LMFDB - Embedded newform 336.4.bc.e.257.8

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			257.8
Root			$-2.81518 + 1.03671i$ of defining polynomial
Character	$\chi$	$=$	336.257
Dual form			336.4.bc.e.17.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.87603 - 1.79564i) q^{3} +(-9.90442 + 17.1550i) q^{5} +(-18.4277 + 1.84901i) q^{7} +(20.5514 - 17.5112i) q^{9} +(4.28742 - 2.47535i) q^{11} -17.7414i q^{13} +(-17.4901 + 101.433i) q^{15} +(-0.947671 - 1.64141i) q^{17} +(-83.9968 - 48.4956i) q^{19} +(-86.5340 + 42.1054i) q^{21} +(-135.935 - 78.4822i) q^{23} +(-133.695 - 231.567i) q^{25} +(68.7652 - 122.288i) q^{27} -92.0138i q^{29} +(-67.3521 + 38.8857i) q^{31} +(16.4608 - 19.7685i) q^{33} +(150.796 - 334.440i) q^{35} +(-124.469 + 215.587i) q^{37} +(-31.8571 - 86.5074i) q^{39} -343.701 q^{41} +24.5859 q^{43} +(96.8547 + 525.996i) q^{45} +(-235.248 + 407.461i) q^{47} +(336.162 - 68.1462i) q^{49} +(-7.56826 - 6.30191i) q^{51} +(344.910 - 199.134i) q^{53} +98.0675i q^{55} +(-496.652 - 85.6379i) q^{57} +(335.568 + 581.220i) q^{59} +(-273.703 - 158.023i) q^{61} +(-346.336 + 360.691i) q^{63} +(304.352 + 175.718i) q^{65} +(-116.895 - 202.469i) q^{67} +(-803.750 - 138.591i) q^{69} +152.225i q^{71} +(539.897 - 311.709i) q^{73} +(-1067.71 - 889.059i) q^{75} +(-74.4305 + 53.5425i) q^{77} +(151.191 - 261.870i) q^{79} +(115.716 - 719.757i) q^{81} -856.438 q^{83} +37.5446 q^{85} +(-165.224 - 448.662i) q^{87} +(-453.577 + 785.618i) q^{89} +(32.8040 + 326.933i) q^{91} +(-258.586 + 310.548i) q^{93} +(1663.88 - 960.642i) q^{95} +70.3731i q^{97} +(44.7661 - 125.950i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.87603	−	1.79564i	0.938393	−	0.345571i
$3$	4.87603	−	1.79564i	0.938393	−	0.345571i
$4$		0			0
$5$	−9.90442	+	17.1550i	−0.885879	+	1.53439i	−0.0411754	+	0.999152i	$0.513110\pi$
$5$	−9.90442	+	17.1550i	−0.885879	+	1.53439i	−0.844703	+	0.535235i	$0.820223\pi$
$6$		0			0
$7$	−18.4277	+	1.84901i	−0.995004	+	0.0998373i
$7$	−18.4277	+	1.84901i	−0.995004	+	0.0998373i
$8$		0			0
$9$	20.5514	−	17.5112i	0.761161	−	0.648563i
$10$		0			0
$11$	4.28742	−	2.47535i	0.117519	−	0.0678495i	−0.440088	−	0.897954i	$-0.645053\pi$
$11$	4.28742	−	2.47535i	0.117519	−	0.0678495i	0.557607	+	0.830105i	$0.311720\pi$
$12$		0			0
$13$		−	17.7414i		−	0.378505i	−0.981928	−	0.189253i	$-0.939394\pi$
$13$		−	17.7414i		−	0.378505i	0.981928	−	0.189253i	$-0.0606065\pi$
$14$		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	$-0.170970\pi$
$17$	−0.947671	−	1.64141i	−0.0135202	−	0.0234177i	−0.872706	+	0.488245i	$0.837637\pi$
$18$		0			0
$19$	−83.9968	−	48.4956i	−1.01422	−	0.585561i	−0.101796	−	0.994805i	$-0.532459\pi$
$19$	−83.9968	−	48.4956i	−1.01422	−	0.585561i	−0.912425	+	0.409245i	$0.865792\pi$
$20$		0			0
$21$	−86.5340	+	42.1054i	−0.899203	+	0.437531i
$22$		0			0
$23$	−135.935	−	78.4822i	−1.23237	−	0.711508i	−0.264845	−	0.964291i	$-0.585321\pi$
$23$	−135.935	−	78.4822i	−1.23237	−	0.711508i	−0.967523	+	0.252783i	$0.918654\pi$
$24$		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	−0.682255	−	0.731114i	$-0.739001\pi$
$31$	−67.3521	+	38.8857i	−0.390219	+	0.225293i	0.292036	+	0.956407i	$0.405667\pi$
$32$		0			0
$33$	16.4608	−	19.7685i	0.0868319	−	0.104281i
$34$		0			0
$35$	150.796	−	334.440i	0.728264	−	1.61516i
$36$		0			0
$37$	−124.469	+	215.587i	−0.553044	+	0.957901i	0.445009	+	0.895526i	$0.353201\pi$
$37$	−124.469	+	215.587i	−0.553044	+	0.957901i	−0.998053	+	0.0623743i	$0.980133\pi$
$38$		0			0
$39$	−31.8571	−	86.5074i	−0.130800	−	0.355186i
$40$		0			0
$41$	−343.701			−1.30920			−0.654598	−	0.755977i	$-0.727162\pi$
$41$	−343.701			−1.30920			−0.654598	+	0.755977i	$0.727162\pi$
$42$		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
$45$	96.8547	+	525.996i	0.320850	+	1.74246i
$46$		0			0
$47$	−235.248	+	407.461i	−0.730093	+	1.26456i	0.226750	+	0.973953i	$0.427190\pi$
$47$	−235.248	+	407.461i	−0.730093	+	1.26456i	−0.956843	+	0.290606i	$0.906143\pi$
$48$		0			0
$49$	336.162	−	68.1462i	0.980065	−	0.198677i
$50$		0			0
$51$	−7.56826	−	6.30191i	−0.0207798	−	0.0173028i
$52$		0			0
$53$	344.910	−	199.134i	0.893907	−	0.516097i	0.0186885	−	0.999825i	$-0.494051\pi$
$53$	344.910	−	199.134i	0.893907	−	0.516097i	0.875218	+	0.483728i	$0.160718\pi$
$54$		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	0.952286	+	0.305208i	$0.0987261\pi$
$59$	335.568	+	581.220i	0.740461	+	1.28252i	−0.211825	+	0.977308i	$0.567941\pi$
$60$		0			0
$61$	−273.703	−	158.023i	−0.574494	−	0.331684i	0.184448	−	0.982842i	$-0.440950\pi$
$61$	−273.703	−	158.023i	−0.574494	−	0.331684i	−0.758942	+	0.651158i	$0.774284\pi$
$62$		0			0
$63$	−346.336	+	360.691i	−0.692607	+	0.721315i
$64$		0			0
$65$	304.352	+	175.718i	0.580773	+	0.335310i
$66$		0			0
$67$	−116.895	−	202.469i	−0.213150	−	0.369186i	0.739549	−	0.673103i	$-0.235039\pi$
$67$	−116.895	−	202.469i	−0.213150	−	0.369186i	−0.952699	+	0.303917i	$0.901706\pi$
