Properties

 Label 48.2.j.a.13.4 Level $48$ Weight $2$ Character 48.13 Analytic conductor $0.383$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,2,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$48 = 2^{4} \cdot 3$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 48.j (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: $$0.383281929702$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.18939904.2 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2$$ x^8 - 4*x^7 + 14*x^6 - 28*x^5 + 43*x^4 - 44*x^3 + 30*x^2 - 12*x + 2 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

 Embedding label 13.4 Root $$0.500000 + 0.0297061i$$ of defining polynomial Character $$\chi$$ $$=$$ 48.13 Dual form 48.2.j.a.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(0.874559 + 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 + 1.94392i) q^{4} +(-0.334904 + 0.334904i) q^{5} +(0.167452 - 1.40426i) q^{6} -4.55765i q^{7} +(-2.57172 + 1.17740i) q^{8} +1.00000i q^{9} +O(q^{10})$$ $$q+(0.874559 + 1.11137i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.470294 + 1.94392i) q^{4} +(-0.334904 + 0.334904i) q^{5} +(0.167452 - 1.40426i) q^{6} -4.55765i q^{7} +(-2.57172 + 1.17740i) q^{8} +1.00000i q^{9} +(-0.665096 - 0.0793096i) q^{10} +(-2.47363 + 2.47363i) q^{11} +(1.70711 - 1.04201i) q^{12} +(-0.0594122 - 0.0594122i) q^{13} +(5.06524 - 3.98593i) q^{14} +0.473626 q^{15} +(-3.55765 - 1.82843i) q^{16} +3.61706 q^{17} +(-1.11137 + 0.874559i) q^{18} +(2.55765 + 2.55765i) q^{19} +(-0.493523 - 0.808530i) q^{20} +(-3.22274 + 3.22274i) q^{21} +(-4.91245 - 0.585786i) q^{22} +2.82843i q^{23} +(2.65103 + 0.985930i) q^{24} +4.77568i q^{25} +(0.0140696 - 0.117988i) q^{26} +(0.707107 - 0.707107i) q^{27} +(8.85970 + 2.14343i) q^{28} +(-5.16333 - 5.16333i) q^{29} +(0.414214 + 0.526374i) q^{30} -0.557647 q^{31} +(-1.07931 - 5.55294i) q^{32} +3.49824 q^{33} +(3.16333 + 4.01990i) q^{34} +(1.52637 + 1.52637i) q^{35} +(-1.94392 - 0.470294i) q^{36} +(4.38607 - 4.38607i) q^{37} +(-0.605684 + 5.07931i) q^{38} +0.0840215i q^{39} +(0.466962 - 1.25559i) q^{40} -9.27391i q^{41} +(-6.40014 - 0.763187i) q^{42} +(-1.61040 + 1.61040i) q^{43} +(-3.64520 - 5.97186i) q^{44} +(-0.334904 - 0.334904i) q^{45} +(-3.14343 + 2.47363i) q^{46} +2.82843 q^{47} +(1.22274 + 3.80853i) q^{48} -13.7721 q^{49} +(-5.30755 + 4.17661i) q^{50} +(-2.55765 - 2.55765i) q^{51} +(0.143434 - 0.0875513i) q^{52} +(-0.493523 + 0.493523i) q^{53} +(1.40426 + 0.167452i) q^{54} -1.65685i q^{55} +(5.36618 + 11.7210i) q^{56} -3.61706i q^{57} +(1.22274 - 10.2540i) q^{58} +(4.00000 - 4.00000i) q^{59} +(-0.222743 + 0.920690i) q^{60} +(2.72922 + 2.72922i) q^{61} +(-0.487695 - 0.619753i) q^{62} +4.55765 q^{63} +(5.22746 - 6.05588i) q^{64} +0.0397948 q^{65} +(3.05941 + 3.88784i) q^{66} +(3.77568 + 3.77568i) q^{67} +(-1.70108 + 7.03127i) q^{68} +(2.00000 - 2.00000i) q^{69} +(-0.361465 + 3.03127i) q^{70} +9.11529i q^{71} +(-1.17740 - 2.57172i) q^{72} -0.541560i q^{73} +(8.71044 + 1.03868i) q^{74} +(3.37691 - 3.37691i) q^{75} +(-6.17471 + 3.76901i) q^{76} +(11.2739 + 11.2739i) q^{77} +(-0.0933792 + 0.0734818i) q^{78} -10.9937 q^{79} +(1.80382 - 0.579123i) q^{80} -1.00000 q^{81} +(10.3068 - 8.11058i) q^{82} +(-10.6417 - 10.6417i) q^{83} +(-4.74912 - 7.78039i) q^{84} +(-1.21137 + 1.21137i) q^{85} +(-3.19813 - 0.381362i) q^{86} +7.30205i q^{87} +(3.44902 - 9.27391i) q^{88} +14.6533i q^{89} +(0.0793096 - 0.665096i) q^{90} +(-0.270780 + 0.270780i) q^{91} +(-5.49824 - 1.33019i) q^{92} +(0.394316 + 0.394316i) q^{93} +(2.47363 + 3.14343i) q^{94} -1.71313 q^{95} +(-3.16333 + 4.68971i) q^{96} +4.31724 q^{97} +(-12.0446 - 15.3060i) q^{98} +(-2.47363 - 2.47363i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 4 q^{4} - 12 q^{8}+O(q^{10})$$ 8 * q - 4 * q^4 - 12 * q^8 $$8 q - 4 q^{4} - 12 q^{8} - 8 q^{10} - 8 q^{11} + 8 q^{12} + 12 q^{14} - 8 q^{15} + 4 q^{18} - 8 q^{19} + 16 q^{20} + 4 q^{24} + 20 q^{26} + 8 q^{28} - 16 q^{29} - 8 q^{30} + 24 q^{31} + 24 q^{35} - 4 q^{36} - 16 q^{37} - 8 q^{38} + 16 q^{40} - 20 q^{42} - 8 q^{43} - 40 q^{44} - 8 q^{46} - 16 q^{48} - 8 q^{49} - 36 q^{50} + 8 q^{51} - 16 q^{52} + 16 q^{53} + 4 q^{54} - 16 q^{58} + 32 q^{59} + 24 q^{60} + 16 q^{61} - 12 q^{62} + 8 q^{63} + 8 q^{64} - 16 q^{65} + 24 q^{66} - 16 q^{67} + 32 q^{68} + 16 q^{69} + 32 q^{70} - 4 q^{72} + 52 q^{74} + 16 q^{75} + 8 q^{76} + 16 q^{77} - 12 q^{78} - 24 q^{79} + 8 q^{80} - 8 q^{81} + 40 q^{82} - 40 q^{83} - 24 q^{84} - 16 q^{85} - 16 q^{86} + 32 q^{88} - 8 q^{90} - 8 q^{91} - 16 q^{92} + 8 q^{94} - 48 q^{95} - 40 q^{98} - 8 q^{99}+O(q^{100})$$ 8 * q - 4 * q^4 - 12 * q^8 - 8 * q^10 - 8 * q^11 + 8 * q^12 + 12 * q^14 - 8 * q^15 + 4 * q^18 - 8 * q^19 + 16 * q^20 + 4 * q^24 + 20 * q^26 + 8 * q^28 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 24 * q^35 - 4 * q^36 - 16 * q^37 - 8 * q^38 + 16 * q^40 - 20 * q^42 - 8 * q^43 - 40 * q^44 - 8 * q^46 - 16 * q^48 - 8 * q^49 - 36 * q^50 + 8 * q^51 - 16 * q^52 + 16 * q^53 + 4 * q^54 - 16 * q^58 + 32 * q^59 + 24 * q^60 + 16 * q^61 - 12 * q^62 + 8 * q^63 + 8 * q^64 - 16 * q^65 + 24 * q^66 - 16 * q^67 + 32 * q^68 + 16 * q^69 + 32 * q^70 - 4 * q^72 + 52 * q^74 + 16 * q^75 + 8 * q^76 + 16 * q^77 - 12 * q^78 - 24 * q^79 + 8 * q^80 - 8 * q^81 + 40 * q^82 - 40 * q^83 - 24 * q^84 - 16 * q^85 - 16 * q^86 + 32 * q^88 - 8 * q^90 - 8 * q^91 - 16 * q^92 + 8 * q^94 - 48 * q^95 - 40 * q^98 - 8 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$$.

