LMFDB - Embedded newform 936.2.ed.e.19.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(19,936)] 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("936.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ed (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	936.19
Dual form			936.2.ed.e.739.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.764112 + 1.19001i) q^{2} +(-0.832266 - 1.81861i) q^{4} +(0.513065 + 0.513065i) q^{5} +(-1.43100 - 0.383434i) q^{7} +(2.80011 + 0.399211i) q^{8} +(-1.00259 + 0.218515i) q^{10} +(-1.43129 + 0.383513i) q^{11} +(-0.967164 - 3.47341i) q^{13} +(1.54973 - 1.40992i) q^{14} +(-2.61467 + 3.02713i) q^{16} +(-1.08804 + 0.628178i) q^{17} +(6.19113 + 1.65891i) q^{19} +(0.506057 - 1.36007i) q^{20} +(0.637280 - 1.99630i) q^{22} +(1.68941 - 2.92615i) q^{23} -4.47353i q^{25} +(4.87243 + 1.50314i) q^{26} +(0.493654 + 2.92154i) q^{28} +(-5.98829 - 3.45734i) q^{29} +(1.65000 + 1.65000i) q^{31} +(-1.60443 - 5.42455i) q^{32} +(0.0838407 - 1.77478i) q^{34} +(-0.537467 - 0.930920i) q^{35} +(-0.944898 - 3.52641i) q^{37} +(-6.70484 + 6.09994i) q^{38} +(1.23182 + 1.64146i) q^{40} +(-0.503062 - 1.87745i) q^{41} +(7.93214 - 4.57963i) q^{43} +(1.88867 + 2.28377i) q^{44} +(2.19126 + 4.24633i) q^{46} +(2.96711 - 2.96711i) q^{47} +(-4.16145 - 2.40261i) q^{49} +(5.32356 + 3.41828i) q^{50} +(-5.51184 + 4.64970i) q^{52} +0.513310i q^{53} +(-0.931112 - 0.537578i) q^{55} +(-3.85388 - 1.64493i) q^{56} +(8.69000 - 4.48435i) q^{58} +(3.60773 - 13.4642i) q^{59} +(12.2267 - 7.05906i) q^{61} +(-3.22431 + 0.702740i) q^{62} +(7.68126 + 2.23567i) q^{64} +(1.28587 - 2.27830i) q^{65} +(1.88176 + 7.02284i) q^{67} +(2.04795 + 1.45590i) q^{68} +(1.51849 + 0.0717338i) q^{70} +(-0.979852 + 3.65686i) q^{71} +(-4.42114 - 4.42114i) q^{73} +(4.91848 + 1.57013i) q^{74} +(-2.13577 - 12.6399i) q^{76} +2.19522 q^{77} +3.24902i q^{79} +(-2.89461 + 0.211622i) q^{80} +(2.61859 + 0.835933i) q^{82} +(2.89926 - 2.89926i) q^{83} +(-0.880529 - 0.235937i) q^{85} +(-0.611226 + 12.9387i) q^{86} +(-4.16088 + 0.502494i) q^{88} +(2.05252 - 0.549972i) q^{89} +(0.0521823 + 5.34128i) q^{91} +(-6.72756 - 0.637043i) q^{92} +(1.26370 + 5.79811i) q^{94} +(2.32532 + 4.02758i) q^{95} +(1.09430 + 0.293217i) q^{97} +(6.03896 - 3.11632i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{8} + 28 q^{14} + 12 q^{16} - 8 q^{19} + 4 q^{20} + 10 q^{22} - 34 q^{26} - 14 q^{28} + 30 q^{32} + 56 q^{34} - 28 q^{40} - 40 q^{41} + 44 q^{44} - 18 q^{46} + 24 q^{49} + 72 q^{50} + 32 q^{52}+ \cdots - 4 q^{98}+O(q^{100}) $ 56 * q + 12 * q^8 + 28 * q^14 + 12 * q^16 - 8 * q^19 + 4 * q^20 + 10 * q^22 - 34 * q^26 - 14 * q^28 + 30 * q^32 + 56 * q^34 - 28 * q^40 - 40 * q^41 + 44 * q^44 - 18 * q^46 + 24 * q^49 + 72 * q^50 + 32 * q^52 + 54 * q^56 - 16 * q^58 - 32 * q^59 - 48 * q^65 - 24 * q^67 + 26 * q^68 + 64 * q^70 + 44 * q^73 + 6 * q^74 + 6 * q^76 + 4 * q^80 - 30 * q^82 - 40 * q^83 + 28 * q^86 + 126 * q^88 + 68 * q^89 - 72 * q^91 - 52 * q^92 + 34 * q^94 - 4 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.764112	+	1.19001i	−0.540309	+	0.841467i
$2$	−0.764112	+	1.19001i	−0.540309	+	0.841467i
$3$		0			0
$3$		0			0
$4$	−0.832266	−	1.81861i	−0.416133	−	0.909304i
$5$	0.513065	+	0.513065i	0.229449	+	0.229449i	0.812463	−	0.583013i	$-0.198126\pi$
$5$	0.513065	+	0.513065i	0.229449	+	0.229449i	−0.583013	+	0.812463i	$0.698126\pi$
$6$		0			0
$7$	−1.43100	−	0.383434i	−0.540866	−	0.144925i	−0.0219645	−	0.999759i	$-0.506992\pi$
$7$	−1.43100	−	0.383434i	−0.540866	−	0.144925i	−0.518901	+	0.854834i	$0.673659\pi$
$8$	2.80011	+	0.399211i	0.989989	+	0.141142i
$9$		0			0
$10$	−1.00259	+	0.218515i	−0.317048	+	0.0691006i
$11$	−1.43129	+	0.383513i	−0.431550	+	0.115634i	−0.468054	−	0.883700i	$-0.655045\pi$
$11$	−1.43129	+	0.383513i	−0.431550	+	0.115634i	0.0365035	+	0.999334i	$0.488378\pi$
$12$		0			0
$13$	−0.967164	−	3.47341i	−0.268243	−	0.963351i
$13$	−0.967164	−	3.47341i	−0.268243	−	0.963351i
$14$	1.54973	−	1.40992i	0.414184	−	0.376817i
$15$		0			0
$16$	−2.61467	+	3.02713i	−0.653666	+	0.756783i
$17$	−1.08804	+	0.628178i	−0.263888	+	0.152356i	−0.626107	−	0.779737i	$-0.715353\pi$
$17$	−1.08804	+	0.628178i	−0.263888	+	0.152356i	0.362219	+	0.932093i	$0.382019\pi$
$18$		0			0
$19$	6.19113	+	1.65891i	1.42034	+	0.380580i	0.885605	−	0.464439i	$-0.153744\pi$
$19$	6.19113	+	1.65891i	1.42034	+	0.380580i	0.534737	+	0.845018i	$0.320411\pi$
$20$	0.506057	−	1.36007i	0.113158	−	0.304121i
$21$		0			0
$22$	0.637280	−	1.99630i	0.135869	−	0.425613i
$23$	1.68941	−	2.92615i	0.352267	−	0.610144i	−0.634379	−	0.773022i	$-0.718744\pi$
$23$	1.68941	−	2.92615i	0.352267	−	0.610144i	0.986646	+	0.162878i	$0.0520776\pi$
$24$		0			0
$25$		−	4.47353i		−	0.894706i
$26$	4.87243	+	1.50314i	0.955562	+	0.294789i
$27$		0			0
$28$	0.493654	+	2.92154i	0.0932918	+	0.552119i
$29$	−5.98829	−	3.45734i	−1.11200	−	0.642012i	−0.172651	−	0.984983i	$-0.555233\pi$
$29$	−5.98829	−	3.45734i	−1.11200	−	0.642012i	−0.939346	+	0.342971i	$0.888567\pi$
$30$		0			0
$31$	1.65000	+	1.65000i	0.296349	+	0.296349i	0.839582	−	0.543233i	$-0.182800\pi$
$31$	1.65000	+	1.65000i	0.296349	+	0.296349i	−0.543233	+	0.839582i	$0.682800\pi$
$32$	−1.60443	−	5.42455i	−0.283626	−	0.958935i
$33$		0			0
$34$	0.0838407	−	1.77478i	0.0143786	−	0.304372i
$35$	−0.537467	−	0.930920i	−0.0908485	−	0.157354i
$36$		0			0
$37$	−0.944898	−	3.52641i	−0.155340	−	0.579738i	−0.999076	−	0.0429788i	$-0.986315\pi$
$37$	−0.944898	−	3.52641i	−0.155340	−	0.579738i	0.843736	−	0.536759i	$-0.180351\pi$
$38$	−6.70484	+	6.09994i	−1.08767	+	0.989541i
$39$		0			0
$40$	1.23182	+	1.64146i	0.194768	+	0.259538i
$41$	−0.503062	−	1.87745i	−0.0785651	−	0.293209i	0.915453	−	0.402425i	$-0.131833\pi$
$41$	−0.503062	−	1.87745i	−0.0785651	−	0.293209i	−0.994018	+	0.109216i	$0.965166\pi$
$42$		0			0
$43$	7.93214	−	4.57963i	1.20964	−	0.698386i	0.246960	−	0.969026i	$-0.420568\pi$
$43$	7.93214	−	4.57963i	1.20964	−	0.698386i	0.962681	+	0.270639i	$0.0872351\pi$
$44$	1.88867	+	2.28377i	0.284728	+	0.344291i
$45$		0			0
$46$	2.19126	+	4.24633i	0.323083	+	0.626087i
$47$	2.96711	−	2.96711i	0.432797	−	0.432797i	−0.456781	−	0.889579i	$-0.650998\pi$
$47$	2.96711	−	2.96711i	0.432797	−	0.432797i	0.889579	+	0.456781i	$0.150998\pi$
$48$		0			0
$49$	−4.16145	−	2.40261i	−0.594493	−	0.343231i
$50$	5.32356	+	3.41828i	0.752865	+	0.483417i
$51$		0			0
$52$	−5.51184	+	4.64970i	−0.764354	+	0.644797i
$53$			0.513310i			0.0705086i	0.999378	+	0.0352543i	$0.0112241\pi$
$53$			0.513310i			0.0705086i	−0.999378	+	0.0352543i	$0.988776\pi$
$54$		0			0
$55$	−0.931112	−	0.537578i	−0.125551	−	0.0724869i
$56$	−3.85388	−	1.64493i	−0.514996	−	0.219813i
$57$		0			0
$58$	8.69000	−	4.48435i	1.14105	−	0.588824i
$59$	3.60773	−	13.4642i	0.469687	−	1.75290i	−0.171176	−	0.985241i	$-0.554757\pi$
$59$	3.60773	−	13.4642i	0.469687	−	1.75290i	0.640863	−	0.767655i	$-0.278577\pi$
$60$		0			0
$61$	12.2267	−	7.05906i	1.56546	−	0.903820i	0.568775	−	0.822493i	$-0.307417\pi$
$61$	12.2267	−	7.05906i	1.56546	−	0.903820i	0.996687	−	0.0813276i	$-0.0259160\pi$
$62$	−3.22431	+	0.702740i	−0.409488	+	0.0892481i
$63$		0			0
$64$	7.68126	+	2.23567i	0.960158	+	0.279459i
$65$	1.28587	−	2.27830i	0.159492	−	0.282589i
$66$		0			0
$67$	1.88176	+	7.02284i	0.229894	+	0.857977i	0.980384	+	0.197095i	$0.0631507\pi$
$67$	1.88176	+	7.02284i	0.229894	+	0.857977i	−0.750490	+	0.660881i	$0.770183\pi$
$68$	2.04795	+	1.45590i	0.248350	+	0.176554i
$69$		0			0
$70$	1.51849	+	0.0717338i	0.181495	+	0.00857383i
$71$	−0.979852	+	3.65686i	−0.116287	+	0.433989i	−0.999380	−	0.0352090i	$-0.988790\pi$
$71$	−0.979852	+	3.65686i	−0.116287	+	0.433989i	0.883093	+	0.469198i	$0.155457\pi$
$72$		0			0
