# Properties

 Label 380.2.k.d.267.13 Level $380$ Weight $2$ Character 380.267 Analytic conductor $3.034$ Analytic rank $0$ Dimension $52$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$380 = 2^{2} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 380.k (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$3.03431527681$$ Analytic rank: $$0$$ Dimension: $$52$$ Relative dimension: $$26$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 267.13 Character $$\chi$$ $$=$$ 380.267 Dual form 380.2.k.d.343.13

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.00522099 + 1.41420i) q^{2} +(-0.212700 - 0.212700i) q^{3} +(-1.99995 + 0.0147671i) q^{4} +(2.19176 + 0.442915i) q^{5} +(0.299691 - 0.301912i) q^{6} +(2.65088 - 2.65088i) q^{7} +(-0.0313254 - 2.82825i) q^{8} -2.90952i q^{9} +O(q^{10})$$ $$q+(0.00522099 + 1.41420i) q^{2} +(-0.212700 - 0.212700i) q^{3} +(-1.99995 + 0.0147671i) q^{4} +(2.19176 + 0.442915i) q^{5} +(0.299691 - 0.301912i) q^{6} +(2.65088 - 2.65088i) q^{7} +(-0.0313254 - 2.82825i) q^{8} -2.90952i q^{9} +(-0.614930 + 3.10191i) q^{10} -2.04453i q^{11} +(0.428530 + 0.422248i) q^{12} +(-0.226183 + 0.226183i) q^{13} +(3.76272 + 3.73504i) q^{14} +(-0.371981 - 0.560397i) q^{15} +(3.99956 - 0.0590668i) q^{16} +(-3.06235 - 3.06235i) q^{17} +(4.11465 - 0.0151906i) q^{18} -1.00000 q^{19} +(-4.38995 - 0.853441i) q^{20} -1.12768 q^{21} +(2.89139 - 0.0106745i) q^{22} +(5.40599 + 5.40599i) q^{23} +(-0.594908 + 0.608234i) q^{24} +(4.60765 + 1.94153i) q^{25} +(-0.321050 - 0.318688i) q^{26} +(-1.25696 + 1.25696i) q^{27} +(-5.26246 + 5.34075i) q^{28} +6.50979i q^{29} +(0.790574 - 0.528982i) q^{30} +5.78891i q^{31} +(0.104414 + 5.65589i) q^{32} +(-0.434873 + 0.434873i) q^{33} +(4.31480 - 4.34677i) q^{34} +(6.98421 - 4.63598i) q^{35} +(0.0429651 + 5.81888i) q^{36} +(-6.86987 - 6.86987i) q^{37} +(-0.00522099 - 1.41420i) q^{38} +0.0962184 q^{39} +(1.18402 - 6.21274i) q^{40} +6.57779 q^{41} +(-0.00588763 - 1.59478i) q^{42} +(-3.72596 - 3.72596i) q^{43} +(0.0301918 + 4.08895i) q^{44} +(1.28867 - 6.37697i) q^{45} +(-7.61695 + 7.67340i) q^{46} +(1.24109 - 1.24109i) q^{47} +(-0.863272 - 0.838145i) q^{48} -7.05428i q^{49} +(-2.72166 + 6.52630i) q^{50} +1.30273i q^{51} +(0.449014 - 0.455694i) q^{52} +(-6.74839 + 6.74839i) q^{53} +(-1.78416 - 1.77103i) q^{54} +(0.905555 - 4.48113i) q^{55} +(-7.58039 - 7.41431i) q^{56} +(0.212700 + 0.212700i) q^{57} +(-9.20617 + 0.0339876i) q^{58} +4.42510 q^{59} +(0.752216 + 1.11527i) q^{60} +0.777701 q^{61} +(-8.18670 + 0.0302239i) q^{62} +(-7.71277 - 7.71277i) q^{63} +(-7.99804 + 0.177192i) q^{64} +(-0.595919 + 0.395560i) q^{65} +(-0.617269 - 0.612728i) q^{66} +(-5.08912 + 5.08912i) q^{67} +(6.16975 + 6.07931i) q^{68} -2.29971i q^{69} +(6.59268 + 9.85289i) q^{70} +1.53345i q^{71} +(-8.22885 + 0.0911417i) q^{72} +(-7.28339 + 7.28339i) q^{73} +(9.67952 - 9.75126i) q^{74} +(-0.567085 - 1.39301i) q^{75} +(1.99995 - 0.0147671i) q^{76} +(-5.41980 - 5.41980i) q^{77} +(0.000502356 + 0.136072i) q^{78} +16.5071 q^{79} +(8.79226 + 1.64201i) q^{80} -8.19384 q^{81} +(0.0343426 + 9.30234i) q^{82} +(4.29909 + 4.29909i) q^{83} +(2.25531 - 0.0166526i) q^{84} +(-5.35558 - 8.06830i) q^{85} +(5.24981 - 5.28872i) q^{86} +(1.38464 - 1.38464i) q^{87} +(-5.78246 + 0.0640457i) q^{88} -8.74189i q^{89} +(9.02507 + 1.78915i) q^{90} +1.19917i q^{91} +(-10.8915 - 10.7319i) q^{92} +(1.23130 - 1.23130i) q^{93} +(1.76164 + 1.74868i) q^{94} +(-2.19176 - 0.442915i) q^{95} +(1.18080 - 1.22522i) q^{96} +(-2.60382 - 2.60382i) q^{97} +(9.97619 - 0.0368304i) q^{98} -5.94860 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10})$$ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 $$52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100})$$ 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$77$$ $$191$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.00522099 + 1.41420i 0.00369180 + 0.999993i
$$3$$ −0.212700 0.212700i −0.122803 0.122803i 0.643035 0.765837i $$-0.277675\pi$$
−0.765837 + 0.643035i $$0.777675\pi$$
$$4$$ −1.99995 + 0.0147671i −0.999973 + 0.00738355i
$$5$$ 2.19176 + 0.442915i 0.980186 + 0.198078i
$$6$$ 0.299691 0.301912i 0.122348 0.123255i
$$7$$ 2.65088 2.65088i 1.00194 1.00194i 0.00193869 0.999998i $$-0.499383\pi$$
0.999998 0.00193869i $$-0.000617103\pi$$
$$8$$ −0.0313254 2.82825i −0.0110752 0.999939i
$$9$$ 2.90952i 0.969839i
$$10$$ −0.614930 + 3.10191i −0.194458 + 0.980911i
$$11$$ 2.04453i 0.616450i −0.951314 0.308225i $$-0.900265\pi$$
0.951314 0.308225i $$-0.0997349\pi$$
$$12$$ 0.428530 + 0.422248i 0.123706 + 0.121893i
$$13$$ −0.226183 + 0.226183i −0.0627319 + 0.0627319i −0.737777 0.675045i $$-0.764124\pi$$
0.675045 + 0.737777i $$0.264124\pi$$
$$14$$ 3.76272 + 3.73504i 1.00563 + 0.998231i
$$15$$ −0.371981 0.560397i −0.0960450 0.144694i
$$16$$ 3.99956 0.0590668i 0.999891 0.0147667i
$$17$$ −3.06235 3.06235i −0.742729 0.742729i 0.230374 0.973102i $$-0.426005\pi$$
−0.973102 + 0.230374i $$0.926005\pi$$
$$18$$ 4.11465 0.0151906i 0.969832 0.00358045i
$$19$$ −1.00000 −0.229416
$$20$$ −4.38995 0.853441i −0.981622 0.190835i
$$21$$ −1.12768 −0.246081
$$22$$ 2.89139 0.0106745i 0.616445 0.00227581i
$$23$$ 5.40599 + 5.40599i 1.12723 + 1.12723i 0.990626 + 0.136600i $$0.0436176\pi$$
0.136600 + 0.990626i $$0.456382\pi$$
$$24$$ −0.594908 + 0.608234i −0.121435 + 0.124155i
$$25$$ 4.60765 + 1.94153i 0.921530 + 0.388306i
$$26$$ −0.321050 0.318688i −0.0629630 0.0624999i
$$27$$ −1.25696 + 1.25696i −0.241901 + 0.241901i
$$28$$ −5.26246 + 5.34075i −0.994512 + 1.00931i
$$29$$ 6.50979i 1.20884i 0.796667 + 0.604419i $$0.206595\pi$$
−0.796667 + 0.604419i $$0.793405\pi$$
$$30$$ 0.790574 0.528982i 0.144338 0.0965785i
$$31$$ 5.78891i 1.03972i 0.854252 + 0.519860i $$0.174016\pi$$
−0.854252 + 0.519860i $$0.825984\pi$$
$$32$$ 0.104414 + 5.65589i 0.0184580 + 0.999830i
$$33$$ −0.434873 + 0.434873i −0.0757016 + 0.0757016i
$$34$$ 4.31480 4.34677i 0.739982 0.745466i
$$35$$ 6.98421 4.63598i 1.18055 0.783623i
$$36$$ 0.0429651 + 5.81888i 0.00716085 + 0.969813i
