Properties

Label 324.2.l.a.143.12
Level $324$
Weight $2$
Character 324.143
Analytic conductor $2.587$
Analytic rank $0$
Dimension $96$
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] = [324,2,Mod(35,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.35");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.l (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: \(2.58715302549\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 143.12
Character \(\chi\) \(=\) 324.143
Dual form 324.2.l.a.179.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.818446 - 1.15332i) q^{2} +(-0.660291 - 1.88786i) q^{4} +(-0.532084 + 0.0938207i) q^{5} +(1.18790 - 1.41568i) q^{7} +(-2.71772 - 0.783586i) q^{8} +O(q^{10})\) \(q+(0.818446 - 1.15332i) q^{2} +(-0.660291 - 1.88786i) q^{4} +(-0.532084 + 0.0938207i) q^{5} +(1.18790 - 1.41568i) q^{7} +(-2.71772 - 0.783586i) q^{8} +(-0.327277 + 0.690450i) q^{10} +(0.867520 - 4.91995i) q^{11} +(-1.52553 - 0.555249i) q^{13} +(-0.660503 - 2.52869i) q^{14} +(-3.12803 + 2.49307i) q^{16} +(0.683630 - 0.394694i) q^{17} +(2.86200 + 1.65238i) q^{19} +(0.528451 + 0.942551i) q^{20} +(-4.96425 - 5.02724i) q^{22} +(3.15234 - 2.64512i) q^{23} +(-4.42415 + 1.61026i) q^{25} +(-1.88895 + 1.30499i) q^{26} +(-3.45697 - 1.30783i) q^{28} +(3.24174 + 8.90660i) q^{29} +(-3.70462 - 4.41499i) q^{31} +(0.315184 + 5.64807i) q^{32} +(0.104306 - 1.11148i) q^{34} +(-0.499242 + 0.864712i) q^{35} +(5.53013 + 9.57846i) q^{37} +(4.24812 - 1.94842i) q^{38} +(1.51957 + 0.161955i) q^{40} +(2.62821 - 7.22095i) q^{41} +(7.88044 + 1.38953i) q^{43} +(-9.86099 + 1.61084i) q^{44} +(-0.470654 - 5.80054i) q^{46} +(2.39693 + 2.01126i) q^{47} +(0.622483 + 3.53027i) q^{49} +(-1.76379 + 6.42037i) q^{50} +(-0.0409360 + 3.24662i) q^{52} -0.933485i q^{53} +2.69922i q^{55} +(-4.33769 + 2.91661i) q^{56} +(12.9253 + 3.55082i) q^{58} +(-0.461077 - 2.61490i) q^{59} +(-4.29949 - 3.60770i) q^{61} +(-8.12393 + 0.659173i) q^{62} +(6.77199 + 4.25913i) q^{64} +(0.863806 + 0.152312i) q^{65} +(-2.15593 + 5.92336i) q^{67} +(-1.19652 - 1.02998i) q^{68} +(0.588687 + 1.28351i) q^{70} +(4.53203 + 7.84970i) q^{71} +(5.77108 - 9.99580i) q^{73} +(15.5731 + 1.46145i) q^{74} +(1.22970 - 6.49411i) q^{76} +(-5.93457 - 7.07254i) q^{77} +(0.275423 + 0.756719i) q^{79} +(1.43047 - 1.62000i) q^{80} +(-6.17702 - 8.94113i) q^{82} +(-15.0247 + 5.46855i) q^{83} +(-0.326718 + 0.274149i) q^{85} +(8.05230 - 7.95141i) q^{86} +(-6.21288 + 12.6913i) q^{88} +(5.41508 + 3.12640i) q^{89} +(-2.59824 + 1.50009i) q^{91} +(-7.07508 - 4.20462i) q^{92} +(4.28138 - 1.11831i) q^{94} +(-1.67785 - 0.610689i) q^{95} +(1.63933 - 9.29708i) q^{97} +(4.58100 + 2.17142i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.818446 1.15332i 0.578729 0.815520i
\(3\) 0 0
\(4\) −0.660291 1.88786i −0.330145 0.943930i
\(5\) −0.532084 + 0.0938207i −0.237955 + 0.0419579i −0.291354 0.956615i \(-0.594106\pi\)
0.0533987 + 0.998573i \(0.482995\pi\)
\(6\) 0 0
\(7\) 1.18790 1.41568i 0.448984 0.535078i −0.493315 0.869851i \(-0.664215\pi\)
0.942299 + 0.334773i \(0.108659\pi\)
\(8\) −2.71772 0.783586i −0.960859 0.277039i
\(9\) 0 0
\(10\) −0.327277 + 0.690450i −0.103494 + 0.218339i
\(11\) 0.867520 4.91995i 0.261567 1.48342i −0.517068 0.855944i \(-0.672977\pi\)
0.778635 0.627477i \(-0.215912\pi\)
\(12\) 0 0
\(13\) −1.52553 0.555249i −0.423107 0.153998i 0.121687 0.992569i \(-0.461170\pi\)
−0.544793 + 0.838570i \(0.683392\pi\)
\(14\) −0.660503 2.52869i −0.176527 0.675821i
\(15\) 0 0
\(16\) −3.12803 + 2.49307i −0.782008 + 0.623268i
\(17\) 0.683630 0.394694i 0.165805 0.0957273i −0.414802 0.909912i \(-0.636149\pi\)
0.580606 + 0.814185i \(0.302816\pi\)
\(18\) 0 0
\(19\) 2.86200 + 1.65238i 0.656589 + 0.379082i 0.790976 0.611847i \(-0.209573\pi\)
−0.134387 + 0.990929i \(0.542907\pi\)
\(20\) 0.528451 + 0.942551i 0.118165 + 0.210761i
\(21\) 0 0
\(22\) −4.96425 5.02724i −1.05838 1.07181i
\(23\) 3.15234 2.64512i 0.657307 0.551546i −0.251971 0.967735i \(-0.581079\pi\)
0.909278 + 0.416188i \(0.136634\pi\)
\(24\) 0 0
\(25\) −4.42415 + 1.61026i −0.884830 + 0.322052i
\(26\) −1.88895 + 1.30499i −0.370453 + 0.255929i
\(27\) 0 0
\(28\) −3.45697 1.30783i −0.653306 0.247156i
\(29\) 3.24174 + 8.90660i 0.601976 + 1.65391i 0.747266 + 0.664525i \(0.231366\pi\)
−0.145290 + 0.989389i \(0.546412\pi\)
\(30\) 0 0
\(31\) −3.70462 4.41499i −0.665369 0.792956i 0.322777 0.946475i \(-0.395384\pi\)
−0.988146 + 0.153519i \(0.950939\pi\)
\(32\) 0.315184 + 5.64807i 0.0557172 + 0.998447i
\(33\) 0 0
\(34\) 0.104306 1.11148i 0.0178884 0.190617i
\(35\) −0.499242 + 0.864712i −0.0843873 + 0.146163i
\(36\) 0 0
\(37\) 5.53013 + 9.57846i 0.909147 + 1.57469i 0.815251 + 0.579108i \(0.196599\pi\)
0.0938963 + 0.995582i \(0.470068\pi\)
\(38\) 4.24812 1.94842i 0.689136 0.316076i
\(39\) 0 0
\(40\) 1.51957 + 0.161955i 0.240265 + 0.0256074i
\(41\) 2.62821 7.22095i 0.410458 1.12772i −0.546491 0.837465i \(-0.684037\pi\)
0.956948 0.290258i \(-0.0937412\pi\)
\(42\) 0 0
\(43\) 7.88044 + 1.38953i 1.20176 + 0.211902i 0.738458 0.674300i \(-0.235555\pi\)
0.463299 + 0.886202i \(0.346666\pi\)
\(44\) −9.86099 + 1.61084i −1.48660 + 0.242844i
\(45\) 0 0
\(46\) −0.470654 5.80054i −0.0693942 0.855243i
\(47\) 2.39693 + 2.01126i 0.349628 + 0.293372i 0.800640 0.599145i \(-0.204493\pi\)
−0.451013 + 0.892517i \(0.648937\pi\)
\(48\) 0 0
\(49\) 0.622483 + 3.53027i 0.0889261 + 0.504325i
\(50\) −1.76379 + 6.42037i −0.249437 + 0.907978i
\(51\) 0 0
\(52\) −0.0409360 + 3.24662i −0.00567681 + 0.450225i
\(53\) 0.933485i 0.128224i −0.997943 0.0641120i \(-0.979579\pi\)
0.997943 0.0641120i \(-0.0204215\pi\)
\(54\) 0 0
\(55\) 2.69922i 0.363962i
\(56\) −4.33769 + 2.91661i −0.579648 + 0.389748i
\(57\) 0 0
\(58\) 12.9253 + 3.55082i 1.69718 + 0.466245i
\(59\) −0.461077 2.61490i −0.0600271 0.340431i 0.939973 0.341250i \(-0.110850\pi\)
−1.00000 0.000819421i \(0.999739\pi\)
\(60\) 0 0
\(61\) −4.29949 3.60770i −0.550493 0.461919i 0.324615 0.945846i \(-0.394765\pi\)
−0.875108 + 0.483928i \(0.839210\pi\)
\(62\) −8.12393 + 0.659173i −1.03174 + 0.0837151i
\(63\) 0 0
\(64\) 6.77199 + 4.25913i 0.846498 + 0.532392i
\(65\) 0.863806 + 0.152312i 0.107142 + 0.0188920i
\(66\) 0 0
\(67\) −2.15593 + 5.92336i −0.263388 + 0.723653i 0.735545 + 0.677476i \(0.236926\pi\)
−0.998933 + 0.0461775i \(0.985296\pi\)
\(68\) −1.19652 1.02998i −0.145100 0.124904i
\(69\) 0 0
\(70\) 0.588687 + 1.28351i 0.0703615 + 0.153408i
\(71\) 4.53203 + 7.84970i 0.537853 + 0.931588i 0.999019 + 0.0442746i \(0.0140977\pi\)
−0.461167 + 0.887313i \(0.652569\pi\)
