# Properties

 Label 546.2.i.j.235.1 Level $546$ Weight $2$ Character 546.235 Analytic conductor $4.360$ 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] = [546,2,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.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: $$4.35983195036$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{7})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} + 7x^{2} + 49$$ x^4 + 7*x^2 + 49 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 235.1 Root $$-1.32288 - 2.29129i$$ of defining polynomial Character $$\chi$$ $$=$$ 546.235 Dual form 546.2.i.j.79.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} -1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.822876 - 1.42526i) q^{5} -1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.822876 - 1.42526i) q^{10} +(2.32288 - 4.02334i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(1.32288 - 2.29129i) q^{14} +1.64575 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.677124 - 1.17281i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.50000 - 4.33013i) q^{19} +1.64575 q^{20} +2.64575 q^{21} +4.64575 q^{22} +(3.82288 + 6.62141i) q^{23} +(0.500000 - 0.866025i) q^{24} +(1.14575 - 1.98450i) q^{25} +(0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +2.64575 q^{28} -6.29150 q^{29} +(0.822876 + 1.42526i) q^{30} +(3.64575 - 6.31463i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.32288 + 4.02334i) q^{33} +1.35425 q^{34} +(-2.17712 + 3.77089i) q^{35} +1.00000 q^{36} +(-0.177124 - 0.306788i) q^{37} +(2.50000 - 4.33013i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(0.822876 + 1.42526i) q^{40} -7.64575 q^{41} +(1.32288 + 2.29129i) q^{42} +5.29150 q^{43} +(2.32288 + 4.02334i) q^{44} +(-0.822876 + 1.42526i) q^{45} +(-3.82288 + 6.62141i) q^{46} +(-1.50000 - 2.59808i) q^{47} +1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} +2.29150 q^{50} +(0.677124 + 1.17281i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(1.50000 - 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} -7.64575 q^{55} +(1.32288 + 2.29129i) q^{56} +5.00000 q^{57} +(-3.14575 - 5.44860i) q^{58} +(-3.96863 + 6.87386i) q^{59} +(-0.822876 + 1.42526i) q^{60} +(-1.96863 - 3.40976i) q^{61} +7.29150 q^{62} +(-1.32288 + 2.29129i) q^{63} +1.00000 q^{64} +(-0.822876 - 1.42526i) q^{65} +(-2.32288 + 4.02334i) q^{66} +(6.79150 - 11.7632i) q^{67} +(0.677124 + 1.17281i) q^{68} -7.64575 q^{69} -4.35425 q^{70} +5.70850 q^{71} +(0.500000 + 0.866025i) q^{72} +(4.17712 - 7.23499i) q^{73} +(0.177124 - 0.306788i) q^{74} +(1.14575 + 1.98450i) q^{75} +5.00000 q^{76} -12.2915 q^{77} -1.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(-0.822876 + 1.42526i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.82288 - 6.62141i) q^{82} -2.70850 q^{83} +(-1.32288 + 2.29129i) q^{84} -2.22876 q^{85} +(2.64575 + 4.58258i) q^{86} +(3.14575 - 5.44860i) q^{87} +(-2.32288 + 4.02334i) q^{88} +(-0.531373 - 0.920365i) q^{89} -1.64575 q^{90} +(-1.32288 - 2.29129i) q^{91} -7.64575 q^{92} +(3.64575 + 6.31463i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-4.11438 + 7.12631i) q^{95} +(0.500000 + 0.866025i) q^{96} -14.9373 q^{97} -7.00000 q^{98} -4.64575 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10})$$ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 $$4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{20} + 8 q^{22} + 10 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 4 q^{27} - 4 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{33} + 16 q^{34} - 14 q^{35} + 4 q^{36} - 6 q^{37} + 10 q^{38} - 2 q^{39} - 2 q^{40} - 20 q^{41} + 4 q^{44} + 2 q^{45} - 10 q^{46} - 6 q^{47} + 4 q^{48} - 14 q^{49} - 12 q^{50} + 8 q^{51} - 2 q^{52} + 6 q^{53} + 2 q^{54} - 20 q^{55} + 20 q^{57} - 2 q^{58} + 2 q^{60} + 8 q^{61} + 8 q^{62} + 4 q^{64} + 2 q^{65} - 4 q^{66} + 6 q^{67} + 8 q^{68} - 20 q^{69} - 28 q^{70} + 44 q^{71} + 2 q^{72} + 22 q^{73} + 6 q^{74} - 6 q^{75} + 20 q^{76} - 28 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{80} - 2 q^{81} - 10 q^{82} - 32 q^{83} + 44 q^{85} + 2 q^{87} - 4 q^{88} - 18 q^{89} + 4 q^{90} - 20 q^{92} + 4 q^{93} + 6 q^{94} + 10 q^{95} + 2 q^{96} - 28 q^{97} - 28 q^{98} - 8 q^{99}+O(q^{100})$$ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 - 4 * q^6 - 4 * q^8 - 2 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^15 - 2 * q^16 + 8 * q^17 + 2 * q^18 - 10 * q^19 - 4 * q^20 + 8 * q^22 + 10 * q^23 + 2 * q^24 - 6 * q^25 + 2 * q^26 + 4 * q^27 - 4 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 4 * q^33 + 16 * q^34 - 14 * q^35 + 4 * q^36 - 6 * q^37 + 10 * q^38 - 2 * q^39 - 2 * q^40 - 20 * q^41 + 4 * q^44 + 2 * q^45 - 10 * q^46 - 6 * q^47 + 4 * q^48 - 14 * q^49 - 12 * q^50 + 8 * q^51 - 2 * q^52 + 6 * q^53 + 2 * q^54 - 20 * q^55 + 20 * q^57 - 2 * q^58 + 2 * q^60 + 8 * q^61 + 8 * q^62 + 4 * q^64 + 2 * q^65 - 4 * q^66 + 6 * q^67 + 8 * q^68 - 20 * q^69 - 28 * q^70 + 44 * q^71 + 2 * q^72 + 22 * q^73 + 6 * q^74 - 6 * q^75 + 20 * q^76 - 28 * q^77 - 4 * q^78 + 20 * q^79 + 2 * q^80 - 2 * q^81 - 10 * q^82 - 32 * q^83 + 44 * q^85 + 2 * q^87 - 4 * q^88 - 18 * q^89 + 4 * q^90 - 20 * q^92 + 4 * q^93 + 6 * q^94 + 10 * q^95 + 2 * q^96 - 28 * q^97 - 28 * q^98 - 8 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$$.

