# Properties

 Label 189.2.bd.a.47.12 Level $189$ Weight $2$ Character 189.47 Analytic conductor $1.509$ Analytic rank $0$ Dimension $132$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 189.bd (of order $$18$$, degree $$6$$, 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: $$1.50917259820$$ Analytic rank: $$0$$ Dimension: $$132$$ Relative dimension: $$22$$ over $$\Q(\zeta_{18})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

## Embedding invariants

 Embedding label 47.12 Character $$\chi$$ $$=$$ 189.47 Dual form 189.2.bd.a.185.12

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.0159182 + 0.00280680i) q^{2} +(-0.402650 - 1.68460i) q^{3} +(-1.87914 - 0.683951i) q^{4} +(3.75147 + 1.36542i) q^{5} +(-0.00168110 - 0.0279459i) q^{6} +(0.157938 - 2.64103i) q^{7} +(-0.0559891 - 0.0323253i) q^{8} +(-2.67575 + 1.35661i) q^{9} +O(q^{10})$$ $$q+(0.0159182 + 0.00280680i) q^{2} +(-0.402650 - 1.68460i) q^{3} +(-1.87914 - 0.683951i) q^{4} +(3.75147 + 1.36542i) q^{5} +(-0.00168110 - 0.0279459i) q^{6} +(0.157938 - 2.64103i) q^{7} +(-0.0559891 - 0.0323253i) q^{8} +(-2.67575 + 1.35661i) q^{9} +(0.0558840 + 0.0322646i) q^{10} +(-1.76436 - 4.84753i) q^{11} +(-0.395548 + 3.44099i) q^{12} +(-0.220791 + 0.606618i) q^{13} +(0.00992693 - 0.0415971i) q^{14} +(0.789663 - 6.86951i) q^{15} +(3.06298 + 2.57014i) q^{16} +(1.69383 - 2.93380i) q^{17} +(-0.0464007 + 0.0140844i) q^{18} +(0.328436 - 0.189623i) q^{19} +(-6.11565 - 5.13164i) q^{20} +(-4.51267 + 0.797349i) q^{21} +(-0.0144792 - 0.0821158i) q^{22} +(-0.993035 + 0.175099i) q^{23} +(-0.0319112 + 0.107335i) q^{24} +(8.37891 + 7.03074i) q^{25} +(-0.00521724 + 0.00903653i) q^{26} +(3.36272 + 3.96132i) q^{27} +(-2.10312 + 4.85485i) q^{28} +(1.97120 + 5.41582i) q^{29} +(0.0318513 - 0.107133i) q^{30} +(-2.20741 + 6.06480i) q^{31} +(0.124656 + 0.148560i) q^{32} +(-7.45572 + 4.92408i) q^{33} +(0.0351973 - 0.0419465i) q^{34} +(4.19863 - 9.69210i) q^{35} +(5.95595 - 0.719172i) q^{36} +6.16814 q^{37} +(0.00576033 - 0.00209659i) q^{38} +(1.11081 + 0.127690i) q^{39} +(-0.165904 - 0.197716i) q^{40} +(0.266252 + 0.0969077i) q^{41} +(-0.0740714 + 2.61403e-5i) q^{42} +(-1.45052 + 8.22633i) q^{43} +10.3159i q^{44} +(-11.8903 + 1.43574i) q^{45} -0.0162988 q^{46} +(6.91258 - 2.51597i) q^{47} +(3.09635 - 6.19475i) q^{48} +(-6.95011 - 0.834239i) q^{49} +(0.113643 + 0.135434i) q^{50} +(-5.62430 - 1.67213i) q^{51} +(0.829794 - 0.988910i) q^{52} +(1.71989 - 0.992981i) q^{53} +(0.0424097 + 0.0724954i) q^{54} -20.5944i q^{55} +(-0.0942150 + 0.142764i) q^{56} +(-0.451683 - 0.476932i) q^{57} +(0.0161767 + 0.0917427i) q^{58} +(-2.62371 + 2.20155i) q^{59} +(-6.18229 + 12.3687i) q^{60} +(-2.75545 - 7.57053i) q^{61} +(-0.0521605 + 0.0903447i) q^{62} +(3.16024 + 7.28100i) q^{63} +(-3.99687 - 6.92277i) q^{64} +(-1.65658 + 1.97424i) q^{65} +(-0.132502 + 0.0574556i) q^{66} +(1.63911 + 9.29584i) q^{67} +(-5.18952 + 4.35453i) q^{68} +(0.694817 + 1.60236i) q^{69} +(0.0940381 - 0.142496i) q^{70} +(8.57363 - 4.94999i) q^{71} +(0.193665 + 0.0105392i) q^{72} +7.08887i q^{73} +(0.0981854 + 0.0173127i) q^{74} +(8.47022 - 16.9460i) q^{75} +(-0.746871 + 0.131693i) q^{76} +(-13.0811 + 3.89411i) q^{77} +(0.0173236 + 0.00515040i) q^{78} +(-0.222353 + 1.26102i) q^{79} +(7.98133 + 13.8241i) q^{80} +(5.31924 - 7.25987i) q^{81} +(0.00396624 + 0.00228991i) q^{82} +(-8.07527 + 2.93916i) q^{83} +(9.02529 + 1.58812i) q^{84} +(10.3602 - 8.69327i) q^{85} +(-0.0461793 + 0.126877i) q^{86} +(8.32979 - 5.50136i) q^{87} +(-0.0579132 + 0.328442i) q^{88} +(-2.67849 - 4.63928i) q^{89} +(-0.193302 - 0.0105194i) q^{90} +(1.56723 + 0.678924i) q^{91} +(1.98581 + 0.350152i) q^{92} +(11.1056 + 1.27661i) q^{93} +(0.117097 - 0.0206474i) q^{94} +(1.49103 - 0.262910i) q^{95} +(0.200071 - 0.269813i) q^{96} +(-7.39427 - 1.30381i) q^{97} +(-0.108291 - 0.0327871i) q^{98} +(11.2971 + 10.5772i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10})$$ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 $$132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100})$$ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$136$$ $$\chi(n)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.0159182 + 0.00280680i 0.0112558 + 0.00198471i 0.179273 0.983799i $$-0.442625\pi$$
−0.168017 + 0.985784i $$0.553736\pi$$
$$3$$ −0.402650 1.68460i −0.232470 0.972604i
$$4$$ −1.87914 0.683951i −0.939570 0.341975i
$$5$$ 3.75147 + 1.36542i 1.67771 + 0.610636i 0.992993 0.118175i $$-0.0377045\pi$$
0.684715 + 0.728811i $$0.259927\pi$$
$$6$$ −0.00168110 0.0279459i −0.000686308 0.0114088i
$$7$$ 0.157938 2.64103i 0.0596949 0.998217i
$$8$$ −0.0559891 0.0323253i −0.0197951 0.0114287i
$$9$$ −2.67575 + 1.35661i −0.891916 + 0.452202i
$$10$$ 0.0558840 + 0.0322646i 0.0176721 + 0.0102030i
$$11$$ −1.76436 4.84753i −0.531973 1.46158i −0.856719 0.515783i $$-0.827501\pi$$
0.324746 0.945801i $$-0.394721\pi$$
$$12$$ −0.395548 + 3.44099i −0.114185 + 0.993328i
$$13$$ −0.220791 + 0.606618i −0.0612364 + 0.168246i −0.966538 0.256524i $$-0.917423\pi$$
0.905301 + 0.424770i $$0.139645\pi$$
$$14$$ 0.00992693 0.0415971i 0.00265308 0.0111173i
$$15$$ 0.789663 6.86951i 0.203890 1.77370i
$$16$$ 3.06298 + 2.57014i 0.765744 + 0.642536i
$$17$$ 1.69383 2.93380i 0.410815 0.711552i −0.584165 0.811635i $$-0.698578\pi$$
0.994979 + 0.100084i $$0.0319111\pi$$
$$18$$ −0.0464007 + 0.0140844i −0.0109367 + 0.00331972i
$$19$$ 0.328436 0.189623i 0.0753485 0.0435025i −0.461852 0.886957i $$-0.652815\pi$$
0.537201 + 0.843454i $$0.319482\pi$$
$$20$$ −6.11565 5.13164i −1.36750 1.14747i
$$21$$ −4.51267 + 0.797349i −0.984746 + 0.173996i
$$22$$ −0.0144792 0.0821158i −0.00308698 0.0175072i
$$23$$ −0.993035 + 0.175099i −0.207062 + 0.0365106i −0.276217 0.961095i $$-0.589081\pi$$
0.0691549 + 0.997606i $$0.477970\pi$$
$$24$$ −0.0319112 + 0.107335i −0.00651385 + 0.0219097i
$$25$$ 8.37891 + 7.03074i 1.67578 + 1.40615i
$$26$$ −0.00521724 + 0.00903653i −0.00102318 + 0.00177221i
$$27$$ 3.36272 + 3.96132i 0.647157 + 0.762357i
$$28$$ −2.10312 + 4.85485i −0.397453 + 0.917480i
$$29$$ 1.97120 + 5.41582i 0.366042 + 1.00569i 0.976852 + 0.213916i $$0.0686218\pi$$
−0.610810 + 0.791777i $$0.709156\pi$$
$$30$$ 0.0318513 0.107133i 0.00581523 0.0195598i
$$31$$ −2.20741 + 6.06480i −0.396462 + 1.08927i 0.567533 + 0.823351i $$0.307898\pi$$
−0.963995 + 0.265920i $$0.914324\pi$$
$$32$$ 0.124656 + 0.148560i 0.0220363 + 0.0262619i