$$37$$ −6.86987 6.86987i −1.12940 1.12940i −0.990275 0.139124i $$-0.955571\pi$$
−0.139124 0.990275i $$-0.544429\pi$$
$$38$$ −0.00522099 1.41420i −0.000846957 0.229414i
$$39$$ 0.0962184 0.0154073
$$40$$ 1.18402 6.21274i 0.187210 0.982320i
$$41$$ 6.57779 1.02728 0.513639 0.858006i $$-0.328297\pi$$
0.513639 + 0.858006i $$0.328297\pi$$
$$42$$ −0.00588763 1.59478i −0.000908481 0.246079i
$$43$$ −3.72596 3.72596i −0.568203 0.568203i 0.363422 0.931625i $$-0.381608\pi$$
−0.931625 + 0.363422i $$0.881608\pi$$
$$44$$ 0.0301918 + 4.08895i 0.00455158 + 0.616433i
$$45$$ 1.28867 6.37697i 0.192104 0.950623i
$$46$$ −7.61695 + 7.67340i −1.12306 + 1.13138i
$$47$$ 1.24109 1.24109i 0.181032 0.181032i −0.610773 0.791805i $$-0.709141\pi$$
0.791805 + 0.610773i $$0.209141\pi$$
$$48$$ −0.863272 0.838145i −0.124603 0.120976i
$$49$$ 7.05428i 1.00775i
$$50$$ −2.72166 + 6.52630i −0.384902 + 0.922958i
$$51$$ 1.30273i 0.182418i
$$52$$ 0.449014 0.455694i 0.0622670 0.0631933i
$$53$$ −6.74839 + 6.74839i −0.926962 + 0.926962i −0.997509 0.0705463i $$-0.977526\pi$$
0.0705463 + 0.997509i $$0.477526\pi$$
$$54$$ −1.78416 1.77103i −0.242793 0.241007i
$$55$$ 0.905555 4.48113i 0.122105 0.604235i
$$56$$ −7.58039 7.41431i −1.01297 0.990779i
$$57$$ 0.212700 + 0.212700i 0.0281729 + 0.0281729i
$$58$$ −9.20617 + 0.0339876i −1.20883 + 0.00446279i
$$59$$ 4.42510 0.576098 0.288049 0.957616i $$-0.406993\pi$$
0.288049 + 0.957616i $$0.406993\pi$$
$$60$$ 0.752216 + 1.11527i 0.0971107 + 0.143981i
$$61$$ 0.777701 0.0995745 0.0497872 0.998760i $$-0.484146\pi$$
0.0497872 + 0.998760i $$0.484146\pi$$
$$62$$ −8.18670 + 0.0302239i −1.03971 + 0.00383844i
$$63$$ −7.71277 7.71277i −0.971717 0.971717i
$$64$$ −7.99804 + 0.177192i −0.999755 + 0.0221490i
$$65$$ −0.595919 + 0.395560i −0.0739147 + 0.0490631i
$$66$$ −0.617269 0.612728i −0.0759806 0.0754216i
$$67$$ −5.08912 + 5.08912i −0.621734 + 0.621734i −0.945975 0.324240i $$-0.894891\pi$$
0.324240 + 0.945975i $$0.394891\pi$$
$$68$$ 6.16975 + 6.07931i 0.748192 + 0.737224i
$$69$$ 2.29971i 0.276853i
$$70$$ 6.59268 + 9.85289i 0.787976 + 1.17765i
$$71$$ 1.53345i 0.181986i 0.995852 + 0.0909932i $$0.0290042\pi$$
−0.995852 + 0.0909932i $$0.970996\pi$$
$$72$$ −8.22885 + 0.0911417i −0.969780 + 0.0107412i
$$73$$ −7.28339 + 7.28339i −0.852457 + 0.852457i −0.990435 0.137979i $$-0.955939\pi$$
0.137979 + 0.990435i $$0.455939\pi$$
$$74$$ 9.67952 9.75126i 1.12522 1.13356i
$$75$$ −0.567085 1.39301i −0.0654813 0.160851i
$$76$$ 1.99995 0.0147671i 0.229409 0.00169390i
$$77$$ −5.41980 5.41980i −0.617644 0.617644i
$$78$$ 0.000502356 0.136072i 5.68806e−5 0.0154072i
$$79$$ 16.5071 1.85720 0.928599 0.371086i $$-0.121014\pi$$
0.928599 + 0.371086i $$0.121014\pi$$
$$80$$ 8.79226 + 1.64201i 0.983004 + 0.183582i
$$81$$ −8.19384 −0.910427
$$82$$ 0.0343426 + 9.30234i 0.00379250 + 1.02727i
$$83$$ 4.29909 + 4.29909i 0.471887 + 0.471887i 0.902525 0.430638i $$-0.141711\pi$$
−0.430638 + 0.902525i $$0.641711\pi$$
$$84$$ 2.25531 0.0166526i 0.246074 0.00181695i
$$85$$ −5.35558 8.06830i −0.580894 0.875131i
$$86$$ 5.24981 5.28872i 0.566102 0.570297i
$$87$$ 1.38464 1.38464i 0.148449 0.148449i
$$88$$ −5.78246 + 0.0640457i −0.616412 + 0.00682730i
$$89$$ 8.74189i 0.926639i −0.886191 0.463319i $$-0.846658\pi$$
0.886191 0.463319i $$-0.153342\pi$$
$$90$$ 9.02507 + 1.78915i 0.951326 + 0.188593i
$$91$$ 1.19917i 0.125707i
$$92$$ −10.8915 10.7319i −1.13552 1.11887i
$$93$$ 1.23130 1.23130i 0.127680 0.127680i
$$94$$ 1.76164 + 1.74868i 0.181699 + 0.180363i
$$95$$ −2.19176 0.442915i −0.224870 0.0454422i
$$96$$ 1.18080 1.22522i 0.120515 0.125048i
$$97$$ −2.60382 2.60382i −0.264377 0.264377i 0.562452 0.826830i $$-0.309858\pi$$
−0.826830 + 0.562452i $$0.809858\pi$$
$$98$$ 9.97619 0.0368304i 1.00775 0.00372043i
$$99$$ −5.94860 −0.597857
$$100$$ −9.24372 3.81492i −0.924372 0.381492i
$$101$$ 13.0511 1.29864 0.649318 0.760517i $$-0.275054\pi$$
0.649318 + 0.760517i $$0.275054\pi$$
$$102$$ −1.84232 + 0.00680152i −0.182417 + 0.000673451i
$$103$$ −12.4417 12.4417i −1.22591 1.22591i −0.965496 0.260419i $$-0.916139\pi$$
−0.260419 0.965496i $$-0.583861\pi$$
$$104$$ 0.646788 + 0.632618i 0.0634228 + 0.0620333i
$$105$$ −2.47162 0.499469i −0.241205 0.0487432i
$$106$$ −9.57883 9.50836i −0.930378 0.923534i
$$107$$ 0.931552 0.931552i 0.0900565 0.0900565i −0.660643 0.750700i $$-0.729716\pi$$
0.750700 + 0.660643i $$0.229716\pi$$
$$108$$ 2.49528 2.53241i 0.240109 0.243681i
$$109$$ 20.2411i 1.93874i 0.245597 + 0.969372i $$0.421016\pi$$
−0.245597 + 0.969372i $$0.578984\pi$$
$$110$$ 6.34196 + 1.25724i 0.604682 + 0.119873i
$$111$$ 2.92245i 0.277386i
$$112$$ 10.4458 10.7589i 0.987032 1.01662i
$$113$$ 3.01028 3.01028i 0.283183 0.283183i −0.551194 0.834377i $$-0.685828\pi$$
0.834377 + 0.551194i $$0.185828\pi$$
$$114$$ −0.299691 + 0.301912i −0.0280687 + 0.0282767i
$$115$$ 9.45425 + 14.2430i 0.881614 + 1.32817i
$$116$$ −0.0961307 13.0192i −0.00892551 1.20881i
$$117$$ 0.658083 + 0.658083i 0.0608398 + 0.0608398i
$$118$$ 0.0231034 + 6.25799i 0.00212684 + 0.576094i
$$119$$ −16.2358 −1.48833
$$120$$ −1.57329 + 1.06961i −0.143621 + 0.0976416i
$$121$$ 6.81989 0.619990
$$122$$ 0.00406037 + 1.09983i 0.000367609 + 0.0995738i
$$123$$ −1.39910 1.39910i −0.126152 0.126152i
$$124$$ −0.0854854 11.5775i −0.00767682 1.03969i
$$125$$ 9.23895 + 6.29618i 0.826357 + 0.563147i
$$126$$ 10.8672 10.9477i 0.968123 0.975298i
$$127$$ 6.14286 6.14286i 0.545091 0.545091i −0.379926 0.925017i $$-0.624051\pi$$
0.925017 + 0.379926i $$0.124051\pi$$
$$128$$ −0.292344 11.3099i −0.0258398 0.999666i
$$129$$ 1.58503i 0.139554i
$$130$$ −0.562513 0.840686i −0.0493357 0.0737331i
$$131$$ 8.30018i 0.725190i 0.931947 + 0.362595i $$0.118109\pi$$
−0.931947 + 0.362595i $$0.881891\pi$$
$$132$$ 0.863300 0.876144i 0.0751406 0.0762585i
$$133$$ −2.65088 + 2.65088i −0.229860 + 0.229860i
$$134$$ −7.22362 7.17048i −0.624026 0.619435i
$$135$$ −3.31168 + 2.19823i −0.285024 + 0.189193i
$$136$$ −8.56517 + 8.75703i −0.734457 + 0.750909i
