Properties

Label 855.2.k.k.676.1
Level $855$
Weight $2$
Character 855.676
Analytic conductor $6.827$
Analytic rank $0$
Dimension $12$
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] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + 14 x^{3} + 46 x^{2} + 12 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 676.1
Root \(1.50733 - 2.61078i\) of defining polynomial
Character \(\chi\) \(=\) 855.676
Dual form 855.2.k.k.406.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00733 + 1.74475i) q^{2} +(-1.02944 - 1.78305i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.66469 q^{7} +0.118641 q^{8} +O(q^{10})\) \(q+(-1.00733 + 1.74475i) q^{2} +(-1.02944 - 1.78305i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.66469 q^{7} +0.118641 q^{8} +(1.00733 + 1.74475i) q^{10} -0.745446 q^{11} +(0.269815 + 0.467333i) q^{13} +(-1.67690 + 2.90447i) q^{14} +(1.93938 - 3.35910i) q^{16} +(-0.705067 + 1.22121i) q^{17} +(4.17330 - 1.25841i) q^{19} -2.05889 q^{20} +(0.750913 - 1.30062i) q^{22} +(-0.437471 - 0.757722i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.08718 q^{26} +(-1.71370 - 2.96822i) q^{28} +(3.70083 + 6.41003i) q^{29} +7.02934 q^{31} +(4.02584 + 6.97297i) q^{32} +(-1.42048 - 2.46034i) q^{34} +(0.832344 - 1.44166i) q^{35} +7.84476 q^{37} +(-2.00828 + 8.54902i) q^{38} +(0.0593204 - 0.102746i) q^{40} +(4.36591 - 7.56198i) q^{41} +(-2.93324 + 5.08052i) q^{43} +(0.767395 + 1.32917i) q^{44} +1.76272 q^{46} +(3.29875 + 5.71360i) q^{47} -4.22881 q^{49} +2.01467 q^{50} +(0.555519 - 0.962187i) q^{52} +(3.85018 + 6.66871i) q^{53} +(-0.372723 + 0.645575i) q^{55} +0.197500 q^{56} -14.9119 q^{58} +(2.45356 - 4.24969i) q^{59} +(2.60473 + 4.51153i) q^{61} +(-7.08089 + 12.2645i) q^{62} -8.46397 q^{64} +0.539630 q^{65} +(-0.443531 - 0.768219i) q^{67} +2.90331 q^{68} +(1.67690 + 2.90447i) q^{70} +(1.41061 - 2.44324i) q^{71} +(-0.524369 + 0.908233i) q^{73} +(-7.90230 + 13.6872i) q^{74} +(-6.53999 - 6.14573i) q^{76} -1.24094 q^{77} +(-2.88624 + 4.99911i) q^{79} +(-1.93938 - 3.35910i) q^{80} +(8.79587 + 15.2349i) q^{82} -3.61555 q^{83} +(0.705067 + 1.22121i) q^{85} +(-5.90950 - 10.2356i) q^{86} -0.0884403 q^{88} +(-0.464416 - 0.804392i) q^{89} +(0.449158 + 0.777964i) q^{91} +(-0.900704 + 1.56007i) q^{92} -13.2918 q^{94} +(0.996831 - 4.24339i) q^{95} +(-0.00920110 + 0.0159368i) q^{97} +(4.25983 - 7.37824i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 5 q^{4} + 6 q^{5} + 4 q^{7} - 12 q^{8} - 3 q^{10} - 8 q^{13} + 10 q^{14} - 3 q^{16} + 4 q^{17} - 6 q^{19} - 10 q^{20} - 2 q^{23} - 6 q^{25} - 40 q^{26} - 26 q^{28} + 4 q^{29} + 24 q^{31} + 15 q^{32} + 7 q^{34} + 2 q^{35} - 29 q^{38} - 6 q^{40} + 12 q^{41} - 4 q^{43} + 6 q^{44} + 48 q^{46} + 6 q^{47} + 32 q^{49} - 6 q^{50} - 20 q^{52} + 26 q^{53} - 44 q^{56} - 20 q^{58} + 16 q^{59} + 20 q^{61} - 25 q^{62} + 28 q^{64} - 16 q^{65} - 12 q^{67} + 54 q^{68} - 10 q^{70} - 8 q^{71} - 4 q^{73} - 16 q^{74} - 66 q^{76} + 48 q^{77} - 12 q^{79} + 3 q^{80} + 26 q^{82} - 44 q^{83} - 4 q^{85} - 44 q^{86} - 32 q^{88} - 8 q^{89} + 2 q^{91} + 36 q^{92} - 14 q^{94} - 6 q^{95} + 30 q^{97} + 49 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00733 + 1.74475i −0.712293 + 1.23373i 0.251702 + 0.967805i \(0.419010\pi\)
−0.963994 + 0.265922i \(0.914323\pi\)
\(3\) 0 0
\(4\) −1.02944 1.78305i −0.514722 0.891525i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 1.66469 0.629193 0.314596 0.949226i \(-0.398131\pi\)
0.314596 + 0.949226i \(0.398131\pi\)
\(8\) 0.118641 0.0419458
\(9\) 0 0
\(10\) 1.00733 + 1.74475i 0.318547 + 0.551740i
\(11\) −0.745446 −0.224760 −0.112380 0.993665i \(-0.535847\pi\)
−0.112380 + 0.993665i \(0.535847\pi\)
\(12\) 0 0
\(13\) 0.269815 + 0.467333i 0.0748332 + 0.129615i 0.901014 0.433791i \(-0.142824\pi\)
−0.826181 + 0.563405i \(0.809491\pi\)
\(14\) −1.67690 + 2.90447i −0.448170 + 0.776252i
\(15\) 0 0
\(16\) 1.93938 3.35910i 0.484844 0.839775i
\(17\) −0.705067 + 1.22121i −0.171004 + 0.296187i −0.938771 0.344542i \(-0.888034\pi\)
0.767767 + 0.640729i \(0.221368\pi\)
\(18\) 0 0
\(19\) 4.17330 1.25841i 0.957420 0.288700i
\(20\) −2.05889 −0.460381
\(21\) 0 0
\(22\) 0.750913 1.30062i 0.160095 0.277293i
\(23\) −0.437471 0.757722i −0.0912190 0.157996i 0.816805 0.576913i \(-0.195743\pi\)
−0.908024 + 0.418917i \(0.862410\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −1.08718 −0.213213
\(27\) 0 0
\(28\) −1.71370 2.96822i −0.323859 0.560941i
\(29\) 3.70083 + 6.41003i 0.687228 + 1.19031i 0.972731 + 0.231935i \(0.0745058\pi\)
−0.285504 + 0.958378i \(0.592161\pi\)
\(30\) 0 0
\(31\) 7.02934 1.26251 0.631253 0.775577i \(-0.282541\pi\)
0.631253 + 0.775577i \(0.282541\pi\)
\(32\) 4.02584 + 6.97297i 0.711675 + 1.23266i
\(33\) 0 0
\(34\) −1.42048 2.46034i −0.243610 0.421944i
\(35\) 0.832344 1.44166i 0.140692 0.243685i
\(36\) 0 0
\(37\) 7.84476 1.28967 0.644836 0.764321i \(-0.276926\pi\)
0.644836 + 0.764321i \(0.276926\pi\)
\(38\) −2.00828 + 8.54902i −0.325787 + 1.38683i
\(39\) 0 0
\(40\) 0.0593204 0.102746i 0.00937937 0.0162455i
\(41\) 4.36591 7.56198i 0.681841 1.18098i −0.292577 0.956242i \(-0.594513\pi\)
0.974418 0.224742i \(-0.0721538\pi\)
\(42\) 0 0
\(43\) −2.93324 + 5.08052i −0.447315 + 0.774772i −0.998210 0.0598025i \(-0.980953\pi\)
0.550896 + 0.834574i \(0.314286\pi\)
\(44\) 0.767395 + 1.32917i 0.115689 + 0.200380i
\(45\) 0 0
\(46\) 1.76272 0.259899
\(47\) 3.29875 + 5.71360i 0.481172 + 0.833414i 0.999767 0.0216064i \(-0.00687808\pi\)
−0.518595 + 0.855020i \(0.673545\pi\)
\(48\) 0 0
\(49\) −4.22881 −0.604116
\(50\) 2.01467 0.284917
\(51\) 0 0
\(52\) 0.555519 0.962187i 0.0770366 0.133431i
\(53\) 3.85018 + 6.66871i 0.528863 + 0.916018i 0.999434 + 0.0336552i \(0.0107148\pi\)
−0.470570 + 0.882362i \(0.655952\pi\)
\(54\) 0 0
\(55\) −0.372723 + 0.645575i −0.0502580 + 0.0870494i
\(56\) 0.197500 0.0263920
\(57\) 0 0
\(58\) −14.9119 −1.95803
\(59\) 2.45356 4.24969i 0.319426 0.553263i −0.660942 0.750437i \(-0.729843\pi\)
