LMFDB - Embedded newform 207.2.i.d.64.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(55,207)] 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("207.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			64.1
Root			$-1.30051 - 1.50087i$ of defining polynomial
Character	$\chi$	$=$	207.64
Dual form			207.2.i.d.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.54781 - 0.454477i) q^{2} +(0.506650 + 0.325604i) q^{4} +(-0.0749695 + 0.521424i) q^{5} +(0.200934 + 0.439985i) q^{7} +(1.47656 + 1.70404i) q^{8} +(0.353014 - 0.772992i) q^{10} +(3.21327 - 0.943501i) q^{11} +(0.853105 - 1.86804i) q^{13} +(-0.111045 - 0.772332i) q^{14} +(-2.01136 - 4.40426i) q^{16} +(0.919522 - 0.590941i) q^{17} +(6.19469 + 3.98109i) q^{19} +(-0.207761 + 0.239769i) q^{20} -5.40232 q^{22} +(1.81662 - 4.43846i) q^{23} +(4.53120 + 1.33048i) q^{25} +(-2.16942 + 2.50365i) q^{26} +(-0.0414575 + 0.288343i) q^{28} +(3.03219 - 1.94867i) q^{29} +(-3.65525 - 4.21838i) q^{31} +(0.469783 + 3.26741i) q^{32} +(-1.69181 + 0.496761i) q^{34} +(-0.244483 + 0.0717866i) q^{35} +(0.491920 + 3.42138i) q^{37} +(-7.77887 - 8.97730i) q^{38} +(-0.999226 + 0.642164i) q^{40} +(-1.47926 + 10.2885i) q^{41} +(-5.05496 + 5.83373i) q^{43} +(1.93521 + 0.568229i) q^{44} +(-4.82895 + 6.04426i) q^{46} -10.7974 q^{47} +(4.43081 - 5.11343i) q^{49} +(-6.40875 - 4.11866i) q^{50} +(1.04047 - 0.668668i) q^{52} +(3.06811 + 6.71822i) q^{53} +(0.251067 + 1.74621i) q^{55} +(-0.453061 + 0.992066i) q^{56} +(-5.57887 + 1.63811i) q^{58} +(0.390317 - 0.854675i) q^{59} +(-3.75616 - 4.33483i) q^{61} +(3.74046 + 8.19046i) q^{62} +(-0.620289 + 4.31421i) q^{64} +(0.910084 + 0.584876i) q^{65} +(-12.3567 - 3.62825i) q^{67} +0.658289 q^{68} +0.411037 q^{70} +(5.99541 + 1.76041i) q^{71} +(-0.00713288 - 0.00458402i) q^{73} +(0.793542 - 5.51920i) q^{74} +(1.84228 + 4.03404i) q^{76} +(1.06078 + 1.22421i) q^{77} +(4.29440 - 9.40343i) q^{79} +(2.44728 - 0.718585i) q^{80} +(6.96548 - 15.2523i) q^{82} +(-0.861534 - 5.99210i) q^{83} +(0.239195 + 0.523763i) q^{85} +(10.4754 - 6.73213i) q^{86} +(6.35236 + 4.08241i) q^{88} +(1.84618 - 2.13061i) q^{89} +0.993327 q^{91} +(2.36557 - 1.65724i) q^{92} +(16.7123 + 4.90718i) q^{94} +(-2.54025 + 2.93160i) q^{95} +(-2.61142 + 18.1628i) q^{97} +(-9.18198 + 5.90090i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29}+ \cdots - 85 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.54781	−	0.454477i	−1.09446	−	0.321364i	−0.315814	−	0.948821i	$-0.602278\pi$
$2$	−1.54781	−	0.454477i	−1.09446	−	0.321364i	−0.778651	+	0.627457i	$0.784096\pi$
$3$		0			0
$3$		0			0
$4$	0.506650	+	0.325604i	0.253325	+	0.162802i
$5$	−0.0749695	+	0.521424i	−0.0335274	+	0.233188i	−0.999694	−	0.0247301i	$-0.992127\pi$
$5$	−0.0749695	+	0.521424i	−0.0335274	+	0.233188i	0.966167	+	0.257918i	$0.0830364\pi$
$6$		0			0
$7$	0.200934	+	0.439985i	0.0759460	+	0.166299i	0.943797	−	0.330526i	$-0.107226\pi$
$7$	0.200934	+	0.439985i	0.0759460	+	0.166299i	−0.867851	+	0.496825i	$0.834499\pi$
$8$	1.47656	+	1.70404i	0.522043	+	0.602470i
$9$		0			0
$10$	0.353014	−	0.772992i	0.111633	−	0.244441i
$11$	3.21327	−	0.943501i	0.968837	−	0.284476i	0.241228	−	0.970468i	$-0.422450\pi$
$11$	3.21327	−	0.943501i	0.968837	−	0.284476i	0.727609	+	0.685992i	$0.240632\pi$
$12$		0			0
$13$	0.853105	−	1.86804i	0.236609	−	0.518101i	−0.753661	−	0.657264i	$-0.771714\pi$
$13$	0.853105	−	1.86804i	0.236609	−	0.518101i	0.990270	+	0.139163i	$0.0444411\pi$
$14$	−0.111045	−	0.772332i	−0.0296779	−	0.206414i
$15$		0			0
$16$	−2.01136	−	4.40426i	−0.502839	−	1.10106i
$17$	0.919522	−	0.590941i	0.223017	−	0.143324i	−0.424362	−	0.905493i	$-0.639502\pi$
$17$	0.919522	−	0.590941i	0.223017	−	0.143324i	0.647379	+	0.762168i	$0.275865\pi$
$18$		0			0
$19$	6.19469	+	3.98109i	1.42116	+	0.913324i	0.999980	+	0.00634685i	$0.00202028\pi$
$19$	6.19469	+	3.98109i	1.42116	+	0.913324i	0.421180	+	0.906977i	$0.361616\pi$
$20$	−0.207761	+	0.239769i	−0.0464568	+	0.0536140i
$21$		0			0
$22$	−5.40232			−1.15178
$23$	1.81662	−	4.43846i	0.378791	−	0.925482i
$23$	1.81662	−	4.43846i	0.378791	−	0.925482i
$24$		0			0
$25$	4.53120	+	1.33048i	0.906240	+	0.266096i
$26$	−2.16942	+	2.50365i	−0.425459	+	0.491006i
$27$		0			0
$28$	−0.0414575	+	0.288343i	−0.00783474	+	0.0544918i
$29$	3.03219	−	1.94867i	0.563064	−	0.361859i	−0.227935	−	0.973676i	$-0.573198\pi$
$29$	3.03219	−	1.94867i	0.563064	−	0.361859i	0.790999	+	0.611817i	$0.209561\pi$
$30$		0			0
$31$	−3.65525	−	4.21838i	−0.656502	−	0.757643i	0.325700	−	0.945473i	$-0.394400\pi$
$31$	−3.65525	−	4.21838i	−0.656502	−	0.757643i	−0.982202	+	0.187830i	$0.939855\pi$
$32$	0.469783	+	3.26741i	0.0830466	+	0.577602i
$33$		0			0
$34$	−1.69181	+	0.496761i	−0.290143	+	0.0851938i
$35$	−0.244483	+	0.0717866i	−0.0413251	+	0.0121341i
$36$		0			0
$37$	0.491920	+	3.42138i	0.0808712	+	0.562471i	0.989463	+	0.144786i	$0.0462494\pi$
$37$	0.491920	+	3.42138i	0.0808712	+	0.562471i	−0.908592	+	0.417685i	$0.862841\pi$
$38$	−7.77887	−	8.97730i	−1.26190	−	1.45631i
$39$		0			0
$40$	−0.999226	+	0.642164i	−0.157991	+	0.101535i
$41$	−1.47926	+	10.2885i	−0.231021	+	1.60679i	0.462680	+	0.886525i	$0.346888\pi$
$41$	−1.47926	+	10.2885i	−0.231021	+	1.60679i	−0.693701	+	0.720263i	$0.744021\pi$
$42$		0			0
$43$	−5.05496	+	5.83373i	−0.770874	+	0.889636i	−0.996415	−	0.0845976i	$-0.973040\pi$
$43$	−5.05496	+	5.83373i	−0.770874	+	0.889636i	0.225541	+	0.974234i	$0.427585\pi$
$44$	1.93521	+	0.568229i	0.291744	+	0.0856638i
$45$		0			0
$46$	−4.82895	+	6.04426i	−0.711990	+	0.891178i
$47$	−10.7974			−1.57497			−0.787483	−	0.616336i	$-0.788616\pi$
$47$	−10.7974			−1.57497			−0.787483	+	0.616336i	$0.788616\pi$
$48$		0			0
$49$	4.43081	−	5.11343i	0.632973	−	0.730490i
$50$	−6.40875	−	4.11866i	−0.906335	−	0.582466i
$51$		0			0
$52$	1.04047	−	0.668668i	0.144287	−	0.0927276i
$53$	3.06811	+	6.71822i	0.421437	+	0.922819i	0.994639	+	0.103405i	$0.0329737\pi$
$53$	3.06811	+	6.71822i	0.421437	+	0.922819i	−0.573202	+	0.819414i	$0.694299\pi$
$54$		0			0
$55$	0.251067	+	1.74621i	0.0338539	+	0.235459i
$56$	−0.453061	+	0.992066i	−0.0605428	+	0.132570i
$57$		0			0
$58$	−5.57887	+	1.63811i	−0.732542	+	0.215094i
$59$	0.390317	−	0.854675i	0.0508149	−	0.111269i	−0.882522	−	0.470272i	$-0.844156\pi$
$59$	0.390317	−	0.854675i	0.0508149	−	0.111269i	0.933337	+	0.359003i	$0.116883\pi$
$60$		0			0
$61$	−3.75616	−	4.33483i	−0.480926	−	0.555019i	0.462492	−	0.886623i	$-0.346955\pi$
$61$	−3.75616	−	4.33483i	−0.480926	−	0.555019i	−0.943418	+	0.331605i	$0.892410\pi$
$62$	3.74046	+	8.19046i	0.475039	+	1.04019i
$63$		0			0
$64$	−0.620289	+	4.31421i	−0.0775362	+	0.539276i
$65$	0.910084	+	0.584876i	0.112882	+	0.0725449i
$66$		0			0
$67$	−12.3567	−	3.62825i	−1.50961	−	0.443262i	−0.580872	−	0.813995i	$-0.697288\pi$
$67$	−12.3567	−	3.62825i	−1.50961	−	0.443262i	−0.928739	+	0.370733i	$0.879106\pi$
$68$	0.658289			0.0798292
$69$		0			0
$70$	0.411037			0.0491284
$71$	5.99541	+	1.76041i	0.711525	+	0.208923i	0.617413	−	0.786639i	$-0.288181\pi$
$71$	5.99541	+	1.76041i	0.711525	+	0.208923i	0.0941117	+	0.995562i	$0.469999\pi$
$72$		0			0
$73$	−0.00713288	−	0.00458402i	−0.000834840	−	0.000536519i	0.540223	−	0.841522i	$-0.318340\pi$
$73$	−0.00713288	−	0.00458402i	−0.000834840	−	0.000536519i	−0.541058	+	0.840985i	$0.681976\pi$
$74$	0.793542	−	5.51920i	0.0922473	−	0.641594i
$75$		0			0
$76$	1.84228	+	4.03404i	0.211324	+	0.462736i
$77$	1.06078	+	1.22421i	0.120887	+	0.139512i
$78$		0			0
$79$	4.29440	−	9.40343i	0.483158	−	1.05797i	−0.498425	−	0.866933i	$-0.666088\pi$
$79$	4.29440	−	9.40343i	0.483158	−	1.05797i	0.981583	−	0.191036i	$-0.0611846\pi$
