# Properties

 Label 380.2.u.b.81.2 Level $380$ Weight $2$ Character 380.81 Analytic conductor $3.034$ Analytic rank $0$ Dimension $18$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(61,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("380.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.u (of order $$9$$, degree $$6$$, 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: $$3.03431527681$$ Analytic rank: $$0$$ Dimension: $$18$$ Relative dimension: $$3$$ over $$\Q(\zeta_{9})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329$$ x^18 - 3*x^17 + 21*x^16 - 30*x^15 + 192*x^14 - 207*x^13 + 1178*x^12 - 705*x^11 + 4413*x^10 - 2224*x^9 + 11430*x^8 - 4101*x^7 + 19237*x^6 - 7125*x^5 + 21573*x^4 - 5266*x^3 + 13851*x^2 - 3285*x + 5329 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 81.2 Root $$-0.478554 - 0.828880i$$ of defining polynomial Character $$\chi$$ $$=$$ 380.81 Dual form 380.2.u.b.61.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.166200 - 0.942568i) q^{3} +(0.766044 + 0.642788i) q^{5} +(-2.28066 - 3.95023i) q^{7} +(1.95827 + 0.712751i) q^{9} +O(q^{10})$$ $$q+(0.166200 - 0.942568i) q^{3} +(0.766044 + 0.642788i) q^{5} +(-2.28066 - 3.95023i) q^{7} +(1.95827 + 0.712751i) q^{9} +(-0.558879 + 0.968007i) q^{11} +(-0.897380 - 5.08930i) q^{13} +(0.733187 - 0.615217i) q^{15} +(6.80290 - 2.47605i) q^{17} +(-3.68742 - 2.32442i) q^{19} +(-4.10240 + 1.49315i) q^{21} +(-3.31875 + 2.78477i) q^{23} +(0.173648 + 0.984808i) q^{25} +(2.43294 - 4.21398i) q^{27} +(2.51115 + 0.913983i) q^{29} +(1.37022 + 2.37328i) q^{31} +(0.819526 + 0.687664i) q^{33} +(0.792067 - 4.49203i) q^{35} -0.491893 q^{37} -4.94615 q^{39} +(1.45408 - 8.24648i) q^{41} +(3.16372 + 2.65467i) q^{43} +(1.04197 + 1.80475i) q^{45} +(2.48547 + 0.904639i) q^{47} +(-6.90286 + 11.9561i) q^{49} +(-1.20320 - 6.82371i) q^{51} +(-10.4500 + 8.76856i) q^{53} +(-1.05035 + 0.382296i) q^{55} +(-2.80377 + 3.08933i) q^{57} +(2.45313 - 0.892868i) q^{59} +(3.64703 - 3.06022i) q^{61} +(-1.65062 - 9.36114i) q^{63} +(2.58390 - 4.47545i) q^{65} +(11.9079 + 4.33411i) q^{67} +(2.07325 + 3.59098i) q^{69} +(0.524118 + 0.439787i) q^{71} +(-2.28024 + 12.9319i) q^{73} +0.957108 q^{75} +5.09846 q^{77} +(-2.75095 + 15.6014i) q^{79} +(1.22158 + 1.02502i) q^{81} +(1.88033 + 3.25683i) q^{83} +(6.80290 + 2.47605i) q^{85} +(1.27884 - 2.21502i) q^{87} +(2.04379 + 11.5909i) q^{89} +(-18.0573 + 15.1518i) q^{91} +(2.46471 - 0.897081i) q^{93} +(-1.33063 - 4.15084i) q^{95} +(3.27804 - 1.19311i) q^{97} +(-1.78438 + 1.49727i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$18 q + 3 q^{3} + 15 q^{9}+O(q^{10})$$ 18 * q + 3 * q^3 + 15 * q^9 $$18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100})$$ 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$77$$ $$191$$ $$\chi(n)$$ $$e\left(\frac{8}{9}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.166200 0.942568i 0.0959557 0.544192i −0.898495 0.438984i $$-0.855338\pi$$
0.994450 0.105207i $$-0.0335506\pi$$
$$4$$ 0 0
$$5$$ 0.766044 + 0.642788i 0.342585 + 0.287463i
$$6$$ 0 0
$$7$$ −2.28066 3.95023i −0.862010 1.49305i −0.869985 0.493077i $$-0.835872\pi$$
0.00797511 0.999968i $$-0.497461\pi$$
$$8$$ 0 0
$$9$$ 1.95827 + 0.712751i 0.652756 + 0.237584i
$$10$$ 0 0
$$11$$ −0.558879 + 0.968007i −0.168508 + 0.291865i −0.937896 0.346918i $$-0.887228\pi$$
0.769387 + 0.638783i $$0.220562\pi$$
$$12$$ 0 0
$$13$$ −0.897380 5.08930i −0.248889 1.41152i −0.811286 0.584650i $$-0.801232\pi$$
0.562397 0.826867i $$-0.309879\pi$$
$$14$$ 0 0
$$15$$ 0.733187 0.615217i 0.189308 0.158848i
$$16$$ 0 0
$$17$$ 6.80290 2.47605i 1.64994 0.600531i 0.661209 0.750202i $$-0.270044\pi$$
0.988736 + 0.149671i $$0.0478216\pi$$
$$18$$ 0 0
$$19$$ −3.68742 2.32442i −0.845953 0.533257i
$$20$$ 0 0
$$21$$ −4.10240 + 1.49315i −0.895218 + 0.325833i
$$22$$ 0 0
$$23$$ −3.31875 + 2.78477i −0.692008 + 0.580664i −0.919488 0.393119i $$-0.871396\pi$$
0.227480 + 0.973783i $$0.426952\pi$$
$$24$$ 0 0
$$25$$ 0.173648 + 0.984808i 0.0347296 + 0.196962i
$$26$$ 0 0
$$27$$ 2.43294 4.21398i 0.468220 0.810981i
$$28$$ 0 0
$$29$$ 2.51115 + 0.913983i 0.466308 + 0.169722i 0.564479 0.825447i $$-0.309077\pi$$
−0.0981710 + 0.995170i $$0.531299\pi$$
$$30$$ 0 0
$$31$$ 1.37022 + 2.37328i 0.246098 + 0.426254i 0.962440 0.271495i $$-0.0875181\pi$$
−0.716342 + 0.697750i $$0.754185\pi$$
$$32$$ 0 0
$$33$$ 0.819526 + 0.687664i 0.142661 + 0.119707i
$$34$$ 0 0
$$35$$ 0.792067 4.49203i 0.133884 0.759292i
$$36$$ 0 0