0.980368 + 0.197174i \(0.0631765\pi\)
\(60\) 0 0
\(61\) 2.60473 + 4.51153i 0.333502 + 0.577643i 0.983196 0.182553i \(-0.0584362\pi\)
−0.649694 + 0.760196i \(0.725103\pi\)
\(62\) −7.08089 + 12.2645i −0.899274 + 1.55759i
\(63\) 0 0
\(64\) −8.46397 −1.05800
\(65\) 0.539630 0.0669329
\(66\) 0 0
\(67\) −0.443531 0.768219i −0.0541860 0.0938528i 0.837660 0.546192i \(-0.183923\pi\)
−0.891846 + 0.452339i \(0.850590\pi\)
\(68\) 2.90331 0.352078
\(69\) 0 0
\(70\) 1.67690 + 2.90447i 0.200428 + 0.347151i
\(71\) 1.41061 2.44324i 0.167408 0.289959i −0.770100 0.637923i \(-0.779794\pi\)
0.937508 + 0.347964i \(0.113127\pi\)
\(72\) 0 0
\(73\) −0.524369 + 0.908233i −0.0613727 + 0.106301i −0.895079 0.445907i \(-0.852881\pi\)
0.833707 + 0.552208i \(0.186214\pi\)
\(74\) −7.90230 + 13.6872i −0.918624 + 1.59110i
\(75\) 0 0
\(76\) −6.53999 6.14573i −0.750188 0.704963i
\(77\) −1.24094 −0.141418
\(78\) 0 0
\(79\) −2.88624 + 4.99911i −0.324727 + 0.562444i −0.981457 0.191682i \(-0.938606\pi\)
0.656730 + 0.754126i \(0.271939\pi\)
\(80\) −1.93938 3.35910i −0.216829 0.375559i
\(81\) 0 0
\(82\) 8.79587 + 15.2349i 0.971341 + 1.68241i
\(83\) −3.61555 −0.396858 −0.198429 0.980115i \(-0.563584\pi\)
−0.198429 + 0.980115i \(0.563584\pi\)
\(84\) 0 0
\(85\) 0.705067 + 1.22121i 0.0764752 + 0.132459i
\(86\) −5.90950 10.2356i −0.637238 1.10373i
\(87\) 0 0
\(88\) −0.0884403 −0.00942776
\(89\) −0.464416 0.804392i −0.0492280 0.0852654i 0.840361 0.542026i \(-0.182343\pi\)
−0.889589 + 0.456761i \(0.849009\pi\)
\(90\) 0 0
\(91\) 0.449158 + 0.777964i 0.0470845 + 0.0815528i
\(92\) −0.900704 + 1.56007i −0.0939049 + 0.162648i
\(93\) 0 0
\(94\) −13.2918 −1.37094
\(95\) 0.996831 4.24339i 0.102273 0.435362i
\(96\) 0 0
\(97\) −0.00920110 + 0.0159368i −0.000934230 + 0.00161813i −0.866492 0.499191i \(-0.833631\pi\)
0.865558 + 0.500809i \(0.166964\pi\)
\(98\) 4.25983 7.37824i 0.430308 0.745315i
\(99\) 0 0
\(100\) −1.02944 + 1.78305i −0.102944 + 0.178305i
\(101\) −7.93725 13.7477i −0.789786 1.36795i −0.926098 0.377284i \(-0.876858\pi\)
0.136312 0.990666i \(-0.456475\pi\)
\(102\) 0 0
\(103\) −8.55819 −0.843264 −0.421632 0.906767i \(-0.638543\pi\)
−0.421632 + 0.906767i \(0.638543\pi\)
\(104\) 0.0320110 + 0.0554448i 0.00313894 + 0.00543681i
\(105\) 0 0
\(106\) −15.5137 −1.50682
\(107\) 11.6508 1.12632 0.563162 0.826347i \(-0.309585\pi\)
0.563162 + 0.826347i \(0.309585\pi\)
\(108\) 0 0
\(109\) 1.12075 1.94119i 0.107348 0.185932i −0.807347 0.590077i \(-0.799097\pi\)
0.914695 + 0.404145i \(0.132431\pi\)
\(110\) −0.750913 1.30062i −0.0715968 0.124009i
\(111\) 0 0
\(112\) 3.22846 5.59185i 0.305061 0.528380i
\(113\) −8.94383 −0.841364 −0.420682 0.907208i \(-0.638209\pi\)
−0.420682 + 0.907208i \(0.638209\pi\)
\(114\) 0 0
\(115\) −0.874942 −0.0815888
\(116\) 7.61960 13.1975i 0.707462 1.22536i
\(117\) 0 0
\(118\) 4.94311 + 8.56172i 0.455050 + 0.788170i
\(119\) −1.17372 + 2.03294i −0.107594 + 0.186359i
\(120\) 0 0
\(121\) −10.4443 −0.949483
\(122\) −10.4954 −0.950205
\(123\) 0 0
\(124\) −7.23631 12.5337i −0.649840 1.12556i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 9.91270 + 17.1693i 0.879609 + 1.52353i 0.851770 + 0.523916i \(0.175529\pi\)
0.0278395 + 0.999612i \(0.491137\pi\)
\(128\) 0.474357 0.821611i 0.0419276 0.0726208i
\(129\) 0 0
\(130\) −0.543588 + 0.941522i −0.0476758 + 0.0825769i
\(131\) 0.917977 1.58998i 0.0802040 0.138917i −0.823133 0.567848i \(-0.807776\pi\)
0.903337 + 0.428931i \(0.141109\pi\)
\(132\) 0 0
\(133\) 6.94723 2.09486i 0.602402 0.181648i
\(134\) 1.78714 0.154385
\(135\) 0 0
\(136\) −0.0836496 + 0.144885i −0.00717290 + 0.0124238i
\(137\) 1.98094 + 3.43109i 0.169243 + 0.293138i 0.938154 0.346218i \(-0.112534\pi\)
−0.768911 + 0.639356i \(0.779201\pi\)
\(138\) 0 0
\(139\) 0.889046 + 1.53987i 0.0754079 + 0.130610i 0.901264 0.433271i \(-0.142641\pi\)
−0.825856 + 0.563882i \(0.809307\pi\)
\(140\) −3.42741 −0.289669
\(141\) 0 0
\(142\) 2.84190 + 4.92232i 0.238487 + 0.413072i
\(143\) −0.201133 0.348372i −0.0168196 0.0291323i
\(144\) 0 0
\(145\) 7.40167 0.614675
\(146\) −1.05643 1.82979i −0.0874307 0.151434i
\(147\) 0 0
\(148\) −8.07575 13.9876i −0.663822 1.14977i
\(149\) 9.55320 16.5466i 0.782629 1.35555i −0.147777 0.989021i \(-0.547212\pi\)
0.930405 0.366532i \(-0.119455\pi\)
\(150\) 0 0
\(151\) 2.44644 0.199088 0.0995442 0.995033i \(-0.468262\pi\)
0.0995442 + 0.995033i \(0.468262\pi\)
\(152\) 0.495123 0.149299i 0.0401598 0.0121097i
\(153\) 0 0
\(154\) 1.25004 2.16513i 0.100731 0.174471i
\(155\) 3.51467 6.08758i 0.282305 0.488967i
\(156\) 0 0
\(157\) −4.60586 + 7.97759i −0.367588 + 0.636681i −0.989188 0.146654i \(-0.953150\pi\)
0.621600 + 0.783335i \(0.286483\pi\)
\(158\) −5.81481 10.0715i −0.462601 0.801249i
\(159\) 0 0
\(160\) 8.05169 0.636542
\(161\) −0.728253 1.26137i −0.0573944 0.0994100i
\(162\) 0 0
\(163\) 1.09691 0.0859164 0.0429582 0.999077i \(-0.486322\pi\)
0.0429582 + 0.999077i \(0.486322\pi\)
\(164\) −17.9779 −1.40383
\(165\) 0 0
\(166\) 3.64207 6.30824i 0.282679 0.489615i
\(167\) 6.24438 + 10.8156i 0.483205 + 0.836935i 0.999814 0.0192861i \(-0.00613933\pi\)
−0.516609 + 0.856221i \(0.672806\pi\)
\(168\) 0 0
\(169\) 6.35440 11.0061i 0.488800 0.846626i
\(170\) −2.84095 −0.217891
\(171\) 0 0
\(172\) 12.0784 0.920971
\(173\) 2.15558 3.73357i 0.163886 0.283858i −0.772373 0.635169i \(-0.780931\pi\)
0.936259 + 0.351310i \(0.114264\pi\)
\(174\) 0 0
\(175\) −0.832344 1.44166i −0.0629193 0.108979i
\(176\) −1.44570 + 2.50403i −0.108974 + 0.188748i
\(177\) 0 0
\(178\) 1.87129 0.140259
\(179\) 12.6038 0.942052 0.471026 0.882119i \(-0.343884\pi\)
0.471026 + 0.882119i \(0.343884\pi\)
\(180\) 0 0
\(181\) −1.84534 3.19623i −0.137163 0.237574i 0.789259 0.614061i \(-0.210465\pi\)
−0.926422 + 0.376487i \(0.877132\pi\)
\(182\) −1.80981 −0.134152
\(183\) 0 0
\(184\) −0.0519019 0.0898967i −0.00382626 0.00662727i
\(185\) 3.92238 6.79377i 0.288379 0.499488i
\(186\) 0 0
\(187\) 0.525589 0.910348i 0.0384349 0.0665712i
