# Properties

 Label 30.3.b.a.29.1 Level $30$ Weight $3$ Character 30.29 Analytic conductor $0.817$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,3,Mod(29,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("30.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$30 = 2 \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 30.b (of order $$2$$, degree $$1$$, 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: $$0.817440793081$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-17})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 16x^{2} + 81$$ x^4 + 16*x^2 + 81 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 29.1 Root $$0.707107 + 2.91548i$$ of defining polynomial Character $$\chi$$ $$=$$ 30.29 Dual form 30.3.b.a.29.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.41421 q^{2} +(0.707107 - 2.91548i) q^{3} +2.00000 q^{4} +(2.82843 - 4.12311i) q^{5} +(-1.00000 + 4.12311i) q^{6} +5.83095i q^{7} -2.82843 q^{8} +(-8.00000 - 4.12311i) q^{9} +O(q^{10})$$ $$q-1.41421 q^{2} +(0.707107 - 2.91548i) q^{3} +2.00000 q^{4} +(2.82843 - 4.12311i) q^{5} +(-1.00000 + 4.12311i) q^{6} +5.83095i q^{7} -2.82843 q^{8} +(-8.00000 - 4.12311i) q^{9} +(-4.00000 + 5.83095i) q^{10} +16.4924i q^{11} +(1.41421 - 5.83095i) q^{12} -8.24621i q^{14} +(-10.0208 - 11.1617i) q^{15} +4.00000 q^{16} +11.3137 q^{17} +(11.3137 + 5.83095i) q^{18} +12.0000 q^{19} +(5.65685 - 8.24621i) q^{20} +(17.0000 + 4.12311i) q^{21} -23.3238i q^{22} -24.0416 q^{23} +(-2.00000 + 8.24621i) q^{24} +(-9.00000 - 23.3238i) q^{25} +(-17.6777 + 20.4083i) q^{27} +11.6619i q^{28} +(14.1716 + 15.7850i) q^{30} -32.0000 q^{31} -5.65685 q^{32} +(48.0833 + 11.6619i) q^{33} -16.0000 q^{34} +(24.0416 + 16.4924i) q^{35} +(-16.0000 - 8.24621i) q^{36} +23.3238i q^{37} -16.9706 q^{38} +(-8.00000 + 11.6619i) q^{40} -57.7235i q^{41} +(-24.0416 - 5.83095i) q^{42} -40.8167i q^{43} +32.9848i q^{44} +(-39.6274 + 21.3229i) q^{45} +34.0000 q^{46} +35.3553 q^{47} +(2.82843 - 11.6619i) q^{48} +15.0000 q^{49} +(12.7279 + 32.9848i) q^{50} +(8.00000 - 32.9848i) q^{51} -67.8823 q^{53} +(25.0000 - 28.8617i) q^{54} +(68.0000 + 46.6476i) q^{55} -16.4924i q^{56} +(8.48528 - 34.9857i) q^{57} +16.4924i q^{59} +(-20.0416 - 22.3234i) q^{60} -16.0000 q^{61} +45.2548 q^{62} +(24.0416 - 46.6476i) q^{63} +8.00000 q^{64} +(-68.0000 - 16.4924i) q^{66} -5.83095i q^{67} +22.6274 q^{68} +(-17.0000 + 70.0928i) q^{69} +(-34.0000 - 23.3238i) q^{70} +(22.6274 + 11.6619i) q^{72} +116.619i q^{73} -32.9848i q^{74} +(-74.3640 + 9.74686i) q^{75} +24.0000 q^{76} -96.1665 q^{77} -72.0000 q^{79} +(11.3137 - 16.4924i) q^{80} +(47.0000 + 65.9697i) q^{81} +81.6333i q^{82} +43.8406 q^{83} +(34.0000 + 8.24621i) q^{84} +(32.0000 - 46.6476i) q^{85} +57.7235i q^{86} -46.6476i q^{88} -65.9697i q^{89} +(56.0416 - 30.1552i) q^{90} -48.0833 q^{92} +(-22.6274 + 93.2952i) q^{93} -50.0000 q^{94} +(33.9411 - 49.4773i) q^{95} +(-4.00000 + 16.4924i) q^{96} -163.267i q^{97} -21.2132 q^{98} +(68.0000 - 131.939i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 8 q^{4} - 4 q^{6} - 32 q^{9}+O(q^{10})$$ 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9 $$4 q + 8 q^{4} - 4 q^{6} - 32 q^{9} - 16 q^{10} + 8 q^{15} + 16 q^{16} + 48 q^{19} + 68 q^{21} - 8 q^{24} - 36 q^{25} + 68 q^{30} - 128 q^{31} - 64 q^{34} - 64 q^{36} - 32 q^{40} - 68 q^{45} + 136 q^{46} + 60 q^{49} + 32 q^{51} + 100 q^{54} + 272 q^{55} + 16 q^{60} - 64 q^{61} + 32 q^{64} - 272 q^{66} - 68 q^{69} - 136 q^{70} - 272 q^{75} + 96 q^{76} - 288 q^{79} + 188 q^{81} + 136 q^{84} + 128 q^{85} + 128 q^{90} - 200 q^{94} - 16 q^{96} + 272 q^{99}+O(q^{100})$$ 4 * q + 8 * q^4 - 4 * q^6 - 32 * q^9 - 16 * q^10 + 8 * q^15 + 16 * q^16 + 48 * q^19 + 68 * q^21 - 8 * q^24 - 36 * q^25 + 68 * q^30 - 128 * q^31 - 64 * q^34 - 64 * q^36 - 32 * q^40 - 68 * q^45 + 136 * q^46 + 60 * q^49 + 32 * q^51 + 100 * q^54 + 272 * q^55 + 16 * q^60 - 64 * q^61 + 32 * q^64 - 272 * q^66 - 68 * q^69 - 136 * q^70 - 272 * q^75 + 96 * q^76 - 288 * q^79 + 188 * q^81 + 136 * q^84 + 128 * q^85 + 128 * q^90 - 200 * q^94 - 16 * q^96 + 272 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$$.