 $$n$$ $$157$$ $$365$$ $$379$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.500000 + 0.866025i 0.353553 + 0.612372i
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ −0.500000 + 0.866025i −0.250000 + 0.433013i
$$5$$ −0.822876 1.42526i −0.368001 0.637397i 0.621252 0.783611i $$-0.286624\pi$$
−0.989253 + 0.146214i $$0.953291\pi$$
$$6$$ −1.00000 −0.408248
$$7$$ −1.32288 2.29129i −0.500000 0.866025i
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0.822876 1.42526i 0.260216 0.450708i
$$11$$ 2.32288 4.02334i 0.700373 1.21308i −0.267962 0.963429i $$-0.586350\pi$$
0.968335 0.249653i $$-0.0803165\pi$$
$$12$$ −0.500000 0.866025i −0.144338 0.250000i
$$13$$ 1.00000 0.277350
$$14$$ 1.32288 2.29129i 0.353553 0.612372i
$$15$$ 1.64575 0.424931
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 0.677124 1.17281i 0.164227 0.284449i −0.772154 0.635436i $$-0.780820\pi$$
0.936380 + 0.350987i $$0.114154\pi$$
$$18$$ 0.500000 0.866025i 0.117851 0.204124i
$$19$$ −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i $$-0.972237\pi$$
0.422659 0.906289i $$-0.361097\pi$$
$$20$$ 1.64575 0.368001
$$21$$ 2.64575 0.577350
$$22$$ 4.64575 0.990478
$$23$$ 3.82288 + 6.62141i 0.797125 + 1.38066i 0.921481 + 0.388423i $$0.126980\pi$$
−0.124357 + 0.992238i $$0.539687\pi$$
$$24$$ 0.500000 0.866025i 0.102062 0.176777i
$$25$$ 1.14575 1.98450i 0.229150 0.396900i
$$26$$ 0.500000 + 0.866025i 0.0980581 + 0.169842i
$$27$$ 1.00000 0.192450
$$28$$ 2.64575 0.500000
$$29$$ −6.29150 −1.16830 −0.584151 0.811645i $$-0.698573\pi$$
−0.584151 + 0.811645i $$0.698573\pi$$
$$30$$ 0.822876 + 1.42526i 0.150236 + 0.260216i
$$31$$ 3.64575 6.31463i 0.654796 1.13414i −0.327149 0.944973i $$-0.606088\pi$$
0.981945 0.189167i $$-0.0605789\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 2.32288 + 4.02334i 0.404361 + 0.700373i
$$34$$ 1.35425 0.232252
$$35$$ −2.17712 + 3.77089i −0.368001 + 0.637397i
$$36$$ 1.00000 0.166667
$$37$$ −0.177124 0.306788i −0.0291191 0.0504357i 0.851099 0.525006i $$-0.175937\pi$$
−0.880218 + 0.474570i $$0.842604\pi$$
$$38$$ 2.50000 4.33013i 0.405554 0.702439i
$$39$$ −0.500000 + 0.866025i −0.0800641 + 0.138675i
$$40$$ 0.822876 + 1.42526i 0.130108 + 0.225354i
$$41$$ −7.64575 −1.19407 −0.597033 0.802217i $$-0.703654\pi$$
−0.597033 + 0.802217i $$0.703654\pi$$
$$42$$ 1.32288 + 2.29129i 0.204124 + 0.353553i
$$43$$ 5.29150 0.806947 0.403473 0.914991i $$-0.367803\pi$$
0.403473 + 0.914991i $$0.367803\pi$$
$$44$$ 2.32288 + 4.02334i 0.350187 + 0.606541i
$$45$$ −0.822876 + 1.42526i −0.122667 + 0.212466i
$$46$$ −3.82288 + 6.62141i −0.563652 + 0.976274i
$$47$$ −1.50000 2.59808i −0.218797 0.378968i 0.735643 0.677369i $$-0.236880\pi$$
−0.954441 + 0.298401i $$0.903547\pi$$
$$48$$ 1.00000 0.144338
$$49$$ −3.50000 + 6.06218i −0.500000 + 0.866025i
$$50$$ 2.29150 0.324067
$$51$$ 0.677124 + 1.17281i 0.0948164 + 0.164227i
$$52$$ −0.500000 + 0.866025i −0.0693375 + 0.120096i
$$53$$ 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i $$-0.767275\pi$$
0.950464 + 0.310835i $$0.100609\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ −7.64575 −1.03095
$$56$$ 1.32288 + 2.29129i 0.176777 + 0.306186i
$$57$$ 5.00000 0.662266
$$58$$ −3.14575 5.44860i −0.413057 0.715436i
$$59$$ −3.96863 + 6.87386i −0.516671 + 0.894901i 0.483141 + 0.875542i $$0.339496\pi$$
−0.999813 + 0.0193585i $$0.993838\pi$$
$$60$$ −0.822876 + 1.42526i −0.106233 + 0.184001i
$$61$$ −1.96863 3.40976i −0.252057 0.436575i 0.712035 0.702144i $$-0.247774\pi$$
−0.964092 + 0.265569i $$0.914440\pi$$
$$62$$ 7.29150 0.926022
$$63$$ −1.32288 + 2.29129i −0.166667 + 0.288675i
$$64$$ 1.00000 0.125000
$$65$$ −0.822876 1.42526i −0.102065 0.176782i
$$66$$ −2.32288 + 4.02334i −0.285926 + 0.495239i
$$67$$ 6.79150 11.7632i 0.829714 1.43711i −0.0685485 0.997648i $$-0.521837\pi$$
0.898263 0.439459i $$-0.144830\pi$$
$$68$$ 0.677124 + 1.17281i 0.0821134 + 0.142225i
$$69$$ −7.64575 −0.920440
$$70$$ −4.35425 −0.520432
$$71$$ 5.70850 0.677474 0.338737 0.940881i $$-0.390000\pi$$
0.338737 + 0.940881i $$0.390000\pi$$
$$72$$ 0.500000 + 0.866025i 0.0589256 + 0.102062i
$$73$$ 4.17712 7.23499i 0.488895 0.846792i −0.511023 0.859567i $$-0.670733\pi$$
0.999918 + 0.0127753i $$0.00406663\pi$$
$$74$$ 0.177124 0.306788i 0.0205903 0.0356634i
$$75$$ 1.14575 + 1.98450i 0.132300 + 0.229150i
$$76$$ 5.00000 0.573539
$$77$$ −12.2915 −1.40075
$$78$$ −1.00000 −0.113228
$$79$$ 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i $$0.0235106\pi$$
−0.434730 + 0.900561i $$0.643156\pi$$
$$80$$ −0.822876 + 1.42526i −0.0920003 + 0.159349i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ −3.82288 6.62141i −0.422166 0.731213i
$$83$$ −2.70850 −0.297296 −0.148648 0.988890i $$-0.547492\pi$$
−0.148648 + 0.988890i $$0.547492\pi$$
$$84$$ −1.32288 + 2.29129i −0.144338 + 0.250000i
$$85$$ −2.22876 −0.241743
$$86$$ 2.64575 + 4.58258i 0.285299 + 0.494152i
$$87$$ 3.14575 5.44860i 0.337260 0.584151i
$$88$$ −2.32288 + 4.02334i −0.247619 + 0.428889i
$$89$$ −0.531373 0.920365i −0.0563254 0.0975585i 0.836488 0.547985i $$-0.184605\pi$$
−0.892813 + 0.450427i $$0.851272\pi$$
$$90$$ −1.64575 −0.173477
$$91$$ −1.32288 2.29129i −0.138675 0.240192i
$$92$$ −7.64575 −0.797125
$$93$$ 3.64575 + 6.31463i 0.378047 + 0.654796i
$$94$$ 1.50000 2.59808i 0.154713 0.267971i
$$95$$ −4.11438 + 7.12631i −0.422126 + 0.731144i
$$96$$ 0.500000 + 0.866025i 0.0510310 + 0.0883883i
$$97$$ −14.9373 −1.51665 −0.758324 0.651878i $$-0.773982\pi$$
−0.758324 + 0.651878i $$0.773982\pi$$
$$98$$ −7.00000 −0.707107
$$99$$ −4.64575 −0.466916
$$100$$ 1.14575 + 1.98450i 0.114575 + 0.198450i
$$101$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$102$$ −0.677124 + 1.17281i −0.0670453 + 0.116126i
$$103$$ −2.64575 4.58258i −0.260694 0.451535i 0.705733 0.708478i $$-0.250618\pi$$
−0.966426 + 0.256943i $$0.917285\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ −2.17712 3.77089i −0.212466 0.368001i
