# Properties

 Label 1323.2.f.c.442.1 Level $1323$ Weight $2$ Character 1323.442 Analytic conductor $10.564$ Analytic rank $0$ Dimension $6$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1323 = 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1323.f (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: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 442.1 Root $$0.500000 - 2.05195i$$ of defining polynomial Character $$\chi$$ $$=$$ 1323.442 Dual form 1323.2.f.c.883.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.23025 - 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(1.29679 - 2.24611i) q^{5} +5.05408 q^{8} +O(q^{10})$$ $$q+(-1.23025 - 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(1.29679 - 2.24611i) q^{5} +5.05408 q^{8} -6.38151 q^{10} +(2.25729 + 3.90975i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-2.16372 - 3.74766i) q^{16} -0.945916 q^{17} +4.05408 q^{19} +(5.25729 + 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +(-0.136673 + 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} -2.46050 q^{26} +(1.23025 + 2.13086i) q^{29} +(1.16372 - 2.01561i) q^{31} +(-0.269748 + 0.467216i) q^{32} +(1.16372 + 2.01561i) q^{34} +1.78074 q^{37} +(-4.98755 - 8.63868i) q^{38} +(6.55408 - 11.3520i) q^{40} +(3.20321 - 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} -18.3025 q^{44} +0.672570 q^{46} +(6.08113 + 10.5328i) q^{47} +(-2.12422 + 3.67926i) q^{50} +(2.02704 + 3.51094i) q^{52} +6.27335 q^{53} +11.7089 q^{55} +(3.02704 - 5.24299i) q^{58} +(1.36333 - 2.36135i) q^{59} +(-1.13667 - 1.96878i) q^{61} -5.72665 q^{62} -7.32743 q^{64} +(-1.29679 - 2.24611i) q^{65} +(7.90856 - 13.6980i) q^{67} +(1.91741 - 3.32105i) q^{68} -3.27335 q^{71} +1.50739 q^{73} +(-2.19076 - 3.79450i) q^{74} +(-8.21780 + 14.2336i) q^{76} +(-7.35447 - 12.7383i) q^{79} -11.2235 q^{80} -15.7630 q^{82} +(0.472958 + 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +(12.8384 - 22.2368i) q^{86} +(11.4086 + 19.7602i) q^{88} -14.3566 q^{89} +(-0.554084 - 0.959702i) q^{92} +(14.9626 - 25.9161i) q^{94} +(5.25729 - 9.10590i) q^{95} +(-5.74484 - 9.95036i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q - q^{2} - 3 q^{4} + 5 q^{5} + 12 q^{8}+O(q^{10})$$ 6 * q - q^2 - 3 * q^4 + 5 * q^5 + 12 * q^8 $$6 q - q^{2} - 3 q^{4} + 5 q^{5} + 12 q^{8} - 2 q^{11} + 3 q^{13} - 3 q^{16} - 24 q^{17} + 6 q^{19} + 16 q^{20} + 15 q^{22} - 6 q^{25} - 2 q^{26} + q^{29} - 3 q^{31} - 8 q^{32} - 3 q^{34} - 6 q^{37} - 8 q^{38} + 21 q^{40} + 22 q^{41} + 3 q^{43} - 46 q^{44} + 24 q^{46} + 9 q^{47} + 10 q^{50} + 3 q^{52} + 36 q^{53} + 12 q^{55} + 9 q^{58} + 9 q^{59} - 6 q^{61} - 36 q^{62} - 24 q^{64} - 5 q^{65} - 6 q^{68} - 18 q^{71} - 6 q^{73} + 6 q^{74} - 21 q^{76} - 15 q^{79} + 22 q^{80} - 18 q^{82} + 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} - 4 q^{89} + 15 q^{92} + 24 q^{94} + 16 q^{95} + 3 q^{97}+O(q^{100})$$ 6 * q - q^2 - 3 * q^4 + 5 * q^5 + 12 * q^8 - 2 * q^11 + 3 * q^13 - 3 * q^16 - 24 * q^17 + 6 * q^19 + 16 * q^20 + 15 * q^22 - 6 * q^25 - 2 * q^26 + q^29 - 3 * q^31 - 8 * q^32 - 3 * q^34 - 6 * q^37 - 8 * q^38 + 21 * q^40 + 22 * q^41 + 3 * q^43 - 46 * q^44 + 24 * q^46 + 9 * q^47 + 10 * q^50 + 3 * q^52 + 36 * q^53 + 12 * q^55 + 9 * q^58 + 9 * q^59 - 6 * q^61 - 36 * q^62 - 24 * q^64 - 5 * q^65 - 6 * q^68 - 18 * q^71 - 6 * q^73 + 6 * q^74 - 21 * q^76 - 15 * q^79 + 22 * q^80 - 18 * q^82 + 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 - 4 * q^89 + 15 * q^92 + 24 * q^94 + 16 * q^95 + 3 * q^97

## Character values

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

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.23025 2.13086i −0.869920 1.50675i −0.862078 0.506776i $$-0.830837\pi$$
−0.00784213 0.999969i $$-0.502496\pi$$
$$3$$ 0 0
$$4$$ −2.02704 + 3.51094i −1.01352 + 1.75547i
$$5$$ 1.29679 2.24611i 0.579942 1.00449i −0.415543 0.909573i $$-0.636409\pi$$
0.995485 0.0949156i $$-0.0302581\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 5.05408 1.78689
