Properties

Label 495.2.n.f.91.1
Level $495$
Weight $2$
Character 495.91
Analytic conductor $3.953$
Analytic rank $0$
Dimension $8$
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] = [495,2,Mod(91,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("495.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), degree \(4\), 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: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.159390625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.1
Root \(0.453245 + 1.39494i\) of defining polynomial
Character \(\chi\) \(=\) 495.91
Dual form 495.2.n.f.136.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0756511 - 0.0549637i) q^{2} +(-0.615332 + 1.89380i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.39815 - 4.30308i) q^{7} +(0.115332 + 0.354955i) q^{8} +O(q^{10})\) \(q+(0.0756511 - 0.0549637i) q^{2} +(-0.615332 + 1.89380i) q^{4} +(0.809017 + 0.587785i) q^{5} +(1.39815 - 4.30308i) q^{7} +(0.115332 + 0.354955i) q^{8} +0.0935099 q^{10} +(2.39815 - 2.29104i) q^{11} +(0.924349 - 0.671579i) q^{13} +(-0.130741 - 0.402380i) q^{14} +(-3.19369 - 2.32035i) q^{16} +(2.72899 + 1.98273i) q^{17} +(1.88030 + 5.78696i) q^{19} +(-1.61096 + 1.17043i) q^{20} +(0.0554990 - 0.305131i) q^{22} +5.45258 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.0330155 - 0.101611i) q^{26} +(7.28883 + 5.29564i) q^{28} +(-1.02619 + 3.15830i) q^{29} +(-1.44887 + 1.05267i) q^{31} -1.11558 q^{32} +0.315430 q^{34} +(3.66042 - 2.65945i) q^{35} +(0.460067 - 1.41594i) q^{37} +(0.460319 + 0.334441i) q^{38} +(-0.115332 + 0.354955i) q^{40} +(0.539933 + 1.66174i) q^{41} -0.263041 q^{43} +(2.86310 + 5.95137i) q^{44} +(0.412494 - 0.299694i) q^{46} +(-2.13986 - 6.58580i) q^{47} +(-10.8985 - 7.91824i) q^{49} +(0.0756511 + 0.0549637i) q^{50} +(0.703052 + 2.16377i) q^{52} +(-1.16479 + 0.846269i) q^{53} +(3.28679 - 0.443888i) q^{55} +1.68865 q^{56} +(0.0959593 + 0.295332i) q^{58} +(2.18416 - 6.72216i) q^{59} +(-2.02452 - 1.47090i) q^{61} +(-0.0517503 + 0.159271i) q^{62} +(6.30297 - 4.57938i) q^{64} +1.14256 q^{65} -0.516598 q^{67} +(-5.43413 + 3.94812i) q^{68} +(0.130741 - 0.402380i) q^{70} +(-8.68098 - 6.30710i) q^{71} +(-1.75560 + 5.40317i) q^{73} +(-0.0430208 - 0.132404i) q^{74} -12.1163 q^{76} +(-6.50552 - 13.5227i) q^{77} +(9.14460 - 6.64394i) q^{79} +(-1.21988 - 3.75440i) q^{80} +(0.132182 + 0.0960360i) q^{82} +(3.62511 + 2.63380i) q^{83} +(1.04238 + 3.20812i) q^{85} +(-0.0198994 + 0.0144577i) q^{86} +(1.08980 + 0.587008i) q^{88} -13.2676 q^{89} +(-1.59747 - 4.91652i) q^{91} +(-3.35515 + 10.3261i) q^{92} +(-0.523863 - 0.380608i) q^{94} +(-1.88030 + 5.78696i) q^{95} +(2.71551 - 1.97293i) q^{97} -1.25970 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} - 6 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8} + 6 q^{10} + 5 q^{11} + 4 q^{13} - 16 q^{14} - 20 q^{16} - q^{17} - q^{19} + q^{20} + 33 q^{22} + 18 q^{23} - 2 q^{25} + 14 q^{26} + 4 q^{28} - 19 q^{29} + 6 q^{31} - 12 q^{32} - 20 q^{34} + 8 q^{35} + 4 q^{37} + 6 q^{38} - 2 q^{40} + 4 q^{41} + 42 q^{43} + 28 q^{44} - 41 q^{46} - 4 q^{47} - 15 q^{49} + 4 q^{50} - 26 q^{52} - 3 q^{53} + 5 q^{55} - 30 q^{56} - 6 q^{58} + 19 q^{59} - 2 q^{61} + 38 q^{62} + 6 q^{64} - 14 q^{65} - 2 q^{67} - 35 q^{68} + 16 q^{70} - 40 q^{71} - 23 q^{73} - 48 q^{74} + 16 q^{76} + 28 q^{77} + 17 q^{79} - 15 q^{80} + 2 q^{82} + 25 q^{83} - 4 q^{85} + 31 q^{86} + 22 q^{88} - 12 q^{91} - 81 q^{92} + 33 q^{94} + q^{95} + 12 q^{97} + 84 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0756511 0.0549637i 0.0534934 0.0388652i −0.560717 0.828007i \(-0.689475\pi\)
0.614211 + 0.789142i \(0.289475\pi\)
\(3\) 0 0
\(4\) −0.615332 + 1.89380i −0.307666 + 0.946898i
\(5\) 0.809017 + 0.587785i 0.361803 + 0.262866i
\(6\) 0 0
\(7\) 1.39815 4.30308i 0.528453 1.62641i −0.228932 0.973442i \(-0.573523\pi\)
0.757385 0.652968i \(-0.226477\pi\)
\(8\) 0.115332 + 0.354955i 0.0407760 + 0.125496i
\(9\) 0 0
\(10\) 0.0935099 0.0295704
\(11\) 2.39815 2.29104i 0.723071 0.690774i
\(12\) 0 0
\(13\) 0.924349 0.671579i 0.256368 0.186262i −0.452176 0.891929i \(-0.649352\pi\)
0.708544 + 0.705666i \(0.249352\pi\)
\(14\) −0.130741 0.402380i −0.0349421 0.107541i
\(15\) 0 0
\(16\) −3.19369 2.32035i −0.798421 0.580087i
\(17\) 2.72899 + 1.98273i 0.661878 + 0.480883i 0.867297 0.497792i \(-0.165856\pi\)
−0.205418 + 0.978674i \(0.565856\pi\)
\(18\) 0 0
\(19\) 1.88030 + 5.78696i 0.431369 + 1.32762i 0.896762 + 0.442514i \(0.145913\pi\)
−0.465392 + 0.885105i \(0.654087\pi\)
\(20\) −1.61096 + 1.17043i −0.360222 + 0.261716i
\(21\) 0 0
\(22\) 0.0554990 0.305131i 0.0118324 0.0650542i
\(23\) 5.45258 1.13694 0.568471 0.822703i \(-0.307535\pi\)
0.568471 + 0.822703i \(0.307535\pi\)
\(24\) 0 0
\(25\) 0.309017 + 0.951057i 0.0618034 + 0.190211i
\(26\) 0.0330155 0.101611i 0.00647488 0.0199276i
\(27\) 0 0
\(28\) 7.28883 + 5.29564i 1.37746 + 1.00078i
\(29\) −1.02619 + 3.15830i −0.190559 + 0.586482i −1.00000 0.000720503i \(-0.999771\pi\)
0.809440 + 0.587202i \(0.199771\pi\)
\(30\) 0 0
\(31\) −1.44887 + 1.05267i −0.260225 + 0.189065i −0.710246 0.703953i \(-0.751416\pi\)
0.450021 + 0.893018i \(0.351416\pi\)
\(32\) −1.11558 −0.197209
\(33\) 0 0
\(34\) 0.315430 0.0540957
\(35\) 3.66042 2.65945i 0.618723 0.449529i
\(36\) 0 0
\(37\) 0.460067 1.41594i 0.0756345 0.232779i −0.906091 0.423084i \(-0.860948\pi\)
0.981725 + 0.190305i \(0.0609476\pi\)
\(38\) 0.460319 + 0.334441i 0.0746736 + 0.0542536i
\(39\) 0 0
\(40\) −0.115332 + 0.354955i −0.0182356 + 0.0561233i
\(41\) 0.539933 + 1.66174i 0.0843234 + 0.259521i 0.984325 0.176367i \(-0.0564345\pi\)
−0.900001 + 0.435888i \(0.856434\pi\)
\(42\) 0 0
\(43\) −0.263041 −0.0401134 −0.0200567 0.999799i \(-0.506385\pi\)
−0.0200567 + 0.999799i \(0.506385\pi\)
\(44\) 2.86310 + 5.95137i 0.431628 + 0.897202i
\(45\) 0 0
\(46\) 0.412494 0.299694i 0.0608189 0.0441875i
\(47\) −2.13986 6.58580i −0.312130 0.960638i −0.976920 0.213607i \(-0.931479\pi\)
0.664790 0.747031i \(-0.268521\pi\)
\(48\) 0 0
\(49\) −10.8985 7.91824i −1.55693 1.13118i
\(50\) 0.0756511 + 0.0549637i 0.0106987 + 0.00777305i
\(51\) 0 0
\(52\) 0.703052 + 2.16377i 0.0974958 + 0.300061i
\(53\) −1.16479 + 0.846269i −0.159996 + 0.116244i −0.664903 0.746930i \(-0.731527\pi\)
0.504907 + 0.863174i \(0.331527\pi\)
\(54\) 0 0
\(55\) 3.28679 0.443888i 0.443190 0.0598539i
\(56\) 1.68865 0.225656
\(57\) 0 0
\(58\) 0.0959593 + 0.295332i 0.0126001 + 0.0387790i
