Properties

Label 287.2.e.c.247.4
Level $287$
Weight $2$
Character 287.247
Analytic conductor $2.292$
Analytic rank $0$
Dimension $10$
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] = [287,2,Mod(165,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.e (of order \(3\), 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: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} + 4x^{7} + 32x^{6} + 3x^{5} + 30x^{4} - 7x^{3} + 26x^{2} - 5x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 247.4
Root \(0.100998 - 0.174933i\) of defining polynomial
Character \(\chi\) \(=\) 287.247
Dual form 287.2.e.c.165.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.894706 - 1.54968i) q^{2} +(1.16033 + 2.00974i) q^{3} +(-0.600998 - 1.04096i) q^{4} +(-1.16033 + 2.00974i) q^{5} +4.15260 q^{6} +(-1.87001 + 1.87165i) q^{7} +1.42796 q^{8} +(-1.19271 + 2.06584i) q^{9} +O(q^{10})\) \(q+(0.894706 - 1.54968i) q^{2} +(1.16033 + 2.00974i) q^{3} +(-0.600998 - 1.04096i) q^{4} +(-1.16033 + 2.00974i) q^{5} +4.15260 q^{6} +(-1.87001 + 1.87165i) q^{7} +1.42796 q^{8} +(-1.19271 + 2.06584i) q^{9} +(2.07630 + 3.59626i) q^{10} +(-1.05503 - 1.82737i) q^{11} +(1.39471 - 2.41570i) q^{12} +2.32065 q^{13} +(1.22734 + 4.57248i) q^{14} -5.38542 q^{15} +(2.47960 - 4.29479i) q^{16} +(0.622267 + 1.07780i) q^{17} +(2.13425 + 3.69663i) q^{18} +(1.21965 - 2.11250i) q^{19} +2.78941 q^{20} +(-5.93135 - 1.58652i) q^{21} -3.77577 q^{22} +(2.93363 - 5.08120i) q^{23} +(1.65690 + 2.86983i) q^{24} +(-0.192711 - 0.333784i) q^{25} +(2.07630 - 3.59626i) q^{26} +1.42622 q^{27} +(3.07218 + 0.821745i) q^{28} -6.48184 q^{29} +(-4.81837 + 8.34566i) q^{30} +(-1.26649 - 2.19362i) q^{31} +(-3.00907 - 5.21185i) q^{32} +(2.44836 - 4.24068i) q^{33} +2.22698 q^{34} +(-1.59171 - 5.92996i) q^{35} +2.86727 q^{36} +(0.200618 - 0.347480i) q^{37} +(-2.18246 - 3.78014i) q^{38} +(2.69271 + 4.66391i) q^{39} +(-1.65690 + 2.86983i) q^{40} -1.00000 q^{41} +(-7.76540 + 7.77221i) q^{42} -0.872387 q^{43} +(-1.26814 + 2.19649i) q^{44} +(-2.76786 - 4.79408i) q^{45} +(-5.24948 - 9.09236i) q^{46} +(1.99209 - 3.45041i) q^{47} +11.5086 q^{48} +(-0.00613483 - 7.00000i) q^{49} -0.689677 q^{50} +(-1.44406 + 2.50119i) q^{51} +(-1.39471 - 2.41570i) q^{52} +(-6.03889 - 10.4597i) q^{53} +(1.27605 - 2.21018i) q^{54} +4.89672 q^{55} +(-2.67030 + 2.67264i) q^{56} +5.66078 q^{57} +(-5.79935 + 10.0448i) q^{58} +(5.25973 + 9.11011i) q^{59} +(3.23663 + 5.60600i) q^{60} +(-1.91374 + 3.31470i) q^{61} -4.53254 q^{62} +(-1.63614 - 6.09546i) q^{63} -0.850520 q^{64} +(-2.69271 + 4.66391i) q^{65} +(-4.38112 - 7.58833i) q^{66} +(6.54117 + 11.3296i) q^{67} +(0.747962 - 1.29551i) q^{68} +13.6159 q^{69} +(-10.6136 - 2.83893i) q^{70} -8.22415 q^{71} +(-1.70314 + 2.94993i) q^{72} +(-3.22464 - 5.58524i) q^{73} +(-0.358988 - 0.621786i) q^{74} +(0.447214 - 0.774597i) q^{75} -2.93204 q^{76} +(5.39311 + 1.44255i) q^{77} +9.63674 q^{78} +(-2.09053 + 3.62090i) q^{79} +(5.75428 + 9.96671i) q^{80} +(5.23301 + 9.06385i) q^{81} +(-0.894706 + 1.54968i) q^{82} +4.83369 q^{83} +(1.91323 + 7.12778i) q^{84} -2.88813 q^{85} +(-0.780530 + 1.35192i) q^{86} +(-7.52105 - 13.0268i) q^{87} +(-1.50654 - 2.60941i) q^{88} +(-6.26243 + 10.8469i) q^{89} -9.90570 q^{90} +(-4.33964 + 4.34344i) q^{91} -7.05243 q^{92} +(2.93907 - 5.09063i) q^{93} +(-3.56467 - 6.17420i) q^{94} +(2.83039 + 4.90238i) q^{95} +(6.98299 - 12.0949i) q^{96} -12.4400 q^{97} +(-10.8532 - 6.25343i) q^{98} +5.03339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{2} + 2 q^{3} - 6 q^{4} - 2 q^{5} + 2 q^{6} + 8 q^{7} - 6 q^{8} - 5 q^{9} + q^{10} + 6 q^{11} + 7 q^{12} + 4 q^{13} - 24 q^{14} - 40 q^{15} + 12 q^{16} + 3 q^{17} + 8 q^{18} - 7 q^{19} + 14 q^{20} - 15 q^{21} - 26 q^{22} - 16 q^{24} + 5 q^{25} + q^{26} + 26 q^{27} - 5 q^{28} - 20 q^{29} - 14 q^{30} + 6 q^{31} + 3 q^{32} + 17 q^{33} + 2 q^{34} - 9 q^{35} - 30 q^{36} + 18 q^{37} + 7 q^{38} + 20 q^{39} + 16 q^{40} - 10 q^{41} - 35 q^{42} - 28 q^{43} - 2 q^{44} + 7 q^{45} + 3 q^{46} - 3 q^{47} + 18 q^{48} - 8 q^{49} - 8 q^{50} - 7 q^{52} + 9 q^{53} + 25 q^{54} + 34 q^{55} - 15 q^{56} + 62 q^{57} + 5 q^{58} + 19 q^{59} + 3 q^{60} + 23 q^{61} + 72 q^{62} + 13 q^{63} - 2 q^{64} - 20 q^{65} - 23 q^{66} + 11 q^{67} + 24 q^{68} + 38 q^{69} - 40 q^{70} - 25 q^{72} - 13 q^{73} - 2 q^{74} - 11 q^{75} + 24 q^{76} + 23 q^{77} + 28 q^{78} + 41 q^{79} + 9 q^{80} + 7 q^{81} - 2 q^{82} - 4 q^{83} - 23 q^{84} - 20 q^{86} - 32 q^{87} + 10 q^{88} - 14 q^{89} + 44 q^{90} - 6 q^{91} + 34 q^{92} + 15 q^{93} - 10 q^{94} + 31 q^{95} + 33 q^{96} - 54 q^{97} - 85 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.894706 1.54968i 0.632653 1.09579i −0.354355 0.935111i \(-0.615299\pi\)
0.987007 0.160675i \(-0.0513673\pi\)
\(3\) 1.16033 + 2.00974i 0.669914 + 1.16033i 0.977928 + 0.208944i \(0.0670025\pi\)
−0.308013 + 0.951382i \(0.599664\pi\)
\(4\) −0.600998 1.04096i −0.300499 0.520479i
\(5\) −1.16033 + 2.00974i −0.518913 + 0.898784i 0.480845 + 0.876806i \(0.340330\pi\)
−0.999758 + 0.0219787i \(0.993003\pi\)
\(6\) 4.15260 1.69529
\(7\) −1.87001 + 1.87165i −0.706797 + 0.707417i
\(8\) 1.42796 0.504860
\(9\) −1.19271 + 2.06584i −0.397570 + 0.688612i
\(10\) 2.07630 + 3.59626i 0.656584 + 1.13724i
\(11\) −1.05503 1.82737i −0.318104 0.550972i 0.661988 0.749514i \(-0.269713\pi\)
−0.980092 + 0.198542i \(0.936379\pi\)
\(12\) 1.39471 2.41570i 0.402617 0.697353i
\(13\) 2.32065 0.643633 0.321816 0.946802i \(-0.395707\pi\)
0.321816 + 0.946802i \(0.395707\pi\)
\(14\) 1.22734 + 4.57248i 0.328021 + 1.22205i
\(15\) −5.38542 −1.39051
\(16\) 2.47960 4.29479i 0.619900 1.07370i
\(17\) 0.622267 + 1.07780i 0.150922 + 0.261404i 0.931567 0.363571i \(-0.118442\pi\)
−0.780645 + 0.624975i \(0.785109\pi\)
\(18\) 2.13425 + 3.69663i 0.503048 + 0.871304i
\(19\) 1.21965 2.11250i 0.279808 0.484641i −0.691529 0.722349i \(-0.743063\pi\)
0.971337 + 0.237708i \(0.0763960\pi\)
\(20\) 2.78941 0.623731
\(21\) −5.93135 1.58652i −1.29433 0.346206i
\(22\) −3.77577 −0.804997
\(23\) 2.93363 5.08120i 0.611705 1.05950i −0.379248 0.925295i \(-0.623817\pi\)
0.990953 0.134209i \(-0.0428493\pi\)
\(24\) 1.65690 + 2.86983i 0.338213 + 0.585802i
\(25\) −0.192711 0.333784i −0.0385421 0.0667569i
\(26\) 2.07630 3.59626i 0.407196 0.705284i
\(27\) 1.42622 0.274477
\(28\) 3.07218 + 0.821745i 0.580587 + 0.155295i
\(29\) −6.48184 −1.20365 −0.601824 0.798629i \(-0.705559\pi\)
−0.601824 + 0.798629i \(0.705559\pi\)
\(30\) −4.81837 + 8.34566i −0.879710 + 1.52370i
\(31\) −1.26649 2.19362i −0.227468 0.393986i 0.729589 0.683886i \(-0.239711\pi\)
−0.957057 + 0.289900i \(0.906378\pi\)
\(32\) −3.00907 5.21185i −0.531933 0.921334i
\(33\) 2.44836 4.24068i 0.426205 0.738208i
\(34\) 2.22698 0.381924
\(35\) −1.59171 5.92996i −0.269049 1.00235i
\(36\) 2.86727 0.477878
\(37\) 0.200618 0.347480i 0.0329814 0.0571254i −0.849064 0.528291i \(-0.822833\pi\)
0.882045 + 0.471165i \(0.156166\pi\)
\(38\) −2.18246 3.78014i −0.354042 0.613219i
\(39\) 2.69271 + 4.66391i 0.431179 + 0.746824i
\(40\) −1.65690 + 2.86983i −0.261978 + 0.453760i
\(41\) −1.00000 −0.156174
\(42\) −7.76540 + 7.77221i −1.19823 + 1.19928i
\(43\) −0.872387 −0.133038 −0.0665189 0.997785i \(-0.521189\pi\)
−0.0665189 + 0.997785i \(0.521189\pi\)
\(44\) −1.26814 + 2.19649i −0.191180 + 0.331133i
\(45\) −2.76786 4.79408i −0.412609 0.714660i
\(46\) −5.24948 9.09236i −0.773993 1.34060i
