# Properties

 Label 666.2.be.c.125.2 Level $666$ Weight $2$ Character 666.125 Analytic conductor $5.318$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

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 125.2 Root $$-0.965926 + 0.258819i$$ of defining polynomial Character $$\chi$$ $$=$$ 666.125 Dual form 666.2.be.c.341.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.448288 - 1.67303i) q^{5} +(0.633975 + 1.09808i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$$ $$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.448288 - 1.67303i) q^{5} +(0.633975 + 1.09808i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.73205 q^{10} +2.44949 q^{11} +(0.366025 + 0.0980762i) q^{13} +(-0.896575 + 0.896575i) q^{14} +(0.500000 - 0.866025i) q^{16} +(6.24384 - 1.67303i) q^{17} +(-5.09808 - 1.36603i) q^{19} +(0.448288 + 1.67303i) q^{20} +(0.633975 + 2.36603i) q^{22} +(2.44949 + 2.44949i) q^{23} +(1.73205 + 1.00000i) q^{25} +0.378937i q^{26} +(-1.09808 - 0.633975i) q^{28} +(6.12372 - 6.12372i) q^{29} +(5.73205 + 5.73205i) q^{31} +(0.965926 + 0.258819i) q^{32} +(3.23205 + 5.59808i) q^{34} +(2.12132 - 0.568406i) q^{35} +(-4.69615 + 3.86603i) q^{37} -5.27792i q^{38} +(-1.50000 + 0.866025i) q^{40} +(2.89778 + 5.01910i) q^{41} +(0.267949 - 0.267949i) q^{43} +(-2.12132 + 1.22474i) q^{44} +(-1.73205 + 3.00000i) q^{46} -4.24264i q^{47} +(2.69615 - 4.66987i) q^{49} +(-0.517638 + 1.93185i) q^{50} +(-0.366025 + 0.0980762i) q^{52} +(-5.22715 - 3.01790i) q^{53} +(1.09808 - 4.09808i) q^{55} +(0.328169 - 1.22474i) q^{56} +(7.50000 + 4.33013i) q^{58} +(-5.79555 + 1.55291i) q^{59} +(-2.86603 + 10.6962i) q^{61} +(-4.05317 + 7.02030i) q^{62} +1.00000i q^{64} +(0.328169 - 0.568406i) q^{65} +(-3.63397 + 2.09808i) q^{67} +(-4.57081 + 4.57081i) q^{68} +(1.09808 + 1.90192i) q^{70} +(2.12132 - 1.22474i) q^{71} -6.39230i q^{73} +(-4.94975 - 3.53553i) q^{74} +(5.09808 - 1.36603i) q^{76} +(1.55291 + 2.68973i) q^{77} +(-3.36603 - 0.901924i) q^{79} +(-1.22474 - 1.22474i) q^{80} +(-4.09808 + 4.09808i) q^{82} +(-3.10583 - 1.79315i) q^{83} -11.1962i q^{85} +(0.328169 + 0.189469i) q^{86} +(-1.73205 - 1.73205i) q^{88} +(-1.10463 - 4.12252i) q^{89} +(0.124356 + 0.464102i) q^{91} +(-3.34607 - 0.896575i) q^{92} +(4.09808 - 1.09808i) q^{94} +(-4.57081 + 7.91688i) q^{95} +(0.366025 - 0.366025i) q^{97} +(5.20857 + 1.39563i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 12 q^{7}+O(q^{10})$$ 8 * q + 12 * q^7 $$8 q + 12 q^{7} - 4 q^{13} + 4 q^{16} - 20 q^{19} + 12 q^{22} + 12 q^{28} + 32 q^{31} + 12 q^{34} + 4 q^{37} - 12 q^{40} + 16 q^{43} - 20 q^{49} + 4 q^{52} - 12 q^{55} + 60 q^{58} - 16 q^{61} - 36 q^{67} - 12 q^{70} + 20 q^{76} - 20 q^{79} - 12 q^{82} - 96 q^{91} + 12 q^{94} - 4 q^{97}+O(q^{100})$$ 8 * q + 12 * q^7 - 4 * q^13 + 4 * q^16 - 20 * q^19 + 12 * q^22 + 12 * q^28 + 32 * q^31 + 12 * q^34 + 4 * q^37 - 12 * q^40 + 16 * q^43 - 20 * q^49 + 4 * q^52 - 12 * q^55 + 60 * q^58 - 16 * q^61 - 36 * q^67 - 12 * q^70 + 20 * q^76 - 20 * q^79 - 12 * q^82 - 96 * q^91 + 12 * q^94 - 4 * 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
$$5$$ 0.448288 1.67303i 0.200480 0.748203i −0.790299 0.612721i $$-0.790075\pi$$
0.990780 0.135482i $$-0.0432583\pi$$
$$6$$ 0 0
$$7$$ 0.633975 + 1.09808i 0.239620 + 0.415034i 0.960605 0.277916i $$-0.0896439\pi$$
−0.720985 + 0.692950i $$0.756311\pi$$
$$8$$ −0.707107 0.707107i −0.250000 0.250000i
$$9$$ 0 0
$$10$$ 1.73205 0.547723
$$11$$ 2.44949 0.738549 0.369274 0.929320i $$-0.379606\pi$$
0.369274 + 0.929320i $$0.379606\pi$$
$$12$$ 0 0
$$13$$ 0.366025 + 0.0980762i 0.101517 + 0.0272014i 0.309220 0.950991i $$-0.399932\pi$$
−0.207703 + 0.978192i $$0.566599\pi$$
$$14$$ −0.896575 + 0.896575i −0.239620 + 0.239620i
$$15$$ 0 0
$$16$$ 0.500000 0.866025i 0.125000 0.216506i
$$17$$ 6.24384 1.67303i 1.51435 0.405770i 0.596476 0.802631i $$-0.296567\pi$$
0.917879 + 0.396861i $$0.129901\pi$$
$$18$$ 0 0
$$19$$ −5.09808 1.36603i −1.16958 0.313388i −0.378793 0.925481i $$-0.623661\pi$$
−0.790785 + 0.612093i $$0.790328\pi$$
$$20$$ 0.448288 + 1.67303i 0.100240 + 0.374101i
$$21$$ 0 0
$$22$$ 0.633975 + 2.36603i 0.135164 + 0.504438i
$$23$$ 2.44949 + 2.44949i 0.510754 + 0.510754i 0.914757 0.404004i $$-0.132382\pi$$
−0.404004 + 0.914757i $$0.632382\pi$$
$$24$$ 0 0
$$25$$ 1.73205 + 1.00000i 0.346410 + 0.200000i
$$26$$ 0.378937i 0.0743157i
$$27$$ 0 0
$$28$$ −1.09808 0.633975i −0.207517 0.119810i
$$29$$ 6.12372 6.12372i 1.13715 1.13715i 0.148188 0.988959i $$-0.452656\pi$$
0.988959 0.148188i $$-0.0473440\pi$$
$$30$$ 0 0
$$31$$ 5.73205 + 5.73205i 1.02951 + 1.02951i 0.999551 + 0.0299555i $$0.00953655\pi$$
0.0299555 + 0.999551i $$0.490463\pi$$
$$32$$ 0.965926 + 0.258819i 0.170753 + 0.0457532i
$$33$$ 0 0
$$34$$ 3.23205 + 5.59808i 0.554292 + 0.960062i
$$35$$ 2.12132 0.568406i 0.358569 0.0960782i
$$36$$ 0 0
$$37$$ −4.69615 + 3.86603i −0.772043 + 0.635571i
$$38$$ 5.27792i 0.856191i
$$39$$ 0 0
$$40$$ −1.50000 + 0.866025i −0.237171 + 0.136931i
