Properties

Label 1365.2.f.c.274.1
Level $1365$
Weight $2$
Character 1365.274
Analytic conductor $10.900$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1365,2,Mod(274,1365)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1365, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1365.274");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1365 = 3 \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1365.f (of order \(2\), degree \(1\), 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: \(10.8995798759\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 274.1
Root \(-0.587785 - 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 1365.274
Dual form 1365.2.f.c.274.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.61803i q^{2} -1.00000i q^{3} -0.618034 q^{4} +(-1.90211 - 1.17557i) q^{5} -1.61803 q^{6} +1.00000i q^{7} -2.23607i q^{8} -1.00000 q^{9} +(-1.90211 + 3.07768i) q^{10} -4.80423 q^{11} +0.618034i q^{12} -1.00000i q^{13} +1.61803 q^{14} +(-1.17557 + 1.90211i) q^{15} -4.85410 q^{16} +3.24669i q^{17} +1.61803i q^{18} +0.891491 q^{19} +(1.17557 + 0.726543i) q^{20} +1.00000 q^{21} +7.77340i q^{22} -1.41164i q^{23} -2.23607 q^{24} +(2.23607 + 4.47214i) q^{25} -1.61803 q^{26} +1.00000i q^{27} -0.618034i q^{28} -0.459650 q^{29} +(3.07768 + 1.90211i) q^{30} +0.340519 q^{31} +3.38197i q^{32} +4.80423i q^{33} +5.25325 q^{34} +(1.17557 - 1.90211i) q^{35} +0.618034 q^{36} -1.71592i q^{37} -1.44246i q^{38} -1.00000 q^{39} +(-2.62866 + 4.25325i) q^{40} -3.07768 q^{41} -1.61803i q^{42} +11.8885i q^{43} +2.96917 q^{44} +(1.90211 + 1.17557i) q^{45} -2.28408 q^{46} -4.50953i q^{47} +4.85410i q^{48} -1.00000 q^{49} +(7.23607 - 3.61803i) q^{50} +3.24669 q^{51} +0.618034i q^{52} +0.405074i q^{53} +1.61803 q^{54} +(9.13818 + 5.64771i) q^{55} +2.23607 q^{56} -0.891491i q^{57} +0.743729i q^{58} -8.94241 q^{59} +(0.726543 - 1.17557i) q^{60} -10.3138 q^{61} -0.550972i q^{62} -1.00000i q^{63} -4.23607 q^{64} +(-1.17557 + 1.90211i) q^{65} +7.77340 q^{66} +8.24367i q^{67} -2.00656i q^{68} -1.41164 q^{69} +(-3.07768 - 1.90211i) q^{70} +7.57763 q^{71} +2.23607i q^{72} -2.48276i q^{73} -2.77642 q^{74} +(4.47214 - 2.23607i) q^{75} -0.550972 q^{76} -4.80423i q^{77} +1.61803i q^{78} +9.07112 q^{79} +(9.23305 + 5.70634i) q^{80} +1.00000 q^{81} +4.97980i q^{82} +3.83035i q^{83} -0.618034 q^{84} +(3.81671 - 6.17557i) q^{85} +19.2360 q^{86} +0.459650i q^{87} +10.7426i q^{88} -15.2935 q^{89} +(1.90211 - 3.07768i) q^{90} +1.00000 q^{91} +0.872441i q^{92} -0.340519i q^{93} -7.29657 q^{94} +(-1.69572 - 1.04801i) q^{95} +3.38197 q^{96} -10.4893i q^{97} +1.61803i q^{98} +4.80423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 4 q^{6} - 8 q^{9} - 8 q^{11} + 4 q^{14} - 12 q^{16} + 4 q^{19} + 8 q^{21} - 4 q^{26} + 12 q^{29} - 4 q^{31} + 8 q^{34} - 4 q^{36} - 8 q^{39} - 4 q^{44} - 12 q^{46} - 8 q^{49} + 40 q^{50}+ \cdots + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1365\mathbb{Z}\right)^\times\).

\(n\) \(106\) \(547\) \(911\) \(976\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.61803i 1.14412i −0.820211 0.572061i \(-0.806144\pi\)
0.820211 0.572061i \(-0.193856\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −0.618034 −0.309017
\(5\) −1.90211 1.17557i −0.850651 0.525731i
\(6\) −1.61803 −0.660560
\(7\) 1.00000i 0.377964i
\(8\) 2.23607i 0.790569i
\(9\) −1.00000 −0.333333
\(10\) −1.90211 + 3.07768i −0.601501 + 0.973249i
\(11\) −4.80423 −1.44853 −0.724264 0.689522i \(-0.757820\pi\)
−0.724264 + 0.689522i \(0.757820\pi\)
\(12\) 0.618034i 0.178411i
\(13\) 1.00000i 0.277350i
\(14\) 1.61803 0.432438
\(15\) −1.17557 + 1.90211i −0.303531 + 0.491123i
\(16\) −4.85410 −1.21353
\(17\) 3.24669i 0.787438i 0.919231 + 0.393719i \(0.128812\pi\)
−0.919231 + 0.393719i \(0.871188\pi\)
\(18\) 1.61803i 0.381374i
\(19\) 0.891491 0.204522 0.102261 0.994758i \(-0.467392\pi\)
0.102261 + 0.994758i \(0.467392\pi\)
\(20\) 1.17557 + 0.726543i 0.262866 + 0.162460i
\(21\) 1.00000 0.218218
\(22\) 7.77340i 1.65729i
\(23\) 1.41164i 0.294347i −0.989111 0.147173i \(-0.952982\pi\)
0.989111 0.147173i \(-0.0470176\pi\)
\(24\) −2.23607 −0.456435
\(25\) 2.23607 + 4.47214i 0.447214 + 0.894427i
\(26\) −1.61803 −0.317323
\(27\) 1.00000i 0.192450i
\(28\) 0.618034i 0.116797i
\(29\) −0.459650 −0.0853548 −0.0426774 0.999089i \(-0.513589\pi\)
−0.0426774 + 0.999089i \(0.513589\pi\)
\(30\) 3.07768 + 1.90211i 0.561906 + 0.347277i
\(31\) 0.340519 0.0611591 0.0305795 0.999532i \(-0.490265\pi\)
0.0305795 + 0.999532i \(0.490265\pi\)
\(32\) 3.38197i 0.597853i
\(33\) 4.80423i 0.836308i
\(34\) 5.25325 0.900926
\(35\) 1.17557 1.90211i 0.198708 0.321516i
\(36\) 0.618034 0.103006
\(37\) 1.71592i 0.282096i −0.990003 0.141048i \(-0.954953\pi\)
0.990003 0.141048i \(-0.0450471\pi\)
\(38\) 1.44246i 0.233998i
\(39\) −1.00000 −0.160128
\(40\) −2.62866 + 4.25325i −0.415627 + 0.672499i
\(41\) −3.07768 −0.480653 −0.240327 0.970692i \(-0.577255\pi\)
−0.240327 + 0.970692i \(0.577255\pi\)
\(42\) 1.61803i 0.249668i
\(43\) 11.8885i 1.81298i 0.422232 + 0.906488i \(0.361247\pi\)
−0.422232 + 0.906488i \(0.638753\pi\)
\(44\) 2.96917 0.447620
\(45\) 1.90211 + 1.17557i 0.283550 + 0.175244i
\(46\) −2.28408 −0.336769
\(47\) 4.50953i 0.657782i −0.944368 0.328891i \(-0.893325\pi\)
0.944368 0.328891i \(-0.106675\pi\)
\(48\) 4.85410i 0.700629i
\(49\) −1.00000 −0.142857
\(50\) 7.23607 3.61803i 1.02333 0.511667i
\(51\) 3.24669 0.454627
\(52\) 0.618034i 0.0857059i
\(53\) 0.405074i 0.0556412i 0.999613 + 0.0278206i \(0.00885671\pi\)
−0.999613 + 0.0278206i \(0.991143\pi\)
\(54\) 1.61803 0.220187
\(55\) 9.13818 + 5.64771i 1.23219 + 0.761537i
\(56\) 2.23607 0.298807
\(57\) 0.891491i 0.118081i
\(58\) 0.743729i 0.0976563i
\(59\) −8.94241 −1.16420 −0.582101 0.813116i \(-0.697769\pi\)
−0.582101 + 0.813116i \(0.697769\pi\)
\(60\) 0.726543 1.17557i 0.0937962 0.151765i
