LMFDB - Embedded newform 912.2.bo.b.385.1

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			385.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	912.385
Dual form			912.2.bo.b.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 - 0.984808i) q^{3} +(-1.93969 - 1.62760i) q^{5} +(0.266044 + 0.460802i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-2.55303 + 4.42198i) q^{11} +(0.705737 + 4.00243i) q^{13} +(-1.93969 + 1.62760i) q^{15} +(-1.82635 + 0.664738i) q^{17} +(-2.23396 - 3.74292i) q^{19} +(0.500000 - 0.181985i) q^{21} +(-2.33022 + 1.95529i) q^{23} +(0.245100 + 1.39003i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-1.51367 - 0.550931i) q^{29} +(4.93969 + 8.55580i) q^{31} +(3.91147 + 3.28212i) q^{33} +(0.233956 - 1.32683i) q^{35} +6.10607 q^{37} +4.06418 q^{39} +(-1.47178 + 8.34689i) q^{41} +(0.135630 + 0.113807i) q^{43} +(1.26604 + 2.19285i) q^{45} +(7.10354 + 2.58548i) q^{47} +(3.35844 - 5.81699i) q^{49} +(0.337496 + 1.91404i) q^{51} +(-7.58512 + 6.36467i) q^{53} +(12.1493 - 4.42198i) q^{55} +(-4.07398 + 1.55007i) q^{57} +(-3.58512 + 1.30488i) q^{59} +(-10.6702 + 8.95340i) q^{61} +(-0.0923963 - 0.524005i) q^{63} +(5.14543 - 8.91215i) q^{65} +(-9.59627 - 3.49276i) q^{67} +(1.52094 + 2.63435i) q^{69} +(-2.92855 - 2.45734i) q^{71} +(-0.322481 + 1.82888i) q^{73} +1.41147 q^{75} -2.71688 q^{77} +(-1.82635 + 10.3578i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-5.73783 - 9.93821i) q^{83} +(4.62449 + 1.68317i) q^{85} +(-0.805407 + 1.39501i) q^{87} +(-1.02869 - 5.83396i) q^{89} +(-1.65657 + 1.39003i) q^{91} +(9.28359 - 3.37895i) q^{93} +(-1.75877 + 10.8961i) q^{95} +(6.39053 - 2.32596i) q^{97} +(3.91147 - 3.28212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$	$1$

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
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$		0			0
$5$	−1.93969	−	1.62760i	−0.867457	−	0.727883i	0.0961041	−	0.995371i	$-0.469362\pi$
$5$	−1.93969	−	1.62760i	−0.867457	−	0.727883i	−0.963561	+	0.267489i	$0.913806\pi$
$6$		0			0
$7$	0.266044	+	0.460802i	0.100555	+	0.174167i	0.911914	−	0.410382i	$-0.134605\pi$
$7$	0.266044	+	0.460802i	0.100555	+	0.174167i	−0.811358	+	0.584549i	$0.801271\pi$
$8$		0			0
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$		0			0
$11$	−2.55303	+	4.42198i	−0.769769	+	1.33328i	0.167920	+	0.985801i	$0.446295\pi$
$11$	−2.55303	+	4.42198i	−0.769769	+	1.33328i	−0.937688	+	0.347478i	$0.887038\pi$
$12$		0			0
$13$	0.705737	+	4.00243i	0.195736	+	1.11008i	0.911366	+	0.411596i	$0.135029\pi$
$13$	0.705737	+	4.00243i	0.195736	+	1.11008i	−0.715630	+	0.698479i	$0.753860\pi$
$14$		0			0
$15$	−1.93969	+	1.62760i	−0.500826	+	0.420243i
$16$		0			0
$17$	−1.82635	+	0.664738i	−0.442955	+	0.161223i	−0.553862	−	0.832608i	$-0.686847\pi$
$17$	−1.82635	+	0.664738i	−0.442955	+	0.161223i	0.110907	+	0.993831i	$0.464624\pi$
$18$		0			0
$19$	−2.23396	−	3.74292i	−0.512505	−	0.858685i
$19$	−2.23396	−	3.74292i	−0.512505	−	0.858685i
$20$		0			0
$21$	0.500000	−	0.181985i	0.109109	−	0.0397124i
$22$		0			0
$23$	−2.33022	+	1.95529i	−0.485885	+	0.407706i	−0.852549	−	0.522648i	$-0.824944\pi$
$23$	−2.33022	+	1.95529i	−0.485885	+	0.407706i	0.366664	+	0.930353i	$0.380500\pi$
$24$		0			0
$25$	0.245100	+	1.39003i	0.0490200	+	0.278006i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	−1.51367	−	0.550931i	−0.281082	−	0.102305i	0.197633	−	0.980276i	$-0.436675\pi$
$29$	−1.51367	−	0.550931i	−0.281082	−	0.102305i	−0.478714	+	0.877971i	$0.658897\pi$
$30$		0			0
$31$	4.93969	+	8.55580i	0.887195	+	1.53667i	0.843177	+	0.537636i	$0.180683\pi$
$31$	4.93969	+	8.55580i	0.887195	+	1.53667i	0.0440180	+	0.999031i	$0.485984\pi$
$32$		0			0
$33$	3.91147	+	3.28212i	0.680900	+	0.571343i
$34$		0			0
$35$	0.233956	−	1.32683i	0.0395457	−	0.224275i
$36$		0			0
$37$	6.10607			1.00383			0.501916	−	0.864917i	$-0.332629\pi$
$37$	6.10607			1.00383			0.501916	+	0.864917i	$0.332629\pi$
$38$		0			0
$39$	4.06418			0.650789
$40$		0			0
$41$	−1.47178	+	8.34689i	−0.229854	+	1.30356i	0.623332	+	0.781957i	$0.285779\pi$
$41$	−1.47178	+	8.34689i	−0.229854	+	1.30356i	−0.853186	+	0.521607i	$0.825333\pi$
$42$		0			0
$43$	0.135630	+	0.113807i	0.0206833	+	0.0173554i	0.653071	−	0.757297i	$-0.273480\pi$
$43$	0.135630	+	0.113807i	0.0206833	+	0.0173554i	−0.632387	+	0.774652i	$0.717925\pi$
$44$		0			0
$45$	1.26604	+	2.19285i	0.188731	+	0.326891i
$46$		0			0
$47$	7.10354	+	2.58548i	1.03616	+	0.377131i	0.803422	−	0.595409i	$-0.203010\pi$
$47$	7.10354	+	2.58548i	1.03616	+	0.377131i	0.232735	+	0.972540i	$0.425232\pi$
$48$		0			0
$49$	3.35844	−	5.81699i	0.479777	−	0.830999i
$50$		0			0
$51$	0.337496	+	1.91404i	0.0472589	+	0.268019i
$52$		0			0
$53$	−7.58512	+	6.36467i	−1.04190	+	0.874255i	−0.992218	−	0.124510i	$-0.960264\pi$
$53$	−7.58512	+	6.36467i	−1.04190	+	0.874255i	−0.0496783	+	0.998765i	$0.515820\pi$
$54$		0			0
$55$	12.1493	−	4.42198i	1.63821	−	0.596260i
$56$		0			0
$57$	−4.07398	+	1.55007i	−0.539612	+	0.205311i
$58$		0			0
$59$	−3.58512	+	1.30488i	−0.466743	+	0.169881i	−0.564676	−	0.825312i	$-0.690999\pi$
$59$	−3.58512	+	1.30488i	−0.466743	+	0.169881i	0.0979333	+	0.995193i	$0.468777\pi$
$60$		0			0
$61$	−10.6702	+	8.95340i	−1.36618	+	1.14637i	−0.392167	+	0.919894i	$0.628274\pi$
$61$	−10.6702	+	8.95340i	−1.36618	+	1.14637i	−0.974018	+	0.226471i	$0.927281\pi$
$62$		0			0
$63$	−0.0923963	−	0.524005i	−0.0116408	−	0.0660185i
$64$		0			0
$65$	5.14543	−	8.91215i	0.638212	−	1.10542i
$66$		0			0
$67$	−9.59627	−	3.49276i	−1.17237	−	0.426708i	−0.318869	−	0.947799i	$-0.603303\pi$
$67$	−9.59627	−	3.49276i	−1.17237	−	0.426708i	−0.853501	+	0.521091i	$0.825525\pi$
$68$		0			0
$69$	1.52094	+	2.63435i	0.183100	+	0.317139i
$70$		0			0
$71$	−2.92855	−	2.45734i	−0.347555	−	0.291633i	0.452253	−	0.891890i	$-0.350621\pi$
$71$	−2.92855	−	2.45734i	−0.347555	−	0.291633i	−0.799807	+	0.600257i	$0.795065\pi$
$72$		0			0
$73$	−0.322481	+	1.82888i	−0.0377436	+	0.214055i	−0.997847	−	0.0655924i	$-0.979106\pi$
$73$	−0.322481	+	1.82888i	−0.0377436	+	0.214055i	0.960103	+	0.279647i	$0.0902174\pi$
$74$		0			0
$75$	1.41147			0.162983
$76$		0			0
$77$	−2.71688			−0.309617
$78$		0			0
$79$	−1.82635	+	10.3578i	−0.205481	+	1.16534i	0.691201	+	0.722663i	$0.257082\pi$
$79$	−1.82635	+	10.3578i	−0.205481	+	1.16534i	−0.896682	+	0.442676i	$0.854029\pi$
$80$		0			0
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$		0			0
$83$	−5.73783	−	9.93821i	−0.629808	−	1.09086i	−0.987590	−	0.157055i	$-0.949800\pi$
$83$	−5.73783	−	9.93821i	−0.629808	−	1.09086i	0.357782	−	0.933805i	$-0.383533\pi$
$84$		0			0
$85$	4.62449	+	1.68317i	0.501596	+	0.182566i
$86$		0			0
$87$	−0.805407	+	1.39501i	−0.0863487	+	0.149560i
$88$		0			0
