Properties

Label 460.2.e.b.91.2
Level $460$
Weight $2$
Character 460.91
Analytic conductor $3.673$
Analytic rank $0$
Dimension $32$
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] = [460,2,Mod(91,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("460.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.e (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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.2
Character \(\chi\) \(=\) 460.91
Dual form 460.2.e.b.91.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39466 - 0.234385i) q^{2} -1.37989i q^{3} +(1.89013 + 0.653773i) q^{4} +1.00000i q^{5} +(-0.323424 + 1.92446i) q^{6} +2.31854 q^{7} +(-2.48284 - 1.35481i) q^{8} +1.09592 q^{9} +O(q^{10})\) \(q+(-1.39466 - 0.234385i) q^{2} -1.37989i q^{3} +(1.89013 + 0.653773i) q^{4} +1.00000i q^{5} +(-0.323424 + 1.92446i) q^{6} +2.31854 q^{7} +(-2.48284 - 1.35481i) q^{8} +1.09592 q^{9} +(0.234385 - 1.39466i) q^{10} +1.65400 q^{11} +(0.902131 - 2.60816i) q^{12} -3.48270 q^{13} +(-3.23356 - 0.543431i) q^{14} +1.37989 q^{15} +(3.14516 + 2.47143i) q^{16} +5.56745i q^{17} +(-1.52843 - 0.256867i) q^{18} +6.63011 q^{19} +(-0.653773 + 1.89013i) q^{20} -3.19932i q^{21} +(-2.30676 - 0.387673i) q^{22} +(-0.716404 + 4.74202i) q^{23} +(-1.86948 + 3.42604i) q^{24} -1.00000 q^{25} +(4.85717 + 0.816294i) q^{26} -5.65189i q^{27} +(4.38233 + 1.51580i) q^{28} +4.94862 q^{29} +(-1.92446 - 0.323424i) q^{30} -3.53020i q^{31} +(-3.80715 - 4.18397i) q^{32} -2.28233i q^{33} +(1.30493 - 7.76468i) q^{34} +2.31854i q^{35} +(2.07142 + 0.716481i) q^{36} -9.38162i q^{37} +(-9.24672 - 1.55400i) q^{38} +4.80573i q^{39} +(1.35481 - 2.48284i) q^{40} -6.37131 q^{41} +(-0.749872 + 4.46194i) q^{42} +12.8813 q^{43} +(3.12628 + 1.08134i) q^{44} +1.09592i q^{45} +(2.11060 - 6.44557i) q^{46} -8.60850i q^{47} +(3.41029 - 4.33996i) q^{48} -1.62438 q^{49} +(1.39466 + 0.234385i) q^{50} +7.68244 q^{51} +(-6.58275 - 2.27690i) q^{52} -2.04707i q^{53} +(-1.32472 + 7.88245i) q^{54} +1.65400i q^{55} +(-5.75656 - 3.14117i) q^{56} -9.14879i q^{57} +(-6.90162 - 1.15988i) q^{58} +9.50571i q^{59} +(2.60816 + 0.902131i) q^{60} +3.86641i q^{61} +(-0.827425 + 4.92341i) q^{62} +2.54093 q^{63} +(4.32901 + 6.72753i) q^{64} -3.48270i q^{65} +(-0.534945 + 3.18307i) q^{66} +4.67720 q^{67} +(-3.63985 + 10.5232i) q^{68} +(6.54344 + 0.988556i) q^{69} +(0.543431 - 3.23356i) q^{70} -10.9401i q^{71} +(-2.72099 - 1.48475i) q^{72} +6.51430 q^{73} +(-2.19891 + 13.0841i) q^{74} +1.37989i q^{75} +(12.5318 + 4.33459i) q^{76} +3.83487 q^{77} +(1.12639 - 6.70234i) q^{78} -4.23483 q^{79} +(-2.47143 + 3.14516i) q^{80} -4.51121 q^{81} +(8.88578 + 1.49334i) q^{82} -5.44089 q^{83} +(2.09163 - 6.04711i) q^{84} -5.56745 q^{85} +(-17.9649 - 3.01918i) q^{86} -6.82852i q^{87} +(-4.10663 - 2.24085i) q^{88} +7.48765i q^{89} +(0.256867 - 1.52843i) q^{90} -8.07478 q^{91} +(-4.45430 + 8.49466i) q^{92} -4.87126 q^{93} +(-2.01770 + 12.0059i) q^{94} +6.63011i q^{95} +(-5.77340 + 5.25343i) q^{96} +19.0123i q^{97} +(2.26545 + 0.380731i) q^{98} +1.81265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48} - 12 q^{49} - 4 q^{50} + 16 q^{52} + 42 q^{54} - 10 q^{58} - 36 q^{62} - 22 q^{64} - 44 q^{69} - 42 q^{70} - 32 q^{72} - 8 q^{73} - 72 q^{77} + 122 q^{78} - 32 q^{81} + 20 q^{82} - 44 q^{85} + 64 q^{92} + 40 q^{93} - 26 q^{94} + 16 q^{96} + 62 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39466 0.234385i −0.986170 0.165735i
\(3\) 1.37989i 0.796677i −0.917238 0.398339i \(-0.869587\pi\)
0.917238 0.398339i \(-0.130413\pi\)
\(4\) 1.89013 + 0.653773i 0.945064 + 0.326886i
\(5\) 1.00000i 0.447214i
\(6\) −0.323424 + 1.92446i −0.132037 + 0.785659i
\(7\) 2.31854 0.876325 0.438162 0.898896i \(-0.355629\pi\)
0.438162 + 0.898896i \(0.355629\pi\)
\(8\) −2.48284 1.35481i −0.877817 0.478996i
\(9\) 1.09592 0.365306
\(10\) 0.234385 1.39466i 0.0741191 0.441029i
\(11\) 1.65400 0.498701 0.249350 0.968413i \(-0.419783\pi\)
0.249350 + 0.968413i \(0.419783\pi\)
\(12\) 0.902131 2.60816i 0.260423 0.752910i
\(13\) −3.48270 −0.965928 −0.482964 0.875640i \(-0.660440\pi\)
−0.482964 + 0.875640i \(0.660440\pi\)
\(14\) −3.23356 0.543431i −0.864206 0.145238i
\(15\) 1.37989 0.356285
\(16\) 3.14516 + 2.47143i 0.786291 + 0.617857i
\(17\) 5.56745i 1.35031i 0.737678 + 0.675153i \(0.235922\pi\)
−0.737678 + 0.675153i \(0.764078\pi\)
\(18\) −1.52843 0.256867i −0.360254 0.0605440i
\(19\) 6.63011 1.52105 0.760526 0.649307i \(-0.224941\pi\)
0.760526 + 0.649307i \(0.224941\pi\)
\(20\) −0.653773 + 1.89013i −0.146188 + 0.422645i
\(21\) 3.19932i 0.698148i
\(22\) −2.30676 0.387673i −0.491804 0.0826523i
\(23\) −0.716404 + 4.74202i −0.149381 + 0.988780i
\(24\) −1.86948 + 3.42604i −0.381605 + 0.699337i
\(25\) −1.00000 −0.200000
\(26\) 4.85717 + 0.816294i 0.952570 + 0.160088i
\(27\) 5.65189i 1.08771i
\(28\) 4.38233 + 1.51580i 0.828183 + 0.286459i
\(29\) 4.94862 0.918935 0.459468 0.888194i \(-0.348040\pi\)
0.459468 + 0.888194i \(0.348040\pi\)
\(30\) −1.92446 0.323424i −0.351357 0.0590489i
\(31\) 3.53020i 0.634042i −0.948419 0.317021i \(-0.897317\pi\)
0.948419 0.317021i \(-0.102683\pi\)
\(32\) −3.80715 4.18397i −0.673016 0.739628i
\(33\) 2.28233i 0.397303i
\(34\) 1.30493 7.76468i 0.223793 1.33163i
\(35\) 2.31854i 0.391904i
\(36\) 2.07142 + 0.716481i 0.345237 + 0.119413i
\(37\) 9.38162i 1.54233i −0.636636 0.771164i \(-0.719675\pi\)
0.636636 0.771164i \(-0.280325\pi\)
\(38\) −9.24672 1.55400i −1.50002 0.252092i
\(39\) 4.80573i 0.769533i
\(40\) 1.35481 2.48284i 0.214213 0.392572i
\(41\) −6.37131 −0.995031 −0.497516 0.867455i \(-0.665754\pi\)
−0.497516 + 0.867455i \(0.665754\pi\)
\(42\) −0.749872 + 4.46194i −0.115708 + 0.688493i
\(43\) 12.8813 1.96438 0.982188 0.187900i \(-0.0601680\pi\)
0.982188 + 0.187900i \(0.0601680\pi\)
\(44\) 3.12628 + 1.08134i 0.471304 + 0.163018i
\(45\) 1.09592i 0.163370i
\(46\) 2.11060 6.44557i 0.311190 0.950348i
\(47\) 8.60850i 1.25568i −0.778343 0.627840i \(-0.783939\pi\)
0.778343 0.627840i \(-0.216061\pi\)
\(48\) 3.41029 4.33996i 0.492232 0.626420i
\(49\) −1.62438 −0.232055
\(50\) 1.39466 + 0.234385i 0.197234 + 0.0331470i
\(51\) 7.68244 1.07576
\(52\) −6.58275 2.27690i −0.912864 0.315749i
\(53\) 2.04707i 0.281187i −0.990067 0.140594i \(-0.955099\pi\)
0.990067 0.140594i \(-0.0449011\pi\)
\(54\) −1.32472 + 7.88245i −0.180271 + 1.07267i
\(55\) 1.65400i 0.223026i
\(56\) −5.75656 3.14117i −0.769253 0.419756i
\(57\) 9.14879i 1.21179i
\(58\) −6.90162 1.15988i −0.906227 0.152300i
\(59\) 9.50571i 1.23754i 0.785573 + 0.618769i \(0.212368\pi\)
−0.785573 + 0.618769i \(0.787632\pi\)
\(60\) 2.60816 + 0.902131i 0.336712 + 0.116465i
\(61\) 3.86641i 0.495043i 0.968882 + 0.247521i \(0.0796161\pi\)
−0.968882 + 0.247521i \(0.920384\pi\)