\(61\) −10.3138 −1.32054 −0.660270 0.751028i \(-0.729558\pi\)
−0.660270 + 0.751028i \(0.729558\pi\)
\(62\) 0.550972i 0.0699735i
\(63\) 1.00000i 0.125988i
\(64\) −4.23607 −0.529508
\(65\) −1.17557 + 1.90211i −0.145812 + 0.235928i
\(66\) 7.77340 0.956840
\(67\) 8.24367i 1.00712i 0.863959 + 0.503562i \(0.167978\pi\)
−0.863959 + 0.503562i \(0.832022\pi\)
\(68\) 2.00656i 0.243332i
\(69\) −1.41164 −0.169941
\(70\) −3.07768 1.90211i −0.367854 0.227346i
\(71\) 7.57763 0.899299 0.449649 0.893205i \(-0.351549\pi\)
0.449649 + 0.893205i \(0.351549\pi\)
\(72\) 2.23607i 0.263523i
\(73\) 2.48276i 0.290585i −0.989389 0.145292i \(-0.953588\pi\)
0.989389 0.145292i \(-0.0464123\pi\)
\(74\) −2.77642 −0.322752
\(75\) 4.47214 2.23607i 0.516398 0.258199i
\(76\) −0.550972 −0.0632008
\(77\) 4.80423i 0.547492i
\(78\) 1.61803i 0.183206i
\(79\) 9.07112 1.02058 0.510290 0.860002i \(-0.329538\pi\)
0.510290 + 0.860002i \(0.329538\pi\)
\(80\) 9.23305 + 5.70634i 1.03229 + 0.637988i
\(81\) 1.00000 0.111111
\(82\) 4.97980i 0.549927i
\(83\) 3.83035i 0.420436i 0.977655 + 0.210218i \(0.0674173\pi\)
−0.977655 + 0.210218i \(0.932583\pi\)
\(84\) −0.618034 −0.0674330
\(85\) 3.81671 6.17557i 0.413981 0.669835i
\(86\) 19.2360 2.07427
\(87\) 0.459650i 0.0492796i
\(88\) 10.7426i 1.14516i
\(89\) −15.2935 −1.62111 −0.810556 0.585661i \(-0.800835\pi\)
−0.810556 + 0.585661i \(0.800835\pi\)
\(90\) 1.90211 3.07768i 0.200500 0.324416i
\(91\) 1.00000 0.104828
\(92\) 0.872441i 0.0909582i
\(93\) 0.340519i 0.0353102i
\(94\) −7.29657 −0.752583
\(95\) −1.69572 1.04801i −0.173977 0.107524i
\(96\) 3.38197 0.345170
\(97\) 10.4893i 1.06503i −0.846421 0.532515i \(-0.821247\pi\)
0.846421 0.532515i \(-0.178753\pi\)
\(98\) 1.61803i 0.163446i
\(99\) 4.80423 0.482843
\(100\) −1.38197 2.76393i −0.138197 0.276393i
\(101\) 2.46151 0.244930 0.122465 0.992473i \(-0.460920\pi\)
0.122465 + 0.992473i \(0.460920\pi\)
\(102\) 5.25325i 0.520150i
\(103\) 4.66906i 0.460056i 0.973184 + 0.230028i \(0.0738818\pi\)
−0.973184 + 0.230028i \(0.926118\pi\)
\(104\) −2.23607 −0.219265
\(105\) −1.90211 1.17557i −0.185627 0.114724i
\(106\) 0.655423 0.0636604
\(107\) 6.28949i 0.608028i −0.952668 0.304014i \(-0.901673\pi\)
0.952668 0.304014i \(-0.0983270\pi\)
\(108\) 0.618034i 0.0594703i
\(109\) 3.92045 0.375511 0.187756 0.982216i \(-0.439879\pi\)
0.187756 + 0.982216i \(0.439879\pi\)
\(110\) 9.13818 14.7859i 0.871291 1.40978i
\(111\) −1.71592 −0.162868
\(112\) 4.85410i 0.458670i
\(113\) 2.43841i 0.229386i 0.993401 + 0.114693i \(0.0365884\pi\)
−0.993401 + 0.114693i \(0.963412\pi\)
\(114\) −1.44246 −0.135099
\(115\) −1.65948 + 2.68510i −0.154747 + 0.250386i
\(116\) 0.284079 0.0263761
\(117\) 1.00000i 0.0924500i
\(118\) 14.4691i 1.33199i
\(119\) −3.24669 −0.297624
\(120\) 4.25325 + 2.62866i 0.388267 + 0.239962i
\(121\) 12.0806 1.09824
\(122\) 16.6880i 1.51086i
\(123\) 3.07768i 0.277505i
\(124\) −0.210453 −0.0188992
\(125\) 1.00406 11.1352i 0.0898056 0.995959i
\(126\) −1.61803 −0.144146
\(127\) 13.3974i 1.18882i −0.804161 0.594412i \(-0.797385\pi\)
0.804161 0.594412i \(-0.202615\pi\)
\(128\) 13.6180i 1.20368i
\(129\) 11.8885 1.04672
\(130\) 3.07768 + 1.90211i 0.269931 + 0.166826i
\(131\) −20.5593 −1.79627 −0.898137 0.439716i \(-0.855079\pi\)
−0.898137 + 0.439716i \(0.855079\pi\)
\(132\) 2.96917i 0.258434i
\(133\) 0.891491i 0.0773021i
\(134\) 13.3385 1.15227
\(135\) 1.17557 1.90211i 0.101177 0.163708i
\(136\) 7.25982 0.622524
\(137\) 4.74258i 0.405186i −0.979263 0.202593i \(-0.935063\pi\)
0.979263 0.202593i \(-0.0649368\pi\)
\(138\) 2.28408i 0.194434i
\(139\) −14.9069 −1.26439 −0.632193 0.774811i \(-0.717845\pi\)
−0.632193 + 0.774811i \(0.717845\pi\)
\(140\) −0.726543 + 1.17557i −0.0614041 + 0.0993538i
\(141\) −4.50953 −0.379771
\(142\) 12.2609i 1.02891i
\(143\) 4.80423i 0.401750i
\(144\) 4.85410 0.404508
\(145\) 0.874305 + 0.540350i 0.0726071 + 0.0448737i
\(146\) −4.01719 −0.332465
\(147\) 1.00000i 0.0824786i
\(148\) 1.06050i 0.0871724i
\(149\) 9.09372 0.744986 0.372493 0.928035i \(-0.378503\pi\)
0.372493 + 0.928035i \(0.378503\pi\)
\(150\) −3.61803 7.23607i −0.295411 0.590822i
\(151\) −12.9864 −1.05682 −0.528408 0.848991i \(-0.677211\pi\)
−0.528408 + 0.848991i \(0.677211\pi\)
\(152\) 1.99344i 0.161689i
\(153\) 3.24669i 0.262479i
\(154\) −7.77340 −0.626399
\(155\) −0.647706 0.400305i −0.0520250 0.0321532i
\(156\) 0.618034 0.0494823
\(157\) 2.55703i 0.204073i 0.994781 + 0.102036i \(0.0325358\pi\)
−0.994781 + 0.102036i \(0.967464\pi\)
\(158\) 14.6774i 1.16767i
\(159\) 0.405074 0.0321245
\(160\) 3.97574 6.43288i 0.314310 0.508564i
\(161\) 1.41164 0.111253
\(162\) 1.61803i 0.127125i
\(163\) 25.2136i 1.97488i −0.157999 0.987439i \(-0.550504\pi\)
0.157999 0.987439i \(-0.449496\pi\)
\(164\) 1.90211 0.148530
\(165\) 5.64771 9.13818i 0.439673 0.711406i
\(166\) 6.19764 0.481030
\(167\) 14.4068i 1.11483i −0.830235 0.557414i \(-0.811794\pi\)
0.830235 0.557414i \(-0.188206\pi\)
\(168\) 2.23607i 0.172516i
\(169\) −1.00000 −0.0769231
\(170\) −9.99228 6.17557i −0.766373 0.473645i
\(171\) −0.891491 −0.0681741
\(172\) 7.34748i 0.560240i
\(173\) 10.0659i 0.765297i 0.923894 + 0.382648i \(0.124988\pi\)
−0.923894 + 0.382648i \(0.875012\pi\)
\(174\) 0.743729 0.0563819
\(175\) −4.47214 + 2.23607i −0.338062 + 0.169031i
\(176\) 23.3202 1.75783
\(177\) 8.94241i 0.672152i
\(178\) 24.7455i 1.85475i
\(179\) −8.15910 −0.609840 −0.304920 0.952378i \(-0.598630\pi\)
−0.304920 + 0.952378i \(0.598630\pi\)
\(180\) −1.17557 0.726543i −0.0876219 0.0541533i
\(181\) −20.5509 −1.52753 −0.763767 0.645492i \(-0.776652\pi\)
−0.763767 + 0.645492i \(0.776652\pi\)
\(182\) 1.61803i 0.119937i
\(183\) 10.3138i 0.762414i
\(184\) −3.15652 −0.232702
\(185\) −2.01719 + 3.26388i −0.148306 + 0.239965i
\(186\) −0.550972 −0.0403992
\(187\) 15.5978i 1.14063i
\(188\) 2.78704i 0.203266i
\(189\) −1.00000 −0.0727393