\(72\) 0 0
\(73\) 5.77108 9.99580i 0.675454 1.16992i −0.300882 0.953661i \(-0.597281\pi\)
0.976336 0.216259i \(-0.0693855\pi\)
\(74\) 15.5731 + 1.46145i 1.81034 + 0.169891i
\(75\) 0 0
\(76\) 1.22970 6.49411i 0.141057 0.744926i
\(77\) −5.93457 7.07254i −0.676307 0.805991i
\(78\) 0 0
\(79\) 0.275423 + 0.756719i 0.0309875 + 0.0851375i 0.954222 0.299100i \(-0.0966865\pi\)
−0.923234 + 0.384238i \(0.874464\pi\)
\(80\) 1.43047 1.62000i 0.159932 0.181121i
\(81\) 0 0
\(82\) −6.17702 8.94113i −0.682137 0.987383i
\(83\) −15.0247 + 5.46855i −1.64918 + 0.600252i −0.988608 0.150513i \(-0.951907\pi\)
−0.660570 + 0.750765i \(0.729685\pi\)
\(84\) 0 0
\(85\) −0.326718 + 0.274149i −0.0354375 + 0.0297356i
\(86\) 8.05230 7.95141i 0.868302 0.857422i
\(87\) 0 0
\(88\) −6.21288 + 12.6913i −0.662295 + 1.35289i
\(89\) 5.41508 + 3.12640i 0.573997 + 0.331398i 0.758744 0.651389i \(-0.225813\pi\)
−0.184747 + 0.982786i \(0.559147\pi\)
\(90\) 0 0
\(91\) −2.59824 + 1.50009i −0.272369 + 0.157252i
\(92\) −7.07508 4.20462i −0.737628 0.438362i
\(93\) 0 0
\(94\) 4.28138 1.11831i 0.441591 0.115345i
\(95\) −1.67785 0.610689i −0.172144 0.0626553i
\(96\) 0 0
\(97\) 1.63933 9.29708i 0.166448 0.943975i −0.781110 0.624393i \(-0.785346\pi\)
0.947559 0.319582i \(-0.103543\pi\)
\(98\) 4.58100 + 2.17142i 0.462751 + 0.219346i
\(99\) 0 0
\(100\) 5.96117 + 7.28894i 0.596117 + 0.728894i
\(101\) −6.31653 + 7.52775i −0.628518 + 0.749039i −0.982510 0.186210i \(-0.940380\pi\)
0.353992 + 0.935249i \(0.384824\pi\)
\(102\) 0 0
\(103\) 6.85056 1.20794i 0.675005 0.119022i 0.174370 0.984680i \(-0.444211\pi\)
0.500635 + 0.865658i \(0.333100\pi\)
\(104\) 3.71089 + 2.70440i 0.363882 + 0.265188i
\(105\) 0 0
\(106\) −1.07661 0.764008i −0.104569 0.0742070i
\(107\) 2.51779 0.243404 0.121702 0.992567i \(-0.461165\pi\)
0.121702 + 0.992567i \(0.461165\pi\)
\(108\) 0 0
\(109\) 5.76924 0.552593 0.276296 0.961072i \(-0.410893\pi\)
0.276296 + 0.961072i \(0.410893\pi\)
\(110\) 3.11306 + 2.20916i 0.296819 + 0.210636i
\(111\) 0 0
\(112\) −0.186384 + 7.38983i −0.0176116 + 0.698273i
\(113\) −4.36693 + 0.770007i −0.410806 + 0.0724362i −0.375232 0.926931i \(-0.622437\pi\)
−0.0355738 + 0.999367i \(0.511326\pi\)
\(114\) 0 0
\(115\) −1.42914 + 1.70318i −0.133268 + 0.158823i
\(116\) 14.6739 12.0009i 1.36244 1.11426i
\(117\) 0 0
\(118\) −3.39318 1.60838i −0.312367 0.148064i
\(119\) 0.253322 1.43666i 0.0232220 0.131698i
\(120\) 0 0
\(121\) −13.1167 4.77409i −1.19243 0.434008i
\(122\) −7.67973 + 2.00598i −0.695290 + 0.181612i
\(123\) 0 0
\(124\) −5.88876 + 9.90898i −0.528826 + 0.889853i
\(125\) 4.54248 2.62260i 0.406292 0.234573i
\(126\) 0 0
\(127\) −3.47118 2.00409i −0.308018 0.177834i 0.338021 0.941138i \(-0.390242\pi\)
−0.646039 + 0.763304i \(0.723576\pi\)
\(128\) 10.4546 4.32439i 0.924069 0.382226i
\(129\) 0 0
\(130\) 0.882643 0.871584i 0.0774129 0.0764430i
\(131\) −1.84218 + 1.54577i −0.160952 + 0.135055i −0.719707 0.694278i \(-0.755724\pi\)
0.558755 + 0.829333i \(0.311279\pi\)
\(132\) 0 0
\(133\) 5.73902 2.08883i 0.497636 0.181125i
\(134\) 5.06701 + 7.33442i 0.437723 + 0.633598i
\(135\) 0 0
\(136\) −2.16719 + 0.536984i −0.185835 + 0.0460460i
\(137\) −1.46523 4.02570i −0.125183 0.343939i 0.861231 0.508213i \(-0.169694\pi\)
−0.986415 + 0.164275i \(0.947472\pi\)
\(138\) 0 0
\(139\) −11.4619 13.6598i −0.972187 1.15861i −0.987323 0.158722i \(-0.949263\pi\)
0.0151364 0.999885i \(-0.495182\pi\)
\(140\) 1.96210 + 0.371537i 0.165828 + 0.0314006i
\(141\) 0 0
\(142\) 12.7624 + 1.19769i 1.07100 + 0.100508i
\(143\) −4.05523 + 7.02386i −0.339115 + 0.587365i
\(144\) 0 0
\(145\) −2.56050 4.43492i −0.212638 0.368300i
\(146\) −6.80503 14.8369i −0.563188 1.22791i
\(147\) 0 0
\(148\) 14.4313 16.7647i 1.18625 1.37805i
\(149\) −4.08657 + 11.2278i −0.334785 + 0.919814i 0.652063 + 0.758165i \(0.273904\pi\)
−0.986848 + 0.161650i \(0.948319\pi\)
\(150\) 0 0
\(151\) −18.0852 3.18891i −1.47175 0.259510i −0.620475 0.784226i \(-0.713060\pi\)
−0.851277 + 0.524716i \(0.824171\pi\)
\(152\) −6.48334 6.73333i −0.525868 0.546145i
\(153\) 0 0
\(154\) −13.0140 + 1.05595i −1.04870 + 0.0850912i
\(155\) 2.38539 + 2.00158i 0.191599 + 0.160770i
\(156\) 0 0
\(157\) 3.60079 + 20.4211i 0.287374 + 1.62978i 0.696680 + 0.717382i \(0.254660\pi\)
−0.409306 + 0.912397i \(0.634229\pi\)
\(158\) 1.09816 + 0.301683i 0.0873647 + 0.0240006i
\(159\) 0 0
\(160\) −0.697610 2.97567i −0.0551509 0.235248i
\(161\) 7.60485i 0.599346i
\(162\) 0 0
\(163\) 2.03697i 0.159548i −0.996813 0.0797739i \(-0.974580\pi\)
0.996813 0.0797739i \(-0.0254198\pi\)
\(164\) −15.3675 0.193767i −1.20000 0.0151306i
\(165\) 0 0
\(166\) −5.98994 + 21.8040i −0.464910 + 1.69232i
\(167\) −1.07213 6.08034i −0.0829637 0.470511i −0.997777 0.0666346i \(-0.978774\pi\)
0.914814 0.403876i \(-0.132337\pi\)
\(168\) 0 0
\(169\) −7.93963 6.66214i −0.610741 0.512472i
\(170\) 0.0487801 + 0.601186i 0.00374126 + 0.0461089i
\(171\) 0 0
\(172\) −2.58014 15.7947i −0.196734 1.20433i
\(173\) −14.6443 2.58218i −1.11338 0.196320i −0.413450 0.910527i \(-0.635676\pi\)
−0.699934 + 0.714207i \(0.746787\pi\)
\(174\) 0 0
\(175\) −2.97583 + 8.17603i −0.224952 + 0.618050i
\(176\) 9.55217 + 17.5526i 0.720022 + 1.32307i
\(177\) 0 0
\(178\) 8.03769 3.68653i 0.602450 0.276317i
\(179\) −2.80761 4.86292i −0.209850 0.363472i 0.741817 0.670603i \(-0.233964\pi\)
−0.951667 + 0.307131i \(0.900631\pi\)
\(180\) 0 0
\(181\) −3.04279 + 5.27027i −0.226169 + 0.391736i −0.956670 0.291176i \(-0.905954\pi\)
0.730500 + 0.682912i \(0.239287\pi\)
\(182\) −0.396432 + 4.22434i −0.0293855 + 0.313129i
\(183\) 0 0
\(184\) −10.6398 + 4.71857i −0.784379 + 0.347858i
\(185\) −3.84115 4.57770i −0.282407 0.336560i
\(186\) 0 0
\(187\) −1.34881 3.70583i −0.0986349 0.270997i
\(188\) 2.21431 5.85308i 0.161495 0.426880i
\(189\) 0 0
\(190\) −2.07755 + 1.43528i −0.150721 + 0.104126i
\(191\) −4.55974 + 1.65961i −0.329931 + 0.120085i −0.501674 0.865057i \(-0.667282\pi\)
0.171743 + 0.985142i \(0.445060\pi\)
\(192\) 0 0
\(193\) 4.04332 3.39275i 0.291044 0.244215i −0.485561 0.874203i \(-0.661385\pi\)
0.776605 + 0.629988i \(0.216940\pi\)
\(194\) −9.38080 9.49982i −0.673502 0.682048i
\(195\) 0 0
\(196\) 6.25364 3.50617i 0.446689 0.250441i
\(197\) −2.31117 1.33435i −0.164664 0.0950687i 0.415403 0.909637i \(-0.363640\pi\)
−0.580067 + 0.814569i \(0.696974\pi\)
\(198\) 0 0
\(199\) −9.82614 + 5.67313i −0.696557 + 0.402157i −0.806064 0.591829i \(-0.798406\pi\)
0.109507 + 0.993986i \(0.465073\pi\)
\(200\) 13.2854 0.909529i 0.939418 0.0643134i
\(201\) 0 0
