Properties

Label 273.2.bl.d.121.5
Level $273$
Weight $2$
Character 273.121
Analytic conductor $2.180$
Analytic rank $0$
Dimension $20$
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] = [273,2,Mod(88,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.88");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bl (of order \(6\), degree \(2\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + 27166 x^{4} + 6435 x^{2} + 576 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 121.5
Root \(0.560998i\) of defining polynomial
Character \(\chi\) \(=\) 273.121
Dual form 273.2.bl.d.88.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.485838 + 0.280499i) q^{2} -1.00000 q^{3} +(-0.842641 + 1.45950i) q^{4} +(-0.449963 - 0.259786i) q^{5} +(0.485838 - 0.280499i) q^{6} +(-1.87423 - 1.86743i) q^{7} -2.06743i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.485838 + 0.280499i) q^{2} -1.00000 q^{3} +(-0.842641 + 1.45950i) q^{4} +(-0.449963 - 0.259786i) q^{5} +(0.485838 - 0.280499i) q^{6} +(-1.87423 - 1.86743i) q^{7} -2.06743i q^{8} +1.00000 q^{9} +0.291479 q^{10} -2.16751i q^{11} +(0.842641 - 1.45950i) q^{12} +(3.29920 - 1.45439i) q^{13} +(1.43438 + 0.381548i) q^{14} +(0.449963 + 0.259786i) q^{15} +(-1.10537 - 1.91455i) q^{16} +(2.48051 - 4.29637i) q^{17} +(-0.485838 + 0.280499i) q^{18} +5.52084i q^{19} +(0.758315 - 0.437813i) q^{20} +(1.87423 + 1.86743i) q^{21} +(0.607984 + 1.05306i) q^{22} +(-3.39752 - 5.88468i) q^{23} +2.06743i q^{24} +(-2.36502 - 4.09634i) q^{25} +(-1.19492 + 1.63202i) q^{26} -1.00000 q^{27} +(4.30480 - 1.16186i) q^{28} +(3.81357 - 6.60529i) q^{29} -0.291479 q^{30} +(-5.15974 + 2.97898i) q^{31} +(4.65496 + 2.68754i) q^{32} +2.16751i q^{33} +2.78312i q^{34} +(0.358201 + 1.32717i) q^{35} +(-0.842641 + 1.45950i) q^{36} +(-5.06378 + 2.92358i) q^{37} +(-1.54859 - 2.68224i) q^{38} +(-3.29920 + 1.45439i) q^{39} +(-0.537091 + 0.930269i) q^{40} +(-9.23279 - 5.33055i) q^{41} +(-1.43438 - 0.381548i) q^{42} +(-2.11946 - 3.67102i) q^{43} +(3.16347 + 1.82643i) q^{44} +(-0.449963 - 0.259786i) q^{45} +(3.30129 + 1.90600i) q^{46} +(9.69377 + 5.59670i) q^{47} +(1.10537 + 1.91455i) q^{48} +(0.0254470 + 6.99995i) q^{49} +(2.29804 + 1.32677i) q^{50} +(-2.48051 + 4.29637i) q^{51} +(-0.657365 + 6.04071i) q^{52} +(1.04639 + 1.81239i) q^{53} +(0.485838 - 0.280499i) q^{54} +(-0.563089 + 0.975299i) q^{55} +(-3.86078 + 3.87484i) q^{56} -5.52084i q^{57} +4.27880i q^{58} +(-2.63992 - 1.52416i) q^{59} +(-0.758315 + 0.437813i) q^{60} +6.24908 q^{61} +(1.67120 - 2.89460i) q^{62} +(-1.87423 - 1.86743i) q^{63} +1.40606 q^{64} +(-1.86235 - 0.202666i) q^{65} +(-0.607984 - 1.05306i) q^{66} -1.98125i q^{67} +(4.18036 + 7.24059i) q^{68} +(3.39752 + 5.88468i) q^{69} +(-0.546298 - 0.544315i) q^{70} +(-8.61474 + 4.97372i) q^{71} -2.06743i q^{72} +(2.47088 - 1.42656i) q^{73} +(1.64012 - 2.84077i) q^{74} +(2.36502 + 4.09634i) q^{75} +(-8.05765 - 4.65209i) q^{76} +(-4.04766 + 4.06240i) q^{77} +(1.19492 - 1.63202i) q^{78} +(2.48141 - 4.29793i) q^{79} +1.14864i q^{80} +1.00000 q^{81} +5.98086 q^{82} -3.65923i q^{83} +(-4.30480 + 1.16186i) q^{84} +(-2.23228 + 1.28880i) q^{85} +(2.05943 + 1.18901i) q^{86} +(-3.81357 + 6.60529i) q^{87} -4.48118 q^{88} +(-2.19138 + 1.26519i) q^{89} +0.291479 q^{90} +(-8.89942 - 3.43516i) q^{91} +11.4516 q^{92} +(5.15974 - 2.97898i) q^{93} -6.27947 q^{94} +(1.43424 - 2.48418i) q^{95} +(-4.65496 - 2.68754i) q^{96} +(8.01957 - 4.63010i) q^{97} +(-1.97584 - 3.39371i) q^{98} -2.16751i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.485838 + 0.280499i −0.343540 + 0.198343i −0.661836 0.749649i \(-0.730223\pi\)
0.318297 + 0.947991i \(0.396889\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.842641 + 1.45950i −0.421320 + 0.729748i
\(5\) −0.449963 0.259786i −0.201230 0.116180i 0.395999 0.918251i \(-0.370398\pi\)
−0.597229 + 0.802071i \(0.703732\pi\)
\(6\) 0.485838 0.280499i 0.198343 0.114513i
\(7\) −1.87423 1.86743i −0.708391 0.705820i
\(8\) 2.06743i 0.730948i
\(9\) 1.00000 0.333333
\(10\) 0.291479 0.0921738
\(11\) 2.16751i 0.653528i −0.945106 0.326764i \(-0.894042\pi\)
0.945106 0.326764i \(-0.105958\pi\)
\(12\) 0.842641 1.45950i 0.243249 0.421320i
\(13\) 3.29920 1.45439i 0.915035 0.403375i
\(14\) 1.43438 + 0.381548i 0.383355 + 0.101973i
\(15\) 0.449963 + 0.259786i 0.116180 + 0.0670766i
\(16\) −1.10537 1.91455i −0.276342 0.478639i
\(17\) 2.48051 4.29637i 0.601612 1.04202i −0.390965 0.920405i \(-0.627859\pi\)
0.992577 0.121617i \(-0.0388079\pi\)
\(18\) −0.485838 + 0.280499i −0.114513 + 0.0661142i
\(19\) 5.52084i 1.26657i 0.773919 + 0.633284i \(0.218294\pi\)
−0.773919 + 0.633284i \(0.781706\pi\)
\(20\) 0.758315 0.437813i 0.169564 0.0978980i
\(21\) 1.87423 + 1.86743i 0.408990 + 0.407506i
\(22\) 0.607984 + 1.05306i 0.129623 + 0.224513i
\(23\) −3.39752 5.88468i −0.708432 1.22704i −0.965439 0.260631i \(-0.916069\pi\)
0.257006 0.966410i \(-0.417264\pi\)
\(24\) 2.06743i 0.422013i
\(25\) −2.36502 4.09634i −0.473004 0.819268i
\(26\) −1.19492 + 1.63202i −0.234344 + 0.320066i
\(27\) −1.00000 −0.192450
\(28\) 4.30480 1.16186i 0.813531 0.219571i
\(29\) 3.81357 6.60529i 0.708161 1.22657i −0.257377 0.966311i \(-0.582858\pi\)
0.965538 0.260260i \(-0.0838084\pi\)
\(30\) −0.291479 −0.0532166
\(31\) −5.15974 + 2.97898i −0.926717 + 0.535040i −0.885772 0.464121i \(-0.846370\pi\)
−0.0409451 + 0.999161i \(0.513037\pi\)
\(32\) 4.65496 + 2.68754i 0.822889 + 0.475095i
\(33\) 2.16751i 0.377315i
\(34\) 2.78312i 0.477301i
\(35\) 0.358201 + 1.32717i 0.0605471 + 0.224333i
\(36\) −0.842641 + 1.45950i −0.140440 + 0.243249i
\(37\) −5.06378 + 2.92358i −0.832481 + 0.480633i −0.854701 0.519120i \(-0.826260\pi\)
0.0222205 + 0.999753i \(0.492926\pi\)
\(38\) −1.54859 2.68224i −0.251215 0.435116i
\(39\) −3.29920 + 1.45439i −0.528295 + 0.232889i
\(40\) −0.537091 + 0.930269i −0.0849216 + 0.147089i
\(41\) −9.23279 5.33055i −1.44192 0.832492i −0.443941 0.896056i \(-0.646420\pi\)
−0.997978 + 0.0635633i \(0.979754\pi\)
\(42\) −1.43438 0.381548i −0.221330 0.0588742i
\(43\) −2.11946 3.67102i −0.323215 0.559825i 0.657934 0.753075i \(-0.271430\pi\)
−0.981150 + 0.193250i \(0.938097\pi\)
\(44\) 3.16347 + 1.82643i 0.476911 + 0.275345i
\(45\) −0.449963 0.259786i −0.0670766 0.0387267i
\(46\) 3.30129 + 1.90600i 0.486749 + 0.281025i
\(47\) 9.69377 + 5.59670i 1.41398 + 0.816363i 0.995761 0.0919829i \(-0.0293205\pi\)
0.418221 + 0.908345i \(0.362654\pi\)
\(48\) 1.10537 + 1.91455i 0.159546 + 0.276342i
\(49\) 0.0254470 + 6.99995i 0.00363529 + 0.999993i
\(50\) 2.29804 + 1.32677i 0.324991 + 0.187634i
\(51\) −2.48051 + 4.29637i −0.347341 + 0.601612i
\(52\) −0.657365 + 6.04071i −0.0911602 + 0.837695i
\(53\) 1.04639 + 1.81239i 0.143732 + 0.248951i 0.928899 0.370333i \(-0.120756\pi\)
−0.785167 + 0.619284i \(0.787423\pi\)
\(54\) 0.485838 0.280499i 0.0661142 0.0381711i
\(55\) −0.563089 + 0.975299i −0.0759269 + 0.131509i
\(56\) −3.86078 + 3.87484i −0.515918 + 0.517797i
\(57\) 5.52084i 0.731254i
\(58\) 4.27880i 0.561834i
\(59\) −2.63992 1.52416i −0.343688 0.198428i 0.318214 0.948019i \(-0.396917\pi\)
−0.661902 + 0.749591i \(0.730250\pi\)
\(60\) −0.758315 + 0.437813i −0.0978980 + 0.0565214i
\(61\) 6.24908 0.800112 0.400056 0.916491i \(-0.368991\pi\)
0.400056 + 0.916491i \(0.368991\pi\)
\(62\) 1.67120 2.89460i 0.212243 0.367615i
\(63\) −1.87423 1.86743i −0.236130 0.235273i
\(64\) 1.40606 0.175758
\(65\) −1.86235 0.202666i −0.230996 0.0251376i
