LMFDB - Embedded newform 855.2.dl.a.298.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(127,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.dl (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,12,0,0,12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			298.4
Character	$\chi$	$=$	855.298
Dual form			855.2.dl.a.307.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.297624 + 0.0260387i) q^{2} +(-1.88171 - 0.331797i) q^{4} +(-1.13754 + 1.92510i) q^{5} +(0.0866366 + 0.323332i) q^{7} +(-1.12856 - 0.302398i) q^{8} +(-0.388686 + 0.543336i) q^{10} +(-0.885063 - 1.53297i) q^{11} +(-0.968521 + 2.07700i) q^{13} +(0.0173660 + 0.0984873i) q^{14} +(3.26301 + 1.18764i) q^{16} +(0.238918 - 2.73085i) q^{17} +(-0.174252 - 4.35541i) q^{19} +(2.77926 - 3.24505i) q^{20} +(-0.223499 - 0.479296i) q^{22} +(7.04590 - 4.93359i) q^{23} +(-2.41202 - 4.37975i) q^{25} +(-0.342337 + 0.592946i) q^{26} +(-0.0557446 - 0.637164i) q^{28} +(-4.70481 - 3.94780i) q^{29} +(-1.80927 - 1.04458i) q^{31} +(3.05804 + 1.42599i) q^{32} +(0.142216 - 0.806545i) q^{34} +(-0.720999 - 0.201018i) q^{35} +(-4.27833 - 4.27833i) q^{37} +(0.0615479 - 1.30081i) q^{38} +(1.86593 - 1.82861i) q^{40} +(-2.08289 + 5.72270i) q^{41} +(3.06524 - 4.37761i) q^{43} +(1.15680 + 3.17828i) q^{44} +(2.22549 - 1.28489i) q^{46} +(-5.75408 + 0.503417i) q^{47} +(5.96514 - 3.44398i) q^{49} +(-0.603830 - 1.36632i) q^{50} +(2.51162 - 3.58697i) q^{52} +(-1.22167 - 1.74473i) q^{53} +(3.95792 + 0.0399817i) q^{55} -0.391100i q^{56} +(-1.29747 - 1.29747i) q^{58} +(1.26888 - 1.06472i) q^{59} +(1.59718 - 9.05803i) q^{61} +(-0.511282 - 0.358003i) q^{62} +(-5.14139 - 2.96838i) q^{64} +(-2.89670 - 4.22716i) q^{65} +(0.957732 + 10.9469i) q^{67} +(-1.35566 + 5.05941i) q^{68} +(-0.209352 - 0.0786018i) q^{70} +(15.3710 - 2.71031i) q^{71} +(-2.33808 - 5.01402i) q^{73} +(-1.16193 - 1.38473i) q^{74} +(-1.11722 + 8.25346i) q^{76} +(0.418981 - 0.418981i) q^{77} +(-14.0660 - 5.11962i) q^{79} +(-5.99811 + 4.93063i) q^{80} +(-0.768931 + 1.64898i) q^{82} +(3.20933 - 0.859936i) q^{83} +(4.98538 + 3.56639i) q^{85} +(1.02628 - 1.22307i) q^{86} +(0.535283 + 1.99770i) q^{88} +(-9.75391 + 3.55013i) q^{89} +(-0.755470 - 0.133210i) q^{91} +(-14.8953 + 6.94580i) q^{92} -1.72566 q^{94} +(8.58282 + 4.61900i) q^{95} +(5.97565 + 0.522802i) q^{97} +(1.86504 - 0.869685i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	0.297624	+	0.0260387i	0.210452	+	0.0184122i	0.191894	−	0.981416i	$-0.438537\pi$
$2$	0.297624	+	0.0260387i	0.210452	+	0.0184122i	0.0185578	+	0.999828i	$0.494093\pi$
$3$		0			0
$3$		0			0
$4$	−1.88171	−	0.331797i	−0.940857	−	0.165898i
$5$	−1.13754	+	1.92510i	−0.508722	+	0.860931i
$5$	−1.13754	+	1.92510i	−0.508722	+	0.860931i
$6$		0			0
$7$	0.0866366	+	0.323332i	0.0327456	+	0.122208i	0.980364	−	0.197197i	$-0.0631837\pi$
$7$	0.0866366	+	0.323332i	0.0327456	+	0.122208i	−0.947618	+	0.319405i	$0.896517\pi$
$8$	−1.12856	−	0.302398i	−0.399008	−	0.106914i
$9$		0			0
$10$	−0.388686	+	0.543336i	−0.122913	+	0.171818i
$11$	−0.885063	−	1.53297i	−0.266856	−	0.462209i	0.701192	−	0.712973i	$-0.252652\pi$
$11$	−0.885063	−	1.53297i	−0.266856	−	0.462209i	−0.968048	+	0.250764i	$0.919318\pi$
$12$		0			0
$13$	−0.968521	+	2.07700i	−0.268619	+	0.576056i	−0.993631	−	0.112680i	$-0.964056\pi$
$13$	−0.968521	+	2.07700i	−0.268619	+	0.576056i	0.725012	+	0.688736i	$0.241834\pi$
$14$	0.0173660	+	0.0984873i	0.00464125	+	0.0263218i
$15$		0			0
$16$	3.26301	+	1.18764i	0.815752	+	0.296909i
$17$	0.238918	−	2.73085i	0.0579462	−	0.662328i	−0.910566	−	0.413363i	$-0.864354\pi$
$17$	0.238918	−	2.73085i	0.0579462	−	0.662328i	0.968512	−	0.248965i	$-0.0800905\pi$
$18$		0			0
$19$	−0.174252	−	4.35541i	−0.0399761	−	0.999201i
$19$	−0.174252	−	4.35541i	−0.0399761	−	0.999201i
$20$	2.77926	−	3.24505i	0.621462	−	0.725616i
$21$		0			0
$22$	−0.223499	−	0.479296i	−0.0476502	−	0.102186i
$23$	7.04590	−	4.93359i	1.46917	−	1.02872i	0.480772	−	0.876845i	$-0.340356\pi$
$23$	7.04590	−	4.93359i	1.46917	−	1.02872i	0.988399	−	0.151879i	$-0.0485325\pi$
$24$		0			0
$25$	−2.41202	−	4.37975i	−0.482403	−	0.875949i
$26$	−0.342337	+	0.592946i	−0.0671379	+	0.116286i
$27$		0			0
$28$	−0.0557446	−	0.637164i	−0.0105347	−	0.120413i
$29$	−4.70481	−	3.94780i	−0.873661	−	0.733089i	0.0912048	−	0.995832i	$-0.470928\pi$
$29$	−4.70481	−	3.94780i	−0.873661	−	0.733089i	−0.964866	+	0.262744i	$0.915373\pi$
$30$		0			0
$31$	−1.80927	−	1.04458i	−0.324954	−	0.187612i	0.328645	−	0.944454i	$-0.393408\pi$
$31$	−1.80927	−	1.04458i	−0.324954	−	0.187612i	−0.653599	+	0.756841i	$0.726742\pi$
$32$	3.05804	+	1.42599i	0.540590	+	0.252081i
$33$		0			0
$34$	0.142216	−	0.806545i	0.0243898	−	0.138321i
$35$	−0.720999	−	0.201018i	−0.121871	−	0.0339783i
$36$		0			0
$37$	−4.27833	−	4.27833i	−0.703353	−	0.703353i	0.261776	−	0.965129i	$-0.415692\pi$
$37$	−4.27833	−	4.27833i	−0.703353	−	0.703353i	−0.965129	+	0.261776i	$0.915692\pi$
$38$	0.0615479	−	1.30081i	0.00998439	−	0.211020i
$39$		0			0
$40$	1.86593	−	1.82861i	0.295030	−	0.289129i
$41$	−2.08289	+	5.72270i	−0.325293	+	0.893736i	0.663992	+	0.747740i	$0.268861\pi$
$41$	−2.08289	+	5.72270i	−0.325293	+	0.893736i	−0.989285	+	0.145996i	$0.953361\pi$
$42$		0			0
$43$	3.06524	−	4.37761i	0.467444	−	0.667580i	−0.514338	−	0.857587i	$-0.671962\pi$
$43$	3.06524	−	4.37761i	0.467444	−	0.667580i	0.981783	+	0.190008i	$0.0608513\pi$
$44$	1.15680	+	3.17828i	0.174394	+	0.479144i
$45$		0			0
$46$	2.22549	−	1.28489i	0.328131	−	0.189446i
$47$	−5.75408	+	0.503417i	−0.839319	+	0.0734309i	−0.498704	−	0.866772i	$-0.666191\pi$
$47$	−5.75408	+	0.503417i	−0.839319	+	0.0734309i	−0.340615	+	0.940203i	$0.610635\pi$
$48$		0			0
$49$	5.96514	−	3.44398i	0.852163	−	0.491996i
$50$	−0.603830	−	1.36632i	−0.0853945	−	0.193227i
$51$		0			0
$52$	2.51162	−	3.58697i	0.348299	−	0.497423i
$53$	−1.22167	−	1.74473i	−0.167809	−	0.239656i	0.726436	−	0.687235i	$-0.241176\pi$
$53$	−1.22167	−	1.74473i	−0.167809	−	0.239656i	−0.894245	+	0.447578i	$0.852287\pi$
$54$		0			0
$55$	3.95792	+	0.0399817i	0.533686	+	0.00539113i
$56$		−	0.391100i		−	0.0522629i
$57$		0			0
$58$	−1.29747	−	1.29747i	−0.170366	−	0.170366i
$59$	1.26888	−	1.06472i	0.165194	−	0.138614i	−0.556443	−	0.830886i	$-0.687834\pi$
$59$	1.26888	−	1.06472i	0.165194	−	0.138614i	0.721637	+	0.692271i	$0.243390\pi$
$60$		0			0
$61$	1.59718	−	9.05803i	0.204497	−	1.15976i	−0.693731	−	0.720234i	$-0.744035\pi$
$61$	1.59718	−	9.05803i	0.204497	−	1.15976i	0.898229	−	0.439528i	$-0.144854\pi$
$62$	−0.511282	−	0.358003i	−0.0649329	−	0.0454665i
$63$		0			0
$64$	−5.14139	−	2.96838i	−0.642674	−	0.371048i
$65$	−2.89670	−	4.22716i	−0.359292	−	0.524315i
$66$		0			0
$67$	0.957732	+	10.9469i	0.117006	+	1.33738i	0.796918	+	0.604087i	$0.206462\pi$
$67$	0.957732	+	10.9469i	0.117006	+	1.33738i	−0.679913	+	0.733293i	$0.737982\pi$
$68$	−1.35566	+	5.05941i	−0.164398	+	0.613543i
$69$		0			0
$70$	−0.209352	−	0.0786018i	−0.0250224	−	0.00939471i
$71$	15.3710	−	2.71031i	1.82420	−	0.321655i	0.846614	−	0.532208i	$-0.178637\pi$
$71$	15.3710	−	2.71031i	1.82420	−	0.321655i	0.977583	+	0.210553i	$0.0675263\pi$
$72$		0			0
$73$	−2.33808	−	5.01402i	−0.273651	−	0.586846i	0.720669	−	0.693279i	$-0.243835\pi$
$73$	−2.33808	−	5.01402i	−0.273651	−	0.586846i	−0.994320	+	0.106433i	$0.966057\pi$
$74$	−1.16193	−	1.38473i	−0.135072	−	0.160972i
$75$		0			0
$76$	−1.11722	+	8.25346i	−0.128154	+	0.946737i
$77$	0.418981	−	0.418981i	0.0477473	−	0.0477473i
$78$		0			0
$79$	−14.0660	−	5.11962i	−1.58255	−	0.576002i	−0.606796	−	0.794857i	$-0.707546\pi$
$79$	−14.0660	−	5.11962i	−1.58255	−	0.576002i	−0.975757	+	0.218855i	$0.929768\pi$
$80$	−5.99811	+	4.93063i	−0.670609	+	0.551261i
$81$		0			0
$82$	−0.768931	+	1.64898i	−0.0849142	+	0.182099i
