LMFDB - Embedded newform 567.2.be.a.62.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(62,567)] 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("567.62"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.be (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			62.17
Character	$\chi$	$=$	567.62
Dual form			567.2.be.a.503.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.681310 + 1.87188i) q^{2} +(-1.50768 + 1.26509i) q^{4} +(-0.291735 - 1.65451i) q^{5} +(0.496759 - 2.59870i) q^{7} +(0.0549773 + 0.0317412i) q^{8} +(2.89829 - 1.67333i) q^{10} +(3.13877 + 0.553450i) q^{11} +(0.877617 - 2.41123i) q^{13} +(5.20291 - 0.840643i) q^{14} +(-0.705484 + 4.00100i) q^{16} +(-0.934264 - 1.61819i) q^{17} +(5.71942 + 3.30211i) q^{19} +(2.53295 + 2.12540i) q^{20} +(1.10248 + 6.25248i) q^{22} +(-4.62225 - 5.50858i) q^{23} +(2.04616 - 0.744740i) q^{25} +5.11148 q^{26} +(2.53864 + 4.54644i) q^{28} +(3.25414 + 8.94067i) q^{29} +(0.942831 + 1.12362i) q^{31} +(-7.84502 + 1.38329i) q^{32} +(2.39254 - 2.85132i) q^{34} +(-4.44450 - 0.0637627i) q^{35} +(-0.322537 - 0.558651i) q^{37} +(-2.28447 + 12.9559i) q^{38} +(0.0364774 - 0.100221i) q^{40} +(-0.477380 - 0.173752i) q^{41} +(-0.197774 + 1.12163i) q^{43} +(-5.43241 + 3.13640i) q^{44} +(7.16224 - 12.4054i) q^{46} +(-8.83196 - 7.41090i) q^{47} +(-6.50646 - 2.58185i) q^{49} +(2.78813 + 3.32277i) q^{50} +(1.72727 + 4.74562i) q^{52} -1.23939i q^{53} -5.35460i q^{55} +(0.109796 - 0.127102i) q^{56} +(-14.5188 + 12.1827i) q^{58} +(0.0973892 + 0.552322i) q^{59} +(-4.58297 + 5.46178i) q^{61} +(-1.46093 + 2.53041i) q^{62} +(-3.87153 - 6.70568i) q^{64} +(-4.24545 - 0.748587i) q^{65} +(8.34610 + 3.03773i) q^{67} +(3.45573 + 1.25778i) q^{68} +(-2.90873 - 8.36303i) q^{70} +(5.31767 - 3.07016i) q^{71} +(-5.75058 - 3.32010i) q^{73} +(0.825982 - 0.984367i) q^{74} +(-12.8005 + 2.25707i) q^{76} +(2.99746 - 7.88178i) q^{77} +(0.814895 - 0.296597i) q^{79} +6.82552 q^{80} -1.01198i q^{82} +(-7.67310 + 2.79278i) q^{83} +(-2.40476 + 2.01784i) q^{85} +(-2.23431 + 0.393970i) q^{86} +(0.154994 + 0.130055i) q^{88} +(-3.77720 + 6.54230i) q^{89} +(-5.83010 - 3.47846i) q^{91} +(13.9377 + 2.45759i) q^{92} +(7.85503 - 21.5815i) q^{94} +(3.79483 - 10.4262i) q^{95} +(9.45944 + 1.66796i) q^{97} +(0.400014 - 13.9384i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) $ 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.681310	+	1.87188i	0.481759	+	1.32362i	0.907984	+	0.419005i	$0.137621\pi$
$2$	0.681310	+	1.87188i	0.481759	+	1.32362i	−0.426225	+	0.904617i	$0.640157\pi$
$3$		0			0
$3$		0			0
$4$	−1.50768	+	1.26509i	−0.753838	+	0.632545i
$5$	−0.291735	−	1.65451i	−0.130468	−	0.739921i	−0.977909	−	0.209031i	$-0.932969\pi$
$5$	−0.291735	−	1.65451i	−0.130468	−	0.739921i	0.847441	−	0.530890i	$-0.178142\pi$
$6$		0			0
$7$	0.496759	−	2.59870i	0.187757	−	0.982215i
$7$	0.496759	−	2.59870i	0.187757	−	0.982215i
$8$	0.0549773	+	0.0317412i	0.0194374	+	0.0112222i
$9$		0			0
$10$	2.89829	−	1.67333i	0.916521	−	0.529154i
$11$	3.13877	+	0.553450i	0.946374	+	0.166871i	0.625477	−	0.780243i	$-0.284904\pi$
$11$	3.13877	+	0.553450i	0.946374	+	0.166871i	0.320897	+	0.947114i	$0.396016\pi$
$12$		0			0
$13$	0.877617	−	2.41123i	0.243407	−	0.668756i	−0.756484	−	0.654012i	$-0.773085\pi$
$13$	0.877617	−	2.41123i	0.243407	−	0.668756i	0.999891	−	0.0147436i	$-0.00469320\pi$
$14$	5.20291	−	0.840643i	1.39054	−	0.224671i
$15$		0			0
$16$	−0.705484	+	4.00100i	−0.176371	+	1.00025i
$17$	−0.934264	−	1.61819i	−0.226592	−	0.392469i	0.730204	−	0.683229i	$-0.239425\pi$
$17$	−0.934264	−	1.61819i	−0.226592	−	0.392469i	−0.956796	+	0.290760i	$0.906092\pi$
$18$		0			0
$19$	5.71942	+	3.30211i	1.31213	+	0.757556i	0.982448	−	0.186538i	$-0.0597267\pi$
$19$	5.71942	+	3.30211i	1.31213	+	0.757556i	0.329677	+	0.944094i	$0.393060\pi$
$20$	2.53295	+	2.12540i	0.566385	+	0.475254i
$21$		0			0
$22$	1.10248	+	6.25248i	0.235050	+	1.33303i
$23$	−4.62225	−	5.50858i	−0.963805	−	1.14862i	−0.988848	−	0.148932i	$-0.952417\pi$
$23$	−4.62225	−	5.50858i	−0.963805	−	1.14862i	0.0250426	−	0.999686i	$-0.492028\pi$
$24$		0			0
$25$	2.04616	−	0.744740i	0.409231	−	0.148948i
$26$	5.11148			1.00244
$27$		0			0
$28$	2.53864	+	4.54644i	0.479757	+	0.859196i
$29$	3.25414	+	8.94067i	0.604278	+	1.66024i	0.742506	+	0.669840i	$0.233637\pi$
$29$	3.25414	+	8.94067i	0.604278	+	1.66024i	−0.138228	+	0.990400i	$0.544141\pi$
$30$		0			0
$31$	0.942831	+	1.12362i	0.169337	+	0.201809i	0.844038	−	0.536283i	$-0.180172\pi$
$31$	0.942831	+	1.12362i	0.169337	+	0.201809i	−0.674701	+	0.738091i	$0.735727\pi$
$32$	−7.84502	+	1.38329i	−1.38682	+	0.244533i
$33$		0			0
$34$	2.39254	−	2.85132i	0.410318	−	0.488998i
$35$	−4.44450	−	0.0637627i	−0.751258	−	0.0107779i
$36$		0			0
$37$	−0.322537	−	0.558651i	−0.0530248	−	0.0918416i	0.838295	−	0.545217i	$-0.183553\pi$
$37$	−0.322537	−	0.558651i	−0.0530248	−	0.0918416i	−0.891319	+	0.453376i	$0.850220\pi$
$38$	−2.28447	+	12.9559i	−0.370589	+	2.10172i
$39$		0			0
$40$	0.0364774	−	0.100221i	0.00576758	−	0.0158463i
$41$	−0.477380	−	0.173752i	−0.0745542	−	0.0271355i	0.304474	−	0.952521i	$-0.401519\pi$
$41$	−0.477380	−	0.173752i	−0.0745542	−	0.0271355i	−0.379028	+	0.925385i	$0.623742\pi$
$42$		0			0
$43$	−0.197774	+	1.12163i	−0.0301603	+	0.171048i	−0.996167	−	0.0874683i	$-0.972122\pi$
$43$	−0.197774	+	1.12163i	−0.0301603	+	0.171048i	0.966007	+	0.258516i	$0.0832334\pi$
$44$	−5.43241	+	3.13640i	−0.818967	+	0.472831i
$45$		0			0
$46$	7.16224	−	12.4054i	1.05601	−	1.82907i
$47$	−8.83196	−	7.41090i	−1.28827	−	1.08099i	−0.992046	−	0.125873i	$-0.959827\pi$
$47$	−8.83196	−	7.41090i	−1.28827	−	1.08099i	−0.296228	−	0.955117i	$-0.595729\pi$
$48$		0			0
$49$	−6.50646	−	2.58185i	−0.929494	−	0.368836i
$50$	2.78813	+	3.32277i	0.394302	+	0.469911i
$51$		0			0
$52$	1.72727	+	4.74562i	0.239529	+	0.658099i
$53$		−	1.23939i		−	0.170243i	−0.996371	−	0.0851215i	$-0.972872\pi$
$53$		−	1.23939i		−	0.170243i	0.996371	−	0.0851215i	$-0.0271278\pi$
$54$		0			0
$55$		−	5.35460i		−	0.722013i
$56$	0.109796	−	0.127102i	0.0146721	−	0.0169847i
$57$		0			0
$58$	−14.5188	+	12.1827i	−1.90641	+	1.59967i
$59$	0.0973892	+	0.552322i	0.0126790	+	0.0719062i	0.990491	−	0.137579i	$-0.0439322\pi$
$59$	0.0973892	+	0.552322i	0.0126790	+	0.0719062i	−0.977812	+	0.209486i	$0.932821\pi$
$60$		0			0
$61$	−4.58297	+	5.46178i	−0.586790	+	0.699309i	−0.974986	−	0.222268i	$-0.928654\pi$
$61$	−4.58297	+	5.46178i	−0.586790	+	0.699309i	0.388196	+	0.921577i	$0.373098\pi$
$62$	−1.46093	+	2.53041i	−0.185538	+	0.321362i
$63$		0			0
$64$	−3.87153	−	6.70568i	−0.483941	−	0.838210i
$65$	−4.24545	−	0.748587i	−0.526583	−	0.0928508i
$66$		0			0
$67$	8.34610	+	3.03773i	1.01964	+	0.371118i	0.797127	−	0.603812i	$-0.206352\pi$
$67$	8.34610	+	3.03773i	1.01964	+	0.371118i	0.222512	+	0.974930i	$0.428574\pi$
$68$	3.45573	+	1.25778i	0.419068	+	0.152528i
$69$		0			0
$70$	−2.90873	−	8.36303i	−0.347659	−	0.999574i
$71$	5.31767	−	3.07016i	0.631092	−	0.364361i	−0.150083	−	0.988673i	$-0.547954\pi$
$71$	5.31767	−	3.07016i	0.631092	−	0.364361i	0.781175	+	0.624312i	$0.214621\pi$
$72$		0			0
$73$	−5.75058	−	3.32010i	−0.673055	−	0.388588i	0.124178	−	0.992260i	$-0.460371\pi$
$73$	−5.75058	−	3.32010i	−0.673055	−	0.388588i	−0.797233	+	0.603671i	$0.793704\pi$
$74$	0.825982	−	0.984367i	0.0960184	−	0.114430i
$75$		0			0
$76$	−12.8005	+	2.25707i	−1.46832	+	0.258904i
$77$	2.99746	−	7.88178i	0.341592	−	0.898212i
$78$		0			0
$79$	0.814895	−	0.296597i	0.0916828	−	0.0333698i	−0.295772	−	0.955259i	$-0.595577\pi$
