LMFDB - Embedded newform 336.4.bc.e.17.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(17,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.17"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$19.8246417619$
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} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{11} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Root			$2.30541 + 1.91966i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.e.257.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.99309 + 3.32495i) q^{3} +(9.90442 + 17.1550i) q^{5} +(-18.4277 - 1.84901i) q^{7} +(4.88947 + 26.5536i) q^{9} +(-4.28742 - 2.47535i) q^{11} +17.7414i q^{13} +(-17.4901 + 101.433i) q^{15} +(0.947671 - 1.64141i) q^{17} +(-83.9968 + 48.4956i) q^{19} +(-67.4356 - 68.6545i) q^{21} +(135.935 - 78.4822i) q^{23} +(-133.695 + 231.567i) q^{25} +(-68.7652 + 122.288i) q^{27} -92.0138i q^{29} +(-67.3521 - 38.8857i) q^{31} +(-8.88966 - 24.1397i) q^{33} +(-150.796 - 334.440i) q^{35} +(-124.469 - 215.587i) q^{37} +(-58.9891 + 70.8428i) q^{39} +343.701 q^{41} +24.5859 q^{43} +(-407.099 + 346.877i) q^{45} +(235.248 + 407.461i) q^{47} +(336.162 + 68.1462i) q^{49} +(9.24175 - 3.40335i) q^{51} +(-344.910 - 199.134i) q^{53} -98.0675i q^{55} +(-496.652 - 85.6379i) q^{57} +(-335.568 + 581.220i) q^{59} +(-273.703 + 158.023i) q^{61} +(-41.0038 - 498.363i) q^{63} +(-304.352 + 175.718i) q^{65} +(-116.895 + 202.469i) q^{67} +(803.750 + 138.591i) q^{69} +152.225i q^{71} +(539.897 + 311.709i) q^{73} +(-1303.80 + 480.137i) q^{75} +(74.4305 + 53.5425i) q^{77} +(151.191 + 261.870i) q^{79} +(-681.186 + 259.666i) q^{81} +856.438 q^{83} +37.5446 q^{85} +(305.941 - 367.419i) q^{87} +(453.577 + 785.618i) q^{89} +(32.8040 - 326.933i) q^{91} +(-139.650 - 379.216i) q^{93} +(-1663.88 - 960.642i) q^{95} -70.3731i q^{97} +(44.7661 - 125.950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 80 q^{7} + 18 q^{9} + 342 q^{19} - 450 q^{21} - 194 q^{25} - 804 q^{31} + 1332 q^{33} - 962 q^{37} - 594 q^{39} - 1732 q^{43} - 2394 q^{45} + 820 q^{49} - 1638 q^{51} - 2664 q^{57} - 4620 q^{61}+ \cdots + 4284 q^{99}+O(q^{100}) $ 16 * q - 80 * q^7 + 18 * q^9 + 342 * q^19 - 450 * q^21 - 194 * q^25 - 804 * q^31 + 1332 * q^33 - 962 * q^37 - 594 * q^39 - 1732 * q^43 - 2394 * q^45 + 820 * q^49 - 1638 * q^51 - 2664 * q^57 - 4620 * q^61 + 2016 * q^63 + 706 * q^67 + 3294 * q^73 - 6174 * q^75 + 2656 * q^79 + 126 * q^81 + 5232 * q^85 - 1026 * q^87 - 4098 * q^91 + 2016 * q^93 + 4284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	3.99309	+	3.32495i	0.768470	+	0.639886i
$3$	3.99309	+	3.32495i	0.768470	+	0.639886i
$4$		0			0
$5$	9.90442	+	17.1550i	0.885879	+	1.53439i	0.844703	+	0.535235i	$0.179777\pi$
$5$	9.90442	+	17.1550i	0.885879	+	1.53439i	0.0411754	+	0.999152i	$0.486890\pi$
$6$		0			0
$7$	−18.4277	−	1.84901i	−0.995004	−	0.0998373i
$7$	−18.4277	−	1.84901i	−0.995004	−	0.0998373i
$8$		0			0
$9$	4.88947	+	26.5536i	0.181091	+	0.983466i
$10$		0			0
$11$	−4.28742	−	2.47535i	−0.117519	−	0.0678495i	0.440088	−	0.897954i	$-0.354947\pi$
$11$	−4.28742	−	2.47535i	−0.117519	−	0.0678495i	−0.557607	+	0.830105i	$0.688280\pi$
$12$		0			0
$13$			17.7414i			0.378505i	0.981928	+	0.189253i	$0.0606065\pi$
$13$			17.7414i			0.378505i	−0.981928	+	0.189253i	$0.939394\pi$
$14$		0			0
$15$	−17.4901	+	101.433i	−0.301062	+	1.74599i
$16$		0			0
$17$	0.947671	−	1.64141i	0.0135202	−	0.0234177i	−0.859186	−	0.511663i	$-0.829030\pi$
$17$	0.947671	−	1.64141i	0.0135202	−	0.0234177i	0.872706	+	0.488245i	$0.162363\pi$
$18$		0			0
$19$	−83.9968	+	48.4956i	−1.01422	+	0.585561i	−0.912425	−	0.409245i	$-0.865792\pi$
$19$	−83.9968	+	48.4956i	−1.01422	+	0.585561i	−0.101796	+	0.994805i	$0.532459\pi$
$20$		0			0
$21$	−67.4356	−	68.6545i	−0.700746	−	0.713411i
$22$		0			0
$23$	135.935	−	78.4822i	1.23237	−	0.711508i	0.264845	−	0.964291i	$-0.414679\pi$
$23$	135.935	−	78.4822i	1.23237	−	0.711508i	0.967523	+	0.252783i	$0.0813460\pi$
$24$		0			0
$25$	−133.695	+	231.567i	−1.06956	+	1.85254i
$26$		0			0
$27$	−68.7652	+	122.288i	−0.490143	+	0.871642i
$28$		0			0
$29$		−	92.0138i		−	0.589191i	−0.955622	−	0.294595i	$-0.904815\pi$
$29$		−	92.0138i		−	0.589191i	0.955622	−	0.294595i	$-0.0951849\pi$
$30$		0			0
$31$	−67.3521	−	38.8857i	−0.390219	−	0.225293i	0.292036	−	0.956407i	$-0.405667\pi$
$31$	−67.3521	−	38.8857i	−0.390219	−	0.225293i	−0.682255	+	0.731114i	$0.739001\pi$
$32$		0			0
$33$	−8.88966	−	24.1397i	−0.0468937	−	0.127339i
$34$		0			0
$35$	−150.796	−	334.440i	−0.728264	−	1.61516i
$36$		0			0
$37$	−124.469	−	215.587i	−0.553044	−	0.957901i	−0.998053	−	0.0623743i	$-0.980133\pi$
$37$	−124.469	−	215.587i	−0.553044	−	0.957901i	0.445009	−	0.895526i	$-0.353201\pi$
$38$		0			0
$39$	−58.9891	+	70.8428i	−0.242200	+	0.290870i
$40$		0			0
$41$	343.701			1.30920			0.654598	−	0.755977i	$-0.272838\pi$
$41$	343.701			1.30920			0.654598	+	0.755977i	$0.272838\pi$
$42$		0			0
$43$	24.5859			0.0871934			0.0435967	−	0.999049i	$-0.486118\pi$
$43$	24.5859			0.0871934			0.0435967	+	0.999049i	$0.486118\pi$
$44$		0			0
$45$	−407.099	+	346.877i	−1.34859	+	1.14910i
$46$		0			0
$47$	235.248	+	407.461i	0.730093	+	1.26456i	0.956843	+	0.290606i	$0.0938568\pi$
$47$	235.248	+	407.461i	0.730093	+	1.26456i	−0.226750	+	0.973953i	$0.572810\pi$
$48$		0			0
$49$	336.162	+	68.1462i	0.980065	+	0.198677i
$50$		0			0
$51$	9.24175	−	3.40335i	0.0253746	−	0.00934441i
$52$		0			0
$53$	−344.910	−	199.134i	−0.893907	−	0.516097i	−0.0186885	−	0.999825i	$-0.505949\pi$
$53$	−344.910	−	199.134i	−0.893907	−	0.516097i	−0.875218	+	0.483728i	$0.839282\pi$
$54$		0			0
$55$		−	98.0675i		−	0.240426i
$56$		0			0
$57$	−496.652	−	85.6379i	−1.15409	−	0.199000i
$58$		0			0
$59$	−335.568	+	581.220i	−0.740461	+	1.28252i	0.211825	+	0.977308i	$0.432059\pi$
$59$	−335.568	+	581.220i	−0.740461	+	1.28252i	−0.952286	+	0.305208i	$0.901274\pi$
$60$		0			0
$61$	−273.703	+	158.023i	−0.574494	+	0.331684i	−0.758942	−	0.651158i	$-0.774284\pi$
$61$	−273.703	+	158.023i	−0.574494	+	0.331684i	0.184448	+	0.982842i	$0.440950\pi$
$62$		0			0
$63$	−41.0038	−	498.363i	−0.0819999	−	0.996632i
$64$		0			0
$65$	−304.352	+	175.718i	−0.580773	+	0.335310i
$66$		0			0
$67$	−116.895	+	202.469i	−0.213150	+	0.369186i	−0.952699	−	0.303917i	$-0.901706\pi$
$67$	−116.895	+	202.469i	−0.213150	+	0.369186i	0.739549	+	0.673103i	$0.235039\pi$
$68$		0			0
$69$	803.750	+	138.591i	1.40232	+	0.241803i
$70$		0			0
$71$			152.225i			0.254447i	0.991874	+	0.127224i	$0.0406066\pi$
$71$			152.225i			0.254447i	−0.991874	+	0.127224i	$0.959393\pi$
$72$		0			0
$73$	539.897	+	311.709i	0.865618	+	0.499765i	0.865890	−	0.500235i	$-0.166753\pi$
$73$	539.897	+	311.709i	0.865618	+	0.499765i	−0.000271580		1.00000i	$0.500086\pi$