$$41$$ 2.89778 + 5.01910i 0.452557 + 0.783851i 0.998544 0.0539421i $$-0.0171786\pi$$
−0.545987 + 0.837793i $$0.683845\pi$$
$$42$$ 0 0
$$43$$ 0.267949 0.267949i 0.0408619 0.0408619i −0.686381 0.727242i $$-0.740802\pi$$
0.727242 + 0.686381i $$0.240802\pi$$
$$44$$ −2.12132 + 1.22474i −0.319801 + 0.184637i
$$45$$ 0 0
$$46$$ −1.73205 + 3.00000i −0.255377 + 0.442326i
$$47$$ 4.24264i 0.618853i −0.950923 0.309426i $$-0.899863\pi$$
0.950923 0.309426i $$-0.100137\pi$$
$$48$$ 0 0
$$49$$ 2.69615 4.66987i 0.385165 0.667125i
$$50$$ −0.517638 + 1.93185i −0.0732051 + 0.273205i
$$51$$ 0 0
$$52$$ −0.366025 + 0.0980762i −0.0507586 + 0.0136007i
$$53$$ −5.22715 3.01790i −0.718004 0.414540i 0.0960135 0.995380i $$-0.469391\pi$$
−0.814018 + 0.580840i $$0.802724\pi$$
$$54$$ 0 0
$$55$$ 1.09808 4.09808i 0.148065 0.552584i
$$56$$ 0.328169 1.22474i 0.0438535 0.163663i
$$57$$ 0 0
$$58$$ 7.50000 + 4.33013i 0.984798 + 0.568574i
$$59$$ −5.79555 + 1.55291i −0.754517 + 0.202172i −0.615521 0.788121i $$-0.711054\pi$$
−0.138996 + 0.990293i $$0.544388\pi$$
$$60$$ 0 0
$$61$$ −2.86603 + 10.6962i −0.366957 + 1.36950i 0.497792 + 0.867297i $$0.334144\pi$$
−0.864748 + 0.502205i $$0.832522\pi$$
$$62$$ −4.05317 + 7.02030i −0.514753 + 0.891579i
$$63$$ 0 0
$$64$$ 1.00000i 0.125000i
$$65$$ 0.328169 0.568406i 0.0407044 0.0705021i
$$66$$ 0 0
$$67$$ −3.63397 + 2.09808i −0.443961 + 0.256321i −0.705276 0.708933i $$-0.749177\pi$$
0.261316 + 0.965253i $$0.415844\pi$$
$$68$$ −4.57081 + 4.57081i −0.554292 + 0.554292i
$$69$$ 0 0
$$70$$ 1.09808 + 1.90192i 0.131245 + 0.227323i
$$71$$ 2.12132 1.22474i 0.251754 0.145350i −0.368813 0.929504i $$-0.620236\pi$$
0.620567 + 0.784153i $$0.286902\pi$$
$$72$$ 0 0
$$73$$ 6.39230i 0.748163i −0.927396 0.374081i $$-0.877958\pi$$
0.927396 0.374081i $$-0.122042\pi$$
$$74$$ −4.94975 3.53553i −0.575396 0.410997i
$$75$$ 0 0
$$76$$ 5.09808 1.36603i 0.584789 0.156694i
$$77$$ 1.55291 + 2.68973i 0.176971 + 0.306523i
$$78$$ 0 0
$$79$$ −3.36603 0.901924i −0.378707 0.101474i 0.0644435 0.997921i $$-0.479473\pi$$
−0.443151 + 0.896447i $$0.646139\pi$$
$$80$$ −1.22474 1.22474i −0.136931 0.136931i
$$81$$ 0 0
$$82$$ −4.09808 + 4.09808i −0.452557 + 0.452557i
$$83$$ −3.10583 1.79315i −0.340909 0.196824i 0.319765 0.947497i $$-0.396396\pi$$
−0.660674 + 0.750673i $$0.729729\pi$$
$$84$$ 0 0
$$85$$ 11.1962i 1.21439i
$$86$$ 0.328169 + 0.189469i 0.0353874 + 0.0204309i
$$87$$ 0 0
$$88$$ −1.73205 1.73205i −0.184637 0.184637i
$$89$$ −1.10463 4.12252i −0.117090 0.436986i 0.882345 0.470604i $$-0.155964\pi$$
−0.999435 + 0.0336174i $$0.989297\pi$$
$$90$$ 0 0
$$91$$ 0.124356 + 0.464102i 0.0130360 + 0.0486511i
$$92$$ −3.34607 0.896575i −0.348851 0.0934745i
$$93$$ 0 0
$$94$$ 4.09808 1.09808i 0.422684 0.113258i
$$95$$ −4.57081 + 7.91688i −0.468955 + 0.812254i
$$96$$ 0 0
$$97$$ 0.366025 0.366025i 0.0371642 0.0371642i −0.688280 0.725445i $$-0.741634\pi$$
0.725445 + 0.688280i $$0.241634\pi$$
$$98$$ 5.20857 + 1.39563i 0.526145 + 0.140980i
$$99$$ 0 0
$$100$$ −2.00000 −0.200000
$$101$$ −2.20925 −0.219829 −0.109914 0.993941i $$-0.535058\pi$$
−0.109914 + 0.993941i $$0.535058\pi$$
$$102$$ 0 0
$$103$$ −3.73205 3.73205i −0.367730 0.367730i 0.498919 0.866649i $$-0.333731\pi$$
−0.866649 + 0.498919i $$0.833731\pi$$
$$104$$ −0.189469 0.328169i −0.0185789 0.0321797i
$$105$$ 0 0
$$106$$ 1.56218 5.83013i 0.151732 0.566272i
$$107$$ −9.46979 + 5.46739i −0.915479 + 0.528552i −0.882190 0.470894i $$-0.843932\pi$$
−0.0332891 + 0.999446i $$0.510598\pi$$
$$108$$ 0 0
$$109$$ −0.794229 2.96410i −0.0760733 0.283909i 0.917401 0.397964i $$-0.130283\pi$$
−0.993475 + 0.114054i $$0.963616\pi$$
$$110$$ 4.24264 0.404520
$$111$$ 0 0
$$112$$ 1.26795 0.119810
$$113$$ −2.03339 7.58871i −0.191285 0.713885i −0.993197 0.116444i $$-0.962851\pi$$
0.801912 0.597442i $$-0.203816\pi$$
$$114$$ 0 0
$$115$$ 5.19615 3.00000i 0.484544 0.279751i
$$116$$ −2.24144 + 8.36516i −0.208112 + 0.776686i
$$117$$ 0 0
$$118$$ −3.00000 5.19615i −0.276172 0.478345i
$$119$$ 5.79555 + 5.79555i 0.531278 + 0.531278i
$$120$$ 0 0
$$121$$ −5.00000 −0.454545
$$122$$ −11.0735 −1.00255
$$123$$ 0 0
$$124$$ −7.83013 2.09808i −0.703166 0.188413i
$$125$$ 8.57321 8.57321i 0.766812 0.766812i
$$126$$ 0 0
$$127$$ −1.19615 + 2.07180i −0.106141 + 0.183842i −0.914204 0.405254i $$-0.867183\pi$$
0.808063 + 0.589097i $$0.200516\pi$$
$$128$$ −0.965926 + 0.258819i −0.0853766 + 0.0228766i
$$129$$ 0 0
$$130$$ 0.633975 + 0.169873i 0.0556033 + 0.0148988i
$$131$$ 2.03339 + 7.58871i 0.177658 + 0.663028i 0.996084 + 0.0884160i $$0.0281805\pi$$
−0.818426 + 0.574612i $$0.805153\pi$$
$$132$$ 0 0
$$133$$ −1.73205 6.46410i −0.150188 0.560509i
$$134$$ −2.96713 2.96713i −0.256321 0.256321i
$$135$$ 0 0
$$136$$ −5.59808 3.23205i −0.480031 0.277146i
$$137$$ 16.0740i 1.37329i −0.726991 0.686647i $$-0.759082\pi$$
0.726991 0.686647i $$-0.240918\pi$$
$$138$$ 0 0
$$139$$ 0.339746 + 0.196152i 0.0288169 + 0.0166374i 0.514339 0.857587i $$-0.328037\pi$$