\(59\) 2.18416 6.72216i 0.284354 0.875150i −0.702238 0.711942i \(-0.747816\pi\)
0.986592 0.163208i \(-0.0521842\pi\)
\(60\) 0 0
\(61\) −2.02452 1.47090i −0.259214 0.188330i 0.450587 0.892733i \(-0.351215\pi\)
−0.709800 + 0.704403i \(0.751215\pi\)
\(62\) −0.0517503 + 0.159271i −0.00657229 + 0.0202274i
\(63\) 0 0
\(64\) 6.30297 4.57938i 0.787872 0.572422i
\(65\) 1.14256 0.141717
\(66\) 0 0
\(67\) −0.516598 −0.0631124 −0.0315562 0.999502i \(-0.510046\pi\)
−0.0315562 + 0.999502i \(0.510046\pi\)
\(68\) −5.43413 + 3.94812i −0.658984 + 0.478780i
\(69\) 0 0
\(70\) 0.130741 0.402380i 0.0156266 0.0480937i
\(71\) −8.68098 6.30710i −1.03024 0.748515i −0.0618853 0.998083i \(-0.519711\pi\)
−0.968357 + 0.249568i \(0.919711\pi\)
\(72\) 0 0
\(73\) −1.75560 + 5.40317i −0.205477 + 0.632393i 0.794216 + 0.607635i \(0.207882\pi\)
−0.999693 + 0.0247584i \(0.992118\pi\)
\(74\) −0.0430208 0.132404i −0.00500106 0.0153917i
\(75\) 0 0
\(76\) −12.1163 −1.38984
\(77\) −6.50552 13.5227i −0.741373 1.54105i
\(78\) 0 0
\(79\) 9.14460 6.64394i 1.02885 0.747502i 0.0607700 0.998152i \(-0.480644\pi\)
0.968078 + 0.250650i \(0.0806444\pi\)
\(80\) −1.21988 3.75440i −0.136387 0.419755i
\(81\) 0 0
\(82\) 0.132182 + 0.0960360i 0.0145971 + 0.0106054i
\(83\) 3.62511 + 2.63380i 0.397907 + 0.289097i 0.768688 0.639624i \(-0.220910\pi\)
−0.370781 + 0.928720i \(0.620910\pi\)
\(84\) 0 0
\(85\) 1.04238 + 3.20812i 0.113062 + 0.347970i
\(86\) −0.0198994 + 0.0144577i −0.00214580 + 0.00155902i
\(87\) 0 0
\(88\) 1.08980 + 0.587008i 0.116173 + 0.0625752i
\(89\) −13.2676 −1.40637 −0.703183 0.711009i \(-0.748238\pi\)
−0.703183 + 0.711009i \(0.748238\pi\)
\(90\) 0 0
\(91\) −1.59747 4.91652i −0.167461 0.515391i
\(92\) −3.35515 + 10.3261i −0.349798 + 1.07657i
\(93\) 0 0
\(94\) −0.523863 0.380608i −0.0540323 0.0392568i
\(95\) −1.88030 + 5.78696i −0.192914 + 0.593729i
\(96\) 0 0
\(97\) 2.71551 1.97293i 0.275718 0.200321i −0.441330 0.897345i \(-0.645493\pi\)
0.717048 + 0.697024i \(0.245493\pi\)
\(98\) −1.25970 −0.127249
\(99\) 0 0
\(100\) −1.99126 −0.199126
\(101\) −7.55216 + 5.48696i −0.751468 + 0.545973i −0.896282 0.443486i \(-0.853742\pi\)
0.144814 + 0.989459i \(0.453742\pi\)
\(102\) 0 0
\(103\) −4.30027 + 13.2349i −0.423718 + 1.30407i 0.480498 + 0.876996i \(0.340456\pi\)
−0.904216 + 0.427075i \(0.859544\pi\)
\(104\) 0.344987 + 0.250648i 0.0338288 + 0.0245781i
\(105\) 0 0
\(106\) −0.0416035 + 0.128042i −0.00404089 + 0.0124366i
\(107\) 5.18787 + 15.9666i 0.501531 + 1.54355i 0.806526 + 0.591198i \(0.201345\pi\)
−0.304996 + 0.952354i \(0.598655\pi\)
\(108\) 0 0
\(109\) −3.65293 −0.349888 −0.174944 0.984578i \(-0.555974\pi\)
−0.174944 + 0.984578i \(0.555974\pi\)
\(110\) 0.224251 0.214235i 0.0213815 0.0204265i
\(111\) 0 0
\(112\) −14.4499 + 10.4985i −1.36539 + 0.992012i
\(113\) 3.67802 + 11.3198i 0.345999 + 1.06488i 0.961047 + 0.276386i \(0.0891369\pi\)
−0.615047 + 0.788490i \(0.710863\pi\)
\(114\) 0 0
\(115\) 4.41123 + 3.20495i 0.411350 + 0.298863i
\(116\) −5.34973 3.88681i −0.496710 0.360881i
\(117\) 0 0
\(118\) −0.204241 0.628588i −0.0188019 0.0578662i
\(119\) 12.3474 8.97091i 1.13188 0.822362i
\(120\) 0 0
\(121\) 0.502293 10.9885i 0.0456630 0.998957i
\(122\) −0.234004 −0.0211857
\(123\) 0 0
\(124\) −1.10200 3.39161i −0.0989626 0.304576i
\(125\) −0.309017 + 0.951057i −0.0276393 + 0.0850651i
\(126\) 0 0
\(127\) −15.9883 11.6162i −1.41873 1.03077i −0.991979 0.126404i \(-0.959656\pi\)
−0.426756 0.904367i \(-0.640344\pi\)
\(128\) 0.914596 2.81484i 0.0808397 0.248799i
\(129\) 0 0
\(130\) 0.0864358 0.0627993i 0.00758092 0.00550786i
\(131\) 1.93479 0.169043 0.0845215 0.996422i \(-0.473064\pi\)
0.0845215 + 0.996422i \(0.473064\pi\)
\(132\) 0 0
\(133\) 27.5307 2.38721
\(134\) −0.0390812 + 0.0283941i −0.00337610 + 0.00245288i
\(135\) 0 0
\(136\) −0.389040 + 1.19734i −0.0333599 + 0.102671i
\(137\) −10.1413 7.36808i −0.866429 0.629498i 0.0631970 0.998001i \(-0.479870\pi\)
−0.929626 + 0.368503i \(0.879870\pi\)
\(138\) 0 0
\(139\) −3.47491 + 10.6947i −0.294738 + 0.907111i 0.688571 + 0.725169i \(0.258238\pi\)
−0.983309 + 0.181942i \(0.941762\pi\)
\(140\) 2.78408 + 8.56853i 0.235298 + 0.724173i
\(141\) 0 0
\(142\) −1.00339 −0.0842024
\(143\) 0.678120 3.72827i 0.0567072 0.311773i
\(144\) 0 0
\(145\) −2.68661 + 1.95194i −0.223111 + 0.162100i
\(146\) 0.164166 + 0.505250i 0.0135864 + 0.0418148i
\(147\) 0 0
\(148\) 2.39841 + 1.74255i 0.197148 + 0.143236i
\(149\) −14.0232 10.1885i −1.14883 0.834672i −0.160503 0.987035i \(-0.551312\pi\)
−0.988325 + 0.152363i \(0.951312\pi\)
\(150\) 0 0
\(151\) −0.00166997 0.00513965i −0.000135901 0.000418259i 0.950989 0.309226i \(-0.100070\pi\)
−0.951124 + 0.308808i \(0.900070\pi\)
\(152\) −1.83725 + 1.33484i −0.149021 + 0.108270i
\(153\) 0 0
\(154\) −1.23541 0.665437i −0.0995519 0.0536225i
\(155\) −1.79091 −0.143849
\(156\) 0 0
\(157\) 0.171454 + 0.527682i 0.0136835 + 0.0421136i 0.957665 0.287884i \(-0.0929519\pi\)
−0.943982 + 0.329998i \(0.892952\pi\)
\(158\) 0.326623 1.00524i 0.0259847 0.0799728i
\(159\) 0 0
\(160\) −0.902527 0.655724i −0.0713510 0.0518395i
\(161\) 7.62356 23.4629i 0.600820 1.84914i
\(162\) 0 0
\(163\) 6.44324 4.68129i 0.504673 0.366667i −0.306126 0.951991i \(-0.599033\pi\)
0.810799 + 0.585324i \(0.199033\pi\)
\(164\) −3.47924 −0.271683
\(165\) 0 0
\(166\) 0.419007 0.0325212
\(167\) 2.77204 2.01400i 0.214507 0.155848i −0.475344 0.879800i \(-0.657676\pi\)
0.689850 + 0.723952i \(0.257676\pi\)
\(168\) 0 0
\(169\) −3.61382 + 11.1222i −0.277986 + 0.855553i
\(170\) 0.255188 + 0.185405i 0.0195720 + 0.0142199i
\(171\) 0 0
\(172\) 0.161858 0.498147i 0.0123415 0.0379834i
\(173\) −6.35552 19.5603i −0.483201 1.48714i −0.834569 0.550903i \(-0.814283\pi\)
0.351368 0.936237i \(-0.385717\pi\)
\(174\) 0 0
\(175\) 4.52452 0.342022
\(176\) −12.9750 + 1.75230i −0.978024 + 0.132084i
\(177\) 0 0
\(178\) −1.00371 + 0.729238i −0.0752313 + 0.0546587i
\(179\) 0.792419 + 2.43882i 0.0592282 + 0.182286i 0.976293 0.216452i \(-0.0694484\pi\)
−0.917065 + 0.398738i \(0.869448\pi\)
\(180\) 0 0
\(181\) −10.8545 7.88624i −0.806807 0.586179i 0.106096 0.994356i \(-0.466165\pi\)
−0.912903 + 0.408177i \(0.866165\pi\)
\(182\) −0.391081 0.284137i −0.0289888 0.0210616i
\(183\) 0 0
\(184\) 0.628857 + 1.93542i 0.0463599 + 0.142681i
\(185\) 1.20447 0.875099i 0.0885544 0.0643385i
\(186\) 0 0
\(187\) 11.0871 1.49733i 0.810766 0.109496i
\(188\) 13.7889 1.00566
\(189\) 0 0
\(190\) 0.175826 + 0.541138i 0.0127558 + 0.0392583i
\(191\) −5.62097 + 17.2996i −0.406719 + 1.25175i 0.512733 + 0.858548i \(0.328633\pi\)