\(188\) 6.79175 11.7637i 0.495339 0.857953i
\(189\) 0 0
\(190\) 6.39952 + 6.01373i 0.464270 + 0.436282i
\(191\) 6.23634 0.451246 0.225623 0.974215i \(-0.427558\pi\)
0.225623 + 0.974215i \(0.427558\pi\)
\(192\) 0 0
\(193\) 9.46275 16.3900i 0.681143 1.17978i −0.293489 0.955963i \(-0.594816\pi\)
0.974632 0.223813i \(-0.0718503\pi\)
\(194\) −0.0185372 0.0321073i −0.00133089 0.00230517i
\(195\) 0 0
\(196\) 4.35333 + 7.54019i 0.310952 + 0.538585i
\(197\) −6.85139 −0.488141 −0.244071 0.969757i \(-0.578483\pi\)
−0.244071 + 0.969757i \(0.578483\pi\)
\(198\) 0 0
\(199\) −9.99420 17.3105i −0.708470 1.22711i −0.965424 0.260683i \(-0.916052\pi\)
0.256954 0.966424i \(-0.417281\pi\)
\(200\) −0.0593204 0.102746i −0.00419458 0.00726523i
\(201\) 0 0
\(202\) 31.9819 2.25024
\(203\) 6.16073 + 10.6707i 0.432399 + 0.748936i
\(204\) 0 0
\(205\) −4.36591 7.56198i −0.304929 0.528152i
\(206\) 8.62096 14.9319i 0.600651 1.04036i
\(207\) 0 0
\(208\) 2.09309 0.145130
\(209\) −3.11097 + 0.938079i −0.215190 + 0.0648883i
\(210\) 0 0
\(211\) −7.41451 + 12.8423i −0.510436 + 0.884101i 0.489491 + 0.872008i \(0.337183\pi\)
−0.999927 + 0.0120925i \(0.996151\pi\)
\(212\) 7.92709 13.7301i 0.544435 0.942989i
\(213\) 0 0
\(214\) −11.7362 + 20.3278i −0.802272 + 1.38958i
\(215\) 2.93324 + 5.08052i 0.200045 + 0.346488i
\(216\) 0 0
\(217\) 11.7017 0.794360
\(218\) 2.25793 + 3.91085i 0.152926 + 0.264876i
\(219\) 0 0
\(220\) 1.53479 0.103476
\(221\) −0.760951 −0.0511871
\(222\) 0 0
\(223\) 9.44388 16.3573i 0.632409 1.09536i −0.354649 0.934999i \(-0.615400\pi\)
0.987058 0.160365i \(-0.0512670\pi\)
\(224\) 6.70177 + 11.6078i 0.447781 + 0.775579i
\(225\) 0 0
\(226\) 9.00942 15.6048i 0.599298 1.03801i
\(227\) −15.7322 −1.04418 −0.522090 0.852890i \(-0.674848\pi\)
−0.522090 + 0.852890i \(0.674848\pi\)
\(228\) 0 0
\(229\) −19.0417 −1.25831 −0.629157 0.777278i \(-0.716600\pi\)
−0.629157 + 0.777278i \(0.716600\pi\)
\(230\) 0.881359 1.52656i 0.0581151 0.100658i
\(231\) 0 0
\(232\) 0.439070 + 0.760491i 0.0288263 + 0.0499287i
\(233\) 0.594442 1.02960i 0.0389432 0.0674515i −0.845897 0.533346i \(-0.820934\pi\)
0.884840 + 0.465895i \(0.154268\pi\)
\(234\) 0 0
\(235\) 6.59749 0.430373
\(236\) −10.1032 −0.657663
\(237\) 0 0
\(238\) −2.36465 4.09569i −0.153277 0.265484i
\(239\) 25.9446 1.67822 0.839108 0.543965i \(-0.183078\pi\)
0.839108 + 0.543965i \(0.183078\pi\)
\(240\) 0 0
\(241\) 4.52815 + 7.84299i 0.291684 + 0.505211i 0.974208 0.225652i \(-0.0724512\pi\)
−0.682524 + 0.730863i \(0.739118\pi\)
\(242\) 10.5209 18.2228i 0.676310 1.17140i
\(243\) 0 0
\(244\) 5.36286 9.28874i 0.343322 0.594651i
\(245\) −2.11441 + 3.66226i −0.135085 + 0.233973i
\(246\) 0 0
\(247\) 1.71412 + 1.61078i 0.109067 + 0.102492i
\(248\) 0.833966 0.0529569
\(249\) 0 0
\(250\) 1.00733 1.74475i 0.0637094 0.110348i
\(251\) −1.46528 2.53794i −0.0924876 0.160193i 0.816070 0.577954i \(-0.196149\pi\)
−0.908557 + 0.417760i \(0.862815\pi\)
\(252\) 0 0
\(253\) 0.326111 + 0.564841i 0.0205024 + 0.0355113i
\(254\) −39.9416 −2.50616
\(255\) 0 0
\(256\) −7.50830 13.0047i −0.469268 0.812797i
\(257\) −5.42535 9.39698i −0.338424 0.586168i 0.645712 0.763581i \(-0.276561\pi\)
−0.984136 + 0.177413i \(0.943227\pi\)
\(258\) 0 0
\(259\) 13.0591 0.811452
\(260\) −0.555519 0.962187i −0.0344518 0.0596723i
\(261\) 0 0
\(262\) 1.84942 + 3.20329i 0.114257 + 0.197900i
\(263\) 8.42898 14.5994i 0.519753 0.900239i −0.479983 0.877278i \(-0.659357\pi\)
0.999736 0.0229610i \(-0.00730935\pi\)
\(264\) 0 0
\(265\) 7.70036 0.473029
\(266\) −3.34317 + 14.2314i −0.204983 + 0.872586i
\(267\) 0 0
\(268\) −0.913181 + 1.58168i −0.0557814 + 0.0966163i
\(269\) 14.7731 25.5878i 0.900733 1.56012i 0.0741891 0.997244i \(-0.476363\pi\)
0.826544 0.562872i \(-0.190304\pi\)
\(270\) 0 0
\(271\) −10.6224 + 18.3985i −0.645262 + 1.11763i 0.338979 + 0.940794i \(0.389919\pi\)
−0.984241 + 0.176833i \(0.943415\pi\)
\(272\) 2.73478 + 4.73678i 0.165821 + 0.287210i
\(273\) 0 0
\(274\) −7.98188 −0.482203
\(275\) 0.372723 + 0.645575i 0.0224760 + 0.0389297i
\(276\) 0 0
\(277\) −28.3656 −1.70432 −0.852161 0.523279i \(-0.824708\pi\)
−0.852161 + 0.523279i \(0.824708\pi\)
\(278\) −3.58226 −0.214850
\(279\) 0 0
\(280\) 0.0987499 0.171040i 0.00590143 0.0102216i
\(281\) 8.80909 + 15.2578i 0.525506 + 0.910204i 0.999559 + 0.0297069i \(0.00945740\pi\)
−0.474052 + 0.880497i \(0.657209\pi\)
\(282\) 0 0
\(283\) 8.54552 14.8013i 0.507978 0.879844i −0.491979 0.870607i \(-0.663726\pi\)
0.999957 0.00923712i \(-0.00294031\pi\)
\(284\) −5.80856 −0.344675
\(285\) 0 0
\(286\) 0.810431 0.0479218
\(287\) 7.26788 12.5883i 0.429010 0.743066i
\(288\) 0 0
\(289\) 7.50576 + 13.0004i 0.441515 + 0.764727i
\(290\) −7.45595 + 12.9141i −0.437829 + 0.758341i
\(291\) 0 0
\(292\) 2.15923 0.126360
\(293\) −22.2555 −1.30018 −0.650089 0.759858i \(-0.725268\pi\)
−0.650089 + 0.759858i \(0.725268\pi\)
\(294\) 0 0
\(295\) −2.45356 4.24969i −0.142852 0.247427i
\(296\) 0.930708 0.0540963
\(297\) 0 0
\(298\) 19.2465 + 33.3360i 1.11492 + 1.93110i
\(299\) 0.236073 0.408890i 0.0136524 0.0236467i
\(300\) 0 0
\(301\) −4.88293 + 8.45747i −0.281447 + 0.487481i
\(302\) −2.46438 + 4.26843i −0.141809 + 0.245621i
\(303\) 0 0
\(304\) 3.86646 16.4591i 0.221757 0.943992i
\(305\) 5.20947 0.298293
\(306\) 0 0
\(307\) 13.2964 23.0300i 0.758863 1.31439i −0.184568 0.982820i \(-0.559088\pi\)
0.943431 0.331570i \(-0.107578\pi\)
\(308\) 1.27747 + 2.21265i 0.0727908 + 0.126077i
\(309\) 0 0
\(310\) 7.08089 + 12.2645i 0.402168 + 0.696575i
\(311\) −11.1894 −0.634493 −0.317247 0.948343i \(-0.602758\pi\)
−0.317247 + 0.948343i \(0.602758\pi\)
\(312\) 0 0
\(313\) −10.2321 17.7225i −0.578351 1.00173i −0.995669 0.0929730i \(-0.970363\pi\)
0.417317 0.908761i \(-0.362970\pi\)
\(314\) −9.27928 16.0722i −0.523660 0.907006i
\(315\) 0 0
\(316\) 11.8849 0.668577
\(317\) −7.76650 13.4520i −0.436210 0.755538i 0.561183 0.827692i \(-0.310346\pi\)
−0.997394 + 0.0721532i \(0.977013\pi\)
