LMFDB - Embedded newform 912.2.bo.b.481.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(289,912)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("912.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			481.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	912.481
Dual form			912.2.bo.b.529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.939693 - 0.342020i) q^{3} +(-0.233956 - 1.32683i) q^{5} +(-0.326352 + 0.565258i) q^{7} +(0.766044 + 0.642788i) q^{9} +(1.97178 + 3.41523i) q^{11} +(-1.59240 + 0.579585i) q^{13} +(-0.233956 + 1.32683i) q^{15} +(-2.93969 + 2.46669i) q^{17} +(-2.82635 + 3.31839i) q^{19} +(0.500000 - 0.419550i) q^{21} +(0.631759 - 3.58288i) q^{23} +(2.99273 - 1.08926i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(8.05690 + 6.76055i) q^{29} +(3.23396 - 5.60138i) q^{31} +(-0.684793 - 3.88365i) q^{33} +(0.826352 + 0.300767i) q^{35} -2.94356 q^{37} +1.69459 q^{39} +(1.41875 + 0.516382i) q^{41} +(1.62701 + 9.22724i) q^{43} +(0.673648 - 1.16679i) q^{45} +(9.77972 + 8.20616i) q^{47} +(3.28699 + 5.69323i) q^{49} +(3.60607 - 1.31250i) q^{51} +(-1.87551 + 10.6366i) q^{53} +(4.07011 - 3.41523i) q^{55} +(3.79086 - 2.15160i) q^{57} +(2.12449 - 1.78265i) q^{59} +(0.748970 - 4.24762i) q^{61} +(-0.613341 + 0.223238i) q^{63} +(1.14156 + 1.97724i) q^{65} +(-6.04189 - 5.06975i) q^{67} +(-1.81908 + 3.15074i) q^{69} +(0.932419 + 5.28801i) q^{71} +(-5.51114 - 2.00589i) q^{73} -3.18479 q^{75} -2.57398 q^{77} +(-2.93969 - 1.06996i) q^{79} +(0.173648 + 0.984808i) q^{81} +(-2.25490 + 3.90560i) q^{83} +(3.96064 + 3.32337i) q^{85} +(-5.25877 - 9.10846i) q^{87} +(10.4620 - 3.80785i) q^{89} +(0.192066 - 1.08926i) q^{91} +(-4.95471 + 4.15749i) q^{93} +(5.06418 + 2.97373i) q^{95} +(5.13429 - 4.30818i) q^{97} +(-0.684793 + 3.88365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{5} - 3 q^{7} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 12 q^{17} - 18 q^{19} + 3 q^{21} + 9 q^{23} - 3 q^{27} + 12 q^{29} + 24 q^{31} + 3 q^{33} + 6 q^{35} + 12 q^{37} + 6 q^{39} + 6 q^{41} - 18 q^{43}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^5 - 3 * q^7 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 12 * q^17 - 18 * q^19 + 3 * q^21 + 9 * q^23 - 3 * q^27 + 12 * q^29 + 24 * q^31 + 3 * q^33 + 6 * q^35 + 12 * q^37 + 6 * q^39 + 6 * q^41 - 18 * q^43 + 3 * q^45 + 33 * q^47 + 12 * q^49 - 3 * q^51 - 24 * q^53 + 33 * q^55 - 9 * q^57 - 21 * q^61 + 3 * q^63 + 15 * q^65 - 30 * q^67 + 6 * q^69 - 18 * q^71 - 27 * q^73 - 12 * q^75 - 12 * q^79 - 15 * q^83 + 15 * q^85 - 9 * q^87 + 45 * q^89 + 12 * q^91 + 6 * q^93 + 12 * q^95 + 21 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$		0			0
$5$	−0.233956	−	1.32683i	−0.104628	−	0.593375i	−0.991368	−	0.131107i	$-0.958147\pi$
$5$	−0.233956	−	1.32683i	−0.104628	−	0.593375i	0.886740	−	0.462268i	$-0.152964\pi$
$6$		0			0
$7$	−0.326352	+	0.565258i	−0.123349	+	0.213647i	−0.921087	−	0.389358i	$-0.872697\pi$
$7$	−0.326352	+	0.565258i	−0.123349	+	0.213647i	0.797737	+	0.603005i	$0.206030\pi$
$8$		0			0
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$		0			0
$11$	1.97178	+	3.41523i	0.594514	+	1.02973i	0.993615	+	0.112822i	$0.0359891\pi$
$11$	1.97178	+	3.41523i	0.594514	+	1.02973i	−0.399101	+	0.916907i	$0.630678\pi$
$12$		0			0
$13$	−1.59240	+	0.579585i	−0.441651	+	0.160748i	−0.553268	−	0.833003i	$-0.686619\pi$
$13$	−1.59240	+	0.579585i	−0.441651	+	0.160748i	0.111617	+	0.993751i	$0.464397\pi$
$14$		0			0
$15$	−0.233956	+	1.32683i	−0.0604071	+	0.342585i
$16$		0			0
$17$	−2.93969	+	2.46669i	−0.712980	+	0.598261i	−0.925434	−	0.378910i	$-0.876299\pi$
$17$	−2.93969	+	2.46669i	−0.712980	+	0.598261i	0.212453	+	0.977171i	$0.431855\pi$
$18$		0			0
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$20$		0			0
$21$	0.500000	−	0.419550i	0.109109	−	0.0915533i
$22$		0			0
$23$	0.631759	−	3.58288i	0.131731	−	0.747083i	−0.845350	−	0.534213i	$-0.820608\pi$
$23$	0.631759	−	3.58288i	0.131731	−	0.747083i	0.977081	−	0.212870i	$-0.0682810\pi$
$24$		0			0
$25$	2.99273	−	1.08926i	0.598545	−	0.217853i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	8.05690	+	6.76055i	1.49613	+	1.25540i	0.886512	+	0.462706i	$0.153122\pi$
$29$	8.05690	+	6.76055i	1.49613	+	1.25540i	0.609618	+	0.792695i	$0.291323\pi$
$30$		0			0
$31$	3.23396	−	5.60138i	0.580836	−	1.00604i	−0.414545	−	0.910029i	$-0.636059\pi$
$31$	3.23396	−	5.60138i	0.580836	−	1.00604i	0.995381	−	0.0960079i	$-0.0306074\pi$
$32$		0			0
$33$	−0.684793	−	3.88365i	−0.119207	−	0.676057i
$34$		0			0
$35$	0.826352	+	0.300767i	0.139679	+	0.0508390i
$36$		0			0
$37$	−2.94356			−0.483919			−0.241959	−	0.970286i	$-0.577790\pi$
$37$	−2.94356			−0.483919			−0.241959	+	0.970286i	$0.577790\pi$
$38$		0			0
$39$	1.69459			0.271352
$40$		0			0
$41$	1.41875	+	0.516382i	0.221571	+	0.0806453i	0.450421	−	0.892817i	$-0.351274\pi$
$41$	1.41875	+	0.516382i	0.221571	+	0.0806453i	−0.228849	+	0.973462i	$0.573496\pi$
$42$		0			0
$43$	1.62701	+	9.22724i	0.248117	+	1.40714i	0.813141	+	0.582067i	$0.197756\pi$
$43$	1.62701	+	9.22724i	0.248117	+	1.40714i	−0.565024	+	0.825074i	$0.691133\pi$
$44$		0			0
$45$	0.673648	−	1.16679i	0.100422	−	0.173935i
$46$		0			0
$47$	9.77972	+	8.20616i	1.42652	+	1.19699i	0.947735	+	0.319057i	$0.103366\pi$
$47$	9.77972	+	8.20616i	1.42652	+	1.19699i	0.478783	+	0.877933i	$0.341078\pi$
$48$		0			0
$49$	3.28699	+	5.69323i	0.469570	+	0.813319i
$50$		0			0
$51$	3.60607	−	1.31250i	0.504950	−	0.183787i
$52$		0			0
$53$	−1.87551	+	10.6366i	−0.257622	+	1.46105i	0.531630	+	0.846976i	$0.321580\pi$
$53$	−1.87551	+	10.6366i	−0.257622	+	1.46105i	−0.789252	+	0.614069i	$0.789532\pi$
$54$		0			0
$55$	4.07011	−	3.41523i	0.548813	−	0.460509i
$56$		0			0
$57$	3.79086	−	2.15160i	0.502112	−	0.284986i
$58$		0			0
$59$	2.12449	−	1.78265i	0.276584	−	0.232082i	−0.493934	−	0.869499i	$-0.664442\pi$
$59$	2.12449	−	1.78265i	0.276584	−	0.232082i	0.770519	+	0.637417i	$0.219997\pi$
$60$		0			0
$61$	0.748970	−	4.24762i	0.0958958	−	0.543852i	−0.898573	−	0.438823i	$-0.855395\pi$
$61$	0.748970	−	4.24762i	0.0958958	−	0.543852i	0.994469	−	0.105029i	$-0.0334935\pi$
$62$		0			0
$63$	−0.613341	+	0.223238i	−0.0772737	+	0.0281253i
$64$		0			0
$65$	1.14156	+	1.97724i	0.141593	+	0.245246i
$66$		0			0
$67$	−6.04189	−	5.06975i	−0.738134	−	0.619368i	0.194202	−	0.980962i	$-0.437788\pi$
$67$	−6.04189	−	5.06975i	−0.738134	−	0.619368i	−0.932336	+	0.361593i	$0.882233\pi$
$68$		0			0
$69$	−1.81908	+	3.15074i	−0.218991	+	0.379304i
$70$		0			0
$71$	0.932419	+	5.28801i	0.110658	+	0.627571i	0.988809	+	0.149188i	$0.0476659\pi$
$71$	0.932419	+	5.28801i	0.110658	+	0.627571i	−0.878151	+	0.478383i	$0.841223\pi$
$72$		0			0
$73$	−5.51114	−	2.00589i	−0.645031	−	0.234772i	−0.00127039	−	0.999999i	$-0.500404\pi$
$73$	−5.51114	−	2.00589i	−0.645031	−	0.234772i	−0.643760	+	0.765227i	$0.722627\pi$
$74$		0			0
$75$	−3.18479			−0.367748
