LMFDB - Embedded newform 912.2.bb.e.559.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(31,912)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("912.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.3
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	912.559
Dual form			912.2.bb.e.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(1.33641 - 2.31473i) q^{5} +3.93569i q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(1.33641 - 2.31473i) q^{5} +3.93569i q^{7} +(-0.500000 - 0.866025i) q^{9} +2.20364i q^{11} +(-3.60083 + 2.07894i) q^{13} +(1.33641 + 2.31473i) q^{15} +(-0.571993 + 0.990721i) q^{17} +(-4.24482 + 0.990721i) q^{19} +(-3.40841 - 1.96784i) q^{21} +(3.19243 - 1.84315i) q^{23} +(-1.07199 - 1.85675i) q^{25} +1.00000 q^{27} +(-2.10083 + 1.21292i) q^{29} +3.67282 q^{31} +(-1.90841 - 1.10182i) q^{33} +(9.11007 + 5.25970i) q^{35} +10.0478i q^{37} -4.15788i q^{39} +(8.01847 + 4.62947i) q^{41} +(-0.490764 - 0.283343i) q^{43} -2.67282 q^{45} +(-10.6336 + 6.13932i) q^{47} -8.48963 q^{49} +(-0.571993 - 0.990721i) q^{51} +(4.09159 - 2.36228i) q^{53} +(5.10083 + 2.94497i) q^{55} +(1.26442 - 4.17148i) q^{57} +(-1.33641 + 2.31473i) q^{59} +(-6.41764 - 11.1157i) q^{61} +(3.40841 - 1.96784i) q^{63} +11.1133i q^{65} +(1.73558 + 3.00612i) q^{67} +3.68630i q^{69} +(-6.24482 + 10.8163i) q^{71} +(1.35601 - 2.34868i) q^{73} +2.14399 q^{75} -8.67282 q^{77} +(-3.50924 + 6.07817i) q^{79} +(-0.500000 + 0.866025i) q^{81} +1.98144i q^{83} +(1.52884 + 2.64802i) q^{85} -2.42583i q^{87} +(12.9269 - 7.46334i) q^{89} +(-8.18206 - 14.1717i) q^{91} +(-1.83641 + 3.18076i) q^{93} +(-3.37957 + 11.1496i) q^{95} +(2.91764 + 1.68450i) q^{97} +(1.90841 - 1.10182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 2 q^{5} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 2 * q^5 - 3 * q^9	$ 6 q - 3 q^{3} - 2 q^{5} - 3 q^{9} - 3 q^{13} - 2 q^{15} - 2 q^{17} - 4 q^{19} - 9 q^{21} + 12 q^{23} - 5 q^{25} + 6 q^{27} + 6 q^{29} + 2 q^{31} + 6 q^{35} - 12 q^{41} - 33 q^{43} + 4 q^{45} - 18 q^{47} - 8 q^{49} - 2 q^{51} + 36 q^{53} + 12 q^{55} - q^{57} + 2 q^{59} + 3 q^{61} + 9 q^{63} + 19 q^{67} - 16 q^{71} + 11 q^{73} + 10 q^{75} - 32 q^{77} + 9 q^{79} - 3 q^{81} - 8 q^{85} + 6 q^{89} + q^{91} - q^{93} - 26 q^{95} - 24 q^{97}+O(q^{100}) $ 6 * q - 3 * q^3 - 2 * q^5 - 3 * q^9 - 3 * q^13 - 2 * q^15 - 2 * q^17 - 4 * q^19 - 9 * q^21 + 12 * q^23 - 5 * q^25 + 6 * q^27 + 6 * q^29 + 2 * q^31 + 6 * q^35 - 12 * q^41 - 33 * q^43 + 4 * q^45 - 18 * q^47 - 8 * q^49 - 2 * q^51 + 36 * q^53 + 12 * q^55 - q^57 + 2 * q^59 + 3 * q^61 + 9 * q^63 + 19 * q^67 - 16 * q^71 + 11 * q^73 + 10 * q^75 - 32 * q^77 + 9 * q^79 - 3 * q^81 - 8 * q^85 + 6 * q^89 + q^91 - q^93 - 26 * q^95 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$-1$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	1.33641	−	2.31473i	0.597662	−	1.03518i	−0.395504	−	0.918464i	$-0.629430\pi$
$5$	1.33641	−	2.31473i	0.597662	−	1.03518i	0.993165	−	0.116716i	$-0.0372367\pi$
$6$		0			0
$7$			3.93569i			1.48755i	0.668430	+	0.743775i	$0.266967\pi$
$7$			3.93569i			1.48755i	−0.668430	+	0.743775i	$0.733033\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$			2.20364i			0.664421i	0.943205	+	0.332211i	$0.107795\pi$
$11$			2.20364i			0.664421i	−0.943205	+	0.332211i	$0.892205\pi$
$12$		0			0
$13$	−3.60083	+	2.07894i	−0.998691	+	0.576594i	−0.907861	−	0.419272i	$-0.862285\pi$
$13$	−3.60083	+	2.07894i	−0.998691	+	0.576594i	−0.0908300	+	0.995866i	$0.528952\pi$
$14$		0			0
$15$	1.33641	+	2.31473i	0.345060	+	0.597662i
$16$		0			0
$17$	−0.571993	+	0.990721i	−0.138729	+	0.240285i	−0.927016	−	0.375023i	$-0.877635\pi$
$17$	−0.571993	+	0.990721i	−0.138729	+	0.240285i	0.788287	+	0.615308i	$0.210968\pi$
$18$		0			0
$19$	−4.24482	+	0.990721i	−0.973828	+	0.227287i
$19$	−4.24482	+	0.990721i	−0.973828	+	0.227287i
$20$		0			0
$21$	−3.40841	−	1.96784i	−0.743775	−	0.429419i
$22$		0			0
$23$	3.19243	−	1.84315i	0.665667	−	0.384323i	−0.128766	−	0.991675i	$-0.541102\pi$
$23$	3.19243	−	1.84315i	0.665667	−	0.384323i	0.794433	+	0.607352i	$0.207768\pi$
$24$		0			0
$25$	−1.07199	−	1.85675i	−0.214399	−	0.371349i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.10083	+	1.21292i	−0.390114	+	0.225233i	−0.682210	−	0.731157i	$-0.738981\pi$
$29$	−2.10083	+	1.21292i	−0.390114	+	0.225233i	0.292095	+	0.956389i	$0.405648\pi$
$30$		0			0
$31$	3.67282			0.659659			0.329829	−	0.944041i	$-0.393009\pi$
$31$	3.67282			0.659659			0.329829	+	0.944041i	$0.393009\pi$
$32$		0			0
$33$	−1.90841	−	1.10182i	−0.332211	−	0.191802i
$34$		0			0
$35$	9.11007	+	5.25970i	1.53988	+	0.889051i
$36$		0			0
$37$			10.0478i			1.65185i	0.563780	+	0.825925i	$0.309347\pi$
$37$			10.0478i			1.65185i	−0.563780	+	0.825925i	$0.690653\pi$
$38$		0			0
$39$		−	4.15788i		−	0.665794i
$40$		0			0
$41$	8.01847	+	4.62947i	1.25227	+	0.723001i	0.971561	−	0.236790i	$-0.0760954\pi$
$41$	8.01847	+	4.62947i	1.25227	+	0.723001i	0.280714	+	0.959791i	$0.409429\pi$
$42$		0			0
$43$	−0.490764	−	0.283343i	−0.0748409	−	0.0432094i	0.462113	−	0.886821i	$-0.347092\pi$
$43$	−0.490764	−	0.283343i	−0.0748409	−	0.0432094i	−0.536953	+	0.843612i	$0.680425\pi$
$44$		0			0
$45$	−2.67282			−0.398441
$46$		0			0
$47$	−10.6336	+	6.13932i	−1.55107	+	0.895512i	−0.553018	+	0.833169i	$0.686524\pi$
$47$	−10.6336	+	6.13932i	−1.55107	+	0.895512i	−0.998055	+	0.0623432i	$0.980143\pi$
$48$		0			0
$49$	−8.48963			−1.21280
$50$		0			0
$51$	−0.571993	−	0.990721i	−0.0800951	−	0.138729i
$52$		0			0
$53$	4.09159	−	2.36228i	0.562024	−	0.324485i	−0.191934	−	0.981408i	$-0.561476\pi$
$53$	4.09159	−	2.36228i	0.562024	−	0.324485i	0.753957	+	0.656923i	$0.228142\pi$
$54$		0			0
$55$	5.10083	+	2.94497i	0.687796	+	0.397099i
$56$		0			0
$57$	1.26442	−	4.17148i	0.167476	−	0.552526i
$58$		0			0
$59$	−1.33641	+	2.31473i	−0.173986	+	0.301353i	−0.939810	−	0.341698i	$-0.888998\pi$
$59$	−1.33641	+	2.31473i	−0.173986	+	0.301353i	0.765824	+	0.643050i	$0.222331\pi$
$60$		0			0
$61$	−6.41764	−	11.1157i	−0.821695	−	1.42322i	−0.904419	−	0.426645i	$-0.859696\pi$
$61$	−6.41764	−	11.1157i	−0.821695	−	1.42322i	0.0827247	−	0.996572i	$-0.473638\pi$
$62$		0			0
$63$	3.40841	−	1.96784i	0.429419	−	0.247925i
$64$		0			0
$65$			11.1133i			1.37843i
$66$		0			0
$67$	1.73558	+	3.00612i	0.212035	+	0.367255i	0.952351	−	0.305003i	$-0.0986576\pi$
$67$	1.73558	+	3.00612i	0.212035	+	0.367255i	−0.740316	+	0.672259i	$0.765324\pi$
$68$		0			0
$69$			3.68630i			0.443778i
$70$		0			0
$71$	−6.24482	+	10.8163i	−0.741123	+	1.28366i	0.210861	+	0.977516i	$0.432373\pi$