$74$		0			0
$75$	−1303.80	+	480.137i	−2.00734	+	0.739220i
$76$		0			0
$77$	74.4305	+	53.5425i	0.110158	+	0.0792433i
$78$		0			0
$79$	151.191	+	261.870i	0.215320	+	0.372945i	0.953371	−	0.301799i	$-0.0975873\pi$
$79$	151.191	+	261.870i	0.215320	+	0.372945i	−0.738052	+	0.674744i	$0.764254\pi$
$80$		0			0
$81$	−681.186	+	259.666i	−0.934412	+	0.356194i
$82$		0			0
$83$	856.438			1.13261			0.566303	−	0.824197i	$-0.308373\pi$
$83$	856.438			1.13261			0.566303	+	0.824197i	$0.308373\pi$
$84$		0			0
$85$	37.5446			0.0479092
$86$		0			0
$87$	305.941	−	367.419i	0.377015	−	0.452775i
$88$		0			0
$89$	453.577	+	785.618i	0.540214	+	0.935678i	0.998891	+	0.0470750i	$0.0149900\pi$
$89$	453.577	+	785.618i	0.540214	+	0.935678i	−0.458678	+	0.888603i	$0.651677\pi$
$90$		0			0
$91$	32.8040	−	326.933i	0.0377889	−	0.376614i
$92$		0			0
$93$	−139.650	−	379.216i	−0.155710	−	0.422827i
$94$		0			0
$95$	−1663.88	−	960.642i	−1.79695	−	1.03747i
$96$		0			0
$97$		−	70.3731i		−	0.0736629i	−0.999321	−	0.0368315i	$-0.988274\pi$
$97$		−	70.3731i		−	0.0736629i	0.999321	−	0.0368315i	$-0.0117265\pi$
$98$		0			0
$99$	44.7661	−	125.950i	0.0454461	−	0.127863i
$100$		0			0
$101$	119.274	−	206.588i	0.117507	−	0.203527i	−0.801272	−	0.598300i	$-0.795843\pi$
$101$	119.274	−	206.588i	0.117507	−	0.203527i	0.918779	+	0.394772i	$0.129177\pi$
$102$		0			0
$103$	16.9592	−	9.79138i	0.0162237	−	0.00936674i	−0.491866	−	0.870671i	$-0.663685\pi$
$103$	16.9592	−	9.79138i	0.0162237	−	0.00936674i	0.508090	+	0.861304i	$0.330352\pi$
$104$		0			0
$105$	509.854	−	1836.84i	0.473873	−	1.70721i
$106$		0			0
$107$	419.010	−	241.915i	0.378572	−	0.218569i	−0.298625	−	0.954371i	$-0.596528\pi$
$107$	419.010	−	241.915i	0.378572	−	0.218569i	0.677197	+	0.735802i	$0.263195\pi$
$108$		0			0
$109$	−21.4023	+	37.0698i	−0.0188070	+	0.0325747i	−0.875276	−	0.483624i	$-0.839320\pi$
$109$	−21.4023	+	37.0698i	−0.0188070	+	0.0325747i	0.856469	+	0.516199i	$0.172653\pi$
$110$		0			0
$111$	219.799	−	1274.71i	0.187950	−	1.09000i
$112$		0			0
$113$			378.359i			0.314983i	0.987520	+	0.157491i	$0.0503406\pi$
$113$			378.359i			0.314983i	−0.987520	+	0.157491i	$0.949659\pi$
$114$		0			0
$115$	2692.72	+	1554.64i	2.18346	+	1.26062i
$116$		0			0
$117$	−471.097	+	86.7457i	−0.372247	+	0.0685440i
$118$		0			0
$119$	−20.4984	+	28.4953i	−0.0157906	+	0.0219509i
$120$		0			0
$121$	−653.245	−	1131.45i	−0.490793	−	0.850078i
$122$		0			0
$123$	1372.43	+	1142.79i	1.00608	+	0.837737i
$124$		0			0
$125$	−2820.59			−2.01825
$126$		0			0
$127$	−112.805			−0.0788177			−0.0394088	−	0.999223i	$-0.512547\pi$
$127$	−112.805			−0.0788177			−0.0394088	+	0.999223i	$0.512547\pi$
$128$		0			0
$129$	98.1736	+	81.7468i	0.0670054	+	0.0557938i
$130$		0			0
$131$	790.927	+	1369.93i	0.527508	+	0.913671i	0.999486	+	0.0320608i	$0.0102070\pi$
$131$	790.927	+	1369.93i	0.527508	+	0.913671i	−0.471977	+	0.881611i	$0.656460\pi$
$132$		0			0
$133$	1637.54	−	738.353i	1.06761	−	0.481378i
$134$		0			0
$135$	−2778.93	+	31.5271i	−1.77164	+	0.0200994i
$136$		0			0
$137$	1597.31	+	922.210i	0.996115	+	0.575107i	0.907097	−	0.420923i	$-0.138294\pi$
$137$	1597.31	+	922.210i	0.996115	+	0.575107i	0.0890187	+	0.996030i	$0.471627\pi$
$138$		0			0
$139$			55.8671i			0.0340905i	0.999855	+	0.0170453i	$0.00542594\pi$
$139$			55.8671i			0.0340905i	−0.999855	+	0.0170453i	$0.994574\pi$
$140$		0			0
$141$	−415.421	+	2409.21i	−0.248119	+	1.43895i
$142$		0			0
$143$	43.9160	−	76.0647i	0.0256814	−	0.0444815i
$144$		0			0
$145$	1578.49	−	911.344i	0.904046	−	0.521951i
$146$		0			0
$147$	1115.74	+	1389.84i	0.626020	+	0.779807i
$148$		0			0
$149$	2951.20	−	1703.87i	1.62263	−	0.936824i	0.636414	−	0.771348i	$-0.280417\pi$
$149$	2951.20	−	1703.87i	1.62263	−	0.936824i	0.986214	−	0.165477i	$-0.0529163\pi$
$150$		0			0
$151$	1627.89	−	2819.59i	0.877324	−	1.51957i	0.0230569	−	0.999734i	$-0.492660\pi$
$151$	1627.89	−	2819.59i	0.877324	−	1.51957i	0.854267	−	0.519835i	$-0.174007\pi$
$152$		0			0
$153$	48.2191	+	17.1384i	0.0254790	+	0.00905595i
$154$		0			0
$155$		−	1540.56i		−	0.798329i
$156$		0			0
$157$	2199.76	+	1270.03i	1.11822	+	0.645602i	0.940945	−	0.338560i	$-0.109940\pi$
$157$	2199.76	+	1270.03i	1.11822	+	0.645602i	0.177271	+	0.984162i	$0.443273\pi$
$158$		0			0
$159$	−715.146	−	1941.97i	−0.356697	−	0.968604i
$160$		0			0
$161$	−2650.09	+	1194.90i	−1.29725	+	0.584917i
$162$		0			0
$163$	862.851	+	1494.50i	0.414624	+	0.718150i	0.995389	−	0.0959216i	$-0.0305798\pi$
$163$	862.851	+	1494.50i	0.414624	+	0.718150i	−0.580765	+	0.814071i	$0.697246\pi$
$164$		0			0
$165$	326.069	−	391.592i	0.153845	−	0.184760i
$166$		0			0
$167$	−485.621			−0.225021			−0.112510	−	0.993651i	$-0.535889\pi$
$167$	−485.621			−0.225021			−0.112510	+	0.993651i	$0.535889\pi$
$168$		0			0
$169$	1882.24			0.856734
$170$		0			0
$171$	−1698.43	−	1993.30i	−0.759546	−	0.891412i
$172$		0			0
$173$	−726.552	−	1258.43i	−0.319299	−	0.553042i	0.661043	−	0.750348i	$-0.270114\pi$
$173$	−726.552	−	1258.43i	−0.319299	−	0.553042i	−0.980342	+	0.197306i	$0.936781\pi$
$174$		0			0
$175$	2891.87	−	4020.05i	1.24917	−	1.73650i
$176$		0			0
$177$	−3272.48	+	1205.12i	−1.38969	+	0.511764i
$178$		0			0
$179$	−1099.44	−	634.760i	−0.459082	−	0.265051i	0.252576	−	0.967577i	$-0.418722\pi$
$179$	−1099.44	−	634.760i	−0.459082	−	0.265051i	−0.711658	+	0.702526i	$0.752056\pi$
$180$		0			0
$181$		−	3289.26i		−	1.35076i	−0.737468	−	0.675382i	$-0.763979\pi$
$181$		−	3289.26i		−	1.35076i	0.737468	−	0.675382i	$-0.236021\pi$
$182$		0			0
$183$	−1618.34	−	279.051i	−0.653721	−	0.112721i
$184$		0			0
$185$	2465.59	−	4270.53i	0.979860	−	1.69717i
$186$		0			0
$187$	−8.12614	+	4.69163i	−0.00317776	+	0.00183468i
$188$		0			0
$189$	1493.30	−	2126.34i	0.574717	−	0.818352i
$190$		0			0
$191$	1713.46	−	989.265i	0.649117	−	0.374768i	−0.139001	−	0.990292i	$-0.544389\pi$
$191$	1713.46	−	989.265i	0.649117	−	0.374768i	0.788118	+	0.615524i	$0.211056\pi$
$192$		0			0
$193$	459.923	−	796.611i	0.171534	−	0.297105i	−0.767423	−	0.641142i	$-0.778461\pi$
$193$	459.923	−	796.611i	0.171534	−	0.297105i	0.938956	+	0.344037i	$0.111794\pi$
$194$		0			0
$195$	−1799.56	−	310.299i	−0.660867	−	0.113954i
$196$		0			0
$197$		−	3061.98i		−	1.10740i	−0.832717	−	0.553699i	$-0.813216\pi$
$197$		−	3061.98i		−	1.10740i	0.832717	−	0.553699i	$-0.186784\pi$
$198$		0			0
$199$	451.592	+	260.727i	0.160867	+	0.0928766i	0.578272	−	0.815844i	$-0.303727\pi$
$199$	451.592	+	260.727i	0.160867	+	0.0928766i	−0.417405	+	0.908720i	$0.637060\pi$
$200$		0			0
$201$	−1139.97	+	419.804i	−0.400036	+	0.147317i
$202$		0			0
$203$	−170.135	+	1695.60i	−0.0588232	+	0.586247i
$204$		0			0
$205$	3404.16	+	5896.18i	1.15979	+	2.00881i
$206$		0			0
