# Properties

 Label 48.2.j.a.37.1 Level $48$ Weight $2$ Character 48.37 Analytic conductor $0.383$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Learn more

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 37.1 Root $$0.500000 - 2.10607i$$ of defining polynomial Character $$\chi$$ $$=$$ 48.37 Dual form 48.2.j.a.13.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.34277 + 0.443806i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.60607 - 1.19186i) q^{4} +(1.27133 + 1.27133i) q^{5} +(-0.635665 + 1.26330i) q^{6} -0.158942i q^{7} +(-1.62764 + 2.31318i) q^{8} -1.00000i q^{9} +O(q^{10})$$ $$q+(-1.34277 + 0.443806i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.60607 - 1.19186i) q^{4} +(1.27133 + 1.27133i) q^{5} +(-0.635665 + 1.26330i) q^{6} -0.158942i q^{7} +(-1.62764 + 2.31318i) q^{8} -1.00000i q^{9} +(-2.27133 - 1.14288i) q^{10} +(-3.79793 - 3.79793i) q^{11} +(0.292893 - 1.97844i) q^{12} +(-4.21215 + 4.21215i) q^{13} +(0.0705392 + 0.213422i) q^{14} +1.79793 q^{15} +(1.15894 - 3.82843i) q^{16} +3.05320 q^{17} +(0.443806 + 1.34277i) q^{18} +(-2.15894 + 2.15894i) q^{19} +(3.55710 + 0.526602i) q^{20} +(-0.112389 - 0.112389i) q^{21} +(6.78530 + 3.41421i) q^{22} +2.82843i q^{23} +(0.484753 + 2.78658i) q^{24} -1.76744i q^{25} +(3.78658 - 7.52533i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.189436 - 0.255272i) q^{28} +(2.09976 - 2.09976i) q^{29} +(-2.41421 + 0.797933i) q^{30} +4.15894 q^{31} +(0.142883 + 5.65505i) q^{32} -5.37109 q^{33} +(-4.09976 + 1.35503i) q^{34} +(0.202067 - 0.202067i) q^{35} +(-1.19186 - 1.60607i) q^{36} +(-5.98737 - 5.98737i) q^{37} +(1.94082 - 3.85712i) q^{38} +5.95687i q^{39} +(-5.01008 + 0.871553i) q^{40} -2.60365i q^{41} +(0.200791 + 0.101034i) q^{42} +(5.75481 + 5.75481i) q^{43} +(-10.6264 - 1.57316i) q^{44} +(1.27133 - 1.27133i) q^{45} +(-1.25527 - 3.79793i) q^{46} -2.82843 q^{47} +(-1.88761 - 3.52660i) q^{48} +6.97474 q^{49} +(0.784399 + 2.37327i) q^{50} +(2.15894 - 2.15894i) q^{51} +(-1.74473 + 11.7853i) q^{52} +(3.55710 + 3.55710i) q^{53} +(1.26330 + 0.635665i) q^{54} -9.65685i q^{55} +(0.367661 + 0.258699i) q^{56} +3.05320i q^{57} +(-1.88761 + 3.75138i) q^{58} +(4.00000 + 4.00000i) q^{59} +(2.88761 - 2.14288i) q^{60} +(3.66949 - 3.66949i) q^{61} +(-5.58451 + 1.84576i) q^{62} -0.158942 q^{63} +(-2.70160 - 7.53003i) q^{64} -10.7101 q^{65} +(7.21215 - 2.38372i) q^{66} +(0.767438 - 0.767438i) q^{67} +(4.90367 - 3.63899i) q^{68} +(2.00000 + 2.00000i) q^{69} +(-0.181652 + 0.361009i) q^{70} +0.317883i q^{71} +(2.31318 + 1.62764i) q^{72} -1.33897i q^{73} +(10.6969 + 5.38244i) q^{74} +(-1.24977 - 1.24977i) q^{75} +(-0.894263 + 6.04057i) q^{76} +(-0.603650 + 0.603650i) q^{77} +(-2.64369 - 7.99872i) q^{78} -9.69382 q^{79} +(6.34059 - 3.39380i) q^{80} -1.00000 q^{81} +(1.15551 + 3.49611i) q^{82} +(0.115816 - 0.115816i) q^{83} +(-0.314456 - 0.0465529i) q^{84} +(3.88163 + 3.88163i) q^{85} +(-10.2814 - 5.17338i) q^{86} -2.96951i q^{87} +(14.9670 - 2.60365i) q^{88} +14.3990i q^{89} +(-1.14288 + 2.27133i) q^{90} +(0.669485 + 0.669485i) q^{91} +(3.37109 + 4.54266i) q^{92} +(2.94082 - 2.94082i) q^{93} +(3.79793 - 1.25527i) q^{94} -5.48946 q^{95} +(4.09976 + 3.89769i) q^{96} -0.571533 q^{97} +(-9.36548 + 3.09543i) q^{98} +(-3.79793 + 3.79793i) 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 $$\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$$.

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

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.34277 + 0.443806i −0.949483 + 0.313818i
$$3$$ 0.707107 0.707107i 0.408248 0.408248i
$$4$$ 1.60607 1.19186i 0.803037 0.595930i
$$5$$ 1.27133 + 1.27133i 0.568556 + 0.568556i 0.931724 0.363168i $$-0.118305\pi$$
−0.363168 + 0.931724i $$0.618305\pi$$
$$6$$ −0.635665 + 1.26330i −0.259509 + 0.515741i
$$7$$ 0.158942i 0.0600743i −0.999549 0.0300371i $$-0.990437\pi$$
0.999549 0.0300371i $$-0.00956256\pi$$
$$8$$ −1.62764 + 2.31318i −0.575456 + 0.817833i
$$9$$ 1.00000i 0.333333i
$$10$$ −2.27133 1.14288i −0.718258 0.361411i
$$11$$ −3.79793 3.79793i −1.14512 1.14512i −0.987500 0.157620i $$-0.949618\pi$$
−0.157620 0.987500i $$-0.550382\pi$$
$$12$$ 0.292893 1.97844i 0.0845510 0.571126i
$$13$$ −4.21215 + 4.21215i −1.16824 + 1.16824i −0.185617 + 0.982622i $$0.559428\pi$$
−0.982622 + 0.185617i $$0.940572\pi$$
$$14$$ 0.0705392 + 0.213422i 0.0188524 + 0.0570395i
$$15$$ 1.79793 0.464224
$$16$$ 1.15894 3.82843i 0.289735 0.957107i
$$17$$ 3.05320 0.740511 0.370255 0.928930i $$-0.379270\pi$$
0.370255 + 0.928930i $$0.379270\pi$$
$$18$$ 0.443806 + 1.34277i 0.104606 + 0.316494i
$$19$$ −2.15894 + 2.15894i −0.495295 + 0.495295i −0.909970 0.414675i $$-0.863895\pi$$
0.414675 + 0.909970i $$0.363895\pi$$
$$20$$ 3.55710 + 0.526602i 0.795391 + 0.117752i
$$21$$ −0.112389 0.112389i −0.0245252 0.0245252i
$$22$$ 6.78530 + 3.41421i 1.44663 + 0.727913i
$$23$$ 2.82843i 0.589768i 0.955533 + 0.294884i $$0.0952810\pi$$
−0.955533 + 0.294884i $$0.904719\pi$$
$$24$$ 0.484753 + 2.78658i 0.0989497 + 0.568808i
$$25$$ 1.76744i 0.353488i
$$26$$ 3.78658 7.52533i 0.742609 1.47584i
$$27$$ −0.707107 0.707107i −0.136083 0.136083i
$$28$$ −0.189436 0.255272i −0.0358001 0.0482419i
$$29$$ 2.09976 2.09976i 0.389915 0.389915i −0.484742 0.874657i $$-0.661087\pi$$
0.874657 + 0.484742i $$0.161087\pi$$
$$30$$ −2.41421 + 0.797933i −0.440773 + 0.145682i
$$31$$ 4.15894 0.746968 0.373484 0.927637i $$-0.378163\pi$$
0.373484 + 0.927637i $$0.378163\pi$$
$$32$$ 0.142883 + 5.65505i 0.0252584 + 0.999681i
$$33$$ −5.37109 −0.934986
$$34$$ −4.09976 + 1.35503i −0.703103 + 0.232386i
$$35$$ 0.202067 0.202067i 0.0341556 0.0341556i
$$36$$ −1.19186 1.60607i −0.198643 0.267679i
$$37$$ −5.98737 5.98737i −0.984317 0.984317i 0.0155615 0.999879i $$-0.495046\pi$$
−0.999879 + 0.0155615i $$0.995046\pi$$
$$38$$ 1.94082 3.85712i 0.314842 0.625707i
