# Properties

 Label 729.2.e.p.406.2 Level $729$ Weight $2$ Character 729.406 Analytic conductor $5.821$ Analytic rank $0$ Dimension $12$ CM no Inner twists $12$

# 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: $$0$$ Dimension: $$12$$ Relative dimension: $$2$$ over $$\Q(\zeta_{9})$$ Coefficient field: 12.0.101559956668416.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} - 8x^{6} + 64$$ x^12 - 8*x^6 + 64 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$3^{3}$$ Twist minimal: no (minimal twist has level 243) Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 406.2 Root $$1.39273 + 0.245576i$$ of defining polynomial Character $$\chi$$ $$=$$ 729.406 Dual form 729.2.e.p.325.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.87642 + 1.57450i) q^{2} +(0.694593 + 3.93923i) q^{4} +(2.30177 + 0.837775i) q^{5} +(0.347296 - 1.96962i) q^{7} +(-2.44949 + 4.24264i) q^{8} +O(q^{10})$$ $$q+(1.87642 + 1.57450i) q^{2} +(0.694593 + 3.93923i) q^{4} +(2.30177 + 0.837775i) q^{5} +(0.347296 - 1.96962i) q^{7} +(-2.44949 + 4.24264i) q^{8} +(3.00000 + 5.19615i) q^{10} +(-2.30177 + 0.837775i) q^{11} +(-0.766044 + 0.642788i) q^{13} +(3.75284 - 3.14900i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(3.67423 + 6.36396i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-1.70140 + 9.64911i) q^{20} +(-5.63816 - 2.05212i) q^{22} +(-0.425349 - 2.41228i) q^{23} +(0.766044 + 0.642788i) q^{25} -2.44949 q^{26} +8.00000 q^{28} +(-3.75284 - 3.14900i) q^{29} +(-0.173648 - 0.984808i) q^{31} +(-3.12567 + 17.7265i) q^{34} +(2.44949 - 4.24264i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(2.30177 - 0.837775i) q^{38} +(-9.19253 + 7.71345i) q^{40} +(3.75284 - 3.14900i) q^{41} +(-10.3366 + 3.76222i) q^{43} +(-4.89898 - 8.48528i) q^{44} +(3.00000 - 5.19615i) q^{46} +(1.70140 - 9.64911i) q^{47} +(2.81908 + 1.02606i) q^{49} +(0.425349 + 2.41228i) q^{50} +(-3.06418 - 2.57115i) q^{52} +7.34847 q^{53} -6.00000 q^{55} +(7.50567 + 6.29801i) q^{56} +(-2.08378 - 11.8177i) q^{58} +(2.30177 + 0.837775i) q^{59} +(0.868241 - 4.92404i) q^{61} +(1.22474 - 2.12132i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-2.30177 + 0.837775i) q^{65} +(-5.36231 + 4.49951i) q^{67} +(-22.5170 + 18.8940i) q^{68} +(11.2763 - 4.10424i) q^{70} +(-3.67423 - 6.36396i) q^{71} +(-5.50000 + 9.52628i) q^{73} +(3.40280 - 19.2982i) q^{74} +(3.75877 + 1.36808i) q^{76} +(0.850699 + 4.82455i) q^{77} +(-5.36231 - 4.49951i) q^{79} -9.79796 q^{80} +12.0000 q^{82} +(-9.38209 - 7.87251i) q^{83} +(3.12567 + 17.7265i) q^{85} +(-25.3194 - 9.21552i) q^{86} +(2.08378 - 11.8177i) q^{88} +(1.00000 + 1.73205i) q^{91} +(9.20707 - 3.35110i) q^{92} +(18.3851 - 15.4269i) q^{94} +(1.87642 - 1.57450i) q^{95} +(6.57785 - 2.39414i) q^{97} +(3.67423 + 6.36396i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q+O(q^{10})$$ 12 * q $$12 q + 36 q^{10} + 6 q^{19} + 96 q^{28} - 48 q^{37} + 36 q^{46} - 72 q^{55} + 48 q^{64} - 66 q^{73} + 144 q^{82} + 12 q^{91}+O(q^{100})$$ 12 * q + 36 * q^10 + 6 * q^19 + 96 * q^28 - 48 * q^37 + 36 * q^46 - 72 * q^55 + 48 * q^64 - 66 * q^73 + 144 * q^82 + 12 * q^91

## Character values

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

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.87642 + 1.57450i 1.32683 + 1.11334i 0.984808 + 0.173648i $$0.0555556\pi$$
0.342020 + 0.939693i $$0.388889\pi$$
$$3$$ 0 0
$$4$$ 0.694593 + 3.93923i 0.347296 + 1.96962i
$$5$$ 2.30177 + 0.837775i 1.02938 + 0.374664i 0.800845 0.598871i $$-0.204384\pi$$
0.228536 + 0.973535i $$0.426606\pi$$
$$6$$ 0 0
$$7$$ 0.347296 1.96962i 0.131266 0.744445i −0.846122 0.532989i $$-0.821069\pi$$
0.977388 0.211455i $$-0.0678203\pi$$
$$8$$ −2.44949 + 4.24264i −0.866025 + 1.50000i
$$9$$ 0 0
$$10$$ 3.00000 + 5.19615i 0.948683 + 1.64317i
$$11$$ −2.30177 + 0.837775i −0.694009 + 0.252599i −0.664851 0.746976i $$-0.731505\pi$$
−0.0291582 + 0.999575i $$0.509283\pi$$
$$12$$ 0 0
$$13$$ −0.766044 + 0.642788i −0.212463 + 0.178277i −0.742808 0.669504i $$-0.766507\pi$$
0.530346 + 0.847781i $$0.322062\pi$$
$$14$$ 3.75284 3.14900i 1.00299 0.841607i
$$15$$ 0 0
$$16$$ −3.75877 + 1.36808i −0.939693 + 0.342020i
$$17$$ 3.67423 + 6.36396i 0.891133 + 1.54349i 0.838519 + 0.544872i $$0.183422\pi$$
0.0526138 + 0.998615i $$0.483245\pi$$
$$18$$ 0 0
$$19$$ 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i $$-0.796740\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ −1.70140 + 9.64911i −0.380444 + 2.15761i
$$21$$ 0 0
$$22$$ −5.63816 2.05212i −1.20206 0.437514i
$$23$$ −0.425349 2.41228i −0.0886915 0.502994i −0.996499 0.0836069i $$-0.973356\pi$$
0.907807 0.419387i $$-0.137755\pi$$
$$24$$ 0 0
$$25$$ 0.766044 + 0.642788i 0.153209 + 0.128558i
$$26$$ −2.44949 −0.480384
$$27$$ 0 0
$$28$$ 8.00000 1.51186
$$29$$ −3.75284 3.14900i −0.696884 0.584755i 0.224001 0.974589i $$-0.428088\pi$$
−0.920885 + 0.389834i $$0.872533\pi$$
$$30$$ 0 0
$$31$$ −0.173648 0.984808i −0.0311881 0.176877i 0.965235 0.261385i $$-0.0841792\pi$$
