# Properties

 Label 666.2.be.b.125.1 Level $666$ Weight $2$ Character 666.125 Analytic conductor $5.318$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(125,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

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

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

chi := DirichletCharacter("666.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$666 = 2 \cdot 3^{2} \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 666.be (of order $$12$$, degree $$4$$, 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: $$5.31803677462$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$2$$ over $$\Q(\zeta_{12})$$ Coefficient field: $$\Q(\zeta_{24})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - x^{4} + 1$$ x^8 - x^4 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 125.1 Root $$0.965926 - 0.258819i$$ of defining polynomial Character $$\chi$$ $$=$$ 666.125 Dual form 666.2.be.b.341.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.896575 - 3.34607i) q^{5} +(0.500000 + 0.866025i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$$ $$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.896575 - 3.34607i) q^{5} +(0.500000 + 0.866025i) q^{7} +(0.707107 + 0.707107i) q^{8} -3.46410 q^{10} +3.86370 q^{11} +(5.59808 + 1.50000i) q^{13} +(0.707107 - 0.707107i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.63896 - 0.707107i) q^{17} +(-6.09808 - 1.63397i) q^{19} +(0.896575 + 3.34607i) q^{20} +(-1.00000 - 3.73205i) q^{22} +(-1.93185 - 1.93185i) q^{23} +(-6.06218 - 3.50000i) q^{25} -5.79555i q^{26} +(-0.866025 - 0.500000i) q^{28} +(0.138701 - 0.138701i) q^{29} +(-3.63397 - 3.63397i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.36603 - 2.36603i) q^{34} +(3.34607 - 0.896575i) q^{35} +(6.00000 - 1.00000i) q^{37} +6.31319i q^{38} +(3.00000 - 1.73205i) q^{40} +(1.03528 + 1.79315i) q^{41} +(-7.56218 + 7.56218i) q^{43} +(-3.34607 + 1.93185i) q^{44} +(-1.36603 + 2.36603i) q^{46} -8.76268i q^{47} +(3.00000 - 5.19615i) q^{49} +(-1.81173 + 6.76148i) q^{50} +(-5.59808 + 1.50000i) q^{52} +(-2.44949 - 1.41421i) q^{53} +(3.46410 - 12.9282i) q^{55} +(-0.258819 + 0.965926i) q^{56} +(-0.169873 - 0.0980762i) q^{58} +(4.57081 - 1.22474i) q^{59} +(-0.633975 + 2.36603i) q^{61} +(-2.56961 + 4.45069i) q^{62} +1.00000i q^{64} +(10.0382 - 17.3867i) q^{65} +(-2.59808 + 1.50000i) q^{67} +(-1.93185 + 1.93185i) q^{68} +(-1.73205 - 3.00000i) q^{70} +(2.44949 - 1.41421i) q^{71} +15.3923i q^{73} +(-2.51884 - 5.53674i) q^{74} +(6.09808 - 1.63397i) q^{76} +(1.93185 + 3.34607i) q^{77} +(-0.133975 - 0.0358984i) q^{79} +(-2.44949 - 2.44949i) q^{80} +(1.46410 - 1.46410i) q^{82} +(-13.9527 - 8.05558i) q^{83} -9.46410i q^{85} +(9.26174 + 5.34727i) q^{86} +(2.73205 + 2.73205i) q^{88} +(2.17209 + 8.10634i) q^{89} +(1.50000 + 5.59808i) q^{91} +(2.63896 + 0.707107i) q^{92} +(-8.46410 + 2.26795i) q^{94} +(-10.9348 + 18.9396i) q^{95} +(11.0263 - 11.0263i) q^{97} +(-5.79555 - 1.55291i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4 q^{7}+O(q^{10})$$ 8 * q + 4 * q^7 $$8 q + 4 q^{7} + 24 q^{13} + 4 q^{16} - 28 q^{19} - 8 q^{22} - 36 q^{31} - 4 q^{34} + 48 q^{37} + 24 q^{40} - 12 q^{43} - 4 q^{46} + 24 q^{49} - 24 q^{52} - 36 q^{58} - 12 q^{61} + 28 q^{76} - 8 q^{79} - 16 q^{82} + 8 q^{88} + 12 q^{91} - 40 q^{94} + 12 q^{97}+O(q^{100})$$ 8 * q + 4 * q^7 + 24 * q^13 + 4 * q^16 - 28 * q^19 - 8 * q^22 - 36 * q^31 - 4 * q^34 + 48 * q^37 + 24 * q^40 - 12 * q^43 - 4 * q^46 + 24 * q^49 - 24 * q^52 - 36 * q^58 - 12 * q^61 + 28 * q^76 - 8 * q^79 - 16 * q^82 + 8 * q^88 + 12 * q^91 - 40 * q^94 + 12 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$$.

 $$n$$ $$371$$ $$631$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.258819 0.965926i −0.183013 0.683013i
$$3$$ 0 0
$$4$$ −0.866025 + 0.500000i −0.433013 + 0.250000i
$$5$$ 0.896575 3.34607i 0.400961 1.49641i −0.410425 0.911894i $$-0.634620\pi$$
0.811386 0.584511i $$-0.198714\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i $$-0.106148\pi$$
−0.755929 + 0.654654i $$0.772814\pi$$
$$8$$ 0.707107 + 0.707107i 0.250000 + 0.250000i
$$9$$ 0 0
$$10$$ −3.46410 −1.09545
$$11$$ 3.86370 1.16495 0.582475 0.812848i $$-0.302084\pi$$
0.582475 + 0.812848i $$0.302084\pi$$
$$12$$ 0 0
$$13$$ 5.59808 + 1.50000i 1.55263 + 0.416025i 0.930320 0.366748i $$-0.119529\pi$$
0.622307 + 0.782773i $$0.286196\pi$$
$$14$$ 0.707107 0.707107i 0.188982 0.188982i
$$15$$ 0 0
$$16$$ 0.500000 0.866025i 0.125000 0.216506i
$$17$$ 2.63896 0.707107i 0.640041 0.171499i 0.0758192 0.997122i $$-0.475843\pi$$
0.564222 + 0.825623i $$0.309176\pi$$
$$18$$ 0 0
$$19$$ −6.09808 1.63397i −1.39899 0.374859i −0.521011 0.853550i $$-0.674445\pi$$
−0.877984 + 0.478691i $$0.841112\pi$$
$$20$$ 0.896575 + 3.34607i 0.200480 + 0.748203i
$$21$$ 0 0
$$22$$ −1.00000 3.73205i −0.213201 0.795676i
$$23$$ −1.93185 1.93185i −0.402819 0.402819i 0.476406 0.879225i $$-0.341939\pi$$
−0.879225 + 0.476406i $$0.841939\pi$$
$$24$$ 0 0
$$25$$ −6.06218 3.50000i −1.21244 0.700000i
