# Properties

 Label 729.2.g.d.28.1 Level $729$ Weight $2$ Character 729.28 Analytic conductor $5.821$ Analytic rank $0$ Dimension $144$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$729 = 3^{6}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 729.g (of order $$27$$, degree $$18$$, 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: $$144$$ Relative dimension: $$8$$ over $$\Q(\zeta_{27})$$ Twist minimal: no (minimal twist has level 81) Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

## Embedding invariants

 Embedding label 28.1 Character $$\chi$$ $$=$$ 729.28 Dual form 729.2.g.d.703.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.76633 + 1.16173i) q^{2} +(0.978129 - 2.26756i) q^{4} +(-2.05186 + 2.17484i) q^{5} +(3.48897 + 0.407803i) q^{7} +(0.172370 + 0.977557i) q^{8} +O(q^{10})$$ $$q+(-1.76633 + 1.16173i) q^{2} +(0.978129 - 2.26756i) q^{4} +(-2.05186 + 2.17484i) q^{5} +(3.48897 + 0.407803i) q^{7} +(0.172370 + 0.977557i) q^{8} +(1.09767 - 6.22518i) q^{10} +(0.562324 - 1.87829i) q^{11} +(-0.0969288 + 1.66420i) q^{13} +(-6.63642 + 3.33294i) q^{14} +(1.94926 + 2.06610i) q^{16} +(3.65626 - 1.33077i) q^{17} +(-0.0155726 - 0.00566795i) q^{19} +(2.92460 + 6.77998i) q^{20} +(1.18882 + 3.97095i) q^{22} +(7.67257 - 0.896795i) q^{23} +(-0.229093 - 3.93338i) q^{25} +(-1.76215 - 3.05213i) q^{26} +(4.33738 - 7.51257i) q^{28} +(4.12997 + 2.07415i) q^{29} +(-6.12985 - 8.23381i) q^{31} +(-7.77505 - 1.84272i) q^{32} +(-4.91215 + 6.59816i) q^{34} +(-8.04578 + 6.75121i) q^{35} +(5.48325 + 4.60100i) q^{37} +(0.0340908 - 0.00807968i) q^{38} +(-2.47971 - 1.63093i) q^{40} +(4.72613 + 3.10842i) q^{41} +(-4.44056 + 1.05243i) q^{43} +(-3.70912 - 3.11232i) q^{44} +(-12.5104 + 10.4975i) q^{46} +(-1.71778 + 2.30738i) q^{47} +(5.19533 + 1.23132i) q^{49} +(4.97418 + 6.68148i) q^{50} +(3.67887 + 1.84760i) q^{52} +(-1.40413 + 2.43202i) q^{53} +(2.93118 + 5.07695i) q^{55} +(0.202743 + 3.48096i) q^{56} +(-9.70447 + 1.13429i) q^{58} +(1.42165 + 4.74864i) q^{59} +(3.71633 + 8.61543i) q^{61} +(20.3928 + 7.42236i) q^{62} +(10.5356 - 3.83466i) q^{64} +(-3.42049 - 3.62551i) q^{65} +(-4.00634 + 2.01206i) q^{67} +(0.558696 - 9.59244i) q^{68} +(6.36838 - 21.2719i) q^{70} +(-1.33743 + 7.58494i) q^{71} +(-0.696188 - 3.94828i) q^{73} +(-15.0303 - 1.75679i) q^{74} +(-0.0280844 + 0.0297677i) q^{76} +(2.72791 - 6.32400i) q^{77} +(-6.81054 + 4.47936i) q^{79} -8.49305 q^{80} -11.9590 q^{82} +(-4.30784 + 2.83331i) q^{83} +(-4.60790 + 10.6823i) q^{85} +(6.62083 - 7.01767i) q^{86} +(1.93307 + 0.225943i) q^{88} +(0.829745 + 4.70572i) q^{89} +(-1.01685 + 5.76683i) q^{91} +(5.47123 - 18.2752i) q^{92} +(0.353607 - 6.07119i) q^{94} +(0.0442795 - 0.0222380i) q^{95} +(7.98151 + 8.45991i) q^{97} +(-10.6071 + 3.86067i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10})$$ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 $$144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100})$$ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

## Character values

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

 $$n$$ $$2$$ $$\chi(n)$$ $$e\left(\frac{22}{27}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.76633 + 1.16173i −1.24898 + 0.821468i −0.989535 0.144290i $$-0.953910\pi$$
−0.259446 + 0.965758i $$0.583540\pi$$
$$3$$ 0 0
$$4$$ 0.978129 2.26756i 0.489065 1.13378i
$$5$$ −2.05186 + 2.17484i −0.917618 + 0.972618i −0.999712 0.0240065i $$-0.992358\pi$$
0.0820939 + 0.996625i $$0.473839\pi$$
$$6$$ 0 0
$$7$$ 3.48897 + 0.407803i 1.31871 + 0.154135i 0.746177 0.665748i $$-0.231887\pi$$
0.572532 + 0.819883i $$0.305961\pi$$
$$8$$ 0.172370 + 0.977557i 0.0609419 + 0.345618i
$$9$$ 0 0
$$10$$ 1.09767 6.22518i 0.347113 1.96858i
$$11$$ 0.562324 1.87829i 0.169547 0.566327i −0.830411 0.557152i $$-0.811894\pi$$
0.999958 0.00917522i $$-0.00292060\pi$$
$$12$$ 0 0
$$13$$ −0.0969288 + 1.66420i −0.0268832 + 0.461567i 0.957825 + 0.287353i $$0.0927754\pi$$
−0.984708 + 0.174214i $$0.944262\pi$$
$$14$$ −6.63642 + 3.33294i −1.77366 + 0.890765i
$$15$$ 0 0
$$16$$ 1.94926 + 2.06610i 0.487316 + 0.516525i
$$17$$ 3.65626 1.33077i 0.886772 0.322759i 0.141833 0.989891i $$-0.454700\pi$$
0.744940 + 0.667132i $$0.232478\pi$$
$$18$$ 0 0
$$19$$ −0.0155726 0.00566795i −0.00357259 0.00130032i 0.340233 0.940341i $$-0.389494\pi$$
−0.343806 + 0.939041i $$0.611716\pi$$
$$20$$ 2.92460 + 6.77998i 0.653960 + 1.51605i
$$21$$ 0 0
$$22$$ 1.18882 + 3.97095i 0.253458 + 0.846609i
$$23$$ 7.67257 0.896795i 1.59984 0.186995i 0.731103 0.682267i $$-0.239006\pi$$
0.868738 + 0.495272i $$0.164932\pi$$
$$24$$ 0 0
$$25$$ −0.229093 3.93338i −0.0458186 0.786675i
$$26$$ −1.76215 3.05213i −0.345586 0.598572i
$$27$$ 0 0
$$28$$ 4.33738 7.51257i 0.819689 1.41974i
$$29$$ 4.12997 + 2.07415i 0.766916 + 0.385159i 0.788839 0.614600i $$-0.210683\pi$$
−0.0219232 + 0.999760i $$0.506979\pi$$
$$30$$ 0 0
$$31$$ −6.12985 8.23381i −1.10095 1.47884i −0.861382 0.507957i $$-0.830401\pi$$
−0.239571 0.970879i $$-0.577007\pi$$
$$32$$ −7.77505 1.84272i −1.37445 0.325750i
$$33$$ 0 0
$$34$$ −4.91215 + 6.59816i −0.842426 + 1.13157i
$$35$$ −8.04578 + 6.75121i −1.35998 + 1.14116i
$$36$$ 0 0
