# Properties

 Label 1323.2.h.d.226.3 Level $1323$ Weight $2$ Character 1323.226 Analytic conductor $10.564$ Analytic rank $0$ 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] = [1323,2,Mod(226,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.h (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$10.5642081874$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.309123.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3$$ x^6 - 3*x^5 + 10*x^4 - 15*x^3 + 19*x^2 - 12*x + 3 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 226.3 Root $$0.500000 - 2.05195i$$ of defining polynomial Character $$\chi$$ $$=$$ 1323.226 Dual form 1323.2.h.d.802.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+2.46050 q^{2} +4.05408 q^{4} +(-1.29679 - 2.24611i) q^{5} +5.05408 q^{8} +O(q^{10})$$ $$q+2.46050 q^{2} +4.05408 q^{4} +(-1.29679 - 2.24611i) q^{5} +5.05408 q^{8} +(-3.19076 - 5.52655i) q^{10} +(2.25729 - 3.90975i) q^{11} +(-0.500000 + 0.866025i) q^{13} +4.32743 q^{16} +(-0.472958 - 0.819187i) q^{17} +(2.02704 - 3.51094i) q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +(-0.136673 - 0.236725i) q^{23} +(-0.863327 + 1.49533i) q^{25} +(-1.23025 + 2.13086i) q^{26} +(1.23025 + 2.13086i) q^{29} +2.32743 q^{31} +0.539495 q^{32} +(-1.16372 - 2.01561i) q^{34} +(-0.890369 + 1.54216i) q^{37} +(4.98755 - 8.63868i) q^{38} +(-6.55408 - 11.3520i) q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} +(9.15126 - 15.8505i) q^{44} +(-0.336285 - 0.582462i) q^{46} +12.1623 q^{47} +(-2.12422 + 3.67926i) q^{50} +(-2.02704 + 3.51094i) q^{52} +(-3.13667 - 5.43288i) q^{53} -11.7089 q^{55} +(3.02704 + 5.24299i) q^{58} +2.72665 q^{59} -2.27335 q^{61} +5.72665 q^{62} -7.32743 q^{64} +2.59358 q^{65} -15.8171 q^{67} +(-1.91741 - 3.32105i) q^{68} -3.27335 q^{71} +(0.753696 + 1.30544i) q^{73} +(-2.19076 + 3.79450i) q^{74} +(8.21780 - 14.2336i) q^{76} +14.7089 q^{79} +(-5.61177 - 9.71987i) q^{80} +(-7.88151 + 13.6512i) q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +(12.8384 + 22.2368i) q^{86} +(11.4086 - 19.7602i) q^{88} +(-7.17830 + 12.4332i) q^{89} +(-0.554084 - 0.959702i) q^{92} +29.9253 q^{94} -10.5146 q^{95} +(5.74484 + 9.95036i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 12 q^{8}+O(q^{10})$$ 6 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 12 * q^8 $$6 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 12 q^{8} - 2 q^{11} - 3 q^{13} + 6 q^{16} - 12 q^{17} + 3 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} - q^{26} + q^{29} - 6 q^{31} + 16 q^{32} + 3 q^{34} + 3 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} + 18 q^{47} + 10 q^{50} - 3 q^{52} - 18 q^{53} - 12 q^{55} + 9 q^{58} + 18 q^{59} - 12 q^{61} + 36 q^{62} - 24 q^{64} + 10 q^{65} + 6 q^{68} - 18 q^{71} - 3 q^{73} + 6 q^{74} + 21 q^{76} + 30 q^{79} + 11 q^{80} - 9 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} - 2 q^{89} + 15 q^{92} + 48 q^{94} - 32 q^{95} - 3 q^{97}+O(q^{100})$$ 6 * q + 2 * q^2 + 6 * q^4 - 5 * q^5 + 12 * q^8 - 2 * q^11 - 3 * q^13 + 6 * q^16 - 12 * q^17 + 3 * q^19 - 16 * q^20 + 15 * q^22 - 6 * q^25 - q^26 + q^29 - 6 * q^31 + 16 * q^32 + 3 * q^34 + 3 * q^37 + 8 * q^38 - 21 * q^40 - 22 * q^41 + 3 * q^43 + 23 * q^44 - 12 * q^46 + 18 * q^47 + 10 * q^50 - 3 * q^52 - 18 * q^53 - 12 * q^55 + 9 * q^58 + 18 * q^59 - 12 * q^61 + 36 * q^62 - 24 * q^64 + 10 * q^65 + 6 * q^68 - 18 * q^71 - 3 * q^73 + 6 * q^74 + 21 * q^76 + 30 * q^79 + 11 * q^80 - 9 * q^82 - 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 - 2 * q^89 + 15 * q^92 + 48 * q^94 - 32 * q^95 - 3 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$$.

 $$n$$ $$785$$ $$1081$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.46050 1.73984 0.869920 0.493193i $$-0.164170\pi$$
0.869920 + 0.493193i $$0.164170\pi$$
$$3$$ 0 0
$$4$$ 4.05408 2.02704
$$5$$ −1.29679 2.24611i −0.579942 1.00449i −0.995485 0.0949156i $$-0.969742\pi$$
0.415543 0.909573i $$-0.363591\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 5.05408 1.78689
$$9$$ 0 0
$$10$$ −3.19076 5.52655i −1.00901 1.74765i
$$11$$ 2.25729 3.90975i 0.680600 1.17883i −0.294198 0.955744i $$-0.595053\pi$$
0.974798 0.223089i $$-0.0716141\pi$$
$$12$$ 0 0
$$13$$ −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i $$-0.877618\pi$$
0.788320 + 0.615265i $$0.210951\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 4.32743 1.08186
$$17$$ −0.472958 0.819187i −0.114709 0.198682i 0.802954 0.596041i $$-0.203260\pi$$
−0.917663 + 0.397359i $$0.869927\pi$$
$$18$$ 0 0
$$19$$ 2.02704 3.51094i 0.465035 0.805465i −0.534168 0.845378i $$-0.679375\pi$$
0.999203 + 0.0399136i $$0.0127083\pi$$
$$20$$ −5.25729 9.10590i −1.17557 2.03614i
$$21$$ 0 0
