Properties

Label 950.2.u.g.899.4
Level $950$
Weight $2$
Character 950.899
Analytic conductor $7.586$
Analytic rank $0$
Dimension $36$
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] = [950,2,Mod(99,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 899.4
Character \(\chi\) \(=\) 950.899
Dual form 950.2.u.g.149.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.642788 + 0.766044i) q^{2} +(-0.811037 + 2.22831i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(2.73267 + 1.57771i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.00943 - 1.68611i) q^{9} +O(q^{10})\) \(q+(0.642788 + 0.766044i) q^{2} +(-0.811037 + 2.22831i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.22831 + 0.811037i) q^{6} +(2.73267 + 1.57771i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.00943 - 1.68611i) q^{9} +(-0.688886 - 1.19319i) q^{11} +(-2.05362 - 1.18566i) q^{12} +(1.47931 + 4.06437i) q^{13} +(0.547933 + 3.10748i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(0.833438 + 0.993253i) q^{17} -2.62313i q^{18} +(-1.08907 + 4.22066i) q^{19} +(-5.73192 + 4.80965i) q^{21} +(0.471226 - 1.29468i) q^{22} +(-2.09271 - 0.369001i) q^{23} +(-0.411774 - 2.33529i) q^{24} +(-2.16260 + 3.74574i) q^{26} +(-0.773953 + 0.446842i) q^{27} +(-2.02826 + 2.41719i) q^{28} +(0.0998515 + 0.0837854i) q^{29} +(-0.173355 + 0.300259i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(3.21749 - 0.567331i) q^{33} +(-0.225152 + 1.27690i) q^{34} +(2.00943 - 1.68611i) q^{36} -10.3150i q^{37} +(-3.93325 + 1.87871i) q^{38} -10.2564 q^{39} +(-10.3451 - 3.76531i) q^{41} +(-7.36881 - 1.29932i) q^{42} +(11.3501 - 2.00132i) q^{43} +(1.29468 - 0.471226i) q^{44} +(-1.06250 - 1.84030i) q^{46} +(0.0491361 - 0.0585581i) q^{47} +(1.52425 - 1.81653i) q^{48} +(1.47834 + 2.56055i) q^{49} +(-2.88922 + 1.05159i) q^{51} +(-4.25950 + 0.751065i) q^{52} +(6.12511 + 1.08002i) q^{53} +(-0.839788 - 0.305658i) q^{54} -3.15542 q^{56} +(-8.52164 - 5.84988i) q^{57} +0.130347i q^{58} +(6.27104 - 5.26202i) q^{59} +(1.36244 - 7.72680i) q^{61} +(-0.341442 + 0.0602055i) q^{62} +(-2.83092 - 7.77790i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.50277 + 2.10007i) q^{66} +(-0.662508 + 0.789546i) q^{67} +(-1.12289 + 0.648300i) q^{68} +(2.51951 - 4.36392i) q^{69} +(2.02349 + 11.4758i) q^{71} +(2.58328 + 0.455501i) q^{72} +(-4.18756 + 11.5052i) q^{73} +(7.90176 - 6.63036i) q^{74} +(-3.96742 - 1.80543i) q^{76} -4.34745i q^{77} +(-6.59270 - 7.85688i) q^{78} +(13.1650 + 4.79168i) q^{79} +(-1.73450 - 9.83684i) q^{81} +(-3.76531 - 10.3451i) q^{82} +(-9.85443 - 5.68946i) q^{83} +(-3.74124 - 6.48003i) q^{84} +(8.82879 + 7.40823i) q^{86} +(-0.267683 + 0.154547i) q^{87} +(1.19319 + 0.688886i) q^{88} +(-17.1195 + 6.23099i) q^{89} +(-2.36992 + 13.4405i) q^{91} +(0.726790 - 1.99684i) q^{92} +(-0.528473 - 0.629809i) q^{93} +0.0764422 q^{94} +2.37131 q^{96} +(10.4271 + 12.4265i) q^{97} +(-1.01124 + 2.77836i) q^{98} +(-0.627577 + 3.55916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 36 q^{9} - 24 q^{11} - 12 q^{14} + 24 q^{21} - 18 q^{26} + 12 q^{29} - 12 q^{31} - 36 q^{34} - 36 q^{36} - 96 q^{39} - 42 q^{41} - 6 q^{44} + 36 q^{46} + 78 q^{49} + 84 q^{51} + 108 q^{54} + 60 q^{59} + 96 q^{61} + 18 q^{64} + 48 q^{66} + 60 q^{69} + 60 q^{71} + 6 q^{74} - 42 q^{76} - 60 q^{79} + 36 q^{81} - 12 q^{84} + 72 q^{86} - 60 q^{89} - 120 q^{91} - 12 q^{94} - 342 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.642788 + 0.766044i 0.454519 + 0.541675i
\(3\) −0.811037 + 2.22831i −0.468252 + 1.28651i 0.450887 + 0.892581i \(0.351108\pi\)
−0.919140 + 0.393932i \(0.871115\pi\)
\(4\) −0.173648 + 0.984808i −0.0868241 + 0.492404i
\(5\) 0 0
\(6\) −2.22831 + 0.811037i −0.909702 + 0.331104i
\(7\) 2.73267 + 1.57771i 1.03285 + 0.596318i 0.917801 0.397041i \(-0.129963\pi\)
0.115053 + 0.993359i \(0.463296\pi\)
\(8\) −0.866025 + 0.500000i −0.306186 + 0.176777i
\(9\) −2.00943 1.68611i −0.669811 0.562038i
\(10\) 0 0
\(11\) −0.688886 1.19319i −0.207707 0.359759i 0.743285 0.668975i \(-0.233267\pi\)
−0.950992 + 0.309216i \(0.899933\pi\)
\(12\) −2.05362 1.18566i −0.592828 0.342270i
\(13\) 1.47931 + 4.06437i 0.410286 + 1.12725i 0.957039 + 0.289958i \(0.0936415\pi\)
−0.546753 + 0.837294i \(0.684136\pi\)
\(14\) 0.547933 + 3.10748i 0.146441 + 0.830509i
\(15\) 0 0
\(16\) −0.939693 0.342020i −0.234923 0.0855050i
\(17\) 0.833438 + 0.993253i 0.202138 + 0.240899i 0.857585 0.514342i \(-0.171964\pi\)
−0.655446 + 0.755242i \(0.727520\pi\)
\(18\) 2.62313i 0.618277i
\(19\) −1.08907 + 4.22066i −0.249849 + 0.968285i
\(20\) 0 0
\(21\) −5.73192 + 4.80965i −1.25081 + 1.04955i
\(22\) 0.471226 1.29468i 0.100466 0.276027i
\(23\) −2.09271 0.369001i −0.436360 0.0769420i −0.0488468 0.998806i \(-0.515555\pi\)
−0.387513 + 0.921864i \(0.626666\pi\)
\(24\) −0.411774 2.33529i −0.0840531 0.476689i
\(25\) 0 0
\(26\) −2.16260 + 3.74574i −0.424122 + 0.734600i
\(27\) −0.773953 + 0.446842i −0.148947 + 0.0859948i
\(28\) −2.02826 + 2.41719i −0.383306 + 0.456806i
\(29\) 0.0998515 + 0.0837854i 0.0185420 + 0.0155586i 0.652012 0.758209i \(-0.273925\pi\)
−0.633470 + 0.773768i \(0.718370\pi\)
\(30\) 0 0
\(31\) −0.173355 + 0.300259i −0.0311355 + 0.0539282i −0.881173 0.472793i \(-0.843246\pi\)
0.850038 + 0.526722i \(0.176579\pi\)
\(32\) −0.342020 0.939693i −0.0604612 0.166116i
\(33\) 3.21749 0.567331i 0.560094 0.0987596i
\(34\) −0.225152 + 1.27690i −0.0386133 + 0.218987i
\(35\) 0 0
\(36\) 2.00943 1.68611i 0.334905 0.281019i
\(37\) 10.3150i 1.69578i −0.530174 0.847889i \(-0.677873\pi\)
0.530174 0.847889i \(-0.322127\pi\)
\(38\) −3.93325 + 1.87871i −0.638057 + 0.304768i
\(39\) −10.2564 −1.64234
\(40\) 0 0
\(41\) −10.3451 3.76531i −1.61563 0.588042i −0.633089 0.774079i \(-0.718213\pi\)
−0.982543 + 0.186037i \(0.940436\pi\)
\(42\) −7.36881 1.29932i −1.13703 0.200490i
\(43\) 11.3501 2.00132i 1.73087 0.305199i 0.782567 0.622566i \(-0.213910\pi\)
0.948303 + 0.317367i \(0.102799\pi\)
\(44\) 1.29468 0.471226i 0.195181 0.0710400i
\(45\) 0 0
\(46\) −1.06250 1.84030i −0.156656 0.271337i
\(47\) 0.0491361 0.0585581i 0.00716723 0.00854158i −0.762449 0.647048i \(-0.776003\pi\)
0.769616 + 0.638507i \(0.220448\pi\)
\(48\) 1.52425 1.81653i 0.220007 0.262194i
\(49\) 1.47834 + 2.56055i 0.211191 + 0.365793i
\(50\) 0 0
\(51\) −2.88922 + 1.05159i −0.404572 + 0.147252i
\(52\) −4.25950 + 0.751065i −0.590686 + 0.104154i
\(53\) 6.12511 + 1.08002i 0.841348 + 0.148352i 0.577682 0.816262i \(-0.303957\pi\)
0.263666 + 0.964614i \(0.415068\pi\)
\(54\) −0.839788 0.305658i −0.114281 0.0415948i
\(55\) 0 0
\(56\) −3.15542 −0.421661
\(57\) −8.52164 5.84988i −1.12872 0.774835i
\(58\) 0.130347i 0.0171154i
\(59\) 6.27104 5.26202i 0.816419 0.685057i −0.135711 0.990748i \(-0.543332\pi\)
0.952131 + 0.305691i \(0.0988875\pi\)
\(60\) 0 0
\(61\) 1.36244 7.72680i 0.174443 0.989315i −0.764342 0.644811i \(-0.776936\pi\)
0.938785 0.344504i \(-0.111953\pi\)
\(62\) −0.341442 + 0.0602055i −0.0433632 + 0.00764611i
