LMFDB - Embedded newform 48.2.j.a.37.1

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 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^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

Display 100 coefficients 10 coefficients

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \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
$2$	−1.34277	+	0.443806i	−0.949483	+	0.313818i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	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	$-0.118305\pi$
$5$	1.27133	+	1.27133i	0.568556	+	0.568556i	−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	$-0.990437\pi$
$7$		−	0.158942i		−	0.0600743i	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	$-0.949618\pi$
$11$	−3.79793	−	3.79793i	−1.14512	−	1.14512i	−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	$0.559428\pi$
$13$	−4.21215	+	4.21215i	−1.16824	+	1.16824i	−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	$-0.379270\pi$
$17$	3.05320			0.740511			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	$-0.863895\pi$
$19$	−2.15894	+	2.15894i	−0.495295	+	0.495295i	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	$0.0952810\pi$
$23$			2.82843i			0.589768i	−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	$-0.661087\pi$
$29$	2.09976	−	2.09976i	0.389915	−	0.389915i	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	$-0.378163\pi$
$31$	4.15894			0.746968			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	$-0.495046\pi$
$37$	−5.98737	−	5.98737i	−0.984317	−	0.984317i	−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	$-0.934830\pi$
$41$		−	2.60365i		−	0.406622i	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	$-0.0369066\pi$
$43$	5.75481	+	5.75481i	0.877600	+	0.877600i	−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	$-0.566137\pi$
$47$	−2.82843			−0.412568			−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	$-0.137711\pi$
$53$	3.55710	+	3.55710i	0.488605	+	0.488605i	−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	$-0.129964\pi$
$59$	4.00000	+	4.00000i	0.520756	+	0.520756i	−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	$-0.642202\pi$
$61$	3.66949	−	3.66949i	0.469829	−	0.469829i	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	$-0.728882\pi$
$67$	0.767438	−	0.767438i	0.0937575	−	0.0937575i	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	$0.00600460\pi$
$71$			0.317883i			0.0377258i	−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	$-0.975032\pi$
$73$		−	1.33897i		−	0.156715i	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	$-0.683592\pi$
$79$	−9.69382			−1.09064			−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	$-0.747139\pi$
$83$	0.115816	−	0.115816i	0.0127125	−	0.0127125i	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	$0.276347\pi$
$89$			14.3990i			1.52629i	−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	$-0.509237\pi$
$97$	−0.571533			−0.0580304			−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	$-0.417874\pi$
$101$	−7.15296	−	7.15296i	−0.711746	−	0.711746i	−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	$-0.811106\pi$
$103$		−	11.3507i		−	1.11841i	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	$-0.265717\pi$
$107$	−0.722018	−	0.722018i	−0.0698001	−	0.0698001i	−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	$-0.781196\pi$
$109$	−1.44471	+	1.44471i	−0.138378	+	0.138378i	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	$-0.553171\pi$
$113$	−3.53488			−0.332533			−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	$-0.521170\pi$
$127$	−1.49791			−0.132918			−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	$-0.527267\pi$
$131$	10.4243	−	10.4243i	0.910775	−	0.910775i	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	$-0.799400\pi$
$137$		−	13.7954i		−	1.17862i	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	$-0.296447\pi$
$139$	−2.42429	−	2.42429i	−0.205626	−	0.205626i	−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	$-0.195744\pi$
$149$	2.92818	+	2.92818i	0.239886	+	0.239886i	−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	$0.373611\pi$
$151$			22.6644i			1.84440i	−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	$-0.800146\pi$
$157$	−2.78007	+	2.78007i	−0.221874	+	0.221874i	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	$-0.847362\pi$
$163$	−5.43692	+	5.43692i	−0.425853	+	0.425853i	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	$-0.951104\pi$
$167$		−	3.95458i		−	0.306015i	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	$0.579016\pi$
$173$	−15.9814	+	15.9814i	−1.21504	+	1.21504i	−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	$-0.973752\pi$
$179$	−12.2316	+	12.2316i	−0.914235	+	0.914235i	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	$-0.152054\pi$
$181$	5.76259	+	5.76259i	0.428330	+	0.428330i	−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	$-0.698873\pi$
$191$	−16.1674			−1.16983			−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	$-0.793597\pi$
$193$	−22.1454			−1.59406			−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	$-0.993964\pi$
