# Properties

 Label 273.2.k.d.211.2 Level $273$ Weight $2$ Character 273.211 Analytic conductor $2.180$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, 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("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.k (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$2.17991597518$$ Analytic rank: $$0$$ Dimension: $$6$$ Relative dimension: $$3$$ over $$\Q(\zeta_{3})$$ Coefficient field: 6.0.771147.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1$$ x^6 - x^5 + 5*x^4 + 6*x^3 + 15*x^2 + 4*x + 1 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 211.2 Root $$-0.688601 - 1.19269i$$ of defining polynomial Character $$\chi$$ $$=$$ 273.211 Dual form 273.2.k.d.22.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.636945 + 1.10322i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.188601 - 0.326667i) q^{4} +1.10331 q^{5} +(-0.636945 + 1.10322i) q^{6} +(0.500000 - 0.866025i) q^{7} +3.02830 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.636945 + 1.10322i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.188601 - 0.326667i) q^{4} +1.10331 q^{5} +(-0.636945 + 1.10322i) q^{6} +(0.500000 - 0.866025i) q^{7} +3.02830 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.702750 + 1.21720i) q^{10} +(0.174453 + 0.302162i) q^{11} +0.377203 q^{12} +(-3.47664 - 0.955496i) q^{13} +1.27389 q^{14} +(0.551656 + 0.955496i) q^{15} +(1.55166 + 2.68755i) q^{16} +(-0.363055 + 0.628829i) q^{17} -1.27389 q^{18} +(-1.15109 + 1.99375i) q^{19} +(0.208086 - 0.360416i) q^{20} +1.00000 q^{21} +(-0.222234 + 0.384921i) q^{22} +(-0.0375080 - 0.0649658i) q^{23} +(1.51415 + 2.62258i) q^{24} -3.78270 q^{25} +(-1.16031 - 4.44410i) q^{26} -1.00000 q^{27} +(-0.188601 - 0.326667i) q^{28} +(-0.240258 - 0.416138i) q^{29} +(-0.702750 + 1.21720i) q^{30} -6.85772 q^{31} +(1.05166 - 1.82152i) q^{32} +(-0.174453 + 0.302162i) q^{33} -0.924984 q^{34} +(0.551656 - 0.955496i) q^{35} +(0.188601 + 0.326667i) q^{36} +(0.551656 + 0.955496i) q^{37} -2.93273 q^{38} +(-0.910836 - 3.48861i) q^{39} +3.34116 q^{40} +(-1.54778 - 2.68084i) q^{41} +(0.636945 + 1.10322i) q^{42} +(2.31140 - 4.00346i) q^{43} +0.131609 q^{44} +(-0.551656 + 0.955496i) q^{45} +(0.0477811 - 0.0827593i) q^{46} +4.70769 q^{47} +(-1.55166 + 2.68755i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.40937 - 4.17316i) q^{50} -0.726109 q^{51} +(-0.967829 + 0.955496i) q^{52} +5.54778 q^{53} +(-0.636945 - 1.10322i) q^{54} +(0.192476 + 0.333379i) q^{55} +(1.51415 - 2.62258i) q^{56} -2.30219 q^{57} +(0.306062 - 0.530115i) q^{58} +(1.96249 - 3.39914i) q^{59} +0.416173 q^{60} +(-2.77389 + 4.80452i) q^{61} +(-4.36799 - 7.56558i) q^{62} +(0.500000 + 0.866025i) q^{63} +8.88601 q^{64} +(-3.83582 - 1.05421i) q^{65} -0.444469 q^{66} +(-4.06193 - 7.03547i) q^{67} +(0.136945 + 0.237196i) q^{68} +(0.0375080 - 0.0649658i) q^{69} +1.40550 q^{70} +(4.76468 - 8.25267i) q^{71} +(-1.51415 + 2.62258i) q^{72} -10.4338 q^{73} +(-0.702750 + 1.21720i) q^{74} +(-1.89135 - 3.27592i) q^{75} +(0.434196 + 0.752049i) q^{76} +0.348907 q^{77} +(3.26855 - 3.22691i) q^{78} +17.1054 q^{79} +(1.71196 + 2.96520i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.97170 - 3.41509i) q^{82} -11.9143 q^{83} +(0.188601 - 0.326667i) q^{84} +(-0.400563 + 0.693795i) q^{85} +5.88894 q^{86} +(0.240258 - 0.416138i) q^{87} +(0.528296 + 0.915036i) q^{88} +(5.98052 + 10.3586i) q^{89} -1.40550 q^{90} +(-2.56580 + 2.53311i) q^{91} -0.0282963 q^{92} +(-3.42886 - 5.93896i) q^{93} +(2.99854 + 5.19362i) q^{94} +(-1.27002 + 2.19973i) q^{95} +2.10331 q^{96} +(-5.05166 + 8.74973i) q^{97} +(0.636945 - 1.10322i) q^{98} -0.348907 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10})$$ 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 $$6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} - 13 q^{10} + 8 q^{11} - 8 q^{12} + 4 q^{14} + 6 q^{16} - 4 q^{17} - 4 q^{18} + 7 q^{19} + 13 q^{20} + 6 q^{21} - q^{22} - 9 q^{23} - 3 q^{24} + 22 q^{25} - 26 q^{26} - 6 q^{27} + 4 q^{28} + 7 q^{29} + 13 q^{30} - 14 q^{31} + 3 q^{32} - 8 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{38} + 26 q^{40} - 2 q^{41} + 2 q^{42} + 19 q^{43} - 30 q^{44} - 7 q^{46} - 34 q^{47} - 6 q^{48} - 3 q^{49} + 16 q^{50} - 8 q^{51} - 26 q^{52} + 26 q^{53} - 2 q^{54} - 3 q^{56} + 14 q^{57} - 22 q^{58} + 3 q^{59} + 26 q^{60} - 13 q^{61} + 17 q^{62} + 3 q^{63} + 2 q^{64} - 2 q^{66} - 5 q^{67} - q^{68} + 9 q^{69} - 26 q^{70} - 8 q^{71} + 3 q^{72} - 4 q^{73} + 13 q^{74} + 11 q^{75} + 18 q^{76} + 16 q^{77} - 13 q^{78} - 2 q^{79} + 26 q^{80} - 3 q^{81} + 36 q^{82} + 4 q^{83} - 4 q^{84} - 13 q^{85} + 34 q^{86} - 7 q^{87} - 21 q^{88} + 19 q^{89} + 26 q^{90} + 24 q^{92} - 7 q^{93} - 7 q^{94} + 6 q^{96} - 27 q^{97} + 2 q^{98} - 16 q^{99}+O(q^{100})$$ 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 - 13 * q^10 + 8 * q^11 - 8 * q^12 + 4 * q^14 + 6 * q^16 - 4 * q^17 - 4 * q^18 + 7 * q^19 + 13 * q^20 + 6 * q^21 - q^22 - 9 * q^23 - 3 * q^24 + 22 * q^25 - 26 * q^26 - 6 * q^27 + 4 * q^28 + 7 * q^29 + 13 * q^30 - 14 * q^31 + 3 * q^32 - 8 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^38 + 26 * q^40 - 2 * q^41 + 2 * q^42 + 19 * q^43 - 30 * q^44 - 7 * q^46 - 34 * q^47 - 6 * q^48 - 3 * q^49 + 16 * q^50 - 8 * q^51 - 26 * q^52 + 26 * q^53 - 2 * q^54 - 3 * q^56 + 14 * q^57 - 22 * q^58 + 3 * q^59 + 26 * q^60 - 13 * q^61 + 17 * q^62 + 3 * q^63 + 2 * q^64 - 2 * q^66 - 5 * q^67 - q^68 + 9 * q^69 - 26 * q^70 - 8 * q^71 + 3 * q^72 - 4 * q^73 + 13 * q^74 + 11 * q^75 + 18 * q^76 + 16 * q^77 - 13 * q^78 - 2 * q^79 + 26 * q^80 - 3 * q^81 + 36 * q^82 + 4 * q^83 - 4 * q^84 - 13 * q^85 + 34 * q^86 - 7 * q^87 - 21 * q^88 + 19 * q^89 + 26 * q^90 + 24 * q^92 - 7 * q^93 - 7 * q^94 + 6 * q^96 - 27 * q^97 + 2 * q^98 - 16 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$$.

