# Properties

 Label 390.2.p.g.281.2 Level $390$ Weight $2$ Character 390.281 Analytic conductor $3.114$ Analytic rank $0$ Dimension $8$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(161,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("390.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$390 = 2 \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 390.p (of order $$4$$, 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: $$3.11416567883$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.40960000.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} + 7x^{4} + 1$$ x^8 + 7*x^4 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 281.2 Root $$-1.14412 - 1.14412i$$ of defining polynomial Character $$\chi$$ $$=$$ 390.281 Dual form 390.2.p.g.161.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.707107 + 0.707107i) q^{2} +(1.58114 - 0.707107i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.618034 + 1.61803i) q^{6} +(0.707107 + 0.707107i) q^{8} +(2.00000 - 2.23607i) q^{9} +O(q^{10})$$ $$q+(-0.707107 + 0.707107i) q^{2} +(1.58114 - 0.707107i) q^{3} -1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.618034 + 1.61803i) q^{6} +(0.707107 + 0.707107i) q^{8} +(2.00000 - 2.23607i) q^{9} -1.00000i q^{10} +(1.41421 + 1.41421i) q^{11} +(-0.707107 - 1.58114i) q^{12} +(3.58114 - 0.418861i) q^{13} +(-0.618034 + 1.61803i) q^{15} -1.00000 q^{16} +1.64371 q^{17} +(0.166925 + 2.99535i) q^{18} +(1.16228 + 1.16228i) q^{19} +(0.707107 + 0.707107i) q^{20} -2.00000 q^{22} +4.47214 q^{23} +(1.61803 + 0.618034i) q^{24} -1.00000i q^{25} +(-2.23607 + 2.82843i) q^{26} +(1.58114 - 4.94975i) q^{27} -4.47214i q^{29} +(-0.707107 - 1.58114i) q^{30} +(-3.00000 - 3.00000i) q^{31} +(0.707107 - 0.707107i) q^{32} +(3.23607 + 1.23607i) q^{33} +(-1.16228 + 1.16228i) q^{34} +(-2.23607 - 2.00000i) q^{36} +(-4.00000 + 4.00000i) q^{37} -1.64371 q^{38} +(5.36610 - 3.19453i) q^{39} -1.00000 q^{40} +(-2.23607 + 2.23607i) q^{41} -0.837722i q^{43} +(1.41421 - 1.41421i) q^{44} +(0.166925 + 2.99535i) q^{45} +(-3.16228 + 3.16228i) q^{46} +(1.64371 + 1.64371i) q^{47} +(-1.58114 + 0.707107i) q^{48} +7.00000i q^{49} +(0.707107 + 0.707107i) q^{50} +(2.59893 - 1.16228i) q^{51} +(-0.418861 - 3.58114i) q^{52} -1.41421i q^{53} +(2.38197 + 4.61803i) q^{54} -2.00000 q^{55} +(2.65958 + 1.01587i) q^{57} +(3.16228 + 3.16228i) q^{58} +(3.05792 + 3.05792i) q^{59} +(1.61803 + 0.618034i) q^{60} -14.6491 q^{61} +4.24264 q^{62} +1.00000i q^{64} +(-2.23607 + 2.82843i) q^{65} +(-3.16228 + 1.41421i) q^{66} +(0.837722 + 0.837722i) q^{67} -1.64371i q^{68} +(7.07107 - 3.16228i) q^{69} +(-9.53663 + 9.53663i) q^{71} +(2.99535 - 0.166925i) q^{72} +(1.16228 - 1.16228i) q^{73} -5.65685i q^{74} +(-0.707107 - 1.58114i) q^{75} +(1.16228 - 1.16228i) q^{76} +(-1.53553 + 6.05327i) q^{78} -10.0000 q^{79} +(0.707107 - 0.707107i) q^{80} +(-1.00000 - 8.94427i) q^{81} -3.16228i q^{82} +(5.65685 - 5.65685i) q^{83} +(-1.16228 + 1.16228i) q^{85} +(0.592359 + 0.592359i) q^{86} +(-3.16228 - 7.07107i) q^{87} +2.00000i q^{88} +(-5.06450 - 5.06450i) q^{89} +(-2.23607 - 2.00000i) q^{90} -4.47214i q^{92} +(-6.86474 - 2.62210i) q^{93} -2.32456 q^{94} -1.64371 q^{95} +(0.618034 - 1.61803i) q^{96} +(5.16228 + 5.16228i) q^{97} +(-4.94975 - 4.94975i) q^{98} +(5.99070 - 0.333851i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{6} + 16 q^{9}+O(q^{10})$$ 8 * q + 4 * q^6 + 16 * q^9 $$8 q + 4 q^{6} + 16 q^{9} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 16 q^{19} - 16 q^{22} + 4 q^{24} - 24 q^{31} + 8 q^{33} + 16 q^{34} - 32 q^{37} + 20 q^{39} - 8 q^{40} - 16 q^{52} + 28 q^{54} - 16 q^{55} + 40 q^{57} + 4 q^{60} - 16 q^{61} + 32 q^{67} - 16 q^{73} - 16 q^{76} + 16 q^{78} - 80 q^{79} - 8 q^{81} + 16 q^{85} + 32 q^{94} - 4 q^{96} + 16 q^{97}+O(q^{100})$$ 8 * q + 4 * q^6 + 16 * q^9 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 16 * q^19 - 16 * q^22 + 4 * q^24 - 24 * q^31 + 8 * q^33 + 16 * q^34 - 32 * q^37 + 20 * q^39 - 8 * q^40 - 16 * q^52 + 28 * q^54 - 16 * q^55 + 40 * q^57 + 4 * q^60 - 16 * q^61 + 32 * q^67 - 16 * q^73 - 16 * q^76 + 16 * q^78 - 80 * q^79 - 8 * q^81 + 16 * q^85 + 32 * q^94 - 4 * q^96 + 16 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$$.

 $$n$$ $$131$$ $$157$$ $$301$$ $$\chi(n)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 + 0.707107i −0.500000 + 0.500000i
$$3$$ 1.58114 0.707107i 0.912871 0.408248i
$$4$$ 1.00000i 0.500000i
$$5$$ −0.707107 + 0.707107i −0.316228 + 0.316228i
$$6$$ −0.618034 + 1.61803i −0.252311 + 0.660560i
$$7$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$8$$ 0.707107 + 0.707107i 0.250000 + 0.250000i
$$9$$ 2.00000 2.23607i 0.666667 0.745356i
$$10$$ 1.00000i 0.316228i
$$11$$ 1.41421 + 1.41421i 0.426401 + 0.426401i 0.887401 0.460999i $$-0.152509\pi$$
−0.460999 + 0.887401i $$0.652509\pi$$
$$12$$ −0.707107 1.58114i −0.204124 0.456435i
$$13$$ 3.58114 0.418861i 0.993229 0.116171i
$$14$$ 0 0
$$15$$ −0.618034 + 1.61803i −0.159576 + 0.417775i
$$16$$ −1.00000 −0.250000
$$17$$ 1.64371 0.398658 0.199329 0.979933i $$-0.436124\pi$$
0.199329 + 0.979933i $$0.436124\pi$$
$$18$$ 0.166925 + 2.99535i 0.0393447 + 0.706011i
$$19$$ 1.16228 + 1.16228i 0.266645 + 0.266645i 0.827747 0.561102i $$-0.189622\pi$$
−0.561102 + 0.827747i $$0.689622\pi$$
$$20$$ 0.707107 + 0.707107i 0.158114 + 0.158114i
$$21$$ 0 0
$$22$$ −2.00000 −0.426401
$$23$$ 4.47214 0.932505 0.466252 0.884652i $$-0.345604\pi$$