$$33$$ −7.45572 + 4.92408i −1.29787 + 0.857173i
$$34$$ 0.0351973 0.0419465i 0.00603628 0.00719376i
$$35$$ 4.19863 9.69210i 0.709697 1.63826i
$$36$$ 5.95595 0.719172i 0.992659 0.119862i
$$37$$ 6.16814 1.01404 0.507018 0.861936i $$-0.330748\pi$$
0.507018 + 0.861936i $$0.330748\pi$$
$$38$$ 0.00576033 0.00209659i 0.000934449 0.000340112i
$$39$$ 1.11081 + 0.127690i 0.177872 + 0.0204467i
$$40$$ −0.165904 0.197716i −0.0262317 0.0312617i
$$41$$ 0.266252 + 0.0969077i 0.0415816 + 0.0151344i 0.362727 0.931895i $$-0.381846\pi$$
−0.321146 + 0.947030i $$0.604068\pi$$
$$42$$ −0.0740714 2.61403e-5i −0.0114295 4.03353e-6i
$$43$$ −1.45052 + 8.22633i −0.221203 + 1.25450i 0.648610 + 0.761121i $$0.275351\pi$$
−0.869812 + 0.493383i $$0.835760\pi$$
$$44$$ 10.3159i 1.55518i
$$45$$ −11.8903 + 1.43574i −1.77250 + 0.214027i
$$46$$ −0.0162988 −0.00240312
$$47$$ 6.91258 2.51597i 1.00830 0.366992i 0.215522 0.976499i $$-0.430855\pi$$
0.792781 + 0.609507i $$0.208632\pi$$
$$48$$ 3.09635 6.19475i 0.446920 0.894136i
$$49$$ −6.95011 0.834239i −0.992873 0.119177i
$$50$$ 0.113643 + 0.135434i 0.0160715 + 0.0191533i
$$51$$ −5.62430 1.67213i −0.787560 0.234145i
$$52$$ 0.829794 0.988910i 0.115072 0.137137i
$$53$$ 1.71989 0.992981i 0.236246 0.136396i −0.377204 0.926130i $$-0.623115\pi$$
0.613450 + 0.789734i $$0.289781\pi$$
$$54$$ 0.0424097 + 0.0724954i 0.00577123 + 0.00986538i
$$55$$ 20.5944i 2.77695i
$$56$$ −0.0942150 + 0.142764i −0.0125900 + 0.0190776i
$$57$$ −0.451683 0.476932i −0.0598269 0.0631712i
$$58$$ 0.0161767 + 0.0917427i 0.00212411 + 0.0120464i
$$59$$ −2.62371 + 2.20155i −0.341578 + 0.286618i −0.797398 0.603454i $$-0.793791\pi$$
0.455820 + 0.890072i $$0.349346\pi$$
$$60$$ −6.18229 + 12.3687i −0.798130 + 1.59679i
$$61$$ −2.75545 7.57053i −0.352799 0.969307i −0.981467 0.191633i $$-0.938622\pi$$
0.628668 0.777674i $$-0.283601\pi$$
$$62$$ −0.0521605 + 0.0903447i −0.00662439 + 0.0114738i
$$63$$ 3.16024 + 7.28100i 0.398153 + 0.917319i
$$64$$ −3.99687 6.92277i −0.499608 0.865347i
$$65$$ −1.65658 + 1.97424i −0.205474 + 0.244874i
$$66$$ −0.132502 + 0.0574556i −0.0163099 + 0.00707230i
$$67$$ 1.63911 + 9.29584i 0.200249 + 1.13567i 0.904743 + 0.425958i $$0.140063\pi$$
−0.704494 + 0.709710i $$0.748826\pi$$
$$68$$ −5.18952 + 4.35453i −0.629322 + 0.528064i
$$69$$ 0.694817 + 1.60236i 0.0836461 + 0.192902i
$$70$$ 0.0940381 0.142496i 0.0112397 0.0170315i
$$71$$ 8.57363 4.94999i 1.01750 0.587456i 0.104123 0.994564i $$-0.466796\pi$$
0.913380 + 0.407109i $$0.133463\pi$$
$$72$$ 0.193665 + 0.0105392i 0.0228237 + 0.00124206i
$$73$$ 7.08887i 0.829690i 0.909892 + 0.414845i $$0.136164\pi$$
−0.909892 + 0.414845i $$0.863836\pi$$
$$74$$ 0.0981854 + 0.0173127i 0.0114138 + 0.00201256i
$$75$$ 8.47022 16.9460i 0.978056 1.95676i
$$76$$ −0.746871 + 0.131693i −0.0856719 + 0.0151063i
$$77$$ −13.0811 + 3.89411i −1.49073 + 0.443775i
$$78$$ 0.0173236 + 0.00515040i 0.00196152 + 0.000583168i
$$79$$ −0.222353 + 1.26102i −0.0250166 + 0.141876i −0.994758 0.102259i $$-0.967393\pi$$
0.969741 + 0.244135i $$0.0785041\pi$$
$$80$$ 7.98133 + 13.8241i 0.892340 + 1.54558i
$$81$$ 5.31924 7.25987i 0.591027 0.806652i
$$82$$ 0.00396624 + 0.00228991i 0.000437998 + 0.000252878i
$$83$$ −8.07527 + 2.93916i −0.886376 + 0.322614i −0.744780 0.667310i $$-0.767446\pi$$
−0.141596 + 0.989925i $$0.545223\pi$$
$$84$$ 9.02529 + 1.58812i 0.984740 + 0.173278i
$$85$$ 10.3602 8.69327i 1.12373 0.942918i
$$86$$ −0.0461793 + 0.126877i −0.00497964 + 0.0136815i
$$87$$ 8.32979 5.50136i 0.893047 0.589807i
$$88$$ −0.0579132 + 0.328442i −0.00617356 + 0.0350120i
$$89$$ −2.67849 4.63928i −0.283920 0.491763i 0.688427 0.725306i $$-0.258302\pi$$
−0.972347 + 0.233543i $$0.924968\pi$$
$$90$$ −0.193302 0.0105194i −0.0203758 0.00110885i
$$91$$ 1.56723 + 0.678924i 0.164290 + 0.0711706i
$$92$$ 1.98581 + 0.350152i 0.207035 + 0.0365059i
$$93$$ 11.1056 + 1.27661i 1.15159 + 0.132378i
$$94$$ 0.117097 0.0206474i 0.0120777 0.00212962i
$$95$$ 1.49103 0.262910i 0.152977 0.0269739i
$$96$$ 0.200071 0.269813i 0.0204196 0.0275377i
$$97$$ −7.39427 1.30381i −0.750774 0.132382i −0.214849 0.976647i $$-0.568926\pi$$
−0.535925 + 0.844265i $$0.680037\pi$$
$$98$$ −0.108291 0.0327871i −0.0109391 0.00331200i
$$99$$ 11.2971 + 10.5772i 1.13541 + 1.06305i
$$100$$ −10.9365 18.9425i −1.09365 1.89425i
$$101$$ 1.98008 11.2296i 0.197025 1.11738i −0.712480 0.701692i $$-0.752428\pi$$
0.909505 0.415693i $$-0.136461\pi$$
$$102$$ −0.0848351 0.0424035i −0.00839993 0.00419858i
$$103$$ −3.27445 + 8.99648i −0.322641 + 0.886449i 0.667277 + 0.744810i $$0.267460\pi$$
−0.989918 + 0.141640i $$0.954763\pi$$
$$104$$ 0.0319710 0.0268269i 0.00313502 0.00263059i
$$105$$ −18.0179 3.17048i −1.75836 0.309407i
$$106$$ 0.0301646 0.0109790i 0.00292985 0.00106638i
$$107$$ −12.0916 6.98107i −1.16894 0.674885i −0.215507 0.976502i $$-0.569140\pi$$
−0.953429 + 0.301617i $$0.902474\pi$$
$$108$$ −3.60968 9.74382i −0.347342 0.937599i
$$109$$ 0.912496 + 1.58049i 0.0874012 + 0.151383i 0.906412 0.422395i $$-0.138810\pi$$
−0.819011 + 0.573778i $$0.805477\pi$$
$$110$$ 0.0578044 0.327825i 0.00551144 0.0312569i
$$111$$ −2.48360 10.3908i −0.235733 0.986255i
$$112$$ 7.27159 7.68350i 0.687101 0.726023i
$$113$$ 4.07591 0.718692i 0.383429 0.0676089i 0.0213886 0.999771i $$-0.493191\pi$$
0.362041 + 0.932162i $$0.382080\pi$$
$$114$$ −0.00585131 0.00885966i −0.000548025 0.000829783i
$$115$$ −3.96442 0.699035i −0.369684 0.0651853i
$$116$$ 11.5253i 1.07010i
$$117$$ −0.232161 1.92268i −0.0214633 0.177752i
$$118$$ −0.0479439 + 0.0276804i −0.00441360 + 0.00254819i
$$119$$ −7.48075 4.93682i −0.685759 0.452558i
$$120$$ −0.266271 + 0.359091i −0.0243071 + 0.0327804i
$$121$$ −11.9591 + 10.0349i −1.08719 + 0.912259i
$$122$$ −0.0226127 0.128243i −0.00204726 0.0116106i
$$123$$ 0.0560445 0.487547i 0.00505336 0.0439607i
$$124$$ 8.29605 9.88685i 0.745008 0.887866i
$$125$$ 11.8527 + 20.5295i 1.06014 + 1.83622i
$$126$$ 0.0298689 + 0.124770i 0.00266093 + 0.0111154i
$$127$$ −3.16383 + 5.47991i −0.280744 + 0.486263i −0.971568 0.236760i $$-0.923915\pi$$
0.690824 + 0.723023i $$0.257248\pi$$
$$128$$ −0.176848 0.485887i −0.0156313 0.0429467i
$$129$$ 14.4421 0.868777i 1.27156 0.0764915i
$$130$$ −0.0319110 + 0.0267765i −0.00279878 + 0.00234845i
$$131$$ 0.681494 + 3.86494i 0.0595424 + 0.337682i 0.999997 0.00223629i $$-0.000711832\pi$$
−0.940455 + 0.339918i $$0.889601\pi$$
$$132$$ 17.3782 4.15370i 1.51258 0.361533i
$$133$$ −0.448928 0.897360i −0.0389270 0.0778110i