$$106$$ 3.00000 0.291386
$$107$$ 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i $$0.0302972\pi$$
−0.415432 + 0.909624i $$0.636370\pi$$
$$108$$ −0.500000 + 0.866025i −0.0481125 + 0.0833333i
$$109$$ 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i $$-0.771977\pi$$
0.945769 + 0.324840i $$0.105310\pi$$
$$110$$ −3.82288 6.62141i −0.364497 0.631327i
$$111$$ 0.354249 0.0336238
$$112$$ −1.32288 + 2.29129i −0.125000 + 0.216506i
$$113$$ −11.2288 −1.05631 −0.528156 0.849147i $$-0.677116\pi$$
−0.528156 + 0.849147i $$0.677116\pi$$
$$114$$ 2.50000 + 4.33013i 0.234146 + 0.405554i
$$115$$ 6.29150 10.8972i 0.586686 1.01617i
$$116$$ 3.14575 5.44860i 0.292076 0.505890i
$$117$$ −0.500000 0.866025i −0.0462250 0.0800641i
$$118$$ −7.93725 −0.730683
$$119$$ −3.58301 −0.328454
$$120$$ −1.64575 −0.150236
$$121$$ −5.29150 9.16515i −0.481046 0.833196i
$$122$$ 1.96863 3.40976i 0.178231 0.308705i
$$123$$ 3.82288 6.62141i 0.344697 0.597033i
$$124$$ 3.64575 + 6.31463i 0.327398 + 0.567070i
$$125$$ −12.0000 −1.07331
$$126$$ −2.64575 −0.235702
$$127$$ 16.2288 1.44007 0.720035 0.693938i $$-0.244126\pi$$
0.720035 + 0.693938i $$0.244126\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ −2.64575 + 4.58258i −0.232945 + 0.403473i
$$130$$ 0.822876 1.42526i 0.0721710 0.125004i
$$131$$ 2.46863 + 4.27579i 0.215685 + 0.373577i 0.953484 0.301443i $$-0.0974683\pi$$
−0.737799 + 0.675020i $$0.764135\pi$$
$$132$$ −4.64575 −0.404361
$$133$$ −6.61438 + 11.4564i −0.573539 + 0.993399i
$$134$$ 13.5830 1.17339
$$135$$ −0.822876 1.42526i −0.0708219 0.122667i
$$136$$ −0.677124 + 1.17281i −0.0580629 + 0.100568i
$$137$$ −8.76013 + 15.1730i −0.748428 + 1.29632i 0.200147 + 0.979766i $$0.435858\pi$$
−0.948576 + 0.316550i $$0.897475\pi$$
$$138$$ −3.82288 6.62141i −0.325425 0.563652i
$$139$$ 4.22876 0.358678 0.179339 0.983787i $$-0.442604\pi$$
0.179339 + 0.983787i $$0.442604\pi$$
$$140$$ −2.17712 3.77089i −0.184001 0.318698i
$$141$$ 3.00000 0.252646
$$142$$ 2.85425 + 4.94370i 0.239523 + 0.414866i
$$143$$ 2.32288 4.02334i 0.194249 0.336448i
$$144$$ −0.500000 + 0.866025i −0.0416667 + 0.0721688i
$$145$$ 5.17712 + 8.96704i 0.429937 + 0.744672i
$$146$$ 8.35425 0.691403
$$147$$ −3.50000 6.06218i −0.288675 0.500000i
$$148$$ 0.354249 0.0291191
$$149$$ 11.4686 + 19.8642i 0.939547 + 1.62734i 0.766319 + 0.642461i $$0.222086\pi$$
0.173228 + 0.984882i $$0.444580\pi$$
$$150$$ −1.14575 + 1.98450i −0.0935502 + 0.162034i
$$151$$ −10.9686 + 18.9982i −0.892614 + 1.54605i −0.0558844 + 0.998437i $$0.517798\pi$$
−0.836730 + 0.547616i $$0.815536\pi$$
$$152$$ 2.50000 + 4.33013i 0.202777 + 0.351220i
$$153$$ −1.35425 −0.109485
$$154$$ −6.14575 10.6448i −0.495239 0.857779i
$$155$$ −12.0000 −0.963863
$$156$$ −0.500000 0.866025i −0.0400320 0.0693375i
$$157$$ 1.32288 2.29129i 0.105577 0.182865i −0.808397 0.588638i $$-0.799664\pi$$
0.913974 + 0.405773i $$0.132998\pi$$
$$158$$ −5.00000 + 8.66025i −0.397779 + 0.688973i
$$159$$ 1.50000 + 2.59808i 0.118958 + 0.206041i
$$160$$ −1.64575 −0.130108
$$161$$ 10.1144 17.5186i 0.797125 1.38066i
$$162$$ −1.00000 −0.0785674
$$163$$ −11.7915 20.4235i −0.923582 1.59969i −0.793826 0.608145i $$-0.791914\pi$$
−0.129755 0.991546i $$-0.541419\pi$$
$$164$$ 3.82288 6.62141i 0.298516 0.517046i
$$165$$ 3.82288 6.62141i 0.297610 0.515476i
$$166$$ −1.35425 2.34563i −0.105110 0.182056i
$$167$$ 24.8745 1.92485 0.962424 0.271553i $$-0.0875371\pi$$
0.962424 + 0.271553i $$0.0875371\pi$$
$$168$$ −2.64575 −0.204124
$$169$$ 1.00000 0.0769231
$$170$$ −1.11438 1.93016i −0.0854689 0.148036i
$$171$$ −2.50000 + 4.33013i −0.191180 + 0.331133i
$$172$$ −2.64575 + 4.58258i −0.201737 + 0.349418i
$$173$$ 5.85425 + 10.1399i 0.445090 + 0.770919i 0.998059 0.0622834i $$-0.0198382\pi$$
−0.552968 + 0.833202i $$0.686505\pi$$
$$174$$ 6.29150 0.476958
$$175$$ −6.06275 −0.458301
$$176$$ −4.64575 −0.350187
$$177$$ −3.96863 6.87386i −0.298300 0.516671i
$$178$$ 0.531373 0.920365i 0.0398281 0.0689843i
$$179$$ 3.00000 5.19615i 0.224231 0.388379i −0.731858 0.681457i $$-0.761346\pi$$
0.956088 + 0.293079i $$0.0946798\pi$$
$$180$$ −0.822876 1.42526i −0.0613335 0.106233i
$$181$$ 9.35425 0.695296 0.347648 0.937625i $$-0.386980\pi$$
0.347648 + 0.937625i $$0.386980\pi$$
$$182$$ 1.32288 2.29129i 0.0980581 0.169842i
$$183$$ 3.93725 0.291050
$$184$$ −3.82288 6.62141i −0.281826 0.488137i
$$185$$ −0.291503 + 0.504897i −0.0214317 + 0.0371208i
$$186$$ −3.64575 + 6.31463i −0.267319 + 0.463011i
$$187$$ −3.14575 5.44860i −0.230040 0.398441i
$$188$$ 3.00000 0.218797
$$189$$ −1.32288 2.29129i −0.0962250 0.166667i
$$190$$ −8.22876 −0.596977
$$191$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$192$$ −0.500000 + 0.866025i −0.0360844 + 0.0625000i
$$193$$ −1.53137 + 2.65242i −0.110231 + 0.190925i −0.915863 0.401490i $$-0.868492\pi$$
0.805633 + 0.592416i $$0.201826\pi$$
$$194$$ −7.46863 12.9360i −0.536216 0.928754i
$$195$$ 1.64575 0.117855
$$196$$ −3.50000 6.06218i −0.250000 0.433013i
$$197$$ 20.8118 1.48278 0.741388 0.671076i $$-0.234168\pi$$
0.741388 + 0.671076i $$0.234168\pi$$
$$198$$ −2.32288 4.02334i −0.165080 0.285926i
$$199$$ −2.11438 + 3.66221i −0.149884 + 0.259607i −0.931185 0.364548i $$-0.881223\pi$$
0.781300 + 0.624155i $$0.214557\pi$$
$$200$$ −1.14575 + 1.98450i −0.0810169 + 0.140325i
$$201$$ 6.79150 + 11.7632i 0.479036 + 0.829714i
$$202$$ 0 0
$$203$$ 8.32288 + 14.4156i 0.584151 + 1.01178i
$$204$$ −1.35425 −0.0948164
$$205$$ 6.29150 + 10.8972i 0.439418 + 0.761094i
$$206$$ 2.64575 4.58258i 0.184338 0.319283i
$$207$$ 3.82288 6.62141i 0.265708 0.460220i
$$208$$ −0.500000 0.866025i −0.0346688 0.0600481i
$$209$$ −23.2288 −1.60677
$$210$$ 2.17712 3.77089i 0.150236 0.260216i
$$211$$ −11.6458 −0.801727 −0.400863 0.916138i $$-0.631290\pi$$
−0.400863 + 0.916138i $$0.631290\pi$$
$$212$$ 1.50000 + 2.59808i 0.103020 + 0.178437i
$$213$$ −2.85425 + 4.94370i −0.195570 + 0.338737i
