# Properties

 Label 285.2.i.d.106.2 Level $285$ Weight $2$ Character 285.106 Analytic conductor $2.276$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$285 = 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 285.i (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: $$2.27573645761$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 2x^{2} + 4$$ x^4 + 2*x^2 + 4 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 106.2 Root $$0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 285.106 Dual form 285.2.i.d.121.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.207107 - 0.358719i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.207107 - 0.358719i) q^{6} +1.82843 q^{7} +1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.207107 - 0.358719i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.207107 - 0.358719i) q^{6} +1.82843 q^{7} +1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.207107 - 0.358719i) q^{10} -2.82843 q^{11} +1.82843 q^{12} +(0.914214 + 1.58346i) q^{13} +(0.378680 - 0.655892i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(0.585786 - 1.01461i) q^{17} -0.414214 q^{18} +(4.00000 - 1.73205i) q^{19} +1.82843 q^{20} +(0.914214 - 1.58346i) q^{21} +(-0.585786 + 1.01461i) q^{22} +(0.414214 + 0.717439i) q^{23} +(0.792893 - 1.37333i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.757359 q^{26} -1.00000 q^{27} +(1.67157 + 2.89525i) q^{28} +(-4.82843 - 8.36308i) q^{29} -0.414214 q^{30} -5.00000 q^{31} +(2.20711 + 3.82282i) q^{32} +(-1.41421 + 2.44949i) q^{33} +(-0.242641 - 0.420266i) q^{34} +(0.914214 - 1.58346i) q^{35} +(0.914214 - 1.58346i) q^{36} -2.17157 q^{37} +(0.207107 - 1.79360i) q^{38} +1.82843 q^{39} +(0.792893 - 1.37333i) q^{40} +(-1.41421 + 2.44949i) q^{41} +(-0.378680 - 0.655892i) q^{42} +(-3.91421 + 6.77962i) q^{43} +(-2.58579 - 4.47871i) q^{44} -1.00000 q^{45} +0.343146 q^{46} +(1.58579 + 2.74666i) q^{47} +(1.50000 + 2.59808i) q^{48} -3.65685 q^{49} -0.414214 q^{50} +(-0.585786 - 1.01461i) q^{51} +(-1.67157 + 2.89525i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-0.207107 + 0.358719i) q^{54} +(-1.41421 + 2.44949i) q^{55} +2.89949 q^{56} +(0.500000 - 4.33013i) q^{57} -4.00000 q^{58} +(0.914214 - 1.58346i) q^{60} +(4.15685 + 7.19988i) q^{61} +(-1.03553 + 1.79360i) q^{62} +(-0.914214 - 1.58346i) q^{63} -4.17157 q^{64} +1.82843 q^{65} +(0.585786 + 1.01461i) q^{66} +(-2.74264 - 4.75039i) q^{67} +2.14214 q^{68} +0.828427 q^{69} +(-0.378680 - 0.655892i) q^{70} +(-5.00000 + 8.66025i) q^{71} +(-0.792893 - 1.37333i) q^{72} +(-4.74264 + 8.21449i) q^{73} +(-0.449747 + 0.778985i) q^{74} -1.00000 q^{75} +(6.39949 + 4.75039i) q^{76} -5.17157 q^{77} +(0.378680 - 0.655892i) q^{78} +(1.67157 - 2.89525i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.585786 + 1.01461i) q^{82} -8.00000 q^{83} +3.34315 q^{84} +(-0.585786 - 1.01461i) q^{85} +(1.62132 + 2.80821i) q^{86} -9.65685 q^{87} -4.48528 q^{88} +(-6.24264 - 10.8126i) q^{89} +(-0.207107 + 0.358719i) q^{90} +(1.67157 + 2.89525i) q^{91} +(-0.757359 + 1.31178i) q^{92} +(-2.50000 + 4.33013i) q^{93} +1.31371 q^{94} +(0.500000 - 4.33013i) q^{95} +4.41421 q^{96} +(3.00000 - 5.19615i) q^{97} +(-0.757359 + 1.31178i) q^{98} +(1.41421 + 2.44949i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9}+O(q^{10})$$ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9 $$4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{12} - 2 q^{13} + 10 q^{14} - 2 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} + 16 q^{19} - 4 q^{20} - 2 q^{21} - 8 q^{22} - 4 q^{23} + 6 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 20 q^{31} + 6 q^{32} + 16 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} - 2 q^{38} - 4 q^{39} + 6 q^{40} - 10 q^{42} - 10 q^{43} - 16 q^{44} - 4 q^{45} + 24 q^{46} + 12 q^{47} + 6 q^{48} + 8 q^{49} + 4 q^{50} - 8 q^{51} - 18 q^{52} + 4 q^{53} + 2 q^{54} - 28 q^{56} + 2 q^{57} - 16 q^{58} - 2 q^{60} - 6 q^{61} + 10 q^{62} + 2 q^{63} - 28 q^{64} - 4 q^{65} + 8 q^{66} + 6 q^{67} - 48 q^{68} - 8 q^{69} - 10 q^{70} - 20 q^{71} - 6 q^{72} - 2 q^{73} + 18 q^{74} - 4 q^{75} - 14 q^{76} - 32 q^{77} + 10 q^{78} + 18 q^{79} + 6 q^{80} - 2 q^{81} + 8 q^{82} - 32 q^{83} + 36 q^{84} - 8 q^{85} - 2 q^{86} - 16 q^{87} + 16 q^{88} - 8 q^{89} + 2 q^{90} + 18 q^{91} - 20 q^{92} - 10 q^{93} - 40 q^{94} + 2 q^{95} + 12 q^{96} + 12 q^{97} - 20 q^{98}+O(q^{100})$$ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^12 - 2 * q^13 + 10 * q^14 - 2 * q^15 - 6 * q^16 + 8 * q^17 + 4 * q^18 + 16 * q^19 - 4 * q^20 - 2 * q^21 - 8 * q^22 - 4 * q^23 + 6 * q^24 - 2 * q^25 + 20 * q^26 - 4 * q^27 + 18 * q^28 - 8 * q^29 + 4 * q^30 - 20 * q^31 + 6 * q^32 + 16 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 - 2 * q^38 - 4 * q^39 + 6 * q^40 - 10 * q^42 - 10 * q^43 - 16 * q^44 - 4 * q^45 + 24 * q^46 + 12 * q^47 + 6 * q^48 + 8 * q^49 + 4 * q^50 - 8 * q^51 - 18 * q^52 + 4 * q^53 + 2 * q^54 - 28 * q^56 + 2 * q^57 - 16 * q^58 - 2 * q^60 - 6 * q^61 + 10 * q^62 + 2 * q^63 - 28 * q^64 - 4 * q^65 + 8 * q^66 + 6 * q^67 - 48 * q^68 - 8 * q^69 - 10 * q^70 - 20 * q^71 - 6 * q^72 - 2 * q^73 + 18 * q^74 - 4 * q^75 - 14 * q^76 - 32 * q^77 + 10 * q^78 + 18 * q^79 + 6 * q^80 - 2 * q^81 + 8 * q^82 - 32 * q^83 + 36 * q^84 - 8 * q^85 - 2 * q^86 - 16 * q^87 + 16 * q^88 - 8 * q^89 + 2 * q^90 + 18 * q^91 - 20 * q^92 - 10 * q^93 - 40 * q^94 + 2 * q^95 + 12 * q^96 + 12 * q^97 - 20 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$$.

