Properties

Label 1040.2.da.f.881.1
Level $1040$
Weight $2$
Character 1040.881
Analytic conductor $8.304$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1040,2,Mod(641,1040)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("1040.641");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.da (of order \(6\), degree \(2\), 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: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 520)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.1
Root \(1.97402i\) of defining polynomial
Character \(\chi\) \(=\) 1040.881
Dual form 1040.2.da.f.641.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.43538 - 2.48615i) q^{3} -1.00000i q^{5} +(-0.0113994 - 0.00658143i) q^{7} +(-2.62062 + 4.53905i) q^{9} +O(q^{10})\) \(q+(-1.43538 - 2.48615i) q^{3} -1.00000i q^{5} +(-0.0113994 - 0.00658143i) q^{7} +(-2.62062 + 4.53905i) q^{9} +(-0.541191 + 0.312457i) q^{11} +(1.97232 + 3.01827i) q^{13} +(-2.48615 + 1.43538i) q^{15} +(-3.78024 + 6.54756i) q^{17} +(-6.29517 - 3.63452i) q^{19} +0.0377874i q^{21} +(1.22985 + 2.13017i) q^{23} -1.00000 q^{25} +6.43407 q^{27} +(-1.15977 - 2.00878i) q^{29} +8.02362i q^{31} +(1.55363 + 0.896987i) q^{33} +(-0.00658143 + 0.0113994i) q^{35} +(-3.65201 + 2.10849i) q^{37} +(4.67284 - 9.23584i) q^{39} +(3.29811 - 1.90416i) q^{41} +(-1.39758 + 2.42068i) q^{43} +(4.53905 + 2.62062i) q^{45} +4.00926i q^{47} +(-3.49991 - 6.06203i) q^{49} +21.7043 q^{51} +6.25234 q^{53} +(0.312457 + 0.541191i) q^{55} +20.8676i q^{57} +(11.6836 + 6.74554i) q^{59} +(3.28736 - 5.69387i) q^{61} +(0.0597469 - 0.0344949i) q^{63} +(3.01827 - 1.97232i) q^{65} +(-5.81605 + 3.35790i) q^{67} +(3.53061 - 6.11520i) q^{69} +(-13.2257 - 7.63585i) q^{71} +2.98937i q^{73} +(1.43538 + 2.48615i) q^{75} +0.00822564 q^{77} -2.02435 q^{79} +(-1.37345 - 2.37889i) q^{81} -2.35696i q^{83} +(6.54756 + 3.78024i) q^{85} +(-3.32941 + 5.76671i) q^{87} +(4.50245 - 2.59949i) q^{89} +(-0.00261866 - 0.0473870i) q^{91} +(19.9479 - 11.5169i) q^{93} +(-3.63452 + 6.29517i) q^{95} +(7.02150 + 4.05387i) q^{97} -3.27532i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.43538 2.48615i −0.828716 1.43538i −0.899046 0.437855i \(-0.855738\pi\)
0.0703297 0.997524i \(-0.477595\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −0.0113994 0.00658143i −0.00430856 0.00248755i 0.497844 0.867266i \(-0.334125\pi\)
−0.502153 + 0.864779i \(0.667458\pi\)
\(8\) 0 0
\(9\) −2.62062 + 4.53905i −0.873541 + 1.51302i
\(10\) 0 0
\(11\) −0.541191 + 0.312457i −0.163175 + 0.0942092i −0.579364 0.815069i \(-0.696699\pi\)
0.416189 + 0.909278i \(0.363366\pi\)
\(12\) 0 0
\(13\) 1.97232 + 3.01827i 0.547023 + 0.837118i
\(14\) 0 0
\(15\) −2.48615 + 1.43538i −0.641921 + 0.370613i
\(16\) 0 0
\(17\) −3.78024 + 6.54756i −0.916842 + 1.58802i −0.112661 + 0.993633i \(0.535937\pi\)
−0.804181 + 0.594384i \(0.797396\pi\)
\(18\) 0 0
\(19\) −6.29517 3.63452i −1.44421 0.833815i −0.446084 0.894991i \(-0.647182\pi\)
−0.998127 + 0.0611757i \(0.980515\pi\)
\(20\) 0 0
\(21\) 0.0377874i 0.00824588i
\(22\) 0 0
\(23\) 1.22985 + 2.13017i 0.256442 + 0.444171i 0.965286 0.261194i \(-0.0841163\pi\)
−0.708844 + 0.705365i \(0.750783\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 6.43407 1.23824
\(28\) 0 0
\(29\) −1.15977 2.00878i −0.215364 0.373021i 0.738021 0.674777i \(-0.235760\pi\)
−0.953385 + 0.301757i \(0.902427\pi\)
\(30\) 0 0
\(31\) 8.02362i 1.44109i 0.693411 + 0.720543i \(0.256107\pi\)
−0.693411 + 0.720543i \(0.743893\pi\)
\(32\) 0 0
\(33\) 1.55363 + 0.896987i 0.270452 + 0.156145i
\(34\) 0 0
\(35\) −0.00658143 + 0.0113994i −0.00111246 + 0.00192684i
\(36\) 0 0
\(37\) −3.65201 + 2.10849i −0.600387 + 0.346634i −0.769194 0.639016i \(-0.779342\pi\)
0.168807 + 0.985649i \(0.446009\pi\)
\(38\) 0 0
\(39\) 4.67284 9.23584i 0.748254 1.47892i
\(40\) 0 0
\(41\) 3.29811 1.90416i 0.515078 0.297380i −0.219840 0.975536i \(-0.570554\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(42\) 0 0
\(43\) −1.39758 + 2.42068i −0.213129 + 0.369151i −0.952692 0.303937i \(-0.901699\pi\)
0.739563 + 0.673087i \(0.235032\pi\)
\(44\) 0 0
\(45\) 4.53905 + 2.62062i 0.676642 + 0.390659i
\(46\) 0 0