$$37$$ −0.491893 −0.0808666 −0.0404333 0.999182i $$-0.512874\pi$$
−0.0404333 + 0.999182i $$0.512874\pi$$
$$38$$ 0 0
$$39$$ −4.94615 −0.792018
$$40$$ 0 0
$$41$$ 1.45408 8.24648i 0.227089 1.28788i −0.631563 0.775325i $$-0.717586\pi$$
0.858652 0.512560i $$-0.171303\pi$$
$$42$$ 0 0
$$43$$ 3.16372 + 2.65467i 0.482462 + 0.404834i 0.851316 0.524654i $$-0.175805\pi$$
−0.368853 + 0.929488i $$0.620250\pi$$
$$44$$ 0 0
$$45$$ 1.04197 + 1.80475i 0.155328 + 0.269036i
$$46$$ 0 0
$$47$$ 2.48547 + 0.904639i 0.362544 + 0.131955i 0.516868 0.856065i $$-0.327098\pi$$
−0.154324 + 0.988020i $$0.549320\pi$$
$$48$$ 0 0
$$49$$ −6.90286 + 11.9561i −0.986124 + 1.70802i
$$50$$ 0 0
$$51$$ −1.20320 6.82371i −0.168482 0.955510i
$$52$$ 0 0
$$53$$ −10.4500 + 8.76856i −1.43541 + 1.20445i −0.492988 + 0.870036i $$0.664095\pi$$
−0.942425 + 0.334418i $$0.891460\pi$$
$$54$$ 0 0
$$55$$ −1.05035 + 0.382296i −0.141629 + 0.0515488i
$$56$$ 0 0
$$57$$ −2.80377 + 3.08933i −0.371368 + 0.409192i
$$58$$ 0 0
$$59$$ 2.45313 0.892868i 0.319371 0.116241i −0.177360 0.984146i $$-0.556756\pi$$
0.496731 + 0.867905i $$0.334534\pi$$
$$60$$ 0 0
$$61$$ 3.64703 3.06022i 0.466954 0.391821i −0.378728 0.925508i $$-0.623638\pi$$
0.845682 + 0.533687i $$0.179194\pi$$
$$62$$ 0 0
$$63$$ −1.65062 9.36114i −0.207959 1.17939i
$$64$$ 0 0
$$65$$ 2.58390 4.47545i 0.320494 0.555112i
$$66$$ 0 0
$$67$$ 11.9079 + 4.33411i 1.45478 + 0.529495i 0.943921 0.330171i $$-0.107107\pi$$
0.510855 + 0.859667i $$0.329329\pi$$
$$68$$ 0 0
$$69$$ 2.07325 + 3.59098i 0.249590 + 0.432303i
$$70$$ 0 0
$$71$$ 0.524118 + 0.439787i 0.0622013 + 0.0521931i 0.673358 0.739316i $$-0.264851\pi$$
−0.611157 + 0.791509i $$0.709296\pi$$
$$72$$ 0 0
$$73$$ −2.28024 + 12.9319i −0.266882 + 1.51356i 0.496741 + 0.867899i $$0.334530\pi$$
−0.763623 + 0.645662i $$0.776581\pi$$
$$74$$ 0 0
$$75$$ 0.957108 0.110517
$$76$$ 0 0
$$77$$ 5.09846 0.581024
$$78$$ 0 0
$$79$$ −2.75095 + 15.6014i −0.309506 + 1.75529i 0.291993 + 0.956420i $$0.405681\pi$$
−0.601499 + 0.798874i $$0.705430\pi$$
$$80$$ 0 0
$$81$$ 1.22158 + 1.02502i 0.135731 + 0.113892i
$$82$$ 0 0
$$83$$ 1.88033 + 3.25683i 0.206393 + 0.357484i 0.950576 0.310493i $$-0.100494\pi$$
−0.744182 + 0.667976i $$0.767161\pi$$
$$84$$ 0 0
$$85$$ 6.80290 + 2.47605i 0.737878 + 0.268565i
$$86$$ 0 0
$$87$$ 1.27884 2.21502i 0.137106 0.237475i
$$88$$ 0 0
$$89$$ 2.04379 + 11.5909i 0.216642 + 1.22864i 0.878035 + 0.478597i $$0.158854\pi$$
−0.661393 + 0.750039i $$0.730035\pi$$
$$90$$ 0 0
$$91$$ −18.0573 + 15.1518i −1.89292 + 1.58834i
$$92$$ 0 0
$$93$$ 2.46471 0.897081i 0.255579 0.0930230i
$$94$$ 0 0
$$95$$ −1.33063 4.15084i −0.136519 0.425867i
$$96$$ 0 0
$$97$$ 3.27804 1.19311i 0.332835 0.121142i −0.170197 0.985410i $$-0.554440\pi$$
0.503031 + 0.864268i $$0.332218\pi$$
$$98$$ 0 0
$$99$$ −1.78438 + 1.49727i −0.179337 + 0.150482i
$$100$$ 0 0
$$101$$ 1.83378 + 10.3999i 0.182468 + 1.03483i 0.929165 + 0.369665i $$0.120527\pi$$
−0.746697 + 0.665164i $$0.768362\pi$$
$$102$$ 0 0
$$103$$ 5.77623 10.0047i 0.569149 0.985794i −0.427502 0.904015i $$-0.640606\pi$$
0.996650 0.0817799i $$-0.0260605\pi$$
$$104$$ 0 0
$$105$$ −4.10240 1.49315i −0.400354 0.145717i
$$106$$ 0 0
$$107$$ −3.88420 6.72763i −0.375499 0.650384i 0.614902 0.788603i $$-0.289195\pi$$
−0.990402 + 0.138219i $$0.955862\pi$$
$$108$$ 0 0
$$109$$ −10.1216 8.49299i −0.969469 0.813481i 0.0129986 0.999916i $$-0.495862\pi$$
−0.982467 + 0.186435i $$0.940307\pi$$
$$110$$ 0 0
$$111$$ −0.0817526 + 0.463642i −0.00775961 + 0.0440070i
$$112$$ 0 0
$$113$$ −1.84103 −0.173190 −0.0865950 0.996244i $$-0.527599\pi$$
−0.0865950 + 0.996244i $$0.527599\pi$$
$$114$$ 0 0
$$115$$ −4.33233 −0.403991
$$116$$ 0 0
$$117$$ 1.87009 10.6058i 0.172890 0.980507i
$$118$$ 0 0
$$119$$ −25.2961 21.2259i −2.31889 1.94578i
$$120$$ 0 0
$$121$$ 4.87531 + 8.44428i 0.443210 + 0.767662i
$$122$$ 0 0
$$123$$ −7.53120 2.74113i −0.679066 0.247160i
$$124$$ 0 0
$$125$$ −0.500000 + 0.866025i −0.0447214 + 0.0774597i
$$126$$ 0 0
$$127$$ −0.731989 4.15132i −0.0649536 0.368370i −0.999908 0.0136008i $$-0.995671\pi$$
0.934954 0.354769i $$-0.115441\pi$$
$$128$$ 0 0
$$129$$ 3.02802 2.54081i 0.266602 0.223706i
$$130$$ 0 0
$$131$$ −2.58430 + 0.940609i −0.225791 + 0.0821814i −0.452439 0.891796i $$-0.649446\pi$$
0.226647 + 0.973977i $$0.427224\pi$$
$$132$$ 0 0
$$133$$ −0.772191 + 19.8674i −0.0669574 + 1.72272i
$$134$$ 0 0
$$135$$ 4.57244 1.66423i 0.393533 0.143234i
$$136$$ 0 0
$$137$$ 1.69224 1.41996i 0.144578 0.121315i −0.567630 0.823284i $$-0.692140\pi$$