−0.919452 + 0.393203i \(0.871367\pi\)
\(192\) 0 0
\(193\) −12.6924 9.22156i −0.913618 0.663782i 0.0283094 0.999599i \(-0.490988\pi\)
−0.941927 + 0.335817i \(0.890988\pi\)
\(194\) 0.0969914 0.298509i 0.00696358 0.0214317i
\(195\) 0 0
\(196\) 21.7018 15.7672i 1.55013 1.12623i
\(197\) 21.8486 1.55665 0.778325 0.627862i \(-0.216070\pi\)
0.778325 + 0.627862i \(0.216070\pi\)
\(198\) 0 0
\(199\) −4.55200 −0.322683 −0.161341 0.986899i \(-0.551582\pi\)
−0.161341 + 0.986899i \(0.551582\pi\)
\(200\) −0.301943 + 0.219374i −0.0213506 + 0.0155121i
\(201\) 0 0
\(202\) −0.269745 + 0.830190i −0.0189792 + 0.0584119i
\(203\) 12.1556 + 8.83159i 0.853158 + 0.619856i
\(204\) 0 0
\(205\) −0.539933 + 1.66174i −0.0377106 + 0.116061i
\(206\) 0.402118 + 1.23759i 0.0280169 + 0.0862271i
\(207\) 0 0
\(208\) −4.51038 −0.312738
\(209\) 17.7674 + 9.57019i 1.22900 + 0.661984i
\(210\) 0 0
\(211\) −15.3393 + 11.1447i −1.05600 + 0.767230i −0.973345 0.229348i \(-0.926341\pi\)
−0.0826575 + 0.996578i \(0.526341\pi\)
\(212\) −0.885929 2.72661i −0.0608459 0.187264i
\(213\) 0 0
\(214\) 1.27005 + 0.922748i 0.0868191 + 0.0630778i
\(215\) −0.212805 0.154612i −0.0145132 0.0105444i
\(216\) 0 0
\(217\) 2.50396 + 7.70641i 0.169980 + 0.523145i
\(218\) −0.276348 + 0.200779i −0.0187167 + 0.0135985i
\(219\) 0 0
\(220\) −1.18183 + 6.49764i −0.0796790 + 0.438071i
\(221\) 3.85410 0.259255
\(222\) 0 0
\(223\) 1.50785 + 4.64070i 0.100973 + 0.310764i 0.988764 0.149483i \(-0.0477609\pi\)
−0.887791 + 0.460247i \(0.847761\pi\)
\(224\) −1.55976 + 4.80045i −0.104216 + 0.320743i
\(225\) 0 0
\(226\) 0.900424 + 0.654197i 0.0598953 + 0.0435165i
\(227\) −5.04404 + 15.5240i −0.334785 + 1.03036i 0.632043 + 0.774933i \(0.282216\pi\)
−0.966828 + 0.255428i \(0.917784\pi\)
\(228\) 0 0
\(229\) 3.90890 2.83998i 0.258307 0.187671i −0.451093 0.892477i \(-0.648966\pi\)
0.709401 + 0.704806i \(0.248966\pi\)
\(230\) 0.509871 0.0336199
\(231\) 0 0
\(232\) −1.23941 −0.0813711
\(233\) −6.81172 + 4.94900i −0.446251 + 0.324220i −0.788114 0.615530i \(-0.788942\pi\)
0.341863 + 0.939750i \(0.388942\pi\)
\(234\) 0 0
\(235\) 2.13986 6.58580i 0.139589 0.429610i
\(236\) 11.3864 + 8.27272i 0.741193 + 0.538508i
\(237\) 0 0
\(238\) 0.441019 1.35732i 0.0285870 0.0879819i
\(239\) 7.01245 + 21.5821i 0.453598 + 1.39603i 0.872773 + 0.488126i \(0.162319\pi\)
−0.419175 + 0.907905i \(0.637681\pi\)
\(240\) 0 0
\(241\) 11.6065 0.747638 0.373819 0.927502i \(-0.378048\pi\)
0.373819 + 0.927502i \(0.378048\pi\)
\(242\) −0.565971 0.858902i −0.0363820 0.0552123i
\(243\) 0 0
\(244\) 4.03135 2.92894i 0.258080 0.187506i
\(245\) −4.16287 12.8120i −0.265956 0.818528i
\(246\) 0 0
\(247\) 5.62445 + 4.08640i 0.357875 + 0.260011i
\(248\) −0.540751 0.392879i −0.0343377 0.0249478i
\(249\) 0 0
\(250\) 0.0288961 + 0.0889332i 0.00182755 + 0.00562463i
\(251\) 2.68032 1.94736i 0.169180 0.122917i −0.499973 0.866041i \(-0.666657\pi\)
0.669153 + 0.743124i \(0.266657\pi\)
\(252\) 0 0
\(253\) 13.0761 12.4921i 0.822090 0.785370i
\(254\) −1.84800 −0.115954
\(255\) 0 0
\(256\) 4.72952 + 14.5560i 0.295595 + 0.909748i
\(257\) 8.29606 25.5326i 0.517494 1.59268i −0.261204 0.965284i \(-0.584120\pi\)
0.778698 0.627399i \(-0.215880\pi\)
\(258\) 0 0
\(259\) −5.44965 3.95940i −0.338625 0.246025i
\(260\) −0.703052 + 2.16377i −0.0436015 + 0.134192i
\(261\) 0 0
\(262\) 0.146369 0.106343i 0.00904269 0.00656990i
\(263\) −12.1682 −0.750324 −0.375162 0.926959i \(-0.622413\pi\)
−0.375162 + 0.926959i \(0.622413\pi\)
\(264\) 0 0
\(265\) −1.43976 −0.0884436
\(266\) 2.08273 1.51319i 0.127700 0.0927795i
\(267\) 0 0
\(268\) 0.317879 0.978331i 0.0194176 0.0597611i
\(269\) −1.69369 1.23053i −0.103266 0.0750270i 0.534954 0.844881i \(-0.320329\pi\)
−0.638220 + 0.769854i \(0.720329\pi\)
\(270\) 0 0
\(271\) 4.67938 14.4017i 0.284252 0.874838i −0.702370 0.711812i \(-0.747875\pi\)
0.986622 0.163026i \(-0.0521254\pi\)
\(272\) −4.11492 12.6644i −0.249504 0.767894i
\(273\) 0 0
\(274\) −1.17218 −0.0708138
\(275\) 2.91998 + 1.57281i 0.176081 + 0.0948441i
\(276\) 0 0
\(277\) −6.69110 + 4.86137i −0.402029 + 0.292091i −0.770367 0.637601i \(-0.779927\pi\)
0.368338 + 0.929692i \(0.379927\pi\)
\(278\) 0.324939 + 1.00006i 0.0194885 + 0.0599795i
\(279\) 0 0
\(280\) 1.36615 + 0.992564i 0.0816429 + 0.0593171i
\(281\) 1.97985 + 1.43844i 0.118108 + 0.0858104i 0.645271 0.763954i \(-0.276744\pi\)
−0.527163 + 0.849764i \(0.676744\pi\)
\(282\) 0 0
\(283\) 8.06372 + 24.8176i 0.479339 + 1.47525i 0.840016 + 0.542562i \(0.182546\pi\)
−0.360677 + 0.932691i \(0.617454\pi\)
\(284\) 17.2860 12.5590i 1.02574 0.745242i
\(285\) 0 0
\(286\) −0.153619 0.319320i −0.00908369 0.0188818i
\(287\) 7.90553 0.466648
\(288\) 0 0
\(289\) −1.73710 5.34624i −0.102182 0.314485i
\(290\) −0.0959593 + 0.295332i −0.00563492 + 0.0173425i
\(291\) 0 0
\(292\) −9.15223 6.64949i −0.535594 0.389132i
\(293\) −4.15719 + 12.7945i −0.242866 + 0.747463i 0.753115 + 0.657889i \(0.228551\pi\)
−0.995980 + 0.0895739i \(0.971449\pi\)
\(294\) 0 0
\(295\) 5.71821 4.15452i 0.332927 0.241886i
\(296\) 0.555655 0.0322968
\(297\) 0 0
\(298\) −1.62087 −0.0938944
\(299\) 5.04009 3.66184i 0.291476 0.211770i
\(300\) 0 0
\(301\) −0.367773 + 1.13189i −0.0211981 + 0.0652409i
\(302\) −0.000408830 0 0.000297032i −2.35255e−5 0 1.70923e-5i
\(303\) 0 0
\(304\) 7.42268 22.8447i 0.425720 1.31023i
\(305\) −0.773299 2.37997i −0.0442790 0.136277i
\(306\) 0 0
\(307\) 27.1844 1.55150 0.775748 0.631042i \(-0.217373\pi\)
0.775748 + 0.631042i \(0.217373\pi\)
\(308\) 29.6123 3.99921i 1.68731 0.227876i
\(309\) 0 0
\(310\) −0.135484 + 0.0984349i −0.00769497 + 0.00559072i
\(311\) 4.07872 + 12.5530i 0.231283 + 0.711817i 0.997593 + 0.0693450i \(0.0220909\pi\)
−0.766310 + 0.642472i \(0.777909\pi\)
\(312\) 0 0
\(313\) −13.0833 9.50561i −0.739515 0.537289i 0.153044 0.988219i \(-0.451092\pi\)
−0.892559 + 0.450931i \(0.851092\pi\)
\(314\) 0.0419741 + 0.0304959i 0.00236873 + 0.00172099i
\(315\) 0 0
\(316\) 6.95531 + 21.4062i 0.391267 + 1.20420i
\(317\) −4.35344 + 3.16296i −0.244514 + 0.177650i −0.703292 0.710901i \(-0.748287\pi\)
0.458778 + 0.888551i \(0.348287\pi\)
\(318\) 0 0
\(319\) 4.77481 + 9.92514i 0.267338 + 0.555701i
\(320\) 7.79091 0.435525
\(321\) 0 0
\(322\) −0.712878 2.19401i −0.0397271 0.122268i
\(323\) −6.34266 + 19.5207i −0.352915 + 1.08616i
\(324\) 0 0
\(325\) 0.924349 + 0.671579i 0.0512737 + 0.0372525i
\(326\) 0.230137 0.708289i 0.0127461 0.0392285i
\(327\) 0 0
\(328\) −0.527573 + 0.383304i −0.0291304 + 0.0211644i
