\) 0.848356 0.626318i 0.0485767 0.0358629i
\(306\) 0.298292 0.142184i 0.0170522 0.00812810i
\(307\) −12.3556 + 12.3556i −0.705171 + 0.705171i −0.965516 0.260345i \(-0.916164\pi\)
0.260345 + 0.965516i \(0.416164\pi\)
\(308\) 3.07098 + 11.4610i 0.174985 + 0.653053i
\(309\) −4.04938 17.9064i −0.230361 1.01866i
\(310\) 0.621463 + 1.58274i 0.0352967 + 0.0898936i
\(311\) 7.49228 4.32567i 0.424848 0.245286i −0.272301 0.962212i \(-0.587785\pi\)
0.697149 + 0.716926i \(0.254451\pi\)
\(312\) −1.82493 1.15177i −0.103316 0.0652064i
\(313\) −18.1094 + 4.85240i −1.02360 + 0.274274i −0.731303 0.682052i \(-0.761088\pi\)
−0.292301 + 0.956326i \(0.594421\pi\)
\(314\) −4.03949 −0.227962
\(315\) −11.9650 11.1878i −0.674151 0.630358i
\(316\) 14.7357 0.828946
\(317\) 18.7418 5.02186i 1.05265 0.282056i 0.309301 0.950964i \(-0.399905\pi\)
0.743345 + 0.668908i \(0.233238\pi\)
\(318\) −0.113855 + 2.88834i −0.00638468 + 0.161970i
\(319\) 13.7434 7.93476i 0.769484 0.444262i
\(320\) 6.36570 14.5965i 0.355854 0.815970i
\(321\) 24.4661 + 7.60037i 1.36556 + 0.424211i
\(322\) 0.860886 + 3.21287i 0.0479753 + 0.179046i
\(323\) 1.73205 1.73205i 0.0963739 0.0963739i
\(324\) 13.7229 + 11.1243i 0.762382 + 0.618015i
\(325\) −7.20704 + 3.81190i −0.399775 + 0.211446i
\(326\) −0.573535 0.331131i −0.0317652 0.0183396i
\(327\) −0.276716 0.526114i −0.0153024 0.0290942i
\(328\) 1.48968 5.55956i 0.0822538 0.306975i
\(329\) 3.68372 + 6.38039i 0.203090 + 0.351763i
\(330\) 1.81579 + 0.347034i 0.0999557 + 0.0191036i
\(331\) 17.1969 29.7859i 0.945226 1.63718i 0.189929 0.981798i \(-0.439174\pi\)
0.755298 0.655382i \(-0.227492\pi\)
\(332\) 15.3258 + 15.3258i 0.841114 + 0.841114i
\(333\) 0.132764 + 0.717358i 0.00727540 + 0.0393110i
\(334\) 1.64333i 0.0899191i
\(335\) −2.99569 2.38822i −0.163672 0.130482i
\(336\) 15.5867 3.52481i 0.850326 0.192294i
\(337\) 30.9291 + 8.28744i 1.68482 + 0.451445i 0.969044 0.246888i \(-0.0794079\pi\)
0.715773 + 0.698333i \(0.246075\pi\)
\(338\) 1.92596 + 0.516060i 0.104758 + 0.0280700i
\(339\) 9.08161 2.05373i 0.493245 0.111543i
\(340\) 1.96054 + 1.56298i 0.106325 + 0.0847644i
\(341\) 9.76331i 0.528713i
\(342\) −2.33775 0.828518i −0.126411 0.0448011i
\(343\) 13.8776 + 13.8776i 0.749320 + 0.749320i
\(344\) 1.95871 3.39259i 0.105607 0.182916i
\(345\) −26.8746 5.13629i −1.44688 0.276528i
\(346\) −1.70397 2.95136i −0.0916059 0.158666i
\(347\) −4.15647 + 15.5122i −0.223131 + 0.832737i 0.760014 + 0.649907i \(0.225192\pi\)
−0.983145 + 0.182829i \(0.941474\pi\)
\(348\) −10.1450 19.2885i −0.543830 1.03397i
\(349\) −15.1664 8.75630i −0.811837 0.468714i 0.0357566 0.999361i \(-0.488616\pi\)
−0.847593 + 0.530646i \(0.821949\pi\)
\(350\) −0.693197 + 2.24977i −0.0370529 + 0.120255i
\(351\) 7.86849 + 3.14273i 0.419989 + 0.167746i
\(352\) −3.95028 + 3.95028i −0.210550 + 0.210550i
\(353\) 4.95294 + 18.4846i 0.263618 + 0.983837i 0.963091 + 0.269177i \(0.0867517\pi\)
−0.699472 + 0.714660i \(0.746582\pi\)
\(354\) −1.44942 0.450262i −0.0770360 0.0239312i
\(355\) −3.13374 + 7.18566i −0.166322 + 0.381375i
\(356\) −4.93169 + 2.84731i −0.261379 + 0.150907i
\(357\) −0.0951692 + 2.41430i −0.00503689 + 0.127778i
\(358\) −1.54728 + 0.414594i −0.0817766 + 0.0219120i
\(359\) −23.0127 −1.21457 −0.607283 0.794486i \(-0.707741\pi\)
−0.607283 + 0.794486i \(0.707741\pi\)
\(360\) 1.15975 4.99270i 0.0611242 0.263138i
\(361\) 0.614846 0.0323603
\(362\) −0.881728 + 0.236258i −0.0463426 + 0.0124175i
\(363\) −7.13557 4.50350i −0.374521 0.236372i
\(364\) 6.76842 3.90775i 0.354762 0.204822i
\(365\) −7.96146 20.2762i −0.416722 1.06131i
\(366\) 0.0347385 + 0.153614i 0.00181581 + 0.00802953i
\(367\) −7.01692 26.1875i −0.366280 1.36698i −0.865677 0.500603i \(-0.833112\pi\)
0.499397 0.866373i \(-0.333555\pi\)
\(368\) 18.8743 18.8743i 0.983891 0.983891i
\(369\) −1.77884 + 22.5282i −0.0926029 + 1.17277i
\(370\) 0.0843487 0.0622724i 0.00438508 0.00323739i
\(371\) −18.3039 10.5678i −0.950293 0.548652i
\(372\) 13.3977 + 0.528121i 0.694636 + 0.0273818i
\(373\) −7.76440 + 28.9771i −0.402025 + 1.50038i 0.407451 + 0.913227i \(0.366418\pi\)
−0.809477 + 0.587152i \(0.800249\pi\)
\(374\) −0.136339 0.236147i −0.00704994 0.0122109i
\(375\) −14.1753 13.1932i −0.732008 0.681296i
\(376\) −1.15266 + 1.99647i −0.0594440 + 0.102960i
\(377\) −7.39138 7.39138i −0.380675 0.380675i
\(378\) 2.24819 0.964871i 0.115634 0.0496276i
\(379\) 20.0943i 1.03218i 0.856535 + 0.516089i \(0.172612\pi\)
−0.856535 + 0.516089i \(0.827388\pi\)
\(380\) −2.10998 18.7005i −0.108240 0.959315i
\(381\) −2.61015 + 8.40224i −0.133722 + 0.430460i
\(382\) −0.720223 0.192983i −0.0368498 0.00987388i
\(383\) −26.6536 7.14181i −1.36194 0.364929i −0.497409 0.867516i \(-0.665715\pi\)
−0.864527 + 0.502587i \(0.832382\pi\)
\(384\) 6.91987 + 7.48780i 0.353128 + 0.382110i
\(385\) −8.42614 + 10.5694i −0.429436 + 0.538667i
\(386\) 3.31162i 0.168557i
\(387\) −5.13797 + 14.4973i −0.261178 + 0.736941i
\(388\) 2.03579 + 2.03579i 0.103352 + 0.103352i
\(389\) 6.71184 11.6253i 0.340304 0.589424i −0.644185 0.764870i \(-0.722803\pi\)
0.984489 + 0.175446i \(0.0561367\pi\)
\(390\) −0.0887583 1.21444i −0.00449445 0.0614953i
\(391\) 2.01790 + 3.49510i 0.102049 + 0.176755i
\(392\) −0.205111 + 0.765487i −0.0103597 + 0.0386629i