 $$n$$ $$92$$ $$106$$ $$157$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.636945 + 1.10322i 0.450388 + 0.780095i 0.998410 0.0563687i $$-0.0179522\pi$$
−0.548022 + 0.836464i $$0.684619\pi$$
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i
$$4$$ 0.188601 0.326667i 0.0943007 0.163334i
$$5$$ 1.10331 0.493416 0.246708 0.969090i $$-0.420651\pi$$
0.246708 + 0.969090i $$0.420651\pi$$
$$6$$ −0.636945 + 1.10322i −0.260032 + 0.450388i
$$7$$ 0.500000 0.866025i 0.188982 0.327327i
$$8$$ 3.02830 1.07066
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0.702750 + 1.21720i 0.222229 + 0.384912i
$$11$$ 0.174453 + 0.302162i 0.0525996 + 0.0911053i 0.891126 0.453755i $$-0.149916\pi$$
−0.838527 + 0.544860i $$0.816583\pi$$
$$12$$ 0.377203 0.108889
$$13$$ −3.47664 0.955496i −0.964246 0.265007i
$$14$$ 1.27389 0.340462
$$15$$ 0.551656 + 0.955496i 0.142437 + 0.246708i
$$16$$ 1.55166 + 2.68755i 0.387914 + 0.671887i
$$17$$ −0.363055 + 0.628829i −0.0880537 + 0.152513i −0.906688 0.421801i $$-0.861398\pi$$
0.818635 + 0.574315i $$0.194731\pi$$
$$18$$ −1.27389 −0.300259
$$19$$ −1.15109 + 1.99375i −0.264079 + 0.457398i −0.967322 0.253551i $$-0.918401\pi$$
0.703243 + 0.710950i $$0.251735\pi$$
$$20$$ 0.208086 0.360416i 0.0465295 0.0805915i
$$21$$ 1.00000 0.218218
$$22$$ −0.222234 + 0.384921i −0.0473805 + 0.0820655i
$$23$$ −0.0375080 0.0649658i −0.00782096 0.0135463i 0.862088 0.506758i $$-0.169156\pi$$
−0.869909 + 0.493212i $$0.835823\pi$$
$$24$$ 1.51415 + 2.62258i 0.309074 + 0.535332i
$$25$$ −3.78270 −0.756540
$$26$$ −1.16031 4.44410i −0.227555 0.871560i
$$27$$ −1.00000 −0.192450
$$28$$ −0.188601 0.326667i −0.0356423 0.0617343i
$$29$$ −0.240258 0.416138i −0.0446147 0.0772749i 0.842856 0.538140i $$-0.180873\pi$$
−0.887470 + 0.460865i $$0.847539\pi$$
$$30$$ −0.702750 + 1.21720i −0.128304 + 0.222229i
$$31$$ −6.85772 −1.23168 −0.615841 0.787870i $$-0.711184\pi$$
−0.615841 + 0.787870i $$0.711184\pi$$
$$32$$ 1.05166 1.82152i 0.185908 0.322003i
$$33$$ −0.174453 + 0.302162i −0.0303684 + 0.0525996i
$$34$$ −0.924984 −0.158633
$$35$$ 0.551656 0.955496i 0.0932469 0.161508i
$$36$$ 0.188601 + 0.326667i 0.0314336 + 0.0544445i
$$37$$ 0.551656 + 0.955496i 0.0906917 + 0.157083i 0.907802 0.419398i $$-0.137759\pi$$
−0.817111 + 0.576481i $$0.804426\pi$$
$$38$$ −2.93273 −0.475752
$$39$$ −0.910836 3.48861i −0.145850 0.558624i
$$40$$ 3.34116 0.528283
$$41$$ −1.54778 2.68084i −0.241723 0.418676i 0.719482 0.694511i $$-0.244379\pi$$
−0.961205 + 0.275835i $$0.911046\pi$$
$$42$$ 0.636945 + 1.10322i 0.0982828 + 0.170231i
$$43$$ 2.31140 4.00346i 0.352485 0.610522i −0.634199 0.773170i $$-0.718670\pi$$
0.986684 + 0.162648i $$0.0520034\pi$$
$$44$$ 0.131609 0.0198407
$$45$$ −0.551656 + 0.955496i −0.0822360 + 0.142437i
$$46$$ 0.0477811 0.0827593i 0.00704494 0.0122022i
$$47$$ 4.70769 0.686687 0.343343 0.939210i $$-0.388441\pi$$
0.343343 + 0.939210i $$0.388441\pi$$
$$48$$ −1.55166 + 2.68755i −0.223962 + 0.387914i
$$49$$ −0.500000 0.866025i −0.0714286 0.123718i
$$50$$ −2.40937 4.17316i −0.340737 0.590174i
$$51$$ −0.726109 −0.101676
$$52$$ −0.967829 + 0.955496i −0.134214 + 0.132504i
$$53$$ 5.54778 0.762046 0.381023 0.924565i $$-0.375572\pi$$
0.381023 + 0.924565i $$0.375572\pi$$
$$54$$ −0.636945 1.10322i −0.0866773 0.150129i
$$55$$ 0.192476 + 0.333379i 0.0259535 + 0.0449528i
$$56$$ 1.51415 2.62258i 0.202337 0.350457i
$$57$$ −2.30219 −0.304932
$$58$$ 0.306062 0.530115i 0.0401879 0.0696075i
$$59$$ 1.96249 3.39914i 0.255495 0.442530i −0.709535 0.704670i $$-0.751095\pi$$
0.965030 + 0.262140i $$0.0844283\pi$$
$$60$$ 0.416173 0.0537276
$$61$$ −2.77389 + 4.80452i −0.355160 + 0.615156i −0.987145 0.159825i $$-0.948907\pi$$
0.631985 + 0.774981i $$0.282240\pi$$
$$62$$ −4.36799 7.56558i −0.554735 0.960830i
$$63$$ 0.500000 + 0.866025i 0.0629941 + 0.109109i
$$64$$ 8.88601 1.11075
$$65$$ −3.83582 1.05421i −0.475775 0.130759i
$$66$$ −0.444469 −0.0547103
$$67$$ −4.06193 7.03547i −0.496244 0.859519i 0.503747 0.863851i $$-0.331954\pi$$
−0.999991 + 0.00433206i $$0.998621\pi$$
$$68$$ 0.136945 + 0.237196i 0.0166071 + 0.0287643i
$$69$$ 0.0375080 0.0649658i 0.00451543 0.00782096i
$$70$$ 1.40550 0.167989
$$71$$ 4.76468 8.25267i 0.565463 0.979411i −0.431543 0.902092i $$-0.642031\pi$$
0.997006 0.0773189i $$-0.0246360\pi$$
$$72$$ −1.51415 + 2.62258i −0.178444 + 0.309074i
$$73$$ −10.4338 −1.22118 −0.610592 0.791946i $$-0.709068\pi$$
−0.610592 + 0.791946i $$0.709068\pi$$
$$74$$ −0.702750 + 1.21720i −0.0816930 + 0.141496i
$$75$$ −1.89135 3.27592i −0.218394 0.378270i
$$76$$ 0.434196 + 0.752049i 0.0498057 + 0.0862659i
$$77$$ 0.348907 0.0397616
$$78$$ 3.26855 3.22691i 0.370091 0.365375i
$$79$$ 17.1054 1.92451 0.962256 0.272146i $$-0.0877335\pi$$
0.962256 + 0.272146i $$0.0877335\pi$$
$$80$$ 1.71196 + 2.96520i 0.191403 + 0.331520i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 1.97170 3.41509i 0.217738 0.377134i
$$83$$ −11.9143 −1.30777 −0.653883 0.756596i $$-0.726861\pi$$
−0.653883 + 0.756596i $$0.726861\pi$$
$$84$$ 0.188601 0.326667i 0.0205781 0.0356423i
$$85$$ −0.400563 + 0.693795i −0.0434471 + 0.0752526i
$$86$$ 5.88894 0.635020
$$87$$ 0.240258 0.416138i 0.0257583 0.0446147i
$$88$$ 0.528296 + 0.915036i 0.0563166 + 0.0975432i
$$89$$ 5.98052 + 10.3586i 0.633933 + 1.09800i 0.986740 + 0.162309i $$0.0518940\pi$$
−0.352807 + 0.935696i $$0.614773\pi$$
$$90$$ −1.40550 −0.148153
$$91$$ −2.56580 + 2.53311i −0.268969 + 0.265542i
$$92$$ −0.0282963 −0.00295009
$$93$$ −3.42886 5.93896i −0.355556 0.615841i
$$94$$ 2.99854 + 5.19362i 0.309276 + 0.535681i
$$95$$ −1.27002 + 2.19973i −0.130301 + 0.225688i
$$96$$ 2.10331 0.214668
$$97$$ −5.05166 + 8.74973i −0.512918 + 0.888400i 0.486970 + 0.873419i $$0.338102\pi$$
−0.999888 + 0.0149812i $$0.995231\pi$$
$$98$$ 0.636945 1.10322i 0.0643412 0.111442i
$$99$$ −0.348907 −0.0350664
$$100$$ −0.713423 + 1.23568i −0.0713423 + 0.123568i
$$101$$ −2.03751 3.52907i −0.202740 0.351155i 0.746671 0.665194i $$-0.231651\pi$$
−0.949410 + 0.314039i $$0.898318\pi$$
$$102$$ −0.462492 0.801060i −0.0457935 0.0793167i
$$103$$ −4.11106 −0.405075 −0.202538 0.979275i $$-0.564919\pi$$
