# Properties

 Label 1638.2.bj.c.127.1 Level $1638$ Weight $2$ Character 1638.127 Analytic conductor $13.079$ Analytic rank $0$ Dimension $4$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1638.bj (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: $$13.0794958511$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 182) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 127.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1638.127 Dual form 1638.2.bj.c.1135.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(-0.633975 + 0.366025i) q^{11} +(2.59808 + 2.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.86603 - 4.96410i) q^{17} +(-1.26795 - 0.732051i) q^{19} +(0.866025 + 0.500000i) q^{20} +(0.366025 - 0.633975i) q^{22} +(-0.633975 - 1.09808i) q^{23} +4.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(-1.50000 - 2.59808i) q^{29} +5.26795i q^{31} +(0.866025 + 0.500000i) q^{32} +5.73205i q^{34} +(0.500000 - 0.866025i) q^{35} +(4.50000 - 2.59808i) q^{37} +1.46410 q^{38} -1.00000 q^{40} +(2.13397 - 1.23205i) q^{41} +(-6.09808 + 10.5622i) q^{43} +0.732051i q^{44} +(1.09808 + 0.633975i) q^{46} +2.92820i q^{47} +(0.500000 + 0.866025i) q^{49} +(-3.46410 + 2.00000i) q^{50} +(3.46410 - 1.00000i) q^{52} -1.53590 q^{53} +(-0.366025 - 0.633975i) q^{55} +(0.500000 - 0.866025i) q^{56} +(2.59808 + 1.50000i) q^{58} +(9.29423 + 5.36603i) q^{59} +(5.86603 - 10.1603i) q^{61} +(-2.63397 - 4.56218i) q^{62} -1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +(10.0981 - 5.83013i) q^{67} +(-2.86603 - 4.96410i) q^{68} +1.00000i q^{70} +(12.0000 + 6.92820i) q^{71} +11.3923i q^{73} +(-2.59808 + 4.50000i) q^{74} +(-1.26795 + 0.732051i) q^{76} +0.732051 q^{77} -3.80385 q^{79} +(0.866025 - 0.500000i) q^{80} +(-1.23205 + 2.13397i) q^{82} +3.80385i q^{83} +(4.96410 + 2.86603i) q^{85} -12.1962i q^{86} +(-0.366025 - 0.633975i) q^{88} +(-2.19615 + 1.26795i) q^{89} +(-1.00000 - 3.46410i) q^{91} -1.26795 q^{92} +(-1.46410 - 2.53590i) q^{94} +(0.732051 - 1.26795i) q^{95} +(-4.73205 - 2.73205i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{4}+O(q^{10})$$ 4 * q + 2 * q^4 $$4 q + 2 q^{4} - 2 q^{10} - 6 q^{11} + 4 q^{14} - 2 q^{16} + 8 q^{17} - 12 q^{19} - 2 q^{22} - 6 q^{23} + 16 q^{25} - 14 q^{26} - 6 q^{29} + 2 q^{35} + 18 q^{37} - 8 q^{38} - 4 q^{40} + 12 q^{41} - 14 q^{43} - 6 q^{46} + 2 q^{49} - 20 q^{53} + 2 q^{55} + 2 q^{56} + 6 q^{59} + 20 q^{61} - 14 q^{62} - 4 q^{64} - 10 q^{65} + 30 q^{67} - 8 q^{68} + 48 q^{71} - 12 q^{76} - 4 q^{77} - 36 q^{79} + 2 q^{82} + 6 q^{85} + 2 q^{88} + 12 q^{89} - 4 q^{91} - 12 q^{92} + 8 q^{94} - 4 q^{95} - 12 q^{97}+O(q^{100})$$ 4 * q + 2 * q^4 - 2 * q^10 - 6 * q^11 + 4 * q^14 - 2 * q^16 + 8 * q^17 - 12 * q^19 - 2 * q^22 - 6 * q^23 + 16 * q^25 - 14 * q^26 - 6 * q^29 + 2 * q^35 + 18 * q^37 - 8 * q^38 - 4 * q^40 + 12 * q^41 - 14 * q^43 - 6 * q^46 + 2 * q^49 - 20 * q^53 + 2 * q^55 + 2 * q^56 + 6 * q^59 + 20 * q^61 - 14 * q^62 - 4 * q^64 - 10 * q^65 + 30 * q^67 - 8 * q^68 + 48 * q^71 - 12 * q^76 - 4 * q^77 - 36 * q^79 + 2 * q^82 + 6 * q^85 + 2 * q^88 + 12 * q^89 - 4 * q^91 - 12 * q^92 + 8 * q^94 - 4 * q^95 - 12 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$$.

 $$n$$ $$379$$ $$703$$ $$911$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ 0 0
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 1.00000i 0.447214i 0.974679 + 0.223607i $$0.0717831\pi$$
−0.974679 + 0.223607i $$0.928217\pi$$
$$6$$ 0 0
$$7$$ −0.866025 0.500000i −0.327327 0.188982i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ −0.500000 0.866025i −0.158114 0.273861i
$$11$$ −0.633975 + 0.366025i −0.191151 + 0.110361i −0.592521 0.805555i $$-0.701867\pi$$
0.401371 + 0.915916i $$0.368534\pi$$
$$12$$ 0 0
$$13$$ 2.59808 + 2.50000i 0.720577 + 0.693375i
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 2.86603 4.96410i 0.695113 1.20397i −0.275029 0.961436i $$-0.588688\pi$$
0.970143 0.242536i $$-0.0779791\pi$$
$$18$$ 0 0
$$19$$ −1.26795 0.732051i −0.290887 0.167944i 0.347455 0.937697i $$-0.387046\pi$$
−0.638342 + 0.769753i $$0.720379\pi$$
$$20$$ 0.866025 + 0.500000i 0.193649 + 0.111803i
$$21$$ 0 0
$$22$$ 0.366025 0.633975i 0.0780369 0.135164i
$$23$$ −0.633975 1.09808i −0.132193 0.228965i 0.792329 0.610094i $$-0.208868\pi$$
−0.924522 + 0.381130i $$0.875535\pi$$
$$24$$ 0 0
$$25$$ 4.00000 0.800000
$$26$$ −3.50000 0.866025i −0.686406 0.169842i
$$27$$ 0 0
$$28$$ −0.866025 + 0.500000i −0.163663 + 0.0944911i
$$29$$ −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i $$-0.256518\pi$$
−0.971023 + 0.238987i $$0.923185\pi$$
$$30$$ 0 0
$$31$$ 5.26795i 0.946152i 0.881022 + 0.473076i $$0.156856\pi$$
−0.881022 + 0.473076i $$0.843144\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ 5.73205i 0.983039i