\(202\) 3.51216 + 13.4460i 0.247114 + 0.946060i
\(203\) 16.4598 + 5.99087i 1.15525 + 0.420477i
\(204\) 0 0
\(205\) −0.720954 + 4.08873i −0.0503536 + 0.285570i
\(206\) 4.21368 8.88951i 0.293581 0.619362i
\(207\) 0 0
\(208\) 6.15619 2.06643i 0.426855 0.143281i
\(209\) 10.6125 12.6474i 0.734080 0.874842i
\(210\) 0 0
\(211\) 4.51015 0.795260i 0.310491 0.0547480i −0.0162314 0.999868i \(-0.505167\pi\)
0.326723 + 0.945120i \(0.394056\pi\)
\(212\) −1.76229 + 0.616372i −0.121035 + 0.0423326i
\(213\) 0 0
\(214\) 2.06067 2.90381i 0.140865 0.198501i
\(215\) −4.32342 −0.294855
\(216\) 0 0
\(217\) −10.6509 −0.723033
\(218\) 4.72181 6.65378i 0.319802 0.450651i
\(219\) 0 0
\(220\) 5.09574 1.78227i 0.343555 0.120161i
\(221\) −1.26205 + 0.222534i −0.0848949 + 0.0149693i
\(222\) 0 0
\(223\) 11.8712 14.1475i 0.794953 0.947388i −0.204552 0.978856i \(-0.565574\pi\)
0.999505 + 0.0314676i \(0.0100181\pi\)
\(224\) 8.37028 + 6.26314i 0.559263 + 0.418473i
\(225\) 0 0
\(226\) −2.68603 + 5.66667i −0.178672 + 0.376941i
\(227\) 2.30342 13.0633i 0.152883 0.867043i −0.807813 0.589439i \(-0.799349\pi\)
0.960696 0.277604i \(-0.0895402\pi\)
\(228\) 0 0
\(229\) 3.24361 + 1.18058i 0.214344 + 0.0780147i 0.446960 0.894554i \(-0.352507\pi\)
−0.232617 + 0.972569i \(0.574729\pi\)
\(230\) 0.794639 + 3.04222i 0.0523969 + 0.200598i
\(231\) 0 0
\(232\) −1.83104 26.7458i −0.120214 1.75595i
\(233\) 14.1574 8.17379i 0.927483 0.535483i 0.0414686 0.999140i \(-0.486796\pi\)
0.886015 + 0.463657i \(0.153463\pi\)
\(234\) 0 0
\(235\) −1.46406 0.845277i −0.0955050 0.0551398i
\(236\) −4.63212 + 2.59704i −0.301525 + 0.169053i
\(237\) 0 0
\(238\) −1.44960 1.46799i −0.0939634 0.0951557i
\(239\) −0.797855 + 0.669480i −0.0516089 + 0.0433050i −0.668227 0.743957i \(-0.732947\pi\)
0.616618 + 0.787262i \(0.288502\pi\)
\(240\) 0 0
\(241\) 15.4743 5.63219i 0.996788 0.362801i 0.208443 0.978035i \(-0.433160\pi\)
0.788345 + 0.615233i \(0.210938\pi\)
\(242\) −16.2414 + 11.2204i −1.04403 + 0.721275i
\(243\) 0 0
\(244\) −3.97192 + 10.4990i −0.254276 + 0.672128i
\(245\) −0.662426 1.82000i −0.0423208 0.116276i
\(246\) 0 0
\(247\) −3.44860 4.10988i −0.219429 0.261506i
\(248\) 6.60858 + 14.9016i 0.419645 + 0.946252i
\(249\) 0 0
\(250\) 0.693078 7.38539i 0.0438341 0.467093i
\(251\) 6.70961 11.6214i 0.423507 0.733535i −0.572773 0.819714i \(-0.694132\pi\)
0.996280 + 0.0861790i \(0.0274657\pi\)
\(252\) 0 0
\(253\) −10.2792 17.8040i −0.646245 1.11933i
\(254\) −5.15233 + 2.36314i −0.323286 + 0.148277i
\(255\) 0 0
\(256\) 3.56916 15.5968i 0.223073 0.974802i
\(257\) −0.987706 + 2.71370i −0.0616114 + 0.169276i −0.966679 0.255992i \(-0.917598\pi\)
0.905068 + 0.425268i \(0.139820\pi\)
\(258\) 0 0
\(259\) 20.1293 + 3.54934i 1.25077 + 0.220545i
\(260\) −0.282819 1.73131i −0.0175397 0.107372i
\(261\) 0 0
\(262\) 0.275044 + 3.38975i 0.0169922 + 0.209420i
\(263\) 10.7439 + 9.01519i 0.662496 + 0.555900i 0.910834 0.412773i \(-0.135440\pi\)
−0.248338 + 0.968674i \(0.579884\pi\)
\(264\) 0 0
\(265\) 0.0875803 + 0.496692i 0.00538001 + 0.0305116i
\(266\) 2.28799 8.32852i 0.140286 0.510654i
\(267\) 0 0
\(268\) 12.6060 + 0.158947i 0.770035 + 0.00970923i
\(269\) 20.1185i 1.22665i 0.789831 + 0.613325i \(0.210168\pi\)
−0.789831 + 0.613325i \(0.789832\pi\)
\(270\) 0 0
\(271\) 19.1968i 1.16612i 0.812428 + 0.583062i \(0.198145\pi\)
−0.812428 + 0.583062i \(0.801855\pi\)
\(272\) −1.15441 + 2.93895i −0.0699967 + 0.178200i
\(273\) 0 0
\(274\) −5.84213 1.60493i −0.352936 0.0969577i
\(275\) 4.08436 + 23.1635i 0.246296 + 1.39681i
\(276\) 0 0
\(277\) 20.3674 + 17.0903i 1.22376 + 1.02686i 0.998619 + 0.0525311i \(0.0167289\pi\)
0.225141 + 0.974326i \(0.427716\pi\)
\(278\) −25.1350 + 2.03945i −1.50750 + 0.122318i
\(279\) 0 0
\(280\) 2.03437 1.95885i 0.121577 0.117063i
\(281\) −2.17919 0.384249i −0.129999 0.0229224i 0.108270 0.994122i \(-0.465469\pi\)
−0.238269 + 0.971199i \(0.576580\pi\)
\(282\) 0 0
\(283\) −8.19432 + 22.5137i −0.487102 + 1.33830i 0.416192 + 0.909277i \(0.363365\pi\)
−0.903293 + 0.429024i \(0.858858\pi\)
\(284\) 11.8267 13.7389i 0.701784 0.815255i
\(285\) 0 0
\(286\) 4.78177 + 10.4256i 0.282752 + 0.616480i
\(287\) −7.10053 12.2985i −0.419131 0.725957i
\(288\) 0 0
\(289\) −8.18843 + 14.1828i −0.481673 + 0.834281i
\(290\) −7.21051 0.676667i −0.423416 0.0397353i
\(291\) 0 0
\(292\) −22.6813 4.29485i −1.32732 0.251337i
\(293\) 17.5281 + 20.8891i 1.02400 + 1.22036i 0.975149 + 0.221550i \(0.0711116\pi\)
0.0488514 + 0.998806i \(0.484444\pi\)
\(294\) 0 0
\(295\) 0.490663 + 1.34809i 0.0285675 + 0.0784886i
\(296\) −7.52378 30.3649i −0.437311 1.76492i
\(297\) 0 0
\(298\) 9.60456 + 13.9024i 0.556377 + 0.805347i
\(299\) −6.27769 + 2.28489i −0.363048 + 0.132139i
\(300\) 0 0
\(301\) 11.3283 9.50559i 0.652953 0.547893i
\(302\) −18.4796 + 18.2481i −1.06338 + 1.05006i
\(303\) 0 0
\(304\) −13.0719 + 1.96649i −0.749727 + 0.112786i
\(305\) 2.62617 + 1.51622i 0.150374 + 0.0868184i
\(306\) 0 0
\(307\) 21.0055 12.1276i 1.19885 0.692156i 0.238551 0.971130i \(-0.423328\pi\)
0.960299 + 0.278974i \(0.0899944\pi\)
\(308\) −9.43343 + 15.8736i −0.537519 + 0.904480i
\(309\) 0 0
\(310\) 4.26077 1.11293i 0.241995 0.0632101i
\(311\) −18.0900 6.58424i −1.02579 0.373358i −0.226315 0.974054i \(-0.572668\pi\)
−0.799477 + 0.600696i \(0.794890\pi\)
\(312\) 0 0
\(313\) −1.18433 + 6.71666i −0.0669422 + 0.379648i 0.932869 + 0.360216i \(0.117297\pi\)
−0.999811 + 0.0194321i \(0.993814\pi\)
\(314\) 26.4991 + 12.5607i 1.49543 + 0.708841i
\(315\) 0 0
\(316\) 1.24672 1.01961i 0.0701335 0.0573578i
\(317\) 7.41728 8.83957i 0.416596 0.496480i −0.516409 0.856342i \(-0.672732\pi\)
0.933006 + 0.359862i \(0.117176\pi\)
\(318\) 0 0
\(319\) 46.6323 8.22253i 2.61091 0.460373i
\(320\) −4.00286 1.63086i −0.223767 0.0911680i
\(321\) 0 0
\(322\) −8.77082 6.22416i −0.488779 0.346859i
\(323\) 2.60873 0.145154
\(324\) 0 0
\(325\) 7.64329 0.423973
\(326\) −2.34928 1.66715i −0.130114 0.0923349i
\(327\) 0 0
\(328\) −12.8010 + 17.5651i −0.706816 + 0.969870i
\(329\) 5.69461 1.00411i 0.313954 0.0553586i
\(330\) 0 0
\(331\) −13.2173 + 15.7517i −0.726487 + 0.865793i −0.995244 0.0974147i \(-0.968943\pi\)
0.268757 + 0.963208i \(0.413387\pi\)
\(332\) 20.2446 + 24.7537i 1.11106 + 1.35854i
\(333\) 0 0
\(334\) −7.89005 3.73993i −0.431724 0.204640i
\(335\) 0.591400 3.35399i 0.0323116 0.183248i
\(336\) 0 0
\(337\) −10.0326 3.65156i −0.546509 0.198913i 0.0539858 0.998542i \(-0.482807\pi\)
−0.600495 + 0.799629i \(0.705030\pi\)
\(338\) −14.1817 + 3.70432i −0.771384 + 0.201489i
\(339\) 0 0
