Properties

Label 260.2.o.a.183.1
Level $260$
Weight $2$
Character 260.183
Analytic conductor $2.076$
Analytic rank $0$
Dimension $72$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [260,2,Mod(27,260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(260, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("260.27");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.o (of order \(4\), 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: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 183.1
Character \(\chi\) \(=\) 260.183
Dual form 260.2.o.a.27.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41404 - 0.0221303i) q^{2} +(0.798638 - 0.798638i) q^{3} +(1.99902 + 0.0625863i) q^{4} +(-1.57330 + 1.58893i) q^{5} +(-1.14698 + 1.11163i) q^{6} +(1.30625 + 1.30625i) q^{7} +(-2.82531 - 0.132739i) q^{8} +1.72435i q^{9} +(2.25988 - 2.21200i) q^{10} +3.52160i q^{11} +(1.64648 - 1.54651i) q^{12} +(-0.707107 - 0.707107i) q^{13} +(-1.81818 - 1.87599i) q^{14} +(0.0124834 + 2.52548i) q^{15} +(3.99217 + 0.250223i) q^{16} +(-1.96348 + 1.96348i) q^{17} +(0.0381605 - 2.43831i) q^{18} +2.70752 q^{19} +(-3.24451 + 3.07785i) q^{20} +2.08644 q^{21} +(0.0779341 - 4.97969i) q^{22} +(4.89998 - 4.89998i) q^{23} +(-2.36241 + 2.15039i) q^{24} +(-0.0494285 - 4.99976i) q^{25} +(0.984229 + 1.01553i) q^{26} +(3.77305 + 3.77305i) q^{27} +(2.52946 + 2.69297i) q^{28} +6.90940i q^{29} +(0.0382377 - 3.57141i) q^{30} +4.15716i q^{31} +(-5.63955 - 0.442173i) q^{32} +(2.81248 + 2.81248i) q^{33} +(2.81989 - 2.73299i) q^{34} +(-4.13066 + 0.0204178i) q^{35} +(-0.107921 + 3.44702i) q^{36} +(-6.10784 + 6.10784i) q^{37} +(-3.82854 - 0.0599183i) q^{38} -1.12944 q^{39} +(4.65599 - 4.28040i) q^{40} +8.91075 q^{41} +(-2.95031 - 0.0461735i) q^{42} +(7.58581 - 7.58581i) q^{43} +(-0.220404 + 7.03975i) q^{44} +(-2.73989 - 2.71293i) q^{45} +(-7.03720 + 6.82033i) q^{46} +(-5.48290 - 5.48290i) q^{47} +(3.38813 - 2.98846i) q^{48} -3.58744i q^{49} +(-0.0407522 + 7.07095i) q^{50} +3.13622i q^{51} +(-1.36927 - 1.45778i) q^{52} +(-4.55558 - 4.55558i) q^{53} +(-5.25175 - 5.41874i) q^{54} +(-5.59559 - 5.54055i) q^{55} +(-3.51716 - 3.86394i) q^{56} +(2.16233 - 2.16233i) q^{57} +(0.152907 - 9.77017i) q^{58} -2.28885 q^{59} +(-0.133106 + 5.04928i) q^{60} -7.76763 q^{61} +(0.0919991 - 5.87839i) q^{62} +(-2.25243 + 2.25243i) q^{63} +(7.96476 + 0.750055i) q^{64} +(2.23604 - 0.0110527i) q^{65} +(-3.91473 - 4.03921i) q^{66} +(-0.898523 - 0.898523i) q^{67} +(-4.04792 + 3.80215i) q^{68} -7.82662i q^{69} +(5.84138 + 0.0625413i) q^{70} -14.2978i q^{71} +(0.228888 - 4.87184i) q^{72} +(3.84146 + 3.84146i) q^{73} +(8.77190 - 8.50156i) q^{74} +(-4.03247 - 3.95352i) q^{75} +(5.41239 + 0.169454i) q^{76} +(-4.60008 + 4.60008i) q^{77} +(1.59708 + 0.0249950i) q^{78} -0.766856 q^{79} +(-6.67848 + 5.94962i) q^{80} +0.853540 q^{81} +(-12.6002 - 0.197198i) q^{82} +(-0.727706 + 0.727706i) q^{83} +(4.17083 + 0.130582i) q^{84} +(-0.0306909 - 6.20899i) q^{85} +(-10.8945 + 10.5588i) q^{86} +(5.51811 + 5.51811i) q^{87} +(0.467452 - 9.94962i) q^{88} -0.442426i q^{89} +(3.81427 + 3.89683i) q^{90} -1.84731i q^{91} +(10.1018 - 9.48848i) q^{92} +(3.32006 + 3.32006i) q^{93} +(7.63170 + 7.87438i) q^{94} +(-4.25975 + 4.30208i) q^{95} +(-4.85709 + 4.15082i) q^{96} +(5.22374 - 5.22374i) q^{97} +(-0.0793912 + 5.07279i) q^{98} -6.07249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48}+ \cdots - 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41404 0.0221303i −0.999878 0.0156485i
\(3\) 0.798638 0.798638i 0.461094 0.461094i −0.437920 0.899014i \(-0.644285\pi\)
0.899014 + 0.437920i \(0.144285\pi\)
\(4\) 1.99902 + 0.0625863i 0.999510 + 0.0312932i
\(5\) −1.57330 + 1.58893i −0.703603 + 0.710593i
\(6\) −1.14698 + 1.11163i −0.468253 + 0.453822i
\(7\) 1.30625 + 1.30625i 0.493715 + 0.493715i 0.909474 0.415760i \(-0.136484\pi\)
−0.415760 + 0.909474i \(0.636484\pi\)
\(8\) −2.82531 0.132739i −0.998898 0.0469301i
\(9\) 1.72435i 0.574785i
\(10\) 2.25988 2.21200i 0.714637 0.699496i
\(11\) 3.52160i 1.06180i 0.847434 + 0.530901i \(0.178146\pi\)
−0.847434 + 0.530901i \(0.821854\pi\)
\(12\) 1.64648 1.54651i 0.475297 0.446439i
\(13\) −0.707107 0.707107i −0.196116 0.196116i
\(14\) −1.81818 1.87599i −0.485928 0.501380i
\(15\) 0.0124834 + 2.52548i 0.00322320 + 0.652077i
\(16\) 3.99217 + 0.250223i 0.998041 + 0.0625557i
\(17\) −1.96348 + 1.96348i −0.476214 + 0.476214i −0.903919 0.427705i \(-0.859322\pi\)
0.427705 + 0.903919i \(0.359322\pi\)
\(18\) 0.0381605 2.43831i 0.00899451 0.574714i
\(19\) 2.70752 0.621148 0.310574 0.950549i \(-0.399479\pi\)
0.310574 + 0.950549i \(0.399479\pi\)
\(20\) −3.24451 + 3.07785i −0.725495 + 0.688227i
\(21\) 2.08644 0.455298
\(22\) 0.0779341 4.97969i 0.0166156 1.06167i
\(23\) 4.89998 4.89998i 1.02172 1.02172i 0.0219567 0.999759i \(-0.493010\pi\)
0.999759 0.0219567i \(-0.00698959\pi\)
\(24\) −2.36241 + 2.15039i −0.482225 + 0.438947i
\(25\) −0.0494285 4.99976i −0.00988571 0.999951i
\(26\) 0.984229 + 1.01553i 0.193023 + 0.199161i
\(27\) 3.77305 + 3.77305i 0.726124 + 0.726124i
\(28\) 2.52946 + 2.69297i 0.478023 + 0.508923i
\(29\) 6.90940i 1.28304i 0.767105 + 0.641522i \(0.221697\pi\)
−0.767105 + 0.641522i \(0.778303\pi\)
\(30\) 0.0382377 3.57141i 0.00698122 0.652048i
\(31\) 4.15716i 0.746647i 0.927701 + 0.373324i \(0.121782\pi\)
−0.927701 + 0.373324i \(0.878218\pi\)
\(32\) −5.63955 0.442173i −0.996940 0.0781658i
\(33\) 2.81248 + 2.81248i 0.489591 + 0.489591i
\(34\) 2.81989 2.73299i 0.483608 0.468703i
\(35\) −4.13066 + 0.0204178i −0.698210 + 0.00345123i
\(36\) −0.107921 + 3.44702i −0.0179868 + 0.574503i
\(37\) −6.10784 + 6.10784i −1.00412 + 1.00412i −0.00413068 + 0.999991i \(0.501315\pi\)
−0.999991 + 0.00413068i \(0.998685\pi\)
\(38\) −3.82854 0.0599183i −0.621072 0.00972003i
\(39\) −1.12944 −0.180856
\(40\) 4.65599 4.28040i 0.736176 0.676790i
\(41\) 8.91075 1.39162 0.695812 0.718224i \(-0.255045\pi\)
0.695812 + 0.718224i \(0.255045\pi\)
\(42\) −2.95031 0.0461735i −0.455242 0.00712472i
\(43\) 7.58581 7.58581i 1.15683 1.15683i 0.171671 0.985154i \(-0.445083\pi\)
0.985154 0.171671i \(-0.0549166\pi\)
\(44\) −0.220404 + 7.03975i −0.0332271 + 1.06128i
\(45\) −2.73989 2.71293i −0.408438 0.404420i
\(46\) −7.03720 + 6.82033i −1.03758 + 1.00560i
\(47\) −5.48290 5.48290i −0.799763 0.799763i 0.183295 0.983058i \(-0.441324\pi\)
−0.983058 + 0.183295i \(0.941324\pi\)
\(48\) 3.38813 2.98846i 0.489035 0.431347i
\(49\) 3.58744i 0.512492i
\(50\) −0.0407522 + 7.07095i −0.00576323 + 0.999983i
\(51\) 3.13622i 0.439159i
\(52\) −1.36927 1.45778i −0.189883 0.202157i
\(53\) −4.55558 4.55558i −0.625757 0.625757i 0.321241 0.946998i \(-0.395900\pi\)
−0.946998 + 0.321241i \(0.895900\pi\)
\(54\) −5.25175 5.41874i −0.714672 0.737398i
\(55\) −5.59559 5.54055i −0.754510 0.747087i
\(56\) −3.51716 3.86394i −0.470001 0.516341i
\(57\) 2.16233 2.16233i 0.286408 0.286408i
\(58\) 0.152907 9.77017i 0.0200777 1.28289i
\(59\) −2.28885 −0.297982 −0.148991 0.988839i \(-0.547603\pi\)
−0.148991 + 0.988839i \(0.547603\pi\)
\(60\) −0.133106 + 5.04928i −0.0171839 + 0.651859i
\(61\) −7.76763 −0.994543 −0.497272 0.867595i \(-0.665665\pi\)
−0.497272 + 0.867595i \(0.665665\pi\)
\(62\) 0.0919991 5.87839i 0.0116839 0.746556i
\(63\) −2.25243 + 2.25243i −0.283780 + 0.283780i
\(64\) 7.96476 + 0.750055i 0.995595 + 0.0937569i
\(65\) 2.23604 0.0110527i 0.277347 0.00137092i
\(66\) −3.91473 4.03921i −0.481869 0.497192i
\(67\) −0.898523 0.898523i −0.109772 0.109772i 0.650087 0.759859i \(-0.274732\pi\)
−0.759859 + 0.650087i \(0.774732\pi\)
