Properties

Label 162.3.f.a.71.6
Level $162$
Weight $3$
Character 162.71
Analytic conductor $4.414$
Analytic rank $0$
Dimension $36$
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] = [162,3,Mod(17,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.f (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: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 71.6
Character \(\chi\) \(=\) 162.71
Dual form 162.3.f.a.89.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.39273 - 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(5.37469 - 6.40531i) q^{5} +(-8.61655 - 3.13617i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})\) \(q+(1.39273 - 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(5.37469 - 6.40531i) q^{5} +(-8.61655 - 3.13617i) q^{7} +(2.44949 - 1.41421i) q^{8} +(5.91250 - 10.2407i) q^{10} +(4.22940 + 5.04040i) q^{11} +(1.04310 - 5.91570i) q^{13} +(-12.7707 - 2.25182i) q^{14} +(3.06418 - 2.57115i) q^{16} +(0.880022 + 0.508081i) q^{17} +(10.5593 + 18.2893i) q^{19} +(5.71963 - 15.7145i) q^{20} +(7.12821 + 5.98128i) q^{22} +(7.33348 + 20.1486i) q^{23} +(-7.79945 - 44.2329i) q^{25} -8.49512i q^{26} -18.3391 q^{28} +(47.7181 - 8.41399i) q^{29} +(-6.20863 + 2.25976i) q^{31} +(3.63616 - 4.33340i) q^{32} +(1.35040 + 0.491507i) q^{34} +(-66.3994 + 38.3357i) q^{35} +(-33.2994 + 57.6763i) q^{37} +(19.1977 + 22.8789i) q^{38} +(4.10678 - 23.2907i) q^{40} +(-52.2291 - 9.20941i) q^{41} +(-36.3861 + 30.5315i) q^{43} +(11.3965 + 6.57978i) q^{44} +(15.1616 + 26.2606i) q^{46} +(2.23172 - 6.13159i) q^{47} +(26.8732 + 22.5493i) q^{49} +(-21.7250 - 59.6890i) q^{50} +(-2.08619 - 11.8314i) q^{52} +39.7705i q^{53} +55.0170 q^{55} +(-25.5414 + 4.50363i) q^{56} +(64.3921 - 23.4368i) q^{58} +(18.0238 - 21.4799i) q^{59} +(38.6125 + 14.0538i) q^{61} +(-8.09199 + 4.67191i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-32.2855 - 38.4764i) q^{65} +(-2.57695 + 14.6146i) q^{67} +(2.00145 + 0.352909i) q^{68} +(-83.0620 + 69.6973i) q^{70} +(65.6502 + 37.9031i) q^{71} +(-26.5140 - 45.9236i) q^{73} +(-32.2131 + 88.5049i) q^{74} +(32.3556 + 27.1496i) q^{76} +(-20.6353 - 56.6950i) q^{77} +(-14.2149 - 80.6166i) q^{79} -33.4461i q^{80} -75.0026 q^{82} +(-46.2126 + 8.14852i) q^{83} +(7.98426 - 2.90603i) q^{85} +(-43.1781 + 51.4577i) q^{86} +(17.4881 + 6.36514i) q^{88} +(-20.2996 + 11.7200i) q^{89} +(-27.5405 + 47.7016i) q^{91} +(27.5649 + 32.8505i) q^{92} +(1.60241 - 9.08769i) q^{94} +(173.902 + 30.6635i) q^{95} +(26.8130 - 22.4988i) q^{97} +(42.9647 + 24.8057i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39273 0.245576i 0.696364 0.122788i
\(3\) 0 0
\(4\) 1.87939 0.684040i 0.469846 0.171010i
\(5\) 5.37469 6.40531i 1.07494 1.28106i 0.117297 0.993097i \(-0.462577\pi\)
0.957641 0.287964i \(-0.0929785\pi\)
\(6\) 0 0
\(7\) −8.61655 3.13617i −1.23094 0.448024i −0.357018 0.934098i \(-0.616206\pi\)
−0.873918 + 0.486074i \(0.838429\pi\)
\(8\) 2.44949 1.41421i 0.306186 0.176777i
\(9\) 0 0
\(10\) 5.91250 10.2407i 0.591250 1.02407i
\(11\) 4.22940 + 5.04040i 0.384491 + 0.458218i 0.923226 0.384257i \(-0.125542\pi\)
−0.538735 + 0.842475i \(0.681098\pi\)
\(12\) 0 0
\(13\) 1.04310 5.91570i 0.0802382 0.455053i −0.918045 0.396477i \(-0.870233\pi\)
0.998283 0.0585766i \(-0.0186562\pi\)
\(14\) −12.7707 2.25182i −0.912192 0.160844i
\(15\) 0 0
\(16\) 3.06418 2.57115i 0.191511 0.160697i
\(17\) 0.880022 + 0.508081i 0.0517660 + 0.0298871i 0.525660 0.850695i \(-0.323819\pi\)
−0.473894 + 0.880582i \(0.657152\pi\)
\(18\) 0 0
\(19\) 10.5593 + 18.2893i 0.555754 + 0.962594i 0.997844 + 0.0656235i \(0.0209036\pi\)
−0.442091 + 0.896970i \(0.645763\pi\)
\(20\) 5.71963 15.7145i 0.285981 0.785727i
\(21\) 0 0
\(22\) 7.12821 + 5.98128i 0.324009 + 0.271876i
\(23\) 7.33348 + 20.1486i 0.318847 + 0.876025i 0.990788 + 0.135421i \(0.0432386\pi\)
−0.671941 + 0.740605i \(0.734539\pi\)
\(24\) 0 0
\(25\) −7.79945 44.2329i −0.311978 1.76932i
\(26\) 8.49512i 0.326735i
\(27\) 0 0
\(28\) −18.3391 −0.654967
\(29\) 47.7181 8.41399i 1.64545 0.290138i 0.727287 0.686334i \(-0.240781\pi\)
0.918166 + 0.396196i \(0.129670\pi\)
\(30\) 0 0
\(31\) −6.20863 + 2.25976i −0.200278 + 0.0728954i −0.440212 0.897894i \(-0.645097\pi\)
0.239933 + 0.970789i \(0.422874\pi\)
\(32\) 3.63616 4.33340i 0.113630 0.135419i
\(33\) 0 0
\(34\) 1.35040 + 0.491507i 0.0397177 + 0.0144561i
\(35\) −66.3994 + 38.3357i −1.89713 + 1.09531i
\(36\) 0 0
\(37\) −33.2994 + 57.6763i −0.899984 + 1.55882i −0.0724711 + 0.997371i \(0.523089\pi\)
−0.827513 + 0.561447i \(0.810245\pi\)
\(38\) 19.1977 + 22.8789i 0.505202 + 0.602076i
\(39\) 0 0
\(40\) 4.10678 23.2907i 0.102669 0.582267i
\(41\) −52.2291 9.20941i −1.27388 0.224620i −0.504501 0.863411i \(-0.668324\pi\)
−0.769380 + 0.638791i \(0.779435\pi\)
\(42\) 0 0
\(43\) −36.3861 + 30.5315i −0.846188 + 0.710036i −0.958947 0.283587i \(-0.908476\pi\)
0.112759 + 0.993622i \(0.464031\pi\)
\(44\) 11.3965 + 6.57978i 0.259012 + 0.149540i
\(45\) 0 0
\(46\) 15.1616 + 26.2606i 0.329599 + 0.570882i
\(47\) 2.23172 6.13159i 0.0474833 0.130459i −0.913684 0.406425i \(-0.866775\pi\)
0.961168 + 0.275965i \(0.0889975\pi\)
\(48\) 0 0
\(49\) 26.8732 + 22.5493i 0.548433 + 0.460190i
\(50\) −21.7250 59.6890i −0.434501 1.19378i
\(51\) 0 0
\(52\) −2.08619 11.8314i −0.0401191 0.227527i
\(53\) 39.7705i 0.750386i 0.926947 + 0.375193i \(0.122424\pi\)
−0.926947 + 0.375193i \(0.877576\pi\)
\(54\) 0 0
\(55\) 55.0170 1.00031
\(56\) −25.5414 + 4.50363i −0.456096 + 0.0804220i
\(57\) 0 0
\(58\) 64.3921 23.4368i 1.11021 0.404083i
\(59\) 18.0238 21.4799i 0.305488 0.364067i −0.591358 0.806409i \(-0.701408\pi\)
0.896846 + 0.442342i \(0.145852\pi\)
\(60\) 0 0
\(61\) 38.6125 + 14.0538i 0.632992 + 0.230390i 0.638533 0.769594i \(-0.279542\pi\)
−0.00554114 + 0.999985i \(0.501764\pi\)
\(62\) −8.09199 + 4.67191i −0.130516 + 0.0753535i
\(63\) 0 0
\(64\) 4.00000 6.92820i 0.0625000 0.108253i
\(65\) −32.2855 38.4764i −0.496700 0.591944i
\(66\) 0 0
\(67\) −2.57695 + 14.6146i −0.0384619 + 0.218128i −0.997981 0.0635158i \(-0.979769\pi\)
0.959519 + 0.281644i \(0.0908798\pi\)
\(68\) 2.00145 + 0.352909i 0.0294331 + 0.00518984i
\(69\) 0 0
\(70\) −83.0620 + 69.6973i −1.18660 + 0.995676i
\(71\) 65.6502 + 37.9031i 0.924650 + 0.533847i 0.885116 0.465371i \(-0.154079\pi\)
