LMFDB - Embedded newform 1008.2.df.c.689.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(689,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))

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

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

chi := DirichletCharacter("1008.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.df (of order $6$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.7
Root			$-1.70672 + 0.295146i$ of defining polynomial
Character	$\chi$	$=$	1008.689
Dual form			1008.2.df.c.929.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72571 - 0.148116i) q^{3} +0.967324 q^{5} +(-2.40137 + 1.11060i) q^{7} +(2.95612 - 0.511208i) q^{9} +O(q^{10})$	\(q+(1.72571 - 0.148116i) q^{3} +0.967324 q^{5} +(-2.40137 + 1.11060i) q^{7} +(2.95612 - 0.511208i) q^{9} +5.57361i q^{11} +(3.76893 + 2.17600i) q^{13} +(1.66932 - 0.143276i) q^{15} +(-1.97267 + 3.41677i) q^{17} +(-3.86796 + 2.23317i) q^{19} +(-3.97956 + 2.27225i) q^{21} -2.65334i q^{23} -4.06428 q^{25} +(5.02568 - 1.32004i) q^{27} +(4.61157 - 2.66249i) q^{29} +(5.34038 - 3.08327i) q^{31} +(0.825539 + 9.61842i) q^{33} +(-2.32290 + 1.07431i) q^{35} +(0.243608 + 0.421942i) q^{37} +(6.82637 + 3.19689i) q^{39} +(-0.0818856 + 0.141830i) q^{41} +(4.35045 + 7.53520i) q^{43} +(2.85953 - 0.494504i) q^{45} +(4.74500 - 8.21859i) q^{47} +(4.53314 - 5.33392i) q^{49} +(-2.89818 + 6.18852i) q^{51} +(1.74520 + 1.00759i) q^{53} +5.39149i q^{55} +(-6.34420 + 4.42670i) q^{57} +(-0.836931 - 1.44961i) q^{59} +(-4.47927 - 2.58611i) q^{61} +(-6.53099 + 4.51067i) q^{63} +(3.64578 + 2.10489i) q^{65} +(-2.72126 - 4.71336i) q^{67} +(-0.393002 - 4.57889i) q^{69} -3.64006i q^{71} +(-2.15468 - 1.24401i) q^{73} +(-7.01376 + 0.601984i) q^{75} +(-6.19005 - 13.3843i) q^{77} +(2.30121 - 3.98581i) q^{79} +(8.47733 - 3.02239i) q^{81} +(-4.20979 - 7.29158i) q^{83} +(-1.90821 + 3.30512i) q^{85} +(7.56386 - 5.27772i) q^{87} +(2.05811 + 3.56475i) q^{89} +(-11.4673 - 1.03959i) q^{91} +(8.75925 - 6.11182i) q^{93} +(-3.74157 + 2.16020i) q^{95} +(-10.2669 + 5.92762i) q^{97} +(2.84928 + 16.4763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q - 2 * q^7 - 6 * q^9	$ 16 q - 2 q^{7} - 6 q^{9} - 6 q^{13} + 18 q^{15} + 18 q^{17} - 18 q^{21} + 16 q^{25} + 36 q^{27} + 6 q^{29} - 6 q^{31} + 18 q^{33} + 30 q^{35} - 2 q^{37} + 30 q^{39} + 6 q^{41} + 2 q^{43} + 12 q^{45} + 18 q^{47} + 10 q^{49} + 36 q^{53} + 6 q^{57} - 30 q^{59} - 60 q^{61} - 42 q^{63} + 42 q^{65} - 14 q^{67} + 42 q^{69} - 30 q^{75} - 18 q^{77} + 16 q^{79} + 54 q^{81} - 12 q^{85} + 48 q^{87} + 24 q^{89} + 12 q^{91} + 30 q^{93} + 66 q^{95} - 6 q^{97} - 18 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 - 6 * q^9 - 6 * q^13 + 18 * q^15 + 18 * q^17 - 18 * q^21 + 16 * q^25 + 36 * q^27 + 6 * q^29 - 6 * q^31 + 18 * q^33 + 30 * q^35 - 2 * q^37 + 30 * q^39 + 6 * q^41 + 2 * q^43 + 12 * q^45 + 18 * q^47 + 10 * q^49 + 36 * q^53 + 6 * q^57 - 30 * q^59 - 60 * q^61 - 42 * q^63 + 42 * q^65 - 14 * q^67 + 42 * q^69 - 30 * q^75 - 18 * q^77 + 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 + 24 * q^89 + 12 * q^91 + 30 * q^93 + 66 * q^95 - 6 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.72571	−	0.148116i	0.996337	−	0.0855146i
$3$	1.72571	−	0.148116i	0.996337	−	0.0855146i
$4$		0			0
$5$	0.967324			0.432600			0.216300	−	0.976327i	$-0.430601\pi$
$5$	0.967324			0.432600			0.216300	+	0.976327i	$0.430601\pi$
$6$		0			0
$7$	−2.40137	+	1.11060i	−0.907632	+	0.419767i
$7$	−2.40137	+	1.11060i	−0.907632	+	0.419767i
$8$		0			0
$9$	2.95612	−	0.511208i	0.985375	−	0.170403i
$10$		0			0
$11$			5.57361i			1.68051i	0.542193	+	0.840254i	$0.317594\pi$
$11$			5.57361i			1.68051i	−0.542193	+	0.840254i	$0.682406\pi$
$12$		0			0
$13$	3.76893	+	2.17600i	1.04531	+	0.603512i	0.921334	−	0.388772i	$-0.127101\pi$
$13$	3.76893	+	2.17600i	1.04531	+	0.603512i	0.123980	+	0.992285i	$0.460434\pi$
$14$		0			0
$15$	1.66932	−	0.143276i	0.431016	−	0.0369937i
$16$		0			0
$17$	−1.97267	+	3.41677i	−0.478443	+	0.828688i	−0.999695	−	0.0247150i	$-0.992132\pi$
$17$	−1.97267	+	3.41677i	−0.478443	+	0.828688i	0.521251	+	0.853403i	$0.325465\pi$
$18$		0			0
$19$	−3.86796	+	2.23317i	−0.887371	+	0.512324i	−0.873082	−	0.487574i	$-0.837882\pi$
$19$	−3.86796	+	2.23317i	−0.887371	+	0.512324i	−0.0142896	+	0.999898i	$0.504549\pi$
$20$		0			0
$21$	−3.97956	+	2.27225i	−0.868411	+	0.495845i
$22$		0			0
$23$		−	2.65334i		−	0.553260i	−0.960976	−	0.276630i	$-0.910782\pi$
$23$		−	2.65334i		−	0.553260i	0.960976	−	0.276630i	$-0.0892177\pi$
$24$		0			0
$25$	−4.06428			−0.812857
$26$		0			0
$27$	5.02568	−	1.32004i	0.967193	−	0.254042i
$28$		0			0
$29$	4.61157	−	2.66249i	0.856347	−	0.494412i	−0.00644015	−	0.999979i	$-0.502050\pi$
$29$	4.61157	−	2.66249i	0.856347	−	0.494412i	0.862787	+	0.505567i	$0.168717\pi$
$30$		0			0
$31$	5.34038	−	3.08327i	0.959161	−	0.553772i	0.0632466	−	0.997998i	$-0.479855\pi$
$31$	5.34038	−	3.08327i	0.959161	−	0.553772i	0.895915	+	0.444226i	$0.146521\pi$
$32$		0			0
$33$	0.825539	+	9.61842i	0.143708	+	1.67435i
$34$		0			0
$35$	−2.32290	+	1.07431i	−0.392642	+	0.181592i
$36$		0			0
$37$	0.243608	+	0.421942i	0.0400490	+	0.0693669i	0.885355	−	0.464915i	$-0.153915\pi$
$37$	0.243608	+	0.421942i	0.0400490	+	0.0693669i	−0.845306	+	0.534282i	$0.820582\pi$
$38$		0			0
$39$	6.82637	+	3.19689i	1.09309	+	0.511912i
$40$		0			0
$41$	−0.0818856	+	0.141830i	−0.0127884	+	0.0221501i	−0.872349	−	0.488884i	$-0.837404\pi$
$41$	−0.0818856	+	0.141830i	−0.0127884	+	0.0221501i	0.859560	+	0.511034i	$0.170737\pi$
$42$		0			0
$43$	4.35045	+	7.53520i	0.663437	+	1.14911i	0.979707	+	0.200437i	$0.0642362\pi$
$43$	4.35045	+	7.53520i	0.663437	+	1.14911i	−0.316270	+	0.948669i	$0.602430\pi$
$44$		0			0
$45$	2.85953	−	0.494504i	0.426273	−	0.0737163i
$46$		0			0
$47$	4.74500	−	8.21859i	0.692130	−	1.19880i	−0.279009	−	0.960289i	$-0.590006\pi$
$47$	4.74500	−	8.21859i	0.692130	−	1.19880i	0.971139	−	0.238516i	$-0.0766609\pi$
$48$		0			0
$49$	4.53314	−	5.33392i	0.647591	−	0.761988i
$50$		0			0
$51$	−2.89818	+	6.18852i	−0.405826	+	0.866567i
$52$		0			0
$53$	1.74520	+	1.00759i	0.239722	+	0.138403i	0.615049	−	0.788489i	$-0.289136\pi$
$53$	1.74520	+	1.00759i	0.239722	+	0.138403i	−0.375327	+	0.926892i	$0.622470\pi$
$54$		0			0
$55$			5.39149i			0.726988i
$56$		0			0
$57$	−6.34420	+	4.42670i	−0.840310	+	0.586331i
$58$		0			0
$59$	−0.836931	−	1.44961i	−0.108959	−	0.188723i	0.806390	−	0.591384i	$-0.201418\pi$
$59$	−0.836931	−	1.44961i	−0.108959	−	0.188723i	−0.915349	+	0.402662i	$0.868085\pi$
$60$		0			0
$61$	−4.47927	−	2.58611i	−0.573512	−	0.331117i	0.185039	−	0.982731i	$-0.440759\pi$
$61$	−4.47927	−	2.58611i	−0.573512	−	0.331117i	−0.758551	+	0.651614i	$0.774092\pi$
$62$		0			0
$63$	−6.53099	+	4.51067i	−0.822828	+	0.568291i
$64$		0			0
$65$	3.64578	+	2.10489i	0.452203	+	0.261080i
$66$		0			0
$67$	−2.72126	−	4.71336i	−0.332455	−	0.575828i	0.650538	−	0.759474i	$-0.274544\pi$
$67$	−2.72126	−	4.71336i	−0.332455	−	0.575828i	−0.982993	+	0.183645i	$0.941210\pi$
$68$		0			0