$$9$$ 0 0
$$10$$ −6.38151 −2.01801
$$11$$ 2.25729 + 3.90975i 0.680600 + 1.17883i 0.974798 + 0.223089i $$0.0716141\pi$$
−0.294198 + 0.955744i $$0.595053\pi$$
$$12$$ 0 0
$$13$$ 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i $$-0.789049\pi$$
0.926995 + 0.375073i $$0.122382\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −2.16372 3.74766i −0.540929 0.936916i
$$17$$ −0.945916 −0.229418 −0.114709 0.993399i $$-0.536594\pi$$
−0.114709 + 0.993399i $$0.536594\pi$$
$$18$$ 0 0
$$19$$ 4.05408 0.930071 0.465035 0.885292i $$-0.346042\pi$$
0.465035 + 0.885292i $$0.346042\pi$$
$$20$$ 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 −0.879923 0.475117i $$-0.842406\pi$$
0.851425 + 0.524477i $$0.175739\pi$$
$$24$$ 0 0
$$25$$ −0.863327 1.49533i −0.172665 0.299065i
$$26$$ −2.46050 −0.482545
$$27$$ 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
$$31$$ 1.16372 2.01561i 0.209009 0.362015i −0.742393 0.669964i $$-0.766309\pi$$
0.951403 + 0.307949i $$0.0996427\pi$$
$$32$$ −0.269748 + 0.467216i −0.0476851 + 0.0825930i
$$33$$ 0 0
$$34$$ 1.16372 + 2.01561i 0.199576 + 0.345675i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 1.78074 0.292752 0.146376 0.989229i $$-0.453239\pi$$
0.146376 + 0.989229i $$0.453239\pi$$
$$38$$ −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 $$-0.666572\pi$$
1.00000 0.000297253i $$-9.46187e-5\pi$$
$$42$$ 0 0
$$43$$ 5.21780 + 9.03749i 0.795707 + 1.37820i 0.922389 + 0.386262i $$0.126234\pi$$
−0.126682 + 0.991943i $$0.540433\pi$$
$$44$$ −18.3025 −2.75921
$$45$$ 0 0
$$46$$ 0.672570 0.0991650
$$47$$ 6.08113 + 10.5328i 0.887023 + 1.53637i 0.843377 + 0.537323i $$0.180564\pi$$
0.0436467 + 0.999047i $$0.486102\pi$$
$$48$$ 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
$$53$$ 6.27335 0.861710 0.430855 0.902421i $$-0.358212\pi$$
0.430855 + 0.902421i $$0.358212\pi$$
$$54$$ 0 0
$$55$$ 11.7089 1.57883
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 3.02704 5.24299i 0.397470 0.688438i
$$59$$ 1.36333 2.36135i 0.177490 0.307422i −0.763530 0.645772i $$-0.776536\pi$$
0.941020 + 0.338350i $$0.109869\pi$$
$$60$$ 0 0
$$61$$ −1.13667 1.96878i −0.145536 0.252076i 0.784037 0.620714i $$-0.213157\pi$$
−0.929573 + 0.368639i $$0.879824\pi$$
$$62$$ −5.72665 −0.727286
$$63$$ 0 0
$$64$$ −7.32743 −0.915929
$$65$$ −1.29679 2.24611i −0.160847 0.278595i
$$66$$ 0 0
$$67$$ 7.90856 13.6980i 0.966184 1.67348i 0.259784 0.965667i $$-0.416349\pi$$
0.706400 0.707813i $$-0.250318\pi$$
$$68$$ 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
$$73$$ 1.50739 0.176427 0.0882134 0.996102i $$-0.471884\pi$$
0.0882134 + 0.996102i $$0.471884\pi$$
$$74$$ −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
$$79$$ −7.35447 12.7383i −0.827443 1.43317i −0.900038 0.435811i $$-0.856461\pi$$
0.0725952 0.997361i $$-0.476872\pi$$
$$80$$ −11.2235 −1.25483
$$81$$ 0 0
$$82$$ −15.7630 −1.74074
$$83$$ 0.472958 + 0.819187i 0.0519139 + 0.0899175i 0.890815 0.454367i $$-0.150135\pi$$
−0.838901 + 0.544285i $$0.816801\pi$$
$$84$$ 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
$$89$$ −14.3566 −1.52180 −0.760899 0.648871i $$-0.775242\pi$$
−0.760899 + 0.648871i $$0.775242\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −0.554084 0.959702i −0.0577673 0.100056i
$$93$$ 0 0
$$94$$ 14.9626 25.9161i 1.54328 2.67304i
$$95$$ 5.25729 9.10590i 0.539387 0.934246i
$$96$$ 0 0
$$97$$ −5.74484 9.95036i −0.583300 1.01031i −0.995085 0.0990246i $$-0.968428\pi$$
0.411785 0.911281i $$-0.364906\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 7.00000 0.700000
$$101$$ 1.83988 + 3.18677i 0.183075 + 0.317096i 0.942926 0.333002i $$-0.108061\pi$$
−0.759851 + 0.650097i $$0.774728\pi$$
$$102$$ 0 0
$$103$$ −4.86333 + 8.42353i −0.479198 + 0.829995i −0.999715 0.0238560i $$-0.992406\pi$$
0.520518 + 0.853851i $$0.325739\pi$$
$$104$$ 2.52704 4.37697i 0.247797 0.429197i
$$105$$ 0 0
$$106$$ −7.71780 13.3676i −0.749619 1.29838i