$80$	2.44728	−	0.718585i	0.273614	−	0.0803402i
$81$		0			0
$82$	6.96548	−	15.2523i	0.769208	−	1.68433i
$83$	−0.861534	−	5.99210i	−0.0945656	−	0.657719i	−0.980877	−	0.194629i	$-0.937650\pi$
$83$	−0.861534	−	5.99210i	−0.0945656	−	0.657719i	0.886311	−	0.463090i	$-0.153259\pi$
$84$		0			0
$85$	0.239195	+	0.523763i	0.0259443	+	0.0568101i
$86$	10.4754	−	6.73213i	1.12959	−	0.725944i
$87$		0			0
$88$	6.35236	+	4.08241i	0.677164	+	0.435187i
$89$	1.84618	−	2.13061i	0.195695	−	0.225844i	−0.649418	−	0.760431i	$-0.724988\pi$
$89$	1.84618	−	2.13061i	0.195695	−	0.225844i	0.845113	+	0.534588i	$0.179533\pi$
$90$		0			0
$91$	0.993327			0.104129
$92$	2.36557	−	1.65724i	0.246628	−	0.172780i
$93$		0			0
$94$	16.7123	+	4.90718i	1.72375	+	0.506137i
$95$	−2.54025	+	2.93160i	−0.260624	+	0.300776i
$96$		0			0
$97$	−2.61142	+	18.1628i	−0.265150	+	1.84416i	0.227311	+	0.973822i	$0.427007\pi$
$97$	−2.61142	+	18.1628i	−0.265150	+	1.84416i	−0.492461	+	0.870335i	$0.663903\pi$
$98$	−9.18198	+	5.90090i	−0.927520	+	0.596081i
$99$		0			0
$100$	1.86252	+	2.14947i	0.186252	+	0.214947i
$101$	−0.923803	−	6.42519i	−0.0919219	−	0.639331i	−0.982743	−	0.184976i	$-0.940779\pi$
$101$	−0.923803	−	6.42519i	−0.0919219	−	0.639331i	0.890821	−	0.454354i	$-0.150130\pi$
$102$		0			0
$103$	13.1354	−	3.85690i	1.29427	−	0.380032i	0.439127	−	0.898425i	$-0.355288\pi$
$103$	13.1354	−	3.85690i	1.29427	−	0.380032i	0.855142	+	0.518394i	$0.173470\pi$
$104$	4.44288	−	1.30455i	0.435660	−	0.127921i
$105$		0			0
$106$	−1.69556	−	11.7929i	−0.164688	−	1.14543i
$107$	−7.86436	−	9.07596i	−0.760277	−	0.877406i	0.235245	−	0.971936i	$-0.424411\pi$
$107$	−7.86436	−	9.07596i	−0.760277	−	0.877406i	−0.995522	+	0.0945299i	$0.969865\pi$
$108$		0			0
$109$	10.5081	−	6.75317i	1.00650	−	0.646837i	0.0700133	−	0.997546i	$-0.477696\pi$
$109$	10.5081	−	6.75317i	1.00650	−	0.646837i	0.936484	+	0.350709i	$0.114059\pi$
$110$	0.405009	−	2.81690i	0.0386161	−	0.268581i
$111$		0			0
$112$	1.53366	−	1.76993i	0.144917	−	0.167243i
$113$	2.99845	+	0.880423i	0.282070	+	0.0828233i	0.419707	−	0.907659i	$-0.362133\pi$
$113$	2.99845	+	0.880423i	0.282070	+	0.0828233i	−0.137637	+	0.990483i	$0.543951\pi$
$114$		0			0
$115$	2.17813	+	1.27998i	0.203111	+	0.119359i
$116$	2.17076			0.201550
$117$		0			0
$118$	−0.992565	+	1.14548i	−0.0913731	+	0.105450i
$119$	0.444769	+	0.285835i	0.0407719	+	0.0262025i
$120$		0			0
$121$	0.181123	−	0.116401i	0.0164657	−	0.0105819i
$122$	3.84372	+	8.41657i	0.347994	+	0.762001i
$123$		0			0
$124$	−0.478409	−	3.32741i	−0.0429624	−	0.298810i
$125$	−2.12762	+	4.65884i	−0.190300	+	0.416699i
$126$		0			0
$127$	−10.4847	+	3.07860i	−0.930370	+	0.273181i	−0.711592	−	0.702593i	$-0.752025\pi$
$127$	−10.4847	+	3.07860i	−0.930370	+	0.273181i	−0.218779	+	0.975775i	$0.570207\pi$
$128$	5.66338	−	12.4011i	0.500576	−	1.09611i
$129$		0			0
$130$	−1.14282	−	1.31889i	−0.100232	−	0.115674i
$131$	0.244434	+	0.535236i	0.0213563	+	0.0467638i	0.920010	−	0.391896i	$-0.128181\pi$
$131$	0.244434	+	0.535236i	0.0213563	+	0.0467638i	−0.898653	+	0.438660i	$0.855453\pi$
$132$		0			0
$133$	−0.506892	+	3.52551i	−0.0439531	+	0.305700i
$134$	17.4768	+	11.2317i	1.50977	+	0.970269i
$135$		0			0
$136$	2.36472	+	0.694344i	0.202773	+	0.0595395i
$137$	−17.9223			−1.53121			−0.765603	−	0.643314i	$-0.777559\pi$
$137$	−17.9223			−1.53121			−0.765603	+	0.643314i	$0.777559\pi$
$138$		0			0
$139$	−13.3492			−1.13227			−0.566133	−	0.824314i	$-0.691561\pi$
$139$	−13.3492			−1.13227			−0.566133	+	0.824314i	$0.691561\pi$
$140$	−0.147241	−	0.0432339i	−0.0124441	−	0.00365393i
$141$		0			0
$142$	−8.47968	−	5.44956i	−0.711599	−	0.457317i
$143$	0.978760	−	6.80742i	0.0818480	−	0.569265i
$144$		0			0
$145$	0.788762	+	1.72715i	0.0655031	+	0.143432i
$146$	0.00895698	+	0.0103369i	0.000741285	+	0.000855489i
$147$		0			0
$148$	−0.864785	+	1.89361i	−0.0710849	+	0.155654i
$149$	7.76039	−	2.27866i	0.635756	−	0.186675i	0.0520557	−	0.998644i	$-0.483423\pi$
$149$	7.76039	−	2.27866i	0.635756	−	0.186675i	0.583700	+	0.811969i	$0.301604\pi$
$150$		0			0
$151$	1.87350	−	4.10240i	0.152464	−	0.333849i	−0.817953	−	0.575285i	$-0.804891\pi$
$151$	1.87350	−	4.10240i	0.152464	−	0.333849i	0.970417	+	0.241436i	$0.0776185\pi$
$152$	2.36290	+	16.4343i	0.191657	+	1.33300i
$153$		0			0
$154$	−1.08551	−	2.37694i	−0.0874731	−	0.191539i
$155$	2.47360	−	1.58968i	0.198684	−	0.127686i
$156$		0			0
$157$	1.74744	+	1.12301i	0.139461	+	0.0896263i	0.608511	−	0.793545i	$-0.291767\pi$
$157$	1.74744	+	1.12301i	0.139461	+	0.0896263i	−0.469050	+	0.883172i	$0.655404\pi$
$158$	−10.9205	+	12.6030i	−0.868792	+	1.00264i
$159$		0			0
$160$	−1.73893			−0.137474
$161$	2.31787	−	0.0925529i	0.182674	−	0.00729419i
$162$		0			0
$163$	−16.6050	−	4.87566i	−1.30060	−	0.381891i	−0.443147	−	0.896449i	$-0.646138\pi$
$163$	−16.6050	−	4.87566i	−1.30060	−	0.381891i	−0.857456	+	0.514558i	$0.827956\pi$
$164$	−4.09943	+	4.73100i	−0.320112	+	0.369429i
$165$		0			0
$166$	−1.38978	+	9.66616i	−0.107868	+	0.750240i
$167$	−14.4834	+	9.30794i	−1.12076	+	0.720270i	−0.963612	−	0.267305i	$-0.913867\pi$
$167$	−14.4834	+	9.30794i	−1.12076	+	0.720270i	−0.157150	+	0.987575i	$0.550231\pi$
$168$		0			0
$169$	5.75140	+	6.63747i	0.442416	+	0.510575i
$170$	−0.132189	−	0.919393i	−0.0101384	−	0.0705142i
$171$		0			0
$172$	−4.46058	+	1.30975i	−0.340116	+	0.0998672i
$173$	−11.8788	+	3.48793i	−0.903129	+	0.265183i	−0.700146	−	0.714000i	$-0.746882\pi$
$173$	−11.8788	+	3.48793i	−0.903129	+	0.265183i	−0.202983	+	0.979182i	$0.565064\pi$
$174$		0			0
$175$	0.325083	+	2.26100i	0.0245739	+	0.170916i
$176$	−10.6185	−	12.2543i	−0.800396	−	0.923706i
$177$		0			0
$178$	−3.82584	+	2.45872i	−0.286759	+	0.184289i
$179$	−0.511848	+	3.55998i	−0.0382573	+	0.266085i	−0.999968	−	0.00798071i	$-0.997460\pi$
$179$	−0.511848	+	3.55998i	−0.0382573	+	0.266085i	0.961711	+	0.274066i	$0.0883687\pi$
$180$		0			0
$181$	−6.81072	+	7.85999i	−0.506237	+	0.584229i	−0.950131	−	0.311851i	$-0.899051\pi$
$181$	−6.81072	+	7.85999i	−0.506237	+	0.584229i	0.443894	+	0.896079i	$0.353597\pi$
$182$	−1.53748	−	0.451445i	−0.113966	−	0.0334633i
$183$		0			0
$184$	10.2457	−	3.45805i	0.755321	−	0.254931i
$185$	−1.82087			−0.133873
$186$		0			0
$187$	2.39712	−	2.76642i	0.175295	−	0.202301i
$188$	−5.47052	−	3.51569i	−0.398979	−	0.256408i
$189$		0			0
$190$	5.26416	−	3.38307i	0.381902	−	0.245434i
$191$	2.78682	+	6.10229i	0.201647	+	0.441546i	0.983258	−	0.182221i	$-0.0583286\pi$
$191$	2.78682	+	6.10229i	0.201647	+	0.441546i	−0.781610	+	0.623767i	$0.785601\pi$
$192$		0			0
$193$	1.89436	+	13.1756i	0.136359	+	0.948398i	0.937019	+	0.349279i	$0.113573\pi$
$193$	1.89436	+	13.1756i	0.136359	+	0.948398i	−0.800660	+	0.599119i	$0.795517\pi$
$194$	12.2966	−	26.9257i	0.882842	−	1.93316i
$195$		0			0
$196$	3.90983	−	1.14803i	0.279273	−	0.0820021i
$197$	7.95982	−	17.4296i	0.567114	−	1.24181i	−0.381206	−	0.924490i	$-0.624491\pi$
$197$	7.95982	−	17.4296i	0.567114	−	1.24181i	0.948320	−	0.317316i	$-0.102781\pi$
$198$		0			0
$199$	−15.2770	−	17.6306i	−1.08296	−	1.24980i	−0.966518	−	0.256600i	$-0.917398\pi$
$199$	−15.2770	−	17.6306i	−1.08296	−	1.24980i	−0.116438	−	0.993198i	$-0.537148\pi$
$200$	4.42340	+	9.68590i	0.312782	+	0.684897i
$201$		0			0
$202$	−1.49023	+	10.3648i	−0.104853	+	0.729265i
$203$	1.46666	+	0.942563i	0.102939	+	0.0661550i
$204$		0			0
$205$	−5.25375	−	1.54264i	−0.366938	−	0.107743i
$206$	−22.0839			−1.53866
$207$		0			0
$208$	−9.94323			−0.689439
$209$	23.6614	+	6.94761i	1.63669	+	0.480576i
$210$		0			0
$211$	−1.72239	−	1.10691i	−0.118574	−	0.0762030i	0.480009	−	0.877263i	$-0.340633\pi$
