LMFDB - Embedded newform 162.3.d.c.107.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,3,Mod(53,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.53"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,8,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.2
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.3.d.c.53.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(1.34486 - 0.776457i) q^{5} +(-6.19615 + 10.7321i) q^{7} -2.82843i q^{8} -2.19615 q^{10} +(-12.7279 - 7.34847i) q^{11} +(5.40192 + 9.35641i) q^{13} +(15.1774 - 8.76268i) q^{14} +(-2.00000 + 3.46410i) q^{16} +28.9778i q^{17} +3.60770 q^{19} +(2.68973 + 1.55291i) q^{20} +(10.3923 + 18.0000i) q^{22} +(-12.7279 + 7.34847i) q^{23} +(-11.2942 + 19.5622i) q^{25} -15.2789i q^{26} -24.7846 q^{28} +(24.3748 + 14.0728i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(4.89898 - 2.82843i) q^{32} +(20.4904 - 35.4904i) q^{34} +19.2442i q^{35} +22.5692 q^{37} +(-4.41851 - 2.55103i) q^{38} +(-2.19615 - 3.80385i) q^{40} +(-21.7816 + 12.5756i) q^{41} +(26.5885 - 46.0526i) q^{43} -29.3939i q^{44} +20.7846 q^{46} +(-14.6969 - 8.48528i) q^{47} +(-52.2846 - 90.5596i) q^{49} +(27.6651 - 15.9725i) q^{50} +(-10.8038 + 18.7128i) q^{52} -84.5482i q^{53} -22.8231 q^{55} +(30.3548 + 17.5254i) q^{56} +(-19.9019 - 34.4711i) q^{58} +(-78.8641 + 45.5322i) q^{59} +(6.50000 - 11.2583i) q^{61} +11.3137i q^{62} -8.00000 q^{64} +(14.5297 + 8.38872i) q^{65} +(20.5885 + 35.6603i) q^{67} +(-50.1910 + 28.9778i) q^{68} +(13.6077 - 23.5692i) q^{70} -16.3613i q^{71} +71.5885 q^{73} +(-27.6415 - 15.9588i) q^{74} +(3.60770 + 6.24871i) q^{76} +(157.728 - 91.0645i) q^{77} +(23.3731 - 40.4833i) q^{79} +6.21166i q^{80} +35.5692 q^{82} +(13.2555 + 7.65308i) q^{83} +(22.5000 + 38.9711i) q^{85} +(-65.1282 + 37.6018i) q^{86} +(-20.7846 + 36.0000i) q^{88} +78.9756i q^{89} -133.885 q^{91} +(-25.4558 - 14.6969i) q^{92} +(12.0000 + 20.7846i) q^{94} +(4.85186 - 2.80122i) q^{95} +(-45.5692 + 78.9282i) q^{97} +147.883i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 8 q^{7} + 24 q^{10} + 64 q^{13} - 16 q^{16} + 112 q^{19} - 28 q^{25} - 32 q^{28} - 32 q^{31} + 60 q^{34} - 152 q^{37} + 24 q^{40} + 88 q^{43} - 252 q^{49} - 128 q^{52} - 432 q^{55} - 180 q^{58}+ \cdots - 32 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^7 + 24 * q^10 + 64 * q^13 - 16 * q^16 + 112 * q^19 - 28 * q^25 - 32 * q^28 - 32 * q^31 + 60 * q^34 - 152 * q^37 + 24 * q^40 + 88 * q^43 - 252 * q^49 - 128 * q^52 - 432 * q^55 - 180 * q^58 + 52 * q^61 - 64 * q^64 + 40 * q^67 + 192 * q^70 + 448 * q^73 + 112 * q^76 - 104 * q^79 - 48 * q^82 + 180 * q^85 + 176 * q^91 + 96 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	1.34486	−	0.776457i	0.268973	−	0.155291i	−0.359448	−	0.933165i	$-0.617035\pi$
$5$	1.34486	−	0.776457i	0.268973	−	0.155291i	0.628421	+	0.777874i	$0.283702\pi$
$6$		0			0
$7$	−6.19615	+	10.7321i	−0.885165	+	1.53315i	−0.0396398	+	0.999214i	$0.512621\pi$
$7$	−6.19615	+	10.7321i	−0.885165	+	1.53315i	−0.845525	+	0.533936i	$0.820712\pi$
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	−2.19615			−0.219615
$11$	−12.7279	−	7.34847i	−1.15708	−	0.668043i	−0.206480	−	0.978451i	$-0.566201\pi$
$11$	−12.7279	−	7.34847i	−1.15708	−	0.668043i	−0.950603	+	0.310408i	$0.899534\pi$
$12$		0			0
$13$	5.40192	+	9.35641i	0.415533	+	0.719724i	0.995484	−	0.0949274i	$-0.0302619\pi$
$13$	5.40192	+	9.35641i	0.415533	+	0.719724i	−0.579952	+	0.814651i	$0.696929\pi$
$14$	15.1774	−	8.76268i	1.08410	−	0.625906i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$			28.9778i			1.70457i	0.523074	+	0.852287i	$0.324785\pi$
$17$			28.9778i			1.70457i	−0.523074	+	0.852287i	$0.675215\pi$
$18$		0			0
$19$	3.60770			0.189879			0.0949393	−	0.995483i	$-0.469734\pi$
$19$	3.60770			0.189879			0.0949393	+	0.995483i	$0.469734\pi$
$20$	2.68973	+	1.55291i	0.134486	+	0.0776457i
$21$		0			0
$22$	10.3923	+	18.0000i	0.472377	+	0.818182i
$23$	−12.7279	+	7.34847i	−0.553388	+	0.319499i	−0.750487	−	0.660885i	$-0.770181\pi$
$23$	−12.7279	+	7.34847i	−0.553388	+	0.319499i	0.197099	+	0.980384i	$0.436848\pi$
$24$		0			0
$25$	−11.2942	+	19.5622i	−0.451769	+	0.782487i
$26$		−	15.2789i		−	0.587652i
$27$		0			0
$28$	−24.7846			−0.885165
$29$	24.3748	+	14.0728i	0.840510	+	0.485268i	0.857437	−	0.514588i	$-0.172055\pi$
$29$	24.3748	+	14.0728i	0.840510	+	0.485268i	−0.0169278	+	0.999857i	$0.505389\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.129032	−	0.223490i	0.794270	−	0.607565i	$-0.207854\pi$
$31$	−4.00000	−	6.92820i	−0.129032	−	0.223490i	−0.923302	+	0.384075i	$0.874520\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$		0			0
$34$	20.4904	−	35.4904i	0.602658	−	1.04383i
$35$			19.2442i			0.549834i
$36$		0			0
$37$	22.5692			0.609979			0.304989	−	0.952356i	$-0.401347\pi$
$37$	22.5692			0.609979			0.304989	+	0.952356i	$0.401347\pi$
$38$	−4.41851	−	2.55103i	−0.116276	−	0.0671323i
$39$		0			0
$40$	−2.19615	−	3.80385i	−0.0549038	−	0.0950962i
$41$	−21.7816	+	12.5756i	−0.531259	+	0.306722i	−0.741529	−	0.670921i	$-0.765899\pi$
$41$	−21.7816	+	12.5756i	−0.531259	+	0.306722i	0.210270	+	0.977643i	$0.432566\pi$
$42$		0			0
$43$	26.5885	−	46.0526i	0.618336	−	1.07099i	−0.371453	−	0.928452i	$-0.621140\pi$
$43$	26.5885	−	46.0526i	0.618336	−	1.07099i	0.989789	−	0.142538i	$-0.0455263\pi$
$44$		−	29.3939i		−	0.668043i
$45$		0			0
$46$	20.7846			0.451839
$47$	−14.6969	−	8.48528i	−0.312701	−	0.180538i	0.335434	−	0.942064i	$-0.391117\pi$
$47$	−14.6969	−	8.48528i	−0.312701	−	0.180538i	−0.648134	+	0.761526i	$0.724451\pi$
$48$		0			0
$49$	−52.2846	−	90.5596i	−1.06703	−	1.84816i
$50$	27.6651	−	15.9725i	0.553302	−	0.319449i
$51$		0			0
$52$	−10.8038	+	18.7128i	−0.207766	+	0.359862i
$53$		−	84.5482i		−	1.59525i	−0.603154	−	0.797625i	$-0.706090\pi$
$53$		−	84.5482i		−	1.59525i	0.603154	−	0.797625i	$-0.293910\pi$
$54$		0			0
$55$	−22.8231			−0.414965
$56$	30.3548	+	17.5254i	0.542050	+	0.312953i
$57$		0			0
$58$	−19.9019	−	34.4711i	−0.343137	−	0.594330i
$59$	−78.8641	+	45.5322i	−1.33668	+	0.771733i	−0.986314	−	0.164880i	$-0.947276\pi$
$59$	−78.8641	+	45.5322i	−1.33668	+	0.771733i	−0.350367	+	0.936613i	$0.613943\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.106557	−	0.184563i	−0.807816	−	0.589435i	$-0.799351\pi$
$61$	6.50000	−	11.2583i	0.106557	−	0.184563i	0.914373	+	0.404872i	$0.132684\pi$
$62$			11.3137i			0.182479i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	14.5297	+	8.38872i	0.223534	+	0.129057i
$66$		0			0
$67$	20.5885	+	35.6603i	0.307290	+	0.532243i	0.977769	−	0.209687i	$-0.0672444\pi$
$67$	20.5885	+	35.6603i	0.307290	+	0.532243i	−0.670478	+	0.741929i	$0.733911\pi$
$68$	−50.1910	+	28.9778i	−0.738103	+	0.426144i
$69$		0			0
$70$	13.6077	−	23.5692i	0.194396	−	0.336703i
$71$		−	16.3613i		−	0.230442i	−0.993340	−	0.115221i	$-0.963242\pi$
$71$		−	16.3613i		−	0.230442i	0.993340	−	0.115221i	$-0.0367575\pi$
$72$		0			0
$73$	71.5885			0.980664			0.490332	−	0.871536i	$-0.336876\pi$
$73$	71.5885			0.980664			0.490332	+	0.871536i	$0.336876\pi$
$74$	−27.6415	−	15.9588i	−0.373534	−	0.215660i
$75$		0			0
$76$	3.60770	+	6.24871i	0.0474697	+	0.0822199i
