# Properties

 Label 380.2.r.a.49.3 Level $380$ Weight $2$ Character 380.49 Analytic conductor $3.034$ Analytic rank $0$ Dimension $20$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(49,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("380.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.r (of order $$6$$, degree $$2$$, 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: $$20$$ Relative dimension: $$10$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + 124617 x^{4} - 24768 x^{2} + 4096$$ x^20 - 20*x^18 + 261*x^16 - 1994*x^14 + 11074*x^12 - 39211*x^10 + 99376*x^8 - 134299*x^6 + 124617*x^4 - 24768*x^2 + 4096 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 49.3 Root $$-1.74361 + 1.00667i$$ of defining polynomial Character $$\chi$$ $$=$$ 380.49 Dual form 380.2.r.a.349.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.74361 - 1.00667i) q^{3} +(-1.95659 + 1.08248i) q^{5} +1.34403i q^{7} +(0.526784 + 0.912416i) q^{9} +O(q^{10})$$ $$q+(-1.74361 - 1.00667i) q^{3} +(-1.95659 + 1.08248i) q^{5} +1.34403i q^{7} +(0.526784 + 0.912416i) q^{9} +5.25594 q^{11} +(2.10918 - 1.21773i) q^{13} +(4.50123 + 0.0822214i) q^{15} +(-1.17765 - 0.679914i) q^{17} +(2.89815 + 3.25587i) q^{19} +(1.35300 - 2.34346i) q^{21} +(7.05514 - 4.07329i) q^{23} +(2.65647 - 4.23594i) q^{25} +3.91884i q^{27} +(-1.03597 - 1.79435i) q^{29} -0.513207 q^{31} +(-9.16431 - 5.29102i) q^{33} +(-1.45488 - 2.62971i) q^{35} +5.57175i q^{37} -4.90344 q^{39} +(2.70353 - 4.68265i) q^{41} +(11.0197 + 6.36221i) q^{43} +(-2.01837 - 1.21499i) q^{45} +(-2.82785 + 1.63266i) q^{47} +5.19359 q^{49} +(1.36890 + 2.37101i) q^{51} +(-10.1892 + 5.88276i) q^{53} +(-10.2837 + 5.68946i) q^{55} +(-1.77564 - 8.59447i) q^{57} +(0.0175979 - 0.0304805i) q^{59} +(0.518372 + 0.897846i) q^{61} +(-1.22631 + 0.708011i) q^{63} +(-2.80861 + 4.66574i) q^{65} +(-0.664028 + 0.383377i) q^{67} -16.4019 q^{69} +(5.68450 - 9.84583i) q^{71} +(1.86429 + 1.07635i) q^{73} +(-8.89606 + 4.71162i) q^{75} +7.06413i q^{77} +(-6.48576 + 11.2337i) q^{79} +(5.52535 - 9.57019i) q^{81} +4.20304i q^{83} +(3.04016 + 0.0555329i) q^{85} +4.17153i q^{87} +(-3.65426 - 6.32937i) q^{89} +(1.63667 + 2.83479i) q^{91} +(0.894833 + 0.516632i) q^{93} +(-9.19491 - 3.23321i) q^{95} +(-0.721716 - 0.416683i) q^{97} +(2.76875 + 4.79561i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20 q + q^{5} + 10 q^{9}+O(q^{10})$$ 20 * q + q^5 + 10 * q^9 $$20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65} + 48 q^{69} - 2 q^{71} + 46 q^{75} - 16 q^{79} + 26 q^{81} - 39 q^{85} - 40 q^{89} - 4 q^{91} - 43 q^{95} - 20 q^{99}+O(q^{100})$$ 20 * q + q^5 + 10 * q^9 - 5 * q^15 + 14 * q^19 - 8 * q^21 + 9 * q^25 - 16 * q^29 + 8 * q^31 - 2 * q^35 - 8 * q^39 + 26 * q^41 - 32 * q^45 - 44 * q^49 + 26 * q^51 - 12 * q^55 + 4 * q^59 + 2 * q^61 - 18 * q^65 + 48 * q^69 - 2 * q^71 + 46 * q^75 - 16 * q^79 + 26 * q^81 - 39 * q^85 - 40 * q^89 - 4 * q^91 - 43 * q^95 - 20 * q^99

## Character values

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

 $$n$$ $$21$$ $$77$$ $$191$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$

## 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
$$3$$ −1.74361 1.00667i −1.00667 0.581203i −0.0964577 0.995337i $$-0.530751\pi$$
−0.910216 + 0.414134i $$0.864085\pi$$
$$4$$ 0 0
$$5$$ −1.95659 + 1.08248i −0.875013 + 0.484100i
$$6$$ 0 0
$$7$$ 1.34403i 0.507994i 0.967205 + 0.253997i $$0.0817454\pi$$
−0.967205 + 0.253997i $$0.918255\pi$$
$$8$$ 0 0
$$9$$ 0.526784 + 0.912416i 0.175595 + 0.304139i
$$10$$ 0 0
$$11$$ 5.25594 1.58473 0.792363 0.610050i $$-0.208851\pi$$
0.792363 + 0.610050i $$0.208851\pi$$
$$12$$ 0 0
$$13$$ 2.10918 1.21773i 0.584980 0.337738i −0.178130 0.984007i $$-0.557005\pi$$
0.763110 + 0.646269i $$0.223671\pi$$
$$14$$ 0 0
$$15$$ 4.50123 + 0.0822214i 1.16221 + 0.0212295i
$$16$$ 0 0
$$17$$ −1.17765 0.679914i −0.285621 0.164903i 0.350344 0.936621i $$-0.386065\pi$$
−0.635965 + 0.771718i $$0.719398\pi$$
$$18$$ 0 0
$$19$$ 2.89815 + 3.25587i 0.664882 + 0.746949i
$$20$$ 0 0
$$21$$ 1.35300 2.34346i 0.295248 0.511384i
$$22$$ 0 0
$$23$$ 7.05514 4.07329i 1.47110 0.849339i 0.471625 0.881799i $$-0.343668\pi$$
0.999473 + 0.0324603i $$0.0103342\pi$$
$$24$$ 0 0
$$25$$ 2.65647 4.23594i 0.531294 0.847187i
$$26$$ 0 0
$$27$$ 3.91884i 0.754182i
$$28$$ 0 0
$$29$$ −1.03597 1.79435i −0.192375 0.333203i 0.753662 0.657262i $$-0.228286\pi$$
