# Properties

 Label 855.2.k.f.406.1 Level $855$ Weight $2$ Character 855.406 Analytic conductor $6.827$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$855 = 3^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 855.k (of order $$3$$, 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: $$6.82720937282$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 285) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 406.1 Root $$-0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 855.406 Dual form 855.2.k.f.676.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.207107 - 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.82843 q^{7} -1.58579 q^{8} +O(q^{10})$$ $$q+(-0.207107 - 0.358719i) q^{2} +(0.914214 - 1.58346i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.82843 q^{7} -1.58579 q^{8} +(-0.207107 + 0.358719i) q^{10} +2.82843 q^{11} +(0.914214 - 1.58346i) q^{13} +(-0.378680 - 0.655892i) q^{14} +(-1.50000 - 2.59808i) q^{16} +(-0.585786 - 1.01461i) q^{17} +(4.00000 + 1.73205i) q^{19} -1.82843 q^{20} +(-0.585786 - 1.01461i) q^{22} +(-0.414214 + 0.717439i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.757359 q^{26} +(1.67157 - 2.89525i) q^{28} +(4.82843 - 8.36308i) q^{29} -5.00000 q^{31} +(-2.20711 + 3.82282i) q^{32} +(-0.242641 + 0.420266i) q^{34} +(-0.914214 - 1.58346i) q^{35} -2.17157 q^{37} +(-0.207107 - 1.79360i) q^{38} +(0.792893 + 1.37333i) q^{40} +(1.41421 + 2.44949i) q^{41} +(-3.91421 - 6.77962i) q^{43} +(2.58579 - 4.47871i) q^{44} +0.343146 q^{46} +(-1.58579 + 2.74666i) q^{47} -3.65685 q^{49} +0.414214 q^{50} +(-1.67157 - 2.89525i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-1.41421 - 2.44949i) q^{55} -2.89949 q^{56} -4.00000 q^{58} +(4.15685 - 7.19988i) q^{61} +(1.03553 + 1.79360i) q^{62} -4.17157 q^{64} -1.82843 q^{65} +(-2.74264 + 4.75039i) q^{67} -2.14214 q^{68} +(-0.378680 + 0.655892i) q^{70} +(5.00000 + 8.66025i) q^{71} +(-4.74264 - 8.21449i) q^{73} +(0.449747 + 0.778985i) q^{74} +(6.39949 - 4.75039i) q^{76} +5.17157 q^{77} +(1.67157 + 2.89525i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(0.585786 - 1.01461i) q^{82} +8.00000 q^{83} +(-0.585786 + 1.01461i) q^{85} +(-1.62132 + 2.80821i) q^{86} -4.48528 q^{88} +(6.24264 - 10.8126i) q^{89} +(1.67157 - 2.89525i) q^{91} +(0.757359 + 1.31178i) q^{92} +1.31371 q^{94} +(-0.500000 - 4.33013i) q^{95} +(3.00000 + 5.19615i) q^{97} +(0.757359 + 1.31178i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10})$$ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 12 * q^8 $$4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 12 q^{8} + 2 q^{10} - 2 q^{13} - 10 q^{14} - 6 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} + 4 q^{23} - 2 q^{25} - 20 q^{26} + 18 q^{28} + 8 q^{29} - 20 q^{31} - 6 q^{32} + 16 q^{34} + 2 q^{35} - 20 q^{37} + 2 q^{38} + 6 q^{40} - 10 q^{43} + 16 q^{44} + 24 q^{46} - 12 q^{47} + 8 q^{49} - 4 q^{50} - 18 q^{52} - 4 q^{53} + 28 q^{56} - 16 q^{58} - 6 q^{61} - 10 q^{62} - 28 q^{64} + 4 q^{65} + 6 q^{67} + 48 q^{68} - 10 q^{70} + 20 q^{71} - 2 q^{73} - 18 q^{74} - 14 q^{76} + 32 q^{77} + 18 q^{79} - 6 q^{80} + 8 q^{82} + 32 q^{83} - 8 q^{85} + 2 q^{86} + 16 q^{88} + 8 q^{89} + 18 q^{91} + 20 q^{92} - 40 q^{94} - 2 q^{95} + 12 q^{97} + 20 q^{98}+O(q^{100})$$ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 - 12 * q^8 + 2 * q^10 - 2 * q^13 - 10 * q^14 - 6 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^20 - 8 * q^22 + 4 * q^23 - 2 * q^25 - 20 * q^26 + 18 * q^28 + 8 * q^29 - 20 * q^31 - 6 * q^32 + 16 * q^34 + 2 * q^35 - 20 * q^37 + 2 * q^38 + 6 * q^40 - 10 * q^43 + 16 * q^44 + 24 * q^46 - 12 * q^47 + 8 * q^49 - 4 * q^50 - 18 * q^52 - 4 * q^53 + 28 * q^56 - 16 * q^58 - 6 * q^61 - 10 * q^62 - 28 * q^64 + 4 * q^65 + 6 * q^67 + 48 * q^68 - 10 * q^70 + 20 * q^71 - 2 * q^73 - 18 * q^74 - 14 * q^76 + 32 * q^77 + 18 * q^79 - 6 * q^80 + 8 * q^82 + 32 * q^83 - 8 * q^85 + 2 * q^86 + 16 * q^88 + 8 * q^89 + 18 * q^91 + 20 * q^92 - 40 * q^94 - 2 * q^95 + 12 * q^97 + 20 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$$.

 $$n$$ $$172$$ $$191$$ $$496$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.207107 0.358719i −0.146447 0.253653i 0.783465 0.621436i $$-0.213450\pi$$
−0.929912 + 0.367783i $$0.880117\pi$$
$$3$$ 0 0
$$4$$ 0.914214 1.58346i 0.457107 0.791732i
$$5$$ −0.500000 0.866025i −0.223607 0.387298i
$$6$$ 0 0
$$7$$ 1.82843 0.691080 0.345540 0.938404i $$-0.387696\pi$$
0.345540 + 0.938404i $$0.387696\pi$$
$$8$$ −1.58579 −0.560660
$$9$$ 0 0
$$10$$ −0.207107 + 0.358719i −0.0654929 + 0.113437i
$$11$$ 2.82843 0.852803 0.426401 0.904534i $$-0.359781\pi$$
0.426401 + 0.904534i $$0.359781\pi$$
$$12$$ 0 0
$$13$$ 0.914214 1.58346i 0.253557 0.439174i −0.710945 0.703247i $$-0.751733\pi$$
0.964503 + 0.264073i $$0.0850661\pi$$
$$14$$ −0.378680 0.655892i −0.101206 0.175295i
$$15$$ 0 0
