LMFDB - Embedded newform 1530.2.m.i.647.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1530,2,Mod(647,1530)] 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("1530.647"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1530, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.1573541673494879666176.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 2 x^{14} + 24 x^{13} + 2 x^{12} - 48 x^{11} + 88 x^{10} - 72 x^{9} + 18 x^{8} + \cdots + 1 $ x^16 - 4x^15 - 2x^14 + 24x^13 + 2x^12 - 48x^11 + 88x^10 - 72x^9 + 18x^8 - 20x^7 + 66x^6 + 84x^5 + 40x^4 + 24x^3 + 20x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.4
Root			$1.29693 + 0.537207i$ of defining polynomial
Character	$\chi$	$=$	1530.647
Dual form			1530.2.m.i.953.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.23580 + 0.0345211i) q^{5} +(0.796815 + 0.796815i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.60536 + 1.55654i) q^{10} -2.14883i q^{11} +(3.95872 - 3.95872i) q^{13} -1.12687 q^{14} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} -4.73017i q^{19} +(0.0345211 - 2.23580i) q^{20} +(1.51945 + 1.51945i) q^{22} +(-5.76432 - 5.76432i) q^{23} +(4.99762 + 0.154365i) q^{25} +5.59847i q^{26} +(0.796815 - 0.796815i) q^{28} +6.62043 q^{29} -1.21072 q^{31} +(0.707107 - 0.707107i) q^{32} -1.00000i q^{34} +(1.75401 + 1.80903i) q^{35} +(-8.37262 - 8.37262i) q^{37} +(3.34474 + 3.34474i) q^{38} +(1.55654 + 1.60536i) q^{40} +9.89612i q^{41} +(2.47817 - 2.47817i) q^{43} -2.14883 q^{44} +8.15198 q^{46} +(-8.42690 + 8.42690i) q^{47} -5.73017i q^{49} +(-3.64300 + 3.42470i) q^{50} +(-3.95872 - 3.95872i) q^{52} +(-0.461295 - 0.461295i) q^{53} +(0.0741799 - 4.80435i) q^{55} +1.12687i q^{56} +(-4.68135 + 4.68135i) q^{58} -4.07935 q^{59} +11.7456 q^{61} +(0.856109 - 0.856109i) q^{62} +1.00000i q^{64} +(8.98756 - 8.71424i) q^{65} +(2.22854 + 2.22854i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-2.51945 - 0.0389007i) q^{70} -3.51868i q^{71} +(-3.15436 + 3.15436i) q^{73} +11.8407 q^{74} -4.73017 q^{76} +(1.71222 - 1.71222i) q^{77} -16.2647i q^{79} +(-2.23580 - 0.0345211i) q^{80} +(-6.99762 - 6.99762i) q^{82} +(11.0370 + 11.0370i) q^{83} +(-1.60536 + 1.55654i) q^{85} +3.50466i q^{86} +(1.51945 - 1.51945i) q^{88} -10.8272 q^{89} +6.30873 q^{91} +(-5.76432 + 5.76432i) q^{92} -11.9174i q^{94} +(0.163291 - 10.5757i) q^{95} +(1.47817 + 1.47817i) q^{97} +(4.05184 + 4.05184i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{10} - 16 q^{16} + 8 q^{22} - 16 q^{25} + 40 q^{31} - 24 q^{37} + 4 q^{40} - 40 q^{43} + 56 q^{46} - 8 q^{55} - 8 q^{58} + 88 q^{61} + 48 q^{67} - 24 q^{70} - 72 q^{73} - 16 q^{82} + 4 q^{85}+ \cdots - 56 q^{97}+O(q^{100}) $ 16 * q + 4 * q^10 - 16 * q^16 + 8 * q^22 - 16 * q^25 + 40 * q^31 - 24 * q^37 + 4 * q^40 - 40 * q^43 + 56 * q^46 - 8 * q^55 - 8 * q^58 + 88 * q^61 + 48 * q^67 - 24 * q^70 - 72 * q^73 - 16 * q^82 + 4 * q^85 + 8 * q^88 + 144 * q^91 - 56 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	2.23580	+	0.0345211i	0.999881	+	0.0154383i
$5$	2.23580	+	0.0345211i	0.999881	+	0.0154383i
$6$		0			0
$7$	0.796815	+	0.796815i	0.301168	+	0.301168i	0.841471	−	0.540303i	$-0.181690\pi$
$7$	0.796815	+	0.796815i	0.301168	+	0.301168i	−0.540303	+	0.841471i	$0.681690\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−1.60536	+	1.55654i	−0.507660	+	0.492221i
$11$		−	2.14883i		−	0.647896i	−0.946075	−	0.323948i	$-0.894990\pi$
$11$		−	2.14883i		−	0.647896i	0.946075	−	0.323948i	$-0.105010\pi$
$12$		0			0
$13$	3.95872	−	3.95872i	1.09795	−	1.09795i	0.103300	−	0.994650i	$-0.467060\pi$
$13$	3.95872	−	3.95872i	1.09795	−	1.09795i	0.994650	−	0.103300i	$-0.0329402\pi$
$14$	−1.12687			−0.301168
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$		0			0
$19$		−	4.73017i		−	1.08518i	−0.839999	−	0.542588i	$-0.817445\pi$
$19$		−	4.73017i		−	1.08518i	0.839999	−	0.542588i	$-0.182555\pi$
$20$	0.0345211	−	2.23580i	0.00771915	−	0.499940i
$21$		0			0
$22$	1.51945	+	1.51945i	0.323948	+	0.323948i
$23$	−5.76432	−	5.76432i	−1.20194	−	1.20194i	−0.973575	−	0.228370i	$-0.926661\pi$
$23$	−5.76432	−	5.76432i	−1.20194	−	1.20194i	−0.228370	−	0.973575i	$-0.573339\pi$
$24$		0			0
$25$	4.99762	+	0.154365i	0.999523	+	0.0308729i
$26$			5.59847i			1.09795i
$27$		0			0
$28$	0.796815	−	0.796815i	0.150584	−	0.150584i
$29$	6.62043			1.22938			0.614692	−	0.788768i	$-0.289281\pi$
$29$	6.62043			1.22938			0.614692	+	0.788768i	$0.289281\pi$
$30$		0			0
$31$	−1.21072			−0.217452			−0.108726	−	0.994072i	$-0.534677\pi$
$31$	−1.21072			−0.217452			−0.108726	+	0.994072i	$0.534677\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	1.00000i		−	0.171499i
$35$	1.75401	+	1.80903i	0.296482	+	0.305781i
$36$		0			0
$37$	−8.37262	−	8.37262i	−1.37645	−	1.37645i	−0.850540	−	0.525911i	$-0.823725\pi$
$37$	−8.37262	−	8.37262i	−1.37645	−	1.37645i	−0.525911	−	0.850540i	$-0.676275\pi$
$38$	3.34474	+	3.34474i	0.542588	+	0.542588i
$39$		0			0
$40$	1.55654	+	1.60536i	0.246111	+	0.253830i
$41$			9.89612i			1.54551i	0.634701	+	0.772757i	$0.281123\pi$
$41$			9.89612i			1.54551i	−0.634701	+	0.772757i	$0.718877\pi$
$42$		0			0
$43$	2.47817	−	2.47817i	0.377917	−	0.377917i	−0.492433	−	0.870350i	$-0.663892\pi$
$43$	2.47817	−	2.47817i	0.377917	−	0.377917i	0.870350	+	0.492433i	$0.163892\pi$
$44$	−2.14883			−0.323948
$45$		0			0
$46$	8.15198			1.20194
$47$	−8.42690	+	8.42690i	−1.22919	+	1.22919i	−0.264918	+	0.964271i	$0.585345\pi$
$47$	−8.42690	+	8.42690i	−1.22919	+	1.22919i	−0.964271	+	0.264918i	$0.914655\pi$
$48$		0			0
$49$		−	5.73017i		−	0.818596i
$50$	−3.64300	+	3.42470i	−0.515198	+	0.484325i
$51$		0			0
$52$	−3.95872	−	3.95872i	−0.548975	−	0.548975i
$53$	−0.461295	−	0.461295i	−0.0633638	−	0.0633638i	0.674715	−	0.738079i	$-0.264267\pi$
$53$	−0.461295	−	0.461295i	−0.0633638	−	0.0633638i	−0.738079	+	0.674715i	$0.764267\pi$
$54$		0			0
$55$	0.0741799	−	4.80435i	0.0100024	−	0.647819i
$56$			1.12687i			0.150584i
$57$		0			0
$58$	−4.68135	+	4.68135i	−0.614692	+	0.614692i
$59$	−4.07935			−0.531086			−0.265543	−	0.964099i	$-0.585551\pi$
$59$	−4.07935			−0.531086			−0.265543	+	0.964099i	$0.585551\pi$
$60$		0			0
$61$	11.7456			1.50387			0.751936	−	0.659236i	$-0.229120\pi$
$61$	11.7456			1.50387			0.751936	+	0.659236i	$0.229120\pi$
$62$	0.856109	−	0.856109i	0.108726	−	0.108726i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	8.98756	−	8.71424i	1.11477	−	1.08087i
$66$		0			0
$67$	2.22854	+	2.22854i	0.272260	+	0.272260i	0.830009	−	0.557749i	$-0.188335\pi$
$67$	2.22854	+	2.22854i	0.272260	+	0.272260i	−0.557749	+	0.830009i	$0.688335\pi$
$68$	0.707107	+	0.707107i	0.0857493	+	0.0857493i
$69$		0			0
$70$	−2.51945	−	0.0389007i	−0.301132	−	0.00464952i
$71$		−	3.51868i		−	0.417591i	−0.977959	−	0.208796i	$-0.933046\pi$
$71$		−	3.51868i		−	0.417591i	0.977959	−	0.208796i	$-0.0669543\pi$
$72$		0			0
$73$	−3.15436	+	3.15436i	−0.369190	+	0.369190i	−0.867182	−	0.497991i	$-0.834071\pi$
