# Properties

 Label 729.2.e.a.568.1 Level $729$ Weight $2$ Character 729.568 Analytic conductor $5.821$ Analytic rank $1$ Dimension $6$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$729 = 3^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 729.e (of order $$9$$, 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: $$5.82109430735$$ Analytic rank: $$1$$ Dimension: $$6$$ Coefficient field: $$\Q(\zeta_{18})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - x^{3} + 1$$ x^6 - x^3 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 243) Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 568.1 Root $$-0.173648 - 0.984808i$$ of defining polynomial Character $$\chi$$ $$=$$ 729.568 Dual form 729.2.e.a.163.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.826352 - 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(-0.673648 + 3.82045i) q^{5} +(-1.67365 + 1.40436i) q^{7} +(1.41875 + 2.45734i) q^{8} +O(q^{10})$$ $$q+(-0.826352 - 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(-0.673648 + 3.82045i) q^{5} +(-1.67365 + 1.40436i) q^{7} +(1.41875 + 2.45734i) q^{8} +(1.70574 - 2.95442i) q^{10} +(-0.0282185 - 0.160035i) q^{11} +(-2.26604 + 0.824773i) q^{13} +(1.80541 - 0.657115i) q^{14} +(-0.00727396 - 0.0412527i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.79813 - 3.11446i) q^{19} +(3.64543 - 3.05888i) q^{20} +(-0.0248149 + 0.140732i) q^{22} +(-2.17365 - 1.82391i) q^{23} +(-9.44356 - 3.43718i) q^{25} +2.12061 q^{26} +2.68004 q^{28} +(6.31180 + 2.29731i) q^{29} +(-3.97178 - 3.33272i) q^{31} +(0.979055 - 5.55250i) q^{32} +(-2.02094 + 1.69577i) q^{34} +(-4.23783 - 7.34013i) q^{35} +(3.31908 - 5.74881i) q^{37} +(0.549163 + 3.11446i) q^{38} +(-10.3439 + 3.76487i) q^{40} +(-5.45084 + 1.98394i) q^{41} +(-1.08125 - 6.13208i) q^{43} +(-0.0996702 + 0.172634i) q^{44} +(1.24763 + 2.16095i) q^{46} +(-5.66637 + 4.75465i) q^{47} +(-0.386659 + 2.19285i) q^{49} +(6.76991 + 5.68063i) q^{50} +(2.77972 + 1.01173i) q^{52} -1.40373 q^{53} +0.630415 q^{55} +(-5.82547 - 2.12030i) q^{56} +(-4.52481 - 3.79677i) q^{58} +(0.889185 - 5.04282i) q^{59} +(-2.89646 + 2.43042i) q^{61} +(2.27972 + 3.94858i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(-1.62449 - 9.21291i) q^{65} +(5.51114 - 2.00589i) q^{67} +(-3.45811 + 1.25865i) q^{68} +(1.29426 + 7.34013i) q^{70} +(-7.65910 + 13.2660i) q^{71} +(-4.34002 - 7.51714i) q^{73} +(-4.47178 + 3.75227i) q^{74} +(-0.766044 + 4.34445i) q^{76} +(0.271974 + 0.228213i) q^{77} +(1.19207 + 0.433877i) q^{79} +0.162504 q^{80} +5.10101 q^{82} +(-7.96451 - 2.89884i) q^{83} +(8.91534 + 7.48086i) q^{85} +(-0.950837 + 5.39246i) q^{86} +(0.353226 - 0.296392i) q^{88} +(3.86097 + 6.68739i) q^{89} +(2.63429 - 4.56272i) q^{91} +(0.604418 + 3.42782i) q^{92} +(6.11246 - 2.22475i) q^{94} +(13.1099 - 4.77163i) q^{95} +(-0.678396 - 3.84737i) q^{97} +(0.979055 - 1.69577i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - 6 q^{2} - 3 q^{5} - 9 q^{7} + 6 q^{8}+O(q^{10})$$ 6 * q - 6 * q^2 - 3 * q^5 - 9 * q^7 + 6 * q^8 $$6 q - 6 q^{2} - 3 q^{5} - 9 q^{7} + 6 q^{8} - 15 q^{11} - 9 q^{13} + 15 q^{14} - 18 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} + 27 q^{22} - 12 q^{23} - 27 q^{25} + 24 q^{26} - 24 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} - 6 q^{35} + 3 q^{37} + 15 q^{38} - 18 q^{40} - 21 q^{41} - 9 q^{43} - 15 q^{44} - 9 q^{46} - 15 q^{47} - 9 q^{49} + 12 q^{50} - 9 q^{52} - 36 q^{53} + 18 q^{55} + 21 q^{56} - 3 q^{59} - 27 q^{61} - 12 q^{62} - 12 q^{64} + 3 q^{65} + 27 q^{67} - 27 q^{68} + 18 q^{70} - 9 q^{71} - 6 q^{73} - 12 q^{74} + 24 q^{77} + 18 q^{79} + 6 q^{80} + 36 q^{82} - 15 q^{83} + 9 q^{85} + 6 q^{86} + 27 q^{88} + 6 q^{91} + 51 q^{92} - 27 q^{94} + 30 q^{95} - 36 q^{97} + 9 q^{98}+O(q^{100})$$ 6 * q - 6 * q^2 - 3 * q^5 - 9 * q^7 + 6 * q^8 - 15 * q^11 - 9 * q^13 + 15 * q^14 - 18 * q^16 + 9 * q^17 + 3 * q^19 + 6 * q^20 + 27 * q^22 - 12 * q^23 - 27 * q^25 + 24 * q^26 - 24 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^32 - 9 * q^34 - 6 * q^35 + 3 * q^37 + 15 * q^38 - 18 * q^40 - 21 * q^41 - 9 * q^43 - 15 * q^44 - 9 * q^46 - 15 * q^47 - 9 * q^49 + 12 * q^50 - 9 * q^52 - 36 * q^53 + 18 * q^55 + 21 * q^56 - 3 * q^59 - 27 * q^61 - 12 * q^62 - 12 * q^64 + 3 * q^65 + 27 * q^67 - 27 * q^68 + 18 * q^70 - 9 * q^71 - 6 * q^73 - 12 * q^74 + 24 * q^77 + 18 * q^79 + 6 * q^80 + 36 * q^82 - 15 * q^83 + 9 * q^85 + 6 * q^86 + 27 * q^88 + 6 * q^91 + 51 * q^92 - 27 * q^94 + 30 * q^95 - 36 * q^97 + 9 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{1}{9}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.826352 0.300767i −0.584319 0.212675i 0.0329100 0.999458i $$-0.489523\pi$$
−0.617229 + 0.786784i $$0.711745\pi$$
$$3$$ 0 0
$$4$$ −0.939693 0.788496i −0.469846 0.394248i
$$5$$ −0.673648 + 3.82045i −0.301265 + 1.70856i 0.339322 + 0.940670i $$0.389802\pi$$
−0.640586 + 0.767886i $$0.721309\pi$$
$$6$$ 0 0
$$7$$ −1.67365 + 1.40436i −0.632580 + 0.530797i −0.901729 0.432301i $$-0.857702\pi$$
0.269150 + 0.963098i $$0.413257\pi$$
$$8$$ 1.41875 + 2.45734i 0.501603 + 0.868802i
$$9$$ 0 0
$$10$$ 1.70574 2.95442i 0.539401 0.934271i
$$11$$ −0.0282185 0.160035i −0.00850820 0.0482524i 0.980258 0.197722i $$-0.0633544\pi$$