$$35$$ 0.500000 0.866025i 0.0845154 0.146385i
$$36$$ 0 0
$$37$$ 4.50000 2.59808i 0.739795 0.427121i −0.0821995 0.996616i $$-0.526194\pi$$
0.821995 + 0.569495i $$0.192861\pi$$
$$38$$ 1.46410 0.237509
$$39$$ 0 0
$$40$$ −1.00000 −0.158114
$$41$$ 2.13397 1.23205i 0.333271 0.192414i −0.324021 0.946050i $$-0.605035\pi$$
0.657292 + 0.753636i $$0.271702\pi$$
$$42$$ 0 0
$$43$$ −6.09808 + 10.5622i −0.929948 + 1.61072i −0.146544 + 0.989204i $$0.546815\pi$$
−0.783404 + 0.621513i $$0.786518\pi$$
$$44$$ 0.732051i 0.110361i
$$45$$ 0 0
$$46$$ 1.09808 + 0.633975i 0.161903 + 0.0934745i
$$47$$ 2.92820i 0.427122i 0.976930 + 0.213561i $$0.0685063\pi$$
−0.976930 + 0.213561i $$0.931494\pi$$
$$48$$ 0 0
$$49$$ 0.500000 + 0.866025i 0.0714286 + 0.123718i
$$50$$ −3.46410 + 2.00000i −0.489898 + 0.282843i
$$51$$ 0 0
$$52$$ 3.46410 1.00000i 0.480384 0.138675i
$$53$$ −1.53590 −0.210972 −0.105486 0.994421i $$-0.533640\pi$$
−0.105486 + 0.994421i $$0.533640\pi$$
$$54$$ 0 0
$$55$$ −0.366025 0.633975i −0.0493549 0.0854851i
$$56$$ 0.500000 0.866025i 0.0668153 0.115728i
$$57$$ 0 0
$$58$$ 2.59808 + 1.50000i 0.341144 + 0.196960i
$$59$$ 9.29423 + 5.36603i 1.21001 + 0.698597i 0.962760 0.270356i $$-0.0871414\pi$$
0.247245 + 0.968953i $$0.420475\pi$$
$$60$$ 0 0
$$61$$ 5.86603 10.1603i 0.751068 1.30089i −0.196238 0.980556i $$-0.562873\pi$$
0.947306 0.320331i $$-0.103794\pi$$
$$62$$ −2.63397 4.56218i −0.334515 0.579397i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −2.50000 + 2.59808i −0.310087 + 0.322252i
$$66$$ 0 0
$$67$$ 10.0981 5.83013i 1.23368 0.712263i 0.265882 0.964006i $$-0.414337\pi$$
0.967794 + 0.251742i $$0.0810035\pi$$
$$68$$ −2.86603 4.96410i −0.347557 0.601986i
$$69$$ 0 0
$$70$$ 1.00000i 0.119523i
$$71$$ 12.0000 + 6.92820i 1.42414 + 0.822226i 0.996649 0.0817942i $$-0.0260650\pi$$
0.427489 + 0.904021i $$0.359398\pi$$
$$72$$ 0 0
$$73$$ 11.3923i 1.33337i 0.745340 + 0.666684i $$0.232287\pi$$
−0.745340 + 0.666684i $$0.767713\pi$$
$$74$$ −2.59808 + 4.50000i −0.302020 + 0.523114i
$$75$$ 0 0
$$76$$ −1.26795 + 0.732051i −0.145444 + 0.0839720i
$$77$$ 0.732051 0.0834249
$$78$$ 0 0
$$79$$ −3.80385 −0.427966 −0.213983 0.976837i $$-0.568644\pi$$
−0.213983 + 0.976837i $$0.568644\pi$$
$$80$$ 0.866025 0.500000i 0.0968246 0.0559017i
$$81$$ 0 0
$$82$$ −1.23205 + 2.13397i −0.136057 + 0.235658i
$$83$$ 3.80385i 0.417527i 0.977966 + 0.208763i $$0.0669438\pi$$
−0.977966 + 0.208763i $$0.933056\pi$$
$$84$$ 0 0
$$85$$ 4.96410 + 2.86603i 0.538432 + 0.310864i
$$86$$ 12.1962i 1.31514i
$$87$$ 0 0
$$88$$ −0.366025 0.633975i −0.0390184 0.0675819i
$$89$$ −2.19615 + 1.26795i −0.232792 + 0.134402i −0.611859 0.790967i $$-0.709578\pi$$
0.379068 + 0.925369i $$0.376245\pi$$
$$90$$ 0 0
$$91$$ −1.00000 3.46410i −0.104828 0.363137i
$$92$$ −1.26795 −0.132193
$$93$$ 0 0
$$94$$ −1.46410 2.53590i −0.151011 0.261558i
$$95$$ 0.732051 1.26795i 0.0751068 0.130089i
$$96$$ 0 0
$$97$$ −4.73205 2.73205i −0.480467 0.277398i 0.240144 0.970737i $$-0.422805\pi$$
−0.720611 + 0.693340i $$0.756139\pi$$
$$98$$ −0.866025 0.500000i −0.0874818 0.0505076i
$$99$$ 0 0
$$100$$ 2.00000 3.46410i 0.200000 0.346410i
$$101$$ −0.598076 1.03590i −0.0595108 0.103076i 0.834735 0.550652i $$-0.185621\pi$$
−0.894246 + 0.447576i $$0.852287\pi$$
$$102$$ 0 0
$$103$$ 8.39230 0.826918 0.413459 0.910523i $$-0.364320\pi$$
0.413459 + 0.910523i $$0.364320\pi$$
$$104$$ −2.50000 + 2.59808i −0.245145 + 0.254762i
$$105$$ 0 0
$$106$$ 1.33013 0.767949i 0.129193 0.0745898i
$$107$$ 5.46410 + 9.46410i 0.528235 + 0.914929i 0.999458 + 0.0329154i $$0.0104792\pi$$
−0.471224 + 0.882014i $$0.656187\pi$$
$$108$$ 0 0
$$109$$ 10.0000i 0.957826i −0.877862 0.478913i $$-0.841031\pi$$
0.877862 0.478913i $$-0.158969\pi$$
$$110$$ 0.633975 + 0.366025i 0.0604471 + 0.0348992i
$$111$$ 0 0
$$112$$ 1.00000i 0.0944911i
$$113$$ 5.69615 9.86603i 0.535849 0.928118i −0.463273 0.886216i $$-0.653325\pi$$
0.999122 0.0419019i $$-0.0133417\pi$$
$$114$$ 0 0
$$115$$ 1.09808 0.633975i 0.102396 0.0591184i
$$116$$ −3.00000 −0.278543
$$117$$ 0 0
$$118$$ −10.7321 −0.987965
$$119$$ −4.96410 + 2.86603i −0.455058 + 0.262728i
$$120$$ 0 0
$$121$$ −5.23205 + 9.06218i −0.475641 + 0.823834i
$$122$$ 11.7321i 1.06217i
$$123$$ 0 0
$$124$$ 4.56218 + 2.63397i 0.409696 + 0.236538i
$$125$$ 9.00000i 0.804984i
$$126$$ 0 0
$$127$$ 4.92820 + 8.53590i 0.437307 + 0.757438i 0.997481 0.0709368i $$-0.0225989\pi$$
−0.560173 + 0.828375i $$0.689266\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ 0.866025 3.50000i 0.0759555 0.306970i
$$131$$ 5.07180 0.443125 0.221562 0.975146i $$-0.428884\pi$$
0.221562 + 0.975146i $$0.428884\pi$$
$$132$$ 0 0
$$133$$ 0.732051 + 1.26795i 0.0634769 + 0.109945i
$$134$$ −5.83013 + 10.0981i −0.503646 + 0.872341i
$$135$$ 0 0
$$136$$ 4.96410 + 2.86603i 0.425668 + 0.245760i