−0.485522 + 0.874224i $$0.661371\pi$$
$$140$$ −1.55291 + 1.55291i −0.131245 + 0.131245i
$$141$$ 0 0
$$142$$ 1.73205 + 1.73205i 0.145350 + 0.145350i
$$143$$ 0.896575 + 0.240237i 0.0749754 + 0.0200896i
$$144$$ 0 0
$$145$$ −7.50000 12.9904i −0.622841 1.07879i
$$146$$ 6.17449 1.65445i 0.511005 0.136923i
$$147$$ 0 0
$$148$$ 2.13397 5.69615i 0.175412 0.468221i
$$149$$ 15.5935i 1.27747i −0.769427 0.638735i $$-0.779458\pi$$
0.769427 0.638735i $$-0.220542\pi$$
$$150$$ 0 0
$$151$$ 15.0000 8.66025i 1.22068 0.704761i 0.255619 0.966778i $$-0.417721\pi$$
0.965064 + 0.262016i $$0.0843873\pi$$
$$152$$ 2.63896 + 4.57081i 0.214048 + 0.370742i
$$153$$ 0 0
$$154$$ −2.19615 + 2.19615i −0.176971 + 0.176971i
$$155$$ 12.1595 7.02030i 0.976676 0.563884i
$$156$$ 0 0
$$157$$ −3.06218 + 5.30385i −0.244388 + 0.423293i −0.961959 0.273192i $$-0.911921\pi$$
0.717571 + 0.696485i $$0.245254\pi$$
$$158$$ 3.48477i 0.277233i
$$159$$ 0 0
$$160$$ 0.866025 1.50000i 0.0684653 0.118585i
$$161$$ −1.13681 + 4.24264i −0.0895933 + 0.334367i
$$162$$ 0 0
$$163$$ −0.366025 + 0.0980762i −0.0286693 + 0.00768192i −0.273125 0.961978i $$-0.588057\pi$$
0.244456 + 0.969660i $$0.421391\pi$$
$$164$$ −5.01910 2.89778i −0.391926 0.226278i
$$165$$ 0 0
$$166$$ 0.928203 3.46410i 0.0720425 0.268866i
$$167$$ −6.45189 + 24.0788i −0.499263 + 1.86327i 0.00544916 + 0.999985i $$0.498265\pi$$
−0.504712 + 0.863288i $$0.668401\pi$$
$$168$$ 0 0
$$169$$ −11.1340 6.42820i −0.856460 0.494477i
$$170$$ 10.8147 2.89778i 0.829446 0.222249i
$$171$$ 0 0
$$172$$ −0.0980762 + 0.366025i −0.00747824 + 0.0279092i
$$173$$ −8.03699 + 13.9205i −0.611041 + 1.05835i 0.380024 + 0.924977i $$0.375916\pi$$
−0.991065 + 0.133378i $$0.957418\pi$$
$$174$$ 0 0
$$175$$ 2.53590i 0.191696i
$$176$$ 1.22474 2.12132i 0.0923186 0.159901i
$$177$$ 0 0
$$178$$ 3.69615 2.13397i 0.277038 0.159948i
$$179$$ −15.8338 + 15.8338i −1.18347 + 1.18347i −0.204631 + 0.978839i $$0.565599\pi$$
−0.978839 + 0.204631i $$0.934401\pi$$
$$180$$ 0 0
$$181$$ −8.59808 14.8923i −0.639090 1.10694i −0.985633 0.168902i $$-0.945978\pi$$
0.346543 0.938034i $$-0.387356\pi$$
$$182$$ −0.416102 + 0.240237i −0.0308435 + 0.0178075i
$$183$$ 0 0
$$184$$ 3.46410i 0.255377i
$$185$$ 4.36276 + 9.58991i 0.320756 + 0.705064i
$$186$$ 0 0
$$187$$ 15.2942 4.09808i 1.11842 0.299681i
$$188$$ 2.12132 + 3.67423i 0.154713 + 0.267971i
$$189$$ 0 0
$$190$$ −8.83013 2.36603i −0.640605 0.171650i
$$191$$ −9.14162 9.14162i −0.661464 0.661464i 0.294261 0.955725i $$-0.404927\pi$$
−0.955725 + 0.294261i $$0.904927\pi$$
$$192$$ 0 0
$$193$$ −2.90192 + 2.90192i −0.208885 + 0.208885i −0.803793 0.594908i $$-0.797188\pi$$
0.594908 + 0.803793i $$0.297188\pi$$
$$194$$ 0.448288 + 0.258819i 0.0321852 + 0.0185821i
$$195$$ 0 0
$$196$$ 5.39230i 0.385165i
$$197$$ 9.67784 + 5.58750i 0.689518 + 0.398093i 0.803431 0.595397i $$-0.203005\pi$$
−0.113914 + 0.993491i $$0.536339\pi$$
$$198$$ 0 0
$$199$$ 19.5885 + 19.5885i 1.38859 + 1.38859i 0.828291 + 0.560297i $$0.189313\pi$$
0.560297 + 0.828291i $$0.310687\pi$$
$$200$$ −0.517638 1.93185i −0.0366025 0.136603i
$$201$$ 0 0
$$202$$ −0.571797 2.13397i −0.0402315 0.150146i
$$203$$ 10.6066 + 2.84203i 0.744438 + 0.199471i
$$204$$ 0 0
$$205$$ 9.69615 2.59808i 0.677209 0.181458i
$$206$$ 2.63896 4.57081i 0.183865 0.318463i
$$207$$ 0 0
$$208$$ 0.267949 0.267949i 0.0185789 0.0185789i
$$209$$ −12.4877 3.34607i −0.863791 0.231452i
$$210$$ 0 0
$$211$$ −17.8038 −1.22567 −0.612834 0.790212i $$-0.709970\pi$$
−0.612834 + 0.790212i $$0.709970\pi$$
$$212$$ 6.03579 0.414540
$$213$$ 0 0
$$214$$ −7.73205 7.73205i −0.528552 0.528552i
$$215$$ −0.328169 0.568406i −0.0223810 0.0387650i
$$216$$ 0 0
$$217$$ −2.66025 + 9.92820i −0.180590 + 0.673970i
$$218$$ 2.65754 1.53433i 0.179991 0.103918i
$$219$$ 0 0
$$220$$ 1.09808 + 4.09808i 0.0740323 + 0.276292i
$$221$$ 2.44949 0.164771
$$222$$ 0 0
$$223$$ 18.3923 1.23164 0.615820 0.787887i $$-0.288825\pi$$
0.615820 + 0.787887i $$0.288825\pi$$
$$224$$ 0.328169 + 1.22474i 0.0219267 + 0.0818317i
$$225$$ 0 0
$$226$$ 6.80385 3.92820i 0.452585 0.261300i
$$227$$ 5.22715 19.5080i 0.346938 1.29479i −0.543394 0.839478i $$-0.682861\pi$$
0.890332 0.455312i $$-0.150472\pi$$
$$228$$ 0 0
$$229$$ −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i $$-0.177186\pi$$
−0.882073 + 0.471113i $$0.843853\pi$$
$$230$$ 4.24264 + 4.24264i 0.279751 + 0.279751i
$$231$$ 0 0
$$232$$ −8.66025 −0.568574
$$233$$ −9.38186 −0.614626 −0.307313 0.951609i $$-0.599430\pi$$
−0.307313 + 0.951609i $$0.599430\pi$$
$$234$$ 0 0
$$235$$ −7.09808 1.90192i −0.463027 0.124068i
$$236$$ 4.24264 4.24264i 0.276172 0.276172i
$$237$$ 0 0
$$238$$ −4.09808 + 7.09808i −0.265639 + 0.460100i
$$239$$ −22.8541 + 6.12372i −1.47831 + 0.396111i −0.905770 0.423769i $$-0.860707\pi$$
−0.572535 + 0.819880i $$0.694040\pi$$
$$240$$ 0 0
$$241$$ −13.2942 3.56218i −0.856357 0.229460i −0.196178 0.980568i $$-0.562853\pi$$
−0.660179 + 0.751108i $$0.729520\pi$$