\(63\) −2.83092 7.77790i −0.356663 0.979923i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) 0 0
\(66\) 2.50277 + 2.10007i 0.308069 + 0.258501i
\(67\) −0.662508 + 0.789546i −0.0809382 + 0.0964584i −0.804994 0.593283i \(-0.797831\pi\)
0.724056 + 0.689742i \(0.242276\pi\)
\(68\) −1.12289 + 0.648300i −0.136170 + 0.0786179i
\(69\) 2.51951 4.36392i 0.303313 0.525354i
\(70\) 0 0
\(71\) 2.02349 + 11.4758i 0.240144 + 1.36192i 0.831505 + 0.555517i \(0.187480\pi\)
−0.591361 + 0.806407i \(0.701409\pi\)
\(72\) 2.58328 + 0.455501i 0.304442 + 0.0536813i
\(73\) −4.18756 + 11.5052i −0.490117 + 1.34659i 0.410456 + 0.911881i \(0.365370\pi\)
−0.900573 + 0.434705i \(0.856853\pi\)
\(74\) 7.90176 6.63036i 0.918561 0.770764i
\(75\) 0 0
\(76\) −3.96742 1.80543i −0.455094 0.207097i
\(77\) 4.34745i 0.495438i
\(78\) −6.59270 7.85688i −0.746477 0.889616i
\(79\) 13.1650 + 4.79168i 1.48118 + 0.539106i 0.951111 0.308848i \(-0.0999436\pi\)
0.530070 + 0.847954i \(0.322166\pi\)
\(80\) 0 0
\(81\) −1.73450 9.83684i −0.192722 1.09298i
\(82\) −3.76531 10.3451i −0.415808 1.14242i
\(83\) −9.85443 5.68946i −1.08166 0.624499i −0.150319 0.988637i \(-0.548030\pi\)
−0.931345 + 0.364138i \(0.881364\pi\)
\(84\) −3.74124 6.48003i −0.408203 0.707029i
\(85\) 0 0
\(86\) 8.82879 + 7.40823i 0.952033 + 0.798850i
\(87\) −0.267683 + 0.154547i −0.0286986 + 0.0165691i
\(88\) 1.19319 + 0.688886i 0.127194 + 0.0734355i
\(89\) −17.1195 + 6.23099i −1.81466 + 0.660484i −0.818348 + 0.574723i \(0.805110\pi\)
−0.996316 + 0.0857608i \(0.972668\pi\)
\(90\) 0 0
\(91\) −2.36992 + 13.4405i −0.248436 + 1.40895i
\(92\) 0.726790 1.99684i 0.0757731 0.208185i
\(93\) −0.528473 0.629809i −0.0548000 0.0653082i
\(94\) 0.0764422 0.00788441
\(95\) 0 0
\(96\) 2.37131 0.242021
\(97\) 10.4271 + 12.4265i 1.05871 + 1.26172i 0.963910 + 0.266227i \(0.0857771\pi\)
0.0948014 + 0.995496i \(0.469778\pi\)
\(98\) −1.01124 + 2.77836i −0.102151 + 0.280657i
\(99\) −0.627577 + 3.55916i −0.0630738 + 0.357710i
\(100\) 0 0
\(101\) −6.22381 + 2.26528i −0.619293 + 0.225404i −0.632564 0.774508i \(-0.717998\pi\)
0.0132716 + 0.999912i \(0.495775\pi\)
\(102\) −2.66272 1.53732i −0.263649 0.152218i
\(103\) −10.7020 + 6.17880i −1.05450 + 0.608815i −0.923906 0.382621i \(-0.875022\pi\)
−0.130594 + 0.991436i \(0.541688\pi\)
\(104\) −3.31330 2.78019i −0.324896 0.272620i
\(105\) 0 0
\(106\) 3.10980 + 5.38633i 0.302050 + 0.523167i
\(107\) 9.48714 + 5.47740i 0.917156 + 0.529521i 0.882727 0.469887i \(-0.155705\pi\)
0.0344297 + 0.999407i \(0.489039\pi\)
\(108\) −0.305658 0.839788i −0.0294120 0.0808087i
\(109\) −1.29211 7.32792i −0.123762 0.701887i −0.982036 0.188695i \(-0.939574\pi\)
0.858274 0.513192i \(-0.171537\pi\)
\(110\) 0 0
\(111\) 22.9850 + 8.36586i 2.18164 + 0.794052i
\(112\) −2.02826 2.41719i −0.191653 0.228403i
\(113\) 11.6014i 1.09137i −0.837990 0.545686i \(-0.816269\pi\)
0.837990 0.545686i \(-0.183731\pi\)
\(114\) −0.996338 10.2882i −0.0933156 0.963577i
\(115\) 0 0
\(116\) −0.0998515 + 0.0837854i −0.00927098 + 0.00777928i
\(117\) 3.88041 10.6613i 0.358744 0.985642i
\(118\) 8.06189 + 1.42153i 0.742157 + 0.130862i
\(119\) 0.710449 + 4.02916i 0.0651268 + 0.369352i
\(120\) 0 0
\(121\) 4.55087 7.88234i 0.413716 0.716577i
\(122\) 6.79483 3.92300i 0.615175 0.355172i
\(123\) 16.7805 19.9982i 1.51305 1.80318i
\(124\) −0.265595 0.222861i −0.0238511 0.0200135i
\(125\) 0 0
\(126\) 4.13853 7.16815i 0.368690 0.638589i
\(127\) 5.60862 + 15.4096i 0.497685 + 1.36738i 0.893507 + 0.449050i \(0.148237\pi\)
−0.395822 + 0.918327i \(0.629540\pi\)
\(128\) 0.984808 0.173648i 0.0870455 0.0153485i
\(129\) −4.74577 + 26.9146i −0.417841 + 2.36970i
\(130\) 0 0
\(131\) 8.53118 7.15851i 0.745373 0.625442i −0.188902 0.981996i \(-0.560493\pi\)
0.934275 + 0.356554i \(0.116048\pi\)
\(132\) 3.26713i 0.284367i
\(133\) −9.63503 + 9.81545i −0.835463 + 0.851107i
\(134\) −1.03068 −0.0890371
\(135\) 0 0
\(136\) −1.21840 0.443463i −0.104477 0.0380266i
\(137\) −7.23011 1.27486i −0.617710 0.108919i −0.143968 0.989582i \(-0.545986\pi\)
−0.473743 + 0.880663i \(0.657097\pi\)
\(138\) 4.96247 0.875017i 0.422433 0.0744864i
\(139\) 11.0992 4.03978i 0.941422 0.342650i 0.174695 0.984623i \(-0.444106\pi\)
0.766727 + 0.641973i \(0.221884\pi\)
\(140\) 0 0
\(141\) 0.0906342 + 0.156983i 0.00763277 + 0.0132203i
\(142\) −7.49028 + 8.92657i −0.628570 + 0.749101i
\(143\) 3.83047 4.56497i 0.320320 0.381742i
\(144\) 1.31156 + 2.27169i 0.109297 + 0.189308i
\(145\) 0 0
\(146\) −11.5052 + 4.18756i −0.952180 + 0.346565i
\(147\) −6.90468 + 1.21748i −0.569488 + 0.100416i
\(148\) 10.1583 + 1.79118i 0.835007 + 0.147234i
\(149\) 3.30256 + 1.20203i 0.270556 + 0.0984745i 0.473736 0.880667i \(-0.342905\pi\)
−0.203179 + 0.979142i \(0.565127\pi\)
\(150\) 0 0
\(151\) −0.212620 −0.0173028 −0.00865139 0.999963i \(-0.502754\pi\)
−0.00865139 + 0.999963i \(0.502754\pi\)
\(152\) −1.16717 4.19973i −0.0946700 0.340643i
\(153\) 3.40114i 0.274966i
\(154\) 3.33034 2.79449i 0.268366 0.225186i
\(155\) 0 0
\(156\) 1.78101 10.1006i 0.142595 0.808696i
\(157\) 7.57072 1.33492i 0.604210 0.106538i 0.136829 0.990595i \(-0.456309\pi\)
0.467381 + 0.884056i \(0.345198\pi\)
\(158\) 4.79168 + 13.1650i 0.381205 + 1.04735i
\(159\) −7.37431 + 12.7727i −0.584821 + 1.01294i
\(160\) 0 0
\(161\) −5.13651 4.31004i −0.404814 0.339679i
\(162\) 6.42054 7.65170i 0.504445 0.601174i
\(163\) −6.34537 + 3.66350i −0.497008 + 0.286948i −0.727477 0.686132i \(-0.759307\pi\)
0.230469 + 0.973080i \(0.425974\pi\)
\(164\) 5.50451 9.53409i 0.429830 0.744487i
\(165\) 0 0
\(166\) −1.97593 11.2060i −0.153362 0.869758i
\(167\) 15.6032 + 2.75126i 1.20741 + 0.212899i 0.740899 0.671617i \(-0.234400\pi\)
0.466511 + 0.884515i \(0.345511\pi\)
\(168\) 2.55916 7.03124i 0.197444 0.542472i
\(169\) −4.37215 + 3.66867i −0.336319 + 0.282205i
\(170\) 0 0
\(171\) 9.30491 6.64483i 0.711564 0.508143i
\(172\) 11.5252i 0.878786i
\(173\) 10.6961 + 12.7471i 0.813211 + 0.969147i 0.999912 0.0132697i \(-0.00422402\pi\)
−0.186701 + 0.982417i \(0.559780\pi\)
\(174\) −0.290453 0.105716i −0.0220192 0.00801432i
\(175\) 0 0
\(176\) 0.239248 + 1.35684i 0.0180340 + 0.102276i
\(177\) 6.63936 + 18.2415i 0.499045 + 1.37111i
\(178\) −15.7774 9.10910i −1.18257 0.682756i
\(179\) −2.28553 3.95866i −0.170829 0.295884i 0.767881 0.640592i \(-0.221311\pi\)
−0.938710 + 0.344708i \(0.887978\pi\)
\(180\) 0 0
\(181\) 1.29338 + 1.08527i 0.0961360 + 0.0806677i 0.689589 0.724201i \(-0.257791\pi\)
−0.593453 + 0.804869i \(0.702236\pi\)
\(182\) −11.8194 + 6.82392i −0.876111 + 0.505823i
\(183\) 16.1127 + 9.30266i 1.19108 + 0.687673i
\(184\) 1.99684 0.726790i 0.147209 0.0535796i
\(185\) 0 0
\(186\) 0.142766 0.809667i 0.0104681 0.0593677i
\(187\) 0.610991 1.67868i 0.0446801 0.122758i
\(188\) 0.0491361 + 0.0585581i 0.00358362 + 0.00427079i
\(189\) −2.81995 −0.205121
\(190\) 0 0
\(191\) 11.2207 0.811901 0.405951 0.913895i \(-0.366941\pi\)
0.405951 + 0.913895i \(0.366941\pi\)
\(192\) 1.52425 + 1.81653i 0.110003 + 0.131097i
\(193\) −7.34927 + 20.1920i −0.529012 + 1.45345i 0.331223 + 0.943552i \(0.392539\pi\)