\(47\) 4.00926i 0.584810i 0.956295 + 0.292405i \(0.0944556\pi\)
−0.956295 + 0.292405i \(0.905544\pi\)
\(48\) 0 0
\(49\) −3.49991 6.06203i −0.499988 0.866004i
\(50\) 0 0
\(51\) 21.7043 3.03921
\(52\) 0 0
\(53\) 6.25234 0.858824 0.429412 0.903109i \(-0.358721\pi\)
0.429412 + 0.903109i \(0.358721\pi\)
\(54\) 0 0
\(55\) 0.312457 + 0.541191i 0.0421316 + 0.0729741i
\(56\) 0 0
\(57\) 20.8676i 2.76399i
\(58\) 0 0
\(59\) 11.6836 + 6.74554i 1.52108 + 0.878195i 0.999691 + 0.0248747i \(0.00791868\pi\)
0.521387 + 0.853320i \(0.325415\pi\)
\(60\) 0 0
\(61\) 3.28736 5.69387i 0.420903 0.729025i −0.575125 0.818065i \(-0.695047\pi\)
0.996028 + 0.0890404i \(0.0283800\pi\)
\(62\) 0 0
\(63\) 0.0597469 0.0344949i 0.00752740 0.00434594i
\(64\) 0 0
\(65\) 3.01827 1.97232i 0.374370 0.244636i
\(66\) 0 0
\(67\) −5.81605 + 3.35790i −0.710544 + 0.410233i −0.811262 0.584682i \(-0.801219\pi\)
0.100718 + 0.994915i \(0.467886\pi\)
\(68\) 0 0
\(69\) 3.53061 6.11520i 0.425036 0.736183i
\(70\) 0 0
\(71\) −13.2257 7.63585i −1.56960 0.906209i −0.996215 0.0869220i \(-0.972297\pi\)
−0.573384 0.819287i \(-0.694370\pi\)
\(72\) 0 0
\(73\) 2.98937i 0.349879i 0.984579 + 0.174940i \(0.0559730\pi\)
−0.984579 + 0.174940i \(0.944027\pi\)
\(74\) 0 0
\(75\) 1.43538 + 2.48615i 0.165743 + 0.287076i
\(76\) 0 0
\(77\) 0.00822564 0.000937399
\(78\) 0 0
\(79\) −2.02435 −0.227758 −0.113879 0.993495i \(-0.536328\pi\)
−0.113879 + 0.993495i \(0.536328\pi\)
\(80\) 0 0
\(81\) −1.37345 2.37889i −0.152606 0.264321i
\(82\) 0 0
\(83\) 2.35696i 0.258710i −0.991598 0.129355i \(-0.958709\pi\)
0.991598 0.129355i \(-0.0412907\pi\)
\(84\) 0 0
\(85\) 6.54756 + 3.78024i 0.710183 + 0.410024i
\(86\) 0 0
\(87\) −3.32941 + 5.76671i −0.356951 + 0.618257i
\(88\) 0 0
\(89\) 4.50245 2.59949i 0.477259 0.275545i −0.242015 0.970273i \(-0.577808\pi\)
0.719273 + 0.694727i \(0.244475\pi\)
\(90\) 0 0
\(91\) −0.00261866 0.0473870i −0.000274510 0.00496751i
\(92\) 0 0
\(93\) 19.9479 11.5169i 2.06850 1.19425i
\(94\) 0 0
\(95\) −3.63452 + 6.29517i −0.372894 + 0.645871i
\(96\) 0 0
\(97\) 7.02150 + 4.05387i 0.712925 + 0.411608i 0.812143 0.583458i \(-0.198301\pi\)
−0.0992179 + 0.995066i \(0.531634\pi\)
\(98\) 0 0
\(99\) 3.27532i 0.329182i
\(100\) 0 0
\(101\) −5.68537 9.84736i −0.565716 0.979848i −0.996983 0.0776241i \(-0.975267\pi\)
0.431267 0.902224i \(-0.358067\pi\)
\(102\) 0 0
\(103\) −13.9614 −1.37566 −0.687829 0.725873i \(-0.741436\pi\)
−0.687829 + 0.725873i \(0.741436\pi\)
\(104\) 0 0
\(105\) 0.0377874 0.00368767
\(106\) 0 0
\(107\) 7.33282 + 12.7008i 0.708891 + 1.22783i 0.965269 + 0.261258i \(0.0841374\pi\)
−0.256378 + 0.966576i \(0.582529\pi\)
\(108\) 0 0
\(109\) 6.16019i 0.590039i 0.955491 + 0.295020i \(0.0953262\pi\)
−0.955491 + 0.295020i \(0.904674\pi\)
\(110\) 0 0
\(111\) 10.4840 + 6.05296i 0.995101 + 0.574522i
\(112\) 0 0
\(113\) −3.38917 + 5.87021i −0.318826 + 0.552223i −0.980243 0.197795i \(-0.936622\pi\)
0.661417 + 0.750018i \(0.269955\pi\)
\(114\) 0 0
\(115\) 2.13017 1.22985i 0.198639 0.114684i
\(116\) 0 0
\(117\) −18.8688 + 1.04271i −1.74442 + 0.0963984i
\(118\) 0 0
\(119\) 0.0861846 0.0497587i 0.00790053 0.00456137i
\(120\) 0 0
\(121\) −5.30474 + 9.18808i −0.482249 + 0.835280i
\(122\) 0 0
\(123\) −9.46807 5.46639i −0.853707 0.492888i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 1.52888 + 2.64810i 0.135666 + 0.234981i 0.925852 0.377887i \(-0.123349\pi\)
−0.790185 + 0.612868i \(0.790016\pi\)
\(128\) 0 0
\(129\) 8.02424 0.706495
\(130\) 0 0
\(131\) 15.5729 1.36061 0.680307 0.732927i \(-0.261846\pi\)
0.680307 + 0.732927i \(0.261846\pi\)
\(132\) 0 0
\(133\) 0.0478406 + 0.0828624i 0.00414831 + 0.00718508i
\(134\) 0 0
\(135\) 6.43407i 0.553756i
\(136\) 0 0
\(137\) −15.4959 8.94656i −1.32390 0.764356i −0.339555 0.940586i \(-0.610276\pi\)
−0.984349 + 0.176230i \(0.943610\pi\)
\(138\) 0 0
\(139\) −10.4203 + 18.0485i −0.883841 + 1.53086i −0.0368049 + 0.999322i \(0.511718\pi\)
−0.847036 + 0.531535i \(0.821615\pi\)
\(140\) 0 0
\(141\) 9.96761 5.75480i 0.839424 0.484642i
\(142\) 0 0
\(143\) −2.01048 1.01720i −0.168125 0.0850622i
\(144\) 0 0
\(145\) −2.00878 + 1.15977i −0.166820 + 0.0963135i
\(146\) 0 0
\(147\) −10.0474 + 17.4026i −0.828696 + 1.43534i
\(148\) 0 0