\(318\) 0 0
\(319\) −2.75877 4.77833i −0.154462 0.267535i
\(320\) −4.23198 + 7.33001i −0.236575 + 0.409760i
\(321\) 0 0
\(322\) 2.93438 0.163526
\(323\) −1.40567 + 5.98374i −0.0782133 + 0.332944i
\(324\) 0 0
\(325\) 0.269815 0.467333i 0.0149666 0.0259230i
\(326\) −1.10495 + 1.91383i −0.0611976 + 0.105997i
\(327\) 0 0
\(328\) 0.517975 0.897159i 0.0286004 0.0495373i
\(329\) 5.49138 + 9.51135i 0.302750 + 0.524378i
\(330\) 0 0
\(331\) −16.3063 −0.896278 −0.448139 0.893964i \(-0.647913\pi\)
−0.448139 + 0.893964i \(0.647913\pi\)
\(332\) 3.72201 + 6.44670i 0.204272 + 0.353809i
\(333\) 0 0
\(334\) −25.1607 −1.37673
\(335\) −0.887063 −0.0484654
\(336\) 0 0
\(337\) −14.5604 + 25.2193i −0.793155 + 1.37378i 0.130849 + 0.991402i \(0.458230\pi\)
−0.924004 + 0.382382i \(0.875104\pi\)
\(338\) 12.8020 + 22.1737i 0.696337 + 1.20609i
\(339\) 0 0
\(340\) 1.45165 2.51434i 0.0787270 0.136359i
\(341\) −5.23999 −0.283761
\(342\) 0 0
\(343\) −18.6925 −1.00930
\(344\) −0.348001 + 0.602756i −0.0187630 + 0.0324984i
\(345\) 0 0
\(346\) 4.34278 + 7.52191i 0.233469 + 0.404381i
\(347\) 1.36152 2.35823i 0.0730904 0.126596i −0.827164 0.561961i \(-0.810047\pi\)
0.900254 + 0.435364i \(0.143380\pi\)
\(348\) 0 0
\(349\) −5.70995 −0.305647 −0.152823 0.988254i \(-0.548837\pi\)
−0.152823 + 0.988254i \(0.548837\pi\)
\(350\) 3.35379 0.179268
\(351\) 0 0
\(352\) −3.00105 5.19797i −0.159956 0.277053i
\(353\) −27.6435 −1.47131 −0.735657 0.677354i \(-0.763126\pi\)
−0.735657 + 0.677354i \(0.763126\pi\)
\(354\) 0 0
\(355\) −1.41061 2.44324i −0.0748672 0.129674i
\(356\) −0.956181 + 1.65615i −0.0506775 + 0.0877760i
\(357\) 0 0
\(358\) −12.6962 + 21.9905i −0.671017 + 1.16224i
\(359\) 2.11633 3.66559i 0.111696 0.193463i −0.804758 0.593603i \(-0.797705\pi\)
0.916454 + 0.400140i \(0.131038\pi\)
\(360\) 0 0
\(361\) 15.8328 10.5035i 0.833305 0.552813i
\(362\) 7.43550 0.390801
\(363\) 0 0
\(364\) 0.924766 1.60174i 0.0484709 0.0839540i
\(365\) 0.524369 + 0.908233i 0.0274467 + 0.0475391i
\(366\) 0 0
\(367\) −0.769642 1.33306i −0.0401750 0.0695852i 0.845239 0.534389i \(-0.179458\pi\)
−0.885414 + 0.464804i \(0.846125\pi\)
\(368\) −3.39369 −0.176908
\(369\) 0 0
\(370\) 7.90230 + 13.6872i 0.410821 + 0.711563i
\(371\) 6.40935 + 11.1013i 0.332757 + 0.576352i
\(372\) 0 0
\(373\) 0.490289 0.0253862 0.0126931 0.999919i \(-0.495960\pi\)
0.0126931 + 0.999919i \(0.495960\pi\)
\(374\) 1.05889 + 1.83405i 0.0547538 + 0.0948364i
\(375\) 0 0
\(376\) 0.391366 + 0.677865i 0.0201831 + 0.0349582i
\(377\) −1.99708 + 3.45905i −0.102855 + 0.178150i
\(378\) 0 0
\(379\) −34.6250 −1.77857 −0.889283 0.457358i \(-0.848796\pi\)
−0.889283 + 0.457358i \(0.848796\pi\)
\(380\) −8.59235 + 2.59093i −0.440778 + 0.132912i
\(381\) 0 0
\(382\) −6.28208 + 10.8809i −0.321419 + 0.556714i
\(383\) −11.9762 + 20.7433i −0.611953 + 1.05993i 0.378958 + 0.925414i \(0.376283\pi\)
−0.990911 + 0.134520i \(0.957051\pi\)
\(384\) 0 0
\(385\) −0.620468 + 1.07468i −0.0316220 + 0.0547708i
\(386\) 19.0643 + 33.0203i 0.970347 + 1.68069i
\(387\) 0 0
\(388\) 0.0378881 0.00192348
\(389\) −8.75864 15.1704i −0.444081 0.769171i 0.553907 0.832579i \(-0.313136\pi\)
−0.997988 + 0.0634081i \(0.979803\pi\)
\(390\) 0 0
\(391\) 1.23379 0.0623952
\(392\) −0.501710 −0.0253402
\(393\) 0 0
\(394\) 6.90164 11.9540i 0.347699 0.602233i
\(395\) 2.88624 + 4.99911i 0.145222 + 0.251532i
\(396\) 0 0
\(397\) −4.44472 + 7.69848i −0.223074 + 0.386376i −0.955740 0.294213i \(-0.904943\pi\)
0.732666 + 0.680589i \(0.238276\pi\)
\(398\) 40.2700 2.01855
\(399\) 0 0
\(400\) −3.87876 −0.193938
\(401\) −18.1428 + 31.4242i −0.906007 + 1.56925i −0.0864475 + 0.996256i \(0.527551\pi\)
−0.819560 + 0.572994i \(0.805782\pi\)
\(402\) 0 0
\(403\) 1.89662 + 3.28504i 0.0944774 + 0.163640i
\(404\) −16.3419 + 28.3050i −0.813041 + 1.40823i
\(405\) 0 0
\(406\) −24.8237 −1.23198
\(407\) −5.84785 −0.289867
\(408\) 0 0
\(409\) 8.69791 + 15.0652i 0.430084 + 0.744928i 0.996880 0.0789306i \(-0.0251505\pi\)
−0.566796 + 0.823858i \(0.691817\pi\)
\(410\) 17.5917 0.868794
\(411\) 0 0
\(412\) 8.81018 + 15.2597i 0.434046 + 0.751790i
\(413\) 4.08441 7.07441i 0.200981 0.348109i
\(414\) 0 0
\(415\) −1.80777 + 3.13116i −0.0887402 + 0.153702i
\(416\) −2.17247 + 3.76282i −0.106514 + 0.184487i
\(417\) 0 0
\(418\) 1.49707 6.37283i 0.0732240 0.311705i
\(419\) 30.9259 1.51083 0.755414 0.655248i \(-0.227436\pi\)
0.755414 + 0.655248i \(0.227436\pi\)
\(420\) 0 0
\(421\) 5.81345 10.0692i 0.283330 0.490742i −0.688873 0.724882i \(-0.741894\pi\)
0.972203 + 0.234140i \(0.0752275\pi\)
\(422\) −14.9378 25.8730i −0.727160 1.25948i
\(423\) 0 0
\(424\) 0.456788 + 0.791180i 0.0221836 + 0.0384231i
\(425\) 1.41013 0.0684015
\(426\) 0 0
\(427\) 4.33607 + 7.51029i 0.209837 + 0.363449i
\(428\) −11.9938 20.7739i −0.579744 1.00415i
\(429\) 0 0
\(430\) −11.8190 −0.569963
\(431\) 12.2150 + 21.1569i 0.588374 + 1.01909i 0.994446 + 0.105252i \(0.0335650\pi\)
−0.406072 + 0.913841i \(0.633102\pi\)
\(432\) 0 0
\(433\) −10.4503 18.1004i −0.502208 0.869851i −0.999997 0.00255203i \(-0.999188\pi\)
0.497788 0.867299i \(-0.334146\pi\)
\(434\) −11.7875 + 20.4165i −0.565817 + 0.980023i
\(435\) 0 0
\(436\) −4.61498 −0.221017
\(437\) −2.77922 2.61168i −0.132948 0.124934i
\(438\) 0 0
\(439\) −8.21019 + 14.2205i −0.391851 + 0.678706i −0.992694 0.120661i \(-0.961498\pi\)
0.600843 + 0.799367i \(0.294832\pi\)
\(440\) −0.0442201 + 0.0765915i −0.00210811 + 0.00365136i
\(441\) 0 0
\(442\) 0.766531 1.32767i 0.0364602 0.0631509i
\(443\) 1.32291 + 2.29135i 0.0628533 + 0.108865i 0.895740 0.444579i \(-0.146647\pi\)
−0.832886 + 0.553444i \(0.813313\pi\)
\(444\) 0 0
\(445\) −0.928832 −0.0440309
\(446\) 19.0263 + 32.9545i 0.900920 + 1.56044i
\(447\) 0 0
\(448\) −14.0899 −0.665683
\(449\) −8.17261 −0.385689 −0.192845 0.981229i \(-0.561771\pi\)
−0.192845 + 0.981229i \(0.561771\pi\)
\(450\) 0 0
\(451\) −3.25455 + 5.63705i −0.153251 + 0.265438i
\(452\) 9.20717 + 15.9473i 0.433069 + 0.750097i