−0.860236 + 0.509897i \(0.829684\pi\)
\(194\) −2.81687 + 15.9752i −0.202239 + 1.14696i
\(195\) 0 0
\(196\) −2.77836 + 1.01124i −0.198455 + 0.0722315i
\(197\) 13.2315 + 7.63921i 0.942705 + 0.544271i 0.890807 0.454381i \(-0.150140\pi\)
0.0518981 + 0.998652i \(0.483473\pi\)
\(198\) −3.12988 + 1.80704i −0.222431 + 0.128420i
\(199\) −0.542940 0.455581i −0.0384880 0.0322953i 0.623341 0.781950i \(-0.285775\pi\)
−0.661829 + 0.749655i \(0.730219\pi\)
\(200\) 0 0
\(201\) −1.22203 2.11662i −0.0861955 0.149295i
\(202\) −5.73590 3.31162i −0.403576 0.233005i
\(203\) 0.140673 + 0.386495i 0.00987328 + 0.0271266i
\(204\) −0.533906 3.02793i −0.0373809 0.211998i
\(205\) 0 0
\(206\) −11.6123 4.22655i −0.809071 0.294478i
\(207\) 3.58298 + 4.27002i 0.249034 + 0.296787i
\(208\) 4.32521i 0.299899i
\(209\) 5.78627 1.60809i 0.400244 0.111234i
\(210\) 0 0
\(211\) 10.7852 9.04988i 0.742486 0.623020i −0.191018 0.981586i \(-0.561179\pi\)
0.933504 + 0.358567i \(0.116735\pi\)
\(212\) −2.12723 + 5.84451i −0.146099 + 0.401403i
\(213\) −27.2126 4.79832i −1.86458 0.328776i
\(214\) 1.90228 + 10.7884i 0.130037 + 0.737478i
\(215\) 0 0
\(216\) 0.446842 0.773953i 0.0304038 0.0526608i
\(217\) −0.947444 + 0.547007i −0.0643167 + 0.0371333i
\(218\) 4.78296 5.70011i 0.323943 0.386060i
\(219\) −22.2409 18.6623i −1.50290 1.26108i
\(220\) 0 0
\(221\) −2.80403 + 4.85673i −0.188620 + 0.326699i
\(222\) 8.36586 + 22.9850i 0.561479 + 1.54265i
\(223\) −11.5389 + 2.03461i −0.772699 + 0.136248i −0.546077 0.837735i \(-0.683879\pi\)
−0.226622 + 0.973983i \(0.572768\pi\)
\(224\) 0.547933 3.10748i 0.0366103 0.207627i
\(225\) 0 0
\(226\) 8.88722 7.45727i 0.591169 0.496050i
\(227\) 10.2265i 0.678758i 0.940650 + 0.339379i \(0.110217\pi\)
−0.940650 + 0.339379i \(0.889783\pi\)
\(228\) 7.24077 7.37636i 0.479532 0.488511i
\(229\) 5.05689 0.334169 0.167084 0.985943i \(-0.446565\pi\)
0.167084 + 0.985943i \(0.446565\pi\)
\(230\) 0 0
\(231\) 9.68744 + 3.52594i 0.637387 + 0.231990i
\(232\) −0.128367 0.0226345i −0.00842768 0.00148603i
\(233\) 7.14818 1.26042i 0.468293 0.0825727i 0.0654778 0.997854i \(-0.479143\pi\)
0.402815 + 0.915281i \(0.368032\pi\)
\(234\) 10.6613 3.88041i 0.696954 0.253671i
\(235\) 0 0
\(236\) 4.09313 + 7.08951i 0.266440 + 0.461488i
\(237\) −21.3546 + 25.4495i −1.38713 + 1.65312i
\(238\) −2.62985 + 3.13413i −0.170468 + 0.203155i
\(239\) 7.98657 + 13.8331i 0.516608 + 0.894792i 0.999814 + 0.0192850i \(0.00613899\pi\)
−0.483206 + 0.875507i \(0.660528\pi\)
\(240\) 0 0
\(241\) −20.8564 + 7.59111i −1.34348 + 0.488986i −0.910906 0.412613i \(-0.864616\pi\)
−0.432572 + 0.901599i \(0.642394\pi\)
\(242\) 8.96347 1.58050i 0.576194 0.101598i
\(243\) 20.6859 + 3.64748i 1.32700 + 0.233986i
\(244\) 7.37283 + 2.68349i 0.471997 + 0.171793i
\(245\) 0 0
\(246\) 26.1058 1.66445
\(247\) −18.7654 + 1.81729i −1.19401 + 0.115632i
\(248\) 0.346710i 0.0220161i
\(249\) 20.6702 17.3443i 1.30992 1.09915i
\(250\) 0 0
\(251\) 3.91622 22.2100i 0.247190 1.40188i −0.568162 0.822917i \(-0.692345\pi\)
0.815352 0.578966i \(-0.196544\pi\)
\(252\) 8.15132 1.43730i 0.513485 0.0905412i
\(253\) 1.00135 + 2.75119i 0.0629544 + 0.172966i
\(254\) −8.19925 + 14.2015i −0.514467 + 0.891083i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) 6.88718 8.20783i 0.429611 0.511990i −0.507199 0.861829i \(-0.669319\pi\)
0.936810 + 0.349839i \(0.113764\pi\)
\(258\) −23.6683 + 13.6649i −1.47352 + 0.850739i
\(259\) 16.2741 28.1876i 1.01122 1.75149i
\(260\) 0 0
\(261\) −0.0593732 0.336722i −0.00367511 0.0208426i
\(262\) 10.9675 + 1.93386i 0.677573 + 0.119474i
\(263\) 9.12051 25.0584i 0.562395 1.54517i −0.253720 0.967278i \(-0.581654\pi\)
0.816115 0.577890i \(-0.196124\pi\)
\(264\) −2.50277 + 2.10007i −0.154035 + 0.129250i
\(265\) 0 0
\(266\) −13.7123 1.07161i −0.840758 0.0657049i
\(267\) 43.2011i 2.64386i
\(268\) −0.662508 0.789546i −0.0404691 0.0482292i
\(269\) 1.34180 + 0.488375i 0.0818110 + 0.0297768i 0.382601 0.923913i \(-0.375028\pi\)
−0.300790 + 0.953690i \(0.597250\pi\)
\(270\) 0 0
\(271\) 1.27969 + 7.25749i 0.0777357 + 0.440861i 0.998689 + 0.0511882i \(0.0163008\pi\)
−0.920953 + 0.389673i \(0.872588\pi\)
\(272\) −0.443463 1.21840i −0.0268889 0.0738766i
\(273\) −28.0275 16.1817i −1.69630 0.979359i
\(274\) −3.67083 6.35806i −0.221763 0.384104i
\(275\) 0 0
\(276\) 3.86011 + 3.23902i 0.232351 + 0.194966i
\(277\) 2.18698 1.26266i 0.131403 0.0758656i −0.432857 0.901462i \(-0.642495\pi\)
0.564261 + 0.825597i \(0.309161\pi\)
\(278\) 10.2291 + 5.90576i 0.613500 + 0.354204i
\(279\) 0.854616 0.311055i 0.0511645 0.0186224i
\(280\) 0 0
\(281\) 2.99175 16.9671i 0.178473 1.01217i −0.755586 0.655050i \(-0.772648\pi\)
0.934058 0.357120i \(-0.116241\pi\)
\(282\) −0.0619974 + 0.170336i −0.00369189 + 0.0101434i
\(283\) 18.1400 + 21.6184i 1.07831 + 1.28508i 0.956248 + 0.292556i \(0.0945058\pi\)
0.122061 + 0.992523i \(0.461050\pi\)
\(284\) −11.6528 −0.691467
\(285\) 0 0
\(286\) 5.95915 0.352372
\(287\) −22.3292 26.6109i −1.31805 1.57079i
\(288\) −0.897162 + 2.46493i −0.0528658 + 0.145248i
\(289\) 2.66009 15.0861i 0.156476 0.887418i
\(290\) 0 0
\(291\) −36.1469 + 13.1564i −2.11897 + 0.771241i
\(292\) −10.6033 6.12181i −0.620510 0.358252i
\(293\) −10.9276 + 6.30904i −0.638396 + 0.368578i −0.783996 0.620766i \(-0.786822\pi\)
0.145601 + 0.989343i \(0.453489\pi\)
\(294\) −5.37089 4.50671i −0.313237 0.262837i
\(295\) 0 0
\(296\) 5.15751 + 8.93306i 0.299774 + 0.519224i
\(297\) 1.06633 + 0.615647i 0.0618748 + 0.0357234i
\(298\) 1.20203 + 3.30256i 0.0696320 + 0.191312i
\(299\) −1.59601 9.05140i −0.0922994 0.523456i
\(300\) 0 0
\(301\) 34.1735 + 12.4382i 1.96973 + 0.716923i
\(302\) −0.136670 0.162877i −0.00786445 0.00937249i
\(303\) 15.7058i 0.902274i
\(304\) 2.46694 3.59364i 0.141488 0.206109i
\(305\) 0 0
\(306\) 2.60543 2.18621i 0.148942 0.124978i
\(307\) −3.10031 + 8.51802i −0.176944 + 0.486149i −0.996182 0.0873047i \(-0.972175\pi\)
0.819238 + 0.573454i \(0.194397\pi\)
\(308\) 4.28140 + 0.754926i 0.243955 + 0.0430159i
\(309\) −5.08854 28.8586i −0.289477 1.64171i
\(310\) 0 0
\(311\) 10.8562 18.8035i 0.615599 1.06625i −0.374680 0.927154i \(-0.622247\pi\)
0.990279 0.139095i \(-0.0444192\pi\)
\(312\) 8.88232 5.12821i 0.502863 0.290328i
\(313\) 6.45746 7.69570i 0.364997 0.434987i −0.552022 0.833829i \(-0.686144\pi\)
0.917019 + 0.398843i \(0.130588\pi\)
\(314\) 5.88898 + 4.94144i 0.332334 + 0.278862i
\(315\) 0 0
\(316\) −7.00496 + 12.1330i −0.394060 + 0.682532i
\(317\) −0.721135 1.98130i −0.0405030 0.111281i 0.917792 0.397061i \(-0.129970\pi\)
−0.958295 + 0.285780i \(0.907747\pi\)
\(318\) −14.5245 + 2.56107i −0.814496 + 0.143618i
\(319\) 0.0311852 0.176860i 0.00174604 0.00990226i
\(320\) 0 0
\(321\) −19.8997 + 16.6979i −1.11070 + 0.931984i
\(322\) 6.70524i 0.373668i
\(323\) −5.09985 + 2.43594i −0.283763 + 0.135539i
\(324\) 9.98859 0.554921
\(325\) 0 0
\(326\) −6.88513 2.50598i −0.381332 0.138794i
\(327\) 17.3768 + 3.06400i 0.960939 + 0.169439i