\(149\) −14.1504 8.16975i −1.15925 0.669292i −0.208125 0.978102i \(-0.566736\pi\)
−0.951124 + 0.308810i \(0.900069\pi\)
\(150\) 0 0
\(151\) 6.34453i 0.516311i −0.966103 0.258155i \(-0.916885\pi\)
0.966103 0.258155i \(-0.0831147\pi\)
\(152\) 0 0
\(153\) −19.8132 34.3174i −1.60180 2.77440i
\(154\) 0 0
\(155\) 8.02362 0.644473
\(156\) 0 0
\(157\) −0.454894 −0.0363045 −0.0181523 0.999835i \(-0.505778\pi\)
−0.0181523 + 0.999835i \(0.505778\pi\)
\(158\) 0 0
\(159\) −8.97447 15.5442i −0.711722 1.23274i
\(160\) 0 0
\(161\) 0.0323768i 0.00255165i
\(162\) 0 0
\(163\) −8.27406 4.77703i −0.648074 0.374166i 0.139644 0.990202i \(-0.455404\pi\)
−0.787718 + 0.616036i \(0.788738\pi\)
\(164\) 0 0
\(165\) 0.896987 1.55363i 0.0698303 0.120950i
\(166\) 0 0
\(167\) −8.71320 + 5.03057i −0.674248 + 0.389277i −0.797684 0.603075i \(-0.793942\pi\)
0.123436 + 0.992352i \(0.460609\pi\)
\(168\) 0 0
\(169\) −5.21992 + 11.9060i −0.401532 + 0.915845i
\(170\) 0 0
\(171\) 32.9945 19.0494i 2.52315 1.45674i
\(172\) 0 0
\(173\) 2.81853 4.88184i 0.214289 0.371159i −0.738763 0.673965i \(-0.764590\pi\)
0.953052 + 0.302805i \(0.0979232\pi\)
\(174\) 0 0
\(175\) 0.0113994 + 0.00658143i 0.000861711 + 0.000497509i
\(176\) 0 0
\(177\) 38.7296i 2.91110i
\(178\) 0 0
\(179\) 2.05404 + 3.55770i 0.153526 + 0.265915i 0.932521 0.361115i \(-0.117604\pi\)
−0.778995 + 0.627030i \(0.784270\pi\)
\(180\) 0 0
\(181\) −26.2588 −1.95180 −0.975899 0.218222i \(-0.929974\pi\)
−0.975899 + 0.218222i \(0.929974\pi\)
\(182\) 0 0
\(183\) −18.8744 −1.39524
\(184\) 0 0
\(185\) 2.10849 + 3.65201i 0.155019 + 0.268501i
\(186\) 0 0
\(187\) 4.72464i 0.345500i
\(188\) 0 0
\(189\) −0.0733443 0.0423453i −0.00533501 0.00308017i
\(190\) 0 0
\(191\) 7.89188 13.6691i 0.571037 0.989064i −0.425423 0.904995i \(-0.639875\pi\)
0.996460 0.0840699i \(-0.0267919\pi\)
\(192\) 0 0
\(193\) 0.684803 0.395371i 0.0492932 0.0284594i −0.475151 0.879904i \(-0.657607\pi\)
0.524444 + 0.851445i \(0.324273\pi\)
\(194\) 0 0
\(195\) −9.23584 4.67284i −0.661392 0.334629i
\(196\) 0 0
\(197\) 2.71134 1.56539i 0.193175 0.111530i −0.400293 0.916387i \(-0.631092\pi\)
0.593468 + 0.804858i \(0.297758\pi\)
\(198\) 0 0
\(199\) −3.01204 + 5.21701i −0.213518 + 0.369824i −0.952813 0.303557i \(-0.901826\pi\)
0.739295 + 0.673382i \(0.235159\pi\)
\(200\) 0 0
\(201\) 16.6965 + 9.63971i 1.17768 + 0.679933i
\(202\) 0 0
\(203\) 0.0305317i 0.00214291i
\(204\) 0 0
\(205\) −1.90416 3.29811i −0.132993 0.230350i
\(206\) 0 0
\(207\) −12.8919 −0.896051
\(208\) 0 0
\(209\) 4.54252 0.314212
\(210\) 0 0
\(211\) −12.5479 21.7335i −0.863830 1.49620i −0.868204 0.496207i \(-0.834726\pi\)
0.00437417 0.999990i \(-0.498608\pi\)
\(212\) 0 0
\(213\) 43.8413i 3.00396i
\(214\) 0 0
\(215\) 2.42068 + 1.39758i 0.165089 + 0.0953144i
\(216\) 0 0
\(217\) 0.0528069 0.0914642i 0.00358477 0.00620900i
\(218\) 0 0
\(219\) 7.43201 4.29088i 0.502209 0.289950i
\(220\) 0 0
\(221\) −27.2182 + 1.50410i −1.83089 + 0.101177i
\(222\) 0 0
\(223\) 0.211215 0.121945i 0.0141440 0.00816606i −0.492911 0.870080i \(-0.664067\pi\)
0.507055 + 0.861913i \(0.330734\pi\)
\(224\) 0 0
\(225\) 2.62062 4.53905i 0.174708 0.302603i
\(226\) 0 0
\(227\) −7.79411 4.49993i −0.517313 0.298671i 0.218521 0.975832i \(-0.429877\pi\)
−0.735835 + 0.677161i \(0.763210\pi\)
\(228\) 0 0
\(229\) 23.1995i 1.53306i −0.642206 0.766532i \(-0.721981\pi\)
0.642206 0.766532i \(-0.278019\pi\)
\(230\) 0 0
\(231\) −0.0118069 0.0204502i −0.000776837 0.00134552i
\(232\) 0 0
\(233\) 3.05984 0.200457 0.100228 0.994964i \(-0.468043\pi\)
0.100228 + 0.994964i \(0.468043\pi\)
\(234\) 0 0
\(235\) 4.00926 0.261535
\(236\) 0 0
\(237\) 2.90572 + 5.03285i 0.188746 + 0.326918i
\(238\) 0 0
\(239\) 14.5625i 0.941967i 0.882142 + 0.470983i \(0.156101\pi\)
−0.882142 + 0.470983i \(0.843899\pi\)
\(240\) 0 0
\(241\) 18.7917 + 10.8494i 1.21048 + 0.698872i 0.962864 0.269986i \(-0.0870191\pi\)
0.247617 + 0.968858i \(0.420352\pi\)
\(242\) 0 0
\(243\) 5.70825 9.88698i 0.366184 0.634250i
\(244\) 0 0
\(245\) −6.06203 + 3.49991i −0.387289 + 0.223601i
\(246\) 0 0
\(247\) −1.44612 26.1690i −0.0920146 1.66509i
\(248\) 0 0
\(249\) −5.85976 + 3.38313i −0.371347 + 0.214397i
\(250\) 0 0
