Properties

 Label 140.2.q.b.9.1 Level $140$ Weight $2$ Character 140.9 Analytic conductor $1.118$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(9,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("140.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$140 = 2^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 140.q (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: $$1.11790562830$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{-19})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} - 4x^{2} - 5x + 25$$ x^4 - x^3 - 4*x^2 - 5*x + 25 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 9.1 Root $$-1.63746 - 1.52274i$$ of defining polynomial Character $$\chi$$ $$=$$ 140.9 Dual form 140.2.q.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.50000 - 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(-1.13746 - 2.38876i) q^{7} +O(q^{10})$$ $$q+(1.50000 - 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(-1.13746 - 2.38876i) q^{7} +(2.63746 + 4.56821i) q^{11} +2.62685i q^{13} +(-2.63746 - 2.83616i) q^{15} +(-0.362541 + 0.209313i) q^{17} +(1.63746 - 2.83616i) q^{19} +(-3.77492 - 2.59808i) q^{21} +(6.77492 + 3.91150i) q^{23} +(-4.50000 + 2.17945i) q^{25} +5.19615i q^{27} -4.27492 q^{29} +(-1.63746 - 2.83616i) q^{31} +(7.91238 + 4.56821i) q^{33} +(-4.63746 + 3.67341i) q^{35} +(-8.63746 - 4.98684i) q^{37} +(2.27492 + 3.94027i) q^{39} -3.72508 q^{41} -2.15068i q^{43} +(5.63746 + 3.25479i) q^{47} +(-4.41238 + 5.43424i) q^{49} +(-0.362541 + 0.627940i) q^{51} +(-4.91238 + 2.83616i) q^{53} +(8.63746 - 8.03231i) q^{55} -5.67232i q^{57} +(-1.63746 - 2.83616i) q^{59} +(6.77492 - 11.7345i) q^{61} +(5.72508 - 1.31342i) q^{65} +(-3.04983 + 1.76082i) q^{67} +13.5498 q^{69} -4.54983 q^{71} +(5.63746 - 3.25479i) q^{73} +(-4.86254 + 7.16629i) q^{75} +(7.91238 - 11.4964i) q^{77} +(3.63746 - 6.30026i) q^{79} +(4.50000 + 7.79423i) q^{81} -7.40437i q^{83} +(0.637459 + 0.685484i) q^{85} +(-6.41238 + 3.70219i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(6.27492 - 2.98793i) q^{91} +(-4.91238 - 2.83616i) q^{93} +(-7.00000 - 2.15068i) q^{95} +6.92820i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 6 q^{3} - 2 q^{5} + 3 q^{7}+O(q^{10})$$ 4 * q + 6 * q^3 - 2 * q^5 + 3 * q^7 $$4 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 3 q^{11} - 3 q^{15} - 9 q^{17} - q^{19} + 12 q^{23} - 18 q^{25} - 2 q^{29} + q^{31} + 9 q^{33} - 11 q^{35} - 27 q^{37} - 6 q^{39} - 30 q^{41} + 15 q^{47} + 5 q^{49} - 9 q^{51} + 3 q^{53} + 27 q^{55} + q^{59} + 12 q^{61} + 38 q^{65} + 18 q^{67} + 24 q^{69} + 12 q^{71} + 15 q^{73} - 27 q^{75} + 9 q^{77} + 7 q^{79} + 18 q^{81} - 5 q^{85} - 3 q^{87} - 14 q^{89} + 10 q^{91} + 3 q^{93} - 28 q^{95}+O(q^{100})$$ 4 * q + 6 * q^3 - 2 * q^5 + 3 * q^7 + 3 * q^11 - 3 * q^15 - 9 * q^17 - q^19 + 12 * q^23 - 18 * q^25 - 2 * q^29 + q^31 + 9 * q^33 - 11 * q^35 - 27 * q^37 - 6 * q^39 - 30 * q^41 + 15 * q^47 + 5 * q^49 - 9 * q^51 + 3 * q^53 + 27 * q^55 + q^59 + 12 * q^61 + 38 * q^65 + 18 * q^67 + 24 * q^69 + 12 * q^71 + 15 * q^73 - 27 * q^75 + 9 * q^77 + 7 * q^79 + 18 * q^81 - 5 * q^85 - 3 * q^87 - 14 * q^89 + 10 * q^91 + 3 * q^93 - 28 * q^95

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$$.

 $$n$$ $$57$$ $$71$$ $$101$$ $$\chi(n)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.50000 0.866025i 0.866025 0.500000i 1.00000i $$-0.5\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ 0 0
$$5$$ −0.500000 2.17945i −0.223607 0.974679i
$$6$$ 0 0
$$7$$ −1.13746 2.38876i −0.429919 0.902867i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 2.63746 + 4.56821i 0.795224 + 1.37737i 0.922697 + 0.385526i $$0.125980\pi$$
−0.127473 + 0.991842i $$0.540687\pi$$
$$12$$ 0 0
$$13$$ 2.62685i 0.728557i 0.931290 + 0.364278i $$0.118684\pi$$
−0.931290 + 0.364278i $$0.881316\pi$$
$$14$$ 0 0
$$15$$ −2.63746 2.83616i −0.680989 0.732294i
$$16$$ 0 0
$$17$$ −0.362541 + 0.209313i −0.0879292 + 0.0507659i −0.543320 0.839526i $$-0.682833\pi$$
0.455391 + 0.890292i $$0.349500\pi$$
$$18$$ 0 0
$$19$$ 1.63746 2.83616i 0.375659 0.650660i −0.614767 0.788709i $$-0.710750\pi$$
0.990425 + 0.138049i $$0.0440831\pi$$
$$20$$ 0 0
$$21$$ −3.77492 2.59808i −0.823754 0.566947i
$$22$$ 0 0
$$23$$ 6.77492 + 3.91150i 1.41267 + 0.815604i 0.995639 0.0932891i $$-0.0297381\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ 0 0