$$214$$ −6.00000 + 10.3923i −0.410152 + 0.710403i
$$215$$ −4.35425 7.54178i −0.296957 0.514345i
$$216$$ −1.00000 −0.0680414
$$217$$ −19.2915 −1.30959
$$218$$ 4.00000 0.270914
$$219$$ 4.17712 + 7.23499i 0.282264 + 0.488895i
$$220$$ 3.82288 6.62141i 0.257738 0.446416i
$$221$$ 0.677124 1.17281i 0.0455483 0.0788920i
$$222$$ 0.177124 + 0.306788i 0.0118878 + 0.0205903i
$$223$$ 16.5203 1.10628 0.553139 0.833089i $$-0.313430\pi$$
0.553139 + 0.833089i $$0.313430\pi$$
$$224$$ −2.64575 −0.176777
$$225$$ −2.29150 −0.152767
$$226$$ −5.61438 9.72439i −0.373463 0.646857i
$$227$$ 7.64575 13.2428i 0.507466 0.878957i −0.492496 0.870315i $$-0.663915\pi$$
0.999963 0.00864295i $$-0.00275117\pi$$
$$228$$ −2.50000 + 4.33013i −0.165567 + 0.286770i
$$229$$ 13.2288 + 22.9129i 0.874181 + 1.51413i 0.857633 + 0.514263i $$0.171934\pi$$
0.0165480 + 0.999863i $$0.494732\pi$$
$$230$$ 12.5830 0.829699
$$231$$ 6.14575 10.6448i 0.404361 0.700373i
$$232$$ 6.29150 0.413057
$$233$$ 2.32288 + 4.02334i 0.152177 + 0.263578i 0.932027 0.362388i $$-0.118038\pi$$
−0.779851 + 0.625965i $$0.784705\pi$$
$$234$$ 0.500000 0.866025i 0.0326860 0.0566139i
$$235$$ −2.46863 + 4.27579i −0.161035 + 0.278922i
$$236$$ −3.96863 6.87386i −0.258336 0.447450i
$$237$$ −10.0000 −0.649570
$$238$$ −1.79150 3.10297i −0.116126 0.201136i
$$239$$ 3.00000 0.194054 0.0970269 0.995282i $$-0.469067\pi$$
0.0970269 + 0.995282i $$0.469067\pi$$
$$240$$ −0.822876 1.42526i −0.0531164 0.0920003i
$$241$$ −8.93725 + 15.4798i −0.575699 + 0.997140i 0.420266 + 0.907401i $$0.361937\pi$$
−0.995965 + 0.0897393i $$0.971397\pi$$
$$242$$ 5.29150 9.16515i 0.340151 0.589158i
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 3.93725 0.252057
$$245$$ 11.5203 0.736002
$$246$$ 7.64575 0.487475
$$247$$ −2.50000 4.33013i −0.159071 0.275519i
$$248$$ −3.64575 + 6.31463i −0.231505 + 0.400979i
$$249$$ 1.35425 2.34563i 0.0858220 0.148648i
$$250$$ −6.00000 10.3923i −0.379473 0.657267i
$$251$$ −2.70850 −0.170959 −0.0854794 0.996340i $$-0.527242\pi$$
−0.0854794 + 0.996340i $$0.527242\pi$$
$$252$$ −1.32288 2.29129i −0.0833333 0.144338i
$$253$$ 35.5203 2.23314
$$254$$ 8.11438 + 14.0545i 0.509141 + 0.881859i
$$255$$ 1.11438 1.93016i 0.0697851 0.120871i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −7.93725 13.7477i −0.495112 0.857560i 0.504872 0.863194i $$-0.331540\pi$$
−0.999984 + 0.00563467i $$0.998206\pi$$
$$258$$ −5.29150 −0.329435
$$259$$ −0.468627 + 0.811686i −0.0291191 + 0.0504357i
$$260$$ 1.64575 0.102065
$$261$$ 3.14575 + 5.44860i 0.194717 + 0.337260i
$$262$$ −2.46863 + 4.27579i −0.152512 + 0.264159i
$$263$$ −0.822876 + 1.42526i −0.0507407 + 0.0878854i −0.890280 0.455413i $$-0.849492\pi$$
0.839539 + 0.543299i $$0.182825\pi$$
$$264$$ −2.32288 4.02334i −0.142963 0.247619i
$$265$$ −4.93725 −0.303293
$$266$$ −13.2288 −0.811107
$$267$$ 1.06275 0.0650390
$$268$$ 6.79150 + 11.7632i 0.414857 + 0.718553i
$$269$$ 12.4373 21.5420i 0.758313 1.31344i −0.185398 0.982664i $$-0.559357\pi$$
0.943710 0.330773i $$-0.107309\pi$$
$$270$$ 0.822876 1.42526i 0.0500786 0.0867387i
$$271$$ 8.67712 + 15.0292i 0.527098 + 0.912960i 0.999501 + 0.0315777i $$0.0100532\pi$$
−0.472404 + 0.881382i $$0.656613\pi$$
$$272$$ −1.35425 −0.0821134
$$273$$ 2.64575 0.160128
$$274$$ −17.5203 −1.05844
$$275$$ −5.32288 9.21949i −0.320981 0.555956i
$$276$$ 3.82288 6.62141i 0.230110 0.398562i
$$277$$ 9.26013 16.0390i 0.556387 0.963691i −0.441407 0.897307i $$-0.645520\pi$$
0.997794 0.0663840i $$-0.0211462\pi$$
$$278$$ 2.11438 + 3.66221i 0.126812 + 0.219645i
$$279$$ −7.29150 −0.436531
$$280$$ 2.17712 3.77089i 0.130108 0.225354i
$$281$$ 18.5830 1.10857 0.554285 0.832327i $$-0.312992\pi$$
0.554285 + 0.832327i $$0.312992\pi$$
$$282$$ 1.50000 + 2.59808i 0.0893237 + 0.154713i
$$283$$ 13.4686 23.3283i 0.800627 1.38673i −0.118577 0.992945i $$-0.537833\pi$$
0.919204 0.393781i $$-0.128833\pi$$
$$284$$ −2.85425 + 4.94370i −0.169368 + 0.293355i
$$285$$ −4.11438 7.12631i −0.243715 0.422126i
$$286$$ 4.64575 0.274709
$$287$$ 10.1144 + 17.5186i 0.597033 + 1.03409i
$$288$$ −1.00000 −0.0589256
$$289$$ 7.58301 + 13.1342i 0.446059 + 0.772597i
$$290$$ −5.17712 + 8.96704i −0.304011 + 0.526563i
$$291$$ 7.46863 12.9360i 0.437819 0.758324i
$$292$$ 4.17712 + 7.23499i 0.244448 + 0.423396i
$$293$$ −29.5203 −1.72459 −0.862296 0.506405i $$-0.830974\pi$$
−0.862296 + 0.506405i $$0.830974\pi$$
$$294$$ 3.50000 6.06218i 0.204124 0.353553i
$$295$$ 13.0627 0.760542
$$296$$ 0.177124 + 0.306788i 0.0102951 + 0.0178317i
$$297$$ 2.32288 4.02334i 0.134787 0.233458i
$$298$$ −11.4686 + 19.8642i −0.664360 + 1.15070i
$$299$$ 3.82288 + 6.62141i 0.221083 + 0.382926i
$$300$$ −2.29150 −0.132300
$$301$$ −7.00000 12.1244i −0.403473 0.698836i
$$302$$ −21.9373 −1.26235
$$303$$ 0 0
$$304$$ −2.50000 + 4.33013i −0.143385 + 0.248350i
$$305$$ −3.23987 + 5.61162i −0.185514 + 0.321320i
$$306$$ −0.677124 1.17281i −0.0387086 0.0670453i
$$307$$ 11.5830 0.661077 0.330539 0.943793i $$-0.392770\pi$$
0.330539 + 0.943793i $$0.392770\pi$$
$$308$$ 6.14575 10.6448i 0.350187 0.606541i
$$309$$ 5.29150 0.301023
$$310$$ −6.00000 10.3923i −0.340777 0.590243i
$$311$$ 8.46863 14.6681i 0.480212 0.831751i −0.519531 0.854452i $$-0.673893\pi$$
0.999742 + 0.0227007i $$0.00722647\pi$$
$$312$$ 0.500000 0.866025i 0.0283069 0.0490290i
$$313$$ 14.5830 + 25.2585i 0.824280 + 1.42770i 0.902468 + 0.430757i $$0.141753\pi$$
−0.0781880 + 0.996939i $$0.524913\pi$$
$$314$$ 2.64575 0.149308
$$315$$ 4.35425 0.245334
$$316$$ −10.0000 −0.562544
$$317$$ 1.35425 + 2.34563i 0.0760622 + 0.131744i 0.901548 0.432680i $$-0.142432\pi$$
−0.825486 + 0.564423i $$0.809099\pi$$
$$318$$ −1.50000 + 2.59808i −0.0841158 + 0.145693i
$$319$$ −14.6144 + 25.3128i −0.818248 + 1.41725i
$$320$$ −0.822876 1.42526i −0.0460001 0.0796746i
$$321$$ −12.0000 −0.669775
$$322$$ 20.2288 1.12730
$$323$$ −6.77124 −0.376762