0.466252 + 0.884652i $$0.345604\pi$$
$$24$$ 1.61803 + 0.618034i 0.330280 + 0.126156i
$$25$$ 1.00000i 0.200000i
$$26$$ −2.23607 + 2.82843i −0.438529 + 0.554700i
$$27$$ 1.58114 4.94975i 0.304290 0.952579i
$$28$$ 0 0
$$29$$ 4.47214i 0.830455i −0.909718 0.415227i $$-0.863702\pi$$
0.909718 0.415227i $$-0.136298\pi$$
$$30$$ −0.707107 1.58114i −0.129099 0.288675i
$$31$$ −3.00000 3.00000i −0.538816 0.538816i 0.384365 0.923181i $$-0.374420\pi$$
−0.923181 + 0.384365i $$0.874420\pi$$
$$32$$ 0.707107 0.707107i 0.125000 0.125000i
$$33$$ 3.23607 + 1.23607i 0.563327 + 0.215172i
$$34$$ −1.16228 + 1.16228i −0.199329 + 0.199329i
$$35$$ 0 0
$$36$$ −2.23607 2.00000i −0.372678 0.333333i
$$37$$ −4.00000 + 4.00000i −0.657596 + 0.657596i −0.954811 0.297215i $$-0.903942\pi$$
0.297215 + 0.954811i $$0.403942\pi$$
$$38$$ −1.64371 −0.266645
$$39$$ 5.36610 3.19453i 0.859263 0.511533i
$$40$$ −1.00000 −0.158114
$$41$$ −2.23607 + 2.23607i −0.349215 + 0.349215i −0.859817 0.510602i $$-0.829423\pi$$
0.510602 + 0.859817i $$0.329423\pi$$
$$42$$ 0 0
$$43$$ 0.837722i 0.127751i −0.997958 0.0638757i $$-0.979654\pi$$
0.997958 0.0638757i $$-0.0203461\pi$$
$$44$$ 1.41421 1.41421i 0.213201 0.213201i
$$45$$ 0.166925 + 2.99535i 0.0248837 + 0.446521i
$$46$$ −3.16228 + 3.16228i −0.466252 + 0.466252i
$$47$$ 1.64371 + 1.64371i 0.239760 + 0.239760i 0.816751 0.576991i $$-0.195773\pi$$
−0.576991 + 0.816751i $$0.695773\pi$$
$$48$$ −1.58114 + 0.707107i −0.228218 + 0.102062i
$$49$$ 7.00000i 1.00000i
$$50$$ 0.707107 + 0.707107i 0.100000 + 0.100000i
$$51$$ 2.59893 1.16228i 0.363923 0.162751i
$$52$$ −0.418861 3.58114i −0.0580856 0.496615i
$$53$$ 1.41421i 0.194257i −0.995272 0.0971286i $$-0.969034\pi$$
0.995272 0.0971286i $$-0.0309658\pi$$
$$54$$ 2.38197 + 4.61803i 0.324145 + 0.628435i
$$55$$ −2.00000 −0.269680
$$56$$ 0 0
$$57$$ 2.65958 + 1.01587i 0.352270 + 0.134555i
$$58$$ 3.16228 + 3.16228i 0.415227 + 0.415227i
$$59$$ 3.05792 + 3.05792i 0.398108 + 0.398108i 0.877565 0.479458i $$-0.159167\pi$$
−0.479458 + 0.877565i $$0.659167\pi$$
$$60$$ 1.61803 + 0.618034i 0.208887 + 0.0797878i
$$61$$ −14.6491 −1.87563 −0.937813 0.347140i $$-0.887153\pi$$
−0.937813 + 0.347140i $$0.887153\pi$$
$$62$$ 4.24264 0.538816
$$63$$ 0 0
$$64$$ 1.00000i 0.125000i
$$65$$ −2.23607 + 2.82843i −0.277350 + 0.350823i
$$66$$ −3.16228 + 1.41421i −0.389249 + 0.174078i
$$67$$ 0.837722 + 0.837722i 0.102344 + 0.102344i 0.756425 0.654081i $$-0.226944\pi$$
−0.654081 + 0.756425i $$0.726944\pi$$
$$68$$ 1.64371i 0.199329i
$$69$$ 7.07107 3.16228i 0.851257 0.380693i
$$70$$ 0 0
$$71$$ −9.53663 + 9.53663i −1.13179 + 1.13179i −0.141910 + 0.989880i $$0.545324\pi$$
−0.989880 + 0.141910i $$0.954676\pi$$
$$72$$ 2.99535 0.166925i 0.353006 0.0196723i
$$73$$ 1.16228 1.16228i 0.136034 0.136034i −0.635811 0.771845i $$-0.719334\pi$$
0.771845 + 0.635811i $$0.219334\pi$$
$$74$$ 5.65685i 0.657596i
$$75$$ −0.707107 1.58114i −0.0816497 0.182574i
$$76$$ 1.16228 1.16228i 0.133322 0.133322i
$$77$$ 0 0
$$78$$ −1.53553 + 6.05327i −0.173865 + 0.685398i
$$79$$ −10.0000 −1.12509 −0.562544 0.826767i $$-0.690177\pi$$
−0.562544 + 0.826767i $$0.690177\pi$$
$$80$$ 0.707107 0.707107i 0.0790569 0.0790569i
$$81$$ −1.00000 8.94427i −0.111111 0.993808i
$$82$$ 3.16228i 0.349215i
$$83$$ 5.65685 5.65685i 0.620920 0.620920i −0.324846 0.945767i $$-0.605313\pi$$
0.945767 + 0.324846i $$0.105313\pi$$
$$84$$ 0 0
$$85$$ −1.16228 + 1.16228i −0.126067 + 0.126067i
$$86$$ 0.592359 + 0.592359i 0.0638757 + 0.0638757i
$$87$$ −3.16228 7.07107i −0.339032 0.758098i
$$88$$ 2.00000i 0.213201i
$$89$$ −5.06450 5.06450i −0.536835 0.536835i 0.385763 0.922598i $$-0.373938\pi$$
−0.922598 + 0.385763i $$0.873938\pi$$
$$90$$ −2.23607 2.00000i −0.235702 0.210819i
$$91$$ 0 0
$$92$$ 4.47214i 0.466252i
$$93$$ −6.86474 2.62210i −0.711840 0.271899i
$$94$$ −2.32456 −0.239760
$$95$$ −1.64371 −0.168641
$$96$$ 0.618034 1.61803i 0.0630778 0.165140i
$$97$$ 5.16228 + 5.16228i 0.524150 + 0.524150i 0.918822 0.394672i $$-0.129142\pi$$
−0.394672 + 0.918822i $$0.629142\pi$$
$$98$$ −4.94975 4.94975i −0.500000 0.500000i
$$99$$ 5.99070 0.333851i 0.602088 0.0335532i
$$100$$ −1.00000 −0.100000
$$101$$ −15.7858 −1.57075 −0.785375 0.619020i $$-0.787530\pi$$
−0.785375 + 0.619020i $$0.787530\pi$$
$$102$$ −1.01587 + 2.65958i −0.100586 + 0.263337i
$$103$$ 6.64911i 0.655156i −0.944824 0.327578i $$-0.893768\pi$$
0.944824 0.327578i $$-0.106232\pi$$
$$104$$ 2.82843 + 2.23607i 0.277350 + 0.219265i
$$105$$ 0 0
$$106$$ 1.00000 + 1.00000i 0.0971286 + 0.0971286i
$$107$$ 10.3585i 1.00139i −0.865623 0.500696i $$-0.833077\pi$$
0.865623 0.500696i $$-0.166923\pi$$
$$108$$ −4.94975 1.58114i −0.476290 0.152145i
$$109$$ −11.1623 11.1623i −1.06915 1.06915i −0.997424 0.0717281i $$-0.977149\pi$$
−0.0717281 0.997424i $$-0.522851\pi$$
$$110$$ 1.41421 1.41421i 0.134840 0.134840i
$$111$$ −3.49613 + 9.15298i −0.331838 + 0.868763i
$$112$$ 0 0
$$113$$ 10.5880i 0.996033i −0.867167 0.498017i $$-0.834062\pi$$
0.867167 0.498017i $$-0.165938\pi$$
$$114$$ −2.59893 + 1.16228i −0.243412 + 0.108857i
$$115$$ −3.16228 + 3.16228i −0.294884 + 0.294884i
$$116$$ −4.47214 −0.415227
$$117$$ 6.22568 8.84539i 0.575564 0.817757i
$$118$$ −4.32456 −0.398108
$$119$$ 0 0
$$120$$ −1.58114 + 0.707107i −0.144338 + 0.0645497i
$$121$$ 7.00000i 0.636364i
$$122$$ 10.3585 10.3585i 0.937813 0.937813i
$$123$$ −1.95440 + 5.11667i −0.176222 + 0.461355i
$$124$$ −3.00000 + 3.00000i −0.269408 + 0.269408i
$$125$$ 0.707107 + 0.707107i 0.0632456 + 0.0632456i
