LMFDB - Embedded newform 972.2.l.d.107.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [972,2,Mod(107,972)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(972, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("972.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,3,0,3,6,0,0,-9,0,-3,0,0,6,33] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	972.107
Dual form			972.2.l.d.863.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41292 + 0.0603944i) q^{2} +(1.99271 - 0.170665i) q^{4} +(-0.0476648 + 0.130958i) q^{5} +(4.57823 + 0.807266i) q^{7} +(-2.80523 + 0.361485i) q^{8} +(0.0594376 - 0.187912i) q^{10} +(0.987987 - 0.359598i) q^{11} +(1.19199 - 1.00020i) q^{13} +(-6.51745 - 0.864105i) q^{14} +(3.94175 - 0.680171i) q^{16} +(5.25631 - 3.03473i) q^{17} +(-3.80088 - 2.19444i) q^{19} +(-0.0726319 + 0.269095i) q^{20} +(-1.37423 + 0.567753i) q^{22} +(0.440052 + 2.49566i) q^{23} +(3.81534 + 3.20145i) q^{25} +(-1.62379 + 1.48520i) q^{26} +(9.26084 + 0.827297i) q^{28} +(0.395532 - 0.471376i) q^{29} +(-4.88457 + 0.861281i) q^{31} +(-5.52831 + 1.19909i) q^{32} +(-7.24349 + 4.60530i) q^{34} +(-0.323938 + 0.561078i) q^{35} +(-1.43991 - 2.49400i) q^{37} +(5.50288 + 2.87102i) q^{38} +(0.0863714 - 0.384598i) q^{40} +(-4.23420 - 5.04612i) q^{41} +(-0.748529 - 2.05657i) q^{43} +(1.90740 - 0.885188i) q^{44} +(-0.772484 - 3.49960i) q^{46} +(-1.91917 + 10.8842i) q^{47} +(13.7307 + 4.99756i) q^{49} +(-5.58414 - 4.29298i) q^{50} +(2.20459 - 2.19654i) q^{52} -8.73360i q^{53} +0.146525i q^{55} +(-13.1348 - 0.609605i) q^{56} +(-0.530388 + 0.689907i) q^{58} +(7.71009 + 2.80624i) q^{59} +(1.94148 - 11.0107i) q^{61} +(6.84951 - 1.51193i) q^{62} +(7.73866 - 2.02810i) q^{64} +(0.0741682 + 0.203776i) q^{65} +(3.62786 + 4.32351i) q^{67} +(9.95636 - 6.94440i) q^{68} +(0.423814 - 0.812324i) q^{70} +(2.33277 + 4.04048i) q^{71} +(-5.64518 + 9.77774i) q^{73} +(2.18511 + 3.43687i) q^{74} +(-7.94854 - 3.72419i) q^{76} +(4.81353 - 0.848755i) q^{77} +(1.07643 - 1.28284i) q^{79} +(-0.0988087 + 0.548623i) q^{80} +(6.28736 + 6.87406i) q^{82} +(-1.79797 - 1.50867i) q^{83} +(0.146881 + 0.833006i) q^{85} +(1.18182 + 2.86056i) q^{86} +(-2.64154 + 1.36590i) q^{88} +(7.63741 + 4.40946i) q^{89} +(6.26466 - 3.61690i) q^{91} +(1.30282 + 4.89801i) q^{92} +(2.05430 - 15.4944i) q^{94} +(0.468547 - 0.393158i) q^{95} +(5.29482 - 1.92716i) q^{97} +(-19.7022 - 6.23192i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} + 33 q^{14} + 3 q^{16} - 18 q^{17} - 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 30 q^{29} + 33 q^{32} + 15 q^{34} - 6 q^{37} - 63 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) $ 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 + 33 * q^14 + 3 * q^16 - 18 * q^17 - 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 30 * q^29 + 33 * q^32 + 15 * q^34 - 6 * q^37 - 63 * q^38 + 33 * q^40 - 24 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 21 * q^50 + 57 * q^52 - 18 * q^56 + 57 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 + 30 * q^65 - 102 * q^68 + 51 * q^70 - 6 * q^73 + 75 * q^74 + 27 * q^76 - 42 * q^77 - 12 * q^82 - 24 * q^85 - 111 * q^86 + 27 * q^88 + 147 * q^92 + 30 * q^94 - 12 * q^97 - 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	−1.41292	+	0.0603944i	−0.999088	+	0.0427053i
$2$	−1.41292	+	0.0603944i	−0.999088	+	0.0427053i
$3$		0			0
$3$		0			0
$4$	1.99271	−	0.170665i	0.996353	−	0.0853327i
$5$	−0.0476648	+	0.130958i	−0.0213163	+	0.0585662i	−0.949894	−	0.312571i	$-0.898810\pi$
$5$	−0.0476648	+	0.130958i	−0.0213163	+	0.0585662i	0.928578	+	0.371137i	$0.121032\pi$
$6$		0			0
$7$	4.57823	+	0.807266i	1.73041	+	0.305118i	0.948147	−	0.317831i	$-0.102955\pi$
$7$	4.57823	+	0.807266i	1.73041	+	0.305118i	0.782262	+	0.622949i	$0.214066\pi$
$8$	−2.80523	+	0.361485i	−0.991799	+	0.127804i
$9$		0			0
$10$	0.0594376	−	0.187912i	0.0187958	−	0.0594231i
$11$	0.987987	−	0.359598i	0.297889	−	0.108423i	−0.188752	−	0.982025i	$-0.560444\pi$
$11$	0.987987	−	0.359598i	0.297889	−	0.108423i	0.486641	+	0.873602i	$0.338222\pi$
$12$		0			0
$13$	1.19199	−	1.00020i	0.330600	−	0.277406i	−0.462344	−	0.886700i	$-0.652992\pi$
$13$	1.19199	−	1.00020i	0.330600	−	0.277406i	0.792944	+	0.609294i	$0.208547\pi$
$14$	−6.51745	−	0.864105i	−1.74186	−	0.230942i
$15$		0			0
$16$	3.94175	−	0.680171i	0.985437	−	0.170043i
$17$	5.25631	−	3.03473i	1.27484	−	0.736031i	0.298948	−	0.954269i	$-0.403364\pi$
$17$	5.25631	−	3.03473i	1.27484	−	0.736031i	0.975895	+	0.218238i	$0.0700310\pi$
$18$		0			0
$19$	−3.80088	−	2.19444i	−0.871981	−	0.503439i	−0.00397518	−	0.999992i	$-0.501265\pi$
$19$	−3.80088	−	2.19444i	−0.871981	−	0.503439i	−0.868006	+	0.496553i	$0.834599\pi$
$20$	−0.0726319	+	0.269095i	−0.0162410	+	0.0601715i
$21$		0			0
$22$	−1.37423	+	0.567753i	−0.292987	+	0.121045i
$23$	0.440052	+	2.49566i	0.0917572	+	0.520381i	0.995693	+	0.0927127i	$0.0295538\pi$
$23$	0.440052	+	2.49566i	0.0917572	+	0.520381i	−0.903936	+	0.427668i	$0.859335\pi$
$24$		0			0
$25$	3.81534	+	3.20145i	0.763069	+	0.640291i
$26$	−1.62379	+	1.48520i	−0.318451	+	0.291271i
$27$		0			0
$28$	9.26084	+	0.827297i	1.75013	+	0.156345i
$29$	0.395532	−	0.471376i	0.0734484	−	0.0875324i	−0.728069	−	0.685504i	$-0.759582\pi$
$29$	0.395532	−	0.471376i	0.0734484	−	0.0875324i	0.801517	+	0.597971i	$0.204026\pi$
$30$		0			0
$31$	−4.88457	+	0.861281i	−0.877295	+	0.154691i	−0.594119	−	0.804377i	$-0.702499\pi$
$31$	−4.88457	+	0.861281i	−0.877295	+	0.154691i	−0.283176	+	0.959068i	$0.591388\pi$
$32$	−5.52831	+	1.19909i	−0.977276	+	0.211971i
$33$		0			0
$34$	−7.24349	+	4.60530i	−1.24225	+	0.789802i
$35$	−0.323938	+	0.561078i	−0.0547556	+	0.0948394i
$36$		0			0
$37$	−1.43991	−	2.49400i	−0.236720	−	0.410012i	0.723051	−	0.690795i	$-0.242739\pi$
$37$	−1.43991	−	2.49400i	−0.236720	−	0.410012i	−0.959771	+	0.280783i	$0.909406\pi$
$38$	5.50288	+	2.87102i	0.892685	+	0.465741i
$39$		0			0
$40$	0.0863714	−	0.384598i	0.0136565	−	0.0608102i
$41$	−4.23420	−	5.04612i	−0.661271	−	0.788072i	0.326297	−	0.945267i	$-0.394199\pi$
$41$	−4.23420	−	5.04612i	−0.661271	−	0.788072i	−0.987568	+	0.157196i	$0.949755\pi$
$42$		0			0
$43$	−0.748529	−	2.05657i	−0.114150	−	0.313623i	0.869441	−	0.494036i	$-0.164479\pi$
$43$	−0.748529	−	2.05657i	−0.114150	−	0.313623i	−0.983591	+	0.180413i	$0.942257\pi$
$44$	1.90740	−	0.885188i	0.287551	−	0.133447i
$45$		0			0
$46$	−0.772484	−	3.49960i	−0.113897	−	0.515988i
$47$	−1.91917	+	10.8842i	−0.279940	+	1.58762i	0.442878	+	0.896582i	$0.353958\pi$
$47$	−1.91917	+	10.8842i	−0.279940	+	1.58762i	−0.722818	+	0.691038i	$0.757154\pi$
$48$		0			0
$49$	13.7307	+	4.99756i	1.96153	+	0.713938i
$50$	−5.58414	−	4.29298i	−0.789716	−	0.607120i
$51$		0			0
$52$	2.20459	−	2.19654i	0.305722	−	0.304605i
$53$		−	8.73360i		−	1.19965i	−0.800130	−	0.599826i	$-0.795236\pi$
$53$		−	8.73360i		−	1.19965i	0.800130	−	0.599826i	$-0.204764\pi$
$54$		0			0
$55$			0.146525i			0.0197574i
$56$	−13.1348	−	0.609605i	−1.75521	−	0.0814619i
$57$		0			0
$58$	−0.530388	+	0.689907i	−0.0696433	+	0.0905892i
$59$	7.71009	+	2.80624i	1.00377	+	0.365342i	0.791036	−	0.611769i	$-0.209542\pi$
$59$	7.71009	+	2.80624i	1.00377	+	0.365342i	0.212732	+	0.977111i	$0.431764\pi$
$60$		0			0
$61$	1.94148	−	11.0107i	0.248581	−	1.40977i	−0.563448	−	0.826152i	$-0.690525\pi$
$61$	1.94148	−	11.0107i	0.248581	−	1.40977i	0.812028	−	0.583618i	$-0.198364\pi$
$62$	6.84951	−	1.51193i	0.869888	−	0.192015i
$63$		0			0
$64$	7.73866	−	2.02810i	0.967332	−	0.253513i
$65$	0.0741682	+	0.203776i	0.00919944	+	0.0252752i
$66$		0			0
$67$	3.62786	+	4.32351i	0.443213	+	0.528201i	0.940686	−	0.339279i	$-0.110183\pi$
$67$	3.62786	+	4.32351i	0.443213	+	0.528201i	−0.497473	+	0.867480i	$0.665739\pi$
$68$	9.95636	−	6.94440i	1.20739	−	0.842132i
$69$		0			0
$70$	0.423814	−	0.812324i	0.0506555	−	0.0970913i
$71$	2.33277	+	4.04048i	0.276849	+	0.479517i	0.970600	−	0.240698i	$-0.0773764\pi$
$71$	2.33277	+	4.04048i	0.276849	+	0.479517i	−0.693751	+	0.720215i	$0.744043\pi$