$211$	−1.72239	−	1.10691i	−0.118574	−	0.0762030i	−0.598584	+	0.801060i	$0.704270\pi$
$212$	−0.633024	+	4.40278i	−0.0434763	+	0.302384i
$213$		0			0
$214$	8.04770	+	17.6220i	0.550130	+	1.20462i
$215$	−2.66288	−	3.07313i	−0.181607	−	0.209586i
$216$		0			0
$217$	1.12156	−	2.45587i	0.0761363	−	0.166715i
$218$	−19.3337	+	5.67690i	−1.30945	+	0.384488i
$219$		0			0
$220$	−0.441370	+	0.966466i	−0.0297572	+	0.0651591i
$221$	−0.319452	−	2.22184i	−0.0214887	−	0.149457i
$222$		0			0
$223$	0.267566	+	0.585889i	0.0179176	+	0.0392340i	0.918379	−	0.395701i	$-0.129498\pi$
$223$	0.267566	+	0.585889i	0.0179176	+	0.0392340i	−0.900462	+	0.434935i	$0.856771\pi$
$224$	−1.34322	+	0.863232i	−0.0897474	+	0.0576771i
$225$		0			0
$226$	−4.24088	−	2.72545i	−0.282099	−	0.181294i
$227$	16.3006	−	18.8119i	1.08191	−	1.24859i	0.115030	−	0.993362i	$-0.463303\pi$
$227$	16.3006	−	18.8119i	1.08191	−	1.24859i	0.966880	−	0.255230i	$-0.0821511\pi$
$228$		0			0
$229$	2.91045			0.192328			0.0961640	−	0.995366i	$-0.469343\pi$
$229$	2.91045			0.192328			0.0961640	+	0.995366i	$0.469343\pi$
$230$	−2.78960	−	2.97107i	−0.183941	−	0.195906i
$231$		0			0
$232$	7.79784	+	2.28965i	0.511953	+	0.150323i
$233$	3.99921	−	4.61533i	0.261997	−	0.302360i	−0.609476	−	0.792805i	$-0.708620\pi$
$233$	3.99921	−	4.61533i	0.261997	−	0.302360i	0.871472	+	0.490444i	$0.163166\pi$
$234$		0			0
$235$	0.809477	−	5.63004i	0.0528045	−	0.367263i
$236$	0.476040	−	0.305932i	0.0309876	−	0.0199145i
$237$		0			0
$238$	−0.558510	−	0.644555i	−0.0362028	−	0.0417803i
$239$	4.26924	+	29.6932i	0.276154	+	1.92069i	0.377828	+	0.925876i	$0.376671\pi$
$239$	4.26924	+	29.6932i	0.276154	+	1.92069i	−0.101674	+	0.994818i	$0.532420\pi$
$240$		0			0
$241$	−2.92074	+	0.857606i	−0.188141	+	0.0552433i	−0.374446	−	0.927249i	$-0.622167\pi$
$241$	−2.92074	+	0.857606i	−0.188141	+	0.0552433i	0.186305	+	0.982492i	$0.440349\pi$
$242$	−0.333245	+	0.0978496i	−0.0214218	+	0.00629001i
$243$		0			0
$244$	−0.491616	−	3.41926i	−0.0314725	−	0.218896i
$245$	2.33409	+	2.69368i	0.149120	+	0.172093i
$246$		0			0
$247$	12.7216	−	8.17565i	0.809453	−	0.520204i
$248$	1.79110	−	12.4574i	0.113735	−	0.791045i
$249$		0			0
$250$	5.41048	−	6.24403i	0.342189	−	0.394907i
$251$	−3.39713	−	0.997487i	−0.214425	−	0.0629608i	0.172756	−	0.984965i	$-0.444733\pi$
$251$	−3.39713	−	0.997487i	−0.214425	−	0.0629608i	−0.387181	+	0.922004i	$0.626551\pi$
$252$		0			0
$253$	1.64960	−	15.9759i	0.103710	−	1.00440i
$254$	17.6275			1.10605
$255$		0			0
$256$	−8.69330	+	10.0326i	−0.543331	+	0.627038i
$257$	−7.38840	−	4.74824i	−0.460876	−	0.296187i	0.289524	−	0.957171i	$-0.406503\pi$
$257$	−7.38840	−	4.74824i	−0.460876	−	0.296187i	−0.750400	+	0.660984i	$0.770139\pi$
$258$		0			0
$259$	−1.40651	+	0.903910i	−0.0873964	+	0.0561663i
$260$	0.270656	+	0.592655i	0.0167854	+	0.0367549i
$261$		0			0
$262$	−0.135084	−	0.939532i	−0.00834553	−	0.0580445i
$263$	−3.85133	+	8.43323i	−0.237483	+	0.520015i	−0.990422	−	0.138076i	$-0.955908\pi$
$263$	−3.85133	+	8.43323i	−0.237483	+	0.520015i	0.752939	+	0.658091i	$0.228636\pi$
$264$		0			0
$265$	−3.73306	+	1.09612i	−0.229320	+	0.0673344i
$266$	2.38683	−	5.22644i	0.146346	−	0.320453i
$267$		0			0
$268$	−5.07915	−	5.86165i	−0.310258	−	0.358057i
$269$	−5.27658	−	11.5541i	−0.321719	−	0.704466i	0.677807	−	0.735239i	$-0.262930\pi$
$269$	−5.27658	−	11.5541i	−0.321719	−	0.704466i	−0.999526	+	0.0307732i	$0.990203\pi$
$270$		0			0
$271$	0.696557	−	4.84466i	0.0423129	−	0.294292i	−0.957667	−	0.287880i	$-0.907050\pi$
$271$	0.696557	−	4.84466i	0.0423129	−	0.294292i	0.999979	−	0.00641267i	$-0.00204123\pi$
$272$	−4.45214	−	2.86122i	−0.269951	−	0.173487i
$273$		0			0
$274$	27.7403	+	8.14528i	1.67585	+	0.492074i
$275$	15.8153			0.953698
$276$		0			0
$277$	3.82724			0.229957			0.114978	−	0.993368i	$-0.463320\pi$
$277$	3.82724			0.229957			0.114978	+	0.993368i	$0.463320\pi$
$278$	20.6620	+	6.06691i	1.23922	+	0.363869i
$279$		0			0
$280$	−0.483321	−	0.310612i	−0.0288840	−	0.0185626i
$281$	−2.81648	+	19.5891i	−0.168017	+	1.16859i	0.714958	+	0.699167i	$0.246446\pi$
$281$	−2.81648	+	19.5891i	−0.168017	+	1.16859i	−0.882976	+	0.469419i	$0.844463\pi$
$282$		0			0
$283$	−4.06513	−	8.90139i	−0.241647	−	0.529133i	0.749484	−	0.662023i	$-0.230302\pi$
$283$	−4.06513	−	8.90139i	−0.241647	−	0.529133i	−0.991131	+	0.132890i	$0.957574\pi$
$284$	2.46438	+	2.84405i	0.146234	+	0.168763i
$285$		0			0
$286$	−4.60875	+	10.0918i	−0.272521	+	0.596738i
$287$	−4.82400	+	1.41645i	−0.284752	+	0.0836107i
$288$		0			0
$289$	−6.56575	+	14.3770i	−0.386220	+	0.845705i
$290$	−0.435902	−	3.03177i	−0.0255971	−	0.178031i
$291$		0			0
$292$	−0.00212130	−	0.00464499i	−0.000124139	−	0.000271827i
$293$	7.48457	−	4.81004i	0.437253	−	0.281006i	−0.303438	−	0.952851i	$-0.598134\pi$
$293$	7.48457	−	4.81004i	0.437253	−	0.281006i	0.740691	+	0.671846i	$0.234498\pi$
$294$		0			0
$295$	0.416386	+	0.267595i	0.0242429	+	0.0155800i
$296$	−5.10383	+	5.89013i	−0.296654	+	0.342357i
$297$		0			0
$298$	−13.0472			−0.755803
$299$	−6.74144	−	7.17999i	−0.389868	−	0.415230i
$300$		0			0
$301$	−3.58247	−	1.05191i	−0.206490	−	0.0606310i
$302$	−4.76427	+	5.49826i	−0.274153	+	0.316389i
$303$		0			0
$304$	5.07399	−	35.2904i	0.291013	−	2.02404i
$305$	2.54188	−	1.63357i	0.145548	−	0.0935379i
$306$		0			0
$307$	8.53152	+	9.84590i	0.486920	+	0.561935i	0.945040	−	0.326955i	$-0.106023\pi$
$307$	8.53152	+	9.84590i	0.486920	+	0.561935i	−0.458120	+	0.888890i	$0.651477\pi$
$308$	0.138838	+	0.965641i	0.00791104	+	0.0550225i
$309$		0			0
$310$	−4.55112	+	1.33633i	−0.258486	+	0.0758985i
$311$	−26.8983	+	7.89805i	−1.52526	+	0.447857i	−0.933597	−	0.358326i	$-0.883348\pi$
$311$	−26.8983	+	7.89805i	−1.52526	+	0.447857i	−0.591666	+	0.806183i	$0.701529\pi$
$312$		0			0
$313$	2.09112	+	14.5440i	0.118197	+	0.822077i	0.959539	+	0.281575i	$0.0908568\pi$
$313$	2.09112	+	14.5440i	0.118197	+	0.822077i	−0.841342	+	0.540502i	$0.818234\pi$
$314$	−2.19432	−	2.53238i	−0.123833	−	0.142911i
$315$		0			0
$316$	5.23756	−	3.36597i	0.294636	−	0.189351i
$317$	−1.75470	+	12.2042i	−0.0985540	+	0.685458i	0.879315	+	0.476241i	$0.158001\pi$
$317$	−1.75470	+	12.2042i	−0.0985540	+	0.685458i	−0.977869	+	0.209218i	$0.932908\pi$
$318$		0			0
$319$	7.90468	−	9.12248i	0.442577	−	0.510761i
$320$	−2.20303	−	0.646868i	−0.123153	−	0.0361610i
$321$		0			0
$322$	−3.62969	−	0.910167i	−0.202275	−	0.0507216i
$323$	8.04874			0.447844
$324$		0			0
$325$	6.35098	−	7.32943i	0.352289	−	0.406563i
$326$	23.4854	+	15.0932i	1.30074	+	0.835933i
$327$		0			0
$328$	−19.7162	+	12.6708i	−1.08864	+	0.699630i
$329$	−2.16957	−	4.75071i	−0.119613	−	0.261915i
$330$		0			0
$331$	0.479124	+	3.33238i	0.0263350	+	0.183164i	0.998743	−	0.0501223i	$-0.0159611\pi$
$331$	0.479124	+	3.33238i	0.0263350	+	0.183164i	−0.972408	+	0.233286i	$0.925052\pi$
$332$	1.51456	−	3.31642i	0.0831221	−	0.182012i
$333$		0			0
$334$	26.6478	−	7.82450i	1.45810	−	0.428138i
$335$	2.81823	−	6.17107i	0.153977	−	0.337162i
$336$		0			0
$337$	1.48464	+	1.71336i	0.0808732	+	0.0933327i	0.794744	−	0.606945i	$-0.207605\pi$
$337$	1.48464	+	1.71336i	0.0808732	+	0.0933327i	−0.713871	+	0.700277i	$0.753060\pi$
$338$	−5.88548	−	12.8874i	−0.320128	−	0.700983i
$339$		0			0
$340$	−0.0493515	+	0.343248i	−0.00267646	+	0.0186152i
$341$	−15.7253	−	10.1061i	−0.851575	−	0.547274i
$342$		0			0
$343$	6.38885	+	1.87594i	0.344966	+	0.101291i
$344$	−17.4049			−0.938409
$345$		0			0
$346$	19.9713			1.07366
$347$	−12.9692	−	3.80810i	−0.696224	−	0.204430i	−0.0855754	−	0.996332i	$-0.527273\pi$