\(340\) 0.733284 + 0.435780i 0.0397679 + 0.0236335i
\(341\) −24.9354 + 14.3964i −1.35033 + 0.779611i
\(342\) 0 0
\(343\) 16.9404 + 9.78053i 0.914694 + 0.528099i
\(344\) −20.3280 9.95137i −1.09601 0.536542i
\(345\) 0 0
\(346\) −14.9636 + 14.7762i −0.804451 + 0.794371i
\(347\) 0.957389 0.803344i 0.0513953 0.0431258i −0.616728 0.787176i \(-0.711542\pi\)
0.668123 + 0.744050i \(0.267098\pi\)
\(348\) 0 0
\(349\) −18.0738 + 6.57834i −0.967470 + 0.352130i −0.776957 0.629554i \(-0.783238\pi\)
−0.190514 + 0.981685i \(0.561015\pi\)
\(350\) 6.99401 + 10.1237i 0.373846 + 0.541136i
\(351\) 0 0
\(352\) 28.0616 + 3.34912i 1.49569 + 0.178509i
\(353\) 2.12947 + 5.85067i 0.113340 + 0.311400i 0.983374 0.181593i \(-0.0581253\pi\)
−0.870034 + 0.492992i \(0.835903\pi\)
\(354\) 0 0
\(355\) −3.14788 3.75150i −0.167072 0.199109i
\(356\) 2.32667 12.2872i 0.123313 0.651223i
\(357\) 0 0
\(358\) −7.90637 0.741970i −0.417865 0.0392143i
\(359\) −4.51666 + 7.82308i −0.238380 + 0.412886i −0.960250 0.279143i \(-0.909950\pi\)
0.721870 + 0.692029i \(0.243283\pi\)
\(360\) 0 0
\(361\) −4.03929 6.99626i −0.212594 0.368224i
\(362\) 3.58794 + 7.82275i 0.188578 + 0.411155i
\(363\) 0 0
\(364\) 4.54756 + 3.91461i 0.238357 + 0.205181i
\(365\) −2.13288 + 5.86005i −0.111640 + 0.306729i
\(366\) 0 0
\(367\) −7.28951 1.28534i −0.380509 0.0670941i −0.0198778 0.999802i \(-0.506328\pi\)
−0.360632 + 0.932708i \(0.617439\pi\)
\(368\) −3.26612 + 16.1330i −0.170258 + 0.840993i
\(369\) 0 0
\(370\) −8.42333 + 0.683467i −0.437908 + 0.0355318i
\(371\) −1.32152 1.10889i −0.0686099 0.0575705i
\(372\) 0 0
\(373\) 0.532880 + 3.02211i 0.0275915 + 0.156479i 0.995491 0.0948598i \(-0.0302403\pi\)
−0.967899 + 0.251339i \(0.919129\pi\)
\(374\) −5.37793 1.47741i −0.278086 0.0763952i
\(375\) 0 0
\(376\) −4.93817 7.34423i −0.254667 0.378750i
\(377\) 15.3873i 0.792486i
\(378\) 0 0
\(379\) 30.1832i 1.55041i −0.631712 0.775203i \(-0.717647\pi\)
0.631712 0.775203i \(-0.282353\pi\)
\(380\) −0.0450234 + 3.57078i −0.00230965 + 0.183177i
\(381\) 0 0
\(382\) −1.81784 + 6.61714i −0.0930090 + 0.338562i
\(383\) −3.37652 19.1492i −0.172532 0.978479i −0.940954 0.338535i \(-0.890069\pi\)
0.768422 0.639944i \(-0.221042\pi\)
\(384\) 0 0
\(385\) 3.82124 + 3.20640i 0.194748 + 0.163413i
\(386\) −0.603681 7.44002i −0.0307266 0.378687i
\(387\) 0 0
\(388\) −18.6340 + 3.04396i −0.945999 + 0.154534i
\(389\) 20.0904 + 3.54247i 1.01862 + 0.179610i 0.657933 0.753076i \(-0.271431\pi\)
0.360688 + 0.932687i \(0.382542\pi\)
\(390\) 0 0
\(391\) 1.11102 3.05249i 0.0561865 0.154371i
\(392\) 1.07454 10.0821i 0.0542725 0.509221i
\(393\) 0 0
\(394\) −3.43050 + 1.57342i −0.172826 + 0.0792676i
\(395\) −0.217544 0.376797i −0.0109458 0.0189587i
\(396\) 0 0
\(397\) −8.78858 + 15.2223i −0.441086 + 0.763984i −0.997770 0.0667406i \(-0.978740\pi\)
0.556684 + 0.830724i \(0.312073\pi\)
\(398\) −1.49924 + 15.9758i −0.0751504 + 0.800796i
\(399\) 0 0
\(400\) 9.82439 16.0667i 0.491220 0.803334i
\(401\) 15.5813 + 18.5691i 0.778094 + 0.927297i 0.998846 0.0480334i \(-0.0152954\pi\)
−0.220751 + 0.975330i \(0.570851\pi\)
\(402\) 0 0
\(403\) 3.20010 + 8.79220i 0.159408 + 0.437971i
\(404\) 18.3821 + 6.95422i 0.914543 + 0.345986i
\(405\) 0 0
\(406\) 20.3808 14.0802i 1.01148 0.698788i
\(407\) 51.9231 18.8984i 2.57373 0.936761i
\(408\) 0 0
\(409\) 15.8369 13.2887i 0.783085 0.657086i −0.160939 0.986964i \(-0.551452\pi\)
0.944024 + 0.329878i \(0.107008\pi\)
\(410\) 4.12555 + 4.17790i 0.203747 + 0.206332i
\(411\) 0 0
\(412\) −6.80378 12.1353i −0.335198 0.597863i
\(413\) −4.24958 2.45350i −0.209108 0.120729i
\(414\) 0 0
\(415\) 7.48135 4.31936i 0.367245 0.212029i
\(416\) 2.65526 8.79132i 0.130185 0.431030i
\(417\) 0 0
\(418\) −5.90081 22.5908i −0.288618 1.10495i
\(419\) −8.00463 2.91345i −0.391052 0.142331i 0.139009 0.990291i \(-0.455608\pi\)
−0.530060 + 0.847960i \(0.677831\pi\)
\(420\) 0 0
\(421\) −2.47727 + 14.0493i −0.120735 + 0.684721i 0.863015 + 0.505178i \(0.168573\pi\)
−0.983750 + 0.179543i \(0.942538\pi\)
\(422\) 2.77412 5.85252i 0.135042 0.284896i
\(423\) 0 0
\(424\) −0.731466 + 2.53695i −0.0355231 + 0.123205i
\(425\) −2.38892 + 2.84701i −0.115880 + 0.138100i
\(426\) 0 0
\(427\) −10.2147 + 1.80113i −0.494325 + 0.0871629i
\(428\) −1.66247 4.75323i −0.0803586 0.229756i
\(429\) 0 0
\(430\) −3.53849 + 4.98629i −0.170641 + 0.240460i
\(431\) −1.49028 −0.0717841 −0.0358920 0.999356i \(-0.511427\pi\)
−0.0358920 + 0.999356i \(0.511427\pi\)
\(432\) 0 0
\(433\) 2.83288 0.136139 0.0680697 0.997681i \(-0.478316\pi\)
0.0680697 + 0.997681i \(0.478316\pi\)
\(434\) −8.71723 + 12.2839i −0.418440 + 0.589648i
\(435\) 0 0
\(436\) −3.80938 10.8915i −0.182436 0.521609i
\(437\) 13.3927 2.36150i 0.640662 0.112966i
\(438\) 0 0
\(439\) −17.2666 + 20.5775i −0.824089 + 0.982112i −0.999997 0.00229504i \(-0.999269\pi\)
0.175908 + 0.984407i \(0.443714\pi\)
\(440\) 2.11507 7.33571i 0.100832 0.349716i
\(441\) 0 0
\(442\) −0.776270 + 1.63768i −0.0369234 + 0.0778966i
\(443\) −4.52430 + 25.6586i −0.214956 + 1.21908i 0.666027 + 0.745928i \(0.267994\pi\)
−0.880983 + 0.473148i \(0.843118\pi\)
\(444\) 0 0
\(445\) −3.17460 1.15546i −0.150490 0.0547740i
\(446\) −6.60069 25.2703i −0.312552 1.19658i
\(447\) 0 0
\(448\) 14.0740 4.52757i 0.664935 0.213908i
\(449\) −19.5356 + 11.2789i −0.921940 + 0.532282i −0.884254 0.467007i \(-0.845332\pi\)
−0.0376867 + 0.999290i \(0.511999\pi\)
\(450\) 0 0
\(451\) −33.2467 19.1950i −1.56553 0.903857i
\(452\) 4.33711 + 7.73572i 0.204000 + 0.363858i
\(453\) 0 0
\(454\) −13.1810 13.3482i −0.618613 0.626462i
\(455\) 1.24174 1.04194i 0.0582137 0.0488471i
\(456\) 0 0
\(457\) −13.9247 + 5.06817i −0.651370 + 0.237079i −0.646506 0.762909i \(-0.723770\pi\)
−0.00486385 + 0.999988i \(0.501548\pi\)
\(458\) 4.01630 2.77468i 0.187669 0.129652i
\(459\) 0 0
\(460\) 4.15902 + 1.57342i 0.193915 + 0.0733611i
\(461\) −10.5924 29.1025i −0.493339 1.35544i −0.897606 0.440798i \(-0.854696\pi\)
0.404267 0.914641i \(-0.367527\pi\)
\(462\) 0 0
\(463\) 14.7162 + 17.5380i 0.683918 + 0.815062i 0.990606 0.136748i \(-0.0436651\pi\)
−0.306687 + 0.951810i \(0.599221\pi\)
\(464\) −32.3451 19.7782i −1.50158 0.918182i
\(465\) 0 0
\(466\) 2.16010 23.0178i 0.100065 1.06628i
\(467\) 17.9763 31.1359i 0.831844 1.44080i −0.0647308 0.997903i \(-0.520619\pi\)
0.896575 0.442893i \(-0.146048\pi\)
\(468\) 0 0
\(469\) 5.82458 + 10.0885i 0.268954 + 0.465842i
\(470\) −2.17313 + 0.996718i −0.100239 + 0.0459752i
\(471\) 0 0
\(472\) −0.795920 + 7.46785i −0.0366352 + 0.343736i
\(473\) 13.6729 37.5659i 0.628680 1.72728i