\(47\) 1.99209 3.45041i 0.290577 0.503293i −0.683370 0.730073i \(-0.739486\pi\)
0.973946 + 0.226779i \(0.0728196\pi\)
\(48\) 11.5086 1.66112
\(49\) −0.00613483 7.00000i −0.000876404 1.00000i
\(50\) −0.689677 −0.0975351
\(51\) −1.44406 + 2.50119i −0.202209 + 0.350237i
\(52\) −1.39471 2.41570i −0.193411 0.334998i
\(53\) −6.03889 10.4597i −0.829505 1.43675i −0.898427 0.439123i \(-0.855289\pi\)
0.0689215 0.997622i \(-0.478044\pi\)
\(54\) 1.27605 2.21018i 0.173648 0.300768i
\(55\) 4.89672 0.660274
\(56\) −2.67030 + 2.67264i −0.356833 + 0.357146i
\(57\) 5.66078 0.749789
\(58\) −5.79935 + 10.0448i −0.761491 + 1.31894i
\(59\) 5.25973 + 9.11011i 0.684758 + 1.18604i 0.973513 + 0.228633i \(0.0734254\pi\)
−0.288755 + 0.957403i \(0.593241\pi\)
\(60\) 3.23663 + 5.60600i 0.417847 + 0.723732i
\(61\) −1.91374 + 3.31470i −0.245029 + 0.424403i −0.962140 0.272556i \(-0.912131\pi\)
0.717110 + 0.696960i \(0.245464\pi\)
\(62\) −4.53254 −0.575633
\(63\) −1.63614 6.09546i −0.206134 0.767956i
\(64\) −0.850520 −0.106315
\(65\) −2.69271 + 4.66391i −0.333990 + 0.578487i
\(66\) −4.38112 7.58833i −0.539279 0.934059i
\(67\) 6.54117 + 11.3296i 0.799131 + 1.38414i 0.920182 + 0.391490i \(0.128040\pi\)
−0.121051 + 0.992646i \(0.538626\pi\)
\(68\) 0.747962 1.29551i 0.0907037 0.157103i
\(69\) 13.6159 1.63916
\(70\) −10.6136 2.83893i −1.26857 0.339317i
\(71\) −8.22415 −0.976028 −0.488014 0.872836i \(-0.662278\pi\)
−0.488014 + 0.872836i \(0.662278\pi\)
\(72\) −1.70314 + 2.94993i −0.200717 + 0.347652i
\(73\) −3.22464 5.58524i −0.377416 0.653703i 0.613270 0.789874i \(-0.289854\pi\)
−0.990685 + 0.136170i \(0.956521\pi\)
\(74\) −0.358988 0.621786i −0.0417315 0.0722811i
\(75\) 0.447214 0.774597i 0.0516398 0.0894428i
\(76\) −2.93204 −0.336328
\(77\) 5.39311 + 1.44255i 0.614602 + 0.164393i
\(78\) 9.63674 1.09115
\(79\) −2.09053 + 3.62090i −0.235203 + 0.407384i −0.959332 0.282281i \(-0.908909\pi\)
0.724129 + 0.689665i \(0.242242\pi\)
\(80\) 5.75428 + 9.96671i 0.643348 + 1.11431i
\(81\) 5.23301 + 9.06385i 0.581446 + 1.00709i
\(82\) −0.894706 + 1.54968i −0.0988038 + 0.171133i
\(83\) 4.83369 0.530566 0.265283 0.964171i \(-0.414535\pi\)
0.265283 + 0.964171i \(0.414535\pi\)
\(84\) 1.91323 + 7.12778i 0.208751 + 0.777705i
\(85\) −2.88813 −0.313261
\(86\) −0.780530 + 1.35192i −0.0841667 + 0.145781i
\(87\) −7.52105 13.0268i −0.806341 1.39662i
\(88\) −1.50654 2.60941i −0.160598 0.278164i
\(89\) −6.26243 + 10.8469i −0.663817 + 1.14976i 0.315788 + 0.948830i \(0.397731\pi\)
−0.979605 + 0.200934i \(0.935602\pi\)
\(90\) −9.90570 −1.04415
\(91\) −4.33964 + 4.34344i −0.454918 + 0.455316i
\(92\) −7.05243 −0.735266
\(93\) 2.93907 5.09063i 0.304768 0.527873i
\(94\) −3.56467 6.17420i −0.367668 0.636820i
\(95\) 2.83039 + 4.90238i 0.290392 + 0.502973i
\(96\) 6.98299 12.0949i 0.712698 1.23443i
\(97\) −12.4400 −1.26309 −0.631546 0.775338i \(-0.717580\pi\)
−0.631546 + 0.775338i \(0.717580\pi\)
\(98\) −10.8532 6.25343i −1.09634 0.631692i
\(99\) 5.03339 0.505875
\(100\) −0.231637 + 0.401207i −0.0231637 + 0.0401207i
\(101\) −7.79974 13.5095i −0.776103 1.34425i −0.934172 0.356822i \(-0.883860\pi\)
0.158069 0.987428i \(-0.449473\pi\)
\(102\) 2.58403 + 4.47566i 0.255857 + 0.443157i
\(103\) −9.22730 + 15.9822i −0.909193 + 1.57477i −0.0940059 + 0.995572i \(0.529967\pi\)
−0.815187 + 0.579197i \(0.803366\pi\)
\(104\) 3.31379 0.324944
\(105\) 10.0708 10.0796i 0.982808 0.983670i
\(106\) −21.6121 −2.09916
\(107\) 5.21481 9.03232i 0.504135 0.873187i −0.495854 0.868406i \(-0.665145\pi\)
0.999989 0.00478099i \(-0.00152184\pi\)
\(108\) −0.857157 1.48464i −0.0824800 0.142859i
\(109\) 10.1898 + 17.6492i 0.976002 + 1.69048i 0.676590 + 0.736360i \(0.263457\pi\)
0.299412 + 0.954124i \(0.403210\pi\)
\(110\) 4.38112 7.58833i 0.417724 0.723519i
\(111\) 0.931128 0.0883788
\(112\) 3.40147 + 12.6722i 0.321408 + 1.19741i
\(113\) 1.84834 0.173878 0.0869388 0.996214i \(-0.472292\pi\)
0.0869388 + 0.996214i \(0.472292\pi\)
\(114\) 5.06473 8.77238i 0.474356 0.821608i
\(115\) 6.80794 + 11.7917i 0.634843 + 1.09958i
\(116\) 3.89557 + 6.74733i 0.361695 + 0.626474i
\(117\) −2.76786 + 4.79408i −0.255889 + 0.443213i
\(118\) 18.8236 1.73286
\(119\) −3.18090 0.850826i −0.291593 0.0779951i
\(120\) −7.69016 −0.702012
\(121\) 3.27382 5.67042i 0.297620 0.515492i
\(122\) 3.42447 + 5.93136i 0.310037 + 0.537000i
\(123\) −1.16033 2.00974i −0.104623 0.181212i
\(124\) −1.52231 + 2.63672i −0.136708 + 0.236785i
\(125\) −10.7088 −0.957827
\(126\) −10.9099 2.91816i −0.971928 0.259971i
\(127\) 5.93689 0.526814 0.263407 0.964685i \(-0.415154\pi\)
0.263407 + 0.964685i \(0.415154\pi\)
\(128\) 5.25717 9.10568i 0.464672 0.804836i
\(129\) −1.01225 1.75327i −0.0891239 0.154367i
\(130\) 4.81837 + 8.34566i 0.422599 + 0.731963i
\(131\) 10.1034 17.4996i 0.882737 1.52894i 0.0344504 0.999406i \(-0.489032\pi\)
0.848286 0.529538i \(-0.177635\pi\)
\(132\) −5.88584 −0.512296
\(133\) 1.67310 + 6.23316i 0.145076 + 0.540483i
\(134\) 23.4097 2.02229
\(135\) −1.65488 + 2.86634i −0.142430 + 0.246695i
\(136\) 0.888571 + 1.53905i 0.0761944 + 0.131972i
\(137\) −9.71980 16.8352i −0.830418 1.43833i −0.897707 0.440593i \(-0.854768\pi\)
0.0672883 0.997734i \(-0.478565\pi\)
\(138\) 12.1822 21.1002i 1.03702 1.79617i
\(139\) 3.36678 0.285566 0.142783 0.989754i \(-0.454395\pi\)
0.142783 + 0.989754i \(0.454395\pi\)
\(140\) −5.21622 + 5.22080i −0.440851 + 0.441238i
\(141\) 9.24590 0.778646
\(142\) −7.35820 + 12.7448i −0.617486 + 1.06952i
\(143\) −2.44836 4.24068i −0.204742 0.354624i
\(144\) 5.91489 + 10.2449i 0.492907 + 0.853740i
\(145\) 7.52105 13.0268i 0.624589 1.08182i
\(146\) −11.5404 −0.955092
\(147\) 14.0611 8.13460i 1.15974 0.670931i
\(148\) −0.482284 −0.0396435
\(149\) 4.76024 8.24497i 0.389974 0.675454i −0.602472 0.798140i \(-0.705817\pi\)
0.992446 + 0.122686i \(0.0391508\pi\)
\(150\) −0.800250 1.38607i −0.0653401 0.113172i
\(151\) 5.05882 + 8.76213i 0.411681 + 0.713052i 0.995074 0.0991381i \(-0.0316085\pi\)
−0.583393 + 0.812190i \(0.698275\pi\)
\(152\) 1.74161 3.01657i 0.141264 0.244676i
\(153\) −2.96874 −0.240008
\(154\) 7.06073 7.06692i 0.568970 0.569468i
\(155\) 5.87815 0.472144
\(156\) 3.23663 5.60600i 0.259137 0.448839i
\(157\) −4.91666 8.51590i −0.392392 0.679643i 0.600372 0.799721i \(-0.295019\pi\)
−0.992765 + 0.120077i \(0.961686\pi\)
\(158\) 3.74082 + 6.47929i 0.297604 + 0.515465i
\(159\) 14.0142 24.2732i 1.11139 1.92499i
\(160\) 13.9660 1.10411
\(161\) 4.02430 + 14.9926i 0.317159 + 1.18158i
\(162\) 18.7280 1.47141
\(163\) 6.81792 11.8090i 0.534020 0.924950i −0.465190 0.885211i \(-0.654014\pi\)
0.999210 0.0397393i \(-0.0126528\pi\)
\(164\) 0.600998 + 1.04096i 0.0469300 + 0.0812852i
\(165\) 5.68179 + 9.84115i 0.442327 + 0.766132i
\(166\) 4.32473 7.49065i 0.335664 0.581387i
\(167\) 4.66022 0.360619 0.180309 0.983610i \(-0.442290\pi\)
0.180309 + 0.983610i \(0.442290\pi\)
\(168\) −8.46972 2.26548i −0.653453 0.174785i
\(169\) −7.61458 −0.585737
\(170\) −2.58403 + 4.47566i −0.198186 + 0.343268i
\(171\) 2.90939 + 5.03921i 0.222486 + 0.385358i
\(172\) 0.524302 + 0.908118i 0.0399777 + 0.0692434i
\(173\) −2.98483 + 5.16988i −0.226932 + 0.393058i −0.956897 0.290426i \(-0.906203\pi\)
0.729965 + 0.683484i \(0.239536\pi\)
\(174\) −26.9165 −2.04054
\(175\) 0.985097 + 0.263493i 0.0744664 + 0.0199182i
\(176\) −10.4642 −0.788770
\(177\) −12.2060 + 21.1414i −0.917458 + 1.58908i