$$137$$ 5.30385 + 3.06218i 0.453138 + 0.261620i 0.709155 0.705053i $$-0.249077\pi$$
−0.256016 + 0.966672i $$0.582410\pi$$
$$138$$ 0 0
$$139$$ 0.169873 0.294229i 0.0144084 0.0249561i −0.858731 0.512426i $$-0.828747\pi$$
0.873140 + 0.487470i $$0.162080\pi$$
$$140$$ −0.500000 0.866025i −0.0422577 0.0731925i
$$141$$ 0 0
$$142$$ −13.8564 −1.16280
$$143$$ −2.56218 0.633975i −0.214260 0.0530156i
$$144$$ 0 0
$$145$$ 2.59808 1.50000i 0.215758 0.124568i
$$146$$ −5.69615 9.86603i −0.471417 0.816518i
$$147$$ 0 0
$$148$$ 5.19615i 0.427121i
$$149$$ 14.8923 + 8.59808i 1.22003 + 0.704382i 0.964923 0.262532i $$-0.0845576\pi$$
0.255102 + 0.966914i $$0.417891\pi$$
$$150$$ 0 0
$$151$$ 12.3923i 1.00847i 0.863566 + 0.504236i $$0.168226\pi$$
−0.863566 + 0.504236i $$0.831774\pi$$
$$152$$ 0.732051 1.26795i 0.0593772 0.102844i
$$153$$ 0 0
$$154$$ −0.633975 + 0.366025i −0.0510871 + 0.0294952i
$$155$$ −5.26795 −0.423132
$$156$$ 0 0
$$157$$ 13.7321 1.09594 0.547968 0.836499i $$-0.315401\pi$$
0.547968 + 0.836499i $$0.315401\pi$$
$$158$$ 3.29423 1.90192i 0.262075 0.151309i
$$159$$ 0 0
$$160$$ −0.500000 + 0.866025i −0.0395285 + 0.0684653i
$$161$$ 1.26795i 0.0999284i
$$162$$ 0 0
$$163$$ −0.633975 0.366025i −0.0496567 0.0286693i 0.474966 0.880004i $$-0.342460\pi$$
−0.524623 + 0.851335i $$0.675794\pi$$
$$164$$ 2.46410i 0.192414i
$$165$$ 0 0
$$166$$ −1.90192 3.29423i −0.147618 0.255682i
$$167$$ 4.56218 2.63397i 0.353032 0.203823i −0.312988 0.949757i $$-0.601330\pi$$
0.666020 + 0.745934i $$0.267997\pi$$
$$168$$ 0 0
$$169$$ 0.500000 + 12.9904i 0.0384615 + 0.999260i
$$170$$ −5.73205 −0.439628
$$171$$ 0 0
$$172$$ 6.09808 + 10.5622i 0.464974 + 0.805359i
$$173$$ 10.4641 18.1244i 0.795571 1.37797i −0.126905 0.991915i $$-0.540504\pi$$
0.922476 0.386054i $$-0.126162\pi$$
$$174$$ 0 0
$$175$$ −3.46410 2.00000i −0.261861 0.151186i
$$176$$ 0.633975 + 0.366025i 0.0477876 + 0.0275902i
$$177$$ 0 0
$$178$$ 1.26795 2.19615i 0.0950368 0.164609i
$$179$$ −8.19615 14.1962i −0.612609 1.06107i −0.990799 0.135342i $$-0.956787\pi$$
0.378190 0.925728i $$-0.376547\pi$$
$$180$$ 0 0
$$181$$ 3.19615 0.237568 0.118784 0.992920i $$-0.462100\pi$$
0.118784 + 0.992920i $$0.462100\pi$$
$$182$$ 2.59808 + 2.50000i 0.192582 + 0.185312i
$$183$$ 0 0
$$184$$ 1.09808 0.633975i 0.0809513 0.0467372i
$$185$$ 2.59808 + 4.50000i 0.191014 + 0.330847i
$$186$$ 0 0
$$187$$ 4.19615i 0.306853i
$$188$$ 2.53590 + 1.46410i 0.184949 + 0.106781i
$$189$$ 0 0
$$190$$ 1.46410i 0.106217i
$$191$$ 3.56218 6.16987i 0.257750 0.446436i −0.707889 0.706324i $$-0.750352\pi$$
0.965639 + 0.259888i $$0.0836855\pi$$
$$192$$ 0 0
$$193$$ −20.0885 + 11.5981i −1.44600 + 0.834848i −0.998240 0.0593065i $$-0.981111\pi$$
−0.447759 + 0.894154i $$0.647778\pi$$
$$194$$ 5.46410 0.392300
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ −6.12436 + 3.53590i −0.436342 + 0.251922i −0.702045 0.712133i $$-0.747729\pi$$
0.265703 + 0.964055i $$0.414396\pi$$
$$198$$ 0 0
$$199$$ −2.73205 + 4.73205i −0.193670 + 0.335446i −0.946464 0.322810i $$-0.895372\pi$$
0.752794 + 0.658256i $$0.228706\pi$$
$$200$$ 4.00000i 0.282843i
$$201$$ 0 0
$$202$$ 1.03590 + 0.598076i 0.0728856 + 0.0420805i
$$203$$ 3.00000i 0.210559i
$$204$$ 0 0
$$205$$ 1.23205 + 2.13397i 0.0860502 + 0.149043i
$$206$$ −7.26795 + 4.19615i −0.506382 + 0.292360i
$$207$$ 0 0
$$208$$ 0.866025 3.50000i 0.0600481 0.242681i
$$209$$ 1.07180 0.0741377
$$210$$ 0 0
$$211$$ 10.6340 + 18.4186i 0.732073 + 1.26799i 0.955996 + 0.293381i $$0.0947804\pi$$
−0.223923 + 0.974607i $$0.571886\pi$$
$$212$$ −0.767949 + 1.33013i −0.0527430 + 0.0913535i
$$213$$ 0 0
$$214$$ −9.46410 5.46410i −0.646953 0.373518i
$$215$$ −10.5622 6.09808i −0.720335 0.415885i
$$216$$ 0 0
$$217$$ 2.63397 4.56218i 0.178806 0.309701i
$$218$$ 5.00000 + 8.66025i 0.338643 + 0.586546i
$$219$$ 0 0
$$220$$ −0.732051 −0.0493549
$$221$$ 19.8564 5.73205i 1.33569 0.385579i
$$222$$ 0 0
$$223$$ 10.7321 6.19615i 0.718671 0.414925i −0.0955922 0.995421i $$-0.530474\pi$$
0.814263 + 0.580496i $$0.197141\pi$$
$$224$$ −0.500000 0.866025i −0.0334077 0.0578638i
$$225$$ 0 0
$$226$$ 11.3923i 0.757805i
$$227$$ −1.09808 0.633975i −0.0728819 0.0420784i 0.463116 0.886298i $$-0.346731\pi$$
−0.535998 + 0.844219i $$0.680065\pi$$
$$228$$ 0 0
$$229$$ 24.3923i 1.61189i −0.591991 0.805944i $$-0.701658\pi$$
0.591991 0.805944i $$-0.298342\pi$$
$$230$$ −0.633975 + 1.09808i −0.0418030 + 0.0724050i
$$231$$ 0 0
$$232$$ 2.59808 1.50000i 0.170572 0.0984798i
$$233$$ −4.39230 −0.287749 −0.143875 0.989596i $$-0.545956\pi$$
−0.143875 + 0.989596i $$0.545956\pi$$
$$234$$ 0 0
$$235$$ −2.92820 −0.191015
$$236$$ 9.29423 5.36603i 0.605003 0.349299i
$$237$$ 0 0
$$238$$ 2.86603 4.96410i 0.185777 0.321775i
$$239$$ 29.5167i 1.90927i 0.297772 + 0.954637i $$0.403756\pi$$