0.0395346 + 0.999218i \(0.487412\pi\)
\(72\) 0 0
\(73\) −26.5140 45.9236i −0.363205 0.629090i 0.625281 0.780400i \(-0.284984\pi\)
−0.988486 + 0.151310i \(0.951651\pi\)
\(74\) −32.2131 + 88.5049i −0.435313 + 1.19601i
\(75\) 0 0
\(76\) 32.3556 + 27.1496i 0.425732 + 0.357232i
\(77\) −20.6353 56.6950i −0.267991 0.736299i
\(78\) 0 0
\(79\) −14.2149 80.6166i −0.179935 1.02046i −0.932292 0.361708i \(-0.882194\pi\)
0.752356 0.658756i \(-0.228917\pi\)
\(80\) 33.4461i 0.418077i
\(81\) 0 0
\(82\) −75.0026 −0.914666
\(83\) −46.2126 + 8.14852i −0.556778 + 0.0981749i −0.444955 0.895553i \(-0.646780\pi\)
−0.111823 + 0.993728i \(0.535669\pi\)
\(84\) 0 0
\(85\) 7.98426 2.90603i 0.0939324 0.0341886i
\(86\) −43.1781 + 51.4577i −0.502071 + 0.598345i
\(87\) 0 0
\(88\) 17.4881 + 6.36514i 0.198728 + 0.0723311i
\(89\) −20.2996 + 11.7200i −0.228085 + 0.131685i −0.609689 0.792641i \(-0.708705\pi\)
0.381603 + 0.924326i \(0.375372\pi\)
\(90\) 0 0
\(91\) −27.5405 + 47.7016i −0.302643 + 0.524193i
\(92\) 27.5649 + 32.8505i 0.299618 + 0.357071i
\(93\) 0 0
\(94\) 1.60241 9.08769i 0.0170469 0.0966776i
\(95\) 173.902 + 30.6635i 1.83054 + 0.322774i
\(96\) 0 0
\(97\) 26.8130 22.4988i 0.276423 0.231946i −0.494028 0.869446i \(-0.664476\pi\)
0.770450 + 0.637500i \(0.220031\pi\)
\(98\) 42.9647 + 24.8057i 0.438415 + 0.253119i
\(99\) 0 0
\(100\) −44.9152 77.7955i −0.449152 0.777955i
\(101\) 41.4761 113.955i 0.410655 1.12826i −0.546189 0.837662i \(-0.683922\pi\)
0.956844 0.290603i \(-0.0938559\pi\)
\(102\) 0 0
\(103\) −144.726 121.440i −1.40511 1.17903i −0.958776 0.284161i \(-0.908285\pi\)
−0.446334 0.894866i \(-0.647271\pi\)
\(104\) −5.81100 15.9656i −0.0558750 0.153515i
\(105\) 0 0
\(106\) 9.76666 + 55.3895i 0.0921383 + 0.522542i
\(107\) 76.4765i 0.714733i −0.933964 0.357367i \(-0.883675\pi\)
0.933964 0.357367i \(-0.116325\pi\)
\(108\) 0 0
\(109\) 43.7808 0.401659 0.200829 0.979626i \(-0.435636\pi\)
0.200829 + 0.979626i \(0.435636\pi\)
\(110\) 76.6238 13.5108i 0.696580 0.122826i
\(111\) 0 0
\(112\) −34.4662 + 12.5447i −0.307734 + 0.112006i
\(113\) 0.133455 0.159046i 0.00118102 0.00140749i −0.765454 0.643491i \(-0.777485\pi\)
0.766635 + 0.642084i \(0.221930\pi\)
\(114\) 0 0
\(115\) 168.473 + 61.3192i 1.46498 + 0.533210i
\(116\) 83.9252 48.4543i 0.723493 0.417709i
\(117\) 0 0
\(118\) 19.8273 34.3419i 0.168028 0.291033i
\(119\) −5.98932 7.13780i −0.0503305 0.0599815i
\(120\) 0 0
\(121\) 13.4936 76.5260i 0.111517 0.632446i
\(122\) 57.2280 + 10.0908i 0.469082 + 0.0827118i
\(123\) 0 0
\(124\) −10.1226 + 8.49390i −0.0816342 + 0.0684992i
\(125\) −144.212 83.2610i −1.15370 0.666088i
\(126\) 0 0
\(127\) 77.5448 + 134.312i 0.610589 + 1.05757i 0.991141 + 0.132812i \(0.0424006\pi\)
−0.380552 + 0.924759i \(0.624266\pi\)
\(128\) 3.86952 10.6314i 0.0302306 0.0830579i
\(129\) 0 0
\(130\) −54.4138 45.6586i −0.418568 0.351220i
\(131\) 46.3122 + 127.242i 0.353529 + 0.971312i 0.981227 + 0.192855i \(0.0617748\pi\)
−0.627699 + 0.778456i \(0.716003\pi\)
\(132\) 0 0
\(133\) −33.6267 190.706i −0.252832 1.43388i
\(134\) 20.9870i 0.156619i
\(135\) 0 0
\(136\) 2.87414 0.0211334
\(137\) −46.2957 + 8.16317i −0.337924 + 0.0595852i −0.340036 0.940413i \(-0.610439\pi\)
0.00211111 + 0.999998i \(0.499328\pi\)
\(138\) 0 0
\(139\) −45.5216 + 16.5685i −0.327494 + 0.119198i −0.500534 0.865717i \(-0.666863\pi\)
0.173040 + 0.984915i \(0.444641\pi\)
\(140\) −98.5669 + 117.467i −0.704049 + 0.839053i
\(141\) 0 0
\(142\) 100.741 + 36.6667i 0.709443 + 0.258216i
\(143\) 34.2292 19.7622i 0.239365 0.138197i
\(144\) 0 0
\(145\) 202.576 350.872i 1.39708 2.41981i
\(146\) −48.2045 57.4479i −0.330168 0.393479i
\(147\) 0 0
\(148\) −23.1295 + 131.174i −0.156281 + 0.886311i
\(149\) −82.6444 14.5724i −0.554660 0.0978015i −0.110710 0.993853i \(-0.535312\pi\)
−0.443951 + 0.896051i \(0.646423\pi\)
\(150\) 0 0
\(151\) −98.8811 + 82.9711i −0.654842 + 0.549477i −0.908536 0.417807i \(-0.862799\pi\)
0.253694 + 0.967284i \(0.418354\pi\)
\(152\) 51.7299 + 29.8663i 0.340328 + 0.196489i
\(153\) 0 0
\(154\) −42.6623 73.8932i −0.277028 0.479826i
\(155\) −18.8950 + 51.9137i −0.121903 + 0.334927i
\(156\) 0 0
\(157\) 159.054 + 133.462i 1.01308 + 0.850079i 0.988743 0.149625i \(-0.0478066\pi\)
0.0243416 + 0.999704i \(0.492251\pi\)
\(158\) −39.5950 108.786i −0.250601 0.688521i
\(159\) 0 0
\(160\) −8.21355 46.5814i −0.0513347 0.291134i
\(161\) 196.610i 1.22118i
\(162\) 0 0
\(163\) −171.033 −1.04928 −0.524641 0.851324i \(-0.675800\pi\)
−0.524641 + 0.851324i \(0.675800\pi\)
\(164\) −104.458 + 18.4188i −0.636941 + 0.112310i
\(165\) 0 0
\(166\) −62.3605 + 22.6974i −0.375665 + 0.136731i
\(167\) 101.372 120.810i 0.607015 0.723413i −0.371765 0.928327i \(-0.621247\pi\)
0.978780 + 0.204914i \(0.0656916\pi\)
\(168\) 0 0
\(169\) 124.901 + 45.4601i 0.739057 + 0.268995i
\(170\) 10.4063 6.00805i 0.0612132 0.0353415i
\(171\) 0 0
\(172\) −47.4986 + 82.2700i −0.276155 + 0.478314i
\(173\) 10.7700 + 12.8352i 0.0622543 + 0.0741918i 0.796273 0.604938i \(-0.206802\pi\)
−0.734019 + 0.679129i \(0.762358\pi\)
\(174\) 0 0
\(175\) −71.5174 + 405.595i −0.408671 + 2.31769i
\(176\) 25.9193 + 4.57027i 0.147269 + 0.0259674i
\(177\) 0 0
\(178\) −25.3937 + 21.3078i −0.142661 + 0.119707i
\(179\) 94.2561 + 54.4188i 0.526570 + 0.304016i 0.739619 0.673026i \(-0.235006\pi\)
−0.213048 + 0.977042i \(0.568339\pi\)
\(180\) 0 0
\(181\) −18.5784 32.1787i −0.102643 0.177783i 0.810130 0.586251i \(-0.199397\pi\)
−0.912773 + 0.408468i \(0.866063\pi\)
\(182\) −26.6421 + 73.1986i −0.146385 + 0.402190i
\(183\) 0 0
\(184\) 46.4577 + 38.9826i 0.252487 + 0.211862i
\(185\) 190.460 + 523.285i 1.02951 + 2.82857i
\(186\) 0 0
\(187\) 1.16103 + 6.58454i 0.00620873 + 0.0352115i
\(188\) 13.0502i 0.0694160i
\(189\) 0 0
\(190\) 249.728 1.31436
\(191\) −211.469 + 37.2877i −1.10717 + 0.195223i −0.697200 0.716877i \(-0.745571\pi\)
−0.409967 + 0.912100i \(0.634460\pi\)
\(192\) 0 0
\(193\) −266.703 + 97.0720i −1.38188 + 0.502964i −0.922748 0.385403i \(-0.874062\pi\)
−0.459134 + 0.888367i \(0.651840\pi\)
\(194\) 31.8181 37.9193i 0.164011 0.195460i
\(195\) 0 0
\(196\) 65.9298 + 23.9965i 0.336376 + 0.122431i
\(197\) 154.203 89.0292i 0.782756 0.451925i −0.0546498 0.998506i \(-0.517404\pi\)
0.837406 + 0.546581i \(0.184071\pi\)
