Properties

Label 1470.2.m.d.1273.7
Level $1470$
Weight $2$
Character 1470.1273
Analytic conductor $11.738$
Analytic rank $0$
Dimension $16$
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] = [1470,2,Mod(97,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.m (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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1273.7
Root \(0.117630 - 0.893490i\) of defining polynomial
Character \(\chi\) \(=\) 1470.1273
Dual form 1470.2.m.d.97.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.19306 - 1.89119i) q^{5} +1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.19306 - 1.89119i) q^{5} +1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(-0.493652 - 2.18090i) q^{10} -1.97875 q^{11} +(0.707107 + 0.707107i) q^{12} +(2.19222 - 2.19222i) q^{13} +(0.493652 + 2.18090i) q^{15} -1.00000 q^{16} +(3.25469 + 3.25469i) q^{17} +(-0.707107 - 0.707107i) q^{18} +4.21878 q^{19} +(-1.89119 - 1.19306i) q^{20} +(-1.39919 + 1.39919i) q^{22} +(-4.15953 - 4.15953i) q^{23} +1.00000 q^{24} +(-2.15321 - 4.51262i) q^{25} -3.10026i q^{26} +(0.707107 + 0.707107i) q^{27} -8.94996i q^{29} +(1.89119 + 1.19306i) q^{30} -1.73386i q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.39919 - 1.39919i) q^{33} +4.60282 q^{34} -1.00000 q^{36} +(-1.96004 + 1.96004i) q^{37} +(2.98313 - 2.98313i) q^{38} +3.10026i q^{39} +(-2.18090 + 0.493652i) q^{40} +6.55691i q^{41} +(-6.33724 - 6.33724i) q^{43} +1.97875i q^{44} +(-1.89119 - 1.19306i) q^{45} -5.88246 q^{46} +(-4.29932 - 4.29932i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-4.71345 - 1.66835i) q^{50} -4.60282 q^{51} +(-2.19222 - 2.19222i) q^{52} +(8.08484 + 8.08484i) q^{53} +1.00000 q^{54} +(-2.36077 + 3.74220i) q^{55} +(-2.98313 + 2.98313i) q^{57} +(-6.32858 - 6.32858i) q^{58} -4.20702 q^{59} +(2.18090 - 0.493652i) q^{60} -11.1200i q^{61} +(-1.22602 - 1.22602i) q^{62} +1.00000i q^{64} +(-1.53045 - 6.76135i) q^{65} -1.97875i q^{66} +(3.89769 - 3.89769i) q^{67} +(3.25469 - 3.25469i) q^{68} +5.88246 q^{69} -3.86002 q^{71} +(-0.707107 + 0.707107i) q^{72} +(10.7621 - 10.7621i) q^{73} +2.77192i q^{74} +(4.71345 + 1.66835i) q^{75} -4.21878i q^{76} +(2.19222 + 2.19222i) q^{78} +2.55514i q^{79} +(-1.19306 + 1.89119i) q^{80} -1.00000 q^{81} +(4.63643 + 4.63643i) q^{82} +(-9.52969 + 9.52969i) q^{83} +(10.0383 - 2.27219i) q^{85} -8.96222 q^{86} +(6.32858 + 6.32858i) q^{87} +(1.39919 + 1.39919i) q^{88} +6.19187 q^{89} +(-2.18090 + 0.493652i) q^{90} +(-4.15953 + 4.15953i) q^{92} +(1.22602 + 1.22602i) q^{93} -6.08016 q^{94} +(5.03327 - 7.97853i) q^{95} -1.00000i q^{96} +(1.48031 + 1.48031i) q^{97} +1.97875i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{10} - 8 q^{11} - 16 q^{13} + 4 q^{15} - 16 q^{16} + 24 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{25} + 8 q^{30} - 4 q^{33} + 16 q^{34} - 16 q^{36} + 16 q^{37} + 8 q^{38} - 24 q^{43} - 8 q^{45} + 8 q^{46} + 24 q^{47} - 16 q^{51} + 16 q^{52} - 16 q^{53} + 16 q^{54} - 56 q^{55} - 8 q^{57} - 36 q^{58} - 16 q^{59} + 8 q^{62} - 32 q^{65} + 48 q^{67} + 24 q^{68} - 8 q^{69} - 32 q^{71} + 56 q^{73} - 16 q^{78} - 16 q^{81} + 24 q^{82} - 16 q^{83} + 8 q^{85} + 16 q^{86} + 36 q^{87} - 4 q^{88} + 32 q^{89} + 8 q^{92} - 8 q^{93} - 16 q^{94} - 24 q^{95} + 44 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 1.19306 1.89119i 0.533554 0.845766i
\(6\) 1.00000i 0.408248i
\(7\) 0 0
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −0.493652 2.18090i −0.156106 0.689660i
\(11\) −1.97875 −0.596616 −0.298308 0.954470i \(-0.596422\pi\)
−0.298308 + 0.954470i \(0.596422\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 2.19222 2.19222i 0.608011 0.608011i −0.334415 0.942426i \(-0.608539\pi\)
0.942426 + 0.334415i \(0.108539\pi\)
\(14\) 0 0
\(15\) 0.493652 + 2.18090i 0.127460 + 0.563105i
\(16\) −1.00000 −0.250000
\(17\) 3.25469 + 3.25469i 0.789378 + 0.789378i 0.981392 0.192014i \(-0.0615020\pi\)
−0.192014 + 0.981392i \(0.561502\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) 4.21878 0.967856 0.483928 0.875108i \(-0.339210\pi\)
0.483928 + 0.875108i \(0.339210\pi\)
\(20\) −1.89119 1.19306i −0.422883 0.266777i
\(21\) 0 0
\(22\) −1.39919 + 1.39919i −0.298308 + 0.298308i
\(23\) −4.15953 4.15953i −0.867322 0.867322i 0.124854 0.992175i \(-0.460154\pi\)
−0.992175 + 0.124854i \(0.960154\pi\)
\(24\) 1.00000 0.204124
\(25\) −2.15321 4.51262i −0.430641 0.902523i
\(26\) 3.10026i 0.608011i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0 0
\(29\) 8.94996i 1.66197i −0.556298 0.830983i \(-0.687779\pi\)
0.556298 0.830983i \(-0.312221\pi\)
\(30\) 1.89119 + 1.19306i 0.345283 + 0.217822i
\(31\) 1.73386i 0.311411i −0.987804 0.155705i \(-0.950235\pi\)
0.987804 0.155705i \(-0.0497650\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 1.39919 1.39919i 0.243568 0.243568i
\(34\) 4.60282 0.789378
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −1.96004 + 1.96004i −0.322229 + 0.322229i −0.849622 0.527393i \(-0.823170\pi\)
0.527393 + 0.849622i \(0.323170\pi\)
\(38\) 2.98313 2.98313i 0.483928 0.483928i
\(39\) 3.10026i 0.496439i
\(40\) −2.18090 + 0.493652i −0.344830 + 0.0780532i
\(41\) 6.55691i 1.02402i 0.858980 + 0.512008i \(0.171098\pi\)
−0.858980 + 0.512008i \(0.828902\pi\)
\(42\) 0 0
\(43\) −6.33724 6.33724i −0.966421 0.966421i 0.0330335 0.999454i \(-0.489483\pi\)
−0.999454 + 0.0330335i \(0.989483\pi\)
\(44\) 1.97875i 0.298308i
\(45\) −1.89119 1.19306i −0.281922 0.177851i
\(46\) −5.88246 −0.867322
\(47\) −4.29932 4.29932i −0.627120 0.627120i 0.320222 0.947343i \(-0.396242\pi\)
−0.947343 + 0.320222i \(0.896242\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 0 0
\(50\) −4.71345 1.66835i −0.666582 0.235941i
\(51\) −4.60282 −0.644524
\(52\) −2.19222 2.19222i −0.304006 0.304006i
\(53\) 8.08484 + 8.08484i 1.11054 + 1.11054i 0.993077 + 0.117461i \(0.0374756\pi\)
0.117461 + 0.993077i \(0.462524\pi\)
\(54\) 1.00000 0.136083
\(55\) −2.36077 + 3.74220i −0.318327 + 0.504598i
\(56\) 0 0
\(57\) −2.98313 + 2.98313i −0.395125 + 0.395125i
\(58\) −6.32858 6.32858i −0.830983 0.830983i
\(59\) −4.20702 −0.547708 −0.273854 0.961771i \(-0.588298\pi\)
−0.273854 + 0.961771i \(0.588298\pi\)
\(60\) 2.18090 0.493652i 0.281552 0.0637302i
\(61\) 11.1200i 1.42377i −0.702298 0.711883i \(-0.747843\pi\)
0.702298 0.711883i \(-0.252157\pi\)
\(62\) −1.22602 1.22602i −0.155705 0.155705i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −1.53045 6.76135i −0.189829 0.838642i
\(66\) 1.97875i 0.243568i