\(178\) 11.2061 + 19.4095i 0.839931 + 1.45480i
\(179\) −7.56674 13.1060i −0.565564 0.979586i −0.996997 0.0774412i \(-0.975325\pi\)
0.431432 0.902145i \(-0.358008\pi\)
\(180\) −3.32696 + 5.76247i −0.247977 + 0.429509i
\(181\) −17.8789 −1.32893 −0.664464 0.747320i \(-0.731340\pi\)
−0.664464 + 0.747320i \(0.731340\pi\)
\(182\) 2.84823 + 10.6111i 0.211125 + 0.786550i
\(183\) −8.88225 −0.656595
\(184\) 4.18911 7.25575i 0.308825 0.534901i
\(185\) 0.465564 + 0.806381i 0.0342290 + 0.0592863i
\(186\) −5.25922 9.10923i −0.385624 0.667921i
\(187\) 1.31302 2.27422i 0.0960177 0.166307i
\(188\) −4.78897 −0.349272
\(189\) −2.66705 + 2.66939i −0.193999 + 0.194169i
\(190\) 10.1295 0.734869
\(191\) 4.39059 7.60473i 0.317692 0.550259i −0.662314 0.749226i \(-0.730425\pi\)
0.980006 + 0.198968i \(0.0637588\pi\)
\(192\) −0.986880 1.70933i −0.0712219 0.123360i
\(193\) 13.4981 + 23.3794i 0.971614 + 1.68289i 0.690684 + 0.723157i \(0.257310\pi\)
0.280930 + 0.959728i \(0.409357\pi\)
\(194\) −11.1302 + 19.2780i −0.799099 + 1.38408i
\(195\) −12.4977 −0.894978
\(196\) −7.28302 + 4.21337i −0.520216 + 0.300955i
\(197\) −20.8256 −1.48376 −0.741881 0.670531i \(-0.766066\pi\)
−0.741881 + 0.670531i \(0.766066\pi\)
\(198\) 4.50340 7.80012i 0.320043 0.554331i
\(199\) 6.19940 + 10.7377i 0.439464 + 0.761173i 0.997648 0.0685435i \(-0.0218352\pi\)
−0.558184 + 0.829717i \(0.688502\pi\)
\(200\) −0.275183 0.476630i −0.0194584 0.0337029i
\(201\) −15.1798 + 26.2921i −1.07070 + 1.85450i
\(202\) −27.9139 −1.96402
\(203\) 12.1211 12.1317i 0.850735 0.851481i
\(204\) 3.47152 0.243055
\(205\) 1.16033 2.00974i 0.0810406 0.140367i
\(206\) 16.5114 + 28.5987i 1.15041 + 1.99256i
\(207\) 6.99795 + 12.1208i 0.486391 + 0.842454i
\(208\) 5.75428 9.96671i 0.398988 0.691067i
\(209\) −5.14709 −0.356032
\(210\) −6.60975 24.6247i −0.456116 1.69927i
\(211\) −18.9338 −1.30346 −0.651728 0.758453i \(-0.725956\pi\)
−0.651728 + 0.758453i \(0.725956\pi\)
\(212\) −7.25872 + 12.5725i −0.498531 + 0.863481i
\(213\) −9.54270 16.5284i −0.653855 1.13251i
\(214\) −9.33144 16.1625i −0.637884 1.10485i
\(215\) 1.01225 1.75327i 0.0690350 0.119572i
\(216\) 2.03659 0.138572
\(217\) 6.47403 + 1.73167i 0.439486 + 0.117553i
\(218\) 36.4673 2.46988
\(219\) 7.48327 12.9614i 0.505672 0.875850i
\(220\) −2.94292 5.09728i −0.198411 0.343659i
\(221\) 1.44406 + 2.50119i 0.0971382 + 0.168248i
\(222\) 0.833086 1.44295i 0.0559131 0.0968443i
\(223\) −10.7618 −0.720664 −0.360332 0.932824i \(-0.617337\pi\)
−0.360332 + 0.932824i \(0.617337\pi\)
\(224\) 15.3817 + 4.11430i 1.02774 + 0.274898i
\(225\) 0.919392 0.0612928
\(226\) 1.65373 2.86434i 0.110004 0.190533i
\(227\) 10.9523 + 18.9699i 0.726927 + 1.25907i 0.958176 + 0.286180i \(0.0923855\pi\)
−0.231249 + 0.972895i \(0.574281\pi\)
\(228\) −3.40212 5.89264i −0.225311 0.390249i
\(229\) −5.91869 + 10.2515i −0.391118 + 0.677437i −0.992597 0.121452i \(-0.961245\pi\)
0.601479 + 0.798889i \(0.294578\pi\)
\(230\) 24.3644 1.60654
\(231\) 3.35861 + 12.5126i 0.220981 + 0.823268i
\(232\) −9.25581 −0.607674
\(233\) −8.44540 + 14.6279i −0.553276 + 0.958303i 0.444759 + 0.895650i \(0.353289\pi\)
−0.998035 + 0.0626525i \(0.980044\pi\)
\(234\) 4.95285 + 8.57859i 0.323778 + 0.560800i
\(235\) 4.62295 + 8.00719i 0.301568 + 0.522331i
\(236\) 6.32217 10.9503i 0.411538 0.712805i
\(237\) −9.70278 −0.630263
\(238\) −4.16448 + 4.16813i −0.269943 + 0.270180i
\(239\) −8.87322 −0.573961 −0.286980 0.957936i \(-0.592651\pi\)
−0.286980 + 0.957936i \(0.592651\pi\)
\(240\) −13.3537 + 23.1293i −0.861977 + 1.49299i
\(241\) 1.12830 + 1.95427i 0.0726801 + 0.125886i 0.900075 0.435735i \(-0.143511\pi\)
−0.827395 + 0.561620i \(0.810178\pi\)
\(242\) −5.85821 10.1467i −0.376580 0.652255i
\(243\) −10.0047 + 17.3286i −0.641800 + 1.11163i
\(244\) 4.60062 0.294524
\(245\) 14.0753 + 8.10995i 0.899239 + 0.518125i
\(246\) −4.15260 −0.264760
\(247\) 2.83039 4.90238i 0.180093 0.311931i
\(248\) −1.80849 3.13240i −0.114839 0.198908i
\(249\) 5.60865 + 9.71446i 0.355434 + 0.615629i
\(250\) −9.58125 + 16.5952i −0.605972 + 1.04957i
\(251\) 5.06165 0.319488 0.159744 0.987158i \(-0.448933\pi\)
0.159744 + 0.987158i \(0.448933\pi\)
\(252\) −5.36181 + 5.36651i −0.337762 + 0.338059i
\(253\) −12.3803 −0.778343
\(254\) 5.31177 9.20026i 0.333290 0.577276i
\(255\) −3.35117 5.80439i −0.209858 0.363485i
\(256\) −10.2578 17.7670i −0.641110 1.11043i
\(257\) −5.77331 + 9.99966i −0.360129 + 0.623762i −0.987982 0.154570i \(-0.950601\pi\)
0.627853 + 0.778332i \(0.283934\pi\)
\(258\) −3.62267 −0.225538
\(259\) 0.275204 + 1.02528i 0.0171003 + 0.0637076i
\(260\) 6.47325 0.401454
\(261\) 7.73096 13.3904i 0.478535 0.828846i
\(262\) −18.0791 31.3139i −1.11693 1.93458i
\(263\) −1.77693 3.07773i −0.109570 0.189781i 0.806026 0.591880i \(-0.201614\pi\)
−0.915596 + 0.402099i \(0.868281\pi\)
\(264\) 3.49616 6.05552i 0.215174 0.372692i
\(265\) 28.0283 1.72177
\(266\) 11.1563 + 2.98408i 0.684037 + 0.182966i
\(267\) −29.0658 −1.77880
\(268\) 7.86246 13.6182i 0.480276 0.831863i
\(269\) 0.777216 + 1.34618i 0.0473877 + 0.0820779i 0.888746 0.458399i \(-0.151577\pi\)
−0.841359 + 0.540477i \(0.818244\pi\)
\(270\) 2.96127 + 5.12907i 0.180217 + 0.312145i
\(271\) 8.13015 14.0818i 0.493871 0.855410i −0.506104 0.862473i \(-0.668915\pi\)
0.999975 + 0.00706233i \(0.00224803\pi\)
\(272\) 6.17189 0.374226
\(273\) −13.7646 3.68175i −0.833071 0.222830i
\(274\) −34.7855 −2.10147
\(275\) −0.406631 + 0.704306i −0.0245208 + 0.0424713i
\(276\) −8.18311 14.1736i −0.492565 0.853148i
\(277\) −8.05385 13.9497i −0.483909 0.838155i 0.515920 0.856637i \(-0.327450\pi\)
−0.999829 + 0.0184818i \(0.994117\pi\)
\(278\) 3.01228 5.21741i 0.180664 0.312920i
\(279\) 6.04221 0.361738
\(280\) −2.27290 8.46774i −0.135832 0.506044i
\(281\) 31.5830 1.88409 0.942043 0.335492i \(-0.108903\pi\)
0.942043 + 0.335492i \(0.108903\pi\)
\(282\) 8.27237 14.3282i 0.492612 0.853229i
\(283\) 1.94072 + 3.36143i 0.115364 + 0.199816i 0.917925 0.396754i \(-0.129863\pi\)
−0.802561 + 0.596570i \(0.796530\pi\)
\(284\) 4.94270 + 8.56100i 0.293295 + 0.508002i
\(285\) −6.56835 + 11.3767i −0.389075 + 0.673898i
\(286\) −8.76225 −0.518123
\(287\) 1.87001 1.87165i 0.110383 0.110480i
\(288\) 14.3558 0.845922
\(289\) 7.72557 13.3811i 0.454445 0.787122i
\(290\) −13.4583 23.3104i −0.790296 1.36883i
\(291\) −14.4345 25.0012i −0.846164 1.46560i
\(292\) −3.87601 + 6.71344i −0.226826 + 0.392874i
\(293\) 5.31620 0.310576 0.155288 0.987869i \(-0.450370\pi\)
0.155288 + 0.987869i \(0.450370\pi\)
\(294\) −0.0254755 29.0682i −0.00148576 1.69529i
\(295\) −24.4120 −1.42132
\(296\) 0.286474 0.496188i 0.0166510 0.0288403i
\(297\) −1.50471 2.60624i −0.0873122 0.151229i
\(298\) −8.51802 14.7536i −0.493436 0.854656i
\(299\) 6.80794 11.7917i 0.393713 0.681931i
\(300\) −1.07510 −0.0620708
\(301\) 1.63137 1.63280i 0.0940306 0.0941131i
\(302\) 18.1046 1.04180
\(303\) 18.1005 31.3509i 1.03985 1.80106i
\(304\) −6.04850 10.4763i −0.346905 0.600858i
\(305\) −4.44113 7.69226i −0.254298 0.440457i
\(306\) −2.65615 + 4.60058i −0.151842 + 0.262998i
\(307\) −5.13586 −0.293119 −0.146559 0.989202i \(-0.546820\pi\)
−0.146559 + 0.989202i \(0.546820\pi\)
\(308\) −1.73962 6.48097i −0.0991238 0.369288i
\(309\) −42.8267 −2.43633
\(310\) 5.25922 9.10923i 0.298703 0.517369i
\(311\) 14.1344 + 24.4815i 0.801488 + 1.38822i 0.918636 + 0.395104i \(0.129291\pi\)
−0.117148 + 0.993114i \(0.537375\pi\)