$71$	−6.24482	+	10.8163i	−0.741123	+	1.28366i	−0.951984	+	0.306147i	$0.900960\pi$
$72$		0			0
$73$	1.35601	−	2.34868i	0.158709	−	0.274893i	−0.775694	−	0.631109i	$-0.782600\pi$
$73$	1.35601	−	2.34868i	0.158709	−	0.274893i	0.934404	+	0.356216i	$0.115933\pi$
$74$		0			0
$75$	2.14399			0.247566
$76$		0			0
$77$	−8.67282			−0.988360
$78$		0			0
$79$	−3.50924	+	6.07817i	−0.394820	+	0.683848i	−0.993078	−	0.117455i	$-0.962526\pi$
$79$	−3.50924	+	6.07817i	−0.394820	+	0.683848i	0.598258	+	0.801303i	$0.295860\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			1.98144i			0.217492i	0.994070	+	0.108746i	$0.0346835\pi$
$83$			1.98144i			0.217492i	−0.994070	+	0.108746i	$0.965317\pi$
$84$		0			0
$85$	1.52884	+	2.64802i	0.165826	+	0.287218i
$86$		0			0
$87$		−	2.42583i		−	0.260076i
$88$		0			0
$89$	12.9269	−	7.46334i	1.37025	−	0.791112i	0.379287	−	0.925279i	$-0.376169\pi$
$89$	12.9269	−	7.46334i	1.37025	−	0.791112i	0.990959	+	0.134167i	$0.0428358\pi$
$90$		0			0
$91$	−8.18206	−	14.1717i	−0.857713	−	1.48560i
$92$		0			0
$93$	−1.83641	+	3.18076i	−0.190427	+	0.329829i
$94$		0			0
$95$	−3.37957	+	11.1496i	−0.346736	+	1.14393i
$96$		0			0
$97$	2.91764	+	1.68450i	0.296242	+	0.171035i	0.640753	−	0.767747i	$-0.278622\pi$
$97$	2.91764	+	1.68450i	0.296242	+	0.171035i	−0.344512	+	0.938782i	$0.611956\pi$
$98$		0			0
$99$	1.90841	−	1.10182i	0.191802	−	0.110737i
$100$		0			0
$101$	−5.10083	−	8.83490i	−0.507552	−	0.879105i	−0.999962	−	0.00874190i	$-0.997217\pi$
$101$	−5.10083	−	8.83490i	−0.507552	−	0.879105i	0.492410	−	0.870363i	$-0.336116\pi$
$102$		0			0
$103$	16.4504			1.62091			0.810455	−	0.585802i	$-0.199220\pi$
$103$	16.4504			1.62091			0.810455	+	0.585802i	$0.199220\pi$
$104$		0			0
$105$	−9.11007	+	5.25970i	−0.889051	+	0.513294i
$106$		0			0
$107$	−4.85601			−0.469449			−0.234724	−	0.972062i	$-0.575419\pi$
$107$	−4.85601			−0.469449			−0.234724	+	0.972062i	$0.575419\pi$
$108$		0			0
$109$	−12.7345	−	7.35224i	−1.21974	−	0.704217i	−0.254877	−	0.966973i	$-0.582035\pi$
$109$	−12.7345	−	7.35224i	−1.21974	−	0.704217i	−0.964862	+	0.262757i	$0.915368\pi$
$110$		0			0
$111$	−8.70166	−	5.02391i	−0.825925	−	0.476848i
$112$		0			0
$113$			14.4823i			1.36238i	0.732107	+	0.681189i	$0.238537\pi$
$113$			14.4823i			1.36238i	−0.732107	+	0.681189i	$0.761463\pi$
$114$		0			0
$115$		−	9.85282i		−	0.918780i
$116$		0			0
$117$	3.60083	+	2.07894i	0.332897	+	0.192198i
$118$		0			0
$119$	−3.89917	−	2.25119i	−0.357436	−	0.206366i
$120$		0			0
$121$	6.14399			0.558544
$122$		0			0
$123$	−8.01847	+	4.62947i	−0.723001	+	0.417425i
$124$		0			0
$125$	7.63362			0.682772
$126$		0			0
$127$	−5.81681	−	10.0750i	−0.516158	−	0.894013i	−0.999824	−	0.0187598i	$-0.994028\pi$
$127$	−5.81681	−	10.0750i	−0.516158	−	0.894013i	0.483666	−	0.875253i	$-0.339305\pi$
$128$		0			0
$129$	0.490764	−	0.283343i	0.0432094	−	0.0249470i
$130$		0			0
$131$	10.7160	+	6.18687i	0.936260	+	0.540550i	0.888786	−	0.458323i	$-0.151550\pi$
$131$	10.7160	+	6.18687i	0.936260	+	0.540550i	0.0474737	+	0.998872i	$0.484883\pi$
$132$		0			0
$133$	−3.89917	−	16.7063i	−0.338101	−	1.44862i
$134$		0			0
$135$	1.33641	−	2.31473i	0.115020	−	0.199221i
$136$		0			0
$137$	4.71598	+	8.16832i	0.402913	+	0.697866i	0.994076	−	0.108686i	$-0.0346643\pi$
$137$	4.71598	+	8.16832i	0.402913	+	0.697866i	−0.591163	+	0.806552i	$0.701331\pi$
$138$		0			0
$139$	11.8941	−	6.86705i	1.00884	−	0.582456i	0.0979905	−	0.995187i	$-0.468759\pi$
$139$	11.8941	−	6.86705i	1.00884	−	0.582456i	0.910853	+	0.412731i	$0.135425\pi$
$140$		0			0
$141$		−	12.2786i		−	1.03405i
$142$		0			0
$143$	−4.58123	−	7.93492i	−0.383102	−	0.663551i
$144$		0			0
$145$			6.48382i			0.538452i
$146$		0			0
$147$	4.24482	−	7.35224i	0.350107	−	0.606402i
$148$		0			0
$149$	8.15322	−	14.1218i	0.667938	−	1.15690i	−0.310542	−	0.950560i	$-0.600510\pi$
$149$	8.15322	−	14.1218i	0.667938	−	1.15690i	0.978480	−	0.206343i	$-0.0661562\pi$
$150$		0			0
$151$	−7.05767			−0.574345			−0.287173	−	0.957879i	$-0.592715\pi$
$151$	−7.05767			−0.574345			−0.287173	+	0.957879i	$0.592715\pi$
$152$		0			0
$153$	1.14399			0.0924858
$154$		0			0
$155$	4.90841	−	8.50161i	0.394253	−	0.682866i
$156$		0			0
$157$	5.66246	−	9.80766i	0.451913	−	0.782737i	−0.546592	−	0.837399i	$-0.684075\pi$
$157$	5.66246	−	9.80766i	0.451913	−	0.782737i	0.998505	+	0.0546625i	$0.0174083\pi$
$158$		0			0
$159$			4.72457i			0.374683i
$160$		0			0
$161$	7.25405	+	12.5644i	0.571699	+	0.990212i
$162$		0			0
$163$			0.915973i			0.0717445i	0.999356	+	0.0358723i	$0.0114209\pi$
$163$			0.915973i			0.0717445i	−0.999356	+	0.0358723i	$0.988579\pi$
$164$		0			0
$165$	−5.10083	+	2.94497i	−0.397099	+	0.229265i
$166$		0			0
$167$	0.192425	+	0.333290i	0.0148903	+	0.0257908i	0.873375	−	0.487049i	$-0.161927\pi$
$167$	0.192425	+	0.333290i	0.0148903	+	0.0257908i	−0.858484	+	0.512840i	$0.828593\pi$
$168$		0			0
$169$	2.14399	−	3.71349i	0.164922	−	0.285653i
$170$		0			0
$171$	2.98040	+	3.18076i	0.227917	+	0.243239i
$172$		0			0
$173$	9.34960	+	5.39799i	0.710837	+	0.410402i	0.811371	−	0.584532i	$-0.198722\pi$
$173$	9.34960	+	5.39799i	0.710837	+	0.410402i	−0.100534	+	0.994934i	$0.532055\pi$
$174$		0			0
$175$	7.30757	−	4.21903i	0.552401	−	0.318929i
$176$		0			0
$177$	−1.33641	−	2.31473i	−0.100451	−	0.173986i
$178$		0			0
$179$	1.03920			0.0776737			0.0388368	−	0.999246i	$-0.487635\pi$
$179$	1.03920			0.0776737			0.0388368	+	0.999246i	$0.487635\pi$
$180$		0			0
$181$	−6.73445	+	3.88814i	−0.500568	+	0.289003i	−0.728948	−	0.684569i	$-0.759990\pi$
$181$	−6.73445	+	3.88814i	−0.500568	+	0.289003i	0.228380	+	0.973572i	$0.426657\pi$
$182$		0			0
$183$	12.8353			0.948811
$184$		0			0
$185$	23.2580	+	13.4280i	1.70996	+	0.987247i
$186$		0			0
$187$	−2.18319	−	1.26047i	−0.159651	−	0.0921743i
$188$		0			0
$189$			3.93569i			0.286279i
$190$		0			0
$191$		−	26.2621i		−	1.90026i	−0.311851	−	0.950131i	$-0.600949\pi$
$191$		−	26.2621i		−	1.90026i	0.311851	−	0.950131i	$-0.399051\pi$
$192$		0			0
$193$	8.23445	+	4.75416i	0.592729	+	0.342212i	0.766176	−	0.642631i	$-0.222157\pi$
$193$	8.23445	+	4.75416i	0.592729	+	0.342212i	−0.173447	+	0.984843i	$0.555491\pi$
$194$		0			0
$195$	−9.62438	−	5.55664i	−0.689217	−	0.397919i
$196$		0			0
$197$	27.9322			1.99008			0.995042	−	0.0994560i	$-0.0317103\pi$
$197$	27.9322			1.99008			0.995042	+	0.0994560i	$0.0317103\pi$
$198$		0			0
$199$	−6.87562	+	3.96964i	−0.487399	+	0.281400i	−0.723495	−	0.690330i	$-0.757466\pi$
$199$	−6.87562	+	3.96964i	−0.487399	+	0.281400i	0.236096	+	0.971730i	$0.424132\pi$