$$137$$ 3.16161 + 3.16161i 0.270115 + 0.270115i 0.829146 0.559032i $$-0.188827\pi$$
−0.559032 + 0.829146i $$0.688827\pi$$
$$138$$ 3.25226 0.0120068i 0.276851 0.00102208i
$$139$$ −16.9908 −1.44114 −0.720572 0.693380i $$-0.756121\pi$$
−0.720572 + 0.693380i $$0.756121\pi$$
$$140$$ −13.8996 + 9.37484i −1.17473 + 0.792319i
$$141$$ −0.527962 −0.0444625
$$142$$ −2.16860 + 0.00800611i −0.181985 + 0.000671857i
$$143$$ 0.462438 + 0.462438i 0.0386710 + 0.0386710i
$$144$$ −0.171856 11.6368i −0.0143213 0.969733i
$$145$$ −2.88329 + 14.2679i −0.239444 + 1.18489i
$$146$$ −10.3382 10.2622i −0.855598 0.849304i
$$147$$ −1.50045 + 1.50045i −0.123755 + 0.123755i
$$148$$ 13.8408 + 13.6379i 1.13771 + 1.12103i
$$149$$ 9.77519i 0.800815i −0.916337 0.400407i $$-0.868869\pi$$
0.916337 0.400407i $$-0.131131\pi$$
$$150$$ 1.96705 0.809247i 0.160609 0.0660747i
$$151$$ 4.21919i 0.343353i 0.985153 + 0.171676i $$0.0549184\pi$$
−0.985153 + 0.171676i $$0.945082\pi$$
$$152$$ 0.0313254 + 2.82825i 0.00254082 + 0.229402i
$$153$$ −8.90996 + 8.90996i −0.720327 + 0.720327i
$$154$$ 7.63641 7.69300i 0.615359 0.619920i
$$155$$ −2.56400 + 12.6879i −0.205945 + 1.01912i
$$156$$ −0.192432 + 0.00142087i −0.0154069 + 0.000113760i
$$157$$ 8.55712 + 8.55712i 0.682933 + 0.682933i 0.960660 0.277727i $$-0.0895812\pi$$
−0.277727 + 0.960660i $$0.589581\pi$$
$$158$$ 0.0861836 + 23.3444i 0.00685640 + 1.85718i
$$159$$ 2.87077 0.227667
$$160$$ −2.27623 + 12.4426i −0.179952 + 0.983675i
$$161$$ 28.6612 2.25882
$$162$$ −0.0427800 11.5878i −0.00336111 0.910421i
$$163$$ −11.5235 11.5235i −0.902586 0.902586i 0.0930729 0.995659i $$-0.470331\pi$$
−0.995659 + 0.0930729i $$0.970331\pi$$
$$164$$ −13.1552 + 0.0971348i −1.02725 + 0.00758496i
$$165$$ −1.14575 + 0.760526i −0.0891965 + 0.0592069i
$$166$$ −6.05735 + 6.10224i −0.470141 + 0.473625i
$$167$$ −3.64071 + 3.64071i −0.281727 + 0.281727i −0.833797 0.552071i $$-0.813838\pi$$
0.552071 + 0.833797i $$0.313838\pi$$
$$168$$ 0.0353252 + 3.18938i 0.00272539 + 0.246066i
$$169$$ 12.8977i 0.992129i
$$170$$ 11.3823 7.61601i 0.872980 0.584121i
$$171$$ 2.90952i 0.222496i
$$172$$ 7.50673 + 7.39669i 0.572383 + 0.563992i
$$173$$ 1.45513 1.45513i 0.110632 0.110632i −0.649624 0.760256i $$-0.725074\pi$$
0.760256 + 0.649624i $$0.225074\pi$$
$$174$$ 1.96539 + 1.95093i 0.148996 + 0.147899i
$$175$$ 17.3611 7.06755i 1.31237 0.534257i
$$176$$ −0.120764 8.17724i −0.00910292 0.616382i
$$177$$ −0.941220 0.941220i −0.0707464 0.0707464i
$$178$$ 12.3628 0.0456413i 0.926632 0.00342096i
$$179$$ −2.19695 −0.164208 −0.0821038 0.996624i $$-0.526164\pi$$
−0.0821038 + 0.996624i $$0.526164\pi$$
$$180$$ −2.48310 + 12.7726i −0.185079 + 0.952015i
$$181$$ −4.48272 −0.333198 −0.166599 0.986025i $$-0.553279\pi$$
−0.166599 + 0.986025i $$0.553279\pi$$
$$182$$ −1.69587 + 0.00626084i −0.125706 + 0.000464084i
$$183$$ −0.165417 0.165417i −0.0122280 0.0122280i
$$184$$ 15.1202 15.4589i 1.11467 1.13964i
$$185$$ −12.0143 18.0999i −0.883312 1.33073i
$$186$$ 1.74774 + 1.73489i 0.128151 + 0.127208i
$$187$$ −6.26107 + 6.26107i −0.457855 + 0.457855i
$$188$$ −2.46379 + 2.50045i −0.179691 + 0.182364i
$$189$$ 6.66407i 0.484740i
$$190$$ 0.614930 3.10191i 0.0446117 0.225036i
$$191$$ 6.36037i 0.460220i −0.973165 0.230110i $$-0.926091\pi$$
0.973165 0.230110i $$-0.0739087\pi$$
$$192$$ 1.73887 + 1.66350i 0.125492 + 0.120053i
$$193$$ −13.5977 + 13.5977i −0.978787 + 0.978787i −0.999780 0.0209930i $$-0.993317\pi$$
0.0209930 + 0.999780i $$0.493317\pi$$
$$194$$ 3.66873 3.69592i 0.263400 0.265352i
$$195$$ 0.210888 + 0.0426166i 0.0151020 + 0.00305184i
$$196$$ 0.104171 + 14.1082i 0.00744080 + 1.00773i
$$197$$ 7.28242 + 7.28242i 0.518851 + 0.518851i 0.917224 0.398373i $$-0.130425\pi$$
−0.398373 + 0.917224i $$0.630425\pi$$
$$198$$ −0.0310576 8.41253i −0.00220717 0.597853i
$$199$$ −21.1117 −1.49657 −0.748284 0.663378i $$-0.769122\pi$$
−0.748284 + 0.663378i $$0.769122\pi$$
$$200$$ 5.34681 13.0924i 0.378076 0.925774i
$$201$$ 2.16491 0.152701
$$202$$ 0.0681399 + 18.4570i 0.00479430 + 1.29863i
$$203$$ 17.2566 + 17.2566i 1.21118 + 1.21118i
$$204$$ −0.0192375 2.60538i −0.00134689 0.182413i
$$205$$ 14.4170 + 2.91340i 1.00692 + 0.203481i
$$206$$ 17.5301 17.6600i 1.22138 1.23043i
$$207$$ 15.7288 15.7288i 1.09323 1.09323i
$$208$$ −0.891273 + 0.917993i −0.0617987 + 0.0636514i
$$209$$ 2.04453i 0.141423i
$$210$$ 0.693447 3.49798i 0.0478524 0.241384i
$$211$$ 13.4524i 0.926098i 0.886333 + 0.463049i $$0.153245\pi$$
−0.886333 + 0.463049i $$0.846755\pi$$
$$212$$ 13.3968 13.5961i 0.920093 0.933781i
$$213$$ 0.326164 0.326164i 0.0223484 0.0223484i
$$214$$ 1.32227 + 1.31254i 0.0903883 + 0.0897234i
$$215$$ −6.51613 9.81670i −0.444397 0.669494i
$$216$$ 3.59437 + 3.51562i 0.244566 + 0.239207i
$$217$$ 15.3457 + 15.3457i 1.04173 + 1.04173i
$$218$$ −28.6250 + 0.105679i −1.93873 + 0.00715745i
$$219$$ 3.09836 0.209368
$$220$$ −1.74489 + 8.97539i −0.117640 + 0.605121i
$$221$$ 1.38530 0.0931855
$$222$$ −4.13293 + 0.0152581i −0.277384 + 0.00102405i
$$223$$ 1.88885 + 1.88885i 0.126486 + 0.126486i 0.767516 0.641030i $$-0.221492\pi$$
−0.641030 + 0.767516i $$0.721492\pi$$
$$224$$ 15.2699 + 14.7163i 1.02026 + 0.983272i
$$225$$ 5.64892 13.4060i 0.376595 0.893736i
$$226$$ 4.27286 + 4.24143i 0.284226 + 0.282136i
$$227$$ 1.46448 1.46448i 0.0972007 0.0972007i −0.656834 0.754035i $$-0.728105\pi$$
0.754035 + 0.656834i $$0.228105\pi$$
$$228$$ −0.428530 0.422248i −0.0283801 0.0279641i
$$229$$ 3.08873i 0.204109i 0.994779 + 0.102055i $$0.0325417\pi$$
−0.994779 + 0.102055i $$0.967458\pi$$
$$230$$ −20.0932 + 13.4446i −1.32491 + 0.886511i
$$231$$ 2.30559i 0.151697i
$$232$$ 18.4113 0.203922i 1.20876 0.0133881i
$$233$$ 0.275351 0.275351i 0.0180388 0.0180388i −0.698030 0.716069i $$-0.745940\pi$$
0.716069 + 0.698030i $$0.245940\pi$$
$$234$$ −0.927228 + 0.934100i −0.0606148 + 0.0610640i
$$235$$ 3.26988 2.17048i 0.213304 0.141587i
$$236$$ −8.84995 + 0.0653458i −0.576083 + 0.00425365i
$$237$$ −3.51107 3.51107i −0.228069 0.228069i
$$238$$ −0.0847670 22.9607i −0.00549463 1.48832i