$$25$$ −4.50000 + 2.17945i −0.900000 + 0.435890i
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ 0 0
$$29$$ −4.27492 −0.793832 −0.396916 0.917855i $$-0.629920\pi$$
−0.396916 + 0.917855i $$0.629920\pi$$
$$30$$ 0 0
$$31$$ −1.63746 2.83616i −0.294096 0.509390i 0.680678 0.732583i $$-0.261685\pi$$
−0.974774 + 0.223193i $$0.928352\pi$$
$$32$$ 0 0
$$33$$ 7.91238 + 4.56821i 1.37737 + 0.795224i
$$34$$ 0 0
$$35$$ −4.63746 + 3.67341i −0.783874 + 0.620920i
$$36$$ 0 0
$$37$$ −8.63746 4.98684i −1.41999 0.819831i −0.423692 0.905806i $$-0.639266\pi$$
−0.996297 + 0.0859750i $$0.972599\pi$$
$$38$$ 0 0
$$39$$ 2.27492 + 3.94027i 0.364278 + 0.630949i
$$40$$ 0 0
$$41$$ −3.72508 −0.581760 −0.290880 0.956760i $$-0.593948\pi$$
−0.290880 + 0.956760i $$0.593948\pi$$
$$42$$ 0 0
$$43$$ 2.15068i 0.327975i −0.986462 0.163988i $$-0.947564\pi$$
0.986462 0.163988i $$-0.0524357\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 5.63746 + 3.25479i 0.822308 + 0.474760i 0.851212 0.524823i $$-0.175868\pi$$
−0.0289038 + 0.999582i $$0.509202\pi$$
$$48$$ 0 0
$$49$$ −4.41238 + 5.43424i −0.630339 + 0.776320i
$$50$$ 0 0
$$51$$ −0.362541 + 0.627940i −0.0507659 + 0.0879292i
$$52$$ 0 0
$$53$$ −4.91238 + 2.83616i −0.674767 + 0.389577i −0.797880 0.602816i $$-0.794045\pi$$
0.123114 + 0.992393i $$0.460712\pi$$
$$54$$ 0 0
$$55$$ 8.63746 8.03231i 1.16467 1.08308i
$$56$$ 0 0
$$57$$ 5.67232i 0.751318i
$$58$$ 0 0
$$59$$ −1.63746 2.83616i −0.213179 0.369237i 0.739529 0.673125i $$-0.235048\pi$$
−0.952708 + 0.303888i $$0.901715\pi$$
$$60$$ 0 0
$$61$$ 6.77492 11.7345i 0.867439 1.50245i 0.00283468 0.999996i $$-0.499098\pi$$
0.864605 0.502453i $$-0.167569\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 5.72508 1.31342i 0.710109 0.162910i
$$66$$ 0 0
$$67$$ −3.04983 + 1.76082i −0.372597 + 0.215119i −0.674592 0.738191i $$-0.735681\pi$$
0.301996 + 0.953309i $$0.402347\pi$$
$$68$$ 0 0
$$69$$ 13.5498 1.63121
$$70$$ 0 0
$$71$$ −4.54983 −0.539966 −0.269983 0.962865i $$-0.587018\pi$$
−0.269983 + 0.962865i $$0.587018\pi$$
$$72$$ 0 0
$$73$$ 5.63746 3.25479i 0.659815 0.380944i −0.132392 0.991197i $$-0.542266\pi$$
0.792206 + 0.610253i $$0.208932\pi$$
$$74$$ 0 0
$$75$$ −4.86254 + 7.16629i −0.561478 + 0.827492i
$$76$$ 0 0
$$77$$ 7.91238 11.4964i 0.901699 1.31014i
$$78$$ 0 0
$$79$$ 3.63746 6.30026i 0.409246 0.708835i −0.585559 0.810630i $$-0.699125\pi$$
0.994805 + 0.101795i $$0.0324584\pi$$
$$80$$ 0 0
$$81$$ 4.50000 + 7.79423i 0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 7.40437i 0.812736i −0.913710 0.406368i $$-0.866795\pi$$
0.913710 0.406368i $$-0.133205\pi$$
$$84$$ 0 0
$$85$$ 0.637459 + 0.685484i 0.0691421 + 0.0743512i
$$86$$ 0 0
$$87$$ −6.41238 + 3.70219i −0.687479 + 0.396916i
$$88$$ 0 0
$$89$$ −3.50000 + 6.06218i −0.370999 + 0.642590i −0.989720 0.143022i $$-0.954318\pi$$
0.618720 + 0.785611i $$0.287651\pi$$
$$90$$ 0 0
$$91$$ 6.27492 2.98793i 0.657790 0.313220i
$$92$$ 0 0
$$93$$ −4.91238 2.83616i −0.509390 0.294096i
$$94$$ 0 0
$$95$$ −7.00000 2.15068i −0.718185 0.220655i
$$96$$ 0 0
$$97$$ 6.92820i 0.703452i 0.936103 + 0.351726i $$0.114405\pi$$
−0.936103 + 0.351726i $$0.885595\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 6.77492 + 11.7345i 0.674129 + 1.16763i 0.976723 + 0.214507i $$0.0688144\pi$$
−0.302593 + 0.953120i $$0.597852\pi$$
$$102$$ 0 0
$$103$$ −9.77492 5.64355i −0.963151 0.556076i −0.0660098 0.997819i $$-0.521027\pi$$
−0.897141 + 0.441743i $$0.854360\pi$$
$$104$$ 0 0
$$105$$ −3.77492 + 9.52628i −0.368394 + 0.929670i
$$106$$ 0 0
$$107$$ 3.04983 + 1.76082i 0.294839 + 0.170225i 0.640122 0.768273i $$-0.278884\pi$$
−0.345283 + 0.938499i $$0.612217\pi$$
$$108$$ 0 0
$$109$$ −5.77492 10.0025i −0.553137 0.958061i −0.998046 0.0624852i $$-0.980097\pi$$
0.444909 0.895576i $$-0.353236\pi$$
$$110$$ 0 0
$$111$$ −17.2749 −1.63966
$$112$$ 0 0
$$113$$ 4.30136i 0.404637i 0.979320 + 0.202319i $$0.0648477\pi$$
−0.979320 + 0.202319i $$0.935152\pi$$
$$114$$ 0 0
$$115$$ 5.13746 16.7213i 0.479070 1.55927i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0.912376 + 0.627940i 0.0836374 + 0.0575632i
$$120$$ 0 0
$$121$$ −8.41238 + 14.5707i −0.764761 + 1.32461i
$$122$$ 0 0
$$123$$ −5.58762 + 3.22602i −0.503819 + 0.290880i
$$124$$ 0 0