\(67\) 3.89769 3.89769i 0.476179 0.476179i −0.427729 0.903907i \(-0.640686\pi\)
0.903907 + 0.427729i \(0.140686\pi\)
\(68\) 3.25469 3.25469i 0.394689 0.394689i
\(69\) 5.88246 0.708165
\(70\) 0 0
\(71\) −3.86002 −0.458100 −0.229050 0.973415i \(-0.573562\pi\)
−0.229050 + 0.973415i \(0.573562\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) 10.7621 10.7621i 1.25961 1.25961i 0.308328 0.951280i \(-0.400231\pi\)
0.951280 0.308328i \(-0.0997693\pi\)
\(74\) 2.77192i 0.322229i
\(75\) 4.71345 + 1.66835i 0.544262 + 0.192645i
\(76\) 4.21878i 0.483928i
\(77\) 0 0
\(78\) 2.19222 + 2.19222i 0.248220 + 0.248220i
\(79\) 2.55514i 0.287476i 0.989616 + 0.143738i \(0.0459123\pi\)
−0.989616 + 0.143738i \(0.954088\pi\)
\(80\) −1.19306 + 1.89119i −0.133388 + 0.211442i
\(81\) −1.00000 −0.111111
\(82\) 4.63643 + 4.63643i 0.512008 + 0.512008i
\(83\) −9.52969 + 9.52969i −1.04602 + 1.04602i −0.0471311 + 0.998889i \(0.515008\pi\)
−0.998889 + 0.0471311i \(0.984992\pi\)
\(84\) 0 0
\(85\) 10.0383 2.27219i 1.08880 0.246454i
\(86\) −8.96222 −0.966421
\(87\) 6.32858 + 6.32858i 0.678495 + 0.678495i
\(88\) 1.39919 + 1.39919i 0.149154 + 0.149154i
\(89\) 6.19187 0.656337 0.328168 0.944619i \(-0.393569\pi\)
0.328168 + 0.944619i \(0.393569\pi\)
\(90\) −2.18090 + 0.493652i −0.229887 + 0.0520355i
\(91\) 0 0
\(92\) −4.15953 + 4.15953i −0.433661 + 0.433661i
\(93\) 1.22602 + 1.22602i 0.127133 + 0.127133i
\(94\) −6.08016 −0.627120
\(95\) 5.03327 7.97853i 0.516403 0.818580i
\(96\) 1.00000i 0.102062i
\(97\) 1.48031 + 1.48031i 0.150303 + 0.150303i 0.778253 0.627951i \(-0.216106\pi\)
−0.627951 + 0.778253i \(0.716106\pi\)
\(98\) 0 0
\(99\) 1.97875i 0.198872i
\(100\) −4.51262 + 2.15321i −0.451262 + 0.215321i
\(101\) 10.0472i 0.999733i −0.866102 0.499866i \(-0.833382\pi\)
0.866102 0.499866i \(-0.166618\pi\)
\(102\) −3.25469 + 3.25469i −0.322262 + 0.322262i
\(103\) 3.52695 3.52695i 0.347521 0.347521i −0.511665 0.859185i \(-0.670971\pi\)
0.859185 + 0.511665i \(0.170971\pi\)
\(104\) −3.10026 −0.304006
\(105\) 0 0
\(106\) 11.4337 1.11054
\(107\) 4.27775 4.27775i 0.413545 0.413545i −0.469426 0.882972i \(-0.655539\pi\)
0.882972 + 0.469426i \(0.155539\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) 9.74899i 0.933784i −0.884314 0.466892i \(-0.845374\pi\)
0.884314 0.466892i \(-0.154626\pi\)
\(110\) 0.976815 + 4.31545i 0.0931356 + 0.411462i
\(111\) 2.77192i 0.263099i
\(112\) 0 0
\(113\) 6.02504 + 6.02504i 0.566788 + 0.566788i 0.931227 0.364439i \(-0.118739\pi\)
−0.364439 + 0.931227i \(0.618739\pi\)
\(114\) 4.21878i 0.395125i
\(115\) −12.8290 + 2.90389i −1.19631 + 0.270789i
\(116\) −8.94996 −0.830983
\(117\) −2.19222 2.19222i −0.202670 0.202670i
\(118\) −2.97481 + 2.97481i −0.273854 + 0.273854i
\(119\) 0 0
\(120\) 1.19306 1.89119i 0.108911 0.172641i
\(121\) −7.08454 −0.644049
\(122\) −7.86301 7.86301i −0.711883 0.711883i
\(123\) −4.63643 4.63643i −0.418053 0.418053i
\(124\) −1.73386 −0.155705
\(125\) −11.1031 1.31171i −0.993094 0.117323i
\(126\) 0 0
\(127\) −8.92770 + 8.92770i −0.792205 + 0.792205i −0.981852 0.189647i \(-0.939266\pi\)
0.189647 + 0.981852i \(0.439266\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 8.96222 0.789079
\(130\) −5.86319 3.69881i −0.514236 0.324407i
\(131\) 5.12160i 0.447476i 0.974649 + 0.223738i \(0.0718260\pi\)
−0.974649 + 0.223738i \(0.928174\pi\)
\(132\) −1.39919 1.39919i −0.121784 0.121784i
\(133\) 0 0
\(134\) 5.51217i 0.476179i
\(135\) 2.18090 0.493652i 0.187702 0.0424868i
\(136\) 4.60282i 0.394689i
\(137\) −8.18996 + 8.18996i −0.699715 + 0.699715i −0.964349 0.264634i \(-0.914749\pi\)
0.264634 + 0.964349i \(0.414749\pi\)
\(138\) 4.15953 4.15953i 0.354083 0.354083i
\(139\) −2.87054 −0.243476 −0.121738 0.992562i \(-0.538847\pi\)
−0.121738 + 0.992562i \(0.538847\pi\)
\(140\) 0 0
\(141\) 6.08016 0.512042
\(142\) −2.72944 + 2.72944i −0.229050 + 0.229050i
\(143\) −4.33785 + 4.33785i −0.362750 + 0.362750i
\(144\) 1.00000i 0.0833333i
\(145\) −16.9261 10.6779i −1.40563 0.886748i
\(146\) 15.2199i 1.25961i
\(147\) 0 0
\(148\) 1.96004 + 1.96004i 0.161114 + 0.161114i
\(149\) 15.5796i 1.27633i −0.769898 0.638167i \(-0.779693\pi\)
0.769898 0.638167i \(-0.220307\pi\)
\(150\) 4.51262 2.15321i 0.368454 0.175809i
\(151\) 21.1906 1.72446 0.862232 0.506513i \(-0.169066\pi\)
0.862232 + 0.506513i \(0.169066\pi\)
\(152\) −2.98313 2.98313i −0.241964 0.241964i
\(153\) 3.25469 3.25469i 0.263126 0.263126i
\(154\) 0 0
\(155\) −3.27906 2.06860i −0.263381 0.166154i
\(156\) 3.10026 0.248220
\(157\) 10.7362 + 10.7362i 0.856846 + 0.856846i 0.990965 0.134119i \(-0.0428206\pi\)
−0.134119 + 0.990965i \(0.542821\pi\)
\(158\) 1.80676 + 1.80676i 0.143738 + 0.143738i
\(159\) −11.4337 −0.906751
\(160\) 0.493652 + 2.18090i 0.0390266 + 0.172415i
\(161\) 0 0
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) 15.7848 + 15.7848i 1.23636 + 1.23636i 0.961479 + 0.274879i \(0.0886378\pi\)
0.274879 + 0.961479i \(0.411362\pi\)
\(164\) 6.55691 0.512008
\(165\) −0.976815 4.31545i −0.0760449 0.335958i
\(166\) 13.4770i 1.04602i
\(167\) 6.91224 + 6.91224i 0.534885 + 0.534885i 0.922022 0.387137i \(-0.126536\pi\)
−0.387137 + 0.922022i \(0.626536\pi\)
\(168\) 0 0
\(169\) 3.38837i 0.260644i
\(170\) 5.49145 8.70482i 0.421175 0.667629i
\(171\) 4.21878i 0.322619i
\(172\) −6.33724 + 6.33724i −0.483210 + 0.483210i
\(173\) −3.20151 + 3.20151i −0.243406 + 0.243406i −0.818258 0.574852i \(-0.805060\pi\)
0.574852 + 0.818258i \(0.305060\pi\)
\(174\) 8.94996 0.678495
\(175\) 0 0
\(176\) 1.97875 0.149154
\(177\) 2.97481 2.97481i 0.223601 0.223601i
\(178\) 4.37831 4.37831i 0.328168 0.328168i
\(179\) 2.06788i 0.154561i −0.997009 0.0772803i \(-0.975376\pi\)
0.997009 0.0772803i \(-0.0246236\pi\)
\(180\) −1.19306 + 1.89119i −0.0889256 + 0.140961i
\(181\) 6.13199i 0.455787i 0.973686 + 0.227894i \(0.0731839\pi\)
−0.973686 + 0.227894i \(0.926816\pi\)
\(182\) 0 0
\(183\) 7.86301 + 7.86301i 0.581250 + 0.581250i
\(184\) 5.88246i 0.433661i
\(185\) 1.36836 + 6.04526i 0.100604 + 0.444456i
\(186\) 1.73386 0.127133
\(187\) −6.44022 6.44022i −0.470956 0.470956i
\(188\) −4.29932 + 4.29932i −0.313560 + 0.313560i
\(189\) 0 0
\(190\) −2.08261 9.20073i −0.151088 0.667491i
\(191\) −16.1661 −1.16974 −0.584869 0.811128i \(-0.698854\pi\)
−0.584869 + 0.811128i \(0.698854\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) 15.4085 + 15.4085i 1.10913 + 1.10913i 0.993265 + 0.115864i \(0.0369636\pi\)
0.115864 + 0.993265i \(0.463036\pi\)
\(194\) 2.09348 0.150303
\(195\) 5.86319 + 3.69881i 0.419872 + 0.264877i
\(196\) 0 0
