LMFDB - Embedded newform 144.2.k.b.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("144.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14984578911$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.4
Root			$0.500000 + 2.10607i$ of defining polynomial
Character	$\chi$	$=$	144.109
Dual form			144.2.k.b.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34277 + 0.443806i) q^{2} +(1.60607 + 1.19186i) q^{4} +(-1.27133 + 1.27133i) q^{5} +0.158942i q^{7} +(1.62764 + 2.31318i) q^{8} +O(q^{10})$	\(q+(1.34277 + 0.443806i) q^{2} +(1.60607 + 1.19186i) q^{4} +(-1.27133 + 1.27133i) q^{5} +0.158942i q^{7} +(1.62764 + 2.31318i) q^{8} +(-2.27133 + 1.14288i) q^{10} +(3.79793 - 3.79793i) q^{11} +(-4.21215 - 4.21215i) q^{13} +(-0.0705392 + 0.213422i) q^{14} +(1.15894 + 3.82843i) q^{16} -3.05320 q^{17} +(-2.15894 - 2.15894i) q^{19} +(-3.55710 + 0.526602i) q^{20} +(6.78530 - 3.41421i) q^{22} +2.82843i q^{23} +1.76744i q^{25} +(-3.78658 - 7.52533i) q^{26} +(-0.189436 + 0.255272i) q^{28} +(-2.09976 - 2.09976i) q^{29} +4.15894 q^{31} +(-0.142883 + 5.65505i) q^{32} +(-4.09976 - 1.35503i) q^{34} +(-0.202067 - 0.202067i) q^{35} +(-5.98737 + 5.98737i) q^{37} +(-1.94082 - 3.85712i) q^{38} +(-5.01008 - 0.871553i) q^{40} -2.60365i q^{41} +(5.75481 - 5.75481i) q^{43} +(10.6264 - 1.57316i) q^{44} +(-1.25527 + 3.79793i) q^{46} +2.82843 q^{47} +6.97474 q^{49} +(-0.784399 + 2.37327i) q^{50} +(-1.74473 - 11.7853i) q^{52} +(-3.55710 + 3.55710i) q^{53} +9.65685i q^{55} +(-0.367661 + 0.258699i) q^{56} +(-1.88761 - 3.75138i) q^{58} +(-4.00000 + 4.00000i) q^{59} +(3.66949 + 3.66949i) q^{61} +(5.58451 + 1.84576i) q^{62} +(-2.70160 + 7.53003i) q^{64} +10.7101 q^{65} +(0.767438 + 0.767438i) q^{67} +(-4.90367 - 3.63899i) q^{68} +(-0.181652 - 0.361009i) q^{70} +0.317883i q^{71} +1.33897i q^{73} +(-10.6969 + 5.38244i) q^{74} +(-0.894263 - 6.04057i) q^{76} +(0.603650 + 0.603650i) q^{77} -9.69382 q^{79} +(-6.34059 - 3.39380i) q^{80} +(1.15551 - 3.49611i) q^{82} +(-0.115816 - 0.115816i) q^{83} +(3.88163 - 3.88163i) q^{85} +(10.2814 - 5.17338i) q^{86} +(14.9670 + 2.60365i) q^{88} +14.3990i q^{89} +(0.669485 - 0.669485i) q^{91} +(-3.37109 + 4.54266i) q^{92} +(3.79793 + 1.25527i) q^{94} +5.48946 q^{95} -0.571533 q^{97} +(9.36548 + 3.09543i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 12 q^{14} - 8 q^{19} - 16 q^{20} - 20 q^{26} + 8 q^{28} + 16 q^{29} + 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{38} + 16 q^{40} - 8 q^{43} + 40 q^{44} - 8 q^{46} - 8 q^{49} + 36 q^{50} - 16 q^{52} - 16 q^{53} - 16 q^{58} - 32 q^{59} + 16 q^{61} + 12 q^{62} + 8 q^{64} + 16 q^{65} - 16 q^{67} - 32 q^{68} + 32 q^{70} - 52 q^{74} + 8 q^{76} - 16 q^{77} - 24 q^{79} - 8 q^{80} + 40 q^{82} + 40 q^{83} - 16 q^{85} + 16 q^{86} + 32 q^{88} - 8 q^{91} + 16 q^{92} + 8 q^{94} + 48 q^{95} + 40 q^{98}+O(q^{100}) $ 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^10 + 8 * q^11 - 12 * q^14 - 8 * q^19 - 16 * q^20 - 20 * q^26 + 8 * q^28 + 16 * q^29 + 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^38 + 16 * q^40 - 8 * q^43 + 40 * q^44 - 8 * q^46 - 8 * q^49 + 36 * q^50 - 16 * q^52 - 16 * q^53 - 16 * q^58 - 32 * q^59 + 16 * q^61 + 12 * q^62 + 8 * q^64 + 16 * q^65 - 16 * q^67 - 32 * q^68 + 32 * q^70 - 52 * q^74 + 8 * q^76 - 16 * q^77 - 24 * q^79 - 8 * q^80 + 40 * q^82 + 40 * q^83 - 16 * q^85 + 16 * q^86 + 32 * q^88 - 8 * q^91 + 16 * q^92 + 8 * q^94 + 48 * q^95 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (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			0
$3$		0			0
$4$	1.60607	+	1.19186i	0.803037	+	0.595930i
$5$	−1.27133	+	1.27133i	−0.568556	+	0.568556i	−0.931724	−	0.363168i	$-0.881695\pi$
$5$	−1.27133	+	1.27133i	−0.568556	+	0.568556i	0.363168	+	0.931724i	$0.381695\pi$
$6$		0			0
$7$			0.158942i			0.0600743i	0.999549	+	0.0300371i	$0.00956256\pi$
$7$			0.158942i			0.0600743i	−0.999549	+	0.0300371i	$0.990437\pi$
$8$	1.62764	+	2.31318i	0.575456	+	0.817833i
$9$		0			0
$10$	−2.27133	+	1.14288i	−0.718258	+	0.361411i
$11$	3.79793	−	3.79793i	1.14512	−	1.14512i	0.157620	−	0.987500i	$-0.449618\pi$
$11$	3.79793	−	3.79793i	1.14512	−	1.14512i	0.987500	−	0.157620i	$-0.0503821\pi$
$12$		0			0
$13$	−4.21215	−	4.21215i	−1.16824	−	1.16824i	−0.982622	−	0.185617i	$-0.940572\pi$
$13$	−4.21215	−	4.21215i	−1.16824	−	1.16824i	−0.185617	−	0.982622i	$-0.559428\pi$
$14$	−0.0705392	+	0.213422i	−0.0188524	+	0.0570395i
$15$		0			0
$16$	1.15894	+	3.82843i	0.289735	+	0.957107i
$17$	−3.05320			−0.740511			−0.370255	−	0.928930i	$-0.620730\pi$
$17$	−3.05320			−0.740511			−0.370255	+	0.928930i	$0.620730\pi$
$18$		0			0
$19$	−2.15894	−	2.15894i	−0.495295	−	0.495295i	0.414675	−	0.909970i	$-0.363895\pi$
$19$	−2.15894	−	2.15894i	−0.495295	−	0.495295i	−0.909970	+	0.414675i	$0.863895\pi$
$20$	−3.55710	+	0.526602i	−0.795391	+	0.117752i
$21$		0			0
$22$	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			0
$25$			1.76744i			0.353488i
$26$	−3.78658	−	7.52533i	−0.742609	−	1.47584i
$27$		0			0
$28$	−0.189436	+	0.255272i	−0.0358001	+	0.0482419i
$29$	−2.09976	−	2.09976i	−0.389915	−	0.389915i	0.484742	−	0.874657i	$-0.338913\pi$
$29$	−2.09976	−	2.09976i	−0.389915	−	0.389915i	−0.874657	+	0.484742i	$0.838913\pi$
$30$		0			0
$31$	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
$33$		0			0
$34$	−4.09976	−	1.35503i	−0.703103	−	0.232386i
$35$	−0.202067	−	0.202067i	−0.0341556	−	0.0341556i
$36$		0			0
$37$	−5.98737	+	5.98737i	−0.984317	+	0.984317i	−0.999879	−	0.0155615i	$-0.995046\pi$
$37$	−5.98737	+	5.98737i	−0.984317	+	0.984317i	0.0155615	+	0.999879i	$0.495046\pi$
$38$	−1.94082	−	3.85712i	−0.314842	−	0.625707i
$39$		0			0
$40$	−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			0
$43$	5.75481	−	5.75481i	0.877600	−	0.877600i	−0.115686	−	0.993286i	$-0.536907\pi$
$43$	5.75481	−	5.75481i	0.877600	−	0.877600i	0.993286	+	0.115686i	$0.0369066\pi$
$44$	10.6264	−	1.57316i	1.60198	−	0.237162i
$45$		0			0
$46$	−1.25527	+	3.79793i	−0.185080	+	0.559975i
$47$	2.82843			0.412568			0.206284	−	0.978492i	$-0.433863\pi$
$47$	2.82843			0.412568			0.206284	+	0.978492i	$0.433863\pi$
$48$		0			0
$49$	6.97474			0.996391
$50$	−0.784399	+	2.37327i	−0.110931	+	0.335631i
$51$		0			0
$52$	−1.74473	−	11.7853i	−0.241950	−	1.63433i
$53$	−3.55710	+	3.55710i	−0.488605	+	0.488605i	−0.907866	−	0.419261i	$-0.862289\pi$
$53$	−3.55710	+	3.55710i	−0.488605	+	0.488605i	0.419261	+	0.907866i	$0.362289\pi$
$54$		0			0
$55$			9.65685i			1.30213i
$56$	−0.367661	+	0.258699i	−0.0491307	+	0.0345701i
$57$		0			0
$58$	−1.88761	−	3.75138i	−0.247856	−	0.492580i
$59$	−4.00000	+	4.00000i	−0.520756	+	0.520756i	−0.917800	−	0.397044i	$-0.870036\pi$
$59$	−4.00000	+	4.00000i	−0.520756	+	0.520756i	0.397044	+	0.917800i	$0.370036\pi$
$60$		0			0
$61$	3.66949	+	3.66949i	0.469829	+	0.469829i	0.901859	−	0.432030i	$-0.142202\pi$
$61$	3.66949	+	3.66949i	0.469829	+	0.469829i	−0.432030	+	0.901859i	$0.642202\pi$
$62$	5.58451	+	1.84576i	0.709234	+	0.234412i
$63$		0			0
$64$	−2.70160	+	7.53003i	−0.337700	+	0.941254i
$65$	10.7101			1.32842