\(329\) −31.3311 −1.72734
\(330\) 0 0
\(331\) −18.5702 −1.02071 −0.510356 0.859963i \(-0.670486\pi\)
−0.510356 + 0.859963i \(0.670486\pi\)
\(332\) −7.21852 + 5.24456i −0.396168 + 0.287833i
\(333\) 0 0
\(334\) 0.0990106 0.304723i 0.00541762 0.0166737i
\(335\) −0.417936 0.303648i −0.0228343 0.0165901i
\(336\) 0 0
\(337\) 2.78305 8.56535i 0.151603 0.466585i −0.846198 0.532868i \(-0.821114\pi\)
0.997801 + 0.0662836i \(0.0211142\pi\)
\(338\) 0.337928 + 1.04003i 0.0183808 + 0.0565704i
\(339\) 0 0
\(340\) −6.71695 −0.364278
\(341\) −1.06292 + 5.84388i −0.0575604 + 0.316464i
\(342\) 0 0
\(343\) −23.6877 + 17.2101i −1.27902 + 0.929260i
\(344\) −0.0303371 0.0933679i −0.00163567 0.00503406i
\(345\) 0 0
\(346\) −1.55591 1.13043i −0.0836461 0.0607725i
\(347\) 8.30939 + 6.03712i 0.446071 + 0.324090i 0.788043 0.615621i \(-0.211095\pi\)
−0.341971 + 0.939710i \(0.611095\pi\)
\(348\) 0 0
\(349\) 5.33402 + 16.4164i 0.285524 + 0.878752i 0.986241 + 0.165313i \(0.0528633\pi\)
−0.700718 + 0.713439i \(0.747137\pi\)
\(350\) 0.342285 0.248685i 0.0182959 0.0132928i
\(351\) 0 0
\(352\) −2.67534 + 2.55585i −0.142596 + 0.136227i
\(353\) 22.8096 1.21403 0.607017 0.794689i \(-0.292366\pi\)
0.607017 + 0.794689i \(0.292366\pi\)
\(354\) 0 0
\(355\) −3.31584 10.2051i −0.175986 0.541631i
\(356\) 8.16399 25.1262i 0.432691 1.33169i
\(357\) 0 0
\(358\) 0.193994 + 0.140945i 0.0102529 + 0.00744916i
\(359\) 4.96736 15.2879i 0.262167 0.806867i −0.730166 0.683270i \(-0.760557\pi\)
0.992333 0.123597i \(-0.0394429\pi\)
\(360\) 0 0
\(361\) −14.5820 + 10.5945i −0.767475 + 0.557603i
\(362\) −1.25461 −0.0659408
\(363\) 0 0
\(364\) 10.2939 0.539545
\(365\) −4.59621 + 3.33934i −0.240577 + 0.174789i
\(366\) 0 0
\(367\) 6.79759 20.9208i 0.354832 1.09206i −0.601276 0.799042i \(-0.705341\pi\)
0.956107 0.293017i \(-0.0946594\pi\)
\(368\) −17.4138 12.6519i −0.907759 0.659525i
\(369\) 0 0
\(370\) 0.0430208 0.132404i 0.00223654 0.00688337i
\(371\) 2.01301 + 6.19539i 0.104510 + 0.321649i
\(372\) 0 0
\(373\) −20.2604 −1.04905 −0.524523 0.851396i \(-0.675756\pi\)
−0.524523 + 0.851396i \(0.675756\pi\)
\(374\) 0.756449 0.722661i 0.0391151 0.0373679i
\(375\) 0 0
\(376\) 2.09087 1.51911i 0.107828 0.0783419i
\(377\) 1.17249 + 3.60854i 0.0603861 + 0.185849i
\(378\) 0 0
\(379\) 3.01578 + 2.19109i 0.154910 + 0.112549i 0.662540 0.749026i \(-0.269478\pi\)
−0.507630 + 0.861575i \(0.669478\pi\)
\(380\) −9.80231 7.12180i −0.502848 0.365341i
\(381\) 0 0
\(382\) 0.525616 + 1.61768i 0.0268928 + 0.0827677i
\(383\) −8.89708 + 6.46411i −0.454620 + 0.330301i −0.791417 0.611277i \(-0.790656\pi\)
0.336797 + 0.941577i \(0.390656\pi\)
\(384\) 0 0
\(385\) 2.68535 14.7639i 0.136858 0.752439i
\(386\) −1.46704 −0.0746706
\(387\) 0 0
\(388\) 2.06539 + 6.35663i 0.104854 + 0.322709i
\(389\) −2.89926 + 8.92300i −0.146998 + 0.452414i −0.997263 0.0739418i \(-0.976442\pi\)
0.850264 + 0.526356i \(0.176442\pi\)
\(390\) 0 0
\(391\) 14.8801 + 10.8110i 0.752517 + 0.546736i
\(392\) 1.55367 4.78171i 0.0784723 0.241513i
\(393\) 0 0
\(394\) 1.65287 1.20088i 0.0832705 0.0604996i
\(395\) 11.3033 0.568733
\(396\) 0 0
\(397\) 22.3136 1.11989 0.559945 0.828530i \(-0.310822\pi\)
0.559945 + 0.828530i \(0.310822\pi\)
\(398\) −0.344364 + 0.250195i −0.0172614 + 0.0125411i
\(399\) 0 0
\(400\) 1.21988 3.75440i 0.0609940 0.187720i
\(401\) −19.9683 14.5078i −0.997171 0.724487i −0.0356909 0.999363i \(-0.511363\pi\)
−0.961480 + 0.274876i \(0.911363\pi\)
\(402\) 0 0
\(403\) −0.632315 + 1.94606i −0.0314978 + 0.0969404i
\(404\) −5.74411 17.6786i −0.285780 0.879541i
\(405\) 0 0
\(406\) 1.40500 0.0697292
\(407\) −2.14066 4.44967i −0.106109 0.220562i
\(408\) 0 0
\(409\) −23.8705 + 17.3429i −1.18032 + 0.857553i −0.992208 0.124594i \(-0.960237\pi\)
−0.188113 + 0.982147i \(0.560237\pi\)
\(410\) 0.0504891 + 0.155390i 0.00249348 + 0.00767414i
\(411\) 0 0
\(412\) −22.4181 16.2877i −1.10446 0.802437i
\(413\) −25.8722 18.7972i −1.27309 0.924951i
\(414\) 0 0
\(415\) 1.38467 + 4.26157i 0.0679707 + 0.209192i
\(416\) −1.03119 + 0.749203i −0.0505582 + 0.0367327i
\(417\) 0 0
\(418\) 1.87013 0.252566i 0.0914713 0.0123534i
\(419\) −9.03564 −0.441420 −0.220710 0.975339i \(-0.570837\pi\)
−0.220710 + 0.975339i \(0.570837\pi\)
\(420\) 0 0
\(421\) 4.39426 + 13.5242i 0.214163 + 0.659127i 0.999212 + 0.0396928i \(0.0126379\pi\)
−0.785049 + 0.619434i \(0.787362\pi\)
\(422\) −0.547884 + 1.68621i −0.0266706 + 0.0820835i
\(423\) 0 0
\(424\) −0.434725 0.315846i −0.0211121 0.0153388i
\(425\) −1.04238 + 3.20812i −0.0505630 + 0.155617i
\(426\) 0 0
\(427\) −9.16001 + 6.65514i −0.443284 + 0.322065i
\(428\) −33.4298 −1.61589
\(429\) 0 0
\(430\) −0.0245970 −0.00118617
\(431\) −1.40086 + 1.01778i −0.0674769 + 0.0490248i −0.621012 0.783801i \(-0.713278\pi\)
0.553535 + 0.832826i \(0.313278\pi\)
\(432\) 0 0
\(433\) 5.70062 17.5447i 0.273955 0.843145i −0.715540 0.698572i \(-0.753819\pi\)
0.989494 0.144573i \(-0.0461809\pi\)
\(434\) 0.613000 + 0.445371i 0.0294250 + 0.0213785i
\(435\) 0 0
\(436\) 2.24777 6.91791i 0.107649 0.331308i
\(437\) 10.2525 + 31.5539i 0.490442 + 1.50943i
\(438\) 0 0
\(439\) −17.1704 −0.819499 −0.409750 0.912198i \(-0.634384\pi\)
−0.409750 + 0.912198i \(0.634384\pi\)
\(440\) 0.536632 + 1.11547i 0.0255829 + 0.0531778i
\(441\) 0 0
\(442\) 0.291567 0.211836i 0.0138684 0.0100760i
\(443\) −11.3098 34.8079i −0.537344 1.65377i −0.738529 0.674221i \(-0.764479\pi\)
0.201185 0.979553i \(-0.435521\pi\)
\(444\) 0 0
\(445\) −10.7337 7.79852i −0.508828 0.369685i
\(446\) 0.369141 + 0.268196i 0.0174793 + 0.0126995i
\(447\) 0 0
\(448\) −10.8929 33.5249i −0.514641 1.58390i
\(449\) −13.4320 + 9.75895i −0.633897 + 0.460553i −0.857748 0.514070i \(-0.828137\pi\)
0.223851 + 0.974623i \(0.428137\pi\)
\(450\) 0 0
\(451\) 5.10196 + 2.74811i 0.240242 + 0.129404i
\(452\) −23.7006 −1.11478
\(453\) 0 0
\(454\) 0.471667 + 1.45164i 0.0221365 + 0.0681290i
\(455\) 1.59747 4.91652i 0.0748907 0.230490i
\(456\) 0 0
\(457\) 25.6178 + 18.6124i 1.19835 + 0.870651i 0.994121 0.108272i \(-0.0345318\pi\)
0.204227 + 0.978923i \(0.434532\pi\)
\(458\) 0.139617 0.429696i 0.00652385 0.0200784i
\(459\) 0 0
\(460\) −8.78389 + 6.38187i −0.409551 + 0.297556i
\(461\) 25.4351 1.18463 0.592315 0.805706i \(-0.298214\pi\)
0.592315 + 0.805706i \(0.298214\pi\)
\(462\) 0 0
\(463\) −16.3319 −0.759007 −0.379503 0.925190i \(-0.623905\pi\)
−0.379503 + 0.925190i \(0.623905\pi\)
\(464\) 10.6057 7.70549i 0.492357 0.357718i
\(465\) 0 0