−0.946037 + 0.324059i $$0.894952\pi$$
$$30$$ 0 0
$$31$$ −0.513207 −0.0921747 −0.0460873 0.998937i $$-0.514675\pi$$
−0.0460873 + 0.998937i $$0.514675\pi$$
$$32$$ 0 0
$$33$$ −9.16431 5.29102i −1.59530 0.921048i
$$34$$ 0 0
$$35$$ −1.45488 2.62971i −0.245920 0.444501i
$$36$$ 0 0
$$37$$ 5.57175i 0.915991i 0.888955 + 0.457995i $$0.151432\pi$$
−0.888955 + 0.457995i $$0.848568\pi$$
$$38$$ 0 0
$$39$$ −4.90344 −0.785179
$$40$$ 0 0
$$41$$ 2.70353 4.68265i 0.422220 0.731307i −0.573936 0.818900i $$-0.694584\pi$$
0.996156 + 0.0875933i $$0.0279176\pi$$
$$42$$ 0 0
$$43$$ 11.0197 + 6.36221i 1.68048 + 0.970228i 0.961339 + 0.275369i $$0.0888000\pi$$
0.719146 + 0.694859i $$0.244533\pi$$
$$44$$ 0 0
$$45$$ −2.01837 1.21499i −0.300881 0.181120i
$$46$$ 0 0
$$47$$ −2.82785 + 1.63266i −0.412485 + 0.238148i −0.691857 0.722035i $$-0.743207\pi$$
0.279372 + 0.960183i $$0.409874\pi$$
$$48$$ 0 0
$$49$$ 5.19359 0.741942
$$50$$ 0 0
$$51$$ 1.36890 + 2.37101i 0.191685 + 0.332008i
$$52$$ 0 0
$$53$$ −10.1892 + 5.88276i −1.39960 + 0.808060i −0.994351 0.106146i $$-0.966149\pi$$
−0.405250 + 0.914206i $$0.632815\pi$$
$$54$$ 0 0
$$55$$ −10.2837 + 5.68946i −1.38666 + 0.767166i
$$56$$ 0 0
$$57$$ −1.77564 8.59447i −0.235190 1.13837i
$$58$$ 0 0
$$59$$ 0.0175979 0.0304805i 0.00229105 0.00396822i −0.864878 0.501983i $$-0.832604\pi$$
0.867169 + 0.498015i $$0.165937\pi$$
$$60$$ 0 0
$$61$$ 0.518372 + 0.897846i 0.0663707 + 0.114957i 0.897301 0.441419i $$-0.145525\pi$$
−0.830930 + 0.556376i $$0.812191\pi$$
$$62$$ 0 0
$$63$$ −1.22631 + 0.708011i −0.154501 + 0.0892010i
$$64$$ 0 0
$$65$$ −2.80861 + 4.66574i −0.348366 + 0.578714i
$$66$$ 0 0
$$67$$ −0.664028 + 0.383377i −0.0811239 + 0.0468369i −0.540013 0.841657i $$-0.681581\pi$$
0.458889 + 0.888493i $$0.348247\pi$$
$$68$$ 0 0
$$69$$ −16.4019 −1.97455
$$70$$ 0 0
$$71$$ 5.68450 9.84583i 0.674625 1.16849i −0.301953 0.953323i $$-0.597638\pi$$
0.976578 0.215163i $$-0.0690282\pi$$
$$72$$ 0 0
$$73$$ 1.86429 + 1.07635i 0.218199 + 0.125977i 0.605116 0.796137i $$-0.293127\pi$$
−0.386917 + 0.922115i $$0.626460\pi$$
$$74$$ 0 0
$$75$$ −8.89606 + 4.71162i −1.02723 + 0.544051i
$$76$$ 0 0
$$77$$ 7.06413i 0.805032i
$$78$$ 0 0
$$79$$ −6.48576 + 11.2337i −0.729705 + 1.26389i 0.227302 + 0.973824i $$0.427009\pi$$
−0.957008 + 0.290062i $$0.906324\pi$$
$$80$$ 0 0
$$81$$ 5.52535 9.57019i 0.613928 1.06335i
$$82$$ 0 0
$$83$$ 4.20304i 0.461343i 0.973032 + 0.230672i $$0.0740923\pi$$
−0.973032 + 0.230672i $$0.925908\pi$$
$$84$$ 0 0
$$85$$ 3.04016 + 0.0555329i 0.329752 + 0.00602339i
$$86$$ 0 0
$$87$$ 4.17153i 0.447235i
$$88$$ 0 0
$$89$$ −3.65426 6.32937i −0.387351 0.670912i 0.604741 0.796422i $$-0.293277\pi$$
−0.992092 + 0.125510i $$0.959943\pi$$
$$90$$ 0 0
$$91$$ 1.63667 + 2.83479i 0.171569 + 0.297166i
$$92$$ 0 0
$$93$$ 0.894833 + 0.516632i 0.0927898 + 0.0535722i
$$94$$ 0 0
$$95$$ −9.19491 3.23321i −0.943378 0.331720i
$$96$$ 0 0
$$97$$ −0.721716 0.416683i −0.0732791 0.0423077i 0.462913 0.886404i $$-0.346804\pi$$
−0.536192 + 0.844096i $$0.680138\pi$$
$$98$$ 0 0
$$99$$ 2.76875 + 4.79561i 0.278269 + 0.481977i
$$100$$ 0 0
$$101$$ −7.40992 12.8344i −0.737315 1.27707i −0.953700 0.300759i $$-0.902760\pi$$
0.216385 0.976308i $$-0.430573\pi$$
$$102$$ 0 0
$$103$$ 9.40773i 0.926971i −0.886104 0.463486i $$-0.846599\pi$$
0.886104 0.463486i $$-0.153401\pi$$
$$104$$ 0 0
$$105$$ −0.110508 + 6.04977i −0.0107845 + 0.590397i
$$106$$ 0 0
$$107$$ 12.8130i 1.23868i −0.785124 0.619338i $$-0.787401\pi$$
0.785124 0.619338i $$-0.212599\pi$$
$$108$$ 0 0
$$109$$ 0.996875 1.72664i 0.0954833 0.165382i −0.814327 0.580406i $$-0.802894\pi$$
0.909810 + 0.415025i $$0.136227\pi$$
$$110$$ 0 0
$$111$$ 5.60894 9.71497i 0.532377 0.922104i
$$112$$ 0 0
$$113$$ 8.34647i 0.785170i 0.919716 + 0.392585i $$0.128419\pi$$
−0.919716 + 0.392585i $$0.871581\pi$$
$$114$$ 0 0
$$115$$ −9.39474 + 15.6068i −0.876064 + 1.45534i
$$116$$ 0 0
$$117$$ 2.22216 + 1.28296i 0.205439 + 0.118610i
$$118$$ 0 0
$$119$$ 0.913823 1.58279i 0.0837700 0.145094i
$$120$$ 0 0
$$121$$ 16.6249 1.51136
$$122$$ 0 0
$$123$$ −9.42780 + 5.44314i −0.850076 + 0.490791i
$$124$$ 0 0
$$125$$ −0.612300 + 11.1636i −0.0547658 + 0.998499i
$$126$$ 0 0
$$127$$ 17.8240 10.2907i 1.58163 0.913153i 0.587005 0.809583i $$-0.300307\pi$$
0.994622 0.103569i $$-0.0330264\pi$$
$$128$$ 0 0
$$129$$ −12.8093 22.1864i −1.12780 1.95341i
$$130$$ 0 0