\(62\) −0.827425 + 4.92341i −0.105083 + 0.625273i
\(63\) 2.54093 0.320127
\(64\) 4.32901 + 6.72753i 0.541126 + 0.840942i
\(65\) 3.48270i 0.431976i
\(66\) −0.534945 + 3.18307i −0.0658472 + 0.391809i
\(67\) 4.67720 0.571411 0.285705 0.958318i \(-0.407772\pi\)
0.285705 + 0.958318i \(0.407772\pi\)
\(68\) −3.63985 + 10.5232i −0.441396 + 1.27612i
\(69\) 6.54344 + 0.988556i 0.787738 + 0.119008i
\(70\) 0.543431 3.23356i 0.0649524 0.386484i
\(71\) 10.9401i 1.29835i −0.760639 0.649175i \(-0.775114\pi\)
0.760639 0.649175i \(-0.224886\pi\)
\(72\) −2.72099 1.48475i −0.320672 0.174980i
\(73\) 6.51430 0.762441 0.381220 0.924484i \(-0.375504\pi\)
0.381220 + 0.924484i \(0.375504\pi\)
\(74\) −2.19891 + 13.0841i −0.255618 + 1.52100i
\(75\) 1.37989i 0.159335i
\(76\) 12.5318 + 4.33459i 1.43749 + 0.497211i
\(77\) 3.83487 0.437024
\(78\) 1.12639 6.70234i 0.127539 0.758891i
\(79\) −4.23483 −0.476456 −0.238228 0.971209i \(-0.576566\pi\)
−0.238228 + 0.971209i \(0.576566\pi\)
\(80\) −2.47143 + 3.14516i −0.276314 + 0.351640i
\(81\) −4.51121 −0.501246
\(82\) 8.88578 + 1.49334i 0.981270 + 0.164912i
\(83\) −5.44089 −0.597215 −0.298608 0.954376i \(-0.596522\pi\)
−0.298608 + 0.954376i \(0.596522\pi\)
\(84\) 2.09163 6.04711i 0.228215 0.659794i
\(85\) −5.56745 −0.603875
\(86\) −17.9649 3.01918i −1.93721 0.325566i
\(87\) 6.82852i 0.732095i
\(88\) −4.10663 2.24085i −0.437768 0.238876i
\(89\) 7.48765i 0.793689i 0.917886 + 0.396845i \(0.129895\pi\)
−0.917886 + 0.396845i \(0.870105\pi\)
\(90\) 0.256867 1.52843i 0.0270761 0.161110i
\(91\) −8.07478 −0.846467
\(92\) −4.45430 + 8.49466i −0.464393 + 0.885629i
\(93\) −4.87126 −0.505127
\(94\) −2.01770 + 12.0059i −0.208110 + 1.23831i
\(95\) 6.63011i 0.680235i
\(96\) −5.77340 + 5.25343i −0.589245 + 0.536176i
\(97\) 19.0123i 1.93040i 0.261509 + 0.965201i \(0.415780\pi\)
−0.261509 + 0.965201i \(0.584220\pi\)
\(98\) 2.26545 + 0.380731i 0.228845 + 0.0384596i
\(99\) 1.81265 0.182178
\(100\) −1.89013 0.653773i −0.189013 0.0653773i
\(101\) 4.06769 0.404750 0.202375 0.979308i \(-0.435134\pi\)
0.202375 + 0.979308i \(0.435134\pi\)
\(102\) −10.7144 1.80065i −1.06088 0.178291i
\(103\) −15.5279 −1.53001 −0.765005 0.644025i \(-0.777263\pi\)
−0.765005 + 0.644025i \(0.777263\pi\)
\(104\) 8.64700 + 4.71839i 0.847908 + 0.462676i
\(105\) 3.19932 0.312221
\(106\) −0.479803 + 2.85496i −0.0466026 + 0.277298i
\(107\) −16.9678 −1.64034 −0.820168 0.572123i \(-0.806120\pi\)
−0.820168 + 0.572123i \(0.806120\pi\)
\(108\) 3.69505 10.6828i 0.355557 1.02795i
\(109\) 4.30718i 0.412553i −0.978494 0.206276i \(-0.933865\pi\)
0.978494 0.206276i \(-0.0661346\pi\)
\(110\) 0.387673 2.30676i 0.0369632 0.219941i
\(111\) −12.9456 −1.22874
\(112\) 7.29218 + 5.73010i 0.689046 + 0.541443i
\(113\) 5.36983i 0.505151i 0.967577 + 0.252575i \(0.0812776\pi\)
−0.967577 + 0.252575i \(0.918722\pi\)
\(114\) −2.14434 + 12.7594i −0.200836 + 1.19503i
\(115\) −4.74202 0.716404i −0.442196 0.0668050i
\(116\) 9.35352 + 3.23527i 0.868452 + 0.300387i
\(117\) −3.81676 −0.352859
\(118\) 2.22800 13.2572i 0.205104 1.22042i
\(119\) 12.9083i 1.18331i
\(120\) −3.42604 1.86948i −0.312753 0.170659i
\(121\) −8.26427 −0.751298
\(122\) 0.906228 5.39231i 0.0820460 0.488196i
\(123\) 8.79167i 0.792718i
\(124\) 2.30795 6.67252i 0.207260 0.599210i
\(125\) 1.00000i 0.0894427i
\(126\) −3.54372 0.595555i −0.315699 0.0530562i
\(127\) 2.29388i 0.203549i 0.994808 + 0.101774i \(0.0324520\pi\)
−0.994808 + 0.101774i \(0.967548\pi\)
\(128\) −4.46064 10.3972i −0.394268 0.918995i
\(129\) 17.7747i 1.56497i
\(130\) −0.816294 + 4.85717i −0.0715937 + 0.426002i
\(131\) 13.9868i 1.22203i −0.791619 0.611015i \(-0.790761\pi\)
0.791619 0.611015i \(-0.209239\pi\)
\(132\) 1.49213 4.31390i 0.129873 0.375477i
\(133\) 15.3722 1.33294
\(134\) −6.52308 1.09627i −0.563508 0.0947029i
\(135\) 5.65189 0.486438
\(136\) 7.54281 13.8231i 0.646791 1.18532i
\(137\) 12.2230i 1.04428i 0.852860 + 0.522139i \(0.174866\pi\)
−0.852860 + 0.522139i \(0.825134\pi\)
\(138\) −8.89415 2.91238i −0.757120 0.247918i
\(139\) 1.61414i 0.136910i 0.997654 + 0.0684549i \(0.0218069\pi\)
−0.997654 + 0.0684549i \(0.978193\pi\)
\(140\) −1.51580 + 4.38233i −0.128108 + 0.370375i
\(141\) −11.8787 −1.00037
\(142\) −2.56419 + 15.2577i −0.215182 + 1.28039i
\(143\) −5.76040 −0.481709
\(144\) 3.44684 + 2.70848i 0.287236 + 0.225707i
\(145\) 4.94862i 0.410960i
\(146\) −9.08520 1.52685i −0.751897 0.126363i
\(147\) 2.24146i 0.184873i
\(148\) 6.13344 17.7325i 0.504166 1.45760i
\(149\) 4.80668i 0.393779i 0.980426 + 0.196889i \(0.0630840\pi\)
−0.980426 + 0.196889i \(0.936916\pi\)
\(150\) 0.323424 1.92446i 0.0264075 0.157132i
\(151\) 9.37662i 0.763059i −0.924357 0.381529i \(-0.875398\pi\)
0.924357 0.381529i \(-0.124602\pi\)
\(152\) −16.4615 8.98251i −1.33521 0.728578i
\(153\) 6.10147i 0.493274i
\(154\) −5.34832 0.898836i −0.430980 0.0724302i
\(155\) 3.53020 0.283552
\(156\) −3.14186 + 9.08344i −0.251550 + 0.727258i
\(157\) 14.5957i 1.16486i −0.812879 0.582432i \(-0.802101\pi\)
0.812879 0.582432i \(-0.197899\pi\)
\(158\) 5.90613 + 0.992581i 0.469866 + 0.0789655i
\(159\) −2.82472 −0.224015
\(160\) 4.18397 3.80715i 0.330772 0.300982i
\(161\) −1.66101 + 10.9946i −0.130906 + 0.866492i
\(162\) 6.29159 + 1.05736i 0.494314 + 0.0830741i
\(163\) 5.23715i 0.410205i 0.978740 + 0.205103i \(0.0657529\pi\)
−0.978740 + 0.205103i \(0.934247\pi\)
\(164\) −12.0426 4.16539i −0.940368 0.325262i
\(165\) 2.28233 0.177679
\(166\) 7.58817 + 1.27526i 0.588956 + 0.0989796i
\(167\) 2.65734i 0.205631i −0.994700 0.102816i \(-0.967215\pi\)
0.994700 0.102816i \(-0.0327852\pi\)
\(168\) −4.33445 + 7.94339i −0.334410 + 0.612846i
\(169\) −0.870770 −0.0669823
\(170\) 7.76468 + 1.30493i 0.595524 + 0.100083i
\(171\) 7.26606 0.555649
\(172\) 24.3473 + 8.42143i 1.85646 + 0.642128i
\(173\) −8.91998 −0.678173 −0.339087 0.940755i \(-0.610118\pi\)
−0.339087 + 0.940755i \(0.610118\pi\)
\(174\) −1.60050 + 9.52344i −0.121334 + 0.721970i
\(175\) −2.31854 −0.175265
\(176\) 5.20211 + 4.08775i 0.392124 + 0.308126i
\(177\) 13.1168 0.985918
\(178\) 1.75499 10.4427i 0.131542 0.782713i
\(179\) 1.37963i 0.103119i −0.998670 0.0515593i \(-0.983581\pi\)
0.998670 0.0515593i \(-0.0164191\pi\)
\(180\) −0.716481 + 2.07142i −0.0534033 + 0.154395i
\(181\) 20.6166i 1.53242i 0.642592 + 0.766208i \(0.277859\pi\)
−0.642592 + 0.766208i \(0.722141\pi\)
\(182\) 11.2615 + 1.89261i 0.834761 + 0.140289i
\(183\) 5.33520 0.394389
\(184\) 8.20323 10.8031i 0.604750 0.796415i
\(185\) 9.38162 0.689750
\(186\) 6.79373 + 1.14175i 0.498141 + 0.0837173i
\(187\) 9.20858i 0.673398i
\(188\) 5.62800 16.2712i 0.410464 1.18670i
\(189\) 13.1041i 0.953185i
\(190\) 1.55400 9.24672i 0.112739 0.670828i
\(191\) −7.65350 −0.553788 −0.276894 0.960901i \(-0.589305\pi\)