$72$		0			0
$73$	−5.64518	+	9.77774i	−0.660718	+	1.14440i	0.319709	+	0.947516i	$0.396415\pi$
$73$	−5.64518	+	9.77774i	−0.660718	+	1.14440i	−0.980427	+	0.196882i	$0.936918\pi$
$74$	2.18511	+	3.43687i	0.254014	+	0.399528i
$75$		0			0
$76$	−7.94854	−	3.72419i	−0.911761	−	0.427194i
$77$	4.81353	−	0.848755i	0.548552	−	0.0967246i
$78$		0			0
$79$	1.07643	−	1.28284i	0.121108	−	0.144330i	−0.702084	−	0.712094i	$-0.747747\pi$
$79$	1.07643	−	1.28284i	0.121108	−	0.144330i	0.823192	+	0.567764i	$0.192191\pi$
$80$	−0.0988087	+	0.548623i	−0.0110471	+	0.0613379i
$81$		0			0
$82$	6.28736	+	6.87406i	0.694322	+	0.759113i
$83$	−1.79797	−	1.50867i	−0.197353	−	0.165598i	0.538756	−	0.842462i	$-0.318894\pi$
$83$	−1.79797	−	1.50867i	−0.197353	−	0.165598i	−0.736109	+	0.676863i	$0.763339\pi$
$84$		0			0
$85$	0.146881	+	0.833006i	0.0159315	+	0.0903522i
$86$	1.18182	+	2.86056i	0.127439	+	0.308462i
$87$		0			0
$88$	−2.64154	+	1.36590i	−0.281590	+	0.145605i
$89$	7.63741	+	4.40946i	0.809564	+	0.467402i	0.846804	−	0.531905i	$-0.178524\pi$
$89$	7.63741	+	4.40946i	0.809564	+	0.467402i	−0.0372408	+	0.999306i	$0.511857\pi$
$90$		0			0
$91$	6.26466	−	3.61690i	0.656715	−	0.379154i
$92$	1.30282	+	4.89801i	0.135828	+	0.510653i
$93$		0			0
$94$	2.05430	−	15.4944i	0.211885	−	1.59813i
$95$	0.468547	−	0.393158i	0.0480719	−	0.0403371i
$96$		0			0
$97$	5.29482	−	1.92716i	0.537607	−	0.195673i	−0.0589247	−	0.998262i	$-0.518767\pi$
$97$	5.29482	−	1.92716i	0.537607	−	0.195673i	0.596532	+	0.802589i	$0.296545\pi$
$98$	−19.7022	−	6.23192i	−1.99023	−	0.629519i
$99$		0			0
$100$	8.14923	+	5.72841i	0.814923	+	0.572841i
$101$	10.2986	+	1.81591i	1.02474	+	0.180690i	0.660667	−	0.750679i	$-0.270273\pi$
$101$	10.2986	+	1.81591i	1.02474	+	0.180690i	0.364077	+	0.931369i	$0.381385\pi$
$102$		0			0
$103$	0.528403	−	1.45178i	0.0520651	−	0.143048i	−0.910934	−	0.412552i	$-0.864638\pi$
$103$	0.528403	−	1.45178i	0.0520651	−	0.143048i	0.962999	+	0.269504i	$0.0868598\pi$
$104$	−2.98226	+	3.23669i	−0.292435	+	0.317383i
$105$		0			0
$106$	0.527461	+	12.3399i	0.0512315	+	1.19856i
$107$	7.89051			0.762805			0.381402	−	0.924409i	$-0.375441\pi$
$107$	7.89051			0.762805			0.381402	+	0.924409i	$0.375441\pi$
$108$		0			0
$109$	1.78550			0.171020			0.0855098	−	0.996337i	$-0.472748\pi$
$109$	1.78550			0.171020			0.0855098	+	0.996337i	$0.472748\pi$
$110$	−0.00884928	−	0.207028i	−0.000843746	−	0.0197394i
$111$		0			0
$112$	18.5953	+	0.0680555i	1.75709	+	0.00643064i
$113$	3.63295	−	9.98146i	0.341759	−	0.938976i	−0.643125	−	0.765762i	$-0.722362\pi$
$113$	3.63295	−	9.98146i	0.341759	−	0.938976i	0.984884	−	0.173215i	$-0.0554155\pi$
$114$		0			0
$115$	−0.347801	−	0.0613268i	−0.0324327	−	0.00571875i
$116$	0.707730	−	1.00682i	0.0657111	−	0.0934807i
$117$		0			0
$118$	−11.0632	−	3.49936i	−1.01845	−	0.322142i
$119$	26.5145	−	9.65048i	2.43058	−	0.884658i
$120$		0			0
$121$	−7.57968	+	6.36011i	−0.689062	+	0.578192i
$122$	−2.07817	+	15.6745i	−0.188149	+	1.41910i
$123$		0			0
$124$	−9.58652	+	2.54991i	−0.860894	+	0.228988i
$125$	−1.20457	+	0.695459i	−0.107740	+	0.0622038i
$126$		0			0
$127$	−2.89596	−	1.67198i	−0.256975	−	0.148364i	0.365979	−	0.930623i	$-0.380734\pi$
$127$	−2.89596	−	1.67198i	−0.256975	−	0.148364i	−0.622954	+	0.782259i	$0.714067\pi$
$128$	−10.8116	+	3.33292i	−0.955623	+	0.294591i
$129$		0			0
$130$	−0.117101	−	0.283440i	−0.0102704	−	0.0248593i
$131$	0.455284	+	2.58205i	0.0397784	+	0.225594i	0.998216	−	0.0597082i	$-0.0190170\pi$
$131$	0.455284	+	2.58205i	0.0397784	+	0.225594i	−0.958438	+	0.285303i	$0.907906\pi$
$132$		0			0
$133$	−15.6298	−	13.1150i	−1.35528	−	1.13721i
$134$	−5.38700	−	5.88969i	−0.465366	−	0.508791i
$135$		0			0
$136$	−13.6482	+	10.4132i	−1.17032	+	0.892926i
$137$	5.73036	−	6.82918i	0.489578	−	0.583456i	−0.463532	−	0.886080i	$-0.653418\pi$
$137$	5.73036	−	6.82918i	0.489578	−	0.583456i	0.953110	+	0.302624i	$0.0978626\pi$
$138$		0			0
$139$	−14.7775	+	2.60567i	−1.25341	+	0.221010i	−0.760654	−	0.649158i	$-0.775121\pi$
$139$	−14.7775	+	2.60567i	−1.25341	+	0.221010i	−0.492756	+	0.870168i	$0.664010\pi$
$140$	−0.549757	+	1.17335i	−0.0464630	+	0.0991660i
$141$		0			0
$142$	−3.54005	−	5.56800i	−0.297074	−	0.467256i
$143$	0.818005	−	1.41683i	0.0684050	−	0.118481i
$144$		0			0
$145$	0.0428775	+	0.0742661i	0.00356079	+	0.00616746i
$146$	7.38569	−	14.1561i	0.611244	−	1.17157i
$147$		0			0
$148$	−3.29496	−	4.72407i	−0.270844	−	0.388316i
$149$	11.6384	+	13.8701i	0.953455	+	1.13628i	0.990575	+	0.136972i	$0.0437372\pi$
$149$	11.6384	+	13.8701i	0.953455	+	1.13628i	−0.0371200	+	0.999311i	$0.511818\pi$
$150$		0			0
$151$	4.99425	+	13.7216i	0.406427	+	1.11665i	0.959055	+	0.283220i	$0.0914027\pi$
$151$	4.99425	+	13.7216i	0.406427	+	1.11665i	−0.552628	+	0.833428i	$0.686375\pi$
$152$	11.4556	+	4.78195i	0.929172	+	0.387867i
$153$		0			0
$154$	−6.74988	+	1.48994i	−0.543921	+	0.120062i
$155$	0.120030	−	0.680726i	0.00964107	−	0.0546772i
$156$		0			0
$157$	−0.128774	−	0.0468700i	−0.0102773	−	0.00374063i	0.336876	−	0.941549i	$-0.390630\pi$
$157$	−0.128774	−	0.0468700i	−0.0102773	−	0.00374063i	−0.347154	+	0.937808i	$0.612852\pi$
$158$	−1.44343	+	1.87756i	−0.114833	+	0.149371i
$159$		0			0
$160$	0.106475	−	0.781130i	0.00841762	−	0.0617537i
$161$			11.7810i			0.928469i
$162$		0			0
$163$		−	12.0210i		−	0.941554i	−0.882252	−	0.470777i	$-0.843974\pi$
$163$		−	12.0210i		−	0.941554i	0.882252	−	0.470777i	$-0.156026\pi$
$164$	−9.29871	−	9.33280i	−0.726107	−	0.728769i
$165$		0			0
$166$	2.63151	+	2.02305i	0.204244	+	0.157019i
$167$	−10.5733	−	3.84838i	−0.818189	−	0.297797i	−0.101187	−	0.994867i	$-0.532264\pi$
$167$	−10.5733	−	3.84838i	−0.818189	−	0.297797i	−0.717002	+	0.697071i	$0.754486\pi$
$168$		0			0
$169$	−1.83698	+	10.4180i	−0.141306	+	0.801387i
$170$	−0.257841	−	1.16810i	−0.0197755	−	0.0895894i
$171$		0			0
$172$	−1.84258	−	3.97038i	−0.140496	−	0.302739i
$173$	−1.95052	−	5.35901i	−0.148295	−	0.407438i	0.843197	−	0.537605i	$-0.180671\pi$
$173$	−1.95052	−	5.35901i	−0.148295	−	0.407438i	−0.991492	+	0.130167i	$0.958449\pi$
$174$		0			0
$175$	14.8831	+	17.7370i	1.12506	+	1.34079i
$176$	3.64981	−	2.08944i	0.275115	−	0.157498i
$177$		0			0
$178$	−11.0574	−	5.76897i	−0.828786	−	0.432403i
$179$	6.20187	+	10.7419i	0.463549	+	0.802891i	0.999135	−	0.0415901i	$-0.0132424\pi$
$179$	6.20187	+	10.7419i	0.463549	+	0.802891i	−0.535585	+	0.844481i	$0.679909\pi$
$180$		0			0
$181$	0.582122	−	1.00827i	0.0432688	−	0.0749437i	−0.843580	−	0.537004i	$-0.819556\pi$
$181$	0.582122	−	1.00827i	0.0432688	−	0.0749437i	0.886849	+	0.462060i	$0.152889\pi$
$182$	−8.63304	+	5.48876i	−0.639924	+	0.406854i
$183$		0			0
$184$	−2.13659	−	6.84183i	−0.157512	−	0.504387i
$185$	0.395243	−	0.0696919i	0.0290588	−	0.00512385i
$186$		0			0
$187$	4.10189	−	4.88844i	0.299960	−	0.357478i
$188$	−1.96680	+	22.0165i	−0.143443	+	1.60572i
$189$		0			0
$190$	−0.638277	+	0.583799i	−0.0463055	+	0.0423533i
$191$	−11.0185	−	9.24558i	−0.797267	−	0.668987i	0.150265	−	0.988646i	$-0.451987\pi$
$191$	−11.0185	−	9.24558i	−0.797267	−	0.668987i	−0.947533	+	0.319659i	$0.896432\pi$
$192$		0			0
$193$	−3.19429	−	18.1157i	−0.229930	−	1.30400i	−0.853032	−	0.521859i	$-0.825239\pi$
$193$	−3.19429	−	18.1157i	−0.229930	−	1.30400i	0.623102	−	0.782141i	$-0.285872\pi$
$194$	−7.36478	+	3.04270i	−0.528760	+	0.218453i
$195$		0			0
$196$	28.2141	+	7.61532i	2.01529	+	0.543951i
$197$	−18.3471	−	10.5927i	−1.30718	−	0.754699i	−0.325553	−	0.945524i	$-0.605550\pi$
$197$	−18.3471	−	10.5927i	−1.30718	−	0.754699i	−0.981624	+	0.190825i	$0.938884\pi$
$198$		0			0
$199$	−5.80763	+	3.35304i	−0.411692	+	0.237691i	−0.691517	−	0.722361i	$-0.743057\pi$
$199$	−5.80763	+	3.35304i	−0.411692	+	0.237691i	0.279824	+	0.960051i	$0.409724\pi$
$200$	−11.8602	−	7.60163i	−0.838643	−	0.537517i
$201$		0			0
$202$	−14.6607	−	1.94377i	−1.03153	−	0.136763i
$203$	2.19136	−	1.83877i	0.153803	−	0.129056i
$204$		0			0
$205$	0.862652	−	0.313980i	0.0602502	−	0.0219293i
$206$	−0.658914	+	2.08316i	−0.0459087	+	0.145141i