$$26$$ 5.79555i 1.13660i
$$27$$ 0 0
$$28$$ −0.866025 0.500000i −0.163663 0.0944911i
$$29$$ 0.138701 0.138701i 0.0257561 0.0257561i −0.694111 0.719868i $$-0.744203\pi$$
0.719868 + 0.694111i $$0.244203\pi$$
$$30$$ 0 0
$$31$$ −3.63397 3.63397i −0.652681 0.652681i 0.300957 0.953638i $$-0.402694\pi$$
−0.953638 + 0.300957i $$0.902694\pi$$
$$32$$ −0.965926 0.258819i −0.170753 0.0457532i
$$33$$ 0 0
$$34$$ −1.36603 2.36603i −0.234271 0.405770i
$$35$$ 3.34607 0.896575i 0.565588 0.151549i
$$36$$ 0 0
$$37$$ 6.00000 1.00000i 0.986394 0.164399i
$$38$$ 6.31319i 1.02414i
$$39$$ 0 0
$$40$$ 3.00000 1.73205i 0.474342 0.273861i
$$41$$ 1.03528 + 1.79315i 0.161683 + 0.280043i 0.935472 0.353400i $$-0.114974\pi$$
−0.773789 + 0.633443i $$0.781641\pi$$
$$42$$ 0 0
$$43$$ −7.56218 + 7.56218i −1.15322 + 1.15322i −0.167318 + 0.985903i $$0.553511\pi$$
−0.985903 + 0.167318i $$0.946489\pi$$
$$44$$ −3.34607 + 1.93185i −0.504438 + 0.291238i
$$45$$ 0 0
$$46$$ −1.36603 + 2.36603i −0.201409 + 0.348851i
$$47$$ 8.76268i 1.27817i −0.769137 0.639084i $$-0.779313\pi$$
0.769137 0.639084i $$-0.220687\pi$$
$$48$$ 0 0
$$49$$ 3.00000 5.19615i 0.428571 0.742307i
$$50$$ −1.81173 + 6.76148i −0.256218 + 0.956218i
$$51$$ 0 0
$$52$$ −5.59808 + 1.50000i −0.776313 + 0.208013i
$$53$$ −2.44949 1.41421i −0.336463 0.194257i 0.322244 0.946657i $$-0.395563\pi$$
−0.658707 + 0.752400i $$0.728896\pi$$
$$54$$ 0 0
$$55$$ 3.46410 12.9282i 0.467099 1.74324i
$$56$$ −0.258819 + 0.965926i −0.0345861 + 0.129077i
$$57$$ 0 0
$$58$$ −0.169873 0.0980762i −0.0223054 0.0128780i
$$59$$ 4.57081 1.22474i 0.595069 0.159448i 0.0513000 0.998683i $$-0.483664\pi$$
0.543769 + 0.839235i $$0.316997\pi$$
$$60$$ 0 0
$$61$$ −0.633975 + 2.36603i −0.0811721 + 0.302939i −0.994562 0.104148i $$-0.966789\pi$$
0.913390 + 0.407086i $$0.133455\pi$$
$$62$$ −2.56961 + 4.45069i −0.326341 + 0.565238i
$$63$$ 0 0
$$64$$ 1.00000i 0.125000i
$$65$$ 10.0382 17.3867i 1.24508 2.15655i
$$66$$ 0 0
$$67$$ −2.59808 + 1.50000i −0.317406 + 0.183254i −0.650236 0.759733i $$-0.725330\pi$$
0.332830 + 0.942987i $$0.391996\pi$$
$$68$$ −1.93185 + 1.93185i −0.234271 + 0.234271i
$$69$$ 0 0
$$70$$ −1.73205 3.00000i −0.207020 0.358569i
$$71$$ 2.44949 1.41421i 0.290701 0.167836i −0.347557 0.937659i $$-0.612989\pi$$
0.638258 + 0.769823i $$0.279655\pi$$
$$72$$ 0 0
$$73$$ 15.3923i 1.80153i 0.434304 + 0.900767i $$0.356994\pi$$
−0.434304 + 0.900767i $$0.643006\pi$$
$$74$$ −2.51884 5.53674i −0.292809 0.643632i
$$75$$ 0 0
$$76$$ 6.09808 1.63397i 0.699497 0.187430i
$$77$$ 1.93185 + 3.34607i 0.220155 + 0.381320i
$$78$$ 0 0
$$79$$ −0.133975 0.0358984i −0.0150733 0.00403888i 0.251275 0.967916i $$-0.419150\pi$$
−0.266348 + 0.963877i $$0.585817\pi$$
$$80$$ −2.44949 2.44949i −0.273861 0.273861i
$$81$$ 0 0
$$82$$ 1.46410 1.46410i 0.161683 0.161683i
$$83$$ −13.9527 8.05558i −1.53150 0.884214i −0.999293 0.0376028i $$-0.988028\pi$$
−0.532211 0.846611i $$-0.678639\pi$$
$$84$$ 0 0
$$85$$ 9.46410i 1.02653i
$$86$$ 9.26174 + 5.34727i 0.998719 + 0.576611i
$$87$$ 0 0
$$88$$ 2.73205 + 2.73205i 0.291238 + 0.291238i
$$89$$ 2.17209 + 8.10634i 0.230241 + 0.859271i 0.980237 + 0.197828i $$0.0633888\pi$$
−0.749996 + 0.661443i $$0.769945\pi$$
$$90$$ 0 0
$$91$$ 1.50000 + 5.59808i 0.157243 + 0.586838i
$$92$$ 2.63896 + 0.707107i 0.275130 + 0.0737210i
$$93$$ 0 0
$$94$$ −8.46410 + 2.26795i −0.873005 + 0.233921i
$$95$$ −10.9348 + 18.9396i −1.12188 + 1.94316i
$$96$$ 0 0
$$97$$ 11.0263 11.0263i 1.11955 1.11955i 0.127742 0.991807i $$-0.459227\pi$$
0.991807 0.127742i $$-0.0407728\pi$$
$$98$$ −5.79555 1.55291i −0.585439 0.156868i
$$99$$ 0 0
$$100$$ 7.00000 0.700000
$$101$$ −16.8690 −1.67853 −0.839265 0.543722i $$-0.817015\pi$$
−0.839265 + 0.543722i $$0.817015\pi$$
$$102$$ 0 0
$$103$$ 13.3923 + 13.3923i 1.31958 + 1.31958i 0.914105 + 0.405478i $$0.132895\pi$$
0.405478 + 0.914105i $$0.367105\pi$$
$$104$$ 2.89778 + 5.01910i 0.284150 + 0.492163i
$$105$$ 0 0
$$106$$ −0.732051 + 2.73205i −0.0711031 + 0.265360i
$$107$$ −1.13681 + 0.656339i −0.109900 + 0.0634507i −0.553942 0.832555i $$-0.686877\pi$$
0.444043 + 0.896006i $$0.353544\pi$$
$$108$$ 0 0
$$109$$ 3.33013 + 12.4282i 0.318968 + 1.19041i 0.920238 + 0.391360i $$0.127995\pi$$
−0.601269 + 0.799046i $$0.705338\pi$$
$$110$$ −13.3843 −1.27614
$$111$$ 0 0
$$112$$ 1.00000 0.0944911
$$113$$ 3.62347 + 13.5230i 0.340867 + 1.27213i 0.897367 + 0.441285i $$0.145477\pi$$
−0.556500 + 0.830848i $$0.687856\pi$$
$$114$$ 0 0
$$115$$ −8.19615 + 4.73205i −0.764295 + 0.441266i
$$116$$ −0.0507680 + 0.189469i −0.00471369 + 0.0175917i
$$117$$ 0 0
$$118$$ −2.36603 4.09808i −0.217810 0.377258i
$$119$$ 1.93185 + 1.93185i 0.177093 + 0.177093i
$$120$$ 0 0
$$121$$ 3.92820 0.357109
$$122$$ 2.44949 0.221766
$$123$$ 0 0
$$124$$ 4.96410 + 1.33013i 0.445789 + 0.119449i
$$125$$ −4.89898 + 4.89898i −0.438178 + 0.438178i
$$126$$ 0 0
$$127$$ 0.133975 0.232051i 0.0118883 0.0205912i −0.860020 0.510260i $$-0.829549\pi$$
0.871908 + 0.489669i $$0.162882\pi$$
$$128$$ 0.965926 0.258819i 0.0853766 0.0228766i
