LMFDB - Embedded newform 1008.2.ca.c.353.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(257,1008)]

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, 5]))

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

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

chi := DirichletCharacter("1008.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.ca (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:	$\Z[a_1, \ldots, a_{11}]$
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			353.5
Root			$-1.70672 - 0.295146i$ of defining polynomial
Character	$\chi$	$=$	1008.353
Dual form			1008.2.ca.c.257.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.734581 + 1.56856i) q^{3} +(0.483662 - 0.837727i) q^{5} +(2.16249 + 1.52435i) q^{7} +(-1.92078 + 2.30447i) q^{9} +(-4.82689 + 2.78681i) q^{11} +(-3.76893 + 2.17600i) q^{13} +(1.66932 + 0.143276i) q^{15} +(1.97267 - 3.41677i) q^{17} +(-3.86796 + 2.23317i) q^{19} +(-0.802507 + 4.51176i) q^{21} +(-2.29786 - 1.32667i) q^{23} +(2.03214 + 3.51977i) q^{25} +(-5.02568 - 1.32004i) q^{27} +(4.61157 + 2.66249i) q^{29} +6.16655i q^{31} +(-7.91702 - 5.52415i) q^{33} +(2.32290 - 1.07431i) q^{35} +(0.243608 + 0.421942i) q^{37} +(-6.18177 - 4.31337i) q^{39} +(0.0818856 + 0.141830i) q^{41} +(4.35045 - 7.53520i) q^{43} +(1.00151 + 2.72368i) q^{45} +9.49001 q^{47} +(2.35274 + 6.59277i) q^{49} +(6.80851 + 0.584367i) q^{51} +(-1.74520 - 1.00759i) q^{53} +5.39149i q^{55} +(-6.34420 - 4.42670i) q^{57} -1.67386 q^{59} +5.17221i q^{61} +(-7.66649 + 2.05547i) q^{63} +4.20979i q^{65} +5.44252 q^{67} +(0.393002 - 4.57889i) q^{69} +3.64006i q^{71} +(-2.15468 - 1.24401i) q^{73} +(-4.02821 + 5.77310i) q^{75} +(-14.6862 - 1.33140i) q^{77} -4.60242 q^{79} +(-1.62120 - 8.85278i) q^{81} +(4.20979 - 7.29158i) q^{83} +(-1.90821 - 3.30512i) q^{85} +(-0.788713 + 9.18936i) q^{87} +(-2.05811 - 3.56475i) q^{89} +(-11.4673 - 1.03959i) q^{91} +(-9.67262 + 4.52983i) q^{93} +4.32040i q^{95} +(10.2669 + 5.92762i) q^{97} +(2.84928 - 16.4763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49}+ \cdots - 18 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Character values

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

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

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
$3$	0.734581	+	1.56856i	0.424111	+	0.905610i
$3$	0.734581	+	1.56856i	0.424111	+	0.905610i
$4$		0			0
$5$	0.483662	−	0.837727i	0.216300	−	0.374643i	−0.737374	−	0.675485i	$-0.763934\pi$
$5$	0.483662	−	0.837727i	0.216300	−	0.374643i	0.953674	+	0.300842i	$0.0972677\pi$
$6$		0			0
$7$	2.16249	+	1.52435i	0.817345	+	0.576149i
$7$	2.16249	+	1.52435i	0.817345	+	0.576149i
$8$		0			0
$9$	−1.92078	+	2.30447i	−0.640260	+	0.768158i
$10$		0			0
$11$	−4.82689	+	2.78681i	−1.45536	+	0.840254i	−0.998778	−	0.0494264i	$-0.984261\pi$
$11$	−4.82689	+	2.78681i	−1.45536	+	0.840254i	−0.456584	+	0.889680i	$0.650927\pi$
$12$		0			0
$13$	−3.76893	+	2.17600i	−1.04531	+	0.603512i	−0.921334	−	0.388772i	$-0.872899\pi$
$13$	−3.76893	+	2.17600i	−1.04531	+	0.603512i	−0.123980	+	0.992285i	$0.539566\pi$
$14$		0			0
$15$	1.66932	+	0.143276i	0.431016	+	0.0369937i
$16$		0			0
$17$	1.97267	−	3.41677i	0.478443	−	0.828688i	−0.521251	−	0.853403i	$-0.674535\pi$
$17$	1.97267	−	3.41677i	0.478443	−	0.828688i	0.999695	+	0.0247150i	$0.00786784\pi$
$18$		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
$21$	−0.802507	+	4.51176i	−0.175121	+	0.984547i
$22$		0			0
$23$	−2.29786	−	1.32667i	−0.479137	−	0.276630i	0.240920	−	0.970545i	$-0.422551\pi$
$23$	−2.29786	−	1.32667i	−0.479137	−	0.276630i	−0.720057	+	0.693915i	$0.755884\pi$
$24$		0			0
$25$	2.03214	+	3.51977i	0.406428	+	0.703955i
$26$		0			0
$27$	−5.02568	−	1.32004i	−0.967193	−	0.254042i
$28$		0			0
$29$	4.61157	+	2.66249i	0.856347	+	0.494412i	0.862787	−	0.505567i	$-0.168717\pi$
$29$	4.61157	+	2.66249i	0.856347	+	0.494412i	−0.00644015	+	0.999979i	$0.502050\pi$
$30$		0			0
$31$			6.16655i			1.10754i	0.832668	+	0.553772i	$0.186812\pi$
$31$			6.16655i			1.10754i	−0.832668	+	0.553772i	$0.813188\pi$
$32$		0			0
$33$	−7.91702	−	5.52415i	−1.37818	−	0.961631i
$34$		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
$39$	−6.18177	−	4.31337i	−0.989876	−	0.690691i
$40$		0			0
$41$	0.0818856	+	0.141830i	0.0127884	+	0.0221501i	0.872349	−	0.488884i	$-0.162596\pi$
$41$	0.0818856	+	0.141830i	0.0127884	+	0.0221501i	−0.859560	+	0.511034i	$0.829263\pi$
$42$		0			0
$43$	4.35045	−	7.53520i	0.663437	−	1.14911i	−0.316270	−	0.948669i	$-0.602430\pi$
$43$	4.35045	−	7.53520i	0.663437	−	1.14911i	0.979707	−	0.200437i	$-0.0642362\pi$
$44$		0			0
$45$	1.00151	+	2.72368i	0.149297	+	0.406022i
$46$		0			0
$47$	9.49001			1.38426			0.692130	−	0.721773i	$-0.256672\pi$
$47$	9.49001			1.38426			0.692130	+	0.721773i	$0.256672\pi$
$48$		0			0
$49$	2.35274	+	6.59277i	0.336106	+	0.941824i
$50$		0			0
$51$	6.80851	+	0.584367i	0.953382	+	0.0818278i
$52$		0			0
$53$	−1.74520	−	1.00759i	−0.239722	−	0.138403i	0.375327	−	0.926892i	$-0.377530\pi$
$53$	−1.74520	−	1.00759i	−0.239722	−	0.138403i	−0.615049	+	0.788489i	$0.710864\pi$
$54$		0			0
$55$			5.39149i			0.726988i
$56$		0			0
$57$	−6.34420	−	4.42670i	−0.840310	−	0.586331i
$58$		0			0
$59$	−1.67386			−0.217918			−0.108959	−	0.994046i	$-0.534752\pi$
$59$	−1.67386			−0.217918			−0.108959	+	0.994046i	$0.534752\pi$
$60$		0			0
$61$			5.17221i			0.662234i	0.943590	+	0.331117i	$0.107426\pi$
$61$			5.17221i			0.662234i	−0.943590	+	0.331117i	$0.892574\pi$
$62$		0			0
$63$	−7.66649	+	2.05547i	−0.965887	+	0.258965i
$64$		0			0
$65$			4.20979i			0.522160i
$66$		0			0
$67$	5.44252			0.664909			0.332455	−	0.943119i	$-0.392123\pi$
$67$	5.44252			0.664909			0.332455	+	0.943119i	$0.392123\pi$
$68$		0			0