 $$n$$ $$17$$ $$31$$ $$37$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{3}{4}\right)$$

Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.874559 + 1.11137i 0.618406 + 0.785858i
$$3$$ −0.707107 0.707107i −0.408248 0.408248i
$$4$$ −0.470294 + 1.94392i −0.235147 + 0.971960i
$$5$$ −0.334904 + 0.334904i −0.149774 + 0.149774i −0.778017 0.628243i $$-0.783774\pi$$
0.628243 + 0.778017i $$0.283774\pi$$
$$6$$ 0.167452 1.40426i 0.0683620 0.573289i
$$7$$ 4.55765i 1.72263i −0.508072 0.861314i $$-0.669642\pi$$
0.508072 0.861314i $$-0.330358\pi$$
$$8$$ −2.57172 + 1.17740i −0.909239 + 0.416274i
$$9$$ 1.00000i 0.333333i
$$10$$ −0.665096 0.0793096i −0.210322 0.0250799i
$$11$$ −2.47363 + 2.47363i −0.745826 + 0.745826i −0.973692 0.227866i $$-0.926825\pi$$
0.227866 + 0.973692i $$0.426825\pi$$
$$12$$ 1.70711 1.04201i 0.492799 0.300803i
$$13$$ −0.0594122 0.0594122i −0.0164780 0.0164780i 0.698820 0.715298i $$-0.253709\pi$$
−0.715298 + 0.698820i $$0.753709\pi$$
$$14$$ 5.06524 3.98593i 1.35374 1.06528i
$$15$$ 0.473626 0.122290
$$16$$ −3.55765 1.82843i −0.889412 0.457107i
$$17$$ 3.61706 0.877266 0.438633 0.898666i $$-0.355463\pi$$
0.438633 + 0.898666i $$0.355463\pi$$
$$18$$ −1.11137 + 0.874559i −0.261953 + 0.206135i
$$19$$ 2.55765 + 2.55765i 0.586765 + 0.586765i 0.936754 0.349989i $$-0.113815\pi$$
−0.349989 + 0.936754i $$0.613815\pi$$
$$20$$ −0.493523 0.808530i −0.110355 0.180793i
$$21$$ −3.22274 + 3.22274i −0.703260 + 0.703260i
$$22$$ −4.91245 0.585786i −1.04734 0.124890i
$$23$$ 2.82843i 0.589768i 0.955533 + 0.294884i $$0.0952810\pi$$
−0.955533 + 0.294884i $$0.904719\pi$$
$$24$$ 2.65103 + 0.985930i 0.541139 + 0.201252i
$$25$$ 4.77568i 0.955136i
$$26$$ 0.0140696 0.117988i 0.00275927 0.0231394i
$$27$$ 0.707107 0.707107i 0.136083 0.136083i
$$28$$ 8.85970 + 2.14343i 1.67433 + 0.405071i
$$29$$ −5.16333 5.16333i −0.958807 0.958807i 0.0403780 0.999184i $$-0.487144\pi$$
−0.999184 + 0.0403780i $$0.987144\pi$$
$$30$$ 0.414214 + 0.526374i 0.0756247 + 0.0961023i
$$31$$ −0.557647 −0.100156 −0.0500782 0.998745i $$-0.515947\pi$$
−0.0500782 + 0.998745i $$0.515947\pi$$
$$32$$ −1.07931 5.55294i −0.190797 0.981630i
$$33$$ 3.49824 0.608965
$$34$$ 3.16333 + 4.01990i 0.542507 + 0.689407i
$$35$$ 1.52637 + 1.52637i 0.258004 + 0.258004i
$$36$$ −1.94392 0.470294i −0.323987 0.0783823i
$$37$$ 4.38607 4.38607i 0.721066 0.721066i −0.247756 0.968822i $$-0.579693\pi$$
0.968822 + 0.247756i $$0.0796932\pi$$
$$38$$ −0.605684 + 5.07931i −0.0982549 + 0.823973i
$$39$$ 0.0840215i 0.0134542i
$$40$$ 0.466962 1.25559i 0.0738332 0.198527i
$$41$$ 9.27391i 1.44834i −0.689620 0.724171i $$-0.742223\pi$$
0.689620 0.724171i $$-0.257777\pi$$
$$42$$ −6.40014 0.763187i −0.987564 0.117762i
$$43$$ −1.61040 + 1.61040i −0.245583 + 0.245583i −0.819155 0.573572i $$-0.805557\pi$$
0.573572 + 0.819155i $$0.305557\pi$$
$$44$$ −3.64520 5.97186i −0.549534 0.900292i
$$45$$ −0.334904 0.334904i −0.0499245 0.0499245i
$$46$$ −3.14343 + 2.47363i −0.463474 + 0.364716i
$$47$$ 2.82843 0.412568 0.206284 0.978492i $$-0.433863\pi$$
0.206284 + 0.978492i $$0.433863\pi$$
$$48$$ 1.22274 + 3.80853i 0.176488 + 0.549714i
$$49$$ −13.7721 −1.96745
$$50$$ −5.30755 + 4.17661i −0.750601 + 0.590662i
$$51$$ −2.55765 2.55765i −0.358142 0.358142i
$$52$$ 0.143434 0.0875513i 0.0198907 0.0121412i
$$53$$ −0.493523 + 0.493523i −0.0677906 + 0.0677906i −0.740189 0.672399i $$-0.765264\pi$$
0.672399 + 0.740189i $$0.265264\pi$$
$$54$$ 1.40426 + 0.167452i 0.191096 + 0.0227873i
$$55$$ 1.65685i 0.223410i
$$56$$ 5.36618 + 11.7210i 0.717086 + 1.56628i
$$57$$ 3.61706i 0.479091i
$$58$$ 1.22274 10.2540i 0.160554 1.34642i
$$59$$ 4.00000 4.00000i 0.520756 0.520756i −0.397044 0.917800i $$-0.629964\pi$$
0.917800 + 0.397044i $$0.129964\pi$$
$$60$$ −0.222743 + 0.920690i −0.0287560 + 0.118861i
$$61$$ 2.72922 + 2.72922i 0.349441 + 0.349441i 0.859901 0.510460i $$-0.170525\pi$$
−0.510460 + 0.859901i $$0.670525\pi$$
$$62$$ −0.487695 0.619753i −0.0619374 0.0787088i
$$63$$ 4.55765 0.574210
$$64$$ 5.22746 6.05588i 0.653432 0.756985i
$$65$$ 0.0397948 0.00493593
$$66$$ 3.05941 + 3.88784i 0.376588 + 0.478560i
$$67$$ 3.77568 + 3.77568i 0.461273 + 0.461273i 0.899072 0.437800i $$-0.144242\pi$$
−0.437800 + 0.899072i $$0.644242\pi$$
$$68$$ −1.70108 + 7.03127i −0.206286 + 0.852667i
$$69$$ 2.00000 2.00000i 0.240772 0.240772i
$$70$$ −0.361465 + 3.03127i −0.0432033 + 0.362306i
$$71$$ 9.11529i 1.08179i 0.841091 + 0.540893i $$0.181914\pi$$
−0.841091 + 0.540893i $$0.818086\pi$$
$$72$$ −1.17740 2.57172i −0.138758 0.303080i
$$73$$ 0.541560i 0.0633848i −0.999498 0.0316924i $$-0.989910\pi$$
0.999498 0.0316924i $$-0.0100897\pi$$
$$74$$ 8.71044 + 1.03868i 1.01257 + 0.120744i
$$75$$ 3.37691 3.37691i 0.389933 0.389933i
$$76$$ −6.17471 + 3.76901i −0.708287 + 0.432336i
$$77$$ 11.2739 + 11.2739i 1.28478 + 1.28478i
$$78$$ −0.0933792 + 0.0734818i −0.0105731 + 0.00832017i
$$79$$ −10.9937 −1.23689 −0.618445 0.785828i $$-0.712237\pi$$
−0.618445 + 0.785828i $$0.712237\pi$$
$$80$$ 1.80382 0.579123i 0.201673 0.0647479i
$$81$$ −1.00000 −0.111111
$$82$$ 10.3068 8.11058i 1.13819 0.895664i
$$83$$ −10.6417 10.6417i −1.16807 1.16807i −0.982660 0.185415i $$-0.940637\pi$$
−0.185415 0.982660i $$-0.559363\pi$$
$$84$$ −4.74912 7.78039i −0.518171 0.848910i
$$85$$ −1.21137 + 1.21137i −0.131391 + 0.131391i
$$86$$ −3.19813 0.381362i −0.344864 0.0411234i
$$87$$ 7.30205i 0.782862i
$$88$$ 3.44902 9.27391i 0.367666 0.988603i
$$89$$ 14.6533i 1.55325i 0.629964 + 0.776625i $$0.283070\pi$$
−0.629964 + 0.776625i $$0.716930\pi$$
$$90$$ 0.0793096 0.665096i 0.00835996 0.0701073i
$$91$$ −0.270780 + 0.270780i −0.0283854 + 0.0283854i
$$92$$ −5.49824 1.33019i −0.573231 0.138682i
$$93$$ 0.394316 + 0.394316i 0.0408887 + 0.0408887i
$$94$$ 2.47363 + 3.14343i 0.255135 + 0.324220i
$$95$$ −1.71313 −0.175764
$$96$$ −3.16333 + 4.68971i −0.322856 + 0.478641i
$$97$$ 4.31724 0.438349 0.219175 0.975686i $$-0.429664\pi$$
0.219175 + 0.975686i $$0.429664\pi$$
$$98$$ −12.0446 15.3060i −1.21668 1.54614i
$$99$$ −2.47363 2.47363i −0.248609 0.248609i
$$100$$ −9.28354 2.24597i −0.928354 0.224597i
$$101$$ −0.453728 + 0.453728i −0.0451477 + 0.0451477i −0.729320 0.684173i $$-0.760164\pi$$