$89$	−1.02869	−	5.83396i	−0.109040	−	0.618399i	−0.989529	−	0.144332i	$-0.953897\pi$
$89$	−1.02869	−	5.83396i	−0.109040	−	0.618399i	0.880489	−	0.474067i	$-0.157214\pi$
$90$		0			0
$91$	−1.65657	+	1.39003i	−0.173656	+	0.145715i
$92$		0			0
$93$	9.28359	−	3.37895i	0.962663	−	0.350381i
$94$		0			0
$95$	−1.75877	+	10.8961i	−0.180446	+	1.11792i
$96$		0			0
$97$	6.39053	−	2.32596i	0.648860	−	0.236166i	0.00344055	−	0.999994i	$-0.498905\pi$
$97$	6.39053	−	2.32596i	0.648860	−	0.236166i	0.645419	+	0.763828i	$0.276683\pi$
$98$		0			0
$99$	3.91147	−	3.28212i	0.393118	−	0.329865i
$100$		0			0
$101$	−1.52094	−	8.62571i	−0.151340	−	0.858290i	−0.962056	−	0.272851i	$-0.912033\pi$
$101$	−1.52094	−	8.62571i	−0.151340	−	0.858290i	0.810717	−	0.585439i	$-0.199078\pi$
$102$		0			0
$103$	−1.92262	+	3.33007i	−0.189441	+	0.328122i	−0.945064	−	0.326885i	$-0.894001\pi$
$103$	−1.92262	+	3.33007i	−0.189441	+	0.328122i	0.755623	+	0.655007i	$0.227334\pi$
$104$		0			0
$105$	−1.26604	−	0.460802i	−0.123553	−	0.0449697i
$106$		0			0
$107$	−2.83750	−	4.91469i	−0.274311	−	0.475121i	0.695650	−	0.718381i	$-0.255116\pi$
$107$	−2.83750	−	4.91469i	−0.274311	−	0.475121i	−0.969961	+	0.243260i	$0.921783\pi$
$108$		0			0
$109$	−1.59833	−	1.34115i	−0.153092	−	0.128459i	0.563025	−	0.826440i	$-0.309638\pi$
$109$	−1.59833	−	1.34115i	−0.153092	−	0.128459i	−0.716116	+	0.697981i	$0.754082\pi$
$110$		0			0
$111$	1.06031	−	6.01330i	0.100640	−	0.570757i
$112$		0			0
$113$	7.27631			0.684498			0.342249	−	0.939609i	$-0.388811\pi$
$113$	7.27631			0.684498			0.342249	+	0.939609i	$0.388811\pi$
$114$		0			0
$115$	7.70233			0.718246
$116$		0			0
$117$	0.705737	−	4.00243i	0.0652454	−	0.370025i
$118$		0			0
$119$	−0.792204	−	0.664738i	−0.0726212	−	0.0609364i
$120$		0			0
$121$	−7.53596	−	13.0527i	−0.685087	−	1.18661i
$122$		0			0
$123$	7.96451	+	2.89884i	0.718135	+	0.261380i
$124$		0			0
$125$	−4.54323	+	7.86911i	−0.406359	+	0.703835i
$126$		0			0
$127$	−0.317734	−	1.80196i	−0.0281943	−	0.159898i	0.967460	−	0.253024i	$-0.0814251\pi$
$127$	−0.317734	−	1.80196i	−0.0281943	−	0.159898i	−0.995654	+	0.0931261i	$0.970314\pi$
$128$		0			0
$129$	0.135630	−	0.113807i	0.0119415	−	0.0100201i
$130$		0			0
$131$	−8.25624	+	3.00503i	−0.721351	+	0.262550i	−0.676499	−	0.736443i	$-0.736504\pi$
$131$	−8.25624	+	3.00503i	−0.721351	+	0.262550i	−0.0448520	+	0.998994i	$0.514282\pi$
$132$		0			0
$133$	1.13041	−	2.02520i	0.0980194	−	0.175607i
$134$		0			0
$135$	2.37939	−	0.866025i	0.204785	−	0.0745356i
$136$		0			0
$137$	−9.67546	+	8.11867i	−0.826630	+	0.693625i	−0.954515	−	0.298164i	$-0.903626\pi$
$137$	−9.67546	+	8.11867i	−0.826630	+	0.693625i	0.127884	+	0.991789i	$0.459181\pi$
$138$		0			0
$139$	0.703211	+	3.98811i	0.0596456	+	0.338267i	0.999998	−	0.00193468i	$-0.000615830\pi$
$139$	0.703211	+	3.98811i	0.0596456	+	0.338267i	−0.940353	+	0.340201i	$0.889505\pi$
$140$		0			0
$141$	3.77972	−	6.54666i	0.318309	−	0.551328i
$142$		0			0
$143$	−19.5005	−	7.09759i	−1.63071	−	0.593530i
$144$		0			0
$145$	2.03936	+	3.53228i	0.169360	+	0.293340i
$146$		0			0
$147$	−5.14543	−	4.31753i	−0.424388	−	0.356104i
$148$		0			0
$149$	1.05391	−	5.97702i	0.0863397	−	0.489657i	−0.910720	−	0.413025i	$-0.864472\pi$
$149$	1.05391	−	5.97702i	0.0863397	−	0.489657i	0.997059	−	0.0766320i	$-0.0244167\pi$
$150$		0			0
$151$	0.162504			0.0132244			0.00661219	−	0.999978i	$-0.497895\pi$
$151$	0.162504			0.0132244			0.00661219	+	0.999978i	$0.497895\pi$
$152$		0			0
$153$	1.94356			0.157128
$154$		0			0
$155$	4.34389	−	24.6354i	0.348910	−	1.97877i
$156$		0			0
$157$	5.10220	+	4.28125i	0.407200	+	0.341681i	0.823269	−	0.567652i	$-0.192148\pi$
$157$	5.10220	+	4.28125i	0.407200	+	0.341681i	−0.416069	+	0.909333i	$0.636593\pi$
$158$		0			0
$159$	4.95084	+	8.57510i	0.392627	+	0.680050i
$160$		0			0
$161$	−1.52094	−	0.553579i	−0.119867	−	0.0436281i
$162$		0			0
$163$	−0.224155	+	0.388249i	−0.0175572	+	0.0304100i	−0.874671	−	0.484718i	$-0.838922\pi$
$163$	−0.224155	+	0.388249i	−0.0175572	+	0.0304100i	0.857113	+	0.515128i	$0.172256\pi$
$164$		0			0
$165$	−2.24510	−	12.7326i	−0.174781	−	0.991231i
$166$		0			0
$167$	−2.59627	+	2.17853i	−0.200905	+	0.168579i	−0.737690	−	0.675140i	$-0.764083\pi$
$167$	−2.59627	+	2.17853i	−0.200905	+	0.168579i	0.536785	+	0.843719i	$0.319639\pi$
$168$		0			0
$169$	−3.30541	+	1.20307i	−0.254262	+	0.0925438i
$170$		0			0
$171$	0.819078	+	4.28125i	0.0626364	+	0.327395i
$172$		0			0
$173$	1.51842	−	0.552659i	0.115443	−	0.0420179i	−0.283653	−	0.958927i	$-0.591546\pi$
$173$	1.51842	−	0.552659i	0.115443	−	0.0420179i	0.399096	+	0.916909i	$0.369324\pi$
$174$		0			0
$175$	−0.575322	+	0.482753i	−0.0434903	+	0.0364927i
$176$		0			0
$177$	0.662504	+	3.75725i	0.0497968	+	0.282412i
$178$		0			0
$179$	1.05690	−	1.83061i	0.0789967	−	0.136826i	−0.823821	−	0.566851i	$-0.808162\pi$
$179$	1.05690	−	1.83061i	0.0789967	−	0.136826i	0.902817	+	0.430024i	$0.141495\pi$
$180$		0			0
$181$	−8.22416	−	2.99335i	−0.611297	−	0.222494i	0.0177739	−	0.999842i	$-0.494342\pi$
$181$	−8.22416	−	2.99335i	−0.611297	−	0.222494i	−0.629071	+	0.777348i	$0.716564\pi$
$182$		0			0
$183$	6.96451	+	12.0629i	0.514831	+	0.891714i
$184$		0			0
$185$	−11.8439	−	9.93821i	−0.870780	−	0.730671i
$186$		0			0
$187$	1.72328	−	9.77320i	0.126019	−	0.714687i
$188$		0			0
$189$	−0.532089			−0.0387038
$190$		0			0
$191$	19.0719			1.38000			0.689998	−	0.723811i	$-0.257611\pi$
$191$	19.0719			1.38000			0.689998	+	0.723811i	$0.257611\pi$
$192$		0			0
$193$	−4.13903	+	23.4736i	−0.297934	+	1.68967i	0.357098	+	0.934067i	$0.383766\pi$
$193$	−4.13903	+	23.4736i	−0.297934	+	1.68967i	−0.655032	+	0.755601i	$0.727345\pi$
$194$		0			0
$195$	−7.88326	−	6.61484i	−0.564532	−	0.473698i
$196$		0			0
$197$	2.19459	+	3.80115i	0.156358	+	0.270820i	0.933553	−	0.358440i	$-0.116691\pi$
$197$	2.19459	+	3.80115i	0.156358	+	0.270820i	−0.777195	+	0.629260i	$0.783358\pi$
$198$		0			0
$199$	−18.8293	−	6.85332i	−1.33478	−	0.485819i	−0.426613	−	0.904434i	$-0.640293\pi$
$199$	−18.8293	−	6.85332i	−1.33478	−	0.485819i	−0.908164	+	0.418615i	$0.862516\pi$
$200$		0			0
$201$	−5.10607	+	8.84397i	−0.360154	+	0.623805i
$202$		0			0
$203$	−0.148833	−	0.844075i	−0.0104460	−	0.0592425i
$204$		0			0
$205$	16.4402	−	13.7949i	1.14823	−	0.963480i
$206$		0			0
$207$	2.85844	−	1.04039i	0.198675	−	0.0723119i
$208$		0			0
$209$	22.2545	−	0.322718i	1.53938	−	0.0223228i
$210$		0			0
$211$	25.5526	−	9.30039i	1.75912	−	0.640266i	0.759172	−	0.650891i	$-0.225604\pi$
$211$	25.5526	−	9.30039i	1.75912	−	0.640266i	0.999944	+	0.0106250i	$0.00338212\pi$
$212$		0			0
$213$	−2.92855	+	2.45734i	−0.200661	+	0.168374i
$214$		0			0
$215$	−0.0778483	−	0.441500i	−0.00530921	−	0.0301100i
$216$		0			0
$217$	−2.62836	+	4.55245i	−0.178424	+	0.309040i