\(393\) 15.4980 24.5558i 0.781771 1.23868i
\(394\) −2.60673 1.50500i −0.131325 0.0758207i
\(395\) 9.97057 + 13.5053i 0.501674 + 0.679523i
\(396\) 8.25973 12.0114i 0.415067 0.603594i
\(397\) −12.8716 + 12.8716i −0.646008 + 0.646008i −0.952026 0.306018i \(-0.901003\pi\)
0.306018 + 0.952026i \(0.401003\pi\)
\(398\) 0.179722 + 0.670732i 0.00900866 + 0.0336208i
\(399\) 13.3186 12.3084i 0.666764 0.616191i
\(400\) 18.4166 4.20949i 0.920832 0.210475i
\(401\) −21.7606 + 12.5635i −1.08667 + 0.627391i −0.932689 0.360682i \(-0.882544\pi\)
−0.153985 + 0.988073i \(0.549211\pi\)
\(402\) 0.506417 0.266356i 0.0252578 0.0132846i
\(403\) 6.21180 1.66445i 0.309432 0.0829120i
\(404\) −34.8046 −1.73159
\(405\) −0.910113 + 20.1040i −0.0452239 + 0.998977i
\(406\) −3.01824 −0.149793
\(407\) 0.581494 0.155811i 0.0288236 0.00772325i
\(408\) −0.669129 + 0.351936i −0.0331268 + 0.0174234i
\(409\) −9.81878 + 5.66888i −0.485508 + 0.280308i −0.722709 0.691153i \(-0.757103\pi\)
0.237201 + 0.971461i \(0.423770\pi\)
\(410\) 3.02302 1.18699i 0.149296 0.0586213i
\(411\) −8.13478 + 7.51777i −0.401259 + 0.370824i
\(412\) 5.38461 + 20.0957i 0.265281 + 0.990042i
\(413\) 7.84719 7.84719i 0.386135 0.386135i
\(414\) 2.31545 3.36714i 0.113798 0.165486i
\(415\) −3.67625 + 24.4160i −0.180460 + 1.19853i
\(416\) 3.18676 + 1.83988i 0.156244 + 0.0902074i
\(417\) 9.70771 15.3814i 0.475389 0.753231i
\(418\) −0.529711 + 1.97691i −0.0259090 + 0.0966938i
\(419\) 4.26264 + 7.38311i 0.208244 + 0.360688i 0.951161 0.308694i \(-0.0998920\pi\)
−0.742918 + 0.669383i \(0.766559\pi\)
\(420\) 14.0480 + 12.1345i 0.685474 + 0.592101i
\(421\) 1.10329 1.91095i 0.0537710 0.0931341i −0.837887 0.545844i \(-0.816209\pi\)
0.891658 + 0.452710i \(0.149543\pi\)
\(422\) 2.60683 + 2.60683i 0.126898 + 0.126898i
\(423\) 3.02359 8.53138i 0.147012 0.414810i
\(424\) 6.61346i 0.321178i
\(425\) −0.105917 + 2.85439i −0.00513772 + 0.138458i
\(426\) −0.794637 0.859856i −0.0385003 0.0416601i
\(427\) −1.11233 0.298048i −0.0538294 0.0144235i
\(428\) −28.0436 7.51426i −1.35554 0.363215i
\(429\) 2.07419 6.67695i 0.100143 0.322366i
\(430\) 2.19651 0.247833i 0.105925 0.0119516i
\(431\) 1.95738i 0.0942838i 0.998888 + 0.0471419i \(0.0150113\pi\)
−0.998888 + 0.0471419i \(0.984989\pi\)
\(432\) −15.7263 11.7528i −0.756630 0.565458i
\(433\) −9.71652 9.71652i −0.466946 0.466946i 0.433978 0.900924i \(-0.357110\pi\)
−0.900924 + 0.433978i \(0.857110\pi\)
\(434\) 0.928445 1.60811i 0.0445668 0.0771919i
\(435\) 10.8136 22.3491i 0.518470 1.07156i
\(436\) 0.336825 + 0.583398i 0.0161310 + 0.0279397i
\(437\) 7.84002 29.2593i 0.375039 1.39966i
\(438\) 3.25085 + 0.128145i 0.155332 + 0.00612302i
\(439\) −4.68008 2.70205i −0.223368 0.128962i 0.384141 0.923275i \(-0.374498\pi\)
−0.607509 + 0.794313i \(0.707831\pi\)
\(440\) −4.18245 0.629740i −0.199391 0.0300217i
\(441\) 0.244926 3.10188i 0.0116631 0.147708i
\(442\) −0.127003 + 0.127003i −0.00604090 + 0.00604090i
\(443\) 6.98940 + 26.0848i 0.332077 + 1.23933i 0.907004 + 0.421122i \(0.138364\pi\)
−0.574927 + 0.818204i \(0.694970\pi\)
\(444\) −0.182356 0.806380i −0.00865424 0.0382691i
\(445\) −5.94648 2.59333i −0.281890 0.122935i
\(446\) 0.697588 0.402752i 0.0330317 0.0190709i
\(447\) −14.5471 9.18114i −0.688053 0.434253i
\(448\) −16.7974 + 4.50086i −0.793604 + 0.212646i
\(449\) 23.8541 1.12574 0.562872 0.826544i \(-0.309696\pi\)
0.562872 + 0.826544i \(0.309696\pi\)
\(450\) 2.65512 1.14678i 0.125164 0.0540599i
\(451\) 18.6479 0.878093
\(452\) −10.1920 + 2.73093i −0.479389 + 0.128452i
\(453\) −0.949576 + 24.0893i −0.0446150 + 1.13182i
\(454\) 2.29672 1.32601i 0.107790 0.0622328i
\(455\) 8.16116 + 3.55917i 0.382601 + 0.166856i
\(456\) 5.41914 + 1.68345i 0.253774 + 0.0788349i
\(457\) −5.13035 19.1467i −0.239988 0.895647i −0.975837 0.218501i \(-0.929883\pi\)
0.735849 0.677146i \(-0.236783\pi\)
\(458\) −2.08902 + 2.08902i −0.0976133 + 0.0976133i
\(459\) 2.33185 1.83682i 0.108842 0.0857356i
\(460\) 30.6609 + 4.61653i 1.42957 + 0.215247i
\(461\) −1.14371 0.660321i −0.0532679 0.0307542i 0.473130 0.880993i \(-0.343124\pi\)
−0.526397 + 0.850239i \(0.676458\pi\)
\(462\) −0.939758 1.78674i −0.0437215 0.0831269i
\(463\) 3.98780 14.8827i 0.185329 0.691656i −0.809231 0.587490i \(-0.800116\pi\)
0.994560 0.104166i \(-0.0332172\pi\)
\(464\) 12.1104 + 20.9759i 0.562213 + 0.973782i
\(465\) 8.58120 + 12.6363i 0.397944 + 0.585994i
\(466\) −0.407058 + 0.705045i −0.0188566 + 0.0326606i
\(467\) −1.77645 1.77645i −0.0822044 0.0822044i 0.664809 0.747013i \(-0.268513\pi\)
−0.747013 + 0.664809i \(0.768513\pi\)
\(468\) −9.05022 3.20747i −0.418346 0.148265i
\(469\) 4.18380i 0.193190i
\(470\) −1.29260 + 0.145844i −0.0596233 + 0.00672730i
\(471\) −35.3933 + 8.00390i −1.63084 + 0.368800i
\(472\) 3.35419 + 0.898753i 0.154389 + 0.0413685i
\(473\) 12.2596 + 3.28495i 0.563697 + 0.151042i
\(474\) −2.44543 + 0.553014i −0.112322 + 0.0254008i
\(475\) 15.7113 14.5871i 0.720886 0.669301i
\(476\) 2.73810i 0.125501i
\(477\) 4.72541 + 25.5327i 0.216361 + 1.16906i
\(478\) 0.707436 + 0.707436i 0.0323574 + 0.0323574i
\(479\) 18.9907 32.8928i 0.867705 1.50291i 0.00336919 0.999994i \(-0.498928\pi\)
0.864336 0.502915i \(-0.167739\pi\)
\(480\) −1.64071 + 8.58469i −0.0748878 + 0.391836i
\(481\) −0.198266 0.343406i −0.00904014 0.0156580i