$69$	−0.393002	−	4.57889i	−0.0473118	−	0.551234i
$70$		0			0
$71$		−	3.64006i		−	0.431996i	−0.976394	−	0.215998i	$-0.930700\pi$
$71$		−	3.64006i		−	0.431996i	0.976394	−	0.215998i	$-0.0693005\pi$
$72$		0			0
$73$	−2.15468	−	1.24401i	−0.252186	−	0.145600i	0.368579	−	0.929597i	$-0.379845\pi$
$73$	−2.15468	−	1.24401i	−0.252186	−	0.145600i	−0.620765	+	0.783997i	$0.713178\pi$
$74$		0			0
$75$	−7.01376	+	0.601984i	−0.809879	+	0.0695111i
$76$		0			0
$77$	−6.19005	−	13.3843i	−0.705422	−	1.52528i
$78$		0			0
$79$	2.30121	−	3.98581i	0.258906	−	0.448438i	−0.707043	−	0.707170i	$-0.749971\pi$
$79$	2.30121	−	3.98581i	0.258906	−	0.448438i	0.965949	+	0.258732i	$0.0833046\pi$
$80$		0			0
$81$	8.47733	−	3.02239i	0.941926	−	0.335821i
$82$		0			0
$83$	−4.20979	−	7.29158i	−0.462085	−	0.800355i	0.536980	−	0.843595i	$-0.319565\pi$
$83$	−4.20979	−	7.29158i	−0.462085	−	0.800355i	−0.999065	+	0.0432405i	$0.986232\pi$
$84$		0			0
$85$	−1.90821	+	3.30512i	−0.206975	+	0.358491i
$86$		0			0
$87$	7.56386	−	5.27772i	0.810931	−	0.565831i
$88$		0			0
$89$	2.05811	+	3.56475i	0.218159	+	0.377863i	0.954245	−	0.299025i	$-0.0966615\pi$
$89$	2.05811	+	3.56475i	0.218159	+	0.377863i	−0.736086	+	0.676888i	$0.763328\pi$
$90$		0			0
$91$	−11.4673	−	1.03959i	−1.20210	−	0.108978i
$92$		0			0
$93$	8.75925	−	6.11182i	0.908292	−	0.633766i
$94$		0			0
$95$	−3.74157	+	2.16020i	−0.383877	+	0.221632i
$96$		0			0
$97$	−10.2669	+	5.92762i	−1.04245	+	0.601859i	−0.920526	−	0.390681i	$-0.872240\pi$
$97$	−10.2669	+	5.92762i	−1.04245	+	0.601859i	−0.121924	+	0.992539i	$0.538906\pi$
$98$		0			0
$99$	2.84928	+	16.4763i	0.286363	+	1.65593i
$100$		0			0
$101$	5.31626			0.528988			0.264494	−	0.964387i	$-0.414795\pi$
$101$	5.31626			0.528988			0.264494	+	0.964387i	$0.414795\pi$
$102$		0			0
$103$			8.94450i			0.881327i	0.897672	+	0.440664i	$0.145257\pi$
$103$			8.94450i			0.881327i	−0.897672	+	0.440664i	$0.854743\pi$
$104$		0			0
$105$	−3.84952	+	2.19800i	−0.375675	+	0.214503i
$106$		0			0
$107$	16.5898	−	9.57813i	1.60380	−	0.925953i	0.613079	−	0.790022i	$-0.289931\pi$
$107$	16.5898	−	9.57813i	1.60380	−	0.925953i	0.990718	−	0.135931i	$-0.0434026\pi$
$108$		0			0
$109$	−9.62168	+	16.6652i	−0.921590	+	1.59624i	−0.124635	+	0.992203i	$0.539776\pi$
$109$	−9.62168	+	16.6652i	−0.921590	+	1.59624i	−0.796955	+	0.604038i	$0.793557\pi$
$110$		0			0
$111$	0.482893	+	0.692066i	0.0458342	+	0.0656880i
$112$		0			0
$113$	7.31199	+	4.22158i	0.687854	+	0.397133i	0.802808	−	0.596238i	$-0.203339\pi$
$113$	7.31199	+	4.22158i	0.687854	+	0.397133i	−0.114953	+	0.993371i	$0.536672\pi$
$114$		0			0
$115$		−	2.56664i		−	0.239341i
$116$		0			0
$117$	12.2538	+	4.50580i	1.13287	+	0.416561i
$118$		0			0
$119$	0.942449	−	10.3958i	0.0863942	−	0.952979i
$120$		0			0
$121$	−20.0652			−1.82411
$122$		0			0
$123$	−0.120303	+	0.256885i	−0.0108474	+	0.0231626i
$124$		0			0
$125$	−8.76810			−0.784243
$126$		0			0
$127$	−3.31883			−0.294498			−0.147249	−	0.989099i	$-0.547042\pi$
$127$	−3.31883			−0.294498			−0.147249	+	0.989099i	$0.547042\pi$
$128$		0			0
$129$	8.62367	+	12.3592i	0.759272	+	1.08816i
$130$		0			0
$131$	18.7467			1.63791			0.818954	−	0.573859i	$-0.194554\pi$
$131$	18.7467			1.63791			0.818954	+	0.573859i	$0.194554\pi$
$132$		0			0
$133$	6.80824	−	9.65842i	0.590350	−	0.837491i
$134$		0			0
$135$	4.86146	−	1.27691i	0.418408	−	0.109899i
$136$		0			0
$137$		−	16.9343i		−	1.44680i	−0.690430	−	0.723399i	$-0.742579\pi$
$137$		−	16.9343i		−	1.44680i	0.690430	−	0.723399i	$-0.257421\pi$
$138$		0			0
$139$	−10.5033	−	6.06406i	−0.890875	−	0.514347i	−0.0166466	−	0.999861i	$-0.505299\pi$
$139$	−10.5033	−	6.06406i	−0.890875	−	0.514347i	−0.874229	+	0.485514i	$0.838632\pi$
$140$		0			0
$141$	6.97118	−	14.8857i	0.587079	−	1.25360i
$142$		0			0
$143$	−12.1282	+	21.0066i	−1.01421	+	1.75666i
$144$		0			0
$145$	4.46088	−	2.57549i	0.370456	−	0.213883i
$146$		0			0
$147$	7.03282	−	9.87620i	0.580058	−	0.814576i
$148$		0			0
$149$		−	8.74051i		−	0.716051i	−0.933712	−	0.358025i	$-0.883450\pi$
$149$		−	8.74051i		−	0.716051i	0.933712	−	0.358025i	$-0.116550\pi$
$150$		0			0
$151$	−22.0941			−1.79799			−0.898997	−	0.437954i	$-0.855703\pi$
$151$	−22.0941			−1.79799			−0.898997	+	0.437954i	$0.855703\pi$
$152$		0			0
$153$	−4.08478	+	11.1088i	−0.330235	+	0.898096i
$154$		0			0
$155$	5.16588	−	2.98252i	0.414934	−	0.239562i
$156$		0			0
$157$	1.23372	−	0.712287i	0.0984614	−	0.0568467i	−0.449961	−	0.893048i	$-0.648562\pi$
$157$	1.23372	−	0.712287i	0.0984614	−	0.0568467i	0.548422	+	0.836202i	$0.315229\pi$
$158$		0			0
$159$	3.16094	+	1.48032i	0.250679	+	0.117397i
$160$		0			0
$161$	2.94680	+	6.37165i	0.232241	+	0.502157i
$162$		0			0
$163$	3.72148	+	6.44579i	0.291489	+	0.504873i	0.974162	−	0.225851i	$-0.0725161\pi$
$163$	3.72148	+	6.44579i	0.291489	+	0.504873i	−0.682673	+	0.730724i	$0.739183\pi$
$164$		0			0
$165$	0.798564	+	9.30413i	0.0621681	+	0.724325i
$166$		0			0
$167$	−3.24855	+	5.62665i	−0.251380	+	0.435404i	−0.963906	−	0.266242i	$-0.914218\pi$
$167$	−3.24855	+	5.62665i	−0.251380	+	0.435404i	0.712526	+	0.701646i	$0.247551\pi$
$168$		0			0
$169$	2.96991	+	5.14404i	0.228455	+	0.395695i
$170$		0			0
$171$	−10.2926	+	8.57886i	−0.787092	+	0.656042i
$172$		0			0
$173$	5.90938	−	10.2354i	0.449282	−	0.778179i	−0.549057	−	0.835785i	$-0.685013\pi$
$173$	5.90938	−	10.2354i	0.449282	−	0.778179i	0.998339	+	0.0576053i	$0.0183465\pi$
$174$		0			0
$175$	9.75984	−	4.51379i	0.737775	−	0.341211i
$176$		0			0
$177$	−1.65901	−	2.37763i	−0.124699	−	0.178714i
$178$		0			0
$179$	−2.10764	−	1.21685i	−0.157533	−	0.0909515i	0.419161	−	0.907912i	$-0.362324\pi$
$179$	−2.10764	−	1.21685i	−0.157533	−	0.0909515i	−0.576694	+	0.816960i	$0.695657\pi$
$180$		0			0
$181$		−	11.5342i		−	0.857327i	−0.903464	−	0.428663i	$-0.858985\pi$
$181$		−	11.5342i		−	0.857327i	0.903464	−	0.428663i	$-0.141015\pi$
$182$		0			0
$183$	−8.11294	−	3.79941i	−0.599726	−	0.280861i
$184$		0			0
$185$	0.235648	+	0.408155i	0.0173252	+	0.0300081i
$186$		0			0
$187$	−19.0438	−	10.9949i	−1.39262	−	0.804028i
$188$		0			0
$189$	−10.6025	+	8.75143i	−0.771216	+	0.636573i
$190$		0			0
$191$	−19.1122	−	11.0345i	−1.38291	−	0.798425i	−0.390409	−	0.920641i	$-0.627666\pi$
$191$	−19.1122	−	11.0345i	−1.38291	−	0.798425i	−0.992503	+	0.122216i	$0.961000\pi$
$192$		0			0
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	0.961932	+	0.273289i	$0.0881116\pi$
$193$	9.96979	+	17.2682i	0.717641	+	1.24299i	−0.244291	+	0.969702i	$0.578555\pi$
$194$		0			0
$195$	6.60331	+	3.09243i	0.472873	+	0.221453i
$196$		0			0
$197$		−	4.62560i		−	0.329560i	−0.986330	−	0.164780i	$-0.947309\pi$
$197$		−	4.62560i		−	0.329560i	0.986330	−	0.164780i	$-0.0526914\pi$
$198$		0			0
$199$	18.1024	+	10.4514i	1.28324	+	0.740882i	0.977440	−	0.211212i	$-0.0677412\pi$
$199$	18.1024	+	10.4514i	1.28324	+	0.740882i	0.305805	+	0.952094i	$0.401075\pi$
$200$		0			0
$201$	−5.39422	−	7.73081i	−0.380479	−	0.545289i
$202$		0			0
$203$	−8.11712	+	11.5152i	−0.569710	+	0.808211i
$204$		0			0
$205$	−0.0792099	+	0.137196i	−0.00553226	+	0.00958215i
$206$		0			0