0.684173 + 0.729320i $$0.260164\pi$$
$$102$$ 0.605684 5.07931i 0.0599716 0.502927i
$$103$$ 1.33686i 0.131724i 0.997829 + 0.0658622i $$0.0209798\pi$$
−0.997829 + 0.0658622i $$0.979020\pi$$
$$104$$ 0.222743 + 0.0828394i 0.0218418 + 0.00812307i
$$105$$ 2.15862i 0.210660i
$$106$$ −0.980103 0.116873i −0.0951960 0.0113517i
$$107$$ 6.06255 6.06255i 0.586088 0.586088i −0.350481 0.936570i $$-0.613982\pi$$
0.936570 + 0.350481i $$0.113982\pi$$
$$108$$ 1.04201 + 1.70711i 0.100268 + 0.164266i
$$109$$ 5.71627 + 5.71627i 0.547519 + 0.547519i 0.925722 0.378203i $$-0.123458\pi$$
−0.378203 + 0.925722i $$0.623458\pi$$
$$110$$ 1.84138 1.44902i 0.175569 0.138158i
$$111$$ −6.20285 −0.588748
$$112$$ −8.33333 + 16.2145i −0.787425 + 1.53213i
$$113$$ −9.55136 −0.898516 −0.449258 0.893402i $$-0.648312\pi$$
−0.449258 + 0.893402i $$0.648312\pi$$
$$114$$ 4.01990 3.16333i 0.376498 0.296273i
$$115$$ −0.947252 0.947252i −0.0883317 0.0883317i
$$116$$ 12.4654 7.60882i 1.15738 0.706461i
$$117$$ 0.0594122 0.0594122i 0.00549266 0.00549266i
$$118$$ 7.94372 + 0.947252i 0.731279 + 0.0872016i
$$119$$ 16.4853i 1.51120i
$$120$$ −1.21803 + 0.557647i −0.111191 + 0.0509060i
$$121$$ 1.23765i 0.112514i
$$122$$ −0.646314 + 5.42004i −0.0585146 + 0.490707i
$$123$$ −6.55765 + 6.55765i −0.591283 + 0.591283i
$$124$$ 0.262258 1.08402i 0.0235515 0.0973480i
$$125$$ −3.27391 3.27391i −0.292828 0.292828i
$$126$$ 3.98593 + 5.06524i 0.355095 + 0.451247i
$$127$$ 5.09921 0.452481 0.226241 0.974071i $$-0.427356\pi$$
0.226241 + 0.974071i $$0.427356\pi$$
$$128$$ 11.3021 + 0.513421i 0.998970 + 0.0453804i
$$129$$ 2.27744 0.200518
$$130$$ 0.0348029 + 0.0442268i 0.00305241 + 0.00387894i
$$131$$ 2.11882 + 2.11882i 0.185123 + 0.185123i 0.793584 0.608461i $$-0.208213\pi$$
−0.608461 + 0.793584i $$0.708213\pi$$
$$132$$ −1.64520 + 6.80029i −0.143196 + 0.591889i
$$133$$ 11.6569 11.6569i 1.01078 1.01078i
$$134$$ −0.894129 + 7.49824i −0.0772410 + 0.647749i
$$135$$ 0.473626i 0.0407632i
$$136$$ −9.30205 + 4.25873i −0.797644 + 0.365183i
$$137$$ 3.37941i 0.288723i −0.989525 0.144361i $$-0.953887\pi$$
0.989525 0.144361i $$-0.0461127\pi$$
$$138$$ 3.97186 + 0.473626i 0.338107 + 0.0403177i
$$139$$ 5.88118 5.88118i 0.498835 0.498835i −0.412240 0.911075i $$-0.635254\pi$$
0.911075 + 0.412240i $$0.135254\pi$$
$$140$$ −3.68499 + 2.24930i −0.311439 + 0.190101i
$$141$$ −2.00000 2.00000i −0.168430 0.168430i
$$142$$ −10.1305 + 7.97186i −0.850131 + 0.668984i
$$143$$ 0.293927 0.0245794
$$144$$ 1.82843 3.55765i 0.152369 0.296471i
$$145$$ 3.45844 0.287208
$$146$$ 0.601874 0.473626i 0.0498115 0.0391975i
$$147$$ 9.73838 + 9.73838i 0.803208 + 0.803208i
$$148$$ 6.46343 + 10.5889i 0.531291 + 0.870404i
$$149$$ −9.99176 + 9.99176i −0.818557 + 0.818557i −0.985899 0.167342i $$-0.946482\pi$$
0.167342 + 0.985899i $$0.446482\pi$$
$$150$$ 6.70632 + 0.799697i 0.547569 + 0.0652950i
$$151$$ 9.97685i 0.811905i 0.913894 + 0.405952i $$0.133060\pi$$
−0.913894 + 0.405952i $$0.866940\pi$$
$$152$$ −9.58892 3.56617i −0.777764 0.289255i
$$153$$ 3.61706i 0.292422i
$$154$$ −2.66981 + 22.3892i −0.215139 + 1.80417i
$$155$$ 0.186758 0.186758i 0.0150008 0.0150008i
$$156$$ −0.163331 0.0395148i −0.0130770 0.00316372i
$$157$$ −16.1618 16.1618i −1.28985 1.28985i −0.934877 0.354971i $$-0.884491\pi$$
−0.354971 0.934877i $$-0.615509\pi$$
$$158$$ −9.61465 12.2181i −0.764900 0.972020i
$$159$$ 0.697947 0.0553508
$$160$$ 2.22117 + 1.49824i 0.175599 + 0.118446i
$$161$$ 12.8910 1.01595
$$162$$ −0.874559 1.11137i −0.0687118 0.0873176i
$$163$$ −7.50490 7.50490i −0.587829 0.587829i 0.349214 0.937043i $$-0.386449\pi$$
−0.937043 + 0.349214i $$0.886449\pi$$
$$164$$ 18.0277 + 4.36147i 1.40773 + 0.340573i
$$165$$ −1.17157 + 1.17157i −0.0912068 + 0.0912068i
$$166$$ 2.52008 21.1336i 0.195596 1.64029i
$$167$$ 5.83822i 0.451775i −0.974153 0.225888i $$-0.927472\pi$$
0.974153 0.225888i $$-0.0725282\pi$$
$$168$$ 4.49352 12.0824i 0.346683 0.932181i
$$169$$ 12.9929i 0.999457i
$$170$$ −2.40569 0.286867i −0.184508 0.0220017i
$$171$$ −2.55765 + 2.55765i −0.195588 + 0.195588i
$$172$$ −2.37312 3.88784i −0.180949 0.296445i
$$173$$ −3.62530 3.62530i −0.275627 0.275627i 0.555734 0.831360i $$-0.312437\pi$$
−0.831360 + 0.555734i $$0.812437\pi$$
$$174$$ −8.11529 + 6.38607i −0.615219 + 0.484127i
$$175$$ 21.7659 1.64534
$$176$$ 13.3231 4.27744i 1.00427 0.322424i
$$177$$ −5.65685 −0.425195
$$178$$ −16.2853 + 12.8152i −1.22063 + 0.960539i
$$179$$ 9.28334 + 9.28334i 0.693869 + 0.693869i 0.963081 0.269212i $$-0.0867632\pi$$
−0.269212 + 0.963081i $$0.586763\pi$$
$$180$$ 0.808530 0.493523i 0.0602642 0.0367850i
$$181$$ −10.8316 + 10.8316i −0.805104 + 0.805104i −0.983888 0.178785i $$-0.942783\pi$$
0.178785 + 0.983888i $$0.442783\pi$$
$$182$$ −0.537750 0.0641242i −0.0398607 0.00475320i
$$183$$ 3.85970i 0.285317i
$$184$$ −3.33019 7.27391i −0.245505 0.536240i
$$185$$ 2.93783i 0.215993i
$$186$$ −0.0933792 + 0.783085i −0.00684689 + 0.0574185i
$$187$$ −8.94725 + 8.94725i −0.654288 + 0.654288i
$$188$$ −1.33019 + 5.49824i −0.0970142 + 0.401000i
$$189$$ −3.22274 3.22274i −0.234420 0.234420i
$$190$$ −1.49824 1.90393i −0.108693 0.138125i
$$191$$ −8.63001 −0.624446 −0.312223 0.950009i $$-0.601074\pi$$
−0.312223 + 0.950009i $$0.601074\pi$$
$$192$$ −7.97852 + 0.585786i −0.575800 + 0.0422755i
$$193$$ 11.4514 0.824288 0.412144 0.911119i $$-0.364780\pi$$
0.412144 + 0.911119i $$0.364780\pi$$
$$194$$ 3.77568 + 4.79806i 0.271078 + 0.344480i
$$195$$ −0.0281391 0.0281391i −0.00201509 0.00201509i
$$196$$ 6.47696 26.7720i 0.462640 1.91228i
$$197$$ 7.48999 7.48999i 0.533640 0.533640i −0.388014 0.921654i $$-0.626839\pi$$
0.921654 + 0.388014i $$0.126839\pi$$
$$198$$ 0.585786 4.91245i 0.0416300 0.349113i
$$199$$ 3.68000i 0.260868i −0.991457 0.130434i $$-0.958363\pi$$
0.991457 0.130434i $$-0.0416371\pi$$
$$200$$ −5.62289 12.2817i −0.397598 0.868447i
$$201$$ 5.33962i 0.376627i
$$202$$ −0.901073 0.107449i −0.0633993 0.00756007i
$$203$$ −23.5326 + 23.5326i −1.65167 + 1.65167i
$$204$$ 6.17471 3.76901i 0.432316 0.263884i
$$205$$ 3.10587 + 3.10587i 0.216923 + 0.216923i
$$206$$ −1.48574 + 1.16916i −0.103517 + 0.0814592i
$$207$$ −2.82843 −0.196589
$$208$$ 0.102737 + 0.319999i 0.00712351 + 0.0221879i
