# Properties

 Label 855.2.k.h.676.1 Level $855$ Weight $2$ Character 855.676 Analytic conductor $6.827$ Analytic rank $0$ Dimension $8$ 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: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: 8.0.4601315889.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9$$ x^8 - x^7 + 6*x^6 - 3*x^5 + 26*x^4 - 14*x^3 + 31*x^2 + 12*x + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 95) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 676.1 Root $$1.07988 - 1.87040i$$ of defining polynomial Character $$\chi$$ $$=$$ 855.676 Dual form 855.2.k.h.406.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.832272 + 1.44154i) q^{2} +(-0.385355 - 0.667454i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.43525 q^{7} -2.04621 q^{8} +O(q^{10})$$ $$q+(-0.832272 + 1.44154i) q^{2} +(-0.385355 - 0.667454i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.43525 q^{7} -2.04621 q^{8} +(0.832272 + 1.44154i) q^{10} +5.75477 q^{11} +(0.797505 + 1.38132i) q^{13} +(2.02680 - 3.51051i) q^{14} +(2.47371 - 4.28460i) q^{16} +(-2.99203 + 5.18234i) q^{17} +(0.149412 + 4.35634i) q^{19} -0.770710 q^{20} +(-4.78953 + 8.29572i) q^{22} +(-0.470022 - 0.814102i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.65497 q^{26} +(0.938437 + 1.62542i) q^{28} +(1.30917 + 2.26755i) q^{29} -5.26913 q^{31} +(2.07140 + 3.58777i) q^{32} +(-4.98037 - 8.62625i) q^{34} +(-1.21763 + 2.10899i) q^{35} -2.89384 q^{37} +(-6.40418 - 3.41028i) q^{38} +(-1.02310 + 1.77207i) q^{40} +(-3.15767 + 5.46925i) q^{41} +(-2.26961 + 3.93108i) q^{43} +(-2.21763 - 3.84104i) q^{44} +1.56475 q^{46} +(4.47718 + 7.75471i) q^{47} -1.06953 q^{49} +1.66454 q^{50} +(0.614645 - 1.06460i) q^{52} +(-1.09819 - 1.90213i) q^{53} +(2.87738 - 4.98377i) q^{55} +4.98304 q^{56} -4.35834 q^{58} +(-5.39939 + 9.35202i) q^{59} +(5.26434 + 9.11811i) q^{61} +(4.38535 - 7.59566i) q^{62} +2.99898 q^{64} +1.59501 q^{65} +(-0.504789 - 0.874320i) q^{67} +4.61197 q^{68} +(-2.02680 - 3.51051i) q^{70} +(4.41694 - 7.65036i) q^{71} +(5.12499 - 8.87674i) q^{73} +(2.40846 - 4.17157i) q^{74} +(2.85008 - 1.77846i) q^{76} -14.0143 q^{77} +(-3.80229 + 6.58577i) q^{79} +(-2.47371 - 4.28460i) q^{80} +(-5.25609 - 9.10381i) q^{82} -3.11355 q^{83} +(2.99203 + 5.18234i) q^{85} +(-3.77787 - 6.54346i) q^{86} -11.7755 q^{88} +(-5.55706 - 9.62511i) q^{89} +(-1.94213 - 3.36387i) q^{91} +(-0.362251 + 0.627436i) q^{92} -14.9049 q^{94} +(3.84741 + 2.04877i) q^{95} +(-2.02888 + 3.51412i) q^{97} +(0.890144 - 1.54177i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8}+O(q^{10})$$ 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8 $$8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8} - q^{10} + 4 q^{11} - 7 q^{13} - q^{14} - 7 q^{16} - q^{17} + 5 q^{19} - 10 q^{20} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 6 q^{26} + 19 q^{28} - q^{29} + 30 q^{32} - 15 q^{34} - 4 q^{35} - 4 q^{37} - 13 q^{38} - 12 q^{40} - 8 q^{41} - q^{43} - 12 q^{44} + 24 q^{46} - 12 q^{47} - 20 q^{49} - 2 q^{50} + 3 q^{52} - 5 q^{53} + 2 q^{55} + 82 q^{56} - 54 q^{58} - 5 q^{59} + 37 q^{62} + 112 q^{64} - 14 q^{65} - 4 q^{67} - 32 q^{68} + q^{70} + 20 q^{71} + 20 q^{73} + 25 q^{74} + 63 q^{76} - 28 q^{77} - 17 q^{79} + 7 q^{80} - 21 q^{82} - 2 q^{83} + q^{85} + 8 q^{86} - 14 q^{88} + 11 q^{89} - 6 q^{91} - q^{92} - 62 q^{94} + 4 q^{95} - q^{97} + 9 q^{98}+O(q^{100})$$ 8 * q + q^2 - 5 * q^4 + 4 * q^5 - 8 * q^7 - 24 * q^8 - q^10 + 4 * q^11 - 7 * q^13 - q^14 - 7 * q^16 - q^17 + 5 * q^19 - 10 * q^20 - 2 * q^22 + 2 * q^23 - 4 * q^25 - 6 * q^26 + 19 * q^28 - q^29 + 30 * q^32 - 15 * q^34 - 4 * q^35 - 4 * q^37 - 13 * q^38 - 12 * q^40 - 8 * q^41 - q^43 - 12 * q^44 + 24 * q^46 - 12 * q^47 - 20 * q^49 - 2 * q^50 + 3 * q^52 - 5 * q^53 + 2 * q^55 + 82 * q^56 - 54 * q^58 - 5 * q^59 + 37 * q^62 + 112 * q^64 - 14 * q^65 - 4 * q^67 - 32 * q^68 + q^70 + 20 * q^71 + 20 * q^73 + 25 * q^74 + 63 * q^76 - 28 * q^77 - 17 * q^79 + 7 * q^80 - 21 * q^82 - 2 * q^83 + q^85 + 8 * q^86 - 14 * q^88 + 11 * q^89 - 6 * q^91 - q^92 - 62 * q^94 + 4 * q^95 - q^97 + 9 * q^98

## Character values

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

 $$n$$ $$172$$ $$191$$ $$496$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.832272 + 1.44154i −0.588506 + 1.01932i 0.405923 + 0.913907i $$0.366950\pi$$
−0.994428 + 0.105414i $$0.966383\pi$$
$$3$$ 0 0
$$4$$ −0.385355 0.667454i −0.192677 0.333727i
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ 0 0
$$7$$ −2.43525 −0.920440 −0.460220 0.887805i $$-0.652229\pi$$
−0.460220 + 0.887805i $$0.652229\pi$$
$$8$$ −2.04621 −0.723444
$$9$$ 0 0
$$10$$ 0.832272 + 1.44154i 0.263188 + 0.455854i
$$11$$ 5.75477 1.73513 0.867564 0.497326i $$-0.165685\pi$$
0.867564 + 0.497326i $$0.165685\pi$$
$$12$$ 0 0
$$13$$ 0.797505 + 1.38132i 0.221188 + 0.383109i 0.955169 0.296061i $$-0.0956732\pi$$