$$16$$ −1.50000 2.59808i −0.375000 0.649519i
$$17$$ −0.585786 1.01461i −0.142074 0.246080i 0.786203 0.617968i $$-0.212044\pi$$
−0.928278 + 0.371888i $$0.878710\pi$$
$$18$$ 0 0
$$19$$ 4.00000 + 1.73205i 0.917663 + 0.397360i
$$20$$ −1.82843 −0.408849
$$21$$ 0 0
$$22$$ −0.585786 1.01461i −0.124890 0.216316i
$$23$$ −0.414214 + 0.717439i −0.0863695 + 0.149596i −0.905974 0.423333i $$-0.860860\pi$$
0.819604 + 0.572930i $$0.194193\pi$$
$$24$$ 0 0
$$25$$ −0.500000 + 0.866025i −0.100000 + 0.173205i
$$26$$ −0.757359 −0.148530
$$27$$ 0 0
$$28$$ 1.67157 2.89525i 0.315898 0.547151i
$$29$$ 4.82843 8.36308i 0.896616 1.55299i 0.0648251 0.997897i $$-0.479351\pi$$
0.831791 0.555089i $$-0.187316\pi$$
$$30$$ 0 0
$$31$$ −5.00000 −0.898027 −0.449013 0.893525i $$-0.648224\pi$$
−0.449013 + 0.893525i $$0.648224\pi$$
$$32$$ −2.20711 + 3.82282i −0.390165 + 0.675786i
$$33$$ 0 0
$$34$$ −0.242641 + 0.420266i −0.0416125 + 0.0720750i
$$35$$ −0.914214 1.58346i −0.154530 0.267654i
$$36$$ 0 0
$$37$$ −2.17157 −0.357004 −0.178502 0.983940i $$-0.557125\pi$$
−0.178502 + 0.983940i $$0.557125\pi$$
$$38$$ −0.207107 1.79360i −0.0335972 0.290960i
$$39$$ 0 0
$$40$$ 0.792893 + 1.37333i 0.125367 + 0.217143i
$$41$$ 1.41421 + 2.44949i 0.220863 + 0.382546i 0.955070 0.296379i $$-0.0957793\pi$$
−0.734207 + 0.678925i $$0.762446\pi$$
$$42$$ 0 0
$$43$$ −3.91421 6.77962i −0.596912 1.03388i −0.993274 0.115788i $$-0.963061\pi$$
0.396362 0.918094i $$-0.370273\pi$$
$$44$$ 2.58579 4.47871i 0.389822 0.675191i
$$45$$ 0 0
$$46$$ 0.343146 0.0505941
$$47$$ −1.58579 + 2.74666i −0.231311 + 0.400642i −0.958194 0.286119i $$-0.907635\pi$$
0.726883 + 0.686761i $$0.240968\pi$$
$$48$$ 0 0
$$49$$ −3.65685 −0.522408
$$50$$ 0.414214 0.0585786
$$51$$ 0 0
$$52$$ −1.67157 2.89525i −0.231805 0.401499i
$$53$$ −1.00000 + 1.73205i −0.137361 + 0.237915i −0.926497 0.376303i $$-0.877195\pi$$
0.789136 + 0.614218i $$0.210529\pi$$
$$54$$ 0 0
$$55$$ −1.41421 2.44949i −0.190693 0.330289i
$$56$$ −2.89949 −0.387461
$$57$$ 0 0
$$58$$ −4.00000 −0.525226
$$59$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$60$$ 0 0
$$61$$ 4.15685 7.19988i 0.532231 0.921851i −0.467061 0.884225i $$-0.654687\pi$$
0.999292 0.0376256i $$-0.0119794\pi$$
$$62$$ 1.03553 + 1.79360i 0.131513 + 0.227787i
$$63$$ 0 0
$$64$$ −4.17157 −0.521447
$$65$$ −1.82843 −0.226788
$$66$$ 0 0
$$67$$ −2.74264 + 4.75039i −0.335067 + 0.580353i −0.983498 0.180921i $$-0.942092\pi$$
0.648431 + 0.761274i $$0.275426\pi$$
$$68$$ −2.14214 −0.259772
$$69$$ 0 0
$$70$$ −0.378680 + 0.655892i −0.0452609 + 0.0783941i
$$71$$ 5.00000 + 8.66025i 0.593391 + 1.02778i 0.993772 + 0.111434i $$0.0355445\pi$$
−0.400381 + 0.916349i $$0.631122\pi$$
$$72$$ 0 0
$$73$$ −4.74264 8.21449i −0.555084 0.961434i −0.997897 0.0648198i $$-0.979353\pi$$
0.442813 0.896614i $$-0.353981\pi$$
$$74$$ 0.449747 + 0.778985i 0.0522821 + 0.0905552i
$$75$$ 0 0
$$76$$ 6.39949 4.75039i 0.734072 0.544907i
$$77$$ 5.17157 0.589355
$$78$$ 0 0
$$79$$ 1.67157 + 2.89525i 0.188067 + 0.325741i 0.944606 0.328208i $$-0.106445\pi$$
−0.756539 + 0.653949i $$0.773111\pi$$
$$80$$ −1.50000 + 2.59808i −0.167705 + 0.290474i
$$81$$ 0 0
$$82$$ 0.585786 1.01461i 0.0646893 0.112045i
$$83$$ 8.00000 0.878114 0.439057 0.898459i $$-0.355313\pi$$
0.439057 + 0.898459i $$0.355313\pi$$
$$84$$ 0 0
$$85$$ −0.585786 + 1.01461i −0.0635375 + 0.110050i
$$86$$ −1.62132 + 2.80821i −0.174831 + 0.302817i
$$87$$ 0 0
$$88$$ −4.48528 −0.478133
$$89$$ 6.24264 10.8126i 0.661719 1.14613i −0.318445 0.947941i $$-0.603161\pi$$
0.980164 0.198189i $$-0.0635060\pi$$
$$90$$ 0 0
$$91$$ 1.67157 2.89525i 0.175228 0.303505i
$$92$$ 0.757359 + 1.31178i 0.0789602 + 0.136763i
$$93$$ 0 0
$$94$$ 1.31371 0.135499
$$95$$ −0.500000 4.33013i −0.0512989 0.444262i
$$96$$ 0 0
$$97$$ 3.00000 + 5.19615i 0.304604 + 0.527589i 0.977173 0.212445i $$-0.0681426\pi$$
−0.672569 + 0.740034i $$0.734809\pi$$
$$98$$ 0.757359 + 1.31178i 0.0765048 + 0.132510i
$$99$$ 0 0
$$100$$ 0.914214 + 1.58346i 0.0914214 + 0.158346i
$$101$$ 6.07107 10.5154i 0.604094 1.04632i −0.388100 0.921617i $$-0.626869\pi$$
0.992194 0.124704i $$-0.0397981\pi$$
$$102$$ 0 0
$$103$$ 9.82843 0.968424 0.484212 0.874951i $$-0.339106\pi$$
0.484212 + 0.874951i $$0.339106\pi$$
$$104$$ −1.44975 + 2.51104i −0.142159 + 0.246227i
$$105$$ 0 0
$$106$$ 0.828427 0.0804640
$$107$$ −14.0000 −1.35343 −0.676716 0.736245i $$-0.736597\pi$$
−0.676716 + 0.736245i $$0.736597\pi$$
$$108$$ 0 0
$$109$$ 8.65685 + 14.9941i 0.829176 + 1.43618i 0.898685 + 0.438594i $$0.144523\pi$$
−0.0695090 + 0.997581i $$0.522143\pi$$
$$110$$ −0.585786 + 1.01461i −0.0558525 + 0.0967394i
$$111$$ 0 0
$$112$$ −2.74264 4.75039i −0.259155 0.448870i
$$113$$ −4.00000 −0.376288 −0.188144 0.982141i $$-0.560247\pi$$
−0.188144 + 0.982141i $$0.560247\pi$$
$$114$$ 0 0
$$115$$ 0.828427 0.0772512
$$116$$ −8.82843 15.2913i −0.819699 1.41976i