−0.988766 + 0.149470i $$0.952243\pi$$
$$12$$ 0 0
$$13$$ −2.26604 + 0.824773i −0.628488 + 0.228751i −0.636573 0.771217i $$-0.719649\pi$$
0.00808527 + 0.999967i $$0.497426\pi$$
$$14$$ 1.80541 0.657115i 0.482515 0.175621i
$$15$$ 0 0
$$16$$ −0.00727396 0.0412527i −0.00181849 0.0103132i
$$17$$ 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i $$-0.714811\pi$$
0.988583 + 0.150675i $$0.0481447\pi$$
$$18$$ 0 0
$$19$$ −1.79813 3.11446i −0.412520 0.714506i 0.582645 0.812727i $$-0.302018\pi$$
−0.995165 + 0.0982214i $$0.968685\pi$$
$$20$$ 3.64543 3.05888i 0.815143 0.683986i
$$21$$ 0 0
$$22$$ −0.0248149 + 0.140732i −0.00529056 + 0.0300043i
$$23$$ −2.17365 1.82391i −0.453237 0.380311i 0.387398 0.921912i $$-0.373374\pi$$
−0.840635 + 0.541601i $$0.817818\pi$$
$$24$$ 0 0
$$25$$ −9.44356 3.43718i −1.88871 0.687435i
$$26$$ 2.12061 0.415887
$$27$$ 0 0
$$28$$ 2.68004 0.506481
$$29$$ 6.31180 + 2.29731i 1.17207 + 0.426600i 0.853396 0.521264i $$-0.174539\pi$$
0.318677 + 0.947863i $$0.396761\pi$$
$$30$$ 0 0
$$31$$ −3.97178 3.33272i −0.713353 0.598574i 0.212185 0.977230i $$-0.431942\pi$$
−0.925538 + 0.378655i $$0.876387\pi$$
$$32$$ 0.979055 5.55250i 0.173074 0.981553i
$$33$$ 0 0
$$34$$ −2.02094 + 1.69577i −0.346589 + 0.290823i
$$35$$ −4.23783 7.34013i −0.716323 1.24071i
$$36$$ 0 0
$$37$$ 3.31908 5.74881i 0.545653 0.945099i −0.452912 0.891555i $$-0.649615\pi$$
0.998566 0.0535438i $$-0.0170517\pi$$
$$38$$ 0.549163 + 3.11446i 0.0890860 + 0.505232i
$$39$$ 0 0
$$40$$ −10.3439 + 3.76487i −1.63551 + 0.595278i
$$41$$ −5.45084 + 1.98394i −0.851278 + 0.309840i −0.730561 0.682847i $$-0.760741\pi$$
−0.120717 + 0.992687i $$0.538519\pi$$
$$42$$ 0 0
$$43$$ −1.08125 6.13208i −0.164889 0.935134i −0.949178 0.314739i $$-0.898083\pi$$
0.784289 0.620396i $$-0.213028\pi$$
$$44$$ −0.0996702 + 0.172634i −0.0150259 + 0.0260255i
$$45$$ 0 0
$$46$$ 1.24763 + 2.16095i 0.183952 + 0.318615i
$$47$$ −5.66637 + 4.75465i −0.826526 + 0.693537i −0.954490 0.298241i $$-0.903600\pi$$
0.127965 + 0.991779i $$0.459156\pi$$
$$48$$ 0 0
$$49$$ −0.386659 + 2.19285i −0.0552370 + 0.313265i
$$50$$ 6.76991 + 5.68063i 0.957411 + 0.803363i
$$51$$ 0 0
$$52$$ 2.77972 + 1.01173i 0.385477 + 0.140302i
$$53$$ −1.40373 −0.192818 −0.0964088 0.995342i $$-0.530736\pi$$
−0.0964088 + 0.995342i $$0.530736\pi$$
$$54$$ 0 0
$$55$$ 0.630415 0.0850051
$$56$$ −5.82547 2.12030i −0.778462 0.283337i
$$57$$ 0 0
$$58$$ −4.52481 3.79677i −0.594137 0.498540i
$$59$$ 0.889185 5.04282i 0.115762 0.656519i −0.870608 0.491977i $$-0.836274\pi$$
0.986370 0.164542i $$-0.0526146\pi$$
$$60$$ 0 0
$$61$$ −2.89646 + 2.43042i −0.370854 + 0.311183i −0.809099 0.587672i $$-0.800044\pi$$
0.438246 + 0.898855i $$0.355600\pi$$
$$62$$ 2.27972 + 3.94858i 0.289524 + 0.501470i
$$63$$ 0 0
$$64$$ −2.52094 + 4.36640i −0.315118 + 0.545801i
$$65$$ −1.62449 9.21291i −0.201493 1.14272i
$$66$$ 0 0
$$67$$ 5.51114 2.00589i 0.673293 0.245059i 0.0173282 0.999850i $$-0.494484\pi$$
0.655965 + 0.754791i $$0.272262\pi$$
$$68$$ −3.45811 + 1.25865i −0.419358 + 0.152634i
$$69$$ 0 0
$$70$$ 1.29426 + 7.34013i 0.154694 + 0.877313i
$$71$$ −7.65910 + 13.2660i −0.908968 + 1.57438i −0.0934675 + 0.995622i $$0.529795\pi$$
−0.815500 + 0.578756i $$0.803538\pi$$
$$72$$ 0 0
$$73$$ −4.34002 7.51714i −0.507961 0.879815i −0.999958 0.00921733i $$-0.997066\pi$$
0.491996 0.870597i $$-0.336267\pi$$
$$74$$ −4.47178 + 3.75227i −0.519834 + 0.436193i
$$75$$ 0 0
$$76$$ −0.766044 + 4.34445i −0.0878713 + 0.498343i
$$77$$ 0.271974 + 0.228213i 0.0309943 + 0.0260073i
$$78$$ 0 0
$$79$$ 1.19207 + 0.433877i 0.134118 + 0.0488149i 0.408207 0.912889i $$-0.366154\pi$$
−0.274089 + 0.961704i $$0.588376\pi$$
$$80$$ 0.162504 0.0181685
$$81$$ 0 0
$$82$$ 5.10101 0.563313
$$83$$ −7.96451 2.89884i −0.874218 0.318189i −0.134344 0.990935i $$-0.542893\pi$$
−0.739874 + 0.672745i $$0.765115\pi$$
$$84$$ 0 0
$$85$$ 8.91534 + 7.48086i 0.967005 + 0.811413i
$$86$$ −0.950837 + 5.39246i −0.102531 + 0.581484i
$$87$$ 0 0
$$88$$ 0.353226 0.296392i 0.0376540 0.0315955i
$$89$$ 3.86097 + 6.68739i 0.409262 + 0.708862i 0.994807 0.101778i $$-0.0324530\pi$$
−0.585546 + 0.810640i $$0.699120\pi$$
$$90$$ 0 0
$$91$$ 2.63429 4.56272i 0.276148 0.478303i
$$92$$ 0.604418 + 3.42782i 0.0630149 + 0.357375i
$$93$$ 0 0
$$94$$ 6.11246 2.22475i 0.630452 0.229466i
$$95$$ 13.1099 4.77163i 1.34505 0.489559i
$$96$$ 0 0
$$97$$ −0.678396 3.84737i −0.0688807 0.390642i −0.999684 0.0251223i $$-0.992002\pi$$
0.930804 0.365519i $$-0.119109\pi$$
$$98$$ 0.979055 1.69577i 0.0988995 0.171299i
$$99$$ 0 0
$$100$$ 6.16385 + 10.6761i 0.616385 + 1.06761i
$$101$$ 6.21554 5.21546i 0.618469 0.518957i −0.278853 0.960334i $$-0.589954\pi$$
0.897322 + 0.441377i $$0.145510\pi$$
$$102$$ 0 0
$$103$$ 3.23783 18.3626i 0.319032 1.80932i −0.229629 0.973278i $$-0.573751\pi$$
0.548661 0.836045i $$-0.315138\pi$$
$$104$$ −5.24170 4.39831i −0.513991 0.431289i
$$105$$ 0 0
$$106$$ 1.15998 + 0.422197i 0.112667 + 0.0410074i
$$107$$ −7.59627 −0.734359 −0.367179 0.930150i $$-0.619676\pi$$
−0.367179 + 0.930150i $$0.619676\pi$$
$$108$$ 0 0
$$109$$ −15.6382 −1.49786 −0.748932 0.662647i $$-0.769433\pi$$
−0.748932 + 0.662647i $$0.769433\pi$$
$$110$$ −0.520945 0.189608i −0.0496701 0.0180784i
$$111$$ 0 0
$$112$$ 0.0701076 + 0.0588272i 0.00662454 + 0.00555865i