 $$n$$ $$7$$ $$11$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.41421 −0.707107
$$3$$ 0.707107 2.91548i 0.235702 0.971825i
$$4$$ 2.00000 0.500000
$$5$$ 2.82843 4.12311i 0.565685 0.824621i
$$6$$ −1.00000 + 4.12311i −0.166667 + 0.687184i
$$7$$ 5.83095i 0.832993i 0.909137 + 0.416497i $$0.136742\pi$$
−0.909137 + 0.416497i $$0.863258\pi$$
$$8$$ −2.82843 −0.353553
$$9$$ −8.00000 4.12311i −0.888889 0.458123i
$$10$$ −4.00000 + 5.83095i −0.400000 + 0.583095i
$$11$$ 16.4924i 1.49931i 0.661828 + 0.749656i $$0.269781\pi$$
−0.661828 + 0.749656i $$0.730219\pi$$
$$12$$ 1.41421 5.83095i 0.117851 0.485913i
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 8.24621i 0.589015i
$$15$$ −10.0208 11.1617i −0.668054 0.744112i
$$16$$ 4.00000 0.250000
$$17$$ 11.3137 0.665512 0.332756 0.943013i $$-0.392021\pi$$
0.332756 + 0.943013i $$0.392021\pi$$
$$18$$ 11.3137 + 5.83095i 0.628539 + 0.323942i
$$19$$ 12.0000 0.631579 0.315789 0.948829i $$-0.397731\pi$$
0.315789 + 0.948829i $$0.397731\pi$$
$$20$$ 5.65685 8.24621i 0.282843 0.412311i
$$21$$ 17.0000 + 4.12311i 0.809524 + 0.196338i
$$22$$ 23.3238i 1.06017i
$$23$$ −24.0416 −1.04529 −0.522644 0.852551i $$-0.675054\pi$$
−0.522644 + 0.852551i $$0.675054\pi$$
$$24$$ −2.00000 + 8.24621i −0.0833333 + 0.343592i
$$25$$ −9.00000 23.3238i −0.360000 0.932952i
$$26$$ 0 0
$$27$$ −17.6777 + 20.4083i −0.654729 + 0.755864i
$$28$$ 11.6619i 0.416497i
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 14.1716 + 15.7850i 0.472386 + 0.526167i
$$31$$ −32.0000 −1.03226 −0.516129 0.856511i $$-0.672628\pi$$
−0.516129 + 0.856511i $$0.672628\pi$$
$$32$$ −5.65685 −0.176777
$$33$$ 48.0833 + 11.6619i 1.45707 + 0.353391i
$$34$$ −16.0000 −0.470588
$$35$$ 24.0416 + 16.4924i 0.686904 + 0.471212i
$$36$$ −16.0000 8.24621i −0.444444 0.229061i
$$37$$ 23.3238i 0.630373i 0.949030 + 0.315187i $$0.102067\pi$$
−0.949030 + 0.315187i $$0.897933\pi$$
$$38$$ −16.9706 −0.446594
$$39$$ 0 0
$$40$$ −8.00000 + 11.6619i −0.200000 + 0.291548i
$$41$$ 57.7235i 1.40789i −0.710255 0.703945i $$-0.751420\pi$$
0.710255 0.703945i $$-0.248580\pi$$
$$42$$ −24.0416 5.83095i −0.572420 0.138832i
$$43$$ 40.8167i 0.949225i −0.880195 0.474612i $$-0.842588\pi$$
0.880195 0.474612i $$-0.157412\pi$$
$$44$$ 32.9848i 0.749656i
$$45$$ −39.6274 + 21.3229i −0.880609 + 0.473843i
$$46$$ 34.0000 0.739130
$$47$$ 35.3553 0.752241 0.376121 0.926571i $$-0.377258\pi$$
0.376121 + 0.926571i $$0.377258\pi$$
$$48$$ 2.82843 11.6619i 0.0589256 0.242956i
$$49$$ 15.0000 0.306122
$$50$$ 12.7279 + 32.9848i 0.254558 + 0.659697i
$$51$$ 8.00000 32.9848i 0.156863 0.646762i
$$52$$ 0 0
$$53$$ −67.8823 −1.28080 −0.640399 0.768043i $$-0.721231\pi$$
−0.640399 + 0.768043i $$0.721231\pi$$
$$54$$ 25.0000 28.8617i 0.462963 0.534477i
$$55$$ 68.0000 + 46.6476i 1.23636 + 0.848138i
$$56$$ 16.4924i 0.294508i
$$57$$ 8.48528 34.9857i 0.148865 0.613784i
$$58$$ 0 0
$$59$$ 16.4924i 0.279533i 0.990185 + 0.139766i $$0.0446351\pi$$
−0.990185 + 0.139766i $$0.955365\pi$$
$$60$$ −20.0416 22.3234i −0.334027 0.372056i
$$61$$ −16.0000 −0.262295 −0.131148 0.991363i $$-0.541866\pi$$
−0.131148 + 0.991363i $$0.541866\pi$$
$$62$$ 45.2548 0.729917
$$63$$ 24.0416 46.6476i 0.381613 0.740438i
$$64$$ 8.00000 0.125000
$$65$$ 0 0
$$66$$ −68.0000 16.4924i −1.03030 0.249885i
$$67$$ 5.83095i 0.0870291i −0.999053 0.0435146i $$-0.986145\pi$$
0.999053 0.0435146i $$-0.0138555\pi$$
$$68$$ 22.6274 0.332756
$$69$$ −17.0000 + 70.0928i −0.246377 + 1.01584i
$$70$$ −34.0000 23.3238i −0.485714 0.333197i
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ 22.6274 + 11.6619i 0.314270 + 0.161971i
$$73$$ 116.619i 1.59752i 0.601649 + 0.798761i $$0.294511\pi$$
−0.601649 + 0.798761i $$0.705489\pi$$
$$74$$ 32.9848i 0.445741i
$$75$$ −74.3640 + 9.74686i −0.991519 + 0.129958i
$$76$$ 24.0000 0.315789
$$77$$ −96.1665 −1.24892
$$78$$ 0 0
$$79$$ −72.0000 −0.911392 −0.455696 0.890135i $$-0.650610\pi$$
−0.455696 + 0.890135i $$0.650610\pi$$
$$80$$ 11.3137 16.4924i 0.141421 0.206155i
$$81$$ 47.0000 + 65.9697i 0.580247 + 0.814441i
$$82$$ 81.6333i 0.995528i
$$83$$ 43.8406 0.528200 0.264100 0.964495i $$-0.414925\pi$$
0.264100 + 0.964495i $$0.414925\pi$$
$$84$$ 34.0000 + 8.24621i 0.404762 + 0.0981692i
$$85$$ 32.0000 46.6476i 0.376471 0.548795i
$$86$$ 57.7235i 0.671203i
$$87$$ 0 0
$$88$$ 46.6476i 0.530087i
$$89$$ 65.9697i 0.741232i −0.928786 0.370616i $$-0.879147\pi$$
0.928786 0.370616i $$-0.120853\pi$$
$$90$$ 56.0416 30.1552i 0.622685 0.335058i
$$91$$ 0 0
$$92$$ −48.0833 −0.522644
$$93$$ −22.6274 + 93.2952i −0.243306 + 1.00317i
$$94$$ −50.0000 −0.531915
$$95$$ 33.9411 49.4773i 0.357275 0.520813i
$$96$$ −4.00000 + 16.4924i −0.0416667 + 0.171796i
$$97$$ 163.267i 1.68316i −0.540131 0.841581i $$-0.681625\pi$$
0.540131 0.841581i $$-0.318375\pi$$
$$98$$ −21.2132 −0.216461
$$99$$ 68.0000 131.939i 0.686869 1.33272i
$$100$$ −18.0000 46.6476i −0.180000 0.466476i
$$101$$ 131.939i 1.30633i 0.757215 + 0.653165i $$0.226559\pi$$
−0.757215 + 0.653165i $$0.773441\pi$$
$$102$$ −11.3137 + 46.6476i −0.110919 + 0.457330i
$$103$$ 99.1262i 0.962390i −0.876614 0.481195i $$-0.840203\pi$$
0.876614 0.481195i $$-0.159797\pi$$
$$104$$ 0 0
$$105$$ 65.0833 58.4309i 0.619841 0.556485i