 $$n$$ $$172$$ $$191$$ $$211$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.207107 0.358719i 0.146447 0.253653i −0.783465 0.621436i $$-0.786550\pi$$
0.929912 + 0.367783i $$0.119883\pi$$
$$3$$ 0.500000 0.866025i 0.288675 0.500000i
$$4$$ 0.914214 + 1.58346i 0.457107 + 0.791732i
$$5$$ 0.500000 0.866025i 0.223607 0.387298i
$$6$$ −0.207107 0.358719i −0.0845510 0.146447i
$$7$$ 1.82843 0.691080 0.345540 0.938404i $$-0.387696\pi$$
0.345540 + 0.938404i $$0.387696\pi$$
$$8$$ 1.58579 0.560660
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ −0.207107 0.358719i −0.0654929 0.113437i
$$11$$ −2.82843 −0.852803 −0.426401 0.904534i $$-0.640219\pi$$
−0.426401 + 0.904534i $$0.640219\pi$$
$$12$$ 1.82843 0.527821
$$13$$ 0.914214 + 1.58346i 0.253557 + 0.439174i 0.964503 0.264073i $$-0.0850661\pi$$
−0.710945 + 0.703247i $$0.751733\pi$$
$$14$$ 0.378680 0.655892i 0.101206 0.175295i
$$15$$ −0.500000 0.866025i −0.129099 0.223607i
$$16$$ −1.50000 + 2.59808i −0.375000 + 0.649519i
$$17$$ 0.585786 1.01461i 0.142074 0.246080i −0.786203 0.617968i $$-0.787956\pi$$
0.928278 + 0.371888i $$0.121290\pi$$
$$18$$ −0.414214 −0.0976311
$$19$$ 4.00000 1.73205i 0.917663 0.397360i
$$20$$ 1.82843 0.408849
$$21$$ 0.914214 1.58346i 0.199498 0.345540i
$$22$$ −0.585786 + 1.01461i −0.124890 + 0.216316i
$$23$$ 0.414214 + 0.717439i 0.0863695 + 0.149596i 0.905974 0.423333i $$-0.139140\pi$$
−0.819604 + 0.572930i $$0.805807\pi$$
$$24$$ 0.792893 1.37333i 0.161849 0.280330i
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0.757359 0.148530
$$27$$ −1.00000 −0.192450
$$28$$ 1.67157 + 2.89525i 0.315898 + 0.547151i
$$29$$ −4.82843 8.36308i −0.896616 1.55299i −0.831791 0.555089i $$-0.812684\pi$$
−0.0648251 0.997897i $$-0.520649\pi$$
$$30$$ −0.414214 −0.0756247
$$31$$ −5.00000 −0.898027 −0.449013 0.893525i $$-0.648224\pi$$
−0.449013 + 0.893525i $$0.648224\pi$$
$$32$$ 2.20711 + 3.82282i 0.390165 + 0.675786i
$$33$$ −1.41421 + 2.44949i −0.246183 + 0.426401i
$$34$$ −0.242641 0.420266i −0.0416125 0.0720750i
$$35$$ 0.914214 1.58346i 0.154530 0.267654i
$$36$$ 0.914214 1.58346i 0.152369 0.263911i
$$37$$ −2.17157 −0.357004 −0.178502 0.983940i $$-0.557125\pi$$
−0.178502 + 0.983940i $$0.557125\pi$$
$$38$$ 0.207107 1.79360i 0.0335972 0.290960i
$$39$$ 1.82843 0.292783
$$40$$ 0.792893 1.37333i 0.125367 0.217143i
$$41$$ −1.41421 + 2.44949i −0.220863 + 0.382546i −0.955070 0.296379i $$-0.904221\pi$$
0.734207 + 0.678925i $$0.237554\pi$$
$$42$$ −0.378680 0.655892i −0.0584315 0.101206i
$$43$$ −3.91421 + 6.77962i −0.596912 + 1.03388i 0.396362 + 0.918094i $$0.370273\pi$$
−0.993274 + 0.115788i $$0.963061\pi$$
$$44$$ −2.58579 4.47871i −0.389822 0.675191i
$$45$$ −1.00000 −0.149071
$$46$$ 0.343146 0.0505941
$$47$$ 1.58579 + 2.74666i 0.231311 + 0.400642i 0.958194 0.286119i $$-0.0923653\pi$$
−0.726883 + 0.686761i $$0.759032\pi$$
$$48$$ 1.50000 + 2.59808i 0.216506 + 0.375000i
$$49$$ −3.65685 −0.522408
$$50$$ −0.414214 −0.0585786
$$51$$ −0.585786 1.01461i −0.0820265 0.142074i
$$52$$ −1.67157 + 2.89525i −0.231805 + 0.401499i
$$53$$ 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i $$-0.122805\pi$$
−0.789136 + 0.614218i $$0.789471\pi$$
$$54$$ −0.207107 + 0.358719i −0.0281837 + 0.0488155i
$$55$$ −1.41421 + 2.44949i −0.190693 + 0.330289i
$$56$$ 2.89949 0.387461
$$57$$ 0.500000 4.33013i 0.0662266 0.573539i
$$58$$ −4.00000 −0.525226
$$59$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$60$$ 0.914214 1.58346i 0.118024 0.204424i
$$61$$ 4.15685 + 7.19988i 0.532231 + 0.921851i 0.999292 + 0.0376256i $$0.0119794\pi$$
−0.467061 + 0.884225i $$0.654687\pi$$
$$62$$ −1.03553 + 1.79360i −0.131513 + 0.227787i
$$63$$ −0.914214 1.58346i −0.115180 0.199498i
$$64$$ −4.17157 −0.521447
$$65$$ 1.82843 0.226788
$$66$$ 0.585786 + 1.01461i 0.0721053 + 0.124890i
$$67$$ −2.74264 4.75039i −0.335067 0.580353i 0.648431 0.761274i $$-0.275426\pi$$
−0.983498 + 0.180921i $$0.942092\pi$$
$$68$$ 2.14214 0.259772
$$69$$ 0.828427 0.0997309
$$70$$ −0.378680 0.655892i −0.0452609 0.0783941i
$$71$$ −5.00000 + 8.66025i −0.593391 + 1.02778i 0.400381 + 0.916349i $$0.368878\pi$$
−0.993772 + 0.111434i $$0.964456\pi$$
$$72$$ −0.792893 1.37333i −0.0934434 0.161849i
$$73$$ −4.74264 + 8.21449i −0.555084 + 0.961434i 0.442813 + 0.896614i $$0.353981\pi$$
−0.997897 + 0.0648198i $$0.979353\pi$$
$$74$$ −0.449747 + 0.778985i −0.0522821 + 0.0905552i
$$75$$ −1.00000 −0.115470
$$76$$ 6.39949 + 4.75039i 0.734072 + 0.544907i
$$77$$ −5.17157 −0.589355
$$78$$ 0.378680 0.655892i 0.0428770 0.0742652i
$$79$$ 1.67157 2.89525i 0.188067 0.325741i −0.756539 0.653949i $$-0.773111\pi$$
0.944606 + 0.328208i $$0.106445\pi$$
$$80$$ 1.50000 + 2.59808i 0.167705 + 0.290474i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0.585786 + 1.01461i 0.0646893 + 0.112045i
$$83$$ −8.00000 −0.878114 −0.439057 0.898459i $$-0.644687\pi$$
−0.439057 + 0.898459i $$0.644687\pi$$
$$84$$ 3.34315 0.364767
$$85$$ −0.585786 1.01461i −0.0635375 0.110050i
$$86$$ 1.62132 + 2.80821i 0.174831 + 0.302817i
$$87$$ −9.65685 −1.03532
$$88$$ −4.48528 −0.478133
$$89$$ −6.24264 10.8126i −0.661719 1.14613i −0.980164 0.198189i $$-0.936494\pi$$
0.318445 0.947941i $$-0.396839\pi$$
$$90$$ −0.207107 + 0.358719i −0.0218310 + 0.0378124i
$$91$$ 1.67157 + 2.89525i 0.175228 + 0.303505i
$$92$$ −0.757359 + 1.31178i −0.0789602 + 0.136763i
$$93$$ −2.50000 + 4.33013i −0.259238 + 0.449013i
$$94$$ 1.31371 0.135499
$$95$$ 0.500000 4.33013i 0.0512989 0.444262i
$$96$$ 4.41421 0.450524
$$97$$ 3.00000 5.19615i 0.304604 0.527589i −0.672569 0.740034i $$-0.734809\pi$$
0.977173 + 0.212445i $$0.0681426\pi$$
$$98$$ −0.757359 + 1.31178i −0.0765048 + 0.132510i
$$99$$ 1.41421 + 2.44949i 0.142134 + 0.246183i
$$100$$ 0.914214 1.58346i 0.0914214 0.158346i
$$101$$ −6.07107 10.5154i −0.604094 1.04632i −0.992194 0.124704i $$-0.960202\pi$$
0.388100 0.921617i $$-0.373131\pi$$
$$102$$ −0.485281 −0.0480500
$$103$$ 9.82843 0.968424 0.484212 0.874951i $$-0.339106\pi$$