$207$		0			0
$208$	4.01823	−	4.75330i	0.278614	−	0.329582i
$209$	−4.54433	−	0.801289i	−0.314338	−	0.0554263i
$210$		0			0
$211$	6.01877	−	16.5364i	0.414349	−	1.13841i	−0.540505	−	0.841340i	$-0.681767\pi$
$211$	6.01877	−	16.5364i	0.414349	−	1.13841i	0.954854	−	0.297074i	$-0.0960108\pi$
$212$	−1.49052	−	17.4035i	−0.102370	−	1.19528i
$213$		0			0
$214$	−11.1487	+	0.476543i	−0.762109	+	0.0325758i
$215$	0.305002			0.0208010
$216$		0			0
$217$	−23.0580			−1.56528
$218$	−2.52277	+	0.107834i	−0.170864	+	0.00730345i
$219$		0			0
$220$	0.0250067	+	0.291981i	0.00168595	+	0.0196853i
$221$	3.23015	−	8.87476i	0.217283	−	0.596981i
$222$		0			0
$223$	−9.12995	−	1.60986i	−0.611386	−	0.107804i	−0.140623	−	0.990063i	$-0.544910\pi$
$223$	−9.12995	−	1.60986i	−0.611386	−	0.107804i	−0.470764	+	0.882259i	$0.656022\pi$
$224$	−26.2779	+	1.02690i	−1.75576	+	0.0686123i
$225$		0			0
$226$	−4.53026	+	14.3224i	−0.301348	+	0.952715i
$227$	−20.9726	+	7.63340i	−1.39200	+	0.506647i	−0.925794	−	0.378029i	$-0.876602\pi$
$227$	−20.9726	+	7.63340i	−1.39200	+	0.506647i	−0.466207	+	0.884676i	$0.654380\pi$
$228$		0			0
$229$	−20.1745	+	16.9284i	−1.33317	+	1.11866i	−0.349840	+	0.936810i	$0.613764\pi$
$229$	−20.1745	+	16.9284i	−1.33317	+	1.11866i	−0.983326	+	0.181849i	$0.941792\pi$
$230$	0.495121	+	0.0656448i	0.0326473	+	0.00432849i
$231$		0			0
$232$	−0.939163	+	1.46530i	−0.0616591	+	0.0962016i
$233$	−6.49629	+	3.75063i	−0.425586	+	0.245712i	−0.697464	−	0.716619i	$-0.745688\pi$
$233$	−6.49629	+	3.75063i	−0.425586	+	0.245712i	0.271878	+	0.962332i	$0.412355\pi$
$234$		0			0
$235$	−1.33389	−	0.770123i	−0.0870135	−	0.0502373i
$236$	15.8429	+	4.27617i	1.03128	+	0.278355i
$237$		0			0
$238$	−36.8801	+	15.2367i	−2.39058	+	0.987649i
$239$	0.596327	+	3.38194i	0.0385732	+	0.218759i	0.998001	−	0.0631941i	$-0.0201287\pi$
$239$	0.596327	+	3.38194i	0.0385732	+	0.218759i	−0.959428	+	0.281954i	$0.909018\pi$
$240$		0			0
$241$	−1.30402	−	1.09420i	−0.0839993	−	0.0704838i	0.599821	−	0.800134i	$-0.295238\pi$
$241$	−1.30402	−	1.09420i	−0.0839993	−	0.0704838i	−0.683820	+	0.729650i	$0.739683\pi$
$242$	10.3254	−	9.44411i	0.663741	−	0.607091i
$243$		0			0
$244$	1.98965	−	22.2723i	0.127374	−	1.42584i
$245$	−1.30894	+	1.55993i	−0.0836252	+	0.0996606i
$246$		0			0
$247$	−6.72551	+	1.18589i	−0.427934	+	0.0754563i
$248$	13.3910	−	4.18179i	0.850330	−	0.265544i
$249$		0			0
$250$	1.65996	−	1.05538i	0.104985	−	0.0667481i
$251$	−7.79783	+	13.5062i	−0.492195	+	0.852506i	−0.999960	−	0.00898943i	$-0.997139\pi$
$251$	−7.79783	+	13.5062i	−0.492195	+	0.852506i	0.507765	+	0.861496i	$0.330472\pi$
$252$		0			0
$253$	1.33220	+	2.30744i	0.0837547	+	0.145067i
$254$	4.19274	+	2.18748i	0.263076	+	0.137255i
$255$		0			0
$256$	15.0747	−	5.36213i	0.942171	−	0.335133i
$257$	−6.38236	−	7.60620i	−0.398121	−	0.474462i	0.529325	−	0.848419i	$-0.322445\pi$
$257$	−6.38236	−	7.60620i	−0.398121	−	0.474462i	−0.927446	+	0.373957i	$0.878001\pi$
$258$		0			0
$259$	−4.57894	−	12.5805i	−0.284521	−	0.781716i
$260$	0.182573	+	0.393407i	0.0113227	+	0.0243980i
$261$		0			0
$262$	−0.799223	−	3.62074i	−0.0493761	−	0.223690i
$263$	−4.54071	+	25.7516i	−0.279992	+	1.58791i	0.442652	+	0.896693i	$0.354038\pi$
$263$	−4.54071	+	25.7516i	−0.279992	+	1.58791i	−0.722644	+	0.691220i	$0.757074\pi$
$264$		0			0
$265$	1.14373	+	0.416285i	0.0702590	+	0.0255722i
$266$	22.8758	+	17.5865i	1.40261	+	1.07830i
$267$		0			0
$268$	7.96712	+	7.99633i	0.486669	+	0.488454i
$269$			0.465194i			0.0283634i	0.999899	+	0.0141817i	$0.00451432\pi$
$269$			0.465194i			0.0283634i	−0.999899	+	0.0141817i	$0.995486\pi$
$270$		0			0
$271$			15.6578i			0.951143i	0.879677	+	0.475571i	$0.157759\pi$
$271$			15.6578i			0.951143i	−0.879677	+	0.475571i	$0.842241\pi$
$272$	18.6549	−	15.5373i	1.13112	−	0.942090i
$273$		0			0
$274$	−7.68412	+	9.99519i	−0.464215	+	0.603831i
$275$	4.92075	+	1.79101i	0.296732	+	0.108002i
$276$		0			0
$277$	−1.71249	+	9.71201i	−0.102893	+	0.583538i	0.889147	+	0.457621i	$0.151298\pi$
$277$	−1.71249	+	9.71201i	−0.102893	+	0.583538i	−0.992041	+	0.125917i	$0.959813\pi$
$278$	20.7221	−	4.57409i	1.24283	−	0.274335i
$279$		0			0
$280$	0.705901	−	1.69105i	0.0421857	−	0.101060i
$281$	−5.83636	−	16.0353i	−0.348168	−	0.956584i	−0.982947	−	0.183890i	$-0.941131\pi$
$281$	−5.83636	−	16.0353i	−0.348168	−	0.956584i	0.634779	−	0.772694i	$-0.281091\pi$
$282$		0			0
$283$	−6.10047	−	7.27025i	−0.362635	−	0.432172i	0.553619	−	0.832770i	$-0.313247\pi$
$283$	−6.10047	−	7.27025i	−0.362635	−	0.432172i	−0.916254	+	0.400599i	$0.868802\pi$
$284$	5.33810	+	7.65336i	0.316758	+	0.454143i
$285$		0			0
$286$	−1.07021	+	2.05127i	−0.0632828	+	0.121294i
$287$	−15.3116	−	26.5204i	−0.903814	−	1.56545i
$288$		0			0
$289$	9.91922	−	17.1806i	0.583484	−	1.01062i
$290$	−0.0650679	−	0.102343i	−0.00382092	−	0.00600977i
$291$		0			0
$292$	−9.58046	+	20.4476i	−0.560654	+	1.19660i
$293$	−2.23373	+	0.393868i	−0.130496	+	0.0230100i	−0.238515	−	0.971139i	$-0.576661\pi$
$293$	−2.23373	+	0.393868i	−0.130496	+	0.0230100i	0.108019	+	0.994149i	$0.465549\pi$
$294$		0			0
$295$	−0.734999	+	0.875938i	−0.0427933	+	0.0509991i
$296$	4.94084	+	6.47575i	0.287180	+	0.376395i
$297$		0			0
$298$	−17.2818	−	18.8945i	−1.00111	−	1.09453i
$299$	3.02070	+	2.53467i	0.174692	+	0.146584i
$300$		0			0
$301$	−1.76674	−	10.0197i	−0.101833	−	0.577526i
$302$	−7.88521	−	19.0859i	−0.453743	−	1.09827i
$303$		0			0
$304$	−16.4747	−	6.06467i	−0.944889	−	0.347833i
$305$	1.34939	+	0.779072i	0.0772660	+	0.0446095i
$306$		0			0
$307$	−10.5153	+	6.07100i	−0.600138	+	0.346490i	−0.769096	−	0.639133i	$-0.779293\pi$
$307$	−10.5153	+	6.07100i	−0.600138	+	0.346490i	0.168958	+	0.985623i	$0.445960\pi$
$308$	9.44709	−	2.51282i	0.538298	−	0.143181i
$309$		0			0
$310$	−0.128482	+	0.969063i	−0.00729727	+	0.0550391i
$311$	−13.3085	+	11.1672i	−0.754656	+	0.633232i	−0.936730	−	0.350053i	$-0.886164\pi$
$311$	−13.3085	+	11.1672i	−0.754656	+	0.633232i	0.182074	+	0.983285i	$0.441719\pi$
$312$		0			0
$313$	−15.2929	+	5.56618i	−0.864408	+	0.314619i	−0.735901	−	0.677090i	$-0.763241\pi$
$313$	−15.2929	+	5.56618i	−0.864408	+	0.314619i	−0.128508	+	0.991709i	$0.541019\pi$
$314$	0.184779	+	0.0584465i	0.0104277	+	0.00329832i
$315$		0			0
$316$	1.92607	−	2.74002i	0.108350	−	0.154138i
$317$	−28.6958	−	5.05984i	−1.61171	−	0.284189i	−0.706043	−	0.708169i	$-0.749521\pi$
$317$	−28.6958	−	5.05984i	−1.61171	−	0.284189i	−0.905671	+	0.423980i	$0.860633\pi$
$318$		0			0
$319$	0.221274	−	0.607946i	0.0123890	−	0.0340385i
$320$	−0.103266	+	1.11011i	−0.00577272	+	0.0620569i
$321$		0			0
$322$	−0.711504	−	16.6456i	−0.0396505	−	0.927622i
$323$	−26.6381			−1.48219
$324$		0			0
$325$	7.74997			0.429891
$326$	0.725998	+	16.9847i	0.0402093	+	0.940695i
$327$		0			0
$328$	13.7020	+	12.6249i	0.756567	+	0.697096i
$329$	−17.5729	+	48.2810i	−0.968823	+	2.66182i
$330$		0			0
$331$	2.69396	+	0.475018i	0.148074	+	0.0261094i	0.247194	−	0.968966i	$-0.420492\pi$
$331$	2.69396	+	0.475018i	0.148074	+	0.0261094i	−0.0991200	+	0.995075i	$0.531603\pi$
$332$	−3.84030	−	2.69949i	−0.210764	−	0.148154i
$333$		0			0
$334$	15.1717	+	4.79889i	0.830160	+	0.262584i
$335$	−0.739119	+	0.269017i	−0.0403824	+	0.0146980i
$336$		0			0
$337$	5.28333	−	4.43324i	0.287801	−	0.241494i	−0.487444	−	0.873154i	$-0.662071\pi$
$337$	5.28333	−	4.43324i	0.287801	−	0.241494i	0.775245	+	0.631660i	$0.217626\pi$
$338$	1.96632	−	14.8308i	0.106954	−	0.806690i
$339$		0			0
$340$	0.434857	+	1.63487i	0.0235834	+	0.0886631i
$341$	−4.51618	+	2.60742i	−0.244565	+	0.141199i
$342$		0			0
$343$	30.6457	+	17.6933i	1.65471	+	0.955349i
$344$	2.84322	+	5.49856i	0.153296	+	0.296463i
$345$		0			0
$346$	3.07959	+	7.45407i	0.165560	+	0.400733i
$347$	−3.97755	−	22.5578i	−0.213526	−	1.21097i	−0.883446	−	0.468533i	$-0.844783\pi$
$347$	−3.97755	−	22.5578i	−0.213526	−	1.21097i	0.669920	−	0.742433i	$-0.266328\pi$
$348$		0			0
$349$	20.7811	+	17.4374i	1.11238	+	0.933401i	0.998195	−	0.0600575i	$-0.0191284\pi$