$76$		0			0
$77$	−2.57398			−0.293332
$78$		0			0
$79$	−2.93969	−	1.06996i	−0.330741	−	0.120380i	0.171312	−	0.985217i	$-0.445200\pi$
$79$	−2.93969	−	1.06996i	−0.330741	−	0.120380i	−0.502053	+	0.864837i	$0.667422\pi$
$80$		0			0
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$		0			0
$83$	−2.25490	+	3.90560i	−0.247507	+	0.428695i	−0.962834	−	0.270095i	$-0.912945\pi$
$83$	−2.25490	+	3.90560i	−0.247507	+	0.428695i	0.715326	+	0.698791i	$0.246278\pi$
$84$		0			0
$85$	3.96064	+	3.32337i	0.429591	+	0.360470i
$86$		0			0
$87$	−5.25877	−	9.10846i	−0.563799	−	0.976529i
$88$		0			0
$89$	10.4620	−	3.80785i	1.10897	−	0.403631i	0.278353	−	0.960479i	$-0.410211\pi$
$89$	10.4620	−	3.80785i	1.10897	−	0.403631i	0.830615	+	0.556848i	$0.187989\pi$
$90$		0			0
$91$	0.192066	−	1.08926i	0.0201340	−	0.114186i
$92$		0			0
$93$	−4.95471	+	4.15749i	−0.513779	+	0.431112i
$94$		0			0
$95$	5.06418	+	2.97373i	0.519574	+	0.305098i
$96$		0			0
$97$	5.13429	−	4.30818i	0.521308	−	0.437429i	−0.343780	−	0.939050i	$-0.611707\pi$
$97$	5.13429	−	4.30818i	0.521308	−	0.437429i	0.865087	+	0.501621i	$0.167263\pi$
$98$		0			0
$99$	−0.684793	+	3.88365i	−0.0688242	+	0.390322i
$100$		0			0
$101$	1.81908	−	0.662090i	0.181005	−	0.0658804i	−0.249928	−	0.968265i	$-0.580407\pi$
$101$	1.81908	−	0.662090i	0.181005	−	0.0658804i	0.430933	+	0.902384i	$0.358185\pi$
$102$		0			0
$103$	0.518418	+	0.897927i	0.0510813	+	0.0884754i	0.890435	−	0.455110i	$-0.150400\pi$
$103$	0.518418	+	0.897927i	0.0510813	+	0.0884754i	−0.839354	+	0.543585i	$0.817067\pi$
$104$		0			0
$105$	−0.673648	−	0.565258i	−0.0657413	−	0.0551635i
$106$		0			0
$107$	−6.10607	+	10.5760i	−0.590296	+	1.02242i	0.403897	+	0.914805i	$0.367656\pi$
$107$	−6.10607	+	10.5760i	−0.590296	+	1.02242i	−0.994192	+	0.107618i	$0.965678\pi$
$108$		0			0
$109$	−0.699340	−	3.96616i	−0.0669847	−	0.379889i	−0.999809	−	0.0195568i	$-0.993774\pi$
$109$	−0.699340	−	3.96616i	−0.0669847	−	0.379889i	0.932824	−	0.360332i	$-0.117337\pi$
$110$		0			0
$111$	2.76604	+	1.00676i	0.262541	+	0.0955572i
$112$		0			0
$113$	−13.1925			−1.24105			−0.620525	−	0.784187i	$-0.713080\pi$
$113$	−13.1925			−1.24105			−0.620525	+	0.784187i	$0.713080\pi$
$114$		0			0
$115$	−4.90167			−0.457083
$116$		0			0
$117$	−1.59240	−	0.579585i	−0.147217	−	0.0535826i
$118$		0			0
$119$	−0.434945	−	2.46669i	−0.0398713	−	0.226122i
$120$		0			0
$121$	−2.27584	+	3.94188i	−0.206895	+	0.358353i
$122$		0			0
$123$	−1.15657	−	0.970481i	−0.104285	−	0.0875053i
$124$		0			0
$125$	−5.51367	−	9.54996i	−0.493158	−	0.854174i
$126$		0			0
$127$	12.4500	−	4.53141i	1.10476	−	0.402098i	0.275688	−	0.961247i	$-0.411094\pi$
$127$	12.4500	−	4.53141i	1.10476	−	0.402098i	0.829067	+	0.559149i	$0.188872\pi$
$128$		0			0
$129$	1.62701	−	9.22724i	0.143250	−	0.812413i
$130$		0			0
$131$	−13.1591	+	11.0418i	−1.14972	+	0.964726i	−0.999713	−	0.0239593i	$-0.992373\pi$
$131$	−13.1591	+	11.0418i	−1.14972	+	0.964726i	−0.150003	+	0.988686i	$0.547928\pi$
$132$		0			0
$133$	−0.953363	−	2.68058i	−0.0826671	−	0.232436i
$134$		0			0
$135$	−1.03209	+	0.866025i	−0.0888281	+	0.0745356i
$136$		0			0
$137$	−1.83140	+	10.3864i	−0.156467	+	0.887371i	0.800965	+	0.598712i	$0.204321\pi$
$137$	−1.83140	+	10.3864i	−0.156467	+	0.887371i	−0.957432	+	0.288659i	$0.906791\pi$
$138$		0			0
$139$	10.1309	−	3.68734i	0.859290	−	0.312756i	0.125468	−	0.992098i	$-0.459957\pi$
$139$	10.1309	−	3.68734i	0.859290	−	0.312756i	0.733822	+	0.679342i	$0.237735\pi$
$140$		0			0
$141$	−6.38326	−	11.0561i	−0.537567	−	0.931094i
$142$		0			0
$143$	−5.11927	−	4.29558i	−0.428095	−	0.359214i
$144$		0			0
$145$	7.08512	−	12.2718i	0.588387	−	1.01912i
$146$		0			0
$147$	−1.14156	−	6.47410i	−0.0941542	−	0.533975i
$148$		0			0
$149$	18.5608	+	6.75557i	1.52056	+	0.553438i	0.961287	−	0.275547i	$-0.0888591\pi$
$149$	18.5608	+	6.75557i	1.52056	+	0.553438i	0.559270	+	0.828985i	$0.311081\pi$
$150$		0			0
$151$	−3.10607			−0.252768			−0.126384	−	0.991981i	$-0.540337\pi$
$151$	−3.10607			−0.252768			−0.126384	+	0.991981i	$0.540337\pi$
$152$		0			0
$153$	−3.83750			−0.310243
$154$		0			0
$155$	−8.18866	−	2.98043i	−0.657729	−	0.239394i
$156$		0			0
$157$	0.127889	+	0.725293i	0.0102066	+	0.0578847i	0.989486	−	0.144631i	$-0.0461995\pi$
$157$	0.127889	+	0.725293i	0.0102066	+	0.0578847i	−0.979279	+	0.202516i	$0.935088\pi$
$158$		0			0
$159$	5.40033	−	9.35365i	0.428274	−	0.741792i
$160$		0			0
$161$	1.81908	+	1.52639i	0.143363	+	0.120296i
$162$		0			0
$163$	−6.31180	−	10.9324i	−0.494379	−	0.856289i	0.505600	−	0.862768i	$-0.331271\pi$
$163$	−6.31180	−	10.9324i	−0.494379	−	0.856289i	−0.999979	+	0.00647887i	$0.997938\pi$
$164$		0			0
$165$	−4.99273	+	1.81720i	−0.388683	+	0.141469i
$166$		0			0
$167$	0.958111	−	5.43372i	0.0741409	−	0.420474i	−0.925035	−	0.379882i	$-0.875965\pi$
$167$	0.958111	−	5.43372i	0.0741409	−	0.420474i	0.999176	−	0.0405917i	$-0.0129243\pi$
$168$		0			0
$169$	−7.75877	+	6.51038i	−0.596828	+	0.500799i
$170$		0			0
$171$	−4.29813	+	0.725293i	−0.328686	+	0.0554645i
$172$		0			0
$173$	9.90420	−	8.31061i	0.753002	−	0.631844i	−0.183293	−	0.983058i	$-0.558676\pi$
$173$	9.90420	−	8.31061i	0.753002	−	0.631844i	0.936295	+	0.351214i	$0.114231\pi$
$174$		0			0
$175$	−0.360967	+	2.04715i	−0.0272865	+	0.154750i
$176$		0			0
$177$	−2.60607	+	0.948531i	−0.195884	+	0.0712959i
$178$		0			0
$179$	−7.54323	−	13.0653i	−0.563808	−	0.976544i	−0.997160	−	0.0753188i	$-0.976003\pi$
$179$	−7.54323	−	13.0653i	−0.563808	−	0.976544i	0.433352	−	0.901225i	$-0.357331\pi$
$180$		0			0
$181$	−14.3118	−	12.0090i	−1.06379	−	0.892624i	−0.0693127	−	0.997595i	$-0.522081\pi$
$181$	−14.3118	−	12.0090i	−1.06379	−	0.892624i	−0.994475	+	0.104971i	$0.966525\pi$
$182$		0			0
$183$	−2.15657	+	3.73530i	−0.159419	+	0.276121i
$184$		0			0
$185$	0.688663	+	3.90560i	0.0506315	+	0.287146i
$186$		0			0
$187$	−14.2208	−	5.17593i	−1.03992	−	0.378502i
$188$		0			0
$189$	0.652704			0.0474772
$190$		0			0
$191$	8.55169			0.618779			0.309389	−	0.950935i	$-0.399875\pi$
$191$	8.55169			0.618779			0.309389	+	0.950935i	$0.399875\pi$
$192$		0			0
$193$	−15.9363	−	5.80033i	−1.14712	−	0.417517i	−0.302640	−	0.953105i	$-0.597868\pi$
$193$	−15.9363	−	5.80033i	−1.14712	−	0.417517i	−0.844480	+	0.535588i	$0.820090\pi$
$194$		0			0
$195$	−0.396459	−	2.24843i	−0.0283910	−	0.161014i
$196$		0			0
$197$	−2.25877	+	3.91231i	−0.160931	+	0.278740i	−0.935203	−	0.354113i	$-0.884783\pi$
$197$	−2.25877	+	3.91231i	−0.160931	+	0.278740i	0.774272	+	0.632853i	$0.218116\pi$
$198$		0			0
$199$	6.16431	+	5.17247i	0.436977	+	0.366667i	0.834577	−	0.550892i	$-0.185712\pi$
$199$	6.16431	+	5.17247i	0.436977	+	0.366667i	−0.397600	+	0.917559i	$0.630157\pi$
$200$		0			0
$201$	3.94356	+	6.83045i	0.278157	+	0.481783i
$202$		0			0
$203$	−6.45084	+	2.34791i	−0.452760	+	0.164791i
$204$		0			0
$205$	0.353226	−	2.00324i	0.0246704	−	0.139913i
$206$		0			0