$207$	2748.64	+	3225.83i	0.922915	+	1.08314i
$208$		0			0
$209$	480.173			0.158920
$210$		0			0
$211$	−99.6288			−0.0325058			−0.0162529	−	0.999868i	$-0.505174\pi$
$211$	−99.6288			−0.0325058			−0.0162529	+	0.999868i	$0.505174\pi$
$212$		0			0
$213$	−506.140	+	607.847i	−0.162817	+	0.195535i
$214$		0			0
$215$	243.509	+	421.770i	0.0772427	+	0.133788i
$216$		0			0
$217$	1169.25	+	841.111i	0.365777	+	0.263126i
$218$		0			0
$219$	1119.44	+	3039.81i	0.345409	+	0.937951i
$220$		0			0
$221$	29.1209	+	16.8130i	0.00886373	+	0.00511748i
$222$		0			0
$223$		−	1782.29i		−	0.535206i	−0.963529	−	0.267603i	$-0.913768\pi$
$223$		−	1782.29i		−	0.535206i	0.963529	−	0.267603i	$-0.0862316\pi$
$224$		0			0
$225$	−6802.63	−	2417.85i	−2.01559	−	0.716400i
$226$		0			0
$227$	1721.58	−	2981.86i	0.503370	−	0.871863i	−0.496622	−	0.867967i	$-0.665427\pi$
$227$	1721.58	−	2981.86i	0.503370	−	0.871863i	0.999992	−	0.00389579i	$-0.00124007\pi$
$228$		0			0
$229$	−4706.78	+	2717.46i	−1.35822	+	0.784169i	−0.989384	−	0.145325i	$-0.953577\pi$
$229$	−4706.78	+	2717.46i	−1.35822	+	0.784169i	−0.368837	+	0.929494i	$0.620244\pi$
$230$		0			0
$231$	119.182	+	461.277i	0.0339462	+	0.131384i
$232$		0			0
$233$	−3815.33	+	2202.78i	−1.07275	+	0.619351i	−0.928931	−	0.370253i	$-0.879271\pi$
$233$	−3815.33	+	2202.78i	−1.07275	+	0.619351i	−0.143817	+	0.989604i	$0.545938\pi$
$234$		0			0
$235$	−4659.98	+	8071.33i	−1.29355	+	2.24049i
$236$		0			0
$237$	−266.986	+	1548.37i	−0.0731755	+	0.424377i
$238$		0			0
$239$			2020.29i			0.546786i	0.961902	+	0.273393i	$0.0881459\pi$
$239$			2020.29i			0.546786i	−0.961902	+	0.273393i	$0.911854\pi$
$240$		0			0
$241$	−1966.82	−	1135.54i	−0.525700	−	0.303513i	0.213563	−	0.976929i	$-0.431493\pi$
$241$	−1966.82	−	1135.54i	−0.525700	−	0.303513i	−0.739264	+	0.673416i	$0.764826\pi$
$242$		0			0
$243$	−3583.41	−	1228.04i	−0.945991	−	0.324193i
$244$		0			0
$245$	2160.45	+	6441.80i	0.563371	+	1.67980i
$246$		0			0
$247$	−860.378	−	1490.22i	−0.221638	−	0.383888i
$248$		0			0
$249$	3419.83	+	2847.61i	0.870373	+	0.724738i
$250$		0			0
$251$	−4513.50			−1.13502			−0.567510	−	0.823367i	$-0.692093\pi$
$251$	−4513.50			−1.13502			−0.567510	+	0.823367i	$0.692093\pi$
$252$		0			0
$253$	−777.082			−0.193102
$254$		0			0
$255$	149.919	+	124.834i	0.0368167	+	0.0306564i
$256$		0			0
$257$	2969.31	+	5142.99i	0.720701	+	1.24829i	0.960719	+	0.277523i	$0.0895134\pi$
$257$	2969.31	+	5142.99i	0.720701	+	1.24829i	−0.240018	+	0.970769i	$0.577153\pi$
$258$		0			0
$259$	1895.06	+	4202.93i	0.454647	+	1.00833i
$260$		0			0
$261$	2443.30	−	449.898i	0.579449	−	0.106697i
$262$		0			0
$263$	4727.20	+	2729.25i	1.10833	+	0.639897i	0.938397	−	0.345558i	$-0.112310\pi$
$263$	4727.20	+	2729.25i	1.10833	+	0.639897i	0.169936	+	0.985455i	$0.445644\pi$
$264$		0			0
$265$		−	7889.23i		−	1.82880i
$266$		0			0
$267$	−800.967	+	4645.16i	−0.183589	+	1.06472i
$268$		0			0
$269$	−2642.46	+	4576.87i	−0.598935	+	1.03739i	0.394043	+	0.919092i	$0.371076\pi$
$269$	−2642.46	+	4576.87i	−0.598935	+	1.03739i	−0.992979	+	0.118294i	$0.962257\pi$
$270$		0			0
$271$	5436.74	−	3138.90i	1.21866	−	0.703596i	0.254033	−	0.967196i	$-0.418243\pi$
$271$	5436.74	−	3138.90i	1.21866	−	0.703596i	0.964632	+	0.263599i	$0.0849096\pi$
$272$		0			0
$273$	1218.02	−	1196.40i	0.270030	−	0.265236i
$274$		0			0
$275$	1146.42	−	661.884i	0.251387	−	0.145139i
$276$		0			0
$277$	−3748.17	+	6492.02i	−0.813017	+	1.40819i	0.0977256	+	0.995213i	$0.468843\pi$
$277$	−3748.17	+	6492.02i	−0.813017	+	1.40819i	−0.910743	+	0.412974i	$0.864490\pi$
$278$		0			0
$279$	703.240	−	1978.57i	0.150903	−	0.424566i
$280$		0			0
$281$		−	745.889i		−	0.158349i	−0.996861	−	0.0791744i	$-0.974772\pi$
$281$		−	745.889i		−	0.158349i	0.996861	−	0.0791744i	$-0.0252284\pi$
$282$		0			0
$283$	−2280.55	−	1316.68i	−0.479027	−	0.276566i	0.240984	−	0.970529i	$-0.422530\pi$
$283$	−2280.55	−	1316.68i	−0.479027	−	0.276566i	−0.720011	+	0.693963i	$0.755863\pi$
$284$		0			0
$285$	−3449.94	−	9368.24i	−0.717040	−	1.94711i
$286$		0			0
$287$	−6333.63	−	635.507i	−1.30266	−	0.130707i
$288$		0			0
$289$	2454.70	+	4251.67i	0.499634	+	0.865392i
$290$		0			0
$291$	233.987	−	281.006i	0.0471359	−	0.0566077i
$292$		0			0
$293$	−889.363			−0.177328			−0.0886640	−	0.996062i	$-0.528260\pi$
$293$	−889.363			−0.177328			−0.0886640	+	0.996062i	$0.528260\pi$
$294$		0			0
$295$	−13294.4			−2.62383
$296$		0			0
$297$	597.530	−	354.083i	0.116742	−	0.0691783i
$298$		0			0
$299$	1392.38	+	2411.68i	0.269309	+	0.466457i
$300$		0			0
$301$	−453.062	−	45.4596i	−0.0867577	−	0.00870515i
$302$		0			0
$303$	1163.16	−	428.345i	0.220534	−	0.0812137i
$304$		0			0
$305$	−5421.75	−	3130.25i	−1.01786	−	0.587664i
$306$		0			0
$307$		−	3995.12i		−	0.742715i	−0.928490	−	0.371357i	$-0.878893\pi$
$307$		−	3995.12i		−	0.742715i	0.928490	−	0.371357i	$-0.121107\pi$
$308$		0			0
$309$	100.275	+	17.2905i	0.0184610	+	0.00318325i
$310$		0			0
$311$	−256.008	+	443.420i	−0.0466782	+	0.0808489i	−0.888420	−	0.459031i	$-0.848197\pi$
$311$	−256.008	+	443.420i	−0.0466782	+	0.0808489i	0.841742	+	0.539879i	$0.181530\pi$
$312$		0			0
$313$	−1271.68	+	734.205i	−0.229647	+	0.132587i	−0.610409	−	0.792086i	$-0.708995\pi$
$313$	−1271.68	+	734.205i	−0.229647	+	0.132587i	0.380762	+	0.924673i	$0.375662\pi$
$314$		0			0
$315$	8143.28	−	5639.42i	1.45658	−	1.00871i
$316$		0			0
$317$	6545.26	−	3778.91i	1.15968	−	0.669542i	0.208453	−	0.978032i	$-0.433157\pi$
$317$	6545.26	−	3778.91i	1.15968	−	0.669542i	0.951227	+	0.308491i	$0.0998239\pi$
$318$		0			0
$319$	−227.766	+	394.502i	−0.0399763	+	0.0692410i
$320$		0			0
$321$	2477.50	+	427.196i	0.430780	+	0.0742796i
$322$		0			0
$323$			183.832i			0.0316677i
$324$		0			0
$325$	−4108.31	−	2371.93i	−0.701194	−	0.404835i
$326$		0			0
$327$	−208.716	+	76.8616i	−0.0352968	+	0.0129983i
$328$		0			0
$329$	−3581.68	−	7943.55i	−0.600196	−	1.33113i
$330$		0			0
$331$	2932.76	+	5079.69i	0.487007	+	0.843520i	0.999888	−	0.0149389i	$-0.00475537\pi$
$331$	2932.76	+	5079.69i	0.487007	+	0.843520i	−0.512882	+	0.858459i	$0.671422\pi$
$332$		0			0
$333$	5116.03	−	4359.21i	0.841911	−	0.717368i
$334$		0			0
$335$	−4631.12			−0.755300
$336$		0			0
$337$	−8489.10			−1.37220			−0.686099	−	0.727508i	$-0.740678\pi$
$337$	−8489.10			−1.37220			−0.686099	+	0.727508i	$0.740678\pi$
$338$		0			0
$339$	−1258.02	+	1510.82i	−0.201553	+	0.242055i
$340$		0			0
$341$	192.511	+	333.439i	0.0305720	+	0.0529523i
$342$		0			0
$343$	−6068.70	−	1877.35i	−0.955333	−	0.295531i
$344$		0			0
$345$	5583.16	+	15161.0i	0.871267	+	2.36591i
$346$		0			0
$347$	−968.873	−	559.379i	−0.149890	−	0.0865390i	0.423179	−	0.906046i	$-0.360914\pi$
$347$	−968.873	−	559.379i	−0.149890	−	0.0865390i	−0.573069	+	0.819507i	$0.694247\pi$