$200$		0			0
$201$	−3.47116			−0.244837
$202$		0			0
$203$	−4.77365	−	8.26821i	−0.335045	−	0.580315i
$204$		0			0
$205$	21.4320	−	12.3737i	1.49687	−	0.864220i
$206$		0			0
$207$	−3.19243	−	1.84315i	−0.221889	−	0.128108i
$208$		0			0
$209$	−2.18319	−	9.35403i	−0.151014	−	0.647032i
$210$		0			0
$211$	4.32605	−	7.49293i	0.297817	−	0.515835i	−0.677819	−	0.735229i	$-0.737075\pi$
$211$	4.32605	−	7.49293i	0.297817	−	0.515835i	0.975636	+	0.219394i	$0.0704081\pi$
$212$		0			0
$213$	−6.24482	−	10.8163i	−0.427888	−	0.741123i
$214$		0			0
$215$	−1.31173	+	0.757326i	−0.0894590	+	0.0516492i
$216$		0			0
$217$			14.4551i			0.981275i
$218$		0			0
$219$	1.35601	+	2.34868i	0.0916309	+	0.158709i
$220$		0			0
$221$		−	4.75656i		−	0.319961i
$222$		0			0
$223$	7.18206	−	12.4397i	0.480946	−	0.833023i	−0.518815	−	0.854887i	$-0.673627\pi$
$223$	7.18206	−	12.4397i	0.480946	−	0.833023i	0.999761	+	0.0218634i	$0.00695988\pi$
$224$		0			0
$225$	−1.07199	+	1.85675i	−0.0714662	+	0.123783i
$226$		0			0
$227$	−14.1832			−0.941371			−0.470686	−	0.882301i	$-0.655993\pi$
$227$	−14.1832			−0.941371			−0.470686	+	0.882301i	$0.655993\pi$
$228$		0			0
$229$	−16.5473			−1.09348			−0.546738	−	0.837303i	$-0.684131\pi$
$229$	−16.5473			−1.09348			−0.546738	+	0.837303i	$0.684131\pi$
$230$		0			0
$231$	4.33641	−	7.51089i	0.285315	−	0.494180i
$232$		0			0
$233$	13.1193	−	22.7233i	0.859474	−	1.48865i	−0.0129574	−	0.999916i	$-0.504125\pi$
$233$	13.1193	−	22.7233i	0.859474	−	1.48865i	0.872431	−	0.488737i	$-0.162542\pi$
$234$		0			0
$235$			32.8187i			2.14085i
$236$		0			0
$237$	−3.50924	−	6.07817i	−0.227949	−	0.394820i
$238$		0			0
$239$		−	1.26047i		−	0.0815327i	−0.999169	−	0.0407664i	$-0.987020\pi$
$239$		−	1.26047i		−	0.0815327i	0.999169	−	0.0407664i	$-0.0129799\pi$
$240$		0			0
$241$	−18.1336	+	10.4695i	−1.16809	+	0.674397i	−0.953229	−	0.302248i	$-0.902263\pi$
$241$	−18.1336	+	10.4695i	−1.16809	+	0.674397i	−0.214860	+	0.976645i	$0.568930\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−11.3456	+	19.6512i	−0.724847	+	1.25547i
$246$		0			0
$247$	13.2252	−	12.3921i	0.841500	−	0.788493i
$248$		0			0
$249$	−1.71598	−	0.990721i	−0.108746	−	0.0627844i
$250$		0			0
$251$	24.6521	−	14.2329i	1.55603	−	0.898372i	0.558396	−	0.829575i	$-0.311417\pi$
$251$	24.6521	−	14.2329i	1.55603	−	0.898372i	0.997631	−	0.0687973i	$-0.0219162\pi$
$252$		0			0
$253$	4.06163	+	7.03494i	0.255352	+	0.442283i
$254$		0			0
$255$	−3.05767			−0.191479
$256$		0			0
$257$	10.4764	−	6.04858i	0.653503	−	0.377300i	−0.136294	−	0.990668i	$-0.543519\pi$
$257$	10.4764	−	6.04858i	0.653503	−	0.377300i	0.789797	+	0.613368i	$0.210186\pi$
$258$		0			0
$259$	−39.5450			−2.45721
$260$		0			0
$261$	2.10083	+	1.21292i	0.130038	+	0.0750776i
$262$		0			0
$263$	−1.11930	−	0.646229i	−0.0690191	−	0.0398482i	0.465093	−	0.885262i	$-0.346021\pi$
$263$	−1.11930	−	0.646229i	−0.0690191	−	0.0398482i	−0.534112	+	0.845413i	$0.679354\pi$
$264$		0			0
$265$		−	12.6279i		−	0.775728i
$266$		0			0
$267$			14.9267i			0.913497i
$268$		0			0
$269$	−24.5420	−	14.1693i	−1.49635	−	0.863920i	−0.496363	−	0.868115i	$-0.665331\pi$
$269$	−24.5420	−	14.1693i	−1.49635	−	0.863920i	−0.999991	+	0.00419513i	$0.998665\pi$
$270$		0			0
$271$	−13.2017	−	7.62198i	−0.801944	−	0.463002i	0.0422066	−	0.999109i	$-0.486561\pi$
$271$	−13.2017	−	7.62198i	−0.801944	−	0.463002i	−0.844150	+	0.536106i	$0.819895\pi$
$272$		0			0
$273$	16.3641			0.990402
$274$		0			0
$275$	4.09159	−	2.36228i	0.246732	−	0.142451i
$276$		0			0
$277$	−15.8353			−0.951450			−0.475725	−	0.879594i	$-0.657814\pi$
$277$	−15.8353			−0.951450			−0.475725	+	0.879594i	$0.657814\pi$
$278$		0			0
$279$	−1.83641	−	3.18076i	−0.109943	−	0.190427i
$280$		0			0
$281$	−15.8445	+	9.14784i	−0.945205	+	0.545714i	−0.891588	−	0.452847i	$-0.850408\pi$
$281$	−15.8445	+	9.14784i	−0.945205	+	0.545714i	−0.0536166	+	0.998562i	$0.517075\pi$
$282$		0			0
$283$	−25.4218	−	14.6773i	−1.51117	−	0.872474i	−0.999915	−	0.0130439i	$-0.995848\pi$
$283$	−25.4218	−	14.6773i	−1.51117	−	0.872474i	−0.511254	−	0.859430i	$-0.670819\pi$
$284$		0			0
$285$	−7.96608	−	8.50161i	−0.471870	−	0.503592i
$286$		0			0
$287$	−18.2201	+	31.5582i	−1.07550	+	1.86282i
$288$		0			0
$289$	7.84565	+	13.5891i	0.461509	+	0.799356i
$290$		0			0
$291$	−2.91764	+	1.68450i	−0.171035	+	0.0987472i
$292$		0			0
$293$			19.6512i			1.14804i	0.818842	+	0.574019i	$0.194616\pi$
$293$			19.6512i			1.14804i	−0.818842	+	0.574019i	$0.805384\pi$
$294$		0			0
$295$	3.57199	+	6.18687i	0.207969	+	0.360214i
$296$		0			0
$297$			2.20364i			0.127868i
$298$		0			0
$299$	−7.66359	+	13.2737i	−0.443197	+	0.767639i
$300$		0			0
$301$	1.11515	−	1.93150i	0.0642761	−	0.111330i
$302$		0			0
$303$	10.2017			0.586070
$304$		0			0
$305$	−34.3064			−1.96438
$306$		0			0
$307$	−3.59046	+	6.21887i	−0.204919	+	0.354929i	−0.950107	−	0.311925i	$-0.899026\pi$
$307$	−3.59046	+	6.21887i	−0.204919	+	0.354929i	0.745188	+	0.666854i	$0.232360\pi$
$308$		0			0
$309$	−8.22522	+	14.2465i	−0.467916	+	0.810455i
$310$		0			0
$311$		−	29.1868i		−	1.65503i	−0.561444	−	0.827515i	$-0.689754\pi$
$311$		−	29.1868i		−	1.65503i	0.561444	−	0.827515i	$-0.310246\pi$
$312$		0			0
$313$	7.24482	+	12.5484i	0.409501	+	0.709277i	0.994834	−	0.101516i	$-0.0323694\pi$
$313$	7.24482	+	12.5484i	0.409501	+	0.709277i	−0.585333	+	0.810793i	$0.699036\pi$
$314$		0			0
$315$		−	10.5194i		−	0.592701i
$316$		0			0
$317$	−2.37562	+	1.37156i	−0.133428	+	0.0770346i	−0.565228	−	0.824935i	$-0.691212\pi$
$317$	−2.37562	+	1.37156i	−0.133428	+	0.0770346i	0.431800	+	0.901969i	$0.357879\pi$
$318$		0			0
$319$	−2.67282	−	4.62947i	−0.149649	−	0.259200i
$320$		0			0
$321$	2.42801	−	4.20543i	0.135518	−	0.234724i
$322$		0			0
$323$	1.44648	−	4.77212i	0.0804842	−	0.265528i
$324$		0			0
$325$	7.72013	+	4.45722i	0.428236	+	0.247242i
$326$		0			0
$327$	12.7345	−	7.35224i	0.704217	−	0.406580i
$328$		0			0
$329$	−24.1625	−	41.8506i	−1.33212	−	2.30730i
$330$		0			0
$331$	10.0761			0.553835			0.276918	−	0.960894i	$-0.410687\pi$
$331$	10.0761			0.553835			0.276918	+	0.960894i	$0.410687\pi$
$332$		0			0
$333$	8.70166	−	5.02391i	0.476848	−	0.275308i
$334$		0			0
$335$	9.27781			0.506901
$336$		0			0
$337$	3.76555	+	2.17404i	0.205123	+	0.118428i	0.599043	−	0.800717i	$-0.295548\pi$
$337$	3.76555	+	2.17404i	0.205123	+	0.118428i	−0.393920	+	0.919145i	$0.628881\pi$
$338$		0			0
$339$	−12.5420	−	7.24114i	−0.681189	−	0.393285i
$340$		0			0
$341$			8.09357i			0.438291i
$342$		0			0
$343$		−	5.86273i		−	0.316558i
$344$		0			0
$345$	8.53279	+	4.92641i	0.459390	+	0.265229i