$83$	3.20933	−	0.859936i	0.352269	−	0.0943903i	−0.0783450	−	0.996926i	$-0.524964\pi$
$83$	3.20933	−	0.859936i	0.352269	−	0.0943903i	0.430614	+	0.902536i	$0.358297\pi$
$84$		0			0
$85$	4.98538	+	3.56639i	0.540740	+	0.386829i
$86$	1.02628	−	1.22307i	0.110666	−	0.131887i
$87$		0			0
$88$	0.535283	+	1.99770i	0.0570613	+	0.212956i
$89$	−9.75391	+	3.55013i	−1.03391	+	0.376313i	−0.802569	−	0.596559i	$-0.796534\pi$
$89$	−9.75391	+	3.55013i	−1.03391	+	0.376313i	−0.231343	+	0.972872i	$0.574312\pi$
$90$		0			0
$91$	−0.755470	−	0.133210i	−0.0791948	−	0.0139642i
$92$	−14.8953	+	6.94580i	−1.55294	+	0.724150i
$93$		0			0
$94$	−1.72566			−0.177988
$95$	8.58282	+	4.61900i	0.880579	+	0.473899i
$96$		0			0
$97$	5.97565	+	0.522802i	0.606736	+	0.0530825i	0.386384	−	0.922338i	$-0.373724\pi$
$97$	5.97565	+	0.522802i	0.606736	+	0.0530825i	0.220352	+	0.975420i	$0.429280\pi$
$98$	1.86504	−	0.869685i	0.188398	−	0.0878514i
$99$		0			0
$100$	3.08554	+	9.04173i	0.308554	+	0.904173i
$101$	−10.0826	+	3.66976i	−1.00326	+	0.365155i	−0.790839	−	0.612024i	$-0.790355\pi$
$101$	−10.0826	+	3.66976i	−1.00326	+	0.365155i	−0.212416	+	0.977179i	$0.568133\pi$
$102$		0			0
$103$	−10.3664	−	2.77767i	−1.02143	−	0.273692i	−0.291033	−	0.956713i	$-0.593999\pi$
$103$	−10.3664	−	2.77767i	−1.02143	−	0.273692i	−0.730398	+	0.683021i	$0.760666\pi$
$104$	1.72112	−	2.05115i	0.168770	−	0.201132i
$105$		0			0
$106$	−0.318168	−	0.551083i	−0.0309032	−	0.0535259i
$107$	2.12744	−	0.570046i	0.205668	−	0.0551085i	−0.154514	−	0.987991i	$-0.549381\pi$
$107$	2.12744	−	0.570046i	0.205668	−	0.0551085i	0.360182	+	0.932882i	$0.382715\pi$
$108$		0			0
$109$	1.51271	+	8.57902i	0.144892	+	0.821721i	0.967454	+	0.253046i	$0.0814325\pi$
$109$	1.51271	+	8.57902i	0.144892	+	0.821721i	−0.822563	+	0.568675i	$0.807456\pi$
$110$	1.17693	+	0.114959i	0.112216	+	0.0109609i
$111$		0			0
$112$	−0.101306	+	1.15793i	−0.00957247	+	0.109414i
$113$	8.30039	−	8.30039i	0.780835	−	0.780835i	−0.199137	−	0.979972i	$-0.563814\pi$
$113$	8.30039	−	8.30039i	0.780835	−	0.780835i	0.979972	+	0.199137i	$0.0638138\pi$
$114$		0			0
$115$	1.48268	+	19.1762i	0.138260	+	1.78819i
$116$	7.54323	+	8.98967i	0.700372	+	0.834670i
$117$		0			0
$118$	0.405372	−	0.283845i	0.0373176	−	0.0261300i
$119$	0.903671	−	0.159342i	0.0828394	−	0.0146068i
$120$		0			0
$121$	3.93333	−	6.81272i	0.357575	−	0.619338i
$122$	0.711217	−	2.65430i	0.0643906	−	0.240309i
$123$		0			0
$124$	3.05794	+	2.56591i	0.274611	+	0.230426i
$125$	11.1752	+	0.338758i	0.999541	+	0.0302994i
$126$		0			0
$127$	−6.06809	−	2.82960i	−0.538456	−	0.251086i	0.134313	−	0.990939i	$-0.457117\pi$
$127$	−6.06809	−	2.82960i	−0.538456	−	0.251086i	−0.672769	+	0.739853i	$0.734895\pi$
$128$	−6.98083	−	4.88803i	−0.617024	−	0.432045i
$129$		0			0
$130$	−0.752058	−	1.33353i	−0.0659598	−	0.116958i
$131$	−5.62950	+	4.72371i	−0.491851	+	0.412712i	−0.854689	−	0.519140i	$-0.826252\pi$
$131$	−5.62950	+	4.72371i	−0.491851	+	0.412712i	0.362838	+	0.931852i	$0.381808\pi$
$132$		0			0
$133$	1.39315	−	0.433679i	0.120801	−	0.0376048i
$134$			3.28301i			0.283609i
$135$		0			0
$136$	−1.09544	+	3.00969i	−0.0939331	+	0.258079i
$137$	−3.01799	−	4.31014i	−0.257845	−	0.368240i	0.669269	−	0.743020i	$-0.266607\pi$
$137$	−3.01799	−	4.31014i	−0.257845	−	0.368240i	−0.927114	+	0.374780i	$0.877718\pi$
$138$		0			0
$139$	6.35505	+	17.4603i	0.539028	+	1.48097i	0.848052	+	0.529913i	$0.177775\pi$
$139$	6.35505	+	17.4603i	0.539028	+	1.48097i	−0.309024	+	0.951054i	$0.600002\pi$
$140$	1.29002	+	0.617484i	0.109026	+	0.0521870i
$141$		0			0
$142$	4.64534	−	0.406414i	0.389828	−	0.0341055i
$143$	4.04119	−	0.353558i	0.337941	−	0.0295660i
$144$		0			0
$145$	12.9518	−	4.56645i	1.07559	−	0.379223i
$146$	−0.565308	−	1.55317i	−0.0467853	−	0.128541i
$147$		0			0
$148$	6.63105	+	9.47012i	0.545069	+	0.778439i
$149$	−6.71169	+	18.4402i	−0.549843	+	1.51068i	0.284080	+	0.958800i	$0.408312\pi$
$149$	−6.71169	+	18.4402i	−0.549843	+	1.51068i	−0.833923	+	0.551880i	$0.813910\pi$
$150$		0			0
$151$		−	1.28151i		−	0.104288i	−0.998640	−	0.0521440i	$-0.983395\pi$
$151$		−	1.28151i		−	0.104288i	0.998640	−	0.0521440i	$-0.0166055\pi$
$152$	−1.12041	+	4.96806i	−0.0908776	+	0.402963i
$153$		0			0
$154$	0.135608	−	0.113789i	0.0109276	−	0.00916938i
$155$	4.06903	−	2.29477i	0.326833	−	0.184320i
$156$		0			0
$157$	−13.3302	−	9.33390i	−1.06387	−	0.744926i	−0.0957434	−	0.995406i	$-0.530523\pi$
$157$	−13.3302	−	9.33390i	−1.06387	−	0.744926i	−0.968122	+	0.250480i	$0.919412\pi$
$158$	−4.05308	−	1.88998i	−0.322446	−	0.150359i
$159$		0			0
$160$	−6.22381	+	4.26492i	−0.492035	+	0.337171i
$161$	2.20562	+	1.85074i	0.173827	+	0.145858i
$162$		0			0
$163$	2.63825	−	9.84609i	0.206644	−	0.771205i	−0.782298	−	0.622904i	$-0.785953\pi$
$163$	2.63825	−	9.84609i	0.206644	−	0.771205i	0.988942	−	0.148301i	$-0.0473806\pi$
$164$	5.81818	−	10.0774i	0.454324	−	0.786912i
$165$		0			0
$166$	0.977564	−	0.172371i	0.0758737	−	0.0133786i
$167$	−2.13302	+	1.49356i	−0.165058	+	0.115575i	−0.653187	−	0.757197i	$-0.726568\pi$
$167$	−2.13302	+	1.49356i	−0.165058	+	0.115575i	0.488129	+	0.872772i	$0.337680\pi$
$168$		0			0
$169$	4.98034	+	5.93534i	0.383103	+	0.456565i
$170$	1.39090	+	1.19125i	0.106677	+	0.0913651i
$171$		0			0
$172$	−7.22038	+	7.22038i	−0.550549	+	0.550549i
$173$	1.59591	−	18.2413i	0.121335	−	1.38686i	−0.654565	−	0.756006i	$-0.727148\pi$
$173$	1.59591	−	18.2413i	0.121335	−	1.38686i	0.775900	−	0.630856i	$-0.217296\pi$
$174$		0			0
$175$	1.20714	−	1.15933i	0.0912515	−	0.0876370i
$176$	−1.06735	−	6.05324i	−0.0804545	−	0.456280i
$177$		0			0
$178$	−2.99544	+	0.802625i	−0.224518	+	0.0601593i
$179$	3.88436	+	6.72790i	0.290331	+	0.502867i	0.973888	−	0.227030i	$-0.0729014\pi$
$179$	3.88436	+	6.72790i	0.290331	+	0.502867i	−0.683557	+	0.729897i	$0.739568\pi$
$180$		0			0
$181$	−12.3085	+	14.6688i	−0.914887	+	1.09032i	0.0807244	+	0.996736i	$0.474277\pi$
$181$	−12.3085	+	14.6688i	−0.914887	+	1.09032i	−0.995611	+	0.0935835i	$0.970168\pi$
$182$	−0.221377	−	0.0593179i	−0.0164096	−	0.00439693i
$183$		0			0
$184$	−9.44366	+	3.43721i	−0.696196	+	0.253395i
$185$	13.1030	−	3.36945i	0.963349	−	0.247727i
$186$		0			0
$187$	−4.39778	+	2.05072i	−0.321597	+	0.149963i
$188$	10.9946	+	0.961900i	0.801861	+	0.0701538i
$189$		0			0
$190$	2.43418	+	1.59821i	0.176594	+	0.115946i
$191$	−15.8411			−1.14622			−0.573110	−	0.819478i	$-0.694263\pi$
$191$	−15.8411			−1.14622			−0.573110	+	0.819478i	$0.694263\pi$
$192$		0			0
$193$	24.5928	−	11.4678i	1.77023	−	0.825470i	0.794252	−	0.607589i	$-0.207863\pi$
$193$	24.5928	−	11.4678i	1.77023	−	0.825470i	0.975975	−	0.217882i	$-0.0699147\pi$
$194$	1.76488	+	0.311197i	0.126711	+	0.0223426i
$195$		0			0
$196$	−12.3674	+	4.50136i	−0.883385	+	0.321526i
$197$	−3.74333	−	13.9703i	−0.266701	−	0.995343i	−0.961201	−	0.275850i	$-0.911041\pi$
$197$	−3.74333	−	13.9703i	−0.266701	−	0.995343i	0.694499	−	0.719493i	$-0.255626\pi$
$198$		0			0
$199$	2.04942	−	2.44240i	0.145279	−	0.173137i	−0.688498	−	0.725239i	$-0.741729\pi$
$199$	2.04942	−	2.44240i	0.145279	−	0.173137i	0.833777	+	0.552101i	$0.186174\pi$
$200$	1.39769	+	5.67222i	0.0988315	+	0.401086i
$201$		0			0
$202$	−3.09638	+	0.829671i	−0.217860	+	0.0583755i
$203$	0.868843	−	1.86324i	0.0609808	−	0.130774i
$204$		0			0
$205$	−8.64740	−	10.5196i	−0.603961	−	0.734718i
$206$	−3.01296	−	1.09663i	−0.209923	−	0.0764057i
$207$		0			0
$208$	−5.62701	+	5.62701i	−0.390163	+	0.390163i
$209$	−6.52251	+	4.12194i	−0.451172	+	0.285120i
$210$		0			0
$211$	0.360006	+	0.429039i	0.0247838	+	0.0295362i	0.778294	−	0.627900i	$-0.216085\pi$
$211$	0.360006	+	0.429039i	0.0247838	+	0.0295362i	−0.753510	+	0.657436i	$0.771641\pi$
$212$	1.71994	+	3.68842i	0.118126	+	0.253322i
$213$		0			0