0.712208 + 0.701968i $$0.247695\pi$$
$$138$$ 0 0
$$139$$ 1.53264 + 8.69203i 0.129997 + 0.737248i 0.978214 + 0.207600i $$0.0665651\pi$$
−0.848217 + 0.529649i $$0.822324\pi$$
$$140$$ 0 0
$$141$$ 1.26577 2.19238i 0.106597 0.184631i
$$142$$ 0 0
$$143$$ 5.42800 + 1.97563i 0.453912 + 0.165211i
$$144$$ 0 0
$$145$$ 1.33615 + 2.31429i 0.110962 + 0.192191i
$$146$$ 0 0
$$147$$ 10.1222 + 8.49352i 0.834864 + 0.700534i
$$148$$ 0 0
$$149$$ 3.62671 20.5681i 0.297111 1.68500i −0.361383 0.932417i $$-0.617695\pi$$
0.658495 0.752585i $$-0.271194\pi$$
$$150$$ 0 0
$$151$$ 5.73130 0.466407 0.233203 0.972428i $$-0.425079\pi$$
0.233203 + 0.972428i $$0.425079\pi$$
$$152$$ 0 0
$$153$$ 15.0867 1.21969
$$154$$ 0 0
$$155$$ −0.475871 + 2.69880i −0.0382229 + 0.216773i
$$156$$ 0 0
$$157$$ −14.1251 11.8523i −1.12730 0.945919i −0.128352 0.991729i $$-0.540969\pi$$
−0.998950 + 0.0458101i $$0.985413\pi$$
$$158$$ 0 0
$$159$$ 6.52818 + 11.3071i 0.517718 + 0.896714i
$$160$$ 0 0
$$161$$ 18.5694 + 6.75872i 1.46348 + 0.532661i
$$162$$ 0 0
$$163$$ −1.74094 + 3.01540i −0.136361 + 0.236185i −0.926117 0.377237i $$-0.876874\pi$$
0.789755 + 0.613422i $$0.210207\pi$$
$$164$$ 0 0
$$165$$ 0.185772 + 1.05356i 0.0144623 + 0.0820198i
$$166$$ 0 0
$$167$$ 16.4620 13.8132i 1.27387 1.06890i 0.279806 0.960056i $$-0.409730\pi$$
0.994059 0.108843i $$-0.0347147\pi$$
$$168$$ 0 0
$$169$$ −12.8797 + 4.68781i −0.990742 + 0.360601i
$$170$$ 0 0
$$171$$ −5.56423 7.18004i −0.425507 0.549071i
$$172$$ 0 0
$$173$$ −10.3262 + 3.75842i −0.785084 + 0.285747i −0.703291 0.710902i $$-0.748287\pi$$
−0.0817929 + 0.996649i $$0.526065\pi$$
$$174$$ 0 0
$$175$$ 3.49418 2.93197i 0.264135 0.221636i
$$176$$ 0 0
$$177$$ −0.433877 2.46064i −0.0326122 0.184953i
$$178$$ 0 0
$$179$$ 8.54852 14.8065i 0.638946 1.10669i −0.346718 0.937969i $$-0.612704\pi$$
0.985664 0.168718i $$-0.0539627\pi$$
$$180$$ 0 0
$$181$$ −10.8910 3.96399i −0.809519 0.294641i −0.0960938 0.995372i $$-0.530635\pi$$
−0.713425 + 0.700732i $$0.752857\pi$$
$$182$$ 0 0
$$183$$ −2.27833 3.94618i −0.168419 0.291710i
$$184$$ 0 0
$$185$$ −0.376812 0.316182i −0.0277037 0.0232462i
$$186$$ 0 0
$$187$$ −1.40516 + 7.96907i −0.102756 + 0.582756i
$$188$$ 0 0
$$189$$ −22.1949 −1.61444
$$190$$ 0 0
$$191$$ 25.8688 1.87180 0.935901 0.352262i $$-0.114587\pi$$
0.935901 + 0.352262i $$0.114587\pi$$
$$192$$ 0 0
$$193$$ 2.44272 13.8534i 0.175831 0.997187i −0.761349 0.648342i $$-0.775463\pi$$
0.937180 0.348845i $$-0.113426\pi$$
$$194$$ 0 0
$$195$$ −3.78897 3.17932i −0.271334 0.227676i
$$196$$ 0 0
$$197$$ −1.70220 2.94830i −0.121277 0.210057i 0.798995 0.601338i $$-0.205365\pi$$
−0.920271 + 0.391281i $$0.872032\pi$$
$$198$$ 0 0
$$199$$ 17.3891 + 6.32911i 1.23268 + 0.448659i 0.874515 0.484999i $$-0.161180\pi$$
0.358166 + 0.933658i $$0.383402\pi$$
$$200$$ 0 0
$$201$$ 6.06427 10.5036i 0.427741 0.740869i
$$202$$ 0 0
$$203$$ −2.11665 12.0041i −0.148559 0.842522i
$$204$$ 0 0
$$205$$ 6.41463 5.38251i 0.448017 0.375931i
$$206$$ 0 0
$$207$$ −8.48385 + 3.08787i −0.589668 + 0.214622i
$$208$$ 0 0
$$209$$ 4.31087 2.27039i 0.298189 0.157046i
$$210$$ 0 0
$$211$$ −14.8432 + 5.40250i −1.02185 + 0.371923i −0.797972 0.602694i $$-0.794094\pi$$
−0.223878 + 0.974617i $$0.571872\pi$$
$$212$$ 0 0
$$213$$ 0.501638 0.420924i 0.0343716 0.0288412i
$$214$$ 0 0
$$215$$ 0.717156 + 4.06720i 0.0489097 + 0.277380i
$$216$$ 0 0
$$217$$ 6.25001 10.8253i 0.424278 0.734871i
$$218$$ 0 0
$$219$$ 11.8102 + 4.29856i 0.798058 + 0.290469i
$$220$$ 0 0
$$221$$ −18.7061 32.4000i −1.25831 2.17946i
$$222$$ 0 0
$$223$$ −17.0138 14.2763i −1.13933 0.956008i −0.139910 0.990164i $$-0.544681\pi$$
−0.999417 + 0.0341558i $$0.989126\pi$$
$$224$$ 0 0
$$225$$ −0.361873 + 2.05228i −0.0241249 + 0.136819i
$$226$$ 0 0
$$227$$ −5.60932 −0.372304 −0.186152 0.982521i $$-0.559602\pi$$
−0.186152 + 0.982521i $$0.559602\pi$$
$$228$$ 0 0
$$229$$ 1.04017 0.0687366 0.0343683 0.999409i $$-0.489058\pi$$
0.0343683 + 0.999409i $$0.489058\pi$$
$$230$$ 0 0
$$231$$ 0.847365 4.80565i 0.0557525 0.316188i
$$232$$ 0 0
$$233$$ 9.15779 + 7.68430i 0.599947 + 0.503415i 0.891428 0.453161i $$-0.149704\pi$$
−0.291482 + 0.956576i $$0.594148\pi$$
$$234$$ 0 0
$$235$$ 1.32249 + 2.29063i 0.0862699 + 0.149424i
$$236$$ 0 0
$$237$$ 14.2482 + 5.18591i 0.925517 + 0.336861i
$$238$$ 0 0
$$239$$ 4.50416 7.80144i 0.291350 0.504633i −0.682779 0.730625i $$-0.739229\pi$$
0.974129 + 0.225992i $$0.0725622\pi$$
$$240$$ 0 0