$77$	157.728	−	91.0645i	2.04842	−	1.18266i
$78$		0			0
$79$	23.3731	−	40.4833i	0.295862	−	0.512447i	−0.679323	−	0.733839i	$-0.737727\pi$
$79$	23.3731	−	40.4833i	0.295862	−	0.512447i	0.975185	+	0.221392i	$0.0710599\pi$
$80$			6.21166i			0.0776457i
$81$		0			0
$82$	35.5692			0.433771
$83$	13.2555	+	7.65308i	0.159705	+	0.0922057i	0.577723	−	0.816233i	$-0.303942\pi$
$83$	13.2555	+	7.65308i	0.159705	+	0.0922057i	−0.418017	+	0.908439i	$0.637275\pi$
$84$		0			0
$85$	22.5000	+	38.9711i	0.264706	+	0.458484i
$86$	−65.1282	+	37.6018i	−0.757304	+	0.437230i
$87$		0			0
$88$	−20.7846	+	36.0000i	−0.236189	+	0.409091i
$89$			78.9756i			0.887367i	0.896184	+	0.443683i	$0.146329\pi$
$89$			78.9756i			0.887367i	−0.896184	+	0.443683i	$0.853671\pi$
$90$		0			0
$91$	−133.885			−1.47126
$92$	−25.4558	−	14.6969i	−0.276694	−	0.159749i
$93$		0			0
$94$	12.0000	+	20.7846i	0.127660	+	0.221113i
$95$	4.85186	−	2.80122i	0.0510722	−	0.0294865i
$96$		0			0
$97$	−45.5692	+	78.9282i	−0.469786	+	0.813693i	−0.999403	−	0.0345438i	$-0.989002\pi$
$97$	−45.5692	+	78.9282i	−0.469786	+	0.813693i	0.529617	+	0.848237i	$0.322336\pi$
$98$			147.883i			1.50901i
$99$		0			0
$100$	−45.1769			−0.451769
$101$	76.6313	+	44.2431i	0.758726	+	0.438051i	0.828838	−	0.559488i	$-0.189002\pi$
$101$	76.6313	+	44.2431i	0.758726	+	0.438051i	−0.0701121	+	0.997539i	$0.522336\pi$
$102$		0			0
$103$	76.3538	+	132.249i	0.741299	+	1.28397i	0.951904	+	0.306397i	$0.0991234\pi$
$103$	76.3538	+	132.249i	0.741299	+	1.28397i	−0.210605	+	0.977571i	$0.567543\pi$
$104$	26.4639	−	15.2789i	0.254461	−	0.146913i
$105$		0			0
$106$	−59.7846	+	103.550i	−0.564006	+	0.976887i
$107$		−	60.0062i		−	0.560805i	−0.959882	−	0.280403i	$-0.909532\pi$
$107$		−	60.0062i		−	0.560805i	0.959882	−	0.280403i	$-0.0904680\pi$
$108$		0			0
$109$	−93.9423			−0.861856			−0.430928	−	0.902386i	$-0.641814\pi$
$109$	−93.9423			−0.861856			−0.430928	+	0.902386i	$0.641814\pi$
$110$	27.9525	+	16.1384i	0.254113	+	0.146712i
$111$		0			0
$112$	−24.7846	−	42.9282i	−0.221291	−	0.383288i
$113$	76.7279	−	44.2989i	0.679008	−	0.392025i	−0.120473	−	0.992717i	$-0.538441\pi$
$113$	76.7279	−	44.2989i	0.679008	−	0.392025i	0.799481	+	0.600691i	$0.205108\pi$
$114$		0			0
$115$	−11.4115	+	19.7654i	−0.0992308	+	0.171873i
$116$			56.2911i			0.485268i
$117$		0			0
$118$	128.785			1.09139
$119$	−310.991	−	179.551i	−2.61337	−	1.50883i
$120$		0			0
$121$	47.5000	+	82.2724i	0.392562	+	0.679937i
$122$	−15.9217	+	9.19239i	−0.130506	+	0.0753474i
$123$		0			0
$124$	8.00000	−	13.8564i	0.0645161	−	0.111745i
$125$			73.9008i			0.591206i
$126$		0			0
$127$	78.8231			0.620654			0.310327	−	0.950630i	$-0.399561\pi$
$127$	78.8231			0.620654			0.310327	+	0.950630i	$0.399561\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−11.8634	−	20.5481i	−0.0912573	−	0.158062i
$131$	71.5157	−	41.2896i	0.545921	−	0.315188i	−0.201554	−	0.979477i	$-0.564599\pi$
$131$	71.5157	−	41.2896i	0.545921	−	0.315188i	0.747475	+	0.664290i	$0.231266\pi$
$132$		0			0
$133$	−22.3538	+	38.7180i	−0.168074	+	0.291113i
$134$		−	58.2330i		−	0.434574i
$135$		0			0
$136$	81.9615			0.602658
$137$	185.970	+	107.370i	1.35745	+	0.783723i	0.989279	−	0.146036i	$-0.0466515\pi$
$137$	185.970	+	107.370i	1.35745	+	0.783723i	0.368169	+	0.929759i	$0.379985\pi$
$138$		0			0
$139$	30.3923	+	52.6410i	0.218650	+	0.378712i	0.954395	−	0.298546i	$-0.0965015\pi$
$139$	30.3923	+	52.6410i	0.218650	+	0.378712i	−0.735746	+	0.677258i	$0.763168\pi$
$140$	−33.3319	+	19.2442i	−0.238085	+	0.137458i
$141$		0			0
$142$	−11.5692	+	20.0385i	−0.0814734	+	0.141116i
$143$		−	158.783i		−	1.11037i
$144$		0			0
$145$	43.7077			0.301432
$146$	−87.6776	−	50.6207i	−0.600531	−	0.346717i
$147$		0			0
$148$	22.5692	+	39.0910i	0.152495	+	0.264129i
$149$	26.5369	−	15.3211i	0.178100	−	0.102826i	−0.408300	−	0.912848i	$-0.633878\pi$
$149$	26.5369	−	15.3211i	0.178100	−	0.102826i	0.586400	+	0.810022i	$0.300545\pi$
$150$		0			0
$151$	−16.0000	+	27.7128i	−0.105960	+	0.183529i	−0.914130	−	0.405421i	$-0.867125\pi$
$151$	−16.0000	+	27.7128i	−0.105960	+	0.183529i	0.808170	+	0.588949i	$0.200458\pi$
$152$		−	10.2041i		−	0.0671323i
$153$		0			0
$154$	−257.569			−1.67253
$155$	−10.7589	−	6.21166i	−0.0694123	−	0.0400752i
$156$		0			0
$157$	−124.854	−	216.253i	−0.795247	−	1.37741i	−0.922682	−	0.385562i	$-0.874008\pi$
$157$	−124.854	−	216.253i	−0.795247	−	1.37741i	0.127435	−	0.991847i	$-0.459326\pi$
$158$	−57.2521	+	33.0545i	−0.362355	+	0.209206i
$159$		0			0
$160$	4.39230	−	7.60770i	0.0274519	−	0.0475481i
$161$		−	182.129i		−	1.13124i
$162$		0			0
$163$	−12.7846			−0.0784332			−0.0392166	−	0.999231i	$-0.512486\pi$
$163$	−12.7846			−0.0784332			−0.0392166	+	0.999231i	$0.512486\pi$
$164$	−43.5632	−	25.1512i	−0.265629	−	0.153361i
$165$		0			0
$166$	−10.8231	−	18.7461i	−0.0651993	−	0.112929i
$167$	−201.292	+	116.216i	−1.20534	+	0.695902i	−0.961737	−	0.273973i	$-0.911662\pi$
$167$	−201.292	+	116.216i	−1.20534	+	0.695902i	−0.243601	+	0.969876i	$0.578329\pi$
$168$		0			0
$169$	26.1384	−	45.2731i	0.154665	−	0.267888i
$170$		−	63.6396i		−	0.374351i
$171$		0			0
$172$	106.354			0.618336
$173$	18.6608	+	10.7738i	0.107866	+	0.0622765i	0.552963	−	0.833206i	$-0.313497\pi$
$173$	18.6608	+	10.7738i	0.107866	+	0.0622765i	−0.445096	+	0.895483i	$0.646831\pi$
$174$		0			0
$175$	−139.962	−	242.420i	−0.799780	−	1.38526i
$176$	50.9117	−	29.3939i	0.289271	−	0.167011i
$177$		0			0
$178$	55.8442	−	96.7250i	0.313732	−	0.543399i
$179$			277.741i			1.55162i	0.630964	+	0.775812i	$0.282659\pi$
$179$			277.741i			1.55162i	−0.630964	+	0.775812i	$0.717341\pi$
$180$		0			0
$181$	174.277			0.962856			0.481428	−	0.876486i	$-0.340118\pi$
$181$	174.277			0.962856			0.481428	+	0.876486i	$0.340118\pi$
$182$	163.974	+	94.6707i	0.900958	+	0.520169i
$183$		0			0
$184$	20.7846	+	36.0000i	0.112960	+	0.195652i
$185$	30.3525	−	17.5240i	0.164068	−	0.0947245i
$186$		0			0
$187$	212.942	−	368.827i	1.13873	−	1.97234i
$188$		−	33.9411i		−	0.180538i
$189$		0			0
$190$	−7.92305			−0.0417003
$191$	131.745	+	76.0629i	0.689764	+	0.398235i	0.803523	−	0.595273i	$-0.202956\pi$
$191$	131.745	+	76.0629i	0.689764	+	0.398235i	−0.113760	+	0.993508i	$0.536289\pi$
$192$		0			0
$193$	27.5000	+	47.6314i	0.142487	+	0.246795i	0.928433	−	0.371501i	$-0.121157\pi$
$193$	27.5000	+	47.6314i	0.142487	+	0.246795i	−0.785946	+	0.618296i	$0.787823\pi$
$194$	111.621	−	64.4446i	0.575368	−	0.332189i
$195$		0			0
$196$	104.569	−	181.119i	0.533516	−	0.924078i
$197$			133.298i			0.676638i	0.941031	+	0.338319i	$0.109858\pi$
$197$			133.298i			0.676638i	−0.941031	+	0.338319i	$0.890142\pi$
$198$		0			0
$199$	−208.862			−1.04956			−0.524778	−	0.851239i	$-0.675852\pi$
$199$	−208.862			−1.04956			−0.524778	+	0.851239i	$0.675852\pi$
$200$	55.3302	+	31.9449i	0.276651	+	0.159725i
$201$		0			0
$202$	−62.5692	−	108.373i	−0.309749	−	0.536500i
$203$	−302.060	+	174.394i	−1.48798	+	0.859085i
$204$		0			0
$205$	−19.5289	+	33.8250i	−0.0952627	+	0.165000i
$206$		−	215.961i		−	1.04836i
$207$		0			0
$208$	−43.2154			−0.207766
$209$	−45.9185	−	26.5110i	−0.219706	−	0.126847i
$210$		0			0
