Properties

 Label 570.2.u.h.301.1 Level $570$ Weight $2$ Character 570.301 Analytic conductor $4.551$ Analytic rank $0$ Dimension $6$ Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.u (of order $$9$$, 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: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: $$\Q(\zeta_{18})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{6} - x^{3} + 1$$ x^6 - x^3 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

 Embedding label 301.1 Root $$0.939693 - 0.342020i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.301 Dual form 570.2.u.h.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.766044 + 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(-0.939693 - 0.342020i) q^{6} +(0.733956 + 1.27125i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$$ $$q+(0.766044 + 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(-0.939693 - 0.342020i) q^{6} +(0.733956 + 1.27125i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-0.766044 + 0.642788i) q^{10} +(-1.67365 + 2.89884i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(2.09240 + 0.761570i) q^{13} +(-0.254900 + 1.44561i) q^{14} +(-0.173648 - 0.984808i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.43969 - 2.04715i) q^{17} +1.00000 q^{18} +(-4.07398 - 1.55007i) q^{19} -1.00000 q^{20} +(-1.12449 - 0.943555i) q^{21} +(-3.14543 + 1.14484i) q^{22} +(0.745100 + 4.22567i) q^{23} +(0.173648 - 0.984808i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(1.11334 + 1.92836i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-1.12449 + 0.943555i) q^{28} +(-5.08512 + 4.26692i) q^{29} +(0.500000 - 0.866025i) q^{30} +(5.40033 + 9.35365i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.581252 - 3.29644i) q^{33} +(-0.553033 - 3.13641i) q^{34} +(-1.37939 + 0.502055i) q^{35} +(0.766044 + 0.642788i) q^{36} -3.02229 q^{37} +(-2.12449 - 3.80612i) q^{38} -2.22668 q^{39} +(-0.766044 - 0.642788i) q^{40} +(2.93242 - 1.06731i) q^{41} +(-0.254900 - 1.44561i) q^{42} +(0.578726 - 3.28212i) q^{43} +(-3.14543 - 1.14484i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-2.14543 + 3.71599i) q^{46} +(-0.592396 + 0.497079i) q^{47} +(0.766044 - 0.642788i) q^{48} +(2.42262 - 4.19610i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.99273 + 1.08926i) q^{51} +(-0.386659 + 2.19285i) q^{52} +(-1.30928 - 7.42528i) q^{53} +(-0.939693 + 0.342020i) q^{54} +(-2.56418 - 2.15160i) q^{55} -1.46791 q^{56} +(4.35844 + 0.0632028i) q^{57} -6.63816 q^{58} +(3.37939 + 2.83564i) q^{59} +(0.939693 - 0.342020i) q^{60} +(1.16385 + 6.60051i) q^{61} +(-1.87551 + 10.6366i) q^{62} +(1.37939 + 0.502055i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.11334 + 1.92836i) q^{65} +(2.56418 - 2.15160i) q^{66} +(10.6985 - 8.97708i) q^{67} +(1.59240 - 2.75811i) q^{68} +(-2.14543 - 3.71599i) q^{69} +(-1.37939 - 0.502055i) q^{70} +(-1.47519 + 8.36619i) q^{71} +(0.173648 + 0.984808i) q^{72} +(13.0706 - 4.75730i) q^{73} +(-2.31521 - 1.94269i) q^{74} +1.00000 q^{75} +(0.819078 - 4.28125i) q^{76} -4.91353 q^{77} +(-1.70574 - 1.43128i) q^{78} +(1.49273 - 0.543308i) q^{79} +(-0.173648 - 0.984808i) q^{80} +(0.173648 - 0.984808i) q^{81} +(2.93242 + 1.06731i) q^{82} +(-0.397804 - 0.689016i) q^{83} +(0.733956 - 1.27125i) q^{84} +(2.43969 - 2.04715i) q^{85} +(2.55303 - 2.14225i) q^{86} +(3.31908 - 5.74881i) q^{87} +(-1.67365 - 2.89884i) q^{88} +(10.2442 + 3.72859i) q^{89} +(-0.173648 + 0.984808i) q^{90} +(0.567581 + 3.21891i) q^{91} +(-4.03209 + 1.46756i) q^{92} +(-8.27379 - 6.94253i) q^{93} -0.773318 q^{94} +(2.23396 - 3.74292i) q^{95} +1.00000 q^{96} +(5.36231 + 4.49951i) q^{97} +(4.55303 - 1.65717i) q^{98} +(0.581252 + 3.29644i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6 q + 9 q^{7} - 3 q^{8}+O(q^{10})$$ 6 * q + 9 * q^7 - 3 * q^8 $$6 q + 9 q^{7} - 3 q^{8} - 9 q^{11} - 3 q^{12} + 9 q^{13} - 3 q^{14} - 9 q^{17} + 6 q^{18} - 9 q^{19} - 6 q^{20} + 6 q^{21} - 3 q^{22} + 3 q^{23} - 3 q^{27} + 6 q^{28} - 9 q^{29} + 3 q^{30} + 18 q^{31} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 6 q^{37} - 6 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 3 q^{45} + 3 q^{46} - 12 q^{49} - 3 q^{50} - 9 q^{52} + 12 q^{53} + 3 q^{55} - 18 q^{56} + 18 q^{57} - 6 q^{58} + 9 q^{59} + 3 q^{61} - 24 q^{62} - 3 q^{63} - 3 q^{64} - 3 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} + 3 q^{70} - 36 q^{71} + 21 q^{73} - 21 q^{74} + 6 q^{75} - 12 q^{76} - 60 q^{77} - 9 q^{79} - 6 q^{82} - 3 q^{83} + 9 q^{84} + 9 q^{85} + 3 q^{86} + 3 q^{87} - 9 q^{88} + 3 q^{89} + 27 q^{91} - 15 q^{92} + 3 q^{93} - 18 q^{94} + 18 q^{95} + 6 q^{96} + 15 q^{98} + 6 q^{99}+O(q^{100})$$ 6 * q + 9 * q^7 - 3 * q^8 - 9 * q^11 - 3 * q^12 + 9 * q^13 - 3 * q^14 - 9 * q^17 + 6 * q^18 - 9 * q^19 - 6 * q^20 + 6 * q^21 - 3 * q^22 + 3 * q^23 - 3 * q^27 + 6 * q^28 - 9 * q^29 + 3 * q^30 + 18 * q^31 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 6 * q^37 - 6 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 3 * q^45 + 3 * q^46 - 12 * q^49 - 3 * q^50 - 9 * q^52 + 12 * q^53 + 3 * q^55 - 18 * q^56 + 18 * q^57 - 6 * q^58 + 9 * q^59 + 3 * q^61 - 24 * q^62 - 3 * q^63 - 3 * q^64 - 3 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 + 3 * q^70 - 36 * q^71 + 21 * q^73 - 21 * q^74 + 6 * q^75 - 12 * q^76 - 60 * q^77 - 9 * q^79 - 6 * q^82 - 3 * q^83 + 9 * q^84 + 9 * q^85 + 3 * q^86 + 3 * q^87 - 9 * q^88 + 3 * q^89 + 27 * q^91 - 15 * q^92 + 3 * q^93 - 18 * q^94 + 18 * q^95 + 6 * q^96 + 15 * q^98 + 6 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.766044 + 0.642788i 0.541675 + 0.454519i
$$3$$ −0.939693 + 0.342020i −0.542532 + 0.197465i
$$4$$ 0.173648 + 0.984808i 0.0868241 + 0.492404i
$$5$$ −0.173648 + 0.984808i −0.0776578 + 0.440419i
$$6$$ −0.939693 0.342020i −0.383628 0.139629i
$$7$$ 0.733956 + 1.27125i 0.277409 + 0.480487i 0.970740 0.240133i $$-0.0771909\pi$$
−0.693331 + 0.720619i $$0.743858\pi$$
$$8$$ −0.500000 + 0.866025i −0.176777 + 0.306186i
$$9$$ 0.766044 0.642788i 0.255348 0.214263i
$$10$$ −0.766044 + 0.642788i −0.242245 + 0.203267i
$$11$$ −1.67365 + 2.89884i −0.504624 + 0.874034i 0.495362 + 0.868687i $$0.335036\pi$$
−0.999986 + 0.00534749i $$0.998298\pi$$
$$12$$ −0.500000 0.866025i −0.144338 0.250000i
$$13$$ 2.09240 + 0.761570i 0.580326 + 0.211222i 0.615469 0.788161i $$-0.288966\pi$$
−0.0351431 + 0.999382i $$0.511189\pi$$