0.484212 + 0.874951i $$0.339106\pi$$
$$104$$ 1.44975 + 2.51104i 0.142159 + 0.246227i
$$105$$ −0.914214 1.58346i −0.0892181 0.154530i
$$106$$ 0.828427 0.0804640
$$107$$ 14.0000 1.35343 0.676716 0.736245i $$-0.263403\pi$$
0.676716 + 0.736245i $$0.263403\pi$$
$$108$$ −0.914214 1.58346i −0.0879702 0.152369i
$$109$$ 8.65685 14.9941i 0.829176 1.43618i −0.0695090 0.997581i $$-0.522143\pi$$
0.898685 0.438594i $$-0.144523\pi$$
$$110$$ 0.585786 + 1.01461i 0.0558525 + 0.0967394i
$$111$$ −1.08579 + 1.88064i −0.103058 + 0.178502i
$$112$$ −2.74264 + 4.75039i −0.259155 + 0.448870i
$$113$$ 4.00000 0.376288 0.188144 0.982141i $$-0.439753\pi$$
0.188144 + 0.982141i $$0.439753\pi$$
$$114$$ −1.44975 1.07616i −0.135781 0.100791i
$$115$$ 0.828427 0.0772512
$$116$$ 8.82843 15.2913i 0.819699 1.41976i
$$117$$ 0.914214 1.58346i 0.0845191 0.146391i
$$118$$ 0 0
$$119$$ 1.07107 1.85514i 0.0981846 0.170061i
$$120$$ −0.792893 1.37333i −0.0723809 0.125367i
$$121$$ −3.00000 −0.272727
$$122$$ 3.44365 0.311773
$$123$$ 1.41421 + 2.44949i 0.127515 + 0.220863i
$$124$$ −4.57107 7.91732i −0.410494 0.710996i
$$125$$ −1.00000 −0.0894427
$$126$$ −0.757359 −0.0674709
$$127$$ −6.48528 11.2328i −0.575476 0.996753i −0.995990 0.0894671i $$-0.971484\pi$$
0.420514 0.907286i $$-0.361850\pi$$
$$128$$ −5.27817 + 9.14207i −0.466529 + 0.808052i
$$129$$ 3.91421 + 6.77962i 0.344627 + 0.596912i
$$130$$ 0.378680 0.655892i 0.0332124 0.0575256i
$$131$$ −3.24264 + 5.61642i −0.283311 + 0.490709i −0.972198 0.234160i $$-0.924766\pi$$
0.688887 + 0.724868i $$0.258099\pi$$
$$132$$ −5.17157 −0.450128
$$133$$ 7.31371 3.16693i 0.634179 0.274608i
$$134$$ −2.27208 −0.196278
$$135$$ −0.500000 + 0.866025i −0.0430331 + 0.0745356i
$$136$$ 0.928932 1.60896i 0.0796553 0.137967i
$$137$$ 5.24264 + 9.08052i 0.447909 + 0.775801i 0.998250 0.0591390i $$-0.0188355\pi$$
−0.550341 + 0.834940i $$0.685502\pi$$
$$138$$ 0.171573 0.297173i 0.0146053 0.0252970i
$$139$$ 8.15685 + 14.1281i 0.691855 + 1.19833i 0.971229 + 0.238146i $$0.0765398\pi$$
−0.279374 + 0.960182i $$0.590127\pi$$
$$140$$ 3.34315 0.282547
$$141$$ 3.17157 0.267095
$$142$$ 2.07107 + 3.58719i 0.173800 + 0.301031i
$$143$$ −2.58579 4.47871i −0.216234 0.374529i
$$144$$ 3.00000 0.250000
$$145$$ −9.65685 −0.801958
$$146$$ 1.96447 + 3.40256i 0.162580 + 0.281597i
$$147$$ −1.82843 + 3.16693i −0.150806 + 0.261204i
$$148$$ −1.98528 3.43861i −0.163189 0.282652i
$$149$$ 0.585786 1.01461i 0.0479895 0.0831202i −0.841033 0.540984i $$-0.818052\pi$$
0.889022 + 0.457864i $$0.151385\pi$$
$$150$$ −0.207107 + 0.358719i −0.0169102 + 0.0292893i
$$151$$ 10.3431 0.841713 0.420857 0.907127i $$-0.361730\pi$$
0.420857 + 0.907127i $$0.361730\pi$$
$$152$$ 6.34315 2.74666i 0.514497 0.222784i
$$153$$ −1.17157 −0.0947161
$$154$$ −1.07107 + 1.85514i −0.0863091 + 0.149492i
$$155$$ −2.50000 + 4.33013i −0.200805 + 0.347804i
$$156$$ 1.67157 + 2.89525i 0.133833 + 0.231805i
$$157$$ 9.91421 17.1719i 0.791240 1.37047i −0.133959 0.990987i $$-0.542769\pi$$
0.925199 0.379482i $$-0.123898\pi$$
$$158$$ −0.692388 1.19925i −0.0550834 0.0954073i
$$159$$ 2.00000 0.158610
$$160$$ 4.41421 0.348974
$$161$$ 0.757359 + 1.31178i 0.0596883 + 0.103383i
$$162$$ 0.207107 + 0.358719i 0.0162718 + 0.0281837i
$$163$$ 15.1421 1.18602 0.593012 0.805194i $$-0.297939\pi$$
0.593012 + 0.805194i $$0.297939\pi$$
$$164$$ −5.17157 −0.403832
$$165$$ 1.41421 + 2.44949i 0.110096 + 0.190693i
$$166$$ −1.65685 + 2.86976i −0.128597 + 0.222736i
$$167$$ 12.4853 + 21.6251i 0.966140 + 1.67340i 0.706520 + 0.707693i $$0.250264\pi$$
0.259620 + 0.965711i $$0.416403\pi$$
$$168$$ 1.44975 2.51104i 0.111850 0.193731i
$$169$$ 4.82843 8.36308i 0.371417 0.643314i
$$170$$ −0.485281 −0.0372194
$$171$$ −3.50000 2.59808i −0.267652 0.198680i
$$172$$ −14.3137 −1.09141
$$173$$ −3.65685 + 6.33386i −0.278025 + 0.481554i −0.970894 0.239510i $$-0.923013\pi$$
0.692868 + 0.721064i $$0.256347\pi$$
$$174$$ −2.00000 + 3.46410i −0.151620 + 0.262613i
$$175$$ −0.914214 1.58346i −0.0691080 0.119699i
$$176$$ 4.24264 7.34847i 0.319801 0.553912i
$$177$$ 0 0
$$178$$ −5.17157 −0.387626
$$179$$ 16.1421 1.20652 0.603260 0.797545i $$-0.293868\pi$$
0.603260 + 0.797545i $$0.293868\pi$$
$$180$$ −0.914214 1.58346i −0.0681415 0.118024i
$$181$$ −12.6569 21.9223i −0.940777 1.62947i −0.763994 0.645223i $$-0.776765\pi$$
−0.176782 0.984250i $$-0.556569\pi$$
$$182$$ 1.38478 0.102646
$$183$$ 8.31371 0.614567
$$184$$ 0.656854 + 1.13770i 0.0484239 + 0.0838727i
$$185$$ −1.08579 + 1.88064i −0.0798286 + 0.138267i
$$186$$ 1.03553 + 1.79360i 0.0759290 + 0.131513i
$$187$$ −1.65685 + 2.86976i −0.121161 + 0.209857i
$$188$$ −2.89949 + 5.02207i −0.211467 + 0.366272i
$$189$$ −1.82843 −0.132999
$$190$$ −1.44975 1.07616i −0.105176 0.0780727i
$$191$$ −16.8284 −1.21766 −0.608831 0.793300i $$-0.708361\pi$$
−0.608831 + 0.793300i $$0.708361\pi$$
$$192$$ −2.08579 + 3.61269i −0.150529 + 0.260723i
$$193$$ 12.3995 21.4766i 0.892535 1.54592i 0.0557094 0.998447i $$-0.482258\pi$$
0.836826 0.547469i $$-0.184409\pi$$
$$194$$ −1.24264 2.15232i −0.0892164 0.154527i
$$195$$ 0.914214 1.58346i 0.0654682 0.113394i
$$196$$ −3.34315 5.79050i −0.238796 0.413607i
$$197$$ 17.6569 1.25800 0.628999 0.777406i $$-0.283465\pi$$
0.628999 + 0.777406i $$0.283465\pi$$
$$198$$ 1.17157 0.0832601
$$199$$ 8.50000 + 14.7224i 0.602549 + 1.04365i 0.992434 + 0.122782i $$0.0391815\pi$$
−0.389885 + 0.920864i $$0.627485\pi$$
$$200$$ −0.792893 1.37333i −0.0560660 0.0971092i
$$201$$ −5.48528 −0.386902
$$202$$ −5.02944 −0.353870
$$203$$ −8.82843 15.2913i −0.619634 1.07324i
$$204$$ 1.07107 1.85514i 0.0749897 0.129886i
$$205$$ 1.41421 + 2.44949i 0.0987730 + 0.171080i
$$206$$ 2.03553 3.52565i 0.141822 0.245644i
$$207$$ 0.414214 0.717439i 0.0287898 0.0498655i
$$208$$ −5.48528 −0.380336
$$209$$ −11.3137 + 4.89898i −0.782586 + 0.338869i
$$210$$ −0.757359 −0.0522628
$$211$$ 0.156854 0.271680i 0.0107983 0.0187032i −0.860576 0.509322i $$-0.829896\pi$$
0.871374 + 0.490619i $$0.163229\pi$$