$$242$$ −1.29410 4.82963i −0.0831876 0.310460i
$$243$$ 0 0
$$244$$ −2.86603 10.6962i −0.183478 0.684751i
$$245$$ −6.60420 6.60420i −0.421927 0.421927i
$$246$$ 0 0
$$247$$ −1.73205 1.00000i −0.110208 0.0636285i
$$248$$ 8.10634i 0.514753i
$$249$$ 0 0
$$250$$ 10.5000 + 6.06218i 0.664078 + 0.383406i
$$251$$ −5.13922 + 5.13922i −0.324384 + 0.324384i −0.850446 0.526062i $$-0.823668\pi$$
0.526062 + 0.850446i $$0.323668\pi$$
$$252$$ 0 0
$$253$$ 6.00000 + 6.00000i 0.377217 + 0.377217i
$$254$$ −2.31079 0.619174i −0.144992 0.0388504i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −5.91567 + 1.58510i −0.369010 + 0.0988758i −0.438558 0.898703i $$-0.644511\pi$$
0.0695487 + 0.997579i $$0.477844\pi$$
$$258$$ 0 0
$$259$$ −7.22243 2.70577i −0.448780 0.168128i
$$260$$ 0.656339i 0.0407044i
$$261$$ 0 0
$$262$$ −6.80385 + 3.92820i −0.420343 + 0.242685i
$$263$$ −2.20925 3.82654i −0.136228 0.235954i 0.789838 0.613316i $$-0.210165\pi$$
−0.926066 + 0.377361i $$0.876831\pi$$
$$264$$ 0 0
$$265$$ −7.39230 + 7.39230i −0.454106 + 0.454106i
$$266$$ 5.79555 3.34607i 0.355348 0.205160i
$$267$$ 0 0
$$268$$ 2.09808 3.63397i 0.128160 0.221980i
$$269$$ 4.24264i 0.258678i 0.991600 + 0.129339i $$0.0412856\pi$$
−0.991600 + 0.129339i $$0.958714\pi$$
$$270$$ 0 0
$$271$$ 13.5622 23.4904i 0.823844 1.42694i −0.0789562 0.996878i $$-0.525159\pi$$
0.902800 0.430061i $$-0.141508\pi$$
$$272$$ 1.67303 6.24384i 0.101443 0.378589i
$$273$$ 0 0
$$274$$ 15.5263 4.16025i 0.937977 0.251330i
$$275$$ 4.24264 + 2.44949i 0.255841 + 0.147710i
$$276$$ 0 0
$$277$$ −7.06218 + 26.3564i −0.424325 + 1.58360i 0.341067 + 0.940039i $$0.389212\pi$$
−0.765392 + 0.643564i $$0.777455\pi$$
$$278$$ −0.101536 + 0.378937i −0.00608972 + 0.0227272i
$$279$$ 0 0
$$280$$ −1.90192 1.09808i −0.113662 0.0656226i
$$281$$ 27.5450 7.38065i 1.64320 0.440293i 0.685499 0.728073i $$-0.259584\pi$$
0.957696 + 0.287780i $$0.0929173\pi$$
$$282$$ 0 0
$$283$$ −5.22243 + 19.4904i −0.310441 + 1.15858i 0.617718 + 0.786400i $$0.288057\pi$$
−0.928159 + 0.372183i $$0.878609\pi$$
$$284$$ −1.22474 + 2.12132i −0.0726752 + 0.125877i
$$285$$ 0 0
$$286$$ 0.928203i 0.0548858i
$$287$$ −3.67423 + 6.36396i −0.216883 + 0.375653i
$$288$$ 0 0
$$289$$ 21.4641 12.3923i 1.26259 0.728959i
$$290$$ 10.6066 10.6066i 0.622841 0.622841i
$$291$$ 0 0
$$292$$ 3.19615 + 5.53590i 0.187041 + 0.323964i
$$293$$ −10.2462 + 5.91567i −0.598592 + 0.345597i −0.768488 0.639865i $$-0.778990\pi$$
0.169895 + 0.985462i $$0.445657\pi$$
$$294$$ 0 0
$$295$$ 10.3923i 0.605063i
$$296$$ 6.05437 + 0.586988i 0.351903 + 0.0341180i
$$297$$ 0 0
$$298$$ 15.0622 4.03590i 0.872529 0.233793i
$$299$$ 0.656339 + 1.13681i 0.0379571 + 0.0657435i
$$300$$ 0 0
$$301$$ 0.464102 + 0.124356i 0.0267504 + 0.00716774i
$$302$$ 12.2474 + 12.2474i 0.704761 + 0.704761i
$$303$$ 0 0
$$304$$ −3.73205 + 3.73205i −0.214048 + 0.214048i
$$305$$ 16.6102 + 9.58991i 0.951098 + 0.549117i
$$306$$ 0 0
$$307$$ 33.1244i 1.89051i 0.326337 + 0.945253i $$0.394186\pi$$
−0.326337 + 0.945253i $$0.605814\pi$$
$$308$$ −2.68973 1.55291i −0.153261 0.0884855i
$$309$$ 0 0
$$310$$ 9.92820 + 9.92820i 0.563884 + 0.563884i
$$311$$ 0.744272 + 2.77766i 0.0422038 + 0.157507i 0.983812 0.179204i $$-0.0573522\pi$$
−0.941608 + 0.336711i $$0.890686\pi$$
$$312$$ 0 0
$$313$$ 4.52628 + 16.8923i 0.255840 + 0.954810i 0.967621 + 0.252408i $$0.0812224\pi$$
−0.711781 + 0.702402i $$0.752111\pi$$
$$314$$ −5.91567 1.58510i −0.333841 0.0894524i
$$315$$ 0 0
$$316$$ 3.36603 0.901924i 0.189354 0.0507372i
$$317$$ 7.70882 13.3521i 0.432971 0.749927i −0.564157 0.825668i $$-0.690799\pi$$
0.997128 + 0.0757404i $$0.0241320\pi$$
$$318$$ 0 0
$$319$$ 15.0000 15.0000i 0.839839 0.839839i
$$320$$ 1.67303 + 0.448288i 0.0935254 + 0.0250600i
$$321$$ 0 0
$$322$$ −4.39230 −0.244774
$$323$$ −34.1170 −1.89832
$$324$$ 0 0
$$325$$ 0.535898 + 0.535898i 0.0297263 + 0.0297263i
$$326$$ −0.189469 0.328169i −0.0104937 0.0181756i
$$327$$ 0 0
$$328$$ 1.50000 5.59808i 0.0828236 0.309102i
$$329$$ 4.65874 2.68973i 0.256845 0.148289i
$$330$$ 0 0
$$331$$ 5.85641 + 21.8564i 0.321897 + 1.20134i 0.917394 + 0.397979i $$0.130288\pi$$
−0.595497 + 0.803357i $$0.703045\pi$$
$$332$$ 3.58630 0.196824
$$333$$ 0 0
$$334$$ −24.9282 −1.36401
$$335$$ 1.88108 + 7.02030i 0.102775 + 0.383560i
$$336$$ 0 0
$$337$$ −31.2846 + 18.0622i −1.70418 + 0.983910i −0.762757 + 0.646685i $$0.776155\pi$$
−0.941424 + 0.337224i $$0.890512\pi$$
$$338$$ 3.32748 12.4183i 0.180991 0.675468i
$$339$$ 0 0
$$340$$ 5.59808 + 9.69615i 0.303598 + 0.525848i
$$341$$ 14.0406 + 14.0406i 0.760341 + 0.760341i
$$342$$ 0 0
$$343$$ 15.7128 0.848412
$$344$$ −0.378937 −0.0204309
$$345$$ 0 0
$$346$$ −15.5263 4.16025i −0.834698 0.223657i
$$347$$ 13.3843 13.3843i 0.718505 0.718505i −0.249794 0.968299i $$-0.580363\pi$$
0.968299 + 0.249794i $$0.0803630\pi$$
$$348$$ 0 0
$$349$$ −2.76795 + 4.79423i −0.148165 + 0.256629i −0.930549 0.366167i $$-0.880670\pi$$
0.782384 + 0.622796i $$0.214003\pi$$