\(197\) −0.628120 + 0.628120i −0.0447517 + 0.0447517i −0.729129 0.684377i \(-0.760074\pi\)
0.684377 + 0.729129i \(0.260074\pi\)
\(198\) 1.39919 + 1.39919i 0.0994361 + 0.0994361i
\(199\) −9.62495 −0.682295 −0.341147 0.940010i \(-0.610816\pi\)
−0.341147 + 0.940010i \(0.610816\pi\)
\(200\) −1.66835 + 4.71345i −0.117970 + 0.333291i
\(201\) 5.51217i 0.388798i
\(202\) −7.10444 7.10444i −0.499866 0.499866i
\(203\) 0 0
\(204\) 4.60282i 0.322262i
\(205\) 12.4004 + 7.82280i 0.866079 + 0.546368i
\(206\) 4.98786i 0.347521i
\(207\) −4.15953 + 4.15953i −0.289107 + 0.289107i
\(208\) −2.19222 + 2.19222i −0.152003 + 0.152003i
\(209\) −8.34793 −0.577439
\(210\) 0 0
\(211\) 11.2669 0.775648 0.387824 0.921733i \(-0.373227\pi\)
0.387824 + 0.921733i \(0.373227\pi\)
\(212\) 8.08484 8.08484i 0.555269 0.555269i
\(213\) 2.72944 2.72944i 0.187018 0.187018i
\(214\) 6.04965i 0.413545i
\(215\) −19.5457 + 4.42421i −1.33300 + 0.301729i
\(216\) 1.00000i 0.0680414i
\(217\) 0 0
\(218\) −6.89357 6.89357i −0.466892 0.466892i
\(219\) 15.2199i 1.02847i
\(220\) 3.74220 + 2.36077i 0.252299 + 0.159163i
\(221\) 14.2700 0.959901
\(222\) −1.96004 1.96004i −0.131549 0.131549i
\(223\) 13.1718 13.1718i 0.882048 0.882048i −0.111694 0.993743i \(-0.535628\pi\)
0.993743 + 0.111694i \(0.0356277\pi\)
\(224\) 0 0
\(225\) −4.51262 + 2.15321i −0.300841 + 0.143547i
\(226\) 8.52069 0.566788
\(227\) 19.0312 + 19.0312i 1.26314 + 1.26314i 0.949561 + 0.313583i \(0.101529\pi\)
0.313583 + 0.949561i \(0.398471\pi\)
\(228\) 2.98313 + 2.98313i 0.197563 + 0.197563i
\(229\) 26.8905 1.77697 0.888486 0.458904i \(-0.151758\pi\)
0.888486 + 0.458904i \(0.151758\pi\)
\(230\) −7.01814 + 11.1249i −0.462762 + 0.733551i
\(231\) 0 0
\(232\) −6.32858 + 6.32858i −0.415491 + 0.415491i
\(233\) −0.651418 0.651418i −0.0426758 0.0426758i 0.685447 0.728123i \(-0.259607\pi\)
−0.728123 + 0.685447i \(0.759607\pi\)
\(234\) −3.10026 −0.202670
\(235\) −13.2602 + 3.00148i −0.865000 + 0.195795i
\(236\) 4.20702i 0.273854i
\(237\) −1.80676 1.80676i −0.117362 0.117362i
\(238\) 0 0
\(239\) 25.3432i 1.63931i −0.572856 0.819656i \(-0.694164\pi\)
0.572856 0.819656i \(-0.305836\pi\)
\(240\) −0.493652 2.18090i −0.0318651 0.140776i
\(241\) 21.1200i 1.36046i 0.732999 + 0.680230i \(0.238120\pi\)
−0.732999 + 0.680230i \(0.761880\pi\)
\(242\) −5.00952 + 5.00952i −0.322024 + 0.322024i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −11.1200 −0.711883
\(245\) 0 0
\(246\) −6.55691 −0.418053
\(247\) 9.24849 9.24849i 0.588467 0.588467i
\(248\) −1.22602 + 1.22602i −0.0778527 + 0.0778527i
\(249\) 13.4770i 0.854072i
\(250\) −8.77861 + 6.92358i −0.555208 + 0.437886i
\(251\) 2.70623i 0.170816i 0.996346 + 0.0854078i \(0.0272193\pi\)
−0.996346 + 0.0854078i \(0.972781\pi\)
\(252\) 0 0
\(253\) 8.23068 + 8.23068i 0.517458 + 0.517458i
\(254\) 12.6257i 0.792205i
\(255\) −5.49145 + 8.70482i −0.343888 + 0.545117i
\(256\) 1.00000 0.0625000
\(257\) 16.9862 + 16.9862i 1.05957 + 1.05957i 0.998110 + 0.0614577i \(0.0195749\pi\)
0.0614577 + 0.998110i \(0.480425\pi\)
\(258\) 6.33724 6.33724i 0.394540 0.394540i
\(259\) 0 0
\(260\) −6.76135 + 1.53045i −0.419321 + 0.0949145i
\(261\) −8.94996 −0.553989
\(262\) 3.62152 + 3.62152i 0.223738 + 0.223738i
\(263\) 0.601271 + 0.601271i 0.0370759 + 0.0370759i 0.725402 0.688326i \(-0.241654\pi\)
−0.688326 + 0.725402i \(0.741654\pi\)
\(264\) −1.97875 −0.121784
\(265\) 24.9357 5.64426i 1.53179 0.346724i
\(266\) 0 0
\(267\) −4.37831 + 4.37831i −0.267948 + 0.267948i
\(268\) −3.89769 3.89769i −0.238089 0.238089i
\(269\) −11.6434 −0.709912 −0.354956 0.934883i \(-0.615504\pi\)
−0.354956 + 0.934883i \(0.615504\pi\)
\(270\) 1.19306 1.89119i 0.0726074 0.115094i
\(271\) 23.3447i 1.41809i 0.705162 + 0.709046i \(0.250874\pi\)
−0.705162 + 0.709046i \(0.749126\pi\)
\(272\) −3.25469 3.25469i −0.197344 0.197344i
\(273\) 0 0
\(274\) 11.5824i 0.699715i
\(275\) 4.26066 + 8.92935i 0.256928 + 0.538460i
\(276\) 5.88246i 0.354083i
\(277\) 6.68198 6.68198i 0.401481 0.401481i −0.477274 0.878755i \(-0.658375\pi\)
0.878755 + 0.477274i \(0.158375\pi\)
\(278\) −2.02978 + 2.02978i −0.121738 + 0.121738i
\(279\) −1.73386 −0.103804
\(280\) 0 0
\(281\) −11.7320 −0.699871 −0.349935 0.936774i \(-0.613796\pi\)
−0.349935 + 0.936774i \(0.613796\pi\)
\(282\) 4.29932 4.29932i 0.256021 0.256021i
\(283\) −2.57938 + 2.57938i −0.153328 + 0.153328i −0.779603 0.626275i \(-0.784579\pi\)
0.626275 + 0.779603i \(0.284579\pi\)
\(284\) 3.86002i 0.229050i
\(285\) 2.08261 + 9.20073i 0.123363 + 0.545004i
\(286\) 6.13465i 0.362750i
\(287\) 0 0
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 4.18598i 0.246234i
\(290\) −19.5189 + 4.41816i −1.14619 + 0.259443i
\(291\) −2.09348 −0.122722
\(292\) −10.7621 10.7621i −0.629804 0.629804i
\(293\) −8.62354 + 8.62354i −0.503793 + 0.503793i −0.912614 0.408822i \(-0.865940\pi\)
0.408822 + 0.912614i \(0.365940\pi\)
\(294\) 0 0
\(295\) −5.01924 + 7.95628i −0.292231 + 0.463233i
\(296\) 2.77192 0.161114
\(297\) −1.39919 1.39919i −0.0811892 0.0811892i
\(298\) −11.0165 11.0165i −0.638167 0.638167i
\(299\) −18.2372 −1.05468
\(300\) 1.66835 4.71345i 0.0963225 0.272131i
\(301\) 0 0
\(302\) 14.9840 14.9840i 0.862232 0.862232i
\(303\) 7.10444 + 7.10444i 0.408139 + 0.408139i
\(304\) −4.21878 −0.241964
\(305\) −21.0300 13.2668i −1.20417 0.759656i
\(306\) 4.60282i 0.263126i
\(307\) 15.9933 + 15.9933i 0.912785 + 0.912785i 0.996490 0.0837060i \(-0.0266757\pi\)
−0.0837060 + 0.996490i \(0.526676\pi\)
\(308\) 0 0
\(309\) 4.98786i 0.283750i
\(310\) −3.78137 + 0.855923i −0.214767 + 0.0486132i
\(311\) 7.74252i 0.439038i 0.975608 + 0.219519i \(0.0704488\pi\)
−0.975608 + 0.219519i \(0.929551\pi\)
\(312\) 2.19222 2.19222i 0.124110 0.124110i
\(313\) 14.1742 14.1742i 0.801171 0.801171i −0.182108 0.983279i \(-0.558292\pi\)
0.983279 + 0.182108i \(0.0582920\pi\)
\(314\) 15.1833 0.856846
\(315\) 0 0
\(316\) 2.55514 0.143738
\(317\) −2.10741 + 2.10741i −0.118364 + 0.118364i −0.763808 0.645444i \(-0.776672\pi\)
0.645444 + 0.763808i \(0.276672\pi\)
\(318\) −8.08484 + 8.08484i −0.453375 + 0.453375i
\(319\) 17.7098i 0.991556i
\(320\) 1.89119 + 1.19306i 0.105721 + 0.0666942i
\(321\) 6.04965i 0.337658i
\(322\) 0 0
\(323\) 13.7308 + 13.7308i 0.764004 + 0.764004i
\(324\) 1.00000i 0.0555556i
\(325\) −14.6129 5.17234i −0.810579 0.286910i
\(326\) 22.3230 1.23636
\(327\) 6.89357 + 6.89357i 0.381216 + 0.381216i
\(328\) 4.63643 4.63643i 0.256004 0.256004i
\(329\) 0 0
\(330\) −3.74220 2.36077i −0.206001 0.129956i
\(331\) 27.8372 1.53007 0.765035 0.643989i \(-0.222722\pi\)
0.765035 + 0.643989i \(0.222722\pi\)