$214$	0.648021	−	0.114264i	0.0442978	−	0.00781090i
$215$	4.94052	+	10.8806i	0.336940	+	0.742050i
$216$		0			0
$217$	0.180998	−	0.675493i	0.0122869	−	0.0458555i
$218$	0.226833	+	2.59271i	0.0153630	+	0.175600i
$219$		0			0
$220$	−7.43440	−	1.38846i	−0.501227	−	0.0936099i
$221$	5.44058	+	3.14112i	0.365973	+	0.211294i
$222$		0			0
$223$	18.4399	+	12.9118i	1.23483	+	0.864635i	0.994364	−	0.106023i	$-0.0338117\pi$
$223$	18.4399	+	12.9118i	1.23483	+	0.864635i	0.240463	+	0.970658i	$0.422701\pi$
$224$	−0.196130	+	1.11231i	−0.0131045	+	0.0743191i
$225$		0			0
$226$	2.68653	−	2.25426i	0.178705	−	0.149951i
$227$	−11.5076	−	11.5076i	−0.763785	−	0.763785i	0.213220	−	0.977004i	$-0.431605\pi$
$227$	−11.5076	−	11.5076i	−0.763785	−	0.763785i	−0.977004	+	0.213220i	$0.931605\pi$
$228$		0			0
$229$		−	11.5082i		−	0.760486i	−0.924887	−	0.380243i	$-0.875840\pi$
$229$		−	11.5082i		−	0.760486i	0.924887	−	0.380243i	$-0.124160\pi$
$230$	−0.0580433	+	5.74590i	−0.00382726	+	0.378874i
$231$		0			0
$232$	4.11587	+	5.87808i	0.270220	+	0.385915i
$233$	−10.0958	+	14.4183i	−0.661398	+	0.944574i	0.338596	+	0.940932i	$0.390048\pi$
$233$	−10.0958	+	14.4183i	−0.661398	+	0.944574i	−0.999993	+	0.00364164i	$0.998841\pi$
$234$		0			0
$235$	5.57636	−	11.6498i	0.363761	−	0.759951i
$236$	−2.74094	+	1.58248i	−0.178420	+	0.103011i
$237$		0			0
$238$	0.273103	−	0.0238934i	0.0177026	−	0.00154878i
$239$	2.74935	−	1.58734i	0.177841	−	0.102676i	−0.408437	−	0.912786i	$-0.633926\pi$
$239$	2.74935	−	1.58734i	0.177841	−	0.102676i	0.586278	+	0.810110i	$0.300593\pi$
$240$		0			0
$241$	2.63620	+	7.24289i	0.169812	+	0.466555i	0.995183	−	0.0980359i	$-0.0312560\pi$
$241$	2.63620	+	7.24289i	0.169812	+	0.466555i	−0.825371	+	0.564591i	$0.809034\pi$
$242$	1.34805	−	1.92521i	0.0866557	−	0.123757i
$243$		0			0
$244$	−6.01085	+	16.5147i	−0.384805	+	1.05724i
$245$	−0.155578	+	15.4011i	−0.00993949	+	0.983943i
$246$		0			0
$247$	9.21496	+	3.85639i	0.586334	+	0.245376i
$248$	1.72600	+	1.72600i	0.109601	+	0.109601i
$249$		0			0
$250$	3.31719	+	0.391810i	0.209797	+	0.0247803i
$251$	0.155567	−	0.882266i	0.00981932	−	0.0556881i	−0.979504	−	0.201423i	$-0.935443\pi$
$251$	0.155567	−	0.882266i	0.00981932	−	0.0556881i	0.989324	+	0.145735i	$0.0465546\pi$
$252$		0			0
$253$	−13.7991	−	6.43464i	−0.867544	−	0.404542i
$254$	−1.73233	−	1.00016i	−0.108696	−	0.0627557i
$255$		0			0
$256$	7.14527	+	5.99559i	0.446579	+	0.374725i
$257$	0.187810	+	2.14668i	0.0117153	+	0.133906i	0.999800	−	0.0200056i	$-0.00636840\pi$
$257$	0.187810	+	2.14668i	0.0117153	+	0.133906i	−0.988085	+	0.153912i	$0.950813\pi$
$258$		0			0
$259$	1.01266	−	1.75398i	0.0629237	−	0.108987i
$260$	4.04820	+	8.91543i	0.251059	+	0.552911i
$261$		0			0
$262$	−1.79847	+	1.25930i	−0.111110	+	0.0778000i
$263$	−12.4532	−	26.7060i	−0.767899	−	1.64676i	−0.762679	−	0.646778i	$-0.776116\pi$
$263$	−12.4532	−	26.7060i	−0.767899	−	1.64676i	−0.00522005	−	0.999986i	$-0.501662\pi$
$264$		0			0
$265$	4.74847	−	0.367145i	0.291696	−	0.0225535i
$266$	0.425927	−	0.0927976i	0.0261153	−	0.00568978i
$267$		0			0
$268$	1.82998	−	20.9168i	0.111784	−	1.27769i
$269$	−5.89502	−	2.14561i	−0.359426	−	0.130820i	0.155994	−	0.987758i	$-0.450142\pi$
$269$	−5.89502	−	2.14561i	−0.359426	−	0.130820i	−0.515420	+	0.856938i	$0.672364\pi$
$270$		0			0
$271$	−1.04597	−	5.93198i	−0.0635381	−	0.360342i	−0.999955	−	0.00945382i	$-0.996991\pi$
$271$	−1.04597	−	5.93198i	−0.0635381	−	0.360342i	0.936417	−	0.350889i	$-0.114120\pi$
$272$	4.02285	−	8.62703i	0.243921	−	0.523091i
$273$		0			0
$274$	−0.785996	−	1.36139i	−0.0474838	−	0.0822443i
$275$	−4.57925	+	7.57391i	−0.276139	+	0.456724i
$276$		0			0
$277$	−21.8337	−	5.85032i	−1.31186	−	0.351512i	−0.465937	−	0.884818i	$-0.654283\pi$
$277$	−21.8337	−	5.85032i	−1.31186	−	0.351512i	−0.845922	+	0.533306i	$0.820949\pi$
$278$	1.43677	+	5.36209i	0.0861716	+	0.321597i
$279$		0			0
$280$	0.752906	+	0.444891i	0.0449948	+	0.0265873i
$281$	11.8624	+	2.09165i	0.707649	+	0.124778i	0.515878	−	0.856662i	$-0.327466\pi$
$281$	11.8624	+	2.09165i	0.707649	+	0.124778i	0.191771	+	0.981440i	$0.438577\pi$
$282$		0			0
$283$	−11.6168	−	1.01634i	−0.690549	−	0.0604152i	−0.263521	−	0.964654i	$-0.584884\pi$
$283$	−11.6168	−	1.01634i	−0.690549	−	0.0604152i	−0.427028	+	0.904238i	$0.640439\pi$
$284$	−29.8230			−1.76967
$285$		0			0
$286$	1.21196			0.0716647
$287$	−2.03079	−	0.177671i	−0.119874	−	0.0104876i
$288$		0			0
$289$	9.34127	+	1.64712i	0.549487	+	0.0968893i
$290$	3.97367	−	1.02184i	0.233342	−	0.0600043i
$291$		0			0
$292$	2.73595	+	10.2107i	0.160109	+	0.597537i
$293$	−12.1638	−	3.25928i	−0.710616	−	0.190409i	−0.114635	−	0.993408i	$-0.536570\pi$
$293$	−12.1638	−	3.25928i	−0.710616	−	0.190409i	−0.595981	+	0.802999i	$0.703237\pi$
$294$		0			0
$295$	0.606286	+	3.65387i	0.0352993	+	0.212737i
$296$	3.53461	+	6.12213i	0.205445	+	0.355841i
$297$		0			0
$298$	−2.47772	+	5.31348i	−0.143530	+	0.307802i
$299$	3.42297	+	19.4126i	0.197955	+	1.12266i
$300$		0			0
$301$	1.68098	+	0.611828i	0.0968903	+	0.0352652i
$302$	0.0333690	−	0.381409i	0.00192017	−	0.0219476i
$303$		0			0
$304$	4.60407	−	14.4187i	0.264061	−	0.826969i
$305$	15.6208	+	13.3786i	0.894442	+	0.766055i
$306$		0			0
$307$	−6.97832	−	14.9650i	−0.398273	−	0.854100i	−0.998525	−	0.0542891i	$-0.982711\pi$
$307$	−6.97832	−	14.9650i	−0.398273	−	0.854100i	0.600252	−	0.799811i	$-0.295067\pi$
$308$	−0.927419	+	0.649385i	−0.0528446	+	0.0370022i
$309$		0			0
$310$	1.27079	−	0.577026i	0.0721763	−	0.0327729i
$311$	−2.66572	+	4.61716i	−0.151159	+	0.261815i	−0.931654	−	0.363347i	$-0.881634\pi$
$311$	−2.66572	+	4.61716i	−0.151159	+	0.261815i	0.780495	+	0.625162i	$0.214967\pi$
$312$		0			0
$313$	1.71309	+	19.5807i	0.0968296	+	1.10677i	0.876769	+	0.480912i	$0.159694\pi$
$313$	1.71309	+	19.5807i	0.0968296	+	1.10677i	−0.779939	+	0.625855i	$0.784750\pi$
$314$	−3.72434	−	3.12509i	−0.210177	−	0.176359i
$315$		0			0
$316$	24.7696	+	14.3007i	1.39340	+	0.804479i
$317$	16.5516	+	7.71815i	0.929632	+	0.433495i	0.827620	−	0.561289i	$-0.189694\pi$
$317$	16.5516	+	7.71815i	0.929632	+	0.433495i	0.102012	+	0.994783i	$0.467472\pi$
$318$		0			0
$319$	−1.88783	+	10.7064i	−0.105698	+	0.599443i
$320$	11.5630	−	6.52104i	0.646389	−	0.364537i
$321$		0			0
$322$	0.608255	+	0.608255i	0.0338967	+	0.0338967i
$323$	−11.9356	−	0.564733i	−0.664115	−	0.0314226i
$324$		0			0
$325$	11.4328	−	0.767879i	0.634179	−	0.0425943i
$326$	1.04159	−	2.86174i	0.0576881	−	0.158497i
$327$		0			0
$328$	4.08121	−	5.82858i	0.225347	−	0.321829i
$329$	−0.661285	−	1.81687i	−0.0364578	−	0.100167i
$330$		0			0
$331$	−10.5135	+	6.06999i	−0.577875	+	0.333637i	−0.760289	−	0.649585i	$-0.774942\pi$
$331$	−10.5135	+	6.06999i	−0.577875	+	0.333637i	0.182413	+	0.983222i	$0.441609\pi$
$332$	−6.32436	+	0.553310i	−0.347094	+	0.0303668i
$333$		0			0
$334$	−0.673729	+	0.388978i	−0.0368648	+	0.0212839i
$335$	−22.1634	−	10.6088i	−1.21092	−	0.579622i
$336$		0			0
$337$	11.9360	−	17.0464i	0.650195	−	0.928575i	−0.349771	−	0.936835i	$-0.613741\pi$
$337$	11.9360	−	17.0464i	0.650195	−	0.928575i	0.999966	+	0.00826058i	$0.00262945\pi$
$338$	1.32772	+	1.89618i	0.0722185	+	0.103139i
$339$		0			0
$340$	−8.19774	−	8.36505i	−0.444585	−	0.453659i
$341$			3.69808i			0.200262i
$342$		0			0
$343$	3.28722	+	3.28722i	0.177493	+	0.177493i
$344$	−4.78310	+	4.01350i	−0.257888	+	0.216393i
$345$		0			0
$346$	0.949961	−	5.38750i	0.0510702	−	0.289634i
$347$	7.40032	+	5.18176i	0.397270	+	0.278171i	0.755093	−	0.655618i	$-0.227592\pi$
$347$	7.40032	+	5.18176i	0.397270	+	0.278171i	−0.357823	+	0.933790i	$0.616481\pi$
$348$		0			0
$349$	1.17548	+	0.678665i	0.0629221	+	0.0363281i	0.531131	−	0.847290i	$-0.321767\pi$
$349$	1.17548	+	0.678665i	0.0629221	+	0.0363281i	−0.468209	+	0.883618i	$0.655101\pi$