$$14$$ −0.254900 + 1.44561i −0.0681249 + 0.386356i
$$15$$ −0.173648 0.984808i −0.0448358 0.254276i
$$16$$ −0.939693 + 0.342020i −0.234923 + 0.0855050i
$$17$$ −2.43969 2.04715i −0.591712 0.496506i 0.297057 0.954860i $$-0.403995\pi$$
−0.888770 + 0.458354i $$0.848439\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −4.07398 1.55007i −0.934635 0.355609i
$$20$$ −1.00000 −0.223607
$$21$$ −1.12449 0.943555i −0.245383 0.205901i
$$22$$ −3.14543 + 1.14484i −0.670608 + 0.244081i
$$23$$ 0.745100 + 4.22567i 0.155364 + 0.881113i 0.958452 + 0.285253i $$0.0920777\pi$$
−0.803088 + 0.595860i $$0.796811\pi$$
$$24$$ 0.173648 0.984808i 0.0354458 0.201023i
$$25$$ −0.939693 0.342020i −0.187939 0.0684040i
$$26$$ 1.11334 + 1.92836i 0.218344 + 0.378183i
$$27$$ −0.500000 + 0.866025i −0.0962250 + 0.166667i
$$28$$ −1.12449 + 0.943555i −0.212508 + 0.178315i
$$29$$ −5.08512 + 4.26692i −0.944284 + 0.792348i −0.978326 0.207072i $$-0.933606\pi$$
0.0340421 + 0.999420i $$0.489162\pi$$
$$30$$ 0.500000 0.866025i 0.0912871 0.158114i
$$31$$ 5.40033 + 9.35365i 0.969928 + 1.67996i 0.695748 + 0.718286i $$0.255073\pi$$
0.274180 + 0.961678i $$0.411594\pi$$
$$32$$ −0.939693 0.342020i −0.166116 0.0604612i
$$33$$ 0.581252 3.29644i 0.101183 0.573837i
$$34$$ −0.553033 3.13641i −0.0948444 0.537890i
$$35$$ −1.37939 + 0.502055i −0.233159 + 0.0848628i
$$36$$ 0.766044 + 0.642788i 0.127674 + 0.107131i
$$37$$ −3.02229 −0.496861 −0.248431 0.968650i $$-0.579915\pi$$
−0.248431 + 0.968650i $$0.579915\pi$$
$$38$$ −2.12449 3.80612i −0.344637 0.617434i
$$39$$ −2.22668 −0.356554
$$40$$ −0.766044 0.642788i −0.121122 0.101634i
$$41$$ 2.93242 1.06731i 0.457967 0.166686i −0.102727 0.994710i $$-0.532757\pi$$
0.560694 + 0.828023i $$0.310535\pi$$
$$42$$ −0.254900 1.44561i −0.0393319 0.223063i
$$43$$ 0.578726 3.28212i 0.0882548 0.500518i −0.908352 0.418207i $$-0.862659\pi$$
0.996607 0.0823112i $$-0.0262302\pi$$
$$44$$ −3.14543 1.14484i −0.474191 0.172592i
$$45$$ 0.500000 + 0.866025i 0.0745356 + 0.129099i
$$46$$ −2.14543 + 3.71599i −0.316326 + 0.547893i
$$47$$ −0.592396 + 0.497079i −0.0864099 + 0.0725065i −0.684969 0.728572i $$-0.740184\pi$$
0.598560 + 0.801078i $$0.295740\pi$$
$$48$$ 0.766044 0.642788i 0.110569 0.0927784i
$$49$$ 2.42262 4.19610i 0.346088 0.599443i
$$50$$ −0.500000 0.866025i −0.0707107 0.122474i
$$51$$ 2.99273 + 1.08926i 0.419065 + 0.152527i
$$52$$ −0.386659 + 2.19285i −0.0536200 + 0.304094i
$$53$$ −1.30928 7.42528i −0.179843 1.01994i −0.932404 0.361418i $$-0.882293\pi$$
0.752561 0.658523i $$-0.228818\pi$$
$$54$$ −0.939693 + 0.342020i −0.127876 + 0.0465430i
$$55$$ −2.56418 2.15160i −0.345754 0.290122i
$$56$$ −1.46791 −0.196158
$$57$$ 4.35844 + 0.0632028i 0.577290 + 0.00837141i
$$58$$ −6.63816 −0.871633
$$59$$ 3.37939 + 2.83564i 0.439958 + 0.369169i 0.835694 0.549196i $$-0.185066\pi$$
−0.395735 + 0.918365i $$0.629510\pi$$
$$60$$ 0.939693 0.342020i 0.121314 0.0441546i
$$61$$ 1.16385 + 6.60051i 0.149015 + 0.845109i 0.964055 + 0.265703i $$0.0856041\pi$$
−0.815039 + 0.579406i $$0.803285\pi$$
$$62$$ −1.87551 + 10.6366i −0.238191 + 1.35085i
$$63$$ 1.37939 + 0.502055i 0.173786 + 0.0632530i
$$64$$ −0.500000 0.866025i −0.0625000 0.108253i
$$65$$ −1.11334 + 1.92836i −0.138093 + 0.239184i
$$66$$ 2.56418 2.15160i 0.315628 0.264844i
$$67$$ 10.6985 8.97708i 1.30703 1.09672i 0.318140 0.948044i $$-0.396942\pi$$
0.988885 0.148681i $$-0.0475027\pi$$
$$68$$ 1.59240 2.75811i 0.193106 0.334470i
$$69$$ −2.14543 3.71599i −0.258279 0.447353i
$$70$$ −1.37939 0.502055i −0.164868 0.0600071i
$$71$$ −1.47519 + 8.36619i −0.175072 + 0.992884i 0.762988 + 0.646412i $$0.223731\pi$$
−0.938060 + 0.346472i $$0.887380\pi$$
$$72$$ 0.173648 + 0.984808i 0.0204646 + 0.116061i
$$73$$ 13.0706 4.75730i 1.52980 0.556800i 0.566224 0.824252i $$-0.308404\pi$$
0.963571 + 0.267452i $$0.0861816\pi$$
$$74$$ −2.31521 1.94269i −0.269137 0.225833i
$$75$$ 1.00000 0.115470
$$76$$ 0.819078 4.28125i 0.0939547 0.491093i
$$77$$ −4.91353 −0.559949
$$78$$ −1.70574 1.43128i −0.193137 0.162061i
$$79$$ 1.49273 0.543308i 0.167945 0.0611269i −0.256679 0.966497i $$-0.582628\pi$$
0.424624 + 0.905370i $$0.360406\pi$$
$$80$$ −0.173648 0.984808i −0.0194145 0.110105i
$$81$$ 0.173648 0.984808i 0.0192942 0.109423i
$$82$$ 2.93242 + 1.06731i 0.323831 + 0.117865i
$$83$$ −0.397804 0.689016i −0.0436646 0.0756293i 0.843367 0.537338i $$-0.180570\pi$$
−0.887032 + 0.461708i $$0.847237\pi$$
$$84$$ 0.733956 1.27125i 0.0800811 0.138705i
$$85$$ 2.43969 2.04715i 0.264622 0.222044i
$$86$$ 2.55303 2.14225i 0.275301 0.231005i
$$87$$ 3.31908 5.74881i 0.355842 0.616337i
$$88$$ −1.67365 2.89884i −0.178411 0.309018i
$$89$$ 10.2442 + 3.72859i 1.08589 + 0.395230i 0.822095 0.569350i $$-0.192805\pi$$
0.263790 + 0.964580i $$0.415027\pi$$
$$90$$ −0.173648 + 0.984808i −0.0183041 + 0.103808i
$$91$$ 0.567581 + 3.21891i 0.0594987 + 0.337434i
$$92$$ −4.03209 + 1.46756i −0.420374 + 0.153004i
$$93$$ −8.27379 6.94253i −0.857952 0.719907i
$$94$$ −0.773318 −0.0797617
$$95$$ 2.23396 3.74292i 0.229199 0.384015i
$$96$$ 1.00000 0.102062
$$97$$ 5.36231 + 4.49951i 0.544460 + 0.456856i 0.873060 0.487613i $$-0.162132\pi$$
−0.328600 + 0.944469i $$0.606577\pi$$
$$98$$ 4.55303 1.65717i 0.459926 0.167399i
$$99$$ 0.581252 + 3.29644i 0.0584180 + 0.331305i
$$100$$ 0.173648 0.984808i 0.0173648 0.0984808i
$$101$$ 4.65910 + 1.69577i 0.463598 + 0.168736i 0.563250 0.826287i $$-0.309551\pi$$
−0.0996522 + 0.995022i $$0.531773\pi$$
$$102$$ 1.59240 + 2.75811i 0.157671 + 0.273094i
$$103$$ 1.02822 1.78093i 0.101313 0.175480i −0.810913 0.585167i $$-0.801029\pi$$
0.912226 + 0.409687i $$0.134362\pi$$
$$104$$ −1.70574 + 1.43128i −0.167261 + 0.140349i
$$105$$ 1.12449 0.943555i 0.109739 0.0920815i
$$106$$ 3.76991 6.52968i 0.366166 0.634219i
$$107$$ 0.481582 + 0.834124i 0.0465563 + 0.0806378i 0.888364 0.459139i $$-0.151842\pi$$
−0.841808 + 0.539777i $$0.818509\pi$$
$$108$$ −0.939693 0.342020i −0.0904220 0.0329109i
$$109$$ 2.07398 11.7621i 0.198651 1.12661i −0.708471 0.705739i $$-0.750615\pi$$
0.907123 0.420867i $$-0.138274\pi$$
$$110$$ −0.581252 3.29644i −0.0554202 0.314304i
$$111$$ 2.84002 1.03368i 0.269563 0.0981129i
$$112$$ −1.12449 0.943555i −0.106254 0.0891576i
$$113$$ −14.4534 −1.35966 −0.679829 0.733371i $$-0.737946\pi$$
−0.679829 + 0.733371i $$0.737946\pi$$
$$114$$ 3.29813 + 2.84997i 0.308898 + 0.266924i
