Properties

Label 504.2.p.g.307.15
Level $504$
Weight $2$
Character 504.307
Analytic conductor $4.024$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(307,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.p (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 307.15
Root \(-0.310478 - 1.37971i\) of defining polynomial
Character \(\chi\) \(=\) 504.307
Dual form 504.2.p.g.307.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37971 + 0.310478i) q^{2} +(1.80721 + 0.856739i) q^{4} -2.33443 q^{5} +(0.490487 + 2.59989i) q^{7} +(2.22743 + 1.74315i) q^{8} +O(q^{10})\) \(q+(1.37971 + 0.310478i) q^{2} +(1.80721 + 0.856739i) q^{4} -2.33443 q^{5} +(0.490487 + 2.59989i) q^{7} +(2.22743 + 1.74315i) q^{8} +(-3.22084 - 0.724789i) q^{10} +0.304570 q^{11} +5.46072 q^{13} +(-0.130477 + 3.73938i) q^{14} +(2.53200 + 3.09661i) q^{16} +6.37384i q^{17} -0.840438i q^{19} +(-4.21880 - 2.00000i) q^{20} +(0.420219 + 0.0945622i) q^{22} +0.111550i q^{23} +0.449578 q^{25} +(7.53421 + 1.69543i) q^{26} +(-1.34102 + 5.11876i) q^{28} -5.46072i q^{29} -7.64576 q^{31} +(2.53200 + 5.05856i) q^{32} +(-1.97893 + 8.79406i) q^{34} +(-1.14501 - 6.06927i) q^{35} -6.44169i q^{37} +(0.260937 - 1.15956i) q^{38} +(-5.19978 - 4.06927i) q^{40} -8.66385i q^{41} +6.06927 q^{43} +(0.550422 + 0.260937i) q^{44} +(-0.0346336 + 0.153906i) q^{46} +8.21451 q^{47} +(-6.51885 + 2.55042i) q^{49} +(0.620289 + 0.139584i) q^{50} +(9.86864 + 4.67841i) q^{52} -10.1296i q^{53} -0.710999 q^{55} +(-3.43947 + 6.64605i) q^{56} +(1.69543 - 7.53421i) q^{58} +1.70998i q^{59} -2.75380 q^{61} +(-10.5489 - 2.37384i) q^{62} +(1.92286 + 7.76548i) q^{64} -12.7477 q^{65} -8.35928 q^{67} +(-5.46072 + 11.5188i) q^{68} +(0.304591 - 8.72934i) q^{70} -2.07350i q^{71} -12.7477i q^{73} +(2.00000 - 8.88767i) q^{74} +(0.720036 - 1.51885i) q^{76} +(0.149388 + 0.791849i) q^{77} +7.90670i q^{79} +(-5.91078 - 7.22883i) q^{80} +(2.68993 - 11.9536i) q^{82} +11.6468i q^{83} -14.8793i q^{85} +(8.37384 + 1.88437i) q^{86} +(0.678408 + 0.530912i) q^{88} -4.08382i q^{89} +(2.67841 + 14.1973i) q^{91} +(-0.0955689 + 0.201593i) q^{92} +(11.3337 + 2.55042i) q^{94} +1.96195i q^{95} +6.42855i q^{97} +(-9.78597 + 1.49489i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} + 2 q^{4} + 10 q^{8} + 8 q^{11} + 14 q^{14} + 18 q^{16} + 8 q^{22} + 16 q^{25} - 10 q^{28} + 18 q^{32} - 24 q^{35} - 8 q^{43} + 52 q^{46} - 8 q^{49} + 34 q^{50} - 50 q^{56} + 24 q^{58} + 2 q^{64} - 40 q^{67} - 24 q^{70} + 32 q^{74} + 32 q^{86} - 88 q^{88} - 56 q^{91} - 44 q^{92} - 66 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37971 + 0.310478i 0.975603 + 0.219541i
\(3\) 0 0
\(4\) 1.80721 + 0.856739i 0.903604 + 0.428370i
\(5\) −2.33443 −1.04399 −0.521995 0.852948i \(-0.674812\pi\)
−0.521995 + 0.852948i \(0.674812\pi\)
\(6\) 0 0
\(7\) 0.490487 + 2.59989i 0.185387 + 0.982666i
\(8\) 2.22743 + 1.74315i 0.787514 + 0.616297i
\(9\) 0 0
\(10\) −3.22084 0.724789i −1.01852 0.229198i
\(11\) 0.304570 0.0918314 0.0459157 0.998945i \(-0.485379\pi\)
0.0459157 + 0.998945i \(0.485379\pi\)
\(12\) 0 0
\(13\) 5.46072 1.51453 0.757265 0.653108i \(-0.226535\pi\)
0.757265 + 0.653108i \(0.226535\pi\)
\(14\) −0.130477 + 3.73938i −0.0348715 + 0.999392i
\(15\) 0 0
\(16\) 2.53200 + 3.09661i 0.632999 + 0.774152i
\(17\) 6.37384i 1.54588i 0.634477 + 0.772941i \(0.281215\pi\)
−0.634477 + 0.772941i \(0.718785\pi\)
\(18\) 0 0
\(19\) 0.840438i 0.192810i −0.995342 0.0964049i \(-0.969266\pi\)
0.995342 0.0964049i \(-0.0307344\pi\)
\(20\) −4.21880 2.00000i −0.943353 0.447214i
\(21\) 0 0
\(22\) 0.420219 + 0.0945622i 0.0895910 + 0.0201607i
\(23\) 0.111550i 0.0232597i 0.999932 + 0.0116298i \(0.00370198\pi\)
−0.999932 + 0.0116298i \(0.996298\pi\)
\(24\) 0 0
\(25\) 0.449578 0.0899157
\(26\) 7.53421 + 1.69543i 1.47758 + 0.332501i
\(27\) 0 0
\(28\) −1.34102 + 5.11876i −0.253428 + 0.967354i
\(29\) 5.46072i 1.01403i −0.861937 0.507015i \(-0.830749\pi\)
0.861937 0.507015i \(-0.169251\pi\)
\(30\) 0 0
\(31\) −7.64576 −1.37322 −0.686610 0.727026i \(-0.740902\pi\)
−0.686610 + 0.727026i \(0.740902\pi\)
\(32\) 2.53200 + 5.05856i 0.447598 + 0.894235i
\(33\) 0 0
\(34\) −1.97893 + 8.79406i −0.339384 + 1.50817i
\(35\) −1.14501 6.06927i −0.193542 1.02589i
\(36\) 0 0
\(37\) 6.44169i 1.05901i −0.848308 0.529504i \(-0.822378\pi\)
0.848308 0.529504i \(-0.177622\pi\)
\(38\) 0.260937 1.15956i 0.0423296 0.188106i
\(39\) 0 0
\(40\) −5.19978 4.06927i −0.822157 0.643408i
\(41\) 8.66385i 1.35307i −0.736412 0.676533i \(-0.763481\pi\)
0.736412 0.676533i \(-0.236519\pi\)
\(42\) 0 0
\(43\) 6.06927 0.925555 0.462777 0.886475i \(-0.346853\pi\)
0.462777 + 0.886475i \(0.346853\pi\)
\(44\) 0.550422 + 0.260937i 0.0829792 + 0.0393378i
\(45\) 0 0
\(46\) −0.0346336 + 0.153906i −0.00510645 + 0.0226922i
\(47\) 8.21451 1.19821 0.599105 0.800671i \(-0.295523\pi\)
0.599105 + 0.800671i \(0.295523\pi\)
\(48\) 0 0
\(49\) −6.51885 + 2.55042i −0.931264 + 0.364346i
\(50\) 0.620289 + 0.139584i 0.0877220 + 0.0197402i
\(51\) 0 0
\(52\) 9.86864 + 4.67841i 1.36853 + 0.648778i
\(53\) 10.1296i 1.39141i −0.718330 0.695703i \(-0.755093\pi\)
0.718330 0.695703i \(-0.244907\pi\)
\(54\) 0 0
\(55\) −0.710999 −0.0958711
\(56\) −3.43947 + 6.64605i −0.459619 + 0.888116i
\(57\) 0 0
\(58\) 1.69543 7.53421i 0.222621 0.989290i
\(59\) 1.70998i 0.222621i 0.993786 + 0.111310i \(0.0355048\pi\)
−0.993786 + 0.111310i \(0.964495\pi\)
\(60\) 0 0
\(61\) −2.75380 −0.352587 −0.176294 0.984338i \(-0.556411\pi\)
−0.176294 + 0.984338i \(0.556411\pi\)
\(62\) −10.5489 2.37384i −1.33972 0.301478i
\(63\) 0 0
\(64\) 1.92286 + 7.76548i 0.240357 + 0.970685i
\(65\) −12.7477 −1.58115
\(66\) 0 0
\(67\) −8.35928 −1.02125 −0.510625 0.859804i \(-0.670586\pi\)
−0.510625 + 0.859804i \(0.670586\pi\)
\(68\) −5.46072 + 11.5188i −0.662209 + 1.39687i