$347$	−12.9692	−	3.80810i	−0.696224	−	0.204430i	−0.610648	+	0.791902i	$0.709091\pi$
$348$		0			0
$349$	17.9744	+	11.5514i	0.962145	+	0.618333i	0.924591	−	0.380961i	$-0.124407\pi$
$349$	17.9744	+	11.5514i	0.962145	+	0.618333i	0.0375543	+	0.999295i	$0.488043\pi$
$350$	0.524407	−	3.64733i	0.0280308	−	0.194958i
$351$		0			0
$352$	4.59235	+	10.0558i	0.244773	+	0.535978i
$353$	19.1742	+	22.1282i	1.02054	+	1.17777i	0.983952	+	0.178436i	$0.0571036\pi$
$353$	19.1742	+	22.1282i	1.02054	+	1.17777i	0.0365884	+	0.999330i	$0.488351\pi$
$354$		0			0
$355$	−1.36739	+	2.99418i	−0.0725738	+	0.158914i
$356$	1.62910	−	0.478347i	0.0863422	−	0.0253524i
$357$		0			0
$358$	2.41017	−	5.27754i	0.127382	−	0.278927i
$359$	−4.14017	−	28.7955i	−0.218510	−	1.51977i	−0.743544	−	0.668687i	$-0.766857\pi$
$359$	−4.14017	−	28.7955i	−0.218510	−	1.51977i	0.525035	−	0.851081i	$-0.324052\pi$
$360$		0			0
$361$	14.6323	+	32.0402i	0.770120	+	1.68633i
$362$	14.1139	−	9.07043i	0.741808	−	0.476731i
$363$		0			0
$364$	0.503270	+	0.323432i	0.0263785	+	0.0169524i
$365$	0.00292497	−	0.00337559i	0.000153100	−	0.000176687i
$366$		0			0
$367$	−14.9673			−0.781284			−0.390642	−	0.920543i	$-0.627747\pi$
$367$	−14.9673			−0.781284			−0.390642	+	0.920543i	$0.627747\pi$
$368$	−23.2020	+	0.926456i	−1.20949	+	0.0482949i
$369$		0			0
$370$	2.81835	+	0.827543i	0.146519	+	0.0430219i
$371$	−2.33943	+	2.69984i	−0.121457	+	0.140169i
$372$		0			0
$373$	4.71393	−	32.7861i	0.244078	−	1.69760i	−0.387160	−	0.922012i	$-0.626544\pi$
$373$	4.71393	−	32.7861i	0.244078	−	1.69760i	0.631238	−	0.775589i	$-0.282547\pi$
$374$	−4.96755	+	3.19245i	−0.256866	+	0.165078i
$375$		0			0
$376$	−15.9431	−	18.3993i	−0.822201	−	0.948871i
$377$	−1.05342	−	7.32668i	−0.0542537	−	0.377343i
$378$		0			0
$379$	18.0864	−	5.31066i	0.929038	−	0.272790i	0.218004	−	0.975948i	$-0.430045\pi$
$379$	18.0864	−	5.31066i	0.929038	−	0.272790i	0.711034	+	0.703158i	$0.248227\pi$
$380$	−2.24156	+	0.658181i	−0.114990	+	0.0337640i
$381$		0			0
$382$	−1.54011	−	10.7117i	−0.0787990	−	0.548059i
$383$	12.0320	+	13.8856i	0.614805	+	0.709523i	0.974712	−	0.223466i	$-0.0717370\pi$
$383$	12.0320	+	13.8856i	0.614805	+	0.709523i	−0.359907	+	0.932988i	$0.617192\pi$
$384$		0			0
$385$	−0.717858	+	0.461339i	−0.0365854	+	0.0235120i
$386$	3.05589	−	21.2542i	0.155541	−	1.08181i
$387$		0			0
$388$	−7.23697	+	8.35191i	−0.367402	+	0.424004i
$389$	−4.28212	−	1.25735i	−0.217112	−	0.0637499i	0.171367	−	0.985207i	$-0.445181\pi$
$389$	−4.28212	−	1.25735i	−0.217112	−	0.0637499i	−0.388480	+	0.921457i	$0.627000\pi$
$390$		0			0
$391$	−0.952443	−	5.15477i	−0.0481671	−	0.260688i
$392$	15.2559			0.770538
$393$		0			0
$394$	−20.2416	+	23.3601i	−1.01976	+	1.17686i
$395$	4.58122	+	2.94417i	0.230506	+	0.148137i
$396$		0			0
$397$	−11.9955	+	7.70906i	−0.602039	+	0.386907i	−0.805864	−	0.592100i	$-0.798299\pi$
$397$	−11.9955	+	7.70906i	−0.602039	+	0.386907i	0.203825	+	0.979007i	$0.434663\pi$
$398$	15.6331	+	34.2317i	0.783617	+	1.71588i
$399$		0			0
$400$	−3.25408	−	22.6326i	−0.162704	−	1.13163i
$401$	14.9051	−	32.6376i	0.744324	−	1.62984i	−0.0319840	−	0.999488i	$-0.510183\pi$
$401$	14.9051	−	32.6376i	0.744324	−	1.62984i	0.776308	−	0.630354i	$-0.217090\pi$
$402$		0			0
$403$	−10.9984	+	3.22942i	−0.547870	+	0.160869i
$404$	1.62403	−	3.55612i	0.0807983	−	0.176924i
$405$		0			0
$406$	−1.84173	−	2.12547i	−0.0914035	−	0.105485i
$407$	4.80875	+	10.5297i	0.238361	+	0.521937i
$408$		0			0
$409$	−1.67097	+	11.6218i	−0.0826241	+	0.574663i	0.905887	+	0.423518i	$0.139205\pi$
$409$	−1.67097	+	11.6218i	−0.0826241	+	0.574663i	−0.988512	+	0.151145i	$0.951704\pi$
$410$	7.43070	+	4.77542i	0.366976	+	0.235841i
$411$		0			0
$412$	7.91087	+	2.32284i	0.389741	+	0.114438i
$413$	0.454472			0.0223631
$414$		0			0
$415$	3.18901			0.156543
$416$	6.50443	+	1.90987i	0.318906	+	0.0936392i
$417$		0			0
$418$	−33.4657	−	21.5071i	−1.63686	−	1.05195i
$419$	−4.58075	+	31.8598i	−0.223784	+	1.55645i	0.499752	+	0.866169i	$0.333424\pi$
$419$	−4.58075	+	31.8598i	−0.223784	+	1.55645i	−0.723536	+	0.690286i	$0.757485\pi$
$420$		0			0
$421$	−10.6956	−	23.4201i	−0.521271	−	1.14142i	−0.968956	−	0.247233i	$-0.920479\pi$
$421$	−10.6956	−	23.4201i	−0.521271	−	1.14142i	0.447685	−	0.894191i	$-0.352249\pi$
$422$	2.16286	+	2.49607i	0.105286	+	0.121507i
$423$		0			0
$424$	−6.91789	+	15.1481i	−0.335962	+	0.735655i
$425$	4.95277	−	1.45427i	0.240245	−	0.0705423i
$426$		0			0
$427$	1.15252	−	2.52367i	0.0557744	−	0.122129i
$428$	−1.02931	−	7.15901i	−0.0497536	−	0.346044i
$429$		0			0
$430$	2.72496	+	5.96683i	0.131409	+	0.287746i
$431$	5.05580	−	3.24916i	0.243529	−	0.156507i	−0.413183	−	0.910648i	$-0.635583\pi$
$431$	5.05580	−	3.24916i	0.243529	−	0.156507i	0.656712	+	0.754141i	$0.271947\pi$
$432$		0			0
$433$	−24.9572	−	16.0390i	−1.19937	−	0.770787i	−0.220521	−	0.975382i	$-0.570776\pi$
$433$	−24.9572	−	16.0390i	−1.19937	−	0.770787i	−0.978847	+	0.204595i	$0.934412\pi$
$434$	−2.85209	+	3.29149i	−0.136905	+	0.157997i
$435$		0			0
$436$	7.52281			0.360277
$437$	28.9233	−	20.2627i	1.38359	−	0.969299i
$438$		0			0
$439$	−3.60675	−	1.05904i	−0.172141	−	0.0505451i	0.194526	−	0.980897i	$-0.437683\pi$
$439$	−3.60675	−	1.05904i	−0.172141	−	0.0505451i	−0.366667	+	0.930352i	$0.619501\pi$
$440$	−2.60490	+	3.00622i	−0.124184	+	0.143316i
$441$		0			0
$442$	−0.515325	+	3.58416i	−0.0245115	+	0.170481i
$443$	9.98016	−	6.41386i	0.474172	−	0.304732i	−0.281641	−	0.959520i	$-0.590879\pi$
$443$	9.98016	−	6.41386i	0.474172	−	0.304732i	0.755812	+	0.654788i	$0.227242\pi$
$444$		0			0
$445$	0.972542	+	1.12237i	0.0461029	+	0.0532056i
$446$	−0.147868	−	1.02845i	−0.00700176	−	0.0486983i
$447$		0			0
$448$	−2.02282	+	0.593955i	−0.0955694	+	0.0280617i
$449$	−28.3526	+	8.32507i	−1.33804	+	0.392885i	−0.870971	−	0.491335i	$-0.836509\pi$
$449$	−28.3526	+	8.32507i	−1.33804	+	0.392885i	−0.467071	+	0.884220i	$0.654691\pi$
$450$		0			0
$451$	4.95392	+	34.4553i	0.233271	+	1.62244i
$452$	1.23249	+	1.42237i	0.0579716	+	0.0669028i
$453$		0			0
$454$	−33.7798	+	21.7090i	−1.58537	+	1.01885i
$455$	−0.0744692	+	0.517945i	−0.00349117	+	0.0242816i
$456$		0			0
$457$	17.3259	−	19.9951i	0.810470	−	0.935332i	−0.188436	−	0.982085i	$-0.560342\pi$
$457$	17.3259	−	19.9951i	0.810470	−	0.935332i	0.998906	+	0.0467529i	$0.0148874\pi$
$458$	−4.50482	−	1.32273i	−0.210496	−	0.0618073i
$459$		0			0
$460$	0.686782	+	1.35771i	0.0320214	+	0.0633035i
$461$	−39.8046			−1.85388			−0.926942	−	0.375205i	$-0.877572\pi$
$461$	−39.8046			−1.85388			−0.926942	+	0.375205i	$0.877572\pi$
$462$		0			0
$463$	−19.4034	+	22.3927i	−0.901752	+	1.04068i	0.0972160	+	0.995263i	$0.469006\pi$
$463$	−19.4034	+	22.3927i	−0.901752	+	1.04068i	−0.998968	+	0.0454143i	$0.985539\pi$
$464$	−14.6813	−	9.43508i	−0.681561	−	0.438012i
$465$		0			0
$466$	−8.28756	+	5.32609i	−0.383914	+	0.246726i
$467$	−1.73407	−	3.79709i	−0.0802432	−	0.175708i	0.865258	−	0.501327i	$-0.167155\pi$
$467$	−1.73407	−	3.79709i	−0.0802432	−	0.175708i	−0.945501	+	0.325619i	$0.894427\pi$
$468$		0			0
$469$	−0.886508	−	6.16580i	−0.0409352	−	0.284710i
$470$	−3.81164	+	8.34633i	−0.175818	+	0.384987i
$471$		0			0
$472$	2.03273	−	0.596863i	0.0935640	−	0.0274729i
$473$	−10.7388	+	23.5147i	−0.493771	+	1.08121i
$474$		0			0
$475$	22.7726	+	26.2810i	1.04488	+	1.20586i
$476$	0.132273	+	0.289637i	0.00606271	+	0.0132755i
$477$		0			0
$478$	6.88693	−	47.8996i	0.315001	−	2.19088i
$479$	−13.8273	−	8.88625i	−0.631784	−	0.406023i	0.185186	−	0.982704i	$-0.440711\pi$
$479$	−13.8273	−	8.88625i	−0.631784	−	0.406023i	−0.816970	+	0.576681i	$0.804348\pi$
$480$		0			0
$481$	6.81093	+	1.99987i	0.310552	+	0.0911863i