$$324$$ −0.500000 0.866025i −0.0277778 0.0481125i
$$325$$ 1.14575 1.98450i 0.0635548 0.110080i
$$326$$ 11.7915 20.4235i 0.653071 1.13115i
$$327$$ 2.00000 + 3.46410i 0.110600 + 0.191565i
$$328$$ 7.64575 0.422166
$$329$$ −3.96863 + 6.87386i −0.218797 + 0.378968i
$$330$$ 7.64575 0.420885
$$331$$ −16.2915 28.2177i −0.895462 1.55099i −0.833232 0.552924i $$-0.813512\pi$$
−0.0622301 0.998062i $$-0.519821\pi$$
$$332$$ 1.35425 2.34563i 0.0743241 0.128733i
$$333$$ −0.177124 + 0.306788i −0.00970635 + 0.0168119i
$$334$$ 12.4373 + 21.5420i 0.680536 + 1.17872i
$$335$$ −22.3542 −1.22134
$$336$$ −1.32288 2.29129i −0.0721688 0.125000i
$$337$$ 5.58301 0.304126 0.152063 0.988371i $$-0.451408\pi$$
0.152063 + 0.988371i $$0.451408\pi$$
$$338$$ 0.500000 + 0.866025i 0.0271964 + 0.0471056i
$$339$$ 5.61438 9.72439i 0.304931 0.528156i
$$340$$ 1.11438 1.93016i 0.0604356 0.104678i
$$341$$ −16.9373 29.3362i −0.917204 1.58864i
$$342$$ −5.00000 −0.270369
$$343$$ 18.5203 1.00000
$$344$$ −5.29150 −0.285299
$$345$$ 6.29150 + 10.8972i 0.338723 + 0.586686i
$$346$$ −5.85425 + 10.1399i −0.314726 + 0.545122i
$$347$$ 13.1144 22.7148i 0.704017 1.21939i −0.263029 0.964788i $$-0.584721\pi$$
0.967045 0.254605i $$-0.0819453\pi$$
$$348$$ 3.14575 + 5.44860i 0.168630 + 0.292076i
$$349$$ 3.06275 0.163945 0.0819725 0.996635i $$-0.473878\pi$$
0.0819725 + 0.996635i $$0.473878\pi$$
$$350$$ −3.03137 5.25049i −0.162034 0.280651i
$$351$$ 1.00000 0.0533761
$$352$$ −2.32288 4.02334i −0.123810 0.214445i
$$353$$ −0.291503 + 0.504897i −0.0155151 + 0.0268730i −0.873679 0.486503i $$-0.838272\pi$$
0.858164 + 0.513376i $$0.171605\pi$$
$$354$$ 3.96863 6.87386i 0.210930 0.365342i
$$355$$ −4.69738 8.13611i −0.249311 0.431820i
$$356$$ 1.06275 0.0563254
$$357$$ 1.79150 3.10297i 0.0948164 0.164227i
$$358$$ 6.00000 0.317110
$$359$$ 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i $$-0.116054\pi$$
−0.775934 + 0.630814i $$0.782721\pi$$
$$360$$ 0.822876 1.42526i 0.0433694 0.0751179i
$$361$$ −3.00000 + 5.19615i −0.157895 + 0.273482i
$$362$$ 4.67712 + 8.10102i 0.245824 + 0.425780i
$$363$$ 10.5830 0.555464
$$364$$ 2.64575 0.138675
$$365$$ −13.7490 −0.719656
$$366$$ 1.96863 + 3.40976i 0.102902 + 0.178231i
$$367$$ −10.2915 + 17.8254i −0.537212 + 0.930479i 0.461841 + 0.886963i $$0.347189\pi$$
−0.999053 + 0.0435157i $$0.986144\pi$$
$$368$$ 3.82288 6.62141i 0.199281 0.345165i
$$369$$ 3.82288 + 6.62141i 0.199011 + 0.344697i
$$370$$ −0.583005 −0.0303090
$$371$$ −7.93725 −0.412082
$$372$$ −7.29150 −0.378047
$$373$$ −4.67712 8.10102i −0.242172 0.419455i 0.719160 0.694844i $$-0.244527\pi$$
−0.961333 + 0.275389i $$0.911193\pi$$
$$374$$ 3.14575 5.44860i 0.162663 0.281740i
$$375$$ 6.00000 10.3923i 0.309839 0.536656i
$$376$$ 1.50000 + 2.59808i 0.0773566 + 0.133986i
$$377$$ −6.29150 −0.324029
$$378$$ 1.32288 2.29129i 0.0680414 0.117851i
$$379$$ 33.1660 1.70362 0.851812 0.523848i $$-0.175504\pi$$
0.851812 + 0.523848i $$0.175504\pi$$
$$380$$ −4.11438 7.12631i −0.211063 0.365572i
$$381$$ −8.11438 + 14.0545i −0.415712 + 0.720035i
$$382$$ 0 0
$$383$$ 18.8745 + 32.6916i 0.964442 + 1.67046i 0.711106 + 0.703085i $$0.248195\pi$$
0.253336 + 0.967378i $$0.418472\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 10.1144 + 17.5186i 0.515476 + 0.892831i
$$386$$ −3.06275 −0.155890
$$387$$ −2.64575 4.58258i −0.134491 0.232945i
$$388$$ 7.46863 12.9360i 0.379162 0.656728i
$$389$$ −9.14575 + 15.8409i −0.463708 + 0.803166i −0.999142 0.0414111i $$-0.986815\pi$$
0.535434 + 0.844577i $$0.320148\pi$$
$$390$$ 0.822876 + 1.42526i 0.0416679 + 0.0721710i
$$391$$ 10.3542 0.523637
$$392$$ 3.50000 6.06218i 0.176777 0.306186i
$$393$$ −4.93725 −0.249052
$$394$$ 10.4059 + 18.0235i 0.524241 + 0.908012i
$$395$$ 8.22876 14.2526i 0.414034 0.717127i
$$396$$ 2.32288 4.02334i 0.116729 0.202180i
$$397$$ −0.468627 0.811686i −0.0235197 0.0407373i 0.854026 0.520230i $$-0.174154\pi$$
−0.877546 + 0.479493i $$0.840821\pi$$
$$398$$ −4.22876 −0.211968
$$399$$ −6.61438 11.4564i −0.331133 0.573539i
$$400$$ −2.29150 −0.114575
$$401$$ −4.11438 7.12631i −0.205462 0.355871i 0.744818 0.667268i $$-0.232536\pi$$
−0.950280 + 0.311397i $$0.899203\pi$$
$$402$$ −6.79150 + 11.7632i −0.338729 + 0.586696i
$$403$$ 3.64575 6.31463i 0.181608 0.314554i
$$404$$ 0 0
$$405$$ 1.64575 0.0817780
$$406$$ −8.32288 + 14.4156i −0.413057 + 0.715436i
$$407$$ −1.64575 −0.0815769
$$408$$ −0.677124 1.17281i −0.0335227 0.0580629i
$$409$$ 5.53137 9.58062i 0.273509 0.473731i −0.696249 0.717800i $$-0.745149\pi$$
0.969758 + 0.244069i $$0.0784824\pi$$
$$410$$ −6.29150 + 10.8972i −0.310715 + 0.538174i
$$411$$ −8.76013 15.1730i −0.432105 0.748428i
$$412$$ 5.29150 0.260694
$$413$$ 21.0000 1.03334
$$414$$ 7.64575 0.375768
$$415$$ 2.22876 + 3.86032i 0.109405 + 0.189496i
$$416$$ 0.500000 0.866025i 0.0245145 0.0424604i
$$417$$ −2.11438 + 3.66221i −0.103542 + 0.179339i
$$418$$ −11.6144 20.1167i −0.568078 0.983940i
$$419$$ −22.4575 −1.09712 −0.548561 0.836111i $$-0.684824\pi$$
−0.548561 + 0.836111i $$0.684824\pi$$
$$420$$ 4.35425 0.212466
$$421$$ −29.6458 −1.44485 −0.722423 0.691452i $$-0.756972\pi$$
−0.722423 + 0.691452i $$0.756972\pi$$
$$422$$ −5.82288 10.0855i −0.283453 0.490955i
$$423$$ −1.50000 + 2.59808i −0.0729325 + 0.126323i
$$424$$ −1.50000 + 2.59808i −0.0728464 + 0.126174i
$$425$$ −1.55163 2.68751i −0.0752652 0.130363i
$$426$$ −5.70850 −0.276578
$$427$$ −5.20850 + 9.02138i −0.252057 + 0.436575i
$$428$$ −12.0000 −0.580042
$$429$$ 2.32288 + 4.02334i 0.112149 + 0.194249i
$$430$$ 4.35425 7.54178i 0.209981 0.363697i
$$431$$ 0.291503 0.504897i 0.0140412 0.0243200i −0.858919 0.512111i $$-0.828864\pi$$
0.872961 + 0.487791i $$0.162197\pi$$
$$432$$ −0.500000 0.866025i −0.0240563 0.0416667i
$$433$$ −12.4170 −0.596723 −0.298361 0.954453i $$-0.596440\pi$$
−0.298361 + 0.954453i $$0.596440\pi$$
$$434$$ −9.64575 16.7069i −0.463011 0.801958i
$$435$$ −10.3542 −0.496448