$$126$$ 0 0
$$127$$ 20.9737i 1.86111i 0.366150 + 0.930556i $$0.380676\pi$$
−0.366150 + 0.930556i $$0.619324\pi$$
$$128$$ −0.707107 0.707107i −0.0625000 0.0625000i
$$129$$ −0.592359 1.32456i −0.0521543 0.116621i
$$130$$ −0.418861 3.58114i −0.0367366 0.314087i
$$131$$ 17.4296i 1.52283i 0.648266 + 0.761414i $$0.275494\pi$$
−0.648266 + 0.761414i $$0.724506\pi$$
$$132$$ 1.23607 3.23607i 0.107586 0.281664i
$$133$$ 0 0
$$134$$ −1.18472 −0.102344
$$135$$ 2.38197 + 4.61803i 0.205007 + 0.397457i
$$136$$ 1.16228 + 1.16228i 0.0996645 + 0.0996645i
$$137$$ −5.42736 5.42736i −0.463691 0.463691i 0.436173 0.899863i $$-0.356334\pi$$
−0.899863 + 0.436173i $$0.856334\pi$$
$$138$$ −2.76393 + 7.23607i −0.235282 + 0.615975i
$$139$$ −6.32456 −0.536442 −0.268221 0.963357i $$-0.586436\pi$$
−0.268221 + 0.963357i $$0.586436\pi$$
$$140$$ 0 0
$$141$$ 3.76121 + 1.43665i 0.316751 + 0.120988i
$$142$$ 13.4868i 1.13179i
$$143$$ 5.65685 + 4.47214i 0.473050 + 0.373979i
$$144$$ −2.00000 + 2.23607i −0.166667 + 0.186339i
$$145$$ 3.16228 + 3.16228i 0.262613 + 0.262613i
$$146$$ 1.64371i 0.136034i
$$147$$ 4.94975 + 11.0680i 0.408248 + 0.912871i
$$148$$ 4.00000 + 4.00000i 0.328798 + 0.328798i
$$149$$ −11.5432 + 11.5432i −0.945656 + 0.945656i −0.998598 0.0529415i $$-0.983140\pi$$
0.0529415 + 0.998598i $$0.483140\pi$$
$$150$$ 1.61803 + 0.618034i 0.132112 + 0.0504623i
$$151$$ 13.3246 13.3246i 1.08434 1.08434i 0.0882375 0.996099i $$-0.471877\pi$$
0.996099 0.0882375i $$-0.0281234\pi$$
$$152$$ 1.64371i 0.133322i
$$153$$ 3.28742 3.67544i 0.265772 0.297142i
$$154$$ 0 0
$$155$$ 4.24264 0.340777
$$156$$ −3.19453 5.36610i −0.255767 0.429632i
$$157$$ 16.8377 1.34380 0.671898 0.740643i $$-0.265479\pi$$
0.671898 + 0.740643i $$0.265479\pi$$
$$158$$ 7.07107 7.07107i 0.562544 0.562544i
$$159$$ −1.00000 2.23607i −0.0793052 0.177332i
$$160$$ 1.00000i 0.0790569i
$$161$$ 0 0
$$162$$ 7.03166 + 5.61745i 0.552460 + 0.441348i
$$163$$ −10.3246 + 10.3246i −0.808682 + 0.808682i −0.984434 0.175753i $$-0.943764\pi$$
0.175753 + 0.984434i $$0.443764\pi$$
$$164$$ 2.23607 + 2.23607i 0.174608 + 0.174608i
$$165$$ −3.16228 + 1.41421i −0.246183 + 0.110096i
$$166$$ 8.00000i 0.620920i
$$167$$ 7.30056 + 7.30056i 0.564935 + 0.564935i 0.930705 0.365771i $$-0.119195\pi$$
−0.365771 + 0.930705i $$0.619195\pi$$
$$168$$ 0 0
$$169$$ 12.6491 3.00000i 0.973009 0.230769i
$$170$$ 1.64371i 0.126067i
$$171$$ 4.92349 0.274377i 0.376508 0.0209821i
$$172$$ −0.837722 −0.0638757
$$173$$ −13.6459 −1.03748 −0.518739 0.854932i $$-0.673599\pi$$
−0.518739 + 0.854932i $$0.673599\pi$$
$$174$$ 7.23607 + 2.76393i 0.548565 + 0.209533i
$$175$$ 0 0
$$176$$ −1.41421 1.41421i −0.106600 0.106600i
$$177$$ 6.99728 + 2.67272i 0.525948 + 0.200894i
$$178$$ 7.16228 0.536835
$$179$$ 17.4296 1.30275 0.651373 0.758758i $$-0.274193\pi$$
0.651373 + 0.758758i $$0.274193\pi$$
$$180$$ 2.99535 0.166925i 0.223260 0.0124419i
$$181$$ 8.32456i 0.618759i −0.950939 0.309380i $$-0.899879\pi$$
0.950939 0.309380i $$-0.100121\pi$$
$$182$$ 0 0
$$183$$ −23.1623 + 10.3585i −1.71220 + 0.765721i
$$184$$ 3.16228 + 3.16228i 0.233126 + 0.233126i
$$185$$ 5.65685i 0.415900i
$$186$$ 6.70820 3.00000i 0.491869 0.219971i
$$187$$ 2.32456 + 2.32456i 0.169988 + 0.169988i
$$188$$ 1.64371 1.64371i 0.119880 0.119880i
$$189$$ 0 0
$$190$$ 1.16228 1.16228i 0.0843205 0.0843205i
$$191$$ 24.7301i 1.78941i 0.446659 + 0.894704i $$0.352614\pi$$
−0.446659 + 0.894704i $$0.647386\pi$$
$$192$$ 0.707107 + 1.58114i 0.0510310 + 0.114109i
$$193$$ 15.4868 15.4868i 1.11477 1.11477i 0.122270 0.992497i $$-0.460983\pi$$
0.992497 0.122270i $$-0.0390173\pi$$
$$194$$ −7.30056 −0.524150
$$195$$ −1.53553 + 6.05327i −0.109962 + 0.433484i
$$196$$ 7.00000 0.500000
$$197$$ −8.94427 + 8.94427i −0.637253 + 0.637253i −0.949877 0.312624i $$-0.898792\pi$$
0.312624 + 0.949877i $$0.398792\pi$$
$$198$$ −4.00000 + 4.47214i −0.284268 + 0.317821i
$$199$$ 2.00000i 0.141776i −0.997484 0.0708881i $$-0.977417\pi$$
0.997484 0.0708881i $$-0.0225833\pi$$
$$200$$ 0.707107 0.707107i 0.0500000 0.0500000i
$$201$$ 1.91691 + 0.732196i 0.135209 + 0.0516451i
$$202$$ 11.1623 11.1623i 0.785375 0.785375i
$$203$$ 0 0
$$204$$ −1.16228 2.59893i −0.0813757 0.181962i
$$205$$ 3.16228i 0.220863i
$$206$$ 4.70163 + 4.70163i 0.327578 + 0.327578i
$$207$$ 8.94427 10.0000i 0.621670 0.695048i
$$208$$ −3.58114 + 0.418861i −0.248307 + 0.0290428i
$$209$$ 3.28742i 0.227395i
$$210$$ 0 0
$$211$$ 28.6491 1.97229 0.986143 0.165897i $$-0.0530520\pi$$
0.986143 + 0.165897i $$0.0530520\pi$$
$$212$$ −1.41421 −0.0971286
$$213$$ −8.33532 + 21.8222i −0.571127 + 1.49523i
$$214$$ 7.32456 + 7.32456i 0.500696 + 0.500696i
$$215$$ 0.592359 + 0.592359i 0.0403986 + 0.0403986i
$$216$$ 4.61803 2.38197i 0.314217 0.162072i
$$217$$ 0 0
$$218$$ 15.7858 1.06915
$$219$$ 1.01587 2.65958i 0.0686460 0.179718i
$$220$$ 2.00000i 0.134840i
$$221$$ 5.88635 0.688486i 0.395959 0.0463126i
$$222$$ −4.00000 8.94427i −0.268462 0.600300i
$$223$$ −8.64911 8.64911i −0.579187 0.579187i 0.355492 0.934679i $$-0.384313\pi$$
−0.934679 + 0.355492i $$0.884313\pi$$
$$224$$ 0 0
$$225$$ −2.23607 2.00000i −0.149071 0.133333i
$$226$$ 7.48683 + 7.48683i 0.498017 + 0.498017i
$$227$$ −12.7279 + 12.7279i −0.844782 + 0.844782i −0.989476 0.144695i $$-0.953780\pi$$
0.144695 + 0.989476i $$0.453780\pi$$
$$228$$ 1.01587 2.65958i 0.0672775 0.176135i
$$229$$ 17.8114 17.8114i 1.17701 1.17701i 0.196507 0.980502i $$-0.437040\pi$$
0.980502 0.196507i $$-0.0629599\pi$$