$$115$$ −4.29086 −0.400125
$$116$$ −5.08512 4.26692i −0.472142 0.396174i
$$117$$ 2.09240 0.761570i 0.193442 0.0704072i
$$118$$ 0.766044 + 4.34445i 0.0705201 + 0.399939i
$$119$$ 0.811804 4.60397i 0.0744179 0.422045i
$$120$$ 0.939693 + 0.342020i 0.0857818 + 0.0312220i
$$121$$ −0.102196 0.177009i −0.00929059 0.0160918i
$$122$$ −3.35117 + 5.80439i −0.303400 + 0.525505i
$$123$$ −2.39053 + 2.00589i −0.215547 + 0.180865i
$$124$$ −8.27379 + 6.94253i −0.743008 + 0.623458i
$$125$$ 0.500000 0.866025i 0.0447214 0.0774597i
$$126$$ 0.733956 + 1.27125i 0.0653860 + 0.113252i
$$127$$ 17.7738 + 6.46913i 1.57717 + 0.574042i 0.974586 0.224014i $$-0.0719162\pi$$
0.602583 + 0.798057i $$0.294138\pi$$
$$128$$ 0.173648 0.984808i 0.0153485 0.0870455i
$$129$$ 0.578726 + 3.28212i 0.0509540 + 0.288974i
$$130$$ −2.09240 + 0.761570i −0.183515 + 0.0667941i
$$131$$ 12.4311 + 10.4309i 1.08611 + 0.911353i 0.996414 0.0846165i $$-0.0269665\pi$$
0.0896944 + 0.995969i $$0.471411\pi$$
$$132$$ 3.34730 0.291345
$$133$$ −1.01960 6.31672i −0.0884106 0.547729i
$$134$$ 13.9659 1.20647
$$135$$ −0.766044 0.642788i −0.0659306 0.0553223i
$$136$$ 2.99273 1.08926i 0.256624 0.0934035i
$$137$$ −2.17112 12.3130i −0.185491 1.05197i −0.925322 0.379181i $$-0.876206\pi$$
0.739831 0.672793i $$-0.234906\pi$$
$$138$$ 0.745100 4.22567i 0.0634271 0.359713i
$$139$$ −10.2378 3.72626i −0.868361 0.316058i −0.130858 0.991401i $$-0.541773\pi$$
−0.737503 + 0.675344i $$0.763995\pi$$
$$140$$ −0.733956 1.27125i −0.0620306 0.107440i
$$141$$ 0.386659 0.669713i 0.0325626 0.0564000i
$$142$$ −6.50774 + 5.46064i −0.546117 + 0.458247i
$$143$$ −5.70961 + 4.79093i −0.477461 + 0.400638i
$$144$$ −0.500000 + 0.866025i −0.0416667 + 0.0721688i
$$145$$ −3.31908 5.74881i −0.275634 0.477413i
$$146$$ 13.0706 + 4.75730i 1.08173 + 0.393717i
$$147$$ −0.841367 + 4.77163i −0.0693947 + 0.393557i
$$148$$ −0.524815 2.97637i −0.0431395 0.244656i
$$149$$ 4.39053 1.59802i 0.359686 0.130915i −0.155855 0.987780i $$-0.549813\pi$$
0.515541 + 0.856865i $$0.327591\pi$$
$$150$$ 0.766044 + 0.642788i 0.0625473 + 0.0524834i
$$151$$ 9.31820 0.758304 0.379152 0.925334i $$-0.376216\pi$$
0.379152 + 0.925334i $$0.376216\pi$$
$$152$$ 3.37939 2.75314i 0.274104 0.223309i
$$153$$ −3.18479 −0.257475
$$154$$ −3.76399 3.15836i −0.303311 0.254508i
$$155$$ −10.1493 + 3.69404i −0.815211 + 0.296713i
$$156$$ −0.386659 2.19285i −0.0309575 0.175569i
$$157$$ 3.82682 21.7030i 0.305413 1.73209i −0.316139 0.948713i $$-0.602387\pi$$
0.621553 0.783372i $$-0.286502\pi$$
$$158$$ 1.49273 + 0.543308i 0.118755 + 0.0432233i
$$159$$ 3.76991 + 6.52968i 0.298974 + 0.517838i
$$160$$ 0.500000 0.866025i 0.0395285 0.0684653i
$$161$$ −4.82501 + 4.04866i −0.380264 + 0.319079i
$$162$$ 0.766044 0.642788i 0.0601861 0.0505022i
$$163$$ 4.28699 7.42528i 0.335783 0.581593i −0.647852 0.761766i $$-0.724332\pi$$
0.983635 + 0.180173i $$0.0576658\pi$$
$$164$$ 1.56031 + 2.70253i 0.121840 + 0.211032i
$$165$$ 3.14543 + 1.14484i 0.244871 + 0.0891259i
$$166$$ 0.138156 0.783520i 0.0107230 0.0608129i
$$167$$ 2.27719 + 12.9146i 0.176214 + 0.999360i 0.936733 + 0.350044i $$0.113834\pi$$
−0.760519 + 0.649316i $$0.775055\pi$$
$$168$$ 1.37939 0.502055i 0.106422 0.0387344i
$$169$$ −6.16044 5.16923i −0.473880 0.397633i
$$170$$ 3.18479 0.244262
$$171$$ −4.11721 + 1.43128i −0.314851 + 0.109453i
$$172$$ 3.33275 0.254120
$$173$$ −1.67159 1.40263i −0.127089 0.106640i 0.577028 0.816724i $$-0.304212\pi$$
−0.704117 + 0.710084i $$0.748657\pi$$
$$174$$ 6.23783 2.27038i 0.472888 0.172117i
$$175$$ −0.254900 1.44561i −0.0192686 0.109278i
$$176$$ 0.581252 3.29644i 0.0438135 0.248479i
$$177$$ −4.14543 1.50881i −0.311590 0.113409i
$$178$$ 5.45084 + 9.44113i 0.408558 + 0.707642i
$$179$$ −10.2121 + 17.6879i −0.763291 + 1.32206i 0.177855 + 0.984057i $$0.443084\pi$$
−0.941146 + 0.338002i $$0.890249\pi$$
$$180$$ −0.766044 + 0.642788i −0.0570976 + 0.0479106i
$$181$$ −15.7895 + 13.2490i −1.17363 + 0.984789i −1.00000 2.31067e-5i $$-0.999993\pi$$
−0.173625 + 0.984812i $$0.555548\pi$$
$$182$$ −1.63429 + 2.83067i −0.121141 + 0.209823i
$$183$$ −3.35117 5.80439i −0.247725 0.429073i
$$184$$ −4.03209 1.46756i −0.297250 0.108190i
$$185$$ 0.524815 2.97637i 0.0385852 0.218827i
$$186$$ −1.87551 10.6366i −0.137519 0.779911i
$$187$$ 10.0175 3.64609i 0.732555 0.266628i
$$188$$ −0.592396 0.497079i −0.0432049 0.0362532i
$$189$$ −1.46791 −0.106775
$$190$$ 4.11721 1.43128i 0.298694 0.103836i
$$191$$ −13.9067 −1.00626 −0.503128 0.864212i $$-0.667817\pi$$
−0.503128 + 0.864212i $$0.667817\pi$$
$$192$$ 0.766044 + 0.642788i 0.0552845 + 0.0463892i
$$193$$ 4.27719 1.55677i 0.307879 0.112059i −0.183460 0.983027i $$-0.558730\pi$$
0.491339 + 0.870968i $$0.336508\pi$$
$$194$$ 1.21554 + 6.89365i 0.0872705 + 0.494936i
$$195$$ 0.386659 2.19285i 0.0276892 0.157033i
$$196$$ 4.55303 + 1.65717i 0.325217 + 0.118369i
$$197$$ 3.84137 + 6.65344i 0.273686 + 0.474038i 0.969803 0.243890i $$-0.0784237\pi$$
−0.696117 + 0.717929i $$0.745090\pi$$
$$198$$ −1.67365 + 2.89884i −0.118941 + 0.206012i
$$199$$ −8.48680 + 7.12127i −0.601613 + 0.504813i −0.891964 0.452107i $$-0.850672\pi$$
0.290351 + 0.956920i $$0.406228\pi$$
$$200$$ 0.766044 0.642788i 0.0541675 0.0454519i
$$201$$ −6.98293 + 12.0948i −0.492538 + 0.853100i
$$202$$ 2.47906 + 4.29385i 0.174426 + 0.302114i
$$203$$ −9.15657 3.33272i −0.642666 0.233911i
$$204$$ −0.553033 + 3.13641i −0.0387201 + 0.219593i
$$205$$ 0.541889 + 3.07321i 0.0378472 + 0.214642i
$$206$$ 1.93242 0.703343i 0.134638 0.0490042i
$$207$$ 3.28699 + 2.75811i 0.228462 + 0.191702i
$$208$$ −2.22668 −0.154393
$$209$$ 11.3118 9.21556i 0.782454 0.637454i
$$210$$ 1.46791 0.101295
$$211$$ 5.96972 + 5.00919i 0.410973 + 0.344847i 0.824717 0.565546i $$-0.191335\pi$$
−0.413744 + 0.910393i $$0.635779\pi$$
$$212$$ 7.08512 2.57877i 0.486608 0.177111i
$$213$$ −1.47519 8.36619i −0.101078 0.573242i
$$214$$ −0.167252 + 0.948531i −0.0114331 + 0.0648402i
$$215$$ 3.13176 + 1.13987i 0.213584 + 0.0777383i
$$216$$ −0.500000 0.866025i −0.0340207 0.0589256i
$$217$$ −7.92720 + 13.7303i −0.538134 + 0.932075i
$$218$$ 9.14930 7.67717i 0.619669 0.519964i
$$219$$ −10.6552 + 8.94080i −0.720014 + 0.604163i
$$220$$ 1.67365 2.89884i 0.112837 0.195440i
$$221$$ −3.54576 6.14144i −0.238514 0.413118i
$$222$$ 2.84002 + 1.03368i 0.190610 + 0.0693763i
$$223$$ −1.82934 + 10.3747i −0.122502 + 0.694743i 0.860258 + 0.509859i $$0.170302\pi$$