$482$	4.91050			0.223667
$483$		0			0
$484$	0.129667			0.00589394
$485$	−9.27476	−	2.72332i	−0.421145	−	0.123659i
$486$		0			0
$487$	18.8374	+	12.1061i	0.853603	+	0.548578i	0.892697	−	0.450658i	$-0.148811\pi$
$487$	18.8374	+	12.1061i	0.853603	+	0.548578i	−0.0390933	+	0.999236i	$0.512447\pi$
$488$	1.84055	−	12.8013i	0.0833177	−	0.579488i
$489$		0			0
$490$	−2.38850	−	5.23009i	−0.107902	−	0.236272i
$491$	−7.83692	−	9.04429i	−0.353675	−	0.408163i	0.550835	−	0.834614i	$-0.314309\pi$
$491$	−7.83692	−	9.04429i	−0.353675	−	0.408163i	−0.904511	+	0.426451i	$0.859764\pi$
$492$		0			0
$493$	1.63662	−	3.58369i	0.0737095	−	0.161401i
$494$	−23.4062	+	6.87267i	−1.05309	+	0.309216i
$495$		0			0
$496$	−11.2268	+	24.5833i	−0.504099	+	1.10382i
$497$	0.430130	+	2.99162i	0.0192940	+	0.134192i
$498$		0			0
$499$	4.66181	+	10.2079i	0.208691	+	0.456970i	0.984814	−	0.173611i	$-0.0555436\pi$
$499$	4.66181	+	10.2079i	0.208691	+	0.456970i	−0.776123	+	0.630582i	$0.782816\pi$
$500$	−2.59490	+	1.66764i	−0.116047	+	0.0745791i
$501$		0			0
$502$	4.80477	+	3.08784i	0.214447	+	0.137817i
$503$	9.14150	−	10.5499i	0.407599	−	0.470395i	−0.514420	−	0.857538i	$-0.671993\pi$
$503$	9.14150	−	10.5499i	0.407599	−	0.470395i	0.922019	+	0.387144i	$0.126538\pi$
$504$		0			0
$505$	3.41951			0.152166
$506$	−9.81397	+	23.9780i	−0.436284	+	1.06595i
$507$		0			0
$508$	−6.31450	−	1.85410i	−0.280161	−	0.0822626i
$509$	−16.8921	+	19.4945i	−0.748730	+	0.864080i	−0.994445	−	0.105262i	$-0.966432\pi$
$509$	−16.8921	+	19.4945i	−0.748730	+	0.864080i	0.245715	+	0.969342i	$0.420977\pi$
$510$		0			0
$511$	0.000583660	−	0.00405944i	2.58196e−5	−	0.000179579i
$512$	−4.92257	+	3.16355i	−0.217549	+	0.139810i
$513$		0			0
$514$	9.27785	+	10.7072i	0.409229	+	0.472275i
$515$	1.02633	+	7.13826i	0.0452254	+	0.314549i
$516$		0			0
$517$	−34.6951	+	10.1874i	−1.52589	+	0.448041i
$518$	2.58782	−	0.759851i	0.113702	−	0.0333859i
$519$		0			0
$520$	0.347142	+	2.41443i	0.0152232	+	0.105880i
$521$	15.2342	+	17.5812i	0.667421	+	0.770245i	0.983971	−	0.178331i	$-0.0570697\pi$
$521$	15.2342	+	17.5812i	0.667421	+	0.770245i	−0.316549	+	0.948576i	$0.602524\pi$
$522$		0			0
$523$	9.64326	−	6.19735i	0.421670	−	0.270991i	−0.312551	−	0.949901i	$-0.601184\pi$
$523$	9.64326	−	6.19735i	0.421670	−	0.270991i	0.734222	+	0.678910i	$0.237547\pi$
$524$	−0.0504326	+	0.350766i	−0.00220316	+	0.0153233i
$525$		0			0
$526$	9.79382	−	11.3027i	0.427031	−	0.492820i
$527$	−5.85389	−	1.71886i	−0.255000	−	0.0748746i
$528$		0			0
$529$	−16.3998	−	16.1260i	−0.713034	−	0.701129i
$530$	6.27622			0.272621
$531$		0			0
$532$	−1.40474	+	1.62115i	−0.0609031	+	0.0702859i
$533$	17.9573	+	11.5405i	0.777817	+	0.499873i
$534$		0			0
$535$	5.32201	−	3.42025i	0.230091	−	0.147870i
$536$	−12.0627	−	26.4137i	−0.521030	−	1.14090i
$537$		0			0
$538$	2.91606	+	20.2816i	0.125720	+	0.874402i
$539$	9.41287	−	20.6113i	0.405441	−	0.887792i
$540$		0			0
$541$	22.5066	−	6.60855i	0.967636	−	0.284124i	0.240525	−	0.970643i	$-0.422680\pi$
$541$	22.5066	−	6.60855i	0.967636	−	0.284124i	0.727112	+	0.686519i	$0.240862\pi$
$542$	−3.27993	+	7.18203i	−0.140885	+	0.308495i
$543$		0			0
$544$	2.36282	+	2.72684i	0.101305	+	0.116912i
$545$	2.73348	+	5.98548i	0.117089	+	0.256390i
$546$		0			0
$547$	2.11351	−	14.6998i	0.0903670	−	0.628516i	−0.893426	−	0.449210i	$-0.851706\pi$
$547$	2.11351	−	14.6998i	0.0903670	−	0.628516i	0.983793	−	0.179306i	$-0.0573853\pi$
$548$	−9.08033	−	5.83558i	−0.387893	−	0.249283i
$549$		0			0
$550$	−24.4790	−	7.18769i	−1.04379	−	0.306484i
$551$	26.5413			1.13070
$552$		0			0
$553$	5.00026			0.212633
$554$	−5.92383	−	1.73939i	−0.251680	−	0.0738998i
$555$		0			0
$556$	−6.76338	−	4.34656i	−0.286831	−	0.184335i
$557$	3.28296	−	22.8335i	0.139103	−	0.967485i	−0.794011	−	0.607904i	$-0.792011\pi$
$557$	3.28296	−	22.8335i	0.139103	−	0.967485i	0.933114	−	0.359581i	$-0.117080\pi$
$558$		0			0
$559$	6.58524	+	14.4197i	0.278526	+	0.609886i
$560$	0.807908	+	0.932376i	0.0341404	+	0.0394001i
$561$		0			0
$562$	13.2622	−	29.0401i	0.559430	−	1.22498i
$563$	−26.0066	+	7.63624i	−1.09605	+	0.321829i	−0.779281	−	0.626674i	$-0.784416\pi$
$563$	−26.0066	+	7.63624i	−1.09605	+	0.321829i	−0.316768	+	0.948503i	$0.602598\pi$
$564$		0			0
$565$	−0.683866	+	1.49746i	−0.0287704	+	0.0629985i
$566$	2.24656	+	15.6251i	0.0944298	+	0.656774i
$567$		0			0
$568$	5.85278	+	12.8158i	0.245577	+	0.537739i
$569$	−14.0899	+	9.05501i	−0.590678	+	0.379606i	−0.801568	−	0.597904i	$-0.796000\pi$
$569$	−14.0899	+	9.05501i	−0.590678	+	0.379606i	0.210890	+	0.977510i	$0.432364\pi$
$570$		0			0
$571$	−6.90227	−	4.43582i	−0.288851	−	0.185633i	0.388188	−	0.921580i	$-0.373101\pi$
$571$	−6.90227	−	4.43582i	−0.288851	−	0.185633i	−0.677039	+	0.735947i	$0.736737\pi$
$572$	2.71241	−	3.13029i	0.113412	−	0.130884i
$573$		0			0
$574$	8.11037			0.338520
$575$	14.1368	−	17.6946i	0.589543	−	0.737914i
$576$		0			0
$577$	−0.910674	−	0.267398i	−0.0379119	−	0.0111319i	0.262722	−	0.964872i	$-0.415380\pi$
$577$	−0.910674	−	0.267398i	−0.0379119	−	0.0111319i	−0.300633	+	0.953740i	$0.597198\pi$
$578$	16.6965	−	19.2688i	0.694484	−	0.801477i
$579$		0			0
$580$	−0.162740	+	1.13188i	−0.00675743	+	0.0469989i
$581$	2.46332	−	1.58308i	0.102196	−	0.0656773i
$582$		0			0
$583$	16.1973	+	18.6927i	0.670824	+	0.774173i
$584$	−0.00272076	−	0.0189233i	−0.000112586	−	0.000783052i
$585$		0			0
$586$	−13.7707	+	4.04345i	−0.568864	+	0.167033i
$587$	27.0571	−	7.94468i	1.11677	−	0.327912i	0.329272	−	0.944235i	$-0.393197\pi$
$587$	27.0571	−	7.94468i	1.11677	−	0.327912i	0.787494	+	0.616323i	$0.211378\pi$
$588$		0			0
$589$	−5.84939	−	40.6834i	−0.241020	−	1.67633i
$590$	−0.522870	−	0.603424i	−0.0215262	−	0.0248426i
$591$		0			0
$592$	14.0792	−	9.04816i	0.578652	−	0.371877i
$593$	0.686106	−	4.77197i	0.0281750	−	0.195961i	−0.970873	−	0.239597i	$-0.922985\pi$
$593$	0.686106	−	4.77197i	0.0281750	−	0.195961i	0.999048	+	0.0436352i	$0.0138939\pi$
$594$		0			0
$595$	−0.182385	+	0.210484i	−0.00747708	+	0.00862901i
$596$	4.67374	+	1.37233i	0.191444	+	0.0562130i
$597$		0			0
$598$	7.17131	+	14.1771i	0.293257	+	0.579744i
$599$	48.1882			1.96892			0.984458	−	0.175619i	$-0.0561926\pi$
$599$	48.1882			1.96892			0.984458	+	0.175619i	$0.0561926\pi$
$600$		0			0
$601$	20.4011	−	23.5441i	0.832177	−	0.960383i	−0.167498	−	0.985872i	$-0.553569\pi$
$601$	20.4011	−	23.5441i	0.832177	−	0.960383i	0.999675	+	0.0254891i	$0.00811432\pi$
$602$	5.06690	+	3.25630i	0.206512	+	0.132717i
$603$		0			0
$604$	2.28497	−	1.46846i	0.0929741	−	0.0597508i
$605$	0.0471155	+	0.103168i	0.00191552	+	0.00419440i
$606$		0			0
$607$	1.14997	+	7.99823i	0.0466759	+	0.324638i	0.999759	+	0.0219309i	$0.00698137\pi$
$607$	1.14997	+	7.99823i	0.0466759	+	0.324638i	−0.953084	+	0.302707i	$0.902110\pi$
$608$	−10.0977	+	22.1109i	−0.409515	+	0.896713i
$609$		0			0
$610$	−4.67677	+	1.37322i	−0.189357	+	0.0556001i
$611$	−9.21134	+	20.1700i	−0.372651	+	0.815992i
$612$		0			0
$613$	−8.27956	−	9.55512i	−0.334408	−	0.385928i	0.563496	−	0.826119i	$-0.309456\pi$
$613$	−8.27956	−	9.55512i	−0.334408	−	0.385928i	−0.897904	+	0.440191i	$0.854911\pi$
$614$	−8.73041	−	19.1169i	−0.352331	−	0.771497i
$615$		0			0
$616$	−0.519793	+	3.61524i	−0.0209430	+	0.145662i
$617$	21.9713	+	14.1201i	0.884531	+	0.568454i	0.902165	−	0.431391i	$-0.141977\pi$
$617$	21.9713	+	14.1201i	0.884531	+	0.568454i	−0.0176341	+	0.999845i	$0.505613\pi$
$618$		0			0
$619$	−16.2418	−	4.76902i	−0.652812	−	0.191683i	−0.0614767	−	0.998109i	$-0.519581\pi$
$619$	−16.2418	−	4.76902i	−0.652812	−	0.191683i	−0.591336	+	0.806426i	$0.701399\pi$