\(453\) 0 0
\(454\) 15.8476 27.4488i 0.743763 1.28823i
\(455\) 0.898315 0.0421137
\(456\) 0 0
\(457\) −8.94164 −0.418272 −0.209136 0.977887i \(-0.567065\pi\)
−0.209136 + 0.977887i \(0.567065\pi\)
\(458\) 19.1814 33.2232i 0.896288 1.55242i
\(459\) 0 0
\(460\) 0.900704 + 1.56007i 0.0419956 + 0.0727384i
\(461\) −8.82526 + 15.2858i −0.411033 + 0.711930i −0.995003 0.0998450i \(-0.968165\pi\)
0.583970 + 0.811775i \(0.301499\pi\)
\(462\) 0 0
\(463\) −20.8670 −0.969771 −0.484885 0.874578i \(-0.661139\pi\)
−0.484885 + 0.874578i \(0.661139\pi\)
\(464\) 28.7093 1.33279
\(465\) 0 0
\(466\) 1.19760 + 2.07431i 0.0554779 + 0.0960905i
\(467\) 24.4820 1.13289 0.566445 0.824099i \(-0.308318\pi\)
0.566445 + 0.824099i \(0.308318\pi\)
\(468\) 0 0
\(469\) −0.738341 1.27884i −0.0340934 0.0590515i
\(470\) −6.64588 + 11.5110i −0.306552 + 0.530963i
\(471\) 0 0
\(472\) 0.291092 0.504186i 0.0133986 0.0232071i
\(473\) 2.18657 3.78725i 0.100539 0.174138i
\(474\) 0 0
\(475\) −3.17646 2.98497i −0.145746 0.136960i
\(476\) 4.83310 0.221525
\(477\) 0 0
\(478\) −26.1349 + 45.2669i −1.19538 + 2.07046i
\(479\) 1.65218 + 2.86165i 0.0754898 + 0.130752i 0.901299 0.433197i \(-0.142615\pi\)
−0.825809 + 0.563949i \(0.809281\pi\)
\(480\) 0 0
\(481\) 2.11664 + 3.66612i 0.0965103 + 0.167161i
\(482\) −18.2454 −0.831057
\(483\) 0 0
\(484\) 10.7518 + 18.6227i 0.488720 + 0.846487i
\(485\) 0.00920110 + 0.0159368i 0.000417800 + 0.000723652i
\(486\) 0 0
\(487\) 32.6648 1.48019 0.740093 0.672505i \(-0.234782\pi\)
0.740093 + 0.672505i \(0.234782\pi\)
\(488\) 0.309028 + 0.535252i 0.0139890 + 0.0242297i
\(489\) 0 0
\(490\) −4.25983 7.37824i −0.192439 0.333315i
\(491\) −6.51626 + 11.2865i −0.294075 + 0.509352i −0.974769 0.223215i \(-0.928345\pi\)
0.680694 + 0.732567i \(0.261678\pi\)
\(492\) 0 0
\(493\) −10.4373 −0.470074
\(494\) −4.53710 + 1.36811i −0.204134 + 0.0615544i
\(495\) 0 0
\(496\) 13.6325 23.6122i 0.612119 1.06022i
\(497\) 2.34822 4.06723i 0.105332 0.182440i
\(498\) 0 0
\(499\) −15.1552 + 26.2496i −0.678441 + 1.17509i 0.297009 + 0.954875i \(0.404011\pi\)
−0.975450 + 0.220220i \(0.929323\pi\)
\(500\) 1.02944 + 1.78305i 0.0460381 + 0.0797404i
\(501\) 0 0
\(502\) 5.90411 0.263513
\(503\) 19.0259 + 32.9539i 0.848324 + 1.46934i 0.882703 + 0.469931i \(0.155721\pi\)
−0.0343796 + 0.999409i \(0.510946\pi\)
\(504\) 0 0
\(505\) −15.8745 −0.706406
\(506\) −1.31401 −0.0584150
\(507\) 0 0
\(508\) 20.4091 35.3497i 0.905509 1.56839i
\(509\) −11.8719 20.5627i −0.526212 0.911427i −0.999534 0.0305368i \(-0.990278\pi\)
0.473321 0.880890i \(-0.343055\pi\)
\(510\) 0 0
\(511\) −0.872910 + 1.51192i −0.0386153 + 0.0668836i
\(512\) 32.1509 1.42088
\(513\) 0 0
\(514\) 21.8606 0.964228
\(515\) −4.27910 + 7.41161i −0.188559 + 0.326595i
\(516\) 0 0
\(517\) −2.45904 4.25918i −0.108148 0.187318i
\(518\) −13.1549 + 22.7849i −0.577991 + 1.00111i
\(519\) 0 0
\(520\) 0.0640221 0.00280755
\(521\) −29.8052 −1.30579 −0.652896 0.757448i \(-0.726446\pi\)
−0.652896 + 0.757448i \(0.726446\pi\)
\(522\) 0 0
\(523\) −2.97546 5.15365i −0.130108 0.225353i 0.793610 0.608427i \(-0.208199\pi\)
−0.923718 + 0.383073i \(0.874866\pi\)
\(524\) −3.78002 −0.165131
\(525\) 0 0
\(526\) 16.9816 + 29.4130i 0.740433 + 1.28247i
\(527\) −4.95615 + 8.58431i −0.215893 + 0.373938i
\(528\) 0 0
\(529\) 11.1172 19.2556i 0.483358 0.837201i
\(530\) −7.75684 + 13.4352i −0.336936 + 0.583589i
\(531\) 0 0
\(532\) −10.8870 10.2307i −0.472013 0.443558i
\(533\) 4.71196 0.204097
\(534\) 0 0
\(535\) 5.82539 10.0899i 0.251854 0.436223i
\(536\) −0.0526209 0.0911420i −0.00227288 0.00393674i
\(537\) 0 0
\(538\) 29.7629 + 51.5509i 1.28317 + 2.22252i
\(539\) 3.15235 0.135781
\(540\) 0 0
\(541\) −2.20614 3.82115i −0.0948496 0.164284i 0.814696 0.579888i \(-0.196904\pi\)
−0.909546 + 0.415604i \(0.863570\pi\)
\(542\) −21.4005 37.0668i −0.919231 1.59216i
\(543\) 0 0
\(544\) −11.3540 −0.486797
\(545\) −1.12075 1.94119i −0.0480075 0.0831514i
\(546\) 0 0
\(547\) −22.2986 38.6224i −0.953421 1.65137i −0.737942 0.674865i \(-0.764202\pi\)
−0.215479 0.976508i \(-0.569131\pi\)
\(548\) 4.07854 7.06424i 0.174227 0.301769i
\(549\) 0 0
\(550\) −1.50183 −0.0640381
\(551\) 23.5111 + 22.0938i 1.00161 + 0.941227i
\(552\) 0 0
\(553\) −4.80468 + 8.32195i −0.204316 + 0.353885i
\(554\) 28.5736 49.4910i 1.21398 2.10267i
\(555\) 0 0
\(556\) 1.83045 3.17043i 0.0776282 0.134456i
\(557\) −6.46476 11.1973i −0.273921 0.474444i 0.695942 0.718098i \(-0.254987\pi\)
−0.969862 + 0.243654i \(0.921654\pi\)
\(558\) 0 0
\(559\) −3.16573 −0.133896
\(560\) −3.22846 5.59185i −0.136427 0.236299i
\(561\) 0 0
\(562\) −35.4948 −1.49726
\(563\) −31.7105 −1.33644 −0.668219 0.743964i \(-0.732943\pi\)
−0.668219 + 0.743964i \(0.732943\pi\)
\(564\) 0 0
\(565\) −4.47191 + 7.74558i −0.188135 + 0.325859i
\(566\) 17.2164 + 29.8196i 0.723659 + 1.25341i
\(567\) 0 0
\(568\) 0.167355 0.289868i 0.00702207 0.0121626i
\(569\) −28.4382 −1.19219 −0.596095 0.802914i \(-0.703282\pi\)
−0.596095 + 0.802914i \(0.703282\pi\)
\(570\) 0 0
\(571\) −7.32088 −0.306369 −0.153185 0.988198i \(-0.548953\pi\)
−0.153185 + 0.988198i \(0.548953\pi\)
\(572\) −0.414110 + 0.717259i −0.0173148 + 0.0299901i
\(573\) 0 0
\(574\) 14.6424 + 25.3613i 0.611161 + 1.05856i
\(575\) −0.437471 + 0.757722i −0.0182438 + 0.0315992i
\(576\) 0 0
\(577\) −13.8157 −0.575156 −0.287578 0.957757i \(-0.592850\pi\)
−0.287578 + 0.957757i \(0.592850\pi\)
\(578\) −30.2432 −1.25795
\(579\) 0 0
\(580\) −7.61960 13.1975i −0.316387 0.547998i
\(581\) −6.01876 −0.249700
\(582\) 0 0
\(583\) −2.87010 4.97116i −0.118868 0.205885i
\(584\) −0.0622115 + 0.107753i −0.00257433 + 0.00445887i
\(585\) 0 0
\(586\) 22.4187 38.8303i 0.926108 1.60407i
\(587\) 9.94338 17.2224i 0.410407 0.710846i −0.584527 0.811374i \(-0.698720\pi\)
0.994934 + 0.100528i \(0.0320533\pi\)
\(588\) 0 0
\(589\) 29.3355 8.84580i 1.20875 0.364485i
\(590\) 9.88622 0.407009
\(591\) 0 0
\(592\) 15.2140 26.3514i 0.625290 1.08303i