$$107$$ 1.37432 0.132860 0.0664301 0.997791i $$-0.478839\pi$$
0.0664301 + 0.997791i $$0.478839\pi$$
$$108$$ 0 0
$$109$$ −3.39922 −0.325587 −0.162793 0.986660i $$-0.552050\pi$$
−0.162793 + 0.986660i $$0.552050\pi$$
$$110$$ −14.4050 24.9501i −1.37346 2.37890i
$$111$$ 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
$$116$$ −9.97509 −0.926164
$$117$$ 0 0
$$118$$ −6.70895 −0.617608
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −4.69076 + 8.12463i −0.426432 + 0.738603i
$$122$$ −2.79679 + 4.84418i −0.253209 + 0.438572i
$$123$$ 0 0
$$124$$ 4.71780 + 8.17147i 0.423671 + 0.733820i
$$125$$ 8.48968 0.759340
$$126$$ 0 0
$$127$$ 0.672570 0.0596809 0.0298405 0.999555i $$-0.490500\pi$$
0.0298405 + 0.999555i $$0.490500\pi$$
$$128$$ 9.55408 + 16.5482i 0.844470 + 1.46266i
$$129$$ 0 0
$$130$$ −3.19076 + 5.52655i −0.279848 + 0.484711i
$$131$$ −3.95691 + 6.85356i −0.345717 + 0.598799i −0.985484 0.169770i $$-0.945697\pi$$
0.639767 + 0.768569i $$0.279031\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −38.9181 −3.36201
$$135$$ 0 0
$$136$$ −4.78074 −0.409945
$$137$$ −1.83628 3.18054i −0.156884 0.271732i 0.776859 0.629674i $$-0.216812\pi$$
−0.933744 + 0.357943i $$0.883478\pi$$
$$138$$ 0 0
$$139$$ −1.02704 + 1.77889i −0.0871126 + 0.150883i −0.906289 0.422658i $$-0.861097\pi$$
0.819177 + 0.573541i $$0.194431\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 4.02704 + 6.97504i 0.337942 + 0.585332i
$$143$$ 4.51459 0.377529
$$144$$ 0 0
$$145$$ 6.38151 0.529956
$$146$$ −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 0.443147 + 0.896449i $$0.353862\pi$$
−0.997921 + 0.0644482i $$0.979471\pi$$
$$150$$ 0 0
$$151$$ −4.96410 8.59808i −0.403973 0.699702i 0.590228 0.807236i $$-0.299038\pi$$
−0.994201 + 0.107535i $$0.965704\pi$$
$$152$$ 20.4897 1.66193
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3.01819 5.22765i −0.242427 0.419895i
$$156$$ 0 0
$$157$$ 3.02704 5.24299i 0.241584 0.418436i −0.719581 0.694408i $$-0.755666\pi$$
0.961166 + 0.275972i $$0.0889996\pi$$
$$158$$ −18.0957 + 31.3427i −1.43962 + 2.49349i
$$159$$ 0 0
$$160$$ 0.699612 + 1.21176i 0.0553092 + 0.0957983i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 17.8171 1.39554 0.697772 0.716320i $$-0.254175\pi$$
0.697772 + 0.716320i $$0.254175\pi$$
$$164$$ 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 −0.654415 0.756136i $$-0.727085\pi$$
0.982040 + 0.188672i $$0.0604183\pi$$
$$168$$ 0 0
$$169$$ 6.00000 + 10.3923i 0.461538 + 0.799408i
$$170$$ 6.03638 0.462969
$$171$$ 0 0
$$172$$ −42.3068 −3.22586
$$173$$ −8.67830 15.0313i −0.659799 1.14281i −0.980667 0.195682i $$-0.937308\pi$$
0.320868 0.947124i $$-0.396025\pi$$
$$174$$ 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
$$179$$ 11.3494 0.848295 0.424147 0.905593i $$-0.360574\pi$$
0.424147 + 0.905593i $$0.360574\pi$$
$$180$$ 0 0
$$181$$ −21.8889 −1.62699 −0.813495 0.581572i $$-0.802438\pi$$
−0.813495 + 0.581572i $$0.802438\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −0.690757 + 1.19643i −0.0509233 + 0.0882018i
$$185$$ 2.30924 3.99973i 0.169779 0.294066i
$$186$$ 0 0
$$187$$ −2.13521 3.69829i −0.156142 0.270446i
$$188$$ −49.3068 −3.59607
$$189$$ 0 0
$$190$$ −25.8712 −1.87689
$$191$$ −0.350874 0.607731i −0.0253883 0.0439739i 0.853052 0.521826i $$-0.174749\pi$$
−0.878440 + 0.477852i $$0.841416\pi$$
$$192$$ 0 0
$$193$$ −6.07227 + 10.5175i −0.437092 + 0.757065i −0.997464 0.0711760i $$-0.977325\pi$$
0.560372 + 0.828241i $$0.310658\pi$$
$$194$$ −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
$$199$$ −22.7060 −1.60959 −0.804794 0.593555i $$-0.797724\pi$$
−0.804794 + 0.593555i $$0.797724\pi$$
$$200$$ −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
$$205$$ −8.30778 14.3895i −0.580241 1.00501i
$$206$$ 23.9325 1.66745
$$207$$ 0 0
$$208$$ −4.32743 −0.300053
$$209$$ 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
$$215$$ 27.0656 1.84586
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 4.18190 + 7.24327i 0.283234 + 0.490576i