$$212$$ −1.82843 + 3.16693i −0.125577 + 0.217506i
$$213$$ 5.00000 + 8.66025i 0.342594 + 0.593391i
$$214$$ 2.89949 5.02207i 0.198205 0.343302i
$$215$$ 3.91421 + 6.77962i 0.266947 + 0.462366i
$$216$$ −1.58579 −0.107899
$$217$$ −9.14214 −0.620609
$$218$$ −3.58579 6.21076i −0.242860 0.420646i
$$219$$ 4.74264 + 8.21449i 0.320478 + 0.555084i
$$220$$ −5.17157 −0.348667
$$221$$ 2.14214 0.144096
$$222$$ 0.449747 + 0.778985i 0.0301851 + 0.0522821i
$$223$$ −2.91421 + 5.04757i −0.195150 + 0.338010i −0.946950 0.321382i $$-0.895853\pi$$
0.751800 + 0.659392i $$0.229186\pi$$
$$224$$ 4.03553 + 6.98975i 0.269635 + 0.467022i
$$225$$ −0.500000 + 0.866025i −0.0333333 + 0.0577350i
$$226$$ 0.828427 1.43488i 0.0551062 0.0954467i
$$227$$ −18.9706 −1.25912 −0.629560 0.776952i $$-0.716765\pi$$
−0.629560 + 0.776952i $$0.716765\pi$$
$$228$$ 7.31371 3.16693i 0.484362 0.209735i
$$229$$ −4.65685 −0.307734 −0.153867 0.988092i $$-0.549173\pi$$
−0.153867 + 0.988092i $$0.549173\pi$$
$$230$$ 0.171573 0.297173i 0.0113132 0.0195950i
$$231$$ −2.58579 + 4.47871i −0.170132 + 0.294678i
$$232$$ −7.65685 13.2621i −0.502697 0.870697i
$$233$$ 12.6569 21.9223i 0.829178 1.43618i −0.0695057 0.997582i $$-0.522142\pi$$
0.898684 0.438597i $$-0.144524\pi$$
$$234$$ −0.378680 0.655892i −0.0247551 0.0428770i
$$235$$ 3.17157 0.206891
$$236$$ 0 0
$$237$$ −1.67157 2.89525i −0.108580 0.188067i
$$238$$ −0.443651 0.768426i −0.0287576 0.0498096i
$$239$$ −24.6274 −1.59302 −0.796508 0.604629i $$-0.793322\pi$$
−0.796508 + 0.604629i $$0.793322\pi$$
$$240$$ 3.00000 0.193649
$$241$$ −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i $$-0.218151\pi$$
−0.935242 + 0.354010i $$0.884818\pi$$
$$242$$ −0.621320 + 1.07616i −0.0399400 + 0.0691781i
$$243$$ 0.500000 + 0.866025i 0.0320750 + 0.0555556i
$$244$$ −7.60051 + 13.1645i −0.486572 + 0.842768i
$$245$$ −1.82843 + 3.16693i −0.116814 + 0.202328i
$$246$$ 1.17157 0.0746968
$$247$$ 6.39949 + 4.75039i 0.407190 + 0.302260i
$$248$$ −7.92893 −0.503488
$$249$$ −4.00000 + 6.92820i −0.253490 + 0.439057i
$$250$$ −0.207107 + 0.358719i −0.0130986 + 0.0226874i
$$251$$ 8.17157 + 14.1536i 0.515785 + 0.893366i 0.999832 + 0.0183240i $$0.00583304\pi$$
−0.484047 + 0.875042i $$0.660834\pi$$
$$252$$ 1.67157 2.89525i 0.105299 0.182384i
$$253$$ −1.17157 2.02922i −0.0736562 0.127576i
$$254$$ −5.37258 −0.337106
$$255$$ −1.17157 −0.0733667
$$256$$ −1.98528 3.43861i −0.124080 0.214913i
$$257$$ 8.41421 + 14.5738i 0.524864 + 0.909091i 0.999581 + 0.0289528i $$0.00921724\pi$$
−0.474717 + 0.880139i $$0.657449\pi$$
$$258$$ 3.24264 0.201878
$$259$$ −3.97056 −0.246719
$$260$$ 1.67157 + 2.89525i 0.103667 + 0.179556i
$$261$$ −4.82843 + 8.36308i −0.298872 + 0.517662i
$$262$$ 1.34315 + 2.32640i 0.0829798 + 0.143725i
$$263$$ −12.8995 + 22.3426i −0.795417 + 1.37770i 0.127157 + 0.991883i $$0.459415\pi$$
−0.922574 + 0.385820i $$0.873919\pi$$
$$264$$ −2.24264 + 3.88437i −0.138025 + 0.239066i
$$265$$ 2.00000 0.122859
$$266$$ 0.378680 3.27946i 0.0232183 0.201077i
$$267$$ −12.4853 −0.764087
$$268$$ 5.01472 8.68575i 0.306323 0.530566i
$$269$$ −0.828427 + 1.43488i −0.0505101 + 0.0874860i −0.890175 0.455619i $$-0.849418\pi$$
0.839665 + 0.543105i $$0.182751\pi$$
$$270$$ 0.207107 + 0.358719i 0.0126041 + 0.0218310i
$$271$$ −6.82843 + 11.8272i −0.414797 + 0.718450i −0.995407 0.0957318i $$-0.969481\pi$$
0.580610 + 0.814182i $$0.302814\pi$$
$$272$$ 1.75736 + 3.04384i 0.106556 + 0.184560i
$$273$$ 3.34315 0.202336
$$274$$ 4.34315 0.262379
$$275$$ 1.41421 + 2.44949i 0.0852803 + 0.147710i
$$276$$ 0.757359 + 1.31178i 0.0455877 + 0.0789602i
$$277$$ 6.00000 0.360505 0.180253 0.983620i $$-0.442309\pi$$
0.180253 + 0.983620i $$0.442309\pi$$
$$278$$ 6.75736 0.405279
$$279$$ 2.50000 + 4.33013i 0.149671 + 0.259238i
$$280$$ 1.44975 2.51104i 0.0866390 0.150063i
$$281$$ 3.48528 + 6.03668i 0.207914 + 0.360118i 0.951057 0.309014i $$-0.0999991\pi$$
−0.743143 + 0.669133i $$0.766666\pi$$
$$282$$ 0.656854 1.13770i 0.0391151 0.0677493i
$$283$$ 10.4853 18.1610i 0.623285 1.07956i −0.365584 0.930778i $$-0.619131\pi$$
0.988870 0.148784i $$-0.0475358\pi$$
$$284$$ −18.2843 −1.08497
$$285$$ −3.50000 2.59808i −0.207322 0.153897i
$$286$$ −2.14214 −0.126667
$$287$$ −2.58579 + 4.47871i −0.152634 + 0.264370i
$$288$$ 2.20711 3.82282i 0.130055 0.225262i
$$289$$ 7.81371 + 13.5337i 0.459630 + 0.796102i
$$290$$ −2.00000 + 3.46410i −0.117444 + 0.203419i
$$291$$ −3.00000 5.19615i −0.175863 0.304604i
$$292$$ −17.3431 −1.01493
$$293$$ −5.31371 −0.310430 −0.155215 0.987881i $$-0.549607\pi$$
−0.155215 + 0.987881i $$0.549607\pi$$
$$294$$ 0.757359 + 1.31178i 0.0441701 + 0.0765048i
$$295$$ 0 0
$$296$$ −3.44365 −0.200158
$$297$$ 2.82843 0.164122
$$298$$ −0.242641 0.420266i −0.0140558 0.0243454i
$$299$$ −0.757359 + 1.31178i −0.0437992 + 0.0758625i
$$300$$ −0.914214 1.58346i −0.0527821 0.0914214i
$$301$$ −7.15685 + 12.3960i −0.412514 + 0.714496i
$$302$$ 2.14214 3.71029i 0.123266 0.213503i
$$303$$ −12.1421 −0.697547
$$304$$ −1.50000 + 12.9904i −0.0860309 + 0.745049i
$$305$$ 8.31371 0.476042
$$306$$ −0.242641 + 0.420266i −0.0138708 + 0.0240250i
$$307$$ 8.82843 15.2913i 0.503865 0.872720i −0.496125 0.868251i $$-0.665244\pi$$
0.999990 0.00446862i $$-0.00142241\pi$$
$$308$$ −4.72792 8.18900i −0.269398 0.466612i
$$309$$ 4.91421 8.51167i 0.279560 0.484212i
$$310$$ 1.03553 + 1.79360i 0.0588144 + 0.101869i
$$311$$ −4.00000 −0.226819 −0.113410 0.993548i $$-0.536177\pi$$
−0.113410 + 0.993548i $$0.536177\pi$$
$$312$$ 2.89949 0.164152
$$313$$ 3.00000 + 5.19615i 0.169570 + 0.293704i 0.938269 0.345907i $$-0.112429\pi$$
−0.768699 + 0.639611i $$0.779095\pi$$
$$314$$ −4.10660 7.11284i −0.231749 0.401401i
$$315$$ −1.82843 −0.103020
$$316$$ 6.11270 0.343866
$$317$$ −2.65685 4.60181i −0.149224 0.258463i 0.781717 0.623633i $$-0.214344\pi$$
−0.930941 + 0.365170i $$0.881011\pi$$
$$318$$ 0.414214 0.717439i 0.0232279 0.0402320i
$$319$$ 13.6569 + 23.6544i 0.764637 + 1.32439i
$$320$$ −2.08579 + 3.61269i −0.116599 + 0.201955i