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −1.07107 1.85514i −0.0981846 0.170061i
$$120$$ 0 0
$$121$$ −3.00000 −0.272727
$$122$$ −3.44365 −0.311773
$$123$$ 0 0
$$124$$ −4.57107 + 7.91732i −0.410494 + 0.710996i
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ −6.48528 + 11.2328i −0.575476 + 0.996753i 0.420514 + 0.907286i $$0.361850\pi$$
−0.995990 + 0.0894671i $$0.971484\pi$$
$$128$$ 5.27817 + 9.14207i 0.466529 + 0.808052i
$$129$$ 0 0
$$130$$ 0.378680 + 0.655892i 0.0332124 + 0.0575256i
$$131$$ 3.24264 + 5.61642i 0.283311 + 0.490709i 0.972198 0.234160i $$-0.0752339\pi$$
−0.688887 + 0.724868i $$0.741901\pi$$
$$132$$ 0 0
$$133$$ 7.31371 + 3.16693i 0.634179 + 0.274608i
$$134$$ 2.27208 0.196278
$$135$$ 0 0
$$136$$ 0.928932 + 1.60896i 0.0796553 + 0.137967i
$$137$$ −5.24264 + 9.08052i −0.447909 + 0.775801i −0.998250 0.0591390i $$-0.981164\pi$$
0.550341 + 0.834940i $$0.314498\pi$$
$$138$$ 0 0
$$139$$ 8.15685 14.1281i 0.691855 1.19833i −0.279374 0.960182i $$-0.590127\pi$$
0.971229 0.238146i $$-0.0765398\pi$$
$$140$$ −3.34315 −0.282547
$$141$$ 0 0
$$142$$ 2.07107 3.58719i 0.173800 0.301031i
$$143$$ 2.58579 4.47871i 0.216234 0.374529i
$$144$$ 0 0
$$145$$ −9.65685 −0.801958
$$146$$ −1.96447 + 3.40256i −0.162580 + 0.281597i
$$147$$ 0 0
$$148$$ −1.98528 + 3.43861i −0.163189 + 0.282652i
$$149$$ −0.585786 1.01461i −0.0479895 0.0831202i 0.841033 0.540984i $$-0.181948\pi$$
−0.889022 + 0.457864i $$0.848615\pi$$
$$150$$ 0 0
$$151$$ 10.3431 0.841713 0.420857 0.907127i $$-0.361730\pi$$
0.420857 + 0.907127i $$0.361730\pi$$
$$152$$ −6.34315 2.74666i −0.514497 0.222784i
$$153$$ 0 0
$$154$$ −1.07107 1.85514i −0.0863091 0.149492i
$$155$$ 2.50000 + 4.33013i 0.200805 + 0.347804i
$$156$$ 0 0
$$157$$ 9.91421 + 17.1719i 0.791240 + 1.37047i 0.925199 + 0.379482i $$0.123898\pi$$
−0.133959 + 0.990987i $$0.542769\pi$$
$$158$$ 0.692388 1.19925i 0.0550834 0.0954073i
$$159$$ 0 0
$$160$$ 4.41421 0.348974
$$161$$ −0.757359 + 1.31178i −0.0596883 + 0.103383i
$$162$$ 0 0
$$163$$ 15.1421 1.18602 0.593012 0.805194i $$-0.297939\pi$$
0.593012 + 0.805194i $$0.297939\pi$$
$$164$$ 5.17157 0.403832
$$165$$ 0 0
$$166$$ −1.65685 2.86976i −0.128597 0.222736i
$$167$$ −12.4853 + 21.6251i −0.966140 + 1.67340i −0.259620 + 0.965711i $$0.583597\pi$$
−0.706520 + 0.707693i $$0.749736\pi$$
$$168$$ 0 0
$$169$$ 4.82843 + 8.36308i 0.371417 + 0.643314i
$$170$$ 0.485281 0.0372194
$$171$$ 0 0
$$172$$ −14.3137 −1.09141
$$173$$ 3.65685 + 6.33386i 0.278025 + 0.481554i 0.970894 0.239510i $$-0.0769867\pi$$
−0.692868 + 0.721064i $$0.743653\pi$$
$$174$$ 0 0
$$175$$ −0.914214 + 1.58346i −0.0691080 + 0.119699i
$$176$$ −4.24264 7.34847i −0.319801 0.553912i
$$177$$ 0 0
$$178$$ −5.17157 −0.387626
$$179$$ −16.1421 −1.20652 −0.603260 0.797545i $$-0.706132\pi$$
−0.603260 + 0.797545i $$0.706132\pi$$
$$180$$ 0 0
$$181$$ −12.6569 + 21.9223i −0.940777 + 1.62947i −0.176782 + 0.984250i $$0.556569\pi$$
−0.763994 + 0.645223i $$0.776765\pi$$
$$182$$ −1.38478 −0.102646
$$183$$ 0 0
$$184$$ 0.656854 1.13770i 0.0484239 0.0838727i
$$185$$ 1.08579 + 1.88064i 0.0798286 + 0.138267i
$$186$$ 0 0
$$187$$ −1.65685 2.86976i −0.121161 0.209857i
$$188$$ 2.89949 + 5.02207i 0.211467 + 0.366272i
$$189$$ 0 0
$$190$$ −1.44975 + 1.07616i −0.105176 + 0.0780727i
$$191$$ 16.8284 1.21766 0.608831 0.793300i $$-0.291639\pi$$
0.608831 + 0.793300i $$0.291639\pi$$
$$192$$ 0 0
$$193$$ 12.3995 + 21.4766i 0.892535 + 1.54592i 0.836826 + 0.547469i $$0.184409\pi$$
0.0557094 + 0.998447i $$0.482258\pi$$
$$194$$ 1.24264 2.15232i 0.0892164 0.154527i
$$195$$ 0 0
$$196$$ −3.34315 + 5.79050i −0.238796 + 0.413607i
$$197$$ −17.6569 −1.25800 −0.628999 0.777406i $$-0.716535\pi$$
−0.628999 + 0.777406i $$0.716535\pi$$
$$198$$ 0 0
$$199$$ 8.50000 14.7224i 0.602549 1.04365i −0.389885 0.920864i $$-0.627485\pi$$
0.992434 0.122782i $$-0.0391815\pi$$
$$200$$ 0.792893 1.37333i 0.0560660 0.0971092i
$$201$$ 0 0
$$202$$ −5.02944 −0.353870
$$203$$ 8.82843 15.2913i 0.619634 1.07324i
$$204$$ 0 0
$$205$$ 1.41421 2.44949i 0.0987730 0.171080i
$$206$$ −2.03553 3.52565i −0.141822 0.245644i
$$207$$ 0 0
$$208$$ −5.48528 −0.380336
$$209$$ 11.3137 + 4.89898i 0.782586 + 0.338869i
$$210$$ 0 0
$$211$$ 0.156854 + 0.271680i 0.0107983 + 0.0187032i 0.871374 0.490619i $$-0.163229\pi$$
−0.860576 + 0.509322i $$0.829896\pi$$
$$212$$ 1.82843 + 3.16693i 0.125577 + 0.217506i
$$213$$ 0 0
$$214$$ 2.89949 + 5.02207i 0.198205 + 0.343302i
$$215$$ −3.91421 + 6.77962i −0.266947 + 0.462366i
$$216$$ 0 0
$$217$$ −9.14214 −0.620609
$$218$$ 3.58579 6.21076i 0.242860 0.420646i
$$219$$ 0 0
$$220$$ −5.17157 −0.348667
$$221$$ −2.14214 −0.144096
$$222$$ 0 0
$$223$$ −2.91421 5.04757i −0.195150 0.338010i 0.751800 0.659392i $$-0.229186\pi$$
−0.946950 + 0.321382i $$0.895853\pi$$
$$224$$ −4.03553 + 6.98975i −0.269635 + 0.467022i
$$225$$ 0 0
$$226$$ 0.828427 + 1.43488i 0.0551062 + 0.0954467i