$$230$$ 4.47214i 0.294884i
$$231$$ 0 0
$$232$$ 3.16228 3.16228i 0.207614 0.207614i
$$233$$ 12.9574 0.848869 0.424434 0.905459i $$-0.360473\pi$$
0.424434 + 0.905459i $$0.360473\pi$$
$$234$$ 1.85242 + 10.6569i 0.121096 + 0.696660i
$$235$$ −2.32456 −0.151637
$$236$$ 3.05792 3.05792i 0.199054 0.199054i
$$237$$ −15.8114 + 7.07107i −1.02706 + 0.459315i
$$238$$ 0 0
$$239$$ −3.42079 + 3.42079i −0.221272 + 0.221272i −0.809034 0.587762i $$-0.800009\pi$$
0.587762 + 0.809034i $$0.300009\pi$$
$$240$$ 0.618034 1.61803i 0.0398939 0.104444i
$$241$$ −17.6491 + 17.6491i −1.13688 + 1.13688i −0.147873 + 0.989006i $$0.547243\pi$$
−0.989006 + 0.147873i $$0.952757\pi$$
$$242$$ 4.94975 + 4.94975i 0.318182 + 0.318182i
$$243$$ −7.90569 13.4350i −0.507151 0.861858i
$$244$$ 14.6491i 0.937813i
$$245$$ −4.94975 4.94975i −0.316228 0.316228i
$$246$$ −2.23607 5.00000i −0.142566 0.318788i
$$247$$ 4.64911 + 3.67544i 0.295816 + 0.233863i
$$248$$ 4.24264i 0.269408i
$$249$$ 4.94427 12.9443i 0.313331 0.820310i
$$250$$ −1.00000 −0.0632456
$$251$$ 3.28742 0.207500 0.103750 0.994603i $$-0.466916\pi$$
0.103750 + 0.994603i $$0.466916\pi$$
$$252$$ 0 0
$$253$$ 6.32456 + 6.32456i 0.397621 + 0.397621i
$$254$$ −14.8306 14.8306i −0.930556 0.930556i
$$255$$ −1.01587 + 2.65958i −0.0636161 + 0.166549i
$$256$$ 1.00000 0.0625000
$$257$$ −7.30056 −0.455397 −0.227698 0.973732i $$-0.573120\pi$$
−0.227698 + 0.973732i $$0.573120\pi$$
$$258$$ 1.35546 + 0.517741i 0.0843875 + 0.0322331i
$$259$$ 0 0
$$260$$ 2.82843 + 2.23607i 0.175412 + 0.138675i
$$261$$ −10.0000 8.94427i −0.618984 0.553637i
$$262$$ −12.3246 12.3246i −0.761414 0.761414i
$$263$$ 10.1290i 0.624580i −0.949987 0.312290i $$-0.898904\pi$$
0.949987 0.312290i $$-0.101096\pi$$
$$264$$ 1.41421 + 3.16228i 0.0870388 + 0.194625i
$$265$$ 1.00000 + 1.00000i 0.0614295 + 0.0614295i
$$266$$ 0 0
$$267$$ −11.5888 4.42653i −0.709224 0.270899i
$$268$$ 0.837722 0.837722i 0.0511720 0.0511720i
$$269$$ 4.47214i 0.272671i −0.990663 0.136335i $$-0.956467\pi$$
0.990663 0.136335i $$-0.0435325\pi$$
$$270$$ −4.94975 1.58114i −0.301232 0.0962250i
$$271$$ 5.32456 5.32456i 0.323444 0.323444i −0.526643 0.850087i $$-0.676549\pi$$
0.850087 + 0.526643i $$0.176549\pi$$
$$272$$ −1.64371 −0.0996645
$$273$$ 0 0
$$274$$ 7.67544 0.463691
$$275$$ 1.41421 1.41421i 0.0852803 0.0852803i
$$276$$ −3.16228 7.07107i −0.190347 0.425628i
$$277$$ 3.16228i 0.190003i 0.995477 + 0.0950014i $$0.0302856\pi$$
−0.995477 + 0.0950014i $$0.969714\pi$$
$$278$$ 4.47214 4.47214i 0.268221 0.268221i
$$279$$ −12.7082 + 0.708204i −0.760820 + 0.0423991i
$$280$$ 0 0
$$281$$ −22.0351 22.0351i −1.31450 1.31450i −0.918060 0.396441i $$-0.870245\pi$$
−0.396441 0.918060i $$-0.629755\pi$$
$$282$$ −3.67544 + 1.64371i −0.218870 + 0.0978814i
$$283$$ 19.1623i 1.13908i 0.821964 + 0.569540i $$0.192878\pi$$
−0.821964 + 0.569540i $$0.807122\pi$$
$$284$$ 9.53663 + 9.53663i 0.565895 + 0.565895i
$$285$$ −2.59893 + 1.16228i −0.153947 + 0.0688474i
$$286$$ −7.16228 + 0.837722i −0.423514 + 0.0495356i
$$287$$ 0 0
$$288$$ −0.166925 2.99535i −0.00983617 0.176503i
$$289$$ −14.2982 −0.841072
$$290$$ −4.47214 −0.262613
$$291$$ 11.8126 + 4.51200i 0.692464 + 0.264498i
$$292$$ −1.16228 1.16228i −0.0680172 0.0680172i
$$293$$ −2.82843 2.82843i −0.165238 0.165238i 0.619644 0.784883i $$-0.287277\pi$$
−0.784883 + 0.619644i $$0.787277\pi$$
$$294$$ −11.3262 4.32624i −0.660560 0.252311i
$$295$$ −4.32456 −0.251785
$$296$$ −5.65685 −0.328798
$$297$$ 9.23607 4.76393i 0.535931 0.276431i
$$298$$ 16.3246i 0.945656i
$$299$$ 16.0153 1.87320i 0.926191 0.108330i
$$300$$ −1.58114 + 0.707107i −0.0912871 + 0.0408248i
$$301$$ 0 0
$$302$$ 18.8438i 1.08434i
$$303$$ −24.9596 + 11.1623i −1.43389 + 0.641256i
$$304$$ −1.16228 1.16228i −0.0666612 0.0666612i
$$305$$ 10.3585 10.3585i 0.593125 0.593125i
$$306$$ 0.274377 + 4.92349i 0.0156851 + 0.281457i
$$307$$ 0.837722 0.837722i 0.0478113 0.0478113i −0.682797 0.730608i $$-0.739237\pi$$
0.730608 + 0.682797i $$0.239237\pi$$
$$308$$ 0 0
$$309$$ −4.70163 10.5132i −0.267466 0.598073i
$$310$$ −3.00000 + 3.00000i −0.170389 + 0.170389i
$$311$$ 32.4897 1.84232 0.921160 0.389184i $$-0.127243\pi$$
0.921160 + 0.389184i $$0.127243\pi$$
$$312$$ 6.05327 + 1.53553i 0.342699 + 0.0869325i
$$313$$ 6.64911 0.375830 0.187915 0.982185i $$-0.439827\pi$$
0.187915 + 0.982185i $$0.439827\pi$$
$$314$$ −11.9061 + 11.9061i −0.671898 + 0.671898i
$$315$$ 0 0
$$316$$ 10.0000i 0.562544i
$$317$$ −17.8885 + 17.8885i −1.00472 + 1.00472i −0.00473191 + 0.999989i $$0.501506\pi$$
−0.999989 + 0.00473191i $$0.998494\pi$$
$$318$$ 2.28825 + 0.874032i 0.128318 + 0.0490133i
$$319$$ 6.32456 6.32456i 0.354107 0.354107i
$$320$$ −0.707107 0.707107i −0.0395285 0.0395285i
$$321$$ −7.32456 16.3782i −0.408817 0.914142i
$$322$$ 0 0
$$323$$ 1.91045 + 1.91045i 0.106300 + 0.106300i
$$324$$ −8.94427 + 1.00000i −0.496904 + 0.0555556i
$$325$$ −0.418861 3.58114i −0.0232342 0.198646i
$$326$$ 14.6011i 0.808682i
$$327$$ −25.5420 9.75619i −1.41248 0.539518i
$$328$$ −3.16228 −0.174608
$$329$$ 0 0
$$330$$ 1.23607 3.23607i 0.0680433 0.178140i
$$331$$ 9.48683 + 9.48683i 0.521443 + 0.521443i 0.918007 0.396564i $$-0.129797\pi$$
−0.396564 + 0.918007i $$0.629797\pi$$
$$332$$ −5.65685 5.65685i −0.310460 0.310460i
$$333$$ 0.944272 + 16.9443i 0.0517458 + 0.928540i
$$334$$ −10.3246 −0.564935
$$335$$ −1.18472 −0.0647281
$$336$$ 0 0
$$337$$ 5.35089i 0.291482i 0.989323 + 0.145741i $$0.0465565\pi$$
−0.989323 + 0.145741i $$0.953443\pi$$