$$37$$ 5.48325 + 4.60100i 0.901441 + 0.756399i 0.970472 0.241215i $$-0.0775460\pi$$
−0.0690302 + 0.997615i $$0.521990\pi$$
$$38$$ 0.0340908 0.00807968i 0.00553026 0.00131070i
$$39$$ 0 0
$$40$$ −2.47971 1.63093i −0.392076 0.257873i
$$41$$ 4.72613 + 3.10842i 0.738097 + 0.485454i 0.862043 0.506835i $$-0.169185\pi$$
−0.123946 + 0.992289i $$0.539555\pi$$
$$42$$ 0 0
$$43$$ −4.44056 + 1.05243i −0.677179 + 0.160494i −0.554793 0.831988i $$-0.687203\pi$$
−0.122386 + 0.992483i $$0.539054\pi$$
$$44$$ −3.70912 3.11232i −0.559170 0.469199i
$$45$$ 0 0
$$46$$ −12.5104 + 10.4975i −1.84456 + 1.54777i
$$47$$ −1.71778 + 2.30738i −0.250564 + 0.336566i −0.909554 0.415586i $$-0.863577\pi$$
0.658990 + 0.752152i $$0.270984\pi$$
$$48$$ 0 0
$$49$$ 5.19533 + 1.23132i 0.742190 + 0.175902i
$$50$$ 4.97418 + 6.68148i 0.703455 + 0.944904i
$$51$$ 0 0
$$52$$ 3.67887 + 1.84760i 0.510167 + 0.256216i
$$53$$ −1.40413 + 2.43202i −0.192872 + 0.334063i −0.946201 0.323580i $$-0.895113\pi$$
0.753329 + 0.657644i $$0.228447\pi$$
$$54$$ 0 0
$$55$$ 2.93118 + 5.07695i 0.395240 + 0.684576i
$$56$$ 0.202743 + 3.48096i 0.0270927 + 0.465163i
$$57$$ 0 0
$$58$$ −9.70447 + 1.13429i −1.27426 + 0.148940i
$$59$$ 1.42165 + 4.74864i 0.185083 + 0.618221i 0.999291 + 0.0376473i $$0.0119863\pi$$
−0.814208 + 0.580573i $$0.802828\pi$$
$$60$$ 0 0
$$61$$ 3.71633 + 8.61543i 0.475828 + 1.10309i 0.972024 + 0.234882i $$0.0754705\pi$$
−0.496196 + 0.868211i $$0.665270\pi$$
$$62$$ 20.3928 + 7.42236i 2.58989 + 0.942641i
$$63$$ 0 0
$$64$$ 10.5356 3.83466i 1.31695 0.479332i
$$65$$ −3.42049 3.62551i −0.424260 0.449689i
$$66$$ 0 0
$$67$$ −4.00634 + 2.01206i −0.489453 + 0.245812i −0.676368 0.736564i $$-0.736447\pi$$
0.186916 + 0.982376i $$0.440151\pi$$
$$68$$ 0.558696 9.59244i 0.0677518 1.16325i
$$69$$ 0 0
$$70$$ 6.36838 21.2719i 0.761167 2.54247i
$$71$$ −1.33743 + 7.58494i −0.158724 + 0.900166i 0.796578 + 0.604535i $$0.206641\pi$$
−0.955302 + 0.295631i $$0.904470\pi$$
$$72$$ 0 0
$$73$$ −0.696188 3.94828i −0.0814827 0.462111i −0.998060 0.0622545i $$-0.980171\pi$$
0.916578 0.399857i $$-0.130940\pi$$
$$74$$ −15.0303 1.75679i −1.74724 0.204223i
$$75$$ 0 0
$$76$$ −0.0280844 + 0.0297677i −0.00322150 + 0.00341459i
$$77$$ 2.72791 6.32400i 0.310874 0.720687i
$$78$$ 0 0
$$79$$ −6.81054 + 4.47936i −0.766245 + 0.503967i −0.871451 0.490483i $$-0.836820\pi$$
0.105205 + 0.994451i $$0.466450\pi$$
$$80$$ −8.49305 −0.949552
$$81$$ 0 0
$$82$$ −11.9590 −1.32065
$$83$$ −4.30784 + 2.83331i −0.472846 + 0.310996i −0.763472 0.645841i $$-0.776507\pi$$
0.290626 + 0.956837i $$0.406137\pi$$
$$84$$ 0 0
$$85$$ −4.60790 + 10.6823i −0.499797 + 1.15866i
$$86$$ 6.62083 7.01767i 0.713943 0.756735i
$$87$$ 0 0
$$88$$ 1.93307 + 0.225943i 0.206066 + 0.0240856i
$$89$$ 0.829745 + 4.70572i 0.0879528 + 0.498805i 0.996680 + 0.0814153i $$0.0259440\pi$$
−0.908727 + 0.417390i $$0.862945\pi$$
$$90$$ 0 0
$$91$$ −1.01685 + 5.76683i −0.106595 + 0.604528i
$$92$$ 5.47123 18.2752i 0.570415 1.90532i
$$93$$ 0 0
$$94$$ 0.353607 6.07119i 0.0364717 0.626196i
$$95$$ 0.0442795 0.0222380i 0.00454298 0.00228157i
$$96$$ 0 0
$$97$$ 7.98151 + 8.45991i 0.810400 + 0.858974i 0.992238 0.124355i $$-0.0396861\pi$$
−0.181838 + 0.983329i $$0.558205\pi$$
$$98$$ −10.6071 + 3.86067i −1.07148 + 0.389986i
$$99$$ 0 0
$$100$$ −9.14325 3.32787i −0.914325 0.332787i
$$101$$ 1.13250 + 2.62543i 0.112688 + 0.261240i 0.965222 0.261431i $$-0.0841945\pi$$
−0.852534 + 0.522672i $$0.824935\pi$$
$$102$$ 0 0
$$103$$ 0.820517 + 2.74072i 0.0808479 + 0.270051i 0.988850 0.148915i $$-0.0475780\pi$$
−0.908002 + 0.418966i $$0.862393\pi$$
$$104$$ −1.64356 + 0.192105i −0.161164 + 0.0188374i
$$105$$ 0 0
$$106$$ −0.345206 5.92695i −0.0335293 0.575676i
$$107$$ −7.89300 13.6711i −0.763045 1.32163i −0.941274 0.337644i $$-0.890370\pi$$
0.178229 0.983989i $$-0.442963\pi$$
$$108$$ 0 0
$$109$$ 0.145393 0.251828i 0.0139261 0.0241207i −0.858978 0.512012i $$-0.828900\pi$$
0.872904 + 0.487891i $$0.162234\pi$$
$$110$$ −11.0755 5.56231i −1.05600 0.530346i
$$111$$ 0 0
$$112$$ 5.95837 + 8.00349i 0.563013 + 0.756258i
$$113$$ −3.14646 0.745724i −0.295994 0.0701518i 0.0799359 0.996800i $$-0.474528\pi$$
−0.375930 + 0.926648i $$0.622677\pi$$
$$114$$ 0 0
$$115$$ −13.7926 + 18.5267i −1.28617 + 1.72762i
$$116$$ 8.74289 7.33616i 0.811757 0.681145i
$$117$$ 0 0
$$118$$ −8.02774 6.73608i −0.739014 0.620106i
$$119$$ 13.2993 3.15199i 1.21914 0.288942i
$$120$$ 0 0
$$121$$ 5.97859 + 3.93218i 0.543508 + 0.357471i
$$122$$ −16.5731 10.9003i −1.50046 0.986865i
$$123$$ 0 0
$$124$$ −24.6664 + 5.84605i −2.21511 + 0.524991i
$$125$$ −2.42779 2.03716i −0.217149 0.182209i
$$126$$ 0 0
$$127$$ 10.0576 8.43933i 0.892468 0.748870i −0.0762356 0.997090i $$-0.524290\pi$$
0.968704 + 0.248220i $$0.0798457\pi$$
$$128$$ −4.61142 + 6.19421i −0.407596 + 0.547496i
$$129$$ 0 0
$$130$$ 10.2536 + 2.43014i 0.899297 + 0.213137i
$$131$$ −0.000192729 0 0.000258880i −1.68388e−5 0 2.26184e-5i 0.802115 0.597170i $$-0.203708\pi$$
−0.802132 + 0.597147i $$0.796301\pi$$
$$132$$ 0 0
$$133$$ −0.0520209 0.0261259i −0.00451078 0.00226540i
$$134$$ 4.73903 8.20825i 0.409390 0.709085i
$$135$$ 0 0
$$136$$ 1.93113 + 3.34481i 0.165593 + 0.286815i
