LMFDB - Embedded newform 432.2.u.b.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.2
Root			$0.500000 - 0.168222i$ of defining polynomial
Character	$\chi$	$=$	432.49
Dual form			432.2.u.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36085 + 1.07149i) q^{3} +(0.696050 - 0.253341i) q^{5} +(-0.717657 - 4.07003i) q^{7} +(0.703829 + 2.91627i) q^{9} +(4.27215 + 1.55493i) q^{11} +(0.662744 + 0.556108i) q^{13} +(1.21867 + 0.401049i) q^{15} +(2.17975 - 3.77544i) q^{17} +(0.777964 + 1.34747i) q^{19} +(3.38437 - 6.30767i) q^{21} +(0.608539 - 3.45119i) q^{23} +(-3.40992 + 2.86126i) q^{25} +(-2.16694 + 4.72275i) q^{27} +(-2.50318 + 2.10042i) q^{29} +(-1.85778 + 10.5360i) q^{31} +(4.14766 + 6.69359i) q^{33} +(-1.53063 - 2.65113i) q^{35} +(0.880842 - 1.52566i) q^{37} +(0.306033 + 1.46690i) q^{39} +(-1.97401 - 1.65639i) q^{41} +(-2.58757 - 0.941797i) q^{43} +(1.22871 + 1.85156i) q^{45} +(-1.68378 - 9.54918i) q^{47} +(-9.47229 + 3.44763i) q^{49} +(7.01165 - 2.80223i) q^{51} +4.00839 q^{53} +3.36756 q^{55} +(-0.385108 + 2.66729i) q^{57} +(1.34517 - 0.489601i) q^{59} +(-0.751711 - 4.26317i) q^{61} +(11.3642 - 4.95749i) q^{63} +(0.602188 + 0.219178i) q^{65} +(-10.0444 - 8.42825i) q^{67} +(4.52604 - 4.04452i) q^{69} +(-2.54213 + 4.40310i) q^{71} +(0.286636 + 0.496469i) q^{73} +(-7.70620 + 0.240065i) q^{75} +(3.26270 - 18.5037i) q^{77} +(-5.17820 + 4.34502i) q^{79} +(-8.00925 + 4.10511i) q^{81} +(-7.06556 + 5.92871i) q^{83} +(0.560740 - 3.18011i) q^{85} +(-5.65702 + 0.176229i) q^{87} +(6.19947 + 10.7378i) q^{89} +(1.78776 - 3.09648i) q^{91} +(-13.8173 + 12.3473i) q^{93} +(0.882872 + 0.740818i) q^{95} +(-5.40770 - 1.96824i) q^{97} +(-1.52774 + 13.5531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9} + 12 q^{11} + 12 q^{13} + 18 q^{15} - 6 q^{17} + 9 q^{19} + 24 q^{21} - 30 q^{23} - 9 q^{25} + 15 q^{29} + 36 q^{33} - 3 q^{35} - 15 q^{37} + 42 q^{39} - 12 q^{41} - 9 q^{43}+ \cdots - 9 q^{99}+O(q^{100}) $ 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9 + 12 * q^11 + 12 * q^13 + 18 * q^15 - 6 * q^17 + 9 * q^19 + 24 * q^21 - 30 * q^23 - 9 * q^25 + 15 * q^29 + 36 * q^33 - 3 * q^35 - 15 * q^37 + 42 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^45 + 9 * q^47 - 39 * q^49 + 27 * q^51 - 12 * q^53 - 18 * q^55 + 18 * q^57 - 12 * q^59 - 36 * q^61 - 3 * q^63 - 15 * q^65 - 36 * q^67 + 18 * q^69 - 12 * q^71 - 21 * q^73 - 30 * q^75 + 3 * q^77 - 39 * q^79 - 18 * q^83 + 45 * q^85 - 27 * q^87 + 12 * q^89 + 6 * q^91 - 33 * q^93 + 15 * q^95 + 39 * q^97 - 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.36085	+	1.07149i	0.785688	+	0.618624i
$3$	1.36085	+	1.07149i	0.785688	+	0.618624i
$4$		0			0
$5$	0.696050	−	0.253341i	0.311283	−	0.113298i	−0.181655	−	0.983362i	$-0.558145\pi$
$5$	0.696050	−	0.253341i	0.311283	−	0.113298i	0.492938	+	0.870065i	$0.335923\pi$
$6$		0			0
$7$	−0.717657	−	4.07003i	−0.271249	−	1.53833i	−0.750631	−	0.660722i	$-0.770250\pi$
$7$	−0.717657	−	4.07003i	−0.271249	−	1.53833i	0.479382	−	0.877606i	$-0.340861\pi$
$8$		0			0
$9$	0.703829	+	2.91627i	0.234610	+	0.972090i
$10$		0			0
$11$	4.27215	+	1.55493i	1.28810	+	0.468830i	0.893103	−	0.449852i	$-0.148523\pi$
$11$	4.27215	+	1.55493i	1.28810	+	0.468830i	0.394998	+	0.918682i	$0.370745\pi$
$12$		0			0
$13$	0.662744	+	0.556108i	0.183812	+	0.154237i	0.730051	−	0.683393i	$-0.239496\pi$
$13$	0.662744	+	0.556108i	0.183812	+	0.154237i	−0.546239	+	0.837630i	$0.683941\pi$
$14$		0			0
$15$	1.21867	+	0.401049i	0.314660	+	0.103550i
$16$		0			0
$17$	2.17975	−	3.77544i	0.528667	−	0.915678i	−0.470774	−	0.882254i	$-0.656025\pi$
$17$	2.17975	−	3.77544i	0.528667	−	0.915678i	0.999441	−	0.0334246i	$-0.0106414\pi$
$18$		0			0
$19$	0.777964	+	1.34747i	0.178477	+	0.309132i	0.941359	−	0.337406i	$-0.109550\pi$
$19$	0.777964	+	1.34747i	0.178477	+	0.309132i	−0.762882	+	0.646538i	$0.776216\pi$
$20$		0			0
$21$	3.38437	−	6.30767i	0.738529	−	1.37645i
$22$		0			0
$23$	0.608539	−	3.45119i	0.126889	−	0.719624i	−0.853279	−	0.521455i	$-0.825389\pi$
$23$	0.608539	−	3.45119i	0.126889	−	0.719624i	0.980168	−	0.198169i	$-0.0634994\pi$
$24$		0			0
$25$	−3.40992	+	2.86126i	−0.681984	+	0.572252i
$26$		0			0
$27$	−2.16694	+	4.72275i	−0.417028	+	0.908894i
$28$		0			0
$29$	−2.50318	+	2.10042i	−0.464829	+	0.390038i	−0.844904	−	0.534918i	$-0.820343\pi$
$29$	−2.50318	+	2.10042i	−0.464829	+	0.390038i	0.380075	+	0.924956i	$0.375898\pi$
$30$		0			0
$31$	−1.85778	+	10.5360i	−0.333667	+	1.89232i	0.106350	+	0.994329i	$0.466084\pi$
$31$	−1.85778	+	10.5360i	−0.333667	+	1.89232i	−0.440016	+	0.897990i	$0.645027\pi$
$32$		0			0
$33$	4.14766	+	6.69359i	0.722015	+	1.16520i
$34$		0			0
$35$	−1.53063	−	2.65113i	−0.258724	−	0.448123i
$36$		0			0
$37$	0.880842	−	1.52566i	0.144810	−	0.250817i	−0.784492	−	0.620139i	$-0.787076\pi$
$37$	0.880842	−	1.52566i	0.144810	−	0.250817i	0.929302	+	0.369321i	$0.120410\pi$
$38$		0			0
$39$	0.306033	+	1.46690i	0.0490044	+	0.234892i
$40$		0			0
$41$	−1.97401	−	1.65639i	−0.308289	−	0.258685i	0.475495	−	0.879718i	$-0.342269\pi$
$41$	−1.97401	−	1.65639i	−0.308289	−	0.258685i	−0.783784	+	0.621033i	$0.786713\pi$
$42$		0			0
$43$	−2.58757	−	0.941797i	−0.394600	−	0.143623i	0.137096	−	0.990558i	$-0.456223\pi$
$43$	−2.58757	−	0.941797i	−0.394600	−	0.143623i	−0.531696	+	0.846935i	$0.678445\pi$
$44$		0			0
$45$	1.22871	+	1.85156i	0.183166	+	0.276014i
$46$		0			0
$47$	−1.68378	−	9.54918i	−0.245604	−	1.39289i	−0.819085	−	0.573672i	$-0.805519\pi$
$47$	−1.68378	−	9.54918i	−0.245604	−	1.39289i	0.573481	−	0.819219i	$-0.305593\pi$
$48$		0			0
$49$	−9.47229	+	3.44763i	−1.35318	+	0.492519i
$50$		0			0
$51$	7.01165	−	2.80223i	0.981827	−	0.392391i
$52$		0			0
$53$	4.00839			0.550595			0.275297	−	0.961359i	$-0.411224\pi$
$53$	4.00839			0.550595			0.275297	+	0.961359i	$0.411224\pi$
$54$		0			0
$55$	3.36756			0.454081
$56$		0			0
$57$	−0.385108	+	2.66729i	−0.0510088	+	0.353291i
$58$		0			0
$59$	1.34517	−	0.489601i	0.175126	−	0.0637406i	−0.252969	−	0.967474i	$-0.581407\pi$
$59$	1.34517	−	0.489601i	0.175126	−	0.0637406i	0.428095	+	0.903734i	$0.359185\pi$
$60$		0			0
$61$	−0.751711	−	4.26317i	−0.0962468	−	0.545843i	−0.994358	−	0.106075i	$-0.966172\pi$
$61$	−0.751711	−	4.26317i	−0.0962468	−	0.545843i	0.898111	−	0.439768i	$-0.144939\pi$
$62$		0			0
$63$	11.3642	−	4.95749i	1.43175	−	0.624585i
$64$		0			0
$65$	0.602188	+	0.219178i	0.0746922	+	0.0271857i
$66$		0			0
$67$	−10.0444	−	8.42825i	−1.22712	−	1.02967i	−0.998421	−	0.0561764i	$-0.982109\pi$
$67$	−10.0444	−	8.42825i	−1.22712	−	1.02967i	−0.228697	−	0.973498i	$-0.573446\pi$
$68$		0			0
$69$	4.52604	−	4.04452i	0.544871	−	0.486903i
$70$		0			0
$71$	−2.54213	+	4.40310i	−0.301695	+	0.522551i	−0.976520	−	0.215427i	$-0.930886\pi$
$71$	−2.54213	+	4.40310i	−0.301695	+	0.522551i	0.674825	+	0.737978i	$0.264219\pi$
$72$		0			0
$73$	0.286636	+	0.496469i	0.0335483	+	0.0581073i	0.882312	−	0.470665i	$-0.155986\pi$
$73$	0.286636	+	0.496469i	0.0335483	+	0.0581073i	−0.848764	+	0.528772i	$0.822653\pi$
$74$		0			0