$68$		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	−0.000271580	−	1.00000i	$-0.500086\pi$
$73$	539.897	−	311.709i	0.865618	−	0.499765i	0.865890	+	0.500235i	$0.166753\pi$
$74$		0			0
$75$	−1067.71	−	889.059i	−1.64385	−	1.36880i
$76$		0			0
$77$	−74.4305	+	53.5425i	−0.110158	+	0.0792433i
$78$		0			0
$79$	151.191	−	261.870i	0.215320	−	0.372945i	−0.738052	−	0.674744i	$-0.764254\pi$
$79$	151.191	−	261.870i	0.215320	−	0.372945i	0.953371	+	0.301799i	$0.0975873\pi$
$80$		0			0
$81$	115.716	−	719.757i	0.158733	−	0.987322i
$82$		0			0
$83$	−856.438			−1.13261			−0.566303	−	0.824197i	$-0.691627\pi$
$83$	−856.438			−1.13261			−0.566303	+	0.824197i	$0.691627\pi$
$84$		0			0
$85$	37.5446			0.0479092
$86$		0			0
$87$	−165.224	−	448.662i	−0.203607	−	0.552892i
$88$		0			0
$89$	−453.577	+	785.618i	−0.540214	+	0.935678i	0.458678	+	0.888603i	$0.348323\pi$
$89$	−453.577	+	785.618i	−0.540214	+	0.935678i	−0.998891	+	0.0470750i	$0.985010\pi$
$90$		0			0
$91$	32.8040	+	326.933i	0.0377889	+	0.376614i
$92$		0			0
$93$	−258.586	+	310.548i	−0.288324	+	0.346262i
$94$		0			0
$95$	1663.88	−	960.642i	1.79695	−	1.03747i
$96$		0			0
$97$			70.3731i			0.0736629i	0.999321	+	0.0368315i	$0.0117265\pi$
$97$			70.3731i			0.0736629i	−0.999321	+	0.0368315i	$0.988274\pi$
$98$		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	$-0.204157\pi$
$101$	−119.274	−	206.588i	−0.117507	−	0.203527i	−0.918779	+	0.394772i	$0.870823\pi$
$102$		0			0
$103$	16.9592	+	9.79138i	0.0162237	+	0.00936674i	0.508090	−	0.861304i	$-0.330352\pi$
$103$	16.9592	+	9.79138i	0.0162237	+	0.00936674i	−0.491866	+	0.870671i	$0.663685\pi$
$104$		0			0
$105$	134.753	−	1901.52i	0.125243	−	1.76733i
$106$		0			0
$107$	−419.010	−	241.915i	−0.378572	−	0.218569i	0.298625	−	0.954371i	$-0.403472\pi$
$107$	−419.010	−	241.915i	−0.378572	−	0.218569i	−0.677197	+	0.735802i	$0.736805\pi$
$108$		0			0
$109$	−21.4023	−	37.0698i	−0.0188070	−	0.0325747i	0.856469	−	0.516199i	$-0.172653\pi$
$109$	−21.4023	−	37.0698i	−0.0188070	−	0.0325747i	−0.875276	+	0.483624i	$0.839320\pi$
$110$		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
$117$	−310.672	−	364.609i	−0.245484	−	0.288103i
$118$		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
$123$	−1675.90	+	617.163i	−1.22854	+	0.452421i
$124$		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
$129$	119.882	−	44.1474i	0.0818216	−	0.0301315i
$130$		0			0
$131$	−790.927	+	1369.93i	−0.527508	+	0.913671i	0.471977	+	0.881611i	$0.343540\pi$
$131$	−790.927	+	1369.93i	−0.527508	+	0.913671i	−0.999486	+	0.0320608i	$0.989793\pi$
$132$		0			0
$133$	1637.54	+	738.353i	1.06761	+	0.481378i
$134$		0			0
$135$	1416.77	+	2390.86i	0.903228	+	1.52424i
$136$		0			0
$137$	−1597.31	+	922.210i	−0.996115	+	0.575107i	−0.907097	−	0.420923i	$-0.861706\pi$
$137$	−1597.31	+	922.210i	−0.996115	+	0.575107i	−0.0890187	+	0.996030i	$0.528373\pi$
$138$		0			0
$139$		−	55.8671i		−	0.0340905i	−0.999855	−	0.0170453i	$-0.994574\pi$
$139$		−	55.8671i		−	0.0340905i	0.999855	−	0.0170453i	$-0.00542594\pi$
$140$		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
$147$	1516.77	−	935.910i	0.851029	−	0.525119i
$148$		0			0
$149$	−2951.20	−	1703.87i	−1.62263	−	0.936824i	−0.986214	−	0.165477i	$-0.947084\pi$
$149$	−2951.20	−	1703.87i	−1.62263	−	0.936824i	−0.636414	−	0.771348i	$-0.719583\pi$
$150$		0			0
$151$	1627.89	+	2819.59i	0.877324	+	1.51957i	0.854267	+	0.519835i	$0.174007\pi$
$151$	1627.89	+	2819.59i	0.877324	+	1.51957i	0.0230569	+	0.999734i	$0.492660\pi$
$152$		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	0.177271	−	0.984162i	$-0.443273\pi$
$157$	2199.76	−	1270.03i	1.11822	−	0.645602i	0.940945	+	0.338560i	$0.109940\pi$
$158$		0			0
$159$	1324.22	−	1590.32i	0.660487	−	0.793210i
$160$		0			0
$161$	2650.09	+	1194.90i	1.29725	+	0.584917i
$162$		0			0
$163$	862.851	−	1494.50i	0.414624	−	0.718150i	−0.580765	−	0.814071i	$-0.697246\pi$
$163$	862.851	−	1494.50i	0.414624	−	0.718150i	0.995389	+	0.0959216i	$0.0305798\pi$
$164$		0			0
$165$	176.094	+	478.180i	0.0830842	+	0.225614i
$166$		0			0
$167$	485.621			0.225021			0.112510	−	0.993651i	$-0.464111\pi$
$167$	485.621			0.225021			0.112510	+	0.993651i	$0.464111\pi$
$168$		0			0
$169$	1882.24			0.856734
$170$		0			0
$171$	−2575.46	+	474.235i	−1.15176	+	0.212080i
$172$		0			0
$173$	726.552	−	1258.43i	0.319299	−	0.553042i	−0.661043	−	0.750348i	$-0.729886\pi$
$173$	726.552	−	1258.43i	0.319299	−	0.553042i	0.980342	+	0.197306i	$0.0632192\pi$
$174$		0			0
$175$	2891.87	+	4020.05i	1.24917	+	1.73650i
$176$		0			0
$177$	2679.90	+	2231.49i	1.13804	+	0.947622i
$178$		0			0
$179$	1099.44	−	634.760i	0.459082	−	0.265051i	−0.252576	−	0.967577i	$-0.581278\pi$
$179$	1099.44	−	634.760i	0.459082	−	0.265051i	0.711658	+	0.702526i	$0.247944\pi$
$180$		0			0
$181$			3289.26i			1.35076i	0.737468	+	0.675382i	$0.236021\pi$
$181$			3289.26i			1.35076i	−0.737468	+	0.675382i	$0.763979\pi$
$182$		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