−0.202538 + 0.979275i $$0.564919\pi$$
$$104$$ −10.5283 2.89353i −1.03238 0.283734i
$$105$$ 1.10331 0.107672
$$106$$ 3.53363 + 6.12043i 0.343217 + 0.594469i
$$107$$ 3.08529 + 5.34388i 0.298266 + 0.516612i 0.975739 0.218935i $$-0.0702584\pi$$
−0.677473 + 0.735547i $$0.736925\pi$$
$$108$$ −0.188601 + 0.326667i −0.0181482 + 0.0314336i
$$109$$ −8.82167 −0.844963 −0.422481 0.906372i $$-0.638841\pi$$
−0.422481 + 0.906372i $$0.638841\pi$$
$$110$$ −0.245194 + 0.424688i −0.0233783 + 0.0404924i
$$111$$ −0.551656 + 0.955496i −0.0523609 + 0.0906917i
$$112$$ 3.10331 0.293235
$$113$$ −6.00494 + 10.4009i −0.564897 + 0.978430i 0.432162 + 0.901796i $$0.357751\pi$$
−0.997059 + 0.0766343i $$0.975583\pi$$
$$114$$ −1.46637 2.53982i −0.137338 0.237876i
$$115$$ −0.0413831 0.0716776i −0.00385899 0.00668397i
$$116$$ −0.181252 −0.0168288
$$117$$ 2.56580 2.53311i 0.237209 0.234186i
$$118$$ 5.00000 0.460287
$$119$$ 0.363055 + 0.628829i 0.0332812 + 0.0576447i
$$120$$ 1.67058 + 2.89353i 0.152502 + 0.264142i
$$121$$ 5.43913 9.42085i 0.494467 0.856441i
$$122$$ −7.06727 −0.639840
$$123$$ 1.54778 2.68084i 0.139559 0.241723i
$$124$$ −1.29338 + 2.24019i −0.116149 + 0.201175i
$$125$$ −9.69006 −0.866706
$$126$$ −0.636945 + 1.10322i −0.0567436 + 0.0982828i
$$127$$ 2.92886 + 5.07293i 0.259894 + 0.450150i 0.966213 0.257744i $$-0.0829790\pi$$
−0.706319 + 0.707894i $$0.749646\pi$$
$$128$$ 3.55659 + 6.16020i 0.314361 + 0.544490i
$$129$$ 4.62280 0.407015
$$130$$ −1.28018 4.90323i −0.112279 0.430042i
$$131$$ 22.4055 1.95758 0.978789 0.204872i $$-0.0656778\pi$$
0.978789 + 0.204872i $$0.0656778\pi$$
$$132$$ 0.0658043 + 0.113976i 0.00572753 + 0.00992037i
$$133$$ 1.15109 + 1.99375i 0.0998125 + 0.172880i
$$134$$ 5.17445 8.96242i 0.447005 0.774235i
$$135$$ −1.10331 −0.0949580
$$136$$ −1.09944 + 1.90428i −0.0942760 + 0.163291i
$$137$$ −10.1044 + 17.5013i −0.863275 + 1.49524i 0.00547505 + 0.999985i $$0.498257\pi$$
−0.868750 + 0.495251i $$0.835076\pi$$
$$138$$ 0.0955622 0.00813480
$$139$$ −2.13695 + 3.70130i −0.181253 + 0.313940i −0.942308 0.334748i $$-0.891349\pi$$
0.761054 + 0.648688i $$0.224682\pi$$
$$140$$ −0.208086 0.360416i −0.0175865 0.0304607i
$$141$$ 2.35384 + 4.07698i 0.198229 + 0.343343i
$$142$$ 12.1394 1.01871
$$143$$ −0.317797 1.21720i −0.0265755 0.101787i
$$144$$ −3.10331 −0.258609
$$145$$ −0.265079 0.459131i −0.0220136 0.0381287i
$$146$$ −6.64576 11.5108i −0.550007 0.952640i
$$147$$ 0.500000 0.866025i 0.0412393 0.0714286i
$$148$$ 0.416173 0.0342092
$$149$$ 2.44834 4.24066i 0.200576 0.347408i −0.748138 0.663543i $$-0.769052\pi$$
0.948714 + 0.316135i $$0.102385\pi$$
$$150$$ 2.40937 4.17316i 0.196725 0.340737i
$$151$$ −8.94553 −0.727977 −0.363988 0.931403i $$-0.618585\pi$$
−0.363988 + 0.931403i $$0.618585\pi$$
$$152$$ −3.48585 + 6.03767i −0.282740 + 0.489720i
$$153$$ −0.363055 0.628829i −0.0293512 0.0508378i
$$154$$ 0.222234 + 0.384921i 0.0179082 + 0.0310178i
$$155$$ −7.56620 −0.607732
$$156$$ −1.31140 0.360416i −0.104996 0.0288564i
$$157$$ 6.59450 0.526298 0.263149 0.964755i $$-0.415239\pi$$
0.263149 + 0.964755i $$0.415239\pi$$
$$158$$ 10.8952 + 18.8711i 0.866778 + 1.50130i
$$159$$ 2.77389 + 4.80452i 0.219984 + 0.381023i
$$160$$ 1.16031 2.00971i 0.0917302 0.158881i
$$161$$ −0.0750160 −0.00591209
$$162$$ 0.636945 1.10322i 0.0500431 0.0866773i
$$163$$ 4.95222 8.57749i 0.387888 0.671841i −0.604277 0.796774i $$-0.706538\pi$$
0.992165 + 0.124933i $$0.0398715\pi$$
$$164$$ −1.16765 −0.0911785
$$165$$ −0.192476 + 0.333379i −0.0149843 + 0.0259535i
$$166$$ −7.58876 13.1441i −0.589002 1.02018i
$$167$$ 8.37826 + 14.5116i 0.648330 + 1.12294i 0.983522 + 0.180790i $$0.0578654\pi$$
−0.335192 + 0.942150i $$0.608801\pi$$
$$168$$ 3.02830 0.233638
$$169$$ 11.1741 + 6.64383i 0.859543 + 0.511064i
$$170$$ −1.02055 −0.0782723
$$171$$ −1.15109 1.99375i −0.0880263 0.152466i
$$172$$ −0.871866 1.51012i −0.0664792 0.115145i
$$173$$ −6.85918 + 11.8804i −0.521494 + 0.903254i 0.478194 + 0.878254i $$0.341292\pi$$
−0.999687 + 0.0249993i $$0.992042\pi$$
$$174$$ 0.612124 0.0464050
$$175$$ −1.89135 + 3.27592i −0.142973 + 0.247636i
$$176$$ −0.541383 + 0.937703i −0.0408083 + 0.0706820i
$$177$$ 3.92498 0.295020
$$178$$ −7.61852 + 13.1957i −0.571032 + 0.989057i
$$179$$ 11.0152 + 19.0789i 0.823315 + 1.42602i 0.903200 + 0.429220i $$0.141211\pi$$
−0.0798846 + 0.996804i $$0.525455\pi$$
$$180$$ 0.208086 + 0.360416i 0.0155098 + 0.0268638i
$$181$$ 9.43380 0.701208 0.350604 0.936524i $$-0.385976\pi$$
0.350604 + 0.936524i $$0.385976\pi$$
$$182$$ −4.42886 1.21720i −0.328289 0.0902247i
$$183$$ −5.54778 −0.410104
$$184$$ −0.113585 0.196736i −0.00837363 0.0145035i
$$185$$ 0.608649 + 1.05421i 0.0447488 + 0.0775071i
$$186$$ 4.36799 7.56558i 0.320277 0.554735i
$$187$$ −0.253344 −0.0185264
$$188$$ 0.887876 1.53785i 0.0647550 0.112159i
$$189$$ −0.500000 + 0.866025i −0.0363696 + 0.0629941i
$$190$$ −3.23572 −0.234744
$$191$$ 1.68860 2.92474i 0.122183 0.211627i −0.798445 0.602067i $$-0.794344\pi$$
0.920628 + 0.390440i $$0.127677\pi$$
$$192$$ 4.44301 + 7.69551i 0.320646 + 0.555376i
$$193$$ −11.1614 19.3321i −0.803413 1.39155i −0.917357 0.398065i $$-0.869682\pi$$
0.113945 0.993487i $$-0.463651\pi$$
$$194$$ −12.8705 −0.924049
$$195$$ −1.00494 3.84902i −0.0719650 0.275634i
$$196$$ −0.377203 −0.0269431
$$197$$ 12.7257 + 22.0416i 0.906669 + 1.57040i 0.818661 + 0.574277i $$0.194717\pi$$
0.0880085 + 0.996120i $$0.471950\pi$$
$$198$$ −0.222234 0.384921i −0.0157935 0.0273552i
$$199$$ 11.1702 19.3473i 0.791833 1.37149i −0.132998 0.991116i $$-0.542460\pi$$
0.924831 0.380379i $$-0.124206\pi$$
$$200$$ −11.4551 −0.810001
$$201$$ 4.06193 7.03547i 0.286506 0.496244i
$$202$$ 2.59556 4.49565i 0.182623 0.316313i
$$203$$ −0.480515 −0.0337256
$$204$$ −0.136945 + 0.237196i −0.00958809 + 0.0166071i
$$205$$ −1.70769 2.95780i −0.119270 0.206582i
$$206$$ −2.61852 4.53541i −0.182441 0.315997i
$$207$$ 0.0750160 0.00521397
$$208$$ −2.82661 10.8262i −0.195990 0.750664i
$$209$$ −0.803248 −0.0555618
$$210$$ 0.702750 + 1.21720i 0.0484943 + 0.0839946i
$$211$$ −5.01908 8.69331i −0.345528 0.598472i 0.639922 0.768440i $$-0.278967\pi$$