$$106$$ 96.0000 0.905660
$$107$$ 55.1543 0.515461 0.257731 0.966217i $$-0.417025\pi$$
0.257731 + 0.966217i $$0.417025\pi$$
$$108$$ −35.3553 + 40.8167i −0.327364 + 0.377932i
$$109$$ 80.0000 0.733945 0.366972 0.930232i $$-0.380394\pi$$
0.366972 + 0.930232i $$0.380394\pi$$
$$110$$ −96.1665 65.9697i −0.874241 0.599724i
$$111$$ 68.0000 + 16.4924i 0.612613 + 0.148580i
$$112$$ 23.3238i 0.208248i
$$113$$ 152.735 1.35164 0.675819 0.737068i $$-0.263790\pi$$
0.675819 + 0.737068i $$0.263790\pi$$
$$114$$ −12.0000 + 49.4773i −0.105263 + 0.434011i
$$115$$ −68.0000 + 99.1262i −0.591304 + 0.861967i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 23.3238i 0.197659i
$$119$$ 65.9697i 0.554367i
$$120$$ 28.3431 + 31.5700i 0.236193 + 0.263083i
$$121$$ −151.000 −1.24793
$$122$$ 22.6274 0.185471
$$123$$ −168.291 40.8167i −1.36822 0.331843i
$$124$$ −64.0000 −0.516129
$$125$$ −121.622 28.8617i −0.972979 0.230894i
$$126$$ −34.0000 + 65.9697i −0.269841 + 0.523569i
$$127$$ 40.8167i 0.321391i 0.987004 + 0.160696i $$0.0513737\pi$$
−0.987004 + 0.160696i $$0.948626\pi$$
$$128$$ −11.3137 −0.0883883
$$129$$ −119.000 28.8617i −0.922481 0.223734i
$$130$$ 0 0
$$131$$ 49.4773i 0.377689i 0.982007 + 0.188845i $$0.0604742\pi$$
−0.982007 + 0.188845i $$0.939526\pi$$
$$132$$ 96.1665 + 23.3238i 0.728534 + 0.176696i
$$133$$ 69.9714i 0.526101i
$$134$$ 8.24621i 0.0615389i
$$135$$ 34.1457 + 130.610i 0.252931 + 0.967484i
$$136$$ −32.0000 −0.235294
$$137$$ 50.9117 0.371618 0.185809 0.982586i $$-0.440509\pi$$
0.185809 + 0.982586i $$0.440509\pi$$
$$138$$ 24.0416 99.1262i 0.174215 0.718306i
$$139$$ 44.0000 0.316547 0.158273 0.987395i $$-0.449407\pi$$
0.158273 + 0.987395i $$0.449407\pi$$
$$140$$ 48.0833 + 32.9848i 0.343452 + 0.235606i
$$141$$ 25.0000 103.078i 0.177305 0.731047i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −32.0000 16.4924i −0.222222 0.114531i
$$145$$ 0 0
$$146$$ 164.924i 1.12962i
$$147$$ 10.6066 43.7321i 0.0721538 0.297498i
$$148$$ 46.6476i 0.315187i
$$149$$ 8.24621i 0.0553437i −0.999617 0.0276718i $$-0.991191\pi$$
0.999617 0.0276718i $$-0.00880935\pi$$
$$150$$ 105.167 13.7841i 0.701110 0.0918943i
$$151$$ 136.000 0.900662 0.450331 0.892862i $$-0.351306\pi$$
0.450331 + 0.892862i $$0.351306\pi$$
$$152$$ −33.9411 −0.223297
$$153$$ −90.5097 46.6476i −0.591566 0.304886i
$$154$$ 136.000 0.883117
$$155$$ −90.5097 + 131.939i −0.583933 + 0.851222i
$$156$$ 0 0
$$157$$ 116.619i 0.742796i 0.928474 + 0.371398i $$0.121122\pi$$
−0.928474 + 0.371398i $$0.878878\pi$$
$$158$$ 101.823 0.644452
$$159$$ −48.0000 + 197.909i −0.301887 + 1.24471i
$$160$$ −16.0000 + 23.3238i −0.100000 + 0.145774i
$$161$$ 140.186i 0.870718i
$$162$$ −66.4680 93.2952i −0.410297 0.575896i
$$163$$ 99.1262i 0.608136i −0.952650 0.304068i $$-0.901655\pi$$
0.952650 0.304068i $$-0.0983450\pi$$
$$164$$ 115.447i 0.703945i
$$165$$ 184.083 165.268i 1.11566 1.00162i
$$166$$ −62.0000 −0.373494
$$167$$ −292.742 −1.75295 −0.876474 0.481450i $$-0.840110\pi$$
−0.876474 + 0.481450i $$0.840110\pi$$
$$168$$ −48.0833 11.6619i −0.286210 0.0694161i
$$169$$ 169.000 1.00000
$$170$$ −45.2548 + 65.9697i −0.266205 + 0.388057i
$$171$$ −96.0000 49.4773i −0.561404 0.289341i
$$172$$ 81.6333i 0.474612i
$$173$$ 164.049 0.948259 0.474129 0.880455i $$-0.342763\pi$$
0.474129 + 0.880455i $$0.342763\pi$$
$$174$$ 0 0
$$175$$ 136.000 52.4786i 0.777143 0.299878i
$$176$$ 65.9697i 0.374828i
$$177$$ 48.0833 + 11.6619i 0.271657 + 0.0658865i
$$178$$ 93.2952i 0.524131i
$$179$$ 16.4924i 0.0921364i 0.998938 + 0.0460682i $$0.0146692\pi$$
−0.998938 + 0.0460682i $$0.985331\pi$$
$$180$$ −79.2548 + 42.6459i −0.440305 + 0.236922i
$$181$$ −82.0000 −0.453039 −0.226519 0.974007i $$-0.572735\pi$$
−0.226519 + 0.974007i $$0.572735\pi$$
$$182$$ 0 0
$$183$$ −11.3137 + 46.6476i −0.0618235 + 0.254905i
$$184$$ 68.0000 0.369565
$$185$$ 96.1665 + 65.9697i 0.519819 + 0.356593i
$$186$$ 32.0000 131.939i 0.172043 0.709352i
$$187$$ 186.590i 0.997810i
$$188$$ 70.7107 0.376121
$$189$$ −119.000 103.078i −0.629630 0.545384i
$$190$$ −48.0000 + 69.9714i −0.252632 + 0.368271i
$$191$$ 296.864i 1.55426i −0.629340 0.777130i $$-0.716675\pi$$
0.629340 0.777130i $$-0.283325\pi$$
$$192$$ 5.65685 23.3238i 0.0294628 0.121478i
$$193$$ 116.619i 0.604244i 0.953269 + 0.302122i $$0.0976950\pi$$
−0.953269 + 0.302122i $$0.902305\pi$$
$$194$$ 230.894i 1.19017i
$$195$$ 0 0
$$196$$ 30.0000 0.153061
$$197$$ 192.333 0.976310 0.488155 0.872757i $$-0.337670\pi$$
0.488155 + 0.872757i $$0.337670\pi$$
$$198$$ −96.1665 + 186.590i −0.485690 + 0.942376i
$$199$$ −312.000 −1.56784 −0.783920 0.620862i $$-0.786783\pi$$
−0.783920 + 0.620862i $$0.786783\pi$$
$$200$$ 25.4558 + 65.9697i 0.127279 + 0.329848i
$$201$$ −17.0000 4.12311i −0.0845771 0.0205130i
$$202$$ 186.590i 0.923715i
$$203$$ 0 0
$$204$$ 16.0000 65.9697i 0.0784314 0.323381i
$$205$$ −238.000 163.267i −1.16098 0.796423i
$$206$$ 140.186i 0.680513i
$$207$$ 192.333 + 99.1262i 0.929145 + 0.478870i
$$208$$ 0 0
$$209$$ 197.909i 0.946933i
$$210$$ −92.0416 + 82.6338i −0.438293 + 0.393494i
$$211$$ −12.0000 −0.0568720 −0.0284360 0.999596i $$-0.509053\pi$$
−0.0284360 + 0.999596i $$0.509053\pi$$
$$212$$ −135.765 −0.640399