$218$		0			0
$219$	1.74510	+	0.635164i	0.117923	+	0.0429204i
$220$		0			0
$221$	−3.94949	−	6.84072i	−0.265672	−	0.460157i
$222$		0			0
$223$	9.20233	+	7.72167i	0.616234	+	0.517082i	0.896617	−	0.442807i	$-0.146017\pi$
$223$	9.20233	+	7.72167i	0.616234	+	0.517082i	−0.280383	+	0.959888i	$0.590462\pi$
$224$		0			0
$225$	0.245100	−	1.39003i	0.0163400	−	0.0926687i
$226$		0			0
$227$	−4.34049			−0.288088			−0.144044	−	0.989571i	$-0.546011\pi$
$227$	−4.34049			−0.288088			−0.144044	+	0.989571i	$0.546011\pi$
$228$		0			0
$229$	3.29591			0.217800			0.108900	−	0.994053i	$-0.465267\pi$
$229$	3.29591			0.217800			0.108900	+	0.994053i	$0.465267\pi$
$230$		0			0
$231$	−0.471782	+	2.67561i	−0.0310409	+	0.176042i
$232$		0			0
$233$	−11.8209	−	9.91890i	−0.774412	−	0.649809i	0.167423	−	0.985885i	$-0.446456\pi$
$233$	−11.8209	−	9.91890i	−0.774412	−	0.649809i	−0.941835	+	0.336076i	$0.890900\pi$
$234$		0			0
$235$	−9.57057	−	16.5767i	−0.624315	−	1.08135i
$236$		0			0
$237$	9.88326	+	3.59721i	0.641986	+	0.233664i
$238$		0			0
$239$	7.91147	−	13.7031i	0.511751	−	0.886378i	−0.488156	−	0.872756i	$-0.662330\pi$
$239$	7.91147	−	13.7031i	0.511751	−	0.886378i	0.999907	−	0.0136221i	$-0.00433619\pi$
$240$		0			0
$241$	−4.10607	−	23.2867i	−0.264495	−	1.50003i	−0.770469	−	0.637477i	$-0.779978\pi$
$241$	−4.10607	−	23.2867i	−0.264495	−	1.50003i	0.505974	−	0.862549i	$-0.331133\pi$
$242$		0			0
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$		0			0
$245$	−15.9820	+	5.81699i	−1.02106	+	0.371634i
$246$		0			0
$247$	13.4042	−	11.5828i	0.852889	−	0.736994i
$248$		0			0
$249$	−10.7836	+	3.92490i	−0.683382	+	0.248731i
$250$		0			0
$251$	−14.8701	+	12.4775i	−0.938589	+	0.787570i	−0.977339	−	0.211679i	$-0.932107\pi$
$251$	−14.8701	+	12.4775i	−0.938589	+	0.787570i	0.0387499	+	0.999249i	$0.487662\pi$
$252$		0			0
$253$	−2.69712	−	15.2961i	−0.169566	−	0.961659i
$254$		0			0
$255$	2.46064	−	4.26195i	0.154091	−	0.266894i
$256$		0			0
$257$	−11.5544	−	4.20545i	−0.720742	−	0.262329i	−0.0445014	−	0.999009i	$-0.514170\pi$
$257$	−11.5544	−	4.20545i	−0.720742	−	0.262329i	−0.676241	+	0.736681i	$0.736392\pi$
$258$		0			0
$259$	1.62449	+	2.81369i	0.100941	+	0.174834i
$260$		0			0
$261$	1.23396	+	1.03541i	0.0763799	+	0.0640904i
$262$		0			0
$263$	−1.10101	+	6.24416i	−0.0678915	+	0.385032i	0.931862	+	0.362814i	$0.118184\pi$
$263$	−1.10101	+	6.24416i	−0.0678915	+	0.385032i	−0.999753	+	0.0222179i	$0.992927\pi$
$264$		0			0
$265$	25.0719			1.54016
$266$		0			0
$267$	−5.92396			−0.362541
$268$		0			0
$269$	−0.403733	+	2.28969i	−0.0246161	+	0.139605i	−0.994639	−	0.103409i	$-0.967025\pi$
$269$	−0.403733	+	2.28969i	−0.0246161	+	0.139605i	0.970023	+	0.243014i	$0.0781360\pi$
$270$		0			0
$271$	−11.4474	−	9.60554i	−0.695382	−	0.583495i	0.225074	−	0.974342i	$-0.427738\pi$
$271$	−11.4474	−	9.60554i	−0.695382	−	0.583495i	−0.920456	+	0.390847i	$0.872182\pi$
$272$		0			0
$273$	1.08125	+	1.87278i	0.0654403	+	0.113346i
$274$		0			0
$275$	−6.77244	−	2.46497i	−0.408394	−	0.148643i
$276$		0			0
$277$	11.9829	−	20.7550i	0.719984	−	1.24705i	−0.241021	−	0.970520i	$-0.577482\pi$
$277$	11.9829	−	20.7550i	0.719984	−	1.24705i	0.961005	−	0.276529i	$-0.0891843\pi$
$278$		0			0
$279$	−1.71554	−	9.72930i	−0.102707	−	0.582478i
$280$		0			0
$281$	19.5804	−	16.4299i	1.16807	−	0.980125i	0.168083	−	0.985773i	$-0.446242\pi$
$281$	19.5804	−	16.4299i	1.16807	−	0.980125i	0.999984	+	0.00564805i	$0.00179784\pi$
$282$		0			0
$283$	−7.05778	+	2.56882i	−0.419542	+	0.152701i	−0.543160	−	0.839629i	$-0.682772\pi$
$283$	−7.05778	+	2.56882i	−0.419542	+	0.152701i	0.123619	+	0.992330i	$0.460550\pi$
$284$		0			0
$285$	10.4251	+	3.62414i	0.617532	+	0.214675i
$286$		0			0
$287$	−4.23783	+	1.54244i	−0.250151	+	0.0910475i
$288$		0			0
$289$	−10.1291	+	8.49930i	−0.595828	+	0.499959i
$290$		0			0
$291$	−1.18092	−	6.69734i	−0.0692269	−	0.392605i
$292$		0			0
$293$	−7.38326	+	12.7882i	−0.431334	+	0.747093i	−0.996989	−	0.0775495i	$-0.975290\pi$
$293$	−7.38326	+	12.7882i	−0.431334	+	0.747093i	0.565654	+	0.824643i	$0.308624\pi$
$294$		0			0
$295$	9.07785	+	3.30407i	0.528533	+	0.192370i
$296$		0			0
$297$	−2.55303	−	4.42198i	−0.148142	−	0.256590i
$298$		0			0
$299$	−9.47044	−	7.94664i	−0.547690	−	0.459566i
$300$		0			0
$301$	−0.0163589	+	0.0927760i	−0.000942912	+	0.00534752i
$302$		0			0
$303$	−8.75877			−0.503178
$304$		0			0
$305$	35.2695			2.01953
$306$		0			0
$307$	−0.957234	+	5.42874i	−0.0546322	+	0.309835i	−0.999863	−	0.0165689i	$-0.994726\pi$
$307$	−0.957234	+	5.42874i	−0.0546322	+	0.309835i	0.945231	+	0.326404i	$0.105837\pi$
$308$		0			0
$309$	2.94562	+	2.47167i	0.167571	+	0.140608i
$310$		0			0
$311$	8.69981	+	15.0685i	0.493321	+	0.854457i	0.999970	−	0.00769537i	$-0.00244954\pi$
$311$	8.69981	+	15.0685i	0.493321	+	0.854457i	−0.506650	+	0.862152i	$0.669116\pi$
$312$		0			0
$313$	−14.9820	−	5.45302i	−0.846835	−	0.308223i	−0.118086	−	0.993003i	$-0.537676\pi$
$313$	−14.9820	−	5.45302i	−0.846835	−	0.308223i	−0.728749	+	0.684780i	$0.759898\pi$
$314$		0			0
$315$	−0.673648	+	1.16679i	−0.0379558	+	0.0657413i
$316$		0			0
$317$	0.342711	+	1.94361i	0.0192486	+	0.109164i	0.992918	−	0.118799i	$-0.0379045\pi$
$317$	0.342711	+	1.94361i	0.0192486	+	0.109164i	−0.973670	+	0.227963i	$0.926793\pi$
$318$		0			0
$319$	6.30066	−	5.28688i	0.352769	−	0.296009i
$320$		0			0
$321$	−5.33275	+	1.94096i	−0.297645	+	0.108334i
$322$		0			0
$323$	6.56805	+	5.35089i	0.365456	+	0.297732i
$324$		0			0
$325$	−5.39053	+	1.96199i	−0.299013	+	0.108832i
$326$		0			0
$327$	−1.59833	+	1.34115i	−0.0883876	+	0.0741660i
$328$		0			0
$329$	0.698463	+	3.96118i	0.0385075	+	0.218387i
$330$		0			0
$331$	−0.418748	+	0.725293i	−0.0230165	+	0.0398657i	−0.877304	−	0.479935i	$-0.840660\pi$
$331$	−0.418748	+	0.725293i	−0.0230165	+	0.0398657i	0.854288	+	0.519800i	$0.173994\pi$
$332$		0			0
$333$	−5.73783	−	2.08840i	−0.314431	−	0.114443i
$334$		0			0
$335$	12.9290	+	22.3937i	0.706388	+	1.22350i
$336$		0			0
$337$	−2.54916	−	2.13900i	−0.138862	−	0.116519i	0.570711	−	0.821151i	$-0.306668\pi$
$337$	−2.54916	−	2.13900i	−0.138862	−	0.116519i	−0.709573	+	0.704632i	$0.751112\pi$
$338$		0			0
$339$	1.26352	−	7.16577i	0.0686249	−	0.389191i
$340$		0			0
$341$	−50.4448			−2.73174
$342$		0			0
$343$	7.29860			0.394087
$344$		0			0
$345$	1.33750	−	7.58532i	0.0720084	−	0.408380i
$346$		0			0
$347$	−3.07011	−	2.57613i	−0.164812	−	0.138294i	0.556652	−	0.830746i	$-0.312086\pi$
$347$	−3.07011	−	2.57613i	−0.164812	−	0.138294i	−0.721464	+	0.692452i	$0.756530\pi$
$348$		0			0
$349$	13.9513	+	24.1644i	0.746796	+	1.29349i	0.949351	+	0.314218i	$0.101742\pi$
$349$	13.9513	+	24.1644i	0.746796	+	1.29349i	−0.202555	+	0.979271i	$0.564924\pi$
$350$		0			0