$$134$$ 0.152573i 0.0131803i
$$135$$ 7.20627 + 19.4523i 0.620217 + 1.67419i
$$136$$ −0.189672 + 0.109507i −0.0162643 + 0.00939017i
$$137$$ 4.16810 4.96735i 0.356105 0.424389i −0.558017 0.829830i $$-0.688437\pi$$
0.914121 + 0.405441i $$0.132882\pi$$
$$138$$ 0.00656268 + 0.0274569i 0.000558653 + 0.00233728i
$$139$$ −3.60990 4.30212i −0.306188 0.364901i 0.590906 0.806740i $$-0.298770\pi$$
−0.897094 + 0.441840i $$0.854326\pi$$
$$140$$ −14.5187 + 15.3412i −1.22706 + 1.29656i
$$141$$ −7.02175 10.6319i −0.591338 0.895365i
$$142$$ 0.150370 0.0547302i 0.0126188 0.00459286i
$$143$$ 3.33015 0.278481
$$144$$ −11.6824 2.72180i −0.973535 0.226817i
$$145$$ 23.0088i 1.91078i
$$146$$ −0.0198970 + 0.112842i −0.00164669 + 0.00933885i
$$147$$ 1.39310 + 12.0441i 0.114901 + 0.993377i
$$148$$ −11.5908 4.21870i −0.952757 0.346775i
$$149$$ 2.28030 + 2.71756i 0.186810 + 0.222631i 0.851318 0.524649i $$-0.175804\pi$$
−0.664509 + 0.747280i $$0.731359\pi$$
$$150$$ 0.182394 0.245975i 0.0148924 0.0200838i
$$151$$ 15.0731 5.48616i 1.22663 0.446457i 0.354188 0.935174i $$-0.384757\pi$$
0.872442 + 0.488717i $$0.162535\pi$$
$$152$$ −0.0245185 −0.00198871
$$153$$ −0.552251 + 10.1480i −0.0446469 + 0.820415i
$$154$$ −0.219157 + 0.0252709i −0.0176602 + 0.00203639i
$$155$$ −16.5620 + 19.7379i −1.33030 + 1.58538i
$$156$$ −2.00003 0.999686i −0.160131 0.0800390i
$$157$$ −3.94390 4.70015i −0.314757 0.375113i 0.585351 0.810780i $$-0.300957\pi$$
−0.900108 + 0.435667i $$0.856512\pi$$
$$158$$ −0.00707889 + 0.0194491i −0.000563166 + 0.00154729i
$$159$$ −2.36529 2.49751i −0.187580 0.198065i
$$160$$ 0.264798 + 0.727525i 0.0209341 + 0.0575159i
$$161$$ 0.305604 + 2.65029i 0.0240850 + 0.208872i
$$162$$ 0.105049 0.100634i 0.00825347 0.00790652i
$$163$$ −1.58197 + 2.74005i −0.123910 + 0.214618i −0.921306 0.388838i $$-0.872877\pi$$
0.797397 + 0.603456i $$0.206210\pi$$
$$164$$ −0.434044 0.364206i −0.0338932 0.0284397i
$$165$$ −34.6934 + 8.29234i −2.70087 + 0.645558i
$$166$$ −0.136793 + 0.0241203i −0.0106172 + 0.00187210i
$$167$$ 1.33048 + 7.54555i 0.102956 + 0.583892i 0.992017 + 0.126104i $$0.0402472\pi$$
−0.889061 + 0.457788i $$0.848642\pi$$
$$168$$ 0.278435 + 0.101231i 0.0214817 + 0.00781013i
$$169$$ 9.63934 + 8.08837i 0.741488 + 0.622182i
$$170$$ 0.189316 0.109302i 0.0145199 0.00838306i
$$171$$ −0.621569 + 0.952941i −0.0475326 + 0.0728732i
$$172$$ 8.35214 14.4663i 0.636845 1.10305i
$$173$$ 1.21193 + 1.01693i 0.0921413 + 0.0773157i 0.687695 0.726000i $$-0.258623\pi$$
−0.595553 + 0.803316i $$0.703067\pi$$
$$174$$ 0.148036 0.0641914i 0.0112226 0.00486634i
$$175$$ 19.8918 21.0186i 1.50368 1.58885i
$$176$$ 7.05465 19.3825i 0.531765 1.46101i
$$177$$ 4.76517 + 3.53344i 0.358172 + 0.265590i
$$178$$ −0.0296151 0.0813668i −0.00221975 0.00609870i
$$179$$ 7.54113 + 4.35388i 0.563651 + 0.325424i 0.754610 0.656174i $$-0.227826\pi$$
−0.190959 + 0.981598i $$0.561160\pi$$
$$180$$ 23.3255 + 5.43444i 1.73858 + 0.405059i
$$181$$ 1.08680 + 0.627465i 0.0807813 + 0.0466391i 0.539847 0.841763i $$-0.318482\pi$$
−0.459065 + 0.888403i $$0.651816\pi$$
$$182$$ 0.0230418 + 0.0152061i 0.00170797 + 0.00112715i
$$183$$ −11.6438 + 7.69010i −0.860737 + 0.568468i
$$184$$ 0.0612593 + 0.0222965i 0.00451609 + 0.00164372i
$$185$$ 23.1396 + 8.42212i 1.70126 + 0.619206i
$$186$$ 0.173197 + 0.0514923i 0.0126994 + 0.00377560i
$$187$$ −17.2102 3.03462i −1.25853 0.221914i
$$188$$ −14.7105 −1.07287
$$189$$ 10.9931 8.25542i 0.799629 0.600494i
$$190$$ 0.0244724 0.00177542
$$191$$ 8.73361 + 1.53997i 0.631942 + 0.111428i 0.480439 0.877028i $$-0.340477\pi$$
0.151503 + 0.988457i $$0.451589\pi$$
$$192$$ −10.0528 + 9.52057i −0.725496 + 0.687088i
$$193$$ −23.6910 8.62281i −1.70531 0.620684i −0.708901 0.705308i $$-0.750809\pi$$
−0.996413 + 0.0846240i $$0.973031\pi$$
$$194$$ −0.114044 0.0415085i −0.00818785 0.00298013i
$$195$$ 3.99282 + 1.99575i 0.285932 + 0.142919i
$$196$$ 12.4897 + 6.32119i 0.892118 + 0.451513i
$$197$$ −11.0546 6.38238i −0.787608 0.454726i 0.0515117 0.998672i $$-0.483596\pi$$
−0.839120 + 0.543947i $$0.816929\pi$$
$$198$$ 0.150142 + 0.200079i 0.0106701 + 0.0142190i
$$199$$ −17.6420 10.1856i −1.25061 0.722038i −0.279377 0.960182i $$-0.590128\pi$$
−0.971230 + 0.238144i $$0.923461\pi$$
$$200$$ −0.241857 0.664496i −0.0171019 0.0469870i
$$201$$ 14.9998 6.50421i 1.05800 0.458771i
$$202$$ 0.0630384 0.173196i 0.00443536 0.0121861i
$$203$$ 14.6147 4.35064i 1.02575 0.305355i
$$204$$ 9.42519 + 6.98892i 0.659895 + 0.489322i
$$205$$ 0.866515 + 0.727093i 0.0605201 + 0.0507824i
$$206$$ −0.0773745 + 0.134017i −0.00539094 + 0.00933738i
$$207$$ 2.41957 1.81568i 0.168172 0.126198i
$$208$$ −2.23537 + 1.29059i −0.154995 + 0.0894866i
$$209$$ −1.49868 1.25754i −0.103666 0.0869860i
$$210$$ −0.277912 0.101041i −0.0191778 0.00697248i
$$211$$ −0.149574 0.848277i −0.0102971 0.0583978i 0.979226 0.202771i $$-0.0649946\pi$$
−0.989523 + 0.144373i $$0.953884\pi$$
$$212$$ −3.91107 + 0.689627i −0.268613 + 0.0473638i
$$213$$ −11.7909 12.4500i −0.807900 0.853061i
$$214$$ −0.172881 0.145064i −0.0118179 0.00991639i
$$215$$ −16.6740 + 28.8802i −1.13716 + 1.96962i
$$216$$ −0.0602249 0.330492i −0.00409778 0.0224871i
$$217$$ 15.6687 + 6.78770i 1.06366 + 0.460779i
$$218$$ 0.0100891 + 0.0277197i 0.000683322 + 0.00187741i
$$219$$ 11.9419 2.85433i 0.806959 0.192878i
$$220$$ −14.0856 + 38.6998i −0.949650 + 2.60914i
$$221$$ 1.40572 + 1.67527i 0.0945586 + 0.112691i
$$222$$ −0.0103693 0.172374i −0.000695941 0.0115690i
$$223$$ −10.1302 + 12.0727i −0.678367 + 0.808446i −0.989897 0.141790i $$-0.954714\pi$$
0.311530 + 0.950236i $$0.399159\pi$$
$$224$$ 0.412039 0.305758i 0.0275305 0.0204293i
$$225$$ −31.9578 7.44561i −2.13052 0.496374i
$$226$$ 0.0668981 0.00445000
$$227$$ 8.89407 3.23718i 0.590320 0.214859i −0.0295500 0.999563i $$-0.509407\pi$$
0.619870 + 0.784704i $$0.287185\pi$$
$$228$$ 0.522578 + 1.20515i 0.0346085 + 0.0798131i
$$229$$ −1.18329 1.41019i −0.0781938 0.0931878i 0.725529 0.688191i $$-0.241595\pi$$
−0.803723 + 0.595004i $$0.797151\pi$$
$$230$$ −0.0611442 0.0222547i −0.00403173 0.00146743i
$$231$$ 11.8271 + 20.4685i 0.778168 + 1.34673i
$$232$$ 0.0647026 0.366947i 0.00424793 0.0240912i
$$233$$ 10.5523i 0.691304i −0.938363 0.345652i $$-0.887658\pi$$
0.938363 0.345652i $$-0.112342\pi$$
$$234$$ 0.00170101 0.0312572i 0.000111199 0.00204335i
$$235$$ 29.3677 1.91574
$$236$$ 6.43607 2.34254i 0.418953 0.152486i