$79$	0.814895	−	0.296597i	0.0916828	−	0.0333698i	0.387454	+	0.921889i	$0.373354\pi$
$80$	6.82552			0.763117
$81$		0			0
$82$		−	1.01198i		−	0.111754i
$83$	−7.67310	+	2.79278i	−0.842232	+	0.306547i	−0.726869	−	0.686776i	$-0.759025\pi$
$83$	−7.67310	+	2.79278i	−0.842232	+	0.306547i	−0.115363	+	0.993323i	$0.536803\pi$
$84$		0			0
$85$	−2.40476	+	2.01784i	−0.260833	+	0.218865i
$86$	−2.23431	+	0.393970i	−0.240932	+	0.0424829i
$87$		0			0
$88$	0.154994	+	0.130055i	0.0165224	+	0.0138639i
$89$	−3.77720	+	6.54230i	−0.400383	+	0.693483i	−0.993772	−	0.111433i	$-0.964456\pi$
$89$	−3.77720	+	6.54230i	−0.400383	+	0.693483i	0.593389	+	0.804915i	$0.297789\pi$
$90$		0			0
$91$	−5.83010	−	3.47846i	−0.611161	−	0.364642i
$92$	13.9377	+	2.45759i	1.45311	+	0.256222i
$93$		0			0
$94$	7.85503	−	21.5815i	0.810185	−	2.22596i
$95$	3.79483	−	10.4262i	0.389341	−	1.06971i
$96$		0			0
$97$	9.45944	+	1.66796i	0.960461	+	0.169355i	0.631833	−	0.775104i	$-0.282303\pi$
$97$	9.45944	+	1.66796i	0.960461	+	0.169355i	0.328628	+	0.944460i	$0.393414\pi$
$98$	0.400014	−	13.9384i	0.0404075	−	1.40799i
$99$		0			0
$100$	−2.14278	+	3.71140i	−0.214278	+	0.371140i
$101$	0.579504	+	0.486261i	0.0576628	+	0.0483848i	0.671164	−	0.741309i	$-0.265795\pi$
$101$	0.579504	+	0.486261i	0.0576628	+	0.0483848i	−0.613501	+	0.789694i	$0.710239\pi$
$102$		0			0
$103$	−17.6544	+	3.11294i	−1.73954	+	0.306727i	−0.951214	−	0.308533i	$-0.900162\pi$
$103$	−17.6544	+	3.11294i	−1.73954	+	0.306727i	−0.788324	+	0.615260i	$0.789051\pi$
$104$	0.124784	−	0.104707i	0.0122361	−	0.0102673i
$105$		0			0
$106$	2.31999	−	0.844407i	0.225337	−	0.0820161i
$107$			5.82280i			0.562912i	0.959574	+	0.281456i	$0.0908173\pi$
$107$			5.82280i			0.562912i	−0.959574	+	0.281456i	$0.909183\pi$
$108$		0			0
$109$	−9.44448			−0.904617			−0.452309	−	0.891861i	$-0.649399\pi$
$109$	−9.44448			−0.904617			−0.452309	+	0.891861i	$0.649399\pi$
$110$	10.0232	−	3.64814i	0.955673	−	0.347836i
$111$		0			0
$112$	10.0469	+	3.82087i	0.949346	+	0.361039i
$113$	19.8413	−	3.49856i	1.86652	−	0.329117i	0.877812	−	0.479005i	$-0.159002\pi$
$113$	19.8413	−	3.49856i	1.86652	−	0.329117i	0.988703	+	0.149888i	$0.0478913\pi$
$114$		0			0
$115$	−7.76554	+	9.25462i	−0.724141	+	0.862997i
$116$	−16.2169	−	9.36285i	−1.50570	−	0.869319i
$117$		0			0
$118$	−0.967530	+	0.558604i	−0.0890683	+	0.0514236i
$119$	−4.66930	+	1.62402i	−0.428034	+	0.148873i
$120$		0			0
$121$	−0.791060	−	0.287922i	−0.0719145	−	0.0261748i
$122$	−13.3462	−	4.85763i	−1.20831	−	0.439789i
$123$		0			0
$124$	−2.84297	−	0.501292i	−0.255306	−	0.0450174i
$125$	−6.02921	−	10.4429i	−0.539269	−	0.934042i
$126$		0			0
$127$	−6.79079	+	11.7620i	−0.602585	+	1.04371i	0.389843	+	0.920881i	$0.372529\pi$
$127$	−6.79079	+	11.7620i	−0.602585	+	1.04371i	−0.992428	+	0.122827i	$0.960804\pi$
$128$	−0.326404	+	0.388993i	−0.0288503	+	0.0343824i
$129$		0			0
$130$	−1.49120	−	8.45701i	−0.130787	−	0.741728i
$131$	−2.75723	+	2.31359i	−0.240901	+	0.202140i	−0.755242	−	0.655446i	$-0.772481\pi$
$131$	−2.75723	+	2.31359i	−0.240901	+	0.202140i	0.514342	+	0.857585i	$0.328036\pi$
$132$		0			0
$133$	11.4224	−	13.2227i	0.990444	−	1.14655i
$134$			17.6926i			1.52840i
$135$		0			0
$136$		−	0.118619i		−	0.0101715i
$137$	−0.743270	−	2.04212i	−0.0635018	−	0.174470i	0.903884	−	0.427778i	$-0.140704\pi$
$137$	−0.743270	−	2.04212i	−0.0635018	−	0.174470i	−0.967386	+	0.253308i	$0.918481\pi$
$138$		0			0
$139$	13.3535	+	15.9141i	1.13263	+	1.34982i	0.928701	+	0.370830i	$0.120927\pi$
$139$	13.3535	+	15.9141i	1.13263	+	1.34982i	0.203929	+	0.978986i	$0.434629\pi$
$140$	6.78154	−	5.52657i	0.573145	−	0.467080i
$141$		0			0
$142$	9.36997	+	7.86234i	0.786310	+	0.659793i
$143$	4.08913	−	7.08258i	0.341950	−	0.592275i
$144$		0			0
$145$	13.8431	−	7.99232i	1.14961	−	0.663726i
$146$	2.29691	−	13.0264i	0.190094	−	1.07808i
$147$		0			0
$148$	1.19303	+	0.434226i	0.0980661	+	0.0356931i
$149$	−0.460486	+	1.26518i	−0.0377245	+	0.103647i	−0.957125	−	0.289676i	$-0.906452\pi$
$149$	−0.460486	+	1.26518i	−0.0377245	+	0.103647i	0.919400	+	0.393323i	$0.128675\pi$
$150$		0			0
$151$	−0.578521	+	3.28095i	−0.0470794	+	0.267000i	−0.999257	−	0.0385451i	$-0.987728\pi$
$151$	−0.578521	+	3.28095i	−0.0470794	+	0.267000i	0.952178	+	0.305545i	$0.0988388\pi$
$152$	0.209626	+	0.363082i	0.0170029	+	0.0294499i
$153$		0			0
$154$	16.7960	+	0.240962i	1.35346	+	0.0194173i
$155$	1.58399	−	1.88773i	0.127229	−	0.151626i
$156$		0			0
$157$	17.2240	−	3.03706i	1.37463	−	0.242384i	0.562950	−	0.826491i	$-0.309666\pi$
$157$	17.2240	−	3.03706i	1.37463	−	0.242384i	0.811676	+	0.584107i	$0.198555\pi$
$158$	1.11039	+	1.32331i	0.0883380	+	0.105277i
$159$		0			0
$160$	4.57734	+	12.5761i	0.361871	+	0.994231i
$161$	−16.6113	+	9.27538i	−1.30915	+	0.731003i
$162$		0			0
$163$	−20.1830			−1.58085			−0.790425	−	0.612558i	$-0.790141\pi$
$163$	−20.1830			−1.58085			−0.790425	+	0.612558i	$0.790141\pi$
$164$	0.939546	−	0.341967i	0.0733662	−	0.0267031i
$165$		0			0
$166$	−10.4555	−	12.4604i	−0.811506	−	0.967115i
$167$	0.218933	+	1.24163i	0.0169415	+	0.0960802i	0.992106	−	0.125401i	$-0.0400219\pi$
$167$	0.218933	+	1.24163i	0.0169415	+	0.0960802i	−0.975165	+	0.221482i	$0.928911\pi$
$168$		0			0
$169$	4.91475	+	4.12396i	0.378057	+	0.317228i
$170$	−5.41554	−	3.12667i	−0.415353	−	0.239804i
$171$		0			0
$172$	−1.12079	−	1.94126i	−0.0854594	−	0.148020i
$173$	3.14577	−	17.8405i	0.239168	−	1.35639i	−0.594486	−	0.804106i	$-0.702645\pi$
$173$	3.14577	−	17.8405i	0.239168	−	1.35639i	0.833655	−	0.552286i	$-0.186244\pi$
$174$		0			0
$175$	−0.918908	−	5.68730i	−0.0694629	−	0.429920i
$176$	−4.42870	+	12.1678i	−0.333826	+	0.917179i
$177$		0			0
$178$	−14.8199	−	2.61314i	−1.11080	−	0.195863i
$179$	−5.04916	+	2.91514i	−0.377392	+	0.217887i	−0.676683	−	0.736274i	$-0.736583\pi$
$179$	−5.04916	+	2.91514i	−0.377392	+	0.217887i	0.299291	+	0.954162i	$0.403250\pi$
$180$		0			0
$181$	−21.6062	−	12.4743i	−1.60598	−	0.927210i	−0.990258	−	0.139243i	$-0.955533\pi$
$181$	−21.6062	−	12.4743i	−1.60598	−	0.927210i	−0.615717	−	0.787967i	$-0.711134\pi$
$182$	2.53917	−	13.2832i	0.188216	−	0.984615i
$183$		0			0
$184$	−0.0792700	−	0.449562i	−0.00584386	−	0.0331422i
$185$	−0.830200	+	0.696620i	−0.0610375	+	0.0512166i
$186$		0			0
$187$	−2.03685	−	5.59620i	−0.148949	−	0.409235i
$188$	22.6912			1.65493
$189$		0			0
$190$	22.1021			1.60345
$191$	−1.74057	−	4.78218i	−0.125943	−	0.346026i	0.860656	−	0.509186i	$-0.170054\pi$
$191$	−1.74057	−	4.78218i	−0.125943	−	0.346026i	−0.986600	+	0.163160i	$0.947831\pi$
$192$		0			0
$193$	−1.96765	+	1.65106i	−0.141635	+	0.118846i	−0.710852	−	0.703341i	$-0.751691\pi$
$193$	−1.96765	+	1.65106i	−0.141635	+	0.118846i	0.569218	+	0.822187i	$0.307246\pi$
$194$	3.32260	+	18.8434i	0.238548	+	1.35288i
$195$		0			0
$196$	13.0759	−	4.33866i	0.933994	−	0.309904i
$197$	2.15214	+	1.24254i	0.153334	+	0.0885272i	0.574704	−	0.818362i	$-0.305117\pi$
$197$	2.15214	+	1.24254i	0.153334	+	0.0885272i	−0.421370	+	0.906889i	$0.638451\pi$
$198$		0			0
$199$	−16.9476	+	9.78473i	−1.20139	+	0.693621i	−0.960863	−	0.277023i	$-0.910652\pi$
$199$	−16.9476	+	9.78473i	−1.20139	+	0.693621i	−0.240523	+	0.970643i	$0.577319\pi$
$200$	0.136131	+	0.0240036i	0.00962593	+	0.00169731i
$201$		0			0
$202$	−0.515403	+	1.41606i	−0.0362636	+	0.0996335i
$203$	24.8506	−	4.01516i	1.74417	−	0.281809i
$204$		0			0
$205$	−0.148206	+	0.840521i	−0.0103512	+	0.0587045i
$206$	−17.8552	−	30.9261i	−1.24403	−	2.15472i
$207$		0			0
$208$	9.02819	+	5.21243i	0.625993	+	0.361417i
$209$	16.1244	+	13.5300i	1.11535	+	0.935887i
$210$		0			0