$73$	−3.15436	+	3.15436i	−0.369190	+	0.369190i	0.497991	+	0.867182i	$0.334071\pi$
$74$	11.8407			1.37645
$75$		0			0
$76$	−4.73017			−0.542588
$77$	1.71222	−	1.71222i	0.195125	−	0.195125i
$78$		0			0
$79$		−	16.2647i		−	1.82992i	−0.403543	−	0.914961i	$-0.632222\pi$
$79$		−	16.2647i		−	1.82992i	0.403543	−	0.914961i	$-0.367778\pi$
$80$	−2.23580	−	0.0345211i	−0.249970	−	0.00385958i
$81$		0			0
$82$	−6.99762	−	6.99762i	−0.772757	−	0.772757i
$83$	11.0370	+	11.0370i	1.21147	+	1.21147i	0.970543	+	0.240927i	$0.0774514\pi$
$83$	11.0370	+	11.0370i	1.21147	+	1.21147i	0.240927	+	0.970543i	$0.422549\pi$
$84$		0			0
$85$	−1.60536	+	1.55654i	−0.174126	+	0.168830i
$86$			3.50466i			0.377917i
$87$		0			0
$88$	1.51945	−	1.51945i	0.161974	−	0.161974i
$89$	−10.8272			−1.14768			−0.573841	−	0.818967i	$-0.694547\pi$
$89$	−10.8272			−1.14768			−0.573841	+	0.818967i	$0.694547\pi$
$90$		0			0
$91$	6.30873			0.661335
$92$	−5.76432	+	5.76432i	−0.600972	+	0.600972i
$93$		0			0
$94$		−	11.9174i		−	1.22919i
$95$	0.163291	−	10.5757i	0.0167533	−	1.08505i
$96$		0			0
$97$	1.47817	+	1.47817i	0.150085	+	0.150085i	0.778156	−	0.628071i	$-0.216155\pi$
$97$	1.47817	+	1.47817i	0.150085	+	0.150085i	−0.628071	+	0.778156i	$0.716155\pi$
$98$	4.05184	+	4.05184i	0.409298	+	0.409298i
$99$		0			0
$100$	0.154365	−	4.99762i	0.0154365	−	0.499762i
$101$		−	4.02434i		−	0.400436i	−0.979751	−	0.200218i	$-0.935835\pi$
$101$		−	4.02434i		−	0.400436i	0.979751	−	0.200218i	$-0.0641651\pi$
$102$		0			0
$103$	−6.24962	+	6.24962i	−0.615794	+	0.615794i	−0.944450	−	0.328656i	$-0.893404\pi$
$103$	−6.24962	+	6.24962i	−0.615794	+	0.615794i	0.328656	+	0.944450i	$0.393404\pi$
$104$	5.59847			0.548975
$105$		0			0
$106$	0.652370			0.0633638
$107$	11.3654	−	11.3654i	1.09873	−	1.09873i	0.104171	−	0.994559i	$-0.466781\pi$
$107$	11.3654	−	11.3654i	1.09873	−	1.09873i	0.994559	−	0.104171i	$-0.0332188\pi$
$108$		0			0
$109$			9.10831i			0.872418i	0.899845	+	0.436209i	$0.143679\pi$
$109$			9.10831i			0.872418i	−0.899845	+	0.436209i	$0.856321\pi$
$110$	3.34474	+	3.44964i	0.318908	+	0.328911i
$111$		0			0
$112$	−0.796815	−	0.796815i	−0.0752920	−	0.0752920i
$113$	5.30047	+	5.30047i	0.498626	+	0.498626i	0.911010	−	0.412384i	$-0.135304\pi$
$113$	5.30047	+	5.30047i	0.498626	+	0.498626i	−0.412384	+	0.911010i	$0.635304\pi$
$114$		0			0
$115$	−12.6889	−	13.0869i	−1.18324	−	1.22036i
$116$		−	6.62043i		−	0.614692i
$117$		0			0
$118$	2.88454	−	2.88454i	0.265543	−	0.265543i
$119$	−1.12687			−0.103300
$120$		0			0
$121$	6.38254			0.580231
$122$	−8.30540	+	8.30540i	−0.751936	+	0.751936i
$123$		0			0
$124$			1.21072i			0.108726i
$125$	11.1683	+	0.517652i	0.998928	+	0.0463002i
$126$		0			0
$127$	13.4170	+	13.4170i	1.19057	+	1.19057i	0.976908	+	0.213663i	$0.0685393\pi$
$127$	13.4170	+	13.4170i	1.19057	+	1.19057i	0.213663	+	0.976908i	$0.431461\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−0.193265	+	12.5171i	−0.0169505	+	1.09782i
$131$		−	19.1126i		−	1.66988i	−0.550341	−	0.834940i	$-0.685502\pi$
$131$		−	19.1126i		−	1.66988i	0.550341	−	0.834940i	$-0.314498\pi$
$132$		0			0
$133$	3.76907	−	3.76907i	0.326820	−	0.326820i
$134$	−3.15164			−0.272260
$135$		0			0
$136$	−1.00000			−0.0857493
$137$	−8.18391	+	8.18391i	−0.699198	+	0.699198i	−0.964238	−	0.265039i	$-0.914615\pi$
$137$	−8.18391	+	8.18391i	−0.699198	+	0.699198i	0.265039	+	0.964238i	$0.414615\pi$
$138$		0			0
$139$			6.95633i			0.590028i	0.955493	+	0.295014i	$0.0953244\pi$
$139$			6.95633i			0.590028i	−0.955493	+	0.295014i	$0.904676\pi$
$140$	1.80903	−	1.75401i	0.152891	−	0.148241i
$141$		0			0
$142$	2.48809	+	2.48809i	0.208796	+	0.208796i
$143$	−8.50660	−	8.50660i	−0.711357	−	0.711357i
$144$		0			0
$145$	14.8020	+	0.228545i	1.22924	+	0.0189796i
$146$		−	4.46095i		−	0.369190i
$147$		0			0
$148$	−8.37262	+	8.37262i	−0.688225	+	0.688225i
$149$	12.0450			0.986761			0.493380	−	0.869814i	$-0.335761\pi$
$149$	12.0450			0.986761			0.493380	+	0.869814i	$0.335761\pi$
$150$		0			0
$151$	11.9174			0.969827			0.484913	−	0.874562i	$-0.338851\pi$
$151$	11.9174			0.969827			0.484913	+	0.874562i	$0.338851\pi$
$152$	3.34474	−	3.34474i	0.271294	−	0.271294i
$153$		0			0
$154$			2.42144i			0.195125i
$155$	−2.70693	−	0.0417954i	−0.217426	−	0.00335709i
$156$		0			0
$157$	5.09526	+	5.09526i	0.406646	+	0.406646i	0.880567	−	0.473921i	$-0.157162\pi$
$157$	5.09526	+	5.09526i	0.406646	+	0.406646i	−0.473921	+	0.880567i	$0.657162\pi$
$158$	11.5009	+	11.5009i	0.914961	+	0.914961i
$159$		0			0
$160$	1.60536	−	1.55654i	0.126915	−	0.123055i
$161$		−	9.18620i		−	0.723974i
$162$		0			0
$163$	10.6476	−	10.6476i	0.833985	−	0.833985i	−0.154075	−	0.988059i	$-0.549240\pi$
$163$	10.6476	−	10.6476i	0.833985	−	0.833985i	0.988059	+	0.154075i	$0.0492396\pi$
$164$	9.89612			0.772757
$165$		0			0
$166$	−15.6087			−1.21147
$167$	−8.28357	+	8.28357i	−0.641002	+	0.641002i	−0.950802	−	0.309800i	$-0.899738\pi$
$167$	−8.28357	+	8.28357i	−0.641002	+	0.641002i	0.309800	+	0.950802i	$0.399738\pi$
$168$		0			0
$169$		−	18.3429i		−	1.41099i
$170$	0.0345211	−	2.23580i	0.00264765	−	0.171478i
$171$		0			0
$172$	−2.47817	−	2.47817i	−0.188958	−	0.188958i
$173$	8.92662	+	8.92662i	0.678678	+	0.678678i	0.959701	−	0.281023i	$-0.0906737\pi$
$173$	8.92662	+	8.92662i	0.678678	+	0.678678i	−0.281023	+	0.959701i	$0.590674\pi$
$174$		0			0
$175$	3.85918	+	4.10518i	0.291726	+	0.310322i
$176$			2.14883i			0.161974i
$177$		0			0
$178$	7.65599	−	7.65599i	0.573841	−	0.573841i
$179$	16.9885			1.26978			0.634890	−	0.772602i	$-0.281045\pi$
$179$	16.9885			1.26978			0.634890	+	0.772602i	$0.281045\pi$
$180$		0			0
$181$	11.2258			0.834407			0.417203	−	0.908813i	$-0.363010\pi$
$181$	11.2258			0.834407			0.417203	+	0.908813i	$0.363010\pi$
$182$	−4.46095	+	4.46095i	−0.330667	+	0.330667i
$183$		0			0
$184$		−	8.15198i		−	0.600972i
$185$	−18.4305	−	19.0086i	−1.35504	−	1.39754i
$186$		0			0
$187$	1.51945	+	1.51945i	0.111113	+	0.111113i
$188$	8.42690	+	8.42690i	0.614595	+	0.614595i
$189$		0			0
$190$	7.36270	+	7.59363i	0.534147	+	0.550900i
$191$			4.43574i			0.320959i	0.987039	+	0.160479i	$0.0513040\pi$
$191$			4.43574i			0.320959i	−0.987039	+	0.160479i	$0.948696\pi$
$192$		0			0
$193$	−19.0869	+	19.0869i	−1.37390	+	1.37390i	−0.519328	+	0.854575i	$0.673818\pi$
$193$	−19.0869	+	19.0869i	−1.37390	+	1.37390i	−0.854575	+	0.519328i	$0.826182\pi$
$194$	−2.09044			−0.150085
$195$		0			0
$196$	−5.73017			−0.409298
$197$	−2.74011	+	2.74011i	−0.195225	+	0.195225i	−0.797949	−	0.602725i	$-0.794082\pi$
$197$	−2.74011	+	2.74011i	−0.195225	+	0.195225i	0.602725	+	0.797949i	$0.294082\pi$
$198$		0			0
$199$			11.7408i			0.832286i	0.909299	+	0.416143i	$0.136619\pi$
$199$			11.7408i			0.832286i	−0.909299	+	0.416143i	$0.863381\pi$
$200$	3.42470	+	3.64300i	0.242163	+	0.257599i
$201$		0			0
$202$	2.84564	+	2.84564i	0.200218	+	0.200218i
$203$	5.27526	+	5.27526i	0.370251	+	0.370251i
$204$		0			0