$$321$$ 7.00000 12.1244i 0.390702 0.676716i
$$322$$ 0.627417 0.0349646
$$323$$ 0.585786 5.07306i 0.0325940 0.282273i
$$324$$ −1.82843 −0.101579
$$325$$ 0.914214 1.58346i 0.0507114 0.0878348i
$$326$$ 3.13604 5.43178i 0.173689 0.300838i
$$327$$ −8.65685 14.9941i −0.478725 0.829176i
$$328$$ −2.24264 + 3.88437i −0.123829 + 0.214478i
$$329$$ 2.89949 + 5.02207i 0.159854 + 0.276876i
$$330$$ 1.17157 0.0644930
$$331$$ −5.34315 −0.293686 −0.146843 0.989160i $$-0.546911\pi$$
−0.146843 + 0.989160i $$0.546911\pi$$
$$332$$ −7.31371 12.6677i −0.401392 0.695231i
$$333$$ 1.08579 + 1.88064i 0.0595007 + 0.103058i
$$334$$ 10.3431 0.565952
$$335$$ −5.48528 −0.299693
$$336$$ 2.74264 + 4.75039i 0.149623 + 0.259155i
$$337$$ −8.74264 + 15.1427i −0.476242 + 0.824875i −0.999629 0.0272195i $$-0.991335\pi$$
0.523387 + 0.852095i $$0.324668\pi$$
$$338$$ −2.00000 3.46410i −0.108786 0.188422i
$$339$$ 2.00000 3.46410i 0.108625 0.188144i
$$340$$ 1.07107 1.85514i 0.0580868 0.100609i
$$341$$ 14.1421 0.765840
$$342$$ −1.65685 + 0.717439i −0.0895924 + 0.0387947i
$$343$$ −19.4853 −1.05211
$$344$$ −6.20711 + 10.7510i −0.334665 + 0.579656i
$$345$$ 0.414214 0.717439i 0.0223005 0.0386256i
$$346$$ 1.51472 + 2.62357i 0.0814318 + 0.141044i
$$347$$ 17.7279 30.7057i 0.951685 1.64837i 0.209906 0.977722i $$-0.432684\pi$$
0.741779 0.670645i $$-0.233982\pi$$
$$348$$ −8.82843 15.2913i −0.473253 0.819699i
$$349$$ −31.6274 −1.69298 −0.846488 0.532407i $$-0.821288\pi$$
−0.846488 + 0.532407i $$0.821288\pi$$
$$350$$ −0.757359 −0.0404826
$$351$$ −0.914214 1.58346i −0.0487971 0.0845191i
$$352$$ −6.24264 10.8126i −0.332734 0.576312i
$$353$$ −1.31371 −0.0699216 −0.0349608 0.999389i $$-0.511131\pi$$
−0.0349608 + 0.999389i $$0.511131\pi$$
$$354$$ 0 0
$$355$$ 5.00000 + 8.66025i 0.265372 + 0.459639i
$$356$$ 11.4142 19.7700i 0.604952 1.04781i
$$357$$ −1.07107 1.85514i −0.0566869 0.0981846i
$$358$$ 3.34315 5.79050i 0.176691 0.306037i
$$359$$ −4.58579 + 7.94282i −0.242029 + 0.419206i −0.961292 0.275532i $$-0.911146\pi$$
0.719263 + 0.694737i $$0.244479\pi$$
$$360$$ −1.58579 −0.0835783
$$361$$ 13.0000 13.8564i 0.684211 0.729285i
$$362$$ −10.4853 −0.551094
$$363$$ −1.50000 + 2.59808i −0.0787296 + 0.136364i
$$364$$ −3.05635 + 5.29375i −0.160196 + 0.277468i
$$365$$ 4.74264 + 8.21449i 0.248241 + 0.429966i
$$366$$ 1.72183 2.98229i 0.0900013 0.155887i
$$367$$ 17.0563 + 29.5425i 0.890334 + 1.54210i 0.839475 + 0.543398i $$0.182863\pi$$
0.0508591 + 0.998706i $$0.483804\pi$$
$$368$$ −2.48528 −0.129554
$$369$$ 2.82843 0.147242
$$370$$ 0.449747 + 0.778985i 0.0233813 + 0.0404975i
$$371$$ 1.82843 + 3.16693i 0.0949272 + 0.164419i
$$372$$ −9.14214 −0.473998
$$373$$ −11.6569 −0.603569 −0.301785 0.953376i $$-0.597582\pi$$
−0.301785 + 0.953376i $$0.597582\pi$$
$$374$$ 0.686292 + 1.18869i 0.0354873 + 0.0614658i
$$375$$ −0.500000 + 0.866025i −0.0258199 + 0.0447214i
$$376$$ 2.51472 + 4.35562i 0.129687 + 0.224624i
$$377$$ 8.82843 15.2913i 0.454687 0.787541i
$$378$$ −0.378680 + 0.655892i −0.0194772 + 0.0337355i
$$379$$ 1.68629 0.0866190 0.0433095 0.999062i $$-0.486210\pi$$
0.0433095 + 0.999062i $$0.486210\pi$$
$$380$$ 7.31371 3.16693i 0.375185 0.162460i
$$381$$ −12.9706 −0.664502
$$382$$ −3.48528 + 6.03668i −0.178323 + 0.308864i
$$383$$ 16.9706 29.3939i 0.867155 1.50196i 0.00226413 0.999997i $$-0.499279\pi$$
0.864891 0.501960i $$-0.167387\pi$$
$$384$$ 5.27817 + 9.14207i 0.269351 + 0.466529i
$$385$$ −2.58579 + 4.47871i −0.131784 + 0.228256i
$$386$$ −5.13604 8.89588i −0.261418 0.452788i
$$387$$ 7.82843 0.397941
$$388$$ 10.9706 0.556946
$$389$$ 7.72792 + 13.3852i 0.391821 + 0.678654i 0.992690 0.120694i $$-0.0385118\pi$$
−0.600869 + 0.799348i $$0.705179\pi$$
$$390$$ −0.378680 0.655892i −0.0191752 0.0332124i
$$391$$ 0.970563 0.0490835
$$392$$ −5.79899 −0.292893
$$393$$ 3.24264 + 5.61642i 0.163570 + 0.283311i
$$394$$ 3.65685 6.33386i 0.184230 0.319095i
$$395$$ −1.67157 2.89525i −0.0841060 0.145676i
$$396$$ −2.58579 + 4.47871i −0.129941 + 0.225064i
$$397$$ 11.9142 20.6360i 0.597957 1.03569i −0.395165 0.918610i $$-0.629313\pi$$
0.993122 0.117082i $$-0.0373541\pi$$
$$398$$ 7.04163 0.352965
$$399$$ 0.914214 7.91732i 0.0457679 0.396362i
$$400$$ 3.00000 0.150000
$$401$$ 11.3137 19.5959i 0.564980 0.978573i −0.432072 0.901839i $$-0.642217\pi$$
0.997052 0.0767343i $$-0.0244493\pi$$
$$402$$ −1.13604 + 1.96768i −0.0566605 + 0.0981388i
$$403$$ −4.57107 7.91732i −0.227701 0.394390i
$$404$$ 11.1005 19.2266i 0.552271 0.956561i
$$405$$ 0.500000 + 0.866025i 0.0248452 + 0.0430331i
$$406$$ −7.31371 −0.362973
$$407$$ 6.14214 0.304454
$$408$$ −0.928932 1.60896i −0.0459890 0.0796553i
$$409$$ −3.00000 5.19615i −0.148340 0.256933i 0.782274 0.622935i $$-0.214060\pi$$
−0.930614 + 0.366002i $$0.880726\pi$$
$$410$$ 1.17157 0.0578599
$$411$$ 10.4853 0.517201
$$412$$ 8.98528 + 15.5630i 0.442673 + 0.766732i
$$413$$ 0 0
$$414$$ −0.171573 0.297173i −0.00843235 0.0146053i
$$415$$ −4.00000 + 6.92820i −0.196352 + 0.340092i
$$416$$ −4.03553 + 6.98975i −0.197858 + 0.342701i
$$417$$ 16.3137 0.798886
$$418$$ −0.585786 + 5.07306i −0.0286518 + 0.248131i
$$419$$ 3.31371 0.161885 0.0809426 0.996719i $$-0.474207\pi$$
0.0809426 + 0.996719i $$0.474207\pi$$
$$420$$ 1.67157 2.89525i 0.0815644 0.141274i
$$421$$ 3.82843 6.63103i 0.186586 0.323177i −0.757524 0.652808i $$-0.773591\pi$$
0.944110 + 0.329631i $$0.106924\pi$$
$$422$$ −0.0649712 0.112533i −0.00316275 0.00547804i
$$423$$ 1.58579 2.74666i 0.0771036 0.133547i
$$424$$ 1.58579 + 2.74666i 0.0770126 + 0.133390i
$$425$$ −1.17157 −0.0568296
$$426$$ 4.14214 0.200687
$$427$$ 7.60051 + 13.1645i 0.367814 + 0.637073i
$$428$$ 12.7990 + 22.1685i 0.618663 + 1.07155i
$$429$$ −5.17157 −0.249686
$$430$$ 3.24264 0.156374
$$431$$ 1.24264 + 2.15232i 0.0598559 + 0.103673i 0.894401 0.447267i $$-0.147603\pi$$
−0.834545 + 0.550940i $$0.814269\pi$$
$$432$$ 1.50000 2.59808i 0.0721688 0.125000i
$$433$$ 19.9142 + 34.4924i 0.957016 + 1.65760i 0.729686 + 0.683783i $$0.239666\pi$$