\(466\) −0.243298 + 0.748795i −0.0112706 + 0.0346873i
\(467\) 6.90020 + 5.01329i 0.319303 + 0.231987i 0.735878 0.677114i \(-0.236770\pi\)
−0.416575 + 0.909101i \(0.636770\pi\)
\(468\) 0 0
\(469\) −0.722284 + 2.22296i −0.0333520 + 0.102647i
\(470\) −0.200098 0.615837i −0.00922982 0.0284065i
\(471\) 0 0
\(472\) 2.63797 0.121422
\(473\) −0.630814 + 0.602638i −0.0290049 + 0.0277093i
\(474\) 0 0
\(475\) −4.92268 + 3.57654i −0.225868 + 0.164103i
\(476\) 9.39133 + 28.9036i 0.430451 + 1.32479i
\(477\) 0 0
\(478\) 1.71673 + 1.24728i 0.0785216 + 0.0570493i
\(479\) 24.2283 + 17.6029i 1.10702 + 0.804296i 0.982192 0.187882i \(-0.0601623\pi\)
0.124827 + 0.992178i \(0.460162\pi\)
\(480\) 0 0
\(481\) −0.525653 1.61779i −0.0239677 0.0737650i
\(482\) 0.878041 0.637934i 0.0399937 0.0290571i
\(483\) 0 0
\(484\) 20.5010 + 7.71283i 0.931862 + 0.350583i
\(485\) 3.35655 0.152413
\(486\) 0 0
\(487\) −6.05768 18.6436i −0.274500 0.844823i −0.989351 0.145547i \(-0.953506\pi\)
0.714852 0.699276i \(-0.246494\pi\)
\(488\) 0.288612 0.888257i 0.0130649 0.0402095i
\(489\) 0 0
\(490\) −1.01912 0.740434i −0.0460391 0.0334494i
\(491\) 4.87911 15.0163i 0.220191 0.677678i −0.778553 0.627579i \(-0.784046\pi\)
0.998744 0.0500997i \(-0.0159539\pi\)
\(492\) 0 0
\(493\) −9.06253 + 6.58432i −0.408156 + 0.296543i
\(494\) 0.650099 0.0292494
\(495\) 0 0
\(496\) 7.06980 0.317443
\(497\) −39.2773 + 28.5366i −1.76183 + 1.28004i
\(498\) 0 0
\(499\) 3.46350 10.6596i 0.155048 0.477188i −0.843118 0.537729i \(-0.819283\pi\)
0.998166 + 0.0605408i \(0.0192825\pi\)
\(500\) −1.61096 1.17043i −0.0720443 0.0523433i
\(501\) 0 0
\(502\) 0.0957345 0.294640i 0.00427284 0.0131504i
\(503\) 0.105965 + 0.326125i 0.00472473 + 0.0145412i 0.953391 0.301737i \(-0.0975666\pi\)
−0.948666 + 0.316279i \(0.897567\pi\)
\(504\) 0 0
\(505\) −9.33498 −0.415401
\(506\) 0.302613 1.66375i 0.0134528 0.0739628i
\(507\) 0 0
\(508\) 31.8368 23.1308i 1.41253 1.02626i
\(509\) 6.04518 + 18.6052i 0.267948 + 0.824659i 0.991000 + 0.133865i \(0.0427389\pi\)
−0.723052 + 0.690794i \(0.757261\pi\)
\(510\) 0 0
\(511\) 20.7957 + 15.1089i 0.919946 + 0.668380i
\(512\) 5.94673 + 4.32055i 0.262811 + 0.190943i
\(513\) 0 0
\(514\) −0.775763 2.38755i −0.0342175 0.105311i
\(515\) −11.2583 + 8.17961i −0.496098 + 0.360436i
\(516\) 0 0
\(517\) −20.2200 10.8913i −0.889275 0.478998i
\(518\) −0.629896 −0.0276760
\(519\) 0 0
\(520\) 0.131773 + 0.405557i 0.00577865 + 0.0177848i
\(521\) −12.9869 + 39.9695i −0.568966 + 1.75110i 0.0868981 + 0.996217i \(0.472305\pi\)
−0.655864 + 0.754879i \(0.727695\pi\)
\(522\) 0 0
\(523\) −24.2790 17.6398i −1.06165 0.771333i −0.0872555 0.996186i \(-0.527810\pi\)
−0.974393 + 0.224853i \(0.927810\pi\)
\(524\) −1.19054 + 3.66409i −0.0520088 + 0.160067i
\(525\) 0 0
\(526\) −0.920538 + 0.668810i −0.0401374 + 0.0291615i
\(527\) −6.04112 −0.263155
\(528\) 0 0
\(529\) 6.73067 0.292638
\(530\) −0.108919 + 0.0791345i −0.00473115 + 0.00343738i
\(531\) 0 0
\(532\) −16.9405 + 52.1375i −0.734464 + 2.26045i
\(533\) 1.61508 + 1.17342i 0.0699568 + 0.0508266i
\(534\) 0 0
\(535\) −5.18787 + 15.9666i −0.224291 + 0.690298i
\(536\) −0.0595802 0.183369i −0.00257347 0.00792033i
\(537\) 0 0
\(538\) −0.195764 −0.00843998
\(539\) −44.2773 + 5.97976i −1.90716 + 0.257567i
\(540\) 0 0
\(541\) 8.35196 6.06806i 0.359079 0.260886i −0.393589 0.919287i \(-0.628767\pi\)
0.752668 + 0.658400i \(0.228767\pi\)
\(542\) −0.437568 1.34670i −0.0187952 0.0578456i
\(543\) 0 0
\(544\) −3.04442 2.21190i −0.130529 0.0948346i
\(545\) −2.95529 2.14714i −0.126591 0.0919734i
\(546\) 0 0
\(547\) 12.9221 + 39.7702i 0.552510 + 1.70045i 0.702431 + 0.711752i \(0.252098\pi\)
−0.149921 + 0.988698i \(0.547902\pi\)
\(548\) 20.1939 14.6717i 0.862641 0.626746i
\(549\) 0 0
\(550\) 0.307347 0.0415079i 0.0131053 0.00176990i
\(551\) −20.2065 −0.860826
\(552\) 0 0
\(553\) −15.8038 48.6392i −0.672047 2.06835i
\(554\) −0.238990 + 0.735536i −0.0101537 + 0.0312499i
\(555\) 0 0
\(556\) −18.1153 13.1616i −0.768261 0.558174i
\(557\) 11.8918 36.5993i 0.503874 1.55076i −0.298782 0.954321i \(-0.596580\pi\)
0.802656 0.596442i \(-0.203420\pi\)
\(558\) 0 0
\(559\) −0.243142 + 0.176653i −0.0102838 + 0.00747163i
\(560\) −17.8611 −0.754768
\(561\) 0 0
\(562\) 0.228840 0.00965303
\(563\) 24.8258 18.0370i 1.04628 0.760170i 0.0747817 0.997200i \(-0.476174\pi\)
0.971502 + 0.237030i \(0.0761740\pi\)
\(564\) 0 0
\(565\) −3.67802 + 11.3198i −0.154736 + 0.476227i
\(566\) 1.97410 + 1.43427i 0.0829775 + 0.0602867i
\(567\) 0 0
\(568\) 1.23754 3.80877i 0.0519262 0.159812i
\(569\) −4.03220 12.4098i −0.169039 0.520247i 0.830273 0.557357i \(-0.188185\pi\)
−0.999311 + 0.0371104i \(0.988185\pi\)
\(570\) 0 0
\(571\) 16.1300 0.675018 0.337509 0.941322i \(-0.390416\pi\)
0.337509 + 0.941322i \(0.390416\pi\)
\(572\) 6.64331 + 3.57834i 0.277771 + 0.149618i
\(573\) 0 0
\(574\) 0.598062 0.434517i 0.0249626 0.0181364i
\(575\) 1.68494 + 5.18572i 0.0702669 + 0.216259i
\(576\) 0 0
\(577\) 11.7885 + 8.56487i 0.490763 + 0.356560i 0.805478 0.592626i \(-0.201909\pi\)
−0.314715 + 0.949186i \(0.601909\pi\)
\(578\) −0.425263 0.308972i −0.0176886 0.0128515i
\(579\) 0 0
\(580\) −2.04341 6.28898i −0.0848482 0.261136i
\(581\) 16.4019 11.9167i 0.680465 0.494387i
\(582\) 0 0
\(583\) −0.854511 + 4.69806i −0.0353902 + 0.194574i
\(584\) −2.12036 −0.0877411
\(585\) 0 0
\(586\) 0.388738 + 1.19641i 0.0160586 + 0.0494234i
\(587\) 8.61360 26.5099i 0.355521 1.09418i −0.600185 0.799861i \(-0.704906\pi\)
0.955707 0.294321i \(-0.0950936\pi\)
\(588\) 0 0
\(589\) −8.81605 6.40524i −0.363259 0.263923i
\(590\) 0.204241 0.628588i 0.00840846 0.0258786i
\(591\) 0 0
\(592\) −4.75478 + 3.45455i −0.195420 + 0.141981i
\(593\) −15.1037 −0.620236 −0.310118 0.950698i \(-0.600369\pi\)
−0.310118 + 0.950698i \(0.600369\pi\)
\(594\) 0 0
\(595\) 15.2622 0.625690
\(596\) 27.9238 20.2878i 1.14380 0.831023i
\(597\) 0 0
\(598\) 0.180020 0.554044i 0.00736156 0.0226566i
\(599\) −20.9339 15.2093i −0.855334 0.621437i 0.0712774 0.997457i \(-0.477292\pi\)
−0.926612 + 0.376020i \(0.877292\pi\)
\(600\) 0 0
\(601\) −14.5321 + 44.7252i −0.592776 + 1.82438i −0.0272781 + 0.999628i \(0.508684\pi\)
−0.565498 + 0.824750i \(0.691316\pi\)
\(602\) 0.0343904 + 0.105843i 0.00140165 + 0.00431383i
\(603\) 0 0
\(604\) 0.0107610 0.000437861
\(605\) 6.86526 8.59466i 0.279112 0.349423i
\(606\) 0 0
\(607\) 28.4967 20.7041i 1.15665 0.840353i 0.167297 0.985907i \(-0.446496\pi\)
0.989350 + 0.145553i \(0.0464963\pi\)
\(608\) −2.09763 6.45584i −0.0850701 0.261819i