\(198\) 0 0
\(199\) −72.8436 + 126.169i −0.366048 + 0.634014i −0.988944 0.148291i \(-0.952623\pi\)
0.622896 + 0.782305i \(0.285956\pi\)
\(200\) −81.6594 97.3179i −0.408297 0.486590i
\(201\) 0 0
\(202\) 29.7805 168.894i 0.147428 0.836107i
\(203\) −437.553 77.1525i −2.15544 0.380061i
\(204\) 0 0
\(205\) −339.705 + 285.046i −1.65710 + 1.39047i
\(206\) −231.387 133.591i −1.12324 0.648502i
\(207\) 0 0
\(208\) −12.0139 20.8087i −0.0577592 0.100042i
\(209\) −47.5258 + 130.576i −0.227396 + 0.624765i
\(210\) 0 0
\(211\) −227.718 191.078i −1.07923 0.905584i −0.0833757 0.996518i \(-0.526570\pi\)
−0.995857 + 0.0909345i \(0.971015\pi\)
\(212\) 27.2046 + 74.7440i 0.128324 + 0.352566i
\(213\) 0 0
\(214\) −18.7808 106.511i −0.0877605 0.497715i
\(215\) 397.161i 1.84726i
\(216\) 0 0
\(217\) 60.5839 0.279189
\(218\) 60.9748 10.7515i 0.279701 0.0493188i
\(219\) 0 0
\(220\) 103.398 37.6339i 0.469992 0.171063i
\(221\) 3.92360 4.67596i 0.0177538 0.0211582i
\(222\) 0 0
\(223\) 198.549 + 72.2658i 0.890352 + 0.324062i 0.746380 0.665520i \(-0.231790\pi\)
0.143972 + 0.989582i \(0.454012\pi\)
\(224\) −44.9214 + 25.9354i −0.200542 + 0.115783i
\(225\) 0 0
\(226\) 0.146809 0.254281i 0.000649599 0.00112514i
\(227\) −10.3430 12.3263i −0.0455638 0.0543008i 0.742781 0.669534i \(-0.233506\pi\)
−0.788345 + 0.615233i \(0.789062\pi\)
\(228\) 0 0
\(229\) 45.3854 257.394i 0.198190 1.12399i −0.709613 0.704592i \(-0.751130\pi\)
0.907803 0.419398i \(-0.137759\pi\)
\(230\) 249.696 + 44.0281i 1.08563 + 0.191426i
\(231\) 0 0
\(232\) 104.986 88.0936i 0.452525 0.379714i
\(233\) −278.614 160.858i −1.19577 0.690377i −0.236159 0.971715i \(-0.575889\pi\)
−0.959609 + 0.281338i \(0.909222\pi\)
\(234\) 0 0
\(235\) −27.2799 47.2502i −0.116085 0.201065i
\(236\) 19.1805 52.6981i 0.0812735 0.223297i
\(237\) 0 0
\(238\) −10.0944 8.47018i −0.0424133 0.0355890i
\(239\) −26.9782 74.1219i −0.112879 0.310133i 0.870370 0.492398i \(-0.163879\pi\)
−0.983250 + 0.182265i \(0.941657\pi\)
\(240\) 0 0
\(241\) 52.6081 + 298.355i 0.218291 + 1.23799i 0.875104 + 0.483935i \(0.160793\pi\)
−0.656813 + 0.754053i \(0.728096\pi\)
\(242\) 109.894i 0.454106i
\(243\) 0 0
\(244\) 82.1811 0.336808
\(245\) 288.870 50.9357i 1.17906 0.207901i
\(246\) 0 0
\(247\) 119.208 43.3882i 0.482624 0.175661i
\(248\) −12.0122 + 14.3156i −0.0484363 + 0.0577241i
\(249\) 0 0
\(250\) −221.295 80.5449i −0.885182 0.322180i
\(251\) 71.3813 41.2120i 0.284387 0.164191i −0.351021 0.936368i \(-0.614165\pi\)
0.635408 + 0.772177i \(0.280832\pi\)
\(252\) 0 0
\(253\) −70.5407 + 122.180i −0.278817 + 0.482925i
\(254\) 140.982 + 168.016i 0.555049 + 0.661482i
\(255\) 0 0
\(256\) 2.77837 15.7569i 0.0108530 0.0615505i
\(257\) 21.2643 + 3.74948i 0.0827406 + 0.0145894i 0.214865 0.976644i \(-0.431069\pi\)
−0.132125 + 0.991233i \(0.542180\pi\)
\(258\) 0 0
\(259\) 467.808 392.538i 1.80621 1.51559i
\(260\) −86.9963 50.2274i −0.334601 0.193182i
\(261\) 0 0
\(262\) 95.7479 + 165.840i 0.365450 + 0.632978i
\(263\) 17.1583 47.1420i 0.0652407 0.179247i −0.902789 0.430085i \(-0.858484\pi\)
0.968029 + 0.250837i \(0.0807059\pi\)
\(264\) 0 0
\(265\) 254.742 + 213.754i 0.961291 + 0.806619i
\(266\) −93.6657 257.344i −0.352127 0.967460i
\(267\) 0 0
\(268\) 5.15390 + 29.2292i 0.0192310 + 0.109064i
\(269\) 119.776i 0.445263i 0.974903 + 0.222632i \(0.0714648\pi\)
−0.974903 + 0.222632i \(0.928535\pi\)
\(270\) 0 0
\(271\) −146.752 −0.541522 −0.270761 0.962647i \(-0.587275\pi\)
−0.270761 + 0.962647i \(0.587275\pi\)
\(272\) 4.00289 0.705818i 0.0147165 0.00259492i
\(273\) 0 0
\(274\) −62.4726 + 22.7382i −0.228002 + 0.0829860i
\(275\) 189.965 226.391i 0.690780 0.823240i
\(276\) 0 0
\(277\) −306.464 111.544i −1.10637 0.402685i −0.276707 0.960954i \(-0.589243\pi\)
−0.829659 + 0.558270i \(0.811465\pi\)
\(278\) −59.3305 + 34.2545i −0.213419 + 0.123217i
\(279\) 0 0
\(280\) −108.430 + 187.806i −0.387249 + 0.670735i
\(281\) 8.78420 + 10.4686i 0.0312605 + 0.0372548i 0.781448 0.623970i \(-0.214481\pi\)
−0.750188 + 0.661225i \(0.770037\pi\)
\(282\) 0 0
\(283\) 79.1142 448.679i 0.279555 1.58544i −0.444554 0.895752i \(-0.646638\pi\)
0.724109 0.689685i \(-0.242251\pi\)
\(284\) 149.309 + 26.3272i 0.525737 + 0.0927016i
\(285\) 0 0
\(286\) 42.8188 35.9293i 0.149716 0.125627i
\(287\) 421.153 + 243.153i 1.46743 + 0.847222i
\(288\) 0 0
\(289\) −143.984 249.387i −0.498214 0.862931i
\(290\) 195.968 538.417i 0.675751 1.85661i
\(291\) 0 0
\(292\) −81.2436 68.1715i −0.278231 0.233464i
\(293\) −166.845 458.404i −0.569438 1.56452i −0.805384 0.592753i \(-0.798041\pi\)
0.235946 0.971766i \(-0.424181\pi\)
\(294\) 0 0
\(295\) −40.7132 230.896i −0.138011 0.782698i
\(296\) 188.370i 0.636385i
\(297\) 0 0
\(298\) −118.680 −0.398254
\(299\) 126.842 22.3657i 0.424222 0.0748018i
\(300\) 0 0
\(301\) 409.274 148.964i 1.35972 0.494896i
\(302\) −117.339 + 139.839i −0.388539 + 0.463043i
\(303\) 0 0
\(304\) 79.3801 + 28.8920i 0.261119 + 0.0950395i
\(305\) 297.549 171.790i 0.975571 0.563246i
\(306\) 0 0
\(307\) 4.37352 7.57515i 0.0142460 0.0246748i −0.858815 0.512287i \(-0.828799\pi\)
0.873061 + 0.487612i \(0.162132\pi\)
\(308\) −77.5633 92.4364i −0.251829 0.300118i
\(309\) 0 0
\(310\) −13.5669 + 76.9418i −0.0437642 + 0.248199i
\(311\) −51.0927 9.00901i −0.164285 0.0289679i 0.0909005 0.995860i \(-0.471025\pi\)
−0.255186 + 0.966892i \(0.582137\pi\)
\(312\) 0 0
\(313\) −279.972 + 234.925i −0.894481 + 0.750558i −0.969104 0.246653i \(-0.920669\pi\)
0.0746231 + 0.997212i \(0.476225\pi\)
\(314\) 254.294 + 146.817i 0.809855 + 0.467570i
\(315\) 0 0
\(316\) −81.8603 141.786i −0.259052 0.448690i
\(317\) −156.797 + 430.796i −0.494627 + 1.35898i 0.401776 + 0.915738i \(0.368393\pi\)
−0.896403 + 0.443239i \(0.853829\pi\)
\(318\) 0 0
\(319\) 244.229 + 204.932i 0.765608 + 0.642421i
\(320\) −22.8785 62.8582i −0.0714953 0.196432i
\(321\) 0 0
\(322\) −48.2827 273.825i −0.149946 0.850387i
\(323\) 21.4600i 0.0664395i
\(324\) 0 0
\(325\) −269.804 −0.830166
\(326\) −238.202 + 42.0015i −0.730682 + 0.128839i
\(327\) 0 0
\(328\) −140.959 + 51.3048i −0.429753 + 0.156417i
\(329\) −38.4594 + 45.8341i −0.116898 + 0.139313i
\(330\) 0 0
\(331\) −417.551 151.976i −1.26148 0.459143i −0.377218 0.926125i \(-0.623119\pi\)
−0.884267 + 0.466982i \(0.845341\pi\)