$$237$$ 2.21385 0.133176i 0.143805 0.00865070i
$$238$$ −0.105223 0.0995821i −0.00682059 0.00645495i
$$239$$ −3.07353 3.66289i −0.198810 0.236933i 0.657424 0.753521i $$-0.271646\pi$$
−0.856234 + 0.516588i $$0.827202\pi$$
$$240$$ 20.0743 19.0116i 1.29579 1.22719i
$$241$$ −5.60988 + 6.68559i −0.361364 + 0.430657i −0.915840 0.401543i $$-0.868474\pi$$
0.554476 + 0.832199i $$0.312919\pi$$
$$242$$ −0.218532 + 0.126170i −0.0140478 + 0.00811049i
$$243$$ −14.3718 6.03761i −0.921948 0.387313i
$$244$$ 16.1107i 1.03138i
$$245$$ −24.9340 12.6195i −1.59298 0.806228i
$$246$$ 0.00226057 0.00760355i 0.000144129 0.000484784i
$$247$$ 0.0425129 + 0.241103i 0.00270503 + 0.0153410i
$$248$$ 0.319637 0.268208i 0.0202970 0.0170312i
$$249$$ 8.20280 + 12.4201i 0.519832 + 0.787094i
$$250$$ 0.131051 + 0.360060i 0.00828840 + 0.0227722i
$$251$$ 5.48464 9.49967i 0.346187 0.599614i −0.639382 0.768890i $$-0.720810\pi$$
0.985569 + 0.169276i $$0.0541429\pi$$
$$252$$ −0.958687 15.8435i −0.0603916 0.998044i
$$253$$ 2.60086 + 4.50483i 0.163515 + 0.283216i
$$254$$ −0.0657433 + 0.0783498i −0.00412510 + 0.00491610i
$$255$$ −18.8162 13.9525i −1.17832 0.873740i
$$256$$ 2.77474 + 15.7363i 0.173421 + 0.983522i
$$257$$ −9.83062 + 8.24887i −0.613217 + 0.514550i −0.895663 0.444733i $$-0.853299\pi$$
0.282446 + 0.959283i $$0.408854\pi$$
$$258$$ 0.232330 + 0.0267068i 0.0144643 + 0.00166269i
$$259$$ 0.974183 16.2903i 0.0605328 1.01223i
$$260$$ 4.46323 2.57685i 0.276798 0.159809i
$$261$$ −12.6216 11.8172i −0.781255 0.731468i
$$262$$ 0.0634356i 0.00391906i
$$263$$ −2.43598 0.429529i −0.150209 0.0264859i 0.0980380 0.995183i $$-0.468743\pi$$
−0.248247 + 0.968697i $$0.579854\pi$$
$$264$$ 0.576612 0.0346865i 0.0354880 0.00213481i
$$265$$ 7.80796 1.37675i 0.479639 0.0845734i
$$266$$ −0.00462739 0.0155444i −0.000283723 0.000953086i
$$267$$ −6.73684 + 6.38019i −0.412288 + 0.390461i
$$268$$ 3.27779 18.5893i 0.200223 1.13552i
$$269$$ −13.2754 22.9936i −0.809413 1.40195i −0.913271 0.407353i $$-0.866452\pi$$
0.103858 0.994592i $$-0.466881\pi$$
$$270$$ 0.0601118 + 0.329872i 0.00365829 + 0.0200753i
$$271$$ −17.4414 10.0698i −1.05949 0.611698i −0.134200 0.990954i $$-0.542846\pi$$
−0.925292 + 0.379257i $$0.876180\pi$$
$$272$$ 12.7285 4.63278i 0.771776 0.280904i
$$273$$ 0.512672 2.91352i 0.0310283 0.176334i
$$274$$ 0.0802908 0.0673720i 0.00485054 0.00407009i
$$275$$ 19.2983 53.0217i 1.16373 3.19733i
$$276$$ −0.209720 3.48628i −0.0126237 0.209850i
$$277$$ −4.06457 + 23.0513i −0.244216 + 1.38502i 0.578090 + 0.815973i $$0.303798\pi$$
−0.822306 + 0.569046i $$0.807313\pi$$
$$278$$ −0.0453878 0.0786140i −0.00272218 0.00471496i
$$279$$ −2.32108 19.2225i −0.138960 1.15082i
$$280$$ −0.548377 + 0.406930i −0.0327718 + 0.0243187i
$$281$$ 8.66178 + 1.52731i 0.516719 + 0.0911114i 0.425925 0.904758i $$-0.359949\pi$$
0.0907933 + 0.995870i $$0.471060\pi$$
$$282$$ −0.0819318 0.188948i −0.00487897 0.0112517i
$$283$$ 29.3925 5.18270i 1.74721 0.308079i 0.793444 0.608643i $$-0.208286\pi$$
0.953762 + 0.300564i $$0.0971748\pi$$
$$284$$ −19.4966 + 3.43778i −1.15691 + 0.203995i
$$285$$ −1.04326 2.40593i −0.0617975 0.142515i
$$286$$ 0.0530099 + 0.00934707i 0.00313454 + 0.000552704i
$$287$$ 0.297988 0.687874i 0.0175897 0.0406039i
$$288$$ −0.535086 0.228398i −0.0315302 0.0134585i
$$289$$ 2.76187 + 4.78370i 0.162463 + 0.281394i
$$290$$ −0.0645811 + 0.366258i −0.00379233 + 0.0215074i
$$291$$ 0.780903 + 12.9814i 0.0457774 + 0.760981i
$$292$$ 4.84844 13.3210i 0.283734 0.779552i
$$293$$ 1.70777 1.43299i 0.0997691 0.0837162i −0.591539 0.806277i $$-0.701479\pi$$
0.691308 + 0.722560i $$0.257035\pi$$
$$294$$ −0.0116297 + 0.195629i −0.000678255 + 0.0114093i
$$295$$ −12.8488 + 4.67659i −0.748087 + 0.272281i
$$296$$ −0.345348 0.199387i −0.0200730 0.0115891i
$$297$$ 13.2696 23.2901i 0.769979 1.35143i
$$298$$ 0.0286706 + 0.0496589i 0.00166084 + 0.00287666i
$$299$$ 0.113035 0.641054i 0.00653698 0.0370731i
$$300$$ −27.5070 + 26.0508i −1.58812 + 1.50404i
$$301$$ 21.4969 + 5.13013i 1.23906 + 0.295696i
$$302$$ 0.255334 0.0450223i 0.0146928 0.00259074i
$$303$$ −19.7146 + 1.18595i −1.13257 + 0.0681309i
$$304$$ 1.49335 + 0.263318i 0.0856495 + 0.0151023i
$$305$$ 32.1630i 1.84165i
$$306$$ −0.0372741 + 0.159987i −0.00213082 + 0.00914584i
$$307$$ 12.9614 7.48325i 0.739744 0.427091i −0.0822321 0.996613i $$-0.526205\pi$$
0.821976 + 0.569522i $$0.192872\pi$$
$$308$$ 27.2447 + 1.62927i 1.55241 + 0.0928365i
$$309$$ 16.4739 + 1.89371i 0.937168 + 0.107729i
$$310$$ −0.319037 + 0.267704i −0.0181201 + 0.0152046i
$$311$$ 0.786394 + 4.45986i 0.0445923 + 0.252896i 0.998952 0.0457630i $$-0.0145719\pi$$
−0.954360 + 0.298659i $$0.903461\pi$$
$$312$$ −0.0580656 0.0430565i −0.00328732 0.00243759i
$$313$$ −7.81741 + 9.31643i −0.441866 + 0.526596i −0.940307 0.340328i $$-0.889462\pi$$
0.498440 + 0.866924i $$0.333906\pi$$
$$314$$ −0.0495872 0.0858875i −0.00279836 0.00484691i
$$315$$ 1.91390 + 31.6295i 0.107836 + 1.78212i
$$316$$ 1.28031 2.21756i 0.0720231 0.124748i
$$317$$ 11.6274 + 31.9461i 0.653061 + 1.79427i 0.606121 + 0.795372i $$0.292725\pi$$
0.0469397 + 0.998898i $$0.485053\pi$$
$$318$$ −0.0306410 0.0463946i −0.00171826 0.00260168i
$$319$$ 22.7755 19.1109i 1.27518 1.07000i
$$320$$ −5.54160 31.4280i −0.309785 1.75688i
$$321$$ −6.89164 + 23.1804i −0.384654 + 1.29380i
$$322$$ −0.00257419 + 0.0430455i −0.000143454 + 0.00239883i
$$323$$ 1.28476i 0.0714858i
$$324$$ −14.9610 + 10.0042i −0.831166 + 0.555789i
$$325$$ −6.11497 + 3.53048i −0.339197 + 0.195836i
$$326$$ −0.0328728 + 0.0391763i −0.00182066 + 0.00216978i
$$327$$ 2.29507 2.17357i 0.126918 0.120199i
$$328$$ −0.0117746 0.0140325i −0.000650145 0.000774813i
$$329$$ −5.55301 18.6537i −0.306147 1.02841i
$$330$$ −0.575529 + 0.0346214i −0.0316818 + 0.00190584i
$$331$$ 31.2817 11.3856i 1.71940 0.625810i 0.721611 0.692299i $$-0.243402\pi$$
0.997787 + 0.0664891i $$0.0211798\pi$$
$$332$$ 17.1848 0.943138
$$333$$ −16.5044 + 8.36773i −0.904434 + 0.458549i
$$334$$ 0.123846i 0.00677653i
$$335$$ −6.54370 + 37.1111i −0.357520 + 2.02760i
$$336$$ −15.8715 9.15596i −0.865862 0.499499i
$$337$$ −26.0769 9.49121i −1.42050 0.517019i −0.486306 0.873789i $$-0.661656\pi$$
−0.934192 + 0.356770i $$0.883878\pi$$
$$338$$ 0.130738 + 0.155808i 0.00711121 + 0.00847481i
$$339$$ −2.85187 6.57689i −0.154892 0.357208i
$$340$$ −25.4141 + 9.24998i −1.37827 + 0.501650i
$$341$$ 33.2939 1.80297
$$342$$ −0.0125689 + 0.0134244i −0.000679651 + 0.000725911i