$$131$$ −5.36554 + 9.29339i −0.468790 + 0.811967i −0.999364 0.0356712i $$-0.988643\pi$$
0.530574 + 0.847639i $$0.321976\pi$$
$$132$$ 0 0
$$133$$ −4.37598 + 3.89519i −0.379446 + 0.337756i
$$134$$ 0 0
$$135$$ −4.24207 7.66756i −0.365100 0.659919i
$$136$$ 0 0
$$137$$ 14.8771 8.58931i 1.27104 0.733834i 0.295855 0.955233i $$-0.404396\pi$$
0.975183 + 0.221399i $$0.0710622\pi$$
$$138$$ 0 0
$$139$$ 3.66394 + 6.34613i 0.310771 + 0.538272i 0.978530 0.206106i $$-0.0660793\pi$$
−0.667758 + 0.744378i $$0.732746\pi$$
$$140$$ 0 0
$$141$$ 6.57423 0.553650
$$142$$ 0 0
$$143$$ 11.0857 6.40033i 0.927033 0.535223i
$$144$$ 0 0
$$145$$ 3.96932 + 2.38939i 0.329634 + 0.198428i
$$146$$ 0 0
$$147$$ −9.05560 5.22825i −0.746893 0.431219i
$$148$$ 0 0
$$149$$ −6.12292 + 10.6052i −0.501609 + 0.868812i 0.498389 + 0.866953i $$0.333925\pi$$
−0.999998 + 0.00185904i $$0.999408\pi$$
$$150$$ 0 0
$$151$$ −11.5577 −0.940549 −0.470274 0.882520i $$-0.655845\pi$$
−0.470274 + 0.882520i $$0.655845\pi$$
$$152$$ 0 0
$$153$$ 1.43267i 0.115825i
$$154$$ 0 0
$$155$$ 1.00413 0.555537i 0.0806540 0.0446218i
$$156$$ 0 0
$$157$$ −3.58528 2.06996i −0.286137 0.165201i 0.350062 0.936727i $$-0.386161\pi$$
−0.636198 + 0.771526i $$0.719494\pi$$
$$158$$ 0 0
$$159$$ 23.6881 1.87859
$$160$$ 0 0
$$161$$ 5.47460 + 9.48229i 0.431459 + 0.747309i
$$162$$ 0 0
$$163$$ 9.41672i 0.737575i −0.929514 0.368787i $$-0.879773\pi$$
0.929514 0.368787i $$-0.120227\pi$$
$$164$$ 0 0
$$165$$ 23.6582 + 0.432151i 1.84179 + 0.0336429i
$$166$$ 0 0
$$167$$ −11.8395 + 6.83551i −0.916164 + 0.528948i −0.882409 0.470482i $$-0.844080\pi$$
−0.0337550 + 0.999430i $$0.510747\pi$$
$$168$$ 0 0
$$169$$ −3.53425 + 6.12151i −0.271866 + 0.470885i
$$170$$ 0 0
$$171$$ −1.44401 + 4.35946i −0.110426 + 0.333376i
$$172$$ 0 0
$$173$$ 10.1999 + 5.88891i 0.775484 + 0.447726i 0.834827 0.550512i $$-0.185567\pi$$
−0.0593437 + 0.998238i $$0.518901\pi$$
$$174$$ 0 0
$$175$$ 5.69321 + 3.57037i 0.430366 + 0.269894i
$$176$$ 0 0
$$177$$ −0.0613678 + 0.0354307i −0.00461269 + 0.00266314i
$$178$$ 0 0
$$179$$ 16.5727 1.23870 0.619350 0.785115i $$-0.287396\pi$$
0.619350 + 0.785115i $$0.287396\pi$$
$$180$$ 0 0
$$181$$ 7.19552 + 12.4630i 0.534839 + 0.926368i 0.999171 + 0.0407069i $$0.0129610\pi$$
−0.464332 + 0.885661i $$0.653706\pi$$
$$182$$ 0 0
$$183$$ 2.08733i 0.154300i
$$184$$ 0 0
$$185$$ −6.03132 10.9016i −0.443431 0.801504i
$$186$$ 0 0
$$187$$ −6.18964 3.57359i −0.452631 0.261327i
$$188$$ 0 0
$$189$$ −5.26703 −0.383120
$$190$$ 0 0
$$191$$ −5.97170 −0.432097 −0.216049 0.976383i $$-0.569317\pi$$
−0.216049 + 0.976383i $$0.569317\pi$$
$$192$$ 0 0
$$193$$ −14.1046 8.14331i −1.01527 0.586168i −0.102542 0.994729i $$-0.532698\pi$$
−0.912731 + 0.408560i $$0.866031\pi$$
$$194$$ 0 0
$$195$$ 9.59401 5.30788i 0.687041 0.380105i
$$196$$ 0 0
$$197$$ 11.5233i 0.820998i −0.911861 0.410499i $$-0.865355\pi$$
0.911861 0.410499i $$-0.134645\pi$$
$$198$$ 0 0
$$199$$ 4.79943 + 8.31285i 0.340222 + 0.589283i 0.984474 0.175531i $$-0.0561643\pi$$
−0.644251 + 0.764814i $$0.722831\pi$$
$$200$$ 0 0
$$201$$ 1.54374 0.108887
$$202$$ 0 0
$$203$$ 2.41166 1.39237i 0.169265 0.0977253i
$$204$$ 0 0
$$205$$ −0.220814 + 12.0885i −0.0154223 + 0.844299i
$$206$$ 0 0
$$207$$ 7.43307 + 4.29148i 0.516634 + 0.298279i
$$208$$ 0 0
$$209$$ 15.2325 + 17.1127i 1.05366 + 1.18371i
$$210$$ 0 0
$$211$$ 7.28207 12.6129i 0.501318 0.868308i −0.498681 0.866786i $$-0.666182\pi$$
0.999999 0.00152265i $$-0.000484675\pi$$
$$212$$ 0 0
$$213$$ −19.8231 + 11.4449i −1.35826 + 0.784189i
$$214$$ 0 0
$$215$$ −28.4479 0.519642i −1.94013 0.0354393i
$$216$$ 0 0
$$217$$ 0.689764i 0.0468242i
$$218$$ 0 0
$$219$$ −2.16707 3.75347i −0.146437 0.253636i
$$220$$ 0 0
$$221$$ −3.31182 −0.222777
$$222$$ 0 0
$$223$$ 6.55816 + 3.78635i 0.439167 + 0.253553i 0.703244 0.710949i $$-0.251734\pi$$
−0.264077 + 0.964501i $$0.585067\pi$$
$$224$$ 0 0
$$225$$ 5.26432 + 0.192385i 0.350955 + 0.0128257i
$$226$$ 0 0
$$227$$ 6.86640i 0.455739i −0.973692 0.227869i $$-0.926824\pi$$
0.973692 0.227869i $$-0.0731759\pi$$
$$228$$ 0 0
$$229$$ −22.1011 −1.46048 −0.730240 0.683191i $$-0.760592\pi$$
−0.730240 + 0.683191i $$0.760592\pi$$
$$230$$ 0 0
$$231$$ 7.11127 12.3171i 0.467887 0.810404i
$$232$$ 0 0
$$233$$ −2.57806 1.48844i −0.168894 0.0975111i 0.413170 0.910654i $$-0.364421\pi$$
−0.582064 + 0.813143i $$0.697755\pi$$
$$234$$ 0 0
$$235$$ 3.76562 6.25555i 0.245642 0.408067i