\(190\) −1.69572 + 2.74373i −0.123020 + 0.199051i
\(191\) 14.8310 1.07313 0.536567 0.843858i \(-0.319721\pi\)
0.536567 + 0.843858i \(0.319721\pi\)
\(192\) 4.23607i 0.305712i
\(193\) 4.38447i 0.315601i 0.987471 + 0.157801i \(0.0504403\pi\)
−0.987471 + 0.157801i \(0.949560\pi\)
\(194\) −16.9721 −1.21852
\(195\) 1.90211 + 1.17557i 0.136213 + 0.0841844i
\(196\) 0.618034 0.0441453
\(197\) 5.40321i 0.384963i −0.981301 0.192481i \(-0.938347\pi\)
0.981301 0.192481i \(-0.0616535\pi\)
\(198\) 7.77340i 0.552432i
\(199\) 11.5692 0.820119 0.410059 0.912059i \(-0.365508\pi\)
0.410059 + 0.912059i \(0.365508\pi\)
\(200\) 10.0000 5.00000i 0.707107 0.353553i
\(201\) 8.24367 0.581464
\(202\) 3.98281i 0.280230i
\(203\) 0.459650i 0.0322611i
\(204\) −2.00656 −0.140488
\(205\) 5.85410 + 3.61803i 0.408868 + 0.252694i
\(206\) 7.55470 0.526361
\(207\) 1.41164i 0.0981157i
\(208\) 4.85410i 0.336571i
\(209\) −4.28293 −0.296256
\(210\) −1.90211 + 3.07768i −0.131258 + 0.212380i
\(211\) −10.7653 −0.741113 −0.370556 0.928810i \(-0.620833\pi\)
−0.370556 + 0.928810i \(0.620833\pi\)
\(212\) 0.250349i 0.0171941i
\(213\) 7.57763i 0.519210i
\(214\) −10.1766 −0.695659
\(215\) 13.9757 22.6132i 0.953138 1.54221i
\(216\) 2.23607 0.152145
\(217\) 0.340519i 0.0231160i
\(218\) 6.34342i 0.429631i
\(219\) −2.48276 −0.167769
\(220\) −5.64771 3.49047i −0.380768 0.235328i
\(221\) 3.24669 0.218396
\(222\) 2.77642i 0.186341i
\(223\) 9.65948i 0.646847i 0.946254 + 0.323423i \(0.104834\pi\)
−0.946254 + 0.323423i \(0.895166\pi\)
\(224\) −3.38197 −0.225967
\(225\) −2.23607 4.47214i −0.149071 0.298142i
\(226\) 3.94542 0.262446
\(227\) 27.8250i 1.84681i 0.383825 + 0.923406i \(0.374607\pi\)
−0.383825 + 0.923406i \(0.625393\pi\)
\(228\) 0.550972i 0.0364890i
\(229\) −8.53026 −0.563695 −0.281848 0.959459i \(-0.590947\pi\)
−0.281848 + 0.959459i \(0.590947\pi\)
\(230\) 4.34458 + 2.68510i 0.286473 + 0.177050i
\(231\) −4.80423 −0.316095
\(232\) 1.02781i 0.0674789i
\(233\) 21.1471i 1.38540i −0.721228 0.692698i \(-0.756422\pi\)
0.721228 0.692698i \(-0.243578\pi\)
\(234\) 1.61803 0.105774
\(235\) −5.30127 + 8.57763i −0.345816 + 0.559543i
\(236\) 5.52671 0.359758
\(237\) 9.07112i 0.589233i
\(238\) 5.25325i 0.340518i
\(239\) −18.1840 −1.17623 −0.588113 0.808779i \(-0.700129\pi\)
−0.588113 + 0.808779i \(0.700129\pi\)
\(240\) 5.70634 9.23305i 0.368343 0.595991i
\(241\) −11.7022 −0.753803 −0.376901 0.926253i \(-0.623010\pi\)
−0.376901 + 0.926253i \(0.623010\pi\)
\(242\) 19.5468i 1.25652i
\(243\) 1.00000i 0.0641500i
\(244\) 6.37425 0.408069
\(245\) 1.90211 + 1.17557i 0.121522 + 0.0751044i
\(246\) 4.97980 0.317500
\(247\) 0.891491i 0.0567242i
\(248\) 0.761425i 0.0483505i
\(249\) 3.83035 0.242739
\(250\) −18.0171 1.62460i −1.13950 0.102749i
\(251\) 6.64185 0.419230 0.209615 0.977784i \(-0.432779\pi\)
0.209615 + 0.977784i \(0.432779\pi\)
\(252\) 0.618034i 0.0389325i
\(253\) 6.78183i 0.426370i
\(254\) −21.6774 −1.36016
\(255\) −6.17557 3.81671i −0.386729 0.239012i
\(256\) 13.5623 0.847644
\(257\) 16.4358i 1.02524i −0.858617 0.512618i \(-0.828676\pi\)
0.858617 0.512618i \(-0.171324\pi\)
\(258\) 19.2360i 1.19758i
\(259\) 1.71592 0.106622
\(260\) 0.726543 1.17557i 0.0450583 0.0729058i
\(261\) 0.459650 0.0284516
\(262\) 33.2656i 2.05516i
\(263\) 27.9057i 1.72074i 0.509673 + 0.860368i \(0.329766\pi\)
−0.509673 + 0.860368i \(0.670234\pi\)
\(264\) 10.7426 0.661160
\(265\) 0.476193 0.770497i 0.0292523 0.0473312i
\(266\) 1.44246 0.0884431
\(267\) 15.2935i 0.935950i
\(268\) 5.09487i 0.311219i
\(269\) −27.3788 −1.66932 −0.834659 0.550768i \(-0.814335\pi\)
−0.834659 + 0.550768i \(0.814335\pi\)
\(270\) −3.07768 1.90211i −0.187302 0.115759i
\(271\) −3.10600 −0.188676 −0.0943381 0.995540i \(-0.530073\pi\)
−0.0943381 + 0.995540i \(0.530073\pi\)
\(272\) 15.7598i 0.955576i
\(273\) 1.00000i 0.0605228i
\(274\) −7.67365 −0.463582
\(275\) −10.7426 21.4852i −0.647802 1.29560i
\(276\) 0.872441 0.0525148
\(277\) 30.2146i 1.81542i 0.419599 + 0.907710i \(0.362171\pi\)
−0.419599 + 0.907710i \(0.637829\pi\)
\(278\) 24.1198i 1.44661i
\(279\) −0.340519 −0.0203864
\(280\) −4.25325 2.62866i −0.254181 0.157092i
\(281\) −0.922959 −0.0550591 −0.0275296 0.999621i \(-0.508764\pi\)
−0.0275296 + 0.999621i \(0.508764\pi\)
\(282\) 7.29657i 0.434504i
\(283\) 16.7953i 0.998376i 0.866494 + 0.499188i \(0.166368\pi\)
−0.866494 + 0.499188i \(0.833632\pi\)
\(284\) −4.68323 −0.277899
\(285\) −1.04801 + 1.69572i −0.0620788 + 0.100446i
\(286\) 7.77340 0.459651
\(287\) 3.07768i 0.181670i
\(288\) 3.38197i 0.199284i
\(289\) 6.45901 0.379942
\(290\) 0.874305 1.41466i 0.0513410 0.0830715i
\(291\) −10.4893 −0.614895
\(292\) 1.53443i 0.0897956i
\(293\) 5.53066i 0.323104i −0.986864 0.161552i \(-0.948350\pi\)
0.986864 0.161552i \(-0.0516500\pi\)
\(294\) 1.61803 0.0943657
\(295\) 17.0095 + 10.5124i 0.990330 + 0.612057i
\(296\) −3.83692 −0.223016
\(297\) 4.80423i 0.278769i
\(298\) 14.7139i 0.852356i
\(299\) −1.41164 −0.0816372
\(300\) −2.76393 + 1.38197i −0.159576 + 0.0797878i
\(301\) −11.8885 −0.685240
\(302\) 21.0124i 1.20913i
\(303\) 2.46151i 0.141410i
\(304\) −4.32739 −0.248193
\(305\) 19.6179 + 12.1245i 1.12332 + 0.694249i
\(306\) −5.25325 −0.300309
\(307\) 31.3957i 1.79185i −0.444208 0.895923i \(-0.646515\pi\)
0.444208 0.895923i \(-0.353485\pi\)
\(308\) 2.96917i 0.169184i
\(309\) 4.66906 0.265614
\(310\) −0.647706 + 1.04801i −0.0367873 + 0.0595230i
\(311\) 2.73362 0.155009 0.0775046 0.996992i \(-0.475305\pi\)
0.0775046 + 0.996992i \(0.475305\pi\)
\(312\) 2.23607i 0.126592i
\(313\) 2.92489i 0.165325i 0.996578 + 0.0826624i \(0.0263423\pi\)
−0.996578 + 0.0826624i \(0.973658\pi\)
\(314\) 4.13736 0.233485
\(315\) −1.17557 + 1.90211i −0.0662359 + 0.107172i
\(316\) −5.60626 −0.315377
\(317\) 0.810148i 0.0455024i 0.999741 + 0.0227512i \(0.00724256\pi\)
−0.999741 + 0.0227512i \(0.992757\pi\)
\(318\) 0.655423i 0.0367543i
\(319\) 2.20826 0.123639