$$129$$ 0 0
$$130$$ −19.3923 5.19615i −1.70082 0.455733i
$$131$$ 1.08604 + 4.05317i 0.0948881 + 0.354127i 0.997002 0.0773698i $$-0.0246522\pi$$
−0.902114 + 0.431497i $$0.857986\pi$$
$$132$$ 0 0
$$133$$ −1.63397 6.09808i −0.141684 0.528770i
$$134$$ 2.12132 + 2.12132i 0.183254 + 0.183254i
$$135$$ 0 0
$$136$$ 2.36603 + 1.36603i 0.202885 + 0.117136i
$$137$$ 13.3843i 1.14349i −0.820430 0.571747i $$-0.806266\pi$$
0.820430 0.571747i $$-0.193734\pi$$
$$138$$ 0 0
$$139$$ 8.59808 + 4.96410i 0.729279 + 0.421050i 0.818158 0.574993i $$-0.194995\pi$$
−0.0888792 + 0.996042i $$0.528328\pi$$
$$140$$ −2.44949 + 2.44949i −0.207020 + 0.207020i
$$141$$ 0 0
$$142$$ −2.00000 2.00000i −0.167836 0.167836i
$$143$$ 21.6293 + 5.79555i 1.80873 + 0.484649i
$$144$$ 0 0
$$145$$ −0.339746 0.588457i −0.0282144 0.0488687i
$$146$$ 14.8678 3.98382i 1.23047 0.329703i
$$147$$ 0 0
$$148$$ −4.69615 + 3.86603i −0.386021 + 0.317785i
$$149$$ 7.07107i 0.579284i −0.957135 0.289642i $$-0.906464\pi$$
0.957135 0.289642i $$-0.0935363\pi$$
$$150$$ 0 0
$$151$$ −9.40192 + 5.42820i −0.765118 + 0.441741i −0.831130 0.556078i $$-0.812306\pi$$
0.0660125 + 0.997819i $$0.478972\pi$$
$$152$$ −3.15660 5.46739i −0.256034 0.443464i
$$153$$ 0 0
$$154$$ 2.73205 2.73205i 0.220155 0.220155i
$$155$$ −15.4176 + 8.90138i −1.23838 + 0.714976i
$$156$$ 0 0
$$157$$ 2.50000 4.33013i 0.199522 0.345582i −0.748852 0.662738i $$-0.769394\pi$$
0.948373 + 0.317156i $$0.102728\pi$$
$$158$$ 0.138701i 0.0110344i
$$159$$ 0 0
$$160$$ −1.73205 + 3.00000i −0.136931 + 0.237171i
$$161$$ 0.707107 2.63896i 0.0557278 0.207979i
$$162$$ 0 0
$$163$$ 2.83013 0.758330i 0.221673 0.0593970i −0.146273 0.989244i $$-0.546728\pi$$
0.367946 + 0.929847i $$0.380061\pi$$
$$164$$ −1.79315 1.03528i −0.140022 0.0808415i
$$165$$ 0 0
$$166$$ −4.16987 + 15.5622i −0.323645 + 1.20786i
$$167$$ −4.19187 + 15.6443i −0.324377 + 1.21059i 0.590560 + 0.806994i $$0.298907\pi$$
−0.914937 + 0.403597i $$0.867760\pi$$
$$168$$ 0 0
$$169$$ 17.8301 + 10.2942i 1.37155 + 0.791864i
$$170$$ −9.14162 + 2.44949i −0.701130 + 0.187867i
$$171$$ 0 0
$$172$$ 2.76795 10.3301i 0.211054 0.787665i
$$173$$ 12.2982 21.3011i 0.935016 1.61950i 0.160411 0.987050i $$-0.448718\pi$$
0.774605 0.632445i $$-0.217949\pi$$
$$174$$ 0 0
$$175$$ 7.00000i 0.529150i
$$176$$ 1.93185 3.34607i 0.145619 0.252219i
$$177$$ 0 0
$$178$$ 7.26795 4.19615i 0.544756 0.314515i
$$179$$ −6.31319 + 6.31319i −0.471870 + 0.471870i −0.902519 0.430649i $$-0.858285\pi$$
0.430649 + 0.902519i $$0.358285\pi$$
$$180$$ 0 0
$$181$$ 9.42820 + 16.3301i 0.700793 + 1.21381i 0.968188 + 0.250222i $$0.0805036\pi$$
−0.267396 + 0.963587i $$0.586163\pi$$
$$182$$ 5.01910 2.89778i 0.372040 0.214798i
$$183$$ 0 0
$$184$$ 2.73205i 0.201409i
$$185$$ 2.03339 20.9730i 0.149498 1.54196i
$$186$$ 0 0
$$187$$ 10.1962 2.73205i 0.745617 0.199787i
$$188$$ 4.38134 + 7.58871i 0.319542 + 0.553463i
$$189$$ 0 0
$$190$$ 21.1244 + 5.66025i 1.53252 + 0.410638i
$$191$$ 13.6245 + 13.6245i 0.985834 + 0.985834i 0.999901 0.0140670i $$-0.00447782\pi$$
−0.0140670 + 0.999901i $$0.504478\pi$$
$$192$$ 0 0
$$193$$ −4.56218 + 4.56218i −0.328393 + 0.328393i −0.851975 0.523582i $$-0.824595\pi$$
0.523582 + 0.851975i $$0.324595\pi$$
$$194$$ −13.5044 7.79676i −0.969558 0.559775i
$$195$$ 0 0
$$196$$ 6.00000i 0.428571i
$$197$$ −1.31268 0.757875i −0.0935244 0.0539963i 0.452508 0.891760i $$-0.350529\pi$$
−0.546033 + 0.837764i $$0.683863\pi$$
$$198$$ 0 0
$$199$$ 12.8301 + 12.8301i 0.909504 + 0.909504i 0.996232 0.0867284i $$-0.0276412\pi$$
−0.0867284 + 0.996232i $$0.527641\pi$$
$$200$$ −1.81173 6.76148i −0.128109 0.478109i
$$201$$ 0 0
$$202$$ 4.36603 + 16.2942i 0.307192 + 1.14646i
$$203$$ 0.189469 + 0.0507680i 0.0132981 + 0.00356321i
$$204$$ 0 0
$$205$$ 6.92820 1.85641i 0.483887 0.129657i
$$206$$ 9.46979 16.4022i 0.659792 1.14279i
$$207$$ 0 0
$$208$$ 4.09808 4.09808i 0.284150 0.284150i
$$209$$ −23.5612 6.31319i −1.62976 0.436693i
$$210$$ 0 0
$$211$$ 0.607695 0.0418355 0.0209177 0.999781i $$-0.493341\pi$$
0.0209177 + 0.999781i $$0.493341\pi$$
$$212$$ 2.82843 0.194257
$$213$$ 0 0
$$214$$ 0.928203 + 0.928203i 0.0634507 + 0.0634507i
$$215$$ 18.5235 + 32.0836i 1.26329 + 2.18808i
$$216$$ 0 0
$$217$$ 1.33013 4.96410i 0.0902949 0.336985i
$$218$$ 11.1428 6.43331i 0.754687 0.435719i
$$219$$ 0 0
$$220$$ 3.46410 + 12.9282i 0.233550 + 0.871619i
$$221$$ 15.8338 1.06509
$$222$$ 0 0
$$223$$ −13.5885 −0.909950 −0.454975 0.890504i $$-0.650352\pi$$
−0.454975 + 0.890504i $$0.650352\pi$$
$$224$$ −0.258819 0.965926i −0.0172931 0.0645386i
$$225$$ 0 0
$$226$$ 12.1244 7.00000i 0.806500 0.465633i
$$227$$ −2.60179 + 9.71003i −0.172687 + 0.644477i 0.824247 + 0.566231i $$0.191599\pi$$
−0.996934 + 0.0782466i $$0.975068\pi$$
$$228$$ 0 0
$$229$$ −0.330127 0.571797i −0.0218154 0.0377854i 0.854912 0.518774i $$-0.173611\pi$$
−0.876727 + 0.480988i $$0.840278\pi$$
$$230$$ 6.69213 + 6.69213i 0.441266 + 0.441266i
$$231$$ 0 0
$$232$$ 0.196152 0.0128780
$$233$$ −22.0454 −1.44424 −0.722121 0.691766i $$-0.756833\pi$$
−0.722121 + 0.691766i $$0.756833\pi$$