$$343$$ −3.30094 + 18.2237i −0.178234 + 0.983988i
$$344$$ 0.347132 0.413696i 0.0187161 0.0223050i
$$345$$ 0.418680 + 6.95993i 0.0225410 + 0.374710i
$$346$$ 0.0164374 + 0.0195893i 0.000883678 + 0.00105313i
$$347$$ 4.17679 11.4756i 0.224222 0.616044i −0.775664 0.631146i $$-0.782585\pi$$
0.999886 + 0.0151019i $$0.00480726\pi$$
$$348$$ −19.4155 + 4.64065i −1.04078 + 0.248765i
$$349$$ −3.80673 10.4589i −0.203770 0.559853i 0.795145 0.606419i $$-0.207394\pi$$
−0.998915 + 0.0465660i $$0.985172\pi$$
$$350$$ 0.375635 0.278744i 0.0200785 0.0148995i
$$351$$ −3.14547 + 1.16527i −0.167893 + 0.0621973i
$$352$$ 0.500209 0.866387i 0.0266612 0.0461786i
$$353$$ 15.0431 + 12.6227i 0.800664 + 0.671837i 0.948360 0.317196i $$-0.102741\pi$$
−0.147696 + 0.989033i $$0.547186\pi$$
$$354$$ 0.0659350 + 0.0696208i 0.00350441 + 0.00370030i
$$355$$ 38.9225 6.86309i 2.06579 0.364255i
$$356$$ 1.86022 + 10.5498i 0.0985913 + 0.559139i
$$357$$ −5.30445 + 14.5899i −0.280741 + 0.772178i
$$358$$ 0.107820 + 0.0904721i 0.00569849 + 0.00478160i
$$359$$ −25.9840 + 15.0019i −1.37138 + 0.791768i −0.991102 0.133103i $$-0.957506\pi$$
−0.380281 + 0.924871i $$0.624173\pi$$
$$360$$ 0.712139 + 0.303973i 0.0375330 + 0.0160208i
$$361$$ −9.42809 + 16.3299i −0.496215 + 0.859470i
$$362$$ 0.0155387 + 0.0130385i 0.000816695 + 0.000685289i
$$363$$ 21.7200 + 16.1057i 1.14000 + 0.845330i
$$364$$ −2.48069 2.34770i −0.130023 0.123053i
$$365$$ −9.67931 + 26.5937i −0.506638 + 1.39198i
$$366$$ −0.206933 + 0.0897302i −0.0108165 + 0.00469027i
$$367$$ −0.00927887 0.0254935i −0.000484353 0.00133075i 0.939450 0.342685i $$-0.111336\pi$$
−0.939935 + 0.341355i $$0.889114\pi$$
$$368$$ −3.49167 2.01592i −0.182016 0.105087i
$$369$$ −0.843888 + 0.101898i −0.0439311 + 0.00530461i
$$370$$ 0.344700 + 0.199013i 0.0179201 + 0.0103462i
$$371$$ −2.35086 4.69912i −0.122051 0.243966i
$$372$$ −19.9958 9.99459i −1.03673 0.518195i
$$373$$ 26.4258 + 9.61822i 1.36828 + 0.498012i 0.918604 0.395180i $$-0.129318\pi$$
0.449674 + 0.893193i $$0.351540\pi$$
$$374$$ −0.265437 0.0966112i −0.0137254 0.00499565i
$$375$$ 29.8115 28.2333i 1.53946 1.45796i
$$376$$ −0.468359 0.0825843i −0.0241538 0.00425896i
$$377$$ −3.72056 −0.191619
$$378$$ 0.198161 0.100556i 0.0101923 0.00517203i
$$379$$ 0.592745 0.0304473 0.0152236 0.999884i $$-0.495154\pi$$
0.0152236 + 0.999884i $$0.495154\pi$$
$$380$$ −2.98168 0.525750i −0.152957 0.0269704i
$$381$$ 10.5054 + 3.12330i 0.538206 + 0.160011i
$$382$$ 0.134701 + 0.0490270i 0.00689188 + 0.00250844i
$$383$$ −11.0275 4.01368i −0.563478 0.205089i 0.0445466 0.999007i $$-0.485816\pi$$
−0.608025 + 0.793918i $$0.708038\pi$$
$$384$$ −0.747316 + 0.493561i −0.0381363 + 0.0251869i
$$385$$ −54.3906 3.25264i −2.77200 0.165770i
$$386$$ −0.352914 0.203755i −0.0179629 0.0103709i
$$387$$ −7.27865 23.9794i −0.369995 1.21894i
$$388$$ 13.0031 + 7.50736i 0.660134 + 0.381128i
$$389$$ −5.24004 14.3969i −0.265680 0.729951i −0.998759 0.0498070i $$-0.984139\pi$$
0.733078 0.680144i $$-0.238083\pi$$
$$390$$ 0.0579566 + 0.0429757i 0.00293475 + 0.00217616i
$$391$$ −1.16833 + 3.20996i −0.0590849 + 0.162335i
$$392$$ 0.362163 + 0.271373i 0.0182920 + 0.0137064i
$$393$$ 6.23647 2.70426i 0.314589 0.136412i
$$394$$ −0.158055 0.132624i −0.00796269 0.00668149i
$$395$$ −2.55598 + 4.42709i −0.128605 + 0.222751i
$$396$$ −13.9946 27.6028i −0.703256 1.38709i
$$397$$ −19.7438 + 11.3991i −0.990914 + 0.572104i −0.905547 0.424245i $$-0.860539\pi$$
−0.0853663 + 0.996350i $$0.527206\pi$$
$$398$$ −0.252239 0.211653i −0.0126436 0.0106092i
$$399$$ −1.33093 + 1.11758i −0.0666299 + 0.0559492i
$$400$$ 7.59440 + 43.0700i 0.379720 + 2.15350i
$$401$$ 2.88795 0.509224i 0.144218 0.0254294i −0.101073 0.994879i $$-0.532228\pi$$
0.245291 + 0.969450i $$0.421117\pi$$
$$402$$ 0.257025 0.0614336i 0.0128192 0.00306403i
$$403$$ −3.19164 2.67811i −0.158987 0.133406i
$$404$$ −11.4013 + 19.7477i −0.567237 + 0.982483i
$$405$$ 29.8678 19.9721i 1.48414 0.992424i
$$406$$ 0.244850 0.0282336i 0.0121517 0.00140121i
$$407$$ −10.8828 29.9002i −0.539440 1.48210i
$$408$$ 0.260847 + 0.275428i 0.0129139 + 0.0136357i
$$409$$ 6.88596 18.9190i 0.340489 0.935485i −0.644764 0.764381i $$-0.723045\pi$$
0.985253 0.171103i $$-0.0547332\pi$$
$$410$$ 0.0117525 + 0.0140061i 0.000580416 + 0.000691712i
$$411$$ −10.0463 5.02148i −0.495546 0.247691i
$$412$$ 12.3063 14.6661i 0.606288 0.722546i
$$413$$ 5.39999 + 7.27701i 0.265716 + 0.358078i
$$414$$ 0.0436113 0.0221110i 0.00214338 0.00108670i
$$415$$ −34.3073 −1.68408
$$416$$ −0.117642 + 0.0428182i −0.00576787 + 0.00209933i
$$417$$ −5.79381 + 7.81349i −0.283724 + 0.382628i
$$418$$ −0.0203265 0.0242242i −0.000994204 0.00118485i
$$419$$ −13.5738 4.94048i −0.663126 0.241358i −0.0115404 0.999933i $$-0.503674\pi$$
−0.651585 + 0.758575i $$0.725896\pi$$
$$420$$ 31.6897 + 18.2811i 1.54630 + 0.892027i
$$421$$ 1.54410 8.75701i 0.0752547 0.426791i −0.923782 0.382918i $$-0.874919\pi$$
0.999037 0.0438728i $$-0.0139696\pi$$
$$422$$ 0.0139228i 0.000677753i
$$423$$ −15.0831 + 16.1098i −0.733367 + 0.783283i
$$424$$ −0.128394 −0.00623535
$$425$$ 34.8193 12.6732i 1.68898 0.614740i
$$426$$ −0.152745 0.231276i −0.00740051 0.0112054i
$$427$$ −20.4292 + 6.08155i −0.988639 + 0.294307i
$$428$$ 17.9470 + 21.3884i 0.867503 + 1.03385i
$$429$$ −1.34088 5.60997i −0.0647385 0.270852i
$$430$$ −0.346481 + 0.412919i −0.0167088 + 0.0199127i
$$431$$ −27.2881 + 15.7548i −1.31442 + 0.758881i −0.982825 0.184541i $$-0.940920\pi$$
−0.331595 + 0.943422i $$0.607587\pi$$
$$432$$ 0.118782 + 20.7761i 0.00571488 + 0.999592i
$$433$$ 35.8271i 1.72174i 0.508824 + 0.860870i $$0.330080\pi$$
−0.508824 + 0.860870i $$0.669920\pi$$
$$434$$ 0.230365 + 0.152027i 0.0110579 + 0.00729751i
$$435$$ 38.7606 9.26449i 1.85843 0.444198i
$$436$$ −0.633730 3.59406i −0.0303502 0.172124i
$$437$$ −0.292946 + 0.245811i −0.0140135 + 0.0117587i
$$438$$ 0.198105 0.0119171i 0.00946581 0.000569423i
$$439$$ −12.3813 34.0174i −0.590928 1.62356i −0.768786 0.639506i $$-0.779139\pi$$
0.177858 0.984056i $$-0.443083\pi$$
$$440$$ −0.665722 + 1.15306i −0.0317370 + 0.0549701i
$$441$$ 19.7285 7.19635i 0.939451 0.342683i
$$442$$ 0.0176743 + 0.0306127i 0.000840678 + 0.00145610i
$$443$$ −15.4246 + 18.3824i −0.732847 + 0.873373i −0.995811 0.0914326i $$-0.970855\pi$$
0.262964 + 0.964806i $$0.415300\pi$$
$$444$$ −2.43980 + 21.2245i −0.115788 + 1.00727i
$$445$$ −3.71369 21.0614i −0.176046 0.998406i