$$39$$ 5.95687i 0.953863i
$$40$$ −5.01008 + 0.871553i −0.792163 + 0.137805i
$$41$$ 2.60365i 0.406622i −0.979114 0.203311i $$-0.934830\pi$$
0.979114 0.203311i $$-0.0651702\pi$$
$$42$$ 0.200791 + 0.101034i 0.0309828 + 0.0155898i
$$43$$ 5.75481 + 5.75481i 0.877600 + 0.877600i 0.993286 0.115686i $$-0.0369066\pi$$
−0.115686 + 0.993286i $$0.536907\pi$$
$$44$$ −10.6264 1.57316i −1.60198 0.237162i
$$45$$ 1.27133 1.27133i 0.189519 0.189519i
$$46$$ −1.25527 3.79793i −0.185080 0.559975i
$$47$$ −2.82843 −0.412568 −0.206284 0.978492i $$-0.566137\pi$$
−0.206284 + 0.978492i $$0.566137\pi$$
$$48$$ −1.88761 3.52660i −0.272453 0.509021i
$$49$$ 6.97474 0.996391
$$50$$ 0.784399 + 2.37327i 0.110931 + 0.335631i
$$51$$ 2.15894 2.15894i 0.302312 0.302312i
$$52$$ −1.74473 + 11.7853i −0.241950 + 1.63433i
$$53$$ 3.55710 + 3.55710i 0.488605 + 0.488605i 0.907866 0.419261i $$-0.137711\pi$$
−0.419261 + 0.907866i $$0.637711\pi$$
$$54$$ 1.26330 + 0.635665i 0.171914 + 0.0865031i
$$55$$ 9.65685i 1.30213i
$$56$$ 0.367661 + 0.258699i 0.0491307 + 0.0345701i
$$57$$ 3.05320i 0.404407i
$$58$$ −1.88761 + 3.75138i −0.247856 + 0.492580i
$$59$$ 4.00000 + 4.00000i 0.520756 + 0.520756i 0.917800 0.397044i $$-0.129964\pi$$
−0.397044 + 0.917800i $$0.629964\pi$$
$$60$$ 2.88761 2.14288i 0.372789 0.276645i
$$61$$ 3.66949 3.66949i 0.469829 0.469829i −0.432030 0.901859i $$-0.642202\pi$$
0.901859 + 0.432030i $$0.142202\pi$$
$$62$$ −5.58451 + 1.84576i −0.709234 + 0.234412i
$$63$$ −0.158942 −0.0200248
$$64$$ −2.70160 7.53003i −0.337700 0.941254i
$$65$$ −10.7101 −1.32842
$$66$$ 7.21215 2.38372i 0.887754 0.293416i
$$67$$ 0.767438 0.767438i 0.0937575 0.0937575i −0.658672 0.752430i $$-0.728882\pi$$
0.752430 + 0.658672i $$0.228882\pi$$
$$68$$ 4.90367 3.63899i 0.594657 0.441292i
$$69$$ 2.00000 + 2.00000i 0.240772 + 0.240772i
$$70$$ −0.181652 + 0.361009i −0.0217115 + 0.0431488i
$$71$$ 0.317883i 0.0377258i 0.999822 + 0.0188629i $$0.00600460\pi$$
−0.999822 + 0.0188629i $$0.993995\pi$$
$$72$$ 2.31318 + 1.62764i 0.272611 + 0.191819i
$$73$$ 1.33897i 0.156715i −0.996925 0.0783573i $$-0.975032\pi$$
0.996925 0.0783573i $$-0.0249675\pi$$
$$74$$ 10.6969 + 5.38244i 1.24349 + 0.625696i
$$75$$ −1.24977 1.24977i −0.144311 0.144311i
$$76$$ −0.894263 + 6.04057i −0.102579 + 0.692901i
$$77$$ −0.603650 + 0.603650i −0.0687923 + 0.0687923i
$$78$$ −2.64369 7.99872i −0.299339 0.905677i
$$79$$ −9.69382 −1.09064 −0.545320 0.838228i $$-0.683592\pi$$
−0.545320 + 0.838228i $$0.683592\pi$$
$$80$$ 6.34059 3.39380i 0.708900 0.379438i
$$81$$ −1.00000 −0.111111
$$82$$ 1.15551 + 3.49611i 0.127605 + 0.386081i
$$83$$ 0.115816 0.115816i 0.0127125 0.0127125i −0.700722 0.713434i $$-0.747139\pi$$
0.713434 + 0.700722i $$0.247139\pi$$
$$84$$ −0.314456 0.0465529i −0.0343100 0.00507934i
$$85$$ 3.88163 + 3.88163i 0.421022 + 0.421022i
$$86$$ −10.2814 5.17338i −1.10867 0.557860i
$$87$$ 2.96951i 0.318364i
$$88$$ 14.9670 2.60365i 1.59548 0.277550i
$$89$$ 14.3990i 1.52629i 0.646225 + 0.763147i $$0.276347\pi$$
−0.646225 + 0.763147i $$0.723653\pi$$
$$90$$ −1.14288 + 2.27133i −0.120470 + 0.239419i
$$91$$ 0.669485 + 0.669485i 0.0701811 + 0.0701811i
$$92$$ 3.37109 + 4.54266i 0.351460 + 0.473605i
$$93$$ 2.94082 2.94082i 0.304948 0.304948i
$$94$$ 3.79793 1.25527i 0.391727 0.129471i
$$95$$ −5.48946 −0.563206
$$96$$ 4.09976 + 3.89769i 0.418430 + 0.397806i
$$97$$ −0.571533 −0.0580304 −0.0290152 0.999579i $$-0.509237\pi$$
−0.0290152 + 0.999579i $$0.509237\pi$$
$$98$$ −9.36548 + 3.09543i −0.946057 + 0.312685i
$$99$$ −3.79793 + 3.79793i −0.381707 + 0.381707i
$$100$$ −2.10654 2.83863i −0.210654 0.283863i
$$101$$ −7.15296 7.15296i −0.711746 0.711746i 0.255154 0.966900i $$-0.417874\pi$$
−0.966900 + 0.255154i $$0.917874\pi$$
$$102$$ −1.94082 + 3.85712i −0.192169 + 0.381911i
$$103$$ 11.3507i 1.11841i −0.829028 0.559207i $$-0.811106\pi$$
0.829028 0.559207i $$-0.188894\pi$$
$$104$$ −2.88761 16.5993i −0.283154 1.62769i
$$105$$ 0.285766i 0.0278879i
$$106$$ −6.35503 3.19771i −0.617255 0.310589i
$$107$$ −0.722018 0.722018i −0.0698001 0.0698001i 0.671345 0.741145i $$-0.265717\pi$$
−0.741145 + 0.671345i $$0.765717\pi$$
$$108$$ −1.97844 0.292893i −0.190375 0.0281837i
$$109$$ −1.44471 + 1.44471i −0.138378 + 0.138378i −0.772903 0.634525i $$-0.781196\pi$$
0.634525 + 0.772903i $$0.281196\pi$$
$$110$$ 4.28577 + 12.9670i 0.408632 + 1.23635i
$$111$$ −8.46742 −0.803692
$$112$$ −0.608497 0.184204i −0.0574975 0.0174057i
$$113$$ −3.53488 −0.332533 −0.166267 0.986081i $$-0.553171\pi$$
−0.166267 + 0.986081i $$0.553171\pi$$
$$114$$ −1.35503 4.09976i −0.126910 0.383977i
$$115$$ −3.59587 + 3.59587i −0.335316 + 0.335316i
$$116$$ 0.869748 5.87498i 0.0807541 0.545478i
$$117$$ 4.21215 + 4.21215i 0.389413 + 0.389413i
$$118$$ −7.14631 3.59587i −0.657871 0.331026i
$$119$$ 0.485281i 0.0444857i
$$120$$ −2.92638 + 4.15894i −0.267141 + 0.379658i
$$121$$ 17.8486i 1.62260i
$$122$$ −3.29874 + 6.55582i −0.298654 + 0.593536i
$$123$$ −1.84106 1.84106i −0.166003 0.166003i
$$124$$ 6.67956 4.95687i 0.599843 0.445140i
$$125$$ 8.60365 8.60365i 0.769534 0.769534i
$$126$$ 0.213422 0.0705392i 0.0190132 0.00628413i
$$127$$ −1.49791 −0.132918 −0.0664591 0.997789i $$-0.521170\pi$$
−0.0664591 + 0.997789i $$0.521170\pi$$
$$128$$ 6.96951 + 8.91213i 0.616023 + 0.787728i
$$129$$ 8.13853 0.716557
$$130$$ 14.3812 4.75318i 1.26131 0.416882i
$$131$$ 10.4243 10.4243i 0.910775 0.910775i −0.0855585 0.996333i $$-0.527267\pi$$
0.996333 + 0.0855585i $$0.0272675\pi$$
$$132$$ −8.62636 + 6.40158i −0.750828 + 0.557186i
$$133$$ 0.343146 + 0.343146i 0.0297545 + 0.0297545i
$$134$$ −0.689901 + 1.37109i −0.0595984 + 0.118444i
$$135$$ 1.79793i 0.154741i
$$136$$ −4.96951 + 7.06261i −0.426132 + 0.605614i
$$137$$ 13.7954i 1.17862i −0.807907 0.589309i $$-0.799400\pi$$
0.807907 0.589309i $$-0.200600\pi$$