\(69\) 0 0
\(70\) 0.304591 8.72934i 0.0364055 1.04336i
\(71\) 2.07350i 0.246079i −0.992402 0.123039i \(-0.960736\pi\)
0.992402 0.123039i \(-0.0392641\pi\)
\(72\) 0 0
\(73\) 12.7477i 1.49200i −0.665945 0.746001i \(-0.731971\pi\)
0.665945 0.746001i \(-0.268029\pi\)
\(74\) 2.00000 8.88767i 0.232495 1.03317i
\(75\) 0 0
\(76\) 0.720036 1.51885i 0.0825938 0.174224i
\(77\) 0.149388 + 0.791849i 0.0170243 + 0.0902395i
\(78\) 0 0
\(79\) 7.90670i 0.889573i 0.895637 + 0.444787i \(0.146720\pi\)
−0.895637 + 0.444787i \(0.853280\pi\)
\(80\) −5.91078 7.22883i −0.660845 0.808208i
\(81\) 0 0
\(82\) 2.68993 11.9536i 0.297053 1.32006i
\(83\) 11.6468i 1.27841i 0.769038 + 0.639203i \(0.220736\pi\)
−0.769038 + 0.639203i \(0.779264\pi\)
\(84\) 0 0
\(85\) 14.8793i 1.61389i
\(86\) 8.37384 + 1.88437i 0.902974 + 0.203197i
\(87\) 0 0
\(88\) 0.678408 + 0.530912i 0.0723185 + 0.0565954i
\(89\) 4.08382i 0.432884i −0.976295 0.216442i \(-0.930555\pi\)
0.976295 0.216442i \(-0.0694452\pi\)
\(90\) 0 0
\(91\) 2.67841 + 14.1973i 0.280773 + 1.48828i
\(92\) −0.0955689 + 0.201593i −0.00996374 + 0.0210175i
\(93\) 0 0
\(94\) 11.3337 + 2.55042i 1.16898 + 0.263056i
\(95\) 1.96195i 0.201291i
\(96\) 0 0
\(97\) 6.42855i 0.652720i 0.945245 + 0.326360i \(0.105822\pi\)
−0.945245 + 0.326360i \(0.894178\pi\)
\(98\) −9.78597 + 1.49489i −0.988533 + 0.151007i
\(99\) 0 0
\(100\) 0.812482 + 0.385171i 0.0812482 + 0.0385171i
\(101\) 7.00330 0.696854 0.348427 0.937336i \(-0.386716\pi\)
0.348427 + 0.937336i \(0.386716\pi\)
\(102\) 0 0
\(103\) 9.60771 0.946676 0.473338 0.880881i \(-0.343049\pi\)
0.473338 + 0.880881i \(0.343049\pi\)
\(104\) 12.1633 + 9.51885i 1.19271 + 0.933400i
\(105\) 0 0
\(106\) 3.14501 13.9759i 0.305470 1.35746i
\(107\) −6.01455 −0.581449 −0.290724 0.956807i \(-0.593896\pi\)
−0.290724 + 0.956807i \(0.593896\pi\)
\(108\) 0 0
\(109\) 9.85961i 0.944379i −0.881497 0.472190i \(-0.843464\pi\)
0.881497 0.472190i \(-0.156536\pi\)
\(110\) −0.980973 0.220749i −0.0935321 0.0210476i
\(111\) 0 0
\(112\) −6.80893 + 8.10176i −0.643384 + 0.765544i
\(113\) 14.7477 1.38734 0.693672 0.720291i \(-0.255992\pi\)
0.693672 + 0.720291i \(0.255992\pi\)
\(114\) 0 0
\(115\) 0.260405i 0.0242829i
\(116\) 4.67841 9.86864i 0.434379 0.916281i
\(117\) 0 0
\(118\) −0.530912 + 2.35928i −0.0488744 + 0.217190i
\(119\) −16.5713 + 3.12628i −1.51909 + 0.286586i
\(120\) 0 0
\(121\) −10.9072 −0.991567
\(122\) −3.79944 0.854992i −0.343985 0.0774073i
\(123\) 0 0
\(124\) −13.8175 6.55042i −1.24085 0.588245i
\(125\) 10.6227 0.950119
\(126\) 0 0
\(127\) 2.49286i 0.221205i −0.993865 0.110603i \(-0.964722\pi\)
0.993865 0.110603i \(-0.0352781\pi\)
\(128\) 0.241980 + 11.3111i 0.0213882 + 0.999771i
\(129\) 0 0
\(130\) −17.5881 3.95787i −1.54258 0.347128i
\(131\) 4.60914i 0.402702i −0.979519 0.201351i \(-0.935467\pi\)
0.979519 0.201351i \(-0.0645333\pi\)
\(132\) 0 0
\(133\) 2.18505 0.412224i 0.189467 0.0357443i
\(134\) −11.5334 2.59537i −0.996334 0.224206i
\(135\) 0 0
\(136\) −11.1106 + 14.1973i −0.952722 + 1.21740i
\(137\) 0.899157 0.0768202 0.0384101 0.999262i \(-0.487771\pi\)
0.0384101 + 0.999262i \(0.487771\pi\)
\(138\) 0 0
\(139\) 23.1762i 1.96578i −0.184189 0.982891i \(-0.558966\pi\)
0.184189 0.982891i \(-0.441034\pi\)
\(140\) 3.13051 11.9494i 0.264576 1.00991i
\(141\) 0 0
\(142\) 0.643774 2.86083i 0.0540243 0.240075i
\(143\) 1.66317 0.139081
\(144\) 0 0
\(145\) 12.7477i 1.05864i
\(146\) 3.95787 17.5881i 0.327555 1.45560i
\(147\) 0 0
\(148\) 5.51885 11.6415i 0.453646 0.956923i
\(149\) 6.58394i 0.539377i 0.962948 + 0.269689i \(0.0869208\pi\)
−0.962948 + 0.269689i \(0.913079\pi\)
\(150\) 0 0
\(151\) 20.5670i 1.67372i 0.547419 + 0.836858i \(0.315610\pi\)
−0.547419 + 0.836858i \(0.684390\pi\)
\(152\) 1.46501 1.87201i 0.118828 0.151840i
\(153\) 0 0
\(154\) −0.0397395 + 1.13890i −0.00320230 + 0.0917755i
\(155\) 17.8485 1.43363
\(156\) 0 0
\(157\) −12.0915 −0.965009 −0.482505 0.875893i \(-0.660273\pi\)
−0.482505 + 0.875893i \(0.660273\pi\)
\(158\) −2.45485 + 10.9090i −0.195298 + 0.867870i
\(159\) 0 0
\(160\) −5.91078 11.8089i −0.467288 0.933573i
\(161\) −0.290017 + 0.0547136i −0.0228565 + 0.00431203i
\(162\) 0 0
\(163\) 0.359284 0.0281413 0.0140706 0.999901i \(-0.495521\pi\)
0.0140706 + 0.999901i \(0.495521\pi\)
\(164\) 7.42266 15.6574i 0.579612 1.22264i
\(165\) 0 0
\(166\) −3.61608 + 16.0693i −0.280662 + 1.24722i
\(167\) −7.91574 −0.612538 −0.306269 0.951945i \(-0.599081\pi\)
−0.306269 + 0.951945i \(0.599081\pi\)
\(168\) 0 0
\(169\) 16.8194 1.29380
\(170\) 4.61969 20.5291i 0.354314 1.57451i
\(171\) 0 0
\(172\) 10.9684 + 5.19978i 0.836335 + 0.396479i
\(173\) −12.5109 −0.951185 −0.475593 0.879666i \(-0.657766\pi\)
−0.475593 + 0.879666i \(0.657766\pi\)
\(174\) 0 0
\(175\) 0.220512 + 1.16885i 0.0166692 + 0.0883571i
\(176\) 0.771171 + 0.943135i 0.0581292 + 0.0710915i
\(177\) 0 0
\(178\) 1.26793 5.63449i 0.0950357 0.422323i
\(179\) −15.3423 −1.14673 −0.573367 0.819298i \(-0.694363\pi\)
−0.573367 + 0.819298i \(0.694363\pi\)
\(180\) 0 0
\(181\) −0.493074 −0.0366499 −0.0183249 0.999832i \(-0.505833\pi\)
−0.0183249 + 0.999832i \(0.505833\pi\)
\(182\) −0.712499 + 20.4197i −0.0528140 + 1.51361i
\(183\) 0 0
\(184\) −0.194448 + 0.248468i −0.0143349 + 0.0183173i
\(185\) 15.0377i 1.10559i
\(186\) 0 0
\(187\) 1.94128i 0.141961i
\(188\) 14.8453 + 7.03769i 1.08271 + 0.513276i
\(189\) 0 0
\(190\) −0.609140 + 2.70692i −0.0441917 + 0.196381i
\(191\) 21.8108i 1.57817i 0.614282 + 0.789087i \(0.289446\pi\)
−0.614282 + 0.789087i \(0.710554\pi\)
\(192\) 0 0
\(193\) 7.58811 0.546204 0.273102 0.961985i \(-0.411950\pi\)
0.273102 + 0.961985i \(0.411950\pi\)
\(194\) −1.99592 + 8.86955i −0.143299 + 0.636796i
\(195\) 0 0
\(196\) −13.9660 0.975809i −0.997568 0.0697006i