$$350$$ −2.44949 + 0.656339i −0.130931 + 0.0350828i
$$351$$ 0 0
$$352$$ 2.36603 + 0.633975i 0.126110 + 0.0337910i
$$353$$ −6.48408 24.1989i −0.345113 1.28798i −0.892480 0.451086i $$-0.851037\pi$$
0.547368 0.836892i $$-0.315630\pi$$
$$354$$ 0 0
$$355$$ −1.09808 4.09808i −0.0582798 0.217503i
$$356$$ 3.01790 + 3.01790i 0.159948 + 0.159948i
$$357$$ 0 0
$$358$$ −19.3923 11.1962i −1.02492 0.591735i
$$359$$ 3.10583i 0.163919i 0.996636 + 0.0819597i $$0.0261179\pi$$
−0.996636 + 0.0819597i $$0.973882\pi$$
$$360$$ 0 0
$$361$$ 7.66987 + 4.42820i 0.403678 + 0.233063i
$$362$$ 12.1595 12.1595i 0.639090 0.639090i
$$363$$ 0 0
$$364$$ −0.339746 0.339746i −0.0178075 0.0178075i
$$365$$ −10.6945 2.86559i −0.559778 0.149992i
$$366$$ 0 0
$$367$$ 14.5885 + 25.2679i 0.761511 + 1.31898i 0.942071 + 0.335412i $$0.108876\pi$$
−0.180560 + 0.983564i $$0.557791\pi$$
$$368$$ 3.34607 0.896575i 0.174426 0.0467372i
$$369$$ 0 0
$$370$$ −8.13397 + 6.69615i −0.422865 + 0.348116i
$$371$$ 7.65308i 0.397328i
$$372$$ 0 0
$$373$$ −6.06218 + 3.50000i −0.313888 + 0.181223i −0.648665 0.761074i $$-0.724672\pi$$
0.334777 + 0.942297i $$0.391339\pi$$
$$374$$ 7.91688 + 13.7124i 0.409372 + 0.709053i
$$375$$ 0 0
$$376$$ −3.00000 + 3.00000i −0.154713 + 0.154713i
$$377$$ 2.84203 1.64085i 0.146372 0.0845079i
$$378$$ 0 0
$$379$$ −4.56218 + 7.90192i −0.234343 + 0.405895i −0.959082 0.283130i $$-0.908627\pi$$
0.724738 + 0.689024i $$0.241961\pi$$
$$380$$ 9.14162i 0.468955i
$$381$$ 0 0
$$382$$ 6.46410 11.1962i 0.330732 0.572845i
$$383$$ −4.81105 + 17.9551i −0.245833 + 0.917461i 0.727130 + 0.686500i $$0.240854\pi$$
−0.972963 + 0.230961i $$0.925813\pi$$
$$384$$ 0 0
$$385$$ 5.19615 1.39230i 0.264820 0.0709584i
$$386$$ −3.55412 2.05197i −0.180900 0.104443i
$$387$$ 0 0
$$388$$ −0.133975 + 0.500000i −0.00680153 + 0.0253837i
$$389$$ 0.536220 2.00120i 0.0271875 0.101465i −0.950999 0.309194i $$-0.899941\pi$$
0.978186 + 0.207729i $$0.0666073\pi$$
$$390$$ 0 0
$$391$$ 19.3923 + 11.1962i 0.980711 + 0.566214i
$$392$$ −5.20857 + 1.39563i −0.263072 + 0.0704900i
$$393$$ 0 0
$$394$$ −2.89230 + 10.7942i −0.145712 + 0.543805i
$$395$$ −3.01790 + 5.22715i −0.151847 + 0.263006i
$$396$$ 0 0
$$397$$ 7.58846i 0.380854i 0.981701 + 0.190427i $$0.0609872\pi$$
−0.981701 + 0.190427i $$0.939013\pi$$
$$398$$ −13.8511 + 23.9909i −0.694294 + 1.20255i
$$399$$ 0 0
$$400$$ 1.73205 1.00000i 0.0866025 0.0500000i
$$401$$ −12.0716 + 12.0716i −0.602826 + 0.602826i −0.941062 0.338235i $$-0.890170\pi$$
0.338235 + 0.941062i $$0.390170\pi$$
$$402$$ 0 0
$$403$$ 1.53590 + 2.66025i 0.0765085 + 0.132517i
$$404$$ 1.91327 1.10463i 0.0951887 0.0549572i
$$405$$ 0 0
$$406$$ 10.9808i 0.544966i
$$407$$ −11.5032 + 9.46979i −0.570191 + 0.469400i
$$408$$ 0 0
$$409$$ 27.2583 7.30385i 1.34784 0.361152i 0.488501 0.872563i $$-0.337544\pi$$
0.859336 + 0.511411i $$0.170877\pi$$
$$410$$ 5.01910 + 8.69333i 0.247876 + 0.429333i
$$411$$ 0 0
$$412$$ 5.09808 + 1.36603i 0.251164 + 0.0672992i
$$413$$ −5.37945 5.37945i −0.264706 0.264706i
$$414$$ 0 0
$$415$$ −4.39230 + 4.39230i −0.215610 + 0.215610i
$$416$$ 0.328169 + 0.189469i 0.0160898 + 0.00928947i
$$417$$ 0 0
$$418$$ 12.9282i 0.632339i
$$419$$ 17.5390 + 10.1261i 0.856835 + 0.494694i 0.862951 0.505288i $$-0.168614\pi$$
−0.00611634 + 0.999981i $$0.501947\pi$$
$$420$$ 0 0
$$421$$ −10.8301 10.8301i −0.527828 0.527828i 0.392096 0.919924i $$-0.371750\pi$$
−0.919924 + 0.392096i $$0.871750\pi$$
$$422$$ −4.60797 17.1972i −0.224313 0.837146i
$$423$$ 0 0
$$424$$ 1.56218 + 5.83013i 0.0758661 + 0.283136i
$$425$$ 12.4877 + 3.34607i 0.605742 + 0.162308i
$$426$$ 0 0
$$427$$ −13.5622 + 3.63397i −0.656320 + 0.175860i
$$428$$ 5.46739 9.46979i 0.264276 0.457740i
$$429$$ 0 0
$$430$$ 0.464102 0.464102i 0.0223810 0.0223810i
$$431$$ 19.5080 + 5.22715i 0.939667 + 0.251783i 0.695972 0.718069i $$-0.254974\pi$$
0.243695 + 0.969852i $$0.421640\pi$$
$$432$$ 0 0
$$433$$ 18.8038 0.903655 0.451828 0.892105i $$-0.350772\pi$$
0.451828 + 0.892105i $$0.350772\pi$$
$$434$$ −10.2784 −0.493381
$$435$$ 0 0
$$436$$ 2.16987 + 2.16987i 0.103918 + 0.103918i
$$437$$ −9.14162 15.8338i −0.437303 0.757431i
$$438$$ 0 0
$$439$$ 7.66025 28.5885i 0.365604 1.36445i −0.500996 0.865449i $$-0.667033\pi$$
0.866600 0.499003i $$-0.166300\pi$$
$$440$$ −3.67423 + 2.12132i −0.175162 + 0.101130i
$$441$$ 0 0
$$442$$ 0.633975 + 2.36603i 0.0301551 + 0.112540i
$$443$$ 23.6627 1.12425 0.562124 0.827053i $$-0.309984\pi$$
0.562124 + 0.827053i $$0.309984\pi$$
$$444$$ 0 0
$$445$$ −7.39230 −0.350429
$$446$$ 4.76028 + 17.7656i 0.225406 + 0.841226i
$$447$$ 0 0
$$448$$ −1.09808 + 0.633975i −0.0518792 + 0.0299525i
$$449$$ 4.00240 14.9372i 0.188885 0.704929i −0.804880 0.593437i $$-0.797771\pi$$
0.993765 0.111492i $$-0.0355628\pi$$
$$450$$ 0 0
$$451$$ 7.09808 + 12.2942i 0.334235 + 0.578913i
$$452$$ 5.55532 + 5.55532i 0.261300 + 0.261300i
$$453$$ 0 0
$$454$$ 20.1962 0.947852
$$455$$ 0.832204 0.0390143
$$456$$ 0 0
$$457$$ 0.669873 + 0.179492i 0.0313353 + 0.00839628i 0.274453 0.961601i $$-0.411503\pi$$