−0.276894 + 0.960901i \(0.589305\pi\)
\(192\) 9.28322 5.97353i 0.669959 0.431102i
\(193\) −3.72049 −0.267807 −0.133904 0.990994i \(-0.542751\pi\)
−0.133904 + 0.990994i \(0.542751\pi\)
\(194\) 4.45619 26.5155i 0.319936 1.90371i
\(195\) −4.80573 −0.344146
\(196\) −3.07029 1.06198i −0.219306 0.0758555i
\(197\) 2.90083 0.206675 0.103338 0.994646i \(-0.467048\pi\)
0.103338 + 0.994646i \(0.467048\pi\)
\(198\) −2.52802 0.424858i −0.179659 0.0301933i
\(199\) −12.0631 −0.855130 −0.427565 0.903985i \(-0.640628\pi\)
−0.427565 + 0.903985i \(0.640628\pi\)
\(200\) 2.48284 + 1.35481i 0.175563 + 0.0957992i
\(201\) 6.45400i 0.455230i
\(202\) −5.67303 0.953406i −0.399153 0.0670814i
\(203\) 11.4736 0.805286
\(204\) 14.5208 + 5.02257i 1.01666 + 0.351650i
\(205\) 6.37131i 0.444991i
\(206\) 21.6561 + 3.63951i 1.50885 + 0.253576i
\(207\) −0.785120 + 5.19686i −0.0545696 + 0.361207i
\(208\) −10.9537 8.60725i −0.759500 0.596805i
\(209\) 10.9662 0.758550
\(210\) −4.46194 0.749872i −0.307903 0.0517461i
\(211\) 14.7717i 1.01692i −0.861084 0.508462i \(-0.830214\pi\)
0.861084 0.508462i \(-0.169786\pi\)
\(212\) 1.33832 3.86923i 0.0919162 0.265740i
\(213\) −15.0961 −1.03437
\(214\) 23.6642 + 3.97699i 1.61765 + 0.271862i
\(215\) 12.8813i 0.878496i
\(216\) −7.65722 + 14.0328i −0.521008 + 0.954808i
\(217\) 8.18489i 0.555627i
\(218\) −1.00954 + 6.00703i −0.0683746 + 0.406847i
\(219\) 8.98898i 0.607419i
\(220\) −1.08134 + 3.12628i −0.0729040 + 0.210773i
\(221\) 19.3898i 1.30430i
\(222\) 18.0546 + 3.03424i 1.21174 + 0.203645i
\(223\) 23.6624i 1.58455i 0.610164 + 0.792275i \(0.291104\pi\)
−0.610164 + 0.792275i \(0.708896\pi\)
\(224\) −8.82703 9.70069i −0.589781 0.648155i
\(225\) −1.09592 −0.0730611
\(226\) 1.25861 7.48906i 0.0837213 0.498165i
\(227\) 26.1645 1.73660 0.868298 0.496042i \(-0.165214\pi\)
0.868298 + 0.496042i \(0.165214\pi\)
\(228\) 5.98123 17.2924i 0.396117 1.14522i
\(229\) 19.1863i 1.26787i 0.773387 + 0.633934i \(0.218561\pi\)
−0.773387 + 0.633934i \(0.781439\pi\)
\(230\) 6.44557 + 2.11060i 0.425008 + 0.139169i
\(231\) 5.29168i 0.348167i
\(232\) −12.2866 6.70441i −0.806657 0.440166i
\(233\) 27.4651 1.79930 0.899651 0.436611i \(-0.143821\pi\)
0.899651 + 0.436611i \(0.143821\pi\)
\(234\) 5.32306 + 0.894590i 0.347979 + 0.0584812i
\(235\) 8.60850 0.561557
\(236\) −6.21458 + 17.9670i −0.404534 + 1.16955i
\(237\) 5.84358i 0.379581i
\(238\) 3.02552 18.0027i 0.196116 1.16694i
\(239\) 0.599617i 0.0387860i 0.999812 + 0.0193930i \(0.00617337\pi\)
−0.999812 + 0.0193930i \(0.993827\pi\)
\(240\) 4.33996 + 3.41029i 0.280143 + 0.220133i
\(241\) 14.3108i 0.921840i −0.887442 0.460920i \(-0.847519\pi\)
0.887442 0.460920i \(-0.152481\pi\)
\(242\) 11.5258 + 1.93702i 0.740907 + 0.124517i
\(243\) 10.7307i 0.688377i
\(244\) −2.52775 + 7.30800i −0.161823 + 0.467847i
\(245\) 1.62438i 0.103778i
\(246\) 2.06064 12.2614i 0.131381 0.781755i
\(247\) −23.0907 −1.46923
\(248\) −4.78273 + 8.76492i −0.303703 + 0.556573i
\(249\) 7.50780i 0.475788i
\(250\) −0.234385 + 1.39466i −0.0148238 + 0.0882058i
\(251\) −18.5184 −1.16887 −0.584437 0.811439i \(-0.698685\pi\)
−0.584437 + 0.811439i \(0.698685\pi\)
\(252\) 4.80267 + 1.66119i 0.302540 + 0.104645i
\(253\) −1.18493 + 7.84332i −0.0744962 + 0.493105i
\(254\) 0.537650 3.19917i 0.0337352 0.200734i
\(255\) 7.68244i 0.481093i
\(256\) 3.78410 + 15.5461i 0.236506 + 0.971630i
\(257\) −20.7306 −1.29314 −0.646569 0.762855i \(-0.723797\pi\)
−0.646569 + 0.762855i \(0.723797\pi\)
\(258\) −4.16612 + 24.7896i −0.259371 + 1.54333i
\(259\) 21.7516i 1.35158i
\(260\) 2.27690 6.58275i 0.141207 0.408245i
\(261\) 5.42328 0.335692
\(262\) −3.27829 + 19.5067i −0.202534 + 1.20513i
\(263\) 8.63352 0.532366 0.266183 0.963923i \(-0.414238\pi\)
0.266183 + 0.963923i \(0.414238\pi\)
\(264\) −3.09212 + 5.66667i −0.190307 + 0.348760i
\(265\) 2.04707 0.125751
\(266\) −21.4389 3.60301i −1.31450 0.220914i
\(267\) 10.3321 0.632314
\(268\) 8.84050 + 3.05782i 0.540019 + 0.186786i
\(269\) −29.2749 −1.78492 −0.892461 0.451125i \(-0.851023\pi\)
−0.892461 + 0.451125i \(0.851023\pi\)
\(270\) −7.88245 1.32472i −0.479710 0.0806199i
\(271\) 7.04520i 0.427966i −0.976837 0.213983i \(-0.931356\pi\)
0.976837 0.213983i \(-0.0686437\pi\)
\(272\) −13.7596 + 17.5105i −0.834295 + 1.06173i
\(273\) 11.1423i 0.674361i
\(274\) 2.86488 17.0468i 0.173074 1.02984i
\(275\) −1.65400 −0.0997401
\(276\) 11.7217 + 6.14642i 0.705561 + 0.369971i
\(277\) −17.7450 −1.06619 −0.533095 0.846055i \(-0.678971\pi\)
−0.533095 + 0.846055i \(0.678971\pi\)
\(278\) 0.378331 2.25117i 0.0226908 0.135016i
\(279\) 3.86880i 0.231619i
\(280\) 3.14117 5.75656i 0.187721 0.344020i
\(281\) 12.8863i 0.768735i −0.923180 0.384367i \(-0.874420\pi\)
0.923180 0.384367i \(-0.125580\pi\)
\(282\) 16.5668 + 2.78420i 0.986536 + 0.165797i
\(283\) −4.81508 −0.286227 −0.143113 0.989706i \(-0.545711\pi\)
−0.143113 + 0.989706i \(0.545711\pi\)
\(284\) 7.15233 20.6782i 0.424413 1.22702i
\(285\) 9.14879 0.541928
\(286\) 8.03378 + 1.35015i 0.475047 + 0.0798362i
\(287\) −14.7721 −0.871971
\(288\) −4.17232 4.58528i −0.245857 0.270190i
\(289\) −13.9965 −0.823325
\(290\) 1.15988 6.90162i 0.0681106 0.405277i
\(291\) 26.2347 1.53791
\(292\) 12.3129 + 4.25887i 0.720555 + 0.249232i
\(293\) 13.6754i 0.798926i −0.916749 0.399463i \(-0.869197\pi\)
0.916749 0.399463i \(-0.130803\pi\)
\(294\) 0.525365 3.12607i 0.0306399 0.182316i
\(295\) −9.50571 −0.553444
\(296\) −12.7103 + 23.2931i −0.738769 + 1.35388i
\(297\) 9.34825i 0.542440i
\(298\) 1.12661 6.70367i 0.0652630 0.388333i
\(299\) 2.49502 16.5151i 0.144291 0.955090i
\(300\) −0.902131 + 2.60816i −0.0520846 + 0.150582i
\(301\) 29.8657 1.72143
\(302\) −2.19774 + 13.0772i −0.126466 + 0.752506i
\(303\) 5.61294i 0.322455i
\(304\) 20.8528 + 16.3858i 1.19599 + 0.939793i
\(305\) −3.86641 −0.221390
\(306\) 1.43009 8.50944i 0.0817529 0.486452i
\(307\) 8.25398i 0.471079i 0.971865 + 0.235540i \(0.0756858\pi\)
−0.971865 + 0.235540i \(0.924314\pi\)
\(308\) 7.24839 + 2.50713i 0.413015 + 0.142857i
\(309\) 21.4267i 1.21892i
\(310\) −4.92341 0.827425i −0.279631 0.0469946i
\(311\) 1.09686i 0.0621970i −0.999516 0.0310985i \(-0.990099\pi\)
0.999516 0.0310985i \(-0.00990055\pi\)
\(312\) 6.51083 11.9319i 0.368603 0.675509i
\(313\) 30.9986i 1.75214i −0.482180 0.876072i \(-0.660155\pi\)
0.482180 0.876072i \(-0.339845\pi\)
\(314\) −3.42101 + 20.3560i −0.193059 + 1.14875i
\(315\) 2.54093i 0.143165i
\(316\) −8.00437 2.76862i −0.450281 0.155747i
\(317\) −8.23636 −0.462600 −0.231300 0.972882i \(-0.574298\pi\)
−0.231300 + 0.972882i \(0.574298\pi\)
\(318\) 3.93952 + 0.662073i 0.220917 + 0.0371272i
\(319\) 8.18503 0.458274
\(320\) −6.72753 + 4.32901i −0.376081 + 0.241999i
\(321\) 23.4136i 1.30682i
\(322\) 4.89350 14.9443i 0.272704 0.832813i
\(323\) 36.9128i 2.05389i