−0.996423 + 0.0845082i $$0.973068\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ −3.12567 + 17.7265i −0.536048 + 3.04008i
$$35$$ 2.44949 4.24264i 0.414039 0.717137i
$$36$$ 0 0
$$37$$ −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i $$-0.938240\pi$$
0.323640 0.946180i $$-0.395093\pi$$
$$38$$ 2.30177 0.837775i 0.373396 0.135905i
$$39$$ 0 0
$$40$$ −9.19253 + 7.71345i −1.45347 + 1.21960i
$$41$$ 3.75284 3.14900i 0.586095 0.491792i −0.300848 0.953672i $$-0.597270\pi$$
0.886942 + 0.461881i $$0.152825\pi$$
$$42$$ 0 0
$$43$$ −10.3366 + 3.76222i −1.57632 + 0.573733i −0.974400 0.224823i $$-0.927820\pi$$
−0.601920 + 0.798556i $$0.705597\pi$$
$$44$$ −4.89898 8.48528i −0.738549 1.27920i
$$45$$ 0 0
$$46$$ 3.00000 5.19615i 0.442326 0.766131i
$$47$$ 1.70140 9.64911i 0.248174 1.40747i −0.564829 0.825208i $$-0.691058\pi$$
0.813003 0.582259i $$-0.197831\pi$$
$$48$$ 0 0
$$49$$ 2.81908 + 1.02606i 0.402725 + 0.146580i
$$50$$ 0.425349 + 2.41228i 0.0601535 + 0.341147i
$$51$$ 0 0
$$52$$ −3.06418 2.57115i −0.424925 0.356554i
$$53$$ 7.34847 1.00939 0.504695 0.863298i $$-0.331605\pi$$
0.504695 + 0.863298i $$0.331605\pi$$
$$54$$ 0 0
$$55$$ −6.00000 −0.809040
$$56$$ 7.50567 + 6.29801i 1.00299 + 0.841607i
$$57$$ 0 0
$$58$$ −2.08378 11.8177i −0.273613 1.55174i
$$59$$ 2.30177 + 0.837775i 0.299665 + 0.109069i 0.487477 0.873136i $$-0.337917\pi$$
−0.187812 + 0.982205i $$0.560140\pi$$
$$60$$ 0 0
$$61$$ 0.868241 4.92404i 0.111167 0.630459i −0.877410 0.479741i $$-0.840731\pi$$
0.988577 0.150717i $$-0.0481583\pi$$
$$62$$ 1.22474 2.12132i 0.155543 0.269408i
$$63$$ 0 0
$$64$$ 4.00000 + 6.92820i 0.500000 + 0.866025i
$$65$$ −2.30177 + 0.837775i −0.285499 + 0.103913i
$$66$$ 0 0
$$67$$ −5.36231 + 4.49951i −0.655111 + 0.549703i −0.908617 0.417631i $$-0.862861\pi$$
0.253506 + 0.967334i $$0.418416\pi$$
$$68$$ −22.5170 + 18.8940i −2.73059 + 2.29124i
$$69$$ 0 0
$$70$$ 11.2763 4.10424i 1.34778 0.490551i
$$71$$ −3.67423 6.36396i −0.436051 0.755263i 0.561329 0.827592i $$-0.310290\pi$$
−0.997381 + 0.0723293i $$0.976957\pi$$
$$72$$ 0 0
$$73$$ −5.50000 + 9.52628i −0.643726 + 1.11497i 0.340868 + 0.940111i $$0.389279\pi$$
−0.984594 + 0.174855i $$0.944054\pi$$
$$74$$ 3.40280 19.2982i 0.395567 2.24337i
$$75$$ 0 0
$$76$$ 3.75877 + 1.36808i 0.431161 + 0.156930i
$$77$$ 0.850699 + 4.82455i 0.0969461 + 0.549809i
$$78$$ 0 0
$$79$$ −5.36231 4.49951i −0.603307 0.506235i 0.289200 0.957269i $$-0.406611\pi$$
−0.892507 + 0.451034i $$0.851055\pi$$
$$80$$ −9.79796 −1.09545
$$81$$ 0 0
$$82$$ 12.0000 1.32518
$$83$$ −9.38209 7.87251i −1.02982 0.864120i −0.0389889 0.999240i $$-0.512414\pi$$
−0.990829 + 0.135120i $$0.956858\pi$$
$$84$$ 0 0
$$85$$ 3.12567 + 17.7265i 0.339026 + 1.92271i
$$86$$ −25.3194 9.21552i −2.73027 0.993735i
$$87$$ 0 0
$$88$$ 2.08378 11.8177i 0.222131 1.25977i
$$89$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$90$$ 0 0
$$91$$ 1.00000 + 1.73205i 0.104828 + 0.181568i
$$92$$ 9.20707 3.35110i 0.959903 0.349376i
$$93$$ 0 0
$$94$$ 18.3851 15.4269i 1.89627 1.59116i
$$95$$ 1.87642 1.57450i 0.192516 0.161540i
$$96$$ 0 0
$$97$$ 6.57785 2.39414i 0.667879 0.243088i 0.0142448 0.999899i $$-0.495466\pi$$
0.653635 + 0.756810i $$0.273243\pi$$
$$98$$ 3.67423 + 6.36396i 0.371154 + 0.642857i
$$99$$ 0 0
$$100$$ −2.00000 + 3.46410i −0.200000 + 0.346410i
$$101$$ −0.850699 + 4.82455i −0.0846477 + 0.480061i 0.912784 + 0.408442i $$0.133928\pi$$
−0.997432 + 0.0716191i $$0.977183\pi$$
$$102$$ 0 0
$$103$$ 6.57785 + 2.39414i 0.648135 + 0.235902i 0.645105 0.764094i $$-0.276813\pi$$
0.00302937 + 0.999995i $$0.499036\pi$$
$$104$$ −0.850699 4.82455i −0.0834179 0.473086i
$$105$$ 0 0
$$106$$ 13.7888 + 11.5702i 1.33929 + 1.12379i
$$107$$ 14.6969 1.42081 0.710403 0.703795i $$-0.248513\pi$$
0.710403 + 0.703795i $$0.248513\pi$$
$$108$$ 0 0
$$109$$ −1.00000 −0.0957826 −0.0478913 0.998853i $$-0.515250\pi$$
−0.0478913 + 0.998853i $$0.515250\pi$$
$$110$$ −11.2585 9.44701i −1.07346 0.900737i
$$111$$ 0 0
$$112$$ 1.38919 + 7.87846i 0.131266 + 0.744445i
$$113$$ 9.20707 + 3.35110i 0.866128 + 0.315245i 0.736598 0.676331i $$-0.236431\pi$$
0.129530 + 0.991575i $$0.458653\pi$$
$$114$$ 0 0
$$115$$ 1.04189 5.90885i 0.0971567 0.551003i
$$116$$ 9.79796 16.9706i 0.909718 1.57568i
$$117$$ 0 0
$$118$$ 3.00000 + 5.19615i 0.276172 + 0.478345i
$$119$$ 13.8106 5.02665i 1.26602 0.460792i
$$120$$ 0 0
$$121$$ −3.83022 + 3.21394i −0.348202 + 0.292176i
$$122$$ 9.38209 7.87251i 0.849415 0.712743i
$$123$$ 0 0
$$124$$ 3.75877 1.36808i 0.337548 0.122857i
$$125$$ −4.89898 8.48528i −0.438178 0.758947i
$$126$$ 0 0
$$127$$ 9.50000 16.4545i 0.842989 1.46010i −0.0443678 0.999015i $$-0.514127\pi$$
0.887357 0.461084i $$-0.152539\pi$$
$$128$$ −3.40280 + 19.2982i −0.300767 + 1.70574i
$$129$$ 0 0
$$130$$ −5.63816 2.05212i −0.494499 0.179983i
$$131$$ 2.12675 + 12.0614i 0.185815 + 1.05381i 0.924904 + 0.380200i $$0.124145\pi$$
−0.739089 + 0.673607i $$0.764744\pi$$
$$132$$ 0 0
$$133$$ −1.53209 1.28558i −0.132849 0.111474i
$$134$$ −17.1464 −1.48123
$$135$$ 0 0