$73$	−4.42114	−	4.42114i	−0.517455	−	0.517455i	0.399345	−	0.916801i	$-0.369237\pi$
$73$	−4.42114	−	4.42114i	−0.517455	−	0.517455i	−0.916801	+	0.399345i	$0.869237\pi$
$74$	4.91848	+	1.57013i	0.571762	+	0.182524i
$75$		0			0
$76$	−2.13577	−	12.6399i	−0.244989	−	1.44989i
$77$	2.19522			0.250169
$78$		0			0
$79$			3.24902i			0.365543i	0.983155	+	0.182771i	$0.0585068\pi$
$79$			3.24902i			0.365543i	−0.983155	+	0.182771i	$0.941493\pi$
$80$	−2.89461	+	0.211622i	−0.323627	+	0.0236600i
$81$		0			0
$82$	2.61859	+	0.835933i	0.289175	+	0.0923134i
$83$	2.89926	−	2.89926i	0.318235	−	0.318235i	−0.529854	−	0.848089i	$-0.677753\pi$
$83$	2.89926	−	2.89926i	0.318235	−	0.318235i	0.848089	+	0.529854i	$0.177753\pi$
$84$		0			0
$85$	−0.880529	−	0.235937i	−0.0955068	−	0.0255910i
$86$	−0.611226	+	12.9387i	−0.0659102	+	1.39522i
$87$		0			0
$88$	−4.16088	+	0.502494i	−0.443551	+	0.0535660i
$89$	2.05252	−	0.549972i	0.217567	−	0.0582969i	−0.148389	−	0.988929i	$-0.547409\pi$
$89$	2.05252	−	0.549972i	0.217567	−	0.0582969i	0.365956	+	0.930632i	$0.380742\pi$
$90$		0			0
$91$	0.0521823	+	5.34128i	0.00547019	+	0.559919i
$92$	−6.72756	−	0.637043i	−0.701396	−	0.0664163i
$93$		0			0
$94$	1.26370	+	5.79811i	0.130341	+	0.598029i
$95$	2.32532	+	4.02758i	0.238573	+	0.413221i
$96$		0			0
$97$	1.09430	+	0.293217i	0.111109	+	0.0297716i	0.313945	−	0.949441i	$-0.398349\pi$
$97$	1.09430	+	0.293217i	0.111109	+	0.0297716i	−0.202836	+	0.979213i	$0.565016\pi$
$98$	6.03896	−	3.11632i	0.610027	−	0.314796i
$99$		0			0
$100$	−8.13559	+	3.72317i	−0.813559	+	0.372317i
$101$	−5.72724	+	9.91986i	−0.569881	+	0.987063i	0.426696	+	0.904395i	$0.359677\pi$
$101$	−5.72724	+	9.91986i	−0.569881	+	0.987063i	−0.996577	+	0.0826680i	$0.973656\pi$
$102$		0			0
$103$	2.48901			0.245249			0.122625	−	0.992453i	$-0.460869\pi$
$103$	2.48901			0.245249			0.122625	+	0.992453i	$0.460869\pi$
$104$	−1.32154	−	10.1120i	−0.129588	−	0.991568i
$105$		0			0
$106$	−0.610846	−	0.392226i	−0.0593307	−	0.0380964i
$107$	5.13018	−	8.88572i	0.495953	−	0.859015i	−0.504036	−	0.863682i	$-0.668152\pi$
$107$	5.13018	−	8.88572i	0.495953	−	0.859015i	0.999989	+	0.00466706i	$0.00148558\pi$
$108$		0			0
$109$	7.21056	+	7.21056i	0.690646	+	0.690646i	0.962374	−	0.271728i	$-0.0875951\pi$
$109$	7.21056	+	7.21056i	0.690646	+	0.690646i	−0.271728	+	0.962374i	$0.587595\pi$
$110$	1.35120	−	0.697266i	0.128832	−	0.0664817i
$111$		0			0
$112$	4.90228	−	3.32926i	0.463222	−	0.314586i
$113$	2.37145	+	4.10748i	0.223088	+	0.386399i	0.955744	−	0.294200i	$-0.0950531\pi$
$113$	2.37145	+	4.10748i	0.223088	+	0.386399i	−0.732656	+	0.680599i	$0.761720\pi$
$114$		0			0
$115$	2.36808	−	0.634526i	0.220825	−	0.0591698i
$116$	−1.30369	+	13.7678i	−0.121045	+	1.27831i
$117$		0			0
$118$	13.2659	+	14.5814i	1.22123	+	1.34233i
$119$	1.79784	−	0.481730i	0.164808	−	0.0441601i
$120$		0			0
$121$	−7.62477	+	4.40216i	−0.693161	+	0.400197i
$122$	−0.942148	+	19.9438i	−0.0852981	+	1.80563i
$123$		0			0
$124$	1.62747	−	4.37395i	0.146151	−	0.392792i
$125$	4.86053	−	4.86053i	0.434739	−	0.434739i
$126$		0			0
$127$	−9.40686	+	16.2932i	−0.834724	+	1.44578i	0.0595311	+	0.998226i	$0.481039\pi$
$127$	−9.40686	+	16.2932i	−0.834724	+	1.44578i	−0.894255	+	0.447558i	$0.852294\pi$
$128$	−8.52982	+	7.43251i	−0.753937	+	0.656947i
$129$		0			0
$130$	1.72867	+	3.27108i	0.151614	+	0.286893i
$131$	1.40105			0.122410			0.0612050	−	0.998125i	$-0.480506\pi$
$131$	1.40105			0.122410			0.0612050	+	0.998125i	$0.480506\pi$
$132$		0			0
$133$	−8.22340	−	4.74778i	−0.713059	−	0.411685i
$134$	−9.79516	−	3.12691i	−0.846173	−	0.270124i
$135$		0			0
$136$	−3.29740	+	1.32461i	−0.282750	+	0.113585i
$137$	4.33906	−	16.1936i	0.370711	−	1.38351i	−0.488800	−	0.872396i	$-0.662565\pi$
$137$	4.33906	−	16.1936i	0.370711	−	1.38351i	0.859511	−	0.511117i	$-0.170768\pi$
$138$		0			0
$139$	−7.57593	−	13.1219i	−0.642582	−	1.11298i	−0.984854	−	0.173384i	$-0.944530\pi$
$139$	−7.57593	−	13.1219i	−0.642582	−	1.11298i	0.342273	−	0.939601i	$-0.388803\pi$
$140$	−1.24566	+	1.75221i	−0.105278	+	0.148089i
$141$		0			0
$142$	−3.60299	−	3.96028i	−0.302357	−	0.332340i
$143$	2.71639	+	4.60054i	0.227156	+	0.384717i
$144$		0			0
$145$	−1.29854	−	4.84622i	−0.107838	−	0.402456i
$146$	8.63946	−	1.88297i	0.715007	−	0.155836i
$147$		0			0
$148$	−5.62674	+	4.65331i	−0.462515	+	0.382499i
$149$	2.01396	−	7.51621i	0.164990	−	0.615752i	−0.833051	−	0.553196i	$-0.813408\pi$
$149$	2.01396	−	7.51621i	0.164990	−	0.615752i	0.998041	−	0.0625561i	$-0.0199252\pi$
$150$		0			0
$151$	−6.96070	+	6.96070i	−0.566453	+	0.566453i	−0.931133	−	0.364680i	$-0.881178\pi$
$151$	−6.96070	+	6.96070i	−0.566453	+	0.566453i	0.364680	+	0.931133i	$0.381178\pi$
$152$	16.6736	+	7.11669i	1.35241	+	0.577240i
$153$		0			0
$154$	−1.67740	+	2.61235i	−0.135168	+	0.210509i
$155$			1.69312i			0.135994i
$156$		0			0
$157$		−	10.6185i		−	0.847450i	−0.905791	−	0.423725i	$-0.860722\pi$
$157$		−	10.6185i		−	0.847450i	0.905791	−	0.423725i	$-0.139278\pi$
$158$	−3.86637	−	2.48261i	−0.307592	−	0.197506i
$159$		0			0
$160$	1.95997	−	3.60632i	0.154949	−	0.285105i
$161$	−3.53953	+	3.53953i	−0.278954	+	0.278954i
$162$		0			0
$163$	2.99986	−	11.1956i	0.234967	−	0.876908i	−0.743197	−	0.669073i	$-0.766692\pi$
$163$	2.99986	−	11.1956i	0.234967	−	0.876908i	0.978164	−	0.207835i	$-0.0666418\pi$
$164$	−2.99567	+	2.47741i	−0.233922	+	0.193453i
$165$		0			0
$166$	1.23480	+	5.66552i	0.0958391	+	0.439729i
$167$	2.32855	+	8.69026i	0.180189	+	0.672473i	0.995609	+	0.0936043i	$0.0298389\pi$
$167$	2.32855	+	8.69026i	0.180189	+	0.672473i	−0.815421	+	0.578868i	$0.803494\pi$
$168$		0			0
$169$	−11.1292	+	6.71872i	−0.856091	+	0.516824i
$170$	0.953591	−	0.867560i	0.0731371	−	0.0665388i
$171$		0			0
$172$	−14.9302	−	10.6140i	−1.13842	−	0.809309i
$173$	−6.97351	−	12.0785i	−0.530186	−	0.918309i	−0.999380	−	0.0352137i	$-0.988789\pi$
$173$	−6.97351	−	12.0785i	−0.530186	−	0.918309i	0.469194	−	0.883095i	$-0.344545\pi$
$174$		0			0
$175$	−1.71530	+	6.40160i	−0.129665	+	0.483916i
$176$	2.58140	−	5.33546i	0.194580	−	0.402176i
$177$		0			0
$178$	−0.913883	+	2.86277i	−0.0684984	+	0.214574i
$179$	8.03592	+	4.63954i	0.600633	+	0.346776i	0.769291	−	0.638899i	$-0.220610\pi$
$179$	8.03592	+	4.63954i	0.600633	+	0.346776i	−0.168658	+	0.985675i	$0.553943\pi$
$180$		0			0
$181$	−20.7868			−1.54507			−0.772535	−	0.634973i	$-0.781011\pi$
$181$	−20.7868			−1.54507			−0.772535	+	0.634973i	$0.781011\pi$
$182$	−6.39607	−	4.01924i	−0.474109	−	0.297926i
$183$		0			0
$184$	5.89870	−	7.51912i	0.434858	−	0.554317i
$185$	1.32448	−	2.29407i	0.0973778	−	0.168663i
$186$		0			0
$187$	1.31638	−	1.31638i	0.0962634	−	0.0962634i
$188$	−7.86543	−	2.92658i	−0.573646	−	0.213443i
$189$		0			0
$190$	−6.56968	−	0.310353i	−0.476615	−	0.0225153i
$191$	−22.5621	+	13.0262i	−1.63254	+	0.942545i	−0.649228	+	0.760593i	$0.724908\pi$
$191$	−22.5621	+	13.0262i	−1.63254	+	0.942545i	−0.983307	+	0.181952i	$0.941759\pi$
$192$		0			0
$193$	−14.5165	+	3.88969i	−1.04492	+	0.279986i	−0.740152	−	0.672439i	$-0.765247\pi$
$193$	−14.5165	+	3.88969i	−1.04492	+	0.279986i	−0.304771	+	0.952426i	$0.598580\pi$
$194$	−1.18510	+	1.07818i	−0.0850851	+	0.0774089i
$195$		0			0
$196$	−0.905977	+	9.56766i	−0.0647126	+	0.683404i
$197$	19.2785	−	5.16566i	1.37354	−	0.368038i	0.504767	−	0.863255i	$-0.331578\pi$
$197$	19.2785	−	5.16566i	1.37354	−	0.368038i	0.868769	+	0.495217i	$0.164912\pi$
$198$		0			0
$199$	5.62998	+	9.75141i	0.399098	+	0.691259i	0.993615	−	0.112825i	$-0.0359898\pi$
$199$	5.62998	+	9.75141i	0.399098	+	0.691259i	−0.594516	+	0.804083i	$0.702656\pi$
$200$	1.78588	−	12.5264i	0.126281	−	0.885749i
$201$		0			0
$202$	−7.42853	−	14.3954i	−0.522669	−	1.01285i
$203$	7.24355	+	7.24355i	0.508398	+	0.508398i
$204$		0			0