$207$	2.78699	−	2.33856i	0.193709	−	0.162541i
$208$		0			0
$209$	−16.9060	−	3.10948i	−1.16941	−	0.215087i
$210$		0			0
$211$	−15.3851	+	12.9096i	−1.05915	+	0.888734i	−0.994026	−	0.109143i	$-0.965189\pi$
$211$	−15.3851	+	12.9096i	−1.05915	+	0.888734i	−0.0651256	+	0.997877i	$0.520745\pi$
$212$		0			0
$213$	0.932419	−	5.28801i	0.0638883	−	0.362328i
$214$		0			0
$215$	11.8623	−	4.31753i	0.809003	−	0.294453i
$216$		0			0
$217$	2.11081	+	3.65604i	0.143291	+	0.248188i
$218$		0			0
$219$	4.49273	+	3.76984i	0.303590	+	0.254743i
$220$		0			0
$221$	3.25150	−	5.63176i	0.218719	−	0.378833i
$222$		0			0
$223$	−3.40167	−	19.2919i	−0.227793	−	1.29188i	−0.857273	−	0.514862i	$-0.827843\pi$
$223$	−3.40167	−	19.2919i	−0.227793	−	1.29188i	0.629480	−	0.777016i	$-0.283268\pi$
$224$		0			0
$225$	2.99273	+	1.08926i	0.199515	+	0.0726175i
$226$		0			0
$227$	18.4979			1.22775			0.613876	−	0.789403i	$-0.289610\pi$
$227$	18.4979			1.22775			0.613876	+	0.789403i	$0.289610\pi$
$228$		0			0
$229$	−28.1634			−1.86109			−0.930546	−	0.366175i	$-0.880667\pi$
$229$	−28.1634			−1.86109			−0.930546	+	0.366175i	$0.880667\pi$
$230$		0			0
$231$	2.41875	+	0.880352i	0.159142	+	0.0579229i
$232$		0			0
$233$	0.0270364	+	0.153331i	0.00177122	+	0.0100451i	0.985681	−	0.168623i	$-0.0539322\pi$
$233$	0.0270364	+	0.153331i	0.00177122	+	0.0100451i	−0.983909	+	0.178668i	$0.942821\pi$
$234$		0			0
$235$	8.60014	−	14.8959i	0.561011	−	0.971700i
$236$		0			0
$237$	2.39646	+	2.01087i	0.155667	+	0.130620i
$238$		0			0
$239$	3.31521	+	5.74211i	0.214443	+	0.371426i	0.953100	−	0.302655i	$-0.0978731\pi$
$239$	3.31521	+	5.74211i	0.214443	+	0.371426i	−0.738657	+	0.674081i	$0.764540\pi$
$240$		0			0
$241$	4.94356	−	1.79931i	0.318443	−	0.115904i	−0.177853	−	0.984057i	$-0.556915\pi$
$241$	4.94356	−	1.79931i	0.318443	−	0.115904i	0.496296	+	0.868153i	$0.334693\pi$
$242$		0			0
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$		0			0
$245$	6.78493	−	5.69323i	0.433473	−	0.363727i
$246$		0			0
$247$	2.57738	−	6.92231i	0.163995	−	0.440456i
$248$		0			0
$249$	3.45471	−	2.89884i	0.218933	−	0.183707i
$250$		0			0
$251$	−2.57263	+	14.5901i	−0.162383	+	0.920921i	0.789338	+	0.613958i	$0.210424\pi$
$251$	−2.57263	+	14.5901i	−0.162383	+	0.920921i	−0.951722	+	0.306963i	$0.900687\pi$
$252$		0			0
$253$	13.4820	−	4.90706i	0.847609	−	0.308504i
$254$		0			0
$255$	−2.58512	−	4.47756i	−0.161887	−	0.280396i
$256$		0			0
$257$	−14.6800	−	12.3180i	−0.915716	−	0.768377i	0.0574818	−	0.998347i	$-0.481693\pi$
$257$	−14.6800	−	12.3180i	−0.915716	−	0.768377i	−0.973198	+	0.229970i	$0.926137\pi$
$258$		0			0
$259$	0.960637	−	1.66387i	0.0596911	−	0.103388i
$260$		0			0
$261$	1.82635	+	10.3578i	0.113048	+	0.641129i
$262$		0			0
$263$	−15.5030	−	5.64263i	−0.955956	−	0.347939i	−0.183508	−	0.983018i	$-0.558745\pi$
$263$	−15.5030	−	5.64263i	−0.955956	−	0.347939i	−0.772447	+	0.635079i	$0.780968\pi$
$264$		0			0
$265$	14.5517			0.893903
$266$		0			0
$267$	−11.1334			−0.681354
$268$		0			0
$269$	−3.95811	−	1.44063i	−0.241330	−	0.0878370i	0.218524	−	0.975832i	$-0.429876\pi$
$269$	−3.95811	−	1.44063i	−0.241330	−	0.0878370i	−0.459854	+	0.887995i	$0.652098\pi$
$270$		0			0
$271$	−1.59105	−	9.02330i	−0.0966495	−	0.548127i	−0.994229	−	0.107275i	$-0.965788\pi$
$271$	−1.59105	−	9.02330i	−0.0966495	−	0.548127i	0.897580	−	0.440852i	$-0.145324\pi$
$272$		0			0
$273$	−0.553033	+	0.957882i	−0.0334711	+	0.0579737i
$274$		0			0
$275$	9.62108	+	8.07305i	0.580173	+	0.486823i
$276$		0			0
$277$	11.2476	+	19.4815i	0.675804	+	1.17053i	0.976233	+	0.216723i	$0.0695369\pi$
$277$	11.2476	+	19.4815i	0.675804	+	1.17053i	−0.300429	+	0.953804i	$0.597130\pi$
$278$		0			0
$279$	6.07785	−	2.21216i	0.363871	−	0.132438i
$280$		0			0
$281$	−4.08559	+	23.1705i	−0.243726	+	1.38224i	0.579707	+	0.814825i	$0.303167\pi$
$281$	−4.08559	+	23.1705i	−0.243726	+	1.38224i	−0.823433	+	0.567413i	$0.807944\pi$
$282$		0			0
$283$	−20.4893	+	17.1926i	−1.21796	+	1.02199i	−0.219035	+	0.975717i	$0.570291\pi$
$283$	−20.4893	+	17.1926i	−1.21796	+	1.02199i	−0.998929	+	0.0462760i	$0.985265\pi$
$284$		0			0
$285$	−3.74170	−	4.52644i	−0.221639	−	0.268123i
$286$		0			0
$287$	−0.754900	+	0.633436i	−0.0445603	+	0.0373906i
$288$		0			0
$289$	−0.394811	+	2.23908i	−0.0232241	+	0.131711i
$290$		0			0
$291$	−6.29813	+	2.29233i	−0.369203	+	0.134379i
$292$		0			0
$293$	0.103541	+	0.179338i	0.00604891	+	0.0104770i	0.869034	−	0.494752i	$-0.164741\pi$
$293$	0.103541	+	0.179338i	0.00604891	+	0.0104770i	−0.862985	+	0.505229i	$0.831408\pi$
$294$		0			0
$295$	−2.86231	−	2.40176i	−0.166650	−	0.139836i
$296$		0			0
$297$	1.97178	−	3.41523i	0.114414	−	0.198171i
$298$		0			0
$299$	1.07057	+	6.07153i	0.0619129	+	0.351126i
$300$		0			0
$301$	−5.74675	−	2.09165i	−0.331237	−	0.120560i
$302$		0			0
$303$	−1.93582			−0.111210
$304$		0			0
$305$	−5.81109			−0.332742
$306$		0			0
$307$	14.3944	+	5.23913i	0.821532	+	0.299013i	0.718379	−	0.695652i	$-0.244885\pi$
$307$	14.3944	+	5.23913i	0.821532	+	0.299013i	0.103153	+	0.994665i	$0.467107\pi$
$308$		0			0
$309$	−0.180045	−	1.02108i	−0.0102424	−	0.0580875i
$310$		0			0
$311$	7.82160	−	13.5474i	0.443522	−	0.768203i	−0.554426	−	0.832233i	$-0.687062\pi$
$311$	7.82160	−	13.5474i	0.443522	−	0.768203i	0.997948	+	0.0640299i	$0.0203953\pi$
$312$		0			0
$313$	7.78493	+	6.53233i	0.440030	+	0.369229i	0.835721	−	0.549155i	$-0.185050\pi$
$313$	7.78493	+	6.53233i	0.440030	+	0.369229i	−0.395690	+	0.918384i	$0.629495\pi$
$314$		0			0
$315$	0.439693	+	0.761570i	0.0247739	+	0.0429096i
$316$		0			0
$317$	7.18644	−	2.61565i	0.403631	−	0.146910i	−0.132224	−	0.991220i	$-0.542212\pi$
$317$	7.18644	−	2.61565i	0.403631	−	0.146910i	0.535855	+	0.844310i	$0.319990\pi$
$318$		0			0
$319$	−7.20233	+	40.8465i	−0.403253	+	2.28696i
$320$		0			0
$321$	9.35504	−	7.84981i	0.522147	−	0.438134i
$322$		0			0
$323$	0.123141	−	16.7268i	0.00685175	−	0.930704i
$324$		0			0
$325$	−4.13429	+	3.46908i	−0.229329	+	0.192430i
$326$		0			0
$327$	−0.699340	+	3.96616i	−0.0386736	+	0.219329i
$328$		0			0
$329$	−7.83022	+	2.84997i	−0.431694	+	0.157124i
$330$		0			0
$331$	−2.05303	−	3.55596i	−0.112845	−	0.195453i	0.804071	−	0.594533i	$-0.202663\pi$
$331$	−2.05303	−	3.55596i	−0.112845	−	0.195453i	−0.916916	+	0.399080i	$0.869330\pi$
$332$		0			0
$333$	−2.25490	−	1.89209i	−0.123568	−	0.103686i
$334$		0			0
$335$	−5.31315	+	9.20264i	−0.290288	+	0.502794i
$336$		0			0
$337$	−2.09967	−	11.9078i	−0.114376	−	0.648660i	−0.987057	−	0.160369i	$-0.948732\pi$
$337$	−2.09967	−	11.9078i	−0.114376	−	0.648660i	0.872681	−	0.488291i	$-0.162380\pi$
$338$		0			0
$339$	12.3969	+	4.51211i	0.673309	+	0.245064i
$340$		0			0
$341$	25.5066			1.38126
$342$		0			0
$343$	−8.85978			−0.478383
$344$		0			0
$345$	4.60607	+	1.67647i	0.247982	+	0.0902582i
$346$		0			0
$347$	0.719408	+	4.07996i	0.0386198	+	0.219024i	0.998010	−	0.0630592i	$-0.0200857\pi$