\(609\) 0 0
\(610\) −0.189313 0.137544i −0.00766506 0.00556899i
\(611\) −6.40086 4.65049i −0.258951 0.188139i
\(612\) 0 0
\(613\) −7.23461 22.2658i −0.292203 0.899309i −0.984147 0.177357i \(-0.943245\pi\)
0.691943 0.721952i \(-0.256755\pi\)
\(614\) 2.05653 1.49416i 0.0829948 0.0602993i
\(615\) 0 0
\(616\) 4.04965 3.86876i 0.163165 0.155877i
\(617\) −22.8910 −0.921557 −0.460778 0.887515i \(-0.652430\pi\)
−0.460778 + 0.887515i \(0.652430\pi\)
\(618\) 0 0
\(619\) 0.657441 + 2.02339i 0.0264248 + 0.0813271i 0.963399 0.268071i \(-0.0863861\pi\)
−0.936974 + 0.349398i \(0.886386\pi\)
\(620\) 1.10200 3.39161i 0.0442574 0.136210i
\(621\) 0 0
\(622\) 0.998521 + 0.725468i 0.0400370 + 0.0290886i
\(623\) −18.5502 + 57.0916i −0.743198 + 2.28733i
\(624\) 0 0
\(625\) −0.809017 + 0.587785i −0.0323607 + 0.0235114i
\(626\) −1.51223 −0.0604410
\(627\) 0 0
\(628\) −1.10482 −0.0440873
\(629\) 4.06294 2.95190i 0.162000 0.117700i
\(630\) 0 0
\(631\) 4.77702 14.7022i 0.190170 0.585284i −0.809829 0.586666i \(-0.800440\pi\)
0.999999 + 0.00138227i \(0.000439991\pi\)
\(632\) 3.41296 + 2.47966i 0.135760 + 0.0986357i
\(633\) 0 0
\(634\) −0.155494 + 0.478563i −0.00617547 + 0.0190062i
\(635\) −6.10700 18.7954i −0.242349 0.745873i
\(636\) 0 0
\(637\) −15.3918 −0.609844
\(638\) 0.906743 + 0.488406i 0.0358983 + 0.0193362i
\(639\) 0 0
\(640\) 2.39444 1.73967i 0.0946487 0.0687663i
\(641\) −4.38201 13.4864i −0.173079 0.532682i 0.826461 0.562993i \(-0.190350\pi\)
−0.999541 + 0.0303108i \(0.990350\pi\)
\(642\) 0 0
\(643\) 10.0270 + 7.28504i 0.395426 + 0.287294i 0.767675 0.640839i \(-0.221413\pi\)
−0.372249 + 0.928133i \(0.621413\pi\)
\(644\) 39.7429 + 28.8749i 1.56609 + 1.13783i
\(645\) 0 0
\(646\) 0.593101 + 1.82538i 0.0233352 + 0.0718185i
\(647\) 26.8970 19.5418i 1.05743 0.768267i 0.0838181 0.996481i \(-0.473289\pi\)
0.973611 + 0.228214i \(0.0732885\pi\)
\(648\) 0 0
\(649\) −10.1628 21.1248i −0.398923 0.829220i
\(650\) 0.106840 0.00419063
\(651\) 0 0
\(652\) 4.90068 + 15.0827i 0.191925 + 0.590685i
\(653\) 10.7558 33.1030i 0.420908 1.29542i −0.485951 0.873986i \(-0.661526\pi\)
0.906858 0.421435i \(-0.138474\pi\)
\(654\) 0 0
\(655\) 1.56528 + 1.13724i 0.0611604 + 0.0444356i
\(656\) 2.13145 6.55992i 0.0832191 0.256122i
\(657\) 0 0
\(658\) −2.37023 + 1.72207i −0.0924011 + 0.0671334i
\(659\) 34.4953 1.34375 0.671873 0.740666i \(-0.265490\pi\)
0.671873 + 0.740666i \(0.265490\pi\)
\(660\) 0 0
\(661\) 1.77827 0.0691668 0.0345834 0.999402i \(-0.488990\pi\)
0.0345834 + 0.999402i \(0.488990\pi\)
\(662\) −1.40486 + 1.02069i −0.0546014 + 0.0396702i
\(663\) 0 0
\(664\) −0.516788 + 1.59051i −0.0200553 + 0.0617238i
\(665\) 22.2728 + 16.1821i 0.863701 + 0.627516i
\(666\) 0 0
\(667\) −5.59541 + 17.2209i −0.216655 + 0.666796i
\(668\) 2.10839 + 6.48896i 0.0815761 + 0.251065i
\(669\) 0 0
\(670\) −0.0483070 −0.00186626
\(671\) −8.22502 + 1.11081i −0.317523 + 0.0428823i
\(672\) 0 0
\(673\) −15.6111 + 11.3422i −0.601765 + 0.437208i −0.846505 0.532381i \(-0.821297\pi\)
0.244740 + 0.969589i \(0.421297\pi\)
\(674\) −0.260243 0.800945i −0.0100242 0.0308513i
\(675\) 0 0
\(676\) −18.8395 13.6877i −0.724595 0.526449i
\(677\) −13.6805 9.93949i −0.525786 0.382006i 0.292993 0.956114i \(-0.405349\pi\)
−0.818779 + 0.574109i \(0.805349\pi\)
\(678\) 0 0
\(679\) −4.69298 14.4435i −0.180100 0.554291i
\(680\) −1.01852 + 0.739998i −0.0390585 + 0.0283776i
\(681\) 0 0
\(682\) 0.240791 + 0.500518i 0.00922035 + 0.0191658i
\(683\) −4.14018 −0.158420 −0.0792098 0.996858i \(-0.525240\pi\)
−0.0792098 + 0.996858i \(0.525240\pi\)
\(684\) 0 0
\(685\) −3.87363 11.9218i −0.148004 0.455509i
\(686\) −0.846069 + 2.60393i −0.0323031 + 0.0994186i
\(687\) 0 0
\(688\) 0.840072 + 0.610348i 0.0320274 + 0.0232693i
\(689\) −0.508335 + 1.56450i −0.0193660 + 0.0596025i
\(690\) 0 0
\(691\) 37.4996 27.2450i 1.42655 1.03645i 0.435904 0.899993i \(-0.356429\pi\)
0.990646 0.136457i \(-0.0435714\pi\)
\(692\) 40.9539 1.55684
\(693\) 0 0
\(694\) 0.960437 0.0364577
\(695\) −9.09743 + 6.60967i −0.345085 + 0.250719i
\(696\) 0 0
\(697\) −1.82132 + 5.60543i −0.0689872 + 0.212321i
\(698\) 1.30583 + 0.948743i 0.0494265 + 0.0359105i
\(699\) 0 0
\(700\) −2.78408 + 8.56853i −0.105228 + 0.323860i
\(701\) 14.0465 + 43.2306i 0.530528 + 1.63280i 0.753119 + 0.657884i \(0.228548\pi\)
−0.222591 + 0.974912i \(0.571452\pi\)
\(702\) 0 0
\(703\) 9.05904 0.341668
\(704\) 4.62398 25.4224i 0.174273 0.958143i
\(705\) 0 0
\(706\) 1.72557 1.25370i 0.0649428 0.0471837i
\(707\) 13.0518 + 40.1692i 0.490862 + 1.51072i
\(708\) 0 0
\(709\) 11.3458 + 8.24318i 0.426099 + 0.309579i 0.780087 0.625671i \(-0.215175\pi\)
−0.353988 + 0.935250i \(0.615175\pi\)
\(710\) −0.811757 0.589776i −0.0304647 0.0221339i
\(711\) 0 0
\(712\) −1.53018 4.70941i −0.0573460 0.176493i
\(713\) −7.90010 + 5.73976i −0.295861 + 0.214956i
\(714\) 0 0
\(715\) 2.74003 2.61764i 0.102471 0.0978943i
\(716\) −5.10622 −0.190829
\(717\) 0 0
\(718\) −0.464497 1.42957i −0.0173349 0.0533512i
\(719\) −4.05999 + 12.4954i −0.151412 + 0.465998i −0.997780 0.0666007i \(-0.978785\pi\)
0.846368 + 0.532599i \(0.178785\pi\)
\(720\) 0 0
\(721\) 50.9383 + 37.0088i 1.89704 + 1.37828i
\(722\) −0.520835 + 1.60297i −0.0193835 + 0.0596562i
\(723\) 0 0
\(724\) 21.6140 15.7035i 0.803279 0.583616i
\(725\) −3.32083 −0.123333
\(726\) 0 0
\(727\) −18.3635 −0.681063 −0.340532 0.940233i \(-0.610607\pi\)
−0.340532 + 0.940233i \(0.610607\pi\)
\(728\) 1.56090 1.13406i 0.0578509 0.0420312i
\(729\) 0 0
\(730\) −0.164166 + 0.505250i −0.00607604 + 0.0187001i
\(731\) −0.717839 0.521540i −0.0265502 0.0192899i
\(732\) 0 0
\(733\) −11.4329 + 35.1869i −0.422284 + 1.29966i 0.483287 + 0.875462i \(0.339443\pi\)
−0.905571 + 0.424195i \(0.860557\pi\)
\(734\) −0.635642 1.95631i −0.0234620 0.0722086i
\(735\) 0 0
\(736\) −6.08282 −0.224216
\(737\) −1.23888 + 1.18354i −0.0456348 + 0.0435964i
\(738\) 0 0
\(739\) −7.96909 + 5.78988i −0.293148 + 0.212984i −0.724632 0.689136i \(-0.757990\pi\)
0.431484 + 0.902121i \(0.357990\pi\)
\(740\) 0.916110 + 2.81950i 0.0336769 + 0.103647i
\(741\) 0 0
\(742\) 0.492808 + 0.358046i 0.0180915 + 0.0131443i
\(743\) 22.2052 + 16.1330i 0.814629 + 0.591862i 0.915169 0.403071i \(-0.132057\pi\)
−0.100540 + 0.994933i \(0.532057\pi\)
\(744\) 0 0
\(745\) −5.35640 16.4853i −0.196243 0.603974i
\(746\) −1.53272 + 1.11359i −0.0561170 + 0.0407714i
\(747\) 0 0
\(748\) −3.98658 + 21.9180i −0.145764 + 0.801401i
\(749\) 75.9591 2.77549
\(750\) 0 0