$$436$$ 2.00000 + 3.46410i 0.0957826 + 0.165900i
$$437$$ 19.1144 33.1071i 0.914365 1.58373i
$$438$$ −4.17712 + 7.23499i −0.199591 + 0.345701i
$$439$$ −9.17712 15.8952i −0.438000 0.758639i 0.559535 0.828807i $$-0.310980\pi$$
−0.997535 + 0.0701681i $$0.977646\pi$$
$$440$$ 7.64575 0.364497
$$441$$ 7.00000 0.333333
$$442$$ 1.35425 0.0644150
$$443$$ −17.4686 30.2565i −0.829960 1.43753i −0.898069 0.439854i $$-0.855030\pi$$
0.0681097 0.997678i $$-0.478303\pi$$
$$444$$ −0.177124 + 0.306788i −0.00840595 + 0.0145595i
$$445$$ −0.874508 + 1.51469i −0.0414556 + 0.0718033i
$$446$$ 8.26013 + 14.3070i 0.391128 + 0.677454i
$$447$$ −22.9373 −1.08489
$$448$$ −1.32288 2.29129i −0.0625000 0.108253i
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ −1.14575 1.98450i −0.0540112 0.0935502i
$$451$$ −17.7601 + 30.7614i −0.836292 + 1.44850i
$$452$$ 5.61438 9.72439i 0.264078 0.457397i
$$453$$ −10.9686 18.9982i −0.515351 0.892614i
$$454$$ 15.2915 0.717666
$$455$$ −2.17712 + 3.77089i −0.102065 + 0.176782i
$$456$$ −5.00000 −0.234146
$$457$$ −2.88562 4.99804i −0.134984 0.233799i 0.790608 0.612323i $$-0.209765\pi$$
−0.925591 + 0.378525i $$0.876432\pi$$
$$458$$ −13.2288 + 22.9129i −0.618139 + 1.07065i
$$459$$ 0.677124 1.17281i 0.0316055 0.0547423i
$$460$$ 6.29150 + 10.8972i 0.293343 + 0.508085i
$$461$$ 16.4575 0.766503 0.383251 0.923644i $$-0.374804\pi$$
0.383251 + 0.923644i $$0.374804\pi$$
$$462$$ 12.2915 0.571852
$$463$$ −17.1660 −0.797772 −0.398886 0.917000i $$-0.630603\pi$$
−0.398886 + 0.917000i $$0.630603\pi$$
$$464$$ 3.14575 + 5.44860i 0.146038 + 0.252945i
$$465$$ 6.00000 10.3923i 0.278243 0.481932i
$$466$$ −2.32288 + 4.02334i −0.107605 + 0.186378i
$$467$$ 0.239870 + 0.415468i 0.0110999 + 0.0192256i 0.871522 0.490356i $$-0.163133\pi$$
−0.860422 + 0.509582i $$0.829800\pi$$
$$468$$ 1.00000 0.0462250
$$469$$ −35.9373 −1.65943
$$470$$ −4.93725 −0.227739
$$471$$ 1.32288 + 2.29129i 0.0609549 + 0.105577i
$$472$$ 3.96863 6.87386i 0.182671 0.316395i
$$473$$ 12.2915 21.2895i 0.565164 0.978893i
$$474$$ −5.00000 8.66025i −0.229658 0.397779i
$$475$$ −11.4575 −0.525707
$$476$$ 1.79150 3.10297i 0.0821134 0.142225i
$$477$$ −3.00000 −0.137361
$$478$$ 1.50000 + 2.59808i 0.0686084 + 0.118833i
$$479$$ −14.3745 + 24.8974i −0.656788 + 1.13759i 0.324654 + 0.945833i $$0.394752\pi$$
−0.981442 + 0.191757i $$0.938581\pi$$
$$480$$ 0.822876 1.42526i 0.0375590 0.0650540i
$$481$$ −0.177124 0.306788i −0.00807617 0.0139883i
$$482$$ −17.8745 −0.814162
$$483$$ 10.1144 + 17.5186i 0.460220 + 0.797125i
$$484$$ 10.5830 0.481046
$$485$$ 12.2915 + 21.2895i 0.558128 + 0.966707i
$$486$$ 0.500000 0.866025i 0.0226805 0.0392837i
$$487$$ 4.03137 6.98254i 0.182679 0.316409i −0.760113 0.649791i $$-0.774856\pi$$
0.942792 + 0.333382i $$0.108190\pi$$
$$488$$ 1.96863 + 3.40976i 0.0891156 + 0.154353i
$$489$$ 23.5830 1.06646
$$490$$ 5.76013 + 9.97684i 0.260216 + 0.450708i
$$491$$ −31.1660 −1.40650 −0.703251 0.710941i $$-0.748269\pi$$
−0.703251 + 0.710941i $$0.748269\pi$$
$$492$$ 3.82288 + 6.62141i 0.172349 + 0.298516i
$$493$$ −4.26013 + 7.37876i −0.191867 + 0.332323i
$$494$$ 2.50000 4.33013i 0.112480 0.194822i
$$495$$ 3.82288 + 6.62141i 0.171825 + 0.297610i
$$496$$ −7.29150 −0.327398
$$497$$ −7.55163 13.0798i −0.338737 0.586710i
$$498$$ 2.70850 0.121371
$$499$$ 9.35425 + 16.2020i 0.418754 + 0.725303i 0.995814 0.0913986i $$-0.0291337\pi$$
−0.577061 + 0.816701i $$0.695800\pi$$
$$500$$ 6.00000 10.3923i 0.268328 0.464758i
$$501$$ −12.4373 + 21.5420i −0.555656 + 0.962424i
$$502$$ −1.35425 2.34563i −0.0604431 0.104690i
$$503$$ −16.4575 −0.733804 −0.366902 0.930260i $$-0.619582\pi$$
−0.366902 + 0.930260i $$0.619582\pi$$
$$504$$ 1.32288 2.29129i 0.0589256 0.102062i
$$505$$ 0 0
$$506$$ 17.7601 + 30.7614i 0.789534 + 1.36751i
$$507$$ −0.500000 + 0.866025i −0.0222058 + 0.0384615i
$$508$$ −8.11438 + 14.0545i −0.360017 + 0.623568i
$$509$$ −12.0000 20.7846i −0.531891 0.921262i −0.999307 0.0372243i $$-0.988148\pi$$
0.467416 0.884037i $$-0.345185\pi$$
$$510$$ 2.22876 0.0986910
$$511$$ −22.1033 −0.977791
$$512$$ −1.00000 −0.0441942
$$513$$ −2.50000 4.33013i −0.110378 0.191180i
$$514$$ 7.93725 13.7477i 0.350097 0.606386i
$$515$$ −4.35425 + 7.54178i −0.191871 + 0.332331i
$$516$$ −2.64575 4.58258i −0.116473 0.201737i
$$517$$ −13.9373 −0.612960
$$518$$ −0.937254 −0.0411806
$$519$$ −11.7085 −0.513946
$$520$$ 0.822876 + 1.42526i 0.0360855 + 0.0625019i
$$521$$ −9.00000 + 15.5885i −0.394297 + 0.682943i −0.993011 0.118020i $$-0.962345\pi$$
0.598714 + 0.800963i $$0.295679\pi$$
$$522$$ −3.14575 + 5.44860i −0.137686 + 0.238479i
$$523$$ 18.6458 + 32.2954i 0.815322 + 1.41218i 0.909097 + 0.416585i $$0.136773\pi$$
−0.0937748 + 0.995593i $$0.529893\pi$$
$$524$$ −4.93725 −0.215685
$$525$$ 3.03137 5.25049i 0.132300 0.229150i
$$526$$ −1.64575 −0.0717582
$$527$$ −4.93725 8.55157i −0.215070 0.372512i
$$528$$ 2.32288 4.02334i 0.101090 0.175093i
$$529$$ −17.7288 + 30.7071i −0.770816 + 1.33509i
$$530$$ −2.46863 4.27579i −0.107230 0.185728i
$$531$$ 7.93725 0.344447
$$532$$ −6.61438 11.4564i −0.286770 0.496700i
$$533$$ −7.64575 −0.331174
$$534$$ 0.531373 + 0.920365i 0.0229948 + 0.0398281i
$$535$$ 9.87451 17.1031i 0.426912 0.739434i
$$536$$ −6.79150 + 11.7632i −0.293348 + 0.508094i
$$537$$ 3.00000 + 5.19615i 0.129460 + 0.224231i
$$538$$ 24.8745 1.07242
$$539$$ 16.2601 + 28.1634i 0.700373 + 1.21308i
$$540$$ 1.64575 0.0708219
$$541$$ −18.1771 31.4837i −0.781496 1.35359i −0.931070 0.364840i $$-0.881124\pi$$
0.149575 0.988750i $$-0.452210\pi$$
$$542$$ −8.67712 + 15.0292i −0.372714 + 0.645560i
$$543$$ −4.67712 + 8.10102i −0.200715 + 0.347648i
$$544$$ −0.677124 1.17281i −0.0290315 0.0502840i
$$545$$ −6.58301 −0.281985
$$546$$ 1.32288 + 2.29129i 0.0566139 + 0.0980581i
$$547$$ −5.06275 −0.216467 −0.108234 0.994125i $$-0.534519\pi$$
−0.108234 + 0.994125i $$0.534519\pi$$
$$548$$ −8.76013 15.1730i −0.374214 0.648158i