\(251\) −6.66885 + 11.5508i −0.420934 + 0.729079i −0.996031 0.0890063i \(-0.971631\pi\)
0.575097 + 0.818085i \(0.304964\pi\)
\(252\) 0 0
\(253\) −1.33117 0.768552i −0.0836900 0.0483184i
\(254\) 0 0
\(255\) 21.7043i 1.35918i
\(256\) 0 0
\(257\) 10.6087 + 18.3747i 0.661750 + 1.14619i 0.980155 + 0.198230i \(0.0635194\pi\)
−0.318405 + 0.947955i \(0.603147\pi\)
\(258\) 0 0
\(259\) 0.0555075 0.00344907
\(260\) 0 0
\(261\) 12.1573 0.752516
\(262\) 0 0
\(263\) 5.15581 + 8.93013i 0.317921 + 0.550656i 0.980054 0.198731i \(-0.0636820\pi\)
−0.662133 + 0.749386i \(0.730349\pi\)
\(264\) 0 0
\(265\) 6.25234i 0.384078i
\(266\) 0 0
\(267\) −12.9254 7.46251i −0.791024 0.456698i
\(268\) 0 0
\(269\) −13.7790 + 23.8659i −0.840119 + 1.45513i 0.0496753 + 0.998765i \(0.484181\pi\)
−0.889794 + 0.456363i \(0.849152\pi\)
\(270\) 0 0
\(271\) −9.57787 + 5.52978i −0.581814 + 0.335910i −0.761854 0.647749i \(-0.775711\pi\)
0.180040 + 0.983659i \(0.442377\pi\)
\(272\) 0 0
\(273\) −0.114052 + 0.0745287i −0.00690277 + 0.00451068i
\(274\) 0 0
\(275\) 0.541191 0.312457i 0.0326350 0.0188418i
\(276\) 0 0
\(277\) −11.9360 + 20.6738i −0.717165 + 1.24217i 0.244953 + 0.969535i \(0.421227\pi\)
−0.962118 + 0.272632i \(0.912106\pi\)
\(278\) 0 0
\(279\) −36.4196 21.0269i −2.18039 1.25885i
\(280\) 0 0
\(281\) 2.59106i 0.154570i −0.997009 0.0772848i \(-0.975375\pi\)
0.997009 0.0772848i \(-0.0246251\pi\)
\(282\) 0 0
\(283\) 7.56534 + 13.1036i 0.449713 + 0.778925i 0.998367 0.0571240i \(-0.0181930\pi\)
−0.548654 + 0.836049i \(0.684860\pi\)
\(284\) 0 0
\(285\) 20.8676 1.23609
\(286\) 0 0
\(287\) −0.0501285 −0.00295899
\(288\) 0 0
\(289\) −20.0804 34.7803i −1.18120 2.04590i
\(290\) 0 0
\(291\) 23.2753i 1.36442i
\(292\) 0 0
\(293\) 27.7087 + 15.9976i 1.61876 + 0.934590i 0.987242 + 0.159226i \(0.0508997\pi\)
0.631514 + 0.775364i \(0.282434\pi\)
\(294\) 0 0
\(295\) 6.74554 11.6836i 0.392741 0.680247i
\(296\) 0 0
\(297\) −3.48206 + 2.01037i −0.202049 + 0.116653i
\(298\) 0 0
\(299\) −4.00376 + 7.91341i −0.231544 + 0.457644i
\(300\) 0 0
\(301\) 0.0318631 0.0183962i 0.00183656 0.00106034i
\(302\) 0 0
\(303\) −16.3213 + 28.2694i −0.937636 + 1.62403i
\(304\) 0 0
\(305\) −5.69387 3.28736i −0.326030 0.188233i
\(306\) 0 0
\(307\) 19.7355i 1.12637i −0.826332 0.563183i \(-0.809577\pi\)
0.826332 0.563183i \(-0.190423\pi\)
\(308\) 0 0
\(309\) 20.0399 + 34.7101i 1.14003 + 1.97459i
\(310\) 0 0
\(311\) 24.2206 1.37342 0.686711 0.726930i \(-0.259054\pi\)
0.686711 + 0.726930i \(0.259054\pi\)
\(312\) 0 0
\(313\) 17.0003 0.960915 0.480457 0.877018i \(-0.340471\pi\)
0.480457 + 0.877018i \(0.340471\pi\)
\(314\) 0 0
\(315\) −0.0344949 0.0597469i −0.00194357 0.00336635i
\(316\) 0 0
\(317\) 29.1303i 1.63612i −0.575131 0.818061i \(-0.695049\pi\)
0.575131 0.818061i \(-0.304951\pi\)
\(318\) 0 0
\(319\) 1.25531 + 0.724755i 0.0702840 + 0.0405785i
\(320\) 0 0
\(321\) 21.0507 36.4610i 1.17494 2.03505i
\(322\) 0 0
\(323\) 47.5945 27.4787i 2.64823 1.52895i
\(324\) 0 0
\(325\) −1.97232 3.01827i −0.109405 0.167424i
\(326\) 0 0
\(327\) 15.3151 8.84220i 0.846930 0.488975i
\(328\) 0 0
\(329\) 0.0263866 0.0457030i 0.00145474 0.00251969i
\(330\) 0 0
\(331\) −1.23105 0.710748i −0.0676647 0.0390662i 0.465786 0.884897i \(-0.345772\pi\)
−0.533451 + 0.845831i \(0.679105\pi\)
\(332\) 0 0
\(333\) 22.1022i 1.21119i
\(334\) 0 0
\(335\) 3.35790 + 5.81605i 0.183462 + 0.317765i
\(336\) 0 0
\(337\) −20.5875 −1.12147 −0.560735 0.827995i \(-0.689481\pi\)
−0.560735 + 0.827995i \(0.689481\pi\)
\(338\) 0 0
\(339\) 19.4590 1.05687
\(340\) 0 0
\(341\) −2.50703 4.34231i −0.135763 0.235149i
\(342\) 0 0
\(343\) 0.184278i 0.00995006i
\(344\) 0 0
\(345\) −6.11520 3.53061i −0.329231 0.190082i
\(346\) 0 0
\(347\) 2.06238 3.57214i 0.110714 0.191763i −0.805344 0.592807i \(-0.798020\pi\)
0.916058 + 0.401045i \(0.131353\pi\)
\(348\) 0 0
\(349\) −8.23537 + 4.75470i −0.440829 + 0.254513i −0.703949 0.710250i \(-0.748582\pi\)
0.263120 + 0.964763i \(0.415249\pi\)
\(350\) 0 0
\(351\) 12.6900 + 19.4198i 0.677344 + 1.03655i
\(352\) 0 0
\(353\) −17.8996 + 10.3343i −0.952700 + 0.550041i −0.893918 0.448230i \(-0.852055\pi\)
−0.0587811 + 0.998271i \(0.518721\pi\)
\(354\) 0 0