\(328\) 10.8418 1.91170i 0.598636 0.105556i
\(329\) 0.226661 0.0824977i 0.0124962 0.00454824i
\(330\) 0 0
\(331\) 1.72204 + 2.98267i 0.0946521 + 0.163942i 0.909463 0.415784i \(-0.136493\pi\)
−0.814811 + 0.579726i \(0.803159\pi\)
\(332\) 7.31423 8.71676i 0.401420 0.478394i
\(333\) −17.3923 + 20.7273i −0.953091 + 1.13585i
\(334\) 7.92194 + 13.7212i 0.433469 + 0.750791i
\(335\) 0 0
\(336\) 7.03124 2.55916i 0.383586 0.139614i
\(337\) −25.4658 + 4.49031i −1.38721 + 0.244603i −0.816877 0.576811i \(-0.804297\pi\)
−0.570332 + 0.821414i \(0.693186\pi\)
\(338\) −5.62072 0.991085i −0.305727 0.0539079i
\(339\) 25.8516 + 9.40920i 1.40406 + 0.511038i
\(340\) 0 0
\(341\) 0.477687 0.0258682
\(342\) 11.0713 + 2.85676i 0.598668 + 0.154476i
\(343\) 12.7584i 0.688889i
\(344\) −8.82879 + 7.40823i −0.476016 + 0.399425i
\(345\) 0 0
\(346\) −2.88954 + 16.3874i −0.155343 + 0.880992i
\(347\) 2.48488 0.438152i 0.133395 0.0235212i −0.106552 0.994307i \(-0.533981\pi\)
0.239947 + 0.970786i \(0.422870\pi\)
\(348\) −0.105716 0.290453i −0.00566698 0.0155699i
\(349\) 1.83973 3.18650i 0.0984782 0.170569i −0.812577 0.582854i \(-0.801936\pi\)
0.911055 + 0.412285i \(0.135269\pi\)
\(350\) 0 0
\(351\) −2.96105 2.48461i −0.158049 0.132619i
\(352\) −0.885615 + 1.05543i −0.0472034 + 0.0562548i
\(353\) 2.42172 1.39818i 0.128895 0.0744175i −0.434166 0.900833i \(-0.642957\pi\)
0.563061 + 0.826415i \(0.309624\pi\)
\(354\) −9.70609 + 16.8114i −0.515873 + 0.893518i
\(355\) 0 0
\(356\) −3.16356 17.9414i −0.167668 0.950893i
\(357\) −9.55440 1.68470i −0.505672 0.0891637i
\(358\) 1.56340 4.29540i 0.0826281 0.227019i
\(359\) −15.4284 + 12.9460i −0.814280 + 0.683262i −0.951625 0.307261i \(-0.900587\pi\)
0.137345 + 0.990523i \(0.456143\pi\)
\(360\) 0 0
\(361\) −16.6279 9.19314i −0.875151 0.483849i
\(362\) 1.68838i 0.0887395i
\(363\) 13.8733 + 16.5336i 0.728162 + 0.867789i
\(364\) −12.8248 4.66784i −0.672201 0.244661i
\(365\) 0 0
\(366\) 3.23078 + 18.3227i 0.168876 + 0.957741i
\(367\) −1.54639 4.24866i −0.0807207 0.221778i 0.892767 0.450520i \(-0.148761\pi\)
−0.973487 + 0.228741i \(0.926539\pi\)
\(368\) 1.84030 + 1.06250i 0.0959321 + 0.0553864i
\(369\) 14.4390 + 25.0091i 0.751666 + 1.30192i
\(370\) 0 0
\(371\) 15.0340 + 12.6150i 0.780524 + 0.654938i
\(372\) 0.712009 0.411079i 0.0369160 0.0213134i
\(373\) −20.1528 11.6352i −1.04347 0.602449i −0.122657 0.992449i \(-0.539142\pi\)
−0.920815 + 0.390000i \(0.872475\pi\)
\(374\) 1.67868 0.610991i 0.0868027 0.0315936i
\(375\) 0 0
\(376\) −0.0132740 + 0.0752808i −0.000684556 + 0.00388231i
\(377\) −0.192823 + 0.529778i −0.00993091 + 0.0272849i
\(378\) −1.81263 2.16021i −0.0932315 0.111109i
\(379\) −9.34667 −0.480106 −0.240053 0.970760i \(-0.577165\pi\)
−0.240053 + 0.970760i \(0.577165\pi\)
\(380\) 0 0
\(381\) −38.8860 −1.99219
\(382\) 7.21252 + 8.59555i 0.369025 + 0.439787i
\(383\) 11.2306 30.8559i 0.573858 1.57666i −0.224497 0.974475i \(-0.572074\pi\)
0.798355 0.602187i \(-0.205704\pi\)
\(384\) −0.411774 + 2.33529i −0.0210133 + 0.119172i
\(385\) 0 0
\(386\) −20.1920 + 7.34927i −1.02774 + 0.374068i
\(387\) −26.1817 15.1160i −1.33089 0.768389i
\(388\) −14.0484 + 8.11084i −0.713199 + 0.411766i
\(389\) −8.17650 6.86090i −0.414565 0.347862i 0.411526 0.911398i \(-0.364996\pi\)
−0.826091 + 0.563537i \(0.809440\pi\)
\(390\) 0 0
\(391\) −1.37763 2.38613i −0.0696698 0.120672i
\(392\) −2.56055 1.47834i −0.129327 0.0746673i
\(393\) 9.03225 + 24.8159i 0.455617 + 1.25180i
\(394\) 2.65307 + 15.0463i 0.133660 + 0.758022i
\(395\) 0 0
\(396\) −3.39612 1.23608i −0.170661 0.0621156i
\(397\) −6.46404 7.70354i −0.324421 0.386630i 0.579041 0.815299i \(-0.303427\pi\)
−0.903462 + 0.428669i \(0.858983\pi\)
\(398\) 0.708758i 0.0355268i
\(399\) −14.0574 29.4305i −0.703753 1.47337i
\(400\) 0 0
\(401\) 9.25312 7.76429i 0.462079 0.387730i −0.381817 0.924238i \(-0.624701\pi\)
0.843895 + 0.536508i \(0.180257\pi\)
\(402\) 0.835919 2.29667i 0.0416918 0.114547i
\(403\) −1.47681 0.260401i −0.0735651 0.0129715i
\(404\) −1.15011 6.52262i −0.0572203 0.324513i
\(405\) 0 0
\(406\) −0.205650 + 0.356196i −0.0102062 + 0.0176777i
\(407\) −12.3077 + 7.10587i −0.610071 + 0.352225i
\(408\) 1.97634 2.35531i 0.0978435 0.116605i
\(409\) 30.2942 + 25.4198i 1.49795 + 1.25693i 0.883911 + 0.467655i \(0.154901\pi\)
0.614040 + 0.789275i \(0.289543\pi\)
\(410\) 0 0
\(411\) 8.70468 15.0769i 0.429370 0.743691i
\(412\) −4.22655 11.6123i −0.208227 0.572099i
\(413\) 25.4386 4.48552i 1.25175 0.220718i
\(414\) −0.967936 + 5.48944i −0.0475715 + 0.269791i
\(415\) 0 0
\(416\) 3.31330 2.78019i 0.162448 0.136310i
\(417\) 28.0088i 1.37160i
\(418\) 4.95121 + 3.39887i 0.242172 + 0.166244i
\(419\) −28.5326 −1.39391 −0.696954 0.717116i \(-0.745462\pi\)
−0.696954 + 0.717116i \(0.745462\pi\)
\(420\) 0 0
\(421\) −1.91607 0.697393i −0.0933836 0.0339888i 0.294906 0.955526i \(-0.404712\pi\)
−0.388289 + 0.921537i \(0.626934\pi\)
\(422\) 13.8652 + 2.44481i 0.674949 + 0.119012i
\(423\) −0.197471 + 0.0348195i −0.00960138 + 0.00169298i
\(424\) −5.84451 + 2.12723i −0.283834 + 0.103307i
\(425\) 0 0
\(426\) −13.8162 23.9304i −0.669398 1.15943i
\(427\) 15.9138 18.9653i 0.770121 0.917794i
\(428\) −7.04161 + 8.39187i −0.340369 + 0.405636i
\(429\) 7.06551 + 12.2378i 0.341126 + 0.590847i
\(430\) 0 0
\(431\) −12.7523 + 4.64147i −0.614258 + 0.223572i −0.630365 0.776299i \(-0.717095\pi\)
0.0161074 + 0.999870i \(0.494873\pi\)
\(432\) 0.880107 0.155187i 0.0423442 0.00746642i
\(433\) 28.5238 + 5.02952i 1.37077 + 0.241703i 0.810078 0.586323i \(-0.199425\pi\)
0.560690 + 0.828026i \(0.310536\pi\)
\(434\) −1.02804 0.374175i −0.0493474 0.0179610i
\(435\) 0 0
\(436\) 7.44096 0.356357
\(437\) 3.83652 8.43073i 0.183526 0.403297i
\(438\) 29.0334i 1.38727i
\(439\) 8.59028 7.20810i 0.409992 0.344024i −0.414349 0.910118i \(-0.635991\pi\)
0.824341 + 0.566094i \(0.191546\pi\)
\(440\) 0 0
\(441\) 1.34677 7.63790i 0.0641318 0.363710i
\(442\) −5.52286 + 0.973830i −0.262696 + 0.0463204i
\(443\) −2.54804 7.00068i −0.121061 0.332612i 0.864329 0.502927i \(-0.167744\pi\)
−0.985390 + 0.170315i \(0.945521\pi\)
\(444\) −12.2301 + 21.1831i −0.580413 + 1.00530i
\(445\) 0 0
\(446\) −8.97564 7.53146i −0.425009 0.356625i
\(447\) −5.35700 + 6.38422i −0.253377 + 0.301963i
\(448\) 2.73267 1.57771i 0.129107 0.0745398i
\(449\) 2.65192 4.59326i 0.125152 0.216769i −0.796640 0.604453i \(-0.793392\pi\)
0.921792 + 0.387684i \(0.126725\pi\)
\(450\) 0 0
\(451\) 2.63388 + 14.9375i 0.124025 + 0.703378i
\(452\) 11.4252 + 2.01457i 0.537396 + 0.0947574i
\(453\) 0.172443 0.473783i 0.00810207 0.0222603i
\(454\) −7.83397 + 6.57348i −0.367667 + 0.308509i
\(455\) 0 0
\(456\) 10.3049 + 0.805323i 0.482571 + 0.0377127i
\(457\) 14.9890i 0.701154i −0.936534 0.350577i \(-0.885986\pi\)
0.936534 0.350577i \(-0.114014\pi\)
\(458\) 3.25051 + 3.87381i 0.151886 + 0.181011i
\(459\) −1.08887 0.396316i −0.0508241 0.0184984i
\(460\) 0 0
\(461\) −1.19157 6.75771i −0.0554968 0.314738i 0.944405 0.328786i \(-0.106639\pi\)