$346$		0			0
$347$	0.542026	+	0.312939i	0.0290975	+	0.0167994i	0.514478	−	0.857503i	$-0.327986\pi$
$347$	0.542026	+	0.312939i	0.0290975	+	0.0167994i	−0.485381	+	0.874303i	$0.661319\pi$
$348$		0			0
$349$	6.79834			0.363907			0.181953	−	0.983307i	$-0.441758\pi$
$349$	6.79834			0.363907			0.181953	+	0.983307i	$0.441758\pi$
$350$		0			0
$351$	−3.60083	+	2.07894i	−0.192198	+	0.110966i
$352$		0			0
$353$	20.0185			1.06548			0.532738	−	0.846280i	$-0.321163\pi$
$353$	20.0185			1.06548			0.532738	+	0.846280i	$0.321163\pi$
$354$		0			0
$355$	16.6913	+	28.9102i	0.885882	+	1.53439i
$356$		0			0
$357$	3.89917	−	2.25119i	0.206366	−	0.119145i
$358$		0			0
$359$	14.7882	+	8.53796i	0.780490	+	0.450616i	0.836604	−	0.547808i	$-0.184538\pi$
$359$	14.7882	+	8.53796i	0.780490	+	0.450616i	−0.0561140	+	0.998424i	$0.517871\pi$
$360$		0			0
$361$	17.0369	−	8.41086i	0.896681	−	0.442677i
$362$		0			0
$363$	−3.07199	+	5.32085i	−0.161238	+	0.279272i
$364$		0			0
$365$	−3.62438	−	6.27762i	−0.189709	−	0.328586i
$366$		0			0
$367$	25.5277	−	14.7384i	1.33254	−	0.769340i	0.346848	−	0.937921i	$-0.387252\pi$
$367$	25.5277	−	14.7384i	1.33254	−	0.769340i	0.985688	+	0.168582i	$0.0539187\pi$
$368$		0			0
$369$		−	9.25893i		−	0.482001i
$370$		0			0
$371$	9.29721	+	16.1032i	0.482687	+	0.836038i
$372$		0			0
$373$			26.6745i			1.38116i	0.723258	+	0.690578i	$0.242644\pi$
$373$			26.6745i			1.38116i	−0.723258	+	0.690578i	$0.757356\pi$
$374$		0			0
$375$	−3.81681	+	6.61091i	−0.197099	+	0.341386i
$376$		0			0
$377$	5.04316	−	8.73500i	0.259736	−	0.449876i
$378$		0			0
$379$	6.80890			0.349750			0.174875	−	0.984591i	$-0.444048\pi$
$379$	6.80890			0.349750			0.174875	+	0.984591i	$0.444048\pi$
$380$		0			0
$381$	11.6336			0.596008
$382$		0			0
$383$	−5.23558	+	9.06829i	−0.267526	+	0.463368i	−0.968222	−	0.250091i	$-0.919539\pi$
$383$	−5.23558	+	9.06829i	−0.267526	+	0.463368i	0.700697	+	0.713459i	$0.252873\pi$
$384$		0			0
$385$	−11.5905	+	20.0753i	−0.590705	+	1.02313i
$386$		0			0
$387$			0.566686i			0.0288063i
$388$		0			0
$389$	−1.25405	−	2.17208i	−0.0635830	−	0.110129i	0.832482	−	0.554053i	$-0.186919\pi$
$389$	−1.25405	−	2.17208i	−0.0635830	−	0.110129i	−0.896065	+	0.443924i	$0.853586\pi$
$390$		0			0
$391$			4.21707i			0.213267i
$392$		0			0
$393$	−10.7160	+	6.18687i	−0.540550	+	0.312087i
$394$		0			0
$395$	9.37957	+	16.2459i	0.471937	+	0.817419i
$396$		0			0
$397$	−4.54316	+	7.86898i	−0.228014	+	0.394933i	−0.957220	−	0.289363i	$-0.906557\pi$
$397$	−4.54316	+	7.86898i	−0.228014	+	0.394933i	0.729205	+	0.684295i	$0.239890\pi$
$398$		0			0
$399$	16.4176	+	4.97636i	0.821910	+	0.249129i
$400$		0			0
$401$	−9.97399	−	5.75848i	−0.498077	−	0.287565i	0.229842	−	0.973228i	$-0.426179\pi$
$401$	−9.97399	−	5.75848i	−0.498077	−	0.287565i	−0.727919	+	0.685663i	$0.759512\pi$
$402$		0			0
$403$	−13.2252	+	7.63558i	−0.658795	+	0.380355i
$404$		0			0
$405$	1.33641	+	2.31473i	0.0664068	+	0.115020i
$406$		0			0
$407$	−22.1417			−1.09752
$408$		0			0
$409$	16.1664	−	9.33368i	0.799378	−	0.461521i	−0.0438759	−	0.999037i	$-0.513971\pi$
$409$	16.1664	−	9.33368i	0.799378	−	0.461521i	0.843253	+	0.537516i	$0.180637\pi$
$410$		0			0
$411$	−9.43196			−0.465244
$412$		0			0
$413$	−9.11007	−	5.25970i	−0.448277	−	0.258813i
$414$		0			0
$415$	4.58651	+	2.64802i	0.225143	+	0.129986i
$416$		0			0
$417$			13.7341i			0.672562i
$418$		0			0
$419$			27.2053i			1.32907i	0.747259	+	0.664533i	$0.231370\pi$
$419$			27.2053i			1.32907i	−0.747259	+	0.664533i	$0.768630\pi$
$420$		0			0
$421$	−1.11930	−	0.646229i	−0.0545514	−	0.0314953i	0.472476	−	0.881343i	$-0.343360\pi$
$421$	−1.11930	−	0.646229i	−0.0545514	−	0.0314953i	−0.527028	+	0.849848i	$0.676694\pi$
$422$		0			0
$423$	10.6336	+	6.13932i	0.517024	+	0.298504i
$424$		0			0
$425$	2.45269			0.118973
$426$		0			0
$427$	43.7478	−	25.2578i	2.11711	−	1.22231i
$428$		0			0
$429$	9.16246			0.442368
$430$		0			0
$431$	10.6336	+	18.4180i	0.512203	+	0.887162i	0.999900	+	0.0141492i	$0.00450397\pi$
$431$	10.6336	+	18.4180i	0.512203	+	0.887162i	−0.487696	+	0.873013i	$0.662163\pi$
$432$		0			0
$433$	33.3890	−	19.2771i	1.60457	−	0.926401i	0.614017	−	0.789293i	$-0.289553\pi$
$433$	33.3890	−	19.2771i	1.60457	−	0.926401i	0.990556	−	0.137108i	$-0.0437807\pi$
$434$		0			0
$435$	−5.61515	−	3.24191i	−0.269226	−	0.155438i
$436$		0			0
$437$	−11.7252	+	10.9866i	−0.560893	+	0.525562i
$438$		0			0
$439$	−12.3692	+	21.4241i	−0.590350	+	1.02252i	0.403835	+	0.914832i	$0.367677\pi$
$439$	−12.3692	+	21.4241i	−0.590350	+	1.02252i	−0.994185	+	0.107684i	$0.965656\pi$
$440$		0			0
$441$	4.24482	+	7.35224i	0.202134	+	0.350107i
$442$		0			0
$443$	31.5513	−	18.2161i	1.49905	−	0.865474i	0.499046	−	0.866575i	$-0.333684\pi$
$443$	31.5513	−	18.2161i	1.49905	−	0.865474i	0.999999	+	0.00110093i	$0.000350438\pi$
$444$		0			0
$445$		−	39.8964i		−	1.89127i
$446$		0			0
$447$	8.15322	+	14.1218i	0.385634	+	0.667938i
$448$		0			0
$449$			28.9509i			1.36628i	0.730289	+	0.683138i	$0.239385\pi$
$449$			28.9509i			1.36628i	−0.730289	+	0.683138i	$0.760615\pi$
$450$		0			0
$451$	−10.2017	+	17.6698i	−0.480377	+	0.832038i
$452$		0			0
$453$	3.52884	−	6.11213i	0.165799	−	0.287173i
$454$		0			0
$455$	−43.7384			−2.05049
$456$		0			0
$457$	−14.2224			−0.665295			−0.332648	−	0.943051i	$-0.607942\pi$
$457$	−14.2224			−0.665295			−0.332648	+	0.943051i	$0.607942\pi$
$458$		0			0
$459$	−0.571993	+	0.990721i	−0.0266984	+	0.0462429i
$460$		0			0
$461$	−18.1677	+	31.4674i	−0.846156	+	1.46559i	0.0384575	+	0.999260i	$0.487756\pi$
$461$	−18.1677	+	31.4674i	−0.846156	+	1.46559i	−0.884613	+	0.466325i	$0.845578\pi$
$462$		0			0
$463$			29.6264i			1.37685i	0.725306	+	0.688427i	$0.241698\pi$
$463$			29.6264i			1.37685i	−0.725306	+	0.688427i	$0.758302\pi$
$464$		0			0
$465$	4.90841	+	8.50161i	0.227622	+	0.394253i
$466$		0			0
$467$		−	30.4879i		−	1.41081i	−0.708803	−	0.705407i	$-0.750764\pi$
$467$		−	30.4879i		−	1.41081i	0.708803	−	0.705407i	$-0.249236\pi$
$468$		0			0
$469$	−11.8311	+	6.83071i	−0.546311	+	0.315413i
$470$		0			0
$471$	5.66246	+	9.80766i	0.260912	+	0.451913i
$472$		0			0
$473$	0.624385	−	1.08147i	0.0287092	−	0.0497259i
$474$		0			0
$475$	6.38993	+	6.81950i	0.293190	+	0.312900i
$476$		0			0
$477$	−4.09159	−	2.36228i	−0.187341	−	0.108162i
$478$		0			0
$479$	−20.5882	+	11.8866i	−0.940699	+	0.543113i	−0.890179	−	0.455610i	$-0.849421\pi$
$479$	−20.5882	+	11.8866i	−0.940699	+	0.543113i	−0.0505196	+	0.998723i	$0.516088\pi$
$480$		0			0
$481$	−20.8888	−	36.1805i	−0.952447	−	1.64969i
$482$		0			0