\(355\) −7.63585 + 13.2257i −0.405269 + 0.701946i
\(356\) 0 0
\(357\) −0.247415 0.142845i −0.0130946 0.00756017i
\(358\) 0 0
\(359\) 4.18621i 0.220939i 0.993879 + 0.110470i \(0.0352355\pi\)
−0.993879 + 0.110470i \(0.964764\pi\)
\(360\) 0 0
\(361\) 16.9194 + 29.3053i 0.890497 + 1.54239i
\(362\) 0 0
\(363\) 30.4572 1.59859
\(364\) 0 0
\(365\) 2.98937 0.156471
\(366\) 0 0
\(367\) 4.18853 + 7.25476i 0.218640 + 0.378695i 0.954392 0.298555i \(-0.0965047\pi\)
−0.735753 + 0.677250i \(0.763171\pi\)
\(368\) 0 0
\(369\) 19.9604i 1.03910i
\(370\) 0 0
\(371\) −0.0712727 0.0411493i −0.00370029 0.00213636i
\(372\) 0 0
\(373\) −16.8805 + 29.2379i −0.874040 + 1.51388i −0.0162579 + 0.999868i \(0.505175\pi\)
−0.857782 + 0.514014i \(0.828158\pi\)
\(374\) 0 0
\(375\) 2.48615 1.43538i 0.128384 0.0741226i
\(376\) 0 0
\(377\) 3.77560 7.46245i 0.194453 0.384336i
\(378\) 0 0
\(379\) 2.75279 1.58932i 0.141401 0.0816380i −0.427630 0.903954i \(-0.640652\pi\)
0.569032 + 0.822316i \(0.307318\pi\)
\(380\) 0 0
\(381\) 4.38905 7.60206i 0.224858 0.389465i
\(382\) 0 0
\(383\) 21.2084 + 12.2447i 1.08370 + 0.625675i 0.931892 0.362735i \(-0.118157\pi\)
0.151809 + 0.988410i \(0.451490\pi\)
\(384\) 0 0
\(385\) 0.00822564i 0.000419217i
\(386\) 0 0
\(387\) −7.32507 12.6874i −0.372354 0.644937i
\(388\) 0 0
\(389\) −10.9858 −0.557005 −0.278502 0.960436i \(-0.589838\pi\)
−0.278502 + 0.960436i \(0.589838\pi\)
\(390\) 0 0
\(391\) −18.5966 −0.940469
\(392\) 0 0
\(393\) −22.3531 38.7166i −1.12756 1.95300i
\(394\) 0 0
\(395\) 2.02435i 0.101856i
\(396\) 0 0
\(397\) −24.6162 14.2122i −1.23545 0.713289i −0.267291 0.963616i \(-0.586128\pi\)
−0.968161 + 0.250327i \(0.919462\pi\)
\(398\) 0 0
\(399\) 0.137339 0.237878i 0.00687554 0.0119088i
\(400\) 0 0
\(401\) 17.2287 9.94697i 0.860358 0.496728i −0.00377395 0.999993i \(-0.501201\pi\)
0.864132 + 0.503265i \(0.167868\pi\)
\(402\) 0 0
\(403\) −24.2175 + 15.8251i −1.20636 + 0.788307i
\(404\) 0 0
\(405\) −2.37889 + 1.37345i −0.118208 + 0.0682475i
\(406\) 0 0
\(407\) 1.31762 2.28219i 0.0653122 0.113124i
\(408\) 0 0
\(409\) 20.6919 + 11.9464i 1.02315 + 0.590714i 0.915014 0.403423i \(-0.132180\pi\)
0.108133 + 0.994136i \(0.465513\pi\)
\(410\) 0 0
\(411\) 51.3668i 2.53374i
\(412\) 0 0
\(413\) −0.0887906 0.153790i −0.00436910 0.00756750i
\(414\) 0 0
\(415\) −2.35696 −0.115699
\(416\) 0 0
\(417\) 59.8285 2.92981
\(418\) 0 0
\(419\) 5.67470 + 9.82886i 0.277227 + 0.480171i 0.970695 0.240317i \(-0.0772512\pi\)
−0.693467 + 0.720488i \(0.743918\pi\)
\(420\) 0 0
\(421\) 23.8328i 1.16154i −0.814068 0.580769i \(-0.802752\pi\)
0.814068 0.580769i \(-0.197248\pi\)
\(422\) 0 0
\(423\) −18.1982 10.5067i −0.884828 0.510855i
\(424\) 0 0
\(425\) 3.78024 6.54756i 0.183368 0.317604i
\(426\) 0 0
\(427\) −0.0749475 + 0.0432710i −0.00362697 + 0.00209403i
\(428\) 0 0
\(429\) 0.356898 + 6.45841i 0.0172312 + 0.311815i
\(430\) 0 0
\(431\) −1.44588 + 0.834781i −0.0696457 + 0.0402100i −0.534418 0.845220i \(-0.679469\pi\)
0.464773 + 0.885430i \(0.346136\pi\)
\(432\) 0 0
\(433\) −13.5317 + 23.4376i −0.650292 + 1.12634i 0.332760 + 0.943012i \(0.392020\pi\)
−0.983052 + 0.183328i \(0.941313\pi\)
\(434\) 0 0
\(435\) 5.76671 + 3.32941i 0.276493 + 0.159633i
\(436\) 0 0
\(437\) 17.8797i 0.855302i
\(438\) 0 0
\(439\) 2.17711 + 3.77087i 0.103908 + 0.179974i 0.913291 0.407307i \(-0.133532\pi\)
−0.809384 + 0.587280i \(0.800199\pi\)
\(440\) 0 0
\(441\) 36.6878 1.74704
\(442\) 0 0
\(443\) −26.7538 −1.27111 −0.635556 0.772055i \(-0.719229\pi\)
−0.635556 + 0.772055i \(0.719229\pi\)
\(444\) 0 0
\(445\) −2.59949 4.50245i −0.123228 0.213437i
\(446\) 0 0
\(447\) 46.9067i 2.21861i
\(448\) 0 0
\(449\) −6.11442 3.53016i −0.288557 0.166599i 0.348734 0.937222i \(-0.386612\pi\)
−0.637291 + 0.770623i \(0.719945\pi\)
\(450\) 0 0
\(451\) −1.18994 + 2.06103i −0.0560319 + 0.0970502i
\(452\) 0 0
\(453\) −15.7735 + 9.10681i −0.741102 + 0.427875i
\(454\) 0 0
\(455\) −0.0473870 + 0.00261866i −0.00222154 + 0.000122764i
\(456\) 0 0
\(457\) −24.8408 + 14.3419i −1.16200 + 0.670884i −0.951784 0.306770i \(-0.900752\pi\)
−0.210221 + 0.977654i \(0.567418\pi\)
\(458\) 0 0
\(459\) −24.3223 + 42.1275i −1.13527 + 1.96634i
\(460\) 0 0