−0.297772 + 0.954637i $$0.596244\pi$$
$$240$$ 0 0
$$241$$ −13.3301 7.69615i −0.858669 0.495753i 0.00489737 0.999988i $$-0.498441\pi$$
−0.863566 + 0.504235i $$0.831774\pi$$
$$242$$ 10.4641i 0.672658i
$$243$$ 0 0
$$244$$ −5.86603 10.1603i −0.375534 0.650444i
$$245$$ −0.866025 + 0.500000i −0.0553283 + 0.0319438i
$$246$$ 0 0
$$247$$ −1.46410 5.07180i −0.0931586 0.322711i
$$248$$ −5.26795 −0.334515
$$249$$ 0 0
$$250$$ −4.50000 7.79423i −0.284605 0.492950i
$$251$$ −11.4641 + 19.8564i −0.723608 + 1.25333i 0.235937 + 0.971768i $$0.424184\pi$$
−0.959545 + 0.281557i $$0.909149\pi$$
$$252$$ 0 0
$$253$$ 0.803848 + 0.464102i 0.0505375 + 0.0291778i
$$254$$ −8.53590 4.92820i −0.535590 0.309223i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −0.669873 1.16025i −0.0417855 0.0723747i 0.844376 0.535751i $$-0.179971\pi$$
−0.886162 + 0.463376i $$0.846638\pi$$
$$258$$ 0 0
$$259$$ −5.19615 −0.322873
$$260$$ 1.00000 + 3.46410i 0.0620174 + 0.214834i
$$261$$ 0 0
$$262$$ −4.39230 + 2.53590i −0.271357 + 0.156668i
$$263$$ −10.2942 17.8301i −0.634769 1.09945i −0.986564 0.163376i $$-0.947762\pi$$
0.351795 0.936077i $$-0.385572\pi$$
$$264$$ 0 0
$$265$$ 1.53590i 0.0943495i
$$266$$ −1.26795 0.732051i −0.0777430 0.0448849i
$$267$$ 0 0
$$268$$ 11.6603i 0.712263i
$$269$$ −14.3923 + 24.9282i −0.877514 + 1.51990i −0.0234543 + 0.999725i $$0.507466\pi$$
−0.854060 + 0.520174i $$0.825867\pi$$
$$270$$ 0 0
$$271$$ 6.16987 3.56218i 0.374793 0.216387i −0.300757 0.953701i $$-0.597239\pi$$
0.675550 + 0.737314i $$0.263906\pi$$
$$272$$ −5.73205 −0.347557
$$273$$ 0 0
$$274$$ −6.12436 −0.369986
$$275$$ −2.53590 + 1.46410i −0.152920 + 0.0882886i
$$276$$ 0 0
$$277$$ 4.69615 8.13397i 0.282164 0.488723i −0.689753 0.724045i $$-0.742281\pi$$
0.971918 + 0.235321i $$0.0756143\pi$$
$$278$$ 0.339746i 0.0203766i
$$279$$ 0 0
$$280$$ 0.866025 + 0.500000i 0.0517549 + 0.0298807i
$$281$$ 16.6603i 0.993867i 0.867789 + 0.496934i $$0.165541\pi$$
−0.867789 + 0.496934i $$0.834459\pi$$
$$282$$ 0 0
$$283$$ −5.29423 9.16987i −0.314709 0.545092i 0.664666 0.747140i $$-0.268574\pi$$
−0.979376 + 0.202048i $$0.935240\pi$$
$$284$$ 12.0000 6.92820i 0.712069 0.411113i
$$285$$ 0 0
$$286$$ 2.53590 0.732051i 0.149951 0.0432871i
$$287$$ −2.46410 −0.145451
$$288$$ 0 0
$$289$$ −7.92820 13.7321i −0.466365 0.807768i
$$290$$ −1.50000 + 2.59808i −0.0880830 + 0.152564i
$$291$$ 0 0
$$292$$ 9.86603 + 5.69615i 0.577365 + 0.333342i
$$293$$ −15.0622 8.69615i −0.879942 0.508035i −0.00930260 0.999957i $$-0.502961\pi$$
−0.870639 + 0.491922i $$0.836294\pi$$
$$294$$ 0 0
$$295$$ −5.36603 + 9.29423i −0.312422 + 0.541131i
$$296$$ 2.59808 + 4.50000i 0.151010 + 0.261557i
$$297$$ 0 0
$$298$$ −17.1962 −0.996146
$$299$$ 1.09808 4.43782i 0.0635034 0.256646i
$$300$$ 0 0
$$301$$ 10.5622 6.09808i 0.608794 0.351487i
$$302$$ −6.19615 10.7321i −0.356549 0.617560i
$$303$$ 0 0
$$304$$ 1.46410i 0.0839720i
$$305$$ 10.1603 + 5.86603i 0.581774 + 0.335888i
$$306$$ 0 0
$$307$$ 23.5167i 1.34217i −0.741382 0.671083i $$-0.765829\pi$$
0.741382 0.671083i $$-0.234171\pi$$
$$308$$ 0.366025 0.633975i 0.0208562 0.0361241i
$$309$$ 0 0
$$310$$ 4.56218 2.63397i 0.259114 0.149600i
$$311$$ −10.1962 −0.578171 −0.289085 0.957303i $$-0.593351\pi$$
−0.289085 + 0.957303i $$0.593351\pi$$
$$312$$ 0 0
$$313$$ −32.0000 −1.80875 −0.904373 0.426742i $$-0.859661\pi$$
−0.904373 + 0.426742i $$0.859661\pi$$
$$314$$ −11.8923 + 6.86603i −0.671122 + 0.387472i
$$315$$ 0 0
$$316$$ −1.90192 + 3.29423i −0.106992 + 0.185315i
$$317$$ 7.05256i 0.396111i −0.980191 0.198056i $$-0.936537\pi$$
0.980191 0.198056i $$-0.0634627\pi$$
$$318$$ 0 0
$$319$$ 1.90192 + 1.09808i 0.106487 + 0.0614805i
$$320$$ 1.00000i 0.0559017i
$$321$$ 0 0
$$322$$ −0.633975 1.09808i −0.0353300 0.0611934i
$$323$$ −7.26795 + 4.19615i −0.404400 + 0.233480i
$$324$$ 0 0
$$325$$ 10.3923 + 10.0000i 0.576461 + 0.554700i
$$326$$ 0.732051 0.0405445
$$327$$ 0 0
$$328$$ 1.23205 + 2.13397i 0.0680286 + 0.117829i
$$329$$ 1.46410 2.53590i 0.0807185 0.139809i
$$330$$ 0 0
$$331$$ 3.75833 + 2.16987i 0.206577 + 0.119267i 0.599719 0.800210i $$-0.295279\pi$$
−0.393143 + 0.919477i $$0.628612\pi$$
$$332$$ 3.29423 + 1.90192i 0.180794 + 0.104382i
$$333$$ 0 0
$$334$$ −2.63397 + 4.56218i −0.144125 + 0.249631i
$$335$$ 5.83013 + 10.0981i 0.318534 + 0.551717i
$$336$$ 0 0
$$337$$ −6.32051 −0.344300 −0.172150 0.985071i $$-0.555071\pi$$
−0.172150 + 0.985071i $$0.555071\pi$$
$$338$$ −6.92820 11.0000i −0.376845 0.598321i
$$339$$ 0 0
$$340$$ 4.96410 2.86603i 0.269216 0.155432i
$$341$$ −1.92820 3.33975i −0.104418 0.180857i
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ −10.5622 6.09808i −0.569474 0.328786i
$$345$$ 0 0
$$346$$ 20.9282i 1.12511i
$$347$$ 14.4904 25.0981i 0.777884 1.34734i −0.155275 0.987871i $$-0.549626\pi$$