$$22$$ 5.55408 9.61996i 1.18413 2.05098i
$$23$$ −0.136673 0.236725i −0.0284983 0.0493605i 0.851425 0.524477i $$-0.175739\pi$$
−0.879923 + 0.475117i $$0.842406\pi$$
$$24$$ 0 0
$$25$$ −0.863327 + 1.49533i −0.172665 + 0.299065i
$$26$$ −1.23025 + 2.13086i −0.241272 + 0.417896i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 1.23025 + 2.13086i 0.228452 + 0.395691i 0.957350 0.288932i $$-0.0933002\pi$$
−0.728897 + 0.684623i $$0.759967\pi$$
$$30$$ 0 0
$$31$$ 2.32743 0.418019 0.209009 0.977914i $$-0.432976\pi$$
0.209009 + 0.977914i $$0.432976\pi$$
$$32$$ 0.539495 0.0953702
$$33$$ 0 0
$$34$$ −1.16372 2.01561i −0.199576 0.345675i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −0.890369 + 1.54216i −0.146376 + 0.253530i −0.929885 0.367849i $$-0.880094\pi$$
0.783510 + 0.621380i $$0.213428\pi$$
$$38$$ 4.98755 8.63868i 0.809087 1.40138i
$$39$$ 0 0
$$40$$ −6.55408 11.3520i −1.03629 1.79491i
$$41$$ −3.20321 + 5.54812i −0.500257 + 0.866471i 0.499743 + 0.866174i $$0.333428\pi$$
−1.00000 0.000297253i $$0.999905\pi$$
$$42$$ 0 0
$$43$$ 5.21780 + 9.03749i 0.795707 + 1.37820i 0.922389 + 0.386262i $$0.126234\pi$$
−0.126682 + 0.991943i $$0.540433\pi$$
$$44$$ 9.15126 15.8505i 1.37960 2.38955i
$$45$$ 0 0
$$46$$ −0.336285 0.582462i −0.0495825 0.0858794i
$$47$$ 12.1623 1.77405 0.887023 0.461724i $$-0.152769\pi$$
0.887023 + 0.461724i $$0.152769\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ −2.12422 + 3.67926i −0.300410 + 0.520326i
$$51$$ 0 0
$$52$$ −2.02704 + 3.51094i −0.281100 + 0.486880i
$$53$$ −3.13667 5.43288i −0.430855 0.746263i 0.566092 0.824342i $$-0.308455\pi$$
−0.996947 + 0.0780790i $$0.975121\pi$$
$$54$$ 0 0
$$55$$ −11.7089 −1.57883
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 3.02704 + 5.24299i 0.397470 + 0.688438i
$$59$$ 2.72665 0.354980 0.177490 0.984123i $$-0.443202\pi$$
0.177490 + 0.984123i $$0.443202\pi$$
$$60$$ 0 0
$$61$$ −2.27335 −0.291072 −0.145536 0.989353i $$-0.546491\pi$$
−0.145536 + 0.989353i $$0.546491\pi$$
$$62$$ 5.72665 0.727286
$$63$$ 0 0
$$64$$ −7.32743 −0.915929
$$65$$ 2.59358 0.321694
$$66$$ 0 0
$$67$$ −15.8171 −1.93237 −0.966184 0.257854i $$-0.916985\pi$$
−0.966184 + 0.257854i $$0.916985\pi$$
$$68$$ −1.91741 3.32105i −0.232520 0.402737i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −3.27335 −0.388475 −0.194237 0.980955i $$-0.562223\pi$$
−0.194237 + 0.980955i $$0.562223\pi$$
$$72$$ 0 0
$$73$$ 0.753696 + 1.30544i 0.0882134 + 0.152790i 0.906756 0.421656i $$-0.138551\pi$$
−0.818543 + 0.574446i $$0.805218\pi$$
$$74$$ −2.19076 + 3.79450i −0.254670 + 0.441102i
$$75$$ 0 0
$$76$$ 8.21780 14.2336i 0.942646 1.63271i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 14.7089 1.65489 0.827443 0.561550i $$-0.189795\pi$$
0.827443 + 0.561550i $$0.189795\pi$$
$$80$$ −5.61177 9.71987i −0.627415 1.08671i
$$81$$ 0 0
$$82$$ −7.88151 + 13.6512i −0.870368 + 1.50752i
$$83$$ −0.472958 0.819187i −0.0519139 0.0899175i 0.838901 0.544285i $$-0.183199\pi$$
−0.890815 + 0.454367i $$0.849865\pi$$
$$84$$ 0 0
$$85$$ −1.22665 + 2.12463i −0.133049 + 0.230448i
$$86$$ 12.8384 + 22.2368i 1.38440 + 2.39786i
$$87$$ 0 0
$$88$$ 11.4086 19.7602i 1.21616 2.10644i
$$89$$ −7.17830 + 12.4332i −0.760899 + 1.31792i 0.181489 + 0.983393i $$0.441908\pi$$
−0.942388 + 0.334522i $$0.891425\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −0.554084 0.959702i −0.0577673 0.100056i
$$93$$ 0 0
$$94$$ 29.9253 3.08656
$$95$$ −10.5146 −1.07877
$$96$$ 0 0
$$97$$ 5.74484 + 9.95036i 0.583300 + 1.01031i 0.995085 + 0.0990246i $$0.0315722\pi$$
−0.411785 + 0.911281i $$0.635094\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ −3.50000 + 6.06218i −0.350000 + 0.606218i
$$101$$ −1.83988 + 3.18677i −0.183075 + 0.317096i −0.942926 0.333002i $$-0.891939\pi$$
0.759851 + 0.650097i $$0.225272\pi$$
$$102$$ 0 0
$$103$$ 4.86333 + 8.42353i 0.479198 + 0.829995i 0.999715 0.0238560i $$-0.00759431\pi$$
−0.520518 + 0.853851i $$0.674261\pi$$
$$104$$ −2.52704 + 4.37697i −0.247797 + 0.429197i
$$105$$ 0 0
$$106$$ −7.71780 13.3676i −0.749619 1.29838i
$$107$$ −0.687159 + 1.19019i −0.0664301 + 0.115060i −0.897327 0.441365i $$-0.854494\pi$$
0.830897 + 0.556426i $$0.187828\pi$$
$$108$$ 0 0
$$109$$ 1.69961 + 2.94381i 0.162793 + 0.281966i 0.935869 0.352347i $$-0.114616\pi$$
−0.773076 + 0.634313i $$0.781283\pi$$
$$110$$ −28.8099 −2.74692
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 5.19436 8.99689i 0.488644 0.846356i −0.511271 0.859420i $$-0.670825\pi$$
0.999915 + 0.0130636i $$0.00415840\pi$$
$$114$$ 0 0
$$115$$ −0.354473 + 0.613964i −0.0330547 + 0.0572525i
$$116$$ 4.98755 + 8.63868i 0.463082 + 0.802082i
$$117$$ 0 0
$$118$$ 6.70895 0.617608
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −4.69076 8.12463i −0.426432 0.738603i