$$241$$ −2.31012 13.1014i −0.148808 0.843933i −0.964230 0.265066i $$-0.914606\pi$$
0.815422 0.578867i $$-0.196505\pi$$
$$242$$ 0 0
$$243$$ 12.3516 10.3642i 0.792358 0.664867i
$$244$$ 0 0
$$245$$ −12.9731 + 4.72184i −0.828824 + 0.301667i
$$246$$ 0 0
$$247$$ −8.52062 + 20.8523i −0.542154 + 1.32680i
$$248$$ 0 0
$$249$$ 3.38230 1.23105i 0.214344 0.0780149i
$$250$$ 0 0
$$251$$ −17.0043 + 14.2683i −1.07330 + 0.900609i −0.995348 0.0963480i $$-0.969284\pi$$
−0.0779560 + 0.996957i $$0.524839\pi$$
$$252$$ 0 0
$$253$$ −0.840890 4.76892i −0.0528663 0.299820i
$$254$$ 0 0
$$255$$ 3.46449 6.00067i 0.216955 0.375776i
$$256$$ 0 0
$$257$$ 2.37388 + 0.864022i 0.148079 + 0.0538962i 0.414996 0.909823i $$-0.363783\pi$$
−0.266918 + 0.963719i $$0.586005\pi$$
$$258$$ 0 0
$$259$$ 1.12184 + 1.94309i 0.0697079 + 0.120738i
$$260$$ 0 0
$$261$$ 4.26605 + 3.57964i 0.264062 + 0.221574i
$$262$$ 0 0
$$263$$ −2.18211 + 12.3753i −0.134554 + 0.763096i 0.840615 + 0.541634i $$0.182194\pi$$
−0.975169 + 0.221462i $$0.928917\pi$$
$$264$$ 0 0
$$265$$ −13.6415 −0.837988
$$266$$ 0 0
$$267$$ 11.2649 0.689401
$$268$$ 0 0
$$269$$ −3.59540 + 20.3905i −0.219216 + 1.24323i 0.654224 + 0.756301i $$0.272995\pi$$
−0.873439 + 0.486933i $$0.838116\pi$$
$$270$$ 0 0
$$271$$ −1.02160 0.857226i −0.0620579 0.0520728i 0.611231 0.791452i $$-0.290675\pi$$
−0.673289 + 0.739379i $$0.735119\pi$$
$$272$$ 0 0
$$273$$ 11.2805 + 19.5384i 0.682728 + 1.18252i
$$274$$ 0 0
$$275$$ −1.05035 0.382296i −0.0633384 0.0230533i
$$276$$ 0 0
$$277$$ −14.1070 + 24.4340i −0.847606 + 1.46810i 0.0357322 + 0.999361i $$0.488624\pi$$
−0.883338 + 0.468736i $$0.844710\pi$$
$$278$$ 0 0
$$279$$ 0.991688 + 5.62414i 0.0593708 + 0.336709i
$$280$$ 0 0
$$281$$ 9.31199 7.81369i 0.555507 0.466126i −0.321294 0.946980i $$-0.604118\pi$$
0.876801 + 0.480854i $$0.159673\pi$$
$$282$$ 0 0
$$283$$ −1.65082 + 0.600850i −0.0981312 + 0.0357168i −0.390619 0.920552i $$-0.627739\pi$$
0.292488 + 0.956269i $$0.405517\pi$$
$$284$$ 0 0
$$285$$ −4.13359 + 0.564335i −0.244853 + 0.0334283i
$$286$$ 0 0
$$287$$ −35.8918 + 13.0635i −2.11862 + 0.771116i
$$288$$ 0 0
$$289$$ 27.1258 22.7612i 1.59564 1.33890i
$$290$$ 0 0
$$291$$ −0.579775 3.28807i −0.0339870 0.192750i
$$292$$ 0 0
$$293$$ 3.85056 6.66937i 0.224952 0.389629i −0.731353 0.681999i $$-0.761111\pi$$
0.956305 + 0.292370i $$0.0944440\pi$$
$$294$$ 0 0
$$295$$ 2.45313 + 0.892868i 0.142827 + 0.0519848i
$$296$$ 0 0
$$297$$ 2.71944 + 4.71021i 0.157798 + 0.273314i
$$298$$ 0 0
$$299$$ 17.1507 + 14.3911i 0.991850 + 0.832261i
$$300$$ 0 0
$$301$$ 3.27119 18.5518i 0.188548 1.06931i
$$302$$ 0 0
$$303$$ 10.1074 0.580654
$$304$$ 0 0
$$305$$ 4.76086 0.272606
$$306$$ 0 0
$$307$$ −1.11720 + 6.33598i −0.0637623 + 0.361614i 0.936187 + 0.351503i $$0.114329\pi$$
−0.999949 + 0.0101104i $$0.996782\pi$$
$$308$$ 0 0
$$309$$ −8.47012 7.10727i −0.481848 0.404319i
$$310$$ 0 0
$$311$$ 14.5028 + 25.1196i 0.822379 + 1.42440i 0.903906 + 0.427731i $$0.140687\pi$$
−0.0815274 + 0.996671i $$0.525980\pi$$
$$312$$ 0 0
$$313$$ −12.8655 4.68265i −0.727200 0.264679i −0.0482209 0.998837i $$-0.515355\pi$$
−0.678979 + 0.734158i $$0.737577\pi$$
$$314$$ 0 0
$$315$$ 4.75278 8.23205i 0.267789 0.463824i
$$316$$ 0 0
$$317$$ −0.782232 4.43626i −0.0439345 0.249165i 0.954929 0.296836i $$-0.0959314\pi$$
−0.998863 + 0.0476705i $$0.984820\pi$$
$$318$$ 0 0
$$319$$ −2.28817 + 1.92000i −0.128113 + 0.107500i
$$320$$ 0 0
$$321$$ −6.98680 + 2.54299i −0.389965 + 0.141936i
$$322$$ 0 0
$$323$$ −30.8405 6.68250i −1.71601 0.371824i
$$324$$ 0 0
$$325$$ 4.85615 1.76749i 0.269371 0.0980430i
$$326$$ 0 0
$$327$$ −9.68742 + 8.12871i −0.535715 + 0.449519i
$$328$$ 0 0
$$329$$ −2.09501 11.8814i −0.115501 0.655041i
$$330$$ 0 0
$$331$$ −7.72326 + 13.3771i −0.424509 + 0.735271i −0.996374 0.0850767i $$-0.972886\pi$$
0.571866 + 0.820347i $$0.306220\pi$$
$$332$$ 0 0
$$333$$ −0.963257 0.350597i −0.0527862 0.0192126i
$$334$$ 0 0
$$335$$ 6.33604 + 10.9743i 0.346175 + 0.599592i
$$336$$ 0 0
$$337$$ −16.3175 13.6920i −0.888869 0.745850i 0.0791136 0.996866i $$-0.474791\pi$$
−0.967983 + 0.251016i $$0.919235\pi$$
$$338$$ 0 0
$$339$$ −0.305980 + 1.73530i −0.0166186 + 0.0942485i
$$340$$ 0 0
$$341$$ −3.06314 −0.165878
$$342$$ 0 0
$$343$$ 31.0432 1.67617
$$344$$ 0 0
$$345$$ −0.720033 + 4.08351i −0.0387653 + 0.219849i
$$346$$ 0 0
$$347$$ 2.69463 + 2.26106i 0.144655 + 0.121380i 0.712244 0.701932i $$-0.247679\pi$$
−0.567588 + 0.823312i $$0.692124\pi$$
$$348$$ 0 0
$$349$$ −4.55638 7.89188i −0.243897 0.422443i 0.717924 0.696122i $$-0.245093\pi$$