$483$	−14.5081			−0.660142
$484$		0			0
$485$	7.79834	−	4.50237i	0.354104	−	0.204442i
$486$		0			0
$487$	−10.2880			−0.466193			−0.233096	−	0.972454i	$-0.574886\pi$
$487$	−10.2880			−0.466193			−0.233096	+	0.972454i	$0.574886\pi$
$488$		0			0
$489$	−0.793256	−	0.457986i	−0.0358723	−	0.0207109i
$490$		0			0
$491$	28.5513	+	16.4841i	1.28850	+	0.743916i	0.978387	−	0.206783i	$-0.0662996\pi$
$491$	28.5513	+	16.4841i	1.28850	+	0.743916i	0.310114	+	0.950699i	$0.399633\pi$
$492$		0			0
$493$		−	2.77512i		−	0.124985i
$494$		0			0
$495$		−	5.88993i		−	0.264733i
$496$		0			0
$497$	−42.5697	−	24.5776i	−1.90951	−	1.10246i
$498$		0			0
$499$	−14.2067	−	8.20227i	−0.635981	−	0.367184i	0.147084	−	0.989124i	$-0.453011\pi$
$499$	−14.2067	−	8.20227i	−0.635981	−	0.367184i	−0.783065	+	0.621940i	$0.786345\pi$
$500$		0			0
$501$	−0.384851			−0.0171939
$502$		0			0
$503$	−12.8521	+	7.42014i	−0.573045	+	0.330848i	−0.758365	−	0.651831i	$-0.774001\pi$
$503$	−12.8521	+	7.42014i	−0.573045	+	0.330848i	0.185320	+	0.982678i	$0.440668\pi$
$504$		0			0
$505$	−27.2672			−1.21338
$506$		0			0
$507$	2.14399	+	3.71349i	0.0952178	+	0.164922i
$508$		0			0
$509$	24.8168	−	14.3280i	1.09999	−	0.635077i	0.163769	−	0.986499i	$-0.447635\pi$
$509$	24.8168	−	14.3280i	1.09999	−	0.635077i	0.936217	+	0.351422i	$0.114302\pi$
$510$		0			0
$511$	9.24369	+	5.33684i	0.408917	+	0.236088i
$512$		0			0
$513$	−4.24482	+	0.990721i	−0.187413	+	0.0437414i
$514$		0			0
$515$	21.9846	−	38.0784i	0.968755	−	1.67793i
$516$		0			0
$517$	−13.5288	−	23.4326i	−0.594998	−	1.03057i
$518$		0			0
$519$	−9.34960	+	5.39799i	−0.410402	+	0.236946i
$520$		0			0
$521$			0.911178i			0.0399194i	0.999801	+	0.0199597i	$0.00635380\pi$
$521$			0.911178i			0.0399194i	−0.999801	+	0.0199597i	$0.993646\pi$
$522$		0			0
$523$	5.12043	+	8.86885i	0.223901	+	0.387808i	0.955989	−	0.293402i	$-0.0947875\pi$
$523$	5.12043	+	8.86885i	0.223901	+	0.387808i	−0.732088	+	0.681210i	$0.761454\pi$
$524$		0			0
$525$			8.43806i			0.368267i
$526$		0			0
$527$	−2.10083	+	3.63875i	−0.0915136	+	0.158506i
$528$		0			0
$529$	−4.70561	+	8.15036i	−0.204592	+	0.354364i
$530$		0			0
$531$	2.67282			0.115991
$532$		0			0
$533$	−38.4975			−1.66751
$534$		0			0
$535$	−6.48963	+	11.2404i	−0.280571	+	0.485964i
$536$		0			0
$537$	−0.519602	+	0.899976i	−0.0224225	+	0.0388368i
$538$		0			0
$539$		−	18.7081i		−	0.805813i
$540$		0			0
$541$	19.6233	+	33.9885i	0.843670	+	1.46128i	0.886772	+	0.462208i	$0.152943\pi$
$541$	19.6233	+	33.9885i	0.843670	+	1.46128i	−0.0431020	+	0.999071i	$0.513724\pi$
$542$		0			0
$543$		−	7.77627i		−	0.333712i
$544$		0			0
$545$	−34.0369	+	19.6512i	−1.45798	+	0.841767i
$546$		0			0
$547$	5.81794	+	10.0770i	0.248757	+	0.430860i	0.963181	−	0.268853i	$-0.0866446\pi$
$547$	5.81794	+	10.0770i	0.248757	+	0.430860i	−0.714424	+	0.699713i	$0.753311\pi$
$548$		0			0
$549$	−6.41764	+	11.1157i	−0.273898	+	0.474406i
$550$		0			0
$551$	7.71598	−	7.22994i	0.328712	−	0.308006i
$552$		0			0
$553$	−23.9218	−	13.8113i	−1.01726	−	0.587314i
$554$		0			0
$555$	−23.2580	+	13.4280i	−0.987247	+	0.569988i
$556$		0			0
$557$	−0.514319	−	0.890827i	−0.0217924	−	0.0377455i	0.854924	−	0.518754i	$-0.173604\pi$
$557$	−0.514319	−	0.890827i	−0.0217924	−	0.0377455i	−0.876716	+	0.481008i	$0.840271\pi$
$558$		0			0
$559$	2.35621			0.0996572
$560$		0			0
$561$	2.18319	−	1.26047i	0.0921743	−	0.0532169i
$562$		0			0
$563$	4.29588			0.181050			0.0905249	−	0.995894i	$-0.471146\pi$
$563$	4.29588			0.181050			0.0905249	+	0.995894i	$0.471146\pi$
$564$		0			0
$565$	33.5226	+	19.3543i	1.41031	+	0.814241i
$566$		0			0
$567$	−3.40841	−	1.96784i	−0.143140	−	0.0826417i
$568$		0			0
$569$		−	25.9992i		−	1.08995i	−0.838454	−	0.544973i	$-0.816540\pi$
$569$		−	25.9992i		−	1.08995i	0.838454	−	0.544973i	$-0.183460\pi$
$570$		0			0
$571$			35.2310i			1.47437i	0.675691	+	0.737185i	$0.263846\pi$
$571$			35.2310i			1.47437i	−0.675691	+	0.737185i	$0.736154\pi$
$572$		0			0
$573$	22.7437	+	13.1311i	0.950131	+	0.548558i
$574$		0			0
$575$	−6.84452	−	3.95168i	−0.285436	−	0.164797i
$576$		0			0
$577$	9.51037			0.395922			0.197961	−	0.980210i	$-0.436568\pi$
$577$	9.51037			0.395922			0.197961	+	0.980210i	$0.436568\pi$
$578$		0			0
$579$	−8.23445	+	4.75416i	−0.342212	+	0.197576i
$580$		0			0
$581$	−7.79834			−0.323530
$582$		0			0
$583$	5.20561	+	9.01639i	0.215594	+	0.373421i
$584$		0			0
$585$	9.62438	−	5.55664i	0.397919	−	0.229739i
$586$		0			0
$587$	−9.84452	−	5.68373i	−0.406327	−	0.234593i	0.282884	−	0.959154i	$-0.408709\pi$
$587$	−9.84452	−	5.68373i	−0.406327	−	0.234593i	−0.689210	+	0.724561i	$0.742042\pi$
$588$		0			0
$589$	−15.5905	+	3.63875i	−0.642394	+	0.149932i
$590$		0			0
$591$	−13.9661	+	24.1900i	−0.574488	+	0.995042i
$592$		0			0
$593$	12.9269	+	22.3900i	0.530843	+	0.919447i	0.999352	+	0.0359886i	$0.0114580\pi$
$593$	12.9269	+	22.3900i	0.530843	+	0.919447i	−0.468509	+	0.883459i	$0.655209\pi$
$594$		0			0
$595$	−10.4218	+	6.01702i	−0.427252	+	0.246674i
$596$		0			0
$597$		−	7.93928i		−	0.324933i
$598$		0			0
$599$	−2.56276	−	4.43883i	−0.104711	−	0.181366i	0.808909	−	0.587934i	$-0.200059\pi$
$599$	−2.56276	−	4.43883i	−0.104711	−	0.181366i	−0.913620	+	0.406569i	$0.866725\pi$
$600$		0			0
$601$		−	12.7822i		−	0.521398i	−0.965420	−	0.260699i	$-0.916047\pi$
$601$		−	12.7822i		−	0.521398i	0.965420	−	0.260699i	$-0.0839530\pi$
$602$		0			0
$603$	1.73558	−	3.00612i	0.0706783	−	0.122418i
$604$		0			0
$605$	8.21090	−	14.2217i	0.333820	−	0.578194i
$606$		0			0
$607$	−31.7882			−1.29024			−0.645121	−	0.764080i	$-0.723193\pi$
$607$	−31.7882			−1.29024			−0.645121	+	0.764080i	$0.723193\pi$
$608$		0			0
$609$	9.54731			0.386876
$610$		0			0
$611$	25.5266	−	44.2133i	1.03269	−	1.78868i
$612$		0			0
$613$	−21.1664	+	36.6613i	−0.854903	+	1.48074i	0.0218315	+	0.999762i	$0.493050\pi$
$613$	−21.1664	+	36.6613i	−0.854903	+	1.48074i	−0.876735	+	0.480974i	$0.840283\pi$
$614$		0			0
$615$			24.7475i			0.997915i
$616$		0			0
$617$	−10.1717	−	17.6179i	−0.409497	−	0.709270i	0.585336	−	0.810791i	$-0.300962\pi$
$617$	−10.1717	−	17.6179i	−0.409497	−	0.709270i	−0.994833	+	0.101521i	$0.967629\pi$
$618$		0			0
$619$			13.1402i			0.528150i	0.964502	+	0.264075i	$0.0850667\pi$
$619$			13.1402i			0.528150i	−0.964502	+	0.264075i	$0.914933\pi$
$620$		0			0
$621$	3.19243	−	1.84315i	0.128108	−	0.0739630i
$622$		0			0
$623$	29.3734	+	50.8761i	1.17682	+	2.03831i
$624$		0			0
$625$	15.5616	−	26.9535i	0.622465	−	1.07814i
$626$		0			0
$627$	9.19243	+	2.78632i	0.367110	+	0.111275i
$628$		0			0