−0.733981 + 0.679170i $$0.762340\pi$$
$$14$$ 2.02680 3.51051i 0.541684 0.938224i
$$15$$ 0 0
$$16$$ 2.47371 4.28460i 0.618428 1.07115i
$$17$$ −2.99203 + 5.18234i −0.725673 + 1.25690i 0.233023 + 0.972471i $$0.425138\pi$$
−0.958696 + 0.284432i $$0.908195\pi$$
$$18$$ 0 0
$$19$$ 0.149412 + 4.35634i 0.0342775 + 0.999412i
$$20$$ −0.770710 −0.172336
$$21$$ 0 0
$$22$$ −4.78953 + 8.29572i −1.02113 + 1.76865i
$$23$$ −0.470022 0.814102i −0.0980064 0.169752i 0.812853 0.582469i $$-0.197913\pi$$
−0.910859 + 0.412717i $$0.864580\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ −2.65497 −0.520682
$$27$$ 0 0
$$28$$ 0.938437 + 1.62542i 0.177348 + 0.307176i
$$29$$ 1.30917 + 2.26755i 0.243106 + 0.421073i 0.961598 0.274463i $$-0.0885002\pi$$
−0.718491 + 0.695536i $$0.755167\pi$$
$$30$$ 0 0
$$31$$ −5.26913 −0.946364 −0.473182 0.880965i $$-0.656895\pi$$
−0.473182 + 0.880965i $$0.656895\pi$$
$$32$$ 2.07140 + 3.58777i 0.366175 + 0.634233i
$$33$$ 0 0
$$34$$ −4.98037 8.62625i −0.854126 1.47939i
$$35$$ −1.21763 + 2.10899i −0.205817 + 0.356485i
$$36$$ 0 0
$$37$$ −2.89384 −0.475744 −0.237872 0.971297i $$-0.576450\pi$$
−0.237872 + 0.971297i $$0.576450\pi$$
$$38$$ −6.40418 3.41028i −1.03889 0.553220i
$$39$$ 0 0
$$40$$ −1.02310 + 1.77207i −0.161767 + 0.280189i
$$41$$ −3.15767 + 5.46925i −0.493145 + 0.854153i −0.999969 0.00789701i $$-0.997486\pi$$
0.506823 + 0.862050i $$0.330820\pi$$
$$42$$ 0 0
$$43$$ −2.26961 + 3.93108i −0.346113 + 0.599485i −0.985555 0.169354i $$-0.945832\pi$$
0.639443 + 0.768839i $$0.279165\pi$$
$$44$$ −2.21763 3.84104i −0.334320 0.579059i
$$45$$ 0 0
$$46$$ 1.56475 0.230709
$$47$$ 4.47718 + 7.75471i 0.653064 + 1.13114i 0.982375 + 0.186919i $$0.0598502\pi$$
−0.329311 + 0.944221i $$0.606816\pi$$
$$48$$ 0 0
$$49$$ −1.06953 −0.152791
$$50$$ 1.66454 0.235402
$$51$$ 0 0
$$52$$ 0.614645 1.06460i 0.0852359 0.147633i
$$53$$ −1.09819 1.90213i −0.150848 0.261277i 0.780691 0.624917i $$-0.214867\pi$$
−0.931540 + 0.363640i $$0.881534\pi$$
$$54$$ 0 0
$$55$$ 2.87738 4.98377i 0.387986 0.672012i
$$56$$ 4.98304 0.665887
$$57$$ 0 0
$$58$$ −4.35834 −0.572278
$$59$$ −5.39939 + 9.35202i −0.702941 + 1.21753i 0.264489 + 0.964389i $$0.414797\pi$$
−0.967430 + 0.253140i $$0.918537\pi$$
$$60$$ 0 0
$$61$$ 5.26434 + 9.11811i 0.674030 + 1.16745i 0.976751 + 0.214375i $$0.0687716\pi$$
−0.302721 + 0.953079i $$0.597895\pi$$
$$62$$ 4.38535 7.59566i 0.556941 0.964649i
$$63$$ 0 0
$$64$$ 2.99898 0.374873
$$65$$ 1.59501 0.197837
$$66$$ 0 0
$$67$$ −0.504789 0.874320i −0.0616698 0.106815i 0.833542 0.552456i $$-0.186309\pi$$
−0.895212 + 0.445641i $$0.852976\pi$$
$$68$$ 4.61197 0.559284
$$69$$ 0 0
$$70$$ −2.02680 3.51051i −0.242248 0.419587i
$$71$$ 4.41694 7.65036i 0.524194 0.907931i −0.475409 0.879765i $$-0.657700\pi$$
0.999603 0.0281662i $$-0.00896677\pi$$
$$72$$ 0 0
$$73$$ 5.12499 8.87674i 0.599835 1.03894i −0.393011 0.919534i $$-0.628566\pi$$
0.992845 0.119410i $$-0.0381003\pi$$
$$74$$ 2.40846 4.17157i 0.279978 0.484936i
$$75$$ 0 0
$$76$$ 2.85008 1.77846i 0.326927 0.204004i
$$77$$ −14.0143 −1.59708
$$78$$ 0 0
$$79$$ −3.80229 + 6.58577i −0.427792 + 0.740957i −0.996677 0.0814604i $$-0.974042\pi$$
0.568885 + 0.822417i $$0.307375\pi$$
$$80$$ −2.47371 4.28460i −0.276570 0.479032i
$$81$$ 0 0
$$82$$ −5.25609 9.10381i −0.580438 1.00535i
$$83$$ −3.11355 −0.341756 −0.170878 0.985292i $$-0.554660\pi$$
−0.170878 + 0.985292i $$0.554660\pi$$
$$84$$ 0 0
$$85$$ 2.99203 + 5.18234i 0.324531 + 0.562104i
$$86$$ −3.77787 6.54346i −0.407378 0.705600i
$$87$$ 0 0
$$88$$ −11.7755 −1.25527
$$89$$ −5.55706 9.62511i −0.589047 1.02026i −0.994358 0.106081i $$-0.966170\pi$$
0.405310 0.914179i $$-0.367163\pi$$
$$90$$ 0 0
$$91$$ −1.94213 3.36387i −0.203590 0.352629i
$$92$$ −0.362251 + 0.627436i −0.0377672 + 0.0654148i
$$93$$ 0 0
$$94$$ −14.9049 −1.53733
$$95$$ 3.84741 + 2.04877i 0.394735 + 0.210200i
$$96$$ 0 0
$$97$$ −2.02888 + 3.51412i −0.206002 + 0.356805i −0.950451 0.310873i $$-0.899379\pi$$
0.744450 + 0.667678i $$0.232712\pi$$
$$98$$ 0.890144 1.54177i 0.0899181 0.155743i
$$99$$ 0 0
$$100$$ −0.385355 + 0.667454i −0.0385355 + 0.0667454i
$$101$$ −5.56503 9.63892i −0.553741 0.959108i −0.998000 0.0632098i $$-0.979866\pi$$
0.444259 0.895898i $$-0.353467\pi$$
$$102$$ 0 0
$$103$$ 11.5791 1.14092 0.570460 0.821326i $$-0.306765\pi$$
0.570460 + 0.821326i $$0.306765\pi$$
$$104$$ −1.63186 2.82647i −0.160017 0.277158i
$$105$$ 0 0
$$106$$ 3.65598 0.355101
$$107$$ −17.9177 −1.73217 −0.866086 0.499894i $$-0.833372\pi$$
−0.866086 + 0.499894i $$0.833372\pi$$
$$108$$ 0 0
$$109$$ −2.81235 + 4.87113i −0.269374 + 0.466570i −0.968700 0.248233i $$-0.920150\pi$$
0.699326 + 0.714803i $$0.253484\pi$$
$$110$$ 4.78953 + 8.29572i 0.456664 + 0.790965i
$$111$$ 0 0
$$112$$ −6.02412 + 10.4341i −0.569226 + 0.985928i
$$113$$ 15.6789 1.47494 0.737472 0.675378i $$-0.236019\pi$$