$$213$$ 0 0
$$214$$ −78.0000 −0.364486
$$215$$ −168.291 115.447i −0.782751 0.536963i
$$216$$ 50.0000 57.7235i 0.231481 0.267238i
$$217$$ 186.590i 0.859864i
$$218$$ −113.137 −0.518977
$$219$$ 340.000 + 82.4621i 1.55251 + 0.376539i
$$220$$ 136.000 + 93.2952i 0.618182 + 0.424069i
$$221$$ 0 0
$$222$$ −96.1665 23.3238i −0.433183 0.105062i
$$223$$ 40.8167i 0.183034i −0.995803 0.0915172i $$-0.970828\pi$$
0.995803 0.0915172i $$-0.0291716\pi$$
$$224$$ 32.9848i 0.147254i
$$225$$ −24.1665 + 223.698i −0.107407 + 0.994215i
$$226$$ −216.000 −0.955752
$$227$$ 159.806 0.703992 0.351996 0.936002i $$-0.385503\pi$$
0.351996 + 0.936002i $$0.385503\pi$$
$$228$$ 16.9706 69.9714i 0.0744323 0.306892i
$$229$$ 82.0000 0.358079 0.179039 0.983842i $$-0.442701\pi$$
0.179039 + 0.983842i $$0.442701\pi$$
$$230$$ 96.1665 140.186i 0.418115 0.609503i
$$231$$ −68.0000 + 280.371i −0.294372 + 1.21373i
$$232$$ 0 0
$$233$$ −192.333 −0.825464 −0.412732 0.910853i $$-0.635425\pi$$
−0.412732 + 0.910853i $$0.635425\pi$$
$$234$$ 0 0
$$235$$ 100.000 145.774i 0.425532 0.620314i
$$236$$ 32.9848i 0.139766i
$$237$$ −50.9117 + 209.914i −0.214817 + 0.885714i
$$238$$ 93.2952i 0.391997i
$$239$$ 461.788i 1.93217i −0.258231 0.966083i $$-0.583139\pi$$
0.258231 0.966083i $$-0.416861\pi$$
$$240$$ −40.0833 44.6467i −0.167014 0.186028i
$$241$$ 304.000 1.26141 0.630705 0.776022i $$-0.282766\pi$$
0.630705 + 0.776022i $$0.282766\pi$$
$$242$$ 213.546 0.882423
$$243$$ 225.567 90.3798i 0.928260 0.371933i
$$244$$ −32.0000 −0.131148
$$245$$ 42.4264 61.8466i 0.173169 0.252435i
$$246$$ 238.000 + 57.7235i 0.967480 + 0.234648i
$$247$$ 0 0
$$248$$ 90.5097 0.364958
$$249$$ 31.0000 127.816i 0.124498 0.513318i
$$250$$ 172.000 + 40.8167i 0.688000 + 0.163267i
$$251$$ 346.341i 1.37984i 0.723884 + 0.689922i $$0.242355\pi$$
−0.723884 + 0.689922i $$0.757645\pi$$
$$252$$ 48.0833 93.2952i 0.190807 0.370219i
$$253$$ 396.505i 1.56721i
$$254$$ 57.7235i 0.227258i
$$255$$ −113.373 126.280i −0.444598 0.495216i
$$256$$ 16.0000 0.0625000
$$257$$ −390.323 −1.51877 −0.759383 0.650644i $$-0.774499\pi$$
−0.759383 + 0.650644i $$0.774499\pi$$
$$258$$ 168.291 + 40.8167i 0.652292 + 0.158204i
$$259$$ −136.000 −0.525097
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 69.9714i 0.267066i
$$263$$ −295.571 −1.12384 −0.561921 0.827191i $$-0.689938\pi$$
−0.561921 + 0.827191i $$0.689938\pi$$
$$264$$ −136.000 32.9848i −0.515152 0.124943i
$$265$$ −192.000 + 279.886i −0.724528 + 1.05617i
$$266$$ 98.9545i 0.372010i
$$267$$ −192.333 46.6476i −0.720348 0.174710i
$$268$$ 11.6619i 0.0435146i
$$269$$ 74.2159i 0.275896i 0.990440 + 0.137948i $$0.0440506\pi$$
−0.990440 + 0.137948i $$0.955949\pi$$
$$270$$ −48.2893 184.711i −0.178849 0.684115i
$$271$$ 40.0000 0.147601 0.0738007 0.997273i $$-0.476487\pi$$
0.0738007 + 0.997273i $$0.476487\pi$$
$$272$$ 45.2548 0.166378
$$273$$ 0 0
$$274$$ −72.0000 −0.262774
$$275$$ 384.666 148.432i 1.39879 0.539752i
$$276$$ −34.0000 + 140.186i −0.123188 + 0.507919i
$$277$$ 443.152i 1.59983i 0.600115 + 0.799914i $$0.295122\pi$$
−0.600115 + 0.799914i $$0.704878\pi$$
$$278$$ −62.2254 −0.223832
$$279$$ 256.000 + 131.939i 0.917563 + 0.472901i
$$280$$ −68.0000 46.6476i −0.242857 0.166599i
$$281$$ 519.511i 1.84879i 0.381431 + 0.924397i $$0.375431\pi$$
−0.381431 + 0.924397i $$0.624569\pi$$
$$282$$ −35.3553 + 145.774i −0.125374 + 0.516928i
$$283$$ 320.702i 1.13322i 0.823985 + 0.566612i $$0.191746\pi$$
−0.823985 + 0.566612i $$0.808254\pi$$
$$284$$ 0 0
$$285$$ −120.250 133.940i −0.421929 0.469966i
$$286$$ 0 0
$$287$$ 336.583 1.17276
$$288$$ 45.2548 + 23.3238i 0.157135 + 0.0809854i
$$289$$ −161.000 −0.557093
$$290$$ 0 0
$$291$$ −476.000 115.447i −1.63574 0.396725i
$$292$$ 233.238i 0.798761i
$$293$$ −84.8528 −0.289600 −0.144800 0.989461i $$-0.546254\pi$$
−0.144800 + 0.989461i $$0.546254\pi$$
$$294$$ −15.0000 + 61.8466i −0.0510204 + 0.210363i
$$295$$ 68.0000 + 46.6476i 0.230508 + 0.158128i
$$296$$ 65.9697i 0.222871i
$$297$$ −336.583 291.548i −1.13328 0.981642i
$$298$$ 11.6619i 0.0391339i
$$299$$ 0 0
$$300$$ −148.728 + 19.4937i −0.495760 + 0.0649791i
$$301$$ 238.000 0.790698
$$302$$ −192.333 −0.636864
$$303$$ 384.666 + 93.2952i 1.26953 + 0.307905i
$$304$$ 48.0000 0.157895
$$305$$ −45.2548 + 65.9697i −0.148377 + 0.216294i
$$306$$ 128.000 + 65.9697i 0.418301 + 0.215587i
$$307$$ 367.350i 1.19658i −0.801280 0.598290i $$-0.795847\pi$$
0.801280 0.598290i $$-0.204153\pi$$
$$308$$ −192.333 −0.624458
$$309$$ −289.000 70.0928i −0.935275 0.226838i
$$310$$ 128.000 186.590i 0.412903 0.601905i
$$311$$ 98.9545i 0.318182i −0.987264 0.159091i $$-0.949144\pi$$
0.987264 0.159091i $$-0.0508563\pi$$
$$312$$ 0 0
$$313$$ 186.590i 0.596136i 0.954545 + 0.298068i $$0.0963422\pi$$
−0.954545 + 0.298068i $$0.903658\pi$$
$$314$$ 164.924i 0.525236i
$$315$$ −124.333 231.066i −0.394708 0.733541i
$$316$$ −144.000 −0.455696
$$317$$ 520.431 1.64174 0.820868 0.571117i $$-0.193490\pi$$
0.820868 + 0.571117i $$0.193490\pi$$
$$318$$ 67.8823 279.886i 0.213466 0.880144i
$$319$$ 0 0
$$320$$ 22.6274 32.9848i 0.0707107 0.103078i
$$321$$ 39.0000 160.801i 0.121495 0.500938i
$$322$$ 198.252i 0.615691i
$$323$$ 135.765 0.420324
$$324$$ 94.0000 + 131.939i 0.290123 + 0.407220i