$$227$$ 18.9706 1.25912 0.629560 0.776952i $$-0.283235\pi$$
0.629560 + 0.776952i $$0.283235\pi$$
$$228$$ 0 0
$$229$$ −4.65685 −0.307734 −0.153867 0.988092i $$-0.549173\pi$$
−0.153867 + 0.988092i $$0.549173\pi$$
$$230$$ −0.171573 0.297173i −0.0113132 0.0195950i
$$231$$ 0 0
$$232$$ −7.65685 + 13.2621i −0.502697 + 0.870697i
$$233$$ −12.6569 21.9223i −0.829178 1.43618i −0.898684 0.438597i $$-0.855476\pi$$
0.0695057 0.997582i $$-0.477858\pi$$
$$234$$ 0 0
$$235$$ 3.17157 0.206891
$$236$$ 0 0
$$237$$ 0 0
$$238$$ −0.443651 + 0.768426i −0.0287576 + 0.0498096i
$$239$$ 24.6274 1.59302 0.796508 0.604629i $$-0.206678\pi$$
0.796508 + 0.604629i $$0.206678\pi$$
$$240$$ 0 0
$$241$$ −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i $$-0.884818\pi$$
0.774202 + 0.632938i $$0.218151\pi$$
$$242$$ 0.621320 + 1.07616i 0.0399400 + 0.0691781i
$$243$$ 0 0
$$244$$ −7.60051 13.1645i −0.486572 0.842768i
$$245$$ 1.82843 + 3.16693i 0.116814 + 0.202328i
$$246$$ 0 0
$$247$$ 6.39949 4.75039i 0.407190 0.302260i
$$248$$ 7.92893 0.503488
$$249$$ 0 0
$$250$$ −0.207107 0.358719i −0.0130986 0.0226874i
$$251$$ −8.17157 + 14.1536i −0.515785 + 0.893366i 0.484047 + 0.875042i $$0.339166\pi$$
−0.999832 + 0.0183240i $$0.994167\pi$$
$$252$$ 0 0
$$253$$ −1.17157 + 2.02922i −0.0736562 + 0.127576i
$$254$$ 5.37258 0.337106
$$255$$ 0 0
$$256$$ −1.98528 + 3.43861i −0.124080 + 0.214913i
$$257$$ −8.41421 + 14.5738i −0.524864 + 0.909091i 0.474717 + 0.880139i $$0.342551\pi$$
−0.999581 + 0.0289528i $$0.990783\pi$$
$$258$$ 0 0
$$259$$ −3.97056 −0.246719
$$260$$ −1.67157 + 2.89525i −0.103667 + 0.179556i
$$261$$ 0 0
$$262$$ 1.34315 2.32640i 0.0829798 0.143725i
$$263$$ 12.8995 + 22.3426i 0.795417 + 1.37770i 0.922574 + 0.385820i $$0.126081\pi$$
−0.127157 + 0.991883i $$0.540585\pi$$
$$264$$ 0 0
$$265$$ 2.00000 0.122859
$$266$$ −0.378680 3.27946i −0.0232183 0.201077i
$$267$$ 0 0
$$268$$ 5.01472 + 8.68575i 0.306323 + 0.530566i
$$269$$ 0.828427 + 1.43488i 0.0505101 + 0.0874860i 0.890175 0.455619i $$-0.150582\pi$$
−0.839665 + 0.543105i $$0.817249\pi$$
$$270$$ 0 0
$$271$$ −6.82843 11.8272i −0.414797 0.718450i 0.580610 0.814182i $$-0.302814\pi$$
−0.995407 + 0.0957318i $$0.969481\pi$$
$$272$$ −1.75736 + 3.04384i −0.106556 + 0.184560i
$$273$$ 0 0
$$274$$ 4.34315 0.262379
$$275$$ −1.41421 + 2.44949i −0.0852803 + 0.147710i
$$276$$ 0 0
$$277$$ 6.00000 0.360505 0.180253 0.983620i $$-0.442309\pi$$
0.180253 + 0.983620i $$0.442309\pi$$
$$278$$ −6.75736 −0.405279
$$279$$ 0 0
$$280$$ 1.44975 + 2.51104i 0.0866390 + 0.150063i
$$281$$ −3.48528 + 6.03668i −0.207914 + 0.360118i −0.951057 0.309014i $$-0.900001\pi$$
0.743143 + 0.669133i $$0.233334\pi$$
$$282$$ 0 0
$$283$$ 10.4853 + 18.1610i 0.623285 + 1.07956i 0.988870 + 0.148784i $$0.0475358\pi$$
−0.365584 + 0.930778i $$0.619131\pi$$
$$284$$ 18.2843 1.08497
$$285$$ 0 0
$$286$$ −2.14214 −0.126667
$$287$$ 2.58579 + 4.47871i 0.152634 + 0.264370i
$$288$$ 0 0
$$289$$ 7.81371 13.5337i 0.459630 0.796102i
$$290$$ 2.00000 + 3.46410i 0.117444 + 0.203419i
$$291$$ 0 0
$$292$$ −17.3431 −1.01493
$$293$$ 5.31371 0.310430 0.155215 0.987881i $$-0.450393\pi$$
0.155215 + 0.987881i $$0.450393\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 3.44365 0.200158
$$297$$ 0 0
$$298$$ −0.242641 + 0.420266i −0.0140558 + 0.0243454i
$$299$$ 0.757359 + 1.31178i 0.0437992 + 0.0758625i
$$300$$ 0 0
$$301$$ −7.15685 12.3960i −0.412514 0.714496i
$$302$$ −2.14214 3.71029i −0.123266 0.213503i
$$303$$ 0 0
$$304$$ −1.50000 12.9904i −0.0860309 0.745049i
$$305$$ −8.31371 −0.476042
$$306$$ 0 0
$$307$$ 8.82843 + 15.2913i 0.503865 + 0.872720i 0.999990 + 0.00446862i $$0.00142241\pi$$
−0.496125 + 0.868251i $$0.665244\pi$$
$$308$$ 4.72792 8.18900i 0.269398 0.466612i
$$309$$ 0 0
$$310$$ 1.03553 1.79360i 0.0588144 0.101869i
$$311$$ 4.00000 0.226819 0.113410 0.993548i $$-0.463823\pi$$
0.113410 + 0.993548i $$0.463823\pi$$
$$312$$ 0 0
$$313$$ 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i $$-0.779095\pi$$
0.938269 + 0.345907i $$0.112429\pi$$
$$314$$ 4.10660 7.11284i 0.231749 0.401401i
$$315$$ 0 0
$$316$$ 6.11270 0.343866
$$317$$ 2.65685 4.60181i 0.149224 0.258463i −0.781717 0.623633i $$-0.785656\pi$$
0.930941 + 0.365170i $$0.118989\pi$$
$$318$$ 0 0
$$319$$ 13.6569 23.6544i 0.764637 1.32439i
$$320$$ 2.08579 + 3.61269i 0.116599 + 0.201955i
$$321$$ 0 0
$$322$$ 0.627417 0.0349646
$$323$$ −0.585786 5.07306i −0.0325940 0.282273i
$$324$$ 0 0
$$325$$ 0.914214 + 1.58346i 0.0507114 + 0.0878348i
$$326$$ −3.13604 5.43178i −0.173689 0.300838i
$$327$$ 0 0
$$328$$ −2.24264 3.88437i −0.123829 0.214478i
$$329$$ −2.89949 + 5.02207i −0.159854 + 0.276876i
$$330$$ 0 0
$$331$$ −5.34315 −0.293686 −0.146843 0.989160i $$-0.546911\pi$$
−0.146843 + 0.989160i $$0.546911\pi$$
$$332$$ 7.31371 12.6677i 0.401392 0.695231i
$$333$$ 0 0
$$334$$ 10.3431 0.565952
$$335$$ 5.48528 0.299693
$$336$$ 0 0