$620$	1.77086			0.0711193
$621$		0			0
$622$	45.2228			1.81327
$623$	1.30840	+	0.384180i	0.0524198	+	0.0153918i
$624$		0			0
$625$	17.5944	+	11.3072i	0.703774	+	0.452288i
$626$	3.37329	−	23.4617i	0.134824	−	0.937719i
$627$		0			0
$628$	0.519685	+	1.13795i	0.0207377	+	0.0454092i
$629$	2.47416	+	2.85534i	0.0986514	+	0.113850i
$630$		0			0
$631$	3.87646	−	8.48826i	0.154319	−	0.337912i	−0.816643	−	0.577142i	$-0.804168\pi$
$631$	3.87646	−	8.48826i	0.154319	−	0.337912i	0.970963	+	0.239230i	$0.0768950\pi$
$632$	22.3648	−	6.56690i	0.889624	−	0.261217i
$633$		0			0
$634$	8.26249	−	18.0923i	0.328145	−	0.718538i
$635$	−0.819220	−	5.69780i	−0.0325097	−	0.226110i
$636$		0			0
$637$	−5.77214	−	12.6392i	−0.228701	−	0.500785i
$638$	−16.3809	+	10.5273i	−0.648525	+	0.416782i
$639$		0			0
$640$	6.04163	+	3.88272i	0.238816	+	0.153478i
$641$	16.4777	−	19.0163i	0.650830	−	0.751097i	−0.330421	−	0.943834i	$-0.607191\pi$
$641$	16.4777	−	19.0163i	0.650830	−	0.751097i	0.981251	+	0.192736i	$0.0617362\pi$
$642$		0			0
$643$	15.1602			0.597859			0.298930	−	0.954275i	$-0.403370\pi$
$643$	15.1602			0.597859			0.298930	+	0.954275i	$0.403370\pi$
$644$	1.20449	+	0.707818i	0.0474634	+	0.0278919i
$645$		0			0
$646$	−12.4579	−	3.65797i	−0.490149	−	0.143921i
$647$	2.75310	−	3.17725i	0.108236	−	0.124910i	−0.699047	−	0.715076i	$-0.746392\pi$
$647$	2.75310	−	3.17725i	0.108236	−	0.124910i	0.807282	+	0.590166i	$0.200938\pi$
$648$		0			0
$649$	0.447807	−	3.11457i	0.0175780	−	0.122257i
$650$	−13.1612	+	8.45816i	−0.516223	+	0.331756i
$651$		0			0
$652$	−6.82538	−	7.87691i	−0.267302	−	0.308483i
$653$	1.36644	+	9.50381i	0.0534730	+	0.371913i	0.998933	+	0.0461756i	$0.0147034\pi$
$653$	1.36644	+	9.50381i	0.0534730	+	0.371913i	−0.945460	+	0.325737i	$0.894388\pi$
$654$		0			0
$655$	−0.297410	+	0.0873274i	−0.0116208	+	0.00341217i
$656$	48.2883	−	14.1787i	1.88534	−	0.553587i
$657$		0			0
$658$	1.19900	+	8.33920i	0.0467417	+	0.325096i
$659$	−0.317667	−	0.366608i	−0.0123746	−	0.0142810i	0.749529	−	0.661972i	$-0.230280\pi$
$659$	−0.317667	−	0.366608i	−0.0123746	−	0.0142810i	−0.761903	+	0.647691i	$0.775735\pi$
$660$		0			0
$661$	−16.0121	+	10.2903i	−0.622797	+	0.400247i	−0.813636	−	0.581374i	$-0.802515\pi$
$661$	−16.0121	+	10.2903i	−0.622797	+	0.400247i	0.190840	+	0.981621i	$0.438879\pi$
$662$	0.772899	−	5.37563i	0.0300396	−	0.208930i
$663$		0			0
$664$	8.93869	−	10.3158i	0.346888	−	0.400331i
$665$	−1.80028	−	0.528611i	−0.0698120	−	0.0204986i
$666$		0			0
$667$	−3.14075	−	16.9982i	−0.121610	−	0.658175i
$668$	−10.3687			−0.401179
$669$		0			0
$670$	−7.16669	+	8.27081i	−0.276874	+	0.319529i
$671$	−16.1595	−	10.3851i	−0.623829	−	0.400911i
$672$		0			0
$673$	1.05038	−	0.675039i	0.0404892	−	0.0260208i	−0.520240	−	0.854020i	$-0.674157\pi$
$673$	1.05038	−	0.675039i	0.0404892	−	0.0260208i	0.560729	+	0.827999i	$0.310521\pi$
$674$	−1.51925	−	3.32668i	−0.0585192	−	0.128139i
$675$		0			0
$676$	0.752760	+	5.23556i	0.0289523	+	0.201368i
$677$	−12.5543	+	27.4900i	−0.482499	+	1.05653i	0.499270	+	0.866447i	$0.333602\pi$
$677$	−12.5543	+	27.4900i	−0.482499	+	1.05653i	−0.981769	+	0.190079i	$0.939126\pi$
$678$		0			0
$679$	−8.51610	+	2.50055i	−0.326818	+	0.0959624i
$680$	−0.539329	+	1.18097i	−0.0206823	+	0.0452880i
$681$		0			0
$682$	19.7468	+	22.7890i	0.756145	+	0.872638i
$683$	6.59875	+	14.4493i	0.252494	+	0.552885i	0.992855	−	0.119324i	$-0.0380727\pi$
$683$	6.59875	+	14.4493i	0.252494	+	0.552885i	−0.740361	+	0.672209i	$0.765345\pi$
$684$		0			0
$685$	1.34362	−	9.34512i	0.0513373	−	0.357059i
$686$	−9.03614	−	5.80717i	−0.345001	−	0.221719i
$687$		0			0
$688$	35.8606	+	10.5296i	1.36717	+	0.401438i
$689$	15.1673			0.577829
$690$		0			0
$691$	−17.1403			−0.652047			−0.326024	−	0.945362i	$-0.605709\pi$
$691$	−17.1403			−0.652047			−0.326024	+	0.945362i	$0.605709\pi$
$692$	−7.15408	−	2.10063i	−0.271957	−	0.0798539i
$693$		0			0
$694$	18.3431	+	11.7884i	0.696296	+	0.447482i
$695$	1.00078	−	6.96060i	0.0379619	−	0.264031i
$696$		0			0
$697$	4.71966	+	10.3346i	0.178770	+	0.391452i
$698$	−22.5710	−	26.0483i	−0.854324	−	0.985943i
$699$		0			0
$700$	−0.571488	+	1.25138i	−0.0216002	+	0.0472979i
$701$	24.0907	−	7.07366i	0.909892	−	0.267168i	0.206897	−	0.978363i	$-0.433664\pi$
$701$	24.0907	−	7.07366i	0.909892	−	0.267168i	0.702995	+	0.711194i	$0.251845\pi$
$702$		0			0
$703$	−10.5735	+	23.1528i	−0.398788	+	0.873223i
$704$	2.07730	+	14.4480i	0.0782913	+	0.544528i
$705$		0			0
$706$	−19.6212	−	42.9644i	−0.738454	−	1.61699i
$707$	2.64136	−	1.69750i	0.0993387	−	0.0638411i
$708$		0			0
$709$	−36.0468	−	23.1659i	−1.35377	−	0.870013i	−0.355851	−	0.934543i	$-0.615809\pi$
$709$	−36.0468	−	23.1659i	−1.35377	−	0.870013i	−0.997916	+	0.0645293i	$0.979445\pi$
$710$	3.47725	−	4.01296i	0.130499	−	0.150604i
$711$		0			0
$712$	6.35664			0.238225
$713$	−25.3633	+	8.56046i	−0.949862	+	0.320592i
$714$		0			0
$715$	3.47618	+	1.02070i	0.130002	+	0.0381719i
$716$	−1.41847	+	1.63700i	−0.0530108	+	0.0611777i
$717$		0			0
$718$	−6.67871	+	46.4515i	−0.249247	+	1.73355i
$719$	−12.1284	+	7.79448i	−0.452315	+	0.290685i	−0.746895	−	0.664942i	$-0.768456\pi$
$719$	−12.1284	+	7.79448i	−0.452315	+	0.290685i	0.294581	+	0.955627i	$0.404820\pi$
$720$		0			0
$721$	4.33633	+	5.00439i	0.161493	+	0.186373i
$722$	−8.08639	−	56.2421i	−0.300944	−	2.09311i
$723$		0			0
$724$	−6.00990	+	1.76467i	−0.223356	+	0.0655833i
$725$	16.3321	−	4.79555i	0.606561	−	0.178102i
$726$		0			0
$727$	−2.80380	−	19.5008i	−0.103987	−	0.723246i	−0.973392	−	0.229146i	$-0.926407\pi$
$727$	−2.80380	−	19.5008i	−0.103987	−	0.723246i	0.869405	−	0.494100i	$-0.164502\pi$
$728$	1.46671	+	1.69267i	0.0543599	+	0.0627346i
$729$		0			0
$730$	−0.00606141	+	0.00389543i	−0.000224343	+	0.000144176i
$731$	−1.20075	+	8.35143i	−0.0444115	+	0.308889i
$732$		0			0
$733$	15.3498	−	17.7146i	0.566956	−	0.654302i	−0.397793	−	0.917475i	$-0.630224\pi$
$733$	15.3498	−	17.7146i	0.566956	−	0.654302i	0.964749	+	0.263173i	$0.0847691\pi$
$734$	23.1664	+	6.80228i	0.855088	+	0.251077i
$735$		0			0
$736$	15.3557	+	3.85053i	0.566018	+	0.141933i
$737$	−43.1287			−1.58867
$738$		0			0
$739$	1.33631	−	1.54218i	0.0491570	−	0.0567302i	−0.730639	−	0.682764i	$-0.760778\pi$
$739$	1.33631	−	1.54218i	0.0491570	−	0.0567302i	0.779796	+	0.626034i	$0.215323\pi$
$740$	−0.922543	−	0.592883i	−0.0339134	−	0.0217948i
$741$		0			0
$742$	4.84800	−	3.11562i	0.177976	−	0.114378i
$743$	−18.5746	−	40.6727i	−0.681436	−	1.49214i	−0.861114	−	0.508412i	$-0.830233\pi$
$743$	−18.5746	−	40.6727i	−0.681436	−	1.49214i	0.179678	−	0.983726i	$-0.442495\pi$
$744$		0			0
$745$	0.606354	+	4.21728i	0.0222151	+	0.154509i
$746$	−22.1968	+	48.6042i	−0.812683	+	1.77953i
$747$		0			0
$748$	2.11526	−	0.621096i	0.0773416	−	0.0227095i
$749$	2.41306	−	5.28387i	0.0881714	−	0.193069i
$750$		0			0
$751$	35.7344	+	41.2397i	1.30397	+	1.50486i	0.722742	+	0.691118i	$0.242882\pi$
$751$	35.7344	+	41.2397i	1.30397	+	1.50486i	0.581227	+	0.813742i	$0.302573\pi$
$752$	21.7175	+	47.5546i	0.791955	+	1.73414i
$753$		0			0
$754$	−1.69932	+	11.8190i	−0.0618856	+	0.430424i
$755$	1.99864	+	1.28444i	0.0727378	+	0.0467457i
$756$		0			0
$757$	−46.5029	−	13.6545i	−1.69018	−	0.496281i	−0.711673	−	0.702511i	$-0.752062\pi$
$757$	−46.5029	−	13.6545i	−1.69018	−	0.496281i	−0.978504	+	0.206230i	$0.933880\pi$
$758$	−30.4079			−1.10446
$759$		0			0
$760$	−8.74641			−0.317265
$761$	−41.4432	−	12.1688i	−1.50232	−	0.441120i	−0.575868	−	0.817542i	$-0.695336\pi$
$761$	−41.4432	−	12.1688i	−1.50232	−	0.441120i	−0.926448	+	0.376423i	$0.877154\pi$
$762$		0			0
$763$	5.08274	+	3.26648i	0.184008	+	0.118255i