0.933159 0.359464i $$-0.117040\pi$$
$$348$$ 0 0
$$349$$ −1.73205 + 1.00000i −0.0927146 + 0.0535288i −0.545640 0.838019i $$-0.683714\pi$$
0.452926 + 0.891548i $$0.350380\pi$$
$$350$$ 4.00000 0.213809
$$351$$ 0 0
$$352$$ −0.732051 −0.0390184
$$353$$ 31.3301 18.0885i 1.66753 0.962751i 0.698573 0.715539i $$-0.253819\pi$$
0.968961 0.247213i $$-0.0795147\pi$$
$$354$$ 0 0
$$355$$ −6.92820 + 12.0000i −0.367711 + 0.636894i
$$356$$ 2.53590i 0.134402i
$$357$$ 0 0
$$358$$ 14.1962 + 8.19615i 0.750290 + 0.433180i
$$359$$ 16.3923i 0.865153i −0.901597 0.432576i $$-0.857605\pi$$
0.901597 0.432576i $$-0.142395\pi$$
$$360$$ 0 0
$$361$$ −8.42820 14.5981i −0.443590 0.768320i
$$362$$ −2.76795 + 1.59808i −0.145480 + 0.0839930i
$$363$$ 0 0
$$364$$ −3.50000 0.866025i −0.183450 0.0453921i
$$365$$ −11.3923 −0.596300
$$366$$ 0 0
$$367$$ −16.9545 29.3660i −0.885017 1.53289i −0.845694 0.533667i $$-0.820813\pi$$
−0.0393224 0.999227i $$-0.512520\pi$$
$$368$$ −0.633975 + 1.09808i −0.0330482 + 0.0572412i
$$369$$ 0 0
$$370$$ −4.50000 2.59808i −0.233944 0.135068i
$$371$$ 1.33013 + 0.767949i 0.0690568 + 0.0398699i
$$372$$ 0 0
$$373$$ 16.2321 28.1147i 0.840464 1.45573i −0.0490394 0.998797i $$-0.515616\pi$$
0.889503 0.456929i $$-0.151051\pi$$
$$374$$ −2.09808 3.63397i −0.108489 0.187908i
$$375$$ 0 0
$$376$$ −2.92820 −0.151011
$$377$$ 2.59808 10.5000i 0.133808 0.540778i
$$378$$ 0 0
$$379$$ 19.2224 11.0981i 0.987390 0.570070i 0.0828969 0.996558i $$-0.473583\pi$$
0.904493 + 0.426488i $$0.140249\pi$$
$$380$$ −0.732051 1.26795i −0.0375534 0.0650444i
$$381$$ 0 0
$$382$$ 7.12436i 0.364514i
$$383$$ −28.2224 16.2942i −1.44210 0.832596i −0.444109 0.895973i $$-0.646480\pi$$
−0.997990 + 0.0633765i $$0.979813\pi$$
$$384$$ 0 0
$$385$$ 0.732051i 0.0373088i
$$386$$ 11.5981 20.0885i 0.590327 1.02248i
$$387$$ 0 0
$$388$$ −4.73205 + 2.73205i −0.240233 + 0.138699i
$$389$$ 24.3205 1.23310 0.616549 0.787316i $$-0.288530\pi$$
0.616549 + 0.787316i $$0.288530\pi$$
$$390$$ 0 0
$$391$$ −7.26795 −0.367556
$$392$$ −0.866025 + 0.500000i −0.0437409 + 0.0252538i
$$393$$ 0 0
$$394$$ 3.53590 6.12436i 0.178136 0.308541i
$$395$$ 3.80385i 0.191392i
$$396$$ 0 0
$$397$$ −25.5167 14.7321i −1.28064 0.739380i −0.303678 0.952775i $$-0.598215\pi$$
−0.976966 + 0.213394i $$0.931548\pi$$
$$398$$ 5.46410i 0.273891i
$$399$$ 0 0
$$400$$ −2.00000 3.46410i −0.100000 0.173205i
$$401$$ 28.6244 16.5263i 1.42943 0.825283i 0.432356 0.901703i $$-0.357682\pi$$
0.997076 + 0.0764198i $$0.0243489\pi$$
$$402$$ 0 0
$$403$$ −13.1699 + 13.6865i −0.656038 + 0.681775i
$$404$$ −1.19615 −0.0595108
$$405$$ 0 0
$$406$$ −1.50000 2.59808i −0.0744438 0.128940i
$$407$$ −1.90192 + 3.29423i −0.0942749 + 0.163289i
$$408$$ 0 0
$$409$$ 22.7942 + 13.1603i 1.12710 + 0.650733i 0.943204 0.332213i $$-0.107795\pi$$
0.183898 + 0.982945i $$0.441129\pi$$
$$410$$ −2.13397 1.23205i −0.105389 0.0608467i
$$411$$ 0 0
$$412$$ 4.19615 7.26795i 0.206730 0.358066i
$$413$$ −5.36603 9.29423i −0.264045 0.457339i
$$414$$ 0 0
$$415$$ −3.80385 −0.186724
$$416$$ 1.00000 + 3.46410i 0.0490290 + 0.169842i
$$417$$ 0 0
$$418$$ −0.928203 + 0.535898i −0.0453999 + 0.0262116i
$$419$$ 2.56218 + 4.43782i 0.125171 + 0.216802i 0.921800 0.387667i $$-0.126719\pi$$
−0.796629 + 0.604469i $$0.793386\pi$$
$$420$$ 0 0
$$421$$ 14.1244i 0.688379i 0.938900 + 0.344189i $$0.111846\pi$$
−0.938900 + 0.344189i $$0.888154\pi$$
$$422$$ −18.4186 10.6340i −0.896603 0.517654i
$$423$$ 0 0
$$424$$ 1.53590i 0.0745898i
$$425$$ 11.4641 19.8564i 0.556091 0.963177i
$$426$$ 0 0
$$427$$ −10.1603 + 5.86603i −0.491689 + 0.283877i
$$428$$ 10.9282 0.528235
$$429$$ 0 0
$$430$$ 12.1962 0.588151
$$431$$ −22.9808 + 13.2679i −1.10694 + 0.639095i −0.938036 0.346537i $$-0.887357\pi$$
−0.168908 + 0.985632i $$0.554024\pi$$
$$432$$ 0 0
$$433$$ 10.8660 18.8205i 0.522188 0.904456i −0.477479 0.878643i $$-0.658449\pi$$
0.999667 0.0258127i $$-0.00821735\pi$$
$$434$$ 5.26795i 0.252870i
$$435$$ 0 0
$$436$$ −8.66025 5.00000i −0.414751 0.239457i
$$437$$ 1.85641i 0.0888040i
$$438$$ 0 0
$$439$$ −9.63397 16.6865i −0.459805 0.796405i 0.539146 0.842212i $$-0.318747\pi$$
−0.998950 + 0.0458077i $$0.985414\pi$$
$$440$$ 0.633975 0.366025i 0.0302236 0.0174496i
$$441$$ 0 0
$$442$$ −14.3301 + 14.8923i −0.681615 + 0.708355i
$$443$$ −35.3205 −1.67813 −0.839064 0.544033i $$-0.816897\pi$$
−0.839064 + 0.544033i $$0.816897\pi$$
$$444$$ 0 0
$$445$$ −1.26795 2.19615i −0.0601066 0.104108i
$$446$$ −6.19615 + 10.7321i −0.293396 + 0.508177i
$$447$$ 0 0
$$448$$ 0.866025 + 0.500000i 0.0409159 + 0.0236228i
$$449$$ −15.5885 9.00000i −0.735665 0.424736i 0.0848262 0.996396i $$-0.472967\pi$$
−0.820491 + 0.571660i $$0.806300\pi$$
$$450$$ 0 0
$$451$$ −0.901924 + 1.56218i −0.0424699 + 0.0735601i
$$452$$ −5.69615 9.86603i −0.267924 0.464059i