$$137$$ −0.749748 12.8727i −0.0640553 1.09979i −0.865236 0.501365i $$-0.832832\pi$$
0.801181 0.598422i $$-0.204206\pi$$
$$138$$ 0 0
$$139$$ −0.637020 + 0.0744569i −0.0540313 + 0.00631535i −0.143066 0.989713i $$-0.545696\pi$$
0.0890343 + 0.996029i $$0.471622\pi$$
$$140$$ 7.43895 + 24.8478i 0.628706 + 2.10003i
$$141$$ 0 0
$$142$$ −6.44932 14.9512i −0.541215 1.25468i
$$143$$ 3.07136 + 1.11788i 0.256840 + 0.0934820i
$$144$$ 0 0
$$145$$ −12.9850 + 4.72617i −1.07835 + 0.392487i
$$146$$ 5.81653 + 6.16517i 0.481380 + 0.510233i
$$147$$ 0 0
$$148$$ 15.7964 7.93323i 1.29845 0.652108i
$$149$$ −0.751391 + 12.9009i −0.0615563 + 1.05688i 0.816199 + 0.577772i $$0.196078\pi$$
−0.877755 + 0.479110i $$0.840959\pi$$
$$150$$ 0 0
$$151$$ 4.81347 16.0781i 0.391714 1.30842i −0.503968 0.863722i $$-0.668127\pi$$
0.895682 0.444695i $$-0.146688\pi$$
$$152$$ 0.00285650 0.0162000i 0.000231693 0.00131400i
$$153$$ 0 0
$$154$$ 2.52841 + 14.3393i 0.203745 + 1.15550i
$$155$$ 30.4848 + 3.56316i 2.44860 + 0.286200i
$$156$$ 0 0
$$157$$ 5.90236 6.25613i 0.471059 0.499294i −0.447660 0.894204i $$-0.647743\pi$$
0.918720 + 0.394910i $$0.129224\pi$$
$$158$$ 6.82582 15.8240i 0.543033 1.25889i
$$159$$ 0 0
$$160$$ 19.9609 13.1285i 1.57805 1.03790i
$$161$$ 27.1351 2.13855
$$162$$ 0 0
$$163$$ 0.674482 0.0528295 0.0264148 0.999651i $$-0.491591\pi$$
0.0264148 + 0.999651i $$0.491591\pi$$
$$164$$ 11.6713 7.67634i 0.911376 0.599421i
$$165$$ 0 0
$$166$$ 4.31750 10.0091i 0.335103 0.776856i
$$167$$ 11.0620 11.7251i 0.856004 0.907312i −0.140565 0.990071i $$-0.544892\pi$$
0.996570 + 0.0827597i $$0.0263734\pi$$
$$168$$ 0 0
$$169$$ 10.1519 + 1.18659i 0.780917 + 0.0912761i
$$170$$ −4.27092 24.2216i −0.327565 1.85771i
$$171$$ 0 0
$$172$$ −1.95699 + 11.0986i −0.149219 + 0.846263i
$$173$$ −4.62618 + 15.4525i −0.351722 + 1.17483i 0.580898 + 0.813976i $$0.302701\pi$$
−0.932621 + 0.360858i $$0.882484\pi$$
$$174$$ 0 0
$$175$$ 0.804742 13.8169i 0.0608327 1.04446i
$$176$$ 4.97686 2.49947i 0.375145 0.188405i
$$177$$ 0 0
$$178$$ −6.93238 7.34790i −0.519604 0.550748i
$$179$$ 7.45990 2.71518i 0.557579 0.202942i −0.0478318 0.998855i $$-0.515231\pi$$
0.605411 + 0.795913i $$0.293009\pi$$
$$180$$ 0 0
$$181$$ 13.0001 + 4.73166i 0.966292 + 0.351702i 0.776496 0.630122i $$-0.216995\pi$$
0.189796 + 0.981824i $$0.439217\pi$$
$$182$$ −4.90342 11.3674i −0.363466 0.842609i
$$183$$ 0 0
$$184$$ 2.19919 + 7.34579i 0.162126 + 0.541539i
$$185$$ −21.2573 + 2.48462i −1.56287 + 0.182673i
$$186$$ 0 0
$$187$$ −0.443573 7.61585i −0.0324372 0.556926i
$$188$$ 3.55191 + 6.15209i 0.259050 + 0.448687i
$$189$$ 0 0
$$190$$ −0.0523775 + 0.0907205i −0.00379986 + 0.00658155i
$$191$$ −12.8453 6.45115i −0.929453 0.466789i −0.0813890 0.996682i $$-0.525936\pi$$
−0.848064 + 0.529893i $$0.822232\pi$$
$$192$$ 0 0
$$193$$ −2.49845 3.35600i −0.179842 0.241570i 0.703056 0.711135i $$-0.251818\pi$$
−0.882898 + 0.469564i $$0.844411\pi$$
$$194$$ −23.9261 5.67059i −1.71779 0.407125i
$$195$$ 0 0
$$196$$ 7.87378 10.5763i 0.562413 0.755452i
$$197$$ −0.181162 + 0.152013i −0.0129073 + 0.0108305i −0.649218 0.760602i $$-0.724904\pi$$
0.636311 + 0.771432i $$0.280459\pi$$
$$198$$ 0 0
$$199$$ 19.9860 + 16.7702i 1.41677 + 1.18881i 0.953044 + 0.302832i $$0.0979322\pi$$
0.463726 + 0.885979i $$0.346512\pi$$
$$200$$ 3.80561 0.901946i 0.269097 0.0637772i
$$201$$ 0 0
$$202$$ −5.05042 3.32171i −0.355346 0.233715i
$$203$$ 13.5635 + 8.92086i 0.951972 + 0.626122i
$$204$$ 0 0
$$205$$ −16.4577 + 3.90054i −1.14945 + 0.272425i
$$206$$ −4.63328 3.88778i −0.322816 0.270874i
$$207$$ 0 0
$$208$$ −3.62735 + 3.04371i −0.251511 + 0.211043i
$$209$$ −0.0194029 + 0.0260626i −0.00134213 + 0.00180279i
$$210$$ 0 0
$$211$$ −11.4811 2.72107i −0.790390 0.187326i −0.184456 0.982841i $$-0.559052\pi$$
−0.605934 + 0.795515i $$0.707200\pi$$
$$212$$ 4.14133 + 5.56277i 0.284427 + 0.382052i
$$213$$ 0 0
$$214$$ 29.8237 + 14.9780i 2.03871 + 1.02388i
$$215$$ 6.82251 11.8169i 0.465292 0.805909i
$$216$$ 0 0
$$217$$ −18.0291 31.2273i −1.22390 2.11985i
$$218$$ 0.0357450 + 0.613717i 0.00242095 + 0.0415662i
$$219$$ 0 0
$$220$$ 14.3794 1.68071i 0.969456 0.113313i
$$221$$ 1.86027 + 6.21374i 0.125135 + 0.417982i
$$222$$ 0 0
$$223$$ −10.4312 24.1822i −0.698524 1.61936i −0.782320 0.622877i $$-0.785964\pi$$
0.0837965 0.996483i $$-0.473295\pi$$
$$224$$ −26.3755 9.59989i −1.76229 0.641420i
$$225$$ 0 0
$$226$$ 6.42400 2.33814i 0.427318 0.155531i
$$227$$ 0.699631 + 0.741565i 0.0464361 + 0.0492194i 0.750175 0.661239i $$-0.229969\pi$$
−0.703739 + 0.710458i $$0.748488\pi$$
$$228$$ 0 0
$$229$$ 23.3073 11.7054i 1.54019 0.773512i 0.542410 0.840114i $$-0.317512\pi$$
0.997780 + 0.0666015i $$0.0212156\pi$$
$$230$$ 2.83922 48.7475i 0.187213 3.21432i
$$231$$ 0 0
$$232$$ −1.31572 + 4.39480i −0.0863810 + 0.288533i
$$233$$ 0.779551 4.42105i 0.0510701 0.289633i −0.948567 0.316577i $$-0.897467\pi$$
0.999637 + 0.0269441i $$0.00857761\pi$$
$$234$$ 0 0
$$235$$ −1.49355 8.47032i −0.0974282 0.552543i
$$236$$ 12.1584 + 1.42111i 0.791443 + 0.0925065i
$$237$$ 0 0
$$238$$ −19.8291 + 21.0176i −1.28533 + 1.36237i
$$239$$ −0.604016 + 1.40027i −0.0390706 + 0.0905757i −0.936634 0.350310i $$-0.886076\pi$$
0.897563 + 0.440886i $$0.145336\pi$$