\(332\) −81.2773 + 46.9255i −0.244811 + 0.141342i
\(333\) 0 0
\(334\) 111.515 193.150i 0.333877 0.578293i
\(335\) 79.7607 + 95.0551i 0.238092 + 0.283747i
\(336\) 0 0
\(337\) −15.6199 + 88.5848i −0.0463498 + 0.262863i −0.999173 0.0406634i \(-0.987053\pi\)
0.952823 + 0.303526i \(0.0981640\pi\)
\(338\) 185.117 + 32.6410i 0.547682 + 0.0965712i
\(339\) 0 0
\(340\) 13.0177 10.9231i 0.0382872 0.0321268i
\(341\) −37.6489 21.7366i −0.110407 0.0637436i
\(342\) 0 0
\(343\) 63.8177 + 110.536i 0.186058 + 0.322261i
\(344\) −45.9492 + 126.244i −0.133573 + 0.366989i
\(345\) 0 0
\(346\) 18.1517 + 15.2311i 0.0524615 + 0.0440204i
\(347\) −169.850 466.660i −0.489483 1.34484i −0.901150 0.433508i \(-0.857276\pi\)
0.411667 0.911334i \(-0.364947\pi\)
\(348\) 0 0
\(349\) 58.8946 + 334.008i 0.168752 + 0.957042i 0.945111 + 0.326750i \(0.105954\pi\)
−0.776358 + 0.630292i \(0.782935\pi\)
\(350\) 582.447i 1.66413i
\(351\) 0 0
\(352\) 37.2209 0.105741
\(353\) 217.451 38.3425i 0.616008 0.108619i 0.143067 0.989713i \(-0.454304\pi\)
0.472941 + 0.881094i \(0.343192\pi\)
\(354\) 0 0
\(355\) 595.631 216.792i 1.67783 0.610681i
\(356\) −30.1338 + 35.9121i −0.0846456 + 0.100877i
\(357\) 0 0
\(358\) 144.637 + 52.6436i 0.404014 + 0.147049i
\(359\) −494.204 + 285.329i −1.37661 + 0.794788i −0.991750 0.128185i \(-0.959085\pi\)
−0.384864 + 0.922973i \(0.625751\pi\)
\(360\) 0 0
\(361\) −42.4986 + 73.6098i −0.117725 + 0.203905i
\(362\) −33.7770 40.2539i −0.0933066 0.111198i
\(363\) 0 0
\(364\) −19.1294 + 108.488i −0.0525534 + 0.298045i
\(365\) −436.659 76.9948i −1.19633 0.210945i
\(366\) 0 0
\(367\) −161.979 + 135.917i −0.441360 + 0.370345i −0.836218 0.548397i \(-0.815238\pi\)
0.394858 + 0.918742i \(0.370794\pi\)
\(368\) 74.2761 + 42.8833i 0.201837 + 0.116531i
\(369\) 0 0
\(370\) 393.765 + 682.021i 1.06423 + 1.84330i
\(371\) 124.727 342.684i 0.336191 0.923677i
\(372\) 0 0
\(373\) −53.2124 44.6505i −0.142661 0.119706i 0.568665 0.822569i \(-0.307460\pi\)
−0.711325 + 0.702863i \(0.751905\pi\)
\(374\) 3.23401 + 8.88536i 0.00864707 + 0.0237576i
\(375\) 0 0
\(376\) −3.20481 18.1754i −0.00852343 0.0483388i
\(377\) 291.063i 0.772049i
\(378\) 0 0
\(379\) 390.211 1.02958 0.514791 0.857316i \(-0.327870\pi\)
0.514791 + 0.857316i \(0.327870\pi\)
\(380\) 347.803 61.3271i 0.915271 0.161387i
\(381\) 0 0
\(382\) −285.362 + 103.863i −0.747020 + 0.271893i
\(383\) 116.563 138.915i 0.304342 0.362701i −0.592098 0.805866i \(-0.701700\pi\)
0.896440 + 0.443165i \(0.146144\pi\)
\(384\) 0 0
\(385\) −474.057 172.543i −1.23132 0.448163i
\(386\) −347.607 + 200.691i −0.900535 + 0.519924i
\(387\) 0 0
\(388\) 35.0019 60.6250i 0.0902110 0.156250i
\(389\) 432.550 + 515.493i 1.11195 + 1.32518i 0.940427 + 0.339996i \(0.110426\pi\)
0.171527 + 0.985179i \(0.445130\pi\)
\(390\) 0 0
\(391\) −3.78348 + 21.4572i −0.00967642 + 0.0548777i
\(392\) 97.7152 + 17.2298i 0.249274 + 0.0439536i
\(393\) 0 0
\(394\) 192.900 161.862i 0.489593 0.410817i
\(395\) −592.775 342.239i −1.50070 0.866427i
\(396\) 0 0
\(397\) 226.822 + 392.867i 0.571340 + 0.989590i 0.996429 + 0.0844384i \(0.0269096\pi\)
−0.425089 + 0.905152i \(0.639757\pi\)
\(398\) −70.4674 + 193.608i −0.177054 + 0.486451i
\(399\) 0 0
\(400\) −137.628 115.484i −0.344071 0.288710i
\(401\) 107.387 + 295.043i 0.267798 + 0.735769i 0.998586 + 0.0531643i \(0.0169307\pi\)
−0.730788 + 0.682605i \(0.760847\pi\)
\(402\) 0 0
\(403\) 6.89183 + 39.0855i 0.0171013 + 0.0969864i
\(404\) 242.536i 0.600337i
\(405\) 0 0
\(406\) −628.340 −1.54763
\(407\) −431.548 + 76.0936i −1.06031 + 0.186962i
\(408\) 0 0
\(409\) −1.59923 + 0.582072i −0.00391009 + 0.00142316i −0.343974 0.938979i \(-0.611773\pi\)
0.340064 + 0.940402i \(0.389551\pi\)
\(410\) −403.116 + 480.415i −0.983209 + 1.17174i
\(411\) 0 0
\(412\) −355.066 129.234i −0.861812 0.313674i
\(413\) −222.668 + 128.557i −0.539147 + 0.311277i
\(414\) 0 0
\(415\) −196.184 + 339.801i −0.472733 + 0.818798i
\(416\) −21.8422 26.0305i −0.0525053 0.0625734i
\(417\) 0 0
\(418\) −34.1242 + 193.528i −0.0816369 + 0.462986i
\(419\) 98.5462 + 17.3764i 0.235194 + 0.0414710i 0.290003 0.957026i \(-0.406344\pi\)
−0.0548088 + 0.998497i \(0.517455\pi\)
\(420\) 0 0
\(421\) 486.614 408.318i 1.15585 0.969876i 0.156012 0.987755i \(-0.450136\pi\)
0.999840 + 0.0178796i \(0.00569155\pi\)
\(422\) −364.074 210.198i −0.862734 0.498099i
\(423\) 0 0
\(424\) 56.2439 + 97.4173i 0.132651 + 0.229758i
\(425\) 15.6102 42.8886i 0.0367299 0.100914i
\(426\) 0 0
\(427\) −288.632 242.191i −0.675952 0.567191i
\(428\) −52.3130 143.729i −0.122227 0.335815i
\(429\) 0 0
\(430\) 97.5332 + 553.138i 0.226821 + 1.28637i
\(431\) 180.242i 0.418195i −0.977895 0.209098i \(-0.932947\pi\)
0.977895 0.209098i \(-0.0670526\pi\)
\(432\) 0 0
\(433\) 161.992 0.374115 0.187058 0.982349i \(-0.440105\pi\)
0.187058 + 0.982349i \(0.440105\pi\)
\(434\) 84.3770 14.8779i 0.194417 0.0342810i
\(435\) 0 0
\(436\) 82.2810 29.9478i 0.188718 0.0686877i
\(437\) −291.066 + 346.880i −0.666056 + 0.793775i
\(438\) 0 0
\(439\) 302.339 + 110.043i 0.688700 + 0.250666i 0.662579 0.748992i \(-0.269462\pi\)
0.0261216 + 0.999659i \(0.491684\pi\)
\(440\) 134.764 77.8059i 0.306281 0.176831i
\(441\) 0 0
\(442\) 4.31621 7.47589i 0.00976517 0.0169138i
\(443\) −325.041 387.368i −0.733726 0.874421i 0.262161 0.965024i \(-0.415565\pi\)
−0.995887 + 0.0906036i \(0.971120\pi\)
\(444\) 0 0
\(445\) −34.0340 + 193.016i −0.0764809 + 0.433745i
\(446\) 294.271 + 51.8879i 0.659800 + 0.116341i
\(447\) 0 0
\(448\) −56.1942 + 47.1525i −0.125434 + 0.105251i
\(449\) 621.494 + 358.820i 1.38417 + 0.799153i 0.992651 0.121015i \(-0.0386148\pi\)
0.391524 + 0.920168i \(0.371948\pi\)
\(450\) 0 0
\(451\) −174.479 302.206i −0.386871 0.670080i
\(452\) 0.142020 0.390198i 0.000314204 0.000863269i
\(453\) 0 0
\(454\) −17.4320 14.6272i −0.0383965 0.0322185i
\(455\) 157.521 + 432.787i 0.346201 + 0.951179i
\(456\) 0 0
\(457\) 72.4920 + 411.123i 0.158626 + 0.899612i 0.955396 + 0.295329i \(0.0954292\pi\)
−0.796770 + 0.604283i \(0.793460\pi\)
\(458\) 369.625i 0.807041i
\(459\) 0 0
\(460\) 358.570 0.779501
\(461\) 807.492 142.383i 1.75161 0.308856i 0.796397 0.604774i \(-0.206737\pi\)
0.955213 + 0.295918i \(0.0956255\pi\)
\(462\) 0 0
\(463\) −800.359 + 291.307i −1.72864 + 0.629173i −0.998532 0.0541620i \(-0.982751\pi\)