\(482\) 0.185513 0.692346i 0.00844991 0.0315355i
\(483\) 13.9089 + 26.4448i 0.632879 + 1.20328i
\(484\) 8.28104 + 4.78106i 0.376411 + 0.217321i
\(485\) −0.488332 + 3.24328i −0.0221740 + 0.147270i
\(486\) −2.69484 1.33110i −0.122240 0.0603800i
\(487\) 23.6900 23.6900i 1.07350 1.07350i 0.0764213 0.997076i \(-0.475651\pi\)
0.997076 0.0764213i \(-0.0243494\pi\)
\(488\) −0.0932612 0.348056i −0.00422174 0.0157557i
\(489\) −5.68131 1.76490i −0.256918 0.0798114i
\(490\) −0.416235 + 0.163435i −0.0188036 + 0.00738322i
\(491\) 18.9114 10.9185i 0.853460 0.492746i −0.00835660 0.999965i \(-0.502660\pi\)
0.861817 + 0.507220i \(0.169327\pi\)
\(492\) 1.00871 25.5894i 0.0454761 1.15366i
\(493\) −3.53734 + 0.947827i −0.159314 + 0.0426880i
\(494\) 1.34809 0.0606535
\(495\) 16.5972 0.557174i 0.745988 0.0250431i
\(496\) −14.9013 −0.669086
\(497\) 8.26913 2.21571i 0.370921 0.0993881i
\(498\) −3.11853 1.96821i −0.139745 0.0881974i
\(499\) −2.74862 + 1.58691i −0.123045 + 0.0710401i −0.560259 0.828317i \(-0.689298\pi\)
0.437214 + 0.899357i \(0.355965\pi\)
\(500\) 16.6404 + 14.3067i 0.744180 + 0.639816i
\(501\) 3.25612 + 14.3986i 0.145473 + 0.643281i
\(502\) −0.198253 0.739889i −0.00884845 0.0330229i
\(503\) −7.00484 + 7.00484i −0.312330 + 0.312330i −0.845812 0.533481i \(-0.820883\pi\)
0.533481 + 0.845812i \(0.320883\pi\)
\(504\) −5.05277 + 2.40845i −0.225068 + 0.107281i
\(505\) −23.5498 31.8985i −1.04795 1.41946i
\(506\) −2.92030 1.68603i −0.129823 0.0749534i
\(507\) 17.8974 + 0.705498i 0.794853 + 0.0313323i
\(508\) 2.58058 9.63084i 0.114495 0.427299i
\(509\) 8.36206 + 14.4835i 0.370642 + 0.641971i 0.989664 0.143403i \(-0.0458044\pi\)
−0.619023 + 0.785373i \(0.712471\pi\)
\(510\) −0.384014 0.185804i −0.0170044 0.00822755i
\(511\) −11.8942 + 20.6013i −0.526167 + 0.911347i
\(512\) −10.1119 10.1119i −0.446886 0.446886i
\(513\) −22.1246 2.62727i −0.976824 0.115997i
\(514\) 3.29603i 0.145382i
\(515\) −14.7743 + 18.5323i −0.651034 + 0.816630i
\(516\) 5.17091 16.6455i 0.227637 0.732777i
\(517\) −7.21452 1.93313i −0.317294 0.0850188i
\(518\) −0.110595 0.0296337i −0.00485925 0.00130203i
\(519\) −20.7777 22.4830i −0.912040 0.986894i
\(520\) 0.312358 + 2.76840i 0.0136978 + 0.121402i
\(521\) 1.34092i 0.0587466i −0.999569 0.0293733i \(-0.990649\pi\)
0.999569 0.0293733i \(-0.00935116\pi\)
\(522\) 2.40748 + 2.82026i 0.105372 + 0.123440i
\(523\) −9.19187 9.19187i −0.401933 0.401933i 0.476981 0.878914i \(-0.341731\pi\)
−0.878914 + 0.476981i \(0.841731\pi\)
\(524\) −16.4532 + 28.4978i −0.718761 + 1.24493i
\(525\) −1.61595 + 21.0856i −0.0705258 + 0.920249i
\(526\) 1.03237 + 1.78811i 0.0450133 + 0.0779653i
\(527\) 0.583126 2.17625i 0.0254014 0.0947991i
\(528\) −8.64667 + 13.7002i −0.376298 + 0.596226i
\(529\) 23.3034 + 13.4542i 1.01319 + 0.584967i
\(530\) 3.00219 2.21644i 0.130407 0.0962759i
\(531\) −13.5917 1.07321i −0.589831 0.0465734i
\(532\) −14.5320 + 14.5320i −0.630043 + 0.630043i
\(533\) −3.17908 11.8645i −0.137701 0.513908i
\(534\) 0.711572 0.657601i 0.0307927 0.0284572i
\(535\) −12.0883 30.7863i −0.522621 1.33101i
\(536\) −1.13375 + 0.654569i −0.0489704 + 0.0282731i
\(537\) −12.7355 + 6.69840i −0.549579 + 0.289057i
\(538\) 2.95987 0.793096i 0.127609 0.0341928i
\(539\) −2.56759 −0.110594
\(540\) 0.133203 22.8056i 0.00573215 0.981395i
\(541\) −34.0389 −1.46345 −0.731724 0.681601i \(-0.761284\pi\)
−0.731724 + 0.681601i \(0.761284\pi\)
\(542\) 0.181438 0.0486162i 0.00779343 0.00208824i
\(543\) −7.25741 + 3.81712i −0.311445 + 0.163808i
\(544\) 1.11646 0.644587i 0.0478677 0.0276364i
\(545\) −0.306779 + 0.703444i −0.0131410 + 0.0301322i
\(546\) −0.976587 + 0.902515i −0.0417941 + 0.0386241i
\(547\) 2.44487 + 9.12437i 0.104535 + 0.390130i 0.998292 0.0584215i \(-0.0186067\pi\)
−0.893757 + 0.448552i \(0.851940\pi\)
\(548\) 8.87591 8.87591i 0.379160 0.379160i
\(549\) 0.608745 + 1.27711i 0.0259806 + 0.0545055i
\(550\) −1.11584 2.10968i −0.0475794 0.0899571i
\(551\) 23.8043 + 13.7434i 1.01410 + 0.585489i
\(552\) −4.99005 + 7.90650i −0.212391 + 0.336523i
\(553\) 4.74472 17.7075i 0.201766 0.753001i
\(554\) 2.30343 + 3.98967i 0.0978636 + 0.169505i
\(555\) 0.615661 0.712749i 0.0261333 0.0302545i
\(556\) −10.3060 + 17.8506i −0.437073 + 0.757033i
\(557\) 1.48579 + 1.48579i 0.0629551 + 0.0629551i 0.737883 0.674928i \(-0.235825\pi\)
−0.674928 + 0.737883i \(0.735825\pi\)
\(558\) −2.24320 + 0.415156i −0.0949623 + 0.0175750i
\(559\) 8.36006i 0.353593i
\(560\) −16.1316 12.8604i −0.681683 0.543451i
\(561\) −1.66248 1.79893i −0.0701901 0.0759509i
\(562\) −5.14501 1.37860i −0.217029 0.0581527i
\(563\) −20.6371 5.52969i −0.869750 0.233049i −0.203770 0.979019i \(-0.565319\pi\)
−0.665979 + 0.745970i \(0.731986\pi\)
\(564\) −3.04297 + 9.79553i −0.128132 + 0.412466i
\(565\) −9.39906 7.49312i −0.395421 0.315238i
\(566\) 3.28436i 0.138052i
\(567\) 17.7864 12.9086i 0.746959 0.542111i
\(568\) 1.89416 + 1.89416i 0.0794771 + 0.0794771i
\(569\) 5.82589 10.0907i 0.244234 0.423026i −0.717682 0.696371i \(-0.754797\pi\)
0.961916 + 0.273345i \(0.0881301\pi\)
\(570\) 1.05197 + 3.02422i 0.0440620 + 0.126671i
\(571\) 10.5623 + 18.2945i 0.442020 + 0.765601i 0.997839 0.0657023i \(-0.0209288\pi\)
−0.555819 + 0.831303i \(0.687595\pi\)
\(572\) −2.05069 + 7.65328i −0.0857436 + 0.320000i