$$240$$ 0 0
$$241$$ −0.703622 + 0.462779i −0.0453243 + 0.0298102i −0.571969 0.820275i $$-0.693820\pi$$
0.526645 + 0.850086i $$0.323450\pi$$
$$242$$ −15.1283 −0.972482
$$243$$ 0 0
$$244$$ 23.1711 1.48337
$$245$$ −13.3380 + 8.77253i −0.852132 + 0.560456i
$$246$$ 0 0
$$247$$ 0.0109420 0.0253665i 0.000696225 0.00161403i
$$248$$ 6.99242 7.41153i 0.444019 0.470633i
$$249$$ 0 0
$$250$$ 6.65491 + 0.777848i 0.420894 + 0.0491954i
$$251$$ 2.59126 + 14.6958i 0.163559 + 0.927590i 0.950538 + 0.310609i $$0.100533\pi$$
−0.786978 + 0.616980i $$0.788356\pi$$
$$252$$ 0 0
$$253$$ 2.63003 14.9156i 0.165348 0.937737i
$$254$$ −7.96078 + 26.5908i −0.499503 + 1.66846i
$$255$$ 0 0
$$256$$ −0.354552 + 6.08743i −0.0221595 + 0.380464i
$$257$$ −8.24289 + 4.13974i −0.514178 + 0.258230i −0.686914 0.726738i $$-0.741035\pi$$
0.172737 + 0.984968i $$0.444739\pi$$
$$258$$ 0 0
$$259$$ 17.2546 + 18.2888i 1.07215 + 1.13641i
$$260$$ −11.5667 + 4.20995i −0.717339 + 0.261090i
$$261$$ 0 0
$$262$$ 0.000641171 0 0.000233367i 3.96117e−5 0 1.44175e-5i
$$263$$ 0.0942800 + 0.218566i 0.00581355 + 0.0134773i 0.921098 0.389330i $$-0.127294\pi$$
−0.915285 + 0.402808i $$0.868034\pi$$
$$264$$ 0 0
$$265$$ −2.40819 8.04390i −0.147934 0.494133i
$$266$$ 0.122237 0.0142875i 0.00749483 0.000876020i
$$267$$ 0 0
$$268$$ 0.643745 + 11.0527i 0.0393230 + 0.675150i
$$269$$ 7.21026 + 12.4885i 0.439617 + 0.761439i 0.997660 0.0683731i $$-0.0217808\pi$$
−0.558043 + 0.829812i $$0.688447\pi$$
$$270$$ 0 0
$$271$$ −8.33200 + 14.4314i −0.506133 + 0.876648i 0.493842 + 0.869552i $$0.335592\pi$$
−0.999975 + 0.00709598i $$0.997741\pi$$
$$272$$ 9.87651 + 4.96017i 0.598851 + 0.300755i
$$273$$ 0 0
$$274$$ 16.2789 + 21.8663i 0.983444 + 1.32099i
$$275$$ −7.51686 1.78153i −0.453284 0.107430i
$$276$$ 0 0
$$277$$ 14.8198 19.9065i 0.890436 1.19606i −0.0893469 0.996001i $$-0.528478\pi$$
0.979783 0.200063i $$-0.0641146\pi$$
$$278$$ 1.03869 0.871561i 0.0622962 0.0522727i
$$279$$ 0 0
$$280$$ −7.98654 6.70150i −0.477287 0.400491i
$$281$$ −18.8042 + 4.45667i −1.12176 + 0.265862i −0.749330 0.662197i $$-0.769624\pi$$
−0.372432 + 0.928059i $$0.621476\pi$$
$$282$$ 0 0
$$283$$ −0.932620 0.613394i −0.0554385 0.0364625i 0.521487 0.853259i $$-0.325377\pi$$
−0.576926 + 0.816797i $$0.695748\pi$$
$$284$$ 15.8911 + 10.4517i 0.942964 + 0.620197i
$$285$$ 0 0
$$286$$ −6.72369 + 1.59354i −0.397580 + 0.0942283i
$$287$$ 15.2217 + 12.7725i 0.898510 + 0.753939i
$$288$$ 0 0
$$289$$ −1.42549 + 1.19613i −0.0838523 + 0.0703605i
$$290$$ 17.4453 23.4331i 1.02442 1.37604i
$$291$$ 0 0
$$292$$ −9.63392 2.28328i −0.563783 0.133619i
$$293$$ −4.79976 6.44720i −0.280405 0.376650i 0.639500 0.768792i $$-0.279142\pi$$
−0.919905 + 0.392142i $$0.871734\pi$$
$$294$$ 0 0
$$295$$ −13.2446 6.65167i −0.771128 0.387275i
$$296$$ −3.55259 + 6.15326i −0.206490 + 0.357651i
$$297$$ 0 0
$$298$$ −13.6602 23.6601i −0.791311 1.37059i
$$299$$ 0.748755 + 12.8556i 0.0433016 + 0.743461i
$$300$$ 0 0
$$301$$ −15.9222 + 1.86104i −0.917739 + 0.107268i
$$302$$ 10.1763 + 33.9911i 0.585579 + 1.95597i
$$303$$ 0 0
$$304$$ −0.0186445 0.0432228i −0.00106933 0.00247900i
$$305$$ −26.3626 9.59519i −1.50952 0.549419i
$$306$$ 0 0
$$307$$ −15.7796 + 5.74331i −0.900590 + 0.327788i −0.750489 0.660883i $$-0.770182\pi$$
−0.150101 + 0.988671i $$0.547960\pi$$
$$308$$ −11.6718 12.3714i −0.665062 0.704925i
$$309$$ 0 0
$$310$$ −57.9855 + 29.1214i −3.29336 + 1.65399i
$$311$$ 0.299735 5.14625i 0.0169964 0.291817i −0.979090 0.203429i $$-0.934791\pi$$
0.996086 0.0883881i $$-0.0281716\pi$$
$$312$$ 0 0
$$313$$ −8.01329 + 26.7663i −0.452938 + 1.51292i 0.361334 + 0.932436i $$0.382321\pi$$
−0.814273 + 0.580483i $$0.802864\pi$$
$$314$$ −3.15754 + 17.9073i −0.178191 + 1.01057i
$$315$$ 0 0
$$316$$ 3.49563 + 19.8247i 0.196644 + 1.11523i
$$317$$ 9.13214 + 1.06739i 0.512912 + 0.0599508i 0.368612 0.929583i $$-0.379833\pi$$
0.144300 + 0.989534i $$0.453907\pi$$
$$318$$ 0 0
$$319$$ 6.21824 6.59095i 0.348155 0.369022i
$$320$$ −13.2778 + 30.7815i −0.742254 + 1.72074i
$$321$$ 0 0
$$322$$ −47.9295 + 31.5237i −2.67100 + 1.75675i
$$323$$ −0.0644800 −0.00358776
$$324$$ 0 0
$$325$$ 6.56814 0.364335
$$326$$ −1.19136 + 0.783567i −0.0659831 + 0.0433978i
$$327$$ 0 0
$$328$$ −2.22402 + 5.15586i −0.122801 + 0.284685i
$$329$$ −6.93426 + 7.34988i −0.382298 + 0.405212i
$$330$$ 0 0
$$331$$ −16.8364 1.96789i −0.925411 0.108165i −0.359979 0.932960i $$-0.617216\pi$$
−0.565431 + 0.824795i $$0.691290\pi$$
$$332$$ 2.21107 + 12.5396i 0.121348 + 0.688201i
$$333$$ 0 0
$$334$$ −5.91777 + 33.5613i −0.323806 + 1.83640i
$$335$$ 3.84453 12.8416i 0.210049 0.701613i
$$336$$ 0 0
$$337$$ −0.758539 + 13.0236i −0.0413203 + 0.709442i 0.912502 + 0.409071i $$0.134147\pi$$
−0.953823 + 0.300370i $$0.902890\pi$$
$$338$$ −19.3101 + 9.69790i −1.05033 + 0.527496i
$$339$$ 0 0
$$340$$ 19.7157 + 20.8974i 1.06923 + 1.13332i
$$341$$ −18.9125 + 6.88358i −1.02417 + 0.372767i
$$342$$ 0 0
$$343$$ −5.48195 1.99527i −0.295997 0.107734i
$$344$$ −1.79423 4.15949i −0.0967383 0.224265i
$$345$$ 0 0
$$346$$ −9.78033 32.6686i −0.525794 1.75627i
$$347$$ 14.2961 1.67098i 0.767457 0.0897029i 0.276650 0.960971i $$-0.410776\pi$$
0.490808 + 0.871268i $$0.336702\pi$$