\(66\) −0.607984 1.05306i −0.0748376 0.129623i
\(67\) 1.98125i 0.242049i −0.992650 0.121024i \(-0.961382\pi\)
0.992650 0.121024i \(-0.0386179\pi\)
\(68\) 4.18036 + 7.24059i 0.506943 + 0.878050i
\(69\) 3.39752 + 5.88468i 0.409014 + 0.708432i
\(70\) −0.546298 0.544315i −0.0652951 0.0650581i
\(71\) −8.61474 + 4.97372i −1.02238 + 0.590272i −0.914793 0.403923i \(-0.867646\pi\)
−0.107589 + 0.994195i \(0.534313\pi\)
\(72\) 2.06743i 0.243649i
\(73\) 2.47088 1.42656i 0.289195 0.166967i −0.348384 0.937352i \(-0.613269\pi\)
0.637579 + 0.770385i \(0.279936\pi\)
\(74\) 1.64012 2.84077i 0.190660 0.330233i
\(75\) 2.36502 + 4.09634i 0.273089 + 0.473004i
\(76\) −8.05765 4.65209i −0.924276 0.533631i
\(77\) −4.04766 + 4.06240i −0.461274 + 0.462953i
\(78\) 1.19492 1.63202i 0.135299 0.184790i
\(79\) 2.48141 4.29793i 0.279181 0.483555i −0.692001 0.721897i \(-0.743271\pi\)
0.971181 + 0.238342i \(0.0766039\pi\)
\(80\) 1.14864i 0.128422i
\(81\) 1.00000 0.111111
\(82\) 5.98086 0.660475
\(83\) 3.65923i 0.401653i −0.979627 0.200826i \(-0.935637\pi\)
0.979627 0.200826i \(-0.0643627\pi\)
\(84\) −4.30480 + 1.16186i −0.469692 + 0.126769i
\(85\) −2.23228 + 1.28880i −0.242124 + 0.139791i
\(86\) 2.05943 + 1.18901i 0.222074 + 0.128215i
\(87\) −3.81357 + 6.60529i −0.408857 + 0.708161i
\(88\) −4.48118 −0.477696
\(89\) −2.19138 + 1.26519i −0.232285 + 0.134110i −0.611626 0.791147i \(-0.709484\pi\)
0.379341 + 0.925257i \(0.376151\pi\)
\(90\) 0.291479 0.0307246
\(91\) −8.89942 3.43516i −0.932913 0.360103i
\(92\) 11.4516 1.19391
\(93\) 5.15974 2.97898i 0.535040 0.308906i
\(94\) −6.27947 −0.647678
\(95\) 1.43424 2.48418i 0.147150 0.254871i
\(96\) −4.65496 2.68754i −0.475095 0.274296i
\(97\) 8.01957 4.63010i 0.814264 0.470116i −0.0341702 0.999416i \(-0.510879\pi\)
0.848435 + 0.529300i \(0.177545\pi\)
\(98\) −1.97584 3.39371i −0.199590 0.342816i
\(99\) 2.16751i 0.217843i
\(100\) 7.97146 0.797146
\(101\) −9.04398 −0.899909 −0.449955 0.893051i \(-0.648560\pi\)
−0.449955 + 0.893051i \(0.648560\pi\)
\(102\) 2.78312i 0.275570i
\(103\) −8.82890 + 15.2921i −0.869937 + 1.50678i −0.00787730 + 0.999969i \(0.502507\pi\)
−0.862060 + 0.506806i \(0.830826\pi\)
\(104\) −3.00686 6.82089i −0.294847 0.668843i
\(105\) −0.358201 1.32717i −0.0349569 0.129519i
\(106\) −1.01675 0.587020i −0.0987553 0.0570164i
\(107\) −9.73005 16.8529i −0.940639 1.62923i −0.764256 0.644913i \(-0.776894\pi\)
−0.176383 0.984322i \(-0.556440\pi\)
\(108\) 0.842641 1.45950i 0.0810831 0.140440i
\(109\) 14.1408 8.16420i 1.35444 0.781989i 0.365576 0.930782i \(-0.380872\pi\)
0.988868 + 0.148793i \(0.0475388\pi\)
\(110\) 0.631783i 0.0602382i
\(111\) 5.06378 2.92358i 0.480633 0.277494i
\(112\) −1.50358 + 5.65250i −0.142075 + 0.534111i
\(113\) 6.19998 + 10.7387i 0.583245 + 1.01021i 0.995092 + 0.0989565i \(0.0315505\pi\)
−0.411847 + 0.911253i \(0.635116\pi\)
\(114\) 1.54859 + 2.68224i 0.145039 + 0.251215i
\(115\) 3.53052i 0.329223i
\(116\) 6.42693 + 11.1318i 0.596726 + 1.03356i
\(117\) 3.29920 1.45439i 0.305012 0.134458i
\(118\) 1.71010 0.157427
\(119\) −12.6722 + 3.42020i −1.16166 + 0.313529i
\(120\) 0.537091 0.930269i 0.0490295 0.0849216i
\(121\) 6.30191 0.572901
\(122\) −3.03604 + 1.75286i −0.274870 + 0.158696i
\(123\) 9.23279 + 5.33055i 0.832492 + 0.480640i
\(124\) 10.0408i 0.901693i
\(125\) 5.05547i 0.452175i
\(126\) 1.43438 + 0.381548i 0.127785 + 0.0339910i
\(127\) 10.1675 17.6107i 0.902223 1.56270i 0.0776210 0.996983i \(-0.475268\pi\)
0.824602 0.565713i \(-0.191399\pi\)
\(128\) −9.99304 + 5.76949i −0.883269 + 0.509955i
\(129\) 2.11946 + 3.67102i 0.186608 + 0.323215i
\(130\) 0.961649 0.423925i 0.0843422 0.0371806i
\(131\) 6.88948 11.9329i 0.601937 1.04258i −0.390591 0.920564i \(-0.627729\pi\)
0.992528 0.122020i \(-0.0389374\pi\)
\(132\) −3.16347 1.82643i −0.275345 0.158970i
\(133\) 10.3098 10.3473i 0.893970 0.897226i
\(134\) 0.555739 + 0.962568i 0.0480085 + 0.0831532i
\(135\) 0.449963 + 0.259786i 0.0387267 + 0.0223589i
\(136\) −8.88246 5.12829i −0.761665 0.439747i
\(137\) −1.40407 0.810643i −0.119958 0.0692579i 0.438820 0.898575i \(-0.355396\pi\)
−0.558778 + 0.829317i \(0.688730\pi\)
\(138\) −3.30129 1.90600i −0.281025 0.162250i
\(139\) 3.66875 + 6.35446i 0.311179 + 0.538979i 0.978618 0.205686i \(-0.0659426\pi\)
−0.667439 + 0.744665i \(0.732609\pi\)
\(140\) −2.23884 0.595535i −0.189216 0.0503319i
\(141\) −9.69377 5.59670i −0.816363 0.471327i
\(142\) 2.79025 4.83285i 0.234152 0.405564i
\(143\) −3.15240 7.15105i −0.263617 0.598001i
\(144\) −1.10537 1.91455i −0.0921140 0.159546i
\(145\) −3.43193 + 1.98142i −0.285006 + 0.164548i
\(146\) −0.800299 + 1.38616i −0.0662332 + 0.114719i
\(147\) −0.0254470 6.99995i −0.00209884 0.577346i
\(148\) 9.85410i 0.810002i
\(149\) 1.07489i 0.0880585i 0.999030 + 0.0440293i \(0.0140195\pi\)
−0.999030 + 0.0440293i \(0.985981\pi\)
\(150\) −2.29804 1.32677i −0.187634 0.108330i
\(151\) −10.8708 + 6.27625i −0.884652 + 0.510754i −0.872189 0.489168i \(-0.837300\pi\)
−0.0124624 + 0.999922i \(0.503967\pi\)
\(152\) 11.4140 0.925796
\(153\) 2.48051 4.29637i 0.200537 0.347341i
\(154\) 0.827009 3.10903i 0.0666423 0.250533i
\(155\) 3.09559 0.248644
\(156\) 0.657365 6.04071i 0.0526313 0.483644i
\(157\) 0.346108 + 0.599476i 0.0276224 + 0.0478434i 0.879506 0.475888i \(-0.157873\pi\)
−0.851884 + 0.523731i \(0.824540\pi\)
\(158\) 2.78413i 0.221494i
\(159\) −1.04639 1.81239i −0.0829838 0.143732i
\(160\) −1.39637 2.41859i −0.110393 0.191206i
\(161\) −4.62148 + 17.3738i −0.364223 + 1.36925i
\(162\) −0.485838 + 0.280499i −0.0381711 + 0.0220381i
\(163\) 10.3974i 0.814384i −0.913343 0.407192i \(-0.866508\pi\)
0.913343 0.407192i \(-0.133492\pi\)
\(164\) 15.5598 8.98348i 1.21502 0.701492i
\(165\) 0.563089 0.975299i 0.0438364 0.0759269i
\(166\) 1.02641 + 1.77779i 0.0796648 + 0.137984i
\(167\) 20.9105 + 12.0727i 1.61810 + 0.934213i 0.987410 + 0.158181i \(0.0505629\pi\)
0.630694 + 0.776032i \(0.282770\pi\)
\(168\) 3.86078 3.87484i 0.297866 0.298950i
\(169\) 8.76949 9.59666i 0.674577 0.738205i
\(170\) 0.723017 1.25230i 0.0554528 0.0960471i
\(171\) 5.52084i 0.422190i
\(172\) 7.14379 0.544709
\(173\) 3.73858 0.284239 0.142119 0.989850i \(-0.454608\pi\)
0.142119 + 0.989850i \(0.454608\pi\)
\(174\) 4.27880i 0.324375i
\(175\) −3.21702 + 12.0940i −0.243184 + 0.914218i
\(176\) −4.14981 + 2.39590i −0.312804 + 0.180597i
\(177\) 2.63992 + 1.52416i 0.198428 + 0.114563i
\(178\) 0.709770 1.22936i 0.0531995 0.0921442i
\(179\) −5.67810 −0.424401 −0.212200 0.977226i \(-0.568063\pi\)
−0.212200 + 0.977226i \(0.568063\pi\)
\(180\) 0.758315 0.437813i 0.0565214 0.0326327i
\(181\) −9.94903 −0.739506 −0.369753 0.929130i \(-0.620558\pi\)
−0.369753 + 0.929130i \(0.620558\pi\)
\(182\) 5.28724 0.827345i 0.391916 0.0613269i
\(183\) −6.24908 −0.461945
\(184\) −12.1662 + 7.02415i −0.896904 + 0.517827i
\(185\) 3.03802 0.223360
\(186\) −1.67120 + 2.89460i −0.122538 + 0.212243i
\(187\) −9.31241 5.37652i −0.680991 0.393170i
\(188\) −16.3367 + 9.43201i −1.19148 + 0.687900i
\(189\) 1.87423 + 1.86743i 0.136330 + 0.135835i
\(190\) 1.60921i 0.116744i
\(191\) 9.50875 0.688029 0.344014 0.938964i \(-0.388213\pi\)
0.344014 + 0.938964i \(0.388213\pi\)
\(192\) −1.40606 −0.101474
\(193\) 3.11196i 0.224004i −0.993708 0.112002i \(-0.964274\pi\)
0.993708 0.112002i \(-0.0357263\pi\)
\(194\) −2.59748 + 4.49896i −0.186488 + 0.323007i
\(195\) 1.86235 + 0.202666i 0.133366 + 0.0145132i