\(593\) −4.92452 8.52952i −0.202226 0.350266i 0.747019 0.664802i \(-0.231484\pi\)
−0.949245 + 0.314537i \(0.898151\pi\)
\(594\) 0 0
\(595\) 1.17372 + 2.03294i 0.0481177 + 0.0833423i
\(596\) −39.3380 −1.61135
\(597\) 0 0
\(598\) 0.475608 + 0.823777i 0.0194491 + 0.0336867i
\(599\) −3.58661 6.21220i −0.146545 0.253823i 0.783403 0.621514i \(-0.213482\pi\)
−0.929948 + 0.367690i \(0.880149\pi\)
\(600\) 0 0
\(601\) 39.2040 1.59916 0.799582 0.600557i \(-0.205054\pi\)
0.799582 + 0.600557i \(0.205054\pi\)
\(602\) −9.83747 17.0390i −0.400946 0.694458i
\(603\) 0 0
\(604\) −2.51847 4.36212i −0.102475 0.177492i
\(605\) −5.22215 + 9.04504i −0.212311 + 0.367733i
\(606\) 0 0
\(607\) 44.1741 1.79297 0.896485 0.443074i \(-0.146112\pi\)
0.896485 + 0.443074i \(0.146112\pi\)
\(608\) 25.5759 + 24.0341i 1.03724 + 0.974711i
\(609\) 0 0
\(610\) −5.24768 + 9.08924i −0.212472 + 0.368013i
\(611\) −1.78010 + 3.08323i −0.0720152 + 0.124734i
\(612\) 0 0
\(613\) 3.75407 6.50224i 0.151625 0.262623i −0.780200 0.625531i \(-0.784883\pi\)
0.931825 + 0.362907i \(0.118216\pi\)
\(614\) 26.7877 + 46.3977i 1.08107 + 1.87246i
\(615\) 0 0
\(616\) −0.147225 −0.00593188
\(617\) 7.53673 + 13.0540i 0.303417 + 0.525534i 0.976908 0.213662i \(-0.0685390\pi\)
−0.673490 + 0.739196i \(0.735206\pi\)
\(618\) 0 0
\(619\) 43.5536 1.75057 0.875283 0.483610i \(-0.160675\pi\)
0.875283 + 0.483610i \(0.160675\pi\)
\(620\) −14.4726 −0.581234
\(621\) 0 0
\(622\) 11.2715 19.5228i 0.451945 0.782792i
\(623\) −0.773108 1.33906i −0.0309739 0.0536484i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 41.2285 1.64782
\(627\) 0 0
\(628\) 18.9659 0.756822
\(629\) −5.53108 + 9.58012i −0.220539 + 0.381984i
\(630\) 0 0
\(631\) −13.9200 24.1101i −0.554146 0.959809i −0.997969 0.0636948i \(-0.979712\pi\)
0.443823 0.896114i \(-0.353622\pi\)
\(632\) −0.342425 + 0.593098i −0.0136209 + 0.0235922i
\(633\) 0 0
\(634\) 31.2939 1.24284
\(635\) 19.8254 0.786747
\(636\) 0 0
\(637\) −1.14100 1.97627i −0.0452080 0.0783025i
\(638\) 11.1160 0.440088
\(639\) 0 0
\(640\) −0.474357 0.821611i −0.0187506 0.0324770i
\(641\) 2.21833 3.84226i 0.0876187 0.151760i −0.818885 0.573957i \(-0.805408\pi\)
0.906504 + 0.422197i \(0.138741\pi\)
\(642\) 0 0
\(643\) 3.32952 5.76690i 0.131304 0.227425i −0.792876 0.609383i \(-0.791417\pi\)
0.924179 + 0.381959i \(0.124750\pi\)
\(644\) −1.49939 + 2.59702i −0.0590843 + 0.102337i
\(645\) 0 0
\(646\) −9.02418 8.48017i −0.355052 0.333648i
\(647\) −1.27795 −0.0502415 −0.0251208 0.999684i \(-0.507997\pi\)
−0.0251208 + 0.999684i \(0.507997\pi\)
\(648\) 0 0
\(649\) −1.82900 + 3.16792i −0.0717944 + 0.124352i
\(650\) 0.543588 + 0.941522i 0.0213213 + 0.0369295i
\(651\) 0 0
\(652\) −1.12920 1.95584i −0.0442231 0.0765966i
\(653\) −45.2709 −1.77159 −0.885795 0.464078i \(-0.846386\pi\)
−0.885795 + 0.464078i \(0.846386\pi\)
\(654\) 0 0
\(655\) −0.917977 1.58998i −0.0358683 0.0621257i
\(656\) −16.9343 29.3311i −0.661174 1.14519i
\(657\) 0 0
\(658\) −22.1266 −0.862586
\(659\) −6.80538 11.7873i −0.265100 0.459167i 0.702490 0.711694i \(-0.252072\pi\)
−0.967590 + 0.252527i \(0.918738\pi\)
\(660\) 0 0
\(661\) 14.5259 + 25.1596i 0.564991 + 0.978594i 0.997050 + 0.0767486i \(0.0244539\pi\)
−0.432059 + 0.901845i \(0.642213\pi\)
\(662\) 16.4259 28.4506i 0.638412 1.10576i
\(663\) 0 0
\(664\) −0.428951 −0.0166465
\(665\) 1.65941 7.06391i 0.0643493 0.273927i
\(666\) 0 0
\(667\) 3.23802 5.60841i 0.125376 0.217158i
\(668\) 12.8565 22.2681i 0.497432 0.861578i
\(669\) 0 0
\(670\) 0.893568 1.54771i 0.0345216 0.0597931i
\(671\) −1.94169 3.36311i −0.0749581 0.129831i
\(672\) 0 0
\(673\) −13.4534 −0.518591 −0.259296 0.965798i \(-0.583490\pi\)
−0.259296 + 0.965798i \(0.583490\pi\)
\(674\) −29.3344 50.8086i −1.12992 1.95707i
\(675\) 0 0
\(676\) −26.1660 −1.00638
\(677\) −48.1048 −1.84882 −0.924409 0.381404i \(-0.875441\pi\)
−0.924409 + 0.381404i \(0.875441\pi\)
\(678\) 0 0
\(679\) −0.0153170 + 0.0265298i −0.000587811 + 0.00101812i
\(680\) 0.0836496 + 0.144885i 0.00320782 + 0.00555610i
\(681\) 0 0
\(682\) 5.27842 9.14250i 0.202121 0.350084i
\(683\) 31.7434 1.21463 0.607314 0.794462i \(-0.292247\pi\)
0.607314 + 0.794462i \(0.292247\pi\)
\(684\) 0 0
\(685\) 3.96188 0.151376
\(686\) 18.8296 32.6138i 0.718916 1.24520i
\(687\) 0 0
\(688\) 11.3773 + 19.7061i 0.433756 + 0.751287i
\(689\) −2.07767 + 3.59864i −0.0791530 + 0.137097i
\(690\) 0 0
\(691\) 5.63348 0.214308 0.107154 0.994242i \(-0.465826\pi\)
0.107154 + 0.994242i \(0.465826\pi\)
\(692\) −8.87620 −0.337422
\(693\) 0 0
\(694\) 2.74302 + 4.75105i 0.104124 + 0.180347i
\(695\) 1.77809 0.0674469
\(696\) 0 0
\(697\) 6.15652 + 10.6634i 0.233195 + 0.403905i
\(698\) 5.75183 9.96246i 0.217710 0.377085i
\(699\) 0 0
\(700\) −1.71370 + 2.96822i −0.0647719 + 0.112188i
\(701\) 14.9878 25.9596i 0.566080 0.980480i −0.430868 0.902415i \(-0.641793\pi\)
0.996948 0.0780649i \(-0.0248741\pi\)
\(702\) 0 0
\(703\) 32.7385 9.87195i 1.23476 0.372328i
\(704\) 6.30943 0.237796
\(705\) 0 0
\(706\) 27.8462 48.2311i 1.04801 1.81520i
\(707\) −13.2130 22.8857i −0.496928 0.860704i
\(708\) 0 0
\(709\) −1.14344 1.98050i −0.0429429 0.0743793i 0.843755 0.536728i \(-0.180340\pi\)
−0.886698 + 0.462349i \(0.847007\pi\)
\(710\) 5.68380 0.213309
\(711\) 0 0
\(712\) −0.0550987 0.0954337i −0.00206491 0.00357653i
\(713\) −3.07513 5.32628i −0.115165 0.199471i
\(714\) 0 0
\(715\) −0.402265 −0.0150439
\(716\) −12.9749 22.4732i −0.484895 0.839863i
\(717\) 0 0
\(718\) 4.26370 + 7.38495i 0.159120 + 0.275604i
\(719\) −22.1981 + 38.4483i −0.827850 + 1.43388i 0.0718716 + 0.997414i \(0.477103\pi\)
−0.899722 + 0.436464i \(0.856231\pi\)
\(720\) 0 0
\(721\) −14.2467 −0.530575
\(722\) 2.37702 + 38.2048i 0.0884636 + 1.42184i
\(723\) 0 0
\(724\) −3.79935 + 6.58067i −0.141202 + 0.244569i
\(725\) 3.70083 6.41003i 0.137446 0.238063i
\(726\) 0 0
\(727\) 4.39956 7.62026i 0.163171 0.282620i −0.772834 0.634609i \(-0.781161\pi\)
0.936004 + 0.351989i \(0.114495\pi\)