$$348$$ 0 0
$$349$$ −0.472908 8.11951i −0.0253142 0.434627i −0.987026 0.160563i $$-0.948669\pi$$
0.961711 0.274064i $$-0.0883681\pi$$
$$350$$ 14.6301 + 25.3400i 0.782010 + 1.35448i
$$351$$ 0 0
$$352$$ −7.83327 + 13.5676i −0.417515 + 0.723157i
$$353$$ −24.2226 12.1651i −1.28924 0.647481i −0.333795 0.942646i $$-0.608329\pi$$
−0.955446 + 0.295165i $$0.904626\pi$$
$$354$$ 0 0
$$355$$ −13.7518 18.4719i −0.729871 0.980386i
$$356$$ 11.4821 + 2.72131i 0.608550 + 0.144229i
$$357$$ 0 0
$$358$$ −10.0223 + 13.4623i −0.529695 + 0.711504i
$$359$$ 19.0992 16.0261i 1.00802 0.845828i 0.0199431 0.999801i $$-0.493651\pi$$
0.988075 + 0.153974i $$0.0492071\pi$$
$$360$$ 0 0
$$361$$ −14.5546 12.2128i −0.766033 0.642778i
$$362$$ −28.4594 + 6.74500i −1.49579 + 0.354509i
$$363$$ 0 0
$$364$$ 12.0820 + 7.94647i 0.633270 + 0.416508i
$$365$$ 10.0154 + 6.58720i 0.524228 + 0.344790i
$$366$$ 0 0
$$367$$ 12.7392 3.01925i 0.664982 0.157604i 0.115756 0.993278i $$-0.463071\pi$$
0.549226 + 0.835674i $$0.314923\pi$$
$$368$$ 16.8087 + 14.1042i 0.876216 + 0.735232i
$$369$$ 0 0
$$370$$ 34.6608 29.0839i 1.80193 1.51200i
$$371$$ −5.89074 + 7.91264i −0.305832 + 0.410804i
$$372$$ 0 0
$$373$$ −27.9998 6.63609i −1.44978 0.343604i −0.571045 0.820919i $$-0.693462\pi$$
−0.878732 + 0.477315i $$0.841610\pi$$
$$374$$ 9.63106 + 12.9368i 0.498010 + 0.668944i
$$375$$ 0 0
$$376$$ −2.55169 1.28151i −0.131593 0.0660887i
$$377$$ −3.85211 + 6.67206i −0.198394 + 0.343628i
$$378$$ 0 0
$$379$$ 10.4915 + 18.1718i 0.538912 + 0.933422i 0.998963 + 0.0455300i $$0.0144977\pi$$
−0.460051 + 0.887892i $$0.652169\pi$$
$$380$$ −0.00711490 0.122158i −0.000364987 0.00626658i
$$381$$ 0 0
$$382$$ 30.1835 3.52794i 1.54432 0.180505i
$$383$$ −7.02527 23.4660i −0.358974 1.19906i −0.926688 0.375832i $$-0.877357\pi$$
0.567714 0.823226i $$-0.307828\pi$$
$$384$$ 0 0
$$385$$ 8.15642 + 18.9087i 0.415690 + 0.963677i
$$386$$ 8.31185 + 3.02526i 0.423062 + 0.153982i
$$387$$ 0 0
$$388$$ 26.9903 9.82366i 1.37022 0.498721i
$$389$$ 10.8199 + 11.4684i 0.548589 + 0.581470i 0.941037 0.338304i $$-0.109853\pi$$
−0.392448 + 0.919774i $$0.628372\pi$$
$$390$$ 0 0
$$391$$ 26.8595 13.4893i 1.35834 0.682184i
$$392$$ −0.308164 + 5.29097i −0.0155646 + 0.267234i
$$393$$ 0 0
$$394$$ 0.143393 0.478966i 0.00722403 0.0241300i
$$395$$ 4.23235 24.0028i 0.212953 1.20771i
$$396$$ 0 0
$$397$$ −4.48471 25.4340i −0.225081 1.27650i −0.862530 0.506005i $$-0.831122\pi$$
0.637449 0.770492i $$-0.279989\pi$$
$$398$$ −54.7843 6.40337i −2.74609 0.320972i
$$399$$ 0 0
$$400$$ 7.68019 8.14052i 0.384009 0.407026i
$$401$$ 6.48724 15.0391i 0.323957 0.751017i −0.675944 0.736953i $$-0.736264\pi$$
0.999901 0.0140640i $$-0.00447687\pi$$
$$402$$ 0 0
$$403$$ 14.2969 9.40321i 0.712179 0.468407i
$$404$$ 7.06106 0.351301
$$405$$ 0 0
$$406$$ −34.3212 −1.70333
$$407$$ 11.7254 7.71191i 0.581206 0.382265i
$$408$$ 0 0
$$409$$ −10.0430 + 23.2823i −0.496596 + 1.15124i 0.467093 + 0.884208i $$0.345301\pi$$
−0.963688 + 0.267030i $$0.913958\pi$$
$$410$$ 24.5382 26.0090i 1.21186 1.28449i
$$411$$ 0 0
$$412$$ 7.01731 + 0.820206i 0.345718 + 0.0404086i
$$413$$ 3.02359 + 17.1476i 0.148781 + 0.843781i
$$414$$ 0 0
$$415$$ 2.67707 15.1824i 0.131412 0.745275i
$$416$$ 3.82029 12.7606i 0.187305 0.625642i
$$417$$ 0 0
$$418$$ 0.00399410 0.0685760i 0.000195358 0.00335416i
$$419$$ −5.68329 + 2.85426i −0.277647 + 0.139440i −0.582174 0.813064i $$-0.697798\pi$$
0.304527 + 0.952504i $$0.401502\pi$$
$$420$$ 0 0
$$421$$ −18.0240 19.1043i −0.878434 0.931086i 0.119658 0.992815i $$-0.461820\pi$$
−0.998093 + 0.0617290i $$0.980339\pi$$
$$422$$ 23.4405 8.53163i 1.14106 0.415313i
$$423$$ 0 0
$$424$$ −2.61946 0.953407i −0.127212 0.0463015i
$$425$$ −6.07204 14.0766i −0.294537 0.682814i
$$426$$ 0 0
$$427$$ 9.45280 + 31.5746i 0.457453 + 1.52800i
$$428$$ −38.7203 + 4.52576i −1.87162 + 0.218761i
$$429$$ 0 0
$$430$$ 1.67732 + 28.7985i 0.0808876 + 1.38879i
$$431$$ 6.16440 + 10.6771i 0.296929 + 0.514296i 0.975432 0.220302i $$-0.0707042\pi$$
−0.678503 + 0.734598i $$0.737371\pi$$
$$432$$ 0 0
$$433$$ 3.37556 5.84664i 0.162219 0.280972i −0.773445 0.633863i $$-0.781468\pi$$
0.935664 + 0.352891i $$0.114802\pi$$
$$434$$ 68.1230 + 34.2127i 3.27001 + 1.64226i
$$435$$ 0 0
$$436$$ −0.428821 0.576007i −0.0205368 0.0275857i
$$437$$ −0.124564 0.0295223i −0.00595873 0.00141224i
$$438$$ 0 0
$$439$$ −2.66717 + 3.58263i −0.127297 + 0.170989i −0.861202 0.508262i $$-0.830288\pi$$
0.733905 + 0.679252i $$0.237695\pi$$
$$440$$ −4.45776 + 3.74051i −0.212516 + 0.178322i
$$441$$ 0 0
$$442$$ −10.5045 8.81436i −0.499650 0.419256i
$$443$$ 27.4508 6.50597i 1.30423 0.309108i 0.480952 0.876747i $$-0.340291\pi$$
0.823277 + 0.567639i $$0.192143\pi$$
$$444$$ 0 0
$$445$$ −11.9367 7.85090i −0.565854 0.372168i
$$446$$ 46.5181 + 30.5954i 2.20269 + 1.44873i
$$447$$ 0 0
$$448$$ 38.3224 9.08256i 1.81056 0.429111i
$$449$$ −20.0933 16.8603i −0.948260 0.795685i 0.0307434 0.999527i $$-0.490213\pi$$
−0.979004 + 0.203842i $$0.934657\pi$$
$$450$$ 0 0
$$451$$ 8.49615 7.12912i 0.400068 0.335697i
$$452$$ −4.76862 + 6.40536i −0.224297 + 0.301283i
$$453$$ 0 0
$$454$$ −2.09728 0.497063i −0.0984300 0.0233283i