$$549$$ −1.96863 + 3.40976i −0.0840190 + 0.145525i
$$550$$ 5.32288 9.21949i 0.226968 0.393120i
$$551$$ 15.7288 + 27.2430i 0.670068 + 1.16059i
$$552$$ 7.64575 0.325425
$$553$$ 13.2288 22.9129i 0.562544 0.974355i
$$554$$ 18.5203 0.786850
$$555$$ −0.291503 0.504897i −0.0123736 0.0214317i
$$556$$ −2.11438 + 3.66221i −0.0896696 + 0.155312i
$$557$$ 15.5830 26.9906i 0.660273 1.14363i −0.320271 0.947326i $$-0.603774\pi$$
0.980544 0.196301i $$-0.0628928\pi$$
$$558$$ −3.64575 6.31463i −0.154337 0.267319i
$$559$$ 5.29150 0.223807
$$560$$ 4.35425 0.184001
$$561$$ 6.29150 0.265627
$$562$$ 9.29150 + 16.0934i 0.391938 + 0.678857i
$$563$$ −23.5203 + 40.7383i −0.991261 + 1.71691i −0.381387 + 0.924416i $$0.624553\pi$$
−0.609874 + 0.792498i $$0.708780\pi$$
$$564$$ −1.50000 + 2.59808i −0.0631614 + 0.109399i
$$565$$ 9.23987 + 16.0039i 0.388724 + 0.673290i
$$566$$ 26.9373 1.13226
$$567$$ 2.64575 0.111111
$$568$$ −5.70850 −0.239523
$$569$$ 3.38562 + 5.86407i 0.141933 + 0.245835i 0.928224 0.372021i $$-0.121335\pi$$
−0.786292 + 0.617855i $$0.788002\pi$$
$$570$$ 4.11438 7.12631i 0.172332 0.298488i
$$571$$ 8.00000 13.8564i 0.334790 0.579873i −0.648655 0.761083i $$-0.724668\pi$$
0.983444 + 0.181210i $$0.0580014\pi$$
$$572$$ 2.32288 + 4.02334i 0.0971243 + 0.168224i
$$573$$ 0 0
$$574$$ −10.1144 + 17.5186i −0.422166 + 0.731213i
$$575$$ 17.5203 0.730645
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −4.29150 + 7.43310i −0.178658 + 0.309444i −0.941421 0.337234i $$-0.890509\pi$$
0.762763 + 0.646678i $$0.223842\pi$$
$$578$$ −7.58301 + 13.1342i −0.315411 + 0.546309i
$$579$$ −1.53137 2.65242i −0.0636417 0.110231i
$$580$$ −10.3542 −0.429937
$$581$$ 3.58301 + 6.20595i 0.148648 + 0.257466i
$$582$$ 14.9373 0.619169
$$583$$ −6.96863 12.0700i −0.288611 0.499889i
$$584$$ −4.17712 + 7.23499i −0.172851 + 0.299386i
$$585$$ −0.822876 + 1.42526i −0.0340217 + 0.0589273i
$$586$$ −14.7601 25.5653i −0.609735 1.05609i
$$587$$ 16.0627 0.662980 0.331490 0.943459i $$-0.392449\pi$$
0.331490 + 0.943459i $$0.392449\pi$$
$$588$$ 7.00000 0.288675
$$589$$ −36.4575 −1.50221
$$590$$ 6.53137 + 11.3127i 0.268892 + 0.465735i
$$591$$ −10.4059 + 18.0235i −0.428041 + 0.741388i
$$592$$ −0.177124 + 0.306788i −0.00727977 + 0.0126089i
$$593$$ −3.23987 5.61162i −0.133046 0.230442i 0.791804 0.610776i $$-0.209142\pi$$
−0.924849 + 0.380334i $$0.875809\pi$$
$$594$$ 4.64575 0.190617
$$595$$ 2.94837 + 5.10672i 0.120871 + 0.209355i
$$596$$ −22.9373 −0.939547
$$597$$ −2.11438 3.66221i −0.0865357 0.149884i
$$598$$ −3.82288 + 6.62141i −0.156329 + 0.270770i
$$599$$ −7.40588 + 12.8274i −0.302596 + 0.524112i −0.976723 0.214504i $$-0.931187\pi$$
0.674127 + 0.738615i $$0.264520\pi$$
$$600$$ −1.14575 1.98450i −0.0467751 0.0810169i
$$601$$ −16.8745 −0.688326 −0.344163 0.938910i $$-0.611837\pi$$
−0.344163 + 0.938910i $$0.611837\pi$$
$$602$$ 7.00000 12.1244i 0.285299 0.494152i
$$603$$ −13.5830 −0.553143
$$604$$ −10.9686 18.9982i −0.446307 0.773027i
$$605$$ −8.70850 + 15.0836i −0.354051 + 0.613234i
$$606$$ 0 0
$$607$$ 15.4059 + 26.6838i 0.625305 + 1.08306i 0.988482 + 0.151340i $$0.0483589\pi$$
−0.363176 + 0.931720i $$0.618308\pi$$
$$608$$ −5.00000 −0.202777
$$609$$ −16.6458 −0.674520
$$610$$ −6.47974 −0.262357
$$611$$ −1.50000 2.59808i −0.0606835 0.105107i
$$612$$ 0.677124 1.17281i 0.0273711 0.0474082i
$$613$$ −5.06275 + 8.76893i −0.204482 + 0.354174i −0.949968 0.312348i $$-0.898884\pi$$
0.745485 + 0.666522i $$0.232218\pi$$
$$614$$ 5.79150 + 10.0312i 0.233726 + 0.404825i
$$615$$ −12.5830 −0.507396
$$616$$ 12.2915 0.495239
$$617$$ −21.2915 −0.857164 −0.428582 0.903503i $$-0.640987\pi$$
−0.428582 + 0.903503i $$0.640987\pi$$
$$618$$ 2.64575 + 4.58258i 0.106428 + 0.184338i
$$619$$ −10.8745 + 18.8352i −0.437083 + 0.757051i −0.997463 0.0711852i $$-0.977322\pi$$
0.560380 + 0.828236i $$0.310655\pi$$
$$620$$ 6.00000 10.3923i 0.240966 0.417365i
$$621$$ 3.82288 + 6.62141i 0.153407 + 0.265708i
$$622$$ 16.9373 0.679122
$$623$$ −1.40588 + 2.43506i −0.0563254 + 0.0975585i
$$624$$ 1.00000 0.0400320
$$625$$ 4.14575 + 7.18065i 0.165830 + 0.287226i
$$626$$ −14.5830 + 25.2585i −0.582854 + 1.00953i
$$627$$ 11.6144 20.1167i 0.463834 0.803383i
$$628$$ 1.32288 + 2.29129i 0.0527885 + 0.0914323i
$$629$$ −0.479741 −0.0191285
$$630$$ 2.17712 + 3.77089i 0.0867387 + 0.150236i
$$631$$ −38.4575 −1.53097 −0.765485 0.643454i $$-0.777501\pi$$
−0.765485 + 0.643454i $$0.777501\pi$$
$$632$$ −5.00000 8.66025i −0.198889 0.344486i
$$633$$ 5.82288 10.0855i 0.231439 0.400863i
$$634$$ −1.35425 + 2.34563i −0.0537841 + 0.0931568i
$$635$$ −13.3542 23.1302i −0.529947 0.917895i
$$636$$ −3.00000 −0.118958
$$637$$ −3.50000 + 6.06218i −0.138675 + 0.240192i
$$638$$ −29.2288 −1.15718
$$639$$ −2.85425 4.94370i −0.112912 0.195570i
$$640$$ 0.822876 1.42526i 0.0325270 0.0563384i
$$641$$ 21.2915 36.8780i 0.840964 1.45659i −0.0481170 0.998842i $$-0.515322\pi$$
0.889081 0.457750i $$-0.151345\pi$$
$$642$$ −6.00000 10.3923i −0.236801 0.410152i
$$643$$ 20.8745 0.823210 0.411605 0.911362i $$-0.364968\pi$$
0.411605 + 0.911362i $$0.364968\pi$$
$$644$$ 10.1144 + 17.5186i 0.398562 + 0.690330i
$$645$$ 8.70850 0.342897
$$646$$ −3.38562 5.86407i −0.133206 0.230719i
$$647$$ 18.8745 32.6916i 0.742033 1.28524i −0.209535 0.977801i $$-0.567195\pi$$
0.951568 0.307438i $$-0.0994718\pi$$
$$648$$ 0.500000 0.866025i 0.0196419 0.0340207i
$$649$$ 18.4373 + 31.9343i 0.723726 + 1.25353i
$$650$$ 2.29150 0.0898801
$$651$$ 9.64575 16.7069i 0.378047 0.654796i
$$652$$ 23.5830 0.923582
$$653$$ −6.00000 10.3923i −0.234798 0.406682i 0.724416 0.689363i $$-0.242110\pi$$
−0.959214 + 0.282681i $$0.908776\pi$$
$$654$$ −2.00000 + 3.46410i −0.0782062 + 0.135457i
$$655$$ 4.06275 7.03688i 0.158745 0.274954i
$$656$$ 3.82288 + 6.62141i 0.149258 + 0.258523i
$$657$$ −8.35425 −0.325930
$$658$$ −7.93725 −0.309426
$$659$$ −1.06275 −0.0413987 −0.0206994 0.999786i $$-0.506589\pi$$