$$236$$ 0 0
$$237$$ 22.6173 13.0581i 1.46915 0.848214i
$$238$$ 0 0
$$239$$ 9.71289 0.628275 0.314137 0.949378i $$-0.398285\pi$$
0.314137 + 0.949378i $$0.398285\pi$$
$$240$$ 0 0
$$241$$ 9.34287 + 16.1823i 0.601827 + 1.04239i 0.992544 + 0.121884i $$0.0388937\pi$$
−0.390717 + 0.920511i $$0.627773\pi$$
$$242$$ 0 0
$$243$$ −9.08665 + 5.24618i −0.582909 + 0.336543i
$$244$$ 0 0
$$245$$ −10.1617 + 5.62196i −0.649209 + 0.359174i
$$246$$ 0 0
$$247$$ 10.0775 + 3.33803i 0.641216 + 0.212394i
$$248$$ 0 0
$$249$$ 4.23109 7.32846i 0.268134 0.464422i
$$250$$ 0 0
$$251$$ 2.10091 + 3.63888i 0.132608 + 0.229684i 0.924681 0.380742i $$-0.124332\pi$$
−0.792073 + 0.610426i $$0.790998\pi$$
$$252$$ 0 0
$$253$$ 37.0814 21.4090i 2.33129 1.34597i
$$254$$ 0 0
$$255$$ −5.24495 3.15728i −0.328452 0.197716i
$$256$$ 0 0
$$257$$ −24.3946 + 14.0842i −1.52169 + 0.878548i −0.522018 + 0.852934i $$0.674821\pi$$
−0.999672 + 0.0256140i $$0.991846\pi$$
$$258$$ 0 0
$$259$$ −7.48859 −0.465318
$$260$$ 0 0
$$261$$ 1.09146 1.89047i 0.0675599 0.117017i
$$262$$ 0 0
$$263$$ −2.34563 1.35425i −0.144637 0.0835065i 0.425935 0.904754i $$-0.359945\pi$$
−0.570572 + 0.821247i $$0.693279\pi$$
$$264$$ 0 0
$$265$$ 13.5682 22.5398i 0.833486 1.38461i
$$266$$ 0 0
$$267$$ 14.7146i 0.900519i
$$268$$ 0 0
$$269$$ 5.64101 9.77052i 0.343938 0.595719i −0.641222 0.767356i $$-0.721572\pi$$
0.985160 + 0.171637i $$0.0549055\pi$$
$$270$$ 0 0
$$271$$ −3.16690 + 5.48523i −0.192375 + 0.333204i −0.946037 0.324059i $$-0.894952\pi$$
0.753662 + 0.657263i $$0.228286\pi$$
$$272$$ 0 0
$$273$$ 6.59035i 0.398866i
$$274$$ 0 0
$$275$$ 13.9623 22.2638i 0.841956 1.34256i
$$276$$ 0 0
$$277$$ 11.1435i 0.669549i 0.942298 + 0.334774i $$0.108660\pi$$
−0.942298 + 0.334774i $$0.891340\pi$$
$$278$$ 0 0
$$279$$ −0.270349 0.468258i −0.0161854 0.0280339i
$$280$$ 0 0
$$281$$ −12.9061 22.3541i −0.769916 1.33353i −0.937608 0.347694i $$-0.886965\pi$$
0.167693 0.985839i $$-0.446368\pi$$
$$282$$ 0 0
$$283$$ 24.9942 + 14.4304i 1.48575 + 0.857799i 0.999868 0.0162249i $$-0.00516476\pi$$
0.485883 + 0.874024i $$0.338498\pi$$
$$284$$ 0 0
$$285$$ 12.7775 + 14.8937i 0.756877 + 0.882228i
$$286$$ 0 0
$$287$$ 6.29360 + 3.63361i 0.371500 + 0.214485i
$$288$$ 0 0
$$289$$ −7.57543 13.1210i −0.445614 0.771826i
$$290$$ 0 0
$$291$$ 0.838927 + 1.45306i 0.0491788 + 0.0851801i
$$292$$ 0 0
$$293$$ 22.7742i 1.33048i −0.746628 0.665242i $$-0.768328\pi$$
0.746628 0.665242i $$-0.231672\pi$$
$$294$$ 0 0
$$295$$ −0.00143733 + 0.0786871i −8.36848e−5 + 0.00458134i
$$296$$ 0 0
$$297$$ 20.5972i 1.19517i
$$298$$ 0 0
$$299$$ 9.92035 17.1825i 0.573709 0.993692i
$$300$$ 0 0
$$301$$ −8.55098 + 14.8107i −0.492870 + 0.853676i
$$302$$ 0 0
$$303$$ 29.8375i 1.71412i
$$304$$ 0 0
$$305$$ −1.98614 1.19559i −0.113726 0.0684592i
$$306$$ 0 0
$$307$$ −14.0275 8.09880i −0.800593 0.462223i 0.0430854 0.999071i $$-0.486281\pi$$
−0.843679 + 0.536849i $$0.819615\pi$$
$$308$$ 0 0
$$309$$ −9.47052 + 16.4034i −0.538759 + 0.933158i
$$310$$ 0 0
$$311$$ −28.3483 −1.60749 −0.803743 0.594977i $$-0.797161\pi$$
−0.803743 + 0.594977i $$0.797161\pi$$
$$312$$ 0 0
$$313$$ −2.67539 + 1.54464i −0.151222 + 0.0873081i −0.573702 0.819064i $$-0.694493\pi$$
0.422480 + 0.906372i $$0.361160\pi$$
$$314$$ 0 0
$$315$$ 1.63298 2.71275i 0.0920079 0.152846i
$$316$$ 0 0
$$317$$ −20.8236 + 12.0225i −1.16957 + 0.675251i −0.953579 0.301144i $$-0.902632\pi$$
−0.215991 + 0.976395i $$0.569298\pi$$
$$318$$ 0 0
$$319$$ −5.44500 9.43101i −0.304861 0.528035i
$$320$$ 0 0
$$321$$ −12.8985 + 22.3408i −0.719923 + 1.24694i
$$322$$ 0 0
$$323$$ −1.19928 5.80476i −0.0667298 0.322986i
$$324$$ 0 0
$$325$$ 0.444724 12.1692i 0.0246689 0.675026i
$$326$$ 0 0
$$327$$ −3.47632 + 2.00706i −0.192241 + 0.110990i
$$328$$ 0 0
$$329$$ −2.19434 3.80071i −0.120978 0.209540i
$$330$$ 0 0
$$331$$ −20.7717 −1.14171 −0.570857 0.821049i $$-0.693389\pi$$
−0.570857 + 0.821049i $$0.693389\pi$$
$$332$$ 0 0
$$333$$ −5.08376 + 2.93511i −0.278588 + 0.160843i
$$334$$ 0 0
$$335$$ 0.884231 1.46891i 0.0483107 0.0802550i
$$336$$ 0 0
$$337$$ 2.10139 + 1.21324i 0.114470 + 0.0660892i 0.556142 0.831087i $$-0.312281\pi$$
−0.441672 + 0.897177i $$0.645614\pi$$
$$338$$ 0 0
$$339$$ 8.40217 14.5530i 0.456343 0.790410i
$$340$$ 0 0
$$341$$ −2.69739 −0.146072
$$342$$ 0 0
$$343$$ 16.3885i 0.884896i
$$344$$ 0 0
$$345$$ 32.0917 17.7547i 1.72776 0.955882i
$$346$$ 0 0