$$122$$ −5.59358 −0.506419
$$123$$ 0 0
$$124$$ 9.43560 0.847342
$$125$$ −8.48968 −0.759340
$$126$$ 0 0
$$127$$ 0.672570 0.0596809 0.0298405 0.999555i $$-0.490500\pi$$
0.0298405 + 0.999555i $$0.490500\pi$$
$$128$$ −19.1082 −1.68894
$$129$$ 0 0
$$130$$ 6.38151 0.559696
$$131$$ 3.95691 + 6.85356i 0.345717 + 0.598799i 0.985484 0.169770i $$-0.0543026\pi$$
−0.639767 + 0.768569i $$0.720969\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −38.9181 −3.36201
$$135$$ 0 0
$$136$$ −2.39037 4.14024i −0.204972 0.355023i
$$137$$ −1.83628 + 3.18054i −0.156884 + 0.271732i −0.933744 0.357943i $$-0.883478\pi$$
0.776859 + 0.629674i $$0.216812\pi$$
$$138$$ 0 0
$$139$$ 1.02704 1.77889i 0.0871126 0.150883i −0.819177 0.573541i $$-0.805569\pi$$
0.906289 + 0.422658i $$0.138903\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −8.05408 −0.675884
$$143$$ 2.25729 + 3.90975i 0.188764 + 0.326950i
$$144$$ 0 0
$$145$$ 3.19076 5.52655i 0.264978 0.458955i
$$146$$ 1.85447 + 3.21204i 0.153477 + 0.265830i
$$147$$ 0 0
$$148$$ −3.60963 + 6.25206i −0.296710 + 0.513917i
$$149$$ −6.77188 11.7292i −0.554774 0.960897i −0.997921 0.0644482i $$-0.979471\pi$$
0.443147 0.896449i $$-0.353862\pi$$
$$150$$ 0 0
$$151$$ −4.96410 + 8.59808i −0.403973 + 0.699702i −0.994201 0.107535i $$-0.965704\pi$$
0.590228 + 0.807236i $$0.299038\pi$$
$$152$$ 10.2448 17.7446i 0.830966 1.43928i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3.01819 5.22765i −0.242427 0.419895i
$$156$$ 0 0
$$157$$ 6.05408 0.483169 0.241584 0.970380i $$-0.422333\pi$$
0.241584 + 0.970380i $$0.422333\pi$$
$$158$$ 36.1914 2.87924
$$159$$ 0 0
$$160$$ −0.699612 1.21176i −0.0553092 0.0957983i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −8.90856 + 15.4301i −0.697772 + 1.20858i 0.271465 + 0.962448i $$0.412492\pi$$
−0.969237 + 0.246128i $$0.920842\pi$$
$$164$$ −12.9861 + 22.4926i −1.01404 + 1.75637i
$$165$$ 0 0
$$166$$ −1.16372 2.01561i −0.0903218 0.156442i
$$167$$ −4.23385 + 7.33325i −0.327625 + 0.567464i −0.982040 0.188672i $$-0.939582\pi$$
0.654415 + 0.756136i $$0.272915\pi$$
$$168$$ 0 0
$$169$$ 6.00000 + 10.3923i 0.461538 + 0.799408i
$$170$$ −3.01819 + 5.22765i −0.231484 + 0.400943i
$$171$$ 0 0
$$172$$ 21.1534 + 36.6388i 1.61293 + 2.79368i
$$173$$ −17.3566 −1.31960 −0.659799 0.751442i $$-0.729359\pi$$
−0.659799 + 0.751442i $$0.729359\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 9.76829 16.9192i 0.736312 1.27533i
$$177$$ 0 0
$$178$$ −17.6623 + 30.5919i −1.32384 + 2.29296i
$$179$$ −5.67471 9.82888i −0.424147 0.734645i 0.572193 0.820119i $$-0.306093\pi$$
−0.996340 + 0.0854741i $$0.972759\pi$$
$$180$$ 0 0
$$181$$ 21.8889 1.62699 0.813495 0.581572i $$-0.197562\pi$$
0.813495 + 0.581572i $$0.197562\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −0.690757 1.19643i −0.0509233 0.0882018i
$$185$$ 4.61849 0.339558
$$186$$ 0 0
$$187$$ −4.27042 −0.312284
$$188$$ 49.3068 3.59607
$$189$$ 0 0
$$190$$ −25.8712 −1.87689
$$191$$ 0.701748 0.0507767 0.0253883 0.999678i $$-0.491918\pi$$
0.0253883 + 0.999678i $$0.491918\pi$$
$$192$$ 0 0
$$193$$ 12.1445 0.874183 0.437092 0.899417i $$-0.356009\pi$$
0.437092 + 0.899417i $$0.356009\pi$$
$$194$$ 14.1352 + 24.4829i 1.01485 + 1.75777i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 16.4107 1.16921 0.584607 0.811317i $$-0.301249\pi$$
0.584607 + 0.811317i $$0.301249\pi$$
$$198$$ 0 0
$$199$$ −11.3530 19.6640i −0.804794 1.39394i −0.916430 0.400194i $$-0.868943\pi$$
0.111637 0.993749i $$-0.464391\pi$$
$$200$$ −4.36333 + 7.55750i −0.308534 + 0.534396i
$$201$$ 0 0
$$202$$ −4.52704 + 7.84107i −0.318522 + 0.551696i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 16.6156 1.16048
$$206$$ 11.9662 + 20.7261i 0.833727 + 1.44406i
$$207$$ 0 0
$$208$$ −2.16372 + 3.74766i −0.150027 + 0.259854i
$$209$$ −9.15126 15.8505i −0.633006 1.09640i
$$210$$ 0 0
$$211$$ −2.28074 + 3.95035i −0.157012 + 0.271954i −0.933790 0.357822i $$-0.883520\pi$$
0.776778 + 0.629775i $$0.216853\pi$$
$$212$$ −12.7163 22.0253i −0.873362 1.51271i
$$213$$ 0 0
$$214$$ −1.69076 + 2.92848i −0.115578 + 0.200187i
$$215$$ 13.5328 23.4395i 0.922928 1.59856i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 4.18190 + 7.24327i 0.283234 + 0.490576i
$$219$$ 0 0
$$220$$ −47.4690 −3.20036
$$221$$ 0.945916 0.0636292
$$222$$ 0 0
$$223$$ −6.66225 11.5394i −0.446137 0.772733i 0.551993 0.833849i $$-0.313867\pi$$
−0.998131 + 0.0611159i $$0.980534\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 12.7807 22.1369i 0.850162 1.47252i
$$227$$ 0.690757 1.19643i 0.0458472 0.0794096i −0.842191 0.539179i $$-0.818735\pi$$
0.888038 + 0.459769i $$0.152068\pi$$
$$228$$ 0 0
$$229$$ 8.98968 + 15.5706i 0.594055 + 1.02893i 0.993679 + 0.112254i $$0.0358072\pi$$