$$446$$ −0.195139 + 0.163741i −0.00924011 + 0.00775338i
$$447$$ 3.65983 4.93562i 0.173104 0.233447i
$$448$$ −18.9145 + 9.46248i −0.893628 + 0.447060i
$$449$$ −27.8837 + 16.0987i −1.31591 + 0.759743i −0.983069 0.183238i $$-0.941342\pi$$
−0.332845 + 0.942981i $$0.608009\pi$$
$$450$$ −0.487811 0.208219i −0.0229956 0.00981556i
$$451$$ 1.46164i 0.0688261i
$$452$$ −8.15075 1.43720i −0.383379 0.0676001i
$$453$$ −15.3111 23.1831i −0.719380 1.08924i
$$454$$ 0.150663 0.0265660i 0.00707098 0.00124680i
$$455$$ 4.95239 + 4.68689i 0.232171 + 0.219725i
$$456$$ 0.00987235 + 0.0413038i 0.000462315 + 0.00193423i
$$457$$ 0.192143 1.08970i 0.00898809 0.0509740i −0.979984 0.199077i $$-0.936206\pi$$
0.988972 + 0.148103i $$0.0473167\pi$$
$$458$$ −0.0148776 0.0257688i −0.000695186 0.00120410i
$$459$$ 17.3176 3.15576i 0.808318 0.147298i
$$460$$ 6.97160 + 4.02506i 0.325053 + 0.187669i
$$461$$ 19.7443 7.18634i 0.919584 0.334701i 0.161511 0.986871i $$-0.448363\pi$$
0.758073 + 0.652170i $$0.226141\pi$$
$$462$$ 0.130815 + 0.359017i 0.00608607 + 0.0167030i
$$463$$ −17.5556 + 14.7309i −0.815876 + 0.684601i −0.952003 0.306090i $$-0.900979\pi$$
0.136126 + 0.990691i $$0.456535\pi$$
$$464$$ −7.88170 + 21.6548i −0.365899 + 1.00530i
$$465$$ 39.9191 + 19.9530i 1.85120 + 0.925296i
$$466$$ 0.0296182 0.167973i 0.00137203 0.00778120i
$$467$$ 17.0089 + 29.4602i 0.787076 + 1.36326i 0.927751 + 0.373200i $$0.121740\pi$$
−0.140674 + 0.990056i $$0.544927\pi$$
$$468$$ −0.878758 + 3.77178i −0.0406206 + 0.174350i
$$469$$ 24.8095 2.86077i 1.14560 0.132098i
$$470$$ 0.467479 + 0.0824292i 0.0215632 + 0.00380218i
$$471$$ −6.32986 + 8.53640i −0.291665 + 0.393336i
$$472$$ 0.218065 0.0384507i 0.0100373 0.00176984i
$$473$$ 42.4366 7.48272i 1.95124 0.344056i
$$474$$ 0.0356142 + 0.00409392i 0.00163581 + 0.000188040i
$$475$$ 4.08513 + 0.720319i 0.187439 + 0.0330505i
$$476$$ 10.6808 + 14.3934i 0.489555 + 0.659723i
$$477$$ −3.25492 + 4.99018i −0.149032 + 0.228485i
$$478$$ −0.0386439 0.0669333i −0.00176753 0.00306146i
$$479$$ −6.61372 + 37.5083i −0.302189 + 1.71380i 0.334263 + 0.942480i $$0.391513\pi$$
−0.636451 + 0.771317i $$0.719598\pi$$
$$480$$ 1.11897 0.739015i 0.0510736 0.0337313i
$$481$$ −1.36187 + 3.74171i −0.0620959 + 0.170607i
$$482$$ −0.108064 + 0.0906764i −0.00492218 + 0.00413020i
$$483$$ 4.34163 1.58196i 0.197551 0.0719816i
$$484$$ 29.3361 10.6775i 1.33346 0.485340i
$$485$$ −25.9591 14.9875i −1.17874 0.680548i
$$486$$ −0.211825 0.136446i −0.00960860 0.00618932i
$$487$$ 10.4173 + 18.0433i 0.472053 + 0.817619i 0.999489 0.0319755i $$-0.0101799\pi$$
−0.527436 + 0.849595i $$0.676847\pi$$
$$488$$ −0.0904448 + 0.512938i −0.00409424 + 0.0232196i
$$489$$ 5.25287 + 1.56171i 0.237543 + 0.0706228i
$$490$$ −0.361483 0.270863i −0.0163302 0.0122364i
$$491$$ 2.73237 0.481790i 0.123310 0.0217429i −0.111653 0.993747i $$-0.535614\pi$$
0.234962 + 0.972004i $$0.424503\pi$$
$$492$$ −0.438774 + 0.877838i −0.0197815 + 0.0395760i
$$493$$ 19.2278 + 3.39039i 0.865978 + 0.152695i
$$494$$ 0.00395723i 0.000178044i
$$495$$ 27.9385 + 55.1055i 1.25574 + 2.47681i
$$496$$ −22.3486 + 12.9030i −1.00348 + 0.579362i
$$497$$ −11.7190 23.4250i −0.525668 1.05076i
$$498$$ 0.0957126 + 0.220729i 0.00428899 + 0.00989112i
$$499$$ −3.11754 + 2.61593i −0.139560 + 0.117105i −0.709895 0.704307i $$-0.751258\pi$$
0.570335 + 0.821412i $$0.306813\pi$$
$$500$$ −8.23174 46.6845i −0.368134 2.08779i
$$501$$ 12.1755 5.27954i 0.543961 0.235873i
$$502$$ 0.113969 0.135823i 0.00508668 0.00606207i
$$503$$ −20.5736 35.6344i −0.917329 1.58886i −0.803455 0.595366i $$-0.797007\pi$$
−0.113875 0.993495i $$-0.536326\pi$$
$$504$$ 0.0584216 0.509812i 0.00260230 0.0227088i
$$505$$ 22.7613 39.4238i 1.01287 1.75433i
$$506$$ 0.0287568 + 0.0790086i 0.00127840 + 0.00351236i
$$507$$ 9.74438 19.4952i 0.432763 0.865812i
$$508$$ 9.69326 8.13361i 0.430069 0.360871i
$$509$$ −6.67420 37.8513i −0.295829 1.67773i −0.663814 0.747897i $$-0.731064\pi$$
0.367986 0.929831i $$-0.380048\pi$$
$$510$$ −0.260358 0.274911i −0.0115288 0.0121733i
$$511$$ 18.7219 + 1.11960i 0.828210 + 0.0495283i
$$512$$ 1.29242i 0.0571175i
$$513$$ 1.85560 + 0.663393i 0.0819267 + 0.0292895i
$$514$$ −0.179638 + 0.103714i −0.00792350 + 0.00457463i
$$515$$ −24.5680 + 29.2790i −1.08260 + 1.29019i
$$516$$ −27.7330 8.24515i −1.22088 0.362972i
$$517$$ −24.3925 29.0698i −1.07278 1.27849i
$$518$$ 0.0612307 0.256576i 0.00269032 0.0112733i
$$519$$ 1.22514 2.45108i 0.0537775 0.107591i
$$520$$ 0.156568 0.0569862i 0.00686597 0.00249901i
$$521$$ −27.2574 −1.19417 −0.597084 0.802178i $$-0.703674\pi$$
−0.597084 + 0.802178i $$0.703674\pi$$
$$522$$ −0.167743 0.223535i −0.00734193 0.00978385i
$$523$$ 14.0528i 0.614487i −0.951631 0.307244i $$-0.900593\pi$$
0.951631 0.307244i $$-0.0994067\pi$$
$$524$$ 1.36281 7.72887i 0.0595346 0.337637i
$$525$$ −43.4173 25.0465i −1.89488 1.09312i
$$526$$ −0.0375707 0.0136746i −0.00163816 0.000596241i
$$527$$ 14.0540 + 16.7489i 0.612200 + 0.729591i
$$528$$ −35.4923 4.07991i −1.54460 0.177555i
$$529$$ −20.6575 + 7.51870i −0.898151 + 0.326900i
$$530$$ 0.128153 0.00556659
$$531$$ 4.03374 9.45014i 0.175049 0.410101i
$$532$$ 0.229847 + 1.99331i 0.00996515 + 0.0864209i
$$533$$ −0.117572 + 0.140117i −0.00509261 + 0.00606914i
$$534$$ −0.125146 + 0.0826519i −0.00541559 + 0.00357670i
$$535$$ −35.8290 42.6994i −1.54902 1.84605i
$$536$$ 0.208719 0.573451i 0.00901528 0.0247693i
$$537$$ 4.29810 14.4569i 0.185477 0.623860i
$$538$$ −0.146781 0.403277i −0.00632817 0.0173865i
$$539$$ 8.21847 + 35.1627i 0.353995 + 1.51457i
$$540$$ −0.237164 41.4824i −0.0102059 1.78512i
$$541$$ 10.7693 18.6530i 0.463010 0.801957i −0.536099 0.844155i $$-0.680103\pi$$
0.999109 + 0.0421981i $$0.0134361\pi$$
$$542$$ −0.249371 0.209247i −0.0107114 0.00898795i
$$543$$ 0.619426 2.08347i 0.0265821 0.0894103i
$$544$$ 0.646991 0.114082i 0.0277395 0.00489123i
$$545$$ 1.26516 + 7.17510i 0.0541936 + 0.307347i
$$546$$ 0.0163384 0.0449389i 0.000699221 0.00192321i
$$547$$ −20.2027 16.9521i −0.863805 0.724819i 0.0989790 0.995090i $$-0.468442\pi$$
−0.962784 + 0.270271i $$0.912887\pi$$
$$548$$ −11.2299 + 6.48357i −0.479716 + 0.276964i
$$549$$ 17.6431 + 16.5188i 0.752989 + 0.705004i
$$550$$ 0.456015 0.789841i 0.0194445 0.0336789i
$$551$$ 1.67438 + 1.40497i 0.0713309 + 0.0598537i
$$552$$ 0.0128947 0.112175i 0.000548836 0.00477448i
$$553$$ 3.29529 + 0.786404i 0.140130 + 0.0334413i
$$554$$ −0.129401 + 0.355526i −0.00549771 + 0.0151048i