$$219$$ 0 0
$$220$$ −23.7345 + 41.1094i −1.60018 + 2.77160i
$$221$$ −0.472958 + 0.819187i −0.0318146 + 0.0551045i
$$222$$ 0 0
$$223$$ 6.66225 + 11.5394i 0.446137 + 0.772733i 0.998131 0.0611159i $$-0.0194659\pi$$
−0.551993 + 0.833849i $$0.686133\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −25.5615 −1.70032
$$227$$ −0.690757 1.19643i −0.0458472 0.0794096i 0.842191 0.539179i $$-0.181265\pi$$
−0.888038 + 0.459769i $$0.847932\pi$$
$$228$$ 0 0
$$229$$ −8.98968 + 15.5706i −0.594055 + 1.02893i 0.399625 + 0.916679i $$0.369141\pi$$
−0.993679 + 0.112254i $$0.964193\pi$$
$$230$$ 0.872181 1.51066i 0.0575099 0.0996101i
$$231$$ 0 0
$$232$$ 6.21780 + 10.7695i 0.408219 + 0.707055i
$$233$$ 18.9823 1.24357 0.621786 0.783187i $$-0.286408\pi$$
0.621786 + 0.783187i $$0.286408\pi$$
$$234$$ 0 0
$$235$$ 31.5438 2.05769
$$236$$ 5.52704 + 9.57312i 0.359780 + 0.623157i
$$237$$ 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 −0.887745 0.460336i $$-0.847729\pi$$
0.0452094 0.998978i $$-0.485604\pi$$
$$242$$ 23.0833 1.48385
$$243$$ 0 0
$$244$$ 9.21634 0.590016
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 2.02704 3.51094i 0.128978 0.223396i
$$248$$ 5.88151 10.1871i 0.373477 0.646880i
$$249$$ 0 0
$$250$$ −10.4445 18.0903i −0.660565 1.14413i
$$251$$ 18.4576 1.16503 0.582516 0.812819i $$-0.302068\pi$$
0.582516 + 0.812819i $$0.302068\pi$$
$$252$$ 0 0
$$253$$ −1.23405 −0.0775838
$$254$$ −0.827430 1.43315i −0.0519176 0.0899239i
$$255$$ 0 0
$$256$$ 16.1804 28.0253i 1.01128 1.75158i
$$257$$ 5.86693 10.1618i 0.365969 0.633876i −0.622962 0.782252i $$-0.714071\pi$$
0.988931 + 0.148375i $$0.0474044\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 10.5146 0.652087
$$261$$ 0 0
$$262$$ 19.4720 1.20298
$$263$$ −3.76089 6.51406i −0.231907 0.401674i 0.726463 0.687206i $$-0.241163\pi$$
−0.958369 + 0.285532i $$0.907830\pi$$
$$264$$ 0 0
$$265$$ 8.13521 14.0906i 0.499742 0.865579i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 32.0620 + 55.5329i 1.95850 + 3.39221i
$$269$$ −18.8348 −1.14838 −0.574190 0.818722i $$-0.694683\pi$$
−0.574190 + 0.818722i $$0.694683\pi$$
$$270$$ 0 0
$$271$$ 23.9823 1.45682 0.728410 0.685141i $$-0.240260\pi$$
0.728410 + 0.685141i $$0.240260\pi$$
$$272$$ 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 0.738156 0.674630i $$-0.235697\pi$$
−0.953325 + 0.301947i $$0.902364\pi$$
$$278$$ 5.05408 0.303124
$$279$$ 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
$$283$$ 9.99854 17.3180i 0.594351 1.02945i −0.399287 0.916826i $$-0.630742\pi$$
0.993638 0.112621i $$-0.0359245\pi$$
$$284$$ 6.63521 11.4925i 0.393727 0.681956i
$$285$$ 0 0
$$286$$ −5.55408 9.61996i −0.328420 0.568840i
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −16.1052 −0.947367
$$290$$ −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 −0.997694 0.0678705i $$-0.978380\pi$$
0.557625 + 0.830093i $$0.311713\pi$$
$$294$$ 0 0
$$295$$ −3.53590 6.12435i −0.205868 0.356574i
$$296$$ 9.00000 0.523114
$$297$$ 0 0
$$298$$ 33.3245 1.93044
$$299$$ 0.136673 + 0.236725i 0.00790401 + 0.0136901i
$$300$$ 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
$$305$$ −5.89610 −0.337610
$$306$$ 0 0
$$307$$ 27.2704 1.55641 0.778203 0.628013i $$-0.216132\pi$$
0.778203 + 0.628013i $$0.216132\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −7.42627 + 12.8627i −0.421784 + 0.730551i
$$311$$ 7.99115 13.8411i 0.453136 0.784855i −0.545443 0.838148i $$-0.683638\pi$$
0.998579 + 0.0532931i $$0.0169718\pi$$
$$312$$ 0 0
$$313$$ 5.79893 + 10.0440i 0.327775 + 0.567722i 0.982070 0.188517i $$-0.0603680\pi$$
−0.654295 + 0.756239i $$0.727035\pi$$
$$314$$ −14.8961 −0.840636
$$315$$ 0 0
$$316$$ 59.6313 3.35452
$$317$$ −1.00885 1.74739i −0.0566629 0.0981430i 0.836303 0.548268i $$-0.184713\pi$$
−0.892965 + 0.450125i $$0.851379\pi$$
$$318$$ 0 0
$$319$$ −5.55408 + 9.61996i −0.310969 + 0.538614i
$$320$$ −9.50214 + 16.4582i −0.531186 + 0.920040i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −3.83482 −0.213375