$69$	0.393002	−	4.57889i	0.0473118	−	0.551234i
$70$		0			0
$71$			3.64006i			0.431996i	0.976394	+	0.215998i	$0.0693005\pi$
$71$			3.64006i			0.431996i	−0.976394	+	0.215998i	$0.930700\pi$
$72$		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
$75$	−4.02821	+	5.77310i	−0.465138	+	0.666620i
$76$		0			0
$77$	−14.6862	−	1.33140i	−1.67364	−	0.151728i
$78$		0			0
$79$	−4.60242			−0.517812			−0.258906	−	0.965902i	$-0.583362\pi$
$79$	−4.60242			−0.517812			−0.258906	+	0.965902i	$0.583362\pi$
$80$		0			0
$81$	−1.62120	−	8.85278i	−0.180133	−	0.983642i
$82$		0			0
$83$	4.20979	−	7.29158i	0.462085	−	0.800355i	−0.536980	−	0.843595i	$-0.680435\pi$
$83$	4.20979	−	7.29158i	0.462085	−	0.800355i	0.999065	+	0.0432405i	$0.0137682\pi$
$84$		0			0
$85$	−1.90821	−	3.30512i	−0.206975	−	0.358491i
$86$		0			0
$87$	−0.788713	+	9.18936i	−0.0845589	+	0.985202i
$88$		0			0
$89$	−2.05811	−	3.56475i	−0.218159	−	0.377863i	0.736086	−	0.676888i	$-0.236672\pi$
$89$	−2.05811	−	3.56475i	−0.218159	−	0.377863i	−0.954245	+	0.299025i	$0.903338\pi$
$90$		0			0
$91$	−11.4673	−	1.03959i	−1.20210	−	0.108978i
$92$		0			0
$93$	−9.67262	+	4.52983i	−1.00300	+	0.469721i
$94$		0			0
$95$			4.32040i			0.443263i
$96$		0			0
$97$	10.2669	+	5.92762i	1.04245	+	0.601859i	0.920526	−	0.390681i	$-0.127760\pi$
$97$	10.2669	+	5.92762i	1.04245	+	0.601859i	0.121924	+	0.992539i	$0.461094\pi$
$98$		0			0
$99$	2.84928	−	16.4763i	0.286363	−	1.65593i
$100$		0			0
$101$	2.65813	+	4.60402i	0.264494	+	0.458117i	0.967431	−	0.253135i	$-0.0814618\pi$
$101$	2.65813	+	4.60402i	0.264494	+	0.458117i	−0.702937	+	0.711252i	$0.748128\pi$
$102$		0			0
$103$	−7.74616	−	4.47225i	−0.763252	−	0.440664i	0.0672102	−	0.997739i	$-0.478590\pi$
$103$	−7.74616	−	4.47225i	−0.763252	−	0.440664i	−0.830462	+	0.557075i	$0.811924\pi$
$104$		0			0
$105$	3.39148	+	2.85445i	0.330975	+	0.278566i
$106$		0			0
$107$	−16.5898	+	9.57813i	−1.60380	+	0.925953i	−0.613079	+	0.790022i	$0.710069\pi$
$107$	−16.5898	+	9.57813i	−1.60380	+	0.925953i	−0.990718	+	0.135931i	$0.956597\pi$
$108$		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	−0.114953	−	0.993371i	$-0.536672\pi$
$113$	7.31199	−	4.22158i	0.687854	−	0.397133i	0.802808	+	0.596238i	$0.203339\pi$
$114$		0			0
$115$	−2.22278	+	1.28332i	−0.207275	+	0.119670i
$116$		0			0
$117$	2.22477	−	12.8650i	0.205680	−	1.18937i
$118$		0			0
$119$	9.47423	−	4.38170i	0.868501	−	0.401670i
$120$		0			0
$121$	10.0326	−	17.3769i	0.912053	−	1.57972i
$122$		0			0
$123$	−0.162318	+	0.232628i	−0.0146357	+	0.0209754i
$124$		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
$129$	15.0152	+	1.28874i	1.32201	+	0.113467i
$130$		0			0
$131$	9.37335	−	16.2351i	0.818954	−	1.41847i	−0.0875000	−	0.996165i	$-0.527888\pi$
$131$	9.37335	−	16.2351i	0.818954	−	1.41847i	0.906454	−	0.422305i	$-0.138779\pi$
$132$		0			0
$133$	−11.7686	−	1.06690i	−1.02046	−	0.0925121i
$134$		0			0
$135$	−3.53657	+	3.57170i	−0.304379	+	0.307403i
$136$		0			0
$137$	14.6656	−	8.46717i	1.25296	−	0.723399i	0.281267	−	0.959630i	$-0.409245\pi$
$137$	14.6656	−	8.46717i	1.25296	−	0.723399i	0.971697	+	0.236230i	$0.0759120\pi$
$138$		0			0
$139$	10.5033	−	6.06406i	0.890875	−	0.514347i	0.0166466	−	0.999861i	$-0.494701\pi$
$139$	10.5033	−	6.06406i	0.890875	−	0.514347i	0.874229	+	0.485514i	$0.161368\pi$
$140$		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
$147$	−8.61290	+	8.53335i	−0.710380	+	0.703819i
$148$		0			0
$149$	−7.56951	−	4.37026i	−0.620118	−	0.358025i	0.156797	−	0.987631i	$-0.449883\pi$
$149$	−7.56951	−	4.37026i	−0.620118	−	0.358025i	−0.776915	+	0.629606i	$0.783217\pi$
$150$		0			0
$151$	11.0471	+	19.1341i	0.898997	+	1.55711i	0.828778	+	0.559578i	$0.189037\pi$
$151$	11.0471	+	19.1341i	0.898997	+	1.55711i	0.0702195	+	0.997532i	$0.477630\pi$
$152$		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
$157$			1.42457i			0.113693i	0.998383	+	0.0568467i	$0.0181046\pi$
$157$			1.42457i			0.113693i	−0.998383	+	0.0568467i	$0.981895\pi$
$158$		0			0
$159$	0.298480	−	3.47761i	0.0236710	−	0.275793i
$160$		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
$165$	−8.45689	+	3.96049i	−0.658368	+	0.308323i
$166$		0			0
$167$	3.24855	+	5.62665i	0.251380	+	0.435404i	0.963906	−	0.266242i	$-0.0857822\pi$
$167$	3.24855	+	5.62665i	0.251380	+	0.435404i	−0.712526	+	0.701646i	$0.752449\pi$
$168$		0			0
$169$	2.96991	−	5.14404i	0.228455	−	0.395695i
$170$		0			0
$171$	2.28323	−	13.2030i	0.174603	−	1.00966i
$172$		0			0
$173$	11.8188			0.898564			0.449282	−	0.893390i	$-0.351680\pi$
$173$	11.8188			0.898564			0.449282	+	0.893390i	$0.351680\pi$
$174$		0			0
$175$	−0.970861	+	10.7092i	−0.0733902	+	0.809537i
$176$		0			0
$177$	−1.22959	−	2.62556i	−0.0924215	−	0.197349i
$178$		0			0
$179$	2.10764	+	1.21685i	0.157533	+	0.0909515i	0.576694	−	0.816960i	$-0.304343\pi$
$179$	2.10764	+	1.21685i	0.157533	+	0.0909515i	−0.419161	+	0.907912i	$0.637676\pi$
$180$		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
$185$	0.471297			0.0346504
$186$		0			0
$187$			21.9898i			1.60806i
$188$		0			0
$189$	−8.85579	−	10.5155i	−0.644164	−	0.764887i
$190$		0			0
$191$		−	22.0689i		−	1.59685i	−0.602094	−	0.798425i	$-0.705667\pi$
$191$		−	22.0689i		−	1.59685i	0.602094	−	0.798425i	$-0.294333\pi$
$192$		0			0
$193$	−19.9396			−1.43528			−0.717641	−	0.696413i	$-0.754778\pi$
$193$	−19.9396			−1.43528			−0.717641	+	0.696413i	$0.754778\pi$
$194$		0			0
$195$	−6.60331	+	3.09243i	−0.472873	+	0.221453i
$196$		0			0
$197$			4.62560i			0.329560i	0.986330	+	0.164780i	$0.0526914\pi$
$197$			4.62560i			0.329560i	−0.986330	+	0.164780i	$0.947309\pi$
$198$		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
$201$	3.99797	+	8.53693i	0.281995	+	0.602149i
$202$		0			0
$203$	5.91393	+	12.7872i	0.415076	+	0.897489i
$204$		0			0
$205$	0.158420			0.0110645