$348$		0			0
$349$		−	2364.44i		−	0.362652i	−0.983423	−	0.181326i	$-0.941961\pi$
$349$		−	2364.44i		−	0.362652i	0.983423	−	0.181326i	$-0.0580389\pi$
$350$		0			0
$351$	−2169.55	−	1219.99i	−0.329921	−	0.185522i
$352$		0			0
$353$	1411.12	−	2444.13i	0.212766	−	0.368522i	−0.739813	−	0.672812i	$-0.765086\pi$
$353$	1411.12	−	2444.13i	0.212766	−	0.368522i	0.952579	+	0.304291i	$0.0984194\pi$
$354$		0			0
$355$	−2611.41	+	1507.70i	−0.390421	+	0.225410i
$356$		0			0
$357$	−176.597	+	45.6280i	−0.0261807	+	0.00676439i
$358$		0			0
$359$	4504.97	−	2600.95i	0.662293	−	0.382375i	−0.130857	−	0.991401i	$-0.541773\pi$
$359$	4504.97	−	2600.95i	0.662293	−	0.382375i	0.793150	+	0.609026i	$0.208440\pi$
$360$		0			0
$361$	1274.15	−	2206.89i	0.185763	−	0.321751i
$362$		0			0
$363$	1153.56	−	6690.00i	0.166794	−	0.967311i
$364$		0			0
$365$			12349.2i			1.77092i
$366$		0			0
$367$	4876.42	+	2815.40i	0.693589	+	0.400444i	0.804955	−	0.593336i	$-0.202189\pi$
$367$	4876.42	+	2815.40i	0.693589	+	0.400444i	−0.111366	+	0.993779i	$0.535523\pi$
$368$		0			0
$369$	1680.51	+	9126.49i	0.237084	+	1.28755i
$370$		0			0
$371$	5987.71	+	4307.33i	0.837915	+	0.602764i
$372$		0			0
$373$	−3422.23	−	5927.47i	−0.475057	−	0.822822i	0.524535	−	0.851389i	$-0.324239\pi$
$373$	−3422.23	−	5927.47i	−0.475057	−	0.822822i	−0.999592	+	0.0285664i	$0.990906\pi$
$374$		0			0
$375$	−11262.9	−	9378.32i	−1.55096	−	1.29145i
$376$		0			0
$377$	1632.45			0.223012
$378$		0			0
$379$	−5690.62			−0.771260			−0.385630	−	0.922654i	$-0.626016\pi$
$379$	−5690.62			−0.771260			−0.385630	+	0.922654i	$0.626016\pi$
$380$		0			0
$381$	−450.441	−	375.071i	−0.0605690	−	0.0504343i
$382$		0			0
$383$	−2151.66	−	3726.78i	−0.287062	−	0.497206i	0.686045	−	0.727559i	$-0.259345\pi$
$383$	−2151.66	−	3726.78i	−0.287062	−	0.497206i	−0.973107	+	0.230353i	$0.926012\pi$
$384$		0			0
$385$	−181.328	+	1807.16i	−0.0240035	+	0.239225i
$386$		0			0
$387$	120.212	+	652.844i	0.0157900	+	0.0857517i
$388$		0			0
$389$	−6143.61	−	3547.01i	−0.800754	−	0.462315i	0.0429809	−	0.999076i	$-0.486315\pi$
$389$	−6143.61	−	3547.01i	−0.800754	−	0.462315i	−0.843735	+	0.536760i	$0.819648\pi$
$390$		0			0
$391$		−	297.501i		−	0.0384790i
$392$		0			0
$393$	−1396.69	+	8100.02i	−0.179271	+	1.03967i
$394$		0			0
$395$	−2994.91	+	5187.34i	−0.381494	+	0.660768i
$396$		0			0
$397$	3898.27	−	2250.67i	0.492817	−	0.284528i	−0.232925	−	0.972495i	$-0.574830\pi$
$397$	3898.27	−	2250.67i	0.492817	−	0.284528i	0.725742	+	0.687967i	$0.241496\pi$
$398$		0			0
$399$	8993.82	+	2496.43i	1.12846	+	0.313227i
$400$		0			0
$401$	6038.64	−	3486.41i	0.752008	−	0.434172i	−0.0744107	−	0.997228i	$-0.523708\pi$
$401$	6038.64	−	3486.41i	0.752008	−	0.434172i	0.826419	+	0.563055i	$0.190374\pi$
$402$		0			0
$403$	689.886	−	1194.92i	0.0852746	−	0.147700i
$404$		0			0
$405$	−11201.3	−	9113.89i	−1.37432	−	1.11820i
$406$		0			0
$407$			1232.42i			0.150095i
$408$		0			0
$409$	12431.9	+	7177.56i	1.50298	+	0.867745i	0.999994	+	0.00344923i	$0.00109793\pi$
$409$	12431.9	+	7177.56i	1.50298	+	0.867745i	0.502984	+	0.864296i	$0.332235\pi$
$410$		0			0
$411$	3311.92	+	8993.45i	0.397481	+	1.07935i
$412$		0			0
$413$	7258.43	−	10090.1i	0.864804	−	1.20218i
$414$		0			0
$415$	8482.52	+	14692.2i	1.00335	+	1.73785i
$416$		0			0
$417$	−185.755	+	223.082i	−0.0218141	+	0.0261975i
$418$		0			0
$419$	14839.8			1.73024			0.865122	−	0.501562i	$-0.167241\pi$
$419$	14839.8			1.73024			0.865122	+	0.501562i	$0.167241\pi$
$420$		0			0
$421$	−11073.0			−1.28187			−0.640935	−	0.767595i	$-0.721453\pi$
$421$	−11073.0			−1.28187			−0.640935	+	0.767595i	$0.721453\pi$
$422$		0			0
$423$	−9669.31	+	8238.93i	−1.11144	+	0.947023i
$424$		0			0
$425$	253.398	+	438.899i	0.0289215	+	0.0500934i
$426$		0			0
$427$	5335.92	−	2405.92i	0.604738	−	0.272671i
$428$		0			0
$429$	428.271	−	157.715i	0.0481984	−	0.0177495i
$430$		0			0
$431$	−5552.06	−	3205.49i	−0.620495	−	0.358243i	0.156566	−	0.987667i	$-0.449957\pi$
$431$	−5552.06	−	3205.49i	−0.620495	−	0.358243i	−0.777062	+	0.629424i	$0.783291\pi$
$432$		0			0
$433$		−	12881.0i		−	1.42961i	−0.699322	−	0.714807i	$-0.746514\pi$
$433$		−	12881.0i		−	1.42961i	0.699322	−	0.714807i	$-0.253486\pi$
$434$		0			0
$435$	9333.23	+	1609.33i	1.02872	+	0.177383i
$436$		0			0
$437$	−7612.09	+	13184.5i	−0.833262	+	1.44325i
$438$		0			0
$439$	8024.85	−	4633.15i	0.872449	−	0.503709i	0.00428790	−	0.999991i	$-0.498635\pi$
$439$	8024.85	−	4633.15i	0.872449	−	0.503709i	0.868161	+	0.496282i	$0.165302\pi$
$440$		0			0
$441$	−165.872	+	9259.51i	−0.0179108	+	0.999840i
$442$		0			0
$443$	−7691.54	+	4440.71i	−0.824912	+	0.476263i	−0.852108	−	0.523367i	$-0.824676\pi$
$443$	−7691.54	+	4440.71i	−0.824912	+	0.476263i	0.0271952	+	0.999630i	$0.491342\pi$
$444$		0			0
$445$	−8984.83	+	15562.2i	−0.957128	+	1.65779i
$446$		0			0
$447$	17449.7	+	3008.86i	1.84640	+	0.318376i
$448$		0			0
$449$		−	6080.93i		−	0.639147i	−0.947562	−	0.319573i	$-0.896460\pi$
$449$		−	6080.93i		−	0.639147i	0.947562	−	0.319573i	$-0.103540\pi$
$450$		0			0
$451$	−1473.59	−	850.778i	−0.153855	−	0.0888283i
$452$		0			0
$453$	15875.3	−	5846.21i	1.64655	−	0.606356i
$454$		0			0
$455$	5933.43	−	2675.33i	0.611348	−	0.275652i
$456$		0			0
$457$	−278.827	−	482.943i	−0.0285404	−	0.0494335i	0.851402	−	0.524513i	$-0.175753\pi$
$457$	−278.827	−	482.943i	−0.0285404	−	0.0494335i	−0.879943	+	0.475080i	$0.842419\pi$
$458$		0			0
$459$	135.558	+	228.761i	0.0137850	+	0.0232629i
$460$		0			0
$461$	7422.24			0.749866			0.374933	−	0.927052i	$-0.377666\pi$
$461$	7422.24			0.749866			0.374933	+	0.927052i	$0.377666\pi$
$462$		0			0
$463$	−10478.8			−1.05182			−0.525908	−	0.850541i	$-0.676274\pi$
$463$	−10478.8			−1.05182			−0.525908	+	0.850541i	$0.676274\pi$
$464$		0			0
$465$	5122.29	−	6151.60i	0.510840	−	0.613492i
$466$		0			0
$467$	−4708.74	−	8155.78i	−0.466584	−	0.808147i	0.532688	−	0.846312i	$-0.321182\pi$
$467$	−4708.74	−	8155.78i	−0.466584	−	0.808147i	−0.999271	+	0.0381650i	$0.987849\pi$
$468$		0			0
$469$	2528.48	−	3514.90i	0.248943	−	0.346062i
$470$		0			0
$471$	4561.04	+	12385.4i	0.446203	+	1.21166i
$472$		0			0
$473$	−105.410	−	60.8586i	−0.0102469	−	0.00591603i
$474$		0			0
$475$		−	25934.5i		−	2.50517i
$476$		0			0
$477$	3601.30	−	10132.3i	0.345686	−	0.972588i
$478$		0			0
$479$	5303.15	−	9185.32i	0.505860	−	0.876176i	−0.494117	−	0.869396i	$-0.664508\pi$
$479$	5303.15	−	9185.32i	0.505860	−	0.876176i	0.999977	−	0.00678003i	$-0.00215817\pi$
$480$		0			0
$481$	3824.81	−	2208.25i	0.362570	−	0.209330i
$482$		0			0
$483$	−14555.0	−	4040.06i	−1.37117	−	0.380599i
$484$		0			0
$485$	1207.25	−	697.005i	0.113027	−	0.0652564i
$486$		0			0
$487$	−6387.19	+	11062.9i	−0.594314	+	1.02938i	0.399329	+	0.916808i	$0.369243\pi$