$$136$$ −36.0000 −3.08697
$$137$$ 7.50567 + 6.29801i 0.641253 + 0.538075i 0.904403 0.426680i $$-0.140317\pi$$
−0.263150 + 0.964755i $$0.584761\pi$$
$$138$$ 0 0
$$139$$ −1.73648 9.84808i −0.147286 0.835303i −0.965503 0.260393i $$-0.916148\pi$$
0.818216 0.574910i $$-0.194963\pi$$
$$140$$ 18.4141 + 6.70220i 1.55628 + 0.566439i
$$141$$ 0 0
$$142$$ 3.12567 17.7265i 0.262300 1.48758i
$$143$$ 1.22474 2.12132i 0.102418 0.177394i
$$144$$ 0 0
$$145$$ −6.00000 10.3923i −0.498273 0.863034i
$$146$$ −25.3194 + 9.21552i −2.09545 + 0.762682i
$$147$$ 0 0
$$148$$ 24.5134 20.5692i 2.01499 1.69078i
$$149$$ 9.38209 7.87251i 0.768611 0.644941i −0.171742 0.985142i $$-0.554940\pi$$
0.940353 + 0.340201i $$0.110495\pi$$
$$150$$ 0 0
$$151$$ −4.69846 + 1.71010i −0.382356 + 0.139166i −0.526045 0.850457i $$-0.676326\pi$$
0.143689 + 0.989623i $$0.454103\pi$$
$$152$$ 2.44949 + 4.24264i 0.198680 + 0.344124i
$$153$$ 0 0
$$154$$ −6.00000 + 10.3923i −0.483494 + 0.837436i
$$155$$ 0.425349 2.41228i 0.0341649 0.193759i
$$156$$ 0 0
$$157$$ −15.9748 5.81434i −1.27493 0.464035i −0.386175 0.922426i $$-0.626204\pi$$
−0.888751 + 0.458391i $$0.848426\pi$$
$$158$$ −2.97745 16.8859i −0.236873 1.34337i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −4.89898 −0.386094
$$162$$ 0 0
$$163$$ −10.0000 −0.783260 −0.391630 0.920123i $$-0.628089\pi$$
−0.391630 + 0.920123i $$0.628089\pi$$
$$164$$ 15.0113 + 12.5960i 1.17219 + 0.983583i
$$165$$ 0 0
$$166$$ −5.20945 29.5442i −0.404331 2.29308i
$$167$$ −4.60353 1.67555i −0.356232 0.129658i 0.157704 0.987486i $$-0.449591\pi$$
−0.513936 + 0.857829i $$0.671813\pi$$
$$168$$ 0 0
$$169$$ −2.08378 + 11.8177i −0.160291 + 0.909053i
$$170$$ −22.0454 + 38.1838i −1.69081 + 2.92856i
$$171$$ 0 0
$$172$$ −22.0000 38.1051i −1.67748 2.90549i
$$173$$ −9.20707 + 3.35110i −0.700001 + 0.254779i −0.667411 0.744689i $$-0.732598\pi$$
−0.0325894 + 0.999469i $$0.510375\pi$$
$$174$$ 0 0
$$175$$ 1.53209 1.28558i 0.115815 0.0971804i
$$176$$ 7.50567 6.29801i 0.565761 0.474730i
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 7.34847 + 12.7279i 0.549250 + 0.951330i 0.998326 + 0.0578359i $$0.0184200\pi$$
−0.449076 + 0.893494i $$0.648247\pi$$
$$180$$ 0 0
$$181$$ −4.00000 + 6.92820i −0.297318 + 0.514969i −0.975521 0.219905i $$-0.929425\pi$$
0.678204 + 0.734874i $$0.262759\pi$$
$$182$$ −0.850699 + 4.82455i −0.0630580 + 0.357620i
$$183$$ 0 0
$$184$$ 11.2763 + 4.10424i 0.831301 + 0.302569i
$$185$$ −3.40280 19.2982i −0.250178 1.41883i
$$186$$ 0 0
$$187$$ −13.7888 11.5702i −1.00834 0.846095i
$$188$$ 39.1918 2.85836
$$189$$ 0 0
$$190$$ 6.00000 0.435286
$$191$$ 7.50567 + 6.29801i 0.543091 + 0.455708i 0.872594 0.488447i $$-0.162436\pi$$
−0.329502 + 0.944155i $$0.606881\pi$$
$$192$$ 0 0
$$193$$ 1.91013 + 10.8329i 0.137494 + 0.779768i 0.973090 + 0.230424i $$0.0740113\pi$$
−0.835596 + 0.549344i $$0.814878\pi$$
$$194$$ 16.1124 + 5.86442i 1.15680 + 0.421041i
$$195$$ 0 0
$$196$$ −2.08378 + 11.8177i −0.148841 + 0.844121i
$$197$$ −7.34847 + 12.7279i −0.523557 + 0.906827i 0.476067 + 0.879409i $$0.342062\pi$$
−0.999624 + 0.0274180i $$0.991271\pi$$
$$198$$ 0 0
$$199$$ 0.500000 + 0.866025i 0.0354441 + 0.0613909i 0.883203 0.468990i $$-0.155382\pi$$
−0.847759 + 0.530381i $$0.822049\pi$$
$$200$$ −4.60353 + 1.67555i −0.325519 + 0.118479i
$$201$$ 0 0
$$202$$ −9.19253 + 7.71345i −0.646784 + 0.542717i
$$203$$ −7.50567 + 6.29801i −0.526795 + 0.442033i
$$204$$ 0 0
$$205$$ 11.2763 4.10424i 0.787572 0.286653i
$$206$$ 8.57321 + 14.8492i 0.597324 + 1.03460i
$$207$$ 0 0
$$208$$ 2.00000 3.46410i 0.138675 0.240192i
$$209$$ −0.425349 + 2.41228i −0.0294220 + 0.166861i
$$210$$ 0 0
$$211$$ 0.939693 + 0.342020i 0.0646911 + 0.0235456i 0.374163 0.927363i $$-0.377930\pi$$
−0.309472 + 0.950909i $$0.600152\pi$$
$$212$$ 5.10419 + 28.9473i 0.350557 + 1.98811i
$$213$$ 0 0
$$214$$ 27.5776 + 23.1404i 1.88517 + 1.58184i
$$215$$ −26.9444 −1.83759
$$216$$ 0 0
$$217$$ −2.00000 −0.135769
$$218$$ −1.87642 1.57450i −0.127087 0.106639i
$$219$$ 0 0
$$220$$ −4.16756 23.6354i −0.280977 1.59350i
$$221$$ −6.90530 2.51332i −0.464501 0.169065i
$$222$$ 0 0
$$223$$ −1.21554 + 6.89365i −0.0813984 + 0.461633i 0.916677 + 0.399628i $$0.130861\pi$$
−0.998076 + 0.0620053i $$0.980250\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 12.0000 + 20.7846i 0.798228 + 1.38257i
$$227$$ −9.20707 + 3.35110i −0.611095 + 0.222420i −0.628982 0.777420i $$-0.716528\pi$$
0.0178875 + 0.999840i $$0.494306\pi$$
$$228$$ 0 0
$$229$$ −0.766044 + 0.642788i −0.0506216 + 0.0424766i −0.667747 0.744388i $$-0.732741\pi$$
0.617126 + 0.786864i $$0.288297\pi$$
$$230$$ 11.2585 9.44701i 0.742364 0.622917i
$$231$$ 0 0
$$232$$ 22.5526 8.20848i 1.48065 0.538913i
$$233$$ 3.67423 + 6.36396i 0.240707 + 0.416917i 0.960916 0.276840i $$-0.0892873\pi$$
−0.720209 + 0.693757i $$0.755954\pi$$
$$234$$ 0 0
$$235$$ 12.0000 20.7846i 0.782794 1.35584i
$$236$$ −1.70140 + 9.64911i −0.110752 + 0.628103i
$$237$$ 0 0
$$238$$ 33.8289 + 12.3127i 2.19280 + 0.798115i