$$239$$ −2.55298 −0.165139 −0.0825693 0.996585i $$-0.526313\pi$$
−0.0825693 + 0.996585i $$0.526313\pi$$
$$240$$ −1.52086 2.21937i −0.0981712 0.143260i
$$241$$ −10.8689 −0.700128 −0.350064 0.936726i $$-0.613840\pi$$
−0.350064 + 0.936726i $$0.613840\pi$$
$$242$$ 0.0356066 + 9.64471i 0.00228888 + 0.619986i
$$243$$ 5.51370 + 5.51370i 0.353704 + 0.353704i
$$244$$ −1.55536 + 0.0114844i −0.0995718 + 0.000735213i
$$245$$ 3.12445 15.4613i 0.199614 0.987787i
$$246$$ 1.97131 1.98592i 0.125686 0.126617i
$$247$$ 0.226183 0.226183i 0.0143917 0.0143917i
$$248$$ 16.3725 0.181340i 1.03966 0.0115151i
$$249$$ 1.82884i 0.115898i
$$250$$ −8.85584 + 13.0986i −0.560093 + 0.828430i
$$251$$ 21.9355i 1.38456i 0.721630 + 0.692279i $$0.243393\pi$$
−0.721630 + 0.692279i $$0.756607\pi$$
$$252$$ 15.5390 + 15.3112i 0.978866 + 0.964516i
$$253$$ 11.0527 11.0527i 0.694878 0.694878i
$$254$$ 8.71933 + 8.65519i 0.547099 + 0.543075i
$$255$$ −0.576997 + 2.85527i −0.0361330 + 0.178804i
$$256$$ 15.9930 0.472483i 0.999564 0.0295302i
$$257$$ −8.89886 8.89886i −0.555096 0.555096i 0.372811 0.927907i $$-0.378394\pi$$
−0.927907 + 0.372811i $$0.878394\pi$$
$$258$$ −2.24155 + 0.00827541i −0.139553 + 0.000515204i
$$259$$ −36.4223 −2.26317
$$260$$ 1.18597 0.799898i 0.0735504 0.0496075i
$$261$$ 18.9404 1.17238
$$262$$ −11.7381 + 0.0433352i −0.725185 + 0.00267725i
$$263$$ −16.0413 16.0413i −0.989151 0.989151i 0.0107906 0.999942i $$-0.496565\pi$$
−0.999942 + 0.0107906i $$0.996565\pi$$
$$264$$ 1.24355 + 1.21631i 0.0765354 + 0.0748586i
$$265$$ −17.7798 + 11.8019i −1.09221 + 0.724985i
$$266$$ −3.76272 3.73504i −0.230707 0.229010i
$$267$$ −1.85940 + 1.85940i −0.113794 + 0.113794i
$$268$$ 10.1028 10.2531i 0.617127 0.626308i
$$269$$ 6.96525i 0.424679i −0.977196 0.212339i $$-0.931892\pi$$
0.977196 0.212339i $$-0.0681083\pi$$
$$270$$ −3.12603 4.67191i −0.190244 0.284323i
$$271$$ 7.23572i 0.439539i −0.975552 0.219769i $$-0.929470\pi$$
0.975552 0.219769i $$-0.0705305\pi$$
$$272$$ −12.4289 12.0672i −0.753615 0.731680i
$$273$$ 0.255063 0.255063i 0.0154371 0.0154371i
$$274$$ −4.45466 + 4.48767i −0.269116 + 0.271110i
$$275$$ 3.96952 9.42049i 0.239371 0.568077i
$$276$$ 0.0339601 + 4.59930i 0.00204416 + 0.276845i
$$277$$ −15.1164 15.1164i −0.908254 0.908254i 0.0878773 0.996131i $$-0.471992\pi$$
−0.996131 + 0.0878773i $$0.971992\pi$$
$$278$$ −0.0887090 24.0285i −0.00532041 1.44113i
$$279$$ 16.8429 1.00836
$$280$$ −13.3305 19.6079i −0.796650 1.17179i
$$281$$ 10.0095 0.597118 0.298559 0.954391i $$-0.403494\pi$$
0.298559 + 0.954391i $$0.403494\pi$$
$$282$$ −0.00275649 0.746646i −0.000164146 0.0444622i
$$283$$ 8.48356 + 8.48356i 0.504295 + 0.504295i 0.912770 0.408474i $$-0.133939\pi$$
−0.408474 + 0.912770i $$0.633939\pi$$
$$284$$ −0.0226445 3.06681i −0.00134371 0.181982i
$$285$$ 0.371981 + 0.560397i 0.0220342 + 0.0331951i
$$286$$ −0.651568 + 0.656397i −0.0385280 + 0.0388135i
$$287$$ 17.4369 17.4369i 1.02927 1.02927i
$$288$$ 16.4559 0.303795i 0.969674 0.0179013i
$$289$$ 1.75596i 0.103292i
$$290$$ −20.1928 4.00306i −1.18576 0.235068i
$$291$$ 1.10767i 0.0649325i
$$292$$ 14.4588 14.6739i 0.846139 0.858727i
$$293$$ 10.3132 10.3132i 0.602501 0.602501i −0.338475 0.940976i $$-0.609911\pi$$
0.940976 + 0.338475i $$0.109911\pi$$
$$294$$ −2.12977 2.11411i −0.124211 0.123297i
$$295$$ 9.69876 + 1.95994i 0.564684 + 0.114112i
$$296$$ −19.2145 + 19.6449i −1.11682 + 1.14184i
$$297$$ 2.56989 + 2.56989i 0.149120 + 0.149120i
$$298$$ 13.8241 0.0510362i 0.800809 0.00295645i
$$299$$ −2.44549 −0.141426
$$300$$ 1.15471 + 2.77758i 0.0666672 + 0.160364i
$$301$$ −19.7541 −1.13861
$$302$$ −5.96680 + 0.0220284i −0.343351 + 0.00126759i
$$303$$ −2.77598 2.77598i −0.159476 0.159476i
$$304$$ −3.99956 + 0.0590668i −0.229391 + 0.00338771i
$$305$$ 1.70454 + 0.344456i 0.0976015 + 0.0197235i
$$306$$ −12.6470 12.5540i −0.722982 0.717663i
$$307$$ −3.77726 + 3.77726i −0.215579 + 0.215579i −0.806633 0.591053i $$-0.798712\pi$$
0.591053 + 0.806633i $$0.298712\pi$$
$$308$$ 10.9193 + 10.7593i 0.622187 + 0.613066i
$$309$$ 5.29270i 0.301091i
$$310$$ −17.9567 3.55977i −1.01987 0.202182i
$$311$$ 21.5006i 1.21919i −0.792715 0.609593i $$-0.791333\pi$$
0.792715 0.609593i $$-0.208667\pi$$
$$312$$ −0.00301408 0.272130i −0.000170639 0.0154063i
$$313$$ −12.1932 + 12.1932i −0.689200 + 0.689200i −0.962055 0.272855i $$-0.912032\pi$$
0.272855 + 0.962055i $$0.412032\pi$$
$$314$$ −12.0568 + 12.1462i −0.680407 + 0.685449i
$$315$$ −13.4885 20.3207i −0.759988 1.14494i
$$316$$ −33.0134 + 0.243762i −1.85715 + 0.0137127i
$$317$$ 0.231233 + 0.231233i 0.0129873 + 0.0129873i 0.713571 0.700583i $$-0.247077\pi$$
−0.700583 + 0.713571i $$0.747077\pi$$
$$318$$ 0.0149883 + 4.05985i 0.000840500 + 0.227665i
$$319$$ 13.3095 0.745188
$$320$$ −17.6083 3.15409i −0.984333 0.176319i
$$321$$ −0.396283 −0.0221183
$$322$$ 0.149640 + 40.5328i 0.00833911 + 2.25880i
$$323$$ 3.06235 + 3.06235i 0.170394 + 0.170394i
$$324$$ 16.3872 0.120999i 0.910402 0.00672218i
$$325$$ −1.48131 + 0.603031i −0.0821685 + 0.0334501i
$$326$$ 16.2363 16.3567i 0.899248 0.905912i
$$327$$ 4.30529 4.30529i 0.238083 0.238083i
$$328$$ −0.206052 18.6037i −0.0113773 1.02722i
$$329$$ 6.57997i 0.362766i
$$330$$ −1.08152 1.61635i −0.0595358 0.0889773i
$$331$$ 22.4492i 1.23392i −0.786994 0.616960i $$-0.788364\pi$$
0.786994 0.616960i $$-0.211636\pi$$
$$332$$ −8.66143 8.53446i −0.475358 0.468389i
$$333$$ −19.9880 + 19.9880i −1.09534 + 1.09534i
$$334$$ −5.16772 5.12970i −0.282765 0.280685i
$$335$$ −13.4082 + 8.90009i −0.732567 + 0.486264i
$$336$$ −4.51025 + 0.0666087i −0.246054 + 0.00363380i
$$337$$ −4.72972 4.72972i −0.257644 0.257644i 0.566451 0.824095i $$-0.308316\pi$$
−0.824095 + 0.566451i $$0.808316\pi$$
$$338$$ −18.2400 + 0.0673387i −0.992123 + 0.00366274i
$$339$$ −1.28057 −0.0695512
$$340$$ 10.8300 + 16.0571i 0.587340 + 0.870818i
$$341$$ 11.8356 0.640935
$$342$$ −4.11465 + 0.0151906i −0.222495 + 0.000821412i
$$343$$ −0.143898 0.143898i −0.00776975 0.00776975i
$$344$$ −10.4212 + 10.6547i −0.561875 + 0.574461i
$$345$$ 1.01858 5.04042i 0.0548384 0.271367i