\(196\) −10.2379 5.86131i −0.731275 0.418665i
\(197\) 4.41349 + 2.54813i 0.314448 + 0.181547i 0.648915 0.760861i \(-0.275223\pi\)
−0.334467 + 0.942407i \(0.608556\pi\)
\(198\) 0.607984 + 1.05306i 0.0432075 + 0.0748376i
\(199\) −6.95536 + 12.0470i −0.493053 + 0.853992i −0.999968 0.00800358i \(-0.997452\pi\)
0.506915 + 0.861996i \(0.330786\pi\)
\(200\) −8.46891 + 4.88953i −0.598842 + 0.345742i
\(201\) 1.98125i 0.139747i
\(202\) 4.39391 2.53683i 0.309154 0.178490i
\(203\) −19.4824 + 5.25826i −1.36739 + 0.369057i
\(204\) −4.18036 7.24059i −0.292683 0.506943i
\(205\) 2.76961 + 4.79711i 0.193438 + 0.335044i
\(206\) 9.90598i 0.690183i
\(207\) −3.39752 5.88468i −0.236144 0.409014i
\(208\) −6.43135 4.70887i −0.445934 0.326501i
\(209\) 11.9665 0.827738
\(210\) 0.546298 + 0.544315i 0.0376981 + 0.0375613i
\(211\) −6.30791 + 10.9256i −0.434255 + 0.752151i −0.997234 0.0743195i \(-0.976322\pi\)
0.562980 + 0.826471i \(0.309655\pi\)
\(212\) −3.52691 −0.242229
\(213\) 8.61474 4.97372i 0.590272 0.340794i
\(214\) 9.45446 + 5.45853i 0.646293 + 0.373138i
\(215\) 2.20243i 0.150205i
\(216\) 2.06743i 0.140671i
\(217\) 15.2335 + 4.05215i 1.03412 + 0.275078i
\(218\) −4.58010 + 7.93296i −0.310203 + 0.537288i
\(219\) −2.47088 + 1.42656i −0.166967 + 0.0963982i
\(220\) −0.948964 1.64365i −0.0639791 0.110815i
\(221\) 1.93511 17.7822i 0.130169 1.19616i
\(222\) −1.64012 + 2.84077i −0.110078 + 0.190660i
\(223\) 0.659526 + 0.380777i 0.0441651 + 0.0254987i 0.521920 0.852994i \(-0.325216\pi\)
−0.477755 + 0.878493i \(0.658549\pi\)
\(224\) −3.70567 13.7299i −0.247595 0.917365i
\(225\) −2.36502 4.09634i −0.157668 0.273089i
\(226\) −6.02437 3.47817i −0.400735 0.231365i
\(227\) 1.33416 + 0.770280i 0.0885515 + 0.0511252i 0.543622 0.839330i \(-0.317053\pi\)
−0.455070 + 0.890455i \(0.650386\pi\)
\(228\) 8.05765 + 4.65209i 0.533631 + 0.308092i
\(229\) 4.86535 + 2.80901i 0.321512 + 0.185625i 0.652066 0.758162i \(-0.273902\pi\)
−0.330555 + 0.943787i \(0.607236\pi\)
\(230\) −0.990307 1.71526i −0.0652989 0.113101i
\(231\) 4.04766 4.06240i 0.266316 0.267286i
\(232\) −13.6560 7.88430i −0.896560 0.517629i
\(233\) −8.57478 + 14.8520i −0.561753 + 0.972984i 0.435591 + 0.900145i \(0.356539\pi\)
−0.997344 + 0.0728395i \(0.976794\pi\)
\(234\) −1.19492 + 1.63202i −0.0781147 + 0.106689i
\(235\) −2.90789 5.03662i −0.189690 0.328553i
\(236\) 4.44900 2.56863i 0.289605 0.167204i
\(237\) −2.48141 + 4.29793i −0.161185 + 0.279181i
\(238\) 5.19727 5.21620i 0.336889 0.338116i
\(239\) 25.6658i 1.66018i 0.557628 + 0.830091i \(0.311711\pi\)
−0.557628 + 0.830091i \(0.688289\pi\)
\(240\) 1.14864i 0.0741443i
\(241\) 4.08520 + 2.35859i 0.263151 + 0.151930i 0.625771 0.780007i \(-0.284784\pi\)
−0.362620 + 0.931937i \(0.618118\pi\)
\(242\) −3.06171 + 1.76768i −0.196814 + 0.113631i
\(243\) −1.00000 −0.0641500
\(244\) −5.26573 + 9.12050i −0.337104 + 0.583880i
\(245\) 1.80704 3.15633i 0.115448 0.201651i
\(246\) −5.98086 −0.381325
\(247\) 8.02947 + 18.2144i 0.510903 + 1.15895i
\(248\) 6.15884 + 10.6674i 0.391087 + 0.677382i
\(249\) 3.65923i 0.231894i
\(250\) −1.41805 2.45614i −0.0896855 0.155340i
\(251\) −0.0982527 0.170179i −0.00620165 0.0107416i 0.862908 0.505361i \(-0.168641\pi\)
−0.869110 + 0.494620i \(0.835307\pi\)
\(252\) 4.30480 1.16186i 0.271177 0.0731902i
\(253\) −12.7551 + 7.36416i −0.801906 + 0.462981i
\(254\) 11.4079i 0.715797i
\(255\) 2.23228 1.28880i 0.139791 0.0807081i
\(256\) 1.83061 3.17070i 0.114413 0.198169i
\(257\) 0.753004 + 1.30424i 0.0469711 + 0.0813563i 0.888555 0.458770i \(-0.151710\pi\)
−0.841584 + 0.540126i \(0.818376\pi\)
\(258\) −2.05943 1.18901i −0.128215 0.0740248i
\(259\) 14.9502 + 3.97679i 0.928962 + 0.247106i
\(260\) 1.86508 2.54732i 0.115668 0.157978i
\(261\) 3.81357 6.60529i 0.236054 0.408857i
\(262\) 7.72996i 0.477559i
\(263\) 6.88599 0.424608 0.212304 0.977204i \(-0.431903\pi\)
0.212304 + 0.977204i \(0.431903\pi\)
\(264\) 4.48118 0.275798
\(265\) 1.08735i 0.0667952i
\(266\) −2.10647 + 7.91900i −0.129156 + 0.485545i
\(267\) 2.19138 1.26519i 0.134110 0.0774285i
\(268\) 2.89163 + 1.66948i 0.176634 + 0.101980i
\(269\) 5.93548 10.2806i 0.361893 0.626816i −0.626380 0.779518i \(-0.715464\pi\)
0.988272 + 0.152702i \(0.0487974\pi\)
\(270\) −0.291479 −0.0177389
\(271\) −11.9020 + 6.87163i −0.722995 + 0.417422i −0.815854 0.578258i \(-0.803733\pi\)
0.0928589 + 0.995679i \(0.470399\pi\)
\(272\) −10.9675 −0.665003
\(273\) 8.89942 + 3.43516i 0.538617 + 0.207905i
\(274\) 0.909537 0.0549472
\(275\) −8.87885 + 5.12620i −0.535415 + 0.309122i
\(276\) −11.4516 −0.689303
\(277\) −5.60801 + 9.71335i −0.336952 + 0.583619i −0.983858 0.178951i \(-0.942729\pi\)
0.646905 + 0.762570i \(0.276063\pi\)
\(278\) −3.56484 2.05816i −0.213805 0.123440i
\(279\) −5.15974 + 2.97898i −0.308906 + 0.178347i
\(280\) 2.74384 0.740558i 0.163976 0.0442568i
\(281\) 1.81616i 0.108343i −0.998532 0.0541714i \(-0.982748\pi\)
0.998532 0.0541714i \(-0.0172517\pi\)
\(282\) 6.27947 0.373937
\(283\) 30.8377 1.83311 0.916556 0.399905i \(-0.130957\pi\)
0.916556 + 0.399905i \(0.130957\pi\)
\(284\) 16.7642i 0.994775i
\(285\) −1.43424 + 2.48418i −0.0849571 + 0.147150i
\(286\) 3.53742 + 2.59001i 0.209172 + 0.153150i
\(287\) 7.34992 + 27.2322i 0.433852 + 1.60747i
\(288\) 4.65496 + 2.68754i 0.274296 + 0.158365i
\(289\) −3.80585 6.59193i −0.223874 0.387760i
\(290\) 1.11157 1.92530i 0.0652739 0.113058i
\(291\) −8.01957 + 4.63010i −0.470116 + 0.271421i
\(292\) 4.80832i 0.281386i
\(293\) −0.948761 + 0.547767i −0.0554272 + 0.0320009i −0.527458 0.849581i \(-0.676855\pi\)
0.472030 + 0.881582i \(0.343521\pi\)
\(294\) 1.97584 + 3.39371i 0.115233 + 0.197925i
\(295\) 0.791910 + 1.37163i 0.0461068 + 0.0798593i
\(296\) 6.04430 + 10.4690i 0.351318 + 0.608501i
\(297\) 2.16751i 0.125772i
\(298\) −0.301506 0.522223i −0.0174658 0.0302516i
\(299\) −19.7677 14.4734i −1.14320 0.837020i
\(300\) −7.97146 −0.460232
\(301\) −2.88300 + 10.8383i −0.166173 + 0.624707i
\(302\) 3.52096 6.09848i 0.202609 0.350928i
\(303\) 9.04398 0.519563
\(304\) 10.5700 6.10257i 0.606229 0.350006i
\(305\) −2.81185 1.62342i −0.161006 0.0929570i
\(306\) 2.78312i 0.159100i
\(307\) 4.90247i 0.279799i −0.990166 0.139899i \(-0.955322\pi\)
0.990166 0.139899i \(-0.0446779\pi\)
\(308\) −2.51834 9.33069i −0.143496 0.531665i
\(309\) 8.82890 15.2921i 0.502258 0.869937i
\(310\) −1.50396 + 0.868310i −0.0854190 + 0.0493167i
\(311\) −5.78751 10.0243i −0.328179 0.568423i 0.653971 0.756519i \(-0.273102\pi\)
−0.982151 + 0.188096i \(0.939768\pi\)
\(312\) 3.00686 + 6.82089i 0.170230 + 0.386157i
\(313\) 2.53480 4.39041i 0.143275 0.248160i −0.785453 0.618922i \(-0.787570\pi\)
0.928728 + 0.370761i \(0.120903\pi\)
\(314\) −0.336305 0.194166i −0.0189788 0.0109574i
\(315\) 0.358201 + 1.32717i 0.0201824 + 0.0747776i
\(316\) 4.18188 + 7.24322i 0.235249 + 0.407463i
\(317\) −14.8929 8.59841i −0.836468 0.482935i 0.0195943 0.999808i \(-0.493763\pi\)
−0.856062 + 0.516873i \(0.827096\pi\)
\(318\) 1.01675 + 0.587020i 0.0570164 + 0.0329184i
\(319\) −14.3170 8.26593i −0.801599 0.462803i
\(320\) −0.632676 0.365276i −0.0353677 0.0204195i
\(321\) 9.73005 + 16.8529i 0.543078 + 0.940639i
\(322\) −2.62805 9.73719i −0.146456 0.542633i
\(323\) 23.7196 + 13.6945i 1.31979 + 0.761983i
\(324\) −0.842641 + 1.45950i −0.0468134 + 0.0810831i
\(325\) −13.7604 10.0750i −0.763288 0.558860i
\(326\) 2.91645 + 5.05143i 0.161527 + 0.279773i
\(327\) −14.1408 + 8.16420i −0.781989 + 0.451481i