−0.985450 + 0.169968i $$0.945634\pi$$
$$212$$ 1.04632 1.81228i 0.0718615 0.124468i
$$213$$ 9.52936 0.652941
$$214$$ −3.93032 + 6.80752i −0.268671 + 0.465352i
$$215$$ 2.55019 4.41707i 0.173922 0.301241i
$$216$$ −3.02830 −0.206049
$$217$$ −3.42886 + 5.93896i −0.232766 + 0.403163i
$$218$$ −5.61892 9.73226i −0.380561 0.659152i
$$219$$ −5.21690 9.03593i −0.352525 0.610592i
$$220$$ 0.145205 0.00978974
$$221$$ 1.86305 1.83932i 0.125323 0.123726i
$$222$$ −1.40550 −0.0943309
$$223$$ 2.56727 + 4.44664i 0.171917 + 0.297769i 0.939090 0.343671i $$-0.111671\pi$$
−0.767173 + 0.641440i $$0.778337\pi$$
$$224$$ −1.05166 1.82152i −0.0702667 0.121706i
$$225$$ 1.89135 3.27592i 0.126090 0.218394i
$$226$$ −15.2993 −1.01769
$$227$$ 14.4855 25.0895i 0.961433 1.66525i 0.242526 0.970145i $$-0.422024\pi$$
0.718907 0.695106i $$-0.244643\pi$$
$$228$$ −0.434196 + 0.752049i −0.0287553 + 0.0498057i
$$229$$ 0.679390 0.0448953 0.0224477 0.999748i $$-0.492854\pi$$
0.0224477 + 0.999748i $$0.492854\pi$$
$$230$$ 0.0527175 0.0913094i 0.00347609 0.00602076i
$$231$$ 0.174453 + 0.302162i 0.0114782 + 0.0198808i
$$232$$ −0.727571 1.26019i −0.0477674 0.0827355i
$$233$$ −18.3022 −1.19902 −0.599508 0.800369i $$-0.704637\pi$$
−0.599508 + 0.800369i $$0.704637\pi$$
$$234$$ 4.42886 + 1.21720i 0.289524 + 0.0795707i
$$235$$ 5.19405 0.338822
$$236$$ −0.740258 1.28216i −0.0481867 0.0834618i
$$237$$ 8.55272 + 14.8137i 0.555559 + 0.962256i
$$238$$ −0.462492 + 0.801060i −0.0299789 + 0.0519250i
$$239$$ −5.45222 −0.352675 −0.176337 0.984330i $$-0.556425\pi$$
−0.176337 + 0.984330i $$0.556425\pi$$
$$240$$ −1.71196 + 2.96520i −0.110507 + 0.191403i
$$241$$ 7.73105 13.3906i 0.498000 0.862562i −0.501997 0.864869i $$-0.667401\pi$$
0.999997 + 0.00230736i $$0.000734455\pi$$
$$242$$ 13.8577 0.890808
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ 1.04632 + 1.81228i 0.0669837 + 0.116019i
$$245$$ −0.551656 0.955496i −0.0352440 0.0610444i
$$246$$ 3.94341 0.251422
$$247$$ 5.90696 5.83169i 0.375851 0.371062i
$$248$$ −20.7672 −1.31872
$$249$$ −5.95716 10.3181i −0.377519 0.653883i
$$250$$ −6.17204 10.6903i −0.390354 0.676113i
$$251$$ 4.14722 7.18319i 0.261770 0.453399i −0.704942 0.709265i $$-0.749027\pi$$
0.966712 + 0.255866i $$0.0823604\pi$$
$$252$$ 0.377203 0.0237615
$$253$$ 0.0130868 0.0226670i 0.000822760 0.00142506i
$$254$$ −3.73105 + 6.46236i −0.234107 + 0.405485i
$$255$$ −0.801125 −0.0501684
$$256$$ 4.35530 7.54361i 0.272207 0.471476i
$$257$$ 7.51908 + 13.0234i 0.469028 + 0.812380i 0.999373 0.0354019i $$-0.0112711\pi$$
−0.530346 + 0.847782i $$0.677938\pi$$
$$258$$ 2.94447 + 5.09997i 0.183315 + 0.317510i
$$259$$ 1.10331 0.0685565
$$260$$ −1.06782 + 1.05421i −0.0662232 + 0.0653794i
$$261$$ 0.480515 0.0297431
$$262$$ 14.2711 + 24.7182i 0.881670 + 1.52710i
$$263$$ 8.62240 + 14.9344i 0.531680 + 0.920896i 0.999316 + 0.0369754i $$0.0117723\pi$$
−0.467636 + 0.883921i $$0.654894\pi$$
$$264$$ −0.528296 + 0.915036i −0.0325144 + 0.0563166i
$$265$$ 6.12094 0.376006
$$266$$ −1.46637 + 2.53982i −0.0899087 + 0.155726i
$$267$$ −5.98052 + 10.3586i −0.366002 + 0.633933i
$$268$$ −3.06434 −0.187185
$$269$$ 12.1472 21.0396i 0.740629 1.28281i −0.211580 0.977361i $$-0.567861\pi$$
0.952209 0.305446i $$-0.0988057\pi$$
$$270$$ −0.702750 1.21720i −0.0427680 0.0740763i
$$271$$ −9.16630 15.8765i −0.556813 0.964429i −0.997760 0.0668956i $$-0.978691\pi$$
0.440947 0.897533i $$-0.354643\pi$$
$$272$$ −2.25334 −0.136629
$$273$$ −3.47664 0.955496i −0.210416 0.0578293i
$$274$$ −25.7437 −1.55524
$$275$$ −0.659905 1.14299i −0.0397938 0.0689248i
$$276$$ −0.0141481 0.0245053i −0.000851617 0.00147504i
$$277$$ −4.22717 + 7.32167i −0.253986 + 0.439917i −0.964620 0.263646i $$-0.915075\pi$$
0.710634 + 0.703562i $$0.248408\pi$$
$$278$$ −5.44447 −0.326538
$$279$$ 3.42886 5.93896i 0.205280 0.355556i
$$280$$ 1.67058 2.89353i 0.0998361 0.172921i
$$281$$ −25.0120 −1.49209 −0.746045 0.665895i $$-0.768050\pi$$
−0.746045 + 0.665895i $$0.768050\pi$$
$$282$$ −2.99854 + 5.19362i −0.178560 + 0.309276i
$$283$$ −13.5707 23.5052i −0.806697 1.39724i −0.915140 0.403137i $$-0.867920\pi$$
0.108443 0.994103i $$-0.465414\pi$$
$$284$$ −1.79725 3.11293i −0.106647 0.184718i
$$285$$ −2.54003 −0.150458
$$286$$ 1.14042 1.12589i 0.0674344 0.0665752i
$$287$$ −3.09556 −0.182725
$$288$$ 1.05166 + 1.82152i 0.0619694 + 0.107334i
$$289$$ 8.23638 + 14.2658i 0.484493 + 0.839167i
$$290$$ 0.337682 0.584882i 0.0198294 0.0343455i
$$291$$ −10.1033 −0.592267
$$292$$ −1.96783 + 3.40838i −0.115158 + 0.199460i
$$293$$ 5.27002 9.12793i 0.307878 0.533260i −0.670020 0.742343i $$-0.733715\pi$$
0.977898 + 0.209083i $$0.0670479\pi$$
$$294$$ 1.27389 0.0742948
$$295$$ 2.16524 3.75031i 0.126065 0.218351i
$$296$$ 1.67058 + 2.89353i 0.0971004 + 0.168183i
$$297$$ −0.174453 0.302162i −0.0101228 0.0175332i
$$298$$ 6.23784 0.361349
$$299$$ 0.0683273 + 0.261701i 0.00395147 + 0.0151346i
$$300$$ −1.42685 −0.0823790
$$301$$ −2.31140 4.00346i −0.133227 0.230756i
$$302$$ −5.69781 9.86890i −0.327872 0.567891i
$$303$$ 2.03751 3.52907i 0.117052 0.202740i
$$304$$ −7.14440 −0.409760
$$305$$ −3.06047 + 5.30089i −0.175242 + 0.303528i
$$306$$ 0.462492 0.801060i 0.0264389 0.0457935i
$$307$$ −4.40842 −0.251602 −0.125801 0.992055i $$-0.540150\pi$$
−0.125801 + 0.992055i $$0.540150\pi$$
$$308$$ 0.0658043 0.113976i 0.00374955 0.00649441i
$$309$$ −2.05553 3.56028i −0.116935 0.202538i
$$310$$ −4.81926 8.34720i −0.273715 0.474089i
$$311$$ −2.32836 −0.132029 −0.0660146 0.997819i $$-0.521028\pi$$
−0.0660146 + 0.997819i $$0.521028\pi$$
$$312$$ −2.75828 10.5645i −0.156157 0.598099i
$$313$$ 12.6687 0.716078 0.358039 0.933707i $$-0.383445\pi$$
0.358039 + 0.933707i $$0.383445\pi$$
$$314$$ 4.20034 + 7.27520i 0.237039 + 0.410563i
$$315$$ 0.551656 + 0.955496i 0.0310823 + 0.0538361i
$$316$$ 3.22611 5.58779i 0.181483 0.314337i
$$317$$ −12.2915 −0.690360 −0.345180 0.938536i $$-0.612182\pi$$
−0.345180 + 0.938536i $$0.612182\pi$$
$$318$$ −3.53363 + 6.12043i −0.198156 + 0.343217i
$$319$$ 0.0838275 0.145193i 0.00469344 0.00812927i
$$320$$ 9.80405 0.548063