$$125$$ 7.00000 + 8.71780i 0.626099 + 0.779744i
$$126$$ 0 0
$$127$$ 15.6460i 1.38836i 0.719802 + 0.694179i $$0.244232\pi$$
−0.719802 + 0.694179i $$0.755768\pi$$
$$128$$ 0 0
$$129$$ −1.86254 3.22602i −0.163988 0.284035i
$$130$$ 0 0
$$131$$ 5.36254 9.28819i 0.468527 0.811513i −0.530826 0.847481i $$-0.678118\pi$$
0.999353 + 0.0359678i $$0.0114514\pi$$
$$132$$ 0 0
$$133$$ −8.63746 0.685484i −0.748963 0.0594390i
$$134$$ 0 0
$$135$$ 11.3248 2.59808i 0.974679 0.223607i
$$136$$ 0 0
$$137$$ 18.4622 10.6592i 1.57733 0.910674i 0.582103 0.813115i $$-0.302230\pi$$
0.995230 0.0975588i $$-0.0311034\pi$$
$$138$$ 0 0
$$139$$ −13.0997 −1.11110 −0.555550 0.831483i $$-0.687492\pi$$
−0.555550 + 0.831483i $$0.687492\pi$$
$$140$$ 0 0
$$141$$ 11.2749 0.949519
$$142$$ 0 0
$$143$$ −12.0000 + 6.92820i −1.00349 + 0.579365i
$$144$$ 0 0
$$145$$ 2.13746 + 9.31697i 0.177506 + 0.773732i
$$146$$ 0 0
$$147$$ −1.91238 + 11.9726i −0.157730 + 0.987482i
$$148$$ 0 0
$$149$$ −3.77492 + 6.53835i −0.309253 + 0.535642i −0.978199 0.207669i $$-0.933412\pi$$
0.668946 + 0.743311i $$0.266746\pi$$
$$150$$ 0 0
$$151$$ 6.36254 + 11.0202i 0.517776 + 0.896815i 0.999787 + 0.0206494i $$0.00657337\pi$$
−0.482011 + 0.876165i $$0.660093\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −5.36254 + 4.98684i −0.430730 + 0.400553i
$$156$$ 0 0
$$157$$ 1.91238 1.10411i 0.152624 0.0881176i −0.421743 0.906715i $$-0.638582\pi$$
0.574367 + 0.818598i $$0.305248\pi$$
$$158$$ 0 0
$$159$$ −4.91238 + 8.50848i −0.389577 + 0.674767i
$$160$$ 0 0
$$161$$ 1.63746 20.6328i 0.129050 1.62610i
$$162$$ 0 0
$$163$$ −4.91238 2.83616i −0.384767 0.222145i 0.295123 0.955459i $$-0.404639\pi$$
−0.679890 + 0.733314i $$0.737973\pi$$
$$164$$ 0 0
$$165$$ 6.00000 19.5287i 0.467099 1.52031i
$$166$$ 0 0
$$167$$ 0.476171i 0.0368472i 0.999830 + 0.0184236i $$0.00586474\pi$$
−0.999830 + 0.0184236i $$0.994135\pi$$
$$168$$ 0 0
$$169$$ 6.09967 0.469205
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −17.7371 10.2405i −1.34853 0.778573i −0.360488 0.932764i $$-0.617390\pi$$
−0.988041 + 0.154190i $$0.950723\pi$$
$$174$$ 0 0
$$175$$ 10.3248 + 8.27040i 0.780478 + 0.625183i
$$176$$ 0 0
$$177$$ −4.91238 2.83616i −0.369237 0.213179i
$$178$$ 0 0
$$179$$ −3.63746 6.30026i −0.271876 0.470904i 0.697466 0.716618i $$-0.254311\pi$$
−0.969342 + 0.245714i $$0.920978\pi$$
$$180$$ 0 0
$$181$$ −24.2749 −1.80434 −0.902170 0.431380i $$-0.858027\pi$$
−0.902170 + 0.431380i $$0.858027\pi$$
$$182$$ 0 0
$$183$$ 23.4690i 1.73488i
$$184$$ 0 0
$$185$$ −6.54983 + 21.3183i −0.481553 + 1.56735i
$$186$$ 0 0
$$187$$ −1.91238 1.10411i −0.139847 0.0807406i
$$188$$ 0 0
$$189$$ 12.4124 5.91041i 0.902867 0.429919i
$$190$$ 0 0
$$191$$ −0.0876242 + 0.151770i −0.00634026 + 0.0109817i −0.869178 0.494499i $$-0.835352\pi$$
0.862838 + 0.505481i $$0.168685\pi$$
$$192$$ 0 0
$$193$$ 18.4622 10.6592i 1.32894 0.767263i 0.343803 0.939042i $$-0.388285\pi$$
0.985136 + 0.171778i $$0.0549513\pi$$
$$194$$ 0 0
$$195$$ 7.45017 6.92820i 0.533517 0.496139i
$$196$$ 0 0
$$197$$ 8.60271i 0.612918i −0.951884 0.306459i $$-0.900856\pi$$
0.951884 0.306459i $$-0.0991442\pi$$
$$198$$ 0 0
$$199$$ 8.63746 + 14.9605i 0.612293 + 1.06052i 0.990853 + 0.134946i $$0.0430861\pi$$
−0.378560 + 0.925577i $$0.623581\pi$$
$$200$$ 0 0
$$201$$ −3.04983 + 5.28247i −0.215119 + 0.372597i
$$202$$ 0 0
$$203$$ 4.86254 + 10.2118i 0.341284 + 0.716725i
$$204$$ 0 0
$$205$$ 1.86254 + 8.11863i 0.130086 + 0.567030i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 17.2749 1.19493
$$210$$ 0 0
$$211$$ 25.6495 1.76578 0.882892 0.469576i $$-0.155593\pi$$
0.882892 + 0.469576i $$0.155593\pi$$
$$212$$ 0 0
$$213$$ −6.82475 + 3.94027i −0.467624 + 0.269983i
$$214$$ 0 0
$$215$$ −4.68729 + 1.07534i −0.319671 + 0.0733375i
$$216$$ 0 0
$$217$$ −4.91238 + 7.13752i −0.333474 + 0.484526i
$$218$$ 0 0
$$219$$ 5.63746 9.76436i 0.380944 0.659815i
$$220$$ 0 0
$$221$$ −0.549834 0.952341i −0.0369859 0.0640614i
$$222$$ 0 0
$$223$$ 8.71780i 0.583787i −0.956451 0.291893i $$-0.905715\pi$$
0.956451 0.291893i $$-0.0942853\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 16.9124 9.76436i 1.12251 0.648084i 0.180472 0.983580i $$-0.442237\pi$$
0.942041 + 0.335496i $$0.108904\pi$$
$$228$$ 0 0
$$229$$ 1.63746 2.83616i 0.108206 0.187419i −0.806837 0.590774i $$-0.798823\pi$$