$$234$$ 0 0
$$235$$ −29.3205 7.85641i −1.91266 0.512495i
$$236$$ −3.34607 + 3.34607i −0.217810 + 0.217810i
$$237$$ 0 0
$$238$$ 1.36603 2.36603i 0.0885463 0.153367i
$$239$$ −0.845807 + 0.226633i −0.0547107 + 0.0146597i −0.286071 0.958209i $$-0.592349\pi$$
0.231360 + 0.972868i $$0.425683\pi$$
$$240$$ 0 0
$$241$$ −22.5263 6.03590i −1.45105 0.388806i −0.554658 0.832078i $$-0.687151\pi$$
−0.896387 + 0.443272i $$0.853818\pi$$
$$242$$ −1.01669 3.79435i −0.0653556 0.243910i
$$243$$ 0 0
$$244$$ −0.633975 2.36603i −0.0405861 0.151469i
$$245$$ −14.6969 14.6969i −0.938953 0.938953i
$$246$$ 0 0
$$247$$ −31.6865 18.2942i −2.01617 1.16403i
$$248$$ 5.13922i 0.326341i
$$249$$ 0 0
$$250$$ 6.00000 + 3.46410i 0.379473 + 0.219089i
$$251$$ 17.1464 17.1464i 1.08227 1.08227i 0.0859757 0.996297i $$-0.472599\pi$$
0.996297 0.0859757i $$-0.0274007\pi$$
$$252$$ 0 0
$$253$$ −7.46410 7.46410i −0.469264 0.469264i
$$254$$ −0.258819 0.0693504i −0.0162398 0.00435143i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ 0.896575 0.240237i 0.0559268 0.0149856i −0.230747 0.973014i $$-0.574117\pi$$
0.286674 + 0.958028i $$0.407450\pi$$
$$258$$ 0 0
$$259$$ 3.86603 + 4.69615i 0.240223 + 0.291805i
$$260$$ 20.0764i 1.24508i
$$261$$ 0 0
$$262$$ 3.63397 2.09808i 0.224508 0.129620i
$$263$$ 2.91636 + 5.05128i 0.179830 + 0.311475i 0.941822 0.336111i $$-0.109112\pi$$
−0.761992 + 0.647587i $$0.775778\pi$$
$$264$$ 0 0
$$265$$ −6.92820 + 6.92820i −0.425596 + 0.425596i
$$266$$ −5.46739 + 3.15660i −0.335227 + 0.193543i
$$267$$ 0 0
$$268$$ 1.50000 2.59808i 0.0916271 0.158703i
$$269$$ 14.4195i 0.879175i 0.898200 + 0.439587i $$0.144875\pi$$
−0.898200 + 0.439587i $$0.855125\pi$$
$$270$$ 0 0
$$271$$ 12.6244 21.8660i 0.766875 1.32827i −0.172375 0.985031i $$-0.555144\pi$$
0.939250 0.343235i $$-0.111523\pi$$
$$272$$ 0.707107 2.63896i 0.0428746 0.160010i
$$273$$ 0 0
$$274$$ −12.9282 + 3.46410i −0.781021 + 0.209274i
$$275$$ −23.4225 13.5230i −1.41243 0.815465i
$$276$$ 0 0
$$277$$ −4.90192 + 18.2942i −0.294528 + 1.09919i 0.647063 + 0.762436i $$0.275997\pi$$
−0.941591 + 0.336757i $$0.890670\pi$$
$$278$$ 2.56961 9.58991i 0.154115 0.575164i
$$279$$ 0 0
$$280$$ 3.00000 + 1.73205i 0.179284 + 0.103510i
$$281$$ −3.01790 + 0.808643i −0.180033 + 0.0482396i −0.347709 0.937603i $$-0.613040\pi$$
0.167676 + 0.985842i $$0.446374\pi$$
$$282$$ 0 0
$$283$$ −1.79423 + 6.69615i −0.106656 + 0.398045i −0.998528 0.0542431i $$-0.982725\pi$$
0.891872 + 0.452288i $$0.149392\pi$$
$$284$$ −1.41421 + 2.44949i −0.0839181 + 0.145350i
$$285$$ 0 0
$$286$$ 22.3923i 1.32408i
$$287$$ −1.03528 + 1.79315i −0.0611104 + 0.105846i
$$288$$ 0 0
$$289$$ −8.25833 + 4.76795i −0.485784 + 0.280468i
$$290$$ −0.480473 + 0.480473i −0.0282144 + 0.0282144i
$$291$$ 0 0
$$292$$ −7.69615 13.3301i −0.450383 0.780087i
$$293$$ −19.5080 + 11.2629i −1.13967 + 0.657988i −0.946349 0.323148i $$-0.895259\pi$$
−0.193320 + 0.981136i $$0.561926\pi$$
$$294$$ 0 0
$$295$$ 16.3923i 0.954397i
$$296$$ 4.94975 + 3.53553i 0.287698 + 0.205499i
$$297$$ 0 0
$$298$$ −6.83013 + 1.83013i −0.395659 + 0.106016i
$$299$$ −7.91688 13.7124i −0.457845 0.793010i
$$300$$ 0 0
$$301$$ −10.3301 2.76795i −0.595419 0.159542i
$$302$$ 7.67664 + 7.67664i 0.441741 + 0.441741i
$$303$$ 0 0
$$304$$ −4.46410 + 4.46410i −0.256034 + 0.256034i
$$305$$ 7.34847 + 4.24264i 0.420772 + 0.242933i
$$306$$ 0 0
$$307$$ 24.2679i 1.38505i −0.721396 0.692523i $$-0.756499\pi$$
0.721396 0.692523i $$-0.243501\pi$$
$$308$$ −3.34607 1.93185i −0.190660 0.110077i
$$309$$ 0 0
$$310$$ 12.5885 + 12.5885i 0.714976 + 0.714976i
$$311$$ 8.05558 + 30.0638i 0.456790 + 1.70476i 0.682772 + 0.730631i $$0.260774\pi$$
−0.225982 + 0.974131i $$0.572559\pi$$
$$312$$ 0 0
$$313$$ −6.57180 24.5263i −0.371460 1.38631i −0.858449 0.512899i $$-0.828571\pi$$
0.486989 0.873408i $$-0.338095\pi$$
$$314$$ −4.82963 1.29410i −0.272552 0.0730300i
$$315$$ 0 0
$$316$$ 0.133975 0.0358984i 0.00753666 0.00201944i
$$317$$ 9.71003 16.8183i 0.545369 0.944608i −0.453214 0.891402i $$-0.649723\pi$$
0.998584 0.0532059i $$-0.0169440\pi$$
$$318$$ 0 0
$$319$$ 0.535898 0.535898i 0.0300045 0.0300045i
$$320$$ 3.34607 + 0.896575i 0.187051 + 0.0501201i
$$321$$ 0 0
$$322$$ −2.73205 −0.152251
$$323$$ −17.2480 −0.959702
$$324$$ 0 0
$$325$$ −28.6865 28.6865i −1.59124 1.59124i
$$326$$ −1.46498 2.53742i −0.0811378 0.140535i
$$327$$ 0 0
$$328$$ −0.535898 + 2.00000i −0.0295900 + 0.110432i
$$329$$ 7.58871 4.38134i 0.418379 0.241551i
$$330$$ 0 0
$$331$$ 4.74167 + 17.6962i 0.260626 + 0.972669i 0.964874 + 0.262714i $$0.0846177\pi$$
−0.704248 + 0.709954i $$0.748716\pi$$
$$332$$ 16.1112 0.884214
$$333$$ 0 0
$$334$$ 16.1962 0.886214
$$335$$ 2.68973 + 10.0382i 0.146955 + 0.548445i
$$336$$ 0 0
$$337$$ −0.232051 + 0.133975i −0.0126406 + 0.00729806i −0.506307 0.862353i $$-0.668990\pi$$
0.493666 + 0.869651i $$0.335656\pi$$
$$338$$ 5.32868 19.8869i 0.289842 1.08171i
$$339$$ 0 0
$$340$$ 4.73205 + 8.19615i 0.256631 + 0.444499i
$$341$$ −14.0406 14.0406i −0.760341 0.760341i
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ −10.6945 −0.576611