$$347$$ −2.48834 1.43664i −0.133581 0.0771230i 0.431720 0.902008i $$-0.357907\pi$$
−0.565301 + 0.824885i $$0.691240\pi$$
$$348$$ 0 0
$$349$$ 5.89385 0.315490 0.157745 0.987480i $$-0.449578\pi$$
0.157745 + 0.987480i $$0.449578\pi$$
$$350$$ 0 0
$$351$$ 4.77211 + 8.26553i 0.254716 + 0.441181i
$$352$$ 0 0
$$353$$ 12.0238i 0.639962i −0.947424 0.319981i $$-0.896324\pi$$
0.947424 0.319981i $$-0.103676\pi$$
$$354$$ 0 0
$$355$$ −0.464289 + 25.4176i −0.0246419 + 1.34903i
$$356$$ 0 0
$$357$$ −3.18670 + 1.83984i −0.168658 + 0.0973748i
$$358$$ 0 0
$$359$$ −2.26590 + 3.92466i −0.119590 + 0.207136i −0.919605 0.392844i $$-0.871491\pi$$
0.800015 + 0.599979i $$0.204825\pi$$
$$360$$ 0 0
$$361$$ −2.20143 + 18.8720i −0.115865 + 0.993265i
$$362$$ 0 0
$$363$$ −28.9874 16.7359i −1.52144 0.878406i
$$364$$ 0 0
$$365$$ −4.81278 0.0879123i −0.251912 0.00460154i
$$366$$ 0 0
$$367$$ −29.9143 + 17.2710i −1.56151 + 0.901539i −0.564407 + 0.825496i $$0.690895\pi$$
−0.997105 + 0.0760429i $$0.975771\pi$$
$$368$$ 0 0
$$369$$ 5.69670 0.296558
$$370$$ 0 0
$$371$$ −7.90659 13.6946i −0.410490 0.710989i
$$372$$ 0 0
$$373$$ 24.0801i 1.24682i 0.781894 + 0.623411i $$0.214254\pi$$
−0.781894 + 0.623411i $$0.785746\pi$$
$$374$$ 0 0
$$375$$ 12.3057 18.8485i 0.635462 0.973333i
$$376$$ 0 0
$$377$$ −4.37008 2.52307i −0.225071 0.129945i
$$378$$ 0 0
$$379$$ −30.1565 −1.54904 −0.774518 0.632552i $$-0.782008\pi$$
−0.774518 + 0.632552i $$0.782008\pi$$
$$380$$ 0 0
$$381$$ −41.4375 −2.12291
$$382$$ 0 0
$$383$$ −33.6192 19.4101i −1.71786 0.991809i −0.922797 0.385286i $$-0.874103\pi$$
−0.795066 0.606522i $$-0.792564\pi$$
$$384$$ 0 0
$$385$$ −7.64678 13.8216i −0.389716 0.704413i
$$386$$ 0 0
$$387$$ 13.4060i 0.681467i
$$388$$ 0 0
$$389$$ 18.6935 + 32.3781i 0.947799 + 1.64164i 0.750048 + 0.661383i $$0.230030\pi$$
0.197750 + 0.980252i $$0.436636\pi$$
$$390$$ 0 0
$$391$$ −11.0779 −0.560236
$$392$$ 0 0
$$393$$ 18.7108 10.8027i 0.943836 0.544924i
$$394$$ 0 0
$$395$$ 0.529733 29.0004i 0.0266538 1.45917i
$$396$$ 0 0
$$397$$ 13.4790 + 7.78211i 0.676492 + 0.390573i 0.798532 0.601952i $$-0.205610\pi$$
−0.122040 + 0.992525i $$0.538944\pi$$
$$398$$ 0 0
$$399$$ 11.5512 2.38651i 0.578283 0.119475i
$$400$$ 0 0
$$401$$ −11.3113 + 19.5918i −0.564860 + 0.978366i 0.432203 + 0.901777i $$0.357737\pi$$
−0.997063 + 0.0765898i $$0.975597\pi$$
$$402$$ 0 0
$$403$$ −1.08244 + 0.624949i −0.0539203 + 0.0311309i
$$404$$ 0 0
$$405$$ −0.451290 + 24.7060i −0.0224248 + 1.22765i
$$406$$ 0 0
$$407$$ 29.2848i 1.45159i
$$408$$ 0 0
$$409$$ −18.1239 31.3915i −0.896169 1.55221i −0.832351 0.554249i $$-0.813005\pi$$
−0.0638187 0.997962i $$-0.520328\pi$$
$$410$$ 0 0
$$411$$ −34.5865 −1.70603
$$412$$ 0 0
$$413$$ 0.0409666 + 0.0236521i 0.00201583 + 0.00116384i
$$414$$ 0 0
$$415$$ −4.54970 8.22361i −0.223336 0.403681i
$$416$$ 0 0
$$417$$ 14.7536i 0.722486i
$$418$$ 0 0
$$419$$ 14.5598 0.711293 0.355647 0.934621i $$-0.384261\pi$$
0.355647 + 0.934621i $$0.384261\pi$$
$$420$$ 0 0
$$421$$ −0.784161 + 1.35821i −0.0382177 + 0.0661950i −0.884502 0.466537i $$-0.845501\pi$$
0.846284 + 0.532732i $$0.178835\pi$$
$$422$$ 0 0
$$423$$ −2.97934 1.72012i −0.144860 0.0836351i
$$424$$ 0 0
$$425$$ −6.00846 + 3.18226i −0.291453 + 0.154362i
$$426$$ 0 0
$$427$$ −1.20673 + 0.696705i −0.0583977 + 0.0337159i
$$428$$ 0 0
$$429$$ −25.7722 −1.24429
$$430$$ 0 0
$$431$$ 12.7303 + 22.0495i 0.613197 + 1.06209i 0.990698 + 0.136080i $$0.0434503\pi$$
−0.377500 + 0.926009i $$0.623216\pi$$
$$432$$ 0 0
$$433$$ −14.6212 + 8.44155i −0.702650 + 0.405675i −0.808334 0.588725i $$-0.799630\pi$$
0.105684 + 0.994400i $$0.466297\pi$$
$$434$$ 0 0
$$435$$ −4.51560 8.16197i −0.216507 0.391337i
$$436$$ 0 0
$$437$$ 33.7090 + 11.1656i 1.61252 + 0.534125i
$$438$$ 0 0
$$439$$ 9.93240 17.2034i 0.474048 0.821075i −0.525511 0.850787i $$-0.676126\pi$$
0.999558 + 0.0297121i $$0.00945905\pi$$
$$440$$ 0 0
$$441$$ 2.73590 + 4.73872i 0.130281 + 0.225653i
$$442$$ 0 0
$$443$$ −4.46422 + 2.57742i −0.212101 + 0.122457i −0.602288 0.798279i $$-0.705744\pi$$
0.390186 + 0.920736i $$0.372411\pi$$
$$444$$ 0 0
$$445$$ 14.0013 + 8.42830i 0.663726 + 0.399540i
$$446$$ 0 0
$$447$$ 21.3520 12.3276i 1.00991 0.583074i
$$448$$ 0 0
$$449$$ 33.2207 1.56778 0.783892 0.620897i $$-0.213232\pi$$
0.783892 + 0.620897i $$0.213232\pi$$
$$450$$ 0 0
$$451$$ 14.2096 24.6117i 0.669103 1.15892i
$$452$$ 0 0