$$453$$ 0 0
$$454$$ 1.26795 0.0595078
$$455$$ 3.46410 1.00000i 0.162400 0.0468807i
$$456$$ 0 0
$$457$$ −12.3564 + 7.13397i −0.578008 + 0.333713i −0.760341 0.649524i $$-0.774968\pi$$
0.182333 + 0.983237i $$0.441635\pi$$
$$458$$ 12.1962 + 21.1244i 0.569889 + 0.987076i
$$459$$ 0 0
$$460$$ 1.26795i 0.0591184i
$$461$$ −7.20577 4.16025i −0.335606 0.193762i 0.322721 0.946494i $$-0.395402\pi$$
−0.658327 + 0.752732i $$0.728736\pi$$
$$462$$ 0 0
$$463$$ 3.94744i 0.183453i −0.995784 0.0917266i $$-0.970761\pi$$
0.995784 0.0917266i $$-0.0292386\pi$$
$$464$$ −1.50000 + 2.59808i −0.0696358 + 0.120613i
$$465$$ 0 0
$$466$$ 3.80385 2.19615i 0.176210 0.101735i
$$467$$ −24.7321 −1.14446 −0.572231 0.820092i $$-0.693922\pi$$
−0.572231 + 0.820092i $$0.693922\pi$$
$$468$$ 0 0
$$469$$ −11.6603 −0.538421
$$470$$ 2.53590 1.46410i 0.116972 0.0675340i
$$471$$ 0 0
$$472$$ −5.36603 + 9.29423i −0.246991 + 0.427802i
$$473$$ 8.92820i 0.410519i
$$474$$ 0 0
$$475$$ −5.07180 2.92820i −0.232710 0.134355i
$$476$$ 5.73205i 0.262728i
$$477$$ 0 0
$$478$$ −14.7583 25.5622i −0.675030 1.16919i
$$479$$ −27.8827 + 16.0981i −1.27399 + 0.735540i −0.975737 0.218946i $$-0.929738\pi$$
−0.298256 + 0.954486i $$0.596405\pi$$
$$480$$ 0 0
$$481$$ 18.1865 + 4.50000i 0.829235 + 0.205182i
$$482$$ 15.3923 0.701100
$$483$$ 0 0
$$484$$ 5.23205 + 9.06218i 0.237820 + 0.411917i
$$485$$ 2.73205 4.73205i 0.124056 0.214871i
$$486$$ 0 0
$$487$$ 27.1244 + 15.6603i 1.22912 + 0.709634i 0.966846 0.255359i $$-0.0821937\pi$$
0.262276 + 0.964993i $$0.415527\pi$$
$$488$$ 10.1603 + 5.86603i 0.459933 + 0.265542i
$$489$$ 0 0
$$490$$ 0.500000 0.866025i 0.0225877 0.0391230i
$$491$$ 13.8564 + 24.0000i 0.625331 + 1.08310i 0.988477 + 0.151373i $$0.0483693\pi$$
−0.363146 + 0.931732i $$0.618297\pi$$
$$492$$ 0 0
$$493$$ −17.1962 −0.774476
$$494$$ 3.80385 + 3.66025i 0.171143 + 0.164683i
$$495$$ 0 0
$$496$$ 4.56218 2.63397i 0.204848 0.118269i
$$497$$ −6.92820 12.0000i −0.310772 0.538274i
$$498$$ 0 0
$$499$$ 11.2679i 0.504423i 0.967672 + 0.252211i $$0.0811578\pi$$
−0.967672 + 0.252211i $$0.918842\pi$$
$$500$$ 7.79423 + 4.50000i 0.348569 + 0.201246i
$$501$$ 0 0
$$502$$ 22.9282i 1.02334i
$$503$$ 10.3660 17.9545i 0.462198 0.800551i −0.536872 0.843664i $$-0.680394\pi$$
0.999070 + 0.0431129i $$0.0137275\pi$$
$$504$$ 0 0
$$505$$ 1.03590 0.598076i 0.0460969 0.0266140i
$$506$$ −0.928203 −0.0412637
$$507$$ 0 0
$$508$$ 9.85641 0.437307
$$509$$ 23.7224 13.6962i 1.05148 0.607071i 0.128415 0.991720i $$-0.459011\pi$$
0.923063 + 0.384649i $$0.125678\pi$$
$$510$$ 0 0
$$511$$ 5.69615 9.86603i 0.251983 0.436447i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 1.16025 + 0.669873i 0.0511766 + 0.0295468i
$$515$$ 8.39230i 0.369809i
$$516$$ 0 0
$$517$$ −1.07180 1.85641i −0.0471376 0.0816447i
$$518$$ 4.50000 2.59808i 0.197719 0.114153i
$$519$$ 0 0
$$520$$ −2.59808 2.50000i −0.113933 0.109632i
$$521$$ −44.3731 −1.94402 −0.972010 0.234941i $$-0.924510\pi$$
−0.972010 + 0.234941i $$0.924510\pi$$
$$522$$ 0 0
$$523$$ −10.7321 18.5885i −0.469280 0.812816i 0.530103 0.847933i $$-0.322153\pi$$
−0.999383 + 0.0351165i $$0.988820\pi$$
$$524$$ 2.53590 4.39230i 0.110781 0.191879i
$$525$$ 0 0
$$526$$ 17.8301 + 10.2942i 0.777430 + 0.448850i
$$527$$ 26.1506 + 15.0981i 1.13914 + 0.657683i
$$528$$ 0 0
$$529$$ 10.6962 18.5263i 0.465050 0.805490i
$$530$$ 0.767949 + 1.33013i 0.0333576 + 0.0577770i
$$531$$ 0 0
$$532$$ 1.46410 0.0634769
$$533$$ 8.62436 + 2.13397i 0.373562 + 0.0924327i
$$534$$ 0 0
$$535$$ −9.46410 + 5.46410i −0.409169 + 0.236234i
$$536$$ 5.83013 + 10.0981i 0.251823 + 0.436170i
$$537$$ 0 0
$$538$$ 28.7846i 1.24099i
$$539$$ −0.633975 0.366025i −0.0273072 0.0157658i
$$540$$ 0 0
$$541$$ 8.26795i 0.355467i 0.984079 + 0.177733i $$0.0568765\pi$$
−0.984079 + 0.177733i $$0.943124\pi$$
$$542$$ −3.56218 + 6.16987i −0.153009 + 0.265019i
$$543$$ 0 0
$$544$$ 4.96410 2.86603i 0.212834 0.122880i
$$545$$ 10.0000 0.428353
$$546$$ 0 0
$$547$$ −30.4449 −1.30173 −0.650864 0.759194i $$-0.725593\pi$$
−0.650864 + 0.759194i $$0.725593\pi$$
$$548$$ 5.30385 3.06218i 0.226569 0.130810i
$$549$$ 0 0
$$550$$ 1.46410 2.53590i 0.0624295 0.108131i
$$551$$ 4.39230i 0.187118i
$$552$$ 0 0
$$553$$ 3.29423 + 1.90192i 0.140085 + 0.0808780i
$$554$$ 9.39230i 0.399041i
$$555$$ 0 0
$$556$$ −0.169873 0.294229i −0.00720422 0.0124781i
$$557$$ −22.6244 + 13.0622i −0.958625 + 0.553462i −0.895749 0.444559i $$-0.853360\pi$$
−0.0628752 + 0.998021i $$0.520027\pi$$
$$558$$ 0 0
$$559$$ −42.2487 + 12.1962i −1.78693 + 0.515842i
$$560$$ −1.00000 −0.0422577
$$561$$ 0 0
$$562$$ −8.33013 14.4282i −0.351385 0.608617i
$$563$$ 14.2224 24.6340i 0.599404 1.03820i −0.393505 0.919322i $$-0.628738\pi$$
0.992909 0.118876i $$-0.0379290\pi$$
$$564$$ 0 0