$$138$$ −3.57316 1.79793i −0.304167 0.153050i
$$139$$ −2.42429 2.42429i −0.205626 0.205626i 0.596779 0.802405i $$-0.296447\pi$$
−0.802405 + 0.596779i $$0.796447\pi$$
$$140$$ 0.0836990 0.565371i 0.00707386 0.0477826i
$$141$$ −2.00000 + 2.00000i −0.168430 + 0.168430i
$$142$$ −0.141078 0.426845i −0.0118390 0.0358200i
$$143$$ 31.9949 2.67555
$$144$$ −3.82843 1.15894i −0.319036 0.0965785i
$$145$$ 5.33897 0.443377
$$146$$ 0.594243 + 1.79793i 0.0491799 + 0.148798i
$$147$$ 4.93188 4.93188i 0.406775 0.406775i
$$148$$ −16.7523 2.48005i −1.37703 0.203859i
$$149$$ 2.92818 + 2.92818i 0.239886 + 0.239886i 0.816803 0.576917i $$-0.195744\pi$$
−0.576917 + 0.816803i $$0.695744\pi$$
$$150$$ 2.23281 + 1.12350i 0.182308 + 0.0917333i
$$151$$ 22.6644i 1.84440i 0.386712 + 0.922201i $$0.373611\pi$$
−0.386712 + 0.922201i $$0.626389\pi$$
$$152$$ −1.48005 8.50799i −0.120048 0.690089i
$$153$$ 3.05320i 0.246837i
$$154$$ 0.542661 1.07847i 0.0437288 0.0869053i
$$155$$ 5.28739 + 5.28739i 0.424693 + 0.424693i
$$156$$ 7.09976 + 9.56718i 0.568436 + 0.765987i
$$157$$ −2.78007 + 2.78007i −0.221874 + 0.221874i −0.809287 0.587413i $$-0.800146\pi$$
0.587413 + 0.809287i $$0.300146\pi$$
$$158$$ 13.0166 4.30217i 1.03554 0.342262i
$$159$$ 5.03049 0.398944
$$160$$ −7.00778 + 7.37109i −0.554014 + 0.582736i
$$161$$ 0.449555 0.0354299
$$162$$ 1.34277 0.443806i 0.105498 0.0348687i
$$163$$ −5.43692 + 5.43692i −0.425853 + 0.425853i −0.887213 0.461360i $$-0.847362\pi$$
0.461360 + 0.887213i $$0.347362\pi$$
$$164$$ −3.10318 4.18165i −0.242318 0.326532i
$$165$$ −6.82843 6.82843i −0.531592 0.531592i
$$166$$ −0.104115 + 0.206914i −0.00808086 + 0.0160597i
$$167$$ 3.95458i 0.306015i −0.988225 0.153007i $$-0.951104\pi$$
0.988225 0.153007i $$-0.0488958\pi$$
$$168$$ 0.442903 0.0770474i 0.0341707 0.00594434i
$$169$$ 22.4844i 1.72957i
$$170$$ −6.93484 3.48946i −0.531878 0.267629i
$$171$$ 2.15894 + 2.15894i 0.165098 + 0.165098i
$$172$$ 16.1016 + 2.38372i 1.22773 + 0.181757i
$$173$$ −15.9814 + 15.9814i −1.21504 + 1.21504i −0.245695 + 0.969347i $$0.579016\pi$$
−0.969347 + 0.245695i $$0.920984\pi$$
$$174$$ 1.31788 + 3.98737i 0.0999085 + 0.302282i
$$175$$ −0.280920 −0.0212355
$$176$$ −18.9417 + 10.1385i −1.42778 + 0.764220i
$$177$$ 5.65685 0.425195
$$178$$ −6.39037 19.3346i −0.478979 1.44919i
$$179$$ −12.2316 + 12.2316i −0.914235 + 0.914235i −0.996602 0.0823670i $$-0.973752\pi$$
0.0823670 + 0.996602i $$0.473752\pi$$
$$180$$ 0.526602 3.55710i 0.0392506 0.265130i
$$181$$ 5.76259 + 5.76259i 0.428330 + 0.428330i 0.888059 0.459729i $$-0.152054\pi$$
−0.459729 + 0.888059i $$0.652054\pi$$
$$182$$ −1.19609 0.601845i −0.0886599 0.0446117i
$$183$$ 5.18944i 0.383614i
$$184$$ −6.54266 4.60365i −0.482331 0.339386i
$$185$$ 15.2238i 1.11928i
$$186$$ −2.64369 + 5.25400i −0.193845 + 0.385242i
$$187$$ −11.5959 11.5959i −0.847974 0.847974i
$$188$$ −4.54266 + 3.37109i −0.331308 + 0.245862i
$$189$$ −0.112389 + 0.112389i −0.00817508 + 0.00817508i
$$190$$ 7.37109 2.43625i 0.534755 0.176744i
$$191$$ −16.1674 −1.16983 −0.584916 0.811094i $$-0.698873\pi$$
−0.584916 + 0.811094i $$0.698873\pi$$
$$192$$ −7.23486 3.41421i −0.522131 0.246400i
$$193$$ −22.1454 −1.59406 −0.797030 0.603940i $$-0.793597\pi$$
−0.797030 + 0.603940i $$0.793597\pi$$
$$194$$ 0.767438 0.253649i 0.0550989 0.0182110i
$$195$$ −7.57316 + 7.57316i −0.542325 + 0.542325i
$$196$$ 11.2019 8.31291i 0.800138 0.593779i
$$197$$ −14.2993 14.2993i −1.01878 1.01878i −0.999820 0.0189608i $$-0.993964\pi$$
−0.0189608 0.999820i $$-0.506036\pi$$
$$198$$ 3.41421 6.78530i 0.242638 0.482210i
$$199$$ 25.0075i 1.77274i 0.462981 + 0.886368i $$0.346780\pi$$
−0.462981 + 0.886368i $$0.653220\pi$$
$$200$$ 4.08840 + 2.87675i 0.289094 + 0.203417i
$$201$$ 1.08532i 0.0765527i
$$202$$ 12.7793 + 6.43027i 0.899150 + 0.452432i
$$203$$ −0.333739 0.333739i −0.0234239 0.0234239i
$$204$$ 0.894263 6.04057i 0.0626109 0.422925i
$$205$$ 3.31010 3.31010i 0.231187 0.231187i
$$206$$ 5.03749 + 15.2414i 0.350979 + 1.06192i
$$207$$ 2.82843 0.196589
$$208$$ 11.2443 + 21.0075i 0.779649 + 1.45661i
$$209$$ 16.3990 1.13434
$$210$$ 0.126825 + 0.383719i 0.00875174 + 0.0264791i
$$211$$ 18.4243 18.4243i 1.26838 1.26838i 0.321456 0.946924i $$-0.395828\pi$$
0.946924 0.321456i $$-0.104172\pi$$
$$212$$ 9.95252 + 1.47340i 0.683542 + 0.101193i
$$213$$ 0.224777 + 0.224777i 0.0154015 + 0.0154015i
$$214$$ 1.28994 + 0.649070i 0.0881786 + 0.0443695i
$$215$$ 14.6325i 0.997930i
$$216$$ 2.78658 0.484753i 0.189603 0.0329832i
$$217$$ 0.661029i 0.0448736i
$$218$$ 1.29874 2.58108i 0.0879620 0.174813i
$$219$$ −0.946795 0.946795i −0.0639785 0.0639785i
$$220$$ −11.5096 15.5096i −0.775978 1.04566i
$$221$$ −12.8605 + 12.8605i −0.865094 + 0.865094i
$$222$$ 11.3698 3.75789i 0.763092 0.252213i
$$223$$ 18.3465 1.22857 0.614286 0.789083i $$-0.289444\pi$$
0.614286 + 0.789083i $$0.289444\pi$$
$$224$$ 0.898823 0.0227101i 0.0600551 0.00151738i
$$225$$ −1.76744 −0.117829
$$226$$ 4.74653 1.56880i 0.315735 0.104355i
$$227$$ −0.115816 + 0.115816i −0.00768697 + 0.00768697i −0.710940 0.703253i $$-0.751730\pi$$
0.703253 + 0.710940i $$0.251730\pi$$
$$228$$ 3.63899 + 4.90367i 0.240998 + 0.324753i
$$229$$ 2.84791 + 2.84791i 0.188195 + 0.188195i 0.794916 0.606720i $$-0.207515\pi$$
−0.606720 + 0.794916i $$0.707515\pi$$
$$230$$ 3.23256 6.42429i 0.213149 0.423605i
$$231$$ 0.853690i 0.0561687i
$$232$$ 1.43948 + 8.27476i 0.0945062 + 0.543264i
$$233$$ 11.7211i 0.767874i 0.923359 + 0.383937i $$0.125432\pi$$
−0.923359 + 0.383937i $$0.874568\pi$$
$$234$$ −7.52533 3.78658i −0.491946 0.247536i
$$235$$ −3.59587 3.59587i −0.234568 0.234568i
$$236$$ 11.1917 + 1.65685i 0.728520 + 0.107852i
$$237$$ −6.85456 + 6.85456i −0.445252 + 0.445252i
$$238$$ 0.215371 + 0.651622i 0.0139604 + 0.0422384i
$$239$$ −13.6517 −0.883058 −0.441529 0.897247i $$-0.645564\pi$$
−0.441529 + 0.897247i $$0.645564\pi$$