−0.999901 + 0.0140479i \(0.995528\pi\)
\(462\) 3.52594 + 9.68744i 0.164042 + 0.450701i
\(463\) −17.8738 10.3194i −0.830665 0.479585i 0.0234152 0.999726i \(-0.492546\pi\)
−0.854080 + 0.520141i \(0.825879\pi\)
\(464\) −0.0651735 0.112884i −0.00302560 0.00524050i
\(465\) 0 0
\(466\) 5.56030 + 4.66564i 0.257576 + 0.216132i
\(467\) 10.4226 6.01750i 0.482301 0.278457i −0.239074 0.971001i \(-0.576844\pi\)
0.721375 + 0.692545i \(0.243510\pi\)
\(468\) 9.82555 + 5.67279i 0.454186 + 0.262225i
\(469\) −3.05609 + 1.11233i −0.141117 + 0.0513625i
\(470\) 0 0
\(471\) −3.16552 + 17.9526i −0.145859 + 0.827210i
\(472\) −2.79986 + 7.69256i −0.128874 + 0.354079i
\(473\) −10.2069 12.1641i −0.469312 0.559304i
\(474\) −33.2219 −1.52593
\(475\) 0 0
\(476\) −4.09132 −0.187525
\(477\) −10.4869 12.4979i −0.480164 0.572238i
\(478\) −5.46314 + 15.0098i −0.249878 + 0.686534i
\(479\) −3.95553 + 22.4329i −0.180733 + 1.02499i 0.750583 + 0.660776i \(0.229773\pi\)
−0.931316 + 0.364211i \(0.881339\pi\)
\(480\) 0 0
\(481\) 41.9240 15.2591i 1.91157 0.695754i
\(482\) −19.2214 11.0975i −0.875509 0.505475i
\(483\) 13.7700 7.95011i 0.626556 0.361743i
\(484\) 6.97234 + 5.85049i 0.316925 + 0.265931i
\(485\) 0 0
\(486\) 10.5025 + 18.1909i 0.476403 + 0.825155i
\(487\) 5.58510 + 3.22456i 0.253085 + 0.146119i 0.621176 0.783671i \(-0.286655\pi\)
−0.368091 + 0.929790i \(0.619989\pi\)
\(488\) 2.68349 + 7.37283i 0.121476 + 0.333752i
\(489\) −3.01707 17.1107i −0.136437 0.773771i
\(490\) 0 0
\(491\) 22.8944 + 8.33289i 1.03321 + 0.376058i 0.802303 0.596917i \(-0.203608\pi\)
0.230908 + 0.972975i \(0.425830\pi\)
\(492\) 16.7805 + 19.9982i 0.756524 + 0.901590i
\(493\) 0.169008i 0.00761173i
\(494\) −13.4543 13.2070i −0.605336 0.594209i
\(495\) 0 0
\(496\) 0.265595 0.222861i 0.0119256 0.0100067i
\(497\) −12.5759 + 34.5520i −0.564106 + 1.54987i
\(498\) 26.5730 + 4.68554i 1.19077 + 0.209964i
\(499\) −0.282127 1.60002i −0.0126298 0.0716269i 0.977841 0.209347i \(-0.0671337\pi\)
−0.990471 + 0.137720i \(0.956023\pi\)
\(500\) 0 0
\(501\) −18.7854 + 32.5373i −0.839270 + 1.45366i
\(502\) 19.5311 11.2763i 0.871717 0.503286i
\(503\) −22.6234 + 26.9615i −1.00873 + 1.20215i −0.0294632 + 0.999566i \(0.509380\pi\)
−0.979264 + 0.202588i \(0.935065\pi\)
\(504\) 6.34060 + 5.32040i 0.282433 + 0.236989i
\(505\) 0 0
\(506\) −1.46388 + 2.53551i −0.0650772 + 0.112717i
\(507\) −4.62894 12.7179i −0.205578 0.564822i
\(508\) −16.1494 + 2.84757i −0.716513 + 0.126341i
\(509\) 4.20711 23.8597i 0.186477 1.05756i −0.737567 0.675274i \(-0.764025\pi\)
0.924043 0.382288i \(-0.124864\pi\)
\(510\) 0 0
\(511\) −29.5952 + 24.8333i −1.30921 + 1.09856i
\(512\) 1.00000i 0.0441942i
\(513\) −1.04308 3.75323i −0.0460532 0.165709i
\(514\) 10.7146 0.472599
\(515\) 0 0
\(516\) −25.6816 9.34733i −1.13057 0.411493i
\(517\) −0.103720 0.0182886i −0.00456159 0.000804332i
\(518\) 32.0537 5.65193i 1.40836 0.248332i
\(519\) −37.0795 + 13.4958i −1.62761 + 0.592401i
\(520\) 0 0
\(521\) 3.95859 + 6.85648i 0.173429 + 0.300388i 0.939616 0.342229i \(-0.111182\pi\)
−0.766187 + 0.642617i \(0.777849\pi\)
\(522\) 0.219780 0.261923i 0.00961950 0.0114641i
\(523\) 1.57943 1.88229i 0.0690637 0.0823069i −0.730406 0.683013i \(-0.760669\pi\)
0.799470 + 0.600706i \(0.205114\pi\)
\(524\) 5.56833 + 9.64464i 0.243254 + 0.421328i
\(525\) 0 0
\(526\) 25.0584 9.12051i 1.09260 0.397673i
\(527\) −0.442714 + 0.0780624i −0.0192849 + 0.00340045i
\(528\) −3.21749 0.567331i −0.140023 0.0246899i
\(529\) −17.3697 6.32204i −0.755203 0.274871i
\(530\) 0 0
\(531\) −21.4736 −0.931874
\(532\) −7.99322 11.1931i −0.346550 0.485282i
\(533\) 47.6163i 2.06249i
\(534\) 33.0939 27.7691i 1.43211 1.20169i
\(535\) 0 0
\(536\) 0.178976 1.01502i 0.00773057 0.0438422i
\(537\) 10.6748 1.88225i 0.460650 0.0812250i
\(538\) 0.488375 + 1.34180i 0.0210554 + 0.0578491i
\(539\) 2.03681 3.52786i 0.0877316 0.151956i
\(540\) 0 0
\(541\) 17.2132 + 14.4436i 0.740054 + 0.620979i 0.932852 0.360260i \(-0.117312\pi\)
−0.192798 + 0.981238i \(0.561756\pi\)
\(542\) −4.73699 + 5.64532i −0.203471 + 0.242487i
\(543\) −3.46730 + 2.00184i −0.148796 + 0.0859074i
\(544\) 0.648300 1.12289i 0.0277956 0.0481434i
\(545\) 0 0
\(546\) −5.61983 31.8717i −0.240507 1.36398i
\(547\) 26.3908 + 4.65342i 1.12839 + 0.198966i 0.706522 0.707691i \(-0.250263\pi\)
0.421869 + 0.906657i \(0.361374\pi\)
\(548\) 2.51099 6.89889i 0.107264 0.294706i
\(549\) −15.7660 + 13.2292i −0.672876 + 0.564610i
\(550\) 0 0
\(551\) −0.462374 + 0.330191i −0.0196978 + 0.0140666i
\(552\) 5.03902i 0.214475i
\(553\) 28.4158 + 33.8647i 1.20836 + 1.44007i
\(554\) 2.37302 + 0.863707i 0.100820 + 0.0366954i
\(555\) 0 0
\(556\) 2.05105 + 11.6321i 0.0869839 + 0.493310i
\(557\) −13.3749 36.7473i −0.566714 1.55704i −0.809601 0.586980i \(-0.800317\pi\)
0.242887 0.970055i \(-0.421906\pi\)
\(558\) 0.787619 + 0.454732i 0.0333426 + 0.0192503i
\(559\) 24.9244 + 43.1703i 1.05419 + 1.82591i
\(560\) 0 0
\(561\) 3.24508 + 2.72295i 0.137008 + 0.114963i
\(562\) 14.9206 8.61440i 0.629387 0.363377i
\(563\) −7.46645 4.31076i −0.314673 0.181677i 0.334343 0.942452i \(-0.391486\pi\)
−0.649016 + 0.760775i \(0.724819\pi\)
\(564\) −0.170336 + 0.0619974i −0.00717246 + 0.00261056i
\(565\) 0 0
\(566\) −4.90049 + 27.7920i −0.205983 + 1.16819i
\(567\) 10.7799 29.6174i 0.452711 1.24381i
\(568\) −7.49028 8.92657i −0.314285 0.374550i
\(569\) −23.0260 −0.965300 −0.482650 0.875813i \(-0.660326\pi\)
−0.482650 + 0.875813i \(0.660326\pi\)
\(570\) 0 0
\(571\) −29.9673 −1.25409 −0.627047 0.778981i \(-0.715737\pi\)
−0.627047 + 0.778981i \(0.715737\pi\)
\(572\) 3.83047 + 4.56497i 0.160160 + 0.190871i
\(573\) −9.10040 + 25.0031i −0.380175 + 1.04452i
\(574\) 6.03220 34.2103i 0.251779 1.42791i
\(575\) 0 0
\(576\) −2.46493 + 0.897162i −0.102706 + 0.0373818i
\(577\) 3.93622 + 2.27258i 0.163867 + 0.0946087i 0.579691 0.814837i \(-0.303173\pi\)
−0.415824 + 0.909445i \(0.636507\pi\)
\(578\) 13.2665 7.65941i 0.551813 0.318590i
\(579\) −39.0333 32.7529i −1.62217 1.36116i
\(580\) 0 0
\(581\) −17.9526 31.0949i −0.744800 1.29003i
\(582\) −33.3131 19.2334i −1.38087 0.797248i
\(583\) −2.93083 8.05240i −0.121383 0.333496i
\(584\) −2.12608 12.0576i −0.0879779 0.498947i
\(585\) 0 0
\(586\) −11.8571 4.31563i −0.489813 0.178277i
\(587\) −11.8709 14.1471i −0.489963 0.583915i 0.463245 0.886230i \(-0.346685\pi\)
−0.953208 + 0.302315i \(0.902240\pi\)
\(588\) 7.01120i 0.289137i
\(589\) −1.07850 1.05867i −0.0444387 0.0436219i
\(590\) 0 0
\(591\) −27.7537 + 23.2881i −1.14164 + 0.957946i
\(592\) −3.52794 + 9.69294i −0.144998 + 0.398377i
\(593\) −15.7488 2.77694i −0.646726 0.114035i −0.159343 0.987223i \(-0.550938\pi\)
−0.487384 + 0.873188i \(0.662049\pi\)
\(594\) 0.213812 + 1.21259i 0.00877280 + 0.0497530i
\(595\) 0 0
\(596\) −1.75726 + 3.04366i −0.0719800 + 0.124673i
\(597\) 1.45552 0.840343i 0.0595704 0.0343930i
\(598\) 5.90788 7.04074i 0.241591 0.287917i
\(599\) −3.02967 2.54220i −0.123789 0.103871i 0.578792 0.815476i \(-0.303524\pi\)
−0.702581 + 0.711604i \(0.747969\pi\)