$$455$$ −10.4555 14.0442i −0.490162 0.658402i
$$456$$ 0 0
$$457$$ −21.5678 10.8317i −1.00890 0.506687i −0.133992 0.990982i $$-0.542780\pi$$
−0.874905 + 0.484295i $$0.839076\pi$$
$$458$$ −27.5698 + 47.7523i −1.28825 + 2.23132i
$$459$$ 0 0
$$460$$ 28.5194 + 49.3971i 1.32972 + 2.30315i
$$461$$ 1.09933 + 18.8747i 0.0512007 + 0.879082i 0.921939 + 0.387335i $$0.126604\pi$$
−0.870738 + 0.491747i $$0.836359\pi$$
$$462$$ 0 0
$$463$$ −1.68749 + 0.197239i −0.0784242 + 0.00916647i −0.155215 0.987881i $$-0.549607\pi$$
0.0767903 + 0.997047i $$0.475533\pi$$
$$464$$ 3.76500 + 12.5760i 0.174786 + 0.583825i
$$465$$ 0 0
$$466$$ 3.75913 + 8.71465i 0.174138 + 0.403698i
$$467$$ −1.44533 0.526058i −0.0668820 0.0243431i 0.308362 0.951269i $$-0.400219\pi$$
−0.375245 + 0.926926i $$0.622441\pi$$
$$468$$ 0 0
$$469$$ −14.7986 + 5.38623i −0.683334 + 0.248713i
$$470$$ 12.4783 + 13.2262i 0.575582 + 0.610081i
$$471$$ 0 0
$$472$$ −4.39702 + 2.20827i −0.202389 + 0.101644i
$$473$$ −0.520258 + 8.93248i −0.0239215 + 0.410716i
$$474$$ 0 0
$$475$$ −0.0187266 + 0.0625512i −0.000859236 + 0.00287005i
$$476$$ 5.86110 33.2399i 0.268643 1.52355i
$$477$$ 0 0
$$478$$ −0.559844 3.17503i −0.0256067 0.145223i
$$479$$ −15.7830 1.84476i −0.721142 0.0842895i −0.252398 0.967623i $$-0.581219\pi$$
−0.468744 + 0.883334i $$0.655293\pi$$
$$480$$ 0 0
$$481$$ −8.18848 + 8.67928i −0.373362 + 0.395741i
$$482$$ 0.705200 1.63484i 0.0321210 0.0744648i
$$483$$ 0 0
$$484$$ 14.7643 9.71062i 0.671104 0.441392i
$$485$$ −34.7759 −1.57909
$$486$$ 0 0
$$487$$ 39.0750 1.77066 0.885330 0.464964i $$-0.153933\pi$$
0.885330 + 0.464964i $$0.153933\pi$$
$$488$$ −7.78149 + 5.11797i −0.352251 + 0.231679i
$$489$$ 0 0
$$490$$ 13.3679 30.9903i 0.603900 1.40000i
$$491$$ 26.4780 28.0650i 1.19494 1.26656i 0.239655 0.970858i $$-0.422966\pi$$
0.955281 0.295700i $$-0.0955528\pi$$
$$492$$ 0 0
$$493$$ 17.8604 + 2.08758i 0.804393 + 0.0940201i
$$494$$ 0.0101418 + 0.0575172i 0.000456303 + 0.00258782i
$$495$$ 0 0
$$496$$ 5.06319 28.7147i 0.227344 1.28933i
$$497$$ −7.75941 + 25.9182i −0.348057 + 1.16259i
$$498$$ 0 0
$$499$$ −0.309871 + 5.32027i −0.0138717 + 0.238168i 0.984244 + 0.176814i $$0.0565790\pi$$
−0.998116 + 0.0613544i $$0.980458\pi$$
$$500$$ −6.99408 + 3.51256i −0.312785 + 0.157086i
$$501$$ 0 0
$$502$$ −21.6496 22.9472i −0.966267 1.02418i
$$503$$ 21.2859 7.74742i 0.949090 0.345440i 0.179341 0.983787i $$-0.442604\pi$$
0.769749 + 0.638347i $$0.220381\pi$$
$$504$$ 0 0
$$505$$ −8.03363 2.92400i −0.357492 0.130116i
$$506$$ 12.6825 + 29.4012i 0.563804 + 1.30704i
$$507$$ 0 0
$$508$$ −9.29904 31.0610i −0.412578 1.37811i
$$509$$ −31.0714 + 3.63172i −1.37721 + 0.160973i −0.772270 0.635294i $$-0.780879\pi$$
−0.604945 + 0.796268i $$0.706805\pi$$
$$510$$ 0 0
$$511$$ −0.818864 14.0594i −0.0362244 0.621949i
$$512$$ −14.1680 24.5396i −0.626141 1.08451i
$$513$$ 0 0
$$514$$ 9.75038 16.8881i 0.430071 0.744904i
$$515$$ −7.64420 3.83906i −0.336844 0.169169i
$$516$$ 0 0
$$517$$ 3.36799 + 4.52400i 0.148124 + 0.198965i
$$518$$ −51.7240 12.2588i −2.27262 0.538622i
$$519$$ 0 0
$$520$$ 2.95455 3.96865i 0.129566 0.174037i
$$521$$ −22.0317 + 18.4868i −0.965226 + 0.809921i −0.981795 0.189942i $$-0.939170\pi$$
0.0165695 + 0.999863i $$0.494726\pi$$
$$522$$ 0 0
$$523$$ −5.64380 4.73571i −0.246786 0.207078i 0.511001 0.859580i $$-0.329275\pi$$
−0.757787 + 0.652502i $$0.773719\pi$$
$$524$$ −0.000775539 0 0.000183806i −3.38796e−5 0 8.02961e-6i
$$525$$ 0 0
$$526$$ −0.420443 0.276530i −0.0183322 0.0120573i
$$527$$ −33.3696 21.9475i −1.45360 0.956049i
$$528$$ 0 0
$$529$$ 35.6840 8.45727i 1.55148 0.367707i
$$530$$ 13.5985 + 11.4105i 0.590680 + 0.495640i
$$531$$ 0 0
$$532$$ −0.110125 + 0.0924059i −0.00477453 + 0.00400630i
$$533$$ −5.63115 + 7.56394i −0.243912 + 0.327631i
$$534$$ 0 0
$$535$$ 45.9277 + 10.8851i 1.98563 + 0.470602i
$$536$$ −2.65748 3.56961i −0.114785 0.154184i
$$537$$ 0 0
$$538$$ −27.2440 13.6824i −1.17457 0.589892i
$$539$$ 5.23423 9.06595i 0.225454 0.390498i
$$540$$ 0 0
$$541$$ 12.6202 + 21.8588i 0.542583 + 0.939782i 0.998755 + 0.0498899i $$0.0158870\pi$$
−0.456171 + 0.889892i $$0.650780\pi$$
$$542$$ −2.04843 35.1702i −0.0879876 1.51069i
$$543$$ 0 0
$$544$$ −30.8798 + 3.60933i −1.32396 + 0.154749i
$$545$$ 0.249360 + 0.832920i 0.0106814 + 0.0356784i
$$546$$ 0 0
$$547$$ 7.17326 + 16.6295i 0.306706 + 0.711025i 0.999953 0.00967491i $$-0.00307967\pi$$
−0.693247 + 0.720700i $$0.743820\pi$$
$$548$$ −29.9229 10.8910i −1.27824 0.465242i
$$549$$ 0 0
$$550$$ 15.3469 5.58581i 0.654393 0.238180i
$$551$$ −0.0525580 0.0557082i −0.00223905 0.00237325i
$$552$$ 0 0
$$553$$ −25.5885 + 12.8510i −1.08813 + 0.546481i
$$554$$ −3.05067 + 52.3779i −0.129610 + 2.22533i
$$555$$ 0 0
$$556$$ −0.454252 + 1.51731i −0.0192646 + 0.0643482i
$$557$$ 1.58101 8.96634i 0.0669894 0.379916i −0.932819 0.360345i $$-0.882659\pi$$
0.999808 0.0195708i $$-0.00622998\pi$$
$$558$$ 0 0
$$559$$ −1.32104 7.49200i −0.0558741 0.316878i
$$560$$ −29.6320 3.46349i −1.25218 0.146359i
$$561$$ 0 0
$$562$$ 28.0368 29.7173i 1.18266 1.25355i
$$563$$ −7.00644 + 16.2428i −0.295286 + 0.684550i −0.999681 0.0252581i $$-0.991959\pi$$
0.704395 + 0.709808i $$0.251219\pi$$
$$564$$ 0 0