−0.399625 + 0.916679i $$0.630859\pi$$
$$230$$ −0.872181 + 1.51066i −0.0575099 + 0.0996101i
$$231$$ 0 0
$$232$$ 6.21780 + 10.7695i 0.408219 + 0.707055i
$$233$$ −9.49115 + 16.4391i −0.621786 + 1.07696i 0.367367 + 0.930076i $$0.380259\pi$$
−0.989153 + 0.146888i $$0.953074\pi$$
$$234$$ 0 0
$$235$$ −15.7719 27.3177i −1.02884 1.78201i
$$236$$ 11.0541 0.719560
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 2.44592 4.23645i 0.158213 0.274033i −0.776011 0.630719i $$-0.782760\pi$$
0.934224 + 0.356686i $$0.116093\pi$$
$$240$$ 0 0
$$241$$ 13.0797 22.6546i 0.842535 1.45931i −0.0452094 0.998978i $$-0.514396\pi$$
0.887745 0.460336i $$-0.152271\pi$$
$$242$$ −11.5416 19.9907i −0.741924 1.28505i
$$243$$ 0 0
$$244$$ −9.21634 −0.590016
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 2.02704 + 3.51094i 0.128978 + 0.223396i
$$248$$ 11.7630 0.746953
$$249$$ 0 0
$$250$$ −20.8889 −1.32113
$$251$$ −18.4576 −1.16503 −0.582516 0.812819i $$-0.697932\pi$$
−0.582516 + 0.812819i $$0.697932\pi$$
$$252$$ 0 0
$$253$$ −1.23405 −0.0775838
$$254$$ 1.65486 0.103835
$$255$$ 0 0
$$256$$ −32.3609 −2.02256
$$257$$ −5.86693 10.1618i −0.365969 0.633876i 0.622962 0.782252i $$-0.285929\pi$$
−0.988931 + 0.148375i $$0.952596\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 10.5146 0.652087
$$261$$ 0 0
$$262$$ 9.73599 + 16.8632i 0.601491 + 1.04181i
$$263$$ −3.76089 + 6.51406i −0.231907 + 0.401674i −0.958369 0.285532i $$-0.907830\pi$$
0.726463 + 0.687206i $$0.241163\pi$$
$$264$$ 0 0
$$265$$ −8.13521 + 14.0906i −0.499742 + 0.865579i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −64.1239 −3.91699
$$269$$ −9.41741 16.3114i −0.574190 0.994526i −0.996129 0.0879017i $$-0.971984\pi$$
0.421939 0.906624i $$-0.361349\pi$$
$$270$$ 0 0
$$271$$ 11.9911 20.7693i 0.728410 1.26164i −0.229145 0.973392i $$-0.573593\pi$$
0.957555 0.288251i $$-0.0930738\pi$$
$$272$$ −2.04669 3.54498i −0.124099 0.214946i
$$273$$ 0 0
$$274$$ −4.51819 + 7.82573i −0.272954 + 0.472770i
$$275$$ 3.89757 + 6.75078i 0.235032 + 0.407088i
$$276$$ 0 0
$$277$$ −3.58113 + 6.20269i −0.215169 + 0.372684i −0.953325 0.301947i $$-0.902364\pi$$
0.738156 + 0.674630i $$0.235697\pi$$
$$278$$ 2.52704 4.37697i 0.151562 0.262513i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 7.44085 + 12.8879i 0.443884 + 0.768830i 0.997974 0.0636271i $$-0.0202668\pi$$
−0.554090 + 0.832457i $$0.686933\pi$$
$$282$$ 0 0
$$283$$ 19.9971 1.18870 0.594351 0.804205i $$-0.297409\pi$$
0.594351 + 0.804205i $$0.297409\pi$$
$$284$$ −13.2704 −0.787455
$$285$$ 0 0
$$286$$ 5.55408 + 9.61996i 0.328420 + 0.568840i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 8.05262 13.9475i 0.473684 0.820444i
$$290$$ 7.85087 13.5981i 0.461019 0.798509i
$$291$$ 0 0
$$292$$ 3.05555 + 5.29236i 0.178812 + 0.309712i
$$293$$ 7.53278 13.0472i 0.440070 0.762223i −0.557625 0.830093i $$-0.688287\pi$$
0.997694 + 0.0678705i $$0.0216205\pi$$
$$294$$ 0 0
$$295$$ −3.53590 6.12435i −0.205868 0.356574i
$$296$$ −4.50000 + 7.79423i −0.261557 + 0.453030i
$$297$$ 0 0
$$298$$ −16.6623 28.8599i −0.965218 1.67181i
$$299$$ 0.273346 0.0158080
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −12.2142 + 21.1556i −0.702848 + 1.21737i
$$303$$ 0 0
$$304$$ 8.77188 15.1933i 0.503102 0.871398i
$$305$$ 2.94805 + 5.10618i 0.168805 + 0.292379i
$$306$$ 0 0
$$307$$ −27.2704 −1.55641 −0.778203 0.628013i $$-0.783868\pi$$
−0.778203 + 0.628013i $$0.783868\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −7.42627 12.8627i −0.421784 0.730551i
$$311$$ 15.9823 0.906273 0.453136 0.891441i $$-0.350305\pi$$
0.453136 + 0.891441i $$0.350305\pi$$
$$312$$ 0 0
$$313$$ 11.5979 0.655549 0.327775 0.944756i $$-0.393701\pi$$
0.327775 + 0.944756i $$0.393701\pi$$
$$314$$ 14.8961 0.840636
$$315$$ 0 0
$$316$$ 59.6313 3.35452
$$317$$ 2.01771 0.113326 0.0566629 0.998393i $$-0.481954\pi$$
0.0566629 + 0.998393i $$0.481954\pi$$
$$318$$ 0 0
$$319$$ 11.1082 0.621938
$$320$$ 9.50214 + 16.4582i 0.531186 + 0.920040i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −3.83482 −0.213375
$$324$$ 0 0
$$325$$ −0.863327 1.49533i −0.0478888 0.0829458i
$$326$$ −21.9195 + 37.9658i −1.21401 + 2.10273i
$$327$$ 0 0
$$328$$ −16.1893 + 28.0407i −0.893904 + 1.54829i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −19.7089 −1.08330 −0.541651 0.840604i $$-0.682200\pi$$
−0.541651 + 0.840604i $$0.682200\pi$$
$$332$$ −1.91741 3.32105i −0.105232 0.182266i
$$333$$ 0 0
$$334$$ −10.4174 + 18.0435i −0.570015 + 0.987296i
$$335$$ 20.5115 + 35.5269i 1.12066 + 1.94104i
$$336$$ 0 0
$$337$$ 14.5256 25.1590i 0.791259 1.37050i −0.133929 0.990991i $$-0.542759\pi$$
0.925188 0.379509i $$-0.123907\pi$$
$$338$$ 14.7630 + 25.5703i 0.803003 + 1.39084i