$$113$$ 0.401674 2.27801i 0.0377863 0.214297i −0.960068 0.279766i $$-0.909743\pi$$
0.997855 + 0.0654689i $$0.0208543\pi$$
$$114$$ 0 0
$$115$$ 8.43242 7.07564i 0.786327 0.659807i
$$116$$ −4.11974 7.13559i −0.382508 0.662523i
$$117$$ 0 0
$$118$$ −2.25150 + 3.89971i −0.207267 + 0.358997i
$$119$$ 1.13816 + 6.45480i 0.104335 + 0.591711i
$$120$$ 0 0
$$121$$ 10.3118 3.75319i 0.937437 0.341199i
$$122$$ 3.12449 1.13722i 0.282878 0.102959i
$$123$$ 0 0
$$124$$ 1.10442 + 6.26347i 0.0991797 + 0.562476i
$$125$$ 9.79473 16.9650i 0.876067 1.51739i
$$126$$ 0 0
$$127$$ −0.0209445 0.0362770i −0.00185853 0.00321906i 0.865095 0.501609i $$-0.167258\pi$$
−0.866953 + 0.498390i $$0.833925\pi$$
$$128$$ −5.24170 + 4.39831i −0.463305 + 0.388759i
$$129$$ 0 0
$$130$$ −1.42855 + 8.10170i −0.125292 + 0.710566i
$$131$$ −14.0556 11.7940i −1.22804 1.03045i −0.998364 0.0571807i $$-0.981789\pi$$
−0.229676 0.973267i $$-0.573767\pi$$
$$132$$ 0 0
$$133$$ 7.38326 + 2.68729i 0.640209 + 0.233017i
$$134$$ −5.15745 −0.445536
$$135$$ 0 0
$$136$$ 8.51249 0.729940
$$137$$ 13.4500 + 4.89538i 1.14911 + 0.418241i 0.845195 0.534459i $$-0.179485\pi$$
0.303913 + 0.952700i $$0.401707\pi$$
$$138$$ 0 0
$$139$$ 8.03983 + 6.74622i 0.681929 + 0.572207i 0.916569 0.399876i $$-0.130947\pi$$
−0.234640 + 0.972082i $$0.575391\pi$$
$$140$$ −1.80541 + 10.2390i −0.152585 + 0.865351i
$$141$$ 0 0
$$142$$ 10.3191 8.65873i 0.865958 0.726625i
$$143$$ 0.195937 + 0.339373i 0.0163851 + 0.0283798i
$$144$$ 0 0
$$145$$ −13.0287 + 22.5663i −1.08197 + 1.87403i
$$146$$ 1.32547 + 7.51714i 0.109697 + 0.622123i
$$147$$ 0 0
$$148$$ −7.65183 + 2.78504i −0.628976 + 0.228929i
$$149$$ −1.19459 + 0.434796i −0.0978648 + 0.0356199i −0.390489 0.920608i $$-0.627694\pi$$
0.292624 + 0.956228i $$0.405472\pi$$
$$150$$ 0 0
$$151$$ 1.36437 + 7.73773i 0.111031 + 0.629688i 0.988639 + 0.150309i $$0.0480268\pi$$
−0.877608 + 0.479379i $$0.840862\pi$$
$$152$$ 5.10220 8.83726i 0.413843 0.716797i
$$153$$ 0 0
$$154$$ −0.156107 0.270386i −0.0125795 0.0217883i
$$155$$ 15.4081 12.9289i 1.23761 1.03847i
$$156$$ 0 0
$$157$$ −2.14496 + 12.1647i −0.171187 + 0.970848i 0.771267 + 0.636512i $$0.219623\pi$$
−0.942454 + 0.334336i $$0.891488\pi$$
$$158$$ −0.854570 0.717070i −0.0679860 0.0570470i
$$159$$ 0 0
$$160$$ 20.5535 + 7.48086i 1.62490 + 0.591414i
$$161$$ 6.19934 0.488576
$$162$$ 0 0
$$163$$ −13.7469 −1.07674 −0.538371 0.842708i $$-0.680960\pi$$
−0.538371 + 0.842708i $$0.680960\pi$$
$$164$$ 6.68644 + 2.43367i 0.522123 + 0.190037i
$$165$$ 0 0
$$166$$ 5.70961 + 4.79093i 0.443151 + 0.371848i
$$167$$ 0.645430 3.66041i 0.0499448 0.283251i −0.949598 0.313469i $$-0.898509\pi$$
0.999543 + 0.0302175i $$0.00961999\pi$$
$$168$$ 0 0
$$169$$ −5.50387 + 4.61830i −0.423375 + 0.355254i
$$170$$ −5.11721 8.86327i −0.392472 0.679782i
$$171$$ 0 0
$$172$$ −3.81908 + 6.61484i −0.291202 + 0.504377i
$$173$$ 0.270792 + 1.53574i 0.0205879 + 0.116760i 0.993370 0.114963i $$-0.0366749\pi$$
−0.972782 + 0.231723i $$0.925564\pi$$
$$174$$ 0 0
$$175$$ 20.6322 7.50952i 1.55965 0.567666i
$$176$$ −0.00639661 + 0.00232818i −0.000482163 + 0.000175493i
$$177$$ 0 0
$$178$$ −1.17917 6.68739i −0.0883823 0.501241i
$$179$$ −6.09627 + 10.5590i −0.455656 + 0.789220i −0.998726 0.0504679i $$-0.983929\pi$$
0.543069 + 0.839688i $$0.317262\pi$$
$$180$$ 0 0
$$181$$ 8.43629 + 14.6121i 0.627064 + 1.08611i 0.988138 + 0.153570i $$0.0490771\pi$$
−0.361073 + 0.932537i $$0.617590\pi$$
$$182$$ −3.54916 + 2.97810i −0.263081 + 0.220752i
$$183$$ 0 0
$$184$$ 1.39811 7.92907i 0.103070 0.584538i
$$185$$ 19.7271 + 16.5530i 1.45037 + 1.21700i
$$186$$ 0 0
$$187$$ −0.458111 0.166739i −0.0335004 0.0121931i
$$188$$ 9.07367 0.661766
$$189$$ 0 0
$$190$$ −12.2686 −0.890056
$$191$$ −16.4217 5.97702i −1.18824 0.432482i −0.329132 0.944284i $$-0.606756\pi$$
−0.859104 + 0.511802i $$0.828978\pi$$
$$192$$ 0 0
$$193$$ −1.52616 1.28060i −0.109855 0.0921796i 0.586205 0.810162i $$-0.300621\pi$$
−0.696061 + 0.717983i $$0.745066\pi$$
$$194$$ −0.596571 + 3.38332i −0.0428313 + 0.242909i
$$195$$ 0 0
$$196$$ 2.09240 1.75573i 0.149457 0.125409i
$$197$$ 10.5963 + 18.3533i 0.754953 + 1.30762i 0.945398 + 0.325919i $$0.105674\pi$$
−0.190445 + 0.981698i $$0.560993\pi$$
$$198$$ 0 0
$$199$$ 1.54189 2.67063i 0.109302 0.189316i −0.806186 0.591662i $$-0.798472\pi$$
0.915488 + 0.402346i $$0.131805\pi$$
$$200$$ −4.95171 28.0826i −0.350139 1.98574i
$$201$$ 0 0
$$202$$ −6.70486 + 2.44037i −0.471752 + 0.171704i
$$203$$ −13.7900 + 5.01914i −0.967867 + 0.352275i
$$204$$ 0 0
$$205$$ −3.90760 22.1611i −0.272919 1.54780i
$$206$$ −8.19846 + 14.2002i −0.571214 + 0.989372i
$$207$$ 0 0
$$208$$ 0.0505072 + 0.0874810i 0.00350204 + 0.00606572i
$$209$$ −0.447682 + 0.375650i −0.0309668 + 0.0259842i
$$210$$ 0 0
$$211$$ 0.174992 0.992431i 0.0120470 0.0683218i −0.978192 0.207705i $$-0.933401\pi$$
0.990239 + 0.139383i $$0.0445118\pi$$
$$212$$ 1.31908 + 1.10684i 0.0905946 + 0.0760179i
$$213$$ 0 0
$$214$$ 6.27719 + 2.28471i 0.429100 + 0.156180i
$$215$$ 24.1557 1.64740
$$216$$ 0 0
$$217$$ 11.3277 0.768974
$$218$$ 12.9226 + 4.70345i 0.875230 + 0.318558i
$$219$$ 0 0
$$220$$ −0.592396 0.497079i −0.0399393 0.0335131i
$$221$$ −1.25624 + 7.12452i −0.0845041 + 0.479247i
$$222$$ 0 0