$$324$$ 0 0
$$325$$ −1.72665 −0.0957775
$$326$$ −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
$$331$$ 9.85447 + 17.0684i 0.541651 + 0.938167i 0.998809 + 0.0487815i $$0.0155338\pi$$
−0.457159 + 0.889385i $$0.651133\pi$$
$$332$$ −3.83482 −0.210463
$$333$$ 0 0
$$334$$ −20.8348 −1.14003
$$335$$ −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
$$341$$ 10.5074 0.569007
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 26.3712 + 45.6763i 1.42184 + 2.46270i
$$345$$ 0 0
$$346$$ −21.3530 + 36.9845i −1.14794 + 1.98830i
$$347$$ 14.5416 25.1868i 0.780636 1.35210i −0.150936 0.988544i $$-0.548229\pi$$
0.931572 0.363557i $$-0.118438\pi$$
$$348$$ 0 0
$$349$$ 12.3815 + 21.4454i 0.662767 + 1.14795i 0.979885 + 0.199561i $$0.0639515\pi$$
−0.317118 + 0.948386i $$0.602715\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −2.43560 −0.129818
$$353$$ 16.6513 + 28.8408i 0.886257 + 1.53504i 0.844266 + 0.535925i $$0.180037\pi$$
0.0419914 + 0.999118i $$0.486630\pi$$
$$354$$ 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
$$359$$ −25.5366 −1.34777 −0.673884 0.738837i $$-0.735375\pi$$
−0.673884 + 0.738837i $$0.735375\pi$$
$$360$$ 0 0
$$361$$ −2.56440 −0.134968
$$362$$ 26.9289 + 46.6422i 1.41535 + 2.45146i
$$363$$ 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 0.962398 + 0.271644i $$0.0875672\pi$$
−0.245949 + 0.969283i $$0.579100\pi$$
$$368$$ 1.18289 0.0616622
$$369$$ 0 0
$$370$$ −11.3638 −0.590776
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −8.16372 + 14.1400i −0.422701 + 0.732140i −0.996203 0.0870646i $$-0.972251\pi$$
0.573502 + 0.819204i $$0.305585\pi$$
$$374$$ −5.25370 + 9.09967i −0.271662 + 0.470533i
$$375$$ 0 0
$$376$$ 30.7345 + 53.2338i 1.58501 + 2.74532i
$$377$$ 2.46050 0.126722
$$378$$ 0 0
$$379$$ 12.0364 0.618267 0.309134 0.951019i $$-0.399961\pi$$
0.309134 + 0.951019i $$0.399961\pi$$
$$380$$ 21.3135 + 36.9161i 1.09336 + 1.89376i
$$381$$ 0 0
$$382$$ −0.863327 + 1.49533i −0.0441716 + 0.0765075i
$$383$$ 6.21780 10.7695i 0.317715 0.550298i −0.662296 0.749242i $$-0.730418\pi$$
0.980011 + 0.198944i $$0.0637512\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 29.8817 1.52094
$$387$$ 0 0
$$388$$ 46.5801 2.36475
$$389$$ 10.3004 + 17.8408i 0.522250 + 0.904564i 0.999665 + 0.0258860i $$0.00824070\pi$$
−0.477414 + 0.878678i $$0.658426\pi$$
$$390$$ 0 0
$$391$$ 0.129281 0.223922i 0.00653803 0.0113242i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −20.1893 34.9689i −1.01712 1.76171i
$$395$$ −38.1488 −1.91948
$$396$$ 0 0
$$397$$ 23.6372 1.18631 0.593157 0.805087i $$-0.297881\pi$$
0.593157 + 0.805087i $$0.297881\pi$$
$$398$$ 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 −0.896263 0.443522i $$-0.853729\pi$$
0.832233 + 0.554426i $$0.187062\pi$$
$$402$$ 0 0
$$403$$ −1.16372 2.01561i −0.0579688 0.100405i
$$404$$ −14.9181 −0.742202
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 4.01965 + 6.96224i 0.199247 + 0.345105i
$$408$$ 0 0
$$409$$ −17.1623 + 29.7259i −0.848619 + 1.46985i 0.0338223 + 0.999428i $$0.489232\pi$$
−0.882441 + 0.470423i $$0.844101\pi$$
$$410$$ −20.4413 + 35.4054i −1.00953 + 1.74855i
$$411$$ 0 0
$$412$$ −19.7163 34.1497i −0.971354 1.68243i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 2.45331 0.120428
$$416$$ 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 −0.911312 0.411717i $$-0.864929\pi$$
0.812213 + 0.583361i $$0.198263\pi$$
$$420$$ 0 0
$$421$$ 10.5344 + 18.2462i 0.513417 + 0.889264i 0.999879 + 0.0155624i $$0.00495387\pi$$
−0.486462 + 0.873702i $$0.661713\pi$$
$$422$$ 11.2235 0.546353
$$423$$ 0 0
$$424$$ 31.7060 1.53978
$$425$$ 0.816635 + 1.41445i 0.0396126 + 0.0686110i
$$426$$ 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
$$431$$ −22.6185 −1.08949 −0.544747 0.838600i $$-0.683374\pi$$
−0.544747 + 0.838600i $$0.683374\pi$$
$$432$$ 0 0
$$433$$ −2.41789 −0.116196 −0.0580982 0.998311i $$-0.518504\pi$$