\(68\) −4.04792 + 3.80215i −0.490883 + 0.461078i
\(69\) 7.82662i 0.942214i
\(70\) 5.84138 + 0.0625413i 0.698178 + 0.00747512i
\(71\) 14.2978i 1.69683i −0.529331 0.848416i \(-0.677557\pi\)
0.529331 0.848416i \(-0.322443\pi\)
\(72\) 0.228888 4.87184i 0.0269747 0.574151i
\(73\) 3.84146 + 3.84146i 0.449609 + 0.449609i 0.895224 0.445616i \(-0.147015\pi\)
−0.445616 + 0.895224i \(0.647015\pi\)
\(74\) 8.77190 8.50156i 1.01971 0.988286i
\(75\) −4.03247 3.95352i −0.465630 0.456513i
\(76\) 5.41239 + 0.169454i 0.620844 + 0.0194377i
\(77\) −4.60008 + 4.60008i −0.524228 + 0.524228i
\(78\) 1.59708 + 0.0249950i 0.180834 + 0.00283012i
\(79\) −0.766856 −0.0862780 −0.0431390 0.999069i \(-0.513736\pi\)
−0.0431390 + 0.999069i \(0.513736\pi\)
\(80\) −6.67848 + 5.94962i −0.746677 + 0.665187i
\(81\) 0.853540 0.0948378
\(82\) −12.6002 0.197198i −1.39145 0.0217768i
\(83\) −0.727706 + 0.727706i −0.0798761 + 0.0798761i −0.745916 0.666040i \(-0.767988\pi\)
0.666040 + 0.745916i \(0.267988\pi\)
\(84\) 4.17083 + 0.130582i 0.455075 + 0.0142477i
\(85\) −0.0306909 6.20899i −0.00332889 0.673460i
\(86\) −10.8945 + 10.5588i −1.17479 + 1.13858i
\(87\) 5.51811 + 5.51811i 0.591603 + 0.591603i
\(88\) 0.467452 9.94962i 0.0498305 1.06063i
\(89\) 0.442426i 0.0468970i −0.999725 0.0234485i \(-0.992535\pi\)
0.999725 0.0234485i \(-0.00746458\pi\)
\(90\) 3.81427 + 3.89683i 0.402060 + 0.410762i
\(91\) 1.84731i 0.193651i
\(92\) 10.1018 9.48848i 1.05319 0.989243i
\(93\) 3.32006 + 3.32006i 0.344274 + 0.344274i
\(94\) 7.63170 + 7.87438i 0.787150 + 0.812180i
\(95\) −4.25975 + 4.30208i −0.437042 + 0.441384i
\(96\) −4.85709 + 4.15082i −0.495725 + 0.423641i
\(97\) 5.22374 5.22374i 0.530390 0.530390i −0.390298 0.920688i \(-0.627628\pi\)
0.920688 + 0.390298i \(0.127628\pi\)
\(98\) −0.0793912 + 5.07279i −0.00801972 + 0.512429i
\(99\) −6.07249 −0.610308
\(100\) 0.214108 9.99771i 0.0214108 0.999771i
\(101\) 3.42179 0.340481 0.170240 0.985403i \(-0.445546\pi\)
0.170240 + 0.985403i \(0.445546\pi\)
\(102\) 0.0694055 4.43474i 0.00687217 0.439105i
\(103\) −9.11709 + 9.11709i −0.898333 + 0.898333i −0.995289 0.0969555i \(-0.969090\pi\)
0.0969555 + 0.995289i \(0.469090\pi\)
\(104\) 1.90394 + 2.09166i 0.186696 + 0.205104i
\(105\) −3.28260 + 3.31521i −0.320349 + 0.323532i
\(106\) 6.34096 + 6.54259i 0.615888 + 0.635473i
\(107\) 0.884982 + 0.884982i 0.0855545 + 0.0855545i 0.748589 0.663034i \(-0.230732\pi\)
−0.663034 + 0.748589i \(0.730732\pi\)
\(108\) 7.30626 + 7.77854i 0.703045 + 0.748491i
\(109\) 1.15044i 0.110192i −0.998481 0.0550959i \(-0.982454\pi\)
0.998481 0.0550959i \(-0.0175465\pi\)
\(110\) 7.78978 + 7.95839i 0.742727 + 0.758803i
\(111\) 9.75590i 0.925989i
\(112\) 4.88790 + 5.54160i 0.461863 + 0.523632i
\(113\) 2.17872 + 2.17872i 0.204956 + 0.204956i 0.802120 0.597163i \(-0.203706\pi\)
−0.597163 + 0.802120i \(0.703706\pi\)
\(114\) −3.10547 + 3.00977i −0.290854 + 0.281891i
\(115\) 0.0765909 + 15.4949i 0.00714214 + 1.44491i
\(116\) −0.432434 + 13.8120i −0.0401505 + 1.28241i
\(117\) 1.21930 1.21930i 0.112725 0.112725i
\(118\) 3.23652 + 0.0506529i 0.297946 + 0.00466298i
\(119\) −5.12958 −0.470228
\(120\) 0.299960 7.13694i 0.0273824 0.651510i
\(121\) −1.40167 −0.127425
\(122\) 10.9837 + 0.171900i 0.994422 + 0.0155631i
\(123\) 7.11646 7.11646i 0.641670 0.641670i
\(124\) −0.260181 + 8.31024i −0.0233649 + 0.746282i
\(125\) 8.02205 + 7.78760i 0.717514 + 0.696544i
\(126\) 3.23488 3.13518i 0.288186 0.279304i
\(127\) 7.30276 + 7.30276i 0.648015 + 0.648015i 0.952513 0.304498i \(-0.0984887\pi\)
−0.304498 + 0.952513i \(0.598489\pi\)
\(128\) −11.2459 1.23687i −0.994006 0.109325i
\(129\) 12.1166i 1.06681i
\(130\) −3.16210 0.0338553i −0.277334 0.00296931i
\(131\) 4.60019i 0.401920i 0.979599 + 0.200960i \(0.0644061\pi\)
−0.979599 + 0.200960i \(0.935594\pi\)
\(132\) 5.44619 + 5.79824i 0.474030 + 0.504672i
\(133\) 3.53669 + 3.53669i 0.306670 + 0.306670i
\(134\) 1.25066 + 1.29043i 0.108041 + 0.111476i
\(135\) −11.9313 + 0.0589760i −1.02688 + 0.00507585i
\(136\) 5.80807 5.28681i 0.498038 0.453340i
\(137\) 11.8882 11.8882i 1.01568 1.01568i 0.0158002 0.999875i \(-0.494970\pi\)
0.999875 0.0158002i \(-0.00502957\pi\)
\(138\) −0.173205 + 11.0672i −0.0147442 + 0.942098i
\(139\) 10.1337 0.859532 0.429766 0.902940i \(-0.358596\pi\)
0.429766 + 0.902940i \(0.358596\pi\)
\(140\) −8.25856 0.217707i −0.697976 0.0183996i
\(141\) −8.75771 −0.737532
\(142\) −0.316414 + 20.2176i −0.0265528 + 1.69662i
\(143\) 2.49015 2.49015i 0.208237 0.208237i
\(144\) −0.431472 + 6.88391i −0.0359560 + 0.573659i
\(145\) −10.9786 10.8706i −0.911722 0.902753i
\(146\) −5.34696 5.51699i −0.442518 0.456589i
\(147\) −2.86507 2.86507i −0.236307 0.236307i
\(148\) −12.5920 + 11.8274i −1.03505 + 0.972208i
\(149\) 13.1713i 1.07904i −0.841974 0.539519i \(-0.818606\pi\)
0.841974 0.539519i \(-0.181394\pi\)
\(150\) 5.61458 + 5.67968i 0.458429 + 0.463744i
\(151\) 19.6586i 1.59979i −0.600137 0.799897i \(-0.704887\pi\)
0.600137 0.799897i \(-0.295113\pi\)
\(152\) −7.64959 0.359392i −0.620464 0.0291506i
\(153\) −3.38573 3.38573i −0.273720 0.273720i
\(154\) 6.60650 6.40290i 0.532367 0.515960i
\(155\) −6.60545 6.54047i −0.530562 0.525343i
\(156\) −2.25778 0.0706878i −0.180767 0.00565955i
\(157\) −10.9745 + 10.9745i −0.875863 + 0.875863i −0.993104 0.117241i \(-0.962595\pi\)
0.117241 + 0.993104i \(0.462595\pi\)
\(158\) 1.08437 + 0.0169708i 0.0862675 + 0.00135012i
\(159\) −7.27652 −0.577066
\(160\) 9.57531 8.26520i 0.756994 0.653421i
\(161\) 12.8012 1.00887
\(162\) −1.20694 0.0188891i −0.0948261 0.00148407i
\(163\) 4.24886 4.24886i 0.332796 0.332796i −0.520851 0.853648i \(-0.674385\pi\)
0.853648 + 0.520851i \(0.174385\pi\)
\(164\) 17.8128 + 0.557691i 1.39094 + 0.0435483i
\(165\) −8.89375 + 0.0439616i −0.692377 + 0.00342240i
\(166\) 1.04511 1.01290i 0.0811163 0.0786164i
\(167\) 12.8152 + 12.8152i 0.991668 + 0.991668i 0.999966 0.00829711i \(-0.00264108\pi\)
−0.00829711 + 0.999966i \(0.502641\pi\)
\(168\) −5.89483 0.276950i −0.454796 0.0213672i
\(169\) 1.00000i 0.0769231i
\(170\) −0.0940088 + 8.78045i −0.00721014 + 0.673429i
\(171\) 4.66873i 0.357026i
\(172\) 15.6390 14.6894i 1.19246 1.12006i
\(173\) 3.57993 + 3.57993i 0.272177 + 0.272177i 0.829976 0.557799i \(-0.188354\pi\)
−0.557799 + 0.829976i \(0.688354\pi\)
\(174\) −7.68071 7.92495i −0.582273 0.600789i
\(175\) 6.46635 6.59548i 0.488810 0.498571i
\(176\) −0.881184 + 14.0588i −0.0664217 + 1.05972i
\(177\) −1.82796 + 1.82796i −0.137398 + 0.137398i
\(178\) −0.00979101 + 0.625608i −0.000733868 + 0.0468913i
\(179\) 2.63043 0.196608 0.0983039 0.995156i \(-0.468658\pi\)
0.0983039 + 0.995156i \(0.468658\pi\)
\(180\) −5.30730 5.59469i −0.395583 0.417004i
\(181\) 18.4843 1.37393 0.686963 0.726692i \(-0.258943\pi\)
0.686963 + 0.726692i \(0.258943\pi\)
\(182\) −0.0408816 + 2.61217i −0.00303034 + 0.193627i
\(183\) −6.20353 + 6.20353i −0.458578 + 0.458578i
\(184\) −14.4944 + 13.1935i −1.06854 + 0.972641i
\(185\) −0.0954708 19.3144i −0.00701915 1.42003i
\(186\) −4.62123 4.76818i −0.338845 0.349620i
\(187\) −6.91459 6.91459i −0.505645 0.505645i
\(188\) −10.6173 11.3036i −0.774344 0.824398i
\(189\) 9.85706i 0.716996i
\(190\) 6.11867 5.98904i 0.443895 0.434491i
\(191\) 23.2986i 1.68582i −0.538051 0.842912i \(-0.680839\pi\)
0.538051 0.842912i \(-0.319161\pi\)
\(192\) 6.95998 5.76194i 0.502294 0.415832i
\(193\) 2.67458 + 2.67458i 0.192520 + 0.192520i 0.796784 0.604264i \(-0.206533\pi\)
−0.604264 + 0.796784i \(0.706533\pi\)
\(194\) −7.50218 + 7.27097i −0.538625 + 0.522025i
\(195\) 1.77696 1.79461i 0.127251 0.128515i
\(196\) 0.224525 7.17137i 0.0160375 0.512241i