$$338$$ −6.82295 + 11.0656i −0.371120 + 0.601889i
$$339$$ −7.48683 16.7411i −0.406629 0.909250i
$$340$$ 1.16228 + 1.16228i 0.0630334 + 0.0630334i
$$341$$ 8.48528i 0.459504i
$$342$$ −3.28742 + 3.67544i −0.177763 + 0.198745i
$$343$$ 0 0
$$344$$ 0.592359 0.592359i 0.0319379 0.0319379i
$$345$$ −2.76393 + 7.23607i −0.148805 + 0.389577i
$$346$$ 9.64911 9.64911i 0.518739 0.518739i
$$347$$ 10.3585i 0.556073i 0.960571 + 0.278036i $$0.0896836\pi$$
−0.960571 + 0.278036i $$0.910316\pi$$
$$348$$ −7.07107 + 3.16228i −0.379049 + 0.169516i
$$349$$ −7.16228 + 7.16228i −0.383388 + 0.383388i −0.872321 0.488933i $$-0.837386\pi$$
0.488933 + 0.872321i $$0.337386\pi$$
$$350$$ 0 0
$$351$$ 3.58902 18.3880i 0.191568 0.981479i
$$352$$ 2.00000 0.106600
$$353$$ 17.6590 17.6590i 0.939896 0.939896i −0.0583971 0.998293i $$-0.518599\pi$$
0.998293 + 0.0583971i $$0.0185990\pi$$
$$354$$ −6.83772 + 3.05792i −0.363421 + 0.162527i
$$355$$ 13.4868i 0.715807i
$$356$$ −5.06450 + 5.06450i −0.268418 + 0.268418i
$$357$$ 0 0
$$358$$ −12.3246 + 12.3246i −0.651373 + 0.651373i
$$359$$ 0.133369 + 0.133369i 0.00703893 + 0.00703893i 0.710617 0.703579i $$-0.248416\pi$$
−0.703579 + 0.710617i $$0.748416\pi$$
$$360$$ −2.00000 + 2.23607i −0.105409 + 0.117851i
$$361$$ 16.2982i 0.857801i
$$362$$ 5.88635 + 5.88635i 0.309380 + 0.309380i
$$363$$ −4.94975 11.0680i −0.259794 0.580918i
$$364$$ 0 0
$$365$$ 1.64371i 0.0860357i
$$366$$ 9.05365 23.7028i 0.473242 1.23896i
$$367$$ −6.64911 −0.347081 −0.173540 0.984827i $$-0.555521\pi$$
−0.173540 + 0.984827i $$0.555521\pi$$
$$368$$ −4.47214 −0.233126
$$369$$ 0.527864 + 9.47214i 0.0274795 + 0.493100i
$$370$$ 4.00000 + 4.00000i 0.207950 + 0.207950i
$$371$$ 0 0
$$372$$ −2.62210 + 6.86474i −0.135949 + 0.355920i
$$373$$ 8.83772 0.457600 0.228800 0.973473i $$-0.426520\pi$$
0.228800 + 0.973473i $$0.426520\pi$$
$$374$$ −3.28742 −0.169988
$$375$$ 1.61803 + 0.618034i 0.0835549 + 0.0319151i
$$376$$ 2.32456i 0.119880i
$$377$$ −1.87320 16.0153i −0.0964749 0.824832i
$$378$$ 0 0
$$379$$ −6.83772 6.83772i −0.351230 0.351230i 0.509337 0.860567i $$-0.329891\pi$$
−0.860567 + 0.509337i $$0.829891\pi$$
$$380$$ 1.64371i 0.0843205i
$$381$$ 14.8306 + 33.1623i 0.759796 + 1.69895i
$$382$$ −17.4868 17.4868i −0.894704 0.894704i
$$383$$ 21.9017 21.9017i 1.11912 1.11912i 0.127254 0.991870i $$-0.459384\pi$$
0.991870 0.127254i $$-0.0406163\pi$$
$$384$$ −1.61803 0.618034i −0.0825700 0.0315389i
$$385$$ 0 0
$$386$$ 21.9017i 1.11477i
$$387$$ −1.87320 1.67544i −0.0952203 0.0851676i
$$388$$ 5.16228 5.16228i 0.262075 0.262075i
$$389$$ 20.9837 1.06392 0.531958 0.846771i $$-0.321456\pi$$
0.531958 + 0.846771i $$0.321456\pi$$
$$390$$ −3.19453 5.36610i −0.161761 0.271723i
$$391$$ 7.35089 0.371750
$$392$$ −4.94975 + 4.94975i −0.250000 + 0.250000i
$$393$$ 12.3246 + 27.5585i 0.621692 + 1.39014i
$$394$$ 12.6491i 0.637253i
$$395$$ 7.07107 7.07107i 0.355784 0.355784i
$$396$$ −0.333851 5.99070i −0.0167766 0.301044i
$$397$$ −19.1623 + 19.1623i −0.961727 + 0.961727i −0.999294 0.0375670i $$-0.988039\pi$$
0.0375670 + 0.999294i $$0.488039\pi$$
$$398$$ 1.41421 + 1.41421i 0.0708881 + 0.0708881i
$$399$$ 0 0
$$400$$ 1.00000i 0.0500000i
$$401$$ −1.77708 1.77708i −0.0887430 0.0887430i 0.661342 0.750085i $$-0.269987\pi$$
−0.750085 + 0.661342i $$0.769987\pi$$
$$402$$ −1.87320 + 0.837722i −0.0934269 + 0.0417818i
$$403$$ −12.0000 9.48683i −0.597763 0.472573i
$$404$$ 15.7858i 0.785375i
$$405$$ 7.03166 + 5.61745i 0.349406 + 0.279133i
$$406$$ 0 0
$$407$$ −11.3137 −0.560800
$$408$$ 2.65958 + 1.01587i 0.131669 + 0.0502930i
$$409$$ 23.3246 + 23.3246i 1.15333 + 1.15333i 0.985882 + 0.167443i $$0.0535511\pi$$
0.167443 + 0.985882i $$0.446449\pi$$
$$410$$ 2.23607 + 2.23607i 0.110432 + 0.110432i
$$411$$ −12.4191 4.74369i −0.612591 0.233989i
$$412$$ −6.64911 −0.327578
$$413$$ 0 0
$$414$$ 0.746512 + 13.3956i 0.0366891 + 0.658359i
$$415$$ 8.00000i 0.392705i
$$416$$ 2.23607 2.82843i 0.109632 0.138675i
$$417$$ −10.0000 + 4.47214i −0.489702 + 0.219001i
$$418$$ −2.32456 2.32456i −0.113698 0.113698i
$$419$$ 4.73887i 0.231509i −0.993278 0.115755i $$-0.963071\pi$$
0.993278 0.115755i $$-0.0369286\pi$$
$$420$$ 0 0
$$421$$ −19.1623 19.1623i −0.933912 0.933912i 0.0640354 0.997948i $$-0.479603\pi$$
−0.997948 + 0.0640354i $$0.979603\pi$$
$$422$$ −20.2580 + 20.2580i −0.986143 + 0.986143i
$$423$$ 6.96286 0.388027i 0.338546 0.0188665i
$$424$$ 1.00000 1.00000i 0.0485643 0.0485643i
$$425$$ 1.64371i 0.0797316i
$$426$$ −9.53663 21.3246i −0.462051 1.03318i
$$427$$ 0 0
$$428$$ −10.3585 −0.500696
$$429$$ 12.1065 + 3.07107i 0.584510 + 0.148273i
$$430$$ −0.837722 −0.0403986
$$431$$ 15.1935 15.1935i 0.731844 0.731844i −0.239141 0.970985i $$-0.576866\pi$$
0.970985 + 0.239141i $$0.0768657\pi$$
$$432$$ −1.58114 + 4.94975i −0.0760726 + 0.238145i
$$433$$ 11.2982i 0.542958i 0.962444 + 0.271479i $$0.0875127\pi$$
−0.962444 + 0.271479i $$0.912487\pi$$
$$434$$ 0 0
$$435$$ 7.23607 + 2.76393i 0.346943 + 0.132520i
$$436$$ −11.1623 + 11.1623i −0.534576 + 0.534576i
$$437$$ 5.19786 + 5.19786i 0.248648 + 0.248648i
$$438$$ 1.16228 + 2.59893i 0.0555358 + 0.124182i
$$439$$ 28.6491i 1.36735i 0.729788 + 0.683674i $$0.239619\pi$$
−0.729788 + 0.683674i $$0.760381\pi$$
$$440$$ −1.41421 1.41421i −0.0674200 0.0674200i
$$441$$ 15.6525 + 14.0000i 0.745356 + 0.666667i
$$442$$ −3.67544 + 4.64911i −0.174823 + 0.221136i
$$443$$ 7.53006i 0.357764i 0.983871 + 0.178882i $$0.0572480\pi$$
−0.983871 + 0.178882i $$0.942752\pi$$