$$240$$ 2.08370 6.88325i 0.134502 0.444312i
$$241$$ 2.13167 0.137313 0.0686565 0.997640i $$-0.478129\pi$$
0.0686565 + 0.997640i $$0.478129\pi$$
$$242$$ −7.92130 23.9666i −0.509201 1.54063i
$$243$$ −0.707107 + 0.707107i −0.0453609 + 0.0453609i
$$244$$ 1.51995 10.2670i 0.0973049 0.657276i
$$245$$ 8.86720 + 8.86720i 0.566504 + 0.566504i
$$246$$ 3.28919 + 1.65505i 0.209711 + 0.105522i
$$247$$ 18.1876i 1.15725i
$$248$$ −6.76924 + 9.62038i −0.429847 + 0.610895i
$$249$$ 0.163788i 0.0103797i
$$250$$ −7.73439 + 15.3711i −0.489166 + 0.972153i
$$251$$ −4.43370 4.43370i −0.279853 0.279853i 0.553198 0.833050i $$-0.313407\pi$$
−0.833050 + 0.553198i $$0.813407\pi$$
$$252$$ −0.255272 + 0.189436i −0.0160806 + 0.0119334i
$$253$$ 10.7422 10.7422i 0.675355 0.675355i
$$254$$ 2.01136 0.664782i 0.126204 0.0417121i
$$255$$ 5.48946 0.343763
$$256$$ −13.3137 8.87385i −0.832107 0.554615i
$$257$$ 15.0853 0.940997 0.470498 0.882401i $$-0.344074\pi$$
0.470498 + 0.882401i $$0.344074\pi$$
$$258$$ −10.9282 + 3.61192i −0.680359 + 0.224869i
$$259$$ −0.951642 + 0.951642i −0.0591322 + 0.0591322i
$$260$$ −17.2011 + 12.7649i −1.06677 + 0.791645i
$$261$$ −2.09976 2.09976i −0.129972 0.129972i
$$262$$ −9.37109 + 18.6238i −0.578948 + 1.15058i
$$263$$ 26.1706i 1.61375i −0.590722 0.806875i $$-0.701157\pi$$
0.590722 0.806875i $$-0.298843\pi$$
$$264$$ 8.74218 12.4243i 0.538044 0.764662i
$$265$$ 9.04449i 0.555599i
$$266$$ −0.613057 0.308476i −0.0375889 0.0189139i
$$267$$ 10.1817 + 10.1817i 0.623107 + 0.623107i
$$268$$ 0.317883 2.14724i 0.0194178 0.131164i
$$269$$ 8.59700 8.59700i 0.524168 0.524168i −0.394659 0.918828i $$-0.629137\pi$$
0.918828 + 0.394659i $$0.129137\pi$$
$$270$$ 0.797933 + 2.41421i 0.0485606 + 0.146924i
$$271$$ 10.6644 0.647815 0.323907 0.946089i $$-0.395003\pi$$
0.323907 + 0.946089i $$0.395003\pi$$
$$272$$ 3.53849 11.6890i 0.214552 0.708748i
$$273$$ 0.946795 0.0573027
$$274$$ 6.12247 + 18.5240i 0.369872 + 1.11908i
$$275$$ −6.71261 + 6.71261i −0.404786 + 0.404786i
$$276$$ 5.59587 + 0.828427i 0.336832 + 0.0498655i
$$277$$ −2.66170 2.66170i −0.159926 0.159926i 0.622608 0.782534i $$-0.286073\pi$$
−0.782534 + 0.622608i $$0.786073\pi$$
$$278$$ 4.33119 + 2.17936i 0.259767 + 0.130709i
$$279$$ 4.15894i 0.248989i
$$280$$ 0.138526 + 0.796310i 0.00827851 + 0.0475886i
$$281$$ 10.4496i 0.623368i 0.950186 + 0.311684i $$0.100893\pi$$
−0.950186 + 0.311684i $$0.899107\pi$$
$$282$$ 1.79793 3.57316i 0.107065 0.212778i
$$283$$ −12.4853 12.4853i −0.742173 0.742173i 0.230823 0.972996i $$-0.425858\pi$$
−0.972996 + 0.230823i $$0.925858\pi$$
$$284$$ 0.378872 + 0.510544i 0.0224819 + 0.0302952i
$$285$$ −3.88163 + 3.88163i −0.229928 + 0.229928i
$$286$$ −42.9618 + 14.1995i −2.54039 + 0.839635i
$$287$$ −0.413828 −0.0244275
$$288$$ 5.65505 0.142883i 0.333227 0.00841947i
$$289$$ −7.67794 −0.451644
$$290$$ −7.16902 + 2.36947i −0.420979 + 0.139140i
$$291$$ −0.404135 + 0.404135i −0.0236908 + 0.0236908i
$$292$$ −1.59587 2.15049i −0.0933910 0.125848i
$$293$$ 21.7410 + 21.7410i 1.27013 + 1.27013i 0.946022 + 0.324104i $$0.105063\pi$$
0.324104 + 0.946022i $$0.394937\pi$$
$$294$$ −4.43360 + 8.81119i −0.258573 + 0.513879i
$$295$$ 10.1706i 0.592158i
$$296$$ 23.5951 4.10460i 1.37144 0.238575i
$$297$$ 5.37109i 0.311662i
$$298$$ −5.23143 2.63234i −0.303049 0.152487i
$$299$$ −11.9137 11.9137i −0.688990 0.688990i
$$300$$ −3.49677 0.517671i −0.201886 0.0298877i
$$301$$ 0.914679 0.914679i 0.0527212 0.0527212i
$$302$$ −10.0586 30.4331i −0.578806 1.75123i
$$303$$ −10.1158 −0.581138
$$304$$ 5.76326 + 10.7674i 0.330546 + 0.617555i
$$305$$ 9.33026 0.534249
$$306$$ 1.35503 + 4.09976i 0.0774619 + 0.234368i
$$307$$ 15.0601 15.0601i 0.859523 0.859523i −0.131759 0.991282i $$-0.542062\pi$$
0.991282 + 0.131759i $$0.0420624\pi$$
$$308$$ −0.250040 + 1.68897i −0.0142473 + 0.0962381i
$$309$$ −8.02614 8.02614i −0.456591 0.456591i
$$310$$ −9.44633 4.75318i −0.536516 0.269963i
$$311$$ 1.77883i 0.100868i −0.998727 0.0504342i $$-0.983939\pi$$
0.998727 0.0504342i $$-0.0160605\pi$$
$$312$$ −13.7793 9.69562i −0.780100 0.548907i
$$313$$ 2.70320i 0.152794i −0.997077 0.0763971i $$-0.975658\pi$$
0.997077 0.0763971i $$-0.0243417\pi$$
$$314$$ 2.49919 4.96681i 0.141037 0.280293i
$$315$$ −0.202067 0.202067i −0.0113852 0.0113852i
$$316$$ −15.5690 + 11.5537i −0.875824 + 0.649945i
$$317$$ 15.6025 15.6025i 0.876325 0.876325i −0.116828 0.993152i $$-0.537272\pi$$
0.993152 + 0.116828i $$0.0372725\pi$$
$$318$$ −6.75481 + 2.23256i −0.378791 + 0.125196i
$$319$$ −15.9495 −0.892999
$$320$$ 6.13853 13.0078i 0.343154 0.727157i
$$321$$ −1.02109 −0.0569916
$$322$$ −0.603650 + 0.199515i −0.0336401 + 0.0111185i
$$323$$ −6.59169 + 6.59169i −0.366771 + 0.366771i
$$324$$ −1.60607 + 1.19186i −0.0892263 + 0.0662144i
$$325$$ 7.44471 + 7.44471i 0.412958 + 0.412958i
$$326$$ 4.88761 9.71349i 0.270700 0.537980i
$$327$$ 2.04313i 0.112985i
$$328$$ 6.02271 + 4.23779i 0.332549 + 0.233993i
$$329$$ 0.449555i 0.0247848i
$$330$$ 12.1995 + 6.13853i 0.671561 + 0.337915i
$$331$$ 15.4454 + 15.4454i 0.848955 + 0.848955i 0.990003 0.141048i $$-0.0450472\pi$$
−0.141048 + 0.990003i $$0.545047\pi$$
$$332$$ 0.0479725 0.324045i 0.00263284 0.0177843i
$$333$$ −5.98737 + 5.98737i −0.328106 + 0.328106i
$$334$$ 1.75506 + 5.31010i 0.0960329 + 0.290556i
$$335$$ 1.95133 0.106613
$$336$$ −0.560524 + 0.300020i −0.0305791 + 0.0163674i
$$337$$ −18.8738 −1.02812 −0.514062 0.857753i $$-0.671860\pi$$
−0.514062 + 0.857753i $$0.671860\pi$$
$$338$$ 9.97868 + 30.1914i 0.542769 + 1.64219i
$$339$$ −2.49954 + 2.49954i −0.135756 + 0.135756i
$$340$$ 10.8605 + 1.60782i 0.588996 + 0.0871965i
$$341$$ −15.7954 15.7954i −0.855368 0.855368i
$$342$$ −3.85712 1.94082i −0.208569 0.104947i
$$343$$ 2.22117i 0.119932i
$$344$$ −22.6786 + 3.94517i −1.22275 + 0.212709i
$$345$$ 5.08532i 0.273785i
$$346$$ 14.3667 28.5520i 0.772360 1.53496i