$$209$$ −12.6533 −0.875249
$$210$$ 2.39903 1.88784i 0.165549 0.130273i
$$211$$ 10.1188 + 10.1188i 0.696609 + 0.696609i 0.963677 0.267069i $$-0.0860551\pi$$
−0.267069 + 0.963677i $$0.586055\pi$$
$$212$$ −0.727268 1.19147i −0.0499490 0.0818305i
$$213$$ 6.44549 6.44549i 0.441637 0.441637i
$$214$$ 12.0398 + 1.43569i 0.823023 + 0.0981417i
$$215$$ 1.07866i 0.0735637i
$$216$$ −0.985930 + 2.65103i −0.0670841 + 0.180380i
$$217$$ 2.54156i 0.172532i
$$218$$ −1.35369 + 11.3521i −0.0916832 + 0.768862i
$$219$$ −0.382941 + 0.382941i −0.0258767 + 0.0258767i
$$220$$ 3.22079 + 0.779208i 0.217146 + 0.0525342i
$$221$$ −0.214897 0.214897i −0.0144556 0.0144556i
$$222$$ −5.42475 6.89367i −0.364086 0.462673i
$$223$$ −4.86156 −0.325554 −0.162777 0.986663i $$-0.552045\pi$$
−0.162777 + 0.986663i $$0.552045\pi$$
$$224$$ −25.3083 + 4.91911i −1.69098 + 0.328672i
$$225$$ −4.77568 −0.318379
$$226$$ −8.35322 10.6151i −0.555648 0.706106i
$$227$$ 10.6417 + 10.6417i 0.706312 + 0.706312i 0.965758 0.259445i $$-0.0835398\pi$$
−0.259445 + 0.965758i $$0.583540\pi$$
$$228$$ 7.03127 + 1.70108i 0.465657 + 0.112657i
$$229$$ −20.1712 + 20.1712i −1.33295 + 1.33295i −0.430229 + 0.902720i $$0.641567\pi$$
−0.902720 + 0.430229i $$0.858433\pi$$
$$230$$ 0.224321 1.88118i 0.0147913 0.124041i
$$231$$ 15.9437i 1.04902i
$$232$$ 19.3579 + 7.19932i 1.27091 + 0.472658i
$$233$$ 13.5702i 0.889014i 0.895775 + 0.444507i $$0.146621\pi$$
−0.895775 + 0.444507i $$0.853379\pi$$
$$234$$ 0.117988 + 0.0140696i 0.00771315 + 0.000919757i
$$235$$ −0.947252 + 0.947252i −0.0617919 + 0.0617919i
$$236$$ 5.89450 + 9.65685i 0.383699 + 0.628608i
$$237$$ 7.77373 + 7.77373i 0.504958 + 0.504958i
$$238$$ 18.3213 14.4173i 1.18759 0.934538i
$$239$$ 29.3629 1.89933 0.949665 0.313267i $$-0.101424\pi$$
0.949665 + 0.313267i $$0.101424\pi$$
$$240$$ −1.68499 0.865990i −0.108766 0.0558994i
$$241$$ 24.0063 1.54638 0.773190 0.634175i $$-0.218660\pi$$
0.773190 + 0.634175i $$0.218660\pi$$
$$242$$ 1.37549 1.08240i 0.0884197 0.0695791i
$$243$$ 0.707107 + 0.707107i 0.0453609 + 0.0453609i
$$244$$ −6.58892 + 4.02185i −0.421812 + 0.257473i
$$245$$ 4.61235 4.61235i 0.294672 0.294672i
$$246$$ −13.0230 1.55294i −0.830318 0.0990115i
$$247$$ 0.303911i 0.0193374i
$$248$$ 1.43411 0.656574i 0.0910661 0.0416925i
$$249$$ 15.0496i 0.953729i
$$250$$ 0.775305 6.50176i 0.0490346 0.411208i
$$251$$ 15.7570 15.7570i 0.994571 0.994571i −0.00541463 0.999985i $$-0.501724\pi$$
0.999985 + 0.00541463i $$0.00172354\pi$$
$$252$$ −2.14343 + 8.85970i −0.135024 + 0.558109i
$$253$$ −6.99647 6.99647i −0.439864 0.439864i
$$254$$ 4.45956 + 5.66711i 0.279817 + 0.355586i
$$255$$ 1.71313 0.107281
$$256$$ 9.31371 + 13.0098i 0.582107 + 0.813112i
$$257$$ 8.66038 0.540220 0.270110 0.962829i $$-0.412940\pi$$
0.270110 + 0.962829i $$0.412940\pi$$
$$258$$ 1.99176 + 2.53109i 0.124001 + 0.157579i
$$259$$ −19.9902 19.9902i −1.24213 1.24213i
$$260$$ −0.0187152 + 0.0773578i −0.00116067 + 0.00479753i
$$261$$ 5.16333 5.16333i 0.319602 0.319602i
$$262$$ −0.501765 + 4.20784i −0.0309991 + 0.259961i
$$263$$ 13.3208i 0.821394i 0.911772 + 0.410697i $$0.134715\pi$$
−0.911772 + 0.410697i $$0.865285\pi$$
$$264$$ −8.99647 + 4.11882i −0.553694 + 0.253496i
$$265$$ 0.330566i 0.0203065i
$$266$$ 23.1497 + 2.76049i 1.41940 + 0.169257i
$$267$$ 10.3615 10.3615i 0.634111 0.634111i
$$268$$ −9.11529 + 5.56394i −0.556805 + 0.339872i
$$269$$ −11.6714 11.6714i −0.711616 0.711616i 0.255257 0.966873i $$-0.417840\pi$$
−0.966873 + 0.255257i $$0.917840\pi$$
$$270$$ −0.526374 + 0.414214i −0.0320341 + 0.0252082i
$$271$$ −21.9769 −1.33500 −0.667499 0.744610i $$-0.732635\pi$$
−0.667499 + 0.744610i $$0.732635\pi$$
$$272$$ −12.8682 6.61353i −0.780251 0.401004i
$$273$$ 0.382941 0.0231766
$$274$$ 3.75578 2.95549i 0.226895 0.178548i
$$275$$ −11.8132 11.8132i −0.712365 0.712365i
$$276$$ 2.94725 + 4.82843i 0.177404 + 0.290637i
$$277$$ −10.9504 + 10.9504i −0.657945 + 0.657945i −0.954893 0.296949i $$-0.904031\pi$$
0.296949 + 0.954893i $$0.404031\pi$$
$$278$$ 11.6796 + 1.39274i 0.700496 + 0.0835309i
$$279$$ 0.557647i 0.0333855i
$$280$$ −5.72256 2.12825i −0.341988 0.127187i
$$281$$ 22.8910i 1.36556i −0.730624 0.682780i $$-0.760771\pi$$
0.730624 0.682780i $$-0.239229\pi$$
$$282$$ 0.473626 3.97186i 0.0282040 0.236521i
$$283$$ 4.48528 4.48528i 0.266622 0.266622i −0.561115 0.827738i $$-0.689628\pi$$
0.827738 + 0.561115i $$0.189628\pi$$
$$284$$ −17.7194 4.28687i −1.05145 0.254379i
$$285$$ 1.21137 + 1.21137i 0.0717552 + 0.0717552i
$$286$$ 0.257057 + 0.326662i 0.0152001 + 0.0193159i
$$287$$ −42.2672 −2.49496
$$288$$ 5.55294 1.07931i 0.327210 0.0635989i
$$289$$ −3.91688 −0.230405
$$290$$ 3.02461 + 3.84361i 0.177611 + 0.225705i
$$291$$ −3.05275 3.05275i −0.178955 0.178955i
$$292$$ 1.05275 + 0.254692i 0.0616074 + 0.0149047i
$$293$$ 21.6221 21.6221i 1.26318 1.26318i 0.313636 0.949543i $$-0.398453\pi$$
0.949543 0.313636i $$-0.101547\pi$$
$$294$$ −2.30617 + 19.3397i −0.134499 + 1.12792i
$$295$$ 2.67923i 0.155991i
$$296$$ −6.11557 + 16.4439i −0.355461 + 0.955783i
$$297$$ 3.49824i 0.202988i
$$298$$ −19.8429 2.36618i −1.14947 0.137069i
$$299$$ 0.168043 0.168043i 0.00971818 0.00971818i
$$300$$ 4.97631 + 8.15259i 0.287307 + 0.470690i
$$301$$ 7.33962 + 7.33962i 0.423048 + 0.423048i
$$302$$ −11.0880 + 8.72534i −0.638042 + 0.502087i
$$303$$ 0.641669 0.0368629
$$304$$ −4.42274 13.7757i −0.253661 0.790089i
$$305$$ −1.82805 −0.104674
$$306$$ −4.01990 + 3.16333i −0.229802 + 0.180836i
$$307$$ −12.1118 12.1118i −0.691255 0.691255i 0.271253 0.962508i $$-0.412562\pi$$
−0.962508 + 0.271253i $$0.912562\pi$$
$$308$$ −27.2176 + 16.6135i −1.55087 + 0.946644i
$$309$$ 0.945300 0.945300i 0.0537762 0.0537762i
$$310$$ 0.370889 + 0.0442268i 0.0210651 + 0.00251191i
$$311$$ 26.8651i 1.52338i −0.647943 0.761689i $$-0.724370\pi$$
0.647943 0.761689i $$-0.275630\pi$$
$$312$$ −0.0989270 0.216080i −0.00560064 0.0122331i
$$313$$ 19.6890i 1.11289i 0.830885 + 0.556445i $$0.187835\pi$$
−0.830885 + 0.556445i $$0.812165\pi$$
$$314$$ 3.82731 32.0961i 0.215988 1.81129i
$$315$$ −1.52637 + 1.52637i −0.0860014 + 0.0860014i
$$316$$ 5.17027 21.3709i 0.290851 1.20221i
$$317$$ 21.3447 + 21.3447i 1.19884 + 1.19884i 0.974515 + 0.224323i $$0.0720171\pi$$