$206$		0			0
$207$	7.47097	−	2.74712i	0.519268	−	0.190938i
$208$		0			0
$209$	12.4468	−	21.5585i	0.860965	−	1.49123i
$210$		0			0
$211$	3.34310	+	5.79042i	0.230148	+	0.398629i	0.957852	−	0.287263i	$-0.0927455\pi$
$211$	3.34310	+	5.79042i	0.230148	+	0.398629i	−0.727703	+	0.685892i	$0.759412\pi$
$212$		0			0
$213$	−5.70967	+	2.67392i	−0.391220	+	0.183214i
$214$		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
$219$	0.368514	−	4.29358i	0.0249018	−	0.290133i
$220$		0			0
$221$			17.1701i			1.15499i
$222$		0			0
$223$	−7.08622	−	4.09123i	−0.474528	−	0.273969i	0.243605	−	0.969875i	$-0.421670\pi$
$223$	−7.08622	−	4.09123i	−0.474528	−	0.273969i	−0.718133	+	0.695905i	$0.755003\pi$
$224$		0			0
$225$	−12.0145	−	2.07770i	−0.800968	−	0.138513i
$226$		0			0
$227$	5.34688	+	9.26106i	0.354885	+	0.614678i	0.987098	−	0.160116i	$-0.0511868\pi$
$227$	5.34688	+	9.26106i	0.354885	+	0.614678i	−0.632214	+	0.774794i	$0.717853\pi$
$228$		0			0
$229$	25.2942	+	14.6036i	1.67149	+	0.965034i	0.966806	+	0.255510i	$0.0822435\pi$
$229$	25.2942	+	14.6036i	1.67149	+	0.965034i	0.704682	+	0.709524i	$0.251090\pi$
$230$		0			0
$231$	−8.69979	−	24.0142i	−0.572404	−	1.58002i
$232$		0			0
$233$	5.57664	−	3.21967i	0.365338	−	0.210928i	−0.306082	−	0.952005i	$-0.599018\pi$
$233$	5.57664	−	3.21967i	0.365338	−	0.210928i	0.671420	+	0.741077i	$0.265685\pi$
$234$		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	−0.364510	−	0.931200i	$-0.618763\pi$
$239$	4.01452	−	2.31778i	0.259678	−	0.149925i	0.624187	+	0.781275i	$0.285430\pi$
$240$		0			0
$241$	9.08846	−	5.24722i	0.585439	−	0.338003i	−0.177853	−	0.984057i	$-0.556915\pi$
$241$	9.08846	−	5.24722i	0.585439	−	0.338003i	0.763292	+	0.646054i	$0.223582\pi$
$242$		0			0
$243$	12.6952	−	9.04604i	0.814400	−	0.580304i
$244$		0			0
$245$	6.66087	+	1.21772i	0.425548	+	0.0777971i
$246$		0			0
$247$	9.71873	−	16.8333i	0.618388	−	1.07108i
$248$		0			0
$249$	14.5297	+	1.24707i	0.920785	+	0.0790300i
$250$		0			0
$251$	−7.85271			−0.495659			−0.247829	−	0.968804i	$-0.579717\pi$
$251$	−7.85271			−0.495659			−0.247829	+	0.968804i	$0.579717\pi$
$252$		0			0
$253$	14.7887			0.929758
$254$		0			0
$255$	3.78256	−	5.42104i	0.236873	−	0.339478i
$256$		0			0
$257$	−1.71568	+	2.97164i	−0.107021	+	0.185366i	−0.914562	−	0.404445i	$-0.867465\pi$
$257$	−1.71568	+	2.97164i	−0.107021	+	0.185366i	0.807541	+	0.589811i	$0.200798\pi$
$258$		0			0
$259$	−0.116385	+	1.28379i	−0.00723178	+	0.0797708i
$260$		0			0
$261$	−14.9935	+	5.51318i	−0.928072	+	0.341257i
$262$		0			0
$263$	3.17080	−	1.83066i	0.195520	−	0.112883i	−0.399044	−	0.916932i	$-0.630658\pi$
$263$	3.17080	−	1.83066i	0.195520	−	0.112883i	0.594564	+	0.804048i	$0.297325\pi$
$264$		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	−0.992009	−	0.126166i	$-0.959733\pi$
$269$	−6.34303	+	10.9865i	−0.386741	+	0.669856i	0.605268	+	0.796022i	$0.293066\pi$
$270$		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
$273$	−6.79297	−	18.7508i	−0.411129	−	1.13485i
$274$		0			0
$275$	−19.6179	−	11.3264i	−1.18300	−	0.683006i
$276$		0			0
$277$	3.73302	+	6.46579i	0.224296	+	0.388491i	0.956108	−	0.293015i	$-0.0946585\pi$
$277$	3.73302	+	6.46579i	0.224296	+	0.388491i	−0.731812	+	0.681506i	$0.761325\pi$
$278$		0			0
$279$	−14.2106	−	11.8446i	−0.850769	−	0.709117i
$280$		0			0
$281$	−19.2746	−	11.1282i	−1.14983	−	0.663854i	−0.200983	−	0.979595i	$-0.564414\pi$
$281$	−19.2746	−	11.1282i	−1.14983	−	0.663854i	−0.948845	+	0.315741i	$0.897747\pi$
$282$		0			0
$283$		−	16.1802i		−	0.961815i	−0.876771	−	0.480908i	$-0.840307\pi$
$283$		−	16.1802i		−	0.961815i	0.876771	−	0.480908i	$-0.159693\pi$
$284$		0			0
$285$	−6.77681	+	3.17368i	−0.401424	+	0.187993i
$286$		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
$291$	−1.75595	+	20.4587i	−0.102935	+	1.19931i
$292$		0			0
$293$	−4.43406	−	7.68002i	−0.259041	−	0.448672i	0.706944	−	0.707269i	$-0.250073\pi$
$293$	−4.43406	−	7.68002i	−0.259041	−	0.448672i	−0.965985	+	0.258597i	$0.916740\pi$
$294$		0			0
$295$	−0.809584	+	1.40224i	−0.0471358	+	0.0816416i
$296$		0			0
$297$	27.9371	−	7.63390i	1.62108	−	0.442964i
$298$		0			0
$299$	11.5473			0.667799
$300$		0			0
$301$	20.8940	−	9.66321i	1.20431	−	0.556978i
$302$		0			0
$303$	−5.26908	+	7.55147i	−0.302701	+	0.433821i
$304$		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
$311$	−16.8955			−0.958055			−0.479028	−	0.877800i	$-0.659011\pi$
$311$	−16.8955			−0.958055			−0.479028	+	0.877800i	$0.659011\pi$
$312$		0			0
$313$		−	4.27739i		−	0.241772i	−0.992666	−	0.120886i	$-0.961426\pi$
$313$		−	4.27739i		−	0.241772i	0.992666	−	0.120886i	$-0.0385736\pi$
$314$		0			0
$315$	−1.98606	+	7.41658i	−0.111902	+	0.417877i
$316$		0			0
$317$		−	6.62940i		−	0.372344i	−0.982517	−	0.186172i	$-0.940392\pi$
$317$		−	6.62940i		−	0.372344i	0.982517	−	0.186172i	$-0.0596082\pi$
$318$		0			0
$319$	−29.6794			−1.66173
$320$		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
$327$	−33.2084	−	2.85024i	−1.83643	−	0.157619i
$328$		0			0
$329$	20.5221	+	14.4661i	1.13142	+	0.797539i
$330$		0			0
$331$	0.757792			0.0416520			0.0208260	−	0.999783i	$-0.493370\pi$
$331$	0.757792			0.0416520			0.0208260	+	0.999783i	$0.493370\pi$
$332$		0			0
$333$	−1.44027	−	0.249069i	−0.0789265	−	0.0136489i
$334$		0			0
$335$	2.63234	−	4.55935i	0.143820	−	0.249104i
$336$		0			0
$337$	1.01088	+	1.75089i	0.0550660	+	0.0953772i	0.892244	−	0.451553i	$-0.149130\pi$
$337$	1.01088	+	1.75089i	0.0550660	+	0.0953772i	−0.837178	+	0.546930i	$0.815796\pi$
$338$		0			0
$339$	11.9931	+	8.36823i	0.651374	+	0.454500i
$340$		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
$345$	−3.64578	−	2.54386i	−0.196282	−	0.136957i
$346$		0			0
$347$			20.9661i			1.12552i	0.826620	+	0.562761i	$0.190261\pi$