$$325$$ 0 0
$$326$$ 140.186i 0.430017i
$$327$$ 56.5685 233.238i 0.172992 0.713266i
$$328$$ 163.267i 0.497764i
$$329$$ 206.155i 0.626612i
$$330$$ −260.333 + 233.724i −0.788888 + 0.708253i
$$331$$ 292.000 0.882175 0.441088 0.897464i $$-0.354593\pi$$
0.441088 + 0.897464i $$0.354593\pi$$
$$332$$ 87.6812 0.264100
$$333$$ 96.1665 186.590i 0.288788 0.560332i
$$334$$ 414.000 1.23952
$$335$$ −24.0416 16.4924i −0.0717661 0.0492311i
$$336$$ 68.0000 + 16.4924i 0.202381 + 0.0490846i
$$337$$ 326.533i 0.968942i −0.874807 0.484471i $$-0.839012\pi$$
0.874807 0.484471i $$-0.160988\pi$$
$$338$$ −239.002 −0.707107
$$339$$ 108.000 445.295i 0.318584 1.31356i
$$340$$ 64.0000 93.2952i 0.188235 0.274398i
$$341$$ 527.758i 1.54768i
$$342$$ 135.765 + 69.9714i 0.396972 + 0.204595i
$$343$$ 373.181i 1.08799i
$$344$$ 115.447i 0.335602i
$$345$$ 240.917 + 268.345i 0.698309 + 0.777812i
$$346$$ −232.000 −0.670520
$$347$$ −394.566 −1.13708 −0.568538 0.822657i $$-0.692491\pi$$
−0.568538 + 0.822657i $$0.692491\pi$$
$$348$$ 0 0
$$349$$ 254.000 0.727794 0.363897 0.931439i $$-0.381446\pi$$
0.363897 + 0.931439i $$0.381446\pi$$
$$350$$ −192.333 + 74.2159i −0.549523 + 0.212045i
$$351$$ 0 0
$$352$$ 93.2952i 0.265043i
$$353$$ −345.068 −0.977530 −0.488765 0.872415i $$-0.662552\pi$$
−0.488765 + 0.872415i $$0.662552\pi$$
$$354$$ −68.0000 16.4924i −0.192090 0.0465888i
$$355$$ 0 0
$$356$$ 131.939i 0.370616i
$$357$$ 192.333 + 46.6476i 0.538748 + 0.130666i
$$358$$ 23.3238i 0.0651503i
$$359$$ 395.818i 1.10256i 0.834321 + 0.551279i $$0.185860\pi$$
−0.834321 + 0.551279i $$0.814140\pi$$
$$360$$ 112.083 60.3104i 0.311342 0.167529i
$$361$$ −217.000 −0.601108
$$362$$ 115.966 0.320347
$$363$$ −106.773 + 440.237i −0.294141 + 1.21277i
$$364$$ 0 0
$$365$$ 480.833 + 329.848i 1.31735 + 0.903694i
$$366$$ 16.0000 65.9697i 0.0437158 0.180245i
$$367$$ 413.998i 1.12806i −0.825755 0.564029i $$-0.809250\pi$$
0.825755 0.564029i $$-0.190750\pi$$
$$368$$ −96.1665 −0.261322
$$369$$ −238.000 + 461.788i −0.644986 + 1.25146i
$$370$$ −136.000 93.2952i −0.367568 0.252149i
$$371$$ 395.818i 1.06690i
$$372$$ −45.2548 + 186.590i −0.121653 + 0.501587i
$$373$$ 629.743i 1.68832i −0.536092 0.844159i $$-0.680100\pi$$
0.536092 0.844159i $$-0.319900\pi$$
$$374$$ 263.879i 0.705558i
$$375$$ −170.146 + 334.179i −0.453722 + 0.891143i
$$376$$ −100.000 −0.265957
$$377$$ 0 0
$$378$$ 168.291 + 145.774i 0.445215 + 0.385645i
$$379$$ −572.000 −1.50923 −0.754617 0.656165i $$-0.772178\pi$$
−0.754617 + 0.656165i $$0.772178\pi$$
$$380$$ 67.8823 98.9545i 0.178638 0.260407i
$$381$$ 119.000 + 28.8617i 0.312336 + 0.0757526i
$$382$$ 419.829i 1.09903i
$$383$$ 193.747 0.505868 0.252934 0.967484i $$-0.418605\pi$$
0.252934 + 0.967484i $$0.418605\pi$$
$$384$$ −8.00000 + 32.9848i −0.0208333 + 0.0858980i
$$385$$ −272.000 + 396.505i −0.706494 + 1.02988i
$$386$$ 164.924i 0.427265i
$$387$$ −168.291 + 326.533i −0.434862 + 0.843755i
$$388$$ 326.533i 0.841581i
$$389$$ 387.572i 0.996329i −0.867083 0.498164i $$-0.834008\pi$$
0.867083 0.498164i $$-0.165992\pi$$
$$390$$ 0 0
$$391$$ −272.000 −0.695652
$$392$$ −42.4264 −0.108231
$$393$$ 144.250 + 34.9857i 0.367048 + 0.0890222i
$$394$$ −272.000 −0.690355
$$395$$ −203.647 + 296.864i −0.515561 + 0.751553i
$$396$$ 136.000 263.879i 0.343434 0.666361i
$$397$$ 513.124i 1.29250i 0.763124 + 0.646252i $$0.223664\pi$$
−0.763124 + 0.646252i $$0.776336\pi$$
$$398$$ 441.235 1.10863
$$399$$ 204.000 + 49.4773i 0.511278 + 0.124003i
$$400$$ −36.0000 93.2952i −0.0900000 0.233238i
$$401$$ 65.9697i 0.164513i −0.996611 0.0822565i $$-0.973787\pi$$
0.996611 0.0822565i $$-0.0262127\pi$$
$$402$$ 24.0416 + 5.83095i 0.0598051 + 0.0145049i
$$403$$ 0 0
$$404$$ 263.879i 0.653165i
$$405$$ 404.936 7.19550i 0.999842 0.0177667i
$$406$$ 0 0
$$407$$ −384.666 −0.945126
$$408$$ −22.6274 + 93.2952i −0.0554594 + 0.228665i
$$409$$ 640.000 1.56479 0.782396 0.622781i $$-0.213997\pi$$
0.782396 + 0.622781i $$0.213997\pi$$
$$410$$ 336.583 + 230.894i 0.820934 + 0.563156i
$$411$$ 36.0000 148.432i 0.0875912 0.361148i
$$412$$ 198.252i 0.481195i
$$413$$ −96.1665 −0.232849
$$414$$ −272.000 140.186i −0.657005 0.338613i
$$415$$ 124.000 180.760i 0.298795 0.435565i
$$416$$ 0 0
$$417$$ 31.1127 128.281i 0.0746108 0.307628i
$$418$$ 279.886i 0.669583i
$$419$$ 577.235i 1.37765i 0.724928 + 0.688824i $$0.241873\pi$$
−0.724928 + 0.688824i $$0.758127\pi$$
$$420$$ 130.167 116.862i 0.309920 0.278242i
$$421$$ −656.000 −1.55819 −0.779097 0.626903i $$-0.784322\pi$$
−0.779097 + 0.626903i $$0.784322\pi$$
$$422$$ 16.9706 0.0402146
$$423$$ −282.843 145.774i −0.668659 0.344619i
$$424$$ 192.000 0.452830
$$425$$ −101.823 263.879i −0.239584 0.620891i
$$426$$ 0 0
$$427$$ 93.2952i 0.218490i
$$428$$ 110.309 0.257731
$$429$$ 0 0
$$430$$ 238.000 + 163.267i 0.553488 + 0.379690i
$$431$$ 362.833i 0.841841i 0.907098 + 0.420920i $$0.138293\pi$$
−0.907098 + 0.420920i $$0.861707\pi$$
$$432$$ −70.7107 + 81.6333i −0.163682 + 0.188966i
$$433$$ 163.267i 0.377059i −0.982068 0.188530i $$-0.939628\pi$$
0.982068 0.188530i $$-0.0603722\pi$$
$$434$$ 263.879i 0.608016i
$$435$$ 0 0
$$436$$ 160.000 0.366972
$$437$$ −288.500 −0.660182
$$438$$ −480.833 116.619i −1.09779 0.266254i