\(332\) 9.52969 + 9.52969i 0.523010 + 0.523010i
\(333\) 1.96004 + 1.96004i 0.107410 + 0.107410i
\(334\) 9.77538 0.534885
\(335\) −2.72109 12.0215i −0.148669 0.656803i
\(336\) 0 0
\(337\) −17.1567 + 17.1567i −0.934583 + 0.934583i −0.997988 0.0634051i \(-0.979804\pi\)
0.0634051 + 0.997988i \(0.479804\pi\)
\(338\) 2.39594 + 2.39594i 0.130322 + 0.130322i
\(339\) −8.52069 −0.462780
\(340\) −2.27219 10.0383i −0.123227 0.544402i
\(341\) 3.43088i 0.185793i
\(342\) −2.98313 2.98313i −0.161309 0.161309i
\(343\) 0 0
\(344\) 8.96222i 0.483210i
\(345\) 7.01814 11.1249i 0.377844 0.598942i
\(346\) 4.52762i 0.243406i
\(347\) −17.7080 + 17.7080i −0.950613 + 0.950613i −0.998837 0.0482236i \(-0.984644\pi\)
0.0482236 + 0.998837i \(0.484644\pi\)
\(348\) 6.32858 6.32858i 0.339247 0.339247i
\(349\) −18.0130 −0.964212 −0.482106 0.876113i \(-0.660128\pi\)
−0.482106 + 0.876113i \(0.660128\pi\)
\(350\) 0 0
\(351\) 3.10026 0.165480
\(352\) 1.39919 1.39919i 0.0745770 0.0745770i
\(353\) −5.37260 + 5.37260i −0.285955 + 0.285955i −0.835478 0.549524i \(-0.814809\pi\)
0.549524 + 0.835478i \(0.314809\pi\)
\(354\) 4.20702i 0.223601i
\(355\) −4.60524 + 7.30003i −0.244421 + 0.387445i
\(356\) 6.19187i 0.328168i
\(357\) 0 0
\(358\) −1.46221 1.46221i −0.0772803 0.0772803i
\(359\) 3.28672i 0.173466i 0.996232 + 0.0867332i \(0.0276428\pi\)
−0.996232 + 0.0867332i \(0.972357\pi\)
\(360\) 0.493652 + 2.18090i 0.0260177 + 0.114943i
\(361\) −1.20185 −0.0632555
\(362\) 4.33597 + 4.33597i 0.227894 + 0.227894i
\(363\) 5.00952 5.00952i 0.262932 0.262932i
\(364\) 0 0
\(365\) −7.51333 33.1930i −0.393266 1.73740i
\(366\) 11.1200 0.581250
\(367\) −2.29639 2.29639i −0.119871 0.119871i 0.644627 0.764497i \(-0.277013\pi\)
−0.764497 + 0.644627i \(0.777013\pi\)
\(368\) 4.15953 + 4.15953i 0.216830 + 0.216830i
\(369\) 6.55691 0.341339
\(370\) 5.24222 + 3.30707i 0.272530 + 0.171926i
\(371\) 0 0
\(372\) 1.22602 1.22602i 0.0635664 0.0635664i
\(373\) −11.1484 11.1484i −0.577243 0.577243i 0.356900 0.934143i \(-0.383834\pi\)
−0.934143 + 0.356900i \(0.883834\pi\)
\(374\) −9.10785 −0.470956
\(375\) 8.77861 6.92358i 0.453326 0.357532i
\(376\) 6.08016i 0.313560i
\(377\) −19.6203 19.6203i −1.01049 1.01049i
\(378\) 0 0
\(379\) 21.7428i 1.11685i −0.829555 0.558426i \(-0.811406\pi\)
0.829555 0.558426i \(-0.188594\pi\)
\(380\) −7.97853 5.03327i −0.409290 0.258201i
\(381\) 12.6257i 0.646833i
\(382\) −11.4312 + 11.4312i −0.584869 + 0.584869i
\(383\) −12.6486 + 12.6486i −0.646316 + 0.646316i −0.952101 0.305785i \(-0.901081\pi\)
0.305785 + 0.952101i \(0.401081\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 21.7909 1.10913
\(387\) −6.33724 + 6.33724i −0.322140 + 0.322140i
\(388\) 1.48031 1.48031i 0.0751514 0.0751514i
\(389\) 5.03599i 0.255335i 0.991817 + 0.127667i \(0.0407490\pi\)
−0.991817 + 0.127667i \(0.959251\pi\)
\(390\) 6.76135 1.53045i 0.342374 0.0774973i
\(391\) 27.0759i 1.36929i
\(392\) 0 0
\(393\) −3.62152 3.62152i −0.182681 0.182681i
\(394\) 0.888296i 0.0447517i
\(395\) 4.83226 + 3.04844i 0.243138 + 0.153384i
\(396\) 1.97875 0.0994361
\(397\) 10.4332 + 10.4332i 0.523625 + 0.523625i 0.918664 0.395039i \(-0.129269\pi\)
−0.395039 + 0.918664i \(0.629269\pi\)
\(398\) −6.80587 + 6.80587i −0.341147 + 0.341147i
\(399\) 0 0
\(400\) 2.15321 + 4.51262i 0.107660 + 0.225631i
\(401\) −8.69371 −0.434143 −0.217072 0.976156i \(-0.569651\pi\)
−0.217072 + 0.976156i \(0.569651\pi\)
\(402\) 3.89769 + 3.89769i 0.194399 + 0.194399i
\(403\) −3.80100 3.80100i −0.189341 0.189341i
\(404\) −10.0472 −0.499866
\(405\) −1.19306 + 1.89119i −0.0592837 + 0.0939740i
\(406\) 0 0
\(407\) 3.87844 3.87844i 0.192247 0.192247i
\(408\) 3.25469 + 3.25469i 0.161131 + 0.161131i
\(409\) 18.9819 0.938595 0.469297 0.883040i \(-0.344507\pi\)
0.469297 + 0.883040i \(0.344507\pi\)
\(410\) 14.2999 3.23683i 0.706223 0.159856i
\(411\) 11.5824i 0.571315i
\(412\) −3.52695 3.52695i −0.173760 0.173760i
\(413\) 0 0
\(414\) 5.88246i 0.289107i
\(415\) 6.65295 + 29.3920i 0.326581 + 1.44280i
\(416\) 3.10026i 0.152003i
\(417\) 2.02978 2.02978i 0.0993985 0.0993985i
\(418\) −5.90288 + 5.90288i −0.288719 + 0.288719i
\(419\) 11.9171 0.582188 0.291094 0.956695i \(-0.405981\pi\)
0.291094 + 0.956695i \(0.405981\pi\)
\(420\) 0 0
\(421\) 6.95263 0.338850 0.169425 0.985543i \(-0.445809\pi\)
0.169425 + 0.985543i \(0.445809\pi\)
\(422\) 7.96693 7.96693i 0.387824 0.387824i
\(423\) −4.29932 + 4.29932i −0.209040 + 0.209040i
\(424\) 11.4337i 0.555269i
\(425\) 7.67914 21.6952i 0.372493 1.05237i
\(426\) 3.86002i 0.187018i
\(427\) 0 0
\(428\) −4.27775 4.27775i −0.206773 0.206773i
\(429\) 6.13465i 0.296184i
\(430\) −10.6925 + 16.9493i −0.515637 + 0.817366i
\(431\) 6.24783 0.300947 0.150474 0.988614i \(-0.451920\pi\)
0.150474 + 0.988614i \(0.451920\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) 15.1544 15.1544i 0.728274 0.728274i −0.242002 0.970276i \(-0.577804\pi\)
0.970276 + 0.242002i \(0.0778040\pi\)
\(434\) 0 0
\(435\) 19.5189 4.41816i 0.935861 0.211835i
\(436\) −9.74899 −0.466892
\(437\) −17.5482 17.5482i −0.839442 0.839442i
\(438\) 10.7621 + 10.7621i 0.514233 + 0.514233i
\(439\) −32.7459 −1.56288 −0.781438 0.623983i \(-0.785513\pi\)
−0.781438 + 0.623983i \(0.785513\pi\)
\(440\) 4.31545 0.976815i 0.205731 0.0465678i
\(441\) 0 0
\(442\) 10.0904 10.0904i 0.479951 0.479951i
\(443\) 21.7443 + 21.7443i 1.03310 + 1.03310i 0.999433 + 0.0336677i \(0.0107188\pi\)
0.0336677 + 0.999433i \(0.489281\pi\)
\(444\) −2.77192 −0.131549
\(445\) 7.38728 11.7100i 0.350191 0.555107i
\(446\) 18.6277i 0.882048i
\(447\) 11.0165 + 11.0165i 0.521061 + 0.521061i
\(448\) 0 0
\(449\) 16.8713i 0.796207i −0.917341 0.398103i \(-0.869669\pi\)
0.917341 0.398103i \(-0.130331\pi\)
\(450\) −1.66835 + 4.71345i −0.0786470 + 0.222194i
\(451\) 12.9745i 0.610945i
\(452\) 6.02504 6.02504i 0.283394 0.283394i
\(453\) −14.9840 + 14.9840i −0.704010 + 0.704010i
\(454\) 26.9142 1.26314
\(455\) 0 0
\(456\) 4.21878 0.197563
\(457\) 14.0344 14.0344i 0.656503 0.656503i −0.298048 0.954551i \(-0.596336\pi\)
0.954551 + 0.298048i \(0.0963356\pi\)
\(458\) 19.0144 19.0144i 0.888486 0.888486i
\(459\) 4.60282i 0.214841i
\(460\) 2.90389 + 12.8290i 0.135394 + 0.598157i
\(461\) 15.7775i 0.734830i 0.930057 + 0.367415i \(0.119757\pi\)
−0.930057 + 0.367415i \(0.880243\pi\)
\(462\) 0 0
\(463\) 4.48617 + 4.48617i 0.208490 + 0.208490i 0.803625 0.595135i \(-0.202902\pi\)
−0.595135 + 0.803625i \(0.702902\pi\)
\(464\) 8.94996i 0.415491i
\(465\) 3.78137 0.855923i 0.175357 0.0396925i
\(466\) −0.921244 −0.0426758