$211$	−4.93177	−	27.9694i	−0.339517	−	1.92550i	−0.377033	−	0.926200i	$-0.623056\pi$
$211$	−4.93177	−	27.9694i	−0.339517	−	1.92550i	0.0375160	−	0.999296i	$-0.488055\pi$
$212$	1.56794	+	1.86860i	0.107686	+	0.128336i
$213$		0			0
$214$	−10.8996	+	3.96713i	−0.745082	+	0.271188i
$215$	1.91346			0.130497
$216$		0			0
$217$	3.38832	−	1.89196i	0.230014	−	0.128435i
$218$	−6.43462	−	17.6790i	−0.435807	−	1.19737i
$219$		0			0
$220$	6.77405	+	8.07300i	0.456706	+	0.544281i
$221$	−4.72176	+	0.832574i	−0.317620	+	0.0560050i
$222$		0			0
$223$	−8.91266	+	10.6217i	−0.596836	+	0.711281i	−0.976904	−	0.213677i	$-0.931456\pi$
$223$	−8.91266	+	10.6217i	−0.596836	+	0.711281i	0.380069	+	0.924958i	$0.375900\pi$
$224$	−0.302336	+	21.0740i	−0.0202007	+	1.40807i
$225$		0			0
$226$	20.0670	+	34.7571i	1.33484	+	2.31200i
$227$	−3.16640	+	17.9575i	−0.210161	+	1.19188i	0.678947	+	0.734187i	$0.262436\pi$
$227$	−3.16640	+	17.9575i	−0.210161	+	1.19188i	−0.889109	+	0.457696i	$0.848675\pi$
$228$		0			0
$229$	−2.80126	+	7.69640i	−0.185113	+	0.508593i	−0.997186	−	0.0749621i	$-0.976116\pi$
$229$	−2.80126	+	7.69640i	−0.185113	+	0.508593i	0.812074	+	0.583555i	$0.198339\pi$
$230$	−22.6143	−	8.23093i	−1.49114	−	0.542732i
$231$		0			0
$232$	−0.104884	+	0.594824i	−0.00688594	+	0.0390521i
$233$	−7.85946	+	4.53766i	−0.514890	+	0.297272i	−0.734841	−	0.678239i	$-0.762743\pi$
$233$	−7.85946	+	4.53766i	−0.514890	+	0.297272i	0.219951	+	0.975511i	$0.429410\pi$
$234$		0			0
$235$	−9.68483	+	16.7746i	−0.631769	+	1.09426i
$236$	−0.845569	−	0.709516i	−0.0550418	−	0.0461856i
$237$		0			0
$238$	−6.22121	−	7.63392i	−0.403261	−	0.494834i
$239$	−12.1412	−	14.4693i	−0.785349	−	0.935943i	0.213813	−	0.976875i	$-0.431412\pi$
$239$	−12.1412	−	14.4693i	−0.785349	−	0.935943i	−0.999162	+	0.0409317i	$0.986967\pi$
$240$		0			0
$241$	3.70352	+	10.1753i	0.238565	+	0.655452i	0.999974	+	0.00718031i	$0.00228558\pi$
$241$	3.70352	+	10.1753i	0.238565	+	0.655452i	−0.761409	+	0.648271i	$0.775492\pi$
$242$		−	1.67694i		−	0.107798i
$243$		0			0
$244$		−	14.0325i		−	0.898337i
$245$	−2.37355	+	11.5182i	−0.151640	+	0.735874i
$246$		0			0
$247$	12.9816	−	10.8929i	0.826000	−	0.693097i
$248$	0.0161692	+	0.0917003i	0.00102675	+	0.00582298i
$249$		0			0
$250$	15.4401	−	18.4008i	0.976520	−	1.16377i
$251$	−6.39471	+	11.0760i	−0.403630	+	0.699108i	−0.994161	−	0.107907i	$-0.965585\pi$
$251$	−6.39471	+	11.0760i	−0.403630	+	0.699108i	0.590531	+	0.807015i	$0.298919\pi$
$252$		0			0
$253$	−11.4594	−	19.8483i	−0.720449	−	1.24785i
$254$	−26.6437	−	4.69800i	−1.67177	−	0.294779i
$255$		0			0
$256$	−15.5027	−	5.64253i	−0.968920	−	0.352658i
$257$	15.5948	+	5.67604i	0.972777	+	0.354062i	0.779028	−	0.626989i	$-0.215713\pi$
$257$	15.5948	+	5.67604i	0.972777	+	0.354062i	0.193749	+	0.981051i	$0.437935\pi$
$258$		0			0
$259$	−1.61199	+	0.560662i	−0.100164	+	0.0348378i
$260$	7.34779	−	4.24225i	0.455691	−	0.263093i
$261$		0			0
$262$	−6.20931	−	3.58495i	−0.383613	−	0.221479i
$263$	−10.7230	+	12.7791i	−0.661206	+	0.787995i	−0.987558	−	0.157254i	$-0.949736\pi$
$263$	−10.7230	+	12.7791i	−0.661206	+	0.787995i	0.326352	+	0.945248i	$0.394180\pi$
$264$		0			0
$265$	−2.05058	+	0.361573i	−0.125966	+	0.0222113i
$266$	32.5335	+	12.3726i	1.99476	+	0.758611i
$267$		0			0
$268$	−16.4262	+	5.97866i	−1.00339	+	0.365205i
$269$	27.3326			1.66650			0.833250	−	0.552896i	$-0.186477\pi$
$269$	27.3326			1.66650			0.833250	+	0.552896i	$0.186477\pi$
$270$		0			0
$271$			18.1849i			1.10465i	0.833628	+	0.552326i	$0.186260\pi$
$271$			18.1849i			1.10465i	−0.833628	+	0.552326i	$0.813740\pi$
$272$	7.13349	−	2.59638i	0.432532	−	0.157429i
$273$		0			0
$274$	3.31621	−	2.78263i	0.200339	−	0.168105i
$275$	6.83459	−	1.20512i	0.412141	−	0.0726716i
$276$		0			0
$277$	2.33912	+	1.96275i	0.140544	+	0.117930i	0.710349	−	0.703849i	$-0.248537\pi$
$277$	2.33912	+	1.96275i	0.140544	+	0.117930i	−0.569805	+	0.821780i	$0.692981\pi$
$278$	−20.6915	+	35.8386i	−1.24099	+	2.14946i
$279$		0			0
$280$	−0.242323	−	0.144579i	−0.0144816	−	0.00864026i
$281$	1.31210	+	0.231358i	0.0782732	+	0.0138017i	0.212648	−	0.977129i	$-0.431791\pi$
$281$	1.31210	+	0.231358i	0.0782732	+	0.0138017i	−0.134374	+	0.990931i	$0.542902\pi$
$282$		0			0
$283$	0.815020	−	2.23925i	0.0484479	−	0.133110i	−0.913109	−	0.407716i	$-0.866325\pi$
$283$	0.815020	−	2.23925i	0.0484479	−	0.133110i	0.961557	+	0.274606i	$0.0885476\pi$
$284$	−4.13330	+	11.3561i	−0.245266	+	0.673863i
$285$		0			0
$286$	16.0437	+	2.82894i	0.948686	+	0.167279i
$287$	−0.688672	+	1.15425i	−0.0406510	+	0.0681334i
$288$		0			0
$289$	6.75430	−	11.6988i	0.397312	−	0.688164i
$290$	24.3921	+	20.4674i	1.43236	+	1.20189i
$291$		0			0
$292$	12.8702	−	2.26937i	0.753174	−	0.132805i
$293$	−19.4216	+	16.2967i	−1.13462	+	0.952061i	−0.999250	−	0.0387342i	$-0.987667\pi$
$293$	−19.4216	+	16.2967i	−1.13462	+	0.952061i	−0.135372	+	0.990795i	$0.543223\pi$
$294$		0			0
$295$	0.885412	−	0.322264i	0.0515507	−	0.0187629i
$296$		−	0.0409508i		−	0.00238022i
$297$		0			0
$298$	−2.68200			−0.155364
$299$	−17.3390	+	6.31089i	−1.00274	+	0.364968i
$300$		0			0
$301$	2.81654	+	1.07114i	0.162343	+	0.0617394i
$302$	−6.53572	+	1.15242i	−0.376088	+	0.0663145i
$303$		0			0
$304$	−17.2467	+	20.5538i	−0.989166	+	1.17884i
$305$	10.3736	+	5.98920i	0.593991	+	0.342941i
$306$		0			0
$307$	9.17503	−	5.29721i	0.523647	−	0.302328i	−0.214779	−	0.976663i	$-0.568903\pi$
$307$	9.17503	−	5.29721i	0.523647	−	0.302328i	0.738425	+	0.674335i	$0.235570\pi$
$308$	5.45197	+	15.6752i	0.310655	+	0.893179i
$309$		0			0
$310$	4.61280	+	1.67892i	0.261989	+	0.0953563i
$311$	−5.82677	−	2.12077i	−0.330406	−	0.120258i	0.171490	−	0.985186i	$-0.445142\pi$
$311$	−5.82677	−	2.12077i	−0.330406	−	0.120258i	−0.501896	+	0.864928i	$0.667364\pi$
$312$		0			0
$313$	14.4632	+	2.55024i	0.817506	+	0.144148i	0.566737	−	0.823899i	$-0.308206\pi$
$313$	14.4632	+	2.55024i	0.817506	+	0.144148i	0.250769	+	0.968047i	$0.419317\pi$
$314$	17.4199	+	30.1722i	0.983063	+	1.70271i
$315$		0			0
$316$	−0.853375	+	1.47809i	−0.0480061	+	0.0831490i
$317$	−7.18858	+	8.56702i	−0.403751	+	0.481172i	−0.929160	−	0.369678i	$-0.879468\pi$
$317$	−7.18858	+	8.56702i	−0.403751	+	0.481172i	0.525409	+	0.850850i	$0.323912\pi$
$318$		0			0
$319$	5.26577	+	29.8637i	0.294827	+	1.67205i
$320$	−9.96518	+	8.36178i	−0.557070	+	0.467438i
$321$		0			0
$322$	−28.6799	−	24.7750i	−1.59827	−	1.38065i
$323$		−	12.3402i		−	0.686625i
$324$		0			0
$325$		−	5.58736i		−	0.309931i
$326$	−13.7508	−	37.7801i	−0.761589	−	2.09245i
$327$		0			0
$328$	−0.0207300	−	0.0247050i	−0.00114462	−	0.00136411i
$329$	−23.6460	+	19.2702i	−1.30365	+	1.06240i
$330$		0			0
$331$	−21.2397	−	17.8222i	−1.16744	−	0.979598i	−0.167460	−	0.985879i	$-0.553556\pi$
$331$	−21.2397	−	17.8222i	−1.16744	−	0.979598i	−0.999980	+	0.00628050i	$0.998001\pi$
$332$	8.03543	−	13.9178i	0.441002	−	0.763837i
$333$		0			0
$334$	−2.17503	+	1.25575i	−0.119012	+	0.0687117i
$335$	2.59112	−	14.6949i	0.141568	−	0.802871i
$336$		0			0
$337$	19.3322	+	7.03635i	1.05309	+	0.383294i	0.809829	−	0.586666i	$-0.199560\pi$
$337$	19.3322	+	7.03635i	1.05309	+	0.383294i	0.243264	+	0.969960i	$0.421782\pi$
$338$	−4.37111	+	12.0095i	−0.237757	+	0.653232i
$339$		0			0
$340$	1.07286	−	6.08449i	0.0581840	−	0.329978i
$341$	2.33746	+	4.04860i	0.126581	+	0.219244i
$342$		0			0
$343$	−9.94160	+	15.6258i	−0.536796	+	0.843712i
$344$	−0.0464751	+	0.0553869i	−0.00250577	+	0.00298626i
$345$		0			0
$346$	35.5387	−	6.26643i	1.91057	−	0.336885i
$347$	11.8767	+	14.1541i	0.637575	+	0.759832i	0.983985	−	0.178251i	$-0.0570439\pi$