−0.0580982 + 0.998311i $$0.518504\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 6.89037 11.9345i 0.329989 0.571557i
$$437$$ −0.554084 + 0.959702i −0.0265054 + 0.0459088i
$$438$$ 0 0
$$439$$ −11.7448 20.3427i −0.560551 0.970902i −0.997448 0.0713911i $$-0.977256\pi$$
0.436898 0.899511i $$-0.356077\pi$$
$$440$$ 59.1780 2.82120
$$441$$ 0 0
$$442$$ 2.32743 0.110705
$$443$$ −6.70895 11.6202i −0.318752 0.552094i 0.661476 0.749966i $$-0.269930\pi$$
−0.980228 + 0.197872i $$0.936597\pi$$
$$444$$ 0 0
$$445$$ −18.6175 + 32.2465i −0.882554 + 1.52863i
$$446$$ 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
$$451$$ 28.9224 1.36190
$$452$$ 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
$$457$$ −4.40856 7.63584i −0.206224 0.357190i 0.744298 0.667847i $$-0.232784\pi$$
−0.950522 + 0.310658i $$0.899451\pi$$
$$458$$ 44.2383 2.06712
$$459$$ 0 0
$$460$$ −2.87412 −0.134007
$$461$$ 2.82957 + 4.90095i 0.131786 + 0.228260i 0.924365 0.381509i $$-0.124595\pi$$
−0.792579 + 0.609769i $$0.791262\pi$$
$$462$$ 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
$$467$$ −21.9971 −1.01790 −0.508952 0.860795i $$-0.669967\pi$$
−0.508952 + 0.860795i $$0.669967\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −38.8068 67.2153i −1.79002 3.10041i
$$471$$ 0 0
$$472$$ 6.89037 11.9345i 0.317155 0.549328i
$$473$$ −23.5562 + 40.8006i −1.08312 + 1.87601i
$$474$$ 0 0
$$475$$ −3.50000 6.06218i −0.160591 0.278152i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −12.0364 −0.550531
$$479$$ −12.4875 21.6291i −0.570571 0.988257i −0.996507 0.0835043i $$-0.973389\pi$$
0.425937 0.904753i $$-0.359945\pi$$
$$480$$ 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
$$485$$ −29.7994 −1.35312
$$486$$ 0 0
$$487$$ −17.5979 −0.797435 −0.398717 0.917074i $$-0.630545\pi$$
−0.398717 + 0.917074i $$0.630545\pi$$
$$488$$ −5.74484 9.95036i −0.260057 0.450432i
$$489$$ 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
$$494$$ −9.97509 −0.448801
$$495$$ 0 0
$$496$$ −10.0718 −0.452237
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −6.54377 + 11.3341i −0.292939 + 0.507386i −0.974503 0.224373i $$-0.927967\pi$$
0.681564 + 0.731758i $$0.261300\pi$$
$$500$$ −17.2089 + 29.8068i −0.769607 + 1.33300i
$$501$$ 0 0
$$502$$ −22.7075 39.3305i −1.01348 1.75541i
$$503$$ −22.3068 −0.994611 −0.497305 0.867576i $$-0.665677\pi$$
−0.497305 + 0.867576i $$0.665677\pi$$
$$504$$ 0 0
$$505$$ 9.54377 0.424692
$$506$$ 1.51819 + 2.62958i 0.0674917 + 0.116899i
$$507$$ 0 0
$$508$$ −1.36333 + 2.36135i −0.0604879 + 0.104768i
$$509$$ 7.94659 13.7639i 0.352226 0.610074i −0.634413 0.772994i $$-0.718758\pi$$
0.986639 + 0.162920i $$0.0520914\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −41.4078 −1.82998
$$513$$ 0 0
$$514$$ −28.8712 −1.27345
$$515$$ 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
$$520$$ −6.55408 11.3520i −0.287416 0.497818i
$$521$$ 4.41789 0.193551 0.0967756 0.995306i $$-0.469147\pi$$
0.0967756 + 0.995306i $$0.469147\pi$$
$$522$$ 0 0
$$523$$ −25.2733 −1.10513 −0.552563 0.833471i $$-0.686350\pi$$
−0.552563 + 0.833471i $$0.686350\pi$$
$$524$$ −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
$$530$$ −40.0335 −1.73894
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −3.20321 5.54812i −0.138746 0.240316i
$$534$$ 0 0
$$535$$ 1.78220 3.08686i 0.0770513 0.133457i
$$536$$ 39.9705 69.2310i 1.72646 2.99032i
$$537$$ 0 0
$$538$$ 23.1716 + 40.1344i 0.998998 + 1.73032i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −3.43852 −0.147834 −0.0739168 0.997264i $$-0.523550\pi$$
−0.0739168 + 0.997264i $$0.523550\pi$$
$$542$$ −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 $$0.786013\pi$$
$$548$$ 14.8889 0.636023
$$549$$ 0 0
$$550$$ −19.1800 −0.817836
$$551$$ 4.98755 + 8.63868i 0.212477 + 0.368020i
$$552$$ 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
$$557$$ −33.5835 −1.42298 −0.711488 0.702698i $$-0.751979\pi$$
−0.711488 + 0.702698i $$0.751979\pi$$
$$558$$ 0 0
$$559$$ 10.4356 0.441379