\(197\) −12.7121 + 12.7121i −0.905697 + 0.905697i −0.995921 0.0902242i \(-0.971242\pi\)
0.0902242 + 0.995921i \(0.471242\pi\)
\(198\) 8.58674 + 0.134386i 0.610233 + 0.00955040i
\(199\) 7.65179 0.542421 0.271211 0.962520i \(-0.412576\pi\)
0.271211 + 0.962520i \(0.412576\pi\)
\(200\) −0.524009 + 14.1324i −0.0370530 + 0.999313i
\(201\) −1.43519 −0.101230
\(202\) −4.83855 0.0757252i −0.340439 0.00532801i
\(203\) −9.02538 + 9.02538i −0.633457 + 0.633457i
\(204\) −0.196284 + 6.26937i −0.0137427 + 0.438944i
\(205\) −14.0193 + 14.1586i −0.979151 + 0.988879i
\(206\) 13.0937 12.6902i 0.912281 0.884166i
\(207\) 8.44929 + 8.44929i 0.587267 + 0.587267i
\(208\) −2.64595 2.99982i −0.183464 0.208000i
\(209\) 9.53481i 0.659537i
\(210\) 4.71509 4.61520i 0.325372 0.318479i
\(211\) 0.696850i 0.0479731i −0.999712 0.0239866i \(-0.992364\pi\)
0.999712 0.0239866i \(-0.00763589\pi\)
\(212\) −8.82158 9.39182i −0.605869 0.645033i
\(213\) −11.4187 11.4187i −0.782399 0.782399i
\(214\) −1.23182 1.27099i −0.0842052 0.0868828i
\(215\) 0.118573 + 23.9881i 0.00808660 + 1.63598i
\(216\) −10.1592 11.1609i −0.691247 0.759401i
\(217\) −5.43027 + 5.43027i −0.368631 + 0.368631i
\(218\) −0.0254595 + 1.62676i −0.00172434 + 0.110178i
\(219\) 6.13587 0.414624
\(220\) −10.8389 11.4259i −0.730762 0.770333i
\(221\) 2.77678 0.186786
\(222\) 0.215901 13.7952i 0.0144903 0.925876i
\(223\) 8.11155 8.11155i 0.543190 0.543190i −0.381273 0.924463i \(-0.624514\pi\)
0.924463 + 0.381273i \(0.124514\pi\)
\(224\) −6.78905 7.94422i −0.453613 0.530796i
\(225\) 8.62135 0.0852323i 0.574757 0.00568215i
\(226\) −3.03258 3.12901i −0.201724 0.208139i
\(227\) −16.3431 16.3431i −1.08473 1.08473i −0.996061 0.0886719i \(-0.971738\pi\)
−0.0886719 0.996061i \(-0.528262\pi\)
\(228\) 4.45787 4.18721i 0.295230 0.277305i
\(229\) 23.0298i 1.52185i −0.648838 0.760926i \(-0.724745\pi\)
0.648838 0.760926i \(-0.275255\pi\)
\(230\) 0.234604 21.9121i 0.0154693 1.44484i
\(231\) 7.34760i 0.483436i
\(232\) 0.917143 19.5212i 0.0602134 1.28163i
\(233\) 12.3099 + 12.3099i 0.806449 + 0.806449i 0.984095 0.177645i \(-0.0568480\pi\)
−0.177645 + 0.984095i \(0.556848\pi\)
\(234\) −1.75113 + 1.69716i −0.114475 + 0.110947i
\(235\) 17.3382 0.0857025i 1.13102 0.00559061i
\(236\) −4.57545 0.143250i −0.297837 0.00932481i
\(237\) −0.612440 + 0.612440i −0.0397823 + 0.0397823i
\(238\) 7.25343 + 0.113519i 0.470170 + 0.00735835i
\(239\) 12.2710 0.793744 0.396872 0.917874i \(-0.370096\pi\)
0.396872 + 0.917874i \(0.370096\pi\)
\(240\) −0.582098 + 10.0853i −0.0375742 + 0.651002i
\(241\) −25.1592 −1.62065 −0.810325 0.585981i \(-0.800709\pi\)
−0.810325 + 0.585981i \(0.800709\pi\)
\(242\) 1.98202 + 0.0310194i 0.127409 + 0.00199400i
\(243\) −10.6375 + 10.6375i −0.682395 + 0.682395i
\(244\) −15.5277 0.486147i −0.994056 0.0311224i
\(245\) 5.70021 + 5.64413i 0.364173 + 0.360591i
\(246\) −10.2205 + 9.90547i −0.651632 + 0.631550i
\(247\) −1.91451 1.91451i −0.121817 0.121817i
\(248\) 0.551815 11.7453i 0.0350403 0.745825i
\(249\) 1.16235i 0.0736608i
\(250\) −11.1712 11.1895i −0.706526 0.707687i
\(251\) 21.2328i 1.34020i −0.742269 0.670102i \(-0.766250\pi\)
0.742269 0.670102i \(-0.233750\pi\)
\(252\) −4.64363 + 4.36169i −0.292521 + 0.274760i
\(253\) 17.2558 + 17.2558i 1.08486 + 1.08486i
\(254\) −10.1648 10.4880i −0.637795 0.658076i
\(255\) −4.98325 4.93423i −0.312063 0.308993i
\(256\) 15.8748 + 1.99786i 0.992174 + 0.124866i
\(257\) −1.09013 + 1.09013i −0.0680006 + 0.0680006i −0.740289 0.672289i \(-0.765311\pi\)
0.672289 + 0.740289i \(0.265311\pi\)
\(258\) −0.268145 + 17.1334i −0.0166940 + 1.06668i
\(259\) −15.9567 −0.991500
\(260\) 4.47058 + 0.117851i 0.277254 + 0.00730881i
\(261\) −11.9143 −0.737474
\(262\) 0.101804 6.50485i 0.00628944 0.401871i
\(263\) 12.5796 12.5796i 0.775689 0.775689i −0.203405 0.979095i \(-0.565201\pi\)
0.979095 + 0.203405i \(0.0652009\pi\)
\(264\) −7.57282 8.31947i −0.466075 0.512028i
\(265\) 14.4058 0.0712077i 0.884943 0.00437425i
\(266\) −4.92275 5.07929i −0.301833 0.311431i
\(267\) −0.353338 0.353338i −0.0216239 0.0216239i
\(268\) −1.73993 1.85240i −0.106283 0.113153i
\(269\) 19.7683i 1.20529i 0.798008 + 0.602647i \(0.205887\pi\)
−0.798008 + 0.602647i \(0.794113\pi\)
\(270\) 16.8726 + 0.180649i 1.02684 + 0.0109939i
\(271\) 21.2849i 1.29296i 0.762929 + 0.646482i \(0.223761\pi\)
−0.762929 + 0.646482i \(0.776239\pi\)
\(272\) −8.32984 + 7.34723i −0.505071 + 0.445491i
\(273\) −1.47533 1.47533i −0.0892912 0.0892912i
\(274\) −17.0734 + 16.5473i −1.03144 + 0.999657i
\(275\) 17.6071 0.174068i 1.06175 0.0104967i
\(276\) 0.489839 15.6456i 0.0294848 0.941752i
\(277\) −13.0098 + 13.0098i −0.781685 + 0.781685i −0.980115 0.198430i \(-0.936416\pi\)
0.198430 + 0.980115i \(0.436416\pi\)
\(278\) −14.3295 0.224263i −0.859426 0.0134504i
\(279\) −7.16841 −0.429161
\(280\) 11.6731 + 0.490612i 0.697602 + 0.0293196i
\(281\) 12.4347 0.741790 0.370895 0.928675i \(-0.379051\pi\)
0.370895 + 0.928675i \(0.379051\pi\)
\(282\) 12.3837 + 0.193811i 0.737442 + 0.0115413i
\(283\) −13.2718 + 13.2718i −0.788926 + 0.788926i −0.981318 0.192393i \(-0.938375\pi\)
0.192393 + 0.981318i \(0.438375\pi\)
\(284\) 0.894843 28.5815i 0.0530992 1.69600i
\(285\) 0.0337991 + 6.83780i 0.00200209 + 0.405037i
\(286\) −3.57628 + 3.46606i −0.211470 + 0.204953i
\(287\) 11.6396 + 11.6396i 0.687066 + 0.687066i
\(288\) 0.762462 9.72458i 0.0449285 0.573026i
\(289\) 9.28949i 0.546441i
\(290\) 15.2836 + 15.6144i 0.897484 + 0.916910i
\(291\) 8.34375i 0.489119i
\(292\) 7.43873 + 7.91957i 0.435319 + 0.463458i
\(293\) −6.94563 6.94563i −0.405768 0.405768i 0.474492 0.880260i \(-0.342632\pi\)
−0.880260 + 0.474492i \(0.842632\pi\)
\(294\) 3.98792 + 4.11473i 0.232580 + 0.239976i
\(295\) 3.60105 3.63683i 0.209661 0.211744i
\(296\) 18.0673 16.4458i 1.05014 0.955892i
\(297\) −13.2872 + 13.2872i −0.771000 + 0.771000i
\(298\) −0.291486 + 18.6248i −0.0168853 + 1.07891i
\(299\) −6.92961 −0.400750
\(300\) −7.81356 8.15555i −0.451116 0.470861i
\(301\) 19.8179 1.14228
\(302\) −0.435051 + 27.7981i −0.0250344 + 1.59960i
\(303\) 2.73277 2.73277i 0.156994 0.156994i
\(304\) 10.8089 + 0.677483i 0.619931 + 0.0388563i
\(305\) 12.2208 12.3423i 0.699764 0.706716i
\(306\) 4.71264 + 4.86249i 0.269404 + 0.277970i
\(307\) 4.02072 + 4.02072i 0.229474 + 0.229474i 0.812473 0.582999i \(-0.198121\pi\)
−0.582999 + 0.812473i \(0.698121\pi\)
\(308\) −9.48355 + 8.90775i −0.540376 + 0.507566i
\(309\) 14.5625i 0.828432i
\(310\) 9.19563 + 9.39467i 0.522277 + 0.533581i
\(311\) 25.4676i 1.44413i −0.691823 0.722067i \(-0.743192\pi\)
0.691823 0.722067i \(-0.256808\pi\)
\(312\) 3.19103 + 0.149921i 0.180657 + 0.00848760i
\(313\) 8.61361 + 8.61361i 0.486870 + 0.486870i 0.907317 0.420447i \(-0.138127\pi\)
−0.420447 + 0.907317i \(0.638127\pi\)
\(314\) 15.7613 15.2756i 0.889461 0.862050i
\(315\) −0.0352075 7.12273i −0.00198372 0.401320i
\(316\) −1.53296 0.0479947i −0.0862358 0.00269991i
\(317\) 13.0464 13.0464i 0.732757 0.732757i −0.238408 0.971165i \(-0.576626\pi\)
0.971165 + 0.238408i \(0.0766257\pi\)
\(318\) 10.2893 + 0.161032i 0.576995 + 0.00903021i
\(319\) −24.3321 −1.36234
\(320\) −13.7228 + 11.4754i −0.767127 + 0.641496i
\(321\) 1.41356 0.0788973
\(322\) −18.1013 0.283293i −1.00875 0.0157873i
\(323\) −5.31616 + 5.31616i −0.295799 + 0.295799i
\(324\) 1.70624 + 0.0534199i 0.0947913 + 0.00296777i
\(325\) −3.50041 + 3.57031i −0.194168 + 0.198045i
\(326\) −6.10209 + 5.91403i −0.337963 + 0.327548i
\(327\) −0.918783 0.918783i −0.0508088 0.0508088i
\(328\) −25.1756 1.18280i −1.39009 0.0653092i