$$337$$ −8.74264 15.1427i −0.476242 0.824875i 0.523387 0.852095i $$-0.324668\pi$$
−0.999629 + 0.0272195i $$0.991335\pi$$
$$338$$ 2.00000 3.46410i 0.108786 0.188422i
$$339$$ 0 0
$$340$$ 1.07107 + 1.85514i 0.0580868 + 0.100609i
$$341$$ −14.1421 −0.765840
$$342$$ 0 0
$$343$$ −19.4853 −1.05211
$$344$$ 6.20711 + 10.7510i 0.334665 + 0.579656i
$$345$$ 0 0
$$346$$ 1.51472 2.62357i 0.0814318 0.141044i
$$347$$ −17.7279 30.7057i −0.951685 1.64837i −0.741779 0.670645i $$-0.766018\pi$$
−0.209906 0.977722i $$-0.567316\pi$$
$$348$$ 0 0
$$349$$ −31.6274 −1.69298 −0.846488 0.532407i $$-0.821288\pi$$
−0.846488 + 0.532407i $$0.821288\pi$$
$$350$$ 0.757359 0.0404826
$$351$$ 0 0
$$352$$ −6.24264 + 10.8126i −0.332734 + 0.576312i
$$353$$ 1.31371 0.0699216 0.0349608 0.999389i $$-0.488869\pi$$
0.0349608 + 0.999389i $$0.488869\pi$$
$$354$$ 0 0
$$355$$ 5.00000 8.66025i 0.265372 0.459639i
$$356$$ −11.4142 19.7700i −0.604952 1.04781i
$$357$$ 0 0
$$358$$ 3.34315 + 5.79050i 0.176691 + 0.306037i
$$359$$ 4.58579 + 7.94282i 0.242029 + 0.419206i 0.961292 0.275532i $$-0.0888539\pi$$
−0.719263 + 0.694737i $$0.755521\pi$$
$$360$$ 0 0
$$361$$ 13.0000 + 13.8564i 0.684211 + 0.729285i
$$362$$ 10.4853 0.551094
$$363$$ 0 0
$$364$$ −3.05635 5.29375i −0.160196 0.277468i
$$365$$ −4.74264 + 8.21449i −0.248241 + 0.429966i
$$366$$ 0 0
$$367$$ 17.0563 29.5425i 0.890334 1.54210i 0.0508591 0.998706i $$-0.483804\pi$$
0.839475 0.543398i $$-0.182863\pi$$
$$368$$ 2.48528 0.129554
$$369$$ 0 0
$$370$$ 0.449747 0.778985i 0.0233813 0.0404975i
$$371$$ −1.82843 + 3.16693i −0.0949272 + 0.164419i
$$372$$ 0 0
$$373$$ −11.6569 −0.603569 −0.301785 0.953376i $$-0.597582\pi$$
−0.301785 + 0.953376i $$0.597582\pi$$
$$374$$ −0.686292 + 1.18869i −0.0354873 + 0.0614658i
$$375$$ 0 0
$$376$$ 2.51472 4.35562i 0.129687 0.224624i
$$377$$ −8.82843 15.2913i −0.454687 0.787541i
$$378$$ 0 0
$$379$$ 1.68629 0.0866190 0.0433095 0.999062i $$-0.486210\pi$$
0.0433095 + 0.999062i $$0.486210\pi$$
$$380$$ −7.31371 3.16693i −0.375185 0.162460i
$$381$$ 0 0
$$382$$ −3.48528 6.03668i −0.178323 0.308864i
$$383$$ −16.9706 29.3939i −0.867155 1.50196i −0.864891 0.501960i $$-0.832613\pi$$
−0.00226413 0.999997i $$-0.500721\pi$$
$$384$$ 0 0
$$385$$ −2.58579 4.47871i −0.131784 0.228256i
$$386$$ 5.13604 8.89588i 0.261418 0.452788i
$$387$$ 0 0
$$388$$ 10.9706 0.556946
$$389$$ −7.72792 + 13.3852i −0.391821 + 0.678654i −0.992690 0.120694i $$-0.961488\pi$$
0.600869 + 0.799348i $$0.294821\pi$$
$$390$$ 0 0
$$391$$ 0.970563 0.0490835
$$392$$ 5.79899 0.292893
$$393$$ 0 0
$$394$$ 3.65685 + 6.33386i 0.184230 + 0.319095i
$$395$$ 1.67157 2.89525i 0.0841060 0.145676i
$$396$$ 0 0
$$397$$ 11.9142 + 20.6360i 0.597957 + 1.03569i 0.993122 + 0.117082i $$0.0373541\pi$$
−0.395165 + 0.918610i $$0.629313\pi$$
$$398$$ −7.04163 −0.352965
$$399$$ 0 0
$$400$$ 3.00000 0.150000
$$401$$ −11.3137 19.5959i −0.564980 0.978573i −0.997052 0.0767343i $$-0.975551\pi$$
0.432072 0.901839i $$-0.357783\pi$$
$$402$$ 0 0
$$403$$ −4.57107 + 7.91732i −0.227701 + 0.394390i
$$404$$ −11.1005 19.2266i −0.552271 0.956561i
$$405$$ 0 0
$$406$$ −7.31371 −0.362973
$$407$$ −6.14214 −0.304454
$$408$$ 0 0
$$409$$ −3.00000 + 5.19615i −0.148340 + 0.256933i −0.930614 0.366002i $$-0.880726\pi$$
0.782274 + 0.622935i $$0.214060\pi$$
$$410$$ −1.17157 −0.0578599
$$411$$ 0 0
$$412$$ 8.98528 15.5630i 0.442673 0.766732i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −4.00000 6.92820i −0.196352 0.340092i
$$416$$ 4.03553 + 6.98975i 0.197858 + 0.342701i
$$417$$ 0 0
$$418$$ −0.585786 5.07306i −0.0286518 0.248131i
$$419$$ −3.31371 −0.161885 −0.0809426 0.996719i $$-0.525793\pi$$
−0.0809426 + 0.996719i $$0.525793\pi$$
$$420$$ 0 0
$$421$$ 3.82843 + 6.63103i 0.186586 + 0.323177i 0.944110 0.329631i $$-0.106924\pi$$
−0.757524 + 0.652808i $$0.773591\pi$$
$$422$$ 0.0649712 0.112533i 0.00316275 0.00547804i
$$423$$ 0 0
$$424$$ 1.58579 2.74666i 0.0770126 0.133390i
$$425$$ 1.17157 0.0568296
$$426$$ 0 0
$$427$$ 7.60051 13.1645i 0.367814 0.637073i
$$428$$ −12.7990 + 22.1685i −0.618663 + 1.07155i
$$429$$ 0 0
$$430$$ 3.24264 0.156374
$$431$$ −1.24264 + 2.15232i −0.0598559 + 0.103673i −0.894401 0.447267i $$-0.852397\pi$$
0.834545 + 0.550940i $$0.185731\pi$$
$$432$$ 0 0
$$433$$ 19.9142 34.4924i 0.957016 1.65760i 0.227330 0.973818i $$-0.427000\pi$$
0.729686 0.683783i $$-0.239666\pi$$
$$434$$ 1.89340 + 3.27946i 0.0908860 + 0.157419i
$$435$$ 0 0
$$436$$ 31.6569 1.51609
$$437$$ −2.89949 + 2.15232i −0.138702 + 0.102959i
$$438$$ 0 0
$$439$$ −8.50000 14.7224i −0.405683 0.702663i 0.588718 0.808339i $$-0.299633\pi$$
−0.994401 + 0.105675i $$0.966300\pi$$
$$440$$ 2.24264 + 3.88437i 0.106914 + 0.185180i
$$441$$ 0 0
$$442$$ 0.443651 + 0.768426i 0.0211023 + 0.0365503i
$$443$$ 9.07107 15.7116i 0.430979 0.746478i −0.565978 0.824420i $$-0.691501\pi$$
0.996958 + 0.0779417i $$0.0248348\pi$$
$$444$$ 0 0