$75$	−7.70620	+	0.240065i	−0.889835	+	0.0277203i
$76$		0			0
$77$	3.26270	−	18.5037i	0.371819	−	2.10869i
$78$		0			0
$79$	−5.17820	+	4.34502i	−0.582593	+	0.488853i	−0.885797	−	0.464072i	$-0.846388\pi$
$79$	−5.17820	+	4.34502i	−0.582593	+	0.488853i	0.303205	+	0.952925i	$0.401943\pi$
$80$		0			0
$81$	−8.00925	+	4.10511i	−0.889916	+	0.456124i
$82$		0			0
$83$	−7.06556	+	5.92871i	−0.775546	+	0.650761i	−0.942123	−	0.335268i	$-0.891173\pi$
$83$	−7.06556	+	5.92871i	−0.775546	+	0.650761i	0.166577	+	0.986029i	$0.446729\pi$
$84$		0			0
$85$	0.560740	−	3.18011i	0.0608208	−	0.344932i
$86$		0			0
$87$	−5.65702	+	0.176229i	−0.606497	+	0.0188937i
$88$		0			0
$89$	6.19947	+	10.7378i	0.657142	+	1.13820i	0.981352	+	0.192219i	$0.0615683\pi$
$89$	6.19947	+	10.7378i	0.657142	+	1.13820i	−0.324210	+	0.945985i	$0.605098\pi$
$90$		0			0
$91$	1.78776	−	3.09648i	0.187408	−	0.324600i
$92$		0			0
$93$	−13.8173	+	12.3473i	−1.43279	+	1.28036i
$94$		0			0
$95$	0.882872	+	0.740818i	0.0905808	+	0.0760063i
$96$		0			0
$97$	−5.40770	−	1.96824i	−0.549069	−	0.199845i	0.0525637	−	0.998618i	$-0.483261\pi$
$97$	−5.40770	−	1.96824i	−0.549069	−	0.199845i	−0.601633	+	0.798773i	$0.705483\pi$
$98$		0			0
$99$	−1.52774	+	13.5531i	−0.153544	+	1.36214i
$100$		0			0
$101$	−1.91700	−	10.8718i	−0.190748	−	1.08179i	−0.918345	−	0.395782i	$-0.870474\pi$
$101$	−1.91700	−	10.8718i	−0.190748	−	1.08179i	0.727596	−	0.686006i	$-0.240637\pi$
$102$		0			0
$103$	−6.03419	+	2.19627i	−0.594567	+	0.216405i	−0.621737	−	0.783226i	$-0.713573\pi$
$103$	−6.03419	+	2.19627i	−0.594567	+	0.216405i	0.0271702	+	0.999631i	$0.491350\pi$
$104$		0			0
$105$	0.757693	−	5.24785i	0.0739433	−	0.512138i
$106$		0			0
$107$	17.2923			1.67171			0.835854	−	0.548952i	$-0.184973\pi$
$107$	17.2923			1.67171			0.835854	+	0.548952i	$0.184973\pi$
$108$		0			0
$109$	−9.94570			−0.952626			−0.476313	−	0.879276i	$-0.658027\pi$
$109$	−9.94570			−0.952626			−0.476313	+	0.879276i	$0.658027\pi$
$110$		0			0
$111$	2.83342	−	1.13239i	0.268937	−	0.107482i
$112$		0			0
$113$	−2.30350	+	0.838405i	−0.216695	+	0.0788705i	−0.448087	−	0.893990i	$-0.647894\pi$
$113$	−2.30350	+	0.838405i	−0.216695	+	0.0788705i	0.231392	+	0.972861i	$0.425672\pi$
$114$		0			0
$115$	−0.450757	−	2.55637i	−0.0420333	−	0.238383i
$116$		0			0
$117$	−1.15530	+	2.32414i	−0.106808	+	0.214867i
$118$		0			0
$119$	−16.9305	−	6.16219i	−1.55201	−	0.564887i
$120$		0			0
$121$	7.40693	+	6.21515i	0.673357	+	0.565014i
$122$		0			0
$123$	−0.911532	−	4.36924i	−0.0821901	−	0.393961i
$124$		0			0
$125$	−3.50040	+	6.06287i	−0.313085	+	0.542279i
$126$		0			0
$127$	4.05136	+	7.01715i	0.359500	+	0.622672i	0.987877	−	0.155237i	$-0.0496140\pi$
$127$	4.05136	+	7.01715i	0.359500	+	0.622672i	−0.628378	+	0.777908i	$0.716281\pi$
$128$		0			0
$129$	−2.51217	−	4.05419i	−0.221184	−	0.356951i
$130$		0			0
$131$	2.76007	−	15.6532i	0.241149	−	1.36762i	−0.588120	−	0.808773i	$-0.700132\pi$
$131$	2.76007	−	15.6532i	0.241149	−	1.36762i	0.829269	−	0.558849i	$-0.188757\pi$
$132$		0			0
$133$	4.92595	−	4.13336i	0.427134	−	0.358408i
$134$		0			0
$135$	−0.311829	+	3.83624i	−0.0268379	+	0.330171i
$136$		0			0
$137$	−9.46551	+	7.94250i	−0.808693	+	0.678574i	−0.950295	−	0.311350i	$-0.899219\pi$
$137$	−9.46551	+	7.94250i	−0.808693	+	0.678574i	0.141603	+	0.989924i	$0.454775\pi$
$138$		0			0
$139$	0.761169	−	4.31680i	0.0645615	−	0.366146i	−0.935361	−	0.353695i	$-0.884925\pi$
$139$	0.761169	−	4.31680i	0.0645615	−	0.366146i	0.999922	−	0.0124519i	$-0.00396366\pi$
$140$		0			0
$141$	7.94045	−	14.7992i	0.668707	−	1.24631i
$142$		0			0
$143$	1.96663	+	3.40630i	0.164458	+	0.284849i
$144$		0			0
$145$	−1.21021	+	2.09615i	−0.100503	+	0.174076i
$146$		0			0
$147$	−16.5845	−	5.45773i	−1.36786	−	0.450146i
$148$		0			0
$149$	5.23476	+	4.39248i	0.428848	+	0.359846i	0.831517	−	0.555499i	$-0.187473\pi$
$149$	5.23476	+	4.39248i	0.428848	+	0.359846i	−0.402669	+	0.915346i	$0.631917\pi$
$150$		0			0
$151$	−4.89254	−	1.78074i	−0.398149	−	0.144915i	0.135182	−	0.990821i	$-0.456838\pi$
$151$	−4.89254	−	1.78074i	−0.398149	−	0.144915i	−0.533332	+	0.845906i	$0.679060\pi$
$152$		0			0
$153$	12.5444	+	3.69947i	1.01415	+	0.299085i
$154$		0			0
$155$	1.37609	+	7.80422i	0.110531	+	0.626850i
$156$		0			0
$157$	−3.73260	+	1.35856i	−0.297894	+	0.108424i	−0.486643	−	0.873601i	$-0.661779\pi$
$157$	−3.73260	+	1.35856i	−0.297894	+	0.108424i	0.188749	+	0.982025i	$0.439557\pi$
$158$		0			0
$159$	5.45482	+	4.29494i	0.432595	+	0.340611i
$160$		0			0
$161$	−14.4832			−1.14144
$162$		0			0
$163$	−2.34707			−0.183837			−0.0919184	−	0.995767i	$-0.529300\pi$
$163$	−2.34707			−0.183837			−0.0919184	+	0.995767i	$0.529300\pi$
$164$		0			0
$165$	4.58274	+	3.60829i	0.356766	+	0.280905i
$166$		0			0
$167$	−0.989141	+	0.360018i	−0.0765420	+	0.0278590i	−0.380007	−	0.924983i	$-0.624079\pi$
$167$	−0.989141	+	0.360018i	−0.0765420	+	0.0278590i	0.303465	+	0.952842i	$0.401856\pi$
$168$		0			0
$169$	−2.12745	−	12.0654i	−0.163650	−	0.928107i
$170$		0			0
$171$	−3.38204	+	3.21714i	−0.258631	+	0.246021i
$172$		0			0
$173$	−6.42081	−	2.33699i	−0.488166	−	0.177678i	0.0861981	−	0.996278i	$-0.472528\pi$
$173$	−6.42081	−	2.33699i	−0.488166	−	0.177678i	−0.574364	+	0.818600i	$0.694750\pi$
$174$		0			0
$175$	14.0926	+	11.8251i	1.06530	+	0.893892i
$176$		0			0
$177$	2.35517	+	0.775057i	0.177026	+	0.0582568i
$178$		0			0
$179$	−1.09877	+	1.90312i	−0.0821258	+	0.142246i	−0.904163	−	0.427188i	$-0.859504\pi$
$179$	−1.09877	+	1.90312i	−0.0821258	+	0.142246i	0.822037	+	0.569434i	$0.192838\pi$
$180$		0			0
$181$	7.86998	+	13.6312i	0.584971	+	1.01320i	0.994879	+	0.101073i	$0.0322275\pi$
$181$	7.86998	+	13.6312i	0.584971	+	1.01320i	−0.409908	+	0.912127i	$0.634439\pi$
$182$		0			0
$183$	3.54496	−	6.60698i	0.262051	−	0.488402i
$184$		0			0
$185$	0.226596	−	1.28509i	0.0166597	−	0.0944818i
$186$		0			0
$187$	15.1828	−	12.7399i	1.11027	−	0.931631i
$188$		0			0
$189$	20.7769	+	5.43020i	1.51129	+	0.394989i
$190$		0			0
$191$	−6.00686	+	5.04036i	−0.434641	+	0.364707i	−0.833700	−	0.552218i	$-0.813782\pi$
$191$	−6.00686	+	5.04036i	−0.434641	+	0.364707i	0.399058	+	0.916926i	$0.369337\pi$
$192$		0			0
$193$	−2.87224	+	16.2893i	−0.206748	+	1.17253i	0.687916	+	0.725790i	$0.258526\pi$
$193$	−2.87224	+	16.2893i	−0.206748	+	1.17253i	−0.894665	+	0.446738i	$0.852586\pi$
$194$		0			0
$195$	0.584641	+	0.943505i	0.0418670	+	0.0675658i
$196$		0			0
$197$	5.68810	+	9.85208i	0.405260	+	0.701931i	0.994352	−	0.106135i	$-0.0338476\pi$
$197$	5.68810	+	9.85208i	0.405260	+	0.701931i	−0.589091	+	0.808066i	$0.700514\pi$
$198$		0			0
$199$	0.936258	−	1.62165i	0.0663696	−	0.114955i	−0.830931	−	0.556375i	$-0.812192\pi$
$199$	0.936258	−	1.62165i	0.0663696	−	0.114955i	0.897301	+	0.441420i	$0.145525\pi$
$200$		0			0
$201$	−4.63816	−	22.2320i	−0.327151	−	1.56813i
$202$		0			0
$203$	10.3452	+	8.68065i	0.726090	+	0.609262i
$204$		0			0
$205$	−1.79364	−	0.652833i	−0.125274	−	0.0455958i
$206$		0			0
$207$	10.4929	−	0.654390i	0.729308	−	0.0454832i
$208$		0			0