$$555$$ 4.87075 42.3721i 0.206752 1.79859i
$$556$$ 3.84108 + 10.5533i 0.162898 + 0.447559i
$$557$$ 26.6538 + 15.3886i 1.12936 + 0.652036i 0.943774 0.330592i $$-0.107248\pi$$
0.185586 + 0.982628i $$0.440582\pi$$
$$558$$ 0.0170062 0.312501i 0.000719932 0.0132292i
$$559$$ −4.66998 2.69621i −0.197519 0.114038i
$$560$$ 37.7704 18.8956i 1.59609 0.798485i
$$561$$ 1.81756 + 30.2142i 0.0767373 + 1.27564i
$$562$$ 0.133593 + 0.0486238i 0.00563527 + 0.00205107i
$$563$$ −18.2008 6.62454i −0.767071 0.279191i −0.0713000 0.997455i $$-0.522715\pi$$
−0.695771 + 0.718264i $$0.744937\pi$$
$$564$$ 5.92318 + 24.7813i 0.249411 + 1.04348i
$$565$$ 16.2720 + 2.86919i 0.684566 + 0.120708i
$$566$$ 0.482422 0.0202777
$$567$$ −18.3334 15.1949i −0.769932 0.638126i
$$568$$ −0.640040 −0.0268555
$$569$$ 41.8969 + 7.38755i 1.75641 + 0.309702i 0.956784 0.290799i $$-0.0939209\pi$$
0.799624 + 0.600501i $$0.205032\pi$$
$$570$$ −0.00985382 0.0412262i −0.000412731 0.00172678i
$$571$$ −28.7214 10.4537i −1.20195 0.437476i −0.338048 0.941129i $$-0.609767\pi$$
−0.863906 + 0.503653i $$0.831989\pi$$
$$572$$ −6.25782 2.27766i −0.261653 0.0952338i
$$573$$ −0.922351 15.3327i −0.0385317 0.640533i
$$574$$ 0.00667414 0.0101133i 0.000278573 0.000422121i
$$575$$ −9.55163 5.51464i −0.398331 0.229976i
$$576$$ 20.0861 + 13.1014i 0.836920 + 0.545892i
$$577$$ 6.22559 + 3.59435i 0.259175 + 0.149635i 0.623958 0.781458i $$-0.285524\pi$$
−0.364783 + 0.931092i $$0.618857\pi$$
$$578$$ 0.0305370 + 0.0838996i 0.00127017 + 0.00348976i
$$579$$ −4.98682 + 43.3818i −0.207245 + 1.80289i
$$580$$ 15.7369 43.2368i 0.653439 1.79531i
$$581$$ 6.48702 + 21.7913i 0.269127 + 0.904054i
$$582$$ −0.0240055 + 0.208831i −0.000995061 + 0.00865632i
$$583$$ −7.84800 6.58526i −0.325031 0.272733i
$$584$$ 0.229150 0.396900i 0.00948230 0.0164238i
$$585$$ 1.75433 7.52988i 0.0725326 0.311322i
$$586$$ 0.0312067 0.0180172i 0.00128914 0.000744283i
$$587$$ −17.1076 14.3550i −0.706107 0.592495i 0.217396 0.976083i $$-0.430244\pi$$
−0.923504 + 0.383589i $$0.874688\pi$$
$$588$$ 5.61971 23.5853i 0.231753 0.972640i
$$589$$ 0.425032 + 2.41048i 0.0175131 + 0.0993220i
$$590$$ −0.217656 + 0.0383786i −0.00896074 + 0.00158002i
$$591$$ −6.30062 + 21.1924i −0.259173 + 0.871741i
$$592$$ 18.8929 + 15.8530i 0.776492 + 0.651554i
$$593$$ 17.8613 30.9367i 0.733476 1.27042i −0.221913 0.975066i $$-0.571230\pi$$
0.955389 0.295351i $$-0.0954364\pi$$
$$594$$ 0.276598 0.333490i 0.0113489 0.0136833i
$$595$$ −21.3229 28.7347i −0.874155 1.17801i
$$596$$ −2.42633 6.66629i −0.0993863 0.273062i
$$597$$ −10.0551 + 33.8209i −0.411529 + 1.38420i
$$598$$ 0.00359862 0.00988712i 0.000147158 0.000404314i
$$599$$ 23.8068 + 28.3718i 0.972718 + 1.15924i 0.987223 + 0.159345i $$0.0509382\pi$$
−0.0145052 + 0.999895i $$0.504617\pi$$
$$600$$ −1.02203 + 0.674991i −0.0417240 + 0.0275564i
$$601$$ 1.43732 1.71293i 0.0586295 0.0698719i −0.735933 0.677055i $$-0.763256\pi$$
0.794562 + 0.607183i $$0.207700\pi$$
$$602$$ 0.327792 + 0.142000i 0.0133598 + 0.00578748i
$$603$$ −16.9966 22.6497i −0.692156 0.922367i
$$604$$ −32.0767 −1.30518
$$605$$ −58.5659 + 21.3162i −2.38104 + 0.866628i
$$606$$ −0.317149 0.0364569i −0.0128833 0.00148096i
$$607$$ 20.5333 + 24.4707i 0.833422 + 0.993233i 0.999974 + 0.00720065i $$0.00229206\pi$$
−0.166552 + 0.986033i $$0.553263\pi$$
$$608$$ 0.0691120 + 0.0251547i 0.00280286 + 0.00102016i
$$609$$ −13.2137 22.8681i −0.535445 0.926663i
$$610$$ 0.0902750 0.511975i 0.00365513 0.0207293i
$$611$$ 4.74880i 0.192116i
$$612$$ 7.97847 18.6917i 0.322511 0.755569i
$$613$$ −10.0436 −0.405657 −0.202828 0.979214i $$-0.565013\pi$$
−0.202828 + 0.979214i $$0.565013\pi$$
$$614$$ 0.227325 0.0827395i 0.00917409 0.00333909i
$$615$$ 0.875958 1.75249i 0.0353220 0.0706674i
$$616$$ 0.858279 + 0.204824i 0.0345811 + 0.00825260i
$$617$$ 20.1274 + 23.9869i 0.810298 + 0.965675i 0.999869 0.0161920i $$-0.00515428\pi$$
−0.189571 + 0.981867i $$0.560710\pi$$
$$618$$ 0.256919 + 0.0763833i 0.0103348 + 0.00307259i
$$619$$ 18.5528 22.1104i 0.745701 0.888691i −0.251154 0.967947i $$-0.580810\pi$$
0.996854 + 0.0792558i $$0.0252544\pi$$
$$620$$ 44.6221 25.7626i 1.79207 1.03465i
$$621$$ −4.03293 3.34492i −0.161836 0.134227i
$$622$$ 0.0732000i 0.00293505i
$$623$$ −12.6755 + 6.34127i −0.507835 + 0.254057i
$$624$$ 3.07420 + 3.24605i 0.123067 + 0.129946i
$$625$$ 6.93691 + 39.3412i 0.277476 + 1.57365i
$$626$$ −0.150588 + 0.126358i −0.00601871 + 0.00505030i
$$627$$ −1.51501 + 3.03102i −0.0605037 + 0.121047i
$$628$$ 4.19646 + 11.5297i 0.167457 + 0.460084i
$$629$$ 10.4478 18.0961i 0.416581 0.721539i
$$630$$ −0.0583119 + 0.508855i −0.00232320 + 0.0202733i
$$631$$ 4.47416 + 7.74947i 0.178113 + 0.308501i 0.941234 0.337754i $$-0.109667\pi$$
−0.763121 + 0.646256i $$0.776334\pi$$
$$632$$ 0.0532123 0.0634160i 0.00211667 0.00252255i
$$633$$ −1.36878 + 0.593531i −0.0544041 + 0.0235907i
$$634$$ 0.0954208 + 0.541158i 0.00378964 + 0.0214921i
$$635$$ −19.3514 + 16.2377i −0.767937 + 0.644375i
$$636$$ 2.73654 + 6.31091i 0.108511 + 0.250244i
$$637$$ 2.04059 4.03187i 0.0808510 0.159749i
$$638$$ 0.416183 0.240284i 0.0164769 0.00951292i
$$639$$ −16.2257 + 24.8760i −0.641878 + 0.984078i
$$640$$ 2.06426i 0.0815971i
$$641$$ −28.5119 5.02742i −1.12615 0.198571i −0.420613 0.907240i $$-0.638185\pi$$
−0.705541 + 0.708669i $$0.749296\pi$$
$$642$$ −0.174765 + 0.349645i −0.00689742 + 0.0137994i
$$643$$ −12.3352 + 2.17502i −0.486451 + 0.0857744i −0.411494 0.911412i $$-0.634993\pi$$
−0.0749567 + 0.997187i $$0.523882\pi$$
$$644$$ 1.23840 5.18929i 0.0487997 0.204487i
$$645$$ 55.3654 + 16.4604i 2.18001 + 0.648128i
$$646$$ 0.00360605 0.0204509i 0.000141878 0.000804632i
$$647$$ −4.53468 7.85429i −0.178277 0.308784i 0.763014 0.646382i $$-0.223719\pi$$
−0.941290 + 0.337598i $$0.890385\pi$$
$$648$$ −0.532497 + 0.234527i −0.0209185 + 0.00921310i
$$649$$ 15.3012 + 8.83418i 0.600626 + 0.346772i
$$650$$ −0.107248 + 0.0390352i −0.00420662 + 0.00153109i
$$651$$ 5.12555 29.1286i 0.200886 1.14164i
$$652$$ 4.84681 4.06695i 0.189816 0.159274i
$$653$$ 8.08778 22.2210i 0.316499 0.869575i −0.674806 0.737995i $$-0.735773\pi$$
0.991306 0.131580i $$-0.0420049\pi$$
$$654$$ 0.0426341 0.0281574i 0.00166713 0.00110104i
$$655$$ −2.72068 + 15.4297i −0.106306 + 0.602890i
$$656$$ 0.566457 + 0.981131i 0.0221164 + 0.0383067i
$$657$$ −9.61681 18.9680i −0.375187 0.740013i
$$658$$ −0.0360364 0.312519i −0.00140484 0.0121833i