$487$	−6387.19	+	11062.9i	−0.594314	+	1.02938i	−0.993643	+	0.112575i	$0.964090\pi$
$488$		0			0
$489$	−1523.70	+	8836.61i	−0.140908	+	0.817188i
$490$		0			0
$491$		−	18689.8i		−	1.71784i	−0.512110	−	0.858920i	$-0.671136\pi$
$491$		−	18689.8i		−	1.71784i	0.512110	−	0.858920i	$-0.328864\pi$
$492$		0			0
$493$	−151.033	−	87.1988i	−0.0137975	−	0.00796600i
$494$		0			0
$495$	2604.04	−	479.497i	0.236451	−	0.0435390i
$496$		0			0
$497$	281.466	−	2805.16i	0.0254033	−	0.253176i
$498$		0			0
$499$	−6862.74	−	11886.6i	−0.615668	−	1.06637i	−0.990267	−	0.139182i	$-0.955553\pi$
$499$	−6862.74	−	11886.6i	−0.615668	−	1.06637i	0.374599	−	0.927187i	$-0.377780\pi$
$500$		0			0
$501$	−1939.13	−	1614.66i	−0.172922	−	0.143988i
$502$		0			0
$503$	−5480.28			−0.485793			−0.242896	−	0.970052i	$-0.578098\pi$
$503$	−5480.28			−0.485793			−0.242896	+	0.970052i	$0.578098\pi$
$504$		0			0
$505$	4725.34			0.416386
$506$		0			0
$507$	7515.96	+	6258.36i	0.658374	+	0.548212i
$508$		0			0
$509$	−5331.28	−	9234.05i	−0.464253	−	0.804111i	0.534914	−	0.844906i	$-0.320344\pi$
$509$	−5331.28	−	9234.05i	−0.464253	−	0.804111i	−0.999168	+	0.0407959i	$0.987011\pi$
$510$		0			0
$511$	−9372.71	−	6742.37i	−0.811398	−	0.583689i
$512$		0			0
$513$	−154.368	−	13606.6i	−0.0132856	−	1.17105i
$514$		0			0
$515$	335.942	+	193.956i	0.0287444	+	0.0165956i
$516$		0			0
$517$		−	2329.28i		−	0.198146i
$518$		0			0
$519$	1283.01	−	7440.75i	0.108512	−	0.629311i
$520$		0			0
$521$	−5750.00	+	9959.29i	−0.483517	+	0.837475i	−0.999821	−	0.0189300i	$-0.993974\pi$
$521$	−5750.00	+	9959.29i	−0.483517	+	0.837475i	0.516304	+	0.856405i	$0.327307\pi$
$522$		0			0
$523$	−8319.57	+	4803.31i	−0.695582	+	0.401594i	−0.805700	−	0.592324i	$-0.798211\pi$
$523$	−8319.57	+	4803.31i	−0.695582	+	0.401594i	0.110118	+	0.993919i	$0.464877\pi$
$524$		0			0
$525$	24913.9	−	6437.09i	2.07111	−	0.535119i
$526$		0			0
$527$	−127.655	+	73.7018i	−0.0105517	+	0.00609203i
$528$		0			0
$529$	6235.42	−	10800.1i	0.512486	−	0.887653i
$530$		0			0
$531$	−17074.2	−	6068.67i	−1.39540	−	0.495966i
$532$		0			0
$533$			6097.72i			0.495538i
$534$		0			0
$535$	8300.10	+	4792.07i	0.670738	+	0.387251i
$536$		0			0
$537$	−2279.60	−	6190.22i	−0.183188	−	0.497444i
$538$		0			0
$539$	−1272.58	−	1124.29i	−0.101696	−	0.0898452i
$540$		0			0
$541$	8782.28	+	15211.3i	0.697929	+	1.20885i	0.969183	+	0.246341i	$0.0792282\pi$
$541$	8782.28	+	15211.3i	0.697929	+	1.20885i	−0.271254	+	0.962508i	$0.587438\pi$
$542$		0			0
$543$	10936.6	−	13134.3i	0.864336	−	1.03802i
$544$		0			0
$545$	−847.909			−0.0666430
$546$		0			0
$547$	14541.1			1.13662			0.568311	−	0.822814i	$-0.307597\pi$
$547$	14541.1			1.13662			0.568311	+	0.822814i	$0.307597\pi$
$548$		0			0
$549$	−5534.33	−	6495.16i	−0.430236	−	0.504930i
$550$		0			0
$551$	4462.26	+	7728.87i	0.345007	+	0.597570i
$552$		0			0
$553$	−2301.90	−	5105.22i	−0.177010	−	0.392578i
$554$		0			0
$555$	24044.6	−	8854.64i	1.83899	−	0.677223i
$556$		0			0
$557$	11945.8	+	6896.92i	0.908726	+	0.524653i	0.880021	−	0.474935i	$-0.157528\pi$
$557$	11945.8	+	6896.92i	0.908726	+	0.524653i	0.0287052	+	0.999588i	$0.490862\pi$
$558$		0			0
$559$			436.187i			0.0330031i
$560$		0			0
$561$	−48.0478	−	8.28490i	−0.00361600	−	0.000623509i
$562$		0			0
$563$	−4598.06	+	7964.08i	−0.344201	+	0.596174i	−0.985208	−	0.171361i	$-0.945184\pi$
$563$	−4598.06	+	7964.08i	−0.344201	+	0.596174i	0.641007	+	0.767535i	$0.278517\pi$
$564$		0			0
$565$	−6490.74	+	3747.43i	−0.483305	+	0.279036i
$566$		0			0
$567$	13032.8	−	3525.53i	0.965305	−	0.261126i
$568$		0			0
$569$	−15644.0	+	9032.06i	−1.15260	+	0.665455i	−0.949520	−	0.313707i	$-0.898429\pi$
$569$	−15644.0	+	9032.06i	−1.15260	+	0.665455i	−0.203082	+	0.979162i	$0.565096\pi$
$570$		0			0
$571$	7626.26	−	13209.1i	0.558930	−	0.968095i	−0.438656	−	0.898655i	$-0.644545\pi$
$571$	7626.26	−	13209.1i	0.558930	−	0.968095i	0.997586	−	0.0694402i	$-0.0221213\pi$
$572$		0			0
$573$	10131.2	+	1746.93i	0.738636	+	0.127363i
$574$		0			0
$575$			41970.8i			3.04401i
$576$		0			0
$577$	−4709.42	−	2718.99i	−0.339785	−	0.196175i	0.320392	−	0.947285i	$-0.396185\pi$
$577$	−4709.42	−	2718.99i	−0.339785	−	0.196175i	−0.660177	+	0.751110i	$0.729519\pi$
$578$		0			0
$579$	4485.20	−	1651.71i	0.321932	−	0.118554i
$580$		0			0
$581$	−15782.2	−	1583.56i	−1.12695	−	0.113076i
$582$		0			0
$583$	985.851	+	1707.54i	0.0700339	+	0.121302i
$584$		0			0
$585$	−6154.06	−	7222.48i	−0.434939	−	0.510449i
$586$		0			0
$587$	−23972.1			−1.68558			−0.842791	−	0.538241i	$-0.819089\pi$
$587$	−23972.1			−1.68558			−0.842791	+	0.538241i	$0.819089\pi$
$588$		0			0
$589$	7543.15			0.527691
$590$		0			0
$591$	10180.9	−	12226.8i	0.708608	−	0.851001i
$592$		0			0
$593$	697.071	+	1207.36i	0.0482720	+	0.0836095i	0.889152	−	0.457612i	$-0.151295\pi$
$593$	697.071	+	1207.36i	0.0482720	+	0.0836095i	−0.840880	+	0.541222i	$0.817962\pi$
$594$		0			0
$595$	−691.861	−	69.4203i	−0.0476698	−	0.00478312i
$596$		0			0
$597$	936.343	+	2542.62i	0.0641909	+	0.174309i
$598$		0			0
$599$	20811.2	+	12015.4i	1.41957	+	0.819591i	0.996261	−	0.0863929i	$-0.0275340\pi$
$599$	20811.2	+	12015.4i	1.41957	+	0.819591i	0.423312	+	0.905984i	$0.360867\pi$
$600$		0			0
$601$		−	10741.9i		−	0.729073i	−0.931189	−	0.364536i	$-0.881227\pi$
$601$		−	10741.9i		−	0.729073i	0.931189	−	0.364536i	$-0.118773\pi$
$602$		0			0
$603$	−5947.83	−	2114.03i	−0.401682	−	0.142769i
$604$		0			0
$605$	12940.0	−	22412.8i	0.869566	−	1.50613i
$606$		0			0
$607$	−23506.4	+	13571.4i	−1.57182	+	0.907492i	−0.575876	+	0.817537i	$0.695339\pi$
$607$	−23506.4	+	13571.4i	−1.57182	+	0.907492i	−0.995946	+	0.0899549i	$0.971328\pi$
$608$		0			0
$609$	−6317.16	+	6205.01i	−0.420335	+	0.412873i
$610$		0			0
$611$	−7228.91	+	4173.61i	−0.478642	+	0.276344i
$612$		0			0
$613$	−14388.2	+	24921.1i	−0.948015	+	1.64201i	−0.198415	+	0.980118i	$0.563579\pi$
$613$	−14388.2	+	24921.1i	−0.948015	+	1.64201i	−0.749600	+	0.661891i	$0.769754\pi$
$614$		0			0
$615$	−6011.37	+	34862.6i	−0.394149	+	2.28585i
$616$		0			0
$617$		−	2160.03i		−	0.140939i	−0.997514	−	0.0704697i	$-0.977550\pi$
$617$		−	2160.03i		−	0.140939i	0.997514	−	0.0704697i	$-0.0224498\pi$
$618$		0			0
$619$	−2505.32	−	1446.45i	−0.162677	−	0.0939218i	0.416451	−	0.909158i	$-0.363274\pi$
$619$	−2505.32	−	1446.45i	−0.162677	−	0.0939218i	−0.579128	+	0.815236i	$0.696607\pi$
$620$		0			0
$621$	249.820	+	22020.1i	0.0161432	+	1.42292i
$622$		0			0
$623$	−6905.77	−	15315.8i	−0.444099	−	0.984936i
$624$		0			0
$625$	−11224.4	−	19441.3i	−0.718364	−	1.24424i
$626$		0			0
$627$	1917.37	+	1596.55i	0.122125	+	0.101691i
$628$		0			0
$629$	−471.824			−0.0299092
$630$		0			0
$631$	13779.4			0.869335			0.434667	−	0.900591i	$-0.356866\pi$