0.737472 + 0.675378i $$0.236019\pi$$
$$114$$ 0 0
$$115$$ −0.940044 −0.0876595
$$116$$ 1.00899 1.74762i 0.0936822 0.162262i
$$117$$ 0 0
$$118$$ −8.98753 15.5669i −0.827369 1.43304i
$$119$$ 7.28635 12.6203i 0.667939 1.15690i
$$120$$ 0 0
$$121$$ 22.1173 2.01067
$$122$$ −17.5255 −1.58668
$$123$$ 0 0
$$124$$ 2.03049 + 3.51691i 0.182343 + 0.315827i
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −3.05996 5.30000i −0.271527 0.470299i 0.697726 0.716365i $$-0.254195\pi$$
−0.969253 + 0.246066i $$0.920862\pi$$
$$128$$ −6.63877 + 11.4987i −0.586790 + 1.01635i
$$129$$ 0 0
$$130$$ −1.32748 + 2.29927i −0.116428 + 0.201659i
$$131$$ −7.44055 + 12.8874i −0.650084 + 1.12598i 0.333018 + 0.942920i $$0.391933\pi$$
−0.983102 + 0.183058i $$0.941400\pi$$
$$132$$ 0 0
$$133$$ −0.363857 10.6088i −0.0315504 0.919899i
$$134$$ 1.68049 0.145172
$$135$$ 0 0
$$136$$ 6.12231 10.6042i 0.524984 0.909299i
$$137$$ 8.67518 + 15.0258i 0.741170 + 1.28374i 0.951963 + 0.306214i $$0.0990622\pi$$
−0.210793 + 0.977531i $$0.567604\pi$$
$$138$$ 0 0
$$139$$ 3.35267 + 5.80700i 0.284370 + 0.492543i 0.972456 0.233086i $$-0.0748823\pi$$
−0.688086 + 0.725629i $$0.741549\pi$$
$$140$$ 1.87687 0.158625
$$141$$ 0 0
$$142$$ 7.35219 + 12.7344i 0.616982 + 1.06864i
$$143$$ 4.58946 + 7.94917i 0.383790 + 0.664743i
$$144$$ 0 0
$$145$$ 2.61834 0.217441
$$146$$ 8.53077 + 14.7757i 0.706012 + 1.22285i
$$147$$ 0 0
$$148$$ 1.11515 + 1.93150i 0.0916651 + 0.158769i
$$149$$ 7.19642 12.4646i 0.589553 1.02114i −0.404737 0.914433i $$-0.632637\pi$$
0.994291 0.106704i $$-0.0340296\pi$$
$$150$$ 0 0
$$151$$ 12.7219 1.03529 0.517645 0.855595i $$-0.326809\pi$$
0.517645 + 0.855595i $$0.326809\pi$$
$$152$$ −0.305729 8.91398i −0.0247979 0.723019i
$$153$$ 0 0
$$154$$ 11.6637 20.2022i 0.939890 1.62794i
$$155$$ −2.63457 + 4.56320i −0.211614 + 0.366525i
$$156$$ 0 0
$$157$$ 1.68765 2.92309i 0.134689 0.233288i −0.790790 0.612088i $$-0.790330\pi$$
0.925479 + 0.378800i $$0.123663\pi$$
$$158$$ −6.32909 10.9623i −0.503515 0.872114i
$$159$$ 0 0
$$160$$ 4.14280 0.327517
$$161$$ 1.14462 + 1.98255i 0.0902089 + 0.156246i
$$162$$ 0 0
$$163$$ 0.307960 0.0241213 0.0120607 0.999927i $$-0.496161\pi$$
0.0120607 + 0.999927i $$0.496161\pi$$
$$164$$ 4.86730 0.380072
$$165$$ 0 0
$$166$$ 2.59132 4.48830i 0.201125 0.348359i
$$167$$ 7.13215 + 12.3532i 0.551902 + 0.955923i 0.998137 + 0.0610070i $$0.0194312\pi$$
−0.446235 + 0.894916i $$0.647235\pi$$
$$168$$ 0 0
$$169$$ 5.22797 9.05511i 0.402152 0.696547i
$$170$$ −9.96073 −0.763953
$$171$$ 0 0
$$172$$ 3.49842 0.266752
$$173$$ 6.67357 11.5590i 0.507382 0.878811i −0.492581 0.870266i $$-0.663947\pi$$
0.999963 0.00854514i $$-0.00272003\pi$$
$$174$$ 0 0
$$175$$ 1.21763 + 2.10899i 0.0920440 + 0.159425i
$$176$$ 14.2356 24.6569i 1.07305 1.85858i
$$177$$ 0 0
$$178$$ 18.5000 1.38663
$$179$$ 14.2207 1.06291 0.531454 0.847087i $$-0.321646\pi$$
0.531454 + 0.847087i $$0.321646\pi$$
$$180$$ 0 0
$$181$$ −4.94132 8.55861i −0.367285 0.636157i 0.621855 0.783133i $$-0.286379\pi$$
−0.989140 + 0.146976i $$0.953046\pi$$
$$182$$ 6.46552 0.479256
$$183$$ 0 0
$$184$$ 0.961763 + 1.66582i 0.0709021 + 0.122806i
$$185$$ −1.44692 + 2.50613i −0.106379 + 0.184255i
$$186$$ 0 0
$$187$$ −17.2184 + 29.8232i −1.25914 + 2.18089i
$$188$$ 3.45061 5.97663i 0.251661 0.435891i
$$189$$ 0 0
$$190$$ −6.15548 + 3.84104i −0.446565 + 0.278659i
$$191$$ 12.9942 0.940228 0.470114 0.882606i $$-0.344213\pi$$
0.470114 + 0.882606i $$0.344213\pi$$
$$192$$ 0 0
$$193$$ −7.25795 + 12.5711i −0.522439 + 0.904890i 0.477221 + 0.878784i $$0.341644\pi$$
−0.999659 + 0.0261066i $$0.991689\pi$$
$$194$$ −3.37716 5.84942i −0.242466 0.419964i
$$195$$ 0 0
$$196$$ 0.412150 + 0.713865i 0.0294393 + 0.0509904i
$$197$$ 25.0010 1.78125 0.890624 0.454740i $$-0.150268\pi$$
0.890624 + 0.454740i $$0.150268\pi$$
$$198$$ 0 0
$$199$$ 1.12769 + 1.95322i 0.0799401 + 0.138460i 0.903224 0.429170i $$-0.141194\pi$$
−0.823284 + 0.567630i $$0.807860\pi$$
$$200$$ 1.02310 + 1.77207i 0.0723444 + 0.125304i
$$201$$ 0 0
$$202$$ 18.5265 1.30352
$$203$$ −3.18816 5.52205i −0.223765 0.387572i
$$204$$ 0 0
$$205$$ 3.15767 + 5.46925i 0.220541 + 0.381989i
$$206$$ −9.63694 + 16.6917i −0.671437 + 1.16296i
$$207$$ 0 0
$$208$$ 7.89120 0.547156
$$209$$ 0.859833 + 25.0697i 0.0594759 + 1.73411i
$$210$$ 0 0
$$211$$ −11.1081 + 19.2397i −0.764710 + 1.32452i 0.175689 + 0.984446i $$0.443785\pi$$
−0.940400 + 0.340071i $$0.889549\pi$$
$$212$$ −0.846388 + 1.46599i −0.0581302 + 0.100684i
$$213$$ 0 0
$$214$$ 14.9124 25.8291i 1.01939 1.76564i
$$215$$ 2.26961 + 3.93108i 0.154786 + 0.268098i
$$216$$ 0 0
$$217$$ 12.8317 0.871071
$$218$$ −4.68128 8.10822i −0.317057 0.549158i
$$219$$ 0 0
$$220$$ −4.43525 −0.299025
$$221$$ −9.54463 −0.642041
$$222$$ 0 0
$$223$$ −5.10799 + 8.84730i −0.342056 + 0.592459i −0.984814 0.173610i $$-0.944457\pi$$
0.642758 + 0.766069i $$0.277790\pi$$
$$224$$ −5.04438 8.73712i −0.337042 0.583774i