$207$	−1.35641	−	7.84361i	−0.0942770	−	0.545169i
$208$		0			0
$209$	−12.4468	−	21.5585i	−0.860965	−	1.49123i
$210$		0			0
$211$	3.34310	−	5.79042i	0.230148	−	0.398629i	−0.727703	−	0.685892i	$-0.759412\pi$
$211$	3.34310	−	5.79042i	0.230148	−	0.398629i	0.957852	+	0.287263i	$0.0927455\pi$
$212$		0			0
$213$	−0.539150	−	6.28168i	−0.0369420	−	0.430414i
$214$		0			0
$215$	4.20829	+	7.28898i	0.287003	+	0.497104i
$216$		0			0
$217$	−9.39995	+	13.3351i	−0.638110	+	0.905246i
$218$		0			0
$219$	−3.90260	−	1.82765i	−0.263714	−	0.123501i
$220$		0			0
$221$	−14.8697	+	8.58505i	−1.00025	+	0.577493i
$222$		0			0
$223$	7.08622	−	4.09123i	0.474528	−	0.273969i	−0.243605	−	0.969875i	$-0.578330\pi$
$223$	7.08622	−	4.09123i	0.474528	−	0.273969i	0.718133	+	0.695905i	$0.244997\pi$
$224$		0			0
$225$	−12.0145	+	2.07770i	−0.800968	+	0.138513i
$226$		0			0
$227$	10.6938			0.709769			0.354885	−	0.934910i	$-0.384520\pi$
$227$	10.6938			0.709769			0.354885	+	0.934910i	$0.384520\pi$
$228$		0			0
$229$		−	29.2072i		−	1.93007i	−0.262125	−	0.965034i	$-0.584423\pi$
$229$		−	29.2072i		−	1.93007i	0.262125	−	0.965034i	$-0.415577\pi$
$230$		0			0
$231$	−12.6646	−	22.1805i	−0.833272	−	1.45937i
$232$		0			0
$233$	−5.57664	+	3.21967i	−0.365338	+	0.210928i	−0.671420	−	0.741077i	$-0.734315\pi$
$233$	−5.57664	+	3.21967i	−0.365338	+	0.210928i	0.306082	+	0.952005i	$0.400982\pi$
$234$		0			0
$235$	4.58996	−	7.95004i	0.299416	−	0.518603i
$236$		0			0
$237$	3.38085	−	7.21918i	0.219610	−	0.468936i
$238$		0			0
$239$	4.01452	+	2.31778i	0.259678	+	0.149925i	0.624187	−	0.781275i	$-0.285430\pi$
$239$	4.01452	+	2.31778i	0.259678	+	0.149925i	−0.364510	+	0.931200i	$0.618763\pi$
$240$		0			0
$241$			10.4944i			0.676007i	0.941145	+	0.338003i	$0.109752\pi$
$241$			10.4944i			0.676007i	−0.941145	+	0.338003i	$0.890248\pi$
$242$		0			0
$243$	14.1817	−	6.47138i	0.909758	−	0.415139i
$244$		0			0
$245$	4.38501	−	5.15963i	0.280148	−	0.329636i
$246$		0			0
$247$	−19.4375			−1.23678
$248$		0			0
$249$	−8.34486	−	11.9596i	−0.528834	−	0.757908i
$250$		0			0
$251$	7.85271			0.495659			0.247829	−	0.968804i	$-0.420283\pi$
$251$	7.85271			0.495659			0.247829	+	0.968804i	$0.420283\pi$
$252$		0			0
$253$	14.7887			0.929758
$254$		0			0
$255$	−2.80348	+	5.98631i	−0.175560	+	0.374877i
$256$		0			0
$257$	−3.43136			−0.214042			−0.107021	−	0.994257i	$-0.534131\pi$
$257$	−3.43136			−0.214042			−0.107021	+	0.994257i	$0.534131\pi$
$258$		0			0
$259$	−1.05360	−	0.742687i	−0.0654677	−	0.0461483i
$260$		0			0
$261$	12.2713	−	10.2281i	0.759574	−	0.633105i
$262$		0			0
$263$		−	3.66132i		−	0.225767i	−0.993608	−	0.112883i	$-0.963991\pi$
$263$		−	3.66132i		−	0.225767i	0.993608	−	0.112883i	$-0.0360087\pi$
$264$		0			0
$265$	1.68817	+	0.974668i	0.103704	+	0.0598734i
$266$		0			0
$267$	4.07969	+	5.84687i	0.249673	+	0.357823i
$268$		0			0
$269$	6.34303	−	10.9865i	0.386741	−	0.669856i	−0.605268	−	0.796022i	$-0.706934\pi$
$269$	6.34303	−	10.9865i	0.386741	−	0.669856i	0.992009	+	0.126166i	$0.0402673\pi$
$270$		0			0
$271$	17.2136	−	9.93828i	1.04565	−	0.603708i	0.124223	−	0.992254i	$-0.460356\pi$
$271$	17.2136	−	9.93828i	1.04565	−	0.603708i	0.921429	+	0.388547i	$0.127023\pi$
$272$		0			0
$273$	−19.9431	−	0.0955416i	−1.20701	−	0.00578244i
$274$		0			0
$275$		−	22.6527i		−	1.36601i
$276$		0			0
$277$	−7.46605			−0.448591			−0.224296	−	0.974521i	$-0.572008\pi$
$277$	−7.46605			−0.448591			−0.224296	+	0.974521i	$0.572008\pi$
$278$		0			0
$279$	14.2106	−	11.8446i	0.850769	−	0.709117i
$280$		0			0
$281$	−19.2746	+	11.1282i	−1.14983	+	0.663854i	−0.948845	−	0.315741i	$-0.897747\pi$
$281$	−19.2746	+	11.1282i	−1.14983	+	0.663854i	−0.200983	+	0.979595i	$0.564414\pi$
$282$		0			0
$283$	−14.0125	+	8.09012i	−0.832957	+	0.480908i	−0.854864	−	0.518852i	$-0.826359\pi$
$283$	−14.0125	+	8.09012i	−0.832957	+	0.480908i	0.0219073	+	0.999760i	$0.493026\pi$
$284$		0			0
$285$	−6.13690	+	4.28205i	−0.363518	+	0.253647i
$286$		0			0
$287$	0.0391210	−	0.431528i	0.00230924	−	0.0254723i
$288$		0			0
$289$	0.717124	+	1.24210i	0.0421838	+	0.0730644i
$290$		0			0
$291$	−16.8397	+	11.7500i	−0.987164	+	0.688799i
$292$		0			0
$293$	4.43406	−	7.68002i	0.259041	−	0.448672i	−0.706944	−	0.707269i	$-0.749927\pi$
$293$	4.43406	−	7.68002i	0.259041	−	0.448672i	0.965985	+	0.258597i	$0.0832603\pi$
$294$		0			0
$295$	−0.809584	−	1.40224i	−0.0471358	−	0.0816416i
$296$		0			0
$297$	7.35741	+	28.0112i	0.426920	+	1.62538i
$298$		0			0
$299$	5.77366	−	10.0003i	0.333899	−	0.578331i
$300$		0			0
$301$	−18.8156	−	13.2632i	−1.08451	−	0.764476i
$302$		0			0
$303$	9.17430	−	0.787421i	0.527050	−	0.0452362i
$304$		0			0
$305$	−4.33290	−	2.50160i	−0.248101	−	0.143241i
$306$		0			0
$307$		−	27.1427i		−	1.54912i	−0.632501	−	0.774559i	$-0.717972\pi$
$307$		−	27.1427i		−	1.54912i	0.632501	−	0.774559i	$-0.282028\pi$
$308$		0			0
$309$	1.32482	+	15.4356i	0.0753664	+	0.878099i
$310$		0			0
$311$	−8.44774	−	14.6319i	−0.479028	−	0.829700i	0.520683	−	0.853750i	$-0.325677\pi$
$311$	−8.44774	−	14.6319i	−0.479028	−	0.829700i	−0.999711	+	0.0240499i	$0.992344\pi$
$312$		0			0
$313$	3.70433	+	2.13870i	0.209381	+	0.120886i	0.601024	−	0.799231i	$-0.294760\pi$
$313$	3.70433	+	2.13870i	0.209381	+	0.120886i	−0.391643	+	0.920117i	$0.628093\pi$
$314$		0			0
$315$	−6.31759	+	4.36328i	−0.355956	+	0.245843i
$316$		0			0
$317$	−5.74123	−	3.31470i	−0.322460	−	0.186172i	0.330029	−	0.943971i	$-0.392942\pi$
$317$	−5.74123	−	3.31470i	−0.322460	−	0.186172i	−0.652488	+	0.757799i	$0.726275\pi$
$318$		0			0
$319$	14.8397	+	25.7031i	0.830864	+	1.43910i
$320$		0			0
$321$	27.2105	−	18.9862i	1.51874	−	1.05971i
$322$		0			0
$323$		−	17.6212i		−	0.980472i
$324$		0			0
$325$	−15.3180	−	8.84386i	−0.849691	−	0.490569i
$326$		0			0
$327$	−14.1358	+	30.1844i	−0.781712	+	1.66920i
$328$		0			0
$329$	−2.26694	+	25.0057i	−0.124980	+	1.37861i
$330$		0			0
$331$	−0.378896	+	0.656267i	−0.0208260	+	0.0360717i	−0.876251	−	0.481856i	$-0.839963\pi$
$331$	−0.378896	+	0.656267i	−0.0208260	+	0.0360717i	0.855425	+	0.517927i	$0.173296\pi$
$332$		0			0
$333$	0.935837	+	1.12278i	0.0512836	+	0.0615279i
$334$		0			0
$335$	−2.63234	−	4.55935i	−0.143820	−	0.249104i
$336$		0			0
$337$	1.01088	−	1.75089i	0.0550660	−	0.0953772i	−0.837178	−	0.546930i	$-0.815796\pi$
$337$	1.01088	−	1.75089i	0.0550660	−	0.0953772i	0.892244	+	0.451553i	$0.149130\pi$
$338$		0			0
$339$	13.2436	+	6.20219i	0.719295	+	0.336857i
$340$		0			0
$341$	17.1850	+	29.7652i	0.930618	+	1.61188i
$342$		0			0
$343$	−4.96188	+	17.8432i	−0.267916	+	0.963442i
$344$		0			0
$345$	−0.380160	−	4.42927i	−0.0204671	−	0.238464i
$346$		0			0
$347$	−18.1572	+	10.4831i	−0.974730	+	0.562761i	−0.900675	−	0.434494i	$-0.856927\pi$
$347$	−18.1572	+	10.4831i	−0.974730	+	0.562761i	−0.0740550	+	0.997254i	$0.523594\pi$
$348$		0			0
$349$	5.36406	−	3.09694i	0.287132	−	0.165776i	−0.349516	−	0.936930i	$-0.613654\pi$
$349$	5.36406	−	3.09694i	0.287132	−	0.165776i	0.636648	+	0.771155i	$0.280321\pi$
$350$		0			0
$351$	21.8139	+	5.96071i	1.16434	+	0.318159i
$352$		0			0