$189$	−1041.07	+	2380.64i	−0.400672	+	0.916222i
$190$		0			0
$191$	−1713.46	−	989.265i	−0.649117	−	0.374768i	0.139001	−	0.990292i	$-0.455611\pi$
$191$	−1713.46	−	989.265i	−0.649117	−	0.374768i	−0.788118	+	0.615524i	$0.788944\pi$
$192$		0			0
$193$	459.923	+	796.611i	0.171534	+	0.297105i	0.938956	−	0.344037i	$-0.111794\pi$
$193$	459.923	+	796.611i	0.171534	+	0.297105i	−0.767423	+	0.641142i	$0.778461\pi$
$194$		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	−0.417405	−	0.908720i	$-0.637060\pi$
$199$	451.592	−	260.727i	0.160867	−	0.0928766i	0.578272	+	0.815844i	$0.303727\pi$
$200$		0			0
$201$	−933.546	−	777.342i	−0.327598	−	0.272783i
$202$		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
$207$	−4167.97	+	767.472i	−1.39949	+	0.257696i
$208$		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
$213$	273.341	+	742.253i	0.0879297	+	0.238772i
$214$		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
$219$	2072.83	−	2489.36i	0.639585	−	0.768108i
$220$		0			0
$221$	−29.1209	+	16.8130i	−0.00886373	+	0.00511748i
$222$		0			0
$223$			1782.29i			0.535206i	0.963529	+	0.267603i	$0.0862316\pi$
$223$			1782.29i			0.535206i	−0.963529	+	0.267603i	$0.913768\pi$
$224$		0			0
$225$	−6802.63	−	2417.85i	−2.01559	−	0.716400i
$226$		0			0
$227$	−1721.58	−	2981.86i	−0.503370	−	0.871863i	−0.999992	−	0.00389579i	$-0.998760\pi$
$227$	−1721.58	−	2981.86i	−0.503370	−	0.871863i	0.496622	−	0.867967i	$-0.334573\pi$
$228$		0			0
$229$	−4706.78	−	2717.46i	−1.35822	−	0.784169i	−0.368837	−	0.929494i	$-0.620244\pi$
$229$	−4706.78	−	2717.46i	−1.35822	−	0.784169i	−0.989384	+	0.145325i	$0.953577\pi$
$230$		0			0
$231$	−266.782	+	394.725i	−0.0759870	+	0.112429i
$232$		0			0
$233$	3815.33	+	2202.78i	1.07275	+	0.619351i	0.928931	−	0.370253i	$-0.120729\pi$
$233$	3815.33	+	2202.78i	1.07275	+	0.619351i	0.143817	+	0.989604i	$0.454062\pi$
$234$		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	−0.739264	−	0.673416i	$-0.764826\pi$
$241$	−1966.82	+	1135.54i	−0.525700	+	0.303513i	0.213563	+	0.976929i	$0.431493\pi$
$242$		0			0
$243$	−728.191	−	3717.34i	−0.192236	−	0.981349i
$244$		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
$249$	−4176.02	+	1537.85i	−1.06283	+	0.391396i
$250$		0			0
$251$	4513.50			1.13502			0.567510	−	0.823367i	$-0.307907\pi$
$251$	4513.50			1.13502			0.567510	+	0.823367i	$0.307907\pi$
$252$		0			0
$253$	−777.082			−0.193102
$254$		0			0
$255$	183.068	−	67.4165i	0.0449576	−	0.0165560i
$256$		0			0
$257$	−2969.31	+	5142.99i	−0.720701	+	1.24829i	0.240018	+	0.970769i	$0.422847\pi$
$257$	−2969.31	+	5142.99i	−0.720701	+	1.24829i	−0.960719	+	0.277523i	$0.910487\pi$
$258$		0			0
$259$	1895.06	−	4202.93i	0.454647	−	1.00833i
$260$		0			0
$261$	−1611.27	−	1891.01i	−0.382127	−	0.448469i
$262$		0			0
$263$	−4727.20	+	2729.25i	−1.10833	+	0.639897i	−0.938397	−	0.345558i	$-0.887690\pi$
$263$	−4727.20	+	2729.25i	−1.10833	+	0.639897i	−0.169936	+	0.985455i	$0.554356\pi$
$264$		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	0.992979	+	0.118294i	$0.0377427\pi$
$269$	2642.46	+	4576.87i	0.598935	+	1.03739i	−0.394043	+	0.919092i	$0.628924\pi$
$270$		0			0
$271$	5436.74	+	3138.90i	1.21866	+	0.703596i	0.964632	−	0.263599i	$-0.0849096\pi$
$271$	5436.74	+	3138.90i	1.21866	+	0.703596i	0.254033	+	0.967196i	$0.418243\pi$
$272$		0			0
$273$	747.007	+	1535.23i	0.165608	+	0.340353i
$274$		0			0
$275$	−1146.42	−	661.884i	−0.251387	−	0.145139i
$276$		0			0
$277$	−3748.17	−	6492.02i	−0.813017	−	1.40819i	−0.910743	−	0.412974i	$-0.864490\pi$
$277$	−3748.17	−	6492.02i	−0.813017	−	1.40819i	0.0977256	−	0.995213i	$-0.468843\pi$
$278$		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	−0.720011	−	0.693963i	$-0.755863\pi$
$283$	−2280.55	+	1316.68i	−0.479027	+	0.276566i	0.240984	+	0.970529i	$0.422530\pi$
$284$		0			0
$285$	6388.17	−	7671.85i	1.32773	−	1.59453i
$286$		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
$291$	126.365	+	343.141i	0.0254558	+	0.0691247i
$292$		0			0
$293$	889.363			0.177328			0.0886640	−	0.996062i	$-0.471740\pi$
$293$	889.363			0.177328			0.0886640	+	0.996062i	$0.471740\pi$
$294$		0			0
$295$	−13294.4			−2.62383
$296$		0			0
$297$	−7.87936	−	694.518i	−0.00153942	−	0.135690i
$298$		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
$303$	−952.539	−	793.156i	−0.180600	−	0.150382i
$304$		0			0
$305$	5421.75	−	3130.25i	1.01786	−	0.587664i
$306$		0			0
$307$			3995.12i			0.742715i	0.928490	+	0.371357i	$0.121107\pi$
$307$			3995.12i			0.742715i	−0.928490	+	0.371357i	$0.878893\pi$
$308$		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	$-0.151803\pi$
$311$	256.008	+	443.420i	0.0466782	+	0.0808489i	−0.841742	+	0.539879i	$0.818470\pi$
$312$		0			0
$313$	−1271.68	−	734.205i	−0.229647	−	0.132587i	0.380762	−	0.924673i	$-0.375662\pi$
$313$	−1271.68	−	734.205i	−0.229647	−	0.132587i	−0.610409	+	0.792086i	$0.708995\pi$
$314$		0			0
$315$	−2757.38	−	9513.83i	−0.493210	−	1.70173i
$316$		0			0