$$225$$ 0 0
$$226$$ −13.0491 + 22.6017i −0.868012 + 1.50344i
$$227$$ −4.15180 −0.275565 −0.137782 0.990463i $$-0.543997\pi$$
−0.137782 + 0.990463i $$0.543997\pi$$
$$228$$ 0 0
$$229$$ 6.53286 0.431703 0.215852 0.976426i $$-0.430747\pi$$
0.215852 + 0.976426i $$0.430747\pi$$
$$230$$ 0.782373 1.35511i 0.0515881 0.0893533i
$$231$$ 0 0
$$232$$ −2.67883 4.63987i −0.175874 0.304623i
$$233$$ 2.57410 4.45848i 0.168635 0.292084i −0.769305 0.638882i $$-0.779397\pi$$
0.937940 + 0.346797i $$0.112731\pi$$
$$234$$ 0 0
$$235$$ 8.95437 0.584118
$$236$$ 8.32272 0.541763
$$237$$ 0 0
$$238$$ 12.1285 + 21.0071i 0.786171 + 1.36169i
$$239$$ −13.9962 −0.905338 −0.452669 0.891679i $$-0.649528\pi$$
−0.452669 + 0.891679i $$0.649528\pi$$
$$240$$ 0 0
$$241$$ −7.61285 13.1858i −0.490387 0.849375i 0.509552 0.860440i $$-0.329811\pi$$
−0.999939 + 0.0110652i $$0.996478\pi$$
$$242$$ −18.4076 + 31.8830i −1.18329 + 2.04952i
$$243$$ 0 0
$$244$$ 4.05728 7.02742i 0.259741 0.449884i
$$245$$ −0.534767 + 0.926244i −0.0341650 + 0.0591756i
$$246$$ 0 0
$$247$$ −5.89834 + 3.68059i −0.375302 + 0.234190i
$$248$$ 10.7817 0.684642
$$249$$ 0 0
$$250$$ 0.832272 1.44154i 0.0526375 0.0911709i
$$251$$ −3.05630 5.29366i −0.192912 0.334133i 0.753302 0.657674i $$-0.228460\pi$$
−0.946214 + 0.323542i $$0.895126\pi$$
$$252$$ 0 0
$$253$$ −2.70487 4.68497i −0.170053 0.294541i
$$254$$ 10.1869 0.639181
$$255$$ 0 0
$$256$$ −8.05154 13.9457i −0.503221 0.871605i
$$257$$ 0.0613414 + 0.106246i 0.00382637 + 0.00662747i 0.867932 0.496683i $$-0.165449\pi$$
−0.864106 + 0.503310i $$0.832115\pi$$
$$258$$ 0 0
$$259$$ 7.04723 0.437893
$$260$$ −0.614645 1.06460i −0.0381187 0.0660235i
$$261$$ 0 0
$$262$$ −12.3851 21.4517i −0.765156 1.32529i
$$263$$ −5.03027 + 8.71267i −0.310179 + 0.537247i −0.978401 0.206716i $$-0.933722\pi$$
0.668222 + 0.743962i $$0.267056\pi$$
$$264$$ 0 0
$$265$$ −2.19639 −0.134923
$$266$$ 15.5958 + 8.30489i 0.956240 + 0.509206i
$$267$$ 0 0
$$268$$ −0.389046 + 0.673847i −0.0237648 + 0.0411618i
$$269$$ 2.85614 4.94698i 0.174142 0.301623i −0.765722 0.643172i $$-0.777618\pi$$
0.939864 + 0.341549i $$0.110951\pi$$
$$270$$ 0 0
$$271$$ 6.35560 11.0082i 0.386075 0.668702i −0.605843 0.795585i $$-0.707164\pi$$
0.991918 + 0.126883i $$0.0404972\pi$$
$$272$$ 14.8028 + 25.6393i 0.897554 + 1.55461i
$$273$$ 0 0
$$274$$ −28.8804 −1.74473
$$275$$ −2.87738 4.98377i −0.173513 0.300533i
$$276$$ 0 0
$$277$$ 17.6019 1.05760 0.528799 0.848747i $$-0.322642\pi$$
0.528799 + 0.848747i $$0.322642\pi$$
$$278$$ −11.1613 −0.669413
$$279$$ 0 0
$$280$$ 2.49152 4.31544i 0.148897 0.257897i
$$281$$ −10.2502 17.7539i −0.611476 1.05911i −0.990992 0.133922i $$-0.957243\pi$$
0.379516 0.925185i $$-0.376090\pi$$
$$282$$ 0 0
$$283$$ 5.92805 10.2677i 0.352386 0.610350i −0.634281 0.773103i $$-0.718704\pi$$
0.986667 + 0.162752i $$0.0520371\pi$$
$$284$$ −6.80836 −0.404002
$$285$$ 0 0
$$286$$ −15.2787 −0.903449
$$287$$ 7.68973 13.3190i 0.453911 0.786196i
$$288$$ 0 0
$$289$$ −9.40447 16.2890i −0.553204 0.958177i
$$290$$ −2.17917 + 3.77443i −0.127965 + 0.221642i
$$291$$ 0 0
$$292$$ −7.89976 −0.462298
$$293$$ 24.9814 1.45943 0.729715 0.683751i $$-0.239653\pi$$
0.729715 + 0.683751i $$0.239653\pi$$
$$294$$ 0 0
$$295$$ 5.39939 + 9.35202i 0.314365 + 0.544495i
$$296$$ 5.92139 0.344174
$$297$$ 0 0
$$298$$ 11.9788 + 20.7478i 0.693911 + 1.20189i
$$299$$ 0.749690 1.29850i 0.0433557 0.0750943i
$$300$$ 0 0
$$301$$ 5.52708 9.57319i 0.318576 0.551789i
$$302$$ −10.5881 + 18.3391i −0.609274 + 1.05529i
$$303$$ 0 0
$$304$$ 19.0348 + 10.1362i 1.09172 + 0.581348i
$$305$$ 10.5287 0.602871
$$306$$ 0 0
$$307$$ −8.45997 + 14.6531i −0.482836 + 0.836296i −0.999806 0.0197074i $$-0.993727\pi$$
0.516970 + 0.856003i $$0.327060\pi$$
$$308$$ 5.40049 + 9.35392i 0.307721 + 0.532989i
$$309$$ 0 0
$$310$$ −4.38535 7.59566i −0.249071 0.431404i
$$311$$ 15.2133 0.862670 0.431335 0.902192i $$-0.358043\pi$$
0.431335 + 0.902192i $$0.358043\pi$$
$$312$$ 0 0
$$313$$ −12.4637 21.5877i −0.704488 1.22021i −0.966876 0.255246i $$-0.917844\pi$$
0.262389 0.964962i $$-0.415490\pi$$
$$314$$ 2.80917 + 4.86562i 0.158531 + 0.274583i
$$315$$ 0 0
$$316$$ 5.86093 0.329703
$$317$$ −12.6152 21.8502i −0.708541 1.22723i −0.965398 0.260780i $$-0.916020\pi$$
0.256857 0.966449i $$-0.417313\pi$$
$$318$$ 0 0
$$319$$ 7.53396 + 13.0492i 0.421821 + 0.730615i
$$320$$ 1.49949 2.59720i 0.0838241 0.145188i
$$321$$ 0 0
$$322$$ −3.81055 −0.212354
$$323$$ −23.0231 12.2600i −1.28104 0.682163i
$$324$$ 0 0
$$325$$ 0.797505 1.38132i 0.0442376 0.0766218i
$$326$$ −0.256307 + 0.443937i −0.0141955 + 0.0245874i
$$327$$ 0 0
$$328$$ 6.46125 11.1912i 0.356763 0.617932i
$$329$$ −10.9031 18.8847i −0.601106 1.04115i
$$330$$ 0 0
$$331$$ −20.2063 −1.11064 −0.555320 0.831637i $$-0.687404\pi$$
−0.555320 + 0.831637i $$0.687404\pi$$
$$332$$ 1.19982 + 2.07815i 0.0658487 + 0.114053i