$$659$$ 42.5738 + 7.50690i 1.65844 + 0.292427i 0.922895 0.385051i $$-0.125816\pi$$
0.735543 + 0.677478i $$0.236927\pi$$
$$660$$ 70.8652 + 8.14609i 2.75842 + 0.317086i
$$661$$ −15.4143 + 2.71796i −0.599548 + 0.105717i −0.465182 0.885215i $$-0.654011\pi$$
−0.134367 + 0.990932i $$0.542900\pi$$
$$662$$ 0.529904 0.0934364i 0.0205953 0.00363151i
$$663$$ 2.25614 3.04261i 0.0876213 0.118165i
$$664$$ 0.547136 + 0.0964749i 0.0212330 + 0.00374395i
$$665$$ −0.458862 3.97939i −0.0177939 0.154314i
$$666$$ −0.286206 + 0.0868744i −0.0110902 + 0.00336631i
$$667$$ −2.90577 5.03295i −0.112512 0.194877i
$$668$$ 2.66062 15.0891i 0.102942 0.583816i
$$669$$ 24.4165 + 12.2042i 0.943998 + 0.471843i
$$670$$ −0.208327 + 0.572374i −0.00804838 + 0.0221127i
$$671$$ −31.8368 + 26.7142i −1.22904 + 1.03129i
$$672$$ −0.680987 0.571007i −0.0262697 0.0220271i
$$673$$ 0.784137 0.285403i 0.0302263 0.0110015i −0.326863 0.945072i $$-0.605991\pi$$
0.357089 + 0.934070i $$0.383769\pi$$
$$674$$ −0.388456 0.224275i −0.0149628 0.00863875i
$$675$$ 0.324933 + 56.8340i 0.0125067 + 2.18754i
$$676$$ −12.5816 21.7920i −0.483909 0.838154i
$$677$$ −3.61744 + 20.5155i −0.139029 + 0.788475i 0.832939 + 0.553364i $$0.186656\pi$$
−0.971969 + 0.235111i $$0.924455\pi$$
$$678$$ −0.0269365 0.112697i −0.00103449 0.00432808i
$$679$$ −4.61124 + 19.3226i −0.176963 + 0.741533i
$$680$$ −0.861073 + 0.151830i −0.0330206 + 0.00582243i
$$681$$ −9.03454 13.6795i −0.346204 0.524199i
$$682$$ 0.529978 + 0.0934494i 0.0202939 + 0.00357836i
$$683$$ 17.5517i 0.671596i 0.941934 + 0.335798i $$0.109006\pi$$
−0.941934 + 0.335798i $$0.890994\pi$$
$$684$$ 1.81978 1.36559i 0.0695810 0.0522145i
$$685$$ 22.4190 12.9436i 0.856587 0.494551i
$$686$$ −0.103695 + 0.280823i −0.00395910 + 0.0107219i
$$687$$ −1.89915 + 2.56118i −0.0724571 + 0.0977150i
$$688$$ −25.5858 + 21.4690i −0.975448 + 0.818498i
$$689$$ 0.222623 + 1.26256i 0.00848128 + 0.0480997i
$$690$$ −0.0128705 + 0.111964i −0.000489972 + 0.00426241i
$$691$$ −16.8826 + 20.1199i −0.642245 + 0.765398i −0.984723 0.174128i $$-0.944289\pi$$
0.342478 + 0.939526i $$0.388734\pi$$
$$692$$ −1.58186 2.73985i −0.0601331 0.104154i
$$693$$ 29.7190 28.1656i 1.12893 1.06992i
$$694$$ 0.0986965 0.170947i 0.00374647 0.00648907i
$$695$$ −7.66823 21.0683i −0.290873 0.799166i
$$696$$ −0.644210 + 0.0387530i −0.0244187 + 0.00146893i
$$697$$ 0.735294 0.616985i 0.0278512 0.0233700i
$$698$$ −0.0312401 0.177171i −0.00118245 0.00670603i
$$699$$ −17.7764 + 4.24887i −0.672364 + 0.160707i
$$700$$ −51.7551 + 25.8918i −1.95616 + 0.978619i
$$701$$ 8.38616i 0.316741i −0.987380 0.158370i $$-0.949376\pi$$
0.987380 0.158370i $$-0.0506240\pi$$
$$702$$ −0.0533407 + 0.00972017i −0.00201322 + 0.000366864i
$$703$$ 2.02584 1.16962i 0.0764060 0.0441130i
$$704$$ −26.5064 + 31.5891i −0.998999 + 1.19056i
$$705$$ −11.8249 49.4728i −0.445351 1.86325i
$$706$$ 0.204029 + 0.243152i 0.00767874 + 0.00915116i
$$707$$ −29.3450 7.00303i −1.10363 0.263376i
$$708$$ −6.53772 9.89898i −0.245702 0.372026i
$$709$$ 7.49554 2.72815i 0.281501 0.102458i −0.197411 0.980321i $$-0.563253\pi$$
0.478912 + 0.877863i $$0.341031\pi$$
$$710$$ 0.638838 0.0239752
$$711$$ −1.11575 3.67583i −0.0418440 0.137854i
$$712$$ 0.346332i 0.0129794i
$$713$$ 1.13009 6.40908i 0.0423223 0.240022i
$$714$$ −0.125388 + 0.217355i −0.00469252 + 0.00813432i
$$715$$ 12.4930 + 4.54706i 0.467210 + 0.170051i
$$716$$ −11.1930 13.3393i −0.418302 0.498513i
$$717$$ −4.93295 + 6.65253i −0.184224 + 0.248443i
$$718$$ −0.455725 + 0.165870i −0.0170075 + 0.00619022i
$$719$$ −49.6729 −1.85249 −0.926243 0.376926i $$-0.876981\pi$$
−0.926243 + 0.376926i $$0.876981\pi$$
$$720$$ −40.1098 26.1622i −1.49481 0.975007i
$$721$$ 23.2428 + 10.0688i 0.865608 + 0.374982i
$$722$$ −0.195913 + 0.233479i −0.00729111 + 0.00868921i
$$723$$ 13.5214 + 6.75844i 0.502864 + 0.251349i
$$724$$ −1.61310 1.92241i −0.0599502 0.0714459i
$$725$$ −21.5608 + 59.2377i −0.800747 + 2.20003i
$$726$$ 0.300537 + 0.317337i 0.0111540 + 0.0117775i
$$727$$ 10.9113 + 29.9786i 0.404678 + 1.11184i 0.959949 + 0.280174i $$0.0903923\pi$$
−0.555271 + 0.831669i $$0.687386\pi$$
$$728$$ −0.0658012 0.0886735i −0.00243875 0.00328646i
$$729$$ −4.38416 + 26.6417i −0.162376 + 0.986729i
$$730$$ −0.228720 + 0.396154i −0.00846530 + 0.0146623i
$$731$$ 21.6775 + 18.1896i 0.801771 + 0.672766i
$$732$$ 27.1400 6.48696i 1.00312 0.239765i
$$733$$ 36.7025 6.47164i 1.35564 0.239035i 0.551845 0.833946i $$-0.313924\pi$$
0.803792 + 0.594911i $$0.202813\pi$$
$$734$$ −7.61473e−5 0 0.000431853i −2.81065e−6 0 1.59400e-5i
$$735$$ −11.2191 + 47.0851i −0.413821 + 1.73676i
$$736$$ −0.149801 0.125698i −0.00552173 0.00463328i
$$737$$ 42.1699 24.3468i 1.55335 0.896826i
$$738$$ −0.0137191 0.000746594i −0.000505009 2.74825e-5i
$$739$$ 24.4802 42.4009i 0.900518 1.55974i 0.0736953 0.997281i $$-0.476521\pi$$
0.826823 0.562462i $$-0.190146\pi$$
$$740$$ −37.7222 31.6527i −1.38670 1.16358i
$$741$$ 0.389043 0.168697i 0.0142919 0.00619724i
$$742$$ −0.0242318 0.0813998i −0.000889578 0.00298828i
$$743$$ 13.1684 36.1798i 0.483100 1.32731i −0.423721 0.905793i $$-0.639276\pi$$
0.906821 0.421515i $$-0.138501\pi$$
$$744$$ −0.580524 0.430467i −0.0212830 0.0157817i
$$745$$ 4.84387 + 13.3084i 0.177465 + 0.487582i
$$746$$ 0.393654 + 0.227276i 0.0144127 + 0.00832117i
$$747$$ 17.6201 18.8194i 0.644686 0.688566i
$$748$$ 30.2648 + 17.4734i 1.10659 + 0.638891i
$$749$$ −20.3470 + 30.8317i −0.743461 + 1.12656i
$$750$$ 0.553789 0.365747i 0.0202215 0.0133552i
$$751$$ 4.12197 + 1.50028i 0.150413 + 0.0547458i 0.416129 0.909305i $$-0.363386\pi$$
−0.265717 + 0.964051i $$0.585609\pi$$
$$752$$ 27.6395 + 10.0599i 1.00791 + 0.366849i
$$753$$ −18.2115 5.41438i −0.663665 0.197311i
$$754$$ −0.0592244 0.0104429i −0.00215683 0.000380307i
$$755$$ 64.0371 2.33055
$$756$$ −26.3039 + 7.99436i −0.956662 + 0.290752i
$$757$$ 2.14305 0.0778906 0.0389453 0.999241i $$-0.487600\pi$$
0.0389453 + 0.999241i $$0.487600\pi$$
$$758$$ 0.00943540 + 0.00166372i 0.000342709 + 6.04289e-5i
$$759$$ 6.54159 6.19528i 0.237445 0.224874i
$$760$$ −0.0919803 0.0334781i −0.00333648 0.00121438i
$$761$$ −22.3023 8.11738i −0.808459 0.294255i −0.0954716 0.995432i $$-0.530436\pi$$
−0.712987 + 0.701177i $$0.752658\pi$$
$$762$$ 0.158460 + 0.0792036i 0.00574038 + 0.00286924i
$$763$$ 4.31824 2.16031i 0.156331 0.0782085i
$$764$$ −15.3584 8.86719i −0.555648 0.320804i
$$765$$ −15.9280 + 37.3157i −0.575879 + 1.34915i
$$766$$