$211$	43.7269	+	75.7372i	0.207236	+	0.358944i	0.950843	−	0.309673i	$-0.100220\pi$
$211$	43.7269	+	75.7372i	0.207236	+	0.358944i	−0.743607	+	0.668617i	$0.766886\pi$
$212$	146.442	−	84.5482i	0.690763	−	0.398812i
$213$		0			0
$214$	−42.4308	+	73.4923i	−0.198275	+	0.343422i
$215$		−	82.5792i		−	0.384089i
$216$		0			0
$217$	99.1384			0.456859
$218$	115.055	+	66.4272i	0.527777	+	0.304712i
$219$		0			0
$220$	−22.8231	−	39.5307i	−0.103741	−	0.179685i
$221$	−271.128	+	156.536i	−1.22682	+	0.708306i
$222$		0			0
$223$	−111.296	+	192.771i	−0.499086	+	0.864442i	−0.999999	−	0.00105540i	$-0.999664\pi$
$223$	−111.296	+	192.771i	−0.499086	+	0.864442i	0.500914	+	0.865497i	$0.332997\pi$
$224$			70.1015i			0.312953i
$225$		0			0
$226$	−125.296			−0.554408
$227$	260.079	+	150.157i	1.14572	+	0.661484i	0.947842	−	0.318742i	$-0.103260\pi$
$227$	260.079	+	150.157i	1.14572	+	0.661484i	0.197882	+	0.980226i	$0.436594\pi$
$228$		0			0
$229$	−114.971	−	199.136i	−0.502057	−	0.869589i	−0.999997	−	0.00237731i	$-0.999243\pi$
$229$	−114.971	−	199.136i	−0.502057	−	0.869589i	0.497940	−	0.867212i	$-0.334090\pi$
$230$	27.9525	−	16.1384i	0.121532	−	0.0701668i
$231$		0			0
$232$	39.8038	−	68.9423i	0.171568	−	0.297165i
$233$		−	116.246i		−	0.498908i	−0.968387	−	0.249454i	$-0.919749\pi$
$233$		−	116.246i		−	0.498908i	0.968387	−	0.249454i	$-0.0802512\pi$
$234$		0			0
$235$	−26.3538			−0.112144
$236$	−157.728	−	91.0645i	−0.668340	−	0.385866i
$237$		0			0
$238$	253.923	+	439.808i	1.06690	+	1.84793i
$239$	142.362	−	82.1930i	0.595659	−	0.343904i	−0.171673	−	0.985154i	$-0.554917\pi$
$239$	142.362	−	82.1930i	0.595659	−	0.343904i	0.767332	+	0.641250i	$0.221584\pi$
$240$		0			0
$241$	40.6558	−	70.4179i	0.168696	−	0.292190i	−0.769265	−	0.638929i	$-0.779378\pi$
$241$	40.6558	−	70.4179i	0.168696	−	0.292190i	0.937962	+	0.346739i	$0.112711\pi$
$242$		−	134.350i		−	0.555166i
$243$		0			0
$244$	26.0000			0.106557
$245$	−140.631	−	81.1935i	−0.574005	−	0.331402i
$246$		0			0
$247$	19.4885	+	33.7551i	0.0789008	+	0.136660i
$248$	−19.5959	+	11.3137i	−0.0790158	+	0.0456198i
$249$		0			0
$250$	52.2558	−	90.5096i	0.209023	−	0.362038i
$251$			396.371i			1.57917i	0.613642	+	0.789584i	$0.289704\pi$
$251$			396.371i			1.57917i	−0.613642	+	0.789584i	$0.710296\pi$
$252$		0			0
$253$	216.000			0.853755
$254$	−96.5382	−	55.7363i	−0.380072	−	0.219434i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	186.164	−	107.482i	0.724372	−	0.418216i	−0.0919879	−	0.995760i	$-0.529322\pi$
$257$	186.164	−	107.482i	0.724372	−	0.418216i	0.816360	+	0.577544i	$0.195989\pi$
$258$		0			0
$259$	−139.842	+	242.214i	−0.539932	+	0.935189i
$260$			33.5549i			0.129057i
$261$		0			0
$262$	−116.785			−0.445743
$263$	−275.304	−	158.947i	−1.04678	−	0.604360i	−0.125036	−	0.992152i	$-0.539905\pi$
$263$	−275.304	−	158.947i	−1.04678	−	0.604360i	−0.921747	+	0.387792i	$0.873238\pi$
$264$		0			0
$265$	−65.6481	−	113.706i	−0.247729	−	0.429078i
$266$	54.7555	−	31.6131i	0.205848	−	0.118846i
$267$		0			0
$268$	−41.1769	+	71.3205i	−0.153645	+	0.266121i
$269$			208.528i			0.775199i	0.921828	+	0.387599i	$0.126696\pi$
$269$			208.528i			0.775199i	−0.921828	+	0.387599i	$0.873304\pi$
$270$		0			0
$271$	409.885			1.51249			0.756245	−	0.654289i	$-0.227032\pi$
$271$	409.885			1.51249			0.756245	+	0.654289i	$0.227032\pi$
$272$	−100.382	−	57.9555i	−0.369051	−	0.213072i
$273$		0			0
$274$	−151.844	−	263.002i	−0.554176	−	0.959861i
$275$	287.504	−	165.991i	1.04547	−	0.603602i
$276$		0			0
$277$	−248.708	+	430.774i	−0.897862	+	1.55514i	−0.0676390	+	0.997710i	$0.521547\pi$
$277$	−248.708	+	430.774i	−0.897862	+	1.55514i	−0.830223	+	0.557432i	$0.811787\pi$
$278$		−	85.9624i		−	0.309217i
$279$		0			0
$280$	54.4308			0.194396
$281$	−186.427	−	107.634i	−0.663442	−	0.383039i	0.130145	−	0.991495i	$-0.458456\pi$
$281$	−186.427	−	107.634i	−0.663442	−	0.383039i	−0.793587	+	0.608456i	$0.791789\pi$
$282$		0			0
$283$	148.354	+	256.956i	0.524218	+	0.907973i	0.999602	+	0.0281946i	$0.00897581\pi$
$283$	148.354	+	256.956i	0.524218	+	0.907973i	−0.475384	+	0.879778i	$0.657691\pi$
$284$	28.3387	−	16.3613i	0.0997841	−	0.0576104i
$285$		0			0
$286$	−112.277	+	194.469i	−0.392576	+	0.679962i
$287$		−	311.682i		−	1.08600i
$288$		0			0
$289$	−550.711			−1.90558
$290$	−53.5307	−	30.9060i	−0.184589	−	0.106572i
$291$		0			0
$292$	71.5885	+	123.995i	0.245166	+	0.424640i
$293$	−295.284	+	170.482i	−1.00779	+	0.581850i	−0.910545	−	0.413410i	$-0.864338\pi$
$293$	−295.284	+	170.482i	−1.00779	+	0.581850i	−0.0972490	+	0.995260i	$0.531004\pi$
$294$		0			0
$295$	−70.7077	+	122.469i	−0.239687	+	0.415150i
$296$		−	63.8354i		−	0.215660i
$297$		0			0
$298$	−43.3346			−0.145418
$299$	−137.511	−	79.3917i	−0.459901	−	0.265524i
$300$		0			0
$301$	329.492	+	570.697i	1.09466	+	1.89600i
$302$	39.1918	−	22.6274i	0.129774	−	0.0749252i
$303$		0			0
$304$	−7.21539	+	12.4974i	−0.0237348	+	0.0411099i
$305$		−	20.1879i		−	0.0661898i
$306$		0			0
$307$	−114.354			−0.372488			−0.186244	−	0.982504i	$-0.559632\pi$
$307$	−114.354			−0.372488			−0.186244	+	0.982504i	$0.559632\pi$
$308$	315.457	+	182.129i	1.02421	+	0.591328i
$309$		0			0
$310$	8.78461	+	15.2154i	0.0283375	+	0.0490819i
$311$	169.929	−	98.1083i	0.546394	−	0.315461i	−0.201272	−	0.979535i	$-0.564508\pi$
$311$	169.929	−	98.1083i	0.546394	−	0.315461i	0.747666	+	0.664074i	$0.231174\pi$
$312$		0			0
$313$	73.3616	−	127.066i	0.234382	−	0.405962i	−0.724711	−	0.689053i	$-0.758027\pi$
$313$	73.3616	−	127.066i	0.234382	−	0.405962i	0.959093	+	0.283092i	$0.0913600\pi$
$314$			353.140i			1.12465i
$315$		0			0
$316$	93.4923			0.295862
$317$	41.6908	+	24.0702i	0.131517	+	0.0759311i	0.564315	−	0.825560i	$-0.309140\pi$
$317$	41.6908	+	24.0702i	0.131517	+	0.0759311i	−0.432798	+	0.901491i	$0.642474\pi$
$318$		0			0
$319$	−206.827	−	358.235i	−0.648360	−	1.12299i
$320$	−10.7589	+	6.21166i	−0.0336216	+	0.0194114i
$321$		0			0
$322$	−128.785	+	223.061i	−0.399952	+	0.692738i
$323$			104.543i			0.323662i
$324$		0			0
$325$	−244.042			−0.750899
$326$	15.6579	+	9.04008i	0.0480303	+	0.0277303i
$327$		0			0
$328$	35.5692	+	61.6077i	0.108443	+	0.187828i
$329$	182.129	−	105.152i	0.553583	−	0.319612i
$330$		0			0
$331$	49.7269	−	86.1295i	0.150232	−	0.260210i	−0.781080	−	0.624430i	$-0.785331\pi$
$331$	49.7269	−	86.1295i	0.150232	−	0.260210i	0.931313	+	0.364220i	$0.118665\pi$
$332$			30.6123i			0.0922057i
$333$		0			0
$334$	328.708			0.984155
$335$	55.3773	+	31.9721i	0.165305	+	0.0954391i
$336$		0			0
$337$	212.631	+	368.287i	0.630952	+	1.09284i	0.987358	+	0.158509i	$0.0506687\pi$
$337$	212.631	+	368.287i	0.630952	+	1.09284i	−0.356406	+	0.934331i	$0.615998\pi$
$338$	−64.0258	+	36.9653i	−0.189426	+	0.109365i
$339$		0			0
$340$	−45.0000	+	77.9423i	−0.132353	+	0.229242i
$341$			117.576i			0.344796i
$342$		0			0
$343$	688.631			2.00767
$344$	−130.256	−	75.2035i	−0.378652	−	0.218615i
$345$		0			0
$346$	−15.2365	−	26.3904i	−0.0440362	−	0.0762729i
$347$	−33.5768	+	19.3856i	−0.0967630	+	0.0558662i	−0.547601	−	0.836740i	$-0.684459\pi$
$347$	−33.5768	+	19.3856i	−0.0967630	+	0.0558662i	0.450838	+	0.892606i	$0.351125\pi$
$348$		0			0