\(467\) 12.3390 + 12.3390i 0.570982 + 0.570982i 0.932403 0.361421i \(-0.117708\pi\)
−0.361421 + 0.932403i \(0.617708\pi\)
\(468\) −2.19222 + 2.19222i −0.101335 + 0.101335i
\(469\) 0 0
\(470\) −7.25401 + 11.4987i −0.334602 + 0.530397i
\(471\) −15.1833 −0.699612
\(472\) 2.97481 + 2.97481i 0.136927 + 0.136927i
\(473\) 12.5398 + 12.5398i 0.576582 + 0.576582i
\(474\) −2.55514 −0.117362
\(475\) −9.08391 19.0378i −0.416799 0.873512i
\(476\) 0 0
\(477\) 8.08484 8.08484i 0.370180 0.370180i
\(478\) −17.9203 17.9203i −0.819656 0.819656i
\(479\) −31.7496 −1.45068 −0.725339 0.688392i \(-0.758317\pi\)
−0.725339 + 0.688392i \(0.758317\pi\)
\(480\) −1.89119 1.19306i −0.0863207 0.0544556i
\(481\) 8.59367i 0.391837i
\(482\) 14.9341 + 14.9341i 0.680230 + 0.680230i
\(483\) 0 0
\(484\) 7.08454i 0.322024i
\(485\) 4.56565 1.03345i 0.207316 0.0469264i
\(486\) 1.00000i 0.0453609i
\(487\) −21.1482 + 21.1482i −0.958316 + 0.958316i −0.999165 0.0408497i \(-0.986994\pi\)
0.0408497 + 0.999165i \(0.486994\pi\)
\(488\) −7.86301 + 7.86301i −0.355942 + 0.355942i
\(489\) −22.3230 −1.00948
\(490\) 0 0
\(491\) 1.57179 0.0709340 0.0354670 0.999371i \(-0.488708\pi\)
0.0354670 + 0.999371i \(0.488708\pi\)
\(492\) −4.63643 + 4.63643i −0.209027 + 0.209027i
\(493\) 29.1293 29.1293i 1.31192 1.31192i
\(494\) 13.0793i 0.588467i
\(495\) 3.74220 + 2.36077i 0.168199 + 0.106109i
\(496\) 1.73386i 0.0778527i
\(497\) 0 0
\(498\) −9.52969 9.52969i −0.427036 0.427036i
\(499\) 14.2595i 0.638345i −0.947697 0.319172i \(-0.896595\pi\)
0.947697 0.319172i \(-0.103405\pi\)
\(500\) −1.31171 + 11.1031i −0.0586613 + 0.496547i
\(501\) −9.77538 −0.436732
\(502\) 1.91359 + 1.91359i 0.0854078 + 0.0854078i
\(503\) 28.7896 28.7896i 1.28367 1.28367i 0.345100 0.938566i \(-0.387845\pi\)
0.938566 0.345100i \(-0.112155\pi\)
\(504\) 0 0
\(505\) −19.0012 11.9869i −0.845540 0.533411i
\(506\) 11.6399 0.517458
\(507\) −2.39594 2.39594i −0.106407 0.106407i
\(508\) 8.92770 + 8.92770i 0.396102 + 0.396102i
\(509\) −14.6188 −0.647969 −0.323984 0.946062i \(-0.605023\pi\)
−0.323984 + 0.946062i \(0.605023\pi\)
\(510\) 2.27219 + 10.0383i 0.100614 + 0.444502i
\(511\) 0 0
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 2.98313 + 2.98313i 0.131708 + 0.131708i
\(514\) 24.0221 1.05957
\(515\) −2.46227 10.8780i −0.108500 0.479342i
\(516\) 8.96222i 0.394540i
\(517\) 8.50729 + 8.50729i 0.374150 + 0.374150i
\(518\) 0 0
\(519\) 4.52762i 0.198740i
\(520\) −3.69881 + 5.86319i −0.162203 + 0.257118i
\(521\) 15.3751i 0.673597i −0.941577 0.336798i \(-0.890656\pi\)
0.941577 0.336798i \(-0.109344\pi\)
\(522\) −6.32858 + 6.32858i −0.276994 + 0.276994i
\(523\) 16.5574 16.5574i 0.724002 0.724002i −0.245416 0.969418i \(-0.578924\pi\)
0.969418 + 0.245416i \(0.0789244\pi\)
\(524\) 5.12160 0.223738
\(525\) 0 0
\(526\) 0.850325 0.0370759
\(527\) 5.64318 5.64318i 0.245821 0.245821i
\(528\) −1.39919 + 1.39919i −0.0608919 + 0.0608919i
\(529\) 11.6033i 0.504493i
\(530\) 13.6411 21.6233i 0.592532 0.939256i
\(531\) 4.20702i 0.182569i
\(532\) 0 0
\(533\) 14.3742 + 14.3742i 0.622614 + 0.622614i
\(534\) 6.19187i 0.267948i
\(535\) −2.98642 13.1937i −0.129114 0.570411i
\(536\) −5.51217 −0.238089
\(537\) 1.46221 + 1.46221i 0.0630991 + 0.0630991i
\(538\) −8.23314 + 8.23314i −0.354956 + 0.354956i
\(539\) 0 0
\(540\) −0.493652 2.18090i −0.0212434 0.0938508i
\(541\) 7.96874 0.342603 0.171301 0.985219i \(-0.445203\pi\)
0.171301 + 0.985219i \(0.445203\pi\)
\(542\) 16.5072 + 16.5072i 0.709046 + 0.709046i
\(543\) −4.33597 4.33597i −0.186074 0.186074i
\(544\) −4.60282 −0.197344
\(545\) −18.4372 11.6311i −0.789763 0.498224i
\(546\) 0 0
\(547\) −5.88082 + 5.88082i −0.251446 + 0.251446i −0.821563 0.570117i \(-0.806898\pi\)
0.570117 + 0.821563i \(0.306898\pi\)
\(548\) 8.18996 + 8.18996i 0.349858 + 0.349858i
\(549\) −11.1200 −0.474589
\(550\) 9.32675 + 3.30126i 0.397694 + 0.140766i
\(551\) 37.7580i 1.60854i
\(552\) −4.15953 4.15953i −0.177041 0.177041i
\(553\) 0 0
\(554\) 9.44974i 0.401481i
\(555\) −5.24222 3.30707i −0.222520 0.140377i
\(556\) 2.87054i 0.121738i
\(557\) 18.5354 18.5354i 0.785370 0.785370i −0.195361 0.980731i \(-0.562588\pi\)
0.980731 + 0.195361i \(0.0625878\pi\)
\(558\) −1.22602 + 1.22602i −0.0519018 + 0.0519018i
\(559\) −27.7852 −1.17519
\(560\) 0 0
\(561\) 9.10785 0.384534
\(562\) −8.29575 + 8.29575i −0.349935 + 0.349935i
\(563\) −0.618308 + 0.618308i −0.0260586 + 0.0260586i −0.720016 0.693957i \(-0.755866\pi\)
0.693957 + 0.720016i \(0.255866\pi\)
\(564\) 6.08016i 0.256021i
\(565\) 18.5827 4.20625i 0.781782 0.176958i
\(566\) 3.64779i 0.153328i
\(567\) 0 0
\(568\) 2.72944 + 2.72944i 0.114525 + 0.114525i
\(569\) 33.0102i 1.38386i −0.721965 0.691929i \(-0.756761\pi\)
0.721965 0.691929i \(-0.243239\pi\)
\(570\) 7.97853 + 5.03327i 0.334184 + 0.210821i
\(571\) 4.79189 0.200534 0.100267 0.994961i \(-0.468030\pi\)
0.100267 + 0.994961i \(0.468030\pi\)
\(572\) 4.33785 + 4.33785i 0.181375 + 0.181375i
\(573\) 11.4312 11.4312i 0.477544 0.477544i
\(574\) 0 0
\(575\) −9.81403 + 27.7267i −0.409273 + 1.15628i
\(576\) 1.00000 0.0416667
\(577\) 23.0871 + 23.0871i 0.961128 + 0.961128i 0.999272 0.0381442i \(-0.0121446\pi\)
−0.0381442 + 0.999272i \(0.512145\pi\)
\(578\) 2.95994 + 2.95994i 0.123117 + 0.123117i
\(579\) −21.7909 −0.905600
\(580\) −10.6779 + 16.9261i −0.443374 + 0.702817i
\(581\) 0 0
\(582\) −1.48031 + 1.48031i −0.0613609 + 0.0613609i
\(583\) −15.9979 15.9979i −0.662566 0.662566i
\(584\) −15.2199 −0.629804
\(585\) −6.76135 + 1.53045i −0.279547 + 0.0632763i
\(586\) 12.1955i 0.503793i
\(587\) 6.03856 + 6.03856i 0.249238 + 0.249238i 0.820658 0.571420i \(-0.193607\pi\)
−0.571420 + 0.820658i \(0.693607\pi\)
\(588\) 0 0
\(589\) 7.31479i 0.301401i
\(590\) 2.07680 + 9.17508i 0.0855007 + 0.377732i
\(591\) 0.888296i 0.0365396i
\(592\) 1.96004 1.96004i 0.0805572 0.0805572i
\(593\) 2.87821 2.87821i 0.118194 0.118194i −0.645536 0.763730i \(-0.723366\pi\)
0.763730 + 0.645536i \(0.223366\pi\)
\(594\) −1.97875 −0.0811892
\(595\) 0 0
\(596\) −15.5796 −0.638167
\(597\) 6.80587 6.80587i 0.278546 0.278546i
\(598\) −12.8956 + 12.8956i −0.527341 + 0.527341i
\(599\) 34.1269i 1.39439i −0.716884 0.697193i \(-0.754432\pi\)
0.716884 0.697193i \(-0.245568\pi\)
\(600\) −2.15321 4.51262i −0.0879043 0.184227i
\(601\) 9.99405i 0.407666i 0.979006 + 0.203833i \(0.0653399\pi\)
−0.979006 + 0.203833i \(0.934660\pi\)
\(602\) 0 0
\(603\) −3.89769 3.89769i −0.158726 0.158726i
\(604\) 21.1906i 0.862232i
\(605\) −8.45229 + 13.3982i −0.343635 + 0.544715i
\(606\) 10.0472 0.408139