$$439$$ 432.000 0.984055 0.492027 0.870580i $$-0.336256\pi$$
0.492027 + 0.870580i $$0.336256\pi$$
$$440$$ −192.333 131.939i −0.437121 0.299862i
$$441$$ −120.000 61.8466i −0.272109 0.140242i
$$442$$ 0 0
$$443$$ −123.037 −0.277735 −0.138867 0.990311i $$-0.544346\pi$$
−0.138867 + 0.990311i $$0.544346\pi$$
$$444$$ 136.000 + 32.9848i 0.306306 + 0.0742902i
$$445$$ −272.000 186.590i −0.611236 0.419304i
$$446$$ 57.7235i 0.129425i
$$447$$ −24.0416 5.83095i −0.0537844 0.0130446i
$$448$$ 46.6476i 0.104124i
$$449$$ 865.852i 1.92840i −0.265174 0.964201i $$-0.585429\pi$$
0.265174 0.964201i $$-0.414571\pi$$
$$450$$ 34.1766 316.357i 0.0759481 0.703016i
$$451$$ 952.000 2.11086
$$452$$ 305.470 0.675819
$$453$$ 96.1665 396.505i 0.212288 0.875286i
$$454$$ −226.000 −0.497797
$$455$$ 0 0
$$456$$ −24.0000 + 98.9545i −0.0526316 + 0.217006i
$$457$$ 466.476i 1.02074i −0.859956 0.510368i $$-0.829509\pi$$
0.859956 0.510368i $$-0.170491\pi$$
$$458$$ −115.966 −0.253200
$$459$$ −200.000 + 230.894i −0.435730 + 0.503037i
$$460$$ −136.000 + 198.252i −0.295652 + 0.430983i
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 96.1665 396.505i 0.208153 0.858235i
$$463$$ 612.250i 1.32235i 0.750230 + 0.661177i $$0.229943\pi$$
−0.750230 + 0.661177i $$0.770057\pi$$
$$464$$ 0 0
$$465$$ 320.666 + 357.174i 0.689604 + 0.768116i
$$466$$ 272.000 0.583691
$$467$$ 767.918 1.64436 0.822182 0.569225i $$-0.192757\pi$$
0.822182 + 0.569225i $$0.192757\pi$$
$$468$$ 0 0
$$469$$ 34.0000 0.0724947
$$470$$ −141.421 + 206.155i −0.300897 + 0.438628i
$$471$$ 340.000 + 82.4621i 0.721868 + 0.175079i
$$472$$ 46.6476i 0.0988297i
$$473$$ 673.166 1.42318
$$474$$ 72.0000 296.864i 0.151899 0.626295i
$$475$$ −108.000 279.886i −0.227368 0.589233i
$$476$$ 131.939i 0.277184i
$$477$$ 543.058 + 279.886i 1.13849 + 0.586762i
$$478$$ 653.067i 1.36625i
$$479$$ 560.742i 1.17065i −0.810798 0.585326i $$-0.800967\pi$$
0.810798 0.585326i $$-0.199033\pi$$
$$480$$ 56.6863 + 63.1400i 0.118096 + 0.131542i
$$481$$ 0 0
$$482$$ −429.921 −0.891952
$$483$$ −408.708 99.1262i −0.846186 0.205230i
$$484$$ −302.000 −0.623967
$$485$$ −673.166 461.788i −1.38797 0.952140i
$$486$$ −319.000 + 127.816i −0.656379 + 0.262996i
$$487$$ 647.236i 1.32903i 0.747277 + 0.664513i $$0.231361\pi$$
−0.747277 + 0.664513i $$0.768639\pi$$
$$488$$ 45.2548 0.0927353
$$489$$ −289.000 70.0928i −0.591002 0.143339i
$$490$$ −60.0000 + 87.4643i −0.122449 + 0.178499i
$$491$$ 346.341i 0.705379i 0.935740 + 0.352689i $$0.114733\pi$$
−0.935740 + 0.352689i $$0.885267\pi$$
$$492$$ −336.583 81.6333i −0.684111 0.165921i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ −351.667 653.552i −0.710438 1.32031i
$$496$$ −128.000 −0.258065
$$497$$ 0 0
$$498$$ −43.8406 + 180.760i −0.0880334 + 0.362971i
$$499$$ −660.000 −1.32265 −0.661323 0.750102i $$-0.730005\pi$$
−0.661323 + 0.750102i $$0.730005\pi$$
$$500$$ −243.245 57.7235i −0.486489 0.115447i
$$501$$ −207.000 + 853.483i −0.413174 + 1.70356i
$$502$$ 489.800i 0.975697i
$$503$$ 182.434 0.362691 0.181345 0.983419i $$-0.441955\pi$$
0.181345 + 0.983419i $$0.441955\pi$$
$$504$$ −68.0000 + 131.939i −0.134921 + 0.261784i
$$505$$ 544.000 + 373.181i 1.07723 + 0.738972i
$$506$$ 560.742i 1.10819i
$$507$$ 119.501 492.715i 0.235702 0.971825i
$$508$$ 81.6333i 0.160696i
$$509$$ 395.818i 0.777639i 0.921314 + 0.388819i $$0.127117\pi$$
−0.921314 + 0.388819i $$0.872883\pi$$
$$510$$ 160.333 + 178.587i 0.314379 + 0.350171i
$$511$$ −680.000 −1.33072
$$512$$ −22.6274 −0.0441942
$$513$$ −212.132 + 244.900i −0.413513 + 0.477388i
$$514$$ 552.000 1.07393
$$515$$ −408.708 280.371i −0.793607 0.544410i
$$516$$ −238.000 57.7235i −0.461240 0.111867i
$$517$$ 583.095i 1.12784i
$$518$$ 192.333 0.371299
$$519$$ 116.000 478.280i 0.223507 0.921542i
$$520$$ 0 0
$$521$$ 131.939i 0.253243i 0.991951 + 0.126621i $$0.0404133\pi$$
−0.991951 + 0.126621i $$0.959587\pi$$
$$522$$ 0 0
$$523$$ 145.774i 0.278726i 0.990241 + 0.139363i $$0.0445055\pi$$
−0.990241 + 0.139363i $$0.955494\pi$$
$$524$$ 98.9545i 0.188845i
$$525$$ −56.8335 433.613i −0.108254 0.825929i
$$526$$ 418.000 0.794677
$$527$$ −362.039 −0.686980
$$528$$ 192.333 + 46.6476i 0.364267 + 0.0883478i
$$529$$ 49.0000 0.0926276
$$530$$ 271.529 395.818i 0.512319 0.746827i
$$531$$ 68.0000 131.939i 0.128060 0.248473i
$$532$$ 139.943i 0.263050i
$$533$$ 0 0
$$534$$ 272.000 + 65.9697i 0.509363 + 0.123539i
$$535$$ 156.000 227.407i 0.291589 0.425060i
$$536$$ 16.4924i 0.0307694i
$$537$$ 48.0833 + 11.6619i 0.0895405 + 0.0217168i
$$538$$ 104.957i 0.195088i
$$539$$ 247.386i 0.458973i
$$540$$ 68.2914 + 261.221i 0.126466 + 0.483742i
$$541$$ 418.000 0.772643 0.386322 0.922364i $$-0.373745\pi$$
0.386322 + 0.922364i $$0.373745\pi$$
$$542$$ −56.5685 −0.104370
$$543$$ −57.9828 + 239.069i −0.106782 + 0.440274i
$$544$$ −64.0000 −0.117647
$$545$$ 226.274 329.848i 0.415182 0.605227i
$$546$$ 0 0
$$547$$ 285.717i 0.522334i 0.965294 + 0.261167i $$0.0841073\pi$$
−0.965294 + 0.261167i $$0.915893\pi$$
$$548$$ 101.823 0.185809
$$549$$ 128.000 + 65.9697i 0.233151 + 0.120163i
$$550$$ −544.000 + 209.914i −0.989091 + 0.381662i
$$551$$ 0 0
$$552$$ 48.0833 198.252i 0.0871074 0.359153i
$$553$$ 419.829i 0.759184i