$205$	−0.341625	+	22.1258i	−0.0238601	+	1.54533i
$206$		−	8.83830i		−	0.615794i
$207$		0			0
$208$	−3.95872	+	3.95872i	−0.274488	+	0.274488i
$209$	−10.1643			−0.703081
$210$		0			0
$211$	−2.37452			−0.163469			−0.0817344	−	0.996654i	$-0.526046\pi$
$211$	−2.37452			−0.163469			−0.0817344	+	0.996654i	$0.526046\pi$
$212$	−0.461295	+	0.461295i	−0.0316819	+	0.0316819i
$213$		0			0
$214$			16.0730i			1.09873i
$215$	5.62624	−	5.45514i	0.383706	−	0.372037i
$216$		0			0
$217$	−0.964721	−	0.964721i	−0.0654895	−	0.0654895i
$218$	−6.44055	−	6.44055i	−0.436209	−	0.436209i
$219$		0			0
$220$	−4.80435	−	0.0741799i	−0.323909	−	0.00500121i
$221$			5.59847i			0.376594i
$222$		0			0
$223$	−11.0154	+	11.0154i	−0.737648	+	0.737648i	−0.972122	−	0.234474i	$-0.924663\pi$
$223$	−11.0154	+	11.0154i	−0.737648	+	0.737648i	0.234474	+	0.972122i	$0.424663\pi$
$224$	1.12687			0.0752920
$225$		0			0
$226$	−7.49599			−0.498626
$227$	−14.1938	+	14.1938i	−0.942074	+	0.942074i	−0.998412	−	0.0563376i	$-0.982058\pi$
$227$	−14.1938	+	14.1938i	−0.942074	+	0.942074i	0.0563376	+	0.998412i	$0.482058\pi$
$228$		0			0
$229$		−	0.0705584i		−	0.00466263i	−0.999997	−	0.00233132i	$-0.999258\pi$
$229$		−	0.0705584i		−	0.00466263i	0.999997	−	0.00233132i	$-0.000742081\pi$
$230$	18.2262	+	0.281415i	1.20180	+	0.0185560i
$231$		0			0
$232$	4.68135	+	4.68135i	0.307346	+	0.307346i
$233$	4.10456	+	4.10456i	0.268898	+	0.268898i	0.828656	−	0.559758i	$-0.189106\pi$
$233$	4.10456	+	4.10456i	0.268898	+	0.268898i	−0.559758	+	0.828656i	$0.689106\pi$
$234$		0			0
$235$	−19.1318	+	18.5500i	−1.24802	+	1.21007i
$236$			4.07935i			0.265543i
$237$		0			0
$238$	0.796815	−	0.796815i	0.0516499	−	0.0516499i
$239$	−19.2176			−1.24308			−0.621540	−	0.783382i	$-0.713493\pi$
$239$	−19.2176			−1.24308			−0.621540	+	0.783382i	$0.713493\pi$
$240$		0			0
$241$	29.0221			1.86948			0.934740	−	0.355333i	$-0.115633\pi$
$241$	29.0221			1.86948			0.934740	+	0.355333i	$0.115633\pi$
$242$	−4.51314	+	4.51314i	−0.290116	+	0.290116i
$243$		0			0
$244$		−	11.7456i		−	0.751936i
$245$	0.197812	−	12.8115i	0.0126377	−	0.818498i
$246$		0			0
$247$	−18.7254	−	18.7254i	−1.19147	−	1.19147i
$248$	−0.856109	−	0.856109i	−0.0543630	−	0.0543630i
$249$		0			0
$250$	−8.26325	+	7.53118i	−0.522614	+	0.476314i
$251$		−	11.1723i		−	0.705186i	−0.935777	−	0.352593i	$-0.885300\pi$
$251$		−	11.1723i		−	0.705186i	0.935777	−	0.352593i	$-0.114700\pi$
$252$		0			0
$253$	−12.3865	+	12.3865i	−0.778735	+	0.778735i
$254$	−18.9746			−1.19057
$255$		0			0
$256$	1.00000			0.0625000
$257$	20.7951	−	20.7951i	1.29716	−	1.29716i	0.366900	−	0.930261i	$-0.380419\pi$
$257$	20.7951	−	20.7951i	1.29716	−	1.29716i	0.930261	−	0.366900i	$-0.119581\pi$
$258$		0			0
$259$		−	13.3429i		−	0.829085i
$260$	−8.71424	−	8.98756i	−0.540434	−	0.557385i
$261$		0			0
$262$	13.5147	+	13.5147i	0.834940	+	0.834940i
$263$	−8.36851	−	8.36851i	−0.516025	−	0.516025i	0.400341	−	0.916366i	$-0.368892\pi$
$263$	−8.36851	−	8.36851i	−0.516025	−	0.516025i	−0.916366	+	0.400341i	$0.868892\pi$
$264$		0			0
$265$	−1.01544	−	1.04729i	−0.0623780	−	0.0643345i
$266$			5.33027i			0.326820i
$267$		0			0
$268$	2.22854	−	2.22854i	0.136130	−	0.136130i
$269$	−1.70441			−0.103920			−0.0519599	−	0.998649i	$-0.516547\pi$
$269$	−1.70441			−0.103920			−0.0519599	+	0.998649i	$0.516547\pi$
$270$		0			0
$271$	−13.8301			−0.840119			−0.420059	−	0.907497i	$-0.637991\pi$
$271$	−13.8301			−0.840119			−0.420059	+	0.907497i	$0.637991\pi$
$272$	0.707107	−	0.707107i	0.0428746	−	0.0428746i
$273$		0			0
$274$		−	11.5738i		−	0.699198i
$275$	0.331703	−	10.7390i	0.0200024	−	0.647587i
$276$		0			0
$277$	−4.00552	−	4.00552i	−0.240668	−	0.240668i	0.576458	−	0.817127i	$-0.304434\pi$
$277$	−4.00552	−	4.00552i	−0.240668	−	0.240668i	−0.817127	+	0.576458i	$0.804434\pi$
$278$	−4.91887	−	4.91887i	−0.295014	−	0.295014i
$279$		0			0
$280$	−0.0389007	+	2.51945i	−0.00232476	+	0.150566i
$281$			8.96504i			0.534810i	0.963584	+	0.267405i	$0.0861661\pi$
$281$			8.96504i			0.534810i	−0.963584	+	0.267405i	$0.913834\pi$
$282$		0			0
$283$	−2.32857	+	2.32857i	−0.138419	+	0.138419i	−0.772921	−	0.634502i	$-0.781205\pi$
$283$	−2.32857	+	2.32857i	−0.138419	+	0.138419i	0.634502	+	0.772921i	$0.281205\pi$
$284$	−3.51868			−0.208796
$285$		0			0
$286$	12.0301			0.711357
$287$	−7.88538	+	7.88538i	−0.465459	+	0.465459i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	−10.6282	+	10.3050i	−0.624108	+	0.605128i
$291$		0			0
$292$	3.15436	+	3.15436i	0.184595	+	0.184595i
$293$	−19.5156	−	19.5156i	−1.14011	−	1.14011i	−0.988429	−	0.151682i	$-0.951531\pi$
$293$	−19.5156	−	19.5156i	−1.14011	−	1.14011i	−0.151682	−	0.988429i	$-0.548469\pi$
$294$		0			0
$295$	−9.12062	−	0.140824i	−0.531023	−	0.00819907i
$296$		−	11.8407i		−	0.688225i
$297$		0			0
$298$	−8.51707	+	8.51707i	−0.493380	+	0.493380i
$299$	−45.6386			−2.63935
$300$		0			0
$301$	3.94928			0.227633
$302$	−8.42690	+	8.42690i	−0.484913	+	0.484913i
$303$		0			0
$304$			4.73017i			0.271294i
$305$	26.2609	+	0.405471i	1.50369	+	0.0232172i
$306$		0			0
$307$	−18.5090	−	18.5090i	−1.05637	−	1.05637i	−0.998313	−	0.0580536i	$-0.981511\pi$
$307$	−18.5090	−	18.5090i	−1.05637	−	1.05637i	−0.0580536	−	0.998313i	$-0.518489\pi$
$308$	−1.71222	−	1.71222i	−0.0975627	−	0.0975627i
$309$		0			0
$310$	1.94364	−	1.88454i	0.110392	−	0.107034i
$311$			23.5658i			1.33629i	0.744030	+	0.668147i	$0.232912\pi$
$311$			23.5658i			1.33629i	−0.744030	+	0.668147i	$0.767088\pi$
$312$		0			0
$313$	−15.0869	+	15.0869i	−0.852760	+	0.852760i	−0.990472	−	0.137712i	$-0.956025\pi$
$313$	−15.0869	+	15.0869i	−0.852760	+	0.852760i	0.137712	+	0.990472i	$0.456025\pi$
$314$	−7.20578			−0.406646
$315$		0			0
$316$	−16.2647			−0.914961
$317$	9.89019	−	9.89019i	0.555489	−	0.555489i	−0.372531	−	0.928020i	$-0.621510\pi$
$317$	9.89019	−	9.89019i	0.555489	−	0.555489i	0.928020	+	0.372531i	$0.121510\pi$
$318$		0			0
$319$		−	14.2262i		−	0.796512i
$320$	−0.0345211	+	2.23580i	−0.00192979	+	0.124985i
$321$		0			0
$322$	6.49562	+	6.49562i	0.361987	+	0.361987i
$323$	3.34474	+	3.34474i	0.186106	+	0.186106i
$324$		0			0
$325$	20.3952	−	19.1731i	1.13132	−	1.06353i
$326$			15.0580i			0.833985i
$327$		0			0
$328$	−6.99762	+	6.99762i	−0.386379	+	0.386379i
$329$	−13.4294			−0.740384
$330$		0			0
$331$	−2.77709			−0.152643			−0.0763214	−	0.997083i	$-0.524318\pi$
$331$	−2.77709			−0.152643			−0.0763214	+	0.997083i	$0.524318\pi$
$332$	11.0370	−	11.0370i	0.605735	−	0.605735i
$333$		0			0
$334$		−	11.7147i		−	0.641002i
$335$	4.90565	+	5.05952i	0.268024	+	0.276431i
$336$		0			0
$337$	−1.52889	−	1.52889i	−0.0832837	−	0.0832837i	0.664238	−	0.747521i	$-0.268756\pi$
$337$	−1.52889	−	1.52889i	−0.0832837	−	0.0832837i	−0.747521	+	0.664238i	$0.768756\pi$
$338$	12.9704	+	12.9704i	0.705495	+	0.705495i
$339$		0			0
$340$	1.55654	+	1.60536i	0.0844152	+	0.0870629i
$341$			2.60163i			0.140886i
$342$		0			0
$343$	10.1436	−	10.1436i	0.547703	−	0.547703i