$349$	20.7811	+	17.4374i	1.11238	+	0.933401i	0.114190	+	0.993459i	$0.463573\pi$
$350$	−22.0999	−	24.1622i	−1.18129	−	1.29152i
$351$		0			0
$352$	−5.03071	+	3.17265i	−0.268138	+	0.169103i
$353$	−4.32953	+	5.15974i	−0.230438	+	0.274625i	−0.868856	−	0.495064i	$-0.835144\pi$
$353$	−4.32953	+	5.15974i	−0.230438	+	0.274625i	0.638419	+	0.769689i	$0.279589\pi$
$354$		0			0
$355$	−0.640324	+	0.112906i	−0.0339849	+	0.00599245i
$356$	15.9716	+	7.48331i	0.846495	+	0.396615i
$357$		0			0
$358$	−9.41152	−	14.8030i	−0.497414	−	0.782362i
$359$	14.3604	−	24.8729i	0.757913	−	1.31274i	−0.186000	−	0.982550i	$-0.559552\pi$
$359$	14.3604	−	24.8729i	0.757913	−	1.31274i	0.943913	−	0.330194i	$-0.107114\pi$
$360$		0			0
$361$	0.131118	+	0.227104i	0.00690097	+	0.0119528i
$362$	−0.761600	+	1.45976i	−0.0400288	+	0.0767232i
$363$		0			0
$364$	11.8663	−	8.27658i	0.621965	−	0.433811i
$365$	−1.01140	−	1.20533i	−0.0529389	−	0.0630901i
$366$		0			0
$367$	1.33583	+	3.67016i	0.0697298	+	0.191581i	0.969662	−	0.244448i	$-0.0786067\pi$
$367$	1.33583	+	3.67016i	0.0697298	+	0.191581i	−0.899933	+	0.436029i	$0.856385\pi$
$368$	3.43205	+	9.53795i	0.178908	+	0.497200i
$369$		0			0
$370$	−0.554239	+	0.122340i	−0.0288135	+	0.00636014i
$371$	7.05034	−	39.9845i	0.366035	−	2.07589i
$372$		0			0
$373$	10.2477	+	3.72985i	0.530605	+	0.193124i	0.593408	−	0.804902i	$-0.297782\pi$
$373$	10.2477	+	3.72985i	0.530605	+	0.193124i	−0.0628037	+	0.998026i	$0.520004\pi$
$374$	−5.50042	+	7.15472i	−0.284420	+	0.369962i
$375$		0			0
$376$	1.44926	−	31.2264i	0.0747399	−	1.61038i
$377$		−	0.957490i		−	0.0493132i
$378$		0			0
$379$		−	5.95264i		−	0.305766i	−0.988244	−	0.152883i	$-0.951144\pi$
$379$		−	5.95264i		−	0.305766i	0.988244	−	0.152883i	$-0.0488558\pi$
$380$	0.866578	−	0.863412i	0.0444545	−	0.0442921i
$381$		0			0
$382$	16.1266	+	12.3978i	0.825109	+	0.634329i
$383$	6.27333	+	2.28330i	0.320552	+	0.116671i	0.497285	−	0.867588i	$-0.334331\pi$
$383$	6.27333	+	2.28330i	0.320552	+	0.116671i	−0.176732	+	0.984259i	$0.556553\pi$
$384$		0			0
$385$	−0.118285	+	0.670825i	−0.00602834	+	0.0341884i
$386$	5.60738	+	25.4032i	0.285408	+	1.29299i
$387$		0			0
$388$	10.2221	−	4.74389i	0.518949	−	0.240835i
$389$	10.4246	+	28.6413i	0.528548	+	1.45217i	0.860781	+	0.508976i	$0.169976\pi$
$389$	10.4246	+	28.6413i	0.528548	+	1.45217i	−0.332233	+	0.943197i	$0.607802\pi$
$390$		0			0
$391$	9.88672	+	11.7825i	0.499993	+	0.595868i
$392$	−40.3243	−	9.05588i	−2.03669	−	0.457391i
$393$		0			0
$394$	26.5628	+	13.8586i	1.33821	+	0.698187i
$395$	0.116690	+	0.202113i	0.00587131	+	0.0101694i
$396$		0			0
$397$	7.87633	−	13.6422i	0.395302	−	0.684683i	−0.597838	−	0.801617i	$-0.703973\pi$
$397$	7.87633	−	13.6422i	0.395302	−	0.684683i	0.993140	+	0.116934i	$0.0373067\pi$
$398$	8.00323	−	5.08833i	0.401166	−	0.255055i
$399$		0			0
$400$	17.2167	+	10.0242i	0.860833	+	0.501212i
$401$	3.05192	−	0.538136i	0.152406	−	0.0268733i	−0.0969247	−	0.995292i	$-0.530901\pi$
$401$	3.05192	−	0.538136i	0.152406	−	0.0268733i	0.249330	+	0.968418i	$0.419789\pi$
$402$		0			0
$403$	−4.96092	+	5.91220i	−0.247121	+	0.294508i
$404$	20.8319	+	1.86097i	1.03643	+	0.0925868i
$405$		0			0
$406$	−2.98518	+	2.73039i	−0.148152	+	0.135507i
$407$	−2.31945	−	1.94625i	−0.114971	−	0.0964722i
$408$		0			0
$409$	−4.55893	−	25.8550i	−0.225424	−	1.27845i	−0.861872	−	0.507126i	$-0.830708\pi$
$409$	−4.55893	−	25.8550i	−0.225424	−	1.27845i	0.636448	−	0.771320i	$-0.280403\pi$
$410$	−1.19990	+	0.495728i	−0.0592588	+	0.0244823i
$411$		0			0
$412$	0.805184	−	2.98314i	0.0396686	−	0.146969i
$413$	33.0332	+	19.0717i	1.62546	+	0.938458i
$414$		0			0
$415$	0.283273	−	0.163547i	0.0139053	−	0.00802823i
$416$	−5.39038	+	6.95873i	−0.264285	+	0.341180i
$417$		0			0
$418$	6.46919	+	0.857707i	0.316418	+	0.0419518i
$419$	27.7064	−	23.2484i	1.35355	−	1.13576i	0.375628	−	0.926771i	$-0.377427\pi$
$419$	27.7064	−	23.2484i	1.35355	−	1.13576i	0.977918	−	0.208989i	$-0.0670172\pi$
$420$		0			0
$421$	−11.9136	+	4.33621i	−0.580635	+	0.211334i	−0.615605	−	0.788055i	$-0.711088\pi$
$421$	−11.9136	+	4.33621i	−0.580635	+	0.211334i	0.0349706	+	0.999388i	$0.488866\pi$
$422$	−7.50535	+	23.7282i	−0.365355	+	1.15507i
$423$		0			0
$424$	3.15707	+	24.4998i	0.153321	+	1.18981i
$425$	29.7702	+	5.24929i	1.44407	+	0.254628i
$426$		0			0
$427$	17.7771	−	48.8421i	0.860292	−	2.36363i
$428$	15.7235	−	1.34664i	0.760022	−	0.0650921i
$429$		0			0
$430$	−0.430945	+	0.0184204i	−0.0207820	+	0.000888311i
$431$	11.3033			0.544463			0.272231	−	0.962232i	$-0.412238\pi$
$431$	11.3033			0.544463			0.272231	+	0.962232i	$0.412238\pi$
$432$		0			0
$433$	18.1058			0.870111			0.435056	−	0.900404i	$-0.356729\pi$
$433$	18.1058			0.870111			0.435056	+	0.900404i	$0.356729\pi$
$434$	32.5792	−	1.39257i	1.56385	−	0.0668456i
$435$		0			0
$436$	3.55797	−	0.304723i	0.170396	−	0.0145936i
$437$	3.80399	−	10.4514i	0.181969	−	0.499957i
$438$		0			0
$439$	13.4676	+	2.37471i	0.642776	+	0.113339i	0.485529	−	0.874221i	$-0.338627\pi$
$439$	13.4676	+	2.37471i	0.642776	+	0.113339i	0.157247	+	0.987559i	$0.449738\pi$
$440$	−0.0529666	−	0.411036i	−0.00252508	−	0.0195954i
$441$		0			0
$442$	−4.02797	+	12.7344i	−0.191591	+	0.605716i
$443$	−10.2251	+	3.72164i	−0.485811	+	0.176821i	−0.573301	−	0.819345i	$-0.694337\pi$
$443$	−10.2251	+	3.72164i	−0.485811	+	0.176821i	0.0874905	+	0.996165i	$0.472115\pi$
$444$		0			0
$445$	−0.941489	+	0.790003i	−0.0446309	+	0.0374497i
$446$	12.9971	+	1.72321i	0.615432	+	0.0815961i
$447$		0			0
$448$	37.0666	−	3.03796i	1.75123	−	0.143530i
$449$	−6.10203	+	3.52301i	−0.287973	+	0.166261i	−0.637027	−	0.770841i	$-0.719836\pi$
$449$	−6.10203	+	3.52301i	−0.287973	+	0.166261i	0.349055	+	0.937102i	$0.386503\pi$
$450$		0			0
$451$	−5.99791	−	3.46289i	−0.282431	−	0.163061i
$452$	5.53592	−	20.5101i	0.260388	−	0.964715i
$453$		0			0
$454$	29.1717	−	12.0520i	1.36909	−	0.565630i
$455$	0.175058	+	0.992805i	0.00820686	+	0.0465434i
$456$		0			0
$457$	19.4984	+	16.3611i	0.912098	+	0.765341i	0.972517	−	0.232832i	$-0.0747993\pi$
$457$	19.4984	+	16.3611i	0.912098	+	0.765341i	−0.0604193	+	0.998173i	$0.519244\pi$
$458$	27.4826	−	25.1369i	1.28418	−	1.17457i
$459$		0			0
$460$	−0.703532	−	0.0628485i	−0.0328024	−	0.00293033i
$461$	−25.2014	+	30.0339i	−1.17375	+	1.39882i	−0.274382	+	0.961621i	$0.588473\pi$
$461$	−25.2014	+	30.0339i	−1.17375	+	1.39882i	−0.899365	+	0.437198i	$0.855971\pi$
$462$		0			0
$463$	−7.36631	+	1.29888i	−0.342341	+	0.0603640i	−0.342176	−	0.939636i	$-0.611164\pi$
$463$	−7.36631	+	1.29888i	−0.342341	+	0.0603640i	−0.000165553		1.00000i	$0.500053\pi$
$464$	1.23847	−	2.12708i	0.0574945	−	0.0987470i
$465$		0			0
$466$	8.95224	−	5.69170i	0.414704	−	0.263663i
$467$	0.689932	−	1.19500i	0.0319262	−	0.0552979i	−0.849621	−	0.527394i	$-0.823169\pi$
$467$	0.689932	−	1.19500i	0.0319262	−	0.0552979i	0.881547	+	0.472096i	$0.156502\pi$
$468$		0			0
$469$	13.1189	+	22.7227i	0.605777	+	1.04924i
$470$	1.93120	+	1.00757i	0.0890795	+	0.0464755i
$471$		0			0
$472$	−22.6430	−	5.08508i	−1.04223	−	0.234060i
$473$	−1.47907	−	1.76269i	−0.0680079	−	0.0810486i
$474$		0			0
$475$	−7.47627	−	20.5409i	−0.343035	−	0.942480i
$476$	51.1885	−	23.7557i	2.34622	−	1.08884i
$477$		0			0
$478$	−1.04681	−	4.74241i	−0.0478802	−	0.216913i
$479$	2.20993	−	12.5331i	0.100974	−	0.572654i	−0.891778	−	0.452474i	$-0.850542\pi$
$479$	2.20993	−	12.5331i	0.100974	−	0.572654i	0.992752	−	0.120180i	$-0.0383472\pi$
$480$		0			0
$481$	−4.21088	−	1.53263i	−0.191999	−	0.0698821i
$482$	1.90856	+	1.46727i	0.0869327	+	0.0668322i
$483$		0			0
$484$	−14.0186	+	13.9674i	−0.637210	+	0.634882i
$485$			0.785256i			0.0356566i
$486$		0			0
$487$			12.3932i			0.561588i	0.959768	+	0.280794i	$0.0905979\pi$
$487$			12.3932i			0.561588i	−0.959768	+	0.280794i	$0.909402\pi$
$488$	−1.46610	+	31.5893i	−0.0663673	+	1.42998i
$489$		0			0
$490$	1.75522	−	2.28312i	0.0792928	−	0.103141i
$491$	−24.9589	−	9.08428i	−1.12638	−	0.409968i	−0.289402	−	0.957208i	$-0.593456\pi$