$$346$$ 2.06545 + 2.05026i 0.111039 + 0.110223i
$$347$$ −25.6539 + 25.6539i −1.37717 + 1.37717i −0.527809 + 0.849363i $$0.676986\pi$$
−0.849363 + 0.527809i $$0.823014\pi$$
$$348$$ −2.74875 + 2.78964i −0.147348 + 0.149541i
$$349$$ 10.9773i 0.587600i −0.955867 0.293800i $$-0.905080\pi$$
0.955867 0.293800i $$-0.0949199\pi$$
$$350$$ 10.0856 + 24.5152i 0.539098 + 1.31039i
$$351$$ 0.568604i 0.0303499i
$$352$$ 11.5636 0.213478i 0.616345 0.0113784i
$$353$$ 20.5889 20.5889i 1.09584 1.09584i 0.100947 0.994892i $$-0.467813\pi$$
0.994892 0.100947i $$-0.0321874\pi$$
$$354$$ 1.32616 1.33599i 0.0704847 0.0710071i
$$355$$ −0.679187 + 3.36095i −0.0360475 + 0.178381i
$$356$$ 0.129092 + 17.4833i 0.00684188 + 0.926613i
$$357$$ 3.45336 + 3.45336i 0.182771 + 0.182771i
$$358$$ −0.0114702 3.10693i −0.000606221 0.164207i
$$359$$ 21.8842 1.15500 0.577502 0.816390i $$-0.304028\pi$$
0.577502 + 0.816390i $$0.304028\pi$$
$$360$$ −18.0761 3.44492i −0.952692 0.181563i
$$361$$ 1.00000 0.0526316
$$362$$ −0.0234042 6.33948i −0.00123010 0.333196i
$$363$$ −1.45059 1.45059i −0.0761364 0.0761364i
$$364$$ −0.0177082 2.39827i −0.000928162 0.125703i
$$365$$ −19.1894 + 12.7375i −1.00442 + 0.666714i
$$366$$ 0.233070 0.234798i 0.0121828 0.0122731i
$$367$$ 26.0801 26.0801i 1.36137 1.36137i 0.489195 0.872175i $$-0.337291\pi$$
0.872175 0.489195i $$-0.162709\pi$$
$$368$$ 21.9409 + 21.3023i 1.14375 + 1.11046i
$$369$$ 19.1382i 0.996294i
$$370$$ 25.5342 17.0852i 1.32746 0.888219i
$$371$$ 35.7783i 1.85752i
$$372$$ −2.44436 + 2.48072i −0.126734 + 0.128620i
$$373$$ −4.43315 + 4.43315i −0.229540 + 0.229540i −0.812500 0.582961i $$-0.801894\pi$$
0.582961 + 0.812500i $$0.301894\pi$$
$$374$$ −8.88712 8.82174i −0.459542 0.456161i
$$375$$ −0.625929 3.30433i −0.0323228 0.170635i
$$376$$ −3.54901 3.47125i −0.183026 0.179016i
$$377$$ −1.47240 1.47240i −0.0758327 0.0758327i
$$378$$ −9.42436 + 0.0347931i −0.484737 + 0.00178956i
$$379$$ 25.3291 1.30107 0.650534 0.759477i $$-0.274545\pi$$
0.650534 + 0.759477i $$0.274545\pi$$
$$380$$ 4.38995 + 0.853441i 0.225200 + 0.0437806i
$$381$$ −2.61318 −0.133877
$$382$$ 8.99486 0.0332075i 0.460217 0.00169904i
$$383$$ 22.1823 + 22.1823i 1.13346 + 1.13346i 0.989597 + 0.143867i $$0.0459538\pi$$
0.143867 + 0.989597i $$0.454046\pi$$
$$384$$ −2.34345 + 2.46781i −0.119588 + 0.125935i
$$385$$ −9.47841 14.2794i −0.483064 0.727747i
$$386$$ −19.3010 19.1590i −0.982393 0.975166i
$$387$$ −10.8407 + 10.8407i −0.551066 + 0.551066i
$$388$$ 5.24594 + 5.16904i 0.266322 + 0.262418i
$$389$$ 26.6415i 1.35078i 0.737462 + 0.675388i $$0.236024\pi$$
−0.737462 + 0.675388i $$0.763976\pi$$
$$390$$ −0.0591676 + 0.298461i −0.00299607 + 0.0151132i
$$391$$ 33.1100i 1.67445i
$$392$$ −19.9513 + 0.220978i −1.00769 + 0.0111611i
$$393$$ 1.76545 1.76545i 0.0890552 0.0890552i
$$394$$ −10.2608 + 10.3368i −0.516932 + 0.520763i
$$395$$ 36.1797 + 7.31126i 1.82040 + 0.367870i
$$396$$ 11.8969 0.0878435i 0.597841 0.00441430i
$$397$$ −20.3538 20.3538i −1.02153 1.02153i −0.999763 0.0217671i $$-0.993071\pi$$
−0.0217671 0.999763i $$-0.506929\pi$$
$$398$$ −0.110224 29.8562i −0.00552503 1.49656i
$$399$$ 1.12768 0.0564548
$$400$$ 18.5433 + 7.49312i 0.927164 + 0.374656i
$$401$$ −22.5998 −1.12858 −0.564289 0.825577i $$-0.690850\pi$$
−0.564289 + 0.825577i $$0.690850\pi$$
$$402$$ 0.0113030 + 3.06163i 0.000563742 + 0.152700i
$$403$$ −1.30935 1.30935i −0.0652236 0.0652236i
$$404$$ −26.1016 + 0.192727i −1.29860 + 0.00958854i
$$405$$ −17.9590 3.62918i −0.892388 0.180335i
$$406$$ −24.3143 + 24.4945i −1.20670 + 1.21564i
$$407$$ −14.0457 + 14.0457i −0.696217 + 0.696217i
$$408$$ 3.68444 0.0408084i 0.182407 0.00202032i
$$409$$ 3.50326i 0.173225i −0.996242 0.0866126i $$-0.972396\pi$$
0.996242 0.0866126i $$-0.0276042\pi$$
$$410$$ −4.04488 + 20.4037i −0.199762 + 1.00767i
$$411$$ 1.34495i 0.0663416i
$$412$$ 25.0664 + 24.6990i 1.23493 + 1.21683i
$$413$$ 11.7304 11.7304i 0.577214 0.577214i
$$414$$ 22.3259 + 22.1616i 1.09726 + 1.08918i
$$415$$ 7.51846 + 11.3267i 0.369066 + 0.556007i
$$416$$ −1.30288 1.25565i −0.0638791 0.0615633i
$$417$$ 3.61396 + 3.61396i 0.176976 + 0.176976i
$$418$$ −2.89139 + 0.0106745i −0.141422 + 0.000522106i
$$419$$ 12.6029 0.615691 0.307846 0.951436i $$-0.400392\pi$$
0.307846 + 0.951436i $$0.400392\pi$$
$$420$$ 4.95048 + 0.962412i 0.241559 + 0.0469609i
$$421$$ −38.3993 −1.87147 −0.935735 0.352704i $$-0.885262\pi$$
−0.935735 + 0.352704i $$0.885262\pi$$
$$422$$ −19.0244 + 0.0702346i −0.926092 + 0.00341897i
$$423$$ −3.61098 3.61098i −0.175572 0.175572i
$$424$$ 19.2975 + 18.8748i 0.937172 + 0.916639i
$$425$$ −8.16459 20.0559i −0.396041 0.972853i
$$426$$ 0.462966 + 0.459560i 0.0224308 + 0.0222658i
$$427$$ 2.06159 2.06159i 0.0997673 0.0997673i
$$428$$ −1.84930 + 1.87681i −0.0893891 + 0.0907190i
$$429$$ 0.196722i 0.00949781i
$$430$$ 13.8488 9.26639i 0.667848 0.446865i
$$431$$ 22.0058i 1.05998i 0.848003 + 0.529992i $$0.177805\pi$$
−0.848003 + 0.529992i $$0.822195\pi$$
$$432$$ −4.95303 + 5.10152i −0.238303 + 0.245447i
$$433$$ 24.6830 24.6830i 1.18619 1.18619i 0.208077 0.978112i $$-0.433279\pi$$
0.978112 0.208077i $$-0.0667205\pi$$
$$434$$ −21.6218 + 21.7821i −1.03788 + 1.04557i
$$435$$ 3.64807 2.42152i 0.174912 0.116103i
$$436$$ −0.298902 40.4811i −0.0143148 1.93869i
$$437$$ −5.40599 5.40599i −0.258604 0.258604i
$$438$$ 0.0161765 + 4.38171i 0.000772944 + 0.209366i
$$439$$ −14.9623 −0.714113 −0.357056 0.934083i $$-0.616220\pi$$
−0.357056 + 0.934083i $$0.616220\pi$$
$$440$$ −12.7021 2.42077i −0.605551 0.115405i
$$441$$ −20.5246 −0.977360
$$442$$ 0.00723265 + 1.95910i 0.000344022 + 0.0931849i
$$443$$ 4.16446 + 4.16446i 0.197859 + 0.197859i 0.799082 0.601222i $$-0.205319\pi$$
−0.601222 + 0.799082i $$0.705319\pi$$
$$444$$ −0.0431560 5.84473i −0.00204809 0.277379i
$$445$$ 3.87192 19.1602i 0.183547 0.908279i
$$446$$ −2.66135 + 2.68107i −0.126019 + 0.126953i
$$447$$ −2.07919 + 2.07919i −0.0983422 + 0.0983422i
$$448$$ −20.7321 + 21.6715i −0.979499 + 1.02388i
$$449$$ 4.32706i 0.204207i 0.994774 + 0.102103i $$0.0325572\pi$$