\(320\) 8.05748 + 4.97980i 0.450427 + 0.278379i
\(321\) −6.28949 −0.351045
\(322\) 2.28408i 0.127287i
\(323\) 2.89440i 0.161049i
\(324\) −0.618034 −0.0343352
\(325\) 4.47214 2.23607i 0.248069 0.124035i
\(326\) −40.7964 −2.25950
\(327\) 3.92045i 0.216801i
\(328\) 6.88191i 0.379990i
\(329\) 4.50953 0.248618
\(330\) −14.7859 9.13818i −0.813936 0.503040i
\(331\) −5.02278 −0.276077 −0.138038 0.990427i \(-0.544080\pi\)
−0.138038 + 0.990427i \(0.544080\pi\)
\(332\) 2.36729i 0.129922i
\(333\) 1.71592i 0.0940319i
\(334\) −23.3106 −1.27550
\(335\) 9.69102 15.6804i 0.529477 0.856712i
\(336\) −4.85410 −0.264813
\(337\) 14.9881i 0.816455i −0.912880 0.408227i \(-0.866147\pi\)
0.912880 0.408227i \(-0.133853\pi\)
\(338\) 1.61803i 0.0880094i
\(339\) 2.43841 0.132436
\(340\) −2.35886 + 3.81671i −0.127927 + 0.206990i
\(341\) −1.63593 −0.0885907
\(342\) 1.44246i 0.0779995i
\(343\) 1.00000i 0.0539949i
\(344\) 26.5834 1.43328
\(345\) 2.68510 + 1.65948i 0.144561 + 0.0893434i
\(346\) 16.2870 0.875594
\(347\) 3.88544i 0.208581i −0.994547 0.104291i \(-0.966743\pi\)
0.994547 0.104291i \(-0.0332572\pi\)
\(348\) 0.284079i 0.0152282i
\(349\) −33.1267 −1.77323 −0.886616 0.462507i \(-0.846950\pi\)
−0.886616 + 0.462507i \(0.846950\pi\)
\(350\) 3.61803 + 7.23607i 0.193392 + 0.386784i
\(351\) 1.00000 0.0533761
\(352\) 16.2477i 0.866007i
\(353\) 6.16721i 0.328248i −0.986440 0.164124i \(-0.947520\pi\)
0.986440 0.164124i \(-0.0524796\pi\)
\(354\) 14.4691 0.769025
\(355\) −14.4135 8.90803i −0.764989 0.472789i
\(356\) 9.45193 0.500951
\(357\) 3.24669i 0.171833i
\(358\) 13.2017i 0.697731i
\(359\) 4.35926 0.230073 0.115036 0.993361i \(-0.463302\pi\)
0.115036 + 0.993361i \(0.463302\pi\)
\(360\) 2.62866 4.25325i 0.138542 0.224166i
\(361\) −18.2052 −0.958171
\(362\) 33.2520i 1.74769i
\(363\) 12.0806i 0.634066i
\(364\) −0.618034 −0.0323938
\(365\) −2.91866 + 4.72249i −0.152769 + 0.247186i
\(366\) 16.6880 0.872296
\(367\) 35.6921i 1.86311i −0.363600 0.931555i \(-0.618453\pi\)
0.363600 0.931555i \(-0.381547\pi\)
\(368\) 6.85224i 0.357198i
\(369\) 3.07768 0.160218
\(370\) 5.28106 + 3.26388i 0.274549 + 0.169681i
\(371\) −0.405074 −0.0210304
\(372\) 0.210453i 0.0109115i
\(373\) 11.6759i 0.604556i −0.953220 0.302278i \(-0.902253\pi\)
0.953220 0.302278i \(-0.0977471\pi\)
\(374\) −25.2378 −1.30502
\(375\) −11.1352 1.00406i −0.575017 0.0518493i
\(376\) −10.0836 −0.520022
\(377\) 0.459650i 0.0236732i
\(378\) 1.61803i 0.0832227i
\(379\) −20.0941 −1.03217 −0.516083 0.856539i \(-0.672610\pi\)
−0.516083 + 0.856539i \(0.672610\pi\)
\(380\) 1.04801 + 0.647706i 0.0537618 + 0.0332266i
\(381\) −13.3974 −0.686367
\(382\) 23.9971i 1.22780i
\(383\) 0.874948i 0.0447078i 0.999750 + 0.0223539i \(0.00711605\pi\)
−0.999750 + 0.0223539i \(0.992884\pi\)
\(384\) 13.6180 0.694942
\(385\) −5.64771 + 9.13818i −0.287834 + 0.465725i
\(386\) 7.09423 0.361087
\(387\) 11.8885i 0.604325i
\(388\) 6.48276i 0.329112i
\(389\) −32.7010 −1.65801 −0.829004 0.559243i \(-0.811092\pi\)
−0.829004 + 0.559243i \(0.811092\pi\)
\(390\) 1.90211 3.07768i 0.0963172 0.155845i
\(391\) 4.58315 0.231780
\(392\) 2.23607i 0.112938i
\(393\) 20.5593i 1.03708i
\(394\) −8.74258 −0.440445
\(395\) −17.2543 10.6637i −0.868158 0.536551i
\(396\) −2.96917 −0.149207
\(397\) 37.1937i 1.86670i −0.358971 0.933349i \(-0.616872\pi\)
0.358971 0.933349i \(-0.383128\pi\)
\(398\) 18.7194i 0.938316i
\(399\) 0.891491 0.0446304
\(400\) −10.8541 21.7082i −0.542705 1.08541i
\(401\) −3.69636 −0.184587 −0.0922937 0.995732i \(-0.529420\pi\)
−0.0922937 + 0.995732i \(0.529420\pi\)
\(402\) 13.3385i 0.665266i
\(403\) 0.340519i 0.0169625i
\(404\) −1.52130 −0.0756875
\(405\) −1.90211 1.17557i −0.0945168 0.0584146i
\(406\) −0.743729 −0.0369106
\(407\) 8.24367i 0.408624i
\(408\) 7.25982i 0.359415i
\(409\) 5.50837 0.272372 0.136186 0.990683i \(-0.456516\pi\)
0.136186 + 0.990683i \(0.456516\pi\)
\(410\) 5.85410 9.47214i 0.289113 0.467795i
\(411\) −4.74258 −0.233934
\(412\) 2.88564i 0.142165i
\(413\) 8.94241i 0.440027i
\(414\) 2.28408 0.112256
\(415\) 4.50285 7.28576i 0.221036 0.357644i
\(416\) 3.38197 0.165815
\(417\) 14.9069i 0.729993i
\(418\) 6.92992i 0.338953i
\(419\) 24.5229 1.19802 0.599012 0.800740i \(-0.295560\pi\)
0.599012 + 0.800740i \(0.295560\pi\)
\(420\) 1.17557 + 0.726543i 0.0573620 + 0.0354516i
\(421\) −6.91531 −0.337032 −0.168516 0.985699i \(-0.553897\pi\)
−0.168516 + 0.985699i \(0.553897\pi\)
\(422\) 17.4186i 0.847924i
\(423\) 4.50953i 0.219261i
\(424\) 0.905773 0.0439882
\(425\) −14.5196 + 7.25982i −0.704306 + 0.352153i
\(426\) −12.2609 −0.594041
\(427\) 10.3138i 0.499117i
\(428\) 3.88712i 0.187891i
\(429\) 4.80423 0.231950
\(430\) −36.5890 22.6132i −1.76448 1.09051i
\(431\) 6.75428 0.325342 0.162671 0.986680i \(-0.447989\pi\)
0.162671 + 0.986680i \(0.447989\pi\)
\(432\) 4.85410i 0.233543i
\(433\) 26.2842i 1.26314i −0.775320 0.631568i \(-0.782412\pi\)
0.775320 0.631568i \(-0.217588\pi\)
\(434\) 0.550972 0.0264475
\(435\) 0.540350 0.874305i 0.0259078 0.0419197i
\(436\) −2.42297 −0.116039
\(437\) 1.25846i 0.0602005i
\(438\) 4.01719i 0.191949i
\(439\) 21.6867 1.03505 0.517526 0.855668i \(-0.326853\pi\)
0.517526 + 0.855668i \(0.326853\pi\)
\(440\) 12.6287 20.4336i 0.602048 0.974133i
\(441\) 1.00000 0.0476190
\(442\) 5.25325i 0.249872i
\(443\) 30.0870i 1.42948i 0.699391 + 0.714739i \(0.253455\pi\)
−0.699391 + 0.714739i \(0.746545\pi\)
\(444\) 1.06050 0.0503290
\(445\) 29.0901 + 17.9786i 1.37900 + 0.852269i
\(446\) 15.6294 0.740072
\(447\) 9.09372i 0.430118i
\(448\) 4.23607i 0.200135i
\(449\) 37.4141 1.76568 0.882840 0.469673i \(-0.155628\pi\)
0.882840 + 0.469673i \(0.155628\pi\)
\(450\) −7.23607 + 3.61803i −0.341112 + 0.170556i
\(451\) 14.7859 0.696240
\(452\) 1.50702i 0.0708842i
\(453\) 12.9864i 0.610152i
\(454\) 45.0218 2.11298
\(455\) −1.90211 1.17557i −0.0891724 0.0551116i
\(456\) −1.99344 −0.0933512