$$223$$ 14.0064 11.7528i 0.937938 0.787023i −0.0392875 0.999228i $$-0.512509\pi$$
0.977225 + 0.212205i $$0.0680644\pi$$
$$224$$ 6.15910 + 10.6679i 0.411522 + 0.712777i
$$225$$ 0 0
$$226$$ −1.01707 + 1.76162i −0.0676548 + 0.117181i
$$227$$ 0.459293 + 2.60478i 0.0304843 + 0.172885i 0.996249 0.0865353i $$-0.0275795\pi$$
−0.965764 + 0.259421i $$0.916468\pi$$
$$228$$ 0 0
$$229$$ 3.25402 1.18437i 0.215032 0.0782652i −0.232258 0.972654i $$-0.574611\pi$$
0.447290 + 0.894389i $$0.352389\pi$$
$$230$$ −9.09627 + 3.31077i −0.599790 + 0.218306i
$$231$$ 0 0
$$232$$ 3.30958 + 18.7696i 0.217285 + 1.23228i
$$233$$ 3.06283 5.30498i 0.200653 0.347541i −0.748086 0.663602i $$-0.769027\pi$$
0.948739 + 0.316061i $$0.102360\pi$$
$$234$$ 0 0
$$235$$ −14.3478 24.8511i −0.935945 1.62110i
$$236$$ −4.81180 + 4.03758i −0.313222 + 0.262824i
$$237$$ 0 0
$$238$$ 1.00088 5.67626i 0.0648772 0.367937i
$$239$$ 22.1780 + 18.6095i 1.43457 + 1.20375i 0.942946 + 0.332946i $$0.108043\pi$$
0.491629 + 0.870805i $$0.336402\pi$$
$$240$$ 0 0
$$241$$ −20.9795 7.63592i −1.35141 0.491873i −0.438022 0.898964i $$-0.644321\pi$$
−0.913388 + 0.407091i $$0.866543\pi$$
$$242$$ −9.65002 −0.620326
$$243$$ 0 0
$$244$$ 4.63816 0.296927
$$245$$ −8.11721 2.95442i −0.518590 0.188751i
$$246$$ 0 0
$$247$$ 6.64337 + 5.57445i 0.422708 + 0.354694i
$$248$$ 2.55468 14.4883i 0.162222 0.920009i
$$249$$ 0 0
$$250$$ −13.1964 + 11.0731i −0.834614 + 0.700324i
$$251$$ −11.3610 19.6778i −0.717098 1.24205i −0.962145 0.272539i $$-0.912137\pi$$
0.245047 0.969511i $$-0.421197\pi$$
$$252$$ 0 0
$$253$$ −0.230552 + 0.399328i −0.0144947 + 0.0251055i
$$254$$ 0.00639661 + 0.0362770i 0.000401359 + 0.00227622i
$$255$$ 0 0
$$256$$ 15.1300 5.50687i 0.945625 0.344179i
$$257$$ −18.4081 + 6.69999i −1.14826 + 0.417934i −0.844891 0.534938i $$-0.820335\pi$$
−0.303373 + 0.952872i $$0.598113\pi$$
$$258$$ 0 0
$$259$$ 2.51842 + 14.2827i 0.156487 + 0.887481i
$$260$$ −5.73783 + 9.93821i −0.355845 + 0.616341i
$$261$$ 0 0
$$262$$ 8.06758 + 13.9735i 0.498417 + 0.863283i
$$263$$ −13.6361 + 11.4420i −0.840838 + 0.705547i −0.957752 0.287595i $$-0.907144\pi$$
0.116914 + 0.993142i $$0.462700\pi$$
$$264$$ 0 0
$$265$$ 0.945622 5.36289i 0.0580891 0.329440i
$$266$$ −5.29292 4.44129i −0.324530 0.272313i
$$267$$ 0 0
$$268$$ −6.76042 2.46059i −0.412958 0.150305i
$$269$$ −22.7888 −1.38946 −0.694729 0.719272i $$-0.744476\pi$$
−0.694729 + 0.719272i $$0.744476\pi$$
$$270$$ 0 0
$$271$$ −3.44562 −0.209307 −0.104653 0.994509i $$-0.533373\pi$$
−0.104653 + 0.994509i $$0.533373\pi$$
$$272$$ −0.118089 0.0429807i −0.00716017 0.00260609i
$$273$$ 0 0
$$274$$ −9.64203 8.09062i −0.582496 0.488772i
$$275$$ −0.283585 + 1.60829i −0.0171008 + 0.0969837i
$$276$$ 0 0
$$277$$ −2.00206 + 1.67993i −0.120292 + 0.100937i −0.700949 0.713211i $$-0.747240\pi$$
0.580657 + 0.814148i $$0.302796\pi$$
$$278$$ −4.61468 7.99287i −0.276770 0.479380i
$$279$$ 0 0
$$280$$ 12.0248 20.8276i 0.718620 1.24469i
$$281$$ 2.37639 + 13.4772i 0.141764 + 0.803982i 0.969909 + 0.243468i $$0.0782851\pi$$
−0.828145 + 0.560514i $$0.810604\pi$$
$$282$$ 0 0
$$283$$ −21.5005 + 7.82553i −1.27807 + 0.465179i −0.889793 0.456363i $$-0.849152\pi$$
−0.388277 + 0.921543i $$0.626929\pi$$
$$284$$ 17.6573 6.42675i 1.04777 0.381357i
$$285$$ 0 0
$$286$$ −0.0598406 0.339373i −0.00353845 0.0200675i
$$287$$ 6.33662 10.9753i 0.374039 0.647854i
$$288$$ 0 0
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ 17.5535 14.7291i 1.03078 0.864925i
$$291$$ 0 0
$$292$$ −1.84895 + 10.4859i −0.108201 + 0.613640i
$$293$$ −18.6006 15.6078i −1.08666 0.911815i −0.0902023 0.995923i $$-0.528751\pi$$
−0.996457 + 0.0841084i $$0.973196\pi$$
$$294$$ 0 0
$$295$$ 18.6668 + 6.79417i 1.08683 + 0.395572i
$$296$$ 18.8357 1.09481
$$297$$ 0 0
$$298$$ 1.11793 0.0647597
$$299$$ 6.42989 + 2.34029i 0.371850 + 0.135342i
$$300$$ 0 0
$$301$$ 10.4213 + 8.74449i 0.600672 + 0.504024i
$$302$$ 1.19981 6.80445i 0.0690412 0.391552i
$$303$$ 0 0
$$304$$ −0.115400 + 0.0968323i −0.00661865 + 0.00555371i
$$305$$ −7.33409 12.7030i −0.419949 0.727373i
$$306$$ 0 0
$$307$$ 8.07444 13.9853i 0.460833 0.798186i −0.538170 0.842836i $$-0.680884\pi$$
0.999003 + 0.0446505i $$0.0142174\pi$$
$$308$$ −0.0756268 0.428901i −0.00430924 0.0244389i
$$309$$ 0 0
$$310$$ −16.6211 + 6.04958i −0.944014 + 0.343593i
$$311$$ 17.5817 6.39922i 0.996968 0.362867i 0.208553 0.978011i $$-0.433125\pi$$
0.788414 + 0.615144i $$0.210902\pi$$
$$312$$ 0 0
$$313$$ 0.481582 + 2.73119i 0.0272206 + 0.154376i 0.995388 0.0959261i $$-0.0305813\pi$$
−0.968168 + 0.250302i $$0.919470\pi$$
$$314$$ 5.43124 9.40718i 0.306502 0.530878i
$$315$$ 0 0
$$316$$ −0.778066 1.34765i −0.0437696 0.0758112i
$$317$$ −13.3923 + 11.2375i −0.752189 + 0.631161i −0.936081 0.351785i $$-0.885575\pi$$
0.183892 + 0.982946i $$0.441130\pi$$
$$318$$ 0 0
$$319$$ 0.189540 1.07494i 0.0106122 0.0601849i
$$320$$ −14.9834 12.5726i −0.837597 0.702827i
$$321$$ 0 0
$$322$$ −5.12284 1.86456i −0.285485 0.103908i
$$323$$ −10.7888 −0.600305
$$324$$ 0 0
$$325$$ 24.2344 1.34428
$$326$$ 11.3598 + 4.13462i 0.629160 + 0.228996i
$$327$$ 0 0
$$328$$ −12.6086 10.5799i −0.696193 0.584175i
$$329$$ 2.80628 15.9152i 0.154715 0.877435i
$$330$$ 0 0
$$331$$ −24.8653 + 20.8645i −1.36672 + 1.14681i −0.392878 + 0.919590i $$0.628521\pi$$