$347$			20.9661i			1.12552i	−0.826620	+	0.562761i	$0.809739\pi$
$348$		0			0
$349$	−5.36406	−	3.09694i	−0.287132	−	0.165776i	0.349516	−	0.936930i	$-0.386346\pi$
$349$	−5.36406	−	3.09694i	−0.287132	−	0.165776i	−0.636648	+	0.771155i	$0.719679\pi$
$350$		0			0
$351$	21.8139	−	5.96071i	1.16434	−	0.318159i
$352$		0			0
$353$	9.41889	+	16.3140i	0.501317	+	0.868306i	0.999999	+	0.00152110i	$0.000484180\pi$
$353$	9.41889	+	16.3140i	0.501317	+	0.868306i	−0.498682	+	0.866785i	$0.666182\pi$
$354$		0			0
$355$	3.04938	+	1.76056i	0.161844	+	0.0934409i
$356$		0			0
$357$	13.8326	+	11.6422i	0.732097	+	0.616171i
$358$		0			0
$359$	24.0735	−	13.8988i	1.27055	−	0.733553i	0.295459	−	0.955355i	$-0.404527\pi$
$359$	24.0735	−	13.8988i	1.27055	−	0.733553i	0.975092	+	0.221803i	$0.0711942\pi$
$360$		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
$367$	18.8390	−	10.8767i	0.983388	−	0.567759i	0.0800968	−	0.996787i	$-0.474477\pi$
$367$	18.8390	−	10.8767i	0.983388	−	0.567759i	0.903291	+	0.429028i	$0.141144\pi$
$368$		0			0
$369$	−0.484128	−	0.0837212i	−0.0252027	−	0.00435835i
$370$		0			0
$371$	−2.23806	−	4.83920i	−0.116194	−	0.251239i
$372$		0			0
$373$	−5.86560	+	10.1595i	−0.303709	+	0.526040i	−0.976973	−	0.213362i	$-0.931558\pi$
$373$	−5.86560	+	10.1595i	−0.303709	+	0.526040i	0.673264	+	0.739402i	$0.264892\pi$
$374$		0			0
$375$	6.44088	+	13.7533i	0.332606	+	0.710218i
$376$		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
$381$	−2.43795	−	5.20579i	−0.124900	−	0.266701i
$382$		0			0
$383$	−5.92412	+	10.2609i	−0.302708	+	0.524306i	−0.976748	−	0.214389i	$-0.931224\pi$
$383$	−5.92412	+	10.2609i	−0.302708	+	0.524306i	0.674040	+	0.738695i	$0.264557\pi$
$384$		0			0
$385$	−8.21849	+	11.6591i	−0.418853	+	0.594200i
$386$		0			0
$387$	9.00841	+	24.4990i	0.457923	+	1.24535i
$388$		0			0
$389$	−5.50224	+	3.17672i	−0.278975	+	0.161066i	−0.632959	−	0.774185i	$-0.718160\pi$
$389$	−5.50224	+	3.17672i	−0.278975	+	0.161066i	0.353984	+	0.935251i	$0.384827\pi$
$390$		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
$399$	−6.97146	−	19.2435i	−0.349009	−	0.963378i
$400$		0			0
$401$	−20.0216	−	11.5595i	−0.999833	−	0.577254i	−0.0916343	−	0.995793i	$-0.529209\pi$
$401$	−20.0216	−	11.5595i	−0.999833	−	0.577254i	−0.908199	+	0.418539i	$0.862542\pi$
$402$		0			0
$403$	−13.4184	−	23.2413i	−0.668417	−	1.15773i
$404$		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
$409$		−	1.55989i		−	0.0771318i	−0.999256	−	0.0385659i	$-0.987721\pi$
$409$		−	1.55989i		−	0.0771318i	0.999256	−	0.0385659i	$-0.0122790\pi$
$410$		0			0
$411$	24.0543	+	16.7840i	1.18651	+	0.827896i
$412$		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
$417$	17.2274	+	12.0205i	0.843628	+	0.588646i
$418$		0			0
$419$	−3.40822	−	5.90321i	−0.166502	−	0.288391i	0.770685	−	0.637216i	$-0.219914\pi$
$419$	−3.40822	−	5.90321i	−0.166502	−	0.288391i	−0.937188	+	0.348825i	$0.886581\pi$
$420$		0			0
$421$	−6.75727	+	11.7039i	−0.329329	+	0.570415i	−0.982379	−	0.186900i	$-0.940156\pi$
$421$	−6.75727	+	11.7039i	−0.329329	+	0.570415i	0.653050	+	0.757315i	$0.273489\pi$
$422$		0			0
$423$	−18.2282	+	21.8695i	−0.886287	+	1.06333i
$424$		0			0
$425$	16.0350			0.777812
$426$		0			0
$427$	−7.88424	+	11.1849i	−0.381545	+	0.541274i
$428$		0			0
$429$	41.8593	+	3.59274i	2.02098	+	0.173459i
$430$		0			0
$431$	−12.2628	−	7.07990i	−0.590676	−	0.341027i	0.174689	−	0.984624i	$-0.444108\pi$
$431$	−12.2628	−	7.07990i	−0.590676	−	0.341027i	−0.765365	+	0.643597i	$0.777441\pi$
$432$		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
$437$	11.8507			0.566897
$438$		0			0
$439$			4.23080i			0.201925i	0.994890	+	0.100963i	$0.0321922\pi$
$439$			4.23080i			0.201925i	−0.994890	+	0.100963i	$0.967808\pi$
$440$		0			0
$441$	−19.7120	−	7.24144i	−0.938665	−	0.344830i
$442$		0			0
$443$			29.8098i			1.41631i	0.706058	+	0.708154i	$0.250472\pi$
$443$			29.8098i			1.41631i	−0.706058	+	0.708154i	$0.749528\pi$
$444$		0			0
$445$	−3.98172			−0.188751
$446$		0			0
$447$	1.29461	−	15.0836i	0.0612328	−	0.713428i
$448$		0			0
$449$		−	8.41716i		−	0.397230i	−0.980078	−	0.198615i	$-0.936356\pi$
$449$		−	8.41716i		−	0.397230i	0.980078	−	0.198615i	$-0.0636444\pi$
$450$		0			0
$451$	−0.790505	−	0.456399i	−0.0372234	−	0.0214910i
$452$		0			0
$453$	−21.8980	+	31.3836i	−1.02886	+	1.47453i
$454$		0			0
$455$	−6.41717	+	9.10363i	−0.300841	+	0.426785i
$456$		0			0
$457$	−3.88219			−0.181601			−0.0908006	−	0.995869i	$-0.528943\pi$
$457$	−3.88219			−0.181601			−0.0908006	+	0.995869i	$0.528943\pi$
$458$		0			0
$459$	−14.4243	+	14.5676i	−0.673269	+	0.679957i
$460$		0			0
$461$	−17.0423	+	29.5181i	−0.793739	+	1.37480i	0.129898	+	0.991527i	$0.458535\pi$
$461$	−17.0423	+	29.5181i	−0.793739	+	1.37480i	−0.923637	+	0.383269i	$0.874798\pi$
$462$		0			0
$463$	6.10962	+	10.5822i	0.283938	+	0.491796i	0.972351	−	0.233523i	$-0.0750256\pi$
$463$	6.10962	+	10.5822i	0.283938	+	0.491796i	−0.688413	+	0.725319i	$0.741692\pi$
$464$		0			0
$465$	−0.883517	+	10.2939i	−0.0409721	+	0.477369i
$466$		0			0
$467$	−15.4057	−	26.6835i	−0.712893	−	1.23477i	−0.963767	−	0.266747i	$-0.914051\pi$
$467$	−15.4057	−	26.6835i	−0.712893	−	1.23477i	0.250874	−	0.968020i	$-0.419282\pi$
$468$		0			0
$469$	11.7694	+	8.29628i	0.543460	+	0.383087i
$470$		0			0
$471$	−2.23453	+	1.04647i	−0.102962	+	0.0482186i
$472$		0			0
$473$			48.4954i			2.22982i
$474$		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
$479$	20.8747	+	36.1560i	0.953788	+	1.65201i	0.737118	+	0.675764i	$0.236186\pi$
$479$	20.8747	+	36.1560i	0.953788	+	1.65201i	0.216670	+	0.976245i	$0.430481\pi$
$480$		0			0
$481$	−1.83629	−	1.06018i	−0.0837276	−	0.0483401i
$482$		0			0
$483$	7.82967	−	9.30274i	0.356262	−	0.423289i
$484$		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	−0.998992	−	0.0448915i	$-0.985706\pi$