$764$	−0.574988	+	3.99913i	−0.0208023	+	0.144683i
$765$		0			0
$766$	−12.3125	−	26.9605i	−0.444867	−	0.974124i
$767$	−1.26359	−	1.45826i	−0.0456254	−	0.0526545i
$768$		0			0
$769$	−20.6411	+	45.1977i	−0.744337	+	1.62987i	0.0319500	+	0.999489i	$0.489828\pi$
$769$	−20.6411	+	45.1977i	−0.744337	+	1.62987i	−0.776287	+	0.630380i	$0.782899\pi$
$770$	1.32077	−	0.387814i	0.0475974	−	0.0139759i
$771$		0			0
$772$	−3.33024	+	7.29222i	−0.119858	+	0.262453i
$773$	1.52790	+	10.6267i	0.0549546	+	0.382217i	0.998674	+	0.0514717i	$0.0163912\pi$
$773$	1.52790	+	10.6267i	0.0549546	+	0.382217i	−0.943720	+	0.330746i	$0.892700\pi$
$774$		0			0
$775$	−10.9502	−	23.9776i	−0.393342	−	0.861300i
$776$	−34.8062	+	22.3686i	−1.24947	+	0.802985i
$777$		0			0
$778$	6.05647	+	3.89226i	0.217135	+	0.139544i
$779$	−50.1228	+	57.8448i	−1.79584	+	2.07251i
$780$		0			0
$781$	20.9258			0.748785
$782$	−0.868529	+	8.41146i	−0.0310585	+	0.300793i
$783$		0			0
$784$	−31.4328	−	9.22950i	−1.12260	−	0.329625i
$785$	−0.716571	+	0.826968i	−0.0255755	+	0.0295157i
$786$		0			0
$787$	−5.48677	+	38.1613i	−0.195582	+	1.36030i	0.621334	+	0.783546i	$0.286591\pi$
$787$	−5.48677	+	38.1613i	−0.195582	+	1.36030i	−0.816916	+	0.576757i	$0.804318\pi$
$788$	9.70799	−	6.23894i	0.345833	−	0.222253i
$789$		0			0
$790$	−5.75279	−	6.63908i	−0.204675	−	0.236208i
$791$	0.215118	+	1.49618i	0.00764871	+	0.0531980i
$792$		0			0
$793$	−11.3020	+	3.31858i	−0.401347	+	0.117846i
$794$	22.0704	−	6.48045i	0.783248	−	0.229982i
$795$		0			0
$796$	−1.99949	−	13.9068i	−0.0708701	−	0.492913i
$797$	−20.0127	−	23.0959i	−0.708886	−	0.818098i	0.281038	−	0.959697i	$-0.409321\pi$
$797$	−20.0127	−	23.0959i	−0.708886	−	0.818098i	−0.989924	+	0.141598i	$0.954776\pi$
$798$		0			0
$799$	−9.92847	+	6.38064i	−0.351244	+	0.225731i
$800$	−2.21855	+	15.4303i	−0.0784375	+	0.545545i
$801$		0			0
$802$	−37.9032	+	43.7426i	−1.33841	+	1.54461i
$803$	−0.0272449	−	0.00799982i	−0.000961451	−	0.000282308i
$804$		0			0
$805$	−0.125511	+	1.21553i	−0.00442366	+	0.0428420i
$806$	18.4911			0.651322
$807$		0			0
$808$	9.58475	−	11.0614i	0.337190	−	0.389138i
$809$	3.73925	+	2.40307i	0.131465	+	0.0844874i	0.604720	−	0.796438i	$-0.293285\pi$
$809$	3.73925	+	2.40307i	0.131465	+	0.0844874i	−0.473255	+	0.880925i	$0.656921\pi$
$810$		0			0
$811$	27.3210	−	17.5582i	0.959371	−	0.616551i	0.0355474	−	0.999368i	$-0.488683\pi$
$811$	27.3210	−	17.5582i	0.959371	−	0.616551i	0.923824	+	0.382817i	$0.125046\pi$
$812$	0.436179	+	0.955100i	0.0153069	+	0.0335174i
$813$		0			0
$814$	−2.65751	−	18.4834i	−0.0931457	−	0.647843i
$815$	3.78715	−	8.29271i	0.132658	−	0.290481i
$816$		0			0
$817$	−54.5385	+	16.0140i	−1.90806	+	0.560257i
$818$	7.86820	−	17.2290i	0.275105	−	0.602396i
$819$		0			0
$820$	−2.15952	−	2.49222i	−0.0754138	−	0.0870322i
$821$	−14.0204	−	30.7003i	−0.489314	−	1.07145i	−0.979796	−	0.199997i	$-0.935907\pi$
$821$	−14.0204	−	30.7003i	−0.489314	−	1.07145i	0.490482	−	0.871451i	$-0.336821\pi$
$822$		0			0
$823$	−2.52621	+	17.5702i	−0.0880581	+	0.612458i	0.897231	+	0.441562i	$0.145575\pi$
$823$	−2.52621	+	17.5702i	−0.0880581	+	0.612458i	−0.985289	+	0.170896i	$0.945334\pi$
$824$	25.9675	+	16.6883i	0.904622	+	0.581365i
$825$		0			0
$826$	−0.703435	−	0.206547i	−0.0244756	−	0.00718670i
$827$	17.7946			0.618778			0.309389	−	0.950936i	$-0.399875\pi$
$827$	17.7946			0.618778			0.309389	+	0.950936i	$0.399875\pi$
$828$		0			0
$829$	−47.4537			−1.64814			−0.824068	−	0.566491i	$-0.808301\pi$
$829$	−47.4537			−1.64814			−0.824068	+	0.566491i	$0.808301\pi$
$830$	−4.93598	−	1.44933i	−0.171330	−	0.0503071i
$831$		0			0
$832$	7.52994	+	4.83920i	0.261054	+	0.167769i
$833$	1.05249	−	7.32026i	0.0364668	−	0.253632i
$834$		0			0
$835$	−3.76757	−	8.24982i	−0.130382	−	0.285497i
$836$	9.72587	+	11.2243i	0.336376	+	0.388199i
$837$		0			0
$838$	21.5697	−	47.2310i	0.745113	−	1.63157i
$839$	1.56477	−	0.459459i	0.0540220	−	0.0158623i	−0.254610	−	0.967044i	$-0.581947\pi$
$839$	1.56477	−	0.459459i	0.0540220	−	0.0158623i	0.308632	+	0.951182i	$0.400129\pi$
$840$		0			0
$841$	−6.65017	+	14.5618i	−0.229316	+	0.502132i
$842$	5.91082	+	41.1107i	0.203700	+	1.41677i
$843$		0			0
$844$	−0.512234	−	1.12164i	−0.0176318	−	0.0386083i
$845$	−3.89212	+	2.50131i	−0.133893	+	0.0860478i
$846$		0			0
$847$	0.0876085	+	0.0563025i	0.00301026	+	0.00193458i
$848$	23.4177	−	27.0255i	0.804168	−	0.928059i
$849$		0			0
$850$	−8.32687			−0.285609
$851$	16.0793	+	4.03198i	0.551191	+	0.138215i
$852$		0			0
$853$	21.2486	+	6.23916i	0.727539	+	0.213625i	0.624469	−	0.781049i	$-0.285315\pi$
$853$	21.2486	+	6.23916i	0.727539	+	0.213625i	0.103070	+	0.994674i	$0.467133\pi$
$854$	−2.93083	+	3.38236i	−0.100291	+	0.115742i
$855$		0			0
$856$	3.85361	−	26.8024i	0.131714	−	0.916088i
$857$	19.0420	−	12.2376i	0.650463	−	0.418027i	−0.173372	−	0.984856i	$-0.555466\pi$
$857$	19.0420	−	12.2376i	0.650463	−	0.418027i	0.823835	+	0.566829i	$0.191830\pi$
$858$		0			0
$859$	−0.824575	−	0.951611i	−0.0281341	−	0.0324685i	0.741508	−	0.670944i	$-0.234111\pi$
$859$	−0.824575	−	0.951611i	−0.0281341	−	0.0324685i	−0.769642	+	0.638475i	$0.779565\pi$
$860$	−0.348525	−	2.42405i	−0.0118846	−	0.0826593i
$861$		0			0
$862$	−9.30207	+	2.73133i	−0.316830	+	0.0930296i
$863$	7.61520	−	2.23603i	0.259225	−	0.0761152i	−0.149538	−	0.988756i	$-0.547779\pi$
$863$	7.61520	−	2.23603i	0.259225	−	0.0761152i	0.408763	+	0.912641i	$0.365960\pi$
$864$		0			0
$865$	−0.928144	−	6.45538i	−0.0315578	−	0.219490i
$866$	31.3396	+	36.1678i	1.06496	+	1.22903i
$867$		0			0
$868$	1.36788	−	0.879083i	0.0464289	−	0.0298380i
$869$	4.92693	−	34.2675i	0.167135	−	1.16245i
$870$		0			0
$871$	−17.3193	+	19.9875i	−0.586842	+	0.677251i
$872$	27.0236	+	7.93485i	0.915135	+	0.268708i
$873$		0			0
$874$	−53.9766	+	18.2178i	−1.82579	+	0.616228i
$875$	−2.47733			−0.0837491
$876$		0			0
$877$	9.70823	−	11.2039i	0.327824	−	0.378329i	−0.567781	−	0.823180i	$-0.692198\pi$
$877$	9.70823	−	11.2039i	0.327824	−	0.378329i	0.895605	+	0.444851i	$0.146743\pi$
$878$	5.10125	+	3.27837i	0.172159	+	0.110640i
$879$		0			0
$880$	7.18577	−	4.61801i	0.242232	−	0.155673i
$881$	10.8447	+	23.7466i	0.365368	+	0.800043i	0.999637	+	0.0269316i	$0.00857362\pi$
$881$	10.8447	+	23.7466i	0.365368	+	0.800043i	−0.634270	+	0.773112i	$0.718699\pi$
$882$		0			0
$883$	−1.30435	−	9.07195i	−0.0438949	−	0.305296i	−0.999928	−	0.0120354i	$-0.996169\pi$
$883$	−1.30435	−	9.07195i	−0.0438949	−	0.305296i	0.956033	−	0.293260i	$-0.0947402\pi$
$884$	0.561590	−	1.22971i	0.0188883	−	0.0413596i
$885$		0			0
$886$	−18.3623	+	5.39166i	−0.616894	+	0.181136i
$887$	−21.1375	+	46.2846i	−0.709727	+	1.55408i	0.118038	+	0.993009i	$0.462340\pi$
$887$	−21.1375	+	46.2846i	−0.709727	+	1.55408i	−0.827765	+	0.561075i	$0.810388\pi$
$888$		0			0
$889$	−3.46128	−	3.99453i	−0.116088	−	0.133972i
$890$	−0.995214	−	2.17922i	−0.0333597	−	0.0730475i
$891$		0			0
$892$	−0.0552053	+	0.383961i	−0.00184841	+	0.0128560i
$893$	−66.8867	−	42.9855i	−2.23828	−	1.43845i
$894$		0			0
$895$	−1.81789	−	0.533780i	−0.0607652	−	0.0178423i
$896$	6.59425			0.220298
$897$		0			0
$898$	47.6679			1.59070
$899$	−19.3036	−	5.66806i	−0.643812	−	0.189040i
$900$		0			0
$901$	6.79127	+	4.36448i	0.226250	+	0.145402i
$902$	7.99143	−	55.5816i	0.266085	−	1.85066i
$903$		0			0
$904$	2.92711	+	6.40948i	0.0973543	+	0.213176i
$905$	−3.58779	−	4.14053i	−0.119262	−	0.137636i
$906$		0			0
$907$	15.9556	−	34.9378i	0.529795	−	1.16009i	−0.435801	−	0.900043i	$-0.643535\pi$
$907$	15.9556	−	34.9378i	0.529795	−	1.16009i	0.965596	−	0.260047i	$-0.0837380\pi$