$$565$$ 9.86603 + 5.69615i 0.415067 + 0.239639i
$$566$$ 9.16987 + 5.29423i 0.385439 + 0.222533i
$$567$$ 0 0
$$568$$ −6.92820 + 12.0000i −0.290701 + 0.503509i
$$569$$ 5.66025 + 9.80385i 0.237290 + 0.410999i 0.959936 0.280220i $$-0.0904074\pi$$
−0.722646 + 0.691219i $$0.757074\pi$$
$$570$$ 0 0
$$571$$ 5.46410 0.228666 0.114333 0.993443i $$-0.463527\pi$$
0.114333 + 0.993443i $$0.463527\pi$$
$$572$$ −1.83013 + 1.90192i −0.0765215 + 0.0795234i
$$573$$ 0 0
$$574$$ 2.13397 1.23205i 0.0890704 0.0514248i
$$575$$ −2.53590 4.39230i −0.105754 0.183172i
$$576$$ 0 0
$$577$$ 34.1769i 1.42280i 0.702786 + 0.711402i $$0.251939\pi$$
−0.702786 + 0.711402i $$0.748061\pi$$
$$578$$ 13.7321 + 7.92820i 0.571178 + 0.329770i
$$579$$ 0 0
$$580$$ 3.00000i 0.124568i
$$581$$ 1.90192 3.29423i 0.0789051 0.136668i
$$582$$ 0 0
$$583$$ 0.973721 0.562178i 0.0403274 0.0232830i
$$584$$ −11.3923 −0.471417
$$585$$ 0 0
$$586$$ 17.3923 0.718469
$$587$$ 24.9282 14.3923i 1.02890 0.594034i 0.112229 0.993682i $$-0.464201\pi$$
0.916668 + 0.399648i $$0.130868\pi$$
$$588$$ 0 0
$$589$$ 3.85641 6.67949i 0.158900 0.275224i
$$590$$ 10.7321i 0.441832i
$$591$$ 0 0
$$592$$ −4.50000 2.59808i −0.184949 0.106780i
$$593$$ 3.14359i 0.129092i 0.997915 + 0.0645460i $$0.0205599\pi$$
−0.997915 + 0.0645460i $$0.979440\pi$$
$$594$$ 0 0
$$595$$ −2.86603 4.96410i −0.117496 0.203508i
$$596$$ 14.8923 8.59808i 0.610013 0.352191i
$$597$$ 0 0
$$598$$ 1.26795 + 4.39230i 0.0518503 + 0.179615i
$$599$$ −30.9282 −1.26369 −0.631846 0.775094i $$-0.717703\pi$$
−0.631846 + 0.775094i $$0.717703\pi$$
$$600$$ 0 0
$$601$$ 11.5263 + 19.9641i 0.470167 + 0.814353i 0.999418 0.0341125i $$-0.0108604\pi$$
−0.529251 + 0.848465i $$0.677527\pi$$
$$602$$ −6.09808 + 10.5622i −0.248539 + 0.430482i
$$603$$ 0 0
$$604$$ 10.7321 + 6.19615i 0.436681 + 0.252118i
$$605$$ −9.06218 5.23205i −0.368430 0.212713i
$$606$$ 0 0
$$607$$ 4.92820 8.53590i 0.200030 0.346461i −0.748508 0.663126i $$-0.769230\pi$$
0.948538 + 0.316664i $$0.102563\pi$$
$$608$$ −0.732051 1.26795i −0.0296886 0.0514221i
$$609$$ 0 0
$$610$$ −11.7321 −0.475017
$$611$$ −7.32051 + 7.60770i −0.296156 + 0.307774i
$$612$$ 0 0
$$613$$ 13.8397 7.99038i 0.558982 0.322728i −0.193755 0.981050i $$-0.562067\pi$$
0.752737 + 0.658322i $$0.228733\pi$$
$$614$$ 11.7583 + 20.3660i 0.474528 + 0.821906i
$$615$$ 0 0
$$616$$ 0.732051i 0.0294952i
$$617$$ 28.7487 + 16.5981i 1.15738 + 0.668213i 0.950675 0.310190i $$-0.100393\pi$$
0.206705 + 0.978403i $$0.433726\pi$$
$$618$$ 0 0
$$619$$ 34.0526i 1.36869i 0.729159 + 0.684344i $$0.239911\pi$$
−0.729159 + 0.684344i $$0.760089\pi$$
$$620$$ −2.63397 + 4.56218i −0.105783 + 0.183221i
$$621$$ 0 0
$$622$$ 8.83013 5.09808i 0.354056 0.204414i
$$623$$ 2.53590 0.101599
$$624$$ 0 0
$$625$$ 11.0000 0.440000
$$626$$ 27.7128 16.0000i 1.10763 0.639489i
$$627$$ 0 0
$$628$$ 6.86603 11.8923i 0.273984 0.474555i
$$629$$ 29.7846i 1.18759i
$$630$$ 0 0
$$631$$ 9.12436 + 5.26795i 0.363235 + 0.209714i 0.670499 0.741911i $$-0.266080\pi$$
−0.307264 + 0.951624i $$0.599413\pi$$
$$632$$ 3.80385i 0.151309i
$$633$$ 0 0
$$634$$ 3.52628 + 6.10770i 0.140046 + 0.242568i
$$635$$ −8.53590 + 4.92820i −0.338737 + 0.195570i
$$636$$ 0 0
$$637$$ −0.866025 + 3.50000i −0.0343132 + 0.138675i
$$638$$ −2.19615 −0.0869465
$$639$$ 0 0
$$640$$ 0.500000 + 0.866025i 0.0197642 + 0.0342327i
$$641$$ −22.2321 + 38.5070i −0.878113 + 1.52094i −0.0247042 + 0.999695i $$0.507864\pi$$
−0.853409 + 0.521242i $$0.825469\pi$$
$$642$$ 0 0
$$643$$ 30.9282 + 17.8564i 1.21969 + 0.704188i 0.964851 0.262796i $$-0.0846446\pi$$
0.254838 + 0.966984i $$0.417978\pi$$
$$644$$ 1.09808 + 0.633975i 0.0432703 + 0.0249821i
$$645$$ 0 0
$$646$$ 4.19615 7.26795i 0.165095 0.285954i
$$647$$ 6.92820 + 12.0000i 0.272376 + 0.471769i 0.969470 0.245211i $$-0.0788573\pi$$
−0.697094 + 0.716980i $$0.745524\pi$$
$$648$$ 0 0
$$649$$ −7.85641 −0.308391
$$650$$ −14.0000 3.46410i −0.549125 0.135873i
$$651$$ 0 0
$$652$$ −0.633975 + 0.366025i −0.0248284 + 0.0143347i
$$653$$ 6.19615 + 10.7321i 0.242474 + 0.419978i 0.961418 0.275090i $$-0.0887077\pi$$
−0.718944 + 0.695068i $$0.755374\pi$$
$$654$$ 0 0
$$655$$ 5.07180i 0.198171i
$$656$$ −2.13397 1.23205i −0.0833177 0.0481035i
$$657$$ 0 0
$$658$$ 2.92820i 0.114153i
$$659$$ 4.39230 7.60770i 0.171100 0.296354i −0.767705 0.640804i $$-0.778601\pi$$
0.938805 + 0.344450i $$0.111935\pi$$
$$660$$ 0 0
$$661$$ 1.66987 0.964102i 0.0649505 0.0374992i −0.467173 0.884166i $$-0.654727\pi$$
0.532124 + 0.846667i $$0.321394\pi$$
$$662$$ −4.33975 −0.168669
$$663$$ 0 0
$$664$$ −3.80385 −0.147618
$$665$$ −1.26795 + 0.732051i −0.0491690 + 0.0283877i
$$666$$ 0 0
$$667$$ −1.90192 + 3.29423i −0.0736428 + 0.127553i
$$668$$ 5.26795i 0.203823i
$$669$$ 0 0
$$670$$ −10.0981 5.83013i −0.390123 0.225237i
$$671$$ 8.58846i 0.331554i