$491$	−24.9589	−	9.08428i	−1.12638	−	0.409968i	−0.836976	+	0.547240i	$0.815679\pi$
$492$		0			0
$493$	0.648537	−	3.67804i	0.0292086	−	0.165650i
$494$	9.43101	−	2.08175i	0.424321	−	0.0936625i
$495$		0			0
$496$	−18.6679	+	6.71730i	−0.838214	+	0.301616i
$497$	7.41823	+	20.3814i	0.332753	+	0.914232i
$498$		0			0
$499$	−6.19736	−	7.38573i	−0.277432	−	0.330631i	0.609278	−	0.792957i	$-0.291459\pi$
$499$	−6.19736	−	7.38573i	−0.277432	−	0.330631i	−0.886710	+	0.462326i	$0.847015\pi$
$500$	−2.28166	+	1.59142i	−0.102039	+	0.0711706i
$501$		0			0
$502$	10.2020	−	19.5542i	0.455339	−	0.872748i
$503$	−4.28642	−	7.42429i	−0.191122	−	0.331033i	0.754500	−	0.656300i	$-0.227879\pi$
$503$	−4.28642	−	7.42429i	−0.191122	−	0.331033i	−0.945622	+	0.325267i	$0.894546\pi$
$504$		0			0
$505$	−0.728686	+	1.26212i	−0.0324261	+	0.0561637i
$506$	−2.02165	−	3.17978i	−0.0898734	−	0.141358i
$507$		0			0
$508$	−6.05614	−	2.83753i	−0.268698	−	0.125895i
$509$	−30.5338	+	5.38393i	−1.35339	+	0.238638i	−0.802854	−	0.596176i	$-0.796686\pi$
$509$	−30.5338	+	5.38393i	−1.35339	+	0.238638i	−0.550532	+	0.834814i	$0.685575\pi$
$510$		0			0
$511$	−33.7382	+	40.2076i	−1.49249	+	1.77868i
$512$	−20.9756	+	8.48670i	−0.926999	+	0.375063i
$513$		0			0
$514$	9.47716	+	10.3615i	0.418020	+	0.457027i
$515$	0.164935	+	0.138397i	0.00726792	+	0.00609851i
$516$		0			0
$517$	2.01781	+	11.4436i	0.0887431	+	0.503287i
$518$	7.22948	+	17.4988i	0.317645	+	0.768852i
$519$		0			0
$520$	−0.281721	−	0.544827i	−0.0123543	−	0.0238922i
$521$	−25.2374	−	14.5708i	−1.10567	−	0.638359i	−0.167966	−	0.985793i	$-0.553720\pi$
$521$	−25.2374	−	14.5708i	−1.10567	−	0.638359i	−0.937705	+	0.347433i	$0.887053\pi$
$522$		0			0
$523$	−4.50959	+	2.60361i	−0.197190	+	0.113848i	−0.595344	−	0.803471i	$-0.702984\pi$
$523$	−4.50959	+	2.60361i	−0.197190	+	0.113848i	0.398154	+	0.917319i	$0.369651\pi$
$524$	1.34791	+	5.06755i	0.0588838	+	0.221377i
$525$		0			0
$526$	4.86042	−	36.6593i	0.211924	−	1.59842i
$527$	−23.0611	+	19.3505i	−1.00456	+	0.842922i
$528$		0			0
$529$	15.5783	−	5.67002i	0.677316	−	0.246523i
$530$	−1.64115	−	0.519104i	−0.0712870	−	0.0225484i
$531$		0			0
$532$	−33.3839	−	23.4668i	−1.44737	−	1.01741i
$533$	−10.0943	−	1.77989i	−0.437232	−	0.0770958i
$534$		0			0
$535$	−0.376100	+	1.03332i	−0.0162602	+	0.0446745i
$536$	−11.7399	−	10.8170i	−0.507085	−	0.467225i
$537$		0			0
$538$	−0.0280951	−	0.657283i	−0.00121127	−	0.0283375i
$539$	15.3629			0.661725
$540$		0			0
$541$	24.3664			1.04759			0.523797	−	0.851843i	$-0.324515\pi$
$541$	24.3664			1.04759			0.523797	+	0.851843i	$0.324515\pi$
$542$	−0.945643	−	22.1233i	−0.0406188	−	0.950275i
$543$		0			0
$544$	−25.4196	+	23.0797i	−1.08986	+	0.989535i
$545$	−0.0851054	+	0.233825i	−0.00364551	+	0.0100160i
$546$		0			0
$547$	−35.2269	−	6.21145i	−1.50619	−	0.265582i	−0.641202	−	0.767372i	$-0.721564\pi$
$547$	−35.2269	−	6.21145i	−1.50619	−	0.265582i	−0.864990	+	0.501790i	$0.832675\pi$
$548$	10.2534	−	14.5865i	0.438004	−	0.623105i
$549$		0			0
$550$	−7.06081	−	2.23337i	−0.301074	−	0.0952311i
$551$	−2.53777	+	0.923674i	−0.108113	+	0.0393498i
$552$		0			0
$553$	5.96373	−	5.00416i	0.253604	−	0.212799i
$554$	1.83306	−	13.8257i	0.0778795	−	0.587400i
$555$		0			0
$556$	−29.0025	+	7.71433i	−1.22998	+	0.327160i
$557$	10.4040	−	6.00674i	0.440831	−	0.254514i	−0.263119	−	0.964763i	$-0.584751\pi$
$557$	10.4040	−	6.00674i	0.440831	−	0.254514i	0.703950	+	0.710250i	$0.251418\pi$
$558$		0			0
$559$	−2.94922	−	1.70274i	−0.124739	−	0.0720180i
$560$	−0.895254	+	2.43196i	−0.0378314	+	0.102769i
$561$		0			0
$562$	9.21477	+	22.3041i	0.388702	+	0.940843i
$563$	0.829324	+	4.70333i	0.0349518	+	0.198222i	0.997284	−	0.0736557i	$-0.0234666\pi$
$563$	0.829324	+	4.70333i	0.0349518	+	0.198222i	−0.962332	+	0.271877i	$0.912355\pi$
$564$		0			0
$565$	1.13399	+	0.951528i	0.0477072	+	0.0400311i
$566$	9.05857	+	9.90387i	0.380760	+	0.416291i
$567$		0			0
$568$	−8.00454	−	10.4912i	−0.335863	−	0.440202i
$569$	5.10034	−	6.07835i	0.213818	−	0.254818i	−0.648466	−	0.761244i	$-0.724589\pi$
$569$	5.10034	−	6.07835i	0.213818	−	0.254818i	0.862284	+	0.506426i	$0.169034\pi$
$570$		0			0
$571$	15.9498	−	2.81238i	0.667478	−	0.117694i	0.170366	−	0.985381i	$-0.445505\pi$
$571$	15.9498	−	2.81238i	0.667478	−	0.117694i	0.497112	+	0.867686i	$0.334394\pi$
$572$	1.38824	−	2.96292i	0.0580452	−	0.123886i
$573$		0			0
$574$	23.2358	+	36.5466i	0.969843	+	1.52543i
$575$	−6.31079	+	10.9306i	−0.263178	+	0.455838i
$576$		0			0
$577$	−8.09164	−	14.0151i	−0.336859	−	0.583458i	0.646981	−	0.762506i	$-0.276031\pi$
$577$	−8.09164	−	14.0151i	−0.336859	−	0.583458i	−0.983840	+	0.179049i	$0.942698\pi$
$578$	−12.9775	+	24.8739i	−0.539792	+	1.03462i
$579$		0			0
$580$	0.0981169	+	0.140673i	0.00407408	+	0.00584111i
$581$	−7.01361	−	8.35850i	−0.290974	−	0.346769i
$582$		0			0
$583$	−3.14058	−	8.62868i	−0.130070	−	0.357364i
$584$	12.3015	−	29.4695i	0.509041	−	1.21946i
$585$		0			0
$586$	3.13231	−	0.691410i	0.129394	−	0.0285619i
$587$	4.51504	−	25.6061i	0.186356	−	1.05688i	−0.737846	−	0.674969i	$-0.764157\pi$
$587$	4.51504	−	25.6061i	0.186356	−	1.05688i	0.924201	−	0.381906i	$-0.124732\pi$
$588$		0			0
$589$	20.4557	+	7.44526i	0.842862	+	0.306777i
$590$	0.985596	−	1.28202i	0.0405764	−	0.0527801i
$591$		0			0
$592$	−7.37212	−	8.85134i	−0.302992	−	0.363788i
$593$			7.68968i			0.315778i	0.987457	+	0.157889i	$0.0504687\pi$
$593$			7.68968i			0.315778i	−0.987457	+	0.157889i	$0.949531\pi$
$594$		0			0
$595$			3.93227i			0.161207i
$596$	25.5590	+	25.6528i	1.04694	+	1.05078i
$597$		0			0
$598$	−4.42110	−	3.39886i	−0.180792	−	0.138990i
$599$	−28.4951	−	10.3714i	−1.16428	−	0.423762i	−0.313653	−	0.949538i	$-0.601553\pi$
$599$	−28.4951	−	10.3714i	−1.16428	−	0.423762i	−0.850623	+	0.525776i	$0.823775\pi$
$600$		0			0
$601$	3.19123	−	18.0984i	0.130173	−	0.738247i	−0.847927	−	0.530113i	$-0.822150\pi$
$601$	3.19123	−	18.0984i	0.130173	−	0.738247i	0.978100	−	0.208135i	$-0.0667392\pi$
$602$	3.10141	+	14.0504i	0.126404	+	0.572650i
$603$		0			0
$604$	12.2939	+	26.4908i	0.500231	+	1.07789i
$605$	−0.471623	−	1.29577i	−0.0191742	−	0.0526806i
$606$		0			0
$607$	3.65542	+	4.35636i	0.148369	+	0.176819i	0.835110	−	0.550083i	$-0.185404\pi$
$607$	3.65542	+	4.35636i	0.148369	+	0.176819i	−0.686741	+	0.726902i	$0.740959\pi$
$608$	23.6438	+	7.57394i	0.958881	+	0.307164i
$609$		0			0
$610$	−1.95364	−	1.01927i	−0.0791006	−	0.0412692i
$611$	8.59873	+	14.8934i	0.347867	+	0.602524i
$612$		0			0
$613$	−4.98728	+	8.63823i	−0.201434	+	0.348895i	−0.948991	−	0.315304i	$-0.897894\pi$
$613$	−4.98728	+	8.63823i	−0.201434	+	0.348895i	0.747556	+	0.664198i	$0.231227\pi$
$614$	14.4906	−	9.21292i	0.584794	−	0.371803i
$615$		0			0
$616$	−13.1962	+	4.12097i	−0.531692	+	0.166039i
$617$	−19.3416	+	3.41044i	−0.778663	+	0.137299i	−0.548834	−	0.835932i	$-0.684928\pi$
$617$	−19.3416	+	3.41044i	−0.778663	+	0.137299i	−0.229830	+	0.973231i	$0.573817\pi$
$618$		0			0
$619$	22.5368	−	26.8583i	0.905831	−	1.07953i	−0.0906642	−	0.995882i	$-0.528899\pi$
$619$	22.5368	−	26.8583i	0.905831	−	1.07953i	0.996496	−	0.0836462i	$-0.0266566\pi$
$620$	0.123009	−	1.37697i	0.00494015	−	0.0553005i
$621$		0			0
$622$	18.1295	−	16.5821i	0.726926	−	0.664882i
$623$	31.4062	+	26.3530i	1.25826	+	1.05581i
$624$		0			0
$625$	4.29068	+	24.3337i	0.171627	+	0.973347i
$626$	21.2716	−	8.78819i	0.850184	−	0.351247i
$627$		0			0
$628$	−0.264608	−	0.0714208i	−0.0105590	−	0.00285000i
$629$	−15.1373	−	8.73951i	−0.603563	−	0.348467i
$630$		0			0
$631$	20.6478	−	11.9210i	0.821976	−	0.474568i	−0.0291214	−	0.999576i	$-0.509271\pi$
$631$	20.6478	−	11.9210i	0.821976	−	0.474568i	0.851097	+	0.525008i	$0.175938\pi$
$632$	−2.55590	+	3.98777i	−0.101668	+	0.158625i
$633$		0			0
$634$	40.8505	+	5.41610i	1.62238	+	0.215101i
$635$	0.356994	−	0.299554i	0.0141669	−	0.0118874i
$636$		0			0
$637$	21.3655	−	7.77640i	0.846531	−	0.308112i
$638$	−0.275927	+	0.872345i	−0.0109241	+	0.0345365i
$639$		0			0
$640$	0.0788622	−	1.57473i	0.00311730	−	0.0622468i