−0.973842 + 0.227224i $$0.927035\pi$$
$$332$$ 5.19846 + 9.00400i 0.285303 + 0.494159i
$$333$$ 0 0
$$334$$ −1.63429 + 2.83067i −0.0894241 + 0.154887i
$$335$$ 3.95084 + 22.4063i 0.215857 + 1.22419i
$$336$$ 0 0
$$337$$ −7.78611 + 2.83391i −0.424137 + 0.154373i −0.545265 0.838264i $$-0.683571\pi$$
0.121128 + 0.992637i $$0.461349\pi$$
$$338$$ 5.93717 2.16095i 0.322939 0.117540i
$$339$$ 0 0
$$340$$ −2.47906 14.0594i −0.134446 0.762479i
$$341$$ −0.421274 + 0.729669i −0.0228133 + 0.0395138i
$$342$$ 0 0
$$343$$ −10.0792 17.4577i −0.544225 0.942626i
$$344$$ 13.5346 11.3569i 0.729738 0.612323i
$$345$$ 0 0
$$346$$ 0.238131 1.35051i 0.0128020 0.0726037i
$$347$$ −11.4624 9.61814i −0.615336 0.516329i 0.280997 0.959709i $$-0.409335\pi$$
−0.896334 + 0.443380i $$0.853779\pi$$
$$348$$ 0 0
$$349$$ −31.6168 11.5076i −1.69241 0.615986i −0.697483 0.716601i $$-0.745697\pi$$
−0.994925 + 0.100615i $$0.967919\pi$$
$$350$$ −19.3081 −1.03206
$$351$$ 0 0
$$352$$ −0.916222 −0.0488348
$$353$$ −14.8037 5.38809i −0.787919 0.286779i −0.0834482 0.996512i $$-0.526593\pi$$
−0.704471 + 0.709733i $$0.748816\pi$$
$$354$$ 0 0
$$355$$ −45.5223 38.1978i −2.41608 2.02733i
$$356$$ 1.64486 9.32845i 0.0871772 0.494407i
$$357$$ 0 0
$$358$$ 8.21348 6.89193i 0.434096 0.364250i
$$359$$ 9.06283 + 15.6973i 0.478318 + 0.828471i 0.999691 0.0248577i $$-0.00791328\pi$$
−0.521373 + 0.853329i $$0.674580\pi$$
$$360$$ 0 0
$$361$$ 3.03343 5.25406i 0.159654 0.276529i
$$362$$ −2.57650 14.6121i −0.135418 0.767994i
$$363$$ 0 0
$$364$$ −6.07310 + 2.21043i −0.318317 + 0.115858i
$$365$$ 31.6425 11.5169i 1.65624 0.602823i
$$366$$ 0 0
$$367$$ −3.32413 18.8521i −0.173518 0.984071i −0.939840 0.341614i $$-0.889026\pi$$
0.766322 0.642457i $$-0.222085\pi$$
$$368$$ −0.0594300 + 0.102936i −0.00309800 + 0.00536590i
$$369$$ 0 0
$$370$$ −11.3229 19.6119i −0.588652 1.01958i
$$371$$ 2.34936 1.97134i 0.121972 0.102347i
$$372$$ 0 0
$$373$$ −2.64812 + 15.0182i −0.137114 + 0.777614i 0.836250 + 0.548349i $$0.184743\pi$$
−0.973364 + 0.229265i $$0.926368\pi$$
$$374$$ 0.328411 + 0.275570i 0.0169817 + 0.0142494i
$$375$$ 0 0
$$376$$ −19.7230 7.17858i −1.01713 0.370207i
$$377$$ −16.1976 −0.834218
$$378$$ 0 0
$$379$$ 9.84760 0.505837 0.252919 0.967488i $$-0.418610\pi$$
0.252919 + 0.967488i $$0.418610\pi$$
$$380$$ −16.0817 5.85327i −0.824975 0.300266i
$$381$$ 0 0
$$382$$ 11.7724 + 9.87825i 0.602330 + 0.505415i
$$383$$ −4.92989 + 27.9588i −0.251906 + 1.42863i 0.551986 + 0.833853i $$0.313870\pi$$
−0.803892 + 0.594775i $$0.797241\pi$$
$$384$$ 0 0
$$385$$ −1.05509 + 0.885328i −0.0537725 + 0.0451205i
$$386$$ 0.875982 + 1.51724i 0.0445863 + 0.0772257i
$$387$$ 0 0
$$388$$ −2.39615 + 4.15026i −0.121646 + 0.210698i
$$389$$ −1.89006 10.7191i −0.0958300 0.543479i −0.994490 0.104833i $$-0.966569\pi$$
0.898660 0.438646i $$-0.144542\pi$$
$$390$$ 0 0
$$391$$ −7.99912 + 2.91144i −0.404533 + 0.147238i
$$392$$ −5.93717 + 2.16095i −0.299872 + 0.109145i
$$393$$ 0 0
$$394$$ −3.23618 18.3533i −0.163036 0.924624i
$$395$$ −2.46064 + 4.26195i −0.123808 + 0.214442i
$$396$$ 0 0
$$397$$ 9.05350 + 15.6811i 0.454382 + 0.787013i 0.998652 0.0518969i $$-0.0165267\pi$$
−0.544270 + 0.838910i $$0.683193\pi$$
$$398$$ −2.07738 + 1.74313i −0.104130 + 0.0873752i
$$399$$ 0 0
$$400$$ −0.0731006 + 0.414574i −0.00365503 + 0.0207287i
$$401$$ −1.09833 0.921605i −0.0548478 0.0460228i 0.614952 0.788565i $$-0.289176\pi$$
−0.669799 + 0.742542i $$0.733620\pi$$
$$402$$ 0 0
$$403$$ 11.7490 + 4.27628i 0.585258 + 0.213016i
$$404$$ −9.95306 −0.495183
$$405$$ 0 0
$$406$$ 12.9050 0.640463
$$407$$ −1.01367 0.368946i −0.0502458 0.0182880i
$$408$$ 0 0
$$409$$ 6.59105 + 5.53055i 0.325907 + 0.273468i 0.791029 0.611778i $$-0.209545\pi$$
−0.465123 + 0.885246i $$0.653990\pi$$
$$410$$ −3.43629 + 19.4882i −0.169706 + 0.962452i
$$411$$ 0 0
$$412$$ −17.5214 + 14.7022i −0.863218 + 0.724326i
$$413$$ 5.59374 + 9.68864i 0.275250 + 0.476747i
$$414$$ 0 0
$$415$$ 16.4402 28.4752i 0.807016 1.39779i
$$416$$ 2.36097 + 13.3897i 0.115756 + 0.656484i
$$417$$ 0 0
$$418$$ 0.482926 0.175771i 0.0236207 0.00859722i
$$419$$ −11.5689 + 4.21074i −0.565179 + 0.205708i −0.608778 0.793341i $$-0.708340\pi$$
0.0435988 + 0.999049i $$0.486118\pi$$
$$420$$ 0 0
$$421$$ 1.93036 + 10.9476i 0.0940800 + 0.533554i 0.995025 + 0.0996216i $$0.0317632\pi$$
−0.900945 + 0.433932i $$0.857126\pi$$
$$422$$ −0.443096 + 0.767465i −0.0215696 + 0.0373596i
$$423$$ 0 0
$$424$$ −1.99154 3.44946i −0.0967179 0.167520i
$$425$$ −23.0954 + 19.3793i −1.12029 + 0.940036i
$$426$$ 0 0
$$427$$ 1.43448 8.13533i 0.0694193 0.393696i
$$428$$ 7.13816 + 5.98962i 0.345036 + 0.289519i
$$429$$ 0 0
$$430$$ −19.9611 7.26525i −0.962610 0.350361i
$$431$$ 36.8958 1.77721 0.888604 0.458675i $$-0.151676\pi$$
0.888604 + 0.458675i $$0.151676\pi$$
$$432$$ 0 0
$$433$$ −37.9982 −1.82608 −0.913040 0.407871i $$-0.866271\pi$$
−0.913040 + 0.407871i $$0.866271\pi$$
$$434$$ −9.36066 3.40700i −0.449326 0.163541i
$$435$$ 0 0
$$436$$ 14.6951 + 12.3306i 0.703766 + 0.590530i
$$437$$ −1.77197 + 10.0494i −0.0847650 + 0.480726i
$$438$$ 0 0
$$439$$ 0.154763 0.129862i 0.00738644 0.00619796i −0.639087 0.769135i $$-0.720688\pi$$
0.646473 + 0.762937i $$0.276243\pi$$
$$440$$ 0.894400 + 1.54915i 0.0426388 + 0.0738526i
$$441$$ 0 0