$347$	0.719408	+	4.07996i	0.0386198	+	0.219024i	−0.959390	+	0.282083i	$0.908975\pi$
$348$		0			0
$349$	0.0196004	−	0.0339488i	0.00104918	−	0.00181724i	−0.865500	−	0.500908i	$-0.832999\pi$
$349$	0.0196004	−	0.0339488i	0.00104918	−	0.00181724i	0.866550	+	0.499091i	$0.166333\pi$
$350$		0			0
$351$	1.29813	+	1.08926i	0.0692892	+	0.0581406i
$352$		0			0
$353$	−3.58125	−	6.20291i	−0.190611	−	0.330148i	0.754842	−	0.655907i	$-0.227714\pi$
$353$	−3.58125	−	6.20291i	−0.190611	−	0.330148i	−0.945453	+	0.325759i	$0.894380\pi$
$354$		0			0
$355$	6.79813	−	2.47432i	0.360807	−	0.131323i
$356$		0			0
$357$	−0.434945	+	2.46669i	−0.0230197	+	0.130551i
$358$		0			0
$359$	15.6591	−	13.1395i	0.826456	−	0.693479i	−0.128019	−	0.991772i	$-0.540862\pi$
$359$	15.6591	−	13.1395i	0.826456	−	0.693479i	0.954474	+	0.298293i	$0.0964173\pi$
$360$		0			0
$361$	−3.02347	−	18.7579i	−0.159130	−	0.987258i
$362$		0			0
$363$	3.48680	−	2.92577i	0.183009	−	0.153563i
$364$		0			0
$365$	−1.37211	+	7.78163i	−0.0718196	+	0.407309i
$366$		0			0
$367$	−1.49912	+	0.545636i	−0.0782536	+	0.0284820i	−0.380850	−	0.924637i	$-0.624369\pi$
$367$	−1.49912	+	0.545636i	−0.0782536	+	0.0284820i	0.302597	+	0.953119i	$0.402146\pi$
$368$		0			0
$369$	0.754900	+	1.30753i	0.0392985	+	0.0680670i
$370$		0			0
$371$	−5.40033	−	4.53141i	−0.280371	−	0.235259i
$372$		0			0
$373$	6.42602	−	11.1302i	0.332727	−	0.576300i	−0.650319	−	0.759661i	$-0.725365\pi$
$373$	6.42602	−	11.1302i	0.332727	−	0.576300i	0.983046	+	0.183362i	$0.0586980\pi$
$374$		0			0
$375$	1.91488	+	10.8598i	0.0988839	+	0.560798i
$376$		0			0
$377$	−16.7481	−	6.09581i	−0.862571	−	0.313950i
$378$		0			0
$379$	15.7023			0.806575			0.403287	−	0.915073i	$-0.367868\pi$
$379$	15.7023			0.806575			0.403287	+	0.915073i	$0.367868\pi$
$380$		0			0
$381$	−13.2490			−0.678765
$382$		0			0
$383$	−15.4564	−	5.62565i	−0.789783	−	0.287457i	−0.0845371	−	0.996420i	$-0.526941\pi$
$383$	−15.4564	−	5.62565i	−0.789783	−	0.287457i	−0.705246	+	0.708963i	$0.749163\pi$
$384$		0			0
$385$	0.602196	+	3.41523i	0.0306908	+	0.174056i
$386$		0			0
$387$	−4.68479	+	8.11430i	−0.238141	+	0.412473i
$388$		0			0
$389$	5.77063	+	4.84213i	0.292583	+	0.245506i	0.777249	−	0.629193i	$-0.216615\pi$
$389$	5.77063	+	4.84213i	0.292583	+	0.245506i	−0.484666	+	0.874699i	$0.661059\pi$
$390$		0			0
$391$	6.98070	+	12.0909i	0.353029	+	0.611465i
$392$		0			0
$393$	16.1420	−	5.87522i	0.814258	−	0.296365i
$394$		0			0
$395$	−0.731896	+	4.15079i	−0.0368257	+	0.208849i
$396$		0			0
$397$	−8.59421	+	7.21140i	−0.431331	+	0.361930i	−0.832454	−	0.554095i	$-0.813065\pi$
$397$	−8.59421	+	7.21140i	−0.431331	+	0.361930i	0.401123	+	0.916024i	$0.368620\pi$
$398$		0			0
$399$	−0.0209445	+	2.84499i	−0.00104854	+	0.142428i
$400$		0			0
$401$	18.5804	−	15.5908i	0.927860	−	0.778567i	−0.0475723	−	0.998868i	$-0.515148\pi$
$401$	18.5804	−	15.5908i	0.927860	−	0.778567i	0.975432	+	0.220301i	$0.0707040\pi$
$402$		0			0
$403$	−1.90327	+	10.7940i	−0.0948085	+	0.537685i
$404$		0			0
$405$	1.26604	−	0.460802i	0.0629103	−	0.0228975i
$406$		0			0
$407$	−5.80406	−	10.0529i	−0.287697	−	0.498305i
$408$		0			0
$409$	20.1348	+	16.8951i	0.995599	+	0.835407i	0.986369	−	0.164550i	$-0.0526173\pi$
$409$	20.1348	+	16.8951i	0.995599	+	0.835407i	0.00923072	+	0.999957i	$0.497062\pi$
$410$		0			0
$411$	5.27332	−	9.13366i	0.260114	−	0.450530i
$412$		0			0
$413$	0.314330	+	1.78265i	0.0154672	+	0.0877187i
$414$		0			0
$415$	5.70961	+	2.07813i	0.280274	+	0.102011i
$416$		0			0
$417$	−10.7811			−0.527951
$418$		0			0
$419$	−13.2226			−0.645964			−0.322982	−	0.946405i	$-0.604685\pi$
$419$	−13.2226			−0.645964			−0.322982	+	0.946405i	$0.604685\pi$
$420$		0			0
$421$	34.8025	+	12.6671i	1.69617	+	0.617355i	0.995380	−	0.0960141i	$-0.0306094\pi$
$421$	34.8025	+	12.6671i	1.69617	+	0.617355i	0.700789	+	0.713369i	$0.252832\pi$
$422$		0			0
$423$	2.21688	+	12.5726i	0.107788	+	0.611299i
$424$		0			0
$425$	−6.11081	+	10.5842i	−0.296418	+	0.513411i
$426$		0			0
$427$	2.15657	+	1.80958i	0.104364	+	0.0875717i
$428$		0			0
$429$	3.34137	+	5.78742i	0.161323	+	0.279419i
$430$		0			0
$431$	8.90167	−	3.23994i	0.428779	−	0.156063i	−0.118611	−	0.992941i	$-0.537844\pi$
$431$	8.90167	−	3.23994i	0.428779	−	0.156063i	0.547389	+	0.836878i	$0.315622\pi$
$432$		0			0
$433$	−3.91101	+	22.1804i	−0.187951	+	1.06592i	0.734154	+	0.678983i	$0.237579\pi$
$433$	−3.91101	+	22.1804i	−0.187951	+	1.06592i	−0.922105	+	0.386940i	$0.873532\pi$
$434$		0			0
$435$	−10.8550	+	9.10846i	−0.520459	+	0.436717i
$436$		0			0
$437$	10.1038	+	12.2229i	0.483332	+	0.584701i
$438$		0			0
$439$	25.4577	−	21.3615i	1.21503	−	1.01953i	0.215960	−	0.976402i	$-0.430712\pi$
$439$	25.4577	−	21.3615i	1.21503	−	1.01953i	0.999070	−	0.0431289i	$-0.0137326\pi$
$440$		0			0
$441$	−1.14156	+	6.47410i	−0.0543600	+	0.308291i
$442$		0			0
$443$	28.7818	−	10.4757i	1.36747	−	0.497717i	0.449112	−	0.893476i	$-0.351741\pi$
$443$	28.7818	−	10.4757i	1.36747	−	0.497717i	0.918355	+	0.395759i	$0.129518\pi$
$444$		0			0
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$		0			0
$447$	−15.1309	−	12.6963i	−0.715666	−	0.600515i
$448$		0			0
$449$	−7.54623	+	13.0704i	−0.356128	+	0.616833i	−0.987310	−	0.158802i	$-0.949237\pi$
$449$	−7.54623	+	13.0704i	−0.356128	+	0.616833i	0.631182	+	0.775635i	$0.282570\pi$
$450$		0			0
$451$	1.03390	+	5.86354i	0.0486844	+	0.276103i
$452$		0			0
$453$	2.91875	+	1.06234i	0.137135	+	0.0499130i
$454$		0			0
$455$	−1.49020			−0.0698616
$456$		0			0
$457$	19.8462			0.928365			0.464182	−	0.885740i	$-0.346348\pi$
$457$	19.8462			0.928365			0.464182	+	0.885740i	$0.346348\pi$
$458$		0			0
$459$	3.60607	+	1.31250i	0.168317	+	0.0612623i
$460$		0			0
$461$	−6.03684	−	34.2366i	−0.281164	−	1.59456i	−0.718676	−	0.695345i	$-0.755252\pi$
$461$	−6.03684	−	34.2366i	−0.281164	−	1.59456i	0.437512	−	0.899212i	$-0.355860\pi$
$462$		0			0
$463$	−1.71301	+	2.96702i	−0.0796104	+	0.137889i	−0.903082	−	0.429468i	$-0.858701\pi$
$463$	−1.71301	+	2.96702i	−0.0796104	+	0.137889i	0.823472	+	0.567358i	$0.192034\pi$
$464$		0			0
$465$	6.67546	+	5.60138i	0.309567	+	0.259758i
$466$		0			0
$467$	−5.66250	−	9.80774i	−0.262029	−	0.453848i	0.704752	−	0.709454i	$-0.251058\pi$
$467$	−5.66250	−	9.80774i	−0.262029	−	0.453848i	−0.966781	+	0.255606i	$0.917725\pi$
$468$		0			0
$469$	4.83750	−	1.76070i	0.223375	−	0.0813018i
$470$		0			0
$471$	0.127889	−	0.725293i	0.00589280	−	0.0334197i
$472$		0			0
$473$	−28.3050	+	23.7507i	−1.30147	+	1.09206i
$474$		0			0
$475$	−4.84389	+	13.0097i	−0.222253	+	0.596925i
$476$		0			0
$477$	−8.27379	+	6.94253i	−0.378831	+	0.317877i
$478$		0			0
$479$	−2.00862	+	11.3914i	−0.0917761	+	0.520488i	0.903912	+	0.427719i	$0.140683\pi$
$479$	−2.00862	+	11.3914i	−0.0917761	+	0.520488i	−0.995688	+	0.0927688i	$0.970428\pi$
$480$		0			0
$481$	4.68732	−	1.70604i	0.213723	−	0.0777889i
$482$		0			0
$483$	−1.18732	−	2.05650i	−0.0540249	−	0.0935738i