$66$		0			0
$67$	0.767438	+	0.767438i	0.0937575	+	0.0937575i	0.752430	−	0.658672i	$-0.228882\pi$
$67$	0.767438	+	0.767438i	0.0937575	+	0.0937575i	−0.658672	+	0.752430i	$0.728882\pi$
$68$	−4.90367	−	3.63899i	−0.594657	−	0.441292i
$69$		0			0
$70$	−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	$0.993995\pi$
$72$		0			0
$73$			1.33897i			0.156715i	0.996925	+	0.0783573i	$0.0249675\pi$
$73$			1.33897i			0.156715i	−0.996925	+	0.0783573i	$0.975032\pi$
$74$	−10.6969	+	5.38244i	−1.24349	+	0.625696i
$75$		0			0
$76$	−0.894263	−	6.04057i	−0.102579	−	0.692901i
$77$	0.603650	+	0.603650i	0.0687923	+	0.0687923i
$78$		0			0
$79$	−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
$81$		0			0
$82$	1.15551	−	3.49611i	0.127605	−	0.386081i
$83$	−0.115816	−	0.115816i	−0.0127125	−	0.0127125i	0.700722	−	0.713434i	$-0.252861\pi$
$83$	−0.115816	−	0.115816i	−0.0127125	−	0.0127125i	−0.713434	+	0.700722i	$0.752861\pi$
$84$		0			0
$85$	3.88163	−	3.88163i	0.421022	−	0.421022i
$86$	10.2814	−	5.17338i	1.10867	−	0.557860i
$87$		0			0
$88$	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	$0.723653\pi$
$90$		0			0
$91$	0.669485	−	0.669485i	0.0701811	−	0.0701811i
$92$	−3.37109	+	4.54266i	−0.351460	+	0.473605i
$93$		0			0
$94$	3.79793	+	1.25527i	0.391727	+	0.129471i
$95$	5.48946			0.563206
$96$		0			0
$97$	−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
$99$		0			0
$100$	−2.10654	+	2.83863i	−0.210654	+	0.283863i
$101$	7.15296	−	7.15296i	0.711746	−	0.711746i	−0.255154	−	0.966900i	$-0.582126\pi$
$101$	7.15296	−	7.15296i	0.711746	−	0.711746i	0.966900	+	0.255154i	$0.0821262\pi$
$102$		0			0
$103$			11.3507i			1.11841i	0.829028	+	0.559207i	$0.188894\pi$
$103$			11.3507i			1.11841i	−0.829028	+	0.559207i	$0.811106\pi$
$104$	2.88761	−	16.5993i	0.283154	−	1.62769i
$105$		0			0
$106$	−6.35503	+	3.19771i	−0.617255	+	0.310589i
$107$	0.722018	−	0.722018i	0.0698001	−	0.0698001i	−0.671345	−	0.741145i	$-0.734283\pi$
$107$	0.722018	−	0.722018i	0.0698001	−	0.0698001i	0.741145	+	0.671345i	$0.234283\pi$
$108$		0			0
$109$	−1.44471	−	1.44471i	−0.138378	−	0.138378i	0.634525	−	0.772903i	$-0.281196\pi$
$109$	−1.44471	−	1.44471i	−0.138378	−	0.138378i	−0.772903	+	0.634525i	$0.781196\pi$
$110$	−4.28577	+	12.9670i	−0.408632	+	1.23635i
$111$		0			0
$112$	−0.608497	+	0.184204i	−0.0574975	+	0.0174057i
$113$	3.53488			0.332533			0.166267	−	0.986081i	$-0.446829\pi$
$113$	3.53488			0.332533			0.166267	+	0.986081i	$0.446829\pi$
$114$		0			0
$115$	−3.59587	−	3.59587i	−0.335316	−	0.335316i
$116$	−0.869748	−	5.87498i	−0.0807541	−	0.545478i
$117$		0			0
$118$	−7.14631	+	3.59587i	−0.657871	+	0.331026i
$119$		−	0.485281i		−	0.0444857i
$120$		0			0
$121$		−	17.8486i		−	1.62260i
$122$	3.29874	+	6.55582i	0.298654	+	0.593536i
$123$		0			0
$124$	6.67956	+	4.95687i	0.599843	+	0.445140i
$125$	−8.60365	−	8.60365i	−0.769534	−	0.769534i
$126$		0			0
$127$	−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
$129$		0			0
$130$	14.3812	+	4.75318i	1.26131	+	0.416882i
$131$	−10.4243	−	10.4243i	−0.910775	−	0.910775i	0.0855585	−	0.996333i	$-0.472733\pi$
$131$	−10.4243	−	10.4243i	−0.910775	−	0.910775i	−0.996333	+	0.0855585i	$0.972733\pi$
$132$		0			0
$133$	0.343146	−	0.343146i	0.0297545	−	0.0297545i
$134$	0.689901	+	1.37109i	0.0595984	+	0.118444i
$135$		0			0
$136$	−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	$-0.200600\pi$
$138$		0			0
$139$	−2.42429	+	2.42429i	−0.205626	+	0.205626i	−0.802405	−	0.596779i	$-0.796447\pi$
$139$	−2.42429	+	2.42429i	−0.205626	+	0.205626i	0.596779	+	0.802405i	$0.296447\pi$
$140$	−0.0836990	−	0.565371i	−0.00707386	−	0.0477826i
$141$		0			0
$142$	−0.141078	+	0.426845i	−0.0118390	+	0.0358200i
$143$	−31.9949			−2.67555
$144$		0			0
$145$	5.33897			0.443377
$146$	−0.594243	+	1.79793i	−0.0491799	+	0.148798i
$147$		0			0
$148$	−16.7523	+	2.48005i	−1.37703	+	0.203859i
$149$	−2.92818	+	2.92818i	−0.239886	+	0.239886i	−0.816803	−	0.576917i	$-0.804256\pi$
$149$	−2.92818	+	2.92818i	−0.239886	+	0.239886i	0.576917	+	0.816803i	$0.304256\pi$
$150$		0			0
$151$		−	22.6644i		−	1.84440i	−0.386712	−	0.922201i	$-0.626389\pi$
$151$		−	22.6644i		−	1.84440i	0.386712	−	0.922201i	$-0.373611\pi$
$152$	1.48005	−	8.50799i	0.120048	−	0.690089i
$153$		0			0
$154$	0.542661	+	1.07847i	0.0437288	+	0.0869053i
$155$	−5.28739	+	5.28739i	−0.424693	+	0.424693i
$156$		0			0
$157$	−2.78007	−	2.78007i	−0.221874	−	0.221874i	0.587413	−	0.809287i	$-0.300146\pi$
$157$	−2.78007	−	2.78007i	−0.221874	−	0.221874i	−0.809287	+	0.587413i	$0.800146\pi$
$158$	−13.0166	−	4.30217i	−1.03554	−	0.342262i
$159$		0			0
$160$	−7.00778	−	7.37109i	−0.554014	−	0.582736i
$161$	−0.449555			−0.0354299
$162$		0			0
$163$	−5.43692	−	5.43692i	−0.425853	−	0.425853i	0.461360	−	0.887213i	$-0.347362\pi$
$163$	−5.43692	−	5.43692i	−0.425853	−	0.425853i	−0.887213	+	0.461360i	$0.847362\pi$
$164$	3.10318	−	4.18165i	0.242318	−	0.326532i
$165$		0			0
$166$	−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			0
$169$			22.4844i			1.72957i
$170$	6.93484	−	3.48946i	0.531878	−	0.267629i
$171$		0			0
$172$	16.1016	−	2.38372i	1.22773	−	0.181757i
$173$	15.9814	+	15.9814i	1.21504	+	1.21504i	0.969347	+	0.245695i	$0.0790163\pi$
$173$	15.9814	+	15.9814i	1.21504	+	1.21504i	0.245695	+	0.969347i	$0.420984\pi$
$174$		0			0
$175$	−0.280920			−0.0212355
$176$	18.9417	+	10.1385i	1.42778	+	0.764220i
$177$		0			0
$178$	−6.39037	+	19.3346i	−0.478979	+	1.44919i
$179$	12.2316	+	12.2316i	0.914235	+	0.914235i	0.996602	−	0.0823670i	$-0.0262480\pi$
$179$	12.2316	+	12.2316i	0.914235	+	0.914235i	−0.0823670	+	0.996602i	$0.526248\pi$
$180$		0			0
$181$	5.76259	−	5.76259i	0.428330	−	0.428330i	−0.459729	−	0.888059i	$-0.652054\pi$
$181$	5.76259	−	5.76259i	0.428330	−	0.428330i	0.888059	+	0.459729i	$0.152054\pi$
$182$	1.19609	−	0.601845i	0.0886599	−	0.0446117i
$183$		0			0
$184$	−6.54266	+	4.60365i	−0.482331	+	0.339386i
$185$		−	15.2238i		−	1.11928i
$186$		0			0
$187$	−11.5959	+	11.5959i	−0.847974	+	0.847974i
$188$	4.54266	+	3.37109i	0.331308	+	0.245862i
$189$		0			0
$190$	7.37109	+	2.43625i	0.534755	+	0.176744i
$191$	16.1674			1.16983			0.584916	−	0.811094i	$-0.301127\pi$
$191$	16.1674			1.16983			0.584916	+	0.811094i	$0.301127\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	11.2019	+	8.31291i	0.800138	+	0.593779i
$197$	14.2993	−	14.2993i	1.01878	−	1.01878i	0.0189608	−	0.999820i	$-0.493964\pi$
$197$	14.2993	−	14.2993i	1.01878	−	1.01878i	0.999820	−	0.0189608i	$-0.00603576\pi$
$198$		0			0
$199$		−	25.0075i		−	1.77274i	−0.462981	−	0.886368i	$-0.653220\pi$
$199$		−	25.0075i		−	1.77274i	0.462981	−	0.886368i	$-0.346780\pi$
$200$	−4.08840	+	2.87675i	−0.289094	+	0.203417i
$201$		0			0
$202$	12.7793	−	6.43027i	0.899150	−	0.452432i
$203$	0.333739	−	0.333739i	0.0234239	−	0.0234239i
$204$		0			0
$205$	3.31010	+	3.31010i	0.231187	+	0.231187i
$206$	−5.03749	+	15.2414i	−0.350979	+	1.06192i
$207$		0			0
$208$	11.2443	−	21.0075i	0.779649	−	1.45661i
$209$	−16.3990			−1.13434
$210$		0			0
$211$	18.4243	+	18.4243i	1.26838	+	1.26838i	0.946924	+	0.321456i	$0.104172\pi$