$908$	14.3840	−	4.22351i	0.477349	−	0.140162i
$909$		0			0
$910$	0.350658	−	0.767834i	0.0116242	−	0.0254535i
$911$	0.0791753	+	0.550676i	0.00262319	+	0.0182447i	0.991091	−	0.133186i	$-0.0425209\pi$
$911$	0.0791753	+	0.550676i	0.00262319	+	0.0182447i	−0.988468	+	0.151431i	$0.951612\pi$
$912$		0			0
$913$	−8.42190	−	18.4414i	−0.278724	−	0.610321i
$914$	−35.9044	+	23.0744i	−1.18761	+	0.763233i
$915$		0			0
$916$	1.47458	+	0.947655i	0.0487215	+	0.0313114i
$917$	−0.186381	+	0.215095i	−0.00615483	+	0.00710305i
$918$		0			0
$919$	−25.5118			−0.841555			−0.420778	−	0.907164i	$-0.638243\pi$
$919$	−25.5118			−0.841555			−0.420778	+	0.907164i	$0.638243\pi$
$920$	1.03500	+	5.60159i	0.0341230	+	0.184679i
$921$		0			0
$922$	61.6098	+	18.0903i	2.02901	+	0.595771i
$923$	8.40324	−	9.69786i	0.276596	−	0.319209i
$924$		0			0
$925$	−2.32309	+	16.1575i	−0.0763828	+	0.531254i
$926$	40.2097	−	25.8412i	1.32137	−	0.849194i
$927$		0			0
$928$	7.79158	+	8.99196i	0.255771	+	0.295176i
$929$	−3.40247	−	23.6647i	−0.111631	−	0.776413i	−0.966333	−	0.257294i	$-0.917169\pi$
$929$	−3.40247	−	23.6647i	−0.111631	−	0.776413i	0.854702	−	0.519119i	$-0.173740\pi$
$930$		0			0
$931$	47.8045	−	14.0367i	1.56673	−	0.460034i
$932$	3.52897	−	1.03620i	0.115595	−	0.0339418i
$933$		0			0
$934$	0.958319	+	6.66525i	0.0313571	+	0.218094i
$935$	1.26277	+	1.45731i	0.0412969	+	0.0476592i
$936$		0			0
$937$	32.0799	−	20.6165i	1.04800	−	0.673511i	0.101050	−	0.994881i	$-0.467780\pi$
$937$	32.0799	−	20.6165i	1.04800	−	0.673511i	0.946954	+	0.321370i	$0.104143\pi$
$938$	−1.43007	+	9.94637i	−0.0466935	+	0.324760i
$939$		0			0
$940$	2.24329	−	2.58889i	0.0731679	−	0.0844403i
$941$	13.5602	+	3.98163i	0.442050	+	0.129797i	0.495181	−	0.868790i	$-0.335102\pi$
$941$	13.5602	+	3.98163i	0.442050	+	0.129797i	−0.0531310	+	0.998588i	$0.516920\pi$
$942$		0			0
$943$	42.9776	+	25.2558i	1.39954	+	0.822444i
$944$	−4.54927			−0.148066
$945$		0			0
$946$	27.3085	−	31.5157i	0.887876	−	1.02466i
$947$	−16.2633	−	10.4518i	−0.528487	−	0.339638i	0.249034	−	0.968495i	$-0.419887\pi$
$947$	−16.2633	−	10.4518i	−0.528487	−	0.339638i	−0.777521	+	0.628857i	$0.783523\pi$
$948$		0			0
$949$	−0.0146482	+	0.00941384i	−0.000475502	+	0.000305586i
$950$	−23.3035	−	51.0276i	−0.756066	−	1.65555i
$951$		0			0
$952$	0.169652	+	1.17996i	0.00549847	+	0.0382427i
$953$	−5.19078	+	11.3662i	−0.168146	+	0.368188i	−0.974881	−	0.222724i	$-0.928505\pi$
$953$	−5.19078	+	11.3662i	−0.168146	+	0.368188i	0.806735	+	0.590913i	$0.201232\pi$
$954$		0			0
$955$	−3.39081	+	0.995631i	−0.109724	+	0.0322179i
$956$	−7.50522	+	16.4341i	−0.242736	+	0.531518i
$957$		0			0
$958$	17.3633	+	20.0384i	0.560984	+	0.647410i
$959$	−3.60121	−	7.88554i	−0.116289	−	0.254637i
$960$		0			0
$961$	−0.0221369	+	0.153966i	−0.000714095	+	0.00496664i
$962$	−9.63312	−	6.19083i	−0.310584	−	0.199600i
$963$		0			0
$964$	−1.75903	−	0.516499i	−0.0566546	−	0.0166353i
$965$	−7.01208			−0.225727
$966$		0			0
$967$	9.35247			0.300755			0.150378	−	0.988629i	$-0.451951\pi$
$967$	9.35247			0.300755			0.150378	+	0.988629i	$0.451951\pi$
$968$	0.465792	+	0.136769i	0.0149711	+	0.00439591i
$969$		0			0
$970$	13.1179	+	8.43034i	0.421189	+	0.270682i
$971$	−3.37468	+	23.4714i	−0.108299	+	0.753233i	0.861223	+	0.508227i	$0.169699\pi$
$971$	−3.37468	+	23.4714i	−0.108299	+	0.753233i	−0.969522	+	0.245006i	$0.921210\pi$
$972$		0			0
$973$	−2.68232	−	5.87345i	−0.0859911	−	0.188294i
$974$	−23.6547	−	27.2990i	−0.757946	−	0.874716i
$975$		0			0
$976$	−11.5368	+	25.2620i	−0.369283	+	0.808616i
$977$	46.3820	−	13.6190i	1.48389	−	0.435710i	0.563306	−	0.826248i	$-0.309529\pi$
$977$	46.3820	−	13.6190i	1.48389	−	0.435710i	0.920587	+	0.390538i	$0.127711\pi$
$978$		0			0
$979$	3.92205	−	8.58809i	0.125349	−	0.274476i
$980$	0.305492	+	2.12474i	0.00975859	+	0.0678725i
$981$		0			0
$982$	8.01962	+	17.5605i	0.255916	+	0.560379i
$983$	30.2232	−	19.4233i	0.963972	−	0.619507i	0.0388772	−	0.999244i	$-0.487622\pi$
$983$	30.2232	−	19.4233i	0.963972	−	0.619507i	0.925094	+	0.379737i	$0.123986\pi$
$984$		0			0
$985$	8.49146	+	5.45713i	0.270560	+	0.173879i
$986$	−4.16187	+	4.80306i	−0.132541	+	0.152961i
$987$		0			0
$988$	9.10740			0.289745
$989$	16.7098	+	33.0339i	0.531342	+	1.05042i
$990$		0			0
$991$	−24.8432	−	7.29461i	−0.789169	−	0.231721i	−0.137778	−	0.990463i	$-0.543996\pi$
$991$	−24.8432	−	7.29461i	−0.789169	−	0.231721i	−0.651391	+	0.758742i	$0.725814\pi$
$992$	12.0660	−	13.9249i	0.383096	−	0.442116i
$993$		0			0
$994$	0.693864	−	4.82593i	0.0220080	−	0.153069i
$995$	10.3383	−	6.64403i	0.327746	−	0.210630i
$996$		0			0
$997$	−20.0725	−	23.1648i	−0.635701	−	0.733638i	0.342908	−	0.939369i	$-0.388588\pi$
$997$	−20.0725	−	23.1648i	−0.635701	−	0.733638i	−0.978609	+	0.205731i	$0.934043\pi$
$998$	−2.57631	−	17.9186i	−0.0815516	−	0.567204i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.d.64.1		20
3.2	odd	2		69.2.e.c.64.2	yes	20
23.3	even	11		4761.2.a.bt.1.8		10
23.9	even	11	inner	207.2.i.d.55.1		20
23.20	odd	22		4761.2.a.bu.1.8		10
69.20	even	22		1587.2.a.t.1.3		10
69.26	odd	22		1587.2.a.u.1.3		10
69.32	odd	22		69.2.e.c.55.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.55.2	✓	20	69.32	odd	22
69.2.e.c.64.2	yes	20	3.2	odd	2
207.2.i.d.55.1		20	23.9	even	11	inner
207.2.i.d.64.1		20	1.1	even	1	trivial
1587.2.a.t.1.3		10	69.20	even	22
1587.2.a.u.1.3		10	69.26	odd	22
4761.2.a.bt.1.8		10	23.3	even	11
4761.2.a.bu.1.8		10	23.20	odd	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54781 - 0.454477i) q^{2} +(0.506650 + 0.325604i) q^{4} +(-0.0749695 + 0.521424i) q^{5} +(0.200934 + 0.439985i) q^{7} +(1.47656 + 1.70404i) q^{8} +(0.353014 - 0.772992i) q^{10} +(3.21327 - 0.943501i) q^{11} +(0.853105 - 1.86804i) q^{13} +(-0.111045 - 0.772332i) q^{14} +(-2.01136 - 4.40426i) q^{16} +(0.919522 - 0.590941i) q^{17} +(6.19469 + 3.98109i) q^{19} +(-0.207761 + 0.239769i) q^{20} -5.40232 q^{22} +(1.81662 - 4.43846i) q^{23} +(4.53120 + 1.33048i) q^{25} +(-2.16942 + 2.50365i) q^{26} +(-0.0414575 + 0.288343i) q^{28} +(3.03219 - 1.94867i) q^{29} +(-3.65525 - 4.21838i) q^{31} +(0.469783 + 3.26741i) q^{32} +(-1.69181 + 0.496761i) q^{34} +(-0.244483 + 0.0717866i) q^{35} +(0.491920 + 3.42138i) q^{37} +(-7.77887 - 8.97730i) q^{38} +(-0.999226 + 0.642164i) q^{40} +(-1.47926 + 10.2885i) q^{41} +(-5.05496 + 5.83373i) q^{43} +(1.93521 + 0.568229i) q^{44} +(-4.82895 + 6.04426i) q^{46} -10.7974 q^{47} +(4.43081 - 5.11343i) q^{49} +(-6.40875 - 4.11866i) q^{50} +(1.04047 - 0.668668i) q^{52} +(3.06811 + 6.71822i) q^{53} +(0.251067 + 1.74621i) q^{55} +(-0.453061 + 0.992066i) q^{56} +(-5.57887 + 1.63811i) q^{58} +(0.390317 - 0.854675i) q^{59} +(-3.75616 - 4.33483i) q^{61} +(3.74046 + 8.19046i) q^{62} +(-0.620289 + 4.31421i) q^{64} +(0.910084 + 0.584876i) q^{65} +(-12.3567 - 3.62825i) q^{67} +0.658289 q^{68} +0.411037 q^{70} +(5.99541 + 1.76041i) q^{71} +(-0.00713288 - 0.00458402i) q^{73} +(0.793542 - 5.51920i) q^{74} +(1.84228 + 4.03404i) q^{76} +(1.06078 + 1.22421i) q^{77} +(4.29440 - 9.40343i) q^{79} +(2.44728 - 0.718585i) q^{80} +(6.96548 - 15.2523i) q^{82} +(-0.861534 - 5.99210i) q^{83} +(0.239195 + 0.523763i) q^{85} +(10.4754 - 6.73213i) q^{86} +(6.35236 + 4.08241i) q^{88} +(1.84618 - 2.13061i) q^{89} +0.993327 q^{91} +(2.36557 - 1.65724i) q^{92} +(16.7123 + 4.90718i) q^{94} +(-2.54025 + 2.93160i) q^{95} +(-2.61142 + 18.1628i) q^{97} +(-9.18198 + 5.90090i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29}+ \cdots - 85 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Introduction

L-functions

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