\(312\) 3.84508 + 6.65987i 0.217685 + 0.377041i
\(313\) −10.6526 + 18.4508i −0.602120 + 1.04290i 0.390379 + 0.920654i \(0.372344\pi\)
−0.992500 + 0.122249i \(0.960989\pi\)
\(314\) −17.5959 −0.992992
\(315\) 14.1488 + 3.78451i 0.797193 + 0.213233i
\(316\) 5.02561 0.282713
\(317\) −8.36242 + 14.4841i −0.469680 + 0.813510i −0.999399 0.0346631i \(-0.988964\pi\)
0.529719 + 0.848173i \(0.322298\pi\)
\(318\) −25.0771 43.4348i −1.40625 2.43570i
\(319\) 6.83855 + 11.8447i 0.382885 + 0.663177i
\(320\) 0.986880 1.70933i 0.0551683 0.0955542i
\(321\) 24.2035 1.35091
\(322\) 26.8343 + 7.17762i 1.49542 + 0.399993i
\(323\) 3.03580 0.168916
\(324\) 6.29006 10.8947i 0.349448 0.605261i
\(325\) −0.447214 0.774597i −0.0248070 0.0429669i
\(326\) −12.2001 21.1311i −0.675699 1.17034i
\(327\) −23.6469 + 40.9576i −1.30767 + 2.26496i
\(328\) −1.42796 −0.0788458
\(329\) 2.73272 + 10.1808i 0.150659 + 0.561285i
\(330\) 20.3341 1.11936
\(331\) 1.16445 2.01688i 0.0640038 0.110858i −0.832248 0.554404i \(-0.812946\pi\)
0.896252 + 0.443546i \(0.146280\pi\)
\(332\) −2.90503 5.03167i −0.159434 0.276149i
\(333\) 0.478558 + 0.828887i 0.0262248 + 0.0454227i
\(334\) 4.16953 7.22184i 0.228146 0.395161i
\(335\) −30.3596 −1.65872
\(336\) −21.5211 + 21.5400i −1.17407 + 1.17510i
\(337\) 4.30942 0.234749 0.117374 0.993088i \(-0.462552\pi\)
0.117374 + 0.993088i \(0.462552\pi\)
\(338\) −6.81281 + 11.8001i −0.370568 + 0.641843i
\(339\) 2.14468 + 3.71470i 0.116483 + 0.201755i
\(340\) 1.73576 + 3.00642i 0.0941347 + 0.163046i
\(341\) −2.67237 + 4.62868i −0.144717 + 0.250657i
\(342\) 10.4122 0.563026
\(343\) 13.1130 + 13.0786i 0.708036 + 0.706177i
\(344\) −1.24573 −0.0671654
\(345\) −15.7988 + 27.3644i −0.850581 + 1.47325i
\(346\) 5.34109 + 9.25104i 0.287139 + 0.497339i
\(347\) −8.73128 15.1230i −0.468720 0.811846i 0.530641 0.847597i \(-0.321951\pi\)
−0.999361 + 0.0357504i \(0.988618\pi\)
\(348\) −9.04027 + 15.6582i −0.484609 + 0.839368i
\(349\) 25.6363 1.37228 0.686139 0.727471i \(-0.259304\pi\)
0.686139 + 0.727471i \(0.259304\pi\)
\(350\) 1.28970 1.29083i 0.0689375 0.0689979i
\(351\) 3.30977 0.176662
\(352\) −6.34932 + 10.9973i −0.338420 + 0.586160i
\(353\) −8.07544 13.9871i −0.429813 0.744457i 0.567044 0.823688i \(-0.308087\pi\)
−0.996856 + 0.0792305i \(0.974754\pi\)
\(354\) 21.8415 + 37.8307i 1.16086 + 2.01068i
\(355\) 9.54270 16.5284i 0.506474 0.877238i
\(356\) 15.0548 0.797904
\(357\) −1.98094 7.38003i −0.104842 0.390593i
\(358\) −27.0800 −1.43122
\(359\) −1.07240 + 1.85745i −0.0565991 + 0.0980325i −0.892937 0.450182i \(-0.851359\pi\)
0.836338 + 0.548215i \(0.184692\pi\)
\(360\) −3.95240 6.84575i −0.208310 0.360803i
\(361\) 6.52489 + 11.3014i 0.343415 + 0.594813i
\(362\) −15.9964 + 27.7065i −0.840750 + 1.45622i
\(363\) 15.1948 0.797519
\(364\) 7.12946 + 1.90698i 0.373685 + 0.0999531i
\(365\) 14.9665 0.783384
\(366\) −7.94700 + 13.7646i −0.415397 + 0.719488i
\(367\) −2.25245 3.90137i −0.117577 0.203650i 0.801230 0.598357i \(-0.204179\pi\)
−0.918807 + 0.394707i \(0.870846\pi\)
\(368\) −14.5485 25.1987i −0.758391 1.31357i
\(369\) 1.19271 2.06584i 0.0620900 0.107543i
\(370\) 1.66617 0.0866202
\(371\) 30.8696 + 8.25698i 1.60267 + 0.428681i
\(372\) −7.06551 −0.366330
\(373\) −3.57165 + 6.18627i −0.184933 + 0.320313i −0.943554 0.331219i \(-0.892540\pi\)
0.758621 + 0.651532i \(0.225873\pi\)
\(374\) −2.34954 4.06952i −0.121492 0.210430i
\(375\) −12.4257 21.5220i −0.641662 1.11139i
\(376\) 2.84463 4.92704i 0.146700 0.254093i
\(377\) −15.0421 −0.774707
\(378\) 1.75046 + 6.52138i 0.0900341 + 0.335424i
\(379\) −6.99123 −0.359116 −0.179558 0.983747i \(-0.557467\pi\)
−0.179558 + 0.983747i \(0.557467\pi\)
\(380\) 3.40212 5.89264i 0.174525 0.302286i
\(381\) 6.88873 + 11.9316i 0.352920 + 0.611276i
\(382\) −7.85658 13.6080i −0.401978 0.696246i
\(383\) −12.6399 + 21.8929i −0.645868 + 1.11868i 0.338232 + 0.941063i \(0.390171\pi\)
−0.984100 + 0.177614i \(0.943162\pi\)
\(384\) 24.4001 1.24516
\(385\) −9.15691 + 9.16494i −0.466679 + 0.467088i
\(386\) 48.3073 2.45878
\(387\) 1.04050 1.80221i 0.0528918 0.0916113i
\(388\) 7.47643 + 12.9495i 0.379558 + 0.657414i
\(389\) 11.0170 + 19.0820i 0.558583 + 0.967495i 0.997615 + 0.0690231i \(0.0219882\pi\)
−0.439032 + 0.898472i \(0.644678\pi\)
\(390\) −11.1818 + 19.3674i −0.566210 + 0.980705i
\(391\) 7.30201 0.369278
\(392\) −0.00876029 9.99571i −0.000442461 0.504860i
\(393\) 46.8928 2.36543
\(394\) −18.6328 + 32.2729i −0.938706 + 1.62589i
\(395\) −4.85139 8.40285i −0.244100 0.422793i
\(396\) −3.02506 5.23955i −0.152015 0.263297i
\(397\) 11.6891 20.2461i 0.586659 1.01612i −0.408008 0.912978i \(-0.633776\pi\)
0.994666 0.103144i \(-0.0328903\pi\)
\(398\) 22.1866 1.11211
\(399\) −10.5857 + 10.5950i −0.529948 + 0.530413i
\(400\) −1.91138 −0.0955690
\(401\) −3.38442 + 5.86199i −0.169010 + 0.292734i −0.938072 0.346440i \(-0.887390\pi\)
0.769062 + 0.639174i \(0.220724\pi\)
\(402\) 27.1629 + 47.0475i 1.35476 + 2.34652i
\(403\) −2.93907 5.09063i −0.146406 0.253582i
\(404\) −9.37525 + 16.2384i −0.466436 + 0.807891i
\(405\) −24.2880 −1.20688
\(406\) −7.95543 29.6381i −0.394822 1.47092i
\(407\) −0.846633 −0.0419660
\(408\) −2.06206 + 3.57160i −0.102087 + 0.176820i
\(409\) 17.8518 + 30.9202i 0.882713 + 1.52890i 0.848312 + 0.529496i \(0.177619\pi\)
0.0344010 + 0.999408i \(0.489048\pi\)
\(410\) −2.07630 3.59626i −0.102541 0.177607i
\(411\) 22.5563 39.0686i 1.11262 1.92711i
\(412\) 22.1824 1.09285
\(413\) −26.8867 7.19163i −1.32301 0.353877i
\(414\) 25.0444 1.23087
\(415\) −5.60865 + 9.71446i −0.275318 + 0.476864i
\(416\) −6.98299 12.0949i −0.342369 0.593001i
\(417\) 3.90656 + 6.76636i 0.191305 + 0.331350i
\(418\) −4.60513 + 7.97632i −0.225244 + 0.390135i
\(419\) −2.83166 −0.138336 −0.0691678 0.997605i \(-0.522034\pi\)
−0.0691678 + 0.997605i \(0.522034\pi\)
\(420\) −16.5450 4.42544i −0.807312 0.215940i
\(421\) −5.51670 −0.268867 −0.134434 0.990923i \(-0.542922\pi\)
−0.134434 + 0.990923i \(0.542922\pi\)
\(422\) −16.9402 + 29.3412i −0.824635 + 1.42831i
\(423\) 4.75198 + 8.23067i 0.231049 + 0.400189i
\(424\) −8.62329 14.9360i −0.418784 0.725355i
\(425\) 0.239835 0.415406i 0.0116337 0.0201501i
\(426\) −34.1516 −1.65465
\(427\) −2.62523 9.78036i −0.127044 0.473305i
\(428\) −12.5364 −0.605968
\(429\) 5.68179 9.84115i 0.274319 0.475135i
\(430\) −1.81134 3.13733i −0.0873504 0.151295i
\(431\) −11.9637 20.7217i −0.576271 0.998131i −0.995902 0.0904365i \(-0.971174\pi\)
0.419631 0.907695i \(-0.362160\pi\)
\(432\) 3.53646 6.12533i 0.170148 0.294705i
\(433\) −25.9161 −1.24545 −0.622725 0.782441i \(-0.713974\pi\)
−0.622725 + 0.782441i \(0.713974\pi\)
\(434\) 8.47588 8.48331i 0.406855 0.407212i
\(435\) 34.9075 1.67368
\(436\) 12.2480 21.2142i 0.586575 1.01598i
\(437\) −7.15603 12.3946i −0.342319 0.592914i
\(438\) −13.3907 23.1933i −0.639830 1.10822i
\(439\) 5.27036 9.12853i 0.251541 0.435681i −0.712410 0.701764i \(-0.752396\pi\)
0.963950 + 0.266083i \(0.0857295\pi\)
\(440\) 6.99231 0.333346
\(441\) 14.4682 + 8.33630i 0.688960 + 0.396967i
\(442\) 5.16805 0.245819
\(443\) 0.459102 0.795189i 0.0218126 0.0377805i −0.854913 0.518771i \(-0.826390\pi\)
0.876726 + 0.480991i \(0.159723\pi\)
\(444\) −0.559606 0.969266i −0.0265577 0.0459993i
\(445\) −14.5329 25.1718i −0.688926 1.19326i
\(446\) −9.62866 + 16.6773i −0.455930 + 0.789694i
\(447\) 22.0937 1.04500
\(448\) 1.59048 1.59187i 0.0751431 0.0752090i