$349$	325.985	−	564.622i	0.934053	−	1.61783i	0.157739	−	0.987481i	$-0.449579\pi$
$349$	325.985	−	564.622i	0.934053	−	1.61783i	0.776314	−	0.630347i	$-0.217087\pi$
$350$			395.871i			1.13106i
$351$		0			0
$352$	−83.1384			−0.236189
$353$	1.03625	+	0.598281i	0.00293556	+	0.00169485i	0.501467	−	0.865177i	$-0.332794\pi$
$353$	1.03625	+	0.598281i	0.00293556	+	0.00169485i	−0.498532	+	0.866872i	$0.666127\pi$
$354$		0			0
$355$	−12.7039	−	22.0038i	−0.0357856	−	0.0619825i
$356$	−136.790	+	78.9756i	−0.384241	+	0.221842i
$357$		0			0
$358$	196.392	−	340.161i	0.548582	−	0.950172i
$359$		−	534.573i		−	1.48906i	−0.667589	−	0.744530i	$-0.732674\pi$
$359$		−	534.573i		−	1.48906i	0.667589	−	0.744530i	$-0.267326\pi$
$360$		0			0
$361$	−347.985			−0.963946
$362$	−213.445	−	123.232i	−0.589626	−	0.340421i
$363$		0			0
$364$	−133.885	−	231.895i	−0.367815	−	0.637074i
$365$	96.2767	−	55.5854i	0.263772	−	0.152289i
$366$		0			0
$367$	−132.354	+	229.244i	−0.360637	+	0.624642i	−0.988066	−	0.154032i	$-0.950774\pi$
$367$	−132.354	+	229.244i	−0.360637	+	0.624642i	0.627429	+	0.778674i	$0.284107\pi$
$368$		−	58.7878i		−	0.159749i
$369$		0			0
$370$	−49.5654			−0.133961
$371$	907.376	+	523.874i	2.44576	+	1.41206i
$372$		0			0
$373$	−35.5077	−	61.5012i	−0.0951950	−	0.164883i	0.814495	−	0.580171i	$-0.197014\pi$
$373$	−35.5077	−	61.5012i	−0.0951950	−	0.164883i	−0.909690	+	0.415288i	$0.863681\pi$
$374$	−521.600	+	301.146i	−1.39465	+	0.805203i
$375$		0			0
$376$	−24.0000	+	41.5692i	−0.0638298	+	0.110556i
$377$			304.080i			0.806579i
$378$		0			0
$379$	−696.785			−1.83848			−0.919241	−	0.393696i	$-0.871196\pi$
$379$	−696.785			−1.83848			−0.919241	+	0.393696i	$0.871196\pi$
$380$	9.70371	+	5.60244i	0.0255361	+	0.0147433i
$381$		0			0
$382$	−107.569	−	186.315i	−0.281595	−	0.487737i
$383$	376.986	−	217.653i	0.984297	−	0.568284i	0.0807324	−	0.996736i	$-0.474274\pi$
$383$	376.986	−	217.653i	0.984297	−	0.568284i	0.903565	+	0.428452i	$0.140941\pi$
$384$		0			0
$385$	141.415	−	244.939i	0.367313	−	0.636204i
$386$		−	77.7817i		−	0.201507i
$387$		0			0
$388$	−182.277			−0.469786
$389$	45.9374	+	26.5220i	0.118091	+	0.0681799i	0.557882	−	0.829920i	$-0.311614\pi$
$389$	45.9374	+	26.5220i	0.118091	+	0.0681799i	−0.439791	+	0.898100i	$0.644947\pi$
$390$		0			0
$391$	−212.942	−	368.827i	−0.544609	−	0.943291i
$392$	−256.141	+	147.883i	−0.653422	+	0.377253i
$393$		0			0
$394$	94.2558	−	163.256i	0.239228	−	0.414355i
$395$		−	72.5927i		−	0.183779i
$396$		0			0
$397$	63.7077			0.160473			0.0802363	−	0.996776i	$-0.474432\pi$
$397$	63.7077			0.160473			0.0802363	+	0.996776i	$0.474432\pi$
$398$	255.802	+	147.687i	0.642719	+	0.371074i
$399$		0			0
$400$	−45.1769	−	78.2487i	−0.112942	−	0.195622i
$401$	−544.463	+	314.346i	−1.35776	+	0.783904i	−0.989322	−	0.145747i	$-0.953441\pi$
$401$	−544.463	+	314.346i	−1.35776	+	0.783904i	−0.368440	+	0.929651i	$0.620108\pi$
$402$		0			0
$403$	43.2154	−	74.8513i	0.107234	−	0.185735i
$404$			176.972i			0.438051i
$405$		0			0
$406$	493.261			1.21493
$407$	−287.259	−	165.849i	−0.705797	−	0.407492i
$408$		0			0
$409$	−267.640	−	463.567i	−0.654377	−	1.13341i	−0.982050	−	0.188623i	$-0.939597\pi$
$409$	−267.640	−	463.567i	−0.654377	−	1.13341i	0.327672	−	0.944791i	$-0.393736\pi$
$410$	47.8357	−	27.6180i	0.116673	−	0.0673609i
$411$		0			0
$412$	−152.708	+	264.497i	−0.370650	+	0.641984i
$413$		−	1128.50i		−	2.73244i
$414$		0			0
$415$	23.7691			0.0572750
$416$	52.9278	+	30.5579i	0.127230	+	0.0734565i
$417$		0			0
$418$	37.4923	+	64.9385i	0.0896944	+	0.155355i
$419$	333.705	−	192.665i	0.796433	−	0.459821i	−0.0457895	−	0.998951i	$-0.514580\pi$
$419$	333.705	−	192.665i	0.796433	−	0.459821i	0.842222	+	0.539130i	$0.181247\pi$
$420$		0			0
$421$	377.660	−	654.126i	0.897054	−	1.55374i	0.0658113	−	0.997832i	$-0.479036\pi$
$421$	377.660	−	654.126i	0.897054	−	1.55374i	0.831242	−	0.555910i	$-0.187630\pi$
$422$		−	123.678i		−	0.293077i
$423$		0			0
$424$	−239.138			−0.564006
$425$	−566.868	−	327.282i	−1.33381	−	0.770074i
$426$		0			0
$427$	80.5500	+	139.517i	0.188642	+	0.326737i
$428$	103.934	−	60.0062i	0.242836	−	0.140201i
$429$		0			0
$430$	−58.3923	+	101.138i	−0.135796	+	0.235206i
$431$		−	107.709i		−	0.249904i	−0.992163	−	0.124952i	$-0.960122\pi$
$431$		−	107.709i		−	0.249904i	0.992163	−	0.124952i	$-0.0398777\pi$
$432$		0			0
$433$	655.123			1.51299			0.756493	−	0.654002i	$-0.226911\pi$
$433$	655.123			1.51299			0.756493	+	0.654002i	$0.226911\pi$
$434$	−121.419	−	70.1015i	−0.279768	−	0.161524i
$435$		0			0
$436$	−93.9423	−	162.713i	−0.215464	−	0.373195i
$437$	−45.9185	+	26.5110i	−0.105077	+	0.0606660i
$438$		0			0
$439$	236.000	−	408.764i	0.537585	−	0.931125i	−0.461448	−	0.887167i	$-0.652670\pi$
$439$	236.000	−	408.764i	0.537585	−	0.931125i	0.999033	−	0.0439580i	$-0.0139968\pi$
$440$			64.5534i			0.146712i
$441$		0			0
$442$	442.750			1.00170
$443$	728.516	+	420.609i	1.64451	+	0.949455i	0.979203	+	0.202881i	$0.0650304\pi$
$443$	728.516	+	420.609i	1.64451	+	0.949455i	0.665302	+	0.746575i	$0.268303\pi$
$444$		0			0
$445$	61.3212	+	106.211i	0.137800	+	0.238677i
$446$	272.619	−	157.396i	0.611253	−	0.352907i
$447$		0			0
$448$	49.5692	−	85.8564i	0.110646	−	0.191644i
$449$		−	382.751i		−	0.852453i	−0.904616	−	0.426227i	$-0.859843\pi$
$449$		−	382.751i		−	0.852453i	0.904616	−	0.426227i	$-0.140157\pi$
$450$		0			0
$451$	369.646			0.819615
$452$	153.456	+	88.5977i	0.339504	+	0.196013i
$453$		0			0
$454$	−212.354	−	367.808i	−0.467740	−	0.810149i
$455$	−180.056	+	103.956i	−0.395728	+	0.228474i
$456$		0			0
$457$	−161.852	+	280.336i	−0.354162	+	0.613426i	−0.986974	−	0.160879i	$-0.948567\pi$
$457$	−161.852	+	280.336i	−0.354162	+	0.613426i	0.632812	+	0.774305i	$0.281900\pi$
$458$			325.187i			0.710016i
$459$		0			0
$460$	−45.6462			−0.0992308
$461$	−555.582	−	320.765i	−1.20517	−	0.695803i	−0.243467	−	0.969909i	$-0.578285\pi$
$461$	−555.582	−	320.765i	−1.20517	−	0.695803i	−0.961700	+	0.274106i	$0.911618\pi$
$462$		0			0
$463$	−64.7461	−	112.144i	−0.139840	−	0.242211i	0.787596	−	0.616192i	$-0.211326\pi$
$463$	−64.7461	−	112.144i	−0.139840	−	0.242211i	−0.927436	+	0.373982i	$0.877992\pi$
$464$	−97.4991	+	56.2911i	−0.210127	+	0.121317i
$465$		0			0
$466$	−82.1980	+	142.371i	−0.176391	+	0.305518i
$467$			672.730i			1.44054i	0.693696	+	0.720268i	$0.255981\pi$
$467$			672.730i			1.44054i	−0.693696	+	0.720268i	$0.744019\pi$
$468$		0			0
$469$	−510.277			−1.08801
$470$	32.2767	+	18.6350i	0.0686739	+	0.0396489i
$471$		0			0
$472$	128.785	+	223.061i	0.272849	+	0.472588i
$473$	−676.832	+	390.769i	−1.43093	+	0.826150i
$474$		0			0
$475$	−40.7461	+	70.5744i	−0.0857813	+	0.148578i
$476$		−	718.203i		−	1.50883i
$477$		0			0
$478$	−232.477			−0.486353
$479$	−108.786	−	62.8074i	−0.227110	−	0.131122i	0.382128	−	0.924109i	$-0.375191\pi$
$479$	−108.786	−	62.8074i	−0.227110	−	0.131122i	−0.609238	+	0.792987i	$0.708525\pi$
$480$		0			0
$481$	121.917	+	211.167i	0.253466	+	0.439016i
$482$	−99.5859	+	57.4960i	−0.206610	+	0.119286i
$483$		0			0
$484$	−95.0000	+	164.545i	−0.196281	+	0.339969i
$485$			141.530i			0.291815i
$486$		0			0
$487$	−448.631			−0.921213			−0.460606	−	0.887604i	$-0.652368\pi$