$197$	−14.2993	−	14.2993i	−1.01878	−	1.01878i	−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	$0.346780\pi$
$199$			25.0075i			1.77274i	−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	$-0.395828\pi$
$211$	18.4243	−	18.4243i	1.26838	−	1.26838i	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	$-0.289444\pi$
$223$	18.3465			1.22857			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	$-0.751730\pi$
$227$	−0.115816	+	0.115816i	−0.00768697	+	0.00768697i	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	$-0.207515\pi$
$229$	2.84791	+	2.84791i	0.188195	+	0.188195i	−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	$0.125432\pi$
$233$			11.7211i			0.767874i	−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	$-0.645564\pi$
$239$	−13.6517			−0.883058			−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	$-0.478129\pi$
$241$	2.13167			0.137313			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	$-0.313407\pi$
$251$	−4.43370	−	4.43370i	−0.279853	−	0.279853i	−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	$-0.344074\pi$
$257$	15.0853			0.940997			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	$-0.701157\pi$
$263$		−	26.1706i		−	1.61375i	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	$-0.629137\pi$
$269$	8.59700	−	8.59700i	0.524168	−	0.524168i	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	$-0.395003\pi$
$271$	10.6644			0.647815			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	$-0.286073\pi$
$277$	−2.66170	−	2.66170i	−0.159926	−	0.159926i	−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	$0.100893\pi$
$281$			10.4496i			0.623368i	−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	$-0.425858\pi$
$283$	−12.4853	−	12.4853i	−0.742173	−	0.742173i	−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	$0.105063\pi$
$293$	21.7410	+	21.7410i	1.27013	+	1.27013i	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	$-0.542062\pi$
$307$	15.0601	−	15.0601i	0.859523	−	0.859523i	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	$-0.983939\pi$
$311$		−	1.77883i		−	0.100868i	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	$-0.975658\pi$
$313$		−	2.70320i		−	0.152794i	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	$-0.537272\pi$
$317$	15.6025	−	15.6025i	0.876325	−	0.876325i	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	$-0.0450472\pi$
$331$	15.4454	+	15.4454i	0.848955	+	0.848955i	−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	$-0.671860\pi$
$337$	−18.8738			−1.02812			−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	$0.0213337\pi$
$347$	19.8337	+	19.8337i	1.06473	+	1.06473i	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	$-0.600304\pi$
$349$	11.9718	−	11.9718i	0.640836	−	0.640836i	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	$-0.609024\pi$
$353$	−12.6202			−0.671705			−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	$-0.746522\pi$
$359$		−	27.0867i		−	1.42958i	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	$-0.679644\pi$
$367$	−20.4937			−1.06976			−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	$-0.237950\pi$
$373$	1.03372	+	1.03372i	0.0535239	+	0.0535239i	−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	$-0.0282083\pi$
$379$	17.6686	+	17.6686i	0.907573	+	0.907573i	−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	$-0.792246\pi$
$383$	−31.0958			−1.58892			−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	$-0.279270\pi$
$389$	−2.56127	−	2.56127i	−0.129862	−	0.129862i	−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	$-0.807907\pi$
$397$	−5.09795	+	5.09795i	−0.255859	+	0.255859i	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	$-0.624480\pi$
$401$	−15.2660			−0.762349			−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	$-0.909234\pi$
$409$		−	11.3779i		−	0.562603i	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	$-0.452087\pi$
$419$	23.3075	−	23.3075i	1.13865	−	1.13865i	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	$-0.457653\pi$
$421$	−17.6154	−	17.6154i	−0.858520	−	0.858520i	−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	$-0.420038\pi$
$431$	10.3211			0.497151			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	$-0.619945\pi$
$433$	−15.3137			−0.735930			−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	$-0.818920\pi$
$439$		−	22.5735i		−	1.07738i	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	$0.0433752\pi$
$443$	23.7117	+	23.7117i	1.12658	+	1.12658i	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	$-0.513186\pi$
$449$	−1.75506			−0.0828266			−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	$0.215094\pi$
$457$			26.7422i			1.25095i	−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	$-0.651585\pi$
$461$	9.23921	−	9.23921i	0.430313	−	0.430313i	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	$-0.260122\pi$
$463$	29.4474			1.36854			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	$-0.971478\pi$
$467$	−19.5897	+	19.5897i	−0.906503	+	0.906503i	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	$-0.198292\pi$
$479$	35.5499			1.62432			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	$0.0717623\pi$