$211$	18.4243	+	18.4243i	1.26838	+	1.26838i	0.321456	+	0.946924i	$0.395828\pi$
$212$	−9.95252	+	1.47340i	−0.683542	+	0.101193i
$213$		0			0
$214$	1.28994	−	0.649070i	0.0881786	−	0.0443695i
$215$			14.6325i			0.997930i
$216$		0			0
$217$			0.661029i			0.0448736i
$218$	−1.29874	−	2.58108i	−0.0879620	−	0.174813i
$219$		0			0
$220$	−11.5096	+	15.5096i	−0.775978	+	1.04566i
$221$	12.8605	+	12.8605i	0.865094	+	0.865094i
$222$		0			0
$223$	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
$225$		0			0
$226$	4.74653	+	1.56880i	0.315735	+	0.104355i
$227$	0.115816	+	0.115816i	0.00768697	+	0.00768697i	0.710940	−	0.703253i	$-0.248270\pi$
$227$	0.115816	+	0.115816i	0.00768697	+	0.00768697i	−0.703253	+	0.710940i	$0.748270\pi$
$228$		0			0
$229$	2.84791	−	2.84791i	0.188195	−	0.188195i	−0.606720	−	0.794916i	$-0.707515\pi$
$229$	2.84791	−	2.84791i	0.188195	−	0.188195i	0.794916	+	0.606720i	$0.207515\pi$
$230$	−3.23256	−	6.42429i	−0.213149	−	0.423605i
$231$		0			0
$232$	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	$0.874568\pi$
$234$		0			0
$235$	−3.59587	+	3.59587i	−0.234568	+	0.234568i
$236$	−11.1917	+	1.65685i	−0.728520	+	0.107852i
$237$		0			0
$238$	0.215371	−	0.651622i	0.0139604	−	0.0422384i
$239$	13.6517			0.883058			0.441529	−	0.897247i	$-0.354436\pi$
$239$	13.6517			0.883058			0.441529	+	0.897247i	$0.354436\pi$
$240$		0			0
$241$	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			0
$244$	1.51995	+	10.2670i	0.0973049	+	0.657276i
$245$	−8.86720	+	8.86720i	−0.566504	+	0.566504i
$246$		0			0
$247$			18.1876i			1.15725i
$248$	6.76924	+	9.62038i	0.429847	+	0.610895i
$249$		0			0
$250$	−7.73439	−	15.3711i	−0.489166	−	0.972153i
$251$	4.43370	−	4.43370i	0.279853	−	0.279853i	−0.553198	−	0.833050i	$-0.686593\pi$
$251$	4.43370	−	4.43370i	0.279853	−	0.279853i	0.833050	+	0.553198i	$0.186593\pi$
$252$		0			0
$253$	10.7422	+	10.7422i	0.675355	+	0.675355i
$254$	−2.01136	−	0.664782i	−0.126204	−	0.0417121i
$255$		0			0
$256$	−13.3137	+	8.87385i	−0.832107	+	0.554615i
$257$	−15.0853			−0.940997			−0.470498	−	0.882401i	$-0.655926\pi$
$257$	−15.0853			−0.940997			−0.470498	+	0.882401i	$0.655926\pi$
$258$		0			0
$259$	−0.951642	−	0.951642i	−0.0591322	−	0.0591322i
$260$	17.2011	+	12.7649i	1.06677	+	0.791645i
$261$		0			0
$262$	−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	$-0.298843\pi$
$264$		0			0
$265$		−	9.04449i		−	0.555599i
$266$	0.613057	−	0.308476i	0.0375889	−	0.0189139i
$267$		0			0
$268$	0.317883	+	2.14724i	0.0194178	+	0.131164i
$269$	−8.59700	−	8.59700i	−0.524168	−	0.524168i	0.394659	−	0.918828i	$-0.370863\pi$
$269$	−8.59700	−	8.59700i	−0.524168	−	0.524168i	−0.918828	+	0.394659i	$0.870863\pi$
$270$		0			0
$271$	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			0
$274$	6.12247	−	18.5240i	0.369872	−	1.11908i
$275$	6.71261	+	6.71261i	0.404786	+	0.404786i
$276$		0			0
$277$	−2.66170	+	2.66170i	−0.159926	+	0.159926i	−0.782534	−	0.622608i	$-0.786073\pi$
$277$	−2.66170	+	2.66170i	−0.159926	+	0.159926i	0.622608	+	0.782534i	$0.286073\pi$
$278$	−4.33119	+	2.17936i	−0.259767	+	0.130709i
$279$		0			0
$280$	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	$0.899107\pi$
$282$		0			0
$283$	−12.4853	+	12.4853i	−0.742173	+	0.742173i	−0.972996	−	0.230823i	$-0.925858\pi$
$283$	−12.4853	+	12.4853i	−0.742173	+	0.742173i	0.230823	+	0.972996i	$0.425858\pi$
$284$	−0.378872	+	0.510544i	−0.0224819	+	0.0302952i
$285$		0			0
$286$	−42.9618	−	14.1995i	−2.54039	−	0.839635i
$287$	0.413828			0.0244275
$288$		0			0
$289$	−7.67794			−0.451644
$290$	7.16902	+	2.36947i	0.420979	+	0.139140i
$291$		0			0
$292$	−1.59587	+	2.15049i	−0.0933910	+	0.125848i
$293$	−21.7410	+	21.7410i	−1.27013	+	1.27013i	−0.324104	+	0.946022i	$0.605063\pi$
$293$	−21.7410	+	21.7410i	−1.27013	+	1.27013i	−0.946022	+	0.324104i	$0.894937\pi$
$294$		0			0
$295$		−	10.1706i		−	0.592158i
$296$	−23.5951	−	4.10460i	−1.37144	−	0.238575i
$297$		0			0
$298$	−5.23143	+	2.63234i	−0.303049	+	0.152487i
$299$	11.9137	−	11.9137i	0.688990	−	0.688990i
$300$		0			0
$301$	0.914679	+	0.914679i	0.0527212	+	0.0527212i
$302$	10.0586	−	30.4331i	0.578806	−	1.75123i
$303$		0			0
$304$	5.76326	−	10.7674i	0.330546	−	0.617555i
$305$	−9.33026			−0.534249
$306$		0			0
$307$	15.0601	+	15.0601i	0.859523	+	0.859523i	0.991282	−	0.131759i	$-0.0420624\pi$
$307$	15.0601	+	15.0601i	0.859523	+	0.859523i	−0.131759	+	0.991282i	$0.542062\pi$
$308$	0.250040	+	1.68897i	0.0142473	+	0.0962381i
$309$		0			0
$310$	−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	$-0.0160605\pi$
$312$		0			0
$313$			2.70320i			0.152794i	0.997077	+	0.0763971i	$0.0243417\pi$
$313$			2.70320i			0.152794i	−0.997077	+	0.0763971i	$0.975658\pi$
$314$	−2.49919	−	4.96681i	−0.141037	−	0.280293i
$315$		0			0
$316$	−15.5690	−	11.5537i	−0.875824	−	0.649945i
$317$	−15.6025	−	15.6025i	−0.876325	−	0.876325i	0.116828	−	0.993152i	$-0.462728\pi$
$317$	−15.6025	−	15.6025i	−0.876325	−	0.876325i	−0.993152	+	0.116828i	$0.962728\pi$
$318$		0			0
$319$	−15.9495			−0.892999
$320$	−6.13853	−	13.0078i	−0.343154	−	0.727157i
$321$		0			0
$322$	−0.603650	−	0.199515i	−0.0336401	−	0.0111185i
$323$	6.59169	+	6.59169i	0.366771	+	0.366771i
$324$		0			0
$325$	7.44471	−	7.44471i	0.412958	−	0.412958i
$326$	−4.88761	−	9.71349i	−0.270700	−	0.537980i
$327$		0			0
$328$	6.02271	−	4.23779i	0.332549	−	0.233993i
$329$			0.449555i			0.0247848i
$330$		0			0
$331$	15.4454	−	15.4454i	0.848955	−	0.848955i	−0.141048	−	0.990003i	$-0.545047\pi$
$331$	15.4454	−	15.4454i	0.848955	−	0.848955i	0.990003	+	0.141048i	$0.0450472\pi$
$332$	−0.0479725	−	0.324045i	−0.00263284	−	0.0177843i
$333$		0			0
$334$	1.75506	−	5.31010i	0.0960329	−	0.290556i
$335$	−1.95133			−0.106613
$336$		0			0
$337$	−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
$339$		0			0
$340$	10.8605	−	1.60782i	0.588996	−	0.0871965i
$341$	15.7954	−	15.7954i	0.855368	−	0.855368i
$342$		0			0
$343$			2.22117i			0.119932i
$344$	22.6786	+	3.94517i	1.22275	+	0.212709i
$345$		0			0
$346$	14.3667	+	28.5520i	0.772360	+	1.53496i
$347$	−19.8337	+	19.8337i	−1.06473	+	1.06473i	−0.0669717	+	0.997755i	$0.521334\pi$
$347$	−19.8337	+	19.8337i	−1.06473	+	1.06473i	−0.997755	+	0.0669717i	$0.978666\pi$
$348$		0			0
$349$	11.9718	+	11.9718i	0.640836	+	0.640836i	0.950761	−	0.309925i	$-0.100304\pi$
$349$	11.9718	+	11.9718i	0.640836	+	0.640836i	−0.309925	+	0.950761i	$0.600304\pi$
$350$	−0.377211	−	0.124674i	−0.0201628	−	0.00666409i
$351$		0			0
$352$	20.9348	+	22.0202i	1.11583	+	1.17368i
$353$	12.6202			0.671705			0.335853	−	0.941915i	$-0.390976\pi$
$353$	12.6202			0.671705			0.335853	+	0.941915i	$0.390976\pi$
$354$		0			0
$355$	−0.404135	−	0.404135i	−0.0214492	−	0.0214492i
$356$	−17.1616	+	23.1259i	−0.909564	+	1.22567i
$357$		0			0
$358$	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			0
$361$		−	9.67794i		−	0.509365i
$362$	10.2953	−	5.18038i	0.541110	−	0.272274i
$363$		0			0
$364$	1.87318	−	0.277310i	0.0981811	−	0.0145350i
$365$	−1.70227	−	1.70227i	−0.0891011	−	0.0891011i
$366$		0			0