\(197\) 11.7928i 0.840199i −0.907478 0.420099i \(-0.861995\pi\)
0.907478 0.420099i \(-0.138005\pi\)
\(198\) 0 0
\(199\) 24.7858 1.75702 0.878509 0.477726i \(-0.158539\pi\)
0.878509 + 0.477726i \(0.158539\pi\)
\(200\) 1.00140 + 0.783683i 0.0708099 + 0.0554147i
\(201\) 0 0
\(202\) 9.66253 + 2.17437i 0.679853 + 0.152988i
\(203\) 14.1973 2.67841i 0.996452 0.187987i
\(204\) 0 0
\(205\) 20.2252i 1.41259i
\(206\) 13.2559 + 2.98298i 0.923580 + 0.207834i
\(207\) 0 0
\(208\) 13.8265 + 16.9097i 0.958696 + 1.17248i
\(209\) 0.255972i 0.0177060i
\(210\) 0 0
\(211\) 14.0693 0.968568 0.484284 0.874911i \(-0.339080\pi\)
0.484284 + 0.874911i \(0.339080\pi\)
\(212\) 8.67841 18.3063i 0.596035 1.25728i
\(213\) 0 0
\(214\) −8.29835 1.86738i −0.567263 0.127652i
\(215\) −14.1683 −0.966270
\(216\) 0 0
\(217\) −3.75014 19.8781i −0.254576 1.34942i
\(218\) 3.06119 13.6034i 0.207330 0.921339i
\(219\) 0 0
\(220\) −1.28492 0.609140i −0.0866294 0.0410682i
\(221\) 34.8057i 2.34129i
\(222\) 0 0
\(223\) −15.4480 −1.03448 −0.517239 0.855841i \(-0.673040\pi\)
−0.517239 + 0.855841i \(0.673040\pi\)
\(224\) −11.9098 + 9.06406i −0.795755 + 0.605618i
\(225\) 0 0
\(226\) 20.3475 + 4.57882i 1.35350 + 0.304579i
\(227\) 11.0377i 0.732597i −0.930497 0.366299i \(-0.880625\pi\)
0.930497 0.366299i \(-0.119375\pi\)
\(228\) 0 0
\(229\) 7.42266 0.490503 0.245252 0.969459i \(-0.421129\pi\)
0.245252 + 0.969459i \(0.421129\pi\)
\(230\) 0.0808499 0.359284i 0.00533109 0.0236905i
\(231\) 0 0
\(232\) 9.51885 12.1633i 0.624943 0.798562i
\(233\) −13.0668 −0.856034 −0.428017 0.903771i \(-0.640788\pi\)
−0.428017 + 0.903771i \(0.640788\pi\)
\(234\) 0 0
\(235\) −19.1762 −1.25092
\(236\) −1.46501 + 3.09029i −0.0953640 + 0.201161i
\(237\) 0 0
\(238\) −23.8342 0.831641i −1.54494 0.0539073i
\(239\) 8.54916i 0.552999i −0.961014 0.276500i \(-0.910826\pi\)
0.961014 0.276500i \(-0.0891744\pi\)
\(240\) 0 0
\(241\) 7.64683i 0.492576i −0.969197 0.246288i \(-0.920789\pi\)
0.969197 0.246288i \(-0.0792109\pi\)
\(242\) −15.0488 3.38645i −0.967376 0.217689i
\(243\) 0 0
\(244\) −4.97668 2.35928i −0.318599 0.151038i
\(245\) 15.2178 5.95379i 0.972230 0.380374i
\(246\) 0 0
\(247\) 4.58939i 0.292016i
\(248\) −17.0304 13.3277i −1.08143 0.846310i
\(249\) 0 0
\(250\) 14.6562 + 3.29810i 0.926939 + 0.208590i
\(251\) 12.7186i 0.802789i 0.915905 + 0.401394i \(0.131474\pi\)
−0.915905 + 0.401394i \(0.868526\pi\)
\(252\) 0 0
\(253\) 0.0339747i 0.00213597i
\(254\) 0.773977 3.43942i 0.0485636 0.215809i
\(255\) 0 0
\(256\) −3.17799 + 15.6812i −0.198624 + 0.980076i
\(257\) 7.44557i 0.464442i −0.972663 0.232221i \(-0.925401\pi\)
0.972663 0.232221i \(-0.0745993\pi\)
\(258\) 0 0
\(259\) 16.7477 3.15956i 1.04065 0.196326i
\(260\) −23.0377 10.9214i −1.42874 0.677318i
\(261\) 0 0
\(262\) 1.43103 6.35928i 0.0884096 0.392878i
\(263\) 11.5549i 0.712503i 0.934390 + 0.356251i \(0.115945\pi\)
−0.934390 + 0.356251i \(0.884055\pi\)
\(264\) 0 0
\(265\) 23.6468i 1.45261i
\(266\) 3.14272 + 0.109658i 0.192692 + 0.00672357i
\(267\) 0 0
\(268\) −15.1070 7.16172i −0.922804 0.437472i
\(269\) −12.2121 −0.744586 −0.372293 0.928115i \(-0.621428\pi\)
−0.372293 + 0.928115i \(0.621428\pi\)
\(270\) 0 0
\(271\) −18.9454 −1.15085 −0.575427 0.817853i \(-0.695164\pi\)
−0.575427 + 0.817853i \(0.695164\pi\)
\(272\) −19.7373 + 16.1385i −1.19675 + 0.978542i
\(273\) 0 0
\(274\) 1.24058 + 0.279168i 0.0749460 + 0.0168652i
\(275\) 0.136928 0.00825708
\(276\) 0 0
\(277\) 18.1876i 1.09278i 0.837529 + 0.546392i \(0.183999\pi\)
−0.837529 + 0.546392i \(0.816001\pi\)
\(278\) 7.19570 31.9765i 0.431569 1.91782i
\(279\) 0 0
\(280\) 8.02922 15.5148i 0.479838 0.927185i
\(281\) 17.5294 1.04572 0.522858 0.852420i \(-0.324866\pi\)
0.522858 + 0.852420i \(0.324866\pi\)
\(282\) 0 0
\(283\) 18.3358i 1.08995i 0.838452 + 0.544975i \(0.183461\pi\)
−0.838452 + 0.544975i \(0.816539\pi\)
\(284\) 1.77644 3.74724i 0.105413 0.222358i
\(285\) 0 0
\(286\) 2.29470 + 0.516377i 0.135688 + 0.0305340i
\(287\) 22.5251 4.24950i 1.32961 0.250840i
\(288\) 0 0
\(289\) −23.6258 −1.38975
\(290\) −3.95787 + 17.5881i −0.232414 + 1.03281i
\(291\) 0 0
\(292\) 10.9214 23.0377i 0.639128 1.34818i
\(293\) −14.0008 −0.817938 −0.408969 0.912548i \(-0.634112\pi\)
−0.408969 + 0.912548i \(0.634112\pi\)
\(294\) 0 0
\(295\) 3.99184i 0.232414i
\(296\) 11.2288 14.3484i 0.652662 0.833983i
\(297\) 0 0
\(298\) −2.04417 + 9.08393i −0.118415 + 0.526218i
\(299\) 0.609140i 0.0352275i
\(300\) 0 0
\(301\) 2.97689 + 15.7794i 0.171585 + 0.909511i
\(302\) −6.38559 + 28.3765i −0.367449 + 1.63288i
\(303\) 0 0
\(304\) 2.60251 2.12799i 0.149264 0.122048i
\(305\) 6.42855 0.368098
\(306\) 0 0
\(307\) 4.26041i 0.243154i 0.992582 + 0.121577i \(0.0387952\pi\)
−0.992582 + 0.121577i \(0.961205\pi\)
\(308\) −0.408433 + 1.55902i −0.0232726 + 0.0888335i
\(309\) 0 0
\(310\) 24.6258 + 5.54157i 1.39865 + 0.314740i
\(311\) 11.6664 0.661541 0.330771 0.943711i \(-0.392691\pi\)
0.330771 + 0.943711i \(0.392691\pi\)
\(312\) 0 0
\(313\) 4.58003i 0.258879i 0.991587 + 0.129439i \(0.0413178\pi\)
−0.991587 + 0.129439i \(0.958682\pi\)
\(314\) −16.6828 3.75415i −0.941466 0.211859i
\(315\) 0 0
\(316\) −6.77398 + 14.2890i −0.381066 + 0.803821i
\(317\) 12.6315i 0.709454i 0.934970 + 0.354727i \(0.115426\pi\)
−0.934970 + 0.354727i \(0.884574\pi\)
\(318\) 0 0
\(319\) 1.66317i 0.0931197i
\(320\) −4.48878 18.1280i −0.250930 1.01339i
\(321\) 0 0
\(322\) −0.417126 0.0145547i −0.0232455 0.000811101i
\(323\) 5.35682 0.298061
\(324\) 0 0
\(325\) 2.45502 0.136180
\(326\) 0.495708 + 0.111550i 0.0274547 + 0.00617816i
\(327\) 0 0
\(328\) 15.1024 19.2981i 0.833890 1.06556i
\(329\) 4.02911 + 21.3568i 0.222132 + 1.17744i
\(330\) 0 0
\(331\) 25.6870 1.41188 0.705942 0.708269i \(-0.250524\pi\)
0.705942 + 0.708269i \(0.250524\pi\)
\(332\) −9.97830 + 21.0482i −0.547630 + 1.15517i