$351$	−3.81908	−	1.39003i	−0.203847	−	0.0741943i
$352$		0			0
$353$	−6.47178	+	11.2095i	−0.344458	+	0.596619i	−0.985255	−	0.171091i	$-0.945271\pi$
$353$	−6.47178	+	11.2095i	−0.344458	+	0.596619i	0.640797	+	0.767710i	$0.278604\pi$
$354$		0			0
$355$	1.68092	+	9.53298i	0.0892141	+	0.505958i
$356$		0			0
$357$	−0.792204	+	0.664738i	−0.0419279	+	0.0351816i
$358$		0			0
$359$	10.7562	−	3.91495i	0.567693	−	0.206623i	−0.0421972	−	0.999109i	$-0.513436\pi$
$359$	10.7562	−	3.91495i	0.567693	−	0.206623i	0.609890	+	0.792486i	$0.291214\pi$
$360$		0			0
$361$	−9.01889	+	16.7230i	−0.474678	+	0.880159i
$362$		0			0
$363$	−14.1630	+	5.15490i	−0.743363	+	0.270562i
$364$		0			0
$365$	3.60220	−	3.02260i	0.188548	−	0.158210i
$366$		0			0
$367$	4.96657	+	28.1668i	0.259253	+	1.47030i	0.784916	+	0.619602i	$0.212706\pi$
$367$	4.96657	+	28.1668i	0.259253	+	1.47030i	−0.525663	+	0.850693i	$0.676183\pi$
$368$		0			0
$369$	4.23783	−	7.34013i	0.220612	−	0.382112i
$370$		0			0
$371$	−4.95084	−	1.80196i	−0.257035	−	0.0935530i
$372$		0			0
$373$	6.28312	+	10.8827i	0.325328	+	0.563484i	0.981579	−	0.191059i	$-0.0611921\pi$
$373$	6.28312	+	10.8827i	0.325328	+	0.563484i	−0.656251	+	0.754543i	$0.727859\pi$
$374$		0			0
$375$	6.96064	+	5.84067i	0.359446	+	0.301611i
$376$		0			0
$377$	1.13681	−	6.44718i	0.0585488	−	0.332047i
$378$		0			0
$379$	2.19934			0.112973			0.0564863	−	0.998403i	$-0.482010\pi$
$379$	2.19934			0.112973			0.0564863	+	0.998403i	$0.482010\pi$
$380$		0			0
$381$	−1.82976			−0.0937412
$382$		0			0
$383$	1.02940	−	5.83802i	0.0525999	−	0.298309i	−0.947147	−	0.320799i	$-0.896048\pi$
$383$	1.02940	−	5.83802i	0.0525999	−	0.298309i	0.999747	+	0.0224905i	$0.00715956\pi$
$384$		0			0
$385$	5.26991	+	4.42198i	0.268580	+	0.225365i
$386$		0			0
$387$	−0.0885259	−	0.153331i	−0.00450002	−	0.00779427i
$388$		0			0
$389$	31.1215	+	11.3273i	1.57793	+	0.574318i	0.974752	−	0.223292i	$-0.0716804\pi$
$389$	31.1215	+	11.3273i	1.57793	+	0.574318i	0.603174	+	0.797610i	$0.293903\pi$
$390$		0			0
$391$	2.95605	−	5.12003i	0.149494	−	0.258931i
$392$		0			0
$393$	1.52569	+	8.65263i	0.0769610	+	0.436467i
$394$		0			0
$395$	20.4008	−	17.1183i	1.02648	−	0.861315i
$396$		0			0
$397$	24.4786	−	8.90950i	1.22855	−	0.447155i	0.355448	−	0.934696i	$-0.384328\pi$
$397$	24.4786	−	8.90950i	1.22855	−	0.447155i	0.873100	+	0.487541i	$0.162106\pi$
$398$		0			0
$399$	−1.79813	−	1.46491i	−0.0900193	−	0.0733374i
$400$		0			0
$401$	15.0052	−	5.46145i	0.749325	−	0.272732i	0.0610031	−	0.998138i	$-0.480570\pi$
$401$	15.0052	−	5.46145i	0.749325	−	0.272732i	0.688322	+	0.725406i	$0.258348\pi$
$402$		0			0
$403$	−30.7579	+	25.8089i	−1.53216	+	1.28563i
$404$		0			0
$405$	−0.439693	−	2.49362i	−0.0218485	−	0.123909i
$406$		0			0
$407$	−15.5890	+	27.0009i	−0.772718	+	1.33839i
$408$		0			0
$409$	2.77079	+	1.00849i	0.137007	+	0.0498664i	0.409614	−	0.912259i	$-0.365664\pi$
$409$	2.77079	+	1.00849i	0.137007	+	0.0498664i	−0.272607	+	0.962126i	$0.587886\pi$
$410$		0			0
$411$	6.31521	+	10.9383i	0.311506	+	0.539545i
$412$		0			0
$413$	−1.55509	−	1.30488i	−0.0765211	−	0.0642088i
$414$		0			0
$415$	−5.04576	+	28.6159i	−0.247687	+	1.40470i
$416$		0			0
$417$	4.04963			0.198311
$418$		0			0
$419$	33.4962			1.63640			0.818198	−	0.574937i	$-0.194973\pi$
$419$	33.4962			1.63640			0.818198	+	0.574937i	$0.194973\pi$
$420$		0			0
$421$	3.12877	−	17.7441i	0.152487	−	0.864795i	−0.808561	−	0.588412i	$-0.799753\pi$
$421$	3.12877	−	17.7441i	0.152487	−	0.864795i	0.961048	−	0.276383i	$-0.0891357\pi$
$422$		0			0
$423$	−5.79086	−	4.85911i	−0.281561	−	0.236258i
$424$		0			0
$425$	−1.37164	−	2.37576i	−0.0665345	−	0.115241i
$426$		0			0
$427$	−6.96451	−	2.53487i	−0.337036	−	0.122671i
$428$		0			0
$429$	−10.3760	+	17.9717i	−0.500957	+	0.867683i
$430$		0			0
$431$	−3.70233	−	20.9970i	−0.178335	−	1.01139i	−0.934223	−	0.356688i	$-0.883906\pi$
$431$	−3.70233	−	20.9970i	−0.178335	−	1.01139i	0.755888	−	0.654701i	$-0.227205\pi$
$432$		0			0
$433$	−16.8931	+	14.1750i	−0.811828	+	0.681205i	−0.951043	−	0.309057i	$-0.899987\pi$
$433$	−16.8931	+	14.1750i	−0.811828	+	0.681205i	0.139215	+	0.990262i	$0.455542\pi$
$434$		0			0
$435$	3.83275	−	1.39501i	0.183766	−	0.0668854i
$436$		0			0
$437$	12.5241	+	4.35381i	0.599109	+	0.208271i
$438$		0			0
$439$	−3.18257	+	1.15836i	−0.151896	+	0.0552856i	−0.416849	−	0.908976i	$-0.636866\pi$
$439$	−3.18257	+	1.15836i	−0.151896	+	0.0552856i	0.264953	+	0.964261i	$0.414643\pi$
$440$		0			0
$441$	−5.14543	+	4.31753i	−0.245020	+	0.205597i
$442$		0			0
$443$	5.23799	+	29.7061i	0.248864	+	1.41138i	0.811344	+	0.584569i	$0.198736\pi$
$443$	5.23799	+	29.7061i	0.248864	+	1.41138i	−0.562480	+	0.826811i	$0.690153\pi$
$444$		0			0
$445$	−7.50000	+	12.9904i	−0.355534	+	0.615803i
$446$		0			0
$447$	−5.70321	−	2.07580i	−0.269753	−	0.0981819i
$448$		0			0
$449$	15.4559	+	26.7704i	0.729409	+	1.26337i	0.957134	+	0.289647i	$0.0935380\pi$
$449$	15.4559	+	26.7704i	0.729409	+	1.26337i	−0.227725	+	0.973725i	$0.573129\pi$
$450$		0			0
$451$	−33.1523	−	27.8181i	−1.56108	−	1.30990i
$452$		0			0
$453$	0.0282185	−	0.160035i	0.00132582	−	0.00751910i
$454$		0			0
$455$	5.47565			0.256703
$456$		0			0
$457$	−39.0479			−1.82658			−0.913291	−	0.407307i	$-0.866468\pi$
$457$	−39.0479			−1.82658			−0.913291	+	0.407307i	$0.866468\pi$
$458$		0			0
$459$	0.337496	−	1.91404i	0.0157530	−	0.0893395i
$460$		0			0
$461$	−1.15476	−	0.968961i	−0.0537827	−	0.0451290i	0.615500	−	0.788137i	$-0.288954\pi$
$461$	−1.15476	−	0.968961i	−0.0537827	−	0.0451290i	−0.669283	+	0.743008i	$0.733399\pi$
$462$		0			0
$463$	−1.64156	−	2.84326i	−0.0762897	−	0.132138i	0.825357	−	0.564612i	$-0.190974\pi$
$463$	−1.64156	−	2.84326i	−0.0762897	−	0.132138i	−0.901646	+	0.432474i	$0.857641\pi$
$464$		0			0
$465$	−23.5069	−	8.55580i	−1.09010	−	0.396766i
$466$		0			0
$467$	−11.4436	+	19.8208i	−0.529545	+	0.917199i	0.469861	+	0.882740i	$0.344304\pi$
$467$	−11.4436	+	19.8208i	−0.529545	+	0.917199i	−0.999406	+	0.0344584i	$0.989029\pi$
$468$		0			0
$469$	−0.943563	−	5.35121i	−0.0435697	−	0.247096i
$470$		0			0
$471$	5.10220	−	4.28125i	0.235097	−	0.197270i
$472$		0			0
$473$	−0.849518	+	0.309199i	−0.0390609	+	0.0142170i
$474$		0			0
$475$	4.65523	−	4.02266i	0.213597	−	0.184572i
$476$		0			0
$477$	9.30453	−	3.38657i	0.426025	−	0.155060i
$478$		0			0
$479$	7.39827	−	6.20789i	0.338036	−	0.283646i	−0.457929	−	0.888989i	$-0.651409\pi$
$479$	7.39827	−	6.20789i	0.338036	−	0.283646i	0.795965	+	0.605343i	$0.206964\pi$
$480$		0			0
$481$	4.30928	+	24.4391i	0.196486	+	1.11433i
$482$		0			0
$483$	−0.809278	+	1.40171i	−0.0368234	+	0.0637800i
$484$		0			0
$485$	−16.1814	−	5.88954i	−0.734759	−	0.267430i
$486$		0			0
$487$	−11.2554	−	19.4949i	−0.510029	−	0.883397i	−0.999932	−	0.0116199i	$-0.996301\pi$