$487$	−448.631			−0.921213			−0.460606	+	0.887604i	$0.652368\pi$
$488$	−31.8434	−	18.3848i	−0.0652528	−	0.0376737i
$489$		0			0
$490$	114.825	+	198.883i	0.234337	+	0.405883i
$491$	391.579	−	226.078i	0.797514	−	0.460445i	−0.0450873	−	0.998983i	$-0.514357\pi$
$491$	391.579	−	226.078i	0.797514	−	0.460445i	0.842601	+	0.538538i	$0.181023\pi$
$492$		0			0
$493$	−407.798	+	706.327i	−0.827176	+	1.43271i
$494$		−	55.1218i		−	0.111583i
$495$		0			0
$496$	32.0000			0.0645161
$497$	175.591	+	101.377i	0.353301	+	0.203979i
$498$		0			0
$499$	−63.2961	−	109.632i	−0.126846	−	0.219704i	0.795607	−	0.605813i	$-0.207152\pi$
$499$	−63.2961	−	109.632i	−0.126846	−	0.219704i	−0.922453	+	0.386109i	$0.873819\pi$
$500$	−128.000	+	73.9008i	−0.256000	+	0.147802i
$501$		0			0
$502$	280.277	−	485.454i	0.558320	−	0.967039i
$503$		−	296.822i		−	0.590103i	−0.955481	−	0.295051i	$-0.904663\pi$
$503$		−	296.822i		−	0.590103i	0.955481	−	0.295051i	$-0.0953367\pi$
$504$		0			0
$505$	137.412			0.272102
$506$	−264.545	−	152.735i	−0.522816	−	0.301848i
$507$		0			0
$508$	78.8231	+	136.526i	0.155164	+	0.268751i
$509$	567.113	−	327.423i	1.11417	−	0.643267i	0.174265	−	0.984699i	$-0.444245\pi$
$509$	567.113	−	327.423i	1.11417	−	0.643267i	0.939907	+	0.341432i	$0.110912\pi$
$510$		0			0
$511$	−443.573	+	768.291i	−0.868049	+	1.50350i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−304.004			−0.591447
$515$	205.371	+	118.571i	0.398778	+	0.230235i
$516$		0			0
$517$	124.708	+	216.000i	0.241214	+	0.417795i
$518$	342.542	−	197.767i	0.661279	−	0.381789i
$519$		0			0
$520$	23.7269	−	41.0962i	0.0456286	−	0.0790311i
$521$			690.006i			1.32439i	0.749333	+	0.662193i	$0.230374\pi$
$521$			690.006i			1.32439i	−0.749333	+	0.662193i	$0.769626\pi$
$522$		0			0
$523$	616.238			1.17828			0.589138	−	0.808032i	$-0.299467\pi$
$523$	616.238			1.17828			0.589138	+	0.808032i	$0.299467\pi$
$524$	143.031	+	82.5792i	0.272961	+	0.157594i
$525$		0			0
$526$	224.785	+	389.338i	0.427347	+	0.740187i
$527$	200.764	−	115.911i	0.380956	−	0.219945i
$528$		0			0
$529$	−156.500	+	271.066i	−0.295841	+	0.512412i
$530$			185.681i			0.350341i
$531$		0			0
$532$	−89.4153			−0.168074
$533$	−235.325	−	135.865i	−0.441511	−	0.254906i
$534$		0			0
$535$	−46.5922	−	80.7001i	−0.0870883	−	0.150841i
$536$	100.862	−	58.2330i	0.188176	−	0.108644i
$537$		0			0
$538$	147.452	−	255.394i	0.274074	−	0.474710i
$539$			1536.85i			2.85129i
$540$		0			0
$541$	−548.734			−1.01430			−0.507148	−	0.861859i	$-0.669300\pi$
$541$	−548.734			−1.01430			−0.507148	+	0.861859i	$0.669300\pi$
$542$	−502.004	−	289.832i	−0.926207	−	0.534746i
$543$		0			0
$544$	81.9615	+	141.962i	0.150665	+	0.260959i
$545$	−126.340	+	72.9422i	−0.231816	+	0.133839i
$546$		0			0
$547$	409.885	−	709.941i	0.749332	−	1.29788i	−0.198811	−	0.980038i	$-0.563708\pi$
$547$	409.885	−	709.941i	0.749332	−	1.29788i	0.948143	−	0.317843i	$-0.102959\pi$
$548$			429.480i			0.783723i
$549$		0			0
$550$	−469.492			−0.853622
$551$	87.9368	+	50.7703i	0.159595	+	0.0921421i
$552$		0			0
$553$	289.646	+	501.682i	0.523772	+	0.907201i
$554$	609.207	−	351.726i	1.09965	−	0.634884i
$555$		0			0
$556$	−60.7846	+	105.282i	−0.109325	+	0.189356i
$557$			125.808i			0.225867i	0.993603	+	0.112934i	$0.0360247\pi$
$557$			125.808i			0.225867i	−0.993603	+	0.112934i	$0.963975\pi$
$558$		0			0
$559$	574.515			1.02776
$560$	−66.6638	−	38.4884i	−0.119043	−	0.0687292i
$561$		0			0
$562$	152.217	+	263.648i	0.270849	+	0.469125i
$563$	−440.625	+	254.395i	−0.782638	+	0.451856i	−0.837365	−	0.546645i	$-0.815905\pi$
$563$	−440.625	+	254.395i	−0.782638	+	0.451856i	0.0547261	+	0.998501i	$0.482571\pi$
$564$		0			0
$565$	68.7923	−	119.152i	0.121756	−	0.210888i
$566$		−	419.608i		−	0.741357i
$567$		0			0
$568$	−46.2769			−0.0814734
$569$	−83.8832	−	48.4300i	−0.147422	−	0.0851143i	0.424474	−	0.905440i	$-0.360459\pi$
$569$	−83.8832	−	48.4300i	−0.147422	−	0.0851143i	−0.571897	+	0.820326i	$0.693792\pi$
$570$		0			0
$571$	227.100	+	393.349i	0.397723	+	0.688877i	0.993445	−	0.114314i	$-0.0364671\pi$
$571$	227.100	+	393.349i	0.397723	+	0.688877i	−0.595721	+	0.803191i	$0.703134\pi$
$572$	275.021	−	158.783i	0.480806	−	0.277594i
$573$		0			0
$574$	−220.392	+	381.731i	−0.383959	+	0.665036i
$575$		−	331.981i		−	0.577359i
$576$		0			0
$577$	−39.1230			−0.0678041			−0.0339021	−	0.999425i	$-0.510793\pi$
$577$	−39.1230			−0.0678041			−0.0339021	+	0.999425i	$0.510793\pi$
$578$	674.481	+	389.412i	1.16692	+	0.673723i
$579$		0			0
$580$	43.7077	+	75.7039i	0.0753580	+	0.130524i
$581$	−164.266	+	94.8393i	−0.282731	+	0.163235i
$582$		0			0
$583$	−621.300	+	1076.12i	−1.06569	+	1.84584i
$584$		−	202.483i		−	0.346717i
$585$		0			0
$586$	482.196			0.822860
$587$	−363.061	−	209.614i	−0.618503	−	0.357093i	0.157783	−	0.987474i	$-0.449565\pi$
$587$	−363.061	−	209.614i	−0.618503	−	0.357093i	−0.776286	+	0.630381i	$0.782899\pi$
$588$		0			0
$589$	−14.4308	−	24.9948i	−0.0245005	−	0.0424361i
$590$	173.198	−	99.9957i	0.293555	−	0.169484i
$591$		0			0
$592$	−45.1384	+	78.1821i	−0.0762474	+	0.132064i
$593$			329.210i			0.555160i	0.960703	+	0.277580i	$0.0895323\pi$
$593$			329.210i			0.555160i	−0.960703	+	0.277580i	$0.910468\pi$
$594$		0			0
$595$	−557.654			−0.937233
$596$	53.0738	+	30.6422i	0.0890500	+	0.0514131i
$597$		0			0
$598$	112.277	+	194.469i	0.187754	+	0.325199i
$599$	−159.556	+	92.1197i	−0.266371	+	0.153789i	−0.627237	−	0.778828i	$-0.715814\pi$
$599$	−159.556	+	92.1197i	−0.266371	+	0.153789i	0.360867	+	0.932617i	$0.382481\pi$
$600$		0			0
$601$	−109.208	+	189.153i	−0.181710	+	0.314731i	−0.942463	−	0.334311i	$-0.891497\pi$
$601$	−109.208	+	189.153i	−0.181710	+	0.314731i	0.760753	+	0.649041i	$0.224830\pi$
$602$		−	931.945i		−	1.54808i
$603$		0			0
$604$	−64.0000			−0.105960
$605$	127.762	+	73.7634i	0.211177	+	0.121923i
$606$		0			0
$607$	−5.13467	−	8.89350i	−0.00845909	−	0.0146516i	0.861765	−	0.507308i	$-0.169359\pi$
$607$	−5.13467	−	8.89350i	−0.00845909	−	0.0146516i	−0.870224	+	0.492656i	$0.836026\pi$
$608$	17.6740	−	10.2041i	0.0290691	−	0.0167831i
$609$		0			0
$610$	−14.2750	+	24.7250i	−0.0234016	+	0.0405328i
$611$		−	183.347i		−	0.300078i
$612$		0			0
$613$	−180.585			−0.294592			−0.147296	−	0.989092i	$-0.547057\pi$
$613$	−180.585			−0.294592			−0.147296	+	0.989092i	$0.547057\pi$
$614$	140.054	+	80.8604i	0.228101	+	0.131694i
$615$		0			0
$616$	−257.569	−	446.123i	−0.418132	−	0.724226i
$617$	−784.800	+	453.104i	−1.27196	+	0.734367i	−0.975357	−	0.220633i	$-0.929188\pi$
$617$	−784.800	+	453.104i	−1.27196	+	0.734367i	−0.296604	+	0.955000i	$0.595854\pi$
$618$		0			0
$619$	−380.823	+	659.605i	−0.615223	+	1.06560i	0.375122	+	0.926975i	$0.377601\pi$
$619$	−380.823	+	659.605i	−0.615223	+	1.06560i	−0.990345	+	0.138622i	$0.955733\pi$
$620$		−	24.8466i		−	0.0400752i
$621$		0			0
$622$	−277.492			−0.446129
$623$	−847.571	−	489.345i	−1.36047	−	0.785466i
$624$		0			0
$625$	−224.975	−	389.668i	−0.359960	−	0.623469i
$626$	−179.698	+	103.749i	−0.287058	+	0.165733i
$627$		0			0
$628$	249.708	−	432.506i	0.397624	−	0.688704i
$629$			654.006i			1.03975i
$630$		0			0