\(333\) 0 0
\(334\) −10.9214 2.45766i −0.597594 0.134477i
\(335\) 19.5142 1.06617
\(336\) 0 0
\(337\) 24.7136 1.34624 0.673119 0.739535i \(-0.264954\pi\)
0.673119 + 0.739535i \(0.264954\pi\)
\(338\) 23.2059 + 5.22205i 1.26224 + 0.284042i
\(339\) 0 0
\(340\) 12.7477 26.8900i 0.691340 1.45831i
\(341\) −2.32867 −0.126105
\(342\) 0 0
\(343\) −9.82822 15.6973i −0.530674 0.847576i
\(344\) 13.5188 + 10.5796i 0.728887 + 0.570416i
\(345\) 0 0
\(346\) −17.2614 3.88435i −0.927980 0.208824i
\(347\) −17.7999 −0.955550 −0.477775 0.878482i \(-0.658557\pi\)
−0.477775 + 0.878482i \(0.658557\pi\)
\(348\) 0 0
\(349\) −8.70758 −0.466106 −0.233053 0.972464i \(-0.574872\pi\)
−0.233053 + 0.972464i \(0.574872\pi\)
\(350\) −0.0586598 + 1.68115i −0.00313550 + 0.0898610i
\(351\) 0 0
\(352\) 0.771171 + 1.54069i 0.0411035 + 0.0821188i
\(353\) 7.33615i 0.390464i −0.980757 0.195232i \(-0.937454\pi\)
0.980757 0.195232i \(-0.0625459\pi\)
\(354\) 0 0
\(355\) 4.84044i 0.256904i
\(356\) 3.49877 7.38031i 0.185434 0.391156i
\(357\) 0 0
\(358\) −21.1679 4.76343i −1.11876 0.251755i
\(359\) 14.3555i 0.757656i −0.925467 0.378828i \(-0.876327\pi\)
0.925467 0.378828i \(-0.123673\pi\)
\(360\) 0 0
\(361\) 18.2937 0.962824
\(362\) −0.680299 0.153088i −0.0357557 0.00804614i
\(363\) 0 0
\(364\) −7.32290 + 27.9521i −0.383824 + 1.46509i
\(365\) 29.7586i 1.55764i
\(366\) 0 0
\(367\) −17.4100 −0.908794 −0.454397 0.890799i \(-0.650145\pi\)
−0.454397 + 0.890799i \(0.650145\pi\)
\(368\) −0.345426 + 0.282443i −0.0180065 + 0.0147234i
\(369\) 0 0
\(370\) −4.66887 + 20.7477i −0.242723 + 1.07862i
\(371\) 26.3358 4.96842i 1.36729 0.257948i
\(372\) 0 0
\(373\) 1.44007i 0.0745641i −0.999305 0.0372821i \(-0.988130\pi\)
0.999305 0.0372821i \(-0.0118700\pi\)
\(374\) −0.602724 + 2.67841i −0.0311661 + 0.138497i
\(375\) 0 0
\(376\) 18.2972 + 14.3191i 0.943607 + 0.738452i
\(377\) 29.8194i 1.53578i
\(378\) 0 0
\(379\) −24.0061 −1.23311 −0.616556 0.787311i \(-0.711472\pi\)
−0.616556 + 0.787311i \(0.711472\pi\)
\(380\) −1.68088 + 3.54564i −0.0862271 + 0.181888i
\(381\) 0 0
\(382\) −6.77176 + 30.0926i −0.346473 + 1.53967i
\(383\) 19.5821 1.00060 0.500300 0.865852i \(-0.333223\pi\)
0.500300 + 0.865852i \(0.333223\pi\)
\(384\) 0 0
\(385\) −0.348735 1.84852i −0.0177732 0.0942092i
\(386\) 10.4694 + 2.35594i 0.532879 + 0.119914i
\(387\) 0 0
\(388\) −5.50759 + 11.6177i −0.279606 + 0.589801i
\(389\) 31.6057i 1.60247i −0.598347 0.801237i \(-0.704176\pi\)
0.598347 0.801237i \(-0.295824\pi\)
\(390\) 0 0
\(391\) −0.710999 −0.0359568
\(392\) −18.9660 5.68245i −0.957928 0.287007i
\(393\) 0 0
\(394\) 3.66139 16.2706i 0.184458 0.819701i
\(395\) 18.4577i 0.928706i
\(396\) 0 0
\(397\) 6.29944 0.316160 0.158080 0.987426i \(-0.449470\pi\)
0.158080 + 0.987426i \(0.449470\pi\)
\(398\) 34.1972 + 7.69543i 1.71415 + 0.385737i
\(399\) 0 0
\(400\) 1.13833 + 1.39217i 0.0569166 + 0.0696085i
\(401\) −3.10084 −0.154849 −0.0774244 0.996998i \(-0.524670\pi\)
−0.0774244 + 0.996998i \(0.524670\pi\)
\(402\) 0 0
\(403\) −41.7513 −2.07978
\(404\) 12.6564 + 6.00000i 0.629680 + 0.298511i
\(405\) 0 0
\(406\) 20.4197 + 0.712499i 1.01341 + 0.0353608i
\(407\) 1.96195i 0.0972501i
\(408\) 0 0
\(409\) 3.06680i 0.151643i 0.997121 + 0.0758217i \(0.0241580\pi\)
−0.997121 + 0.0758217i \(0.975842\pi\)
\(410\) −6.27947 + 27.9049i −0.310121 + 1.37813i
\(411\) 0 0
\(412\) 17.3631 + 8.23130i 0.855419 + 0.405527i
\(413\) −4.44577 + 0.838724i −0.218762 + 0.0412709i
\(414\) 0 0
\(415\) 27.1888i 1.33464i
\(416\) 13.8265 + 27.6233i 0.677901 + 1.35435i
\(417\) 0 0
\(418\) 0.0794737 0.353168i 0.00388719 0.0172740i
\(419\) 15.5294i 0.758661i 0.925261 + 0.379330i \(0.123846\pi\)
−0.925261 + 0.379330i \(0.876154\pi\)
\(420\) 0 0
\(421\) 17.3631i 0.846227i 0.906077 + 0.423113i \(0.139063\pi\)
−0.906077 + 0.423113i \(0.860937\pi\)
\(422\) 19.4115 + 4.36819i 0.944938 + 0.212640i
\(423\) 0 0
\(424\) 17.6574 22.5629i 0.857518 1.09575i
\(425\) 2.86554i 0.138999i
\(426\) 0 0
\(427\) −1.35070 7.15956i −0.0653649 0.346475i
\(428\) −10.8695 5.15290i −0.525399 0.249075i
\(429\) 0 0
\(430\) −19.5482 4.39894i −0.942696 0.212136i
\(431\) 5.07919i 0.244656i 0.992490 + 0.122328i \(0.0390360\pi\)
−0.992490 + 0.122328i \(0.960964\pi\)
\(432\) 0 0
\(433\) 14.7817i 0.710364i −0.934797 0.355182i \(-0.884419\pi\)
0.934797 0.355182i \(-0.115581\pi\)
\(434\) 0.997598 28.5904i 0.0478863 1.37238i
\(435\) 0 0
\(436\) 8.44711 17.8184i 0.404543 0.853344i
\(437\) 0.0937505 0.00448469
\(438\) 0 0
\(439\) 17.6945 0.844512 0.422256 0.906477i \(-0.361238\pi\)
0.422256 + 0.906477i \(0.361238\pi\)
\(440\) −1.58370 1.23938i −0.0754998 0.0590850i
\(441\) 0 0
\(442\) −10.8064 + 48.0218i −0.514008 + 2.28417i
\(443\) −35.8340 −1.70252 −0.851262 0.524742i \(-0.824162\pi\)
−0.851262 + 0.524742i \(0.824162\pi\)
\(444\) 0 0
\(445\) 9.53341i 0.451927i
\(446\) −21.3138 4.79627i −1.00924 0.227110i
\(447\) 0 0
\(448\) −19.2462 + 8.80807i −0.909299 + 0.416142i
\(449\) −18.1094 −0.854637 −0.427318 0.904101i \(-0.640542\pi\)
−0.427318 + 0.904101i \(0.640542\pi\)
\(450\) 0 0
\(451\) 2.63875i 0.124254i
\(452\) 26.6521 + 12.6349i 1.25361 + 0.594296i
\(453\) 0 0
\(454\) 3.42696 15.2288i 0.160835 0.714724i
\(455\) −6.25256 33.1425i −0.293125 1.55375i
\(456\) 0 0
\(457\) −13.6177 −0.637010 −0.318505 0.947921i \(-0.603181\pi\)
−0.318505 + 0.947921i \(0.603181\pi\)
\(458\) 10.2411 + 2.30457i 0.478537 + 0.107685i
\(459\) 0 0
\(460\) 0.223099 0.470606i 0.0104021 0.0219421i
\(461\) −31.7263 −1.47764 −0.738821 0.673902i \(-0.764617\pi\)
−0.738821 + 0.673902i \(0.764617\pi\)
\(462\) 0 0
\(463\) 24.0983i 1.11994i −0.828511 0.559972i \(-0.810812\pi\)
0.828511 0.559972i \(-0.189188\pi\)
\(464\) 16.9097 13.8265i 0.785013 0.641880i
\(465\) 0 0
\(466\) −18.0284 4.05695i −0.835150 0.187935i