$344$	3.50466			0.188958
$345$		0			0
$346$	−12.6241			−0.678678
$347$	−9.34949	+	9.34949i	−0.501907	+	0.501907i	−0.912030	−	0.410123i	$-0.865486\pi$
$347$	−9.34949	+	9.34949i	−0.501907	+	0.501907i	0.410123	+	0.912030i	$0.365486\pi$
$348$		0			0
$349$			9.26983i			0.496203i	0.968734	+	0.248101i	$0.0798066\pi$
$349$			9.26983i			0.496203i	−0.968734	+	0.248101i	$0.920193\pi$
$350$	−5.63165	−	0.173948i	−0.301024	−	0.00929793i
$351$		0			0
$352$	−1.51945	−	1.51945i	−0.0809870	−	0.0809870i
$353$	6.47454	+	6.47454i	0.344605	+	0.344605i	0.858095	−	0.513490i	$-0.171648\pi$
$353$	6.47454	+	6.47454i	0.344605	+	0.344605i	−0.513490	+	0.858095i	$0.671648\pi$
$354$		0			0
$355$	0.121469	−	7.86708i	0.00644690	−	0.417541i
$356$			10.8272i			0.573841i
$357$		0			0
$358$	−12.0127	+	12.0127i	−0.634890	+	0.634890i
$359$	−11.1533			−0.588647			−0.294323	−	0.955706i	$-0.595094\pi$
$359$	−11.1533			−0.588647			−0.294323	+	0.955706i	$0.595094\pi$
$360$		0			0
$361$	−3.37452			−0.177606
$362$	−7.93783	+	7.93783i	−0.417203	+	0.417203i
$363$		0			0
$364$		−	6.30873i		−	0.330667i
$365$	−7.16143	+	6.94364i	−0.374846	+	0.363447i
$366$		0			0
$367$	2.92534	+	2.92534i	0.152701	+	0.152701i	0.779323	−	0.626622i	$-0.215563\pi$
$367$	2.92534	+	2.92534i	0.152701	+	0.152701i	−0.626622	+	0.779323i	$0.715563\pi$
$368$	5.76432	+	5.76432i	0.300486	+	0.300486i
$369$		0			0
$370$	26.4734	+	0.408753i	1.37629	+	0.0212501i
$371$		−	0.735134i		−	0.0381663i
$372$		0			0
$373$	−23.2707	+	23.2707i	−1.20491	+	1.20491i	−0.232257	+	0.972655i	$0.574611\pi$
$373$	−23.2707	+	23.2707i	−1.20491	+	1.20491i	−0.972655	+	0.232257i	$0.925389\pi$
$374$	−2.14883			−0.111113
$375$		0			0
$376$	−11.9174			−0.614595
$377$	26.2084	−	26.2084i	1.34980	−	1.34980i
$378$		0			0
$379$		−	0.957068i		−	0.0491613i	−0.999698	−	0.0245806i	$-0.992175\pi$
$379$		−	0.957068i		−	0.0491613i	0.999698	−	0.0245806i	$-0.00782505\pi$
$380$	−10.5757	−	0.163291i	−0.542523	−	0.00837664i
$381$		0			0
$382$	−3.13654	−	3.13654i	−0.160479	−	0.160479i
$383$	14.0585	+	14.0585i	0.718358	+	0.718358i	0.968269	−	0.249911i	$-0.0804013\pi$
$383$	14.0585	+	14.0585i	0.718358	+	0.718358i	−0.249911	+	0.968269i	$0.580401\pi$
$384$		0			0
$385$	3.88729	−	3.76907i	0.198115	−	0.192090i
$386$		−	26.9929i		−	1.37390i
$387$		0			0
$388$	1.47817	−	1.47817i	0.0750425	−	0.0750425i
$389$	3.39923			0.172348			0.0861739	−	0.996280i	$-0.472536\pi$
$389$	3.39923			0.172348			0.0861739	+	0.996280i	$0.472536\pi$
$390$		0			0
$391$	8.15198			0.412263
$392$	4.05184	−	4.05184i	0.204649	−	0.204649i
$393$		0			0
$394$		−	3.87510i		−	0.195225i
$395$	0.561475	−	36.3646i	0.0282509	−	1.82970i
$396$		0			0
$397$	−0.319017	−	0.319017i	−0.0160110	−	0.0160110i	0.699056	−	0.715067i	$-0.253604\pi$
$397$	−0.319017	−	0.319017i	−0.0160110	−	0.0160110i	−0.715067	+	0.699056i	$0.753604\pi$
$398$	−8.30203	−	8.30203i	−0.416143	−	0.416143i
$399$		0			0
$400$	−4.99762	−	0.154365i	−0.249881	−	0.00771823i
$401$		−	16.9054i		−	0.844217i	−0.906545	−	0.422109i	$-0.861290\pi$
$401$		−	16.9054i		−	0.844217i	0.906545	−	0.422109i	$-0.138710\pi$
$402$		0			0
$403$	−4.79290	+	4.79290i	−0.238751	+	0.238751i
$404$	−4.02434			−0.200218
$405$		0			0
$406$	−7.46034			−0.370251
$407$	−17.9913	+	17.9913i	−0.891797	+	0.891797i
$408$		0			0
$409$			38.6421i			1.91073i	0.295430	+	0.955364i	$0.404537\pi$
$409$			38.6421i			1.91073i	−0.295430	+	0.955364i	$0.595463\pi$
$410$	−15.4037	−	15.8868i	−0.760735	−	0.784595i
$411$		0			0
$412$	6.24962	+	6.24962i	0.307897	+	0.307897i
$413$	−3.25049	−	3.25049i	−0.159946	−	0.159946i
$414$		0			0
$415$	24.2956	+	25.0576i	1.19262	+	1.23003i
$416$		−	5.59847i		−	0.274488i
$417$		0			0
$418$	7.18726	−	7.18726i	0.351540	−	0.351540i
$419$	−18.9813			−0.927297			−0.463649	−	0.886019i	$-0.653460\pi$
$419$	−18.9813			−0.927297			−0.463649	+	0.886019i	$0.653460\pi$
$420$		0			0
$421$	0.695260			0.0338849			0.0169425	−	0.999856i	$-0.494607\pi$
$421$	0.695260			0.0338849			0.0169425	+	0.999856i	$0.494607\pi$
$422$	1.67904	−	1.67904i	0.0817344	−	0.0817344i
$423$		0			0
$424$		−	0.652370i		−	0.0316819i
$425$	−3.64300	+	3.42470i	−0.176711	+	0.166122i
$426$		0			0
$427$	9.35908	+	9.35908i	0.452918	+	0.452918i
$428$	−11.3654	−	11.3654i	−0.549365	−	0.549365i
$429$		0			0
$430$	−0.120985	+	7.83572i	−0.00583440	+	0.377872i
$431$			14.1579i			0.681963i	0.940070	+	0.340981i	$0.110759\pi$
$431$			14.1579i			0.681963i	−0.940070	+	0.340981i	$0.889241\pi$
$432$		0			0
$433$	−6.79633	+	6.79633i	−0.326611	+	0.326611i	−0.851296	−	0.524685i	$-0.824183\pi$
$433$	−6.79633	+	6.79633i	−0.326611	+	0.326611i	0.524685	+	0.851296i	$0.324183\pi$
$434$	1.36432			0.0654895
$435$		0			0
$436$	9.10831			0.436209
$437$	−27.2662	+	27.2662i	−1.30432	+	1.30432i
$438$		0			0
$439$		−	16.7265i		−	0.798315i	−0.916882	−	0.399157i	$-0.869303\pi$
$439$		−	16.7265i		−	0.798315i	0.916882	−	0.399157i	$-0.130697\pi$
$440$	3.44964	−	3.34474i	0.164455	−	0.159454i
$441$		0			0
$442$	−3.95872	−	3.95872i	−0.188297	−	0.188297i
$443$	7.42694	+	7.42694i	0.352864	+	0.352864i	0.861174	−	0.508310i	$-0.169730\pi$
$443$	7.42694	+	7.42694i	0.352864	+	0.352864i	−0.508310	+	0.861174i	$0.669730\pi$
$444$		0			0
$445$	−24.2075	−	0.373767i	−1.14754	−	0.0177183i
$446$		−	15.5782i		−	0.737648i
$447$		0			0
$448$	−0.796815	+	0.796815i	−0.0376460	+	0.0376460i
$449$	5.09550			0.240472			0.120236	−	0.992745i	$-0.461635\pi$
$449$	5.09550			0.240472			0.120236	+	0.992745i	$0.461635\pi$
$450$		0			0
$451$	21.2651			1.00133
$452$	5.30047	−	5.30047i	0.249313	−	0.249313i
$453$		0			0
$454$		−	20.0730i		−	0.942074i
$455$	14.1051	+	0.217784i	0.661256	+	0.0102099i
$456$		0			0
$457$	−20.3742	−	20.3742i	−0.953063	−	0.953063i	0.0458841	−	0.998947i	$-0.485390\pi$
$457$	−20.3742	−	20.3742i	−0.953063	−	0.953063i	−0.998947	+	0.0458841i	$0.985390\pi$
$458$	0.0498923	+	0.0498923i	0.00233132	+	0.00233132i
$459$		0			0
$460$	−13.0869	+	12.6889i	−0.610178	+	0.591622i
$461$		−	15.8779i		−	0.739509i	−0.929129	−	0.369755i	$-0.879442\pi$
$461$		−	15.8779i		−	0.739509i	0.929129	−	0.369755i	$-0.120558\pi$
$462$		0			0
$463$	−21.0504	+	21.0504i	−0.978293	+	0.978293i	−0.999769	−	0.0214766i	$-0.993163\pi$
$463$	−21.0504	+	21.0504i	−0.978293	+	0.978293i	0.0214766	+	0.999769i	$0.493163\pi$
$464$	−6.62043			−0.307346
$465$		0			0
$466$	−5.80472			−0.268898
$467$	4.07086	−	4.07086i	0.188377	−	0.188377i	−0.606617	−	0.794994i	$-0.707474\pi$
$467$	4.07086	−	4.07086i	0.188377	−	0.188377i	0.794994	+	0.606617i	$0.207474\pi$
$468$		0			0
$469$			3.55148i			0.163992i
$470$	0.411403	−	26.6450i	0.0189766	−	1.22904i
$471$		0			0
$472$	−2.88454	−	2.88454i	−0.132772	−	0.132772i
$473$	−5.32515	−	5.32515i	−0.244851	−	0.244851i
$474$		0			0
$475$	0.730171	−	23.6396i	0.0335026	−	1.08466i
$476$			1.12687i			0.0516499i
$477$		0			0
$478$	13.5889	−	13.5889i	0.621540	−	0.621540i
$479$	0.442145			0.0202021			0.0101011	−	0.999949i	$-0.496785\pi$