\(324\) −8.52677 2.94931i −0.473709 0.163850i
\(325\) 3.48270 0.193186
\(326\) 1.22751 7.30402i 0.0679855 0.404532i
\(327\) −5.94341 −0.328671
\(328\) 15.8190 + 8.63188i 0.873455 + 0.476616i
\(329\) 19.9591i 1.10038i
\(330\) −3.18307 0.534945i −0.175222 0.0294477i
\(331\) 8.65040i 0.475469i 0.971330 + 0.237734i \(0.0764048\pi\)
−0.971330 + 0.237734i \(0.923595\pi\)
\(332\) −10.2840 3.55711i −0.564407 0.195222i
\(333\) 10.2815i 0.563421i
\(334\) −0.622841 + 3.70608i −0.0340804 + 0.202787i
\(335\) 4.67720i 0.255543i
\(336\) 7.90688 10.0624i 0.431355 0.548947i
\(337\) 4.60244i 0.250711i −0.992112 0.125356i \(-0.959993\pi\)
0.992112 0.125356i \(-0.0400071\pi\)
\(338\) 1.21442 + 0.204096i 0.0660560 + 0.0111013i
\(339\) 7.40974 0.402442
\(340\) −10.5232 3.63985i −0.570700 0.197398i
\(341\) 5.83895i 0.316197i
\(342\) −10.1336 1.70305i −0.547965 0.0920906i
\(343\) −19.9960 −1.07968
\(344\) −31.9822 17.4516i −1.72436 0.940928i
\(345\) −0.988556 + 6.54344i −0.0532220 + 0.352287i
\(346\) 12.4403 + 2.09071i 0.668794 + 0.112397i
\(347\) 27.6570i 1.48471i −0.670008 0.742354i \(-0.733709\pi\)
0.670008 0.742354i \(-0.266291\pi\)
\(348\) 4.46430 12.9068i 0.239312 0.691876i
\(349\) 0.443757 0.0237538 0.0118769 0.999929i \(-0.496219\pi\)
0.0118769 + 0.999929i \(0.496219\pi\)
\(350\) 3.23356 + 0.543431i 0.172841 + 0.0290476i
\(351\) 19.6839i 1.05065i
\(352\) −6.29704 6.92030i −0.335633 0.368853i
\(353\) −3.85949 −0.205420 −0.102710 0.994711i \(-0.532751\pi\)
−0.102710 + 0.994711i \(0.532751\pi\)
\(354\) −18.2934 3.07438i −0.972283 0.163401i
\(355\) 10.9401 0.580640
\(356\) −4.89522 + 14.1526i −0.259446 + 0.750087i
\(357\) 17.8120 0.942713
\(358\) −0.323365 + 1.92411i −0.0170904 + 0.101693i
\(359\) −16.8300 −0.888253 −0.444127 0.895964i \(-0.646486\pi\)
−0.444127 + 0.895964i \(0.646486\pi\)
\(360\) 1.48475 2.72099i 0.0782534 0.143409i
\(361\) 24.9584 1.31360
\(362\) 4.83221 28.7530i 0.253975 1.51122i
\(363\) 11.4037i 0.598542i
\(364\) −15.2624 5.27907i −0.799965 0.276699i
\(365\) 6.51430i 0.340974i
\(366\) −7.44076 1.25049i −0.388935 0.0653642i
\(367\) −2.40164 −0.125365 −0.0626824 0.998034i \(-0.519966\pi\)
−0.0626824 + 0.998034i \(0.519966\pi\)
\(368\) −13.9728 + 13.1439i −0.728381 + 0.685172i
\(369\) −6.98243 −0.363491
\(370\) −13.0841 2.19891i −0.680211 0.114316i
\(371\) 4.74621i 0.246411i
\(372\) −9.20731 3.18470i −0.477377 0.165119i
\(373\) 0.740895i 0.0383621i 0.999816 + 0.0191810i \(0.00610589\pi\)
−0.999816 + 0.0191810i \(0.993894\pi\)
\(374\) 2.15835 12.8428i 0.111606 0.664085i
\(375\) −1.37989 −0.0712570
\(376\) −11.6628 + 21.3736i −0.601465 + 1.10226i
\(377\) −17.2346 −0.887626
\(378\) −3.07141 + 18.2757i −0.157976 + 0.940003i
\(379\) −13.8734 −0.712631 −0.356316 0.934366i \(-0.615967\pi\)
−0.356316 + 0.934366i \(0.615967\pi\)
\(380\) −4.33459 + 12.5318i −0.222360 + 0.642866i
\(381\) 3.16529 0.162163
\(382\) 10.6740 + 1.79387i 0.546129 + 0.0917821i
\(383\) 11.6143 0.593463 0.296732 0.954961i \(-0.404103\pi\)
0.296732 + 0.954961i \(0.404103\pi\)
\(384\) −14.3470 + 6.15517i −0.732142 + 0.314105i
\(385\) 3.83487i 0.195443i
\(386\) 5.18881 + 0.872028i 0.264103 + 0.0443851i
\(387\) 14.1168 0.717598
\(388\) −12.4297 + 35.9356i −0.631022 + 1.82435i
\(389\) 5.88082i 0.298170i 0.988824 + 0.149085i \(0.0476327\pi\)
−0.988824 + 0.149085i \(0.952367\pi\)
\(390\) 6.70234 + 1.12639i 0.339386 + 0.0570371i
\(391\) −26.4010 3.98855i −1.33515 0.201709i
\(392\) 4.03308 + 2.20072i 0.203702 + 0.111153i
\(393\) −19.3002 −0.973564
\(394\) −4.04566 0.679911i −0.203817 0.0342534i
\(395\) 4.23483i 0.213077i
\(396\) 3.42614 + 1.18506i 0.172170 + 0.0595516i
\(397\) 25.6253 1.28610 0.643049 0.765825i \(-0.277669\pi\)
0.643049 + 0.765825i \(0.277669\pi\)
\(398\) 16.8239 + 2.82741i 0.843303 + 0.141725i
\(399\) 21.2118i 1.06192i
\(400\) −3.14516 2.47143i −0.157258 0.123571i
\(401\) 12.3949i 0.618972i 0.950904 + 0.309486i \(0.100157\pi\)
−0.950904 + 0.309486i \(0.899843\pi\)
\(402\) −1.51272 + 9.00110i −0.0754476 + 0.448934i
\(403\) 12.2946i 0.612439i
\(404\) 7.68845 + 2.65934i 0.382515 + 0.132307i
\(405\) 4.51121i 0.224164i
\(406\) −16.0017 2.68923i −0.794149 0.133464i
\(407\) 15.5172i 0.769160i
\(408\) −19.0743 10.4082i −0.944318 0.515283i
\(409\) 3.15508 0.156009 0.0780043 0.996953i \(-0.475145\pi\)
0.0780043 + 0.996953i \(0.475145\pi\)
\(410\) −1.49334 + 8.88578i −0.0737508 + 0.438837i
\(411\) 16.8663 0.831953
\(412\) −29.3497 10.1517i −1.44596 0.500139i
\(413\) 22.0394i 1.08449i
\(414\) 2.31304 7.06381i 0.113680 0.347167i
\(415\) 5.44089i 0.267083i
\(416\) 13.2592 + 14.5715i 0.650085 + 0.714428i
\(417\) 2.22733 0.109073
\(418\) −15.2941 2.57032i −0.748059 0.125718i
\(419\) −0.845711 −0.0413157 −0.0206578 0.999787i \(-0.506576\pi\)
−0.0206578 + 0.999787i \(0.506576\pi\)
\(420\) 6.04711 + 2.09163i 0.295069 + 0.102061i
\(421\) 26.0162i 1.26795i −0.773354 0.633975i \(-0.781422\pi\)
0.773354 0.633975i \(-0.218578\pi\)
\(422\) −3.46226 + 20.6014i −0.168540 + 1.00286i
\(423\) 9.43421i 0.458707i
\(424\) −2.77338 + 5.08256i −0.134687 + 0.246831i
\(425\) 5.56745i 0.270061i
\(426\) 21.0538 + 3.53829i 1.02006 + 0.171431i
\(427\) 8.96441i 0.433818i
\(428\) −32.0712 11.0931i −1.55022 0.536204i
\(429\) 7.94869i 0.383767i
\(430\) 3.01918 17.9649i 0.145598 0.866347i
\(431\) 15.1645 0.730447 0.365224 0.930920i \(-0.380993\pi\)
0.365224 + 0.930920i \(0.380993\pi\)
\(432\) 13.9682 17.7761i 0.672048 0.855254i
\(433\) 4.87293i 0.234178i 0.993121 + 0.117089i \(0.0373563\pi\)
−0.993121 + 0.117089i \(0.962644\pi\)
\(434\) −1.91842 + 11.4151i −0.0920869 + 0.547943i
\(435\) 6.82852 0.327403
\(436\) 2.81592 8.14112i 0.134858 0.389889i
\(437\) −4.74984 + 31.4401i −0.227216 + 1.50399i
\(438\) −2.10688 + 12.5365i −0.100671 + 0.599019i
\(439\) 20.7315i 0.989460i 0.869047 + 0.494730i \(0.164733\pi\)
−0.869047 + 0.494730i \(0.835267\pi\)
\(440\) 2.24085 4.10663i 0.106828 0.195776i
\(441\) −1.78019 −0.0847709
\(442\) −4.54468 + 27.0421i −0.216168 + 1.28626i
\(443\) 19.8054i 0.940984i 0.882404 + 0.470492i \(0.155924\pi\)
−0.882404 + 0.470492i \(0.844076\pi\)
\(444\) −24.4687 8.46345i −1.16124 0.401658i
\(445\) −7.48765 −0.354949
\(446\) 5.54611 33.0009i 0.262616 1.56264i
\(447\) 6.63267 0.313715
\(448\) 10.0370 + 15.5980i 0.474202 + 0.736938i
\(449\) 7.22437 0.340939 0.170470 0.985363i \(-0.445472\pi\)
0.170470 + 0.985363i \(0.445472\pi\)
\(450\) 1.52843 + 0.256867i 0.0720507 + 0.0121088i
\(451\) −10.5382 −0.496223
\(452\) −3.51065 + 10.1497i −0.165127 + 0.477400i
\(453\) −12.9387 −0.607911
\(454\) −36.4904 6.13256i −1.71258 0.287815i
\(455\) 8.07478i 0.378552i
\(456\) −12.3948 + 22.7150i −0.580441 + 1.06373i
\(457\) 37.5343i 1.75578i 0.478861 + 0.877891i \(0.341050\pi\)