$491$	−32.3428	+	18.6731i	−1.45961	+	0.842707i	−0.460619	+	0.887598i	$0.652372\pi$
$492$		0			0
$493$	18.1942	−	10.5044i	0.819427	−	0.473097i
$494$		0			0
$495$	−12.4245	−	10.3559i	−0.558442	−	0.465462i
$496$		0			0
$497$	−5.54872	+	7.87161i	−0.248894	+	0.353090i
$498$		0			0
$499$	13.7099	−	23.7462i	0.613738	−	1.06303i	−0.376867	−	0.926267i	$-0.622999\pi$
$499$	13.7099	−	23.7462i	0.613738	−	1.06303i	0.990605	−	0.136758i	$-0.0436681\pi$
$500$		0			0
$501$	−6.43944	+	9.22879i	−0.287693	+	0.412312i
$502$		0			0
$503$	11.2791			0.502909			0.251454	−	0.967869i	$-0.419091\pi$
$503$	11.2791			0.502909			0.251454	+	0.967869i	$0.419091\pi$
$504$		0			0
$505$	5.14255			0.228840
$506$		0			0
$507$	10.2504	+	0.879780i	0.455236	+	0.0390724i
$508$		0			0
$509$	9.31667	−	16.1370i	0.412954	−	0.715258i	−0.582257	−	0.813005i	$-0.697830\pi$
$509$	9.31667	−	16.1370i	0.412954	−	0.715258i	0.995211	+	0.0977470i	$0.0311636\pi$
$510$		0			0
$511$	−2.76319	−	5.97463i	−0.122236	−	0.264302i
$512$		0			0
$513$	22.3870	−	6.11732i	0.988412	−	0.270086i
$514$		0			0
$515$	−7.49305	+	4.32611i	−0.330183	+	0.190631i
$516$		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	−0.983451	−	0.181172i	$-0.942011\pi$
$521$	−7.64255	+	13.2373i	−0.334826	+	0.579936i	0.648625	+	0.761108i	$0.275344\pi$
$522$		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
$525$	−17.5112	+	6.34390i	−0.764251	+	0.276870i
$526$		0			0
$527$	21.0697	+	12.1646i	0.917809	+	0.529897i
$528$		0			0
$529$	−7.97989	−	13.8216i	−0.346952	−	0.600938i
$530$		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
$535$			18.5303i			0.801135i
$536$		0			0
$537$	−0.360468	+	4.19984i	−0.0155554	+	0.181237i
$538$		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
$543$	18.0920	−	8.47277i	0.776404	−	0.363601i
$544$		0			0
$545$	9.30729	+	16.1207i	0.398680	+	0.690535i
$546$		0			0
$547$	9.29831	−	16.1051i	0.397567	−	0.688606i	−0.595858	−	0.803090i	$-0.703188\pi$
$547$	9.29831	−	16.1051i	0.397567	−	0.688606i	0.993425	+	0.114484i	$0.0365213\pi$
$548$		0			0
$549$	−11.9192	−	9.93469i	−0.508700	−	0.424002i
$550$		0			0
$551$	−23.7832			−1.01320
$552$		0			0
$553$	−9.95268	−	7.01567i	−0.423231	−	0.298337i
$554$		0			0
$555$	0.346206	+	0.739259i	0.0146956	+	0.0313798i
$556$		0			0
$557$	23.8694	+	13.7810i	1.01138	+	0.583920i	0.911595	−	0.411089i	$-0.134851\pi$
$557$	23.8694	+	13.7810i	1.01138	+	0.583920i	0.0997845	+	0.995009i	$0.468185\pi$
$558$		0			0
$559$			37.8662i			1.60157i
$560$		0			0
$561$	−34.4924	+	16.1533i	−1.45627	+	0.681993i
$562$		0			0
$563$	18.8515			0.794497			0.397249	−	0.917711i	$-0.369965\pi$
$563$	18.8515			0.794497			0.397249	+	0.917711i	$0.369965\pi$
$564$		0			0
$565$		−	8.16727i		−	0.343600i
$566$		0			0
$567$	9.98886	−	21.6153i	0.419493	−	0.907759i
$568$		0			0
$569$			4.46988i			0.187387i	0.995601	+	0.0936936i	$0.0298674\pi$
$569$			4.46988i			0.187387i	−0.995601	+	0.0936936i	$0.970133\pi$
$570$		0			0
$571$	−18.6249			−0.779428			−0.389714	−	0.920936i	$-0.627426\pi$
$571$	−18.6249			−0.779428			−0.389714	+	0.920936i	$0.627426\pi$
$572$		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
$579$	−14.6472	−	31.2765i	−0.608719	−	1.29981i
$580$		0			0
$581$	20.2185	−	9.35079i	0.838806	−	0.387936i
$582$		0			0
$583$	11.2319			0.465176
$584$		0			0
$585$	−9.70134	−	8.08608i	−0.401101	−	0.334318i
$586$		0			0
$587$	−13.2295	+	22.9141i	−0.546039	+	0.945766i	0.452502	+	0.891763i	$0.350531\pi$
$587$	−13.2295	+	22.9141i	−0.546039	+	0.945766i	−0.998541	+	0.0540032i	$0.982802\pi$
$588$		0			0
$589$	−13.7709	−	23.8520i	−0.567422	−	0.982803i
$590$		0			0
$591$	−7.25554	+	3.39788i	−0.298453	+	0.139770i
$592$		0			0
$593$	−17.3351	−	30.0254i	−0.711869	−	1.23299i	−0.964155	−	0.265341i	$-0.914516\pi$
$593$	−17.3351	−	30.0254i	−0.711869	−	1.23299i	0.252285	−	0.967653i	$-0.418818\pi$
$594$		0			0
$595$	0.911654	−	10.0561i	0.0373742	−	0.412259i
$596$		0			0
$597$	−3.09604	+	36.0722i	−0.126712	+	1.47634i
$598$		0			0
$599$			24.4887i			1.00058i	0.865857	+	0.500291i	$0.166774\pi$
$599$			24.4887i			1.00058i	−0.865857	+	0.500291i	$0.833226\pi$
$600$		0			0
$601$	−19.3812	−	11.1898i	−0.790577	−	0.456440i	0.0495885	−	0.998770i	$-0.484209\pi$
$601$	−19.3812	−	11.1898i	−0.790577	−	0.456440i	−0.840166	+	0.542330i	$0.817542\pi$
$602$		0			0
$603$	−10.4539	+	12.5421i	−0.425715	+	0.510755i
$604$		0			0
$605$	−9.70476	−	16.8091i	−0.394554	−	0.683388i
$606$		0			0
$607$	28.2180	+	16.2917i	1.14533	+	0.661259i	0.947746	−	0.319026i	$-0.103356\pi$
$607$	28.2180	+	16.2917i	1.14533	+	0.661259i	0.197589	+	0.980285i	$0.436689\pi$
$608$		0			0
$609$	−15.7133	+	18.6696i	−0.636737	+	0.756532i
$610$		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	−0.538687	+	0.842506i	$0.681080\pi$
$617$	−38.1947	+	22.0517i	−1.53766	+	0.887770i	−0.998975	+	0.0452639i	$0.985587\pi$
$618$		0			0
$619$	4.28374	−	2.47322i	0.172178	−	0.0994070i	−0.411434	−	0.911439i	$-0.634972\pi$
$619$	4.28374	−	2.47322i	0.172178	−	0.0994070i	0.583612	+	0.812032i	$0.301639\pi$
$620$		0			0
$621$	9.79706	+	9.70071i	0.393143	+	0.389276i
$622$		0			0
$623$	0.983266	−	10.8460i	0.0393937	−	0.434536i
$624$		0			0
$625$	−5.91991	+	10.2536i	−0.236797	+	0.410144i
$626$		0			0
$627$	42.9591	+	3.68714i	1.71562	+	0.147250i
$628$		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
$633$	−6.62686	+	9.49739i	−0.263394	+	0.377487i
$634$		0			0
$635$	−1.60519	+	2.78027i	−0.0637001	+	0.110332i
$636$		0			0
$637$	−23.2132	−	19.7282i	−0.919739	−	0.781658i
$638$		0			0
$639$	−8.38843	−	6.99177i	−0.331841	−	0.276590i
$640$		0			0
$641$	−12.1954	+	7.04105i	−0.481691	+	0.278105i	−0.721121	−	0.692809i	$-0.756373\pi$
$641$	−12.1954	+	7.04105i	−0.481691	+	0.278105i	0.239430	+	0.970914i	$0.423040\pi$