$479$	0.442145			0.0202021			0.0101011	+	0.999949i	$0.496785\pi$
$480$		0			0
$481$	−66.2897			−3.02255
$482$	−20.5217	+	20.5217i	−0.934740	+	0.934740i
$483$		0			0
$484$		−	6.38254i		−	0.290116i
$485$	3.25386	+	3.35591i	0.147750	+	0.152384i
$486$		0			0
$487$	1.58133	+	1.58133i	0.0716568	+	0.0716568i	0.742027	−	0.670370i	$-0.233865\pi$
$487$	1.58133	+	1.58133i	0.0716568	+	0.0716568i	−0.670370	+	0.742027i	$0.733865\pi$
$488$	8.30540	+	8.30540i	0.375968	+	0.375968i
$489$		0			0
$490$	8.91924	+	9.19899i	0.402930	+	0.415568i
$491$			29.7714i			1.34357i	0.740748	+	0.671783i	$0.234471\pi$
$491$			29.7714i			1.34357i	−0.740748	+	0.671783i	$0.765529\pi$
$492$		0			0
$493$	−4.68135	+	4.68135i	−0.210837	+	0.210837i
$494$	26.4817			1.19147
$495$		0			0
$496$	1.21072			0.0543630
$497$	2.80374	−	2.80374i	0.125765	−	0.125765i
$498$		0			0
$499$		−	3.14034i		−	0.140581i	−0.997527	−	0.0702904i	$-0.977607\pi$
$499$		−	3.14034i		−	0.140581i	0.997527	−	0.0702904i	$-0.0223926\pi$
$500$	0.517652	−	11.1683i	0.0231501	−	0.499464i
$501$		0			0
$502$	7.89998	+	7.89998i	0.352593	+	0.352593i
$503$	−21.7449	−	21.7449i	−0.969557	−	0.969557i	0.0299931	−	0.999550i	$-0.490451\pi$
$503$	−21.7449	−	21.7449i	−0.969557	−	0.969557i	−0.999550	+	0.0299931i	$0.990451\pi$
$504$		0			0
$505$	0.138925	−	8.99762i	0.00618206	−	0.400389i
$506$		−	17.5172i		−	0.778735i
$507$		0			0
$508$	13.4170	−	13.4170i	0.595285	−	0.595285i
$509$	10.8452			0.480703			0.240351	−	0.970686i	$-0.422737\pi$
$509$	10.8452			0.480703			0.240351	+	0.970686i	$0.422737\pi$
$510$		0			0
$511$	−5.02689			−0.222377
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			29.4087i			1.29716i
$515$	−14.1887	+	13.7572i	−0.625227	+	0.606213i
$516$		0			0
$517$	18.1079	+	18.1079i	0.796387	+	0.796387i
$518$	9.43483	+	9.43483i	0.414543	+	0.414543i
$519$		0			0
$520$	12.5171	+	0.193265i	0.548910	+	0.00847525i
$521$		−	34.6381i		−	1.51752i	−0.651367	−	0.758762i	$-0.725804\pi$
$521$		−	34.6381i		−	1.51752i	0.651367	−	0.758762i	$-0.274196\pi$
$522$		0			0
$523$	−11.6111	+	11.6111i	−0.507717	+	0.507717i	−0.913825	−	0.406108i	$-0.866886\pi$
$523$	−11.6111	+	11.6111i	−0.507717	+	0.507717i	0.406108	+	0.913825i	$0.366886\pi$
$524$	−19.1126			−0.834940
$525$		0			0
$526$	11.8349			0.516025
$527$	0.856109	−	0.856109i	0.0372927	−	0.0372927i
$528$		0			0
$529$			43.4548i			1.88934i
$530$	1.45857	+	0.0225205i	0.0633562	+	0.000978229i
$531$		0			0
$532$	−3.76907	−	3.76907i	−0.163410	−	0.163410i
$533$	39.1759	+	39.1759i	1.69690	+	1.69690i
$534$		0			0
$535$	25.8030	−	25.0183i	1.11556	−	1.08164i
$536$			3.15164i			0.136130i
$537$		0			0
$538$	1.20520	−	1.20520i	0.0519599	−	0.0519599i
$539$	−12.3131			−0.530365
$540$		0			0
$541$	20.0893			0.863704			0.431852	−	0.901944i	$-0.357860\pi$
$541$	20.0893			0.863704			0.431852	+	0.901944i	$0.357860\pi$
$542$	9.77936	−	9.77936i	0.420059	−	0.420059i
$543$		0			0
$544$			1.00000i			0.0428746i
$545$	−0.314429	+	20.3644i	−0.0134687	+	0.872314i
$546$		0			0
$547$	−20.3539	−	20.3539i	−0.870272	−	0.870272i	0.122230	−	0.992502i	$-0.460995\pi$
$547$	−20.3539	−	20.3539i	−0.870272	−	0.870272i	−0.992502	+	0.122230i	$0.960995\pi$
$548$	8.18391	+	8.18391i	0.349599	+	0.349599i
$549$		0			0
$550$	7.35908	+	7.82818i	0.313792	+	0.333795i
$551$		−	31.3158i		−	1.33410i
$552$		0			0
$553$	12.9600	−	12.9600i	0.551113	−	0.551113i
$554$	5.66466			0.240668
$555$		0			0
$556$	6.95633			0.295014
$557$	−9.44817	+	9.44817i	−0.400332	+	0.400332i	−0.878350	−	0.478018i	$-0.841355\pi$
$557$	−9.44817	+	9.44817i	−0.400332	+	0.400332i	0.478018	+	0.878350i	$0.341355\pi$
$558$		0			0
$559$		−	19.6207i		−	0.829868i
$560$	−1.75401	−	1.80903i	−0.0741206	−	0.0764454i
$561$		0			0
$562$	−6.33924	−	6.33924i	−0.267405	−	0.267405i
$563$	18.4112	+	18.4112i	0.775940	+	0.775940i	0.979138	−	0.203198i	$-0.0651334\pi$
$563$	18.4112	+	18.4112i	0.775940	+	0.775940i	−0.203198	+	0.979138i	$0.565133\pi$
$564$		0			0
$565$	11.6678	+	12.0338i	0.490868	+	0.506264i
$566$		−	3.29309i		−	0.138419i
$567$		0			0
$568$	2.48809	−	2.48809i	0.104398	−	0.104398i
$569$	8.03733			0.336942			0.168471	−	0.985707i	$-0.446117\pi$
$569$	8.03733			0.336942			0.168471	+	0.985707i	$0.446117\pi$
$570$		0			0
$571$	35.7992			1.49815			0.749075	−	0.662485i	$-0.230498\pi$
$571$	35.7992			1.49815			0.749075	+	0.662485i	$0.230498\pi$
$572$	−8.50660	+	8.50660i	−0.355679	+	0.355679i
$573$		0			0
$574$		−	11.1516i		−	0.465459i
$575$	−27.9181	−	29.6977i	−1.16426	−	1.23848i
$576$		0			0
$577$	3.30396	+	3.30396i	0.137546	+	0.137546i	0.772527	−	0.634982i	$-0.218992\pi$
$577$	3.30396	+	3.30396i	0.137546	+	0.137546i	−0.634982	+	0.772527i	$0.718992\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$		0			0
$580$	0.228545	−	14.8020i	0.00948980	−	0.614618i
$581$			17.5889i			0.729712i
$582$		0			0
$583$	−0.991244	+	0.991244i	−0.0410531	+	0.0410531i
$584$	−4.46095			−0.184595
$585$		0			0
$586$	27.5992			1.14011
$587$	−23.4735	+	23.4735i	−0.968857	+	0.968857i	−0.999529	−	0.0306728i	$-0.990235\pi$
$587$	−23.4735	+	23.4735i	−0.968857	+	0.968857i	0.0306728	+	0.999529i	$0.490235\pi$
$588$		0			0
$589$			5.72692i			0.235974i
$590$	6.54883	−	6.34967i	0.269611	−	0.261412i
$591$		0			0
$592$	8.37262	+	8.37262i	0.344113	+	0.344113i
$593$	8.12889	+	8.12889i	0.333814	+	0.333814i	0.854033	−	0.520219i	$-0.174150\pi$
$593$	8.12889	+	8.12889i	0.333814	+	0.333814i	−0.520219	+	0.854033i	$0.674150\pi$
$594$		0			0
$595$	−2.51945	−	0.0389007i	−0.103287	−	0.00159477i
$596$		−	12.0450i		−	0.493380i
$597$		0			0
$598$	32.2714	−	32.2714i	1.31967	−	1.31967i
$599$	−23.0136			−0.940311			−0.470155	−	0.882584i	$-0.655802\pi$
$599$	−23.0136			−0.940311			−0.470155	+	0.882584i	$0.655802\pi$
$600$		0			0
$601$	−12.1508			−0.495643			−0.247821	−	0.968806i	$-0.579715\pi$
$601$	−12.1508			−0.495643			−0.247821	+	0.968806i	$0.579715\pi$
$602$	−2.79256	+	2.79256i	−0.113816	+	0.113816i
$603$		0			0
$604$		−	11.9174i		−	0.484913i
$605$	14.2701	+	0.220332i	0.580162	+	0.00895778i
$606$		0			0
$607$	21.2099	+	21.2099i	0.860882	+	0.860882i	0.991441	−	0.130559i	$-0.0416771\pi$
$607$	21.2099	+	21.2099i	0.860882	+	0.860882i	−0.130559	+	0.991441i	$0.541677\pi$
$608$	−3.34474	−	3.34474i	−0.135647	−	0.135647i
$609$		0			0
$610$	−18.8559	+	18.2825i	−0.763455	+	0.740237i
$611$			66.7194i			2.69918i
$612$		0			0
$613$	6.02145	−	6.02145i	0.243204	−	0.243204i	−0.574970	−	0.818174i	$-0.694986\pi$
$613$	6.02145	−	6.02145i	0.243204	−	0.243204i	0.818174	+	0.574970i	$0.194986\pi$
$614$	26.1757			1.05637
$615$		0			0
$616$	2.42144			0.0975627
$617$	8.91625	−	8.91625i	0.358955	−	0.358955i	−0.504473	−	0.863428i	$-0.668313\pi$
$617$	8.91625	−	8.91625i	0.358955	−	0.358955i	0.863428	+	0.504473i	$0.168313\pi$
$618$		0			0
$619$		−	5.11670i		−	0.205658i	−0.994699	−	0.102829i	$-0.967211\pi$
$619$		−	5.11670i		−	0.205658i	0.994699	−	0.102829i	$-0.0327894\pi$