$353$	18.8378			1.00263			0.501317	−	0.865264i	$-0.332849\pi$
$353$	18.8378			1.00263			0.501317	+	0.865264i	$0.332849\pi$
$354$		0			0
$355$		−	3.52112i		−	0.186882i
$356$		0			0
$357$	0.0866143	−	18.0796i	0.00458411	−	0.956876i
$358$		0			0
$359$	−24.0735	+	13.8988i	−1.27055	+	0.733553i	−0.975092	−	0.221803i	$-0.928806\pi$
$359$	−24.0735	+	13.8988i	−1.27055	+	0.733553i	−0.295459	+	0.955355i	$0.595473\pi$
$360$		0			0
$361$	0.474089	−	0.821146i	0.0249520	−	0.0432182i
$362$		0			0
$363$	−34.6266	+	2.97196i	−1.81742	+	0.155988i
$364$		0			0
$365$	−2.08428	−	1.20336i	−0.109096	−	0.0629866i
$366$		0			0
$367$			21.7534i			1.13552i	0.823195	+	0.567759i	$0.192190\pi$
$367$			21.7534i			1.13552i	−0.823195	+	0.567759i	$0.807810\pi$
$368$		0			0
$369$	−0.169559	+	0.461128i	−0.00882690	+	0.0240053i
$370$		0			0
$371$	−5.30990	−	0.481379i	−0.275676	−	0.0249920i
$372$		0			0
$373$	11.7312			0.607419			0.303709	−	0.952765i	$-0.401775\pi$
$373$	11.7312			0.607419			0.303709	+	0.952765i	$0.401775\pi$
$374$		0			0
$375$	−15.1312	+	1.29869i	−0.781370	+	0.0670642i
$376$		0			0
$377$	23.1743			1.19354
$378$		0			0
$379$	−34.8881			−1.79208			−0.896041	−	0.443971i	$-0.853569\pi$
$379$	−34.8881			−1.79208			−0.896041	+	0.443971i	$0.853569\pi$
$380$		0			0
$381$	−5.72732	+	0.491570i	−0.293420	+	0.0251839i
$382$		0			0
$383$	−11.8482			−0.605416			−0.302708	−	0.953083i	$-0.597891\pi$
$383$	−11.8482			−0.605416			−0.302708	+	0.953083i	$0.597891\pi$
$384$		0			0
$385$	−5.98779	−	12.9470i	−0.305166	−	0.659838i
$386$		0			0
$387$	16.7125	+	20.0510i	0.849545	+	1.01925i
$388$		0			0
$389$			6.35344i			0.322132i	0.986944	+	0.161066i	$0.0514933\pi$
$389$			6.35344i			0.322132i	−0.986944	+	0.161066i	$0.948507\pi$
$390$		0			0
$391$	9.06586	+	5.23418i	0.458480	+	0.264704i
$392$		0			0
$393$	32.3513	−	2.77668i	1.63191	−	0.140065i
$394$		0			0
$395$	2.22601	−	3.85557i	0.112003	−	0.193995i
$396$		0			0
$397$	−7.42647	+	4.28768i	−0.372724	+	0.215192i	−0.674648	−	0.738140i	$-0.735704\pi$
$397$	−7.42647	+	4.28768i	−0.372724	+	0.215192i	0.301924	+	0.953332i	$0.402371\pi$
$398$		0			0
$399$	10.3185	−	17.6760i	0.516569	−	0.884907i
$400$		0			0
$401$		−	23.1190i		−	1.15451i	−0.816565	−	0.577254i	$-0.804124\pi$
$401$		−	23.1190i		−	1.15451i	0.816565	−	0.577254i	$-0.195876\pi$
$402$		0			0
$403$	26.8367			1.33683
$404$		0			0
$405$	8.20033	−	2.92363i	0.407478	−	0.145276i
$406$		0			0
$407$	−2.35174	+	1.35778i	−0.116572	+	0.0673026i
$408$		0			0
$409$	−1.35091	+	0.779947i	−0.0667981	+	0.0385659i	−0.533027	−	0.846098i	$-0.678946\pi$
$409$	−1.35091	+	0.779947i	−0.0667981	+	0.0385659i	0.466229	+	0.884664i	$0.345612\pi$
$410$		0			0
$411$	−2.50824	−	29.2237i	−0.123722	−	1.44150i
$412$		0			0
$413$	3.61971	+	2.55154i	0.178114	+	0.125553i
$414$		0			0
$415$	−4.07224	−	7.05332i	−0.199898	−	0.346234i
$416$		0			0
$417$	−19.0237	−	8.90909i	−0.931596	−	0.436280i
$418$		0			0
$419$	3.40822	−	5.90321i	0.166502	−	0.288391i	−0.770685	−	0.637216i	$-0.780086\pi$
$419$	3.40822	−	5.90321i	0.166502	−	0.288391i	0.937188	+	0.348825i	$0.113419\pi$
$420$		0			0
$421$	−6.75727	−	11.7039i	−0.329329	−	0.570415i	0.653050	−	0.757315i	$-0.273489\pi$
$421$	−6.75727	−	11.7039i	−0.329329	−	0.570415i	−0.982379	+	0.186900i	$0.940156\pi$
$422$		0			0
$423$	9.82541	−	26.7208i	0.477728	−	1.29921i
$424$		0			0
$425$	8.01750	−	13.8867i	0.388906	−	0.673605i
$426$		0			0
$427$	13.6285	+	1.23552i	0.659529	+	0.0597910i
$428$		0			0
$429$	−17.8182	+	38.0476i	−0.860272	+	1.83695i
$430$		0			0
$431$	12.2628	+	7.07990i	0.590676	+	0.341027i	0.765365	−	0.643597i	$-0.222559\pi$
$431$	12.2628	+	7.07990i	0.590676	+	0.341027i	−0.174689	+	0.984624i	$0.555892\pi$
$432$		0			0
$433$		−	23.4830i		−	1.12852i	−0.825597	−	0.564260i	$-0.809161\pi$
$433$		−	23.4830i		−	1.12852i	0.825597	−	0.564260i	$-0.190839\pi$
$434$		0			0
$435$	7.31670	−	5.10527i	0.350809	−	0.244779i
$436$		0			0
$437$	5.92536	+	10.2630i	0.283449	+	0.490947i
$438$		0			0
$439$	−3.66398	−	2.11540i	−0.174872	−	0.100963i	0.410009	−	0.912081i	$-0.365526\pi$
$439$	−3.66398	−	2.11540i	−0.174872	−	0.100963i	−0.584881	+	0.811119i	$0.698859\pi$
$440$		0			0
$441$	10.6738	−	18.0851i	0.508275	−	0.861195i
$442$		0			0
$443$	25.8161	+	14.9049i	1.22656	+	0.708154i	0.966308	−	0.257388i	$-0.0828618\pi$
$443$	25.8161	+	14.9049i	1.22656	+	0.708154i	0.260250	+	0.965541i	$0.416195\pi$
$444$		0			0
$445$	1.99086	+	3.44827i	0.0943757	+	0.163464i
$446$		0			0
$447$	−1.29461	−	15.0836i	−0.0612328	−	0.713428i
$448$		0			0
$449$			8.41716i			0.397230i	0.980078	+	0.198615i	$0.0636444\pi$
$449$			8.41716i			0.397230i	−0.980078	+	0.198615i	$0.936356\pi$
$450$		0			0
$451$	−0.790505	−	0.456399i	−0.0372234	−	0.0214910i
$452$		0			0
$453$	−38.1280	+	3.27249i	−1.79141	+	0.153755i
$454$		0			0
$455$	−11.0926	−	1.00562i	−0.520027	−	0.0471441i
$456$		0			0
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	−0.817048	−	0.576570i	$-0.804391\pi$
$457$	1.94109	−	3.36207i	0.0908006	−	0.157271i	0.907848	+	0.419299i	$0.137724\pi$
$458$		0			0
$459$	−5.40374	+	19.7756i	−0.252225	+	0.923047i
$460$		0			0
$461$	17.0423	+	29.5181i	0.793739	+	1.37480i	0.923637	+	0.383269i	$0.125202\pi$
$461$	17.0423	+	29.5181i	0.793739	+	1.37480i	−0.129898	+	0.991527i	$0.541465\pi$
$462$		0			0
$463$	6.10962	−	10.5822i	0.283938	−	0.491796i	−0.688413	−	0.725319i	$-0.741692\pi$
$463$	6.10962	−	10.5822i	0.283938	−	0.491796i	0.972351	+	0.233523i	$0.0750256\pi$
$464$		0			0
$465$	8.47304	−	5.91211i	0.392928	−	0.274167i
$466$		0			0
$467$	15.4057	+	26.6835i	0.712893	+	1.23477i	0.963767	+	0.266747i	$0.0859488\pi$
$467$	15.4057	+	26.6835i	0.712893	+	1.23477i	−0.250874	+	0.968020i	$0.580718\pi$
$468$		0			0
$469$	11.7694	+	8.29628i	0.543460	+	0.383087i
$470$		0			0
$471$	2.02353	−	1.41193i	0.0932395	−	0.0650583i
$472$		0			0
$473$	−41.9983	+	24.2477i	−1.93108	+	1.11491i
$474$		0			0
$475$	15.7205	−	9.07623i	0.721306	−	0.416446i
$476$		0			0
$477$	5.67412	+	2.08640i	0.259800	+	0.0955299i
$478$		0			0
$479$	41.7493			1.90758			0.953788	−	0.300481i	$-0.0971472\pi$
$479$	41.7493			1.90758			0.953788	+	0.300481i	$0.0971472\pi$
$480$		0			0
$481$			2.12036i			0.0966803i
$482$		0			0
$483$	6.02906	+	10.5591i	0.274332	+	0.480457i
$484$		0			0
$485$	−9.93146	+	5.73393i	−0.450964	+	0.260364i
$486$		0			0
$487$	−10.5832	+	18.3306i	−0.479568	+	0.830637i	−0.999725	−	0.0234338i	$-0.992540\pi$
$487$	−10.5832	+	18.3306i	−0.479568	+	0.830637i	0.520157	+	0.854071i	$0.325873\pi$
$488$		0			0
$489$	7.37690	+	10.5723i	0.333595	+	0.478097i
$490$		0			0
$491$	−32.3428	−	18.6731i	−1.45961	−	0.842707i	−0.460619	−	0.887598i	$-0.652372\pi$
$491$	−32.3428	−	18.6731i	−1.45961	−	0.842707i	−0.998992	+	0.0448915i	$0.985706\pi$
$492$		0			0
$493$			21.0089i			0.946193i
$494$		0			0
$495$	2.75617	+	15.9379i	0.123881	+	0.716356i
$496$		0			0
$497$	4.04266	+	8.74113i	0.181338	+	0.392093i
$498$		0			0
$499$	−27.4197			−1.22748			−0.613738	−	0.789510i	$-0.710335\pi$
$499$	−27.4197			−1.22748			−0.613738	+	0.789510i	$0.710335\pi$