$$321$$ −3.08529 + 5.34388i −0.172204 + 0.298266i
$$322$$ −0.0477811 0.0827593i −0.00266274 0.00461200i
$$323$$ −0.835820 1.44768i −0.0465063 0.0805512i
$$324$$ −0.377203 −0.0209557
$$325$$ 13.1511 + 3.61436i 0.729491 + 0.200489i
$$326$$ 12.6172 0.698800
$$327$$ −4.41084 7.63979i −0.243920 0.422481i
$$328$$ −4.68714 8.11836i −0.258804 0.448262i
$$329$$ 2.35384 4.07698i 0.129772 0.224771i
$$330$$ −0.490388 −0.0269950
$$331$$ −6.64576 + 11.5108i −0.365284 + 0.632690i −0.988822 0.149103i $$-0.952361\pi$$
0.623538 + 0.781793i $$0.285695\pi$$
$$332$$ −2.24706 + 3.89202i −0.123323 + 0.213602i
$$333$$ −1.10331 −0.0604611
$$334$$ −10.6730 + 18.4862i −0.584000 + 1.01152i
$$335$$ −4.48158 7.76232i −0.244855 0.424101i
$$336$$ 1.55166 + 2.68755i 0.0846498 + 0.146618i
$$337$$ −3.40550 −0.185509 −0.0927547 0.995689i $$-0.529567\pi$$
−0.0927547 + 0.995689i $$0.529567\pi$$
$$338$$ −0.212362 + 16.5592i −0.0115510 + 0.900703i
$$339$$ −12.0099 −0.652287
$$340$$ 0.151093 + 0.261701i 0.00819419 + 0.0141928i
$$341$$ −1.19635 2.07214i −0.0647861 0.112213i
$$342$$ 1.46637 2.53982i 0.0792920 0.137338i
$$343$$ −1.00000 −0.0539949
$$344$$ 6.99960 12.1237i 0.377393 0.653664i
$$345$$ 0.0413831 0.0716776i 0.00222799 0.00385899i
$$346$$ −17.4757 −0.939499
$$347$$ 16.7491 29.0102i 0.899137 1.55735i 0.0705378 0.997509i $$-0.477528\pi$$
0.828599 0.559842i $$-0.189138\pi$$
$$348$$ −0.0906258 0.156969i −0.00485806 0.00841440i
$$349$$ 14.0902 + 24.4050i 0.754232 + 1.30637i 0.945755 + 0.324881i $$0.105324\pi$$
−0.191523 + 0.981488i $$0.561342\pi$$
$$350$$ −4.81875 −0.257573
$$351$$ 3.47664 + 0.955496i 0.185569 + 0.0510006i
$$352$$ 0.733860 0.0391148
$$353$$ 1.49612 + 2.59136i 0.0796307 + 0.137924i 0.903091 0.429450i $$-0.141293\pi$$
−0.823460 + 0.567374i $$0.807959\pi$$
$$354$$ 2.50000 + 4.33013i 0.132874 + 0.230144i
$$355$$ 5.25693 9.10527i 0.279009 0.483257i
$$356$$ 4.51173 0.239121
$$357$$ −0.363055 + 0.628829i −0.0192149 + 0.0332812i
$$358$$ −14.0322 + 24.3044i −0.741623 + 1.28453i
$$359$$ 3.80888 0.201025 0.100512 0.994936i $$-0.467952\pi$$
0.100512 + 0.994936i $$0.467952\pi$$
$$360$$ −1.67058 + 2.89353i −0.0880472 + 0.152502i
$$361$$ 6.84997 + 11.8645i 0.360525 + 0.624447i
$$362$$ 6.00881 + 10.4076i 0.315816 + 0.547010i
$$363$$ 10.8783 0.570961
$$364$$ 0.343570 + 1.31591i 0.0180080 + 0.0689726i
$$365$$ −11.5117 −0.602552
$$366$$ −3.53363 6.12043i −0.184706 0.319920i
$$367$$ 13.2257 + 22.9076i 0.690376 + 1.19577i 0.971715 + 0.236158i $$0.0758884\pi$$
−0.281338 + 0.959609i $$0.590778\pi$$
$$368$$ 0.116399 0.201609i 0.00606772 0.0105096i
$$369$$ 3.09556 0.161149
$$370$$ −0.775352 + 1.34295i −0.0403086 + 0.0698166i
$$371$$ 2.77389 4.80452i 0.144013 0.249438i
$$372$$ −2.58675 −0.134117
$$373$$ −1.06580 + 1.84603i −0.0551853 + 0.0955837i −0.892298 0.451446i $$-0.850908\pi$$
0.837113 + 0.547030i $$0.184242\pi$$
$$374$$ −0.161367 0.279495i −0.00834406 0.0144523i
$$375$$ −4.84503 8.39184i −0.250196 0.433353i
$$376$$ 14.2563 0.735211
$$377$$ 0.437670 + 1.67633i 0.0225412 + 0.0863353i
$$378$$ −1.27389 −0.0655219
$$379$$ 6.97170 + 12.0753i 0.358112 + 0.620269i 0.987645 0.156705i $$-0.0500871\pi$$
−0.629533 + 0.776974i $$0.716754\pi$$
$$380$$ 0.479053 + 0.829745i 0.0245749 + 0.0425650i
$$381$$ −2.92886 + 5.07293i −0.150050 + 0.259894i
$$382$$ 4.30219 0.220119
$$383$$ 9.30219 16.1119i 0.475320 0.823278i −0.524281 0.851545i $$-0.675666\pi$$
0.999600 + 0.0282678i $$0.00899913\pi$$
$$384$$ −3.55659 + 6.16020i −0.181497 + 0.314361i
$$385$$ 0.384953 0.0196190
$$386$$ 14.2184 24.6269i 0.723695 1.25348i
$$387$$ 2.31140 + 4.00346i 0.117495 + 0.203507i
$$388$$ 1.90550 + 3.30042i 0.0967371 + 0.167554i
$$389$$ −1.23009 −0.0623682 −0.0311841 0.999514i $$-0.509928\pi$$
−0.0311841 + 0.999514i $$0.509928\pi$$
$$390$$ 3.60624 3.56028i 0.182609 0.180282i
$$391$$ 0.0544699 0.00275466
$$392$$ −1.51415 2.62258i −0.0764760 0.132460i
$$393$$ 11.2027 + 19.4037i 0.565104 + 0.978789i
$$394$$ −16.2112 + 28.0786i −0.816706 + 1.41458i
$$395$$ 18.8726 0.949585
$$396$$ −0.0658043 + 0.113976i −0.00330679 + 0.00572753i
$$397$$ −14.8071 + 25.6467i −0.743148 + 1.28717i 0.207907 + 0.978149i $$0.433335\pi$$
−0.951055 + 0.309022i $$0.899998\pi$$
$$398$$ 28.4592 1.42653
$$399$$ −1.15109 + 1.99375i −0.0576267 + 0.0998125i
$$400$$ −5.86945 10.1662i −0.293473 0.508310i
$$401$$ −4.09023 7.08448i −0.204256 0.353782i 0.745639 0.666350i $$-0.232144\pi$$
−0.949895 + 0.312568i $$0.898811\pi$$
$$402$$ 10.3489 0.516157
$$403$$ 23.8418 + 6.55253i 1.18765 + 0.326405i
$$404$$ −1.53711 −0.0764740
$$405$$ −0.551656 0.955496i −0.0274120 0.0474790i
$$406$$ −0.306062 0.530115i −0.0151896 0.0263092i
$$407$$ −0.192476 + 0.333379i −0.00954070 + 0.0165250i
$$408$$ −2.19887 −0.108861
$$409$$ −5.03363 + 8.71851i −0.248897 + 0.431102i −0.963220 0.268714i $$-0.913401\pi$$
0.714323 + 0.699816i $$0.246735\pi$$
$$410$$ 2.17540 3.76791i 0.107436 0.186084i
$$411$$ −20.2087 −0.996824
$$412$$ −0.775352 + 1.34295i −0.0381989 + 0.0661624i
$$413$$ −1.96249 3.39914i −0.0965679 0.167261i
$$414$$ 0.0477811 + 0.0827593i 0.00234831 + 0.00406740i
$$415$$ −13.1452 −0.645273
$$416$$ −5.39669 + 5.32792i −0.264594 + 0.261223i
$$417$$ −4.27389 −0.209293
$$418$$ −0.511625 0.886161i −0.0250244 0.0433435i
$$419$$ −4.72998 8.19257i −0.231075 0.400233i 0.727050 0.686585i $$-0.240891\pi$$
−0.958125 + 0.286351i $$0.907558\pi$$
$$420$$ 0.208086 0.360416i 0.0101536 0.0175865i
$$421$$ 31.0643 1.51398 0.756992 0.653424i $$-0.226668\pi$$
0.756992 + 0.653424i $$0.226668\pi$$
$$422$$ 6.39376 11.0743i 0.311244 0.539090i
$$423$$ −2.35384 + 4.07698i −0.114448 + 0.198229i
$$424$$ 16.8003 0.815896
$$425$$ 1.37333 2.37867i 0.0666162 0.115383i
$$426$$ 6.06968 + 10.5130i 0.294077 + 0.509356i
$$427$$ 2.77389 + 4.80452i 0.134238 + 0.232507i
$$428$$ 2.32756 0.112507
$$429$$ 0.895226 0.883819i 0.0432219 0.0426712i
$$430$$ 6.49734 0.313329
$$431$$ 12.6093 + 21.8400i 0.607369 + 1.05199i 0.991672 + 0.128787i $$0.0411084\pi$$
−0.384303 + 0.923207i $$0.625558\pi$$
$$432$$ −1.55166 2.68755i −0.0746541 0.129305i