$$239$$ −0.425349 2.41228i −0.0275136 0.156037i 0.967956 0.251121i $$-0.0807992\pi$$
−0.995469 + 0.0950838i $$0.969688\pi$$
$$240$$ 0 0
$$241$$ −12.2567 10.2846i −0.789524 0.662489i 0.156103 0.987741i $$-0.450107\pi$$
−0.945628 + 0.325251i $$0.894551\pi$$
$$242$$ −12.2474 −0.787296
$$243$$ 0 0
$$244$$ 20.0000 1.28037
$$245$$ 5.62925 + 4.72350i 0.359640 + 0.301774i
$$246$$ 0 0
$$247$$ 0.173648 + 0.984808i 0.0110490 + 0.0626618i
$$248$$ 4.60353 + 1.67555i 0.292325 + 0.106398i
$$249$$ 0 0
$$250$$ 4.16756 23.6354i 0.263579 1.49483i
$$251$$ 3.67423 6.36396i 0.231916 0.401690i −0.726456 0.687213i $$-0.758834\pi$$
0.958372 + 0.285523i $$0.0921673\pi$$
$$252$$ 0 0
$$253$$ 3.00000 + 5.19615i 0.188608 + 0.326679i
$$254$$ 43.7336 15.9177i 2.74409 0.998767i
$$255$$ 0 0
$$256$$ −24.5134 + 20.5692i −1.53209 + 1.28558i
$$257$$ −13.1349 + 11.0215i −0.819334 + 0.687503i −0.952816 0.303548i $$-0.901829\pi$$
0.133482 + 0.991051i $$0.457384\pi$$
$$258$$ 0 0
$$259$$ −15.0351 + 5.47232i −0.934235 + 0.340034i
$$260$$ −4.89898 8.48528i −0.303822 0.526235i
$$261$$ 0 0
$$262$$ −15.0000 + 25.9808i −0.926703 + 1.60510i
$$263$$ −4.67884 + 26.5350i −0.288510 + 1.63622i 0.403962 + 0.914776i $$0.367633\pi$$
−0.692472 + 0.721445i $$0.743478\pi$$
$$264$$ 0 0
$$265$$ 16.9145 + 6.15636i 1.03905 + 0.378182i
$$266$$ −0.850699 4.82455i −0.0521597 0.295812i
$$267$$ 0 0
$$268$$ −21.4492 17.9981i −1.31022 1.09941i
$$269$$ −22.0454 −1.34413 −0.672066 0.740491i $$-0.734593\pi$$
−0.672066 + 0.740491i $$0.734593\pi$$
$$270$$ 0 0
$$271$$ −7.00000 −0.425220 −0.212610 0.977137i $$-0.568196\pi$$
−0.212610 + 0.977137i $$0.568196\pi$$
$$272$$ −22.5170 18.8940i −1.36529 1.14562i
$$273$$ 0 0
$$274$$ 4.16756 + 23.6354i 0.251771 + 1.42787i
$$275$$ −2.30177 0.837775i −0.138802 0.0505197i
$$276$$ 0 0
$$277$$ 1.91013 10.8329i 0.114769 0.650885i −0.872096 0.489335i $$-0.837240\pi$$
0.986865 0.161550i $$-0.0516493\pi$$
$$278$$ 12.2474 21.2132i 0.734553 1.27228i
$$279$$ 0 0
$$280$$ 12.0000 + 20.7846i 0.717137 + 1.24212i
$$281$$ 11.5088 4.18887i 0.686560 0.249887i 0.0248982 0.999690i $$-0.492074\pi$$
0.661661 + 0.749803i $$0.269852\pi$$
$$282$$ 0 0
$$283$$ 13.0228 10.9274i 0.774122 0.649566i −0.167639 0.985849i $$-0.553614\pi$$
0.941761 + 0.336283i $$0.109170\pi$$
$$284$$ 22.5170 18.8940i 1.33614 1.12115i
$$285$$ 0 0
$$286$$ 5.63816 2.05212i 0.333391 0.121344i
$$287$$ −4.89898 8.48528i −0.289178 0.500870i
$$288$$ 0 0
$$289$$ −18.5000 + 32.0429i −1.08824 + 1.88488i
$$290$$ 5.10419 28.9473i 0.299729 1.69985i
$$291$$ 0 0
$$292$$ −41.3465 15.0489i −2.41962 0.880669i
$$293$$ 0.850699 + 4.82455i 0.0496984 + 0.281853i 0.999521 0.0309343i $$-0.00984827\pi$$
−0.949823 + 0.312788i $$0.898737\pi$$
$$294$$ 0 0
$$295$$ 4.59627 + 3.85673i 0.267605 + 0.224547i
$$296$$ 39.1918 2.27798
$$297$$ 0 0
$$298$$ 30.0000 1.73785
$$299$$ 1.87642 + 1.57450i 0.108516 + 0.0910558i
$$300$$ 0 0
$$301$$ 3.82026 + 21.6658i 0.220196 + 1.24879i
$$302$$ −11.5088 4.18887i −0.662259 0.241043i
$$303$$ 0 0
$$304$$ −0.694593 + 3.93923i −0.0398376 + 0.225930i
$$305$$ 6.12372 10.6066i 0.350643 0.607332i
$$306$$ 0 0
$$307$$ −1.00000 1.73205i −0.0570730 0.0988534i 0.836077 0.548612i $$-0.184843\pi$$
−0.893150 + 0.449758i $$0.851510\pi$$
$$308$$ −18.4141 + 6.70220i −1.04924 + 0.381893i
$$309$$ 0 0
$$310$$ 4.59627 3.85673i 0.261050 0.219047i
$$311$$ −18.7642 + 15.7450i −1.06402 + 0.892818i −0.994497 0.104762i $$-0.966592\pi$$
−0.0695218 + 0.997580i $$0.522147\pi$$
$$312$$ 0 0
$$313$$ 15.0351 5.47232i 0.849833 0.309314i 0.119861 0.992791i $$-0.461755\pi$$
0.729972 + 0.683477i $$0.239533\pi$$
$$314$$ −20.8207 36.0624i −1.17498 2.03512i
$$315$$ 0 0
$$316$$ 14.0000 24.2487i 0.787562 1.36410i
$$317$$ 1.70140 9.64911i 0.0955600 0.541948i −0.899014 0.437919i $$-0.855716\pi$$
0.994574 0.104029i $$-0.0331733\pi$$
$$318$$ 0 0
$$319$$ 11.2763 + 4.10424i 0.631352 + 0.229793i
$$320$$ 3.40280 + 19.2982i 0.190222 + 1.07880i
$$321$$ 0 0
$$322$$ −9.19253 7.71345i −0.512280 0.429854i
$$323$$ 7.34847 0.408880
$$324$$ 0 0
$$325$$ −1.00000 −0.0554700
$$326$$ −18.7642 15.7450i −1.03925 0.872036i
$$327$$ 0 0
$$328$$ 4.16756 + 23.6354i 0.230115 + 1.30505i
$$329$$ −18.4141 6.70220i −1.01520 0.369504i
$$330$$ 0 0
$$331$$ −1.21554 + 6.89365i −0.0668120 + 0.378910i 0.933007 + 0.359859i $$0.117175\pi$$
−0.999819 + 0.0190501i $$0.993936\pi$$
$$332$$ 24.4949 42.4264i 1.34433 2.32845i
$$333$$ 0 0
$$334$$ −6.00000 10.3923i −0.328305 0.568642i
$$335$$ −16.1124 + 5.86442i −0.880313 + 0.320408i
$$336$$ 0 0
$$337$$ −21.4492 + 17.9981i −1.16841 + 0.980416i −0.999986 0.00529739i $$-0.998314\pi$$
−0.168429 + 0.985714i $$0.553869\pi$$
$$338$$ −22.5170 + 18.8940i −1.22476 + 1.02770i
$$339$$ 0 0
$$340$$ −67.6579 + 24.6255i −3.66926 + 1.33550i
$$341$$ 1.22474 + 2.12132i 0.0663237 + 0.114876i
$$342$$ 0 0
$$343$$ 10.0000 17.3205i 0.539949 0.935220i
$$344$$ 9.35769 53.0701i 0.504533 2.86135i
$$345$$ 0 0
$$346$$ −22.5526 8.20848i −1.21244 0.441291i
$$347$$ −4.25349 24.1228i −0.228340 1.29498i −0.856197 0.516650i $$-0.827179\pi$$