$367$	−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
$369$		0			0
$370$	6.75643	−	20.4422i	0.351250	−	1.06274i
$371$	−0.565371	−	0.565371i	−0.0293526	−	0.0293526i
$372$		0			0
$373$	1.03372	−	1.03372i	0.0535239	−	0.0535239i	−0.679838	−	0.733362i	$-0.737950\pi$
$373$	1.03372	−	1.03372i	0.0535239	−	0.0535239i	0.733362	+	0.679838i	$0.237950\pi$
$374$	−20.7169	+	10.4243i	−1.07125	+	0.539027i
$375$		0			0
$376$	4.60365	+	6.54266i	0.237415	+	0.337412i
$377$			17.6890i			0.911028i
$378$		0			0
$379$	17.6686	−	17.6686i	0.907573	−	0.907573i	−0.0885032	−	0.996076i	$-0.528208\pi$
$379$	17.6686	−	17.6686i	0.907573	−	0.907573i	0.996076	+	0.0885032i	$0.0282083\pi$
$380$	8.81647	+	6.54266i	0.452275	+	0.335631i
$381$		0			0
$382$	21.7091	+	7.17518i	1.11074	+	0.367114i
$383$	31.0958			1.58892			0.794460	−	0.607316i	$-0.207754\pi$
$383$	31.0958			1.58892			0.794460	+	0.607316i	$0.207754\pi$
$384$		0			0
$385$	−1.53488			−0.0782245
$386$	−29.7362	−	9.82824i	−1.51353	−	0.500244i
$387$		0			0
$388$	−0.917923	−	0.681187i	−0.0466005	−	0.0345820i
$389$	2.56127	−	2.56127i	0.129862	−	0.129862i	−0.639188	−	0.769050i	$-0.720730\pi$
$389$	2.56127	−	2.56127i	0.129862	−	0.129862i	0.769050	+	0.639188i	$0.220730\pi$
$390$		0			0
$391$		−	8.63577i		−	0.436729i
$392$	11.3523	+	16.1338i	0.573379	+	0.814881i
$393$		0			0
$394$	25.5468	−	12.8546i	1.28703	−	0.647604i
$395$	12.3240	−	12.3240i	0.620090	−	0.620090i
$396$		0			0
$397$	−5.09795	−	5.09795i	−0.255859	−	0.255859i	0.567509	−	0.823367i	$-0.307907\pi$
$397$	−5.09795	−	5.09795i	−0.255859	−	0.255859i	−0.823367	+	0.567509i	$0.807907\pi$
$398$	11.0985	−	33.5794i	0.556317	−	1.68318i
$399$		0			0
$400$	−6.76651	+	2.04836i	−0.338325	+	0.102418i
$401$	15.2660			0.762349			0.381174	−	0.924503i	$-0.375520\pi$
$401$	15.2660			0.762349			0.381174	+	0.924503i	$0.375520\pi$
$402$		0			0
$403$	−17.5181	−	17.5181i	−0.872637	−	0.872637i
$404$	20.0135	−	2.96285i	0.995709	−	0.147407i
$405$		0			0
$406$	0.596250	−	0.300020i	0.0295914	−	0.0148897i
$407$			45.4792i			2.25432i
$408$		0			0
$409$			11.3779i			0.562603i	0.959619	+	0.281302i	$0.0907661\pi$
$409$			11.3779i			0.562603i	−0.959619	+	0.281302i	$0.909234\pi$
$410$	2.97567	+	5.91375i	0.146958	+	0.292059i
$411$		0			0
$412$	−13.5284	+	18.2300i	−0.666497	+	0.898128i
$413$	−0.635767	−	0.635767i	−0.0312840	−	0.0312840i
$414$		0			0
$415$	0.294481			0.0144555
$416$	24.4217	−	23.2181i	1.19737	−	1.13836i
$417$		0			0
$418$	−22.0202	−	7.27798i	−1.07704	−	0.355978i
$419$	−23.3075	−	23.3075i	−1.13865	−	1.13865i	−0.988693	−	0.149955i	$-0.952087\pi$
$419$	−23.3075	−	23.3075i	−1.13865	−	1.13865i	−0.149955	−	0.988693i	$-0.547913\pi$
$420$		0			0
$421$	−17.6154	+	17.6154i	−0.858520	+	0.858520i	−0.991164	−	0.132644i	$-0.957653\pi$
$421$	−17.6154	+	17.6154i	−0.858520	+	0.858520i	0.132644	+	0.991164i	$0.457653\pi$
$422$	16.5628	+	32.9164i	0.806265	+	1.60235i
$423$		0			0
$424$	−14.0179	−	2.43855i	−0.680768	−	0.118426i
$425$		−	5.39635i		−	0.261761i
$426$		0			0
$427$	−0.583234	+	0.583234i	−0.0282247	+	0.0282247i
$428$	2.02016	−	0.299070i	0.0976480	−	0.0144561i
$429$		0			0
$430$	−6.49400	+	19.6481i	−0.313168	+	0.947517i
$431$	−10.3211			−0.497151			−0.248576	−	0.968612i	$-0.579962\pi$
$431$	−10.3211			−0.497151			−0.248576	+	0.968612i	$0.579962\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	−0.598418	−	4.04220i	−0.0286590	−	0.193586i
$437$	6.10641	−	6.10641i	0.292109	−	0.292109i
$438$		0			0
$439$			22.5735i			1.07738i	0.842505	+	0.538688i	$0.181080\pi$
$439$			22.5735i			1.07738i	−0.842505	+	0.538688i	$0.818920\pi$
$440$	−22.3380	+	15.7178i	−1.06492	+	0.749319i
$441$		0			0
$442$	11.5612	+	22.9764i	0.549910	+	1.09287i
$443$	−23.7117	+	23.7117i	−1.12658	+	1.12658i	−0.135846	+	0.990730i	$0.543375\pi$
$443$	−23.7117	+	23.7117i	−1.12658	+	1.12658i	−0.990730	+	0.135846i	$0.956625\pi$
$444$		0			0
$445$	−18.3059	−	18.3059i	−0.867784	−	0.867784i
$446$	24.6352	+	8.14228i	1.16651	+	0.385548i
$447$		0			0
$448$	−1.19684	−	0.429397i	−0.0565452	−	0.0202871i
$449$	1.75506			0.0828266			0.0414133	−	0.999142i	$-0.486814\pi$
$449$	1.75506			0.0828266			0.0414133	+	0.999142i	$0.486814\pi$
$450$		0			0
$451$	−9.88849	−	9.88849i	−0.465631	−	0.465631i
$452$	5.67727	+	4.21308i	0.267036	+	0.198166i
$453$		0			0
$454$	0.104115	+	0.206914i	0.00488634	+	0.00971096i
$455$			1.70227i			0.0798039i
$456$		0			0
$457$		−	26.7422i		−	1.25095i	−0.780246	−	0.625473i	$-0.784906\pi$
$457$		−	26.7422i		−	1.25095i	0.780246	−	0.625473i	$-0.215094\pi$
$458$	5.08802	−	2.56018i	0.237747	−	0.119629i
$459$		0			0
$460$	−1.48946	−	10.0610i	−0.0694463	−	0.469096i
$461$	−9.23921	−	9.23921i	−0.430313	−	0.430313i	0.458422	−	0.888735i	$-0.348415\pi$
$461$	−9.23921	−	9.23921i	−0.430313	−	0.430313i	−0.888735	+	0.458422i	$0.848415\pi$
$462$		0			0
$463$	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
$465$		0			0
$466$	−5.20189	+	15.7387i	−0.240973	+	0.729083i
$467$	19.5897	+	19.5897i	0.906503	+	0.906503i	0.995988	−	0.0894848i	$-0.0285221\pi$
$467$	19.5897	+	19.5897i	0.906503	+	0.906503i	−0.0894848	+	0.995988i	$0.528522\pi$
$468$		0			0
$469$	−0.121978	+	0.121978i	−0.00563242	+	0.00563242i
$470$	−6.42429	+	3.23256i	−0.296331	+	0.149107i
$471$		0			0
$472$	−15.7633	−	2.74218i	−0.725563	−	0.126219i
$473$		−	43.7127i		−	2.00991i
$474$		0			0
$475$	3.81580	−	3.81580i	0.175081	−	0.175081i
$476$	0.578387	−	0.779397i	0.0265103	−	0.0357236i
$477$		0			0
$478$	18.3312	+	6.05872i	0.838449	+	0.277120i
$479$	−35.5499			−1.62432			−0.812159	−	0.583436i	$-0.801708\pi$
$479$	−35.5499			−1.62432			−0.812159	+	0.583436i	$0.801708\pi$
$480$		0			0
$481$	50.4393			2.29984
$482$	2.86235	+	0.946048i	0.130376	+	0.0430913i
$483$		0			0
$484$	21.2730	−	28.6661i	0.966955	−	1.30301i
$485$	0.726607	−	0.726607i	0.0329935	−	0.0329935i
$486$		0			0
$487$		−	9.86632i		−	0.447086i	−0.974694	−	0.223543i	$-0.928238\pi$
$487$		−	9.86632i		−	0.447086i	0.974694	−	0.223543i	$-0.0717623\pi$
$488$	−2.51559	+	14.4608i	−0.113876	+	0.654608i
$489$		0			0
$490$	−15.8419	+	7.97131i	−0.715666	+	0.360107i
$491$	0.449555	−	0.449555i	0.0202881	−	0.0202881i	−0.696890	−	0.717178i	$-0.745433\pi$
$491$	0.449555	−	0.449555i	0.0202881	−	0.0202881i	0.717178	+	0.696890i	$0.245433\pi$
$492$		0			0
$493$	6.41099	+	6.41099i	0.288736	+	0.288736i
$494$	−8.07174	+	24.4217i	−0.363165	+	1.09879i
$495$		0			0
$496$	4.81997	+	15.9222i	0.216423	+	0.714928i
$497$	−0.0505249			−0.00226635
$498$		0			0
$499$	2.70645	+	2.70645i	0.121157	+	0.121157i	0.765086	−	0.643928i	$-0.222697\pi$
$499$	2.70645	+	2.70645i	0.121157	+	0.121157i	−0.643928	+	0.765086i	$0.722697\pi$
$500$	−3.56375	−	24.0724i	−0.159376	−	1.07655i
$501$		0			0
$502$	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			0
$505$			18.1876i			0.809336i
$506$	9.65685	+	19.1917i	0.429300	+	0.853176i
$507$		0			0
$508$	−2.40576	−	1.78530i	−0.106738	−	0.0792099i
$509$	24.6052	+	24.6052i	1.09061	+	1.09061i	0.995464	+	0.0951425i	$0.0303307\pi$
$509$	24.6052	+	24.6052i	1.09061	+	1.09061i	0.0951425	+	0.995464i	$0.469669\pi$