$317$	−6545.26	−	3778.91i	−1.15968	−	0.669542i	−0.208453	−	0.978032i	$-0.566843\pi$
$317$	−6545.26	−	3778.91i	−1.15968	−	0.669542i	−0.951227	+	0.308491i	$0.900176\pi$
$318$		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
$327$	−170.922	−	142.323i	−0.0289053	−	0.0240687i
$328$		0			0
$329$	3581.68	−	7943.55i	0.600196	−	1.33113i
$330$		0			0
$331$	2932.76	−	5079.69i	0.487007	−	0.843520i	−0.512882	−	0.858459i	$-0.671422\pi$
$331$	2932.76	−	5079.69i	0.487007	−	0.843520i	0.999888	+	0.0149389i	$0.00475537\pi$
$332$		0			0
$333$	1217.18	+	6610.22i	0.200303	+	1.08780i
$334$		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
$339$	679.397	+	1844.89i	0.108849	+	0.295577i
$340$		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
$345$	10338.2	−	12415.6i	1.61331	−	1.93749i
$346$		0			0
$347$	968.873	−	559.379i	0.149890	−	0.0865390i	−0.423179	−	0.906046i	$-0.639086\pi$
$347$	968.873	−	559.379i	0.149890	−	0.0865390i	0.573069	+	0.819507i	$0.305753\pi$
$348$		0			0
$349$			2364.44i			0.362652i	0.983423	+	0.181326i	$0.0580389\pi$
$349$			2364.44i			0.362652i	−0.983423	+	0.181326i	$0.941961\pi$
$350$		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	$-0.234914\pi$
$353$	−1411.12	−	2444.13i	−0.212766	−	0.368522i	−0.952579	+	0.304291i	$0.901581\pi$
$354$		0			0
$355$	−2611.41	−	1507.70i	−0.390421	−	0.225410i
$356$		0			0
$357$	151.118	+	102.136i	0.0224034	+	0.0151418i
$358$		0			0
$359$	−4504.97	−	2600.95i	−0.662293	−	0.382375i	0.130857	−	0.991401i	$-0.458227\pi$
$359$	−4504.97	−	2600.95i	−0.662293	−	0.382375i	−0.793150	+	0.609026i	$0.791560\pi$
$360$		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	−0.111366	−	0.993779i	$-0.535523\pi$
$367$	4876.42	−	2815.40i	0.693589	−	0.400444i	0.804955	+	0.593336i	$0.202189\pi$
$368$		0			0
$369$	−7063.52	+	6018.61i	−0.996510	+	0.849096i
$370$		0			0
$371$	−5987.71	+	4307.33i	−0.837915	+	0.602764i
$372$		0			0
$373$	−3422.23	+	5927.47i	−0.475057	+	0.822822i	−0.999592	−	0.0285664i	$-0.990906\pi$
$373$	−3422.23	+	5927.47i	−0.475057	+	0.822822i	0.524535	+	0.851389i	$0.324239\pi$
$374$		0			0
$375$	13753.3	−	5064.77i	1.89391	−	0.697449i
$376$		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
$381$	−550.042	+	202.558i	−0.0739619	+	0.0272371i
$382$		0			0
$383$	2151.66	−	3726.78i	0.287062	−	0.497206i	−0.686045	−	0.727559i	$-0.740655\pi$
$383$	2151.66	−	3726.78i	0.287062	−	0.497206i	0.973107	+	0.230353i	$0.0739881\pi$
$384$		0			0
$385$	−181.328	−	1807.16i	−0.0240035	−	0.239225i
$386$		0			0
$387$	505.273	−	430.528i	0.0663682	−	0.0565504i
$388$		0			0
$389$	6143.61	−	3547.01i	0.800754	−	0.462315i	−0.0429809	−	0.999076i	$-0.513685\pi$
$389$	6143.61	−	3547.01i	0.800754	−	0.462315i	0.843735	+	0.536760i	$0.180352\pi$
$390$		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	0.725742	−	0.687967i	$-0.241496\pi$
$397$	3898.27	+	2250.67i	0.492817	+	0.284528i	−0.232925	+	0.972495i	$0.574830\pi$
$398$		0			0
$399$	9310.51	+	659.797i	1.16819	+	0.0827848i
$400$		0			0
$401$	−6038.64	−	3486.41i	−0.752008	−	0.434172i	0.0744107	−	0.997228i	$-0.476292\pi$
$401$	−6038.64	−	3486.41i	−0.752008	−	0.434172i	−0.826419	+	0.563055i	$0.809626\pi$
$402$		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	0.502984	−	0.864296i	$-0.332235\pi$
$409$	12431.9	−	7177.56i	1.50298	−	0.867745i	0.999994	−	0.00344923i	$-0.00109793\pi$
$410$		0			0
$411$	−6132.60	+	7364.93i	−0.736007	+	0.883905i
$412$		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
$417$	−100.317	−	272.410i	−0.0117807	−	0.0319903i
$418$		0			0
$419$	−14839.8			−1.73024			−0.865122	−	0.501562i	$-0.832759\pi$
$419$	−14839.8			−1.73024			−0.865122	+	0.501562i	$0.832759\pi$
$420$		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
$423$	2300.47	+	12493.3i	0.264427	+	1.43604i
$424$		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
$429$	−350.721	−	292.037i	−0.0394707	−	0.0328663i
$430$		0			0
$431$	5552.06	−	3205.49i	0.620495	−	0.358243i	−0.156566	−	0.987667i	$-0.550043\pi$
$431$	5552.06	−	3205.49i	0.620495	−	0.358243i	0.777062	+	0.629424i	$0.216709\pi$
$432$		0			0
$433$			12881.0i			1.42961i	0.699322	+	0.714807i	$0.253486\pi$
$433$			12881.0i			1.42961i	−0.699322	+	0.714807i	$0.746514\pi$
$434$		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	0.868161	−	0.496282i	$-0.165302\pi$
$439$	8024.85	+	4633.15i	0.872449	+	0.503709i	0.00428790	+	0.999991i	$0.498635\pi$
$440$		0			0
$441$	5715.27	−	7287.10i	0.617133	−	0.786859i
$442$		0			0
$443$	7691.54	+	4440.71i	0.824912	+	0.476263i	0.852108	−	0.523367i	$-0.175324\pi$
$443$	7691.54	+	4440.71i	0.824912	+	0.476263i	−0.0271952	+	0.999630i	$0.508658\pi$
$444$		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
$453$	13000.6	+	10825.3i	1.34839	+	1.12277i
$454$		0			0
$455$	−5933.43	−	2675.33i	−0.611348	−	0.275652i
$456$		0			0
$457$	−278.827	+	482.943i	−0.0285404	+	0.0494335i	−0.879943	−	0.475080i	$-0.842419\pi$