\(329\) 14.3240i 0.789710i
\(330\) 12.5771 + 0.134658i 0.692346 + 0.00741268i
\(331\) 22.5223i 1.23794i 0.785415 + 0.618970i \(0.212450\pi\)
−0.785415 + 0.618970i \(0.787550\pi\)
\(332\) −1.50024 + 1.40916i −0.0823366 + 0.0773374i
\(333\) −10.5321 10.5321i −0.577154 0.577154i
\(334\) −17.8376 18.4048i −0.976029 1.00707i
\(335\) 2.84134 0.0140447i 0.155239 0.000767343i
\(336\) 8.32940 + 0.522074i 0.454406 + 0.0284814i
\(337\) 18.5334 18.5334i 1.00958 1.00958i 0.00962269 0.999954i \(-0.496937\pi\)
0.999954 0.00962269i \(-0.00306304\pi\)
\(338\) 0.0221303 1.41404i 0.00120373 0.0769137i
\(339\) 3.48001 0.189008
\(340\) 0.327246 12.4138i 0.0177474 0.673234i
\(341\) −14.6398 −0.792792
\(342\) 0.103320 6.60177i 0.00558692 0.356983i
\(343\) 13.8298 13.8298i 0.746739 0.746739i
\(344\) −22.4392 + 20.4253i −1.20984 + 1.10126i
\(345\) 12.4360 + 12.3136i 0.669531 + 0.662944i
\(346\) −4.98295 5.14140i −0.267885 0.276403i
\(347\) 19.0075 + 19.0075i 1.02038 + 1.02038i 0.999788 + 0.0205887i \(0.00655405\pi\)
0.0205887 + 0.999788i \(0.493446\pi\)
\(348\) 10.6855 + 11.3762i 0.572801 + 0.609827i
\(349\) 7.56368i 0.404874i −0.979295 0.202437i \(-0.935114\pi\)
0.979295 0.202437i \(-0.0648862\pi\)
\(350\) −9.28964 + 9.18317i −0.496552 + 0.490861i
\(351\) 5.33590i 0.284809i
\(352\) 1.55716 19.8602i 0.0829967 1.05855i
\(353\) −21.5167 21.5167i −1.14522 1.14522i −0.987481 0.157740i \(-0.949579\pi\)
−0.157740 0.987481i \(-0.550421\pi\)
\(354\) 2.62526 2.54436i 0.139531 0.135231i
\(355\) 22.7182 + 22.4947i 1.20576 + 1.19390i
\(356\) 0.0276898 0.884418i 0.00146756 0.0468740i
\(357\) −4.09668 + 4.09668i −0.216819 + 0.216819i
\(358\) −3.71954 0.0582123i −0.196584 0.00307661i
\(359\) 25.3560 1.33824 0.669120 0.743155i \(-0.266671\pi\)
0.669120 + 0.743155i \(0.266671\pi\)
\(360\) 7.38092 + 8.02857i 0.389009 + 0.423143i
\(361\) −11.6693 −0.614175
\(362\) −26.1375 0.409063i −1.37376 0.0214999i
\(363\) −1.11943 + 1.11943i −0.0587547 + 0.0587547i
\(364\) 0.115616 3.69281i 0.00605995 0.193556i
\(365\) −12.1476 + 0.0600453i −0.635835 + 0.00314292i
\(366\) 8.90932 8.63475i 0.465698 0.451346i
\(367\) 0.233912 + 0.233912i 0.0122101 + 0.0122101i 0.713185 0.700975i \(-0.247252\pi\)
−0.700975 + 0.713185i \(0.747252\pi\)
\(368\) 20.7876 18.3354i 1.08363 0.955800i
\(369\) 15.3653i 0.799885i
\(370\) −0.292435 + 27.3135i −0.0152030 + 1.41996i
\(371\) 11.9014i 0.617891i
\(372\) 6.42908 + 6.84466i 0.333332 + 0.354879i
\(373\) −13.6778 13.6778i −0.708208 0.708208i 0.257950 0.966158i \(-0.416953\pi\)
−0.966158 + 0.257950i \(0.916953\pi\)
\(374\) 9.62449 + 9.93053i 0.497671 + 0.513496i
\(375\) 12.6262 0.187245i 0.652014 0.00966929i
\(376\) 14.7631 + 16.2187i 0.761349 + 0.836415i
\(377\) 4.88568 4.88568i 0.251625 0.251625i
\(378\) 0.218140 13.9383i 0.0112199 0.716908i
\(379\) −27.2977 −1.40219 −0.701093 0.713070i \(-0.747304\pi\)
−0.701093 + 0.713070i \(0.747304\pi\)
\(380\) −8.78459 + 8.33333i −0.450640 + 0.427491i
\(381\) 11.6645 0.597591
\(382\) −0.515604 + 32.9451i −0.0263806 + 1.68562i
\(383\) −10.7069 + 10.7069i −0.547095 + 0.547095i −0.925599 0.378505i \(-0.876438\pi\)
0.378505 + 0.925599i \(0.376438\pi\)
\(384\) −9.96921 + 7.99359i −0.508739 + 0.407921i
\(385\) −0.0719032 14.5465i −0.00366453 0.741361i
\(386\) −3.72277 3.84115i −0.189484 0.195509i
\(387\) 13.0806 + 13.0806i 0.664926 + 0.664926i
\(388\) 10.7693 10.1154i 0.546728 0.513533i
\(389\) 1.85990i 0.0943006i 0.998888 + 0.0471503i \(0.0150140\pi\)
−0.998888 + 0.0471503i \(0.984986\pi\)
\(390\) −2.55241 + 2.49833i −0.129246 + 0.126508i
\(391\) 19.2420i 0.973110i
\(392\) −0.476191 + 10.1356i −0.0240513 + 0.511927i
\(393\) 3.67388 + 3.67388i 0.185323 + 0.185323i
\(394\) 18.2567 17.6941i 0.919759 0.891414i
\(395\) 1.20650 1.21848i 0.0607055 0.0613086i
\(396\) −12.1390 0.380054i −0.610009 0.0190985i
\(397\) 1.54829 1.54829i 0.0777066 0.0777066i −0.667185 0.744892i \(-0.732501\pi\)
0.744892 + 0.667185i \(0.232501\pi\)
\(398\) −10.8199 0.169337i −0.542355 0.00848807i
\(399\) 5.64907 0.282807
\(400\) 1.05372 19.9722i 0.0526862 0.998611i
\(401\) −25.1569 −1.25628 −0.628139 0.778101i \(-0.716183\pi\)
−0.628139 + 0.778101i \(0.716183\pi\)
\(402\) 2.02941 + 0.0317612i 0.101218 + 0.00158410i
\(403\) 2.93955 2.93955i 0.146430 0.146430i
\(404\) 6.84023 + 0.214157i 0.340314 + 0.0106547i
\(405\) −1.34288 + 1.35622i −0.0667281 + 0.0673911i
\(406\) 12.9620 12.5625i 0.643292 0.623467i
\(407\) −21.5094 21.5094i −1.06618 1.06618i
\(408\) 0.416297 8.86079i 0.0206098 0.438675i
\(409\) 17.0509i 0.843112i 0.906802 + 0.421556i \(0.138516\pi\)
−0.906802 + 0.421556i \(0.861484\pi\)
\(410\) 20.1372 19.7106i 0.994506 0.973436i
\(411\) 18.9887i 0.936644i
\(412\) −18.7958 + 17.6546i −0.926005 + 0.869782i
\(413\) −2.98980 2.98980i −0.147118 0.147118i
\(414\) −11.7607 12.1346i −0.578005 0.596384i
\(415\) −0.0113747 2.30118i −0.000558361 0.112961i
\(416\) 3.67510 + 4.30042i 0.180187 + 0.210846i
\(417\) 8.09318 8.09318i 0.396325 0.396325i
\(418\) 0.211008 13.4826i 0.0103208 0.659456i
\(419\) 33.8791 1.65510 0.827551 0.561391i \(-0.189734\pi\)
0.827551 + 0.561391i \(0.189734\pi\)
\(420\) −6.76947 + 6.42173i −0.330316 + 0.313348i
\(421\) −25.0338 −1.22007 −0.610036 0.792374i \(-0.708845\pi\)
−0.610036 + 0.792374i \(0.708845\pi\)
\(422\) −0.0154215 + 0.985374i −0.000750707 + 0.0479672i
\(423\) 9.45446 9.45446i 0.459692 0.459692i
\(424\) 12.2662 + 13.4756i 0.595701 + 0.654434i
\(425\) 9.91397 + 9.71987i 0.480898 + 0.471483i
\(426\) 15.8938 + 16.3992i 0.770059 + 0.794546i
\(427\) −10.1464 10.1464i −0.491021 0.491021i
\(428\) 1.71371 + 1.82449i 0.0828353 + 0.0881898i
\(429\) 3.97745i 0.192033i
\(430\) 0.363198 33.9228i 0.0175150 1.63590i
\(431\) 15.0689i 0.725844i 0.931820 + 0.362922i \(0.118221\pi\)
−0.931820 + 0.362922i \(0.881779\pi\)
\(432\) 14.1185 + 16.0067i 0.679278 + 0.770125i
\(433\) −5.58575 5.58575i −0.268434 0.268434i 0.560035 0.828469i \(-0.310788\pi\)
−0.828469 + 0.560035i \(0.810788\pi\)
\(434\) 7.79879 7.55845i 0.374354 0.362817i
\(435\) −17.4496 + 0.0862528i −0.836643 + 0.00413551i
\(436\) 0.0720016 2.29975i 0.00344825 0.110138i
\(437\) 13.2668 13.2668i 0.634637 0.634637i
\(438\) −8.67637 0.135789i −0.414573 0.00648823i
\(439\) −29.6737 −1.41625 −0.708124 0.706088i \(-0.750458\pi\)
−0.708124 + 0.706088i \(0.750458\pi\)
\(440\) 15.0738 + 16.3965i 0.718618 + 0.781674i
\(441\) 6.18602 0.294572
\(442\) −3.92648 0.0614510i −0.186764 0.00292293i
\(443\) −1.89262 + 1.89262i −0.0899213 + 0.0899213i −0.750637 0.660715i \(-0.770253\pi\)
0.660715 + 0.750637i \(0.270253\pi\)
\(444\) −0.610586 + 19.5022i −0.0289771 + 0.925536i
\(445\) 0.702985 + 0.696070i 0.0333247 + 0.0329969i
\(446\) −11.6496 + 11.2906i −0.551623 + 0.534623i
\(447\) −10.5191 10.5191i −0.497538 0.497538i
\(448\) 9.42418 + 11.3837i 0.445251 + 0.537829i
\(449\) 12.5398i 0.591791i 0.955220 + 0.295895i \(0.0956180\pi\)
−0.955220 + 0.295895i \(0.904382\pi\)
\(450\) −12.1928 0.0702712i −0.574775 0.00331262i
\(451\) 31.3801i 1.47763i
\(452\) 4.21894 + 4.49166i 0.198442 + 0.211270i
\(453\) −15.7001 15.7001i −0.737655 0.737655i
\(454\) 22.7482 + 23.4715i 1.06763 + 1.10157i
\(455\) 2.93526 + 2.90638i 0.137607 + 0.136253i
\(456\) −6.39628 + 5.82223i −0.299533 + 0.272651i
\(457\) 12.2710 12.2710i 0.574015 0.574015i −0.359233 0.933248i \(-0.616962\pi\)
0.933248 + 0.359233i \(0.116962\pi\)
\(458\) −0.509657 + 32.5651i −0.0238147 + 1.52167i
\(459\) −14.8166 −0.691580
\(460\) −0.816661 + 30.9794i −0.0380770 + 1.44442i
\(461\) 6.10051 0.284129 0.142065 0.989857i \(-0.454626\pi\)
0.142065 + 0.989857i \(0.454626\pi\)