$$345$$ 0 0
$$346$$ −23.7583 6.36603i −1.27726 0.342240i
$$347$$ −3.62347 + 3.62347i −0.194518 + 0.194518i −0.797645 0.603127i $$-0.793921\pi$$
0.603127 + 0.797645i $$0.293921\pi$$
$$348$$ 0 0
$$349$$ −6.92820 + 12.0000i −0.370858 + 0.642345i −0.989698 0.143172i $$-0.954270\pi$$
0.618840 + 0.785517i $$0.287603\pi$$
$$350$$ −6.76148 + 1.81173i −0.361416 + 0.0968412i
$$351$$ 0 0
$$352$$ −3.73205 1.00000i −0.198919 0.0533002i
$$353$$ 3.77577 + 14.0914i 0.200964 + 0.750008i 0.990642 + 0.136486i $$0.0435810\pi$$
−0.789678 + 0.613522i $$0.789752\pi$$
$$354$$ 0 0
$$355$$ −2.53590 9.46410i −0.134592 0.502302i
$$356$$ −5.93426 5.93426i −0.314515 0.314515i
$$357$$ 0 0
$$358$$ 7.73205 + 4.46410i 0.408652 + 0.235935i
$$359$$ 19.1427i 1.01031i 0.863028 + 0.505155i $$0.168565\pi$$
−0.863028 + 0.505155i $$0.831435\pi$$
$$360$$ 0 0
$$361$$ 18.0622 + 10.4282i 0.950641 + 0.548853i
$$362$$ 13.3335 13.3335i 0.700793 0.700793i
$$363$$ 0 0
$$364$$ −4.09808 4.09808i −0.214798 0.214798i
$$365$$ 51.5037 + 13.8004i 2.69582 + 0.722344i
$$366$$ 0 0
$$367$$ −7.66987 13.2846i −0.400364 0.693451i 0.593406 0.804904i $$-0.297783\pi$$
−0.993770 + 0.111453i $$0.964450\pi$$
$$368$$ −2.63896 + 0.707107i −0.137565 + 0.0368605i
$$369$$ 0 0
$$370$$ −20.7846 + 3.46410i −1.08054 + 0.180090i
$$371$$ 2.82843i 0.146845i
$$372$$ 0 0
$$373$$ −8.42820 + 4.86603i −0.436396 + 0.251953i −0.702068 0.712110i $$-0.747740\pi$$
0.265672 + 0.964064i $$0.414406\pi$$
$$374$$ −5.27792 9.14162i −0.272915 0.472702i
$$375$$ 0 0
$$376$$ 6.19615 6.19615i 0.319542 0.319542i
$$377$$ 0.984508 0.568406i 0.0507048 0.0292744i
$$378$$ 0 0
$$379$$ 3.66025 6.33975i 0.188015 0.325651i −0.756574 0.653909i $$-0.773128\pi$$
0.944588 + 0.328258i $$0.106461\pi$$
$$380$$ 21.8695i 1.12188i
$$381$$ 0 0
$$382$$ 9.63397 16.6865i 0.492917 0.853757i
$$383$$ 7.50077 27.9933i 0.383272 1.43039i −0.457602 0.889157i $$-0.651291\pi$$
0.840873 0.541232i $$-0.182042\pi$$
$$384$$ 0 0
$$385$$ 12.9282 3.46410i 0.658882 0.176547i
$$386$$ 5.58750 + 3.22595i 0.284396 + 0.164196i
$$387$$ 0 0
$$388$$ −4.03590 + 15.0622i −0.204892 + 0.764666i
$$389$$ −1.07244 + 4.00240i −0.0543749 + 0.202930i −0.987769 0.155922i $$-0.950165\pi$$
0.933394 + 0.358852i $$0.116832\pi$$
$$390$$ 0 0
$$391$$ −6.46410 3.73205i −0.326904 0.188738i
$$392$$ 5.79555 1.55291i 0.292720 0.0784340i
$$393$$ 0 0
$$394$$ −0.392305 + 1.46410i −0.0197640 + 0.0737604i
$$395$$ −0.240237 + 0.416102i −0.0120876 + 0.0209364i
$$396$$ 0 0
$$397$$ 32.5167i 1.63196i −0.578077 0.815982i $$-0.696197\pi$$
0.578077 0.815982i $$-0.303803\pi$$
$$398$$ 9.07227 15.7136i 0.454752 0.787653i
$$399$$ 0 0
$$400$$ −6.06218 + 3.50000i −0.303109 + 0.175000i
$$401$$ 16.4901 16.4901i 0.823476 0.823476i −0.163129 0.986605i $$-0.552159\pi$$
0.986605 + 0.163129i $$0.0521587\pi$$
$$402$$ 0 0
$$403$$ −14.8923 25.7942i −0.741839 1.28490i
$$404$$ 14.6090 8.43451i 0.726825 0.419633i
$$405$$ 0 0
$$406$$ 0.196152i 0.00973488i
$$407$$ 23.1822 3.86370i 1.14910 0.191517i
$$408$$ 0 0
$$409$$ 23.8923 6.40192i 1.18140 0.316555i 0.385917 0.922533i $$-0.373885\pi$$
0.795481 + 0.605979i $$0.207218\pi$$
$$410$$ −3.58630 6.21166i −0.177115 0.306772i
$$411$$ 0 0
$$412$$ −18.2942 4.90192i −0.901292 0.241500i
$$413$$ 3.34607 + 3.34607i 0.164649 + 0.164649i
$$414$$ 0 0
$$415$$ −39.4641 + 39.4641i −1.93722 + 1.93722i
$$416$$ −5.01910 2.89778i −0.246082 0.142075i
$$417$$ 0 0
$$418$$ 24.3923i 1.19307i
$$419$$ −13.2320 7.63947i −0.646423 0.373213i 0.140661 0.990058i $$-0.455077\pi$$
−0.787085 + 0.616845i $$0.788411\pi$$
$$420$$ 0 0
$$421$$ 8.12436 + 8.12436i 0.395957 + 0.395957i 0.876804 0.480847i $$-0.159671\pi$$
−0.480847 + 0.876804i $$0.659671\pi$$
$$422$$ −0.157283 0.586988i −0.00765642 0.0285742i
$$423$$ 0 0
$$424$$ −0.732051 2.73205i −0.0355515 0.132680i
$$425$$ −18.4727 4.94975i −0.896058 0.240098i
$$426$$ 0 0
$$427$$ −2.36603 + 0.633975i −0.114500 + 0.0306802i
$$428$$ 0.656339 1.13681i 0.0317253 0.0549499i
$$429$$ 0 0
$$430$$ 26.1962 26.1962i 1.26329 1.26329i
$$431$$ −15.8338 4.24264i −0.762685 0.204361i −0.143547 0.989643i $$-0.545851\pi$$
−0.619137 + 0.785283i $$0.712518\pi$$
$$432$$ 0 0
$$433$$ 15.8564 0.762010 0.381005 0.924573i $$-0.375578\pi$$
0.381005 + 0.924573i $$0.375578\pi$$
$$434$$ −5.13922 −0.246690
$$435$$ 0 0
$$436$$ −9.09808 9.09808i −0.435719 0.435719i
$$437$$ 8.62398 + 14.9372i 0.412541 + 0.714542i
$$438$$ 0 0
$$439$$ −4.62436 + 17.2583i −0.220708 + 0.823695i 0.763370 + 0.645961i $$0.223543\pi$$
−0.984079 + 0.177734i $$0.943123\pi$$
$$440$$ 11.5911 6.69213i 0.552584 0.319035i
$$441$$ 0 0
$$442$$ −4.09808 15.2942i −0.194926 0.727472i
$$443$$ −32.7028 −1.55376 −0.776878 0.629651i $$-0.783198\pi$$
−0.776878 + 0.629651i $$0.783198\pi$$
$$444$$ 0 0
$$445$$ 29.0718 1.37814
$$446$$ 3.51695 + 13.1254i 0.166532 + 0.621508i
$$447$$ 0 0
$$448$$ −0.866025 + 0.500000i −0.0409159 + 0.0236228i
$$449$$ 5.18998 19.3693i 0.244930 0.914093i −0.728488 0.685059i $$-0.759777\pi$$
0.973418 0.229034i $$-0.0735568\pi$$