−0.730105 + 0.683335i \(0.760529\pi\)
\(464\) 124.583 148.472i 0.268498 0.319984i
\(465\) 0 0
\(466\) −427.536 155.610i −0.917460 0.333928i
\(467\) 557.001 321.585i 1.19272 0.688619i 0.233800 0.972285i \(-0.424884\pi\)
0.958923 + 0.283666i \(0.0915507\pi\)
\(468\) 0 0
\(469\) 68.0383 117.846i 0.145071 0.251270i
\(470\) −49.5970 59.1074i −0.105526 0.125760i
\(471\) 0 0
\(472\) 13.7719 78.1044i 0.0291778 0.165475i
\(473\) −307.782 54.2704i −0.650703 0.114736i
\(474\) 0 0
\(475\) 726.631 609.716i 1.52975 1.28361i
\(476\) −16.1388 9.31774i −0.0339050 0.0195751i
\(477\) 0 0
\(478\) −55.7758 96.6065i −0.116686 0.202106i
\(479\) 103.396 284.077i 0.215857 0.593062i −0.783751 0.621076i \(-0.786696\pi\)
0.999608 + 0.0280135i \(0.00891813\pi\)
\(480\) 0 0
\(481\) 306.461 + 257.151i 0.637132 + 0.534617i
\(482\) 146.538 + 402.609i 0.304020 + 0.835288i
\(483\) 0 0
\(484\) −26.9872 153.052i −0.0557586 0.316223i
\(485\) 292.669i 0.603442i
\(486\) 0 0
\(487\) 584.450 1.20010 0.600052 0.799961i \(-0.295147\pi\)
0.600052 + 0.799961i \(0.295147\pi\)
\(488\) 114.456 20.1817i 0.234541 0.0413559i
\(489\) 0 0
\(490\) 389.810 141.879i 0.795530 0.289549i
\(491\) 177.012 210.954i 0.360513 0.429643i −0.555050 0.831817i \(-0.687301\pi\)
0.915563 + 0.402174i \(0.131745\pi\)
\(492\) 0 0
\(493\) 46.2680 + 16.8402i 0.0938498 + 0.0341586i
\(494\) 155.370 89.7027i 0.314513 0.181584i
\(495\) 0 0
\(496\) −13.2142 + 22.8876i −0.0266415 + 0.0461444i
\(497\) −446.807 532.484i −0.899009 1.07140i
\(498\) 0 0
\(499\) −29.6099 + 167.926i −0.0593384 + 0.336525i −0.999996 0.00283231i \(-0.999098\pi\)
0.940658 + 0.339357i \(0.110210\pi\)
\(500\) −327.984 57.8325i −0.655969 0.115665i
\(501\) 0 0
\(502\) 89.2941 74.9266i 0.177877 0.149256i
\(503\) 13.2176 + 7.63121i 0.0262776 + 0.0151714i 0.513081 0.858340i \(-0.328504\pi\)
−0.486804 + 0.873511i \(0.661837\pi\)
\(504\) 0 0
\(505\) −506.994 878.139i −1.00395 1.73889i
\(506\) −68.2396 + 187.487i −0.134861 + 0.370527i
\(507\) 0 0
\(508\) 237.611 + 199.379i 0.467738 + 0.392479i
\(509\) 177.011 + 486.334i 0.347762 + 0.955470i 0.983073 + 0.183213i \(0.0586498\pi\)
−0.635311 + 0.772257i \(0.719128\pi\)
\(510\) 0 0
\(511\) 84.4351 + 478.855i 0.165235 + 0.937094i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 30.5362 0.0594090
\(515\) −1555.72 + 274.315i −3.02081 + 0.532651i
\(516\) 0 0
\(517\) 40.3445 14.6842i 0.0780358 0.0284027i
\(518\) 555.132 661.581i 1.07168 1.27718i
\(519\) 0 0
\(520\) −133.497 48.5889i −0.256725 0.0934402i
\(521\) −843.550 + 487.024i −1.61910 + 0.934786i −0.631943 + 0.775015i \(0.717742\pi\)
−0.987154 + 0.159771i \(0.948924\pi\)
\(522\) 0 0
\(523\) 159.545 276.340i 0.305058 0.528375i −0.672217 0.740355i \(-0.734658\pi\)
0.977274 + 0.211979i \(0.0679909\pi\)
\(524\) 174.077 + 207.457i 0.332208 + 0.395910i
\(525\) 0 0
\(526\) 12.3199 69.8697i 0.0234219 0.132832i
\(527\) −6.61187 1.16585i −0.0125462 0.00221224i
\(528\) 0 0
\(529\) 53.0522 44.5161i 0.100288 0.0841514i
\(530\) 407.279 + 235.143i 0.768451 + 0.443666i
\(531\) 0 0
\(532\) −193.648 335.409i −0.364001 0.630468i
\(533\) −108.960 + 299.365i −0.204428 + 0.561661i
\(534\) 0 0
\(535\) −489.855 411.037i −0.915617 0.768294i
\(536\) 14.3560 + 39.4427i 0.0267835 + 0.0735871i
\(537\) 0 0
\(538\) 29.4140 + 166.815i 0.0546729 + 0.310066i
\(539\) 230.822i 0.428241i
\(540\) 0 0
\(541\) −604.682 −1.11771 −0.558856 0.829265i \(-0.688759\pi\)
−0.558856 + 0.829265i \(0.688759\pi\)
\(542\) −204.386 + 36.0388i −0.377096 + 0.0664922i
\(543\) 0 0
\(544\) 5.40161 1.96603i 0.00992944 0.00361402i
\(545\) 235.308 280.430i 0.431758 0.514550i
\(546\) 0 0
\(547\) −789.301 287.282i −1.44296 0.525196i −0.502347 0.864666i \(-0.667530\pi\)
−0.940617 + 0.339470i \(0.889752\pi\)
\(548\) −81.4234 + 47.0098i −0.148583 + 0.0857844i
\(549\) 0 0
\(550\) 208.973 361.952i 0.379951 0.658094i
\(551\) 657.757 + 783.884i 1.19375 + 1.42266i
\(552\) 0 0
\(553\) −130.344 + 739.218i −0.235703 + 1.33674i
\(554\) −454.213 80.0900i −0.819879 0.144567i
\(555\) 0 0
\(556\) −74.2192 + 62.2773i −0.133488 + 0.112009i
\(557\) 785.853 + 453.713i 1.41087 + 0.814565i 0.995470 0.0950749i \(-0.0303091\pi\)
0.415398 + 0.909640i \(0.363642\pi\)
\(558\) 0 0
\(559\) 142.661 + 247.096i 0.255208 + 0.442033i
\(560\) −104.893 + 288.190i −0.187308 + 0.514626i
\(561\) 0 0
\(562\) 14.8048 + 12.4227i 0.0263431 + 0.0221045i
\(563\) −23.4667 64.4741i −0.0416815 0.114519i 0.917106 0.398644i \(-0.130519\pi\)
−0.958787 + 0.284125i \(0.908297\pi\)
\(564\) 0 0
\(565\) −0.301457 1.70965i −0.000533552 0.00302592i
\(566\) 644.316i 1.13837i
\(567\) 0 0
\(568\) 214.413 0.377487
\(569\) 459.085 80.9491i 0.806828 0.142265i 0.245004 0.969522i \(-0.421211\pi\)
0.561824 + 0.827257i \(0.310100\pi\)
\(570\) 0 0
\(571\) −496.079 + 180.558i −0.868789 + 0.316213i −0.737677 0.675154i \(-0.764077\pi\)
−0.131113 + 0.991367i \(0.541855\pi\)
\(572\) 50.8116 60.5549i 0.0888315 0.105865i
\(573\) 0 0
\(574\) 646.264 + 235.221i 1.12590 + 0.409792i
\(575\) 834.033 481.529i 1.45049 0.837442i
\(576\) 0 0
\(577\) 171.837 297.630i 0.297811 0.515824i −0.677824 0.735224i \(-0.737077\pi\)
0.975635 + 0.219401i \(0.0704101\pi\)
\(578\) −261.774 311.970i −0.452895 0.539740i
\(579\) 0 0
\(580\) 140.708 797.993i 0.242600 1.37585i
\(581\) 423.748 + 74.7182i 0.729342 + 0.128603i
\(582\) 0 0
\(583\) −200.459 + 168.205i −0.343841 + 0.288517i
\(584\) −129.891 74.9929i −0.222417 0.128412i
\(585\) 0 0
\(586\) −344.943 597.459i −0.588640 1.01956i
\(587\) 56.2267 154.482i 0.0957866 0.263172i −0.882541 0.470236i \(-0.844169\pi\)
0.978327 + 0.207064i \(0.0663910\pi\)
\(588\) 0 0
\(589\) −106.888 89.6899i −0.181474 0.152275i
\(590\) −113.405 311.577i −0.192212 0.528097i
\(591\) 0 0
\(592\) 46.2590 + 262.348i 0.0781403 + 0.443155i
\(593\) 349.285i 0.589014i −0.955649 0.294507i \(-0.904845\pi\)
0.955649 0.294507i \(-0.0951555\pi\)
\(594\) 0 0
\(595\) −77.9106 −0.130942
\(596\) −165.289 + 29.1449i −0.277330 + 0.0489008i
\(597\) 0 0
\(598\) 171.165 62.2988i 0.286228 0.104179i
\(599\) 387.503 461.808i 0.646917 0.770965i −0.338529 0.940956i \(-0.609929\pi\)
0.985446 + 0.169991i \(0.0543737\pi\)
\(600\) 0 0
\(601\) 37.6412 + 13.7003i 0.0626310 + 0.0227958i 0.373146 0.927773i \(-0.378279\pi\)