$$347$$ 19.8337 + 19.8337i 1.06473 + 1.06473i 0.997755 + 0.0669717i $$0.0213337\pi$$
0.0669717 + 0.997755i $$0.478666\pi$$
$$348$$ −3.53923 4.76924i −0.189723 0.255658i
$$349$$ 11.9718 11.9718i 0.640836 0.640836i −0.309925 0.950761i $$-0.600304\pi$$
0.950761 + 0.309925i $$0.100304\pi$$
$$350$$ 0.377211 0.124674i 0.0201628 0.00666409i
$$351$$ 5.95687 0.317954
$$352$$ 20.9348 22.0202i 1.11583 1.17368i
$$353$$ −12.6202 −0.671705 −0.335853 0.941915i $$-0.609024\pi$$
−0.335853 + 0.941915i $$0.609024\pi$$
$$354$$ −7.59587 + 2.51054i −0.403716 + 0.133434i
$$355$$ −0.404135 + 0.404135i −0.0214492 + 0.0214492i
$$356$$ 17.1616 + 23.1259i 0.909564 + 1.22567i
$$357$$ −0.343146 0.343146i −0.0181612 0.0181612i
$$358$$ 10.9958 21.8528i 0.581147 1.15495i
$$359$$ 27.0867i 1.42958i −0.699339 0.714790i $$-0.746522\pi$$
0.699339 0.714790i $$-0.253478\pi$$
$$360$$ 0.871553 + 5.01008i 0.0459349 + 0.264054i
$$361$$ 9.67794i 0.509365i
$$362$$ −10.2953 5.18038i −0.541110 0.272274i
$$363$$ 12.6209 + 12.6209i 0.662423 + 0.662423i
$$364$$ 1.87318 + 0.277310i 0.0981811 + 0.0145350i
$$365$$ 1.70227 1.70227i 0.0891011 0.0891011i
$$366$$ 2.30310 + 6.96823i 0.120385 + 0.364235i
$$367$$ −20.4937 −1.06976 −0.534882 0.844927i $$-0.679644\pi$$
−0.534882 + 0.844927i $$0.679644\pi$$
$$368$$ 10.8284 + 3.27798i 0.564471 + 0.170877i
$$369$$ −2.60365 −0.135541
$$370$$ 6.75643 + 20.4422i 0.351250 + 1.06274i
$$371$$ 0.565371 0.565371i 0.0293526 0.0293526i
$$372$$ 1.21813 8.22820i 0.0631569 0.426613i
$$373$$ 1.03372 + 1.03372i 0.0535239 + 0.0535239i 0.733362 0.679838i $$-0.237950\pi$$
−0.679838 + 0.733362i $$0.737950\pi$$
$$374$$ 20.7169 + 10.4243i 1.07125 + 0.539027i
$$375$$ 12.1674i 0.628322i
$$376$$ 4.60365 6.54266i 0.237415 0.337412i
$$377$$ 17.6890i 0.911028i
$$378$$ 0.101034 0.200791i 0.00519661 0.0103276i
$$379$$ 17.6686 + 17.6686i 0.907573 + 0.907573i 0.996076 0.0885032i $$-0.0282083\pi$$
−0.0885032 + 0.996076i $$0.528208\pi$$
$$380$$ −8.81647 + 6.54266i −0.452275 + 0.335631i
$$381$$ −1.05918 + 1.05918i −0.0542636 + 0.0542636i
$$382$$ 21.7091 7.17518i 1.11074 0.367114i
$$383$$ −31.0958 −1.58892 −0.794460 0.607316i $$-0.792246\pi$$
−0.794460 + 0.607316i $$0.792246\pi$$
$$384$$ 11.2300 + 1.37364i 0.573079 + 0.0700983i
$$385$$ −1.53488 −0.0782245
$$386$$ 29.7362 9.82824i 1.51353 0.500244i
$$387$$ 5.75481 5.75481i 0.292533 0.292533i
$$388$$ −0.917923 + 0.681187i −0.0466005 + 0.0345820i
$$389$$ −2.56127 2.56127i −0.129862 0.129862i 0.639188 0.769050i $$-0.279270\pi$$
−0.769050 + 0.639188i $$0.779270\pi$$
$$390$$ 6.80801 13.5300i 0.344737 0.685120i
$$391$$ 8.63577i 0.436729i
$$392$$ −11.3523 + 16.1338i −0.573379 + 0.814881i
$$393$$ 14.7422i 0.743644i
$$394$$ 25.5468 + 12.8546i 1.28703 + 0.647604i
$$395$$ −12.3240 12.3240i −0.620090 0.620090i
$$396$$ −1.57316 + 10.6264i −0.0790540 + 0.533995i
$$397$$ −5.09795 + 5.09795i −0.255859 + 0.255859i −0.823367 0.567509i $$-0.807907\pi$$
0.567509 + 0.823367i $$0.307907\pi$$
$$398$$ −11.0985 33.5794i −0.556317 1.68318i
$$399$$ 0.485281 0.0242945
$$400$$ −6.76651 2.04836i −0.338325 0.102418i
$$401$$ −15.2660 −0.762349 −0.381174 0.924503i $$-0.624480\pi$$
−0.381174 + 0.924503i $$0.624480\pi$$
$$402$$ 0.481672 + 1.45734i 0.0240236 + 0.0726855i
$$403$$ −17.5181 + 17.5181i −0.872637 + 0.872637i
$$404$$ −20.0135 2.96285i −0.995709 0.147407i
$$405$$ −1.27133 1.27133i −0.0631729 0.0631729i
$$406$$ 0.596250 + 0.300020i 0.0295914 + 0.0148897i
$$407$$ 45.4792i 2.25432i
$$408$$ 1.48005 + 8.50799i 0.0732734 + 0.421208i
$$409$$ 11.3779i 0.562603i −0.959619 0.281302i $$-0.909234\pi$$
0.959619 0.281302i $$-0.0907661\pi$$
$$410$$ −2.97567 + 5.91375i −0.146958 + 0.292059i
$$411$$ −9.75481 9.75481i −0.481169 0.481169i
$$412$$ −13.5284 18.2300i −0.666497 0.898128i
$$413$$ 0.635767 0.635767i 0.0312840 0.0312840i
$$414$$ −3.79793 + 1.25527i −0.186658 + 0.0616932i
$$415$$ 0.294481 0.0144555
$$416$$ −24.4217 23.2181i −1.19737 1.13836i
$$417$$ −3.42847 −0.167893
$$418$$ −22.0202 + 7.27798i −1.07704 + 0.355978i
$$419$$ 23.3075 23.3075i 1.13865 1.13865i 0.149955 0.988693i $$-0.452087\pi$$
0.988693 0.149955i $$-0.0479130\pi$$
$$420$$ −0.340593 0.458962i −0.0166193 0.0223950i
$$421$$ −17.6154 17.6154i −0.858520 0.858520i 0.132644 0.991164i $$-0.457653\pi$$
−0.991164 + 0.132644i $$0.957653\pi$$
$$422$$ −16.5628 + 32.9164i −0.806265 + 1.60235i
$$423$$ 2.82843i 0.137523i
$$424$$ −14.0179 + 2.43855i −0.680768 + 0.118426i
$$425$$ 5.39635i 0.261761i
$$426$$ −0.401582 0.202067i −0.0194567 0.00979020i
$$427$$ −0.583234 0.583234i −0.0282247 0.0282247i
$$428$$ −2.02016 0.299070i −0.0976480 0.0144561i
$$429$$ 22.6238 22.6238i 1.09229 1.09229i
$$430$$ −6.49400 19.6481i −0.313168 0.947517i
$$431$$ 10.3211 0.497151 0.248576 0.968612i $$-0.420038\pi$$
0.248576 + 0.968612i $$0.420038\pi$$
$$432$$ −3.52660 + 1.88761i −0.169674 + 0.0908177i
$$433$$ −15.3137 −0.735930 −0.367965 0.929840i $$-0.619945\pi$$
−0.367965 + 0.929840i $$0.619945\pi$$
$$434$$ 0.293368 + 0.887611i 0.0140821 + 0.0426067i
$$435$$ 3.77522 3.77522i 0.181008 0.181008i
$$436$$ −0.598418 + 4.04220i −0.0286590 + 0.193586i
$$437$$ −6.10641 6.10641i −0.292109 0.292109i
$$438$$ 1.69152 + 0.851137i 0.0808241 + 0.0406689i
$$439$$ 22.5735i 1.07738i −0.842505 0.538688i $$-0.818920\pi$$
0.842505 0.538688i $$-0.181080\pi$$
$$440$$ 22.3380 + 15.7178i 1.06492 + 0.749319i
$$441$$ 6.97474i 0.332130i
$$442$$ 11.5612 22.9764i 0.549910 1.09287i
$$443$$ 23.7117 + 23.7117i 1.12658 + 1.12658i 0.990730 + 0.135846i $$0.0433752\pi$$
0.135846 + 0.990730i $$0.456625\pi$$
$$444$$ −13.5993 + 10.0920i −0.645394 + 0.478944i
$$445$$ −18.3059 + 18.3059i −0.867784 + 0.867784i
$$446$$ −24.6352 + 8.14228i −1.16651 + 0.385548i
$$447$$ 4.14108 0.195866
$$448$$ −1.19684 + 0.429397i −0.0565452 + 0.0202871i
$$449$$ −1.75506 −0.0828266 −0.0414133 0.999142i $$-0.513186\pi$$