$629$	−9.95458	−	5.74728i	−0.396915	−	0.229159i
$630$		0			0
$631$	3.57312	−	2.06294i	0.142244	−	0.0821245i	−0.427189	−	0.904162i	$-0.640496\pi$
$631$	3.57312	−	2.06294i	0.142244	−	0.0821245i	0.569433	+	0.822038i	$0.307163\pi$
$632$		0			0
$633$	4.32605	+	7.49293i	0.171945	+	0.297817i
$634$		0			0
$635$	−31.0946			−1.23395
$636$		0			0
$637$	30.5697	−	17.6494i	1.21122	−	0.699296i
$638$		0			0
$639$	12.4896			0.494082
$640$		0			0
$641$	31.9714	+	18.4587i	1.26279	+	0.729074i	0.973614	−	0.228201i	$-0.0732844\pi$
$641$	31.9714	+	18.4587i	1.26279	+	0.729074i	0.289179	+	0.957275i	$0.406618\pi$
$642$		0			0
$643$	6.62854	+	3.82699i	0.261404	+	0.150922i	0.624975	−	0.780645i	$-0.285109\pi$
$643$	6.62854	+	3.82699i	0.261404	+	0.150922i	−0.363571	+	0.931567i	$0.618443\pi$
$644$		0			0
$645$		−	1.51465i		−	0.0596394i
$646$		0			0
$647$		−	26.5387i		−	1.04335i	−0.853146	−	0.521673i	$-0.825308\pi$
$647$		−	26.5387i		−	1.04335i	0.853146	−	0.521673i	$-0.174692\pi$
$648$		0			0
$649$	−5.10083	−	2.94497i	−0.200225	−	0.115600i
$650$		0			0
$651$	−12.5185	−	7.22754i	−0.490638	−	0.283270i
$652$		0			0
$653$	−2.23860			−0.0876033			−0.0438017	−	0.999040i	$-0.513947\pi$
$653$	−2.23860			−0.0876033			−0.0438017	+	0.999040i	$0.513947\pi$
$654$		0			0
$655$	28.6419	−	16.5364i	1.11913	−	0.646132i
$656$		0			0
$657$	−2.71203			−0.105806
$658$		0			0
$659$	3.43724	+	5.95348i	0.133896	+	0.231915i	0.925175	−	0.379540i	$-0.123918\pi$
$659$	3.43724	+	5.95348i	0.133896	+	0.231915i	−0.791279	+	0.611455i	$0.790585\pi$
$660$		0			0
$661$	32.2386	−	18.6130i	1.25394	−	0.723960i	0.282047	−	0.959400i	$-0.408986\pi$
$661$	32.2386	−	18.6130i	1.25394	−	0.723960i	0.971889	+	0.235440i	$0.0756531\pi$
$662$		0			0
$663$	4.11930	+	2.37828i	0.159980	+	0.0923647i
$664$		0			0
$665$	−43.8815	−	13.3009i	−1.70165	−	0.515788i
$666$		0			0
$667$	−4.47116	+	7.74428i	−0.173124	+	0.299860i
$668$		0			0
$669$	7.18206	+	12.4397i	0.277674	+	0.480946i
$670$		0			0
$671$	24.4949	−	14.1421i	0.945616	−	0.545952i
$672$		0			0
$673$			40.4406i			1.55887i	0.626482	+	0.779436i	$0.284494\pi$
$673$			40.4406i			1.55887i	−0.626482	+	0.779436i	$0.715506\pi$
$674$		0			0
$675$	−1.07199	−	1.85675i	−0.0412610	−	0.0714662i
$676$		0			0
$677$			14.1650i			0.544405i	0.962240	+	0.272202i	$0.0877520\pi$
$677$			14.1650i			0.544405i	−0.962240	+	0.272202i	$0.912248\pi$
$678$		0			0
$679$	−6.62967	+	11.4829i	−0.254423	+	0.440674i
$680$		0			0
$681$	7.09159	−	12.2830i	0.271751	−	0.470686i
$682$		0			0
$683$	−23.8952			−0.914325			−0.457163	−	0.889383i	$-0.651134\pi$
$683$	−23.8952			−0.914325			−0.457163	+	0.889383i	$0.651134\pi$
$684$		0			0
$685$	25.2100			0.963223
$686$		0			0
$687$	8.27365	−	14.3304i	0.315660	−	0.546738i
$688$		0			0
$689$	−9.82209	+	17.0124i	−0.374192	+	0.648119i
$690$		0			0
$691$		−	19.0166i		−	0.723427i	−0.932289	−	0.361714i	$-0.882192\pi$
$691$		−	19.0166i		−	0.723427i	0.932289	−	0.361714i	$-0.117808\pi$
$692$		0			0
$693$	4.33641	+	7.51089i	0.164727	+	0.285315i
$694$		0			0
$695$		−	36.7088i		−	1.39245i
$696$		0			0
$697$	−9.17302	+	5.29605i	−0.347453	+	0.200602i
$698$		0			0
$699$	13.1193	+	22.7233i	0.496218	+	0.859474i
$700$		0			0
$701$	14.2109	−	24.6140i	0.536738	−	0.929658i	−0.462339	−	0.886703i	$-0.652990\pi$
$701$	14.2109	−	24.6140i	0.536738	−	0.929658i	0.999077	−	0.0429544i	$-0.0136770\pi$
$702$		0			0
$703$	−9.95458	−	42.6511i	−0.375444	−	1.60862i
$704$		0			0
$705$	−28.4218	−	16.4093i	−1.07043	−	0.618011i
$706$		0			0
$707$	34.7714	−	20.0753i	1.30771	−	0.755008i
$708$		0			0
$709$	13.8681	+	24.0202i	0.520826	+	0.902098i	0.999707	+	0.0242175i	$0.00770943\pi$
$709$	13.8681	+	24.0202i	0.520826	+	0.902098i	−0.478880	+	0.877880i	$0.658957\pi$
$710$		0			0
$711$	7.01847			0.263213
$712$		0			0
$713$	11.7252	−	6.76956i	0.439113	−	0.253522i
$714$		0			0
$715$	−24.4896			−0.915860
$716$		0			0
$717$	1.09159	+	0.630233i	0.0407664	+	0.0235365i
$718$		0			0
$719$	−0.844517	−	0.487582i	−0.0314952	−	0.0181837i	0.484170	−	0.874974i	$-0.339122\pi$
$719$	−0.844517	−	0.487582i	−0.0314952	−	0.0181837i	−0.515665	+	0.856790i	$0.672455\pi$
$720$		0			0
$721$			64.7438i			2.41118i
$722$		0			0
$723$		−	20.9389i		−	0.778726i
$724$		0			0
$725$	4.50415	+	2.60047i	0.167280	+	0.0965792i
$726$		0			0
$727$	22.6924	+	13.1015i	0.841615	+	0.485907i	0.857813	−	0.513962i	$-0.171823\pi$
$727$	22.6924	+	13.1015i	0.841615	+	0.485907i	−0.0161975	+	0.999869i	$0.505156\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	0.561428	−	0.324141i	0.0207652	−	0.0119888i
$732$		0			0
$733$	27.2751			1.00743			0.503715	−	0.863870i	$-0.331966\pi$
$733$	27.2751			1.00743			0.503715	+	0.863870i	$0.331966\pi$
$734$		0			0
$735$	−11.3456	−	19.6512i	−0.418491	−	0.724847i
$736$		0			0
$737$	−6.62438	+	3.82459i	−0.244012	+	0.140881i
$738$		0			0
$739$	−21.2908	−	12.2922i	−0.783195	−	0.452178i	0.0543667	−	0.998521i	$-0.482686\pi$
$739$	−21.2908	−	12.2922i	−0.783195	−	0.452178i	−0.837561	+	0.546343i	$0.816019\pi$
$740$		0			0
$741$	4.11930	+	17.6494i	0.151326	+	0.648368i
$742$		0			0
$743$	24.1101	−	41.7599i	0.884513	−	1.53202i	0.0382412	−	0.999269i	$-0.487824\pi$
$743$	24.1101	−	41.7599i	0.884513	−	1.53202i	0.846271	−	0.532752i	$-0.178842\pi$
$744$		0			0
$745$	−21.7921	−	37.7451i	−0.798402	−	1.38287i
$746$		0			0
$747$	1.71598	−	0.990721i	0.0627844	−	0.0362486i
$748$		0			0
$749$		−	19.1118i		−	0.698328i
$750$		0			0
$751$	−16.2437	−	28.1349i	−0.592741	−	1.02666i	−0.993861	−	0.110632i	$-0.964713\pi$
$751$	−16.2437	−	28.1349i	−0.592741	−	1.02666i	0.401121	−	0.916025i	$-0.368621\pi$
$752$		0			0
$753$			28.4658i			1.03735i
$754$		0			0
$755$	−9.43196	+	16.3366i	−0.343264	+	0.594551i
$756$		0			0
$757$	−11.5801	+	20.0573i	−0.420886	+	0.728996i	−0.996026	−	0.0890590i	$-0.971614\pi$
$757$	−11.5801	+	20.0573i	−0.420886	+	0.728996i	0.575141	+	0.818055i	$0.304947\pi$
$758$		0			0
$759$	−8.12325			−0.294855
$760$		0			0
$761$	−18.5496			−0.672421			−0.336211	−	0.941787i	$-0.609145\pi$
$761$	−18.5496			−0.672421			−0.336211	+	0.941787i	$0.609145\pi$
$762$		0			0
$763$	28.9361	−	50.1188i	1.04756	−	1.81442i
$764$		0			0
$765$	1.52884	−	2.64802i	0.0552752	−	0.0957395i
$766$		0			0
$767$		−	11.1133i		−	0.401277i
$768$		0			0
$769$	−18.8249	−	32.6057i	−0.678844	−	1.17579i	−0.975329	−	0.220755i	$-0.929148\pi$
$769$	−18.8249	−	32.6057i	−0.678844	−	1.17579i	0.296486	−	0.955037i	$-0.404185\pi$
$770$		0			0
$771$			12.0972i			0.435668i
$772$		0			0
$773$	−0.981529	+	0.566686i	−0.0353031	+	0.0203823i	−0.517548	−	0.855654i	$-0.673155\pi$