$$450$$ 0 0
$$451$$ 4.00000 + 6.92820i 0.188353 + 0.326236i
$$452$$ −9.89949 9.89949i −0.465633 0.465633i
$$453$$ 0 0
$$454$$ 10.0526 0.471790
$$455$$ 20.0764 0.941196
$$456$$ 0 0
$$457$$ −25.6865 6.88269i −1.20157 0.321958i −0.398118 0.917334i $$-0.630337\pi$$
−0.803447 + 0.595376i $$0.797003\pi$$
$$458$$ −0.466870 + 0.466870i −0.0218154 + 0.0218154i
$$459$$ 0 0
$$460$$ 4.73205 8.19615i 0.220633 0.382148i
$$461$$ 21.6293 5.79555i 1.00738 0.269926i 0.282844 0.959166i $$-0.408722\pi$$
0.724533 + 0.689240i $$0.242055\pi$$
$$462$$ 0 0
$$463$$ 19.8923 + 5.33013i 0.924474 + 0.247712i 0.689497 0.724289i $$-0.257832\pi$$
0.234977 + 0.972001i $$0.424498\pi$$
$$464$$ −0.0507680 0.189469i −0.00235684 0.00879586i
$$465$$ 0 0
$$466$$ 5.70577 + 21.2942i 0.264315 + 0.986436i
$$467$$ 2.07055 + 2.07055i 0.0958137 + 0.0958137i 0.753389 0.657575i $$-0.228418\pi$$
−0.657575 + 0.753389i $$0.728418\pi$$
$$468$$ 0 0
$$469$$ −2.59808 1.50000i −0.119968 0.0692636i
$$470$$ 30.3548i 1.40016i
$$471$$ 0 0
$$472$$ 4.09808 + 2.36603i 0.188629 + 0.108905i
$$473$$ −29.2180 + 29.2180i −1.34345 + 1.34345i
$$474$$ 0 0
$$475$$ 31.2487 + 31.2487i 1.43379 + 1.43379i
$$476$$ −2.63896 0.707107i −0.120956 0.0324102i
$$477$$ 0 0
$$478$$ 0.437822 + 0.758330i 0.0200255 + 0.0346852i
$$479$$ 14.2301 3.81294i 0.650188 0.174217i 0.0813744 0.996684i $$-0.474069\pi$$
0.568814 + 0.822466i $$0.307402\pi$$
$$480$$ 0 0
$$481$$ 35.0885 + 3.40192i 1.59990 + 0.155114i
$$482$$ 23.3209i 1.06224i
$$483$$ 0 0
$$484$$ −3.40192 + 1.96410i −0.154633 + 0.0892773i
$$485$$ −27.0088 46.7805i −1.22640 2.12419i
$$486$$ 0 0
$$487$$ −24.6603 + 24.6603i −1.11746 + 1.11746i −0.125350 + 0.992113i $$0.540005\pi$$
−0.992113 + 0.125350i $$0.959995\pi$$
$$488$$ −2.12132 + 1.22474i −0.0960277 + 0.0554416i
$$489$$ 0 0
$$490$$ −10.3923 + 18.0000i −0.469476 + 0.813157i
$$491$$ 31.0112i 1.39951i 0.714381 + 0.699757i $$0.246708\pi$$
−0.714381 + 0.699757i $$0.753292\pi$$
$$492$$ 0 0
$$493$$ 0.267949 0.464102i 0.0120678 0.0209021i
$$494$$ −9.46979 + 35.3417i −0.426066 + 1.59010i
$$495$$ 0 0
$$496$$ −4.96410 + 1.33013i −0.222895 + 0.0597245i
$$497$$ 2.44949 + 1.41421i 0.109875 + 0.0634361i
$$498$$ 0 0
$$499$$ 0.509619 1.90192i 0.0228137 0.0851418i −0.953580 0.301138i $$-0.902633\pi$$
0.976394 + 0.215997i $$0.0693000\pi$$
$$500$$ 1.79315 6.69213i 0.0801921 0.299281i
$$501$$ 0 0
$$502$$ −21.0000 12.1244i −0.937276 0.541136i
$$503$$ −31.8570 + 8.53605i −1.42043 + 0.380604i −0.885637 0.464378i $$-0.846278\pi$$
−0.534795 + 0.844982i $$0.679611\pi$$
$$504$$ 0 0
$$505$$ −15.1244 + 56.4449i −0.673025 + 2.51176i
$$506$$ −5.27792 + 9.14162i −0.234632 + 0.406395i
$$507$$ 0 0
$$508$$ 0.267949i 0.0118883i
$$509$$ −16.5409 + 28.6496i −0.733161 + 1.26987i 0.222365 + 0.974963i $$0.428622\pi$$
−0.955526 + 0.294908i $$0.904711\pi$$
$$510$$ 0 0
$$511$$ −13.3301 + 7.69615i −0.589690 + 0.340458i
$$512$$ −0.707107 + 0.707107i −0.0312500 + 0.0312500i
$$513$$ 0 0
$$514$$ −0.464102 0.803848i −0.0204706 0.0354562i
$$515$$ 56.8187 32.8043i 2.50373 1.44553i
$$516$$ 0 0
$$517$$ 33.8564i 1.48900i
$$518$$ 3.53553 4.94975i 0.155342 0.217479i
$$519$$ 0 0
$$520$$ 19.3923 5.19615i 0.850409 0.227866i
$$521$$ −0.795040 1.37705i −0.0348313 0.0603296i 0.848084 0.529861i $$-0.177756\pi$$
−0.882916 + 0.469532i $$0.844423\pi$$
$$522$$ 0 0
$$523$$ 9.52628 + 2.55256i 0.416555 + 0.111616i 0.461008 0.887396i $$-0.347488\pi$$
−0.0444531 + 0.999011i $$0.514155\pi$$
$$524$$ −2.96713 2.96713i −0.129620 0.129620i
$$525$$ 0 0
$$526$$ 4.12436 4.12436i 0.179830 0.179830i
$$527$$ −12.1595 7.02030i −0.529677 0.305809i
$$528$$ 0 0
$$529$$ 15.5359i 0.675474i
$$530$$ 8.48528 + 4.89898i 0.368577 + 0.212798i
$$531$$ 0 0
$$532$$ 4.46410 + 4.46410i 0.193543 + 0.193543i
$$533$$ 3.10583 + 11.5911i 0.134528 + 0.502067i
$$534$$ 0 0
$$535$$ 1.17691 + 4.39230i 0.0508825 + 0.189896i
$$536$$ −2.89778 0.776457i −0.125165 0.0335378i
$$537$$ 0 0
$$538$$ 13.9282 3.73205i 0.600487 0.160900i
$$539$$ 11.5911 20.0764i 0.499264 0.864751i
$$540$$ 0 0
$$541$$ −6.29423 + 6.29423i −0.270610 + 0.270610i −0.829346 0.558736i $$-0.811287\pi$$
0.558736 + 0.829346i $$0.311287\pi$$
$$542$$ −24.3884 6.53485i −1.04757 0.280696i
$$543$$ 0 0
$$544$$ −2.73205 −0.117136
$$545$$ 44.5713 1.90922
$$546$$ 0 0
$$547$$ −17.9545 17.9545i −0.767678 0.767678i 0.210019 0.977697i $$-0.432647\pi$$
−0.977697 + 0.210019i $$0.932647\pi$$
$$548$$ 6.69213 + 11.5911i 0.285874 + 0.495148i
$$549$$ 0 0
$$550$$ −7.00000 + 26.1244i −0.298481 + 1.11395i
$$551$$ −1.07244 + 0.619174i −0.0456875 + 0.0263777i
$$552$$ 0 0
$$553$$ −0.0358984 0.133975i −0.00152655 0.00569718i
$$554$$ 18.9396 0.804666
$$555$$ 0 0
$$556$$ −9.92820 −0.421050
$$557$$ 1.26191 + 4.70951i 0.0534688 + 0.199548i 0.987493 0.157660i $$-0.0503951\pi$$
−0.934025 + 0.357209i $$0.883728\pi$$
$$558$$ 0 0
$$559$$ −53.6769 + 30.9904i −2.27029 + 1.31075i
$$560$$ 0.896575 3.34607i 0.0378872 0.141397i
$$561$$ 0 0
$$562$$ 1.56218 + 2.70577i 0.0658965 + 0.114136i
$$563$$ −5.37945 5.37945i −0.226717 0.226717i 0.584603 0.811320i $$-0.301250\pi$$