−0.961821 + 0.273679i $$0.911759\pi$$
$$350$$ 0 0
$$351$$ −23.6295 8.60042i −1.26125 0.459057i
$$352$$ 0 0
$$353$$ −12.4350 + 21.5381i −0.661850 + 1.14636i 0.318279 + 0.947997i $$0.396895\pi$$
−0.980129 + 0.198361i $$0.936438\pi$$
$$354$$ 0 0
$$355$$ 0.118808 + 0.673793i 0.00630567 + 0.0357612i
$$356$$ 0 0
$$357$$ −24.2111 + 20.3155i −1.28139 + 1.07521i
$$358$$ 0 0
$$359$$ −18.2882 + 6.65634i −0.965212 + 0.351308i −0.776074 0.630642i $$-0.782792\pi$$
−0.189138 + 0.981951i $$0.560569\pi$$
$$360$$ 0 0
$$361$$ 8.19419 + 17.1422i 0.431273 + 0.902221i
$$362$$ 0 0
$$363$$ 8.76958 3.19187i 0.460284 0.167530i
$$364$$ 0 0
$$365$$ −10.0592 + 8.44068i −0.526523 + 0.441805i
$$366$$ 0 0
$$367$$ 3.57276 + 20.2622i 0.186497 + 1.05768i 0.924017 + 0.382351i $$0.124885\pi$$
−0.737520 + 0.675325i $$0.764003\pi$$
$$368$$ 0 0
$$369$$ 8.72516 15.1124i 0.454214 0.786721i
$$370$$ 0 0
$$371$$ 58.4707 + 21.2816i 3.03565 + 1.10488i
$$372$$ 0 0
$$373$$ 1.84938 + 3.20322i 0.0957572 + 0.165856i 0.909924 0.414774i $$-0.136139\pi$$
−0.814167 + 0.580630i $$0.802806\pi$$
$$374$$ 0 0
$$375$$ 0.733187 + 0.615217i 0.0378616 + 0.0317697i
$$376$$ 0 0
$$377$$ 2.39808 13.6002i 0.123507 0.700444i
$$378$$ 0 0
$$379$$ −6.68304 −0.343285 −0.171642 0.985159i $$-0.554907\pi$$
−0.171642 + 0.985159i $$0.554907\pi$$
$$380$$ 0 0
$$381$$ −4.03456 −0.206697
$$382$$ 0 0
$$383$$ 5.39114 30.5747i 0.275474 1.56229i −0.461977 0.886892i $$-0.652860\pi$$
0.737451 0.675400i $$-0.236029\pi$$
$$384$$ 0 0
$$385$$ 3.90565 + 3.27723i 0.199050 + 0.167023i
$$386$$ 0 0
$$387$$ 4.30328 + 7.45350i 0.218748 + 0.378883i
$$388$$ 0 0
$$389$$ 11.2323 + 4.08822i 0.569500 + 0.207281i 0.610689 0.791870i $$-0.290892\pi$$
−0.0411892 + 0.999151i $$0.513115\pi$$
$$390$$ 0 0
$$391$$ −15.6819 + 27.1619i −0.793068 + 1.37363i
$$392$$ 0 0
$$393$$ 0.457076 + 2.59221i 0.0230564 + 0.130760i
$$394$$ 0 0
$$395$$ −12.1357 + 10.1831i −0.610615 + 0.512367i
$$396$$ 0 0
$$397$$ 4.00480 1.45763i 0.200995 0.0731562i −0.239561 0.970881i $$-0.577004\pi$$
0.440556 + 0.897725i $$0.354781\pi$$
$$398$$ 0 0
$$399$$ 18.5980 + 4.02980i 0.931065 + 0.201742i
$$400$$ 0 0
$$401$$ 0.433821 0.157898i 0.0216640 0.00788506i −0.331165 0.943573i $$-0.607442\pi$$
0.352829 + 0.935688i $$0.385220\pi$$
$$402$$ 0 0
$$403$$ 10.8487 9.10317i 0.540414 0.453461i
$$404$$ 0 0
$$405$$ 0.276909 + 1.57043i 0.0137597 + 0.0780352i
$$406$$ 0 0
$$407$$ 0.274909 0.476156i 0.0136267 0.0236022i
$$408$$ 0 0
$$409$$ 29.7422 + 10.8253i 1.47066 + 0.535276i 0.948279 0.317438i $$-0.102823\pi$$
0.522378 + 0.852714i $$0.325045\pi$$
$$410$$ 0 0
$$411$$ −1.05715 1.83104i −0.0521456 0.0903188i
$$412$$ 0 0
$$413$$ −9.12181 7.65411i −0.448855 0.376634i
$$414$$ 0 0
$$415$$ −0.653033 + 3.70353i −0.0320561 + 0.181799i
$$416$$ 0 0
$$417$$ 8.44755 0.413678
$$418$$ 0 0
$$419$$ 23.8430 1.16481 0.582403 0.812900i $$-0.302112\pi$$
0.582403 + 0.812900i $$0.302112\pi$$
$$420$$ 0 0
$$421$$ 1.32252 7.50041i 0.0644559 0.365547i −0.935470 0.353405i $$-0.885024\pi$$
0.999926 0.0121424i $$-0.00386514\pi$$
$$422$$ 0 0
$$423$$ 4.22244 + 3.54305i 0.205302 + 0.172269i
$$424$$ 0 0
$$425$$ 3.61975 + 6.26958i 0.175583 + 0.304119i
$$426$$ 0 0
$$427$$ −20.4062 7.42726i −0.987526 0.359430i
$$428$$ 0 0
$$429$$ 2.76430 4.78791i 0.133462 0.231162i
$$430$$ 0 0
$$431$$ −1.04802 5.94360i −0.0504812 0.286293i 0.949108 0.314950i $$-0.101988\pi$$
−0.999589 + 0.0286575i $$0.990877\pi$$
$$432$$ 0 0
$$433$$ −14.2376 + 11.9468i −0.684216 + 0.574126i −0.917235 0.398347i $$-0.869584\pi$$
0.233019 + 0.972472i $$0.425140\pi$$
$$434$$ 0 0
$$435$$ 2.40344 0.874781i 0.115236 0.0419425i
$$436$$ 0 0
$$437$$ 18.7106 2.55445i 0.895049 0.122196i
$$438$$ 0 0
$$439$$ −13.0999 + 4.76797i −0.625223 + 0.227563i −0.635151 0.772388i $$-0.719062\pi$$
0.00992755 + 0.999951i $$0.496840\pi$$
$$440$$ 0 0
$$441$$ −22.0394 + 18.4932i −1.04949 + 0.880630i
$$442$$ 0 0
$$443$$ −2.65351 15.0488i −0.126072 0.714991i −0.980665 0.195692i $$-0.937305\pi$$
0.854593 0.519298i $$-0.173807\pi$$
$$444$$ 0 0
$$445$$ −5.88487 + 10.1929i −0.278970 + 0.483189i
$$446$$ 0 0
$$447$$ −18.7840 6.83683i −0.888455 0.323371i
$$448$$ 0 0
$$449$$ 16.3149 + 28.2582i 0.769947 + 1.33359i 0.937591 + 0.347739i $$0.113051\pi$$
−0.167645 + 0.985847i $$0.553616\pi$$
$$450$$ 0 0
$$451$$ 7.17000 + 6.01635i 0.337622 + 0.283299i
$$452$$ 0 0
$$453$$ 0.952543 5.40214i 0.0447544 0.253815i
$$454$$ 0 0
$$455$$ −23.5721 −1.10508
$$456$$ 0 0