\(607\) −12.9256 12.9256i −0.524633 0.524633i 0.394334 0.918967i \(-0.370975\pi\)
−0.918967 + 0.394334i \(0.870975\pi\)
\(608\) −2.98313 + 2.98313i −0.120982 + 0.120982i
\(609\) 0 0
\(610\) −24.2515 + 5.48939i −0.981915 + 0.222259i
\(611\) −18.8501 −0.762593
\(612\) −3.25469 3.25469i −0.131563 0.131563i
\(613\) −21.0944 21.0944i −0.851995 0.851995i 0.138383 0.990379i \(-0.455809\pi\)
−0.990379 + 0.138383i \(0.955809\pi\)
\(614\) 22.6179 0.912785
\(615\) −14.2999 + 3.23683i −0.576629 + 0.130521i
\(616\) 0 0
\(617\) −35.0246 + 35.0246i −1.41004 + 1.41004i −0.650721 + 0.759317i \(0.725533\pi\)
−0.759317 + 0.650721i \(0.774467\pi\)
\(618\) 3.52695 + 3.52695i 0.141875 + 0.141875i
\(619\) 11.5154 0.462843 0.231422 0.972854i \(-0.425662\pi\)
0.231422 + 0.972854i \(0.425662\pi\)
\(620\) −2.06860 + 3.27906i −0.0830771 + 0.131690i
\(621\) 5.88246i 0.236055i
\(622\) 5.47479 + 5.47479i 0.219519 + 0.219519i
\(623\) 0 0
\(624\) 3.10026i 0.124110i
\(625\) −15.7274 + 19.4332i −0.629096 + 0.777327i
\(626\) 20.0453i 0.801171i
\(627\) 5.90288 5.90288i 0.235738 0.235738i
\(628\) 10.7362 10.7362i 0.428423 0.428423i
\(629\) −12.7586 −0.508720
\(630\) 0 0
\(631\) 18.4477 0.734390 0.367195 0.930144i \(-0.380318\pi\)
0.367195 + 0.930144i \(0.380318\pi\)
\(632\) 1.80676 1.80676i 0.0718690 0.0718690i
\(633\) −7.96693 + 7.96693i −0.316657 + 0.316657i
\(634\) 2.98032i 0.118364i
\(635\) 6.23268 + 27.5353i 0.247336 + 1.09270i
\(636\) 11.4337i 0.453375i
\(637\) 0 0
\(638\) 12.5227 + 12.5227i 0.495778 + 0.495778i
\(639\) 3.86002i 0.152700i
\(640\) 2.18090 0.493652i 0.0862075 0.0195133i
\(641\) −19.4846 −0.769594 −0.384797 0.923001i \(-0.625729\pi\)
−0.384797 + 0.923001i \(0.625729\pi\)
\(642\) 4.27775 + 4.27775i 0.168829 + 0.168829i
\(643\) −28.2707 + 28.2707i −1.11489 + 1.11489i −0.122408 + 0.992480i \(0.539062\pi\)
−0.992480 + 0.122408i \(0.960938\pi\)
\(644\) 0 0
\(645\) 10.6925 16.9493i 0.421016 0.667377i
\(646\) 19.4183 0.764004
\(647\) −17.6276 17.6276i −0.693012 0.693012i 0.269882 0.962893i \(-0.413015\pi\)
−0.962893 + 0.269882i \(0.913015\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) 8.32466 0.326771
\(650\) −13.9903 + 6.67550i −0.548744 + 0.261835i
\(651\) 0 0
\(652\) 15.7848 15.7848i 0.618179 0.618179i
\(653\) −35.1733 35.1733i −1.37644 1.37644i −0.850559 0.525880i \(-0.823736\pi\)
−0.525880 0.850559i \(-0.676264\pi\)
\(654\) 9.74899 0.381216
\(655\) 9.68592 + 6.11038i 0.378460 + 0.238752i
\(656\) 6.55691i 0.256004i
\(657\) −10.7621 10.7621i −0.419869 0.419869i
\(658\) 0 0
\(659\) 39.5644i 1.54121i 0.637312 + 0.770606i \(0.280046\pi\)
−0.637312 + 0.770606i \(0.719954\pi\)
\(660\) −4.31545 + 0.976815i −0.167979 + 0.0380225i
\(661\) 2.02066i 0.0785948i −0.999228 0.0392974i \(-0.987488\pi\)
0.999228 0.0392974i \(-0.0125120\pi\)
\(662\) 19.6839 19.6839i 0.765035 0.765035i
\(663\) −10.0904 + 10.0904i −0.391878 + 0.391878i
\(664\) 13.4770 0.523010
\(665\) 0 0
\(666\) 2.77192 0.107410
\(667\) −37.2276 + 37.2276i −1.44146 + 1.44146i
\(668\) 6.91224 6.91224i 0.267442 0.267442i
\(669\) 18.6277i 0.720190i
\(670\) −10.4246 6.57636i −0.402736 0.254067i
\(671\) 22.0037i 0.849442i
\(672\) 0 0
\(673\) −19.7775 19.7775i −0.762366 0.762366i 0.214383 0.976750i \(-0.431226\pi\)
−0.976750 + 0.214383i \(0.931226\pi\)
\(674\) 24.2632i 0.934583i
\(675\) 1.66835 4.71345i 0.0642150 0.181421i
\(676\) 3.38837 0.130322
\(677\) 12.1336 + 12.1336i 0.466332 + 0.466332i 0.900724 0.434392i \(-0.143037\pi\)
−0.434392 + 0.900724i \(0.643037\pi\)
\(678\) −6.02504 + 6.02504i −0.231390 + 0.231390i
\(679\) 0 0
\(680\) −8.70482 5.49145i −0.333815 0.210588i
\(681\) −26.9142 −1.03135
\(682\) 2.42600 + 2.42600i 0.0928963 + 0.0928963i
\(683\) 0.356641 + 0.356641i 0.0136465 + 0.0136465i 0.713897 0.700251i \(-0.246928\pi\)
−0.700251 + 0.713897i \(0.746928\pi\)
\(684\) −4.21878 −0.161309
\(685\) 5.71765 + 25.2599i 0.218460 + 0.965131i
\(686\) 0 0
\(687\) −19.0144 + 19.0144i −0.725445 + 0.725445i
\(688\) 6.33724 + 6.33724i 0.241605 + 0.241605i
\(689\) 35.4475 1.35044
\(690\) −2.90389 12.8290i −0.110549 0.488393i
\(691\) 15.6342i 0.594753i −0.954760 0.297376i \(-0.903888\pi\)
0.954760 0.297376i \(-0.0961116\pi\)
\(692\) 3.20151 + 3.20151i 0.121703 + 0.121703i
\(693\) 0 0
\(694\) 25.0428i 0.950613i
\(695\) −3.42473 + 5.42873i −0.129907 + 0.205924i
\(696\) 8.94996i 0.339247i
\(697\) −21.3407 + 21.3407i −0.808336 + 0.808336i
\(698\) −12.7371 + 12.7371i −0.482106 + 0.482106i
\(699\) 0.921244 0.0348447
\(700\) 0 0
\(701\) 8.02724 0.303185 0.151592 0.988443i \(-0.451560\pi\)
0.151592 + 0.988443i \(0.451560\pi\)
\(702\) 2.19222 2.19222i 0.0827399 0.0827399i
\(703\) −8.26899 + 8.26899i −0.311871 + 0.311871i
\(704\) 1.97875i 0.0745770i
\(705\) 7.25401 11.4987i 0.273202 0.433068i
\(706\) 7.59800i 0.285955i
\(707\) 0 0
\(708\) −2.97481 2.97481i −0.111800 0.111800i
\(709\) 13.6783i 0.513698i −0.966452 0.256849i \(-0.917316\pi\)
0.966452 0.256849i \(-0.0826843\pi\)
\(710\) 1.90550 + 8.41829i 0.0715123 + 0.315933i
\(711\) 2.55514 0.0958253
\(712\) −4.37831 4.37831i −0.164084 0.164084i
\(713\) −7.21204 + 7.21204i −0.270093 + 0.270093i
\(714\) 0 0
\(715\) 3.02838 + 13.3790i 0.113255 + 0.500348i
\(716\) −2.06788 −0.0772803
\(717\) 17.9203 + 17.9203i 0.669246 + 0.669246i
\(718\) 2.32406 + 2.32406i 0.0867332 + 0.0867332i
\(719\) 21.0471 0.784924 0.392462 0.919768i \(-0.371623\pi\)
0.392462 + 0.919768i \(0.371623\pi\)
\(720\) 1.89119 + 1.19306i 0.0704805 + 0.0444628i
\(721\) 0 0
\(722\) −0.849839 + 0.849839i −0.0316277 + 0.0316277i
\(723\) −14.9341 14.9341i −0.555405 0.555405i
\(724\) 6.13199 0.227894
\(725\) −40.3877 + 19.2711i −1.49996 + 0.715711i
\(726\) 7.08454i 0.262932i
\(727\) −11.2251 11.2251i −0.416317 0.416317i 0.467615 0.883932i \(-0.345113\pi\)
−0.883932 + 0.467615i \(0.845113\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) −28.7837 18.1583i −1.06533 0.672068i
\(731\) 41.2515i 1.52574i
\(732\) 7.86301 7.86301i 0.290625 0.290625i
\(733\) 20.3304 20.3304i 0.750922 0.750922i −0.223730 0.974651i \(-0.571823\pi\)
0.974651 + 0.223730i \(0.0718233\pi\)
\(734\) −3.24759 −0.119871
\(735\) 0 0
\(736\) 5.88246 0.216830
\(737\) −7.71257 + 7.71257i −0.284096 + 0.284096i
\(738\) 4.63643 4.63643i 0.170669 0.170669i
\(739\) 41.9841i 1.54441i 0.635373 + 0.772205i \(0.280846\pi\)
−0.635373 + 0.772205i \(0.719154\pi\)
\(740\) 6.04526 1.36836i 0.222228 0.0503019i
\(741\) 13.0793i 0.480482i
\(742\) 0 0
\(743\) 8.63799 + 8.63799i 0.316897 + 0.316897i 0.847574 0.530677i \(-0.178062\pi\)