0.227330 + 0.973818i $$0.427000\pi$$
$$434$$ −1.89340 + 3.27946i −0.0908860 + 0.157419i
$$435$$ −4.82843 + 8.36308i −0.231505 + 0.400979i
$$436$$ 31.6569 1.51609
$$437$$ 2.89949 + 2.15232i 0.138702 + 0.102959i
$$438$$ 3.92893 0.187732
$$439$$ −8.50000 + 14.7224i −0.405683 + 0.702663i −0.994401 0.105675i $$-0.966300\pi$$
0.588718 + 0.808339i $$0.299633\pi$$
$$440$$ −2.24264 + 3.88437i −0.106914 + 0.185180i
$$441$$ 1.82843 + 3.16693i 0.0870680 + 0.150806i
$$442$$ 0.443651 0.768426i 0.0211023 0.0365503i
$$443$$ −9.07107 15.7116i −0.430979 0.746478i 0.565978 0.824420i $$-0.308499\pi$$
−0.996958 + 0.0779417i $$0.975165\pi$$
$$444$$ −3.97056 −0.188435
$$445$$ −12.4853 −0.591859
$$446$$ 1.20711 + 2.09077i 0.0571582 + 0.0990008i
$$447$$ −0.585786 1.01461i −0.0277067 0.0479895i
$$448$$ −7.62742 −0.360362
$$449$$ 13.1716 0.621605 0.310802 0.950475i $$-0.399402\pi$$
0.310802 + 0.950475i $$0.399402\pi$$
$$450$$ 0.207107 + 0.358719i 0.00976311 + 0.0169102i
$$451$$ 4.00000 6.92820i 0.188353 0.326236i
$$452$$ 3.65685 + 6.33386i 0.172004 + 0.297920i
$$453$$ 5.17157 8.95743i 0.242982 0.420857i
$$454$$ −3.92893 + 6.80511i −0.184394 + 0.319380i
$$455$$ 3.34315 0.156729
$$456$$ 0.792893 6.86666i 0.0371306 0.321561i
$$457$$ −4.17157 −0.195138 −0.0975690 0.995229i $$-0.531107\pi$$
−0.0975690 + 0.995229i $$0.531107\pi$$
$$458$$ −0.964466 + 1.67050i −0.0450665 + 0.0780575i
$$459$$ −0.585786 + 1.01461i −0.0273422 + 0.0473580i
$$460$$ 0.757359 + 1.31178i 0.0353121 + 0.0611623i
$$461$$ −15.0711 + 26.1039i −0.701930 + 1.21578i 0.265859 + 0.964012i $$0.414345\pi$$
−0.967788 + 0.251766i $$0.918989\pi$$
$$462$$ 1.07107 + 1.85514i 0.0498306 + 0.0863091i
$$463$$ −22.7990 −1.05956 −0.529779 0.848135i $$-0.677725\pi$$
−0.529779 + 0.848135i $$0.677725\pi$$
$$464$$ 28.9706 1.34492
$$465$$ 2.50000 + 4.33013i 0.115935 + 0.200805i
$$466$$ −5.24264 9.08052i −0.242861 0.420647i
$$467$$ 23.7990 1.10129 0.550643 0.834741i $$-0.314383\pi$$
0.550643 + 0.834741i $$0.314383\pi$$
$$468$$ 3.34315 0.154537
$$469$$ −5.01472 8.68575i −0.231558 0.401071i
$$470$$ 0.656854 1.13770i 0.0302984 0.0524784i
$$471$$ −9.91421 17.1719i −0.456823 0.791240i
$$472$$ 0 0
$$473$$ 11.0711 19.1757i 0.509048 0.881697i
$$474$$ −1.38478 −0.0636049
$$475$$ −3.50000 2.59808i −0.160591 0.119208i
$$476$$ 3.91674 0.179523
$$477$$ 1.00000 1.73205i 0.0457869 0.0793052i
$$478$$ −5.10051 + 8.83433i −0.233292 + 0.404073i
$$479$$ −1.24264 2.15232i −0.0567777 0.0983419i 0.836240 0.548364i $$-0.184749\pi$$
−0.893017 + 0.450022i $$0.851416\pi$$
$$480$$ 2.20711 3.82282i 0.100740 0.174487i
$$481$$ −1.98528 3.43861i −0.0905210 0.156787i
$$482$$ −2.07107 −0.0943346
$$483$$ 1.51472 0.0689221
$$484$$ −2.74264 4.75039i −0.124665 0.215927i
$$485$$ −3.00000 5.19615i −0.136223 0.235945i
$$486$$ 0.414214 0.0187891
$$487$$ −6.34315 −0.287435 −0.143718 0.989619i $$-0.545906\pi$$
−0.143718 + 0.989619i $$0.545906\pi$$
$$488$$ 6.59188 + 11.4175i 0.298401 + 0.516845i
$$489$$ 7.57107 13.1135i 0.342376 0.593012i
$$490$$ 0.757359 + 1.31178i 0.0342140 + 0.0592604i
$$491$$ −11.8284 + 20.4874i −0.533809 + 0.924585i 0.465411 + 0.885095i $$0.345907\pi$$
−0.999220 + 0.0394901i $$0.987427\pi$$
$$492$$ −2.58579 + 4.47871i −0.116576 + 0.201916i
$$493$$ −11.3137 −0.509544
$$494$$ 3.02944 1.31178i 0.136301 0.0590200i
$$495$$ 2.82843 0.127128
$$496$$ 7.50000 12.9904i 0.336760 0.583285i
$$497$$ −9.14214 + 15.8346i −0.410081 + 0.710281i
$$498$$ 1.65685 + 2.86976i 0.0742454 + 0.128597i
$$499$$ 3.67157 6.35935i 0.164362 0.284684i −0.772066 0.635542i $$-0.780777\pi$$
0.936429 + 0.350858i $$0.114110\pi$$
$$500$$ −0.914214 1.58346i −0.0408849 0.0708147i
$$501$$ 24.9706 1.11560
$$502$$ 6.76955 0.302140
$$503$$ −6.92893 12.0013i −0.308946 0.535110i 0.669186 0.743095i $$-0.266643\pi$$
−0.978132 + 0.207985i $$0.933310\pi$$
$$504$$ −1.44975 2.51104i −0.0645769 0.111850i
$$505$$ −12.1421 −0.540318
$$506$$ −0.970563 −0.0431468
$$507$$ −4.82843 8.36308i −0.214438 0.371417i
$$508$$ 11.8579 20.5384i 0.526108 0.911245i
$$509$$ −16.5563 28.6764i −0.733847 1.27106i −0.955227 0.295873i $$-0.904389\pi$$
0.221380 0.975188i $$-0.428944\pi$$
$$510$$ −0.242641 + 0.420266i −0.0107443 + 0.0186097i
$$511$$ −8.67157 + 15.0196i −0.383608 + 0.664428i
$$512$$ −22.7574 −1.00574
$$513$$ −4.00000 + 1.73205i −0.176604 + 0.0764719i
$$514$$ 6.97056 0.307458
$$515$$ 4.91421 8.51167i 0.216546 0.375069i
$$516$$ −7.15685 + 12.3960i −0.315063 + 0.545705i
$$517$$ −4.48528 7.76874i −0.197262 0.341669i
$$518$$ −0.822330 + 1.42432i −0.0361311 + 0.0625809i
$$519$$ 3.65685 + 6.33386i 0.160518 + 0.278025i
$$520$$ 2.89949 0.127151
$$521$$ 6.34315 0.277898 0.138949 0.990300i $$-0.455628\pi$$
0.138949 + 0.990300i $$0.455628\pi$$
$$522$$ 2.00000 + 3.46410i 0.0875376 + 0.151620i
$$523$$ 14.8848 + 25.7812i 0.650866 + 1.12733i 0.982913 + 0.184070i $$0.0589273\pi$$
−0.332047 + 0.943263i $$0.607739\pi$$
$$524$$ −11.8579 −0.518013
$$525$$ −1.82843 −0.0797991
$$526$$ 5.34315 + 9.25460i 0.232972 + 0.403520i
$$527$$ −2.92893 + 5.07306i −0.127586 + 0.220986i
$$528$$ −4.24264 7.34847i −0.184637 0.319801i
$$529$$ 11.1569 19.3242i 0.485081 0.840184i
$$530$$ 0.414214 0.717439i 0.0179923 0.0311636i
$$531$$ 0 0
$$532$$ 11.7010 + 8.68575i 0.507303 + 0.376575i
$$533$$ −5.17157 −0.224006
$$534$$ −2.58579 + 4.47871i −0.111898 + 0.193813i
$$535$$ 7.00000 12.1244i 0.302636 0.524182i
$$536$$ −4.34924 7.53311i −0.187859 0.325381i
$$537$$ 8.07107 13.9795i 0.348292 0.603260i
$$538$$ 0.343146 + 0.594346i 0.0147941 + 0.0256241i
$$539$$ 10.3431 0.445511
$$540$$ −1.82843 −0.0786830
$$541$$ −8.15685 14.1281i −0.350691 0.607414i 0.635680 0.771953i $$-0.280720\pi$$
−0.986371 + 0.164539i $$0.947386\pi$$
$$542$$ 2.82843 + 4.89898i 0.121491 + 0.210429i
$$543$$ −25.3137 −1.08632
$$544$$ 5.17157 0.221729
$$545$$ −8.65685 14.9941i −0.370819 0.642277i
$$546$$ 0.692388 1.19925i 0.0296315 0.0513232i
$$547$$ 6.57107 + 11.3814i 0.280959 + 0.486635i 0.971621 0.236543i $$-0.0760143\pi$$