\(573\) −6.69284 0.263825i −0.279598 0.0110214i
\(574\) −3.07149 1.77332i −0.128201 0.0740171i
\(575\) 16.5150 + 31.2244i 0.688723 + 1.30215i
\(576\) 17.6040 + 12.1056i 0.733500 + 0.504398i
\(577\) 30.1119 30.1119i 1.25357 1.25357i 0.299469 0.954106i \(-0.403191\pi\)
0.954106 0.299469i \(-0.0968094\pi\)
\(578\) −0.832076 3.10535i −0.0346098 0.129166i
\(579\) 6.56168 + 29.0158i 0.272694 + 1.20586i
\(580\) −11.2472 + 25.7898i −0.467016 + 1.07086i
\(581\) 23.3515 13.4820i 0.968782 0.559327i
\(582\) −0.414248 0.261445i −0.0171711 0.0108373i
\(583\) 20.6969 5.54571i 0.857177 0.229680i
\(584\) −7.44353 −0.308015
\(585\) −3.18398 10.4648i −0.131641 0.432666i
\(586\) 5.14140 0.212389
\(587\) −8.53262 + 2.28631i −0.352179 + 0.0943661i −0.430571 0.902556i \(-0.641688\pi\)
0.0783924 + 0.996923i \(0.475021\pi\)
\(588\) −0.138887 + 3.52336i −0.00572761 + 0.145301i
\(589\) −14.6450 + 8.45527i −0.603435 + 0.348393i
\(590\) 0.716134 + 1.82385i 0.0294828 + 0.0750867i
\(591\) −25.8217 8.02150i −1.06216 0.329960i
\(592\) 0.237806 + 0.887505i 0.00977377 + 0.0364762i
\(593\) 24.5829 24.5829i 1.00950 1.00950i 0.00954475 0.999954i \(-0.496962\pi\)
0.999954 0.00954475i \(-0.00303823\pi\)
\(594\) −0.919955 + 2.30330i −0.0377462 + 0.0945056i
\(595\) 2.50947 1.85267i 0.102878 0.0759523i
\(596\) 16.8823 + 9.74700i 0.691526 + 0.399253i
\(597\) 2.90369 + 5.52073i 0.118840 + 0.225948i
\(598\) −0.574869 + 2.14544i −0.0235082 + 0.0877336i
\(599\) −18.8291 32.6129i −0.769335 1.33253i −0.937924 0.346840i \(-0.887255\pi\)
0.168590 0.985686i \(-0.446079\pi\)
\(600\) −5.96669 + 2.86101i −0.243589 + 0.116800i
\(601\) 11.1158 19.2532i 0.453424 0.785354i −0.545172 0.838324i \(-0.683536\pi\)
0.998596 + 0.0529703i \(0.0168689\pi\)
\(602\) −1.70690 1.70690i −0.0695679 0.0695679i
\(603\) 3.90937 3.33718i 0.159202 0.135900i
\(604\) 27.3201i 1.11164i
\(605\) 1.22134 + 10.8246i 0.0496544 + 0.440082i
\(606\) 5.77593 1.30618i 0.234631 0.0530599i
\(607\) −20.8988 5.59982i −0.848257 0.227290i −0.191594 0.981474i \(-0.561366\pi\)
−0.656663 + 0.754184i \(0.728032\pi\)
\(608\) −9.34645 2.50437i −0.379049 0.101566i
\(609\) −26.4452 + 5.98037i −1.07161 + 0.242337i
\(610\) 0.126745 0.158983i 0.00513175 0.00643705i
\(611\) 4.91972i 0.199031i
\(612\) −2.55850 + 2.18403i −0.103421 + 0.0882841i
\(613\) 15.7726 + 15.7726i 0.637051 + 0.637051i 0.949827 0.312776i \(-0.101259\pi\)
−0.312776 + 0.949827i \(0.601259\pi\)
\(614\) −1.68455 + 2.91773i −0.0679830 + 0.117750i
\(615\) 24.1352 16.3900i 0.973227 0.660910i
\(616\) 2.30946 + 4.00010i 0.0930507 + 0.161169i
\(617\) −10.9568 + 40.8914i −0.441104 + 1.64622i 0.284917 + 0.958552i \(0.408034\pi\)
−0.726021 + 0.687672i \(0.758633\pi\)
\(618\) −1.64776 3.13286i −0.0662827 0.126022i
\(619\) 27.5855 + 15.9265i 1.10876 + 0.640141i 0.938507 0.345260i \(-0.112209\pi\)
0.170250 + 0.985401i \(0.445543\pi\)
\(620\) −10.2810 13.9258i −0.412896 0.559272i
\(621\) 13.6158 34.0901i 0.546385 1.36799i
\(622\) 1.17952 1.17952i 0.0472944 0.0472944i
\(623\) 1.83361 + 6.84311i 0.0734619 + 0.274163i
\(624\) 10.1907 + 3.16573i 0.407955 + 0.126731i
\(625\) −1.85278 + 24.9312i −0.0741113 + 0.997250i
\(626\) −3.13060 + 1.80745i −0.125124 + 0.0722403i
\(627\) −0.724161 + 18.3709i −0.0289202 + 0.733663i
\(628\) 39.7206 10.6431i 1.58502 0.424706i
\(629\) −0.138922 −0.00553917
\(630\) −2.78671 1.48654i −0.111025 0.0592253i
\(631\) 15.7931 0.628713 0.314356 0.949305i \(-0.398211\pi\)
0.314356 + 0.949305i \(0.398211\pi\)
\(632\) 5.54081 1.48466i 0.220402 0.0590564i
\(633\) 28.0057 + 17.6753i 1.11313 + 0.702532i
\(634\) 3.23993 1.87057i 0.128674 0.0742899i
\(635\) 10.5728 4.15140i 0.419567 0.164743i
\(636\) −6.49053 28.7012i −0.257366 1.13808i
\(637\) 0.437722 + 1.63360i 0.0173432 + 0.0647256i
\(638\) 2.16364 2.16364i 0.0856594 0.0856594i
\(639\) −8.66619 5.95939i −0.342829 0.235750i
\(640\) 1.95976 13.0158i 0.0774663 0.514497i
\(641\) −8.57453 4.95051i −0.338673 0.195533i 0.321012 0.947075i \(-0.395977\pi\)
−0.659685 + 0.751542i \(0.729310\pi\)
\(642\) 4.93592 + 0.194569i 0.194805 + 0.00767902i
\(643\) −12.2247 + 45.6232i −0.482095 + 1.79920i 0.110706 + 0.993853i \(0.464689\pi\)
−0.592801 + 0.805349i \(0.701978\pi\)
\(644\) −16.9303 29.3241i −0.667147 1.15553i
\(645\) 18.7544 6.52367i 0.738454 0.256869i
\(646\) 0.236147 0.409018i 0.00929107 0.0160926i
\(647\) −9.75824 9.75824i −0.383636 0.383636i 0.488774 0.872410i \(-0.337444\pi\)
−0.872410 + 0.488774i \(0.837444\pi\)
\(648\) 6.28079 + 2.80026i 0.246733 + 0.110005i
\(649\) 11.2506i 0.441625i
\(650\) −1.15203 + 1.06960i −0.0451865 + 0.0419530i
\(651\) 4.94853 15.9296i 0.193948 0.624331i
\(652\) 6.51206 + 1.74490i 0.255032 + 0.0683356i
\(653\) −2.99335 0.802065i −0.117139 0.0313872i 0.199773 0.979842i \(-0.435979\pi\)
−0.316912 + 0.948455i \(0.602646\pi\)
\(654\) −0.0777914 0.0841760i −0.00304189 0.00329154i
\(655\) −37.2509 + 4.20302i −1.45551 + 0.164226i
\(656\) 28.4613i 1.11123i
\(657\) 28.7373 5.31850i 1.12115 0.207494i
\(658\) 1.00447 + 1.00447i 0.0391584 + 0.0391584i
\(659\) 13.5644 23.4942i 0.528393 0.915204i −0.471059 0.882102i \(-0.656128\pi\)
0.999452 0.0331023i \(-0.0105387\pi\)
\(660\) −18.7691 + 1.37176i −0.730585 + 0.0533956i
\(661\) −9.54526 16.5329i −0.371268 0.643055i 0.618493 0.785790i \(-0.287743\pi\)