−0.530677 + 0.847574i \(0.678062\pi\)
\(744\) 1.73386i 0.0635664i
\(745\) −29.4641 18.5875i −1.07948 0.680993i
\(746\) −15.7662 −0.577243
\(747\) 9.52969 + 9.52969i 0.348673 + 0.348673i
\(748\) −6.44022 + 6.44022i −0.235478 + 0.235478i
\(749\) 0 0
\(750\) 1.31171 11.1031i 0.0478968 0.405429i
\(751\) 31.7446 1.15838 0.579188 0.815194i \(-0.303370\pi\)
0.579188 + 0.815194i \(0.303370\pi\)
\(752\) 4.29932 + 4.29932i 0.156780 + 0.156780i
\(753\) −1.91359 1.91359i −0.0697351 0.0697351i
\(754\) −27.7472 −1.01049
\(755\) 25.2817 40.0754i 0.920094 1.45849i
\(756\) 0 0
\(757\) −9.81959 + 9.81959i −0.356899 + 0.356899i −0.862669 0.505770i \(-0.831209\pi\)
0.505770 + 0.862669i \(0.331209\pi\)
\(758\) −15.3745 15.3745i −0.558426 0.558426i
\(759\) −11.6399 −0.422503
\(760\) −9.20073 + 2.08261i −0.333746 + 0.0755442i
\(761\) 31.9432i 1.15794i −0.815349 0.578970i \(-0.803455\pi\)
0.815349 0.578970i \(-0.196545\pi\)
\(762\) −8.92770 8.92770i −0.323416 0.323416i
\(763\) 0 0
\(764\) 16.1661i 0.584869i
\(765\) −2.27219 10.0383i −0.0821513 0.362935i
\(766\) 17.8879i 0.646316i
\(767\) −9.22271 + 9.22271i −0.333013 + 0.333013i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) −26.3715 −0.950981 −0.475490 0.879721i \(-0.657729\pi\)
−0.475490 + 0.879721i \(0.657729\pi\)
\(770\) 0 0
\(771\) −24.0221 −0.865133
\(772\) 15.4085 15.4085i 0.554564 0.554564i
\(773\) 32.5441 32.5441i 1.17053 1.17053i 0.188448 0.982083i \(-0.439654\pi\)
0.982083 0.188448i \(-0.0603457\pi\)
\(774\) 8.96222i 0.322140i
\(775\) −7.82425 + 3.73336i −0.281055 + 0.134106i
\(776\) 2.09348i 0.0751514i
\(777\) 0 0
\(778\) 3.56098 + 3.56098i 0.127667 + 0.127667i
\(779\) 27.6622i 0.991100i
\(780\) 3.69881 5.86319i 0.132438 0.209936i
\(781\) 7.63802 0.273310
\(782\) −19.1456 19.1456i −0.684644 0.684644i
\(783\) 6.32858 6.32858i 0.226165 0.226165i
\(784\) 0 0
\(785\) 33.1133 7.49528i 1.18186 0.267518i
\(786\) −5.12160 −0.182681
\(787\) −8.01108 8.01108i −0.285564 0.285564i 0.549759 0.835323i \(-0.314720\pi\)
−0.835323 + 0.549759i \(0.814720\pi\)
\(788\) 0.628120 + 0.628120i 0.0223759 + 0.0223759i
\(789\) −0.850325 −0.0302724
\(790\) 5.57250 1.26135i 0.198261 0.0448768i
\(791\) 0 0
\(792\) 1.39919 1.39919i 0.0497180 0.0497180i
\(793\) −24.3774 24.3774i −0.865666 0.865666i
\(794\) 14.7547 0.523625
\(795\) −13.6411 + 21.6233i −0.483800 + 0.766899i
\(796\) 9.62495i 0.341147i
\(797\) 24.7239 + 24.7239i 0.875767 + 0.875767i 0.993093 0.117327i \(-0.0374325\pi\)
−0.117327 + 0.993093i \(0.537432\pi\)
\(798\) 0 0
\(799\) 27.9859i 0.990070i
\(800\) 4.71345 + 1.66835i 0.166646 + 0.0589852i
\(801\) 6.19187i 0.218779i
\(802\) −6.14738 + 6.14738i −0.217072 + 0.217072i
\(803\) −21.2955 + 21.2955i −0.751503 + 0.751503i
\(804\) 5.51217 0.194399
\(805\) 0 0
\(806\) −5.37542 −0.189341
\(807\) 8.23314 8.23314i 0.289820 0.289820i
\(808\) −7.10444 + 7.10444i −0.249933 + 0.249933i
\(809\) 5.79908i 0.203885i 0.994790 + 0.101942i \(0.0325057\pi\)
−0.994790 + 0.101942i \(0.967494\pi\)
\(810\) 0.493652 + 2.18090i 0.0173452 + 0.0766289i
\(811\) 28.8064i 1.01153i −0.862671 0.505765i \(-0.831210\pi\)
0.862671 0.505765i \(-0.168790\pi\)
\(812\) 0 0
\(813\) −16.5072 16.5072i −0.578934 0.578934i
\(814\) 5.48494i 0.192247i
\(815\) 48.6842 11.0198i 1.70533 0.386007i
\(816\) 4.60282 0.161131
\(817\) −26.7355 26.7355i −0.935356 0.935356i
\(818\) 13.4222 13.4222i 0.469297 0.469297i
\(819\) 0 0
\(820\) 7.82280 12.4004i 0.273184 0.433039i
\(821\) 4.51799 0.157679 0.0788395 0.996887i \(-0.474879\pi\)
0.0788395 + 0.996887i \(0.474879\pi\)
\(822\) −8.18996 8.18996i −0.285658 0.285658i
\(823\) −15.8260 15.8260i −0.551659 0.551659i 0.375261 0.926919i \(-0.377553\pi\)
−0.926919 + 0.375261i \(0.877553\pi\)
\(824\) −4.98786 −0.173760
\(825\) −9.32675 3.30126i −0.324716 0.114935i
\(826\) 0 0
\(827\) 22.5410 22.5410i 0.783826 0.783826i −0.196648 0.980474i \(-0.563006\pi\)
0.980474 + 0.196648i \(0.0630057\pi\)
\(828\) 4.15953 + 4.15953i 0.144554 + 0.144554i
\(829\) −7.22693 −0.251002 −0.125501 0.992094i \(-0.540054\pi\)
−0.125501 + 0.992094i \(0.540054\pi\)
\(830\) 25.4876 + 16.0789i 0.884688 + 0.558108i
\(831\) 9.44974i 0.327808i
\(832\) 2.19222 + 2.19222i 0.0760014 + 0.0760014i
\(833\) 0 0
\(834\) 2.87054i 0.0993985i
\(835\) 21.3191 4.82563i 0.737777 0.166998i
\(836\) 8.34793i 0.288719i
\(837\) 1.22602 1.22602i 0.0423776 0.0423776i
\(838\) 8.42665 8.42665i 0.291094 0.291094i
\(839\) 5.52622 0.190786 0.0953932 0.995440i \(-0.469589\pi\)
0.0953932 + 0.995440i \(0.469589\pi\)
\(840\) 0 0
\(841\) −51.1018 −1.76213
\(842\) 4.91625 4.91625i 0.169425 0.169425i
\(843\) 8.29575 8.29575i 0.285721 0.285721i
\(844\) 11.2669i 0.387824i
\(845\) 6.40806 + 4.04254i 0.220444 + 0.139068i
\(846\) 6.08016i 0.209040i
\(847\) 0 0
\(848\) −8.08484 8.08484i −0.277635 0.277635i
\(849\) 3.64779i 0.125192i
\(850\) −9.91083 20.7708i −0.339939 0.712432i
\(851\) 16.3057 0.558952
\(852\) −2.72944 2.72944i −0.0935092 0.0935092i
\(853\) −10.4649 + 10.4649i −0.358313 + 0.358313i −0.863191 0.504878i \(-0.831538\pi\)
0.504878 + 0.863191i \(0.331538\pi\)
\(854\) 0 0
\(855\) −7.97853 5.03327i −0.272860 0.172134i
\(856\) −6.04965 −0.206773
\(857\) 1.52003 + 1.52003i 0.0519233 + 0.0519233i 0.732592 0.680668i \(-0.238311\pi\)
−0.680668 + 0.732592i \(0.738311\pi\)
\(858\) −4.33785 4.33785i −0.148092 0.148092i
\(859\) 7.18910 0.245289 0.122644 0.992451i \(-0.460863\pi\)
0.122644 + 0.992451i \(0.460863\pi\)
\(860\) 4.42421 + 19.5457i 0.150864 + 0.666502i
\(861\) 0 0
\(862\) 4.41788 4.41788i 0.150474 0.150474i
\(863\) 28.6663 + 28.6663i 0.975812 + 0.975812i 0.999714 0.0239027i \(-0.00760919\pi\)
−0.0239027 + 0.999714i \(0.507609\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 2.23507 + 9.87426i 0.0759945 + 0.335735i
\(866\) 21.4316i 0.728274i
\(867\) −2.95994 2.95994i −0.100525 0.100525i
\(868\) 0 0
\(869\) 5.05600i 0.171513i
\(870\) 10.6779 16.9261i 0.362013 0.573848i
\(871\) 17.0892i 0.579044i
\(872\) −6.89357 + 6.89357i −0.233446 + 0.233446i
\(873\) 1.48031 1.48031i 0.0501009 0.0501009i
\(874\) −24.8168 −0.839442
\(875\) 0 0
\(876\) 15.2199 0.514233
\(877\) −36.1279 + 36.1279i −1.21995 + 1.21995i −0.252303 + 0.967648i \(0.581188\pi\)
−0.967648 + 0.252303i \(0.918812\pi\)
\(878\) −23.1548 + 23.1548i −0.781438 + 0.781438i
\(879\) 12.1955i 0.411345i
\(880\) 2.36077 3.74220i 0.0795817 0.126150i
\(881\) 27.9972i 0.943251i −0.881799 0.471625i \(-0.843667\pi\)
0.881799 0.471625i \(-0.156333\pi\)
\(882\) 0 0
\(883\) 4.66131 + 4.66131i 0.156865 + 0.156865i 0.781176 0.624311i \(-0.214620\pi\)