\(328\) −11.0206 + 19.0882i −0.608509 + 1.05397i
\(329\) −7.71690 28.5919i −0.425446 1.57632i
\(330\) 0.631783i 0.0347785i
\(331\) 20.4213i 1.12246i −0.827662 0.561228i \(-0.810329\pi\)
0.827662 0.561228i \(-0.189671\pi\)
\(332\) 5.34063 + 3.08342i 0.293105 + 0.169224i
\(333\) −5.06378 + 2.92358i −0.277494 + 0.160211i
\(334\) −13.5455 −0.741177
\(335\) −0.514702 + 0.891491i −0.0281212 + 0.0487073i
\(336\) 1.50358 5.65250i 0.0820268 0.308369i
\(337\) −13.1872 −0.718353 −0.359176 0.933270i \(-0.616942\pi\)
−0.359176 + 0.933270i \(0.616942\pi\)
\(338\) −1.56870 + 7.12226i −0.0853262 + 0.387400i
\(339\) −6.19998 10.7387i −0.336736 0.583245i
\(340\) 4.34400i 0.235586i
\(341\) 6.45696 + 11.1838i 0.349664 + 0.605636i
\(342\) −1.54859 2.68224i −0.0837382 0.145039i
\(343\) 13.0242 13.1670i 0.703240 0.710952i
\(344\) −7.58959 + 4.38185i −0.409203 + 0.236254i
\(345\) 3.53052i 0.190077i
\(346\) −1.81634 + 1.04867i −0.0976473 + 0.0563767i
\(347\) 4.34376 7.52361i 0.233185 0.403889i −0.725558 0.688161i \(-0.758418\pi\)
0.958744 + 0.284272i \(0.0917518\pi\)
\(348\) −6.42693 11.1318i −0.344520 0.596726i
\(349\) 30.2239 + 17.4498i 1.61785 + 0.934064i 0.987476 + 0.157770i \(0.0504303\pi\)
0.630370 + 0.776294i \(0.282903\pi\)
\(350\) −1.82939 6.77808i −0.0977851 0.362304i
\(351\) −3.29920 + 1.45439i −0.176098 + 0.0776296i
\(352\) 5.82527 10.0897i 0.310488 0.537781i
\(353\) 14.5143i 0.772519i −0.922390 0.386259i \(-0.873767\pi\)
0.922390 0.386259i \(-0.126233\pi\)
\(354\) −1.71010 −0.0908906
\(355\) 5.16842 0.274311
\(356\) 4.26441i 0.226013i
\(357\) 12.6722 3.42020i 0.670683 0.181016i
\(358\) 2.75864 1.59270i 0.145798 0.0841768i
\(359\) −0.460772 0.266027i −0.0243186 0.0140404i 0.487791 0.872960i \(-0.337803\pi\)
−0.512110 + 0.858920i \(0.671136\pi\)
\(360\) −0.537091 + 0.930269i −0.0283072 + 0.0490295i
\(361\) −11.4797 −0.604196
\(362\) 4.83362 2.79069i 0.254049 0.146675i
\(363\) −6.30191 −0.330764
\(364\) 12.5126 10.0941i 0.655839 0.529073i
\(365\) −1.48241 −0.0775927
\(366\) 3.03604 1.75286i 0.158696 0.0916234i
\(367\) 5.85266 0.305506 0.152753 0.988264i \(-0.451186\pi\)
0.152753 + 0.988264i \(0.451186\pi\)
\(368\) −7.51103 + 13.0095i −0.391539 + 0.678166i
\(369\) −9.23279 5.33055i −0.480640 0.277497i
\(370\) −1.47599 + 0.852161i −0.0767329 + 0.0443018i
\(371\) 1.42334 5.35088i 0.0738964 0.277804i
\(372\) 10.0408i 0.520593i
\(373\) 24.2517 1.25571 0.627853 0.778332i \(-0.283934\pi\)
0.627853 + 0.778332i \(0.283934\pi\)
\(374\) 6.03243 0.311930
\(375\) 5.05547i 0.261063i
\(376\) 11.5708 20.0412i 0.596719 1.03355i
\(377\) 2.97506 27.3386i 0.153223 1.40801i
\(378\) −1.43438 0.381548i −0.0737766 0.0196247i
\(379\) −1.19932 0.692428i −0.0616050 0.0355677i 0.468881 0.883261i \(-0.344657\pi\)
−0.530486 + 0.847694i \(0.677991\pi\)
\(380\) 2.41710 + 4.18654i 0.123995 + 0.214765i
\(381\) −10.1675 + 17.6107i −0.520899 + 0.902223i
\(382\) −4.61971 + 2.66719i −0.236365 + 0.136465i
\(383\) 19.7383i 1.00858i −0.863534 0.504290i \(-0.831754\pi\)
0.863534 0.504290i \(-0.168246\pi\)
\(384\) 9.99304 5.76949i 0.509955 0.294423i
\(385\) 2.87665 0.776404i 0.146608 0.0395692i
\(386\) 0.872902 + 1.51191i 0.0444295 + 0.0769542i
\(387\) −2.11946 3.67102i −0.107738 0.186608i
\(388\) 15.6061i 0.792277i
\(389\) 2.48623 + 4.30628i 0.126057 + 0.218337i 0.922146 0.386843i \(-0.126434\pi\)
−0.796089 + 0.605180i \(0.793101\pi\)
\(390\) −0.961649 + 0.423925i −0.0486950 + 0.0214663i
\(391\) −33.7103 −1.70480
\(392\) 14.4719 0.0526101i 0.730944 0.00265721i
\(393\) −6.88948 + 11.9329i −0.347528 + 0.601937i
\(394\) −2.85899 −0.144034
\(395\) −2.23309 + 1.28927i −0.112359 + 0.0648704i
\(396\) 3.16347 + 1.82643i 0.158970 + 0.0917816i
\(397\) 9.82615i 0.493161i −0.969122 0.246580i \(-0.920693\pi\)
0.969122 0.246580i \(-0.0793069\pi\)
\(398\) 7.80389i 0.391173i
\(399\) −10.3098 + 10.3473i −0.516134 + 0.518013i
\(400\) −5.22844 + 9.05593i −0.261422 + 0.452796i
\(401\) −25.3395 + 14.6298i −1.26540 + 0.730577i −0.974113 0.226060i \(-0.927416\pi\)
−0.291283 + 0.956637i \(0.594082\pi\)
\(402\) −0.555739 0.962568i −0.0277177 0.0480085i
\(403\) −12.6904 + 17.3325i −0.632156 + 0.863395i
\(404\) 7.62082 13.1997i 0.379150 0.656707i
\(405\) −0.449963 0.259786i −0.0223589 0.0129089i
\(406\) 7.99034 8.01944i 0.396554 0.397998i
\(407\) 6.33688 + 10.9758i 0.314107 + 0.544050i
\(408\) 8.88246 + 5.12829i 0.439747 + 0.253888i
\(409\) 11.1197 + 6.41994i 0.549832 + 0.317446i 0.749054 0.662509i \(-0.230508\pi\)
−0.199222 + 0.979954i \(0.563842\pi\)
\(410\) −2.69117 1.55374i −0.132907 0.0767340i
\(411\) 1.40407 + 0.810643i 0.0692579 + 0.0399861i
\(412\) −14.8792 25.7715i −0.733045 1.26967i
\(413\) 2.10155 + 7.78646i 0.103411 + 0.383147i
\(414\) 3.30129 + 1.90600i 0.162250 + 0.0936749i
\(415\) −0.950618 + 1.64652i −0.0466640 + 0.0808244i
\(416\) 19.2664 + 2.09662i 0.944613 + 0.102795i
\(417\) −3.66875 6.35446i −0.179660 0.311179i
\(418\) −5.81377 + 3.35658i −0.284361 + 0.164176i
\(419\) 13.1853 22.8376i 0.644144 1.11569i −0.340354 0.940297i \(-0.610547\pi\)
0.984498 0.175393i \(-0.0561197\pi\)
\(420\) 2.23884 + 0.595535i 0.109244 + 0.0290591i
\(421\) 2.71377i 0.132261i −0.997811 0.0661306i \(-0.978935\pi\)
0.997811 0.0661306i \(-0.0210654\pi\)
\(422\) 7.07745i 0.344525i
\(423\) 9.69377 + 5.59670i 0.471327 + 0.272121i
\(424\) 3.74700 2.16333i 0.181971 0.105061i
\(425\) −23.4658 −1.13826
\(426\) −2.79025 + 4.83285i −0.135188 + 0.234152i
\(427\) −11.7122 11.6697i −0.566792 0.564735i
\(428\) 32.7957 1.58524
\(429\) 3.15240 + 7.15105i 0.152200 + 0.345256i
\(430\) −0.617779 1.07003i −0.0297920 0.0516012i
\(431\) 37.0866i 1.78640i −0.449659 0.893200i \(-0.648455\pi\)
0.449659 0.893200i \(-0.351545\pi\)
\(432\) 1.10537 + 1.91455i 0.0531821 + 0.0921140i
\(433\) 7.21536 + 12.4974i 0.346748 + 0.600585i 0.985670 0.168686i \(-0.0539525\pi\)
−0.638922 + 0.769272i \(0.720619\pi\)
\(434\) −8.53766 + 2.30430i −0.409821 + 0.110610i
\(435\) 3.43193 1.98142i 0.164548 0.0950020i
\(436\) 27.5180i 1.31787i
\(437\) 32.4884 18.7572i 1.55413 0.897278i
\(438\) 0.800299 1.38616i 0.0382398 0.0662332i
\(439\) −7.31502 12.6700i −0.349127 0.604706i 0.636968 0.770891i \(-0.280188\pi\)
−0.986095 + 0.166185i \(0.946855\pi\)
\(440\) 2.01637 + 1.16415i 0.0961265 + 0.0554987i
\(441\) 0.0254470 + 6.99995i 0.00121176 + 0.333331i
\(442\) 4.04774 + 9.18208i 0.192532 + 0.436747i
\(443\) 18.3045 31.7043i 0.869672 1.50632i 0.00733990 0.999973i \(-0.497664\pi\)
0.862332 0.506343i \(-0.169003\pi\)
\(444\) 9.85410i 0.467655i
\(445\) 1.31472 0.0623236
\(446\) −0.427231 −0.0202300
\(447\) 1.07489i 0.0508406i
\(448\) −2.63528 2.62572i −0.124505 0.124053i
\(449\) −5.59341 + 3.22935i −0.263969 + 0.152403i −0.626144 0.779708i \(-0.715368\pi\)
0.362175 + 0.932110i \(0.382034\pi\)
\(450\) 2.29804 + 1.32677i 0.108330 + 0.0625446i
\(451\) −11.5540 + 20.0121i −0.544057 + 0.942335i
\(452\) −20.8974 −0.982932
\(453\) 10.8708 6.27625i 0.510754 0.294884i
\(454\) −0.864250 −0.0405613
\(455\) 3.11200 + 3.85764i 0.145893 + 0.180849i
\(456\) −11.4140 −0.534509
\(457\) 16.6225 9.59698i 0.777565 0.448928i −0.0580013 0.998317i \(-0.518473\pi\)
0.835567 + 0.549389i \(0.185139\pi\)
\(458\) −3.15170 −0.147269
\(459\) −2.48051 + 4.29637i −0.115780 + 0.200537i
\(460\) −5.15278 2.97496i −0.240250 0.138708i
\(461\) −5.50203 + 3.17660i −0.256255 + 0.147949i −0.622625 0.782520i \(-0.713934\pi\)
0.366370 + 0.930469i \(0.380600\pi\)