$631$	13779.4			0.869335			0.434667	+	0.900591i	$0.356866\pi$
$632$		0			0
$633$	−397.826	−	331.260i	−0.0249797	−	0.0208000i
$634$		0			0
$635$	−1117.27	−	1935.17i	−0.0698229	−	0.120937i
$636$		0			0
$637$	−1209.01	+	5963.98i	−0.0752002	+	0.370960i
$638$		0			0
$639$	−4042.12	+	744.298i	−0.250241	+	0.0460782i
$640$		0			0
$641$	12252.1	+	7073.73i	0.754957	+	0.435875i	0.827482	−	0.561492i	$-0.189772\pi$
$641$	12252.1	+	7073.73i	0.754957	+	0.435875i	−0.0725251	+	0.997367i	$0.523106\pi$
$642$		0			0
$643$		−	4248.35i		−	0.260557i	−0.991477	−	0.130279i	$-0.958413\pi$
$643$		−	4248.35i		−	0.260557i	0.991477	−	0.130279i	$-0.0415872\pi$
$644$		0			0
$645$	−430.010	+	2493.82i	−0.0262506	+	0.152239i
$646$		0			0
$647$	8314.83	−	14401.7i	0.505239	−	0.875100i	−0.494742	−	0.869040i	$-0.664738\pi$
$647$	8314.83	−	14401.7i	0.505239	−	0.875100i	0.999982	−	0.00606041i	$-0.00192910\pi$
$648$		0			0
$649$	2877.44	−	1661.29i	0.174036	−	0.100480i
$650$		0			0
$651$	1872.25	+	7246.30i	0.112718	+	0.436260i
$652$		0			0
$653$	−26164.5	+	15106.1i	−1.56798	+	0.905276i	−0.571581	+	0.820546i	$0.693670\pi$
$653$	−26164.5	+	15106.1i	−1.56798	+	0.905276i	−0.996404	+	0.0847307i	$0.972997\pi$
$654$		0			0
$655$	−15667.4	+	27136.7i	−0.934617	+	1.61880i
$656$		0			0
$657$	−5637.20	+	15860.3i	−0.334746	+	0.941809i
$658$		0			0
$659$		−	533.821i		−	0.0315549i	−0.999876	−	0.0157775i	$-0.994978\pi$
$659$		−	533.821i		−	0.0315549i	0.999876	−	0.0157775i	$-0.00502233\pi$
$660$		0			0
$661$	−6638.24	−	3832.59i	−0.390617	−	0.225523i	0.291811	−	0.956476i	$-0.405742\pi$
$661$	−6638.24	−	3832.59i	−0.390617	−	0.225523i	−0.682427	+	0.730954i	$0.739076\pi$
$662$		0			0
$663$	60.3801	+	163.961i	0.00353691	+	0.00960441i
$664$		0			0
$665$	28885.3	+	20779.0i	1.68440	+	1.21169i
$666$		0			0
$667$	−7221.45	−	12507.9i	−0.419214	−	0.726099i
$668$		0			0
$669$	5926.02	−	7116.84i	0.342471	−	0.411290i
$670$		0			0
$671$	1564.64			0.0900184
$672$		0			0
$673$	−28054.4			−1.60686			−0.803430	−	0.595400i	$-0.796994\pi$
$673$	−28054.4			−1.60686			−0.803430	+	0.595400i	$0.796994\pi$
$674$		0			0
$675$	−19124.3	−	32273.1i	−1.09051	−	1.84028i
$676$		0			0
$677$	−5256.30	−	9104.19i	−0.298399	−	0.516842i	0.677371	−	0.735642i	$-0.263119\pi$
$677$	−5256.30	−	9104.19i	−0.298399	−	0.516842i	−0.975770	+	0.218799i	$0.929786\pi$
$678$		0			0
$679$	−130.121	+	1296.82i	−0.00735431	+	0.0732949i
$680$		0			0
$681$	16788.9	−	6182.66i	0.944717	−	0.347900i
$682$		0			0
$683$	15679.7	+	9052.66i	0.878427	+	0.507160i	0.870140	−	0.492805i	$-0.164029\pi$
$683$	15679.7	+	9052.66i	0.878427	+	0.507160i	0.00828788	+	0.999966i	$0.497362\pi$
$684$		0			0
$685$			36535.8i			2.03790i
$686$		0			0
$687$	−27830.0	−	4798.73i	−1.54553	−	0.266496i
$688$		0			0
$689$	3532.91	−	6119.18i	0.195346	−	0.338348i
$690$		0			0
$691$	−7660.53	+	4422.81i	−0.421737	+	0.243490i	−0.695820	−	0.718216i	$-0.744959\pi$
$691$	−7660.53	+	4422.81i	−0.421737	+	0.243490i	0.274083	+	0.961706i	$0.411626\pi$
$692$		0			0
$693$	−1057.82	+	2238.19i	−0.0579845	+	0.122687i
$694$		0			0
$695$	−958.398	+	553.331i	−0.0523080	+	0.0302001i
$696$		0			0
$697$	325.715	−	564.156i	0.0177006	−	0.0306584i
$698$		0			0
$699$	−22559.0	−	3889.87i	−1.22069	−	0.210484i
$700$		0			0
$701$		−	32985.2i		−	1.77723i	−0.458658	−	0.888613i	$-0.651670\pi$
$701$		−	32985.2i		−	1.77723i	0.458658	−	0.888613i	$-0.348330\pi$
$702$		0			0
$703$	20910.1	+	12072.4i	1.12182	+	0.647682i
$704$		0			0
$705$	−45444.4	+	16735.3i	−2.42771	+	0.894026i
$706$		0			0
$707$	−2579.92	+	3586.41i	−0.137239	+	0.190779i
$708$		0			0
$709$	−7996.91	−	13851.1i	−0.423597	−	0.733692i	0.572691	−	0.819771i	$-0.305899\pi$
$709$	−7996.91	−	13851.1i	−0.423597	−	0.733692i	−0.996288	+	0.0860795i	$0.972566\pi$
$710$		0			0
$711$	−6214.34	+	5295.05i	−0.327786	+	0.279297i
$712$		0			0
$713$	−12207.4			−0.641191
$714$		0			0
$715$	1739.85			0.0910024
$716$		0			0
$717$	−6717.36	+	8067.20i	−0.349881	+	0.420188i
$718$		0			0
$719$	−10462.3	−	18121.2i	−0.542668	−	0.939928i	−0.998750	−	0.0499905i	$-0.984081\pi$
$719$	−10462.3	−	18121.2i	−0.542668	−	0.939928i	0.456082	−	0.889938i	$-0.349252\pi$
$720$		0			0
$721$	−330.623	+	149.075i	−0.0170778	+	0.00770021i
$722$		0			0
$723$	−4078.05	−	11073.9i	−0.209771	−	0.569629i
$724$		0			0
$725$	21307.4	+	12301.8i	1.09150	+	0.630176i
$726$		0			0
$727$			21598.1i			1.10183i	0.834562	+	0.550915i	$0.185721\pi$
$727$			21598.1i			1.10183i	−0.834562	+	0.550915i	$0.814279\pi$
$728$		0			0
$729$	−10225.7	−	16818.3i	−0.519519	−	0.854459i
$730$		0			0
$731$	23.2993	−	40.3557i	0.00117887	−	0.00204187i
$732$		0			0
$733$	8894.03	−	5134.97i	0.448170	−	0.258751i	−0.258887	−	0.965908i	$-0.583356\pi$
$733$	8894.03	−	5134.97i	0.448170	−	0.258751i	0.707057	+	0.707157i	$0.250022\pi$
$734$		0			0
$735$	−12791.8	+	32906.0i	−0.641949	+	1.65137i
$736$		0			0
$737$	1002.36	−	578.713i	0.0500982	−	0.0289242i
$738$		0			0
$739$	−9022.60	+	15627.6i	−0.449123	+	0.777903i	−0.998329	−	0.0577833i	$-0.981597\pi$
$739$	−9022.60	+	15627.6i	−0.449123	+	0.777903i	0.549206	+	0.835687i	$0.314930\pi$
$740$		0			0
$741$	1519.33	−	8811.28i	0.0753226	−	0.436829i
$742$		0			0
$743$		−	29700.6i		−	1.46650i	−0.679960	−	0.733249i	$-0.738003\pi$
$743$		−	29700.6i		−	1.46650i	0.679960	−	0.733249i	$-0.261997\pi$
$744$		0			0
$745$	58459.8	+	33751.8i	2.87490	+	1.65983i
$746$		0			0
$747$	4187.52	+	22741.5i	0.205105	+	1.11388i
$748$		0			0
$749$	−8168.70	+	3683.20i	−0.398502	+	0.179681i
$750$		0			0
$751$	−9431.09	−	16335.1i	−0.458249	−	0.793711i	0.540619	−	0.841267i	$-0.318190\pi$
$751$	−9431.09	−	16335.1i	−0.458249	−	0.793711i	−0.998869	+	0.0475563i	$0.984857\pi$
$752$		0			0
$753$	−18022.8	−	15007.2i	−0.872228	−	0.726283i
$754$		0			0
$755$	64493.3			3.10881
$756$		0			0
$757$	12141.1			0.582929			0.291464	−	0.956582i	$-0.405858\pi$
$757$	12141.1			0.582929			0.291464	+	0.956582i	$0.405858\pi$
$758$		0			0
$759$	−3102.96	−	2583.76i	−0.148393	−	0.123563i
$760$		0			0
$761$	−12563.5	−	21760.6i	−0.598457	−	1.03656i	−0.993049	−	0.117702i	$-0.962447\pi$
$761$	−12563.5	−	21760.6i	−0.598457	−	1.03656i	0.394592	−	0.918856i	$-0.370886\pi$
$762$		0			0
$763$	462.938	−	643.540i	0.0219652	−	0.0305343i
$764$		0			0
$765$	183.573	+	996.943i	0.00867593	+	0.0471170i
$766$		0			0
$767$	−10311.6	−	5953.43i	−0.485439	−	0.280268i
$768$		0			0
$769$		−	23475.2i		−	1.10083i	−0.834892	−	0.550413i	$-0.814470\pi$
$769$		−	23475.2i		−	1.10083i	0.834892	−	0.550413i	$-0.185530\pi$
$770$		0			0
$771$	−5243.47	+	30409.2i	−0.244927	+	1.42044i
$772$		0			0
$773$	15695.6	−	27185.6i	0.730313	−	1.26494i	−0.226436	−	0.974026i	$-0.572708\pi$
$773$	15695.6	−	27185.6i	0.730313	−	1.26494i	0.956749	−	0.290913i	$-0.0939592\pi$