$$333$$ 0 0
$$334$$ −23.7436 −1.29919
$$335$$ −1.00958 −0.0551592
$$336$$ 0 0
$$337$$ 15.9123 27.5610i 0.866800 1.50134i 0.00155051 0.999999i $$-0.499506\pi$$
0.865249 0.501342i $$-0.167160\pi$$
$$338$$ 8.70219 + 15.0726i 0.473337 + 0.819843i
$$339$$ 0 0
$$340$$ 2.30599 3.99408i 0.125060 0.216610i
$$341$$ −30.3226 −1.64206
$$342$$ 0 0
$$343$$ 19.6514 1.06107
$$344$$ 4.64410 8.04382i 0.250393 0.433693i
$$345$$ 0 0
$$346$$ 11.1085 + 19.2404i 0.597194 + 1.03437i
$$347$$ −1.65128 + 2.86009i −0.0886451 + 0.153538i −0.906939 0.421263i $$-0.861587\pi$$
0.818294 + 0.574801i $$0.194920\pi$$
$$348$$ 0 0
$$349$$ 17.8486 0.955416 0.477708 0.878519i $$-0.341468\pi$$
0.477708 + 0.878519i $$0.341468\pi$$
$$350$$ −4.05359 −0.216674
$$351$$ 0 0
$$352$$ 11.9204 + 20.6468i 0.635360 + 1.10048i
$$353$$ 8.29523 0.441511 0.220755 0.975329i $$-0.429148\pi$$
0.220755 + 0.975329i $$0.429148\pi$$
$$354$$ 0 0
$$355$$ −4.41694 7.65036i −0.234427 0.406039i
$$356$$ −4.28288 + 7.41817i −0.226992 + 0.393162i
$$357$$ 0 0
$$358$$ −11.8355 + 20.4997i −0.625527 + 1.08344i
$$359$$ 4.17511 7.23150i 0.220354 0.381664i −0.734562 0.678542i $$-0.762612\pi$$
0.954915 + 0.296878i $$0.0959455\pi$$
$$360$$ 0 0
$$361$$ −18.9554 + 1.30178i −0.997650 + 0.0685148i
$$362$$ 16.4501 0.864598
$$363$$ 0 0
$$364$$ −1.49682 + 2.59256i −0.0784545 + 0.135887i
$$365$$ −5.12499 8.87674i −0.268254 0.464630i
$$366$$ 0 0
$$367$$ −7.20988 12.4879i −0.376353 0.651862i 0.614176 0.789169i $$-0.289489\pi$$
−0.990528 + 0.137307i $$0.956155\pi$$
$$368$$ −4.65080 −0.242440
$$369$$ 0 0
$$370$$ −2.40846 4.17157i −0.125210 0.216870i
$$371$$ 2.67438 + 4.63216i 0.138847 + 0.240490i
$$372$$ 0 0
$$373$$ −24.1157 −1.24866 −0.624332 0.781159i $$-0.714629\pi$$
−0.624332 + 0.781159i $$0.714629\pi$$
$$374$$ −28.6608 49.6420i −1.48202 2.56693i
$$375$$ 0 0
$$376$$ −9.16125 15.8678i −0.472455 0.818317i
$$377$$ −2.08814 + 3.61676i −0.107545 + 0.186273i
$$378$$ 0 0
$$379$$ 16.6757 0.856571 0.428285 0.903644i $$-0.359118\pi$$
0.428285 + 0.903644i $$0.359118\pi$$
$$380$$ −0.115154 3.35747i −0.00590725 0.172235i
$$381$$ 0 0
$$382$$ −10.8147 + 18.7316i −0.553329 + 0.958395i
$$383$$ −5.43895 + 9.42053i −0.277917 + 0.481367i −0.970867 0.239619i $$-0.922977\pi$$
0.692950 + 0.720986i $$0.256311\pi$$
$$384$$ 0 0
$$385$$ −7.00716 + 12.1368i −0.357118 + 0.618546i
$$386$$ −12.0812 20.9252i −0.614916 1.06507i
$$387$$ 0 0
$$388$$ 3.12736 0.158767
$$389$$ 18.2272 + 31.5704i 0.924154 + 1.60068i 0.792917 + 0.609330i $$0.208562\pi$$
0.131237 + 0.991351i $$0.458105\pi$$
$$390$$ 0 0
$$391$$ 5.62528 0.284482
$$392$$ 2.18849 0.110535
$$393$$ 0 0
$$394$$ −20.8077 + 36.0399i −1.04827 + 1.81566i
$$395$$ 3.80229 + 6.58577i 0.191314 + 0.331366i
$$396$$ 0 0
$$397$$ −4.29191 + 7.43380i −0.215405 + 0.373092i −0.953398 0.301717i $$-0.902440\pi$$
0.737993 + 0.674808i $$0.235774\pi$$
$$398$$ −3.75419 −0.188181
$$399$$ 0 0
$$400$$ −4.94743 −0.247371
$$401$$ −8.52785 + 14.7707i −0.425860 + 0.737612i −0.996500 0.0835885i $$-0.973362\pi$$
0.570640 + 0.821200i $$0.306695\pi$$
$$402$$ 0 0
$$403$$ −4.20216 7.27836i −0.209325 0.362561i
$$404$$ −4.28903 + 7.42881i −0.213387 + 0.369597i
$$405$$ 0 0
$$406$$ 10.6137 0.526747
$$407$$ −16.6533 −0.825476
$$408$$ 0 0
$$409$$ 5.89702 + 10.2139i 0.291589 + 0.505047i 0.974186 0.225749i $$-0.0724828\pi$$
−0.682597 + 0.730795i $$0.739149\pi$$
$$410$$ −10.5122 −0.519159
$$411$$ 0 0
$$412$$ −4.46205 7.72850i −0.219829 0.380756i
$$413$$ 13.1489 22.7745i 0.647015 1.12066i
$$414$$ 0 0
$$415$$ −1.55677 + 2.69641i −0.0764190 + 0.132362i
$$416$$ −3.30390 + 5.72252i −0.161987 + 0.280570i
$$417$$ 0 0
$$418$$ −36.8546 19.6253i −1.80261 0.959907i
$$419$$ −1.14280 −0.0558292 −0.0279146 0.999610i $$-0.508887\pi$$
−0.0279146 + 0.999610i $$0.508887\pi$$
$$420$$ 0 0
$$421$$ −9.75944 + 16.9039i −0.475646 + 0.823843i −0.999611 0.0278967i $$-0.991119\pi$$
0.523965 + 0.851740i $$0.324452\pi$$
$$422$$ −18.4899 32.0254i −0.900072 1.55897i
$$423$$ 0 0
$$424$$ 2.24713 + 3.89215i 0.109130 + 0.189019i
$$425$$ 5.98406 0.290269
$$426$$ 0 0
$$427$$ −12.8200 22.2049i −0.620404 1.07457i
$$428$$ 6.90469 + 11.9593i 0.333751 + 0.578073i
$$429$$ 0 0
$$430$$ −7.55574 −0.364370
$$431$$ −18.4392 31.9377i −0.888187 1.53838i −0.842017 0.539451i $$-0.818632\pi$$
−0.0461694 0.998934i $$-0.514701\pi$$
$$432$$ 0 0
$$433$$ −0.184467 0.319506i −0.00886490 0.0153545i 0.861559 0.507658i $$-0.169488\pi$$
−0.870424 + 0.492303i $$0.836155\pi$$
$$434$$ −10.6795 + 18.4974i −0.512630 + 0.887902i
$$435$$ 0 0
$$436$$ 4.33501 0.207609
$$437$$ 3.47628 2.16921i 0.166293 0.103767i
$$438$$ 0 0
$$439$$ 1.13220 1.96102i 0.0540367 0.0935944i −0.837742 0.546067i $$-0.816125\pi$$
0.891778 + 0.452472i $$0.149458\pi$$
$$440$$ −5.88773 + 10.1978i −0.280686 + 0.486163i
$$441$$ 0 0
$$442$$ 7.94373 13.7590i 0.377845 0.654447i