$$433$$ −1.88495 + 3.26483i −0.0905851 + 0.156898i −0.907757 0.419495i $$-0.862207\pi$$
0.817172 + 0.576393i $$0.195540\pi$$
$$434$$ −8.73598 −0.419341
$$435$$ 0.265079 0.459131i 0.0127096 0.0220136i
$$436$$ −1.66378 + 2.88175i −0.0796806 + 0.138011i
$$437$$ 0.172701 0.00826141
$$438$$ 6.64576 11.5108i 0.317547 0.550007i
$$439$$ 11.3174 + 19.6023i 0.540150 + 0.935567i 0.998895 + 0.0469991i $$0.0149658\pi$$
−0.458745 + 0.888568i $$0.651701\pi$$
$$440$$ 0.582876 + 1.00957i 0.0277875 + 0.0481294i
$$441$$ 1.00000 0.0476190
$$442$$ 3.21584 + 0.883819i 0.152962 + 0.0420390i
$$443$$ 4.64334 0.220612 0.110306 0.993898i $$-0.464817\pi$$
0.110306 + 0.993898i $$0.464817\pi$$
$$444$$ 0.208086 + 0.360416i 0.00987534 + 0.0171046i
$$445$$ 6.59838 + 11.4287i 0.312793 + 0.541773i
$$446$$ −3.27042 + 5.66453i −0.154859 + 0.268223i
$$447$$ 4.89669 0.231605
$$448$$ 4.44301 7.69551i 0.209912 0.363579i
$$449$$ −4.71156 + 8.16066i −0.222352 + 0.385125i −0.955522 0.294920i $$-0.904707\pi$$
0.733170 + 0.680046i $$0.238040\pi$$
$$450$$ 4.81875 0.227158
$$451$$ 0.540031 0.935361i 0.0254291 0.0440444i
$$452$$ 2.26508 + 3.92323i 0.106540 + 0.184533i
$$453$$ −4.47277 7.74706i −0.210149 0.363988i
$$454$$ 36.9058 1.73207
$$455$$ −2.83088 + 2.79481i −0.132714 + 0.131023i
$$456$$ −6.97170 −0.326480
$$457$$ −6.35812 11.0126i −0.297420 0.515147i 0.678125 0.734947i $$-0.262793\pi$$
−0.975545 + 0.219800i $$0.929460\pi$$
$$458$$ 0.432734 + 0.749517i 0.0202203 + 0.0350226i
$$459$$ 0.363055 0.628829i 0.0169459 0.0293512i
$$460$$ −0.0312196 −0.00145562
$$461$$ 14.8627 25.7429i 0.692223 1.19897i −0.278885 0.960324i $$-0.589965\pi$$
0.971108 0.238641i $$-0.0767018\pi$$
$$462$$ −0.222234 + 0.384921i −0.0103393 + 0.0179082i
$$463$$ −15.2838 −0.710297 −0.355148 0.934810i $$-0.615570\pi$$
−0.355148 + 0.934810i $$0.615570\pi$$
$$464$$ 0.745594 1.29141i 0.0346133 0.0599521i
$$465$$ −3.78310 6.55253i −0.175437 0.303866i
$$466$$ −11.6575 20.1914i −0.540023 0.935347i
$$467$$ −26.6503 −1.23323 −0.616614 0.787265i $$-0.711496\pi$$
−0.616614 + 0.787265i $$0.711496\pi$$
$$468$$ −0.343570 1.31591i −0.0158815 0.0608281i
$$469$$ −8.12386 −0.375125
$$470$$ 3.30832 + 5.73019i 0.152602 + 0.264314i
$$471$$ 3.29725 + 5.71101i 0.151929 + 0.263149i
$$472$$ 5.94301 10.2936i 0.273549 0.473801i
$$473$$ 1.61292 0.0741623
$$474$$ −10.8952 + 18.8711i −0.500434 + 0.866778i
$$475$$ 4.35424 7.54177i 0.199786 0.346040i
$$476$$ 0.273891 0.0125538
$$477$$ −2.77389 + 4.80452i −0.127008 + 0.219984i
$$478$$ −3.47277 6.01501i −0.158841 0.275120i
$$479$$ 11.1058 + 19.2359i 0.507439 + 0.878909i 0.999963 + 0.00861072i $$0.00274091\pi$$
−0.492524 + 0.870299i $$0.663926\pi$$
$$480$$ 2.32061 0.105921
$$481$$ −1.00494 3.84902i −0.0458212 0.175500i
$$482$$ 19.6970 0.897174
$$483$$ −0.0375080 0.0649658i −0.00170667 0.00295605i
$$484$$ −2.05166 3.55357i −0.0932571 0.161526i
$$485$$ −5.57355 + 9.65368i −0.253082 + 0.438351i
$$486$$ 1.27389 0.0577848
$$487$$ 0.485852 0.841520i 0.0220160 0.0381329i −0.854807 0.518945i $$-0.826325\pi$$
0.876824 + 0.480812i $$0.159658\pi$$
$$488$$ −8.40016 + 14.5495i −0.380257 + 0.658625i
$$489$$ 9.90444 0.447894
$$490$$ 0.702750 1.21720i 0.0317470 0.0549874i
$$491$$ −13.4674 23.3263i −0.607777 1.05270i −0.991606 0.129296i $$-0.958728\pi$$
0.383830 0.923404i $$-0.374605\pi$$
$$492$$ −0.583827 1.01122i −0.0263210 0.0455893i
$$493$$ 0.348907 0.0157140
$$494$$ 10.1961 + 2.80222i 0.458742 + 0.126078i
$$495$$ −0.384953 −0.0173023
$$496$$ −10.6408 18.4304i −0.477787 0.827551i
$$497$$ −4.76468 8.25267i −0.213725 0.370183i
$$498$$ 7.58876 13.1441i 0.340061 0.589002i
$$499$$ −21.1239 −0.945634 −0.472817 0.881161i $$-0.656763\pi$$
−0.472817 + 0.881161i $$0.656763\pi$$
$$500$$ −1.82756 + 3.16543i −0.0817310 + 0.141562i
$$501$$ −8.37826 + 14.5116i −0.374313 + 0.648330i
$$502$$ 10.5662 0.471593
$$503$$ −6.28270 + 10.8820i −0.280132 + 0.485203i −0.971417 0.237379i $$-0.923712\pi$$
0.691285 + 0.722582i $$0.257045\pi$$
$$504$$ 1.51415 + 2.62258i 0.0674455 + 0.116819i
$$505$$ −2.24801 3.89366i −0.100035 0.173266i
$$506$$ 0.0333423 0.00148225
$$507$$ −0.166703 + 12.9989i −0.00740355 + 0.577303i
$$508$$ 2.20955 0.0980328
$$509$$ −13.8032 23.9079i −0.611818 1.05970i −0.990934 0.134351i $$-0.957105\pi$$
0.379116 0.925349i $$-0.376228\pi$$
$$510$$ −0.510273 0.883819i −0.0225953 0.0391362i
$$511$$ −5.21690 + 9.03593i −0.230782 + 0.399726i
$$512$$ 25.3227 1.11912
$$513$$ 1.15109 1.99375i 0.0508220 0.0880263i
$$514$$ −9.57849 + 16.5904i −0.422489 + 0.731773i
$$515$$ −4.53579 −0.199871
$$516$$ 0.871866 1.51012i 0.0383818 0.0664792i
$$517$$ 0.821271 + 1.42248i 0.0361195 + 0.0625608i
$$518$$ 0.702750 + 1.21720i 0.0308770 + 0.0534806i
$$519$$ −13.7184 −0.602169
$$520$$ −11.6160 3.19246i −0.509395 0.139999i
$$521$$ −36.8783 −1.61567 −0.807833 0.589411i $$-0.799360\pi$$
−0.807833 + 0.589411i $$0.799360\pi$$
$$522$$ 0.306062 + 0.530115i 0.0133960 + 0.0232025i
$$523$$ −15.4027 26.6782i −0.673512 1.16656i −0.976901 0.213691i $$-0.931451\pi$$
0.303389 0.952867i $$-0.401882\pi$$
$$524$$ 4.22571 7.31914i 0.184601 0.319738i
$$525$$ −3.78270 −0.165091
$$526$$ −10.9840 + 19.0248i −0.478925 + 0.829522i
$$527$$ 2.48973 4.31233i 0.108454 0.187848i
$$528$$ −1.08277 −0.0471213
$$529$$ 11.4972 19.9137i 0.499878 0.865814i
$$530$$ 3.89870 + 6.75275i 0.169349 + 0.293321i
$$531$$ 1.96249 + 3.39914i 0.0851649 + 0.147510i
$$532$$ 0.868391 0.0376495
$$533$$ 2.81955 + 10.7992i 0.122128 + 0.467765i
$$534$$ −15.2370 −0.659371
$$535$$ 3.40404 + 5.89597i 0.147169 + 0.254905i
$$536$$ −12.3007 21.3055i −0.531310 0.920257i
$$537$$ −11.0152 + 19.0789i −0.475341 + 0.823315i
$$538$$ 30.9485 1.33428
$$539$$ 0.174453 0.302162i 0.00751424 0.0130150i
$$540$$ −0.208086 + 0.360416i −0.00895461 + 0.0155098i
$$541$$ −41.4981 −1.78414 −0.892072 0.451893i $$-0.850749\pi$$
−0.892072 + 0.451893i $$0.850749\pi$$
$$542$$ 11.6769 20.2249i 0.501564 0.868735i
$$543$$ 4.71690 + 8.16991i 0.202421 + 0.350604i
$$544$$ 0.763617 + 1.32262i 0.0327398 + 0.0567070i
$$545$$ −9.73306 −0.416918
$$546$$ −1.16031 4.44410i −0.0496565 0.190190i