$209$	1.22834	+	6.96629i	0.0849663	+	0.481868i
$210$		0			0
$211$	5.14025	−	1.87090i	0.353870	−	0.128798i	−0.158968	−	0.987284i	$-0.550817\pi$
$211$	5.14025	−	1.87090i	0.353870	−	0.128798i	0.512837	+	0.858486i	$0.328594\pi$
$212$		0			0
$213$	−8.17732	+	3.26810i	−0.560301	+	0.223926i
$214$		0			0
$215$	−2.03967			−0.139104
$216$		0			0
$217$	44.2150			3.00151
$218$		0			0
$219$	−0.141891	+	0.982747i	−0.00958809	+	0.0664079i
$220$		0			0
$221$	3.54417	−	1.28997i	0.238407	−	0.0867729i
$222$		0			0
$223$	0.219638	+	1.24563i	0.0147080	+	0.0834134i	0.991278	−	0.131786i	$-0.0420711\pi$
$223$	0.219638	+	1.24563i	0.0147080	+	0.0834134i	−0.976570	+	0.215199i	$0.930960\pi$
$224$		0			0
$225$	−10.7442	−	7.93040i	−0.716281	−	0.528693i
$226$		0			0
$227$	9.34189	+	3.40017i	0.620043	+	0.225677i	0.632892	−	0.774240i	$-0.281868\pi$
$227$	9.34189	+	3.40017i	0.620043	+	0.225677i	−0.0128486	+	0.999917i	$0.504090\pi$
$228$		0			0
$229$	−7.64692	−	6.41653i	−0.505323	−	0.424016i	0.354157	−	0.935186i	$-0.384768\pi$
$229$	−7.64692	−	6.41653i	−0.505323	−	0.424016i	−0.859480	+	0.511170i	$0.829212\pi$
$230$		0			0
$231$	24.2665	−	21.6848i	1.59662	−	1.42676i
$232$		0			0
$233$	13.5765	−	23.5152i	0.889428	−	1.54053i	0.0488748	−	0.998805i	$-0.484436\pi$
$233$	13.5765	−	23.5152i	0.889428	−	1.54053i	0.840553	−	0.541729i	$-0.182230\pi$
$234$		0			0
$235$	−3.59119	−	6.22013i	−0.234264	−	0.405757i
$236$		0			0
$237$	−11.7024	+	0.364555i	−0.760152	+	0.0236804i
$238$		0			0
$239$	3.39241	−	19.2393i	0.219437	−	1.24449i	−0.653602	−	0.756839i	$-0.726743\pi$
$239$	3.39241	−	19.2393i	0.219437	−	1.24449i	0.873039	−	0.487651i	$-0.162146\pi$
$240$		0			0
$241$	12.4216	−	10.4229i	0.800144	−	0.671400i	−0.148090	−	0.988974i	$-0.547312\pi$
$241$	12.4216	−	10.4229i	0.800144	−	0.671400i	0.948234	+	0.317573i	$0.102868\pi$
$242$		0			0
$243$	−15.2980	−	2.99536i	−0.981365	−	0.192153i
$244$		0			0
$245$	−5.71975	+	4.79944i	−0.365422	+	0.306625i
$246$		0			0
$247$	−0.233750	+	1.32566i	−0.0148731	+	0.0843498i
$248$		0			0
$249$	−15.9677	+	0.497429i	−1.01191	+	0.0315233i
$250$		0			0
$251$	11.7303	+	20.3174i	0.740408	+	1.28242i	0.952310	+	0.305133i	$0.0987010\pi$
$251$	11.7303	+	20.3174i	0.740408	+	1.28242i	−0.211902	+	0.977291i	$0.567966\pi$
$252$		0			0
$253$	7.96615	−	13.7978i	0.500827	−	0.867458i
$254$		0			0
$255$	4.17053	−	3.72683i	0.261169	−	0.233383i
$256$		0			0
$257$	16.8456	+	14.1352i	1.05080	+	0.881728i	0.993178	−	0.116611i	$-0.0372030\pi$
$257$	16.8456	+	14.1352i	1.05080	+	0.881728i	0.0576244	+	0.998338i	$0.481647\pi$
$258$		0			0
$259$	−6.84164	−	2.49015i	−0.425119	−	0.154731i
$260$		0			0
$261$	−7.88719	−	5.82161i	−0.488205	−	0.360349i
$262$		0			0
$263$	4.07773	+	23.1260i	0.251444	+	1.42601i	0.805039	+	0.593222i	$0.202144\pi$
$263$	4.07773	+	23.1260i	0.251444	+	1.42601i	−0.553595	+	0.832786i	$0.686745\pi$
$264$		0			0
$265$	2.79004	−	1.01549i	0.171391	−	0.0623811i
$266$		0			0
$267$	−3.06886	+	21.2552i	−0.187811	+	1.30080i
$268$		0			0
$269$	18.3001			1.11578			0.557888	−	0.829916i	$-0.311612\pi$
$269$	18.3001			1.11578			0.557888	+	0.829916i	$0.311612\pi$
$270$		0			0
$271$	16.4825			1.00124			0.500620	−	0.865667i	$-0.333105\pi$
$271$	16.4825			1.00124			0.500620	+	0.865667i	$0.333105\pi$
$272$		0			0
$273$	5.75071	−	2.29829i	0.348049	−	0.139099i
$274$		0			0
$275$	−19.0167	+	6.92153i	−1.14675	+	0.417384i
$276$		0			0
$277$	1.95736	+	11.1008i	0.117606	+	0.666980i	0.985427	+	0.170101i	$0.0544094\pi$
$277$	1.95736	+	11.1008i	0.117606	+	0.666980i	−0.867820	+	0.496878i	$0.834479\pi$
$278$		0			0
$279$	−32.0333	+	1.99776i	−1.91778	+	0.119602i
$280$		0			0
$281$	0.681601	+	0.248083i	0.0406609	+	0.0147994i	0.362271	−	0.932073i	$-0.382002\pi$
$281$	0.681601	+	0.248083i	0.0406609	+	0.0147994i	−0.321610	+	0.946872i	$0.604224\pi$
$282$		0			0
$283$	16.9589	+	14.2302i	1.00810	+	0.845897i	0.988086	−	0.153903i	$-0.0491843\pi$
$283$	16.9589	+	14.2302i	1.00810	+	0.845897i	0.0200144	+	0.999800i	$0.493629\pi$
$284$		0			0
$285$	0.407680	+	1.95413i	0.0241489	+	0.115753i
$286$		0			0
$287$	−5.32491	+	9.22302i	−0.314320	+	0.544418i
$288$		0			0
$289$	−1.00263	−	1.73660i	−0.0589780	−	0.102153i
$290$		0			0
$291$	−5.25013	−	8.47277i	−0.307768	−	0.496683i
$292$		0			0
$293$	−1.13889	+	6.45895i	−0.0665344	+	0.377336i	0.933299	+	0.359100i	$0.116916\pi$
$293$	−1.13889	+	6.45895i	−0.0665344	+	0.377336i	−0.999834	+	0.0182360i	$0.994195\pi$
$294$		0			0
$295$	0.812267	−	0.681573i	0.0472920	−	0.0396827i
$296$		0			0
$297$	−16.6010	+	16.8068i	−0.963290	+	0.975232i
$298$		0			0
$299$	2.32254	−	1.94884i	0.134316	−	0.112705i
$300$		0			0
$301$	−1.97616	+	11.2074i	−0.113904	+	0.645982i
$302$		0			0
$303$	9.04028	−	16.8490i	0.519351	−	0.967948i
$304$		0			0
$305$	−1.60326	−	2.77694i	−0.0918027	−	0.159007i
$306$		0			0
$307$	3.98740	−	6.90639i	0.227573	−	0.394168i	−0.729515	−	0.683965i	$-0.760254\pi$
$307$	3.98740	−	6.90639i	0.227573	−	0.394168i	0.957088	+	0.289796i	$0.0935876\pi$
$308$		0			0
$309$	−10.5649	−	3.47677i	−0.601016	−	0.197787i
$310$		0			0
$311$	−10.8380	−	9.09419i	−0.614569	−	0.515684i	0.281522	−	0.959555i	$-0.409161\pi$
$311$	−10.8380	−	9.09419i	−0.614569	−	0.515684i	−0.896091	+	0.443870i	$0.853605\pi$
$312$		0			0
$313$	−22.5917	−	8.22270i	−1.27696	−	0.464774i	−0.387532	−	0.921856i	$-0.626672\pi$
$313$	−22.5917	−	8.22270i	−1.27696	−	0.464774i	−0.889425	+	0.457082i	$0.848895\pi$
$314$		0			0
$315$	6.65411	−	6.32968i	0.374917	−	0.356637i
$316$		0			0
$317$	3.15913	+	17.9163i	0.177435	+	1.00628i	0.935296	+	0.353866i	$0.115133\pi$
$317$	3.15913	+	17.9163i	0.177435	+	1.00628i	−0.757862	+	0.652415i	$0.773756\pi$
$318$		0			0
$319$	−13.9600	+	5.08101i	−0.781608	+	0.284482i
$320$		0			0
$321$	23.5322	+	18.5285i	1.31344	+	1.03416i
$322$		0			0
$323$	6.78307			0.377420
$324$		0			0
$325$	−3.85107			−0.213619
$326$		0			0
$327$	−13.5346	−	10.6567i	−0.748466	−	0.589317i
$328$		0			0
$329$	−37.6571	+	13.7061i	−2.07610	+	0.755640i
$330$		0			0
$331$	−3.11884	−	17.6878i	−0.171427	−	0.972212i	−0.942187	−	0.335086i	$-0.891234\pi$
$331$	−3.11884	−	17.6878i	−0.171427	−	0.972212i	0.770760	−	0.637125i	$-0.219877\pi$
$332$		0			0
$333$	5.06921	+	1.49497i	0.277791	+	0.0819236i
$334$		0			0
$335$	−9.12662	−	3.32182i	−0.498640	−	0.181490i
$336$		0			0
$337$	−17.9989	−	15.1029i	−0.980462	−	0.822705i	0.00369714	−	0.999993i	$-0.498823\pi$
$337$	−17.9989	−	15.1029i	−0.980462	−	0.822705i	−0.984159	+	0.177288i	$0.943268\pi$
$338$		0			0
$339$	−4.03306	−	1.32723i	−0.219046	−	0.0720850i
$340$		0			0
$341$	−24.3195	+	42.1225i	−1.31697	+	2.28106i
$342$		0			0
$343$	6.36495	+	11.0244i	0.343675	+	0.595263i
$344$		0			0
$345$	2.12571	−	3.96182i	0.114444	−	0.213297i
$346$		0			0
$347$	−1.44691	+	8.20582i	−0.0776741	+	0.440512i	0.921024	+	0.389505i	$0.127354\pi$
$347$	−1.44691	+	8.20582i	−0.0776741	+	0.440512i	−0.998698	+	0.0510063i	$0.983757\pi$
$348$		0			0
$349$	−4.05619	+	3.40354i	−0.217123	+	0.182188i	−0.744861	−	0.667219i	$-0.767484\pi$