−0.989761 + 0.142736i \(0.954410\pi\)
\(662\) 1.71638 6.40560i 0.0667088 0.248961i
\(663\) −0.861129 + 1.36442i −0.0334435 + 0.0529896i
\(664\) 7.30683 + 4.21860i 0.283560 + 0.163713i
\(665\) −23.1514 3.48584i −0.897772 0.135175i
\(666\) 0.0605251 + 0.126978i 0.00234530 + 0.00492028i
\(667\) −32.0231 + 32.0231i −1.23994 + 1.23994i
\(668\) −4.32979 16.1590i −0.167524 0.625210i
\(669\) 5.31412 4.91105i 0.205456 0.189872i
\(670\) −0.677107 0.295294i −0.0261589 0.0114082i
\(671\) 1.01104 0.583723i 0.0390307 0.0225344i
\(672\) 8.44739 4.44300i 0.325865 0.171392i
\(673\) −0.134287 + 0.0359820i −0.00517638 + 0.00138701i −0.261406 0.965229i \(-0.584186\pi\)
0.256230 + 0.966616i \(0.417520\pi\)
\(674\) 6.17391 0.237810
\(675\) 20.9914 15.3088i 0.807961 0.589236i
\(676\) −20.2978 −0.780684
\(677\) −7.80401 + 2.09108i −0.299933 + 0.0803667i −0.405647 0.914030i \(-0.632954\pi\)
0.105714 + 0.994397i \(0.466287\pi\)
\(678\) 1.58890 0.835699i 0.0610213 0.0320948i
\(679\) 3.10188 1.79087i 0.119039 0.0687272i
\(680\) 0.894663 + 0.390172i 0.0343087 + 0.0149624i
\(681\) 17.4961 16.1690i 0.670450 0.619598i
\(682\) 0.487225 + 1.81835i 0.0186568 + 0.0696281i
\(683\) −35.0271 + 35.0271i −1.34027 + 1.34027i −0.444490 + 0.895784i \(0.646615\pi\)
−0.895784 + 0.444490i \(0.853385\pi\)
\(684\) 25.1702 + 1.98745i 0.962406 + 0.0759921i
\(685\) 14.1405 + 2.12909i 0.540279 + 0.0813483i
\(686\) 3.27715 + 1.89206i 0.125122 + 0.0722393i
\(687\) −14.1644 + 22.4428i −0.540404 + 0.856245i
\(688\) −5.01366 + 18.7112i −0.191144 + 0.713359i
\(689\) −7.05680 12.2227i −0.268843 0.465649i
\(690\) −5.26153 + 0.384544i −0.200303 + 0.0146394i
\(691\) −20.5195 + 35.5408i −0.780597 + 1.35203i 0.150997 + 0.988534i \(0.451752\pi\)
−0.931594 + 0.363500i \(0.881582\pi\)
\(692\) 24.5313 + 24.5313i 0.932541 + 0.932541i
\(693\) −11.7743 13.7931i −0.447267 0.523956i
\(694\) 3.09646i 0.117540i
\(695\) −23.3334 + 2.63271i −0.885087 + 0.0998644i
\(696\) −5.75804 6.23062i −0.218258 0.236171i
\(697\) −4.15663 1.11377i −0.157444 0.0421869i
\(698\) −3.26160 0.873943i −0.123453 0.0330792i
\(699\) −2.16958 + 6.98402i −0.0820611 + 0.264160i
\(700\) 0.888649 23.9485i 0.0335878 0.905168i
\(701\) 37.2173i 1.40568i −0.711348 0.702840i \(-0.751915\pi\)
0.711348 0.702840i \(-0.248085\pi\)
\(702\) 1.62228 + 0.192645i 0.0612292 + 0.00727091i
\(703\) 0.737304 + 0.737304i 0.0278080 + 0.0278080i
\(704\) 8.81487 15.2678i 0.332223 0.575427i
\(705\) −11.0366 + 3.83904i −0.415661 + 0.144587i
\(706\) 1.84490 + 3.19546i 0.0694337 + 0.120263i
\(707\) −11.2067 + 41.8240i −0.421471 + 1.57295i
\(708\) 15.4386 + 0.608573i 0.580218 + 0.0228716i
\(709\) −13.3449 7.70466i −0.501177 0.289355i 0.228023 0.973656i \(-0.426774\pi\)
−0.729199 + 0.684301i \(0.760107\pi\)
\(710\) −0.225047 + 1.49466i −0.00844587 + 0.0560938i
\(711\) −20.3307 + 9.69081i −0.762459 + 0.363434i
\(712\) −1.56751 + 1.56751i −0.0587448 + 0.0587448i
\(713\) −7.21120 26.9125i −0.270061 1.00788i
\(714\) 0.102758 + 0.454396i 0.00384562 + 0.0170053i
\(715\) −8.40179 + 3.29896i −0.314209 + 0.123374i
\(716\) 14.1222 8.15345i 0.527771 0.304709i
\(717\) 7.60014 + 4.79670i 0.283833 + 0.179136i
\(718\) −4.28596 + 1.14842i −0.159951 + 0.0428587i
\(719\) −11.9324 −0.445002 −0.222501 0.974932i \(-0.571422\pi\)
−0.222501 + 0.974932i \(0.571422\pi\)
\(720\) 0.850388 + 25.3315i 0.0316921 + 0.944048i
\(721\) 25.8823 0.963908
\(722\) 0.114511 0.0306831i 0.00426165 0.00114191i
\(723\) 0.253613 6.43378i 0.00943196 0.239275i
\(724\) 8.04760 4.64628i 0.299087 0.172678i
\(725\) −31.2466 + 7.14203i −1.16047 + 0.265248i
\(726\) −1.55369 0.482653i −0.0576629 0.0179129i
\(727\) 1.12575 + 4.20134i 0.0417516 + 0.155819i 0.983654 0.180066i \(-0.0576312\pi\)
−0.941903 + 0.335885i \(0.890965\pi\)
\(728\) 2.15130 2.15130i 0.0797326 0.0797326i
\(729\) −26.2491 6.32329i −0.972189 0.234196i
\(730\) −2.49462 3.37900i −0.0923302 0.125062i
\(731\) −2.53649 1.46444i −0.0938153 0.0541643i
\(732\) −0.746322 1.41897i −0.0275848 0.0524465i
\(733\) 12.7796 47.6943i 0.472027 1.76163i −0.160446 0.987045i \(-0.551293\pi\)
0.632473 0.774583i \(-0.282040\pi\)
\(734\) −2.61370 4.52707i −0.0964736 0.167097i
\(735\) −3.32314 + 2.25672i −0.122576 + 0.0832402i
\(736\) 7.97125 13.8066i 0.293824 0.508918i
\(737\) −2.99918 2.99918i −0.110476 0.110476i
\(738\) 0.792945 + 4.28450i 0.0291887 + 0.157715i
\(739\) 16.1890i 0.595523i 0.954640 + 0.297761i \(0.0962400\pi\)
−0.954640 + 0.297761i \(0.903760\pi\)
\(740\) −0.665333 + 0.834567i −0.0244581 + 0.0306793i
\(741\) 11.8117 2.67112i 0.433915 0.0981262i
\(742\) −3.93635 1.05474i −0.144508 0.0387208i
\(743\) 19.2021 + 5.14520i 0.704458 + 0.188759i 0.593227 0.805035i \(-0.297854\pi\)
0.111232 + 0.993795i \(0.464520\pi\)
\(744\) 5.09091 1.15127i 0.186642 0.0422075i
\(745\) 2.48990 + 22.0677i 0.0912230 + 0.808499i
\(746\) 5.78426i 0.211777i
\(747\) −31.2238 11.0660i −1.14242 0.404883i
\(748\) 1.96282 + 1.96282i 0.0717679 + 0.0717679i
\(749\) −18.0595 + 31.2799i −0.659878 + 1.14294i
\(750\) −3.29844 1.74975i −0.120442 0.0638918i
\(751\) 7.95061 + 13.7709i 0.290122 + 0.502506i 0.973838 0.227242i \(-0.0729708\pi\)
−0.683716 + 0.729748i \(0.739637\pi\)
\(752\) 2.95043 11.0112i 0.107591 0.401536i