$457$	−278.827	+	482.943i	−0.0285404	+	0.0494335i	0.851402	+	0.524513i	$0.175753\pi$
$458$		0			0
$459$	−265.892	+	3.01657i	−0.0270387	+	0.000306757i
$460$		0			0
$461$	−7422.24			−0.749866			−0.374933	−	0.927052i	$-0.622334\pi$
$461$	−7422.24			−0.749866			−0.374933	+	0.927052i	$0.622334\pi$
$462$		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
$465$	−2766.30	−	7511.83i	−0.275880	−	0.749146i
$466$		0			0
$467$	4708.74	−	8155.78i	0.466584	−	0.808147i	−0.532688	−	0.846312i	$-0.678818\pi$
$467$	4708.74	−	8155.78i	0.466584	−	0.808147i	0.999271	+	0.0381650i	$0.0121512\pi$
$468$		0			0
$469$	2528.48	+	3514.90i	0.248943	+	0.346062i
$470$		0			0
$471$	8445.57	−	10142.7i	0.826224	−	0.992251i
$472$		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	−0.999977	−	0.00678003i	$-0.997842\pi$
$479$	−5303.15	−	9185.32i	−0.505860	−	0.876176i	0.494117	−	0.869396i	$-0.335492\pi$
$480$		0			0
$481$	3824.81	+	2208.25i	0.362570	+	0.209330i
$482$		0			0
$483$	15067.5	+	1067.77i	1.41946	+	0.100591i
$484$		0			0
$485$	−1207.25	−	697.005i	−0.113027	−	0.0652564i
$486$		0			0
$487$	−6387.19	−	11062.9i	−0.594314	−	1.02938i	−0.993643	−	0.112575i	$-0.964090\pi$
$487$	−6387.19	−	11062.9i	−0.594314	−	1.02938i	0.399329	−	0.916808i	$-0.369243\pi$
$488$		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
$495$	1717.28	+	2015.42i	0.155931	+	0.183003i
$496$		0			0
$497$	−281.466	−	2805.16i	−0.0254033	−	0.253176i
$498$		0			0
$499$	−6862.74	+	11886.6i	−0.615668	+	1.06637i	0.374599	+	0.927187i	$0.377780\pi$
$499$	−6862.74	+	11886.6i	−0.615668	+	1.06637i	−0.990267	+	0.139182i	$0.955553\pi$
$500$		0			0
$501$	2367.90	−	872.001i	0.211158	−	0.0777608i
$502$		0			0
$503$	5480.28			0.485793			0.242896	−	0.970052i	$-0.421902\pi$
$503$	5480.28			0.485793			0.242896	+	0.970052i	$0.421902\pi$
$504$		0			0
$505$	4725.34			0.416386
$506$		0			0
$507$	9177.88	−	3379.83i	0.803953	−	0.296063i
$508$		0			0
$509$	5331.28	−	9234.05i	0.464253	−	0.804111i	−0.534914	−	0.844906i	$-0.679656\pi$
$509$	5331.28	−	9234.05i	0.464253	−	0.804111i	0.999168	+	0.0407959i	$0.0129893\pi$
$510$		0			0
$511$	−9372.71	+	6742.37i	−0.811398	+	0.583689i
$512$		0			0
$513$	−11706.5	+	6936.99i	−1.00751	+	0.597029i
$514$		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	$-0.00602596\pi$
$521$	5750.00	+	9959.29i	0.483517	+	0.837475i	−0.516304	+	0.856405i	$0.672693\pi$
$522$		0			0
$523$	−8319.57	−	4803.31i	−0.695582	−	0.401594i	0.110118	−	0.993919i	$-0.464877\pi$
$523$	−8319.57	−	4803.31i	−0.695582	−	0.401594i	−0.805700	+	0.592324i	$0.798211\pi$
$524$		0			0
$525$	21319.4	+	14409.1i	1.77230	+	1.19784i
$526$		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
$537$	4221.08	−	5069.30i	0.339205	−	0.407368i
$538$		0			0
$539$	1272.58	−	1124.29i	0.101696	−	0.0898452i
$540$		0			0
$541$	8782.28	−	15211.3i	0.697929	−	1.20885i	−0.271254	−	0.962508i	$-0.587438\pi$
$541$	8782.28	−	15211.3i	0.697929	−	1.20885i	0.969183	−	0.246341i	$-0.0792282\pi$
$542$		0			0
$543$	5906.32	+	16038.5i	0.466785	+	1.26755i
$544$		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
$549$	−8392.14	+	1545.29i	−0.652400	+	0.120130i
$550$		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
$555$	−19690.7	−	16395.9i	−1.50599	−	1.25400i
$556$		0			0
$557$	−11945.8	+	6896.92i	−0.908726	+	0.524653i	−0.880021	−	0.474935i	$-0.842472\pi$
$557$	−11945.8	+	6896.92i	−0.908726	+	0.524653i	−0.0287052	+	0.999588i	$0.509138\pi$
$558$		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	$-0.0548165\pi$
$563$	4598.06	+	7964.08i	0.344201	+	0.596174i	−0.641007	+	0.767535i	$0.721483\pi$
$564$		0			0
$565$	−6490.74	−	3747.43i	−0.483305	−	0.279036i
$566$		0			0
$567$	−801.543	+	13477.5i	−0.0593680	+	0.998236i
$568$		0			0
$569$	15644.0	+	9032.06i	1.15260	+	0.665455i	0.949520	−	0.313707i	$-0.101571\pi$
$569$	15644.0	+	9032.06i	1.15260	+	0.665455i	0.203082	+	0.979162i	$0.434904\pi$
$570$		0			0
$571$	7626.26	+	13209.1i	0.558930	+	0.968095i	0.997586	+	0.0694402i	$0.0221213\pi$
$571$	7626.26	+	13209.1i	0.558930	+	0.968095i	−0.438656	+	0.898655i	$0.644545\pi$
$572$		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	−0.660177	−	0.751110i	$-0.729519\pi$
$577$	−4709.42	+	2718.99i	−0.339785	+	0.196175i	0.320392	+	0.947285i	$0.396185\pi$
$578$		0			0
$579$	3673.03	+	3058.44i	0.263637	+	0.219524i
$580$		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
$585$	9331.88	−	1718.33i	0.659531	−	0.121443i
$586$		0			0
$587$	23972.1			1.68558			0.842791	−	0.538241i	$-0.180911\pi$
$587$	23972.1			1.68558			0.842791	+	0.538241i	$0.180911\pi$
$588$		0			0
$589$	7543.15			0.527691
$590$		0			0
$591$	−5498.22	−	14930.3i	−0.382685	−	1.03917i
$592$		0			0
$593$	−697.071	+	1207.36i	−0.0482720	+	0.0836095i	−0.889152	−	0.457612i	$-0.848705\pi$
$593$	−697.071	+	1207.36i	−0.0482720	+	0.0836095i	0.840880	+	0.541222i	$0.182038\pi$
$594$		0			0
$595$	−691.861	+	69.4203i	−0.0476698	+	0.00478312i
$596$		0			0
$597$	1733.81	−	2082.21i	0.118861	−	0.142746i