$510$		0			0
$511$	−0.212818			−0.00941453
$512$	−21.8155	+	6.00685i	−0.964120	+	0.265468i
$513$		0			0
$514$	−20.2561	−	6.69495i	−0.893460	−	0.295302i
$515$	−14.4305	−	14.4305i	−0.635882	−	0.635882i
$516$		0			0
$517$	10.7422	−	10.7422i	0.472440	−	0.472440i
$518$	−0.855494	−	1.70018i	−0.0375883	−	0.0747017i
$519$		0			0
$520$	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	$0.897195\pi$
$522$		0			0
$523$	−19.4979	+	19.4979i	−0.852584	+	0.852584i	−0.990451	−	0.137867i	$-0.955975\pi$
$523$	−19.4979	+	19.4979i	−0.852584	+	0.852584i	0.137867	+	0.990451i	$0.455975\pi$
$524$	−4.31788	−	29.1665i	−0.188628	−	1.27414i
$525$		0			0
$526$	11.6147	−	35.1412i	0.506424	−	1.53223i
$527$	−12.6981			−0.553138
$528$		0			0
$529$	15.0000			0.652174
$530$	4.01400	−	12.1447i	0.174357	−	0.527532i
$531$		0			0
$532$	0.960099	−	0.142136i	0.0416256	−	0.00616236i
$533$	−10.9670	+	10.9670i	−0.475031	+	0.475031i
$534$		0			0
$535$			1.83585i			0.0793706i
$536$	−0.526113	+	3.02433i	−0.0227246	+	0.130631i
$537$		0			0
$538$	−7.72841	−	15.3592i	−0.333195	−	0.662182i
$539$	26.4896	−	26.4896i	1.14099	−	1.14099i
$540$		0			0
$541$	−10.0396	−	10.0396i	−0.431638	−	0.431638i	0.457547	−	0.889185i	$-0.348728\pi$
$541$	−10.0396	−	10.0396i	−0.431638	−	0.431638i	−0.889185	+	0.457547i	$0.848728\pi$
$542$	14.3198	+	4.73291i	0.615089	+	0.203296i
$543$		0			0
$544$	0.436252	−	17.2660i	0.0187041	−	0.740275i
$545$	3.67340			0.157351
$546$		0			0
$547$	−7.19884	−	7.19884i	−0.307800	−	0.307800i	0.536255	−	0.844056i	$-0.319838\pi$
$547$	−7.19884	−	7.19884i	−0.307800	−	0.307800i	−0.844056	+	0.536255i	$0.819838\pi$
$548$	16.4422	−	22.1564i	0.702374	−	0.946474i
$549$		0			0
$550$	6.03441	+	11.9926i	0.257308	+	0.511366i
$551$			9.06651i			0.386246i
$552$		0			0
$553$		−	1.54075i		−	0.0655194i
$554$	−4.75534	+	2.39278i	−0.202035	+	0.101659i
$555$		0			0
$556$	−6.78301	+	1.00417i	−0.287664	+	0.0425865i
$557$	−1.02129	−	1.02129i	−0.0432735	−	0.0432735i	0.685139	−	0.728412i	$-0.259741\pi$
$557$	−1.02129	−	1.02129i	−0.0432735	−	0.0432735i	−0.728412	+	0.685139i	$0.759741\pi$
$558$		0			0
$559$	−48.4802			−2.05049
$560$	0.539416	−	1.00778i	0.0227945	−	0.0425867i
$561$		0			0
$562$	−4.63757	+	14.0314i	−0.195624	+	0.591878i
$563$	−6.70751	−	6.70751i	−0.282688	−	0.282688i	0.551492	−	0.834180i	$-0.314059\pi$
$563$	−6.70751	−	6.70751i	−0.282688	−	0.282688i	−0.834180	+	0.551492i	$0.814059\pi$
$564$		0			0
$565$	−4.49400	+	4.49400i	−0.189064	+	0.189064i
$566$	−22.3059	+	11.2238i	−0.937588	+	0.471774i
$567$		0			0
$568$	−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	$0.939676\pi$
$570$		0			0
$571$	−9.17157	+	9.17157i	−0.383818	+	0.383818i	−0.872476	−	0.488657i	$-0.837487\pi$
$571$	−9.17157	+	9.17157i	−0.383818	+	0.383818i	0.488657	+	0.872476i	$0.337487\pi$
$572$	−51.3861	−	38.1334i	−2.14856	−	1.59444i
$573$		0			0
$574$	0.555677	+	0.183659i	0.0231935	+	0.00766579i
$575$	−4.99907			−0.208476
$576$		0			0
$577$	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
$579$		0			0
$580$	8.57478	+	6.36330i	0.356048	+	0.264222i
$581$	0.0184080	−	0.0184080i	0.000763692	−	0.000763692i
$582$		0			0
$583$			27.0192i			1.11902i
$584$	−3.09728	+	2.17936i	−0.128166	+	0.0901824i
$585$		0			0
$586$	−38.8421	+	19.5445i	−1.60455	+	0.807374i
$587$	−1.82425	+	1.82425i	−0.0752950	+	0.0752950i	−0.743751	−	0.668456i	$-0.766955\pi$
$587$	−1.82425	+	1.82425i	−0.0752950	+	0.0752950i	0.668456	+	0.743751i	$0.266955\pi$
$588$		0			0
$589$	−8.97891	−	8.97891i	−0.369970	−	0.369970i
$590$	4.51379	−	13.6569i	0.185830	−	0.562244i
$591$		0			0
$592$	−29.8612	−	15.9832i	−1.22729	−	0.656905i
$593$	35.4338			1.45509			0.727546	−	0.686058i	$-0.240661\pi$
$593$	35.4338			1.45509			0.727546	+	0.686058i	$0.240661\pi$
$594$		0			0
$595$	0.616953	+	0.616953i	0.0252926	+	0.0252926i
$596$	−8.19286	+	1.21289i	−0.335593	+	0.0496821i
$597$		0			0
$598$	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	$0.812745\pi$
$600$		0			0
$601$			5.33897i			0.217781i	0.994054	+	0.108891i	$0.0347298\pi$
$601$			5.33897i			0.217781i	−0.994054	+	0.108891i	$0.965270\pi$
$602$	0.822265	+	1.63414i	0.0335130	+	0.0666027i
$603$		0			0
$604$	27.0128	−	36.4007i	1.09913	−	1.48112i
$605$	22.6914	+	22.6914i	0.922539	+	0.922539i
$606$		0			0
$607$	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			0
$610$	−12.5284	−	4.14082i	−0.507260	−	0.167657i
$611$	−11.9137	−	11.9137i	−0.481979	−	0.481979i
$612$		0			0
$613$	0.436924	−	0.436924i	0.0176472	−	0.0176472i	−0.698228	−	0.715875i	$-0.746028\pi$
$613$	0.436924	−	0.436924i	0.0176472	−	0.0176472i	0.715875	+	0.698228i	$0.246028\pi$
$614$	13.5385	+	26.9060i	0.546369	+	1.08584i
$615$		0			0
$616$	−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	$-0.0567254\pi$
$618$		0			0
$619$	1.92932	−	1.92932i	0.0775458	−	0.0775458i	−0.667270	−	0.744816i	$-0.732537\pi$
$619$	1.92932	−	1.92932i	0.0775458	−	0.0775458i	0.744816	+	0.667270i	$0.232537\pi$
$620$	−14.7938	+	2.19011i	−0.594132	+	0.0879569i
$621$		0			0
$622$	0.789456	−	2.38857i	0.0316543	−	0.0957728i
$623$	−2.28861			−0.0916910
$624$		0			0
$625$	13.0390			0.521559
$626$	−1.19970	+	3.62979i	−0.0479495	+	0.145075i
$627$		0			0
$628$	−1.15154	−	7.77845i	−0.0459515	−	0.310394i
$629$	18.2807	−	18.2807i	0.728898	−	0.728898i
$630$		0			0
$631$			38.7864i			1.54406i	0.635586	+	0.772030i	$0.280759\pi$
$631$			38.7864i			1.54406i	−0.635586	+	0.772030i	$0.719241\pi$
$632$	−15.7780	−	22.4235i	−0.627615	−	0.891961i
$633$		0			0
$634$	−14.0261	−	27.8751i	−0.557049	−	1.10706i
$635$	1.90434	−	1.90434i	0.0755715	−	0.0755715i
$636$		0			0
$637$	−29.3786	−	29.3786i	−1.16402	−	1.16402i
$638$	−21.4165	−	7.07847i	−0.847888	−	0.280239i
$639$		0			0
$640$	−2.46971	−	20.1908i	−0.0976240	−	0.798111i
$641$	−33.1091			−1.30773			−0.653865	−	0.756611i	$-0.726854\pi$
$641$	−33.1091			−1.30773			−0.653865	+	0.756611i	$0.726854\pi$
$642$		0			0
$643$	−19.2897	−	19.2897i	−0.760711	−	0.760711i	0.215740	−	0.976451i	$-0.430784\pi$
$643$	−19.2897	−	19.2897i	−0.760711	−	0.760711i	−0.976451	+	0.215740i	$0.930784\pi$
$644$	−0.722018	−	0.535806i	−0.0284515	−	0.0211137i
$645$		0			0
$646$	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	$0.692522\pi$
$648$		0			0
$649$			30.3835i			1.19266i
$650$	13.3005	−	6.69254i	0.521690	−	0.262503i
$651$		0			0
$652$	−2.25205	−	15.2121i	−0.0881970	−	0.595754i
$653$	−14.7741	−	14.7741i	−0.578155	−	0.578155i	0.356240	−	0.934395i	$-0.384059\pi$
$653$	−14.7741	−	14.7741i	−0.578155	−	0.578155i	−0.934395	+	0.356240i	$0.884059\pi$
$654$		0			0
$655$	26.5054			1.03565
$656$	9.96788	−	3.01748i	0.389180	−	0.117813i
$657$		0			0
$658$	−0.199515	+	0.603650i	−0.00777790	+	0.0235327i
$659$	2.22839	+	2.22839i	0.0868056	+	0.0868056i	0.749176	−	0.662371i	$-0.230450\pi$
$659$	2.22839	+	2.22839i	0.0868056	+	0.0868056i	−0.662371	+	0.749176i	$0.730450\pi$
$660$		0			0
$661$	−18.0685	+	18.0685i	−0.702784	+	0.702784i	−0.965007	−	0.262223i	$-0.915544\pi$
$661$	−18.0685	+	18.0685i	−0.702784	+	0.702784i	0.262223	+	0.965007i	$0.415544\pi$