\(753\) −3.20308 6.08995i −0.116727 0.221930i
\(754\) −1.74545 1.00774i −0.0635655 0.0366996i
\(755\) 25.0389 18.4856i 0.911259 0.672758i
\(756\) −19.5644 + 15.4111i −0.711550 + 0.560495i
\(757\) 21.3482 21.3482i 0.775914 0.775914i −0.203219 0.979133i \(-0.565140\pi\)
0.979133 + 0.203219i \(0.0651404\pi\)
\(758\) 1.00278 + 3.74243i 0.0364227 + 0.135931i
\(759\) −28.9278 8.98641i −1.05001 0.326186i
\(760\) −2.67750 6.81905i −0.0971232 0.247353i
\(761\) 4.74778 2.74113i 0.172107 0.0993659i −0.411472 0.911422i \(-0.634985\pi\)
0.583579 + 0.812056i \(0.301652\pi\)
\(762\) −0.0668196 + 1.69511i −0.00242062 + 0.0614075i
\(763\) 0.809511 0.216908i 0.0293063 0.00785259i
\(764\) 7.59046 0.274613
\(765\) −3.73282 0.867093i −0.134960 0.0313498i
\(766\) −5.32045 −0.192236
\(767\) 7.15808 1.91800i 0.258463 0.0692550i
\(768\) −19.1997 12.1176i −0.692810 0.437255i
\(769\) −7.13004 + 4.11653i −0.257116 + 0.148446i −0.623018 0.782207i \(-0.714094\pi\)
0.365902 + 0.930653i \(0.380760\pi\)
\(770\) −1.04186 + 2.38897i −0.0375460 + 0.0860927i
\(771\) 6.53080 + 28.8792i 0.235201 + 1.04006i
\(772\) −8.72533 32.5634i −0.314031 1.17198i
\(773\) −14.0889 + 14.0889i −0.506743 + 0.506743i −0.913525 0.406782i \(-0.866651\pi\)
0.406782 + 0.913525i \(0.366651\pi\)
\(774\) −0.233441 + 2.95643i −0.00839088 + 0.106267i
\(775\) 5.80655 18.8451i 0.208578 0.676937i
\(776\) 0.970598 + 0.560375i 0.0348424 + 0.0201163i
\(777\) −1.02773 0.0405119i −0.0368695 0.00145336i
\(778\) 0.669891 2.50007i 0.0240168 0.0896318i
\(779\) 16.1495 + 27.9718i 0.578616 + 1.00219i
\(780\) 4.07251 + 11.7078i 0.145819 + 0.419205i
\(781\) −4.33944 + 7.51612i −0.155277 + 0.268948i
\(782\) 0.550238 + 0.550238i 0.0196765 + 0.0196765i
\(783\) 26.6820 + 19.9404i 0.953536 + 0.712612i
\(784\) 3.91879i 0.139957i
\(785\) 36.6305 + 29.2025i 1.30740 + 1.04228i
\(786\) 1.66097 5.34676i 0.0592448 0.190713i
\(787\) 19.4505 + 5.21175i 0.693336 + 0.185779i 0.588244 0.808684i \(-0.299820\pi\)
0.105092 + 0.994462i \(0.466486\pi\)
\(788\) 29.5975 + 7.93062i 1.05437 + 0.282516i
\(789\) 12.5884 + 13.6215i 0.448158 + 0.484940i
\(790\) 2.53091 + 2.01769i 0.0900457 + 0.0717862i
\(791\) 13.1268i 0.466735i
\(792\) 1.89560 5.34863i 0.0673571 0.190055i
\(793\) −0.543749 0.543749i −0.0193091 0.0193091i
\(794\) −1.75491 + 3.03959i −0.0622793 + 0.107871i
\(795\) 21.9130 25.3686i 0.777173 0.899731i
\(796\) −3.53444 6.12183i −0.125275 0.216982i
\(797\) 11.4576 42.7605i 0.405850 1.51465i −0.396632 0.917978i \(-0.629821\pi\)
0.802483 0.596676i \(-0.203512\pi\)
\(798\) 1.86626 2.95700i 0.0660650 0.104677i
\(799\) 1.49267 + 0.861793i 0.0528068 + 0.0304880i
\(800\) 9.97418 5.27547i 0.352640 0.186516i
\(801\) 4.93169 7.17170i 0.174253 0.253399i
\(802\) −3.42580 + 3.42580i −0.120969 + 0.120969i
\(803\) −6.24176 23.2946i −0.220267 0.822047i
\(804\) −4.27784 + 3.95338i −0.150868 + 0.139425i
\(805\) 15.4201 35.3581i 0.543486 1.24621i
\(806\) 1.07384 0.619983i 0.0378245 0.0218380i
\(807\) 24.3624 12.8137i 0.857597 0.451063i
\(808\) −13.0870 + 3.50665i −0.460399 + 0.123364i
\(809\) 35.4591 1.24667 0.623337 0.781953i \(-0.285777\pi\)
0.623337 + 0.781953i \(0.285777\pi\)
\(810\) 0.833762 + 3.78965i 0.0292954 + 0.133155i
\(811\) −9.68119 −0.339952 −0.169976 0.985448i \(-0.554369\pi\)
−0.169976 + 0.985448i \(0.554369\pi\)
\(812\) 29.6785 7.95233i 1.04151 0.279072i
\(813\) 1.49340 0.785469i 0.0523757 0.0275476i
\(814\) 0.100524 0.0580373i 0.00352335 0.00203421i
\(815\) 2.80704 + 7.14895i 0.0983262 + 0.250417i
\(816\) 2.74562 2.53737i 0.0961158 0.0888256i
\(817\) 5.68970 + 21.2343i 0.199058 + 0.742893i
\(818\) −1.54578 + 1.54578i −0.0540470 + 0.0540470i
\(819\) −6.76842 + 9.84269i −0.236508 + 0.343931i
\(820\) −26.5981 + 19.6367i −0.928847 + 0.685743i
\(821\) 14.6602 + 8.46408i 0.511645 + 0.295398i 0.733510 0.679679i \(-0.237881\pi\)
−0.221865 + 0.975077i \(0.571214\pi\)
\(822\) −1.13988 + 1.80609i −0.0397579 + 0.0629945i
\(823\) 9.19340 34.3102i 0.320462 1.19598i −0.598334 0.801247i \(-0.704170\pi\)
0.918796 0.394733i \(-0.129163\pi\)
\(824\) 4.04938 + 7.01372i 0.141067 + 0.244335i
\(825\) −13.9569 16.2737i −0.485917 0.566578i
\(826\) 1.06988 1.85309i 0.0372259 0.0644772i
\(827\) −31.4545 31.4545i −1.09378 1.09378i −0.995121 0.0986577i \(-0.968545\pi\)
−0.0986577 0.995121i \(-0.531455\pi\)
\(828\) −13.8963 + 39.2100i −0.482931 + 1.36264i
\(829\) 17.3376i 0.602161i 0.953599 + 0.301081i \(0.0973474\pi\)
−0.953599 + 0.301081i \(0.902653\pi\)
\(830\) 0.533773 + 4.73077i 0.0185275 + 0.164207i
\(831\) 28.0874 + 30.3927i 0.974342 + 1.05431i
\(832\) −11.2167 3.00551i −0.388870 0.104197i
\(833\) 0.572320 + 0.153353i 0.0198297 + 0.00531335i
\(834\) 1.04041 3.34913i 0.0360263 0.115971i
\(835\) 11.8801 14.9019i 0.411127 0.515701i
\(836\) 20.8347i 0.720584i
\(837\) −18.8319 + 8.08223i −0.650926 + 0.279363i
\(838\) 1.16233 + 1.16233i 0.0401521 + 0.0401521i
\(839\) −12.8988 + 22.3413i −0.445315 + 0.771308i −0.998074 0.0620331i \(-0.980242\pi\)
0.552759 + 0.833341i \(0.313575\pi\)
\(840\) 6.50483 + 3.14735i 0.224438 + 0.108594i
\(841\) −6.04717 10.4740i −0.208523 0.361173i
\(842\) 0.110116 0.410960i 0.00379486 0.0141626i
\(843\) −47.8112 1.88467i −1.64670 0.0649113i
\(844\) −32.5015 18.7647i −1.11875 0.645909i