\(449\) −18.9072 −0.892285 −0.446143 0.894962i \(-0.647203\pi\)
−0.446143 + 0.894962i \(0.647203\pi\)
\(450\) 0.822585 1.42476i 0.0387770 0.0671638i
\(451\) 1.05503 + 1.82737i 0.0496795 + 0.0860474i
\(452\) −1.11085 1.92405i −0.0522500 0.0904997i
\(453\) −11.7398 + 20.3338i −0.551582 + 0.955367i
\(454\) 39.1962 1.83957
\(455\) −3.69381 13.7614i −0.173168 0.645143i
\(456\) 8.08336 0.378538
\(457\) 19.0894 33.0639i 0.892966 1.54666i 0.0566645 0.998393i \(-0.481953\pi\)
0.836302 0.548269i \(-0.184713\pi\)
\(458\) 10.5910 + 18.3441i 0.494884 + 0.857164i
\(459\) 0.887491 + 1.53718i 0.0414245 + 0.0717494i
\(460\) 8.18311 14.1736i 0.381539 0.660846i
\(461\) −23.1161 −1.07662 −0.538312 0.842745i \(-0.680938\pi\)
−0.538312 + 0.842745i \(0.680938\pi\)
\(462\) 22.3954 + 5.99032i 1.04193 + 0.278695i
\(463\) 10.4597 0.486104 0.243052 0.970013i \(-0.421851\pi\)
0.243052 + 0.970013i \(0.421851\pi\)
\(464\) −16.0724 + 27.8382i −0.746141 + 1.29235i
\(465\) 6.82057 + 11.8136i 0.316296 + 0.547841i
\(466\) 15.1123 + 26.1753i 0.700064 + 1.21255i
\(467\) 16.9301 29.3237i 0.783430 1.35694i −0.146502 0.989210i \(-0.546801\pi\)
0.929932 0.367731i \(-0.119865\pi\)
\(468\) 6.65392 0.307578
\(469\) −33.4372 8.94376i −1.54398 0.412984i
\(470\) 16.5447 0.763152
\(471\) 11.4099 19.7624i 0.525738 0.910605i
\(472\) 7.51067 + 13.0089i 0.345707 + 0.598782i
\(473\) 0.920395 + 1.59417i 0.0423198 + 0.0733001i
\(474\) −8.68114 + 15.0362i −0.398738 + 0.690634i
\(475\) −0.940160 −0.0431375
\(476\) 1.02604 + 3.82253i 0.0470285 + 0.175205i
\(477\) 28.8106 1.31915
\(478\) −7.93892 + 13.7506i −0.363118 + 0.628938i
\(479\) 11.6199 + 20.1262i 0.530926 + 0.919591i 0.999349 + 0.0360861i \(0.0114891\pi\)
−0.468423 + 0.883504i \(0.655178\pi\)
\(480\) 16.2051 + 28.0680i 0.739657 + 1.28112i
\(481\) 0.465564 0.806381i 0.0212279 0.0367678i
\(482\) 4.03798 0.183925
\(483\) −25.4618 + 25.4841i −1.15855 + 1.15957i
\(484\) −7.87023 −0.357738
\(485\) 14.4345 25.0012i 0.655436 1.13525i
\(486\) 17.9025 + 31.0080i 0.812073 + 1.40655i
\(487\) 13.8023 + 23.9063i 0.625442 + 1.08330i 0.988455 + 0.151513i \(0.0484147\pi\)
−0.363013 + 0.931784i \(0.618252\pi\)
\(488\) −2.73274 + 4.73325i −0.123706 + 0.214264i
\(489\) 31.6440 1.43099
\(490\) 25.1611 14.5562i 1.13666 0.657580i
\(491\) 26.6973 1.20483 0.602415 0.798183i \(-0.294205\pi\)
0.602415 + 0.798183i \(0.294205\pi\)
\(492\) −1.39471 + 2.41570i −0.0628782 + 0.108908i
\(493\) −4.03344 6.98612i −0.181657 0.314639i
\(494\) −5.06473 8.77238i −0.227873 0.394688i
\(495\) −5.84037 + 10.1158i −0.262505 + 0.454672i
\(496\) −12.5615 −0.564029
\(497\) 15.3792 15.3927i 0.689853 0.690458i
\(498\) 20.0724 0.899464
\(499\) 1.94594 3.37047i 0.0871122 0.150883i −0.819177 0.573541i \(-0.805569\pi\)
0.906289 + 0.422658i \(0.138903\pi\)
\(500\) 6.43598 + 11.1474i 0.287826 + 0.498529i
\(501\) 5.40738 + 9.36585i 0.241584 + 0.418435i
\(502\) 4.52869 7.84392i 0.202125 0.350091i
\(503\) −29.7118 −1.32478 −0.662392 0.749158i \(-0.730458\pi\)
−0.662392 + 0.749158i \(0.730458\pi\)
\(504\) −2.33634 8.70407i −0.104069 0.387710i
\(505\) 36.2009 1.61092
\(506\) −11.0767 + 19.1855i −0.492421 + 0.852898i
\(507\) −8.83539 15.3033i −0.392393 0.679645i
\(508\) −3.56806 6.18006i −0.158307 0.274196i
\(509\) −16.8364 + 29.1615i −0.746261 + 1.29256i 0.203342 + 0.979108i \(0.434820\pi\)
−0.949603 + 0.313455i \(0.898514\pi\)
\(510\) −11.9932 −0.531070
\(511\) 16.4837 + 4.40906i 0.729197 + 0.195045i
\(512\) −15.6820 −0.693055
\(513\) 1.73950 3.01290i 0.0768007 0.133023i
\(514\) 10.3308 + 17.8935i 0.455673 + 0.789249i
\(515\) −21.4134 37.0890i −0.943585 1.63434i
\(516\) −1.21672 + 2.10743i −0.0535632 + 0.0927742i
\(517\) −8.40688 −0.369734
\(518\) 1.83507 + 0.490845i 0.0806286 + 0.0215665i
\(519\) −13.8535 −0.608101
\(520\) −3.84508 + 6.65987i −0.168618 + 0.292055i
\(521\) 10.8627 + 18.8147i 0.475902 + 0.824286i 0.999619 0.0276065i \(-0.00878854\pi\)
−0.523717 + 0.851892i \(0.675455\pi\)
\(522\) −13.8339 23.9610i −0.605492 1.04874i
\(523\) 12.7245 22.0394i 0.556403 0.963718i −0.441390 0.897315i \(-0.645515\pi\)
0.997793 0.0664025i \(-0.0211521\pi\)
\(524\) −24.2884 −1.06105
\(525\) 0.613480 + 2.28553i 0.0267744 + 0.0997487i
\(526\) −6.35932 −0.277280
\(527\) 1.57619 2.73003i 0.0686597 0.118922i
\(528\) −12.1419 21.0304i −0.528408 0.915230i
\(529\) −5.71240 9.89417i −0.248365 0.430181i
\(530\) 25.0771 43.4348i 1.08928 1.88669i
\(531\) −25.0933 −1.08896
\(532\) 5.48293 5.48774i 0.237715 0.237924i
\(533\) −2.32065 −0.100519
\(534\) −26.0054 + 45.0426i −1.12536 + 1.94919i
\(535\) 12.1018 + 20.9609i 0.523204 + 0.906217i
\(536\) 9.34052 + 16.1783i 0.403449 + 0.698795i
\(537\) 17.5598 30.4144i 0.757759 1.31248i
\(538\) 2.78152 0.119920
\(539\) −12.7851 + 7.39643i −0.550693 + 0.318587i
\(540\) 3.97832 0.171200
\(541\) 9.86020 17.0784i 0.423923 0.734257i −0.572396 0.819977i \(-0.693986\pi\)
0.996319 + 0.0857207i \(0.0273193\pi\)
\(542\) −14.5482 25.1982i −0.624898 1.08236i
\(543\) −20.7453 35.9320i −0.890268 1.54199i
\(544\) 3.74488 6.48633i 0.160560 0.278099i
\(545\) −47.2937 −2.02584
\(546\) −18.0208 + 18.0366i −0.771218 + 0.771895i
\(547\) 24.9225 1.06561 0.532804 0.846239i \(-0.321138\pi\)
0.532804 + 0.846239i \(0.321138\pi\)
\(548\) −11.6832 + 20.2358i −0.499080 + 0.864431i
\(549\) −4.56508 7.90695i −0.194833 0.337460i
\(550\) 0.727631 + 1.26029i 0.0310263 + 0.0537391i
\(551\) −7.90560 + 13.6929i −0.336790 + 0.583337i
\(552\) 19.4429 0.827545
\(553\) −2.86775 10.6839i −0.121949 0.454324i
\(554\) −28.8233 −1.22458
\(555\) −1.08041 + 1.87133i −0.0458609 + 0.0794335i
\(556\) −2.02343 3.50468i −0.0858124 0.148631i
\(557\) 6.47467 + 11.2145i 0.274341 + 0.475172i 0.969969 0.243230i \(-0.0782071\pi\)
−0.695628 + 0.718402i \(0.744874\pi\)
\(558\) 5.40600 9.36347i 0.228854 0.396387i
\(559\) −2.02450 −0.0856274
\(560\) −29.4147 7.86784i −1.24300 0.332477i
\(561\) 6.09413 0.257294
\(562\) 28.2575 48.9435i 1.19197 2.06456i
\(563\) −18.3080 31.7105i −0.771592 1.33644i −0.936690 0.350159i \(-0.886127\pi\)
0.165098 0.986277i \(-0.447206\pi\)
\(564\) −5.55677 9.62460i −0.233982 0.405269i
\(565\) −2.14468 + 3.71470i −0.0902274 + 0.156279i
\(566\) 6.94550 0.291941
\(567\) −26.7501 7.15511i −1.12340 0.300486i
\(568\) −11.7438 −0.492757
\(569\) −7.41077 + 12.8358i −0.310675 + 0.538106i −0.978509 0.206205i \(-0.933889\pi\)
0.667833 + 0.744311i \(0.267222\pi\)
\(570\) 11.7535 + 20.3576i 0.492299 + 0.852687i
\(571\) −5.37734 9.31382i −0.225035 0.389771i 0.731295 0.682061i \(-0.238916\pi\)
−0.956330 + 0.292290i \(0.905583\pi\)
\(572\) −2.94292 + 5.09728i −0.123050 + 0.213128i
\(573\) 20.3781 0.851306
\(574\) −1.22734 4.57248i −0.0512282 0.190852i
\(575\) −2.26137 −0.0943055
\(576\) 1.01442 1.75703i 0.0422677 0.0732097i
\(577\) −4.56980 7.91513i −0.190243 0.329511i 0.755087 0.655624i \(-0.227594\pi\)
−0.945331 + 0.326113i \(0.894261\pi\)
\(578\) −13.8242 23.9443i −0.575012 0.995950i
\(579\) −31.3244 + 54.2554i −1.30180 + 2.25478i
\(580\) −18.0805 −0.750753
\(581\) −9.03903 + 9.04696i −0.375002 + 0.375331i
\(582\) −51.6584 −2.14131
\(583\) −12.7424 + 22.0706i −0.527738 + 0.914069i
\(584\) −4.60466 7.97550i −0.190542 0.330028i
\(585\) −6.42325 11.1254i −0.265569 0.459978i
\(586\) 4.75644 8.23839i 0.196487 0.340325i
\(587\) 20.2730 0.836757 0.418379 0.908273i \(-0.362599\pi\)
0.418379 + 0.908273i \(0.362599\pi\)