\(474\) 0 0
\(475\) −15.3227 2.70181i −0.703054 0.123967i
\(476\) −2.87948 + 0.470377i −0.131981 + 0.0215597i
\(477\) 0 0
\(478\) 0.119122 + 1.46811i 0.00544853 + 0.0671500i
\(479\) −15.6682 13.1472i −0.715899 0.600711i 0.210348 0.977627i \(-0.432540\pi\)
−0.926248 + 0.376916i \(0.876985\pi\)
\(480\) 0 0
\(481\) −3.11797 17.6829i −0.142167 0.806269i
\(482\) 6.16918 22.4565i 0.280998 1.02286i
\(483\) 0 0
\(484\) −0.351972 + 27.9148i −0.0159987 + 1.26885i
\(485\) 5.10063i 0.231608i
\(486\) 0 0
\(487\) 17.0248i 0.771469i −0.922610 0.385734i \(-0.873948\pi\)
0.922610 0.385734i \(-0.126052\pi\)
\(488\) 8.85786 + 13.1737i 0.400976 + 0.596347i
\(489\) 0 0
\(490\) −2.64120 0.725584i −0.119317 0.0327785i
\(491\) 2.46802 + 13.9968i 0.111380 + 0.631668i 0.988479 + 0.151358i \(0.0483647\pi\)
−0.877099 + 0.480310i \(0.840524\pi\)
\(492\) 0 0
\(493\) 5.73153 + 4.80932i 0.258135 + 0.216601i
\(494\) −7.56250 + 0.613620i −0.340253 + 0.0276080i
\(495\) 0 0
\(496\) 22.5951 + 4.57435i 1.01455 + 0.205394i
\(497\) 16.4963 + 2.90874i 0.739960 + 0.130475i
\(498\) 0 0
\(499\) −2.45044 + 6.73253i −0.109697 + 0.301390i −0.982379 0.186899i \(-0.940156\pi\)
0.872682 + 0.488288i \(0.162379\pi\)
\(500\) −7.95046 6.84388i −0.355555 0.306068i
\(501\) 0 0
\(502\) −7.91171 17.2498i −0.353117 0.769896i
\(503\) 2.15953 + 3.74041i 0.0962886 + 0.166777i 0.910146 0.414288i \(-0.135969\pi\)
−0.813857 + 0.581065i \(0.802636\pi\)
\(504\) 0 0
\(505\) 2.65467 4.59802i 0.118131 0.204609i
\(506\) −28.9467 2.71649i −1.28684 0.120763i
\(507\) 0 0
\(508\) −1.49145 + 7.87639i −0.0661723 + 0.349458i
\(509\) −25.4341 30.3112i −1.12735 1.34352i −0.931861 0.362816i \(-0.881815\pi\)
−0.195488 0.980706i \(-0.562629\pi\)
\(510\) 0 0
\(511\) −7.29543 20.0440i −0.322731 0.886696i
\(512\) −15.0670 16.8816i −0.665872 0.746066i
\(513\) 0 0
\(514\) 2.32138 + 3.36016i 0.102392 + 0.148210i
\(515\) −3.53174 + 1.28545i −0.155627 + 0.0566436i
\(516\) 0 0
\(517\) 11.9747 10.0479i 0.526646 0.441908i
\(518\) 20.5683 20.3106i 0.903719 0.892396i
\(519\) 0 0
\(520\) −2.22823 1.09081i −0.0977144 0.0478351i
\(521\) −39.1169 22.5841i −1.71374 0.989429i −0.929380 0.369123i \(-0.879658\pi\)
−0.784360 0.620305i \(-0.787009\pi\)
\(522\) 0 0
\(523\) 2.99933 1.73166i 0.131152 0.0757204i −0.432989 0.901399i \(-0.642541\pi\)
0.564140 + 0.825679i \(0.309208\pi\)
\(524\) 4.13457 + 2.45712i 0.180620 + 0.107340i
\(525\) 0 0
\(526\) 19.1907 5.01268i 0.836754 0.218563i
\(527\) −4.27516 1.55603i −0.186229 0.0677817i
\(528\) 0 0
\(529\) −1.05337 + 5.97395i −0.0457986 + 0.259737i
\(530\) 0.644525 + 0.305508i 0.0279964 + 0.0132704i
\(531\) 0 0
\(532\) −7.73284 9.45523i −0.335261 0.409936i
\(533\) −8.01885 + 9.55650i −0.347335 + 0.413938i
\(534\) 0 0
\(535\) −1.33967 + 0.236221i −0.0579192 + 0.0102127i
\(536\) 10.5007 14.4087i 0.453559 0.622360i
\(537\) 0 0
\(538\) 23.2031 + 16.4660i 1.00036 + 0.709898i
\(539\) 17.9088 0.771386
\(540\) 0 0
\(541\) −14.6206 −0.628588 −0.314294 0.949326i \(-0.601768\pi\)
−0.314294 + 0.949326i \(0.601768\pi\)
\(542\) 22.1401 + 15.7116i 0.950997 + 0.674869i
\(543\) 0 0
\(544\) 2.44473 + 3.73679i 0.104817 + 0.160213i
\(545\) −3.06972 + 0.541274i −0.131492 + 0.0231856i
\(546\) 0 0
\(547\) 8.74169 10.4179i 0.373768 0.445439i −0.546069 0.837740i \(-0.683876\pi\)
0.919837 + 0.392301i \(0.128321\pi\)
\(548\) −6.63247 + 5.42429i −0.283325 + 0.231714i
\(549\) 0 0
\(550\) 30.0578 + 14.2475i 1.28167 + 0.607517i
\(551\) −5.43921 + 30.8473i −0.231718 + 1.31414i
\(552\) 0 0
\(553\) 1.39845 + 0.508994i 0.0594681 + 0.0216446i
\(554\) 36.3802 9.50266i 1.54565 0.403729i
\(555\) 0 0
\(556\) −18.2196 + 30.6579i −0.772681 + 1.30019i
\(557\) −5.66207 + 3.26900i −0.239909 + 0.138512i −0.615135 0.788422i \(-0.710899\pi\)
0.375226 + 0.926933i \(0.377565\pi\)
\(558\) 0 0
\(559\) −11.2503 6.49539i −0.475839 0.274726i
\(560\) −0.594147 3.94949i −0.0251073 0.166897i
\(561\) 0 0
\(562\) −2.22671 + 2.19881i −0.0939280 + 0.0927512i
\(563\) −18.1068 + 15.1934i −0.763110 + 0.640325i −0.938934 0.344096i \(-0.888185\pi\)
0.175824 + 0.984422i \(0.443741\pi\)
\(564\) 0 0
\(565\) 2.25133 0.819417i 0.0947141 0.0344731i
\(566\) 19.2589 + 27.8769i 0.809511 + 1.17175i
\(567\) 0 0
\(568\) −6.16586 24.8845i −0.258714 1.04413i
\(569\) −3.88872 10.6842i −0.163024 0.447904i 0.831104 0.556117i \(-0.187709\pi\)
−0.994128 + 0.108213i \(0.965487\pi\)
\(570\) 0 0
\(571\) −14.2613 16.9960i −0.596818 0.711260i 0.380083 0.924952i \(-0.375895\pi\)
−0.976901 + 0.213692i \(0.931451\pi\)
\(572\) 15.9377 + 3.01791i 0.666388 + 0.126185i
\(573\) 0 0
\(574\) −19.9955 1.87647i −0.834596 0.0783223i
\(575\) −9.68708 + 16.7785i −0.403979 + 0.699712i
\(576\) 0 0
\(577\) 5.30268 + 9.18452i 0.220754 + 0.382357i 0.955037 0.296487i \(-0.0958150\pi\)
−0.734283 + 0.678843i \(0.762482\pi\)
\(578\) 9.65548 + 21.0517i 0.401615 + 0.875636i
\(579\) 0 0
\(580\) −6.68183 + 7.76220i −0.277448 + 0.322308i
\(581\) −10.1061 + 27.7664i −0.419273 + 1.15194i
\(582\) 0 0
\(583\) −4.59270 0.809817i −0.190210 0.0335392i
\(584\) −23.5167 + 22.6436i −0.973129 + 0.937000i
\(585\) 0 0
\(586\) 38.4376 3.11882i 1.58784 0.128837i
\(587\) −8.09141 6.78950i −0.333968 0.280233i 0.460346 0.887740i \(-0.347725\pi\)
−0.794314 + 0.607507i \(0.792170\pi\)
\(588\) 0 0
\(589\) −3.30739 18.7572i −0.136279 0.772875i
\(590\) 1.95636 + 0.537445i 0.0805419 + 0.0221263i
\(591\) 0 0
\(592\) −41.1782 16.1747i −1.69241 0.664777i
\(593\) 27.5676i 1.13207i 0.824383 + 0.566033i \(0.191522\pi\)
−0.824383 + 0.566033i \(0.808478\pi\)
\(594\) 0 0
\(595\) 0.788191i 0.0323127i
\(596\) 23.8948 + 0.301285i 0.978768 + 0.0123411i
\(597\) 0 0
\(598\) −2.50274 + 9.11025i −0.102345 + 0.372546i
\(599\) −2.13432 12.1044i −0.0872061 0.494571i −0.996859 0.0792006i \(-0.974763\pi\)
0.909653 0.415370i \(-0.136348\pi\)
\(600\) 0 0
\(601\) −9.68745 8.12873i −0.395159 0.331578i 0.423460 0.905915i \(-0.360815\pi\)
−0.818619 + 0.574337i \(0.805260\pi\)
\(602\) −1.69136 20.8450i −0.0689346 0.849578i
\(603\) 0 0
\(604\) 5.92128 + 36.2479i 0.240933 + 1.47491i
\(605\) 7.42709 + 1.30960i 0.301954 + 0.0532427i
\(606\) 0 0
\(607\) −2.12432 + 5.83652i −0.0862235 + 0.236897i −0.975309 0.220844i \(-0.929119\pi\)
0.889086 + 0.457741i \(0.151341\pi\)
\(608\) −8.43069 + 16.6856i −0.341909 + 0.676690i
\(609\) 0 0
\(610\) 3.89806 1.78787i 0.157828 0.0723886i
\(611\) −2.53984 4.39913i −0.102751 0.177970i
\(612\) 0 0
\(613\) 12.5009 21.6522i 0.504907 0.874524i −0.495077 0.868849i \(-0.664860\pi\)
0.999984 0.00567529i \(-0.00180651\pi\)