\(461\) 11.3018 + 6.52508i 0.526376 + 0.303903i 0.739539 0.673113i \(-0.235043\pi\)
−0.213163 + 0.977017i \(0.568377\pi\)
\(462\) 0 0
\(463\) 30.1313i 1.40032i −0.713985 0.700161i \(-0.753112\pi\)
0.713985 0.700161i \(-0.246888\pi\)
\(464\) 0 0
\(465\) −11.5169 19.9479i −0.534085 0.925063i
\(466\) 0 0
\(467\) 21.4253 0.991446 0.495723 0.868481i \(-0.334903\pi\)
0.495723 + 0.868481i \(0.334903\pi\)
\(468\) 0 0
\(469\) 0.0883991 0.00408189
\(470\) 0 0
\(471\) 0.652946 + 1.13093i 0.0300861 + 0.0521107i
\(472\) 0 0
\(473\) 1.74674i 0.0803150i
\(474\) 0 0
\(475\) 6.29517 + 3.63452i 0.288842 + 0.166763i
\(476\) 0 0
\(477\) −16.3850 + 28.3797i −0.750218 + 1.29942i
\(478\) 0 0
\(479\) 24.6440 14.2282i 1.12602 0.650105i 0.183085 0.983097i \(-0.441392\pi\)
0.942930 + 0.332992i \(0.108058\pi\)
\(480\) 0 0
\(481\) −13.5669 6.86415i −0.618599 0.312978i
\(482\) 0 0
\(483\) −0.0804935 + 0.0464729i −0.00366258 + 0.00211459i
\(484\) 0 0
\(485\) 4.05387 7.02150i 0.184077 0.318830i
\(486\) 0 0
\(487\) −19.2632 11.1216i −0.872901 0.503969i −0.00458955 0.999989i \(-0.501461\pi\)
−0.868311 + 0.496020i \(0.834794\pi\)
\(488\) 0 0
\(489\) 27.4274i 1.24031i
\(490\) 0 0
\(491\) −18.4112 31.8892i −0.830887 1.43914i −0.897336 0.441349i \(-0.854500\pi\)
0.0664487 0.997790i \(-0.478833\pi\)
\(492\) 0 0
\(493\) 17.5368 0.789818
\(494\) 0 0
\(495\) −3.27532 −0.147215
\(496\) 0 0
\(497\) 0.100510 + 0.174088i 0.00450847 + 0.00780890i
\(498\) 0 0
\(499\) 19.2718i 0.862725i 0.902179 + 0.431362i \(0.141967\pi\)
−0.902179 + 0.431362i \(0.858033\pi\)
\(500\) 0 0
\(501\) 25.0135 + 14.4415i 1.11752 + 0.645201i
\(502\) 0 0
\(503\) 4.00312 6.93361i 0.178490 0.309155i −0.762873 0.646548i \(-0.776212\pi\)
0.941364 + 0.337394i \(0.109545\pi\)
\(504\) 0 0
\(505\) −9.84736 + 5.68537i −0.438202 + 0.252996i
\(506\) 0 0
\(507\) 37.0926 4.11211i 1.64734 0.182625i
\(508\) 0 0
\(509\) −15.3822 + 8.88090i −0.681803 + 0.393639i −0.800534 0.599287i \(-0.795451\pi\)
0.118731 + 0.992926i \(0.462117\pi\)
\(510\) 0 0
\(511\) 0.0196743 0.0340769i 0.000870340 0.00150747i
\(512\) 0 0
\(513\) −40.5035 23.3847i −1.78827 1.03246i
\(514\) 0 0
\(515\) 13.9614i 0.615213i
\(516\) 0 0
\(517\) −1.25272 2.16977i −0.0550945 0.0954265i
\(518\) 0 0
\(519\) −16.1826 −0.710339
\(520\) 0 0
\(521\) 6.32264 0.277000 0.138500 0.990362i \(-0.455772\pi\)
0.138500 + 0.990362i \(0.455772\pi\)
\(522\) 0 0
\(523\) 6.41474 + 11.1107i 0.280497 + 0.485835i 0.971507 0.237010i \(-0.0761674\pi\)
−0.691010 + 0.722845i \(0.742834\pi\)
\(524\) 0 0
\(525\) 0.0377874i 0.00164918i
\(526\) 0 0
\(527\) −52.5352 30.3312i −2.28847 1.32125i
\(528\) 0 0
\(529\) 8.47492 14.6790i 0.368475 0.638217i
\(530\) 0 0
\(531\) −61.2367 + 35.3550i −2.65745 + 1.53428i
\(532\) 0 0
\(533\) 12.2522 + 6.19897i 0.530702 + 0.268507i
\(534\) 0 0
\(535\) 12.7008 7.33282i 0.549104 0.317026i
\(536\) 0 0
\(537\) 5.89665 10.2133i 0.254459 0.440736i
\(538\) 0 0
\(539\) 3.78824 + 2.18714i 0.163171 + 0.0942069i
\(540\) 0 0
\(541\) 26.8783i 1.15559i −0.816183 0.577793i \(-0.803914\pi\)
0.816183 0.577793i \(-0.196086\pi\)
\(542\) 0 0
\(543\) 37.6913 + 65.2832i 1.61749 + 2.80157i
\(544\) 0 0
\(545\) 6.16019 0.263874
\(546\) 0 0
\(547\) −18.7581 −0.802039 −0.401020 0.916069i \(-0.631344\pi\)
−0.401020 + 0.916069i \(0.631344\pi\)
\(548\) 0 0
\(549\) 17.2298 + 29.8429i 0.735351 + 1.27367i
\(550\) 0 0
\(551\) 16.8608i 0.718294i
\(552\) 0 0
\(553\) 0.0230764 + 0.0133231i 0.000981307 + 0.000566558i
\(554\) 0 0
\(555\) 6.05296 10.4840i 0.256934 0.445023i
\(556\) 0 0
\(557\) −0.562910 + 0.324996i −0.0238513 + 0.0137705i −0.511878 0.859058i \(-0.671050\pi\)
0.488027 + 0.872829i \(0.337717\pi\)
\(558\) 0 0
\(559\) −10.0628 + 0.556078i −0.425609 + 0.0235196i
\(560\) 0 0
\(561\) −11.7462 + 6.78165i −0.495923 + 0.286321i
\(562\) 0 0
\(563\) 2.06346 3.57402i 0.0869645 0.150627i −0.819262 0.573419i \(-0.805617\pi\)
0.906227 + 0.422792i \(0.138950\pi\)
\(564\) 0 0
\(565\) 5.87021 + 3.38917i 0.246962 + 0.142583i
\(566\) 0 0
\(567\) 0.0361571i 0.00151846i
\(568\) 0 0
\(569\) 17.6625 + 30.5923i 0.740449 + 1.28250i 0.952291 + 0.305191i \(0.0987204\pi\)
−0.211842 + 0.977304i \(0.567946\pi\)
\(570\) 0 0
\(571\) −21.7114 −0.908596 −0.454298 0.890850i \(-0.650110\pi\)