$500$		0			0
$501$	−4.77265	+	10.1911i	−0.213226	+	0.455305i
$502$		0			0
$503$	−11.2791			−0.502909			−0.251454	−	0.967869i	$-0.580909\pi$
$503$	−11.2791			−0.502909			−0.251454	+	0.967869i	$0.580909\pi$
$504$		0			0
$505$	5.14255			0.228840
$506$		0			0
$507$	5.88710	+	8.43720i	0.261455	+	0.374709i
$508$		0			0
$509$	18.6333			0.825909			0.412954	−	0.910752i	$-0.364497\pi$
$509$	18.6333			0.825909			0.412954	+	0.910752i	$0.364497\pi$
$510$		0			0
$511$	6.55578	+	0.594327i	0.290010	+	0.0262915i
$512$		0			0
$513$	−16.4913	+	16.3291i	−0.728107	+	0.720946i
$514$		0			0
$515$			8.65223i			0.381263i
$516$		0			0
$517$	45.8072	+	26.4468i	2.01460	+	1.16313i
$518$		0			0
$519$	8.68184	−	18.5385i	0.381091	−	0.813749i
$520$		0			0
$521$	7.64255	−	13.2373i	0.334826	−	0.579936i	−0.648625	−	0.761108i	$-0.724656\pi$
$521$	7.64255	−	13.2373i	0.334826	−	0.579936i	0.983451	+	0.181172i	$0.0579891\pi$
$522$		0			0
$523$	31.5991	−	18.2437i	1.38173	−	0.797743i	0.389368	−	0.921082i	$-0.372694\pi$
$523$	31.5991	−	18.2437i	1.38173	−	0.797743i	0.992365	+	0.123339i	$0.0393602\pi$
$524$		0			0
$525$	16.1741	−	9.23507i	0.705894	−	0.403051i
$526$		0			0
$527$			24.3292i			1.05979i
$528$		0			0
$529$	15.9598			0.693903
$530$		0			0
$531$	−3.21512	−	3.85737i	−0.139524	−	0.167396i
$532$		0			0
$533$	−0.617243	+	0.356365i	−0.0267358	+	0.0154359i
$534$		0			0
$535$	16.0477	−	9.26516i	0.693803	−	0.400568i
$536$		0			0
$537$	−3.81740	−	1.78775i	−0.164733	−	0.0771470i
$538$		0			0
$539$	29.7292	+	25.2659i	1.28053	+	1.08828i
$540$		0			0
$541$	2.63647	+	4.56649i	0.113351	+	0.196329i	0.917119	−	0.398613i	$-0.130508\pi$
$541$	2.63647	+	4.56649i	0.113351	+	0.196329i	−0.803769	+	0.594942i	$0.797175\pi$
$542$		0			0
$543$	−1.70839	−	19.9046i	−0.0733140	−	0.854186i
$544$		0			0
$545$	−9.30729	+	16.1207i	−0.398680	+	0.690535i
$546$		0			0
$547$	9.29831	+	16.1051i	0.397567	+	0.688606i	0.993425	−	0.114484i	$-0.0365213\pi$
$547$	9.29831	+	16.1051i	0.397567	+	0.688606i	−0.595858	+	0.803090i	$0.703188\pi$
$548$		0			0
$549$	−14.5633	−	5.35501i	−0.621547	−	0.228546i
$550$		0			0
$551$	−11.8916	+	20.5968i	−0.506599	+	0.877455i
$552$		0			0
$553$	−1.09941	+	12.1271i	−0.0467516	+	0.515697i
$554$		0			0
$555$	0.467114	+	0.669452i	0.0198279	+	0.0284167i
$556$		0			0
$557$	−23.8694	−	13.7810i	−1.01138	−	0.583920i	−0.0997845	−	0.995009i	$-0.531815\pi$
$557$	−23.8694	−	13.7810i	−1.01138	−	0.583920i	−0.911595	+	0.411089i	$0.865149\pi$
$558$		0			0
$559$			37.8662i			1.60157i
$560$		0			0
$561$	−34.4924	−	16.1533i	−1.45627	−	0.681993i
$562$		0			0
$563$	9.42577	+	16.3259i	0.397249	+	0.688055i	0.993385	−	0.114828i	$-0.0366317\pi$
$563$	9.42577	+	16.3259i	0.397249	+	0.688055i	−0.596137	+	0.802883i	$0.703298\pi$
$564$		0			0
$565$	7.07306	+	4.08364i	0.297566	+	0.171800i
$566$		0			0
$567$	−17.0005	+	16.6728i	−0.713955	+	0.700191i
$568$		0			0
$569$	3.87103	+	2.23494i	0.162282	+	0.0936936i	0.578942	−	0.815369i	$-0.303466\pi$
$569$	3.87103	+	2.23494i	0.162282	+	0.0936936i	−0.416659	+	0.909063i	$0.636799\pi$
$570$		0			0
$571$	9.31245	+	16.1296i	0.389714	+	0.675004i	0.992411	−	0.122966i	$-0.0392405\pi$
$571$	9.31245	+	16.1296i	0.389714	+	0.675004i	−0.602697	+	0.797970i	$0.705907\pi$
$572$		0			0
$573$	−34.6165	−	16.2114i	−1.44612	−	0.677241i
$574$		0			0
$575$			10.7839i			0.449721i
$576$		0			0
$577$	31.9418	+	18.4416i	1.32976	+	0.767735i	0.985262	−	0.171053i	$-0.0547170\pi$
$577$	31.9418	+	18.4416i	1.32976	+	0.767735i	0.344495	+	0.938788i	$0.388050\pi$
$578$		0			0
$579$	19.7626	+	28.3231i	0.821306	+	1.17707i
$580$		0			0
$581$	18.2073	+	12.8344i	0.755366	+	0.532459i
$582$		0			0
$583$	−5.61593	+	9.72707i	−0.232588	+	0.402854i
$584$		0			0
$585$	11.8534	+	4.35857i	0.490078	+	0.180205i
$586$		0			0
$587$	13.2295	+	22.9141i	0.546039	+	0.945766i	0.998541	+	0.0540032i	$0.0171981\pi$
$587$	13.2295	+	22.9141i	0.546039	+	0.945766i	−0.452502	+	0.891763i	$0.649469\pi$
$588$		0			0
$589$	−13.7709	+	23.8520i	−0.567422	+	0.982803i
$590$		0			0
$591$	−0.685123	−	7.98242i	−0.0281822	−	0.328353i
$592$		0			0
$593$	17.3351	+	30.0254i	0.711869	+	1.23299i	0.964155	+	0.265341i	$0.0854845\pi$
$593$	17.3351	+	30.0254i	0.711869	+	1.23299i	−0.252285	+	0.967653i	$0.581182\pi$
$594$		0			0
$595$	0.911654	−	10.0561i	0.0373742	−	0.412259i
$596$		0			0
$597$	32.7874	+	15.3548i	1.34190	+	0.628432i
$598$		0			0
$599$	−21.2079	+	12.2444i	−0.866530	+	0.500291i	−0.866193	−	0.499709i	$-0.833440\pi$
$599$	−21.2079	+	12.2444i	−0.866530	+	0.500291i	−0.000336253		1.00000i	$0.500107\pi$
$600$		0			0
$601$	19.3812	−	11.1898i	0.790577	−	0.456440i	−0.0495885	−	0.998770i	$-0.515791\pi$
$601$	19.3812	−	11.1898i	0.790577	−	0.456440i	0.840166	+	0.542330i	$0.182458\pi$
$602$		0			0
$603$	−10.4539	−	12.5421i	−0.425715	−	0.510755i
$604$		0			0
$605$	−19.4095			−0.789109
$606$		0			0
$607$		−	32.5834i		−	1.32252i	−0.750158	−	0.661259i	$-0.770022\pi$
$607$		−	32.5834i		−	1.32252i	0.750158	−	0.661259i	$-0.229978\pi$
$608$		0			0
$609$	−12.3022	+	21.0742i	−0.498509	+	0.853969i
$610$		0			0
$611$	35.7672	−	20.6502i	1.44699	−	0.835418i
$612$		0			0
$613$	5.86931	−	10.1659i	0.237059	−	0.410598i	−0.722810	−	0.691047i	$-0.757150\pi$
$613$	5.86931	−	10.1659i	0.237059	−	0.410598i	0.959869	+	0.280449i	$0.0904832\pi$
$614$		0			0
$615$	−0.116372	+	0.248491i	−0.00469258	+	0.0100201i
$616$		0			0
$617$	−38.1947	−	22.0517i	−1.53766	−	0.887770i	−0.998975	−	0.0452639i	$-0.985587\pi$
$617$	−38.1947	−	22.0517i	−1.53766	−	0.887770i	−0.538687	−	0.842506i	$-0.681080\pi$
$618$		0			0
$619$			4.94644i			0.198814i	0.995047	+	0.0994070i	$0.0316946\pi$
$619$			4.94644i			0.198814i	−0.995047	+	0.0994070i	$0.968305\pi$
$620$		0			0
$621$	−3.50253	−	13.3349i	−0.140552	−	0.535109i
$622$		0			0
$623$	−8.90128	−	6.27454i	−0.356622	−	0.251384i
$624$		0			0
$625$	11.8398			0.473593
$626$		0			0
$627$	−24.6727	−	35.3601i	−0.985333	−	1.41215i
$628$		0			0
$629$	−1.92224			−0.0766447
$630$		0			0
$631$	9.08478			0.361659			0.180830	−	0.983514i	$-0.442122\pi$
$631$	9.08478			0.361659			0.180830	+	0.983514i	$0.442122\pi$
$632$		0			0
$633$	4.91155	−	10.4877i	0.195217	−	0.416850i
$634$		0			0
$635$	−3.21038			−0.127400
$636$		0			0
$637$	28.6917	−	10.2391i	1.13681	−	0.405688i
$638$		0			0
$639$	−1.86083	−	10.7605i	−0.0736133	−	0.425678i
$640$		0			0
$641$			14.0821i			0.556209i	0.960551	+	0.278105i	$0.0897062\pi$
$641$			14.0821i			0.556209i	−0.960551	+	0.278105i	$0.910294\pi$
$642$		0			0
$643$	7.33157	+	4.23288i	0.289129	+	0.166929i	0.637549	−	0.770410i	$-0.279948\pi$
$643$	7.33157	+	4.23288i	0.289129	+	0.166929i	−0.348420	+	0.937339i	$0.613282\pi$
$644$		0			0
$645$	8.34189	+	11.9553i	0.328461	+	0.470740i
$646$		0			0
$647$	−12.1662	+	21.0725i	−0.478304	+	0.828446i	−0.999691	−	0.0248742i	$-0.992081\pi$
$647$	−12.1662	+	21.0725i	−0.478304	+	0.828446i	0.521387	+	0.853320i	$0.325415\pi$
$648$		0			0
$649$	8.07955	−	4.66473i	0.317150	−	0.183107i
$650$		0			0
$651$	−14.2464	+	24.4047i	−0.558361	+	0.956498i
$652$		0			0