\(728\) 0.0532884 + 0.0922982i 0.00197500 + 0.00342080i
\(729\) 0 0
\(730\) −2.11286 −0.0782004
\(731\) −4.13626 7.16421i −0.152985 0.264978i
\(732\) 0 0
\(733\) 28.5385 1.05409 0.527047 0.849836i \(-0.323299\pi\)
0.527047 + 0.849836i \(0.323299\pi\)
\(734\) 3.10115 0.114465
\(735\) 0 0
\(736\) 3.52238 6.10094i 0.129837 0.224884i
\(737\) 0.330629 + 0.572666i 0.0121789 + 0.0210944i
\(738\) 0 0
\(739\) 5.16208 8.94099i 0.189890 0.328900i −0.755323 0.655352i \(-0.772520\pi\)
0.945213 + 0.326453i \(0.105853\pi\)
\(740\) −16.1515 −0.593741
\(741\) 0 0
\(742\) −25.8254 −0.948081
\(743\) −13.5295 + 23.4339i −0.496351 + 0.859705i −0.999991 0.00420839i \(-0.998660\pi\)
0.503640 + 0.863914i \(0.331994\pi\)
\(744\) 0 0
\(745\) −9.55320 16.5466i −0.350002 0.606222i
\(746\) −0.493885 + 0.855434i −0.0180824 + 0.0313196i
\(747\) 0 0
\(748\) −2.16426 −0.0791332
\(749\) 19.3949 0.708675
\(750\) 0 0
\(751\) 25.9995 + 45.0325i 0.948735 + 1.64326i 0.748093 + 0.663593i \(0.230969\pi\)
0.200642 + 0.979665i \(0.435697\pi\)
\(752\) 25.5901 0.933173
\(753\) 0 0
\(754\) −4.02346 6.96883i −0.146526 0.253790i
\(755\) 1.22322 2.11868i 0.0445175 0.0771066i
\(756\) 0 0
\(757\) −26.7487 + 46.3301i −0.972199 + 1.68390i −0.283313 + 0.959028i \(0.591433\pi\)
−0.688886 + 0.724870i \(0.741900\pi\)
\(758\) 34.8789 60.4121i 1.26686 2.19427i
\(759\) 0 0
\(760\) 0.118265 0.503438i 0.00428991 0.0182616i
\(761\) −33.8123 −1.22569 −0.612847 0.790201i \(-0.709976\pi\)
−0.612847 + 0.790201i \(0.709976\pi\)
\(762\) 0 0
\(763\) 1.86569 3.23147i 0.0675426 0.116987i
\(764\) −6.41996 11.1197i −0.232266 0.402297i
\(765\) 0 0
\(766\) −24.1280 41.7909i −0.871780 1.50997i
\(767\) 2.64803 0.0956148
\(768\) 0 0
\(769\) 3.09718 + 5.36447i 0.111687 + 0.193448i 0.916451 0.400148i \(-0.131041\pi\)
−0.804763 + 0.593596i \(0.797708\pi\)
\(770\) −1.25004 2.16513i −0.0450482 0.0780257i
\(771\) 0 0
\(772\) −38.9655 −1.40240
\(773\) −4.36013 7.55197i −0.156823 0.271626i 0.776898 0.629626i \(-0.216792\pi\)
−0.933721 + 0.358001i \(0.883459\pi\)
\(774\) 0 0
\(775\) −3.51467 6.08758i −0.126251 0.218672i
\(776\) −0.00109163 + 0.00189075i −3.91871e−5 + 6.78740e-5i
\(777\) 0 0
\(778\) 35.2915 1.26526
\(779\) 8.70416 37.0525i 0.311859 1.32754i
\(780\) 0 0
\(781\) −1.05153 + 1.82130i −0.0376267 + 0.0651714i
\(782\) −1.24283 + 2.15265i −0.0444437 + 0.0769787i
\(783\) 0 0
\(784\) −8.20127 + 14.2050i −0.292902 + 0.507322i
\(785\) 4.60586 + 7.97759i 0.164390 + 0.284732i
\(786\) 0 0
\(787\) −1.67992 −0.0598826 −0.0299413 0.999552i \(-0.509532\pi\)
−0.0299413 + 0.999552i \(0.509532\pi\)
\(788\) 7.05312 + 12.2164i 0.251257 + 0.435190i
\(789\) 0 0
\(790\) −11.6296 −0.413763
\(791\) −14.8887 −0.529380
\(792\) 0 0
\(793\) −1.40559 + 2.43456i −0.0499141 + 0.0864537i
\(794\) −8.95464 15.5099i −0.317788 0.550425i
\(795\) 0 0
\(796\) −20.5769 + 35.6403i −0.729331 + 1.26324i
\(797\) 15.8793 0.562475 0.281237 0.959638i \(-0.409255\pi\)
0.281237 + 0.959638i \(0.409255\pi\)
\(798\) 0 0
\(799\) −9.30335 −0.329129
\(800\) 4.02584 6.97297i 0.142335 0.246532i
\(801\) 0 0
\(802\) −36.5517 63.3094i −1.29068 2.23553i
\(803\) 0.390889 0.677039i 0.0137942 0.0238922i
\(804\) 0 0
\(805\) −1.45651 −0.0513351
\(806\) −7.64212 −0.269182
\(807\) 0 0
\(808\) −0.941681 1.63104i −0.0331282 0.0573798i
\(809\) 47.8983 1.68402 0.842008 0.539465i \(-0.181373\pi\)
0.842008 + 0.539465i \(0.181373\pi\)
\(810\) 0 0
\(811\) 13.1961 + 22.8564i 0.463379 + 0.802596i 0.999127 0.0417821i \(-0.0133035\pi\)
−0.535748 + 0.844378i \(0.679970\pi\)
\(812\) 12.6843 21.9698i 0.445130 0.770988i
\(813\) 0 0
\(814\) 5.89074 10.2031i 0.206470 0.357617i
\(815\) 0.548453 0.949949i 0.0192115 0.0332753i
\(816\) 0 0
\(817\) −5.84789 + 24.8937i −0.204592 + 0.870921i
\(818\) −35.0468 −1.22538
\(819\) 0 0
\(820\) −8.98893 + 15.5693i −0.313907 + 0.543703i
\(821\) −0.411319 0.712425i −0.0143551 0.0248638i 0.858759 0.512380i \(-0.171236\pi\)
−0.873114 + 0.487517i \(0.837903\pi\)
\(822\) 0 0
\(823\) −7.76958 13.4573i −0.270831 0.469092i 0.698244 0.715860i \(-0.253965\pi\)
−0.969075 + 0.246767i \(0.920632\pi\)
\(824\) −1.01535 −0.0353714
\(825\) 0 0
\(826\) 8.22874 + 14.2526i 0.286314 + 0.495911i
\(827\) 14.1156 + 24.4490i 0.490848 + 0.850174i 0.999944 0.0105355i \(-0.00335363\pi\)
−0.509096 + 0.860710i \(0.670020\pi\)
\(828\) 0 0
\(829\) 4.85357 0.168571 0.0842857 0.996442i \(-0.473139\pi\)
0.0842857 + 0.996442i \(0.473139\pi\)
\(830\) −3.64207 6.30824i −0.126418 0.218962i
\(831\) 0 0
\(832\) −2.28371 3.95549i −0.0791732 0.137132i
\(833\) 2.98160 5.16428i 0.103306 0.178932i
\(834\) 0 0
\(835\) 12.4888 0.432191
\(836\) 4.87521 + 4.58131i 0.168613 + 0.158448i
\(837\) 0 0
\(838\) −31.1527 + 53.9581i −1.07615 + 1.86395i
\(839\) 10.4587 18.1151i 0.361075 0.625401i −0.627063 0.778969i \(-0.715743\pi\)
0.988138 + 0.153568i \(0.0490763\pi\)
\(840\) 0 0
\(841\) −12.8923 + 22.3302i −0.444563 + 0.770006i
\(842\) 11.7122 + 20.2861i 0.403628 + 0.699104i
\(843\) 0 0
\(844\) 30.5313 1.05093
\(845\) −6.35440 11.0061i −0.218598 0.378623i
\(846\) 0 0
\(847\) −17.3865 −0.597408
\(848\) 29.8678 1.02567
\(849\) 0 0
\(850\) −1.42048 + 2.46034i −0.0487219 + 0.0843889i
\(851\) −3.43186 5.94415i −0.117643 0.203763i
\(852\) 0 0
\(853\) 25.9685 44.9788i 0.889146 1.54005i 0.0482595 0.998835i \(-0.484633\pi\)
0.840887 0.541211i \(-0.182034\pi\)
\(854\) −17.4715 −0.597862
\(855\) 0 0
\(856\) 1.38226 0.0472446
\(857\) 3.13726 5.43389i 0.107167 0.185618i −0.807455 0.589930i \(-0.799155\pi\)
0.914621 + 0.404311i \(0.132489\pi\)
\(858\) 0 0
\(859\) 22.7479 + 39.4005i 0.776148 + 1.34433i 0.934147 + 0.356888i \(0.116162\pi\)
−0.157999 + 0.987439i \(0.550504\pi\)
\(860\) 6.03921 10.4602i 0.205935 0.356690i
\(861\) 0 0
\(862\) −49.2182 −1.67638
\(863\) −36.0191 −1.22611 −0.613053 0.790042i \(-0.710059\pi\)
−0.613053 + 0.790042i \(0.710059\pi\)
\(864\) 0 0
\(865\) −2.15558 3.73357i −0.0732919 0.126945i
\(866\) 42.1077 1.43088
\(867\) 0 0