$347$	11.8767	+	14.1541i	0.637575	+	0.759832i	−0.346410	+	0.938083i	$0.612599\pi$
$348$		0			0
$349$	−2.33201	−	6.40713i	−0.124829	−	0.342966i	0.861499	−	0.507760i	$-0.169526\pi$
$349$	−2.33201	−	6.40713i	−0.124829	−	0.342966i	−0.986328	+	0.164794i	$0.947304\pi$
$350$	10.0199	−	5.59490i	0.535586	−	0.299060i
$351$		0			0
$352$	−25.3893			−1.35325
$353$	−1.67606	+	0.610036i	−0.0892077	+	0.0324689i	−0.386238	−	0.922399i	$-0.626226\pi$
$353$	−1.67606	+	0.610036i	−0.0892077	+	0.0324689i	0.297031	+	0.954868i	$0.404004\pi$
$354$		0			0
$355$	−6.63098	−	7.90249i	−0.351936	−	0.419421i
$356$	−2.58181	−	14.6422i	−0.136836	−	0.776034i
$357$		0			0
$358$	−8.89684	−	7.46533i	−0.470213	−	0.394555i
$359$	−20.9229	−	12.0799i	−1.10427	−	0.637550i	−0.166930	−	0.985969i	$-0.553386\pi$
$359$	−20.9229	−	12.0799i	−1.10427	−	0.637550i	−0.937339	+	0.348418i	$0.886719\pi$
$360$		0			0
$361$	12.3079	+	21.3178i	0.647782	+	1.12199i
$362$	8.63000	−	48.9432i	0.453583	−	2.57240i
$363$		0			0
$364$	13.1905	−	2.13121i	0.691369	−	0.111706i
$365$	−3.81550	+	10.4830i	−0.199713	+	0.548706i
$366$		0			0
$367$	12.6882	+	2.23726i	0.662316	+	0.116784i	0.494694	−	0.869067i	$-0.335280\pi$
$367$	12.6882	+	2.23726i	0.662316	+	0.116784i	0.167622	+	0.985851i	$0.446391\pi$
$368$	25.3007	−	14.6074i	1.31889	−	0.761463i
$369$		0			0
$370$	−1.86962	−	1.07942i	−0.0971967	−	0.0561165i
$371$	−3.22079	−	0.615677i	−0.167215	−	0.0319644i
$372$		0			0
$373$	3.00218	+	17.0262i	0.155447	+	0.881585i	0.958376	+	0.285510i	$0.0921629\pi$
$373$	3.00218	+	17.0262i	0.155447	+	0.881585i	−0.802929	+	0.596075i	$0.796726\pi$
$374$	9.08771	−	7.62549i	0.469914	−	0.394305i
$375$		0			0
$376$	−0.250327	−	0.687768i	−0.0129096	−	0.0354689i
$377$	24.4139			1.25738
$378$		0			0
$379$	22.4692			1.15416			0.577082	−	0.816687i	$-0.304191\pi$
$379$	22.4692			1.15416			0.577082	+	0.816687i	$0.304191\pi$
$380$	7.46872	+	20.5201i	0.383137	+	1.05266i
$381$		0			0
$382$	7.76581	−	6.51629i	0.397333	−	0.333402i
$383$	−3.13629	−	17.7868i	−0.160257	−	0.908864i	−0.953821	−	0.300376i	$-0.902888\pi$
$383$	−3.13629	−	17.7868i	−0.160257	−	0.908864i	0.793564	−	0.608487i	$-0.208223\pi$
$384$		0			0
$385$	−13.9150	−	2.65994i	−0.709173	−	0.135563i
$386$	−4.43116	−	2.55833i	−0.225540	−	0.130216i
$387$		0			0
$388$	−16.3719	+	9.45232i	−0.831157	+	0.479869i
$389$	19.1153	+	3.37054i	0.969184	+	0.170893i	0.635762	−	0.771885i	$-0.280686\pi$
$389$	19.1153	+	3.37054i	0.969184	+	0.170893i	0.333421	+	0.942778i	$0.391797\pi$
$390$		0			0
$391$	−4.59554	+	12.6261i	−0.232407	+	0.638532i
$392$	−0.275757	−	0.348466i	−0.0139278	−	0.0176002i
$393$		0			0
$394$	−0.859613	+	4.87511i	−0.0433067	+	0.245604i
$395$	−0.728458	−	1.26173i	−0.0366527	−	0.0634844i
$396$		0			0
$397$	11.5666	+	6.67796i	0.580509	+	0.335157i	0.761336	−	0.648358i	$-0.224544\pi$
$397$	11.5666	+	6.67796i	0.580509	+	0.335157i	−0.180826	+	0.983515i	$0.557877\pi$
$398$	−29.8625	−	25.0576i	−1.49687	−	1.25602i
$399$		0			0
$400$	1.53617	+	8.71208i	0.0768087	+	0.435604i
$401$	−2.35877	−	2.81108i	−0.117792	−	0.140379i	0.703926	−	0.710273i	$-0.251429\pi$
$401$	−2.35877	−	2.81108i	−0.117792	−	0.140379i	−0.821718	+	0.569894i	$0.806984\pi$
$402$		0			0
$403$	3.53676	−	1.28728i	0.176179	−	0.0641238i
$404$	−1.48887			−0.0740740
$405$		0			0
$406$	24.4469	+	43.7819i	1.21328	+	2.17286i
$407$	−0.703185	−	1.93198i	−0.0348556	−	0.0957649i
$408$		0			0
$409$	−1.06836	−	1.27322i	−0.0528271	−	0.0629569i	0.738984	−	0.673723i	$-0.235306\pi$
$409$	−1.06836	−	1.27322i	−0.0528271	−	0.0629569i	−0.791811	+	0.610766i	$0.790862\pi$
$410$	−1.67433	+	0.295230i	−0.0826893	+	0.0145804i
$411$		0			0
$412$	22.6789	−	27.0277i	1.11731	−	1.33156i
$413$	1.48370	+	0.0212857i	0.0730079	+	0.00104740i
$414$		0			0
$415$	6.85921	+	11.8805i	0.336705	+	0.583191i
$416$	−3.54949	+	20.1302i	−0.174028	+	0.986963i
$417$		0			0
$418$	−14.3408	+	39.4011i	−0.701432	+	1.92717i
$419$	−0.883387	−	0.321527i	−0.0431563	−	0.0157076i	0.320352	−	0.947299i	$-0.396199\pi$
$419$	−0.883387	−	0.321527i	−0.0431563	−	0.0157076i	−0.363508	+	0.931591i	$0.618421\pi$
$420$		0			0
$421$	6.25816	−	35.4918i	0.305004	−	1.72976i	−0.318482	−	0.947929i	$-0.603173\pi$
$421$	6.25816	−	35.4918i	0.305004	−	1.72976i	0.623486	−	0.781835i	$-0.285716\pi$
$422$	48.9955	−	28.2876i	2.38506	−	1.37702i
$423$		0			0
$424$	0.0393396	−	0.0681382i	0.00191050	−	0.00330908i
$425$	−3.11678	−	2.61529i	−0.151186	−	0.126860i
$426$		0			0
$427$	11.9169	+	14.6230i	0.576698	+	0.707654i
$428$	−7.36637	−	8.77890i	−0.356067	−	0.424344i
$429$		0			0
$430$	1.30366	+	3.58177i	0.0628679	+	0.172728i
$431$			25.0083i			1.20461i	0.798268	+	0.602303i	$0.205750\pi$
$431$			25.0083i			1.20461i	−0.798268	+	0.602303i	$0.794250\pi$
$432$		0			0
$433$		−	28.5219i		−	1.37068i	−0.728225	−	0.685338i	$-0.759654\pi$
$433$		−	28.5219i		−	1.37068i	0.728225	−	0.685338i	$-0.240346\pi$
$434$	5.85003	+	5.05352i	0.280810	+	0.242577i
$435$		0			0
$436$	14.2392	−	11.9481i	0.681935	−	0.572211i
$437$	−8.24664	−	46.7690i	−0.394490	−	2.23727i
$438$		0			0
$439$	18.7971	−	22.4015i	0.897136	−	1.06917i	−0.100108	−	0.994977i	$-0.531919\pi$
$439$	18.7971	−	22.4015i	0.897136	−	1.06917i	0.997244	−	0.0741886i	$-0.0236367\pi$
$440$	0.169961	−	0.294381i	0.00810258	−	0.0140341i
$441$		0			0
$442$	−4.77547	−	8.27135i	−0.227146	−	0.393428i
$443$	2.26061	+	0.398607i	0.107405	+	0.0189384i	0.227092	−	0.973873i	$-0.427078\pi$
$443$	2.26061	+	0.398607i	0.107405	+	0.0189384i	−0.119687	+	0.992812i	$0.538189\pi$
$444$		0			0
$445$	11.9263	+	4.34081i	0.565360	+	0.205774i
$446$	−25.9549	−	9.44680i	−1.22900	−	0.447319i
$447$		0			0
$448$	−19.3493	+	6.72982i	−0.914166	+	0.317954i
$449$	18.7877	−	10.8471i	0.886646	−	0.511905i	0.0138018	−	0.999905i	$-0.495607\pi$
$449$	18.7877	−	10.8471i	0.886646	−	0.511905i	0.872844	+	0.488000i	$0.162273\pi$
$450$		0			0
$451$	−1.40222	−	0.809573i	−0.0660280	−	0.0381213i
$452$	−25.4883	+	30.3758i	−1.19887	+	1.42876i
$453$		0			0
$454$	−35.7717	+	6.30752i	−1.67885	+	0.296026i
$455$	−4.05432	+	10.6608i	−0.190069	+	0.499785i
$456$		0			0
$457$	0.112432	−	0.0409217i	0.00525933	−	0.00191424i	−0.339389	−	0.940646i	$-0.610220\pi$
$457$	0.112432	−	0.0409217i	0.00525933	−	0.00191424i	0.344648	+	0.938732i	$0.387998\pi$
$458$	−16.3153			−0.762364
$459$		0			0
$460$		−	23.7771i		−	1.10861i
$461$	32.1671	−	11.7079i	1.49817	−	0.545289i	0.542584	−	0.840001i	$-0.317446\pi$
$461$	32.1671	−	11.7079i	1.49817	−	0.545289i	0.955586	+	0.294712i	$0.0952237\pi$
$462$		0			0
$463$	11.1529	−	9.35842i	0.518321	−	0.434923i	−0.345725	−	0.938336i	$-0.612367\pi$
$463$	11.1529	−	9.35842i	0.518321	−	0.434923i	0.864046	+	0.503413i	$0.167923\pi$
$464$	−38.0673	+	6.71230i	−1.76723	+	0.311611i
$465$		0			0
$466$	−13.8487	−	11.6204i	−0.641528	−	0.538306i
$467$	9.08585	−	15.7372i	0.420443	−	0.728229i	−0.575540	−	0.817774i	$-0.695208\pi$
$467$	9.08585	−	15.7372i	0.420443	−	0.728229i	0.995983	+	0.0895452i	$0.0285414\pi$
$468$		0			0
$469$	12.0401	−	20.1800i	0.555962	−	0.931824i
$470$	−37.9985	−	6.70016i	−1.75274	−	0.309056i
$471$		0			0
$472$	−0.0121771	+	0.0334564i	−0.000560498	+	0.00153996i
$473$	−1.24154	+	3.41109i	−0.0570859	+	0.156842i
$474$		0			0
$475$	14.1621	+	2.49715i	0.649799	+	0.114577i
$476$	4.98526	−	8.35558i	0.228499	−	0.382977i
$477$		0			0
$478$	18.8130	−	32.5850i	0.860485	−	1.49040i
$479$	6.32713	+	5.30910i	0.289094	+	0.242579i	0.775788	−	0.630994i	$-0.217353\pi$
$479$	6.32713	+	5.30910i	0.289094	+	0.242579i	−0.486694	+	0.873573i	$0.661797\pi$
$480$		0			0
$481$	−1.63010	+	0.287431i	−0.0743262	+	0.0131057i