$350$	0.389462	−	0.313611i	0.0208176	−	0.0167632i
$351$		0			0
$352$	−0.520556	−	5.94999i	−0.0277457	−	0.317135i
$353$	6.50831	−	24.2894i	0.346403	−	1.29279i	−0.544563	−	0.838720i	$-0.683304\pi$
$353$	6.50831	−	24.2894i	0.346403	−	1.29279i	0.890965	−	0.454072i	$-0.150029\pi$
$354$		0			0
$355$	−12.2674	+	32.6737i	−0.651087	+	1.73414i
$356$	19.5320	−	3.44402i	1.03519	−	0.182533i
$357$		0			0
$358$	0.980892	+	2.10353i	0.0518417	+	0.111175i
$359$	−1.32860	−	1.58336i	−0.0701208	−	0.0835667i	0.729844	−	0.683614i	$-0.239593\pi$
$359$	−1.32860	−	1.58336i	−0.0701208	−	0.0835667i	−0.799964	+	0.600047i	$0.795148\pi$
$360$		0			0
$361$	−18.9393	+	1.51788i	−0.996804	+	0.0798883i
$362$	−4.04527	+	4.04527i	−0.212615	+	0.212615i
$363$		0			0
$364$	1.37738	+	0.501325i	0.0721943	+	0.0262766i
$365$	12.3121	+	1.20261i	0.644446	+	0.0629474i
$366$		0			0
$367$	2.99889	−	6.43114i	0.156541	−	0.335703i	−0.812358	−	0.583158i	$-0.801817\pi$
$367$	2.99889	−	6.43114i	0.156541	−	0.335703i	0.968899	+	0.247456i	$0.0795945\pi$
$368$	28.8501	−	7.73037i	1.50392	−	0.402973i
$369$		0			0
$370$	3.98749	−	0.661643i	0.207300	−	0.0343972i
$371$	0.458284	−	0.546162i	0.0237929	−	0.0283553i
$372$		0			0
$373$	−6.17989	−	23.0637i	−0.319983	−	1.19419i	−0.919260	−	0.393650i	$-0.871212\pi$
$373$	−6.17989	−	23.0637i	−0.319983	−	1.19419i	0.599277	−	0.800541i	$-0.295455\pi$
$374$	−1.36228	+	0.495830i	−0.0704419	+	0.0256388i
$375$		0			0
$376$	6.64609	+	1.17188i	0.342746	+	0.0604353i
$377$	12.7563	−	5.94835i	0.656982	−	0.306356i
$378$		0			0
$379$	16.2074			0.832518			0.416259	−	0.909246i	$-0.363341\pi$
$379$	16.2074			0.832518			0.416259	+	0.909246i	$0.363341\pi$
$380$	−14.6178	−	11.5394i	−0.749880	−	0.591958i
$381$		0			0
$382$	−4.71468	−	0.412481i	−0.241224	−	0.0211044i
$383$	−5.70067	+	2.65826i	−0.291290	+	0.135831i	−0.562771	−	0.826613i	$-0.690265\pi$
$383$	−5.70067	+	2.65826i	−0.291290	+	0.135831i	0.271480	+	0.962444i	$0.412487\pi$
$384$		0			0
$385$	0.329973	+	1.28319i	0.0168170	+	0.0653972i
$386$	7.61801	−	2.77273i	0.387746	−	0.141128i
$387$		0			0
$388$	−11.0710	−	2.96647i	−0.562045	−	0.150600i
$389$	13.5012	−	16.0901i	0.684537	−	0.815799i	−0.306147	−	0.951984i	$-0.599040\pi$
$389$	13.5012	−	16.0901i	0.684537	−	0.815799i	0.990683	+	0.136185i	$0.0434843\pi$
$390$		0			0
$391$	−11.7895	−	20.4200i	−0.596221	−	1.03268i
$392$	−7.77350	+	2.08290i	−0.392621	+	0.105202i
$393$		0			0
$394$	−0.750336	−	4.25537i	−0.0378014	−	0.214382i
$395$	25.8564	−	21.2548i	1.30098	−	1.06944i
$396$		0			0
$397$	0.242726	−	2.77437i	0.0121821	−	0.139242i	−0.987668	−	0.156563i	$-0.949958\pi$
$397$	0.242726	−	2.77437i	0.0121821	−	0.139242i	0.999850	+	0.0173218i	$0.00551397\pi$
$398$	0.673552	−	0.673552i	0.0337621	−	0.0337621i
$399$		0			0
$400$	−2.66887	−	17.1557i	−0.133444	−	0.857787i
$401$	−14.4597	−	17.2324i	−0.722083	−	0.860545i	0.272749	−	0.962085i	$-0.412067\pi$
$401$	−14.4597	−	17.2324i	−0.722083	−	0.860545i	−0.994831	+	0.101541i	$0.967623\pi$
$402$		0			0
$403$	3.92191	−	2.74615i	0.195364	−	0.136795i
$404$	20.1902	−	3.56007i	1.00450	−	0.177120i
$405$		0			0
$406$	0.307105	−	0.531921i	0.0152414	−	0.0263988i
$407$	−2.77197	+	10.3452i	−0.137402	+	0.512790i
$408$		0			0
$409$	−18.6505	−	15.6496i	−0.922209	−	0.773825i	0.0521935	−	0.998637i	$-0.483379\pi$
$409$	−18.6505	−	15.6496i	−0.922209	−	0.773825i	−0.974402	+	0.224812i	$0.927823\pi$
$410$	−2.29976	−	3.35604i	−0.113577	−	0.165743i
$411$		0			0
$412$	18.5850	+	8.66631i	0.915616	+	0.426959i
$413$	0.454188	+	0.318026i	0.0223491	+	0.0156490i
$414$		0			0
$415$	−1.99527	+	7.15648i	−0.0979438	+	0.351298i
$416$	−5.92355	+	4.97045i	−0.290426	+	0.243696i
$417$		0			0
$418$	−2.04859	+	1.05695i	−0.100200	+	0.0516971i
$419$		−	3.10801i		−	0.151836i	−0.997114	−	0.0759182i	$-0.975811\pi$
$419$		−	3.10801i		−	0.151836i	0.997114	−	0.0759182i	$-0.0241888\pi$
$420$		0			0
$421$	−7.35818	+	20.2164i	−0.358616	+	0.985289i	0.620894	+	0.783894i	$0.286770\pi$
$421$	−7.35818	+	20.2164i	−0.358616	+	0.985289i	−0.979510	+	0.201395i	$0.935453\pi$
$422$	0.0959748	+	0.137066i	0.00467198	+	0.00667228i
$423$		0			0
$424$	0.851132	+	2.33847i	0.0413346	+	0.113566i
$425$	−12.5367	+	5.54045i	−0.608120	+	0.268751i
$426$		0			0
$427$	3.06713	−	0.268339i	0.148429	−	0.0129858i
$428$	−4.19238	+	0.366785i	−0.202646	+	0.0177292i
$429$		0			0
$430$	1.18710	+	3.36697i	0.0572470	+	0.162370i
$431$	6.33738	+	17.4118i	0.305261	+	0.838698i	0.993564	+	0.113274i	$0.0361339\pi$
$431$	6.33738	+	17.4118i	0.305261	+	0.838698i	−0.688303	+	0.725424i	$0.741644\pi$
$432$		0			0
$433$	−5.25844	−	7.50983i	−0.252704	−	0.360899i	0.672677	−	0.739936i	$-0.265144\pi$
$433$	−5.25844	−	7.50983i	−0.252704	−	0.360899i	−0.925382	+	0.379037i	$0.876255\pi$
$434$	0.0714583	−	0.196330i	0.00343011	−	0.00942414i
$435$		0			0
$436$		−	16.6452i		−	0.797159i
$437$	−22.7156	−	29.8281i	−1.08663	−	1.42687i
$438$		0			0
$439$	−13.5592	+	11.3775i	−0.647147	+	0.543021i	−0.906204	−	0.422841i	$-0.861033\pi$
$439$	−13.5592	+	11.3775i	−0.647147	+	0.543021i	0.259057	+	0.965862i	$0.416588\pi$
$440$	−4.45468	−	1.24199i	−0.212368	−	0.0592095i
$441$		0			0
$442$	1.53745	+	1.07654i	0.0731293	+	0.0512057i
$443$	4.31463	+	2.01194i	0.204994	+	0.0955903i	0.522404	−	0.852698i	$-0.325035\pi$
$443$	4.31463	+	2.01194i	0.204994	+	0.0955903i	−0.317410	+	0.948288i	$0.602813\pi$
$444$		0			0
$445$	4.26108	−	22.8157i	0.201995	−	1.08157i
$446$	5.15195	+	4.32300i	0.243952	+	0.204700i
$447$		0			0
$448$	0.514341	−	1.91955i	0.0243003	−	0.0906901i
$449$	−1.65599	+	2.86825i	−0.0781508	+	0.135361i	−0.902452	−	0.430790i	$-0.858235\pi$
$449$	−1.65599	+	2.86825i	−0.0781508	+	0.135361i	0.824301	+	0.566151i	$0.191568\pi$
$450$		0			0
$451$	10.6162	−	1.87193i	0.499899	−	0.0881458i
$452$	−18.3730	+	12.8649i	−0.864193	+	0.605115i
$453$		0			0
$454$	−3.12529	−	3.72457i	−0.146677	−	0.174803i
$455$	1.11582	−	1.30282i	0.0523103	−	0.0610773i
$456$		0			0
$457$	20.2603	−	20.2603i	0.947736	−	0.947736i	−0.0509647	−	0.998700i	$-0.516230\pi$
$457$	20.2603	−	20.2603i	0.947736	−	0.947736i	0.998700	+	0.0509647i	$0.0162296\pi$
$458$	0.299660	−	3.42513i	0.0140022	−	0.160046i
$459$		0			0
$460$	3.57263	−	36.5761i	0.166575	−	1.70537i
$461$	−2.78058	−	15.7694i	−0.129504	−	0.734455i	−0.978530	−	0.206104i	$-0.933921\pi$
$461$	−2.78058	−	15.7694i	−0.129504	−	0.734455i	0.849026	−	0.528351i	$-0.177190\pi$
$462$		0			0
$463$	27.3267	−	7.32218i	1.26998	−	0.340291i	0.439958	−	0.898018i	$-0.354993\pi$
$463$	27.3267	−	7.32218i	1.26998	−	0.340291i	0.830024	+	0.557728i	$0.188327\pi$
$464$	−10.6633	−	18.4693i	−0.495029	−	0.857416i
$465$		0			0
$466$	−3.38018	+	4.02835i	−0.156584	+	0.186610i
$467$	1.48896	+	0.398965i	0.0689007	+	0.0184619i	0.293105	−	0.956080i	$-0.405312\pi$
$467$	1.48896	+	0.398965i	0.0689007	+	0.0184619i	−0.224204	+	0.974542i	$0.571978\pi$
$468$		0			0
$469$	−3.45652	+	1.25807i	−0.159607	+	0.0580923i
$470$	1.96300	−	3.32207i	0.0905466	−	0.153236i
$471$		0			0
$472$	−1.75398	+	0.817894i	−0.0807335	+	0.0376466i
$473$	−9.42369	−	0.824466i	−0.433302	−	0.0379090i
$474$		0			0
$475$	−18.6553	+	11.2685i	−0.855965	+	0.517035i
$476$	−1.75332			−0.0803632
$477$		0			0
$478$	0.859605	−	0.400840i	0.0393174	−	0.0183340i
$479$	−16.5181	−	2.91258i	−0.754730	−	0.133079i	−0.216971	−	0.976178i	$-0.569618\pi$
$479$	−16.5181	−	2.91258i	−0.754730	−	0.133079i	−0.537759	+	0.843099i	$0.680729\pi$
$480$		0			0
$481$	13.0297	−	4.74243i	0.594105	−	0.216236i
$482$	0.595999	+	2.22430i	0.0271470	+	0.101314i
$483$		0			0
$484$	−9.66184	+	11.5145i	−0.439174	+	0.523388i
$485$	−7.80398	+	10.9090i	−0.354360	+	0.495353i
$486$		0			0
$487$	3.88785	−	1.04175i	0.176175	−	0.0472060i	−0.169653	−	0.985504i	$-0.554265\pi$