−0.624311 + 0.781176i \(0.714620\pi\)
\(884\) 14.2700i 0.479951i
\(885\) −2.07680 9.17508i −0.0698110 0.308417i
\(886\) 30.7510 1.03310
\(887\) 9.84950 + 9.84950i 0.330714 + 0.330714i 0.852857 0.522144i \(-0.174868\pi\)
−0.522144 + 0.852857i \(0.674868\pi\)
\(888\) −1.96004 + 1.96004i −0.0657747 + 0.0657747i
\(889\) 0 0
\(890\) −3.05663 13.5038i −0.102458 0.452649i
\(891\) 1.97875 0.0662907
\(892\) −13.1718 13.1718i −0.441024 0.441024i
\(893\) −18.1379 18.1379i −0.606962 0.606962i
\(894\) 15.5796 0.521061
\(895\) −3.91075 2.46711i −0.130722 0.0824663i
\(896\) 0 0
\(897\) 12.8956 12.8956i 0.430573 0.430573i
\(898\) −11.9298 11.9298i −0.398103 0.398103i
\(899\) −15.5180 −0.517554
\(900\) 2.15321 + 4.51262i 0.0717735 + 0.150421i
\(901\) 52.6273i 1.75327i
\(902\) −9.17435 9.17435i −0.305473 0.305473i
\(903\) 0 0
\(904\) 8.52069i 0.283394i
\(905\) 11.5968 + 7.31585i 0.385490 + 0.243187i
\(906\) 21.1906i 0.704010i
\(907\) 19.0839 19.0839i 0.633670 0.633670i −0.315316 0.948987i \(-0.602111\pi\)
0.948987 + 0.315316i \(0.102111\pi\)
\(908\) 19.0312 19.0312i 0.631572 0.631572i
\(909\) −10.0472 −0.333244
\(910\) 0 0
\(911\) −15.5364 −0.514744 −0.257372 0.966312i \(-0.582857\pi\)
−0.257372 + 0.966312i \(0.582857\pi\)
\(912\) 2.98313 2.98313i 0.0987814 0.0987814i
\(913\) 18.8569 18.8569i 0.624073 0.624073i
\(914\) 19.8477i 0.656503i
\(915\) 24.2515 5.48939i 0.801730 0.181474i
\(916\) 26.8905i 0.888486i
\(917\) 0 0
\(918\) 3.25469 + 3.25469i 0.107421 + 0.107421i
\(919\) 37.8644i 1.24903i −0.781013 0.624515i \(-0.785297\pi\)
0.781013 0.624515i \(-0.214703\pi\)
\(920\) 11.1249 + 7.01814i 0.366776 + 0.231381i
\(921\) −22.6179 −0.745285
\(922\) 11.1564 + 11.1564i 0.367415 + 0.367415i
\(923\) −8.46199 + 8.46199i −0.278530 + 0.278530i
\(924\) 0 0
\(925\) 13.0653 + 4.62454i 0.429584 + 0.152054i
\(926\) 6.34440 0.208490
\(927\) −3.52695 3.52695i −0.115840 0.115840i
\(928\) 6.32858 + 6.32858i 0.207746 + 0.207746i
\(929\) −17.5137 −0.574606 −0.287303 0.957840i \(-0.592759\pi\)
−0.287303 + 0.957840i \(0.592759\pi\)
\(930\) 2.06860 3.27906i 0.0678322 0.107525i
\(931\) 0 0
\(932\) −0.651418 + 0.651418i −0.0213379 + 0.0213379i
\(933\) −5.47479 5.47479i −0.179236 0.179236i
\(934\) 17.4500 0.570982
\(935\) −19.8633 + 4.49610i −0.649598 + 0.147038i
\(936\) 3.10026i 0.101335i
\(937\) 2.68964 + 2.68964i 0.0878666 + 0.0878666i 0.749674 0.661807i \(-0.230210\pi\)
−0.661807 + 0.749674i \(0.730210\pi\)
\(938\) 0 0
\(939\) 20.0453i 0.654153i
\(940\) 3.00148 + 13.2602i 0.0978975 + 0.432500i
\(941\) 32.4048i 1.05637i 0.849131 + 0.528183i \(0.177126\pi\)
−0.849131 + 0.528183i \(0.822874\pi\)
\(942\) −10.7362 + 10.7362i −0.349806 + 0.349806i
\(943\) 27.2736 27.2736i 0.888152 0.888152i
\(944\) 4.20702 0.136927
\(945\) 0 0
\(946\) 17.7340 0.576582
\(947\) −27.1338 + 27.1338i −0.881729 + 0.881729i −0.993710 0.111982i \(-0.964280\pi\)
0.111982 + 0.993710i \(0.464280\pi\)
\(948\) −1.80676 + 1.80676i −0.0586808 + 0.0586808i
\(949\) 47.1857i 1.53171i
\(950\) −19.8850 7.03843i −0.645155 0.228357i
\(951\) 2.98032i 0.0966436i
\(952\) 0 0
\(953\) 12.2232 + 12.2232i 0.395949 + 0.395949i 0.876801 0.480853i \(-0.159673\pi\)
−0.480853 + 0.876801i \(0.659673\pi\)
\(954\) 11.4337i 0.370180i
\(955\) −19.2872 + 30.5732i −0.624118 + 0.989326i
\(956\) −25.3432 −0.819656
\(957\) −12.5227 12.5227i −0.404801 0.404801i
\(958\) −22.4504 + 22.4504i −0.725339 + 0.725339i
\(959\) 0 0
\(960\) −2.18090 + 0.493652i −0.0703881 + 0.0159325i
\(961\) 27.9937 0.903023
\(962\) 6.07664 + 6.07664i 0.195919 + 0.195919i
\(963\) −4.27775 4.27775i −0.137848 0.137848i
\(964\) 21.1200 0.680230
\(965\) 47.5237 10.7571i 1.52984 0.346284i
\(966\) 0 0
\(967\) 24.7551 24.7551i 0.796071 0.796071i −0.186402 0.982474i \(-0.559683\pi\)
0.982474 + 0.186402i \(0.0596827\pi\)
\(968\) 5.00952 + 5.00952i 0.161012 + 0.161012i
\(969\) −19.4183 −0.623806
\(970\) 2.49765 3.95916i 0.0801946 0.127121i
\(971\) 10.2123i 0.327729i −0.986483 0.163864i \(-0.947604\pi\)
0.986483 0.163864i \(-0.0523959\pi\)
\(972\) −0.707107 0.707107i −0.0226805 0.0226805i
\(973\) 0 0
\(974\) 29.9080i 0.958316i
\(975\) 13.9903 6.67550i 0.448048 0.213787i
\(976\) 11.1200i 0.355942i
\(977\) −11.3259 + 11.3259i −0.362348 + 0.362348i −0.864677 0.502328i \(-0.832477\pi\)
0.502328 + 0.864677i \(0.332477\pi\)
\(978\) −15.7848 + 15.7848i −0.504741 + 0.504741i
\(979\) −12.2522 −0.391581
\(980\) 0 0
\(981\) −9.74899 −0.311261
\(982\) 1.11143 1.11143i 0.0354670 0.0354670i
\(983\) −5.39290 + 5.39290i −0.172007 + 0.172007i −0.787860 0.615854i \(-0.788811\pi\)
0.615854 + 0.787860i \(0.288811\pi\)
\(984\) 6.55691i 0.209027i
\(985\) 0.438509 + 1.93728i 0.0139721 + 0.0617269i
\(986\) 41.1951i 1.31192i
\(987\) 0 0
\(988\) −9.24849 9.24849i −0.294234 0.294234i
\(989\) 52.7199i 1.67640i
\(990\) 4.31545 0.976815i 0.137154 0.0310452i
\(991\) 50.8757 1.61612 0.808060 0.589100i \(-0.200517\pi\)
0.808060 + 0.589100i \(0.200517\pi\)
\(992\) 1.22602 + 1.22602i 0.0389263 + 0.0389263i
\(993\) −19.6839 + 19.6839i −0.624648 + 0.624648i
\(994\) 0 0
\(995\) −11.4832 + 18.2026i −0.364041 + 0.577062i
\(996\) −13.4770 −0.427036
\(997\) −28.7960 28.7960i −0.911980 0.911980i 0.0844482 0.996428i \(-0.473087\pi\)
−0.996428 + 0.0844482i \(0.973087\pi\)
\(998\) −10.0830 10.0830i −0.319172 0.319172i
\(999\) −2.77192 −0.0876995
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 1470.2.m.d.1273.7 16
5.2 odd 4 1470.2.m.e.97.6 16
7.4 even 3 210.2.u.a.103.3 16
7.5 odd 6 210.2.u.b.73.2 yes 16
7.6 odd 2 1470.2.m.e.1273.6 16
21.5 even 6 630.2.bv.b.73.3 16
21.11 odd 6 630.2.bv.a.523.2 16
35.4 even 6 1050.2.bc.h.943.2 16
35.12 even 12 210.2.u.a.157.3 yes 16
35.18 odd 12 1050.2.bc.g.607.4 16
35.19 odd 6 1050.2.bc.g.493.4 16
35.27 even 4 inner 1470.2.m.d.97.7 16
35.32 odd 12 210.2.u.b.187.2 yes 16
35.33 even 12 1050.2.bc.h.157.2 16
105.32 even 12 630.2.bv.b.397.3 16
105.47 odd 12 630.2.bv.a.577.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.u.a.103.3 16 7.4 even 3
210.2.u.a.157.3 yes 16 35.12 even 12
210.2.u.b.73.2 yes 16 7.5 odd 6
210.2.u.b.187.2 yes 16 35.32 odd 12
630.2.bv.a.523.2 16 21.11 odd 6
630.2.bv.a.577.2 16 105.47 odd 12
630.2.bv.b.73.3 16 21.5 even 6
630.2.bv.b.397.3 16 105.32 even 12
1050.2.bc.g.493.4 16 35.19 odd 6
1050.2.bc.g.607.4 16 35.18 odd 12
1050.2.bc.h.157.2 16 35.33 even 12
1050.2.bc.h.943.2 16 35.4 even 6
1470.2.m.d.97.7 16 35.27 even 4 inner
1470.2.m.d.1273.7 16 1.1 even 1 trivial
1470.2.m.e.97.6 16 5.2 odd 4
1470.2.m.e.1273.6 16 7.6 odd 2