$349$	−4.05619	+	3.40354i	−0.217123	+	0.182188i	0.527739	+	0.849407i	$0.323040\pi$
$350$		0			0
$351$	−4.06248	+	1.92492i	−0.216839	+	0.102745i
$352$		0			0
$353$	26.4759	−	22.2159i	1.40917	−	1.18243i	0.452318	−	0.891857i	$-0.350597\pi$
$353$	26.4759	−	22.2159i	1.40917	−	1.18243i	0.956852	−	0.290577i	$-0.0938473\pi$
$354$		0			0
$355$	−0.653961	+	3.70880i	−0.0347087	+	0.196843i
$356$		0			0
$357$	−16.4371	−	26.5266i	−0.869946	−	1.40394i
$358$		0			0
$359$	−12.8489	−	22.2549i	−0.678138	−	1.17457i	−0.975541	−	0.219818i	$-0.929454\pi$
$359$	−12.8489	−	22.2549i	−0.678138	−	1.17457i	0.297403	−	0.954752i	$-0.403880\pi$
$360$		0			0
$361$	8.28954	−	14.3579i	0.436292	−	0.755680i
$362$		0			0
$363$	3.42027	+	16.3943i	0.179518	+	0.860479i
$364$		0			0
$365$	0.325289	+	0.272950i	0.0170264	+	0.0142869i
$366$		0			0
$367$	10.6739	+	3.88499i	0.557174	+	0.202795i	0.605231	−	0.796050i	$-0.293081\pi$
$367$	10.6739	+	3.88499i	0.557174	+	0.202795i	−0.0480573	+	0.998845i	$0.515303\pi$
$368$		0			0
$369$	3.44112	−	6.92257i	0.179138	−	0.360375i
$370$		0			0
$371$	−2.87665	−	16.3143i	−0.149348	−	0.846995i
$372$		0			0
$373$	26.9731	−	9.81739i	1.39661	−	0.508325i	0.469441	−	0.882964i	$-0.344455\pi$
$373$	26.9731	−	9.81739i	1.39661	−	0.508325i	0.927171	+	0.374639i	$0.122233\pi$
$374$		0			0
$375$	−11.2598	+	4.50002i	−0.581454	+	0.232380i
$376$		0			0
$377$	−2.82703			−0.145599
$378$		0			0
$379$	23.0493			1.18396			0.591981	−	0.805952i	$-0.298346\pi$
$379$	23.0493			1.18396			0.591981	+	0.805952i	$0.298346\pi$
$380$		0			0
$381$	−2.00550	+	13.8903i	−0.102745	+	0.711620i
$382$		0			0
$383$	−23.1212	+	8.41541i	−1.18144	+	0.430007i	−0.856709	−	0.515800i	$-0.827495\pi$
$383$	−23.1212	+	8.41541i	−1.18144	+	0.430007i	−0.324727	+	0.945808i	$0.605272\pi$
$384$		0			0
$385$	−2.41675	−	13.7061i	−0.123169	−	0.698525i
$386$		0			0
$387$	0.925328	−	8.20890i	0.0470371	−	0.417282i
$388$		0			0
$389$	−34.8878	−	12.6981i	−1.76888	−	0.643820i	−0.999990	−	0.00444021i	$-0.998587\pi$
$389$	−34.8878	−	12.6981i	−1.76888	−	0.643820i	−0.768891	−	0.639380i	$-0.779191\pi$
$390$		0			0
$391$	−11.7033	−	9.82024i	−0.591862	−	0.496631i
$392$		0			0
$393$	20.5282	−	18.3442i	1.03551	−	0.925344i
$394$		0			0
$395$	−2.50351	+	4.33620i	−0.125965	+	0.218178i
$396$		0			0
$397$	−3.19629	−	5.53614i	−0.160417	−	0.277851i	0.774601	−	0.632450i	$-0.217951\pi$
$397$	−3.19629	−	5.53614i	−0.160417	−	0.277851i	−0.935018	+	0.354599i	$0.884617\pi$
$398$		0			0
$399$	11.1323	−	0.346796i	0.557313	−	0.0173615i
$400$		0			0
$401$	5.67599	−	32.1901i	0.283445	−	1.60750i	−0.427342	−	0.904090i	$-0.640550\pi$
$401$	5.67599	−	32.1901i	0.283445	−	1.60750i	0.710787	−	0.703407i	$-0.248339\pi$
$402$		0			0
$403$	−7.09038	+	5.94953i	−0.353197	+	0.296367i
$404$		0			0
$405$	−4.53484	+	4.88643i	−0.225338	+	0.242809i
$406$		0			0
$407$	6.13539	−	5.14821i	0.304120	−	0.255187i
$408$		0			0
$409$	−3.79522	+	21.5238i	−0.187662	+	1.06428i	0.734826	+	0.678256i	$0.237264\pi$
$409$	−3.79522	+	21.5238i	−0.187662	+	1.06428i	−0.922488	+	0.386027i	$0.873847\pi$
$410$		0			0
$411$	−21.3914	+	0.666390i	−1.05516	+	0.0328706i
$412$		0			0
$413$	−2.95806	−	5.12351i	−0.145557	−	0.252112i
$414$		0			0
$415$	−3.41599	+	5.91668i	−0.167685	+	0.290438i
$416$		0			0
$417$	5.66124	−	5.05894i	0.277232	−	0.247737i
$418$		0			0
$419$	20.0021	+	16.7838i	0.977168	+	0.819941i	0.983660	−	0.180037i	$-0.0576219\pi$
$419$	20.0021	+	16.7838i	0.977168	+	0.819941i	−0.00649160	+	0.999979i	$0.502066\pi$
$420$		0			0
$421$	35.2362	+	12.8249i	1.71731	+	0.625049i	0.997601	−	0.0692288i	$-0.0220539\pi$
$421$	35.2362	+	12.8249i	1.71731	+	0.625049i	0.719707	+	0.694278i	$0.244276\pi$
$422$		0			0
$423$	26.6629	−	11.6313i	1.29639	−	0.565535i
$424$		0			0
$425$	3.36975	+	19.1108i	0.163457	+	0.927009i
$426$		0			0
$427$	−16.8118	+	6.11898i	−0.813578	+	0.296118i
$428$		0			0
$429$	−0.973519	+	6.74268i	−0.0470020	+	0.325540i
$430$		0			0
$431$	−6.13162			−0.295350			−0.147675	−	0.989036i	$-0.547179\pi$
$431$	−6.13162			−0.295350			−0.147675	+	0.989036i	$0.547179\pi$
$432$		0			0
$433$	−20.9401			−1.00632			−0.503158	−	0.864195i	$-0.667829\pi$
$433$	−20.9401			−1.00632			−0.503158	+	0.864195i	$0.667829\pi$
$434$		0			0
$435$	−3.89292	+	1.55582i	−0.186651	+	0.0745960i
$436$		0			0
$437$	5.12381	−	1.86492i	0.245105	−	0.0892110i
$438$		0			0
$439$	4.98629	+	28.2787i	0.237983	+	1.34967i	0.836240	+	0.548363i	$0.184749\pi$
$439$	4.98629	+	28.2787i	0.237983	+	1.34967i	−0.598258	+	0.801304i	$0.704140\pi$
$440$		0			0
$441$	−16.7211	−	25.1972i	−0.796243	−	1.19987i
$442$		0			0
$443$	−14.2882	−	5.20050i	−0.678855	−	0.247083i	−0.0204992	−	0.999790i	$-0.506526\pi$
$443$	−14.2882	−	5.20050i	−0.678855	−	0.247083i	−0.658356	+	0.752707i	$0.728748\pi$
$444$		0			0
$445$	7.03547	+	5.90346i	0.333513	+	0.279851i
$446$		0			0
$447$	2.41723	+	11.5865i	0.114331	+	0.548022i
$448$		0			0
$449$	6.21048	−	10.7569i	0.293091	−	0.507648i	−0.681448	−	0.731866i	$-0.738649\pi$
$449$	6.21048	−	10.7569i	0.293091	−	0.507648i	0.974539	+	0.224218i	$0.0719828\pi$
$450$		0			0
$451$	−5.85769	−	10.1458i	−0.275828	−	0.477748i
$452$		0			0
$453$	−4.74998	−	7.66562i	−0.223173	−	0.360162i
$454$		0			0
$455$	0.459899	−	2.60822i	0.0215604	−	0.122275i
$456$		0			0
$457$	−8.30728	+	6.97064i	−0.388598	+	0.326073i	−0.816067	−	0.577957i	$-0.803850\pi$
$457$	−8.30728	+	6.97064i	−0.388598	+	0.326073i	0.427468	+	0.904030i	$0.359405\pi$
$458$		0			0
$459$	13.1071	+	18.4756i	0.611786	+	0.862365i
$460$		0			0
$461$	−6.28283	+	5.27192i	−0.292621	+	0.245538i	−0.777265	−	0.629173i	$-0.783394\pi$
$461$	−6.28283	+	5.27192i	−0.292621	+	0.245538i	0.484644	+	0.874711i	$0.338949\pi$
$462$		0			0
$463$	5.84350	−	33.1401i	0.271571	−	1.54015i	−0.478078	−	0.878317i	$-0.658667\pi$
$463$	5.84350	−	33.1401i	0.271571	−	1.54015i	0.749649	−	0.661836i	$-0.230222\pi$
$464$		0			0
$465$	−6.48946	+	12.0948i	−0.300942	+	0.560885i
$466$		0			0
$467$	5.43426	+	9.41241i	0.251467	+	0.435554i	0.963930	−	0.266156i	$-0.0857535\pi$
$467$	5.43426	+	9.41241i	0.251467	+	0.435554i	−0.712463	+	0.701710i	$0.752420\pi$
$468$		0			0
$469$	−27.0948	+	46.9296i	−1.25112	+	2.16701i
$470$		0			0
$471$	−6.53519	−	2.15064i	−0.301125	−	0.0990964i
$472$		0			0
$473$	−9.59003	−	8.04699i	−0.440950	−	0.370001i
$474$		0			0
$475$	−6.50827	−	2.36882i	−0.298620	−	0.108689i
$476$		0			0
$477$	2.82122	+	11.6895i	0.129175	+	0.535227i
$478$		0			0
$479$	3.26943	+	18.5418i	0.149384	+	0.847198i	0.963742	+	0.266836i	$0.0859781\pi$
$479$	3.26943	+	18.5418i	0.149384	+	0.847198i	−0.814358	+	0.580363i	$0.802911\pi$
$480$		0			0
$481$	1.43221	−	0.521280i	0.0653030	−	0.0237683i
$482$		0			0
$483$	−19.7095	−	15.5186i	−0.896812	−	0.706119i
$484$		0			0
$485$	−4.26267			−0.193558
$486$		0			0
$487$	−32.9521			−1.49320			−0.746601	−	0.665272i	$-0.768315\pi$
$487$	−32.9521			−1.49320			−0.746601	+	0.665272i	$0.768315\pi$
$488$		0			0
$489$	−3.19401	−	2.51486i	−0.144438	−	0.113726i
$490$		0			0