$487$	3.88785	−	1.04175i	0.176175	−	0.0472060i	0.345828	+	0.938298i	$0.387598\pi$
$488$	−4.54165	+	9.73959i	−0.205591	+	0.440891i
$489$		0			0
$490$	−0.447330	+	4.57970i	−0.0202083	+	0.206890i
$491$	10.9927	+	4.00100i	0.496091	+	0.180563i	0.577935	−	0.816083i	$-0.303859\pi$
$491$	10.9927	+	4.00100i	0.496091	+	0.180563i	−0.0818437	+	0.996645i	$0.526081\pi$
$492$		0			0
$493$	−11.9049	+	11.9049i	−0.536171	+	0.536171i
$494$	2.64218	+	1.38770i	0.118877	+	0.0624355i
$495$		0			0
$496$	−4.66307	−	5.55723i	−0.209378	−	0.249527i
$497$	2.20802	+	4.73511i	0.0990432	+	0.212399i
$498$		0			0
$499$	−25.5639	+	4.50760i	−1.14440	+	0.201788i	−0.713527	−	0.700627i	$-0.752904\pi$
$499$	−25.5639	+	4.50760i	−1.14440	+	0.201788i	−0.430868	+	0.902415i	$0.641792\pi$
$500$	−20.9161	−	4.34534i	−0.935398	−	0.194330i
$501$		0			0
$502$	0.0692736	−	0.258533i	0.00309183	−	0.0115389i
$503$	2.84355	+	32.5020i	0.126788	+	1.44919i	0.747035	+	0.664784i	$0.231477\pi$
$503$	2.84355	+	32.5020i	0.126788	+	1.44919i	−0.620248	+	0.784406i	$0.712968\pi$
$504$		0			0
$505$	4.40467	−	23.5845i	0.196005	−	1.04950i
$506$	−3.93940	−	2.27441i	−0.175128	−	0.101110i
$507$		0			0
$508$	10.4796	+	7.33786i	0.464955	+	0.325565i
$509$	1.27621	−	7.23775i	0.0565671	−	0.320808i	−0.943373	−	0.331733i	$-0.892367\pi$
$509$	1.27621	−	7.23775i	0.0565671	−	0.320808i	0.999940	+	0.0109254i	$0.00347774\pi$
$510$		0			0
$511$	1.41863	−	1.19037i	0.0627565	−	0.0526590i
$512$	14.0224	+	14.0224i	0.619710	+	0.619710i
$513$		0			0
$514$			0.643793i			0.0283965i
$515$	17.1395	−	16.7966i	0.755255	−	0.740149i
$516$		0			0
$517$	5.86445	+	8.37530i	0.257918	+	0.368345i
$518$	0.347063	−	0.495658i	0.0152491	−	0.0217780i
$519$		0			0
$520$	1.99083	+	5.64659i	0.0873036	+	0.247619i
$521$	25.6025	−	14.7816i	1.12166	−	0.647593i	0.179839	−	0.983696i	$-0.442442\pi$
$521$	25.6025	−	14.7816i	1.12166	−	0.647593i	0.941825	+	0.336103i	$0.109109\pi$
$522$		0			0
$523$	−36.7539	+	3.21555i	−1.60714	+	0.140606i	−0.855082	−	0.518494i	$-0.826493\pi$
$523$	−36.7539	+	3.21555i	−1.60714	+	0.140606i	−0.752055	+	0.659100i	$0.770937\pi$
$524$	12.1604	−	7.02082i	0.531230	−	0.306706i
$525$		0			0
$526$	−3.01099	−	8.27262i	−0.131285	−	0.360703i
$527$	−3.28486	+	4.69127i	−0.143091	+	0.204355i
$528$		0			0
$529$	17.4379	−	47.9102i	0.758169	−	2.08305i
$530$	1.42282	+	0.0143729i	0.0618032	+	0.000624317i
$531$		0			0
$532$	−2.76540	+	0.353818i	−0.119895	+	0.0153400i
$533$	−9.86873	−	9.86873i	−0.427462	−	0.427462i
$534$		0			0
$535$	−1.32265	+	4.74399i	−0.0571831	+	0.205100i
$536$	2.22947	−	12.6439i	0.0962983	−	0.546135i
$537$		0			0
$538$	−1.69863	−	0.792084i	−0.0732332	−	0.0341492i
$539$	−10.5590	−	6.09627i	−0.454810	−	0.262585i
$540$		0			0
$541$	30.1856	+	25.3287i	1.29778	+	1.08897i	0.990524	+	0.137341i	$0.0438556\pi$
$541$	30.1856	+	25.3287i	1.29778	+	1.08897i	0.307257	+	0.951627i	$0.400589\pi$
$542$	−0.156844	−	1.79274i	−0.00673703	−	0.0770046i
$543$		0			0
$544$	4.62478	−	8.01036i	0.198286	−	0.343441i
$545$	−18.2362	−	6.84683i	−0.781154	−	0.293286i
$546$		0			0
$547$	3.33017	−	2.33181i	0.142388	−	0.0997010i	−0.500212	−	0.865903i	$-0.666745\pi$
$547$	3.33017	−	2.33181i	0.142388	−	0.0997010i	0.642600	+	0.766202i	$0.277856\pi$
$548$	4.24891	+	9.11181i	0.181504	+	0.389237i
$549$		0			0
$550$	−1.56011	+	2.13494i	−0.0665233	+	0.0910341i
$551$	−16.3745	+	21.1793i	−0.697577	+	0.902269i
$552$		0			0
$553$	0.436704	−	4.99155i	0.0185705	−	0.212262i
$554$	−6.34589	−	2.30972i	−0.269611	−	0.0981304i
$555$		0			0
$556$	−6.16509	−	34.9640i	−0.261458	−	1.48280i
$557$	−0.133737	+	0.286800i	−0.00566663	+	0.0121521i	−0.909121	−	0.416533i	$-0.863245\pi$
$557$	−0.133737	+	0.286800i	−0.00566663	+	0.0121521i	0.903454	+	0.428685i	$0.141023\pi$
$558$		0			0
$559$	6.12355	+	10.6063i	0.258999	+	0.448599i
$560$	−2.11389	−	1.51221i	−0.0893280	−	0.0639025i
$561$		0			0
$562$	3.47606	+	0.931407i	0.146629	+	0.0392890i
$563$	12.0964	+	45.1444i	0.509803	+	1.90261i	0.422330	+	0.906442i	$0.361212\pi$
$563$	12.0964	+	45.1444i	0.509803	+	1.90261i	0.0874723	+	0.996167i	$0.472121\pi$
$564$		0			0
$565$	6.53707	+	25.4211i	0.275017	+	1.06947i
$566$	−3.43098	−	0.604975i	−0.144215	−	0.0254290i
$567$		0			0
$568$	−18.1667	−	1.58938i	−0.762258	−	0.0666889i
$569$	25.5911			1.07283			0.536417	−	0.843953i	$-0.319777\pi$
$569$	25.5911			1.07283			0.536417	+	0.843953i	$0.319777\pi$
$570$		0			0
$571$	−2.95798			−0.123788			−0.0618938	−	0.998083i	$-0.519714\pi$
$571$	−2.95798			−0.123788			−0.0618938	+	0.998083i	$0.519714\pi$
$572$	−7.72167	−	0.675558i	−0.322859	−	0.0282465i
$573$		0			0
$574$	−0.599785	−	0.105758i	−0.0250345	−	0.00441426i
$575$	−38.6027	−	18.9594i	−1.60984	−	0.790660i
$576$		0			0
$577$	−1.90612	−	7.11374i	−0.0793528	−	0.296149i	0.914832	−	0.403834i	$-0.132323\pi$
$577$	−1.90612	−	7.11374i	−0.0793528	−	0.296149i	−0.994185	+	0.107685i	$0.965656\pi$
$578$	2.73730	+	0.733456i	0.113857	+	0.0305078i
$579$		0			0
$580$	−25.8867	+	4.29538i	−1.07489	+	0.178356i
$581$	0.556090	+	0.963176i	0.0230705	+	0.0399593i
$582$		0			0
$583$	−1.59336	+	3.41698i	−0.0659904	+	0.141517i
$584$	1.12244	+	6.36567i	0.0464469	+	0.263413i
$585$		0			0
$586$	−3.53536	−	1.28677i	−0.146045	−	0.0531559i
$587$	−0.255196	+	2.91690i	−0.0105331	+	0.120394i	−0.999641	−	0.0267997i	$-0.991468\pi$
$587$	−0.255196	+	2.91690i	−0.0105331	+	0.120394i	0.989108	+	0.147193i	$0.0470239\pi$
$588$		0			0
$589$	−4.23432	+	8.06213i	−0.174472	+	0.332194i
$590$	0.0853031	+	1.10327i	0.00351187	+	0.0454208i
$591$		0			0
$592$	−8.87911	−	19.0413i	−0.364929	−	0.782593i
$593$	−2.83613	+	1.98588i	−0.116466	+	0.0815502i	−0.630358	−	0.776304i	$-0.717092\pi$
$593$	−2.83613	+	1.98588i	−0.116466	+	0.0815502i	0.513892	+	0.857855i	$0.328203\pi$
$594$		0			0
$595$	−0.721211	+	1.92091i	−0.0295668	+	0.0787498i
$596$	18.7479	−	32.4723i	0.767943	−	1.33012i
$597$		0			0
$598$	0.513277	+	5.86679i	0.0209895	+	0.239911i
$599$	12.9017	+	10.8258i	0.527151	+	0.442332i	0.867116	−	0.498106i	$-0.165971\pi$
$599$	12.9017	+	10.8258i	0.527151	+	0.442332i	−0.339965	+	0.940438i	$0.610415\pi$
$600$		0			0
$601$	3.51772	+	2.03096i	0.143491	+	0.0828445i	0.570027	−	0.821626i	$-0.306933\pi$
$601$	3.51772	+	2.03096i	0.143491	+	0.0828445i	−0.426536	+	0.904471i	$0.640266\pi$
$602$	0.484370	+	0.225865i	0.0197414	+	0.00920559i
$603$		0			0
$604$	−0.425202	+	2.41144i	−0.0173012	+	0.0981201i
$605$	8.64086	+	15.3218i	0.351301	+	0.622919i
$606$		0			0
$607$	24.9122	+	24.9122i	1.01116	+	1.01116i	0.999937	+	0.0112183i	$0.00357098\pi$
$607$	24.9122	+	24.9122i	1.01116	+	1.01116i	0.0112183	+	0.999937i	$0.496429\pi$
$608$	5.67790	−	13.5675i	0.230269	−	0.550236i
$609$		0			0
$610$	4.30075	+	4.38853i	0.174132	+	0.177686i
$611$	4.52735	−	12.4388i	0.183157	−	0.503220i
$612$		0			0
$613$	5.19022	−	7.41240i	0.209631	−	0.299384i	−0.700543	−	0.713610i	$-0.747059\pi$
$613$	5.19022	−	7.41240i	0.209631	−	0.299384i	0.910174	+	0.414226i	$0.135948\pi$
$614$	−1.68724	−	4.63566i	−0.0680916	−	0.187080i
$615$		0			0
$616$	−0.599546	+	0.346148i	−0.0241564	+	0.0139467i
$617$	42.1238	−	3.68535i	1.69584	−	0.148367i	0.802171	−	0.597094i	$-0.203678\pi$
$617$	42.1238	−	3.68535i	1.69584	−	0.148367i	0.893669	+	0.448727i	$0.148122\pi$
$618$		0			0
$619$	15.6339	−	9.02621i	0.628378	−	0.362794i	−0.151746	−	0.988420i	$-0.548489\pi$
$619$	15.6339	−	9.02621i	0.628378	−	0.362794i	0.780124	+	0.625625i	$0.215156\pi$
$620$	−8.41815	+	2.96801i	−0.338081	+	0.119198i
$621$		0			0
$622$	−0.913606	+	1.30476i	−0.0366323	+	0.0523163i
$623$	−1.99292	−	2.84618i	−0.0798446	−	0.114030i
$624$		0			0
$625$	−13.3644	+	21.1280i	−0.534574	+	0.845121i
$626$			5.87229i			0.234704i
$627$		0			0
$628$	21.9866	+	21.9866i	0.877363	+	0.877363i