\(600\) 0 0
\(601\) 1.10855 1.92006i 0.0452186 0.0783209i −0.842530 0.538649i \(-0.818935\pi\)
0.887749 + 0.460328i \(0.152268\pi\)
\(602\) 12.4382 + 34.1735i 0.506941 + 1.39281i
\(603\) 2.66253 0.469476i 0.108427 0.0191185i
\(604\) 0.0369211 0.209390i 0.00150230 0.00851996i
\(605\) 0 0
\(606\) 12.0313 10.0955i 0.488739 0.410101i
\(607\) 17.4964i 0.710155i −0.934837 0.355078i \(-0.884454\pi\)
0.934837 0.355078i \(-0.115546\pi\)
\(608\) 4.33860 0.420163i 0.175954 0.0170399i
\(609\) −0.975319 −0.0395219
\(610\) 0 0
\(611\) 0.310689 + 0.113082i 0.0125691 + 0.00457479i
\(612\) 3.34947 + 0.590603i 0.135394 + 0.0238737i
\(613\) −8.98922 + 1.58504i −0.363071 + 0.0640193i −0.352208 0.935922i \(-0.614569\pi\)
−0.0108633 + 0.999941i \(0.503458\pi\)
\(614\) −8.51802 + 3.10031i −0.343759 + 0.125118i
\(615\) 0 0
\(616\) 2.17372 + 3.76500i 0.0875818 + 0.151696i
\(617\) 1.00026 1.19206i 0.0402689 0.0479906i −0.745534 0.666467i \(-0.767806\pi\)
0.785803 + 0.618477i \(0.212250\pi\)
\(618\) 18.8361 22.4480i 0.757699 0.902990i
\(619\) 16.2140 + 28.0835i 0.651695 + 1.12877i 0.982711 + 0.185144i \(0.0592753\pi\)
−0.331016 + 0.943625i \(0.607391\pi\)
\(620\) 0 0
\(621\) 1.78454 0.649520i 0.0716112 0.0260644i
\(622\) 21.3826 3.77032i 0.857362 0.151176i
\(623\) −56.6127 9.98235i −2.26814 0.399934i
\(624\) 9.63789 + 3.50790i 0.385824 + 0.140429i
\(625\) 0 0
\(626\) 10.0460 0.401520
\(627\) −1.10955 + 14.1978i −0.0443112 + 0.567005i
\(628\) 7.68751i 0.306765i
\(629\) 10.2454 8.59692i 0.408511 0.342782i
\(630\) 0 0
\(631\) −1.67744 + 9.51323i −0.0667778 + 0.378716i 0.933043 + 0.359766i \(0.117143\pi\)
−0.999820 + 0.0189499i \(0.993968\pi\)
\(632\) −13.7971 + 2.43280i −0.548819 + 0.0967715i
\(633\) 11.4187 + 31.3726i 0.453852 + 1.24695i
\(634\) 1.05423 1.82598i 0.0418688 0.0725189i
\(635\) 0 0
\(636\) −11.2981 9.48023i −0.447999 0.375915i
\(637\) −8.22011 + 9.79635i −0.325693 + 0.388145i
\(638\) 0.155528 0.0897942i 0.00615741 0.00355498i
\(639\) 15.2834 26.4716i 0.604602 1.04720i
\(640\) 0 0
\(641\) 7.05763 + 40.0258i 0.278759 + 1.58092i 0.726761 + 0.686891i \(0.241025\pi\)
−0.448001 + 0.894033i \(0.647864\pi\)
\(642\) −25.5826 4.51091i −1.00967 0.178031i
\(643\) −14.3882 + 39.5312i −0.567414 + 1.55896i 0.241112 + 0.970497i \(0.422488\pi\)
−0.808526 + 0.588460i \(0.799734\pi\)
\(644\) 5.13651 4.31004i 0.202407 0.169840i
\(645\) 0 0
\(646\) −5.14416 2.34092i −0.202394 0.0921022i
\(647\) 18.0072i 0.707936i −0.935258 0.353968i \(-0.884832\pi\)
0.935258 0.353968i \(-0.115168\pi\)
\(648\) 6.42054 + 7.65170i 0.252223 + 0.300587i
\(649\) −10.5986 3.85757i −0.416031 0.151423i
\(650\) 0 0
\(651\) −0.450487 2.55484i −0.0176560 0.100132i
\(652\) −2.50598 6.88513i −0.0981419 0.269643i
\(653\) −34.1968 19.7435i −1.33822 0.772624i −0.351680 0.936120i \(-0.614390\pi\)
−0.986544 + 0.163496i \(0.947723\pi\)
\(654\) 8.82243 + 15.2809i 0.344984 + 0.597530i
\(655\) 0 0
\(656\) 8.43340 + 7.07646i 0.329269 + 0.276289i
\(657\) 27.8138 16.0583i 1.08512 0.626493i
\(658\) 0.208891 + 0.120604i 0.00814344 + 0.00470162i
\(659\) 33.6395 12.2438i 1.31041 0.476949i 0.410035 0.912070i \(-0.365516\pi\)
0.900372 + 0.435120i \(0.143294\pi\)
\(660\) 0 0
\(661\) 2.36241 13.3979i 0.0918871 0.521118i −0.903770 0.428019i \(-0.859212\pi\)
0.995657 0.0930988i \(-0.0296772\pi\)
\(662\) −1.17795 + 3.23639i −0.0457822 + 0.125786i
\(663\) −8.54809 10.1872i −0.331980 0.395639i
\(664\) 11.3789 0.441588
\(665\) 0 0
\(666\) −27.0576 −1.04846
\(667\) −0.178043 0.212184i −0.00689386 0.00821578i
\(668\) −5.41893 + 14.8884i −0.209665 + 0.576049i
\(669\) 4.82470 27.3623i 0.186534 1.05789i
\(670\) 0 0
\(671\) −10.1581 + 3.69724i −0.392148 + 0.142730i
\(672\) 6.48003 + 3.74124i 0.249972 + 0.144322i
\(673\) −36.5649 + 21.1108i −1.40947 + 0.813760i −0.995337 0.0964549i \(-0.969250\pi\)
−0.414136 + 0.910215i \(0.635916\pi\)
\(674\) −19.8089 16.6216i −0.763009 0.640241i
\(675\) 0 0
\(676\) −2.85372 4.94278i −0.109758 0.190107i
\(677\) −37.8202 21.8355i −1.45355 0.839207i −0.454869 0.890558i \(-0.650314\pi\)
−0.998681 + 0.0513514i \(0.983647\pi\)
\(678\) 9.40920 + 25.8516i 0.361358 + 0.992824i
\(679\) 8.88840 + 50.4086i 0.341105 + 1.93450i
\(680\) 0 0
\(681\) −22.7878 8.29409i −0.873231 0.317830i
\(682\) 0.307051 + 0.365929i 0.0117576 + 0.0140122i
\(683\) 9.22100i 0.352832i 0.984316 + 0.176416i \(0.0564504\pi\)
−0.984316 + 0.176416i \(0.943550\pi\)
\(684\) 4.92810 + 10.3174i 0.188431 + 0.394496i
\(685\) 0 0
\(686\) 9.77350 8.20094i 0.373154 0.313113i
\(687\) −4.10133 + 11.2683i −0.156475 + 0.429913i
\(688\) −11.3501 2.00132i −0.432717 0.0762998i
\(689\) 4.67132 + 26.4924i 0.177963 + 1.00928i
\(690\) 0 0
\(691\) 20.0044 34.6487i 0.761004 1.31810i −0.181330 0.983422i \(-0.558040\pi\)
0.942334 0.334675i \(-0.108626\pi\)
\(692\) −14.4108 + 8.32010i −0.547818 + 0.316283i
\(693\) −7.33029 + 8.73590i −0.278455 + 0.331849i
\(694\) 1.93290 + 1.62189i 0.0733717 + 0.0615662i
\(695\) 0 0
\(696\) 0.154547 0.267683i 0.00585808 0.0101465i
\(697\) −4.88209 13.4134i −0.184922 0.508070i
\(698\) 3.62355 0.638930i 0.137153 0.0241839i
\(699\) −2.98884 + 16.9506i −0.113048 + 0.641130i
\(700\) 0 0
\(701\) −1.37655 + 1.15507i −0.0519917 + 0.0436262i −0.668413 0.743790i \(-0.733026\pi\)
0.616422 + 0.787416i \(0.288582\pi\)
\(702\) 3.86537i 0.145889i
\(703\) 43.5361 + 11.2337i 1.64200 + 0.423688i
\(704\) −1.37777 −0.0519267
\(705\) 0 0
\(706\) 2.62772 + 0.956410i 0.0988954 + 0.0359950i
\(707\) −20.5816 3.62909i −0.774051 0.136486i
\(708\) −19.1173 + 3.37089i −0.718471 + 0.126686i
\(709\) 31.8904 11.6072i 1.19767 0.435916i 0.335259 0.942126i \(-0.391176\pi\)
0.862410 + 0.506210i \(0.168954\pi\)
\(710\) 0 0
\(711\) −18.3749 31.8263i −0.689113 1.19358i
\(712\) 11.7104 13.9559i 0.438867 0.523021i
\(713\) 0.473577 0.564387i 0.0177356 0.0211365i
\(714\) −4.85090 8.40200i −0.181540 0.314437i
\(715\) 0 0
\(716\) 4.29540 1.56340i 0.160527 0.0584269i
\(717\) −37.3019 + 6.57733i −1.39306 + 0.245635i
\(718\) −19.8344 3.49734i −0.740212 0.130519i
\(719\) −4.77790 1.73901i −0.178186 0.0648542i 0.251387 0.967887i \(-0.419113\pi\)
−0.429572 + 0.903033i \(0.641336\pi\)
\(720\) 0 0
\(721\) −38.9934 −1.45219
\(722\) −3.64584 18.6469i −0.135684 0.693967i
\(723\) 52.6311i 1.95737i
\(724\) −1.29338 + 1.08527i −0.0480680 + 0.0403338i
\(725\) 0 0
\(726\) −3.74786 + 21.2552i −0.139096 + 0.788854i
\(727\) −21.2529 + 3.74747i −0.788228 + 0.138986i −0.553250 0.833015i \(-0.686613\pi\)
−0.234977 + 0.972001i \(0.575502\pi\)
\(728\) −4.66784 12.8248i −0.173002 0.475318i
\(729\) −9.92186 + 17.1852i −0.367476 + 0.636487i
\(730\) 0 0
\(731\) 11.4474 + 9.60551i 0.423397 + 0.355273i
\(732\) −11.9593 + 14.2525i −0.442027 + 0.526788i
\(733\) 8.20601 4.73774i 0.303096 0.174993i −0.340737 0.940159i \(-0.610677\pi\)
0.643833 + 0.765166i \(0.277343\pi\)
\(734\) 2.26066 3.91559i 0.0834426 0.144527i
\(735\) 0 0
\(736\) 0.369001 + 2.09271i 0.0136015 + 0.0771382i
\(737\) 1.39847 + 0.246588i 0.0515132 + 0.00908317i