$$443$$ −8.23137 14.2572i −0.391084 0.677378i 0.601508 0.798866i $$-0.294567\pi$$
−0.992593 + 0.121488i $$0.961233\pi$$
$$444$$ 0 0
$$445$$ −11.1141 −0.526860
$$446$$ −8.50248 14.7267i −0.402604 0.697331i
$$447$$ 0 0
$$448$$ −7.30329 −0.345048
$$449$$ −14.1613 −0.668315 −0.334158 0.942517i $$-0.608452\pi$$
−0.334158 + 0.942517i $$0.608452\pi$$
$$450$$ 0 0
$$451$$ −18.1717 + 31.4742i −0.855670 + 1.48206i
$$452$$ −6.04193 10.4649i −0.284188 0.492229i
$$453$$ 0 0
$$454$$ 3.45543 5.98498i 0.162171 0.280889i
$$455$$ −3.88426 −0.182097
$$456$$ 0 0
$$457$$ 1.22073 0.0571033 0.0285516 0.999592i $$-0.490910\pi$$
0.0285516 + 0.999592i $$0.490910\pi$$
$$458$$ −5.43712 + 9.41736i −0.254060 + 0.440045i
$$459$$ 0 0
$$460$$ 0.362251 + 0.627436i 0.0168900 + 0.0292544i
$$461$$ −4.34580 + 7.52714i −0.202404 + 0.350574i −0.949303 0.314364i $$-0.898209\pi$$
0.746898 + 0.664938i $$0.231542\pi$$
$$462$$ 0 0
$$463$$ −19.7149 −0.916229 −0.458114 0.888893i $$-0.651475\pi$$
−0.458114 + 0.888893i $$0.651475\pi$$
$$464$$ 12.9540 0.601375
$$465$$ 0 0
$$466$$ 4.28471 + 7.42133i 0.198485 + 0.343787i
$$467$$ 11.4795 0.531207 0.265604 0.964082i $$-0.414429\pi$$
0.265604 + 0.964082i $$0.414429\pi$$
$$468$$ 0 0
$$469$$ 1.22929 + 2.12919i 0.0567633 + 0.0983170i
$$470$$ −7.45247 + 12.9081i −0.343757 + 0.595404i
$$471$$ 0 0
$$472$$ 11.0483 19.1362i 0.508538 0.880814i
$$473$$ −13.0611 + 22.6225i −0.600549 + 1.04018i
$$474$$ 0 0
$$475$$ 3.69799 2.30756i 0.169676 0.105878i
$$476$$ −11.2313 −0.514787
$$477$$ 0 0
$$478$$ 11.6486 20.1760i 0.532796 0.922830i
$$479$$ 19.6316 + 34.0029i 0.896989 + 1.55363i 0.831324 + 0.555789i $$0.187584\pi$$
0.0656652 + 0.997842i $$0.479083\pi$$
$$480$$ 0 0
$$481$$ −2.30785 3.99731i −0.105229 0.182262i
$$482$$ 25.3439 1.15438
$$483$$ 0 0
$$484$$ −8.52302 14.7623i −0.387410 0.671014i
$$485$$ 2.02888 + 3.51412i 0.0921267 + 0.159568i
$$486$$ 0 0
$$487$$ 31.5943 1.43168 0.715838 0.698266i $$-0.246045\pi$$
0.715838 + 0.698266i $$0.246045\pi$$
$$488$$ −10.7719 18.6576i −0.487623 0.844588i
$$489$$ 0 0
$$490$$ −0.890144 1.54177i −0.0402126 0.0696503i
$$491$$ −5.53187 + 9.58148i −0.249650 + 0.432406i −0.963429 0.267965i $$-0.913649\pi$$
0.713779 + 0.700371i $$0.246982\pi$$
$$492$$ 0 0
$$493$$ −15.6683 −0.705663
$$494$$ −0.396685 11.5659i −0.0178477 0.520376i
$$495$$ 0 0
$$496$$ −13.0343 + 22.5761i −0.585258 + 1.01370i
$$497$$ −10.7564 + 18.6306i −0.482489 + 0.835696i
$$498$$ 0 0
$$499$$ 10.1868 17.6440i 0.456023 0.789854i −0.542724 0.839911i $$-0.682607\pi$$
0.998746 + 0.0500570i $$0.0159403\pi$$
$$500$$ 0.385355 + 0.667454i 0.0172336 + 0.0298495i
$$501$$ 0 0
$$502$$ 10.1747 0.454118
$$503$$ −6.83622 11.8407i −0.304812 0.527950i 0.672407 0.740181i $$-0.265260\pi$$
−0.977219 + 0.212231i $$0.931927\pi$$
$$504$$ 0 0
$$505$$ −11.1301 −0.495281
$$506$$ 9.00474 0.400310
$$507$$ 0 0
$$508$$ −2.35834 + 4.08476i −0.104634 + 0.181232i
$$509$$ −3.86196 6.68912i −0.171179 0.296490i 0.767654 0.640865i $$-0.221424\pi$$
−0.938832 + 0.344375i $$0.888091\pi$$
$$510$$ 0 0
$$511$$ −12.4807 + 21.6171i −0.552112 + 0.956285i
$$512$$ 0.249240 0.0110150
$$513$$ 0 0
$$514$$ −0.204211 −0.00900736
$$515$$ 5.78953 10.0278i 0.255117 0.441876i
$$516$$ 0 0
$$517$$ 25.7651 + 44.6265i 1.13315 + 1.96267i
$$518$$ −5.86521 + 10.1588i −0.257703 + 0.446354i
$$519$$ 0 0
$$520$$ −3.26372 −0.143124
$$521$$ 2.16876 0.0950151 0.0475075 0.998871i $$-0.484872\pi$$
0.0475075 + 0.998871i $$0.484872\pi$$
$$522$$ 0 0
$$523$$ 11.9466 + 20.6921i 0.522389 + 0.904804i 0.999661 + 0.0260485i $$0.00829243\pi$$
−0.477272 + 0.878756i $$0.658374\pi$$
$$524$$ 11.4690 0.501026
$$525$$ 0 0
$$526$$ −8.37310 14.5026i −0.365085 0.632345i
$$527$$ 15.7654 27.3065i 0.686751 1.18949i
$$528$$ 0 0
$$529$$ 11.0582 19.1533i 0.480790 0.832752i
$$530$$ 1.82799 3.16617i 0.0794029 0.137530i
$$531$$ 0 0
$$532$$ −6.94067 + 4.33101i −0.300916 + 0.187773i
$$533$$ −10.0730 −0.436312
$$534$$ 0 0
$$535$$ −8.95887 + 15.5172i −0.387326 + 0.670868i
$$536$$ 1.03290 + 1.78904i 0.0446147 + 0.0772749i
$$537$$ 0 0
$$538$$ 4.75418 + 8.23448i 0.204967 + 0.355013i
$$539$$ −6.15492 −0.265111
$$540$$ 0 0
$$541$$ −21.2275 36.7671i −0.912641 1.58074i −0.810319 0.585990i $$-0.800706\pi$$
−0.102323 0.994751i $$-0.532627\pi$$
$$542$$ 10.5792 + 18.3237i 0.454415 + 0.787069i
$$543$$ 0 0
$$544$$ −24.7907 −1.06289
$$545$$ 2.81235 + 4.87113i 0.120468 + 0.208656i
$$546$$ 0 0
$$547$$ −6.01535 10.4189i −0.257198 0.445480i 0.708292 0.705919i $$-0.249466\pi$$
−0.965490 + 0.260439i $$0.916133\pi$$
$$548$$ 6.68604 11.5806i 0.285614 0.494697i
$$549$$ 0 0
$$550$$ 9.57907 0.408453
$$551$$ −9.68259 + 6.04198i −0.412492 + 0.257397i
$$552$$ 0 0
$$553$$ 9.25956 16.0380i 0.393756 0.682006i
$$554$$ −14.6496 + 25.3739i −0.622403 + 1.07803i
$$555$$ 0 0
$$556$$ 2.58394 4.47551i 0.109583 0.189804i
$$557$$ −4.37635 7.58006i −0.185432 0.321178i 0.758290 0.651917i $$-0.226035\pi$$