0.224323 + 0.974515i $$0.427983\pi$$
$$318$$ 0.610396 + 0.775679i 0.0342293 + 0.0434979i
$$319$$ 25.5443 1.43021
$$320$$ 0.277444 + 3.77883i 0.0155096 + 0.211243i
$$321$$ −8.57373 −0.478539
$$322$$ 11.2739 + 14.3267i 0.628271 + 0.798394i
$$323$$ 9.25116 + 9.25116i 0.514748 + 0.514748i
$$324$$ 0.470294 1.94392i 0.0261274 0.107996i
$$325$$ 0.283734 0.283734i 0.0157387 0.0157387i
$$326$$ 1.77726 14.9042i 0.0984331 0.825468i
$$327$$ 8.08402i 0.447047i
$$328$$ 10.9191 + 23.8499i 0.602907 + 1.31689i
$$329$$ 12.8910i 0.710702i
$$330$$ −2.32666 0.277444i −0.128079 0.0152728i
$$331$$ 14.6926 14.6926i 0.807576 0.807576i −0.176690 0.984266i $$-0.556539\pi$$
0.984266 + 0.176690i $$0.0565391\pi$$
$$332$$ 25.6913 15.6818i 1.40999 0.860653i
$$333$$ 4.38607 + 4.38607i 0.240355 + 0.240355i
$$334$$ 6.48844 5.10587i 0.355032 0.279381i
$$335$$ −2.52898 −0.138173
$$336$$ 17.3579 5.57283i 0.946953 0.304023i
$$337$$ −23.0098 −1.25342 −0.626712 0.779251i $$-0.715600\pi$$
−0.626712 + 0.779251i $$0.715600\pi$$
$$338$$ 14.4400 11.3631i 0.785432 0.618071i
$$339$$ 6.75383 + 6.75383i 0.366818 + 0.366818i
$$340$$ −1.78510 2.92450i −0.0968108 0.158603i
$$341$$ 1.37941 1.37941i 0.0746993 0.0746993i
$$342$$ −5.07931 0.605684i −0.274658 0.0327516i
$$343$$ 30.8651i 1.66656i
$$344$$ 2.24540 6.03756i 0.121064 0.325524i
$$345$$ 1.33962i 0.0721225i
$$346$$ 0.858518 7.19960i 0.0461542 0.387053i
$$347$$ −10.9026 + 10.9026i −0.585284 + 0.585284i −0.936350 0.351067i $$-0.885819\pi$$
0.351067 + 0.936350i $$0.385819\pi$$
$$348$$ −14.1946 3.43411i −0.760911 0.184088i
$$349$$ 20.0563 + 20.0563i 1.07359 + 1.07359i 0.997068 + 0.0765186i $$0.0243805\pi$$
0.0765186 + 0.997068i $$0.475620\pi$$
$$350$$ 19.0355 + 24.1900i 1.01749 + 1.29301i
$$351$$ −0.0840215 −0.00448474
$$352$$ 16.4057 + 11.0661i 0.874426 + 0.589824i
$$353$$ −12.2117 −0.649965 −0.324983 0.945720i $$-0.605358\pi$$
−0.324983 + 0.945720i $$0.605358\pi$$
$$354$$ −4.94725 6.28687i −0.262943 0.334143i
$$355$$ −3.05275 3.05275i −0.162023 0.162023i
$$356$$ −28.4849 6.89137i −1.50970 0.365242i
$$357$$ −11.6569 + 11.6569i −0.616946 + 0.616946i
$$358$$ −2.19841 + 18.4361i −0.116190 + 0.974376i
$$359$$ 33.4780i 1.76690i 0.468522 + 0.883452i $$0.344786\pi$$
−0.468522 + 0.883452i $$0.655214\pi$$
$$360$$ 1.25559 + 0.466962i 0.0661756 + 0.0246111i
$$361$$ 5.91688i 0.311415i
$$362$$ −21.5107 2.56505i −1.13058 0.134816i
$$363$$ −0.875150 + 0.875150i −0.0459335 + 0.0459335i
$$364$$ −0.399028 0.653720i −0.0209148 0.0342643i
$$365$$ 0.181370 + 0.181370i 0.00949337 + 0.00949337i
$$366$$ 4.28956 3.37553i 0.224219 0.176442i
$$367$$ −0.702379 −0.0366639 −0.0183319 0.999832i $$-0.505836\pi$$
−0.0183319 + 0.999832i $$0.505836\pi$$
$$368$$ 5.17157 10.0625i 0.269587 0.524546i
$$369$$ 9.27391 0.482781
$$370$$ −3.26502 + 2.56930i −0.169740 + 0.133572i
$$371$$ 2.24930 + 2.24930i 0.116778 + 0.116778i
$$372$$ −0.951963 + 0.581074i −0.0493570 + 0.0301273i
$$373$$ 18.9598 18.9598i 0.981702 0.981702i −0.0181339 0.999836i $$-0.505773\pi$$
0.999836 + 0.0181339i $$0.00577250\pi$$
$$374$$ −17.7686 2.11882i −0.918793 0.109562i
$$375$$ 4.63001i 0.239093i
$$376$$ −7.27391 + 3.33019i −0.375123 + 0.171742i
$$377$$ 0.613530i 0.0315984i
$$378$$ 0.763187 6.40014i 0.0392541 0.329188i
$$379$$ −1.77844 + 1.77844i −0.0913523 + 0.0913523i −0.751306 0.659954i $$-0.770576\pi$$
0.659954 + 0.751306i $$0.270576\pi$$
$$380$$ 0.805676 3.33019i 0.0413303 0.170835i
$$381$$ −3.60568 3.60568i −0.184725 0.184725i
$$382$$ −7.54745 9.59115i −0.386161 0.490726i
$$383$$ 25.4880 1.30238 0.651188 0.758916i $$-0.274271\pi$$
0.651188 + 0.758916i $$0.274271\pi$$
$$384$$ −7.62872 8.35480i −0.389301 0.426354i
$$385$$ −7.55136 −0.384853
$$386$$ 10.0149 + 12.7267i 0.509745 + 0.647774i
$$387$$ −1.61040 1.61040i −0.0818610 0.0818610i
$$388$$ −2.03037 + 8.39236i −0.103076 + 0.426058i
$$389$$ −11.7049 + 11.7049i −0.593462 + 0.593462i −0.938565 0.345103i $$-0.887844\pi$$
0.345103 + 0.938565i $$0.387844\pi$$
$$390$$ 0.00666371 0.0558824i 0.000337430 0.00282971i
$$391$$ 10.2306i 0.517383i
$$392$$ 35.4181 16.2153i 1.78888 0.818998i
$$393$$ 2.99647i 0.151152i
$$394$$ 14.8746 + 1.77373i 0.749372 + 0.0893591i
$$395$$ 3.68184 3.68184i 0.185253 0.185253i
$$396$$ 5.97186 3.64520i 0.300097 0.183178i
$$397$$ −9.04646 9.04646i −0.454029 0.454029i 0.442661 0.896689i $$-0.354035\pi$$
−0.896689 + 0.442661i $$0.854035\pi$$
$$398$$ 4.08985 3.21838i 0.205006 0.161323i
$$399$$ −16.4853 −0.825296
$$400$$ 8.73198 16.9902i 0.436599 0.849509i
$$401$$ −18.0853 −0.903137 −0.451568 0.892237i $$-0.649135\pi$$
−0.451568 + 0.892237i $$0.649135\pi$$
$$402$$ 5.93430 4.66981i 0.295976 0.232909i
$$403$$ 0.0331311 + 0.0331311i 0.00165038 + 0.00165038i
$$404$$ −0.668626 1.09540i −0.0332654 0.0544980i
$$405$$ 0.334904 0.334904i 0.0166415 0.0166415i
$$406$$ −46.7342 5.57283i −2.31938 0.276575i
$$407$$ 21.6990i 1.07558i
$$408$$ 9.58892 + 3.56617i 0.474722 + 0.176552i
$$409$$ 25.2271i 1.24740i −0.781665 0.623699i $$-0.785629\pi$$
0.781665 0.623699i $$-0.214371\pi$$
$$410$$ −0.735510 + 6.16804i −0.0363243 + 0.304618i
$$411$$ −2.38960 + 2.38960i −0.117870 + 0.117870i
$$412$$ −2.59874 0.628715i −0.128031 0.0309746i
$$413$$ −18.2306 18.2306i −0.897069 0.897069i
$$414$$ −2.47363 3.14343i −0.121572 0.154491i
$$415$$ 7.12787 0.349894
$$416$$ −0.265788 + 0.394036i −0.0130313 + 0.0193192i
$$417$$ −8.31724 −0.407297
$$418$$ −11.0661 14.0625i −0.541259 0.687822i
$$419$$ 7.25283 + 7.25283i 0.354324 + 0.354324i 0.861716 0.507392i $$-0.169390\pi$$
−0.507392 + 0.861716i $$0.669390\pi$$
$$420$$ 4.19618 + 1.01519i 0.204753 + 0.0495360i
$$421$$ 2.39550 2.39550i 0.116749 0.116749i −0.646318 0.763068i $$-0.723692\pi$$
0.763068 + 0.646318i $$0.223692\pi$$
$$422$$ −2.39627 + 20.0953i −0.116648 + 0.978223i
$$423$$ 2.82843i 0.137523i
$$424$$ 0.688127 1.85028i 0.0334184 0.0898574i
$$425$$ 17.2739i 0.837908i
$$426$$ 12.8003 + 1.52637i 0.620176 + 0.0739531i
$$427$$ 12.4388 12.4388i 0.601957 0.601957i
$$428$$ 8.93392 + 14.6363i 0.431838 + 0.707471i
$$429$$ −0.207838 0.207838i −0.0100345 0.0100345i
$$430$$ 1.19879 0.943348i 0.0578107 0.0454923i
$$431$$ −4.42454 −0.213123 −0.106561 0.994306i $$-0.533984\pi$$