0.627857 0.778328i $$-0.283932\pi$$
$$348$$ 0 0
$$349$$ 15.3209 + 12.8558i 0.820108 + 0.688153i 0.952997 0.302978i $$-0.0979810\pi$$
−0.132889 + 0.991131i $$0.542425\pi$$
$$350$$ 4.89898 0.261861
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1.87642 + 1.57450i 0.0998717 + 0.0838023i 0.691356 0.722514i $$-0.257014\pi$$
−0.591485 + 0.806316i $$0.701458\pi$$
$$354$$ 0 0
$$355$$ −3.12567 17.7265i −0.165893 0.940827i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ −6.25133 + 35.4531i −0.330393 + 1.87375i
$$359$$ −14.6969 + 25.4558i −0.775675 + 1.34351i 0.158740 + 0.987320i $$0.449257\pi$$
−0.934414 + 0.356188i $$0.884076\pi$$
$$360$$ 0 0
$$361$$ 9.00000 + 15.5885i 0.473684 + 0.820445i
$$362$$ −18.4141 + 6.70220i −0.967826 + 0.352260i
$$363$$ 0 0
$$364$$ −6.12836 + 5.14230i −0.321213 + 0.269530i
$$365$$ −20.6406 + 17.3195i −1.08038 + 0.906545i
$$366$$ 0 0
$$367$$ −4.69846 + 1.71010i −0.245258 + 0.0892665i −0.461724 0.887024i $$-0.652769\pi$$
0.216466 + 0.976290i $$0.430547\pi$$
$$368$$ 4.89898 + 8.48528i 0.255377 + 0.442326i
$$369$$ 0 0
$$370$$ 24.0000 41.5692i 1.24770 2.16108i
$$371$$ 2.55210 14.4737i 0.132498 0.751435i
$$372$$ 0 0
$$373$$ −32.8892 11.9707i −1.70294 0.619820i −0.706785 0.707428i $$-0.749855\pi$$
−0.996155 + 0.0876084i $$0.972078\pi$$
$$374$$ −7.65629 43.4210i −0.395897 2.24525i
$$375$$ 0 0
$$376$$ 36.7701 + 30.8538i 1.89627 + 1.59116i
$$377$$ 4.89898 0.252310
$$378$$ 0 0
$$379$$ 8.00000 0.410932 0.205466 0.978664i $$-0.434129\pi$$
0.205466 + 0.978664i $$0.434129\pi$$
$$380$$ 7.50567 + 6.29801i 0.385033 + 0.323081i
$$381$$ 0 0
$$382$$ 4.16756 + 23.6354i 0.213231 + 1.20929i
$$383$$ −32.2247 11.7288i −1.64661 0.599316i −0.658432 0.752641i $$-0.728780\pi$$
−0.988176 + 0.153324i $$0.951002\pi$$
$$384$$ 0 0
$$385$$ −2.08378 + 11.8177i −0.106199 + 0.602285i
$$386$$ −13.4722 + 23.3345i −0.685717 + 1.18770i
$$387$$ 0 0
$$388$$ 14.0000 + 24.2487i 0.710742 + 1.23104i
$$389$$ 25.3194 9.21552i 1.28375 0.467246i 0.392077 0.919932i $$-0.371757\pi$$
0.891670 + 0.452687i $$0.149534\pi$$
$$390$$ 0 0
$$391$$ 13.7888 11.5702i 0.697330 0.585129i
$$392$$ −11.2585 + 9.44701i −0.568641 + 0.477146i
$$393$$ 0 0
$$394$$ −33.8289 + 12.3127i −1.70428 + 0.620306i
$$395$$ −8.57321 14.8492i −0.431365 0.747146i
$$396$$ 0 0
$$397$$ 0.500000 0.866025i 0.0250943 0.0434646i −0.853206 0.521575i $$-0.825345\pi$$
0.878300 + 0.478110i $$0.158678\pi$$
$$398$$ −0.425349 + 2.41228i −0.0213208 + 0.120916i
$$399$$ 0 0
$$400$$ −3.75877 1.36808i −0.187939 0.0684040i
$$401$$ 5.95489 + 33.7719i 0.297373 + 1.68649i 0.657398 + 0.753544i $$0.271657\pi$$
−0.360024 + 0.932943i $$0.617232\pi$$
$$402$$ 0 0
$$403$$ 0.766044 + 0.642788i 0.0381594 + 0.0320195i
$$404$$ −19.5959 −0.974933
$$405$$ 0 0
$$406$$ −24.0000 −1.19110
$$407$$ 15.0113 + 12.5960i 0.744085 + 0.624361i
$$408$$ 0 0
$$409$$ −4.86215 27.5746i −0.240418 1.36348i −0.830898 0.556425i $$-0.812173\pi$$
0.590480 0.807052i $$-0.298938\pi$$
$$410$$ 27.6212 + 10.0533i 1.36411 + 0.496497i
$$411$$ 0 0
$$412$$ −4.86215 + 27.5746i −0.239541 + 1.35850i
$$413$$ 2.44949 4.24264i 0.120532 0.208767i
$$414$$ 0 0
$$415$$ −15.0000 25.9808i −0.736321 1.27535i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ −4.59627 + 3.85673i −0.224811 + 0.188639i
$$419$$ 26.2699 22.0430i 1.28337 1.07687i 0.290596 0.956846i $$-0.406147\pi$$
0.992771 0.120026i $$-0.0382978\pi$$
$$420$$ 0 0
$$421$$ −1.87939 + 0.684040i −0.0915956 + 0.0333381i −0.387412 0.921907i $$-0.626631\pi$$
0.295816 + 0.955245i $$0.404409\pi$$
$$422$$ 1.22474 + 2.12132i 0.0596196 + 0.103264i
$$423$$ 0 0
$$424$$ −18.0000 + 31.1769i −0.874157 + 1.51408i
$$425$$ −1.27605 + 7.23683i −0.0618974 + 0.351038i
$$426$$ 0 0
$$427$$ −9.39693 3.42020i −0.454749 0.165515i
$$428$$ 10.2084 + 57.8946i 0.493441 + 2.79844i
$$429$$ 0 0
$$430$$ −50.5589 42.4240i −2.43817 2.04587i
$$431$$ −7.34847 −0.353963 −0.176982 0.984214i $$-0.556633\pi$$
−0.176982 + 0.984214i $$0.556633\pi$$
$$432$$ 0 0
$$433$$ 17.0000 0.816968 0.408484 0.912766i $$-0.366058\pi$$
0.408484 + 0.912766i $$0.366058\pi$$
$$434$$ −3.75284 3.14900i −0.180142 0.151157i
$$435$$ 0 0
$$436$$ −0.694593 3.93923i −0.0332650 0.188655i
$$437$$ −2.30177 0.837775i −0.110108 0.0400762i
$$438$$ 0 0
$$439$$ 2.43107 13.7873i 0.116029 0.658032i −0.870207 0.492687i $$-0.836015\pi$$
0.986236 0.165346i $$-0.0528740\pi$$
$$440$$ 14.6969 25.4558i 0.700649 1.21356i
$$441$$ 0 0
$$442$$ −9.00000 15.5885i −0.428086 0.741467i
$$443$$ 11.5088 4.18887i 0.546801 0.199019i −0.0538234 0.998550i $$-0.517141\pi$$
0.600625 + 0.799531i $$0.294919\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −13.1349 + 11.0215i −0.621957 + 0.521884i
$$447$$ 0 0
$$448$$ 15.0351 5.47232i 0.710341 0.258543i
$$449$$ −11.0227 19.0919i −0.520194 0.901002i −0.999724 0.0234766i $$-0.992526\pi$$
0.479531 0.877525i $$-0.340807\pi$$
$$450$$ 0 0
$$451$$ −6.00000 + 10.3923i −0.282529 + 0.489355i
$$452$$ −6.80559 + 38.5964i −0.320108 + 1.81542i
$$453$$ 0 0