\(462\) −0.827009 + 3.10903i −0.0384759 + 0.144645i
\(463\) 10.8299i 0.503307i 0.967817 + 0.251653i \(0.0809743\pi\)
−0.967817 + 0.251653i \(0.919026\pi\)
\(464\) −16.8616 −0.782779
\(465\) −3.09559 −0.143555
\(466\) 9.62087i 0.445678i
\(467\) 5.84012 10.1154i 0.270248 0.468084i −0.698677 0.715437i \(-0.746228\pi\)
0.968925 + 0.247353i \(0.0795609\pi\)
\(468\) −0.657365 + 6.04071i −0.0303867 + 0.279232i
\(469\) −3.69984 + 3.71331i −0.170843 + 0.171465i
\(470\) 2.82553 + 1.63132i 0.130332 + 0.0752472i
\(471\) −0.346108 0.599476i −0.0159478 0.0276224i
\(472\) −3.15109 + 5.45785i −0.145041 + 0.251218i
\(473\) −7.95696 + 4.59395i −0.365862 + 0.211230i
\(474\) 2.78413i 0.127879i
\(475\) 22.6152 13.0569i 1.03766 0.599093i
\(476\) 5.68633 21.3770i 0.260632 0.979813i
\(477\) 1.04639 + 1.81239i 0.0479107 + 0.0829838i
\(478\) −7.19922 12.4694i −0.329285 0.570338i
\(479\) 24.0236i 1.09767i 0.835932 + 0.548833i \(0.184928\pi\)
−0.835932 + 0.548833i \(0.815072\pi\)
\(480\) 1.39637 + 2.41859i 0.0637355 + 0.110393i
\(481\) −12.4544 + 17.0102i −0.567873 + 0.775598i
\(482\) −2.64633 −0.120537
\(483\) 4.62148 17.3738i 0.210284 0.790537i
\(484\) −5.31024 + 9.19761i −0.241375 + 0.418073i
\(485\) −4.81135 −0.218472
\(486\) 0.485838 0.280499i 0.0220381 0.0127237i
\(487\) 5.23103 + 3.02014i 0.237041 + 0.136856i 0.613816 0.789449i \(-0.289634\pi\)
−0.376775 + 0.926305i \(0.622967\pi\)
\(488\) 12.9196i 0.584841i
\(489\) 10.3974i 0.470185i
\(490\) 0.00741728 + 2.04034i 0.000335079 + 0.0921732i
\(491\) −7.05626 + 12.2218i −0.318444 + 0.551562i −0.980164 0.198190i \(-0.936494\pi\)
0.661719 + 0.749752i \(0.269827\pi\)
\(492\) −15.5598 + 8.98348i −0.701492 + 0.405007i
\(493\) −18.9192 32.7690i −0.852076 1.47584i
\(494\) −9.01014 6.59699i −0.405385 0.296813i
\(495\) −0.563089 + 0.975299i −0.0253090 + 0.0438364i
\(496\) 11.4068 + 6.58574i 0.512182 + 0.295708i
\(497\) 25.4340 + 6.76550i 1.14087 + 0.303474i
\(498\) −1.02641 1.77779i −0.0459945 0.0796648i
\(499\) 28.4481 + 16.4245i 1.27351 + 0.735263i 0.975647 0.219345i \(-0.0703922\pi\)
0.297865 + 0.954608i \(0.403726\pi\)
\(500\) −7.37844 4.25994i −0.329974 0.190510i
\(501\) −20.9105 12.0727i −0.934213 0.539368i
\(502\) 0.0954698 + 0.0551195i 0.00426103 + 0.00246010i
\(503\) −19.5590 33.8772i −0.872093 1.51051i −0.859828 0.510584i \(-0.829429\pi\)
−0.0122649 0.999925i \(-0.503904\pi\)
\(504\) −3.86078 + 3.87484i −0.171973 + 0.172599i
\(505\) 4.06946 + 2.34950i 0.181088 + 0.104551i
\(506\) 4.13127 7.15558i 0.183658 0.318104i
\(507\) −8.76949 + 9.59666i −0.389467 + 0.426203i
\(508\) 17.1352 + 29.6790i 0.760250 + 1.31679i
\(509\) 0.959846 0.554167i 0.0425444 0.0245630i −0.478577 0.878046i \(-0.658847\pi\)
0.521121 + 0.853483i \(0.325514\pi\)
\(510\) −0.723017 + 1.25230i −0.0320157 + 0.0554528i
\(511\) −7.29499 1.94048i −0.322711 0.0858418i
\(512\) 21.0240i 0.929139i
\(513\) 5.52084i 0.243751i
\(514\) −0.731676 0.422433i −0.0322728 0.0186327i
\(515\) 7.94536 4.58726i 0.350114 0.202139i
\(516\) −7.14379 −0.314488
\(517\) 12.1309 21.0113i 0.533516 0.924077i
\(518\) −8.37888 + 2.26145i −0.368147 + 0.0993622i
\(519\) −3.73858 −0.164105
\(520\) −0.418998 + 3.85029i −0.0183743 + 0.168846i
\(521\) 6.87363 + 11.9055i 0.301139 + 0.521589i 0.976394 0.215996i \(-0.0692997\pi\)
−0.675255 + 0.737584i \(0.735966\pi\)
\(522\) 4.27880i 0.187278i
\(523\) 1.20677 + 2.09020i 0.0527686 + 0.0913979i 0.891203 0.453604i \(-0.149862\pi\)
−0.838435 + 0.545002i \(0.816529\pi\)
\(524\) 11.6107 + 20.1103i 0.507216 + 0.878524i
\(525\) 3.21702 12.0940i 0.140402 0.527824i
\(526\) −3.34548 + 1.93151i −0.145870 + 0.0842179i
\(527\) 29.5575i 1.28755i
\(528\) 4.14981 2.39590i 0.180597 0.104268i
\(529\) −11.5863 + 20.0681i −0.503753 + 0.872525i
\(530\) 0.305000 + 0.528275i 0.0132483 + 0.0229468i
\(531\) −2.63992 1.52416i −0.114563 0.0661427i
\(532\) 6.41444 + 23.7661i 0.278101 + 1.03039i
\(533\) −38.2136 4.15850i −1.65521 0.180125i
\(534\) −0.709770 + 1.22936i −0.0307147 + 0.0531995i
\(535\) 10.1109i 0.437134i
\(536\) −4.09611 −0.176925
\(537\) 5.67810 0.245028
\(538\) 6.65958i 0.287115i
\(539\) 15.1725 0.0551567i 0.653524 0.00237577i
\(540\) −0.758315 + 0.437813i −0.0326327 + 0.0188405i
\(541\) −7.81869 4.51412i −0.336152 0.194077i 0.322417 0.946598i \(-0.395505\pi\)
−0.658569 + 0.752520i \(0.728838\pi\)
\(542\) 3.85497 6.67700i 0.165585 0.286802i
\(543\) 9.94903 0.426954
\(544\) 23.0934 13.3330i 0.990119 0.571646i
\(545\) −8.48379 −0.363406
\(546\) −5.28724 + 0.827345i −0.226273 + 0.0354071i
\(547\) −24.3206 −1.03987 −0.519936 0.854205i \(-0.674044\pi\)
−0.519936 + 0.854205i \(0.674044\pi\)
\(548\) 2.36626 1.36616i 0.101082 0.0583595i
\(549\) 6.24908 0.266704
\(550\) 2.87579 4.98101i 0.122624 0.212391i
\(551\) 36.4668 + 21.0541i 1.55354 + 0.896935i
\(552\) 12.1662 7.02415i 0.517827 0.298968i
\(553\) −12.6768 + 3.42144i −0.539072 + 0.145495i
\(554\) 6.29216i 0.267328i
\(555\) −3.03802 −0.128957
\(556\) −12.3658 −0.524425
\(557\) 27.5933i 1.16916i 0.811335 + 0.584582i \(0.198742\pi\)
−0.811335 + 0.584582i \(0.801258\pi\)
\(558\) 1.67120 2.89460i 0.0707475 0.122538i
\(559\) −12.3316 9.02891i −0.521573 0.381882i
\(560\) 2.14500 2.15281i 0.0906427 0.0909728i
\(561\) 9.31241 + 5.37652i 0.393170 + 0.226997i
\(562\) 0.509430 + 0.882358i 0.0214890 + 0.0372200i
\(563\) 3.85215 6.67211i 0.162349 0.281196i −0.773362 0.633965i \(-0.781426\pi\)
0.935711 + 0.352769i \(0.114760\pi\)
\(564\) 16.3367 9.43201i 0.687900 0.397159i
\(565\) 6.44268i 0.271045i
\(566\) −14.9822 + 8.64995i −0.629747 + 0.363584i
\(567\) −1.87423 1.86743i −0.0787101 0.0784245i
\(568\) 10.2828 + 17.8104i 0.431459 + 0.747308i
\(569\) 11.6240 + 20.1333i 0.487302 + 0.844033i 0.999893 0.0146003i \(-0.00464758\pi\)
−0.512591 + 0.858633i \(0.671314\pi\)
\(570\) 1.60921i 0.0674024i
\(571\) −2.06269 3.57268i −0.0863209 0.149512i 0.819632 0.572890i \(-0.194178\pi\)
−0.905953 + 0.423378i \(0.860844\pi\)
\(572\) 13.0933 + 1.42484i 0.547458 + 0.0595757i
\(573\) −9.50875 −0.397234
\(574\) −11.2095 11.1688i −0.467874 0.466177i
\(575\) −16.0704 + 27.8348i −0.670183 + 1.16079i
\(576\) 1.40606 0.0585859
\(577\) 6.14307 3.54670i 0.255739 0.147651i −0.366650 0.930359i \(-0.619495\pi\)
0.622389 + 0.782708i \(0.286162\pi\)
\(578\) 3.69806 + 2.13507i 0.153819 + 0.0888074i
\(579\) 3.11196i 0.129329i
\(580\) 6.67852i 0.277310i
\(581\) −6.83334 + 6.85822i −0.283495 + 0.284527i
\(582\) 2.59748 4.49896i 0.107669 0.186488i
\(583\) 3.92838 2.26805i 0.162697 0.0939330i
\(584\) −2.94933 5.10838i −0.122044 0.211386i
\(585\) −1.86235 0.202666i −0.0769988 0.00837920i
\(586\) 0.307296 0.532253i 0.0126943 0.0219871i
\(587\) −1.42269 0.821391i −0.0587208 0.0339025i 0.470352 0.882479i \(-0.344127\pi\)
−0.529073 + 0.848576i \(0.677460\pi\)
\(588\) 10.2379 + 5.86131i 0.422202 + 0.241716i
\(589\) −16.4465 28.4861i −0.677665 1.17375i
\(590\) −0.769480 0.444260i −0.0316790 0.0182899i
\(591\) −4.41349 2.54813i −0.181547 0.104816i
\(592\) 11.1947 + 6.46326i 0.460099 + 0.265638i
\(593\) −37.1597 21.4542i −1.52597 0.881016i −0.999525 0.0308039i \(-0.990193\pi\)
−0.526440 0.850212i \(-0.676473\pi\)
\(594\) −0.607984 1.05306i −0.0249459 0.0432075i
\(595\) 6.59054 + 1.75310i 0.270186 + 0.0718699i
\(596\) −1.56880 0.905747i −0.0642606 0.0371009i
\(597\) 6.95536 12.0470i 0.284664 0.493053i
\(598\) 13.6637 + 1.48692i 0.558751 + 0.0608047i