−0.106561 + 0.994306i $$0.533984\pi$$
$$432$$ −3.80853 + 1.22274i −0.183238 + 0.0588293i
$$433$$ 7.31371 0.351474 0.175737 0.984437i $$-0.443769\pi$$
0.175737 + 0.984437i $$0.443769\pi$$
$$434$$ −2.82462 + 2.22274i −0.135586 + 0.106695i
$$435$$ −2.44549 2.44549i −0.117252 0.117252i
$$436$$ −13.8003 + 8.42364i −0.660914 + 0.403419i
$$437$$ −7.23412 + 7.23412i −0.346055 + 0.346055i
$$438$$ −0.760493 0.0906852i −0.0363378 0.00433311i
$$439$$ 29.6533i 1.41527i −0.706576 0.707637i $$-0.749761\pi$$
0.706576 0.707637i $$-0.250239\pi$$
$$440$$ 1.95078 + 4.26096i 0.0929999 + 0.203133i
$$441$$ 13.7721i 0.655817i
$$442$$ 0.0508905 0.426771i 0.00242061 0.0202994i
$$443$$ 10.3056 10.3056i 0.489633 0.489633i −0.418557 0.908190i $$-0.637464\pi$$
0.908190 + 0.418557i $$0.137464\pi$$
$$444$$ 2.91716 12.0578i 0.138442 0.572239i
$$445$$ −4.90746 4.90746i −0.232636 0.232636i
$$446$$ −4.25172 5.40300i −0.201325 0.255839i
$$447$$ 14.1305 0.668349
$$448$$ −27.6006 23.8249i −1.30400 1.12562i
$$449$$ −6.48844 −0.306208 −0.153104 0.988210i $$-0.548927\pi$$
−0.153104 + 0.988210i $$0.548927\pi$$
$$450$$ −4.17661 5.30755i −0.196887 0.250200i
$$451$$ 22.9402 + 22.9402i 1.08021 + 1.08021i
$$452$$ 4.49195 18.5671i 0.211283 0.873322i
$$453$$ 7.05470 7.05470i 0.331459 0.331459i
$$454$$ −2.52008 + 21.1336i −0.118273 + 0.991850i
$$455$$ 0.181370i 0.00850278i
$$456$$ 4.25873 + 9.30205i 0.199433 + 0.435609i
$$457$$ 9.00353i 0.421167i −0.977576 0.210584i $$-0.932464\pi$$
0.977576 0.210584i $$-0.0675364\pi$$
$$458$$ −40.0586 4.77679i −1.87181 0.223205i
$$459$$ 2.55765 2.55765i 0.119381 0.119381i
$$460$$ 2.28687 1.39589i 0.106626 0.0650839i
$$461$$ 14.6218 + 14.6218i 0.681004 + 0.681004i 0.960226 0.279223i $$-0.0900767\pi$$
−0.279223 + 0.960226i $$0.590077\pi$$
$$462$$ 17.7194 13.9437i 0.824381 0.648721i
$$463$$ −18.6435 −0.866437 −0.433219 0.901289i $$-0.642622\pi$$
−0.433219 + 0.901289i $$0.642622\pi$$
$$464$$ 8.92854 + 27.8101i 0.414497 + 1.29105i
$$465$$ −0.264116 −0.0122481
$$466$$ −15.0815 + 11.8679i −0.698639 + 0.549772i
$$467$$ −23.5138 23.5138i −1.08809 1.08809i −0.995725 0.0923633i $$-0.970558\pi$$
−0.0923633 0.995725i $$-0.529442\pi$$
$$468$$ 0.0875513 + 0.143434i 0.00404706 + 0.00663023i
$$469$$ 17.2082 17.2082i 0.794601 0.794601i
$$470$$ −1.88118 0.224321i −0.0867722 0.0103472i
$$471$$ 22.8562i 1.05316i
$$472$$ −5.57726 + 14.9965i −0.256714 + 0.690268i
$$473$$ 7.96703i 0.366325i
$$474$$ −1.84092 + 15.4381i −0.0845562 + 0.709095i
$$475$$ −12.2145 + 12.2145i −0.560440 + 0.560440i
$$476$$ 32.0461 + 7.75293i 1.46883 + 0.355355i
$$477$$ −0.493523 0.493523i −0.0225969 0.0225969i
$$478$$ 25.6796 + 32.6331i 1.17456 + 1.49260i
$$479$$ −1.08864 −0.0497412 −0.0248706 0.999691i $$-0.507917\pi$$
−0.0248706 + 0.999691i $$0.507917\pi$$
$$480$$ −0.511189 2.63001i −0.0233325 0.120043i
$$481$$ −0.521173 −0.0237634
$$482$$ 20.9949 + 26.6799i 0.956291 + 1.21524i
$$483$$ −9.11529 9.11529i −0.414760 0.414760i
$$484$$ 2.40589 + 0.582059i 0.109359 + 0.0264572i
$$485$$ −1.44586 + 1.44586i −0.0656531 + 0.0656531i
$$486$$ −0.167452 + 1.40426i −0.00759578 + 0.0636987i
$$487$$ 35.3298i 1.60095i −0.599369 0.800473i $$-0.704582\pi$$
0.599369 0.800473i $$-0.295418\pi$$
$$488$$ −10.2322 3.80540i −0.463188 0.172262i
$$489$$ 10.6135i 0.479960i
$$490$$ 9.15980 + 1.09226i 0.413798 + 0.0493434i
$$491$$ −12.8910 + 12.8910i −0.581761 + 0.581761i −0.935387 0.353626i $$-0.884949\pi$$
0.353626 + 0.935387i $$0.384949\pi$$
$$492$$ −9.66352 15.8316i −0.435665 0.713742i
$$493$$ −18.6761 18.6761i −0.841128 0.841128i
$$494$$ 0.337758 0.265788i 0.0151964 0.0119584i
$$495$$ 1.65685 0.0744701
$$496$$ 1.98391 + 1.01962i 0.0890803 + 0.0457822i
$$497$$ 41.5443 1.86352
$$498$$ −16.7257 + 13.1618i −0.749496 + 0.589792i
$$499$$ 14.3798 + 14.3798i 0.643728 + 0.643728i 0.951470 0.307742i $$-0.0995734\pi$$
−0.307742 + 0.951470i $$0.599573\pi$$
$$500$$ 7.90393 4.82452i 0.353474 0.215759i
$$501$$ −4.12825 + 4.12825i −0.184437 + 0.184437i
$$502$$ 31.2922 + 3.73145i 1.39664 + 0.166543i
$$503$$ 30.2969i 1.35087i −0.737420 0.675435i $$-0.763956\pi$$
0.737420 0.675435i $$-0.236044\pi$$
$$504$$ −11.7210 + 5.36618i −0.522094 + 0.239029i
$$505$$ 0.303911i 0.0135239i
$$506$$ 1.65685 13.8945i 0.0736562 0.617686i
$$507$$ −9.18740 + 9.18740i −0.408027 + 0.408027i
$$508$$ −2.39813 + 9.91245i −0.106400 + 0.439794i
$$509$$ 10.5825 + 10.5825i 0.469063 + 0.469063i 0.901611 0.432548i $$-0.142385\pi$$
−0.432548 + 0.901611i $$0.642385\pi$$
$$510$$ 1.49824 + 1.90393i 0.0663430 + 0.0843073i
$$511$$ −2.46824 −0.109188
$$512$$ −6.31333 + 21.7288i −0.279013 + 0.960287i
$$513$$ 3.61706 0.159697
$$514$$ 7.57401 + 9.62491i 0.334075 + 0.424536i
$$515$$ −0.447718 0.447718i −0.0197288 0.0197288i
$$516$$ −1.07107 + 4.42717i −0.0471511 + 0.194895i
$$517$$ −6.99647 + 6.99647i −0.307704 + 0.307704i
$$518$$ 4.73393 39.6991i 0.207997 1.74428i
$$519$$ 5.12695i 0.225048i
$$520$$ −0.102341 + 0.0468544i −0.00448794 + 0.00205470i
$$521$$ 24.9049i 1.09110i 0.838078 + 0.545551i $$0.183680\pi$$
−0.838078 + 0.545551i $$0.816320\pi$$
$$522$$ 10.2540 + 1.22274i 0.448806 + 0.0535180i
$$523$$ −12.9008 + 12.9008i −0.564112 + 0.564112i −0.930473 0.366361i $$-0.880604\pi$$
0.366361 + 0.930473i $$0.380604\pi$$
$$524$$ −5.11529 + 3.12235i −0.223463 + 0.136401i
$$525$$ −15.3908 15.3908i −0.671709 0.671709i
$$526$$ −14.8043 + 11.6498i −0.645499 + 0.507955i
$$527$$ −2.01704 −0.0878638
$$528$$ −12.4455 6.39627i −0.541620 0.278362i
$$529$$ 15.0000 0.652174
$$530$$ 0.367381 0.289099i 0.0159580 0.0125577i
$$531$$ 4.00000 + 4.00000i 0.173585 + 0.173585i
$$532$$ 17.1778 + 28.1421i 0.744754 + 1.22012i
$$533$$ −0.550984 + 0.550984i −0.0238657 + 0.0238657i
$$534$$ 20.5771 + 2.45373i 0.890460 + 0.106183i
$$535$$ 4.06074i 0.175561i
$$536$$ −14.1555 5.26449i −0.611423 0.227391i
$$537$$ 13.1286i 0.566542i
$$538$$ 2.76393 23.1785i 0.119161 0.999297i
$$539$$ 34.0671 34.0671i 1.46738 1.46738i
$$540$$ −0.920690 0.222743i −0.0396202 0.00958535i
$$541$$ 18.2767 + 18.2767i 0.785776 + 0.785776i 0.980799 0.195023i $$-0.0624782\pi$$
−0.195023 + 0.980799i $$0.562478\pi$$
$$542$$ −19.2200 24.4245i −0.825572 1.04912i
$$543$$ 15.3181 0.657364