−0.943722 + 0.330740i $$0.892702\pi$$
$$558$$ 0 0
$$559$$ −7.24011 −0.306224
$$560$$ 6.02412 + 10.4341i 0.254566 + 0.440921i
$$561$$ 0 0
$$562$$ 34.1238 1.43943
$$563$$ 35.9707 1.51598 0.757991 0.652265i $$-0.226181\pi$$
0.757991 + 0.652265i $$0.226181\pi$$
$$564$$ 0 0
$$565$$ 7.83943 13.5783i 0.329807 0.571243i
$$566$$ 9.86750 + 17.0910i 0.414762 + 0.718389i
$$567$$ 0 0
$$568$$ −9.03798 + 15.6542i −0.379225 + 0.656837i
$$569$$ 20.3125 0.851543 0.425772 0.904831i $$-0.360003\pi$$
0.425772 + 0.904831i $$0.360003\pi$$
$$570$$ 0 0
$$571$$ 10.1773 0.425906 0.212953 0.977062i $$-0.431692\pi$$
0.212953 + 0.977062i $$0.431692\pi$$
$$572$$ 3.53714 6.12650i 0.147895 0.256162i
$$573$$ 0 0
$$574$$ 12.7999 + 22.1701i 0.534258 + 0.925362i
$$575$$ −0.470022 + 0.814102i −0.0196013 + 0.0339504i
$$576$$ 0 0
$$577$$ −32.7441 −1.36316 −0.681578 0.731745i $$-0.738706\pi$$
−0.681578 + 0.731745i $$0.738706\pi$$
$$578$$ 31.3083 1.30225
$$579$$ 0 0
$$580$$ −1.00899 1.74762i −0.0418960 0.0725660i
$$581$$ 7.58228 0.314566
$$582$$ 0 0
$$583$$ −6.31984 10.9463i −0.261741 0.453349i
$$584$$ −10.4868 + 18.1637i −0.433947 + 0.751618i
$$585$$ 0 0
$$586$$ −20.7913 + 36.0117i −0.858883 + 1.48763i
$$587$$ 4.38663 7.59786i 0.181056 0.313597i −0.761185 0.648535i $$-0.775382\pi$$
0.942240 + 0.334938i $$0.108715\pi$$
$$588$$ 0 0
$$589$$ −0.787274 22.9541i −0.0324390 0.945808i
$$590$$ −17.9751 −0.740021
$$591$$ 0 0
$$592$$ −7.15852 + 12.3989i −0.294213 + 0.509592i
$$593$$ −16.1603 27.9905i −0.663625 1.14943i −0.979656 0.200684i $$-0.935684\pi$$
0.316031 0.948749i $$-0.397650\pi$$
$$594$$ 0 0
$$595$$ −7.28635 12.6203i −0.298711 0.517383i
$$596$$ −11.0927 −0.454375
$$597$$ 0 0
$$598$$ 1.24789 + 2.16141i 0.0510301 + 0.0883868i
$$599$$ −9.77520 16.9311i −0.399404 0.691787i 0.594249 0.804281i $$-0.297449\pi$$
−0.993652 + 0.112494i $$0.964116\pi$$
$$600$$ 0 0
$$601$$ −0.401837 −0.0163913 −0.00819564 0.999966i $$-0.502609\pi$$
−0.00819564 + 0.999966i $$0.502609\pi$$
$$602$$ 9.20008 + 15.9350i 0.374967 + 0.649462i
$$603$$ 0 0
$$604$$ −4.90243 8.49126i −0.199477 0.345505i
$$605$$ 11.0587 19.1542i 0.449599 0.778728i
$$606$$ 0 0
$$607$$ 13.4453 0.545727 0.272863 0.962053i $$-0.412029\pi$$
0.272863 + 0.962053i $$0.412029\pi$$
$$608$$ −15.3200 + 9.55976i −0.621309 + 0.387700i
$$609$$ 0 0
$$610$$ −8.76274 + 15.1775i −0.354793 + 0.614519i
$$611$$ −7.14115 + 12.3688i −0.288900 + 0.500390i
$$612$$ 0 0
$$613$$ 10.3527 17.9313i 0.418140 0.724239i −0.577613 0.816311i $$-0.696016\pi$$
0.995752 + 0.0920716i $$0.0293489\pi$$
$$614$$ −14.0820 24.3907i −0.568303 0.984330i
$$615$$ 0 0
$$616$$ 28.6762 1.15540
$$617$$ −4.63936 8.03560i −0.186773 0.323501i 0.757399 0.652952i $$-0.226470\pi$$
−0.944173 + 0.329451i $$0.893136\pi$$
$$618$$ 0 0
$$619$$ −2.89129 −0.116211 −0.0581053 0.998310i $$-0.518506\pi$$
−0.0581053 + 0.998310i $$0.518506\pi$$
$$620$$ 4.06097 0.163093
$$621$$ 0 0
$$622$$ −12.6616 + 21.9306i −0.507686 + 0.879338i
$$623$$ 13.5329 + 23.4396i 0.542183 + 0.939088i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 41.4926 1.65838
$$627$$ 0 0
$$628$$ −2.60138 −0.103806
$$629$$ 8.65844 14.9969i 0.345234 0.597964i
$$630$$ 0 0
$$631$$ −15.2270 26.3740i −0.606178 1.04993i −0.991864 0.127301i $$-0.959369\pi$$
0.385686 0.922630i $$-0.373965\pi$$
$$632$$ 7.78029 13.4759i 0.309483 0.536041i
$$633$$ 0 0
$$634$$ 41.9972 1.66792
$$635$$ −6.11991 −0.242861
$$636$$ 0 0
$$637$$ −0.852959 1.47737i −0.0337955 0.0585355i
$$638$$ −25.0812 −0.992975
$$639$$ 0 0
$$640$$ 6.63877 + 11.4987i 0.262420 + 0.454525i
$$641$$ −10.0369 + 17.3845i −0.396434 + 0.686645i −0.993283 0.115709i $$-0.963086\pi$$
0.596849 + 0.802354i $$0.296419\pi$$
$$642$$ 0 0
$$643$$ 1.04457 1.80924i 0.0411937 0.0713496i −0.844693 0.535250i $$-0.820217\pi$$
0.885887 + 0.463901i $$0.153551\pi$$
$$644$$ 0.882172 1.52797i 0.0347625 0.0602103i
$$645$$ 0 0
$$646$$ 36.8347 22.9850i 1.44924 0.904334i
$$647$$ 2.10623 0.0828043 0.0414021 0.999143i $$-0.486818\pi$$
0.0414021 + 0.999143i $$0.486818\pi$$
$$648$$ 0 0
$$649$$ −31.0722 + 53.8187i −1.21969 + 2.11257i
$$650$$ 1.32748 + 2.29927i 0.0520682 + 0.0901847i
$$651$$ 0 0
$$652$$ −0.118674 0.205549i −0.00464763 0.00804994i
$$653$$ −1.83067 −0.0716395 −0.0358197 0.999358i $$-0.511404\pi$$
−0.0358197 + 0.999358i $$0.511404\pi$$
$$654$$ 0 0
$$655$$ 7.44055 + 12.8874i 0.290726 + 0.503553i
$$656$$ 15.6223 + 27.0587i 0.609950 + 1.05646i
$$657$$ 0 0
$$658$$ 36.2973 1.41502
$$659$$ 12.0268 + 20.8310i 0.468497 + 0.811460i 0.999352 0.0360024i $$-0.0114624\pi$$
−0.530855 + 0.847463i $$0.678129\pi$$
$$660$$ 0 0
$$661$$ 8.72110 + 15.1054i 0.339211 + 0.587531i 0.984285 0.176589i $$-0.0565065\pi$$
−0.645073 + 0.764121i $$0.723173\pi$$
$$662$$ 16.8172 29.1282i 0.653617 1.13210i
$$663$$ 0 0
$$664$$ 6.37097 0.247241
$$665$$ −9.36941 4.98929i −0.363330 0.193476i
$$666$$ 0 0