$487$	−11.2554	−	19.4949i	−0.510029	−	0.883397i	0.489903	−	0.871777i	$-0.337032\pi$
$488$		0			0
$489$	0.343426	+	0.288169i	0.0155303	+	0.0130314i
$490$		0			0
$491$	−1.26264	+	7.16079i	−0.0569822	+	0.323162i	−0.999953	−	0.00971390i	$-0.996908\pi$
$491$	−1.26264	+	7.16079i	−0.0569822	+	0.323162i	0.942971	+	0.332876i	$0.108019\pi$
$492$		0			0
$493$	3.13072			0.141001
$494$		0			0
$495$	−12.9290			−0.581116
$496$		0			0
$497$	0.353226	−	2.00324i	0.0158444	−	0.0898578i
$498$		0			0
$499$	9.81386	+	8.23481i	0.439329	+	0.368641i	0.835458	−	0.549554i	$-0.185202\pi$
$499$	9.81386	+	8.23481i	0.439329	+	0.368641i	−0.396129	+	0.918195i	$0.629647\pi$
$500$		0			0
$501$	1.69459	+	2.93512i	0.0757088	+	0.131132i
$502$		0			0
$503$	7.86571	+	2.86289i	0.350715	+	0.127650i	0.511370	−	0.859361i	$-0.329138\pi$
$503$	7.86571	+	2.86289i	0.350715	+	0.127650i	−0.160655	+	0.987011i	$0.551361\pi$
$504$		0			0
$505$	−11.0890	+	19.2067i	−0.493454	+	0.854687i
$506$		0			0
$507$	0.610815	+	3.46410i	0.0271272	+	0.153846i
$508$		0			0
$509$	10.4816	−	8.79509i	0.464588	−	0.389836i	−0.380228	−	0.924893i	$-0.624154\pi$
$509$	10.4816	−	8.79509i	0.464588	−	0.389836i	0.844816	+	0.535057i	$0.179710\pi$
$510$		0			0
$511$	−0.928548	+	0.337964i	−0.0410766	+	0.0149506i
$512$		0			0
$513$	4.35844	−	0.0632028i	0.192430	−	0.00279047i
$514$		0			0
$515$	9.14930	−	3.33007i	0.403166	−	0.146741i
$516$		0			0
$517$	−29.5685	+	24.8109i	−1.30042	+	1.09118i
$518$		0			0
$519$	−0.280592	−	1.59132i	−0.0123166	−	0.0698511i
$520$		0			0
$521$	8.48205	−	14.6913i	0.371605	−	0.643639i	−0.618207	−	0.786015i	$-0.712141\pi$
$521$	8.48205	−	14.6913i	0.371605	−	0.643639i	0.989813	+	0.142376i	$0.0454741\pi$
$522$		0			0
$523$	−3.67112	−	1.33618i	−0.160527	−	0.0584270i	0.260507	−	0.965472i	$-0.416110\pi$
$523$	−3.67112	−	1.33618i	−0.160527	−	0.0584270i	−0.421034	+	0.907045i	$0.638333\pi$
$524$		0			0
$525$	0.375515	+	0.650411i	0.0163888	+	0.0283863i
$526$		0			0
$527$	−14.7090	−	12.3423i	−0.640733	−	0.537639i
$528$		0			0
$529$	−2.38713	+	13.5381i	−0.103788	+	0.588611i
$530$		0			0
$531$	3.81521			0.165566
$532$		0			0
$533$	−34.4466			−1.49205
$534$		0			0
$535$	−2.49525	+	14.1513i	−0.107879	+	0.611813i
$536$		0			0
$537$	−1.61927	−	1.35873i	−0.0698767	−	0.0586335i
$538$		0			0
$539$	17.1484	+	29.7019i	0.738635	+	1.27935i
$540$		0			0
$541$	−12.4017	−	4.51384i	−0.533190	−	0.194065i	0.0613724	−	0.998115i	$-0.480452\pi$
$541$	−12.4017	−	4.51384i	−0.533190	−	0.194065i	−0.594562	+	0.804050i	$0.702675\pi$
$542$		0			0
$543$	−4.37598	+	7.57942i	−0.187791	+	0.325264i
$544$		0			0
$545$	0.917404	+	5.20286i	0.0392973	+	0.222866i
$546$		0			0
$547$	24.1878	−	20.2960i	1.03420	−	0.867793i	0.0428509	−	0.999081i	$-0.486356\pi$
$547$	24.1878	−	20.2960i	1.03420	−	0.867793i	0.991344	+	0.131289i	$0.0419115\pi$
$548$		0			0
$549$	13.0890	−	4.76400i	0.558625	−	0.203323i
$550$		0			0
$551$	1.31938	+	6.89630i	0.0562076	+	0.293792i
$552$		0			0
$553$	−5.25877	+	1.91404i	−0.223626	+	0.0813931i
$554$		0			0
$555$	−11.8439	+	9.93821i	−0.502745	+	0.421853i
$556$		0			0
$557$	6.18748	+	35.0909i	0.262172	+	1.48685i	0.776969	+	0.629539i	$0.216756\pi$
$557$	6.18748	+	35.0909i	0.262172	+	1.48685i	−0.514797	+	0.857312i	$0.672133\pi$
$558$		0			0
$559$	−0.359785	+	0.623166i	−0.0152173	+	0.0263571i
$560$		0			0
$561$	−9.32547	−	3.39420i	−0.393722	−	0.143303i
$562$		0			0
$563$	−10.9957	−	19.0451i	−0.463414	−	0.802657i	0.535714	−	0.844399i	$-0.320042\pi$
$563$	−10.9957	−	19.0451i	−0.463414	−	0.802657i	−0.999128	+	0.0417423i	$0.986709\pi$
$564$		0			0
$565$	−14.1138	−	11.8429i	−0.593772	−	0.498234i
$566$		0			0
$567$	−0.0923963	+	0.524005i	−0.00388028	+	0.0220062i
$568$		0			0
$569$	28.7588			1.20563			0.602815	−	0.797881i	$-0.294046\pi$
$569$	28.7588			1.20563			0.602815	+	0.797881i	$0.294046\pi$
$570$		0			0
$571$	−7.30365			−0.305648			−0.152824	−	0.988253i	$-0.548837\pi$
$571$	−7.30365			−0.305648			−0.152824	+	0.988253i	$0.548837\pi$
$572$		0			0
$573$	3.31180	−	18.7822i	0.138353	−	0.784637i
$574$		0			0
$575$	−3.28905	−	2.75984i	−0.137163	−	0.115093i
$576$		0			0
$577$	−15.7545	−	27.2876i	−0.655868	−	1.13600i	−0.981675	−	0.190561i	$-0.938969\pi$
$577$	−15.7545	−	27.2876i	−0.655868	−	1.13600i	0.325807	−	0.945436i	$-0.394364\pi$
$578$		0			0
$579$	22.3983	+	8.15230i	0.930840	+	0.338798i
$580$		0			0
$581$	3.05303	−	5.28801i	0.126661	−	0.219384i
$582$		0			0
$583$	−8.77941	−	49.7905i	−0.363606	−	2.06211i
$584$		0			0
$585$	−7.88326	+	6.61484i	−0.325933	+	0.273490i
$586$		0			0
$587$	25.6434	−	9.33342i	1.05842	−	0.385232i	0.246583	−	0.969122i	$-0.420692\pi$
$587$	25.6434	−	9.33342i	1.05842	−	0.385232i	0.811833	+	0.583890i	$0.198470\pi$
$588$		0			0
$589$	20.9886	−	37.6021i	0.864820	−	1.54937i
$590$		0			0
$591$	4.12449	−	1.50119i	0.169659	−	0.0617507i
$592$		0			0
$593$	26.6366	−	22.3507i	1.09383	−	0.917834i	0.0968375	−	0.995300i	$-0.469127\pi$
$593$	26.6366	−	22.3507i	1.09383	−	0.917834i	0.996995	+	0.0774657i	$0.0246828\pi$
$594$		0			0
$595$	0.454707	+	2.57877i	0.0186412	+	0.105719i
$596$		0			0
$597$	−10.0189	+	17.3532i	−0.410046	+	0.710220i
$598$		0			0
$599$	14.9402	+	5.43777i	0.610438	+	0.222181i	0.628695	−	0.777652i	$-0.283589\pi$
$599$	14.9402	+	5.43777i	0.610438	+	0.222181i	−0.0182567	+	0.999833i	$0.505812\pi$
$600$		0			0
$601$	12.3464	+	21.3846i	0.503621	+	0.872297i	0.999991	+	0.00418616i	$0.00133250\pi$
$601$	12.3464	+	21.3846i	0.503621	+	0.872297i	−0.496370	+	0.868111i	$0.665334\pi$
$602$		0			0
$603$	7.82295	+	6.56423i	0.318575	+	0.267316i
$604$		0			0
$605$	−6.62701	+	37.5836i	−0.269426	+	1.52799i
$606$		0			0
$607$	−4.01455			−0.162945			−0.0814727	−	0.996676i	$-0.525962\pi$
$607$	−4.01455			−0.162945			−0.0814727	+	0.996676i	$0.525962\pi$
$608$		0			0
$609$	−0.857097			−0.0347313
$610$		0			0
$611$	−5.33497	+	30.2561i	−0.215830	+	1.22403i
$612$		0			0
$613$	−30.8082	−	25.8511i	−1.24433	−	1.04412i	−0.997173	−	0.0751409i	$-0.976059\pi$
$613$	−30.8082	−	25.8511i	−1.24433	−	1.04412i	−0.247157	−	0.968976i	$-0.579496\pi$
$614$		0			0
$615$	−10.7306	−	18.5859i	−0.432698	−	0.749454i
$616$		0			0
$617$	20.8427	+	7.58613i	0.839096	+	0.305406i	0.725586	−	0.688131i	$-0.241569\pi$
$617$	20.8427	+	7.58613i	0.839096	+	0.305406i	0.113509	+	0.993537i	$0.463791\pi$
$618$		0			0
$619$	−11.6177	+	20.1224i	−0.466954	+	0.808788i	−0.999287	−	0.0377469i	$-0.987982\pi$
$619$	−11.6177	+	20.1224i	−0.466954	+	0.808788i	0.532333	+	0.846535i	$0.321315\pi$
$620$		0			0
$621$	−0.528218	−	2.99568i	−0.0211967	−	0.120212i
$622$		0			0
$623$	2.41463	−	2.02611i	0.0967401	−	0.0811746i
$624$		0			0
$625$	28.2520	−	10.2829i	1.13008	−	0.411315i
$626$		0			0
$627$	3.54664	−	21.9724i	0.141639	−	0.877494i