\(738\) −9.87687 + 27.1365i −0.363573 + 0.998908i
\(739\) 6.02954 5.05938i 0.221800 0.186112i −0.525116 0.851031i \(-0.675978\pi\)
0.746916 + 0.664918i \(0.231534\pi\)
\(740\) 0 0
\(741\) 11.1699 43.2888i 0.410337 1.59026i
\(742\) 19.6254i 0.720473i
\(743\) 31.1013 + 37.0651i 1.14100 + 1.35979i 0.923442 + 0.383737i \(0.125363\pi\)
0.217553 + 0.976049i \(0.430193\pi\)
\(744\) 0.772575 + 0.281194i 0.0283240 + 0.0103091i
\(745\) 0 0
\(746\) −4.04087 22.9169i −0.147947 0.839048i
\(747\) 10.2087 + 28.0483i 0.373518 + 1.02623i
\(748\) 1.54708 + 0.893209i 0.0565670 + 0.0326590i
\(749\) 17.2835 + 29.9359i 0.631525 + 1.09383i
\(750\) 0 0
\(751\) −9.30243 7.80567i −0.339451 0.284833i 0.457087 0.889422i \(-0.348893\pi\)
−0.796537 + 0.604589i \(0.793337\pi\)
\(752\) −0.0662008 + 0.0382211i −0.00241410 + 0.00139378i
\(753\) 46.3145 + 26.7397i 1.68779 + 0.974447i
\(754\) −0.529778 + 0.192823i −0.0192934 + 0.00702221i
\(755\) 0 0
\(756\) 0.489679 2.77711i 0.0178095 0.101002i
\(757\) −11.9596 + 32.8586i −0.434677 + 1.19427i 0.508233 + 0.861220i \(0.330299\pi\)
−0.942910 + 0.333046i \(0.891923\pi\)
\(758\) −6.00792 7.15997i −0.218218 0.260062i
\(759\) −6.94262 −0.252001
\(760\) 0 0
\(761\) 46.9073 1.70039 0.850194 0.526470i \(-0.176485\pi\)
0.850194 + 0.526470i \(0.176485\pi\)
\(762\) −24.9954 29.7884i −0.905489 1.07912i
\(763\) 8.03041 22.0634i 0.290720 0.798748i
\(764\) −1.94845 + 11.0502i −0.0704926 + 0.399783i
\(765\) 0 0
\(766\) 30.8559 11.2306i 1.11487 0.405779i
\(767\) 30.6636 + 17.7036i 1.10720 + 0.639241i
\(768\) −2.05362 + 1.18566i −0.0741035 + 0.0427837i
\(769\) −1.06182 0.890969i −0.0382900 0.0321292i 0.623442 0.781870i \(-0.285734\pi\)
−0.661732 + 0.749741i \(0.730178\pi\)
\(770\) 0 0
\(771\) 12.7038 + 22.0036i 0.457516 + 0.792440i
\(772\) −18.6090 10.7439i −0.669753 0.386682i
\(773\) −2.20242 6.05111i −0.0792157 0.217643i 0.893762 0.448541i \(-0.148056\pi\)
−0.972978 + 0.230897i \(0.925834\pi\)
\(774\) −5.24973 29.7727i −0.188698 1.07016i
\(775\) 0 0
\(776\) −15.2434 5.54814i −0.547206 0.199167i
\(777\) 49.6116 + 59.1248i 1.77981 + 2.12109i
\(778\) 10.6737i 0.382670i
\(779\) 27.1585 39.5624i 0.973056 1.41747i
\(780\) 0 0
\(781\) 12.2988 10.3199i 0.440085 0.369275i
\(782\) 0.942355 2.58910i 0.0336985 0.0925860i
\(783\) −0.114719 0.0202281i −0.00409973 0.000722893i
\(784\) −0.513421 2.91175i −0.0183365 0.103991i
\(785\) 0 0
\(786\) −13.2043 + 22.8705i −0.470981 + 0.815762i
\(787\) −7.30651 + 4.21842i −0.260449 + 0.150370i −0.624539 0.780993i \(-0.714713\pi\)
0.364090 + 0.931364i \(0.381380\pi\)
\(788\) −9.82078 + 11.7040i −0.349851 + 0.416936i
\(789\) 48.4407 + 40.6466i 1.72453 + 1.44706i
\(790\) 0 0
\(791\) 18.3037 31.7030i 0.650805 1.12723i
\(792\) −1.23608 3.39612i −0.0439224 0.120676i
\(793\) 33.4200 5.89285i 1.18678 0.209261i
\(794\) 1.74625 9.90348i 0.0619721 0.351461i
\(795\) 0 0
\(796\) 0.542940 0.455581i 0.0192440 0.0161476i
\(797\) 32.4342i 1.14888i 0.818548 + 0.574438i \(0.194779\pi\)
−0.818548 + 0.574438i \(0.805221\pi\)
\(798\) 13.5091 29.6862i 0.478217 1.05088i
\(799\) 0.0991149 0.00350643
\(800\) 0 0
\(801\) 44.9066 + 16.3447i 1.58670 + 0.577511i
\(802\) 11.8956 + 2.09751i 0.420047 + 0.0740657i
\(803\) 16.6126 2.92926i 0.586247 0.103371i
\(804\) 2.29667 0.835919i 0.0809973 0.0294806i
\(805\) 0 0
\(806\) −0.749796 1.29868i −0.0264104 0.0457442i
\(807\) −2.17650 + 2.59385i −0.0766164 + 0.0913079i
\(808\) 4.25734 5.07370i 0.149773 0.178492i
\(809\) −9.01013 15.6060i −0.316779 0.548678i 0.663035 0.748589i \(-0.269268\pi\)
−0.979814 + 0.199911i \(0.935935\pi\)
\(810\) 0 0
\(811\) 24.5830 8.94748i 0.863226 0.314189i 0.127805 0.991799i \(-0.459207\pi\)
0.735421 + 0.677611i \(0.236985\pi\)
\(812\) −0.405051 + 0.0714214i −0.0142145 + 0.00250640i
\(813\) −17.2098 3.03455i −0.603573 0.106426i
\(814\) −13.3547 4.86070i −0.468081 0.170367i
\(815\) 0 0
\(816\) 3.07464 0.107634
\(817\) −3.91407 + 50.0843i −0.136936 + 1.75223i
\(818\) 39.5462i 1.38270i
\(819\) 27.4244 23.0118i 0.958287 0.804098i
\(820\) 0 0
\(821\) −4.91249 + 27.8601i −0.171447 + 0.972325i 0.770718 + 0.637176i \(0.219898\pi\)
−0.942165 + 0.335149i \(0.891213\pi\)
\(822\) 17.1449 3.02310i 0.597996 0.105443i
\(823\) −17.0857 46.9427i −0.595571 1.63632i −0.759995 0.649929i \(-0.774799\pi\)
0.164424 0.986390i \(-0.447423\pi\)
\(824\) 6.17880 10.7020i 0.215249 0.372822i
\(825\) 0 0
\(826\) 19.7878 + 16.6039i 0.688504 + 0.577723i
\(827\) −3.41471 + 4.06949i −0.118741 + 0.141510i −0.822140 0.569285i \(-0.807220\pi\)
0.703399 + 0.710795i \(0.251665\pi\)
\(828\) −4.82733 + 2.78706i −0.167761 + 0.0968570i
\(829\) 18.4308 31.9231i 0.640129 1.10874i −0.345275 0.938502i \(-0.612214\pi\)
0.985404 0.170234i \(-0.0544524\pi\)
\(830\) 0 0
\(831\) 1.03986 + 5.89733i 0.0360723 + 0.204576i
\(832\) 4.25950 + 0.751065i 0.147672 + 0.0260385i
\(833\) −1.31118 + 3.60242i −0.0454295 + 0.124817i
\(834\) −21.4560 + 18.0037i −0.742961 + 0.623418i
\(835\) 0 0
\(836\) 0.578889 + 5.97760i 0.0200213 + 0.206740i
\(837\) 0.309849i 0.0107099i
\(838\) −18.3404 21.8572i −0.633558 0.755045i
\(839\) −42.0154 15.2924i −1.45053 0.527951i −0.507793 0.861479i \(-0.669538\pi\)
−0.942740 + 0.333528i \(0.891761\pi\)
\(840\) 0 0
\(841\) −5.03285 28.5427i −0.173546 0.984231i
\(842\) −0.697393 1.91607i −0.0240337 0.0660321i
\(843\) 35.3814 + 20.4275i 1.21860 + 0.703559i
\(844\) 7.03956 + 12.1929i 0.242312 + 0.419696i
\(845\) 0 0
\(846\) −0.153605 0.128890i −0.00528106 0.00443133i
\(847\) 24.8721 14.3599i 0.854615 0.493412i
\(848\) −5.38633 3.10980i −0.184967 0.106791i
\(849\) −62.8845 + 22.8881i −2.15819 + 0.785517i
\(850\) 0 0
\(851\) −3.80625 + 21.5863i −0.130476 + 0.739969i
\(852\) 9.45085 25.9660i 0.323781 0.889581i
\(853\) −18.9389 22.5705i −0.648457 0.772800i 0.337224 0.941424i \(-0.390512\pi\)
−0.985680 + 0.168624i \(0.946068\pi\)
\(854\) 24.7574 0.847181
\(855\) 0 0
\(856\) −10.9548 −0.374428
\(857\) 30.5152 + 36.3667i 1.04238 + 1.24226i 0.969544 + 0.244917i \(0.0787608\pi\)
0.0728369 + 0.997344i \(0.476795\pi\)
\(858\) −4.83309 + 13.2788i −0.164999 + 0.453331i
\(859\) −0.165772 + 0.940140i −0.00565607 + 0.0320772i −0.987505 0.157587i \(-0.949629\pi\)
0.981849 + 0.189664i \(0.0607398\pi\)
\(860\) 0 0
\(861\) 77.4070 28.1739i 2.63802 0.960162i
\(862\) −11.7526 6.78537i −0.400295 0.231111i
\(863\) 40.7257 23.5130i 1.38632 0.800392i 0.393421 0.919359i \(-0.371292\pi\)
0.992898 + 0.118967i \(0.0379583\pi\)
\(864\) 0.684602 + 0.574449i 0.0232906 + 0.0195432i
\(865\) 0 0
\(866\) 14.4819 + 25.0834i 0.492116 + 0.852370i
\(867\) 31.4590 + 18.1629i 1.06840 + 0.616843i
\(868\) −0.374175 1.02804i −0.0127003 0.0348939i
\(869\) −3.35184 19.0092i −0.113703 0.644844i
\(870\) 0 0
\(871\) −4.18906 1.52469i −0.141941 0.0516622i
\(872\) 4.78296 + 5.70011i 0.161971 + 0.193030i
\(873\) 42.5515i 1.44015i
\(874\) 8.92438 2.48023i 0.301872 0.0838949i
\(875\) 0 0
\(876\) 22.2409 18.6623i 0.751451 0.630542i