\(599\) 15.5990 + 27.0183i 0.637358 + 1.10394i 0.986010 + 0.166684i \(0.0533060\pi\)
−0.348653 + 0.937252i \(0.613361\pi\)
\(600\) 8.46891 4.88953i 0.345742 0.199614i
\(601\) −17.5568 + 30.4093i −0.716157 + 1.24042i 0.246354 + 0.969180i \(0.420767\pi\)
−0.962511 + 0.271241i \(0.912566\pi\)
\(602\) −1.63945 6.07432i −0.0668189 0.247571i
\(603\) 1.98125i 0.0806828i
\(604\) 21.1545i 0.860764i
\(605\) −2.83563 1.63715i −0.115285 0.0665596i
\(606\) −4.39391 + 2.53683i −0.178490 + 0.103051i
\(607\) −2.31771 −0.0940730 −0.0470365 0.998893i \(-0.514978\pi\)
−0.0470365 + 0.998893i \(0.514978\pi\)
\(608\) −14.8375 + 25.6993i −0.601741 + 1.04225i
\(609\) 19.4824 5.25826i 0.789465 0.213075i
\(610\) 1.82148 0.0737494
\(611\) 40.1215 + 4.36613i 1.62314 + 0.176635i
\(612\) 4.18036 + 7.24059i 0.168981 + 0.292683i
\(613\) 17.0601i 0.689050i −0.938777 0.344525i \(-0.888040\pi\)
0.938777 0.344525i \(-0.111960\pi\)
\(614\) 1.37514 + 2.38181i 0.0554960 + 0.0961219i
\(615\) −2.76961 4.79711i −0.111681 0.193438i
\(616\) 8.39875 + 8.36827i 0.338395 + 0.337167i
\(617\) −20.5147 + 11.8442i −0.825890 + 0.476828i −0.852443 0.522820i \(-0.824880\pi\)
0.0265537 + 0.999647i \(0.491547\pi\)
\(618\) 9.90598i 0.398477i
\(619\) 13.5416 7.81825i 0.544283 0.314242i −0.202530 0.979276i \(-0.564916\pi\)
0.746813 + 0.665034i \(0.231583\pi\)
\(620\) −2.60847 + 4.51801i −0.104759 + 0.181447i
\(621\) 3.39752 + 5.88468i 0.136338 + 0.236144i
\(622\) 5.62359 + 3.24678i 0.225485 + 0.130184i
\(623\) 6.46979 + 1.72098i 0.259206 + 0.0689494i
\(624\) 6.43135 + 4.70887i 0.257460 + 0.188506i
\(625\) −10.5118 + 18.2069i −0.420471 + 0.728277i
\(626\) 2.84404i 0.113671i
\(627\) −11.9665 −0.477895
\(628\) −1.16658 −0.0465515
\(629\) 29.0078i 1.15662i
\(630\) −0.546298 0.544315i −0.0217650 0.0216860i
\(631\) −19.8241 + 11.4455i −0.789186 + 0.455637i −0.839676 0.543088i \(-0.817255\pi\)
0.0504898 + 0.998725i \(0.483922\pi\)
\(632\) −8.88569 5.13015i −0.353454 0.204067i
\(633\) 6.30791 10.9256i 0.250717 0.434255i
\(634\) 9.64738 0.383146
\(635\) −9.15004 + 5.28278i −0.363108 + 0.209641i
\(636\) 3.52691 0.139851
\(637\) 10.2646 + 23.0573i 0.406699 + 0.913562i
\(638\) 9.27434 0.367175
\(639\) −8.61474 + 4.97372i −0.340794 + 0.196757i
\(640\) 5.99534 0.236986
\(641\) 23.1024 40.0145i 0.912490 1.58048i 0.101954 0.994789i \(-0.467491\pi\)
0.810536 0.585689i \(-0.199176\pi\)
\(642\) −9.45446 5.45853i −0.373138 0.215431i
\(643\) 8.19662 4.73232i 0.323243 0.186625i −0.329594 0.944123i \(-0.606912\pi\)
0.652837 + 0.757498i \(0.273579\pi\)
\(644\) −21.4628 21.3849i −0.845753 0.842684i
\(645\) 2.20243i 0.0867206i
\(646\) −15.3652 −0.604535
\(647\) 5.70593 0.224323 0.112162 0.993690i \(-0.464223\pi\)
0.112162 + 0.993690i \(0.464223\pi\)
\(648\) 2.06743i 0.0812165i
\(649\) −3.30362 + 5.72204i −0.129678 + 0.224610i
\(650\) 9.51134 + 1.03505i 0.373065 + 0.0405979i
\(651\) −15.2335 4.05215i −0.597049 0.158816i
\(652\) 15.1749 + 8.76124i 0.594295 + 0.343117i
\(653\) −16.5067 28.5904i −0.645956 1.11883i −0.984080 0.177727i \(-0.943126\pi\)
0.338124 0.941101i \(-0.390208\pi\)
\(654\) 4.58010 7.93296i 0.179096 0.310203i
\(655\) −6.20002 + 3.57959i −0.242255 + 0.139866i
\(656\) 23.5689i 0.920211i
\(657\) 2.47088 1.42656i 0.0963982 0.0556555i
\(658\) 11.7691 + 11.7264i 0.458809 + 0.457144i
\(659\) −11.4177 19.7760i −0.444770 0.770363i 0.553267 0.833004i \(-0.313381\pi\)
−0.998036 + 0.0626408i \(0.980048\pi\)
\(660\) 0.948964 + 1.64365i 0.0369384 + 0.0639791i
\(661\) 1.83380i 0.0713266i −0.999364 0.0356633i \(-0.988646\pi\)
0.999364 0.0356633i \(-0.0113544\pi\)
\(662\) 5.72815 + 9.92144i 0.222631 + 0.385608i
\(663\) −1.93511 + 17.7822i −0.0751534 + 0.690604i
\(664\) −7.56522 −0.293587
\(665\) −7.32710 + 1.97757i −0.284133 + 0.0766870i
\(666\) 1.64012 2.84077i 0.0635533 0.110078i
\(667\) −51.8267 −2.00674
\(668\) −35.2401 + 20.3459i −1.36348 + 0.787206i
\(669\) −0.659526 0.380777i −0.0254987 0.0147217i
\(670\) 0.577494i 0.0223105i
\(671\) 13.5449i 0.522896i
\(672\) 3.70567 + 13.7299i 0.142949 + 0.529641i
\(673\) 14.8231 25.6743i 0.571387 0.989672i −0.425037 0.905176i \(-0.639739\pi\)
0.996424 0.0844955i \(-0.0269278\pi\)
\(674\) 6.40685 3.69900i 0.246783 0.142480i
\(675\) 2.36502 + 4.09634i 0.0910297 + 0.157668i
\(676\) 6.61677 + 20.8856i 0.254491 + 0.803292i
\(677\) −21.1048 + 36.5546i −0.811124 + 1.40491i 0.100954 + 0.994891i \(0.467811\pi\)
−0.912078 + 0.410017i \(0.865523\pi\)
\(678\) 6.02437 + 3.47817i 0.231365 + 0.133578i
\(679\) −23.6769 6.29809i −0.908635 0.241699i
\(680\) 2.66452 + 4.61508i 0.102180 + 0.176980i
\(681\) −1.33416 0.770280i −0.0511252 0.0295172i
\(682\) −6.27407 3.62234i −0.240247 0.138707i
\(683\) 21.5544 + 12.4444i 0.824757 + 0.476173i 0.852054 0.523454i \(-0.175357\pi\)
−0.0272974 + 0.999627i \(0.508690\pi\)
\(684\) −8.05765 4.65209i −0.308092 0.177877i
\(685\) 0.421188 + 0.729519i 0.0160928 + 0.0278735i
\(686\) −2.63432 + 10.0503i −0.100579 + 0.383723i
\(687\) −4.86535 2.80901i −0.185625 0.107171i
\(688\) −4.68558 + 8.11566i −0.178636 + 0.309407i
\(689\) 6.08817 + 4.45760i 0.231941 + 0.169821i
\(690\) 0.990307 + 1.71526i 0.0377003 + 0.0652989i
\(691\) 32.5266 18.7792i 1.23737 0.714396i 0.268815 0.963192i \(-0.413368\pi\)
0.968556 + 0.248796i \(0.0800347\pi\)
\(692\) −3.15028 + 5.45644i −0.119756 + 0.207423i
\(693\) −4.04766 + 4.06240i −0.153758 + 0.154318i
\(694\) 4.87368i 0.185002i
\(695\) 3.81237i 0.144611i
\(696\) 13.6560 + 7.88430i 0.517629 + 0.298853i
\(697\) −45.8040 + 26.4450i −1.73495 + 1.00167i
\(698\) −19.5785 −0.741059
\(699\) 8.57478 14.8520i 0.324328 0.561753i
\(700\) −14.9403 14.8861i −0.564691 0.562642i
\(701\) 36.1312 1.36466 0.682328 0.731046i \(-0.260968\pi\)
0.682328 + 0.731046i \(0.260968\pi\)
\(702\) 1.19492 1.63202i 0.0450995 0.0615967i
\(703\) −16.1406 27.9564i −0.608755 1.05439i
\(704\) 3.04765i 0.114863i
\(705\) 2.90789 + 5.03662i 0.109518 + 0.189690i
\(706\) 4.07125 + 7.05161i 0.153223 + 0.265391i
\(707\) 16.9505 + 16.8890i 0.637488 + 0.635174i
\(708\) −4.44900 + 2.56863i −0.167204 + 0.0965351i
\(709\) 25.0157i 0.939486i 0.882803 + 0.469743i \(0.155653\pi\)
−0.882803 + 0.469743i \(0.844347\pi\)
\(710\) −2.51102 + 1.44974i −0.0942368 + 0.0544076i
\(711\) 2.48141 4.29793i 0.0930602 0.161185i
\(712\) 2.61570 + 4.53053i 0.0980275 + 0.169789i
\(713\) 35.0607 + 20.2423i 1.31303 + 0.758079i
\(714\) −5.19727 + 5.21620i −0.194503 + 0.195211i
\(715\) −0.439280 + 4.03666i −0.0164281 + 0.150963i
\(716\) 4.78460 8.28716i 0.178809 0.309706i
\(717\) 25.6658i 0.958506i
\(718\) 0.298481 0.0111392
\(719\) −6.63648 −0.247499 −0.123749 0.992314i \(-0.539492\pi\)
−0.123749 + 0.992314i \(0.539492\pi\)
\(720\) 1.14864i 0.0428072i
\(721\) 45.1042 12.1735i 1.67977 0.453367i
\(722\) 5.57729 3.22005i 0.207565 0.119838i
\(723\) −4.08520 2.35859i −0.151930 0.0877170i
\(724\) 8.38346 14.5206i 0.311569 0.539653i
\(725\) −36.0767 −1.33985
\(726\) 3.06171 1.76768i 0.113631 0.0656047i
\(727\) 18.2640 0.677375 0.338688 0.940899i \(-0.390017\pi\)
0.338688 + 0.940899i \(0.390017\pi\)
\(728\) −7.10197 + 18.3990i −0.263216 + 0.681911i
\(729\) 1.00000 0.0370370
\(730\) 0.720210 0.415813i 0.0266562 0.0153899i
\(731\) −21.0294 −0.777800
\(732\) 5.26573 9.12050i 0.194627 0.337104i
\(733\) −26.5047 15.3025i −0.978972 0.565210i −0.0770123 0.997030i \(-0.524538\pi\)
−0.901960 + 0.431820i \(0.857871\pi\)
\(734\) −2.84345 + 1.64166i −0.104953 + 0.0605949i