$629$	−12.7056	+	10.6613i	−0.506607	+	0.425094i
$630$		0			0
$631$	−2.44081	+	13.8425i	−0.0971672	+	0.551062i	0.896895	+	0.442244i	$0.145818\pi$
$631$	−2.44081	+	13.8425i	−0.0971672	+	0.551062i	−0.994062	+	0.108818i	$0.965293\pi$
$632$	14.3263	+	10.0314i	0.569869	+	0.399026i
$633$		0			0
$634$	4.72519	+	2.72809i	0.187661	+	0.108346i
$635$	12.3499	−	8.46290i	0.490092	−	0.335840i
$636$		0			0
$637$	1.37577	+	15.7252i	0.0545101	+	0.623053i
$638$	−0.840643	+	3.13732i	−0.0332814	+	0.124208i
$639$		0			0
$640$	17.3509	−	7.87848i	0.685855	−	0.311424i
$641$	−23.1158	+	4.07593i	−0.913018	+	0.160990i	−0.610374	−	0.792114i	$-0.708981\pi$
$641$	−23.1158	+	4.07593i	−0.913018	+	0.160990i	−0.302645	+	0.953103i	$0.597870\pi$
$642$		0			0
$643$	4.67679	+	10.0294i	0.184435	+	0.395521i	0.976686	−	0.214674i	$-0.0688688\pi$
$643$	4.67679	+	10.0294i	0.184435	+	0.395521i	−0.792251	+	0.610195i	$0.791091\pi$
$644$	−3.53628	−	4.21437i	−0.139349	−	0.166070i
$645$		0			0
$646$	−3.53762	−	0.478866i	−0.139186	−	0.0188407i
$647$	10.3878	−	10.3878i	0.408386	−	0.408386i	−0.472790	−	0.881175i	$-0.656753\pi$
$647$	10.3878	−	10.3878i	0.408386	−	0.408386i	0.881175	+	0.472790i	$0.156753\pi$
$648$		0			0
$649$	−2.75522	−	1.00282i	−0.108152	−	0.0393640i
$650$	3.42267	+	0.0691567i	0.134248	+	0.00271255i
$651$		0			0
$652$	−8.23134	+	17.6522i	−0.322364	+	0.691312i
$653$	19.7746	−	5.29859i	0.773841	−	0.207350i	0.149773	−	0.988720i	$-0.452146\pi$
$653$	19.7746	−	5.29859i	0.773841	−	0.207350i	0.624067	+	0.781370i	$0.285479\pi$
$654$		0			0
$655$	−2.68984	−	16.2107i	−0.105101	−	0.633406i
$656$	−13.5930	+	16.1995i	−0.530717	+	0.632484i
$657$		0			0
$658$	−0.149505	−	0.557961i	−0.00582832	−	0.0217516i
$659$	−1.78757	+	0.650624i	−0.0696340	+	0.0253447i	−0.376602	−	0.926375i	$-0.622908\pi$
$659$	−1.78757	+	0.650624i	−0.0696340	+	0.0253447i	0.306968	+	0.951720i	$0.400685\pi$
$660$		0			0
$661$	14.1497	+	2.49497i	0.550360	+	0.0970433i	0.441911	−	0.897059i	$-0.354301\pi$
$661$	14.1497	+	2.49497i	0.550360	+	0.0970433i	0.108448	+	0.994102i	$0.465412\pi$
$662$	−3.28713	+	1.53281i	−0.127758	+	0.0595745i
$663$		0			0
$664$	−3.88198			−0.150650
$665$	−0.749883	+	3.17528i	−0.0290792	+	0.123132i
$666$		0			0
$667$	−52.6264	−	4.60422i	−2.03770	−	0.178276i
$668$	4.50930	−	2.10272i	0.174470	−	0.0813566i
$669$		0			0
$670$	−6.32011	−	3.73454i	−0.244167	−	0.144278i
$671$	−15.2993	+	5.56850i	−0.590624	+	0.214969i
$672$		0			0
$673$	13.2264	+	3.54401i	0.509842	+	0.136612i	0.504564	−	0.863374i	$-0.331653\pi$
$673$	13.2264	+	3.54401i	0.509842	+	0.136612i	0.00527799	+	0.999986i	$0.498320\pi$
$674$	3.99630	−	4.76261i	0.153932	−	0.183449i
$675$		0			0
$676$	−7.40225	−	12.8211i	−0.284702	−	0.493118i
$677$	30.7746	−	8.24603i	1.18276	−	0.316921i	0.386742	−	0.922188i	$-0.373600\pi$
$677$	30.7746	−	8.24603i	1.18276	−	0.316921i	0.796023	+	0.605267i	$0.206934\pi$
$678$		0			0
$679$	0.348672	+	1.97741i	0.0133808	+	0.0758862i
$680$	−4.54786	−	5.53247i	−0.174402	−	0.212160i
$681$		0			0
$682$	−0.0962933	+	1.10064i	−0.00368726	+	0.0421456i
$683$	1.98056	−	1.98056i	0.0757839	−	0.0757839i	−0.668199	−	0.743983i	$-0.732934\pi$
$683$	1.98056	−	1.98056i	0.0757839	−	0.0757839i	0.743983	+	0.668199i	$0.232934\pi$
$684$		0			0
$685$	11.7305	−	0.906989i	0.448201	−	0.0346543i
$686$	0.892759	+	1.06395i	0.0340857	+	0.0406218i
$687$		0			0
$688$	15.2009	−	10.6438i	0.579529	−	0.405791i
$689$	4.80701	−	0.847605i	0.183132	−	0.0322912i
$690$		0			0
$691$	9.82610	−	17.0193i	0.373802	−	0.647445i	−0.616345	−	0.787476i	$-0.711387\pi$
$691$	9.82610	−	17.0193i	0.373802	−	0.647445i	0.990147	+	0.140032i	$0.0447205\pi$
$692$	−9.05546	+	33.7954i	−0.344237	+	1.28471i
$693$		0			0
$694$	2.06759	+	1.73491i	0.0784845	+	0.0658563i
$695$	−40.8420	−	7.62771i	−1.54923	−	0.289335i
$696$		0			0
$697$	15.1302	+	7.05533i	0.573097	+	0.267240i
$698$	0.332180	+	0.232595i	0.0125732	+	0.00880385i
$699$		0			0
$700$	−2.65616	+	1.78100i	−0.100393	+	0.0673154i
$701$	−25.1461	+	21.1001i	−0.949755	+	0.796939i	−0.979256	−	0.202625i	$-0.935053\pi$
$701$	−25.1461	+	21.1001i	−0.949755	+	0.796939i	0.0295010	+	0.999565i	$0.490608\pi$
$702$		0			0
$703$	−17.8884	+	19.3794i	−0.674673	+	0.730908i
$704$			10.5088i			0.396066i
$705$		0			0
$706$	2.56949	−	7.05962i	0.0967042	−	0.265692i
$707$	−2.06007	−	2.94209i	−0.0774770	−	0.110649i
$708$		0			0
$709$	−6.40035	−	17.5848i	−0.240370	−	0.660412i	−0.999950	−	0.00999760i	$-0.996818\pi$
$709$	−6.40035	−	17.5848i	−0.240370	−	0.660412i	0.759580	−	0.650414i	$-0.225405\pi$
$710$	−4.50186	+	9.40504i	−0.168952	+	0.352965i
$711$		0			0
$712$	12.0815	−	1.05699i	0.452772	−	0.0396125i
$713$	−17.9015	+	1.56617i	−0.670415	+	0.0586537i
$714$		0			0
$715$	−3.91637	+	8.18187i	−0.146464	+	0.305985i
$716$	−5.07695	−	13.9488i	−0.189735	−	0.521291i
$717$		0			0
$718$	−0.354194	−	0.505842i	−0.0132184	−	0.0188778i
$719$	−2.67044	+	7.33697i	−0.0995905	+	0.273623i	−0.979475	−	0.201564i	$-0.935397\pi$
$719$	−2.67044	+	7.33697i	−0.0995905	+	0.273623i	0.879885	+	0.475187i	$0.157620\pi$
$720$		0			0
$721$		−	3.59244i		−	0.133789i
$722$	−5.67630	−	0.0413976i	−0.211250	−	0.00154066i
$723$		0			0
$724$	28.0282	−	23.5185i	1.04166	−	0.874057i
$725$	−5.94231	+	30.1280i	−0.220692	+	1.11893i
$726$		0			0
$727$	24.5663	+	17.2015i	0.911115	+	0.637970i	0.932253	−	0.361807i	$-0.117840\pi$
$727$	24.5663	+	17.2015i	0.911115	+	0.637970i	−0.0211378	+	0.999777i	$0.506729\pi$
$728$	0.812315	+	0.378788i	0.0301064	+	0.0140388i
$729$		0			0
$730$	3.63307	+	0.678517i	0.134466	+	0.0251130i
$731$	−11.2223	−	9.41660i	−0.415070	−	0.348285i
$732$		0			0
$733$	−4.87884	+	18.2081i	−0.180204	+	0.672531i	0.815402	+	0.578895i	$0.196516\pi$
$733$	−4.87884	+	18.2081i	−0.180204	+	0.672531i	−0.995606	+	0.0936365i	$0.970151\pi$
$734$	1.06000	−	1.83597i	0.0391253	−	0.0677670i
$735$		0			0
$736$	28.5819	−	5.03976i	1.05354	−	0.185768i
$737$	15.9337	−	11.1569i	0.586926	−	0.410970i
$738$		0			0
$739$	19.7272	+	23.5100i	0.725678	+	0.864829i	0.995169	−	0.0981738i	$-0.0313001\pi$
$739$	19.7272	+	23.5100i	0.725678	+	0.864829i	−0.269492	+	0.963003i	$0.586856\pi$
$740$	−25.7740	+	1.99281i	−0.947471	+	0.0732572i
$741$		0			0
$742$	0.150618	−	0.150618i	0.00552935	−	0.00552935i
$743$	−1.19259	+	13.6313i	−0.0437517	+	0.500084i	0.942428	+	0.334408i	$0.108536\pi$
$743$	−1.19259	+	13.6313i	−0.0437517	+	0.500084i	−0.986180	+	0.165676i	$0.947019\pi$
$744$		0			0
$745$	−27.8644	−	33.8971i	−1.02087	−	1.24189i
$746$	−1.23874	−	7.02522i	−0.0453533	−	0.257212i
$747$		0			0
$748$	8.95578	−	2.39969i	0.327456	−	0.0877415i
$749$	0.368629	+	0.638484i	0.0134694	+	0.0233297i
$750$		0			0
$751$	−14.7692	+	17.6012i	−0.538934	+	0.642277i	−0.964948	−	0.262440i	$-0.915473\pi$
$751$	−14.7692	+	17.6012i	−0.538934	+	0.642277i	0.426014	+	0.904717i	$0.359917\pi$
$752$	−19.3735	−	5.19111i	−0.706478	−	0.189300i
$753$		0			0
$754$	3.95146	−	1.43822i	0.143904	−	0.0523767i
$755$	2.46704	+	1.45777i	0.0897848	+	0.0530537i
$756$		0			0
$757$	−2.99560	+	1.39687i	−0.108877	+	0.0507702i	−0.476294	−	0.879286i	$-0.658020\pi$
$757$	−2.99560	+	1.39687i	−0.108877	+	0.0507702i	0.367417	+	0.930056i	$0.380242\pi$
$758$	4.82371	+	0.422020i	0.175205	+	0.0153284i
$759$		0			0
$760$	−8.28950	−	7.80827i	−0.300692	−	0.283236i
$761$	39.1861			1.42050			0.710248	−	0.703952i	$-0.248583\pi$
$761$	39.1861			1.42050			0.710248	+	0.703952i	$0.248583\pi$
$762$		0			0
$763$	−2.64282	+	1.23237i	−0.0956764	+	0.0446146i
$764$	29.8084	+	5.25602i	1.07843	+	0.190156i
$765$		0			0
$766$	−1.76587	+	0.642725i	−0.0638036	+	0.0232226i
$767$	0.982478	+	3.66666i	0.0354752	+	0.132395i
$768$		0			0
$769$	−22.2353	+	26.4990i	−0.801825	+	0.955578i	−0.999696	−	0.0246499i	$-0.992153\pi$