$$554$$ 626.712i 1.13125i
$$555$$ 260.333 233.724i 0.469069 0.421124i
$$556$$ 88.0000 0.158273
$$557$$ −424.264 −0.761695 −0.380847 0.924638i $$-0.624368\pi$$
−0.380847 + 0.924638i $$0.624368\pi$$
$$558$$ −362.039 186.590i −0.648815 0.334392i
$$559$$ 0 0
$$560$$ 96.1665 + 65.9697i 0.171726 + 0.117803i
$$561$$ 544.000 + 131.939i 0.969697 + 0.235186i
$$562$$ 734.700i 1.30730i
$$563$$ 813.173 1.44436 0.722178 0.691707i $$-0.243141\pi$$
0.722178 + 0.691707i $$0.243141\pi$$
$$564$$ 50.0000 206.155i 0.0886525 0.365524i
$$565$$ 432.000 629.743i 0.764602 1.11459i
$$566$$ 453.542i 0.801310i
$$567$$ −384.666 + 274.055i −0.678423 + 0.483342i
$$568$$ 0 0
$$569$$ 453.542i 0.797085i 0.917150 + 0.398543i $$0.130484\pi$$
−0.917150 + 0.398543i $$0.869516\pi$$
$$570$$ 170.059 + 189.420i 0.298349 + 0.332316i
$$571$$ 220.000 0.385289 0.192644 0.981269i $$-0.438294\pi$$
0.192644 + 0.981269i $$0.438294\pi$$
$$572$$ 0 0
$$573$$ −865.499 209.914i −1.51047 0.366343i
$$574$$ −476.000 −0.829268
$$575$$ 216.375 + 560.742i 0.376304 + 0.975204i
$$576$$ −64.0000 32.9848i −0.111111 0.0572654i
$$577$$ 46.6476i 0.0808451i −0.999183 0.0404225i $$-0.987130\pi$$
0.999183 0.0404225i $$-0.0128704\pi$$
$$578$$ 227.688 0.393925
$$579$$ 340.000 + 82.4621i 0.587219 + 0.142422i
$$580$$ 0 0
$$581$$ 255.633i 0.439987i
$$582$$ 673.166 + 163.267i 1.15664 + 0.280527i
$$583$$ 1119.54i 1.92031i
$$584$$ 329.848i 0.564809i
$$585$$ 0 0
$$586$$ 120.000 0.204778
$$587$$ −55.1543 −0.0939597 −0.0469798 0.998896i $$-0.514960\pi$$
−0.0469798 + 0.998896i $$0.514960\pi$$
$$588$$ 21.2132 87.4643i 0.0360769 0.148749i
$$589$$ −384.000 −0.651952
$$590$$ −96.1665 65.9697i −0.162994 0.111813i
$$591$$ 136.000 560.742i 0.230118 0.948803i
$$592$$ 93.2952i 0.157593i
$$593$$ −390.323 −0.658217 −0.329109 0.944292i $$-0.606748\pi$$
−0.329109 + 0.944292i $$0.606748\pi$$
$$594$$ 476.000 + 412.311i 0.801347 + 0.694126i
$$595$$ 272.000 + 186.590i 0.457143 + 0.313597i
$$596$$ 16.4924i 0.0276718i
$$597$$ −220.617 + 909.628i −0.369543 + 1.52367i
$$598$$ 0 0
$$599$$ 98.9545i 0.165200i −0.996583 0.0825998i $$-0.973678\pi$$
0.996583 0.0825998i $$-0.0263223\pi$$
$$600$$ 210.333 27.5683i 0.350555 0.0459471i
$$601$$ −880.000 −1.46423 −0.732113 0.681183i $$-0.761466\pi$$
−0.732113 + 0.681183i $$0.761466\pi$$
$$602$$ −336.583 −0.559108
$$603$$ −24.0416 + 46.6476i −0.0398700 + 0.0773592i
$$604$$ 272.000 0.450331
$$605$$ −427.092 + 622.589i −0.705938 + 1.02907i
$$606$$ −544.000 131.939i −0.897690 0.217722i
$$607$$ 425.659i 0.701251i −0.936516 0.350626i $$-0.885969\pi$$
0.936516 0.350626i $$-0.114031\pi$$
$$608$$ −67.8823 −0.111648
$$609$$ 0 0
$$610$$ 64.0000 93.2952i 0.104918 0.152943i
$$611$$ 0 0
$$612$$ −181.019 93.2952i −0.295783 0.152443i
$$613$$ 606.419i 0.989264i 0.869102 + 0.494632i $$0.164697\pi$$
−0.869102 + 0.494632i $$0.835303\pi$$
$$614$$ 519.511i 0.846110i
$$615$$ −644.291 + 578.436i −1.04763 + 0.940547i
$$616$$ 272.000 0.441558
$$617$$ 113.137 0.183366 0.0916832 0.995788i $$-0.470775\pi$$
0.0916832 + 0.995788i $$0.470775\pi$$
$$618$$ 408.708 + 99.1262i 0.661339 + 0.160398i
$$619$$ 52.0000 0.0840065 0.0420032 0.999117i $$-0.486626\pi$$
0.0420032 + 0.999117i $$0.486626\pi$$
$$620$$ −181.019 + 263.879i −0.291967 + 0.425611i
$$621$$ 425.000 490.650i 0.684380 0.790096i
$$622$$ 139.943i 0.224988i
$$623$$ 384.666 0.617442
$$624$$ 0 0
$$625$$ −463.000 + 419.829i −0.740800 + 0.671726i
$$626$$ 263.879i 0.421532i
$$627$$ 576.999 + 139.943i 0.920254 + 0.223194i
$$628$$ 233.238i 0.371398i
$$629$$ 263.879i 0.419521i
$$630$$ 175.833 + 326.776i 0.279101 + 0.518692i
$$631$$ −544.000 −0.862124 −0.431062 0.902322i $$-0.641861\pi$$
−0.431062 + 0.902322i $$0.641861\pi$$
$$632$$ 203.647 0.322226
$$633$$ −8.48528 + 34.9857i −0.0134049 + 0.0552697i
$$634$$ −736.000 −1.16088
$$635$$ 168.291 + 115.447i 0.265026 + 0.181806i
$$636$$ −96.0000 + 395.818i −0.150943 + 0.622356i
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −32.0000 + 46.6476i −0.0500000 + 0.0728869i
$$641$$ 849.360i 1.32505i −0.749038 0.662527i $$-0.769484\pi$$
0.749038 0.662527i $$-0.230516\pi$$
$$642$$ −55.1543 + 227.407i −0.0859102 + 0.354217i
$$643$$ 367.350i 0.571306i −0.958333 0.285653i $$-0.907789\pi$$
0.958333 0.285653i $$-0.0922105\pi$$
$$644$$ 280.371i 0.435359i
$$645$$ −455.583 + 409.016i −0.706330 + 0.634134i
$$646$$ −192.000 −0.297214
$$647$$ 971.565 1.50165 0.750823 0.660504i $$-0.229657\pi$$
0.750823 + 0.660504i $$0.229657\pi$$
$$648$$ −132.936 186.590i −0.205148 0.287948i
$$649$$ −272.000 −0.419106
$$650$$ 0 0
$$651$$ −544.000 131.939i −0.835637 0.202672i
$$652$$ 198.252i 0.304068i
$$653$$ −350.725 −0.537098 −0.268549 0.963266i $$-0.586544\pi$$
−0.268549 + 0.963266i $$0.586544\pi$$
$$654$$ −80.0000 + 329.848i −0.122324 + 0.504355i
$$655$$ 204.000 + 139.943i 0.311450 + 0.213653i
$$656$$ 230.894i 0.351972i
$$657$$ 480.833 932.952i 0.731861 1.42002i
$$658$$ 291.548i 0.443081i
$$659$$ 577.235i 0.875925i −0.898993 0.437963i $$-0.855700\pi$$
0.898993 0.437963i $$-0.144300\pi$$
$$660$$ 368.167 330.535i 0.557828 0.500811i
$$661$$ 80.0000 0.121029 0.0605144 0.998167i $$-0.480726\pi$$
0.0605144 + 0.998167i $$0.480726\pi$$