\(467\) 25.3568i 1.17337i 0.809814 + 0.586687i \(0.199568\pi\)
−0.809814 + 0.586687i \(0.800432\pi\)
\(468\) 0 0
\(469\) −4.10012 21.7332i −0.189326 1.00355i
\(470\) −26.4577 5.95379i −1.22040 0.274628i
\(471\) 0 0
\(472\) −2.98076 + 3.80886i −0.137200 + 0.175317i
\(473\) 1.84852 0.0849950
\(474\) 0 0
\(475\) 0.377843i 0.0173366i
\(476\) −32.6261 8.54741i −1.49542 0.391770i
\(477\) 0 0
\(478\) 2.65432 11.7954i 0.121406 0.539508i
\(479\) −40.2196 −1.83768 −0.918839 0.394632i \(-0.870872\pi\)
−0.918839 + 0.394632i \(0.870872\pi\)
\(480\) 0 0
\(481\) 35.1762i 1.60390i
\(482\) 2.37417 10.5504i 0.108140 0.480559i
\(483\) 0 0
\(484\) −19.7116 9.34466i −0.895984 0.424757i
\(485\) 15.0070i 0.681434i
\(486\) 0 0
\(487\) 34.9584i 1.58412i −0.610446 0.792058i \(-0.709010\pi\)
0.610446 0.792058i \(-0.290990\pi\)
\(488\) −6.13388 4.80028i −0.277668 0.217298i
\(489\) 0 0
\(490\) 22.8447 3.48972i 1.03202 0.157650i
\(491\) −11.4808 −0.518121 −0.259061 0.965861i \(-0.583413\pi\)
−0.259061 + 0.965861i \(0.583413\pi\)
\(492\) 0 0
\(493\) 34.8057 1.56757
\(494\) 1.42490 6.33204i 0.0641094 0.284892i
\(495\) 0 0
\(496\) −19.3590 23.6759i −0.869247 1.06308i
\(497\) 5.39086 1.01702i 0.241813 0.0456197i
\(498\) 0 0
\(499\) −1.23326 −0.0552084 −0.0276042 0.999619i \(-0.508788\pi\)
−0.0276042 + 0.999619i \(0.508788\pi\)
\(500\) 19.1973 + 9.10084i 0.858531 + 0.407002i
\(501\) 0 0
\(502\) −3.94883 + 17.5480i −0.176245 + 0.783203i
\(503\) −5.04712 −0.225040 −0.112520 0.993649i \(-0.535892\pi\)
−0.112520 + 0.993649i \(0.535892\pi\)
\(504\) 0 0
\(505\) −16.3487 −0.727509
\(506\) −0.0105484 + 0.0468753i −0.000468933 + 0.00208386i
\(507\) 0 0
\(508\) 2.13573 4.50511i 0.0947576 0.199882i
\(509\) 35.6387 1.57966 0.789828 0.613328i \(-0.210170\pi\)
0.789828 + 0.613328i \(0.210170\pi\)
\(510\) 0 0
\(511\) 33.1425 6.25256i 1.46614 0.276597i
\(512\) −9.25337 + 20.6489i −0.408945 + 0.912559i
\(513\) 0 0
\(514\) 2.31168 10.2727i 0.101964 0.453111i
\(515\) −22.4286 −0.988320
\(516\) 0 0
\(517\) 2.50190 0.110033
\(518\) 24.0879 + 0.840494i 1.05836 + 0.0369292i
\(519\) 0 0
\(520\) −28.3945 22.2211i −1.24518 0.974460i
\(521\) 3.12151i 0.136756i −0.997659 0.0683780i \(-0.978218\pi\)
0.997659 0.0683780i \(-0.0217824\pi\)
\(522\) 0 0
\(523\) 33.3779i 1.45951i −0.683706 0.729757i \(-0.739633\pi\)
0.683706 0.729757i \(-0.260367\pi\)
\(524\) 3.94883 8.32967i 0.172505 0.363883i
\(525\) 0 0
\(526\) −3.58752 + 15.9424i −0.156423 + 0.695120i
\(527\) 48.7328i 2.12284i
\(528\) 0 0
\(529\) 22.9876 0.999459
\(530\) −7.34181 + 32.6258i −0.318908 + 1.41717i
\(531\) 0 0
\(532\) 4.30200 + 1.12704i 0.186515 + 0.0488634i
\(533\) 47.3108i 2.04926i
\(534\) 0 0
\(535\) 14.0406 0.607027
\(536\) −18.6197 14.5715i −0.804248 0.629392i
\(537\) 0 0
\(538\) −16.8492 3.79159i −0.726420 0.163467i
\(539\) −1.98545 + 0.776782i −0.0855192 + 0.0334584i
\(540\) 0 0
\(541\) 13.8175i 0.594060i 0.954868 + 0.297030i \(0.0959961\pi\)
−0.954868 + 0.297030i \(0.904004\pi\)
\(542\) −26.1392 5.88213i −1.12278 0.252659i
\(543\) 0 0
\(544\) −32.2424 + 16.1385i −1.38238 + 0.691934i
\(545\) 23.0166i 0.985923i
\(546\) 0 0
\(547\) −12.4978 −0.534368 −0.267184 0.963646i \(-0.586093\pi\)
−0.267184 + 0.963646i \(0.586093\pi\)
\(548\) 1.62496 + 0.770343i 0.0694150 + 0.0329074i
\(549\) 0 0
\(550\) 0.188921 + 0.0425131i 0.00805564 + 0.00181277i
\(551\) −4.58939 −0.195515
\(552\) 0 0
\(553\) −20.5565 + 3.87813i −0.874153 + 0.164915i
\(554\) −5.64683 + 25.0936i −0.239911 + 1.06612i
\(555\) 0 0
\(556\) 19.8560 41.8842i 0.842081 1.77629i
\(557\) 7.57008i 0.320755i 0.987056 + 0.160377i \(0.0512711\pi\)
−0.987056 + 0.160377i \(0.948729\pi\)
\(558\) 0 0
\(559\) 33.1425 1.40178
\(560\) 15.8950 18.9130i 0.671686 0.799220i
\(561\) 0 0
\(562\) 24.1855 + 5.44248i 1.02020 + 0.229577i
\(563\) 15.0668i 0.634990i −0.948260 0.317495i \(-0.897158\pi\)
0.948260 0.317495i \(-0.102842\pi\)
\(564\) 0 0
\(565\) −34.4275 −1.44837
\(566\) −5.69285 + 25.2981i −0.239288 + 1.06336i
\(567\) 0 0
\(568\) 3.61441 4.61856i 0.151657 0.193790i
\(569\) −36.7056 −1.53878 −0.769390 0.638780i \(-0.779440\pi\)
−0.769390 + 0.638780i \(0.779440\pi\)
\(570\) 0 0
\(571\) −5.19529 −0.217416 −0.108708 0.994074i \(-0.534671\pi\)
−0.108708 + 0.994074i \(0.534671\pi\)
\(572\) 3.00570 + 1.42490i 0.125674 + 0.0595782i
\(573\) 0 0
\(574\) 32.3975 + 1.13044i 1.35224 + 0.0471835i
\(575\) 0.0501503i 0.00209141i
\(576\) 0 0
\(577\) 43.9319i 1.82891i 0.404688 + 0.914455i \(0.367380\pi\)
−0.404688 + 0.914455i \(0.632620\pi\)
\(578\) −32.5968 7.33528i −1.35585 0.305108i
\(579\) 0 0
\(580\) −10.9214 + 23.0377i −0.453488 + 0.956588i
\(581\) −30.2805 + 5.71262i −1.25625 + 0.236999i
\(582\) 0 0
\(583\) 3.08517i 0.127775i
\(584\) 22.2211 28.3945i 0.919516 1.17497i
\(585\) 0 0
\(586\) −19.3171 4.34695i −0.797983 0.179571i
\(587\) 34.5380i 1.42553i −0.701400 0.712767i \(-0.747441\pi\)
0.701400 0.712767i \(-0.252559\pi\)
\(588\) 0 0
\(589\) 6.42579i 0.264770i
\(590\) 1.23938 5.50759i 0.0510244 0.226744i
\(591\) 0 0
\(592\) 19.9474 16.3103i 0.819833 0.670351i
\(593\) 29.3232i 1.20416i 0.798436 + 0.602080i \(0.205661\pi\)
−0.798436 + 0.602080i \(0.794339\pi\)
\(594\) 0 0
\(595\) 38.6845 7.29810i 1.58591 0.299193i
\(596\) −5.64072 + 11.8985i −0.231053 + 0.487383i
\(597\) 0 0
\(598\) −0.189124 + 0.840438i −0.00773387 + 0.0343681i
\(599\) 19.9925i 0.816870i −0.912787 0.408435i \(-0.866075\pi\)
0.912787 0.408435i \(-0.133925\pi\)
\(600\) 0 0
\(601\) 21.1008i 0.860721i 0.902657 + 0.430361i \(0.141614\pi\)
−0.902657 + 0.430361i \(0.858386\pi\)
\(602\) −0.791902 + 22.6953i −0.0322755 + 0.924992i
\(603\) 0 0
\(604\) −17.6205 + 37.1688i −0.716969 + 1.51238i
\(605\) 25.4622 1.03519
\(606\) 0 0
\(607\) −21.6184 −0.877463 −0.438732 0.898618i \(-0.644572\pi\)