−0.478861 + 0.877891i \(0.658950\pi\)
\(458\) 4.49699 26.7583i 0.210131 1.25033i
\(459\) 31.4667 1.46874
\(460\) −8.49466 4.45430i −0.396065 0.207683i
\(461\) 12.1716 0.566889 0.283444 0.958989i \(-0.408523\pi\)
0.283444 + 0.958989i \(0.408523\pi\)
\(462\) −1.24029 + 7.38007i −0.0577035 + 0.343352i
\(463\) 2.25366i 0.104736i 0.998628 + 0.0523681i \(0.0166769\pi\)
−0.998628 + 0.0523681i \(0.983323\pi\)
\(464\) 15.5642 + 12.2302i 0.722550 + 0.567770i
\(465\) 4.87126i 0.225899i
\(466\) −38.3044 6.43742i −1.77442 0.298208i
\(467\) 4.35631 0.201586 0.100793 0.994907i \(-0.467862\pi\)
0.100793 + 0.994907i \(0.467862\pi\)
\(468\) −7.21415 2.49529i −0.333474 0.115345i
\(469\) 10.8443 0.500741
\(470\) −12.0059 2.01770i −0.553791 0.0930698i
\(471\) −20.1404 −0.928020
\(472\) 12.8784 23.6012i 0.592776 1.08633i
\(473\) 21.3057 0.979636
\(474\) 1.36965 8.14978i 0.0629100 0.374332i
\(475\) −6.63011 −0.304210
\(476\) −8.43912 + 24.3984i −0.386807 + 1.11830i
\(477\) 2.24342i 0.102719i
\(478\) 0.140541 0.836260i 0.00642821 0.0382496i
\(479\) 36.1090 1.64986 0.824932 0.565232i \(-0.191213\pi\)
0.824932 + 0.565232i \(0.191213\pi\)
\(480\) −5.25343 5.77340i −0.239785 0.263518i
\(481\) 32.6734i 1.48978i
\(482\) −3.35424 + 19.9586i −0.152781 + 0.909091i
\(483\) 15.1712 + 2.29200i 0.690315 + 0.104290i
\(484\) −15.6205 5.40296i −0.710024 0.245589i
\(485\) −19.0123 −0.863302
\(486\) −2.51512 + 14.9657i −0.114088 + 0.678856i
\(487\) 18.1513i 0.822514i 0.911519 + 0.411257i \(0.134910\pi\)
−0.911519 + 0.411257i \(0.865090\pi\)
\(488\) 5.23823 9.59968i 0.237123 0.434557i
\(489\) 7.22667 0.326801
\(490\) −0.380731 + 2.26545i −0.0171997 + 0.102343i
\(491\) 22.6804i 1.02355i −0.859119 0.511776i \(-0.828988\pi\)
0.859119 0.511776i \(-0.171012\pi\)
\(492\) −5.74776 + 16.6174i −0.259129 + 0.749169i
\(493\) 27.5512i 1.24084i
\(494\) 32.2036 + 5.41212i 1.44891 + 0.243503i
\(495\) 1.81265i 0.0814726i
\(496\) 8.72462 11.1030i 0.391747 0.498541i
\(497\) 25.3650i 1.13778i
\(498\) 1.75972 10.4708i 0.0788548 0.469208i
\(499\) 31.4754i 1.40903i −0.709688 0.704516i \(-0.751164\pi\)
0.709688 0.704516i \(-0.248836\pi\)
\(500\) 0.653773 1.89013i 0.0292376 0.0845291i
\(501\) −3.66683 −0.163822
\(502\) 25.8268 + 4.34045i 1.15271 + 0.193724i
\(503\) −13.7449 −0.612853 −0.306426 0.951894i \(-0.599133\pi\)
−0.306426 + 0.951894i \(0.599133\pi\)
\(504\) −6.30872 3.44246i −0.281013 0.153339i
\(505\) 4.06769i 0.181010i
\(506\) 3.49093 10.6610i 0.155191 0.473939i
\(507\) 1.20156i 0.0533633i
\(508\) −1.49967 + 4.33572i −0.0665373 + 0.192366i
\(509\) −14.8818 −0.659625 −0.329813 0.944046i \(-0.606986\pi\)
−0.329813 + 0.944046i \(0.606986\pi\)
\(510\) 1.80065 10.7144i 0.0797341 0.474440i
\(511\) 15.1036 0.668146
\(512\) −1.63374 22.5684i −0.0722018 0.997390i
\(513\) 37.4727i 1.65446i
\(514\) 28.9120 + 4.85894i 1.27525 + 0.214319i
\(515\) 15.5279i 0.684241i
\(516\) 11.6206 33.5964i 0.511568 1.47900i
\(517\) 14.2385i 0.626208i
\(518\) −5.09826 + 30.3360i −0.224005 + 1.33289i
\(519\) 12.3085i 0.540285i
\(520\) −4.71839 + 8.64700i −0.206915 + 0.379196i
\(521\) 14.8702i 0.651476i −0.945460 0.325738i \(-0.894387\pi\)
0.945460 0.325738i \(-0.105613\pi\)
\(522\) −7.56360 1.27113i −0.331050 0.0556361i
\(523\) 2.95573 0.129245 0.0646226 0.997910i \(-0.479416\pi\)
0.0646226 + 0.997910i \(0.479416\pi\)
\(524\) 9.14418 26.4368i 0.399465 1.15490i
\(525\) 3.19932i 0.139630i
\(526\) −12.0408 2.02357i −0.525003 0.0882317i
\(527\) 19.6542 0.856150
\(528\) 5.64062 7.17831i 0.245477 0.312396i
\(529\) −21.9735 6.79441i −0.955371 0.295409i
\(530\) −2.85496 0.479803i −0.124012 0.0208413i
\(531\) 10.4175i 0.452080i
\(532\) 29.0554 + 10.0499i 1.25971 + 0.435719i
\(533\) 22.1894 0.961129
\(534\) −14.4097 2.42169i −0.623569 0.104797i
\(535\) 16.9678i 0.733581i
\(536\) −11.6127 6.33669i −0.501594 0.273703i
\(537\) −1.90374 −0.0821523
\(538\) 40.8284 + 6.86160i 1.76024 + 0.295824i
\(539\) −2.68673 −0.115726
\(540\) 10.6828 + 3.69505i 0.459715 + 0.159010i
\(541\) −24.8102 −1.06667 −0.533337 0.845903i \(-0.679062\pi\)
−0.533337 + 0.845903i \(0.679062\pi\)
\(542\) −1.65129 + 9.82563i −0.0709290 + 0.422047i
\(543\) 28.4485 1.22084
\(544\) 23.2940 21.1961i 0.998724 0.908777i
\(545\) 4.30718 0.184499
\(546\) 2.61158 15.5396i 0.111765 0.665035i
\(547\) 14.3225i 0.612386i 0.951969 + 0.306193i \(0.0990553\pi\)
−0.951969 + 0.306193i \(0.900945\pi\)
\(548\) −7.99104 + 23.1030i −0.341360 + 0.986910i
\(549\) 4.23726i 0.180842i
\(550\) 2.30676 + 0.387673i 0.0983607 + 0.0165305i
\(551\) 32.8099 1.39775
\(552\) −14.9070 11.3195i −0.634486 0.481791i
\(553\) −9.81861 −0.417530
\(554\) 24.7481 + 4.15915i 1.05145 + 0.176705i
\(555\) 12.9456i 0.549508i
\(556\) −1.05528 + 3.05094i −0.0447539 + 0.129388i
\(557\) 39.1149i 1.65735i −0.559730 0.828675i \(-0.689095\pi\)
0.559730 0.828675i \(-0.310905\pi\)
\(558\) −0.906789 + 5.39565i −0.0383875 + 0.228416i
\(559\) −44.8617 −1.89745
\(560\) −5.73010 + 7.29218i −0.242141 + 0.308151i
\(561\) 12.7068 0.536481
\(562\) −3.02037 + 17.9720i −0.127406 + 0.758104i
\(563\) 35.3742 1.49085 0.745423 0.666592i \(-0.232247\pi\)
0.745423 + 0.666592i \(0.232247\pi\)
\(564\) −22.4523 7.76600i −0.945414 0.327008i
\(565\) −5.36983 −0.225910
\(566\) 6.71537 + 1.12858i 0.282268 + 0.0474378i
\(567\) −10.4594 −0.439254
\(568\) −14.8217 + 27.1625i −0.621905 + 1.13971i
\(569\) 8.98709i 0.376758i −0.982096 0.188379i \(-0.939677\pi\)
0.982096 0.188379i \(-0.0603234\pi\)
\(570\) −12.7594 2.14434i −0.534433 0.0898165i
\(571\) 16.6329 0.696067 0.348034 0.937482i \(-0.386849\pi\)
0.348034 + 0.937482i \(0.386849\pi\)
\(572\) −10.8879 3.76599i −0.455246 0.157464i
\(573\) 10.5609i 0.441190i
\(574\) 20.6020 + 3.46236i 0.859912 + 0.144516i
\(575\) 0.716404 4.74202i 0.0298761 0.197756i
\(576\) 4.74423 + 7.37282i 0.197676 + 0.307201i
\(577\) −20.6514 −0.859729 −0.429865 0.902893i \(-0.641439\pi\)
−0.429865 + 0.902893i \(0.641439\pi\)
\(578\) 19.5203 + 3.28057i 0.811938 + 0.136454i
\(579\) 5.13385i 0.213356i
\(580\) −3.23527 + 9.35352i −0.134337 + 0.388384i
\(581\) −12.6149 −0.523355
\(582\) −36.5884 6.14903i −1.51664 0.254885i
\(583\) 3.38586i 0.140228i
\(584\) −16.1740 8.82560i −0.669284 0.365206i
\(585\) 3.81676i 0.157803i
\(586\) −3.20531 + 19.0725i −0.132410 + 0.787877i
\(587\) 40.9822i 1.69152i −0.533566 0.845759i \(-0.679148\pi\)
0.533566 0.845759i \(-0.320852\pi\)
\(588\) −1.46541 + 4.23665i −0.0604323 + 0.174716i
\(589\) 23.4056i 0.964411i
\(590\) 13.2572 + 2.22800i 0.545790 + 0.0917252i
\(591\) 4.00281i 0.164654i
\(592\) 23.1860 29.5067i 0.952938 1.21272i
\(593\) 26.5118 1.08871 0.544354 0.838855i \(-0.316775\pi\)
0.544354 + 0.838855i \(0.316775\pi\)
\(594\) −2.19109 + 13.0376i −0.0899015 + 0.534939i
\(595\) −12.9083 −0.529191