$$453$$ 20.1520 + 11.6348i 0.946826 + 0.546650i
$$454$$ 0 0
$$455$$ −6.27088 3.77485i −0.293983 0.176968i
$$456$$ 0 0
$$457$$ 11.7126i 0.547894i −0.961745 0.273947i $$-0.911671\pi$$
0.961745 0.273947i $$-0.0883293\pi$$
$$458$$ 0 0
$$459$$ 2.66448 4.61501i 0.124367 0.215410i
$$460$$ 0 0
$$461$$ 3.68501 6.38263i 0.171628 0.297269i −0.767361 0.641215i $$-0.778431\pi$$
0.938989 + 0.343947i $$0.111764\pi$$
$$462$$ 0 0
$$463$$ 28.8020i 1.33854i −0.743019 0.669271i $$-0.766607\pi$$
0.743019 0.669271i $$-0.233393\pi$$
$$464$$ 0 0
$$465$$ −2.31006 0.0421966i −0.107127 0.00195682i
$$466$$ 0 0
$$467$$ 34.1251i 1.57912i −0.613673 0.789561i $$-0.710309\pi$$
0.613673 0.789561i $$-0.289691\pi$$
$$468$$ 0 0
$$469$$ −0.515268 0.892471i −0.0237929 0.0412105i
$$470$$ 0 0
$$471$$ 4.16756 + 7.21842i 0.192031 + 0.332607i
$$472$$ 0 0
$$473$$ 57.9188 + 33.4394i 2.66311 + 1.53755i
$$474$$ 0 0
$$475$$ 21.4905 3.62725i 0.986053 0.166430i
$$476$$ 0 0
$$477$$ −10.7351 6.19789i −0.491525 0.283782i
$$478$$ 0 0
$$479$$ 14.4130 + 24.9640i 0.658546 + 1.14064i 0.980992 + 0.194048i $$0.0621617\pi$$
−0.322446 + 0.946588i $$0.604505\pi$$
$$480$$ 0 0
$$481$$ 6.78491 + 11.7518i 0.309365 + 0.535836i
$$482$$ 0 0
$$483$$ 22.0446i 1.00306i
$$484$$ 0 0
$$485$$ 1.86315 + 0.0340331i 0.0846013 + 0.00154536i
$$486$$ 0 0
$$487$$ 16.5796i 0.751294i −0.926763 0.375647i $$-0.877421\pi$$
0.926763 0.375647i $$-0.122579\pi$$
$$488$$ 0 0
$$489$$ −9.47957 + 16.4191i −0.428681 + 0.742497i
$$490$$ 0 0
$$491$$ −4.94615 + 8.56698i −0.223217 + 0.386623i −0.955783 0.294073i $$-0.904989\pi$$
0.732566 + 0.680696i $$0.238322\pi$$
$$492$$ 0 0
$$493$$ 2.81748i 0.126893i
$$494$$ 0 0
$$495$$ −10.6084 6.38591i −0.476814 0.287026i
$$496$$ 0 0
$$497$$ 13.2331 + 7.64011i 0.593584 + 0.342706i
$$498$$ 0 0
$$499$$ −15.4949 + 26.8380i −0.693649 + 1.20144i 0.276985 + 0.960874i $$0.410665\pi$$
−0.970634 + 0.240561i $$0.922669\pi$$
$$500$$ 0 0
$$501$$ 27.5245 1.22970
$$502$$ 0 0
$$503$$ −11.1406 + 6.43203i −0.496735 + 0.286790i −0.727364 0.686252i $$-0.759255\pi$$
0.230629 + 0.973042i $$0.425922\pi$$
$$504$$ 0 0
$$505$$ 28.3911 + 17.0905i 1.26339 + 0.760516i
$$506$$ 0 0
$$507$$ 12.3247 7.11568i 0.547360 0.316018i
$$508$$ 0 0
$$509$$ −7.35312 12.7360i −0.325921 0.564512i 0.655777 0.754955i $$-0.272341\pi$$
−0.981698 + 0.190442i $$0.939008\pi$$
$$510$$ 0 0
$$511$$ −1.44664 + 2.50566i −0.0639957 + 0.110844i
$$512$$ 0 0
$$513$$ −12.7593 + 11.3574i −0.563335 + 0.501442i
$$514$$ 0 0
$$515$$ 10.1837 + 18.4071i 0.448747 + 0.811112i
$$516$$ 0 0
$$517$$ −14.8630 + 8.58118i −0.653676 + 0.377400i
$$518$$ 0 0
$$519$$ −11.8564 20.5359i −0.520439 0.901427i
$$520$$ 0 0
$$521$$ 5.35528 0.234619 0.117310 0.993095i $$-0.462573\pi$$
0.117310 + 0.993095i $$0.462573\pi$$
$$522$$ 0 0
$$523$$ 13.8388 7.98981i 0.605127 0.349370i −0.165929 0.986138i $$-0.553062\pi$$
0.771056 + 0.636768i $$0.219729\pi$$
$$524$$ 0 0
$$525$$ −6.33254 11.9565i −0.276375 0.521826i
$$526$$ 0 0
$$527$$ 0.604376 + 0.348937i 0.0263270 + 0.0151999i
$$528$$ 0 0
$$529$$ 21.6833 37.5566i 0.942753 1.63290i
$$530$$ 0 0
$$531$$ 0.0370812 0.00160919
$$532$$ 0 0
$$533$$ 13.1687i 0.570400i
$$534$$ 0 0
$$535$$ 13.8698 + 25.0697i 0.599643 + 1.08386i
$$536$$ 0 0
$$537$$ −28.8963 16.6833i −1.24697 0.719937i
$$538$$ 0 0
$$539$$ 27.2972 1.17577
$$540$$ 0 0
$$541$$ −17.9500 31.0904i −0.771732 1.33668i −0.936613 0.350366i $$-0.886057\pi$$
0.164881 0.986313i $$-0.447276\pi$$
$$542$$ 0 0
$$543$$ 28.9742i 1.24340i
$$544$$ 0 0
$$545$$ −0.0814211 + 4.45742i −0.00348770 + 0.190935i
$$546$$ 0 0
$$547$$ 22.6473 13.0754i 0.968327 0.559064i 0.0696011 0.997575i $$-0.477827\pi$$
0.898726 + 0.438511i $$0.144494\pi$$
$$548$$ 0 0
$$549$$ −0.546140 + 0.945942i −0.0233087 + 0.0403718i
$$550$$ 0 0
$$551$$ 2.83979 8.57329i 0.120979 0.365235i
$$552$$ 0 0
$$553$$ −15.0983 8.71704i −0.642047 0.370686i
$$554$$ 0 0
$$555$$ −0.458118 + 25.0798i −0.0194460 + 1.06458i
$$556$$ 0 0
$$557$$ 3.64444 2.10412i 0.154420 0.0891543i −0.420799 0.907154i $$-0.638250\pi$$
0.575219 + 0.818000i $$0.304917\pi$$
$$558$$ 0 0
$$559$$ 30.9899 1.31073
$$560$$ 0 0
$$561$$ 7.19488 + 12.4619i 0.303768 + 0.526142i
$$562$$ 0 0
$$563$$ 40.5225i 1.70782i 0.520422 + 0.853909i $$0.325775\pi$$
−0.520422 + 0.853909i $$0.674225\pi$$
$$564$$ 0 0
$$565$$ −9.03489 16.3306i −0.380101 0.687034i
$$566$$ 0 0
$$567$$ 12.8626 + 7.42622i 0.540178 + 0.311872i