\(751\) 4.24232 + 13.0565i 0.154804 + 0.476439i 0.998141 0.0609469i \(-0.0194120\pi\)
−0.843337 + 0.537385i \(0.819412\pi\)
\(752\) −8.44732 + 25.9982i −0.308042 + 0.948056i
\(753\) 0 0
\(754\) 0.287039 + 0.208546i 0.0104533 + 0.00759479i
\(755\) 0.00166997 0.00513965i 6.07766e−5 0.000187051i
\(756\) 0 0
\(757\) 18.5507 13.4779i 0.674236 0.489861i −0.197205 0.980362i \(-0.563186\pi\)
0.871440 + 0.490501i \(0.163186\pi\)
\(758\) 0.348578 0.0126609
\(759\) 0 0
\(760\) −2.27097 −0.0823767
\(761\) −16.7319 + 12.1565i −0.606533 + 0.440672i −0.848192 0.529689i \(-0.822308\pi\)
0.241659 + 0.970361i \(0.422308\pi\)
\(762\) 0 0
\(763\) −5.10737 + 15.7189i −0.184899 + 0.569061i
\(764\) −29.3031 21.2899i −1.06015 0.770243i
\(765\) 0 0
\(766\) −0.317783 + 0.978034i −0.0114819 + 0.0353378i
\(767\) −2.49553 7.68046i −0.0901084 0.277325i
\(768\) 0 0
\(769\) 38.4306 1.38584 0.692922 0.721013i \(-0.256323\pi\)
0.692922 + 0.721013i \(0.256323\pi\)
\(770\) −0.608331 1.26450i −0.0219227 0.0455696i
\(771\) 0 0
\(772\) 25.2738 18.3625i 0.909624 0.660880i
\(773\) −15.4325 47.4964i −0.555069 1.70833i −0.695762 0.718272i \(-0.744933\pi\)
0.140693 0.990053i \(-0.455067\pi\)
\(774\) 0 0
\(775\) −1.44887 1.05267i −0.0520451 0.0378129i
\(776\) 1.01349 + 0.736341i 0.0363821 + 0.0264331i
\(777\) 0 0
\(778\) 0.271109 + 0.834389i 0.00971975 + 0.0299143i
\(779\) −8.60121 + 6.24914i −0.308170 + 0.223899i
\(780\) 0 0
\(781\) −35.2681 + 4.76305i −1.26199 + 0.170435i
\(782\) 1.71991 0.0615037
\(783\) 0 0
\(784\) 16.4334 + 50.5767i 0.586906 + 1.80631i
\(785\) −0.171454 + 0.527682i −0.00611946 + 0.0188338i
\(786\) 0 0
\(787\) 12.5834 + 9.14241i 0.448551 + 0.325892i 0.789024 0.614363i \(-0.210587\pi\)
−0.340472 + 0.940255i \(0.610587\pi\)
\(788\) −13.4442 + 41.3769i −0.478928 + 1.47399i
\(789\) 0 0
\(790\) 0.855110 0.621274i 0.0304235 0.0221039i
\(791\) 53.8524 1.91477
\(792\) 0 0
\(793\) −2.85919 −0.101533
\(794\) 1.68805 1.22644i 0.0599067 0.0435248i
\(795\) 0 0
\(796\) 2.80099 8.62057i 0.0992786 0.305548i
\(797\) 37.3012 + 27.1009i 1.32127 + 0.959962i 0.999915 + 0.0130049i \(0.00413972\pi\)
0.321359 + 0.946957i \(0.395860\pi\)
\(798\) 0 0
\(799\) 7.21821 22.2154i 0.255362 0.785923i
\(800\) −0.344735 1.06098i −0.0121882 0.0375114i
\(801\) 0 0
\(802\) −2.30803 −0.0814994
\(803\) 8.16868 + 16.9798i 0.288266 + 0.599203i
\(804\) 0 0
\(805\) 19.9587 14.5009i 0.703453 0.511088i
\(806\) 0.0591277 + 0.181976i 0.00208268 + 0.00640984i
\(807\) 0 0
\(808\) −2.81863 2.04786i −0.0991591 0.0720433i
\(809\) −30.3700 22.0651i −1.06775 0.775767i −0.0922454 0.995736i \(-0.529404\pi\)
−0.975507 + 0.219969i \(0.929404\pi\)
\(810\) 0 0
\(811\) 2.22661 + 6.85281i 0.0781870 + 0.240635i 0.982509 0.186217i \(-0.0596227\pi\)
−0.904322 + 0.426852i \(0.859623\pi\)
\(812\) −24.2050 + 17.5859i −0.849428 + 0.617146i
\(813\) 0 0
\(814\) −0.406514 0.218964i −0.0142483 0.00767468i
\(815\) 7.96428 0.278977
\(816\) 0 0
\(817\) −0.494596 1.52221i −0.0173037 0.0532554i
\(818\) −0.852597 + 2.62402i −0.0298104 + 0.0917469i
\(819\) 0 0
\(820\) −2.81477 2.04505i −0.0982960 0.0714162i
\(821\) 2.66807 8.21147i 0.0931163 0.286582i −0.893642 0.448781i \(-0.851858\pi\)
0.986758 + 0.162198i \(0.0518584\pi\)
\(822\) 0 0
\(823\) 20.2352 14.7017i 0.705354 0.512470i −0.176318 0.984333i \(-0.556419\pi\)
0.881672 + 0.471864i \(0.156419\pi\)
\(824\) −5.19375 −0.180933
\(825\) 0 0
\(826\) −2.99042 −0.104050
\(827\) 39.5387 28.7265i 1.37489 0.998919i 0.377558 0.925986i \(-0.376764\pi\)
0.997337 0.0729332i \(-0.0232360\pi\)
\(828\) 0 0
\(829\) 1.63522 5.03270i 0.0567937 0.174793i −0.918636 0.395106i \(-0.870708\pi\)
0.975429 + 0.220313i \(0.0707079\pi\)
\(830\) 0.338983 + 0.246286i 0.0117663 + 0.00854871i
\(831\) 0 0
\(832\) 2.75073 8.46589i 0.0953645 0.293502i
\(833\) −14.0423 43.2177i −0.486536 1.49740i
\(834\) 0 0
\(835\) 3.42643 0.118576
\(836\) −29.0568 + 27.7590i −1.00495 + 0.960064i
\(837\) 0 0
\(838\) −0.683556 + 0.496633i −0.0236131 + 0.0171559i
\(839\) 4.09196 + 12.5938i 0.141270 + 0.434785i 0.996513 0.0834435i \(-0.0265918\pi\)
−0.855242 + 0.518228i \(0.826592\pi\)
\(840\) 0 0
\(841\) 14.5397 + 10.5637i 0.501369 + 0.364266i
\(842\) 1.07577 + 0.781592i 0.0370734 + 0.0269354i
\(843\) 0 0
\(844\) −11.6670 35.9072i −0.401593 1.23598i
\(845\) −9.46110 + 6.87389i −0.325472 + 0.236469i
\(846\) 0 0
\(847\) −46.5822 17.5251i −1.60058 0.602168i
\(848\) 5.68361 0.195176
\(849\) 0 0
\(850\) 0.0974731 + 0.299991i 0.00334330 + 0.0102896i
\(851\) 2.50855 7.72053i 0.0859920 0.264656i
\(852\) 0 0
\(853\) −1.79509 1.30421i −0.0614626 0.0446552i 0.556630 0.830761i \(-0.312094\pi\)
−0.618092 + 0.786106i \(0.712094\pi\)
\(854\) −0.327174 + 1.00694i −0.0111956 + 0.0344567i
\(855\) 0 0
\(856\) −5.06911 + 3.68292i −0.173259 + 0.125880i
\(857\) −31.4625 −1.07474 −0.537368 0.843348i \(-0.680582\pi\)
−0.537368 + 0.843348i \(0.680582\pi\)
\(858\) 0 0
\(859\) 9.07676 0.309695 0.154848 0.987938i \(-0.450511\pi\)
0.154848 + 0.987938i \(0.450511\pi\)
\(860\) 0.423749 0.307872i 0.0144497 0.0104983i
\(861\) 0 0
\(862\) −0.0500352 + 0.153993i −0.00170421 + 0.00524501i
\(863\) 34.3704 + 24.9716i 1.16998 + 0.850042i 0.991007 0.133811i \(-0.0427215\pi\)
0.178976 + 0.983853i \(0.442721\pi\)
\(864\) 0 0
\(865\) 6.35552 19.5603i 0.216094 0.665069i
\(866\) −0.533065 1.64060i −0.0181143 0.0557500i
\(867\) 0 0
\(868\) −16.1351 −0.547662
\(869\) 6.70865 36.8838i 0.227575 1.25120i
\(870\) 0 0
\(871\) −0.477516 + 0.346936i −0.0161800 + 0.0117555i
\(872\) −0.421300 1.29663i −0.0142670 0.0439094i
\(873\) 0 0
\(874\) 2.50993 + 1.82357i 0.0848996 + 0.0616832i
\(875\) 3.66042 + 2.65945i 0.123745 + 0.0899058i
\(876\) 0 0
\(877\) −9.67537 29.7777i −0.326714 1.00552i −0.970661 0.240452i \(-0.922704\pi\)
0.643947 0.765070i \(-0.277296\pi\)
\(878\) −1.29896 + 0.943750i −0.0438378 + 0.0318500i
\(879\) 0 0
\(880\) −11.5269 6.20885i −0.388573 0.209300i
\(881\) −21.5189 −0.724990 −0.362495 0.931986i \(-0.618075\pi\)
−0.362495 + 0.931986i \(0.618075\pi\)
\(882\) 0 0
\(883\) −0.201650 0.620614i −0.00678605 0.0208853i 0.947606 0.319441i \(-0.103495\pi\)
−0.954392 + 0.298556i \(0.903495\pi\)
\(884\) −2.37155 + 7.29889i −0.0797639 + 0.245488i
\(885\) 0 0
\(886\) −2.76877 2.01163i −0.0930187 0.0675820i
\(887\) 4.52593 13.9294i 0.151966 0.467702i −0.845875 0.533381i \(-0.820921\pi\)
0.997841 + 0.0656786i \(0.0209212\pi\)
\(888\) 0 0
\(889\) −72.3396 + 52.5578i −2.42619 + 1.76273i
\(890\) −1.24065 −0.0415868
\(891\) 0 0
\(892\) −9.71637 −0.325328