$$457$$ −19.5721 −0.915546 −0.457773 0.889069i $$-0.651353\pi$$
−0.457773 + 0.889069i $$0.651353\pi$$
$$458$$ 0 0
$$459$$ 6.11702 34.6914i 0.285518 1.61925i
$$460$$ 0 0
$$461$$ −24.0645 20.1925i −1.12079 0.940457i −0.122149 0.992512i $$-0.538979\pi$$
−0.998644 + 0.0520545i $$0.983423\pi$$
$$462$$ 0 0
$$463$$ 15.2496 + 26.4132i 0.708711 + 1.22752i 0.965335 + 0.261012i $$0.0840563\pi$$
−0.256624 + 0.966511i $$0.582610\pi$$
$$464$$ 0 0
$$465$$ 2.46471 + 0.897081i 0.114298 + 0.0416011i
$$466$$ 0 0
$$467$$ 3.74239 6.48201i 0.173177 0.299952i −0.766352 0.642421i $$-0.777930\pi$$
0.939529 + 0.342469i $$0.111263\pi$$
$$468$$ 0 0
$$469$$ −10.0371 56.9234i −0.463472 2.62848i
$$470$$ 0 0
$$471$$ −13.5192 + 11.3440i −0.622932 + 0.522702i
$$472$$ 0 0
$$473$$ −4.33788 + 1.57886i −0.199456 + 0.0725960i
$$474$$ 0 0
$$475$$ 1.64879 4.03503i 0.0756516 0.185140i
$$476$$ 0 0
$$477$$ −26.7136 + 9.72296i −1.22313 + 0.445184i
$$478$$ 0 0
$$479$$ −4.59620 + 3.85667i −0.210006 + 0.176216i −0.741723 0.670706i $$-0.765991\pi$$
0.531718 + 0.846922i $$0.321547\pi$$
$$480$$ 0 0
$$481$$ 0.441415 + 2.50339i 0.0201268 + 0.114145i
$$482$$ 0 0
$$483$$ 9.45679 16.3796i 0.430299 0.745299i
$$484$$ 0 0
$$485$$ 3.27804 + 1.19311i 0.148848 + 0.0541763i
$$486$$ 0 0
$$487$$ −3.24803 5.62576i −0.147182 0.254927i 0.783003 0.622018i $$-0.213687\pi$$
−0.930185 + 0.367091i $$0.880354\pi$$
$$488$$ 0 0
$$489$$ 2.55288 + 2.14212i 0.115445 + 0.0968699i
$$490$$ 0 0
$$491$$ 5.01124 28.4202i 0.226154 1.28258i −0.634312 0.773077i $$-0.718717\pi$$
0.860467 0.509507i $$-0.170172\pi$$
$$492$$ 0 0
$$493$$ 19.3461 0.871306
$$494$$ 0 0
$$495$$ −2.32935 −0.104696
$$496$$ 0 0
$$497$$ 0.541922 3.07339i 0.0243085 0.137860i
$$498$$ 0 0
$$499$$ −9.63514 8.08484i −0.431328 0.361927i 0.401124 0.916024i $$-0.368619\pi$$
−0.832453 + 0.554096i $$0.813064\pi$$
$$500$$ 0 0
$$501$$ −10.2839 17.8123i −0.459452 0.795794i
$$502$$ 0 0
$$503$$ −14.4854 5.27226i −0.645872 0.235078i −0.00174715 0.999998i $$-0.500556\pi$$
−0.644125 + 0.764920i $$0.722778\pi$$
$$504$$ 0 0
$$505$$ −5.28017 + 9.14552i −0.234964 + 0.406970i
$$506$$ 0 0
$$507$$ 2.27798 + 12.9191i 0.101169 + 0.573755i
$$508$$ 0 0
$$509$$ −4.58561 + 3.84778i −0.203254 + 0.170550i −0.738733 0.673998i $$-0.764575\pi$$
0.535479 + 0.844548i $$0.320131\pi$$
$$510$$ 0 0
$$511$$ 56.2843 20.4858i 2.48987 0.906239i
$$512$$ 0 0
$$513$$ −18.7663 + 9.88356i −0.828554 + 0.436370i
$$514$$ 0 0
$$515$$ 10.8558 3.95117i 0.478362 0.174109i
$$516$$ 0 0
$$517$$ −2.26478 + 1.90037i −0.0996047 + 0.0835783i
$$518$$ 0 0
$$519$$ 1.82635 + 10.3578i 0.0801680 + 0.454655i
$$520$$ 0 0
$$521$$ 8.62104 14.9321i 0.377695 0.654187i −0.613032 0.790058i $$-0.710050\pi$$
0.990726 + 0.135872i $$0.0433835\pi$$
$$522$$ 0 0
$$523$$ 0.113607 + 0.0413496i 0.00496770 + 0.00180809i 0.344503 0.938785i $$-0.388048\pi$$
−0.339535 + 0.940593i $$0.610270\pi$$
$$524$$ 0 0
$$525$$ −2.18284 3.78080i −0.0952671 0.165007i
$$526$$ 0 0
$$527$$ 15.1978 + 12.7525i 0.662027 + 0.555507i
$$528$$ 0 0
$$529$$ −0.734698 + 4.16668i −0.0319434 + 0.181160i
$$530$$ 0 0
$$531$$ 5.44028 0.236088
$$532$$ 0 0
$$533$$ −43.2737 −1.87439
$$534$$ 0 0
$$535$$ 1.34897 7.65037i 0.0583209 0.330754i
$$536$$ 0 0
$$537$$ −12.5353 10.5184i −0.540940 0.453902i
$$538$$ 0 0
$$539$$ −7.71574 13.3640i −0.332340 0.575630i
$$540$$ 0 0
$$541$$ 36.3600 + 13.2340i 1.56324 + 0.568973i 0.971476 0.237139i $$-0.0762097\pi$$
0.591764 + 0.806112i $$0.298432\pi$$
$$542$$ 0 0
$$543$$ −5.54640 + 9.60665i −0.238019 + 0.412261i
$$544$$ 0 0
$$545$$ −2.29437 13.0120i −0.0982800 0.557373i
$$546$$ 0 0
$$547$$ −7.34449 + 6.16276i −0.314028 + 0.263501i −0.786154 0.618030i $$-0.787931\pi$$
0.472127 + 0.881531i $$0.343486\pi$$
$$548$$ 0 0
$$549$$ 9.32303 3.39331i 0.397897 0.144823i
$$550$$ 0 0
$$551$$ −7.13519 9.20719i −0.303969 0.392240i
$$552$$ 0 0
$$553$$ 67.9030 24.7147i 2.88753 1.05098i
$$554$$ 0 0
$$555$$ −0.360649 + 0.302621i −0.0153087 + 0.0128455i
$$556$$ 0 0
$$557$$ 5.99528 + 34.0009i 0.254028 + 1.44067i 0.798555 + 0.601922i $$0.205598\pi$$
−0.544527 + 0.838744i $$0.683291\pi$$
$$558$$ 0 0
$$559$$ 10.6714 18.4834i 0.451351 0.781762i
$$560$$ 0 0
$$561$$ 7.27784 + 2.64892i 0.307271 + 0.111837i
$$562$$ 0 0
$$563$$ 21.6196 + 37.4463i 0.911158 + 1.57817i 0.812431 + 0.583057i $$0.198144\pi$$
0.0987270 + 0.995115i $$0.468523\pi$$
$$564$$ 0 0
$$565$$ −1.41031 1.18339i −0.0593324 0.0497858i
$$566$$ 0 0
$$567$$ 1.26307 7.16324i 0.0530440 0.300828i
$$568$$ 0 0