$$445$$ −12.4853 −0.591859
$$446$$ −1.20711 + 2.09077i −0.0571582 + 0.0990008i
$$447$$ 0 0
$$448$$ −7.62742 −0.360362
$$449$$ −13.1716 −0.621605 −0.310802 0.950475i $$-0.600598\pi$$
−0.310802 + 0.950475i $$0.600598\pi$$
$$450$$ 0 0
$$451$$ 4.00000 + 6.92820i 0.188353 + 0.326236i
$$452$$ −3.65685 + 6.33386i −0.172004 + 0.297920i
$$453$$ 0 0
$$454$$ −3.92893 6.80511i −0.184394 0.319380i
$$455$$ −3.34315 −0.156729
$$456$$ 0 0
$$457$$ −4.17157 −0.195138 −0.0975690 0.995229i $$-0.531107\pi$$
−0.0975690 + 0.995229i $$0.531107\pi$$
$$458$$ 0.964466 + 1.67050i 0.0450665 + 0.0780575i
$$459$$ 0 0
$$460$$ 0.757359 1.31178i 0.0353121 0.0611623i
$$461$$ 15.0711 + 26.1039i 0.701930 + 1.21578i 0.967788 + 0.251766i $$0.0810112\pi$$
−0.265859 + 0.964012i $$0.585655\pi$$
$$462$$ 0 0
$$463$$ −22.7990 −1.05956 −0.529779 0.848135i $$-0.677725\pi$$
−0.529779 + 0.848135i $$0.677725\pi$$
$$464$$ −28.9706 −1.34492
$$465$$ 0 0
$$466$$ −5.24264 + 9.08052i −0.242861 + 0.420647i
$$467$$ −23.7990 −1.10129 −0.550643 0.834741i $$-0.685617\pi$$
−0.550643 + 0.834741i $$0.685617\pi$$
$$468$$ 0 0
$$469$$ −5.01472 + 8.68575i −0.231558 + 0.401071i
$$470$$ −0.656854 1.13770i −0.0302984 0.0524784i
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −11.0711 19.1757i −0.509048 0.881697i
$$474$$ 0 0
$$475$$ −3.50000 + 2.59808i −0.160591 + 0.119208i
$$476$$ −3.91674 −0.179523
$$477$$ 0 0
$$478$$ −5.10051 8.83433i −0.233292 0.404073i
$$479$$ 1.24264 2.15232i 0.0567777 0.0983419i −0.836240 0.548364i $$-0.815251\pi$$
0.893017 + 0.450022i $$0.148584\pi$$
$$480$$ 0 0
$$481$$ −1.98528 + 3.43861i −0.0905210 + 0.156787i
$$482$$ 2.07107 0.0943346
$$483$$ 0 0
$$484$$ −2.74264 + 4.75039i −0.124665 + 0.215927i
$$485$$ 3.00000 5.19615i 0.136223 0.235945i
$$486$$ 0 0
$$487$$ −6.34315 −0.287435 −0.143718 0.989619i $$-0.545906\pi$$
−0.143718 + 0.989619i $$0.545906\pi$$
$$488$$ −6.59188 + 11.4175i −0.298401 + 0.516845i
$$489$$ 0 0
$$490$$ 0.757359 1.31178i 0.0342140 0.0592604i
$$491$$ 11.8284 + 20.4874i 0.533809 + 0.924585i 0.999220 + 0.0394901i $$0.0125734\pi$$
−0.465411 + 0.885095i $$0.654093\pi$$
$$492$$ 0 0
$$493$$ −11.3137 −0.509544
$$494$$ −3.02944 1.31178i −0.136301 0.0590200i
$$495$$ 0 0
$$496$$ 7.50000 + 12.9904i 0.336760 + 0.583285i
$$497$$ 9.14214 + 15.8346i 0.410081 + 0.710281i
$$498$$ 0 0
$$499$$ 3.67157 + 6.35935i 0.164362 + 0.284684i 0.936429 0.350858i $$-0.114110\pi$$
−0.772066 + 0.635542i $$0.780777\pi$$
$$500$$ 0.914214 1.58346i 0.0408849 0.0708147i
$$501$$ 0 0
$$502$$ 6.76955 0.302140
$$503$$ 6.92893 12.0013i 0.308946 0.535110i −0.669186 0.743095i $$-0.733357\pi$$
0.978132 + 0.207985i $$0.0666905\pi$$
$$504$$ 0 0
$$505$$ −12.1421 −0.540318
$$506$$ 0.970563 0.0431468
$$507$$ 0 0
$$508$$ 11.8579 + 20.5384i 0.526108 + 0.911245i
$$509$$ 16.5563 28.6764i 0.733847 1.27106i −0.221380 0.975188i $$-0.571056\pi$$
0.955227 0.295873i $$-0.0956106\pi$$
$$510$$ 0 0
$$511$$ −8.67157 15.0196i −0.383608 0.664428i
$$512$$ 22.7574 1.00574
$$513$$ 0 0
$$514$$ 6.97056 0.307458
$$515$$ −4.91421 8.51167i −0.216546 0.375069i
$$516$$ 0 0
$$517$$ −4.48528 + 7.76874i −0.197262 + 0.341669i
$$518$$ 0.822330 + 1.42432i 0.0361311 + 0.0625809i
$$519$$ 0 0
$$520$$ 2.89949 0.127151
$$521$$ −6.34315 −0.277898 −0.138949 0.990300i $$-0.544372\pi$$
−0.138949 + 0.990300i $$0.544372\pi$$
$$522$$ 0 0
$$523$$ 14.8848 25.7812i 0.650866 1.12733i −0.332047 0.943263i $$-0.607739\pi$$
0.982913 0.184070i $$-0.0589273\pi$$
$$524$$ 11.8579 0.518013
$$525$$ 0 0
$$526$$ 5.34315 9.25460i 0.232972 0.403520i
$$527$$ 2.92893 + 5.07306i 0.127586 + 0.220986i
$$528$$ 0 0
$$529$$ 11.1569 + 19.3242i 0.485081 + 0.840184i
$$530$$ −0.414214 0.717439i −0.0179923 0.0311636i
$$531$$ 0 0
$$532$$ 11.7010 8.68575i 0.507303 0.376575i
$$533$$ 5.17157 0.224006
$$534$$ 0 0
$$535$$ 7.00000 + 12.1244i 0.302636 + 0.524182i
$$536$$ 4.34924 7.53311i 0.187859 0.325381i
$$537$$ 0 0
$$538$$ 0.343146 0.594346i 0.0147941 0.0256241i
$$539$$ −10.3431 −0.445511
$$540$$ 0 0
$$541$$ −8.15685 + 14.1281i −0.350691 + 0.607414i −0.986371 0.164539i $$-0.947386\pi$$
0.635680 + 0.771953i $$0.280720\pi$$
$$542$$ −2.82843 + 4.89898i −0.121491 + 0.210429i
$$543$$ 0 0
$$544$$ 5.17157 0.221729
$$545$$ 8.65685 14.9941i 0.370819 0.642277i
$$546$$ 0 0
$$547$$ 6.57107 11.3814i 0.280959 0.486635i −0.690663 0.723177i $$-0.742681\pi$$
0.971621 + 0.236543i $$0.0760143\pi$$
$$548$$ 9.58579 + 16.6031i 0.409485 + 0.709248i
$$549$$ 0 0
$$550$$ 1.17157 0.0499560
$$551$$ 33.7990 25.0892i 1.43989 1.06884i
$$552$$ 0 0
$$553$$ 3.05635 + 5.29375i 0.129969 + 0.225113i
$$554$$ −1.24264 2.15232i −0.0527947 0.0914432i
$$555$$ 0 0
$$556$$ −14.9142 25.8322i −0.632504 1.09553i
$$557$$ −4.51472 + 7.81972i −0.191295 + 0.331332i −0.945680 0.325100i $$-0.894602\pi$$
0.754385 + 0.656432i $$0.227935\pi$$
$$558$$ 0 0
$$559$$ −14.3137 −0.605405