0.915044 + 0.403355i $$0.132156\pi$$
$$230$$ 0 0
$$231$$ 1.91238 24.0969i 0.125825 1.58546i
$$232$$ 0 0
$$233$$ −12.3625 7.13752i −0.809897 0.467594i 0.0370231 0.999314i $$-0.488212\pi$$
−0.846920 + 0.531720i $$0.821546\pi$$
$$234$$ 0 0
$$235$$ 4.27492 13.9140i 0.278865 0.907646i
$$236$$ 0 0
$$237$$ 12.6005i 0.818492i
$$238$$ 0 0
$$239$$ −0.549834 −0.0355658 −0.0177829 0.999842i $$-0.505661\pi$$
−0.0177829 + 0.999842i $$0.505661\pi$$
$$240$$ 0 0
$$241$$ −4.91238 8.50848i −0.316434 0.548080i 0.663307 0.748347i $$-0.269152\pi$$
−0.979741 + 0.200267i $$0.935819\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 14.0498 + 6.89943i 0.897611 + 0.440788i
$$246$$ 0 0
$$247$$ 7.45017 + 4.30136i 0.474043 + 0.273689i
$$248$$ 0 0
$$249$$ −6.41238 11.1066i −0.406368 0.703850i
$$250$$ 0 0
$$251$$ −20.5498 −1.29709 −0.648547 0.761175i $$-0.724623\pi$$
−0.648547 + 0.761175i $$0.724623\pi$$
$$252$$ 0 0
$$253$$ 41.2657i 2.59435i
$$254$$ 0 0
$$255$$ 1.54983 + 0.476171i 0.0970544 + 0.0298190i
$$256$$ 0 0
$$257$$ −10.0876 5.82409i −0.629249 0.363297i 0.151212 0.988501i $$-0.451682\pi$$
−0.780461 + 0.625204i $$0.785016\pi$$
$$258$$ 0 0
$$259$$ −2.08762 + 26.3052i −0.129719 + 1.63452i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 0.675248 0.389855i 0.0416376 0.0240395i −0.479037 0.877795i $$-0.659014\pi$$
0.520674 + 0.853755i $$0.325681\pi$$
$$264$$ 0 0
$$265$$ 8.63746 + 9.28819i 0.530595 + 0.570569i
$$266$$ 0 0
$$267$$ 12.1244i 0.741999i
$$268$$ 0 0
$$269$$ −7.22508 12.5142i −0.440521 0.763005i 0.557207 0.830374i $$-0.311873\pi$$
−0.997728 + 0.0673687i $$0.978540\pi$$
$$270$$ 0 0
$$271$$ −4.91238 + 8.50848i −0.298406 + 0.516854i −0.975771 0.218793i $$-0.929788\pi$$
0.677366 + 0.735646i $$0.263121\pi$$
$$272$$ 0 0
$$273$$ 6.82475 9.91613i 0.413053 0.600152i
$$274$$ 0 0
$$275$$ −21.8248 14.8087i −1.31608 0.893001i
$$276$$ 0 0
$$277$$ −12.3625 + 7.13752i −0.742793 + 0.428852i −0.823084 0.567920i $$-0.807748\pi$$
0.0802909 + 0.996771i $$0.474415\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 9.46221 5.46301i 0.562470 0.324742i −0.191666 0.981460i $$-0.561389\pi$$
0.754136 + 0.656718i $$0.228056\pi$$
$$284$$ 0 0
$$285$$ −12.3625 + 2.83616i −0.732294 + 0.168000i
$$286$$ 0 0
$$287$$ 4.23713 + 8.89834i 0.250110 + 0.525252i
$$288$$ 0 0
$$289$$ −8.41238 + 14.5707i −0.494846 + 0.857098i
$$290$$ 0 0
$$291$$ 6.00000 + 10.3923i 0.351726 + 0.609208i
$$292$$ 0 0
$$293$$ 6.92820i 0.404750i 0.979308 + 0.202375i $$0.0648660\pi$$
−0.979308 + 0.202375i $$0.935134\pi$$
$$294$$ 0 0
$$295$$ −5.36254 + 4.98684i −0.312219 + 0.290345i
$$296$$ 0 0
$$297$$ −23.7371 + 13.7046i −1.37737 + 0.795224i
$$298$$ 0 0
$$299$$ −10.2749 + 17.7967i −0.594214 + 1.02921i
$$300$$ 0 0
$$301$$ −5.13746 + 2.44631i −0.296118 + 0.141003i
$$302$$ 0 0
$$303$$ 20.3248 + 11.7345i 1.16763 + 0.674129i
$$304$$ 0 0
$$305$$ −28.9622 8.89834i −1.65837 0.509517i
$$306$$ 0 0
$$307$$ 26.5145i 1.51326i −0.653843 0.756631i $$-0.726844\pi$$
0.653843 0.756631i $$-0.273156\pi$$
$$308$$ 0 0
$$309$$ −19.5498 −1.11215
$$310$$ 0 0
$$311$$ 4.91238 + 8.50848i 0.278555 + 0.482472i 0.971026 0.238974i $$-0.0768111\pi$$
−0.692471 + 0.721446i $$0.743478\pi$$
$$312$$ 0 0
$$313$$ 29.0120 + 16.7501i 1.63986 + 0.946772i 0.980881 + 0.194609i $$0.0623438\pi$$
0.658977 + 0.752163i $$0.270990\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 22.1873 + 12.8098i 1.24616 + 0.719472i 0.970342 0.241737i $$-0.0777171\pi$$
0.275821 + 0.961209i $$0.411050\pi$$
$$318$$ 0 0
$$319$$ −11.2749 19.5287i −0.631274 1.09340i
$$320$$ 0 0
$$321$$ 6.09967 0.340450
$$322$$ 0 0
$$323$$ 1.37097i 0.0762827i
$$324$$ 0 0
$$325$$ −5.72508 11.8208i −0.317570 0.655701i
$$326$$ 0 0
$$327$$ −17.3248 10.0025i −0.958061 0.553137i
$$328$$ 0 0
$$329$$ 1.36254 17.1687i 0.0751193 0.946543i
$$330$$ 0 0
$$331$$ −8.91238 + 15.4367i −0.489868 + 0.848477i −0.999932 0.0116596i $$-0.996289\pi$$
0.510064 + 0.860137i $$0.329622\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 5.36254 + 5.76655i 0.292987 + 0.315060i
$$336$$ 0 0
$$337$$ 4.30136i 0.234310i 0.993114 + 0.117155i $$0.0373774\pi$$
−0.993114 + 0.117155i $$0.962623\pi$$
$$338$$ 0 0
$$339$$ 3.72508 + 6.45203i 0.202319 + 0.350426i
$$340$$ 0 0
$$341$$ 8.63746 14.9605i 0.467745 0.810157i
$$342$$ 0 0
$$343$$ 18.0000 + 4.35890i 0.971909 + 0.235358i