−0.454298 + 0.890850i \(0.650110\pi\)
\(572\) 0 0
\(573\) −45.3114 −1.89291
\(574\) 0 0
\(575\) −1.22985 2.13017i −0.0512885 0.0888342i
\(576\) 0 0
\(577\) 27.7388i 1.15478i 0.816468 + 0.577390i \(0.195929\pi\)
−0.816468 + 0.577390i \(0.804071\pi\)
\(578\) 0 0
\(579\) −1.96590 1.13501i −0.0817002 0.0471696i
\(580\) 0 0
\(581\) −0.0155122 + 0.0268679i −0.000643554 + 0.00111467i
\(582\) 0 0
\(583\) −3.38371 + 1.95358i −0.140139 + 0.0809092i
\(584\) 0 0
\(585\) 1.04271 + 18.8688i 0.0431107 + 0.780128i
\(586\) 0 0
\(587\) 26.3980 15.2409i 1.08956 0.629058i 0.156102 0.987741i \(-0.450107\pi\)
0.933460 + 0.358683i \(0.116774\pi\)
\(588\) 0 0
\(589\) 29.1620 50.5101i 1.20160 2.08123i
\(590\) 0 0
\(591\) −7.78360 4.49386i −0.320174 0.184853i
\(592\) 0 0
\(593\) 25.3371i 1.04047i −0.854024 0.520234i \(-0.825845\pi\)
0.854024 0.520234i \(-0.174155\pi\)
\(594\) 0 0
\(595\) −0.0497587 0.0861846i −0.00203991 0.00353323i
\(596\) 0 0
\(597\) 17.2937 0.707784
\(598\) 0 0
\(599\) 13.4736 0.550517 0.275259 0.961370i \(-0.411236\pi\)
0.275259 + 0.961370i \(0.411236\pi\)
\(600\) 0 0
\(601\) −19.4499 33.6883i −0.793380 1.37417i −0.923863 0.382724i \(-0.874986\pi\)
0.130483 0.991451i \(-0.458347\pi\)
\(602\) 0 0
\(603\) 35.1991i 1.43342i
\(604\) 0 0
\(605\) 9.18808 + 5.30474i 0.373549 + 0.215668i
\(606\) 0 0
\(607\) 1.14512 1.98340i 0.0464789 0.0805039i −0.841850 0.539712i \(-0.818533\pi\)
0.888329 + 0.459208i \(0.151867\pi\)
\(608\) 0 0
\(609\) 0.0759064 0.0438246i 0.00307588 0.00177586i
\(610\) 0 0
\(611\) −12.1010 + 7.90753i −0.489555 + 0.319905i
\(612\) 0 0
\(613\) 31.1861 18.0053i 1.25960 0.727228i 0.286599 0.958051i \(-0.407475\pi\)
0.972996 + 0.230823i \(0.0741418\pi\)
\(614\) 0 0
\(615\) −5.46639 + 9.46807i −0.220426 + 0.381789i
\(616\) 0 0
\(617\) 11.2592 + 6.50050i 0.453278 + 0.261700i 0.709214 0.704994i \(-0.249050\pi\)
−0.255935 + 0.966694i \(0.582383\pi\)
\(618\) 0 0
\(619\) 24.6297i 0.989952i 0.868907 + 0.494976i \(0.164823\pi\)
−0.868907 + 0.494976i \(0.835177\pi\)
\(620\) 0 0
\(621\) 7.91296 + 13.7057i 0.317536 + 0.549989i
\(622\) 0 0
\(623\) −0.0684334 −0.00274173
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −6.52023 11.2934i −0.260393 0.451014i
\(628\) 0 0
\(629\) 31.8824i 1.27123i
\(630\) 0 0
\(631\) 28.6992 + 16.5695i 1.14250 + 0.659621i 0.947048 0.321093i \(-0.104050\pi\)
0.195449 + 0.980714i \(0.437384\pi\)
\(632\) 0 0
\(633\) −36.0218 + 62.3917i −1.43174 + 2.47985i
\(634\) 0 0
\(635\) 2.64810 1.52888i 0.105087 0.0606719i
\(636\) 0 0
\(637\) 11.3939 22.5199i 0.451443 0.892272i
\(638\) 0 0
\(639\) 69.3190 40.0214i 2.74222 1.58322i
\(640\) 0 0
\(641\) −18.9022 + 32.7395i −0.746591 + 1.29313i 0.202857 + 0.979208i \(0.434977\pi\)
−0.949448 + 0.313925i \(0.898356\pi\)
\(642\) 0 0
\(643\) 16.3067 + 9.41467i 0.643073 + 0.371278i 0.785797 0.618484i \(-0.212253\pi\)
−0.142724 + 0.989762i \(0.545586\pi\)
\(644\) 0 0
\(645\) 8.02424i 0.315954i
\(646\) 0 0
\(647\) 6.03457 + 10.4522i 0.237243 + 0.410917i 0.959922 0.280266i \(-0.0904228\pi\)
−0.722679 + 0.691184i \(0.757089\pi\)
\(648\) 0 0
\(649\) −8.43076 −0.330936
\(650\) 0 0
\(651\) −0.303191 −0.0118830
\(652\) 0 0
\(653\) 0.180156 + 0.312039i 0.00705004 + 0.0122110i 0.869529 0.493882i \(-0.164423\pi\)
−0.862479 + 0.506093i \(0.831089\pi\)
\(654\) 0 0
\(655\) 15.5729i 0.608485i
\(656\) 0 0
\(657\) −13.5689 7.83401i −0.529373 0.305634i
\(658\) 0 0
\(659\) −8.14247 + 14.1032i −0.317185 + 0.549381i −0.979900 0.199491i \(-0.936071\pi\)
0.662714 + 0.748872i \(0.269404\pi\)
\(660\) 0 0
\(661\) −12.1249 + 7.00033i −0.471605 + 0.272281i −0.716911 0.697164i \(-0.754445\pi\)
0.245306 + 0.969446i \(0.421111\pi\)
\(662\) 0 0
\(663\) 42.8078 + 65.5094i 1.66252 + 2.54417i
\(664\) 0 0
\(665\) 0.0828624 0.0478406i 0.00321327 0.00185518i
\(666\) 0 0
\(667\) 2.85269 4.94101i 0.110457 0.191317i
\(668\) 0 0
\(669\) −0.606348 0.350075i −0.0234428 0.0135347i
\(670\) 0 0
\(671\) 4.10862i 0.158612i
\(672\) 0 0
\(673\) −2.40870 4.17199i −0.0928485 0.160818i 0.815860 0.578249i \(-0.196264\pi\)
−0.908709 + 0.417431i \(0.862931\pi\)
\(674\) 0 0
\(675\) −6.43407 −0.247647
\(676\) 0 0