−0.438732 + 0.898618i \(0.644572\pi\)
\(608\) 4.25140 2.12799i 0.172417 0.0863012i
\(609\) 0 0
\(610\) 8.86955 + 1.99592i 0.359117 + 0.0808125i
\(611\) 44.8571 1.81472
\(612\) 0 0
\(613\) 27.8723i 1.12575i −0.826541 0.562876i \(-0.809695\pi\)
0.826541 0.562876i \(-0.190305\pi\)
\(614\) −1.32276 + 5.87813i −0.0533823 + 0.237222i
\(615\) 0 0
\(616\) −1.04756 + 2.02419i −0.0422074 + 0.0815569i
\(617\) 9.81447 0.395116 0.197558 0.980291i \(-0.436699\pi\)
0.197558 + 0.980291i \(0.436699\pi\)
\(618\) 0 0
\(619\) 22.8992i 0.920395i 0.887817 + 0.460197i \(0.152221\pi\)
−0.887817 + 0.460197i \(0.847779\pi\)
\(620\) 32.2560 + 15.2915i 1.29543 + 0.614122i
\(621\) 0 0
\(622\) 16.0963 + 3.62216i 0.645402 + 0.145235i
\(623\) 10.6175 2.00306i 0.425380 0.0802509i
\(624\) 0 0
\(625\) −27.0458 −1.08183
\(626\) −1.42200 + 6.31912i −0.0568345 + 0.252563i
\(627\) 0 0
\(628\) −21.8519 10.3593i −0.871986 0.413380i
\(629\) 41.0583 1.63710
\(630\) 0 0
\(631\) 15.4442i 0.614823i 0.951577 + 0.307412i \(0.0994628\pi\)
−0.951577 + 0.307412i \(0.900537\pi\)
\(632\) −13.7826 + 17.6116i −0.548241 + 0.700551i
\(633\) 0 0
\(634\) −3.92179 + 17.4278i −0.155754 + 0.692146i
\(635\) 5.81941i 0.230936i
\(636\) 0 0
\(637\) −35.5976 + 13.9271i −1.41043 + 0.551813i
\(638\) 0.516377 2.29470i 0.0204436 0.0908479i
\(639\) 0 0
\(640\) −0.564886 26.4051i −0.0223291 1.04375i
\(641\) 6.58003 0.259896 0.129948 0.991521i \(-0.458519\pi\)
0.129948 + 0.991521i \(0.458519\pi\)
\(642\) 0 0
\(643\) 18.3358i 0.723093i 0.932354 + 0.361546i \(0.117751\pi\)
−0.932354 + 0.361546i \(0.882249\pi\)
\(644\) −0.570995 0.149590i −0.0225004 0.00589466i
\(645\) 0 0
\(646\) 7.39086 + 1.66317i 0.290789 + 0.0654366i
\(647\) 10.4752 0.411824 0.205912 0.978571i \(-0.433984\pi\)
0.205912 + 0.978571i \(0.433984\pi\)
\(648\) 0 0
\(649\) 0.520810i 0.0204436i
\(650\) 3.38722 + 0.762229i 0.132858 + 0.0298971i
\(651\) 0 0
\(652\) 0.649300 + 0.307812i 0.0254286 + 0.0120549i
\(653\) 37.9262i 1.48417i 0.670307 + 0.742084i \(0.266162\pi\)
−0.670307 + 0.742084i \(0.733838\pi\)
\(654\) 0 0
\(655\) 10.7597i 0.420417i
\(656\) 26.8286 21.9368i 1.04748 0.856490i
\(657\) 0 0
\(658\) −1.07181 + 30.7172i −0.0417834 + 1.19748i
\(659\) −11.2037 −0.436435 −0.218218 0.975900i \(-0.570024\pi\)
−0.218218 + 0.975900i \(0.570024\pi\)
\(660\) 0 0
\(661\) −4.78369 −0.186064 −0.0930320 0.995663i \(-0.529656\pi\)
−0.0930320 + 0.995663i \(0.529656\pi\)
\(662\) 35.4406 + 7.97524i 1.37744 + 0.309966i
\(663\) 0 0
\(664\) −20.3022 + 25.9425i −0.787877 + 1.00676i
\(665\) −5.10084 + 0.962308i −0.197802 + 0.0373167i
\(666\) 0 0
\(667\) 0.609140 0.0235860
\(668\) −14.3054 6.78172i −0.553492 0.262393i
\(669\) 0 0
\(670\) 26.9240 + 6.05872i 1.04016 + 0.234069i
\(671\) −0.838724 −0.0323786
\(672\) 0 0
\(673\) −11.4707 −0.442162 −0.221081 0.975255i \(-0.570959\pi\)
−0.221081 + 0.975255i \(0.570959\pi\)
\(674\) 34.0977 + 7.67303i 1.31339 + 0.295554i
\(675\) 0 0
\(676\) 30.3962 + 14.4098i 1.16908 + 0.554225i
\(677\) 39.0226 1.49976 0.749881 0.661573i \(-0.230111\pi\)
0.749881 + 0.661573i \(0.230111\pi\)
\(678\) 0 0
\(679\) −16.7135 + 3.15312i −0.641406 + 0.121006i
\(680\) 25.9368 33.1425i 0.994633 1.27096i
\(681\) 0 0
\(682\) −3.21289 0.723000i −0.123028 0.0276851i
\(683\) 6.36772 0.243654 0.121827 0.992551i \(-0.461125\pi\)
0.121827 + 0.992551i \(0.461125\pi\)
\(684\) 0 0
\(685\) −2.09902 −0.0801995
\(686\) −8.68644 24.7092i −0.331650 0.943403i
\(687\) 0 0
\(688\) 15.3674 + 18.7942i 0.585875 + 0.716520i
\(689\) 55.3148i 2.10732i
\(690\) 0 0
\(691\) 10.3191i 0.392558i −0.980548 0.196279i \(-0.937114\pi\)
0.980548 0.196279i \(-0.0628858\pi\)
\(692\) −22.6098 10.7186i −0.859495 0.407459i
\(693\) 0 0
\(694\) −24.5588 5.52648i −0.932238 0.209782i
\(695\) 54.1034i 2.05226i
\(696\) 0 0
\(697\) 55.2220 2.09168
\(698\) −12.0140 2.70351i −0.454735 0.102329i
\(699\) 0 0
\(700\) −0.602892 + 2.30128i −0.0227872 + 0.0869803i
\(701\) 38.3982i 1.45028i 0.688601 + 0.725141i \(0.258225\pi\)
−0.688601 + 0.725141i \(0.741775\pi\)
\(702\) 0 0
\(703\) −5.41384 −0.204187
\(704\) 0.585645 + 2.36513i 0.0220723 + 0.0891393i
\(705\) 0 0
\(706\) 2.27771 10.1218i 0.0857227 0.380938i
\(707\) 3.43502 + 18.2078i 0.129187 + 0.684775i
\(708\) 0 0
\(709\) 8.88381i 0.333638i −0.985988 0.166819i \(-0.946650\pi\)
0.985988 0.166819i \(-0.0533496\pi\)
\(710\) −1.50285 + 6.67841i −0.0564009 + 0.250636i
\(711\) 0 0
\(712\) 7.11871 9.09641i 0.266785 0.340902i
\(713\) 0.852881i 0.0319407i
\(714\) 0 0
\(715\) −3.88256 −0.145200
\(716\) −27.7266 13.1443i −1.03619 0.491226i
\(717\) 0 0
\(718\) 4.45707 19.8065i 0.166336 0.739171i
\(719\) −40.2196 −1.49994 −0.749968 0.661474i \(-0.769931\pi\)
−0.749968 + 0.661474i \(0.769931\pi\)
\(720\) 0 0
\(721\) 4.71245 + 24.9790i 0.175501 + 0.930266i
\(722\) 25.2400 + 5.67977i 0.939335 + 0.211379i
\(723\) 0 0
\(724\) −0.891086 0.422435i −0.0331170 0.0156997i
\(725\) 2.45502i 0.0911772i
\(726\) 0 0
\(727\) 2.89742 0.107459 0.0537297 0.998556i \(-0.482889\pi\)
0.0537297 + 0.998556i \(0.482889\pi\)
\(728\) −18.7820 + 36.2922i −0.696107 + 1.34508i
\(729\) 0 0
\(730\) −9.23938 + 41.0583i −0.341965 + 1.51963i
\(731\) 38.6845i 1.43080i
\(732\) 0 0
\(733\) −6.37891 −0.235611 −0.117805 0.993037i \(-0.537586\pi\)
−0.117805 + 0.993037i \(0.537586\pi\)
\(734\) −24.0208 5.40541i −0.886623 0.199517i
\(735\) 0 0
\(736\) −0.564280 + 0.282443i −0.0207996 + 0.0104110i
\(737\) −2.54599 −0.0937827
\(738\) 0 0
\(739\) −7.14100 −0.262686 −0.131343 0.991337i \(-0.541929\pi\)
−0.131343 + 0.991337i \(0.541929\pi\)
\(740\) −12.8834 + 27.1762i −0.473602 + 0.999018i
\(741\) 0 0
\(742\) 37.8784 + 1.32168i 1.39056 + 0.0485204i
\(743\) 22.2570i 0.816530i −0.912864 0.408265i \(-0.866134\pi\)
0.912864 0.408265i \(-0.133866\pi\)