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 18.3083 31.7108i 0.772287 1.33764i
$$563$$ −21.2396 + 36.7880i −0.895142 + 1.55043i −0.0615128 + 0.998106i $$0.519593\pi$$
−0.833629 + 0.552325i $$0.813741\pi$$
$$564$$ 0 0
$$565$$ −13.4720 23.3341i −0.566770 0.981675i
$$566$$ −49.2029 −2.06815
$$567$$ 0 0
$$568$$ −16.5438 −0.694161
$$569$$ 5.20175 + 9.00969i 0.218069 + 0.377706i 0.954217 0.299114i $$-0.0966910\pi$$
−0.736149 + 0.676820i $$0.763358\pi$$
$$570$$ 0 0
$$571$$ −8.92480 + 15.4582i −0.373491 + 0.646906i −0.990100 0.140364i $$-0.955173\pi$$
0.616609 + 0.787270i $$0.288506\pi$$
$$572$$ −9.15126 + 15.8505i −0.382633 + 0.662741i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0.471974 0.0196827
$$576$$ 0 0
$$577$$ −11.9430 −0.497193 −0.248597 0.968607i $$-0.579969\pi$$
−0.248597 + 0.968607i $$0.579969\pi$$
$$578$$ 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
$$583$$ 14.1608 + 24.5272i 0.586480 + 1.01581i
$$584$$ 7.61849 0.315255
$$585$$ 0 0
$$586$$ 37.0689 1.53130
$$587$$ −11.9299 20.6631i −0.492398 0.852859i 0.507563 0.861614i $$-0.330546\pi$$
−0.999962 + 0.00875568i $$0.997213\pi$$
$$588$$ 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
$$593$$ 19.5801 0.804060 0.402030 0.915626i $$-0.368305\pi$$
0.402030 + 0.915626i $$0.368305\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −27.4538 47.5514i −1.12455 1.94778i
$$597$$ 0 0
$$598$$ 0.336285 0.582462i 0.0137517 0.0238187i
$$599$$ 9.27335 16.0619i 0.378899 0.656272i −0.612004 0.790855i $$-0.709636\pi$$
0.990902 + 0.134583i $$0.0429696\pi$$
$$600$$ 0 0
$$601$$ −9.09931 15.7605i −0.371169 0.642883i 0.618577 0.785724i $$-0.287710\pi$$
−0.989746 + 0.142841i $$0.954376\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 40.2498 1.63774
$$605$$ 12.1659 + 21.0719i 0.494612 + 0.856693i
$$606$$ 0 0
$$607$$ −11.1549 + 19.3208i −0.452762 + 0.784206i −0.998556 0.0537125i $$-0.982895\pi$$
0.545795 + 0.837919i $$0.316228\pi$$
$$608$$ −1.09358 + 1.89413i −0.0443505 + 0.0768173i
$$609$$ 0 0
$$610$$ 7.25370 + 12.5638i 0.293694 + 0.508692i
$$611$$ 12.1623 0.492032
$$612$$ 0 0
$$613$$ 10.2370 0.413467 0.206734 0.978397i $$-0.433717\pi$$
0.206734 + 0.978397i $$0.433717\pi$$
$$614$$ −33.5495 58.1094i −1.35395 2.34511i
$$615$$ 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 $$-0.111159\pi$$
−0.766141 + 0.642672i $$0.777826\pi$$
$$620$$ 24.4720 0.982818
$$621$$ 0 0
$$622$$ −39.3245 −1.57677
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 15.3260 26.5454i 0.613039 1.06181i
$$626$$ 14.2683 24.7134i 0.570275 0.987746i
$$627$$ 0 0
$$628$$ 12.2719 + 21.2555i 0.489701 + 0.848188i
$$629$$ −1.68443 −0.0671626
$$630$$ 0 0
$$631$$ −14.8535 −0.591308 −0.295654 0.955295i $$-0.595538\pi$$
−0.295654 + 0.955295i $$0.595538\pi$$
$$632$$ −37.1701 64.3805i −1.47855 2.56092i
$$633$$ 0 0
$$634$$ −2.48229 + 4.29945i −0.0985844 + 0.170753i
$$635$$ 0.872181 1.51066i 0.0346115 0.0599488i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 27.3317 1.08207
$$639$$ 0 0
$$640$$ 49.5586 1.95897
$$641$$ −17.0797 29.5828i −0.674606 1.16845i −0.976584 0.215137i $$-0.930980\pi$$
0.301978 0.953315i $$-0.402353\pi$$
$$642$$ 0 0
$$643$$ −5.41741 + 9.38323i −0.213642 + 0.370039i −0.952852 0.303437i $$-0.901866\pi$$
0.739210 + 0.673475i $$0.235199\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 4.71780 + 8.17147i 0.185619 + 0.321502i
$$647$$ 32.9692 1.29615 0.648077 0.761575i $$-0.275573\pi$$
0.648077 + 0.761575i $$0.275573\pi$$
$$648$$ 0 0
$$649$$ 12.3097 0.483199
$$650$$ 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 −0.901919 0.431905i $$-0.857841\pi$$
0.825000 + 0.565132i $$0.191175\pi$$
$$654$$ 0 0
$$655$$ 10.2626 + 17.7753i 0.400991 + 0.694537i
$$656$$ −27.7233 −1.08241
$$657$$ 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
$$661$$ −8.51080 + 14.7411i −0.331032 + 0.573364i −0.982714 0.185128i $$-0.940730\pi$$
0.651683 + 0.758492i $$0.274063\pi$$
$$662$$ 24.2470 41.9970i 0.942386 1.63226i