$$544$$ −3.90393 20.0853i −0.167379 0.861150i
$$545$$ −3.82880 −0.164008
$$546$$ 0.334904 + 0.425589i 0.0143326 + 0.0182135i
$$547$$ 13.7355 + 13.7355i 0.587287 + 0.587287i 0.936896 0.349609i $$-0.113685\pi$$
−0.349609 + 0.936896i $$0.613685\pi$$
$$548$$ 6.56930 + 1.58932i 0.280627 + 0.0678922i
$$549$$ −2.72922 + 2.72922i −0.116480 + 0.116480i
$$550$$ 2.79753 23.4603i 0.119287 1.00035i
$$551$$ 26.4120i 1.12519i
$$552$$ −2.78863 + 7.49824i −0.118692 + 0.319146i
$$553$$ 50.1055i 2.13070i
$$554$$ −21.7467 2.59319i −0.923929 0.110174i
$$555$$ 2.07736 2.07736i 0.0881789 0.0881789i
$$556$$ 8.66665 + 14.1984i 0.367548 + 0.602147i
$$557$$ −27.5525 27.5525i −1.16744 1.16744i −0.982808 0.184631i $$-0.940891\pi$$
−0.184631 0.982808i $$-0.559109\pi$$
$$558$$ 0.619753 0.487695i 0.0262363 0.0206458i
$$559$$ 0.191354 0.00809342
$$560$$ −2.63944 8.22117i −0.111537 0.347408i
$$561$$ 12.6533 0.534224
$$562$$ 25.4404 20.0195i 1.07314 0.844472i
$$563$$ −19.8928 19.8928i −0.838383 0.838383i 0.150263 0.988646i $$-0.451988\pi$$
−0.988646 + 0.150263i $$0.951988\pi$$
$$564$$ 4.82843 2.94725i 0.203313 0.124102i
$$565$$ 3.19879 3.19879i 0.134574 0.134574i
$$566$$ 8.90746 + 1.06217i 0.374408 + 0.0446464i
$$567$$ 4.55765i 0.191403i
$$568$$ −10.7324 23.4420i −0.450320 0.983603i
$$569$$ 13.4849i 0.565317i 0.959221 + 0.282658i $$0.0912163\pi$$
−0.959221 + 0.282658i $$0.908784\pi$$
$$570$$ −0.286867 + 2.40569i −0.0120156 + 0.100763i
$$571$$ −14.8284 + 14.8284i −0.620550 + 0.620550i −0.945672 0.325122i $$-0.894595\pi$$
0.325122 + 0.945672i $$0.394595\pi$$
$$572$$ −0.138232 + 0.571371i −0.00577977 + 0.0238902i
$$573$$ 6.10234 + 6.10234i 0.254929 + 0.254929i
$$574$$ −36.9652 46.9746i −1.54290 1.96068i
$$575$$ −13.5077 −0.563308
$$576$$ 6.05588 + 5.22746i 0.252328 + 0.217811i
$$577$$ −11.6176 −0.483648 −0.241824 0.970320i $$-0.577746\pi$$
−0.241824 + 0.970320i $$0.577746\pi$$
$$578$$ −3.42554 4.35311i −0.142484 0.181066i
$$579$$ −8.09735 8.09735i −0.336514 0.336514i
$$580$$ −1.62648 + 6.72293i −0.0675360 + 0.279154i
$$581$$ −48.5010 + 48.5010i −2.01216 + 2.01216i
$$582$$ 0.722930 6.06255i 0.0299664 0.251301i
$$583$$ 2.44158i 0.101120i
$$584$$ 0.637633 + 1.39274i 0.0263854 + 0.0576319i
$$585$$ 0.0397948i 0.00164531i
$$586$$ 42.9401 + 5.12040i 1.77384 + 0.211522i
$$587$$ −17.0268 + 17.0268i −0.702773 + 0.702773i −0.965005 0.262232i $$-0.915541\pi$$
0.262232 + 0.965005i $$0.415541\pi$$
$$588$$ −23.5105 + 14.3507i −0.969558 + 0.591814i
$$589$$ −1.42627 1.42627i −0.0587682 0.0587682i
$$590$$ −2.97762 + 2.34315i −0.122587 + 0.0964658i
$$591$$ −10.5925 −0.435715
$$592$$ −23.6237 + 7.58449i −0.970929 + 0.311721i
$$593$$ 41.5372 1.70573 0.852865 0.522132i $$-0.174863\pi$$
0.852865 + 0.522132i $$0.174863\pi$$
$$594$$ −3.88784 + 3.05941i −0.159520 + 0.125529i
$$595$$ 5.52099 + 5.52099i 0.226338 + 0.226338i
$$596$$ −14.7241 24.1222i −0.603123 0.988085i
$$597$$ −2.60215 + 2.60215i −0.106499 + 0.106499i
$$598$$ 0.333722 + 0.0397948i 0.0136469 + 0.00162733i
$$599$$ 6.43160i 0.262788i −0.991330 0.131394i $$-0.958055\pi$$
0.991330 0.131394i $$-0.0419453\pi$$
$$600$$ −4.70849 + 12.6605i −0.192223 + 0.516861i
$$601$$ 3.45844i 0.141073i 0.997509 + 0.0705364i $$0.0224711\pi$$
−0.997509 + 0.0705364i $$0.977529\pi$$
$$602$$ −1.73812 + 14.5760i −0.0708403 + 0.594072i
$$603$$ −3.77568 + 3.77568i −0.153758 + 0.153758i
$$604$$ −19.3942 4.69205i −0.789139 0.190917i
$$605$$ 0.414494 + 0.414494i 0.0168516 + 0.0168516i
$$606$$ 0.561177 + 0.713133i 0.0227963 + 0.0289690i
$$607$$ −30.1019 −1.22180 −0.610900 0.791708i $$-0.709192\pi$$
−0.610900 + 0.791708i $$0.709192\pi$$
$$608$$ 11.4420 16.9629i 0.464033 0.687938i
$$609$$ 33.2802 1.34858
$$610$$ −1.59874 2.03165i −0.0647311 0.0822590i
$$611$$ −0.168043 0.168043i −0.00679829 0.00679829i
$$612$$ −7.03127 1.70108i −0.284222 0.0687621i
$$613$$ 2.50490 2.50490i 0.101172 0.101172i −0.654709 0.755881i $$-0.727209\pi$$
0.755881 + 0.654709i $$0.227209\pi$$
$$614$$ 2.86822 24.0531i 0.115752 0.970705i
$$615$$ 4.39236i 0.177117i
$$616$$ −42.2672 15.7194i −1.70300 0.633353i
$$617$$ 22.9098i 0.922315i −0.887318 0.461157i $$-0.847434\pi$$
0.887318 0.461157i $$-0.152566\pi$$
$$618$$ 1.87730 + 0.223859i 0.0755161 + 0.00900494i
$$619$$ −28.6104 + 28.6104i −1.14995 + 1.14995i −0.163386 + 0.986562i $$0.552242\pi$$
−0.986562 + 0.163386i $$0.947758\pi$$
$$620$$ 0.275212 + 0.450874i 0.0110528 + 0.0181076i
$$621$$ 2.00000 + 2.00000i 0.0802572 + 0.0802572i
$$622$$ 29.8571 23.4951i 1.19716 0.942067i
$$623$$ 66.7847 2.67567
$$624$$ 0.153627 0.298919i 0.00615001 0.0119663i
$$625$$ −21.6855 −0.867420
$$626$$ −21.8818 + 17.2192i −0.874574 + 0.688218i
$$627$$ 8.94725 + 8.94725i 0.357319 + 0.357319i
$$628$$ 39.0179 23.8164i 1.55698 0.950377i
$$629$$ 15.8647 15.8647i 0.632567 0.632567i
$$630$$ −3.03127 0.361465i −0.120769 0.0144011i
$$631$$ 11.1851i 0.445270i −0.974902 0.222635i $$-0.928534\pi$$
0.974902 0.222635i $$-0.0714659\pi$$
$$632$$ 28.2727 12.9440i 1.12463 0.514885i
$$633$$ 14.3102i 0.568779i
$$634$$ −5.05470 + 42.3891i −0.200748 + 1.68349i
$$635$$ −1.70774 + 1.70774i −0.0677698 + 0.0677698i
$$636$$ −0.328240 + 1.35675i −0.0130156 + 0.0537988i
$$637$$ 0.818234 + 0.818234i 0.0324196 + 0.0324196i
$$638$$ 22.3400 + 28.3892i 0.884449 + 1.12394i
$$639$$ −9.11529 −0.360595
$$640$$ −3.95705 + 3.61316i −0.156416 + 0.142823i
$$641$$ −6.69312 −0.264362 −0.132181 0.991226i $$-0.542198\pi$$
−0.132181 + 0.991226i $$0.542198\pi$$
$$642$$ −7.49824 9.52861i −0.295932 0.376064i
$$643$$ −17.9410 17.9410i −0.707522 0.707522i 0.258491 0.966014i $$-0.416775\pi$$
−0.966014 + 0.258491i $$0.916775\pi$$
$$644$$ −6.06255 + 25.0590i −0.238898 + 0.987464i
$$645$$ −0.762725 + 0.762725i −0.0300323 + 0.0300323i
$$646$$ −2.19079 + 18.3722i −0.0861957 + 0.722843i
$$647$$ 6.72999i 0.264583i −0.991211 0.132292i $$-0.957766\pi$$
0.991211 0.132292i $$-0.0422335\pi$$
$$648$$ 2.57172 1.17740i 0.101027 0.0462527i
$$649$$ 19.7890i 0.776786i
$$650$$ 0.563475 + 0.0671918i 0.0221013 + 0.00263548i
$$651$$ 1.79715 1.79715i 0.0704360 0.0704360i
$$652$$ 18.1184 11.0594i 0.709572 0.433120i
$$653$$ 26.1731 + 26.1731i 1.02423 + 1.02423i 0.999699 + 0.0245347i $$0.00781042\pi$$