\(588\) −16.9185 9.74812i −0.697706 0.402006i
\(589\) −6.17870 −0.254589
\(590\) −21.8415 + 37.8307i −0.899202 + 1.55746i
\(591\) −24.1645 41.8541i −0.993994 1.72165i
\(592\) −0.994904 1.72322i −0.0408903 0.0708241i
\(593\) 20.6018 35.6834i 0.846015 1.46534i −0.0387213 0.999250i \(-0.512328\pi\)
0.884737 0.466091i \(-0.154338\pi\)
\(594\) −5.38509 −0.220953
\(595\) 5.40082 5.40556i 0.221412 0.221606i
\(596\) −11.4436 −0.468747
\(597\) −14.3866 + 24.9184i −0.588806 + 1.01984i
\(598\) −12.1822 21.1002i −0.498167 0.862851i
\(599\) 11.3643 + 19.6835i 0.464333 + 0.804248i 0.999171 0.0407067i \(-0.0129609\pi\)
−0.534839 + 0.844954i \(0.679628\pi\)
\(600\) 0.638603 1.10609i 0.0260709 0.0451561i
\(601\) 1.17763 0.0480364 0.0240182 0.999712i \(-0.492354\pi\)
0.0240182 + 0.999712i \(0.492354\pi\)
\(602\) −1.07072 3.98897i −0.0436391 0.162578i
\(603\) −31.2069 −1.27084
\(604\) 6.08068 10.5320i 0.247419 0.428543i
\(605\) 7.59739 + 13.1591i 0.308878 + 0.534992i
\(606\) −32.3892 56.0998i −1.31572 2.27890i
\(607\) 5.76102 9.97839i 0.233833 0.405010i −0.725100 0.688644i \(-0.758207\pi\)
0.958933 + 0.283633i \(0.0915399\pi\)
\(608\) −14.6801 −0.595355
\(609\) 38.4461 + 10.2835i 1.55791 + 0.416710i
\(610\) −15.8940 −0.643530
\(611\) 4.62295 8.00719i 0.187025 0.323936i
\(612\) 1.78420 + 3.09033i 0.0721222 + 0.124919i
\(613\) −7.51557 13.0174i −0.303551 0.525766i 0.673387 0.739291i \(-0.264839\pi\)
−0.976938 + 0.213525i \(0.931506\pi\)
\(614\) −4.59508 + 7.95891i −0.185442 + 0.321196i
\(615\) 5.38542 0.217161
\(616\) 7.70114 + 2.05990i 0.310288 + 0.0829956i
\(617\) −14.3301 −0.576909 −0.288454 0.957494i \(-0.593141\pi\)
−0.288454 + 0.957494i \(0.593141\pi\)
\(618\) −38.3173 + 66.3675i −1.54135 + 2.66969i
\(619\) 23.5218 + 40.7410i 0.945422 + 1.63752i 0.754904 + 0.655835i \(0.227683\pi\)
0.190518 + 0.981684i \(0.438983\pi\)
\(620\) −3.53275 6.11891i −0.141879 0.245741i
\(621\) 4.18402 7.24693i 0.167899 0.290809i
\(622\) 50.5845 2.02826
\(623\) −8.59069 32.0048i −0.344179 1.28224i
\(624\) 26.7074 1.06915
\(625\) 13.3893 23.1909i 0.535571 0.927636i
\(626\) 19.0619 + 33.0161i 0.761866 + 1.31959i
\(627\) −5.97230 10.3443i −0.238511 0.413113i
\(628\) −5.90980 + 10.2361i −0.235827 + 0.408464i
\(629\) 0.499351 0.0199104
\(630\) 18.5237 18.5400i 0.738004 0.738651i
\(631\) −1.71098 −0.0681130 −0.0340565 0.999420i \(-0.510843\pi\)
−0.0340565 + 0.999420i \(0.510843\pi\)
\(632\) −2.98519 + 5.17050i −0.118745 + 0.205672i
\(633\) −21.9694 38.0520i −0.873203 1.51243i
\(634\) 14.9638 + 25.9181i 0.594289 + 1.02934i
\(635\) −6.88873 + 11.9316i −0.273371 + 0.473492i
\(636\) −33.6899 −1.33589
\(637\) −0.0142368 16.2446i −0.000564083 0.643633i
\(638\) 24.4740 0.968934
\(639\) 9.80903 16.9897i 0.388039 0.672104i
\(640\) 12.2000 + 21.1311i 0.482249 + 0.835280i
\(641\) −0.179763 0.311359i −0.00710022 0.0122979i 0.862453 0.506136i \(-0.168927\pi\)
−0.869554 + 0.493838i \(0.835593\pi\)
\(642\) 21.6550 37.5076i 0.854656 1.48031i
\(643\) −28.7086 −1.13216 −0.566078 0.824352i \(-0.691540\pi\)
−0.566078 + 0.824352i \(0.691540\pi\)
\(644\) 13.1881 13.1997i 0.519684 0.520140i
\(645\) 4.69817 0.184990
\(646\) 2.71615 4.70450i 0.106865 0.185096i
\(647\) −0.0618297 0.107092i −0.00243078 0.00421023i 0.864807 0.502104i \(-0.167440\pi\)
−0.867238 + 0.497893i \(0.834107\pi\)
\(648\) 7.47253 + 12.9428i 0.293549 + 0.508441i
\(649\) 11.0984 19.2229i 0.435648 0.754565i
\(650\) −1.60050 −0.0627768
\(651\) 4.03177 + 15.0204i 0.158017 + 0.588697i
\(652\) −16.3902 −0.641890
\(653\) 19.6280 33.9967i 0.768103 1.33039i −0.170487 0.985360i \(-0.554534\pi\)
0.938590 0.345034i \(-0.112133\pi\)
\(654\) 42.3140 + 73.2900i 1.65461 + 2.86586i
\(655\) 23.4464 + 40.6104i 0.916128 + 1.58678i
\(656\) −2.47960 + 4.29479i −0.0968121 + 0.167683i
\(657\) 15.3843 0.600197
\(658\) 18.2219 + 4.87399i 0.710364 + 0.190008i
\(659\) −25.6293 −0.998374 −0.499187 0.866494i \(-0.666368\pi\)
−0.499187 + 0.866494i \(0.666368\pi\)
\(660\) 6.82948 11.8290i 0.265837 0.460444i
\(661\) −5.72942 9.92365i −0.222849 0.385985i 0.732823 0.680419i \(-0.238202\pi\)
−0.955672 + 0.294434i \(0.904869\pi\)
\(662\) −2.08367 3.60903i −0.0809843 0.140269i
\(663\) −3.35117 + 5.80439i −0.130149 + 0.225424i
\(664\) 6.90230 0.267861
\(665\) −14.4684 3.87000i −0.561060 0.150072i
\(666\) 1.71268 0.0663648
\(667\) −19.0154 + 32.9356i −0.736277 + 1.27527i
\(668\) −2.80078 4.85110i −0.108366 0.187695i
\(669\) −12.4872 21.6285i −0.482783 0.836205i
\(670\) −27.1629 + 47.0475i −1.04939 + 1.81760i
\(671\) 8.07623 0.311779
\(672\) 9.57914 + 35.6873i 0.369523 + 1.37667i
\(673\) 42.6903 1.64559 0.822795 0.568338i \(-0.192413\pi\)
0.822795 + 0.568338i \(0.192413\pi\)
\(674\) 3.85566 6.67820i 0.148514 0.257235i
\(675\) −0.274848 0.476051i −0.0105789 0.0183232i
\(676\) 4.57634 + 7.92646i 0.176013 + 0.304864i
\(677\) 0.00725772 0.0125707i 0.000278937 0.000483133i −0.865886 0.500242i \(-0.833245\pi\)
0.866165 + 0.499758i \(0.166578\pi\)
\(678\) 7.67544 0.294773
\(679\) 23.2630 23.2833i 0.892750 0.893533i
\(680\) −4.12413 −0.158153
\(681\) −25.4164 + 44.0225i −0.973958 + 1.68694i
\(682\) 4.78197 + 8.28261i 0.183111 + 0.317158i
\(683\) 7.71563 + 13.3639i 0.295230 + 0.511354i 0.975038 0.222036i \(-0.0712703\pi\)
−0.679808 + 0.733390i \(0.737937\pi\)
\(684\) 3.49707 6.05710i 0.133714 0.231599i
\(685\) 45.1125 1.72366
\(686\) 31.9998 8.61943i 1.22176 0.329092i
\(687\) −27.4704 −1.04806
\(688\) −2.16317 + 3.74672i −0.0824700 + 0.142842i
\(689\) −14.0142 24.2732i −0.533897 0.924736i
\(690\) 28.2706 + 48.9662i 1.07625 + 1.86411i
\(691\) 5.05570 8.75673i 0.192328 0.333122i −0.753693 0.657226i \(-0.771730\pi\)
0.946021 + 0.324104i \(0.105063\pi\)
\(692\) 7.17550 0.272772
\(693\) −9.41248 + 9.42073i −0.357551 + 0.357864i
\(694\) −31.2477 −1.18615
\(695\) −3.90656 + 6.76636i −0.148184 + 0.256663i
\(696\) −10.7397 18.6018i −0.407089 0.705099i
\(697\) −0.622267 1.07780i −0.0235700 0.0408245i
\(698\) 22.9369 39.7279i 0.868175 1.50372i
\(699\) −39.1976 −1.48259
\(700\) −0.317756 1.18380i −0.0120100 0.0447436i
\(701\) 12.5561 0.474239 0.237120 0.971480i \(-0.423797\pi\)
0.237120 + 0.971480i \(0.423797\pi\)
\(702\) 2.96127 5.12907i 0.111766 0.193584i
\(703\) −0.489369 0.847611i −0.0184569 0.0319683i
\(704\) 0.897325 + 1.55421i 0.0338192 + 0.0585766i
\(705\) −10.7283 + 18.5819i −0.404050 + 0.699834i
\(706\) −28.9006 −1.08769
\(707\) 39.8707 + 10.6646i 1.49949 + 0.401084i
\(708\) 29.3431 1.10278
\(709\) −18.9610 + 32.8414i −0.712094 + 1.23338i 0.251975 + 0.967734i \(0.418920\pi\)
−0.964070 + 0.265650i \(0.914413\pi\)
\(710\) −17.0758 29.5762i −0.640844 1.10997i
\(711\) −4.98679 8.63738i −0.187019 0.323927i
\(712\) −8.94250 + 15.4889i −0.335134 + 0.580469i
\(713\) −14.8616 −0.556573
\(714\) −13.2090 3.53314i −0.494335 0.132225i
\(715\) 11.3636 0.424974
\(716\) −9.09518 + 15.7533i −0.339903 + 0.588729i
\(717\) −10.2958 17.8329i −0.384504 0.665981i
\(718\) 1.91896 + 3.32374i 0.0716151 + 0.124041i
\(719\) 0.535531 0.927567i 0.0199719 0.0345924i −0.855867 0.517196i \(-0.826976\pi\)
0.875839 + 0.482604i \(0.160309\pi\)
\(720\) −27.4528 −1.02310
\(721\) −12.6578 47.1570i −0.471403 1.75622i
\(722\) 23.3514 0.869051
\(723\) −2.61839 + 4.53518i −0.0973789 + 0.168665i
\(724\) 10.7452 + 18.6112i 0.399342 + 0.691680i
\(725\) 1.24912 + 2.16354i 0.0463911 + 0.0803518i
\(726\) 13.5949 23.5470i 0.504552 0.873910i