$$547$$ −41.3716 −1.76892 −0.884460 0.466615i $$-0.845473\pi$$
−0.884460 + 0.466615i $$0.845473\pi$$
$$548$$ 3.81140 + 6.60154i 0.162815 + 0.282004i
$$549$$ −2.77389 4.80452i −0.118387 0.205052i
$$550$$ 0.840647 1.45604i 0.0358453 0.0620859i
$$551$$ 1.10624 0.0471272
$$552$$ 0.113585 0.196736i 0.00483452 0.00837363i
$$553$$ 8.55272 14.8137i 0.363699 0.629944i
$$554$$ −10.7699 −0.457569
$$555$$ −0.608649 + 1.05421i −0.0258357 + 0.0447488i
$$556$$ 0.806062 + 1.39614i 0.0341846 + 0.0592095i
$$557$$ −15.0075 25.9937i −0.635886 1.10139i −0.986327 0.164803i $$-0.947301\pi$$
0.350440 0.936585i $$-0.386032\pi$$
$$558$$ 8.73598 0.369824
$$559$$ −11.8612 + 11.7101i −0.501675 + 0.495283i
$$560$$ 3.42392 0.144687
$$561$$ −0.126672 0.219403i −0.00534810 0.00926319i
$$562$$ −15.9313 27.5938i −0.672020 1.16397i
$$563$$ −12.9674 + 22.4602i −0.546512 + 0.946586i 0.451998 + 0.892019i $$0.350711\pi$$
−0.998510 + 0.0545676i $$0.982622\pi$$
$$564$$ 1.77575 0.0747727
$$565$$ −6.62532 + 11.4754i −0.278729 + 0.482773i
$$566$$ 17.2876 29.9431i 0.726654 1.25860i
$$567$$ −1.00000 −0.0419961
$$568$$ 14.4289 24.9915i 0.605421 1.04862i
$$569$$ 3.28310 + 5.68650i 0.137635 + 0.238390i 0.926601 0.376046i $$-0.122717\pi$$
−0.788966 + 0.614437i $$0.789383\pi$$
$$570$$ −1.61786 2.80222i −0.0677647 0.117372i
$$571$$ −30.0539 −1.25772 −0.628858 0.777520i $$-0.716477\pi$$
−0.628858 + 0.777520i $$0.716477\pi$$
$$572$$ −0.457556 0.125752i −0.0191314 0.00525794i
$$573$$ 3.37720 0.141085
$$574$$ −1.97170 3.41509i −0.0822973 0.142543i
$$575$$ 0.141882 + 0.245746i 0.00591687 + 0.0102483i
$$576$$ −4.44301 + 7.69551i −0.185125 + 0.320646i
$$577$$ 21.1706 0.881343 0.440671 0.897669i $$-0.354740\pi$$
0.440671 + 0.897669i $$0.354740\pi$$
$$578$$ −10.4922 + 18.1731i −0.436420 + 0.755902i
$$579$$ 11.1614 19.3321i 0.463851 0.803413i
$$580$$ −0.199977 −0.00830360
$$581$$ −5.95716 + 10.3181i −0.247144 + 0.428067i
$$582$$ −6.43526 11.1462i −0.266750 0.462025i
$$583$$ 0.967829 + 1.67633i 0.0400834 + 0.0694264i
$$584$$ −31.5966 −1.30748
$$585$$ 2.83088 2.79481i 0.117043 0.115551i
$$586$$ 13.4268 0.554658
$$587$$ −0.0156098 0.0270370i −0.000644286 0.00111594i 0.865703 0.500558i $$-0.166872\pi$$
−0.866347 + 0.499442i $$0.833538\pi$$
$$588$$ −0.188601 0.326667i −0.00777779 0.0134715i
$$589$$ 7.89387 13.6726i 0.325261 0.563369i
$$590$$ 5.51656 0.227113
$$591$$ −12.7257 + 22.0416i −0.523466 + 0.906669i
$$592$$ −1.71196 + 2.96520i −0.0703612 + 0.121869i
$$593$$ −10.3150 −0.423586 −0.211793 0.977315i $$-0.567930\pi$$
−0.211793 + 0.977315i $$0.567930\pi$$
$$594$$ 0.222234 0.384921i 0.00911839 0.0157935i
$$595$$ 0.400563 + 0.693795i 0.0164215 + 0.0284428i
$$596$$ −0.923522 1.59959i −0.0378289 0.0655217i
$$597$$ 22.3404 0.914330
$$598$$ −0.245194 + 0.242070i −0.0100267 + 0.00989896i
$$599$$ 44.0176 1.79851 0.899256 0.437423i $$-0.144109\pi$$
0.899256 + 0.437423i $$0.144109\pi$$
$$600$$ −5.72757 9.92044i −0.233827 0.405000i
$$601$$ −2.52336 4.37059i −0.102930 0.178280i 0.809961 0.586484i $$-0.199488\pi$$
−0.912891 + 0.408204i $$0.866155\pi$$
$$602$$ 2.94447 5.09997i 0.120008 0.207859i
$$603$$ 8.12386 0.330829
$$604$$ −1.68714 + 2.92221i −0.0686487 + 0.118903i
$$605$$ 6.00106 10.3941i 0.243978 0.422582i
$$606$$ 5.19112 0.210875
$$607$$ −8.32409 + 14.4177i −0.337864 + 0.585198i −0.984031 0.177998i $$-0.943038\pi$$
0.646167 + 0.763196i $$0.276371\pi$$
$$608$$ 2.42111 + 4.19348i 0.0981889 + 0.170068i
$$609$$ −0.240258 0.416138i −0.00973573 0.0168628i
$$610$$ −7.79740 −0.315708
$$611$$ −16.3669 4.49818i −0.662135 0.181977i
$$612$$ −0.273891 −0.0110714
$$613$$ −19.0060 32.9194i −0.767645 1.32960i −0.938837 0.344362i $$-0.888095\pi$$
0.171192 0.985238i $$-0.445238\pi$$
$$614$$ −2.80792 4.86347i −0.113319 0.196274i
$$615$$ 1.70769 2.95780i 0.0688605 0.119270i
$$616$$ 1.05659 0.0425713
$$617$$ −7.83330 + 13.5677i −0.315357 + 0.546214i −0.979513 0.201380i $$-0.935457\pi$$
0.664157 + 0.747593i $$0.268791\pi$$
$$618$$ 2.61852 4.53541i 0.105332 0.182441i
$$619$$ 3.26109 0.131074 0.0655372 0.997850i $$-0.479124\pi$$
0.0655372 + 0.997850i $$0.479124\pi$$
$$620$$ −1.42700 + 2.47163i −0.0573096 + 0.0992631i
$$621$$ 0.0375080 + 0.0649658i 0.00150514 + 0.00260699i
$$622$$ −1.48304 2.56870i −0.0594644 0.102995i
$$623$$ 11.9610 0.479209
$$624$$ 7.96249 7.86103i 0.318755 0.314693i
$$625$$ 8.22234 0.328894
$$626$$ 8.06928 + 13.9764i 0.322513 + 0.558609i
$$627$$ −0.401624 0.695633i −0.0160393 0.0277809i
$$628$$ 1.24373 2.15421i 0.0496303 0.0859622i
$$629$$ −0.801125 −0.0319430
$$630$$ −0.702750 + 1.21720i −0.0279982 + 0.0484943i
$$631$$ −0.799773 + 1.38525i −0.0318385 + 0.0551459i −0.881506 0.472174i $$-0.843470\pi$$
0.849667 + 0.527319i $$0.176803\pi$$
$$632$$ 51.8003 2.06051
$$633$$ 5.01908 8.69331i 0.199491 0.345528i
$$634$$ −7.82902 13.5603i −0.310930 0.538547i
$$635$$ 3.23145 + 5.59703i 0.128236 + 0.222111i
$$636$$ 2.09264 0.0829785
$$637$$ 0.910836 + 3.48861i 0.0360886 + 0.138224i
$$638$$ 0.213574 0.00845548
$$639$$ 4.76468 + 8.25267i 0.188488 + 0.326470i
$$640$$ 3.92403 + 6.79662i 0.155111 + 0.268660i
$$641$$ −15.6779 + 27.1550i −0.619241 + 1.07256i 0.370384 + 0.928879i $$0.379226\pi$$
−0.989625 + 0.143678i $$0.954107\pi$$
$$642$$ −7.86064 −0.310235
$$643$$ 9.33154 16.1627i 0.368000 0.637395i −0.621253 0.783610i $$-0.713376\pi$$
0.989253 + 0.146215i $$0.0467092\pi$$
$$644$$ −0.0141481 + 0.0245053i −0.000557514 + 0.000965643i
$$645$$ 5.10039 0.200828
$$646$$ 1.06474 1.84419i 0.0418918 0.0725586i
$$647$$ −3.26855 5.66130i −0.128500 0.222569i 0.794596 0.607139i $$-0.207683\pi$$
−0.923096 + 0.384570i $$0.874350\pi$$
$$648$$ −1.51415 2.62258i −0.0594814 0.103025i
$$649$$ 1.36945 0.0537557
$$650$$ 4.38909 + 16.8107i 0.172154 + 0.659371i
$$651$$ −6.85772 −0.268775
$$652$$ −1.86799 3.23546i −0.0731562 0.126710i
$$653$$ −7.92605 13.7283i −0.310170 0.537230i 0.668229 0.743956i $$-0.267053\pi$$
−0.978399 + 0.206725i $$0.933719\pi$$
$$654$$ 5.61892 9.73226i 0.219717 0.380561i
$$655$$ 24.7203 0.965901
$$656$$ 4.80325 8.31947i 0.187535 0.324821i
$$657$$ 5.21690 9.03593i 0.203531 0.352525i