$$442$$ 3.18092 5.50952i 0.151301 0.262061i
$$443$$ −3.68644 20.9068i −0.175148 0.993314i −0.937973 0.346709i $$-0.887299\pi$$
0.762825 0.646605i $$-0.223812\pi$$
$$444$$ 0 0
$$445$$ −28.1498 + 10.2457i −1.33443 + 0.485692i
$$446$$ −15.1091 + 5.49925i −0.715435 + 0.260397i
$$447$$ 0 0
$$448$$ −1.91282 10.8481i −0.0903722 0.512526i
$$449$$ −16.6297 + 28.8035i −0.784804 + 1.35932i 0.144312 + 0.989532i $$0.453903\pi$$
−0.929116 + 0.369788i $$0.879430\pi$$
$$450$$ 0 0
$$451$$ 0.471315 + 0.816341i 0.0221933 + 0.0384400i
$$452$$ −2.17365 + 1.82391i −0.102240 + 0.0857894i
$$453$$ 0 0
$$454$$ 0.403895 2.29061i 0.0189558 0.107503i
$$455$$ 15.6570 + 13.1378i 0.734013 + 0.615910i
$$456$$ 0 0
$$457$$ 0.0320889 + 0.0116794i 0.00150105 + 0.000546339i 0.342771 0.939419i $$-0.388635\pi$$
−0.341270 + 0.939965i $$0.610857\pi$$
$$458$$ −3.04519 −0.142292
$$459$$ 0 0
$$460$$ −13.5030 −0.629580
$$461$$ −14.0826 5.12565i −0.655892 0.238725i −0.00743018 0.999972i $$-0.502365\pi$$
−0.648462 + 0.761247i $$0.724587\pi$$
$$462$$ 0 0
$$463$$ −23.3203 19.5680i −1.08378 0.909403i −0.0875549 0.996160i $$-0.527905\pi$$
−0.996230 + 0.0867566i $$0.972350\pi$$
$$464$$ 0.0488583 0.277089i 0.00226819 0.0128635i
$$465$$ 0 0
$$466$$ −4.12654 + 3.46258i −0.191158 + 0.160401i
$$467$$ −0.255367 0.442308i −0.0118170 0.0204676i 0.860056 0.510199i $$-0.170428\pi$$
−0.871873 + 0.489731i $$0.837095\pi$$
$$468$$ 0 0
$$469$$ −6.40673 + 11.0968i −0.295835 + 0.512401i
$$470$$ 4.38191 + 24.8511i 0.202123 + 1.14629i
$$471$$ 0 0
$$472$$ 13.6535 4.96946i 0.628452 0.228738i
$$473$$ −0.950837 + 0.346076i −0.0437195 + 0.0159126i
$$474$$ 0 0
$$475$$ 6.27584 + 35.5921i 0.287955 + 1.63308i
$$476$$ 4.02007 6.96296i 0.184259 0.319147i
$$477$$ 0 0
$$478$$ −12.7297 22.0484i −0.582242 1.00847i
$$479$$ 11.8359 9.93150i 0.540796 0.453782i −0.331014 0.943626i $$-0.607391\pi$$
0.871810 + 0.489844i $$0.162946\pi$$
$$480$$ 0 0
$$481$$ −2.77972 + 15.7645i −0.126744 + 0.718801i
$$482$$ 15.0398 + 12.6199i 0.685045 + 0.574821i
$$483$$ 0 0
$$484$$ −12.6493 4.60397i −0.574968 0.209271i
$$485$$ 15.1557 0.688185
$$486$$ 0 0
$$487$$ 29.5107 1.33726 0.668629 0.743596i $$-0.266881\pi$$
0.668629 + 0.743596i $$0.266881\pi$$
$$488$$ −10.0817 3.66945i −0.456378 0.166108i
$$489$$ 0 0
$$490$$ 5.81908 + 4.88279i 0.262879 + 0.220582i
$$491$$ −0.374638 + 2.12467i −0.0169072 + 0.0958852i −0.992094 0.125500i $$-0.959947\pi$$
0.975187 + 0.221385i $$0.0710577\pi$$
$$492$$ 0 0
$$493$$ 15.4363 12.9526i 0.695215 0.583355i
$$494$$ −3.81315 6.60457i −0.171562 0.297153i
$$495$$ 0 0
$$496$$ −0.108593 + 0.188089i −0.00487597 + 0.00844543i
$$497$$ −5.81150 32.9586i −0.260681 1.47840i
$$498$$ 0 0
$$499$$ −7.04323 + 2.56353i −0.315298 + 0.114759i −0.494822 0.868994i $$-0.664767\pi$$
0.179523 + 0.983754i $$0.442544\pi$$
$$500$$ −22.5808 + 8.21875i −1.00985 + 0.367554i
$$501$$ 0 0
$$502$$ 3.46972 + 19.6778i 0.154861 + 0.878262i
$$503$$ 14.2981 24.7651i 0.637522 1.10422i −0.348453 0.937326i $$-0.613293\pi$$
0.985975 0.166894i $$-0.0533739\pi$$
$$504$$ 0 0
$$505$$ 15.7383 + 27.2595i 0.700345 + 1.21303i
$$506$$ 0.310622 0.260643i 0.0138088 0.0115870i
$$507$$ 0 0
$$508$$ −0.00892283 + 0.0506039i −0.000395887 + 0.00224518i
$$509$$ 1.29607 + 1.08754i 0.0574475 + 0.0482041i 0.671059 0.741404i $$-0.265840\pi$$
−0.613612 + 0.789608i $$0.710284\pi$$
$$510$$ 0 0
$$511$$ 17.8204 + 6.48610i 0.788329 + 0.286928i
$$512$$ −0.473897 −0.0209435
$$513$$ 0 0
$$514$$ 17.2267 0.759836
$$515$$ 67.9723 + 24.7399i 2.99522 + 1.09017i
$$516$$ 0 0
$$517$$ 0.920807 + 0.772649i 0.0404971 + 0.0339811i
$$518$$ 2.21466 12.5600i 0.0973066 0.551853i
$$519$$ 0 0
$$520$$ 20.3346 17.0627i 0.891729 0.748250i
$$521$$ −11.2019 19.4022i −0.490763 0.850026i 0.509181 0.860660i $$-0.329948\pi$$
−0.999943 + 0.0106337i $$0.996615\pi$$
$$522$$ 0 0
$$523$$ −1.21436 + 2.10332i −0.0531000 + 0.0919720i −0.891354 0.453309i $$-0.850244\pi$$
0.838254 + 0.545281i $$0.183577\pi$$
$$524$$ 3.90838 + 22.1655i 0.170738 + 0.968304i
$$525$$ 0 0
$$526$$ 14.7096 5.35386i 0.641369 0.233439i
$$527$$ −14.6163 + 5.31991i −0.636698 + 0.231739i
$$528$$ 0 0
$$529$$ −2.59580 14.7215i −0.112861 0.640066i
$$530$$ −2.39440 + 4.14722i −0.104006 + 0.180144i
$$531$$ 0 0
$$532$$ −4.81908 8.34689i −0.208934 0.361883i
$$533$$ 10.7155 8.99140i 0.464141 0.389461i
$$534$$ 0 0
$$535$$ 5.11721 29.0211i 0.221236 1.25469i
$$536$$ 12.7481 + 10.6969i 0.550634 + 0.462037i
$$537$$ 0 0
$$538$$ 18.8316 + 6.85413i 0.811886 + 0.295503i
$$539$$ 0.361844 0.0155857
$$540$$ 0 0
$$541$$ 38.9394 1.67414 0.837069 0.547098i $$-0.184267\pi$$
0.837069 + 0.547098i $$0.184267\pi$$
$$542$$ 2.84730 + 1.03633i 0.122302 + 0.0445142i
$$543$$ 0 0
$$544$$ −12.9572 10.8724i −0.555537 0.466151i
$$545$$ 10.5346 59.7448i 0.451253 2.55918i
$$546$$ 0 0
$$547$$ −11.2396 + 9.43118i −0.480572 + 0.403248i −0.850633 0.525759i $$-0.823781\pi$$
0.370061 + 0.929007i $$0.379337\pi$$
$$548$$ −8.77884 15.2054i −0.375013 0.649542i
$$549$$ 0 0
$$550$$ 0.718063 1.24372i 0.0306183 0.0530325i
$$551$$ −4.19459 23.7887i −0.178696 1.01343i
$$552$$ 0 0
$$553$$ −2.60442 + 0.947931i −0.110751 + 0.0403101i
$$554$$ 2.15967 0.786057i 0.0917557 0.0333963i
$$555$$ 0 0
$$556$$ −2.23560 12.6787i −0.0948107 0.537698i