\(596\) −3.14248 + 9.08524i −0.128721 + 0.372146i
\(597\) 16.6457i 0.681262i
\(598\) −7.35058 + 22.4480i −0.300588 + 0.917968i
\(599\) 1.77018i 0.0723276i 0.999346 + 0.0361638i \(0.0115138\pi\)
−0.999346 + 0.0361638i \(0.988486\pi\)
\(600\) 1.86948 3.42604i 0.0763210 0.139867i
\(601\) −46.2673 −1.88728 −0.943641 0.330970i \(-0.892624\pi\)
−0.943641 + 0.330970i \(0.892624\pi\)
\(602\) −41.6524 7.00008i −1.69763 0.285302i
\(603\) 5.12582 0.208740
\(604\) 6.13018 17.7230i 0.249433 0.721139i
\(605\) 8.26427i 0.335991i
\(606\) −1.31559 + 7.82812i −0.0534422 + 0.317996i
\(607\) 39.0068i 1.58324i 0.611015 + 0.791619i \(0.290761\pi\)
−0.611015 + 0.791619i \(0.709239\pi\)
\(608\) −25.2419 27.7402i −1.02369 1.12501i
\(609\) 15.8322i 0.641553i
\(610\) 5.39231 + 0.906228i 0.218328 + 0.0366921i
\(611\) 29.9809i 1.21290i
\(612\) −3.98897 + 11.5325i −0.161245 + 0.466176i
\(613\) 0.0667318i 0.00269527i −0.999999 0.00134764i \(-0.999571\pi\)
0.999999 0.00134764i \(-0.000428966\pi\)
\(614\) 1.93461 11.5115i 0.0780744 0.464564i
\(615\) −8.79167 −0.354514
\(616\) −9.52137 5.19550i −0.383627 0.209333i
\(617\) 13.1473i 0.529291i −0.964346 0.264645i \(-0.914745\pi\)
0.964346 0.264645i \(-0.0852549\pi\)
\(618\) 5.02210 29.8829i 0.202019 1.20207i
\(619\) −19.6605 −0.790220 −0.395110 0.918634i \(-0.629294\pi\)
−0.395110 + 0.918634i \(0.629294\pi\)
\(620\) 6.67252 + 2.30795i 0.267975 + 0.0926893i
\(621\) 26.8014 + 4.04904i 1.07550 + 0.162482i
\(622\) −0.257087 + 1.52974i −0.0103082 + 0.0613368i
\(623\) 17.3604i 0.695530i
\(624\) −11.8770 + 15.1148i −0.475461 + 0.605077i
\(625\) 1.00000 0.0400000
\(626\) −7.26561 + 43.2324i −0.290392 + 1.72791i
\(627\) 15.1321i 0.604319i
\(628\) 9.54227 27.5877i 0.380778 1.10087i
\(629\) 52.2317 2.08261
\(630\) 0.595555 3.54372i 0.0237275 0.141185i
\(631\) 3.93430 0.156622 0.0783111 0.996929i \(-0.475047\pi\)
0.0783111 + 0.996929i \(0.475047\pi\)
\(632\) 10.5144 + 5.73737i 0.418241 + 0.228220i
\(633\) −20.3832 −0.810161
\(634\) 11.4869 + 1.93048i 0.456203 + 0.0766691i
\(635\) −2.29388 −0.0910297
\(636\) −5.33909 1.84673i −0.211709 0.0732275i
\(637\) 5.65724 0.224148
\(638\) −11.4153 1.91845i −0.451936 0.0759521i
\(639\) 11.9894i 0.474295i
\(640\) 10.3972 4.46064i 0.410987 0.176322i
\(641\) 17.7243i 0.700067i −0.936737 0.350033i \(-0.886170\pi\)
0.936737 0.350033i \(-0.113830\pi\)
\(642\) 5.48779 32.6539i 0.216586 1.28875i
\(643\) −4.97285 −0.196110 −0.0980551 0.995181i \(-0.531262\pi\)
−0.0980551 + 0.995181i \(0.531262\pi\)
\(644\) −10.3275 + 19.6952i −0.406959 + 0.776099i
\(645\) 17.7747 0.699877
\(646\) 8.65182 51.4807i 0.340401 2.02548i
\(647\) 36.1791i 1.42235i −0.703016 0.711174i \(-0.748164\pi\)
0.703016 0.711174i \(-0.251836\pi\)
\(648\) 11.2006 + 6.11182i 0.440002 + 0.240095i
\(649\) 15.7225i 0.617161i
\(650\) −4.85717 0.816294i −0.190514 0.0320177i
\(651\) −11.2942 −0.442655
\(652\) −3.42391 + 9.89889i −0.134091 + 0.387670i
\(653\) −20.9627 −0.820332 −0.410166 0.912011i \(-0.634529\pi\)
−0.410166 + 0.912011i \(0.634529\pi\)
\(654\) 8.28901 + 1.39305i 0.324126 + 0.0544724i
\(655\) 13.9868 0.546509
\(656\) −20.0388 15.7462i −0.782384 0.614787i
\(657\) 7.13913 0.278524
\(658\) −4.67812 + 27.8361i −0.182372 + 1.08517i
\(659\) 26.4259 1.02941 0.514703 0.857368i \(-0.327902\pi\)
0.514703 + 0.857368i \(0.327902\pi\)
\(660\) 4.31390 + 1.49213i 0.167918 + 0.0580810i
\(661\) 4.30861i 0.167586i 0.996483 + 0.0837928i \(0.0267034\pi\)
−0.996483 + 0.0837928i \(0.973297\pi\)
\(662\) 2.02752 12.0643i 0.0788020 0.468893i
\(663\) −26.7557 −1.03910
\(664\) 13.5089 + 7.37135i 0.524246 + 0.286064i
\(665\) 15.3722i 0.596107i
\(666\) −2.40982 + 14.3391i −0.0933788 + 0.555629i
\(667\) −3.54521 + 23.4665i −0.137271 + 0.908625i
\(668\) 1.73730 5.02271i 0.0672181 0.194335i
\(669\) 32.6514 1.26238
\(670\) 1.09627 6.52308i 0.0423524 0.252009i
\(671\) 6.39505i 0.246878i
\(672\) −13.3858 + 12.1803i −0.516370 + 0.469865i
\(673\) 41.2693 1.59081 0.795407 0.606075i \(-0.207257\pi\)
0.795407 + 0.606075i \(0.207257\pi\)
\(674\) −1.07874 + 6.41882i −0.0415517 + 0.247244i
\(675\) 5.65189i 0.217542i
\(676\) −1.64587 0.569286i −0.0633026 0.0218956i
\(677\) 37.9054i 1.45682i 0.685139 + 0.728412i \(0.259741\pi\)
−0.685139 + 0.728412i \(0.740259\pi\)
\(678\) −10.3340 1.73673i −0.396876 0.0666988i
\(679\) 44.0806i 1.69166i
\(680\) 13.8231 + 7.54281i 0.530092 + 0.289254i
\(681\) 36.1040i 1.38351i
\(682\) −1.36856 + 8.14333i −0.0524050 + 0.311824i
\(683\) 30.0463i 1.14969i 0.818262 + 0.574845i \(0.194938\pi\)
−0.818262 + 0.574845i \(0.805062\pi\)
\(684\) 13.7338 + 4.75035i 0.525124 + 0.181634i
\(685\) −12.2230 −0.467016
\(686\) 27.8875 + 4.68675i 1.06475 + 0.178941i
\(687\) 26.4749 1.01008
\(688\) 40.5137 + 31.8351i 1.54457 + 1.21370i
\(689\) 7.12935i 0.271607i
\(690\) 2.91238 8.89415i 0.110872 0.338594i
\(691\) 31.4123i 1.19498i −0.801876 0.597491i \(-0.796165\pi\)
0.801876 0.597491i \(-0.203835\pi\)
\(692\) −16.8599 5.83164i −0.640917 0.221686i
\(693\) 4.20270 0.159647
\(694\) −6.48239 + 38.5720i −0.246068 + 1.46417i
\(695\) −1.61414 −0.0612279
\(696\) −9.25132 + 16.9541i −0.350670 + 0.642645i
\(697\) 35.4720i 1.34360i
\(698\) −0.618888 0.104010i −0.0234253 0.00393684i
\(699\) 37.8987i 1.43346i
\(700\) −4.38233 1.51580i −0.165637 0.0572917i
\(701\) 27.3698i 1.03374i 0.856063 + 0.516871i \(0.172903\pi\)
−0.856063 + 0.516871i \(0.827097\pi\)
\(702\) 4.61361 27.4522i 0.174129 1.03612i
\(703\) 62.2012i 2.34596i
\(704\) 7.16019 + 11.1274i 0.269860 + 0.419378i
\(705\) 11.8787i 0.447379i
\(706\) 5.38266 + 0.904606i 0.202579 + 0.0340453i
\(707\) 9.43109 0.354693
\(708\) 24.7924 + 8.57540i 0.931756 + 0.322283i
\(709\) 46.7346i 1.75515i −0.479436 0.877577i \(-0.659159\pi\)
0.479436 0.877577i \(-0.340841\pi\)
\(710\) −15.2577 2.56419i −0.572610 0.0962325i
\(711\) −4.64102 −0.174052
\(712\) 10.1443 18.5906i 0.380174 0.696714i
\(713\) 16.7403 + 2.52905i 0.626928 + 0.0947136i
\(714\) −24.8417 4.17487i −0.929675 0.156241i
\(715\) 5.76040i 0.215427i
\(716\) 0.901967 2.60768i 0.0337081 0.0974537i
\(717\) 0.827403 0.0308999
\(718\) 23.4720 + 3.94470i 0.875969 + 0.147215i
\(719\) 23.8230i 0.888447i 0.895916 + 0.444223i \(0.146520\pi\)
−0.895916 + 0.444223i \(0.853480\pi\)
\(720\) −2.70848 + 3.44684i −0.100939 + 0.128456i
\(721\) −36.0020 −1.34079
\(722\) −34.8084 5.84988i −1.29543 0.217710i
\(723\) −19.7473 −0.734409
\(724\) −13.4785 + 38.9679i −0.500926 + 1.44823i
\(725\) −4.94862 −0.183787
\(726\) 2.67287 15.9043i 0.0991994 0.590264i
\(727\) −24.5081 −0.908956 −0.454478 0.890758i \(-0.650174\pi\)
−0.454478 + 0.890758i \(0.650174\pi\)
\(728\) 20.0484 + 10.9398i 0.743043 + 0.405454i
\(729\) −28.3408 −1.04966
\(730\) 1.52685 9.08520i 0.0565114 0.336258i
\(731\) 71.7159i 2.65251i