−0.310515 + 0.950569i \(0.600501\pi\)
\(602\) 533.426 307.974i 0.886090 0.511584i
\(603\) 0 0
\(604\) −129.080 + 223.573i −0.213709 + 0.370154i
\(605\) −417.648 497.734i −0.690328 0.822701i
\(606\) 0 0
\(607\) 173.949 986.513i 0.286572 1.62523i −0.413046 0.910710i \(-0.635535\pi\)
0.699617 0.714518i \(-0.253354\pi\)
\(608\) 117.650 + 20.7449i 0.193504 + 0.0341199i
\(609\) 0 0
\(610\) 372.218 312.328i 0.610193 0.512013i
\(611\) −33.9447 19.5980i −0.0555560 0.0320753i
\(612\) 0 0
\(613\) −45.2825 78.4316i −0.0738704 0.127947i 0.826724 0.562608i \(-0.190202\pi\)
−0.900594 + 0.434660i \(0.856868\pi\)
\(614\) 4.23085 11.6242i 0.00689063 0.0189319i
\(615\) 0 0
\(616\) −130.725 109.691i −0.212216 0.178070i
\(617\) 337.332 + 926.812i 0.546729 + 1.50213i 0.838100 + 0.545516i \(0.183666\pi\)
−0.291371 + 0.956610i \(0.594111\pi\)
\(618\) 0 0
\(619\) 169.172 + 959.420i 0.273298 + 1.54995i 0.744316 + 0.667828i \(0.232776\pi\)
−0.471017 + 0.882124i \(0.656113\pi\)
\(620\) 110.491i 0.178211i
\(621\) 0 0
\(622\) −73.3706 −0.117959
\(623\) 211.668 37.3228i 0.339757 0.0599083i
\(624\) 0 0
\(625\) −253.245 + 92.1738i −0.405193 + 0.147478i
\(626\) −332.234 + 395.941i −0.530725 + 0.632493i
\(627\) 0 0
\(628\) 390.218 + 142.028i 0.621366 + 0.226159i
\(629\) −58.6084 + 33.8376i −0.0931771 + 0.0537958i
\(630\) 0 0
\(631\) 5.01746 8.69050i 0.00795160 0.0137726i −0.862022 0.506870i \(-0.830802\pi\)
0.869974 + 0.493098i \(0.164136\pi\)
\(632\) −148.828 177.367i −0.235488 0.280644i
\(633\) 0 0
\(634\) −112.582 + 638.487i −0.177575 + 1.00708i
\(635\) 1277.09 + 225.185i 2.01116 + 0.354622i
\(636\) 0 0
\(637\) 161.426 135.453i 0.253416 0.212642i
\(638\) 390.471 + 225.439i 0.612024 + 0.353352i
\(639\) 0 0
\(640\) −47.3000 81.9260i −0.0739062 0.128009i
\(641\) 80.7353 221.818i 0.125952 0.346050i −0.860650 0.509197i \(-0.829942\pi\)
0.986602 + 0.163147i \(0.0521645\pi\)
\(642\) 0 0
\(643\) −21.9909 18.4526i −0.0342005 0.0286976i 0.625527 0.780202i \(-0.284884\pi\)
−0.659728 + 0.751505i \(0.729328\pi\)
\(644\) −134.489 369.506i −0.208834 0.573768i
\(645\) 0 0
\(646\) 5.27004 + 29.8879i 0.00815796 + 0.0462661i
\(647\) 230.995i 0.357024i −0.983938 0.178512i \(-0.942872\pi\)
0.983938 0.178512i \(-0.0571284\pi\)
\(648\) 0 0
\(649\) 184.497 0.284280
\(650\) −375.763 + 66.2572i −0.578098 + 0.101934i
\(651\) 0 0
\(652\) −321.437 + 116.993i −0.493001 + 0.179438i
\(653\) −704.150 + 839.173i −1.07833 + 1.28510i −0.122092 + 0.992519i \(0.538960\pi\)
−0.956239 + 0.292586i \(0.905484\pi\)
\(654\) 0 0
\(655\) 1063.94 + 387.241i 1.62433 + 0.591208i
\(656\) −183.718 + 106.070i −0.280058 + 0.161692i
\(657\) 0 0
\(658\) −42.3077 + 73.2791i −0.0642975 + 0.111366i
\(659\) −231.520 275.915i −0.351321 0.418688i 0.561224 0.827664i \(-0.310330\pi\)
−0.912545 + 0.408976i \(0.865886\pi\)
\(660\) 0 0
\(661\) −27.1592 + 154.027i −0.0410880 + 0.233022i −0.998435 0.0559177i \(-0.982192\pi\)
0.957347 + 0.288940i \(0.0933027\pi\)
\(662\) −618.857 109.121i −0.934830 0.164836i
\(663\) 0 0
\(664\) −101.673 + 85.3141i −0.153123 + 0.128485i
\(665\) −1402.27 809.598i −2.10867 1.21744i
\(666\) 0 0
\(667\) 519.470 + 899.749i 0.778816 + 1.34895i
\(668\) 107.877 296.391i 0.161493 0.443698i
\(669\) 0 0
\(670\) 134.428 + 112.799i 0.200639 + 0.168356i
\(671\) 92.4709 + 254.062i 0.137811 + 0.378632i
\(672\) 0 0
\(673\) −131.778 747.351i −0.195807 1.11048i −0.911265 0.411821i \(-0.864893\pi\)
0.715458 0.698656i \(-0.246218\pi\)
\(674\) 127.210i 0.188739i
\(675\) 0 0
\(676\) 265.833 0.393244
\(677\) −1043.94 + 184.074i −1.54200 + 0.271897i −0.879038 0.476752i \(-0.841814\pi\)
−0.662966 + 0.748649i \(0.730703\pi\)
\(678\) 0 0
\(679\) −301.595 + 109.772i −0.444176 + 0.161667i
\(680\) 15.4476 18.4097i 0.0227171 0.0270731i
\(681\) 0 0
\(682\) −57.7726 21.0275i −0.0847106 0.0308321i
\(683\) −927.527 + 535.508i −1.35802 + 0.784053i −0.989357 0.145511i \(-0.953518\pi\)
−0.368663 + 0.929563i \(0.620184\pi\)
\(684\) 0 0
\(685\) −196.537 + 340.412i −0.286916 + 0.496952i
\(686\) 116.026 + 138.274i 0.169134 + 0.201565i
\(687\) 0 0
\(688\) −32.9922 + 187.108i −0.0479538 + 0.271959i
\(689\) 235.270 + 41.4844i 0.341466 + 0.0602096i
\(690\) 0 0
\(691\) 338.945 284.409i 0.490514 0.411590i −0.363696 0.931518i \(-0.618485\pi\)
0.854211 + 0.519927i \(0.174041\pi\)
\(692\) 29.0207 + 16.7551i 0.0419375 + 0.0242126i
\(693\) 0 0
\(694\) −351.156 608.220i −0.505988 0.876398i
\(695\) −138.538 + 380.631i −0.199336 + 0.547670i
\(696\) 0 0
\(697\) −41.2837 34.6411i −0.0592305 0.0497003i
\(698\) 164.048 + 450.719i 0.235026 + 0.645729i
\(699\) 0 0
\(700\) 143.035 + 811.191i 0.204335 + 1.15884i
\(701\) 77.6184i 0.110725i 0.998466 + 0.0553626i \(0.0176315\pi\)
−0.998466 + 0.0553626i \(0.982369\pi\)
\(702\) 0 0
\(703\) −1406.48 −2.00068
\(704\) 51.8385 9.14053i 0.0736343 0.0129837i
\(705\) 0 0
\(706\) 293.434 106.801i 0.415629 0.151277i
\(707\) −714.763 + 851.821i −1.01098 + 1.20484i
\(708\) 0 0
\(709\) −139.805 50.8850i −0.197187 0.0717700i 0.241539 0.970391i \(-0.422348\pi\)
−0.438726 + 0.898621i \(0.644570\pi\)
\(710\) 776.313 448.204i 1.09340 0.631274i
\(711\) 0 0
\(712\) −33.1491 + 57.4159i −0.0465577 + 0.0806404i
\(713\) −91.0618 108.523i −0.127716 0.152206i
\(714\) 0 0
\(715\) 57.3881 325.464i 0.0802631 0.455195i
\(716\) 214.368 + 37.7989i 0.299397 + 0.0527917i
\(717\) 0 0
\(718\) −618.223 + 518.750i −0.861034 + 0.722494i
\(719\) 22.6129 + 13.0556i 0.0314505 + 0.0181580i 0.515643 0.856804i \(-0.327553\pi\)
−0.484192 + 0.874962i \(0.660886\pi\)
\(720\) 0 0
\(721\) 866.187 + 1500.28i 1.20137 + 2.08083i
\(722\) −41.1123 + 112.955i −0.0569422 + 0.156447i
\(723\) 0 0
\(724\) −56.9275 47.7679i −0.0786292 0.0659777i
\(725\) −744.350 2045.09i −1.02669 2.82081i
\(726\) 0 0
\(727\) −159.723 905.834i −0.219701 1.24599i −0.872559 0.488508i \(-0.837541\pi\)
0.652858 0.757480i \(-0.273570\pi\)
\(728\) 155.793i 0.214001i
\(729\) 0 0
\(730\) −627.056 −0.858980
\(731\) −47.5330 + 8.38135i −0.0650246 + 0.0114656i
\(732\) 0 0
\(733\) 332.814 121.134i 0.454044 0.165258i −0.104867 0.994486i \(-0.533442\pi\)
0.558911 + 0.829228i \(0.311219\pi\)
\(734\) −192.215 + 229.073i −0.261874 + 0.312089i
\(735\) 0 0
\(736\) 113.978 + 41.4844i 0.154861 + 0.0563647i