−0.0206994 + 0.999786i $$0.506589\pi$$
$$660$$ 3.82288 + 6.62141i 0.148805 + 0.257738i
$$661$$ 10.7601 18.6371i 0.418521 0.724899i −0.577270 0.816553i $$-0.695882\pi$$
0.995791 + 0.0916543i $$0.0292155\pi$$
$$662$$ 16.2915 28.2177i 0.633187 1.09671i
$$663$$ 0.677124 + 1.17281i 0.0262973 + 0.0455483i
$$664$$ 2.70850 0.105110
$$665$$ 21.7712 0.844253
$$666$$ −0.354249 −0.0137269
$$667$$ −24.0516 41.6586i −0.931283 1.61303i
$$668$$ −12.4373 + 21.5420i −0.481212 + 0.833483i
$$669$$ −8.26013 + 14.3070i −0.319355 + 0.553139i
$$670$$ −11.1771 19.3593i −0.431810 0.747917i
$$671$$ −18.2915 −0.706136
$$672$$ 1.32288 2.29129i 0.0510310 0.0883883i
$$673$$ 14.5830 0.562134 0.281067 0.959688i $$-0.409312\pi$$
0.281067 + 0.959688i $$0.409312\pi$$
$$674$$ 2.79150 + 4.83502i 0.107525 + 0.186238i
$$675$$ 1.14575 1.98450i 0.0441000 0.0763834i
$$676$$ −0.500000 + 0.866025i −0.0192308 + 0.0333087i
$$677$$ 11.0830 + 19.1963i 0.425954 + 0.737775i 0.996509 0.0834849i $$-0.0266050\pi$$
−0.570555 + 0.821260i $$0.693272\pi$$
$$678$$ 11.2288 0.431238
$$679$$ 19.7601 + 34.2255i 0.758324 + 1.31346i
$$680$$ 2.22876 0.0854689
$$681$$ 7.64575 + 13.2428i 0.292986 + 0.507466i
$$682$$ 16.9373 29.3362i 0.648561 1.12334i
$$683$$ −4.35425 + 7.54178i −0.166611 + 0.288578i −0.937226 0.348722i $$-0.886616\pi$$
0.770615 + 0.637300i $$0.219949\pi$$
$$684$$ −2.50000 4.33013i −0.0955899 0.165567i
$$685$$ 28.8340 1.10169
$$686$$ 9.26013 + 16.0390i 0.353553 + 0.612372i
$$687$$ −26.4575 −1.00942
$$688$$ −2.64575 4.58258i −0.100868 0.174709i
$$689$$ 1.50000 2.59808i 0.0571454 0.0989788i
$$690$$ −6.29150 + 10.8972i −0.239513 + 0.414849i
$$691$$ −17.0203 29.4800i −0.647481 1.12147i −0.983722 0.179694i $$-0.942489\pi$$
0.336241 0.941776i $$-0.390844\pi$$
$$692$$ −11.7085 −0.445090
$$693$$ 6.14575 + 10.6448i 0.233458 + 0.404361i
$$694$$ 26.2288 0.995630
$$695$$ −3.47974 6.02709i −0.131994 0.228620i
$$696$$ −3.14575 + 5.44860i −0.119239 + 0.206529i
$$697$$ −5.17712 + 8.96704i −0.196098 + 0.339651i
$$698$$ 1.53137 + 2.65242i 0.0579633 + 0.100395i
$$699$$ −4.64575 −0.175718
$$700$$ 3.03137 5.25049i 0.114575 0.198450i
$$701$$ 12.0000 0.453234 0.226617 0.973984i $$-0.427233\pi$$
0.226617 + 0.973984i $$0.427233\pi$$
$$702$$ 0.500000 + 0.866025i 0.0188713 + 0.0326860i
$$703$$ −0.885622 + 1.53394i −0.0334019 + 0.0578537i
$$704$$ 2.32288 4.02334i 0.0875467 0.151635i
$$705$$ −2.46863 4.27579i −0.0929739 0.161035i
$$706$$ −0.583005 −0.0219417
$$707$$ 0 0
$$708$$ 7.93725 0.298300
$$709$$ −21.7601 37.6897i −0.817219 1.41546i −0.907724 0.419569i $$-0.862181\pi$$
0.0905049 0.995896i $$-0.471152\pi$$
$$710$$ 4.69738 8.13611i 0.176290 0.305343i
$$711$$ 5.00000 8.66025i 0.187515 0.324785i
$$712$$ 0.531373 + 0.920365i 0.0199140 + 0.0344921i
$$713$$ 55.7490 2.08782
$$714$$ 3.58301 0.134091
$$715$$ −7.64575 −0.285935
$$716$$ 3.00000 + 5.19615i 0.112115 + 0.194189i
$$717$$ −1.50000 + 2.59808i −0.0560185 + 0.0970269i
$$718$$ −3.00000 + 5.19615i −0.111959 + 0.193919i
$$719$$ −11.7085 20.2797i −0.436653 0.756306i 0.560776 0.827968i $$-0.310503\pi$$
−0.997429 + 0.0716621i $$0.977170\pi$$
$$720$$ 1.64575 0.0613335
$$721$$ −7.00000 + 12.1244i −0.260694 + 0.451535i
$$722$$ −6.00000 −0.223297
$$723$$ −8.93725 15.4798i −0.332380 0.575699i
$$724$$ −4.67712 + 8.10102i −0.173824 + 0.301072i
$$725$$ −7.20850 + 12.4855i −0.267717 + 0.463699i
$$726$$ 5.29150 + 9.16515i 0.196386 + 0.340151i
$$727$$ 36.4575 1.35213 0.676067 0.736840i $$-0.263683\pi$$
0.676067 + 0.736840i $$0.263683\pi$$
$$728$$ 1.32288 + 2.29129i 0.0490290 + 0.0849208i
$$729$$ 1.00000 0.0370370
$$730$$ −6.87451 11.9070i −0.254437 0.440698i
$$731$$ 3.58301 6.20595i 0.132522 0.229535i
$$732$$ −1.96863 + 3.40976i −0.0727625 + 0.126028i
$$733$$ 6.11438 + 10.5904i 0.225840 + 0.391166i 0.956571 0.291499i $$-0.0941541\pi$$
−0.730731 + 0.682665i $$0.760821\pi$$
$$734$$ −20.5830 −0.759733
$$735$$ −5.76013 + 9.97684i −0.212466 + 0.368001i
$$736$$ 7.64575 0.281826
$$737$$ −31.5516 54.6490i −1.16222 2.01302i
$$738$$ −3.82288 + 6.62141i −0.140722 + 0.243738i
$$739$$ 3.35425 5.80973i 0.123388 0.213714i −0.797714 0.603036i $$-0.793957\pi$$
0.921102 + 0.389322i $$0.127291\pi$$
$$740$$ −0.291503 0.504897i −0.0107158 0.0185604i
$$741$$ 5.00000 0.183680
$$742$$ −3.96863 6.87386i −0.145693 0.252347i
$$743$$ 1.45751 0.0534710 0.0267355 0.999643i $$-0.491489\pi$$
0.0267355 + 0.999643i $$0.491489\pi$$
$$744$$ −3.64575 6.31463i −0.133660 0.231505i
$$745$$ 18.8745 32.6916i 0.691508 1.19773i
$$746$$ 4.67712 8.10102i 0.171242 0.296599i
$$747$$ 1.35425 + 2.34563i 0.0495494 + 0.0858220i
$$748$$ 6.29150 0.230040
$$749$$ 15.8745 27.4955i 0.580042 1.00466i
$$750$$ 12.0000 0.438178
$$751$$ −4.58301 7.93800i −0.167236 0.289662i 0.770211 0.637789i $$-0.220151\pi$$
−0.937447 + 0.348128i $$0.886818\pi$$
$$752$$ −1.50000 + 2.59808i −0.0546994 + 0.0947421i
$$753$$ 1.35425 2.34563i 0.0493516 0.0854794i
$$754$$ −3.14575 5.44860i −0.114562 0.198426i
$$755$$ 36.1033 1.31393
$$756$$ 2.64575 0.0962250
$$757$$ 21.3542 0.776133 0.388067 0.921631i $$-0.373143\pi$$
0.388067 + 0.921631i $$0.373143\pi$$
$$758$$ 16.5830 + 28.7226i 0.602322 + 1.04325i
$$759$$ −17.7601 + 30.7614i −0.644652 + 1.11657i
$$760$$ 4.11438 7.12631i 0.149244 0.258499i
$$761$$ 1.64575 + 2.85052i 0.0596584 + 0.103331i 0.894312 0.447444i $$-0.147666\pi$$
−0.834654 + 0.550775i $$0.814332\pi$$
$$762$$ −16.2288 −0.587906
$$763$$ −10.5830 −0.383131
$$764$$ 0 0
$$765$$ 1.11438 + 1.93016i 0.0402904 + 0.0697851i
$$766$$ −18.8745 + 32.6916i −0.681964 + 1.18120i
$$767$$ −3.96863 + 6.87386i −0.143299 + 0.248201i
$$768$$ −0.500000 0.866025i −0.0180422 0.0312500i
$$769$$ 0.354249 0.0127745 0.00638727 0.999980i $$-0.497967\pi$$
0.00638727 + 0.999980i $$0.497967\pi$$
$$770$$ −10.1144 + 17.5186i −0.364497 + 0.631327i
$$771$$ 15.8745 0.571706
$$772$$ −1.53137 2.65242i −0.0551153 0.0954625i
$$773$$ 22.1660