\(614\) 3.20497 34.1518i 0.129342 1.37826i
\(615\) 0 0
\(616\) 10.5865 + 23.8714i 0.426544 + 0.961807i
\(617\) 20.9893 + 25.0141i 0.844997 + 1.00703i 0.999818 + 0.0190859i \(0.00607561\pi\)
−0.154821 + 0.987943i \(0.549480\pi\)
\(618\) 0 0
\(619\) 13.2843 + 36.4984i 0.533942 + 1.46699i 0.854342 + 0.519711i \(0.173960\pi\)
−0.320401 + 0.947282i \(0.603818\pi\)
\(620\) 2.20365 5.82490i 0.0885006 0.233933i
\(621\) 0 0
\(622\) −22.3995 + 15.4748i −0.898136 + 0.620481i
\(623\) 10.8586 3.95219i 0.435039 0.158341i
\(624\) 0 0
\(625\) 15.8621 13.3099i 0.634483 0.532395i
\(626\) 6.77714 + 6.86313i 0.270869 + 0.274306i
\(627\) 0 0
\(628\) 36.1746 20.2816i 1.44352 0.809325i
\(629\) 7.56112 + 4.36541i 0.301482 + 0.174060i
\(630\) 0 0
\(631\) −27.2601 + 15.7386i −1.08521 + 0.626544i −0.932296 0.361696i \(-0.882198\pi\)
−0.152911 + 0.988240i \(0.548865\pi\)
\(632\) −0.155568 2.27237i −0.00618817 0.0903899i
\(633\) 0 0
\(634\) −4.12420 15.7892i −0.163793 0.627070i
\(635\) 2.03499 + 0.740675i 0.0807560 + 0.0293928i
\(636\) 0 0
\(637\) 1.01056 5.73118i 0.0400399 0.227078i
\(638\) 28.6828 60.5116i 1.13556 2.39568i
\(639\) 0 0
\(640\) −5.15703 + 3.28180i −0.203850 + 0.129725i
\(641\) −6.98262 + 8.32156i −0.275797 + 0.328682i −0.886107 0.463481i \(-0.846600\pi\)
0.610310 + 0.792163i \(0.291045\pi\)
\(642\) 0 0
\(643\) −10.8032 + 1.90489i −0.426036 + 0.0751217i −0.382555 0.923933i \(-0.624956\pi\)
−0.0434808 + 0.999054i \(0.513845\pi\)
\(644\) −14.3569 + 5.02141i −0.565741 + 0.197871i
\(645\) 0 0
\(646\) 2.13511 3.00870i 0.0840047 0.118376i
\(647\) −47.2138 −1.85616 −0.928082 0.372375i \(-0.878544\pi\)
−0.928082 + 0.372375i \(0.878544\pi\)
\(648\) 0 0
\(649\) −13.2652 −0.520703
\(650\) 6.25562 8.81515i 0.245366 0.345759i
\(651\) 0 0
\(652\) −3.84551 + 1.34499i −0.150602 + 0.0526740i
\(653\) 28.9484 5.10438i 1.13284 0.199750i 0.424367 0.905490i \(-0.360497\pi\)
0.708471 + 0.705740i \(0.249385\pi\)
\(654\) 0 0
\(655\) 0.835168 0.995314i 0.0326327 0.0388902i
\(656\) 9.78124 + 29.1397i 0.381893 + 1.13771i
\(657\) 0 0
\(658\) 3.50267 7.38952i 0.136548 0.288074i
\(659\) −0.0149056 + 0.0845336i −0.000580638 + 0.00329296i −0.985097 0.172001i \(-0.944977\pi\)
0.984516 + 0.175294i \(0.0560877\pi\)
\(660\) 0 0
\(661\) −12.6865 4.61752i −0.493449 0.179601i 0.0832963 0.996525i \(-0.473455\pi\)
−0.576745 + 0.816924i \(0.695677\pi\)
\(662\) 7.34915 + 28.1357i 0.285633 + 1.09352i
\(663\) 0 0
\(664\) 45.1181 3.08882i 1.75092 0.119870i
\(665\) −2.85766 + 1.64987i −0.110815 + 0.0639793i
\(666\) 0 0
\(667\) 33.7781 + 19.5018i 1.30789 + 0.755113i
\(668\) −10.7709 + 6.03882i −0.416739 + 0.233649i
\(669\) 0 0
\(670\) −3.38420 3.42714i −0.130743 0.132402i
\(671\) −21.4796 + 18.0235i −0.829211 + 0.695790i
\(672\) 0 0
\(673\) −5.01426 + 1.82504i −0.193285 + 0.0703501i −0.436849 0.899535i \(-0.643906\pi\)
0.243564 + 0.969885i \(0.421683\pi\)
\(674\) −12.4225 + 8.58215i −0.478498 + 0.330572i
\(675\) 0 0
\(676\) −7.33472 + 19.3879i −0.282105 + 0.745687i
\(677\) 8.95953 + 24.6161i 0.344343 + 0.946074i 0.984119 + 0.177512i \(0.0568050\pi\)
−0.639776 + 0.768562i \(0.720973\pi\)
\(678\) 0 0
\(679\) −11.2144 13.3648i −0.430368 0.512892i
\(680\) 1.10275 0.489048i 0.0422884 0.0187541i
\(681\) 0 0
\(682\) −3.80457 + 40.5412i −0.145684 + 1.55240i
\(683\) −16.4032 + 28.4113i −0.627653 + 1.08713i 0.360369 + 0.932810i \(0.382651\pi\)
−0.988021 + 0.154317i \(0.950682\pi\)
\(684\) 0 0
\(685\) 1.15732 + 2.00454i 0.0442190 + 0.0765895i
\(686\) 25.1449 11.5328i 0.960035 0.440325i
\(687\) 0 0
\(688\) −28.1145 + 15.3000i −1.07185 + 0.583308i
\(689\) −0.518316 + 1.42406i −0.0197463 + 0.0542525i
\(690\) 0 0
\(691\) 5.03144 + 0.887178i 0.191405 + 0.0337498i 0.268529 0.963272i \(-0.413463\pi\)
−0.0771239 + 0.997022i \(0.524574\pi\)
\(692\) 4.79469 + 29.3514i 0.182267 + 1.11577i
\(693\) 0 0
\(694\) −0.142941 1.76167i −0.00542598 0.0668721i
\(695\) 7.38027 + 6.19278i 0.279950 + 0.234906i
\(696\) 0 0
\(697\) −1.05334 5.97380i −0.0398982 0.226274i
\(698\) −7.20554 + 26.2289i −0.272734 + 0.992779i
\(699\) 0 0
\(700\) 17.4001 + 0.219395i 0.657662 + 0.00829235i
\(701\) 40.9095i 1.54513i −0.634936 0.772565i \(-0.718974\pi\)
0.634936 0.772565i \(-0.281026\pi\)
\(702\) 0 0
\(703\) 36.5515i 1.37856i
\(704\) 26.8295 29.6230i 1.01118 1.11646i
\(705\) 0 0
\(706\) 8.49054 + 2.33250i 0.319546 + 0.0877848i
\(707\) 3.15351 + 17.8844i 0.118600 + 0.672613i
\(708\) 0 0
\(709\) −12.2104 10.2458i −0.458572 0.384787i 0.384033 0.923319i \(-0.374535\pi\)
−0.842605 + 0.538532i \(0.818979\pi\)
\(710\) −6.90305 + 0.560112i −0.259067 + 0.0210206i
\(711\) 0 0
\(712\) −12.2669 12.7399i −0.459720 0.477446i
\(713\) −23.3564 4.11836i −0.874704 0.154234i
\(714\) 0 0
\(715\) 1.49874 4.11775i 0.0560496 0.153995i
\(716\) −7.32667 + 8.51131i −0.273811 + 0.318083i
\(717\) 0 0
\(718\) 5.32587 + 11.6119i 0.198760 + 0.433353i
\(719\) 15.8103 + 27.3843i 0.589626 + 1.02126i 0.994281 + 0.106793i \(0.0340582\pi\)
−0.404655 + 0.914469i \(0.632608\pi\)
\(720\) 0 0
\(721\) 6.42772 11.1331i 0.239381 0.414619i
\(722\) −11.3749 1.06747i −0.423328 0.0397271i
\(723\) 0 0
\(724\) 11.9587 + 2.26446i 0.444440 + 0.0841578i
\(725\) −28.6839 34.1841i −1.06529 1.26957i
\(726\) 0 0
\(727\) −9.85979 27.0896i −0.365680 1.00470i −0.976986 0.213302i \(-0.931578\pi\)
0.611307 0.791394i \(-0.290644\pi\)
\(728\) 8.23673 2.04089i 0.305273 0.0756403i
\(729\) 0 0
\(730\) 5.01286 + 7.25603i 0.185534 + 0.268558i
\(731\) 5.93575 2.16044i 0.219542 0.0799066i
\(732\) 0 0
\(733\) −25.8057 + 21.6536i −0.953157 + 0.799793i −0.979826 0.199851i \(-0.935954\pi\)
0.0266696 + 0.999644i \(0.491510\pi\)
\(734\) −7.44848 + 7.35515i −0.274928 + 0.271484i
\(735\) 0 0
\(736\) 15.9334 + 16.9709i 0.587313 + 0.625556i
\(737\) 27.2723 + 15.7457i 1.00459 + 0.580000i
\(738\) 0 0
\(739\) 10.3214 5.95905i 0.379678 0.219207i −0.298000 0.954566i \(-0.596320\pi\)
0.677678 + 0.735359i \(0.262986\pi\)
\(740\) −6.10579 + 10.2742i −0.224453 + 0.377686i
\(741\) 0 0
\(742\) −2.36049 + 0.616570i −0.0866564 + 0.0226350i
\(743\) 9.08444 + 3.30647i 0.333276 + 0.121302i 0.503237 0.864148i \(-0.332142\pi\)
−0.169962 + 0.985451i \(0.554364\pi\)
\(744\) 0 0
\(745\) 1.12100 6.35752i 0.0410703 0.232921i
\(746\) 3.92160 + 1.85886i 0.143580 + 0.0680576i
\(747\) 0 0
\(748\) −6.10548 + 4.99329i −0.223238 + 0.182573i
\(749\) 2.99088 3.56439i 0.109284 0.130240i
\(750\) 0 0
\(751\) −22.0213 + 3.88295i −0.803570 + 0.141691i −0.560324 0.828274i \(-0.689323\pi\)
−0.243246 + 0.969965i \(0.578212\pi\)