−0.982760 + 0.184885i $$0.940809\pi$$
$$224$$ −0.254900 1.44561i −0.0170312 0.0965889i
$$225$$ −0.939693 + 0.342020i −0.0626462 + 0.0228013i
$$226$$ −11.0719 9.29044i −0.736493 0.617991i
$$227$$ −22.9445 −1.52288 −0.761440 0.648236i $$-0.775507\pi$$
−0.761440 + 0.648236i $$0.775507\pi$$
$$228$$ 0.694593 + 4.30320i 0.0460005 + 0.284986i
$$229$$ −6.32770 −0.418146 −0.209073 0.977900i $$-0.567045\pi$$
−0.209073 + 0.977900i $$0.567045\pi$$
$$230$$ −3.28699 2.75811i −0.216738 0.181864i
$$231$$ 4.61721 1.68053i 0.303790 0.110571i
$$232$$ −1.15270 6.53731i −0.0756787 0.429195i
$$233$$ 1.84430 10.4596i 0.120824 0.685229i −0.862876 0.505415i $$-0.831339\pi$$
0.983701 0.179814i $$-0.0575495\pi$$
$$234$$ 2.09240 + 0.761570i 0.136784 + 0.0497854i
$$235$$ −0.386659 0.669713i −0.0252229 0.0436873i
$$236$$ −2.20574 + 3.82045i −0.143581 + 0.248690i
$$237$$ −1.21688 + 1.02108i −0.0790449 + 0.0663266i
$$238$$ 3.58125 3.00503i 0.232138 0.194787i
$$239$$ 6.22416 10.7806i 0.402607 0.697336i −0.591433 0.806354i $$-0.701437\pi$$
0.994040 + 0.109018i $$0.0347707\pi$$
$$240$$ 0.500000 + 0.866025i 0.0322749 + 0.0559017i
$$241$$ 11.5239 + 4.19437i 0.742322 + 0.270183i 0.685371 0.728194i $$-0.259640\pi$$
0.0569508 + 0.998377i $$0.481862\pi$$
$$242$$ 0.0354925 0.201288i 0.00228154 0.0129393i
$$243$$ 0.173648 + 0.984808i 0.0111395 + 0.0631754i
$$244$$ −6.29813 + 2.29233i −0.403197 + 0.146752i
$$245$$ 3.71167 + 3.11446i 0.237130 + 0.198975i
$$246$$ −3.12061 −0.198963
$$247$$ −7.34389 6.34597i −0.467281 0.403784i
$$248$$ −10.8007 −0.685843
$$249$$ 0.609470 + 0.511406i 0.0386236 + 0.0324091i
$$250$$ 0.939693 0.342020i 0.0594314 0.0216313i
$$251$$ 2.21941 + 12.5869i 0.140088 + 0.794477i 0.971181 + 0.238344i $$0.0766045\pi$$
−0.831093 + 0.556133i $$0.812284\pi$$
$$252$$ −0.254900 + 1.44561i −0.0160572 + 0.0910649i
$$253$$ −13.4966 4.91236i −0.848524 0.308837i
$$254$$ 9.45723 + 16.3804i 0.593400 + 1.02780i
$$255$$ −1.59240 + 2.75811i −0.0997197 + 0.172720i
$$256$$ 0.766044 0.642788i 0.0478778 0.0401742i
$$257$$ 2.87030 2.40847i 0.179044 0.150236i −0.548861 0.835914i $$-0.684938\pi$$
0.727905 + 0.685677i $$0.240494\pi$$
$$258$$ −1.66637 + 2.88624i −0.103744 + 0.179690i
$$259$$ −2.21823 3.84208i −0.137834 0.238735i
$$260$$ −2.09240 0.761570i −0.129765 0.0472306i
$$261$$ −1.15270 + 6.53731i −0.0713506 + 0.404649i
$$262$$ 2.81790 + 15.9811i 0.174090 + 0.987315i
$$263$$ 11.9474 4.34851i 0.736710 0.268141i 0.0537078 0.998557i $$-0.482896\pi$$
0.683002 + 0.730416i $$0.260674\pi$$
$$264$$ 2.56418 + 2.15160i 0.157814 + 0.132422i
$$265$$ 7.53983 0.463168
$$266$$ 3.27925 5.49427i 0.201064 0.336875i
$$267$$ −10.9017 −0.667172
$$268$$ 10.6985 + 8.97708i 0.653513 + 0.548362i
$$269$$ 15.0890 5.49194i 0.919992 0.334850i 0.161757 0.986831i $$-0.448284\pi$$
0.758235 + 0.651981i $$0.226062\pi$$
$$270$$ −0.173648 0.984808i −0.0105679 0.0599335i
$$271$$ 1.53297 8.69388i 0.0931211 0.528116i −0.902186 0.431347i $$-0.858038\pi$$
0.995307 0.0967683i $$-0.0308506\pi$$
$$272$$ 2.99273 + 1.08926i 0.181461 + 0.0660463i
$$273$$ −1.63429 2.83067i −0.0989114 0.171320i
$$274$$ 6.25150 10.8279i 0.377667 0.654138i
$$275$$ 2.56418 2.15160i 0.154626 0.129746i
$$276$$ 3.28699 2.75811i 0.197853 0.166019i
$$277$$ 1.35978 2.35522i 0.0817016 0.141511i −0.822279 0.569084i $$-0.807298\pi$$
0.903981 + 0.427573i $$0.140631\pi$$
$$278$$ −5.44743 9.43523i −0.326715 0.565888i
$$279$$ 10.1493 + 3.69404i 0.607623 + 0.221157i
$$280$$ 0.254900 1.44561i 0.0152332 0.0863917i
$$281$$ −4.50000 25.5208i −0.268447 1.52244i −0.759035 0.651050i $$-0.774329\pi$$
0.490588 0.871392i $$-0.336782\pi$$
$$282$$ 0.726682 0.264490i 0.0432733 0.0157502i
$$283$$ −18.4140 15.4512i −1.09460 0.918477i −0.0975486 0.995231i $$-0.531100\pi$$
−0.997050 + 0.0767534i $$0.975545\pi$$
$$284$$ −8.49525 −0.504100
$$285$$ −0.819078 + 4.28125i −0.0485180 + 0.253599i
$$286$$ −7.45336 −0.440727
$$287$$ 3.50908 + 2.94447i 0.207135 + 0.173807i
$$288$$ −0.939693 + 0.342020i −0.0553719 + 0.0201537i
$$289$$ −1.19072 6.75292i −0.0700425 0.397231i
$$290$$ 1.15270 6.53731i 0.0676891 0.383884i
$$291$$ −6.57785 2.39414i −0.385600 0.140347i
$$292$$ 6.95471 + 12.0459i 0.406993 + 0.704933i
$$293$$ −4.22328 + 7.31493i −0.246727 + 0.427343i −0.962616 0.270871i $$-0.912688\pi$$
0.715889 + 0.698214i $$0.246022\pi$$
$$294$$ −3.71167 + 3.11446i −0.216469 + 0.181639i
$$295$$ −3.37939 + 2.83564i −0.196755 + 0.165097i
$$296$$ 1.51114 2.61738i 0.0878335 0.152132i
$$297$$ −1.67365 2.89884i −0.0971149 0.168208i
$$298$$ 4.39053 + 1.59802i 0.254337 + 0.0925709i
$$299$$ −1.65910 + 9.40923i −0.0959482 + 0.544150i
$$300$$ 0.173648 + 0.984808i 0.0100256 + 0.0568579i
$$301$$ 4.59714 1.67322i 0.264975 0.0964430i
$$302$$ 7.13816 + 5.98962i 0.410755 + 0.344664i
$$303$$ −4.95811 −0.284836
$$304$$ 4.35844 + 0.0632028i 0.249974 + 0.00362493i
$$305$$ −6.70233 −0.383774
$$306$$ −2.43969 2.04715i −0.139468 0.117028i
$$307$$ −26.9971 + 9.82613i −1.54080 + 0.560807i −0.966238 0.257652i $$-0.917051\pi$$
−0.574566 + 0.818458i $$0.694829\pi$$
$$308$$ −0.853226 4.83889i −0.0486171 0.275721i
$$309$$ −0.357097 + 2.02520i −0.0203145 + 0.115209i
$$310$$ −10.1493 3.69404i −0.576442 0.209808i
$$311$$ −4.70826 8.15495i −0.266981 0.462425i 0.701100 0.713063i $$-0.252693\pi$$
−0.968081 + 0.250638i $$0.919359\pi$$
$$312$$ 1.11334 1.92836i 0.0630305 0.109172i
$$313$$ −20.2331 + 16.9776i −1.14364 + 0.959629i −0.999552 0.0299358i $$-0.990470\pi$$
−0.144089 + 0.989565i $$0.546025\pi$$
$$314$$ 16.8819 14.1656i 0.952701 0.799411i
$$315$$ −0.733956 + 1.27125i −0.0413537 + 0.0716267i
$$316$$ 0.794263 + 1.37570i 0.0446808 + 0.0773894i
$$317$$ −18.7763 6.83402i −1.05458 0.383837i −0.244192 0.969727i $$-0.578523\pi$$
−0.810390 + 0.585890i $$0.800745\pi$$
$$318$$ −1.30928 + 7.42528i −0.0734206 + 0.416389i
$$319$$ −3.85844 21.8823i −0.216031 1.22517i
$$320$$ 0.939693 0.342020i 0.0525304 0.0191195i
$$321$$ −0.737826 0.619109i −0.0411814 0.0345553i
$$322$$ −6.29860 −0.351007
$$323$$ 6.76604 + 12.1217i 0.376473 + 0.674470i
$$324$$ 1.00000 0.0555556
$$325$$ −1.70574 1.43128i −0.0946173 0.0793933i
$$326$$ 8.05690 2.93247i 0.446231 0.162415i
$$327$$ 2.07398 + 11.7621i 0.114691 + 0.650446i
$$328$$ −0.541889 + 3.07321i −0.0299208 + 0.169689i
$$329$$ −1.06670 0.388249i −0.0588093 0.0214048i
$$330$$ 1.67365 + 2.89884i 0.0921313 + 0.159576i