\(868\) −12.0462 20.8646i −0.408875 0.708191i
\(869\) 2.15153 3.72657i 0.0729858 0.126415i
\(870\) 0 0
\(871\) 0.239343 0.414554i 0.00810982 0.0140466i
\(872\) 0.132966 0.230304i 0.00450280 0.00779907i
\(873\) 0 0
\(874\) 7.35635 2.21823i 0.248832 0.0750326i
\(875\) −1.66469 −0.0562767
\(876\) 0 0
\(877\) 11.5506 20.0063i 0.390037 0.675564i −0.602417 0.798182i \(-0.705795\pi\)
0.992454 + 0.122617i \(0.0391288\pi\)
\(878\) −16.5408 28.6495i −0.558225 0.966875i
\(879\) 0 0
\(880\) 1.44570 + 2.50403i 0.0487346 + 0.0844108i
\(881\) 14.4294 0.486141 0.243070 0.970009i \(-0.421845\pi\)
0.243070 + 0.970009i \(0.421845\pi\)
\(882\) 0 0
\(883\) −7.48691 12.9677i −0.251955 0.436398i 0.712109 0.702069i \(-0.247740\pi\)
−0.964064 + 0.265671i \(0.914407\pi\)
\(884\) 0.783356 + 1.35681i 0.0263471 + 0.0456345i
\(885\) 0 0
\(886\) −5.33045 −0.179080
\(887\) 5.39733 + 9.34845i 0.181225 + 0.313890i 0.942298 0.334776i \(-0.108661\pi\)
−0.761073 + 0.648666i \(0.775327\pi\)
\(888\) 0 0
\(889\) 16.5015 + 28.5815i 0.553444 + 0.958593i
\(890\) 0.935644 1.62058i 0.0313629 0.0543221i
\(891\) 0 0
\(892\) −38.8878 −1.30206
\(893\) 20.9567 + 19.6933i 0.701289 + 0.659013i
\(894\) 0 0
\(895\) 6.30190 10.9152i 0.210649 0.364855i
\(896\) 0.789656 1.36773i 0.0263806 0.0456925i
\(897\) 0 0
\(898\) 8.23255 14.2592i 0.274724 0.475835i
\(899\) 26.0144 + 45.0583i 0.867629 + 1.50278i
\(900\) 0 0
\(901\) −10.8585 −0.361750
\(902\) −6.55685 11.3568i −0.218319 0.378140i
\(903\) 0 0
\(904\) −1.06110 −0.0352917
\(905\) −3.69068 −0.122682
\(906\) 0 0
\(907\) −24.5290 + 42.4854i −0.814471 + 1.41071i 0.0952355 + 0.995455i \(0.469640\pi\)
−0.909707 + 0.415251i \(0.863694\pi\)
\(908\) 16.1954 + 28.0512i 0.537463 + 0.930913i
\(909\) 0 0
\(910\) −0.904904 + 1.56734i −0.0299973 + 0.0519568i
\(911\) 21.3969 0.708912 0.354456 0.935073i \(-0.384666\pi\)
0.354456 + 0.935073i \(0.384666\pi\)
\(912\) 0 0
\(913\) 2.69520 0.0891980
\(914\) 9.00722 15.6010i 0.297932 0.516034i
\(915\) 0 0
\(916\) 19.6024 + 33.9524i 0.647682 + 1.12182i
\(917\) 1.52814 2.64682i 0.0504638 0.0874058i
\(918\) 0 0
\(919\) −30.9528 −1.02104 −0.510520 0.859866i \(-0.670547\pi\)
−0.510520 + 0.859866i \(0.670547\pi\)
\(920\) −0.103804 −0.00342231
\(921\) 0 0
\(922\) −17.7800 30.7958i −0.585552 1.01421i
\(923\) 1.52241 0.0501107
\(924\) 0 0
\(925\) −3.92238 6.79377i −0.128967 0.223378i
\(926\) 21.0200 36.4077i 0.690761 1.19643i
\(927\) 0 0
\(928\) −29.7980 + 51.6116i −0.978166 + 1.69423i
\(929\) −25.8861 + 44.8361i −0.849296 + 1.47102i 0.0325418 + 0.999470i \(0.489640\pi\)
−0.881838 + 0.471553i \(0.843694\pi\)
\(930\) 0 0
\(931\) −17.6481 + 5.32159i −0.578393 + 0.174408i
\(932\) −2.44778 −0.0801796
\(933\) 0 0
\(934\) −24.6615 + 42.7150i −0.806950 + 1.39768i
\(935\) −0.525589 0.910348i −0.0171886 0.0297716i
\(936\) 0 0
\(937\) −17.5665 30.4261i −0.573873 0.993977i −0.996163 0.0875161i \(-0.972107\pi\)
0.422290 0.906461i \(-0.361226\pi\)
\(938\) 2.97502 0.0971380
\(939\) 0 0
\(940\) −6.79175 11.7637i −0.221522 0.383688i
\(941\) −26.0465 45.1139i −0.849092 1.47067i −0.882020 0.471212i \(-0.843817\pi\)
0.0329279 0.999458i \(-0.489517\pi\)
\(942\) 0 0
\(943\) −7.63985 −0.248788
\(944\) −9.51676 16.4835i −0.309744 0.536493i
\(945\) 0 0
\(946\) 4.40522 + 7.63006i 0.143226 + 0.248075i
\(947\) −25.0695 + 43.4217i −0.814651 + 1.41102i 0.0949279 + 0.995484i \(0.469738\pi\)
−0.909579 + 0.415532i \(0.863595\pi\)
\(948\) 0 0
\(949\) −0.565930 −0.0183709
\(950\) 8.40781 2.53528i 0.272785 0.0822554i
\(951\) 0 0
\(952\) −0.139251 + 0.241189i −0.00451314 + 0.00781698i
\(953\) −20.3402 + 35.2303i −0.658884 + 1.14122i 0.322021 + 0.946732i \(0.395638\pi\)
−0.980905 + 0.194488i \(0.937696\pi\)
\(954\) 0 0
\(955\) 3.11817 5.40083i 0.100902 0.174767i
\(956\) −26.7085 46.2605i −0.863815 1.49617i
\(957\) 0 0
\(958\) −6.65717 −0.215083
\(959\) 3.29765 + 5.71170i 0.106487 + 0.184440i
\(960\) 0 0
\(961\) 18.4116 0.593922
\(962\) −8.52864 −0.274974
\(963\) 0 0
\(964\) 9.32296 16.1478i 0.300272 0.520087i
\(965\) −9.46275 16.3900i −0.304617 0.527611i
\(966\) 0 0
\(967\) −19.9627 + 34.5763i −0.641956 + 1.11190i 0.343040 + 0.939321i \(0.388543\pi\)
−0.984996 + 0.172579i \(0.944790\pi\)
\(968\) −1.23912 −0.0398268
\(969\) 0 0
\(970\) −0.0370743 −0.00119039
\(971\) 8.58195 14.8644i 0.275408 0.477020i −0.694830 0.719174i \(-0.744520\pi\)
0.970238 + 0.242153i \(0.0778538\pi\)
\(972\) 0 0
\(973\) 1.47998 + 2.56341i 0.0474461 + 0.0821790i
\(974\) −32.9044 + 56.9921i −1.05433 + 1.82614i
\(975\) 0 0
\(976\) 20.2063 0.646787
\(977\) −36.0150 −1.15222 −0.576111 0.817371i \(-0.695431\pi\)
−0.576111 + 0.817371i \(0.695431\pi\)
\(978\) 0 0
\(979\) 0.346197 + 0.599631i 0.0110645 + 0.0191643i
\(980\) 8.70666 0.278124
\(981\) 0 0
\(982\) −13.1281 22.7385i −0.418935 0.725616i
\(983\) 23.8054 41.2321i 0.759273 1.31510i −0.183949 0.982936i \(-0.558888\pi\)
0.943222 0.332164i \(-0.107779\pi\)
\(984\) 0 0
\(985\) −3.42569 + 5.93348i −0.109152 + 0.189056i
\(986\) 10.5139 18.2106i 0.334831 0.579943i
\(987\) 0 0
\(988\) 1.10752 4.71456i 0.0352348 0.149990i
\(989\) 5.13283 0.163214
\(990\) 0 0
\(991\) −15.5005 + 26.8477i −0.492391 + 0.852845i −0.999962 0.00876452i \(-0.997210\pi\)
0.507571 + 0.861610i \(0.330543\pi\)
\(992\) 28.2990 + 49.0153i 0.898494 + 1.55624i
\(993\) 0 0
\(994\) 4.73088 + 8.19412i 0.150054 + 0.259902i
\(995\) −19.9884 −0.633675
\(996\) 0 0
\(997\) 13.8534 + 23.9948i 0.438741 + 0.759921i 0.997593 0.0693461i \(-0.0220913\pi\)
−0.558852 + 0.829268i \(0.688758\pi\)
\(998\) −30.5327 52.8843i −0.966497 1.67402i
\(999\) 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 855.2.k.k.676.1 yes 12
3.2 odd 2 855.2.k.j.676.6 yes 12
19.7 even 3 inner 855.2.k.k.406.1 yes 12
57.26 odd 6 855.2.k.j.406.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
855.2.k.j.406.6 12 57.26 odd 6
855.2.k.j.676.6 yes 12 3.2 odd 2
855.2.k.k.406.1 yes 12 19.7 even 3 inner
855.2.k.k.676.1 yes 12 1.1 even 1 trivial