$628$		0			0
$629$	−11.1518	+	4.05893i	−0.444652	+	0.161840i
$630$		0			0
$631$	−21.4893	+	18.0317i	−0.855476	+	0.717830i	−0.960989	−	0.276588i	$-0.910796\pi$
$631$	−21.4893	+	18.0317i	−0.855476	+	0.717830i	0.105512	+	0.994418i	$0.466352\pi$
$632$		0			0
$633$	−4.72193	−	26.7794i	−0.187680	−	1.06439i
$634$		0			0
$635$	−2.31655	+	4.01239i	−0.0919295	+	0.159227i
$636$		0			0
$637$	25.6523	+	9.33667i	1.01638	+	0.369932i
$638$		0			0
$639$	1.91147	+	3.31077i	0.0756167	+	0.130972i
$640$		0			0
$641$	33.3068	+	27.9477i	1.31554	+	1.10387i	0.987230	+	0.159299i	$0.0509233\pi$
$641$	33.3068	+	27.9477i	1.31554	+	1.10387i	0.328309	+	0.944570i	$0.393521\pi$
$642$		0			0
$643$	−6.83322	+	38.7531i	−0.269476	+	1.52827i	0.486504	+	0.873678i	$0.338272\pi$
$643$	−6.83322	+	38.7531i	−0.269476	+	1.52827i	−0.755980	+	0.654595i	$0.772839\pi$
$644$		0			0
$645$	−0.448311			−0.0176522
$646$		0			0
$647$	−18.8862			−0.742493			−0.371246	−	0.928534i	$-0.621069\pi$
$647$	−18.8862			−0.742493			−0.371246	+	0.928534i	$0.621069\pi$
$648$		0			0
$649$	3.38279	−	19.1847i	0.132786	−	0.753067i
$650$		0			0
$651$	4.02687	+	3.37895i	0.157826	+	0.132431i
$652$		0			0
$653$	23.3714	+	40.4804i	0.914593	+	1.58412i	0.807495	+	0.589874i	$0.200823\pi$
$653$	23.3714	+	40.4804i	0.914593	+	1.58412i	0.107098	+	0.994248i	$0.465844\pi$
$654$		0			0
$655$	20.9055	+	7.60900i	0.816847	+	0.297308i
$656$		0			0
$657$	0.928548	−	1.60829i	0.0362261	−	0.0627455i
$658$		0			0
$659$	−0.362778	−	2.05742i	−0.0141318	−	0.0801455i	0.976926	−	0.213577i	$-0.0685115\pi$
$659$	−0.362778	−	2.05742i	−0.0141318	−	0.0801455i	−0.991058	+	0.133432i	$0.957400\pi$
$660$		0			0
$661$	−9.53596	+	8.00162i	−0.370906	+	0.311227i	−0.809120	−	0.587644i	$-0.800056\pi$
$661$	−9.53596	+	8.00162i	−0.370906	+	0.311227i	0.438214	+	0.898871i	$0.355611\pi$
$662$		0			0
$663$	−7.42262	+	2.70161i	−0.288271	+	0.104922i
$664$		0			0
$665$	−5.48886	+	2.08840i	−0.212849	+	0.0809846i
$666$		0			0
$667$	4.60442	−	1.67587i	0.178284	−	0.0648900i
$668$		0			0
$669$	9.20233	−	7.72167i	0.355783	−	0.298537i
$670$		0			0
$671$	−12.3503	−	70.0420i	−0.476778	−	2.70394i
$672$		0			0
$673$	5.41060	−	9.37143i	0.208563	−	0.361242i	−0.742699	−	0.669625i	$-0.766455\pi$
$673$	5.41060	−	9.37143i	0.208563	−	0.361242i	0.951262	+	0.308383i	$0.0997880\pi$
$674$		0			0
$675$	−1.32635	−	0.482753i	−0.0510513	−	0.0185812i
$676$		0			0
$677$	−2.18092	−	3.77747i	−0.0838196	−	0.145180i	0.821068	−	0.570830i	$-0.193379\pi$
$677$	−2.18092	−	3.77747i	−0.0838196	−	0.145180i	−0.904888	+	0.425651i	$0.860045\pi$
$678$		0			0
$679$	2.77197	+	2.32596i	0.106379	+	0.0892623i
$680$		0			0
$681$	−0.753718	+	4.27455i	−0.0288825	+	0.163801i
$682$		0			0
$683$	44.6441			1.70826			0.854130	−	0.520059i	$-0.174090\pi$
$683$	44.6441			1.70826			0.854130	+	0.520059i	$0.174090\pi$
$684$		0			0
$685$	31.9813			1.22194
$686$		0			0
$687$	0.572329	−	3.24584i	0.0218357	−	0.123837i
$688$		0			0
$689$	−30.8273	−	25.8672i	−1.17443	−	0.985460i
$690$		0			0
$691$	12.1604	+	21.0625i	0.462605	+	0.801256i	0.999090	−	0.0426544i	$-0.0135815\pi$
$691$	12.1604	+	21.0625i	0.462605	+	0.801256i	−0.536485	+	0.843910i	$0.680248\pi$
$692$		0			0
$693$	2.55303	+	0.929228i	0.0969817	+	0.0352985i
$694$		0			0
$695$	5.12701	−	8.88024i	0.194479	−	0.336847i
$696$		0			0
$697$	−2.86050	−	16.2227i	−0.108349	−	0.614479i
$698$		0			0
$699$	−11.8209	+	9.91890i	−0.447107	+	0.375167i
$700$		0			0
$701$	22.1386	−	8.05780i	0.836164	−	0.304339i	0.111778	−	0.993733i	$-0.464345\pi$
$701$	22.1386	−	8.05780i	0.836164	−	0.304339i	0.724386	+	0.689394i	$0.242123\pi$
$702$		0			0
$703$	−13.6407	−	22.8545i	−0.514468	−	0.861974i
$704$		0			0
$705$	−17.9868	+	6.54666i	−0.677422	+	0.246561i
$706$		0			0
$707$	3.57011	−	2.99568i	0.134268	−	0.112664i
$708$		0			0
$709$	−1.06851	−	6.05985i	−0.0401289	−	0.227582i	0.958147	−	0.286276i	$-0.0924175\pi$
$709$	−1.06851	−	6.05985i	−0.0401289	−	0.227582i	−0.998276	+	0.0586939i	$0.981306\pi$
$710$		0			0
$711$	5.25877	−	9.10846i	0.197219	−	0.341594i
$712$		0			0
$713$	−28.2396	−	10.2784i	−1.05758	−	0.384929i
$714$		0			0
$715$	26.2729	+	45.5060i	0.982551	+	1.70183i
$716$		0			0
$717$	−12.1211	−	10.1708i	−0.452670	−	0.379835i
$718$		0			0
$719$	−5.65657	+	32.0800i	−0.210955	+	1.19638i	0.676835	+	0.736134i	$0.263351\pi$
$719$	−5.65657	+	32.0800i	−0.210955	+	1.19638i	−0.887790	+	0.460249i	$0.847760\pi$
$720$		0			0
$721$	−2.04601			−0.0761973
$722$		0			0
$723$	−23.6459			−0.879400
$724$		0			0
$725$	0.394811	−	2.23908i	0.0146629	−	0.0831574i
$726$		0			0
$727$	−24.6896	−	20.7170i	−0.915686	−	0.768352i	0.0575058	−	0.998345i	$-0.481685\pi$
$727$	−24.6896	−	20.7170i	−0.915686	−	0.768352i	−0.973192	+	0.229993i	$0.926130\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	−0.323359	−	0.117693i	−0.0119599	−	0.00435303i
$732$		0			0
$733$	−4.89053	+	8.47065i	−0.180636	+	0.312870i	−0.942097	−	0.335340i	$-0.891149\pi$
$733$	−4.89053	+	8.47065i	−0.180636	+	0.312870i	0.761461	+	0.648210i	$0.224482\pi$
$734$		0			0
$735$	2.95336	+	16.7494i	0.108936	+	0.617809i
$736$		0			0
$737$	39.9445	−	33.5174i	1.47137	−	1.23463i
$738$		0			0
$739$	26.0993	−	9.49935i	0.960077	−	0.349439i	0.186013	−	0.982547i	$-0.440443\pi$
$739$	26.0993	−	9.49935i	0.960077	−	0.349439i	0.774064	+	0.633108i	$0.218221\pi$
$740$		0			0
$741$	−9.07919	−	15.2119i	−0.333532	−	0.558823i
$742$		0			0
$743$	−30.3542	+	11.0480i	−1.11359	+	0.405312i	−0.832308	−	0.554314i	$-0.812981\pi$
$743$	−30.3542	+	11.0480i	−1.11359	+	0.405312i	−0.281278	+	0.959626i	$0.590758\pi$
$744$		0			0
$745$	−11.7724	+	9.87825i	−0.431309	+	0.361911i
$746$		0			0
$747$	1.99273	+	11.3013i	0.0729100	+	0.413493i
$748$		0			0
$749$	1.50980	−	2.61505i	0.0551669	−	0.0955519i
$750$		0			0
$751$	3.27497	+	1.19199i	0.119505	+	0.0434964i	0.401081	−	0.916043i	$-0.368635\pi$
$751$	3.27497	+	1.19199i	0.119505	+	0.0434964i	−0.281575	+	0.959539i	$0.590857\pi$
$752$		0			0
$753$	9.70574	+	16.8108i	0.353697	+	0.612621i
$754$		0			0
$755$	−0.315207	−	0.264490i	−0.0114716	−	0.00962579i
$756$		0			0
$757$	−6.41353	+	36.3730i	−0.233104	+	1.32200i	0.613467	+	0.789721i	$0.289775\pi$
$757$	−6.41353	+	36.3730i	−0.233104	+	1.32200i	−0.846570	+	0.532277i	$0.821337\pi$
$758$		0			0
$759$	−15.5321			−0.563779
$760$		0			0
$761$	31.3429			1.13618			0.568089	−	0.822967i	$-0.307683\pi$
$761$	31.3429			1.13618			0.568089	+	0.822967i	$0.307683\pi$
$762$		0			0
$763$	0.192782	−	1.09332i	0.00697917	−	0.0395808i
$764$		0			0
$765$	−3.76991	−	3.16333i	−0.136302	−	0.114371i
$766$		0			0
$767$	−7.75284	−	13.4283i	−0.279939	−	0.484868i
$768$		0			0
$769$	29.8282	+	10.8566i	1.07563	+	0.391498i	0.818280	−	0.574820i	$-0.194928\pi$