−0.0414133 + 0.999142i $$0.513186\pi$$
$$450$$ 2.37327 0.784399i 0.111877 0.0369769i
$$451$$ −9.88849 + 9.88849i −0.465631 + 0.465631i
$$452$$ −5.67727 + 4.21308i −0.267036 + 0.198166i
$$453$$ 16.0261 + 16.0261i 0.752974 + 0.752974i
$$454$$ 0.104115 0.206914i 0.00488634 0.00971096i
$$455$$ 1.70227i 0.0798039i
$$456$$ −7.06261 4.96951i −0.330737 0.232718i
$$457$$ 26.7422i 1.25095i 0.780246 + 0.625473i $$0.215094\pi$$
−0.780246 + 0.625473i $$0.784906\pi$$
$$458$$ −5.08802 2.56018i −0.237747 0.119629i
$$459$$ −2.15894 2.15894i −0.100771 0.100771i
$$460$$ −1.48946 + 10.0610i −0.0694463 + 0.469096i
$$461$$ 9.23921 9.23921i 0.430313 0.430313i −0.458422 0.888735i $$-0.651585\pi$$
0.888735 + 0.458422i $$0.151585\pi$$
$$462$$ −0.378872 1.14631i −0.0176267 0.0533312i
$$463$$ 29.4474 1.36854 0.684268 0.729231i $$-0.260122\pi$$
0.684268 + 0.729231i $$0.260122\pi$$
$$464$$ −5.60527 10.4723i −0.260218 0.486163i
$$465$$ 7.47750 0.346761
$$466$$ −5.20189 15.7387i −0.240973 0.729083i
$$467$$ −19.5897 + 19.5897i −0.906503 + 0.906503i −0.995988 0.0894848i $$-0.971478\pi$$
0.0894848 + 0.995988i $$0.471478\pi$$
$$468$$ 11.7853 + 1.74473i 0.544776 + 0.0806501i
$$469$$ −0.121978 0.121978i −0.00563242 0.00563242i
$$470$$ 6.42429 + 3.23256i 0.296331 + 0.149107i
$$471$$ 3.93161i 0.181159i
$$472$$ −15.7633 + 2.74218i −0.725563 + 0.126219i
$$473$$ 43.7127i 2.00991i
$$474$$ 6.16202 12.2462i 0.283031 0.562487i
$$475$$ 3.81580 + 3.81580i 0.175081 + 0.175081i
$$476$$ −0.578387 0.779397i −0.0265103 0.0357236i
$$477$$ 3.55710 3.55710i 0.162868 0.162868i
$$478$$ 18.3312 6.05872i 0.838449 0.277120i
$$479$$ 35.5499 1.62432 0.812159 0.583436i $$-0.198292\pi$$
0.812159 + 0.583436i $$0.198292\pi$$
$$480$$ 0.256894 + 10.1674i 0.0117256 + 0.464076i
$$481$$ 50.4393 2.29984
$$482$$ −2.86235 + 0.946048i −0.130376 + 0.0430913i
$$483$$ 0.317883 0.317883i 0.0144642 0.0144642i
$$484$$ 21.2730 + 28.6661i 0.966955 + 1.30301i
$$485$$ −0.726607 0.726607i −0.0329935 0.0329935i
$$486$$ 0.635665 1.26330i 0.0288344 0.0573045i
$$487$$ 9.86632i 0.447086i 0.974694 + 0.223543i $$0.0717623\pi$$
−0.974694 + 0.223543i $$0.928238\pi$$
$$488$$ 2.51559 + 14.4608i 0.113876 + 0.654608i
$$489$$ 7.68897i 0.347707i
$$490$$ −15.8419 7.97131i −0.715666 0.360107i
$$491$$ −0.449555 0.449555i −0.0202881 0.0202881i 0.696890 0.717178i $$-0.254567\pi$$
−0.717178 + 0.696890i $$0.754567\pi$$
$$492$$ −5.15116 0.762591i −0.232232 0.0343803i
$$493$$ 6.41099 6.41099i 0.288736 0.288736i
$$494$$ 8.07174 + 24.4217i 0.363165 + 1.09879i
$$495$$ −9.65685 −0.434043
$$496$$ 4.81997 15.9222i 0.216423 0.714928i
$$497$$ 0.0505249 0.00226635
$$498$$ 0.0726903 + 0.219931i 0.00325733 + 0.00985533i
$$499$$ 2.70645 2.70645i 0.121157 0.121157i −0.643928 0.765086i $$-0.722697\pi$$
0.765086 + 0.643928i $$0.222697\pi$$
$$500$$ 3.56375 24.0724i 0.159376 1.07655i
$$501$$ −2.79631 2.79631i −0.124930 0.124930i
$$502$$ 7.92115 + 3.98575i 0.353538 + 0.177893i
$$503$$ 23.6719i 1.05548i −0.849407 0.527739i $$-0.823040\pi$$
0.849407 0.527739i $$-0.176960\pi$$
$$504$$ 0.258699 0.367661i 0.0115234 0.0163769i
$$505$$ 18.1876i 0.809336i
$$506$$ −9.65685 + 19.1917i −0.429300 + 0.853176i
$$507$$ −15.8988 15.8988i −0.706092 0.706092i
$$508$$ −2.40576 + 1.78530i −0.106738 + 0.0792099i
$$509$$ −24.6052 + 24.6052i −1.09061 + 1.09061i −0.0951425 + 0.995464i $$0.530331\pi$$
−0.995464 + 0.0951425i $$0.969669\pi$$
$$510$$ −7.37109 + 2.43625i −0.326397 + 0.107879i
$$511$$ −0.212818 −0.00941453
$$512$$ 21.8155 + 6.00685i 0.964120 + 0.265468i
$$513$$ 3.05320 0.134802
$$514$$ −20.2561 + 6.69495i −0.893460 + 0.295302i
$$515$$ 14.4305 14.4305i 0.635882 0.635882i
$$516$$ 13.0711 9.69998i 0.575422 0.427018i
$$517$$ 10.7422 + 10.7422i 0.472440 + 0.472440i
$$518$$ 0.855494 1.70018i 0.0375883 0.0747017i
$$519$$ 22.6011i 0.992078i
$$520$$ 17.4321 24.7743i 0.764447 1.08642i
$$521$$ 14.4889i 0.634770i 0.948297 + 0.317385i $$0.102805\pi$$
−0.948297 + 0.317385i $$0.897195\pi$$
$$522$$ 3.75138 + 1.88761i 0.164193 + 0.0826185i
$$523$$ −19.4979 19.4979i −0.852584 0.852584i 0.137867 0.990451i $$-0.455975\pi$$
−0.990451 + 0.137867i $$0.955975\pi$$
$$524$$ 4.31788 29.1665i 0.188628 1.27414i
$$525$$ −0.198640 + 0.198640i −0.00866937 + 0.00866937i
$$526$$ 11.6147 + 35.1412i 0.506424 + 1.53223i
$$527$$ 12.6981 0.553138
$$528$$ −6.22478 + 20.5628i −0.270899 + 0.894882i
$$529$$ 15.0000 0.652174
$$530$$ −4.01400 12.1447i −0.174357 0.527532i
$$531$$ 4.00000 4.00000i 0.173585 0.173585i
$$532$$ 0.960099 + 0.142136i 0.0416256 + 0.00616236i
$$533$$ 10.9670 + 10.9670i 0.475031 + 0.475031i
$$534$$ −18.1903 9.15296i −0.787172 0.396087i
$$535$$ 1.83585i 0.0793706i
$$536$$ 0.526113 + 3.02433i 0.0227246 + 0.130631i
$$537$$ 17.2981i 0.746470i
$$538$$ −7.72841 + 15.3592i −0.333195 + 0.662182i
$$539$$ −26.4896 26.4896i −1.14099 1.14099i
$$540$$ −2.14288 2.88761i −0.0922150 0.124263i
$$541$$ −10.0396 + 10.0396i −0.431638 + 0.431638i −0.889185 0.457547i $$-0.848728\pi$$
0.457547 + 0.889185i $$0.348728\pi$$
$$542$$ −14.3198 + 4.73291i −0.615089 + 0.203296i
$$543$$ 8.14953 0.349730
$$544$$ 0.436252 + 17.2660i 0.0187041 + 0.740275i
$$545$$ −3.67340 −0.157351
$$546$$ −1.27133 + 0.420193i −0.0544079 + 0.0179826i
$$547$$ −7.19884 + 7.19884i −0.307800 + 0.307800i −0.844056 0.536255i $$-0.819838\pi$$
0.536255 + 0.844056i $$0.319838\pi$$
$$548$$ −16.4422 22.1564i −0.702374 0.946474i
$$549$$ −3.66949 3.66949i −0.156610 0.156610i
$$550$$ 6.03441 11.9926i 0.257308 0.511366i
$$551$$ 9.06651i 0.386246i
$$552$$ −7.88163 + 1.37109i −0.335465 + 0.0583574i
$$553$$ 1.54075i 0.0655194i
$$554$$ 4.75534 + 2.39278i 0.202035 + 0.101659i
$$555$$ −10.7649 10.7649i −0.456944 0.456944i
$$556$$ −6.78301 1.00417i −0.287664 0.0425865i
$$557$$ 1.02129 1.02129i 0.0432735 0.0432735i −0.685139 0.728412i $$-0.740259\pi$$