$482$	−16.5238	+	13.8651i	−0.752639	+	0.631539i
$483$		0			0
$484$	1.55691	−	0.566669i	0.0707686	−	0.0257577i
$485$		−	16.1374i		−	0.732761i
$486$		0			0
$487$	11.6289			0.526957			0.263478	−	0.964665i	$-0.415130\pi$
$487$	11.6289			0.526957			0.263478	+	0.964665i	$0.415130\pi$
$488$	−0.425323	+	0.154805i	−0.0192535	+	0.00700769i
$489$		0			0
$490$	−23.1779	+	3.40449i	−1.04707	+	0.153799i
$491$	23.9209	−	4.21791i	1.07954	−	0.190351i	0.394526	−	0.918885i	$-0.370909\pi$
$491$	23.9209	−	4.21791i	1.07954	−	0.190351i	0.685010	+	0.728533i	$0.259798\pi$
$492$		0			0
$493$	11.4275	−	13.6188i	0.514669	−	0.613358i
$494$	29.2347	+	16.8787i	1.31533	+	0.759406i
$495$		0			0
$496$	−5.16077	+	2.97957i	−0.231725	+	0.133787i
$497$	−5.33682	−	15.3442i	−0.239389	−	0.688280i
$498$		0			0
$499$	−15.5923	−	5.67512i	−0.698006	−	0.254053i	−0.0314466	−	0.999505i	$-0.510011\pi$
$499$	−15.5923	−	5.67512i	−0.698006	−	0.254053i	−0.666559	+	0.745452i	$0.732234\pi$
$500$	22.3013	+	8.11702i	0.997345	+	0.363004i
$501$		0			0
$502$	−25.0897	−	4.42399i	−1.11981	−	0.197452i
$503$	−2.75453	−	4.77099i	−0.122819	−	0.212728i	0.798060	−	0.602579i	$-0.205860\pi$
$503$	−2.75453	−	4.77099i	−0.122819	−	0.212728i	−0.920878	+	0.389851i	$0.872527\pi$
$504$		0			0
$505$	0.635464	−	1.10066i	0.0282778	−	0.0489786i
$506$	29.3463	−	34.9736i	1.30460	−	1.55477i
$507$		0			0
$508$	−4.64167	−	26.3242i	−0.205941	−	1.16795i
$509$	28.4889	−	23.9050i	1.26275	−	1.05957i	0.267366	−	0.963595i	$-0.413847\pi$
$509$	28.4889	−	23.9050i	1.26275	−	1.05957i	0.995384	−	0.0959772i	$-0.0305976\pi$
$510$		0			0
$511$	−11.4846	+	13.2947i	−0.508049	+	0.588125i
$512$		−	31.8480i		−	1.40750i
$513$		0			0
$514$			33.0588i			1.45816i
$515$	10.3008	+	28.3013i	0.453908	+	1.24710i
$516$		0			0
$517$	−23.6199	−	28.1491i	−1.03880	−	1.23800i
$518$	−2.14776	−	2.63547i	−0.0943670	−	0.115796i
$519$		0			0
$520$	−0.209642	−	0.175911i	−0.00919343	−	0.00771420i
$521$	−4.68325	+	8.11162i	−0.205177	+	0.355376i	−0.950189	−	0.311674i	$-0.899110\pi$
$521$	−4.68325	+	8.11162i	−0.205177	+	0.355376i	0.745012	+	0.667051i	$0.232444\pi$
$522$		0			0
$523$	−8.64692	+	4.99230i	−0.378104	+	0.218298i	−0.676993	−	0.735990i	$-0.736717\pi$
$523$	−8.64692	+	4.99230i	−0.378104	+	0.218298i	0.298889	+	0.954288i	$0.403384\pi$
$524$	1.23011	−	6.97630i	0.0537376	−	0.304761i
$525$		0			0
$526$	−31.2267	−	11.3656i	−1.36155	−	0.495563i
$527$	0.937384	−	2.57544i	0.0408331	−	0.112188i
$528$		0			0
$529$	−4.98537	+	28.2734i	−0.216755	+	1.22928i
$530$	−2.07391	−	3.59211i	−0.0900847	−	0.156031i
$531$		0			0
$532$	−0.493314	+	34.3859i	−0.0213879	+	1.49082i
$533$	−0.837913	+	0.998586i	−0.0362940	+	0.0432535i
$534$		0			0
$535$	9.63391	−	1.69872i	0.416510	−	0.0734420i
$536$	0.362425	+	0.431921i	0.0156544	+	0.0186562i
$537$		0			0
$538$	18.6220	+	51.1635i	0.802851	+	2.20582i
$539$	−18.9933	−	11.7048i	−0.818101	−	0.504163i
$540$		0			0
$541$	−6.07091			−0.261009			−0.130504	−	0.991448i	$-0.541660\pi$
$541$	−6.07091			−0.261009			−0.130504	+	0.991448i	$0.541660\pi$
$542$	−34.0400	+	12.3895i	−1.46214	+	0.532176i
$543$		0			0
$544$	9.56775	+	11.4024i	0.410214	+	0.488874i
$545$	2.75529	+	15.6260i	0.118024	+	0.669345i
$546$		0			0
$547$	−23.6417	−	19.8377i	−1.01084	−	0.848199i	−0.0223949	−	0.999749i	$-0.507129\pi$
$547$	−23.6417	−	19.8377i	−1.01084	−	0.848199i	−0.988450	+	0.151550i	$0.951574\pi$
$548$	3.70407	+	2.13855i	0.158230	+	0.0913542i
$549$		0			0
$550$	6.91232	+	11.9725i	0.294742	+	0.510509i
$551$	−10.9113	+	61.8810i	−0.464836	+	2.63622i
$552$		0			0
$553$	−0.365961	−	2.26500i	−0.0155622	−	0.0963177i
$554$	−2.08038	+	5.71580i	−0.0883869	+	0.242841i
$555$		0			0
$556$	−40.2655	−	7.09990i	−1.70764	−	0.301103i
$557$	−0.0926294	+	0.0534796i	−0.00392483	+	0.00226600i	−0.501961	−	0.864890i	$-0.667388\pi$
$557$	−0.0926294	+	0.0534796i	−0.00392483	+	0.00226600i	0.498036	+	0.867156i	$0.334055\pi$
$558$		0			0
$559$	2.53095	+	1.46124i	0.107048	+	0.0618041i
$560$	3.39064	−	17.7375i	0.143281	−	0.749545i
$561$		0			0
$562$	0.460870	+	2.61372i	0.0194406	+	0.110253i
$563$	−16.8629	+	14.1497i	−0.710687	+	0.596337i	−0.924792	−	0.380474i	$-0.875761\pi$
$563$	−16.8629	+	14.1497i	−0.710687	+	0.596337i	0.214105	+	0.976811i	$0.431317\pi$
$564$		0			0
$565$	−11.5768	−	31.8071i	−0.487041	−	1.33813i
$566$	4.74689			0.199527
$567$		0			0
$568$	0.389802			0.0163557
$569$	−3.90300	−	10.7234i	−0.163622	−	0.449549i	0.830603	−	0.556866i	$-0.187996\pi$
$569$	−3.90300	−	10.7234i	−0.163622	−	0.449549i	−0.994225	+	0.107317i	$0.965774\pi$
$570$		0			0
$571$	−4.28570	+	3.59613i	−0.179351	+	0.150493i	−0.728044	−	0.685531i	$-0.759570\pi$
$571$	−4.28570	+	3.59613i	−0.179351	+	0.150493i	0.548693	+	0.836024i	$0.315126\pi$
$572$	2.79502	+	15.8514i	0.116866	+	0.662779i
$573$		0			0
$574$	−2.62983	−	0.502709i	−0.109767	−	0.0209827i
$575$	−13.5603	−	7.82905i	−0.565504	−	0.326494i
$576$		0			0
$577$	−1.56687	+	0.904634i	−0.0652297	+	0.0376604i	−0.532260	−	0.846581i	$-0.678657\pi$
$577$	−1.56687	+	0.904634i	−0.0652297	+	0.0376604i	0.467030	+	0.884241i	$0.345324\pi$
$578$	26.5006	+	4.67276i	1.10228	+	0.194361i
$579$		0			0
$580$	−10.7599	+	29.5626i	−0.446781	+	1.22752i
$581$	3.44591	+	21.3274i	0.142960	+	0.884810i
$582$		0			0
$583$	0.685939	−	3.89015i	0.0284087	−	0.161114i
$584$	−0.210768	−	0.365061i	−0.00872164	−	0.0151063i
$585$		0			0
$586$	−43.7376	−	25.2519i	−1.80678	−	1.04315i
$587$	−24.7393	−	20.7587i	−1.02110	−	0.856804i	−0.0313339	−	0.999509i	$-0.509976\pi$
$587$	−24.7393	−	20.7587i	−1.02110	−	0.856804i	−0.989765	+	0.142705i	$0.954420\pi$
$588$		0			0
$589$	1.68212	+	9.53980i	0.0693107	+	0.393081i
$590$	1.20648	+	1.43783i	0.0496700	+	0.0591944i
$591$		0			0
$592$	2.46271	−	0.896352i	0.101217	−	0.0368398i
$593$	6.02328			0.247347			0.123673	−	0.992323i	$-0.460533\pi$
$593$	6.02328			0.247347			0.123673	+	0.992323i	$0.460533\pi$
$594$		0			0
$595$	4.04916	+	7.25163i	0.165999	+	0.297288i
$596$	−0.906298	−	2.49003i	−0.0371234	−	0.101996i
$597$		0			0
$598$	−23.6265	−	28.1570i	−0.966159	−	1.15142i
$599$	8.19802	−	1.44553i	0.334962	−	0.0590629i	−0.00363751	−	0.999993i	$-0.501158\pi$
$599$	8.19802	−	1.44553i	0.334962	−	0.0590629i	0.338600	+	0.940931i	$0.390047\pi$
$600$		0			0
$601$	−13.5043	+	16.0938i	−0.550851	+	0.656479i	−0.967584	−	0.252550i	$-0.918731\pi$
$601$	−13.5043	+	16.0938i	−0.550851	+	0.656479i	0.416733	+	0.909029i	$0.363175\pi$
$602$	−0.0861074	+	6.00202i	−0.00350947	+	0.244624i
$603$		0			0
$604$	−3.27848	−	5.67850i	−0.133400	−	0.231055i
$605$	−0.245591	+	1.39282i	−0.00998470	+	0.0566260i
$606$		0			0
$607$	−13.9808	+	38.4119i	−0.567463	+	1.55909i	0.240989	+	0.970528i	$0.422528\pi$
$607$	−13.9808	+	38.4119i	−0.567463	+	1.55909i	−0.808452	+	0.588563i	$0.799694\pi$
$608$	−49.4368	−	17.9935i	−2.00493	−	0.729733i
$609$		0			0
$610$	−4.14345	+	23.4987i	−0.167763	+	0.951433i
$611$	−25.6205	+	14.7920i	−1.03649	+	0.598420i
$612$		0			0
$613$	7.05243	−	12.2152i	0.284845	−	0.493366i	−0.687727	−	0.725970i	$-0.741391\pi$
$613$	7.05243	−	12.2152i	0.284845	−	0.493366i	0.972572	+	0.232604i	$0.0747245\pi$
$614$	16.1668	+	13.5656i	0.652439	+	0.547461i
$615$		0			0
$616$	0.414969	−	0.338176i	0.0167196	−	0.0136255i
$617$	−19.9970	−	23.8315i	−0.805051	−	0.959422i	0.194720	−	0.980859i	$-0.437620\pi$
$617$	−19.9970	−	23.8315i	−0.805051	−	0.959422i	−0.999770	+	0.0214370i	$0.993176\pi$
$618$		0			0
$619$	−15.2211	−	41.8197i	−0.611789	−	1.68088i	−0.726235	−	0.687446i	$-0.758732\pi$
$619$	−15.2211	−	41.8197i	−0.611789	−	1.68088i	0.114446	−	0.993429i	$-0.463491\pi$