$620$	−0.0417954	+	2.70693i	−0.00167854	+	0.108713i
$621$		0			0
$622$	−16.6635	−	16.6635i	−0.668147	−	0.668147i
$623$	−8.62728	−	8.62728i	−0.345645	−	0.345645i
$624$		0			0
$625$	24.9523	+	1.54291i	0.998094	+	0.0617164i
$626$		−	21.3361i		−	0.852760i
$627$		0			0
$628$	5.09526	−	5.09526i	0.203323	−	0.203323i
$629$	11.8407			0.472119
$630$		0			0
$631$	45.4508			1.80937			0.904684	−	0.426083i	$-0.140107\pi$
$631$	45.4508			1.80937			0.904684	+	0.426083i	$0.140107\pi$
$632$	11.5009	−	11.5009i	0.457480	−	0.457480i
$633$		0			0
$634$			13.9868i			0.555489i
$635$	29.5347	+	30.4610i	1.17205	+	1.20881i
$636$		0			0
$637$	−22.6841	−	22.6841i	−0.898778	−	0.898778i
$638$	10.0594	+	10.0594i	0.398256	+	0.398256i
$639$		0			0
$640$	−1.55654	−	1.60536i	−0.0615277	−	0.0634574i
$641$			34.4653i			1.36130i	0.732611	+	0.680648i	$0.238302\pi$
$641$			34.4653i			1.36130i	−0.732611	+	0.680648i	$0.761698\pi$
$642$		0			0
$643$	−9.57379	+	9.57379i	−0.377553	+	0.377553i	−0.870219	−	0.492665i	$-0.836023\pi$
$643$	−9.57379	+	9.57379i	−0.377553	+	0.377553i	0.492665	+	0.870219i	$0.336023\pi$
$644$	−9.18620			−0.361987
$645$		0			0
$646$	−4.73017			−0.186106
$647$	10.3356	−	10.3356i	0.406334	−	0.406334i	−0.474124	−	0.880458i	$-0.657235\pi$
$647$	10.3356	−	10.3356i	0.406334	−	0.406334i	0.880458	+	0.474124i	$0.157235\pi$
$648$		0			0
$649$			8.76582i			0.344088i
$650$	−0.864206	+	27.9790i	−0.0338969	+	1.09743i
$651$		0			0
$652$	−10.6476	−	10.6476i	−0.416992	−	0.416992i
$653$	17.1902	+	17.1902i	0.672705	+	0.672705i	0.958339	−	0.285634i	$-0.0922040\pi$
$653$	17.1902	+	17.1902i	0.672705	+	0.672705i	−0.285634	+	0.958339i	$0.592204\pi$
$654$		0			0
$655$	0.659790	−	42.7321i	0.0257801	−	1.66968i
$656$		−	9.89612i		−	0.386379i
$657$		0			0
$658$	9.49599	−	9.49599i	0.370192	−	0.370192i
$659$	−9.62048			−0.374761			−0.187380	−	0.982287i	$-0.560000\pi$
$659$	−9.62048			−0.374761			−0.187380	+	0.982287i	$0.560000\pi$
$660$		0			0
$661$	9.45558			0.367779			0.183890	−	0.982947i	$-0.441131\pi$
$661$	9.45558			0.367779			0.183890	+	0.982947i	$0.441131\pi$
$662$	1.96370	−	1.96370i	0.0763214	−	0.0763214i
$663$		0			0
$664$			15.6087i			0.605735i
$665$	8.55701	−	8.29678i	0.331827	−	0.321735i
$666$		0			0
$667$	−38.1623	−	38.1623i	−1.47765	−	1.47765i
$668$	8.28357	+	8.28357i	0.320501	+	0.320501i
$669$		0			0
$670$	−7.04644	−	0.108798i	−0.272228	−	0.00420323i
$671$		−	25.2393i		−	0.974352i
$672$		0			0
$673$	−6.09562	+	6.09562i	−0.234969	+	0.234969i	−0.814763	−	0.579794i	$-0.803133\pi$
$673$	−6.09562	+	6.09562i	−0.234969	+	0.234969i	0.579794	+	0.814763i	$0.303133\pi$
$674$	2.16217			0.0832837
$675$		0			0
$676$	−18.3429			−0.705495
$677$	13.9397	−	13.9397i	0.535748	−	0.535748i	−0.386529	−	0.922277i	$-0.626326\pi$
$677$	13.9397	−	13.9397i	0.535748	−	0.535748i	0.922277	+	0.386529i	$0.126326\pi$
$678$		0			0
$679$			2.35565i			0.0904016i
$680$	−2.23580	−	0.0345211i	−0.0857391	−	0.00132382i
$681$		0			0
$682$	−1.83963	−	1.83963i	−0.0704431	−	0.0704431i
$683$	6.53953	+	6.53953i	0.250228	+	0.250228i	0.821064	−	0.570836i	$-0.193381\pi$
$683$	6.53953	+	6.53953i	0.250228	+	0.250228i	−0.570836	+	0.821064i	$0.693381\pi$
$684$		0			0
$685$	−18.5801	+	18.0151i	−0.709909	+	0.688321i
$686$			14.3452i			0.547703i
$687$		0			0
$688$	−2.47817	+	2.47817i	−0.0944792	+	0.0944792i
$689$	−3.65227			−0.139141
$690$		0			0
$691$	−0.0469211			−0.00178496			−0.000892481	−	1.00000i	$-0.500284\pi$
$691$	−0.0469211			−0.00178496			−0.000892481		1.00000i	$0.500284\pi$
$692$	8.92662	−	8.92662i	0.339339	−	0.339339i
$693$		0			0
$694$		−	13.2222i		−	0.501907i
$695$	−0.240140	+	15.5530i	−0.00910904	+	0.589958i
$696$		0			0
$697$	−6.99762	−	6.99762i	−0.265054	−	0.265054i
$698$	−6.55476	−	6.55476i	−0.248101	−	0.248101i
$699$		0			0
$700$	4.10518	−	3.85918i	0.155161	−	0.145863i
$701$		−	14.7343i		−	0.556505i	−0.960508	−	0.278253i	$-0.910245\pi$
$701$		−	14.7343i		−	0.556505i	0.960508	−	0.278253i	$-0.0897552\pi$
$702$		0			0
$703$	−39.6039	+	39.6039i	−1.49369	+	1.49369i
$704$	2.14883			0.0809870
$705$		0			0
$706$	−9.15638			−0.344605
$707$	3.20665	−	3.20665i	0.120599	−	0.120599i
$708$		0			0
$709$			19.4527i			0.730561i	0.930897	+	0.365281i	$0.119027\pi$
$709$			19.4527i			0.730561i	−0.930897	+	0.365281i	$0.880973\pi$
$710$	5.47697	+	5.64876i	0.205547	+	0.211994i
$711$		0			0
$712$	−7.65599	−	7.65599i	−0.286920	−	0.286920i
$713$	6.97898	+	6.97898i	0.261365	+	0.261365i
$714$		0			0
$715$	−18.7254	−	19.3127i	−0.700290	−	0.722255i
$716$		−	16.9885i		−	0.634890i
$717$		0			0
$718$	7.88655	−	7.88655i	0.294323	−	0.294323i
$719$	8.28101			0.308829			0.154415	−	0.988006i	$-0.450651\pi$
$719$	8.28101			0.308829			0.154415	+	0.988006i	$0.450651\pi$
$720$		0			0
$721$	−9.95959			−0.370914
$722$	2.38615	−	2.38615i	0.0888032	−	0.0888032i
$723$		0			0
$724$		−	11.2258i		−	0.417203i
$725$	33.0864	+	1.02196i	1.22880	+	0.0379547i
$726$		0			0
$727$	27.5606	+	27.5606i	1.02217	+	1.02217i	0.999749	+	0.0224187i	$0.00713671\pi$
$727$	27.5606	+	27.5606i	1.02217	+	1.02217i	0.0224187	+	0.999749i	$0.492863\pi$
$728$	4.46095	+	4.46095i	0.165334	+	0.165334i
$729$		0			0
$730$	0.153997	−	9.97379i	0.00569968	−	0.369146i
$731$			3.50466i			0.129624i
$732$		0			0
$733$	−0.458695	+	0.458695i	−0.0169423	+	0.0169423i	−0.715527	−	0.698585i	$-0.753813\pi$
$733$	−0.458695	+	0.458695i	−0.0169423	+	0.0169423i	0.698585	+	0.715527i	$0.253813\pi$
$734$	−4.13705			−0.152701
$735$		0			0
$736$	−8.15198			−0.300486
$737$	4.78876	−	4.78876i	0.176396	−	0.176396i
$738$		0			0
$739$		−	30.0206i		−	1.10433i	−0.833736	−	0.552163i	$-0.813803\pi$
$739$		−	30.0206i		−	1.10433i	0.833736	−	0.552163i	$-0.186197\pi$
$740$	−19.0086	+	18.4305i	−0.698768	+	0.677518i
$741$		0			0
$742$	0.519818	+	0.519818i	0.0190831	+	0.0190831i
$743$	−13.4426	−	13.4426i	−0.493160	−	0.493160i	0.416140	−	0.909300i	$-0.363383\pi$
$743$	−13.4426	−	13.4426i	−0.493160	−	0.493160i	−0.909300	+	0.416140i	$0.863383\pi$
$744$		0			0
$745$	26.9301	+	0.415805i	0.986643	+	0.0152339i
$746$		−	32.9097i		−	1.20491i
$747$		0			0
$748$	1.51945	−	1.51945i	0.0555566	−	0.0555566i
$749$	18.1122			0.661804
$750$		0			0
$751$	−29.9203			−1.09181			−0.545904	−	0.837848i	$-0.683814\pi$
$751$	−29.9203			−1.09181			−0.545904	+	0.837848i	$0.683814\pi$
$752$	8.42690	−	8.42690i	0.307297	−	0.307297i
$753$		0			0
$754$			37.0643i			1.34980i
$755$	26.6450	+	0.411403i	0.969711	+	0.0149725i
$756$		0			0
$757$	−3.86584	−	3.86584i	−0.140506	−	0.140506i	0.633355	−	0.773861i	$-0.281677\pi$
$757$	−3.86584	−	3.86584i	−0.140506	−	0.140506i	−0.773861	+	0.633355i	$0.781677\pi$
$758$	0.676749	+	0.676749i	0.0245806	+	0.0245806i
$759$		0			0
$760$	7.59363	−	7.36270i	0.275450	−	0.267073i
$761$			28.1664i			1.02103i	0.859868	+	0.510516i	$0.170545\pi$
$761$			28.1664i			1.02103i	−0.859868	+	0.510516i	$0.829455\pi$
$762$		0			0
$763$	−7.25764	+	7.25764i	−0.262744	+	0.262744i