$774$		0			0
$775$	18009.3	−	10397.7i	0.834727	−	0.481930i
$776$		0			0
$777$	−6407.36	+	23083.6i	−0.295834	+	1.06579i
$778$		0			0
$779$	−28869.8	+	16668.0i	−1.32781	+	0.766614i
$780$		0			0
$781$	376.809	−	652.653i	0.0172641	−	0.0299024i
$782$		0			0
$783$	11252.2	+	6327.35i	0.513563	+	0.288788i
$784$		0			0
$785$			50315.7i			2.28770i
$786$		0			0
$787$	4012.16	+	2316.42i	0.181726	+	0.104919i	0.588103	−	0.808786i	$-0.299875\pi$
$787$	4012.16	+	2316.42i	0.181726	+	0.104919i	−0.406378	+	0.913705i	$0.633208\pi$
$788$		0			0
$789$	9801.51	+	26615.8i	0.442260	+	1.20095i
$790$		0			0
$791$	699.591	−	6972.30i	0.0314470	−	0.313409i
$792$		0			0
$793$	−2803.54	−	4855.87i	−0.125544	−	0.217449i
$794$		0			0
$795$	26231.3	−	31502.4i	1.17022	−	1.40538i
$796$		0			0
$797$	−121.248			−0.00538874			−0.00269437	−	0.999996i	$-0.500858\pi$
$797$	−121.248			−0.00538874			−0.00269437	+	0.999996i	$0.500858\pi$
$798$		0			0
$799$	891.749			0.0394841
$800$		0			0
$801$	−18643.2	+	15885.3i	−0.822379	+	0.700725i
$802$		0			0
$803$	−1543.18	−	2672.86i	−0.0678176	−	0.117464i
$804$		0			0
$805$	−46746.2	−	33627.4i	−2.04669	−	1.47231i
$806$		0			0
$807$	−25769.4	+	9489.81i	−1.12407	+	0.413949i
$808$		0			0
$809$	11357.9	+	6557.47i	0.493599	+	0.284979i	0.726066	−	0.687625i	$-0.241347\pi$
$809$	11357.9	+	6557.47i	0.493599	+	0.284979i	−0.232467	+	0.972604i	$0.574680\pi$
$810$		0			0
$811$			2601.55i			0.112642i	0.998413	+	0.0563211i	$0.0179371\pi$
$811$			2601.55i			0.112642i	−0.998413	+	0.0563211i	$0.982063\pi$
$812$		0			0
$813$	32146.0	+	5542.95i	1.38673	+	0.239114i
$814$		0			0
$815$	−17092.1	+	29604.4i	−0.734613	+	1.27239i
$816$		0			0
$817$	−2065.14	+	1192.31i	−0.0884333	+	0.0510570i
$818$		0			0
$819$	8841.64	−	727.463i	0.377230	−	0.0310374i
$820$		0			0
$821$	−13977.1	+	8069.68i	−0.594158	+	0.343038i	−0.766740	−	0.641958i	$-0.778122\pi$
$821$	−13977.1	+	8069.68i	−0.594158	+	0.343038i	0.172582	+	0.984995i	$0.444789\pi$
$822$		0			0
$823$	9786.73	−	16951.1i	0.414513	−	0.717957i	−0.580864	−	0.814000i	$-0.697285\pi$
$823$	9786.73	−	16951.1i	0.414513	−	0.717957i	0.995377	+	0.0960431i	$0.0306187\pi$
$824$		0			0
$825$	6778.47	+	1168.81i	0.286056	+	0.0493247i
$826$		0			0
$827$		−	19041.3i		−	0.800641i	−0.916375	−	0.400320i	$-0.868899\pi$
$827$		−	19041.3i		−	0.800641i	0.916375	−	0.400320i	$-0.131101\pi$
$828$		0			0
$829$	−4754.65	−	2745.10i	−0.199199	−	0.115007i	0.397083	−	0.917783i	$-0.370023\pi$
$829$	−4754.65	−	2745.10i	−0.199199	−	0.115007i	−0.596282	+	0.802775i	$0.703356\pi$
$830$		0			0
$831$	−36552.4	+	13460.7i	−1.52586	+	0.561911i
$832$		0			0
$833$	430.427	−	487.202i	0.0179033	−	0.0202647i
$834$		0			0
$835$	−4809.80	−	8330.82i	−0.199341	−	0.345269i
$836$		0			0
$837$	9386.74	−	5562.36i	0.387638	−	0.229705i
$838$		0			0
$839$	−25774.7			−1.06060			−0.530299	−	0.847811i	$-0.677920\pi$
$839$	−25774.7			−1.06060			−0.530299	+	0.847811i	$0.677920\pi$
$840$		0			0
$841$	15922.5			0.652854
$842$		0			0
$843$	2480.04	−	2978.40i	0.101325	−	0.121686i
$844$		0			0
$845$	18642.5	+	32289.8i	0.758962	+	1.31456i
$846$		0			0
$847$	9945.75	+	22058.0i	0.403471	+	0.894830i
$848$		0			0
$849$	−4728.56	−	12840.3i	−0.191147	−	0.519056i
$850$		0			0
$851$	−33839.5	−	19537.3i	−1.36311	−	0.786990i
$852$		0			0
$853$			15407.3i			0.618447i	0.950989	+	0.309224i	$0.100069\pi$
$853$			15407.3i			0.618447i	−0.950989	+	0.309224i	$0.899931\pi$
$854$		0			0
$855$	17373.0	−	48879.0i	0.694906	−	1.95512i
$856$		0			0
$857$	5708.14	−	9886.78i	0.227522	−	0.394079i	−0.729551	−	0.683926i	$-0.760271\pi$
$857$	5708.14	−	9886.78i	0.227522	−	0.394079i	0.957073	+	0.289847i	$0.0936043\pi$
$858$		0			0
$859$	32407.3	−	18710.4i	1.28722	−	0.743178i	0.309064	−	0.951041i	$-0.399984\pi$
$859$	32407.3	−	18710.4i	1.28722	−	0.743178i	0.978158	+	0.207863i	$0.0666510\pi$
$860$		0			0
$861$	−23177.7	−	23596.6i	−0.917414	−	0.933995i
$862$		0			0
$863$	30175.4	−	17421.8i	1.19025	−	0.687189i	0.231884	−	0.972743i	$-0.425511\pi$
$863$	30175.4	−	17421.8i	1.19025	−	0.687189i	0.958362	+	0.285554i	$0.0921777\pi$
$864$		0			0
$865$	14392.2	−	24928.0i	0.565720	−	0.979856i
$866$		0			0
$867$	−4334.74	+	25139.0i	−0.169799	+	0.984737i
$868$		0			0
$869$		−	1496.99i		−	0.0584374i
$870$		0			0
$871$	−3592.07	−	2073.88i	−0.139739	−	0.0806783i
$872$		0			0
$873$	1868.66	−	344.087i	0.0724450	−	0.0133397i
$874$		0			0
$875$	51977.1	+	5215.31i	2.00817	+	0.201497i
$876$		0			0
$877$	14281.1	+	24735.6i	0.549874	+	0.952409i	0.998283	+	0.0585807i	$0.0186575\pi$
$877$	14281.1	+	24735.6i	0.549874	+	0.952409i	−0.448409	+	0.893828i	$0.648009\pi$
$878$		0			0
$879$	−3551.30	−	2957.08i	−0.136271	−	0.113470i
$880$		0			0
$881$	−25098.4			−0.959804			−0.479902	−	0.877322i	$-0.659328\pi$
$881$	−25098.4			−0.959804			−0.479902	+	0.877322i	$0.659328\pi$
$882$		0			0
$883$	32704.3			1.24642			0.623208	−	0.782056i	$-0.285829\pi$
$883$	32704.3			1.24642			0.623208	+	0.782056i	$0.285829\pi$
$884$		0			0
$885$	−53085.8	−	44203.2i	−2.01634	−	1.67896i
$886$		0			0
$887$	11659.7	+	20195.2i	0.441368	+	0.764472i	0.997791	−	0.0664269i	$-0.0211599\pi$
$887$	11659.7	+	20195.2i	0.441368	+	0.764472i	−0.556423	+	0.830899i	$0.687827\pi$
$888$		0			0
$889$	2078.74	+	208.578i	0.0784239	+	0.00786894i
$890$		0			0
$891$	3563.30	+	572.874i	0.133979	+	0.0215399i
$892$		0			0
$893$	−39520.1	−	22816.9i	−1.48095	−	0.855028i
$894$		0			0
$895$		−	25147.7i		−	0.939213i
$896$		0			0
$897$	−2458.79	+	14259.6i	−0.0915236	+	0.530786i
$898$		0			0
$899$	−3578.02	+	6197.32i	−0.132741	+	0.229913i
$900$		0			0
$901$	−653.723	+	377.427i	−0.0241717	+	0.0139555i
$902$		0			0
$903$	−1657.97	−	1687.93i	−0.0611004	−	0.0622047i
$904$		0			0
$905$	56427.1	−	32578.2i	2.07260	−	1.19661i
$906$		0			0
$907$	−18663.6	+	32326.3i	−0.683258	+	1.18344i	0.290723	+	0.956807i	$0.406104\pi$
$907$	−18663.6	+	32326.3i	−0.683258	+	1.18344i	−0.973981	+	0.226631i	$0.927229\pi$
$908$		0			0
$909$	6068.83	+	2157.04i	0.221442	+	0.0787067i
$910$		0			0
$911$			33130.2i			1.20489i	0.798161	+	0.602444i	$0.205806\pi$
$911$			33130.2i			1.20489i	−0.798161	+	0.602444i	$0.794194\pi$
$912$		0			0
$913$	−3671.91	−	2119.98i	−0.133102	−	0.0768467i
$914$		0			0
$915$	−11241.6	−	30526.4i	−0.406159	−	1.10292i
$916$		0			0
$917$	−12042.0	−	26707.1i	−0.433654	−	0.961772i
$918$		0			0
$919$	−11879.4	−	20575.7i	−0.426404	−	0.738553i	0.570146	−	0.821543i	$-0.306886\pi$
$919$	−11879.4	−	20575.7i	−0.426404	−	0.738553i	−0.996550	+	0.0829898i	$0.973553\pi$
$920$		0			0
$921$	13283.5	−	15952.8i	0.475253	−	0.570754i
$922$		0			0
$923$	−2700.68			−0.0963097
$924$		0			0
$925$	66563.8			2.36606
$926$		0			0