$487$			9.86632i			0.447086i	−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	$-0.254567\pi$
$491$	−0.449555	−	0.449555i	−0.0202881	−	0.0202881i	−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	$-0.722697\pi$
$499$	2.70645	−	2.70645i	0.121157	−	0.121157i	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	$-0.823040\pi$
$503$		−	23.6719i		−	1.05548i	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	$0.530331\pi$
$509$	−24.6052	+	24.6052i	−1.09061	+	1.09061i	−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	$0.102805\pi$
$521$			14.4889i			0.634770i	−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	$-0.455975\pi$
$523$	−19.4979	−	19.4979i	−0.852584	−	0.852584i	−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	$-0.848728\pi$
$541$	−10.0396	+	10.0396i	−0.431638	+	0.431638i	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	$-0.819838\pi$
$547$	−7.19884	+	7.19884i	−0.307800	+	0.307800i	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	$-0.740259\pi$
$557$	1.02129	−	1.02129i	0.0432735	−	0.0432735i	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	$-0.685941\pi$
$563$	6.70751	−	6.70751i	0.282688	−	0.282688i	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	$0.0603235\pi$
$569$			8.98711i			0.376759i	−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	$-0.337487\pi$
$571$	−9.17157	−	9.17157i	−0.383818	−	0.383818i	−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	$-0.289528\pi$
$577$	29.5013			1.22815			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	$-0.233045\pi$
$587$	1.82425	+	1.82425i	0.0752950	+	0.0752950i	−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	$-0.759339\pi$
$593$	−35.4338			−1.45509			−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	$0.187255\pi$
$599$			27.1632i			1.10986i	−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	$-0.965270\pi$
$601$		−	5.33897i		−	0.217781i	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	$-0.393993\pi$
$607$	16.1084			0.653820			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	$-0.246028\pi$
$613$	0.436924	+	0.436924i	0.0176472	+	0.0176472i	−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	$-0.943275\pi$
$617$		−	8.80641i		−	0.354533i	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	$-0.232537\pi$
$619$	1.92932	+	1.92932i	0.0775458	+	0.0775458i	−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	$-0.719241\pi$
$631$		−	38.7864i		−	1.54406i	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	$-0.273146\pi$
$641$	33.1091			1.30773			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	$-0.930784\pi$
$643$	−19.2897	+	19.2897i	−0.760711	+	0.760711i	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	$0.307478\pi$
$647$			41.8477i			1.64520i	−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	$-0.615941\pi$
$653$	14.7741	−	14.7741i	0.578155	−	0.578155i	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	$-0.769550\pi$
$659$	−2.22839	+	2.22839i	−0.0868056	+	0.0868056i	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	$-0.415544\pi$
$661$	−18.0685	−	18.0685i	−0.702784	−	0.702784i	−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	$-0.368714\pi$
$673$	20.7981			0.801706			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	$0.0392413\pi$
$677$	29.0213	+	29.0213i	1.11538	+	1.11538i	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	$-0.419799\pi$
$683$	−18.7938	−	18.7938i	−0.719123	−	0.719123i	−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	$-0.659229\pi$
$691$	10.4580	−	10.4580i	0.397841	−	0.397841i	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	$-0.587151\pi$
$701$	18.3314	−	18.3314i	0.692367	−	0.692367i	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	$-0.123519\pi$
$709$	14.5722	+	14.5722i	0.547271	+	0.547271i	−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	$-0.192730\pi$
$719$	44.0949			1.64446			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	$0.0547792\pi$
$727$			9.23457i			0.342491i	−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	$-0.591603\pi$
$733$	18.2764	−	18.2764i	0.675053	−	0.675053i	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	$-0.604209\pi$
$739$	16.9991	−	16.9991i	0.625321	−	0.625321i	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	$-0.893665\pi$
$743$		−	17.8748i		−	0.655762i	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	$-0.721032\pi$
$751$	−35.0731			−1.27984			−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	$-0.930699\pi$
$757$	−32.8071	−	32.8071i	−1.19239	−	1.19239i	−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	$-0.938738\pi$
$761$		−	10.5531i		−	0.382550i	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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34277 + 0.443806i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.60607 - 1.19186i) q^{4} +(1.27133 + 1.27133i) q^{5} +(-0.635665 + 1.26330i) q^{6} -0.158942i q^{7} +(-1.62764 + 2.31318i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(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

Introduction

L-functions

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