\(737\) −84.5624 + 48.8222i −0.114739 + 0.0662444i
\(738\) 0 0
\(739\) 410.346 710.740i 0.555272 0.961760i −0.442610 0.896714i \(-0.645947\pi\)
0.997882 0.0650455i \(-0.0207192\pi\)
\(740\) 715.896 + 853.171i 0.967427 + 1.15293i
\(741\) 0 0
\(742\) 89.5558 507.896i 0.120695 0.684496i
\(743\) 132.906 + 23.4348i 0.178877 + 0.0315408i 0.262369 0.964968i \(-0.415496\pi\)
−0.0834921 + 0.996508i \(0.526607\pi\)
\(744\) 0 0
\(745\) −537.529 + 451.040i −0.721515 + 0.605423i
\(746\) −85.0755 49.1184i −0.114042 0.0658423i
\(747\) 0 0
\(748\) 6.68612 + 11.5807i 0.00893866 + 0.0154822i
\(749\) −239.843 + 658.963i −0.320218 + 0.879791i
\(750\) 0 0
\(751\) 938.326 + 787.349i 1.24944 + 1.04840i 0.996726 + 0.0808587i \(0.0257663\pi\)
0.252710 + 0.967542i \(0.418678\pi\)
\(752\) −8.92686 24.5264i −0.0118708 0.0326148i
\(753\) 0 0
\(754\) −71.4779 405.371i −0.0947982 0.537627i
\(755\) 1079.31i 1.42955i
\(756\) 0 0
\(757\) 915.003 1.20872 0.604361 0.796710i \(-0.293428\pi\)
0.604361 + 0.796710i \(0.293428\pi\)
\(758\) 543.458 95.8264i 0.716964 0.126420i
\(759\) 0 0
\(760\) 469.335 170.824i 0.617546 0.224768i
\(761\) 482.010 574.437i 0.633391 0.754846i −0.349920 0.936780i \(-0.613791\pi\)
0.983311 + 0.181934i \(0.0582357\pi\)
\(762\) 0 0
\(763\) −377.240 137.304i −0.494416 0.179953i
\(764\) −371.925 + 214.731i −0.486813 + 0.281062i
\(765\) 0 0
\(766\) 128.227 222.095i 0.167398 0.289942i
\(767\) −108.268 129.029i −0.141158 0.168226i
\(768\) 0 0
\(769\) −159.677 + 905.573i −0.207642 + 1.17760i 0.685585 + 0.727993i \(0.259547\pi\)
−0.893227 + 0.449606i \(0.851565\pi\)
\(770\) −702.605 123.888i −0.912474 0.160894i
\(771\) 0 0
\(772\) −434.837 + 364.872i −0.563260 + 0.472632i
\(773\) 240.810 + 139.032i 0.311526 + 0.179860i 0.647609 0.761973i \(-0.275769\pi\)
−0.336083 + 0.941832i \(0.609102\pi\)
\(774\) 0 0
\(775\) 148.379 + 257.001i 0.191457 + 0.331614i
\(776\) 33.8601 93.0298i 0.0436341 0.119884i
\(777\) 0 0
\(778\) 729.018 + 611.718i 0.937041 + 0.786270i
\(779\) −383.071 1052.48i −0.491747 1.35106i
\(780\) 0 0
\(781\) 86.6137 + 491.211i 0.110901 + 0.628951i
\(782\) 30.8132i 0.0394030i
\(783\) 0 0
\(784\) 140.322 0.178982
\(785\) 1709.73 301.472i 2.17801 0.384041i
\(786\) 0 0
\(787\) −770.156 + 280.314i −0.978597 + 0.356180i −0.781295 0.624162i \(-0.785440\pi\)
−0.197303 + 0.980343i \(0.563218\pi\)
\(788\) 228.907 272.801i 0.290492 0.346194i
\(789\) 0 0
\(790\) −909.620 331.075i −1.15142 0.419082i
\(791\) −1.64872 + 0.951889i −0.00208435 + 0.00120340i
\(792\) 0 0
\(793\) 123.415 213.760i 0.155630 0.269559i
\(794\) 412.380 + 491.456i 0.519370 + 0.618962i
\(795\) 0 0
\(796\) −50.5966 + 286.948i −0.0635636 + 0.360487i
\(797\) 1111.67 + 196.018i 1.39482 + 0.245944i 0.820013 0.572344i \(-0.193966\pi\)
0.574807 + 0.818289i \(0.305077\pi\)
\(798\) 0 0
\(799\) 5.07930 4.26204i 0.00635707 0.00533422i
\(800\) −220.039 127.039i −0.275049 0.158799i
\(801\) 0 0
\(802\) 222.016 + 384.544i 0.276828 + 0.479481i
\(803\) 119.335 327.870i 0.148612 0.408307i
\(804\) 0 0
\(805\) −1259.35 1056.72i −1.56441 1.31269i
\(806\) 19.1969 + 52.7430i 0.0238175 + 0.0654380i
\(807\) 0 0
\(808\) −59.5610 337.787i −0.0737141 0.418053i
\(809\) 1010.80i 1.24945i 0.780846 + 0.624724i \(0.214788\pi\)
−0.780846 + 0.624724i \(0.785212\pi\)
\(810\) 0 0
\(811\) 481.599 0.593834 0.296917 0.954903i \(-0.404042\pi\)
0.296917 + 0.954903i \(0.404042\pi\)
\(812\) −875.107 + 154.305i −1.07772 + 0.190031i
\(813\) 0 0
\(814\) −582.343 + 211.955i −0.715409 + 0.260387i
\(815\) −919.249 + 1095.52i −1.12791 + 1.34419i
\(816\) 0 0
\(817\) −942.612 343.083i −1.15375 0.419930i
\(818\) −2.08435 + 1.20340i −0.00254810 + 0.00147115i
\(819\) 0 0
\(820\) −443.453 + 768.083i −0.540796 + 0.936686i
\(821\) −685.546 817.002i −0.835013 0.995130i −0.999961 0.00882774i \(-0.997190\pi\)
0.164948 0.986302i \(-0.447254\pi\)
\(822\) 0 0
\(823\) −14.1302 + 80.1366i −0.0171692 + 0.0973713i −0.992188 0.124750i \(-0.960187\pi\)
0.975019 + 0.222121i \(0.0712982\pi\)
\(824\) −526.248 92.7917i −0.638650 0.112611i
\(825\) 0 0
\(826\) −278.545 + 233.727i −0.337222 + 0.282963i
\(827\) −93.3706 53.9076i −0.112903 0.0651845i 0.442485 0.896776i \(-0.354097\pi\)
−0.555388 + 0.831591i \(0.687430\pi\)
\(828\) 0 0
\(829\) −657.741 1139.24i −0.793415 1.37424i −0.923841 0.382778i \(-0.874968\pi\)
0.130425 0.991458i \(-0.458366\pi\)
\(830\) −189.785 + 521.429i −0.228656 + 0.628228i
\(831\) 0 0
\(832\) −36.8128 30.8896i −0.0442461 0.0371269i
\(833\) 12.1921 + 33.4976i 0.0146364 + 0.0402133i
\(834\) 0 0
\(835\) −228.984 1298.63i −0.274232 1.55525i
\(836\) 277.912i 0.332431i
\(837\) 0 0
\(838\) 141.515 0.168873
\(839\) 1292.61 227.922i 1.54065 0.271659i 0.662141 0.749380i \(-0.269648\pi\)
0.878512 + 0.477721i \(0.158537\pi\)
\(840\) 0 0
\(841\) 1415.94 515.361i 1.68364 0.612796i
\(842\) 577.448 688.176i 0.685806 0.817311i
\(843\) 0 0
\(844\) −558.675 203.341i −0.661937 0.240926i
\(845\) 962.488 555.693i 1.13904 0.657625i
\(846\) 0 0
\(847\) −356.267 + 617.072i −0.420622 + 0.728538i
\(848\) 102.256 + 121.864i 0.120585 + 0.143707i
\(849\) 0 0
\(850\) 11.2084 63.5657i 0.0131863 0.0747832i
\(851\) −1406.30 247.968i −1.65252 0.291384i
\(852\) 0 0
\(853\) 846.044 709.915i 0.991845 0.832257i 0.00601108 0.999982i \(-0.498087\pi\)
0.985834 + 0.167725i \(0.0536422\pi\)
\(854\) −461.461 266.425i −0.540353 0.311973i
\(855\) 0 0
\(856\) −108.154 187.328i −0.126348 0.218841i
\(857\) 547.088 1503.11i 0.638376 1.75392i −0.0183917 0.999831i \(-0.505855\pi\)
0.656768 0.754093i \(-0.271923\pi\)
\(858\) 0 0
\(859\) 852.719 + 715.516i 0.992688 + 0.832964i 0.985955 0.167014i \(-0.0534124\pi\)
0.00673292 + 0.999977i \(0.497857\pi\)
\(860\) 271.674 + 746.419i 0.315900 + 0.867929i
\(861\) 0 0
\(862\) −44.2631 251.028i −0.0513493 0.291216i
\(863\) 172.993i 0.200455i 0.994965 + 0.100227i \(0.0319570\pi\)
−0.994965 + 0.100227i \(0.968043\pi\)
\(864\) 0 0
\(865\) 140.099 0.161964
\(866\) 225.611 39.7813i 0.260520 0.0459368i
\(867\) 0 0
\(868\) 113.861 41.4419i 0.131176 0.0477441i
\(869\) 346.220 412.609i 0.398412 0.474809i
\(870\) 0 0
\(871\) 83.7675 + 30.4889i 0.0961740 + 0.0350045i
\(872\) 107.241 61.9154i 0.122982 0.0710039i
\(873\) 0 0
\(874\) −320.191 + 554.588i −0.366352 + 0.634540i