$205$	0.705151	−	1.22136i	0.0492499	−	0.0853033i
$206$	−1.90188	+	2.96196i	−0.132510	+	0.206369i
$207$		0			0
$208$	13.0433	+	6.15408i	0.904389	+	0.426709i
$209$	−9.49752			−0.656957
$210$		0			0
$211$	0.571787	−	0.990365i	0.0393635	−	0.0681795i	−0.845672	−	0.533702i	$-0.820800\pi$
$211$	0.571787	−	0.990365i	0.0393635	−	0.0681795i	0.885036	+	0.465523i	$0.154134\pi$
$212$	0.933510	−	0.427211i	0.0641137	−	0.0293410i
$213$		0			0
$214$	6.65411	+	12.8947i	0.454865	+	0.881461i
$215$	6.41935	+	1.72006i	0.437796	+	0.117307i
$216$		0			0
$217$	−1.72848	−	2.99382i	−0.117337	−	0.203233i
$218$	−14.0903	+	3.07099i	−0.954318	+	0.207994i
$219$		0			0
$220$	−0.202710	+	2.14073i	−0.0136667	+	0.144328i
$221$	3.23423	+	3.17165i	0.217558	+	0.213348i
$222$		0			0
$223$	14.1824	−	3.80017i	0.949726	−	0.254478i	0.249480	−	0.968380i	$-0.419740\pi$
$223$	14.1824	−	3.80017i	0.949726	−	0.254478i	0.700246	+	0.713902i	$0.253074\pi$
$224$	0.215976	+	8.37771i	0.0144305	+	0.559759i
$225$		0			0
$226$	−6.70001	−	0.316509i	−0.445678	−	0.0210539i
$227$	8.65489	+	2.31907i	0.574445	+	0.153922i	0.534334	−	0.845273i	$-0.320562\pi$
$227$	8.65489	+	2.31907i	0.574445	+	0.153922i	0.0401107	+	0.999195i	$0.487229\pi$
$228$		0			0
$229$	1.63656	−	1.63656i	0.108147	−	0.108147i	−0.650963	−	0.759110i	$-0.725635\pi$
$229$	1.63656	−	1.63656i	0.108147	−	0.108147i	0.759110	+	0.650963i	$0.225635\pi$
$230$	−1.05438	+	3.30290i	−0.0695241	+	0.217787i
$231$		0			0
$232$	−15.3877	−	12.0715i	−1.01025	−	0.792534i
$233$			15.2245i			0.997391i	0.866777	+	0.498695i	$0.166187\pi$
$233$			15.2245i			0.997391i	−0.866777	+	0.498695i	$0.833813\pi$
$234$		0			0
$235$	3.04464			0.198610
$236$	−27.4888	+	4.64479i	−1.78937	+	0.302350i
$237$		0			0
$238$	−0.800486	+	2.50755i	−0.0518878	+	0.162540i
$239$	−20.1260	−	20.1260i	−1.30184	−	1.30184i	−0.927149	−	0.374693i	$-0.877748\pi$
$239$	−20.1260	−	20.1260i	−1.30184	−	1.30184i	−0.374693	−	0.927149i	$-0.622252\pi$
$240$		0			0
$241$	0.968043	−	3.61278i	0.0623571	−	0.232720i	−0.927713	−	0.373294i	$-0.878228\pi$
$241$	0.968043	−	3.61278i	0.0623571	−	0.232720i	0.990070	+	0.140574i	$0.0448949\pi$
$242$	0.587541	−	12.4373i	0.0377686	−	0.799502i
$243$		0			0
$244$	−23.0135	−	16.3605i	−1.47329	−	1.04737i
$245$	−0.902396	−	3.36779i	−0.0576520	−	0.215160i
$246$		0			0
$247$	−0.225764	−	23.1088i	−0.0143650	−	1.47038i
$248$	3.96150	+	5.27889i	0.251555	+	0.335210i
$249$		0			0
$250$	2.07011	+	9.49809i	0.130925	+	0.600712i
$251$	−19.4389	+	11.2231i	−1.22697	+	0.708393i	−0.966395	−	0.257060i	$-0.917246\pi$
$251$	−19.4389	+	11.2231i	−1.22697	+	0.708393i	−0.260577	+	0.965453i	$0.583913\pi$
$252$		0			0
$253$	−1.29582	+	4.83608i	−0.0814678	+	0.304042i
$254$	−12.2012	−	23.6441i	−0.765571	−	1.48356i
$255$		0			0
$256$	−2.32705	−	15.8299i	−0.145441	−	0.989367i
$257$	−25.8091	−	14.9009i	−1.60993	−	0.929494i	−0.989384	−	0.145324i	$-0.953578\pi$
$257$	−25.8091	−	14.9009i	−1.60993	−	0.929494i	−0.620546	−	0.784170i	$-0.713089\pi$
$258$		0			0
$259$			5.40858i			0.336073i
$260$	−5.21352	−	0.442333i	−0.323329	−	0.0274324i
$261$		0			0
$262$	−1.07056	+	1.66727i	−0.0661392	+	0.103004i
$263$	2.11644	+	1.22193i	0.130506	+	0.0753474i	0.563831	−	0.825890i	$-0.309327\pi$
$263$	2.11644	+	1.22193i	0.130506	+	0.0753474i	−0.433326	+	0.901237i	$0.642660\pi$
$264$		0			0
$265$	−0.263361	+	0.263361i	−0.0161782	+	0.0161782i
$266$	11.9335	−	6.15812i	0.731691	−	0.377579i
$267$		0			0
$268$	11.2057	−	9.26706i	0.684495	−	0.566076i
$269$	−22.9614	+	13.2568i	−1.39998	+	0.808280i	−0.994390	−	0.105774i	$-0.966268\pi$
$269$	−22.9614	+	13.2568i	−1.39998	+	0.808280i	−0.405592	+	0.914054i	$0.632935\pi$
$270$		0			0
$271$	1.72024	+	6.42004i	0.104497	+	0.389990i	0.998288	−	0.0584956i	$-0.0186304\pi$
$271$	1.72024	+	6.42004i	0.104497	+	0.389990i	−0.893790	+	0.448485i	$0.851964\pi$
$272$	0.943273	−	4.93610i	0.0571943	−	0.299295i
$273$		0			0
$274$	15.9551	+	17.5373i	0.963882	+	1.05946i
$275$	1.71566	+	6.40292i	0.103458	+	0.386111i
$276$		0			0
$277$	−0.878646	−	1.52186i	−0.0527927	−	0.0914397i	0.838421	−	0.545023i	$-0.183479\pi$
$277$	−0.878646	−	1.52186i	−0.0527927	−	0.0914397i	−0.891214	+	0.453583i	$0.850146\pi$
$278$	21.4041	+	1.01113i	1.28373	+	0.0606437i
$279$		0			0
$280$	−1.13333	−	2.82124i	−0.0677297	−	0.168602i
$281$	−17.3570	−	17.3570i	−1.03543	−	1.03543i	−0.999349	−	0.0360826i	$-0.988512\pi$
$281$	−17.3570	−	17.3570i	−1.03543	−	1.03543i	−0.0360826	−	0.999349i	$-0.511488\pi$
$282$		0			0
$283$	−3.46233	−	1.99897i	−0.205814	−	0.118827i	0.393551	−	0.919303i	$-0.371247\pi$
$283$	−3.46233	−	1.99897i	−0.205814	−	0.118827i	−0.599364	+	0.800476i	$0.704580\pi$
$284$	7.46588	−	1.26151i	0.443019	−	0.0748570i
$285$		0			0
$286$	−7.55034	−	0.282785i	−0.446461	−	0.0167214i
$287$			2.87952i			0.169973i
$288$		0			0
$289$	−7.71078	+	13.3555i	−0.453576	+	0.785616i
$290$	6.75929	+	2.15777i	0.396919	+	0.126709i
$291$		0			0
$292$	−4.36075	+	11.7199i	−0.255194	+	0.685854i
$293$	20.3123	+	5.44266i	1.18666	+	0.317963i	0.797563	−	0.603235i	$-0.206122\pi$
$293$	20.3123	+	5.44266i	1.18666	+	0.317963i	0.389093	+	0.921199i	$0.372789\pi$
$294$		0			0
$295$	8.75903	−	5.05703i	0.509971	−	0.294432i
$296$	−1.23804	−	10.2515i	−0.0719597	−	0.595859i
$297$		0			0
$298$	7.40550	+	8.13987i	0.428989	+	0.471530i
$299$	−11.7977	−	3.03796i	−0.682276	−	0.175690i
$300$		0			0
$301$	−13.1069	+	3.51197i	−0.755466	+	0.202427i
$302$	−2.96458	−	13.6021i	−0.170592	−	0.782711i
$303$		0			0
$304$	−21.2095	+	14.4039i	−1.21645	+	0.826119i
$305$	9.89482	+	2.65131i	0.566576	+	0.151814i
$306$		0			0
$307$	−1.73231	−	1.73231i	−0.0988683	−	0.0988683i	0.655943	−	0.754811i	$-0.272271\pi$
$307$	−1.73231	−	1.73231i	−0.0988683	−	0.0988683i	−0.754811	+	0.655943i	$0.772271\pi$
$308$	−1.82701	−	3.99225i	−0.104104	−	0.227479i
$309$		0			0
$310$	−2.01483	−	1.29373i	−0.114435	−	0.0734790i
$311$	−2.28061			−0.129321			−0.0646606	−	0.997907i	$-0.520596\pi$
$311$	−2.28061			−0.129321			−0.0646606	+	0.997907i	$0.520596\pi$
$312$		0			0
$313$	32.2565			1.82325			0.911623	−	0.411028i	$-0.134830\pi$
$313$	32.2565			1.82325			0.911623	+	0.411028i	$0.134830\pi$
$314$	12.6362	+	8.11373i	0.713101	+	0.457884i
$315$		0			0
$316$	5.90868	−	2.70405i	0.332389	−	0.152115i
$317$	−17.9781	−	17.9781i	−1.00975	−	1.00975i	−0.999952	−	0.00979695i	$-0.996881\pi$
$317$	−17.9781	−	17.9781i	−1.00975	−	1.00975i	−0.00979695	−	0.999952i	$-0.503119\pi$
$318$		0			0
$319$	9.89691	+	2.65187i	0.554121	+	0.148476i
$320$	2.79394	+	5.08803i	0.156186	+	0.284429i
$321$		0			0
$322$	−1.50749	−	6.91668i	−0.0840093	−	0.385452i
$323$	−7.77826	+	2.08418i	−0.432794	+	0.115967i
$324$		0			0
$325$	−15.5384	+	4.32664i	−0.861916	+	0.239999i
$326$	11.0307	+	12.1246i	0.610934	+	0.671518i
$327$		0			0
$328$	−0.659131	−	5.45791i	−0.0363944	−	0.301362i
$329$	−5.38361	+	3.10823i	−0.296808	+	0.171362i
$330$		0			0
$331$	28.0985	+	7.52896i	1.54443	+	0.413829i	0.927694	−	0.373341i	$-0.121788\pi$
$331$	28.0985	+	7.52896i	1.54443	+	0.413829i	0.616736	+	0.787170i	$0.288454\pi$
$332$	−7.68557	−	2.85966i	−0.421800	−	0.156944i
$333$		0			0
$334$	−12.1208	−	3.86933i	−0.663221	−	0.211720i
$335$	−2.63770	+	4.56864i	−0.144113	+	0.249611i
$336$		0			0
$337$			13.9376i			0.759229i	0.925145	+	0.379615i	$0.123943\pi$
$337$			13.9376i			0.759229i	−0.925145	+	0.379615i	$0.876057\pi$
$338$	0.508576	−	18.3777i	0.0276629	−	0.999617i
$339$		0			0
$340$	0.303758	+	1.79770i	0.0164736	+	0.0974939i
$341$	−2.99443	−	1.72884i	−0.162158	−	0.0936217i
$342$		0			0
$343$	12.3667	+	12.3667i	0.667739	+	0.667739i
$344$	24.0391	−	9.65687i	1.29610	−	0.520664i
$345$		0			0
$346$	19.7021	+	0.930729i	1.05919	+	0.0500363i