$631$	601.108			0.952627			0.476313	−	0.879276i	$-0.341973\pi$
$631$	601.108			0.952627			0.476313	+	0.879276i	$0.341973\pi$
$632$	−114.504	−	66.1090i	−0.181177	−	0.104603i
$633$		0			0
$634$	−34.0404	−	58.9596i	−0.0536914	−	0.0929963i
$635$	106.006	−	61.2027i	0.166939	−	0.0963823i
$636$		0			0
$637$	564.875	−	978.392i	0.886774	−	1.53594i
$638$			584.995i			0.916920i
$639$		0			0
$640$	17.5692			0.0274519
$641$	500.089	+	288.727i	0.780170	+	0.450431i	0.836491	−	0.547981i	$-0.184604\pi$
$641$	500.089	+	288.727i	0.780170	+	0.450431i	−0.0563204	+	0.998413i	$0.517937\pi$
$642$		0			0
$643$	−65.0615	−	112.690i	−0.101184	−	0.175256i	0.810989	−	0.585062i	$-0.198930\pi$
$643$	−65.0615	−	112.690i	−0.101184	−	0.175256i	−0.912173	+	0.409806i	$0.865597\pi$
$644$	315.457	−	182.129i	0.489839	−	0.282809i
$645$		0			0
$646$	73.9230	−	128.038i	0.114432	−	0.198202i
$647$		−	985.467i		−	1.52313i	−0.648087	−	0.761567i	$-0.724430\pi$
$647$		−	985.467i		−	1.52313i	0.648087	−	0.761567i	$-0.275570\pi$
$648$		0			0
$649$	1338.37			2.06220
$650$	298.889	+	172.564i	0.459830	+	0.265483i
$651$		0			0
$652$	−12.7846	−	22.1436i	−0.0196083	−	0.0339626i
$653$	519.895	−	300.161i	0.796163	−	0.459665i	−0.0459644	−	0.998943i	$-0.514636\pi$
$653$	519.895	−	300.161i	0.796163	−	0.459665i	0.842128	+	0.539278i	$0.181303\pi$
$654$		0			0
$655$	64.1192	−	111.058i	0.0978919	−	0.169554i
$656$		−	100.605i		−	0.153361i
$657$		0			0
$658$	−297.415			−0.451999
$659$	−13.5004	−	7.79445i	−0.0204862	−	0.0118277i	0.489722	−	0.871879i	$-0.337098\pi$
$659$	−13.5004	−	7.79445i	−0.0204862	−	0.0118277i	−0.510208	+	0.860051i	$0.670432\pi$
$660$		0			0
$661$	−203.915	−	353.192i	−0.308495	−	0.534329i	0.669538	−	0.742778i	$-0.266492\pi$
$661$	−203.915	−	353.192i	−0.308495	−	0.534329i	−0.978033	+	0.208448i	$0.933159\pi$
$662$	−121.806	+	70.3245i	−0.183996	+	0.106230i
$663$		0			0
$664$	21.6462	−	37.4923i	0.0325997	−	0.0564643i
$665$			69.4272i			0.104402i
$666$		0			0
$667$	−413.654			−0.620170
$668$	−402.583	−	232.431i	−0.602669	−	0.347951i
$669$		0			0
$670$	−45.2154	−	78.3154i	−0.0674857	−	0.116889i
$671$	−165.463	+	95.5301i	−0.246592	+	0.142370i
$672$		0			0
$673$	237.285	−	410.989i	0.352577	−	0.610682i	−0.634123	−	0.773232i	$-0.718639\pi$
$673$	237.285	−	410.989i	0.352577	−	0.610682i	0.986700	+	0.162550i	$0.0519720\pi$
$674$		−	601.410i		−	0.892300i
$675$		0			0
$676$	104.554			0.154665
$677$	244.346	+	141.073i	0.360925	+	0.208380i	0.669486	−	0.742824i	$-0.266514\pi$
$677$	244.346	+	141.073i	0.360925	+	0.208380i	−0.308562	+	0.951204i	$0.599848\pi$
$678$		0			0
$679$	−564.708	−	978.102i	−0.831675	−	1.44050i
$680$	110.227	−	63.6396i	0.162099	−	0.0935877i
$681$		0			0
$682$	83.1384	−	144.000i	0.121904	−	0.211144i
$683$		−	1085.46i		−	1.58926i	−0.607095	−	0.794629i	$-0.707665\pi$
$683$		−	1085.46i		−	1.58926i	0.607095	−	0.794629i	$-0.292335\pi$
$684$		0			0
$685$	333.473			0.486822
$686$	−843.397	−	486.935i	−1.22944	−	0.709818i
$687$		0			0
$688$	106.354	+	184.210i	0.154584	+	0.267747i
$689$	791.067	−	456.723i	1.14814	−	0.662878i
$690$		0			0
$691$	503.888	−	872.760i	0.729216	−	1.26304i	−0.227999	−	0.973661i	$-0.573218\pi$
$691$	503.888	−	872.760i	0.729216	−	1.26304i	0.957215	−	0.289378i	$-0.0934484\pi$
$692$			43.0954i			0.0622765i
$693$		0			0
$694$	54.8306			0.0790067
$695$	81.7470	+	47.1966i	0.117622	+	0.0679088i
$696$		0			0
$697$	−364.413	−	631.183i	−0.522831	−	0.905570i
$698$	−798.496	+	461.012i	−1.14398	+	0.660475i
$699$		0			0
$700$	279.923	−	484.841i	0.399890	−	0.692630i
$701$		−	216.731i		−	0.309174i	−0.987979	−	0.154587i	$-0.950595\pi$
$701$		−	216.731i		−	0.309174i	0.987979	−	0.154587i	$-0.0494047\pi$
$702$		0			0
$703$	81.4229			0.115822
$704$	101.823	+	58.7878i	0.144635	+	0.0835053i
$705$		0			0
$706$	−0.846097	−	1.46548i	−0.00119844	−	0.00207575i
$707$	−949.639	+	548.274i	−1.34319	+	0.775494i
$708$		0			0
$709$	−497.248	+	861.259i	−0.701337	+	1.21475i	0.266660	+	0.963791i	$0.414080\pi$
$709$	−497.248	+	861.259i	−0.701337	+	1.21475i	−0.967997	+	0.250961i	$0.919253\pi$
$710$			35.9320i			0.0506085i
$711$		0			0
$712$	223.377			0.313732
$713$	101.823	+	58.7878i	0.142810	+	0.0824513i
$714$		0			0
$715$	−123.289	−	213.542i	−0.172432	−	0.298660i
$716$	−481.061	+	277.741i	−0.671873	+	0.387906i
$717$		0			0
$718$	−378.000	+	654.715i	−0.526462	+	0.911860i
$719$			340.912i			0.474148i	0.971492	+	0.237074i	$0.0761884\pi$
$719$			340.912i			0.474148i	−0.971492	+	0.237074i	$0.923812\pi$
$720$		0			0
$721$	−1892.40			−2.62469
$722$	426.192	+	246.062i	0.590294	+	0.340806i
$723$		0			0
$724$	174.277	+	301.856i	0.240714	+	0.416929i
$725$	−550.589	+	317.883i	−0.759433	+	0.438459i
$726$		0			0
$727$	485.888	−	841.583i	0.668347	−	1.15761i	−0.310019	−	0.950730i	$-0.600335\pi$
$727$	485.888	−	841.583i	0.668347	−	1.15761i	0.978366	−	0.206881i	$-0.0663312\pi$
$728$			378.683i			0.520169i
$729$		0			0
$730$	−157.219			−0.215369
$731$	1334.50	+	770.474i	1.82558	+	1.05400i
$732$		0			0
$733$	−114.585	−	198.466i	−0.156323	−	0.270759i	0.777217	−	0.629233i	$-0.216631\pi$
$733$	−114.585	−	198.466i	−0.156323	−	0.270759i	−0.933540	+	0.358473i	$0.883297\pi$
$734$	324.199	−	187.177i	0.441688	−	0.255009i
$735$		0			0
$736$	−41.5692	+	72.0000i	−0.0564799	+	0.0978261i
$737$		−	605.175i		−	0.821132i
$738$		0			0
$739$	−629.892			−0.852357			−0.426179	−	0.904639i	$-0.640141\pi$
$739$	−629.892			−0.852357			−0.426179	+	0.904639i	$0.640141\pi$
$740$	60.7050	+	35.0481i	0.0820338	+	0.0473622i
$741$		0			0
$742$	−740.869	−	1283.22i	−0.998476	−	1.72941i
$743$	162.825	−	94.0071i	0.219145	−	0.126524i	−0.386409	−	0.922327i	$-0.626285\pi$
$743$	162.825	−	94.0071i	0.219145	−	0.126524i	0.605554	+	0.795804i	$0.292951\pi$
$744$		0			0
$745$	23.7923	−	41.2095i	0.0319360	−	0.0553148i
$746$			100.431i			0.134626i
$747$		0			0
$748$	851.769			1.13873
$749$	643.989	+	371.807i	0.859799	+	0.496405i
$750$		0			0
$751$	693.335	+	1200.89i	0.923215	+	1.59906i	0.794407	+	0.607386i	$0.207782\pi$
$751$	693.335	+	1200.89i	0.923215	+	1.59906i	0.128808	+	0.991670i	$0.458885\pi$
$752$	58.7878	−	33.9411i	0.0781752	−	0.0451345i
$753$		0			0
$754$	215.017	−	372.421i	0.285169	−	0.493927i
$755$			49.6933i			0.0658189i
$756$		0			0
$757$	1222.12			1.61443			0.807215	−	0.590258i	$-0.200974\pi$
$757$	1222.12			1.61443			0.807215	+	0.590258i	$0.200974\pi$
$758$	853.383	+	492.701i	1.12584	+	0.650001i
$759$		0			0
$760$	−7.92305	−	13.7231i	−0.0104251	−	0.0180567i
$761$	489.896	−	282.841i	0.643752	−	0.371671i	−0.142306	−	0.989823i	$-0.545452\pi$
$761$	489.896	−	282.841i	0.643752	−	0.371671i	0.786059	+	0.618152i	$0.212118\pi$
$762$		0			0
$763$	582.081	−	1008.19i	0.762884	−	1.32135i
$764$			304.252i			0.398235i
$765$		0			0
$766$	−615.615			−0.803675
$767$	−852.036	−	491.923i	−1.11087	−	0.641360i
$768$		0			0
$769$	299.408	+	518.589i	0.389347	+	0.674368i	0.992362	−	0.123362i	$-0.0393675\pi$
$769$	299.408	+	518.589i	0.389347	+	0.674368i	−0.603015	+	0.797730i	$0.706034\pi$
$770$	−346.395	+	199.991i	−0.449864	+	0.259729i
$771$		0			0
$772$	−55.0000	+	95.2628i	−0.0712435	+	0.123397i
$773$		−	446.970i		−	0.578228i	−0.957295	−	0.289114i	$-0.906639\pi$