\(875\) 981.492 + 1169.70i 1.12171 + 1.33680i
\(876\) 0 0
\(877\) 185.834 1053.92i 0.211897 1.20173i −0.674313 0.738445i \(-0.735560\pi\)
0.886210 0.463283i \(-0.153329\pi\)
\(878\) 448.100 + 79.0122i 0.510365 + 0.0899911i
\(879\) 0 0
\(880\) 168.582 141.457i 0.191570 0.160747i
\(881\) −347.336 200.535i −0.394253 0.227622i 0.289749 0.957103i \(-0.406428\pi\)
−0.684001 + 0.729481i \(0.739762\pi\)
\(882\) 0 0
\(883\) −165.563 286.763i −0.187500 0.324760i 0.756916 0.653512i \(-0.226705\pi\)
−0.944416 + 0.328752i \(0.893372\pi\)
\(884\) 4.17541 11.4718i 0.00472331 0.0129772i
\(885\) 0 0
\(886\) −547.821 459.677i −0.618309 0.518823i
\(887\) −81.1984 223.091i −0.0915427 0.251511i 0.885469 0.464699i \(-0.153838\pi\)
−0.977011 + 0.213188i \(0.931615\pi\)
\(888\) 0 0
\(889\) −246.945 1400.50i −0.277779 1.57536i
\(890\) 277.177i 0.311435i
\(891\) 0 0
\(892\) 422.582 0.473747
\(893\) 135.708 23.9289i 0.151968 0.0267961i
\(894\) 0 0
\(895\) 855.166 311.255i 0.955493 0.347771i
\(896\) −66.6838 + 79.4706i −0.0744238 + 0.0886949i
\(897\) 0 0
\(898\) 953.690 + 347.115i 1.06202 + 0.386542i
\(899\) −277.251 + 160.071i −0.308399 + 0.178054i
\(900\) 0 0
\(901\) −20.2066 + 34.9989i −0.0224269 + 0.0388445i
\(902\) −317.216 378.043i −0.351681 0.419117i
\(903\) 0 0
\(904\) 0.101973 0.578316i 0.000112802 0.000639730i
\(905\) −305.968 53.9504i −0.338086 0.0596137i
\(906\) 0 0
\(907\) −810.703 + 680.261i −0.893829 + 0.750012i −0.968975 0.247161i \(-0.920502\pi\)
0.0751451 + 0.997173i \(0.476058\pi\)
\(908\) −27.8701 16.0908i −0.0306940 0.0177212i
\(909\) 0 0
\(910\) 325.666 + 564.071i 0.357875 + 0.619858i
\(911\) 616.706 1694.38i 0.676955 1.85992i 0.203573 0.979060i \(-0.434745\pi\)
0.473381 0.880858i \(-0.343033\pi\)
\(912\) 0 0
\(913\) −236.523 198.467i −0.259062 0.217378i
\(914\) 201.923 + 554.780i 0.220923 + 0.606980i
\(915\) 0 0
\(916\) −90.7709 514.787i −0.0990948 0.561995i
\(917\) 1241.63i 1.35401i
\(918\) 0 0
\(919\) 185.717 0.202086 0.101043 0.994882i \(-0.467782\pi\)
0.101043 + 0.994882i \(0.467782\pi\)
\(920\) 499.391 88.0562i 0.542817 0.0957132i
\(921\) 0 0
\(922\) 1089.65 396.601i 1.18184 0.430153i
\(923\) 292.703 348.830i 0.317121 0.377930i
\(924\) 0 0
\(925\) 2810.90 + 1023.09i 3.03882 + 1.10604i
\(926\) −1043.15 + 602.260i −1.12651 + 0.650389i
\(927\) 0 0
\(928\) 137.049 237.376i 0.147682 0.255794i
\(929\) −173.693 206.999i −0.186968 0.222819i 0.664416 0.747363i \(-0.268680\pi\)
−0.851384 + 0.524544i \(0.824236\pi\)
\(930\) 0 0
\(931\) −128.648 + 729.597i −0.138182 + 0.783671i
\(932\) −633.656 111.731i −0.679888 0.119883i
\(933\) 0 0
\(934\) 696.778 584.667i 0.746015 0.625981i
\(935\) 48.4162 + 27.9531i 0.0517820 + 0.0298964i
\(936\) 0 0
\(937\) 96.9914 + 167.994i 0.103513 + 0.179289i 0.913130 0.407669i \(-0.133658\pi\)
−0.809617 + 0.586959i \(0.800325\pi\)
\(938\) 65.8188 180.836i 0.0701693 0.192789i
\(939\) 0 0
\(940\) −83.5905 70.1408i −0.0889261 0.0746178i
\(941\) −18.6872 51.3425i −0.0198588 0.0545617i 0.929367 0.369157i \(-0.120353\pi\)
−0.949226 + 0.314595i \(0.898131\pi\)
\(942\) 0 0
\(943\) −197.465 1119.88i −0.209401 1.18757i
\(944\) 112.160i 0.118814i
\(945\) 0 0
\(946\) −441.985 −0.467214
\(947\) −51.8920 + 9.14995i −0.0547962 + 0.00966204i −0.200979 0.979596i \(-0.564412\pi\)
0.146183 + 0.989258i \(0.453301\pi\)
\(948\) 0 0
\(949\) −299.327 + 108.946i −0.315413 + 0.114801i
\(950\) 862.268 1027.61i 0.907651 1.08170i
\(951\) 0 0
\(952\) −24.7652 9.01378i −0.0260138 0.00946826i
\(953\) 251.736 145.340i 0.264151 0.152508i −0.362076 0.932149i \(-0.617932\pi\)
0.626227 + 0.779641i \(0.284599\pi\)
\(954\) 0 0
\(955\) −897.741 + 1554.93i −0.940042 + 1.62820i
\(956\) −101.405 120.849i −0.106072 0.126412i
\(957\) 0 0
\(958\) 74.2395 421.033i 0.0774943 0.439492i
\(959\) 424.510 + 74.8526i 0.442659 + 0.0780527i
\(960\) 0 0
\(961\) −702.728 + 589.659i −0.731247 + 0.613589i
\(962\) 489.966 + 282.882i 0.509321 + 0.294056i
\(963\) 0 0
\(964\) 302.958 + 524.738i 0.314272 + 0.544334i
\(965\) −811.671 + 2230.05i −0.841110 + 2.31093i
\(966\) 0 0
\(967\) 339.635 + 284.987i 0.351225 + 0.294713i 0.801282 0.598287i \(-0.204152\pi\)
−0.450057 + 0.893000i \(0.648596\pi\)
\(968\) −75.1716 206.532i −0.0776567 0.213360i
\(969\) 0 0
\(970\) −71.8725 407.609i −0.0740953 0.420215i
\(971\) 437.137i 0.450193i −0.974337 0.225096i \(-0.927730\pi\)
0.974337 0.225096i \(-0.0722697\pi\)
\(972\) 0 0
\(973\) 444.201 0.456527
\(974\) 813.981 143.527i 0.835709 0.147358i
\(975\) 0 0
\(976\) 154.450 56.2152i 0.158248 0.0575975i
\(977\) −25.0546 + 29.8589i −0.0256444 + 0.0305618i −0.778714 0.627379i \(-0.784128\pi\)
0.753070 + 0.657941i \(0.228572\pi\)
\(978\) 0 0
\(979\) −144.929 52.7497i −0.148037 0.0538812i
\(980\) 508.057 293.327i 0.518425 0.299313i
\(981\) 0 0
\(982\) 194.724 337.272i 0.198293 0.343454i
\(983\) 1141.74 + 1360.67i 1.16148 + 1.38420i 0.909101 + 0.416575i \(0.136770\pi\)
0.252382 + 0.967628i \(0.418786\pi\)
\(984\) 0 0
\(985\) 258.534 1466.22i 0.262472 1.48855i
\(986\) 68.5743 + 12.0915i 0.0695479 + 0.0122632i
\(987\) 0 0
\(988\) 194.359 163.086i 0.196720 0.165067i
\(989\) −882.004 509.225i −0.891814 0.514889i
\(990\) 0 0
\(991\) −694.188 1202.37i −0.700492 1.21329i −0.968294 0.249814i \(-0.919631\pi\)
0.267802 0.963474i \(-0.413703\pi\)
\(992\) −12.7831 + 35.1213i −0.0128862 + 0.0354045i
\(993\) 0 0
\(994\) −753.047 631.881i −0.757592 0.635695i
\(995\) 416.638 + 1144.70i 0.418732 + 1.15046i
\(996\) 0 0
\(997\) −42.0253 238.337i −0.0421517 0.239054i 0.956451 0.291892i \(-0.0942847\pi\)
−0.998603 + 0.0528372i \(0.983174\pi\)
\(998\) 241.147i 0.241630i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 162.3.f.a.71.6 36
3.2 odd 2 54.3.f.a.41.2 yes 36
12.11 even 2 432.3.bc.c.257.5 36
27.2 odd 18 inner 162.3.f.a.89.6 36
27.5 odd 18 1458.3.b.c.1457.35 36
27.22 even 9 1458.3.b.c.1457.2 36
27.25 even 9 54.3.f.a.29.2 36
108.79 odd 18 432.3.bc.c.353.5 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.f.a.29.2 36 27.25 even 9
54.3.f.a.41.2 yes 36 3.2 odd 2
162.3.f.a.71.6 36 1.1 even 1 trivial
162.3.f.a.89.6 36 27.2 odd 18 inner
432.3.bc.c.257.5 36 12.11 even 2
432.3.bc.c.353.5 36 108.79 odd 18
1458.3.b.c.1457.2 36 27.22 even 9
1458.3.b.c.1457.35 36 27.5 odd 18