\(457\) 8.26452i 0.386598i −0.981140 0.193299i \(-0.938081\pi\)
0.981140 0.193299i \(-0.0619187\pi\)
\(458\) 13.8022i 0.644937i
\(459\) −3.24669 −0.151542
\(460\) 1.02562 1.65948i 0.0478196 0.0773737i
\(461\) 0.874815 0.0407442 0.0203721 0.999792i \(-0.493515\pi\)
0.0203721 + 0.999792i \(0.493515\pi\)
\(462\) 7.77340i 0.361651i
\(463\) 20.4850i 0.952020i 0.879440 + 0.476010i \(0.157917\pi\)
−0.879440 + 0.476010i \(0.842083\pi\)
\(464\) 2.23119 0.103580
\(465\) −0.400305 + 0.647706i −0.0185637 + 0.0300367i
\(466\) −34.2168 −1.58506
\(467\) 12.7298i 0.589063i −0.955642 0.294532i \(-0.904836\pi\)
0.955642 0.294532i \(-0.0951636\pi\)
\(468\) 0.618034i 0.0285686i
\(469\) −8.24367 −0.380657
\(470\) 13.8789 + 8.57763i 0.640186 + 0.395656i
\(471\) 2.55703 0.117822
\(472\) 19.9958i 0.920383i
\(473\) 57.1149i 2.62615i
\(474\) −14.6774 −0.674154
\(475\) 1.99344 + 3.98687i 0.0914651 + 0.182930i
\(476\) 2.00656 0.0919707
\(477\) 0.405074i 0.0185471i
\(478\) 29.4223i 1.34575i
\(479\) −24.9962 −1.14210 −0.571052 0.820914i \(-0.693464\pi\)
−0.571052 + 0.820914i \(0.693464\pi\)
\(480\) −6.43288 3.97574i −0.293620 0.181467i
\(481\) −1.71592 −0.0782393
\(482\) 18.9345i 0.862443i
\(483\) 1.41164i 0.0642318i
\(484\) −7.46621 −0.339373
\(485\) −12.3309 + 19.9519i −0.559919 + 0.905968i
\(486\) −1.61803 −0.0733955
\(487\) 27.6813i 1.25436i 0.778874 + 0.627180i \(0.215791\pi\)
−0.778874 + 0.627180i \(0.784209\pi\)
\(488\) 23.0622i 1.04398i
\(489\) −25.2136 −1.14020
\(490\) 1.90211 3.07768i 0.0859287 0.139036i
\(491\) 5.75969 0.259931 0.129966 0.991518i \(-0.458513\pi\)
0.129966 + 0.991518i \(0.458513\pi\)
\(492\) 1.90211i 0.0857539i
\(493\) 1.49234i 0.0672116i
\(494\) −1.44246 −0.0648995
\(495\) −9.13818 5.64771i −0.410731 0.253846i
\(496\) −1.65292 −0.0742181
\(497\) 7.57763i 0.339903i
\(498\) 6.19764i 0.277723i
\(499\) 35.2238 1.57683 0.788416 0.615143i \(-0.210902\pi\)
0.788416 + 0.615143i \(0.210902\pi\)
\(500\) −0.620541 + 6.88191i −0.0277515 + 0.307768i
\(501\) −14.4068 −0.643646
\(502\) 10.7467i 0.479651i
\(503\) 23.1576i 1.03254i 0.856425 + 0.516272i \(0.172681\pi\)
−0.856425 + 0.516272i \(0.827319\pi\)
\(504\) −2.23607 −0.0996024
\(505\) −4.68208 2.89368i −0.208350 0.128767i
\(506\) 10.9732 0.487820
\(507\) 1.00000i 0.0444116i
\(508\) 8.28002i 0.367367i
\(509\) −7.23722 −0.320784 −0.160392 0.987053i \(-0.551276\pi\)
−0.160392 + 0.987053i \(0.551276\pi\)
\(510\) −6.17557 + 9.99228i −0.273459 + 0.442466i
\(511\) 2.48276 0.109831
\(512\) 5.29180i 0.233867i
\(513\) 0.891491i 0.0393603i
\(514\) −26.5937 −1.17300
\(515\) 5.48881 8.88108i 0.241866 0.391347i
\(516\) −7.34748 −0.323455
\(517\) 21.6648i 0.952816i
\(518\) 2.77642i 0.121989i
\(519\) 10.0659 0.441844
\(520\) 4.25325 + 2.62866i 0.186518 + 0.115274i
\(521\) −16.2953 −0.713910 −0.356955 0.934122i \(-0.616185\pi\)
−0.356955 + 0.934122i \(0.616185\pi\)
\(522\) 0.743729i 0.0325521i
\(523\) 22.1147i 0.967010i 0.875342 + 0.483505i \(0.160637\pi\)
−0.875342 + 0.483505i \(0.839363\pi\)
\(524\) 12.7063 0.555079
\(525\) 2.23607 + 4.47214i 0.0975900 + 0.195180i
\(526\) 45.1523 1.96873
\(527\) 1.10556i 0.0481590i
\(528\) 23.3202i 1.01488i
\(529\) 21.0073 0.913360
\(530\) −1.24669 0.770497i −0.0541527 0.0334682i
\(531\) 8.94241 0.388067
\(532\) 0.550972i 0.0238877i
\(533\) 3.07768i 0.133309i
\(534\) 24.7455 1.07084
\(535\) −7.39374 + 11.9633i −0.319659 + 0.517220i
\(536\) 18.4334 0.796202
\(537\) 8.15910i 0.352091i
\(538\) 44.2999i 1.90990i
\(539\) 4.80423 0.206933
\(540\) −0.726543 + 1.17557i −0.0312654 + 0.0505885i
\(541\) −13.0517 −0.561138 −0.280569 0.959834i \(-0.590523\pi\)
−0.280569 + 0.959834i \(0.590523\pi\)
\(542\) 5.02562i 0.215869i
\(543\) 20.5509i 0.881922i
\(544\) −10.9802 −0.470772
\(545\) −7.45714 4.60877i −0.319429 0.197418i
\(546\) −1.61803 −0.0692455
\(547\) 21.3283i 0.911933i −0.889997 0.455966i \(-0.849294\pi\)
0.889997 0.455966i \(-0.150706\pi\)
\(548\) 2.93107i 0.125209i
\(549\) 10.3138 0.440180
\(550\) −34.7637 + 17.3819i −1.48233 + 0.741165i
\(551\) −0.409774 −0.0174569
\(552\) 3.15652i 0.134350i
\(553\) 9.07112i 0.385743i
\(554\) 48.8882 2.07706
\(555\) 3.26388 + 2.01719i 0.138544 + 0.0856248i
\(556\) 9.21296 0.390717
\(557\) 18.4676i 0.782496i 0.920285 + 0.391248i \(0.127957\pi\)
−0.920285 + 0.391248i \(0.872043\pi\)
\(558\) 0.550972i 0.0233245i
\(559\) 11.8885 0.502829
\(560\) −5.70634 + 9.23305i −0.241137 + 0.390168i
\(561\) −15.5978 −0.658541
\(562\) 1.49338i 0.0629944i
\(563\) 3.69475i 0.155715i −0.996964 0.0778575i \(-0.975192\pi\)
0.996964 0.0778575i \(-0.0248079\pi\)
\(564\) 2.78704 0.117356
\(565\) 2.86652 4.63812i 0.120595 0.195127i
\(566\) 27.1753 1.14226
\(567\) 1.00000i 0.0419961i
\(568\) 16.9441i 0.710958i
\(569\) 31.4370 1.31791 0.658954 0.752183i \(-0.270999\pi\)
0.658954 + 0.752183i \(0.270999\pi\)
\(570\) 2.74373 + 1.69572i 0.114922 + 0.0710258i
\(571\) 32.3772 1.35494 0.677471 0.735549i \(-0.263076\pi\)
0.677471 + 0.735549i \(0.263076\pi\)
\(572\) 2.96917i 0.124147i
\(573\) 14.8310i 0.619574i
\(574\) −4.97980 −0.207853
\(575\) 6.31304 3.15652i 0.263272 0.131636i
\(576\) 4.23607 0.176503
\(577\) 26.6939i 1.11128i −0.831422 0.555642i \(-0.812473\pi\)
0.831422 0.555642i \(-0.187527\pi\)
\(578\) 10.4509i 0.434700i
\(579\) 4.38447 0.182212
\(580\) −0.540350 0.333955i −0.0224368 0.0138667i
\(581\) −3.83035 −0.158910
\(582\) 16.9721i 0.703515i
\(583\) 1.94607i 0.0805979i
\(584\) −5.55161 −0.229727
\(585\) 1.17557 1.90211i 0.0486039 0.0786427i
\(586\) −8.94879 −0.369671
\(587\) 25.0174i 1.03258i −0.856414 0.516289i \(-0.827313\pi\)
0.856414 0.516289i \(-0.172687\pi\)
\(588\) 0.618034i 0.0254873i
\(589\) 0.303570 0.0125084
\(590\) 17.0095 27.5219i 0.700269 1.13306i
\(591\) −5.40321 −0.222258
\(592\) 8.32926i 0.342330i
\(593\) 30.4293i 1.24958i 0.780792 + 0.624791i \(0.214816\pi\)
−0.780792 + 0.624791i \(0.785184\pi\)