$641$	−18.2530	−	3.21850i	−0.720951	−	0.127123i	−0.198879	−	0.980024i	$-0.563730\pi$
$641$	−18.2530	−	3.21850i	−0.720951	−	0.127123i	−0.522073	+	0.852901i	$0.674841\pi$
$642$		0			0
$643$	−12.2412	+	33.6323i	−0.482744	+	1.32633i	0.424387	+	0.905481i	$0.360490\pi$
$643$	−12.2412	+	33.6323i	−0.482744	+	1.32633i	−0.907131	+	0.420848i	$0.861733\pi$
$644$	2.01060	+	23.4760i	0.0792287	+	0.925083i
$645$		0			0
$646$	37.6377	−	1.60879i	1.48083	−	0.0632972i
$647$	−31.4863			−1.23785			−0.618926	−	0.785449i	$-0.712432\pi$
$647$	−31.4863			−1.23785			−0.618926	+	0.785449i	$0.712432\pi$
$648$		0			0
$649$	8.62659			0.338623
$650$	−10.9501	+	0.468055i	−0.429499	+	0.0183586i
$651$		0			0
$652$	−2.05156	−	23.9542i	−0.0803453	−	0.938119i
$653$	9.20421	−	25.2884i	0.360189	−	0.989610i	−0.618774	−	0.785569i	$-0.712370\pi$
$653$	9.20421	−	25.2884i	0.360189	−	0.989610i	0.978962	−	0.204041i	$-0.0654076\pi$
$654$		0			0
$655$	−0.359840	−	0.0634495i	−0.0140601	−	0.00247918i
$656$	−20.1224	−	17.0106i	−0.785647	−	0.664151i
$657$		0			0
$658$	21.9132	−	69.2787i	0.854265	−	2.70076i
$659$	−42.1246	+	15.3321i	−1.64094	+	0.597253i	−0.987203	−	0.159468i	$-0.949022\pi$
$659$	−42.1246	+	15.3321i	−1.64094	+	0.597253i	−0.653737	+	0.756722i	$0.726800\pi$
$660$		0			0
$661$	−15.4928	+	13.0000i	−0.602602	+	0.505643i	−0.892281	−	0.451481i	$-0.850896\pi$
$661$	−15.4928	+	13.0000i	−0.602602	+	0.505643i	0.289679	+	0.957124i	$0.406451\pi$
$662$	−3.83505	−	0.508464i	−0.149053	−	0.0197620i
$663$		0			0
$664$	5.58908	+	3.58224i	0.216898	+	0.139018i
$665$	2.46250	−	1.42173i	0.0954917	−	0.0551322i
$666$		0			0
$667$	1.35045	+	0.779683i	0.0522896	+	0.0301894i
$668$	−21.7263	−	5.86418i	−0.840617	−	0.226892i
$669$		0			0
$670$	1.02807	−	0.424739i	0.0397179	−	0.0164091i
$671$	−2.04126	−	11.5765i	−0.0788018	−	0.446907i
$672$		0			0
$673$	−32.9507	−	27.6490i	−1.27016	−	1.06579i	−0.994522	−	0.104527i	$-0.966667\pi$
$673$	−32.9507	−	27.6490i	−1.27016	−	1.06579i	−0.275636	−	0.961262i	$-0.588888\pi$
$674$	−7.19720	+	6.58291i	−0.277226	+	0.253564i
$675$		0			0
$676$	−1.88256	+	21.0736i	−0.0724062	+	0.810522i
$677$	12.7626	−	15.2099i	0.490506	−	0.584563i	−0.462840	−	0.886442i	$-0.653170\pi$
$677$	12.7626	−	15.2099i	0.490506	−	0.584563i	0.953346	+	0.301879i	$0.0976140\pi$
$678$		0			0
$679$	25.7966	−	4.54864i	0.989984	−	0.174561i
$680$	−0.713156	−	2.28368i	−0.0273483	−	0.0875751i
$681$		0			0
$682$	6.22354	−	3.95683i	0.238312	−	0.151515i
$683$	−16.6637	+	28.8624i	−0.637618	+	1.10439i	0.348336	+	0.937370i	$0.386747\pi$
$683$	−16.6637	+	28.8624i	−0.637618	+	1.10439i	−0.985954	+	0.167017i	$0.946586\pi$
$684$		0			0
$685$	0.621199	+	1.07595i	0.0237348	+	0.0411098i
$686$	−44.3686	−	23.1485i	−1.69400	−	0.883813i
$687$		0			0
$688$	−4.34933	−	7.59733i	−0.165817	−	0.289646i
$689$	−8.73537	−	10.4104i	−0.332791	−	0.396605i
$690$		0			0
$691$	0.668178	+	1.83580i	0.0254187	+	0.0698373i	0.951753	−	0.306865i	$-0.0992801\pi$
$691$	0.668178	+	1.83580i	0.0254187	+	0.0698373i	−0.926334	+	0.376703i	$0.877058\pi$
$692$	−4.80141	−	10.3460i	−0.182522	−	0.393297i
$693$		0			0
$694$	6.98234	+	31.6322i	0.265046	+	1.20074i
$695$	0.363132	−	2.05943i	0.0137744	−	0.0781185i
$696$		0			0
$697$	−37.5699	−	13.6743i	−1.42306	−	0.517952i
$698$	−30.4152	−	23.3826i	−1.15123	−	0.885045i
$699$		0			0
$700$	32.6847	+	32.8046i	1.23537	+	1.23990i
$701$			15.9132i			0.601032i	0.953777	+	0.300516i	$0.0971588\pi$
$701$			15.9132i			0.601032i	−0.953777	+	0.300516i	$0.902841\pi$
$702$		0			0
$703$			12.6392i			0.476697i
$704$	6.91639	−	4.78654i	0.260671	−	0.180400i
$705$		0			0
$706$	5.80568	−	7.55179i	0.218500	−	0.284215i
$707$	45.6832	+	16.6273i	1.71810	+	0.625335i
$708$		0			0
$709$	−5.73424	+	32.5205i	−0.215354	+	1.22133i	0.664937	+	0.746899i	$0.268458\pi$
$709$	−5.73424	+	32.5205i	−0.215354	+	1.22133i	−0.880291	+	0.474434i	$0.842653\pi$
$710$	0.897910	−	0.198200i	0.0336980	−	0.00743832i
$711$		0			0
$712$	−23.0187	−	9.60875i	−0.862661	−	0.360103i
$713$	−4.29893	−	11.8112i	−0.160996	−	0.442334i
$714$		0			0
$715$	0.146555	+	0.174657i	0.00548083	+	0.00653180i
$716$	14.1918	+	20.3471i	0.530371	+	0.760406i
$717$		0			0
$718$	−18.7880	+	36.0109i	−0.701161	+	1.34391i
$719$	4.06158	+	7.03487i	0.151471	+	0.262356i	0.931769	−	0.363053i	$-0.118266\pi$
$719$	4.06158	+	7.03487i	0.151471	+	0.262356i	−0.780297	+	0.625409i	$0.784932\pi$
$720$		0			0
$721$	3.59112	−	6.22000i	0.133740	−	0.231645i
$722$	−0.198976	−	0.312961i	−0.00740512	−	0.0116472i
$723$		0			0
$724$	0.987922	−	2.10852i	0.0367158	−	0.0783626i
$725$	3.01818	−	0.532186i	0.112092	−	0.0197649i
$726$		0			0
$727$	24.2351	−	28.8823i	0.898830	−	1.07118i	−0.0982756	−	0.995159i	$-0.531333\pi$
$727$	24.2351	−	28.8823i	0.898830	−	1.07118i	0.997106	−	0.0760250i	$-0.0242229\pi$
$728$	−16.2664	+	12.4108i	−0.602872	+	0.459976i
$729$		0			0
$730$	1.50182	+	1.64196i	0.0555849	+	0.0607718i
$731$	−10.1756	−	8.53837i	−0.376359	−	0.315803i
$732$		0			0
$733$	−5.07665	−	28.7911i	−0.187510	−	1.06342i	−0.922687	−	0.385549i	$-0.874012\pi$
$733$	−5.07665	−	28.7911i	−0.187510	−	1.06342i	0.735177	−	0.677875i	$-0.237099\pi$
$734$	−2.10908	−	5.10498i	−0.0778477	−	0.188428i
$735$		0			0
$736$	−5.42526	−	13.2691i	−0.199978	−	0.489106i
$737$	5.13900	+	2.96700i	0.189298	+	0.109291i
$738$		0			0
$739$	34.0829	−	19.6778i	1.25376	−	0.723858i	0.281905	−	0.959442i	$-0.409034\pi$
$739$	34.0829	−	19.6778i	1.25376	−	0.723858i	0.971854	+	0.235584i	$0.0757002\pi$
$740$	0.775708	−	0.206330i	0.0285156	−	0.00758483i
$741$		0			0
$742$	−7.54675	+	56.9208i	−0.277050	+	2.08963i
$743$	−8.53663	+	7.16309i	−0.313179	+	0.262788i	−0.785804	−	0.618475i	$-0.787751\pi$
$743$	−8.53663	+	7.16309i	−0.313179	+	0.262788i	0.472626	+	0.881263i	$0.343306\pi$
$744$		0			0
$745$	−2.37114	+	0.863025i	−0.0868719	+	0.0316188i
$746$	−14.7044	−	4.65109i	−0.538368	−	0.170288i
$747$		0			0
$748$	7.33956	−	10.4413i	0.268361	−	0.381770i
$749$	36.1246	+	6.36974i	1.31996	+	0.232745i
$750$		0			0
$751$	−9.99875	+	27.4713i	−0.364860	+	1.00244i	0.612428	+	0.790526i	$0.290193\pi$
$751$	−9.99875	+	27.4713i	−0.364860	+	1.00244i	−0.977288	+	0.211917i	$0.932029\pi$
$752$	−0.161793	+	44.2080i	−0.00590000	+	1.61210i
$753$		0			0
$754$	0.0578270	+	1.35286i	0.00210594	+	0.0492682i
$755$	−2.03500			−0.0740613
$756$		0			0
$757$	−8.57552			−0.311682			−0.155841	−	0.987782i	$-0.549809\pi$
$757$	−8.57552			−0.311682			−0.155841	+	0.987782i	$0.549809\pi$
$758$	0.359506	+	8.41062i	0.0130578	+	0.305487i
$759$		0			0
$760$	−1.17226	+	1.27227i	−0.0425224	+	0.0461501i
$761$	1.92414	−	5.28652i	0.0697499	−	0.191636i	−0.899920	−	0.436056i	$-0.856375\pi$
$761$	1.92414	−	5.28652i	0.0697499	−	0.191636i	0.969670	+	0.244419i	$0.0785973\pi$
$762$		0			0
$763$	8.17443	+	1.44137i	0.295934	+	0.0521812i
$764$	−23.5344	−	16.5432i	−0.851446	−	0.598514i
$765$		0			0
$766$	−9.00163	−	2.84726i	−0.325242	−	0.102876i
$767$	11.9972	−	4.36662i	0.433194	−	0.157670i
$768$		0			0
$769$	1.92270	−	1.61334i	0.0693344	−	0.0581784i	−0.607462	−	0.794349i	$-0.707812\pi$
$769$	1.92270	−	1.61334i	0.0693344	−	0.0581784i	0.676796	+	0.736170i	$0.263368\pi$
$770$	0.126613	−	0.954968i	0.00456281	−	0.0344147i
$771$		0			0
$772$	−9.45702	−	35.5542i	−0.340365	−	1.27962i
$773$	0.0355587	−	0.0205298i	0.00127896	−	0.000738407i	−0.499360	−	0.866394i	$-0.666432\pi$
$773$	0.0355587	−	0.0205298i	0.00127896	−	0.000738407i	0.500639	+	0.865656i	$0.333098\pi$
$774$		0			0
$775$	−21.3937	−	12.3516i	−0.768483	−	0.443684i
$776$	−14.1566	+	7.32012i	−0.508191	+	0.262777i
$777$		0			0
$778$	−16.4589	−	39.8384i	−0.590081	−	1.42828i
$779$	5.02027	+	28.4714i	0.179870	+	1.02009i
$780$		0			0
$781$	3.75770	+	3.15308i	0.134461	+	0.112826i
$782$	−14.6808	−	16.0507i	−0.524983	−	0.573972i
$783$		0			0
$784$	57.5221	+	10.3599i	2.05436	+	0.369997i
$785$	0.0122760	−	0.0146300i	0.000438149	−	0.000522166i
$786$		0			0
$787$	−42.8565	+	7.55676i	−1.52767	+	0.269369i	−0.873442	−	0.486928i	$-0.838117\pi$