$$557$$ −5.55350 + 9.61894i −0.235309 + 0.407568i −0.959363 0.282176i $$-0.908944\pi$$
0.724053 + 0.689744i $$0.242277\pi$$
$$558$$ 0 0
$$559$$ 7.50774 + 13.0038i 0.317544 + 0.550002i
$$560$$ −0.271974 + 0.228213i −0.0114930 + 0.00964378i
$$561$$ 0 0
$$562$$ 2.08976 11.8516i 0.0881514 0.499931i
$$563$$ −12.4927 10.4826i −0.526506 0.441791i 0.340387 0.940285i $$-0.389442\pi$$
−0.866893 + 0.498495i $$0.833886\pi$$
$$564$$ 0 0
$$565$$ 8.43242 + 3.06915i 0.354755 + 0.129120i
$$566$$ 20.1206 0.845733
$$567$$ 0 0
$$568$$ −43.4653 −1.82376
$$569$$ 33.8444 + 12.3183i 1.41883 + 0.516412i 0.933708 0.358035i $$-0.116553\pi$$
0.485121 + 0.874447i $$0.338775\pi$$
$$570$$ 0 0
$$571$$ 29.9971 + 25.1705i 1.25534 + 1.05335i 0.996162 + 0.0875234i $$0.0278953\pi$$
0.259176 + 0.965830i $$0.416549\pi$$
$$572$$ 0.0834734 0.473401i 0.00349020 0.0197939i
$$573$$ 0 0
$$574$$ −8.53730 + 7.16365i −0.356340 + 0.299005i
$$575$$ 14.2579 + 24.6954i 0.594595 + 1.02987i
$$576$$ 0 0
$$577$$ −5.90286 + 10.2240i −0.245739 + 0.425633i −0.962339 0.271852i $$-0.912364\pi$$
0.716600 + 0.697484i $$0.245697\pi$$
$$578$$ −1.22163 6.92820i −0.0508131 0.288175i
$$579$$ 0 0
$$580$$ 30.0364 10.9324i 1.24719 0.453942i
$$581$$ 17.4008 6.33337i 0.721907 0.262753i
$$582$$ 0 0
$$583$$ 0.0396112 + 0.224647i 0.00164053 + 0.00930391i
$$584$$ 12.3148 21.3299i 0.509590 0.882636i
$$585$$ 0 0
$$586$$ 10.6763 + 18.4920i 0.441035 + 0.763896i
$$587$$ 30.6122 25.6867i 1.26350 1.06020i 0.268201 0.963363i $$-0.413571\pi$$
0.995300 0.0968406i $$-0.0308737\pi$$
$$588$$ 0 0
$$589$$ −3.23783 + 18.3626i −0.133412 + 0.756619i
$$590$$ −13.3819 11.2288i −0.550925 0.462281i
$$591$$ 0 0
$$592$$ −0.261297 0.0951042i −0.0107392 0.00390876i
$$593$$ 29.2995 1.20319 0.601594 0.798802i $$-0.294533\pi$$
0.601594 + 0.798802i $$0.294533\pi$$
$$594$$ 0 0
$$595$$ −25.4270 −1.04240
$$596$$ 1.46538 + 0.533356i 0.0600245 + 0.0218471i
$$597$$ 0 0
$$598$$ −4.60947 3.86780i −0.188495 0.158166i
$$599$$ −1.74897 + 9.91890i −0.0714610 + 0.405275i 0.928004 + 0.372570i $$0.121523\pi$$
−0.999465 + 0.0327053i $$0.989588\pi$$
$$600$$ 0 0
$$601$$ −23.3025 + 19.5531i −0.950528 + 0.797587i −0.979386 0.201996i $$-0.935257\pi$$
0.0288587 + 0.999584i $$0.490813\pi$$
$$602$$ −5.98158 10.3604i −0.243791 0.422259i
$$603$$ 0 0
$$604$$ 4.81908 8.34689i 0.196085 0.339630i
$$605$$ 7.39234 + 41.9240i 0.300541 + 1.70445i
$$606$$ 0 0
$$607$$ 21.6827 7.89187i 0.880075 0.320321i 0.137835 0.990455i $$-0.455986\pi$$
0.742240 + 0.670134i $$0.233763\pi$$
$$608$$ −19.0535 + 6.93491i −0.772721 + 0.281248i
$$609$$ 0 0
$$610$$ 2.23989 + 12.7030i 0.0906903 + 0.514330i
$$611$$ 8.91875 15.4477i 0.360814 0.624948i
$$612$$ 0 0
$$613$$ −0.382789 0.663010i −0.0154607 0.0267787i 0.858192 0.513330i $$-0.171588\pi$$
−0.873652 + 0.486551i $$0.838255\pi$$
$$614$$ −10.8787 + 9.12829i −0.439027 + 0.368388i
$$615$$ 0 0
$$616$$ −0.174936 + 0.992112i −0.00704837 + 0.0399733i
$$617$$ 7.11515 + 5.97032i 0.286445 + 0.240356i 0.774676 0.632359i $$-0.217913\pi$$
−0.488231 + 0.872715i $$0.662357\pi$$
$$618$$ 0 0
$$619$$ 32.9666 + 11.9989i 1.32504 + 0.482275i 0.905070 0.425263i $$-0.139818\pi$$
0.419970 + 0.907538i $$0.362040\pi$$
$$620$$ −24.6732 −0.990901
$$621$$ 0 0
$$622$$ −16.4534 −0.659720
$$623$$ −15.8534 5.77016i −0.635153 0.231177i
$$624$$ 0 0
$$625$$ 19.7233 + 16.5498i 0.788931 + 0.661992i
$$626$$ 0.423496 2.40176i 0.0169263 0.0959938i
$$627$$ 0 0
$$628$$ 11.6074 9.73977i 0.463186 0.388659i
$$629$$ −9.95723 17.2464i −0.397021 0.687660i
$$630$$ 0 0
$$631$$ −17.8810 + 30.9709i −0.711833 + 1.23293i 0.252336 + 0.967640i $$0.418801\pi$$
−0.964168 + 0.265291i $$0.914532\pi$$
$$632$$ 0.625058 + 3.54488i 0.0248635 + 0.141008i
$$633$$ 0 0
$$634$$ 14.4467 5.25815i 0.573750 0.208828i
$$635$$ 0.152704 0.0555796i 0.00605986 0.00220561i
$$636$$ 0 0
$$637$$ −0.932419 5.28801i −0.0369438 0.209519i
$$638$$ −0.479933 + 0.831268i −0.0190007 + 0.0329102i
$$639$$ 0 0
$$640$$ −13.2724 22.9885i −0.524639 0.908702i
$$641$$ −2.24170 + 1.88101i −0.0885417 + 0.0742953i −0.685984 0.727616i $$-0.740628\pi$$
0.597442 + 0.801912i $$0.296184\pi$$
$$642$$ 0 0
$$643$$ −3.51666 + 19.9440i −0.138684 + 0.786514i 0.833540 + 0.552459i $$0.186311\pi$$
−0.972223 + 0.234055i $$0.924801\pi$$
$$644$$ −5.82547 4.88815i −0.229556 0.192620i
$$645$$ 0 0
$$646$$ 8.91534 + 3.24492i 0.350770 + 0.127670i
$$647$$ −10.7219 −0.421523 −0.210761 0.977538i $$-0.567594\pi$$
−0.210761 + 0.977538i $$0.567594\pi$$
$$648$$ 0 0
$$649$$ −0.832119 −0.0326635
$$650$$ −20.0262 7.28893i −0.785491 0.285895i
$$651$$ 0 0
$$652$$ 12.9179 + 10.8394i 0.505903 + 0.424503i
$$653$$ −6.20393 + 35.1842i −0.242778 + 1.37686i 0.582818 + 0.812603i $$0.301950\pi$$
−0.825596 + 0.564262i $$0.809161\pi$$
$$654$$ 0 0
$$655$$ 54.5269 45.7535i 2.13054 1.78774i
$$656$$ 0.121492 + 0.210430i 0.00474347 + 0.00821593i
$$657$$ 0 0
$$658$$ −7.10576 + 12.3075i −0.277011 + 0.479798i
$$659$$ −5.35978 30.3969i −0.208788 1.18409i −0.891367 0.453282i $$-0.850253\pi$$
0.682580 0.730811i $$-0.260858\pi$$
$$660$$ 0 0
$$661$$ 9.25402 3.36819i 0.359940 0.131007i −0.155719 0.987801i $$-0.549769\pi$$
0.515659 + 0.856794i $$0.327547\pi$$
$$662$$ 26.8228 9.76272i 1.04250 0.379439i
$$663$$ 0 0