−0.994774 + 0.102103i $$0.967443\pi$$
$$450$$ 18.9884 + 7.91873i 0.895120 + 0.373293i
$$451$$ 13.4485i 0.633265i
$$452$$ −5.97593 + 6.06484i −0.281084 + 0.285266i
$$453$$ 0.897424 0.897424i 0.0421646 0.0421646i
$$454$$ 2.07871 + 2.06342i 0.0975589 + 0.0968412i
$$455$$ −0.531129 + 2.62829i −0.0248997 + 0.123216i
$$456$$ 0.594908 0.608234i 0.0278591 0.0284831i
$$457$$ 11.1732 + 11.1732i 0.522659 + 0.522659i 0.918374 0.395714i $$-0.129503\pi$$
−0.395714 + 0.918374i $$0.629503\pi$$
$$458$$ −4.36810 + 0.0161263i −0.204108 + 0.000753530i
$$459$$ 7.69848 0.359334
$$460$$ −19.1183 28.3457i −0.891396 1.32163i
$$461$$ −28.2155 −1.31413 −0.657064 0.753835i $$-0.728202\pi$$
−0.657064 + 0.753835i $$0.728202\pi$$
$$462$$ −3.26057 + 0.0120375i −0.151695 + 0.000560033i
$$463$$ −23.1500 23.1500i −1.07587 1.07587i −0.996875 0.0789948i $$-0.974829\pi$$
−0.0789948 0.996875i $$-0.525171\pi$$
$$464$$ 0.384512 + 26.0363i 0.0178505 + 1.20871i
$$465$$ 3.24409 2.15336i 0.150441 0.0998599i
$$466$$ 0.390840 + 0.387964i 0.0181053 + 0.0179721i
$$467$$ −12.5001 + 12.5001i −0.578435 + 0.578435i −0.934472 0.356037i $$-0.884128\pi$$
0.356037 + 0.934472i $$0.384128\pi$$
$$468$$ −1.32585 1.30641i −0.0612874 0.0603889i
$$469$$ 26.9812i 1.24588i
$$470$$ 3.08658 + 4.61295i 0.142373 + 0.212780i
$$471$$ 3.64021i 0.167732i
$$472$$ −0.138618 12.5153i −0.00638040 0.576063i
$$473$$ −7.61784 + 7.61784i −0.350269 + 0.350269i
$$474$$ 4.94704 4.98370i 0.227225 0.228909i
$$475$$ −4.60765 1.94153i −0.211414 0.0890836i
$$476$$ 32.4707 0.239756i 1.48829 0.0109892i
$$477$$ 19.6345 + 19.6345i 0.899004 + 0.899004i
$$478$$ −0.0133291 3.61044i −0.000609658 0.165137i
$$479$$ 18.1663 0.830040 0.415020 0.909812i $$-0.363775\pi$$
0.415020 + 0.909812i $$0.363775\pi$$
$$480$$ 3.13071 2.16240i 0.142896 0.0986994i
$$481$$ 3.10769 0.141699
$$482$$ −0.0567465 15.3709i −0.00258473 0.700123i
$$483$$ −6.09625 6.09625i −0.277389 0.277389i
$$484$$ −13.6394 + 0.100710i −0.619973 + 0.00457772i
$$485$$ −4.55368 6.86022i −0.206772 0.311506i
$$486$$ −7.76871 + 7.82629i −0.352396 + 0.355008i
$$487$$ 23.4493 23.4493i 1.06259 1.06259i 0.0646845 0.997906i $$-0.479396\pi$$
0.997906 0.0646845i $$-0.0206041\pi$$
$$488$$ −0.0243618 2.19954i −0.00110281 0.0995684i
$$489$$ 4.90209i 0.221680i
$$490$$ 21.8818 + 4.33789i 0.988518 + 0.195966i
$$491$$ 1.07295i 0.0484217i −0.999707 0.0242108i $$-0.992293\pi$$
0.999707 0.0242108i $$-0.00770731\pi$$
$$492$$ 2.81878 + 2.77746i 0.127080 + 0.125218i
$$493$$ 19.9353 19.9353i 0.897839 0.897839i
$$494$$ 0.321050 + 0.318688i 0.0144447 + 0.0143384i
$$495$$ −13.0379 2.63473i −0.586011 0.118422i
$$496$$ 0.341932 + 23.1531i 0.0153532 + 1.03961i
$$497$$ 4.06497 + 4.06497i 0.182339 + 0.182339i
$$498$$ 2.58635 0.00954834i 0.115897 0.000427871i
$$499$$ 17.3943 0.778674 0.389337 0.921095i $$-0.372704\pi$$
0.389337 + 0.921095i $$0.372704\pi$$
$$500$$ −18.5704 12.4556i −0.830492 0.557030i
$$501$$ 1.54876 0.0691936
$$502$$ −31.0213 + 0.114525i −1.38455 + 0.00511151i
$$503$$ −20.5398 20.5398i −0.915826 0.915826i 0.0808962 0.996723i $$-0.474222\pi$$
−0.996723 + 0.0808962i $$0.974222\pi$$
$$504$$ −21.5721 + 22.0553i −0.960896 + 0.982420i
$$505$$ 28.6050 + 5.78055i 1.27291 + 0.257231i
$$506$$ 15.6885 + 15.5731i 0.697439 + 0.692308i
$$507$$ 2.74334 2.74334i 0.121836 0.121836i
$$508$$ −12.1947 + 12.3761i −0.541051 + 0.549101i
$$509$$ 31.2945i 1.38710i −0.720406 0.693552i $$-0.756045\pi$$
0.720406 0.693552i $$-0.243955\pi$$
$$510$$ −4.04094 0.801085i −0.178936 0.0354726i
$$511$$ 38.6147i 1.70822i
$$512$$ 0.751686 + 22.6149i 0.0332201 + 0.999448i
$$513$$ 1.25696 1.25696i 0.0554960 0.0554960i
$$514$$ 12.5383 12.6313i 0.553043 0.557141i
$$515$$ −21.7586 32.7798i −0.958799 1.44445i
$$516$$ −0.0234062 3.16996i −0.00103040 0.139550i
$$517$$ −2.53746 2.53746i −0.111597 0.111597i
$$518$$ −0.190161 51.5086i −0.00835518 2.26316i
$$519$$ −0.619015 −0.0271717
$$520$$ 1.13741 + 1.67302i 0.0498787 + 0.0733668i
$$521$$ 17.9538 0.786572 0.393286 0.919416i $$-0.371338\pi$$
0.393286 + 0.919416i $$0.371338\pi$$
$$522$$ 0.0988874 + 26.7855i 0.00432818 + 1.17237i
$$523$$ 5.14238 + 5.14238i 0.224861 + 0.224861i 0.810542 0.585681i $$-0.199173\pi$$
−0.585681 + 0.810542i $$0.699173\pi$$
$$524$$ −0.122569 16.5999i −0.00535447 0.725170i
$$525$$ −5.19598 2.18944i −0.226771 0.0955548i
$$526$$ 22.6020 22.7695i 0.985493 0.992796i
$$527$$ 17.7277 17.7277i 0.772230 0.772230i
$$528$$ −1.71362 + 1.76499i −0.0745755 + 0.0768112i
$$529$$ 35.4494i 1.54128i
$$530$$ −16.7831 25.0827i −0.729012 1.08952i
$$531$$ 12.8749i 0.558723i
$$532$$ 5.26246 5.34075i 0.228157 0.231551i
$$533$$ −1.48778 + 1.48778i −0.0644431 + 0.0644431i
$$534$$ −2.63928 2.61987i −0.114213 0.113373i
$$535$$ 2.45434 1.62914i 0.106110 0.0704339i
$$536$$ 14.5527 + 14.2339i 0.628582 + 0.614810i
$$537$$ 0.467292 + 0.467292i 0.0201651 + 0.0201651i
$$538$$ 9.85029 0.0363655i 0.424676 0.00156783i
$$539$$ −14.4227 −0.621230
$$540$$ 6.59071 4.44524i 0.283619 0.191292i
$$541$$ 19.3237 0.830792 0.415396 0.909641i $$-0.363643\pi$$
0.415396 + 0.909641i $$0.363643\pi$$
$$542$$ 10.2328 0.0377776i 0.439536 0.00162269i
$$543$$ 0.953477 + 0.953477i 0.0409176 + 0.0409176i
$$544$$ 17.0006 17.6401i 0.728893 0.756311i
$$545$$ −8.96509 + 44.3637i −0.384022 + 1.90033i
$$546$$ 0.362043 + 0.359380i 0.0154940 + 0.0153800i
$$547$$ 18.3764 18.3764i 0.785719 0.785719i −0.195071 0.980789i $$-0.562494\pi$$
0.980789 + 0.195071i $$0.0624936\pi$$
$$548$$ −6.36974 6.27636i −0.272102 0.268113i
$$549$$ 2.26274i 0.0965712i
$$550$$ 13.3432 + 5.56453i 0.568957 + 0.237272i
$$551$$ 6.50979i 0.277326i
$$552$$ −6.50417 + 0.0720394i −0.276836 + 0.00306620i
$$553$$ 43.7583 43.7583i 1.86079 1.86079i
$$554$$ 21.2987 21.4565i 0.904895 0.911601i
$$555$$ −1.29440 + 6.40531i −0.0549441 + 0.271890i
$$556$$ 33.9808 0.250905i 1.44110 0.0106408i
$$557$$ 22.1345 + 22.1345i 0.937870 + 0.937870i 0.998180 0.0603095i $$-0.0192088\pi$$
−0.0603095 + 0.998180i $$0.519209\pi$$