\(893\) 34.0882 24.7665i 1.14072 0.828780i
\(894\) 0 0
\(895\) −0.792419 + 2.43882i −0.0264877 + 0.0815206i
\(896\) −10.8337 7.87116i −0.361929 0.262957i
\(897\) 0 0
\(898\) −0.479760 + 1.47655i −0.0160098 + 0.0492731i
\(899\) −1.83782 5.65622i −0.0612946 0.188645i
\(900\) 0 0
\(901\) −4.85662 −0.161798
\(902\) 0.537016 0.0725252i 0.0178807 0.00241483i
\(903\) 0 0
\(904\) −3.59382 + 2.61107i −0.119529 + 0.0868428i
\(905\) −4.14604 12.7602i −0.137819 0.424163i
\(906\) 0 0
\(907\) −23.2552 16.8959i −0.772175 0.561018i 0.130445 0.991456i \(-0.458359\pi\)
−0.902620 + 0.430437i \(0.858359\pi\)
\(908\) −26.2955 19.1048i −0.872645 0.634014i
\(909\) 0 0
\(910\) −0.149380 0.459743i −0.00495188 0.0152403i
\(911\) 13.9813 10.1580i 0.463222 0.336550i −0.331572 0.943430i \(-0.607579\pi\)
0.794794 + 0.606880i \(0.207579\pi\)
\(912\) 0 0
\(913\) 14.7277 1.98901i 0.487416 0.0658266i
\(914\) 2.96102 0.0979418
\(915\) 0 0
\(916\) 2.97308 + 9.15020i 0.0982333 + 0.302331i
\(917\) 2.70513 8.32554i 0.0893313 0.274933i
\(918\) 0 0
\(919\) 1.77859 + 1.29222i 0.0586701 + 0.0426263i 0.616734 0.787172i \(-0.288456\pi\)
−0.558064 + 0.829798i \(0.688456\pi\)
\(920\) −0.628857 + 1.93542i −0.0207328 + 0.0638090i
\(921\) 0 0
\(922\) 1.92419 1.39801i 0.0633699 0.0460409i
\(923\) −12.2600 −0.403542
\(924\) 0 0
\(925\) 1.48881 0.0489517
\(926\) −1.23552 + 0.897661i −0.0406019 + 0.0294990i
\(927\) 0 0
\(928\) 1.14481 3.52335i 0.0375801 0.115660i
\(929\) 19.5866 + 14.2305i 0.642616 + 0.466888i 0.860748 0.509031i \(-0.169996\pi\)
−0.218132 + 0.975919i \(0.569996\pi\)
\(930\) 0 0
\(931\) 25.3301 77.9579i 0.830159 2.55497i
\(932\) −5.18094 15.9453i −0.169707 0.522305i
\(933\) 0 0
\(934\) 0.797556 0.0260968
\(935\) 9.84973 + 5.30544i 0.322121 + 0.173506i
\(936\) 0 0
\(937\) 16.8459 12.2393i 0.550333 0.399840i −0.277575 0.960704i \(-0.589531\pi\)
0.827908 + 0.560864i \(0.189531\pi\)
\(938\) 0.0675407 + 0.207869i 0.00220528 + 0.00678716i
\(939\) 0 0
\(940\) 11.1554 + 8.10491i 0.363851 + 0.264353i
\(941\) 27.6787 + 20.1098i 0.902301 + 0.655560i 0.939056 0.343764i \(-0.111702\pi\)
−0.0367552 + 0.999324i \(0.511702\pi\)
\(942\) 0 0
\(943\) 2.94403 + 9.06080i 0.0958709 + 0.295060i
\(944\) −22.5733 + 16.4004i −0.734697 + 0.533789i
\(945\) 0 0
\(946\) −0.0145986 + 0.0802621i −0.000474640 + 0.00260955i
\(947\) −33.8128 −1.09877 −0.549383 0.835570i \(-0.685137\pi\)
−0.549383 + 0.835570i \(0.685137\pi\)
\(948\) 0 0
\(949\) 2.00587 + 6.17344i 0.0651133 + 0.200398i
\(950\) −0.175826 + 0.541138i −0.00570456 + 0.0175568i
\(951\) 0 0
\(952\) 4.60832 + 3.34814i 0.149356 + 0.108514i
\(953\) −7.91027 + 24.3453i −0.256239 + 0.788622i 0.737344 + 0.675517i \(0.236080\pi\)
−0.993583 + 0.113105i \(0.963920\pi\)
\(954\) 0 0
\(955\) −14.7159 + 10.6917i −0.476195 + 0.345976i
\(956\) −45.1871 −1.46146
\(957\) 0 0
\(958\) 2.80042 0.0904774
\(959\) −45.8845 + 33.3371i −1.48169 + 1.07651i
\(960\) 0 0
\(961\) −8.58840 + 26.4324i −0.277045 + 0.852658i
\(962\) −0.128686 0.0934959i −0.00414901 0.00301443i
\(963\) 0 0
\(964\) −7.14182 + 21.9803i −0.230023 + 0.707937i
\(965\) −4.84806 14.9208i −0.156065 0.480317i
\(966\) 0 0
\(967\) 43.8942 1.41154 0.705772 0.708439i \(-0.250600\pi\)
0.705772 + 0.708439i \(0.250600\pi\)
\(968\) 3.95836 1.08904i 0.127227 0.0350029i
\(969\) 0 0
\(970\) 0.253927 0.184489i 0.00815310 0.00592357i
\(971\) −11.2392 34.5906i −0.360682 1.11006i −0.952641 0.304097i \(-0.901645\pi\)
0.591959 0.805968i \(-0.298355\pi\)
\(972\) 0 0
\(973\) 41.1616 + 29.9056i 1.31958 + 0.958730i
\(974\) −1.48299 1.07746i −0.0475182 0.0345240i
\(975\) 0 0
\(976\) 3.05269 + 9.39520i 0.0977141 + 0.300733i
\(977\) 8.37462 6.08452i 0.267928 0.194661i −0.445707 0.895179i \(-0.647048\pi\)
0.713635 + 0.700518i \(0.247048\pi\)
\(978\) 0 0
\(979\) −31.8178 + 30.3966i −1.01690 + 0.971481i
\(980\) 26.8248 0.856888
\(981\) 0 0
\(982\) −0.456245 1.40418i −0.0145594 0.0448091i
\(983\) 6.83416 21.0334i 0.217976 0.670861i −0.780953 0.624590i \(-0.785266\pi\)
0.998929 0.0462712i \(-0.0147338\pi\)
\(984\) 0 0
\(985\) 17.6759 + 12.8423i 0.563201 + 0.409190i
\(986\) −0.323692 + 0.996222i −0.0103085 + 0.0317262i
\(987\) 0 0
\(988\) −11.1997 + 8.13707i −0.356310 + 0.258875i
\(989\) −1.43426 −0.0456067
\(990\) 0 0
\(991\) −55.5911 −1.76591 −0.882955 0.469457i \(-0.844450\pi\)
−0.882955 + 0.469457i \(0.844450\pi\)
\(992\) 1.61634 1.17434i 0.0513189 0.0372853i
\(993\) 0 0
\(994\) −1.40289 + 4.31765i −0.0444970 + 0.136948i
\(995\) −3.68265 2.67560i −0.116748 0.0848222i
\(996\) 0 0
\(997\) 3.33465 10.2630i 0.105609 0.325032i −0.884264 0.466988i \(-0.845339\pi\)
0.989873 + 0.141956i \(0.0453391\pi\)
\(998\) −0.323872 0.996775i −0.0102520 0.0315524i
\(999\) 0 0
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 495.2.n.f.91.1 8
3.2 odd 2 55.2.g.a.36.2 yes 8
11.2 odd 10 5445.2.a.bu.1.2 4
11.4 even 5 inner 495.2.n.f.136.1 8
11.9 even 5 5445.2.a.bg.1.3 4
12.11 even 2 880.2.bo.e.641.1 8
15.2 even 4 275.2.z.b.124.2 16
15.8 even 4 275.2.z.b.124.3 16
15.14 odd 2 275.2.h.b.201.1 8
33.2 even 10 605.2.a.i.1.3 4
33.5 odd 10 605.2.g.j.251.1 8
33.8 even 10 605.2.g.g.511.2 8
33.14 odd 10 605.2.g.j.511.1 8
33.17 even 10 605.2.g.g.251.2 8
33.20 odd 10 605.2.a.l.1.2 4
33.26 odd 10 55.2.g.a.26.2 8
33.29 even 10 605.2.g.n.81.1 8
33.32 even 2 605.2.g.n.366.1 8
132.35 odd 10 9680.2.a.cv.1.1 4
132.59 even 10 880.2.bo.e.81.1 8
132.119 even 10 9680.2.a.cs.1.1 4
165.59 odd 10 275.2.h.b.26.1 8
165.92 even 20 275.2.z.b.224.3 16
165.119 odd 10 3025.2.a.v.1.3 4
165.134 even 10 3025.2.a.be.1.2 4
165.158 even 20 275.2.z.b.224.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.g.a.26.2 8 33.26 odd 10
55.2.g.a.36.2 yes 8 3.2 odd 2
275.2.h.b.26.1 8 165.59 odd 10
275.2.h.b.201.1 8 15.14 odd 2
275.2.z.b.124.2 16 15.2 even 4
275.2.z.b.124.3 16 15.8 even 4
275.2.z.b.224.2 16 165.158 even 20
275.2.z.b.224.3 16 165.92 even 20
495.2.n.f.91.1 8 1.1 even 1 trivial
495.2.n.f.136.1 8 11.4 even 5 inner
605.2.a.i.1.3 4 33.2 even 10
605.2.a.l.1.2 4 33.20 odd 10
605.2.g.g.251.2 8 33.17 even 10
605.2.g.g.511.2 8 33.8 even 10
605.2.g.j.251.1 8 33.5 odd 10
605.2.g.j.511.1 8 33.14 odd 10
605.2.g.n.81.1 8 33.29 even 10
605.2.g.n.366.1 8 33.32 even 2
880.2.bo.e.81.1 8 132.59 even 10
880.2.bo.e.641.1 8 12.11 even 2
3025.2.a.v.1.3 4 165.119 odd 10
3025.2.a.be.1.2 4 165.134 even 10
5445.2.a.bg.1.3 4 11.9 even 5
5445.2.a.bu.1.2 4 11.2 odd 10
9680.2.a.cs.1.1 4 132.119 even 10
9680.2.a.cv.1.1 4 132.35 odd 10