\(594\) −7.77340 −0.318947
\(595\) 6.17557 + 3.81671i 0.253174 + 0.156470i
\(596\) −5.62023 −0.230213
\(597\) 11.5692i 0.473496i
\(598\) 2.28408i 0.0934029i
\(599\) 45.6159 1.86382 0.931908 0.362694i \(-0.118143\pi\)
0.931908 + 0.362694i \(0.118143\pi\)
\(600\) −5.00000 10.0000i −0.204124 0.408248i
\(601\) 30.8212 1.25722 0.628611 0.777720i \(-0.283624\pi\)
0.628611 + 0.777720i \(0.283624\pi\)
\(602\) 19.2360i 0.783999i
\(603\) 8.24367i 0.335708i
\(604\) 8.02601 0.326574
\(605\) −22.9786 14.2016i −0.934215 0.577376i
\(606\) −3.98281 −0.161791
\(607\) 45.7895i 1.85854i −0.369403 0.929269i \(-0.620438\pi\)
0.369403 0.929269i \(-0.379562\pi\)
\(608\) 3.01499i 0.122274i
\(609\) −0.459650 −0.0186259
\(610\) 19.6179 31.7425i 0.794306 1.28521i
\(611\) −4.50953 −0.182436
\(612\) 2.00656i 0.0811106i
\(613\) 42.3482i 1.71043i −0.518276 0.855214i \(-0.673426\pi\)
0.518276 0.855214i \(-0.326574\pi\)
\(614\) −50.7993 −2.05009
\(615\) 3.61803 5.85410i 0.145893 0.236060i
\(616\) −10.7426 −0.432831
\(617\) 20.2302i 0.814438i 0.913331 + 0.407219i \(0.133501\pi\)
−0.913331 + 0.407219i \(0.866499\pi\)
\(618\) 7.55470i 0.303895i
\(619\) 42.9807 1.72754 0.863771 0.503885i \(-0.168097\pi\)
0.863771 + 0.503885i \(0.168097\pi\)
\(620\) 0.400305 + 0.247402i 0.0160766 + 0.00993590i
\(621\) 1.41164 0.0566471
\(622\) 4.42309i 0.177350i
\(623\) 15.2935i 0.612723i
\(624\) 4.85410 0.194320
\(625\) −15.0000 + 20.0000i −0.600000 + 0.800000i
\(626\) 4.73258 0.189152
\(627\) 4.28293i 0.171044i
\(628\) 1.58033i 0.0630620i
\(629\) 5.57106 0.222133
\(630\) 3.07768 + 1.90211i 0.122618 + 0.0757820i
\(631\) −33.9944 −1.35329 −0.676647 0.736307i \(-0.736568\pi\)
−0.676647 + 0.736307i \(0.736568\pi\)
\(632\) 20.2836i 0.806840i
\(633\) 10.7653i 0.427882i
\(634\) 1.31085 0.0520604
\(635\) −15.7495 + 25.4833i −0.625001 + 1.01127i
\(636\) −0.250349 −0.00992700
\(637\) 1.00000i 0.0396214i
\(638\) 3.57304i 0.141458i
\(639\) −7.57763 −0.299766
\(640\) 16.0090 25.9030i 0.632810 1.02391i
\(641\) −4.61668 −0.182348 −0.0911739 0.995835i \(-0.529062\pi\)
−0.0911739 + 0.995835i \(0.529062\pi\)
\(642\) 10.1766i 0.401639i
\(643\) 15.0975i 0.595386i 0.954662 + 0.297693i \(0.0962171\pi\)
−0.954662 + 0.297693i \(0.903783\pi\)
\(644\) −0.872441 −0.0343790
\(645\) −22.6132 13.9757i −0.890395 0.550294i
\(646\) 4.68323 0.184259
\(647\) 24.3079i 0.955642i 0.878457 + 0.477821i \(0.158573\pi\)
−0.878457 + 0.477821i \(0.841427\pi\)
\(648\) 2.23607i 0.0878410i
\(649\) 42.9613 1.68638
\(650\) −3.61803 7.23607i −0.141911 0.283822i
\(651\) 0.340519 0.0133460
\(652\) 15.5828i 0.610271i
\(653\) 36.8251i 1.44108i −0.693415 0.720539i \(-0.743895\pi\)
0.693415 0.720539i \(-0.256105\pi\)
\(654\) −6.34342 −0.248048
\(655\) 39.1061 + 24.1689i 1.52800 + 0.944357i
\(656\) 14.9394 0.583285
\(657\) 2.48276i 0.0968616i
\(658\) 7.29657i 0.284450i
\(659\) −26.7208 −1.04090 −0.520448 0.853893i \(-0.674235\pi\)
−0.520448 + 0.853893i \(0.674235\pi\)
\(660\) −3.49047 + 5.64771i −0.135867 + 0.219837i
\(661\) 27.8739 1.08417 0.542084 0.840324i \(-0.317636\pi\)
0.542084 + 0.840324i \(0.317636\pi\)
\(662\) 8.12703i 0.315866i
\(663\) 3.24669i 0.126091i
\(664\) 8.56493 0.332384
\(665\) 1.04801 1.69572i 0.0406401 0.0657571i
\(666\) 2.77642 0.107584
\(667\) 0.648859i 0.0251239i
\(668\) 8.90387i 0.344501i
\(669\) 9.65948 0.373457
\(670\) −25.3714 15.6804i −0.980183 0.605787i
\(671\) 49.5496 1.91284
\(672\) 3.38197i 0.130462i
\(673\) 2.24554i 0.0865591i 0.999063 + 0.0432795i \(0.0137806\pi\)
−0.999063 + 0.0432795i \(0.986219\pi\)
\(674\) −24.2513 −0.934124
\(675\) −4.47214 + 2.23607i −0.172133 + 0.0860663i
\(676\) 0.618034 0.0237705
\(677\) 3.64602i 0.140128i −0.997542 0.0700640i \(-0.977680\pi\)
0.997542 0.0700640i \(-0.0223204\pi\)
\(678\) 3.94542i 0.151523i
\(679\) 10.4893 0.402543
\(680\) −13.8090 8.53443i −0.529551 0.327280i
\(681\) 27.8250 1.06626
\(682\) 2.64699i 0.101359i
\(683\) 16.3180i 0.624391i 0.950018 + 0.312196i \(0.101064\pi\)
−0.950018 + 0.312196i \(0.898936\pi\)
\(684\) 0.550972 0.0210669
\(685\) −5.57523 + 9.02092i −0.213019 + 0.344671i
\(686\) −1.61803 −0.0617768
\(687\) 8.53026i 0.325450i
\(688\) 57.7079i 2.20009i
\(689\) 0.405074 0.0154321
\(690\) 2.68510 4.34458i 0.102220 0.165395i
\(691\) 25.9174 0.985946 0.492973 0.870045i \(-0.335910\pi\)
0.492973 + 0.870045i \(0.335910\pi\)
\(692\) 6.22107i 0.236490i
\(693\) 4.80423i 0.182497i
\(694\) −6.28677 −0.238642
\(695\) 28.3546 + 17.5241i 1.07555 + 0.664727i
\(696\) 1.02781 0.0389589
\(697\) 9.99228i 0.378485i
\(698\) 53.6001i 2.02879i
\(699\) −21.1471 −0.799858
\(700\) 2.76393 1.38197i 0.104467 0.0522334i
\(701\) 3.27417 0.123664 0.0618318 0.998087i \(-0.480306\pi\)
0.0618318 + 0.998087i \(0.480306\pi\)
\(702\) 1.61803i 0.0610688i
\(703\) 1.52973i 0.0576948i
\(704\) 20.3510 0.767008
\(705\) 8.57763 + 5.30127i 0.323052 + 0.199657i
\(706\) −9.97876 −0.375555
\(707\) 2.46151i 0.0925748i
\(708\) 5.52671i 0.207707i
\(709\) 25.4583 0.956105 0.478052 0.878331i \(-0.341343\pi\)
0.478052 + 0.878331i \(0.341343\pi\)
\(710\) −14.4135 + 23.3215i −0.540929 + 0.875242i
\(711\) −9.07112 −0.340194
\(712\) 34.1974i 1.28160i
\(713\) 0.480690i 0.0180020i
\(714\) 5.25325 0.196598
\(715\) 5.64771 9.13818i 0.211212 0.341749i
\(716\) 5.04260 0.188451
\(717\) 18.1840i 0.679094i
\(718\) 7.05342i 0.263231i
\(719\) 31.3560 1.16938 0.584690 0.811257i \(-0.301216\pi\)
0.584690 + 0.811257i \(0.301216\pi\)
\(720\) −9.23305 5.70634i −0.344095 0.212663i
\(721\) −4.66906 −0.173885
\(722\) 29.4567i 1.09626i
\(723\) 11.7022i 0.435208i
\(724\) 12.7011 0.472034
\(725\) −1.02781 2.05562i −0.0381718 0.0763436i
\(726\) −19.5468 −0.725450
\(727\) 31.0101i 1.15010i 0.818118 + 0.575050i \(0.195017\pi\)
−0.818118 + 0.575050i \(0.804983\pi\)
\(728\) 2.23607i 0.0828742i
\(729\) −1.00000 −0.0370370
\(730\) 7.64114 + 4.72249i 0.282811 + 0.174787i