$$444$$ 9.15298 + 3.49613i 0.434381 + 0.165919i
$$445$$ 7.16228 0.339525
$$446$$ 12.2317 0.579187
$$447$$ −10.0891 + 26.4137i −0.477199 + 1.24932i
$$448$$ 0 0
$$449$$ 8.35191 + 8.35191i 0.394151 + 0.394151i 0.876164 0.482013i $$-0.160094\pi$$
−0.482013 + 0.876164i $$0.660094\pi$$
$$450$$ 2.99535 0.166925i 0.141202 0.00786893i
$$451$$ −6.32456 −0.297812
$$452$$ −10.5880 −0.498017
$$453$$ 11.6461 30.4899i 0.547181 1.43254i
$$454$$ 18.0000i 0.844782i
$$455$$ 0 0
$$456$$ 1.16228 + 2.59893i 0.0544286 + 0.121706i
$$457$$ −15.4868 15.4868i −0.724443 0.724443i 0.245064 0.969507i $$-0.421191\pi$$
−0.969507 + 0.245064i $$0.921191\pi$$
$$458$$ 25.1891i 1.17701i
$$459$$ 2.59893 8.13594i 0.121308 0.379753i
$$460$$ 3.16228 + 3.16228i 0.147442 + 0.147442i
$$461$$ 3.78365 3.78365i 0.176222 0.176222i −0.613485 0.789707i $$-0.710233\pi$$
0.789707 + 0.613485i $$0.210233\pi$$
$$462$$ 0 0
$$463$$ −4.32456 + 4.32456i −0.200979 + 0.200979i −0.800419 0.599440i $$-0.795390\pi$$
0.599440 + 0.800419i $$0.295390\pi$$
$$464$$ 4.47214i 0.207614i
$$465$$ 6.70820 3.00000i 0.311086 0.139122i
$$466$$ −9.16228 + 9.16228i −0.424434 + 0.424434i
$$467$$ 19.7617 0.914465 0.457232 0.889347i $$-0.348841\pi$$
0.457232 + 0.889347i $$0.348841\pi$$
$$468$$ −8.84539 6.22568i −0.408878 0.287782i
$$469$$ 0 0
$$470$$ 1.64371 1.64371i 0.0758186 0.0758186i
$$471$$ 26.6228 11.9061i 1.22671 0.548603i
$$472$$ 4.32456i 0.199054i
$$473$$ 1.18472 1.18472i 0.0544734 0.0544734i
$$474$$ 6.18034 16.1803i 0.283872 0.743188i
$$475$$ 1.16228 1.16228i 0.0533290 0.0533290i
$$476$$ 0 0
$$477$$ −3.16228 2.82843i −0.144791 0.129505i
$$478$$ 4.83772i 0.221272i
$$479$$ −22.4940 22.4940i −1.02778 1.02778i −0.999603 0.0281763i $$-0.991030\pi$$
−0.0281763 0.999603i $$-0.508970\pi$$
$$480$$ 0.707107 + 1.58114i 0.0322749 + 0.0721688i
$$481$$ −12.6491 + 16.0000i −0.576750 + 0.729537i
$$482$$ 24.9596i 1.13688i
$$483$$ 0 0
$$484$$ −7.00000 −0.318182
$$485$$ −7.30056 −0.331501
$$486$$ 15.0902 + 3.90983i 0.684504 + 0.177353i
$$487$$ −18.0000 18.0000i −0.815658 0.815658i 0.169818 0.985476i $$-0.445682\pi$$
−0.985476 + 0.169818i $$0.945682\pi$$
$$488$$ −10.3585 10.3585i −0.468907 0.468907i
$$489$$ −9.02399 + 23.6251i −0.408079 + 1.06836i
$$490$$ 7.00000 0.316228
$$491$$ −28.2843 −1.27645 −0.638226 0.769849i $$-0.720331\pi$$
−0.638226 + 0.769849i $$0.720331\pi$$
$$492$$ 5.11667 + 1.95440i 0.230677 + 0.0881109i
$$493$$ 7.35089i 0.331067i
$$494$$ −5.88635 + 0.688486i −0.264839 + 0.0309764i
$$495$$ −4.00000 + 4.47214i −0.179787 + 0.201008i
$$496$$ 3.00000 + 3.00000i 0.134704 + 0.134704i
$$497$$ 0 0
$$498$$ 5.65685 + 12.6491i 0.253490 + 0.566820i
$$499$$ −4.83772 4.83772i −0.216566 0.216566i 0.590484 0.807050i $$-0.298937\pi$$
−0.807050 + 0.590484i $$0.798937\pi$$
$$500$$ 0.707107 0.707107i 0.0316228 0.0316228i
$$501$$ 16.7055 + 6.38093i 0.746346 + 0.285079i
$$502$$ −2.32456 + 2.32456i −0.103750 + 0.103750i
$$503$$ 19.5323i 0.870900i −0.900213 0.435450i $$-0.856589\pi$$
0.900213 0.435450i $$-0.143411\pi$$
$$504$$ 0 0
$$505$$ 11.1623 11.1623i 0.496715 0.496715i
$$506$$ −8.94427 −0.397621
$$507$$ 17.8787 13.6877i 0.794020 0.607892i
$$508$$ 20.9737 0.930556
$$509$$ −5.42736 + 5.42736i −0.240563 + 0.240563i −0.817083 0.576520i $$-0.804410\pi$$
0.576520 + 0.817083i $$0.304410\pi$$
$$510$$ −1.16228 2.59893i −0.0514665 0.115083i
$$511$$ 0 0
$$512$$ −0.707107 + 0.707107i −0.0312500 + 0.0312500i
$$513$$ 7.59070 3.91526i 0.335138 0.172863i
$$514$$ 5.16228 5.16228i 0.227698 0.227698i
$$515$$ 4.70163 + 4.70163i 0.207179 + 0.207179i
$$516$$ −1.32456 + 0.592359i −0.0583103 + 0.0260772i
$$517$$ 4.64911i 0.204468i
$$518$$ 0 0
$$519$$ −21.5761 + 9.64911i −0.947084 + 0.423549i
$$520$$ −3.58114 + 0.418861i −0.157043 + 0.0183683i
$$521$$ 24.7301i 1.08345i −0.840557 0.541723i $$-0.817772\pi$$
0.840557 0.541723i $$-0.182228\pi$$
$$522$$ 13.3956 0.746512i 0.586310 0.0326740i
$$523$$ −4.18861 −0.183155 −0.0915776 0.995798i $$-0.529191\pi$$
−0.0915776 + 0.995798i $$0.529191\pi$$
$$524$$ 17.4296 0.761414
$$525$$ 0 0
$$526$$ 7.16228 + 7.16228i 0.312290 + 0.312290i
$$527$$ −4.93113 4.93113i −0.214803 0.214803i
$$528$$ −3.23607 1.23607i −0.140832 0.0537930i
$$529$$ −3.00000 −0.130435
$$530$$ −1.41421 −0.0614295
$$531$$ 12.9536 0.721878i 0.562137 0.0313268i
$$532$$ 0 0
$$533$$ −7.07107 + 8.94427i −0.306282 + 0.387419i
$$534$$ 11.3246 5.06450i 0.490061 0.219162i
$$535$$ 7.32456 + 7.32456i 0.316668 + 0.316668i
$$536$$ 1.18472i 0.0511720i
$$537$$ 27.5585 12.3246i 1.18924 0.531844i
$$538$$ 3.16228 + 3.16228i 0.136335 + 0.136335i
$$539$$ −9.89949 + 9.89949i −0.426401 + 0.426401i
$$540$$ 4.61803 2.38197i 0.198729 0.102503i
$$541$$ −1.81139 + 1.81139i −0.0778777 + 0.0778777i −0.744973 0.667095i $$-0.767538\pi$$
0.667095 + 0.744973i $$0.267538\pi$$
$$542$$ 7.53006i 0.323444i
$$543$$ −5.88635 13.1623i −0.252607 0.564847i
$$544$$ 1.16228 1.16228i 0.0498322 0.0498322i
$$545$$ 15.7858 0.676191
$$546$$ 0 0
$$547$$ 9.48683 0.405628 0.202814 0.979217i $$-0.434991\pi$$
0.202814 + 0.979217i $$0.434991\pi$$
$$548$$ −5.42736 + 5.42736i −0.231845 + 0.231845i
$$549$$ −29.2982 + 32.7564i −1.25042 + 1.39801i
$$550$$ 2.00000i 0.0852803i
$$551$$ 5.19786 5.19786i 0.221436 0.221436i
$$552$$ 7.23607 + 2.76393i 0.307988 + 0.117641i
$$553$$ 0 0
$$554$$ −2.23607 2.23607i −0.0950014 0.0950014i
$$555$$ −4.00000 8.94427i −0.169791 0.379663i
$$556$$ 6.32456i 0.268221i
$$557$$ −6.11584 6.11584i −0.259137 0.259137i 0.565566 0.824703i $$-0.308658\pi$$