$$454$$ −22.5526 8.20848i −1.05845 0.385243i
$$455$$ 0.850699 + 4.82455i 0.0398814 + 0.226179i
$$456$$ 0 0
$$457$$ 22.2153 + 18.6408i 1.03919 + 0.871982i 0.991915 0.126900i $$-0.0405028\pi$$
0.0472719 + 0.998882i $$0.484947\pi$$
$$458$$ −2.44949 −0.114457
$$459$$ 0 0
$$460$$ 24.0000 1.11901
$$461$$ −20.6406 17.3195i −0.961328 0.806650i 0.0198402 0.999803i $$-0.493684\pi$$
−0.981169 + 0.193153i $$0.938129\pi$$
$$462$$ 0 0
$$463$$ −3.29932 18.7113i −0.153332 0.869590i −0.960295 0.278987i $$-0.910001\pi$$
0.806963 0.590603i $$-0.201110\pi$$
$$464$$ 18.4141 + 6.70220i 0.854855 + 0.311142i
$$465$$ 0 0
$$466$$ −3.12567 + 17.7265i −0.144794 + 0.821166i
$$467$$ −7.34847 + 12.7279i −0.340047 + 0.588978i −0.984441 0.175715i $$-0.943776\pi$$
0.644394 + 0.764693i $$0.277110\pi$$
$$468$$ 0 0
$$469$$ 7.00000 + 12.1244i 0.323230 + 0.559851i
$$470$$ 55.2424 20.1066i 2.54814 0.927448i
$$471$$ 0 0
$$472$$ −9.19253 + 7.71345i −0.423121 + 0.355040i
$$473$$ 20.6406 17.3195i 0.949056 0.796352i
$$474$$ 0 0
$$475$$ 0.939693 0.342020i 0.0431161 0.0156930i
$$476$$ 29.3939 + 50.9117i 1.34727 + 2.33353i
$$477$$ 0 0
$$478$$ 3.00000 5.19615i 0.137217 0.237666i
$$479$$ −4.67884 + 26.5350i −0.213782 + 1.21242i 0.669226 + 0.743059i $$0.266626\pi$$
−0.883008 + 0.469358i $$0.844485\pi$$
$$480$$ 0 0
$$481$$ 7.51754 + 2.73616i 0.342770 + 0.124758i
$$482$$ −6.80559 38.5964i −0.309986 1.75802i
$$483$$ 0 0
$$484$$ −15.3209 12.8558i −0.696404 0.584352i
$$485$$ 17.1464 0.778579
$$486$$ 0 0
$$487$$ 35.0000 1.58600 0.793001 0.609221i $$-0.208518\pi$$
0.793001 + 0.609221i $$0.208518\pi$$
$$488$$ 18.7642 + 15.7450i 0.849415 + 0.712743i
$$489$$ 0 0
$$490$$ 3.12567 + 17.7265i 0.141203 + 0.800803i
$$491$$ 36.8283 + 13.4044i 1.66204 + 0.604932i 0.990681 0.136203i $$-0.0434899\pi$$
0.671356 + 0.741135i $$0.265712\pi$$
$$492$$ 0 0
$$493$$ 6.25133 35.4531i 0.281546 1.59673i
$$494$$ −1.22474 + 2.12132i −0.0551039 + 0.0954427i
$$495$$ 0 0
$$496$$ 2.00000 + 3.46410i 0.0898027 + 0.155543i
$$497$$ −13.8106 + 5.02665i −0.619490 + 0.225476i
$$498$$ 0 0
$$499$$ 1.53209 1.28558i 0.0685857 0.0575503i −0.607850 0.794052i $$-0.707968\pi$$
0.676436 + 0.736501i $$0.263524\pi$$
$$500$$ 30.0227 25.1920i 1.34266 1.12662i
$$501$$ 0 0
$$502$$ 16.9145 6.15636i 0.754930 0.274772i
$$503$$ 7.34847 + 12.7279i 0.327652 + 0.567510i 0.982045 0.188644i $$-0.0604093\pi$$
−0.654393 + 0.756154i $$0.727076\pi$$
$$504$$ 0 0
$$505$$ −6.00000 + 10.3923i −0.266996 + 0.462451i
$$506$$ −2.55210 + 14.4737i −0.113455 + 0.643433i
$$507$$ 0 0
$$508$$ 71.4166 + 25.9935i 3.16860 + 1.15328i
$$509$$ −1.70140 9.64911i −0.0754131 0.427689i −0.999017 0.0443397i $$-0.985882\pi$$
0.923603 0.383349i $$-0.125229\pi$$
$$510$$ 0 0
$$511$$ 16.8530 + 14.1413i 0.745532 + 0.625575i
$$512$$ −39.1918 −1.73205
$$513$$ 0 0
$$514$$ −42.0000 −1.85254
$$515$$ 13.1349 + 11.0215i 0.578794 + 0.485666i
$$516$$ 0 0
$$517$$ 4.16756 + 23.6354i 0.183289 + 1.03948i
$$518$$ −36.8283 13.4044i −1.61814 0.588955i
$$519$$ 0 0
$$520$$ 2.08378 11.8177i 0.0913797 0.518240i
$$521$$ −11.0227 + 19.0919i −0.482913 + 0.836431i −0.999808 0.0196188i $$-0.993755\pi$$
0.516894 + 0.856049i $$0.327088\pi$$
$$522$$ 0 0
$$523$$ 12.5000 + 21.6506i 0.546587 + 0.946716i 0.998505 + 0.0546569i $$0.0174065\pi$$
−0.451918 + 0.892059i $$0.649260\pi$$
$$524$$ −46.0353 + 16.7555i −2.01106 + 0.731967i
$$525$$ 0 0
$$526$$ −50.5589 + 42.4240i −2.20447 + 1.84977i
$$527$$ 5.62925 4.72350i 0.245214 0.205759i
$$528$$ 0 0
$$529$$ 15.9748 5.81434i 0.694555 0.252797i
$$530$$ 22.0454 + 38.1838i 0.957591 + 1.65860i
$$531$$ 0 0
$$532$$ 4.00000 6.92820i 0.173422 0.300376i
$$533$$ −0.850699 + 4.82455i −0.0368479 + 0.208975i
$$534$$ 0 0
$$535$$ 33.8289 + 12.3127i 1.46255 + 0.532326i
$$536$$ −5.95489 33.7719i −0.257212 1.45872i
$$537$$ 0 0
$$538$$ −41.3664 34.7105i −1.78343 1.49648i
$$539$$ −7.34847 −0.316521
$$540$$ 0 0
$$541$$ −28.0000 −1.20381 −0.601907 0.798566i $$-0.705592\pi$$
−0.601907 + 0.798566i $$0.705592\pi$$
$$542$$ −13.1349 11.0215i −0.564193 0.473414i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −2.30177 0.837775i −0.0985969 0.0358863i
$$546$$ 0 0
$$547$$ −2.25743 + 12.8025i −0.0965206 + 0.547395i 0.897750 + 0.440505i $$0.145201\pi$$
−0.994271 + 0.106891i $$0.965911\pi$$
$$548$$ −19.5959 + 33.9411i −0.837096 + 1.44989i
$$549$$ 0 0
$$550$$ −3.00000 5.19615i −0.127920 0.221565i
$$551$$ −4.60353 + 1.67555i −0.196117 + 0.0713808i
$$552$$ 0 0
$$553$$ −10.7246 + 8.99903i −0.456057 + 0.382678i
$$554$$ 20.6406 17.3195i 0.876935 0.735836i
$$555$$ 0 0
$$556$$ 37.5877 13.6808i 1.59407 0.580195i
$$557$$ −3.67423 6.36396i −0.155682 0.269650i 0.777625 0.628728i $$-0.216424\pi$$
−0.933307 + 0.359079i $$0.883091\pi$$
$$558$$ 0 0
$$559$$ 5.50000 9.52628i 0.232625 0.402919i
$$560$$ −3.40280 + 19.2982i −0.143794 + 0.815498i
$$561$$ 0 0
$$562$$ 28.1908 + 10.2606i 1.18916 + 0.432817i
$$563$$ 2.12675 + 12.0614i 0.0896317 + 0.508327i 0.996261 + 0.0863979i $$0.0275356\pi$$
−0.906629 + 0.421929i $$0.861353\pi$$