$653$		−	41.6446i		−	1.62968i	−0.579686	−	0.814840i	$-0.696825\pi$
$653$		−	41.6446i		−	1.62968i	0.579686	−	0.814840i	$-0.303175\pi$
$654$		0			0
$655$	18.1341			0.708560
$656$		0			0
$657$	−7.00545	−	2.57594i	−0.273309	−	0.100497i
$658$		0			0
$659$	9.09866	−	5.25312i	0.354434	−	0.204632i	−0.312203	−	0.950016i	$-0.601067\pi$
$659$	9.09866	−	5.25312i	0.354434	−	0.204632i	0.666636	+	0.745383i	$0.267733\pi$
$660$		0			0
$661$	−16.8988	+	9.75655i	−0.657289	+	0.379486i	−0.791243	−	0.611502i	$-0.790566\pi$
$661$	−16.8988	+	9.75655i	−0.657289	+	0.379486i	0.133954	+	0.990987i	$0.457232\pi$
$662$		0			0
$663$	−24.3892	+	17.0177i	−0.947199	+	0.660914i
$664$		0			0
$665$	6.58578	−	9.34282i	0.255386	−	0.362299i
$666$		0			0
$667$	−7.06450	−	12.2361i	−0.273539	−	0.473783i
$668$		0			0
$669$	11.6228	−	8.10984i	0.449362	−	0.313545i
$670$		0			0
$671$	14.4140	−	24.9657i	0.556445	−	0.963790i
$672$		0			0
$673$	−3.10277	−	5.37415i	−0.119603	−	0.207158i	0.800007	−	0.599990i	$-0.204829\pi$
$673$	−3.10277	−	5.37415i	−0.119603	−	0.207158i	−0.919610	+	0.392832i	$0.871495\pi$
$674$		0			0
$675$	−20.4258	+	5.36503i	−0.786189	+	0.206500i
$676$		0			0
$677$	12.3765	−	21.4368i	0.475669	−	0.823883i	−0.523942	−	0.851754i	$-0.675539\pi$
$677$	12.3765	−	21.4368i	0.475669	−	0.823883i	0.999612	+	0.0278703i	$0.00887255\pi$
$678$		0			0
$679$	18.0715	−	25.6369i	0.693520	−	0.983852i
$680$		0			0
$681$	18.4543	−	1.58391i	0.707169	−	0.0606956i
$682$		0			0
$683$	−18.3119	−	10.5724i	−0.700687	−	0.404542i	0.106916	−	0.994268i	$-0.465902\pi$
$683$	−18.3119	−	10.5724i	−0.700687	−	0.404542i	−0.807603	+	0.589726i	$0.799236\pi$
$684$		0			0
$685$		−	16.3810i		−	0.625886i
$686$		0			0
$687$	−4.32605	−	50.4031i	−0.165049	−	1.92300i
$688$		0			0
$689$	4.38503	+	7.59509i	0.167056	+	0.289350i
$690$		0			0
$691$	−5.58127	−	3.22235i	−0.212322	−	0.122584i	0.390068	−	0.920786i	$-0.372451\pi$
$691$	−5.58127	−	3.22235i	−0.212322	−	0.122584i	−0.602390	+	0.798202i	$0.705785\pi$
$692$		0			0
$693$	−25.1407	−	36.4012i	−0.955017	−	1.38277i
$694$		0			0
$695$	−10.1601	−	5.86591i	−0.385393	−	0.222507i
$696$		0			0
$697$	−0.323067	−	0.559568i	−0.0122370	−	0.0211952i
$698$		0			0
$699$	−9.14675	+	6.38220i	−0.345962	+	0.241397i
$700$		0			0
$701$		−	24.5717i		−	0.928061i	−0.885819	−	0.464031i	$-0.846403\pi$
$701$		−	24.5717i		−	0.928061i	0.885819	−	0.464031i	$-0.153597\pi$
$702$		0			0
$703$	−1.88454	−	1.08804i	−0.0710767	−	0.0410361i
$704$		0			0
$705$	6.74339	−	14.3993i	0.253971	−	0.542308i
$706$		0			0
$707$	−12.7663	+	5.90424i	−0.480126	+	0.222052i
$708$		0			0
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	0.0655765	+	0.997848i	$0.479111\pi$
$709$	−22.1370	+	38.3424i	−0.831373	+	1.43998i	−0.896950	+	0.442133i	$0.854222\pi$
$710$		0			0
$711$	4.76508	−	12.9589i	0.178704	−	0.485998i
$712$		0			0
$713$	−8.18098	−	14.1699i	−0.306380	−	0.530666i
$714$		0			0
$715$	−11.7319	+	20.3202i	−0.438747	+	0.759931i
$716$		0			0
$717$	7.27118	+	3.40520i	0.271547	+	0.127169i
$718$		0			0
$719$	2.22433	+	3.85266i	0.0829537	+	0.143680i	0.904517	−	0.426437i	$-0.140231\pi$
$719$	2.22433	+	3.85266i	0.0829537	+	0.143680i	−0.821564	+	0.570117i	$0.806898\pi$
$720$		0			0
$721$	−9.93376	−	21.4790i	−0.369952	−	0.799921i
$722$		0			0
$723$	1.55439	+	18.1103i	0.0578084	+	0.673530i
$724$		0			0
$725$	−18.7427	+	10.8211i	−0.696088	+	0.401886i
$726$		0			0
$727$	30.4270	−	17.5670i	1.12848	−	0.651525i	0.184924	−	0.982753i	$-0.440796\pi$
$727$	30.4270	−	17.5670i	1.12848	−	0.651525i	0.943551	+	0.331227i	$0.107463\pi$
$728$		0			0
$729$	23.5150	−	13.2682i	0.870925	−	0.491416i
$730$		0			0
$731$	−34.3280			−1.26967
$732$		0			0
$733$			5.81725i			0.214865i	0.994212	+	0.107433i	$0.0342630\pi$
$733$			5.81725i			0.214865i	−0.994212	+	0.107433i	$0.965737\pi$
$734$		0			0
$735$	6.80302	−	9.55349i	0.250933	−	0.352386i
$736$		0			0
$737$	26.2704	−	15.1672i	0.967684	−	0.558693i
$738$		0			0
$739$	5.51675	−	9.55529i	0.202937	−	0.351497i	−0.746537	−	0.665344i	$-0.768285\pi$
$739$	5.51675	−	9.55529i	0.202937	−	0.351497i	0.949473	+	0.313847i	$0.101618\pi$
$740$		0			0
$741$	−33.5433	+	2.87899i	−1.23225	+	0.105762i
$742$		0			0
$743$	0.543196	+	0.313615i	0.0199279	+	0.0115054i	0.509931	−	0.860215i	$-0.329671\pi$
$743$	0.543196	+	0.313615i	0.0199279	+	0.0115054i	−0.490003	+	0.871721i	$0.663004\pi$
$744$		0			0
$745$		−	8.45491i		−	0.309764i
$746$		0			0
$747$	−16.1722	−	19.4027i	−0.591709	−	0.709909i
$748$		0			0
$749$	−29.2008	+	41.4253i	−1.06697	+	1.51365i
$750$		0			0
$751$	−4.47058			−0.163134			−0.0815668	−	0.996668i	$-0.525992\pi$
$751$	−4.47058			−0.163134			−0.0815668	+	0.996668i	$0.525992\pi$
$752$		0			0
$753$	13.5515	−	1.16311i	0.493843	−	0.0423861i
$754$		0			0
$755$	−21.3722			−0.777813
$756$		0			0
$757$	5.75624			0.209214			0.104607	−	0.994514i	$-0.466642\pi$
$757$	5.75624			0.209214			0.104607	+	0.994514i	$0.466642\pi$
$758$		0			0
$759$	25.5210	−	2.19044i	0.926352	−	0.0795079i
$760$		0			0
$761$	−20.9940			−0.761032			−0.380516	−	0.924774i	$-0.624254\pi$
$761$	−20.9940			−0.761032			−0.380516	+	0.924774i	$0.624254\pi$
$762$		0			0
$763$	4.59678	−	50.7052i	0.166415	−	1.83565i
$764$		0			0
$765$	−3.95131	+	10.7458i	−0.142860	+	0.388517i
$766$		0			0
$767$		−	7.28463i		−	0.263033i
$768$		0			0
$769$	−34.1729	−	19.7298i	−1.23231	−	0.711473i	−0.264797	−	0.964304i	$-0.585305\pi$
$769$	−34.1729	−	19.7298i	−1.23231	−	0.711473i	−0.967511	+	0.252831i	$0.918638\pi$
$770$		0			0
$771$	−5.92151	+	0.508238i	−0.213258	+	0.0183037i
$772$		0			0
$773$	−17.3164	+	29.9929i	−0.622829	+	1.07877i	0.366128	+	0.930565i	$0.380683\pi$
$773$	−17.3164	+	29.9929i	−0.622829	+	1.07877i	−0.988956	+	0.148206i	$0.952650\pi$
$774$		0			0
$775$	−21.7048	+	12.5313i	−0.779661	+	0.450137i
$776$		0			0
$777$	−1.92821	−	1.12560i	−0.0691742	−	0.0403808i
$778$		0			0
$779$		−	0.731457i		−	0.0262072i
$780$		0			0
$781$	20.2883			0.725973
$782$		0			0
$783$	19.6617	−	19.4683i	0.702651	−	0.695741i
$784$		0			0
$785$	1.19340	−	0.689012i	0.0425944	−	0.0245919i
$786$		0			0
$787$	−30.5793	+	17.6550i	−1.09003	+	0.629332i	−0.933586	−	0.358355i	$-0.883338\pi$
$787$	−30.5793	+	17.6550i	−1.09003	+	0.629332i	−0.156449	+	0.987686i	$0.550005\pi$
$788$		0			0
$789$	−0.542299	−	6.31837i	−0.0193064	−	0.224940i
$790$		0			0
$791$	−22.2473	−	2.01687i	−0.791022	−	0.0717116i
$792$		0			0
$793$	−11.2547	−	19.4937i	−0.399667	−	0.692243i
$794$		0			0
$795$	3.05766	+	1.43194i	0.108444	+	0.0507859i
$796$		0			0
$797$	−9.60992	+	16.6449i	−0.340401	+	0.589591i	−0.984507	−	0.175344i	$-0.943896\pi$
$797$	−9.60992	+	16.6449i	−0.340401	+	0.589591i	0.644106	+	0.764936i	$0.277229\pi$
$798$		0			0
$799$	18.7207	+	32.4252i	0.662290	+	1.14712i
$800$		0			0
$801$	7.90635	+	9.48571i	0.279357	+	0.335161i
$802$		0			0
$803$	6.93361	−	12.0094i	0.244682	−	0.423801i
$804$		0			0
$805$	2.85051	+	6.16345i	0.100467	+	0.217233i
$806$		0			0
$807$	9.31894	−	19.8989i	0.328042	−	0.700474i
$808$		0			0
$809$	34.0157	+	19.6390i	1.19593	+	0.690469i	0.959645	−	0.281215i	$-0.0907374\pi$