0.728412 + 0.685139i $$0.240259\pi$$
$$558$$ 1.84576 + 5.58451i 0.0781373 + 0.236411i
$$559$$ −48.4802 −2.05049
$$560$$ −0.539416 1.00778i −0.0227945 0.0425867i
$$561$$ −16.3990 −0.692368
$$562$$ −4.63757 14.0314i −0.195624 0.591878i
$$563$$ 6.70751 6.70751i 0.282688 0.282688i −0.551492 0.834180i $$-0.685941\pi$$
0.834180 + 0.551492i $$0.185941\pi$$
$$564$$ −0.828427 + 5.59587i −0.0348831 + 0.235628i
$$565$$ −4.49400 4.49400i −0.189064 0.189064i
$$566$$ 22.3059 + 11.2238i 0.937588 + 0.471774i
$$567$$ 0.158942i 0.00667492i
$$568$$ −0.735321 0.517398i −0.0308534 0.0217096i
$$569$$ 8.98711i 0.376759i 0.982096 + 0.188380i $$0.0603235\pi$$
−0.982096 + 0.188380i $$0.939676\pi$$
$$570$$ 3.48946 6.93484i 0.146157 0.290468i
$$571$$ −9.17157 9.17157i −0.383818 0.383818i 0.488657 0.872476i $$-0.337487\pi$$
−0.872476 + 0.488657i $$0.837487\pi$$
$$572$$ 51.3861 38.1334i 2.14856 1.59444i
$$573$$ −11.4321 + 11.4321i −0.477582 + 0.477582i
$$574$$ 0.555677 0.183659i 0.0231935 0.00766579i
$$575$$ 4.99907 0.208476
$$576$$ −7.53003 + 2.70160i −0.313751 + 0.112567i
$$577$$ 29.5013 1.22815 0.614077 0.789246i $$-0.289528\pi$$
0.614077 + 0.789246i $$0.289528\pi$$
$$578$$ 10.3097 3.40751i 0.428828 0.141734i
$$579$$ −15.6591 + 15.6591i −0.650772 + 0.650772i
$$580$$ 8.57478 6.36330i 0.356048 0.264222i
$$581$$ −0.0184080 0.0184080i −0.000763692 0.000763692i
$$582$$ 0.363303 0.722018i 0.0150594 0.0299286i
$$583$$ 27.0192i 1.11902i
$$584$$ 3.09728 + 2.17936i 0.128166 + 0.0901824i
$$585$$ 10.7101i 0.442806i
$$586$$ −38.8421 19.5445i −1.60455 0.807374i
$$587$$ 1.82425 + 1.82425i 0.0752950 + 0.0752950i 0.743751 0.668456i $$-0.233045\pi$$
−0.668456 + 0.743751i $$0.733045\pi$$
$$588$$ 2.04285 13.7991i 0.0842459 0.569064i
$$589$$ −8.97891 + 8.97891i −0.369970 + 0.369970i
$$590$$ −4.51379 13.6569i −0.185830 0.562244i
$$591$$ −20.2222 −0.831831
$$592$$ −29.8612 + 15.9832i −1.22729 + 0.656905i
$$593$$ −35.4338 −1.45509 −0.727546 0.686058i $$-0.759339\pi$$
−0.727546 + 0.686058i $$0.759339\pi$$
$$594$$ −2.38372 7.21215i −0.0978052 0.295918i
$$595$$ 0.616953 0.616953i 0.0252926 0.0252926i
$$596$$ 8.19286 + 1.21289i 0.335593 + 0.0496821i
$$597$$ 17.6830 + 17.6830i 0.723717 + 0.723717i
$$598$$ 21.2848 + 10.7101i 0.870402 + 0.437967i
$$599$$ 27.1632i 1.10986i 0.831897 + 0.554930i $$0.187255\pi$$
−0.831897 + 0.554930i $$0.812745\pi$$
$$600$$ 4.92510 0.856771i 0.201067 0.0349775i
$$601$$ 5.33897i 0.217781i −0.994054 0.108891i $$-0.965270\pi$$
0.994054 0.108891i $$-0.0347298\pi$$
$$602$$ −0.822265 + 1.63414i −0.0335130 + 0.0666027i
$$603$$ −0.767438 0.767438i −0.0312525 0.0312525i
$$604$$ 27.0128 + 36.4007i 1.09913 + 1.48112i
$$605$$ −22.6914 + 22.6914i −0.922539 + 0.922539i
$$606$$ 13.5832 4.48946i 0.551781 0.182372i
$$607$$ 16.1084 0.653820 0.326910 0.945055i $$-0.393993\pi$$
0.326910 + 0.945055i $$0.393993\pi$$
$$608$$ −12.5174 11.9004i −0.507648 0.482627i
$$609$$ −0.471978 −0.0191255
$$610$$ −12.5284 + 4.14082i −0.507260 + 0.167657i
$$611$$ 11.9137 11.9137i 0.481979 0.481979i
$$612$$ −3.63899 4.90367i −0.147097 0.198219i
$$613$$ 0.436924 + 0.436924i 0.0176472 + 0.0176472i 0.715875 0.698228i $$-0.246028\pi$$
−0.698228 + 0.715875i $$0.746028\pi$$
$$614$$ −13.5385 + 26.9060i −0.546369 + 1.08584i
$$615$$ 4.68119i 0.188764i
$$616$$ −0.413828 2.37887i −0.0166736 0.0958475i
$$617$$ 8.80641i 0.354533i −0.984163 0.177266i $$-0.943275\pi$$
0.984163 0.177266i $$-0.0567254\pi$$
$$618$$ 14.3393 + 7.21523i 0.576812 + 0.290239i
$$619$$ 1.92932 + 1.92932i 0.0775458 + 0.0775458i 0.744816 0.667270i $$-0.232537\pi$$
−0.667270 + 0.744816i $$0.732537\pi$$
$$620$$ 14.7938 + 2.19011i 0.594132 + 0.0879569i
$$621$$ 2.00000 2.00000i 0.0802572 0.0802572i
$$622$$ 0.789456 + 2.38857i 0.0316543 + 0.0957728i
$$623$$ 2.28861 0.0916910
$$624$$ 22.8055 + 6.90367i 0.912949 + 0.276368i
$$625$$ 13.0390 0.521559
$$626$$ 1.19970 + 3.62979i 0.0479495 + 0.145075i
$$627$$ 11.5959 11.5959i 0.463094 0.463094i
$$628$$ −1.15154 + 7.77845i −0.0459515 + 0.310394i
$$629$$ −18.2807 18.2807i −0.728898 0.728898i
$$630$$ 0.361009 + 0.181652i 0.0143829 + 0.00723718i
$$631$$ 38.7864i 1.54406i −0.635586 0.772030i $$-0.719241\pi$$
0.635586 0.772030i $$-0.280759\pi$$
$$632$$ 15.7780 22.4235i 0.627615 0.891961i
$$633$$ 26.0559i 1.03563i
$$634$$ −14.0261 + 27.8751i −0.557049 + 1.10706i
$$635$$ −1.90434 1.90434i −0.0755715 0.0755715i
$$636$$ 8.07934 5.99564i 0.320367 0.237743i
$$637$$ −29.3786 + 29.3786i −1.16402 + 1.16402i
$$638$$ 21.4165 7.07847i 0.847888 0.280239i
$$639$$ 0.317883 0.0125753
$$640$$ −2.46971 + 20.1908i −0.0976240 + 0.798111i
$$641$$ 33.1091 1.30773 0.653865 0.756611i $$-0.273146\pi$$
0.653865 + 0.756611i $$0.273146\pi$$
$$642$$ 1.37109 0.453164i 0.0541125 0.0178850i
$$643$$ −19.2897 + 19.2897i −0.760711 + 0.760711i −0.976451 0.215740i $$-0.930784\pi$$
0.215740 + 0.976451i $$0.430784\pi$$
$$644$$ 0.722018 0.535806i 0.0284515 0.0211137i
$$645$$ 10.3468 + 10.3468i 0.407403 + 0.407403i
$$646$$ 5.92571 11.7766i 0.233144 0.463343i
$$647$$ 41.8477i 1.64520i 0.568620 + 0.822601i $$0.307478\pi$$
−0.568620 + 0.822601i $$0.692522\pi$$
$$648$$ 1.62764 2.31318i 0.0639396 0.0908703i
$$649$$ 30.3835i 1.19266i
$$650$$ −13.3005 6.69254i −0.521690 0.262503i
$$651$$ −0.467418 0.467418i −0.0183196 0.0183196i
$$652$$ −2.25205 + 15.2121i −0.0881970 + 0.595754i
$$653$$ 14.7741 14.7741i 0.578155 0.578155i −0.356240 0.934395i $$-0.615941\pi$$
0.934395 + 0.356240i $$0.115941\pi$$
$$654$$ −0.906751 2.74345i −0.0354568 0.107277i
$$655$$ 26.5054 1.03565
$$656$$ −9.96788 3.01748i −0.389180 0.117813i
$$657$$ −1.33897 −0.0522382
$$658$$ −0.199515 0.603650i −0.00777790 0.0235327i
$$659$$ −2.22839 + 2.22839i −0.0868056 + 0.0868056i −0.749176 0.662371i $$-0.769550\pi$$
0.662371 + 0.749176i $$0.269550\pi$$
$$660$$ −19.1055 2.82843i −0.743680 0.110096i