$$569$$ −0.172138 −0.00721638 −0.00360819 0.999993i $$-0.501149\pi$$
−0.00360819 + 0.999993i $$0.501149\pi$$
$$570$$ 0 0
$$571$$ −28.8203 −1.20609 −0.603046 0.797706i $$-0.706046\pi$$
−0.603046 + 0.797706i $$0.706046\pi$$
$$572$$ 0 0
$$573$$ 4.29940 24.3831i 0.179610 1.01862i
$$574$$ 0 0
$$575$$ −3.31875 2.78477i −0.138402 0.116133i
$$576$$ 0 0
$$577$$ −1.03745 1.79692i −0.0431898 0.0748069i 0.843622 0.536937i $$-0.180419\pi$$
−0.886812 + 0.462130i $$0.847085\pi$$
$$578$$ 0 0
$$579$$ −12.6517 4.60486i −0.525789 0.191371i
$$580$$ 0 0
$$581$$ 8.57682 14.8555i 0.355826 0.616309i
$$582$$ 0 0
$$583$$ −2.64776 15.0162i −0.109659 0.621908i
$$584$$ 0 0
$$585$$ 8.24986 6.92245i 0.341090 0.286208i
$$586$$ 0 0
$$587$$ −28.5583 + 10.3944i −1.17873 + 0.429022i −0.855752 0.517385i $$-0.826905\pi$$
−0.322975 + 0.946407i $$0.604683\pi$$
$$588$$ 0 0
$$589$$ 0.463930 11.9363i 0.0191159 0.491825i
$$590$$ 0 0
$$591$$ −3.06187 + 1.11443i −0.125949 + 0.0458416i
$$592$$ 0 0
$$593$$ −8.44741 + 7.08822i −0.346894 + 0.291078i −0.799541 0.600611i $$-0.794924\pi$$
0.452648 + 0.891689i $$0.350480\pi$$
$$594$$ 0 0
$$595$$ −5.73416 32.5200i −0.235078 1.33319i
$$596$$ 0 0
$$597$$ 8.85569 15.3385i 0.362439 0.627763i
$$598$$ 0 0
$$599$$ −23.2641 8.46746i −0.950547 0.345971i −0.180225 0.983625i $$-0.557683\pi$$
−0.770322 + 0.637655i $$0.779905\pi$$
$$600$$ 0 0
$$601$$ −20.6916 35.8388i −0.844026 1.46190i −0.886464 0.462797i $$-0.846846\pi$$
0.0424380 0.999099i $$-0.486487\pi$$
$$602$$ 0 0
$$603$$ 20.2296 + 16.9747i 0.823814 + 0.691262i
$$604$$ 0 0
$$605$$ −1.69318 + 9.60248i −0.0688374 + 0.390396i
$$606$$ 0 0
$$607$$ 27.0263 1.09696 0.548481 0.836163i $$-0.315206\pi$$
0.548481 + 0.836163i $$0.315206\pi$$
$$608$$ 0 0
$$609$$ −11.6665 −0.472749
$$610$$ 0 0
$$611$$ 2.37356 13.4611i 0.0960239 0.544579i
$$612$$ 0 0
$$613$$ 5.62519 + 4.72010i 0.227199 + 0.190643i 0.749280 0.662253i $$-0.230400\pi$$
−0.522081 + 0.852896i $$0.674844\pi$$
$$614$$ 0 0
$$615$$ −4.00727 6.94079i −0.161589 0.279880i
$$616$$ 0 0
$$617$$ −15.4866 5.63667i −0.623468 0.226924i 0.0109180 0.999940i $$-0.496525\pi$$
−0.634386 + 0.773017i $$0.718747\pi$$
$$618$$ 0 0
$$619$$ 5.27186 9.13112i 0.211894 0.367011i −0.740413 0.672152i $$-0.765370\pi$$
0.952307 + 0.305141i $$0.0987036\pi$$
$$620$$ 0 0
$$621$$ 3.66061 + 20.7603i 0.146895 + 0.833083i
$$622$$ 0 0
$$623$$ 41.1256 34.5085i 1.64766 1.38255i
$$624$$ 0 0
$$625$$ −0.939693 + 0.342020i −0.0375877 + 0.0136808i
$$626$$ 0 0
$$627$$ −1.42352 4.44063i −0.0568501 0.177342i
$$628$$ 0 0
$$629$$ −3.34629 + 1.21795i −0.133425 + 0.0485629i
$$630$$ 0 0
$$631$$ −12.0300 + 10.0944i −0.478907 + 0.401850i −0.850031 0.526733i $$-0.823417\pi$$
0.371124 + 0.928583i $$0.378972\pi$$
$$632$$ 0 0
$$633$$ 2.62527 + 14.8886i 0.104345 + 0.591771i
$$634$$ 0 0
$$635$$ 2.10768 3.65061i 0.0836407 0.144870i
$$636$$ 0 0
$$637$$ 67.0427 + 24.4016i 2.65633 + 0.966825i
$$638$$ 0 0
$$639$$ 0.712904 + 1.23479i 0.0282020 + 0.0488474i
$$640$$ 0 0
$$641$$ 2.38617 + 2.00224i 0.0942481 + 0.0790836i 0.688694 0.725052i $$-0.258184\pi$$
−0.594446 + 0.804135i $$0.702629\pi$$
$$642$$ 0 0
$$643$$ 3.53665 20.0573i 0.139472 0.790983i −0.832169 0.554522i $$-0.812901\pi$$
0.971641 0.236462i $$-0.0759877\pi$$
$$644$$ 0 0
$$645$$ 3.95280 0.155641
$$646$$ 0 0
$$647$$ −2.01187 −0.0790946 −0.0395473 0.999218i $$-0.512592\pi$$
−0.0395473 + 0.999218i $$0.512592\pi$$
$$648$$ 0 0
$$649$$ −0.506703 + 2.87366i −0.0198898 + 0.112801i
$$650$$ 0 0
$$651$$ −9.16485 7.69022i −0.359199 0.301404i
$$652$$ 0 0
$$653$$ −0.326876 0.566166i −0.0127916 0.0221558i 0.859559 0.511037i $$-0.170738\pi$$
−0.872350 + 0.488881i $$0.837405\pi$$
$$654$$ 0 0
$$655$$ −2.58430 0.940609i −0.100977 0.0367526i
$$656$$ 0 0
$$657$$ −13.6825 + 23.6988i −0.533806 + 0.924579i
$$658$$ 0 0
$$659$$ −0.256516 1.45477i −0.00999243 0.0566699i 0.979404 0.201911i $$-0.0647153\pi$$
−0.989396 + 0.145241i $$0.953604\pi$$
$$660$$ 0 0
$$661$$ −1.31742 + 1.10545i −0.0512418 + 0.0429970i −0.668049 0.744117i $$-0.732870\pi$$
0.616807 + 0.787114i $$0.288426\pi$$
$$662$$ 0 0
$$663$$ −33.6482 + 12.2469i −1.30679 + 0.475631i
$$664$$ 0 0
$$665$$ −13.3620 + 14.7229i −0.518157 + 0.570931i
$$666$$ 0 0
$$667$$ −10.8791 + 3.95967i −0.421241 + 0.153319i
$$668$$ 0 0
$$669$$ −16.2840 + 13.6639i −0.629577 + 0.528278i
$$670$$ 0 0
$$671$$ 0.924067 + 5.24064i 0.0356732 + 0.202313i
$$672$$ 0 0
$$673$$ 15.1537 26.2469i 0.584130 1.01174i −0.410853 0.911702i $$-0.634769\pi$$
0.994983 0.100042i $$-0.0318977\pi$$