\(845\) −13.7341 18.6029i −0.472466 0.639961i
\(846\) 0.137375 1.73980i 0.00472306 0.0598155i
\(847\) 8.41170 8.41170i 0.289030 0.289030i
\(848\) 8.46415 + 31.5886i 0.290660 + 1.08476i
\(849\) −6.50766 28.7769i −0.223342 0.987622i
\(850\) 0.122718 + 0.536896i 0.00420920 + 0.0184154i
\(851\) −1.48780 + 0.858984i −0.0510013 + 0.0294456i
\(852\) 10.0792 + 6.36133i 0.345309 + 0.217936i
\(853\) −13.7160 + 3.67518i −0.469626 + 0.125836i −0.485868 0.874032i \(-0.661496\pi\)
0.0162423 + 0.999868i \(0.494830\pi\)
\(854\) −0.222037 −0.00759796
\(855\) 15.2094 + 24.4133i 0.520149 + 0.834916i
\(856\) −11.3019 −0.386289
\(857\) −48.2115 + 12.9182i −1.64687 + 0.441278i −0.958735 0.284303i \(-0.908238\pi\)
−0.688137 + 0.725581i \(0.741571\pi\)
\(858\) 0.0530991 1.34705i 0.00181277 0.0459874i
\(859\) 35.6374 20.5752i 1.21593 0.702018i 0.251886 0.967757i \(-0.418949\pi\)
0.964045 + 0.265739i \(0.0856158\pi\)
\(860\) −20.9455 + 8.22425i −0.714235 + 0.280444i
\(861\) −30.4255 9.45165i −1.03690 0.322112i
\(862\) 0.0976806 + 0.364549i 0.00332701 + 0.0124166i
\(863\) 20.5637 20.5637i 0.699996 0.699996i −0.264413 0.964410i \(-0.585178\pi\)
0.964410 + 0.264413i \(0.0851783\pi\)
\(864\) −10.8896 4.34937i −0.370471 0.147969i
\(865\) −5.88440 + 39.0816i −0.200076 + 1.32881i
\(866\) −2.29452 1.32474i −0.0779711 0.0450166i
\(867\) −13.4435 25.5598i −0.456564 0.868057i
\(868\) −4.89246 + 18.2589i −0.166061 + 0.619748i
\(869\) 9.29248 + 16.0950i 0.315226 + 0.545987i
\(870\) 0.898648 4.70200i 0.0304670 0.159413i
\(871\) −1.39690 + 2.41950i −0.0473320 + 0.0819815i
\(872\) 0.185430 + 0.185430i 0.00627944 + 0.00627944i
\(873\) −4.14759 1.46994i −0.140375 0.0497499i
\(874\) 5.84059i 0.197561i
\(875\) 22.5501 15.3898i 0.762333 0.520270i
\(876\) −32.3035 + 7.30516i −1.09143 + 0.246819i
\(877\) 48.3556 + 12.9568i 1.63285 + 0.437521i 0.954741 0.297438i \(-0.0961321\pi\)
0.678111 + 0.734959i \(0.262799\pi\)
\(878\) −1.00647 0.269684i −0.0339669 0.00910140i
\(879\) 45.0480 10.1872i 1.51943 0.343607i
\(880\) 20.7831 2.34496i 0.700597 0.0790484i
\(881\) 25.4215i 0.856471i 0.903667 + 0.428235i \(0.140865\pi\)
−0.903667 + 0.428235i \(0.859135\pi\)
\(882\) −0.109179 0.589925i −0.00367626 0.0198638i
\(883\) −27.7207 27.7207i −0.932874 0.932874i 0.0650103 0.997885i \(-0.479292\pi\)
−0.997885 + 0.0650103i \(0.979292\pi\)
\(884\) 0.914203 1.58345i 0.0307480 0.0532571i
\(885\) 9.88843 + 14.5613i 0.332396 + 0.489472i
\(886\) 2.60346 + 4.50932i 0.0874648 + 0.151493i
\(887\) 5.34114 19.9334i 0.179338 0.669298i −0.816434 0.577439i \(-0.804052\pi\)
0.995772 0.0918595i \(-0.0292811\pi\)
\(888\) −0.149813 0.284837i −0.00502740 0.00955850i
\(889\) −10.7423 6.20205i −0.360284 0.208010i
\(890\) −1.23691 0.186238i −0.0414612 0.00624270i
\(891\) −3.49668 + 22.0039i −0.117143 + 0.737159i
\(892\) −5.79827 + 5.79827i −0.194140 + 0.194140i
\(893\) −3.34827 12.4959i −0.112046 0.418160i
\(894\) −3.16746 0.983971i −0.105936 0.0329089i
\(895\) 17.0281 + 7.42615i 0.569187 + 0.248229i
\(896\) −12.4484 + 7.18706i −0.415870 + 0.240103i
\(897\) −0.785896 + 19.9370i −0.0262403 + 0.665677i
\(898\) 4.44266 1.19041i 0.148253 0.0397244i
\(899\) 25.2822 0.843209
\(900\) −23.0865 + 18.2720i −0.769549 + 0.609067i
\(901\) −4.94459 −0.164728
\(902\) 3.47303 0.930596i 0.115639 0.0309855i
\(903\) −18.3376 11.5734i −0.610236 0.385140i
\(904\) −3.55717 + 2.05373i −0.118310 + 0.0683061i
\(905\) 9.70355 + 4.23182i 0.322557 + 0.140671i
\(906\) 1.02529 + 4.53386i 0.0340631 + 0.150627i
\(907\) −10.1886 38.0242i −0.338305 1.26257i −0.900241 0.435392i \(-0.856610\pi\)
0.561935 0.827181i \(-0.310057\pi\)
\(908\) −19.0901 + 19.0901i −0.633526 + 0.633526i
\(909\) 48.0196 22.8890i 1.59271 0.759180i
\(910\) 1.69757 + 0.255599i 0.0562741 + 0.00847302i
\(911\) −42.5747 24.5805i −1.41056 0.814389i −0.415122 0.909766i \(-0.636261\pi\)
−0.995441 + 0.0953768i \(0.969594\pi\)
\(912\) −28.0386 1.10525i −0.928450 0.0365985i
\(913\) −7.07501 + 26.4043i −0.234149 + 0.873854i
\(914\) −1.91099 3.30992i −0.0632098 0.109483i
\(915\) 0.795502 1.64412i 0.0262985 0.0543528i
\(916\) 15.0374 26.0455i 0.496848 0.860567i
\(917\) 28.9474 + 28.9474i 0.955928 + 0.955928i
\(918\) 0.342627 0.458464i 0.0113084 0.0151316i
\(919\) 7.00522i 0.231081i −0.993303 0.115540i \(-0.963140\pi\)
0.993303 0.115540i \(-0.0368600\pi\)
\(920\) 11.9941 1.35329i 0.395432 0.0446166i
\(921\) −8.97851 + 28.9024i −0.295852 + 0.952367i
\(922\) −0.245960 0.0659049i −0.00810028 0.00217046i
\(923\) 5.52184 + 1.47957i 0.181753 + 0.0487007i
\(924\) 13.9483 + 15.0931i 0.458867 + 0.496527i
\(925\) −1.21506 0.0450870i −0.0399511 0.00148245i
\(926\) 2.97080i 0.0976265i
\(927\) −20.6449 24.1846i −0.678066 0.794327i
\(928\) 10.2293 + 10.2293i 0.335793 + 0.335793i
\(929\) −1.96179 + 3.39791i −0.0643641 + 0.111482i −0.896412 0.443222i \(-0.853835\pi\)
0.832048 + 0.554704i \(0.187169\pi\)
\(930\) 2.22879 + 1.92519i 0.0730848 + 0.0631294i
\(931\) −2.22360 3.85139i −0.0728755 0.126224i
\(932\) 2.14500 8.00525i 0.0702618 0.262221i
\(933\) 7.99761 12.6718i 0.261830 0.414857i
\(934\) −0.419503 0.242200i −0.0137266 0.00792504i
\(935\) −0.470828 + 3.12703i −0.0153977 + 0.102265i
\(936\) −3.72616 0.294220i −0.121794 0.00961688i
\(937\) −28.6351 + 28.6351i −0.935468 + 0.935468i −0.998040 0.0625728i \(-0.980069\pi\)