$927$	342.918	+	402.452i	0.0121498	+	0.0142592i
$928$		0			0
$929$	−17720.4	−	30692.6i	−0.625819	−	1.08395i	−0.988382	−	0.151991i	$-0.951431\pi$
$929$	−17720.4	−	30692.6i	−0.625819	−	1.08395i	0.362563	−	0.931959i	$-0.381902\pi$
$930$		0			0
$931$	−31541.4	+	10578.3i	−1.11034	+	0.372385i
$932$		0			0
$933$	−2496.61	+	919.398i	−0.0876049	+	0.0322612i
$934$		0			0
$935$	−160.969	−	92.9357i	−0.00563023	−	0.00325061i
$936$		0			0
$937$			42936.0i			1.49697i	0.663154	+	0.748483i	$0.269218\pi$
$937$			42936.0i			1.49697i	−0.663154	+	0.748483i	$0.730782\pi$
$938$		0			0
$939$	−7519.12	−	1296.53i	−0.261318	−	0.0450591i
$940$		0			0
$941$	−16115.3	+	27912.5i	−0.558282	+	0.966972i	0.439359	+	0.898312i	$0.355206\pi$
$941$	−16115.3	+	27912.5i	−0.558282	+	0.966972i	−0.997640	+	0.0686602i	$0.978128\pi$
$942$		0			0
$943$	46721.1	−	26974.4i	1.61341	−	0.931503i
$944$		0			0
$945$	51267.6	+	4557.29i	1.76480	+	0.156877i
$946$		0			0
$947$	−9522.57	+	5497.86i	−0.326760	+	0.188655i	−0.654402	−	0.756147i	$-0.727079\pi$
$947$	−9522.57	+	5497.86i	−0.326760	+	0.188655i	0.327642	+	0.944802i	$0.393746\pi$
$948$		0			0
$949$	−5530.15	+	9578.50i	−0.189164	+	0.327641i
$950$		0			0
$951$	38700.5	+	6673.14i	1.31961	+	0.227541i
$952$		0			0
$953$		−	10083.0i		−	0.342728i	−0.985208	−	0.171364i	$-0.945183\pi$
$953$		−	10083.0i		−	0.342728i	0.985208	−	0.171364i	$-0.0548174\pi$
$954$		0			0
$955$	33941.6	+	19596.2i	1.15008	+	0.663998i
$956$		0			0
$957$	−2221.19	+	817.971i	−0.0750269	+	0.0276293i
$958$		0			0
$959$	−27729.7	−	19947.7i	−0.933721	−	0.671684i
$960$		0			0
$961$	−11871.3	−	20561.7i	−0.398486	−	0.690198i
$962$		0			0
$963$	8472.46	+	9943.38i	0.283511	+	0.332732i
$964$		0			0
$965$	18221.1			0.607832
$966$		0			0
$967$	24809.9			0.825061			0.412530	−	0.910944i	$-0.364645\pi$
$967$	24809.9			0.825061			0.412530	+	0.910944i	$0.364645\pi$
$968$		0			0
$969$	−611.230	+	734.055i	−0.0202637	+	0.0243357i
$970$		0			0
$971$	3033.74	+	5254.60i	0.100265	+	0.173664i	0.911794	−	0.410648i	$-0.134698\pi$
$971$	3033.74	+	5254.60i	0.100265	+	0.173664i	−0.811529	+	0.584313i	$0.801364\pi$
$972$		0			0
$973$	103.299	−	1029.50i	0.00340351	−	0.0339202i
$974$		0			0
$975$	−8518.28	−	23131.3i	−0.279798	−	0.759788i
$976$		0			0
$977$	−11370.3	−	6564.62i	−0.372331	−	0.214965i	0.302146	−	0.953262i	$-0.402297\pi$
$977$	−11370.3	−	6564.62i	−0.372331	−	0.214965i	−0.674476	+	0.738297i	$0.735630\pi$
$978$		0			0
$979$		−	4491.03i		−	0.146613i
$980$		0			0
$981$	−1088.98	−	387.056i	−0.0354420	−	0.0125971i
$982$		0			0
$983$	−13427.3	+	23256.8i	−0.435671	+	0.754605i	−0.997350	−	0.0727505i	$-0.976822\pi$
$983$	−13427.3	+	23256.8i	−0.435671	+	0.754605i	0.561679	+	0.827355i	$0.310156\pi$
$984$		0			0
$985$	52528.2	−	30327.2i	1.69918	−	0.981019i
$986$		0			0
$987$	12109.9	−	43628.2i	0.390540	−	1.40699i
$988$		0			0
$989$	3342.09	−	1929.56i	0.107454	−	0.0620387i
$990$		0			0
$991$	13495.1	−	23374.1i	0.432578	−	0.749247i	−0.564516	−	0.825422i	$-0.690937\pi$
$991$	13495.1	−	23374.1i	0.432578	−	0.749247i	0.997094	+	0.0761745i	$0.0242706\pi$
$992$		0			0
$993$	−5178.94	+	30034.9i	−0.165507	+	0.959849i
$994$		0			0
$995$			10329.4i			0.329109i
$996$		0			0
$997$	12247.7	+	7071.22i	0.389056	+	0.224622i	0.681751	−	0.731584i	$-0.261219\pi$
$997$	12247.7	+	7071.22i	0.389056	+	0.224622i	−0.292695	+	0.956206i	$0.594552\pi$
$998$		0			0
$999$	34922.9	−	396.203i	1.10602	−	0.0125479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.e.17.6		16
3.2	odd	2	inner	336.4.bc.e.17.8		16
4.3	odd	2		42.4.f.a.17.2	yes	16
7.5	odd	6	inner	336.4.bc.e.257.8		16
12.11	even	2		42.4.f.a.17.5	yes	16
21.5	even	6	inner	336.4.bc.e.257.6		16
28.3	even	6		294.4.d.a.293.5		16
28.11	odd	6		294.4.d.a.293.4		16
28.19	even	6		42.4.f.a.5.5	yes	16
28.23	odd	6		294.4.f.a.215.8		16
28.27	even	2		294.4.f.a.227.3		16
84.11	even	6		294.4.d.a.293.13		16
84.23	even	6		294.4.f.a.215.3		16
84.47	odd	6		42.4.f.a.5.2	✓	16
84.59	odd	6		294.4.d.a.293.12		16
84.83	odd	2		294.4.f.a.227.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.2	✓	16	84.47	odd	6
42.4.f.a.5.5	yes	16	28.19	even	6
42.4.f.a.17.2	yes	16	4.3	odd	2
42.4.f.a.17.5	yes	16	12.11	even	2
294.4.d.a.293.4		16	28.11	odd	6
294.4.d.a.293.5		16	28.3	even	6
294.4.d.a.293.12		16	84.59	odd	6
294.4.d.a.293.13		16	84.11	even	6
294.4.f.a.215.3		16	84.23	even	6
294.4.f.a.215.8		16	28.23	odd	6
294.4.f.a.227.3		16	28.27	even	2
294.4.f.a.227.8		16	84.83	odd	2
336.4.bc.e.17.6		16	1.1	even	1	trivial
336.4.bc.e.17.8		16	3.2	odd	2	inner
336.4.bc.e.257.6		16	21.5	even	6	inner
336.4.bc.e.257.8		16	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.99309 + 3.32495i) q^{3} +(9.90442 + 17.1550i) q^{5} +(-18.4277 - 1.84901i) q^{7} +(4.88947 + 26.5536i) q^{9} +(-4.28742 - 2.47535i) q^{11} +17.7414i q^{13} +(-17.4901 + 101.433i) q^{15} +(0.947671 - 1.64141i) q^{17} +(-83.9968 + 48.4956i) q^{19} +(-67.4356 - 68.6545i) q^{21} +(135.935 - 78.4822i) q^{23} +(-133.695 + 231.567i) q^{25} +(-68.7652 + 122.288i) q^{27} -92.0138i q^{29} +(-67.3521 - 38.8857i) q^{31} +(-8.88966 - 24.1397i) q^{33} +(-150.796 - 334.440i) q^{35} +(-124.469 - 215.587i) q^{37} +(-58.9891 + 70.8428i) q^{39} +343.701 q^{41} +24.5859 q^{43} +(-407.099 + 346.877i) q^{45} +(235.248 + 407.461i) q^{47} +(336.162 + 68.1462i) q^{49} +(9.24175 - 3.40335i) q^{51} +(-344.910 - 199.134i) q^{53} -98.0675i q^{55} +(-496.652 - 85.6379i) q^{57} +(-335.568 + 581.220i) q^{59} +(-273.703 + 158.023i) q^{61} +(-41.0038 - 498.363i) q^{63} +(-304.352 + 175.718i) q^{65} +(-116.895 + 202.469i) q^{67} +(803.750 + 138.591i) q^{69} +152.225i q^{71} +(539.897 + 311.709i) q^{73} +(-1303.80 + 480.137i) q^{75} +(74.4305 + 53.5425i) q^{77} +(151.191 + 261.870i) q^{79} +(-681.186 + 259.666i) q^{81} +856.438 q^{83} +37.5446 q^{85} +(305.941 - 367.419i) q^{87} +(453.577 + 785.618i) q^{89} +(32.8040 - 326.933i) q^{91} +(-139.650 - 379.216i) q^{93} +(-1663.88 - 960.642i) q^{95} -70.3731i q^{97} +(44.7661 - 125.950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 80 q^{7} + 18 q^{9} + 342 q^{19} - 450 q^{21} - 194 q^{25} - 804 q^{31} + 1332 q^{33} - 962 q^{37} - 594 q^{39} - 1732 q^{43} - 2394 q^{45} + 820 q^{49} - 1638 q^{51} - 2664 q^{57} - 4620 q^{61}+ \cdots + 4284 q^{99}+O(q^{100}) \) 16 * q - 80 * q^7 + 18 * q^9 + 342 * q^19 - 450 * q^21 - 194 * q^25 - 804 * q^31 + 1332 * q^33 - 962 * q^37 - 594 * q^39 - 1732 * q^43 - 2394 * q^45 + 820 * q^49 - 1638 * q^51 - 2664 * q^57 - 4620 * q^61 + 2016 * q^63 + 706 * q^67 + 3294 * q^73 - 6174 * q^75 + 2656 * q^79 + 126 * q^81 + 5232 * q^85 - 1026 * q^87 - 4098 * q^91 + 2016 * q^93 + 4284 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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