\(727\) −33.3789 −1.23795 −0.618977 0.785409i \(-0.712453\pi\)
−0.618977 + 0.785409i \(0.712453\pi\)
\(728\) −6.19682 + 6.20226i −0.229670 + 0.229871i
\(729\) −15.0366 −0.556911
\(730\) 13.3907 23.1933i 0.495610 0.858422i
\(731\) −0.542857 0.940256i −0.0200783 0.0347766i
\(732\) 5.33821 + 9.24606i 0.197306 + 0.341744i
\(733\) 0.926857 1.60536i 0.0342343 0.0592955i −0.848401 0.529355i \(-0.822434\pi\)
0.882635 + 0.470059i \(0.155767\pi\)
\(734\) −8.06114 −0.297542
\(735\) 0.0330386 + 37.6979i 0.00121865 + 1.39051i
\(736\) −35.3100 −1.30154
\(737\) 13.8023 23.9063i 0.508414 0.880598i
\(738\) −2.13425 3.69663i −0.0785629 0.136075i
\(739\) 7.58650 + 13.1402i 0.279074 + 0.483370i 0.971155 0.238450i \(-0.0766393\pi\)
−0.692081 + 0.721820i \(0.743306\pi\)
\(740\) 0.559606 0.969266i 0.0205715 0.0356309i
\(741\) 13.1367 0.482588
\(742\) 40.4149 40.4503i 1.48368 1.48498i
\(743\) −11.9780 −0.439430 −0.219715 0.975564i \(-0.570513\pi\)
−0.219715 + 0.975564i \(0.570513\pi\)
\(744\) 4.19688 7.26921i 0.153865 0.266502i
\(745\) 11.0468 + 19.1337i 0.404725 + 0.701004i
\(746\) 6.39115 + 11.0698i 0.233997 + 0.405294i
\(747\) −5.76519 + 9.98560i −0.210937 + 0.365354i
\(748\) −3.15649 −0.115413
\(749\) 7.15358 + 26.6508i 0.261386 + 0.973799i
\(750\) −44.4695 −1.62380
\(751\) 8.56037 14.8270i 0.312372 0.541045i −0.666503 0.745502i \(-0.732210\pi\)
0.978875 + 0.204457i \(0.0655430\pi\)
\(752\) −9.87918 17.1112i −0.360257 0.623983i
\(753\) 5.87316 + 10.1726i 0.214030 + 0.370711i
\(754\) −13.4583 + 23.3104i −0.490121 + 0.848914i
\(755\) −23.4795 −0.854507
\(756\) 4.38161 + 1.17199i 0.159358 + 0.0426249i
\(757\) 33.6949 1.22466 0.612330 0.790602i \(-0.290232\pi\)
0.612330 + 0.790602i \(0.290232\pi\)
\(758\) −6.25510 + 10.8341i −0.227195 + 0.393514i
\(759\) −14.3652 24.8812i −0.521423 0.903131i
\(760\) 4.04168 + 7.00039i 0.146607 + 0.253931i
\(761\) −4.12485 + 7.14444i −0.149526 + 0.258986i −0.931052 0.364886i \(-0.881108\pi\)
0.781527 + 0.623872i \(0.214441\pi\)
\(762\) 24.6535 0.893104
\(763\) −52.0880 13.9325i −1.88571 0.504389i
\(764\) −10.5549 −0.381865
\(765\) 3.44470 5.96640i 0.124543 0.215715i
\(766\) 22.6180 + 39.1755i 0.817221 + 1.41547i
\(767\) 12.2060 + 21.1414i 0.440733 + 0.763371i
\(768\) 23.8047 41.2309i 0.858977 1.48779i
\(769\) −0.583432 −0.0210391 −0.0105196 0.999945i \(-0.503349\pi\)
−0.0105196 + 0.999945i \(0.503349\pi\)
\(770\) 6.00994 + 22.3902i 0.216583 + 0.806886i
\(771\) −26.7957 −0.965022
\(772\) 16.2246 28.1019i 0.583938 1.01141i
\(773\) −12.9555 22.4397i −0.465978 0.807098i 0.533267 0.845947i \(-0.320964\pi\)
−0.999245 + 0.0388489i \(0.987631\pi\)
\(774\) −1.86189 3.22489i −0.0669243 0.115916i
\(775\) −0.488131 + 0.845467i −0.0175342 + 0.0303701i
\(776\) −17.7638 −0.637685
\(777\) −1.74122 + 1.74274i −0.0624658 + 0.0625206i
\(778\) 39.4278 1.41356
\(779\) −1.21965 + 2.11250i −0.0436986 + 0.0756882i
\(780\) 7.51108 + 13.0096i 0.268940 + 0.465817i
\(781\) 8.67674 + 15.0286i 0.310478 + 0.537764i
\(782\) 6.53315 11.3157i 0.233625 0.404650i
\(783\) −9.24456 −0.330374
\(784\) −30.0787 17.3308i −1.07424 0.618958i
\(785\) 22.8197 0.814470
\(786\) 41.9553 72.6687i 1.49650 2.59201i
\(787\) 12.2121 + 21.1520i 0.435315 + 0.753988i 0.997321 0.0731454i \(-0.0233037\pi\)
−0.562006 + 0.827133i \(0.689970\pi\)
\(788\) 12.5161 + 21.6786i 0.445869 + 0.772268i
\(789\) 4.12363 7.14234i 0.146805 0.254274i
\(790\) −17.3623 −0.617722
\(791\) −3.45642 + 3.45945i −0.122896 + 0.123004i
\(792\) 7.18747 0.255396
\(793\) −4.44113 + 7.69226i −0.157709 + 0.273160i
\(794\) −20.9166 36.2286i −0.742302 1.28571i
\(795\) 32.5220 + 56.3297i 1.15344 + 1.99781i
\(796\) 7.45165 12.9066i 0.264117 0.457464i
\(797\) −10.9145 −0.386613 −0.193306 0.981138i \(-0.561921\pi\)
−0.193306 + 0.981138i \(0.561921\pi\)
\(798\) 6.94771 + 25.8838i 0.245946 + 0.916277i
\(799\) 4.95845 0.175417
\(800\) −1.15976 + 2.00876i −0.0410036 + 0.0710203i
\(801\) −14.9385 25.8743i −0.527827 0.914224i
\(802\) 6.05612 + 10.4895i 0.213849 + 0.370398i
\(803\) −6.80420 + 11.7852i −0.240115 + 0.415891i
\(804\) 36.4920 1.28698
\(805\) −34.8008 9.30851i −1.22657 0.328082i
\(806\) −10.5184 −0.370496
\(807\) −1.80365 + 3.12401i −0.0634914 + 0.109970i
\(808\) −11.1377 19.2911i −0.391823 0.678658i
\(809\) 17.3389 + 30.0319i 0.609604 + 1.05586i 0.991306 + 0.131579i \(0.0420047\pi\)
−0.381702 + 0.924285i \(0.624662\pi\)
\(810\) −21.7306 + 37.6385i −0.763536 + 1.32248i
\(811\) 47.9830 1.68491 0.842456 0.538765i \(-0.181109\pi\)
0.842456 + 0.538765i \(0.181109\pi\)
\(812\) −19.9134 5.32643i −0.698823 0.186921i
\(813\) 37.7345 1.32341
\(814\) −0.757488 + 1.31201i −0.0265499 + 0.0459858i
\(815\) 15.8220 + 27.4045i 0.554221 + 0.959938i
\(816\) 7.16140 + 12.4039i 0.250699 + 0.434224i
\(817\) −1.06401 + 1.84292i −0.0372250 + 0.0644755i
\(818\) 63.8884 2.23380
\(819\) −3.79691 14.1454i −0.132675 0.494282i
\(820\) −2.78941 −0.0974105
\(821\) 8.70627 15.0797i 0.303851 0.526285i −0.673154 0.739502i \(-0.735061\pi\)
0.977005 + 0.213217i \(0.0683942\pi\)
\(822\) −40.3624 69.9098i −1.40780 2.43838i
\(823\) −3.36519 5.82867i −0.117303 0.203175i 0.801395 0.598135i \(-0.204092\pi\)
−0.918698 + 0.394961i \(0.870758\pi\)
\(824\) −13.1762 + 22.8219i −0.459015 + 0.795037i
\(825\) −1.88730 −0.0657073
\(826\) −35.2004 + 35.2312i −1.22478 + 1.22585i
\(827\) 23.5885 0.820252 0.410126 0.912029i \(-0.365485\pi\)
0.410126 + 0.912029i \(0.365485\pi\)
\(828\) 8.41150 14.5692i 0.292320 0.506313i
\(829\) −16.1814 28.0270i −0.562004 0.973419i −0.997322 0.0731419i \(-0.976697\pi\)
0.435318 0.900277i \(-0.356636\pi\)
\(830\) 10.0362 + 17.3832i 0.348361 + 0.603379i
\(831\) 18.6902 32.3723i 0.648355 1.12298i
\(832\) −1.97376 −0.0684278
\(833\) 7.54076 4.36248i 0.261272 0.151151i
\(834\) 13.9809 0.484118
\(835\) −5.40738 + 9.36585i −0.187130 + 0.324119i
\(836\) 3.09339 + 5.35791i 0.106987 + 0.185307i
\(837\) −1.80629 3.12859i −0.0624346 0.108140i
\(838\) −2.53350 + 4.38815i −0.0875184 + 0.151586i
\(839\) 32.3692 1.11751 0.558755 0.829333i \(-0.311279\pi\)
0.558755 + 0.829333i \(0.311279\pi\)
\(840\) 14.3807 14.3933i 0.496180 0.496615i
\(841\) 13.0143 0.448769
\(842\) −4.93582 + 8.54909i −0.170100 + 0.294621i
\(843\) 36.6466 + 63.4738i 1.26218 + 2.18615i
\(844\) 11.3792 + 19.7093i 0.391687 + 0.678422i
\(845\) 8.83539 15.3033i 0.303947 0.526451i
\(846\) 17.0065 0.584695
\(847\) 4.49096 + 16.7312i 0.154311 + 0.574890i
\(848\) −59.8961 −2.05684
\(849\) −4.50374 + 7.80070i −0.154568 + 0.267719i
\(850\) −0.429163 0.743332i −0.0147202 0.0254961i
\(851\) −1.17708 2.03876i −0.0403497 0.0698878i
\(852\) −11.4703 + 19.8671i −0.392965 + 0.680636i
\(853\) −1.82393 −0.0624501 −0.0312251 0.999512i \(-0.509941\pi\)
−0.0312251 + 0.999512i \(0.509941\pi\)
\(854\) −17.5052 4.68229i −0.599016 0.160225i
\(855\) −13.5033 −0.461805
\(856\) 7.44653 12.8978i 0.254517 0.440837i
\(857\) −5.09165 8.81900i −0.173928 0.301251i 0.765862 0.643005i \(-0.222313\pi\)
−0.939790 + 0.341754i \(0.888979\pi\)
\(858\) −10.1671 17.6099i −0.347098 0.601191i
\(859\) −13.3722 + 23.1614i −0.456255 + 0.790257i −0.998759 0.0497959i \(-0.984143\pi\)
0.542504 + 0.840053i \(0.317476\pi\)
\(860\) −2.43345 −0.0829798
\(861\) 5.93135 + 1.58652i 0.202140 + 0.0540683i
\(862\) −42.8160 −1.45832
\(863\) −19.8006 + 34.2956i −0.674020 + 1.16744i 0.302734 + 0.953075i \(0.402101\pi\)