$$674$$ 0 0
$$675$$ 4.57244 + 1.66423i 0.175993 + 0.0640563i
$$676$$ 0 0
$$677$$ 13.5349 + 23.4432i 0.520190 + 0.900995i 0.999724 + 0.0234721i $$0.00747210\pi$$
−0.479535 + 0.877523i $$0.659195\pi$$
$$678$$ 0 0
$$679$$ −12.1892 10.2279i −0.467777 0.392512i
$$680$$ 0 0
$$681$$ −0.932270 + 5.28717i −0.0357247 + 0.202605i
$$682$$ 0 0
$$683$$ −49.3960 −1.89008 −0.945042 0.326948i $$-0.893980\pi$$
−0.945042 + 0.326948i $$0.893980\pi$$
$$684$$ 0 0
$$685$$ 2.20906 0.0844038
$$686$$ 0 0
$$687$$ 0.172877 0.980433i 0.00659566 0.0374059i
$$688$$ 0 0
$$689$$ 54.0034 + 45.3142i 2.05737 + 1.72633i
$$690$$ 0 0
$$691$$ 2.99171 + 5.18179i 0.113810 + 0.197125i 0.917303 0.398189i $$-0.130361\pi$$
−0.803493 + 0.595314i $$0.797028\pi$$
$$692$$ 0 0
$$693$$ 9.98415 + 3.63393i 0.379267 + 0.138042i
$$694$$ 0 0
$$695$$ −4.41306 + 7.64364i −0.167397 + 0.289940i
$$696$$ 0 0
$$697$$ −10.5268 59.7003i −0.398730 2.26131i
$$698$$ 0 0
$$699$$ 8.76499 7.35470i 0.331522 0.278180i
$$700$$ 0 0
$$701$$ 11.2185 4.08320i 0.423717 0.154220i −0.121356 0.992609i $$-0.538724\pi$$
0.545073 + 0.838389i $$0.316502\pi$$
$$702$$ 0 0
$$703$$ 1.81382 + 1.14336i 0.0684094 + 0.0431227i
$$704$$ 0 0
$$705$$ 2.37887 0.865837i 0.0895933 0.0326093i
$$706$$ 0 0
$$707$$ 36.8997 30.9625i 1.38776 1.16447i
$$708$$ 0 0
$$709$$ 4.35271 + 24.6854i 0.163469 + 0.927080i 0.950629 + 0.310331i $$0.100440\pi$$
−0.787159 + 0.616750i $$0.788449\pi$$
$$710$$ 0 0
$$711$$ −16.5070 + 28.5909i −0.619061 + 1.07224i
$$712$$ 0 0
$$713$$ −11.1564 4.06061i −0.417812 0.152071i
$$714$$ 0 0
$$715$$ 2.88818 + 5.00248i 0.108012 + 0.187082i
$$716$$ 0 0
$$717$$ −6.60479 5.54208i −0.246660 0.206973i
$$718$$ 0 0
$$719$$ 3.32244 18.8425i 0.123906 0.702706i −0.858046 0.513574i $$-0.828321\pi$$
0.981952 0.189132i $$-0.0605676\pi$$
$$720$$ 0 0
$$721$$ −52.6946 −1.96245
$$722$$ 0 0
$$723$$ −12.7329 −0.473540
$$724$$ 0 0
$$725$$ −0.464041 + 2.63171i −0.0172341 + 0.0977392i
$$726$$ 0 0
$$727$$ −5.68566 4.77084i −0.210870 0.176941i 0.531235 0.847224i $$-0.321728\pi$$
−0.742105 + 0.670284i $$0.766172\pi$$
$$728$$ 0 0
$$729$$ −5.32418 9.22175i −0.197192 0.341546i
$$730$$ 0 0
$$731$$ 28.0955 + 10.2259i 1.03915 + 0.378220i
$$732$$ 0 0
$$733$$ −1.59766 + 2.76722i −0.0590108 + 0.102210i −0.894022 0.448024i $$-0.852128\pi$$
0.835011 + 0.550234i $$0.185461\pi$$
$$734$$ 0 0
$$735$$ 2.29451 + 13.0128i 0.0846344 + 0.479986i
$$736$$ 0 0
$$737$$ −10.8505 + 9.10465i −0.399683 + 0.335374i
$$738$$ 0 0
$$739$$ 1.47844 0.538109i 0.0543853 0.0197946i −0.314684 0.949196i $$-0.601899\pi$$
0.369070 + 0.929402i $$0.379676\pi$$
$$740$$ 0 0
$$741$$ 18.2386 + 11.4969i 0.670010 + 0.422350i
$$742$$ 0 0
$$743$$ −10.6647 + 3.88164i −0.391251 + 0.142404i −0.530152 0.847903i $$-0.677865\pi$$
0.138901 + 0.990306i $$0.455643\pi$$
$$744$$ 0 0
$$745$$ 15.9991 13.4249i 0.586163 0.491849i
$$746$$ 0 0
$$747$$ 1.36088 + 7.71795i 0.0497921 + 0.282385i
$$748$$ 0 0
$$749$$ −17.7171 + 30.6869i −0.647369 + 1.12128i
$$750$$ 0 0
$$751$$ −27.5103 10.0129i −1.00386 0.365377i −0.212791 0.977098i $$-0.568255\pi$$
−0.791074 + 0.611721i $$0.790478\pi$$
$$752$$ 0 0
$$753$$ 10.6227 + 18.3991i 0.387114 + 0.670501i
$$754$$ 0 0
$$755$$ 4.39043 + 3.68401i 0.159784 + 0.134075i
$$756$$ 0 0
$$757$$ 6.71567 38.0865i 0.244085 1.38428i −0.578522 0.815667i $$-0.696370\pi$$
0.822607 0.568610i $$-0.192519\pi$$
$$758$$ 0 0
$$759$$ −4.63479 −0.168232
$$760$$ 0 0
$$761$$ 31.8253 1.15367 0.576833 0.816862i $$-0.304288\pi$$
0.576833 + 0.816862i $$0.304288\pi$$
$$762$$ 0 0
$$763$$ −10.4654 + 59.3521i −0.378872 + 2.14869i
$$764$$ 0 0
$$765$$ 11.5571 + 9.69754i 0.417847 + 0.350615i
$$766$$ 0 0
$$767$$ −6.74546 11.6835i −0.243565 0.421866i
$$768$$ 0 0
$$769$$ −8.83346 3.21512i −0.318543 0.115940i 0.177800 0.984067i $$-0.443102\pi$$
−0.496343 + 0.868127i $$0.665324\pi$$
$$770$$ 0 0
$$771$$ 1.20894 2.09394i 0.0435388 0.0754115i
$$772$$ 0 0
$$773$$ 2.61084 + 14.8068i 0.0939054 + 0.532564i 0.995077 + 0.0991019i $$0.0315970\pi$$
−0.901172 + 0.433462i $$0.857292\pi$$
$$774$$ 0 0
$$775$$ −2.09929 + 1.76152i −0.0754088 + 0.0632755i
$$776$$ 0 0
$$777$$ 2.01794 0.734471i 0.0723933 0.0263490i
$$778$$ 0 0
$$779$$ −24.5301 + 27.0284i −0.878880 + 0.968393i
$$780$$ 0 0
$$781$$ −0.718636 + 0.261562i −0.0257148 + 0.00935942i
$$782$$ 0 0
$$783$$ 9.96098 8.35826i 0.355976 0.298700i
$$784$$ 0 0
$$785$$ −3.20189 18.1588i −0.114280 0.648116i
$$786$$ 0 0
$$787$$ −13.6930 + 23.7170i −0.488104 + 0.845421i