$773$	−0.981529	+	0.566686i	−0.0353031	+	0.0203823i	0.482245	+	0.876037i	$0.339822\pi$
$774$		0			0
$775$	−3.93724	−	6.81950i	−0.141430	−	0.244964i
$776$		0			0
$777$	19.7725	−	34.2470i	0.709335	−	1.22860i
$778$		0			0
$779$	−38.6235	−	11.7072i	−1.38383	−	0.419453i
$780$		0			0
$781$	−23.8353	−	13.7613i	−0.852893	−	0.492418i
$782$		0			0
$783$	−2.10083	+	1.21292i	−0.0750776	+	0.0433460i
$784$		0			0
$785$	−15.1348	−	26.2142i	−0.540182	−	0.935623i
$786$		0			0
$787$	13.9687			0.497930			0.248965	−	0.968512i	$-0.419910\pi$
$787$	13.9687			0.497930			0.248965	+	0.968512i	$0.419910\pi$
$788$		0			0
$789$	1.11930	−	0.646229i	0.0398482	−	0.0230064i
$790$		0			0
$791$	−56.9977			−2.02661
$792$		0			0
$793$	46.2177	+	26.6838i	1.64124	+	0.947569i
$794$		0			0
$795$	10.9361	+	6.31397i	0.387864	+	0.223933i
$796$		0			0
$797$			10.2972i			0.364746i	0.983229	+	0.182373i	$0.0583778\pi$
$797$			10.2972i			0.364746i	−0.983229	+	0.182373i	$0.941622\pi$
$798$		0			0
$799$		−	14.0466i		−	0.496933i
$800$		0			0
$801$	−12.9269	−	7.46334i	−0.456749	−	0.263704i
$802$		0			0
$803$	5.17565	+	2.98816i	0.182645	+	0.105450i
$804$		0			0
$805$	38.7776			1.36673
$806$		0			0
$807$	24.5420	−	14.1693i	0.863920	−	0.498785i
$808$		0			0
$809$	−26.1338			−0.918816			−0.459408	−	0.888225i	$-0.651938\pi$
$809$	−26.1338			−0.918816			−0.459408	+	0.888225i	$0.651938\pi$
$810$		0			0
$811$	−18.0185	−	31.2089i	−0.632714	−	1.09589i	−0.986995	−	0.160754i	$-0.948608\pi$
$811$	−18.0185	−	31.2089i	−0.632714	−	1.09589i	0.354280	−	0.935139i	$-0.384726\pi$
$812$		0			0
$813$	13.2017	−	7.62198i	0.463002	−	0.267315i
$814$		0			0
$815$	2.12023	+	1.22412i	0.0742685	+	0.0428789i
$816$		0			0
$817$	2.36392	+	0.716528i	0.0827031	+	0.0250682i
$818$		0			0
$819$	−8.18206	+	14.1717i	−0.285904	+	0.495201i
$820$		0			0
$821$	−3.89917	−	6.75356i	−0.136082	−	0.235701i	0.789928	−	0.613199i	$-0.210118\pi$
$821$	−3.89917	−	6.75356i	−0.136082	−	0.235701i	−0.926010	+	0.377498i	$0.876784\pi$
$822$		0			0
$823$	23.8824	−	13.7885i	0.832488	−	0.480637i	−0.0222159	−	0.999753i	$-0.507072\pi$
$823$	23.8824	−	13.7885i	0.832488	−	0.480637i	0.854704	+	0.519116i	$0.173739\pi$
$824$		0			0
$825$			4.72457i			0.164488i
$826$		0			0
$827$	1.99605	+	3.45726i	0.0694094	+	0.120221i	0.898641	−	0.438684i	$-0.144555\pi$
$827$	1.99605	+	3.45726i	0.0694094	+	0.120221i	−0.829232	+	0.558904i	$0.811222\pi$
$828$		0			0
$829$			50.8873i			1.76739i	0.468063	+	0.883695i	$0.344952\pi$
$829$			50.8873i			1.76739i	−0.468063	+	0.883695i	$0.655048\pi$
$830$		0			0
$831$	7.91764	−	13.7138i	0.274660	−	0.475725i
$832$		0			0
$833$	4.85601	−	8.41086i	0.168251	−	0.291419i
$834$		0			0
$835$	1.02864			0.0355975
$836$		0			0
$837$	3.67282			0.126951
$838$		0			0
$839$	−25.3117	+	43.8412i	−0.873858	+	1.51357i	−0.0158834	+	0.999874i	$0.505056\pi$
$839$	−25.3117	+	43.8412i	−0.873858	+	1.51357i	−0.857974	+	0.513692i	$0.828277\pi$
$840$		0			0
$841$	−11.5577	+	20.0185i	−0.398540	+	0.690292i
$842$		0			0
$843$		−	18.2957i		−	0.630136i
$844$		0			0
$845$	−5.73050	−	9.92551i	−0.197135	−	0.341448i
$846$		0			0
$847$			24.1808i			0.830862i
$848$		0			0
$849$	25.4218	−	14.6773i	0.872474	−	0.503723i
$850$		0			0
$851$	18.5196	+	32.0769i	0.634844	+	1.09958i
$852$		0			0
$853$	10.3745	−	17.9691i	0.355216	−	0.615251i	−0.631939	−	0.775018i	$-0.717741\pi$
$853$	10.3745	−	17.9691i	0.355216	−	0.615251i	0.987155	+	0.159766i	$0.0510741\pi$
$854$		0			0
$855$	11.3456	−	2.64802i	0.388013	−	0.0905605i
$856$		0			0
$857$	24.6521	+	14.2329i	0.842099	+	0.486186i	0.857977	−	0.513688i	$-0.171721\pi$
$857$	24.6521	+	14.2329i	0.842099	+	0.486186i	−0.0158779	+	0.999874i	$0.505054\pi$
$858$		0			0
$859$	−43.4453	+	25.0832i	−1.48234	+	0.855827i	−0.999799	−	0.0200484i	$-0.993618\pi$
$859$	−43.4453	+	25.0832i	−1.48234	+	0.855827i	−0.482537	+	0.875876i	$0.660285\pi$
$860$		0			0
$861$	−18.2201	−	31.5582i	−0.620940	−	1.07550i
$862$		0			0
$863$	39.5922			1.34773			0.673866	−	0.738853i	$-0.264632\pi$
$863$	39.5922			1.34773			0.673866	+	0.738853i	$0.264632\pi$
$864$		0			0
$865$	24.9898	−	14.4279i	0.849680	−	0.490563i
$866$		0			0
$867$	−15.6913			−0.532904
$868$		0			0
$869$	−13.3941	−	7.73308i	−0.454363	−	0.262327i
$870$		0			0
$871$	−12.4991	−	7.21634i	−0.423515	−	0.244516i
$872$		0			0
$873$		−	3.36900i		−	0.114023i
$874$		0			0
$875$			30.0435i			1.01566i
$876$		0			0
$877$	−41.5924	−	24.0134i	−1.40447	−	0.810873i	−0.409626	−	0.912253i	$-0.634341\pi$
$877$	−41.5924	−	24.0134i	−1.40447	−	0.810873i	−0.994848	+	0.101380i	$0.967674\pi$
$878$		0			0
$879$	−17.0185	−	9.82562i	−0.574019	−	0.331410i
$880$		0			0
$881$	27.9815			0.942722			0.471361	−	0.881940i	$-0.343763\pi$
$881$	27.9815			0.942722			0.471361	+	0.881940i	$0.343763\pi$
$882$		0			0
$883$	−26.3445	+	15.2100i	−0.886564	+	0.511858i	−0.872817	−	0.488048i	$-0.837709\pi$
$883$	−26.3445	+	15.2100i	−0.886564	+	0.511858i	−0.0137467	+	0.999906i	$0.504376\pi$
$884$		0			0
$885$	−7.14399			−0.240142
$886$		0			0
$887$	−2.09555	−	3.62960i	−0.0703616	−	0.121870i	0.828698	−	0.559696i	$-0.189082\pi$
$887$	−2.09555	−	3.62960i	−0.0703616	−	0.121870i	−0.899060	+	0.437826i	$0.855749\pi$
$888$		0			0
$889$	39.6521	−	22.8931i	1.32989	−	0.767811i
$890$		0			0
$891$	−1.90841	−	1.10182i	−0.0639340	−	0.0369123i
$892$		0			0
$893$	39.0554	−	36.5953i	1.30694	−	1.22461i
$894$		0			0
$895$	1.38880	−	2.40548i	0.0464226	−	0.0804063i
$896$		0			0
$897$	−7.66359	−	13.2737i	−0.255880	−	0.443197i
$898$		0			0
$899$	−7.71598	+	4.45482i	−0.257342	+	0.148577i
$900$		0			0
$901$			5.40484i			0.180061i
$902$		0			0
$903$	1.11515	+	1.93150i	0.0371098	+	0.0642761i
$904$		0			0
$905$			20.7846i			0.690904i
$906$		0			0
$907$	4.38485	−	7.59478i	0.145597	−	0.252181i	−0.783999	−	0.620762i	$-0.786823\pi$
$907$	4.38485	−	7.59478i	0.145597	−	0.252181i	0.929595	+	0.368582i	$0.120157\pi$
$908$		0			0
$909$	−5.10083	+	8.83490i	−0.169184	+	0.293035i
$910$		0			0
$911$	1.95854			0.0648892			0.0324446	−	0.999474i	$-0.489671\pi$
$911$	1.95854			0.0648892			0.0324446	+	0.999474i	$0.489671\pi$
$912$		0			0
$913$	−4.36638			−0.144506
$914$		0			0
$915$	17.1532	−	29.7103i	0.567068	−	0.982191i
$916$		0			0
$917$	−24.3496	+	42.1747i	−0.804095	+	1.39273i
$918$		0			0
$919$			43.4284i			1.43257i	0.697808	+	0.716285i	$0.254159\pi$
$919$			43.4284i			1.43257i	−0.697808	+	0.716285i	$0.745841\pi$
$920$		0			0
$921$	−3.59046	−	6.21887i	−0.118310	−	0.204919i
$922$		0			0
$923$		−	51.9304i		−	1.70931i
$924$		0			0
$925$	18.6562	−	10.7712i	0.613414	−	0.354154i