$$344$$ 0 0
$$345$$ −6.77492 29.5312i −0.364749 1.58991i
$$346$$ 0 0
$$347$$ −10.5000 + 6.06218i −0.563670 + 0.325435i −0.754617 0.656165i $$-0.772177\pi$$
0.190947 + 0.981600i $$0.438844\pi$$
$$348$$ 0 0
$$349$$ 3.72508 0.199399 0.0996996 0.995018i $$-0.468212\pi$$
0.0996996 + 0.995018i $$0.468212\pi$$
$$350$$ 0 0
$$351$$ −13.6495 −0.728557
$$352$$ 0 0
$$353$$ 7.08762 4.09204i 0.377236 0.217797i −0.299379 0.954134i $$-0.596779\pi$$
0.676615 + 0.736337i $$0.263446\pi$$
$$354$$ 0 0
$$355$$ 2.27492 + 9.91613i 0.120740 + 0.526294i
$$356$$ 0 0
$$357$$ 1.91238 + 0.151770i 0.101214 + 0.00803249i
$$358$$ 0 0
$$359$$ 18.1873 31.5013i 0.959889 1.66258i 0.237127 0.971479i $$-0.423794\pi$$
0.722762 0.691097i $$-0.242872\pi$$
$$360$$ 0 0
$$361$$ 4.13746 + 7.16629i 0.217761 + 0.377173i
$$362$$ 0 0
$$363$$ 29.1413i 1.52952i
$$364$$ 0 0
$$365$$ −9.91238 10.6592i −0.518837 0.557926i
$$366$$ 0 0
$$367$$ 5.22508 3.01670i 0.272747 0.157471i −0.357388 0.933956i $$-0.616333\pi$$
0.630135 + 0.776485i $$0.282999\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 12.3625 + 8.50848i 0.641831 + 0.441739i
$$372$$ 0 0
$$373$$ −8.63746 4.98684i −0.447231 0.258209i 0.259429 0.965762i $$-0.416466\pi$$
−0.706660 + 0.707553i $$0.749799\pi$$
$$374$$ 0 0
$$375$$ 18.0498 + 7.01452i 0.932089 + 0.362228i
$$376$$ 0 0
$$377$$ 11.2296i 0.578352i
$$378$$ 0 0
$$379$$ 21.6495 1.11206 0.556030 0.831162i $$-0.312324\pi$$
0.556030 + 0.831162i $$0.312324\pi$$
$$380$$ 0 0
$$381$$ 13.5498 + 23.4690i 0.694179 + 1.20235i
$$382$$ 0 0
$$383$$ 5.32475 + 3.07425i 0.272082 + 0.157087i 0.629833 0.776730i $$-0.283123\pi$$
−0.357751 + 0.933817i $$0.616456\pi$$
$$384$$ 0 0
$$385$$ −29.0120 11.4964i −1.47859 0.585912i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 16.1873 + 28.0372i 0.820728 + 1.42154i 0.905141 + 0.425112i $$0.139765\pi$$
−0.0844123 + 0.996431i $$0.526901\pi$$
$$390$$ 0 0
$$391$$ −3.27492 −0.165620
$$392$$ 0 0
$$393$$ 18.5764i 0.937055i
$$394$$ 0 0
$$395$$ −15.5498 4.77753i −0.782397 0.240383i
$$396$$ 0 0
$$397$$ 9.36254 + 5.40547i 0.469892 + 0.271293i 0.716195 0.697901i $$-0.245882\pi$$
−0.246302 + 0.969193i $$0.579216\pi$$
$$398$$ 0 0
$$399$$ −13.5498 + 6.45203i −0.678340 + 0.323006i
$$400$$ 0 0
$$401$$ −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i $$-0.857199\pi$$
0.826139 + 0.563466i $$0.190532\pi$$
$$402$$ 0 0
$$403$$ 7.45017 4.30136i 0.371119 0.214266i
$$404$$ 0 0
$$405$$ 14.7371 13.7046i 0.732294 0.680989i
$$406$$ 0 0
$$407$$ 52.6103i 2.60780i
$$408$$ 0 0
$$409$$ −10.0498 17.4068i −0.496932 0.860712i 0.503061 0.864251i $$-0.332207\pi$$
−0.999994 + 0.00353862i $$0.998874\pi$$
$$410$$ 0 0
$$411$$ 18.4622 31.9775i 0.910674 1.57733i
$$412$$ 0 0
$$413$$ −4.91238 + 7.13752i −0.241722 + 0.351214i
$$414$$ 0 0
$$415$$ −16.1375 + 3.70219i −0.792157 + 0.181733i
$$416$$ 0 0
$$417$$ −19.6495 + 11.3446i −0.962240 + 0.555550i
$$418$$ 0 0
$$419$$ 13.0997 0.639961 0.319980 0.947424i $$-0.396324\pi$$
0.319980 + 0.947424i $$0.396324\pi$$
$$420$$ 0 0
$$421$$ −4.27492 −0.208347 −0.104173 0.994559i $$-0.533220\pi$$
−0.104173 + 0.994559i $$0.533220\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.17525 1.73205i 0.0570079 0.0840168i
$$426$$ 0 0
$$427$$ −35.7371 2.83616i −1.72944 0.137251i
$$428$$ 0 0
$$429$$ −12.0000 + 20.7846i −0.579365 + 1.00349i
$$430$$ 0 0
$$431$$ 9.18729 + 15.9129i 0.442536 + 0.766495i 0.997877 0.0651276i $$-0.0207454\pi$$
−0.555341 + 0.831623i $$0.687412\pi$$
$$432$$ 0 0
$$433$$ 18.1578i 0.872606i −0.899800 0.436303i $$-0.856288\pi$$
0.899800 0.436303i $$-0.143712\pi$$
$$434$$ 0 0
$$435$$ 11.2749 + 12.1244i 0.540591 + 0.581318i
$$436$$ 0 0
$$437$$ 22.1873 12.8098i 1.06136 0.612778i
$$438$$ 0 0
$$439$$ 11.9124 20.6328i 0.568547 0.984752i −0.428163 0.903701i $$-0.640839\pi$$
0.996710 0.0810504i $$-0.0258275\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 10.5000 + 6.06218i 0.498870 + 0.288023i 0.728247 0.685315i $$-0.240335\pi$$
−0.229377 + 0.973338i $$0.573669\pi$$
$$444$$ 0 0
$$445$$ 14.9622 + 4.59698i 0.709277 + 0.217918i
$$446$$ 0 0
$$447$$ 13.0767i 0.618507i
$$448$$ 0 0
$$449$$ 3.17525 0.149849 0.0749246 0.997189i $$-0.476128\pi$$
0.0749246 + 0.997189i $$0.476128\pi$$
$$450$$ 0 0
$$451$$ −9.82475 17.0170i −0.462629 0.801298i
$$452$$ 0 0