$598$		0			0
$599$	−20811.2	+	12015.4i	−1.41957	+	0.819591i	−0.996261	−	0.0863929i	$-0.972466\pi$
$599$	−20811.2	+	12015.4i	−1.41957	+	0.819591i	−0.423312	+	0.905984i	$0.639133\pi$
$600$		0			0
$601$			10741.9i			0.729073i	0.931189	+	0.364536i	$0.118773\pi$
$601$			10741.9i			0.729073i	−0.931189	+	0.364536i	$0.881227\pi$
$602$		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	−0.995946	−	0.0899549i	$-0.971328\pi$
$607$	−23506.4	−	13571.4i	−1.57182	−	0.907492i	−0.575876	−	0.817537i	$-0.695339\pi$
$608$		0			0
$609$	3874.28	+	7962.32i	0.257789	+	0.529802i
$610$		0			0
$611$	7228.91	+	4173.61i	0.478642	+	0.276344i
$612$		0			0
$613$	−14388.2	−	24921.1i	−0.948015	−	1.64201i	−0.749600	−	0.661891i	$-0.769754\pi$
$613$	−14388.2	−	24921.1i	−0.948015	−	1.64201i	−0.198415	−	0.980118i	$-0.563579\pi$
$614$		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	−0.579128	−	0.815236i	$-0.696607\pi$
$619$	−2505.32	+	1446.45i	−0.162677	+	0.0939218i	0.416451	+	0.909158i	$0.363274\pi$
$620$		0			0
$621$	−18945.0	+	11226.4i	−1.22422	+	0.725442i
$622$		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
$627$	−2341.34	+	862.219i	−0.149129	+	0.0549182i
$628$		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
$633$	−485.793	+	178.898i	−0.0305032	+	0.0112331i
$634$		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
$639$	2665.64	+	3128.43i	0.165025	+	0.193676i
$640$		0			0
$641$	−12252.1	+	7073.73i	−0.754957	+	0.435875i	−0.827482	−	0.561492i	$-0.810228\pi$
$641$	−12252.1	+	7073.73i	−0.754957	+	0.435875i	0.0725251	+	0.997367i	$0.476894\pi$
$642$		0			0
$643$			4248.35i			0.260557i	0.991477	+	0.130279i	$0.0415872\pi$
$643$			4248.35i			0.260557i	−0.991477	+	0.130279i	$0.958413\pi$
$644$		0			0
$645$	−430.010	+	2493.82i	−0.0262506	+	0.152239i
$646$		0			0
$647$	−8314.83	−	14401.7i	−0.505239	−	0.875100i	−0.999982	−	0.00606041i	$-0.998071\pi$
$647$	−8314.83	−	14401.7i	−0.505239	−	0.875100i	0.494742	−	0.869040i	$-0.335262\pi$
$648$		0			0
$649$	2877.44	+	1661.29i	0.174036	+	0.100480i
$650$		0			0
$651$	4190.94	−	6200.83i	0.252313	−	0.373317i
$652$		0			0
$653$	26164.5	+	15106.1i	1.56798	+	0.905276i	0.996404	+	0.0847307i	$0.0270030\pi$
$653$	26164.5	+	15106.1i	1.56798	+	0.905276i	0.571581	+	0.820546i	$0.306330\pi$
$654$		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	−0.682427	−	0.730954i	$-0.739076\pi$
$661$	−6638.24	+	3832.59i	−0.390617	+	0.225523i	0.291811	+	0.956476i	$0.405742\pi$
$662$		0			0
$663$	−111.804	+	134.271i	−0.00654921	+	0.00786526i
$664$		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
$669$	3200.35	+	8690.50i	0.184952	+	0.502234i
$670$		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
$675$	−37511.4	+	425.570i	−2.13899	+	0.0242670i
$676$		0			0
$677$	5256.30	−	9104.19i	0.298399	−	0.516842i	−0.677371	−	0.735642i	$-0.736881\pi$
$677$	5256.30	−	9104.19i	0.298399	−	0.516842i	0.975770	+	0.218799i	$0.0702140\pi$
$678$		0			0
$679$	−130.121	−	1296.82i	−0.00735431	−	0.0732949i
$680$		0			0
$681$	−13748.8	−	11448.3i	−0.773649	−	0.644199i
$682$		0			0
$683$	−15679.7	+	9052.66i	−0.878427	+	0.507160i	−0.870140	−	0.492805i	$-0.835971\pi$
$683$	−15679.7	+	9052.66i	−0.878427	+	0.507160i	−0.00828788	+	0.999966i	$0.502638\pi$
$684$		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	0.274083	−	0.961706i	$-0.411626\pi$
$691$	−7660.53	−	4422.81i	−0.421737	−	0.243490i	−0.695820	+	0.718216i	$0.744959\pi$
$692$		0			0
$693$	−592.055	+	2403.74i	−0.0324535	+	0.131761i
$694$		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
$705$	−37215.4	−	30988.4i	−1.98811	−	1.65545i
$706$		0			0
$707$	2579.92	+	3586.41i	0.137239	+	0.190779i
$708$		0			0
$709$	−7996.91	+	13851.1i	−0.423597	+	0.733692i	−0.996288	−	0.0860795i	$-0.972566\pi$
$709$	−7996.91	+	13851.1i	−0.423597	+	0.733692i	0.572691	+	0.819771i	$0.305899\pi$
$710$		0			0
$711$	−1478.48	−	8029.30i	−0.0779851	−	0.423520i
$712$		0			0
$713$	12207.4			0.641191
$714$		0			0
$715$	1739.85			0.0910024
$716$		0			0
$717$	3627.72	+	9851.01i	0.188953	+	0.513100i
$718$		0			0
$719$	10462.3	−	18121.2i	0.542668	−	0.939928i	−0.456082	−	0.889938i	$-0.650748\pi$
$719$	10462.3	−	18121.2i	0.542668	−	0.939928i	0.998750	−	0.0499905i	$-0.0159191\pi$
$720$		0			0
$721$	−330.623	−	149.075i	−0.0170778	−	0.00770021i
$722$		0			0
$723$	−7551.23	+	9068.63i	−0.388428	+	0.466481i
$724$		0			0
$725$	−21307.4	+	12301.8i	−1.09150	+	0.630176i
$726$		0			0
$727$		−	21598.1i		−	1.10183i	−0.834562	−	0.550915i	$-0.814279\pi$
$727$		−	21598.1i		−	1.10183i	0.834562	−	0.550915i	$-0.185721\pi$
$728$		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	0.707057	−	0.707157i	$-0.250022\pi$
$733$	8894.03	+	5134.97i	0.448170	+	0.258751i	−0.258887	+	0.965908i	$0.583356\pi$
$734$		0			0
$735$	1032.75	+	35289.8i	0.0518278	+	1.77100i
$736$		0			0
$737$	−1002.36	−	578.713i	−0.0500982	−	0.0289242i
$738$		0			0
$739$	−9022.60	−	15627.6i	−0.449123	−	0.777903i	0.549206	−	0.835687i	$-0.314930\pi$