−0.824703 + 0.565566i $$0.808658\pi$$
$$558$$ 8.48528 9.48683i 0.359211 0.401610i
$$559$$ −0.350889 3.00000i −0.0148410 0.126886i
$$560$$ 0 0
$$561$$ 5.31915 + 2.03174i 0.224575 + 0.0857800i
$$562$$ 31.1623 1.31450
$$563$$ −42.3892 −1.78649 −0.893245 0.449570i $$-0.851577\pi$$
−0.893245 + 0.449570i $$0.851577\pi$$
$$564$$ 1.43665 3.76121i 0.0604941 0.158375i
$$565$$ 7.48683 + 7.48683i 0.314973 + 0.314973i
$$566$$ −13.5498 13.5498i −0.569540 0.569540i
$$567$$ 0 0
$$568$$ −13.4868 −0.565895
$$569$$ −24.7301 −1.03674 −0.518370 0.855156i $$-0.673461\pi$$
−0.518370 + 0.855156i $$0.673461\pi$$
$$570$$ 1.01587 2.65958i 0.0425500 0.111397i
$$571$$ 18.9737i 0.794023i −0.917814 0.397012i $$-0.870047\pi$$
0.917814 0.397012i $$-0.129953\pi$$
$$572$$ 4.47214 5.65685i 0.186989 0.236525i
$$573$$ 17.4868 + 39.1017i 0.730523 + 1.63350i
$$574$$ 0 0
$$575$$ 4.47214i 0.186501i
$$576$$ 2.23607 + 2.00000i 0.0931695 + 0.0833333i
$$577$$ −14.8377 14.8377i −0.617702 0.617702i 0.327239 0.944942i $$-0.393882\pi$$
−0.944942 + 0.327239i $$0.893882\pi$$
$$578$$ 10.1104 10.1104i 0.420536 0.420536i
$$579$$ 13.5360 35.4377i 0.562536 1.47274i
$$580$$ 3.16228 3.16228i 0.131306 0.131306i
$$581$$ 0 0
$$582$$ −11.5432 + 5.16228i −0.478481 + 0.213983i
$$583$$ 2.00000 2.00000i 0.0828315 0.0828315i
$$584$$ 1.64371 0.0680172
$$585$$ 1.85242 + 10.6569i 0.0765881 + 0.440607i
$$586$$ 4.00000 0.165238
$$587$$ −17.4296 + 17.4296i −0.719395 + 0.719395i −0.968481 0.249087i $$-0.919870\pi$$
0.249087 + 0.968481i $$0.419870\pi$$
$$588$$ 11.0680 4.94975i 0.456435 0.204124i
$$589$$ 6.97367i 0.287345i
$$590$$ 3.05792 3.05792i 0.125893 0.125893i
$$591$$ −7.81758 + 20.4667i −0.321572 + 0.841887i
$$592$$ 4.00000 4.00000i 0.164399 0.164399i
$$593$$ 22.5902 + 22.5902i 0.927667 + 0.927667i 0.997555 0.0698876i $$-0.0222641\pi$$
−0.0698876 + 0.997555i $$0.522264\pi$$
$$594$$ −3.16228 + 9.89949i −0.129750 + 0.406181i
$$595$$ 0 0
$$596$$ 11.5432 + 11.5432i 0.472828 + 0.472828i
$$597$$ −1.41421 3.16228i −0.0578799 0.129423i
$$598$$ −10.0000 + 12.6491i −0.408930 + 0.517261i
$$599$$ 14.8679i 0.607484i 0.952754 + 0.303742i $$0.0982362\pi$$
−0.952754 + 0.303742i $$0.901764\pi$$
$$600$$ 0.618034 1.61803i 0.0252311 0.0660560i
$$601$$ 0.649111 0.0264778 0.0132389 0.999912i $$-0.495786\pi$$
0.0132389 + 0.999912i $$0.495786\pi$$
$$602$$ 0 0
$$603$$ 3.54865 0.197759i 0.144512 0.00805339i
$$604$$ −13.3246 13.3246i −0.542168 0.542168i
$$605$$ 4.94975 + 4.94975i 0.201236 + 0.201236i
$$606$$ 9.75619 25.5420i 0.396318 1.03757i
$$607$$ 41.6228 1.68942 0.844708 0.535227i $$-0.179774\pi$$
0.844708 + 0.535227i $$0.179774\pi$$
$$608$$ 1.64371 0.0666612
$$609$$ 0 0
$$610$$ 14.6491i 0.593125i
$$611$$ 6.57484 + 5.19786i 0.265989 + 0.210283i
$$612$$ −3.67544 3.28742i −0.148571 0.132886i
$$613$$ −9.67544 9.67544i −0.390788 0.390788i 0.484181 0.874968i $$-0.339118\pi$$
−0.874968 + 0.484181i $$0.839118\pi$$
$$614$$ 1.18472i 0.0478113i
$$615$$ −2.23607 5.00000i −0.0901670 0.201619i
$$616$$ 0 0
$$617$$ 18.3848 18.3848i 0.740143 0.740143i −0.232462 0.972605i $$-0.574678\pi$$
0.972605 + 0.232462i $$0.0746782\pi$$
$$618$$ 10.7585 + 4.10938i 0.432770 + 0.165303i
$$619$$ 10.5132 10.5132i 0.422560 0.422560i −0.463524 0.886084i $$-0.653415\pi$$
0.886084 + 0.463524i $$0.153415\pi$$
$$620$$ 4.24264i 0.170389i
$$621$$ 7.07107 22.1359i 0.283752 0.888285i
$$622$$ −22.9737 + 22.9737i −0.921160 + 0.921160i
$$623$$ 0 0
$$624$$ −5.36610 + 3.19453i −0.214816 + 0.127883i
$$625$$ −1.00000 −0.0400000
$$626$$ −4.70163 + 4.70163i −0.187915 + 0.187915i
$$627$$ 2.32456 + 5.19786i 0.0928338 + 0.207583i
$$628$$ 16.8377i 0.671898i
$$629$$ −6.57484 + 6.57484i −0.262156 + 0.262156i
$$630$$ 0 0
$$631$$ 0.675445 0.675445i 0.0268890 0.0268890i −0.693534 0.720423i $$-0.743947\pi$$
0.720423 + 0.693534i $$0.243947\pi$$
$$632$$ −7.07107 7.07107i −0.281272 0.281272i
$$633$$ 45.2982 20.2580i 1.80044 0.805182i
$$634$$ 25.2982i 1.00472i
$$635$$ −14.8306 14.8306i −0.588535 0.588535i
$$636$$ −2.23607 + 1.00000i −0.0886659 + 0.0396526i
$$637$$ 2.93203 + 25.0680i 0.116171 + 0.993229i
$$638$$ 8.94427i 0.354107i
$$639$$ 2.25129 + 40.3978i 0.0890598 + 1.59811i
$$640$$ 1.00000 0.0395285
$$641$$ 35.7771 1.41311 0.706555 0.707658i $$-0.250248\pi$$
0.706555 + 0.707658i $$0.250248\pi$$
$$642$$ 16.7604 + 6.40190i 0.661479 + 0.252663i
$$643$$ 7.35089 + 7.35089i 0.289891 + 0.289891i 0.837037 0.547146i $$-0.184286\pi$$
−0.547146 + 0.837037i $$0.684286\pi$$
$$644$$ 0 0
$$645$$ 1.35546 + 0.517741i 0.0533713 + 0.0203860i
$$646$$ −2.70178 −0.106300
$$647$$ 37.9543 1.49214 0.746068 0.665870i $$-0.231939\pi$$
0.746068 + 0.665870i $$0.231939\pi$$
$$648$$ 5.61745 7.03166i 0.220674 0.276230i
$$649$$ 8.64911i 0.339507i
$$650$$ 2.82843 + 2.23607i 0.110940 + 0.0877058i
$$651$$ 0 0
$$652$$ 10.3246 + 10.3246i 0.404341 + 0.404341i
$$653$$ 48.0460i 1.88019i 0.340918 + 0.940093i $$0.389262\pi$$
−0.340918 + 0.940093i $$0.610738\pi$$
$$654$$ 24.9596 11.1623i 0.975998 0.436480i
$$655$$ −12.3246 12.3246i −0.481560 0.481560i
$$656$$ 2.23607 2.23607i 0.0873038 0.0873038i
$$657$$ −0.274377 4.92349i −0.0107044 0.192084i
$$658$$ 0 0
$$659$$ 8.94427i 0.348419i 0.984709 + 0.174210i $$0.0557371\pi$$
−0.984709 + 0.174210i $$0.944263\pi$$
$$660$$ 1.41421 + 3.16228i 0.0550482 + 0.123091i
$$661$$ −17.1623 + 17.1623i −0.667535 + 0.667535i −0.957145 0.289610i $$-0.906475\pi$$
0.289610 + 0.957145i $$0.406475\pi$$