\(462\) 0.162605 10.3898i 0.00756505 0.483377i
\(463\) −23.1386 + 23.1386i −1.07534 + 1.07534i −0.0784197 + 0.996920i \(0.524987\pi\)
−0.996920 + 0.0784197i \(0.975013\pi\)
\(464\) −1.72889 + 27.5835i −0.0802616 + 1.28053i
\(465\) −10.4988 + 0.0518955i −0.486872 + 0.00240659i
\(466\) −17.1343 17.6791i −0.793731 0.818970i
\(467\) −12.2124 12.2124i −0.565122 0.565122i 0.365636 0.930758i \(-0.380851\pi\)
−0.930758 + 0.365636i \(0.880851\pi\)
\(468\) 2.51372 2.36110i 0.116197 0.109142i
\(469\) 2.34738i 0.108392i
\(470\) −24.5189 0.262514i −1.13097 0.0121089i
\(471\) 17.5294i 0.807710i
\(472\) 6.46670 + 0.303818i 0.297654 + 0.0139844i
\(473\) 26.7142 + 26.7142i 1.22832 + 1.22832i
\(474\) 0.879569 0.852462i 0.0403999 0.0391549i
\(475\) −0.133829 13.5369i −0.00614049 0.621118i
\(476\) −10.2541 0.321041i −0.469997 0.0147149i
\(477\) 7.85543 7.85543i 0.359676 0.359676i
\(478\) −17.3517 0.271561i −0.793646 0.0124209i
\(479\) 21.9564 1.00321 0.501607 0.865096i \(-0.332742\pi\)
0.501607 + 0.865096i \(0.332742\pi\)
\(480\) 1.04630 14.2481i 0.0477568 0.650334i
\(481\) 8.63779 0.393849
\(482\) 35.5762 + 0.556782i 1.62045 + 0.0253607i
\(483\) 10.2235 10.2235i 0.465185 0.465185i
\(484\) −2.80197 0.0877254i −0.127362 0.00398752i
\(485\) 0.0816515 + 16.5187i 0.00370760 + 0.750076i
\(486\) 15.2772 14.8064i 0.692989 0.671633i
\(487\) −19.5227 19.5227i −0.884659 0.884659i 0.109345 0.994004i \(-0.465125\pi\)
−0.994004 + 0.109345i \(0.965125\pi\)
\(488\) 21.9460 + 1.03106i 0.993448 + 0.0466741i
\(489\) 6.78660i 0.306901i
\(490\) −7.93542 8.10718i −0.358486 0.366245i
\(491\) 5.37843i 0.242725i 0.992608 + 0.121363i \(0.0387264\pi\)
−0.992608 + 0.121363i \(0.961274\pi\)
\(492\) 14.6713 13.7806i 0.661435 0.621276i
\(493\) −13.5665 13.5665i −0.611003 0.611003i
\(494\) 2.66482 + 2.74956i 0.119896 + 0.123708i
\(495\) 9.55387 9.64879i 0.429414 0.433681i
\(496\) −1.04021 + 16.5961i −0.0467070 + 0.745185i
\(497\) 18.6764 18.6764i 0.837750 0.837750i
\(498\) 0.0257231 1.64361i 0.00115268 0.0736518i
\(499\) −25.0685 −1.12222 −0.561111 0.827740i \(-0.689626\pi\)
−0.561111 + 0.827740i \(0.689626\pi\)
\(500\) 15.5489 + 16.0696i 0.695366 + 0.718656i
\(501\) 20.4694 0.914505
\(502\) −0.469889 + 30.0241i −0.0209722 + 1.34004i
\(503\) −16.4098 + 16.4098i −0.731676 + 0.731676i −0.970952 0.239276i \(-0.923090\pi\)
0.239276 + 0.970952i \(0.423090\pi\)
\(504\) 6.66280 6.06483i 0.296785 0.270149i
\(505\) −5.38351 + 5.43700i −0.239563 + 0.241943i
\(506\) −24.0185 24.7822i −1.06775 1.10170i
\(507\) 0.798638 + 0.798638i 0.0354688 + 0.0354688i
\(508\) 14.1413 + 15.0554i 0.627419 + 0.667976i
\(509\) 14.9919i 0.664503i 0.943191 + 0.332252i \(0.107808\pi\)
−0.943191 + 0.332252i \(0.892192\pi\)
\(510\) 6.93732 + 7.08748i 0.307190 + 0.313839i
\(511\) 10.0358i 0.443957i
\(512\) −22.4034 3.17637i −0.990098 0.140377i
\(513\) 10.2156 + 10.2156i 0.451030 + 0.451030i
\(514\) 1.56562 1.51737i 0.0690564 0.0669282i
\(515\) −0.142508 28.8304i −0.00627965 1.27042i
\(516\) 0.758335 24.2214i 0.0333839 1.06629i
\(517\) 19.3086 19.3086i 0.849190 0.849190i
\(518\) 22.5634 + 0.353126i 0.991378 + 0.0155155i
\(519\) 5.71814 0.250999
\(520\) −6.31898 0.265581i −0.277105 0.0116465i
\(521\) 13.2279 0.579524 0.289762 0.957099i \(-0.406424\pi\)
0.289762 + 0.957099i \(0.406424\pi\)
\(522\) 16.8472 + 0.263666i 0.737383 + 0.0115404i
\(523\) −13.5227 + 13.5227i −0.591304 + 0.591304i −0.937984 0.346679i \(-0.887309\pi\)
0.346679 + 0.937984i \(0.387309\pi\)
\(524\) −0.287909 + 9.19586i −0.0125773 + 0.401723i
\(525\) −0.103130 10.4317i −0.00450094 0.455276i
\(526\) −18.0664 + 17.5096i −0.787733 + 0.763456i
\(527\) −8.16249 8.16249i −0.355564 0.355564i
\(528\) 10.5242 + 11.9317i 0.458005 + 0.519259i
\(529\) 25.0195i 1.08781i
\(530\) −20.3720 0.218115i −0.884903 0.00947431i
\(531\) 3.94678i 0.171276i
\(532\) 6.84857 + 7.29126i 0.296923 + 0.316116i
\(533\) −6.30085 6.30085i −0.272920 0.272920i
\(534\) 0.491815 + 0.507454i 0.0212829 + 0.0219597i
\(535\) −2.79853 + 0.0138330i −0.120991 + 0.000598055i
\(536\) 2.41934 + 2.65787i 0.104499 + 0.114803i
\(537\) 2.10076 2.10076i 0.0906546 0.0906546i
\(538\) 0.437479 27.9532i 0.0188610 1.20515i
\(539\) 12.6335 0.544165
\(540\) −23.8546 0.628841i −1.02654 0.0270610i
\(541\) 18.3005 0.786799 0.393400 0.919368i \(-0.371299\pi\)
0.393400 + 0.919368i \(0.371299\pi\)
\(542\) 0.471041 30.0977i 0.0202330 1.29281i
\(543\) 14.7623 14.7623i 0.633509 0.633509i
\(544\) 11.9413 10.2049i 0.511980 0.437533i
\(545\) 1.82797 + 1.80999i 0.0783016 + 0.0775313i
\(546\) 2.05353 + 2.11883i 0.0878830 + 0.0906776i
\(547\) −23.1342 23.1342i −0.989147 0.989147i 0.0107946 0.999942i \(-0.496564\pi\)
−0.999942 + 0.0107946i \(0.996564\pi\)
\(548\) 24.5087 23.0207i 1.04696 0.983394i
\(549\) 13.3941i 0.571648i
\(550\) −24.9011 0.143513i −1.06178 0.00611941i
\(551\) 18.7073i 0.796960i
\(552\) −1.03889 + 22.1126i −0.0442182 + 0.941176i
\(553\) −1.00170 1.00170i −0.0425967 0.0425967i
\(554\) 18.6844 18.1085i 0.793822 0.769358i
\(555\) −15.5015 15.3490i −0.658002 0.651529i
\(556\) 20.2575 + 0.634233i 0.859111 + 0.0268975i
\(557\) −12.7940 + 12.7940i −0.542100 + 0.542100i −0.924144 0.382044i \(-0.875220\pi\)
0.382044 + 0.924144i \(0.375220\pi\)
\(558\) 10.1364 + 0.158639i 0.429109 + 0.00671573i
\(559\) −10.7280 −0.453744
\(560\) −16.4954 0.952074i −0.697058 0.0402325i
\(561\) −11.0445 −0.466300
\(562\) −17.5831 0.275183i −0.741699 0.0116079i
\(563\) −25.0765 + 25.0765i −1.05685 + 1.05685i −0.0585642 + 0.998284i \(0.518652\pi\)
−0.998284 + 0.0585642i \(0.981348\pi\)
\(564\) −17.5068 0.548112i −0.737171 0.0230797i
\(565\) −6.88962 + 0.0340552i −0.289849 + 0.00143271i
\(566\) 19.0605 18.4731i 0.801174 0.776483i
\(567\) 1.11493 + 1.11493i 0.0468228 + 0.0468228i
\(568\) −1.89786 + 40.3956i −0.0796325 + 1.69496i
\(569\) 3.78598i 0.158716i 0.996846 + 0.0793582i \(0.0252871\pi\)
−0.996846 + 0.0793582i \(0.974713\pi\)
\(570\) 0.103529 9.66968i 0.00433637 0.405018i
\(571\) 25.5130i 1.06769i −0.845583 0.533843i \(-0.820747\pi\)
0.845583 0.533843i \(-0.179253\pi\)
\(572\) 5.13371 4.82201i 0.214651 0.201618i
\(573\) −18.6071 18.6071i −0.777324 0.777324i
\(574\) −16.2013 16.7165i −0.676230 0.697733i
\(575\) −24.7409 24.2565i −1.03177 1.01157i
\(576\) −1.29336 + 13.7341i −0.0538900 + 0.572253i
\(577\) 4.42706 4.42706i 0.184301 0.184301i −0.608926 0.793227i \(-0.708399\pi\)
0.793227 + 0.608926i \(0.208399\pi\)
\(578\) 0.205579 13.1357i 0.00855098 0.546374i
\(579\) 4.27204 0.177540
\(580\) −21.2661 22.4176i −0.883025 0.930842i
\(581\) −1.90113 −0.0788721
\(582\) −0.184650 + 11.7984i −0.00765398 + 0.489059i
\(583\) 16.0429 16.0429i 0.664430 0.664430i
\(584\) −10.3434 11.3632i −0.428013 0.470213i
\(585\) 0.0190588 + 3.85573i 0.000787983 + 0.159415i
\(586\) 9.66769 + 9.97511i 0.399369 + 0.412068i
\(587\) −23.6571 23.6571i −0.976431 0.976431i 0.0232972 0.999729i \(-0.492584\pi\)
−0.999729 + 0.0232972i \(0.992584\pi\)
\(588\) −5.54801 5.90664i −0.228796 0.243586i
\(589\) 11.2556i 0.463778i
\(590\) −5.17252 + 5.06293i −0.212949 + 0.208438i
\(591\) 20.3047i 0.835223i
\(592\) −25.9118 + 22.8552i −1.06497 + 0.939342i
\(593\) −9.21789 9.21789i −0.378534 0.378534i 0.492039 0.870573i \(-0.336252\pi\)
−0.870573 + 0.492039i \(0.836252\pi\)
\(594\) 19.0826 18.4946i 0.782971 0.758841i
\(595\) 8.07038 8.15056i 0.330853 0.334141i
\(596\) 0.824345 26.3298i 0.0337665 1.07851i
\(597\) 6.11101 6.11101i 0.250107 0.250107i
\(598\) 9.79875 + 0.153354i 0.400701 + 0.00627113i
\(599\) −2.77755 −0.113488 −0.0567438 0.998389i \(-0.518072\pi\)