$347$	14.4501	+	25.0283i	0.775720	+	1.34359i	0.934389	+	0.356255i	$0.115947\pi$
$347$	14.4501	+	25.0283i	0.775720	+	1.34359i	−0.158668	+	0.987332i	$0.550720\pi$
$348$		0			0
$349$	5.08095	+	18.9624i	0.271977	+	1.01503i	0.957840	+	0.287302i	$0.0927583\pi$
$349$	5.08095	+	18.9624i	0.271977	+	1.01503i	−0.685863	+	0.727731i	$0.740575\pi$
$350$	−6.30731	−	6.93278i	−0.337140	−	0.370572i
$351$		0			0
$352$	4.37680	+	7.14879i	0.233284	+	0.381032i
$353$	4.83344	+	18.0387i	0.257258	+	0.960101i	0.966820	+	0.255458i	$0.0822262\pi$
$353$	4.83344	+	18.0387i	0.257258	+	0.960101i	−0.709562	+	0.704643i	$0.751107\pi$
$354$		0			0
$355$	−2.37893	+	1.37348i	−0.126261	+	0.0728966i
$356$	−2.70843	−	3.27501i	−0.143546	−	0.173575i
$357$		0			0
$358$	−11.6615	+	6.01773i	−0.616327	+	0.318047i
$359$	16.3844	−	16.3844i	0.864734	−	0.864734i	−0.127149	−	0.991884i	$-0.540583\pi$
$359$	16.3844	−	16.3844i	0.864734	−	0.864734i	0.991884	+	0.127149i	$0.0405827\pi$
$360$		0			0
$361$	19.1236	+	11.0410i	1.00651	+	0.581107i
$362$	15.8834	−	24.7366i	0.834814	−	1.30012i
$363$		0			0
$364$	9.67027	−	4.54027i	0.506860	−	0.237975i
$365$		−	4.53666i		−	0.237460i
$366$		0			0
$367$	−25.4992	−	14.7220i	−1.33105	−	0.768480i	−0.345587	−	0.938387i	$-0.612320\pi$
$367$	−25.4992	−	14.7220i	−1.33105	−	0.768480i	−0.985460	+	0.169907i	$0.945653\pi$
$368$	4.44059	+	12.7650i	0.231482	+	0.665420i
$369$		0			0
$370$	1.71792	+	3.32907i	0.0893105	+	0.173070i
$371$	0.196821	−	0.734545i	0.0102184	−	0.0381357i
$372$		0			0
$373$	20.6658	−	11.9314i	1.07003	−	0.617785i	0.141844	−	0.989889i	$-0.454697\pi$
$373$	20.6658	−	11.9314i	1.07003	−	0.617785i	0.928191	+	0.372104i	$0.121364\pi$
$374$	0.560650	+	2.57238i	0.0289905	+	0.133014i
$375$		0			0
$376$	9.49274	−	7.12374i	0.489551	−	0.367379i
$377$	−6.21711	+	24.1436i	−0.320197	+	1.24346i
$378$		0			0
$379$	3.24058	+	12.0940i	0.166457	+	0.621227i	0.997850	+	0.0655416i	$0.0208775\pi$
$379$	3.24058	+	12.0940i	0.166457	+	0.621227i	−0.831393	+	0.555686i	$0.812456\pi$
$380$	5.38929	−	7.58087i	0.276465	−	0.388890i
$381$		0			0
$382$	1.73856	−	36.8027i	0.0889527	−	1.88299i
$383$	−8.74431	+	32.6342i	−0.446814	+	1.66753i	0.264290	+	0.964443i	$0.414862\pi$
$383$	−8.74431	+	32.6342i	−0.446814	+	1.66753i	−0.711103	+	0.703088i	$0.751804\pi$
$384$		0			0
$385$	1.12629	+	1.12629i	0.0574011	+	0.0574011i
$386$	6.46347	−	20.2470i	0.328982	−	1.03055i
$387$		0			0
$388$	−0.377503	−	2.23414i	−0.0191648	−	0.113421i
$389$	29.5448			1.49798			0.748990	−	0.662581i	$-0.230539\pi$
$389$	29.5448			1.49798			0.748990	+	0.662581i	$0.230539\pi$
$390$		0			0
$391$			4.24501i			0.214679i
$392$	−10.6934	−	8.38889i	−0.540097	−	0.423703i
$393$		0			0
$394$	−8.58372	+	26.8888i	−0.432442	+	1.35464i
$395$	−1.66696	+	1.66696i	−0.0838736	+	0.0838736i
$396$		0			0
$397$	28.0508	+	7.51619i	1.40783	+	0.377227i	0.881150	−	0.472838i	$-0.156770\pi$
$397$	28.0508	+	7.51619i	1.40783	+	0.377227i	0.526679	+	0.850064i	$0.323437\pi$
$398$	−15.9062	−	0.751413i	−0.797308	−	0.0376649i
$399$		0			0
$400$	13.5420	+	11.6968i	0.677098	+	0.584839i
$401$	5.34143	−	1.43123i	0.266738	−	0.0714723i	−0.122971	−	0.992410i	$-0.539242\pi$
$401$	5.34143	−	1.43123i	0.266738	−	0.0714723i	0.389709	+	0.920938i	$0.372576\pi$
$402$		0			0
$403$	4.13532	−	7.32697i	0.205995	−	0.364982i
$404$	22.8069	+	2.15962i	1.13469	+	0.107445i
$405$		0			0
$406$	−14.1548	+	3.08504i	−0.702491	+	0.153108i
$407$	2.70485	+	4.68493i	0.134074	+	0.232223i
$408$		0			0
$409$	−17.8385	−	4.77981i	−0.882056	−	0.236346i	−0.210762	−	0.977537i	$-0.567595\pi$
$409$	−17.8385	−	4.77981i	−0.882056	−	0.236346i	−0.671294	+	0.741191i	$0.734261\pi$
$410$	0.914619	+	1.77239i	0.0451698	+	0.0875323i
$411$		0			0
$412$	−2.07152	−	4.52653i	−0.102056	−	0.223006i
$413$	−10.3253	+	17.8840i	−0.508075	+	0.880012i
$414$		0			0
$415$	2.97501			0.146038
$416$	−17.2900	+	10.8193i	−0.847710	+	0.530459i
$417$		0			0
$418$	7.25716	−	11.3022i	0.354960	−	0.552808i
$419$	−14.1415	+	24.4939i	−0.690859	+	1.19660i	0.280698	+	0.959796i	$0.409434\pi$
$419$	−14.1415	+	24.4939i	−0.690859	+	1.19660i	−0.971557	+	0.236807i	$0.923899\pi$
$420$		0			0
$421$	−19.6915	−	19.6915i	−0.959704	−	0.959704i	0.0395149	−	0.999219i	$-0.487419\pi$
$421$	−19.6915	−	19.6915i	−0.959704	−	0.959704i	−0.999219	+	0.0395149i	$0.987419\pi$
$422$	0.741639	+	1.43718i	0.0361024	+	0.0699611i
$423$		0			0
$424$	−0.204919	+	1.43733i	−0.00995174	+	0.0698028i
$425$	2.81017	+	4.86736i	0.136313	+	0.236102i
$426$		0			0
$427$	−20.2030	+	5.41337i	−0.977691	+	0.261971i
$428$	−20.4293	−	1.93448i	−0.987488	−	0.0935068i
$429$		0			0
$430$	−6.95199	+	6.32479i	−0.335255	+	0.305009i
$431$	30.7854	−	8.24891i	1.48288	−	0.397336i	0.575553	−	0.817764i	$-0.304787\pi$
$431$	30.7854	−	8.24891i	1.48288	−	0.397336i	0.907326	+	0.420428i	$0.138120\pi$
$432$		0			0
$433$	13.1701	−	7.60376i	0.632915	−	0.365414i	−0.148965	−	0.988842i	$-0.547594\pi$
$433$	13.1701	−	7.60376i	0.632915	−	0.365414i	0.781880	+	0.623429i	$0.214261\pi$
$434$	4.88344	+	0.230694i	0.234412	+	0.0110737i
$435$		0			0
$436$	7.11207	−	19.1143i	0.340606	−	0.915408i
$437$	15.3136	−	15.3136i	0.732548	−	0.732548i
$438$		0			0
$439$	−1.65131	+	2.86016i	−0.0788129	+	0.136508i	−0.902738	−	0.430191i	$-0.858446\pi$
$439$	−1.65131	+	2.86016i	−0.0788129	+	0.136508i	0.823925	+	0.566699i	$0.191780\pi$
$440$	−2.39261	−	1.87699i	−0.114063	−	0.0894819i
$441$		0			0
$442$	−6.24562	+	1.42529i	−0.297074	+	0.0677940i
$443$	12.1161			0.575654			0.287827	−	0.957682i	$-0.407067\pi$
$443$	12.1161			0.575654			0.287827	+	0.957682i	$0.407067\pi$
$444$		0			0
$445$	1.33525	+	0.770906i	0.0632968	+	0.0365444i
$446$	−6.31471	+	19.7810i	−0.299010	+	0.936660i
$447$		0			0
$448$	−10.1346	−	6.14449i	−0.478816	−	0.290300i
$449$	−2.46287	+	9.19155i	−0.116230	+	0.433776i	−0.999376	−	0.0353221i	$-0.988754\pi$
$449$	−2.46287	+	9.19155i	−0.116230	+	0.433776i	0.883146	+	0.469098i	$0.155421\pi$
$450$		0			0
$451$	1.44006	+	2.49425i	0.0678096	+	0.117450i
$452$	5.49621	−	7.73126i	0.258520	−	0.363648i
$453$		0			0
$454$	−9.37303	+	8.52741i	−0.439898	+	0.400211i
$455$	−2.71365	+	2.76720i	−0.127218	+	0.129728i
$456$		0			0
$457$	−3.13824	−	11.7121i	−0.146800	−	0.547867i	−0.999669	−	0.0257405i	$-0.991806\pi$
$457$	−3.13824	−	11.7121i	−0.146800	−	0.547867i	0.852868	−	0.522126i	$-0.174861\pi$
$458$	0.697013	+	3.19804i	0.0325693	+	0.149434i
$459$		0			0
$460$	−3.12483	−	3.77852i	−0.145696	−	0.176174i
$461$	−6.26259	+	23.3723i	−0.291678	+	1.08856i	0.652142	+	0.758097i	$0.273871\pi$
$461$	−6.26259	+	23.3723i	−0.291678	+	1.08856i	−0.943820	+	0.330460i	$0.892796\pi$
$462$		0			0
$463$	−12.7547	+	12.7547i	−0.592763	+	0.592763i	−0.938377	−	0.345614i	$-0.887671\pi$
$463$	−12.7547	+	12.7547i	−0.592763	+	0.592763i	0.345614	+	0.938377i	$0.387671\pi$
$464$	26.1232	−	9.08755i	1.21274	−	0.421879i
$465$		0			0
$466$	−18.1174	−	11.6332i	−0.839271	−	0.538899i
$467$		−	18.1587i		−	0.840286i	−0.907458	−	0.420143i	$-0.861980\pi$
$467$		−	18.1587i		−	0.840286i	0.907458	−	0.420143i	$-0.138020\pi$
$468$		0			0
$469$		−	10.7712i		−	0.497367i
$470$	−2.32644	+	3.62316i	−0.107311	+	0.167124i
$471$		0			0
$472$	15.4771	−	36.2612i	0.712393	−	1.66906i
$473$	−9.59686	+	9.59686i	−0.441264	+	0.441264i
$474$		0			0
$475$	7.42117	−	27.6962i	0.340507	−	1.27079i
$476$	−2.37236	−	2.86864i	−0.108737	−	0.131484i
$477$		0			0
$478$	39.3287	−	8.57170i	1.79885	−	0.392061i
$479$	4.24253	+	15.8334i	0.193846	+	0.723444i	0.992562	+	0.121736i	$0.0388463\pi$
$479$	4.24253	+	15.8334i	0.193846	+	0.723444i	−0.798716	+	0.601708i	$0.794487\pi$
$480$		0			0
$481$	−11.3348	+	6.69263i	−0.516822	+	0.305158i
$482$	3.55957	+	3.91256i	0.162134	+	0.178212i
$483$		0			0
$484$	14.3516	+	10.2027i	0.652347	+	0.463759i