$484$		0			0
$485$	−6.91740	−	5.80439i	−0.314103	−	0.263564i
$486$		0			0
$487$	5.87346	−	10.1731i	0.266152	−	0.460988i	−0.701713	−	0.712460i	$-0.747581\pi$
$487$	5.87346	−	10.1731i	0.266152	−	0.460988i	0.967865	+	0.251471i	$0.0809145\pi$
$488$		0			0
$489$	2.19207	+	12.4318i	0.0991287	+	0.562187i
$490$		0			0
$491$	9.63563	+	3.50708i	0.434850	+	0.158272i	0.550164	−	0.835057i	$-0.314565\pi$
$491$	9.63563	+	3.50708i	0.434850	+	0.158272i	−0.115314	+	0.993329i	$0.536787\pi$
$492$		0			0
$493$	−40.3610			−1.81777
$494$		0			0
$495$	5.31315			0.238808
$496$		0			0
$497$	−3.29339	−	1.19869i	−0.147729	−	0.0537688i
$498$		0			0
$499$	1.12149	+	6.36030i	0.0502049	+	0.284726i	0.999566	−	0.0294612i	$-0.00937914\pi$
$499$	1.12149	+	6.36030i	0.0502049	+	0.284726i	−0.949361	+	0.314187i	$0.898268\pi$
$500$		0			0
$501$	−2.75877	+	4.77833i	−0.123253	+	0.213480i
$502$		0			0
$503$	14.0248	+	11.7682i	0.625336	+	0.524719i	0.899476	−	0.436971i	$-0.143949\pi$
$503$	14.0248	+	11.7682i	0.625336	+	0.524719i	−0.274140	+	0.961690i	$0.588393\pi$
$504$		0			0
$505$	−1.30406	−	2.25870i	−0.0580300	−	0.100511i
$506$		0			0
$507$	9.51754	−	3.46410i	0.422689	−	0.153846i
$508$		0			0
$509$	2.09580	−	11.8859i	0.0928947	−	0.526832i	−0.902477	−	0.430737i	$-0.858254\pi$
$509$	2.09580	−	11.8859i	0.0928947	−	0.526832i	0.995372	−	0.0960949i	$-0.0306352\pi$
$510$		0			0
$511$	2.93242	−	2.46059i	0.129723	−	0.108850i
$512$		0			0
$513$	4.28699	+	0.788496i	0.189275	+	0.0348129i
$514$		0			0
$515$	1.07011	−	0.897927i	0.0471546	−	0.0395674i
$516$		0			0
$517$	−8.74241	+	49.5807i	−0.384491	+	2.18056i
$518$		0			0
$519$	−12.1493	+	4.42198i	−0.533295	+	0.194104i
$520$		0			0
$521$	−14.2849	−	24.7422i	−0.625834	−	1.08398i	−0.988379	−	0.152010i	$-0.951425\pi$
$521$	−14.2849	−	24.7422i	−0.625834	−	1.08398i	0.362545	−	0.931966i	$-0.381908\pi$
$522$		0			0
$523$	−14.2836	−	11.9854i	−0.624578	−	0.524083i	0.274661	−	0.961541i	$-0.411434\pi$
$523$	−14.2836	−	11.9854i	−0.624578	−	0.524083i	−0.899239	+	0.437458i	$0.855879\pi$
$524$		0			0
$525$	1.03936	−	1.80023i	0.0453615	−	0.0785684i
$526$		0			0
$527$	4.31005	+	24.4435i	0.187749	+	1.06478i
$528$		0			0
$529$	9.17499	+	3.33942i	0.398913	+	0.145192i
$530$		0			0
$531$	2.77332			0.120352
$532$		0			0
$533$	−2.55850			−0.110821
$534$		0			0
$535$	15.4611	+	5.62738i	0.668442	+	0.243293i
$536$		0			0
$537$	2.61974	+	14.8573i	0.113050	+	0.641138i
$538$		0			0
$539$	−12.9624	+	22.4516i	−0.558332	+	0.967060i
$540$		0			0
$541$	−13.3007	−	11.1606i	−0.571840	−	0.479831i	0.310416	−	0.950601i	$-0.399532\pi$
$541$	−13.3007	−	11.1606i	−0.571840	−	0.479831i	−0.882256	+	0.470770i	$0.843976\pi$
$542$		0			0
$543$	9.34137	+	16.1797i	0.400876	+	0.694338i
$544$		0			0
$545$	−5.09879	+	1.85581i	−0.218408	+	0.0794941i
$546$		0			0
$547$	−0.877326	+	4.97556i	−0.0375117	+	0.212740i	−0.997802	−	0.0662625i	$-0.978893\pi$
$547$	−0.877326	+	4.97556i	−0.0375117	+	0.212740i	0.960290	+	0.279002i	$0.0900037\pi$
$548$		0			0
$549$	3.30406	−	2.77244i	0.141014	−	0.118325i
$550$		0			0
$551$	−45.2058	+	7.62830i	−1.92583	+	0.324976i
$552$		0			0
$553$	1.56418	−	1.31250i	0.0665156	−	0.0558132i
$554$		0			0
$555$	0.688663	−	3.90560i	0.0292321	−	0.165784i
$556$		0			0
$557$	22.5303	−	8.20037i	0.954641	−	0.347461i	0.182710	−	0.983167i	$-0.441513\pi$
$557$	22.5303	−	8.20037i	0.954641	−	0.347461i	0.771931	+	0.635706i	$0.219291\pi$
$558$		0			0
$559$	−7.93882	−	13.7504i	−0.335776	−	0.581581i
$560$		0			0
$561$	11.5929	+	9.72757i	0.489451	+	0.410698i
$562$		0			0
$563$	21.3418	−	36.9651i	0.899451	−	1.55789i	0.0712538	−	0.997458i	$-0.477300\pi$
$563$	21.3418	−	36.9651i	0.899451	−	1.55789i	0.828197	−	0.560437i	$-0.189367\pi$
$564$		0			0
$565$	3.08647	+	17.5042i	0.129849	+	0.736408i
$566$		0			0
$567$	−0.613341	−	0.223238i	−0.0257579	−	0.00937511i
$568$		0			0
$569$	21.9358			0.919598			0.459799	−	0.888023i	$-0.347922\pi$
$569$	21.9358			0.919598			0.459799	+	0.888023i	$0.347922\pi$
$570$		0			0
$571$	32.3063			1.35198			0.675989	−	0.736912i	$-0.263717\pi$
$571$	32.3063			1.35198			0.675989	+	0.736912i	$0.263717\pi$
$572$		0			0
$573$	−8.03596	−	2.92485i	−0.335707	−	0.122187i
$574$		0			0
$575$	−2.01202	−	11.4107i	−0.0839071	−	0.475861i
$576$		0			0
$577$	23.4060	−	40.5404i	0.974405	−	1.68772i	0.292520	−	0.956259i	$-0.405506\pi$
$577$	23.4060	−	40.5404i	0.974405	−	1.68772i	0.681885	−	0.731460i	$-0.261161\pi$
$578$		0			0
$579$	12.9914	+	10.9011i	0.539903	+	0.453033i
$580$		0			0
$581$	−1.47178	−	2.54920i	−0.0610598	−	0.105759i
$582$		0			0
$583$	−40.0244	+	14.5677i	−1.65764	+	0.603332i
$584$		0			0
$585$	−0.396459	+	2.24843i	−0.0163916	+	0.0929613i
$586$		0			0
$587$	18.9841	−	15.9296i	0.783558	−	0.657483i	−0.160584	−	0.987022i	$-0.551338\pi$
$587$	18.9841	−	15.9296i	0.783558	−	0.657483i	0.944142	+	0.329539i	$0.106893\pi$
$588$		0			0
$589$	9.44727	+	26.5630i	0.389268	+	1.09451i
$590$		0			0
$591$	3.46064	−	2.90382i	0.142352	−	0.119447i
$592$		0			0
$593$	−0.634447	+	3.59813i	−0.0260536	+	0.147758i	−0.995060	−	0.0992801i	$-0.968346\pi$
$593$	−0.634447	+	3.59813i	−0.0260536	+	0.147758i	0.969006	+	0.247038i	$0.0794571\pi$
$594$		0			0
$595$	−3.17112	+	1.15419i	−0.130003	+	0.0473173i
$596$		0			0
$597$	−4.02347	−	6.96886i	−0.164670	−	0.285216i
$598$		0			0
$599$	−1.14677	−	0.962258i	−0.0468559	−	0.0393168i	0.619059	−	0.785344i	$-0.287514\pi$
$599$	−1.14677	−	0.962258i	−0.0468559	−	0.0393168i	−0.665915	+	0.746028i	$0.731959\pi$
$600$		0			0
$601$	−11.9119	+	20.6321i	−0.485898	+	0.841600i	−0.999869	−	0.0162075i	$-0.994841\pi$
$601$	−11.9119	+	20.6321i	−0.485898	+	0.841600i	0.513970	+	0.857808i	$0.328174\pi$
$602$		0			0
$603$	−1.36959	−	7.76730i	−0.0557738	−	0.316309i
$604$		0			0
$605$	5.76264	+	2.09743i	0.234285	+	0.0852726i
$606$		0			0
$607$	−16.4757			−0.668726			−0.334363	−	0.942444i	$-0.608521\pi$
$607$	−16.4757			−0.668726			−0.334363	+	0.942444i	$0.608521\pi$
$608$		0			0
$609$	6.86484			0.278177
$610$		0			0
$611$	−20.3293	−	7.39928i	−0.822437	−	0.299343i
$612$		0			0
$613$	0.231591	+	1.31342i	0.00935389	+	0.0530486i	0.989127	−	0.147061i	$-0.0469813\pi$
$613$	0.231591	+	1.31342i	0.00935389	+	0.0530486i	−0.979774	+	0.200109i	$0.935870\pi$
$614$		0			0
$615$	−1.01707	+	1.76162i	−0.0410124	+	0.0710355i
$616$		0			0
$617$	27.6864	+	23.2317i	1.11461	+	0.935272i	0.998320	−	0.0579425i	$-0.0184540\pi$
$617$	27.6864	+	23.2317i	1.11461	+	0.935272i	0.116294	+	0.993215i	$0.462898\pi$
$618$		0			0
$619$	9.65792	+	16.7280i	0.388185	+	0.672355i	0.992205	−	0.124613i	$-0.0397690\pi$
$619$	9.65792	+	16.7280i	0.388185	+	0.672355i	−0.604021	+	0.796968i	$0.706436\pi$
$620$		0			0
$621$	−3.41875	+	1.24432i	−0.137190	+	0.0499329i
$622$		0			0
$623$	−1.26187	+	7.15642i	−0.0505557	+	0.286716i
$624$		0			0
$625$	0.817267	−	0.685768i	0.0326907	−	0.0274307i
$626$		0			0
$627$	14.8229	+	8.70415i	0.591972	+	0.347610i