$739$	−9022.60	−	15627.6i	−0.449123	−	0.777903i	−0.998329	+	0.0577833i	$0.981597\pi$
$740$		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
$747$	−17600.9	+	14997.2i	−0.862095	+	0.734566i
$748$		0			0
$749$	8168.70	+	3683.20i	0.398502	+	0.179681i
$750$		0			0
$751$	−9431.09	+	16335.1i	−0.458249	+	0.793711i	−0.998869	−	0.0475563i	$-0.984857\pi$
$751$	−9431.09	+	16335.1i	−0.458249	+	0.793711i	0.540619	+	0.841267i	$0.318190\pi$
$752$		0			0
$753$	22008.0	−	8104.63i	1.06509	−	0.392230i
$754$		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
$759$	−3789.08	+	1395.36i	−0.181205	+	0.0667304i
$760$		0			0
$761$	12563.5	−	21760.6i	0.598457	−	1.03656i	−0.394592	−	0.918856i	$-0.629114\pi$
$761$	12563.5	−	21760.6i	0.598457	−	1.03656i	0.993049	−	0.117702i	$-0.0375526\pi$
$762$		0			0
$763$	462.938	+	643.540i	0.0219652	+	0.0305343i
$764$		0			0
$765$	771.591	−	657.450i	0.0364666	−	0.0310721i
$766$		0			0
$767$	10311.6	−	5953.43i	0.485439	−	0.280268i
$768$		0			0
$769$			23475.2i			1.10083i	0.834892	+	0.550413i	$0.185530\pi$
$769$			23475.2i			1.10083i	−0.834892	+	0.550413i	$0.814470\pi$
$770$		0			0
$771$	−5243.47	+	30409.2i	−0.244927	+	1.42044i
$772$		0			0
$773$	−15695.6	−	27185.6i	−0.730313	−	1.26494i	−0.956749	−	0.290913i	$-0.906041\pi$
$773$	−15695.6	−	27185.6i	−0.730313	−	1.26494i	0.226436	−	0.974026i	$-0.427292\pi$
$774$		0			0
$775$	18009.3	+	10397.7i	0.834727	+	0.481930i
$776$		0			0
$777$	1693.44	−	23896.5i	0.0781877	−	1.10332i
$778$		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	−0.406378	−	0.913705i	$-0.633208\pi$
$787$	4012.16	−	2316.42i	0.181726	−	0.104919i	0.588103	+	0.808786i	$0.299875\pi$
$788$		0			0
$789$	−18149.2	+	21796.3i	−0.818922	+	0.983482i
$790$		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
$795$	14166.2	+	38468.1i	0.631980	+	1.71613i
$796$		0			0
$797$	121.248			0.00538874			0.00269437	−	0.999996i	$-0.499142\pi$
$797$	121.248			0.00538874			0.00269437	+	0.999996i	$0.499142\pi$
$798$		0			0
$799$	891.749			0.0394841
$800$		0			0
$801$	4435.49	+	24088.2i	0.195656	+	1.06256i
$802$		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
$807$	21103.1	+	17572.1i	0.920527	+	0.766501i
$808$		0			0
$809$	−11357.9	+	6557.47i	−0.493599	+	0.284979i	−0.726066	−	0.687625i	$-0.758653\pi$
$809$	−11357.9	+	6557.47i	−0.493599	+	0.284979i	0.232467	+	0.972604i	$0.425320\pi$
$810$		0			0
$811$		−	2601.55i		−	0.112642i	−0.998413	−	0.0563211i	$-0.982063\pi$
$811$		−	2601.55i		−	0.112642i	0.998413	−	0.0563211i	$-0.0179371\pi$
$812$		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
$819$	6399.15	+	6144.48i	0.273021	+	0.262155i
$820$		0			0
$821$	13977.1	+	8069.68i	0.594158	+	0.343038i	0.766740	−	0.641958i	$-0.221878\pi$
$821$	13977.1	+	8069.68i	0.594158	+	0.343038i	−0.172582	+	0.984995i	$0.555211\pi$
$822$		0			0
$823$	9786.73	+	16951.1i	0.414513	+	0.717957i	0.995377	−	0.0960431i	$-0.0306187\pi$
$823$	9786.73	+	16951.1i	0.414513	+	0.717957i	−0.580864	+	0.814000i	$0.697285\pi$
$824$		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	−0.596282	−	0.802775i	$-0.703356\pi$
$829$	−4754.65	+	2745.10i	−0.199199	+	0.115007i	0.397083	+	0.917783i	$0.370023\pi$
$830$		0			0
$831$	−29933.5	−	24924.9i	−1.24956	−	1.04048i
$832$		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
$837$	123.779	+	10910.3i	0.00511161	+	0.450557i
$838$		0			0
$839$	25774.7			1.06060			0.530299	−	0.847811i	$-0.322080\pi$
$839$	25774.7			1.06060			0.530299	+	0.847811i	$0.322080\pi$
$840$		0			0
$841$	15922.5			0.652854
$842$		0			0
$843$	−1339.35	−	3636.98i	−0.0547208	−	0.148593i
$844$		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
$849$	−8755.76	+	10515.2i	−0.353942	+	0.425066i
$850$		0			0
$851$	33839.5	−	19537.3i	1.36311	−	0.786990i
$852$		0			0
$853$		−	15407.3i		−	0.618447i	−0.950989	−	0.309224i	$-0.899931\pi$
$853$		−	15407.3i		−	0.618447i	0.950989	−	0.309224i	$-0.100069\pi$
$854$		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	$-0.239729\pi$
$857$	−5708.14	−	9886.78i	−0.227522	−	0.394079i	−0.957073	+	0.289847i	$0.906396\pi$
$858$		0			0
$859$	32407.3	+	18710.4i	1.28722	+	0.743178i	0.978158	−	0.207863i	$-0.0666510\pi$
$859$	32407.3	+	18710.4i	1.28722	+	0.743178i	0.309064	+	0.951041i	$0.399984\pi$
$860$		0			0
$861$	29741.8	−	14471.7i	1.17723	−	0.572814i
$862$		0			0
$863$	−30175.4	−	17421.8i	−1.19025	−	0.687189i	−0.231884	−	0.972743i	$-0.574489\pi$
$863$	−30175.4	−	17421.8i	−1.19025	−	0.687189i	−0.958362	+	0.285554i	$0.907822\pi$
$864$		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
$873$	1232.32	+	1446.26i	0.0477750	+	0.0560694i
$874$		0			0
$875$	−51977.1	+	5215.31i	−2.00817	+	0.201497i
$876$		0			0
$877$	14281.1	−	24735.6i	0.549874	−	0.952409i	−0.448409	−	0.893828i	$-0.648009\pi$
$877$	14281.1	−	24735.6i	0.549874	−	0.952409i	0.998283	−	0.0585807i	$-0.0186575\pi$
$878$		0			0
$879$	4336.56	−	1596.98i	0.166403	−	0.0612795i