$$331$$ −12.3444 + 21.3811i −0.678507 + 1.17521i 0.296923 + 0.954901i $$0.404040\pi$$
−0.975430 + 0.220308i $$0.929294\pi$$
$$332$$ 0.609470 0.511406i 0.0334490 0.0280671i
$$333$$ −2.31521 + 1.94269i −0.126873 + 0.106459i
$$334$$ −6.55690 + 11.3569i −0.358778 + 0.621421i
$$335$$ 6.98293 + 12.0948i 0.381518 + 0.660809i
$$336$$ 1.37939 + 0.502055i 0.0752516 + 0.0273894i
$$337$$ 1.65776 9.40160i 0.0903037 0.512138i −0.905782 0.423744i $$-0.860716\pi$$
0.996086 0.0883937i $$-0.0281733\pi$$
$$338$$ −1.39646 7.91971i −0.0759574 0.430776i
$$339$$ 13.5817 4.94334i 0.737658 0.268485i
$$340$$ 2.43969 + 2.04715i 0.132311 + 0.111022i
$$341$$ −36.1530 −1.95780
$$342$$ −4.07398 1.55007i −0.220295 0.0838180i
$$343$$ 17.3878 0.938851
$$344$$ 2.55303 + 2.14225i 0.137650 + 0.115502i
$$345$$ 4.03209 1.46756i 0.217080 0.0790108i
$$346$$ −0.378918 2.14895i −0.0203708 0.115528i
$$347$$ 3.62819 20.5765i 0.194772 1.10460i −0.717972 0.696072i $$-0.754929\pi$$
0.912744 0.408533i $$-0.133959\pi$$
$$348$$ 6.23783 + 2.27038i 0.334383 + 0.121705i
$$349$$ 16.1766 + 28.0188i 0.865916 + 1.49981i 0.866135 + 0.499810i $$0.166597\pi$$
−0.000219262 1.00000i $$0.500070\pi$$
$$350$$ 0.733956 1.27125i 0.0392316 0.0679511i
$$351$$ −1.70574 + 1.43128i −0.0910455 + 0.0763963i
$$352$$ 2.56418 2.15160i 0.136671 0.114681i
$$353$$ 10.7023 18.5370i 0.569628 0.986624i −0.426975 0.904263i $$-0.640421\pi$$
0.996603 0.0823607i $$-0.0262459\pi$$
$$354$$ −2.20574 3.82045i −0.117234 0.203055i
$$355$$ −7.98293 2.90555i −0.423690 0.154210i
$$356$$ −1.89306 + 10.7361i −0.100332 + 0.569010i
$$357$$ 0.811804 + 4.60397i 0.0429652 + 0.243668i
$$358$$ −19.1925 + 6.98551i −1.01436 + 0.369196i
$$359$$ 11.9081 + 9.99206i 0.628484 + 0.527361i 0.900457 0.434944i $$-0.143232\pi$$
−0.271974 + 0.962305i $$0.587676\pi$$
$$360$$ −1.00000 −0.0527046
$$361$$ 14.1946 + 12.6299i 0.747084 + 0.664730i
$$362$$ −20.6117 −1.08333
$$363$$ 0.156574 + 0.131381i 0.00821801 + 0.00689573i
$$364$$ −3.07145 + 1.11792i −0.160988 + 0.0585948i
$$365$$ 2.41534 + 13.6981i 0.126425 + 0.716991i
$$366$$ 1.16385 6.60051i 0.0608353 0.345014i
$$367$$ 10.0198 + 3.64690i 0.523027 + 0.190366i 0.590022 0.807387i $$-0.299119\pi$$
−0.0669950 + 0.997753i $$0.521341\pi$$
$$368$$ −2.14543 3.71599i −0.111838 0.193710i
$$369$$ 1.56031 2.70253i 0.0812264 0.140688i
$$370$$ 2.31521 1.94269i 0.120362 0.100996i
$$371$$ 8.47843 7.11424i 0.440178 0.369353i
$$372$$ 5.40033 9.35365i 0.279994 0.484964i
$$373$$ 13.5351 + 23.4434i 0.700820 + 1.21386i 0.968179 + 0.250259i $$0.0805157\pi$$
−0.267359 + 0.963597i $$0.586151\pi$$
$$374$$ 10.0175 + 3.64609i 0.517995 + 0.188535i
$$375$$ −0.173648 + 0.984808i −0.00896715 + 0.0508553i
$$376$$ −0.134285 0.761570i −0.00692524 0.0392750i
$$377$$ −13.8897 + 5.05542i −0.715353 + 0.260367i
$$378$$ −1.12449 0.943555i −0.0578373 0.0485312i
$$379$$ −28.3432 −1.45589 −0.727946 0.685635i $$-0.759525\pi$$
−0.727946 + 0.685635i $$0.759525\pi$$
$$380$$ 4.07398 + 1.55007i 0.208991 + 0.0795167i
$$381$$ −18.9145 −0.969018
$$382$$ −10.6532 8.93907i −0.545064 0.457363i
$$383$$ 6.39945 2.32921i 0.326997 0.119017i −0.173305 0.984868i $$-0.555445\pi$$
0.500302 + 0.865851i $$0.333222\pi$$
$$384$$ 0.173648 + 0.984808i 0.00886145 + 0.0502558i
$$385$$ 0.853226 4.83889i 0.0434844 0.246612i
$$386$$ 4.27719 + 1.55677i 0.217703 + 0.0792375i
$$387$$ −1.66637 2.88624i −0.0847066 0.146716i
$$388$$ −3.50000 + 6.06218i −0.177686 + 0.307760i
$$389$$ 5.19072 4.35553i 0.263180 0.220834i −0.501643 0.865075i $$-0.667271\pi$$
0.764823 + 0.644240i $$0.222826\pi$$
$$390$$ 1.70574 1.43128i 0.0863734 0.0724758i
$$391$$ 6.83275 11.8347i 0.345547 0.598505i
$$392$$ 2.42262 + 4.19610i 0.122361 + 0.211935i
$$393$$ −15.2490 5.55017i −0.769209 0.279969i
$$394$$ −1.33409 + 7.56602i −0.0672106 + 0.381170i
$$395$$ 0.275845 + 1.56439i 0.0138792 + 0.0787131i
$$396$$ −3.14543 + 1.14484i −0.158064 + 0.0575305i
$$397$$ 22.2861 + 18.7003i 1.11851 + 0.938540i 0.998528 0.0542368i $$-0.0172726\pi$$
0.119980 + 0.992776i $$0.461717\pi$$
$$398$$ −11.0787 −0.555326
$$399$$ 3.11856 + 5.58705i 0.156123 + 0.279702i
$$400$$ 1.00000 0.0500000
$$401$$ −2.77513 2.32861i −0.138583 0.116285i 0.570861 0.821047i $$-0.306610\pi$$
−0.709444 + 0.704762i $$0.751054\pi$$
$$402$$ −13.1236 + 4.77660i −0.654546 + 0.238235i
$$403$$ 4.17617 + 23.6843i 0.208030 + 1.17980i
$$404$$ −0.860967 + 4.88279i −0.0428347 + 0.242928i
$$405$$ 0.939693 + 0.342020i 0.0466937 + 0.0169951i
$$406$$ −4.87211 8.43874i −0.241799 0.418808i
$$407$$ 5.05825 8.76114i 0.250728 0.434274i
$$408$$ −2.43969 + 2.04715i −0.120783 + 0.101349i
$$409$$ −6.72849 + 5.64588i −0.332703 + 0.279171i −0.793800 0.608179i $$-0.791900\pi$$
0.461097 + 0.887350i $$0.347456\pi$$
$$410$$ −1.56031 + 2.70253i −0.0770581 + 0.133469i
$$411$$ 6.25150 + 10.8279i 0.308364 + 0.534101i
$$412$$ 1.93242 + 0.703343i 0.0952034 + 0.0346512i
$$413$$ −1.12449 + 6.37727i −0.0553323 + 0.313805i
$$414$$ 0.745100 + 4.22567i 0.0366197 + 0.207680i
$$415$$ 0.747626 0.272114i 0.0366995 0.0133575i
$$416$$ −1.70574 1.43128i −0.0836306 0.0701744i
$$417$$ 10.8949 0.533524
$$418$$ 14.5890 + 0.211558i 0.713571 + 0.0103477i
$$419$$ 27.5672 1.34674 0.673372 0.739304i $$-0.264845\pi$$
0.673372 + 0.739304i $$0.264845\pi$$
$$420$$ 1.12449 + 0.943555i 0.0548693 + 0.0460408i
$$421$$ −0.634285 + 0.230861i −0.0309132 + 0.0112515i −0.357430 0.933940i $$-0.616347\pi$$
0.326517 + 0.945191i $$0.394125\pi$$
$$422$$ 1.35323 + 7.67453i 0.0658740 + 0.373590i
$$423$$ −0.134285 + 0.761570i −0.00652918 + 0.0370288i
$$424$$ 7.08512 + 2.57877i 0.344084 + 0.125236i
$$425$$ 1.59240 + 2.75811i 0.0772426 + 0.133788i
$$426$$ 4.24763 7.35710i 0.205798 0.356453i
$$427$$ −7.53667 + 6.32402i −0.364725 + 0.306041i
$$428$$ −0.737826 + 0.619109i −0.0356642 + 0.0299258i
$$429$$ 3.72668 6.45480i 0.179926 0.311641i
$$430$$ 1.66637 + 2.88624i 0.0803597 + 0.139187i
$$431$$ 0.226682 + 0.0825054i 0.0109189 + 0.00397414i 0.347474 0.937690i $$-0.387040\pi$$
−0.336555 + 0.941664i $$0.609262\pi$$
$$432$$ 0.173648 0.984808i 0.00835465 0.0473816i
$$433$$ 5.10488 + 28.9512i 0.245325 + 1.39131i 0.819736 + 0.572741i $$0.194120\pi$$
−0.574411 + 0.818567i $$0.694769\pi$$
$$434$$ −14.8983 + 5.42253i −0.715140 + 0.260290i
$$435$$ 5.08512 + 4.26692i 0.243813 + 0.204583i
$$436$$ 11.9436 0.571993
$$437$$ 3.51455 18.3702i 0.168124 0.878768i