$$453$$ 19.0876 + 11.0202i 0.896815 + 0.517776i
$$454$$ 0 0
$$455$$ −9.64950 12.1819i −0.452376 0.571096i
$$456$$ 0 0
$$457$$ −1.18729 0.685484i −0.0555392 0.0320656i 0.471973 0.881613i $$-0.343542\pi$$
−0.527512 + 0.849547i $$0.676875\pi$$
$$458$$ 0 0
$$459$$ −1.08762 1.88382i −0.0507659 0.0879292i
$$460$$ 0 0
$$461$$ −14.0000 −0.652045 −0.326023 0.945362i $$-0.605709\pi$$
−0.326023 + 0.945362i $$0.605709\pi$$
$$462$$ 0 0
$$463$$ 2.15068i 0.0999505i 0.998750 + 0.0499752i $$0.0159142\pi$$
−0.998750 + 0.0499752i $$0.984086\pi$$
$$464$$ 0 0
$$465$$ −3.72508 + 12.1244i −0.172747 + 0.562254i
$$466$$ 0 0
$$467$$ 13.5997 + 7.85177i 0.629318 + 0.363337i 0.780488 0.625171i $$-0.214971\pi$$
−0.151170 + 0.988508i $$0.548304\pi$$
$$468$$ 0 0
$$469$$ 7.67525 + 5.28247i 0.354410 + 0.243922i
$$470$$ 0 0
$$471$$ 1.91238 3.31233i 0.0881176 0.152624i
$$472$$ 0 0
$$473$$ 9.82475 5.67232i 0.451743 0.260814i
$$474$$ 0 0
$$475$$ −1.18729 + 16.3315i −0.0544767 + 0.749340i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 4.91238 + 8.50848i 0.224452 + 0.388763i 0.956155 0.292861i $$-0.0946074\pi$$
−0.731703 + 0.681624i $$0.761274\pi$$
$$480$$ 0 0
$$481$$ 13.0997 22.6893i 0.597293 1.03454i
$$482$$ 0 0
$$483$$ −15.4124 32.3673i −0.701287 1.47277i
$$484$$ 0 0
$$485$$ 15.0997 3.46410i 0.685641 0.157297i
$$486$$ 0 0
$$487$$ −2.53779 + 1.46519i −0.114998 + 0.0663943i −0.556396 0.830917i $$-0.687816\pi$$
0.441398 + 0.897312i $$0.354483\pi$$
$$488$$ 0 0
$$489$$ −9.82475 −0.444291
$$490$$ 0 0
$$491$$ −28.5498 −1.28844 −0.644218 0.764842i $$-0.722817\pi$$
−0.644218 + 0.764842i $$0.722817\pi$$
$$492$$ 0 0
$$493$$ 1.54983 0.894797i 0.0698010 0.0402996i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 5.17525 + 10.8685i 0.232142 + 0.487518i
$$498$$ 0 0
$$499$$ 0.812707 1.40765i 0.0363818 0.0630151i −0.847261 0.531177i $$-0.821750\pi$$
0.883643 + 0.468161i $$0.155083\pi$$
$$500$$ 0 0
$$501$$ 0.412376 + 0.714256i 0.0184236 + 0.0319106i
$$502$$ 0 0
$$503$$ 31.7682i 1.41647i 0.705975 + 0.708236i $$0.250509\pi$$
−0.705975 + 0.708236i $$0.749491\pi$$
$$504$$ 0 0
$$505$$ 22.1873 20.6328i 0.987322 0.918149i
$$506$$ 0 0
$$507$$ 9.14950 5.28247i 0.406344 0.234603i
$$508$$ 0 0
$$509$$ −7.22508 + 12.5142i −0.320246 + 0.554683i −0.980539 0.196326i $$-0.937099\pi$$
0.660293 + 0.751008i $$0.270432\pi$$
$$510$$ 0 0
$$511$$ −14.1873 9.76436i −0.627609 0.431950i
$$512$$ 0 0
$$513$$ 14.7371 + 8.50848i 0.650660 + 0.375659i
$$514$$ 0 0
$$515$$ −7.41238 + 24.1257i −0.326628 + 1.06311i
$$516$$ 0 0
$$517$$ 34.3375i 1.51016i
$$518$$ 0 0
$$519$$ −35.4743 −1.55715
$$520$$ 0 0
$$521$$ −4.91238 8.50848i −0.215215 0.372763i 0.738124 0.674665i $$-0.235712\pi$$
−0.953339 + 0.301902i $$0.902379\pi$$
$$522$$ 0 0
$$523$$ −6.36254 3.67341i −0.278215 0.160627i 0.354400 0.935094i $$-0.384685\pi$$
−0.632615 + 0.774467i $$0.718018\pi$$
$$524$$ 0 0
$$525$$ 22.6495 + 3.46410i 0.988505 + 0.151186i
$$526$$ 0 0
$$527$$ 1.18729 + 0.685484i 0.0517193 + 0.0298602i
$$528$$ 0 0
$$529$$ 19.0997 + 33.0816i 0.830420 + 1.43833i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 9.78523i 0.423845i
$$534$$ 0 0
$$535$$ 2.31271 7.52737i 0.0999870 0.325437i
$$536$$ 0 0
$$537$$ −10.9124 6.30026i −0.470904 0.271876i
$$538$$ 0 0
$$539$$ −36.4622 5.82409i −1.57054 0.250861i
$$540$$ 0 0
$$541$$ 8.77492 15.1986i 0.377263 0.653439i −0.613400 0.789773i $$-0.710199\pi$$
0.990663 + 0.136334i $$0.0435319\pi$$
$$542$$ 0 0
$$543$$ −36.4124 + 21.0227i −1.56260 + 0.902170i
$$544$$ 0 0
$$545$$ −18.9124 + 17.5874i −0.810117 + 0.753360i
$$546$$ 0 0
$$547$$ 20.5386i 0.878168i 0.898446 + 0.439084i $$0.144697\pi$$
−0.898446 + 0.439084i $$0.855303\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −7.00000 + 12.1244i −0.298210 + 0.516515i
$$552$$ 0 0
$$553$$ −19.1873 1.52274i −0.815927 0.0647534i
$$554$$ 0 0
$$555$$ 8.63746 + 37.6498i 0.366640 + 1.59815i
$$556$$ 0 0
$$557$$ −8.63746 + 4.98684i −0.365981 + 0.211299i −0.671701 0.740822i $$-0.734436\pi$$
0.305720 + 0.952121i $$0.401103\pi$$
$$558$$ 0 0
$$559$$ 5.64950 0.238949
$$560$$ 0 0
$$561$$ −3.82475 −0.161481
$$562$$ 0 0
$$563$$ −19.5997 + 11.3159i −0.826028 + 0.476907i −0.852491 0.522743i $$-0.824909\pi$$
0.0264630 + 0.999650i $$0.491576\pi$$
$$564$$ 0 0
$$565$$ 9.37459 2.15068i 0.394392 0.0904797i
$$566$$ 0 0