$491$	32.5492	−	11.8469i	1.46892	−	0.534645i	0.521116	−	0.853486i	$-0.325516\pi$
$491$	32.5492	−	11.8469i	1.46892	−	0.534645i	0.947808	+	0.318841i	$0.103294\pi$
$492$		0			0
$493$	2.47369	+	14.0290i	0.111409	+	0.631834i
$494$		0			0
$495$	2.37018	+	9.82070i	0.106532	+	0.441407i
$496$		0			0
$497$	19.7451	+	7.18664i	0.885690	+	0.322365i
$498$		0			0
$499$	−18.1706	−	15.2470i	−0.813428	−	0.682547i	0.137995	−	0.990433i	$-0.455934\pi$
$499$	−18.1706	−	15.2470i	−0.813428	−	0.682547i	−0.951423	+	0.307886i	$0.900379\pi$
$500$		0			0
$501$	−1.73183	−	0.569921i	−0.0773724	−	0.0254622i
$502$		0			0
$503$	16.0067	−	27.7243i	0.713701	−	1.23617i	−0.249757	−	0.968309i	$-0.580351\pi$
$503$	16.0067	−	27.7243i	0.713701	−	1.23617i	0.963458	−	0.267858i	$-0.0863160\pi$
$504$		0			0
$505$	−4.08861	−	7.08168i	−0.181941	−	0.315131i
$506$		0			0
$507$	10.0328	−	18.6987i	0.445571	−	0.830440i
$508$		0			0
$509$	6.91488	−	39.2162i	0.306497	−	1.73823i	−0.309879	−	0.950776i	$-0.600289\pi$
$509$	6.91488	−	39.2162i	0.306497	−	1.73823i	0.616376	−	0.787452i	$-0.288600\pi$
$510$		0			0
$511$	1.81494	−	1.52291i	0.0802881	−	0.0673697i
$512$		0			0
$513$	−8.04958	+	0.754239i	−0.355398	+	0.0333005i
$514$		0			0
$515$	−3.64369	+	3.05742i	−0.160560	+	0.134726i
$516$		0			0
$517$	7.65500	−	43.4136i	0.336666	−	1.90933i
$518$		0			0
$519$	−6.23372	−	10.0601i	−0.273630	−	0.441590i
$520$		0			0
$521$	−1.81609	−	3.14555i	−0.0795642	−	0.137809i	0.823498	−	0.567319i	$-0.192020\pi$
$521$	−1.81609	−	3.14555i	−0.0795642	−	0.137809i	−0.903062	+	0.429510i	$0.858686\pi$
$522$		0			0
$523$	6.50104	−	11.2601i	0.284270	−	0.492371i	−0.688162	−	0.725558i	$-0.741582\pi$
$523$	6.50104	−	11.2601i	0.284270	−	0.492371i	0.972432	+	0.233187i	$0.0749153\pi$
$524$		0			0
$525$	6.50748	+	31.1922i	0.284010	+	1.36134i
$526$		0			0
$527$	35.7285	+	29.9797i	1.55636	+	1.30594i
$528$		0			0
$529$	10.0725	+	3.66609i	0.437935	+	0.159395i
$530$		0			0
$531$	2.37458	+	3.57828i	0.103048	+	0.155284i
$532$		0			0
$533$	−0.387131	−	2.19553i	−0.0167685	−	0.0950989i
$534$		0			0
$535$	12.0363	−	4.38085i	0.520374	−	0.189401i
$536$		0			0
$537$	−3.53443	+	1.41255i	−0.152522	+	0.0609560i
$538$		0			0
$539$	−45.8278			−1.97394
$540$		0			0
$541$	−31.1320			−1.33847			−0.669235	−	0.743051i	$-0.733378\pi$
$541$	−31.1320			−1.33847			−0.669235	+	0.743051i	$0.733378\pi$
$542$		0			0
$543$	−3.89580	+	26.9826i	−0.167185	+	1.15794i
$544$		0			0
$545$	−6.92270	+	2.51966i	−0.296536	+	0.107930i
$546$		0			0
$547$	−3.35773	−	19.0426i	−0.143566	−	0.814204i	−0.968507	−	0.248985i	$-0.919903\pi$
$547$	−3.35773	−	19.0426i	−0.143566	−	0.814204i	0.824941	−	0.565219i	$-0.191208\pi$
$548$		0			0
$549$	11.9035	−	5.19274i	0.508027	−	0.221621i
$550$		0			0
$551$	−4.77764	−	1.73892i	−0.203534	−	0.0740804i
$552$		0			0
$553$	21.4005	+	17.9572i	0.910044	+	0.763617i
$554$		0			0
$555$	1.68532	−	1.50602i	0.0715380	−	0.0639271i
$556$		0			0
$557$	0.618509	−	1.07129i	0.0262070	−	0.0453919i	−0.852624	−	0.522524i	$-0.824990\pi$
$557$	0.618509	−	1.07129i	0.0262070	−	0.0453919i	0.878831	+	0.477132i	$0.158324\pi$
$558$		0			0
$559$	−1.19115	−	2.06314i	−0.0503804	−	0.0872614i
$560$		0			0
$561$	34.3121	−	1.06890i	1.44866	−	0.0451289i
$562$		0			0
$563$	3.63180	−	20.5969i	0.153062	−	0.868057i	−0.807474	−	0.589903i	$-0.799166\pi$
$563$	3.63180	−	20.5969i	0.153062	−	0.868057i	0.960536	−	0.278155i	$-0.0897228\pi$
$564$		0			0
$565$	−1.39095	+	1.16714i	−0.0585176	+	0.0491021i
$566$		0			0
$567$	22.4558	+	29.6518i	0.943056	+	1.24526i
$568$		0			0
$569$	−4.70347	+	3.94668i	−0.197180	+	0.165453i	−0.736032	−	0.676947i	$-0.763303\pi$
$569$	−4.70347	+	3.94668i	−0.197180	+	0.165453i	0.538852	+	0.842400i	$0.318858\pi$
$570$		0			0
$571$	−2.98710	+	16.9407i	−0.125006	+	0.708946i	0.856298	+	0.516483i	$0.172759\pi$
$571$	−2.98710	+	16.9407i	−0.125006	+	0.708946i	−0.981304	+	0.192464i	$0.938352\pi$
$572$		0			0
$573$	−13.5751	+	0.422895i	−0.567109	+	0.0176667i
$574$		0			0
$575$	7.79970	+	13.5095i	0.325270	+	0.563384i
$576$		0			0
$577$	7.08481	−	12.2713i	0.294945	−	0.510859i	−0.680027	−	0.733187i	$-0.738032\pi$
$577$	7.08481	−	12.2713i	0.294945	−	0.510859i	0.974972	+	0.222328i	$0.0713655\pi$
$578$		0			0
$579$	−21.3624	+	19.0897i	−0.887793	+	0.793341i
$580$		0			0
$581$	29.2007	+	24.5023i	1.21145	+	1.01653i
$582$		0			0
$583$	17.1244	+	6.23278i	0.709221	+	0.258135i
$584$		0			0
$585$	−0.215346	+	1.91040i	−0.00890345	+	0.0789855i
$586$		0			0
$587$	−5.83795	−	33.1087i	−0.240958	−	1.36654i	−0.829695	−	0.558217i	$-0.811486\pi$
$587$	−5.83795	−	33.1087i	−0.240958	−	1.36654i	0.588737	−	0.808324i	$-0.299625\pi$
$588$		0			0
$589$	−15.6422	+	5.69331i	−0.644527	+	0.234589i
$590$		0			0
$591$	−2.81572	+	19.5019i	−0.115823	+	0.802202i
$592$		0			0
$593$	6.82673			0.280340			0.140170	−	0.990127i	$-0.455235\pi$
$593$	6.82673			0.280340			0.140170	+	0.990127i	$0.455235\pi$
$594$		0			0
$595$	−13.3456			−0.547116
$596$		0			0
$597$	3.01168	−	1.20363i	0.123260	−	0.0492613i
$598$		0			0
$599$	−27.5399	+	10.0237i	−1.12525	+	0.409557i	−0.836565	−	0.547867i	$-0.815440\pi$
$599$	−27.5399	+	10.0237i	−1.12525	+	0.409557i	−0.288684	+	0.957424i	$0.593218\pi$
$600$		0			0
$601$	−0.803257	−	4.55550i	−0.0327655	−	0.185823i	0.964032	−	0.265785i	$-0.0856311\pi$
$601$	−0.803257	−	4.55550i	−0.0327655	−	0.185823i	−0.996798	+	0.0799624i	$0.974520\pi$
$602$		0			0
$603$	17.5095	−	35.2242i	0.713042	−	1.43444i
$604$		0			0
$605$	6.73014	+	2.44957i	0.273619	+	0.0995893i
$606$		0			0
$607$	10.3745	+	8.70526i	0.421089	+	0.353335i	0.828577	−	0.559875i	$-0.189151\pi$
$607$	10.3745	+	8.70526i	0.421089	+	0.353335i	−0.407488	+	0.913210i	$0.633595\pi$
$608$		0			0
$609$	4.77706	+	22.8978i	0.193576	+	0.927866i
$610$		0			0
$611$	4.19446	−	7.26502i	0.169690	−	0.293911i
$612$		0			0
$613$	−14.9136	−	25.8311i	−0.602354	−	1.04331i	−0.992464	−	0.122539i	$-0.960896\pi$
$613$	−14.9136	−	25.8311i	−0.602354	−	1.04331i	0.390110	−	0.920768i	$-0.372437\pi$
$614$		0			0
$615$	−1.74138	−	2.81028i	−0.0702192	−	0.113321i
$616$		0			0
$617$	−5.84851	+	33.1685i	−0.235452	+	1.33531i	0.606208	+	0.795306i	$0.292690\pi$
$617$	−5.84851	+	33.1685i	−0.235452	+	1.33531i	−0.841660	+	0.540008i	$0.818421\pi$
$618$		0			0
$619$	−27.2839	+	22.8939i	−1.09663	+	0.920182i	−0.997194	−	0.0748615i	$-0.976149\pi$
$619$	−27.2839	+	22.8939i	−1.09663	+	0.920182i	−0.0994367	+	0.995044i	$0.531704\pi$
$620$		0			0
$621$	14.9805	+	10.3525i	0.601145	+	0.415432i
$622$		0			0
$623$	39.2541	−	32.9381i	1.57268	−	1.31964i
$624$		0			0
$625$	2.96435	−	16.8117i	0.118574	−	0.672467i
$626$		0			0
$627$	−5.79269	+	10.7962i	−0.231338	+	0.431160i
$628$		0			0
$629$	−3.84003	−	6.65113i	−0.153112	−	0.265198i
$630$		0			0
$631$	−19.6546	+	34.0427i	−0.782436	+	1.35522i	0.148083	+	0.988975i	$0.452690\pi$
$631$	−19.6546	+	34.0427i	−0.782436	+	1.35522i	−0.930519	+	0.366243i	$0.880644\pi$
$632$		0			0
$633$	8.99976	+	2.96170i	0.357708	+	0.117717i
$634$		0			0
$635$	4.59768	+	3.85791i	0.182453	+	0.153097i
$636$		0			0