$773$		−	446.970i		−	0.578228i	0.957295	−	0.289114i	$-0.0933607\pi$
$774$		0			0
$775$	180.708			0.233171
$776$	223.243	+	128.889i	0.287684	+	0.166094i
$777$		0			0
$778$	−37.5077	−	64.9653i	−0.0482105	−	0.0835030i
$779$	−78.5814	+	45.3690i	−0.100875	+	0.0582400i
$780$		0			0
$781$	−120.231	+	208.246i	−0.153945	+	0.266640i
$782$			602.292i			0.770194i
$783$		0			0
$784$	418.277			0.533516
$785$	−335.823	−	193.887i	−0.427800	−	0.246990i
$786$		0			0
$787$	477.650	+	827.314i	0.606925	+	1.05122i	0.991744	+	0.128233i	$0.0409305\pi$
$787$	477.650	+	827.314i	0.606925	+	1.05122i	−0.384819	+	0.922992i	$0.625736\pi$
$788$	−230.878	+	133.298i	−0.292993	+	0.169160i
$789$		0			0
$790$	−51.3308	+	88.9076i	−0.0649757	+	0.112541i
$791$			1097.93i			1.38803i
$792$		0			0
$793$	140.450			0.177112
$794$	−78.0256	−	45.0481i	−0.0982691	−	0.0567357i
$795$		0			0
$796$	−208.862	−	361.759i	−0.262389	−	0.454471i
$797$	−192.141	+	110.933i	−0.241081	+	0.139188i	−0.615673	−	0.788002i	$-0.711116\pi$
$797$	−192.141	+	110.933i	−0.241081	+	0.139188i	0.374593	+	0.927189i	$0.377783\pi$
$798$		0			0
$799$	245.885	−	425.885i	0.307740	−	0.533022i
$800$			127.780i			0.159725i
$801$		0			0
$802$	889.104			1.10861
$803$	−911.172	−	526.066i	−1.13471	−	0.655125i
$804$		0			0
$805$	−141.415	−	244.939i	−0.175671	−	0.304271i
$806$	−105.856	+	61.1158i	−0.131335	+	0.0758260i
$807$		0			0
$808$	125.138	−	216.746i	0.154874	−	0.268250i
$809$		−	1180.17i		−	1.45881i	−0.684084	−	0.729403i	$-0.739798\pi$
$809$		−	1180.17i		−	1.45881i	0.684084	−	0.729403i	$-0.260202\pi$
$810$		0			0
$811$	−627.307			−0.773499			−0.386749	−	0.922185i	$-0.626402\pi$
$811$	−627.307			−0.773499			−0.386749	+	0.922185i	$0.626402\pi$
$812$	−604.119	−	348.788i	−0.743989	−	0.429542i
$813$		0			0
$814$	234.546	+	406.246i	0.288140	+	0.499074i
$815$	−17.1936	+	9.92670i	−0.0210964	+	0.0121800i
$816$		0			0
$817$	95.9230	−	166.144i	0.117409	−	0.203358i
$818$			757.001i			0.925429i
$819$		0			0
$820$	−78.1154			−0.0952627
$821$	338.512	+	195.440i	0.412317	+	0.238051i	0.691785	−	0.722104i	$-0.256825\pi$
$821$	338.512	+	195.440i	0.412317	+	0.238051i	−0.279468	+	0.960155i	$0.590158\pi$
$822$		0			0
$823$	−163.100	−	282.497i	−0.198177	−	0.343253i	0.749760	−	0.661710i	$-0.230169\pi$
$823$	−163.100	−	282.497i	−0.198177	−	0.343253i	−0.947937	+	0.318456i	$0.896836\pi$
$824$	374.056	−	215.961i	0.453951	−	0.262089i
$825$		0			0
$826$	−797.969	+	1382.12i	−0.966064	+	1.67327i
$827$			1103.70i			1.33458i	0.744799	+	0.667289i	$0.232545\pi$
$827$			1103.70i			1.33458i	−0.744799	+	0.667289i	$0.767455\pi$
$828$		0			0
$829$	−441.569			−0.532653			−0.266326	−	0.963883i	$-0.585810\pi$
$829$	−441.569			−0.532653			−0.266326	+	0.963883i	$0.585810\pi$
$830$	−29.1111	−	16.8073i	−0.0350737	−	0.0202498i
$831$		0			0
$832$	−43.2154	−	74.8513i	−0.0519416	−	0.0899654i
$833$	2624.22	−	1515.09i	3.15032	−	1.81884i
$834$		0			0
$835$	−180.473	+	312.588i	−0.216135	+	0.374357i
$836$		−	106.044i		−	0.126847i
$837$		0			0
$838$	−544.939			−0.650285
$839$	436.443	+	251.980i	0.520194	+	0.300334i	0.737014	−	0.675878i	$-0.236235\pi$
$839$	436.443	+	251.980i	0.520194	+	0.300334i	−0.216820	+	0.976212i	$0.569569\pi$
$840$		0			0
$841$	−24.4134	−	42.2853i	−0.0290290	−	0.0502798i
$842$	−925.073	+	534.091i	−1.09866	+	0.634313i
$843$		0			0
$844$	−87.4538	+	151.474i	−0.103618	+	0.179472i
$845$		−	81.1815i		−	0.0960728i
$846$		0			0
$847$	−1177.27			−1.38993
$848$	292.884	+	169.096i	0.345382	+	0.199406i
$849$		0			0
$850$	462.846	+	801.673i	0.544525	+	0.943145i
$851$	−287.259	+	165.849i	−0.337555	+	0.194887i
$852$		0			0
$853$	−472.415	+	818.247i	−0.553828	+	0.959258i	0.444166	+	0.895945i	$0.353500\pi$
$853$	−472.415	+	818.247i	−0.553828	+	0.959258i	−0.997994	+	0.0633136i	$0.979833\pi$
$854$		−	227.830i		−	0.266780i
$855$		0			0
$856$	−169.723			−0.198275
$857$	642.051	+	370.689i	0.749185	+	0.432542i	0.825399	−	0.564549i	$-0.190950\pi$
$857$	642.051	+	370.689i	0.749185	+	0.432542i	−0.0762145	+	0.997091i	$0.524283\pi$
$858$		0			0
$859$	680.631	+	1178.89i	0.792352	+	1.37239i	0.924507	+	0.381165i	$0.124477\pi$
$859$	680.631	+	1178.89i	0.792352	+	1.37239i	−0.132154	+	0.991229i	$0.542189\pi$
$860$	143.031	−	82.5792i	0.166316	−	0.0960223i
$861$		0			0
$862$	−76.1615	+	131.916i	−0.0883544	+	0.153034i
$863$		−	805.003i		−	0.932796i	−0.884575	−	0.466398i	$-0.845551\pi$
$863$		−	805.003i		−	0.932796i	0.884575	−	0.466398i	$-0.154449\pi$
$864$		0			0
$865$	33.4617			0.0386841
$866$	−802.359	−	463.242i	−0.926511	−	0.534921i
$867$		0			0
$868$	99.1384	+	171.713i	0.114215	+	0.197826i
$869$	−594.981	+	343.513i	−0.684673	+	0.395296i
$870$		0			0
$871$	−222.435	+	385.268i	−0.255378	+	0.442328i
$872$			265.709i			0.304712i
$873$		0			0
$874$	74.9845			0.0857947
$875$	−793.107	−	457.901i	−0.906408	−	0.523315i
$876$		0			0
$877$	−21.3461	−	36.9725i	−0.0243399	−	0.0421580i	0.853599	−	0.520931i	$-0.174415\pi$
$877$	−21.3461	−	36.9725i	−0.0243399	−	0.0421580i	−0.877939	+	0.478773i	$0.841082\pi$
$878$	−578.080	+	333.754i	−0.658405	+	0.380130i
$879$		0			0
$880$	45.6462	−	79.0615i	0.0518706	−	0.0898426i
$881$		−	264.567i		−	0.300303i	−0.988663	−	0.150151i	$-0.952024\pi$
$881$		−	264.567i		−	0.300303i	0.988663	−	0.150151i	$-0.0479761\pi$
$882$		0			0
$883$	−393.338			−0.445457			−0.222728	−	0.974881i	$-0.571496\pi$
$883$	−393.338			−0.445457			−0.222728	+	0.974881i	$0.571496\pi$
$884$	−542.256	−	313.071i	−0.613411	−	0.354153i
$885$		0			0
$886$	−594.831	−	1030.28i	−0.671366	−	1.16284i
$887$	1340.65	−	774.026i	1.51145	−	0.872634i	0.511535	−	0.859262i	$-0.329077\pi$
$887$	1340.65	−	774.026i	1.51145	−	0.872634i	0.999911	−	0.0133715i	$-0.00425642\pi$
$888$		0			0
$889$	−488.400	+	845.933i	−0.549381	+	0.951556i
$890$		−	173.443i		−	0.194879i
$891$		0			0
$892$	−445.184			−0.499086
$893$	−53.0221	−	30.6123i	−0.0593752	−	0.0342803i
$894$		0			0
$895$	215.654	+	373.523i	0.240954	+	0.417344i
$896$	−121.419	+	70.1015i	−0.135513	+	0.0782382i
$897$		0			0
$898$	−270.646	+	468.773i	−0.301388	+	0.522019i
$899$		−	225.165i		−	0.250461i
$900$		0			0
$901$	2450.02			2.71922
$902$	−452.722	−	261.379i	−0.501909	−	0.289778i
$903$		0			0
$904$	−125.296	−	217.019i	−0.138602	−	0.240066i
$905$	234.379	−	135.319i	0.258982	−	0.149523i
$906$		0			0
$907$	−688.746	+	1192.94i	−0.759367	+	1.31526i	0.183806	+	0.982962i	$0.441158\pi$
$907$	−688.746	+	1192.94i	−0.759367	+	1.31526i	−0.943174	+	0.332300i	$0.892175\pi$
$908$			600.627i			0.661484i
$909$		0			0
$910$	294.031			0.323111
$911$	−1217.70	−	703.038i	−1.33666	−	0.771721i	−0.350350	−	0.936619i	$-0.613937\pi$
$911$	−1217.70	−	703.038i	−1.33666	−	0.771721i	−0.986311	+	0.164898i	$0.947271\pi$
$912$		0			0
$913$	−112.477	−	194.816i	−0.123195	−	0.213380i
$914$	396.455	−	228.893i	0.433758	−	0.250430i
$915$		0			0
$916$	229.942	−	398.272i	0.251029	−	0.434794i
$917$			1023.35i			1.11597i
$918$		0			0
$919$	479.992			0.522299			0.261149	−	0.965298i	$-0.415899\pi$
$919$	479.992			0.522299			0.261149	+	0.965298i	$0.415899\pi$
$920$	55.9049	+	32.2767i	0.0607662	+	0.0350834i
$921$		0			0