\(877\) 14.6358 40.2114i 0.494215 1.35784i −0.402575 0.915387i \(-0.631885\pi\)
0.896790 0.442457i \(-0.145893\pi\)
\(878\) 11.0435 + 1.94726i 0.372699 + 0.0657168i
\(879\) −5.19580 29.4668i −0.175250 0.993891i
\(880\) 0 0
\(881\) −4.53664 + 7.85770i −0.152843 + 0.264733i −0.932272 0.361759i \(-0.882176\pi\)
0.779428 + 0.626491i \(0.215510\pi\)
\(882\) 6.71666 3.87786i 0.226162 0.130574i
\(883\) 20.1333 23.9939i 0.677539 0.807460i −0.312250 0.950000i \(-0.601083\pi\)
0.989789 + 0.142540i \(0.0455270\pi\)
\(884\) −4.29603 3.60479i −0.144491 0.121242i
\(885\) 0 0
\(886\) 3.72498 6.45186i 0.125143 0.216755i
\(887\) −1.16097 3.18973i −0.0389814 0.107101i 0.918675 0.395015i \(-0.129260\pi\)
−0.957656 + 0.287914i \(0.907038\pi\)
\(888\) −24.0885 + 4.24746i −0.808358 + 0.142535i
\(889\) −8.98528 + 50.9581i −0.301357 + 1.70908i
\(890\) 0 0
\(891\) −10.5423 + 8.84604i −0.353180 + 0.296353i
\(892\) 11.7169i 0.392310i
\(893\) 0.193641 + 0.271160i 0.00647995 + 0.00907402i
\(894\) −8.33401 −0.278731
\(895\) 0 0
\(896\) 2.96512 + 1.07922i 0.0990579 + 0.0360541i
\(897\) 21.4637 + 3.78463i 0.716652 + 0.126365i
\(898\) 5.22326 0.921002i 0.174303 0.0307342i
\(899\) −0.0424671 + 0.0154568i −0.00141636 + 0.000515512i
\(900\) 0 0
\(901\) 4.03216 + 6.98391i 0.134331 + 0.232668i
\(902\) −9.74975 + 11.6193i −0.324631 + 0.386880i
\(903\) −55.4320 + 66.0613i −1.84466 + 2.19838i
\(904\) 5.80072 + 10.0471i 0.192929 + 0.334163i
\(905\) 0 0
\(906\) 0.473783 0.172443i 0.0157404 0.00572903i
\(907\) 39.0053 6.87769i 1.29515 0.228370i 0.516749 0.856137i \(-0.327142\pi\)
0.778401 + 0.627767i \(0.216031\pi\)
\(908\) −10.0712 1.77582i −0.334223 0.0589326i
\(909\) 16.3259 + 5.94213i 0.541494 + 0.197088i
\(910\) 0 0
\(911\) −24.0316 −0.796204 −0.398102 0.917341i \(-0.630331\pi\)
−0.398102 + 0.917341i \(0.630331\pi\)
\(912\) 6.00695 + 8.41166i 0.198910 + 0.278538i
\(913\) 15.6776i 0.518851i
\(914\) 11.4822 9.63471i 0.379798 0.318688i
\(915\) 0 0
\(916\) −0.878120 + 4.98007i −0.0290139 + 0.164546i
\(917\) 34.6070 6.10215i 1.14282 0.201511i
\(918\) −0.396316 1.08887i −0.0130804 0.0359380i
\(919\) 1.92860 3.34044i 0.0636187 0.110191i −0.832462 0.554083i \(-0.813069\pi\)
0.896080 + 0.443892i \(0.146403\pi\)
\(920\) 0 0
\(921\) −16.4663 13.8169i −0.542583 0.455281i
\(922\) 4.41078 5.25656i 0.145261 0.173116i
\(923\) −43.6484 + 25.2004i −1.43670 + 0.829481i
\(924\) −5.15458 + 8.92800i −0.169573 + 0.293710i
\(925\) 0 0
\(926\) −3.58390 20.3253i −0.117774 0.667931i
\(927\) 31.9231 + 5.62890i 1.04849 + 0.184877i
\(928\) 0.0445813 0.122486i 0.00146345 0.00402080i
\(929\) −15.5371 + 13.0371i −0.509755 + 0.427735i −0.861043 0.508532i \(-0.830188\pi\)
0.351288 + 0.936267i \(0.385744\pi\)
\(930\) 0 0
\(931\) −12.4172 + 3.45094i −0.406958 + 0.113100i
\(932\) 7.25845i 0.237759i
\(933\) 33.0952 + 39.4413i 1.08349 + 1.29125i
\(934\) 11.3092 + 4.11621i 0.370048 + 0.134687i
\(935\) 0 0
\(936\) 1.97014 + 11.1732i 0.0643960 + 0.365208i
\(937\) −9.43723 25.9286i −0.308301 0.847050i −0.992988 0.118213i \(-0.962283\pi\)
0.684687 0.728837i \(-0.259939\pi\)
\(938\) −2.81651 1.62611i −0.0919623 0.0530945i
\(939\) 11.9111 + 20.6307i 0.388705 + 0.673257i
\(940\) 0 0
\(941\) −17.5704 14.7433i −0.572780 0.480619i 0.309787 0.950806i \(-0.399742\pi\)
−0.882567 + 0.470187i \(0.844187\pi\)
\(942\) −15.7872 + 9.11475i −0.514375 + 0.296975i
\(943\) 20.2599 + 11.6970i 0.659752 + 0.380908i
\(944\) −7.69256 + 2.79986i −0.250372 + 0.0911278i
\(945\) 0 0
\(946\) 2.75737 15.6378i 0.0896498 0.508429i
\(947\) −9.60233 + 26.3822i −0.312034 + 0.857306i 0.680212 + 0.733016i \(0.261888\pi\)
−0.992246 + 0.124291i \(0.960334\pi\)
\(948\) −21.3546 25.4495i −0.693566 0.826560i
\(949\) −52.9562 −1.71903
\(950\) 0 0
\(951\) 4.99982 0.162130
\(952\) −2.62985 3.13413i −0.0852338 0.101578i
\(953\) 11.7324 32.2346i 0.380050 1.04418i −0.591284 0.806463i \(-0.701379\pi\)
0.971335 0.237717i \(-0.0763989\pi\)
\(954\) 2.83303 16.0669i 0.0917229 0.520186i
\(955\) 0 0
\(956\) −15.0098 + 5.46314i −0.485453 + 0.176690i
\(957\) 0.368806 + 0.212930i 0.0119218 + 0.00688305i
\(958\) −19.7272 + 11.3895i −0.637357 + 0.367978i
\(959\) −17.7462 14.8908i −0.573054 0.480849i
\(960\) 0 0
\(961\) 15.4399 + 26.7427i 0.498061 + 0.862667i
\(962\) 38.6374 + 22.3073i 1.24572 + 0.719216i
\(963\) −9.82824 27.0029i −0.316711 0.870155i
\(964\) −3.85411 21.8577i −0.124132 0.703990i
\(965\) 0 0
\(966\) 14.9413 + 5.43820i 0.480729 + 0.174971i
\(967\) −9.34181 11.1331i −0.300412 0.358017i 0.594629 0.804000i \(-0.297299\pi\)
−0.895042 + 0.445983i \(0.852854\pi\)
\(968\) 9.10174i 0.292541i
\(969\) −1.29185 13.3397i −0.0415002 0.428531i
\(970\) 0 0
\(971\) 37.8612 31.7693i 1.21502 1.01952i 0.215952 0.976404i \(-0.430714\pi\)
0.999070 0.0431208i \(-0.0137300\pi\)
\(972\) −7.18414 + 19.7383i −0.230431 + 0.633105i
\(973\) 36.7041 + 6.47192i 1.17668 + 0.207480i
\(974\) 1.11988 + 6.35114i 0.0358832 + 0.203504i
\(975\) 0 0
\(976\) −3.92300 + 6.79483i −0.125572 + 0.217497i
\(977\) 2.52147 1.45577i 0.0806691 0.0465743i −0.459123 0.888373i \(-0.651836\pi\)
0.539792 + 0.841798i \(0.318503\pi\)
\(978\) 11.1682 13.3097i 0.357120 0.425599i
\(979\) 19.2281 + 16.1343i 0.614533 + 0.515655i
\(980\) 0 0
\(981\) −9.75929 + 16.9036i −0.311590 + 0.539690i
\(982\) 8.33289 + 22.8944i 0.265913 + 0.730591i
\(983\) −40.6242 + 7.16313i −1.29571 + 0.228469i −0.778638 0.627474i \(-0.784089\pi\)
−0.517072 + 0.855942i \(0.672978\pi\)
\(984\) −4.53323 + 25.7092i −0.144514 + 0.819580i
\(985\) 0 0
\(986\) −0.129467 + 0.108636i −0.00412308 + 0.00345968i
\(987\) 0.571978i 0.0182062i
\(988\) 1.46889 18.7958i 0.0467315 0.597975i
\(989\) −24.4909 −0.778764
\(990\) 0 0
\(991\) 27.2089 + 9.90324i 0.864320 + 0.314587i 0.735865 0.677129i \(-0.236776\pi\)
0.128455 + 0.991715i \(0.458998\pi\)
\(992\) 0.341442 + 0.0602055i 0.0108408 + 0.00191153i
\(993\) −8.04294 + 1.41819i −0.255235 + 0.0450048i
\(994\) −34.5520 + 12.5759i −1.09592 + 0.398883i
\(995\) 0 0
\(996\) 13.4915 + 23.3679i 0.427494 + 0.740442i
\(997\) 0.422618 0.503657i 0.0133844 0.0159510i −0.759311 0.650728i \(-0.774464\pi\)
0.772695 + 0.634777i \(0.218908\pi\)
\(998\) 1.04434 1.24460i 0.0330580 0.0393970i
\(999\) 4.60918 + 7.98334i 0.145828 + 0.252582i
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 950.2.u.g.899.4 36
5.2 odd 4 190.2.k.d.101.3 18
5.3 odd 4 950.2.l.i.101.1 18
5.4 even 2 inner 950.2.u.g.899.3 36
19.16 even 9 inner 950.2.u.g.149.3 36
95.42 odd 36 3610.2.a.bi.1.2 9
95.54 even 18 inner 950.2.u.g.149.4 36
95.72 even 36 3610.2.a.bj.1.8 9
95.73 odd 36 950.2.l.i.301.1 18
95.92 odd 36 190.2.k.d.111.3 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.k.d.101.3 18 5.2 odd 4
190.2.k.d.111.3 yes 18 95.92 odd 36
950.2.l.i.101.1 18 5.3 odd 4
950.2.l.i.301.1 18 95.73 odd 36
950.2.u.g.149.3 36 19.16 even 9 inner
950.2.u.g.149.4 36 95.54 even 18 inner
950.2.u.g.899.3 36 5.4 even 2 inner
950.2.u.g.899.4 36 1.1 even 1 trivial
3610.2.a.bi.1.2 9 95.42 odd 36
3610.2.a.bj.1.8 9 95.72 even 36