\(732\) 10.0842 + 3.48801i 0.372723 + 0.128920i
\(733\) 14.8727i 0.549337i 0.961539 + 0.274669i \(0.0885681\pi\)
−0.961539 + 0.274669i \(0.911432\pi\)
\(734\) 3.34947 + 0.562910i 0.123631 + 0.0207774i
\(735\) −2.24146 −0.0826775
\(736\) 22.5679 15.0562i 0.831865 0.554978i
\(737\) 7.73610 0.284963
\(738\) 9.73808 + 1.63658i 0.358464 + 0.0602432i
\(739\) 25.8160i 0.949658i −0.880078 0.474829i \(-0.842510\pi\)
0.880078 0.474829i \(-0.157490\pi\)
\(740\) 17.7325 + 6.13344i 0.651858 + 0.225470i
\(741\) 31.8625i 1.17050i
\(742\) −1.11244 + 6.61933i −0.0408390 + 0.243003i
\(743\) −26.3405 −0.966339 −0.483170 0.875527i \(-0.660515\pi\)
−0.483170 + 0.875527i \(0.660515\pi\)
\(744\) 12.0946 + 6.59961i 0.443409 + 0.241954i
\(745\) −4.80668 −0.176103
\(746\) 0.173655 1.03329i 0.00635795 0.0378316i
\(747\) −5.96277 −0.218166
\(748\) −6.02032 + 17.4054i −0.220125 + 0.636404i
\(749\) −39.3404 −1.43747
\(750\) 1.92446 + 0.323424i 0.0702715 + 0.0118098i
\(751\) −27.2225 −0.993364 −0.496682 0.867933i \(-0.665449\pi\)
−0.496682 + 0.867933i \(0.665449\pi\)
\(752\) 21.2753 27.0751i 0.775830 0.987329i
\(753\) 25.5533i 0.931215i
\(754\) 24.0363 + 4.03953i 0.875350 + 0.147111i
\(755\) 9.37662 0.341250
\(756\) 8.56712 24.7685i 0.311583 0.900821i
\(757\) 28.6707i 1.04205i 0.853540 + 0.521027i \(0.174451\pi\)
−0.853540 + 0.521027i \(0.825549\pi\)
\(758\) 19.3487 + 3.25173i 0.702776 + 0.118108i
\(759\) 10.8229 + 1.63507i 0.392845 + 0.0593494i
\(760\) 8.98251 16.4615i 0.325830 0.597122i
\(761\) −23.3091 −0.844953 −0.422476 0.906374i \(-0.638839\pi\)
−0.422476 + 0.906374i \(0.638839\pi\)
\(762\) −4.41448 0.741896i −0.159920 0.0268761i
\(763\) 9.98636i 0.361530i
\(764\) −14.4661 5.00365i −0.523365 0.181026i
\(765\) −6.10147 −0.220599
\(766\) −16.1980 2.72222i −0.585256 0.0983578i
\(767\) 33.1056i 1.19537i
\(768\) 21.4518 5.22162i 0.774075 0.188419i
\(769\) 48.0354i 1.73220i 0.499871 + 0.866100i \(0.333381\pi\)
−0.499871 + 0.866100i \(0.666619\pi\)
\(770\) 0.898836 5.34832i 0.0323918 0.192740i
\(771\) 28.6058i 1.03021i
\(772\) −7.03221 2.43236i −0.253095 0.0875425i
\(773\) 20.1340i 0.724170i −0.932145 0.362085i \(-0.882065\pi\)
0.932145 0.362085i \(-0.117935\pi\)
\(774\) −19.6881 3.30877i −0.707674 0.118931i
\(775\) 3.53020i 0.126808i
\(776\) 25.7579 47.2044i 0.924655 1.69454i
\(777\) −30.0148 −1.07677
\(778\) 1.37838 8.20172i 0.0494172 0.294046i
\(779\) −42.2425 −1.51349
\(780\) −9.08344 3.14186i −0.325239 0.112496i
\(781\) 18.0949i 0.647488i
\(782\) 35.8854 + 11.7506i 1.28326 + 0.420202i
\(783\) 27.9691i 0.999533i
\(784\) −5.10895 4.01454i −0.182462 0.143377i
\(785\) 14.5957 0.520943
\(786\) 26.9171 + 4.52367i 0.960100 + 0.161354i
\(787\) −7.68977 −0.274111 −0.137055 0.990563i \(-0.543764\pi\)
−0.137055 + 0.990563i \(0.543764\pi\)
\(788\) 5.48294 + 1.89648i 0.195321 + 0.0675594i
\(789\) 11.9133i 0.424123i
\(790\) −0.992581 + 5.90613i −0.0353144 + 0.210131i
\(791\) 12.4501i 0.442676i
\(792\) −4.50052 2.45579i −0.159919 0.0872626i
\(793\) 13.4656i 0.478176i
\(794\) −35.7385 6.00619i −1.26831 0.213152i
\(795\) 2.82472i 0.100183i
\(796\) −22.8008 7.88652i −0.808152 0.279530i
\(797\) 3.88875i 0.137747i −0.997625 0.0688734i \(-0.978060\pi\)
0.997625 0.0688734i \(-0.0219404\pi\)
\(798\) −4.97173 + 29.5832i −0.175997 + 1.04723i
\(799\) 47.9274 1.69555
\(800\) 3.80715 + 4.18397i 0.134603 + 0.147926i
\(801\) 8.20584i 0.289939i
\(802\) 2.90518 17.2866i 0.102586 0.610412i
\(803\) 10.7747 0.380230
\(804\) 4.21945 12.1989i 0.148808 0.430221i
\(805\) −10.9946 1.66101i −0.387507 0.0585429i
\(806\) 2.88168 17.1468i 0.101503 0.603969i
\(807\) 40.3960i 1.42201i
\(808\) −10.0994 5.51093i −0.355297 0.193874i
\(809\) −19.8128 −0.696581 −0.348290 0.937387i \(-0.613238\pi\)
−0.348290 + 0.937387i \(0.613238\pi\)
\(810\) −1.05736 + 6.29159i −0.0371519 + 0.221064i
\(811\) 44.4156i 1.55964i 0.626003 + 0.779821i \(0.284690\pi\)
−0.626003 + 0.779821i \(0.715310\pi\)
\(812\) 21.6865 + 7.50110i 0.761046 + 0.263237i
\(813\) −9.72157 −0.340950
\(814\) −3.63700 + 21.6412i −0.127477 + 0.758523i
\(815\) −5.23715 −0.183449
\(816\) 24.1625 + 18.9866i 0.845858 + 0.664664i
\(817\) 85.4043 2.98792
\(818\) −4.40024 0.739503i −0.153851 0.0258561i
\(819\) −8.84929 −0.309219
\(820\) 4.16539 12.0426i 0.145462 0.420545i
\(821\) 36.9381 1.28915 0.644575 0.764541i \(-0.277034\pi\)
0.644575 + 0.764541i \(0.277034\pi\)
\(822\) −23.5227 3.95321i −0.820447 0.137884i
\(823\) 9.38371i 0.327096i −0.986535 0.163548i \(-0.947706\pi\)
0.986535 0.163548i \(-0.0522938\pi\)
\(824\) 38.5533 + 21.0373i 1.34307 + 0.732868i
\(825\) 2.28233i 0.0794607i
\(826\) 5.16569 30.7373i 0.179738 1.06949i
\(827\) −34.4624 −1.19837 −0.599187 0.800609i \(-0.704509\pi\)
−0.599187 + 0.800609i \(0.704509\pi\)
\(828\) −4.88154 + 9.30944i −0.169645 + 0.323525i
\(829\) 18.3378 0.636897 0.318449 0.947940i \(-0.396838\pi\)
0.318449 + 0.947940i \(0.396838\pi\)
\(830\) −1.27526 + 7.58817i −0.0442650 + 0.263389i
\(831\) 24.4860i 0.849410i
\(832\) −15.0766 23.4300i −0.522689 0.812289i
\(833\) 9.04367i 0.313345i
\(834\) −3.10636 0.522053i −0.107564 0.0180772i
\(835\) 2.65734 0.0919611
\(836\) 20.7276 + 7.16942i 0.716878 + 0.247960i
\(837\) −19.9523 −0.689652
\(838\) 1.17948 + 0.198222i 0.0407443 + 0.00684746i
\(839\) 28.6022 0.987456 0.493728 0.869616i \(-0.335634\pi\)
0.493728 + 0.869616i \(0.335634\pi\)
\(840\) −7.94339 4.33445i −0.274073 0.149553i
\(841\) −4.51118 −0.155558
\(842\) −6.09780 + 36.2836i −0.210144 + 1.25041i
\(843\) −17.7817 −0.612433
\(844\) 9.65732 27.9204i 0.332419 0.961059i
\(845\) 0.870770i 0.0299554i
\(846\) −2.21124 + 13.1575i −0.0760239 + 0.452363i
\(847\) −19.1610 −0.658381
\(848\) 5.05919 6.43838i 0.173733 0.221095i
\(849\) 6.64425i 0.228030i
\(850\) −1.30493 + 7.76468i −0.0447586 + 0.266326i
\(851\) 44.4878 + 6.72103i 1.52502 + 0.230394i
\(852\) −28.5335 9.86940i −0.977542 0.338120i
\(853\) −15.5290 −0.531701 −0.265851 0.964014i \(-0.585653\pi\)
−0.265851 + 0.964014i \(0.585653\pi\)
\(854\) 2.10112 12.5023i 0.0718990 0.427819i
\(855\) 7.26606i 0.248494i
\(856\) 42.1283 + 22.9880i 1.43992 + 0.785714i
\(857\) 5.90572 0.201736 0.100868 0.994900i \(-0.467838\pi\)
0.100868 + 0.994900i \(0.467838\pi\)
\(858\) 1.86305 11.0857i 0.0636036 0.378459i
\(859\) 11.1944i 0.381947i 0.981595 + 0.190973i \(0.0611644\pi\)
−0.981595 + 0.190973i \(0.938836\pi\)
\(860\) −8.42143 + 24.3473i −0.287168 + 0.830235i
\(861\) 20.3838i 0.694679i
\(862\) −21.1492 3.55433i −0.720345 0.121061i
\(863\) 57.7691i 1.96648i −0.182310 0.983241i \(-0.558357\pi\)
0.182310 0.983241i \(-0.441643\pi\)
\(864\) −23.6473 + 21.5176i −0.804499 + 0.732044i
\(865\) 8.91998i 0.303288i
\(866\) 1.14214 6.79606i 0.0388116 0.230939i
\(867\) 19.3136i 0.655924i