$$438$$ −13.9094 −0.664618
$$439$$ −20.3384 17.0660i −0.970700 0.814514i 0.0119602 0.999928i $$-0.496193\pi$$
−0.982660 + 0.185414i $$0.940637\pi$$
$$440$$ 3.14543 1.14484i 0.149952 0.0545782i
$$441$$ −0.841367 4.77163i −0.0400651 0.227220i
$$442$$ 1.23143 6.98378i 0.0585731 0.332185i
$$443$$ −29.6498 10.7916i −1.40870 0.512726i −0.477954 0.878385i $$-0.658621\pi$$
−0.930749 + 0.365659i $$0.880844\pi$$
$$444$$ 1.51114 + 2.61738i 0.0717157 + 0.124215i
$$445$$ −5.45084 + 9.44113i −0.258394 + 0.447552i
$$446$$ −8.07011 + 6.77162i −0.382131 + 0.320646i
$$447$$ −3.57919 + 3.00330i −0.169290 + 0.142051i
$$448$$ 0.733956 1.27125i 0.0346761 0.0600608i
$$449$$ 1.84477 + 3.19524i 0.0870601 + 0.150792i 0.906267 0.422705i $$-0.138919\pi$$
−0.819207 + 0.573498i $$0.805586\pi$$
$$450$$ −0.939693 0.342020i −0.0442975 0.0161230i
$$451$$ −1.81386 + 10.2869i −0.0854115 + 0.484393i
$$452$$ −2.50980 14.2338i −0.118051 0.669501i
$$453$$ −8.75624 + 3.18701i −0.411404 + 0.149739i
$$454$$ −17.5765 14.7484i −0.824906 0.692178i
$$455$$ −3.26857 −0.153233
$$456$$ −2.23396 + 3.74292i −0.104615 + 0.175278i
$$457$$ −7.69728 −0.360064 −0.180032 0.983661i $$-0.557620\pi$$
−0.180032 + 0.983661i $$0.557620\pi$$
$$458$$ −4.84730 4.06736i −0.226499 0.190055i
$$459$$ 2.99273 1.08926i 0.139688 0.0508425i
$$460$$ −0.745100 4.22567i −0.0347405 0.197023i
$$461$$ 2.68938 15.2522i 0.125257 0.710367i −0.855898 0.517144i $$-0.826995\pi$$
0.981155 0.193222i $$-0.0618939\pi$$
$$462$$ 4.61721 + 1.68053i 0.214812 + 0.0781852i
$$463$$ −1.17483 2.03487i −0.0545990 0.0945682i 0.837434 0.546538i $$-0.184055\pi$$
−0.892033 + 0.451970i $$0.850721\pi$$
$$464$$ 3.31908 5.74881i 0.154084 0.266882i
$$465$$ 8.27379 6.94253i 0.383688 0.321952i
$$466$$ 8.13610 6.82700i 0.376897 0.316254i
$$467$$ 18.7913 32.5475i 0.869559 1.50612i 0.00711073 0.999975i $$-0.497737\pi$$
0.862448 0.506145i $$-0.168930\pi$$
$$468$$ 1.11334 + 1.92836i 0.0514642 + 0.0891386i
$$469$$ 19.2643 + 7.01163i 0.889542 + 0.323767i
$$470$$ 0.134285 0.761570i 0.00619412 0.0351286i
$$471$$ 3.82682 + 21.7030i 0.176330 + 1.00002i
$$472$$ −4.14543 + 1.50881i −0.190809 + 0.0694487i
$$473$$ 8.54576 + 7.17074i 0.392934 + 0.329711i
$$474$$ −1.58853 −0.0729634
$$475$$ 3.29813 + 2.84997i 0.151329 + 0.130765i
$$476$$ 4.67499 0.214278
$$477$$ −5.77584 4.84651i −0.264458 0.221906i
$$478$$ 11.6976 4.25757i 0.535035 0.194737i
$$479$$ −2.46404 13.9743i −0.112585 0.638501i −0.987918 0.154980i $$-0.950469\pi$$
0.875333 0.483521i $$-0.160642\pi$$
$$480$$ −0.173648 + 0.984808i −0.00792592 + 0.0449501i
$$481$$ −6.32383 2.30168i −0.288342 0.104948i
$$482$$ 6.13176 + 10.6205i 0.279294 + 0.483751i
$$483$$ 3.14930 5.45475i 0.143298 0.248200i
$$484$$ 0.156574 0.131381i 0.00711700 0.00597187i
$$485$$ −5.36231 + 4.49951i −0.243490 + 0.204312i
$$486$$ −0.500000 + 0.866025i −0.0226805 + 0.0392837i
$$487$$ −2.58260 4.47319i −0.117029 0.202699i 0.801560 0.597914i $$-0.204004\pi$$
−0.918589 + 0.395215i $$0.870670\pi$$
$$488$$ −6.29813 2.29233i −0.285103 0.103769i
$$489$$ −1.48886 + 8.44372i −0.0673284 + 0.381838i
$$490$$ 0.841367 + 4.77163i 0.0380091 + 0.215560i
$$491$$ 11.0505 4.02206i 0.498702 0.181513i −0.0804079 0.996762i $$-0.525622\pi$$
0.579110 + 0.815249i $$0.303400\pi$$
$$492$$ −2.39053 2.00589i −0.107773 0.0904326i
$$493$$ 21.1411 0.952149
$$494$$ −1.54664 9.58186i −0.0695865 0.431108i
$$495$$ −3.34730 −0.150450
$$496$$ −8.27379 6.94253i −0.371504 0.311729i
$$497$$ −11.7182 + 4.26509i −0.525634 + 0.191315i
$$498$$ 0.138156 + 0.783520i 0.00619091 + 0.0351104i
$$499$$ 5.43629 30.8307i 0.243362 1.38017i −0.580905 0.813971i $$-0.697301\pi$$
0.824267 0.566202i $$-0.191588\pi$$
$$500$$ 0.939693 + 0.342020i 0.0420243 + 0.0152956i
$$501$$ −6.55690 11.3569i −0.292941 0.507388i
$$502$$ −6.39053 + 11.0687i −0.285223 + 0.494021i
$$503$$ 19.4520 16.3222i 0.867323 0.727770i −0.0962099 0.995361i $$-0.530672\pi$$
0.963533 + 0.267591i $$0.0862276\pi$$
$$504$$ −1.12449 + 0.943555i −0.0500885 + 0.0420293i
$$505$$ −2.47906 + 4.29385i −0.110317 + 0.191074i
$$506$$ −7.18139 12.4385i −0.319252 0.552960i
$$507$$ 7.55690 + 2.75049i 0.335614 + 0.122153i
$$508$$ −3.28446 + 18.6271i −0.145724 + 0.826445i
$$509$$ −6.11112 34.6579i −0.270871 1.53618i −0.751780 0.659413i $$-0.770805\pi$$
0.480910 0.876770i $$-0.340306\pi$$
$$510$$ −2.99273 + 1.08926i −0.132520 + 0.0482334i
$$511$$ 15.6409 + 13.1243i 0.691914 + 0.580585i
$$512$$ 1.00000 0.0441942
$$513$$ 3.37939 2.75314i 0.149204 0.121554i
$$514$$ 3.74691 0.165269
$$515$$ 1.57532 + 1.32185i 0.0694170 + 0.0582478i
$$516$$ −3.13176 + 1.13987i −0.137868 + 0.0501799i
$$517$$ −0.449493 2.54920i −0.0197687 0.112114i
$$518$$ 0.770382 4.36905i 0.0338486 0.191965i
$$519$$ 2.05051 + 0.746324i 0.0900073 + 0.0327600i
$$520$$ −1.11334 1.92836i −0.0488232 0.0845643i
$$521$$ 5.37164 9.30396i 0.235336 0.407614i −0.724034 0.689764i $$-0.757714\pi$$
0.959370 + 0.282150i $$0.0910476\pi$$
$$522$$ −5.08512 + 4.26692i −0.222570 + 0.186758i
$$523$$ 20.8066 17.4588i 0.909809 0.763420i −0.0622739 0.998059i $$-0.519835\pi$$
0.972083 + 0.234639i $$0.0753908\pi$$
$$524$$ −8.11381 + 14.0535i −0.354453 + 0.613931i
$$525$$ 0.733956 + 1.27125i 0.0320324 + 0.0554818i
$$526$$ 11.9474 + 4.34851i 0.520933 + 0.189604i
$$527$$ 5.97313 33.8753i 0.260193 1.47563i
$$528$$ 0.581252 + 3.29644i 0.0252957 + 0.143459i
$$529$$ 4.31180 1.56937i 0.187470 0.0682334i
$$530$$ 5.77584 + 4.84651i 0.250887 + 0.210519i
$$531$$ 4.41147 0.191442
$$532$$ 6.04370 2.10100i 0.262028 0.0910898i
$$533$$ 6.94862 0.300978
$$534$$ −8.35117 7.00746i −0.361390 0.303242i
$$535$$ −0.905078 + 0.329421i −0.0391299 + 0.0142421i
$$536$$ 2.42514 + 13.7537i 0.104750 + 0.594068i
$$537$$ 3.54664 20.1140i 0.153049 0.867982i
$$538$$ 15.0890 + 5.49194i 0.650533 + 0.236775i
$$539$$ 8.10922 + 14.0456i 0.349289 + 0.604986i
$$540$$ 0.500000 0.866025i 0.0215166 0.0372678i
$$541$$ −9.69846 + 8.13798i −0.416969 + 0.349879i −0.827009 0.562189i $$-0.809959\pi$$
0.410039 + 0.912068i $$0.365515\pi$$
$$542$$ 6.76264 5.67453i 0.290480 0.243742i
$$543$$ 10.3059 17.8503i 0.442267 0.766030i
$$544$$ 1.59240 + 2.75811i 0.0682734 + 0.118253i
$$545$$ 11.2233 + 4.08494i 0.480752 + 0.174980i
$$546$$ 0.567581 3.21891i 0.0242902 0.137757i
$$547$$ 2.96657 + 16.8242i 0.126841 + 0.719352i 0.980197 + 0.198024i $$0.0634523\pi$$