$662$	27.5944	−	13.8849i	1.07249	−	0.539651i
$663$		0			0
$664$	0.0793969	−	0.456409i	0.00308120	−	0.0177121i
$665$			0.872503i			0.0338342i
$666$		0			0
$667$	5.93901	−	5.93901i	0.229959	−	0.229959i
$668$	4.71330	−	6.35134i	0.182363	−	0.245741i
$669$		0			0
$670$	−2.62020	−	0.866013i	−0.101227	−	0.0334570i
$671$	27.8729			1.07602
$672$		0			0
$673$	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
$675$		0			0
$676$	−26.7982	+	36.1115i	−1.03070	+	1.38890i
$677$	−29.0213	+	29.0213i	−1.11538	+	1.11538i	−0.122968	+	0.992411i	$0.539241\pi$
$677$	−29.0213	+	29.0213i	−1.11538	+	1.11538i	−0.992411	+	0.122968i	$0.960759\pi$
$678$		0			0
$679$		−	0.0908404i		−	0.00348613i
$680$	15.2968	+	2.66103i	0.586605	+	0.102046i
$681$		0			0
$682$	28.2197	−	14.1995i	1.08059	−	0.543728i
$683$	18.7938	−	18.7938i	0.719123	−	0.719123i	−0.249303	−	0.968426i	$-0.580201\pi$
$683$	18.7938	−	18.7938i	0.719123	−	0.719123i	0.968426	+	0.249303i	$0.0802013\pi$
$684$		0			0
$685$	17.5385	+	17.5385i	0.670111	+	0.670111i
$686$	−0.985767	+	2.98252i	−0.0376368	+	0.113873i
$687$		0			0
$688$	28.7013	+	15.3624i	1.09423	+	0.585685i
$689$	29.9660			1.14161
$690$		0			0
$691$	10.4580	+	10.4580i	0.397841	+	0.397841i	0.877471	−	0.479630i	$-0.159229\pi$
$691$	10.4580	+	10.4580i	0.397841	+	0.397841i	−0.479630	+	0.877471i	$0.659229\pi$
$692$	6.61971	+	44.7149i	0.251644	+	1.69980i
$693$		0			0
$694$	−35.4344	+	17.8298i	−1.34507	+	0.676810i
$695$		−	6.16415i		−	0.233820i
$696$		0			0
$697$			7.94948i			0.301108i
$698$	10.7622	+	21.3885i	0.407357	+	0.809569i
$699$		0			0
$700$	−0.451177	−	0.334817i	−0.0170529	−	0.0126549i
$701$	−18.3314	−	18.3314i	−0.692367	−	0.692367i	0.270385	−	0.962752i	$-0.412849\pi$
$701$	−18.3314	−	18.3314i	−0.692367	−	0.692367i	−0.962752	+	0.270385i	$0.912849\pi$
$702$		0			0
$703$	25.8528			0.975055
$704$	18.3380	+	38.8590i	0.691141	+	1.46456i
$705$		0			0
$706$	16.9460	+	5.60091i	0.637773	+	0.210793i
$707$	1.13690	+	1.13690i	0.0427577	+	0.0427577i
$708$		0			0
$709$	14.5722	−	14.5722i	0.547271	−	0.547271i	−0.378380	−	0.925650i	$-0.623519\pi$
$709$	14.5722	−	14.5722i	0.547271	−	0.547271i	0.925650	+	0.378380i	$0.123519\pi$
$710$	−0.363303	−	0.722018i	−0.0136345	−	0.0270969i
$711$		0			0
$712$	−33.3075	+	23.4364i	−1.24825	+	0.878315i
$713$			11.7633i			0.440538i
$714$		0			0
$715$	40.6761	−	40.6761i	1.52120	−	1.52120i
$716$	5.06651	+	34.2233i	0.189344	+	1.27898i
$717$		0			0
$718$	12.0212	−	36.3712i	0.448628	−	1.35736i
$719$	−44.0949			−1.64446			−0.822230	−	0.569155i	$-0.807270\pi$
$719$	−44.0949			−1.64446			−0.822230	+	0.569155i	$0.807270\pi$
$720$		0			0
$721$	−1.80409			−0.0671880
$722$	4.29513	−	12.9953i	0.159848	−	0.483634i
$723$		0			0
$724$	16.1233	−	2.38694i	0.599219	−	0.0887101i
$725$	3.71119	−	3.71119i	0.137830	−	0.137830i
$726$		0			0
$727$		−	9.23457i		−	0.342491i	−0.985228	−	0.171246i	$-0.945221\pi$
$727$		−	9.23457i		−	0.342491i	0.985228	−	0.171246i	$-0.0547792\pi$
$728$	2.63832	+	0.458962i	0.0977826	+	0.0170103i
$729$		0			0
$730$	−1.53029	−	3.04125i	−0.0566385	−	0.112562i
$731$	−17.5706	+	17.5706i	−0.649872	+	0.649872i
$732$		0			0
$733$	18.2764	+	18.2764i	0.675053	+	0.675053i	0.958877	−	0.283823i	$-0.0916029\pi$
$733$	18.2764	+	18.2764i	0.675053	+	0.675053i	−0.283823	+	0.958877i	$0.591603\pi$
$734$	−27.5184	−	9.09524i	−1.01572	−	0.335711i
$735$		0			0
$736$	−15.9949	−	0.404135i	−0.589580	−	0.0148966i
$737$	5.82936			0.214727
$738$		0			0
$739$	16.9991	+	16.9991i	0.625321	+	0.625321i	0.946887	−	0.321566i	$-0.104209\pi$
$739$	16.9991	+	16.9991i	0.625321	+	0.625321i	−0.321566	+	0.946887i	$0.604209\pi$
$740$	18.1447	−	24.4506i	0.667012	−	0.898822i
$741$		0			0
$742$	−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	$-0.106335\pi$
$744$		0			0
$745$		−	7.44538i		−	0.272778i
$746$	1.84682	−	0.929278i	0.0676168	−	0.0340233i
$747$		0			0
$748$	−32.4445	+	4.80316i	−1.18629	+	0.175621i
$749$	0.114759	+	0.114759i	0.00419319	+	0.00419319i
$750$		0			0
$751$	−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
$753$		0			0
$754$	−7.85047	+	23.7523i	−0.285897	+	0.865006i
$755$	28.8139	+	28.8139i	1.04865	+	1.04865i
$756$		0			0
$757$	−32.8071	+	32.8071i	−1.19239	+	1.19239i	−0.216000	+	0.976393i	$0.569301\pi$
$757$	−32.8071	+	32.8071i	−1.19239	+	1.19239i	−0.976393	+	0.216000i	$0.930699\pi$
$758$	31.5662	−	15.8834i	1.14654	−	0.576912i
$759$		0			0
$760$	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			0
$763$	0.229624	−	0.229624i	0.00831296	−	0.00831296i
$764$	25.9660	+	19.2693i	0.939418	+	0.697138i
$765$		0			0
$766$	41.7545	+	13.8005i	1.50865	+	0.498632i
$767$	33.6972			1.21673
$768$		0			0
$769$	−35.2068			−1.26959			−0.634795	−	0.772681i	$-0.718915\pi$
$769$	−35.2068			−1.26959			−0.634795	+	0.772681i	$0.718915\pi$
$770$	−2.06099	−	0.681187i	−0.0742729	−	0.0245483i
$771$		0			0
$772$	−35.5671	−	26.3942i	−1.28009	−	0.949947i
$773$	19.3897	−	19.3897i	0.697399	−	0.697399i	−0.266450	−	0.963849i	$-0.585851\pi$
$773$	19.3897	−	19.3897i	0.697399	−	0.697399i	0.963849	+	0.266450i	$0.0858507\pi$
$774$		0			0
$775$			7.35067i			0.264044i
$776$	−0.930247	−	1.32206i	−0.0333939	−	0.0474591i
$777$		0			0
$778$	4.57591	−	2.30250i	0.164054	−	0.0825485i
$779$	−5.62113	+	5.62113i	−0.201398	+	0.201398i
$780$		0			0
$781$	1.20730	+	1.20730i	0.0432006	+	0.0432006i
$782$	3.83260	−	11.5959i	0.137054	−	0.414667i
$783$		0			0
$784$	8.08331	+	26.7023i	0.288690	+	0.953653i
$785$	7.06877			0.252295
$786$		0			0
$787$	−6.68964	−	6.68964i	−0.238460	−	0.238460i	0.577752	−	0.816212i	$-0.303930\pi$
$787$	−6.68964	−	6.68964i	−0.238460	−	0.238460i	−0.816212	+	0.577752i	$0.803930\pi$
$788$	40.0084	−	5.92295i	1.42524	−	0.210996i
$789$		0			0
$790$	22.0179	−	11.0789i	0.783360	−	0.394170i
$791$			0.561839i			0.0199767i
$792$		0			0
$793$		−	30.9128i		−	1.09775i
$794$	−4.58289	−	9.10789i	−0.162641	−	0.323227i
$795$		0			0
$796$	29.8055	−	40.1639i	1.05643	−	1.42357i
$797$	−13.5617	−	13.5617i	−0.480380	−	0.480380i	0.424873	−	0.905253i	$-0.360319\pi$
$797$	−13.5617	−	13.5617i	−0.480380	−	0.480380i	−0.905253	+	0.424873i	$0.860319\pi$
$798$		0			0
$799$	−8.63577			−0.305511
$800$	−9.99495	−	0.252537i	−0.353375	−	0.00892854i
$801$		0			0
$802$	20.4988	+	6.77515i	0.723837	+	0.239239i
$803$	5.08532	+	5.08532i	0.179457	+	0.179457i
$804$		0			0
$805$	0.571533	−	0.571533i	0.0201439	−	0.0201439i
$806$	−15.7482	−	31.2974i	−0.554705	−	1.10240i
$807$		0			0
$808$	28.1885	+	4.90367i	0.991668	+	0.172510i
$809$			43.1578i			1.51735i	0.651472	+	0.758673i	$0.274152\pi$
$809$			43.1578i			1.51735i	−0.651472	+	0.758673i	$0.725848\pi$
$810$		0			0
$811$	2.74017	−	2.74017i	0.0962203	−	0.0962203i	−0.657358	−	0.753578i	$-0.728326\pi$
$811$	2.74017	−	2.74017i	0.0962203	−	0.0962203i	0.753578	+	0.657358i	$0.228326\pi$
$812$	0.933779	−	0.138239i	0.0327692	−	0.00485124i
$813$		0			0
$814$	−20.1839	+	61.0683i	−0.707447	+	2.14044i
$815$	13.8243			0.484242
$816$		0			0
$817$	−24.8486			−0.869342
$818$	−5.04959	+	15.2780i	−0.176555	+	0.534182i
$819$		0			0
$820$	1.37109	+	9.26143i	0.0478805	+	0.323423i