$$339$$ 0 0
$$340$$ −4.97296 + 8.61342i −0.269697 + 0.467128i
$$341$$ 5.25370 9.09967i 0.284504 0.492775i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 26.3712 + 45.6763i 1.42184 + 2.46270i
$$345$$ 0 0
$$346$$ −42.7060 −2.29589
$$347$$ −29.0833 −1.56127 −0.780636 0.624986i $$-0.785105\pi$$
−0.780636 + 0.624986i $$0.785105\pi$$
$$348$$ 0 0
$$349$$ −12.3815 21.4454i −0.662767 1.14795i −0.979885 0.199561i $$-0.936049\pi$$
0.317118 0.948386i $$-0.397285\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.21780 2.10929i 0.0649089 0.112426i
$$353$$ −16.6513 + 28.8408i −0.886257 + 1.53504i −0.0419914 + 0.999118i $$0.513370\pi$$
−0.844266 + 0.535925i $$0.819963\pi$$
$$354$$ 0 0
$$355$$ 4.24484 + 7.35228i 0.225293 + 0.390219i
$$356$$ −29.1015 + 50.4052i −1.54237 + 2.67147i
$$357$$ 0 0
$$358$$ −13.9626 24.1840i −0.737949 1.27816i
$$359$$ 12.7683 22.1153i 0.673884 1.16720i −0.302909 0.953019i $$-0.597958\pi$$
0.976794 0.214182i $$-0.0687087\pi$$
$$360$$ 0 0
$$361$$ 1.28220 + 2.22084i 0.0674842 + 0.116886i
$$362$$ 53.8578 2.83070
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 1.95477 3.38576i 0.102317 0.177219i
$$366$$ 0 0
$$367$$ −13.7252 + 23.7727i −0.716449 + 1.24093i 0.245949 + 0.969283i $$0.420900\pi$$
−0.962398 + 0.271644i $$0.912433\pi$$
$$368$$ −0.591443 1.02441i −0.0308311 0.0534011i
$$369$$ 0 0
$$370$$ 11.3638 0.590776
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −8.16372 14.1400i −0.422701 0.732140i 0.573502 0.819204i $$-0.305585\pi$$
−0.996203 + 0.0870646i $$0.972251\pi$$
$$374$$ −10.5074 −0.543324
$$375$$ 0 0
$$376$$ 61.4690 3.17002
$$377$$ −2.46050 −0.126722
$$378$$ 0 0
$$379$$ 12.0364 0.618267 0.309134 0.951019i $$-0.399961\pi$$
0.309134 + 0.951019i $$0.399961\pi$$
$$380$$ −42.6270 −2.18672
$$381$$ 0 0
$$382$$ 1.72665 0.0883433
$$383$$ −6.21780 10.7695i −0.317715 0.550298i 0.662296 0.749242i $$-0.269582\pi$$
−0.980011 + 0.198944i $$0.936249\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 29.8817 1.52094
$$387$$ 0 0
$$388$$ 23.2901 + 40.3396i 1.18237 + 2.04793i
$$389$$ 10.3004 17.8408i 0.522250 0.904564i −0.477414 0.878678i $$-0.658426\pi$$
0.999665 0.0258860i $$-0.00824070\pi$$
$$390$$ 0 0
$$391$$ −0.129281 + 0.223922i −0.00653803 + 0.0113242i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 40.3786 2.03424
$$395$$ −19.0744 33.0378i −0.959738 1.66231i
$$396$$ 0 0
$$397$$ 11.8186 20.4704i 0.593157 1.02738i −0.400647 0.916233i $$-0.631215\pi$$
0.993804 0.111146i $$-0.0354521\pi$$
$$398$$ −27.9341 48.3833i −1.40021 2.42524i
$$399$$ 0 0
$$400$$ −3.73599 + 6.47092i −0.186799 + 0.323546i
$$401$$ −1.28220 2.22084i −0.0640300 0.110903i 0.832233 0.554426i $$-0.187062\pi$$
−0.896263 + 0.443522i $$0.853729\pi$$
$$402$$ 0 0
$$403$$ −1.16372 + 2.01561i −0.0579688 + 0.100405i
$$404$$ −7.45904 + 12.9194i −0.371101 + 0.642766i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 4.01965 + 6.96224i 0.199247 + 0.345105i
$$408$$ 0 0
$$409$$ −34.3245 −1.69724 −0.848619 0.529005i $$-0.822565\pi$$
−0.848619 + 0.529005i $$0.822565\pi$$
$$410$$ 40.8827 2.01905
$$411$$ 0 0
$$412$$ 19.7163 + 34.1497i 0.971354 + 1.68243i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −1.22665 + 2.12463i −0.0602141 + 0.104294i
$$416$$ −0.269748 + 0.467216i −0.0132255 + 0.0229072i
$$417$$ 0 0
$$418$$ −22.5167 39.0001i −1.10133 1.90756i
$$419$$ 2.02850 3.51347i 0.0990989 0.171644i −0.812213 0.583361i $$-0.801737\pi$$
0.911312 + 0.411717i $$0.135071\pi$$
$$420$$ 0 0
$$421$$ 10.5344 + 18.2462i 0.513417 + 0.889264i 0.999879 + 0.0155624i $$0.00495387\pi$$
−0.486462 + 0.873702i $$0.661713\pi$$
$$422$$ −5.61177 + 9.71987i −0.273177 + 0.473156i
$$423$$ 0 0
$$424$$ −15.8530 27.4582i −0.769890 1.33349i
$$425$$ 1.63327 0.0792252
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −2.78580 + 4.82515i −0.134657 + 0.233232i
$$429$$ 0 0
$$430$$ 33.2975 57.6729i 1.60575 2.78123i
$$431$$ 11.3092 + 19.5882i 0.544747 + 0.943530i 0.998623 + 0.0524646i $$0.0167077\pi$$
−0.453876 + 0.891065i $$0.649959\pi$$
$$432$$ 0 0
$$433$$ 2.41789 0.116196 0.0580982 0.998311i $$-0.481496\pi$$
0.0580982 + 0.998311i $$0.481496\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 6.89037 + 11.9345i 0.329989 + 0.571557i
$$437$$ −1.10817 −0.0530109
$$438$$ 0 0
$$439$$ −23.4897 −1.12110 −0.560551 0.828120i $$-0.689411\pi$$
−0.560551 + 0.828120i $$0.689411\pi$$
$$440$$ −59.1780 −2.82120
$$441$$ 0 0
$$442$$ 2.32743 0.110705
$$443$$ 13.4179 0.637503 0.318752 0.947838i $$-0.396736\pi$$
0.318752 + 0.947838i $$0.396736\pi$$
$$444$$ 0 0
$$445$$ 37.2350 1.76511
$$446$$ −16.3925 28.3927i −0.776208 1.34443i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 9.16225 0.432393 0.216197 0.976350i $$-0.430635\pi$$