$922$	453.631	+	785.711i	0.492007	+	0.852182i
$923$	153.083	−	88.3827i	0.165854	−	0.0957560i
$924$		0			0
$925$	−254.902	+	441.503i	−0.275570	+	0.477301i
$926$			183.130i			0.197764i
$927$		0			0
$928$	159.215			0.171568
$929$	−587.800	−	339.366i	−0.632723	−	0.365303i	0.149083	−	0.988825i	$-0.452368\pi$
$929$	−587.800	−	339.366i	−0.632723	−	0.365303i	−0.781806	+	0.623522i	$0.785701\pi$
$930$		0			0
$931$	−188.627	−	326.711i	−0.202607	−	0.350925i
$932$	201.343	−	116.246i	0.216034	−	0.124727i
$933$		0			0
$934$	475.692	−	823.923i	0.509306	−	0.882145i
$935$		−	661.362i		−	0.707339i
$936$		0			0
$937$	−666.600			−0.711420			−0.355710	−	0.934596i	$-0.615761\pi$
$937$	−666.600			−0.711420			−0.355710	+	0.934596i	$0.615761\pi$
$938$	624.959	+	360.820i	0.666268	+	0.384670i
$939$		0			0
$940$	−26.3538	−	45.6462i	−0.0280360	−	0.0485598i
$941$	1037.46	−	598.978i	1.10251	−	0.636533i	0.165629	−	0.986188i	$-0.447034\pi$
$941$	1037.46	−	598.978i	1.10251	−	0.636533i	0.936879	+	0.349655i	$0.113701\pi$
$942$		0			0
$943$	184.823	−	320.123i	0.195995	−	0.339473i
$944$		−	364.258i		−	0.385866i
$945$		0			0
$946$	1105.26			1.16835
$947$	−393.793	−	227.357i	−0.415832	−	0.240081i	0.277460	−	0.960737i	$-0.410507\pi$
$947$	−393.793	−	227.357i	−0.415832	−	0.240081i	−0.693293	+	0.720656i	$0.743841\pi$
$948$		0			0
$949$	386.715	+	669.811i	0.407498	+	0.705807i
$950$	99.8072	−	57.6237i	0.105060	−	0.0606566i
$951$		0			0
$952$	−507.846	+	879.615i	−0.533452	+	0.923966i
$953$			1060.16i			1.11245i	0.831033	+	0.556224i	$0.187750\pi$
$953$			1060.16i			1.11245i	−0.831033	+	0.556224i	$0.812250\pi$
$954$		0			0
$955$	236.238			0.247370
$956$	284.725	+	164.386i	0.297829	+	0.171952i
$957$		0			0
$958$	88.8231	+	153.846i	0.0927172	+	0.160591i
$959$	−2304.60	+	1330.56i	−2.40313	+	1.38745i
$960$		0			0
$961$	448.500	−	776.825i	0.466701	−	0.808350i
$962$		−	344.834i		−	0.358455i
$963$		0			0
$964$	162.623			0.168696
$965$	73.9675	+	42.7051i	0.0766502	+	0.0442540i
$966$		0			0
$967$	827.657	+	1433.54i	0.855902	+	1.48247i	0.875805	+	0.482664i	$0.160331\pi$
$967$	827.657	+	1433.54i	0.855902	+	1.48247i	−0.0199032	+	0.999802i	$0.506336\pi$
$968$	232.702	−	134.350i	0.240394	−	0.138792i
$969$		0			0
$970$	100.077	−	173.338i	0.103172	−	0.178699i
$971$		−	797.780i		−	0.821606i	−0.911724	−	0.410803i	$-0.865248\pi$
$971$		−	797.780i		−	0.821606i	0.911724	−	0.410803i	$-0.134752\pi$
$972$		0			0
$973$	−753.261			−0.774164
$974$	549.458	+	317.230i	0.564125	+	0.325698i
$975$		0			0
$976$	26.0000	+	45.0333i	0.0266393	+	0.0461407i
$977$	−270.574	+	156.216i	−0.276944	+	0.159894i	−0.632039	−	0.774936i	$-0.717782\pi$
$977$	−270.574	+	156.216i	−0.276944	+	0.159894i	0.355095	+	0.934830i	$0.384448\pi$
$978$		0			0
$979$	580.350	−	1005.20i	0.592799	−	1.02676i
$980$		−	324.774i		−	0.331402i
$981$		0			0
$982$	−639.446			−0.651167
$983$	−320.553	−	185.072i	−0.326097	−	0.188272i	0.328010	−	0.944674i	$-0.393622\pi$
$983$	−320.553	−	185.072i	−0.326097	−	0.188272i	−0.654107	+	0.756402i	$0.726955\pi$
$984$		0			0
$985$	103.500	+	179.267i	0.105076	+	0.181997i
$986$	998.897	−	576.713i	1.01308	−	0.584902i
$987$		0			0
$988$	−38.9770	+	67.5101i	−0.0394504	+	0.0683301i
$989$			781.538i			0.790230i
$990$		0			0
$991$	−1324.48			−1.33651			−0.668256	−	0.743931i	$-0.732959\pi$
$991$	−1324.48			−1.33651			−0.668256	+	0.743931i	$0.732959\pi$
$992$	−39.1918	−	22.6274i	−0.0395079	−	0.0228099i
$993$		0			0
$994$	−143.369	−	248.323i	−0.144235	−	0.249822i
$995$	−280.890	+	162.172i	−0.282302	+	0.162987i
$996$		0			0
$997$	−439.623	+	761.449i	−0.440946	+	0.763741i	−0.997760	−	0.0668966i	$-0.978690\pi$
$997$	−439.623	+	761.449i	−0.440946	+	0.763741i	0.556814	+	0.830637i	$0.312024\pi$
$998$			179.028i			0.179387i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.d.c.107.2		8
3.2	odd	2	inner	162.3.d.c.107.3		8
4.3	odd	2		1296.3.q.o.593.3		8
9.2	odd	6		162.3.b.b.161.1	✓	4
9.4	even	3	inner	162.3.d.c.53.3		8
9.5	odd	6	inner	162.3.d.c.53.2		8
9.7	even	3		162.3.b.b.161.4	yes	4
12.11	even	2		1296.3.q.o.593.2		8
36.7	odd	6		1296.3.e.d.161.3		4
36.11	even	6		1296.3.e.d.161.2		4
36.23	even	6		1296.3.q.o.1025.3		8
36.31	odd	6		1296.3.q.o.1025.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.3.b.b.161.1	✓	4	9.2	odd	6
162.3.b.b.161.4	yes	4	9.7	even	3
162.3.d.c.53.2		8	9.5	odd	6	inner
162.3.d.c.53.3		8	9.4	even	3	inner
162.3.d.c.107.2		8	1.1	even	1	trivial
162.3.d.c.107.3		8	3.2	odd	2	inner
1296.3.e.d.161.2		4	36.11	even	6
1296.3.e.d.161.3		4	36.7	odd	6
1296.3.q.o.593.2		8	12.11	even	2
1296.3.q.o.593.3		8	4.3	odd	2
1296.3.q.o.1025.2		8	36.31	odd	6
1296.3.q.o.1025.3		8	36.23	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(1.34486 - 0.776457i) q^{5} +(-6.19615 + 10.7321i) q^{7} -2.82843i q^{8} -2.19615 q^{10} +(-12.7279 - 7.34847i) q^{11} +(5.40192 + 9.35641i) q^{13} +(15.1774 - 8.76268i) q^{14} +(-2.00000 + 3.46410i) q^{16} +28.9778i q^{17} +3.60770 q^{19} +(2.68973 + 1.55291i) q^{20} +(10.3923 + 18.0000i) q^{22} +(-12.7279 + 7.34847i) q^{23} +(-11.2942 + 19.5622i) q^{25} -15.2789i q^{26} -24.7846 q^{28} +(24.3748 + 14.0728i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(4.89898 - 2.82843i) q^{32} +(20.4904 - 35.4904i) q^{34} +19.2442i q^{35} +22.5692 q^{37} +(-4.41851 - 2.55103i) q^{38} +(-2.19615 - 3.80385i) q^{40} +(-21.7816 + 12.5756i) q^{41} +(26.5885 - 46.0526i) q^{43} -29.3939i q^{44} +20.7846 q^{46} +(-14.6969 - 8.48528i) q^{47} +(-52.2846 - 90.5596i) q^{49} +(27.6651 - 15.9725i) q^{50} +(-10.8038 + 18.7128i) q^{52} -84.5482i q^{53} -22.8231 q^{55} +(30.3548 + 17.5254i) q^{56} +(-19.9019 - 34.4711i) q^{58} +(-78.8641 + 45.5322i) q^{59} +(6.50000 - 11.2583i) q^{61} +11.3137i q^{62} -8.00000 q^{64} +(14.5297 + 8.38872i) q^{65} +(20.5885 + 35.6603i) q^{67} +(-50.1910 + 28.9778i) q^{68} +(13.6077 - 23.5692i) q^{70} -16.3613i q^{71} +71.5885 q^{73} +(-27.6415 - 15.9588i) q^{74} +(3.60770 + 6.24871i) q^{76} +(157.728 - 91.0645i) q^{77} +(23.3731 - 40.4833i) q^{79} +6.21166i q^{80} +35.5692 q^{82} +(13.2555 + 7.65308i) q^{83} +(22.5000 + 38.9711i) q^{85} +(-65.1282 + 37.6018i) q^{86} +(-20.7846 + 36.0000i) q^{88} +78.9756i q^{89} -133.885 q^{91} +(-25.4558 - 14.6969i) q^{92} +(12.0000 + 20.7846i) q^{94} +(4.85186 - 2.80122i) q^{95} +(-45.5692 + 78.9282i) q^{97} +147.883i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 8 q^{7} + 24 q^{10} + 64 q^{13} - 16 q^{16} + 112 q^{19} - 28 q^{25} - 32 q^{28} - 32 q^{31} + 60 q^{34} - 152 q^{37} + 24 q^{40} + 88 q^{43} - 252 q^{49} - 128 q^{52} - 432 q^{55} - 180 q^{58}+ \cdots - 32 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^7 + 24 * q^10 + 64 * q^13 - 16 * q^16 + 112 * q^19 - 28 * q^25 - 32 * q^28 - 32 * q^31 + 60 * q^34 - 152 * q^37 + 24 * q^40 + 88 * q^43 - 252 * q^49 - 128 * q^52 - 432 * q^55 - 180 * q^58 + 52 * q^61 - 64 * q^64 + 40 * q^67 + 192 * q^70 + 448 * q^73 + 112 * q^76 - 104 * q^79 - 48 * q^82 + 180 * q^85 + 176 * q^91 + 96 * q^94 - 32 * q^97

Introduction

L-functions

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Database

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