$628$		0			0
$629$	8.65317	−	7.26087i	0.345025	−	0.289510i
$630$		0			0
$631$	−4.95290	+	28.0893i	−0.197172	+	1.11822i	0.712120	+	0.702057i	$0.247735\pi$
$631$	−4.95290	+	28.0893i	−0.197172	+	1.11822i	−0.909292	+	0.416159i	$0.863376\pi$
$632$		0			0
$633$	18.8726	−	6.86906i	0.750118	−	0.273020i
$634$		0			0
$635$	−8.92514	−	15.4588i	−0.354184	−	0.613464i
$636$		0			0
$637$	−8.53390	−	7.16079i	−0.338125	−	0.283721i
$638$		0			0
$639$	−2.68479	+	4.65020i	−0.106209	+	0.183959i
$640$		0			0
$641$	−5.38342	−	30.5309i	−0.212632	−	1.20590i	−0.884968	−	0.465651i	$-0.845820\pi$
$641$	−5.38342	−	30.5309i	−0.212632	−	1.20590i	0.672336	−	0.740246i	$-0.265291\pi$
$642$		0			0
$643$	22.2358	+	8.09316i	0.876893	+	0.319163i	0.740955	−	0.671554i	$-0.234373\pi$
$643$	22.2358	+	8.09316i	0.876893	+	0.319163i	0.135938	+	0.990717i	$0.456595\pi$
$644$		0			0
$645$	−12.6236			−0.497054
$646$		0			0
$647$	−36.0865			−1.41871			−0.709353	−	0.704854i	$-0.751013\pi$
$647$	−36.0865			−1.41871			−0.709353	+	0.704854i	$0.751013\pi$
$648$		0			0
$649$	10.2772	+	3.74059i	0.403415	+	0.146831i
$650$		0			0
$651$	−0.733078	−	4.15749i	−0.0287316	−	0.162945i
$652$		0			0
$653$	18.7245	−	32.4317i	0.732745	−	1.26915i	−0.222961	−	0.974827i	$-0.571572\pi$
$653$	18.7245	−	32.4317i	0.732745	−	1.26915i	0.955706	−	0.294324i	$-0.0950944\pi$
$654$		0			0
$655$	17.7292	+	14.8766i	0.692737	+	0.581276i
$656$		0			0
$657$	−2.93242	−	5.07910i	−0.114405	−	0.198154i
$658$		0			0
$659$	18.1652	−	6.61159i	0.707615	−	0.257551i	0.0369566	−	0.999317i	$-0.488234\pi$
$659$	18.1652	−	6.61159i	0.707615	−	0.257551i	0.670659	+	0.741766i	$0.266011\pi$
$660$		0			0
$661$	−4.27584	+	24.2495i	−0.166311	+	0.943197i	0.781391	+	0.624041i	$0.214510\pi$
$661$	−4.27584	+	24.2495i	−0.166311	+	0.943197i	−0.947702	+	0.319156i	$0.896601\pi$
$662$		0			0
$663$	−4.98158	+	4.18004i	−0.193469	+	0.162339i
$664$		0			0
$665$	−3.33363	+	1.89209i	−0.129272	+	0.0733719i
$666$		0			0
$667$	29.3123	−	24.5959i	1.13498	−	0.952358i
$668$		0			0
$669$	−3.40167	+	19.2919i	−0.131516	+	0.745866i
$670$		0			0
$671$	15.9834	−	5.81748i	0.617032	−	0.224581i
$672$		0			0
$673$	−21.2173	−	36.7495i	−0.817869	−	1.41659i	−0.907250	−	0.420593i	$-0.861822\pi$
$673$	−21.2173	−	36.7495i	−0.817869	−	1.41659i	0.0893810	−	0.995998i	$-0.471511\pi$
$674$		0			0
$675$	−2.43969	−	2.04715i	−0.0939038	−	0.0787947i
$676$		0			0
$677$	−7.29813	+	12.6407i	−0.280490	+	0.485823i	−0.971506	−	0.237017i	$-0.923830\pi$
$677$	−7.29813	+	12.6407i	−0.280490	+	0.485823i	0.691015	+	0.722840i	$0.257164\pi$
$678$		0			0
$679$	0.759648	+	4.30818i	0.0291526	+	0.165333i
$680$		0			0
$681$	−17.3824	−	6.32667i	−0.666094	−	0.242438i
$682$		0			0
$683$	−17.8043			−0.681262			−0.340631	−	0.940197i	$-0.610641\pi$
$683$	−17.8043			−0.681262			−0.340631	+	0.940197i	$0.610641\pi$
$684$		0			0
$685$	14.2094			0.542915
$686$		0			0
$687$	26.4650	+	9.63246i	1.00970	+	0.367501i
$688$		0			0
$689$	−3.17823	−	18.0247i	−0.121081	−	0.686685i
$690$		0			0
$691$	6.23648	−	10.8019i	0.237247	−	0.410924i	−0.722676	−	0.691187i	$-0.757088\pi$
$691$	6.23648	−	10.8019i	0.237247	−	0.410924i	0.959923	+	0.280263i	$0.0904216\pi$
$692$		0			0
$693$	−1.97178	−	1.65452i	−0.0749018	−	0.0628501i
$694$		0			0
$695$	−7.26264	−	12.5793i	−0.275488	−	0.477159i
$696$		0			0
$697$	−5.44444	+	1.98161i	−0.206223	+	0.0750590i
$698$		0			0
$699$	0.0270364	−	0.153331i	0.00102261	−	0.00579952i
$700$		0			0
$701$	−2.47700	+	2.07845i	−0.0935549	+	0.0785018i	−0.688366	−	0.725364i	$-0.741671\pi$
$701$	−2.47700	+	2.07845i	−0.0935549	+	0.0785018i	0.594811	+	0.803866i	$0.297227\pi$
$702$		0			0
$703$	8.31954	−	9.76790i	0.313778	−	0.368403i
$704$		0			0
$705$	−13.1762	+	11.0561i	−0.496243	+	0.416398i
$706$		0			0
$707$	−0.219408	+	1.24432i	−0.00825167	+	0.0467976i
$708$		0			0
$709$	19.7576	−	7.19117i	0.742012	−	0.270070i	0.0567714	−	0.998387i	$-0.481919\pi$
$709$	19.7576	−	7.19117i	0.742012	−	0.270070i	0.685240	+	0.728317i	$0.259697\pi$
$710$		0			0
$711$	−1.56418	−	2.70924i	−0.0586612	−	0.101604i
$712$		0			0
$713$	−18.0260	−	15.1256i	−0.675079	−	0.566458i
$714$		0			0
$715$	−4.50181	+	7.79737i	−0.168358	+	0.291605i
$716$		0			0
$717$	−1.15136	−	6.52968i	−0.0429983	−	0.243856i
$718$		0			0
$719$	−3.80793	−	1.38597i	−0.142012	−	0.0516881i	0.270036	−	0.962850i	$-0.412964\pi$
$719$	−3.80793	−	1.38597i	−0.142012	−	0.0516881i	−0.412048	+	0.911162i	$0.635187\pi$
$720$		0			0
$721$	−0.676747			−0.0252034
$722$		0			0
$723$	−5.26083			−0.195652
$724$		0			0
$725$	31.4761	+	11.4564i	1.16899	+	0.425479i
$726$		0			0
$727$	7.10623	+	40.3014i	0.263555	+	1.49470i	0.773117	+	0.634263i	$0.218696\pi$
$727$	7.10623	+	40.3014i	0.263555	+	1.49470i	−0.509562	+	0.860434i	$0.670192\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−27.5437	−	23.1119i	−1.01874	−	0.854825i
$732$		0			0
$733$	−3.63429	−	6.29477i	−0.134235	−	0.232503i	0.791070	−	0.611726i	$-0.209524\pi$
$733$	−3.63429	−	6.29477i	−0.134235	−	0.232503i	−0.925305	+	0.379223i	$0.876191\pi$
$734$		0			0
$735$	−8.32295	+	3.02931i	−0.306997	+	0.111738i
$736$		0			0
$737$	5.40104	−	30.6308i	0.198950	−	1.12830i
$738$		0			0
$739$	−3.56212	+	2.98897i	−0.131035	+	0.109951i	−0.705950	−	0.708262i	$-0.749480\pi$
$739$	−3.56212	+	2.98897i	−0.131035	+	0.109951i	0.574915	+	0.818213i	$0.305035\pi$
$740$		0			0
$741$	−4.78952	+	5.62333i	−0.175947	+	0.206578i
$742$		0			0
$743$	2.05484	−	1.72422i	0.0753849	−	0.0632555i	−0.604317	−	0.796744i	$-0.706554\pi$
$743$	2.05484	−	1.72422i	0.0753849	−	0.0632555i	0.679701	+	0.733489i	$0.262109\pi$
$744$		0			0
$745$	4.62108	−	26.2075i	0.169303	−	0.960167i
$746$		0			0
$747$	−4.23783	+	1.54244i	−0.155054	+	0.0564350i
$748$		0			0
$749$	−3.98545	−	6.90301i	−0.145625	−	0.252230i
$750$		0			0
$751$	−24.8444	−	20.8469i	−0.906584	−	0.760714i	0.0648824	−	0.997893i	$-0.479333\pi$
$751$	−24.8444	−	20.8469i	−0.906584	−	0.760714i	−0.971466	+	0.237179i	$0.923777\pi$
$752$		0			0
$753$	7.40760	−	12.8303i	0.269948	−	0.467564i
$754$		0			0
$755$	0.726682	+	4.12122i	0.0264467	+	0.149986i
$756$		0			0
$757$	−4.47266	−	1.62791i	−0.162562	−	0.0591676i	0.259458	−	0.965755i	$-0.416456\pi$
$757$	−4.47266	−	1.62791i	−0.162562	−	0.0591676i	−0.422019	+	0.906587i	$0.638678\pi$
$758$		0			0
$759$	−14.3473			−0.520774
$760$		0			0
$761$	−30.2481			−1.09649			−0.548247	−	0.836316i	$-0.684705\pi$
$761$	−30.2481			−1.09649			−0.548247	+	0.836316i	$0.684705\pi$
$762$		0			0
$763$	2.47013	+	0.899055i	0.0894248	+	0.0325480i
$764$		0			0
$765$	0.897804	+	5.09170i	0.0324602	+	0.184091i
$766$		0			0
$767$	−2.34982	+	4.07001i	−0.0848472	+	0.146960i
$768$		0			0
$769$	24.2108	+	20.3153i	0.873063	+	0.732587i	0.964741	−	0.263202i	$-0.0847784\pi$
$769$	24.2108	+	20.3153i	0.873063	+	0.732587i	−0.0916775	+	0.995789i	$0.529223\pi$
$770$		0			0
$771$	9.58172	+	16.5960i	0.345077	+	0.597691i