$$568$$ 0 0
$$569$$ −23.9522 −1.00413 −0.502064 0.864831i $$-0.667426\pi$$
−0.502064 + 0.864831i $$0.667426\pi$$
$$570$$ 0 0
$$571$$ −7.78949 −0.325980 −0.162990 0.986628i $$-0.552114\pi$$
−0.162990 + 0.986628i $$0.552114\pi$$
$$572$$ 0 0
$$573$$ 10.4123 + 6.01155i 0.434981 + 0.251136i
$$574$$ 0 0
$$575$$ 1.48759 40.7057i 0.0620369 1.69754i
$$576$$ 0 0
$$577$$ 34.1385i 1.42121i −0.703593 0.710603i $$-0.748422\pi$$
0.703593 0.710603i $$-0.251578\pi$$
$$578$$ 0 0
$$579$$ 16.3953 + 28.3975i 0.681366 + 1.18016i
$$580$$ 0 0
$$581$$ −5.64899 −0.234360
$$582$$ 0 0
$$583$$ −53.5541 + 30.9195i −2.21798 + 1.28055i
$$584$$ 0 0
$$585$$ −5.73663 0.104788i −0.237181 0.00433244i
$$586$$ 0 0
$$587$$ −19.1737 11.0700i −0.791384 0.456906i 0.0490654 0.998796i $$-0.484376\pi$$
−0.840450 + 0.541890i $$0.817709\pi$$
$$588$$ 0 0
$$589$$ −1.48735 1.67094i −0.0612853 0.0688498i
$$590$$ 0 0
$$591$$ −11.6002 + 20.0921i −0.477167 + 0.826477i
$$592$$ 0 0
$$593$$ 35.8131 20.6767i 1.47067 0.849089i 0.471208 0.882022i $$-0.343818\pi$$
0.999458 + 0.0329325i $$0.0104846\pi$$
$$594$$ 0 0
$$595$$ −0.0746377 + 4.08606i −0.00305985 + 0.167512i
$$596$$ 0 0
$$597$$ 19.3258i 0.790954i
$$598$$ 0 0
$$599$$ 16.8243 + 29.1406i 0.687423 + 1.19065i 0.972669 + 0.232197i $$0.0745912\pi$$
−0.285246 + 0.958454i $$0.592075\pi$$
$$600$$ 0 0
$$601$$ 38.4939 1.57020 0.785100 0.619369i $$-0.212611\pi$$
0.785100 + 0.619369i $$0.212611\pi$$
$$602$$ 0 0
$$603$$ −0.699598 0.403913i −0.0284899 0.0164486i
$$604$$ 0 0
$$605$$ −32.5281 + 17.9962i −1.32246 + 0.731648i
$$606$$ 0 0
$$607$$ 22.1827i 0.900367i 0.892936 + 0.450183i $$0.148641\pi$$
−0.892936 + 0.450183i $$0.851359\pi$$
$$608$$ 0 0
$$609$$ −5.60665 −0.227193
$$610$$ 0 0
$$611$$ −3.97629 + 6.88714i −0.160864 + 0.278624i
$$612$$ 0 0
$$613$$ −4.13445 2.38703i −0.166989 0.0964111i 0.414176 0.910197i $$-0.364070\pi$$
−0.581165 + 0.813786i $$0.697403\pi$$
$$614$$ 0 0
$$615$$ 12.5542 20.8554i 0.506235 0.840970i
$$616$$ 0 0
$$617$$ 14.0178 8.09317i 0.564335 0.325819i −0.190549 0.981678i $$-0.561027\pi$$
0.754883 + 0.655859i $$0.227693\pi$$
$$618$$ 0 0
$$619$$ −13.4892 −0.542176 −0.271088 0.962555i $$-0.587383\pi$$
−0.271088 + 0.962555i $$0.587383\pi$$
$$620$$ 0 0
$$621$$ 15.9626 + 27.6480i 0.640556 + 1.10948i
$$622$$ 0 0
$$623$$ 8.50684 4.91143i 0.340819 0.196772i
$$624$$ 0 0
$$625$$ −10.8863 22.5053i −0.435453 0.900212i
$$626$$ 0 0
$$627$$ −9.33268 45.1720i −0.372711 1.80400i
$$628$$ 0 0
$$629$$ 3.78832 6.56156i 0.151050 0.261626i
$$630$$ 0 0
$$631$$ 13.2207 + 22.8989i 0.526308 + 0.911592i 0.999530 + 0.0306488i $$0.00975735\pi$$
−0.473222 + 0.880943i $$0.656909\pi$$
$$632$$ 0 0
$$633$$ −25.3942 + 14.6613i −1.00933 + 0.582735i
$$634$$ 0 0
$$635$$ −23.7348 + 39.4288i −0.941886 + 1.56469i
$$636$$ 0 0
$$637$$ 10.9542 6.32441i 0.434021 0.250582i
$$638$$ 0 0
$$639$$ 11.9780 0.473842
$$640$$ 0 0
$$641$$ −4.27817 + 7.41000i −0.168977 + 0.292677i −0.938061 0.346471i $$-0.887380\pi$$
0.769083 + 0.639149i $$0.220713\pi$$
$$642$$ 0 0
$$643$$ 24.2681 + 14.0112i 0.957042 + 0.552548i 0.895261 0.445541i $$-0.146989\pi$$
0.0617804 + 0.998090i $$0.480322\pi$$
$$644$$ 0 0
$$645$$ 49.0790 + 29.5438i 1.93248 + 1.16329i
$$646$$ 0 0
$$647$$ 9.57376i 0.376383i 0.982132 + 0.188192i $$0.0602626\pi$$
−0.982132 + 0.188192i $$0.939737\pi$$
$$648$$ 0 0
$$649$$ 0.0924936 0.160204i 0.00363069 0.00628854i
$$650$$ 0 0
$$651$$ −0.694367 + 1.20268i −0.0272144 + 0.0471367i
$$652$$ 0 0
$$653$$ 16.4168i 0.642439i 0.947005 + 0.321219i $$0.104093\pi$$
−0.947005 + 0.321219i $$0.895907\pi$$
$$654$$ 0 0
$$655$$ 0.438238 23.9914i 0.0171234 0.937423i
$$656$$ 0 0
$$657$$ 2.26801i 0.0884837i
$$658$$ 0 0
$$659$$ 7.08162 + 12.2657i 0.275861 + 0.477805i 0.970352 0.241697i $$-0.0777039\pi$$
−0.694491 + 0.719501i $$0.744371\pi$$
$$660$$ 0 0
$$661$$ −18.5170 32.0724i −0.720229 1.24747i −0.960908 0.276868i $$-0.910704\pi$$
0.240679 0.970605i $$-0.422630\pi$$
$$662$$ 0 0
$$663$$ 5.77452 + 3.33392i 0.224264 + 0.129479i
$$664$$ 0 0
$$665$$ 4.34552 12.3582i 0.168512 0.479230i
$$666$$ 0 0
$$667$$ −14.6178 8.43960i −0.566004 0.326783i
$$668$$ 0 0
$$669$$ −7.62324 13.2038i −0.294732 0.510490i
$$670$$ 0 0
$$671$$ 2.72453 + 4.71903i 0.105179 + 0.182176i
$$672$$ 0 0
$$673$$ 42.3293i 1.63167i −0.578282 0.815837i $$-0.696277\pi$$
0.578282 0.815837i $$-0.303723\pi$$
$$674$$ 0 0
$$675$$ 16.6000 + 10.4103i 0.638933 + 0.400693i