$$560$$ −2.74264 + 4.75039i −0.115898 + 0.200741i
$$561$$ 0 0
$$562$$ 2.88730 0.121793
$$563$$ 12.1421 0.511730 0.255865 0.966713i $$-0.417640\pi$$
0.255865 + 0.966713i $$0.417640\pi$$
$$564$$ 0 0
$$565$$ 2.00000 + 3.46410i 0.0841406 + 0.145736i
$$566$$ 4.34315 7.52255i 0.182556 0.316196i
$$567$$ 0 0
$$568$$ −7.92893 13.7333i −0.332691 0.576237i
$$569$$ −4.97056 −0.208377 −0.104188 0.994558i $$-0.533224\pi$$
−0.104188 + 0.994558i $$0.533224\pi$$
$$570$$ 0 0
$$571$$ 14.3137 0.599010 0.299505 0.954095i $$-0.403178\pi$$
0.299505 + 0.954095i $$0.403178\pi$$
$$572$$ −4.72792 8.18900i −0.197684 0.342399i
$$573$$ 0 0
$$574$$ 1.07107 1.85514i 0.0447055 0.0774322i
$$575$$ −0.414214 0.717439i −0.0172739 0.0299193i
$$576$$ 0 0
$$577$$ −36.3431 −1.51298 −0.756492 0.654002i $$-0.773089\pi$$
−0.756492 + 0.654002i $$0.773089\pi$$
$$578$$ −6.47309 −0.269245
$$579$$ 0 0
$$580$$ −8.82843 + 15.2913i −0.366580 + 0.634936i
$$581$$ 14.6274 0.606848
$$582$$ 0 0
$$583$$ −2.82843 + 4.89898i −0.117141 + 0.202895i
$$584$$ 7.52082 + 13.0264i 0.311214 + 0.539038i
$$585$$ 0 0
$$586$$ −1.10051 1.90613i −0.0454614 0.0787415i
$$587$$ 5.31371 + 9.20361i 0.219320 + 0.379874i 0.954600 0.297890i $$-0.0962827\pi$$
−0.735280 + 0.677763i $$0.762949\pi$$
$$588$$ 0 0
$$589$$ −20.0000 8.66025i −0.824086 0.356840i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 3.25736 + 5.64191i 0.133877 + 0.231881i
$$593$$ −4.92893 + 8.53716i −0.202407 + 0.350579i −0.949303 0.314361i $$-0.898210\pi$$
0.746896 + 0.664940i $$0.231543\pi$$
$$594$$ 0 0
$$595$$ −1.07107 + 1.85514i −0.0439095 + 0.0760535i
$$596$$ −2.14214 −0.0877453
$$597$$ 0 0
$$598$$ 0.313708 0.543359i 0.0128285 0.0222196i
$$599$$ −8.48528 + 14.6969i −0.346699 + 0.600501i −0.985661 0.168738i $$-0.946031\pi$$
0.638962 + 0.769238i $$0.279364\pi$$
$$600$$ 0 0
$$601$$ −35.3431 −1.44168 −0.720838 0.693103i $$-0.756243\pi$$
−0.720838 + 0.693103i $$0.756243\pi$$
$$602$$ −2.96447 + 5.13461i −0.120823 + 0.209271i
$$603$$ 0 0
$$604$$ 9.45584 16.3780i 0.384753 0.666411i
$$605$$ 1.50000 + 2.59808i 0.0609837 + 0.105627i
$$606$$ 0 0
$$607$$ −6.17157 −0.250496 −0.125248 0.992125i $$-0.539973\pi$$
−0.125248 + 0.992125i $$0.539973\pi$$
$$608$$ −15.4497 + 11.4685i −0.626570 + 0.465108i
$$609$$ 0 0
$$610$$ 1.72183 + 2.98229i 0.0697147 + 0.120749i
$$611$$ 2.89949 + 5.02207i 0.117301 + 0.203171i
$$612$$ 0 0
$$613$$ −16.7990 29.0967i −0.678505 1.17520i −0.975431 0.220304i $$-0.929295\pi$$
0.296926 0.954900i $$-0.404038\pi$$
$$614$$ 3.65685 6.33386i 0.147579 0.255614i
$$615$$ 0 0
$$616$$ −8.20101 −0.330428
$$617$$ 12.8284 22.2195i 0.516453 0.894523i −0.483364 0.875419i $$-0.660585\pi$$
0.999818 0.0191037i $$-0.00608126\pi$$
$$618$$ 0 0
$$619$$ 15.6863 0.630485 0.315243 0.949011i $$-0.397914\pi$$
0.315243 + 0.949011i $$0.397914\pi$$
$$620$$ 9.14214 0.367157
$$621$$ 0 0
$$622$$ −0.828427 1.43488i −0.0332169 0.0575334i
$$623$$ 11.4142 19.7700i 0.457301 0.792068i
$$624$$ 0 0
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ −2.48528 −0.0993318
$$627$$ 0 0
$$628$$ 36.2548 1.44673
$$629$$ 1.27208 + 2.20330i 0.0507211 + 0.0878515i
$$630$$ 0 0
$$631$$ 6.64214 11.5045i 0.264419 0.457988i −0.702992 0.711198i $$-0.748153\pi$$
0.967411 + 0.253210i $$0.0814864\pi$$
$$632$$ −2.65076 4.59125i −0.105441 0.182630i
$$633$$ 0 0
$$634$$ −2.20101 −0.0874133
$$635$$ 12.9706 0.514721
$$636$$ 0 0
$$637$$ −3.34315 + 5.79050i −0.132460 + 0.229428i
$$638$$ −11.3137 −0.447914
$$639$$ 0 0
$$640$$ 5.27817 9.14207i 0.208638 0.361372i
$$641$$ 14.0711 + 24.3718i 0.555774 + 0.962628i 0.997843 + 0.0656474i $$0.0209113\pi$$
−0.442069 + 0.896981i $$0.645755\pi$$
$$642$$ 0 0
$$643$$ −2.91421 5.04757i −0.114925 0.199057i 0.802825 0.596215i $$-0.203330\pi$$
−0.917750 + 0.397159i $$0.869996\pi$$
$$644$$ 1.38478 + 2.39850i 0.0545678 + 0.0945143i
$$645$$ 0 0
$$646$$ −1.69848 + 1.26080i −0.0668260 + 0.0496054i
$$647$$ 32.2843 1.26923 0.634613 0.772830i $$-0.281160\pi$$
0.634613 + 0.772830i $$0.281160\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0.378680 0.655892i 0.0148530 0.0257262i
$$651$$ 0 0
$$652$$ 13.8431 23.9770i 0.542139 0.939013i
$$653$$ −39.9411 −1.56302 −0.781509 0.623895i $$-0.785549\pi$$
−0.781509 + 0.623895i $$0.785549\pi$$
$$654$$ 0 0
$$655$$ 3.24264 5.61642i 0.126700 0.219452i
$$656$$ 4.24264 7.34847i 0.165647 0.286910i
$$657$$ 0 0
$$658$$ 2.40202 0.0936405
$$659$$ 3.75736 6.50794i 0.146366 0.253513i −0.783516 0.621372i $$-0.786576\pi$$
0.929882 + 0.367859i $$0.119909\pi$$
$$660$$ 0 0
$$661$$ 3.48528 6.03668i 0.135562 0.234800i −0.790250 0.612784i $$-0.790049\pi$$
0.925812 + 0.377985i $$0.123383\pi$$
$$662$$ 1.10660 + 1.91669i 0.0430093 + 0.0744943i
$$663$$ 0 0
$$664$$ −12.6863 −0.492324
$$665$$ −0.914214 7.91732i −0.0354517 0.307021i
$$666$$ 0 0
$$667$$ 4.00000 + 6.92820i 0.154881 + 0.268261i
$$668$$ 22.8284 + 39.5400i 0.883258 + 1.52985i