$642$		0			0
$643$	−7.33157	+	4.23288i	−0.289129	+	0.166929i	−0.637549	−	0.770410i	$-0.720052\pi$
$643$	−7.33157	+	4.23288i	−0.289129	+	0.166929i	0.348420	+	0.937339i	$0.386718\pi$
$644$		0			0
$645$	8.34189	−	11.9553i	0.328461	−	0.470740i
$646$		0			0
$647$	12.1662	−	21.0725i	0.478304	−	0.828446i	−0.521387	−	0.853320i	$-0.674585\pi$
$647$	12.1662	−	21.0725i	0.478304	−	0.828446i	0.999691	+	0.0248742i	$0.00791854\pi$
$648$		0			0
$649$	8.07955	−	4.66473i	0.317150	−	0.183107i
$650$		0			0
$651$	−27.8220	−	4.94869i	−1.09043	−	0.193955i
$652$		0			0
$653$	−36.0653	−	20.8223i	−1.41134	−	0.814840i	−0.415829	−	0.909443i	$-0.636509\pi$
$653$	−36.0653	−	20.8223i	−1.41134	−	0.814840i	−0.995515	+	0.0946029i	$0.969842\pi$
$654$		0			0
$655$	−9.06707	−	15.7046i	−0.354280	−	0.613631i
$656$		0			0
$657$	7.00545	−	2.57594i	0.273309	−	0.100497i
$658$		0			0
$659$	9.09866	+	5.25312i	0.354434	+	0.204632i	0.666636	−	0.745383i	$-0.267733\pi$
$659$	9.09866	+	5.25312i	0.354434	+	0.204632i	−0.312203	+	0.950016i	$0.601067\pi$
$660$		0			0
$661$		−	19.5131i		−	0.758972i	−0.925198	−	0.379486i	$-0.876101\pi$
$661$		−	19.5131i		−	0.758972i	0.925198	−	0.379486i	$-0.123899\pi$
$662$		0			0
$663$	−26.9324	+	12.6128i	−1.04597	+	0.489842i
$664$		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
$669$	1.21195	−	14.1205i	0.0468567	−	0.545931i
$670$		0			0
$671$	−14.4140	−	24.9657i	−0.556445	−	0.963790i
$672$		0			0
$673$	−3.10277	+	5.37415i	−0.119603	+	0.207158i	−0.919610	−	0.392832i	$-0.871495\pi$
$673$	−3.10277	+	5.37415i	−0.119603	+	0.207158i	0.800007	+	0.599990i	$0.204829\pi$
$674$		0			0
$675$	−5.56665	−	20.3718i	−0.214260	−	0.784110i
$676$		0			0
$677$	24.7531			0.951339			0.475669	−	0.879624i	$-0.342206\pi$
$677$	24.7531			0.951339			0.475669	+	0.879624i	$0.342206\pi$
$678$		0			0
$679$	13.1664	+	28.4688i	0.505281	+	1.09253i
$680$		0			0
$681$	−10.5988	+	15.1899i	−0.406149	+	0.582079i
$682$		0			0
$683$	18.3119	+	10.5724i	0.700687	+	0.404542i	0.807603	−	0.589726i	$-0.200764\pi$
$683$	18.3119	+	10.5724i	0.700687	+	0.404542i	−0.106916	+	0.994268i	$0.534098\pi$
$684$		0			0
$685$		−	16.3810i		−	0.625886i
$686$		0			0
$687$	−4.32605	+	50.4031i	−0.165049	+	1.92300i
$688$		0			0
$689$	8.77006			0.334113
$690$		0			0
$691$			6.44470i			0.245168i	0.992458	+	0.122584i	$0.0391181\pi$
$691$			6.44470i			0.245168i	−0.992458	+	0.122584i	$0.960882\pi$
$692$		0			0
$693$	31.2771	−	31.2866i	1.18812	−	1.18848i
$694$		0			0
$695$		−	11.7318i		−	0.445014i
$696$		0			0
$697$	0.646134			0.0244741
$698$		0			0
$699$	9.14675	+	6.38220i	0.345962	+	0.241397i
$700$		0			0
$701$			24.5717i			0.928061i	0.885819	+	0.464031i	$0.153597\pi$
$701$			24.5717i			0.928061i	−0.885819	+	0.464031i	$0.846403\pi$
$702$		0			0
$703$	−1.88454	−	1.08804i	−0.0710767	−	0.0410361i
$704$		0			0
$705$	15.8418	+	1.35969i	0.596638	+	0.0512088i
$706$		0			0
$707$	−1.26993	+	14.0081i	−0.0477606	+	0.526827i
$708$		0			0
$709$	44.2740			1.66275			0.831373	−	0.555715i	$-0.187555\pi$
$709$	44.2740			1.66275			0.831373	+	0.555715i	$0.187555\pi$
$710$		0			0
$711$	8.84023	−	10.6061i	0.331535	−	0.397762i
$712$		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
$717$	6.58458	+	4.59442i	0.245906	+	0.171582i
$718$		0			0
$719$	−2.22433	−	3.85266i	−0.0829537	−	0.143680i	0.821564	−	0.570117i	$-0.193102\pi$
$719$	−2.22433	−	3.85266i	−0.0829537	−	0.143680i	−0.904517	+	0.426437i	$0.859769\pi$
$720$		0			0
$721$	−9.93376	−	21.4790i	−0.369952	−	0.799921i
$722$		0			0
$723$	14.9068	+	10.4013i	0.554390	+	0.386829i
$724$		0			0
$725$			21.6422i			0.803773i
$726$		0			0
$727$	−30.4270	−	17.5670i	−1.12848	−	0.651525i	−0.184924	−	0.982753i	$-0.559204\pi$
$727$	−30.4270	−	17.5670i	−1.12848	−	0.651525i	−0.943551	+	0.331227i	$0.892537\pi$
$728$		0			0
$729$	23.5150	+	13.2682i	0.870925	+	0.491416i
$730$		0			0
$731$	−17.1640	−	29.7289i	−0.634834	−	1.09956i
$732$		0			0
$733$	−5.03789	−	2.90863i	−0.186079	−	0.107433i	0.404067	−	0.914729i	$-0.367596\pi$
$733$	−5.03789	−	2.90863i	−0.186079	−	0.107433i	−0.590145	+	0.807297i	$0.700930\pi$
$734$		0			0
$735$	2.98289	+	11.3425i	0.110025	+	0.418375i
$736$		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	−0.490003	−	0.871721i	$-0.663004\pi$
$743$	0.543196	−	0.313615i	0.0199279	−	0.0115054i	0.509931	+	0.860215i	$0.329671\pi$
$744$		0			0
$745$	−7.32216	+	4.22745i	−0.268263	+	0.154882i
$746$		0			0
$747$	8.71716	+	23.7069i	0.318944	+	0.867390i
$748$		0			0
$749$	−50.4757	−	4.57598i	−1.84434	−	0.167202i
$750$		0			0
$751$	2.23529	−	3.87163i	0.0815668	−	0.141278i	−0.822356	−	0.568973i	$-0.807341\pi$
$751$	2.23529	−	3.87163i	0.0815668	−	0.141278i	0.903923	+	0.427695i	$0.140674\pi$
$752$		0			0
$753$	−5.76845	−	12.3175i	−0.210214	−	0.448874i
$754$		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
$759$	10.8635	+	23.1970i	0.394320	+	0.841998i
$760$		0			0
$761$	−10.4970	+	18.1813i	−0.380516	+	0.659073i	−0.991136	−	0.132851i	$-0.957587\pi$
$761$	−10.4970	+	18.1813i	−0.380516	+	0.659073i	0.610620	+	0.791924i	$0.290920\pi$
$762$		0			0
$763$	−46.2104	+	21.3717i	−1.67293	+	0.773707i
$764$		0			0
$765$	11.2818	+	1.95099i	0.407895	+	0.0705382i
$766$		0			0
$767$	6.30868	−	3.64232i	0.227793	−	0.131516i
$768$		0			0
$769$	34.1729	−	19.7298i	1.23231	−	0.711473i	0.264797	−	0.964304i	$-0.414695\pi$
$769$	34.1729	−	19.7298i	1.23231	−	0.711473i	0.967511	+	0.252831i	$0.0813616\pi$
$770$		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	$-0.619317\pi$
$773$	17.3164	−	29.9929i	0.622829	−	1.07877i	0.988956	−	0.148206i	$-0.0473499\pi$
$774$		0			0
$775$	−21.7048	+	12.5313i	−0.779661	+	0.450137i
$776$		0			0
$777$	−2.09920	+	0.760492i	−0.0753084	+	0.0272825i
$778$		0			0
$779$	−0.633461	−	0.365729i	−0.0226961	−	0.0131036i
$780$		0			0