$764$	4.43574			0.160479
$765$		0			0
$766$	−19.8818			−0.718358
$767$	−16.1490	+	16.1490i	−0.583106	+	0.583106i
$768$		0			0
$769$			7.43020i			0.267940i	0.990985	+	0.133970i	$0.0427725\pi$
$769$			7.43020i			0.267940i	−0.990985	+	0.133970i	$0.957227\pi$
$770$	−0.0835909	+	5.41386i	−0.00301241	+	0.195102i
$771$		0			0
$772$	19.0869	+	19.0869i	0.686951	+	0.686951i
$773$	−28.8769	−	28.8769i	−1.03863	−	1.03863i	−0.999223	−	0.0394070i	$-0.987453\pi$
$773$	−28.8769	−	28.8769i	−1.03863	−	1.03863i	−0.0394070	−	0.999223i	$-0.512547\pi$
$774$		0			0
$775$	−6.05072	−	0.186893i	−0.217348	−	0.00671338i
$776$			2.09044i			0.0750425i
$777$		0			0
$778$	−2.40362	+	2.40362i	−0.0861739	+	0.0861739i
$779$	46.8104			1.67716
$780$		0			0
$781$	−7.56105			−0.270555
$782$	−5.76432	+	5.76432i	−0.206132	+	0.206132i
$783$		0			0
$784$			5.73017i			0.204649i
$785$	11.2161	+	11.5679i	0.400319	+	0.412875i
$786$		0			0
$787$	1.72312	+	1.72312i	0.0614226	+	0.0614226i	0.737151	−	0.675728i	$-0.236171\pi$
$787$	1.72312	+	1.72312i	0.0614226	+	0.0614226i	−0.675728	+	0.737151i	$0.736171\pi$
$788$	2.74011	+	2.74011i	0.0976124	+	0.0976124i
$789$		0			0
$790$	25.3167	+	26.1107i	0.900726	+	0.928977i
$791$			8.44698i			0.300340i
$792$		0			0
$793$	46.4975	−	46.4975i	1.65118	−	1.65118i
$794$	0.451158			0.0160110
$795$		0			0
$796$	11.7408			0.416143
$797$	11.4513	−	11.4513i	0.405625	−	0.405625i	−0.474585	−	0.880210i	$-0.657402\pi$
$797$	11.4513	−	11.4513i	0.405625	−	0.405625i	0.880210	+	0.474585i	$0.157402\pi$
$798$		0			0
$799$		−	11.9174i		−	0.421608i
$800$	3.64300	−	3.42470i	0.128800	−	0.121081i
$801$		0			0
$802$	11.9539	+	11.9539i	0.422109	+	0.422109i
$803$	6.77818	+	6.77818i	0.239197	+	0.239197i
$804$		0			0
$805$	0.317118	−	20.5385i	0.0111769	−	0.723887i
$806$		−	6.77818i		−	0.238751i
$807$		0			0
$808$	2.84564	−	2.84564i	0.100109	−	0.100109i
$809$	34.0791			1.19816			0.599078	−	0.800691i	$-0.295534\pi$
$809$	34.0791			1.19816			0.599078	+	0.800691i	$0.295534\pi$
$810$		0			0
$811$	−16.9872			−0.596502			−0.298251	−	0.954488i	$-0.596403\pi$
$811$	−16.9872			−0.596502			−0.298251	+	0.954488i	$0.596403\pi$
$812$	5.27526	−	5.27526i	0.185125	−	0.185125i
$813$		0			0
$814$		−	25.4436i		−	0.891797i
$815$	24.1735	−	23.4384i	0.846761	−	0.821010i
$816$		0			0
$817$	−11.7222	−	11.7222i	−0.410106	−	0.410106i
$818$	−27.3241	−	27.3241i	−0.955364	−	0.955364i
$819$		0			0
$820$	22.1258	+	0.341625i	0.772665	+	0.0119301i
$821$		−	17.7259i		−	0.618640i	−0.950958	−	0.309320i	$-0.899899\pi$
$821$		−	17.7259i		−	0.618640i	0.950958	−	0.309320i	$-0.100101\pi$
$822$		0			0
$823$	21.2135	−	21.2135i	0.739456	−	0.739456i	−0.233017	−	0.972473i	$-0.574860\pi$
$823$	21.2135	−	21.2135i	0.739456	−	0.739456i	0.972473	+	0.233017i	$0.0748597\pi$
$824$	−8.83830			−0.307897
$825$		0			0
$826$	4.59688			0.159946
$827$	9.94265	−	9.94265i	0.345740	−	0.345740i	−0.512780	−	0.858520i	$-0.671384\pi$
$827$	9.94265	−	9.94265i	0.345740	−	0.345740i	0.858520	+	0.512780i	$0.171384\pi$
$828$		0			0
$829$		−	30.9159i		−	1.07375i	−0.843660	−	0.536877i	$-0.819604\pi$
$829$		−	30.9159i		−	1.07375i	0.843660	−	0.536877i	$-0.180396\pi$
$830$	−34.8980	−	0.538830i	−1.21133	−	0.0187030i
$831$		0			0
$832$	3.95872	+	3.95872i	0.137244	+	0.137244i
$833$	4.05184	+	4.05184i	0.140388	+	0.140388i
$834$		0			0
$835$	−18.8064	+	18.2345i	−0.650821	+	0.631029i
$836$			10.1643i			0.351540i
$837$		0			0
$838$	13.4218	−	13.4218i	0.463649	−	0.463649i
$839$	−10.3354			−0.356818			−0.178409	−	0.983956i	$-0.557095\pi$
$839$	−10.3354			−0.356818			−0.178409	+	0.983956i	$0.557095\pi$
$840$		0			0
$841$	14.8301			0.511383
$842$	−0.491623	+	0.491623i	−0.0169425	+	0.0169425i
$843$		0			0
$844$			2.37452i			0.0817344i
$845$	0.633216	−	41.0110i	0.0217833	−	1.41082i
$846$		0			0
$847$	5.08571	+	5.08571i	0.174747	+	0.174747i
$848$	0.461295	+	0.461295i	0.0158409	+	0.0158409i
$849$		0			0
$850$	0.154365	−	4.99762i	0.00529466	−	0.171417i
$851$			96.5250i			3.30883i
$852$		0			0
$853$	34.6249	−	34.6249i	1.18553	−	1.18553i	0.207245	−	0.978289i	$-0.433550\pi$
$853$	34.6249	−	34.6249i	1.18553	−	1.18553i	0.978289	−	0.207245i	$-0.0664496\pi$
$854$	−13.2357			−0.452918
$855$		0			0
$856$	16.0730			0.549365
$857$	−6.14336	+	6.14336i	−0.209853	+	0.209853i	−0.804205	−	0.594352i	$-0.797409\pi$
$857$	−6.14336	+	6.14336i	−0.209853	+	0.209853i	0.594352	+	0.804205i	$0.297409\pi$
$858$		0			0
$859$		−	12.3389i		−	0.420997i	−0.977594	−	0.210498i	$-0.932491\pi$
$859$		−	12.3389i		−	0.420997i	0.977594	−	0.210498i	$-0.0675087\pi$
$860$	−5.45514	−	5.62624i	−0.186019	−	0.191853i
$861$		0			0
$862$	−10.0112	−	10.0112i	−0.340981	−	0.340981i
$863$	7.27751	+	7.27751i	0.247729	+	0.247729i	0.820038	−	0.572309i	$-0.193952\pi$
$863$	7.27751	+	7.27751i	0.247729	+	0.247729i	−0.572309	+	0.820038i	$0.693952\pi$
$864$		0			0
$865$	19.6500	+	20.2663i	0.668120	+	0.689075i
$866$		−	9.61146i		−	0.326611i
$867$		0			0
$868$	−0.964721	+	0.964721i	−0.0327448	+	0.0327448i
$869$	−34.9500			−1.18560
$870$		0			0
$871$	17.6443			0.597856
$872$	−6.44055	+	6.44055i	−0.218105	+	0.218105i
$873$		0			0
$874$		−	38.5603i		−	1.30432i
$875$	8.48664	+	9.31158i	0.286901	+	0.314789i
$876$		0			0
$877$	−0.963967	−	0.963967i	−0.0325509	−	0.0325509i	0.690644	−	0.723195i	$-0.257327\pi$
$877$	−0.963967	−	0.963967i	−0.0325509	−	0.0325509i	−0.723195	+	0.690644i	$0.757327\pi$
$878$	11.8275	+	11.8275i	0.399157	+	0.399157i
$879$		0			0
$880$	−0.0741799	+	4.80435i	−0.00250060	+	0.161955i
$881$			32.0589i			1.08009i	0.841636	+	0.540045i	$0.181593\pi$
$881$			32.0589i			1.08009i	−0.841636	+	0.540045i	$0.818407\pi$
$882$		0			0
$883$	−12.7318	+	12.7318i	−0.428460	+	0.428460i	−0.888103	−	0.459644i	$-0.847977\pi$
$883$	−12.7318	+	12.7318i	−0.428460	+	0.428460i	0.459644	+	0.888103i	$0.347977\pi$
$884$	5.59847			0.188297
$885$		0			0
$886$	−10.5033			−0.352864
$887$	9.48728	−	9.48728i	0.318552	−	0.318552i	−0.529659	−	0.848211i	$-0.677680\pi$
$887$	9.48728	−	9.48728i	0.318552	−	0.318552i	0.848211	+	0.529659i	$0.177680\pi$
$888$		0			0
$889$			21.3818i			0.717123i
$890$	17.3816	−	16.8530i	0.582632	−	0.564913i
$891$		0			0
$892$	11.0154	+	11.0154i	0.368824	+	0.368824i
$893$	39.8607	+	39.8607i	1.33389	+	1.33389i
$894$		0			0
$895$	37.9829	+	0.586462i	1.26963	+	0.0196033i
$896$		−	1.12687i		−	0.0376460i
$897$		0			0
$898$	−3.60307	+	3.60307i	−0.120236	+	0.120236i
$899$	−8.01549			−0.267332
$900$		0			0
$901$	0.652370			0.0217336
$902$	−15.0367	+	15.0367i	−0.500666	+	0.500666i
$903$		0			0
$904$			7.49599i			0.249313i
$905$	25.0986	+	0.387527i	0.834307	+	0.0128818i
$906$		0			0
$907$	−12.1634	−	12.1634i	−0.403880	−	0.403880i	0.475718	−	0.879598i	$-0.342188\pi$
$907$	−12.1634	−	12.1634i	−0.403880	−	0.403880i	−0.879598	+	0.475718i	$0.842188\pi$
$908$	14.1938	+	14.1938i	0.471037	+	0.471037i
$909$		0			0
$910$	−10.1278	+	9.81979i	−0.335733	+	0.325523i