\(735\) −1.80704 + 3.15633i −0.0666538 + 0.116423i
\(736\) 36.5240i 1.34629i
\(737\) −4.29438 −0.158186
\(738\) 5.98086 0.220158
\(739\) 34.9923i 1.28721i −0.765356 0.643607i \(-0.777437\pi\)
0.765356 0.643607i \(-0.222563\pi\)
\(740\) −2.55996 + 4.43398i −0.0941060 + 0.162996i
\(741\) −8.02947 18.2144i −0.294970 0.669122i
\(742\) 0.809400 + 2.99891i 0.0297140 + 0.110093i
\(743\) 6.87469 + 3.96910i 0.252208 + 0.145612i 0.620775 0.783989i \(-0.286818\pi\)
−0.368567 + 0.929601i \(0.620151\pi\)
\(744\) −6.15884 10.6674i −0.225794 0.391087i
\(745\) 0.279242 0.483662i 0.0102306 0.0177200i
\(746\) −11.7824 + 6.80258i −0.431385 + 0.249060i
\(747\) 3.65923i 0.133884i
\(748\) 15.6940 9.06096i 0.573831 0.331301i
\(749\) −13.2353 + 49.7563i −0.483607 + 1.81806i
\(750\) 1.41805 + 2.45614i 0.0517800 + 0.0896855i
\(751\) 15.4194 + 26.7072i 0.562662 + 0.974559i 0.997263 + 0.0739360i \(0.0235560\pi\)
−0.434601 + 0.900623i \(0.643111\pi\)
\(752\) 24.7457i 0.902381i
\(753\) 0.0982527 + 0.170179i 0.00358053 + 0.00620165i
\(754\) 6.22305 + 14.1166i 0.226630 + 0.514098i
\(755\) 6.52194 0.237358
\(756\) −4.30480 + 1.16186i −0.156564 + 0.0422564i
\(757\) 3.83594 6.64405i 0.139420 0.241482i −0.787857 0.615858i \(-0.788810\pi\)
0.927277 + 0.374376i \(0.122143\pi\)
\(758\) 0.776901 0.0282183
\(759\) 12.7551 7.36416i 0.462981 0.267302i
\(760\) −5.13587 2.96520i −0.186298 0.107559i
\(761\) 28.3330i 1.02707i −0.858068 0.513535i \(-0.828335\pi\)
0.858068 0.513535i \(-0.171665\pi\)
\(762\) 11.4079i 0.413266i
\(763\) −41.7491 11.1053i −1.51142 0.402041i
\(764\) −8.01246 + 13.8780i −0.289881 + 0.502088i
\(765\) −2.23228 + 1.28880i −0.0807081 + 0.0465968i
\(766\) 5.53657 + 9.58962i 0.200044 + 0.346487i
\(767\) −10.9263 1.18903i −0.394527 0.0429335i
\(768\) −1.83061 + 3.17070i −0.0660563 + 0.114413i
\(769\) 8.61926 + 4.97633i 0.310819 + 0.179451i 0.647293 0.762242i \(-0.275901\pi\)
−0.336474 + 0.941693i \(0.609234\pi\)
\(770\) −1.17981 + 1.18410i −0.0425173 + 0.0426722i
\(771\) −0.753004 1.30424i −0.0271188 0.0469711i
\(772\) 4.54190 + 2.62227i 0.163466 + 0.0943774i
\(773\) −31.8718 18.4012i −1.14635 0.661844i −0.198353 0.980131i \(-0.563559\pi\)
−0.947995 + 0.318286i \(0.896893\pi\)
\(774\) 2.05943 + 1.18901i 0.0740248 + 0.0427382i
\(775\) 24.4058 + 14.0907i 0.876682 + 0.506153i
\(776\) −9.57244 16.5799i −0.343630 0.595185i
\(777\) −14.9502 3.97679i −0.536337 0.142667i
\(778\) −2.41581 1.39477i −0.0866111 0.0500050i
\(779\) 29.4292 50.9728i 1.05441 1.82629i
\(780\) −1.86508 + 2.54732i −0.0667807 + 0.0912087i
\(781\) 10.7806 + 18.6725i 0.385760 + 0.668155i
\(782\) 16.3778 9.45571i 0.585668 0.338136i
\(783\) −3.81357 + 6.60529i −0.136286 + 0.236054i
\(784\) 13.3737 7.78625i 0.477631 0.278080i
\(785\) 0.359656i 0.0128367i
\(786\) 7.72996i 0.275719i
\(787\) −12.4610 7.19437i −0.444187 0.256451i 0.261185 0.965289i \(-0.415887\pi\)
−0.705372 + 0.708837i \(0.749220\pi\)
\(788\) −7.43798 + 4.29432i −0.264967 + 0.152979i
\(789\) −6.88599 −0.245148
\(790\) 0.723279 1.25276i 0.0257331 0.0445711i
\(791\) 8.43351 31.7047i 0.299861 1.12729i
\(792\) −4.48118 −0.159232
\(793\) 20.6170 9.08860i 0.732130 0.322746i
\(794\) 2.75623 + 4.77392i 0.0978148 + 0.169420i
\(795\) 1.08735i 0.0385642i
\(796\) −11.7217 20.3027i −0.415466 0.719609i
\(797\) 15.6589 + 27.1221i 0.554668 + 0.960712i 0.997929 + 0.0643202i \(0.0204879\pi\)
−0.443262 + 0.896392i \(0.646179\pi\)
\(798\) 2.10647 7.91900i 0.0745682 0.280329i
\(799\) 48.0910 27.7653i 1.70134 0.982267i
\(800\) 25.4244i 0.898888i
\(801\) −2.19138 + 1.26519i −0.0774285 + 0.0447034i
\(802\) 8.20728 14.2154i 0.289809 0.501964i
\(803\) −3.09209 5.35565i −0.109117 0.188997i
\(804\) −2.89163 1.66948i −0.101980 0.0588782i
\(805\) 6.59298 6.61699i 0.232372 0.233218i
\(806\) 1.30374 11.9805i 0.0459225 0.421994i
\(807\) −5.93548 + 10.2806i −0.208939 + 0.361893i
\(808\) 18.6978i 0.657787i
\(809\) 55.4621 1.94995 0.974973 0.222325i \(-0.0713647\pi\)
0.974973 + 0.222325i \(0.0713647\pi\)
\(810\) 0.291479 0.0102415
\(811\) 8.46874i 0.297378i −0.988884 0.148689i \(-0.952495\pi\)
0.988884 0.148689i \(-0.0475053\pi\)
\(812\) 8.74223 32.8653i 0.306792 1.15334i
\(813\) 11.9020 6.87163i 0.417422 0.240998i
\(814\) −6.15739 3.55497i −0.215817 0.124602i
\(815\) −2.70109 + 4.67843i −0.0946151 + 0.163878i
\(816\) 10.9675 0.383940
\(817\) 20.2671 11.7012i 0.709057 0.409374i
\(818\) −7.20315 −0.251852
\(819\) −8.89942 3.43516i −0.310971 0.120034i
\(820\) −9.33515 −0.325997
\(821\) −23.0243 + 13.2931i −0.803552 + 0.463931i −0.844712 0.535222i \(-0.820228\pi\)
0.0411597 + 0.999153i \(0.486895\pi\)
\(822\) −0.909537 −0.0317238
\(823\) 24.4813 42.4029i 0.853366 1.47807i −0.0247866 0.999693i \(-0.507891\pi\)
0.878153 0.478381i \(-0.158776\pi\)
\(824\) 31.6154 + 18.2532i 1.10138 + 0.635879i
\(825\) 8.87885 5.12620i 0.309122 0.178472i
\(826\) −3.20511 3.19348i −0.111520 0.111115i
\(827\) 16.8817i 0.587034i −0.955954 0.293517i \(-0.905174\pi\)
0.955954 0.293517i \(-0.0948257\pi\)
\(828\) 11.4516 0.397969
\(829\) 9.44160 0.327920 0.163960 0.986467i \(-0.447573\pi\)
0.163960 + 0.986467i \(0.447573\pi\)
\(830\) 1.06659i 0.0370218i
\(831\) 5.60801 9.71335i 0.194540 0.336952i
\(832\) 4.63889 2.04496i 0.160824 0.0708964i
\(833\) 30.1375 + 17.2541i 1.04420 + 0.597820i
\(834\) 3.56484 + 2.05816i 0.123440 + 0.0712683i
\(835\) −6.27264 10.8645i −0.217074 0.375983i
\(836\) −10.0834 + 17.4650i −0.348743 + 0.604041i
\(837\) 5.15974 2.97898i 0.178347 0.102969i
\(838\) 14.7939i 0.511045i
\(839\) −32.5016 + 18.7648i −1.12208 + 0.647833i −0.941931 0.335806i \(-0.890991\pi\)
−0.180149 + 0.983639i \(0.557658\pi\)
\(840\) −2.74384 + 0.740558i −0.0946714 + 0.0255517i
\(841\) −14.5866 25.2647i −0.502985 0.871195i
\(842\) 0.761211 + 1.31846i 0.0262330 + 0.0454370i
\(843\) 1.81616i 0.0625517i
\(844\) −10.6306 18.4128i −0.365921 0.633793i
\(845\) −6.43903 + 2.03995i −0.221509 + 0.0701764i
\(846\) −6.27947 −0.215893
\(847\) −11.8112 11.7683i −0.405838 0.404365i
\(848\) 2.31328 4.00672i 0.0794385 0.137591i
\(849\) −30.8377 −1.05835
\(850\) 11.4006 6.58214i 0.391037 0.225766i
\(851\) 34.4086 + 19.8658i 1.17951 + 0.680992i
\(852\) 16.7642i 0.574334i
\(853\) 35.3664i 1.21092i −0.795875 0.605461i \(-0.792989\pi\)
0.795875 0.605461i \(-0.207011\pi\)
\(854\) 8.96356 + 2.38432i 0.306727 + 0.0815899i
\(855\) 1.43424 2.48418i 0.0490500 0.0849571i
\(856\) −34.8423 + 20.1162i −1.19089 + 0.687559i
\(857\) −2.53098 4.38379i −0.0864568 0.149748i 0.819554 0.573002i \(-0.194221\pi\)
−0.906011 + 0.423254i \(0.860888\pi\)
\(858\) −3.53742 2.59001i −0.120766 0.0884214i
\(859\) 2.61058 4.52166i 0.0890719 0.154277i −0.818047 0.575151i \(-0.804943\pi\)
0.907119 + 0.420874i \(0.138277\pi\)
\(860\) −3.21444 1.85586i −0.109612 0.0632842i
\(861\) −7.34992 27.2322i −0.250485 0.928071i
\(862\) 10.4028 + 18.0181i 0.354319 + 0.613699i
\(863\) 1.53116 + 0.884017i 0.0521214 + 0.0300923i 0.525834 0.850587i \(-0.323753\pi\)
−0.473713 + 0.880679i \(0.657087\pi\)
\(864\) −4.65496 2.68754i −0.158365 0.0914321i
\(865\) −1.68222 0.971232i −0.0571973 0.0330229i
\(866\) −7.01100 4.04780i −0.238243 0.137550i
\(867\) 3.80585 + 6.59193i 0.129253 + 0.223874i
\(868\) −18.7505 + 18.8188i −0.636434 + 0.638751i
\(869\) −9.31580 5.37848i −0.316017 0.182452i
\(870\) −1.11157 + 1.92530i −0.0376859 + 0.0652739i
\(871\) −2.88152 6.53656i −0.0976364 0.221483i
\(872\) −16.8790 29.2352i −0.571593 0.990029i