\(731\) −38.5982 −1.42761
\(732\) 6.37425i 0.235599i
\(733\) 2.45901i 0.0908255i 0.998968 + 0.0454127i \(0.0144603\pi\)
−0.998968 + 0.0454127i \(0.985540\pi\)
\(734\) −57.7510 −2.13163
\(735\) 1.17557 1.90211i 0.0433616 0.0701605i
\(736\) 4.77411 0.175976
\(737\) 39.6045i 1.45885i
\(738\) 4.97980i 0.183309i
\(739\) 8.78416 0.323130 0.161565 0.986862i \(-0.448346\pi\)
0.161565 + 0.986862i \(0.448346\pi\)
\(740\) 1.24669 2.01719i 0.0458292 0.0741532i
\(741\) −0.891491 −0.0327498
\(742\) 0.655423i 0.0240614i
\(743\) 8.51627i 0.312432i 0.987723 + 0.156216i \(0.0499296\pi\)
−0.987723 + 0.156216i \(0.950070\pi\)
\(744\) −0.761425 −0.0279152
\(745\) −17.2973 10.6903i −0.633723 0.391662i
\(746\) −18.8920 −0.691686
\(747\) 3.83035i 0.140145i
\(748\) 9.63999i 0.352473i
\(749\) 6.28949 0.229813
\(750\) −1.62460 + 18.0171i −0.0593219 + 0.657890i
\(751\) 33.0460 1.20587 0.602933 0.797791i \(-0.293998\pi\)
0.602933 + 0.797791i \(0.293998\pi\)
\(752\) 21.8897i 0.798235i
\(753\) 6.64185i 0.242043i
\(754\) 0.743729 0.0270850
\(755\) 24.7015 + 15.2664i 0.898981 + 0.555601i
\(756\) 0.618034 0.0224777
\(757\) 29.7676i 1.08192i −0.841048 0.540961i \(-0.818061\pi\)
0.841048 0.540961i \(-0.181939\pi\)
\(758\) 32.5130i 1.18092i
\(759\) 6.78183 0.246165
\(760\) −2.34342 + 3.79174i −0.0850049 + 0.137541i
\(761\) 14.2403 0.516209 0.258104 0.966117i \(-0.416902\pi\)
0.258104 + 0.966117i \(0.416902\pi\)
\(762\) 21.6774i 0.785289i
\(763\) 3.92045i 0.141930i
\(764\) −9.16606 −0.331616
\(765\) −3.81671 + 6.17557i −0.137994 + 0.223278i
\(766\) 1.41570 0.0511512
\(767\) 8.94241i 0.322892i
\(768\) 13.5623i 0.489388i
\(769\) 38.0129 1.37078 0.685390 0.728176i \(-0.259632\pi\)
0.685390 + 0.728176i \(0.259632\pi\)
\(770\) 14.7859 + 9.13818i 0.532846 + 0.329317i
\(771\) −16.4358 −0.591920
\(772\) 2.70975i 0.0975262i
\(773\) 39.9492i 1.43687i −0.695593 0.718436i \(-0.744858\pi\)
0.695593 0.718436i \(-0.255142\pi\)
\(774\) −19.2360 −0.691422
\(775\) 0.761425 + 1.52285i 0.0273512 + 0.0547024i
\(776\) −23.4548 −0.841980
\(777\) 1.71592i 0.0615583i
\(778\) 52.9114i 1.89696i
\(779\) −2.74373 −0.0983043
\(780\) −1.17557 0.726543i −0.0420922 0.0260144i
\(781\) −36.4046 −1.30266
\(782\) 7.41570i 0.265185i
\(783\) 0.459650i 0.0164265i
\(784\) 4.85410 0.173361
\(785\) 3.00597 4.86375i 0.107287 0.173595i
\(786\) 33.2656 1.18655
\(787\) 40.2577i 1.43503i −0.696541 0.717517i \(-0.745279\pi\)
0.696541 0.717517i \(-0.254721\pi\)
\(788\) 3.33937i 0.118960i
\(789\) 27.9057 0.993468
\(790\) −17.2543 + 27.9180i −0.613880 + 0.993279i
\(791\) −2.43841 −0.0866998
\(792\) 10.7426i 0.381721i
\(793\) 10.3138i 0.366252i
\(794\) −60.1806 −2.13573
\(795\) −0.770497 0.476193i −0.0273267 0.0168888i
\(796\) −7.15016 −0.253431
\(797\) 15.9645i 0.565493i 0.959195 + 0.282747i \(0.0912455\pi\)
−0.959195 + 0.282747i \(0.908754\pi\)
\(798\) 1.44246i 0.0510627i
\(799\) 14.6410 0.517962
\(800\) −15.1246 + 7.56231i −0.534736 + 0.267368i
\(801\) 15.2935 0.540371
\(802\) 5.98084i 0.211191i
\(803\) 11.9277i 0.420920i
\(804\) −5.09487 −0.179682
\(805\) −2.68510 1.65948i −0.0946372 0.0584890i
\(806\) −0.550972 −0.0194072
\(807\) 27.3788i 0.963781i
\(808\) 5.50411i 0.193634i
\(809\) 31.1877 1.09650 0.548251 0.836314i \(-0.315294\pi\)
0.548251 + 0.836314i \(0.315294\pi\)
\(810\) −1.90211 + 3.07768i −0.0668334 + 0.108139i
\(811\) 43.7661 1.53684 0.768418 0.639948i \(-0.221044\pi\)
0.768418 + 0.639948i \(0.221044\pi\)
\(812\) 0.284079i 0.00996922i
\(813\) 3.10600i 0.108932i
\(814\) 13.3385 0.467516
\(815\) −29.6403 + 47.9590i −1.03826 + 1.67993i
\(816\) −15.7598 −0.551702
\(817\) 10.5985i 0.370794i
\(818\) 8.91273i 0.311626i
\(819\) −1.00000 −0.0349428
\(820\) −3.61803 2.23607i −0.126347 0.0780869i
\(821\) −29.9442 −1.04506 −0.522529 0.852621i \(-0.675011\pi\)
−0.522529 + 0.852621i \(0.675011\pi\)
\(822\) 7.67365i 0.267649i
\(823\) 10.1764i 0.354728i 0.984145 + 0.177364i \(0.0567570\pi\)
−0.984145 + 0.177364i \(0.943243\pi\)
\(824\) 10.4403 0.363707
\(825\) −21.4852 + 10.7426i −0.748017 + 0.374008i
\(826\) −14.4691 −0.503445
\(827\) 36.8304i 1.28072i −0.768075 0.640360i \(-0.778785\pi\)
0.768075 0.640360i \(-0.221215\pi\)
\(828\) 0.872441i 0.0303194i
\(829\) −18.6901 −0.649133 −0.324567 0.945863i \(-0.605218\pi\)
−0.324567 + 0.945863i \(0.605218\pi\)
\(830\) −11.7886 7.28576i −0.409189 0.252892i
\(831\) 30.2146 1.04813
\(832\) 4.23607i 0.146859i
\(833\) 3.24669i 0.112491i
\(834\) 24.1198 0.835202
\(835\) −16.9362 + 27.4033i −0.586100 + 0.948330i
\(836\) 2.64699 0.0915482
\(837\) 0.340519i 0.0117701i
\(838\) 39.6789i 1.37069i
\(839\) −42.0400 −1.45138 −0.725692 0.688020i \(-0.758480\pi\)
−0.725692 + 0.688020i \(0.758480\pi\)
\(840\) −2.62866 + 4.25325i −0.0906972 + 0.146751i
\(841\) −28.7887 −0.992715
\(842\) 11.1892i 0.385606i
\(843\) 0.922959i 0.0317884i
\(844\) 6.65331 0.229016
\(845\) 1.90211 + 1.17557i 0.0654347 + 0.0404409i
\(846\) 7.29657 0.250861
\(847\) 12.0806i 0.415094i
\(848\) 1.96627i 0.0675220i
\(849\) 16.7953 0.576413
\(850\) 11.7466 + 23.4933i 0.402906 + 0.805812i
\(851\) −2.42226 −0.0830340
\(852\) 4.68323i 0.160445i
\(853\) 33.0029i 1.13000i 0.825092 + 0.564998i \(0.191123\pi\)
−0.825092 + 0.564998i \(0.808877\pi\)
\(854\) −16.6880 −0.571052
\(855\) 1.69572 + 1.04801i 0.0579923 + 0.0358412i
\(856\) −14.0637 −0.480688
\(857\) 6.77951i 0.231583i −0.993274 0.115792i \(-0.963059\pi\)
0.993274 0.115792i \(-0.0369405\pi\)
\(858\) 7.77340i 0.265380i
\(859\) 47.5032 1.62079 0.810395 0.585884i \(-0.199253\pi\)
0.810395 + 0.585884i \(0.199253\pi\)
\(860\) −8.63748 + 13.9757i −0.294536 + 0.476569i
\(861\) −3.07768 −0.104887
\(862\) 10.9287i 0.372231i
\(863\) 35.7993i 1.21862i 0.792931 + 0.609311i \(0.208554\pi\)
−0.792931 + 0.609311i \(0.791446\pi\)
\(864\) −3.38197 −0.115057
\(865\) 11.8332 19.1465i 0.402340 0.651000i
\(866\) −42.5287 −1.44518