$781$	−10.1442	−	17.5702i	−0.362986	−	0.628711i
$782$		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
$787$		−	35.3099i		−	1.25866i	−0.777137	−	0.629332i	$-0.783329\pi$
$787$		−	35.3099i		−	1.25866i	0.777137	−	0.629332i	$-0.216671\pi$
$788$		0			0
$789$	5.20072	+	3.62883i	0.185151	+	0.129190i
$790$		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
$795$	−2.76893	−	1.93203i	−0.0982038	−	0.0685222i
$796$		0			0
$797$	9.60992	+	16.6449i	0.340401	+	0.589591i	0.984507	−	0.175344i	$-0.0561039\pi$
$797$	9.60992	+	16.6449i	0.340401	+	0.589591i	−0.644106	+	0.764936i	$0.722771\pi$
$798$		0			0
$799$	18.7207	−	32.4252i	0.662290	−	1.14712i
$800$		0			0
$801$	12.1680	+	2.10424i	0.429937	+	0.0743498i
$802$		0			0
$803$	13.8672			0.489363
$804$		0			0
$805$	−6.76296	−	0.613110i	−0.238363	−	0.0216093i
$806$		0			0
$807$	−21.8924	−	1.87900i	−0.770649	−	0.0661441i
$808$		0			0
$809$	−34.0157	−	19.6390i	−1.19593	−	0.690469i	−0.236283	−	0.971684i	$-0.575929\pi$
$809$	−34.0157	−	19.6390i	−1.19593	−	0.690469i	−0.959645	+	0.281215i	$0.909263\pi$
$810$		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
$815$	7.19975			0.252196
$816$		0			0
$817$			38.8611i			1.35958i
$818$		0			0
$819$	24.4218	−	24.4292i	0.853366	−	0.853625i
$820$		0			0
$821$			12.6924i			0.442968i	0.975164	+	0.221484i	$0.0710900\pi$
$821$			12.6924i			0.442968i	−0.975164	+	0.221484i	$0.928910\pi$
$822$		0			0
$823$	−17.4767			−0.609201			−0.304600	−	0.952480i	$-0.598523\pi$
$823$	−17.4767			−0.609201			−0.304600	+	0.952480i	$0.598523\pi$
$824$		0			0
$825$	3.35523	−	39.0920i	0.116814	−	1.36101i
$826$		0			0
$827$		−	46.9482i		−	1.63255i	−0.577665	−	0.816274i	$-0.696036\pi$
$827$		−	46.9482i		−	1.63255i	0.577665	−	0.816274i	$-0.303964\pi$
$828$		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
$831$	−7.39979	+	10.6051i	−0.256696	+	0.367888i
$832$		0			0
$833$	27.1672	+	4.96661i	0.941286	+	0.172083i
$834$		0			0
$835$	6.28480			0.217495
$836$		0			0
$837$	8.14011	−	30.9911i	0.281363	−	1.07121i
$838$		0			0
$839$	−8.51664	+	14.7513i	−0.294027	+	0.509270i	−0.974758	−	0.223264i	$-0.928329\pi$
$839$	−8.51664	+	14.7513i	−0.294027	+	0.509270i	0.680731	+	0.732533i	$0.261662\pi$
$840$		0			0
$841$	−0.322276	−	0.558199i	−0.0111130	−	0.0192482i
$842$		0			0
$843$	3.29653	−	38.4081i	0.113538	−	1.32284i
$844$		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
$849$	25.3797	−	11.8857i	0.871030	−	0.407916i
$850$		0			0
$851$		−	1.29275i		−	0.0443150i
$852$		0			0
$853$	2.87158	+	1.65791i	0.0983209	+	0.0567656i	0.548354	−	0.836246i	$-0.315255\pi$
$853$	2.87158	+	1.65791i	0.0983209	+	0.0567656i	−0.450033	+	0.893012i	$0.648588\pi$
$854$		0			0
$855$	−9.95624	−	8.29854i	−0.340496	−	0.283804i
$856$		0			0
$857$	−4.74512	−	8.21879i	−0.162090	−	0.280748i	0.773528	−	0.633762i	$-0.218490\pi$
$857$	−4.74512	−	8.21879i	−0.162090	−	0.280748i	−0.935618	+	0.353014i	$0.885157\pi$
$858$		0			0
$859$	25.5104	+	14.7284i	0.870404	+	0.502528i	0.867482	−	0.497468i	$-0.165737\pi$
$859$	25.5104	+	14.7284i	0.870404	+	0.502528i	0.00292142	+	0.999996i	$0.499070\pi$
$860$		0			0
$861$	−0.705617	+	0.255629i	−0.0240474	+	0.00871180i
$862$		0			0
$863$	−13.4610	+	7.77172i	−0.458218	+	0.264553i	−0.711295	−	0.702894i	$-0.751891\pi$
$863$	−13.4610	+	7.77172i	−0.458218	+	0.264553i	0.253076	+	0.967446i	$0.418558\pi$
$864$		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
$871$	−20.5125	+	11.8429i	−0.695039	+	0.401281i
$872$		0			0
$873$	−33.3806	+	12.2742i	−1.12976	+	0.415420i
$874$		0			0
$875$	18.9609	+	13.3656i	0.640997	+	0.451840i
$876$		0			0
$877$	22.7249	−	39.3606i	0.767364	−	1.32911i	−0.171624	−	0.985163i	$-0.554901\pi$
$877$	22.7249	−	39.3606i	0.767364	−	1.32911i	0.938988	−	0.343950i	$-0.111765\pi$
$878$		0			0
$879$	8.78942	−	12.5967i	0.296460	−	0.424877i
$880$		0			0
$881$	15.6912			0.528651			0.264326	−	0.964433i	$-0.414851\pi$
$881$	15.6912			0.528651			0.264326	+	0.964433i	$0.414851\pi$
$882$		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
$885$	−2.79421	−	0.239824i	−0.0939262	−	0.00806159i
$886$		0			0
$887$	−0.0302741	+	0.0524362i	−0.00101650	+	0.00176064i	−0.866533	−	0.499119i	$-0.833657\pi$
$887$	−0.0302741	+	0.0524362i	−0.00101650	+	0.00176064i	0.865517	+	0.500880i	$0.166990\pi$
$888$		0			0
$889$	−7.17694	−	5.05904i	−0.240707	−	0.169675i
$890$		0			0
$891$	32.4963	+	38.2134i	1.08867	+	1.28020i
$892$		0			0
$893$	−36.7070	+	21.1928i	−1.22835	+	0.709190i
$894$		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
$903$	30.5057	+	25.6752i	1.01517	+	0.854418i
$904$		0			0
$905$	−9.66247	−	5.57863i	−0.321192	−	0.185440i
$906$		0			0
$907$	12.0490	+	20.8695i	0.400081	+	0.692961i	0.993735	−	0.111760i	$-0.0356487\pi$
$907$	12.0490	+	20.8695i	0.400081	+	0.692961i	−0.593654	+	0.804720i	$0.702315\pi$
$908$		0			0
$909$	−15.7155	−	2.71772i	−0.521251	−	0.0901410i
$910$		0			0
$911$	−22.0494	−	12.7302i	−0.730528	−	0.421771i	0.0880873	−	0.996113i	$-0.471925\pi$
$911$	−22.0494	−	12.7302i	−0.730528	−	0.421771i	−0.818615	+	0.574342i	$0.805258\pi$
$912$		0			0
$913$			46.9275i			1.55307i
$914$		0			0
$915$	−0.741053	+	8.63406i	−0.0244985	+	0.285433i
$916$		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
$921$	42.5751	−	19.9386i	1.40290	−	0.656998i
$922$		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
$927$	25.1849	−	9.26062i	0.827179	−	0.304159i
$928$		0			0
$929$	28.7973			0.944809			0.472404	−	0.881382i	$-0.343386\pi$
$929$	28.7973			0.944809			0.472404	+	0.881382i	$0.343386\pi$
$930$		0			0
$931$	−23.8231	−	20.2465i	−0.780770	−	0.663553i
$932$		0			0
$933$	−12.4111	−	26.5016i	−0.406321	−	0.867625i
$934$		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
$941$	−45.9021			−1.49637			−0.748184	−	0.663492i	$-0.769074\pi$