$485$	0.411007	+	0.711885i	0.0186629	+	0.0323251i
$486$		0			0
$487$	9.33917	−	34.8542i	0.423198	−	1.57940i	−0.344629	−	0.938739i	$-0.611995\pi$
$487$	9.33917	−	34.8542i	0.423198	−	1.57940i	0.767827	−	0.640658i	$-0.221338\pi$
$488$	37.0541	−	14.8852i	1.67736	−	0.673820i
$489$		0			0
$490$	4.69725	+	1.49950i	0.212200	+	0.0677406i
$491$	12.9846	+	7.49664i	0.585985	+	0.338319i	0.763508	−	0.645798i	$-0.223475\pi$
$491$	12.9846	+	7.49664i	0.585985	+	0.338319i	−0.177523	+	0.984117i	$0.556808\pi$
$492$		0			0
$493$	8.68730			0.391256
$494$	27.6723	+	17.3890i	1.24503	+	0.782369i
$495$		0			0
$496$	−9.30899	+	0.680571i	−0.417986	+	0.0305585i
$497$	2.80433	−	4.85724i	0.125791	−	0.217877i
$498$		0			0
$499$	−30.5157	+	30.5157i	−1.36607	+	1.36607i	−0.500105	+	0.865965i	$0.666705\pi$
$499$	−30.5157	+	30.5157i	−1.36607	+	1.36607i	−0.865965	+	0.500105i	$0.833295\pi$
$500$	−12.8847	−	4.79414i	−0.576219	−	0.214401i
$501$		0			0
$502$	1.49790	−	31.7082i	0.0668546	−	1.41521i
$503$	30.7732	−	17.7669i	1.37211	−	0.792187i	0.380914	−	0.924610i	$-0.375609\pi$
$503$	30.7732	−	17.7669i	1.37211	−	0.792187i	0.991193	+	0.132424i	$0.0422760\pi$
$504$		0			0
$505$	−8.02797	+	2.15109i	−0.357240	+	0.0957222i
$506$	−4.76485	−	5.23736i	−0.211823	−	0.232829i
$507$		0			0
$508$	37.4599	+	3.54714i	1.66201	+	0.157379i
$509$	17.3479	−	4.64835i	0.768931	−	0.206034i	0.147032	−	0.989132i	$-0.453028\pi$
$509$	17.3479	−	4.64835i	0.768931	−	0.206034i	0.621899	+	0.783097i	$0.286361\pi$
$510$		0			0
$511$	4.63141	+	8.02185i	0.204882	+	0.354866i
$512$	20.6159	+	9.32657i	0.911102	+	0.412180i
$513$		0			0
$514$	37.4534	−	19.3273i	1.65200	−	0.852490i
$515$	1.27702	+	1.27702i	0.0562724	+	0.0562724i
$516$		0			0
$517$	−3.10887	+	5.38472i	−0.136728	+	0.236820i
$518$	−6.43628	−	4.13276i	−0.282794	−	0.181583i
$519$		0			0
$520$	4.51010	−	5.86617i	0.197781	−	0.257249i
$521$	33.0188			1.44658			0.723289	−	0.690545i	$-0.242629\pi$
$521$	33.0188			1.44658			0.723289	+	0.690545i	$0.242629\pi$
$522$		0			0
$523$	0.905353	−	1.56812i	0.0395883	−	0.0685690i	−0.845552	−	0.533893i	$-0.820729\pi$
$523$	0.905353	−	1.56812i	0.0395883	−	0.0685690i	0.885141	+	0.465324i	$0.154062\pi$
$524$	−1.16604	−	2.54796i	−0.0509389	−	0.111308i
$525$		0			0
$526$	−3.07131	+	1.58491i	−0.133916	+	0.0691053i
$527$	−2.83176	−	0.758768i	−0.123353	−	0.0330524i
$528$		0			0
$529$	5.79177	+	10.0316i	0.251816	+	0.436158i
$530$	−0.112166	−	0.514641i	−0.00487219	−	0.0223546i
$531$		0			0
$532$	−1.79029	+	18.9066i	−0.0776190	+	0.819703i
$533$	−6.03462	+	3.56315i	−0.261389	+	0.154337i
$534$		0			0
$535$	7.19106	−	1.92684i	0.310897	−	0.0833045i
$536$	2.46556	+	20.4160i	0.106496	+	0.881835i
$537$		0			0
$538$	1.76934	−	37.4541i	0.0762815	−	1.61476i
$539$	6.87768	+	1.84287i	0.296243	+	0.0793780i
$540$		0			0
$541$	27.7884	−	27.7884i	1.19472	−	1.19472i	0.218990	−	0.975727i	$-0.429724\pi$
$541$	27.7884	−	27.7884i	1.19472	−	1.19472i	0.975727	−	0.218990i	$-0.0702761\pi$
$542$	−8.95439	−	2.85851i	−0.384624	−	0.122784i
$543$		0			0
$544$	5.15327	+	4.89424i	0.220945	+	0.209839i
$545$			7.39896i			0.316937i
$546$		0			0
$547$	6.37762			0.272687			0.136344	−	0.990662i	$-0.456465\pi$
$547$	6.37762			0.272687			0.136344	+	0.990662i	$0.456465\pi$
$548$	−33.0611	+	5.58634i	−1.41230	+	0.238637i
$549$		0			0
$550$	−8.93052	−	2.85089i	−0.380799	−	0.121562i
$551$	−31.3388	−	31.3388i	−1.33508	−	1.33508i
$552$		0			0
$553$	1.24578	−	4.64933i	0.0529761	−	0.197710i
$554$	2.48242	+	0.117270i	0.105468	+	0.00498231i
$555$		0			0
$556$	−17.5584	+	24.6985i	−0.744641	+	1.04745i
$557$	−1.53541	−	5.73023i	−0.0650574	−	0.242798i	0.925738	−	0.378166i	$-0.123445\pi$
$557$	−1.53541	−	5.73023i	−0.0650574	−	0.242798i	−0.990795	+	0.135368i	$0.956778\pi$
$558$		0			0
$559$	−23.5786	−	23.1224i	−0.997269	−	0.977972i
$560$	4.22331	+	0.807061i	0.178468	+	0.0341046i
$561$		0			0
$562$	33.9177	−	7.39238i	1.43073	−	0.311829i
$563$	−5.39506	+	3.11484i	−0.227375	+	0.131275i	−0.609360	−	0.792893i	$-0.708574\pi$
$563$	−5.39506	+	3.11484i	−0.227375	+	0.131275i	0.381986	+	0.924168i	$0.375240\pi$
$564$		0			0
$565$	−0.890693	+	3.32411i	−0.0374717	+	0.139846i
$566$	5.02441	−	2.59278i	0.211192	−	0.108982i
$567$		0			0
$568$	−4.20355	+	9.84844i	−0.176377	+	0.413232i
$569$	1.68213	+	0.971181i	0.0705187	+	0.0407140i	0.534845	−	0.844950i	$-0.320370\pi$
$569$	1.68213	+	0.971181i	0.0705187	+	0.0407140i	−0.464326	+	0.885664i	$0.653703\pi$
$570$		0			0
$571$			31.5350i			1.31970i	0.751398	+	0.659850i	$0.229380\pi$
$571$			31.5350i			1.31970i	−0.751398	+	0.659850i	$0.770620\pi$
$572$	6.10582	−	8.76893i	0.255297	−	0.366647i
$573$		0			0
$574$	−3.42667	−	2.20027i	−0.143026	−	0.0918377i
$575$	−13.0902	−	7.55764i	−0.545900	−	0.315175i
$576$		0			0
$577$	17.6927	−	17.6927i	0.736558	−	0.736558i	−0.235352	−	0.971910i	$-0.575624\pi$
$577$	17.6927	−	17.6927i	0.736558	−	0.736558i	0.971910	+	0.235352i	$0.0756242\pi$
$578$	−10.0013	−	19.3810i	−0.415999	−	0.806144i
$579$		0			0
$580$	−7.73263	+	6.39488i	−0.321080	+	0.265533i
$581$	−5.26050	+	3.03715i	−0.218242	+	0.126002i
$582$		0			0
$583$	−0.196861	−	0.734696i	−0.00815316	−	0.0304280i
$584$	−10.6147	−	14.1446i	−0.439240	−	0.585310i
$585$		0			0
$586$	−21.9977	+	20.0131i	−0.908716	+	0.826733i
$587$	−7.64218	−	28.5210i	−0.315427	−	1.17719i	−0.923592	−	0.383377i	$-0.874761\pi$
$587$	−7.64218	−	28.5210i	−0.315427	−	1.17719i	0.608165	−	0.793810i	$-0.291906\pi$
$588$		0			0
$589$	7.47818	+	12.9526i	0.308133	+	0.533702i
$590$	−0.674944	+	14.2875i	−0.0277870	+	0.588207i
$591$		0			0
$592$	13.1455	+	6.36004i	0.540276	+	0.261396i
$593$	20.5469	+	20.5469i	0.843759	+	0.843759i	0.989346	−	0.145586i	$-0.0465069\pi$
$593$	20.5469	+	20.5469i	0.843759	+	0.843759i	−0.145586	+	0.989346i	$0.546507\pi$
$594$		0			0
$595$	1.16957	+	0.675250i	0.0479476	+	0.0276825i
$596$	−15.3452	+	2.59288i	−0.628563	+	0.106209i
$597$		0			0
$598$	12.6300	−	11.7180i	0.516477	−	0.479186i
$599$		−	28.2451i		−	1.15407i	−0.816721	−	0.577033i	$-0.804211\pi$
$599$		−	28.2451i		−	1.15407i	0.816721	−	0.577033i	$-0.195789\pi$
$600$		0			0
$601$	−2.74994	+	4.76304i	−0.112172	+	0.194288i	−0.916646	−	0.399700i	$-0.869114\pi$
$601$	−2.74994	+	4.76304i	−0.112172	+	0.194288i	0.804473	+	0.593989i	$0.202448\pi$
$602$	5.83581	−	18.2809i	0.237850	−	0.745073i
$603$		0			0
$604$	18.4519	+	6.86562i	0.750798	+	0.279358i
$605$	−6.17059	−	1.65341i	−0.250870	−	0.0672205i
$606$		0			0
$607$	1.25794	−	0.726274i	0.0510584	−	0.0294786i	−0.474254	−	0.880388i	$-0.657282\pi$
$607$	1.25794	−	0.726274i	0.0510584	−	0.0294786i	0.525312	+	0.850910i	$0.323949\pi$
$608$	−0.934410	−	36.2457i	−0.0378953	−	1.46996i
$609$		0			0
$610$	−10.7158	+	9.74908i	−0.433872	+	0.394729i
$611$	−13.1757	−	7.43632i	−0.533031	−	0.300841i
$612$		0			0
$613$	−30.9474	+	8.29232i	−1.24995	+	0.334924i	−0.822318	−	0.569028i	$-0.807319\pi$
$613$	−30.9474	+	8.29232i	−1.24995	+	0.334924i	−0.427634	+	0.903952i	$0.640653\pi$
$614$	3.38516	−	0.737796i	0.136614	−	0.0297750i
$615$		0			0
$616$	6.14687	+	0.876356i	0.247665	+	0.0353094i
$617$	4.26824	+	1.14367i	0.171833	+	0.0460425i	0.343710	−	0.939076i	$-0.388316\pi$
$617$	4.26824	+	1.14367i	0.171833	+	0.0460425i	−0.171877	+	0.985118i	$0.554983\pi$
$618$		0			0
$619$	−8.69550	−	8.69550i	−0.349502	−	0.349502i	0.510422	−	0.859924i	$-0.329489\pi$
$619$	−8.69550	−	8.69550i	−0.349502	−	0.349502i	−0.859924	+	0.510422i	$0.829489\pi$
$620$	3.07912	−	1.40912i	0.123660	−	0.0565918i
$621$		0			0
$622$	1.74264	−	2.71395i	0.0698734	−	0.108820i
$623$	−3.14803			−0.126123
$624$		0			0
$625$	−17.3801			−0.695204
$626$	−24.6476	+	38.3857i	−0.985115	+	1.53420i
$627$		0			0
$628$	−19.3109	+	8.83743i	−0.770589	+	0.352652i