\(867\) 6.45901i 0.219359i
\(868\) 0.210453i 0.00714323i
\(869\) −43.5797 −1.47834
\(870\) −1.41466 0.874305i −0.0479613 0.0296417i
\(871\) 8.24367 0.279326
\(872\) 8.76640i 0.296868i
\(873\) 10.4893i 0.355010i
\(874\) −2.03624 −0.0688767
\(875\) 11.1352 + 1.00406i 0.376437 + 0.0339433i
\(876\) 1.53443 0.0518435
\(877\) 0.361560i 0.0122090i 0.999981 + 0.00610451i \(0.00194314\pi\)
−0.999981 + 0.00610451i \(0.998057\pi\)
\(878\) 35.0899i 1.18423i
\(879\) −5.53066 −0.186544
\(880\) −44.3577 27.4145i −1.49530 0.924144i
\(881\) −15.8057 −0.532506 −0.266253 0.963903i \(-0.585786\pi\)
−0.266253 + 0.963903i \(0.585786\pi\)
\(882\) 1.61803i 0.0544820i
\(883\) 16.0987i 0.541765i −0.962612 0.270883i \(-0.912684\pi\)
0.962612 0.270883i \(-0.0873156\pi\)
\(884\) −2.00656 −0.0674881
\(885\) 10.5124 17.0095i 0.353371 0.571767i
\(886\) 48.6819 1.63550
\(887\) 23.3425i 0.783764i 0.920015 + 0.391882i \(0.128176\pi\)
−0.920015 + 0.391882i \(0.871824\pi\)
\(888\) 3.83692i 0.128758i
\(889\) 13.3974 0.449333
\(890\) 29.0901 47.0687i 0.975101 1.57775i
\(891\) −4.80423 −0.160948
\(892\) 5.96989i 0.199887i
\(893\) 4.02020i 0.134531i
\(894\) −14.7139 −0.492108
\(895\) 15.5195 + 9.59159i 0.518760 + 0.320612i
\(896\) −13.6180 −0.454947
\(897\) 1.41164i 0.0471332i
\(898\) 60.5373i 2.02016i
\(899\) −0.156520 −0.00522022
\(900\) 1.38197 + 2.76393i 0.0460655 + 0.0921311i
\(901\) −1.31515 −0.0438140
\(902\) 23.9241i 0.796584i
\(903\) 11.8885i 0.395624i
\(904\) 5.45244 0.181346
\(905\) 39.0901 + 24.1590i 1.29940 + 0.803072i
\(906\) 21.0124 0.698089
\(907\) 43.6032i 1.44782i 0.689894 + 0.723910i \(0.257657\pi\)
−0.689894 + 0.723910i \(0.742343\pi\)
\(908\) 17.1968i 0.570696i
\(909\) −2.46151 −0.0816433
\(910\) −1.90211 + 3.07768i −0.0630544 + 0.102024i
\(911\) −42.3998 −1.40477 −0.702385 0.711798i \(-0.747881\pi\)
−0.702385 + 0.711798i \(0.747881\pi\)
\(912\) 4.32739i 0.143294i
\(913\) 18.4019i 0.609013i
\(914\) −13.3723 −0.442315
\(915\) 12.1245 19.6179i 0.400825 0.648548i
\(916\) 5.27199 0.174191
\(917\) 20.5593i 0.678928i
\(918\) 5.25325i 0.173383i
\(919\) 6.50432 0.214558 0.107279 0.994229i \(-0.465786\pi\)
0.107279 + 0.994229i \(0.465786\pi\)
\(920\) 6.00406 + 3.71071i 0.197948 + 0.122339i
\(921\) −31.3957 −1.03452
\(922\) 1.41548i 0.0466164i
\(923\) 7.57763i 0.249421i
\(924\) 2.96917 0.0976787
\(925\) 7.67383 3.83692i 0.252314 0.126157i
\(926\) 33.1455 1.08923
\(927\) 4.66906i 0.153352i
\(928\) 1.55452i 0.0510296i
\(929\) −44.7854 −1.46936 −0.734681 0.678412i \(-0.762668\pi\)
−0.734681 + 0.678412i \(0.762668\pi\)
\(930\) 1.04801 + 0.647706i 0.0343656 + 0.0212391i
\(931\) −0.891491 −0.0292175
\(932\) 13.0697i 0.428111i
\(933\) 2.73362i 0.0894946i
\(934\) −20.5972 −0.673961
\(935\) −18.3363 + 29.6688i −0.599663 + 0.970275i
\(936\) 2.23607 0.0730882
\(937\) 9.80796i 0.320412i 0.987084 + 0.160206i \(0.0512158\pi\)
−0.987084 + 0.160206i \(0.948784\pi\)
\(938\) 13.3385i 0.435519i
\(939\) 2.92489 0.0954503
\(940\) 3.27636 5.30127i 0.106863 0.172908i
\(941\) 6.56164 0.213903 0.106952 0.994264i \(-0.465891\pi\)
0.106952 + 0.994264i \(0.465891\pi\)
\(942\) 4.13736i 0.134802i
\(943\) 4.34458i 0.141479i
\(944\) 43.4074 1.41279
\(945\) 1.90211 + 1.17557i 0.0618757 + 0.0382413i
\(946\) −92.4139 −3.00463
\(947\) 19.7936i 0.643206i 0.946875 + 0.321603i \(0.104222\pi\)
−0.946875 + 0.321603i \(0.895778\pi\)
\(948\) 5.60626i 0.182083i
\(949\) −2.48276 −0.0805937
\(950\) 6.45089 3.22545i 0.209295 0.104647i
\(951\) 0.810148 0.0262708
\(952\) 7.25982i 0.235292i
\(953\) 15.0734i 0.488275i −0.969741 0.244138i \(-0.921495\pi\)
0.969741 0.244138i \(-0.0785049\pi\)
\(954\) −0.655423 −0.0212201
\(955\) −28.2102 17.4349i −0.912862 0.564179i
\(956\) 11.2383 0.363474
\(957\) 2.20826i 0.0713829i
\(958\) 40.4446i 1.30671i
\(959\) 4.74258 0.153146
\(960\) 4.97980 8.05748i 0.160722 0.260054i
\(961\) −30.8840 −0.996260
\(962\) 2.77642i 0.0895153i
\(963\) 6.28949i 0.202676i
\(964\) 7.23234 0.232938
\(965\) 5.15426 8.33976i 0.165921 0.268467i
\(966\) −2.28408 −0.0734890
\(967\) 2.83139i 0.0910514i 0.998963 + 0.0455257i \(0.0144963\pi\)
−0.998963 + 0.0455257i \(0.985504\pi\)
\(968\) 27.0130i 0.868231i
\(969\) 2.89440 0.0929814
\(970\) 32.2828 + 19.9519i 1.03654 + 0.640616i
\(971\) −2.43707 −0.0782093 −0.0391047 0.999235i \(-0.512451\pi\)
−0.0391047 + 0.999235i \(0.512451\pi\)
\(972\) 0.618034i 0.0198234i
\(973\) 14.9069i 0.477893i
\(974\) 44.7893 1.43514
\(975\) −2.23607 4.47214i −0.0716115 0.143223i
\(976\) 50.0640 1.60251
\(977\) 51.3238i 1.64199i −0.570934 0.820996i \(-0.693419\pi\)
0.570934 0.820996i \(-0.306581\pi\)
\(978\) 40.7964i 1.30452i
\(979\) 73.4737 2.34823
\(980\) −1.17557 0.726543i −0.0375522 0.0232085i
\(981\) −3.92045 −0.125170
\(982\) 9.31938i 0.297393i
\(983\) 10.8569i 0.346283i −0.984897 0.173141i \(-0.944608\pi\)
0.984897 0.173141i \(-0.0553917\pi\)
\(984\) 6.88191 0.219387
\(985\) −6.35185 + 10.2775i −0.202387 + 0.327469i
\(986\) −2.41466 −0.0768983
\(987\) 4.50953i 0.143540i
\(988\) 0.550972i 0.0175288i
\(989\) 16.7822 0.533644
\(990\) −9.13818 + 14.7859i −0.290430 + 0.469926i
\(991\) −5.95012 −0.189012 −0.0945060 0.995524i \(-0.530127\pi\)
−0.0945060 + 0.995524i \(0.530127\pi\)
\(992\) 1.15163i 0.0365641i
\(993\) 5.02278i 0.159393i
\(994\) 12.2609 0.388891
\(995\) −22.0059 13.6004i −0.697635 0.431162i
\(996\) −2.36729 −0.0750104
\(997\) 3.66128i 0.115954i 0.998318 + 0.0579769i \(0.0184650\pi\)
−0.998318 + 0.0579769i \(0.981535\pi\)
\(998\) 56.9932i 1.80409i
\(999\) 1.71592 0.0542893
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 1365.2.f.c.274.1 8
5.2 odd 4 6825.2.a.bm.1.3 4
5.3 odd 4 6825.2.a.be.1.1 4
5.4 even 2 inner 1365.2.f.c.274.7 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1365.2.f.c.274.1 8 1.1 even 1 trivial
1365.2.f.c.274.7 yes 8 5.4 even 2 inner
6825.2.a.be.1.1 4 5.3 odd 4
6825.2.a.bm.1.3 4 5.2 odd 4