$$567$$ 13.5000 19.6150i 0.566947 0.823754i
$$568$$ 0 0
$$569$$ 4.18729 7.25260i 0.175540 0.304045i −0.764808 0.644259i $$-0.777166\pi$$
0.940348 + 0.340214i $$0.110499\pi$$
$$570$$ 0 0
$$571$$ −3.63746 6.30026i −0.152223 0.263658i 0.779821 0.626002i $$-0.215310\pi$$
−0.932044 + 0.362344i $$0.881976\pi$$
$$572$$ 0 0
$$573$$ 0.303539i 0.0126805i
$$574$$ 0 0
$$575$$ −39.0120 2.83616i −1.62691 0.118276i
$$576$$ 0 0
$$577$$ 3.36254 1.94136i 0.139984 0.0808200i −0.428372 0.903602i $$-0.640913\pi$$
0.568357 + 0.822782i $$0.307579\pi$$
$$578$$ 0 0
$$579$$ 18.4622 31.9775i 0.767263 1.32894i
$$580$$ 0 0
$$581$$ −17.6873 + 8.42217i −0.733793 + 0.349410i
$$582$$ 0 0
$$583$$ −25.9124 14.9605i −1.07318 0.619601i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 20.8997i 0.862623i −0.902203 0.431311i $$-0.858051\pi$$
0.902203 0.431311i $$-0.141949\pi$$
$$588$$ 0 0
$$589$$ −10.7251 −0.441919
$$590$$ 0 0
$$591$$ −7.45017 12.9041i −0.306459 0.530802i
$$592$$ 0 0
$$593$$ −28.9124 16.6926i −1.18729 0.685482i −0.229600 0.973285i $$-0.573742\pi$$
−0.957689 + 0.287804i $$0.907075\pi$$
$$594$$ 0 0
$$595$$ 0.912376 2.30245i 0.0374038 0.0943911i
$$596$$ 0 0
$$597$$ 25.9124 + 14.9605i 1.06052 + 0.612293i
$$598$$ 0 0
$$599$$ 2.63746 + 4.56821i 0.107764 + 0.186652i 0.914864 0.403762i $$-0.132298\pi$$
−0.807100 + 0.590414i $$0.798964\pi$$
$$600$$ 0 0
$$601$$ 14.0000 0.571072 0.285536 0.958368i $$-0.407828\pi$$
0.285536 + 0.958368i $$0.407828\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 35.9622 + 11.0490i 1.46207 + 0.449206i
$$606$$ 0 0
$$607$$ 9.87459 + 5.70109i 0.400797 + 0.231400i 0.686828 0.726820i $$-0.259003\pi$$
−0.286031 + 0.958220i $$0.592336\pi$$
$$608$$ 0 0
$$609$$ 16.1375 + 11.1066i 0.653923 + 0.450061i
$$610$$ 0 0
$$611$$ −8.54983 + 14.8087i −0.345889 + 0.599098i
$$612$$ 0 0
$$613$$ −24.5619 + 14.1808i −0.992045 + 0.572757i −0.905885 0.423524i $$-0.860793\pi$$
−0.0861600 + 0.996281i $$0.527460\pi$$
$$614$$ 0 0
$$615$$ 9.82475 + 10.5649i 0.396172 + 0.426019i
$$616$$ 0 0
$$617$$ 31.2920i 1.25977i 0.776689 + 0.629884i $$0.216898\pi$$
−0.776689 + 0.629884i $$0.783102\pi$$
$$618$$ 0 0
$$619$$ −4.46221 7.72877i −0.179351 0.310646i 0.762307 0.647215i $$-0.224067\pi$$
−0.941659 + 0.336570i $$0.890733\pi$$
$$620$$ 0 0
$$621$$ −20.3248 + 35.2035i −0.815604 + 1.41267i
$$622$$ 0 0
$$623$$ 18.4622 + 1.46519i 0.739673 + 0.0587017i
$$624$$ 0 0
$$625$$ 15.5000 19.6150i 0.620000 0.784602i
$$626$$ 0 0
$$627$$ 25.9124 14.9605i 1.03484 0.597466i
$$628$$ 0 0
$$629$$ 4.17525 0.166478
$$630$$ 0 0
$$631$$ 33.0997 1.31768 0.658839 0.752284i $$-0.271048\pi$$
0.658839 + 0.752284i $$0.271048\pi$$
$$632$$ 0 0
$$633$$ 38.4743 22.2131i 1.52921 0.882892i
$$634$$ 0 0
$$635$$ 34.0997 7.82300i 1.35320 0.310446i
$$636$$ 0 0
$$637$$ −14.2749 11.5906i −0.565593 0.459238i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 1.04983 + 1.81837i 0.0414660 + 0.0718212i 0.886014 0.463659i $$-0.153464\pi$$
−0.844548 + 0.535481i $$0.820131\pi$$
$$642$$ 0 0
$$643$$ 31.4071i 1.23857i −0.785164 0.619287i $$-0.787422\pi$$
0.785164 0.619287i $$-0.212578\pi$$
$$644$$ 0 0
$$645$$ −6.09967 + 5.67232i −0.240174 + 0.223348i
$$646$$ 0 0
$$647$$ −23.3248 + 13.4666i −0.916991 + 0.529425i −0.882674 0.469986i $$-0.844259\pi$$
−0.0343169 + 0.999411i $$0.510926\pi$$
$$648$$ 0 0
$$649$$ 8.63746 14.9605i 0.339050 0.587252i
$$650$$ 0 0
$$651$$ −1.18729 + 14.9605i −0.0465337 + 0.586349i
$$652$$ 0 0
$$653$$ −24.5619 14.1808i −0.961181 0.554938i −0.0646444 0.997908i $$-0.520591\pi$$
−0.896536 + 0.442970i $$0.853925\pi$$
$$654$$ 0 0
$$655$$ −22.9244 7.04329i −0.895731 0.275204i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 40.5498 1.57960 0.789799 0.613366i $$-0.210185\pi$$
0.789799 + 0.613366i $$0.210185\pi$$
$$660$$ 0 0
$$661$$ 0.225083 + 0.389855i 0.00875471 + 0.0151636i 0.870370 0.492399i $$-0.163880\pi$$
−0.861615 + 0.507563i $$0.830547\pi$$
$$662$$ 0 0
$$663$$ −1.64950 0.952341i −0.0640614 0.0369859i
$$664$$ 0 0
$$665$$ 2.82475 + 19.1676i 0.109539 + 0.743289i
$$666$$ 0 0
$$667$$ −28.9622 16.7213i −1.12142 0.647453i
$$668$$ 0 0
$$669$$ −7.54983 13.0767i −0.291893 0.505574i
$$670$$ 0 0
$$671$$ 71.4743 2.75923
$$672$$ 0 0
$$673$$ 31.2920i 1.20622i −0.797659 0.603109i $$-0.793928\pi$$
0.797659 0.603109i $$-0.206072\pi$$