$$664$$ −4.17617 23.6843i −0.162067 0.919128i
$$665$$ −15.2404 + 26.3971i −0.590996 + 1.02363i
$$666$$ 0 0
$$667$$ −9.52956 16.5057i −0.368986 0.639103i
$$668$$ −3.49273 + 2.93075i −0.135138 + 0.113394i
$$669$$ 0 0
$$670$$ 3.47431 19.7038i 0.134224 0.761223i
$$671$$ 0.470686 + 0.394952i 0.0181706 + 0.0152470i
$$672$$ 0 0
$$673$$ 18.5094 + 6.73687i 0.713485 + 0.259687i 0.673157 0.739499i $$-0.264938\pi$$
0.0403273 + 0.999187i $$0.487160\pi$$
$$674$$ 7.28642 0.280662
$$675$$ 0 0
$$676$$ 8.81345 0.338979
$$677$$ −26.7408 9.73286i −1.02773 0.374064i −0.227516 0.973774i $$-0.573060\pi$$
−0.800217 + 0.599710i $$0.795283\pi$$
$$678$$ 0 0
$$679$$ 6.53849 + 5.48644i 0.250924 + 0.210550i
$$680$$ −5.73442 + 32.5215i −0.219905 + 1.24714i
$$681$$ 0 0
$$682$$ 0.567581 0.476257i 0.0217338 0.0182368i
$$683$$ 6.25537 + 10.8346i 0.239355 + 0.414575i 0.960529 0.278179i $$-0.0897307\pi$$
−0.721174 + 0.692754i $$0.756397\pi$$
$$684$$ 0 0
$$685$$ −27.7631 + 48.0871i −1.06077 + 1.83731i
$$686$$ 3.07826 + 17.4577i 0.117528 + 0.666537i
$$687$$ 0 0
$$688$$ −0.245100 + 0.0892091i −0.00934435 + 0.00340106i
$$689$$ 3.18092 1.15776i 0.121183 0.0441072i
$$690$$ 0 0
$$691$$ 7.40184 + 41.9779i 0.281579 + 1.59691i 0.717255 + 0.696811i $$0.245398\pi$$
−0.435676 + 0.900104i $$0.643491\pi$$
$$692$$ 0.956462 1.65664i 0.0363592 0.0629760i
$$693$$ 0 0
$$694$$ 6.57919 + 11.3955i 0.249743 + 0.432567i
$$695$$ −31.1896 + 26.1712i −1.18309 + 0.992729i
$$696$$ 0 0
$$697$$ −3.02182 + 17.1376i −0.114460 + 0.649133i
$$698$$ 22.6655 + 19.0186i 0.857902 + 0.719865i
$$699$$ 0 0
$$700$$ −25.3092 9.21179i −0.956597 0.348173i
$$701$$ −51.7701 −1.95533 −0.977665 0.210167i $$-0.932599\pi$$
−0.977665 + 0.210167i $$0.932599\pi$$
$$702$$ 0 0
$$703$$ −23.8726 −0.900371
$$704$$ 0.769915 + 0.280226i 0.0290173 + 0.0105614i
$$705$$ 0 0
$$706$$ 10.6125 + 8.90491i 0.399405 + 0.335141i
$$707$$ −3.07826 + 17.4577i −0.115770 + 0.656563i
$$708$$ 0 0
$$709$$ 11.6120 9.74362i 0.436098 0.365929i −0.398149 0.917321i $$-0.630347\pi$$
0.834247 + 0.551391i $$0.185903\pi$$
$$710$$ 26.1288 + 45.2564i 0.980597 + 1.69844i
$$711$$ 0 0
$$712$$ −10.9555 + 18.9754i −0.410574 + 0.711135i
$$713$$ 2.55468 + 14.4883i 0.0956736 + 0.542592i
$$714$$ 0 0
$$715$$ −1.42855 + 0.519949i −0.0534247 + 0.0194450i
$$716$$ 14.0544 5.11538i 0.525237 0.191171i
$$717$$ 0 0
$$718$$ −2.76786 15.6973i −0.103295 0.585818i
$$719$$ −1.30747 + 2.26460i −0.0487603 + 0.0844553i −0.889375 0.457178i $$-0.848860\pi$$
0.840615 + 0.541633i $$0.182194\pi$$
$$720$$ 0 0
$$721$$ 20.3687 + 35.2796i 0.758570 + 1.31388i
$$722$$ −4.08693 + 3.42934i −0.152100 + 0.127627i
$$723$$ 0 0
$$724$$ 3.59405 20.3828i 0.133572 0.757522i
$$725$$ −51.7097 43.3896i −1.92045 1.61145i
$$726$$ 0 0
$$727$$ 3.85204 + 1.40203i 0.142864 + 0.0519984i 0.412463 0.910974i $$-0.364669\pi$$
−0.269598 + 0.962973i $$0.586891\pi$$
$$728$$ 14.9495 0.554067
$$729$$ 0 0
$$730$$ −29.6117 −1.09598
$$731$$ −17.5535 6.38895i −0.649240 0.236304i
$$732$$ 0 0
$$733$$ −29.2690 24.5596i −1.08108 0.907131i −0.0850668 0.996375i $$-0.527110\pi$$
−0.996010 + 0.0892443i $$0.971555\pi$$
$$734$$ −2.92319 + 16.5782i −0.107897 + 0.611914i
$$735$$ 0 0
$$736$$ −12.2554 + 10.2835i −0.451739 + 0.379054i
$$737$$ −0.476529 0.825373i −0.0175532 0.0304030i
$$738$$ 0 0
$$739$$ 12.1047 20.9660i 0.445279 0.771247i −0.552792 0.833319i $$-0.686438\pi$$
0.998072 + 0.0620725i $$0.0197710\pi$$
$$740$$ −5.48545 31.1095i −0.201649 1.14361i
$$741$$ 0 0
$$742$$ −2.53431 + 0.922414i −0.0930375 + 0.0338629i
$$743$$ −3.11169 + 1.13256i −0.114157 + 0.0415497i −0.398467 0.917183i $$-0.630458\pi$$
0.284310 + 0.958732i $$0.408235\pi$$
$$744$$ 0 0
$$745$$ −0.856381 4.85678i −0.0313754 0.177939i
$$746$$ 6.70527 11.6139i 0.245497 0.425214i
$$747$$ 0 0
$$748$$ 0.299011 + 0.517902i 0.0109329 + 0.0189364i
$$749$$ 12.7135 10.6679i 0.464540 0.389796i
$$750$$ 0 0
$$751$$ 2.38089 13.5027i 0.0868800 0.492721i −0.910055 0.414487i $$-0.863961\pi$$
0.996935 0.0782335i $$-0.0249280\pi$$
$$752$$ 0.237359 + 0.199168i 0.00865560 + 0.00726291i
$$753$$ 0 0
$$754$$ 13.3849 + 4.87171i 0.487449 + 0.177417i
$$755$$ −30.4807 −1.10931
$$756$$ 0 0
$$757$$ 12.3833 0.450079 0.225040 0.974350i $$-0.427749\pi$$
0.225040 + 0.974350i $$0.427749\pi$$
$$758$$ −8.13758 2.96184i −0.295570 0.107579i
$$759$$ 0 0
$$760$$ 30.3252 + 25.4459i 1.10001 + 0.923019i
$$761$$ −1.31671 + 7.46745i −0.0477308 + 0.270695i −0.999328 0.0366529i $$-0.988330\pi$$
0.951597 + 0.307348i $$0.0994415\pi$$
$$762$$ 0 0
$$763$$ 26.1728 21.9616i 0.947518 0.795062i
$$764$$ 10.7185 + 18.5650i 0.387783 + 0.671660i
$$765$$ 0 0
$$766$$ 12.4829 21.6211i 0.451026 0.781201i
$$767$$ 2.14425 + 12.1606i 0.0774243 + 0.439095i
$$768$$ 0 0
$$769$$ −3.02317 + 1.10034i −0.109018 + 0.0396794i −0.395953 0.918271i $$-0.629586\pi$$
0.286935 + 0.957950i $$0.407364\pi$$
$$770$$ 1.13816 0.414255i 0.0410163 0.0149287i
$$771$$ 0 0
$$772$$ 0.424373 + 2.40674i 0.0152735 + 0.0866205i
$$773$$ −0.0922341 + 0.159754i −0.00331743 + 0.00574596i −0.867679 0.497124i $$-0.834389\pi$$
0.864362 + 0.502870i $$0.167723\pi$$
$$774$$ 0 0
$$775$$ 26.0526 + 45.1245i 0.935838 + 1.62092i
$$776$$ 8.49185 7.12551i 0.304840 0.255791i
$$777$$ 0 0
$$778$$ −1.66209 + 9.42620i −0.0595889 + 0.337946i