−0.243117 + 0.969997i $$0.578170\pi$$
$$458$$ 0.707107 0.707107i 0.0330409 0.0330409i
$$459$$ 0 0
$$460$$ −3.00000 + 5.19615i −0.139876 + 0.242272i
$$461$$ 9.14162 2.44949i 0.425768 0.114084i −0.0395711 0.999217i $$-0.512599\pi$$
0.465339 + 0.885133i $$0.345932\pi$$
$$462$$ 0 0
$$463$$ −40.9545 10.9737i −1.90332 0.509992i −0.995979 0.0895888i $$-0.971445\pi$$
−0.907337 0.420403i $$-0.861889\pi$$
$$464$$ −2.24144 8.36516i −0.104056 0.388343i
$$465$$ 0 0
$$466$$ −2.42820 9.06218i −0.112484 0.419797i
$$467$$ −3.76217 3.76217i −0.174092 0.174092i 0.614682 0.788775i $$-0.289284\pi$$
−0.788775 + 0.614682i $$0.789284\pi$$
$$468$$ 0 0
$$469$$ −4.60770 2.66025i −0.212764 0.122839i
$$470$$ 7.34847i 0.338960i
$$471$$ 0 0
$$472$$ 5.19615 + 3.00000i 0.239172 + 0.138086i
$$473$$ 0.656339 0.656339i 0.0301785 0.0301785i
$$474$$ 0 0
$$475$$ −7.46410 7.46410i −0.342476 0.342476i
$$476$$ −7.91688 2.12132i −0.362869 0.0972306i
$$477$$ 0 0
$$478$$ −11.8301 20.4904i −0.541097 0.937208i
$$479$$ −2.68973 + 0.720710i −0.122897 + 0.0329301i −0.319743 0.947504i $$-0.603597\pi$$
0.196846 + 0.980434i $$0.436930\pi$$
$$480$$ 0 0
$$481$$ −2.09808 + 0.954483i −0.0956640 + 0.0435207i
$$482$$ 13.7632i 0.626897i
$$483$$ 0 0
$$484$$ 4.33013 2.50000i 0.196824 0.113636i
$$485$$ −0.448288 0.776457i −0.0203557 0.0352571i
$$486$$ 0 0
$$487$$ −9.26795 + 9.26795i −0.419971 + 0.419971i −0.885194 0.465223i $$-0.845974\pi$$
0.465223 + 0.885194i $$0.345974\pi$$
$$488$$ 9.58991 5.53674i 0.434115 0.250636i
$$489$$ 0 0
$$490$$ 4.66987 8.08846i 0.210963 0.365399i
$$491$$ 22.5259i 1.01658i −0.861186 0.508289i $$-0.830278\pi$$
0.861186 0.508289i $$-0.169722\pi$$
$$492$$ 0 0
$$493$$ 27.9904 48.4808i 1.26062 2.18346i
$$494$$ 0.517638 1.93185i 0.0232896 0.0869181i
$$495$$ 0 0
$$496$$ 7.83013 2.09808i 0.351583 0.0942064i
$$497$$ 2.68973 + 1.55291i 0.120651 + 0.0696577i
$$498$$ 0 0
$$499$$ 0.366025 1.36603i 0.0163855 0.0611517i −0.957249 0.289265i $$-0.906589\pi$$
0.973635 + 0.228113i $$0.0732557\pi$$
$$500$$ −3.13801 + 11.7112i −0.140336 + 0.523742i
$$501$$ 0 0
$$502$$ −6.29423 3.63397i −0.280925 0.162192i
$$503$$ −3.67423 + 0.984508i −0.163826 + 0.0438971i −0.339800 0.940498i $$-0.610359\pi$$
0.175974 + 0.984395i $$0.443693\pi$$
$$504$$ 0 0
$$505$$ −0.990381 + 3.69615i −0.0440714 + 0.164477i
$$506$$ −4.24264 + 7.34847i −0.188608 + 0.326679i
$$507$$ 0 0
$$508$$ 2.39230i 0.106141i
$$509$$ 3.46618 6.00361i 0.153636 0.266105i −0.778926 0.627116i $$-0.784235\pi$$
0.932561 + 0.361011i $$0.117568\pi$$
$$510$$ 0 0
$$511$$ 7.01924 4.05256i 0.310513 0.179275i
$$512$$ 0.707107 0.707107i 0.0312500 0.0312500i
$$513$$ 0 0
$$514$$ −3.06218 5.30385i −0.135067 0.233943i
$$515$$ −7.91688 + 4.57081i −0.348859 + 0.201414i
$$516$$ 0 0
$$517$$ 10.3923i 0.457053i
$$518$$ 0.744272 7.67664i 0.0327014 0.337292i
$$519$$ 0 0
$$520$$ −0.633975 + 0.169873i −0.0278016 + 0.00744942i
$$521$$ 13.9527 + 24.1667i 0.611277 + 1.05876i 0.991025 + 0.133674i $$0.0426774\pi$$
−0.379748 + 0.925090i $$0.623989\pi$$
$$522$$ 0 0
$$523$$ −31.5885 8.46410i −1.38127 0.370109i −0.509686 0.860361i $$-0.670238\pi$$
−0.871581 + 0.490251i $$0.836905\pi$$
$$524$$ −5.55532 5.55532i −0.242685 0.242685i
$$525$$ 0 0
$$526$$ 3.12436 3.12436i 0.136228 0.136228i
$$527$$ 45.3799 + 26.2001i 1.97678 + 1.14129i
$$528$$ 0 0
$$529$$ 11.0000i 0.478261i
$$530$$ −9.05369 5.22715i −0.393267 0.227053i
$$531$$ 0 0
$$532$$ 4.73205 + 4.73205i 0.205160 + 0.205160i
$$533$$ 0.568406 + 2.12132i 0.0246204 + 0.0918846i
$$534$$ 0 0
$$535$$ 4.90192 + 18.2942i 0.211929 + 0.790928i
$$536$$ 4.05317 + 1.08604i 0.175070 + 0.0469100i
$$537$$ 0 0
$$538$$ −4.09808 + 1.09808i −0.176681 + 0.0473414i
$$539$$ 6.60420 11.4388i 0.284463 0.492704i
$$540$$ 0 0
$$541$$ 19.4186 19.4186i 0.834870 0.834870i −0.153308 0.988178i $$-0.548993\pi$$
0.988178 + 0.153308i $$0.0489927\pi$$
$$542$$ 26.2001 + 7.02030i 1.12539 + 0.301548i
$$543$$ 0 0
$$544$$ 6.46410 0.277146
$$545$$ −5.31508 −0.227673
$$546$$ 0 0
$$547$$ −28.3205 28.3205i −1.21090 1.21090i −0.970732 0.240166i $$-0.922798\pi$$
−0.240166 0.970732i $$-0.577202\pi$$
$$548$$ 8.03699 + 13.9205i 0.343323 + 0.594653i
$$549$$ 0 0
$$550$$ −1.26795 + 4.73205i −0.0540655 + 0.201775i
$$551$$ −39.5844 + 22.8541i −1.68635 + 0.973615i
$$552$$ 0 0
$$553$$ −1.14359 4.26795i −0.0486305 0.181492i
$$554$$ −27.2862 −1.15928
$$555$$ 0 0
$$556$$ −0.392305 −0.0166374
$$557$$ −4.53862 16.9384i −0.192308 0.717702i −0.992947 0.118556i $$-0.962174\pi$$
0.800640 0.599146i $$-0.204493\pi$$
$$558$$ 0 0
$$559$$ 0.124356 0.0717968i 0.00525968 0.00303668i
$$560$$ 0.568406 2.12132i 0.0240195 0.0896421i
$$561$$ 0 0
$$562$$ 14.2583 + 24.6962i 0.601451 + 1.04174i
$$563$$ −28.7375 28.7375i −1.21114 1.21114i −0.970651 0.240492i $$-0.922691\pi$$
−0.240492 0.970651i $$-0.577309\pi$$
$$564$$ 0 0
$$565$$ −13.6077 −0.572480
$$566$$ −20.1779 −0.848142
$$567$$ 0 0
$$568$$ −2.36603 0.633975i −0.0992762 0.0266010i