$$667$$ 1.23068 2.13159i 0.0476519 0.0825356i
$$668$$ 5.49682 9.52077i 0.212678 0.368370i
$$669$$ 0 0
$$670$$ 0.840244 1.45535i 0.0324615 0.0562249i
$$671$$ 30.2951 + 52.4726i 1.16953 + 2.02568i
$$672$$ 0 0
$$673$$ 47.5187 1.83171 0.915856 0.401506i $$-0.131513\pi$$
0.915856 + 0.401506i $$0.131513\pi$$
$$674$$ 26.4868 + 45.8765i 1.02023 + 1.76709i
$$675$$ 0 0
$$676$$ −8.05850 −0.309942
$$677$$ −14.5531 −0.559321 −0.279661 0.960099i $$-0.590222\pi$$
−0.279661 + 0.960099i $$0.590222\pi$$
$$678$$ 0 0
$$679$$ 4.94084 8.55778i 0.189612 0.328418i
$$680$$ −6.12231 10.6042i −0.234780 0.406651i
$$681$$ 0 0
$$682$$ 25.2367 43.7112i 0.966363 1.67379i
$$683$$ −3.33714 −0.127692 −0.0638460 0.997960i $$-0.520337\pi$$
−0.0638460 + 0.997960i $$0.520337\pi$$
$$684$$ 0 0
$$685$$ 17.3504 0.662923
$$686$$ −16.3553 + 28.3282i −0.624448 + 1.08158i
$$687$$ 0 0
$$688$$ 11.2287 + 19.4487i 0.428092 + 0.741476i
$$689$$ 1.75163 3.03391i 0.0667318 0.115583i
$$690$$ 0 0
$$691$$ −19.3318 −0.735415 −0.367708 0.929941i $$-0.619857\pi$$
−0.367708 + 0.929941i $$0.619857\pi$$
$$692$$ −10.2868 −0.391044
$$693$$ 0 0
$$694$$ −2.74862 4.76075i −0.104336 0.180716i
$$695$$ 6.70534 0.254348
$$696$$ 0 0
$$697$$ −18.8957 32.7283i −0.715725 1.23967i
$$698$$ −14.8549 + 25.7295i −0.562268 + 0.973876i
$$699$$ 0 0
$$700$$ 0.938437 1.62542i 0.0354696 0.0614351i
$$701$$ 4.96892 8.60643i 0.187674 0.325060i −0.756801 0.653646i $$-0.773239\pi$$
0.944474 + 0.328586i $$0.106572\pi$$
$$702$$ 0 0
$$703$$ −0.432375 12.6065i −0.0163073 0.475464i
$$704$$ 17.2584 0.650452
$$705$$ 0 0
$$706$$ −6.90389 + 11.9579i −0.259831 + 0.450041i
$$707$$ 13.5523 + 23.4732i 0.509686 + 0.882801i
$$708$$ 0 0
$$709$$ −18.6059 32.2264i −0.698760 1.21029i −0.968897 0.247466i $$-0.920402\pi$$
0.270136 0.962822i $$-0.412931\pi$$
$$710$$ 14.7044 0.551846
$$711$$ 0 0
$$712$$ 11.3709 + 19.6950i 0.426143 + 0.738101i
$$713$$ 2.47661 + 4.28961i 0.0927497 + 0.160647i
$$714$$ 0 0
$$715$$ 9.17891 0.343272
$$716$$ −5.48003 9.49169i −0.204798 0.354721i
$$717$$ 0 0
$$718$$ 6.94966 + 12.0372i 0.259359 + 0.449223i
$$719$$ −1.32109 + 2.28819i −0.0492683 + 0.0853351i −0.889608 0.456725i $$-0.849022\pi$$
0.840340 + 0.542060i $$0.182356\pi$$
$$720$$ 0 0
$$721$$ −28.1980 −1.05015
$$722$$ 13.8995 28.4083i 0.517284 1.05725i
$$723$$ 0 0
$$724$$ −3.80832 + 6.59621i −0.141535 + 0.245146i
$$725$$ 1.30917 2.26755i 0.0486213 0.0842145i
$$726$$ 0 0
$$727$$ 5.08653 8.81013i 0.188649 0.326750i −0.756151 0.654397i $$-0.772923\pi$$
0.944800 + 0.327647i $$0.106256\pi$$
$$728$$ 3.97400 + 6.88317i 0.147286 + 0.255107i
$$729$$ 0 0
$$730$$ 17.0615 0.631476
$$731$$ −13.5815 23.5238i −0.502329 0.870060i
$$732$$ 0 0
$$733$$ 14.8222 0.547472 0.273736 0.961805i $$-0.411741\pi$$
0.273736 + 0.961805i $$0.411741\pi$$
$$734$$ 24.0023 0.885942
$$735$$ 0 0
$$736$$ 1.94720 3.37266i 0.0717749 0.124318i
$$737$$ −2.90494 5.03151i −0.107005 0.185338i
$$738$$ 0 0
$$739$$ −17.7433 + 30.7323i −0.652697 + 1.13050i 0.329769 + 0.944062i $$0.393029\pi$$
−0.982466 + 0.186443i $$0.940304\pi$$
$$740$$ 2.23031 0.0819877
$$741$$ 0 0
$$742$$ −8.90325 −0.326849
$$743$$ −4.36941 + 7.56804i −0.160298 + 0.277645i −0.934976 0.354712i $$-0.884579\pi$$
0.774677 + 0.632357i $$0.217912\pi$$
$$744$$ 0 0
$$745$$ −7.19642 12.4646i −0.263656 0.456666i
$$746$$ 20.0708 34.7637i 0.734846 1.27279i
$$747$$ 0 0
$$748$$ 26.5408 0.970428
$$749$$ 43.6342 1.59436
$$750$$ 0 0
$$751$$ −6.54957 11.3442i −0.238997 0.413955i 0.721430 0.692488i $$-0.243485\pi$$
−0.960427 + 0.278533i $$0.910152\pi$$
$$752$$ 44.3011 1.61549
$$753$$ 0 0
$$754$$ −3.47580 6.02026i −0.126581 0.219245i
$$755$$ 6.36093 11.0175i 0.231498 0.400966i
$$756$$ 0 0
$$757$$ 8.21901 14.2357i 0.298725 0.517407i −0.677119 0.735873i $$-0.736772\pi$$
0.975845 + 0.218466i $$0.0701053\pi$$
$$758$$ −13.8787 + 24.0386i −0.504097 + 0.873121i
$$759$$ 0 0
$$760$$ −7.87259 4.19222i −0.285569 0.152068i
$$761$$ −16.3918 −0.594203 −0.297101 0.954846i $$-0.596020\pi$$
−0.297101 + 0.954846i $$0.596020\pi$$
$$762$$ 0 0
$$763$$ 6.84879 11.8625i 0.247943 0.429450i
$$764$$ −5.00738 8.67304i −0.181161 0.313780i
$$765$$ 0 0
$$766$$ −9.05337 15.6809i −0.327112 0.566574i
$$767$$ −17.2242 −0.621929
$$768$$ 0 0
$$769$$ 25.0210 + 43.3377i 0.902282 + 1.56280i 0.824525 + 0.565825i $$0.191442\pi$$
0.0777564 + 0.996972i $$0.475224\pi$$
$$770$$ −11.6637 20.2022i −0.420332 0.728036i
$$771$$ 0 0
$$772$$ 11.1875 0.402649
$$773$$ 24.3436 + 42.1644i 0.875580 + 1.51655i 0.856144 + 0.516737i $$0.172854\pi$$
0.0194356 + 0.999811i $$0.493813\pi$$
$$774$$ 0 0
$$775$$ 2.63457 + 4.56320i 0.0946364 + 0.163915i
$$776$$ 4.15151 7.19063i 0.149031 0.258129i
$$777$$ 0 0
$$778$$ −60.6799 −2.17548
$$779$$ −24.2977 12.9387i −0.870555 0.463577i
$$780$$ 0 0
$$781$$ 25.4185 44.0261i 0.909544 1.57538i
$$782$$ −4.68176 + 8.10905i −0.167419 + 0.289979i
$$783$$ 0 0