0.216197 + 0.976350i $$0.430635\pi$$
$$450$$ 0 0
$$451$$ 14.4612 + 25.0475i 0.680950 + 1.17944i
$$452$$ 21.0584 36.4741i 0.990502 1.71560i
$$453$$ 0 0
$$454$$ 1.69961 2.94381i 0.0797667 0.138160i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 8.81711 0.412447 0.206224 0.978505i $$-0.433883\pi$$
0.206224 + 0.978505i $$0.433883\pi$$
$$458$$ 22.1192 + 38.3115i 1.03356 + 1.79018i
$$459$$ 0 0
$$460$$ −1.43706 + 2.48906i −0.0670033 + 0.116053i
$$461$$ −2.82957 4.90095i −0.131786 0.228260i 0.792579 0.609769i $$-0.208738\pi$$
−0.924365 + 0.381509i $$0.875405\pi$$
$$462$$ 0 0
$$463$$ −7.86333 + 13.6197i −0.365440 + 0.632960i −0.988847 0.148937i $$-0.952415\pi$$
0.623407 + 0.781898i $$0.285748\pi$$
$$464$$ 5.32383 + 9.22115i 0.247153 + 0.428081i
$$465$$ 0 0
$$466$$ −23.3530 + 40.4486i −1.08181 + 1.87375i
$$467$$ −10.9985 + 19.0500i −0.508952 + 0.881530i 0.490995 + 0.871163i $$0.336633\pi$$
−0.999946 + 0.0103675i $$0.996700\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −38.8068 67.2153i −1.79002 3.10041i
$$471$$ 0 0
$$472$$ 13.7807 0.634310
$$473$$ 47.1124 2.16623
$$474$$ 0 0
$$475$$ 3.50000 + 6.06218i 0.160591 + 0.278152i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 6.01819 10.4238i 0.275265 0.476774i
$$479$$ 12.4875 21.6291i 0.570571 0.988257i −0.425937 0.904753i $$-0.640055\pi$$
0.996507 0.0835043i $$-0.0266112\pi$$
$$480$$ 0 0
$$481$$ −0.890369 1.54216i −0.0405973 0.0703166i
$$482$$ 32.1826 55.7419i 1.46588 2.53897i
$$483$$ 0 0
$$484$$ −19.0167 32.9379i −0.864397 1.49718i
$$485$$ 14.8997 25.8070i 0.676561 1.17184i
$$486$$ 0 0
$$487$$ 8.79893 + 15.2402i 0.398717 + 0.690599i 0.993568 0.113238i $$-0.0361221\pi$$
−0.594851 + 0.803836i $$0.702789\pi$$
$$488$$ −11.4897 −0.520114
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 6.89757 11.9469i 0.311283 0.539158i −0.667358 0.744737i $$-0.732575\pi$$
0.978640 + 0.205580i $$0.0659080\pi$$
$$492$$ 0 0
$$493$$ 1.16372 2.01561i 0.0524111 0.0907787i
$$494$$ 4.98755 + 8.63868i 0.224400 + 0.388673i
$$495$$ 0 0
$$496$$ 10.0718 0.452237
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −6.54377 11.3341i −0.292939 0.507386i 0.681564 0.731758i $$-0.261300\pi$$
−0.974503 + 0.224373i $$0.927967\pi$$
$$500$$ −34.4179 −1.53921
$$501$$ 0 0
$$502$$ −45.4150 −2.02697
$$503$$ 22.3068 0.994611 0.497305 0.867576i $$-0.334323\pi$$
0.497305 + 0.867576i $$0.334323\pi$$
$$504$$ 0 0
$$505$$ 9.54377 0.424692
$$506$$ −3.03638 −0.134983
$$507$$ 0 0
$$508$$ 2.72665 0.120976
$$509$$ −7.94659 13.7639i −0.352226 0.610074i 0.634413 0.772994i $$-0.281242\pi$$
−0.986639 + 0.162920i $$0.947909\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −41.4078 −1.82998
$$513$$ 0 0
$$514$$ −14.4356 25.0032i −0.636727 1.10284i
$$515$$ 12.6134 21.8471i 0.555814 0.962698i
$$516$$ 0 0
$$517$$ 27.4538 47.5514i 1.20742 2.09131i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 13.1082 0.574831
$$521$$ 2.20895 + 3.82600i 0.0967756 + 0.167620i 0.910348 0.413843i $$-0.135814\pi$$
−0.813573 + 0.581463i $$0.802480\pi$$
$$522$$ 0 0
$$523$$ −12.6367 + 21.8874i −0.552563 + 0.957067i 0.445526 + 0.895269i $$0.353017\pi$$
−0.998089 + 0.0617982i $$0.980316\pi$$
$$524$$ 16.0416 + 27.7849i 0.700782 + 1.21379i
$$525$$ 0 0
$$526$$ −9.25370 + 16.0279i −0.403480 + 0.698848i
$$527$$ −1.10078 1.90660i −0.0479506 0.0830528i
$$528$$ 0 0
$$529$$ 11.4626 19.8539i 0.498376 0.863212i
$$530$$ −20.0167 + 34.6700i −0.869471 + 1.50597i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −3.20321 5.54812i −0.138746 0.240316i
$$534$$ 0 0
$$535$$ 3.56440 0.154103
$$536$$ −79.9410 −3.45293
$$537$$ 0 0
$$538$$ −23.1716 40.1344i −0.998998 1.73032i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 1.71926 2.97785i 0.0739168 0.128028i −0.826698 0.562646i $$-0.809783\pi$$
0.900615 + 0.434618i $$0.143117\pi$$
$$542$$ 29.5043 51.1029i 1.26732 2.19506i
$$543$$ 0 0
$$544$$ −0.255158 0.441947i −0.0109398 0.0189483i
$$545$$ 4.40808 7.63501i 0.188821 0.327048i
$$546$$ 0 0
$$547$$ 3.46410 + 6.00000i 0.148114 + 0.256542i 0.930531 0.366214i $$-0.119346\pi$$
−0.782416 + 0.622756i $$0.786013\pi$$
$$548$$ −7.44445 + 12.8942i −0.318011 + 0.550812i
$$549$$ 0 0
$$550$$ 9.58998 + 16.6103i 0.408918 + 0.708267i
$$551$$ 9.97509 0.424953
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −8.81138 + 15.2618i −0.374360 + 0.648410i
$$555$$ 0 0
$$556$$ 4.16372 7.21177i 0.176581 0.305847i
$$557$$ 16.7917 + 29.0841i 0.711488 + 1.23233i 0.964298 + 0.264818i $$0.0853119\pi$$
−0.252810 + 0.967516i $$0.581355\pi$$
$$558$$ 0 0
$$559$$ −10.4356 −0.441379
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 18.3083 + 31.7108i 0.772287 + 1.33764i
$$563$$ −42.4792 −1.79028 −0.895142 0.445781i $$-0.852926\pi$$