\(744\) 0 0
\(745\) 15.3698i 0.563105i
\(746\) 0.447110 1.98688i 0.0163699 0.0727450i
\(747\) 0 0
\(748\) −1.66317 + 3.50830i −0.0608116 + 0.128276i
\(749\) −2.95006 15.6372i −0.107793 0.571370i
\(750\) 0 0
\(751\) 21.7697i 0.794387i 0.917735 + 0.397193i \(0.130016\pi\)
−0.917735 + 0.397193i \(0.869984\pi\)
\(752\) 20.7991 + 25.4371i 0.758466 + 0.927597i
\(753\) 0 0
\(754\) 9.25826 41.1422i 0.337166 1.49831i
\(755\) 48.0122i 1.74734i
\(756\) 0 0
\(757\) 4.51372i 0.164054i 0.996630 + 0.0820269i \(0.0261393\pi\)
−0.996630 + 0.0820269i \(0.973861\pi\)
\(758\) −33.1215 7.45336i −1.20303 0.270718i
\(759\) 0 0
\(760\) −3.41997 + 4.37009i −0.124055 + 0.158520i
\(761\) 3.12151i 0.113155i 0.998398 + 0.0565774i \(0.0180188\pi\)
−0.998398 + 0.0565774i \(0.981981\pi\)
\(762\) 0 0
\(763\) 25.6339 4.83601i 0.928009 0.175075i
\(764\) −18.6862 + 39.4166i −0.676041 + 1.42604i
\(765\) 0 0
\(766\) 27.0177 + 6.07982i 0.976189 + 0.219673i
\(767\) 9.33773i 0.337166i
\(768\) 0 0
\(769\) 52.3945i 1.88939i −0.327944 0.944697i \(-0.606356\pi\)
0.327944 0.944697i \(-0.393644\pi\)
\(770\) 0.0927692 2.65870i 0.00334317 0.0958128i
\(771\) 0 0
\(772\) 13.7133 + 6.50103i 0.493552 + 0.233977i
\(773\) −14.5408 −0.522996 −0.261498 0.965204i \(-0.584216\pi\)
−0.261498 + 0.965204i \(0.584216\pi\)
\(774\) 0 0
\(775\) −3.43737 −0.123474
\(776\) −11.2059 + 14.3191i −0.402269 + 0.514027i
\(777\) 0 0
\(778\) 9.81287 43.6068i 0.351808 1.56338i
\(779\) −7.28143 −0.260884
\(780\) 0 0
\(781\) 0.631525i 0.0225977i
\(782\) −0.980973 0.220749i −0.0350795 0.00789398i
\(783\) 0 0
\(784\) −24.4034 13.7287i −0.871548 0.490309i
\(785\) 28.2269 1.00746
\(786\) 0 0
\(787\) 18.0754i 0.644318i −0.946686 0.322159i \(-0.895591\pi\)
0.946686 0.322159i \(-0.104409\pi\)
\(788\) 10.1033 21.3119i 0.359916 0.759207i
\(789\) 0 0
\(790\) 5.73069 25.4662i 0.203889 0.906048i
\(791\) 7.23354 + 38.3423i 0.257195 + 1.36330i
\(792\) 0 0
\(793\) −15.0377 −0.534004
\(794\) 8.69141 + 1.95583i 0.308447 + 0.0694100i
\(795\) 0 0
\(796\) 44.7930 + 21.2349i 1.58765 + 0.752653i
\(797\) −8.28822 −0.293584 −0.146792 0.989167i \(-0.546895\pi\)
−0.146792 + 0.989167i \(0.546895\pi\)
\(798\) 0 0
\(799\) 52.3580i 1.85229i
\(800\) 1.13833 + 2.27422i 0.0402461 + 0.0804058i
\(801\) 0 0
\(802\) −4.27827 0.962742i −0.151071 0.0339956i
\(803\) 3.88256i 0.137013i
\(804\) 0 0
\(805\) 0.677024 0.127725i 0.0238620 0.00450172i
\(806\) −57.6048 12.9629i −2.02904 0.456597i
\(807\) 0 0
\(808\) 15.5993 + 12.2078i 0.548783 + 0.429469i
\(809\) 52.3022 1.83885 0.919425 0.393266i \(-0.128655\pi\)
0.919425 + 0.393266i \(0.128655\pi\)
\(810\) 0 0
\(811\) 16.3945i 0.575689i 0.957677 + 0.287845i \(0.0929386\pi\)
−0.957677 + 0.287845i \(0.907061\pi\)
\(812\) 27.9521 + 7.32290i 0.980926 + 0.256984i
\(813\) 0 0
\(814\) 0.609140 2.70692i 0.0213504 0.0948775i
\(815\) −0.838724 −0.0293792
\(816\) 0 0
\(817\) 5.10084i 0.178456i
\(818\) −0.952172 + 4.23130i −0.0332919 + 0.147944i
\(819\) 0 0
\(820\) −17.3277 + 36.5511i −0.605110 + 1.27642i
\(821\) 14.9459i 0.521614i −0.965391 0.260807i \(-0.916011\pi\)
0.965391 0.260807i \(-0.0839887\pi\)
\(822\) 0 0
\(823\) 21.3876i 0.745526i 0.927927 + 0.372763i \(0.121590\pi\)
−0.927927 + 0.372763i \(0.878410\pi\)
\(824\) 21.4005 + 16.7477i 0.745520 + 0.583433i
\(825\) 0 0
\(826\) −6.39428 0.223114i −0.222485 0.00776313i
\(827\) 16.5605 0.575866 0.287933 0.957650i \(-0.407032\pi\)
0.287933 + 0.957650i \(0.407032\pi\)
\(828\) 0 0
\(829\) −47.4372 −1.64756 −0.823781 0.566908i \(-0.808139\pi\)
−0.823781 + 0.566908i \(0.808139\pi\)
\(830\) 8.44150 37.5126i 0.293009 1.30208i
\(831\) 0 0
\(832\) 10.5002 + 42.4051i 0.364028 + 1.47013i
\(833\) −16.2560 41.5501i −0.563236 1.43962i
\(834\) 0 0
\(835\) 18.4788 0.639484
\(836\) 0.219302 0.462595i 0.00758470 0.0159992i
\(837\) 0 0
\(838\) −4.82153 + 21.4261i −0.166557 + 0.740152i
\(839\) 12.3796 0.427390 0.213695 0.976900i \(-0.431450\pi\)
0.213695 + 0.976900i \(0.431450\pi\)
\(840\) 0 0
\(841\) −0.819411 −0.0282555
\(842\) −5.39086 + 23.9561i −0.185781 + 0.825582i
\(843\) 0 0
\(844\) 25.4261 + 12.0537i 0.875202 + 0.414905i
\(845\) −39.2638 −1.35072
\(846\) 0 0
\(847\) −5.34985 28.3576i −0.183823 0.974379i
\(848\) 31.3674 25.6481i 1.07716 0.880758i
\(849\) 0 0
\(850\) −0.889686 + 3.95362i −0.0305160 + 0.135608i
\(851\) 0.718568 0.0246322
\(852\) 0 0
\(853\) 27.8292 0.952855 0.476428 0.879214i \(-0.341931\pi\)
0.476428 + 0.879214i \(0.341931\pi\)
\(854\) 0.359308 10.2975i 0.0122953 0.352373i
\(855\) 0 0
\(856\) −13.3970 10.4843i −0.457899 0.358345i
\(857\) 19.8278i 0.677306i 0.940911 + 0.338653i \(0.109971\pi\)
−0.940911 + 0.338653i \(0.890029\pi\)
\(858\) 0 0
\(859\) 35.5541i 1.21309i 0.795049 + 0.606545i \(0.207445\pi\)
−0.795049 + 0.606545i \(0.792555\pi\)
\(860\) −25.6051 12.1385i −0.873125 0.413921i
\(861\) 0 0
\(862\) −1.57698 + 7.00782i −0.0537120 + 0.238687i
\(863\) 32.6385i 1.11103i 0.831508 + 0.555513i \(0.187478\pi\)
−0.831508 + 0.555513i \(0.812522\pi\)
\(864\) 0 0
\(865\) 29.2058 0.993028
\(866\) 4.58939 20.3945i 0.155954 0.693034i
\(867\) 0 0
\(868\) 10.2531 39.1368i 0.348012 1.32839i
\(869\) 2.40814i 0.0816907i
\(870\) 0 0
\(871\) −45.6477 −1.54671
\(872\) 17.1868 21.9615i 0.582018 0.743712i
\(873\) 0 0
\(874\) 0.129349 + 0.0291074i 0.00437528 + 0.000984574i
\(875\) 5.21027 + 27.6177i 0.176139 + 0.933649i
\(876\) 0 0
\(877\) 31.1987i 1.05350i 0.850019 + 0.526752i \(0.176590\pi\)
−0.850019 + 0.526752i \(0.823410\pi\)
\(878\) 24.4133 + 5.49374i 0.823909 + 0.185405i
\(879\) 0 0
\(880\) −1.80025 2.20169i −0.0606863 0.0742188i
\(881\) 51.2309i 1.72601i 0.505192 + 0.863007i \(0.331422\pi\)
−0.505192 + 0.863007i \(0.668578\pi\)
\(882\) 0 0
\(883\) −16.9684 −0.571033 −0.285516 0.958374i \(-0.592165\pi\)