$$558$$ 0.0879369 + 23.8194i 0.00372266 + 1.00835i
$$559$$ 1.68550 0.0712889
$$560$$ 27.6599 18.9544i 1.16885 0.800971i
$$561$$ 2.66346 0.112452
$$562$$ 0.0522597 + 14.1555i 0.00220444 + 0.597114i
$$563$$ −4.11064 4.11064i −0.173243 0.173243i 0.615160 0.788403i $$-0.289092\pi$$
−0.788403 + 0.615160i $$0.789092\pi$$
$$564$$ 1.05590 0.00779647i 0.0444612 0.000328291i
$$565$$ 7.93111 5.26451i 0.333664 0.221480i
$$566$$ −11.9532 + 12.0418i −0.502430 + 0.506154i
$$567$$ −21.7209 + 21.7209i −0.912190 + 0.912190i
$$568$$ 4.33697 0.0480358i 0.181975 0.00201554i
$$569$$ 21.3698i 0.895869i 0.894066 + 0.447934i $$0.147840\pi$$
−0.894066 + 0.447934i $$0.852160\pi$$
$$570$$ −0.790574 + 0.528982i −0.0331135 + 0.0221566i
$$571$$ 17.7556i 0.743049i −0.928423 0.371524i $$-0.878835\pi$$
0.928423 0.371524i $$-0.121165\pi$$
$$572$$ −0.931680 0.918023i −0.0389555 0.0383845i
$$573$$ −1.35285 + 1.35285i −0.0565163 + 0.0565163i
$$574$$ 24.7504 + 24.5683i 1.03306 + 1.02546i
$$575$$ 14.4130 + 35.4048i 0.601064 + 1.47648i
$$576$$ 0.515544 + 23.2704i 0.0214810 + 0.969601i
$$577$$ 15.8282 + 15.8282i 0.658936 + 0.658936i 0.955128 0.296193i $$-0.0957170\pi$$
−0.296193 + 0.955128i $$0.595717\pi$$
$$578$$ −2.48329 + 0.00916785i −0.103291 + 0.000381332i
$$579$$ 5.78449 0.240395
$$580$$ 5.55572 28.5776i 0.230689 1.18662i
$$581$$ 22.7927 0.945601
$$582$$ −1.56646 + 0.00578311i −0.0649320 + 0.000239718i
$$583$$ 13.7973 + 13.7973i 0.571425 + 0.571425i
$$584$$ 20.8274 + 20.3711i 0.861845 + 0.842963i
$$585$$ 1.15089 + 1.73384i 0.0475833 + 0.0716854i
$$586$$ 14.6387 + 14.5311i 0.604721 + 0.600272i
$$587$$ −5.07211 + 5.07211i −0.209348 + 0.209348i −0.803991 0.594642i $$-0.797294\pi$$
0.594642 + 0.803991i $$0.297294\pi$$
$$588$$ 2.97866 3.02297i 0.122838 0.124665i
$$589$$ 5.78891i 0.238528i
$$590$$ −2.72112 + 13.7263i −0.112027 + 0.565101i
$$591$$ 3.09795i 0.127433i
$$592$$ −27.8822 27.0707i −1.14595 1.11260i
$$593$$ 14.6665 14.6665i 0.602280 0.602280i −0.338637 0.940917i $$-0.609966\pi$$
0.940917 + 0.338637i $$0.109966\pi$$
$$594$$ −3.62093 + 3.64776i −0.148569 + 0.149670i
$$595$$ −35.5851 7.19109i −1.45884 0.294806i
$$596$$ 0.144351 + 19.5498i 0.00591285 + 0.800793i
$$597$$ 4.49047 + 4.49047i 0.183783 + 0.183783i
$$598$$ −0.0127679 3.45842i −0.000522117 0.141425i
$$599$$ 10.7934 0.441005 0.220502 0.975386i $$-0.429230\pi$$
0.220502 + 0.975386i $$0.429230\pi$$
$$600$$ −3.92203 + 1.64750i −0.160116 + 0.0672588i
$$601$$ −8.15596 −0.332688 −0.166344 0.986068i $$-0.553196\pi$$
−0.166344 + 0.986068i $$0.553196\pi$$
$$602$$ −0.103136 27.9363i −0.00420351 1.13860i
$$603$$ 14.8069 + 14.8069i 0.602982 + 0.602982i
$$604$$ −0.0623052 8.43815i −0.00253516 0.343344i
$$605$$ 14.9476 + 3.02063i 0.607706 + 0.122806i
$$606$$ 3.91131 3.94030i 0.158886 0.160064i
$$607$$ −33.9049 + 33.9049i −1.37616 + 1.37616i −0.525148 + 0.851011i $$0.675990\pi$$
−0.851011 + 0.525148i $$0.824010\pi$$
$$608$$ −0.104414 5.65589i −0.00423455 0.229377i
$$609$$ 7.34099i 0.297472i
$$610$$ −0.478232 + 2.41236i −0.0193630 + 0.0976737i
$$611$$ 0.561429i 0.0227130i
$$612$$ 17.6879 17.9510i 0.714989 0.725626i
$$613$$ −8.50562 + 8.50562i −0.343539 + 0.343539i −0.857696 0.514157i $$-0.828105\pi$$
0.514157 + 0.857696i $$0.328105\pi$$
$$614$$ −5.36153 5.32209i −0.216374 0.214782i
$$615$$ −2.44681 3.68617i −0.0986649 0.148641i
$$616$$ −15.1588 + 15.4983i −0.610765 + 0.624446i
$$617$$ −22.6320 22.6320i −0.911129 0.911129i 0.0852322 0.996361i $$-0.472837\pi$$
−0.996361 + 0.0852322i $$0.972837\pi$$
$$618$$ −7.48496 + 0.0276331i −0.301089 + 0.00111157i
$$619$$ −14.5559 −0.585051 −0.292525 0.956258i $$-0.594496\pi$$
−0.292525 + 0.956258i $$0.594496\pi$$
$$620$$ 4.94049 25.4130i 0.198415 1.02061i
$$621$$ −13.5902 −0.545355
$$622$$ 30.4062 0.112254i 1.21918 0.00450099i
$$623$$ −23.1737 23.1737i −0.928433 0.928433i
$$624$$ 0.384832 0.00568331i 0.0154056 0.000227515i
$$625$$ 17.4609 + 17.8918i 0.698436 + 0.715672i
$$626$$ −17.3073 17.1800i −0.691740 0.686651i
$$627$$ 0.434873 0.434873i 0.0173671 0.0173671i
$$628$$ −17.2401 16.9874i −0.687956 0.677872i
$$629$$ 42.0758i 1.67767i
$$630$$ 28.6671 19.1815i 1.14213 0.764210i
$$631$$ 29.4769i 1.17346i 0.809784 + 0.586728i $$0.199584\pi$$
−0.809784 + 0.586728i $$0.800416\pi$$
$$632$$ −0.517092 46.6864i −0.0205688 1.85708i
$$633$$ 2.86132 2.86132i 0.113727 0.113727i
$$634$$ −0.325803 + 0.328218i −0.0129393 + 0.0130352i
$$635$$ 16.1845 10.7429i 0.642261 0.426320i
$$636$$ −5.74138 + 0.0423929i −0.227661 + 0.00168099i
$$637$$ 1.59556 + 1.59556i 0.0632183 + 0.0632183i
$$638$$ 0.0694887 + 18.8223i 0.00275108 + 0.745183i
$$639$$ 4.46159 0.176498
$$640$$ 4.36859 24.9182i 0.172684 0.984977i
$$641$$ 12.2729 0.484749 0.242374 0.970183i $$-0.422074\pi$$
0.242374 + 0.970183i $$0.422074\pi$$
$$642$$ −0.00206899 0.560425i −8.16565e−5 0.0221182i
$$643$$ −8.55592 8.55592i −0.337413 0.337413i 0.517980 0.855393i $$-0.326684\pi$$
−0.855393 + 0.517980i $$0.826684\pi$$
$$644$$ −57.3209 + 0.423243i −2.25876 + 0.0166781i
$$645$$ −0.702032 + 3.47400i −0.0276425 + 0.136789i
$$646$$ −4.31480 + 4.34677i −0.169763 + 0.171022i
$$647$$ −27.5524 + 27.5524i −1.08320 + 1.08320i −0.0869883 + 0.996209i $$0.527724\pi$$
−0.996209 + 0.0869883i $$0.972276\pi$$
$$648$$ 0.256675 + 23.1743i 0.0100832 + 0.910371i
$$649$$ 9.04725i 0.355136i
$$650$$ −0.860543 2.09173i −0.0337533 0.0820445i
$$651$$ 6.52807i 0.255855i
$$652$$ 23.2164 + 22.8761i 0.909226 + 0.895898i
$$653$$ 9.19195 9.19195i 0.359709 0.359709i −0.503997 0.863706i $$-0.668138\pi$$
0.863706 + 0.503997i $$0.168138\pi$$
$$654$$ 6.11103 + 6.06608i 0.238960 + 0.237202i
$$655$$ −3.67628 + 18.1920i −0.143644 + 0.710821i
$$656$$ 26.3083 0.388529i 1.02717 0.0151695i
$$657$$ 21.1912 + 21.1912i 0.826746 + 0.826746i
$$658$$ 9.30542 0.0343540i 0.362763 0.00133926i
$$659$$ −1.02222 −0.0398199 −0.0199099 0.999802i $$-0.506338\pi$$
−0.0199099 + 0.999802i $$0.506338\pi$$
$$660$$ 2.28021 1.53793i 0.0887569 0.0598639i
$$661$$ −8.72455 −0.339346 −0.169673 0.985500i $$-0.554271\pi$$