$620$			4.84998i			0.194780i
$621$		0			0
$622$		−	12.3519i		−	0.495267i
$623$	15.1251	+	13.0658i	0.605975	+	0.523468i
$624$		0			0
$625$	−7.17877	+	6.02371i	−0.287151	+	0.240948i
$626$	5.08013	+	28.8108i	0.203043	+	1.15151i
$627$		0			0
$628$	−22.1261	+	26.3688i	−0.882927	+	1.05223i
$629$	−0.602670	+	1.04385i	−0.0240300	+	0.0416212i
$630$		0			0
$631$	4.05881	+	7.03007i	0.161579	+	0.279862i	0.935435	−	0.353499i	$-0.115008\pi$
$631$	4.05881	+	7.03007i	0.161579	+	0.279862i	−0.773856	+	0.633361i	$0.781675\pi$
$632$	0.0542151	+	0.00955958i	0.00215656	+	0.000380260i
$633$		0			0
$634$	−20.9341	−	7.61940i	−0.831400	−	0.302605i
$635$	21.4415	+	7.80406i	0.850879	+	0.309695i
$636$		0			0
$637$	−11.9356	+	13.4227i	−0.472907	+	0.531827i
$638$	−52.3137	+	30.2033i	−2.07112	+	1.19576i
$639$		0			0
$640$	0.738818	+	0.426557i	0.0292043	+	0.0168611i
$641$	12.1403	−	14.4683i	0.479514	−	0.571462i	−0.471005	−	0.882131i	$-0.656108\pi$
$641$	12.1403	−	14.4683i	0.479514	−	0.571462i	0.950518	+	0.310669i	$0.100553\pi$
$642$		0			0
$643$	25.9951	−	4.58364i	1.02515	−	0.180761i	0.364300	−	0.931282i	$-0.381308\pi$
$643$	25.9951	−	4.58364i	1.02515	−	0.180761i	0.660847	+	0.750521i	$0.270197\pi$
$644$	13.3102	−	34.9990i	0.524496	−	1.37916i
$645$		0			0
$646$	23.0993	−	8.40748i	0.908832	−	0.330788i
$647$	−25.0360			−0.984267			−0.492133	−	0.870520i	$-0.663783\pi$
$647$	−25.0360			−0.984267			−0.492133	+	0.870520i	$0.663783\pi$
$648$		0			0
$649$			1.78751i			0.0701659i
$650$	10.4589	−	3.80672i	0.410231	−	0.149312i
$651$		0			0
$652$	30.4294	−	25.5333i	1.19171	−	0.999960i
$653$	24.9911	−	4.40660i	0.977977	−	0.172444i	0.338259	−	0.941053i	$-0.390162\pi$
$653$	24.9911	−	4.40660i	0.977977	−	0.172444i	0.639718	+	0.768609i	$0.279051\pi$
$654$		0			0
$655$	4.63226	+	3.88693i	0.180997	+	0.151875i
$656$	1.03197	−	1.78742i	0.0402915	−	0.0697869i
$657$		0			0
$658$	−52.1818	−	31.1337i	−2.03426	−	1.21372i
$659$	28.7214	+	5.06437i	1.11883	+	0.197280i	0.702326	−	0.711855i	$-0.252145\pi$
$659$	28.7214	+	5.06437i	1.11883	+	0.197280i	0.416502	+	0.909135i	$0.363256\pi$
$660$		0			0
$661$	1.91283	−	5.25546i	0.0744005	−	0.204414i	−0.896917	−	0.442198i	$-0.854199\pi$
$661$	1.91283	−	5.25546i	0.0744005	−	0.204414i	0.971318	+	0.237784i	$0.0764211\pi$
$662$	18.8903	−	51.9007i	0.734193	−	2.01718i
$663$		0			0
$664$	−0.510493	−	0.0900136i	−0.0198110	−	0.00349321i
$665$	−25.2094	−	15.0409i	−0.977580	−	0.583262i
$666$		0			0
$667$	34.2089	−	59.2516i	1.32458	−	2.29423i
$668$	−1.90085	−	1.59501i	−0.0735463	−	0.0617126i
$669$		0			0
$670$	29.2726	−	5.16155i	1.13090	−	0.199408i
$671$	−17.4077	+	14.6068i	−0.672017	+	0.563889i
$672$		0			0
$673$	21.3185	−	7.75929i	0.821767	−	0.299099i	0.103292	−	0.994651i	$-0.467063\pi$
$673$	21.3185	−	7.75929i	0.821767	−	0.299099i	0.718475	+	0.695552i	$0.244840\pi$
$674$			40.9816i			1.57855i
$675$		0			0
$676$	−12.6270			−0.485655
$677$	7.76681	−	2.82689i	0.298503	−	0.108646i	−0.188427	−	0.982087i	$-0.560339\pi$
$677$	7.76681	−	2.82689i	0.298503	−	0.108646i	0.486930	+	0.873441i	$0.338117\pi$
$678$		0			0
$679$	9.03358	−	23.7537i	0.346677	−	0.911582i
$680$	−0.196256	+	0.0346052i	−0.00752607	+	0.00132705i
$681$		0			0
$682$	−5.98597	+	7.13381i	−0.229215	+	0.273168i
$683$	−23.0002	−	13.2792i	−0.880080	−	0.508114i	−0.00939496	−	0.999956i	$-0.502991\pi$
$683$	−23.0002	−	13.2792i	−0.880080	−	0.508114i	−0.870685	+	0.491842i	$0.836324\pi$
$684$		0			0
$685$	−3.16187	+	1.82551i	−0.120809	+	0.0697491i
$686$	−36.0229	−	7.96353i	−1.37536	−	0.304049i
$687$		0			0
$688$	−4.34813	−	1.58259i	−0.165771	−	0.0603357i
$689$	−2.98845	−	1.08771i	−0.113851	−	0.0414384i
$690$		0			0
$691$	37.5870	+	6.62760i	1.42988	+	0.252126i	0.834361	−	0.551218i	$-0.185837\pi$
$691$	37.5870	+	6.62760i	1.42988	+	0.252126i	0.595515	+	0.803344i	$0.296948\pi$
$692$	17.8271	+	30.8774i	0.677685	+	1.17378i
$693$		0			0
$694$	−18.4031	+	31.8751i	−0.698573	+	1.20996i
$695$	22.4344	−	26.7363i	0.850985	−	1.01416i
$696$		0			0
$697$	0.164834	+	0.934822i	0.00624355	+	0.0354089i
$698$	10.4046	−	8.73049i	0.393820	−	0.330454i
$699$		0			0
$700$	8.58037	+	7.41211i	0.324307	+	0.280151i
$701$			12.5706i			0.474787i	0.971414	+	0.237393i	$0.0762930\pi$
$701$			12.5706i			0.474787i	−0.971414	+	0.237393i	$0.923707\pi$
$702$		0			0
$703$		−	4.26021i		−	0.160677i
$704$	−8.44057	−	23.1903i	−0.318116	−	0.874016i
$705$		0			0
$706$	−2.28383	−	2.72177i	−0.0859532	−	0.102435i
$707$	1.55152	−	1.26440i	0.0583509	−	0.0475527i
$708$		0			0
$709$	14.2522	+	11.9590i	0.535254	+	0.449131i	0.869911	−	0.493209i	$-0.164176\pi$
$709$	14.2522	+	11.9590i	0.535254	+	0.449131i	−0.334657	+	0.942340i	$0.608620\pi$
$710$	10.2748	−	17.7965i	0.385606	−	0.667889i
$711$		0			0
$712$	−0.415321	+	0.239786i	−0.0155648	+	0.00898634i
$713$	1.83156	−	10.3873i	0.0685926	−	0.389008i
$714$		0			0
$715$	−12.9112	−	4.69928i	−0.482851	−	0.175743i
$716$	3.92459	−	10.7827i	0.146669	−	0.402969i
$717$		0			0
$718$	8.35709	−	47.3954i	0.311884	−	1.76878i
$719$	5.19387	+	8.99605i	0.193699	+	0.335496i	0.946473	−	0.322783i	$-0.104618\pi$
$719$	5.19387	+	8.99605i	0.193699	+	0.335496i	−0.752774	+	0.658278i	$0.771285\pi$
$720$		0			0
$721$	−0.680375	+	47.4248i	−0.0253385	+	1.76619i
$722$	−31.5190	+	37.5629i	−1.17302	+	1.39795i
$723$		0			0
$724$	48.3563	−	8.52652i	1.79715	−	0.316886i
$725$	13.3170	+	15.8705i	0.494579	+	0.589417i
$726$		0			0
$727$	1.63424	+	4.49002i	0.0606104	+	0.166526i	0.966302	−	0.257412i	$-0.0828697\pi$
$727$	1.63424	+	4.49002i	0.0606104	+	0.166526i	−0.905691	+	0.423938i	$0.860648\pi$
$728$	−0.210113	−	0.376291i	−0.00778730	−	0.0139463i
$729$		0			0
$730$	−22.2225			−0.822492
$731$	1.99979	−	0.727865i	0.0739650	−	0.0269211i
$732$		0			0
$733$	−26.9708	−	32.1426i	−0.996189	−	1.18721i	−0.982301	−	0.187309i	$-0.940023\pi$
$733$	−26.9708	−	32.1426i	−0.996189	−	1.18721i	−0.0138884	−	0.999904i	$-0.504421\pi$
$734$	4.45667	+	25.2750i	0.164499	+	0.932918i
$735$		0			0
$736$	43.8816	+	36.8210i	1.61750	+	1.35724i
$737$	24.5152	+	14.1539i	0.903030	+	0.521365i
$738$		0			0
$739$	8.69080	+	15.0529i	0.319696	+	0.553730i	0.980425	−	0.196895i	$-0.0630858\pi$
$739$	8.69080	+	15.0529i	0.319696	+	0.553730i	−0.660728	+	0.750625i	$0.729752\pi$
$740$	0.370385	−	2.10056i	0.0136156	−	0.0772180i
$741$		0			0
$742$	−1.04188	−	6.44842i	−0.0382487	−	0.236729i
$743$	−2.40577	+	6.60980i	−0.0882591	+	0.242490i	−0.975967	−	0.217916i	$-0.930074\pi$
$743$	−2.40577	+	6.60980i	−0.0882591	+	0.242490i	0.887708	+	0.460406i	$0.152296\pi$
$744$		0			0
$745$	2.22759	+	0.392784i	0.0816126	+	0.0143905i
$746$	−29.8257	+	17.2199i	−1.09200	+	0.630465i
$747$		0			0
$748$	10.1506	+	5.86046i	0.371143	+	0.214279i
$749$	15.1317	+	2.89253i	0.552901	+	0.105691i
$750$		0			0
$751$	−3.67514	−	20.8427i	−0.134108	−	0.760562i	−0.975477	−	0.220102i	$-0.929361\pi$
$751$	−3.67514	−	20.8427i	−0.134108	−	0.760562i	0.841369	−	0.540461i	$-0.181750\pi$
$752$	35.8818	−	30.1084i	1.30847	−	1.09794i
$753$		0			0
$754$	16.6334	+	45.7000i	0.605754	+	1.66430i
$755$	5.59716			0.203701
$756$		0			0
$757$	−13.1453			−0.477773			−0.238886	−	0.971048i	$-0.576782\pi$
$757$	−13.1453			−0.477773			−0.238886	+	0.971048i	$0.576782\pi$
$758$	15.3085	+	42.0596i	0.556028	+	1.52768i
$759$		0			0
$760$	0.539569	−	0.452752i	0.0195722	−	0.0164231i
$761$	−4.65271	−	26.3869i	−0.168661	−	0.956523i	−0.945209	−	0.326465i	$-0.894142\pi$
$761$	−4.65271	−	26.3869i	−0.168661	−	0.956523i	0.776548	−	0.630058i	$-0.216969\pi$
$762$		0			0
$763$	−4.69163	+	24.5434i	−0.169849	+	0.888529i