−0.690663 + 0.723177i $$0.742681\pi$$
$$548$$ −9.58579 + 16.6031i −0.409485 + 0.709248i
$$549$$ 4.15685 7.19988i 0.177410 0.307284i
$$550$$ 1.17157 0.0499560
$$551$$ −33.7990 25.0892i −1.43989 1.06884i
$$552$$ 1.31371 0.0559151
$$553$$ 3.05635 5.29375i 0.129969 0.225113i
$$554$$ 1.24264 2.15232i 0.0527947 0.0914432i
$$555$$ 1.08579 + 1.88064i 0.0460891 + 0.0798286i
$$556$$ −14.9142 + 25.8322i −0.632504 + 1.09553i
$$557$$ 4.51472 + 7.81972i 0.191295 + 0.331332i 0.945680 0.325100i $$-0.105398\pi$$
−0.754385 + 0.656432i $$0.772065\pi$$
$$558$$ 2.07107 0.0876753
$$559$$ −14.3137 −0.605405
$$560$$ 2.74264 + 4.75039i 0.115898 + 0.200741i
$$561$$ 1.65685 + 2.86976i 0.0699524 + 0.121161i
$$562$$ 2.88730 0.121793
$$563$$ −12.1421 −0.511730 −0.255865 0.966713i $$-0.582360\pi$$
−0.255865 + 0.966713i $$0.582360\pi$$
$$564$$ 2.89949 + 5.02207i 0.122091 + 0.211467i
$$565$$ 2.00000 3.46410i 0.0841406 0.145736i
$$566$$ −4.34315 7.52255i −0.182556 0.316196i
$$567$$ −0.914214 + 1.58346i −0.0383934 + 0.0664993i
$$568$$ −7.92893 + 13.7333i −0.332691 + 0.576237i
$$569$$ 4.97056 0.208377 0.104188 0.994558i $$-0.466776\pi$$
0.104188 + 0.994558i $$0.466776\pi$$
$$570$$ −1.65685 + 0.717439i −0.0693980 + 0.0300502i
$$571$$ 14.3137 0.599010 0.299505 0.954095i $$-0.403178\pi$$
0.299505 + 0.954095i $$0.403178\pi$$
$$572$$ 4.72792 8.18900i 0.197684 0.342399i
$$573$$ −8.41421 + 14.5738i −0.351509 + 0.608831i
$$574$$ 1.07107 + 1.85514i 0.0447055 + 0.0774322i
$$575$$ 0.414214 0.717439i 0.0172739 0.0299193i
$$576$$ 2.08579 + 3.61269i 0.0869078 + 0.150529i
$$577$$ −36.3431 −1.51298 −0.756492 0.654002i $$-0.773089\pi$$
−0.756492 + 0.654002i $$0.773089\pi$$
$$578$$ 6.47309 0.269245
$$579$$ −12.3995 21.4766i −0.515305 0.892535i
$$580$$ −8.82843 15.2913i −0.366580 0.634936i
$$581$$ −14.6274 −0.606848
$$582$$ −2.48528 −0.103018
$$583$$ −2.82843 4.89898i −0.117141 0.202895i
$$584$$ −7.52082 + 13.0264i −0.311214 + 0.539038i
$$585$$ −0.914214 1.58346i −0.0377981 0.0654682i
$$586$$ −1.10051 + 1.90613i −0.0454614 + 0.0787415i
$$587$$ −5.31371 + 9.20361i −0.219320 + 0.379874i −0.954600 0.297890i $$-0.903717\pi$$
0.735280 + 0.677763i $$0.237051\pi$$
$$588$$ −6.68629 −0.275738
$$589$$ −20.0000 + 8.66025i −0.824086 + 0.356840i
$$590$$ 0 0
$$591$$ 8.82843 15.2913i 0.363153 0.628999i
$$592$$ 3.25736 5.64191i 0.133877 0.231881i
$$593$$ 4.92893 + 8.53716i 0.202407 + 0.350579i 0.949303 0.314361i $$-0.101790\pi$$
−0.746896 + 0.664940i $$0.768457\pi$$
$$594$$ 0.585786 1.01461i 0.0240351 0.0416300i
$$595$$ −1.07107 1.85514i −0.0439095 0.0760535i
$$596$$ 2.14214 0.0877453
$$597$$ 17.0000 0.695764
$$598$$ 0.313708 + 0.543359i 0.0128285 + 0.0222196i
$$599$$ 8.48528 + 14.6969i 0.346699 + 0.600501i 0.985661 0.168738i $$-0.0539691\pi$$
−0.638962 + 0.769238i $$0.720636\pi$$
$$600$$ −1.58579 −0.0647395
$$601$$ −35.3431 −1.44168 −0.720838 0.693103i $$-0.756243\pi$$
−0.720838 + 0.693103i $$0.756243\pi$$
$$602$$ 2.96447 + 5.13461i 0.120823 + 0.209271i
$$603$$ −2.74264 + 4.75039i −0.111689 + 0.193451i
$$604$$ 9.45584 + 16.3780i 0.384753 + 0.666411i
$$605$$ −1.50000 + 2.59808i −0.0609837 + 0.105627i
$$606$$ −2.51472 + 4.35562i −0.102153 + 0.176935i
$$607$$ −6.17157 −0.250496 −0.125248 0.992125i $$-0.539973\pi$$
−0.125248 + 0.992125i $$0.539973\pi$$
$$608$$ 15.4497 + 11.4685i 0.626570 + 0.465108i
$$609$$ −17.6569 −0.715492
$$610$$ 1.72183 2.98229i 0.0697147 0.120749i
$$611$$ −2.89949 + 5.02207i −0.117301 + 0.203171i
$$612$$ −1.07107 1.85514i −0.0432954 0.0749897i
$$613$$ −16.7990 + 29.0967i −0.678505 + 1.17520i 0.296926 + 0.954900i $$0.404038\pi$$
−0.975431 + 0.220304i $$0.929295\pi$$
$$614$$ −3.65685 6.33386i −0.147579 0.255614i
$$615$$ 2.82843 0.114053
$$616$$ −8.20101 −0.330428
$$617$$ −12.8284 22.2195i −0.516453 0.894523i −0.999818 0.0191037i $$-0.993919\pi$$
0.483364 0.875419i $$-0.339415\pi$$
$$618$$ −2.03553 3.52565i −0.0818812 0.141822i
$$619$$ 15.6863 0.630485 0.315243 0.949011i $$-0.397914\pi$$
0.315243 + 0.949011i $$0.397914\pi$$
$$620$$ −9.14214 −0.367157
$$621$$ −0.414214 0.717439i −0.0166218 0.0287898i
$$622$$ −0.828427 + 1.43488i −0.0332169 + 0.0575334i
$$623$$ −11.4142 19.7700i −0.457301 0.792068i
$$624$$ −2.74264 + 4.75039i −0.109793 + 0.190168i
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 2.48528 0.0993318
$$627$$ −1.41421 + 12.2474i −0.0564782 + 0.489116i
$$628$$ 36.2548 1.44673
$$629$$ −1.27208 + 2.20330i −0.0507211 + 0.0878515i
$$630$$ −0.378680 + 0.655892i −0.0150870 + 0.0261314i
$$631$$ 6.64214 + 11.5045i 0.264419 + 0.457988i 0.967411 0.253210i $$-0.0814864\pi$$
−0.702992 + 0.711198i $$0.748153\pi$$
$$632$$ 2.65076 4.59125i 0.105441 0.182630i
$$633$$ −0.156854 0.271680i −0.00623440 0.0107983i
$$634$$ −2.20101 −0.0874133
$$635$$ −12.9706 −0.514721
$$636$$ 1.82843 + 3.16693i 0.0725019 + 0.125577i
$$637$$ −3.34315 5.79050i −0.132460 0.229428i
$$638$$ 11.3137 0.447914
$$639$$ 10.0000 0.395594
$$640$$ 5.27817 + 9.14207i 0.208638 + 0.361372i
$$641$$ −14.0711 + 24.3718i −0.555774 + 0.962628i 0.442069 + 0.896981i $$0.354245\pi$$
−0.997843 + 0.0656474i $$0.979089\pi$$
$$642$$ −2.89949 5.02207i −0.114434 0.198205i
$$643$$ −2.91421 + 5.04757i −0.114925 + 0.199057i −0.917750 0.397159i $$-0.869996\pi$$
0.802825 + 0.596215i $$0.203330\pi$$
$$644$$ −1.38478 + 2.39850i −0.0545678 + 0.0945143i
$$645$$ 7.82843 0.308244
$$646$$ −1.69848 1.26080i −0.0668260 0.0496054i
$$647$$ −32.2843 −1.26923 −0.634613 0.772830i $$-0.718840\pi$$
−0.634613 + 0.772830i $$0.718840\pi$$
$$648$$ −0.792893 + 1.37333i −0.0311478 + 0.0539496i
$$649$$ 0 0
$$650$$ −0.378680 0.655892i −0.0148530 0.0257262i
$$651$$ −4.57107 + 7.91732i −0.179154 + 0.310304i
$$652$$ 13.8431 + 23.9770i 0.542139 + 0.939013i
$$653$$ 39.9411 1.56302 0.781509 0.623895i $$-0.214451\pi$$
0.781509 + 0.623895i $$0.214451\pi$$
$$654$$ −7.17157 −0.280431
$$655$$ 3.24264 + 5.61642i 0.126700 + 0.219452i
$$656$$ −4.24264 7.34847i −0.165647 0.286910i
$$657$$ 9.48528 0.370056