$$661$$ −18.0685 18.0685i −0.702784 0.702784i 0.262223 0.965007i $$-0.415544\pi$$
−0.965007 + 0.262223i $$0.915544\pi$$
$$662$$ −27.5944 13.8849i −1.07249 0.539651i
$$663$$ 18.1876i 0.706346i
$$664$$ 0.0793969 + 0.456409i 0.00308120 + 0.0177121i
$$665$$ 0.872503i 0.0338342i
$$666$$ 5.38244 10.6969i 0.208565 0.414496i
$$667$$ 5.93901 + 5.93901i 0.229959 + 0.229959i
$$668$$ −4.71330 6.35134i −0.182363 0.245741i
$$669$$ 12.9729 12.9729i 0.501563 0.501563i
$$670$$ −2.62020 + 0.866013i −0.101227 + 0.0334570i
$$671$$ −27.8729 −1.07602
$$672$$ 0.619505 0.651622i 0.0238979 0.0251369i
$$673$$ 20.7981 0.801706 0.400853 0.916142i $$-0.368714\pi$$
0.400853 + 0.916142i $$0.368714\pi$$
$$674$$ 25.3433 8.37632i 0.976186 0.322644i
$$675$$ −1.24977 + 1.24977i −0.0481036 + 0.0481036i
$$676$$ −26.7982 36.1115i −1.03070 1.38890i
$$677$$ 29.0213 + 29.0213i 1.11538 + 1.11538i 0.992411 + 0.122968i $$0.0392413\pi$$
0.122968 + 0.992411i $$0.460759\pi$$
$$678$$ 2.24700 4.46561i 0.0862954 0.171501i
$$679$$ 0.0908404i 0.00348613i
$$680$$ −15.2968 + 2.66103i −0.586605 + 0.102046i
$$681$$ 0.163788i 0.00627639i
$$682$$ 28.2197 + 14.1995i 1.08059 + 0.543728i
$$683$$ −18.7938 18.7938i −0.719123 0.719123i 0.249303 0.968426i $$-0.419799\pi$$
−0.968426 + 0.249303i $$0.919799\pi$$
$$684$$ 6.04057 + 0.894263i 0.230967 + 0.0341930i
$$685$$ 17.5385 17.5385i 0.670111 0.670111i
$$686$$ 0.985767 + 2.98252i 0.0376368 + 0.113873i
$$687$$ 4.02756 0.153661
$$688$$ 28.7013 15.3624i 1.09423 0.585685i
$$689$$ −29.9660 −1.14161
$$690$$ −2.25689 6.82843i −0.0859185 0.259954i
$$691$$ 10.4580 10.4580i 0.397841 0.397841i −0.479630 0.877471i $$-0.659229\pi$$
0.877471 + 0.479630i $$0.159229\pi$$
$$692$$ −6.61971 + 44.7149i −0.251644 + 1.69980i
$$693$$ 0.603650 + 0.603650i 0.0229308 + 0.0229308i
$$694$$ −35.4344 17.8298i −1.34507 0.676810i
$$695$$ 6.16415i 0.233820i
$$696$$ 6.86900 + 4.83327i 0.260369 + 0.183205i
$$697$$ 7.94948i 0.301108i
$$698$$ −10.7622 + 21.3885i −0.407357 + 0.809569i
$$699$$ 8.28806 + 8.28806i 0.313483 + 0.313483i
$$700$$ −0.451177 + 0.334817i −0.0170529 + 0.0126549i
$$701$$ 18.3314 18.3314i 0.692367 0.692367i −0.270385 0.962752i $$-0.587151\pi$$
0.962752 + 0.270385i $$0.0871511\pi$$
$$702$$ −7.99872 + 2.64369i −0.301892 + 0.0997798i
$$703$$ 25.8528 0.975055
$$704$$ −18.3380 + 38.8590i −0.691141 + 1.46456i
$$705$$ −5.08532 −0.191524
$$706$$ 16.9460 5.60091i 0.637773 0.210793i
$$707$$ −1.13690 + 1.13690i −0.0427577 + 0.0427577i
$$708$$ 9.08532 6.74218i 0.341447 0.253386i
$$709$$ 14.5722 + 14.5722i 0.547271 + 0.547271i 0.925650 0.378380i $$-0.123519\pi$$
−0.378380 + 0.925650i $$0.623519\pi$$
$$710$$ 0.363303 0.722018i 0.0136345 0.0270969i
$$711$$ 9.69382i 0.363547i
$$712$$ −33.3075 23.4364i −1.24825 0.878315i
$$713$$ 11.7633i 0.440538i
$$714$$ 0.613057 + 0.308476i 0.0229431 + 0.0115444i
$$715$$ 40.6761 + 40.6761i 1.52120 + 1.52120i
$$716$$ −5.06651 + 34.2233i −0.189344 + 1.27898i
$$717$$ −9.65324 + 9.65324i −0.360507 + 0.360507i
$$718$$ 12.0212 + 36.3712i 0.448628 + 1.35736i
$$719$$ 44.0949 1.64446 0.822230 0.569155i $$-0.192730\pi$$
0.822230 + 0.569155i $$0.192730\pi$$
$$720$$ −3.39380 6.34059i −0.126479 0.236300i
$$721$$ −1.80409 −0.0671880
$$722$$ −4.29513 12.9953i −0.159848 0.483634i
$$723$$ 1.50732 1.50732i 0.0560578 0.0560578i
$$724$$ 16.1233 + 2.38694i 0.599219 + 0.0887101i
$$725$$ −3.71119 3.71119i −0.137830 0.137830i
$$726$$ −22.5481 11.3457i −0.836840 0.421079i
$$727$$ 9.23457i 0.342491i 0.985228 + 0.171246i $$0.0547792\pi$$
−0.985228 + 0.171246i $$0.945221\pi$$
$$728$$ −2.63832 + 0.458962i −0.0977826 + 0.0170103i
$$729$$ 1.00000i 0.0370370i
$$730$$ −1.53029 + 3.04125i −0.0566385 + 0.112562i
$$731$$ 17.5706 + 17.5706i 0.649872 + 0.649872i
$$732$$ −6.18508 8.33461i −0.228607 0.308056i
$$733$$ 18.2764 18.2764i 0.675053 0.675053i −0.283823 0.958877i $$-0.591603\pi$$
0.958877 + 0.283823i $$0.0916029\pi$$
$$734$$ 27.5184 9.09524i 1.01572 0.335711i
$$735$$ 12.5401 0.462549
$$736$$ −15.9949 + 0.404135i −0.589580 + 0.0148966i
$$737$$ −5.82936 −0.214727
$$738$$ 3.49611 1.15551i 0.128694 0.0425351i
$$739$$ 16.9991 16.9991i 0.625321 0.625321i −0.321566 0.946887i $$-0.604209\pi$$
0.946887 + 0.321566i $$0.104209\pi$$
$$740$$ −18.1447 24.4506i −0.667012 0.898822i
$$741$$ −12.8605 12.8605i −0.472444 0.472444i
$$742$$ −0.508249 + 1.01008i −0.0186584 + 0.0370812i
$$743$$ 17.8748i 0.655762i −0.944719 0.327881i $$-0.893665\pi$$
0.944719 0.327881i $$-0.106335\pi$$
$$744$$ 2.01606 + 11.5892i 0.0739123 + 0.424881i
$$745$$ 7.44538i 0.272778i
$$746$$ −1.84682 0.929278i −0.0676168 0.0340233i
$$747$$ −0.115816 0.115816i −0.00423748 0.00423748i
$$748$$ −32.4445 4.80316i −1.18629 0.175621i
$$749$$ −0.114759 + 0.114759i −0.00419319 + 0.00419319i
$$750$$ 5.39996 + 16.3380i 0.197179 + 0.596581i
$$751$$ −35.0731 −1.27984 −0.639918 0.768443i $$-0.721032\pi$$
−0.639918 + 0.768443i $$0.721032\pi$$
$$752$$ −3.27798 + 10.8284i −0.119536 + 0.394872i
$$753$$ −6.27020 −0.228499
$$754$$ −7.85047 23.7523i −0.285897 0.865006i
$$755$$ −28.8139 + 28.8139i −1.04865 + 1.04865i
$$756$$ −0.0465529 + 0.314456i −0.00169311 + 0.0114367i
$$757$$ −32.8071 32.8071i −1.19239 1.19239i −0.976393 0.216000i $$-0.930699\pi$$
−0.216000 0.976393i $$-0.569301\pi$$
$$758$$ −31.5662 15.8834i −1.14654 0.576912i
$$759$$ 15.1917i 0.551425i
$$760$$ 8.93484 12.6981i 0.324101 0.460608i
$$761$$ 10.5531i 0.382550i −0.981536 0.191275i $$-0.938738\pi$$
0.981536 0.191275i $$-0.0612623\pi$$
$$762$$ 0.952171 1.89231i 0.0344935 0.0685513i
$$763$$ 0.229624 + 0.229624i 0.00831296 + 0.00831296i
$$764$$ −25.9660 + 19.2693i −0.939418 + 0.697138i
$$765$$ 3.88163 3.88163i 0.140341 0.140341i
$$766$$ 41.7545 13.8005i 1.50865 0.498632i
$$767$$ −33.6972 −1.21673
$$768$$ −15.6890 + 3.13946i −0.566127 + 0.113285i
$$769$$ −35.2068 −1.26959