$769$	29.8282	+	10.8566i	1.07563	+	0.391498i	0.257351	+	0.966318i	$0.417150\pi$
$770$		0			0
$771$	−6.14796	+	10.6486i	−0.221413	+	0.383499i
$772$		0			0
$773$	1.90269	+	10.7907i	0.0684351	+	0.388115i	0.999716	+	0.0238140i	$0.00758095\pi$
$773$	1.90269	+	10.7907i	0.0684351	+	0.388115i	−0.931281	+	0.364301i	$0.881308\pi$
$774$		0			0
$775$	−10.6821	+	8.96335i	−0.383713	+	0.321973i
$776$		0			0
$777$	3.05303	−	1.11121i	0.109527	−	0.0398646i
$778$		0			0
$779$	34.5296	−	13.1378i	1.23715	−	0.470711i
$780$		0			0
$781$	18.3430	−	6.67631i	0.656365	−	0.238897i
$782$		0			0
$783$	1.23396	−	1.03541i	0.0440980	−	0.0370026i
$784$		0			0
$785$	−2.92855	−	16.6086i	−0.104524	−	0.592787i
$786$		0			0
$787$	23.1771	−	40.1439i	0.826175	−	1.43098i	−0.0748436	−	0.997195i	$-0.523846\pi$
$787$	23.1771	−	40.1439i	0.826175	−	1.43098i	0.901018	−	0.433781i	$-0.142821\pi$
$788$		0			0
$789$	5.95811	+	2.16858i	0.212114	+	0.0772033i
$790$		0			0
$791$	1.93582	+	3.35294i	0.0688299	+	0.119217i
$792$		0			0
$793$	−43.3658	−	36.3882i	−1.53996	−	1.29218i
$794$		0			0
$795$	4.35369	−	24.6910i	0.154410	−	0.875700i
$796$		0			0
$797$	−3.47296			−0.123019			−0.0615093	−	0.998107i	$-0.519591\pi$
$797$	−3.47296			−0.123019			−0.0615093	+	0.998107i	$0.519591\pi$
$798$		0			0
$799$	−14.6922			−0.519774
$800$		0			0
$801$	−1.02869	+	5.83396i	−0.0363468	+	0.206133i
$802$		0			0
$803$	−7.26399	−	6.09521i	−0.256340	−	0.215095i
$804$		0			0
$805$	2.04916	+	3.54925i	0.0722235	+	0.125095i
$806$		0			0
$807$	2.18479	+	0.795199i	0.0769083	+	0.0279923i
$808$		0			0
$809$	25.9748	−	44.9896i	0.913224	−	1.58175i	0.103744	−	0.994604i	$-0.466918\pi$
$809$	25.9748	−	44.9896i	0.913224	−	1.58175i	0.809480	−	0.587147i	$-0.199749\pi$
$810$		0			0
$811$	−2.91329	−	16.5221i	−0.102299	−	0.580168i	−0.992265	−	0.124140i	$-0.960383\pi$
$811$	−2.91329	−	16.5221i	−0.102299	−	0.580168i	0.889965	−	0.456028i	$-0.150728\pi$
$812$		0			0
$813$	−11.4474	+	9.60554i	−0.401479	+	0.336881i
$814$		0			0
$815$	1.06670	−	0.388249i	0.0373650	−	0.0135998i
$816$		0			0
$817$	0.122979	−	0.761889i	0.00430249	−	0.0266551i
$818$		0			0
$819$	2.03209	−	0.739620i	0.0710069	−	0.0258444i
$820$		0			0
$821$	−28.5330	+	23.9420i	−0.995809	+	0.835583i	−0.986398	−	0.164372i	$-0.947440\pi$
$821$	−28.5330	+	23.9420i	−0.995809	+	0.835583i	−0.00941101	+	0.999956i	$0.502996\pi$
$822$		0			0
$823$	0.763985	+	4.33277i	0.0266308	+	0.151031i	0.995224	−	0.0976214i	$-0.0311234\pi$
$823$	0.763985	+	4.33277i	0.0266308	+	0.151031i	−0.968593	+	0.248652i	$0.920012\pi$
$824$		0			0
$825$	−3.60354	+	6.24152i	−0.125459	+	0.217302i
$826$		0			0
$827$	−13.0265	−	4.74125i	−0.452975	−	0.164869i	0.105450	−	0.994425i	$-0.466372\pi$
$827$	−13.0265	−	4.74125i	−0.452975	−	0.164869i	−0.558424	+	0.829555i	$0.688594\pi$
$828$		0			0
$829$	−8.18850	−	14.1829i	−0.284398	−	0.492592i	0.688065	−	0.725649i	$-0.258461\pi$
$829$	−8.18850	−	14.1829i	−0.284398	−	0.492592i	−0.972463	+	0.233057i	$0.925127\pi$
$830$		0			0
$831$	−18.3589	−	15.4050i	−0.636863	−	0.534392i
$832$		0			0
$833$	−2.26692	+	12.8564i	−0.0785442	+	0.445446i
$834$		0			0
$835$	8.58172			0.296983
$836$		0			0
$837$	−9.87939			−0.341482
$838$		0			0
$839$	6.64883	−	37.7074i	0.229543	−	1.30180i	−0.624263	−	0.781214i	$-0.714601\pi$
$839$	6.64883	−	37.7074i	0.229543	−	1.30180i	0.853807	−	0.520590i	$-0.174288\pi$
$840$		0			0
$841$	−20.2276	−	16.9730i	−0.697504	−	0.585275i
$842$		0			0
$843$	−12.7802	−	22.1359i	−0.440173	−	0.762402i
$844$		0			0
$845$	8.36959	+	3.04628i	0.287922	+	0.104795i
$846$		0			0
$847$	4.00980	−	6.94518i	0.137778	−	0.238639i
$848$		0			0
$849$	1.30423	+	7.39663i	0.0447609	+	0.253852i
$850$		0			0
$851$	−14.2285	+	11.9391i	−0.487746	+	0.409268i
$852$		0			0
$853$	−20.7579	+	7.55526i	−0.710737	+	0.258687i	−0.671988	−	0.740562i	$-0.734559\pi$
$853$	−20.7579	+	7.55526i	−0.710737	+	0.258687i	−0.0387487	+	0.999249i	$0.512337\pi$
$854$		0			0
$855$	5.37939	−	9.63744i	0.183971	−	0.329593i
$856$		0			0
$857$	−42.2934	+	15.3936i	−1.44472	+	0.525834i	−0.941110	−	0.338100i	$-0.890216\pi$
$857$	−42.2934	+	15.3936i	−1.44472	+	0.525834i	−0.503606	+	0.863933i	$0.667994\pi$
$858$		0			0
$859$	12.2358	−	10.2670i	0.417479	−	0.350306i	−0.409724	−	0.912209i	$-0.634375\pi$
$859$	12.2358	−	10.2670i	0.417479	−	0.350306i	0.827203	+	0.561903i	$0.189931\pi$
$860$		0			0
$861$	0.783119	+	4.44129i	0.0266886	+	0.151359i
$862$		0			0
$863$	20.6288	−	35.7302i	0.702213	−	1.21627i	−0.265475	−	0.964118i	$-0.585529\pi$
$863$	20.6288	−	35.7302i	0.702213	−	1.21627i	0.967688	−	0.252151i	$-0.0811380\pi$
$864$		0			0
$865$	−3.84477	−	1.39938i	−0.130726	−	0.0475804i
$866$		0			0
$867$	6.61128	+	11.4511i	0.224531	+	0.388899i
$868$		0			0
$869$	−41.1391	−	34.5198i	−1.39555	−	1.17100i
$870$		0			0
$871$	7.20708	−	40.8734i	0.244203	−	1.38494i
$872$		0			0
$873$	−6.80066			−0.230167
$874$		0			0
$875$	−4.83481			−0.163446
$876$		0			0
$877$	8.01650	−	45.4638i	0.270698	−	1.53520i	−0.481606	−	0.876388i	$-0.659946\pi$
$877$	8.01650	−	45.4638i	0.270698	−	1.53520i	0.752304	−	0.658817i	$-0.228943\pi$
$878$		0			0
$879$	11.3118	+	9.49173i	0.381538	+	0.320148i
$880$		0			0
$881$	−9.47906	−	16.4182i	−0.319357	−	0.553143i	0.660997	−	0.750389i	$-0.270134\pi$
$881$	−9.47906	−	16.4182i	−0.319357	−	0.553143i	−0.980354	+	0.197245i	$0.936800\pi$
$882$		0			0
$883$	32.9359	+	11.9877i	1.10838	+	0.403418i	0.830399	−	0.557169i	$-0.188112\pi$
$883$	32.9359	+	11.9877i	1.10838	+	0.403418i	0.277981	+	0.960586i	$0.410335\pi$
$884$		0			0
$885$	4.83022	−	8.36619i	0.162366	−	0.281226i
$886$		0			0
$887$	3.09745	+	17.5665i	0.104002	+	0.589825i	0.991614	+	0.129234i	$0.0412517\pi$
$887$	3.09745	+	17.5665i	0.104002	+	0.589825i	−0.887612	+	0.460592i	$0.847637\pi$
$888$		0			0
$889$	0.745815	−	0.625813i	0.0250138	−	0.0209891i
$890$		0			0
$891$	−4.79813	+	1.74638i	−0.160744	+	0.0585059i
$892$		0			0
$893$	−6.19176	−	32.3638i	−0.207199	−	1.08301i
$894$		0			0
$895$	−5.02956	+	1.83061i	−0.168120	+	0.0611906i
$896$		0			0
$897$	−9.47044	+	7.94664i	−0.316209	+	0.265331i
$898$		0			0
$899$	−2.76341	−	15.6721i	−0.0921650	−	0.522693i
$900$		0			0
$901$	9.62226	−	16.6662i	0.320564	−	0.555233i
$902$		0			0
$903$	0.0885259	+	0.0322208i	0.00294596	+	0.00107224i
$904$		0			0
$905$	11.0804	+	19.1918i	0.368324	+	0.637956i
$906$		0			0
$907$	10.9172	+	9.16058i	0.362498	+	0.304172i	0.805786	−	0.592207i	$-0.201743\pi$
$907$	10.9172	+	9.16058i	0.362498	+	0.304172i	−0.443287	+	0.896380i	$0.646188\pi$
$908$		0			0
$909$	−1.52094	+	8.62571i	−0.0504465	+	0.286097i
$910$		0			0
$911$	16.4466			0.544899			0.272449	−	0.962170i	$-0.412166\pi$
$911$	16.4466			0.544899			0.272449	+	0.962170i	$0.412166\pi$
$912$		0			0
$913$	58.5954			1.93923