$769$	−22.2353	+	26.4990i	−0.801825	+	0.955578i	0.197871	+	0.980228i	$0.436597\pi$
$770$	0.0647954	+	0.390499i	0.00233506	+	0.0140726i
$771$		0			0
$772$	−50.0815	+	13.4193i	−1.80247	+	0.482972i
$773$	7.07654	−	15.1757i	0.254526	−	0.545832i	−0.736977	−	0.675918i	$-0.763748\pi$
$773$	7.07654	−	15.1757i	0.254526	−	0.545832i	0.991503	+	0.130086i	$0.0415253\pi$
$774$		0			0
$775$	−0.211019	+	10.4437i	−0.00758004	+	0.375148i
$776$	−6.58582	−	2.39704i	−0.236417	−	0.0860488i
$777$		0			0
$778$	4.43724	−	4.43724i	0.159083	−	0.159083i
$779$	25.2877	+	8.07467i	0.906026	+	0.289305i
$780$		0			0
$781$	−17.7591	−	21.1645i	−0.635470	−	0.757324i
$782$	−2.97713	−	6.38447i	−0.106462	−	0.228308i
$783$		0			0
$784$	23.5545	−	4.15329i	0.841232	−	0.148332i
$785$	33.1323	−	15.0443i	1.18254	−	0.536953i
$786$		0			0
$787$	−11.9180	+	44.4784i	−0.424830	+	1.58549i	0.339465	+	0.940619i	$0.389754\pi$
$787$	−11.9180	+	44.4784i	−0.424830	+	1.58549i	−0.764295	+	0.644867i	$0.776913\pi$
$788$	2.40858	+	27.5301i	0.0858019	+	0.980721i
$789$		0			0
$790$	8.24894	−	5.65266i	0.293484	−	0.201113i
$791$	3.40290	+	1.96467i	0.120993	+	0.0698555i
$792$		0			0
$793$	17.2666	+	12.0902i	0.613156	+	0.429336i
$794$	0.144482	−	0.819399i	0.00512748	−	0.0290794i
$795$		0			0
$796$	−4.66680	+	3.91591i	−0.165410	+	0.138796i
$797$	14.9095	+	14.9095i	0.528121	+	0.528121i	0.920012	−	0.391891i	$-0.128179\pi$
$797$	14.9095	+	14.9095i	0.528121	+	0.528121i	−0.391891	+	0.920012i	$0.628179\pi$
$798$		0			0
$799$			15.8338i			0.560160i
$800$	−1.13058	−	16.8330i	−0.0399719	−	0.595135i
$801$		0			0
$802$	−3.85484	−	5.50528i	−0.136119	−	0.194398i
$803$	−5.61702	+	8.02193i	−0.198220	+	0.283088i
$804$		0			0
$805$	−6.07183	+	2.14076i	−0.214004	+	0.0754518i
$806$	1.23876	−	0.715198i	0.0436335	−	0.0251918i
$807$		0			0
$808$	12.4886	−	1.09261i	0.439347	−	0.0384379i
$809$	0.0883067	−	0.0509839i	0.00310470	−	0.00179250i	−0.498447	−	0.866920i	$-0.666096\pi$
$809$	0.0883067	−	0.0509839i	0.00310470	−	0.00179250i	0.501552	+	0.865128i	$0.332763\pi$
$810$		0			0
$811$	13.8775	+	38.1282i	0.487306	+	1.33886i	0.903111	+	0.429407i	$0.141278\pi$
$811$	13.8775	+	38.1282i	0.487306	+	1.33886i	−0.415805	+	0.909454i	$0.636500\pi$
$812$	−2.25313	+	3.21780i	−0.0790694	+	0.112923i
$813$		0			0
$814$	−1.09438	+	3.00679i	−0.0383580	+	0.105388i
$815$	15.9536	+	16.2792i	0.558830	+	0.570235i
$816$		0			0
$817$	−19.6004	−	12.5876i	−0.685733	−	0.440383i
$818$	−5.14334	−	5.14334i	−0.179833	−	0.179833i
$819$		0			0
$820$	12.7816	+	22.6640i	0.446352	+	0.791461i
$821$	1.91779	−	10.8763i	0.0669314	−	0.379587i	−0.932880	−	0.360186i	$-0.882713\pi$
$821$	1.91779	−	10.8763i	0.0669314	−	0.379587i	0.999812	−	0.0194006i	$-0.00617579\pi$
$822$		0			0
$823$	−41.8739	−	19.5261i	−1.45963	−	0.680638i	−0.479238	−	0.877685i	$-0.659087\pi$
$823$	−41.8739	−	19.5261i	−1.45963	−	0.680638i	−0.980394	+	0.197047i	$0.936865\pi$
$824$	10.8592	+	6.26956i	0.378298	+	0.218410i
$825$		0			0
$826$	0.126896	+	0.106479i	0.00441528	+	0.00370486i
$827$	−1.94055	−	22.1806i	−0.0674796	−	0.771295i	−0.952260	−	0.305287i	$-0.901247\pi$
$827$	−1.94055	−	22.1806i	−0.0674796	−	0.771295i	0.884781	−	0.466008i	$-0.154308\pi$
$828$		0			0
$829$	−13.8403	+	23.9721i	−0.480694	+	0.832587i	−0.999755	−	0.0221506i	$-0.992949\pi$
$829$	−13.8403	+	23.9721i	−0.480694	+	0.832587i	0.519060	+	0.854738i	$0.326282\pi$
$830$	−0.780185	+	2.07799i	−0.0270806	+	0.0721280i
$831$		0			0
$832$	11.1449	−	7.80373i	0.386379	−	0.270545i
$833$	−7.97980	−	17.1127i	−0.276484	−	0.592921i
$834$		0			0
$835$	−0.448855	−	5.80526i	−0.0155333	−	0.200899i
$836$	13.6411	−	5.59216i	0.471789	−	0.193409i
$837$		0			0
$838$	0.0809287	−	0.925019i	0.00279564	−	0.0319543i
$839$	35.1412	+	12.7903i	1.21321	+	0.441572i	0.867815	−	0.496887i	$-0.165524\pi$
$839$	35.1412	+	12.7903i	1.21321	+	0.441572i	0.345393	+	0.938458i	$0.387746\pi$
$840$		0			0
$841$	1.51428	+	8.58788i	0.0522164	+	0.296134i
$842$	−2.71638	+	5.82530i	−0.0936127	+	0.200753i
$843$		0			0
$844$	−0.535075	−	0.926777i	−0.0184180	−	0.0319010i
$845$	−17.0915	+	2.83598i	−0.587964	+	0.0975607i
$846$		0			0
$847$	2.54354	+	0.681540i	0.0873972	+	0.0234180i
$848$	−1.91422	−	7.14395i	−0.0657344	−	0.245324i
$849$		0			0
$850$	−3.87549	+	1.32253i	−0.132928	+	0.0453624i
$851$	−51.2522	−	9.03714i	−1.75690	−	0.309789i
$852$		0			0
$853$	−18.2820	−	1.59947i	−0.625964	−	0.0547648i	−0.230240	−	0.973134i	$-0.573951\pi$
$853$	−18.2820	−	1.59947i	−0.625964	−	0.0547648i	−0.395725	+	0.918369i	$0.629507\pi$
$854$	0.919837			0.0314762
$855$		0			0
$856$	−2.57334			−0.0879549
$857$	−48.7757	−	4.26732i	−1.66615	−	0.145769i	−0.785283	−	0.619138i	$-0.787482\pi$
$857$	−48.7757	−	4.26732i	−1.66615	−	0.145769i	−0.880864	+	0.473369i	$0.843038\pi$
$858$		0			0
$859$	2.01743	+	0.355727i	0.0688338	+	0.0121373i	0.207959	−	0.978138i	$-0.433318\pi$
$859$	2.01743	+	0.355727i	0.0688338	+	0.0121373i	−0.139125	+	0.990275i	$0.544429\pi$
$860$	−5.68649	−	22.1134i	−0.193908	−	0.754061i
$861$		0			0
$862$	1.43278	+	5.34719i	0.0488005	+	0.182126i
$863$	−33.3761	−	8.94309i	−1.13613	−	0.304426i	−0.358738	−	0.933438i	$-0.616793\pi$
$863$	−33.3761	−	8.94309i	−1.13613	−	0.304426i	−0.777396	+	0.629012i	$0.783460\pi$
$864$		0			0
$865$	33.3010	+	23.8225i	1.13227	+	0.809989i
$866$	−1.36949	−	2.37203i	−0.0465372	−	0.0806048i
$867$		0			0
$868$	−0.564713	+	1.21103i	−0.0191676	+	0.0411051i
$869$	4.60109	+	26.0941i	0.156081	+	0.885181i
$870$		0			0
$871$	−23.6644	−	8.61312i	−0.801836	−	0.291844i
$872$	0.887084	−	10.1394i	0.0300405	−	0.343364i
$873$		0			0
$874$	−5.98402	−	9.46905i	−0.202412	−	0.320295i
$875$	0.858651	+	3.64265i	0.0290277	+	0.123144i
$876$		0			0
$877$	17.7162	+	37.9925i	0.598234	+	1.28292i	0.939371	+	0.342903i	$0.111410\pi$
$877$	17.7162	+	37.9925i	0.598234	+	1.28292i	−0.341137	+	0.940014i	$0.610812\pi$
$878$	−4.33181	+	3.03316i	−0.146191	+	0.102364i
$879$		0			0
$880$	12.8672	+	4.83103i	0.433754	+	0.162854i
$881$	−2.70678	+	4.68828i	−0.0911936	+	0.157952i	−0.908014	−	0.418941i	$-0.862402\pi$
$881$	−2.70678	+	4.68828i	−0.0911936	+	0.157952i	0.816820	+	0.576893i	$0.195735\pi$
$882$		0			0
$883$	2.66819	+	30.4975i	0.0897917	+	1.02632i	0.898751	+	0.438459i	$0.144476\pi$
$883$	2.66819	+	30.4975i	0.0897917	+	1.02632i	−0.808959	+	0.587864i	$0.799969\pi$
$884$	−9.19539	−	7.71585i	−0.309275	−	0.259512i
$885$		0			0
$886$	1.23175	+	0.711150i	0.0413814	+	0.0238916i
$887$	33.6111	+	15.6731i	1.12855	+	0.526252i	0.894988	−	0.446090i	$-0.147184\pi$
$887$	33.6111	+	15.6731i	1.12855	+	0.526252i	0.233562	+	0.972342i	$0.424962\pi$
$888$		0			0
$889$	0.389181	−	2.20715i	0.0130527	−	0.0740256i
$890$	1.86229	−	6.67953i	0.0624241	−	0.223898i
$891$		0			0
$892$	−30.4145	−	30.4145i	−1.01835	−	1.01835i
$893$	3.19525	+	24.9737i	0.106925	+	0.835713i
$894$		0			0
$895$	−17.3705	−	0.175471i	−0.580631	−	0.00586536i
$896$	0.975662	−	2.68061i	0.0325946	−	0.0895529i
$897$		0			0
$898$	−0.567547	+	0.810541i	−0.0189393	+	0.0270481i
$899$	4.38846	+	12.0572i	0.146363	+	0.402130i
$900$		0			0
$901$	−5.05646	+	2.91935i	−0.168455	+	0.0972577i
$902$	3.20839	−	0.280698i	0.106828	−	0.00934622i
$903$		0			0
$904$	−11.8776	+	6.85751i	−0.395041	+	0.228077i
$905$	−14.2374	−	40.3814i	−0.473266	−	1.34232i
$906$		0			0
$907$	−0.162899	+	0.232644i	−0.00540896	+	0.00772480i	−0.821847	−	0.569708i	$-0.807056\pi$
$907$	−0.162899	+	0.232644i	−0.00540896	+	0.00772480i	0.816438	+	0.577432i	$0.195945\pi$
$908$	17.8358	+	25.4721i	0.591901	+	0.845323i
$909$		0			0
$910$	0.366018	−	0.358697i	0.0121334	−	0.0118907i
$911$			35.0022i			1.15968i	0.814732	+	0.579838i	$0.196884\pi$
$911$			35.0022i			1.15968i	−0.814732	+	0.579838i	$0.803116\pi$
$912$		0			0
$913$	−4.15872	−	4.15872i	−0.137633	−	0.137633i