0.0625728 + 0.998040i \(0.480069\pi\)
\(938\) 0.208787 + 0.779203i 0.00681713 + 0.0254419i
\(939\) −23.8484 + 22.0396i −0.778264 + 0.719234i
\(940\) 12.3260 4.83980i 0.402029 0.157857i
\(941\) −50.0184 + 28.8781i −1.63055 + 0.941400i −0.646630 + 0.762804i \(0.723822\pi\)
−0.983922 + 0.178596i \(0.942844\pi\)
\(942\) −6.19233 + 3.25693i −0.201757 + 0.106116i
\(943\) −51.4028 + 13.7733i −1.67390 + 0.448521i
\(944\) −17.1713 −0.558877
\(945\) −27.3621 7.50321i −0.890088 0.244079i
\(946\) 2.44720 0.0795653
\(947\) 8.02351 2.14989i 0.260729 0.0698622i −0.126086 0.992019i \(-0.540242\pi\)
0.386816 + 0.922157i \(0.373575\pi\)
\(948\) 22.5890 11.8809i 0.733657 0.385875i
\(949\) −13.7568 + 7.94250i −0.446565 + 0.257824i
\(950\) 2.19818 3.50079i 0.0713184 0.113581i
\(951\) 24.6813 22.8092i 0.800345 0.739640i
\(952\) −0.275870 1.02956i −0.00894101 0.0333683i
\(953\) −27.2237 + 27.2237i −0.881861 + 0.881861i −0.993724 0.111862i \(-0.964318\pi\)
0.111862 + 0.993724i \(0.464318\pi\)
\(954\) 2.15425 + 4.51947i 0.0697463 + 0.146323i
\(955\) 5.13592 + 6.95667i 0.166195 + 0.225112i
\(956\) −8.82018 5.09233i −0.285265 0.164698i
\(957\) 14.6704 23.2445i 0.474225 0.751388i
\(958\) 1.89541 7.07375i 0.0612378 0.228543i
\(959\) −7.80805 13.5239i −0.252135 0.436711i
\(960\) −2.01046 27.5082i −0.0648874 0.887823i
\(961\) 7.72289 13.3764i 0.249126 0.431498i
\(962\) −0.0540628 0.0540628i −0.00174306 0.00174306i
\(963\) 43.6332 8.07532i 1.40606 0.260224i
\(964\) 7.29666i 0.235010i
\(965\) 23.9406 30.0301i 0.770674 0.966702i
\(966\) 3.91014 + 4.23105i 0.125807 + 0.136132i
\(967\) −45.5627 12.2085i −1.46520 0.392598i −0.563916 0.825832i \(-0.690706\pi\)
−0.901282 + 0.433234i \(0.857372\pi\)
\(968\) 3.59549 + 0.963408i 0.115563 + 0.0309651i
\(969\) 1.25864 4.05164i 0.0404334 0.130158i
\(970\) 0.0709034 + 0.628409i 0.00227657 + 0.0201770i
\(971\) 20.4752i 0.657080i −0.944490 0.328540i \(-0.893443\pi\)
0.944490 0.328540i \(-0.106557\pi\)
\(972\) 30.0056 + 5.98855i 0.962431 + 0.192083i
\(973\) 18.1322 + 18.1322i 0.581292 + 0.581292i
\(974\) 3.22988 5.59432i 0.103492 0.179254i
\(975\) −7.97460 + 11.6543i −0.255392 + 0.373235i
\(976\) 0.890908 + 1.54310i 0.0285173 + 0.0493934i
\(977\) 9.36214 34.9400i 0.299521 1.11783i −0.638038 0.770005i \(-0.720254\pi\)
0.937560 0.347824i \(-0.113079\pi\)
\(978\) −1.14618 0.0451812i −0.0366508 0.00144474i
\(979\) −6.21996 3.59109i −0.198791 0.114772i
\(980\) 3.66225 2.70374i 0.116986 0.0863679i
\(981\) −0.848381 0.583398i −0.0270867 0.0186265i
\(982\) 2.97725 2.97725i 0.0950077 0.0950077i
\(983\) 5.10700 + 19.0596i 0.162888 + 0.607906i 0.998300 + 0.0582820i \(0.0185623\pi\)
−0.835412 + 0.549624i \(0.814771\pi\)
\(984\) −2.19891 9.72360i −0.0700987 0.309977i
\(985\) 12.7581 + 32.4922i 0.406506 + 1.03529i
\(986\) −0.611505 + 0.353052i −0.0194743 + 0.0112435i
\(987\) 10.7913 + 6.81073i 0.343490 + 0.216788i
\(988\) −13.2559 + 3.55190i −0.421725 + 0.113001i
\(989\) −36.2199 −1.15172
\(990\) 3.06331 0.932031i 0.0973583 0.0296219i
\(991\) 53.0916 1.68651 0.843255 0.537513i \(-0.180636\pi\)
0.843255 + 0.537513i \(0.180636\pi\)
\(992\) −8.59681 + 2.30351i −0.272949 + 0.0731364i
\(993\) 2.34643 59.5255i 0.0744618 1.88899i
\(994\) 1.42950 0.825320i 0.0453409 0.0261776i
\(995\) 3.21916 7.38152i 0.102054 0.234010i
\(996\) 35.8504 + 11.1369i 1.13596 + 0.352887i
\(997\) 9.82689 + 36.6745i 0.311221 + 1.16149i 0.927457 + 0.373930i \(0.121990\pi\)
−0.616236 + 0.787562i \(0.711343\pi\)
\(998\) −0.432718 + 0.432718i −0.0136974 + 0.0136974i
\(999\) 0.781905 + 0.992629i 0.0247384 + 0.0314054i
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 45.2.l.a.38.3 yes 16
3.2 odd 2 135.2.m.a.8.2 16
4.3 odd 2 720.2.cu.c.353.1 16
5.2 odd 4 inner 45.2.l.a.2.3 16
5.3 odd 4 225.2.p.b.182.2 16
5.4 even 2 225.2.p.b.218.2 16
9.2 odd 6 405.2.f.a.323.5 16
9.4 even 3 135.2.m.a.98.2 16
9.5 odd 6 inner 45.2.l.a.23.3 yes 16
9.7 even 3 405.2.f.a.323.4 16
15.2 even 4 135.2.m.a.62.2 16
15.8 even 4 675.2.q.a.332.3 16
15.14 odd 2 675.2.q.a.143.3 16
20.7 even 4 720.2.cu.c.497.2 16
36.23 even 6 720.2.cu.c.113.2 16
45.2 even 12 405.2.f.a.242.4 16
45.4 even 6 675.2.q.a.368.3 16
45.7 odd 12 405.2.f.a.242.5 16
45.13 odd 12 675.2.q.a.557.3 16
45.14 odd 6 225.2.p.b.68.2 16
45.22 odd 12 135.2.m.a.17.2 16
45.23 even 12 225.2.p.b.32.2 16
45.32 even 12 inner 45.2.l.a.32.3 yes 16
180.167 odd 12 720.2.cu.c.257.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.2.l.a.2.3 16 5.2 odd 4 inner
45.2.l.a.23.3 yes 16 9.5 odd 6 inner
45.2.l.a.32.3 yes 16 45.32 even 12 inner
45.2.l.a.38.3 yes 16 1.1 even 1 trivial
135.2.m.a.8.2 16 3.2 odd 2
135.2.m.a.17.2 16 45.22 odd 12
135.2.m.a.62.2 16 15.2 even 4
135.2.m.a.98.2 16 9.4 even 3
225.2.p.b.32.2 16 45.23 even 12
225.2.p.b.68.2 16 45.14 odd 6
225.2.p.b.182.2 16 5.3 odd 4
225.2.p.b.218.2 16 5.4 even 2
405.2.f.a.242.4 16 45.2 even 12
405.2.f.a.242.5 16 45.7 odd 12
405.2.f.a.323.4 16 9.7 even 3
405.2.f.a.323.5 16 9.2 odd 6
675.2.q.a.143.3 16 15.14 odd 2
675.2.q.a.332.3 16 15.8 even 4
675.2.q.a.368.3 16 45.4 even 6
675.2.q.a.557.3 16 45.13 odd 12
720.2.cu.c.113.2 16 36.23 even 6
720.2.cu.c.257.1 16 180.167 odd 12
720.2.cu.c.353.1 16 4.3 odd 2
720.2.cu.c.497.2 16 20.7 even 4