\(868\) 5.35106 15.4705i 0.181627 0.525103i
\(869\) −7.00442 −0.237609
\(870\) −9.52344 1.60050i −0.322875 0.0542622i
\(871\) −16.2893 −0.551942
\(872\) −5.83539 + 10.6940i −0.197611 + 0.362146i
\(873\) 20.8359i 0.705187i
\(874\) 13.9935 42.7349i 0.473337 1.44553i
\(875\) 2.31854i 0.0783809i
\(876\) 5.87675 16.9903i 0.198557 0.574050i
\(877\) 17.2151 0.581312 0.290656 0.956828i \(-0.406127\pi\)
0.290656 + 0.956828i \(0.406127\pi\)
\(878\) 4.85915 28.9133i 0.163988 0.975776i
\(879\) −18.8705 −0.636486
\(880\) −4.08775 + 5.20211i −0.137798 + 0.175363i
\(881\) 1.23909i 0.0417461i 0.999782 + 0.0208730i \(0.00664457\pi\)
−0.999782 + 0.0208730i \(0.993355\pi\)
\(882\) 2.48275 + 0.417250i 0.0835985 + 0.0140495i
\(883\) 57.4856i 1.93454i −0.253742 0.967272i \(-0.581661\pi\)
0.253742 0.967272i \(-0.418339\pi\)
\(884\) 12.6765 36.6492i 0.426357 1.23264i
\(885\) 13.1168i 0.440916i
\(886\) 4.64210 27.6217i 0.155954 0.927971i
\(887\) 3.53645i 0.118742i −0.998236 0.0593712i \(-0.981090\pi\)
0.998236 0.0593712i \(-0.0189096\pi\)
\(888\) 32.1418 + 17.5387i 1.07861 + 0.588560i
\(889\) 5.31844i 0.178375i
\(890\) 10.4427 + 1.75499i 0.350040 + 0.0588275i
\(891\) −7.46156 −0.249972
\(892\) −15.4698 + 44.7249i −0.517968 + 1.49750i
\(893\) 57.0754i 1.90995i
\(894\) −9.25029 1.55460i −0.309376 0.0519936i
\(895\) 1.37963 0.0461161
\(896\) −10.3422 24.1064i −0.345507 0.805338i
\(897\) −22.7889 3.44285i −0.760899 0.114953i
\(898\) −10.0755 1.69328i −0.336224 0.0565056i
\(899\) 17.4696i 0.582643i
\(900\) −2.07142 0.716481i −0.0690474 0.0238827i
\(901\) 11.3970 0.379688
\(902\) 14.6971 + 2.46999i 0.489360 + 0.0822416i
\(903\) 41.2113i 1.37143i
\(904\) 7.27507 13.3324i 0.241965 0.443430i
\(905\) −20.6166 −0.685318
\(906\) 18.0450 + 3.03263i 0.599504 + 0.100752i
\(907\) 47.5207 1.57790 0.788949 0.614458i \(-0.210625\pi\)
0.788949 + 0.614458i \(0.210625\pi\)
\(908\) 49.4542 + 17.1056i 1.64119 + 0.567670i
\(909\) 4.45785 0.147858
\(910\) −1.89261 + 11.2615i −0.0627393 + 0.373316i
\(911\) −2.29768 −0.0761255 −0.0380628 0.999275i \(-0.512119\pi\)
−0.0380628 + 0.999275i \(0.512119\pi\)
\(912\) 22.6106 28.7744i 0.748711 0.952817i
\(913\) −8.99925 −0.297832
\(914\) 8.79748 52.3474i 0.290995 1.73150i
\(915\) 5.33520i 0.176376i
\(916\) −12.5435 + 36.2646i −0.414449 + 1.19822i
\(917\) 32.4289i 1.07090i
\(918\) −43.8851 7.37531i −1.44843 0.243422i
\(919\) −11.6989 −0.385910 −0.192955 0.981208i \(-0.561807\pi\)
−0.192955 + 0.981208i \(0.561807\pi\)
\(920\) 10.8031 + 8.20323i 0.356168 + 0.270453i
\(921\) 11.3895 0.375298
\(922\) −16.9752 2.85284i −0.559049 0.0939534i
\(923\) 38.1011i 1.25411i
\(924\) 3.45955 10.0019i 0.113811 0.329040i
\(925\) 9.38162i 0.308466i
\(926\) 0.528223 3.14307i 0.0173585 0.103288i
\(927\) −17.0173 −0.558921
\(928\) −18.8401 20.7049i −0.618458 0.679670i
\(929\) 22.6705 0.743796 0.371898 0.928274i \(-0.378707\pi\)
0.371898 + 0.928274i \(0.378707\pi\)
\(930\) −1.14175 + 6.79373i −0.0374395 + 0.222775i
\(931\) −10.7698 −0.352967
\(932\) 51.9126 + 17.9560i 1.70045 + 0.588167i
\(933\) −1.51353 −0.0495509
\(934\) −6.07555 1.02105i −0.198798 0.0334099i
\(935\) −9.20858 −0.301153
\(936\) 9.47640 + 5.17096i 0.309746 + 0.169018i
\(937\) 21.3724i 0.698206i 0.937084 + 0.349103i \(0.113514\pi\)
−0.937084 + 0.349103i \(0.886486\pi\)
\(938\) −15.1240 2.54173i −0.493816 0.0829905i
\(939\) −42.7745 −1.39589
\(940\) 16.2712 + 5.62800i 0.530707 + 0.183565i
\(941\) 19.2671i 0.628091i −0.949408 0.314045i \(-0.898316\pi\)
0.949408 0.314045i \(-0.101684\pi\)
\(942\) 28.0889 + 4.72061i 0.915186 + 0.153806i
\(943\) 4.56443 30.2129i 0.148638 0.983867i
\(944\) −23.4927 + 29.8970i −0.764622 + 0.973065i
\(945\) 13.1041 0.426277
\(946\) −29.7141 4.99373i −0.966088 0.162360i
\(947\) 1.73836i 0.0564891i −0.999601 0.0282446i \(-0.991008\pi\)
0.999601 0.0282446i \(-0.00899172\pi\)
\(948\) −3.82037 + 11.0451i −0.124080 + 0.358728i
\(949\) −22.6874 −0.736463
\(950\) 9.24672 + 1.55400i 0.300003 + 0.0504184i
\(951\) 11.3652i 0.368543i
\(952\) 17.4883 32.0494i 0.566799 1.03873i
\(953\) 49.8435i 1.61459i 0.590149 + 0.807295i \(0.299069\pi\)
−0.590149 + 0.807295i \(0.700931\pi\)
\(954\) −0.525824 + 3.12880i −0.0170242 + 0.101299i
\(955\) 7.65350i 0.247661i
\(956\) −0.392013 + 1.13335i −0.0126786 + 0.0366553i
\(957\) 11.2944i 0.365096i
\(958\) −50.3597 8.46342i −1.62705 0.273441i
\(959\) 28.3394i 0.915127i
\(960\) 5.97353 + 9.28322i 0.192795 + 0.299615i
\(961\) 18.5377 0.597991
\(962\) 7.65816 45.5681i 0.246909 1.46918i
\(963\) −18.5953 −0.599224
\(964\) 9.35602 27.0493i 0.301337 0.871198i
\(965\) 3.72049i 0.119767i
\(966\) −20.6214 6.75246i −0.663483 0.217257i
\(967\) 48.8626i 1.57131i 0.618662 + 0.785657i \(0.287675\pi\)
−0.618662 + 0.785657i \(0.712325\pi\)
\(968\) 20.5189 + 11.1965i 0.659502 + 0.359869i
\(969\) 50.9355 1.63628
\(970\) 26.5155 + 4.45619i 0.851363 + 0.143080i
\(971\) −48.9550 −1.57104 −0.785520 0.618837i \(-0.787604\pi\)
−0.785520 + 0.618837i \(0.787604\pi\)
\(972\) 7.01546 20.2824i 0.225021 0.650560i
\(973\) 3.74245i 0.119977i
\(974\) 4.25439 25.3148i 0.136320 0.811139i
\(975\) 4.80573i 0.153907i
\(976\) −9.55555 + 12.1605i −0.305866 + 0.389248i
\(977\) 28.3251i 0.906201i 0.891459 + 0.453100i \(0.149682\pi\)
−0.891459 + 0.453100i \(0.850318\pi\)
\(978\) −10.0787 1.69382i −0.322282 0.0541625i
\(979\) 12.3846i 0.395813i
\(980\) 1.06198 3.07029i 0.0339236 0.0980768i
\(981\) 4.72031i 0.150708i
\(982\) −5.31594 + 31.6313i −0.169639 + 1.00940i
\(983\) −11.9527 −0.381233 −0.190617 0.981665i \(-0.561049\pi\)
−0.190617 + 0.981665i \(0.561049\pi\)
\(984\) 11.9110 21.8283i 0.379709 0.695862i
\(985\) 2.90083i 0.0924281i
\(986\) 6.45759 38.4244i 0.205651 1.22368i
\(987\) −27.5413 −0.876650
\(988\) −43.6444 15.0961i −1.38851 0.480270i
\(989\) −9.22820 + 61.0833i −0.293440 + 1.94234i
\(990\) 0.424858 2.52802i 0.0135029 0.0803458i
\(991\) 42.6367i 1.35440i −0.735800 0.677199i \(-0.763194\pi\)
0.735800 0.677199i \(-0.236806\pi\)
\(992\) −14.7702 + 13.4400i −0.468955 + 0.426720i
\(993\) 11.9366 0.378795
\(994\) −5.94518 + 35.3755i −0.188570 + 1.12204i
\(995\) 12.0631i 0.382426i
\(996\) −4.90840 + 14.1907i −0.155529 + 0.449650i
\(997\) −4.21192 −0.133393 −0.0666964 0.997773i \(-0.521246\pi\)
−0.0666964 + 0.997773i \(0.521246\pi\)
\(998\) −7.37736 + 43.8973i −0.233526 + 1.38955i
\(999\) −53.0239 −1.67760
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 460.2.e.b.91.2 yes 32
4.3 odd 2 inner 460.2.e.b.91.4 yes 32
23.22 odd 2 inner 460.2.e.b.91.1 32
92.91 even 2 inner 460.2.e.b.91.3 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.e.b.91.1 32 23.22 odd 2 inner
460.2.e.b.91.2 yes 32 1.1 even 1 trivial
460.2.e.b.91.3 yes 32 92.91 even 2 inner
460.2.e.b.91.4 yes 32 4.3 odd 2 inner