$$564$$ 0 0
$$565$$ 18.3851 + 15.4269i 0.773466 + 0.649015i
$$566$$ 41.6413 1.75032
$$567$$ 0 0
$$568$$ 36.0000 1.51053
$$569$$ −9.38209 7.87251i −0.393318 0.330033i 0.424586 0.905387i $$-0.360420\pi$$
−0.817904 + 0.575355i $$0.804864\pi$$
$$570$$ 0 0
$$571$$ −1.73648 9.84808i −0.0726695 0.412129i −0.999342 0.0362604i $$-0.988455\pi$$
0.926673 0.375869i $$-0.122656\pi$$
$$572$$ 9.20707 + 3.35110i 0.384967 + 0.140117i
$$573$$ 0 0
$$574$$ 4.16756 23.6354i 0.173950 0.986522i
$$575$$ 1.22474 2.12132i 0.0510754 0.0884652i
$$576$$ 0 0
$$577$$ 12.5000 + 21.6506i 0.520382 + 0.901328i 0.999719 + 0.0236970i $$0.00754370\pi$$
−0.479337 + 0.877631i $$0.659123\pi$$
$$578$$ −85.1654 + 30.9977i −3.54241 + 1.28933i
$$579$$ 0 0
$$580$$ 36.7701 30.8538i 1.52680 1.28113i
$$581$$ −18.7642 + 15.7450i −0.778469 + 0.653213i
$$582$$ 0 0
$$583$$ −16.9145 + 6.15636i −0.700526 + 0.254970i
$$584$$ −26.9444 46.6690i −1.11497 1.93118i
$$585$$ 0 0
$$586$$ −6.00000 + 10.3923i −0.247858 + 0.429302i
$$587$$ 0.425349 2.41228i 0.0175560 0.0995653i −0.974771 0.223209i $$-0.928347\pi$$
0.992327 + 0.123644i $$0.0394579\pi$$
$$588$$ 0 0
$$589$$ −0.939693 0.342020i −0.0387194 0.0140927i
$$590$$ 2.55210 + 14.4737i 0.105068 + 0.595871i
$$591$$ 0 0
$$592$$ 24.5134 + 20.5692i 1.00750 + 0.845389i
$$593$$ 7.34847 0.301765 0.150883 0.988552i $$-0.451788\pi$$
0.150883 + 0.988552i $$0.451788\pi$$
$$594$$ 0 0
$$595$$ 36.0000 1.47586
$$596$$ 37.5284 + 31.4900i 1.53722 + 1.28988i
$$597$$ 0 0
$$598$$ 1.04189 + 5.90885i 0.0426060 + 0.241631i
$$599$$ 36.8283 + 13.4044i 1.50476 + 0.547689i 0.957289 0.289134i $$-0.0933673\pi$$
0.547474 + 0.836823i $$0.315589\pi$$
$$600$$ 0 0
$$601$$ −1.21554 + 6.89365i −0.0495828 + 0.281198i −0.999511 0.0312703i $$-0.990045\pi$$
0.949928 + 0.312468i $$0.101156\pi$$
$$602$$ −26.9444 + 46.6690i −1.09817 + 1.90209i
$$603$$ 0 0
$$604$$ −10.0000 17.3205i −0.406894 0.704761i
$$605$$ −11.5088 + 4.18887i −0.467901 + 0.170302i
$$606$$ 0 0
$$607$$ 33.7060 28.2827i 1.36808 1.14796i 0.394690 0.918814i $$-0.370852\pi$$
0.973393 0.229143i $$-0.0735924\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 28.1908 10.2606i 1.14141 0.415440i
$$611$$ 4.89898 + 8.48528i 0.198191 + 0.343278i
$$612$$ 0 0
$$613$$ −5.50000 + 9.52628i −0.222143 + 0.384763i −0.955458 0.295126i $$-0.904638\pi$$
0.733316 + 0.679888i $$0.237972\pi$$
$$614$$ 0.850699 4.82455i 0.0343314 0.194703i
$$615$$ 0 0
$$616$$ −22.5526 8.20848i −0.908671 0.330729i
$$617$$ −4.25349 24.1228i −0.171239 0.971146i −0.942396 0.334500i $$-0.891432\pi$$
0.771156 0.636646i $$-0.219679\pi$$
$$618$$ 0 0
$$619$$ −37.5362 31.4966i −1.50871 1.26595i −0.866226 0.499653i $$-0.833461\pi$$
−0.642481 0.766302i $$-0.722095\pi$$
$$620$$ 9.79796 0.393496
$$621$$ 0 0
$$622$$ −60.0000 −2.40578
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −5.03580 28.5594i −0.201432 1.14238i
$$626$$ 36.8283 + 13.4044i 1.47195 + 0.535747i
$$627$$ 0 0
$$628$$ 11.8081 66.9669i 0.471194 2.67227i
$$629$$ 29.3939 50.9117i 1.17201 2.02998i
$$630$$ 0 0
$$631$$ −22.0000 38.1051i −0.875806 1.51694i −0.855901 0.517139i $$-0.826997\pi$$
−0.0199047 0.999802i $$-0.506336\pi$$
$$632$$ 32.2247 11.7288i 1.28183 0.466549i
$$633$$ 0 0
$$634$$ 18.3851 15.4269i 0.730164 0.612681i
$$635$$ 35.6519 29.9155i 1.41480 1.18716i
$$636$$ 0 0
$$637$$ −2.81908 + 1.02606i −0.111696 + 0.0406540i
$$638$$ 14.6969 + 25.4558i 0.581857 + 1.00781i
$$639$$ 0 0
$$640$$ −24.0000 + 41.5692i −0.948683 + 1.64317i
$$641$$ 2.97745 16.8859i 0.117602 0.666954i −0.867827 0.496867i $$-0.834484\pi$$
0.985429 0.170088i $$-0.0544051\pi$$
$$642$$ 0 0
$$643$$ −35.7083 12.9968i −1.40820 0.512542i −0.477598 0.878578i $$-0.658492\pi$$
−0.930601 + 0.366036i $$0.880715\pi$$
$$644$$ −3.40280 19.2982i −0.134089 0.760456i
$$645$$ 0 0
$$646$$ 13.7888 + 11.5702i 0.542513 + 0.455223i
$$647$$ 36.7423 1.44449 0.722245 0.691637i $$-0.243110\pi$$
0.722245 + 0.691637i $$0.243110\pi$$
$$648$$ 0 0
$$649$$ −6.00000 −0.235521
$$650$$ −1.87642 1.57450i −0.0735992 0.0617570i
$$651$$ 0 0
$$652$$ −6.94593 39.3923i −0.272023 1.54272i
$$653$$ 9.20707 + 3.35110i 0.360300 + 0.131139i 0.515826 0.856693i $$-0.327485\pi$$
−0.155526 + 0.987832i $$0.549707\pi$$
$$654$$ 0 0
$$655$$ −5.20945 + 29.5442i −0.203550 + 1.15439i
$$656$$ −9.79796 + 16.9706i −0.382546 + 0.662589i
$$657$$ 0 0
$$658$$ −24.0000 41.5692i −0.935617 1.62054i
$$659$$ 18.4141 6.70220i 0.717313 0.261081i 0.0425284 0.999095i $$-0.486459\pi$$
0.674785 + 0.738015i $$0.264236\pi$$
$$660$$ 0 0
$$661$$ 8.42649 7.07066i 0.327752 0.275017i −0.464031 0.885819i $$-0.653597\pi$$
0.791783 + 0.610802i $$0.209153\pi$$
$$662$$ −13.1349 + 11.0215i −0.510503 + 0.428363i
$$663$$ 0 0
$$664$$ 56.3816 20.5212i 2.18803 0.796377i
$$665$$ −2.44949 4.24264i −0.0949871 0.164523i
$$666$$ 0 0
$$667$$ −6.00000 + 10.3923i −0.232321 + 0.402392i
$$668$$ 3.40280 19.2982i 0.131658 0.746670i
$$669$$ 0 0
$$670$$ −39.4671 14.3648i −1.52475 0.554962i
$$671$$ 2.12675 + 12.0614i 0.0821022 + 0.465625i