−0.853356 + 0.521329i $$0.825437\pi$$
$$548$$ 11.7490 4.27628i 0.501891 0.182673i
$$549$$ 5.13429 + 4.30818i 0.219126 + 0.183869i
$$550$$ 3.34730 0.142729
$$551$$ 27.3307 9.50108i 1.16433 0.404760i
$$552$$ 4.29086 0.182631
$$553$$ 1.78627 + 1.49886i 0.0759601 + 0.0637381i
$$554$$ 2.55556 0.930148i 0.108575 0.0395182i
$$555$$ 0.524815 + 2.97637i 0.0222772 + 0.126340i
$$556$$ 1.89187 10.7293i 0.0802333 0.455026i
$$557$$ −16.9611 6.17334i −0.718665 0.261573i −0.0433061 0.999062i $$-0.513789\pi$$
−0.675359 + 0.737489i $$0.736011\pi$$
$$558$$ 5.40033 + 9.35365i 0.228614 + 0.395971i
$$559$$ 3.71048 6.42675i 0.156937 0.271822i
$$560$$ 1.12449 0.943555i 0.0475182 0.0398725i
$$561$$ −8.16637 + 6.85240i −0.344785 + 0.289309i
$$562$$ 12.9572 22.4426i 0.546568 0.946683i
$$563$$ 18.9718 + 32.8601i 0.799565 + 1.38489i 0.919899 + 0.392154i $$0.128270\pi$$
−0.120334 + 0.992733i $$0.538397\pi$$
$$564$$ 0.726682 + 0.264490i 0.0305988 + 0.0111371i
$$565$$ 2.50980 14.2338i 0.105588 0.598820i
$$566$$ −4.17412 23.6726i −0.175451 0.995033i
$$567$$ 1.37939 0.502055i 0.0579287 0.0210843i
$$568$$ −6.50774 5.46064i −0.273059 0.229123i
$$569$$ 11.5253 0.483165 0.241582 0.970380i $$-0.422334\pi$$
0.241582 + 0.970380i $$0.422334\pi$$
$$570$$ −3.37939 + 2.75314i −0.141547 + 0.115316i
$$571$$ −23.9932 −1.00408 −0.502042 0.864843i $$-0.667418\pi$$
−0.502042 + 0.864843i $$0.667418\pi$$
$$572$$ −5.70961 4.79093i −0.238731 0.200319i
$$573$$ 13.0680 4.75638i 0.545926 0.198701i
$$574$$ 0.795445 + 4.51119i 0.0332012 + 0.188294i
$$575$$ 0.745100 4.22567i 0.0310728 0.176223i
$$576$$ −0.939693 0.342020i −0.0391539 0.0142508i
$$577$$ −4.19119 7.25935i −0.174481 0.302211i 0.765500 0.643436i $$-0.222492\pi$$
−0.939982 + 0.341225i $$0.889158\pi$$
$$578$$ 3.42855 5.93842i 0.142609 0.247006i
$$579$$ −3.48680 + 2.92577i −0.144906 + 0.121591i
$$580$$ 5.08512 4.26692i 0.211148 0.177174i
$$581$$ 0.583940 1.01141i 0.0242259 0.0419605i
$$582$$ −3.50000 6.06218i −0.145080 0.251285i
$$583$$ 23.7160 + 8.63192i 0.982217 + 0.357498i
$$584$$ −2.41534 + 13.6981i −0.0999477 + 0.566831i
$$585$$ 0.386659 + 2.19285i 0.0159864 + 0.0906633i
$$586$$ −7.93717 + 2.88889i −0.327881 + 0.119339i
$$587$$ 11.2337 + 9.42620i 0.463665 + 0.389061i 0.844477 0.535591i $$-0.179911\pi$$
−0.380813 + 0.924652i $$0.624356\pi$$
$$588$$ −4.84524 −0.199814
$$589$$ −7.50206 46.4774i −0.309117 1.91507i
$$590$$ −4.41147 −0.181618
$$591$$ −5.88532 4.93837i −0.242090 0.203137i
$$592$$ 2.84002 1.03368i 0.116724 0.0424841i
$$593$$ 6.76563 + 38.3698i 0.277831 + 1.57566i 0.729822 + 0.683637i $$0.239603\pi$$
−0.451991 + 0.892023i $$0.649286\pi$$
$$594$$ 0.581252 3.29644i 0.0238491 0.135255i
$$595$$ 4.39306 + 1.59894i 0.180098 + 0.0655502i
$$596$$ 2.33615 + 4.04633i 0.0956925 + 0.165744i
$$597$$ 5.53936 9.59446i 0.226711 0.392675i
$$598$$ −7.31908 + 6.14144i −0.299299 + 0.251142i
$$599$$ −21.7781 + 18.2740i −0.889830 + 0.746656i −0.968176 0.250270i $$-0.919481\pi$$
0.0783461 + 0.996926i $$0.475036\pi$$
$$600$$ −0.500000 + 0.866025i −0.0204124 + 0.0353553i
$$601$$ 20.0501 + 34.7278i 0.817861 + 1.41658i 0.907256 + 0.420580i $$0.138173\pi$$
−0.0893951 + 0.995996i $$0.528493\pi$$
$$602$$ 4.59714 + 1.67322i 0.187366 + 0.0681955i
$$603$$ 2.42514 13.7537i 0.0987595 0.560093i
$$604$$ 1.61809 + 9.17664i 0.0658391 + 0.373392i
$$605$$ 0.192066 0.0699065i 0.00780861 0.00284210i
$$606$$ −3.79813 3.18701i −0.154289 0.129464i
$$607$$ −20.0182 −0.812512 −0.406256 0.913759i $$-0.633166\pi$$
−0.406256 + 0.913759i $$0.633166\pi$$
$$608$$ 3.29813 + 2.84997i 0.133757 + 0.115581i
$$609$$ 9.74422 0.394856
$$610$$ −5.13429 4.30818i −0.207881 0.174433i
$$611$$ −1.61809 + 0.588936i −0.0654609 + 0.0238258i
$$612$$ −0.553033 3.13641i −0.0223551 0.126782i
$$613$$ 1.21466 6.88868i 0.0490597 0.278231i −0.950403 0.311022i $$-0.899329\pi$$
0.999462 + 0.0327913i $$0.0104397\pi$$
$$614$$ −26.9971 9.82613i −1.08951 0.396550i
$$615$$ −1.56031 2.70253i −0.0629177 0.108977i
$$616$$ 2.45677 4.25524i 0.0989860 0.171449i
$$617$$ 27.2704 22.8826i 1.09786 0.921217i 0.100585 0.994929i $$-0.467929\pi$$
0.997280 + 0.0737110i $$0.0234843\pi$$
$$618$$ −1.57532 + 1.32185i −0.0633687 + 0.0531727i
$$619$$ −8.40167 + 14.5521i −0.337692 + 0.584899i −0.983998 0.178179i $$-0.942979\pi$$
0.646306 + 0.763078i $$0.276313\pi$$
$$620$$ −5.40033 9.35365i −0.216882 0.375651i
$$621$$ −4.03209 1.46756i −0.161802 0.0588912i
$$622$$ 1.63516 9.27347i 0.0655641 0.371832i
$$623$$ 2.77884 + 15.7596i 0.111332 + 0.631394i
$$624$$ 2.09240 0.761570i 0.0837629 0.0304872i
$$625$$ 0.766044 + 0.642788i 0.0306418 + 0.0257115i
$$626$$ −26.4124 −1.05565
$$627$$ −7.47771 + 12.5287i −0.298631 + 0.500346i
$$628$$ 22.0378 0.879403
$$629$$ 7.37346 + 6.18706i 0.293999 + 0.246694i
$$630$$ −1.37939 + 0.502055i −0.0549560 + 0.0200024i
$$631$$ −7.57516 42.9609i −0.301562 1.71025i −0.639260 0.768991i $$-0.720759\pi$$
0.337698 0.941255i $$-0.390352\pi$$
$$632$$ −0.275845 + 1.56439i −0.0109725 + 0.0622282i
$$633$$ −7.32295 2.66534i −0.291061 0.105938i
$$634$$ −9.99067 17.3043i −0.396780 0.687243i
$$635$$ −9.45723 + 16.3804i −0.375299 + 0.650037i
$$636$$ −5.77584 + 4.84651i −0.229027 + 0.192177i
$$637$$ 8.26470 6.93491i 0.327459 0.274771i
$$638$$ 11.1099 19.2430i 0.439847 0.761837i
$$639$$ 4.24763 + 7.35710i 0.168033 + 0.291043i
$$640$$ 0.939693 + 0.342020i 0.0371446 + 0.0135195i
$$641$$ 5.50387 31.2140i 0.217390 1.23288i −0.659321 0.751861i $$-0.729156\pi$$
0.876711 0.481017i $$-0.159733\pi$$
$$642$$ −0.167252 0.948531i −0.00660089 0.0374355i
$$643$$ 20.1677 7.34045i 0.795337 0.289479i 0.0877843 0.996140i $$-0.472021\pi$$
0.707553 + 0.706660i $$0.249799\pi$$
$$644$$ −4.82501 4.04866i −0.190132 0.159540i
$$645$$ −3.33275 −0.131227
$$646$$ −2.60859 + 13.6349i −0.102634 + 0.536458i
$$647$$ 30.0137 1.17996 0.589981 0.807417i $$-0.299135\pi$$
0.589981 + 0.807417i $$0.299135\pi$$
$$648$$ 0.766044 + 0.642788i 0.0300931 + 0.0252511i
$$649$$ −13.8760 + 5.05044i −0.544680 + 0.198247i
$$650$$ −0.386659 2.19285i −0.0151660 0.0860108i
$$651$$ 2.75309 15.6135i 0.107902 0.611943i
$$652$$ 8.05690 + 2.93247i 0.315533 + 0.114845i
$$653$$ 0.786112 + 1.36159i 0.0307629 + 0.0532829i 0.880997 0.473122i $$-0.156873\pi$$
−0.850234 + 0.526405i $$0.823540\pi$$
$$654$$ −5.97178 + 10.3434i −0.233515 + 0.404460i
$$655$$ −12.4311 + 10.4309i −0.485722 + 0.407569i