$772$		0			0
$773$	−43.6014	+	15.8696i	−1.56823	+	0.570790i	−0.972604	−	0.232470i	$-0.925319\pi$
$773$	−43.6014	+	15.8696i	−1.56823	+	0.570790i	−0.595629	+	0.803260i	$0.703097\pi$
$774$		0			0
$775$	3.57697	−	20.2860i	0.128489	−	0.728695i
$776$		0			0
$777$	−1.47178	+	1.23497i	−0.0527999	+	0.0443043i
$778$		0			0
$779$	−5.72344	+	3.24849i	−0.205064	+	0.116389i
$780$		0			0
$781$	−16.2212	+	13.6112i	−0.580441	+	0.487048i
$782$		0			0
$783$	1.82635	−	10.3578i	0.0652685	−	0.370156i
$784$		0			0
$785$	0.932419	−	0.339373i	0.0332794	−	0.0121127i
$786$		0			0
$787$	−18.4244	−	31.9120i	−0.656760	−	1.13754i	−0.981449	−	0.191721i	$-0.938593\pi$
$787$	−18.4244	−	31.9120i	−0.656760	−	1.13754i	0.324689	−	0.945821i	$-0.394740\pi$
$788$		0			0
$789$	12.6382	+	10.6047i	0.449930	+	0.377536i
$790$		0			0
$791$	4.30541	−	7.45718i	0.153083	−	0.265147i
$792$		0			0
$793$	1.26920	+	7.19799i	0.0450706	+	0.255608i
$794$		0			0
$795$	−13.6741	−	4.97697i	−0.484971	−	0.176515i
$796$		0			0
$797$	18.7939			0.665712			0.332856	−	0.942978i	$-0.391988\pi$
$797$	18.7939			0.665712			0.332856	+	0.942978i	$0.391988\pi$
$798$		0			0
$799$	−48.9914			−1.73319
$800$		0			0
$801$	10.4620	+	3.80785i	0.369656	+	0.134544i
$802$		0			0
$803$	−4.01620	−	22.7770i	−0.141729	−	0.803782i
$804$		0			0
$805$	1.59967	−	2.77071i	0.0563810	−	0.0976547i
$806$		0			0
$807$	3.22668	+	2.70751i	0.113585	+	0.0953088i
$808$		0			0
$809$	−3.02276	−	5.23557i	−0.106274	−	0.184073i	0.807984	−	0.589205i	$-0.200559\pi$
$809$	−3.02276	−	5.23557i	−0.106274	−	0.184073i	−0.914258	+	0.405132i	$0.867226\pi$
$810$		0			0
$811$	8.41370	−	3.06233i	0.295445	−	0.107533i	−0.190045	−	0.981775i	$-0.560863\pi$
$811$	8.41370	−	3.06233i	0.295445	−	0.107533i	0.485490	+	0.874242i	$0.338641\pi$
$812$		0			0
$813$	−1.59105	+	9.02330i	−0.0558006	+	0.316461i
$814$		0			0
$815$	−13.0287	+	10.9324i	−0.456375	+	0.382944i
$816$		0			0
$817$	−35.2181	−	20.6804i	−1.23213	−	0.723514i
$818$		0			0
$819$	0.847296	−	0.710966i	0.0296069	−	0.0248432i
$820$		0			0
$821$	1.41416	−	8.02011i	0.0493546	−	0.279904i	−0.950135	−	0.311838i	$-0.899055\pi$
$821$	1.41416	−	8.02011i	0.0493546	−	0.279904i	0.999490	+	0.0319338i	$0.0101666\pi$
$822$		0			0
$823$	−2.48380	+	0.904030i	−0.0865799	+	0.0315125i	−0.384947	−	0.922939i	$-0.625780\pi$
$823$	−2.48380	+	0.904030i	−0.0865799	+	0.0315125i	0.298367	+	0.954451i	$0.403558\pi$
$824$		0			0
$825$	−6.27972	−	10.8768i	−0.218632	−	0.378681i
$826$		0			0
$827$	28.1464	+	23.6176i	0.978745	+	0.821265i	0.983900	−	0.178722i	$-0.0571963\pi$
$827$	28.1464	+	23.6176i	0.978745	+	0.821265i	−0.00515463	+	0.999987i	$0.501641\pi$
$828$		0			0
$829$	21.8717	−	37.8829i	0.759636	−	1.31573i	−0.183401	−	0.983038i	$-0.558711\pi$
$829$	21.8717	−	37.8829i	0.759636	−	1.31573i	0.943037	−	0.332689i	$-0.107956\pi$
$830$		0			0
$831$	−3.90626	−	22.1535i	−0.135507	−	0.768496i
$832$		0			0
$833$	−23.7062	−	8.62835i	−0.821371	−	0.298955i
$834$		0			0
$835$	−7.43376			−0.257256
$836$		0			0
$837$	−6.46791			−0.223564
$838$		0			0
$839$	12.9508	+	4.71372i	0.447113	+	0.162736i	0.555757	−	0.831345i	$-0.312429\pi$
$839$	12.9508	+	4.71372i	0.447113	+	0.162736i	−0.108644	+	0.994081i	$0.534651\pi$
$840$		0			0
$841$	14.1729	+	80.3787i	0.488722	+	2.77168i
$842$		0			0
$843$	11.7640	−	20.3758i	0.405173	−	0.701781i
$844$		0			0
$845$	10.4534	+	8.77141i	0.359607	+	0.301746i
$846$		0			0
$847$	−1.48545	−	2.57288i	−0.0510407	−	0.0884052i
$848$		0			0
$849$	25.1339	−	9.14798i	0.862592	−	0.313958i
$850$		0			0
$851$	−1.85962	+	10.5464i	−0.0637470	+	0.361527i
$852$		0			0
$853$	8.09673	−	6.79397i	0.277227	−	0.232621i	−0.493564	−	0.869710i	$-0.664306\pi$
$853$	8.09673	−	6.79397i	0.277227	−	0.232621i	0.770790	+	0.637089i	$0.219862\pi$
$854$		0			0
$855$	1.96791	+	5.53320i	0.0673011	+	0.189231i
$856$		0			0
$857$	28.2342	−	23.6913i	0.964461	−	0.809279i	−0.0172120	−	0.999852i	$-0.505479\pi$
$857$	28.2342	−	23.6913i	0.964461	−	0.809279i	0.981673	+	0.190573i	$0.0610346\pi$
$858$		0			0
$859$	6.09745	−	34.5803i	0.208042	−	1.17987i	−0.684538	−	0.728977i	$-0.739996\pi$
$859$	6.09745	−	34.5803i	0.208042	−	1.17987i	0.892580	−	0.450889i	$-0.148893\pi$
$860$		0			0
$861$	0.926022	−	0.337044i	0.0315587	−	0.0114864i
$862$		0			0
$863$	1.50846	+	2.61272i	0.0513484	+	0.0889381i	0.890557	−	0.454871i	$-0.150315\pi$
$863$	1.50846	+	2.61272i	0.0513484	+	0.0889381i	−0.839209	+	0.543809i	$0.816981\pi$
$864$		0			0
$865$	−13.3439	−	11.1969i	−0.453706	−	0.380705i
$866$		0			0
$867$	1.13681	−	1.96902i	0.0386081	−	0.0668713i
$868$		0			0
$869$	−2.14227	−	12.1494i	−0.0726717	−	0.412142i
$870$		0			0
$871$	12.5594	+	4.57126i	0.425560	+	0.154891i
$872$		0			0
$873$	6.70233			0.226840
$874$		0			0
$875$	7.19759			0.243323
$876$		0			0
$877$	−54.6878	−	19.9047i	−1.84668	−	0.672136i	−0.986870	−	0.161517i	$-0.948361\pi$
$877$	−54.6878	−	19.9047i	−1.84668	−	0.672136i	−0.859807	−	0.510619i	$-0.829416\pi$
$878$		0			0
$879$	−0.0359593	−	0.203935i	−0.00121288	−	0.00687856i
$880$		0			0
$881$	−12.8191	+	22.2033i	−0.431886	+	0.748048i	−0.997036	−	0.0769402i	$-0.975485\pi$
$881$	−12.8191	+	22.2033i	−0.431886	+	0.748048i	0.565150	+	0.824988i	$0.308818\pi$
$882$		0			0
$883$	−15.4886	−	12.9965i	−0.521233	−	0.437367i	0.343828	−	0.939033i	$-0.388276\pi$
$883$	−15.4886	−	12.9965i	−0.521233	−	0.437367i	−0.865061	+	0.501666i	$0.832721\pi$
$884$		0			0
$885$	1.86824	+	3.23589i	0.0628002	+	0.108773i
$886$		0			0
$887$	−19.8332	+	7.21870i	−0.665934	+	0.242380i	−0.652796	−	0.757533i	$-0.726404\pi$
$887$	−19.8332	+	7.21870i	−0.665934	+	0.242380i	−0.0131379	+	0.999914i	$0.504182\pi$
$888$		0			0
$889$	−1.50165	+	8.51627i	−0.0503637	+	0.285627i
$890$		0			0
$891$	−3.02094	+	2.53487i	−0.101205	+	0.0849215i
$892$		0			0
$893$	−54.8722	+	9.25946i	−1.83623	+	0.309856i
$894$		0			0
$895$	−15.5706	+	13.0653i	−0.520467	+	0.436724i
$896$		0			0
$897$	1.07057	−	6.07153i	0.0357454	−	0.202722i
$898$		0			0
$899$	63.9240	−	23.2664i	2.13199	−	0.775979i
$900$		0			0
$901$	−20.7237	−	35.8946i	−0.690408	−	1.19582i
$902$		0			0
$903$	4.68479	+	3.93101i	0.155900	+	0.130816i
$904$		0			0
$905$	−12.5856	+	21.7989i	−0.418359	+	0.724619i
$906$		0			0
$907$	−4.48515	−	25.4365i	−0.148927	−	0.844606i	−0.964130	−	0.265431i	$-0.914486\pi$
$907$	−4.48515	−	25.4365i	−0.148927	−	0.844606i	0.815203	−	0.579175i	$-0.196625\pi$
$908$		0			0
$909$	1.81908	+	0.662090i	0.0603350	+	0.0219601i
$910$		0			0
$911$	−15.4415			−0.511600			−0.255800	−	0.966730i	$-0.582339\pi$
$911$	−15.4415			−0.511600			−0.255800	+	0.966730i	$0.582339\pi$
$912$		0			0
$913$	−17.7847			−0.588587
$914$		0			0
$915$	5.46064	+	1.98751i	0.180523	+	0.0657050i
$916$		0			0
$917$	−1.94697	−	11.0418i	−0.0642945	−	0.364632i
$918$		0			0
$919$	4.63223	−	8.02325i	0.152803	−	0.264663i	−0.779454	−	0.626460i	$-0.784503\pi$