−0.895142 + 0.445781i $$0.852926\pi$$
$$564$$ 0 0
$$565$$ −26.9439 −1.13354
$$566$$ 49.2029 2.06815
$$567$$ 0 0
$$568$$ −16.5438 −0.694161
$$569$$ −10.4035 −0.436137 −0.218069 0.975933i $$-0.569976\pi$$
−0.218069 + 0.975933i $$0.569976\pi$$
$$570$$ 0 0
$$571$$ 17.8496 0.746983 0.373491 0.927634i $$-0.378161\pi$$
0.373491 + 0.927634i $$0.378161\pi$$
$$572$$ 9.15126 + 15.8505i 0.382633 + 0.662741i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0.471974 0.0196827
$$576$$ 0 0
$$577$$ −5.97150 10.3429i −0.248597 0.430582i 0.714540 0.699595i $$-0.246636\pi$$
−0.963137 + 0.269013i $$0.913303\pi$$
$$578$$ 19.8135 34.3180i 0.824134 1.42744i
$$579$$ 0 0
$$580$$ 12.9356 22.4051i 0.537122 0.930322i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −28.3216 −1.17296
$$584$$ 3.80924 + 6.59780i 0.157628 + 0.273019i
$$585$$ 0 0
$$586$$ 18.5344 32.1026i 0.765650 1.32615i
$$587$$ 11.9299 + 20.6631i 0.492398 + 0.852859i 0.999962 0.00875568i $$-0.00278706\pi$$
−0.507563 + 0.861614i $$0.669454\pi$$
$$588$$ 0 0
$$589$$ 4.71780 8.17147i 0.194394 0.336699i
$$590$$ −8.70009 15.0690i −0.358177 0.620381i
$$591$$ 0 0
$$592$$ −3.85301 + 6.67361i −0.158358 + 0.274284i
$$593$$ 9.79007 16.9569i 0.402030 0.696336i −0.591941 0.805981i $$-0.701638\pi$$
0.993971 + 0.109645i $$0.0349714\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −27.4538 47.5514i −1.12455 1.94778i
$$597$$ 0 0
$$598$$ 0.672570 0.0275034
$$599$$ −18.5467 −0.757797 −0.378899 0.925438i $$-0.623697\pi$$
−0.378899 + 0.925438i $$0.623697\pi$$
$$600$$ 0 0
$$601$$ 9.09931 + 15.7605i 0.371169 + 0.642883i 0.989746 0.142841i $$-0.0456238\pi$$
−0.618577 + 0.785724i $$0.712290\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −20.1249 + 34.8573i −0.818870 + 1.41832i
$$605$$ −12.1659 + 21.0719i −0.494612 + 0.856693i
$$606$$ 0 0
$$607$$ 11.1549 + 19.3208i 0.452762 + 0.784206i 0.998556 0.0537125i $$-0.0171055\pi$$
−0.545795 + 0.837919i $$0.683772\pi$$
$$608$$ 1.09358 1.89413i 0.0443505 0.0768173i
$$609$$ 0 0
$$610$$ 7.25370 + 12.5638i 0.293694 + 0.508692i
$$611$$ −6.08113 + 10.5328i −0.246016 + 0.426112i
$$612$$ 0 0
$$613$$ −5.11849 8.86548i −0.206734 0.358073i 0.743950 0.668235i $$-0.232950\pi$$
−0.950684 + 0.310162i $$0.899617\pi$$
$$614$$ −67.0990 −2.70790
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −5.66372 + 9.80984i −0.228013 + 0.394929i −0.957219 0.289364i $$-0.906556\pi$$
0.729206 + 0.684294i $$0.239889\pi$$
$$618$$ 0 0
$$619$$ −4.31663 + 7.47663i −0.173500 + 0.300511i −0.939641 0.342161i $$-0.888841\pi$$
0.766141 + 0.642672i $$0.222174\pi$$
$$620$$ −12.2360 21.1934i −0.491409 0.851145i
$$621$$ 0 0
$$622$$ 39.3245 1.57677
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 15.3260 + 26.5454i 0.613039 + 1.06181i
$$626$$ 28.5366 1.14055
$$627$$ 0 0
$$628$$ 24.5438 0.979403
$$629$$ 1.68443 0.0671626
$$630$$ 0 0
$$631$$ −14.8535 −0.591308 −0.295654 0.955295i $$-0.595538\pi$$
−0.295654 + 0.955295i $$0.595538\pi$$
$$632$$ 74.3402 2.95710
$$633$$ 0 0
$$634$$ 4.96458 0.197169
$$635$$ −0.872181 1.51066i −0.0346115 0.0599488i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 27.3317 1.08207
$$639$$ 0 0
$$640$$ 24.7793 + 42.9190i 0.979487 + 1.69652i
$$641$$ −17.0797 + 29.5828i −0.674606 + 1.16845i 0.301978 + 0.953315i $$0.402353\pi$$
−0.976584 + 0.215137i $$0.930980\pi$$
$$642$$ 0 0
$$643$$ 5.41741 9.38323i 0.213642 0.370039i −0.739210 0.673475i $$-0.764801\pi$$
0.952852 + 0.303437i $$0.0981341\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −9.43560 −0.371239
$$647$$ 16.4846 + 28.5522i 0.648077 + 1.12250i 0.983582 + 0.180464i $$0.0577600\pi$$
−0.335504 + 0.942039i $$0.608907\pi$$
$$648$$ 0 0
$$649$$ 6.15486 10.6605i 0.241599 0.418462i
$$650$$ −2.12422 3.67926i −0.0833188 0.144312i
$$651$$ 0 0
$$652$$ −36.1160 + 62.5548i −1.41441 + 2.44984i
$$653$$ −1.96557 3.40446i −0.0769185 0.133227i 0.825000 0.565132i $$-0.191175\pi$$
−0.901919 + 0.431905i $$0.857841\pi$$
$$654$$ 0 0
$$655$$ 10.2626 17.7753i 0.400991 0.694537i
$$656$$ −13.8617 + 24.0091i −0.541207 + 0.937399i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 8.40856 + 14.5640i 0.327551 + 0.567335i 0.982025 0.188749i $$-0.0604434\pi$$
−0.654474 + 0.756084i $$0.727110\pi$$
$$660$$ 0 0
$$661$$ −17.0216 −0.662063 −0.331032 0.943620i $$-0.607397\pi$$
−0.331032 + 0.943620i $$0.607397\pi$$
$$662$$ −48.4940 −1.88477
$$663$$ 0 0
$$664$$ −2.39037 4.14024i −0.0927643 0.160672i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0.336285 0.582462i 0.0130210 0.0225530i
$$668$$ −17.1644 + 29.7296i −0.664110 + 1.15027i
$$669$$ 0 0
$$670$$ 50.4686 + 87.4141i 1.94977 + 3.37710i
$$671$$ −5.13161 + 8.88821i −0.198104 + 0.343126i
$$672$$ 0 0