$914$		0			0
$915$	6.12449	−	34.7337i	0.202469	−	1.14826i
$916$		0			0
$917$	−3.58125	−	3.00503i	−0.118263	−	0.0992347i
$918$		0			0
$919$	−16.9500	−	29.3582i	−0.559128	−	0.968437i	−0.997570	−	0.0696779i	$-0.977803\pi$
$919$	−16.9500	−	29.3582i	−0.559128	−	0.968437i	0.438442	−	0.898760i	$-0.355530\pi$
$920$		0			0
$921$	5.18004	+	1.88538i	0.170688	+	0.0621255i
$922$		0			0
$923$	7.76857	−	13.4556i	0.255706	−	0.442895i
$924$		0			0
$925$	1.49660	+	8.48762i	0.0492078	+	0.279071i
$926$		0			0
$927$	2.94562	−	2.47167i	0.0967469	−	0.0811803i
$928$		0			0
$929$	−20.2358	+	7.36522i	−0.663914	+	0.241645i	−0.651925	−	0.758283i	$-0.726038\pi$
$929$	−20.2358	+	7.36522i	−0.663914	+	0.241645i	−0.0119887	+	0.999928i	$0.503816\pi$
$930$		0			0
$931$	−29.2751	+	0.424525i	−0.959454	+	0.0139133i
$932$		0			0
$933$	16.3503	−	5.95102i	0.535284	−	0.194828i
$934$		0			0
$935$	−19.2494	+	16.1522i	−0.629524	+	0.528233i
$936$		0			0
$937$	1.31386	+	7.45129i	0.0429220	+	0.243423i	0.998719	−	0.0506054i	$-0.0161151\pi$
$937$	1.31386	+	7.45129i	0.0429220	+	0.243423i	−0.955797	+	0.294028i	$0.905004\pi$
$938$		0			0
$939$	−7.97178	+	13.8075i	−0.260149	+	0.450592i
$940$		0			0
$941$	−17.9740	−	6.54200i	−0.585936	−	0.213263i	0.0320052	−	0.999488i	$-0.489811\pi$
$941$	−17.9740	−	6.54200i	−0.585936	−	0.213263i	−0.617941	+	0.786225i	$0.712033\pi$
$942$		0			0
$943$	−12.8910	−	22.3279i	−0.419789	−	0.727095i
$944$		0			0
$945$	1.03209	+	0.866025i	0.0335739	+	0.0281718i
$946$		0			0
$947$	−10.4549	+	59.2925i	−0.339738	+	1.92675i	0.0344768	+	0.999405i	$0.489024\pi$
$947$	−10.4549	+	59.2925i	−0.339738	+	1.92675i	−0.374214	+	0.927342i	$0.622088\pi$
$948$		0			0
$949$	−7.54757			−0.245005
$950$		0			0
$951$	1.97359			0.0639981
$952$		0			0
$953$	−3.42918	+	19.4478i	−0.111082	+	0.629977i	0.877534	+	0.479515i	$0.159187\pi$
$953$	−3.42918	+	19.4478i	−0.111082	+	0.629977i	−0.988616	+	0.150462i	$0.951924\pi$
$954$		0			0
$955$	−36.9937	−	31.0414i	−1.19709	−	1.00448i
$956$		0			0
$957$	−4.11246	−	7.12300i	−0.132937	−	0.230254i
$958$		0			0
$959$	−6.31521	−	2.29855i	−0.203929	−	0.0742240i
$960$		0			0
$961$	−33.3011	+	57.6792i	−1.07423	+	1.86062i
$962$		0			0
$963$	0.985452	+	5.58878i	0.0317557	+	0.180096i
$964$		0			0
$965$	46.2340	−	38.7949i	1.48833	−	1.24885i
$966$		0			0
$967$	−4.85679	+	1.76773i	−0.156184	+	0.0568463i	−0.418929	−	0.908019i	$-0.637594\pi$
$967$	−4.85679	+	1.76773i	−0.156184	+	0.0568463i	0.262745	+	0.964865i	$0.415372\pi$
$968$		0			0
$969$	6.41013	−	5.53909i	0.205923	−	0.177941i
$970$		0			0
$971$	−8.22967	+	2.99536i	−0.264103	+	0.0961256i	−0.470678	−	0.882305i	$-0.655991\pi$
$971$	−8.22967	+	2.99536i	−0.264103	+	0.0961256i	0.206575	+	0.978431i	$0.433768\pi$
$972$		0			0
$973$	−1.65064	+	1.38505i	−0.0529172	+	0.0444028i
$974$		0			0
$975$	0.996130	+	5.64933i	0.0319017	+	0.180923i
$976$		0			0
$977$	−20.3640	+	35.2714i	−0.651501	+	1.12843i	0.331258	+	0.943540i	$0.392527\pi$
$977$	−20.3640	+	35.2714i	−0.651501	+	1.12843i	−0.982759	+	0.184892i	$0.940806\pi$
$978$		0			0
$979$	28.4240	+	10.3455i	0.908434	+	0.330643i
$980$		0			0
$981$	1.04323	+	1.80693i	0.0333079	+	0.0576909i
$982$		0			0
$983$	−3.02616	−	2.53925i	−0.0965195	−	0.0809895i	0.593251	−	0.805018i	$-0.297844\pi$
$983$	−3.02616	−	2.53925i	−0.0965195	−	0.0809895i	−0.689771	+	0.724028i	$0.742289\pi$
$984$		0			0
$985$	1.92989	−	10.9450i	0.0614915	−	0.348736i
$986$		0			0
$987$	4.02229			0.128031
$988$		0			0
$989$	−0.538572			−0.0171256
$990$		0			0
$991$	3.22328	−	18.2801i	0.102391	−	0.580687i	−0.889840	−	0.456273i	$-0.849184\pi$
$991$	3.22328	−	18.2801i	0.102391	−	0.580687i	0.992230	−	0.124414i	$-0.0397050\pi$
$992$		0			0
$993$	0.641559	+	0.538332i	0.0203593	+	0.0170835i
$994$		0			0
$995$	25.3687	+	43.9399i	0.804242	+	1.39299i
$996$		0			0
$997$	−2.57398	−	0.936851i	−0.0815187	−	0.0296704i	0.300939	−	0.953643i	$-0.402700\pi$
$997$	−2.57398	−	0.936851i	−0.0815187	−	0.0296704i	−0.382458	+	0.923973i	$0.624922\pi$
$998$		0			0
$999$	−3.05303	+	5.28801i	−0.0965937	+	0.167305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.b.385.1		6
4.3	odd	2		57.2.i.a.43.1	yes	6
12.11	even	2		171.2.u.a.100.1		6
19.4	even	9	inner	912.2.bo.b.289.1		6
76.23	odd	18		57.2.i.a.4.1	✓	6
76.55	odd	18		1083.2.a.m.1.1		3
76.59	even	18		1083.2.a.n.1.3		3
228.23	even	18		171.2.u.a.118.1		6
228.59	odd	18		3249.2.a.x.1.1		3
228.131	even	18		3249.2.a.w.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.4.1	✓	6	76.23	odd	18
57.2.i.a.43.1	yes	6	4.3	odd	2
171.2.u.a.100.1		6	12.11	even	2
171.2.u.a.118.1		6	228.23	even	18
912.2.bo.b.289.1		6	19.4	even	9	inner
912.2.bo.b.385.1		6	1.1	even	1	trivial
1083.2.a.m.1.1		3	76.55	odd	18
1083.2.a.n.1.3		3	76.59	even	18
3249.2.a.w.1.3		3	228.131	even	18
3249.2.a.x.1.1		3	228.59	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)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{3} +(-1.93969 - 1.62760i) q^{5} +(0.266044 + 0.460802i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(-2.55303 + 4.42198i) q^{11} +(0.705737 + 4.00243i) q^{13} +(-1.93969 + 1.62760i) q^{15} +(-1.82635 + 0.664738i) q^{17} +(-2.23396 - 3.74292i) q^{19} +(0.500000 - 0.181985i) q^{21} +(-2.33022 + 1.95529i) q^{23} +(0.245100 + 1.39003i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(-1.51367 - 0.550931i) q^{29} +(4.93969 + 8.55580i) q^{31} +(3.91147 + 3.28212i) q^{33} +(0.233956 - 1.32683i) q^{35} +6.10607 q^{37} +4.06418 q^{39} +(-1.47178 + 8.34689i) q^{41} +(0.135630 + 0.113807i) q^{43} +(1.26604 + 2.19285i) q^{45} +(7.10354 + 2.58548i) q^{47} +(3.35844 - 5.81699i) q^{49} +(0.337496 + 1.91404i) q^{51} +(-7.58512 + 6.36467i) q^{53} +(12.1493 - 4.42198i) q^{55} +(-4.07398 + 1.55007i) q^{57} +(-3.58512 + 1.30488i) q^{59} +(-10.6702 + 8.95340i) q^{61} +(-0.0923963 - 0.524005i) q^{63} +(5.14543 - 8.91215i) q^{65} +(-9.59627 - 3.49276i) q^{67} +(1.52094 + 2.63435i) q^{69} +(-2.92855 - 2.45734i) q^{71} +(-0.322481 + 1.82888i) q^{73} +1.41147 q^{75} -2.71688 q^{77} +(-1.82635 + 10.3578i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-5.73783 - 9.93821i) q^{83} +(4.62449 + 1.68317i) q^{85} +(-0.805407 + 1.39501i) q^{87} +(-1.02869 - 5.83396i) q^{89} +(-1.65657 + 1.39003i) q^{91} +(9.28359 - 3.37895i) q^{93} +(-1.75877 + 10.8961i) q^{95} +(6.39053 - 2.32596i) q^{97} +(3.91147 - 3.28212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} - 3 q^{7} - 3 q^{11} - 6 q^{13} - 6 q^{15} - 12 q^{17} - 18 q^{19} + 3 q^{21} + 9 q^{23} - 3 q^{27} + 12 q^{29} + 24 q^{31} + 3 q^{33} + 6 q^{35} + 12 q^{37} + 6 q^{39} + 6 q^{41} - 18 q^{43}+ \cdots + 3 q^{99}+O(q^{100}) \) 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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