$809$	34.0157	+	19.6390i	1.19593	+	0.690469i	0.236283	+	0.971684i	$0.424071\pi$
$810$		0			0
$811$		−	9.68436i		−	0.340064i	−0.985439	−	0.170032i	$-0.945613\pi$
$811$		−	9.68436i		−	0.340064i	0.985439	−	0.170032i	$-0.0543871\pi$
$812$		0			0
$813$	28.2336	−	19.7002i	0.990196	−	0.690915i
$814$		0			0
$815$	3.59987	+	6.23517i	0.126098	+	0.218408i
$816$		0			0
$817$	−33.6547	−	19.4306i	−1.17743	−	0.679790i
$818$		0			0
$819$	−34.4301	+	2.78901i	−1.20308	+	0.0974558i
$820$		0			0
$821$	10.9919	+	6.34620i	0.383621	+	0.221484i	0.679393	−	0.733775i	$-0.262243\pi$
$821$	10.9919	+	6.34620i	0.383621	+	0.221484i	−0.295771	+	0.955259i	$0.595577\pi$
$822$		0			0
$823$	8.73837	+	15.1353i	0.304600	+	0.527583i	0.977172	−	0.212448i	$-0.0681438\pi$
$823$	8.73837	+	15.1353i	0.304600	+	0.527583i	−0.672572	+	0.740032i	$0.734810\pi$
$824$		0			0
$825$	−3.35523	−	39.0920i	−0.116814	−	1.36101i
$826$		0			0
$827$			46.9482i			1.63255i	0.577665	+	0.816274i	$0.303964\pi$
$827$			46.9482i			1.63255i	−0.577665	+	0.816274i	$0.696036\pi$
$828$		0			0
$829$	−1.99797	−	1.15353i	−0.0693924	−	0.0400637i	0.464902	−	0.885362i	$-0.346089\pi$
$829$	−1.99797	−	1.15353i	−0.0693924	−	0.0400637i	−0.534295	+	0.845298i	$0.679423\pi$
$830$		0			0
$831$	−12.8842	+	1.10584i	−0.446948	+	0.0383611i
$832$		0			0
$833$	9.28237	+	26.0108i	0.321615	+	0.901219i
$834$		0			0
$835$	−3.14240	+	5.44280i	−0.108747	+	0.188356i
$836$		0			0
$837$	22.7690	−	22.5451i	0.787013	−	0.779272i
$838$		0			0
$839$	8.51664	+	14.7513i	0.294027	+	0.509270i	0.974758	−	0.223264i	$-0.0716711\pi$
$839$	8.51664	+	14.7513i	0.294027	+	0.509270i	−0.680731	+	0.732533i	$0.738338\pi$
$840$		0			0
$841$	−0.322276	+	0.558199i	−0.0111130	+	0.0192482i
$842$		0			0
$843$	−31.6141	+	22.0589i	−1.08885	+	0.759749i
$844$		0			0
$845$	2.87287	+	4.97595i	0.0988296	+	0.171178i
$846$		0			0
$847$	48.1838	−	22.2844i	1.65562	−	0.765700i
$848$		0			0
$849$	−22.9832	+	16.0366i	−0.788781	+	0.550376i
$850$		0			0
$851$	1.11956	−	0.646377i	0.0383779	−	0.0221575i
$852$		0			0
$853$	−2.87158	+	1.65791i	−0.0983209	+	0.0567656i	−0.548354	−	0.836246i	$-0.684745\pi$
$853$	−2.87158	+	1.65791i	−0.0983209	+	0.0567656i	0.450033	+	0.893012i	$0.351412\pi$
$854$		0			0
$855$	−9.95624	+	8.29854i	−0.340496	+	0.283804i
$856$		0			0
$857$	−9.49024			−0.324180			−0.162090	−	0.986776i	$-0.551824\pi$
$857$	−9.49024			−0.324180			−0.162090	+	0.986776i	$0.551824\pi$
$858$		0			0
$859$		−	29.4569i		−	1.00506i	−0.864561	−	0.502528i	$-0.832403\pi$
$859$		−	29.4569i		−	1.00506i	0.864561	−	0.502528i	$-0.167597\pi$
$860$		0			0
$861$	0.00359536	−	0.750485i	0.000122529	−	0.0255765i
$862$		0			0
$863$	13.4610	−	7.77172i	0.458218	−	0.264553i	−0.253076	−	0.967446i	$-0.581442\pi$
$863$	13.4610	−	7.77172i	0.458218	−	0.264553i	0.711295	+	0.702894i	$0.248109\pi$
$864$		0			0
$865$	5.71629	−	9.90090i	0.194360	−	0.336641i
$866$		0			0
$867$	1.42152	+	2.03727i	0.0482773	+	0.0691895i
$868$		0			0
$869$	22.2154	+	12.8260i	0.753604	+	0.435094i
$870$		0			0
$871$		−	23.6858i		−	0.802562i
$872$		0			0
$873$	−27.3201	+	22.7713i	−0.924645	+	0.770692i
$874$		0			0
$875$	21.0554	−	9.73785i	0.711804	−	0.329199i
$876$		0			0
$877$	−45.4497			−1.53473			−0.767364	−	0.641212i	$-0.778432\pi$
$877$	−45.4497			−1.53473			−0.767364	+	0.641212i	$0.778432\pi$
$878$		0			0
$879$	6.51436	−	13.9102i	0.219724	−	0.469180i
$880$		0			0
$881$	−15.6912			−0.528651			−0.264326	−	0.964433i	$-0.585149\pi$
$881$	−15.6912			−0.528651			−0.264326	+	0.964433i	$0.585149\pi$
$882$		0			0
$883$	10.5344			0.354510			0.177255	−	0.984165i	$-0.443278\pi$
$883$	10.5344			0.354510			0.177255	+	0.984165i	$0.443278\pi$
$884$		0			0
$885$	−1.60480	−	2.29994i	−0.0539447	−	0.0773117i
$886$		0			0
$887$	−0.0605481			−0.00203301			−0.00101650	−	0.999999i	$-0.500324\pi$
$887$	−0.0605481			−0.00203301			−0.00101650	+	0.999999i	$0.500324\pi$
$888$		0			0
$889$	7.96973	−	3.68589i	0.267296	−	0.123621i
$890$		0			0
$891$	16.8456	+	47.2494i	0.564350	+	1.58291i
$892$		0			0
$893$			42.3856i			1.41838i
$894$		0			0
$895$	−2.03877	−	1.17709i	−0.0681487	−	0.0393456i
$896$		0			0
$897$	8.48245	−	18.1127i	0.283221	−	0.604766i
$898$		0			0
$899$	16.4184	−	28.4375i	0.547583	−	0.948442i
$900$		0			0
$901$	−6.88542	+	3.97530i	−0.229386	+	0.132436i
$902$		0			0
$903$	−34.4347	−	20.1014i	−1.14592	−	0.668934i
$904$		0			0
$905$		−	11.1573i		−	0.370880i
$906$		0			0
$907$	−24.0980			−0.800162			−0.400081	−	0.916480i	$-0.631018\pi$
$907$	−24.0980			−0.800162			−0.400081	+	0.916480i	$0.631018\pi$
$908$		0			0
$909$	15.7155	−	2.71772i	0.521251	−	0.0901410i
$910$		0			0
$911$	−22.0494	+	12.7302i	−0.730528	+	0.421771i	−0.818615	−	0.574342i	$-0.805258\pi$
$911$	−22.0494	+	12.7302i	−0.730528	+	0.421771i	0.0880873	+	0.996113i	$0.471925\pi$
$912$		0			0
$913$	40.6404	−	23.4638i	1.34500	−	0.776537i
$914$		0			0
$915$	−7.84785	−	3.67526i	−0.259442	−	0.121500i
$916$		0			0
$917$	−45.0177	+	20.8201i	−1.48662	+	0.687540i
$918$		0			0
$919$	−11.4534	−	19.8378i	−0.377812	−	0.654389i	0.612932	−	0.790136i	$-0.289990\pi$
$919$	−11.4534	−	19.8378i	−0.377812	−	0.654389i	−0.990744	+	0.135747i	$0.956657\pi$
$920$		0			0
$921$	−4.02027	−	46.8404i	−0.132472	−	1.54344i
$922$		0			0
$923$	7.92076	−	13.7192i	0.260715	−	0.451572i
$924$		0			0
$925$	−0.990094	−	1.71489i	−0.0325541	−	0.0563853i
$926$		0			0
$927$	4.57250	+	26.4410i	0.150181	+	0.868437i
$928$		0			0
$929$	14.3986	−	24.9392i	0.472404	−	0.818228i	−0.527097	−	0.849805i	$-0.676720\pi$
$929$	14.3986	−	24.9392i	0.472404	−	0.818228i	0.999501	+	0.0315768i	$0.0100529\pi$
$930$		0			0
$931$	−5.62246	+	30.7547i	−0.184269	+	1.00794i
$932$		0			0
$933$	−16.7455	−	23.9992i	−0.548224	−	0.785697i
$934$		0			0
$935$	−18.4215	−	10.6356i	−0.602447	−	0.347823i
$936$		0			0
$937$			53.6825i			1.75373i	0.480736	+	0.876865i	$0.340369\pi$
$937$			53.6825i			1.75373i	−0.480736	+	0.876865i	$0.659631\pi$
$938$		0			0
$939$	6.70936	+	3.14209i	0.218952	+	0.102538i
$940$		0			0
$941$	−22.9511	−	39.7524i	−0.748184	−	1.29589i	−0.948693	−	0.316200i	$-0.897593\pi$
$941$	−22.9511	−	39.7524i	−0.748184	−	1.29589i	0.200509	−	0.979692i	$-0.435740\pi$
$942$		0			0
$943$	0.376324	+	0.217271i	0.0122548	+	0.00707530i
$944$		0			0
$945$	−10.2560	+	8.46547i	−0.333629	+	0.275382i
$946$		0			0
$947$	25.0440	+	14.4591i	0.813820	+	0.469859i	0.848281	−	0.529547i	$-0.177638\pi$
$947$	25.0440	+	14.4591i	0.813820	+	0.469859i	−0.0344607	+	0.999406i	$0.510971\pi$
$948$		0			0
$949$	−5.41390	−	9.37715i	−0.175743	−	0.304395i
$950$		0			0
$951$	−10.3986	−	4.86984i	−0.337199	−	0.157915i
$952$		0			0
$953$		−	12.8715i		−	0.416949i	−0.978028	−	0.208475i	$-0.933150\pi$
$953$		−	12.8715i		−	0.416949i	0.978028	−	0.208475i	$-0.0668498\pi$
$954$		0			0
$955$	−18.4877	−	10.6739i	−0.598249	−	0.345399i
$956$		0			0
$957$	29.4160	+	42.1580i	0.950884	+	1.36278i
$958$		0			0
$959$	18.8073	+	40.6656i	0.607319	+	1.31316i
$960$		0			0
$961$	3.51314	−	6.08494i	0.113327	−	0.196288i
$962$		0			0
$963$	44.1451	−	36.7950i	1.42256	−	1.18570i