$$673$$ −14.3727 24.8942i −0.554025 0.959600i −0.997979 0.0635501i $$-0.979758\pi$$
0.443953 0.896050i $$-0.353576\pi$$
$$674$$ 35.7403 61.9039i 1.37666 2.38445i
$$675$$ 0 0
$$676$$ 24.3245 + 42.1313i 0.935558 + 1.62043i
$$677$$ 6.03638 0.231997 0.115998 0.993249i $$-0.462993\pi$$
0.115998 + 0.993249i $$0.462993\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −6.19961 + 10.7380i −0.237744 + 0.411785i
$$681$$ 0 0
$$682$$ 12.9267 22.3898i 0.494991 0.857349i
$$683$$ 10.2556 + 17.7633i 0.392421 + 0.679693i 0.992768 0.120046i $$-0.0383043\pi$$
−0.600347 + 0.799739i $$0.704971\pi$$
$$684$$ 0 0
$$685$$ 9.52510 0.363935
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 22.5797 + 39.1091i 0.860842 + 1.49102i
$$689$$ 6.27335 0.238995
$$690$$ 0 0
$$691$$ −15.0029 −0.570738 −0.285369 0.958418i $$-0.592116\pi$$
−0.285369 + 0.958418i $$0.592116\pi$$
$$692$$ −70.3652 −2.67488
$$693$$ 0 0
$$694$$ −71.5595 −2.71636
$$695$$ −5.32743 −0.202081
$$696$$ 0 0
$$697$$ 6.05993 0.229536
$$698$$ −30.4648 52.7665i −1.15311 1.99724i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −38.5113 −1.45455 −0.727275 0.686346i $$-0.759214\pi$$
−0.727275 + 0.686346i $$0.759214\pi$$
$$702$$ 0 0
$$703$$ 3.60963 + 6.25206i 0.136140 + 0.235801i
$$704$$ −16.5402 + 28.6484i −0.623381 + 1.07973i
$$705$$ 0 0
$$706$$ −40.9705 + 70.9630i −1.54195 + 2.67073i
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 7.64008 0.286929 0.143465 0.989655i $$-0.454176\pi$$
0.143465 + 0.989655i $$0.454176\pi$$
$$710$$ 10.4445 + 18.0903i 0.391973 + 0.678918i
$$711$$ 0 0
$$712$$ −36.2798 + 62.8384i −1.35964 + 2.35497i
$$713$$ −0.318097 0.550960i −0.0119128 0.0206336i
$$714$$ 0 0
$$715$$ 5.85447 10.1402i 0.218945 0.379224i
$$716$$ −23.0057 39.8471i −0.859765 1.48916i
$$717$$ 0 0
$$718$$ 31.4164 54.4148i 1.17245 2.03074i
$$719$$ −15.0182 + 26.0123i −0.560084 + 0.970094i 0.437405 + 0.899265i $$0.355898\pi$$
−0.997488 + 0.0708289i $$0.977436\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 3.15486 + 5.46438i 0.117412 + 0.203363i
$$723$$ 0 0
$$724$$ 88.7395 3.29798
$$725$$ −4.24844 −0.157783
$$726$$ 0 0
$$727$$ −1.72812 2.99319i −0.0640923 0.111011i 0.832199 0.554478i $$-0.187082\pi$$
−0.896291 + 0.443466i $$0.853749\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 4.80972 8.33068i 0.178016 0.308332i
$$731$$ 4.93560 8.54871i 0.182550 0.316185i
$$732$$ 0 0
$$733$$ −19.2630 33.3645i −0.711496 1.23235i −0.964295 0.264829i $$-0.914685\pi$$
0.252799 0.967519i $$-0.418649\pi$$
$$734$$ −33.7709 + 58.4929i −1.24651 + 2.15901i
$$735$$ 0 0
$$736$$ −0.0737345 0.127712i −0.00271789 0.00470752i
$$737$$ −35.7039 + 61.8409i −1.31517 + 2.27794i
$$738$$ 0 0
$$739$$ −22.5620 39.0785i −0.829955 1.43752i −0.898073 0.439847i $$-0.855033\pi$$
0.0681179 0.997677i $$-0.478301\pi$$
$$740$$ 18.7237 0.688298
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 4.74338 8.21577i 0.174018 0.301407i −0.765803 0.643075i $$-0.777658\pi$$
0.939821 + 0.341668i $$0.110992\pi$$
$$744$$ 0 0
$$745$$ −17.5634 + 30.4207i −0.643474 + 1.11453i
$$746$$ −20.0869 34.7915i −0.735432 1.27381i
$$747$$ 0 0
$$748$$ −17.3126 −0.633013
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 4.91595 + 8.51467i 0.179386 + 0.310705i 0.941670 0.336537i $$-0.109256\pi$$
−0.762285 + 0.647242i $$0.775922\pi$$
$$752$$ 52.6313 1.91927
$$753$$ 0 0
$$754$$ −6.05408 −0.220477
$$755$$ 25.7496 0.937124
$$756$$ 0 0
$$757$$ −41.8171 −1.51987 −0.759934 0.650000i $$-0.774769\pi$$
−0.759934 + 0.650000i $$0.774769\pi$$
$$758$$ 29.6156 1.07569
$$759$$ 0 0
$$760$$ −53.1416 −1.92765
$$761$$ 11.4897 + 19.9007i 0.416501 + 0.721400i 0.995585 0.0938675i $$-0.0299230\pi$$
−0.579084 + 0.815268i $$0.696590\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 2.84494 0.102926
$$765$$ 0 0
$$766$$ −15.2989 26.4985i −0.552773 0.957430i
$$767$$ −1.36333 + 2.36135i −0.0492269 + 0.0852635i
$$768$$ 0 0
$$769$$ −3.04329 + 5.27113i −0.109744 + 0.190082i −0.915666 0.401939i $$-0.868336\pi$$
0.805923 + 0.592021i $$0.201670\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 49.2350 1.77201
$$773$$ −20.9107 36.2184i −0.752105 1.30268i −0.946801 0.321821i $$-0.895705\pi$$
0.194695 0.980864i $$-0.437628\pi$$
$$774$$ 0 0
$$775$$ −2.00933 + 3.48027i −0.0721774 + 0.125015i
$$776$$ 29.0349 + 50.2899i 1.04229 + 1.80530i
$$777$$ 0 0
$$778$$ 25.3442 43.8974i 0.908632 1.57380i
$$779$$ 12.9861 + 22.4926i 0.465275 + 0.805880i
$$780$$ 0 0
$$781$$ −7.38891 + 12.7980i −0.264396 + 0.457947i
$$782$$ −0.318097 + 0.550960i −0.0113751 + 0.0197023i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −7.85087 13.5981i −0.280210 0.485337i
$$786$$ 0 0
$$787$$ 32.2920 1.15109 0.575543 0.817772i $$-0.304791\pi$$