$629$	3.24329	+	3.24329i	0.129319	+	0.129319i
$630$		0			0
$631$	9.04870	+	2.42459i	0.360223	+	0.0965215i	0.434391	−	0.900724i	$-0.356963\pi$
$631$	9.04870	+	2.42459i	0.360223	+	0.0965215i	−0.0741682	+	0.997246i	$0.523630\pi$
$632$	−1.29704	+	9.09761i	−0.0515935	+	0.361884i
$633$		0			0
$634$	35.1314	−	7.65690i	1.39525	−	0.304094i
$635$	−13.1858	+	3.53312i	−0.523261	+	0.140207i
$636$		0			0
$637$	−4.32047	+	16.7782i	−0.171183	+	0.664775i
$638$	−10.7181	+	9.75114i	−0.424334	+	0.386051i
$639$		0			0
$640$	−8.18971	−	0.562992i	−0.323727	−	0.0222542i
$641$	31.6965	−	18.3000i	1.25194	−	0.722805i	0.280442	−	0.959871i	$-0.409519\pi$
$641$	31.6965	−	18.3000i	1.25194	−	0.722805i	0.971494	+	0.237066i	$0.0761856\pi$
$642$		0			0
$643$	−13.8446	−	3.70965i	−0.545977	−	0.146294i	−0.0247210	−	0.999694i	$-0.507870\pi$
$643$	−13.8446	−	3.70965i	−0.545977	−	0.146294i	−0.521256	+	0.853400i	$0.674536\pi$
$644$	9.38284	+	3.49118i	0.369736	+	0.137572i
$645$		0			0
$646$	3.46326	−	10.8488i	0.136260	−	0.426840i
$647$	16.5697	−	28.6996i	0.651422	−	1.12830i	−0.331356	−	0.943506i	$-0.607506\pi$
$647$	16.5697	−	28.6996i	0.651422	−	1.12830i	0.982778	−	0.184790i	$-0.0591606\pi$
$648$		0			0
$649$			20.6549i			0.810774i
$650$	6.72433	−	21.7970i	0.263750	−	0.854947i
$651$		0			0
$652$	−22.8571	+	3.86217i	−0.895153	+	0.151254i
$653$	−35.8657	−	20.7071i	−1.40353	−	0.810330i	−0.408780	−	0.912633i	$-0.634046\pi$
$653$	−35.8657	−	20.7071i	−1.40353	−	0.810330i	−0.994753	+	0.102303i	$0.967379\pi$
$654$		0			0
$655$	0.718828	+	0.718828i	0.0280869	+	0.0280869i
$656$	6.99864	+	3.38608i	0.273251	+	0.132204i
$657$		0			0
$658$	0.414845	−	8.78161i	0.0161723	−	0.342343i
$659$	−14.1419	−	24.4945i	−0.550889	−	0.954168i	−0.998211	−	0.0597950i	$-0.980955\pi$
$659$	−14.1419	−	24.4945i	−0.550889	−	0.954168i	0.447321	−	0.894373i	$-0.352378\pi$
$660$		0			0
$661$	6.42654	+	23.9842i	0.249963	+	0.932876i	0.970823	+	0.239796i	$0.0770804\pi$
$661$	6.42654	+	23.9842i	0.249963	+	0.932876i	−0.720860	+	0.693081i	$0.756253\pi$
$662$	−30.4299	+	27.6846i	−1.18269	+	1.07599i
$663$		0			0
$664$	9.27567	−	6.96084i	0.359966	−	0.270133i
$665$	−1.78322	−	6.65505i	−0.0691502	−	0.258072i
$666$		0			0
$667$	−20.2334	+	11.6817i	−0.783440	+	0.452319i
$668$	13.8662	−	11.4673i	0.536500	−	0.443684i
$669$		0			0
$670$	−3.42124	−	6.62985i	−0.132174	−	0.256134i
$671$	−14.7927	+	14.7927i	−0.571064	+	0.571064i
$672$		0			0
$673$	19.3181	+	11.1533i	0.744658	+	0.429929i	0.823761	−	0.566938i	$-0.191872\pi$
$673$	19.3181	+	11.1533i	0.744658	+	0.429929i	−0.0791022	+	0.996867i	$0.525205\pi$
$674$	−16.5859	−	10.6499i	−0.638866	−	0.410218i
$675$		0			0
$676$	21.4812	+	14.6479i	0.826198	+	0.563379i
$677$			7.36423i			0.283030i	0.989936	+	0.141515i	$0.0451974\pi$
$677$			7.36423i			0.283030i	−0.989936	+	0.141515i	$0.954803\pi$
$678$		0			0
$679$	−1.45351	−	0.839184i	−0.0557805	−	0.0322049i
$680$	−2.37139	−	1.01217i	−0.0909387	−	0.0388148i
$681$		0			0
$682$	4.34542	−	2.24239i	0.166395	−	0.0858656i
$683$	−1.34151	+	5.00660i	−0.0513316	+	0.191572i	−0.986831	−	0.161757i	$-0.948284\pi$
$683$	−1.34151	+	5.00660i	−0.0513316	+	0.191572i	0.935499	+	0.353329i	$0.114951\pi$
$684$		0			0
$685$	10.5346	−	6.08214i	0.402506	−	0.232387i
$686$	−24.1661	+	5.26701i	−0.922666	+	0.201095i
$687$		0			0
$688$	−6.87677	+	35.9858i	−0.262174	+	1.37195i
$689$	1.78294	−	0.496455i	0.0679245	−	0.0189134i
$690$		0			0
$691$	6.75090	+	25.1947i	0.256816	+	0.958451i	0.967071	+	0.254506i	$0.0819130\pi$
$691$	6.75090	+	25.1947i	0.256816	+	0.958451i	−0.710255	+	0.703945i	$0.751420\pi$
$692$	−16.1622	+	22.7346i	−0.614394	+	0.864239i
$693$		0			0
$694$	−40.8254	−	1.92860i	−1.54971	−	0.0732086i
$695$	2.84544	−	10.6193i	0.107934	−	0.402814i
$696$		0			0
$697$	1.72672	+	1.72672i	0.0654044	+	0.0654044i
$698$	−26.4479	−	8.44297i	−1.00107	−	0.319571i
$699$		0			0
$700$	13.0696	−	2.20837i	0.493984	−	0.0834687i
$701$	−2.13901			−0.0807892			−0.0403946	−	0.999184i	$-0.512862\pi$
$701$	−2.13901			−0.0807892			−0.0403946	+	0.999184i	$0.512862\pi$
$702$		0			0
$703$		−	23.3999i		−	0.882545i
$704$	−11.8515	−	0.254028i	−0.446671	−	0.00957402i
$705$		0			0
$706$	−25.1596	−	8.03169i	−0.946892	−	0.302277i
$707$	11.9993	−	11.9993i	0.451279	−	0.451279i
$708$		0			0
$709$	31.8967	+	8.54671i	1.19791	+	0.320978i	0.802007	−	0.597315i	$-0.203766\pi$
$709$	31.8967	+	8.54671i	1.19791	+	0.320978i	0.395901	+	0.918293i	$0.370433\pi$
$710$	0.183313	−	3.88045i	0.00687962	−	0.145631i
$711$		0			0
$712$	5.96685	−	0.720594i	0.223617	−	0.0270054i
$713$	7.61569	−	2.04062i	0.285210	−	0.0764218i
$714$		0			0
$715$	−0.966691	+	3.75406i	−0.0361522	+	0.140394i
$716$	1.74948	−	18.4755i	0.0653810	−	0.690462i
$717$		0			0
$718$	6.97814	+	32.0171i	0.260422	+	1.19487i
$719$	24.1212	+	41.7791i	0.899568	+	1.55810i	0.828047	+	0.560659i	$0.189452\pi$
$719$	24.1212	+	41.7791i	0.899568	+	1.55810i	0.0715216	+	0.997439i	$0.477215\pi$
$720$		0			0
$721$	−3.56176	−	0.954371i	−0.132647	−	0.0355426i
$722$	−27.7516	+	14.3208i	−1.03281	+	0.532965i
$723$		0			0
$724$	17.3001	+	37.8030i	0.642955	+	1.40494i
$725$	−15.4665	+	26.7888i	−0.574412	+	0.994910i
$726$		0			0
$727$	−35.9735			−1.33418			−0.667092	−	0.744976i	$-0.732461\pi$
$727$	−35.9735			−1.33418			−0.667092	+	0.744976i	$0.732461\pi$
$728$	−1.98618	+	14.9770i	−0.0736127	+	0.555085i
$729$		0			0
$730$	5.39869	+	3.46651i	0.199814	+	0.128301i
$731$	−5.75364	+	9.96560i	−0.212806	+	0.368591i
$732$		0			0
$733$	−7.99326	−	7.99326i	−0.295238	−	0.295238i	0.543907	−	0.839145i	$-0.316944\pi$
$733$	−7.99326	−	7.99326i	−0.295238	−	0.295238i	−0.839145	+	0.543907i	$0.816944\pi$
$734$	37.0036	−	19.0952i	1.36583	−	0.704815i
$735$		0			0
$736$	−18.5836	−	4.46951i	−0.685001	−	0.164748i
$737$	−5.38670	−	9.33004i	−0.198422	−	0.343677i
$738$		0			0
$739$	10.6104	−	2.84304i	0.390308	−	0.104583i	−0.0583274	−	0.998298i	$-0.518577\pi$
$739$	10.6104	−	2.84304i	0.390308	−	0.104583i	0.448636	+	0.893715i	$0.351910\pi$
$740$	−5.27433	−	0.499435i	−0.193888	−	0.0183596i
$741$		0			0
$742$	0.723726	+	0.795494i	0.0265688	+	0.0292035i
$743$	9.10445	−	2.43953i	0.334010	−	0.0894977i	−0.0879163	−	0.996128i	$-0.528021\pi$
$743$	9.10445	−	2.43953i	0.334010	−	0.0894977i	0.421926	+	0.906630i	$0.361354\pi$
$744$		0			0
$745$	4.88959	−	2.82301i	0.179141	−	0.103427i
$746$	−1.59244	+	33.7095i	−0.0583035	+	1.23419i
$747$		0			0
$748$	−3.48956	−	1.29840i	−0.127591	−	0.0474742i
$749$	−10.7484	+	10.7484i	−0.392736	+	0.392736i
$750$		0			0
$751$	−11.9625	+	20.7197i	−0.436519	+	0.756073i	−0.997418	−	0.0718109i	$-0.977122\pi$
$751$	−11.9625	+	20.7197i	−0.436519	+	0.756073i	0.560899	+	0.827884i	$0.310456\pi$
$752$	1.22383	+	16.7398i	0.0446286	+	0.610439i
$753$		0			0
$754$	−23.9807	−	25.8469i	−0.873324	−	0.941287i
$755$	−7.14257			−0.259945
$756$		0			0
$757$	−4.03960	−	2.33226i	−0.146822	−	0.0847676i	0.424789	−	0.905292i	$-0.360348\pi$
$757$	−4.03960	−	2.33226i	−0.146822	−	0.0847676i	−0.571611	+	0.820525i	$0.693681\pi$
$758$	−16.8682	−	5.38484i	−0.612680	−	0.195586i
$759$		0			0
$760$	4.90331	+	12.2060i	0.177862	+	0.442757i
$761$	5.39526	−	20.1354i	0.195578	−	0.729907i	−0.796538	−	0.604588i	$-0.793338\pi$
$761$	5.39526	−	20.1354i	0.195578	−	0.729907i	0.992116	−	0.125319i	$-0.0399955\pi$
$762$		0			0
$763$	−7.55350	−	13.0831i	−0.273455	−	0.473638i
$764$	42.4673	+	30.1903i	1.53641	+	1.09225i
$765$		0			0
$766$	−32.1535	−	35.3420i	−1.16175	−	1.27696i
$767$	−50.2562	+	0.490983i	−1.81464	+	0.0177284i
$768$		0			0
$769$	−10.2054	−	38.0871i	−0.368016	−	1.37346i	−0.863285	−	0.504716i	$-0.831597\pi$
$769$	−10.2054	−	38.0871i	−0.368016	−	1.37346i	0.495269	−	0.868740i	$-0.335070\pi$
$770$	−2.20091	+	0.479690i	−0.0793155	+	0.0172868i