$764$	8.67410	+	5.00800i	0.313818	+	0.181183i
$765$		0			0
$766$	31.1581	−	17.9891i	1.12579	−	0.649973i
$767$	1.41725	+	0.249899i	0.0511738	+	0.00902332i
$768$		0			0
$769$	4.19859	−	11.5355i	0.151405	−	0.415982i	−0.840683	−	0.541528i	$-0.817846\pi$
$769$	4.19859	−	11.5355i	0.151405	−	0.415982i	0.992088	+	0.125546i	$0.0400683\pi$
$770$	−4.50130	−	27.8595i	−0.162216	−	1.00399i
$771$		0			0
$772$	0.877846	−	4.97851i	0.0315944	−	0.179181i
$773$	−5.69422	−	9.86268i	−0.204807	−	0.354736i	0.745264	−	0.666769i	$-0.232323\pi$
$773$	−5.69422	−	9.86268i	−0.204807	−	0.354736i	−0.950071	+	0.312033i	$0.898990\pi$
$774$		0			0
$775$	2.76599	+	1.59694i	0.0993572	+	0.0573639i
$776$	0.467112	+	0.391954i	0.0167683	+	0.0140703i
$777$		0			0
$778$	6.71418	+	38.0780i	0.240715	+	1.36516i
$779$	−2.15659	−	2.57012i	−0.0772678	−	0.0920841i
$780$		0			0
$781$	18.3901	−	6.69346i	0.658050	−	0.239511i
$782$	−26.7657			−0.957138
$783$		0			0
$784$	14.9202	−	24.2109i	0.532864	−	0.864675i
$785$	−10.0497	−	27.6113i	−0.358690	−	0.985491i
$786$		0			0
$787$	22.4585	+	26.7650i	0.800558	+	0.954068i	0.999664	−	0.0259096i	$-0.00824820\pi$
$787$	22.4585	+	26.7650i	0.800558	+	0.954068i	−0.199106	+	0.979978i	$0.563804\pi$
$788$	−4.81665	+	0.849306i	−0.171586	+	0.0302553i
$789$		0			0
$790$	1.86550	−	2.22322i	0.0663715	−	0.0790985i
$791$	0.764657	−	53.2996i	0.0271881	−	1.89511i
$792$		0			0
$793$	9.14752	+	15.8440i	0.324838	+	0.562636i
$794$	−4.61995	+	26.2010i	−0.163956	+	0.929840i
$795$		0			0
$796$	13.1730	−	36.1925i	0.466904	−	1.28281i
$797$	21.0051	+	7.64522i	0.744038	+	0.270808i	0.686095	−	0.727512i	$-0.259324\pi$
$797$	21.0051	+	7.64522i	0.744038	+	0.270808i	0.0579433	+	0.998320i	$0.481546\pi$
$798$		0			0
$799$	−3.74087	+	21.2155i	−0.132343	+	0.750552i
$800$	−15.0220	+	8.67293i	−0.531107	+	0.306634i
$801$		0			0
$802$	3.65495	−	6.33057i	0.129061	−	0.223540i
$803$	−16.2122	−	13.6037i	−0.572118	−	0.480064i
$804$		0			0
$805$	20.1923	+	24.7776i	0.711687	+	0.873296i
$806$	4.81926	+	5.74337i	0.169751	+	0.202302i
$807$		0			0
$808$	0.0164251	+	0.0451275i	0.000577831	+	0.00158758i
$809$		−	7.66333i		−	0.269428i	−0.990884	−	0.134714i	$-0.956988\pi$
$809$		−	7.66333i		−	0.269428i	0.990884	−	0.134714i	$-0.0430116\pi$
$810$		0			0
$811$			4.98733i			0.175129i	0.996159	+	0.0875644i	$0.0279084\pi$
$811$			4.98733i			0.175129i	−0.996159	+	0.0875644i	$0.972092\pi$
$812$	−32.3871	+	37.4918i	−1.13657	+	1.31571i
$813$		0			0
$814$	3.13736	−	2.63256i	0.109964	−	0.0922712i
$815$	5.88808	+	33.3930i	0.206251	+	1.16970i
$816$		0			0
$817$	−4.83491	+	5.76202i	−0.169152	+	0.201588i
$818$	1.65544	−	2.86731i	0.0578812	−	0.100253i
$819$		0			0
$820$	−0.839888	−	1.45473i	−0.0293301	−	0.0508013i
$821$	7.38627	+	1.30240i	0.257782	+	0.0454540i	0.301046	−	0.953610i	$-0.402664\pi$
$821$	7.38627	+	1.30240i	0.257782	+	0.0454540i	−0.0432633	+	0.999064i	$0.513775\pi$
$822$		0			0
$823$	−11.9501	−	4.34947i	−0.416553	−	0.151613i	0.125237	−	0.992127i	$-0.460031\pi$
$823$	−11.9501	−	4.34947i	−0.416553	−	0.151613i	−0.541790	+	0.840514i	$0.682253\pi$
$824$	−1.06940	−	0.389229i	−0.0372543	−	0.0135595i
$825$		0			0
$826$	0.971013	+	2.79181i	0.0337859	+	0.0971395i
$827$	−10.6649	+	6.15737i	−0.370854	+	0.214113i	−0.673832	−	0.738885i	$-0.735353\pi$
$827$	−10.6649	+	6.15737i	−0.370854	+	0.214113i	0.302977	+	0.952998i	$0.402019\pi$
$828$		0			0
$829$	10.1850	+	5.88032i	0.353740	+	0.204232i	0.666331	−	0.745656i	$-0.267864\pi$
$829$	10.1850	+	5.88032i	0.353740	+	0.204232i	−0.312591	+	0.949888i	$0.601197\pi$
$830$	−17.5657	+	20.9339i	−0.609713	+	0.726628i
$831$		0			0
$832$	−19.5667	+	3.45013i	−0.678352	+	0.119612i
$833$	1.90081	+	12.9408i	0.0658593	+	0.448373i
$834$		0			0
$835$	1.99042	−	0.724455i	0.0688814	−	0.0250708i
$836$	−41.4270			−1.43278
$837$		0			0
$838$		−	1.87266i		−	0.0646899i
$839$	37.4037	−	13.6138i	1.29132	−	0.470002i	0.397160	−	0.917749i	$-0.369996\pi$
$839$	37.4037	−	13.6138i	1.29132	−	0.470002i	0.894160	+	0.447747i	$0.147774\pi$
$840$		0			0
$841$	−47.1308	+	39.5475i	−1.62520	+	1.36371i
$842$	70.7002	−	12.4664i	2.43649	−	0.429619i
$843$		0			0
$844$	42.8194	+	35.9297i	1.47390	+	1.23675i
$845$	5.38935	−	9.33462i	0.185399	−	0.321121i
$846$		0			0
$847$	−1.14119	+	1.91270i	−0.0392117	+	0.0657211i
$848$	4.95879	+	0.874368i	0.170286	+	0.0300259i
$849$		0			0
$850$	2.77203	−	7.61608i	0.0950797	−	0.261229i
$851$	−1.58653	+	4.35894i	−0.0543854	+	0.149423i
$852$		0			0
$853$	20.0361	+	3.53291i	0.686023	+	0.120964i	0.505786	−	0.862659i	$-0.331202\pi$
$853$	20.0361	+	3.53291i	0.686023	+	0.120964i	0.180237	+	0.983623i	$0.442314\pi$
$854$	−19.2534	+	32.2698i	−0.658837	+	1.10425i
$855$		0			0
$856$	−0.184823	+	0.320122i	−0.00631711	+	0.0109416i
$857$	3.25940	+	2.73496i	0.111339	+	0.0934245i	0.696758	−	0.717307i	$-0.254625\pi$
$857$	3.25940	+	2.73496i	0.111339	+	0.0934245i	−0.585419	+	0.810731i	$0.699070\pi$
$858$		0			0
$859$	−16.4971	+	2.90888i	−0.562872	+	0.0992495i	−0.447842	−	0.894113i	$-0.647807\pi$
$859$	−16.4971	+	2.90888i	−0.562872	+	0.0992495i	−0.115030	+	0.993362i	$0.536696\pi$
$860$	−2.88487	+	2.42070i	−0.0983734	+	0.0825450i
$861$		0			0
$862$	−46.8126	+	17.0384i	−1.59444	+	0.580329i
$863$		−	21.7088i		−	0.738977i	−0.929235	−	0.369488i	$-0.879533\pi$
$863$		−	21.7088i		−	0.738977i	0.929235	−	0.369488i	$-0.120467\pi$
$864$		0			0
$865$	−30.4352			−1.03483
$866$	53.3897	−	19.4323i	1.81426	−	0.660335i
$867$		0			0
$868$	−2.71498	+	7.13900i	−0.0921523	+	0.242313i
$869$	2.72192	−	0.479948i	0.0923347	−	0.0162811i
$870$		0			0
$871$	14.6494	−	17.4584i	0.496374	−	0.591556i
$872$	−0.519232	−	0.299779i	−0.0175834	−	0.0101518i
$873$		0			0
$874$	81.9277	−	47.3010i	2.77125	−	1.59998i
$875$	−30.1330	+	10.4805i	−1.01868	+	0.354305i
$876$		0			0
$877$	35.8799	+	13.0592i	1.21158	+	0.440978i	0.867251	−	0.497872i	$-0.165885\pi$
$877$	35.8799	+	13.0592i	1.21158	+	0.440978i	0.344327	+	0.938850i	$0.388107\pi$
$878$	54.7396	+	19.9236i	1.84737	+	0.672389i
$879$		0			0
$880$	21.4237	+	3.77758i	0.722194	+	0.127342i
$881$	19.9609	+	34.5734i	0.672501	+	1.16481i	0.977193	+	0.212355i	$0.0681132\pi$
$881$	19.9609	+	34.5734i	0.672501	+	1.16481i	−0.304692	+	0.952451i	$0.598553\pi$
$882$		0			0
$883$	−15.2724	+	26.4525i	−0.513957	+	0.890199i	0.485912	+	0.874008i	$0.338487\pi$
$883$	−15.2724	+	26.4525i	−0.513957	+	0.890199i	−0.999869	+	0.0161915i	$0.994846\pi$
$884$	6.06561	−	7.22871i	0.204008	−	0.243128i
$885$		0			0
$886$	0.794032	+	4.50318i	0.0266760	+	0.151287i
$887$	−3.33017	+	2.79434i	−0.111816	+	0.0938248i	−0.696981	−	0.717089i	$-0.745474\pi$
$887$	−3.33017	+	2.79434i	−0.111816	+	0.0938248i	0.585165	+	0.810914i	$0.301030\pi$
$888$		0			0
$889$	27.1925	+	23.4901i	0.912006	+	0.787832i
$890$			25.2820i			0.847456i
$891$		0			0
$892$		−	27.2894i		−	0.913717i
$893$	−26.0421	−	71.5501i	−0.871466	−	2.39433i
$894$		0			0
$895$	6.29615	+	7.50346i	0.210457	+	0.250813i
$896$	0.848731	+	1.04146i	0.0283541	+	0.0347928i
$897$		0			0
$898$	33.1047	+	27.7781i	1.10472	+	0.926968i
$899$	−6.97783	+	12.0860i	−0.232724	+	0.403089i
$900$		0			0
$901$	−2.00557	+	1.15791i	−0.0668151	+	0.0385757i
$902$	0.560079	−	3.17636i	0.0186486	−	0.105761i
$903$		0			0
$904$	1.20187	+	0.437446i	0.0399737	+	0.0145492i
$905$	−14.3357	+	39.3869i	−0.476534	+	1.30927i
$906$		0			0
$907$	−1.87379	+	10.6268i	−0.0622180	+	0.352856i	0.937766	+	0.347267i	$0.112890\pi$
$907$	−1.87379	+	10.6268i	−0.0622180	+	0.352856i	−0.999984	+	0.00558913i	$0.998221\pi$
$908$	−17.9440	−	31.0799i	−0.595493	−	1.03142i
$909$		0			0