$926$		0			0
$927$	−8.22522	−	14.2465i	−0.270152	−	0.467916i
$928$		0			0
$929$	−3.02997	+	5.24806i	−0.0994100	+	0.172183i	−0.911441	−	0.411432i	$-0.865029\pi$
$929$	−3.02997	+	5.24806i	−0.0994100	+	0.172183i	0.812031	+	0.583615i	$0.198362\pi$
$930$		0			0
$931$	36.0369	−	8.41086i	1.18106	−	0.275655i
$932$		0			0
$933$	25.2765	+	14.5934i	0.827515	+	0.477766i
$934$		0			0
$935$	−5.83528	+	3.36900i	−0.190834	+	0.110178i
$936$		0			0
$937$	−12.1297	−	21.0092i	−0.396259	−	0.686341i	0.597002	−	0.802240i	$-0.296358\pi$
$937$	−12.1297	−	21.0092i	−0.396259	−	0.686341i	−0.993261	+	0.115899i	$0.963025\pi$
$938$		0			0
$939$	−14.4896			−0.472851
$940$		0			0
$941$	35.6706	−	20.5944i	1.16283	−	0.671359i	0.210847	−	0.977519i	$-0.432378\pi$
$941$	35.6706	−	20.5944i	1.16283	−	0.671359i	0.951980	+	0.306160i	$0.0990444\pi$
$942$		0			0
$943$	34.1312			1.11146
$944$		0			0
$945$	9.11007	+	5.25970i	0.296350	+	0.171098i
$946$		0			0
$947$	−1.88900	−	1.09062i	−0.0613843	−	0.0354403i	0.468994	−	0.883201i	$-0.344617\pi$
$947$	−1.88900	−	1.09062i	−0.0613843	−	0.0354403i	−0.530378	+	0.847761i	$0.677950\pi$
$948$		0			0
$949$			11.2763i			0.366044i
$950$		0			0
$951$		−	2.74312i		−	0.0889519i
$952$		0			0
$953$	−21.7974	−	12.5847i	−0.706087	−	0.407660i	0.103523	−	0.994627i	$-0.466988\pi$
$953$	−21.7974	−	12.5847i	−0.706087	−	0.407660i	−0.809611	+	0.586967i	$0.800322\pi$
$954$		0			0
$955$	−60.7899	−	35.0970i	−1.96711	−	1.13571i
$956$		0			0
$957$	5.34565			0.172800
$958$		0			0
$959$	−32.1479	+	18.5606i	−1.03811	+	0.599354i
$960$		0			0
$961$	−17.5104			−0.564851
$962$		0			0
$963$	2.42801	+	4.20543i	0.0782414	+	0.135518i
$964$		0			0
$965$	22.0092	−	12.7070i	0.708502	−	0.409054i
$966$		0			0
$967$	−6.65548	−	3.84254i	−0.214026	−	0.123568i	0.389155	−	0.921172i	$-0.372767\pi$
$967$	−6.65548	−	3.84254i	−0.214026	−	0.123568i	−0.603181	+	0.797604i	$0.706100\pi$
$968$		0			0
$969$	3.40954	+	3.63875i	0.109530	+	0.116893i
$970$		0			0
$971$	24.3272	−	42.1359i	0.780696	−	1.35221i	−0.150840	−	0.988558i	$-0.548198\pi$
$971$	24.3272	−	42.1359i	0.780696	−	1.35221i	0.931537	−	0.363647i	$-0.118469\pi$
$972$		0			0
$973$	27.0266	+	46.8114i	0.866432	+	1.50070i
$974$		0			0
$975$	−7.72013	+	4.45722i	−0.247242	+	0.142745i
$976$		0			0
$977$		−	11.2811i		−	0.360914i	−0.983583	−	0.180457i	$-0.942242\pi$
$977$		−	11.2811i		−	0.360914i	0.983583	−	0.180457i	$-0.0577576\pi$
$978$		0			0
$979$	16.4465	+	28.4861i	0.525632	+	0.910421i
$980$		0			0
$981$			14.7045i			0.469478i
$982$		0			0
$983$	19.8485	−	34.3786i	0.633068	−	1.09651i	−0.353853	−	0.935301i	$-0.615129\pi$
$983$	19.8485	−	34.3786i	0.633068	−	1.09651i	0.986921	−	0.161205i	$-0.0515379\pi$
$984$		0			0
$985$	37.3289	−	64.6555i	1.18940	−	2.06010i
$986$		0			0
$987$	48.3249			1.53820
$988$		0			0
$989$	−2.08897			−0.0664254
$990$		0			0
$991$	−7.78930	+	13.4915i	−0.247435	+	0.428571i	−0.962814	−	0.270167i	$-0.912921\pi$
$991$	−7.78930	+	13.4915i	−0.247435	+	0.428571i	0.715378	+	0.698738i	$0.246254\pi$
$992$		0			0
$993$	−5.03807	+	8.72620i	−0.159878	+	0.276918i
$994$		0			0
$995$			21.2203i			0.672728i
$996$		0			0
$997$	16.5185	+	28.6108i	0.523145	+	0.906114i	0.999637	+	0.0269353i	$0.00857480\pi$
$997$	16.5185	+	28.6108i	0.523145	+	0.906114i	−0.476492	+	0.879179i	$0.658092\pi$
$998$		0			0
$999$			10.0478i			0.317899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bb.e.559.3	yes	6
3.2	odd	2		2736.2.bm.n.559.1		6
4.3	odd	2		912.2.bb.f.559.3	yes	6
12.11	even	2		2736.2.bm.o.559.1		6
19.12	odd	6		912.2.bb.f.31.3	yes	6
57.50	even	6		2736.2.bm.o.1855.1		6
76.31	even	6	inner	912.2.bb.e.31.3	✓	6
228.107	odd	6		2736.2.bm.n.1855.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bb.e.31.3	✓	6	76.31	even	6	inner
912.2.bb.e.559.3	yes	6	1.1	even	1	trivial
912.2.bb.f.31.3	yes	6	19.12	odd	6
912.2.bb.f.559.3	yes	6	4.3	odd	2
2736.2.bm.n.559.1		6	3.2	odd	2
2736.2.bm.n.1855.1		6	228.107	odd	6
2736.2.bm.o.559.1		6	12.11	even	2
2736.2.bm.o.1855.1		6	57.50	even	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.33641 - 2.31473i) q^{5} +3.93569i q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(1.33641 - 2.31473i) q^{5} +3.93569i q^{7} +(-0.500000 - 0.866025i) q^{9} +2.20364i q^{11} +(-3.60083 + 2.07894i) q^{13} +(1.33641 + 2.31473i) q^{15} +(-0.571993 + 0.990721i) q^{17} +(-4.24482 + 0.990721i) q^{19} +(-3.40841 - 1.96784i) q^{21} +(3.19243 - 1.84315i) q^{23} +(-1.07199 - 1.85675i) q^{25} +1.00000 q^{27} +(-2.10083 + 1.21292i) q^{29} +3.67282 q^{31} +(-1.90841 - 1.10182i) q^{33} +(9.11007 + 5.25970i) q^{35} +10.0478i q^{37} -4.15788i q^{39} +(8.01847 + 4.62947i) q^{41} +(-0.490764 - 0.283343i) q^{43} -2.67282 q^{45} +(-10.6336 + 6.13932i) q^{47} -8.48963 q^{49} +(-0.571993 - 0.990721i) q^{51} +(4.09159 - 2.36228i) q^{53} +(5.10083 + 2.94497i) q^{55} +(1.26442 - 4.17148i) q^{57} +(-1.33641 + 2.31473i) q^{59} +(-6.41764 - 11.1157i) q^{61} +(3.40841 - 1.96784i) q^{63} +11.1133i q^{65} +(1.73558 + 3.00612i) q^{67} +3.68630i q^{69} +(-6.24482 + 10.8163i) q^{71} +(1.35601 - 2.34868i) q^{73} +2.14399 q^{75} -8.67282 q^{77} +(-3.50924 + 6.07817i) q^{79} +(-0.500000 + 0.866025i) q^{81} +1.98144i q^{83} +(1.52884 + 2.64802i) q^{85} -2.42583i q^{87} +(12.9269 - 7.46334i) q^{89} +(-8.18206 - 14.1717i) q^{91} +(-1.83641 + 3.18076i) q^{93} +(-3.37957 + 11.1496i) q^{95} +(2.91764 + 1.68450i) q^{97} +(1.90841 - 1.10182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 2 q^{5} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 2 * q^5 - 3 * q^9	\( 6 q - 3 q^{3} - 2 q^{5} - 3 q^{9} - 3 q^{13} - 2 q^{15} - 2 q^{17} - 4 q^{19} - 9 q^{21} + 12 q^{23} - 5 q^{25} + 6 q^{27} + 6 q^{29} + 2 q^{31} + 6 q^{35} - 12 q^{41} - 33 q^{43} + 4 q^{45} - 18 q^{47} - 8 q^{49} - 2 q^{51} + 36 q^{53} + 12 q^{55} - q^{57} + 2 q^{59} + 3 q^{61} + 9 q^{63} + 19 q^{67} - 16 q^{71} + 11 q^{73} + 10 q^{75} - 32 q^{77} + 9 q^{79} - 3 q^{81} - 8 q^{85} + 6 q^{89} + q^{91} - q^{93} - 26 q^{95} - 24 q^{97}+O(q^{100}) \) 6 * q - 3 * q^3 - 2 * q^5 - 3 * q^9 - 3 * q^13 - 2 * q^15 - 2 * q^17 - 4 * q^19 - 9 * q^21 + 12 * q^23 - 5 * q^25 + 6 * q^27 + 6 * q^29 + 2 * q^31 + 6 * q^35 - 12 * q^41 - 33 * q^43 + 4 * q^45 - 18 * q^47 - 8 * q^49 - 2 * q^51 + 36 * q^53 + 12 * q^55 - q^57 + 2 * q^59 + 3 * q^61 + 9 * q^63 + 19 * q^67 - 16 * q^71 + 11 * q^73 + 10 * q^75 - 32 * q^77 + 9 * q^79 - 3 * q^81 - 8 * q^85 + 6 * q^89 + q^91 - q^93 - 26 * q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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