−0.0567438 + 0.998389i \(0.518072\pi\)
\(600\) 10.8682 + 11.7052i 0.443692 + 0.477862i
\(601\) −40.0680 −1.63441 −0.817205 0.576348i \(-0.804477\pi\)
−0.817205 + 0.576348i \(0.804477\pi\)
\(602\) −28.0233 0.438576i −1.14214 0.0178750i
\(603\) 1.54937 1.54937i 0.0630953 0.0630953i
\(604\) 1.23036 39.2979i 0.0500626 1.59901i
\(605\) 2.20525 2.22716i 0.0896563 0.0905471i
\(606\) −3.92473 + 3.80377i −0.159431 + 0.154518i
\(607\) 15.4132 + 15.4132i 0.625602 + 0.625602i 0.946958 0.321356i \(-0.104139\pi\)
−0.321356 + 0.946958i \(0.604139\pi\)
\(608\) −15.2692 1.19719i −0.619248 0.0485526i
\(609\) 14.4160i 0.584167i
\(610\) −17.5539 + 17.1820i −0.710737 + 0.695679i
\(611\) 7.75399i 0.313693i
\(612\) −6.55625 6.98005i −0.265021 0.282152i
\(613\) 24.1149 + 24.1149i 0.973991 + 0.973991i 0.999670 0.0256796i \(-0.00817496\pi\)
−0.0256796 + 0.999670i \(0.508175\pi\)
\(614\) −5.59647 5.77443i −0.225855 0.233037i
\(615\) 0.111236 + 22.5040i 0.00448549 + 0.907447i
\(616\) 13.6073 12.3860i 0.548252 0.499048i
\(617\) −9.31246 + 9.31246i −0.374905 + 0.374905i −0.869260 0.494355i \(-0.835404\pi\)
0.494355 + 0.869260i \(0.335404\pi\)
\(618\) 0.322273 20.5920i 0.0129637 0.828331i
\(619\) 20.6325 0.829290 0.414645 0.909983i \(-0.363906\pi\)
0.414645 + 0.909983i \(0.363906\pi\)
\(620\) −12.7951 13.4879i −0.513863 0.541689i
\(621\) 36.9757 1.48378
\(622\) −0.563605 + 36.0122i −0.0225985 + 1.44396i
\(623\) 0.577917 0.577917i 0.0231537 0.0231537i
\(624\) −4.50893 0.282613i −0.180502 0.0113136i
\(625\) −24.9951 + 0.494261i −0.999805 + 0.0197705i
\(626\) −11.9894 12.3706i −0.479192 0.494429i
\(627\) 7.61486 + 7.61486i 0.304108 + 0.304108i
\(628\) −22.6252 + 21.2515i −0.902842 + 0.848025i
\(629\) 23.9852i 0.956354i
\(630\) −0.107843 + 10.0726i −0.00429658 + 0.401302i
\(631\) 0.761372i 0.0303098i −0.999885 0.0151549i \(-0.995176\pi\)
0.999885 0.0151549i \(-0.00482413\pi\)
\(632\) 2.16661 + 0.101791i 0.0861830 + 0.00404904i
\(633\) −0.556531 0.556531i −0.0221201 0.0221201i
\(634\) −18.7368 + 18.1594i −0.744133 + 0.721200i
\(635\) −23.0931 + 0.114148i −0.916420 + 0.00452984i
\(636\) −14.5459 0.455410i −0.576783 0.0180582i
\(637\) −2.53670 + 2.53670i −0.100508 + 0.100508i
\(638\) 34.4066 + 0.538478i 1.36217 + 0.0213185i
\(639\) 24.6544 0.975313
\(640\) 19.6585 15.9230i 0.777071 0.629413i
\(641\) −46.1859 −1.82423 −0.912117 0.409930i \(-0.865553\pi\)
−0.912117 + 0.409930i \(0.865553\pi\)
\(642\) −1.99883 0.0312825i −0.0788876 0.00123462i
\(643\) 24.2799 24.2799i 0.957507 0.957507i −0.0416264 0.999133i \(-0.513254\pi\)
0.999133 + 0.0416264i \(0.0132539\pi\)
\(644\) 25.5898 + 0.801177i 1.00838 + 0.0315708i
\(645\) 19.2525 + 19.0632i 0.758068 + 0.750611i
\(646\) 7.63492 7.39962i 0.300392 0.291134i
\(647\) 0.561905 + 0.561905i 0.0220907 + 0.0220907i 0.718066 0.695975i \(-0.245028\pi\)
−0.695975 + 0.718066i \(0.745028\pi\)
\(648\) −2.41152 0.113298i −0.0947333 0.00445075i
\(649\) 8.06040i 0.316399i
\(650\) 5.02873 4.97110i 0.197243 0.194983i
\(651\) 8.67364i 0.339947i
\(652\) 8.75948 8.22764i 0.343048 0.322219i
\(653\) 9.91131 + 9.91131i 0.387860 + 0.387860i 0.873923 0.486064i \(-0.161568\pi\)
−0.486064 + 0.873923i \(0.661568\pi\)
\(654\) 1.27886 + 1.31953i 0.0500075 + 0.0515977i
\(655\) −7.30940 7.23749i −0.285602 0.282792i
\(656\) 35.5732 + 2.22967i 1.38890 + 0.0870540i
\(657\) −6.62403 + 6.62403i −0.258428 + 0.258428i
\(658\) −0.316995 + 20.2548i −0.0123578 + 0.789613i
\(659\) 30.2716 1.17922 0.589608 0.807690i \(-0.299282\pi\)
0.589608 + 0.807690i \(0.299282\pi\)
\(660\) −17.7815 0.468747i −0.692145 0.0182459i
\(661\) 1.99460 0.0775808 0.0387904 0.999247i \(-0.487650\pi\)
0.0387904 + 0.999247i \(0.487650\pi\)
\(662\) 0.498426 31.8475i 0.0193719 1.23779i
\(663\) 2.21764 2.21764i 0.0861261 0.0861261i
\(664\) 2.15259 1.95940i 0.0835367 0.0760395i
\(665\) −11.1839 + 0.0552815i −0.433691 + 0.00214373i
\(666\) 14.6597 + 15.1259i 0.568052 + 0.586115i
\(667\) 33.8559 + 33.8559i 1.31091 + 1.31091i
\(668\) 24.8158 + 26.4199i 0.960150 + 1.02222i
\(669\) 12.9564i 0.500923i
\(670\) −4.01808 0.0430200i −0.155232 0.00166201i
\(671\) 27.3545i 1.05601i
\(672\) −11.7666 0.922565i −0.453905 0.0355887i
\(673\) −4.18463 4.18463i −0.161306 0.161306i 0.621839 0.783145i \(-0.286386\pi\)
−0.783145 + 0.621839i \(0.786386\pi\)
\(674\) −26.6171 + 25.7968i −1.02525 + 0.993654i
\(675\) 18.6778 19.0508i 0.718910 0.733266i
\(676\) −0.0625863 + 1.99902i −0.00240717 + 0.0768854i
\(677\) −21.7743 + 21.7743i −0.836853 + 0.836853i −0.988443 0.151590i \(-0.951561\pi\)
0.151590 + 0.988443i \(0.451561\pi\)
\(678\) −4.92088 0.0770138i −0.188985 0.00295770i
\(679\) 13.6470 0.523723
\(680\) −0.737461 + 17.5464i −0.0282803 + 0.672874i
\(681\) −26.1045 −1.00033
\(682\) 20.7013 + 0.323984i 0.792695 + 0.0124060i
\(683\) 23.8214 23.8214i 0.911500 0.911500i −0.0848900 0.996390i \(-0.527054\pi\)
0.996390 + 0.0848900i \(0.0270539\pi\)
\(684\) −0.292198 + 9.33288i −0.0111725 + 0.356852i
\(685\) 0.185823 + 37.5933i 0.00709991 + 1.43636i
\(686\) −19.8620 + 19.2498i −0.758333 + 0.734963i
\(687\) −18.3925 18.3925i −0.701717 0.701717i
\(688\) 32.1820 28.3857i 1.22693 1.08219i
\(689\) 6.44256i 0.245442i
\(690\) −17.3125 17.6872i −0.659075 0.673340i
\(691\) 22.6733i 0.862534i 0.902224 + 0.431267i \(0.141933\pi\)
−0.902224 + 0.431267i \(0.858067\pi\)
\(692\) 6.93231 + 7.38042i 0.263527 + 0.280561i
\(693\) −7.93216 7.93216i −0.301318 0.301318i
\(694\) −26.4567 27.2980i −1.00428 1.03622i
\(695\) −15.9434 + 16.1018i −0.604769 + 0.610777i
\(696\) −14.8579 16.3228i −0.563188 0.618716i
\(697\) −17.4961 + 17.4961i −0.662711 + 0.662711i
\(698\) −0.167387 + 10.6953i −0.00633567 + 0.404825i
\(699\) 19.6623 0.743698
\(700\) 13.3391 12.7798i 0.504172 0.483031i
\(701\) −4.26882 −0.161231 −0.0806155 0.996745i \(-0.525689\pi\)
−0.0806155 + 0.996745i \(0.525689\pi\)
\(702\) −0.118085 + 7.54518i −0.00445683 + 0.284774i
\(703\) −16.5371 + 16.5371i −0.623708 + 0.623708i
\(704\) −2.64139 + 28.0487i −0.0995513 + 1.05713i
\(705\) 13.7785 13.9154i 0.518930 0.524085i
\(706\) 29.9494 + 30.9017i 1.12716 + 1.16300i
\(707\) 4.46970 + 4.46970i 0.168100 + 0.168100i
\(708\) −3.76854 + 3.53973i −0.141630 + 0.133031i
\(709\) 25.6567i 0.963558i −0.876293 0.481779i \(-0.839991\pi\)
0.876293 0.481779i \(-0.160009\pi\)
\(710\) −31.6266 32.3112i −1.18693 1.21262i
\(711\) 1.32233i 0.0495913i
\(712\) −0.0587269 + 1.24999i −0.00220088 + 0.0468453i
\(713\) 20.3700 + 20.3700i 0.762861 + 0.762861i
\(714\) 5.88353 5.70220i 0.220185 0.213400i
\(715\) 0.0389232 + 7.87444i 0.00145564 + 0.294487i
\(716\) 5.25829 + 0.164629i 0.196511 + 0.00615248i
\(717\) 9.80007 9.80007i 0.365990 0.365990i
\(718\) −35.8544 0.561137i −1.33808 0.0209414i
\(719\) −44.8441 −1.67240 −0.836201 0.548422i \(-0.815229\pi\)
−0.836201 + 0.548422i \(0.815229\pi\)
\(720\) −10.2592 11.5161i −0.382339 0.429178i
\(721\) −23.8183 −0.887041
\(722\) 16.5009 + 0.258246i 0.614100 + 0.00961091i
\(723\) −20.0931 + 20.0931i −0.747272 + 0.747272i
\(724\) 36.9505 + 1.15686i 1.37325 + 0.0429945i
\(725\) 34.5453 0.341522i 1.28298 0.0126838i
\(726\) 1.60769 1.55814i 0.0596669 0.0578281i
\(727\) −4.22306 4.22306i −0.156625 0.156625i 0.624444 0.781069i \(-0.285325\pi\)
−0.781069 + 0.624444i \(0.785325\pi\)
\(728\) −0.245209 + 5.21923i −0.00908806 + 0.193437i
\(729\) 19.5516i 0.724134i
\(730\) 17.1785 + 0.183924i 0.635806 + 0.00680732i
\(731\) 29.7892i 1.10179i
\(732\) −12.7892 + 12.0127i −0.472704 + 0.444003i
\(733\) 10.7917 + 10.7917i 0.398601 + 0.398601i 0.877739 0.479139i \(-0.159051\pi\)