−0.811320 + 0.584603i $$0.801250\pi$$
$$564$$ 0 0
$$565$$ 48.4974 2.04030
$$566$$ 6.93237 0.291389
$$567$$ 0 0
$$568$$ 2.73205 + 0.732051i 0.114634 + 0.0307162i
$$569$$ −9.55772 + 9.55772i −0.400681 + 0.400681i −0.878473 0.477792i $$-0.841437\pi$$
0.477792 + 0.878473i $$0.341437\pi$$
$$570$$ 0 0
$$571$$ 23.0622 39.9449i 0.965122 1.67164i 0.255835 0.966720i $$-0.417649\pi$$
0.709287 0.704920i $$-0.249017\pi$$
$$572$$ −21.6293 + 5.79555i −0.904367 + 0.242324i
$$573$$ 0 0
$$574$$ 2.00000 + 0.535898i 0.0834784 + 0.0223680i
$$575$$ 4.94975 + 18.4727i 0.206419 + 0.770365i
$$576$$ 0 0
$$577$$ −7.95448 29.6865i −0.331149 1.23587i −0.907984 0.419005i $$-0.862379\pi$$
0.576834 0.816861i $$-0.304288\pi$$
$$578$$ 6.74290 + 6.74290i 0.280468 + 0.280468i
$$579$$ 0 0
$$580$$ 0.588457 + 0.339746i 0.0244344 + 0.0141072i
$$581$$ 16.1112i 0.668403i
$$582$$ 0 0
$$583$$ −9.46410 5.46410i −0.391963 0.226300i
$$584$$ −10.8840 + 10.8840i −0.450383 + 0.450383i
$$585$$ 0 0
$$586$$ 15.9282 + 15.9282i 0.657988 + 0.657988i
$$587$$ −29.0793 7.79178i −1.20023 0.321601i −0.397309 0.917685i $$-0.630056\pi$$
−0.802922 + 0.596084i $$0.796723\pi$$
$$588$$ 0 0
$$589$$ 16.2224 + 28.0981i 0.668434 + 1.15776i
$$590$$ −15.8338 + 4.24264i −0.651865 + 0.174667i
$$591$$ 0 0
$$592$$ 2.13397 5.69615i 0.0877058 0.234110i
$$593$$ 42.7038i 1.75364i 0.480823 + 0.876818i $$0.340338\pi$$
−0.480823 + 0.876818i $$0.659662\pi$$
$$594$$ 0 0
$$595$$ 8.19615 4.73205i 0.336009 0.193995i
$$596$$ 3.53553 + 6.12372i 0.144821 + 0.250838i
$$597$$ 0 0
$$598$$ −11.1962 + 11.1962i −0.457845 + 0.457845i
$$599$$ −37.1349 + 21.4398i −1.51729 + 0.876008i −0.517497 + 0.855685i $$0.673136\pi$$
−0.999793 + 0.0203229i $$0.993531\pi$$
$$600$$ 0 0
$$601$$ −13.7942 + 23.8923i −0.562678 + 0.974587i 0.434583 + 0.900632i $$0.356896\pi$$
−0.997262 + 0.0739558i $$0.976438\pi$$
$$602$$ 10.6945i 0.435877i
$$603$$ 0 0
$$604$$ 5.42820 9.40192i 0.220870 0.382559i
$$605$$ 3.52193 13.1440i 0.143187 0.534381i
$$606$$ 0 0
$$607$$ 39.6147 10.6147i 1.60791 0.430839i 0.660493 0.750832i $$-0.270347\pi$$
0.947420 + 0.319993i $$0.103681\pi$$
$$608$$ 5.46739 + 3.15660i 0.221732 + 0.128017i
$$609$$ 0 0
$$610$$ 2.19615 8.19615i 0.0889196 0.331853i
$$611$$ 13.1440 49.0542i 0.531750 1.98452i
$$612$$ 0 0
$$613$$ 31.2679 + 18.0526i 1.26290 + 0.729136i 0.973635 0.228113i $$-0.0732555\pi$$
0.289266 + 0.957249i $$0.406589\pi$$
$$614$$ −23.4410 + 6.28101i −0.946003 + 0.253481i
$$615$$ 0 0
$$616$$ −1.00000 + 3.73205i −0.0402911 + 0.150369i
$$617$$ 13.9019 24.0788i 0.559669 0.969376i −0.437854 0.899046i $$-0.644261\pi$$
0.997524 0.0703299i $$-0.0224052\pi$$
$$618$$ 0 0
$$619$$ 39.0526i 1.56965i 0.619714 + 0.784827i $$0.287248\pi$$
−0.619714 + 0.784827i $$0.712752\pi$$
$$620$$ 8.90138 15.4176i 0.357488 0.619188i
$$621$$ 0 0
$$622$$ 26.9545 15.5622i 1.08078 0.623986i
$$623$$ −5.93426 + 5.93426i −0.237751 + 0.237751i
$$624$$ 0 0
$$625$$ −5.50000 9.52628i −0.220000 0.381051i
$$626$$ −21.9897 + 12.6957i −0.878884 + 0.507424i
$$627$$ 0 0
$$628$$ 5.00000i 0.199522i
$$629$$ 15.1266 6.88160i 0.603139 0.274387i
$$630$$ 0 0
$$631$$ 13.5263 3.62436i 0.538473 0.144283i 0.0206747 0.999786i $$-0.493419\pi$$
0.517798 + 0.855503i $$0.326752\pi$$
$$632$$ −0.0693504 0.120118i −0.00275861 0.00477805i
$$633$$ 0 0
$$634$$ −18.7583 5.02628i −0.744988 0.199619i
$$635$$ −0.656339 0.656339i −0.0260460 0.0260460i
$$636$$ 0 0
$$637$$ 24.5885 24.5885i 0.974230 0.974230i
$$638$$ −0.656339 0.378937i −0.0259847 0.0150023i
$$639$$ 0 0
$$640$$ 3.46410i 0.136931i
$$641$$ 14.7849 + 8.53605i 0.583967 + 0.337154i 0.762708 0.646742i $$-0.223869\pi$$
−0.178741 + 0.983896i $$0.557202\pi$$
$$642$$ 0 0
$$643$$ 10.1506 + 10.1506i 0.400302 + 0.400302i 0.878339 0.478037i $$-0.158652\pi$$
−0.478037 + 0.878339i $$0.658652\pi$$
$$644$$ 0.707107 + 2.63896i 0.0278639 + 0.103990i
$$645$$ 0 0
$$646$$ 4.46410 + 16.6603i 0.175638 + 0.655489i
$$647$$ 4.38134 + 1.17398i 0.172248 + 0.0461538i 0.343912 0.939002i $$-0.388248\pi$$
−0.171664 + 0.985156i $$0.554914\pi$$
$$648$$ 0 0
$$649$$ 17.6603 4.73205i 0.693226 0.185749i
$$650$$ −20.2844 + 35.1337i −0.795621 + 1.37806i
$$651$$ 0 0
$$652$$ −2.07180 + 2.07180i −0.0811378 + 0.0811378i
$$653$$ −6.69213 1.79315i −0.261883 0.0701714i 0.125488 0.992095i $$-0.459950\pi$$
−0.387372 + 0.921924i $$0.626617\pi$$
$$654$$ 0 0
$$655$$ 14.5359 0.567965
$$656$$ 2.07055 0.0808415
$$657$$ 0 0
$$658$$ −6.19615 6.19615i −0.241551 0.241551i
$$659$$ −15.4548 26.7685i −0.602034 1.04275i −0.992513 0.122142i $$-0.961024\pi$$
0.390479 0.920612i $$-0.372310\pi$$
$$660$$ 0 0
$$661$$ −4.74167 + 17.6962i −0.184430 + 0.688301i 0.810322 + 0.585984i $$0.199292\pi$$
−0.994752 + 0.102316i $$0.967375\pi$$
$$662$$ 15.8659 9.16020i 0.616647 0.356021i
$$663$$ 0 0
$$664$$ −4.16987 15.5622i −0.161822 0.603930i
$$665$$ −21.8695 −0.848064
$$666$$ 0 0
$$667$$ −0.535898 −0.0207501
$$668$$ −4.19187 15.6443i −0.162188 0.605295i
$$669$$ 0 0
$$670$$ 9.00000 5.19615i 0.347700 0.200745i