\(873\) 8.01957 4.63010i 0.271421 0.156705i
\(874\) −10.5227 + 18.2259i −0.355937 + 0.616501i
\(875\) 9.44070 9.47509i 0.319154 0.320316i
\(876\) 4.80832i 0.162458i
\(877\) 56.8326i 1.91910i −0.281537 0.959550i \(-0.590844\pi\)
0.281537 0.959550i \(-0.409156\pi\)
\(878\) 7.10784 + 4.10371i 0.239878 + 0.138494i
\(879\) 0.948761 0.547767i 0.0320009 0.0184757i
\(880\) 2.48968 0.0839272
\(881\) 20.9164 36.2283i 0.704693 1.22056i −0.262110 0.965038i \(-0.584418\pi\)
0.966802 0.255525i \(-0.0822484\pi\)
\(882\) −1.97584 3.39371i −0.0665301 0.114272i
\(883\) −8.23784 −0.277225 −0.138613 0.990347i \(-0.544264\pi\)
−0.138613 + 0.990347i \(0.544264\pi\)
\(884\) 24.3225 + 17.8083i 0.818054 + 0.598958i
\(885\) −0.791910 1.37163i −0.0266198 0.0461068i
\(886\) 20.5375i 0.689972i
\(887\) 27.3772 + 47.4187i 0.919236 + 1.59216i 0.800578 + 0.599229i \(0.204526\pi\)
0.118659 + 0.992935i \(0.462141\pi\)
\(888\) −6.04430 10.4690i −0.202834 0.351318i
\(889\) −51.9429 + 14.0193i −1.74211 + 0.470192i
\(890\) −0.638741 + 0.368777i −0.0214106 + 0.0123614i
\(891\) 2.16751i 0.0726143i
\(892\) −1.11149 + 0.641717i −0.0372153 + 0.0214863i
\(893\) −30.8985 + 53.5178i −1.03398 + 1.79090i
\(894\) 0.301506 + 0.522223i 0.0100839 + 0.0174658i
\(895\) 2.55493 + 1.47509i 0.0854020 + 0.0493069i
\(896\) 29.5033 + 7.84794i 0.985636 + 0.262181i
\(897\) 19.7677 + 14.4734i 0.660026 + 0.483254i
\(898\) 1.81166 3.13789i 0.0604559 0.104713i
\(899\) 45.4421i 1.51558i
\(900\) 7.97146 0.265715
\(901\) 10.3823 0.345884
\(902\) 12.9636i 0.431639i
\(903\) 2.88300 10.8383i 0.0959402 0.360675i
\(904\) 22.2015 12.8180i 0.738411 0.426322i
\(905\) 4.47670 + 2.58462i 0.148810 + 0.0859158i
\(906\) −3.52096 + 6.09848i −0.116976 + 0.202609i
\(907\) 11.5571 0.383748 0.191874 0.981420i \(-0.438543\pi\)
0.191874 + 0.981420i \(0.438543\pi\)
\(908\) −2.24844 + 1.29814i −0.0746171 + 0.0430802i
\(909\) −9.04398 −0.299970
\(910\) −2.59400 1.00128i −0.0859901 0.0331920i
\(911\) 23.9338 0.792961 0.396481 0.918043i \(-0.370231\pi\)
0.396481 + 0.918043i \(0.370231\pi\)
\(912\) −10.5700 + 6.10257i −0.350006 + 0.202076i
\(913\) −7.93141 −0.262491
\(914\) −5.38388 + 9.32516i −0.178083 + 0.308449i
\(915\) 2.81185 + 1.62342i 0.0929570 + 0.0536688i
\(916\) −8.19949 + 4.73398i −0.270919 + 0.156415i
\(917\) −35.1963 + 9.49942i −1.16228 + 0.313698i
\(918\) 2.78312i 0.0918566i
\(919\) 3.13809 0.103516 0.0517580 0.998660i \(-0.483518\pi\)
0.0517580 + 0.998660i \(0.483518\pi\)
\(920\) 7.29912 0.240645
\(921\) 4.90247i 0.161542i
\(922\) 1.78206 3.08662i 0.0586891 0.101653i
\(923\) −21.1880 + 28.9385i −0.697413 + 0.952523i
\(924\) 2.51834 + 9.33069i 0.0828472 + 0.306957i
\(925\) 23.9519 + 13.8286i 0.787534 + 0.454683i
\(926\) −3.03777 5.26157i −0.0998272 0.172906i
\(927\) −8.82890 + 15.2921i −0.289979 + 0.502258i
\(928\) 35.5040 20.4982i 1.16548 0.672888i
\(929\) 21.1971i 0.695455i −0.937596 0.347728i \(-0.886953\pi\)
0.937596 0.347728i \(-0.113047\pi\)
\(930\) 1.50396 0.868310i 0.0493167 0.0284730i
\(931\) −38.6457 + 0.140489i −1.26656 + 0.00460435i
\(932\) −14.4509 25.0297i −0.473356 0.819876i
\(933\) 5.78751 + 10.0243i 0.189474 + 0.328179i
\(934\) 6.55258i 0.214407i
\(935\) 2.79350 + 4.83848i 0.0913571 + 0.158235i
\(936\) −3.00686 6.82089i −0.0982822 0.222948i
\(937\) −26.0293 −0.850339 −0.425169 0.905114i \(-0.639786\pi\)
−0.425169 + 0.905114i \(0.639786\pi\)
\(938\) 0.755943 2.84187i 0.0246824 0.0927904i
\(939\) −2.53480 + 4.39041i −0.0827201 + 0.143275i
\(940\) 9.80124 0.319681
\(941\) −14.2589 + 8.23240i −0.464828 + 0.268369i −0.714072 0.700072i \(-0.753151\pi\)
0.249244 + 0.968441i \(0.419818\pi\)
\(942\) 0.336305 + 0.194166i 0.0109574 + 0.00632625i
\(943\) 72.4427i 2.35906i
\(944\) 6.73902i 0.219336i
\(945\) −0.358201 1.32717i −0.0116523 0.0431729i
\(946\) 2.57720 4.46384i 0.0837919 0.145132i
\(947\) 12.3262 7.11651i 0.400546 0.231255i −0.286173 0.958178i \(-0.592383\pi\)
0.686720 + 0.726922i \(0.259050\pi\)
\(948\) −4.18188 7.24322i −0.135821 0.235249i
\(949\) 6.07716 8.30015i 0.197273 0.269434i
\(950\) −7.32490 + 12.6871i −0.237651 + 0.411624i
\(951\) 14.8929 + 8.59841i 0.482935 + 0.278823i
\(952\) 7.07104 + 26.1989i 0.229174 + 0.849111i
\(953\) −22.2750 38.5815i −0.721559 1.24978i −0.960375 0.278712i \(-0.910092\pi\)
0.238815 0.971065i \(-0.423241\pi\)
\(954\) −1.01675 0.587020i −0.0329184 0.0190055i
\(955\) −4.27859 2.47024i −0.138452 0.0799352i
\(956\) −37.4591 21.6270i −1.21151 0.699468i
\(957\) 14.3170 + 8.26593i 0.462803 + 0.267200i
\(958\) −6.73859 11.6716i −0.217714 0.377092i
\(959\) 1.11774 + 4.14133i 0.0360937 + 0.133731i
\(960\) 0.632676 + 0.365276i 0.0204195 + 0.0117892i
\(961\) 2.24861 3.89472i 0.0725360 0.125636i
\(962\) 1.27950 11.7577i 0.0412527 0.379082i
\(963\) −9.73005 16.8529i −0.313546 0.543078i
\(964\) −6.88471 + 3.97489i −0.221742 + 0.128023i
\(965\) −0.808445 + 1.40027i −0.0260248 + 0.0450762i
\(966\) 2.62805 + 9.73719i 0.0845562 + 0.313289i
\(967\) 17.7030i 0.569289i 0.958633 + 0.284645i \(0.0918756\pi\)
−0.958633 + 0.284645i \(0.908124\pi\)
\(968\) 13.0288i 0.418761i
\(969\) −23.7196 13.6945i −0.761983 0.439931i
\(970\) 2.33754 1.34958i 0.0750538 0.0433324i
\(971\) 6.32688 0.203039 0.101520 0.994834i \(-0.467630\pi\)
0.101520 + 0.994834i \(0.467630\pi\)
\(972\) 0.842641 1.45950i 0.0270277 0.0468134i
\(973\) 4.99042 18.7608i 0.159985 0.601444i
\(974\) −3.38858 −0.108577
\(975\) 13.7604 + 10.0750i 0.440684 + 0.322658i
\(976\) −6.90753 11.9642i −0.221105 0.382965i
\(977\) 9.17489i 0.293531i −0.989171 0.146765i \(-0.953114\pi\)
0.989171 0.146765i \(-0.0468862\pi\)
\(978\) −2.91645 5.05143i −0.0932577 0.161527i
\(979\) 2.74231 + 4.74983i 0.0876447 + 0.151805i
\(980\) 3.08397 + 5.29703i 0.0985138 + 0.169207i
\(981\) 14.1408 8.16420i 0.451481 0.260663i
\(982\) 7.91709i 0.252644i
\(983\) −42.7704 + 24.6935i −1.36416 + 0.787601i −0.990175 0.139832i \(-0.955344\pi\)
−0.373990 + 0.927433i \(0.622010\pi\)
\(984\) 11.0206 19.0882i 0.351323 0.608509i
\(985\) −1.32394 2.29313i −0.0421842 0.0730652i
\(986\) 18.3833 + 10.6136i 0.585444 + 0.338006i
\(987\) 7.71690 + 28.5919i 0.245632 + 0.910089i
\(988\) −33.3498 3.62921i −1.06100 0.115461i
\(989\) −14.4018 + 24.9447i −0.457952 + 0.793196i
\(990\) 0.631783i 0.0200794i
\(991\) 35.8929 1.14018 0.570088 0.821584i \(-0.306909\pi\)
0.570088 + 0.821584i \(0.306909\pi\)
\(992\) −32.0245 −1.01678
\(993\) 20.4213i 0.648050i
\(994\) −14.2545 + 3.84728i −0.452126 + 0.122028i
\(995\) 6.25932 3.61382i 0.198434 0.114566i
\(996\) −5.34063 3.08342i −0.169224 0.0977018i
\(997\) −21.1225 + 36.5853i −0.668957 + 1.15867i 0.309239 + 0.950984i \(0.399926\pi\)
−0.978196 + 0.207684i \(0.933408\pi\)
\(998\) −18.4282 −0.583336
\(999\) 5.06378 2.92358i 0.160211 0.0924979i
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 273.2.bl.d.121.5 yes 20
3.2 odd 2 819.2.do.g.667.6 20
7.4 even 3 273.2.t.d.4.5 20
13.10 even 6 273.2.t.d.205.6 yes 20
21.11 odd 6 819.2.bm.g.550.6 20
39.23 odd 6 819.2.bm.g.478.5 20
91.88 even 6 inner 273.2.bl.d.88.5 yes 20
273.179 odd 6 819.2.do.g.361.6 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.t.d.4.5 20 7.4 even 3
273.2.t.d.205.6 yes 20 13.10 even 6
273.2.bl.d.88.5 yes 20 91.88 even 6 inner
273.2.bl.d.121.5 yes 20 1.1 even 1 trivial
819.2.bm.g.478.5 20 39.23 odd 6
819.2.bm.g.550.6 20 21.11 odd 6
819.2.do.g.361.6 20 273.179 odd 6
819.2.do.g.667.6 20 3.2 odd 2