−0.976754 + 0.214362i \(0.931233\pi\)
\(864\) −4.29160 7.43327i −0.146003 0.252885i
\(865\) −6.92675 11.9975i −0.235516 0.407926i
\(866\) −23.1873 + 40.1616i −0.787937 + 1.36475i
\(867\) 35.8567 1.21776
\(868\) −2.08828 7.77993i −0.0708808 0.264068i
\(869\) 8.82230 0.299276
\(870\) 31.2319 54.0953i 1.05886 1.83400i
\(871\) 15.1798 + 26.2921i 0.514347 + 0.890875i
\(872\) 14.5506 + 25.2023i 0.492744 + 0.853457i
\(873\) 14.8373 25.6990i 0.502168 0.869781i
\(874\) −25.6102 −0.866277
\(875\) 20.0256 20.0432i 0.676989 0.677582i
\(876\) −17.9897 −0.607816
\(877\) −9.91845 + 17.1793i −0.334922 + 0.580103i −0.983470 0.181072i \(-0.942043\pi\)
0.648548 + 0.761174i \(0.275377\pi\)
\(878\) −9.43084 16.3347i −0.318276 0.551269i
\(879\) 6.16852 + 10.6842i 0.208059 + 0.360369i
\(880\) 12.1419 21.0304i 0.409303 0.708934i
\(881\) −42.9749 −1.44786 −0.723930 0.689873i \(-0.757666\pi\)
−0.723930 + 0.689873i \(0.757666\pi\)
\(882\) 25.8633 14.9624i 0.870863 0.503811i
\(883\) −15.8035 −0.531831 −0.265915 0.963996i \(-0.585674\pi\)
−0.265915 + 0.963996i \(0.585674\pi\)
\(884\) 1.73576 3.00642i 0.0583799 0.101117i
\(885\) −28.3258 49.0618i −0.952163 1.64919i
\(886\) −0.821523 1.42292i −0.0275996 0.0478039i
\(887\) −7.06451 + 12.2361i −0.237203 + 0.410848i −0.959911 0.280306i \(-0.909564\pi\)
0.722708 + 0.691154i \(0.242897\pi\)
\(888\) 1.32961 0.0446189
\(889\) −11.1020 + 11.1118i −0.372350 + 0.372677i
\(890\) −52.0108 −1.74340
\(891\) 11.0420 19.1253i 0.369921 0.640721i
\(892\) 6.46782 + 11.2026i 0.216559 + 0.375091i
\(893\) −4.85932 8.41660i −0.162611 0.281651i
\(894\) 19.7674 34.2381i 0.661119 1.14509i
\(895\) 35.1195 1.17392
\(896\) 7.21168 + 26.8673i 0.240925 + 0.897572i
\(897\) 31.5977 1.05502
\(898\) −16.9164 + 29.3000i −0.564507 + 0.977754i
\(899\) 8.20917 + 14.2187i 0.273791 + 0.474220i
\(900\) −0.552552 0.957049i −0.0184184 0.0319016i
\(901\) 7.51560 13.0174i 0.250381 0.433672i
\(902\) 3.77577 0.125719
\(903\) 5.17443 + 1.38405i 0.172194 + 0.0460584i
\(904\) 2.63936 0.0877838
\(905\) 20.7453 35.9320i 0.689599 1.19442i
\(906\) 21.0073 + 36.3856i 0.697919 + 1.20883i
\(907\) −16.7797 29.0633i −0.557161 0.965031i −0.997732 0.0673130i \(-0.978557\pi\)
0.440571 0.897718i \(-0.354776\pi\)
\(908\) 13.1646 22.8017i 0.436882 0.756701i
\(909\) 37.2113 1.23422
\(910\) −24.6305 6.58816i −0.816494 0.218396i
\(911\) 53.2950 1.76574 0.882871 0.469615i \(-0.155607\pi\)
0.882871 + 0.469615i \(0.155607\pi\)
\(912\) 14.0365 24.3119i 0.464794 0.805046i
\(913\) −5.09969 8.83292i −0.168775 0.292327i
\(914\) −34.1589 59.1649i −1.12987 1.95700i
\(915\) 10.3063 17.8510i 0.340716 0.590137i
\(916\) 14.2285 0.470122
\(917\) 13.8596 + 51.6343i 0.457685 + 1.70512i
\(918\) 3.17617 0.104829
\(919\) 20.3007 35.1618i 0.669657 1.15988i −0.308343 0.951275i \(-0.599774\pi\)
0.978000 0.208605i \(-0.0668924\pi\)
\(920\) 9.72145 + 16.8381i 0.320507 + 0.555134i
\(921\) −5.95926 10.3217i −0.196364 0.340113i
\(922\) −20.6821 + 35.8225i −0.681130 + 1.17975i
\(923\) −19.0854 −0.628203
\(924\) 11.0066 11.0162i 0.362089 0.362407i
\(925\) −0.154645 −0.00508469
\(926\) 9.35837 16.2092i 0.307535 0.532666i
\(927\) −22.0110 38.1242i −0.722936 1.25216i
\(928\) 19.5043 + 33.7824i 0.640260 + 1.10896i
\(929\) −21.8395 + 37.8270i −0.716529 + 1.24107i 0.245838 + 0.969311i \(0.420937\pi\)
−0.962367 + 0.271754i \(0.912396\pi\)
\(930\) 24.4096 0.800423
\(931\) −14.7950 8.52461i −0.484886 0.279383i
\(932\) 20.3027 0.665036
\(933\) −32.8010 + 56.8130i −1.07386 + 1.85997i
\(934\) −30.2949 52.4723i −0.991279 1.71694i
\(935\) 3.04707 + 5.27767i 0.0996497 + 0.172598i
\(936\) −3.95240 + 6.84575i −0.129188 + 0.223760i
\(937\) −48.3610 −1.57988 −0.789942 0.613181i \(-0.789890\pi\)
−0.789942 + 0.613181i \(0.789890\pi\)
\(938\) −43.7764 + 43.8147i −1.42935 + 1.43060i
\(939\) −49.4419 −1.61348
\(940\) 5.55677 9.62460i 0.181242 0.313920i
\(941\) 14.8886 + 25.7879i 0.485355 + 0.840660i 0.999858 0.0168284i \(-0.00535691\pi\)
−0.514503 + 0.857489i \(0.672024\pi\)
\(942\) −20.4169 35.3632i −0.665219 1.15219i
\(943\) −2.93363 + 5.08120i −0.0955322 + 0.165467i
\(944\) 52.1680 1.69793
\(945\) −2.27014 8.45744i −0.0738476 0.275121i
\(946\) 3.29393 0.107095
\(947\) −4.64622 + 8.04748i −0.150982 + 0.261508i −0.931589 0.363514i \(-0.881577\pi\)
0.780607 + 0.625022i \(0.214910\pi\)
\(948\) 5.83135 + 10.1002i 0.189393 + 0.328039i
\(949\) −7.48327 12.9614i −0.242917 0.420745i
\(950\) −0.841167 + 1.45694i −0.0272911 + 0.0472695i
\(951\) −38.8125 −1.25858
\(952\) −4.54220 1.21494i −0.147213 0.0393766i
\(953\) 41.8537 1.35577 0.677887 0.735166i \(-0.262896\pi\)
0.677887 + 0.735166i \(0.262896\pi\)
\(954\) 25.7770 44.6471i 0.834561 1.44550i
\(955\) 10.1890 + 17.6479i 0.329709 + 0.571073i
\(956\) 5.33278 + 9.23665i 0.172475 + 0.298735i
\(957\) −15.8699 + 27.4875i −0.513001 + 0.888543i
\(958\) 41.5855 1.34357
\(959\) 49.6857 + 13.2899i 1.60443 + 0.429153i
\(960\) 4.58041 0.147832
\(961\) 12.2920 21.2904i 0.396517 0.686787i
\(962\) −0.833086 1.44295i −0.0268598 0.0465225i
\(963\) 12.4395 + 21.5459i 0.400858 + 0.694306i
\(964\) 1.35621 2.34902i 0.0436806 0.0756570i
\(965\) −62.6487 −2.01673
\(966\) 16.7113 + 62.2584i 0.537678 + 2.00313i
\(967\) 1.00640 0.0323637 0.0161819 0.999869i \(-0.494849\pi\)
0.0161819 + 0.999869i \(0.494849\pi\)
\(968\) 4.67488 8.09712i 0.150256 0.260251i
\(969\) 3.52251 + 6.10117i 0.113159 + 0.195998i
\(970\) −25.8292 44.7375i −0.829326 1.43644i
\(971\) −17.4817 + 30.2792i −0.561015 + 0.971706i 0.436394 + 0.899756i \(0.356256\pi\)
−0.997408 + 0.0719499i \(0.977078\pi\)
\(972\) 24.0511 0.771440
\(973\) −6.29590 + 6.30142i −0.201837 + 0.202014i
\(974\) 49.3960 1.58275
\(975\) 1.03783 1.79757i 0.0332371 0.0575683i
\(976\) 9.49062 + 16.4382i 0.303787 + 0.526175i
\(977\) 13.0893 + 22.6713i 0.418763 + 0.725319i 0.995815 0.0913882i \(-0.0291304\pi\)
−0.577052 + 0.816707i \(0.695797\pi\)
\(978\) 28.3121 49.0380i 0.905320 1.56806i
\(979\) 26.4283 0.844651
\(980\) −0.0171126 19.5259i −0.000546641 0.623731i
\(981\) −48.6137 −1.55212
\(982\) 23.8862 41.3721i 0.762239 1.32024i
\(983\) −15.3146 26.5257i −0.488460 0.846038i 0.511452 0.859312i \(-0.329108\pi\)
−0.999912 + 0.0132743i \(0.995775\pi\)
\(984\) −1.65690 2.86983i −0.0528200 0.0914868i
\(985\) 24.1645 41.8541i 0.769944 1.33358i
\(986\) −14.4350 −0.459703
\(987\) −17.2899 + 17.3051i −0.550344 + 0.550827i
\(988\) −6.80423 −0.216471
\(989\) −2.55926 + 4.43277i −0.0813798 + 0.140954i
\(990\) 10.4508 + 18.1014i 0.332149 + 0.575299i
\(991\) 5.92605 + 10.2642i 0.188247 + 0.326054i 0.944666 0.328034i \(-0.106386\pi\)
−0.756419 + 0.654088i \(0.773053\pi\)
\(992\) −7.62189 + 13.2015i −0.241995 + 0.419148i
\(993\) 5.40455 0.171508
\(994\) −10.0938 37.6048i −0.320157 1.19275i
\(995\) −28.7733 −0.912174
\(996\) 6.74157 11.6767i 0.213615 0.369992i
\(997\) −3.60081 6.23679i −0.114039 0.197521i 0.803356 0.595499i \(-0.203046\pi\)
−0.917395 + 0.397978i \(0.869712\pi\)
\(998\) −3.48209 6.03115i −0.110224 0.190913i
\(999\) 0.286126 0.495585i 0.00905262 0.0156796i
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 287.2.e.c.247.4 yes 10
7.2 even 3 2009.2.a.l.1.2 5
7.4 even 3 inner 287.2.e.c.165.4 10
7.5 odd 6 2009.2.a.m.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.e.c.165.4 10 7.4 even 3 inner
287.2.e.c.247.4 yes 10 1.1 even 1 trivial
2009.2.a.l.1.2 5 7.2 even 3
2009.2.a.m.1.2 5 7.5 odd 6