$771$		0			0
$772$	19.1555	+	23.1626i	0.689420	+	0.833641i
$773$	−12.6898	+	47.3590i	−0.456421	+	1.70339i	0.227456	+	0.973788i	$0.426959\pi$
$773$	−12.6898	+	47.3590i	−0.456421	+	1.70339i	−0.683877	+	0.729597i	$0.739707\pi$
$774$		0			0
$775$	7.38134	−	7.38134i	0.265146	−	0.265146i
$776$	2.94711	+	1.25790i	0.105795	+	0.0451558i
$777$		0			0
$778$	−22.5755	+	35.1587i	−0.809372	+	1.26050i
$779$		−	12.4581i		−	0.446357i
$780$		0			0
$781$		−	5.60981i		−	0.200735i
$782$	−5.05162	−	3.24366i	−0.180646	−	0.115993i
$783$		0			0
$784$	18.1538	−	6.31523i	0.648351	−	0.225544i
$785$	5.44798	−	5.44798i	0.194447	−	0.194447i
$786$		0			0
$787$	4.46886	−	16.6780i	0.159298	−	0.594507i	−0.839401	−	0.543512i	$-0.817094\pi$
$787$	4.46886	−	16.6780i	0.159298	−	0.594507i	0.998699	−	0.0509947i	$-0.0162392\pi$
$788$	−25.4392	−	30.7608i	−0.906232	−	1.09581i
$789$		0			0
$790$	−0.709960	−	3.25744i	−0.0252592	−	0.115895i
$791$	−1.81859	−	6.78708i	−0.0646617	−	0.241321i
$792$		0			0
$793$	−36.3442	−	35.6409i	−1.29062	−	1.26565i
$794$	−30.3783	+	27.6376i	−1.07809	+	0.980823i
$795$		0			0
$796$	13.0483	−	18.3545i	0.462486	−	0.650557i
$797$	−7.88369	−	13.6550i	−0.279255	−	0.483683i	0.691945	−	0.721950i	$-0.256754\pi$
$797$	−7.88369	−	13.6550i	−0.279255	−	0.483683i	−0.971200	+	0.238267i	$0.923421\pi$
$798$		0			0
$799$	−1.36445	+	5.09220i	−0.0482708	+	0.180149i
$800$	−24.2669	+	7.17748i	−0.857965	+	0.253762i
$801$		0			0
$802$	−2.37826	+	7.45000i	−0.0839794	+	0.263069i
$803$	8.02350	+	4.63237i	0.283143	+	0.163473i
$804$		0			0
$805$	−3.63201			−0.128012
$806$	5.55935	+	10.5197i	0.195820	+	0.370541i
$807$		0			0
$808$	−19.9970	+	25.4904i	−0.703493	+	0.896748i
$809$	−16.1331	+	27.9433i	−0.567210	+	0.982436i	0.429631	+	0.903005i	$0.358644\pi$
$809$	−16.1331	+	27.9433i	−0.567210	+	0.982436i	−0.996840	+	0.0794311i	$0.974690\pi$
$810$		0			0
$811$	−2.82597	+	2.82597i	−0.0992332	+	0.0992332i	−0.754980	−	0.655747i	$-0.772354\pi$
$811$	−2.82597	+	2.82597i	−0.0992332	+	0.0992332i	0.655747	+	0.754980i	$0.272354\pi$
$812$	7.14461	−	19.2017i	0.250727	−	0.673849i
$813$		0			0
$814$	−7.64194	−	0.361006i	−0.267850	−	0.0126533i
$815$	7.28319	−	4.20495i	0.255119	−	0.147293i
$816$		0			0
$817$	56.7061	−	15.1944i	1.98390	−	0.531583i
$818$	19.3186	−	17.5757i	0.675460	−	0.614521i
$819$		0			0
$820$	−2.80804	−	0.265898i	−0.0980612	−	0.00928557i
$821$	25.7200	−	6.89166i	0.897635	−	0.240521i	0.219635	−	0.975582i	$-0.429513\pi$
$821$	25.7200	−	6.89166i	0.897635	−	0.240521i	0.678000	+	0.735062i	$0.262847\pi$
$822$		0			0
$823$	1.80298	+	3.12285i	0.0628478	+	0.108856i	0.895737	−	0.444584i	$-0.146648\pi$
$823$	1.80298	+	3.12285i	0.0628478	+	0.108856i	−0.832889	+	0.553439i	$0.813315\pi$
$824$	6.96951	+	0.993639i	0.242794	+	0.0346151i
$825$		0			0
$826$	−13.3925	−	25.9526i	−0.465984	−	0.903007i
$827$	−18.5758	−	18.5758i	−0.645943	−	0.645943i	0.306067	−	0.952010i	$-0.400987\pi$
$827$	−18.5758	−	18.5758i	−0.645943	−	0.645943i	−0.952010	+	0.306067i	$0.900987\pi$
$828$		0			0
$829$	−0.283646	+	0.491289i	−0.00985143	+	0.0170632i	−0.870909	−	0.491444i	$-0.836469\pi$
$829$	−0.283646	+	0.491289i	−0.00985143	+	0.0170632i	0.861058	+	0.508507i	$0.169803\pi$
$830$	−2.27324	+	3.54031i	−0.0789054	+	0.122886i
$831$		0			0
$832$	0.336364	−	28.8424i	0.0116613	−	0.999932i
$833$	6.03708			0.209172
$834$		0			0
$835$	−3.26397	+	5.65336i	−0.112954	+	0.195643i
$836$	7.90446	+	17.2723i	0.273382	+	0.597373i
$837$		0			0
$838$	−18.3423	−	35.5447i	−0.633625	−	1.22787i
$839$	32.7243	+	8.76844i	1.12977	+	0.302720i	0.774830	−	0.632170i	$-0.217836\pi$
$839$	32.7243	+	8.76844i	1.12977	+	0.302720i	0.354937	+	0.934890i	$0.384502\pi$
$840$		0			0
$841$	9.40638	+	16.2923i	0.324358	+	0.561805i
$842$	38.4796	−	8.38665i	1.32610	−	0.289023i
$843$		0			0
$844$	−2.27696	−	0.215609i	−0.0783764	−	0.00742158i
$845$	−9.15713	−	2.26286i	−0.315015	−	0.0778446i
$846$		0			0
$847$	12.5990	−	3.37588i	0.432905	−	0.115997i
$848$	−1.55386	−	1.34213i	−0.0533597	−	0.0460891i
$849$		0			0
$850$	−7.93952	−	0.375064i	−0.272323	−	0.0128646i
$851$	−11.9151	−	3.19264i	−0.408445	−	0.109442i
$852$		0			0
$853$	−15.4913	+	15.4913i	−0.530411	+	0.530411i	−0.920695	−	0.390283i	$-0.872377\pi$
$853$	−15.4913	+	15.4913i	−0.530411	+	0.530411i	0.390283	+	0.920695i	$0.372377\pi$
$854$	8.99535	−	28.1783i	0.307814	−	0.964240i
$855$		0			0
$856$	17.9123	−	22.8330i	0.612231	−	0.780416i
$857$			17.3171i			0.591540i	0.955259	+	0.295770i	$0.0955762\pi$
$857$			17.3171i			0.591540i	−0.955259	+	0.295770i	$0.904424\pi$
$858$		0			0
$859$	−22.9629			−0.783484			−0.391742	−	0.920075i	$-0.628127\pi$
$859$	−22.9629			−0.783484			−0.391742	+	0.920075i	$0.628127\pi$
$860$	−2.21450	−	13.1058i	−0.0755137	−	0.446905i
$861$		0			0
$862$	−13.7071	+	42.9381i	−0.466867	+	1.46248i
$863$	−18.9344	−	18.9344i	−0.644536	−	0.644536i	0.307131	−	0.951667i	$-0.400631\pi$
$863$	−18.9344	−	18.9344i	−0.644536	−	0.644536i	−0.951667	+	0.307131i	$0.900631\pi$
$864$		0			0
$865$	2.61917	−	9.77489i	0.0890546	−	0.332356i
$866$	−1.01485	+	21.4827i	−0.0344859	+	0.730013i
$867$		0			0
$868$	−4.00602	+	5.63508i	−0.135973	+	0.191267i
$869$	−1.24604	−	4.65029i	−0.0422690	−	0.157750i
$870$		0			0
$871$	22.5732	−	13.3284i	0.764865	−	0.451615i
$872$	17.3118	+	23.0689i	0.586253	+	0.781212i
$873$		0			0
$874$	6.52209	+	29.9247i	0.220613	+	1.01222i
$875$	−8.81910	+	5.09171i	−0.298140	+	0.172131i
$876$		0			0
$877$	−11.6288	+	43.3992i	−0.392676	+	1.46549i	0.433027	+	0.901381i	$0.357446\pi$
$877$	−11.6288	+	43.3992i	−0.392676	+	1.46549i	−0.825703	+	0.564106i	$0.809221\pi$
$878$	−2.14184	−	4.15057i	−0.0722837	−	0.140075i
$879$		0			0
$880$	4.06186	−	1.41301i	0.136925	−	0.0476326i
$881$	−2.13057	−	1.23009i	−0.0717808	−	0.0414427i	0.463680	−	0.886003i	$-0.346529\pi$
$881$	−2.13057	−	1.23009i	−0.0717808	−	0.0414427i	−0.535461	+	0.844560i	$0.679862\pi$
$882$		0			0
$883$		−	39.7470i		−	1.33759i	−0.743446	−	0.668796i	$-0.766810\pi$
$883$		−	39.7470i		−	1.33759i	0.743446	−	0.668796i	$-0.233190\pi$
$884$	3.07624	−	8.52145i	0.103465	−	0.286607i
$885$		0			0
$886$	−9.25807	+	14.4184i	−0.311031	+	0.484394i
$887$	17.1497	+	9.90141i	0.575832	+	0.332457i	0.759475	−	0.650536i	$-0.225456\pi$
$887$	17.1497	+	9.90141i	0.575832	+	0.332457i	−0.183643	+	0.982993i	$0.558789\pi$
$888$		0			0
$889$	19.7085	−	19.7085i	0.661003	−	0.661003i
$890$	−1.93767	+	0.999906i	−0.0649508	+	0.0335169i
$891$		0			0
$892$	−18.7146	−	22.6295i	−0.626610	−	0.757692i
$893$	23.2919	−	13.4476i	0.779435	−	0.450007i
$894$		0			0
$895$	1.74256	+	6.50333i	0.0582474	+	0.217382i
$896$	15.0560	−	7.36526i	0.502986	−	0.246056i
$897$		0			0
$898$	−9.05616	−	9.95422i	−0.302208	−	0.332177i
$899$	−4.17607	−	15.5853i	−0.139280	−	0.519799i
$900$		0			0
$901$	−0.322450	−	0.558500i	−0.0107424	−	0.0186063i
$902$	−4.06855	−	0.192199i	−0.135468	−	0.00639953i
$903$		0			0
$904$	5.00059	+	12.4481i	0.166317	+	0.414018i
$905$	−10.6650	−	10.6650i	−0.354515	−	0.354515i
$906$		0			0
$907$	−16.4874	−	9.51900i	−0.547455	−	0.316073i	0.200640	−	0.979665i	$-0.435698\pi$
$907$	−16.4874	−	9.51900i	−0.547455	−	0.316073i	−0.748095	+	0.663592i	$0.769031\pi$
$908$	−2.98569	−	17.6699i	−0.0990838	−	0.586397i
$909$		0			0
$910$	−1.21947	−	5.34373i	−0.0404250	−	0.177143i
$911$			1.28948i			0.0427225i	0.999772	+	0.0213612i	$0.00680001\pi$
$911$			1.28948i			0.0427225i	−0.999772	+	0.0213612i	$0.993200\pi$
$912$		0			0
$913$	−3.03778	+	5.26159i	−0.100536	+	0.174133i
$914$	16.3355	+	5.21477i	0.540329	+	0.172489i
$915$		0			0
$916$	−4.33830	−	1.61420i	−0.143342	−	0.0533347i
$917$	−2.00489	−	0.537210i	−0.0662074	−	0.0177402i
$918$		0			0
$919$	−23.2515	+	13.4243i	−0.766997	+	0.442826i	−0.831802	−	0.555072i	$-0.812691\pi$