0.0245347 + 0.999699i $$0.492190\pi$$
$$654$$ 8.98435 7.06995i 0.351316 0.276457i
$$655$$ −1.41921 −0.0554529
$$656$$ −16.9567 + 32.9933i −0.662047 + 1.28817i
$$657$$ 0.541560 0.0211283
$$658$$ 14.3267 11.2739i 0.558511 0.439503i
$$659$$ 13.9741 + 13.9741i 0.544353 + 0.544353i 0.924802 0.380449i $$-0.124230\pi$$
−0.380449 + 0.924802i $$0.624230\pi$$
$$660$$ −1.72646 2.82843i −0.0672024 0.110096i
$$661$$ 11.9241 11.9241i 0.463794 0.463794i −0.436103 0.899897i $$-0.643642\pi$$
0.899897 + 0.436103i $$0.143642\pi$$
$$662$$ 29.1784 + 3.47939i 1.13405 + 0.135230i
$$663$$ 0.303911i 0.0118029i
$$664$$ 39.8969 + 14.8379i 1.54830 + 0.575820i
$$665$$ 7.80785i 0.302776i
$$666$$ −1.03868 + 8.71044i −0.0402480 + 0.337523i
$$667$$ 14.6041 14.6041i 0.565473 0.565473i
$$668$$ 11.3490 + 2.74568i 0.439108 + 0.106234i
$$669$$ 3.43764 + 3.43764i 0.132907 + 0.132907i
$$670$$ −2.21174 2.81064i −0.0854470 0.108584i
$$671$$ −13.5021 −0.521244
$$672$$ 21.3740 + 14.4173i 0.824521 + 0.556161i
$$673$$ −37.3066 −1.43807 −0.719033 0.694976i $$-0.755415\pi$$
−0.719033 + 0.694976i $$0.755415\pi$$
$$674$$ −20.1234 25.5724i −0.775125 0.985013i
$$675$$ 3.37691 + 3.37691i 0.129978 + 0.129978i
$$676$$ 25.2572 + 6.11050i 0.971432 + 0.235019i
$$677$$ 0.447461 0.447461i 0.0171973 0.0171973i −0.698456 0.715653i $$-0.746129\pi$$
0.715653 + 0.698456i $$0.246129\pi$$
$$678$$ −1.59939 + 13.4126i −0.0614243 + 0.515109i
$$679$$ 19.6764i 0.755113i
$$680$$ 1.68903 4.54156i 0.0647713 0.174161i
$$681$$ 15.0496i 0.576702i
$$682$$ 2.73941 + 0.326662i 0.104898 + 0.0125085i
$$683$$ −4.27521 + 4.27521i −0.163586 + 0.163586i −0.784153 0.620567i $$-0.786902\pi$$
0.620567 + 0.784153i $$0.286902\pi$$
$$684$$ −3.76901 6.17471i −0.144112 0.236096i
$$685$$ 1.13178 + 1.13178i 0.0432430 + 0.0432430i
$$686$$ −34.3026 + 26.9933i −1.30968 + 1.03061i
$$687$$ 28.5264 1.08835
$$688$$ 8.67371 2.78473i 0.330682 0.106167i
$$689$$ 0.0586426 0.00223410
$$690$$ −1.48881 + 1.17157i −0.0566781 + 0.0446010i
$$691$$ 20.0786 + 20.0786i 0.763827 + 0.763827i 0.977012 0.213185i $$-0.0683836\pi$$
−0.213185 + 0.977012i $$0.568384\pi$$
$$692$$ 8.75225 5.34234i 0.332711 0.203085i
$$693$$ −11.2739 + 11.2739i −0.428261 + 0.428261i
$$694$$ −21.6519 2.58188i −0.821893 0.0980069i
$$695$$ 3.93926i 0.149425i
$$696$$ −8.59744 18.7788i −0.325885 0.711809i
$$697$$ 33.5443i 1.27058i
$$698$$ −4.74958 + 39.8303i −0.179774 + 1.50760i
$$699$$ 9.59558 9.59558i 0.362938 0.362938i
$$700$$ −10.2364 + 42.3111i −0.386898 + 1.59921i
$$701$$ −10.4467 10.4467i −0.394565 0.394565i 0.481746 0.876311i $$-0.340003\pi$$
−0.876311 + 0.481746i $$0.840003\pi$$
$$702$$ −0.0734818 0.0933792i −0.00277339 0.00352437i
$$703$$ 22.4361 0.846192
$$704$$ 2.04922 + 27.9108i 0.0772328 + 1.05193i
$$705$$ 1.33962 0.0504529
$$706$$ −10.6799 13.5718i −0.401943 0.510781i
$$707$$ 2.06793 + 2.06793i 0.0777727 + 0.0777727i
$$708$$ 2.66038 10.9965i 0.0999834 0.413273i
$$709$$ 16.0916 16.0916i 0.604332 0.604332i −0.337127 0.941459i $$-0.609455\pi$$
0.941459 + 0.337127i $$0.109455\pi$$
$$710$$ 0.722930 6.06255i 0.0271311 0.227523i
$$711$$ 10.9937i 0.412296i
$$712$$ −17.2528 37.6842i −0.646577 1.41228i
$$713$$ 1.57726i 0.0590690i
$$714$$ −23.1497 2.76049i −0.866356 0.103309i
$$715$$ −0.0984373 + 0.0984373i −0.00368135 + 0.00368135i
$$716$$ −22.4120 + 13.6802i −0.837574 + 0.511252i
$$717$$ −20.7627 20.7627i −0.775398 0.775398i
$$718$$ −37.2065 + 29.2785i −1.38854 + 1.09266i
$$719$$ −30.9957 −1.15594 −0.577972 0.816057i $$-0.696156\pi$$
−0.577972 + 0.816057i $$0.696156\pi$$
$$720$$ 0.579123 + 1.80382i 0.0215826 + 0.0672243i
$$721$$ 6.09292 0.226912
$$722$$ 6.57585 5.17466i 0.244728 0.192581i
$$723$$ −16.9750 16.9750i −0.631307 0.631307i
$$724$$ −15.9617 26.1497i −0.593211 0.971846i
$$725$$ 24.6584 24.6584i 0.915790 0.915790i
$$726$$ −1.73799 0.207247i −0.0645027 0.00769165i
$$727$$ 41.1117i 1.52475i 0.647135 + 0.762375i $$0.275967\pi$$
−0.647135 + 0.762375i $$0.724033\pi$$
$$728$$ 0.377553 1.01519i 0.0139930 0.0376253i
$$729$$ 1.00000i 0.0370370i
$$730$$ −0.0429509 + 0.360189i −0.00158968 + 0.0133312i
$$731$$ −5.82490 + 5.82490i −0.215442 + 0.215442i
$$732$$ 7.50295 + 1.81519i 0.277317 + 0.0670915i
$$733$$ 0.146061 + 0.146061i 0.00539490 + 0.00539490i 0.709799 0.704404i $$-0.248786\pi$$
−0.704404 + 0.709799i $$0.748786\pi$$
$$734$$ −0.614272 0.780604i −0.0226732 0.0288126i
$$735$$ −6.52284 −0.240599
$$736$$ 15.7061 3.05275i 0.578934 0.112526i
$$737$$ −18.6792 −0.688058
$$738$$ 8.11058 + 10.3068i 0.298555 + 0.379397i
$$739$$ −1.50766 1.50766i −0.0554601 0.0554601i 0.678833 0.734293i $$-0.262486\pi$$
−0.734293 + 0.678833i $$0.762486\pi$$
$$740$$ −5.71090 1.38164i −0.209937 0.0507902i
$$741$$ −0.214897 + 0.214897i −0.00789445 + 0.00789445i
$$742$$ −0.532664 + 4.46696i −0.0195547 + 0.163987i
$$743$$ 40.5175i 1.48644i 0.669046 + 0.743221i $$0.266703\pi$$
−0.669046 + 0.743221i $$0.733297\pi$$
$$744$$ −1.47834 0.549801i −0.0541985 0.0201567i
$$745$$ 6.69256i 0.245196i
$$746$$ 37.6529 + 4.48993i 1.37857 + 0.164388i
$$747$$ 10.6417 10.6417i 0.389358 0.389358i
$$748$$ −13.1849 21.6006i −0.482088 0.789795i
$$749$$ −27.6309 27.6309i −1.00961 1.00961i
$$750$$ −5.14567 + 4.04922i −0.187893 + 0.147857i
$$751$$ −12.5843 −0.459208 −0.229604 0.973284i $$-0.573743\pi$$
−0.229604 + 0.973284i $$0.573743\pi$$
$$752$$ −10.0625 5.17157i −0.366943 0.188588i
$$753$$ −22.2837 −0.812064
$$754$$ −0.681859 + 0.536568i −0.0248319 + 0.0195406i
$$755$$ −3.34129 3.34129i −0.121602 0.121602i
$$756$$ 7.78039 4.74912i 0.282970 0.172724i
$$757$$ −7.49900 + 7.49900i −0.272556 + 0.272556i −0.830128 0.557572i $$-0.811733\pi$$
0.557572 + 0.830128i $$0.311733\pi$$
$$758$$ −3.53186 0.421157i −0.128283 0.0152971i
$$759$$ 9.89450i 0.359148i
$$760$$ 4.40569 2.01704i 0.159811 0.0731659i
$$761$$ 42.8182i 1.55216i −0.630635 0.776079i $$-0.717206\pi$$
0.630635 0.776079i $$-0.282794\pi$$
$$762$$ 0.853872 7.16064i 0.0309325 0.259403i
$$763$$ 26.0527 26.0527i 0.943172 0.943172i
$$764$$ 4.05864 16.7761i 0.146837 0.606936i
$$765$$ −1.21137 1.21137i −0.0437971 0.0437971i
$$766$$ 22.2908 + 28.3267i 0.805398 + 1.02348i
$$767$$ −0.475298 −0.0171620
$$768$$ 2.61353