$$676$$ 0 0
$$677$$ 13.9856i 0.537510i 0.963209 + 0.268755i $$0.0866121\pi$$
−0.963209 + 0.268755i $$0.913388\pi$$
$$678$$ 0 0
$$679$$ 0.560033 0.970005i 0.0214921 0.0372254i
$$680$$ 0 0
$$681$$ −6.91222 + 11.9723i −0.264877 + 0.458780i
$$682$$ 0 0
$$683$$ 11.6668i 0.446416i 0.974771 + 0.223208i $$0.0716529\pi$$
−0.974771 + 0.223208i $$0.928347\pi$$
$$684$$ 0 0
$$685$$ −19.8106 + 32.9099i −0.756925 + 1.25742i
$$686$$ 0 0
$$687$$ 38.5356 + 22.2486i 1.47023 + 0.848835i
$$688$$ 0 0
$$689$$ −14.3273 + 24.8156i −0.545825 + 0.945397i
$$690$$ 0 0
$$691$$ −15.7886 −0.600627 −0.300313 0.953841i $$-0.597091\pi$$
−0.300313 + 0.953841i $$0.597091\pi$$
$$692$$ 0 0
$$693$$ −6.44542 + 3.72127i −0.244841 + 0.141359i
$$694$$ 0 0
$$695$$ −14.0384 8.45062i −0.532506 0.320550i
$$696$$ 0 0
$$697$$ −6.36760 + 3.67633i −0.241190 + 0.139251i
$$698$$ 0 0
$$699$$ 2.99675 + 5.19053i 0.113348 + 0.196324i
$$700$$ 0 0
$$701$$ 2.64450 4.58042i 0.0998816 0.173000i −0.811754 0.584000i $$-0.801487\pi$$
0.911635 + 0.411000i $$0.134820\pi$$
$$702$$ 0 0
$$703$$ −18.1409 + 16.1478i −0.684198 + 0.609025i
$$704$$ 0 0
$$705$$ −12.8631 + 7.11648i −0.484451 + 0.268022i
$$706$$ 0 0
$$707$$ 17.2497 9.95913i 0.648743 0.374552i
$$708$$ 0 0
$$709$$ −12.2529 21.2226i −0.460166 0.797031i 0.538803 0.842432i $$-0.318877\pi$$
−0.998969 + 0.0454011i $$0.985543\pi$$
$$710$$ 0 0
$$711$$ −13.6664 −0.512529
$$712$$ 0 0
$$713$$ −3.62075 + 2.09044i −0.135598 + 0.0782875i
$$714$$ 0 0
$$715$$ −14.7619 + 24.5229i −0.552064 + 0.917104i
$$716$$ 0 0
$$717$$ −16.9355 9.77771i −0.632467 0.365155i
$$718$$ 0 0
$$719$$ 22.4239 38.8393i 0.836269 1.44846i −0.0567236 0.998390i $$-0.518065\pi$$
0.892993 0.450071i $$-0.148601\pi$$
$$720$$ 0 0
$$721$$ 12.6442 0.470896
$$722$$ 0 0
$$723$$ 37.6209i 1.39914i
$$724$$ 0 0
$$725$$ −10.3528 0.378343i −0.384493 0.0140513i
$$726$$ 0 0
$$727$$ 28.1376 + 16.2453i 1.04357 + 0.602504i 0.920842 0.389937i $$-0.127503\pi$$
0.122726 + 0.992441i $$0.460836\pi$$
$$728$$ 0 0
$$729$$ −12.0273 −0.445457
$$730$$ 0 0
$$731$$ −8.65152 14.9849i −0.319988 0.554235i
$$732$$ 0 0
$$733$$ 11.1969i 0.413568i −0.978387 0.206784i $$-0.933700\pi$$
0.978387 0.206784i $$-0.0662998\pi$$
$$734$$ 0 0
$$735$$ 23.3776 + 0.427025i 0.862294 + 0.0157510i
$$736$$ 0 0
$$737$$ −3.49009 + 2.01501i −0.128559 + 0.0742237i
$$738$$ 0 0
$$739$$ 0.466361 0.807761i 0.0171554 0.0297140i −0.857320 0.514783i $$-0.827872\pi$$
0.874476 + 0.485069i $$0.161206\pi$$
$$740$$ 0 0
$$741$$ −14.2109 15.9650i −0.522051 0.586488i
$$742$$ 0 0
$$743$$ 23.3370 + 13.4736i 0.856153 + 0.494300i 0.862722 0.505678i $$-0.168758\pi$$
−0.00656939 + 0.999978i $$0.502091\pi$$
$$744$$ 0 0
$$745$$ 0.500098 27.3780i 0.0183222 1.00305i
$$746$$ 0 0
$$747$$ −3.83492 + 2.21409i −0.140312 + 0.0810094i
$$748$$ 0 0
$$749$$ 17.2210 0.629240
$$750$$ 0 0
$$751$$ 2.33645 + 4.04686i 0.0852584 + 0.147672i 0.905501 0.424343i $$-0.139495\pi$$
−0.820243 + 0.572015i $$0.806162\pi$$
$$752$$ 0 0
$$753$$ 8.45971i 0.308289i
$$754$$ 0 0
$$755$$ 22.6136 12.5109i 0.822992 0.455320i
$$756$$ 0 0
$$757$$ −37.0902 21.4140i −1.34807 0.778306i −0.360090 0.932918i $$-0.617254\pi$$
−0.987975 + 0.154612i $$0.950587\pi$$
$$758$$ 0 0
$$759$$ −86.2073 −3.12913
$$760$$ 0 0
$$761$$ −16.7169 −0.605987 −0.302994 0.952993i $$-0.597986\pi$$
−0.302994 + 0.952993i $$0.597986\pi$$
$$762$$ 0 0
$$763$$ 2.32065 + 1.33983i 0.0840131 + 0.0485050i
$$764$$ 0 0
$$765$$ 1.55084 + 2.80315i 0.0560707 + 0.101348i
$$766$$ 0 0
$$767$$ 0.0857182i 0.00309511i
$$768$$ 0 0
$$769$$ −7.70852 13.3516i −0.277976 0.481469i 0.692905 0.721029i $$-0.256330\pi$$
−0.970882 + 0.239559i $$0.922997\pi$$
$$770$$ 0 0
$$771$$ 56.7128 2.04246
$$772$$ 0 0
$$773$$ −28.7343 + 16.5897i −1.03350 + 0.596691i −0.917985 0.396615i $$-0.870185\pi$$
−0.115514 + 0.993306i $$0.536852\pi$$
$$774$$ 0 0
$$775$$ −1.36332 + 2.17391i −0.0489719 + 0.0780892i
$$776$$ 0 0
$$777$$ 13.0572 + 7.53856i 0.468423 + 0.270444i
$$778$$ 0 0
$$779$$ 23.0813 4.76868i 0.826975 0.170856i
$$780$$ 0 0
$$781$$ 29.8774 51.7491i 1.06910 1.85173i
$$782$$ 0 0
$$783$$ 7.03179 4.05980i 0.251296 0.145086i
$$784$$ 0 0
$$785$$ 9.25562 + 0.169067i 0.330347 + 0.00603427i
$$786$$ 0 0
$$787$$ 12.8318i 0.457405i 0.973496 + 0.228702i $$0.0734483\pi$$
−0.973496 + 0.228702i $$0.926552\pi$$
$$788$$ 0 0
$$789$$ 2.72657 + 4.72256i 0.0970685 + 0.168128i