$911$		−	45.4286i		−	1.50512i	−0.658525	−	0.752559i	$-0.728819\pi$
$911$		−	45.4286i		−	1.50512i	0.658525	−	0.752559i	$-0.271181\pi$
$912$		0			0
$913$	23.7166	−	23.7166i	0.784906	−	0.784906i
$914$	28.8134			0.953063
$915$		0			0
$916$	−0.0705584			−0.00233132
$917$	15.2292	−	15.2292i	0.502914	−	0.502914i
$918$		0			0
$919$			46.0422i			1.51879i	0.650630	+	0.759395i	$0.274505\pi$
$919$			46.0422i			1.51879i	−0.650630	+	0.759395i	$0.725495\pi$
$920$	0.281415	−	18.2262i	0.00927799	−	0.600900i
$921$		0			0
$922$	11.2274	+	11.2274i	0.369755	+	0.369755i
$923$	−13.9295	−	13.9295i	−0.458494	−	0.458494i
$924$		0			0
$925$	−40.5507	−	43.1356i	−1.33330	−	1.41829i
$926$		−	29.7697i		−	0.978293i
$927$		0			0
$928$	4.68135	−	4.68135i	0.153673	−	0.153673i
$929$	−46.2717			−1.51813			−0.759063	−	0.651018i	$-0.774342\pi$
$929$	−46.2717			−1.51813			−0.759063	+	0.651018i	$0.774342\pi$
$930$		0			0
$931$	−27.1047			−0.888320
$932$	4.10456	−	4.10456i	0.134449	−	0.134449i
$933$		0			0
$934$			5.75706i			0.188377i
$935$	3.34474	+	3.44964i	0.109385	+	0.112815i
$936$		0			0
$937$	18.9043	+	18.9043i	0.617576	+	0.617576i	0.944909	−	0.327333i	$-0.106150\pi$
$937$	18.9043	+	18.9043i	0.617576	+	0.617576i	−0.327333	+	0.944909i	$0.606150\pi$
$938$	−2.51127	−	2.51127i	−0.0819960	−	0.0819960i
$939$		0			0
$940$	18.5500	+	19.1318i	0.605033	+	0.624010i
$941$		−	21.0595i		−	0.686519i	−0.939241	−	0.343260i	$-0.888469\pi$
$941$		−	21.0595i		−	0.686519i	0.939241	−	0.343260i	$-0.111531\pi$
$942$		0			0
$943$	57.0444	−	57.0444i	1.85762	−	1.85762i
$944$	4.07935			0.132772
$945$		0			0
$946$	7.53090			0.244851
$947$	10.4376	−	10.4376i	0.339178	−	0.339178i	−0.516880	−	0.856058i	$-0.672907\pi$
$947$	10.4376	−	10.4376i	0.339178	−	0.339178i	0.856058	+	0.516880i	$0.172907\pi$
$948$		0			0
$949$			24.9745i			0.810706i
$950$	16.1994	+	17.2320i	0.525578	+	0.559081i
$951$		0			0
$952$	−0.796815	−	0.796815i	−0.0258249	−	0.0258249i
$953$	38.1698	+	38.1698i	1.23644	+	1.23644i	0.961446	+	0.274994i	$0.0886759\pi$
$953$	38.1698	+	38.1698i	1.23644	+	1.23644i	0.274994	+	0.961446i	$0.411324\pi$
$954$		0			0
$955$	−0.153127	+	9.91743i	−0.00495506	+	0.320921i
$956$			19.2176i			0.621540i
$957$		0			0
$958$	−0.312644	+	0.312644i	−0.0101011	+	0.0101011i
$959$	−13.0421			−0.421152
$960$		0			0
$961$	−29.5342			−0.952715
$962$	46.8739	−	46.8739i	1.51127	−	1.51127i
$963$		0			0
$964$		−	29.0221i		−	0.934740i
$965$	−43.3333	+	42.0155i	−1.39495	+	1.35253i
$966$		0			0
$967$	25.2765	+	25.2765i	0.812838	+	0.812838i	0.985058	−	0.172221i	$-0.0550942\pi$
$967$	25.2765	+	25.2765i	0.812838	+	0.812838i	−0.172221	+	0.985058i	$0.555094\pi$
$968$	4.51314	+	4.51314i	0.145058	+	0.145058i
$969$		0			0
$970$	−4.67382	−	0.0721644i	−0.150067	−	0.00231706i
$971$		−	8.47005i		−	0.271817i	−0.990721	−	0.135908i	$-0.956605\pi$
$971$		−	8.47005i		−	0.271817i	0.990721	−	0.135908i	$-0.0433953\pi$
$972$		0			0
$973$	−5.54291	+	5.54291i	−0.177698	+	0.177698i
$974$	−2.23633			−0.0716568
$975$		0			0
$976$	−11.7456			−0.375968
$977$	28.3027	−	28.3027i	0.905485	−	0.905485i	−0.0904191	−	0.995904i	$-0.528821\pi$
$977$	28.3027	−	28.3027i	0.905485	−	0.905485i	0.995904	+	0.0904191i	$0.0288206\pi$
$978$		0			0
$979$			23.2658i			0.743578i
$980$	−12.8115	−	0.197812i	−0.409249	−	0.00631887i
$981$		0			0
$982$	−21.0516	−	21.0516i	−0.671783	−	0.671783i
$983$	−13.4971	−	13.4971i	−0.430490	−	0.430490i	0.458305	−	0.888795i	$-0.348457\pi$
$983$	−13.4971	−	13.4971i	−0.430490	−	0.430490i	−0.888795	+	0.458305i	$0.848457\pi$
$984$		0			0
$985$	−6.22093	+	6.03175i	−0.198215	+	0.192188i
$986$		−	6.62043i		−	0.210837i
$987$		0			0
$988$	−18.7254	+	18.7254i	−0.595734	+	0.595734i
$989$	−28.5699			−0.908470
$990$		0			0
$991$	18.7401			0.595298			0.297649	−	0.954675i	$-0.403798\pi$
$991$	18.7401			0.595298			0.297649	+	0.954675i	$0.403798\pi$
$992$	−0.856109	+	0.856109i	−0.0271815	+	0.0271815i
$993$		0			0
$994$			3.96509i			0.125765i
$995$	−0.405307	+	26.2502i	−0.0128491	+	0.832187i
$996$		0			0
$997$	−31.6882	−	31.6882i	−1.00358	−	1.00358i	−0.999994	−	0.00358261i	$-0.998860\pi$
$997$	−31.6882	−	31.6882i	−1.00358	−	1.00358i	−0.00358261	−	0.999994i	$-0.501140\pi$
$998$	2.22056	+	2.22056i	0.0702904	+	0.0702904i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.m.i.647.4	✓	16
3.2	odd	2	inner	1530.2.m.i.647.5	yes	16
5.3	odd	4	inner	1530.2.m.i.953.5	yes	16
15.8	even	4	inner	1530.2.m.i.953.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.i.647.4	✓	16	1.1	even	1	trivial
1530.2.m.i.647.5	yes	16	3.2	odd	2	inner
1530.2.m.i.953.4	yes	16	15.8	even	4	inner
1530.2.m.i.953.5	yes	16	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(2.23580 + 0.0345211i) q^{5} +(0.796815 + 0.796815i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.60536 + 1.55654i) q^{10} -2.14883i q^{11} +(3.95872 - 3.95872i) q^{13} -1.12687 q^{14} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} -4.73017i q^{19} +(0.0345211 - 2.23580i) q^{20} +(1.51945 + 1.51945i) q^{22} +(-5.76432 - 5.76432i) q^{23} +(4.99762 + 0.154365i) q^{25} +5.59847i q^{26} +(0.796815 - 0.796815i) q^{28} +6.62043 q^{29} -1.21072 q^{31} +(0.707107 - 0.707107i) q^{32} -1.00000i q^{34} +(1.75401 + 1.80903i) q^{35} +(-8.37262 - 8.37262i) q^{37} +(3.34474 + 3.34474i) q^{38} +(1.55654 + 1.60536i) q^{40} +9.89612i q^{41} +(2.47817 - 2.47817i) q^{43} -2.14883 q^{44} +8.15198 q^{46} +(-8.42690 + 8.42690i) q^{47} -5.73017i q^{49} +(-3.64300 + 3.42470i) q^{50} +(-3.95872 - 3.95872i) q^{52} +(-0.461295 - 0.461295i) q^{53} +(0.0741799 - 4.80435i) q^{55} +1.12687i q^{56} +(-4.68135 + 4.68135i) q^{58} -4.07935 q^{59} +11.7456 q^{61} +(0.856109 - 0.856109i) q^{62} +1.00000i q^{64} +(8.98756 - 8.71424i) q^{65} +(2.22854 + 2.22854i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-2.51945 - 0.0389007i) q^{70} -3.51868i q^{71} +(-3.15436 + 3.15436i) q^{73} +11.8407 q^{74} -4.73017 q^{76} +(1.71222 - 1.71222i) q^{77} -16.2647i q^{79} +(-2.23580 - 0.0345211i) q^{80} +(-6.99762 - 6.99762i) q^{82} +(11.0370 + 11.0370i) q^{83} +(-1.60536 + 1.55654i) q^{85} +3.50466i q^{86} +(1.51945 - 1.51945i) q^{88} -10.8272 q^{89} +6.30873 q^{91} +(-5.76432 + 5.76432i) q^{92} -11.9174i q^{94} +(0.163291 - 10.5757i) q^{95} +(1.47817 + 1.47817i) q^{97} +(4.05184 + 4.05184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{10} - 16 q^{16} + 8 q^{22} - 16 q^{25} + 40 q^{31} - 24 q^{37} + 4 q^{40} - 40 q^{43} + 56 q^{46} - 8 q^{55} - 8 q^{58} + 88 q^{61} + 48 q^{67} - 24 q^{70} - 72 q^{73} - 16 q^{82} + 4 q^{85}+ \cdots - 56 q^{97}+O(q^{100}) \) 16 * q + 4 * q^10 - 16 * q^16 + 8 * q^22 - 16 * q^25 + 40 * q^31 - 24 * q^37 + 4 * q^40 - 40 * q^43 + 56 * q^46 - 8 * q^55 - 8 * q^58 + 88 * q^61 + 48 * q^67 - 24 * q^70 - 72 * q^73 - 16 * q^82 + 4 * q^85 + 8 * q^88 + 144 * q^91 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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