−0.169673 + 0.985500i $$0.554271\pi$$
$$662$$ 31.7478 0.117207i 1.23391 0.00455539i
$$663$$ −0.294654 0.294654i −0.0114434 0.0114434i
$$664$$ 12.0242 12.2936i 0.466631 0.477084i
$$665$$ −6.98421 + 4.63598i −0.270836 + 0.179776i
$$666$$ −28.3715 28.1627i −1.09937 1.09128i
$$667$$ −35.1919 + 35.1919i −1.36263 + 1.36263i
$$668$$ 7.22746 7.33499i 0.279639 0.283799i
$$669$$ 0.803516i 0.0310657i
$$670$$ −12.6565 18.9154i −0.488965 0.730767i
$$671$$ 1.59004i 0.0613826i
$$672$$ −0.117746 6.37806i −0.00454216 0.246039i
$$673$$ −15.8449 + 15.8449i −0.610777 + 0.610777i −0.943148 0.332372i $$-0.892151\pi$$
0.332372 + 0.943148i $$0.392151\pi$$
$$674$$ 6.66409 6.71348i 0.256691 0.258594i
$$675$$ −8.23204 + 3.35120i −0.316851 + 0.128988i
$$676$$ −0.190461 25.7947i −0.00732543 0.992102i
$$677$$ −19.7428 19.7428i −0.758777 0.758777i 0.217323 0.976100i $$-0.430268\pi$$
−0.976100 + 0.217323i $$0.930268\pi$$
$$678$$ −0.00668587 1.81099i −0.000256769 0.0695507i
$$679$$ −13.8048 −0.529779
$$680$$ −22.6514 + 15.3997i −0.868643 + 0.590551i
$$681$$ −0.622990 −0.0238730
$$682$$ 0.0617937 + 16.7380i 0.00236620 + 0.640930i
$$683$$ 25.7242 + 25.7242i 0.984311 + 0.984311i 0.999879 0.0155682i $$-0.00495571\pi$$
−0.0155682 + 0.999879i $$0.504956\pi$$
$$684$$ −0.0429651 5.81888i −0.00164281 0.222490i
$$685$$ 5.52918 + 8.32983i 0.211259 + 0.318266i
$$686$$ 0.202749 0.204252i 0.00774101 0.00779838i
$$687$$ 0.656975 0.656975i 0.0250652 0.0250652i
$$688$$ −15.1223 14.6821i −0.576532 0.559751i
$$689$$ 3.05274i 0.116300i
$$690$$ 7.13351 + 1.41416i 0.271568 + 0.0538362i
$$691$$ 28.0903i 1.06861i −0.845293 0.534303i $$-0.820574\pi$$
0.845293 0.534303i $$-0.179426\pi$$
$$692$$ −2.88870 + 2.93167i −0.109812 + 0.111446i
$$693$$ −15.7690 + 15.7690i −0.599015 + 0.599015i
$$694$$ −36.4137 36.1459i −1.38225 1.37208i
$$695$$ −37.2399 7.52550i −1.41259 0.285459i
$$696$$ −3.95947 3.87273i −0.150083 0.146795i
$$697$$ −20.1435 20.1435i −0.762989 0.762989i
$$698$$ 15.5241 0.0573122i 0.587596 0.00216930i
$$699$$ −0.117134 −0.00443043
$$700$$ −34.6168 + 14.3911i −1.30839 + 0.543932i
$$701$$ 17.5957 0.664579 0.332289 0.943177i $$-0.392179\pi$$
0.332289 + 0.943177i $$0.392179\pi$$
$$702$$ 0.804123 0.00296868i 0.0303497 0.000112046i
$$703$$ 6.86987 + 6.86987i 0.259102 + 0.259102i
$$704$$ 0.362275 + 16.3522i 0.0136538 + 0.616298i
$$705$$ −1.15717 0.233843i −0.0435815 0.00880702i
$$706$$ 29.2245 + 29.0095i 1.09988 + 1.09179i
$$707$$ 34.5969 34.5969i 1.30115 1.30115i
$$708$$ 1.89629 + 1.86849i 0.0712668 + 0.0702221i
$$709$$ 40.9442i 1.53769i −0.639434 0.768846i $$-0.720831\pi$$
0.639434 0.768846i $$-0.279169\pi$$
$$710$$ −4.75661 0.942961i −0.178513 0.0353887i
$$711$$ 48.0278i 1.80118i
$$712$$ −24.7243 + 0.273843i −0.926582 + 0.0102627i
$$713$$ −31.2948 + 31.2948i −1.17200 + 1.17200i
$$714$$ −4.86573 + 4.90179i −0.182095 + 0.183445i
$$715$$ 0.808734 + 1.21838i 0.0302449 + 0.0455647i
$$716$$ 4.39378 0.0324425i 0.164203 0.00121243i
$$717$$ 0.543020 + 0.543020i 0.0202795 + 0.0202795i
$$718$$ 0.114257 + 30.9487i 0.00426404 + 1.15500i
$$719$$ 18.4285 0.687266 0.343633 0.939104i $$-0.388342\pi$$
0.343633 + 0.939104i $$0.388342\pi$$
$$720$$ 4.77745 25.5812i 0.178045 0.953356i
$$721$$ −65.9627 −2.45658
$$722$$ 0.00522099 + 1.41420i 0.000194305 + 0.0526312i
$$723$$ 2.31182 + 2.31182i 0.0859775 + 0.0859775i
$$724$$ 8.96520 0.0661968i 0.333189 0.00246018i
$$725$$ −12.6390 + 29.9949i −0.469399 + 1.11398i
$$726$$ 2.04386 2.05901i 0.0758548 0.0764170i
$$727$$ 14.2988 14.2988i 0.530314 0.530314i −0.390352 0.920666i $$-0.627647\pi$$
0.920666 + 0.390352i $$0.127647\pi$$
$$728$$ 3.39155 0.0375643i 0.125699 0.00139223i
$$729$$ 22.2360i 0.823555i
$$730$$ −18.1137 27.0712i −0.670417 1.00195i
$$731$$ 22.8204i 0.844042i
$$732$$ 0.333269 + 0.328383i 0.0123180 + 0.0121374i
$$733$$ 2.66770 2.66770i 0.0985337 0.0985337i −0.656122 0.754655i $$-0.727804\pi$$
0.754655 + 0.656122i $$0.227804\pi$$
$$734$$ 37.0187 + 36.7464i 1.36639 + 1.35633i
$$735$$ −3.95320 + 2.62406i −0.145816 + 0.0967898i
$$736$$ −30.0112 + 31.1401i −1.10623 + 1.14784i
$$737$$ 10.4049 + 10.4049i 0.383268 + 0.383268i
$$738$$ 27.0653 0.0999203i 0.996288 0.00367812i
$$739$$ −38.6731 −1.42261 −0.711307 0.702882i $$-0.751896\pi$$
−0.711307 + 0.702882i $$0.751896\pi$$
$$740$$ 24.2953 + 36.0214i 0.893114 + 1.32417i
$$741$$ −0.0962184 −0.00353467
$$742$$ −50.5978 + 0.186798i −1.85750 + 0.00685757i
$$743$$ −1.38756 1.38756i −0.0509046 0.0509046i 0.681196 0.732101i $$-0.261460\pi$$
−0.732101 + 0.681196i $$0.761460\pi$$
$$744$$ −3.52101 3.44387i −0.129087 0.126258i
$$745$$ 4.32958 21.4249i 0.158624 0.784948i
$$746$$ −6.29252 6.24623i −0.230385 0.228691i
$$747$$ 12.5083 12.5083i 0.457654 0.457654i
$$748$$ 12.4293 12.6143i 0.454462 0.461223i
$$749$$ 4.93885i 0.180462i
$$750$$ 4.66972 0.902442i 0.170514 0.0329525i
$$751$$ 13.6253i 0.497193i 0.968607 + 0.248596i $$0.0799693\pi$$
−0.968607 + 0.248596i $$0.920031\pi$$
$$752$$ 4.89053 5.03714i 0.178339 0.183686i
$$753$$ 4.66569 4.66569i 0.170027 0.170027i
$$754$$ 2.07459 2.08997i 0.0755522 0.0761121i
$$755$$ −1.86874 + 9.24747i −0.0680106 + 0.336550i
$$756$$ −0.0984090 13.3278i −0.00357910 0.484727i
$$757$$ 12.0474 + 12.0474i 0.437871 + 0.437871i 0.891295 0.453424i $$-0.149798\pi$$
−0.453424 + 0.891295i $$0.649798\pi$$
$$758$$ 0.132243 + 35.8205i 0.00480328 + 1.30106i
$$759$$ −4.70184 −0.170666
$$760$$ −1.18402 + 6.21274i −0.0429489 + 0.225360i
$$761$$ −9.84572 −0.356907 −0.178454 0.983948i $$-0.557109\pi$$
−0.178454 + 0.983948i $$0.557109\pi$$
$$762$$ −0.0136434 3.69557i −0.000494248 0.133876i
$$763$$ 53.6566 + 53.6566i 1.94250 + 1.94250i
$$764$$ 0.0939242 + 12.7204i 0.00339806 + 0.460208i
$$765$$ −23.4749 + 15.5822i −0.848736 + 0.563374i
$$766$$ −31.2545 + 31.4862i −1.12927 + 1.13764i
$$767$$ −1.00088 + 1.00088i −0.0361397 + 0.0361397i
$$768$$ −3.50222 3.30123i −0.126375 0.119123i
$$769$$ 32.7080i 1.17948i −0.807593 0.589741i $$-0.799230\pi$$
0.807593 0.589741i $$-0.200770\pi$$
$$770$$ 20.1445 13.4790i 0.725959 0.485748i