$$672$$ 0 0
$$673$$ 22.2153 + 18.6408i 0.856336 + 0.718552i 0.961176 0.275938i $$-0.0889883\pi$$
−0.104839 + 0.994489i $$0.533433\pi$$
$$674$$ −68.5857 −2.64182
$$675$$ 0 0
$$676$$ −48.0000 −1.84615
$$677$$ 35.6519 + 29.9155i 1.37022 + 1.14975i 0.972677 + 0.232162i $$0.0745798\pi$$
0.397538 + 0.917586i $$0.369865\pi$$
$$678$$ 0 0
$$679$$ −2.43107 13.7873i −0.0932961 0.529108i
$$680$$ −82.8636 30.1599i −3.17768 1.15658i
$$681$$ 0 0
$$682$$ −1.04189 + 5.90885i −0.0398960 + 0.226261i
$$683$$ 11.0227 19.0919i 0.421772 0.730531i −0.574341 0.818616i $$-0.694742\pi$$
0.996113 + 0.0880857i $$0.0280749\pi$$
$$684$$ 0 0
$$685$$ 12.0000 + 20.7846i 0.458496 + 0.794139i
$$686$$ 46.0353 16.7555i 1.75764 0.639728i
$$687$$ 0 0
$$688$$ 33.7060 28.2827i 1.28503 1.07827i
$$689$$ −5.62925 + 4.72350i −0.214457 + 0.179951i
$$690$$ 0 0
$$691$$ −44.1656 + 16.0749i −1.68014 + 0.611520i −0.993329 0.115319i $$-0.963211\pi$$
−0.686808 + 0.726839i $$0.740989\pi$$
$$692$$ −19.5959 33.9411i −0.744925 1.29025i
$$693$$ 0 0
$$694$$ 30.0000 51.9615i 1.13878 1.97243i
$$695$$ 4.25349 24.1228i 0.161344 0.915029i
$$696$$ 0 0
$$697$$ 33.8289 + 12.3127i 1.28136 + 0.466378i
$$698$$ 8.50699 + 48.2455i 0.321994 + 1.82612i
$$699$$ 0 0
$$700$$ 6.12836 + 5.14230i 0.231630 + 0.194361i
$$701$$ −14.6969 −0.555096 −0.277548 0.960712i $$-0.589522\pi$$
−0.277548 + 0.960712i $$0.589522\pi$$
$$702$$ 0 0
$$703$$ −8.00000 −0.301726
$$704$$ −15.0113 12.5960i −0.565761 0.474730i
$$705$$ 0 0
$$706$$ 1.04189 + 5.90885i 0.0392120 + 0.222382i
$$707$$ 9.20707 + 3.35110i 0.346267 + 0.126031i
$$708$$ 0 0
$$709$$ −1.21554 + 6.89365i −0.0456505 + 0.258897i −0.999088 0.0426932i $$-0.986406\pi$$
0.953438 + 0.301590i $$0.0975173\pi$$
$$710$$ 22.0454 38.1838i 0.827349 1.43301i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −2.30177 + 0.837775i −0.0862019 + 0.0313749i
$$714$$ 0 0
$$715$$ 4.59627 3.85673i 0.171891 0.144233i
$$716$$ −45.0340 + 37.7880i −1.68300 + 1.41221i
$$717$$ 0 0
$$718$$ −67.6579 + 24.6255i −2.52497 + 0.919014i
$$719$$ 18.3712 + 31.8198i 0.685129 + 1.18668i 0.973396 + 0.229128i $$0.0735876\pi$$
−0.288267 + 0.957550i $$0.593079\pi$$
$$720$$ 0 0
$$721$$ 7.00000 12.1244i 0.260694 0.451535i
$$722$$ −7.65629 + 43.4210i −0.284938 + 1.61596i
$$723$$ 0 0
$$724$$ −30.0702 10.9446i −1.11755 0.406755i
$$725$$ −0.850699 4.82455i −0.0315942 0.179179i
$$726$$ 0 0
$$727$$ 10.7246 + 8.99903i 0.397754 + 0.333755i 0.819625 0.572901i $$-0.194182\pi$$
−0.421871 + 0.906656i $$0.638626\pi$$
$$728$$ −9.79796 −0.363137
$$729$$ 0 0
$$730$$ −66.0000 −2.44277
$$731$$ −61.9218 51.9586i −2.29026 1.92176i
$$732$$ 0 0
$$733$$ 2.95202 + 16.7417i 0.109035 + 0.618370i 0.989532 + 0.144317i $$0.0460984\pi$$
−0.880496 + 0.474053i $$0.842790\pi$$
$$734$$ −11.5088 4.18887i −0.424799 0.154614i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 8.57321 14.8492i 0.315798 0.546979i
$$738$$ 0 0
$$739$$ 0.500000 + 0.866025i 0.0183928 + 0.0318573i 0.875075 0.483987i $$-0.160812\pi$$
−0.856683 + 0.515844i $$0.827478\pi$$
$$740$$ 73.6566 26.8088i 2.70767 0.985511i
$$741$$ 0 0
$$742$$ 27.5776 23.1404i 1.01241 0.849509i
$$743$$ −24.3934 + 20.4685i −0.894908 + 0.750917i −0.969189 0.246320i $$-0.920779\pi$$
0.0742802 + 0.997237i $$0.476334\pi$$
$$744$$ 0 0
$$745$$ 28.1908 10.2606i 1.03283 0.375919i
$$746$$ −42.8661 74.2462i −1.56944 2.71835i
$$747$$ 0 0
$$748$$ 36.0000 62.3538i 1.31629 2.27988i
$$749$$ 5.10419 28.9473i 0.186503 1.05771i
$$750$$ 0 0
$$751$$ −24.4320 8.89252i −0.891537 0.324493i −0.144680 0.989478i $$-0.546215\pi$$
−0.746856 + 0.664986i $$0.768438\pi$$
$$752$$ 6.80559 + 38.5964i 0.248174 + 1.40747i
$$753$$ 0 0
$$754$$ 9.19253 + 7.71345i 0.334772 + 0.280907i
$$755$$ −12.2474 −0.445730
$$756$$ 0 0
$$757$$ −7.00000 −0.254419 −0.127210 0.991876i $$-0.540602\pi$$
−0.127210 + 0.991876i $$0.540602\pi$$
$$758$$ 15.0113 + 12.5960i 0.545237 + 0.457508i
$$759$$ 0 0
$$760$$ 2.08378 + 11.8177i 0.0755866 + 0.428673i
$$761$$ 2.30177 + 0.837775i 0.0834390 + 0.0303693i 0.383402 0.923581i $$-0.374752\pi$$
−0.299963 + 0.953951i $$0.596974\pi$$
$$762$$ 0 0
$$763$$ −0.347296 + 1.96962i −0.0125730 + 0.0713049i
$$764$$ −19.5959 + 33.9411i −0.708955 + 1.22795i
$$765$$ 0 0
$$766$$ −42.0000 72.7461i −1.51752 2.62842i
$$767$$ −2.30177 + 0.837775i −0.0831120 + 0.0302503i
$$768$$ 0 0
$$769$$ −28.3436 + 23.7831i −1.02210 + 0.857642i −0.989890 0.141839i $$-0.954698\pi$$
−0.0322082 + 0.999481i $$0.510254\pi$$
$$770$$ −22.5170 + 18.8940i −0.811457 + 0.680893i
$$771$$ 0 0
$$772$$ −41.3465 + 15.0489i −1.48809 + 0.541621i
$$773$$ 22.0454 + 38.1838i 0.792918 + 1.37337i 0.924153 + 0.382023i $$0.124773\pi$$
−0.131235 + 0.991351i $$0.541894\pi$$
$$774$$ 0 0
$$775$$ 0.500000 0.866025i 0.0179605 0.0311086i
$$776$$ −5.95489 + 33.7719i −0.213768 + 1.21234i
$$777$$ 0 0
$$778$$ 62.0197 + 22.5733i 2.22351 + 0.809293i
$$779$$ −0.850699 4.82455i −0.0304794 0.172858i
$$780$$ 0 0
$$781$$ 13.7888 + 11.5702i 0.493402 + 0.414013i
$$782$$ 44.0908 1.57668
$$783$$