$$662$$ −13.4164 −0.521443
$$663$$ 8.82030 5.25087i 0.342552 0.203927i
$$664$$ 8.00000 0.310460
$$665$$ 0 0
$$666$$ −12.6491 11.3137i −0.490143 0.438397i
$$667$$ 20.0000i 0.774403i
$$668$$ 7.30056 7.30056i 0.282467 0.282467i
$$669$$ −19.7913 7.55960i −0.765175 0.292271i
$$670$$ 0.837722 0.837722i 0.0323640 0.0323640i
$$671$$ −20.7170 20.7170i −0.799770 0.799770i
$$672$$ 0 0
$$673$$ 32.3246i 1.24602i 0.782214 + 0.623010i $$0.214090\pi$$
−0.782214 + 0.623010i $$0.785910\pi$$
$$674$$ −3.78365 3.78365i −0.145741 0.145741i
$$675$$ −4.94975 1.58114i −0.190516 0.0608581i
$$676$$ −3.00000 12.6491i −0.115385 0.486504i
$$677$$ 13.1869i 0.506814i 0.967360 + 0.253407i $$0.0815512\pi$$
−0.967360 + 0.253407i $$0.918449\pi$$
$$678$$ 17.1317 + 6.54373i 0.657939 + 0.251311i
$$679$$ 0 0
$$680$$ −1.64371 −0.0630334
$$681$$ −11.1246 + 29.1246i −0.426296 + 1.11606i
$$682$$ 6.00000 + 6.00000i 0.229752 + 0.229752i
$$683$$ −4.24264 4.24264i −0.162340 0.162340i 0.621262 0.783603i $$-0.286620\pi$$
−0.783603 + 0.621262i $$0.786620\pi$$
$$684$$ −0.274377 4.92349i −0.0104910 0.188254i
$$685$$ 7.67544 0.293264
$$686$$ 0 0
$$687$$ 15.5677 40.7568i 0.593946 1.55497i
$$688$$ 0.837722i 0.0319379i
$$689$$ −0.592359 5.06450i −0.0225671 0.192942i
$$690$$ −3.16228 7.07107i −0.120386 0.269191i
$$691$$ −4.18861 4.18861i −0.159342 0.159342i 0.622933 0.782275i $$-0.285941\pi$$
−0.782275 + 0.622933i $$0.785941\pi$$
$$692$$ 13.6459i 0.518739i
$$693$$ 0 0
$$694$$ −7.32456 7.32456i −0.278036 0.278036i
$$695$$ 4.47214 4.47214i 0.169638 0.169638i
$$696$$ 2.76393 7.23607i 0.104767 0.274282i
$$697$$ −3.67544 + 3.67544i −0.139217 + 0.139217i
$$698$$ 10.1290i 0.383388i
$$699$$ 20.4875 9.16228i 0.774907 0.346549i
$$700$$ 0 0
$$701$$ −5.39012 −0.203582 −0.101791 0.994806i $$-0.532457\pi$$
−0.101791 + 0.994806i $$0.532457\pi$$
$$702$$ 10.4645 + 15.5401i 0.394956 + 0.586524i
$$703$$ −9.29822 −0.350689
$$704$$ −1.41421 + 1.41421i −0.0533002 + 0.0533002i
$$705$$ −3.67544 + 1.64371i −0.138425 + 0.0619057i
$$706$$ 24.9737i 0.939896i
$$707$$ 0 0
$$708$$ 2.67272 6.99728i 0.100447 0.262974i
$$709$$ 3.48683 3.48683i 0.130951 0.130951i −0.638593 0.769544i $$-0.720483\pi$$
0.769544 + 0.638593i $$0.220483\pi$$
$$710$$ 9.53663 + 9.53663i 0.357903 + 0.357903i
$$711$$ −20.0000 + 22.3607i −0.750059 + 0.838591i
$$712$$ 7.16228i 0.268418i
$$713$$ −13.4164 13.4164i −0.502448 0.502448i
$$714$$ 0 0
$$715$$ −7.16228 + 0.837722i −0.267854 + 0.0313290i
$$716$$ 17.4296i 0.651373i
$$717$$ −2.98988 + 7.82760i −0.111659 + 0.292327i
$$718$$ −0.188612 −0.00703893
$$719$$ −24.7301 −0.922278 −0.461139 0.887328i $$-0.652559\pi$$
−0.461139 + 0.887328i $$0.652559\pi$$
$$720$$ −0.166925 2.99535i −0.00622094 0.111630i
$$721$$ 0 0
$$722$$ 11.5246 + 11.5246i 0.428901 + 0.428901i
$$723$$ −15.4259 + 40.3855i −0.573695 + 1.50195i
$$724$$ −8.32456 −0.309380
$$725$$ −4.47214 −0.166091
$$726$$ 11.3262 + 4.32624i 0.420356 + 0.160562i
$$727$$ 32.9737i 1.22293i 0.791273 + 0.611463i $$0.209419\pi$$
−0.791273 + 0.611463i $$0.790581\pi$$
$$728$$ 0 0
$$729$$ −22.0000 15.6525i −0.814815 0.579721i
$$730$$ −1.16228 1.16228i −0.0430178 0.0430178i
$$731$$ 1.37697i 0.0509291i
$$732$$ 10.3585 + 23.1623i 0.382861 + 0.856102i
$$733$$ −14.5132 14.5132i −0.536056 0.536056i 0.386312 0.922368i $$-0.373749\pi$$
−0.922368 + 0.386312i $$0.873749\pi$$
$$734$$ 4.70163 4.70163i 0.173540 0.173540i
$$735$$ −11.3262 4.32624i −0.417775 0.159576i
$$736$$ 3.16228 3.16228i 0.116563 0.116563i
$$737$$ 2.36944i 0.0872793i
$$738$$ −7.07107 6.32456i −0.260290 0.232810i
$$739$$ −32.1359 + 32.1359i −1.18214 + 1.18214i −0.202951 + 0.979189i $$0.565053\pi$$
−0.979189 + 0.202951i $$0.934947\pi$$
$$740$$ −5.65685 −0.207950
$$741$$ 9.94982 + 2.52397i 0.365516 + 0.0927204i
$$742$$ 0 0
$$743$$ 0.725728 0.725728i 0.0266244 0.0266244i −0.693669 0.720294i $$-0.744007\pi$$
0.720294 + 0.693669i $$0.244007\pi$$
$$744$$ −3.00000 6.70820i −0.109985 0.245935i
$$745$$ 16.3246i 0.598085i
$$746$$ −6.24921 + 6.24921i −0.228800 + 0.228800i
$$747$$ −1.33540 23.9628i −0.0488598 0.876754i
$$748$$ 2.32456 2.32456i 0.0849942 0.0849942i
$$749$$ 0 0
$$750$$ −1.58114 + 0.707107i −0.0577350 + 0.0258199i
$$751$$ 28.0000i 1.02173i −0.859660 0.510867i $$-0.829324\pi$$
0.859660 0.510867i $$-0.170676\pi$$
$$752$$ −1.64371 1.64371i −0.0599399 0.0599399i
$$753$$ 5.19786 2.32456i 0.189421 0.0847115i
$$754$$ 12.6491 + 10.0000i 0.460653 + 0.364179i
$$755$$ 18.8438i 0.685795i
$$756$$ 0 0
$$757$$ −23.8114 −0.865440 −0.432720 0.901528i $$-0.642446\pi$$
−0.432720 + 0.901528i $$0.642446\pi$$
$$758$$ 9.67000 0.351230
$$759$$ 14.4721 + 5.52786i 0.525305 + 0.200649i
$$760$$ −1.16228 1.16228i −0.0421602 0.0421602i
$$761$$ 29.7946 + 29.7946i 1.08005 + 1.08005i 0.996504 + 0.0835503i $$0.0266259\pi$$
0.0835503 + 0.996504i $$0.473374\pi$$
$$762$$ −33.9361 12.9624i −1.22938 0.469580i
$$763$$ 0 0
$$764$$ 24.7301 0.894704
$$765$$ 0.274377 + 4.92349i 0.00992010 + 0.178009i
$$766$$ 30.9737i 1.11912i
$$767$$ 12.2317 + 9.67000i 0.441661 + 0.349163i
$$768$$ 1.58114 0.707107i 0.0570544 0.0255155i
$$769$$ 31.6491 + 31.6491i 1.14130 + 1.14130i 0.988213 + 0.153083i $$0.0489201\pi$$
0.153083 + 0.988213i $$0.451080\pi$$
$$770$$ 0 0
$$771$$ −11.5432 + 5.16228i −0.415718 + 0.185915i
$$772$$ −15.4868 15.4868i −0.557383 0.557383i
$$773$$ 16.9706 16.9706i 0.610389 0.610389i −0.332659 0.943047i $$-0.607946\pi$$
0.943047 + 0.332659i $$0.107946\pi$$
$$774$$ 2.50927 0.139837i 0.0901940