$$663$$ 0 0
$$664$$ 2.39037 + 4.14024i 0.0927643 + 0.160672i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −0.672570 −0.0260420
$$668$$ 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 $$-0.353576\pi$$
$$674$$ −71.4805 −2.75333
$$675$$ 0 0
$$676$$ −48.6490 −1.87112
$$677$$ 3.01819 + 5.22765i 0.115998 + 0.200915i 0.918178 0.396167i $$-0.129660\pi$$
−0.802180 + 0.597082i $$0.796327\pi$$
$$678$$ 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
$$683$$ −20.5113 −0.784842 −0.392421 0.919786i $$-0.628362\pi$$
−0.392421 + 0.919786i $$0.628362\pi$$
$$684$$ 0 0
$$685$$ −9.52510 −0.363935
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 22.5797 39.1091i 0.860842 1.49102i
$$689$$ 3.13667 5.43288i 0.119498 0.206976i
$$690$$ 0 0
$$691$$ −7.50146 12.9929i −0.285369 0.494274i 0.687330 0.726346i $$-0.258783\pi$$
−0.972699 + 0.232072i $$0.925450\pi$$
$$692$$ 70.3652 2.67488
$$693$$ 0 0
$$694$$ −71.5595 −2.71636
$$695$$ 2.66372 + 4.61369i 0.101040 + 0.175007i
$$696$$ 0 0
$$697$$ −3.02997 + 5.24806i −0.114768 + 0.198784i
$$698$$ 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
$$703$$ 7.21926 0.272280
$$704$$ −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
$$709$$ −3.82004 6.61650i −0.143465 0.248488i 0.785334 0.619072i $$-0.212491\pi$$
−0.928799 + 0.370584i $$0.879158\pi$$
$$710$$ 20.8889 0.783947
$$711$$ 0 0
$$712$$ −72.5595 −2.71928
$$713$$ 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
$$719$$ −30.0364 −1.12017 −0.560084 0.828436i $$-0.689231\pi$$
−0.560084 + 0.828436i $$0.689231\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 3.15486 + 5.46438i 0.117412 + 0.203363i
$$723$$ 0 0
$$724$$ 44.3697 76.8506i 1.64899 2.85613i
$$725$$ 2.12422 3.67926i 0.0788916 0.136644i
$$726$$ 0 0
$$727$$ 1.72812 + 2.99319i 0.0640923 + 0.111011i 0.896291 0.443466i $$-0.146251\pi$$
−0.832199 + 0.554478i $$0.812918\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −9.61944 −0.356032
$$731$$ −4.93560 8.54871i −0.182550 0.316185i
$$732$$ 0 0
$$733$$ 19.2630 33.3645i 0.711496 1.23235i −0.252799 0.967519i $$-0.581351\pi$$
0.964295 0.264829i $$-0.0853155\pi$$
$$734$$ 33.7709 58.4929i 1.24651 2.15901i
$$735$$ 0 0
$$736$$ −0.0737345 0.127712i −0.00271789 0.00470752i
$$737$$ 71.4078 2.63034
$$738$$ 0 0
$$739$$ 45.1239 1.65991 0.829955 0.557830i $$-0.188366\pi$$
0.829955 + 0.557830i $$0.188366\pi$$
$$740$$ 9.36186 + 16.2152i 0.344149 + 0.596084i
$$741$$ 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
$$746$$ 40.1737 1.47086
$$747$$ 0 0
$$748$$ 17.3126 0.633013
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 4.91595 8.51467i 0.179386 0.310705i −0.762285 0.647242i $$-0.775922\pi$$
0.941670 + 0.336537i $$0.109256\pi$$
$$752$$ 26.3157 45.5800i 0.959633 1.66213i
$$753$$ 0 0
$$754$$ −3.02704 5.24299i −0.110238 0.190938i
$$755$$ −25.7496 −0.937124
$$756$$ 0 0
$$757$$ −41.8171 −1.51987 −0.759934 0.650000i $$-0.774769\pi$$
−0.759934 + 0.650000i $$0.774769\pi$$
$$758$$ −14.8078 25.6478i −0.537843 0.931571i
$$759$$ 0 0
$$760$$ 26.5708 46.0220i 0.963825 1.66939i
$$761$$ −11.4897 + 19.9007i −0.416501 + 0.721400i −0.995585 0.0938675i $$-0.970077\pi$$
0.579084 + 0.815268i $$0.303410\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 2.84494 0.102926
$$765$$ 0 0
$$766$$ −30.5979 −1.10555
$$767$$ −1.36333 2.36135i −0.0492269 0.0852635i
$$768$$ 0 0
$$769$$ 3.04329 5.27113i 0.109744 0.190082i −0.805923 0.592021i $$-0.798330\pi$$
0.915666 + 0.401939i $$0.131664\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −24.6175 42.6388i −0.886003 1.53460i
$$773$$ −41.8214 −1.50421 −0.752105 0.659043i $$-0.770962\pi$$
−0.752105 + 0.659043i $$0.770962\pi$$
$$774$$ 0 0
$$775$$ −4.01867 −0.144355
$$776$$ −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
$$782$$ −0.636194 −0.0227503
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −7.85087 13.5981i −0.280210 0.485337i
$$786$$ 0 0
$$787$$ 16.1460 27.9657i 0.575543 0.996870i −0.420439