$637$	−8.19495	−	2.98272i	−0.324696	−	0.118180i
$638$		0			0
$639$	−14.6298	−	4.31450i	−0.578747	−	0.170679i
$640$		0			0
$641$	−4.79194	−	27.1764i	−0.189270	−	1.07340i	−0.920345	−	0.391107i	$-0.872092\pi$
$641$	−4.79194	−	27.1764i	−0.189270	−	1.07340i	0.731075	−	0.682297i	$-0.239019\pi$
$642$		0			0
$643$	30.6010	−	11.1378i	1.20678	−	0.439234i	0.341197	−	0.939992i	$-0.389168\pi$
$643$	30.6010	−	11.1378i	1.20678	−	0.439234i	0.865587	+	0.500758i	$0.166945\pi$
$644$		0			0
$645$	−2.77569	−	2.18548i	−0.109293	−	0.0860532i
$646$		0			0
$647$	11.8337			0.465232			0.232616	−	0.972569i	$-0.425272\pi$
$647$	11.8337			0.465232			0.232616	+	0.972569i	$0.425272\pi$
$648$		0			0
$649$	6.50805			0.255463
$650$		0			0
$651$	60.1701	+	47.3759i	2.35825	+	1.85681i
$652$		0			0
$653$	1.90882	−	0.694752i	0.0746978	−	0.0271878i	−0.304401	−	0.952544i	$-0.598456\pi$
$653$	1.90882	−	0.694752i	0.0746978	−	0.0271878i	0.379099	+	0.925356i	$0.376234\pi$
$654$		0			0
$655$	−2.04444	−	11.5946i	−0.0798830	−	0.453039i
$656$		0			0
$657$	−1.24609	+	1.18534i	−0.0486147	+	0.0462445i
$658$		0			0
$659$	45.4410	+	16.5392i	1.77013	+	0.644275i	0.999979	+	0.00641394i	$0.00204163\pi$
$659$	45.4410	+	16.5392i	1.77013	+	0.644275i	0.770151	+	0.637861i	$0.220181\pi$
$660$		0			0
$661$	−13.0788	−	10.9744i	−0.508706	−	0.426855i	0.351968	−	0.936012i	$-0.385513\pi$
$661$	−13.0788	−	10.9744i	−0.508706	−	0.426855i	−0.860673	+	0.509157i	$0.829957\pi$
$662$		0			0
$663$	6.20527	+	2.04207i	0.240993	+	0.0793075i
$664$		0			0
$665$	2.38155	−	4.12497i	0.0923527	−	0.159960i
$666$		0			0
$667$	5.72567	+	9.91715i	0.221699	+	0.383993i
$668$		0			0
$669$	−1.03578	+	1.93045i	−0.0400456	+	0.0746356i
$670$		0			0
$671$	3.41752	−	19.3817i	0.131932	−	0.748224i
$672$		0			0
$673$	−22.8356	+	19.1613i	−0.880247	+	0.738615i	−0.966230	−	0.257681i	$-0.917042\pi$
$673$	−22.8356	+	19.1613i	−0.880247	+	0.738615i	0.0859825	+	0.996297i	$0.472597\pi$
$674$		0			0
$675$	−6.12394	−	22.3044i	−0.235711	−	0.858496i
$676$		0			0
$677$	6.10334	−	5.12131i	0.234570	−	0.196828i	−0.517924	−	0.855427i	$-0.673295\pi$
$677$	6.10334	−	5.12131i	0.234570	−	0.196828i	0.752494	+	0.658599i	$0.228851\pi$
$678$		0			0
$679$	−4.12994	+	23.4221i	−0.158493	+	0.898856i
$680$		0			0
$681$	9.06968	+	14.6368i	0.347551	+	0.560885i
$682$		0			0
$683$	−15.1593	−	26.2566i	−0.580054	−	1.00468i	−0.995472	−	0.0950521i	$-0.969698\pi$
$683$	−15.1593	−	26.2566i	−0.580054	−	1.00468i	0.415419	−	0.909630i	$-0.363635\pi$
$684$		0			0
$685$	−4.57630	+	7.92638i	−0.174851	+	0.302851i
$686$		0			0
$687$	−3.53109	−	16.9255i	−0.134719	−	0.645748i
$688$		0			0
$689$	2.65653	+	2.22910i	0.101206	+	0.0849218i
$690$		0			0
$691$	24.9197	+	9.07005i	0.947992	+	0.345041i	0.769317	−	0.638867i	$-0.220597\pi$
$691$	24.9197	+	9.07005i	0.947992	+	0.345041i	0.178675	+	0.983908i	$0.442819\pi$
$692$		0			0
$693$	56.2581	−	3.50853i	2.13707	−	0.133278i
$694$		0			0
$695$	−0.563813	−	3.19754i	−0.0213867	−	0.121290i
$696$		0			0
$697$	−10.5565	+	3.84224i	−0.399855	+	0.145535i
$698$		0			0
$699$	43.6719	−	17.4536i	1.65182	−	0.660158i
$700$		0			0
$701$	46.2262			1.74594			0.872971	−	0.487773i	$-0.162191\pi$
$701$	46.2262			1.74594			0.872971	+	0.487773i	$0.162191\pi$
$702$		0			0
$703$	2.74105			0.103381
$704$		0			0
$705$	1.77771	−	12.3126i	0.0669525	−	0.463719i
$706$		0			0
$707$	−42.8730	+	15.6045i	−1.61240	+	0.586867i
$708$		0			0
$709$	5.30328	+	30.0764i	0.199169	+	1.12954i	0.906355	+	0.422516i	$0.138853\pi$
$709$	5.30328	+	30.0764i	0.199169	+	1.12954i	−0.707186	+	0.707027i	$0.750036\pi$
$710$		0			0
$711$	−16.3158	−	12.0429i	−0.611891	−	0.451642i
$712$		0			0
$713$	35.2312	+	12.8231i	1.31942	+	0.480229i
$714$		0			0
$715$	2.23183	+	1.87272i	0.0834656	+	0.0700359i
$716$		0			0
$717$	25.2313	−	22.5469i	0.942279	−	0.842031i
$718$		0			0
$719$	3.46256	−	5.99733i	0.129132	−	0.223663i	−0.794209	−	0.607645i	$-0.792114\pi$
$719$	3.46256	−	5.99733i	0.129132	−	0.223663i	0.923340	+	0.383982i	$0.125448\pi$
$720$		0			0
$721$	13.2694	+	22.9832i	0.494177	+	0.855939i
$722$		0			0
$723$	28.0720	−	0.874503i	1.04401	−	0.0325231i
$724$		0			0
$725$	2.52580	−	14.3245i	0.0938057	−	0.531999i
$726$		0			0
$727$	16.6231	−	13.9485i	0.616517	−	0.517319i	−0.280189	−	0.959945i	$-0.590397\pi$
$727$	16.6231	−	13.9485i	0.616517	−	0.517319i	0.896707	+	0.442625i	$0.145953\pi$
$728$		0			0
$729$	−17.6088	−	20.4678i	−0.652176	−	0.758067i
$730$		0			0
$731$	−9.19595	+	7.71631i	−0.340124	+	0.285398i
$732$		0			0
$733$	6.80782	−	38.6090i	0.251452	−	1.42606i	−0.553565	−	0.832806i	$-0.686733\pi$
$733$	6.80782	−	38.6090i	0.251452	−	1.42606i	0.805017	−	0.593251i	$-0.202156\pi$
$734$		0			0
$735$	−12.9263	+	0.402682i	−0.476793	+	0.0148531i
$736$		0			0
$737$	−29.8057	−	51.6251i	−1.09791	−	1.90163i
$738$		0			0
$739$	−15.4039	+	26.6804i	−0.566643	+	0.981454i	0.430252	+	0.902709i	$0.358425\pi$
$739$	−15.4039	+	26.6804i	−0.566643	+	0.981454i	−0.996895	+	0.0787451i	$0.974909\pi$
$740$		0			0
$741$	−1.73853	+	1.55357i	−0.0638664	+	0.0570717i
$742$		0			0
$743$	−24.4602	−	20.5245i	−0.897357	−	0.752972i	0.0723153	−	0.997382i	$-0.476961\pi$
$743$	−24.4602	−	20.5245i	−0.897357	−	0.752972i	−0.969672	+	0.244410i	$0.921406\pi$
$744$		0			0
$745$	4.75645	+	1.73121i	0.174263	+	0.0634265i
$746$		0			0
$747$	−22.2627	−	16.4323i	−0.814548	−	0.601226i
$748$		0			0
$749$	−12.4099	−	70.3801i	−0.453448	−	2.57163i
$750$		0			0
$751$	2.85191	−	1.03801i	0.104068	−	0.0378776i	−0.289462	−	0.957190i	$-0.593476\pi$
$751$	2.85191	−	1.03801i	0.104068	−	0.0378776i	0.393529	+	0.919312i	$0.371254\pi$
$752$		0			0
$753$	−5.80672	+	40.2178i	−0.211609	+	1.46562i
$754$		0			0
$755$	−3.85659			−0.140356
$756$		0			0
$757$	10.7254			0.389823			0.194912	−	0.980821i	$-0.437558\pi$
$757$	10.7254			0.389823			0.194912	+	0.980821i	$0.437558\pi$
$758$		0			0
$759$	25.6249	−	10.2411i	0.930124	−	0.371728i
$760$		0			0
$761$	−25.4656	+	9.26871i	−0.923126	+	0.335990i	−0.759481	−	0.650529i	$-0.774547\pi$
$761$	−25.4656	+	9.26871i	−0.923126	+	0.335990i	−0.163645	+	0.986519i	$0.552325\pi$
$762$		0			0
$763$	7.13760	+	40.4793i	0.258398	+	1.46545i
$764$		0			0
$765$	9.66873	−	0.602990i	0.349574	−	0.0218011i
$766$		0			0
$767$	1.16377	+	0.423579i	0.0420214	+	0.0152945i
$768$		0			0
$769$	20.6292	+	17.3100i	0.743910	+	0.624214i	0.933885	−	0.357575i	$-0.116396\pi$
$769$	20.6292	+	17.3100i	0.743910	+	0.624214i	−0.189975	+	0.981789i	$0.560841\pi$
$770$		0			0
$771$	7.77874	+	37.2857i	0.280145	+	1.34281i
$772$		0			0
$773$	7.19832	−	12.4679i	0.258906	−	0.448438i	−0.707043	−	0.707170i	$-0.749971\pi$
$773$	7.19832	−	12.4679i	0.258906	−	0.448438i	0.965949	+	0.258733i	$0.0833048\pi$
$774$		0			0
$775$	−23.8113	−	41.2424i	−0.855328	−	1.48147i
$776$		0			0
$777$	−6.64228	−	10.7195i	−0.238291	−	0.384559i
$778$		0			0
$779$	0.696235	−	3.94855i	0.0249452	−	0.141471i
$780$		0			0
$781$	−17.7069	+	14.8578i	−0.633602	+	0.531655i
$782$		0			0
$783$	−4.49551	−	16.3734i	−0.160656	−	0.585137i
$784$		0			0