$$658$$ 2.40202 0.0936405
$$659$$ −3.75736 6.50794i −0.146366 0.253513i 0.783516 0.621372i $$-0.213424\pi$$
−0.929882 + 0.367859i $$0.880091\pi$$
$$660$$ −2.58579 + 4.47871i −0.100652 + 0.174334i
$$661$$ 3.48528 + 6.03668i 0.135562 + 0.234800i 0.925812 0.377985i $$-0.123383\pi$$
−0.790250 + 0.612784i $$0.790049\pi$$
$$662$$ −1.10660 + 1.91669i −0.0430093 + 0.0744943i
$$663$$ 1.07107 1.85514i 0.0415968 0.0720478i
$$664$$ −12.6863 −0.492324
$$665$$ 0.914214 7.91732i 0.0354517 0.307021i
$$666$$ 0.899495 0.0348547
$$667$$ 4.00000 6.92820i 0.154881 0.268261i
$$668$$ −22.8284 + 39.5400i −0.883258 + 1.52985i
$$669$$ 2.91421 + 5.04757i 0.112670 + 0.195150i
$$670$$ −1.13604 + 1.96768i −0.0438890 + 0.0760180i
$$671$$ −11.7574 20.3643i −0.453888 0.786157i
$$672$$ 8.07107 0.311348
$$673$$ −23.8284 −0.918518 −0.459259 0.888302i $$-0.651885\pi$$
−0.459259 + 0.888302i $$0.651885\pi$$
$$674$$ 3.62132 + 6.27231i 0.139488 + 0.241600i
$$675$$ 0.500000 + 0.866025i 0.0192450 + 0.0333333i
$$676$$ 17.6569 0.679110
$$677$$ −23.4558 −0.901481 −0.450741 0.892655i $$-0.648840\pi$$
−0.450741 + 0.892655i $$0.648840\pi$$
$$678$$ −0.828427 1.43488i −0.0318156 0.0551062i
$$679$$ 5.48528 9.50079i 0.210506 0.364607i
$$680$$ −0.928932 1.60896i −0.0356229 0.0617007i
$$681$$ −9.48528 + 16.4290i −0.363477 + 0.629560i
$$682$$ 2.92893 5.07306i 0.112155 0.194257i
$$683$$ 44.1421 1.68905 0.844526 0.535515i $$-0.179882\pi$$
0.844526 + 0.535515i $$0.179882\pi$$
$$684$$ 0.914214 7.91732i 0.0349558 0.302726i
$$685$$ 10.4853 0.400622
$$686$$ −4.03553 + 6.98975i −0.154077 + 0.266870i
$$687$$ −2.32843 + 4.03295i −0.0888350 + 0.153867i
$$688$$ −11.7426 20.3389i −0.447684 0.775411i
$$689$$ −1.82843 + 3.16693i −0.0696575 + 0.120650i
$$690$$ −0.171573 0.297173i −0.00653167 0.0113132i
$$691$$ 31.3137 1.19123 0.595615 0.803270i $$-0.296908\pi$$
0.595615 + 0.803270i $$0.296908\pi$$
$$692$$ −13.3726 −0.508349
$$693$$ 2.58579 + 4.47871i 0.0982259 + 0.170132i
$$694$$ −7.34315 12.7187i −0.278742 0.482795i
$$695$$ 16.3137 0.618814
$$696$$ −15.3137 −0.580465
$$697$$ 1.65685 + 2.86976i 0.0627578 + 0.108700i
$$698$$ −6.55025 + 11.3454i −0.247931 + 0.429429i
$$699$$ −12.6569 21.9223i −0.478726 0.829178i
$$700$$ 1.67157 2.89525i 0.0631795 0.109430i
$$701$$ −16.0711 + 27.8359i −0.606996 + 1.05135i 0.384737 + 0.923026i $$0.374292\pi$$
−0.991733 + 0.128321i $$0.959041\pi$$
$$702$$ −0.757359 −0.0285847
$$703$$ −8.68629 + 3.76127i −0.327610 + 0.141859i
$$704$$ 11.7990 0.444691
$$705$$ 1.58579 2.74666i 0.0597242 0.103445i
$$706$$ −0.272078 + 0.471253i −0.0102398 + 0.0177358i
$$707$$ −11.1005 19.2266i −0.417477 0.723092i
$$708$$ 0 0
$$709$$ −15.8137 27.3901i −0.593896 1.02866i −0.993702 0.112058i $$-0.964256\pi$$
0.399805 0.916600i $$-0.369078\pi$$
$$710$$ 4.14214 0.155452
$$711$$ −3.34315 −0.125378
$$712$$ −9.89949 17.1464i −0.370999 0.642590i
$$713$$ −2.07107 3.58719i −0.0775621 0.134341i
$$714$$ −0.887302 −0.0332064
$$715$$ −5.17157 −0.193406
$$716$$ 14.7574 + 25.5605i 0.551508 + 0.955241i
$$717$$ −12.3137 + 21.3280i −0.459864 + 0.796508i
$$718$$ 1.89949 + 3.29002i 0.0708885 + 0.122783i
$$719$$ 11.5858 20.0672i 0.432077 0.748379i −0.564975 0.825108i $$-0.691114\pi$$
0.997052 + 0.0767288i $$0.0244476\pi$$
$$720$$ 1.50000 2.59808i 0.0559017 0.0968246i
$$721$$ 17.9706 0.669259
$$722$$ −2.27817 7.53311i −0.0847849 0.280353i
$$723$$ −5.00000 −0.185952
$$724$$ 23.1421 40.0834i 0.860071 1.48969i
$$725$$ −4.82843 + 8.36308i −0.179323 + 0.310597i
$$726$$ 0.621320 + 1.07616i 0.0230594 + 0.0399400i
$$727$$ −18.0858 + 31.3255i −0.670765 + 1.16180i 0.306923 + 0.951734i $$0.400701\pi$$
−0.977688 + 0.210064i $$0.932633\pi$$
$$728$$ 2.65076 + 4.59125i 0.0982436 + 0.170163i
$$729$$ 1.00000 0.0370370
$$730$$ 3.92893 0.145416
$$731$$ 4.58579 + 7.94282i 0.169611 + 0.293776i
$$732$$ 7.60051 + 13.1645i 0.280923 + 0.486572i
$$733$$ 3.65685 0.135069 0.0675345 0.997717i $$-0.478487\pi$$
0.0675345 + 0.997717i $$0.478487\pi$$
$$734$$ 14.1299 0.521546
$$735$$ 1.82843 + 3.16693i 0.0674426 + 0.116814i
$$736$$ −1.82843 + 3.16693i −0.0673967 + 0.116735i
$$737$$ 7.75736 + 13.4361i 0.285746 + 0.494927i
$$738$$ 0.585786 1.01461i 0.0215631 0.0373484i
$$739$$ 20.8137 36.0504i 0.765645 1.32614i −0.174260 0.984700i $$-0.555753\pi$$
0.939905 0.341436i $$-0.110913\pi$$
$$740$$ −3.97056 −0.145961
$$741$$ 7.31371 3.16693i 0.268676 0.116340i
$$742$$ 1.51472 0.0556071
$$743$$ −17.0711 + 29.5680i −0.626277 + 1.08474i 0.362016 + 0.932172i $$0.382089\pi$$
−0.988292 + 0.152571i $$0.951245\pi$$
$$744$$ −3.96447 + 6.86666i −0.145344 + 0.251744i
$$745$$ −0.585786 1.01461i −0.0214616 0.0371725i
$$746$$ −2.41421 + 4.18154i −0.0883906 + 0.153097i
$$747$$ 4.00000 + 6.92820i 0.146352 + 0.253490i
$$748$$ −6.05887 −0.221534
$$749$$ 25.5980 0.935330
$$750$$ 0.207107 + 0.358719i 0.00756247 + 0.0130986i
$$751$$ −13.1569 22.7883i −0.480100 0.831558i 0.519639 0.854386i $$-0.326066\pi$$
−0.999739 + 0.0228276i $$0.992733\pi$$
$$752$$ −9.51472 −0.346966
$$753$$ 16.3431 0.595577
$$754$$ −3.65685 6.33386i −0.133175 0.230665i
$$755$$ 5.17157 8.95743i 0.188213 0.325994i
$$756$$ −1.67157 2.89525i −0.0607945 0.105299i
$$757$$ 16.5711 28.7019i 0.602286 1.04319i −0.390188 0.920735i $$-0.627590\pi$$
0.992474 0.122454i $$-0.0390765\pi$$
$$758$$ 0.349242 0.604906i 0.0126851 0.0219712i
$$759$$ −2.34315 −0.0850508
$$760$$ 0.792893 6.86666i 0.0287613 0.249080i
$$761$$ 51.5980 1.87043 0.935213 0.354087i $$-0.115208\pi$$
0.935213 + 0.354087i $$0.115208\pi$$
$$762$$ −2.68629 + 4.65279i −0.0973141 + 0.168553i
$$763$$ 15.8284 27.4156i 0.573028 0.992513i
$$764$$ −15.3848 26.6472i −0.556602 0.964062i
$$765$$ −0.585786 + 1.01461i −0.0211792 + 0.0366834i
$$766$$ −7.02944 12.1753i −0.253984 0.439913i
$$767$$ 0 0
$$768$$ −3.97056 −0.143275
$$769$$ −7.15685 12.3960i −0.258083 0.447012i 0.707646 0.706568i $$-0.249757\pi$$
−0.965728 + 0.259555i $$0.916424\pi$$
$$770$$ 1.07107 + 1.85514i 0.0385986 + 0.0668547i
$$771$$