$941$	−45.9021			−1.49637			−0.748184	+	0.663492i	$0.769074\pi$
$942$		0			0
$943$		−	0.434541i		−	0.0141506i
$944$		0			0
$945$	−13.0923	+	2.33281i	−0.425893	+	0.0758864i
$946$		0			0
$947$			28.9183i			0.939718i	0.882741	+	0.469859i	$0.155695\pi$
$947$			28.9183i			0.939718i	−0.882741	+	0.469859i	$0.844305\pi$
$948$		0			0
$949$	10.8278			0.351485
$950$		0			0
$951$	10.3986	−	4.86984i	0.337199	−	0.157915i
$952$		0			0
$953$			12.8715i			0.416949i	0.978028	+	0.208475i	$0.0668498\pi$
$953$			12.8715i			0.416949i	−0.978028	+	0.208475i	$0.933150\pi$
$954$		0			0
$955$	−18.4877	−	10.6739i	−0.598249	−	0.345399i
$956$		0			0
$957$	−21.8019	−	46.5540i	−0.704756	−	1.50488i
$958$		0			0
$959$	44.6211	+	4.04521i	1.44089	+	0.130627i
$960$		0			0
$961$	−7.02628			−0.226654
$962$		0			0
$963$	9.79284	−	56.6283i	0.315570	−	1.82482i
$964$		0			0
$965$	−9.64402	+	16.7039i	−0.310452	+	0.537719i
$966$		0			0
$967$	−3.11725	−	5.39923i	−0.100244	−	0.173627i	0.811541	−	0.584295i	$-0.198629\pi$
$967$	−3.11725	−	5.39923i	−0.100244	−	0.173627i	−0.911785	+	0.410668i	$0.865296\pi$
$968$		0			0
$969$	−27.6400	+	12.9442i	−0.887926	+	0.415829i
$970$		0			0
$971$	19.6863	+	34.0977i	0.631764	+	1.09425i	0.987191	+	0.159544i	$0.0510023\pi$
$971$	19.6863	+	34.0977i	0.631764	+	1.09425i	−0.355426	+	0.934704i	$0.615664\pi$
$972$		0			0
$973$	31.9570	+	2.89712i	1.02449	+	0.0928774i
$974$		0			0
$975$	2.61983	−	30.5238i	0.0839017	−	0.977544i
$976$		0			0
$977$		−	26.8438i		−	0.858809i	−0.903112	−	0.429405i	$-0.858723\pi$
$977$		−	26.8438i		−	0.858809i	0.903112	−	0.429405i	$-0.141277\pi$
$978$		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
$983$	−5.98457	−	10.3656i	−0.190878	−	0.330611i	0.754663	−	0.656112i	$-0.227800\pi$
$983$	−5.98457	−	10.3656i	−0.190878	−	0.330611i	−0.945541	+	0.325502i	$0.894467\pi$
$984$		0			0
$985$	3.87499	+	2.23723i	0.123467	+	0.0712839i
$986$		0			0
$987$	−7.61580	+	42.8166i	−0.242414	+	1.36287i
$988$		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
$997$	−11.6653	+	6.73498i	−0.369445	+	0.213299i	−0.673216	−	0.739446i	$-0.735088\pi$
$997$	−11.6653	+	6.73498i	−0.369445	+	0.213299i	0.303771	+	0.952745i	$0.401754\pi$
$998$		0			0
$999$	−0.667317	−	2.44212i	−0.0211130	−	0.0772653i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.7	✓	16	252.131	odd	6
126.2.l.a.101.3	yes	16	4.3	odd	2
126.2.t.a.47.1	yes	16	28.19	even	6
126.2.t.a.59.1	yes	16	36.23	even	6
378.2.l.a.143.6		16	12.11	even	2
378.2.l.a.341.2		16	252.103	even	6
378.2.t.a.17.6		16	36.31	odd	6
378.2.t.a.89.6		16	84.47	odd	6
882.2.l.b.227.2		16	28.27	even	2
882.2.l.b.509.6		16	252.23	even	6
882.2.m.a.293.7		16	252.95	even	6
882.2.m.a.587.7		16	28.3	even	6
882.2.m.b.293.6		16	252.59	odd	6
882.2.m.b.587.6		16	28.11	odd	6
882.2.t.a.803.4		16	28.23	odd	6
882.2.t.a.815.4		16	252.167	odd	6
1008.2.ca.c.257.5		16	63.5	even	6	inner
1008.2.ca.c.353.5		16	1.1	even	1	trivial
1008.2.df.c.689.7		16	9.5	odd	6
1008.2.df.c.929.7		16	7.5	odd	6
1134.2.k.a.647.3		16	36.7	odd	6
1134.2.k.a.971.3		16	252.47	odd	6
1134.2.k.b.647.6		16	36.11	even	6
1134.2.k.b.971.6		16	252.187	even	6
2646.2.l.a.521.7		16	84.83	odd	2
2646.2.l.a.1097.3		16	252.247	odd	6
2646.2.m.a.881.3		16	252.67	odd	6
2646.2.m.a.1763.3		16	84.59	odd	6
2646.2.m.b.881.2		16	252.31	even	6
2646.2.m.b.1763.2		16	84.11	even	6
2646.2.t.b.1979.7		16	84.23	even	6
2646.2.t.b.2285.7		16	252.139	even	6
3024.2.ca.c.2033.4		16	3.2	odd	2
3024.2.ca.c.2609.4		16	63.40	odd	6
3024.2.df.c.17.4		16	9.4	even	3
3024.2.df.c.1601.4		16	21.5	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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.734581 + 1.56856i) q^{3} +(0.483662 - 0.837727i) q^{5} +(2.16249 + 1.52435i) q^{7} +(-1.92078 + 2.30447i) q^{9} +(-4.82689 + 2.78681i) q^{11} +(-3.76893 + 2.17600i) q^{13} +(1.66932 + 0.143276i) q^{15} +(1.97267 - 3.41677i) q^{17} +(-3.86796 + 2.23317i) q^{19} +(-0.802507 + 4.51176i) q^{21} +(-2.29786 - 1.32667i) q^{23} +(2.03214 + 3.51977i) q^{25} +(-5.02568 - 1.32004i) q^{27} +(4.61157 + 2.66249i) q^{29} +6.16655i q^{31} +(-7.91702 - 5.52415i) q^{33} +(2.32290 - 1.07431i) q^{35} +(0.243608 + 0.421942i) q^{37} +(-6.18177 - 4.31337i) q^{39} +(0.0818856 + 0.141830i) q^{41} +(4.35045 - 7.53520i) q^{43} +(1.00151 + 2.72368i) q^{45} +9.49001 q^{47} +(2.35274 + 6.59277i) q^{49} +(6.80851 + 0.584367i) q^{51} +(-1.74520 - 1.00759i) q^{53} +5.39149i q^{55} +(-6.34420 - 4.42670i) q^{57} -1.67386 q^{59} +5.17221i q^{61} +(-7.66649 + 2.05547i) q^{63} +4.20979i q^{65} +5.44252 q^{67} +(0.393002 - 4.57889i) q^{69} +3.64006i q^{71} +(-2.15468 - 1.24401i) q^{73} +(-4.02821 + 5.77310i) q^{75} +(-14.6862 - 1.33140i) q^{77} -4.60242 q^{79} +(-1.62120 - 8.85278i) q^{81} +(4.20979 - 7.29158i) q^{83} +(-1.90821 - 3.30512i) q^{85} +(-0.788713 + 9.18936i) q^{87} +(-2.05811 - 3.56475i) q^{89} +(-11.4673 - 1.03959i) q^{91} +(-9.67262 + 4.52983i) q^{93} +4.32040i q^{95} +(10.2669 + 5.92762i) q^{97} +(2.84928 - 16.4763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} - 12 q^{11} + 6 q^{13} + 18 q^{15} - 18 q^{17} - 12 q^{21} + 6 q^{23} - 8 q^{25} - 36 q^{27} + 6 q^{29} - 30 q^{35} - 2 q^{37} + 12 q^{39} - 6 q^{41} + 2 q^{43} - 30 q^{45} + 36 q^{47} - 8 q^{49}+ \cdots - 18 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 - 12 * q^11 + 6 * q^13 + 18 * q^15 - 18 * q^17 - 12 * q^21 + 6 * q^23 - 8 * q^25 - 36 * q^27 + 6 * q^29 - 30 * q^35 - 2 * q^37 + 12 * q^39 - 6 * q^41 + 2 * q^43 - 30 * q^45 + 36 * q^47 - 8 * q^49 - 6 * q^51 - 36 * q^53 + 6 * q^57 - 60 * q^59 - 36 * q^63 + 28 * q^67 - 42 * q^69 - 60 * q^75 - 42 * q^77 - 32 * q^79 - 36 * q^81 - 12 * q^85 + 24 * q^87 - 24 * q^89 + 12 * q^91 - 42 * q^93 + 6 * q^97 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more