−0.479139 + 0.877739i \(0.659051\pi\)
\(734\) −0.325584 0.335937i −0.0120175 0.0123997i
\(735\) 9.06003 0.0447835i 0.334184 0.00165186i
\(736\) −29.8003 + 25.4670i −1.09845 + 0.938726i
\(737\) 3.16424 3.16424i 0.116556 0.116556i
\(738\) 0.340038 21.7271i 0.0125170 0.799787i
\(739\) 40.5731 1.49250 0.746252 0.665663i \(-0.231851\pi\)
0.746252 + 0.665663i \(0.231851\pi\)
\(740\) 1.01797 38.6159i 0.0374214 1.41955i
\(741\) −3.05800 −0.112338
\(742\) −0.263382 + 16.8291i −0.00966906 + 0.617815i
\(743\) −2.78875 + 2.78875i −0.102309 + 0.102309i −0.756409 0.654099i \(-0.773048\pi\)
0.654099 + 0.756409i \(0.273048\pi\)
\(744\) −8.93951 9.82091i −0.327738 0.360052i
\(745\) 20.9284 + 20.7225i 0.766757 + 0.759214i
\(746\) 19.0382 + 19.6436i 0.697039 + 0.719203i
\(747\) −1.25482 1.25482i −0.0459116 0.0459116i
\(748\) −13.3897 14.2552i −0.489574 0.521221i
\(749\) 2.31201i 0.0844790i
\(750\) −17.8581 0.0146495i −0.652085 0.000534922i
\(751\) 17.6843i 0.645308i −0.946517 0.322654i \(-0.895425\pi\)
0.946517 0.322654i \(-0.104575\pi\)
\(752\) −20.5167 23.2606i −0.748167 0.848226i
\(753\) −16.9573 16.9573i −0.617960 0.617960i
\(754\) −7.01667 + 6.80043i −0.255532 + 0.247657i
\(755\) 31.2362 + 30.9290i 1.13680 + 1.12562i
\(756\) −0.616917 + 19.7045i −0.0224371 + 0.716645i
\(757\) 21.2020 21.2020i 0.770600 0.770600i −0.207611 0.978211i \(-0.566569\pi\)
0.978211 + 0.207611i \(0.0665689\pi\)
\(758\) 38.6000 + 0.604106i 1.40201 + 0.0219421i
\(759\) 27.5622 1.00044
\(760\) 12.6062 11.5893i 0.457274 0.420387i
\(761\) −10.5601 −0.382804 −0.191402 0.981512i \(-0.561303\pi\)
−0.191402 + 0.981512i \(0.561303\pi\)
\(762\) −16.4941 0.258139i −0.597518 0.00935141i
\(763\) 1.50275 1.50275i 0.0544033 0.0544033i
\(764\) 1.45817 46.5743i 0.0527548 1.68500i
\(765\) 10.7065 0.0529220i 0.387094 0.00191340i
\(766\) 15.3769 14.9030i 0.555589 0.538466i
\(767\) 1.61846 + 1.61846i 0.0584392 + 0.0584392i
\(768\) 14.2738 11.0826i 0.515060 0.399910i
\(769\) 1.08776i 0.0392255i −0.999808 0.0196128i \(-0.993757\pi\)
0.999808 0.0196128i \(-0.00624333\pi\)
\(770\) −0.220246 + 20.5710i −0.00793710 + 0.741327i
\(771\) 1.74124i 0.0627094i
\(772\) 5.17914 + 5.51393i 0.186401 + 0.198451i
\(773\) −19.0543 19.0543i −0.685334 0.685334i 0.275863 0.961197i \(-0.411036\pi\)
−0.961197 + 0.275863i \(0.911036\pi\)
\(774\) −18.2071 18.7860i −0.654439 0.675249i
\(775\) 20.7848 0.205482i 0.746611 0.00738114i
\(776\) −15.4521 + 14.0653i −0.554697 + 0.504914i
\(777\) −12.7436 + 12.7436i −0.457175 + 0.457175i
\(778\) 0.0411601 2.62997i 0.00147566 0.0942891i
\(779\) 24.1260 0.864405
\(780\) 3.66450 3.47626i 0.131210 0.124470i
\(781\) 50.3510 1.80170
\(782\) 0.425832 27.2090i 0.0152277 0.972991i
\(783\) −26.0695 + 26.0695i −0.931648 + 0.931648i
\(784\) 0.897659 14.3217i 0.0320592 0.511488i
\(785\) −0.171541 34.7041i −0.00612258 1.23864i
\(786\) −5.11372 5.27632i −0.182400 0.188200i
\(787\) −25.0958 25.0958i −0.894567 0.894567i 0.100382 0.994949i \(-0.467994\pi\)
−0.994949 + 0.100382i \(0.967994\pi\)
\(788\) −26.2073 + 24.6161i −0.933596 + 0.876912i
\(789\) 20.0930i 0.715331i
\(790\) −1.73300 + 1.69629i −0.0616574 + 0.0603511i
\(791\) 5.69188i 0.202380i
\(792\) 17.1567 + 0.806053i 0.609635 + 0.0286418i
\(793\) 5.49255 + 5.49255i 0.195046 + 0.195046i
\(794\) −2.22361 + 2.15509i −0.0789131 + 0.0764811i
\(795\) 11.4482 11.5619i 0.406025 0.410059i
\(796\) 15.2961 + 0.478897i 0.542155 + 0.0169741i
\(797\) 11.3874 11.3874i 0.403363 0.403363i −0.476053 0.879416i \(-0.657933\pi\)
0.879416 + 0.476053i \(0.157933\pi\)
\(798\) −7.98802 0.125016i −0.282773 0.00442551i
\(799\) 21.5311 0.761716
\(800\) −1.93200 + 28.2182i −0.0683066 + 0.997664i
\(801\) 0.762898 0.0269557
\(802\) 35.5729 + 0.556731i 1.25612 + 0.0196588i
\(803\) −13.5281 + 13.5281i −0.477395 + 0.477395i
\(804\) −2.86897 0.0898232i −0.101181 0.00316782i
\(805\) −20.1401 + 20.3402i −0.709845 + 0.716898i
\(806\) −4.22170 + 4.09159i −0.148703 + 0.144120i
\(807\) 15.7877 + 15.7877i 0.555754 + 0.555754i
\(808\) −9.66762 0.454203i −0.340106 0.0159788i
\(809\) 52.3022i 1.83885i 0.393268 + 0.919424i \(0.371345\pi\)
−0.393268 + 0.919424i \(0.628655\pi\)
\(810\) 1.92890 1.88803i 0.0677745 0.0663386i
\(811\) 20.4717i 0.718859i 0.933172 + 0.359430i \(0.117029\pi\)
−0.933172 + 0.359430i \(0.882971\pi\)
\(812\) −18.6068 + 17.4771i −0.652970 + 0.613324i
\(813\) 16.9989 + 16.9989i 0.596178 + 0.596178i
\(814\) 29.9391 + 30.8911i 1.04936 + 1.08273i
\(815\) 0.0664134 + 13.4359i 0.00232636 + 0.470639i
\(816\) −0.784753 + 12.5203i −0.0274719 + 0.438298i
\(817\) 20.5387 20.5387i 0.718560 0.718560i
\(818\) 0.377341 24.1106i 0.0131934 0.843009i
\(819\) 3.18542 0.111308
\(820\) −28.9110 + 27.4259i −1.00962 + 0.957754i
\(821\) 3.26359 0.113900 0.0569500 0.998377i \(-0.481862\pi\)
0.0569500 + 0.998377i \(0.481862\pi\)
\(822\) −0.420226 + 26.8508i −0.0146571 + 0.936529i
\(823\) 34.5355 34.5355i 1.20383 1.20383i 0.230838 0.972992i \(-0.425853\pi\)
0.972992 0.230838i \(-0.0741469\pi\)
\(824\) 26.9688 24.5484i 0.939502 0.855185i
\(825\) 13.9227 14.2008i 0.484727 0.494407i
\(826\) 4.16153 + 4.29386i 0.144798 + 0.149403i
\(827\) 16.0580 + 16.0580i 0.558391 + 0.558391i 0.928849 0.370458i \(-0.120799\pi\)
−0.370458 + 0.928849i \(0.620799\pi\)
\(828\) 16.3615 + 17.4191i 0.568602 + 0.605356i
\(829\) 27.1152i 0.941748i 0.882200 + 0.470874i \(0.156061\pi\)
−0.882200 + 0.470874i \(0.843939\pi\)
\(830\) −0.0348416 + 3.25421i −0.00120937 + 0.112955i
\(831\) 20.7803i 0.720861i
\(832\) −5.10157 6.16231i −0.176865 0.213640i
\(833\) 7.04387 + 7.04387i 0.244056 + 0.244056i
\(834\) −11.6232 + 11.2650i −0.402478 + 0.390074i
\(835\) −40.5247 + 0.200312i −1.40241 + 0.00693210i
\(836\) −0.596748 + 19.0603i −0.0206390 + 0.659214i
\(837\) −15.6852 + 15.6852i −0.542158 + 0.542158i
\(838\) −47.9064 0.749755i −1.65490 0.0258998i
\(839\) 0.563143 0.0194419 0.00972094 0.999953i \(-0.496906\pi\)
0.00972094 + 0.999953i \(0.496906\pi\)
\(840\) 9.71442 8.93078i 0.335179 0.308141i
\(841\) −18.7398 −0.646200
\(842\) 35.3988 + 0.554005i 1.21992 + 0.0190923i
\(843\) 9.93080 9.93080i 0.342035 0.342035i
\(844\) 0.0436132 1.39302i 0.00150123 0.0479496i
\(845\) −1.58893 1.57330i −0.0546610 0.0541233i
\(846\) −13.5782 + 13.1598i −0.466829 + 0.452442i
\(847\) −1.83093 1.83093i −0.0629114 0.0629114i
\(848\) −17.0467 19.3265i −0.585387 0.663676i
\(849\) 21.1987i 0.727538i
\(850\) −13.8037 13.9637i −0.473461 0.478950i
\(851\) 59.8565i 2.05185i
\(852\) −22.1116 23.5409i −0.757532 0.806499i
\(853\) 18.4950 + 18.4950i 0.633258 + 0.633258i 0.948884 0.315626i \(-0.102214\pi\)
−0.315626 + 0.948884i \(0.602214\pi\)
\(854\) 14.1229 + 14.5720i 0.483277 + 0.498644i
\(855\) −7.41830 7.34533i −0.253701 0.251205i
\(856\) −2.38288 2.61782i −0.0814451 0.0894753i
\(857\) −23.2399 + 23.2399i −0.793860 + 0.793860i −0.982119 0.188260i \(-0.939715\pi\)
0.188260 + 0.982119i \(0.439715\pi\)
\(858\) −0.0880223 + 5.62428i −0.00300503 + 0.192010i
\(859\) −29.9848 −1.02307 −0.511534 0.859263i \(-0.670923\pi\)
−0.511534 + 0.859263i \(0.670923\pi\)
\(860\) −1.26430 + 47.9602i −0.0431123 + 1.63543i
\(861\) 18.5917 0.633604
\(862\) 0.333480 21.3080i 0.0113584 0.725755i
\(863\) 1.19082 1.19082i 0.0405360 0.0405360i −0.686548 0.727084i \(-0.740875\pi\)
0.727084 + 0.686548i \(0.240875\pi\)
\(864\) −19.6099 22.9466i −0.667144 0.780660i
\(865\) −11.3206 + 0.0559575i −0.384912 + 0.00190261i
\(866\) 7.77486 + 8.02209i 0.264201 + 0.272602i
\(867\) 7.41894 + 7.41894i 0.251961 + 0.251961i
\(868\) −11.1951 + 10.5154i −0.379986 + 0.356915i