$$662$$ −412.950 −0.623792
$$663$$ 0 0
$$664$$ −124.000 −0.186747
$$665$$ 288.500 + 197.909i 0.433834 + 0.297608i
$$666$$ −136.000 + 263.879i −0.204204 + 0.396214i
$$667$$ 0 0
$$668$$ −585.484 −0.876474
$$669$$ −119.000 28.8617i −0.177877 0.0431416i
$$670$$ 34.0000 + 23.3238i 0.0507463 + 0.0348117i
$$671$$ 263.879i 0.393262i
$$672$$ −96.1665 23.3238i −0.143105 0.0347080i
$$673$$ 489.800i 0.727786i 0.931441 + 0.363893i $$0.118553\pi$$
−0.931441 + 0.363893i $$0.881447\pi$$
$$674$$ 461.788i 0.685145i
$$675$$ 635.099 + 228.636i 0.940887 + 0.338719i
$$676$$ 338.000 0.500000
$$677$$ −192.333 −0.284096 −0.142048 0.989860i $$-0.545369\pi$$
−0.142048 + 0.989860i $$0.545369\pi$$
$$678$$ −152.735 + 629.743i −0.225273 + 0.928824i
$$679$$ 952.000 1.40206
$$680$$ −90.5097 + 131.939i −0.133102 + 0.194029i
$$681$$ 113.000 465.911i 0.165932 0.684157i
$$682$$ 746.362i 1.09437i
$$683$$ −236.174 −0.345789 −0.172894 0.984940i $$-0.555312\pi$$
−0.172894 + 0.984940i $$0.555312\pi$$
$$684$$ −192.000 98.9545i −0.280702 0.144670i
$$685$$ 144.000 209.914i 0.210219 0.306444i
$$686$$ 527.758i 0.769326i
$$687$$ 57.9828 239.069i 0.0843999 0.347990i
$$688$$ 163.267i 0.237306i
$$689$$ 0 0
$$690$$ −340.708 379.497i −0.493779 0.549996i
$$691$$ −548.000 −0.793054 −0.396527 0.918023i $$-0.629785\pi$$
−0.396527 + 0.918023i $$0.629785\pi$$
$$692$$ 328.098 0.474129
$$693$$ 769.332 + 396.505i 1.11015 + 0.572157i
$$694$$ 558.000 0.804035
$$695$$ 124.451 181.417i 0.179066 0.261031i
$$696$$ 0 0
$$697$$ 653.067i 0.936968i
$$698$$ −359.210 −0.514628
$$699$$ −136.000 + 560.742i −0.194564 + 0.802207i
$$700$$ 272.000 104.957i 0.388571 0.149939i
$$701$$ 57.7235i 0.0823445i −0.999152 0.0411722i $$-0.986891\pi$$
0.999152 0.0411722i $$-0.0131092\pi$$
$$702$$ 0 0
$$703$$ 279.886i 0.398130i
$$704$$ 131.939i 0.187414i
$$705$$ −354.289 394.625i −0.502538 0.559752i
$$706$$ 488.000 0.691218
$$707$$ −769.332 −1.08816
$$708$$ 96.1665 + 23.3238i 0.135828 + 0.0329432i
$$709$$ 1230.00 1.73484 0.867419 0.497579i $$-0.165777\pi$$
0.867419 + 0.497579i $$0.165777\pi$$
$$710$$ 0 0
$$711$$ 576.000 + 296.864i 0.810127 + 0.417530i
$$712$$ 186.590i 0.262065i
$$713$$ 769.332 1.07901
$$714$$ −272.000 65.9697i −0.380952 0.0923945i
$$715$$ 0 0
$$716$$ 32.9848i 0.0460682i
$$717$$ −1346.33 326.533i −1.87773 0.455416i
$$718$$ 559.771i 0.779626i
$$719$$ 626.712i 0.871644i 0.900033 + 0.435822i $$0.143542\pi$$
−0.900033 + 0.435822i $$0.856458\pi$$
$$720$$ −158.510 + 85.2918i −0.220152 + 0.118461i
$$721$$ 578.000 0.801664
$$722$$ 306.884 0.425048
$$723$$ 214.960 886.305i 0.297317 1.22587i
$$724$$ −164.000 −0.226519
$$725$$ 0 0
$$726$$ 151.000 622.589i 0.207989 0.857561i
$$727$$ 367.350i 0.505296i 0.967558 + 0.252648i $$0.0813014\pi$$
−0.967558 + 0.252648i $$0.918699\pi$$
$$728$$ 0 0
$$729$$ −104.000 721.543i −0.142661 0.989772i
$$730$$ −680.000 466.476i −0.931507 0.639008i
$$731$$ 461.788i 0.631721i
$$732$$ −22.6274 + 93.2952i −0.0309118 + 0.127453i
$$733$$ 1002.92i 1.36825i 0.729367 + 0.684123i $$0.239815\pi$$
−0.729367 + 0.684123i $$0.760185\pi$$
$$734$$ 585.481i 0.797658i
$$735$$ −150.312 167.425i −0.204506 0.227790i
$$736$$ 136.000 0.184783
$$737$$ 96.1665 0.130484
$$738$$ 336.583 653.067i 0.456074 0.884914i
$$739$$ −340.000 −0.460081 −0.230041 0.973181i $$-0.573886\pi$$
−0.230041 + 0.973181i $$0.573886\pi$$
$$740$$ 192.333 + 131.939i 0.259910 + 0.178296i
$$741$$ 0 0
$$742$$ 559.771i 0.754409i
$$743$$ −1243.09 −1.67307 −0.836537 0.547911i $$-0.815423\pi$$
−0.836537 + 0.547911i $$0.815423\pi$$
$$744$$ 64.0000 263.879i 0.0860215 0.354676i
$$745$$ −34.0000 23.3238i −0.0456376 0.0313071i
$$746$$ 890.591i 1.19382i
$$747$$ −350.725 180.760i −0.469511 0.241981i
$$748$$ 373.181i 0.498905i
$$749$$ 321.602i 0.429375i
$$750$$ 240.622 472.600i 0.320830 0.630133i
$$751$$ −520.000 −0.692410 −0.346205 0.938159i $$-0.612530\pi$$
−0.346205 + 0.938159i $$0.612530\pi$$
$$752$$ 141.421 0.188060
$$753$$ 1009.75 + 244.900i 1.34097 + 0.325232i
$$754$$ 0 0
$$755$$ 384.666 560.742i 0.509492 0.742705i
$$756$$ −238.000 206.155i −0.314815 0.272692i
$$757$$ 816.333i 1.07838i −0.842184 0.539190i $$-0.818731\pi$$
0.842184 0.539190i $$-0.181269\pi$$
$$758$$ 808.930 1.06719
$$759$$ −1156.00 280.371i −1.52306 0.369395i
$$760$$ −96.0000 + 139.943i −0.126316 + 0.184135i
$$761$$ 395.818i 0.520129i 0.965591 + 0.260064i $$0.0837438\pi$$
−0.965591 + 0.260064i $$0.916256\pi$$
$$762$$ −168.291 40.8167i −0.220855 0.0535652i
$$763$$ 466.476i 0.611371i
$$764$$ 593.727i 0.777130i
$$765$$ −448.333 + 241.242i −0.586056 + 0.315348i
$$766$$ −274.000 −0.357702
$$767$$ 0 0
$$768$$ 11.3137 46.6476i 0.0147314 0.0607391i
$$769$$ −306.000 −0.397919 −0.198960 0.980008i $$-0.563756\pi$$
−0.198960 + 0.980008i $$0.563756\pi$$
$$770$$ 384.666 560.742i 0.499566 0.728237i
$$771$$ −276.000 + 1137.98i −0.357977 + 1.47598i
$$772$$ 233.238i 0.302122i
$$773$$ −305.470 −0.395175 −0.197587 0.980285i $$-0.563311\pi$$
−0.197587 + 0.980285i $$0.563311\pi$$
$$774$$ 238.000 461.788i 0.307494 0.596625i
$$775$$ 288.000 + 746.362i 0.371613 + 0.963048i
$$776$$ 461.788i 0.595087i
$$777$$ −96.1665 + 396.505i −0.123766 + 0.510302i
$$778$$ 548.109i 0.704511i