$910$	−22.7180	−	0.325921i	−0.753093	−	0.0108042i
$911$	17.8805	−	21.3091i	0.592407	−	0.706003i	−0.383660	−	0.923474i	$-0.625337\pi$
$911$	17.8805	−	21.3091i	0.592407	−	0.706003i	0.976067	+	0.217472i	$0.0697810\pi$
$912$		0			0
$913$	−25.6297	+	4.51922i	−0.848221	+	0.149564i
$914$	0.153201	+	0.182578i	0.00506745	+	0.00603916i
$915$		0			0
$916$	−5.51325	−	15.1475i	−0.182163	−	0.500489i
$917$	4.64265	+	8.31452i	0.153314	+	0.274570i
$918$		0			0
$919$	−41.7928			−1.37862			−0.689308	−	0.724468i	$-0.742085\pi$
$919$	−41.7928			−1.37862			−0.689308	+	0.724468i	$0.742085\pi$
$920$	−0.720681	+	0.262307i	−0.0237602	+	0.00864799i
$921$		0			0
$922$	43.8315	+	52.2364i	1.44351	+	1.72031i
$923$	−2.73599	−	15.5166i	−0.0900562	−	0.510734i
$924$		0			0
$925$	−1.07601	−	0.902881i	−0.0353791	−	0.0296866i
$926$	25.1165	+	14.5010i	0.825378	+	0.476532i
$927$		0			0
$928$	−37.8963	−	65.6383i	−1.24401	−	2.15468i
$929$	−5.51917	+	31.3007i	−0.181078	+	1.02694i	0.749814	+	0.661649i	$0.230143\pi$
$929$	−5.51917	+	31.3007i	−0.181078	+	1.02694i	−0.930892	+	0.365295i	$0.880968\pi$
$930$		0			0
$931$	−28.6876	−	36.2518i	−0.940199	−	1.18810i
$932$	6.10897	−	16.7842i	0.200106	−	0.549786i
$933$		0			0
$934$	35.6484	+	6.28577i	1.16645	+	0.205677i
$935$	−8.66476	+	5.00260i	−0.283368	+	0.163603i
$936$		0			0
$937$	−12.7723	−	7.37411i	−0.417254	−	0.240902i	0.276648	−	0.960971i	$-0.410777\pi$
$937$	−12.7723	−	7.37411i	−0.417254	−	0.240902i	−0.693902	+	0.720070i	$0.744110\pi$
$938$	45.9776	+	8.78894i	1.50122	+	0.286969i
$939$		0			0
$940$	−6.61983	−	37.5429i	−0.215915	−	1.22451i
$941$	−22.9309	+	19.2413i	−0.747524	+	0.627248i	−0.934847	−	0.355051i	$-0.884464\pi$
$941$	−22.9309	+	19.2413i	−0.747524	+	0.627248i	0.187322	+	0.982298i	$0.440019\pi$
$942$		0			0
$943$	1.24944	+	3.43281i	0.0406874	+	0.111788i
$944$	−2.27855			−0.0741603
$945$		0			0
$946$	−7.23104			−0.235101
$947$	15.8287	+	43.4890i	0.514364	+	1.41320i	0.876647	+	0.481135i	$0.159775\pi$
$947$	15.8287	+	43.4890i	0.514364	+	1.41320i	−0.362283	+	0.932068i	$0.618003\pi$
$948$		0			0
$949$	−13.0523	+	10.9522i	−0.423697	+	0.355524i
$950$	4.97437	+	28.2110i	0.161390	+	0.915287i
$951$		0			0
$952$	−0.308254	−	0.0589248i	−0.00999056	−	0.00190976i
$953$	23.3288	+	13.4689i	0.755694	+	0.436300i	0.827747	−	0.561101i	$-0.189622\pi$
$953$	23.3288	+	13.4689i	0.755694	+	0.436300i	−0.0720539	+	0.997401i	$0.522955\pi$
$954$		0			0
$955$	−7.40439	+	4.27493i	−0.239600	+	0.138333i
$956$	36.6100	+	6.45533i	1.18405	+	0.208780i
$957$		0			0
$958$	−5.62727	+	15.4608i	−0.181809	+	0.499516i
$959$	−5.67607	+	0.917093i	−0.183290	+	0.0296145i
$960$		0			0
$961$	5.00950	−	28.4103i	0.161597	−	0.916460i
$962$	−1.64864	−	2.85553i	−0.0531543	−	0.0920660i
$963$		0			0
$964$	−18.4565	−	10.6558i	−0.594442	−	0.343201i
$965$	3.30573	+	2.77383i	0.106415	+	0.0892929i
$966$		0			0
$967$	−1.68216	−	9.53998i	−0.0540945	−	0.306785i	0.945741	−	0.324921i	$-0.105338\pi$
$967$	−1.68216	−	9.53998i	−0.0540945	−	0.306785i	−0.999836	+	0.0181363i	$0.994227\pi$
$968$	−0.0343514	−	0.0409384i	−0.00110409	−	0.00131581i
$969$		0			0
$970$	30.2073	−	10.9946i	0.969898	−	0.353014i
$971$	−17.2534			−0.553688			−0.276844	−	0.960915i	$-0.589289\pi$
$971$	−17.2534			−0.553688			−0.276844	+	0.960915i	$0.589289\pi$
$972$		0			0
$973$	47.9894	−	26.7963i	1.53847	−	0.859049i
$974$	7.92290	+	21.7680i	0.253866	+	0.697492i
$975$		0			0
$976$	−18.6193	−	22.1897i	−0.595991	−	0.710274i
$977$	−32.3224	+	5.69932i	−1.03409	+	0.182337i	−0.664833	−	0.746992i	$-0.731497\pi$
$977$	−32.3224	+	5.69932i	−1.03409	+	0.182337i	−0.369253	+	0.929329i	$0.620386\pi$
$978$		0			0
$979$	−15.4766	+	18.4443i	−0.494634	+	0.589482i
$980$	−10.9931	−	20.3685i	−0.351161	−	0.650649i
$981$		0			0
$982$	24.1930	+	41.9035i	0.772030	+	1.33719i
$983$	6.82161	−	38.6873i	0.217576	−	1.23393i	−0.658805	−	0.752314i	$-0.728938\pi$
$983$	6.82161	−	38.6873i	0.217576	−	1.23393i	0.876381	−	0.481619i	$-0.159951\pi$
$984$		0			0
$985$	1.42794	−	3.92324i	0.0454980	−	0.125005i
$986$	33.2784	+	12.1123i	1.05980	+	0.385736i
$987$		0			0
$988$	−5.79161	+	32.8458i	−0.184256	+	1.04497i
$989$	7.09277	−	4.09501i	0.225537	−	0.130214i
$990$		0			0
$991$	11.3750	−	19.7020i	0.361338	−	0.625856i	−0.626843	−	0.779145i	$-0.715653\pi$
$991$	11.3750	−	19.7020i	0.361338	−	0.625856i	0.988181	+	0.153289i	$0.0489867\pi$
$992$	−8.95083	−	7.51064i	−0.284189	−	0.238463i
$993$		0			0
$994$	25.0865	−	20.4440i	0.795694	−	0.648445i
$995$	21.1332	+	25.1856i	0.669967	+	0.798436i
$996$		0			0
$997$	−6.82407	−	18.7490i	−0.216120	−	0.593786i	0.783498	−	0.621394i	$-0.213433\pi$
$997$	−6.82407	−	18.7490i	−0.216120	−	0.593786i	−0.999619	+	0.0276077i	$0.991211\pi$
$998$		−	33.0534i		−	1.04629i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.62.17		132
3.2	odd	2		189.2.be.a.20.6	yes	132
7.6	odd	2	inner	567.2.be.a.62.18		132
21.20	even	2		189.2.be.a.20.5	✓	132
27.4	even	9		189.2.be.a.104.5	yes	132
27.23	odd	18	inner	567.2.be.a.503.18		132
189.104	even	18	inner	567.2.be.a.503.17		132
189.139	odd	18		189.2.be.a.104.6	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.5	✓	132	21.20	even	2
189.2.be.a.20.6	yes	132	3.2	odd	2
189.2.be.a.104.5	yes	132	27.4	even	9
189.2.be.a.104.6	yes	132	189.139	odd	18
567.2.be.a.62.17		132	1.1	even	1	trivial
567.2.be.a.62.18		132	7.6	odd	2	inner
567.2.be.a.503.17		132	189.104	even	18	inner
567.2.be.a.503.18		132	27.23	odd	18	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.be (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.681310 + 1.87188i) q^{2} +(-1.50768 + 1.26509i) q^{4} +(-0.291735 - 1.65451i) q^{5} +(0.496759 - 2.59870i) q^{7} +(0.0549773 + 0.0317412i) q^{8} +(2.89829 - 1.67333i) q^{10} +(3.13877 + 0.553450i) q^{11} +(0.877617 - 2.41123i) q^{13} +(5.20291 - 0.840643i) q^{14} +(-0.705484 + 4.00100i) q^{16} +(-0.934264 - 1.61819i) q^{17} +(5.71942 + 3.30211i) q^{19} +(2.53295 + 2.12540i) q^{20} +(1.10248 + 6.25248i) q^{22} +(-4.62225 - 5.50858i) q^{23} +(2.04616 - 0.744740i) q^{25} +5.11148 q^{26} +(2.53864 + 4.54644i) q^{28} +(3.25414 + 8.94067i) q^{29} +(0.942831 + 1.12362i) q^{31} +(-7.84502 + 1.38329i) q^{32} +(2.39254 - 2.85132i) q^{34} +(-4.44450 - 0.0637627i) q^{35} +(-0.322537 - 0.558651i) q^{37} +(-2.28447 + 12.9559i) q^{38} +(0.0364774 - 0.100221i) q^{40} +(-0.477380 - 0.173752i) q^{41} +(-0.197774 + 1.12163i) q^{43} +(-5.43241 + 3.13640i) q^{44} +(7.16224 - 12.4054i) q^{46} +(-8.83196 - 7.41090i) q^{47} +(-6.50646 - 2.58185i) q^{49} +(2.78813 + 3.32277i) q^{50} +(1.72727 + 4.74562i) q^{52} -1.23939i q^{53} -5.35460i q^{55} +(0.109796 - 0.127102i) q^{56} +(-14.5188 + 12.1827i) q^{58} +(0.0973892 + 0.552322i) q^{59} +(-4.58297 + 5.46178i) q^{61} +(-1.46093 + 2.53041i) q^{62} +(-3.87153 - 6.70568i) q^{64} +(-4.24545 - 0.748587i) q^{65} +(8.34610 + 3.03773i) q^{67} +(3.45573 + 1.25778i) q^{68} +(-2.90873 - 8.36303i) q^{70} +(5.31767 - 3.07016i) q^{71} +(-5.75058 - 3.32010i) q^{73} +(0.825982 - 0.984367i) q^{74} +(-12.8005 + 2.25707i) q^{76} +(2.99746 - 7.88178i) q^{77} +(0.814895 - 0.296597i) q^{79} +6.82552 q^{80} -1.01198i q^{82} +(-7.67310 + 2.79278i) q^{83} +(-2.40476 + 2.01784i) q^{85} +(-2.23431 + 0.393970i) q^{86} +(0.154994 + 0.130055i) q^{88} +(-3.77720 + 6.54230i) q^{89} +(-5.83010 - 3.47846i) q^{91} +(13.9377 + 2.45759i) q^{92} +(7.85503 - 21.5815i) q^{94} +(3.79483 - 10.4262i) q^{95} +(9.45944 + 1.66796i) q^{97} +(0.400014 - 13.9384i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Introduction

L-functions

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