\(677\) 1.69491 0.0651407 0.0325703 0.999469i \(-0.489631\pi\)
0.0325703 + 0.999469i \(0.489631\pi\)
\(678\) 0 0
\(679\) −0.0533604 0.0924230i −0.00204779 0.00354687i
\(680\) 0 0
\(681\) 25.8364i 0.990054i
\(682\) 0 0
\(683\) −20.9247 12.0809i −0.800661 0.462262i 0.0430412 0.999073i \(-0.486295\pi\)
−0.843702 + 0.536811i \(0.819629\pi\)
\(684\) 0 0
\(685\) −8.94656 + 15.4959i −0.341830 + 0.592068i
\(686\) 0 0
\(687\) −57.6773 + 33.3000i −2.20053 + 1.27048i
\(688\) 0 0
\(689\) 12.3316 + 18.8712i 0.469797 + 0.718937i
\(690\) 0 0
\(691\) 3.68354 2.12669i 0.140128 0.0809032i −0.428297 0.903638i \(-0.640886\pi\)
0.568425 + 0.822735i \(0.307553\pi\)
\(692\) 0 0
\(693\) −0.0215563 + 0.0373366i −0.000818856 + 0.00141830i
\(694\) 0 0
\(695\) 18.0485 + 10.4203i 0.684620 + 0.395266i
\(696\) 0 0
\(697\) 28.7928i 1.09060i
\(698\) 0 0
\(699\) −4.39203 7.60722i −0.166122 0.287732i
\(700\) 0 0
\(701\) 49.9032 1.88482 0.942408 0.334465i \(-0.108556\pi\)
0.942408 + 0.334465i \(0.108556\pi\)
\(702\) 0 0
\(703\) 30.6534 1.15611
\(704\) 0 0
\(705\) −5.75480 9.96761i −0.216738 0.375402i
\(706\) 0 0
\(707\) 0.149671i 0.00562898i
\(708\) 0 0
\(709\) −29.5571 17.0648i −1.11004 0.640881i −0.171199 0.985236i \(-0.554764\pi\)
−0.938839 + 0.344355i \(0.888098\pi\)
\(710\) 0 0
\(711\) 5.30507 9.18865i 0.198956 0.344601i
\(712\) 0 0
\(713\) −17.0917 + 9.86789i −0.640088 + 0.369555i
\(714\) 0 0
\(715\) −1.01720 + 2.01048i −0.0380410 + 0.0751876i
\(716\) 0 0
\(717\) 36.2044 20.9026i 1.35208 0.780623i
\(718\) 0 0
\(719\) 2.72873 4.72630i 0.101765 0.176261i −0.810647 0.585535i \(-0.800885\pi\)
0.912412 + 0.409274i \(0.134218\pi\)
\(720\) 0 0
\(721\) 0.159151 + 0.0918859i 0.00592710 + 0.00342201i
\(722\) 0 0
\(723\) 62.2920i 2.31667i
\(724\) 0 0
\(725\) 1.15977 + 2.00878i 0.0430727 + 0.0746041i
\(726\) 0 0
\(727\) 35.0650 1.30049 0.650244 0.759725i \(-0.274667\pi\)
0.650244 + 0.759725i \(0.274667\pi\)
\(728\) 0 0
\(729\) −41.0147 −1.51906
\(730\) 0 0
\(731\) −10.5664 18.3015i −0.390812 0.676906i
\(732\) 0 0
\(733\) 11.5520i 0.426683i −0.976978 0.213341i \(-0.931565\pi\)
0.976978 0.213341i \(-0.0684346\pi\)
\(734\) 0 0
\(735\) 17.4026 + 10.0474i 0.641905 + 0.370604i
\(736\) 0 0
\(737\) 2.09840 3.63453i 0.0772954 0.133880i
\(738\) 0 0
\(739\) 9.81858 5.66876i 0.361182 0.208529i −0.308417 0.951251i \(-0.599799\pi\)
0.669599 + 0.742723i \(0.266466\pi\)
\(740\) 0 0
\(741\) −62.9842 + 41.1576i −2.31378 + 1.51196i
\(742\) 0 0
\(743\) −2.22973 + 1.28734i −0.0818009 + 0.0472278i −0.540343 0.841445i \(-0.681705\pi\)
0.458542 + 0.888673i \(0.348372\pi\)
\(744\) 0 0
\(745\) −8.16975 + 14.1504i −0.299317 + 0.518432i
\(746\) 0 0
\(747\) 10.6984 + 6.17671i 0.391433 + 0.225994i
\(748\) 0 0
\(749\) 0.193042i 0.00705359i
\(750\) 0 0
\(751\) −21.2324 36.7756i −0.774782 1.34196i −0.934917 0.354866i \(-0.884526\pi\)
0.160135 0.987095i \(-0.448807\pi\)
\(752\) 0 0
\(753\) 38.2893 1.39534
\(754\) 0 0
\(755\) −6.34453 −0.230901
\(756\) 0 0
\(757\) 22.8791 + 39.6278i 0.831556 + 1.44030i 0.896804 + 0.442428i \(0.145883\pi\)
−0.0652482 + 0.997869i \(0.520784\pi\)
\(758\) 0 0
\(759\) 4.41265i 0.160169i
\(760\) 0 0
\(761\) −7.27193 4.19845i −0.263607 0.152194i 0.362372 0.932034i \(-0.381967\pi\)
−0.625979 + 0.779840i \(0.715300\pi\)
\(762\) 0 0
\(763\) 0.0405428 0.0702223i 0.00146775 0.00254222i
\(764\) 0 0
\(765\) −34.3174 + 19.8132i −1.24075 + 0.716346i
\(766\) 0 0
\(767\) 2.68395 + 48.5687i 0.0969120 + 1.75371i
\(768\) 0 0
\(769\) 33.3508 19.2551i 1.20266 0.694356i 0.241514 0.970397i \(-0.422356\pi\)
0.961146 + 0.276042i \(0.0890229\pi\)
\(770\) 0 0
\(771\) 30.4549 52.7494i 1.09681 1.89972i
\(772\) 0 0
\(773\) −13.8690 8.00728i −0.498834 0.288002i 0.229398 0.973333i \(-0.426324\pi\)
−0.728232 + 0.685331i \(0.759658\pi\)
\(774\) 0 0
\(775\) 8.02362i 0.288217i
\(776\) 0 0
\(777\) −0.0796743 0.138000i −0.00285830 0.00495072i
\(778\) 0 0
\(779\) −27.6829 −0.991842
\(780\) 0 0
\(781\) 9.54348 0.341493
\(782\) 0 0
\(783\) −7.46203 12.9246i −0.266671 0.461888i
\(784\) 0 0
\(785\) 0.454894i 0.0162359i
\(786\) 0 0
\(787\) −22.9063 13.2249i −0.816520 0.471418i 0.0326948 0.999465i \(-0.489591\pi\)
−0.849215 + 0.528047i \(0.822924\pi\)
\(788\) 0 0