\(752\) −12.5119 0.315570i −0.456261 0.0115077i
\(753\) 0 0
\(754\) −17.7465 12.5937i −0.646288 0.458634i
\(755\) 9.92203 0.361100
\(756\) 0 0
\(757\) 3.40365 0.123708 0.0618540 0.998085i \(-0.480299\pi\)
0.0618540 + 0.998085i \(0.480299\pi\)
\(758\) −34.8109 24.7033i −1.26439 0.897265i
\(759\) 0 0
\(760\) 4.08141 + 2.97442i 0.148048 + 0.107894i
\(761\) −43.2514 + 7.62639i −1.56786 + 0.276457i −0.889034 0.457840i \(-0.848623\pi\)
−0.678829 + 0.734297i \(0.737512\pi\)
\(762\) 0 0
\(763\) 6.85328 8.16742i 0.248105 0.295680i
\(764\) 6.14387 + 7.51233i 0.222277 + 0.271787i
\(765\) 0 0
\(766\) −24.8486 11.7784i −0.897818 0.425571i
\(767\) −0.748530 + 4.24513i −0.0270279 + 0.153283i
\(768\) 0 0
\(769\) 43.4127 + 15.8009i 1.56550 + 0.569797i 0.971989 0.235027i \(-0.0755178\pi\)
0.593514 + 0.804823i \(0.297740\pi\)
\(770\) 6.82548 1.78284i 0.245973 0.0642492i
\(771\) 0 0
\(772\) −9.07480 5.39302i −0.326609 0.194099i
\(773\) 35.3857 20.4299i 1.27273 0.734813i 0.297232 0.954805i \(-0.403936\pi\)
0.975502 + 0.219992i \(0.0706031\pi\)
\(774\) 0 0
\(775\) 23.4991 + 13.5672i 0.844112 + 0.487348i
\(776\) −11.7403 + 23.9823i −0.421452 + 0.860914i
\(777\) 0 0
\(778\) 20.5285 20.2713i 0.735982 0.726760i
\(779\) 19.4537 16.3236i 0.697001 0.584853i
\(780\) 0 0
\(781\) 42.5518 15.4876i 1.52262 0.554189i
\(782\) −2.61119 3.77966i −0.0933760 0.135160i
\(783\) 0 0
\(784\) −10.7484 9.49091i −0.383871 0.338961i
\(785\) −3.83184 10.5279i −0.136764 0.375757i
\(786\) 0 0
\(787\) 26.6313 + 31.7379i 0.949302 + 1.13133i 0.991221 + 0.132214i \(0.0422085\pi\)
−0.0419189 + 0.999121i \(0.513347\pi\)
\(788\) −0.993029 + 5.24422i −0.0353752 + 0.186818i
\(789\) 0 0
\(790\) −0.612616 0.0574907i −0.0217959 0.00204543i
\(791\) −4.09738 + 7.09688i −0.145686 + 0.252336i
\(792\) 0 0
\(793\) 4.55584 + 7.89095i 0.161783 + 0.280216i
\(794\) 10.3632 + 22.5946i 0.367774 + 0.801854i
\(795\) 0 0
\(796\) 17.1982 + 14.8045i 0.609573 + 0.524730i
\(797\) −4.25196 + 11.6822i −0.150612 + 0.413803i −0.991938 0.126725i \(-0.959553\pi\)
0.841326 + 0.540528i \(0.181776\pi\)
\(798\) 0 0
\(799\) 2.43244 + 0.428905i 0.0860536 + 0.0151736i
\(800\) −10.4893 24.4804i −0.370852 0.865512i
\(801\) 0 0
\(802\) 34.1686 2.77243i 1.20653 0.0978979i
\(803\) −44.1723 37.0650i −1.55881 1.30799i
\(804\) 0 0
\(805\) 0.713493 + 4.04642i 0.0251473 + 0.142618i
\(806\) 12.7593 + 3.50521i 0.449428 + 0.123466i
\(807\) 0 0
\(808\) 23.0652 15.5088i 0.811431 0.545596i
\(809\) 4.57993i 0.161022i −0.996754 0.0805109i \(-0.974345\pi\)
0.996754 0.0805109i \(-0.0256552\pi\)
\(810\) 0 0
\(811\) 23.9708i 0.841727i −0.907124 0.420864i \(-0.861727\pi\)
0.907124 0.420864i \(-0.138273\pi\)
\(812\) 0.441681 35.0295i 0.0155000 1.22929i
\(813\) 0 0
\(814\) 20.7003 75.3512i 0.725545 2.64106i
\(815\) 0.191110 + 1.08384i 0.00669429 + 0.0379652i
\(816\) 0 0
\(817\) 20.2578 + 16.9983i 0.708731 + 0.594696i
\(818\) −2.36451 29.1411i −0.0826730 1.01890i
\(819\) 0 0
\(820\) 8.19500 1.33869i 0.286182 0.0467492i
\(821\) −7.46457 1.31620i −0.260515 0.0459359i 0.0418649 0.999123i \(-0.486670\pi\)
−0.302380 + 0.953187i \(0.597781\pi\)
\(822\) 0 0
\(823\) 15.9886 43.9282i 0.557326 1.53124i −0.266174 0.963925i \(-0.585760\pi\)
0.823500 0.567316i \(-0.192018\pi\)
\(824\) −19.5644 2.08516i −0.681558 0.0726402i
\(825\) 0 0
\(826\) −6.30772 + 2.89307i −0.219474 + 0.100663i
\(827\) −15.4331 26.7308i −0.536660 0.929522i −0.999081 0.0428620i \(-0.986352\pi\)
0.462421 0.886661i \(-0.346981\pi\)
\(828\) 0 0
\(829\) 5.56407 9.63724i 0.193248 0.334715i −0.753077 0.657933i \(-0.771431\pi\)
0.946325 + 0.323217i \(0.104764\pi\)
\(830\) 1.14148 12.1636i 0.0396215 0.422203i
\(831\) 0 0
\(832\) −7.96601 10.2576i −0.276172 0.355618i
\(833\) 1.81892 + 2.16771i 0.0630220 + 0.0751067i
\(834\) 0 0
\(835\) 1.14092 + 3.13466i 0.0394833 + 0.108479i
\(836\) −30.8839 11.6839i −1.06814 0.404095i
\(837\) 0 0
\(838\) −9.91149 + 6.84739i −0.342387 + 0.236539i
\(839\) 8.74658 3.18349i 0.301965 0.109906i −0.186594 0.982437i \(-0.559745\pi\)
0.488559 + 0.872531i \(0.337523\pi\)
\(840\) 0 0
\(841\) −46.6034 + 39.1049i −1.60701 + 1.34844i
\(842\) 14.1758 + 14.3557i 0.488531 + 0.494730i
\(843\) 0 0
\(844\) −4.47935 7.98942i −0.154186 0.275007i
\(845\) 4.84959 + 2.79991i 0.166831 + 0.0963200i
\(846\) 0 0
\(847\) −22.3399 + 12.8980i −0.767609 + 0.443179i
\(848\) 2.32725 + 2.91997i 0.0799180 + 0.100272i
\(849\) 0 0
\(850\) 1.32830 + 5.08531i 0.0455604 + 0.174425i
\(851\) 42.7690 + 15.5667i 1.46610 + 0.533618i
\(852\) 0 0
\(853\) 2.28870 12.9798i 0.0783634 0.444421i −0.920229 0.391381i \(-0.871998\pi\)
0.998592 0.0530406i \(-0.0168913\pi\)
\(854\) −6.28293 + 13.2550i −0.214997 + 0.453576i
\(855\) 0 0
\(856\) −6.84264 1.97290i −0.233877 0.0674324i
\(857\) 9.69516 11.5542i 0.331180 0.394685i −0.574599 0.818435i \(-0.694842\pi\)
0.905779 + 0.423750i \(0.139286\pi\)
\(858\) 0 0
\(859\) −24.5457 + 4.32808i −0.837490 + 0.147672i −0.575914 0.817511i \(-0.695354\pi\)
−0.261577 + 0.965183i \(0.584242\pi\)
\(860\) 2.85472 + 8.16202i 0.0973451 + 0.278323i
\(861\) 0 0
\(862\) −1.21971 + 1.71876i −0.0415435 + 0.0585413i
\(863\) 22.0216 0.749626 0.374813 0.927101i \(-0.377707\pi\)
0.374813 + 0.927101i \(0.377707\pi\)
\(864\) 0 0
\(865\) 8.03425 0.273173
\(866\) 2.31856 3.26721i 0.0787879 0.111024i
\(867\) 0 0
\(868\) 7.03272 + 20.1075i 0.238706 + 0.682493i
\(869\) 3.96195 0.698599i 0.134400 0.0236984i
\(870\) 0 0
\(871\) 6.57787 7.83921i 0.222883 0.265621i
\(872\) −15.6792 4.52070i −0.530964 0.153090i
\(873\) 0 0
\(874\) 8.23767 17.3789i 0.278643 0.587849i
\(875\) 1.68323 9.54610i 0.0569037 0.322717i
\(876\) 0 0
\(877\) −20.5090 7.46466i −0.692539 0.252064i −0.0283170 0.999599i \(-0.509015\pi\)
−0.664222 + 0.747535i \(0.731237\pi\)
\(878\) 9.60067 + 36.7555i 0.324007 + 1.24044i
\(879\) 0 0
\(880\) −6.72935 8.44324i −0.226846 0.284621i
\(881\) 7.29454 4.21150i 0.245759 0.141889i −0.372062 0.928208i \(-0.621349\pi\)
0.617821 + 0.786319i \(0.288016\pi\)
\(882\) 0 0
\(883\) −21.6426 12.4953i −0.728330 0.420502i 0.0894807 0.995989i \(-0.471479\pi\)
−0.817811 + 0.575487i \(0.804813\pi\)
\(884\) 1.25344 + 2.23564i 0.0421576 + 0.0751928i
\(885\) 0 0
\(886\) 25.8896 + 26.2181i 0.869779 + 0.880815i
\(887\) 34.3044 28.7848i 1.15183 0.966499i 0.152068 0.988370i \(-0.451407\pi\)
0.999761 + 0.0218707i \(0.00696222\pi\)
\(888\) 0 0
\(889\) −6.96058 + 2.53344i −0.233450 + 0.0849689i
\(890\) −3.93085 + 2.71564i −0.131762 + 0.0910286i
\(891\) 0 0
\(892\) −34.5470 13.0696i −1.15672 0.437604i