$$569$$ 17.7148 17.7148i 0.742644 0.742644i −0.230442 0.973086i $$-0.574017\pi$$
0.973086 + 0.230442i $$0.0740171\pi$$
$$570$$ 0 0
$$571$$ 12.9282 22.3923i 0.541028 0.937089i −0.457817 0.889047i $$-0.651368\pi$$
0.998845 0.0480423i $$-0.0152982\pi$$
$$572$$ −0.896575 + 0.240237i −0.0374877 + 0.0100448i
$$573$$ 0 0
$$574$$ −7.09808 1.90192i −0.296268 0.0793848i
$$575$$ 1.79315 + 6.69213i 0.0747796 + 0.279081i
$$576$$ 0 0
$$577$$ −3.70577 13.8301i −0.154273 0.575756i −0.999166 0.0408207i $$-0.987003\pi$$
0.844893 0.534935i $$-0.179664\pi$$
$$578$$ 17.5254 + 17.5254i 0.728959 + 0.728959i
$$579$$ 0 0
$$580$$ 12.9904 + 7.50000i 0.539396 + 0.311421i
$$581$$ 4.54725i 0.188652i
$$582$$ 0 0
$$583$$ −12.8038 7.39230i −0.530281 0.306158i
$$584$$ −4.52004 + 4.52004i −0.187041 + 0.187041i
$$585$$ 0 0
$$586$$ −8.36603 8.36603i −0.345597 0.345597i
$$587$$ −12.4877 3.34607i −0.515422 0.138107i −0.00827376 0.999966i $$-0.502634\pi$$
−0.507148 + 0.861859i $$0.669300\pi$$
$$588$$ 0 0
$$589$$ −21.3923 37.0526i −0.881455 1.52672i
$$590$$ −10.0382 + 2.68973i −0.413266 + 0.110734i
$$591$$ 0 0
$$592$$ 1.00000 + 6.00000i 0.0410997 + 0.246598i
$$593$$ 21.1488i 0.868478i −0.900798 0.434239i $$-0.857017\pi$$
0.900798 0.434239i $$-0.142983\pi$$
$$594$$ 0 0
$$595$$ 12.2942 7.09808i 0.504014 0.290993i
$$596$$ 7.79676 + 13.5044i 0.319368 + 0.553161i
$$597$$ 0 0
$$598$$ −0.928203 + 0.928203i −0.0379571 + 0.0379571i
$$599$$ 14.4331 8.33298i 0.589722 0.340476i −0.175266 0.984521i $$-0.556078\pi$$
0.764988 + 0.644045i $$0.222745\pi$$
$$600$$ 0 0
$$601$$ −12.2321 + 21.1865i −0.498956 + 0.864217i −0.999999 0.00120537i $$-0.999616\pi$$
0.501044 + 0.865422i $$0.332950\pi$$
$$602$$ 0.480473i 0.0195826i
$$603$$ 0 0
$$604$$ −8.66025 + 15.0000i −0.352381 + 0.610341i
$$605$$ −2.24144 + 8.36516i −0.0911274 + 0.340092i
$$606$$ 0 0
$$607$$ −37.4904 + 10.0455i −1.52169 + 0.407735i −0.920297 0.391220i $$-0.872053\pi$$
−0.601391 + 0.798955i $$0.705386\pi$$
$$608$$ −4.57081 2.63896i −0.185371 0.107024i
$$609$$ 0 0
$$610$$ −4.96410 + 18.5263i −0.200991 + 0.750107i
$$611$$ 0.416102 1.55291i 0.0168337 0.0628242i
$$612$$ 0 0
$$613$$ 26.0885 + 15.0622i 1.05370 + 0.608356i 0.923684 0.383156i $$-0.125163\pi$$
0.130019 + 0.991511i $$0.458496\pi$$
$$614$$ −31.9957 + 8.57321i −1.29124 + 0.345987i
$$615$$ 0 0
$$616$$ 0.803848 3.00000i 0.0323879 0.120873i
$$617$$ −17.4746 + 30.2669i −0.703501 + 1.21850i 0.263729 + 0.964597i $$0.415048\pi$$
−0.967230 + 0.253902i $$0.918286\pi$$
$$618$$ 0 0
$$619$$ 44.1962i 1.77639i −0.459463 0.888197i $$-0.651958\pi$$
0.459463 0.888197i $$-0.348042\pi$$
$$620$$ −7.02030 + 12.1595i −0.281942 + 0.488338i
$$621$$ 0 0
$$622$$ −2.49038 + 1.43782i −0.0998552 + 0.0576514i
$$623$$ 3.82654 3.82654i 0.153307 0.153307i
$$624$$ 0 0
$$625$$ −5.50000 9.52628i −0.220000 0.381051i
$$626$$ −15.1452 + 8.74410i −0.605325 + 0.349485i
$$627$$ 0 0
$$628$$ 6.12436i 0.244388i
$$629$$ −22.8541 + 31.9957i −0.911251 + 1.27575i
$$630$$ 0 0
$$631$$ 10.6603 2.85641i 0.424378 0.113712i −0.0403079 0.999187i $$-0.512834\pi$$
0.464686 + 0.885476i $$0.346167\pi$$
$$632$$ 1.74238 + 3.01790i 0.0693083 + 0.120045i
$$633$$ 0 0
$$634$$ 14.8923 + 3.99038i 0.591449 + 0.158478i
$$635$$ 2.92996 + 2.92996i 0.116272 + 0.116272i
$$636$$ 0 0
$$637$$ 1.44486 1.44486i 0.0572476 0.0572476i
$$638$$ 18.3712 + 10.6066i 0.727322 + 0.419919i
$$639$$ 0 0
$$640$$ 1.73205i 0.0684653i
$$641$$ −42.3299 24.4392i −1.67193 0.965288i −0.966557 0.256450i $$-0.917447\pi$$
−0.705371 0.708838i $$-0.749220\pi$$
$$642$$ 0 0
$$643$$ −13.3397 13.3397i −0.526068 0.526068i 0.393329 0.919398i $$-0.371323\pi$$
−0.919398 + 0.393329i $$0.871323\pi$$
$$644$$ −1.13681 4.24264i −0.0447967 0.167183i
$$645$$ 0 0
$$646$$ −8.83013 32.9545i −0.347417 1.29658i
$$647$$ 26.8565 + 7.19617i 1.05584 + 0.282910i 0.744662 0.667442i $$-0.232611\pi$$
0.311175 + 0.950353i $$0.399278\pi$$
$$648$$ 0 0
$$649$$ −14.1962 + 3.80385i −0.557248 + 0.149314i
$$650$$ −0.378937 + 0.656339i −0.0148631 + 0.0257437i
$$651$$ 0 0
$$652$$ 0.267949 0.267949i 0.0104937 0.0104937i
$$653$$ 13.5923 + 3.64205i 0.531908 + 0.142524i 0.514769 0.857329i $$-0.327878\pi$$
0.0171389 + 0.999853i $$0.494544\pi$$
$$654$$ 0 0
$$655$$ 13.6077 0.531697
$$656$$ 5.79555 0.226278
$$657$$ 0 0
$$658$$ 3.80385 + 3.80385i 0.148289 + 0.148289i
$$659$$ −17.8671 30.9468i −0.696005 1.20552i −0.969841 0.243739i $$-0.921626\pi$$
0.273836 0.961776i $$-0.411707\pi$$
$$660$$ 0 0
$$661$$ −7.55256 + 28.1865i −0.293760 + 1.09633i 0.648436 + 0.761269i $$0.275423\pi$$
−0.942197 + 0.335060i $$0.891243\pi$$
$$662$$ −19.5959 + 11.3137i −0.761617 + 0.439720i
$$663$$ 0 0
$$664$$ 0.928203 + 3.46410i 0.0360213 + 0.134433i
$$665$$ −11.5911 −0.449484
$$666$$ 0 0
$$667$$ 30.0000 1.16160
$$668$$ −6.45189 24.0788i −0.249631 0.931637i
$$669$$ 0 0
$$670$$ −6.29423 + 3.63397i −0.243167 + 0.140393i
$$671$$ −7.02030 + 26.2001i −0.271016 + 1.01144i
$$672$$ 0 0