$919$	−23.2515	+	13.4243i	−0.766997	+	0.442826i	0.0648055	+	0.997898i	$0.479357\pi$
$920$	6.88421	−	0.831380i	0.226966	−	0.0274098i
$921$		0			0
$922$	−23.0281	−	25.3116i	−0.758389	−	0.833595i
$923$	13.6494	−	0.133350i	0.449277	−	0.00438926i
$924$		0			0
$925$	−15.7755	+	4.22703i	−0.518695	+	0.138984i
$926$	−5.43227	−	24.9244i	−0.178516	−	0.819066i
$927$		0			0
$928$	−9.14672	+	38.0309i	−0.300256	+	1.24842i
$929$	−37.8024	−	10.1291i	−1.24026	−	0.332326i	−0.421692	−	0.906739i	$-0.638564\pi$
$929$	−37.8024	−	10.1291i	−1.24026	−	0.332326i	−0.818566	+	0.574413i	$0.805230\pi$
$930$		0			0
$931$	−21.7784	−	21.7784i	−0.713757	−	0.713757i
$932$	27.6874	−	12.6708i	0.906931	−	0.415047i
$933$		0			0
$934$	21.6091	+	13.8753i	0.707073	+	0.454014i
$935$	1.35078			0.0441752
$936$		0			0
$937$	46.1571			1.50789			0.753943	−	0.656939i	$-0.228149\pi$
$937$	46.1571			1.50789			0.753943	+	0.656939i	$0.228149\pi$
$938$	12.8179	+	8.23039i	0.418518	+	0.268732i
$939$		0			0
$940$	−2.53395	−	5.53700i	−0.0826484	−	0.180597i
$941$	35.7367	+	35.7367i	1.16498	+	1.16498i	0.983370	+	0.181611i	$0.0581313\pi$
$941$	35.7367	+	35.7367i	1.16498	+	1.16498i	0.181611	+	0.983370i	$0.441869\pi$
$942$		0			0
$943$	−6.34359	−	1.69976i	−0.206576	−	0.0553518i
$944$	31.3250	+	46.1256i	1.01954	+	1.50126i
$945$		0			0
$946$	−4.08732	−	18.7535i	−0.132890	−	0.609728i
$947$	−0.723796	+	0.193941i	−0.0235202	+	0.00630222i	−0.270560	−	0.962703i	$-0.587209\pi$
$947$	−0.723796	+	0.193941i	−0.0235202	+	0.00630222i	0.247040	+	0.969005i	$0.420542\pi$
$948$		0			0
$949$	−11.0805	+	19.6324i	−0.359687	+	0.637295i
$950$	27.2883	+	29.9943i	0.885348	+	0.973143i
$951$		0			0
$952$	5.22647	−	0.631181i	0.169391	−	0.0204567i
$953$	41.5062	−	23.9636i	1.34452	−	0.776257i	0.357050	−	0.934085i	$-0.383783\pi$
$953$	41.5062	−	23.9636i	1.34452	−	0.776257i	0.987467	+	0.157828i	$0.0504492\pi$
$954$		0			0
$955$	−18.2591	−	4.89251i	−0.590851	−	0.158318i
$956$	−19.8511	+	53.3514i	−0.642030	+	1.72551i
$957$		0			0
$958$	−22.0837	−	7.04978i	−0.713491	−	0.227768i
$959$	−12.4184	+	21.5092i	−0.401010	+	0.694569i
$960$		0			0
$961$		−	25.5550i		−	0.824354i
$962$	0.696723	−	18.6025i	0.0224633	−	0.599768i
$963$		0			0
$964$	−7.37591	+	1.24631i	−0.237562	+	0.0401409i
$965$	−9.44359	−	5.45226i	−0.304000	−	0.175514i
$966$		0			0
$967$	−8.44481	−	8.44481i	−0.271567	−	0.271567i	0.558164	−	0.829731i	$-0.311506\pi$
$967$	−8.44481	−	8.44481i	−0.271567	−	0.271567i	−0.829731	+	0.558164i	$0.811506\pi$
$968$	−23.1076	+	9.28266i	−0.742706	+	0.298356i
$969$		0			0
$970$	−1.16121	−	0.0548557i	−0.0372842	−	0.00176131i
$971$	−24.1539	−	41.8358i	−0.775136	−	1.34257i	−0.934718	−	0.355390i	$-0.884348\pi$
$971$	−24.1539	−	41.8358i	−0.775136	−	1.34257i	0.159582	−	0.987185i	$-0.448985\pi$
$972$		0			0
$973$	5.80974	+	21.6822i	0.186252	+	0.695101i
$974$	34.3409	+	37.7463i	1.10035	+	1.20947i
$975$		0			0
$976$	−10.5999	+	55.4688i	−0.339295	+	1.77551i
$977$	−8.21436	−	30.6564i	−0.262801	−	0.980786i	−0.963583	−	0.267410i	$-0.913832\pi$
$977$	−8.21436	−	30.6564i	−0.262801	−	0.980786i	0.700782	−	0.713376i	$-0.252835\pi$
$978$		0			0
$979$	−2.72683	+	1.57434i	−0.0871500	+	0.0503161i
$980$	−5.37365	+	4.44400i	−0.171655	+	0.141958i
$981$		0			0
$982$	−18.8428	+	9.72354i	−0.601297	+	0.310291i
$983$	18.1345	−	18.1345i	0.578400	−	0.578400i	−0.356062	−	0.934462i	$-0.615881\pi$
$983$	18.1345	−	18.1345i	0.578400	−	0.578400i	0.934462	+	0.356062i	$0.115881\pi$
$984$		0			0
$985$	12.5414	+	7.24080i	0.399603	+	0.230711i
$986$	−6.63807	+	10.3380i	−0.211399	+	0.329229i
$987$		0			0
$988$	−41.8379	+	19.6432i	−1.33104	+	0.624935i
$989$		−	30.9475i		−	0.984074i
$990$		0			0
$991$	−15.3411	−	8.85718i	−0.487326	−	0.281358i	0.236139	−	0.971719i	$-0.424118\pi$
$991$	−15.3411	−	8.85718i	−0.487326	−	0.281358i	−0.723464	+	0.690362i	$0.757451\pi$
$992$	6.30322	−	11.5979i	0.200127	−	0.368232i
$993$		0			0
$994$	3.63736	+	7.04866i	0.115370	+	0.223570i
$995$	−2.11456	+	7.89164i	−0.0670360	+	0.250182i
$996$		0			0
$997$	−4.27051	+	2.46558i	−0.135249	+	0.0780858i	−0.566098	−	0.824338i	$-0.691547\pi$
$997$	−4.27051	+	2.46558i	−0.135249	+	0.0780858i	0.430849	+	0.902424i	$0.358214\pi$
$998$	−12.9967	−	59.6315i	−0.411403	−	1.88760i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ed.e.19.5		56
3.2	odd	2		312.2.bt.d.19.10	yes	56
8.3	odd	2	inner	936.2.ed.e.19.12		56
13.11	odd	12	inner	936.2.ed.e.739.12		56
24.11	even	2		312.2.bt.d.19.3	✓	56
39.11	even	12		312.2.bt.d.115.3	yes	56
104.11	even	12	inner	936.2.ed.e.739.5		56
312.11	odd	12		312.2.bt.d.115.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.3	✓	56	24.11	even	2
312.2.bt.d.19.10	yes	56	3.2	odd	2
312.2.bt.d.115.3	yes	56	39.11	even	12
312.2.bt.d.115.10	yes	56	312.11	odd	12
936.2.ed.e.19.5		56	1.1	even	1	trivial
936.2.ed.e.19.12		56	8.3	odd	2	inner
936.2.ed.e.739.5		56	104.11	even	12	inner
936.2.ed.e.739.12		56	13.11	odd	12	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.764112 + 1.19001i) q^{2} +(-0.832266 - 1.81861i) q^{4} +(0.513065 + 0.513065i) q^{5} +(-1.43100 - 0.383434i) q^{7} +(2.80011 + 0.399211i) q^{8} +(-1.00259 + 0.218515i) q^{10} +(-1.43129 + 0.383513i) q^{11} +(-0.967164 - 3.47341i) q^{13} +(1.54973 - 1.40992i) q^{14} +(-2.61467 + 3.02713i) q^{16} +(-1.08804 + 0.628178i) q^{17} +(6.19113 + 1.65891i) q^{19} +(0.506057 - 1.36007i) q^{20} +(0.637280 - 1.99630i) q^{22} +(1.68941 - 2.92615i) q^{23} -4.47353i q^{25} +(4.87243 + 1.50314i) q^{26} +(0.493654 + 2.92154i) q^{28} +(-5.98829 - 3.45734i) q^{29} +(1.65000 + 1.65000i) q^{31} +(-1.60443 - 5.42455i) q^{32} +(0.0838407 - 1.77478i) q^{34} +(-0.537467 - 0.930920i) q^{35} +(-0.944898 - 3.52641i) q^{37} +(-6.70484 + 6.09994i) q^{38} +(1.23182 + 1.64146i) q^{40} +(-0.503062 - 1.87745i) q^{41} +(7.93214 - 4.57963i) q^{43} +(1.88867 + 2.28377i) q^{44} +(2.19126 + 4.24633i) q^{46} +(2.96711 - 2.96711i) q^{47} +(-4.16145 - 2.40261i) q^{49} +(5.32356 + 3.41828i) q^{50} +(-5.51184 + 4.64970i) q^{52} +0.513310i q^{53} +(-0.931112 - 0.537578i) q^{55} +(-3.85388 - 1.64493i) q^{56} +(8.69000 - 4.48435i) q^{58} +(3.60773 - 13.4642i) q^{59} +(12.2267 - 7.05906i) q^{61} +(-3.22431 + 0.702740i) q^{62} +(7.68126 + 2.23567i) q^{64} +(1.28587 - 2.27830i) q^{65} +(1.88176 + 7.02284i) q^{67} +(2.04795 + 1.45590i) q^{68} +(1.51849 + 0.0717338i) q^{70} +(-0.979852 + 3.65686i) q^{71} +(-4.42114 - 4.42114i) q^{73} +(4.91848 + 1.57013i) q^{74} +(-2.13577 - 12.6399i) q^{76} +2.19522 q^{77} +3.24902i q^{79} +(-2.89461 + 0.211622i) q^{80} +(2.61859 + 0.835933i) q^{82} +(2.89926 - 2.89926i) q^{83} +(-0.880529 - 0.235937i) q^{85} +(-0.611226 + 12.9387i) q^{86} +(-4.16088 + 0.502494i) q^{88} +(2.05252 - 0.549972i) q^{89} +(0.0521823 + 5.34128i) q^{91} +(-6.72756 - 0.637043i) q^{92} +(1.26370 + 5.79811i) q^{94} +(2.32532 + 4.02758i) q^{95} +(1.09430 + 0.293217i) q^{97} +(6.03896 - 3.11632i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{8} + 28 q^{14} + 12 q^{16} - 8 q^{19} + 4 q^{20} + 10 q^{22} - 34 q^{26} - 14 q^{28} + 30 q^{32} + 56 q^{34} - 28 q^{40} - 40 q^{41} + 44 q^{44} - 18 q^{46} + 24 q^{49} + 72 q^{50} + 32 q^{52}+ \cdots - 4 q^{98}+O(q^{100}) \) 56 * q + 12 * q^8 + 28 * q^14 + 12 * q^16 - 8 * q^19 + 4 * q^20 + 10 * q^22 - 34 * q^26 - 14 * q^28 + 30 * q^32 + 56 * q^34 - 28 * q^40 - 40 * q^41 + 44 * q^44 - 18 * q^46 + 24 * q^49 + 72 * q^50 + 32 * q^52 + 54 * q^56 - 16 * q^58 - 32 * q^59 - 48 * q^65 - 24 * q^67 + 26 * q^68 + 64 * q^70 + 44 * q^73 + 6 * q^74 + 6 * q^76 + 4 * q^80 - 30 * q^82 - 40 * q^83 + 28 * q^86 + 126 * q^88 + 68 * q^89 - 72 * q^91 - 52 * q^92 + 34 * q^94 - 4 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more