$785$	−2.25390	+	1.89124i	−0.0804450	+	0.0675014i
$786$		0			0
$787$	1.54500	−	8.76212i	0.0550732	−	0.312336i	−0.944810	−	0.327619i	$-0.893754\pi$
$787$	1.54500	−	8.76212i	0.0550732	−	0.312336i	0.999883	+	0.0152831i	$0.00486494\pi$
$788$		0			0
$789$	−19.2300	+	35.8402i	−0.684606	+	1.27595i
$790$		0			0
$791$	5.06546	+	8.77363i	0.180107	+	0.311954i
$792$		0			0
$793$	1.87259	−	3.24342i	0.0664976	−	0.115177i
$794$		0			0
$795$	4.88491	+	1.60756i	0.173250	+	0.0570142i
$796$		0			0
$797$	23.0251	+	19.3204i	0.815592	+	0.684363i	0.951935	−	0.306299i	$-0.0990907\pi$
$797$	23.0251	+	19.3204i	0.815592	+	0.684363i	−0.136344	+	0.990662i	$0.543535\pi$
$798$		0			0
$799$	−39.7225	−	14.4578i	−1.40528	−	0.511481i
$800$		0			0
$801$	−26.9509	+	25.6369i	−0.952264	+	0.905835i
$802$		0			0
$803$	0.452577	+	2.56669i	0.0159711	+	0.0905765i
$804$		0			0
$805$	−10.0810	+	3.66919i	−0.355309	+	0.129322i
$806$		0			0
$807$	24.9037	+	19.6083i	0.876651	+	0.690245i
$808$		0			0
$809$	−22.4607			−0.789676			−0.394838	−	0.918751i	$-0.629199\pi$
$809$	−22.4607			−0.789676			−0.394838	+	0.918751i	$0.629199\pi$
$810$		0			0
$811$	−21.1008			−0.740949			−0.370474	−	0.928843i	$-0.620805\pi$
$811$	−21.1008			−0.740949			−0.370474	+	0.928843i	$0.620805\pi$
$812$		0			0
$813$	22.4302	+	17.6608i	0.786662	+	0.619391i
$814$		0			0
$815$	−1.63368	+	0.594610i	−0.0572252	+	0.0208283i
$816$		0			0
$817$	−0.743987	−	4.21936i	−0.0260288	−	0.147617i
$818$		0			0
$819$	10.2885	+	3.03418i	0.359508	+	0.106023i
$820$		0			0
$821$	6.32803	+	2.30322i	0.220850	+	0.0803828i	0.450075	−	0.892991i	$-0.351397\pi$
$821$	6.32803	+	2.30322i	0.220850	+	0.0803828i	−0.229226	+	0.973373i	$0.573619\pi$
$822$		0			0
$823$	−23.1807	−	19.4509i	−0.808030	−	0.678017i	0.142107	−	0.989851i	$-0.454612\pi$
$823$	−23.1807	−	19.4509i	−0.808030	−	0.678017i	−0.950137	+	0.311834i	$0.899057\pi$
$824$		0			0
$825$	−33.2953	−	10.9570i	−1.15919	−	0.381475i
$826$		0			0
$827$	2.82370	−	4.89079i	0.0981897	−	0.170070i	−0.812746	−	0.582619i	$-0.802028\pi$
$827$	2.82370	−	4.89079i	0.0981897	−	0.170070i	0.910935	+	0.412549i	$0.135361\pi$
$828$		0			0
$829$	−11.3107	−	19.5907i	−0.392837	−	0.680413i	0.599986	−	0.800011i	$-0.295173\pi$
$829$	−11.3107	−	19.5907i	−0.392837	−	0.680413i	−0.992822	+	0.119597i	$0.961840\pi$
$830$		0			0
$831$	−9.23064	+	17.2038i	−0.320207	+	0.596792i
$832$		0			0
$833$	−7.63091	+	43.2770i	−0.264395	+	1.49946i
$834$		0			0
$835$	−0.597284	+	0.501181i	−0.0206699	+	0.0173441i
$836$		0			0
$837$	−45.7331	−	31.6047i	−1.58077	−	1.09242i
$838$		0			0
$839$	8.13447	−	6.82563i	0.280833	−	0.235647i	−0.491480	−	0.870889i	$-0.663544\pi$
$839$	8.13447	−	6.82563i	0.280833	−	0.235647i	0.772313	+	0.635242i	$0.219100\pi$
$840$		0			0
$841$	−3.18164	+	18.0440i	−0.109712	+	0.622206i
$842$		0			0
$843$	0.661740	+	1.06793i	0.0227915	+	0.0367815i
$844$		0			0
$845$	−4.53747	−	7.85914i	−0.156094	−	0.270362i
$846$		0			0
$847$	19.9802	−	34.6068i	0.686529	−	1.18910i
$848$		0			0
$849$	7.83103	+	37.5364i	0.268760	+	1.28825i
$850$		0			0
$851$	−4.72933	−	3.96838i	−0.162119	−	0.136034i
$852$		0			0
$853$	16.0795	+	5.85246i	0.550551	+	0.200384i	0.602291	−	0.798276i	$-0.294255\pi$
$853$	16.0795	+	5.85246i	0.550551	+	0.200384i	−0.0517401	+	0.998661i	$0.516477\pi$
$854$		0			0
$855$	−1.53903	+	3.09610i	−0.0526338	+	0.105884i
$856$		0			0
$857$	5.77848	+	32.7714i	0.197389	+	1.11945i	0.908975	+	0.416850i	$0.136866\pi$
$857$	5.77848	+	32.7714i	0.197389	+	1.11945i	−0.711586	+	0.702599i	$0.752023\pi$
$858$		0			0
$859$	−0.698231	+	0.254135i	−0.0238233	+	0.00867098i	−0.353904	−	0.935282i	$-0.615146\pi$
$859$	−0.698231	+	0.254135i	−0.0238233	+	0.00867098i	0.330081	+	0.943953i	$0.392924\pi$
$860$		0			0
$861$	−17.1288	+	6.84558i	−0.583747	+	0.233297i
$862$		0			0
$863$	−14.4375			−0.491457			−0.245728	−	0.969339i	$-0.579027\pi$
$863$	−14.4375			−0.491457			−0.245728	+	0.969339i	$0.579027\pi$
$864$		0			0
$865$	−5.06126			−0.172088
$866$		0			0
$867$	0.496319	−	3.43755i	0.0168559	−	0.116745i
$868$		0			0
$869$	−28.8782	+	10.5108i	−0.979627	+	0.356555i
$870$		0			0
$871$	−1.96984	−	11.1715i	−0.0667456	−	0.378533i
$872$		0			0
$873$	1.93383	−	17.1556i	0.0654501	−	0.580630i
$874$		0			0
$875$	27.1882	+	9.89568i	0.919127	+	0.334535i
$876$		0			0
$877$	−22.3924	−	18.7895i	−0.756139	−	0.634476i	0.180979	−	0.983487i	$-0.442073\pi$
$877$	−22.3924	−	18.7895i	−0.756139	−	0.634476i	−0.937119	+	0.349011i	$0.886518\pi$
$878$		0			0
$879$	−8.47053	+	7.56936i	−0.285704	+	0.255308i
$880$		0			0
$881$	3.02765	−	5.24404i	0.102004	−	0.176676i	−0.810506	−	0.585730i	$-0.800808\pi$
$881$	3.02765	−	5.24404i	0.102004	−	0.176676i	0.912510	+	0.409054i	$0.134141\pi$
$882$		0			0
$883$	3.06634	+	5.31105i	0.103190	+	0.178731i	0.912997	−	0.407965i	$-0.133762\pi$
$883$	3.06634	+	5.31105i	0.103190	+	0.178731i	−0.809807	+	0.586696i	$0.800428\pi$
$884$		0			0
$885$	1.83567	−	0.0571852i	0.0617054	−	0.00192226i
$886$		0			0
$887$	−9.46864	+	53.6993i	−0.317926	+	1.80305i	0.237399	+	0.971412i	$0.423705\pi$
$887$	−9.46864	+	53.6993i	−0.317926	+	1.80305i	−0.555325	+	0.831634i	$0.687406\pi$
$888$		0			0
$889$	25.6526	−	21.5251i	0.860359	−	0.721927i
$890$		0			0
$891$	−40.5999	+	5.08379i	−1.36015	+	0.170313i
$892$		0			0
$893$	11.5573	−	9.69776i	0.386752	−	0.324523i
$894$		0			0
$895$	−0.282658	+	1.60303i	−0.00944820	+	0.0535834i
$896$		0			0
$897$	5.24879	−	0.163511i	0.175252	−	0.00545949i
$898$		0			0
$899$	−17.4796	−	30.2756i	−0.582978	−	1.00975i
$900$		0			0
$901$	8.73729	−	15.1334i	0.291081	−	0.504168i
$902$		0			0
$903$	−14.6978	+	13.1341i	−0.489113	+	0.437076i
$904$		0			0
$905$	8.93125	+	7.49421i	0.296885	+	0.249116i
$906$		0			0
$907$	−3.63868	−	1.32437i	−0.120820	−	0.0439750i	0.280902	−	0.959736i	$-0.409366\pi$
$907$	−3.63868	−	1.32437i	−0.120820	−	0.0439750i	−0.401723	+	0.915761i	$0.631588\pi$
$908$		0			0
$909$	30.3559	−	13.2424i	1.00684	−	0.439222i
$910$		0			0
$911$	0.755948	+	4.28719i	0.0250457	+	0.142041i	0.994766	−	0.102175i	$-0.0325803\pi$
$911$	0.755948	+	4.28719i	0.0250457	+	0.142041i	−0.969721	+	0.244217i	$0.921469\pi$
$912$		0			0
$913$	−39.4039	+	14.3418i	−1.30408	+	0.474646i
$914$		0			0
$915$	0.793648	−	5.49687i	0.0262372	−	0.181721i
$916$		0			0
$917$	−65.6896			−2.16926
$918$		0			0
$919$	−23.4247			−0.772710			−0.386355	−	0.922350i	$-0.626266\pi$
$919$	−23.4247			−0.772710			−0.386355	+	0.922350i	$0.626266\pi$
$920$		0			0
$921$	12.8264	−	5.12611i	0.422643	−	0.168911i
$922$		0			0
$923$	−4.13338	+	1.50443i	−0.136052	+	0.0495188i
$924$		0			0
$925$	1.36172	+	7.72271i	0.0447731	+	0.253921i
$926$		0			0
$927$	−10.6519	−	16.0515i	−0.349856	−	0.527201i
$928$		0			0
$929$	38.3287	+	13.9505i	1.25752	+	0.457701i	0.882937	−	0.469492i	$-0.155563\pi$
$929$	38.3287	+	13.9505i	1.25752	+	0.457701i	0.374586	+	0.927192i	$0.377785\pi$
$930$		0			0
$931$	−12.0147	−	10.0815i	−0.393765	−	0.330408i
$932$		0			0
$933$	−5.00464	−	23.9887i	−0.163844	−	0.785353i
$934$		0			0