\(893\) 3.53665 + 9.71686i 0.118349 + 0.325162i
\(894\) 0 0
\(895\) 1.95013 + 2.32407i 0.0651855 + 0.0776850i
\(896\) 6.29710 19.9374i 0.210371 0.666062i
\(897\) 0 0
\(898\) −2.98068 + 31.7619i −0.0994666 + 1.05991i
\(899\) 27.3132 47.3078i 0.910945 1.57780i
\(900\) 0 0
\(901\) −0.368441 0.638158i −0.0122745 0.0212601i
\(902\) −49.3486 + 22.6340i −1.64313 + 0.753630i
\(903\) 0 0
\(904\) 12.4714 + 1.32920i 0.414794 + 0.0442085i
\(905\) 1.12456 3.08970i 0.0373817 0.102705i
\(906\) 0 0
\(907\) 31.5142 + 5.55680i 1.04641 + 0.184511i 0.670320 0.742072i \(-0.266157\pi\)
0.376091 + 0.926583i \(0.377268\pi\)
\(908\) −26.1826 + 4.27707i −0.868902 + 0.141939i
\(909\) 0 0
\(910\) −0.185396 2.28490i −0.00614582 0.0757436i
\(911\) 21.9054 + 18.3808i 0.725757 + 0.608983i 0.928971 0.370152i \(-0.120694\pi\)
−0.203214 + 0.979134i \(0.565139\pi\)
\(912\) 0 0
\(913\) 13.8708 + 78.6650i 0.459055 + 2.60343i
\(914\) −5.55139 + 20.2076i −0.183624 + 0.668410i
\(915\) 0 0
\(916\) 0.0870387 6.90300i 0.00287584 0.228082i
\(917\) 4.44416i 0.146759i
\(918\) 0 0
\(919\) 27.7726i 0.916132i 0.888918 + 0.458066i \(0.151458\pi\)
−0.888918 + 0.458066i \(0.848542\pi\)
\(920\) 5.21859 3.50892i 0.172052 0.115686i
\(921\) 0 0
\(922\) −42.2338 11.6024i −1.39090 0.382104i
\(923\) −2.55522 14.4914i −0.0841062 0.476990i
\(924\) 0 0
\(925\) −39.8899 33.4716i −1.31157 1.10054i
\(926\) 32.2714 2.61849i 1.06050 0.0860489i
\(927\) 0 0
\(928\) −49.2833 + 21.1168i −1.61780 + 0.693192i
\(929\) 9.40060 + 1.65758i 0.308424 + 0.0543834i 0.325718 0.945467i \(-0.394394\pi\)
−0.0172941 + 0.999850i \(0.505505\pi\)
\(930\) 0 0
\(931\) −4.05180 + 11.1322i −0.132792 + 0.364844i
\(932\) −24.7790 21.3301i −0.811663 0.698692i
\(933\) 0 0
\(934\) −21.1970 46.2154i −0.693585 1.51222i
\(935\) 1.06536 + 1.84527i 0.0348411 + 0.0603466i
\(936\) 0 0
\(937\) −1.13866 + 1.97222i −0.0371986 + 0.0644298i −0.884025 0.467439i \(-0.845177\pi\)
0.846827 + 0.531869i \(0.178510\pi\)
\(938\) 16.4023 + 1.53927i 0.535555 + 0.0502589i
\(939\) 0 0
\(940\) −0.629058 + 3.32208i −0.0205176 + 0.108354i
\(941\) 4.48164 + 5.34101i 0.146097 + 0.174112i 0.834130 0.551567i \(-0.185970\pi\)
−0.688033 + 0.725679i \(0.741526\pi\)
\(942\) 0 0
\(943\) −10.8153 29.7148i −0.352195 0.967647i
\(944\) 7.96140 + 7.02998i 0.259121 + 0.228806i
\(945\) 0 0
\(946\) −32.1350 46.5149i −1.04480 1.51233i
\(947\) −42.9198 + 15.6215i −1.39471 + 0.507631i −0.926603 0.376042i \(-0.877285\pi\)
−0.468103 + 0.883674i \(0.655063\pi\)
\(948\) 0 0
\(949\) −14.3541 + 12.0445i −0.465955 + 0.390982i
\(950\) −15.6569 + 15.4607i −0.507975 + 0.501611i
\(951\) 0 0
\(952\) −1.81420 + 3.70594i −0.0587987 + 0.120110i
\(953\) 26.2534 + 15.1574i 0.850431 + 0.490997i 0.860796 0.508950i \(-0.169966\pi\)
−0.0103652 + 0.999946i \(0.503299\pi\)
\(954\) 0 0
\(955\) 2.27046 1.31085i 0.0734704 0.0424181i
\(956\) 1.79070 + 1.06419i 0.0579154 + 0.0344183i
\(957\) 0 0
\(958\) −27.9865 + 7.31019i −0.904204 + 0.236181i
\(959\) −7.43966 2.70782i −0.240239 0.0874400i
\(960\) 0 0
\(961\) −0.384864 + 2.18267i −0.0124150 + 0.0704089i
\(962\) −22.9459 10.8765i −0.739805 0.350671i
\(963\) 0 0
\(964\) −20.8503 25.4944i −0.671544 0.821121i
\(965\) −1.83307 + 2.18457i −0.0590088 + 0.0703239i
\(966\) 0 0
\(967\) 30.8569 5.44090i 0.992290 0.174967i 0.346144 0.938181i \(-0.387491\pi\)
0.646146 + 0.763214i \(0.276380\pi\)
\(968\) 31.9066 + 23.2527i 1.02552 + 0.747370i
\(969\) 0 0
\(970\) 5.88265 + 4.17459i 0.188881 + 0.134038i
\(971\) −1.61116 −0.0517047 −0.0258523 0.999666i \(-0.508230\pi\)
−0.0258523 + 0.999666i \(0.508230\pi\)
\(972\) 0 0
\(973\) −32.9535 −1.05644
\(974\) −19.6351 13.9339i −0.629148 0.446471i
\(975\) 0 0
\(976\) 22.4432 + 0.566055i 0.718389 + 0.0181190i
\(977\) −26.4012 + 4.65524i −0.844648 + 0.148934i −0.579194 0.815190i \(-0.696633\pi\)
−0.265453 + 0.964124i \(0.585522\pi\)
\(978\) 0 0
\(979\) 20.0794 23.9297i 0.641741 0.764797i
\(980\) −2.99851 + 2.45230i −0.0957839 + 0.0783358i
\(981\) 0 0
\(982\) 18.1628 + 8.60924i 0.579597 + 0.274732i
\(983\) 4.56612 25.8958i 0.145637 0.825947i −0.821217 0.570616i \(-0.806704\pi\)
0.966854 0.255331i \(-0.0821844\pi\)
\(984\) 0 0
\(985\) 1.35492 + 0.493152i 0.0431715 + 0.0157131i
\(986\) 10.2376 2.67411i 0.326033 0.0851610i
\(987\) 0 0
\(988\) −5.48180 + 9.22419i −0.174399 + 0.293461i
\(989\) 28.5173 16.4645i 0.906797 0.523540i
\(990\) 0 0
\(991\) −20.2827 11.7102i −0.644302 0.371988i 0.141968 0.989871i \(-0.454657\pi\)
−0.786270 + 0.617883i \(0.787990\pi\)
\(992\) 23.7685 22.3155i 0.754652 0.708517i
\(993\) 0 0
\(994\) 16.8560 16.6448i 0.534641 0.527942i
\(995\) 4.69607 3.94047i 0.148876 0.124921i
\(996\) 0 0
\(997\) 5.48788 1.99742i 0.173803 0.0632590i −0.253653 0.967295i \(-0.581632\pi\)
0.427456 + 0.904036i \(0.359410\pi\)
\(998\) 5.75921 + 8.33636i 0.182304 + 0.263883i
\(999\) 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 324.2.l.a.143.12 96
3.2 odd 2 108.2.l.a.47.5 yes 96
4.3 odd 2 inner 324.2.l.a.143.1 96
9.2 odd 6 972.2.l.d.107.16 96
9.4 even 3 972.2.l.b.755.11 96
9.5 odd 6 972.2.l.c.755.6 96
9.7 even 3 972.2.l.a.107.1 96
12.11 even 2 108.2.l.a.47.16 yes 96
27.4 even 9 108.2.l.a.23.16 yes 96
27.5 odd 18 972.2.l.b.215.12 96
27.13 even 9 972.2.l.d.863.7 96
27.14 odd 18 972.2.l.a.863.10 96
27.22 even 9 972.2.l.c.215.5 96
27.23 odd 18 inner 324.2.l.a.179.1 96
36.7 odd 6 972.2.l.a.107.10 96
36.11 even 6 972.2.l.d.107.7 96
36.23 even 6 972.2.l.c.755.5 96
36.31 odd 6 972.2.l.b.755.12 96
108.23 even 18 inner 324.2.l.a.179.12 96
108.31 odd 18 108.2.l.a.23.5 96
108.59 even 18 972.2.l.b.215.11 96
108.67 odd 18 972.2.l.d.863.16 96
108.95 even 18 972.2.l.a.863.1 96
108.103 odd 18 972.2.l.c.215.6 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.2.l.a.23.5 96 108.31 odd 18
108.2.l.a.23.16 yes 96 27.4 even 9
108.2.l.a.47.5 yes 96 3.2 odd 2
108.2.l.a.47.16 yes 96 12.11 even 2
324.2.l.a.143.1 96 4.3 odd 2 inner
324.2.l.a.143.12 96 1.1 even 1 trivial
324.2.l.a.179.1 96 27.23 odd 18 inner
324.2.l.a.179.12 96 108.23 even 18 inner
972.2.l.a.107.1 96 9.7 even 3
972.2.l.a.107.10 96 36.7 odd 6
972.2.l.a.863.1 96 108.95 even 18
972.2.l.a.863.10 96 27.14 odd 18
972.2.l.b.215.11 96 108.59 even 18
972.2.l.b.215.12 96 27.5 odd 18
972.2.l.b.755.11 96 9.4 even 3
972.2.l.b.755.12 96 36.31 odd 6
972.2.l.c.215.5 96 27.22 even 9
972.2.l.c.215.6 96 108.103 odd 18
972.2.l.c.755.5 96 36.23 even 6
972.2.l.c.755.6 96 9.5 odd 6
972.2.l.d.107.7 96 36.11 even 6
972.2.l.d.107.16 96 9.2 odd 6
972.2.l.d.863.7 96 27.13 even 9
972.2.l.d.863.16 96 108.67 odd 18