\(869\) 2.70056i 0.0916102i
\(870\) 24.6763 + 0.264200i 0.836606 + 0.00895721i
\(871\) 1.27070i 0.0430561i
\(872\) −0.152707 + 3.25034i −0.00517132 + 0.110070i
\(873\) 9.00757 + 9.00757i 0.304860 + 0.304860i
\(874\) −19.0534 + 18.4662i −0.644490 + 0.624628i
\(875\) 0.306257 + 20.6513i 0.0103534 + 0.698141i
\(876\) 12.2657 + 0.384021i 0.414420 + 0.0129749i
\(877\) 22.0407 22.0407i 0.744262 0.744262i −0.229133 0.973395i \(-0.573589\pi\)
0.973395 + 0.229133i \(0.0735891\pi\)
\(878\) 41.9598 + 0.656688i 1.41607 + 0.0221621i
\(879\) −11.0941 −0.374194
\(880\) −20.9522 23.5189i −0.706298 0.792823i
\(881\) −51.6638 −1.74060 −0.870299 0.492524i \(-0.836075\pi\)
−0.870299 + 0.492524i \(0.836075\pi\)
\(882\) −8.74728 0.136898i −0.294536 0.00460961i
\(883\) 9.30625 9.30625i 0.313180 0.313180i −0.532960 0.846140i \(-0.678920\pi\)
0.846140 + 0.532960i \(0.178920\pi\)
\(884\) 5.55084 + 0.173788i 0.186695 + 0.00584514i
\(885\) −0.0285726 5.78045i −0.000960458 0.194308i
\(886\) 2.71813 2.63436i 0.0913174 0.0885032i
\(887\) 13.4068 + 13.4068i 0.450157 + 0.450157i 0.895407 0.445249i \(-0.146885\pi\)
−0.445249 + 0.895407i \(0.646885\pi\)
\(888\) 1.29498 27.5635i 0.0434568 0.924969i
\(889\) 19.0784i 0.639869i
\(890\) −0.978646 0.999828i −0.0328043 0.0335143i
\(891\) 3.00583i 0.100699i
\(892\) 16.7228 15.7075i 0.559922 0.525926i
\(893\) −14.8451 14.8451i −0.496771 0.496771i
\(894\) 14.6417 + 15.1073i 0.489691 + 0.505262i
\(895\) −4.13847 + 4.17959i −0.138334 + 0.139708i
\(896\) −13.0743 16.3056i −0.436780 0.544731i
\(897\) −5.53425 + 5.53425i −0.184783 + 0.184783i
\(898\) 0.277510 17.7318i 0.00926064 0.591719i
\(899\) −28.7234 −0.957981
\(900\) 17.2396 + 0.369197i 0.574653 + 0.0123066i
\(901\) 17.8896 0.595988
\(902\) 0.694451 44.3727i 0.0231227 1.47745i
\(903\) 15.8273 15.8273i 0.526700 0.526700i
\(904\) −5.86635 6.44475i −0.195112 0.214349i
\(905\) −29.0814 + 29.3703i −0.966699 + 0.976303i
\(906\) 21.8531 + 22.5480i 0.726022 + 0.749108i
\(907\) −5.06718 5.06718i −0.168253 0.168253i 0.617958 0.786211i \(-0.287960\pi\)
−0.786211 + 0.617958i \(0.787960\pi\)
\(908\) −31.6474 33.6931i −1.05026 1.11815i
\(909\) 5.90038i 0.195703i
\(910\) −4.08625 4.17470i −0.135458 0.138390i
\(911\) 52.2824i 1.73219i −0.499877 0.866097i \(-0.666621\pi\)
0.499877 0.866097i \(-0.333379\pi\)
\(912\) 9.17344 8.09132i 0.303763 0.267930i
\(913\) −2.56269 2.56269i −0.0848127 0.0848127i
\(914\) −17.6233 + 17.0802i −0.582928 + 0.564963i
\(915\) −0.0969665 19.6170i −0.00320561 0.648519i
\(916\) 1.44135 46.0371i 0.0476236 1.52111i
\(917\) −6.00898 + 6.00898i −0.198434 + 0.198434i
\(918\) 20.9513 + 0.327896i 0.691496 + 0.0108222i
\(919\) −36.9830 −1.21996 −0.609979 0.792418i \(-0.708822\pi\)
−0.609979 + 0.792418i \(0.708822\pi\)
\(920\) 1.84038 43.7881i 0.0606754 1.44365i
\(921\) 6.42219 0.211618
\(922\) −8.62637 0.135006i −0.284094 0.00444619i
\(923\) −10.1100 + 10.1100i −0.332776 + 0.332776i
\(924\) −0.459859 + 14.6880i −0.0151282 + 0.483200i
\(925\) 30.8396 + 30.2358i 1.01400 + 0.994147i
\(926\) 33.2309 32.2068i 1.09204 1.05838i
\(927\) −15.7211 15.7211i −0.516348 0.516348i
\(928\) 3.05515 38.9659i 0.100290 1.27912i
\(929\) 13.8125i 0.453175i −0.973991 0.226587i \(-0.927243\pi\)
0.973991 0.226587i \(-0.0727569\pi\)
\(930\) 14.8469 + 0.158960i 0.486850 + 0.00521251i
\(931\) 9.71307i 0.318333i
\(932\) 23.8373 + 25.3782i 0.780818 + 0.831291i
\(933\) −20.3394 20.3394i −0.665881 0.665881i
\(934\) 16.9985 + 17.5391i 0.556209 + 0.573896i
\(935\) 21.8656 0.108081i 0.715081 0.00353463i
\(936\) −3.60676 + 3.28306i −0.117891 + 0.107310i
\(937\) −16.2119 + 16.2119i −0.529619 + 0.529619i −0.920459 0.390840i \(-0.872185\pi\)
0.390840 + 0.920459i \(0.372185\pi\)
\(938\) −0.0519483 + 3.31930i −0.00169617 + 0.108379i
\(939\) 13.7583 0.448986
\(940\) 34.6649 + 0.913815i 1.13064 + 0.0298054i
\(941\) −34.4230 −1.12216 −0.561080 0.827762i \(-0.689614\pi\)
−0.561080 + 0.827762i \(0.689614\pi\)
\(942\) 0.387930 24.7872i 0.0126394 0.807611i
\(943\) 43.6624 43.6624i 1.42184 1.42184i
\(944\) −9.13746 0.572721i −0.297399 0.0186405i
\(945\) −15.6622 15.5082i −0.509493 0.504480i
\(946\) −37.1838 38.3661i −1.20895 1.24739i
\(947\) −26.2388 26.2388i −0.852647 0.852647i 0.137811 0.990458i \(-0.455993\pi\)
−0.990458 + 0.137811i \(0.955993\pi\)
\(948\) −1.26261 + 1.18595i −0.0410077 + 0.0385179i
\(949\) 5.43264i 0.176351i
\(950\) −0.110337 + 19.1448i −0.00357982 + 0.621138i
\(951\) 20.8386i 0.675739i
\(952\) 14.4926 + 0.680892i 0.469709 + 0.0220678i
\(953\) −7.37148 7.37148i −0.238786 0.238786i 0.577562 0.816347i \(-0.304004\pi\)
−0.816347 + 0.577562i \(0.804004\pi\)
\(954\) −11.2817 + 10.9341i −0.365260 + 0.354003i
\(955\) 37.0199 + 36.6557i 1.19794 + 1.18615i
\(956\) 24.5299 + 0.767995i 0.793355 + 0.0248387i
\(957\) −19.4326 + 19.4326i −0.628166 + 0.628166i
\(958\) −31.0473 0.485902i −1.00309 0.0156988i
\(959\) 31.0578 1.00291
\(960\) −1.79483 + 20.1242i −0.0579277 + 0.649507i
\(961\) 13.7181 0.442518
\(962\) −12.2142 0.191157i −0.393801 0.00616314i
\(963\) −1.52602 + 1.52602i −0.0491754 + 0.0491754i
\(964\) −50.2939 1.57462i −1.61986 0.0507152i
\(965\) −8.45765 + 0.0418060i −0.272261 + 0.00134578i
\(966\) −14.6827 + 14.2302i −0.472407 + 0.457848i
\(967\) −12.3132 12.3132i −0.395967 0.395967i 0.480841 0.876808i \(-0.340332\pi\)
−0.876808 + 0.480841i \(0.840332\pi\)
\(968\) 3.96015 + 0.186056i 0.127284 + 0.00598005i
\(969\) 8.49138i 0.272782i
\(970\) 0.250105 23.3599i 0.00803040 0.750042i
\(971\) 35.6856i 1.14521i −0.819833 0.572603i \(-0.805934\pi\)
0.819833 0.572603i \(-0.194066\pi\)
\(972\) −21.9303 + 20.5988i −0.703415 + 0.660706i
\(973\) 13.2371 + 13.2371i 0.424363 + 0.424363i
\(974\) 27.1739 + 28.0380i 0.870707 + 0.898394i
\(975\) 0.0558268 + 5.64695i 0.00178789 + 0.180847i
\(976\) −31.0097 1.94364i −0.992596 0.0622143i
\(977\) −8.96861 + 8.96861i −0.286931 + 0.286931i −0.835865 0.548934i \(-0.815034\pi\)
0.548934 + 0.835865i \(0.315034\pi\)
\(978\) −0.150190 + 9.59653i −0.00480253 + 0.306863i
\(979\) 1.55805 0.0497954
\(980\) 11.0416 + 11.6395i 0.352711 + 0.371810i
\(981\) 1.98376 0.0633366
\(982\) 0.119026 7.60532i 0.00379828 0.242695i
\(983\) −43.0243 + 43.0243i −1.37226 + 1.37226i −0.515180 + 0.857082i \(0.672275\pi\)
−0.857082 + 0.515180i \(0.827725\pi\)
\(984\) −21.0508 + 19.1616i −0.671076 + 0.610849i
\(985\) −0.198701 40.1986i −0.00633113 1.28083i
\(986\) 18.8833 + 19.4838i 0.601367 + 0.620489i
\(987\) −11.4397 11.4397i −0.364130 0.364130i
\(988\) −3.70732 3.94696i −0.117945 0.125570i
\(989\) 74.3406i 2.36389i
\(990\) −13.7231 + 13.4323i −0.436148 + 0.426908i
\(991\) 7.62867i 0.242333i 0.992632 + 0.121166i \(0.0386634\pi\)
−0.992632 + 0.121166i \(0.961337\pi\)
\(992\) 1.83818 23.4445i 0.0583623 0.744363i
\(993\) 17.9872 + 17.9872i 0.570806 + 0.570806i
\(994\) −26.8225 + 25.9959i −0.850757 + 0.824538i
\(995\) −12.0386 + 12.1582i −0.381649 + 0.385441i
\(996\) −0.0727471 + 2.32356i −0.00230508 + 0.0736247i
\(997\) −2.71420 + 2.71420i −0.0859597 + 0.0859597i −0.748779 0.662820i \(-0.769360\pi\)
0.662820 + 0.748779i \(0.269360\pi\)
\(998\) 35.4479 + 0.554775i 1.12208 + 0.0175611i
\(999\) −46.0903 −1.45823
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 260.2.o.a.183.1 yes 72
4.3 odd 2 inner 260.2.o.a.183.19 yes 72
5.2 odd 4 inner 260.2.o.a.27.19 yes 72
20.7 even 4 inner 260.2.o.a.27.1 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.o.a.27.1 72 20.7 even 4 inner
260.2.o.a.27.19 yes 72 5.2 odd 4 inner
260.2.o.a.183.1 yes 72 1.1 even 1 trivial
260.2.o.a.183.19 yes 72 4.3 odd 2 inner