$914$	6.55749	−	5.50239i	0.216903	−	0.182003i
$915$		0			0
$916$	−3.81840	+	21.6552i	−0.126163	+	0.715508i
$917$	−2.01505	−	1.41095i	−0.0665427	−	0.0465937i
$918$		0			0
$919$	10.2856	+	5.93841i	0.339291	+	0.195890i	0.659959	−	0.751302i	$-0.270574\pi$
$919$	10.2856	+	5.93841i	0.339291	+	0.195890i	−0.320667	+	0.947192i	$0.603907\pi$
$920$	4.12555	−	22.0899i	0.136015	−	0.728284i
$921$		0			0
$922$	−0.416950	−	4.76576i	−0.0137315	−	0.156952i
$923$	−9.25777	+	34.5505i	−0.304723	+	1.13724i
$924$		0			0
$925$	−8.41860	+	29.0574i	−0.276802	+	0.955401i
$926$	8.32375	−	1.46770i	0.273535	−	0.0482317i
$927$		0			0
$928$	−8.75798	−	18.7815i	−0.287495	−	0.616534i
$929$	−34.7475	−	41.4104i	−1.14003	−	1.35863i	−0.924067	−	0.382230i	$-0.875156\pi$
$929$	−34.7475	−	41.4104i	−1.14003	−	1.35863i	−0.215960	−	0.976402i	$-0.569288\pi$
$930$		0			0
$931$	−16.0394	−	25.3805i	−0.525669	−	0.831814i
$932$	23.7813	−	23.7813i	0.778984	−	0.778984i
$933$		0			0
$934$	0.432760	+	0.157512i	0.0141604	+	0.00515395i
$935$	1.05480	−	10.7989i	0.0344958	−	0.353163i
$936$		0			0
$937$	7.52427	−	16.1359i	0.245807	−	0.527135i	−0.744233	−	0.667920i	$-0.767185\pi$
$937$	7.52427	−	16.1359i	0.245807	−	0.527135i	0.990040	+	0.140785i	$0.0449626\pi$
$938$	−1.06150	+	0.284428i	−0.0346592	+	0.00928692i
$939$		0			0
$940$	−14.3585	+	20.0714i	−0.468322	+	0.654658i
$941$	−20.1771	+	24.0461i	−0.657754	+	0.783881i	−0.987062	−	0.160342i	$-0.948740\pi$
$941$	−20.1771	+	24.0461i	−0.657754	+	0.783881i	0.329307	+	0.944223i	$0.393185\pi$
$942$		0			0
$943$	13.5576	+	50.5977i	0.441497	+	1.64769i
$944$	5.40486	−	1.96721i	0.175913	−	0.0640271i
$945$		0			0
$946$	−2.78325	−	0.490762i	−0.0904912	−	0.0159560i
$947$	22.7589	−	10.6127i	0.739565	−	0.344865i	−0.0160582	−	0.999871i	$-0.505112\pi$
$947$	22.7589	−	10.6127i	0.739565	−	0.344865i	0.755624	+	0.655006i	$0.227334\pi$
$948$		0			0
$949$	12.6786			0.411564
$950$	−5.84568	+	2.86802i	−0.189659	+	0.0930507i
$951$		0			0
$952$	−1.06804	−	0.0934410i	−0.0346152	−	0.00302844i
$953$	−1.38466	+	0.645677i	−0.0448535	+	0.0209155i	−0.444916	−	0.895572i	$-0.646766\pi$
$953$	−1.38466	+	0.645677i	−0.0448535	+	0.0209155i	0.400062	+	0.916488i	$0.368989\pi$
$954$		0			0
$955$	18.0198	−	30.4956i	0.583108	−	0.986816i
$956$	−5.70017	+	2.07469i	−0.184357	+	0.0671003i
$957$		0			0
$958$	−4.84033	−	1.29696i	−0.156384	−	0.0419030i
$959$	1.13214	−	1.34923i	0.0365587	−	0.0435689i
$960$		0			0
$961$	−13.3177	−	23.0669i	−0.429603	−	0.744095i
$962$	4.00145	−	1.07218i	0.129012	−	0.0345686i
$963$		0			0
$964$	−2.55740	−	14.5037i	−0.0823682	−	0.467133i
$965$	−5.89856	+	60.3886i	−0.189881	+	1.94398i
$966$		0			0
$967$	1.75903	−	20.1058i	0.0565665	−	0.646558i	−0.913998	−	0.405718i	$-0.867022\pi$
$967$	1.75903	−	20.1058i	0.0565665	−	0.646558i	0.970565	−	0.240840i	$-0.0774229\pi$
$968$	−6.49917	+	6.49917i	−0.208891	+	0.208891i
$969$		0			0
$970$	−2.60671	+	3.04358i	−0.0836963	+	0.0977234i
$971$	1.63397	+	1.94730i	0.0524367	+	0.0624917i	0.791625	−	0.611007i	$-0.209235\pi$
$971$	1.63397	+	1.94730i	0.0524367	+	0.0624917i	−0.739189	+	0.673499i	$0.764791\pi$
$972$		0			0
$973$	−5.09491	+	3.56750i	−0.163335	+	0.114369i
$974$	1.18424	−	0.208814i	0.0379456	−	0.00669083i
$975$		0			0
$976$	15.9692	−	27.6595i	0.511163	−	0.885361i
$977$	−15.0379	+	56.1223i	−0.481106	+	1.79551i	0.115882	+	0.993263i	$0.463030\pi$
$977$	−15.0379	+	56.1223i	−0.481106	+	1.79551i	−0.596989	+	0.802250i	$0.703636\pi$
$978$		0			0
$979$	14.0751	+	11.8104i	0.449842	+	0.377462i
$980$	5.40280	−	28.9289i	0.172586	−	0.924100i
$981$		0			0
$982$	3.16750	+	1.47703i	0.101079	+	0.0471338i
$983$	26.9174	+	18.8478i	0.858531	+	0.601150i	0.917778	−	0.397093i	$-0.129981\pi$
$983$	26.9174	+	18.8478i	0.858531	+	0.601150i	−0.0592470	+	0.998243i	$0.518870\pi$
$984$		0			0
$985$	31.1524	+	8.68546i	0.992598	+	0.276742i
$986$	−3.85318	+	3.23320i	−0.122710	+	0.102966i
$987$		0			0
$988$	−16.0604	−	10.3141i	−0.510949	−	0.328136i
$989$		−	45.9668i		−	1.46166i
$990$		0			0
$991$	6.36348	−	17.4835i	0.202143	−	0.555383i	−0.796653	−	0.604436i	$-0.793398\pi$
$991$	6.36348	−	17.4835i	0.202143	−	0.555383i	0.998796	+	0.0490538i	$0.0156206\pi$
$992$	−4.04326	−	5.77437i	−0.128373	−	0.183336i
$993$		0			0
$994$	0.533863	+	1.46678i	0.0169331	+	0.0465233i
$995$	2.37057	+	6.72365i	0.0751522	+	0.213154i
$996$		0			0
$997$	51.6752	−	4.52099i	1.63657	−	0.143181i	0.768577	−	0.639758i	$-0.220965\pi$
$997$	51.6752	−	4.52099i	1.63657	−	0.143181i	0.867993	+	0.496577i	$0.165410\pi$
$998$	−7.72579	+	0.675919i	−0.244555	+	0.0213958i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.dl.a.298.4		96
3.2	odd	2		95.2.r.a.13.5	yes	96
5.2	odd	4	inner	855.2.dl.a.127.5		96
15.2	even	4		95.2.r.a.32.4	yes	96
15.8	even	4		475.2.bb.b.32.5		96
15.14	odd	2		475.2.bb.b.393.4		96
19.3	odd	18	inner	855.2.dl.a.478.5		96
57.41	even	18		95.2.r.a.3.4	✓	96
95.22	even	36	inner	855.2.dl.a.307.4		96
285.98	odd	36		475.2.bb.b.307.4		96
285.212	odd	36		95.2.r.a.22.5	yes	96
285.269	even	18		475.2.bb.b.193.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.3.4	✓	96	57.41	even	18
95.2.r.a.13.5	yes	96	3.2	odd	2
95.2.r.a.22.5	yes	96	285.212	odd	36
95.2.r.a.32.4	yes	96	15.2	even	4
475.2.bb.b.32.5		96	15.8	even	4
475.2.bb.b.193.5		96	285.269	even	18
475.2.bb.b.307.4		96	285.98	odd	36
475.2.bb.b.393.4		96	15.14	odd	2
855.2.dl.a.127.5		96	5.2	odd	4	inner
855.2.dl.a.298.4		96	1.1	even	1	trivial
855.2.dl.a.307.4		96	95.22	even	36	inner
855.2.dl.a.478.5		96	19.3	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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.dl (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.297624 + 0.0260387i) q^{2} +(-1.88171 - 0.331797i) q^{4} +(-1.13754 + 1.92510i) q^{5} +(0.0866366 + 0.323332i) q^{7} +(-1.12856 - 0.302398i) q^{8} +(-0.388686 + 0.543336i) q^{10} +(-0.885063 - 1.53297i) q^{11} +(-0.968521 + 2.07700i) q^{13} +(0.0173660 + 0.0984873i) q^{14} +(3.26301 + 1.18764i) q^{16} +(0.238918 - 2.73085i) q^{17} +(-0.174252 - 4.35541i) q^{19} +(2.77926 - 3.24505i) q^{20} +(-0.223499 - 0.479296i) q^{22} +(7.04590 - 4.93359i) q^{23} +(-2.41202 - 4.37975i) q^{25} +(-0.342337 + 0.592946i) q^{26} +(-0.0557446 - 0.637164i) q^{28} +(-4.70481 - 3.94780i) q^{29} +(-1.80927 - 1.04458i) q^{31} +(3.05804 + 1.42599i) q^{32} +(0.142216 - 0.806545i) q^{34} +(-0.720999 - 0.201018i) q^{35} +(-4.27833 - 4.27833i) q^{37} +(0.0615479 - 1.30081i) q^{38} +(1.86593 - 1.82861i) q^{40} +(-2.08289 + 5.72270i) q^{41} +(3.06524 - 4.37761i) q^{43} +(1.15680 + 3.17828i) q^{44} +(2.22549 - 1.28489i) q^{46} +(-5.75408 + 0.503417i) q^{47} +(5.96514 - 3.44398i) q^{49} +(-0.603830 - 1.36632i) q^{50} +(2.51162 - 3.58697i) q^{52} +(-1.22167 - 1.74473i) q^{53} +(3.95792 + 0.0399817i) q^{55} -0.391100i q^{56} +(-1.29747 - 1.29747i) q^{58} +(1.26888 - 1.06472i) q^{59} +(1.59718 - 9.05803i) q^{61} +(-0.511282 - 0.358003i) q^{62} +(-5.14139 - 2.96838i) q^{64} +(-2.89670 - 4.22716i) q^{65} +(0.957732 + 10.9469i) q^{67} +(-1.35566 + 5.05941i) q^{68} +(-0.209352 - 0.0786018i) q^{70} +(15.3710 - 2.71031i) q^{71} +(-2.33808 - 5.01402i) q^{73} +(-1.16193 - 1.38473i) q^{74} +(-1.11722 + 8.25346i) q^{76} +(0.418981 - 0.418981i) q^{77} +(-14.0660 - 5.11962i) q^{79} +(-5.99811 + 4.93063i) q^{80} +(-0.768931 + 1.64898i) q^{82} +(3.20933 - 0.859936i) q^{83} +(4.98538 + 3.56639i) q^{85} +(1.02628 - 1.22307i) q^{86} +(0.535283 + 1.99770i) q^{88} +(-9.75391 + 3.55013i) q^{89} +(-0.755470 - 0.133210i) q^{91} +(-14.8953 + 6.94580i) q^{92} -1.72566 q^{94} +(8.58282 + 4.61900i) q^{95} +(5.97565 + 0.522802i) q^{97} +(1.86504 - 0.869685i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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