$$672$$ 0 0
$$673$$ 10.8923 + 18.8660i 0.419867 + 0.727232i 0.995926 0.0901768i $$-0.0287432\pi$$
−0.576058 + 0.817409i $$0.695410\pi$$
$$674$$ 5.47372 3.16025i 0.210840 0.121728i
$$675$$ 0 0
$$676$$ 11.5000 + 6.06218i 0.442308 + 0.233161i
$$677$$ −27.8564 −1.07061 −0.535304 0.844659i $$-0.679803\pi$$
−0.535304 + 0.844659i $$0.679803\pi$$
$$678$$ 0 0
$$679$$ 2.73205 + 4.73205i 0.104846 + 0.181599i
$$680$$ −2.86603 + 4.96410i −0.109907 + 0.190365i
$$681$$ 0 0
$$682$$ 3.33975 + 1.92820i 0.127885 + 0.0738347i
$$683$$ −5.66025 3.26795i −0.216584 0.125045i 0.387784 0.921750i $$-0.373241\pi$$
−0.604367 + 0.796706i $$0.706574\pi$$
$$684$$ 0 0
$$685$$ −3.06218 + 5.30385i −0.117000 + 0.202650i
$$686$$ 0.500000 + 0.866025i 0.0190901 + 0.0330650i
$$687$$ 0 0
$$688$$ 12.1962 0.464974
$$689$$ −3.99038 3.83975i −0.152021 0.146283i
$$690$$ 0 0
$$691$$ 5.07180 2.92820i 0.192940 0.111394i −0.400418 0.916333i $$-0.631135\pi$$
0.593358 + 0.804938i $$0.297802\pi$$
$$692$$ −10.4641 18.1244i −0.397785 0.688985i
$$693$$ 0 0
$$694$$ 28.9808i 1.10009i
$$695$$ 0.294229 + 0.169873i 0.0111607 + 0.00644365i
$$696$$ 0 0
$$697$$ 14.1244i 0.534998i
$$698$$ 1.00000 1.73205i 0.0378506 0.0655591i
$$699$$ 0 0
$$700$$ −3.46410 + 2.00000i −0.130931 + 0.0755929i
$$701$$ 14.5359 0.549013 0.274507 0.961585i $$-0.411485\pi$$
0.274507 + 0.961585i $$0.411485\pi$$
$$702$$ 0 0
$$703$$ −7.60770 −0.286930
$$704$$ 0.633975 0.366025i 0.0238938 0.0137951i
$$705$$ 0 0
$$706$$ −18.0885 + 31.3301i −0.680768 + 1.17912i
$$707$$ 1.19615i 0.0449859i
$$708$$ 0 0
$$709$$ −5.64359 3.25833i −0.211950 0.122369i 0.390268 0.920702i $$-0.372383\pi$$
−0.602217 + 0.798332i $$0.705716\pi$$
$$710$$ 13.8564i 0.520022i
$$711$$ 0 0
$$712$$ −1.26795 2.19615i −0.0475184 0.0823043i
$$713$$ 5.78461 3.33975i 0.216635 0.125074i
$$714$$ 0 0
$$715$$ 0.633975 2.56218i 0.0237093 0.0958200i
$$716$$ −16.3923 −0.612609
$$717$$ 0 0
$$718$$ 8.19615 + 14.1962i 0.305878 + 0.529796i
$$719$$ 3.09808 5.36603i 0.115539 0.200119i −0.802456 0.596711i $$-0.796474\pi$$
0.917995 + 0.396592i $$0.129807\pi$$
$$720$$ 0 0
$$721$$ −7.26795 4.19615i −0.270673 0.156273i
$$722$$ 14.5981 + 8.42820i 0.543284 + 0.313665i
$$723$$ 0 0
$$724$$ 1.59808 2.76795i 0.0593920 0.102870i
$$725$$ −6.00000 10.3923i −0.222834 0.385961i
$$726$$ 0 0
$$727$$ −53.8564 −1.99742 −0.998712 0.0507424i $$-0.983841\pi$$
−0.998712 + 0.0507424i $$0.983841\pi$$
$$728$$ 3.46410 1.00000i 0.128388 0.0370625i
$$729$$ 0 0
$$730$$ 9.86603 5.69615i 0.365158 0.210824i
$$731$$ 34.9545 + 60.5429i 1.29284 + 2.23926i
$$732$$ 0 0
$$733$$ 2.46410i 0.0910137i −0.998964 0.0455068i $$-0.985510\pi$$
0.998964 0.0455068i $$-0.0144903\pi$$
$$734$$ 29.3660 + 16.9545i 1.08392 + 0.625801i
$$735$$ 0 0
$$736$$ 1.26795i 0.0467372i
$$737$$ −4.26795 + 7.39230i −0.157212 + 0.272299i
$$738$$ 0 0
$$739$$ 5.66025 3.26795i 0.208216 0.120213i −0.392266 0.919852i $$-0.628309\pi$$
0.600482 + 0.799638i $$0.294975\pi$$
$$740$$ 5.19615 0.191014
$$741$$ 0 0
$$742$$ −1.53590 −0.0563846
$$743$$ 4.39230 2.53590i 0.161138 0.0930331i −0.417262 0.908786i $$-0.637010\pi$$
0.578401 + 0.815753i $$0.303677\pi$$
$$744$$ 0 0
$$745$$ −8.59808 + 14.8923i −0.315009 + 0.545612i
$$746$$ 32.4641i 1.18860i
$$747$$ 0 0
$$748$$ 3.63397 + 2.09808i 0.132871 + 0.0767133i
$$749$$ 10.9282i 0.399308i
$$750$$ 0 0
$$751$$ 3.22243 + 5.58142i 0.117588 + 0.203669i 0.918811 0.394697i $$-0.129150\pi$$
−0.801223 + 0.598366i $$0.795817\pi$$
$$752$$ 2.53590 1.46410i 0.0924747 0.0533903i
$$753$$ 0 0
$$754$$ 3.00000 + 10.3923i 0.109254 + 0.378465i
$$755$$ −12.3923 −0.451002
$$756$$ 0 0
$$757$$ 22.1962 + 38.4449i 0.806733 + 1.39730i 0.915115 + 0.403193i $$0.132100\pi$$
−0.108382 + 0.994109i $$0.534567\pi$$
$$758$$ −11.0981 + 19.2224i −0.403100 + 0.698190i
$$759$$ 0 0
$$760$$ 1.26795 + 0.732051i 0.0459934 + 0.0265543i
$$761$$ −15.8038 9.12436i −0.572889 0.330758i 0.185413 0.982661i $$-0.440638\pi$$
−0.758302 + 0.651903i $$0.773971\pi$$
$$762$$ 0 0
$$763$$ −5.00000 + 8.66025i −0.181012 + 0.313522i
$$764$$ −3.56218 6.16987i −0.128875 0.223218i
$$765$$ 0 0
$$766$$ 32.5885 1.17747
$$767$$ 10.7321 + 37.1769i 0.387512 + 1.34238i
$$768$$ 0 0
$$769$$ 0.339746 0.196152i 0.0122516 0.00707344i −0.493862 0.869540i $$-0.664415\pi$$
0.506113 + 0.862467i $$0.331082\pi$$
$$770$$ −0.366025 0.633975i −0.0131906 0.0228469i
$$771$$ 0 0
$$772$$ 23.1962i 0.834848i
$$773$$ −40.0526 23.1244i −1.44059 0.831725i −0.442701 0.896669i $$-0.645980\pi$$
−0.997889 + 0.0649438i $$0.979313\pi$$
$$774$$ 0 0
$$775$$ 21.0718i 0.756921i
$$776$$ 2.73205 4.73205i 0.0980749 0.169871i
$$777$$ 0 0
$$778$$ −21.0622 + 12.1603i −0.755116 + 0.435966i
$$779$$ −3.60770 −0.129259
$$780$$ 0 0
$$781$$ −10.1436 −0.362966
$$782$$ 6.29423 3.63397i 0.225081 0.129951i