$$669$$ 0 0
$$670$$ −1.13604 1.96768i −0.0438890 0.0760180i
$$671$$ 11.7574 20.3643i 0.453888 0.786157i
$$672$$ 0 0
$$673$$ −23.8284 −0.918518 −0.459259 0.888302i $$-0.651885\pi$$
−0.459259 + 0.888302i $$0.651885\pi$$
$$674$$ −3.62132 + 6.27231i −0.139488 + 0.241600i
$$675$$ 0 0
$$676$$ 17.6569 0.679110
$$677$$ 23.4558 0.901481 0.450741 0.892655i $$-0.351160\pi$$
0.450741 + 0.892655i $$0.351160\pi$$
$$678$$ 0 0
$$679$$ 5.48528 + 9.50079i 0.210506 + 0.364607i
$$680$$ 0.928932 1.60896i 0.0356229 0.0617007i
$$681$$ 0 0
$$682$$ 2.92893 + 5.07306i 0.112155 + 0.194257i
$$683$$ −44.1421 −1.68905 −0.844526 0.535515i $$-0.820118\pi$$
−0.844526 + 0.535515i $$0.820118\pi$$
$$684$$ 0 0
$$685$$ 10.4853 0.400622
$$686$$ 4.03553 + 6.98975i 0.154077 + 0.266870i
$$687$$ 0 0
$$688$$ −11.7426 + 20.3389i −0.447684 + 0.775411i
$$689$$ 1.82843 + 3.16693i 0.0696575 + 0.120650i
$$690$$ 0 0
$$691$$ 31.3137 1.19123 0.595615 0.803270i $$-0.296908\pi$$
0.595615 + 0.803270i $$0.296908\pi$$
$$692$$ 13.3726 0.508349
$$693$$ 0 0
$$694$$ −7.34315 + 12.7187i −0.278742 + 0.482795i
$$695$$ −16.3137 −0.618814
$$696$$ 0 0
$$697$$ 1.65685 2.86976i 0.0627578 0.108700i
$$698$$ 6.55025 + 11.3454i 0.247931 + 0.429429i
$$699$$ 0 0
$$700$$ 1.67157 + 2.89525i 0.0631795 + 0.109430i
$$701$$ 16.0711 + 27.8359i 0.606996 + 1.05135i 0.991733 + 0.128321i $$0.0409589\pi$$
−0.384737 + 0.923026i $$0.625708\pi$$
$$702$$ 0 0
$$703$$ −8.68629 3.76127i −0.327610 0.141859i
$$704$$ −11.7990 −0.444691
$$705$$ 0 0
$$706$$ −0.272078 0.471253i −0.0102398 0.0177358i
$$707$$ 11.1005 19.2266i 0.417477 0.723092i
$$708$$ 0 0
$$709$$ −15.8137 + 27.3901i −0.593896 + 1.02866i 0.399805 + 0.916600i $$0.369078\pi$$
−0.993702 + 0.112058i $$0.964256\pi$$
$$710$$ −4.14214 −0.155452
$$711$$ 0 0
$$712$$ −9.89949 + 17.1464i −0.370999 + 0.642590i
$$713$$ 2.07107 3.58719i 0.0775621 0.134341i
$$714$$ 0 0
$$715$$ −5.17157 −0.193406
$$716$$ −14.7574 + 25.5605i −0.551508 + 0.955241i
$$717$$ 0 0
$$718$$ 1.89949 3.29002i 0.0708885 0.122783i
$$719$$ −11.5858 20.0672i −0.432077 0.748379i 0.564975 0.825108i $$-0.308886\pi$$
−0.997052 + 0.0767288i $$0.975552\pi$$
$$720$$ 0 0
$$721$$ 17.9706 0.669259
$$722$$ 2.27817 7.53311i 0.0847849 0.280353i
$$723$$ 0 0
$$724$$ 23.1421 + 40.0834i 0.860071 + 1.48969i
$$725$$ 4.82843 + 8.36308i 0.179323 + 0.310597i
$$726$$ 0 0
$$727$$ −18.0858 31.3255i −0.670765 1.16180i −0.977688 0.210064i $$-0.932633\pi$$
0.306923 0.951734i $$-0.400701\pi$$
$$728$$ −2.65076 + 4.59125i −0.0982436 + 0.170163i
$$729$$ 0 0
$$730$$ 3.92893 0.145416
$$731$$ −4.58579 + 7.94282i −0.169611 + 0.293776i
$$732$$ 0 0
$$733$$ 3.65685 0.135069 0.0675345 0.997717i $$-0.478487\pi$$
0.0675345 + 0.997717i $$0.478487\pi$$
$$734$$ −14.1299 −0.521546
$$735$$ 0 0
$$736$$ −1.82843 3.16693i −0.0673967 0.116735i
$$737$$ −7.75736 + 13.4361i −0.285746 + 0.494927i
$$738$$ 0 0
$$739$$ 20.8137 + 36.0504i 0.765645 + 1.32614i 0.939905 + 0.341436i $$0.110913\pi$$
−0.174260 + 0.984700i $$0.555753\pi$$
$$740$$ 3.97056 0.145961
$$741$$ 0 0
$$742$$ 1.51472 0.0556071
$$743$$ 17.0711 + 29.5680i 0.626277 + 1.08474i 0.988292 + 0.152571i $$0.0487553\pi$$
−0.362016 + 0.932172i $$0.617911\pi$$
$$744$$ 0 0
$$745$$ −0.585786 + 1.01461i −0.0214616 + 0.0371725i
$$746$$ 2.41421 + 4.18154i 0.0883906 + 0.153097i
$$747$$ 0 0
$$748$$ −6.05887 −0.221534
$$749$$ −25.5980 −0.935330
$$750$$ 0 0
$$751$$ −13.1569 + 22.7883i −0.480100 + 0.831558i −0.999739 0.0228276i $$-0.992733\pi$$
0.519639 + 0.854386i $$0.326066\pi$$
$$752$$ 9.51472 0.346966
$$753$$ 0 0
$$754$$ −3.65685 + 6.33386i −0.133175 + 0.230665i
$$755$$ −5.17157 8.95743i −0.188213 0.325994i
$$756$$ 0 0
$$757$$ 16.5711 + 28.7019i 0.602286 + 1.04319i 0.992474 + 0.122454i $$0.0390765\pi$$
−0.390188 + 0.920735i $$0.627590\pi$$
$$758$$ −0.349242 0.604906i −0.0126851 0.0219712i
$$759$$ 0 0
$$760$$ 0.792893 + 6.86666i 0.0287613 + 0.249080i
$$761$$ −51.5980 −1.87043 −0.935213 0.354087i $$-0.884792\pi$$
−0.935213 + 0.354087i $$0.884792\pi$$
$$762$$ 0 0
$$763$$ 15.8284 + 27.4156i 0.573028 + 0.992513i
$$764$$ 15.3848 26.6472i 0.556602 0.964062i
$$765$$ 0 0
$$766$$ −7.02944 + 12.1753i −0.253984 + 0.439913i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −7.15685 + 12.3960i −0.258083 + 0.447012i −0.965728 0.259555i $$-0.916424\pi$$
0.707646 + 0.706568i $$0.249757\pi$$
$$770$$ −1.07107 + 1.85514i −0.0385986 + 0.0668547i
$$771$$ 0 0
$$772$$ 45.3431 1.63194
$$773$$ −11.0000 + 19.0526i −0.395643 + 0.685273i −0.993183 0.116566i $$-0.962811\pi$$
0.597540 + 0.801839i $$0.296145\pi$$
$$774$$ 0 0
$$775$$ 2.50000 4.33013i 0.0898027 0.155543i
$$776$$ −4.75736 8.23999i −0.170779 0.295798i
$$777$$ 0 0
$$778$$ 6.40202 0.229524
$$779$$ 1.41421 + 12.2474i 0.0506695 + 0.438810i
$$780$$ 0 0
$$781$$ 14.1421 + 24.4949i 0.506045 + 0.876496i
$$782$$ −0.201010 0.348160i −0.00718811 0.0124502i
$$783$$ 0