−0.285516 + 0.958374i \(0.592165\pi\)
\(884\) −29.8194 + 62.9011i −1.00294 + 2.11559i
\(885\) 0 0
\(886\) −49.4405 11.1256i −1.66099 0.373773i
\(887\) 18.7434 0.629342 0.314671 0.949201i \(-0.398106\pi\)
0.314671 + 0.949201i \(0.398106\pi\)
\(888\) 0 0
\(889\) 6.48115 1.22271i 0.217371 0.0410085i
\(890\) −2.95991 + 13.1534i −0.0992164 + 0.440901i
\(891\) 0 0
\(892\) −27.9178 13.2349i −0.934758 0.443139i
\(893\) 6.90379i 0.231026i
\(894\) 0 0
\(895\) 35.8155 1.19718
\(896\) −29.2890 + 6.17707i −0.978476 + 0.206362i
\(897\) 0 0
\(898\) −24.9858 5.62257i −0.833786 0.187628i
\(899\) 41.7513i 1.39248i
\(900\) 0 0
\(901\) 64.5643 2.15095
\(902\) 0.819273 3.64072i 0.0272788 0.121223i
\(903\) 0 0
\(904\) 32.8494 + 25.7074i 1.09255 + 0.855016i
\(905\) 1.15105 0.0382621
\(906\) 0 0
\(907\) 1.15395 0.0383163 0.0191581 0.999816i \(-0.493901\pi\)
0.0191581 + 0.999816i \(0.493901\pi\)
\(908\) 9.45642 19.9474i 0.313822 0.661978i
\(909\) 0 0
\(910\) 1.66328 47.6684i 0.0551373 1.58019i
\(911\) 44.7588i 1.48292i 0.670994 + 0.741462i \(0.265867\pi\)
−0.670994 + 0.741462i \(0.734133\pi\)
\(912\) 0 0
\(913\) 3.54728i 0.117398i
\(914\) −18.7885 4.22800i −0.621469 0.139850i
\(915\) 0 0
\(916\) 13.4143 + 6.35928i 0.443221 + 0.210117i
\(917\) 11.9833 2.26072i 0.395722 0.0746556i
\(918\) 0 0
\(919\) 40.3722i 1.33176i 0.746060 + 0.665878i \(0.231943\pi\)
−0.746060 + 0.665878i \(0.768057\pi\)
\(920\) 0.453925 0.580033i 0.0149655 0.0191231i
\(921\) 0 0
\(922\) −43.7731 9.85031i −1.44159 0.324403i
\(923\) 11.3228i 0.372694i
\(924\) 0 0
\(925\) 2.89604i 0.0952214i
\(926\) 7.48200 33.2488i 0.245874 1.09262i
\(927\) 0 0
\(928\) 27.6233 13.8265i 0.906780 0.453877i
\(929\) 13.4697i 0.441928i −0.975282 0.220964i \(-0.929080\pi\)
0.975282 0.220964i \(-0.0709203\pi\)
\(930\) 0 0
\(931\) 2.14347 + 5.47869i 0.0702494 + 0.179557i
\(932\) −23.6144 11.1948i −0.773516 0.366699i
\(933\) 0 0
\(934\) −7.87272 + 34.9851i −0.257603 + 1.14475i
\(935\) 4.53179i 0.148205i
\(936\) 0 0
\(937\) 11.6055i 0.379135i 0.981868 + 0.189567i \(0.0607086\pi\)
−0.981868 + 0.189567i \(0.939291\pi\)
\(938\) 1.09070 31.2586i 0.0356125 1.02063i
\(939\) 0 0
\(940\) −34.6554 16.4290i −1.13034 0.535856i
\(941\) −29.2387 −0.953154 −0.476577 0.879133i \(-0.658123\pi\)
−0.476577 + 0.879133i \(0.658123\pi\)
\(942\) 0 0
\(943\) 0.966449 0.0314719
\(944\) −5.29515 + 4.32967i −0.172343 + 0.140919i
\(945\) 0 0
\(946\) 2.55042 + 0.573923i 0.0829214 + 0.0186599i
\(947\) 24.0096 0.780208 0.390104 0.920771i \(-0.372439\pi\)
0.390104 + 0.920771i \(0.372439\pi\)
\(948\) 0 0
\(949\) 69.6114i 2.25968i
\(950\) 0.117312 0.521314i 0.00380610 0.0169137i
\(951\) 0 0
\(952\) −42.3609 21.9226i −1.37292 0.710517i
\(953\) −38.6716 −1.25270 −0.626348 0.779544i \(-0.715451\pi\)
−0.626348 + 0.779544i \(0.715451\pi\)
\(954\) 0 0
\(955\) 50.9158i 1.64760i
\(956\) 7.32440 15.4501i 0.236888 0.499692i
\(957\) 0 0
\(958\) −55.4914 12.4873i −1.79284 0.403445i
\(959\) 0.441024 + 2.33771i 0.0142414 + 0.0754885i
\(960\) 0 0
\(961\) 27.4577 0.885731
\(962\) 10.9214 48.5330i 0.352121 1.56477i
\(963\) 0 0
\(964\) 6.55134 13.8194i 0.211004 0.445093i
\(965\) −17.7139 −0.570232
\(966\) 0 0
\(967\) 12.2768i 0.394795i −0.980324 0.197397i \(-0.936751\pi\)
0.980324 0.197397i \(-0.0632489\pi\)
\(968\) −24.2951 19.0130i −0.780873 0.611099i
\(969\) 0 0
\(970\) 4.65934 20.7054i 0.149603 0.664809i
\(971\) 20.5330i 0.658937i −0.944167 0.329468i \(-0.893131\pi\)
0.944167 0.329468i \(-0.106869\pi\)
\(972\) 0 0
\(973\) 60.2556 11.3676i 1.93171 0.364429i
\(974\) 10.8538 48.2325i 0.347778 1.54547i
\(975\) 0 0
\(976\) −6.97260 8.52743i −0.223187 0.272956i
\(977\) 10.7477 0.343849 0.171924 0.985110i \(-0.445002\pi\)
0.171924 + 0.985110i \(0.445002\pi\)
\(978\) 0 0
\(979\) 1.24381i 0.0397523i
\(980\) 32.6026 + 2.27796i 1.04145 + 0.0727668i
\(981\) 0 0
\(982\) −15.8402 3.56453i −0.505481 0.113749i
\(983\) 26.5912 0.848128 0.424064 0.905632i \(-0.360603\pi\)
0.424064 + 0.905632i \(0.360603\pi\)
\(984\) 0 0
\(985\) 27.5294i 0.877159i
\(986\) 48.0218 + 10.8064i 1.52933 + 0.344146i
\(987\) 0 0
\(988\) 3.93191 8.29398i 0.125091 0.263867i
\(989\) 0.677024i 0.0215281i
\(990\) 0 0
\(991\) 30.5203i 0.969510i 0.874650 + 0.484755i \(0.161091\pi\)
−0.874650 + 0.484755i \(0.838909\pi\)
\(992\) −19.3590 38.6765i −0.614650 1.22798i
\(993\) 0 0
\(994\) 7.75359 + 0.270544i 0.245929 + 0.00858114i
\(995\) −57.8607 −1.83431
\(996\) 0 0
\(997\) 23.6105 0.747752 0.373876 0.927479i \(-0.378029\pi\)
0.373876 + 0.927479i \(0.378029\pi\)
\(998\) −1.70155 0.382900i −0.0538615 0.0121205i
\(999\) 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 504.2.p.g.307.15 16
3.2 odd 2 168.2.p.a.139.1 16
4.3 odd 2 2016.2.p.g.559.3 16
7.6 odd 2 inner 504.2.p.g.307.16 16
8.3 odd 2 inner 504.2.p.g.307.14 16
8.5 even 2 2016.2.p.g.559.14 16
12.11 even 2 672.2.p.a.559.15 16
21.20 even 2 168.2.p.a.139.2 yes 16
24.5 odd 2 672.2.p.a.559.10 16
24.11 even 2 168.2.p.a.139.3 yes 16
28.27 even 2 2016.2.p.g.559.13 16
56.13 odd 2 2016.2.p.g.559.4 16
56.27 even 2 inner 504.2.p.g.307.13 16
84.83 odd 2 672.2.p.a.559.2 16
168.83 odd 2 168.2.p.a.139.4 yes 16
168.125 even 2 672.2.p.a.559.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.2.p.a.139.1 16 3.2 odd 2
168.2.p.a.139.2 yes 16 21.20 even 2
168.2.p.a.139.3 yes 16 24.11 even 2
168.2.p.a.139.4 yes 16 168.83 odd 2
504.2.p.g.307.13 16 56.27 even 2 inner
504.2.p.g.307.14 16 8.3 odd 2 inner
504.2.p.g.307.15 16 1.1 even 1 trivial
504.2.p.g.307.16 16 7.6 odd 2 inner
672.2.p.a.559.2 16 84.83 odd 2
672.2.p.a.559.7 16 168.125 even 2
672.2.p.a.559.10 16 24.5 odd 2
672.2.p.a.559.15 16 12.11 even 2
2016.2.p.g.559.3 16 4.3 odd 2
2016.2.p.g.559.4 16 56.13 odd 2
2016.2.p.g.559.13 16 28.27 even 2
2016.2.p.g.559.14 16 8.5 even 2