$$656$$ −2.39053 + 2.00589i −0.0933345 + 0.0783169i
$$657$$ 6.95471 12.0459i 0.271329 0.469956i
$$658$$ −0.567581 0.983080i −0.0221266 0.0383244i
$$659$$ −35.7276 13.0038i −1.39175 0.506556i −0.466031 0.884768i $$-0.654317\pi$$
−0.925719 + 0.378212i $$0.876539\pi$$
$$660$$ −0.581252 + 3.29644i −0.0226252 + 0.128314i
$$661$$ −3.91828 22.2217i −0.152403 0.864323i −0.961121 0.276126i $$-0.910949\pi$$
0.808718 0.588197i $$-0.200162\pi$$
$$662$$ −23.1998 + 8.44404i −0.901686 + 0.328187i
$$663$$ 5.43242 + 4.55834i 0.210978 + 0.177031i
$$664$$ 0.795607 0.0308755
$$665$$ 6.39780 + 0.0927760i 0.248096 + 0.00359770i
$$666$$ −3.02229 −0.117111
$$667$$ −21.8195 18.3088i −0.844856 0.708918i
$$668$$ −12.3229 + 4.48519i −0.476789 + 0.173537i
$$669$$ −1.82934 10.3747i −0.0707266 0.401110i
$$670$$ −2.42514 + 13.7537i −0.0936915 + 0.531351i
$$671$$ −21.0817 7.67312i −0.813851 0.296217i
$$672$$ 0.733956 + 1.27125i 0.0283130 + 0.0490395i
$$673$$ −2.88800 + 5.00217i −0.111324 + 0.192819i −0.916304 0.400482i $$-0.868843\pi$$
0.804980 + 0.593302i $$0.202176\pi$$
$$674$$ 7.31315 6.13646i 0.281692 0.236368i
$$675$$ 0.766044 0.642788i 0.0294851 0.0247409i
$$676$$ 4.02094 6.96448i 0.154652 0.267865i
$$677$$ 24.4167 + 42.2909i 0.938410 + 1.62537i 0.768438 + 0.639924i $$0.221034\pi$$
0.169971 + 0.985449i $$0.445632\pi$$
$$678$$ 13.5817 + 4.94334i 0.521603 + 0.189848i
$$679$$ −1.78430 + 10.1193i −0.0684752 + 0.388342i
$$680$$ 0.553033 + 3.13641i 0.0212079 + 0.120276i
$$681$$ 21.5608 7.84748i 0.826211 0.300716i
$$682$$ −27.6948 23.2387i −1.06049 0.889856i
$$683$$ −0.315836 −0.0120851 −0.00604257 0.999982i $$-0.501923\pi$$
−0.00604257 + 0.999982i $$0.501923\pi$$
$$684$$ −2.12449 3.80612i −0.0812317 0.145531i
$$685$$ 12.5030 0.477715
$$686$$ 13.3198 + 11.1766i 0.508552 + 0.426726i
$$687$$ 5.94609 2.16420i 0.226857 0.0825694i
$$688$$ 0.578726 + 3.28212i 0.0220637 + 0.125130i
$$689$$ 2.91534 16.5337i 0.111066 0.629885i
$$690$$ 4.03209 + 1.46756i 0.153499 + 0.0558691i
$$691$$ −8.34183 14.4485i −0.317338 0.549646i 0.662593 0.748979i $$-0.269456\pi$$
−0.979932 + 0.199333i $$0.936122\pi$$
$$692$$ 1.09105 1.88976i 0.0414756 0.0718378i
$$693$$ −3.76399 + 3.15836i −0.142982 + 0.119976i
$$694$$ 16.0057 13.4304i 0.607567 0.509810i
$$695$$ 5.44743 9.43523i 0.206633 0.357899i
$$696$$ 3.31908 + 5.74881i 0.125809 + 0.217908i
$$697$$ −9.33915 3.39917i −0.353745 0.128753i
$$698$$ −5.61809 + 31.8618i −0.212648 + 1.20599i
$$699$$ 1.84430 + 10.4596i 0.0697580 + 0.395617i
$$700$$ 1.37939 0.502055i 0.0521359 0.0189759i
$$701$$ 0.265329 + 0.222638i 0.0100213 + 0.00840891i 0.647785 0.761824i $$-0.275696\pi$$
−0.637763 + 0.770233i $$0.720140\pi$$
$$702$$ −2.22668 −0.0840407
$$703$$ 12.3127 + 4.68475i 0.464384 + 0.176689i
$$704$$ 3.34730 0.126156
$$705$$ 0.592396 + 0.497079i 0.0223109 + 0.0187211i
$$706$$ 20.1138 7.32083i 0.756993 0.275523i
$$707$$ 1.26382 + 7.16750i 0.0475310 + 0.269561i
$$708$$ 0.766044 4.34445i 0.0287897 0.163275i
$$709$$ 1.95842 + 0.712805i 0.0735498 + 0.0267700i 0.378533 0.925588i $$-0.376429\pi$$
−0.304983 + 0.952358i $$0.598651\pi$$
$$710$$ −4.24763 7.35710i −0.159411 0.276107i
$$711$$ 0.794263 1.37570i 0.0297872 0.0515929i
$$712$$ −8.35117 + 7.00746i −0.312973 + 0.262616i
$$713$$ −35.5016 + 29.7894i −1.32955 + 1.11562i
$$714$$ −2.33750 + 4.04866i −0.0874786 + 0.151517i
$$715$$ −3.72668 6.45480i −0.139370 0.241396i
$$716$$ −19.1925 6.98551i −0.717259 0.261061i
$$717$$ −2.16163 + 12.2592i −0.0807274 + 0.457828i
$$718$$ 2.69934 + 15.3087i 0.100738 + 0.571316i
$$719$$ −9.00134 + 3.27622i −0.335693 + 0.122182i −0.504367 0.863490i $$-0.668274\pi$$
0.168673 + 0.985672i $$0.446052\pi$$
$$720$$ −0.766044 0.642788i −0.0285488 0.0239553i
$$721$$ 3.01867 0.112421
$$722$$ 2.75537 + 18.7991i 0.102544 + 0.699632i
$$723$$ −12.2635 −0.456085
$$724$$ −15.7895 13.2490i −0.586813 0.492394i
$$725$$ 6.23783 2.27038i 0.231667 0.0843199i
$$726$$ 0.0354925 + 0.201288i 0.00131725 + 0.00747049i
$$727$$ −2.20146 + 12.4851i −0.0816475 + 0.463046i 0.916382 + 0.400304i $$0.131096\pi$$
−0.998030 + 0.0627417i $$0.980016\pi$$
$$728$$ −3.07145 1.11792i −0.113836 0.0414328i
$$729$$ −0.500000 0.866025i −0.0185185 0.0320750i
$$730$$ −6.95471 + 12.0459i −0.257405 + 0.445839i
$$731$$ −8.13088 + 6.82262i −0.300732 + 0.252344i
$$732$$ 5.13429 4.30818i 0.189769 0.159235i
$$733$$ −1.77672 + 3.07737i −0.0656247 + 0.113665i −0.896971 0.442090i $$-0.854237\pi$$
0.831346 + 0.555755i $$0.187571\pi$$
$$734$$ 5.33140 + 9.23426i 0.196786 + 0.340843i
$$735$$ −4.55303 1.65717i −0.167941 0.0611256i
$$736$$ 0.745100 4.22567i 0.0274647 0.155760i
$$737$$ 8.11768 + 46.0376i 0.299019 + 1.69582i
$$738$$ 2.93242 1.06731i 0.107944 0.0392883i
$$739$$ −39.6823 33.2974i −1.45974 1.22487i −0.925066 0.379805i $$-0.875991\pi$$
−0.534671 0.845060i $$-0.679565\pi$$
$$740$$ 3.02229 0.111102
$$741$$ 9.07145 + 3.45150i 0.333248 + 0.126794i
$$742$$ 11.0678 0.406312
$$743$$ 29.0822 + 24.4029i 1.06692 + 0.895254i 0.994770 0.102140i $$-0.0325689\pi$$
0.0721519 + 0.997394i $$0.477013\pi$$
$$744$$ 10.1493 3.69404i 0.372091 0.135430i
$$745$$ 0.811337 + 4.60132i 0.0297251 + 0.168579i
$$746$$ −4.70068 + 26.6589i −0.172104 + 0.976052i
$$747$$ −0.747626 0.272114i −0.0273542 0.00995612i
$$748$$ 5.33022 + 9.23222i 0.194892 + 0.337563i
$$749$$ −0.706919 + 1.22442i −0.0258303 + 0.0447393i
$$750$$ −0.766044 + 0.642788i −0.0279720 + 0.0234713i
$$751$$ 24.3214 20.4080i 0.887499 0.744700i −0.0802080 0.996778i $$-0.525558\pi$$
0.967707 + 0.252078i $$0.0811140\pi$$
$$752$$ 0.386659 0.669713i 0.0141000 0.0244219i
$$753$$ −6.39053 11.0687i −0.232884 0.403367i
$$754$$ −13.8897 5.05542i −0.505831 0.184108i
$$755$$ −1.61809 + 9.17664i −0.0588883 + 0.333972i
$$756$$ −0.254900 1.44561i −0.00927063 0.0525763i
$$757$$ −5.02007 + 1.82716i −0.182457 + 0.0664091i −0.431633 0.902049i $$-0.642063\pi$$
0.249176 + 0.968458i $$0.419840\pi$$
$$758$$ −21.7121 18.2186i −0.788620 0.661731i
$$759$$ 14.3628 0.521336
$$760$$ 2.12449 + 3.80612i 0.0770632 + 0.138063i
$$761$$ −15.7948 −0.572561 −0.286280 0.958146i $$-0.592419\pi$$
−0.286280 + 0.958146i $$0.592419\pi$$
$$762$$ −14.4893 12.1580i −0.524893 0.440437i
$$763$$ 16.4748 5.99633i 0.596427 0.217082i
$$764$$ −2.41488 13.6955i −0.0873672 0.495484i
$$765$$ 0.553033 3.13641i 0.0199950 0.113397i
$$766$$ 6.39945 + 2.32921i 0.231222 + 0.0841578i