$821$	−3.97453	+	3.97453i	−0.138712	+	0.138712i	−0.773053	−	0.634341i	$-0.781271\pi$
$821$	−3.97453	+	3.97453i	−0.138712	+	0.138712i	0.634341	+	0.773053i	$0.281271\pi$
$822$		0			0
$823$		−	38.5255i		−	1.34291i	−0.741043	−	0.671457i	$-0.765669\pi$
$823$		−	38.5255i		−	1.34291i	0.741043	−	0.671457i	$-0.234331\pi$
$824$	−26.2561	+	18.4748i	−0.914676	+	0.643599i
$825$		0			0
$826$	−0.571533	−	1.13585i	−0.0198862	−	0.0395212i
$827$	−2.99583	+	2.99583i	−0.104175	+	0.104175i	−0.757273	−	0.653098i	$-0.773469\pi$
$827$	−2.99583	+	2.99583i	−0.104175	+	0.104175i	0.653098	+	0.757273i	$0.273469\pi$
$828$		0			0
$829$	−24.9699	−	24.9699i	−0.867240	−	0.867240i	0.124926	−	0.992166i	$-0.460131\pi$
$829$	−24.9699	−	24.9699i	−0.867240	−	0.867240i	−0.992166	+	0.124926i	$0.960131\pi$
$830$	0.395420	+	0.130692i	0.0137252	+	0.00453639i
$831$		0			0
$832$	43.0971	−	20.3380i	1.49412	−	0.705095i
$833$	−21.2953			−0.737838
$834$		0			0
$835$	5.02758	+	5.02758i	0.173986	+	0.173986i
$836$	−26.3380	−	19.5453i	−0.910920	−	0.675990i
$837$		0			0
$838$	−20.9527	−	41.6407i	−0.723799	−	1.43846i
$839$		−	39.6005i		−	1.36716i	−0.729876	−	0.683580i	$-0.760422\pi$
$839$		−	39.6005i		−	1.36716i	0.729876	−	0.683580i	$-0.239578\pi$
$840$		0			0
$841$		−	20.1820i		−	0.695932i
$842$	−31.4712	+	15.8356i	−1.08457	+	0.545731i
$843$		0			0
$844$	7.63159	+	51.5499i	0.262690	+	1.77442i
$845$	−28.5850	−	28.5850i	−0.983355	−	0.983355i
$846$		0			0
$847$	2.83688			0.0974765
$848$	−17.7406	−	9.49562i	−0.609213	−	0.326081i
$849$		0			0
$850$	2.39493	−	7.24607i	0.0821454	−	0.248538i
$851$	−16.9348	−	16.9348i	−0.580519	−	0.580519i
$852$		0			0
$853$	7.68505	−	7.68505i	0.263131	−	0.263131i	−0.563194	−	0.826325i	$-0.690428\pi$
$853$	7.68505	−	7.68505i	0.263131	−	0.263131i	0.826325	+	0.563194i	$0.190428\pi$
$854$	−1.04199	+	0.524308i	−0.0356563	+	0.0179414i
$855$		0			0
$856$	2.84534	+	0.494975i	0.0972517	+	0.0169179i
$857$		−	34.0082i		−	1.16170i	−0.814011	−	0.580849i	$-0.802721\pi$
$857$		−	34.0082i		−	1.16170i	0.814011	−	0.580849i	$-0.197279\pi$
$858$		0			0
$859$	9.19049	−	9.19049i	0.313576	−	0.313576i	−0.532718	−	0.846293i	$-0.678829\pi$
$859$	9.19049	−	9.19049i	0.313576	−	0.313576i	0.846293	+	0.532718i	$0.178829\pi$
$860$	−17.4399	+	23.5009i	−0.594696	+	0.801374i
$861$		0			0
$862$	−13.8589	−	4.58057i	−0.472037	−	0.156015i
$863$	25.8307			0.879289			0.439644	−	0.898172i	$-0.355104\pi$
$863$	25.8307			0.879289			0.439644	+	0.898172i	$0.355104\pi$
$864$		0			0
$865$	−40.6353			−1.38164
$866$	−20.5628	−	6.79631i	−0.698753	−	0.230948i
$867$		0			0
$868$	−0.787854	+	1.06166i	−0.0267415	+	0.0360351i
$869$	−36.8165	+	36.8165i	−1.24891	+	1.24891i
$870$		0			0
$871$		−	6.46512i		−	0.219062i
$872$	0.990411	−	5.69333i	0.0335395	−	0.192800i
$873$		0			0
$874$	10.9096	−	5.48946i	0.369022	−	0.185684i
$875$	1.36748	−	1.36748i	0.0462292	−	0.0462292i
$876$		0			0
$877$	31.9718	+	31.9718i	1.07961	+	1.07961i	0.996544	+	0.0830670i	$0.0264716\pi$
$877$	31.9718	+	31.9718i	1.07961	+	1.07961i	0.0830670	+	0.996544i	$0.473528\pi$
$878$	−10.0183	+	30.3111i	−0.338100	+	1.02295i
$879$		0			0
$880$	−36.9706	+	11.1917i	−1.24628	+	0.377273i
$881$	−34.7403			−1.17043			−0.585215	−	0.810878i	$-0.698990\pi$
$881$	−34.7403			−1.17043			−0.585215	+	0.810878i	$0.698990\pi$
$882$		0			0
$883$	−34.6034	−	34.6034i	−1.16450	−	1.16450i	−0.983480	−	0.181017i	$-0.942061\pi$
$883$	−34.6034	−	34.6034i	−1.16450	−	1.16450i	−0.181017	−	0.983480i	$-0.557939\pi$
$884$	5.32701	+	35.9829i	0.179167	+	1.21024i
$885$		0			0
$886$	−42.3628	+	21.3160i	−1.42320	+	0.716125i
$887$		−	22.9284i		−	0.769860i	−0.922946	−	0.384930i	$-0.874226\pi$
$887$		−	22.9284i		−	0.769860i	0.922946	−	0.384930i	$-0.125774\pi$
$888$		0			0
$889$		−	0.238081i		−	0.00798497i
$890$	−16.4564	−	32.7050i	−0.551620	−	1.09627i
$891$		0			0
$892$	29.4658	+	21.8664i	0.986588	+	0.732143i
$893$	−6.10641	−	6.10641i	−0.204343	−	0.204343i
$894$		0			0
$895$	−31.1009			−1.03959
$896$	−1.41651	−	1.10774i	−0.0473222	−	0.0370072i
$897$		0			0
$898$	2.35665	+	0.778908i	0.0786425	+	0.0259925i
$899$	−8.73277	−	8.73277i	−0.291254	−	0.291254i
$900$		0			0
$901$	10.8605	−	10.8605i	0.361817	−	0.361817i
$902$	−8.88942	−	17.6665i	−0.295985	−	0.588232i
$903$		0			0
$904$	5.75349	+	8.17680i	0.191358	+	0.271956i
$905$			14.6523i			0.487059i
$906$		0			0
$907$	−16.3822	+	16.3822i	−0.543963	+	0.543963i	−0.924688	−	0.380725i	$-0.875674\pi$
$907$	−16.3822	+	16.3822i	−0.543963	+	0.543963i	0.380725	+	0.924688i	$0.375674\pi$
$908$	0.0479725	+	0.324045i	0.00159202	+	0.0107538i
$909$		0			0
$910$	−0.755479	+	2.28577i	−0.0250439	+	0.0757724i
$911$	29.4078			0.974324			0.487162	−	0.873312i	$-0.338032\pi$
$911$	29.4078			0.974324			0.487162	+	0.873312i	$0.338032\pi$
$912$		0			0
$913$	−0.879722			−0.0291146
$914$	11.8683	−	35.9086i	0.392569	−	1.18775i
$915$		0			0
$916$	7.96827	−	1.17964i	0.263279	−	0.0389765i
$917$	1.65685	−	1.65685i	0.0547141	−	0.0547141i
$918$		0			0
$919$		−	6.86029i		−	0.226300i	−0.993578	−	0.113150i	$-0.963906\pi$
$919$		−	6.86029i		−	0.226300i	0.993578	−	0.113150i	$-0.0360941\pi$
$920$	2.46512	−	14.1706i	0.0812727	−	0.467192i
$921$		0			0
$922$	−8.30574	−	16.5066i	−0.273535	−	0.543615i
$923$	1.33897	−	1.33897i	0.0440728	−	0.0440728i
$924$		0			0
$925$	−10.5823	−	10.5823i	−0.347944	−	0.347944i
$926$	39.5411	+	13.0689i	1.29940	+	0.429471i
$927$		0			0
$928$	12.1743	−	11.5742i	0.399639	−	0.379942i
$929$	−16.1385			−0.529488			−0.264744	−	0.964319i	$-0.585287\pi$
$929$	−16.1385			−0.529488			−0.264744	+	0.964319i	$0.585287\pi$
$930$		0			0
$931$	−15.0581	−	15.0581i	−0.493508	−	0.493508i
$932$	−13.9699	+	18.8249i	−0.457599	+	0.616631i
$933$		0			0
$934$	17.6105	+	34.9985i	0.576233	+	1.14519i
$935$		−	29.4844i		−	0.964241i
$936$		0			0
$937$		−	34.7669i		−	1.13579i	−0.823102	−	0.567893i	$-0.807759\pi$
$937$		−	34.7669i		−	1.13579i	0.823102	−	0.567893i	$-0.192241\pi$
$938$	−0.217923	+	0.109654i	−0.00711544	+	0.00358033i
$939$		0			0
$940$	−10.0610	+	1.48946i	−0.328153	+	0.0485807i
$941$	37.2662	+	37.2662i	1.21484	+	1.21484i	0.969414	+	0.245430i	$0.0789291\pi$
$941$	37.2662	+	37.2662i	1.21484	+	1.21484i	0.245430	+	0.969414i	$0.421071\pi$
$942$		0			0
$943$	7.36423			0.239812
$944$	−19.9495	−	10.6779i	−0.649300	−	0.347537i
$945$		0			0
$946$	19.4000	−	58.6962i	0.630747	−	1.90838i
$947$	−18.5243	−	18.5243i	−0.601957	−	0.601957i	0.338874	−	0.940832i	$-0.389954\pi$
$947$	−18.5243	−	18.5243i	−0.601957	−	0.601957i	−0.940832	+	0.338874i	$0.889954\pi$
$948$		0			0
$949$	5.63994	−	5.63994i	0.183080	−	0.183080i
$950$	6.81722	−	3.43027i	0.221180	−	0.111293i
$951$		0			0
$952$	1.12254	−	0.789861i	0.0363818	−	0.0255996i
$953$		−	11.1752i		−	0.362000i	−0.983483	−	0.181000i	$-0.942067\pi$
$953$		−	11.1752i		−	0.362000i	0.983483	−	0.181000i	$-0.0579333\pi$
$954$		0			0
$955$	−20.5541	+	20.5541i	−0.665115	+	0.665115i
$956$	21.9257	+	16.2710i	0.709128	+	0.526241i
$957$		0			0
$958$	−47.7354	−	15.7773i	−1.54226	−	0.509740i
$959$	2.19266			0.0708047