$$674$$ 0 0
$$675$$ −11.3248 23.3827i −0.435890 0.900000i
$$676$$ 0 0
$$677$$ 40.1873 + 23.2021i 1.54452 + 0.891731i 0.998545 + 0.0539317i $$0.0171753\pi$$
0.545979 + 0.837799i $$0.316158\pi$$
$$678$$ 0 0
$$679$$ 16.5498 7.88054i 0.635124 0.302428i
$$680$$ 0 0
$$681$$ 16.9124 29.2931i 0.648084 1.12251i
$$682$$ 0 0
$$683$$ 16.5997 9.58382i 0.635169 0.366715i −0.147582 0.989050i $$-0.547149\pi$$
0.782751 + 0.622335i $$0.213816\pi$$
$$684$$ 0 0
$$685$$ −32.4622 34.9079i −1.24032 1.33376i
$$686$$ 0 0
$$687$$ 5.67232i 0.216413i
$$688$$ 0 0
$$689$$ −7.45017 12.9041i −0.283829 0.491606i
$$690$$ 0 0
$$691$$ −15.1873 + 26.3052i −0.577752 + 1.00070i 0.417985 + 0.908454i $$0.362737\pi$$
−0.995737 + 0.0922416i $$0.970597\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 6.54983 + 28.5501i 0.248449 + 1.08297i
$$696$$ 0 0
$$697$$ 1.35050 0.779710i 0.0511537 0.0295336i
$$698$$ 0 0
$$699$$ −24.7251 −0.935189
$$700$$ 0 0
$$701$$ 8.82475 0.333306 0.166653 0.986016i $$-0.446704\pi$$
0.166653 + 0.986016i $$0.446704\pi$$
$$702$$ 0 0
$$703$$ −28.2870 + 16.3315i −1.06686 + 0.615954i
$$704$$ 0 0
$$705$$ −5.63746 24.5731i −0.212319 0.925477i
$$706$$ 0 0
$$707$$ 20.3248 29.5312i 0.764391 1.11063i
$$708$$ 0 0
$$709$$ −5.22508 + 9.05011i −0.196232 + 0.339884i −0.947304 0.320337i $$-0.896204\pi$$
0.751072 + 0.660221i $$0.229537\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 25.6197i 0.959465i
$$714$$ 0 0
$$715$$ 21.0997 + 22.6893i 0.789083 + 0.848531i
$$716$$ 0 0
$$717$$ −0.824752 + 0.476171i −0.0308009 + 0.0177829i
$$718$$ 0 0
$$719$$ −15.1873 + 26.3052i −0.566390 + 0.981017i 0.430528 + 0.902577i $$0.358327\pi$$
−0.996919 + 0.0784400i $$0.975006\pi$$
$$720$$ 0 0
$$721$$ −2.36254 + 29.7693i −0.0879856 + 1.10867i
$$722$$ 0 0
$$723$$ −14.7371 8.50848i −0.548080 0.316434i
$$724$$ 0 0
$$725$$ 19.2371 9.31697i 0.714449 0.346023i
$$726$$ 0 0
$$727$$ 3.10302i 0.115085i −0.998343 0.0575423i $$-0.981674\pi$$
0.998343 0.0575423i $$-0.0183264\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 0.450166 + 0.779710i 0.0166500 + 0.0288386i
$$732$$ 0 0
$$733$$ −32.6375 18.8432i −1.20549 0.695991i −0.243721 0.969845i $$-0.578368\pi$$
−0.961771 + 0.273854i $$0.911701\pi$$
$$734$$ 0 0
$$735$$ 27.0498 1.81837i 0.997748 0.0670715i
$$736$$ 0 0
$$737$$ −16.0876 9.28819i −0.592595 0.342135i
$$738$$ 0 0
$$739$$ −10.4622 18.1211i −0.384859 0.666595i 0.606891 0.794785i $$-0.292416\pi$$
−0.991750 + 0.128190i $$0.959083\pi$$
$$740$$ 0 0
$$741$$ 14.9003 0.547377
$$742$$ 0 0
$$743$$ 6.45203i 0.236702i −0.992972 0.118351i $$-0.962239\pi$$
0.992972 0.118351i $$-0.0377608\pi$$
$$744$$ 0 0
$$745$$ 16.1375 + 4.95807i 0.591231 + 0.181650i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0.737127 9.28819i 0.0269341 0.339383i
$$750$$ 0 0
$$751$$ 7.36254 12.7523i 0.268663 0.465338i −0.699854 0.714286i $$-0.746752\pi$$
0.968517 + 0.248948i $$0.0800849\pi$$
$$752$$ 0 0
$$753$$ −30.8248 + 17.7967i −1.12332 + 0.648547i
$$754$$ 0 0
$$755$$ 20.8368 19.3770i 0.758329 0.705200i
$$756$$ 0 0
$$757$$ 35.5934i 1.29366i −0.762633 0.646831i $$-0.776094\pi$$
0.762633 0.646831i $$-0.223906\pi$$
$$758$$ 0 0
$$759$$ 35.7371 + 61.8985i 1.29718 + 2.24677i
$$760$$ 0 0
$$761$$ −11.4622 + 19.8531i −0.415505 + 0.719675i −0.995481 0.0949578i $$-0.969728\pi$$
0.579977 + 0.814633i $$0.303062\pi$$
$$762$$ 0 0
$$763$$ −17.3248 + 25.1723i −0.627198 + 0.911298i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 7.45017 4.30136i 0.269010 0.155313i
$$768$$ 0 0
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ −20.1752 −0.726594
$$772$$ 0 0
$$773$$ −34.9124 + 20.1567i −1.25571 + 0.724985i −0.972238 0.233995i $$-0.924820\pi$$
−0.283473 + 0.958980i $$0.591487\pi$$
$$774$$ 0 0
$$775$$ 13.5498 + 9.19397i 0.486724 + 0.330257i
$$776$$ 0 0
$$777$$ 19.6495 + 41.2657i 0.704922 + 1.48040i
$$778$$ 0 0
$$779$$ −6.09967 + 10.5649i −0.218543 + 0.378528i
$$780$$ 0 0
$$781$$ −12.0000 20.7846i −0.429394 0.743732i
$$782$$ 0 0
$$783$$ 22.2131i 0.793832i
$$784$$ 0 0
$$785$$ −3.36254 3.61587i −0.120014 0.129056i
$$786$$ 0 0
$$787$$ 1.50000 0.866025i 0.0534692 0.0308705i −0.473027 0.881048i $$-0.656839\pi$$
0.526496 + 0.850177i $$0.323505\pi$$
$$788$$ 0 0
$$789$$ 0.675248 1.16956i 0.0240395 0.0416376i
$$790$$ 0 0
$$791$$ 10.2749 4.89261i 0.365334