$919$	4.63223	−	8.02325i	0.152803	−	0.264663i	0.932257	+	0.361797i	$0.117837\pi$
$920$		0			0
$921$	−11.7344	−	9.84635i	−0.386662	−	0.324448i
$922$		0			0
$923$	−4.54963	−	7.88019i	−0.149753	−	0.259380i
$924$		0			0
$925$	−8.80928	+	3.20631i	−0.289647	+	0.105423i
$926$		0			0
$927$	−0.180045	+	1.02108i	−0.00591345	+	0.0335368i
$928$		0			0
$929$	−14.0974	+	11.8292i	−0.462522	+	0.388102i	−0.844058	−	0.536252i	$-0.819840\pi$
$929$	−14.0974	+	11.8292i	−0.462522	+	0.388102i	0.381536	+	0.924354i	$0.375395\pi$
$930$		0			0
$931$	−28.1826	−	5.18355i	−0.923646	−	0.169884i
$932$		0			0
$933$	−11.9834	+	10.0553i	−0.392319	+	0.329194i
$934$		0			0
$935$	−3.54054	+	20.0794i	−0.115788	+	0.656668i
$936$		0			0
$937$	−7.37851	+	2.68556i	−0.241045	+	0.0877333i	−0.459718	−	0.888065i	$-0.652050\pi$
$937$	−7.37851	+	2.68556i	−0.241045	+	0.0877333i	0.218673	+	0.975798i	$0.429827\pi$
$938$		0			0
$939$	−5.08125	−	8.80099i	−0.165820	−	0.287209i
$940$		0			0
$941$	−44.7656	−	37.5628i	−1.45932	−	1.22451i	−0.925408	−	0.378972i	$-0.876278\pi$
$941$	−44.7656	−	37.5628i	−1.45932	−	1.22451i	−0.533910	−	0.845542i	$-0.679278\pi$
$942$		0			0
$943$	2.74644	−	4.75698i	0.0894365	−	0.154909i
$944$		0			0
$945$	−0.152704	−	0.866025i	−0.00496745	−	0.0281718i
$946$		0			0
$947$	−33.8558	−	12.3225i	−1.10017	−	0.400428i	−0.272789	−	0.962074i	$-0.587946\pi$
$947$	−33.8558	−	12.3225i	−1.10017	−	0.400428i	−0.827377	+	0.561646i	$0.810168\pi$
$948$		0			0
$949$	9.93851			0.322618
$950$		0			0
$951$	−7.64765			−0.247992
$952$		0			0
$953$	−12.2138	−	4.44545i	−0.395643	−	0.144002i	0.136534	−	0.990635i	$-0.456404\pi$
$953$	−12.2138	−	4.44545i	−0.395643	−	0.144002i	−0.532177	+	0.846633i	$0.678626\pi$
$954$		0			0
$955$	−2.00072	−	11.3466i	−0.0647416	−	0.367168i
$956$		0			0
$957$	20.7383	−	35.9198i	0.670374	−	1.16112i
$958$		0			0
$959$	−5.27332	−	4.42484i	−0.170284	−	0.142886i
$960$		0			0
$961$	−5.41694	−	9.38241i	−0.174740	−	0.302658i
$962$		0			0
$963$	−11.4757	+	4.17680i	−0.369798	+	0.134595i
$964$		0			0
$965$	−3.96766	+	22.5017i	−0.127724	+	0.724356i
$966$		0			0
$967$	−38.5428	+	32.3413i	−1.23945	+	1.04003i	−0.241887	+	0.970304i	$0.577766\pi$
$967$	−38.5428	+	32.3413i	−1.23945	+	1.04003i	−0.997567	+	0.0697207i	$0.977789\pi$
$968$		0			0
$969$	−5.83662	+	15.6759i	−0.187499	+	0.503584i
$970$		0			0
$971$	23.5155	−	19.7318i	0.754648	−	0.633225i	−0.182080	−	0.983284i	$-0.558283\pi$
$971$	23.5155	−	19.7318i	0.754648	−	0.633225i	0.936728	+	0.350059i	$0.113839\pi$
$972$		0			0
$973$	−1.22193	+	6.92993i	−0.0391734	+	0.222163i
$974$		0			0
$975$	5.07145	−	1.84586i	0.162416	−	0.0591147i
$976$		0			0
$977$	17.5403	+	30.3807i	0.561164	+	0.971964i	0.997395	+	0.0721297i	$0.0229796\pi$
$977$	17.5403	+	30.3807i	0.561164	+	0.971964i	−0.436231	+	0.899834i	$0.643687\pi$
$978$		0			0
$979$	33.6334	+	28.2218i	1.07493	+	0.901972i
$980$		0			0
$981$	2.01367	−	3.48778i	0.0642916	−	0.111356i
$982$		0			0
$983$	−3.26130	−	18.4957i	−0.104019	−	0.589922i	−0.991608	−	0.129285i	$-0.958732\pi$
$983$	−3.26130	−	18.4957i	−0.104019	−	0.589922i	0.887588	−	0.460638i	$-0.152379\pi$
$984$		0			0
$985$	5.71941	+	2.08169i	0.182235	+	0.0663283i
$986$		0			0
$987$	8.33275			0.265234
$988$		0			0
$989$	34.0880			1.08394
$990$		0			0
$991$	−12.7208	−	4.62998i	−0.404088	−	0.147076i	0.131977	−	0.991253i	$-0.457868\pi$
$991$	−12.7208	−	4.62998i	−0.404088	−	0.147076i	−0.536065	+	0.844177i	$0.680090\pi$
$992$		0			0
$993$	0.713011	+	4.04369i	0.0226267	+	0.128323i
$994$		0			0
$995$	5.42081	−	9.38911i	0.171851	−	0.297655i
$996$		0			0
$997$	5.29086	+	4.43956i	0.167563	+	0.140602i	0.722713	−	0.691148i	$-0.242895\pi$
$997$	5.29086	+	4.43956i	0.167563	+	0.140602i	−0.555150	+	0.831750i	$0.687339\pi$
$998$		0			0
$999$	1.47178	+	2.54920i	0.0465651	+	0.0806531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.b.481.1		6
4.3	odd	2		57.2.i.a.25.1	yes	6
12.11	even	2		171.2.u.a.82.1		6
19.16	even	9	inner	912.2.bo.b.529.1		6
76.15	even	18		1083.2.a.n.1.2		3
76.23	odd	18		1083.2.a.m.1.2		3
76.35	odd	18		57.2.i.a.16.1	✓	6
228.23	even	18		3249.2.a.w.1.2		3
228.35	even	18		171.2.u.a.73.1		6
228.167	odd	18		3249.2.a.x.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.16.1	✓	6	76.35	odd	18
57.2.i.a.25.1	yes	6	4.3	odd	2
171.2.u.a.73.1		6	228.35	even	18
171.2.u.a.82.1		6	12.11	even	2
912.2.bo.b.481.1		6	1.1	even	1	trivial
912.2.bo.b.529.1		6	19.16	even	9	inner
1083.2.a.m.1.2		3	76.23	odd	18
1083.2.a.n.1.2		3	76.15	even	18
3249.2.a.w.1.2		3	228.23	even	18
3249.2.a.x.1.2		3	228.167	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{3} +(-0.233956 - 1.32683i) q^{5} +(-0.326352 + 0.565258i) q^{7} +(0.766044 + 0.642788i) q^{9} +(1.97178 + 3.41523i) q^{11} +(-1.59240 + 0.579585i) q^{13} +(-0.233956 + 1.32683i) q^{15} +(-2.93969 + 2.46669i) q^{17} +(-2.82635 + 3.31839i) q^{19} +(0.500000 - 0.419550i) q^{21} +(0.631759 - 3.58288i) q^{23} +(2.99273 - 1.08926i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(8.05690 + 6.76055i) q^{29} +(3.23396 - 5.60138i) q^{31} +(-0.684793 - 3.88365i) q^{33} +(0.826352 + 0.300767i) q^{35} -2.94356 q^{37} +1.69459 q^{39} +(1.41875 + 0.516382i) q^{41} +(1.62701 + 9.22724i) q^{43} +(0.673648 - 1.16679i) q^{45} +(9.77972 + 8.20616i) q^{47} +(3.28699 + 5.69323i) q^{49} +(3.60607 - 1.31250i) q^{51} +(-1.87551 + 10.6366i) q^{53} +(4.07011 - 3.41523i) q^{55} +(3.79086 - 2.15160i) q^{57} +(2.12449 - 1.78265i) q^{59} +(0.748970 - 4.24762i) q^{61} +(-0.613341 + 0.223238i) q^{63} +(1.14156 + 1.97724i) q^{65} +(-6.04189 - 5.06975i) q^{67} +(-1.81908 + 3.15074i) q^{69} +(0.932419 + 5.28801i) q^{71} +(-5.51114 - 2.00589i) q^{73} -3.18479 q^{75} -2.57398 q^{77} +(-2.93969 - 1.06996i) q^{79} +(0.173648 + 0.984808i) q^{81} +(-2.25490 + 3.90560i) q^{83} +(3.96064 + 3.32337i) q^{85} +(-5.25877 - 9.10846i) q^{87} +(10.4620 - 3.80785i) q^{89} +(0.192066 - 1.08926i) q^{91} +(-4.95471 + 4.15749i) q^{93} +(5.06418 + 2.97373i) q^{95} +(5.13429 - 4.30818i) q^{97} +(-0.684793 + 3.88365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} - 3 q^{7} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 12 q^{17} - 18 q^{19} + 3 q^{21} + 9 q^{23} - 3 q^{27} + 12 q^{29} + 24 q^{31} + 3 q^{33} + 6 q^{35} + 12 q^{37} + 6 q^{39} + 6 q^{41} - 18 q^{43}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^5 - 3 * q^7 - 3 * q^11 - 6 * q^13 - 6 * q^15 - 12 * q^17 - 18 * q^19 + 3 * q^21 + 9 * q^23 - 3 * q^27 + 12 * q^29 + 24 * q^31 + 3 * q^33 + 6 * q^35 + 12 * q^37 + 6 * q^39 + 6 * q^41 - 18 * q^43 + 3 * q^45 + 33 * q^47 + 12 * q^49 - 3 * q^51 - 24 * q^53 + 33 * q^55 - 9 * q^57 - 21 * q^61 + 3 * q^63 + 15 * q^65 - 30 * q^67 + 6 * q^69 - 18 * q^71 - 27 * q^73 - 12 * q^75 - 12 * q^79 - 15 * q^83 + 15 * q^85 - 9 * q^87 + 45 * q^89 + 12 * q^91 + 6 * q^93 + 12 * q^95 + 21 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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