$$565$$ 8.07791 5.31292i 0.339840 0.223516i
$$566$$ 2.35991 0.0991944
$$567$$ 0 0
$$568$$ −7.64524 −0.320787
$$569$$ 34.9033 22.9563i 1.46322 0.962377i 0.466249 0.884654i $$-0.345605\pi$$
0.996975 0.0777237i $$-0.0247652\pi$$
$$570$$ 0 0
$$571$$ 7.80567 18.0956i 0.326657 0.757276i −0.673184 0.739475i $$-0.735074\pi$$
0.999842 0.0178017i $$-0.00566675\pi$$
$$572$$ 5.53905 5.87105i 0.231599 0.245481i
$$573$$ 0 0
$$574$$ −41.7248 4.87693i −1.74156 0.203559i
$$575$$ −5.28516 29.9737i −0.220407 1.24999i
$$576$$ 0 0
$$577$$ −1.35567 + 7.68841i −0.0564374 + 0.320073i −0.999936 0.0113037i $$-0.996402\pi$$
0.943499 + 0.331376i $$0.107513\pi$$
$$578$$ 1.12830 3.76879i 0.0469311 0.156761i
$$579$$ 0 0
$$580$$ −1.98418 + 34.0671i −0.0823888 + 1.41456i
$$581$$ −16.1854 + 8.12859i −0.671482 + 0.337231i
$$582$$ 0 0
$$583$$ 3.77847 + 4.00494i 0.156488 + 0.165868i
$$584$$ 3.73967 1.36113i 0.154748 0.0563238i
$$585$$ 0 0
$$586$$ 15.9679 + 5.81183i 0.659626 + 0.240084i
$$587$$ 8.30634 + 19.2563i 0.342839 + 0.794791i 0.999186 + 0.0403319i $$0.0128415\pi$$
−0.656347 + 0.754459i $$0.727899\pi$$
$$588$$ 0 0
$$589$$ 0.0487886 + 0.162965i 0.00201030 + 0.00671486i
$$590$$ 31.1217 3.63760i 1.28126 0.149758i
$$591$$ 0 0
$$592$$ 1.18220 + 20.2975i 0.0485879 + 0.834222i
$$593$$ −11.8196 20.4722i −0.485373 0.840691i 0.514485 0.857499i $$-0.327983\pi$$
−0.999859 + 0.0168078i $$0.994650\pi$$
$$594$$ 0 0
$$595$$ −20.4331 + 35.3912i −0.837677 + 1.45090i
$$596$$ 28.5186 + 14.3226i 1.16817 + 0.586675i
$$597$$ 0 0
$$598$$ −16.2573 21.8374i −0.664812 0.892997i
$$599$$ −1.55457 0.368441i −0.0635182 0.0150541i 0.198734 0.980053i $$-0.436317\pi$$
−0.262252 + 0.964999i $$0.584465\pi$$
$$600$$ 0 0
$$601$$ 18.9415 25.4429i 0.772641 1.03784i −0.225337 0.974281i $$-0.572348\pi$$
0.997978 0.0635563i $$-0.0202443\pi$$
$$602$$ 25.9617 21.7845i 1.05812 0.887869i
$$603$$ 0 0
$$604$$ −31.7498 26.6413i −1.29188 1.08402i
$$605$$ −20.8191 + 4.93421i −0.846415 + 0.200604i
$$606$$ 0 0
$$607$$ −8.88733 5.84529i −0.360726 0.237253i 0.356189 0.934414i $$-0.384076\pi$$
−0.716915 + 0.697161i $$0.754446\pi$$
$$608$$ 0.110633 + 0.0727644i 0.00448676 + 0.00295099i
$$609$$ 0 0
$$610$$ 57.7119 13.6780i 2.33669 0.553805i
$$611$$ −3.67345 3.08239i −0.148612 0.124700i
$$612$$ 0 0
$$613$$ −34.7629 + 29.1695i −1.40406 + 1.17815i −0.444796 + 0.895632i $$0.646724\pi$$
−0.959263 + 0.282513i $$0.908832\pi$$
$$614$$ 21.1998 28.4762i 0.855553 1.14921i
$$615$$ 0 0
$$616$$ 6.65228 + 1.57662i 0.268028 + 0.0635238i
$$617$$ 13.7903 + 18.5236i 0.555178 + 0.745733i 0.987781 0.155851i $$-0.0498121\pi$$
−0.432603 + 0.901585i $$0.642405\pi$$
$$618$$ 0 0
$$619$$ 1.75718 + 0.882490i 0.0706271 + 0.0354703i 0.483762 0.875200i $$-0.339270\pi$$
−0.413135 + 0.910670i $$0.635566\pi$$
$$620$$ 37.8977 65.6408i 1.52201 2.63620i
$$621$$ 0 0
$$622$$ 5.44913 + 9.43817i 0.218490 + 0.378436i
$$623$$ 0.975956 + 16.7565i 0.0391008 + 0.671335i
$$624$$ 0 0
$$625$$ 28.9790 3.38716i 1.15916 0.135486i
$$626$$ −16.9411 56.5872i −0.677103 2.26168i
$$627$$ 0 0
$$628$$ −8.41288 19.5033i −0.335711 0.778264i
$$629$$ 26.1710 + 9.52548i 1.04351 + 0.379806i
$$630$$ 0 0
$$631$$ −45.7709 + 16.6593i −1.82211 + 0.663195i −0.827265 + 0.561812i $$0.810104\pi$$
−0.994848 + 0.101382i $$0.967673\pi$$
$$632$$ −5.55276 5.88558i −0.220877 0.234116i
$$633$$ 0 0
$$634$$ −17.3704 + 8.72372i −0.689865 + 0.346463i
$$635$$ −2.28256 + 39.1900i −0.0905805 + 1.55521i
$$636$$ 0 0
$$637$$ −2.55274 + 8.52673i −0.101143 + 0.337841i
$$638$$ −3.32653 + 18.8657i −0.131699 + 0.746899i
$$639$$ 0 0
$$640$$ −4.00945 22.7387i −0.158487 0.898827i
$$641$$ 24.5011 + 2.86377i 0.967737 + 0.113112i 0.585254 0.810850i $$-0.300995\pi$$
0.382483 + 0.923962i $$0.375069\pi$$
$$642$$ 0 0
$$643$$ 7.26830 7.70395i 0.286634 0.303814i −0.568018 0.823016i $$-0.692289\pi$$
0.854651 + 0.519202i $$0.173771\pi$$
$$644$$ 26.5416 61.5305i 1.04589 2.42464i
$$645$$ 0 0
$$646$$ 0.113893 0.0749084i 0.00448105 0.00294723i
$$647$$ −12.2785 −0.482716 −0.241358 0.970436i $$-0.577593\pi$$
−0.241358 + 0.970436i $$0.577593\pi$$
$$648$$ 0 0
$$649$$ 9.71877 0.381495
$$650$$ −11.6015 + 7.63041i −0.455048 + 0.299289i
$$651$$ 0 0
$$652$$ 0.659731 1.52943i 0.0258371 0.0598970i
$$653$$ 1.96487 2.08264i 0.0768914 0.0815001i −0.687786 0.725914i $$-0.741417\pi$$
0.764677 + 0.644414i $$0.222899\pi$$
$$654$$ 0 0
$$655$$ 0.000958475 0 0.000112030i 3.74507e−5 0 4.37736e-6i
$$656$$ 2.79016 + 15.8238i 0.108938 + 0.617815i
$$657$$ 0 0
$$658$$ 3.70957 21.0380i 0.144614 0.820148i
$$659$$ 13.3973 44.7501i 0.521885 1.74322i −0.136603 0.990626i $$-0.543619\pi$$
0.658488 0.752591i $$-0.271196\pi$$
$$660$$ 0 0
$$661$$ −1.38632 + 23.8022i −0.0539215 + 0.925797i 0.857542 + 0.514415i $$0.171991\pi$$
−0.911463 + 0.411382i $$0.865046\pi$$
$$662$$ 32.0247 16.0834i 1.24467 0.625099i
$$663$$ 0 0
$$664$$ −3.51226 3.72278i −0.136302 0.144472i
$$665$$ 0.163559 0.0595306i 0.00634254 0.00230850i
$$666$$ 0 0
$$667$$ 33.5475 + 12.2103i 1.29897 + 0.472785i
$$668$$ −15.7672 36.5524i −0.610050 1.41425i
$$669$$ 0 0
$$670$$ 8.12781 + 27.1488i 0.314005 + 1.04885i
$$671$$ 18.2721 2.13570i 0.705386 0.0824479i
$$672$$ 0 0