$935$	7.34043	−	12.7140i	0.240058	−	0.415792i
$936$		0			0
$937$	10.2480	+	17.7501i	0.334789	+	0.579871i	0.983444	−	0.181211i	$-0.0580017\pi$
$937$	10.2480	+	17.7501i	0.334789	+	0.579871i	−0.648656	+	0.761082i	$0.724668\pi$
$938$		0			0
$939$	−21.9334	−	35.3965i	−0.715769	−	1.15512i
$940$		0			0
$941$	1.49514	−	8.47935i	0.0487401	−	0.276419i	−0.950691	−	0.310139i	$-0.899624\pi$
$941$	1.49514	−	8.47935i	0.0487401	−	0.276419i	0.999431	+	0.0337201i	$0.0107355\pi$
$942$		0			0
$943$	−6.91780	+	5.80472i	−0.225275	+	0.189028i
$944$		0			0
$945$	15.8374	−	1.48395i	0.515191	−	0.0482730i
$946$		0			0
$947$	−31.4937	+	26.4264i	−1.02341	+	0.858741i	−0.990052	−	0.140702i	$-0.955064\pi$
$947$	−31.4937	+	26.4264i	−1.02341	+	0.858741i	−0.0333562	+	0.999444i	$0.510620\pi$
$948$		0			0
$949$	−0.0861238	+	0.488432i	−0.00279570	+	0.0158552i
$950$		0			0
$951$	−14.8980	+	27.7664i	−0.483101	+	0.900388i
$952$		0			0
$953$	−13.8375	−	23.9672i	−0.448240	−	0.776374i	0.550032	−	0.835144i	$-0.314616\pi$
$953$	−13.8375	−	23.9672i	−0.448240	−	0.776374i	−0.998272	+	0.0587696i	$0.981282\pi$
$954$		0			0
$955$	−2.90414	+	5.03012i	−0.0939759	+	0.162771i
$956$		0			0
$957$	−24.4417	−	8.04343i	−0.790087	−	0.260007i
$958$		0			0
$959$	39.1192	+	32.8249i	1.26323	+	1.05997i
$960$		0			0
$961$	−78.4251	−	28.5444i	−2.52984	−	0.920788i
$962$		0			0
$963$	12.1708	+	50.4289i	0.392199	+	1.62505i
$964$		0			0
$965$	2.12753	+	12.0658i	0.0684875	+	0.388412i
$966$		0			0
$967$	56.1727	−	20.4452i	1.80639	−	0.657474i	0.808805	−	0.588077i	$-0.200115\pi$
$967$	56.1727	−	20.4452i	1.80639	−	0.657474i	0.997589	−	0.0693962i	$-0.0221073\pi$
$968$		0			0
$969$	9.23075	+	7.26797i	0.296534	+	0.233481i
$970$		0			0
$971$	3.80514			0.122113			0.0610564	−	0.998134i	$-0.480553\pi$
$971$	3.80514			0.122113			0.0610564	+	0.998134i	$0.480553\pi$
$972$		0			0
$973$	−18.1158			−0.580765
$974$		0			0
$975$	−5.24074	−	4.12638i	−0.167838	−	0.132150i
$976$		0			0
$977$	−26.6685	+	9.70654i	−0.853201	+	0.310540i	−0.731345	−	0.682008i	$-0.761107\pi$
$977$	−26.6685	+	9.70654i	−0.853201	+	0.310540i	−0.121856	+	0.992548i	$0.538885\pi$
$978$		0			0
$979$	9.78848	+	55.5132i	0.312841	+	1.77421i
$980$		0			0
$981$	−7.00008	−	29.0043i	−0.223495	−	0.926037i
$982$		0			0
$983$	16.6680	+	6.06666i	0.531627	+	0.193496i	0.593865	−	0.804565i	$-0.297601\pi$
$983$	16.6680	+	6.06666i	0.531627	+	0.193496i	−0.0622377	+	0.998061i	$0.519824\pi$
$984$		0			0
$985$	6.45514	+	5.41650i	0.205678	+	0.172584i
$986$		0			0
$987$	−65.9315	−	21.6972i	−2.09862	−	0.690629i
$988$		0			0
$989$	−4.82496	+	8.35707i	−0.153425	+	0.265739i
$990$		0			0
$991$	−6.59603	−	11.4247i	−0.209530	−	0.362916i	0.742037	−	0.670359i	$-0.233860\pi$
$991$	−6.59603	−	11.4247i	−0.209530	−	0.362916i	−0.951566	+	0.307443i	$0.900527\pi$
$992$		0			0
$993$	14.7080	−	27.4123i	0.466745	−	0.869904i
$994$		0			0
$995$	0.240852	−	1.36594i	0.00763552	−	0.0433032i
$996$		0			0
$997$	45.1830	−	37.9130i	1.43096	−	1.20072i	0.485816	−	0.874061i	$-0.338523\pi$
$997$	45.1830	−	37.9130i	1.43096	−	1.20072i	0.945143	−	0.326656i	$-0.105922\pi$
$998$		0			0
$999$	5.29660	+	7.46602i	0.167577	+	0.236214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.b.49.2		12
4.3	odd	2		54.2.e.b.49.1	yes	12
12.11	even	2		162.2.e.b.37.1		12
27.16	even	9	inner	432.2.u.b.97.2		12
36.7	odd	6		486.2.e.h.433.1		12
36.11	even	6		486.2.e.e.433.2		12
36.23	even	6		486.2.e.g.271.2		12
36.31	odd	6		486.2.e.f.271.1		12
108.7	odd	18		486.2.e.f.217.1		12
108.11	even	18		162.2.e.b.127.1		12
108.23	even	18		1458.2.a.f.1.4		6
108.31	odd	18		1458.2.a.g.1.3		6
108.43	odd	18		54.2.e.b.43.1	✓	12
108.47	even	18		486.2.e.g.217.2		12
108.59	even	18		1458.2.c.g.973.3		12
108.67	odd	18		1458.2.c.f.487.4		12
108.79	odd	18		486.2.e.h.55.1		12
108.83	even	18		486.2.e.e.55.2		12
108.95	even	18		1458.2.c.g.487.3		12
108.103	odd	18		1458.2.c.f.973.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.43.1	✓	12	108.43	odd	18
54.2.e.b.49.1	yes	12	4.3	odd	2
162.2.e.b.37.1		12	12.11	even	2
162.2.e.b.127.1		12	108.11	even	18
432.2.u.b.49.2		12	1.1	even	1	trivial
432.2.u.b.97.2		12	27.16	even	9	inner
486.2.e.e.55.2		12	108.83	even	18
486.2.e.e.433.2		12	36.11	even	6
486.2.e.f.217.1		12	108.7	odd	18
486.2.e.f.271.1		12	36.31	odd	6
486.2.e.g.217.2		12	108.47	even	18
486.2.e.g.271.2		12	36.23	even	6
486.2.e.h.55.1		12	108.79	odd	18
486.2.e.h.433.1		12	36.7	odd	6
1458.2.a.f.1.4		6	108.23	even	18
1458.2.a.g.1.3		6	108.31	odd	18
1458.2.c.f.487.4		12	108.67	odd	18
1458.2.c.f.973.4		12	108.103	odd	18
1458.2.c.g.487.3		12	108.95	even	18
1458.2.c.g.973.3		12	108.59	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36085 + 1.07149i) q^{3} +(0.696050 - 0.253341i) q^{5} +(-0.717657 - 4.07003i) q^{7} +(0.703829 + 2.91627i) q^{9} +(4.27215 + 1.55493i) q^{11} +(0.662744 + 0.556108i) q^{13} +(1.21867 + 0.401049i) q^{15} +(2.17975 - 3.77544i) q^{17} +(0.777964 + 1.34747i) q^{19} +(3.38437 - 6.30767i) q^{21} +(0.608539 - 3.45119i) q^{23} +(-3.40992 + 2.86126i) q^{25} +(-2.16694 + 4.72275i) q^{27} +(-2.50318 + 2.10042i) q^{29} +(-1.85778 + 10.5360i) q^{31} +(4.14766 + 6.69359i) q^{33} +(-1.53063 - 2.65113i) q^{35} +(0.880842 - 1.52566i) q^{37} +(0.306033 + 1.46690i) q^{39} +(-1.97401 - 1.65639i) q^{41} +(-2.58757 - 0.941797i) q^{43} +(1.22871 + 1.85156i) q^{45} +(-1.68378 - 9.54918i) q^{47} +(-9.47229 + 3.44763i) q^{49} +(7.01165 - 2.80223i) q^{51} +4.00839 q^{53} +3.36756 q^{55} +(-0.385108 + 2.66729i) q^{57} +(1.34517 - 0.489601i) q^{59} +(-0.751711 - 4.26317i) q^{61} +(11.3642 - 4.95749i) q^{63} +(0.602188 + 0.219178i) q^{65} +(-10.0444 - 8.42825i) q^{67} +(4.52604 - 4.04452i) q^{69} +(-2.54213 + 4.40310i) q^{71} +(0.286636 + 0.496469i) q^{73} +(-7.70620 + 0.240065i) q^{75} +(3.26270 - 18.5037i) q^{77} +(-5.17820 + 4.34502i) q^{79} +(-8.00925 + 4.10511i) q^{81} +(-7.06556 + 5.92871i) q^{83} +(0.560740 - 3.18011i) q^{85} +(-5.65702 + 0.176229i) q^{87} +(6.19947 + 10.7378i) q^{89} +(1.78776 - 3.09648i) q^{91} +(-13.8173 + 12.3473i) q^{93} +(0.882872 + 0.740818i) q^{95} +(-5.40770 - 1.96824i) q^{97} +(-1.52774 + 13.5531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{7} - 12 q^{9} + 12 q^{11} + 12 q^{13} + 18 q^{15} - 6 q^{17} + 9 q^{19} + 24 q^{21} - 30 q^{23} - 9 q^{25} + 15 q^{29} + 36 q^{33} - 3 q^{35} - 15 q^{37} + 42 q^{39} - 12 q^{41} - 9 q^{43}+ \cdots - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^7 - 12 * q^9 + 12 * q^11 + 12 * q^13 + 18 * q^15 - 6 * q^17 + 9 * q^19 + 24 * q^21 - 30 * q^23 - 9 * q^25 + 15 * q^29 + 36 * q^33 - 3 * q^35 - 15 * q^37 + 42 * q^39 - 12 * q^41 - 9 * q^43 + 18 * q^45 + 9 * q^47 - 39 * q^49 + 27 * q^51 - 12 * q^53 - 18 * q^55 + 18 * q^57 - 12 * q^59 - 36 * q^61 - 3 * q^63 - 15 * q^65 - 36 * q^67 + 18 * q^69 - 12 * q^71 - 21 * q^73 - 30 * q^75 + 3 * q^77 - 39 * q^79 - 18 * q^83 + 45 * q^85 - 27 * q^87 + 12 * q^89 + 6 * q^91 - 33 * q^93 + 15 * q^95 + 39 * q^97 - 9 * q^99

Introduction

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