$787$	−42.8565	+	7.55676i	−1.52767	+	0.269369i	−0.654228	+	0.756298i	$0.727006\pi$
$788$	−38.3682	−	17.9769i	−1.36681	−	0.640401i
$789$		0			0
$790$	−0.177080	−	0.278523i	−0.00630024	−	0.00990939i
$791$	24.6902	−	42.7647i	0.877882	−	1.52054i
$792$		0			0
$793$	−8.69865	−	15.0665i	−0.308898	−	0.535028i
$794$	−10.3047	+	19.7511i	−0.365702	+	0.700940i
$795$		0			0
$796$	−11.0006	+	7.67278i	−0.389908	+	0.271954i
$797$	28.8870	+	34.4262i	1.02323	+	1.21944i	0.975368	+	0.220585i	$0.0707966\pi$
$797$	28.8870	+	34.4262i	1.02323	+	1.21944i	0.0478627	+	0.998854i	$0.484759\pi$
$798$		0			0
$799$	22.9428	+	63.0348i	0.811658	+	2.23001i
$800$	−24.9312	−	13.1237i	−0.881452	−	0.463992i
$801$		0			0
$802$	−4.27963	+	0.944665i	−0.151119	+	0.0333573i
$803$	−2.06131	+	11.6903i	−0.0727421	+	0.412541i
$804$		0			0
$805$	−1.54281	−	0.561537i	−0.0543769	−	0.0197916i
$806$	6.65234	−	8.65310i	0.234319	−	0.304792i
$807$		0			0
$808$	−29.5463	−	1.37128i	−1.03943	−	0.0482415i
$809$		−	39.4534i		−	1.38711i	−0.720405	−	0.693553i	$-0.756044\pi$
$809$		−	39.4534i		−	1.38711i	0.720405	−	0.693553i	$-0.243956\pi$
$810$		0			0
$811$		−	49.4348i		−	1.73589i	−0.496659	−	0.867946i	$-0.665440\pi$
$811$		−	49.4348i		−	1.73589i	0.496659	−	0.867946i	$-0.334560\pi$
$812$	4.05292	−	4.03812i	0.142230	−	0.141710i
$813$		0			0
$814$	3.39475	+	2.60982i	0.118986	+	0.0914743i
$815$	1.57424	+	0.572976i	0.0551432	+	0.0200705i
$816$		0			0
$817$	−1.66794	+	9.45936i	−0.0583538	+	0.330941i
$818$	8.00291	+	36.2557i	0.279815	+	1.26765i
$819$		0			0
$820$	1.66543	−	0.772894i	0.0581592	−	0.0269906i
$821$	−7.55911	−	20.7685i	−0.263815	−	0.724825i	−0.998902	−	0.0468524i	$-0.985081\pi$
$821$	−7.55911	−	20.7685i	−0.263815	−	0.724825i	0.735087	−	0.677973i	$-0.237141\pi$
$822$		0			0
$823$	12.5755	+	14.9869i	0.438356	+	0.522412i	0.939314	−	0.343060i	$-0.111463\pi$
$823$	12.5755	+	14.9869i	0.438356	+	0.522412i	−0.500958	+	0.865472i	$0.667019\pi$
$824$	−0.957498	+	4.26358i	−0.0333560	+	0.148529i
$825$		0			0
$826$	−47.8252	−	24.9519i	−1.66405	−	0.868187i
$827$	−8.39197	−	14.5353i	−0.291817	−	0.505442i	0.682422	−	0.730958i	$-0.260927\pi$
$827$	−8.39197	−	14.5353i	−0.291817	−	0.505442i	−0.974239	+	0.225516i	$0.927593\pi$
$828$		0			0
$829$	−18.8116	+	32.5827i	−0.653355	+	1.13164i	0.328949	+	0.944348i	$0.393306\pi$
$829$	−18.8116	+	32.5827i	−0.653355	+	1.13164i	−0.982304	+	0.187296i	$0.940028\pi$
$830$	−0.390365	+	0.248188i	−0.0135498	+	0.00861474i
$831$		0			0
$832$	7.19593	−	10.1577i	0.249474	−	0.352155i
$833$	87.3391	−	15.4002i	3.02612	−	0.533587i
$834$		0			0
$835$	1.00795	−	1.20123i	0.0348816	−	0.0415703i
$836$	−9.19227	−	0.821172i	−0.317921	−	0.0284008i
$837$		0			0
$838$	−37.7429	+	34.5215i	−1.30381	+	1.19253i
$839$	42.1708	+	35.3855i	1.45590	+	1.22164i	0.928130	+	0.372257i	$0.121416\pi$
$839$	42.1708	+	35.3855i	1.45590	+	1.22164i	0.527770	+	0.849387i	$0.323028\pi$
$840$		0			0
$841$	4.97005	+	28.1865i	0.171381	+	0.971950i
$842$	16.5712	−	6.84625i	0.571080	−	0.235937i
$843$		0			0
$844$	9.17143	−	33.9794i	0.315694	−	1.16962i
$845$	−1.27676	−	0.737140i	−0.0439220	−	0.0253584i
$846$		0			0
$847$	−39.8358	+	22.9992i	−1.36878	+	0.790263i
$848$	−5.94034	−	34.4256i	−0.203992	−	1.18218i
$849$		0			0
$850$	−42.3800	−	5.61889i	−1.45362	−	0.192726i
$851$	5.59055	−	4.69103i	0.191642	−	0.160806i
$852$		0			0
$853$	−10.7087	+	3.89766i	−0.366660	+	0.133453i	−0.518778	−	0.854909i	$-0.673613\pi$
$853$	−10.7087	+	3.89766i	−0.366660	+	0.133453i	0.152118	+	0.988362i	$0.451391\pi$
$854$	−22.1678	+	70.0837i	−0.758568	+	2.39822i
$855$		0			0
$856$	−22.1347	+	2.85230i	−0.756549	+	0.0974897i
$857$	−26.1169	−	4.60511i	−0.892135	−	0.157307i	−0.291254	−	0.956646i	$-0.594072\pi$
$857$	−26.1169	−	4.60511i	−0.892135	−	0.157307i	−0.600881	+	0.799338i	$0.705184\pi$
$858$		0			0
$859$	−2.68013	+	7.36359i	−0.0914447	+	0.251242i	−0.976980	−	0.213329i	$-0.931569\pi$
$859$	−2.68013	+	7.36359i	−0.0914447	+	0.251242i	0.885536	+	0.464571i	$0.153792\pi$
$860$	0.607779	−	0.0520533i	0.0207251	−	0.00177500i
$861$		0			0
$862$	−15.9707	+	0.682658i	−0.543966	+	0.0232514i
$863$	32.9090			1.12023			0.560117	−	0.828413i	$-0.310756\pi$
$863$	32.9090			1.12023			0.560117	+	0.828413i	$0.310756\pi$
$864$		0			0
$865$	0.794776			0.0270232
$866$	−25.5822	+	1.09349i	−0.869317	+	0.0371584i
$867$		0			0
$868$	−45.9478	+	3.93520i	−1.55957	+	0.133569i
$869$	0.602192	−	1.65451i	0.0204279	−	0.0561253i
$870$		0			0
$871$	8.64877	+	1.52501i	0.293052	+	0.0516730i
$872$	−5.00874	+	0.645431i	−0.169617	+	0.0218571i
$873$		0			0
$874$	−4.74354	+	14.9967i	−0.160453	+	0.507272i
$875$	−6.07623	+	2.21157i	−0.205414	+	0.0747646i
$876$		0			0
$877$	30.3283	−	25.4485i	1.02411	−	0.859333i	0.0339746	−	0.999423i	$-0.489183\pi$
$877$	30.3283	−	25.4485i	1.02411	−	0.859333i	0.990139	+	0.140089i	$0.0447390\pi$
$878$	−19.1722	−	2.54191i	−0.647029	−	0.0857854i
$879$		0			0
$880$	0.0996620	+	0.577564i	0.00335961	+	0.0194697i
$881$	−20.1797	+	11.6507i	−0.679870	+	0.392523i	−0.799806	−	0.600259i	$-0.795064\pi$
$881$	−20.1797	+	11.6507i	−0.679870	+	0.392523i	0.119936	+	0.992782i	$0.461731\pi$
$882$		0			0
$883$	−44.2753	−	25.5624i	−1.48998	−	0.860242i	−0.490049	−	0.871695i	$-0.663021\pi$
$883$	−44.2753	−	25.5624i	−1.48998	−	0.860242i	−0.999934	+	0.0114524i	$0.996355\pi$
$884$	4.92212	−	18.2361i	0.165549	−	0.613345i
$885$		0			0
$886$	14.2226	−	5.87594i	0.477816	−	0.197406i
$887$	−1.18664	−	6.72976i	−0.0398434	−	0.225963i	0.958384	−	0.285483i	$-0.0921541\pi$
$887$	−1.18664	−	6.72976i	−0.0398434	−	0.225963i	−0.998227	+	0.0595201i	$0.981043\pi$
$888$		0			0
$889$	−11.9086	−	9.99253i	−0.399403	−	0.335139i
$890$	1.28254	−	1.17307i	0.0429908	−	0.0393215i
$891$		0			0
$892$	−18.4680	−	1.64980i	−0.618356	−	0.0552395i
$893$	31.1792	−	37.1579i	1.04337	−	1.24344i
$894$		0			0
$895$	−1.70235	+	0.300171i	−0.0569034	+	0.0100336i
$896$	−52.1888	+	6.53102i	−1.74350	+	0.218186i
$897$		0			0
$898$	8.40893	−	5.34627i	0.280610	−	0.178407i
$899$	−1.52601	+	2.64313i	−0.0508954	+	0.0881535i
$900$		0			0
$901$	−26.5042	−	45.9065i	−0.882981	−	1.52937i
$902$	8.68373	+	4.53056i	0.289136	+	0.150851i
$903$		0			0
$904$	−6.58313	+	29.3136i	−0.218952	+	0.974955i
$905$	0.104294	+	0.124292i	0.00346684	+	0.00413161i
$906$		0			0
$907$	−2.56226	−	7.03975i	−0.0850784	−	0.233751i	0.889857	−	0.456240i	$-0.150804\pi$
$907$	−2.56226	−	7.03975i	−0.0850784	−	0.233751i	−0.974935	+	0.222489i	$0.928582\pi$
$908$	−40.4894	+	18.7904i	−1.34369	+	0.623582i
$909$		0			0
$910$	−0.307304	−	1.39219i	−0.0101870	−	0.0461505i
$911$	4.49855	−	25.5126i	0.149044	−	0.845269i	−0.814987	−	0.579479i	$-0.803256\pi$
$911$	4.49855	−	25.5126i	0.149044	−	0.845269i	0.964031	−	0.265790i	$-0.0856328\pi$
$912$		0			0
$913$	−2.31889	−	0.844005i	−0.0767439	−	0.0279325i
$914$	−28.5379	−	21.9394i	−0.943950	−	0.725691i
$915$		0			0
$916$	−37.3127	+	37.1764i	−1.23285	+	1.22834i
$917$			12.1887i			0.402508i
$918$		0			0
$919$			37.4197i			1.23436i	0.786821	+	0.617182i	$0.211726\pi$
$919$			37.4197i			1.23436i	−0.786821	+	0.617182i	$0.788274\pi$
$920$	0.997833	+	0.0463108i	0.0328976	+	0.00152682i
$921$		0			0
$922$	33.7938	−	43.9576i	1.11294	−	1.44767i
$923$	6.82195	+	2.48299i	0.224547	+	0.0817285i
$924$		0			0
$925$	2.49067	−	14.1253i	0.0818928	−	0.464437i
$926$	10.3296	−	2.28010i	0.339451	−	0.0749287i
$927$		0			0
$928$	−1.62140	+	3.08019i	−0.0532250	+	0.101112i
$929$	4.20155	+	11.5437i	0.137848	+	0.378736i	0.989338	−	0.145636i	$-0.0465227\pi$
$929$	4.20155	+	11.5437i	0.137848	+	0.378736i	−0.851490	+	0.524371i	$0.824300\pi$
$930$		0			0
$931$	−41.2218	−	49.1263i	−1.35099	−	1.61005i
$932$	−12.3051	+	8.58260i	−0.403066	+	0.281132i
$933$		0			0
$934$	−0.902650	+	1.73011i	−0.0295356	+	0.0566109i
$935$	0.444664	+	0.770181i	0.0145421	+	0.0251876i
$936$		0			0
$937$	−20.8028	+	36.0316i	−0.679599	+	1.17710i	0.295503	+	0.955342i	$0.404513\pi$
$937$	−20.8028	+	36.0316i	−0.679599	+	1.17710i	−0.975102	+	0.221758i	$0.928821\pi$