$$673$$ −0.262422 4.50561i −0.0101156 0.173679i −0.999582 0.0289148i $$-0.990795\pi$$
0.989466 0.144764i $$-0.0462422\pi$$
$$674$$ −13.7901 23.8852i −0.531175 0.920023i
$$675$$ 0 0
$$676$$ 12.6206 21.8594i 0.485406 0.840748i
$$677$$ 11.2705 + 5.66027i 0.433162 + 0.217542i 0.652000 0.758219i $$-0.273930\pi$$
−0.218838 + 0.975761i $$0.570227\pi$$
$$678$$ 0 0
$$679$$ 24.3973 + 32.7713i 0.936283 + 1.25765i
$$680$$ −11.2368 2.66318i −0.430913 0.102128i
$$681$$ 0 0
$$682$$ 25.4087 34.1299i 0.972951 1.30690i
$$683$$ −13.8210 + 11.5972i −0.528845 + 0.443754i −0.867702 0.497084i $$-0.834404\pi$$
0.338857 + 0.940838i $$0.389960\pi$$
$$684$$ 0 0
$$685$$ 29.5344 + 24.7823i 1.12845 + 0.946883i
$$686$$ 12.0009 2.84426i 0.458195 0.108594i
$$687$$ 0 0
$$688$$ −10.8303 7.12317i −0.412899 0.271568i
$$689$$ −3.91127 2.57248i −0.149008 0.0980038i
$$690$$ 0 0
$$691$$ −32.3764 + 7.67336i −1.23166 + 0.291908i −0.794382 0.607419i $$-0.792205\pi$$
−0.437276 + 0.899327i $$0.644057\pi$$
$$692$$ 30.5145 + 25.6047i 1.15999 + 0.973345i
$$693$$ 0 0
$$694$$ −23.3104 + 19.5598i −0.884852 + 0.742479i
$$695$$ 1.14514 1.53819i 0.0434377 0.0583469i
$$696$$ 0 0
$$697$$ 21.4165 + 5.07581i 0.811209 + 0.192260i
$$698$$ 10.2680 + 13.7923i 0.388649 + 0.522047i
$$699$$ 0 0
$$700$$ −30.5434 15.3395i −1.15443 0.579778i
$$701$$ −9.13385 + 15.8203i −0.344981 + 0.597524i −0.985350 0.170543i $$-0.945448\pi$$
0.640370 + 0.768067i $$0.278781\pi$$
$$702$$ 0 0
$$703$$ −0.0593101 0.102728i −0.00223692 0.00387446i
$$704$$ −1.27817 21.9453i −0.0481729 0.827096i
$$705$$ 0 0
$$706$$ 56.9176 6.65272i 2.14212 0.250378i
$$707$$ 2.88061 + 9.62191i 0.108337 + 0.361869i
$$708$$ 0 0
$$709$$ 0.783606 + 1.81660i 0.0294290 + 0.0682240i 0.932297 0.361694i $$-0.117802\pi$$
−0.902868 + 0.429918i $$0.858542\pi$$
$$710$$ 45.7496 + 16.6515i 1.71695 + 0.624919i
$$711$$ 0 0
$$712$$ −4.45709 + 1.62225i −0.167036 + 0.0607963i
$$713$$ −54.4157 57.6773i −2.03788 2.16003i
$$714$$ 0 0
$$715$$ −8.73320 + 4.38598i −0.326603 + 0.164026i
$$716$$ 1.13991 19.5716i 0.0426006 0.731423i
$$717$$ 0 0
$$718$$ −15.1174 + 50.4955i −0.564175 + 1.88448i
$$719$$ 2.42853 13.7729i 0.0905690 0.513642i −0.905446 0.424461i $$-0.860464\pi$$
0.996015 0.0891816i $$-0.0284252\pi$$
$$720$$ 0 0
$$721$$ 1.74509 + 9.89690i 0.0649906 + 0.368580i
$$722$$ 39.8962 + 4.66320i 1.48478 + 0.173546i
$$723$$ 0 0
$$724$$ 23.4451 24.8504i 0.871332 0.923558i
$$725$$ 7.21226 16.7199i 0.267856 0.620961i
$$726$$ 0 0
$$727$$ −31.2308 + 20.5408i −1.15829 + 0.761817i −0.975210 0.221281i $$-0.928976\pi$$
−0.183077 + 0.983099i $$0.558606\pi$$
$$728$$ −5.81268 −0.215432
$$729$$ 0 0
$$730$$ −25.3429 −0.937984
$$731$$ −14.8353 + 9.75731i −0.548702 + 0.360887i
$$732$$ 0 0
$$733$$ 10.5389 24.4320i 0.389265 0.902417i −0.605075 0.796168i $$-0.706857\pi$$
0.994340 0.106248i $$-0.0338838\pi$$
$$734$$ −18.9941 + 20.1325i −0.701084 + 0.743105i
$$735$$ 0 0
$$736$$ −61.3071 7.16578i −2.25981 0.264134i
$$737$$ 1.52638 + 8.65652i 0.0562249 + 0.318867i
$$738$$ 0 0
$$739$$ 7.56956 42.9291i 0.278451 1.57917i −0.449332 0.893365i $$-0.648338\pi$$
0.727782 0.685808i $$-0.240551\pi$$
$$740$$ −15.1583 + 50.6324i −0.557232 + 1.86128i
$$741$$ 0 0
$$742$$ 1.21261 20.8198i 0.0445164 0.764317i
$$743$$ 45.4564 22.8291i 1.66763 0.837517i 0.672380 0.740206i $$-0.265272\pi$$
0.995254 0.0973110i $$-0.0310242\pi$$
$$744$$ 0 0
$$745$$ −26.5156 28.1049i −0.971457 1.02968i
$$746$$ 57.1662 20.8068i 2.09300 0.761791i
$$747$$ 0 0
$$748$$ −17.7033 6.44346i −0.647295 0.235596i
$$749$$ −21.9634 50.9168i −0.802524 1.86046i
$$750$$ 0 0
$$751$$ −3.63443 12.1398i −0.132622 0.442989i 0.865721 0.500527i $$-0.166860\pi$$
−0.998343 + 0.0575375i $$0.981675\pi$$
$$752$$ −8.11570 + 0.948589i −0.295949 + 0.0345915i
$$753$$ 0 0
$$754$$ −0.947046 16.2602i −0.0344894 0.592160i
$$755$$ 25.0908 + 43.4585i 0.913146 + 1.58162i
$$756$$ 0 0
$$757$$ 7.49384 12.9797i 0.272368 0.471756i −0.697100 0.716974i $$-0.745526\pi$$
0.969468 + 0.245219i $$0.0788598\pi$$
$$758$$ −39.6421 19.9090i −1.43987 0.723128i
$$759$$ 0 0
$$760$$ 0.0293714 + 0.0394526i 0.00106541 + 0.00143110i
$$761$$ 10.2662 + 2.43313i 0.372149 + 0.0882010i 0.412435 0.910987i $$-0.364679\pi$$
−0.0402853 + 0.999188i $$0.512827\pi$$
$$762$$ 0 0
$$763$$ 0.609968 0.819329i 0.0220823 0.0296617i
$$764$$ −27.1927 + 22.8174i −0.983798 + 0.825505i
$$765$$ 0 0
$$766$$ 39.6701 + 33.2872i 1.43334 + 1.20271i
$$767$$ −8.04050 + 1.90563i −0.290326 + 0.0688085i
$$768$$ 0 0
$$769$$ 32.8627 + 21.6141i 1.18506 + 0.779426i 0.979936 0.199310i $$-0.0638701\pi$$
0.205123 + 0.978736i $$0.434240\pi$$
$$770$$ −36.3737 23.9234i −1.31082 0.862139i
$$771$$ 0 0
$$772$$ −10.0537 + 2.38278i −0.361842 + 0.0857581i
$$773$$ −37.1233 31.1502i −1.33523 1.12039i −0.982824 0.184547i $$-0.940918\pi$$
−0.352409 0.935846i $$-0.614637\pi$$
$$774$$ 0 0
$$775$$ −30.9824 + 25.9973i −1.11292 + 0.933851i
$$776$$ −6.89427 + 9.26061i −0.247490 + 0.332437i
$$777$$ 0 0
$$778$$ −32.4346 7.68714i −1.16284 0.275597i
$$779$$ −0.0559795 0.0751936i −0.00200568 0.00269409i
$$780$$ 0 0
$$781$$ 13.4947 + 6.77728i 0.482877 + 0.242510i
$$782$$ −31.7716 + 55.0300i −1.13615 + 1.96787i
$$783$$ 0