$$658$$ 5.99708 0.233790
$$659$$ 24.8987 43.1258i 0.969916 1.67994i 0.274132 0.961692i $$-0.411610\pi$$
0.695784 0.718251i $$-0.255057\pi$$
$$660$$ 0.0726027 + 0.125752i 0.00282606 + 0.00489487i
$$661$$ −1.78552 3.09260i −0.0694485 0.120288i 0.829210 0.558937i $$-0.188791\pi$$
−0.898659 + 0.438649i $$0.855457\pi$$
$$662$$ −16.9319 −0.658078
$$663$$ 2.52442 + 0.693795i 0.0980404 + 0.0269448i
$$664$$ −36.0801 −1.40018
$$665$$ 1.27002 + 2.19973i 0.0492491 + 0.0853019i
$$666$$ −0.702750 1.21720i −0.0272310 0.0471655i
$$667$$ −0.0180232 + 0.0312170i −0.000697860 + 0.00120873i
$$668$$ 6.32061 0.244552
$$669$$ −2.56727 + 4.44664i −0.0992562 + 0.171917i
$$670$$ 5.70904 9.88834i 0.220559 0.382020i
$$671$$ −1.93566 −0.0747252
$$672$$ 1.05166 1.82152i 0.0405685 0.0702667i
$$673$$ −5.86693 10.1618i −0.226154 0.391709i 0.730511 0.682901i $$-0.239282\pi$$
−0.956665 + 0.291191i $$0.905948\pi$$
$$674$$ −2.16912 3.75702i −0.0835512 0.144715i
$$675$$ 3.78270 0.145596
$$676$$ 4.27777 2.39716i 0.164529 0.0921985i
$$677$$ 17.3326 0.666146 0.333073 0.942901i $$-0.391914\pi$$
0.333073 + 0.942901i $$0.391914\pi$$
$$678$$ −7.64963 13.2496i −0.293782 0.508846i
$$679$$ 5.05166 + 8.74973i 0.193865 + 0.335784i
$$680$$ −1.21302 + 2.10102i −0.0465173 + 0.0805703i
$$681$$ 28.9709 1.11017
$$682$$ 1.52402 2.63968i 0.0583578 0.101079i
$$683$$ −8.48198 + 14.6912i −0.324554 + 0.562144i −0.981422 0.191862i $$-0.938547\pi$$
0.656868 + 0.754005i $$0.271881\pi$$
$$684$$ −0.868391 −0.0332038
$$685$$ −11.1483 + 19.3094i −0.425954 + 0.737774i
$$686$$ −0.636945 1.10322i −0.0243187 0.0421212i
$$687$$ 0.339695 + 0.588369i 0.0129602 + 0.0224477i
$$688$$ 14.3460 0.546935
$$689$$ −19.2876 5.30089i −0.734801 0.201948i
$$690$$ 0.105435 0.00401384
$$691$$ −18.3213 31.7334i −0.696974 1.20719i −0.969511 0.245049i $$-0.921196\pi$$
0.272537 0.962145i $$-0.412137\pi$$
$$692$$ 2.58730 + 4.48134i 0.0983545 + 0.170355i
$$693$$ −0.174453 + 0.302162i −0.00662693 + 0.0114782i
$$694$$ 42.6730 1.61984
$$695$$ −2.35772 + 4.08369i −0.0894333 + 0.154903i
$$696$$ 0.727571 1.26019i 0.0275785 0.0477674i
$$697$$ 2.24772 0.0851384
$$698$$ −17.9494 + 31.0893i −0.679395 + 1.17675i
$$699$$ −9.15109 15.8502i −0.346126 0.599508i
$$700$$ 0.713423 + 1.23568i 0.0269649 + 0.0467045i
$$701$$ −14.6092 −0.551782 −0.275891 0.961189i $$-0.588973\pi$$
−0.275891 + 0.961189i $$0.588973\pi$$
$$702$$ 1.16031 + 4.44410i 0.0437929 + 0.167732i
$$703$$ −2.54003 −0.0957991
$$704$$ 1.55019 + 2.68502i 0.0584252 + 0.101195i
$$705$$ 2.59702 + 4.49818i 0.0978096 + 0.169411i
$$706$$ −1.90590 + 3.30111i −0.0717295 + 0.124239i
$$707$$ −4.07502 −0.153257
$$708$$ 0.740258 1.28216i 0.0278206 0.0481867i
$$709$$ 11.7930 20.4260i 0.442894 0.767116i −0.555008 0.831845i $$-0.687285\pi$$
0.997903 + 0.0647290i $$0.0206183\pi$$
$$710$$ 13.3935 0.502649
$$711$$ −8.55272 + 14.8137i −0.320752 + 0.555559i
$$712$$ 18.1108 + 31.3688i 0.678730 + 1.17559i
$$713$$ 0.257219 + 0.445517i 0.00963294 + 0.0166847i
$$714$$ −0.924984 −0.0346167
$$715$$ −0.350629 1.34295i −0.0131128 0.0502235i
$$716$$ 8.30994 0.310557
$$717$$ −2.72611 4.72176i −0.101808 0.176337i
$$718$$ 2.42605 + 4.20203i 0.0905392 + 0.156819i
$$719$$ −17.0669 + 29.5607i −0.636487 + 1.10243i 0.349711 + 0.936857i $$0.386280\pi$$
−0.986198 + 0.165570i $$0.947054\pi$$
$$720$$ −3.42392 −0.127602
$$721$$ −2.05553 + 3.56028i −0.0765520 + 0.132592i
$$722$$ −8.72611 + 15.1141i −0.324752 + 0.562487i
$$723$$ 15.4621 0.575041
$$724$$ 1.77923 3.08171i 0.0661245 0.114531i
$$725$$ 0.908823 + 1.57413i 0.0337528 + 0.0584616i
$$726$$ 6.92886 + 12.0011i 0.257154 + 0.445404i
$$727$$ −15.3481 −0.569230 −0.284615 0.958642i $$-0.591866\pi$$
−0.284615 + 0.958642i $$0.591866\pi$$
$$728$$ −7.77002 + 7.67101i −0.287976 + 0.284307i
$$729$$ 1.00000 0.0370370
$$730$$ −7.33235 12.7000i −0.271382 0.470048i
$$731$$ 1.67833 + 2.90695i 0.0620752 + 0.107517i
$$732$$ −1.04632 + 1.81228i −0.0386731 + 0.0669837i
$$733$$ 23.2894 0.860213 0.430107 0.902778i $$-0.358476\pi$$
0.430107 + 0.902778i $$0.358476\pi$$
$$734$$ −16.8481 + 29.1818i −0.621875 + 1.07712i
$$735$$ 0.551656 0.955496i 0.0203481 0.0352440i
$$736$$ −0.157782 −0.00581593
$$737$$ 1.41723 2.45472i 0.0522045 0.0904208i
$$738$$ 1.97170 + 3.41509i 0.0725794 + 0.125711i
$$739$$ 5.13307 + 8.89074i 0.188823 + 0.327051i 0.944858 0.327480i $$-0.106199\pi$$
−0.756035 + 0.654531i $$0.772866\pi$$
$$740$$ 0.459168 0.0168794
$$741$$ 8.00388 + 2.19973i 0.294030 + 0.0808092i
$$742$$ 7.06727 0.259447
$$743$$ 22.6741 + 39.2726i 0.831830 + 1.44077i 0.896585 + 0.442871i $$0.146040\pi$$
−0.0647549 + 0.997901i $$0.520627\pi$$
$$744$$ −10.3836 17.9849i −0.380681 0.659359i
$$745$$ 2.70129 4.67877i 0.0989675 0.171417i
$$746$$ −2.71544 −0.0994192
$$747$$ 5.95716 10.3181i 0.217961 0.377519i
$$748$$ −0.0477811 + 0.0827593i −0.00174705 + 0.00302598i
$$749$$ 6.17058 0.225468
$$750$$ 6.17204 10.6903i 0.225371 0.390354i
$$751$$ 14.8057 + 25.6442i 0.540266 + 0.935769i 0.998888 + 0.0471372i $$0.0150098\pi$$
−0.458622 + 0.888631i $$0.651657\pi$$
$$752$$ 7.30471 + 12.6521i 0.266375 + 0.461376i
$$753$$ 8.29444 0.302266
$$754$$ −1.57059 + 1.55058i −0.0571975 + 0.0564687i
$$755$$ −9.86971 −0.359196
$$756$$ 0.188601 + 0.326667i 0.00685937 + 0.0118808i
$$757$$ 12.9908 + 22.5007i 0.472158 + 0.817802i 0.999492 0.0318559i $$-0.0101418\pi$$
−0.527334 + 0.849658i $$0.676808\pi$$
$$758$$ −8.88119 + 15.3827i −0.322579 + 0.558724i
$$759$$ 0.0261736 0.000950041
$$760$$ −3.84598 + 6.66144i −0.139508 + 0.241636i
$$761$$ 27.0332 46.8229i 0.979954 1.69733i 0.317444 0.948277i $$-0.397176\pi$$
0.662510 0.749053i $$-0.269491\pi$$
$$762$$ −7.46209 −0.270323
$$763$$ −4.41084 + 7.63979i −0.159683 + 0.276579i
$$764$$ −0.636945 1.10322i −0.0230439 0.0399132i
$$765$$ −0.400563 0.693795i −0.0144824 0.0250842i
$$766$$ 23.6999 0.856313
$$767$$ −10.0707 + 9.94242i −0.363633 + 0.359000i
$$768$$ 8.71061 0.314317
$$769$$ −12.8967 22.3377i −0.465066 0.805519i 0.534138 0.845397i $$-0.320636\pi$$
−0.999205 + 0.0398785i $$0.987303\pi$$
$$770$$ 0.245194 + 0.424688i 0.00883618 + 0.0153047i