$938$	−19.9084	−	31.3131i	−0.650032	−	1.02241i
$939$		0			0
$940$	−2.78949	−	1.30698i	−0.0909830	−	0.0426289i
$941$	−51.4480	+	9.07167i	−1.67716	+	0.295728i	−0.929627	−	0.368501i	$-0.879871\pi$
$941$	−51.4480	+	9.07167i	−1.67716	+	0.295728i	−0.747529	+	0.664229i	$0.768760\pi$
$942$		0			0
$943$	10.7301	−	12.7877i	0.349421	−	0.416424i
$944$	32.2999	+	5.81732i	1.05127	+	0.189338i
$945$		0			0
$946$	2.19627	+	2.40122i	0.0714070	+	0.0780704i
$947$	−13.5313	−	11.3541i	−0.439707	−	0.368958i	0.395893	−	0.918297i	$-0.370435\pi$
$947$	−13.5313	−	11.3541i	−0.439707	−	0.368958i	−0.835600	+	0.549339i	$0.814880\pi$
$948$		0			0
$949$	3.05069	+	17.3013i	0.0990296	+	0.561625i
$950$	11.8039	+	28.5712i	0.382971	+	0.926971i
$951$		0			0
$952$	−70.8907	+	36.6564i	−2.29758	+	1.18804i
$953$	47.6750	+	27.5252i	1.54435	+	0.891628i	0.998557	+	0.0537052i	$0.0171031\pi$
$953$	47.6750	+	27.5252i	1.54435	+	0.891628i	0.545788	+	0.837923i	$0.316230\pi$
$954$		0			0
$955$	1.73597	−	1.00227i	0.0561748	−	0.0324325i
$956$	1.76548	+	6.63743i	0.0570998	+	0.214670i
$957$		0			0
$958$	−2.36553	+	17.8418i	−0.0764268	+	0.576443i
$959$	31.7479	−	26.6396i	1.02519	−	0.860239i
$960$		0			0
$961$	−6.01326	+	2.18865i	−0.193976	+	0.0706015i
$962$	6.04221	+	1.91118i	0.194809	+	0.0616189i
$963$		0			0
$964$	−2.78527	−	1.95787i	−0.0897075	−	0.0630588i
$965$	2.52466	+	0.445165i	0.0812715	+	0.0143304i
$966$		0			0
$967$	−5.75089	+	15.8004i	−0.184936	+	0.508108i	−0.997166	−	0.0752294i	$-0.976031\pi$
$967$	−5.75089	+	15.8004i	−0.184936	+	0.508108i	0.812230	+	0.583337i	$0.198253\pi$
$968$	18.9637	−	20.5815i	0.609516	−	0.661515i
$969$		0			0
$970$	−0.0474250	−	1.10951i	−0.00152273	−	0.0356241i
$971$	22.4986			0.722013			0.361007	−	0.932563i	$-0.382433\pi$
$971$	22.4986			0.722013			0.361007	+	0.932563i	$0.382433\pi$
$972$		0			0
$973$	−69.7582			−2.23635
$974$	−0.748479	−	17.5106i	−0.0239828	−	0.561076i
$975$		0			0
$976$	0.163674	−	44.7218i	0.00523906	−	1.43151i
$977$	−2.99686	+	8.23381i	−0.0958781	+	0.263423i	−0.978355	−	0.206932i	$-0.933652\pi$
$977$	−2.99686	+	8.23381i	−0.0958781	+	0.263423i	0.882477	+	0.470355i	$0.155874\pi$
$978$		0			0
$979$	9.13129	+	1.61009i	0.291837	+	0.0514588i
$980$	−2.34211	+	3.33188i	−0.0748158	+	0.106433i
$981$		0			0
$982$	35.8136	+	11.3280i	1.14286	+	0.361492i
$983$	−10.2909	+	3.74559i	−0.328230	+	0.119466i	−0.500878	−	0.865518i	$-0.666990\pi$
$983$	−10.2909	+	3.74559i	−0.328230	+	0.119466i	0.172649	+	0.984983i	$0.444767\pi$
$984$		0			0
$985$	2.26171	−	1.89780i	0.0720640	−	0.0604689i
$986$	−0.694200	+	5.23595i	−0.0221078	+	0.166747i
$987$		0			0
$988$	−13.1996	+	3.51094i	−0.419934	+	0.111698i
$989$	4.80310	−	2.77307i	0.152730	−	0.0881785i
$990$		0			0
$991$	31.9842	+	18.4661i	1.01601	+	0.586594i	0.912946	−	0.408081i	$-0.133802\pi$
$991$	31.9842	+	18.4661i	1.01601	+	0.586594i	0.103065	+	0.994675i	$0.467135\pi$
$992$	25.9706	−	10.6185i	0.824569	−	0.337137i
$993$		0			0
$994$	−11.7123	−	28.3494i	−0.371492	−	0.899188i
$995$	−0.162287	−	0.920377i	−0.00514485	−	0.0291779i
$996$		0			0
$997$	−28.8738	−	24.2280i	−0.914443	−	0.767309i	0.0585161	−	0.998286i	$-0.481363\pi$
$997$	−28.8738	−	24.2280i	−0.914443	−	0.767309i	−0.972959	+	0.230978i	$0.925808\pi$
$998$	9.20246	+	10.0612i	0.291299	+	0.318481i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.d.107.1		96
3.2	odd	2		972.2.l.a.107.16		96
4.3	odd	2	inner	972.2.l.d.107.9		96
9.2	odd	6		972.2.l.b.755.6		96
9.4	even	3		108.2.l.a.47.11	yes	96
9.5	odd	6		324.2.l.a.143.6		96
9.7	even	3		972.2.l.c.755.11		96
12.11	even	2		972.2.l.a.107.8		96
27.4	even	9		972.2.l.b.215.4		96
27.5	odd	18	inner	972.2.l.d.863.9		96
27.13	even	9		324.2.l.a.179.14		96
27.14	odd	18		108.2.l.a.23.3	✓	96
27.22	even	9		972.2.l.a.863.8		96
27.23	odd	18		972.2.l.c.215.13		96
36.7	odd	6		972.2.l.c.755.13		96
36.11	even	6		972.2.l.b.755.4		96
36.23	even	6		324.2.l.a.143.14		96
36.31	odd	6		108.2.l.a.47.3	yes	96
108.23	even	18		972.2.l.c.215.11		96
108.31	odd	18		972.2.l.b.215.6		96
108.59	even	18	inner	972.2.l.d.863.1		96
108.67	odd	18		324.2.l.a.179.6		96
108.95	even	18		108.2.l.a.23.11	yes	96
108.103	odd	18		972.2.l.a.863.16		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.3	✓	96	27.14	odd	18
108.2.l.a.23.11	yes	96	108.95	even	18
108.2.l.a.47.3	yes	96	36.31	odd	6
108.2.l.a.47.11	yes	96	9.4	even	3
324.2.l.a.143.6		96	9.5	odd	6
324.2.l.a.143.14		96	36.23	even	6
324.2.l.a.179.6		96	108.67	odd	18
324.2.l.a.179.14		96	27.13	even	9
972.2.l.a.107.8		96	12.11	even	2
972.2.l.a.107.16		96	3.2	odd	2
972.2.l.a.863.8		96	27.22	even	9
972.2.l.a.863.16		96	108.103	odd	18
972.2.l.b.215.4		96	27.4	even	9
972.2.l.b.215.6		96	108.31	odd	18
972.2.l.b.755.4		96	36.11	even	6
972.2.l.b.755.6		96	9.2	odd	6
972.2.l.c.215.11		96	108.23	even	18
972.2.l.c.215.13		96	27.23	odd	18
972.2.l.c.755.11		96	9.7	even	3
972.2.l.c.755.13		96	36.7	odd	6
972.2.l.d.107.1		96	1.1	even	1	trivial
972.2.l.d.107.9		96	4.3	odd	2	inner
972.2.l.d.863.1		96	108.59	even	18	inner
972.2.l.d.863.9		96	27.5	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41292 + 0.0603944i) q^{2} +(1.99271 - 0.170665i) q^{4} +(-0.0476648 + 0.130958i) q^{5} +(4.57823 + 0.807266i) q^{7} +(-2.80523 + 0.361485i) q^{8} +(0.0594376 - 0.187912i) q^{10} +(0.987987 - 0.359598i) q^{11} +(1.19199 - 1.00020i) q^{13} +(-6.51745 - 0.864105i) q^{14} +(3.94175 - 0.680171i) q^{16} +(5.25631 - 3.03473i) q^{17} +(-3.80088 - 2.19444i) q^{19} +(-0.0726319 + 0.269095i) q^{20} +(-1.37423 + 0.567753i) q^{22} +(0.440052 + 2.49566i) q^{23} +(3.81534 + 3.20145i) q^{25} +(-1.62379 + 1.48520i) q^{26} +(9.26084 + 0.827297i) q^{28} +(0.395532 - 0.471376i) q^{29} +(-4.88457 + 0.861281i) q^{31} +(-5.52831 + 1.19909i) q^{32} +(-7.24349 + 4.60530i) q^{34} +(-0.323938 + 0.561078i) q^{35} +(-1.43991 - 2.49400i) q^{37} +(5.50288 + 2.87102i) q^{38} +(0.0863714 - 0.384598i) q^{40} +(-4.23420 - 5.04612i) q^{41} +(-0.748529 - 2.05657i) q^{43} +(1.90740 - 0.885188i) q^{44} +(-0.772484 - 3.49960i) q^{46} +(-1.91917 + 10.8842i) q^{47} +(13.7307 + 4.99756i) q^{49} +(-5.58414 - 4.29298i) q^{50} +(2.20459 - 2.19654i) q^{52} -8.73360i q^{53} +0.146525i q^{55} +(-13.1348 - 0.609605i) q^{56} +(-0.530388 + 0.689907i) q^{58} +(7.71009 + 2.80624i) q^{59} +(1.94148 - 11.0107i) q^{61} +(6.84951 - 1.51193i) q^{62} +(7.73866 - 2.02810i) q^{64} +(0.0741682 + 0.203776i) q^{65} +(3.62786 + 4.32351i) q^{67} +(9.95636 - 6.94440i) q^{68} +(0.423814 - 0.812324i) q^{70} +(2.33277 + 4.04048i) q^{71} +(-5.64518 + 9.77774i) q^{73} +(2.18511 + 3.43687i) q^{74} +(-7.94854 - 3.72419i) q^{76} +(4.81353 - 0.848755i) q^{77} +(1.07643 - 1.28284i) q^{79} +(-0.0988087 + 0.548623i) q^{80} +(6.28736 + 6.87406i) q^{82} +(-1.79797 - 1.50867i) q^{83} +(0.146881 + 0.833006i) q^{85} +(1.18182 + 2.86056i) q^{86} +(-2.64154 + 1.36590i) q^{88} +(7.63741 + 4.40946i) q^{89} +(6.26466 - 3.61690i) q^{91} +(1.30282 + 4.89801i) q^{92} +(2.05430 - 15.4944i) q^{94} +(0.468547 - 0.393158i) q^{95} +(5.29482 - 1.92716i) q^{97} +(-19.7022 - 6.23192i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} + 33 q^{14} + 3 q^{16} - 18 q^{17} - 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 30 q^{29} + 33 q^{32} + 15 q^{34} - 6 q^{37} - 63 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) \) 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 + 33 * q^14 + 3 * q^16 - 18 * q^17 - 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 30 * q^29 + 33 * q^32 + 15 * q^34 - 6 * q^37 - 63 * q^38 + 33 * q^40 - 24 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 21 * q^50 + 57 * q^52 - 18 * q^56 + 57 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 + 30 * q^65 - 102 * q^68 + 51 * q^70 - 6 * q^73 + 75 * q^74 + 27 * q^76 - 42 * q^77 - 12 * q^82 - 24 * q^85 - 111 * q^86 + 27 * q^88 + 147 * q^92 + 30 * q^94 - 12 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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