$$673$$ 11.6603 + 20.1962i 0.449470 + 0.778504i 0.998352 0.0573955i $$-0.0182796\pi$$
−0.548882 + 0.835900i $$0.684946\pi$$
$$674$$ −25.5438 25.5438i −0.983910 0.983910i
$$675$$ 0 0
$$676$$ 12.8564 0.494477
$$677$$ 20.3166 0.780831 0.390416 0.920639i $$-0.372331\pi$$
0.390416 + 0.920639i $$0.372331\pi$$
$$678$$ 0 0
$$679$$ 0.633975 + 0.169873i 0.0243297 + 0.00651913i
$$680$$ −7.91688 + 7.91688i −0.303598 + 0.303598i
$$681$$ 0 0
$$682$$ −9.92820 + 17.1962i −0.380171 + 0.658475i
$$683$$ −14.3688 + 3.85010i −0.549806 + 0.147320i −0.523019 0.852321i $$-0.675194\pi$$
−0.0267869 + 0.999641i $$0.508528\pi$$
$$684$$ 0 0
$$685$$ −26.8923 7.20577i −1.02750 0.275318i
$$686$$ 4.06678 + 15.1774i 0.155270 + 0.579476i
$$687$$ 0 0
$$688$$ −0.0980762 0.366025i −0.00373912 0.0139546i
$$689$$ −1.61729 1.61729i −0.0616137 0.0616137i
$$690$$ 0 0
$$691$$ −19.5622 11.2942i −0.744180 0.429653i 0.0794069 0.996842i $$-0.474697\pi$$
−0.823587 + 0.567190i $$0.808031\pi$$
$$692$$ 16.0740i 0.611041i
$$693$$ 0 0
$$694$$ 16.3923 + 9.46410i 0.622243 + 0.359252i
$$695$$ 0.480473 0.480473i 0.0182254 0.0182254i
$$696$$ 0 0
$$697$$ 26.4904 + 26.4904i 1.00339 + 1.00339i
$$698$$ −5.34727 1.43280i −0.202397 0.0542321i
$$699$$ 0 0
$$700$$ −1.26795 2.19615i −0.0479240 0.0830068i
$$701$$ 15.8338 4.24264i 0.598033 0.160242i 0.0529108 0.998599i $$-0.483150\pi$$
0.545122 + 0.838357i $$0.316483\pi$$
$$702$$ 0 0
$$703$$ 29.2224 13.2942i 1.10214 0.501401i
$$704$$ 2.44949i 0.0923186i
$$705$$ 0 0
$$706$$ 21.6962 12.5263i 0.816545 0.471433i
$$707$$ −1.40061 2.42593i −0.0526754 0.0912364i
$$708$$ 0 0
$$709$$ −25.9282 + 25.9282i −0.973754 + 0.973754i −0.999664 0.0259102i $$-0.991752\pi$$
0.0259102 + 0.999664i $$0.491752\pi$$
$$710$$ 3.67423 2.12132i 0.137892 0.0796117i
$$711$$ 0 0
$$712$$ −2.13397 + 3.69615i −0.0799741 + 0.138519i
$$713$$ 28.0812i 1.05165i
$$714$$ 0 0
$$715$$ 0.803848 1.39230i 0.0300622 0.0520692i
$$716$$ 5.79555 21.6293i 0.216590 0.808325i
$$717$$ 0 0
$$718$$ −3.00000 + 0.803848i −0.111959 + 0.0299993i
$$719$$ 10.8704 + 6.27603i 0.405398 + 0.234056i 0.688810 0.724942i $$-0.258133\pi$$
−0.283413 + 0.958998i $$0.591467\pi$$
$$720$$ 0 0
$$721$$ 1.73205 6.46410i 0.0645049 0.240736i
$$722$$ −2.29221 + 8.55463i −0.0853071 + 0.318370i
$$723$$ 0 0
$$724$$ 14.8923 + 8.59808i 0.553468 + 0.319545i
$$725$$ 16.7303 4.48288i 0.621349 0.166490i
$$726$$ 0 0
$$727$$ −11.4641 + 42.7846i −0.425180 + 1.58679i 0.338350 + 0.941020i $$0.390131\pi$$
−0.763530 + 0.645773i $$0.776535\pi$$
$$728$$ 0.240237 0.416102i 0.00890376 0.0154218i
$$729$$ 0 0
$$730$$ 11.0718i 0.409786i
$$731$$ 1.22474 2.12132i 0.0452988 0.0784599i
$$732$$ 0 0
$$733$$ 6.00000 3.46410i 0.221615 0.127950i −0.385083 0.922882i $$-0.625827\pi$$
0.606698 + 0.794933i $$0.292494\pi$$
$$734$$ −20.6312 + 20.6312i −0.761511 + 0.761511i
$$735$$ 0 0
$$736$$ 1.73205 + 3.00000i 0.0638442 + 0.110581i
$$737$$ −8.90138 + 5.13922i −0.327887 + 0.189305i
$$738$$ 0 0
$$739$$ 28.3923i 1.04443i −0.852815 0.522214i $$-0.825106\pi$$
0.852815 0.522214i $$-0.174894\pi$$
$$740$$ −8.57321 6.12372i −0.315158 0.225113i
$$741$$ 0 0
$$742$$ 7.39230 1.98076i 0.271380 0.0727161i
$$743$$ 2.12132 + 3.67423i 0.0778237 + 0.134795i 0.902311 0.431086i $$-0.141870\pi$$
−0.824487 + 0.565881i $$0.808536\pi$$
$$744$$ 0 0
$$745$$ −26.0885 6.99038i −0.955807 0.256108i
$$746$$ −4.94975 4.94975i −0.181223 0.181223i
$$747$$ 0 0
$$748$$ −11.1962 + 11.1962i −0.409372 + 0.409372i
$$749$$ −12.0072 6.93237i −0.438734 0.253303i
$$750$$ 0 0
$$751$$ 50.5885i 1.84600i −0.384801 0.923000i $$-0.625730\pi$$
0.384801 0.923000i $$-0.374270\pi$$
$$752$$ −3.67423 2.12132i −0.133986 0.0773566i
$$753$$ 0 0
$$754$$ 2.32051 + 2.32051i 0.0845079 + 0.0845079i
$$755$$ −7.76457 28.9778i −0.282582 1.05461i
$$756$$ 0 0
$$757$$ 9.91858 + 37.0167i 0.360497 + 1.34539i 0.873424 + 0.486961i $$0.161895\pi$$
−0.512927 + 0.858432i $$0.671439\pi$$
$$758$$ −8.81345 2.36156i −0.320119 0.0857756i
$$759$$ 0 0
$$760$$ 8.83013 2.36603i 0.320302 0.0858248i
$$761$$ −0.776457 + 1.34486i −0.0281465 + 0.0487513i −0.879756 0.475426i $$-0.842294\pi$$
0.851609 + 0.524178i $$0.175627\pi$$
$$762$$ 0 0
$$763$$ 2.75129 2.75129i 0.0996033 0.0996033i
$$764$$ 12.4877 + 3.34607i 0.451789 + 0.121056i
$$765$$ 0 0
$$766$$ −18.5885 −0.671628
$$767$$ −2.27362 −0.0820958
$$768$$ 0 0
$$769$$ −27.1962 27.1962i −0.980718 0.980718i 0.0190993 0.999818i $$-0.493920\pi$$
−0.999818 + 0.0190993i $$0.993920\pi$$
$$770$$ 2.68973 + 4.65874i 0.0969310 + 0.167889i
$$771$$ 0 0
$$772$$ 1.06218 3.96410i 0.0382286 0.142671i
$$773$$ −14.0728 + 8.12493i −0.506163 + 0.292233i −0.731255 0.682104i $$-0.761065\pi$$
0.225092 + 0.974337i $$0.427732\pi$$
$$774$$ 0 0
$$775$$ 4.19615 + 15.6603i 0.150730 + 0.562533i
$$776$$ −0.517638 −0.0185821
$$777$$ 0 0
$$778$$ 2.07180 0.0742775
$$779$$ −7.91688 29.5462i −0.283651 1.05860i
$$780$$ 0 0
$$781$$ 5.19615 3.00000i 0.185933 0.107348i
$$782$$ −5.79555 + 21.6293i −0.207249