$964$		0			0
$965$	9.64402	+	16.7039i	0.310452	+	0.537719i
$966$		0			0
$967$	−3.11725	+	5.39923i	−0.100244	+	0.173627i	−0.911785	−	0.410668i	$-0.865296\pi$
$967$	−3.11725	+	5.39923i	−0.100244	+	0.173627i	0.811541	+	0.584295i	$0.198629\pi$
$968$		0			0
$969$	−2.60998	−	30.4091i	−0.0838447	−	0.976881i
$970$		0			0
$971$	−19.6863	−	34.0977i	−0.631764	−	1.09425i	−0.987191	−	0.159544i	$-0.948998\pi$
$971$	−19.6863	−	34.0977i	−0.631764	−	1.09425i	0.355426	−	0.934704i	$-0.384336\pi$
$972$		0			0
$973$	31.9570	+	2.89712i	1.02449	+	0.0928774i
$974$		0			0
$975$	−27.7443	−	12.9931i	−0.888529	−	0.416111i
$976$		0			0
$977$	23.2474	−	13.4219i	0.743751	−	0.429405i	−0.0796807	−	0.996820i	$-0.525390\pi$
$977$	23.2474	−	13.4219i	0.743751	−	0.429405i	0.823431	+	0.567416i	$0.192057\pi$
$978$		0			0
$979$	−19.8685	+	11.4711i	−0.635001	+	0.366618i
$980$		0			0
$981$	−19.9235	+	54.1832i	−0.636108	+	1.72994i
$982$		0			0
$983$	−11.9691			−0.381756			−0.190878	−	0.981614i	$-0.561134\pi$
$983$	−11.9691			−0.381756			−0.190878	+	0.981614i	$0.561134\pi$
$984$		0			0
$985$		−	4.47445i		−	0.142568i
$986$		0			0
$987$	−0.208339	+	43.4882i	−0.00663151	+	1.38424i
$988$		0			0
$989$	19.9935	−	11.5432i	0.635755	−	0.367053i
$990$		0			0
$991$	5.40420	−	9.36036i	0.171670	−	0.297342i	−0.767334	−	0.641248i	$-0.778417\pi$
$991$	5.40420	−	9.36036i	0.171670	−	0.297342i	0.939004	+	0.343906i	$0.111750\pi$
$992$		0			0
$993$	−0.556660	+	1.18864i	−0.0176651	+	0.0377205i
$994$		0			0
$995$	17.5109	+	10.1099i	0.555132	+	0.320506i
$996$		0			0
$997$		−	13.4700i		−	0.426598i	−0.976987	−	0.213299i	$-0.931579\pi$
$997$		−	13.4700i		−	0.426598i	0.976987	−	0.213299i	$-0.0684208\pi$
$998$		0			0
$999$	1.78128	+	1.79897i	0.0563572	+	0.0569170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.df.c.689.7		16
3.2	odd	2		3024.2.df.c.17.4		16
4.3	odd	2		126.2.t.a.59.1	yes	16
7.5	odd	6		1008.2.ca.c.257.5		16
9.2	odd	6		1008.2.ca.c.353.5		16
9.7	even	3		3024.2.ca.c.2033.4		16
12.11	even	2		378.2.t.a.17.6		16
21.5	even	6		3024.2.ca.c.2609.4		16
28.3	even	6		882.2.m.b.293.6		16
28.11	odd	6		882.2.m.a.293.7		16
28.19	even	6		126.2.l.a.5.7	✓	16
28.23	odd	6		882.2.l.b.509.6		16
28.27	even	2		882.2.t.a.815.4		16
36.7	odd	6		378.2.l.a.143.6		16
36.11	even	6		126.2.l.a.101.3	yes	16
36.23	even	6		1134.2.k.a.647.3		16
36.31	odd	6		1134.2.k.b.647.6		16
63.47	even	6	inner	1008.2.df.c.929.7		16
63.61	odd	6		3024.2.df.c.1601.4		16
84.11	even	6		2646.2.m.a.881.3		16
84.23	even	6		2646.2.l.a.1097.3		16
84.47	odd	6		378.2.l.a.341.2		16
84.59	odd	6		2646.2.m.b.881.2		16
84.83	odd	2		2646.2.t.b.2285.7		16
252.11	even	6		882.2.m.b.587.6		16
252.47	odd	6		126.2.t.a.47.1	yes	16
252.79	odd	6		2646.2.t.b.1979.7		16
252.83	odd	6		882.2.l.b.227.2		16
252.103	even	6		1134.2.k.a.971.3		16
252.115	even	6		2646.2.m.a.1763.3		16
252.131	odd	6		1134.2.k.b.971.6		16
252.151	odd	6		2646.2.m.b.1763.2		16
252.187	even	6		378.2.t.a.89.6		16
252.191	even	6		882.2.t.a.803.4		16
252.223	even	6		2646.2.l.a.521.7		16
252.227	odd	6		882.2.m.a.587.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.7	✓	16	28.19	even	6
126.2.l.a.101.3	yes	16	36.11	even	6
126.2.t.a.47.1	yes	16	252.47	odd	6
126.2.t.a.59.1	yes	16	4.3	odd	2
378.2.l.a.143.6		16	36.7	odd	6
378.2.l.a.341.2		16	84.47	odd	6
378.2.t.a.17.6		16	12.11	even	2
378.2.t.a.89.6		16	252.187	even	6
882.2.l.b.227.2		16	252.83	odd	6
882.2.l.b.509.6		16	28.23	odd	6
882.2.m.a.293.7		16	28.11	odd	6
882.2.m.a.587.7		16	252.227	odd	6
882.2.m.b.293.6		16	28.3	even	6
882.2.m.b.587.6		16	252.11	even	6
882.2.t.a.803.4		16	252.191	even	6
882.2.t.a.815.4		16	28.27	even	2
1008.2.ca.c.257.5		16	7.5	odd	6
1008.2.ca.c.353.5		16	9.2	odd	6
1008.2.df.c.689.7		16	1.1	even	1	trivial
1008.2.df.c.929.7		16	63.47	even	6	inner
1134.2.k.a.647.3		16	36.23	even	6
1134.2.k.a.971.3		16	252.103	even	6
1134.2.k.b.647.6		16	36.31	odd	6
1134.2.k.b.971.6		16	252.131	odd	6
2646.2.l.a.521.7		16	252.223	even	6
2646.2.l.a.1097.3		16	84.23	even	6
2646.2.m.a.881.3		16	84.11	even	6
2646.2.m.a.1763.3		16	252.115	even	6
2646.2.m.b.881.2		16	84.59	odd	6
2646.2.m.b.1763.2		16	252.151	odd	6
2646.2.t.b.1979.7		16	252.79	odd	6
2646.2.t.b.2285.7		16	84.83	odd	2
3024.2.ca.c.2033.4		16	9.7	even	3
3024.2.ca.c.2609.4		16	21.5	even	6
3024.2.df.c.17.4		16	3.2	odd	2
3024.2.df.c.1601.4		16	63.61	odd	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.72571 - 0.148116i) q^{3} +0.967324 q^{5} +(-2.40137 + 1.11060i) q^{7} +(2.95612 - 0.511208i) q^{9} +O(q^{10})\)	\(q+(1.72571 - 0.148116i) q^{3} +0.967324 q^{5} +(-2.40137 + 1.11060i) q^{7} +(2.95612 - 0.511208i) q^{9} +5.57361i q^{11} +(3.76893 + 2.17600i) q^{13} +(1.66932 - 0.143276i) q^{15} +(-1.97267 + 3.41677i) q^{17} +(-3.86796 + 2.23317i) q^{19} +(-3.97956 + 2.27225i) q^{21} -2.65334i q^{23} -4.06428 q^{25} +(5.02568 - 1.32004i) q^{27} +(4.61157 - 2.66249i) q^{29} +(5.34038 - 3.08327i) q^{31} +(0.825539 + 9.61842i) q^{33} +(-2.32290 + 1.07431i) q^{35} +(0.243608 + 0.421942i) q^{37} +(6.82637 + 3.19689i) q^{39} +(-0.0818856 + 0.141830i) q^{41} +(4.35045 + 7.53520i) q^{43} +(2.85953 - 0.494504i) q^{45} +(4.74500 - 8.21859i) q^{47} +(4.53314 - 5.33392i) q^{49} +(-2.89818 + 6.18852i) q^{51} +(1.74520 + 1.00759i) q^{53} +5.39149i q^{55} +(-6.34420 + 4.42670i) q^{57} +(-0.836931 - 1.44961i) q^{59} +(-4.47927 - 2.58611i) q^{61} +(-6.53099 + 4.51067i) q^{63} +(3.64578 + 2.10489i) q^{65} +(-2.72126 - 4.71336i) q^{67} +(-0.393002 - 4.57889i) q^{69} -3.64006i q^{71} +(-2.15468 - 1.24401i) q^{73} +(-7.01376 + 0.601984i) q^{75} +(-6.19005 - 13.3843i) q^{77} +(2.30121 - 3.98581i) q^{79} +(8.47733 - 3.02239i) q^{81} +(-4.20979 - 7.29158i) q^{83} +(-1.90821 + 3.30512i) q^{85} +(7.56386 - 5.27772i) q^{87} +(2.05811 + 3.56475i) q^{89} +(-11.4673 - 1.03959i) q^{91} +(8.75925 - 6.11182i) q^{93} +(-3.74157 + 2.16020i) q^{95} +(-10.2669 + 5.92762i) q^{97} +(2.84928 + 16.4763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q - 2 * q^7 - 6 * q^9	\( 16 q - 2 q^{7} - 6 q^{9} - 6 q^{13} + 18 q^{15} + 18 q^{17} - 18 q^{21} + 16 q^{25} + 36 q^{27} + 6 q^{29} - 6 q^{31} + 18 q^{33} + 30 q^{35} - 2 q^{37} + 30 q^{39} + 6 q^{41} + 2 q^{43} + 12 q^{45} + 18 q^{47} + 10 q^{49} + 36 q^{53} + 6 q^{57} - 30 q^{59} - 60 q^{61} - 42 q^{63} + 42 q^{65} - 14 q^{67} + 42 q^{69} - 30 q^{75} - 18 q^{77} + 16 q^{79} + 54 q^{81} - 12 q^{85} + 48 q^{87} + 24 q^{89} + 12 q^{91} + 30 q^{93} + 66 q^{95} - 6 q^{97} - 18 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 - 6 * q^9 - 6 * q^13 + 18 * q^15 + 18 * q^17 - 18 * q^21 + 16 * q^25 + 36 * q^27 + 6 * q^29 - 6 * q^31 + 18 * q^33 + 30 * q^35 - 2 * q^37 + 30 * q^39 + 6 * q^41 + 2 * q^43 + 12 * q^45 + 18 * q^47 + 10 * q^49 + 36 * q^53 + 6 * q^57 - 30 * q^59 - 60 * q^61 - 42 * q^63 + 42 * q^65 - 14 * q^67 + 42 * q^69 - 30 * q^75 - 18 * q^77 + 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 + 24 * q^89 + 12 * q^91 + 30 * q^93 + 66 * q^95 - 6 * q^97 - 18 * q^99

Introduction

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