$$671$$ −2.44949 + 9.14162i −0.0945615 + 0.352908i
$$672$$ 0 0
$$673$$ 17.5885 + 30.4641i 0.677985 + 1.17430i 0.975587 + 0.219615i $$0.0704800\pi$$
−0.297601 + 0.954690i $$0.596187\pi$$
$$674$$ 0.189469 + 0.189469i 0.00729806 + 0.00729806i
$$675$$ 0 0
$$676$$ −20.5885 −0.791864
$$677$$ −4.14110 −0.159156 −0.0795778 0.996829i $$-0.525357\pi$$
−0.0795778 + 0.996829i $$0.525357\pi$$
$$678$$ 0 0
$$679$$ 15.0622 + 4.03590i 0.578033 + 0.154884i
$$680$$ 6.69213 6.69213i 0.256631 0.256631i
$$681$$ 0 0
$$682$$ −9.92820 + 17.1962i −0.380171 + 0.658475i
$$683$$ 34.4452 9.22955i 1.31801 0.353159i 0.469776 0.882785i $$-0.344335\pi$$
0.848231 + 0.529626i $$0.177668\pi$$
$$684$$ 0 0
$$685$$ −44.7846 12.0000i −1.71113 0.458496i
$$686$$ −3.36465 12.5570i −0.128463 0.479430i
$$687$$ 0 0
$$688$$ 2.76795 + 10.3301i 0.105527 + 0.393832i
$$689$$ −11.5911 11.5911i −0.441586 0.441586i
$$690$$ 0 0
$$691$$ 11.3827 + 6.57180i 0.433018 + 0.250003i 0.700631 0.713523i $$-0.252902\pi$$
−0.267614 + 0.963526i $$0.586235\pi$$
$$692$$ 24.5964i 0.935016i
$$693$$ 0 0
$$694$$ 4.43782 + 2.56218i 0.168457 + 0.0972589i
$$695$$ 24.3190 24.3190i 0.922473 0.922473i
$$696$$ 0 0
$$697$$ 4.00000 + 4.00000i 0.151511 + 0.151511i
$$698$$ 13.3843 + 3.58630i 0.506602 + 0.135744i
$$699$$ 0 0
$$700$$ 3.50000 + 6.06218i 0.132288 + 0.229129i
$$701$$ −42.3620 + 11.3509i −1.59999 + 0.428717i −0.945040 0.326954i $$-0.893978\pi$$
−0.654952 + 0.755671i $$0.727311\pi$$
$$702$$ 0 0
$$703$$ −38.2224 3.70577i −1.44159 0.139766i
$$704$$ 3.86370i 0.145619i
$$705$$ 0 0
$$706$$ 12.6340 7.29423i 0.475486 0.274522i
$$707$$ −8.43451 14.6090i −0.317213 0.549428i
$$708$$ 0 0
$$709$$ −15.2224 + 15.2224i −0.571690 + 0.571690i −0.932601 0.360910i $$-0.882466\pi$$
0.360910 + 0.932601i $$0.382466\pi$$
$$710$$ −8.48528 + 4.89898i −0.318447 + 0.183855i
$$711$$ 0 0
$$712$$ −4.19615 + 7.26795i −0.157257 + 0.272378i
$$713$$ 14.0406i 0.525825i
$$714$$ 0 0
$$715$$ 38.7846 67.1769i 1.45046 2.51227i
$$716$$ 2.31079 8.62398i 0.0863582 0.322293i
$$717$$ 0 0
$$718$$ 18.4904 4.95448i 0.690055 0.184900i
$$719$$ 32.9802 + 19.0411i 1.22995 + 0.710114i 0.967020 0.254700i $$-0.0819768\pi$$
0.262933 + 0.964814i $$0.415310\pi$$
$$720$$ 0 0
$$721$$ −4.90192 + 18.2942i −0.182557 + 0.681313i
$$722$$ 5.39804 20.1457i 0.200894 0.749747i
$$723$$ 0 0
$$724$$ −16.3301 9.42820i −0.606904 0.350396i
$$725$$ −1.32628 + 0.355376i −0.0492568 + 0.0131983i
$$726$$ 0 0
$$727$$ −7.01666 + 26.1865i −0.260234 + 0.971205i 0.704870 + 0.709336i $$0.251005\pi$$
−0.965104 + 0.261868i $$0.915661\pi$$
$$728$$ −2.89778 + 5.01910i −0.107399 + 0.186020i
$$729$$ 0 0
$$730$$ 53.3205i 1.97348i
$$731$$ −14.6090 + 25.3035i −0.540334 + 0.935885i
$$732$$ 0 0
$$733$$ 8.25833 4.76795i 0.305028 0.176108i −0.339671 0.940544i $$-0.610316\pi$$
0.644700 + 0.764436i $$0.276982\pi$$
$$734$$ −10.8468 + 10.8468i −0.400364 + 0.400364i
$$735$$ 0 0
$$736$$ 1.36603 + 2.36603i 0.0503524 + 0.0872129i
$$737$$ −10.0382 + 5.79555i −0.369762 + 0.213482i
$$738$$ 0 0
$$739$$ 9.32051i 0.342860i 0.985196 + 0.171430i $$0.0548388\pi$$
−0.985196 + 0.171430i $$0.945161\pi$$
$$740$$ 8.72552 + 19.1798i 0.320756 + 0.705064i
$$741$$ 0 0
$$742$$ −2.73205 + 0.732051i −0.100297 + 0.0268744i
$$743$$ −15.4040 26.6806i −0.565120 0.978816i −0.997039 0.0769034i $$-0.975497\pi$$
0.431919 0.901912i $$-0.357837\pi$$
$$744$$ 0 0
$$745$$ −23.6603 6.33975i −0.866845 0.232270i
$$746$$ 6.88160 + 6.88160i 0.251953 + 0.251953i
$$747$$ 0 0
$$748$$ −7.46410 + 7.46410i −0.272915 + 0.272915i
$$749$$ −1.13681 0.656339i −0.0415382 0.0239821i
$$750$$ 0 0
$$751$$ 7.19615i 0.262591i 0.991343 + 0.131296i $$0.0419137\pi$$
−0.991343 + 0.131296i $$0.958086\pi$$
$$752$$ −7.58871 4.38134i −0.276732 0.159771i
$$753$$ 0 0
$$754$$ −0.803848 0.803848i −0.0292744 0.0292744i
$$755$$ 9.73359 + 36.3262i 0.354242 + 1.32205i
$$756$$ 0 0
$$757$$ 4.55256 + 16.9904i 0.165466 + 0.617526i 0.997980 + 0.0635231i $$0.0202337\pi$$
−0.832515 + 0.554003i $$0.813100\pi$$
$$758$$ −7.07107 1.89469i −0.256833 0.0688181i
$$759$$ 0 0
$$760$$ −21.1244 + 5.66025i −0.766261 + 0.205319i
$$761$$ −22.6274 + 39.1918i −0.820243 + 1.42070i 0.0852578 + 0.996359i $$0.472829\pi$$
−0.905501 + 0.424344i $$0.860505\pi$$
$$762$$ 0 0
$$763$$ −9.09808 + 9.09808i −0.329372 + 0.329372i
$$764$$ −18.6114 4.98691i −0.673337 0.180420i
$$765$$ 0 0
$$766$$ −28.9808 −1.04712
$$767$$ 27.4249 0.990254
$$768$$ 0 0
$$769$$ 7.97372 + 7.97372i 0.287540 + 0.287540i 0.836107 0.548567i $$-0.184826\pi$$
−0.548567 + 0.836107i $$0.684826\pi$$
$$770$$ −6.69213 11.5911i −0.241168 0.417715i
$$771$$ 0 0
$$772$$ 1.66987 6.23205i 0.0601000 0.224296i
$$773$$ 6.03579 3.48477i 0.217092 0.125338i −0.387511 0.921865i $$-0.626665\pi$$
0.604603 + 0.796527i $$0.293332\pi$$
$$774$$ 0 0
$$775$$ 9.31089 + 34.7487i 0.334457 + 1.24821i
$$776$$ 15.5935 0.559775
$$777$$ 0 0
$$778$$ 4.14359 0.148555
$$779$$ −3.38323 12.6264i −0.121217 0.452387i
$$780$$ 0 0
$$781$$ 9.46410 5.46410i 0.338652 0.195521i
$$782$$ −1.93185 + 7.20977i −0.0690829 + 0.25