$960$		0			0
$961$	−13.7032			−0.442039
$962$	67.7285	+	22.3853i	2.18366	+	0.721730i
$963$		0			0
$964$	3.42362	+	2.54065i	0.110267	+	0.0818289i
$965$	28.1541	−	28.1541i	0.906312	−	0.906312i
$966$		0			0
$967$			12.8452i			0.413075i	0.978439	+	0.206537i	$0.0662195\pi$
$967$			12.8452i			0.413075i	−0.978439	+	0.206537i	$0.933780\pi$
$968$	41.2870	−	29.0510i	1.32701	−	0.933734i
$969$		0			0
$970$	1.29814	−	0.653195i	0.0416808	−	0.0209728i
$971$	−5.94517	+	5.94517i	−0.190790	+	0.190790i	−0.796037	−	0.605248i	$-0.793074\pi$
$971$	−5.94517	+	5.94517i	−0.190790	+	0.190790i	0.605248	+	0.796037i	$0.293074\pi$
$972$		0			0
$973$	−0.385321	−	0.385321i	−0.0123528	−	0.0123528i
$974$	4.37873	−	13.2482i	0.140304	−	0.424500i
$975$		0			0
$976$	−9.79564	+	18.3011i	−0.313551	+	0.585803i
$977$	−40.4156			−1.29301			−0.646504	−	0.762910i	$-0.723770\pi$
$977$	−40.4156			−1.29301			−0.646504	+	0.762910i	$0.723770\pi$
$978$		0			0
$979$	54.6865	+	54.6865i	1.74779	+	1.74779i
$980$	−24.8098	+	3.67291i	−0.792521	+	0.117327i
$981$		0			0
$982$	0.803165	−	0.404135i	0.0256300	−	0.0128965i
$983$			13.9202i			0.443985i	0.975048	+	0.221993i	$0.0712561\pi$
$983$			13.9202i			0.443985i	−0.975048	+	0.221993i	$0.928744\pi$
$984$		0			0
$985$			36.3582i			1.15847i
$986$	5.76326	+	11.4537i	0.183540	+	0.364761i
$987$		0			0
$988$	−21.6770	+	29.2105i	−0.689638	+	0.929311i
$989$	16.2771	+	16.2771i	0.517580	+	0.517580i
$990$		0			0
$991$	41.0309			1.30339			0.651695	−	0.758481i	$-0.274058\pi$
$991$	41.0309			1.30339			0.651695	+	0.758481i	$0.274058\pi$
$992$	−0.594243	+	23.5190i	−0.0188672	+	0.746730i
$993$		0			0
$994$	−0.0678434	−	0.0224232i	−0.00215186	−	0.000711222i
$995$	31.7928	+	31.7928i	1.00790	+	1.00790i
$996$		0			0
$997$	27.3245	−	27.3245i	0.865375	−	0.865375i	−0.126581	−	0.991956i	$-0.540400\pi$
$997$	27.3245	−	27.3245i	0.865375	−	0.865375i	0.991956	+	0.126581i	$0.0404005\pi$
$998$	2.43301	+	4.83528i	0.0770155	+	0.153058i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.k.b.109.4		8
3.2	odd	2		48.2.j.a.13.1	✓	8
4.3	odd	2		576.2.k.b.145.2		8
8.3	odd	2		1152.2.k.f.289.3		8
8.5	even	2		1152.2.k.c.289.3		8
12.11	even	2		192.2.j.a.145.2		8
16.3	odd	4		1152.2.k.f.865.3		8
16.5	even	4	inner	144.2.k.b.37.4		8
16.11	odd	4		576.2.k.b.433.2		8
16.13	even	4		1152.2.k.c.865.3		8
24.5	odd	2		384.2.j.b.289.1		8
24.11	even	2		384.2.j.a.289.3		8
32.5	even	8		9216.2.a.bo.1.1		4
32.11	odd	8		9216.2.a.x.1.4		4
32.21	even	8		9216.2.a.y.1.4		4
32.27	odd	8		9216.2.a.bn.1.1		4
48.5	odd	4		48.2.j.a.37.1	yes	8
48.11	even	4		192.2.j.a.49.2		8
48.29	odd	4		384.2.j.b.97.1		8
48.35	even	4		384.2.j.a.97.3		8
96.5	odd	8		3072.2.a.i.1.4		4
96.11	even	8		3072.2.a.n.1.1		4
96.29	odd	8		3072.2.d.f.1537.8		8
96.35	even	8		3072.2.d.i.1537.4		8
96.53	odd	8		3072.2.a.t.1.1		4
96.59	even	8		3072.2.a.o.1.4		4
96.77	odd	8		3072.2.d.f.1537.1		8
96.83	even	8		3072.2.d.i.1537.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.j.a.13.1	✓	8	3.2	odd	2
48.2.j.a.37.1	yes	8	48.5	odd	4
144.2.k.b.37.4		8	16.5	even	4	inner
144.2.k.b.109.4		8	1.1	even	1	trivial
192.2.j.a.49.2		8	48.11	even	4
192.2.j.a.145.2		8	12.11	even	2
384.2.j.a.97.3		8	48.35	even	4
384.2.j.a.289.3		8	24.11	even	2
384.2.j.b.97.1		8	48.29	odd	4
384.2.j.b.289.1		8	24.5	odd	2
576.2.k.b.145.2		8	4.3	odd	2
576.2.k.b.433.2		8	16.11	odd	4
1152.2.k.c.289.3		8	8.5	even	2
1152.2.k.c.865.3		8	16.13	even	4
1152.2.k.f.289.3		8	8.3	odd	2
1152.2.k.f.865.3		8	16.3	odd	4
3072.2.a.i.1.4		4	96.5	odd	8
3072.2.a.n.1.1		4	96.11	even	8
3072.2.a.o.1.4		4	96.59	even	8
3072.2.a.t.1.1		4	96.53	odd	8
3072.2.d.f.1537.1		8	96.77	odd	8
3072.2.d.f.1537.8		8	96.29	odd	8
3072.2.d.i.1537.4		8	96.35	even	8
3072.2.d.i.1537.5		8	96.83	even	8
9216.2.a.x.1.4		4	32.11	odd	8
9216.2.a.y.1.4		4	32.21	even	8
9216.2.a.bn.1.1		4	32.27	odd	8
9216.2.a.bo.1.1		4	32.5	even	8

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34277 + 0.443806i) q^{2} +(1.60607 + 1.19186i) q^{4} +(-1.27133 + 1.27133i) q^{5} +0.158942i q^{7} +(1.62764 + 2.31318i) q^{8} +O(q^{10})\)	\(q+(1.34277 + 0.443806i) q^{2} +(1.60607 + 1.19186i) q^{4} +(-1.27133 + 1.27133i) q^{5} +0.158942i q^{7} +(1.62764 + 2.31318i) q^{8} +(-2.27133 + 1.14288i) q^{10} +(3.79793 - 3.79793i) q^{11} +(-4.21215 - 4.21215i) q^{13} +(-0.0705392 + 0.213422i) q^{14} +(1.15894 + 3.82843i) q^{16} -3.05320 q^{17} +(-2.15894 - 2.15894i) q^{19} +(-3.55710 + 0.526602i) q^{20} +(6.78530 - 3.41421i) q^{22} +2.82843i q^{23} +1.76744i q^{25} +(-3.78658 - 7.52533i) q^{26} +(-0.189436 + 0.255272i) q^{28} +(-2.09976 - 2.09976i) q^{29} +4.15894 q^{31} +(-0.142883 + 5.65505i) q^{32} +(-4.09976 - 1.35503i) q^{34} +(-0.202067 - 0.202067i) q^{35} +(-5.98737 + 5.98737i) q^{37} +(-1.94082 - 3.85712i) q^{38} +(-5.01008 - 0.871553i) q^{40} -2.60365i q^{41} +(5.75481 - 5.75481i) q^{43} +(10.6264 - 1.57316i) q^{44} +(-1.25527 + 3.79793i) q^{46} +2.82843 q^{47} +6.97474 q^{49} +(-0.784399 + 2.37327i) q^{50} +(-1.74473 - 11.7853i) q^{52} +(-3.55710 + 3.55710i) q^{53} +9.65685i q^{55} +(-0.367661 + 0.258699i) q^{56} +(-1.88761 - 3.75138i) q^{58} +(-4.00000 + 4.00000i) q^{59} +(3.66949 + 3.66949i) q^{61} +(5.58451 + 1.84576i) q^{62} +(-2.70160 + 7.53003i) q^{64} +10.7101 q^{65} +(0.767438 + 0.767438i) q^{67} +(-4.90367 - 3.63899i) q^{68} +(-0.181652 - 0.361009i) q^{70} +0.317883i q^{71} +1.33897i q^{73} +(-10.6969 + 5.38244i) q^{74} +(-0.894263 - 6.04057i) q^{76} +(0.603650 + 0.603650i) q^{77} -9.69382 q^{79} +(-6.34059 - 3.39380i) q^{80} +(1.15551 - 3.49611i) q^{82} +(-0.115816 - 0.115816i) q^{83} +(3.88163 - 3.88163i) q^{85} +(10.2814 - 5.17338i) q^{86} +(14.9670 + 2.60365i) q^{88} +14.3990i q^{89} +(0.669485 - 0.669485i) q^{91} +(-3.37109 + 4.54266i) q^{92} +(3.79793 + 1.25527i) q^{94} +5.48946 q^{95} -0.571533 q^{97} +(9.36548 + 3.09543i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 + 12 * q^8	\( 8 q - 4 q^{4} + 12 q^{8} - 8 q^{10} + 8 q^{11} - 12 q^{14} - 8 q^{19} - 16 q^{20} - 20 q^{26} + 8 q^{28} + 16 q^{29} + 24 q^{31} - 24 q^{35} - 16 q^{37} + 8 q^{38} + 16 q^{40} - 8 q^{43} + 40 q^{44} - 8 q^{46} - 8 q^{49} + 36 q^{50} - 16 q^{52} - 16 q^{53} - 16 q^{58} - 32 q^{59} + 16 q^{61} + 12 q^{62} + 8 q^{64} + 16 q^{65} - 16 q^{67} - 32 q^{68} + 32 q^{70} - 52 q^{74} + 8 q^{76} - 16 q^{77} - 24 q^{79} - 8 q^{80} + 40 q^{82} + 40 q^{83} - 16 q^{85} + 16 q^{86} + 32 q^{88} - 8 q^{91} + 16 q^{92} + 8 q^{94} + 48 q^{95} + 40 q^{98}+O(q^{100}) \) 8 * q - 4 * q^4 + 12 * q^8 - 8 * q^10 + 8 * q^11 - 12 * q^14 - 8 * q^19 - 16 * q^20 - 20 * q^26 + 8 * q^28 + 16 * q^29 + 24 * q^31 - 24 * q^35 - 16 * q^37 + 8 * q^38 + 16 * q^40 - 8 * q^43 + 40 * q^44 - 8 * q^46 - 8 * q^49 + 36 * q^50 - 16 * q^52 - 16 * q^53 - 16 * q^58 - 32 * q^59 + 16 * q^61 + 12 * q^62 + 8 * q^64 + 16 * q^65 - 16 * q^67 - 32 * q^68 + 32 * q^70 - 52 * q^74 + 8 * q^76 - 16 * q^77 - 24 * q^79 - 8 * q^80 + 40 * q^82 + 40 * q^83 - 16 * q^85 + 16 * q^86 + 32 * q^88 - 8 * q^91 + 16 * q^92 + 8 * q^94 + 48 * q^95 + 40 * q^98

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