$880$		0			0
$881$	25098.4			0.959804			0.479902	−	0.877322i	$-0.340672\pi$
$881$	25098.4			0.959804			0.479902	+	0.877322i	$0.340672\pi$
$882$		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
$885$	−64824.0	+	23872.0i	−2.46219	+	0.906721i
$886$		0			0
$887$	−11659.7	+	20195.2i	−0.441368	+	0.764472i	−0.997791	−	0.0664269i	$-0.978840\pi$
$887$	−11659.7	+	20195.2i	−0.441368	+	0.764472i	0.556423	+	0.830899i	$0.312173\pi$
$888$		0			0
$889$	2078.74	−	208.578i	0.0784239	−	0.00786894i
$890$		0			0
$891$	−1285.52	−	3372.34i	−0.0483352	−	0.126799i
$892$		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
$903$	−2127.52	+	1035.20i	−0.0784045	+	0.0381498i
$904$		0			0
$905$	−56427.1	−	32578.2i	−2.07260	−	1.19661i
$906$		0			0
$907$	−18663.6	−	32326.3i	−0.683258	−	1.18344i	−0.973981	−	0.226631i	$-0.927229\pi$
$907$	−18663.6	−	32326.3i	−0.683258	−	1.18344i	0.290723	−	0.956807i	$-0.406104\pi$
$908$		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
$915$	20815.8	−	24998.7i	0.752076	−	0.903204i
$916$		0			0
$917$	12042.0	−	26707.1i	0.433654	−	0.961772i
$918$		0			0
$919$	−11879.4	+	20575.7i	−0.426404	+	0.738553i	−0.996550	−	0.0829898i	$-0.973553\pi$
$919$	−11879.4	+	20575.7i	−0.426404	+	0.738553i	0.570146	+	0.821543i	$0.306886\pi$
$920$		0			0
$921$	7173.79	+	19480.3i	0.256661	+	0.696958i
$922$		0			0
$923$	2700.68			0.0963097
$924$		0			0
$925$	66563.8			2.36606
$926$		0			0
$927$	519.993	−	95.7493i	0.0184237	−	0.00339247i
$928$		0			0
$929$	17720.4	−	30692.6i	0.625819	−	1.08395i	−0.362563	−	0.931959i	$-0.618098\pi$
$929$	17720.4	−	30692.6i	0.625819	−	1.08395i	0.988382	−	0.151991i	$-0.0485685\pi$
$930$		0			0
$931$	−31541.4	−	10578.3i	−1.11034	−	0.372385i
$932$		0			0
$933$	2044.53	+	1702.43i	0.0717415	+	0.0597374i
$934$		0			0
$935$	160.969	−	92.9357i	0.00563023	−	0.00325061i
$936$		0			0
$937$		−	42936.0i		−	1.49697i	−0.663154	−	0.748483i	$-0.730782\pi$
$937$		−	42936.0i		−	1.49697i	0.663154	−	0.748483i	$-0.269218\pi$
$938$		0			0
$939$	−7519.12	−	1296.53i	−0.261318	−	0.0450591i
$940$		0			0
$941$	16115.3	+	27912.5i	0.558282	+	0.966972i	0.997640	+	0.0686602i	$0.0218724\pi$
$941$	16115.3	+	27912.5i	0.558282	+	0.966972i	−0.439359	+	0.898312i	$0.644794\pi$
$942$		0			0
$943$	46721.1	+	26974.4i	1.61341	+	0.931503i
$944$		0			0
$945$	−30528.5	−	41438.4i	−1.05089	−	1.42645i
$946$		0			0
$947$	9522.57	+	5497.86i	0.326760	+	0.188655i	0.654402	−	0.756147i	$-0.272921\pi$
$947$	9522.57	+	5497.86i	0.326760	+	0.188655i	−0.327642	+	0.944802i	$0.606254\pi$
$948$		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
$957$	−1818.98	−	1514.62i	−0.0614412	−	0.0511606i
$958$		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
$963$	−12847.4	+	2365.67i	−0.429910	+	0.0791618i
$964$		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
$969$	330.095	+	896.368i	0.0109434	+	0.0297167i
$970$		0			0
$971$	−3033.74	+	5254.60i	−0.100265	+	0.173664i	−0.911794	−	0.410648i	$-0.865302\pi$
$971$	−3033.74	+	5254.60i	−0.100265	+	0.173664i	0.811529	+	0.584313i	$0.198636\pi$
$972$		0			0
$973$	103.299	+	1029.50i	0.00340351	+	0.0339202i
$974$		0			0
$975$	−15773.1	+	18942.7i	−0.518096	+	0.622206i
$976$		0			0
$977$	11370.3	−	6564.62i	0.372331	−	0.214965i	−0.302146	−	0.953262i	$-0.597703\pi$
$977$	11370.3	−	6564.62i	0.372331	−	0.214965i	0.674476	+	0.738297i	$0.264370\pi$
$978$		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	$-0.0231777\pi$
$983$	13427.3	+	23256.8i	0.435671	+	0.754605i	−0.561679	+	0.827355i	$0.689844\pi$
$984$		0			0
$985$	52528.2	+	30327.2i	1.69918	+	0.981019i
$986$		0			0
$987$	3200.61	−	45164.4i	0.103218	−	1.45653i
$988$		0			0
$989$	−3342.09	−	1929.56i	−0.107454	−	0.0620387i
$990$		0			0
$991$	13495.1	+	23374.1i	0.432578	+	0.749247i	0.997094	−	0.0761745i	$-0.0242706\pi$
$991$	13495.1	+	23374.1i	0.432578	+	0.749247i	−0.564516	+	0.825422i	$0.690937\pi$
$992$		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	−0.292695	−	0.956206i	$-0.594552\pi$
$997$	12247.7	−	7071.22i	0.389056	−	0.224622i	0.681751	+	0.731584i	$0.261219\pi$
$998$		0			0
$999$	17804.6	+	30046.0i	0.563875	+	0.951565i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.2	✓	16	12.11	even	2
42.4.f.a.5.5	yes	16	4.3	odd	2
42.4.f.a.17.2	yes	16	28.3	even	6
42.4.f.a.17.5	yes	16	84.59	odd	6
294.4.d.a.293.4		16	28.19	even	6
294.4.d.a.293.5		16	28.23	odd	6
294.4.d.a.293.12		16	84.23	even	6
294.4.d.a.293.13		16	84.47	odd	6
294.4.f.a.215.3		16	84.83	odd	2
294.4.f.a.215.8		16	28.27	even	2
294.4.f.a.227.3		16	28.11	odd	6
294.4.f.a.227.8		16	84.11	even	6
336.4.bc.e.17.6		16	7.3	odd	6	inner
336.4.bc.e.17.8		16	21.17	even	6	inner
336.4.bc.e.257.6		16	3.2	odd	2	inner
336.4.bc.e.257.8		16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(4.87603 - 1.79564i) q^{3} +(-9.90442 + 17.1550i) q^{5} +(-18.4277 + 1.84901i) q^{7} +(20.5514 - 17.5112i) q^{9} +(4.28742 - 2.47535i) q^{11} -17.7414i q^{13} +(-17.4901 + 101.433i) q^{15} +(-0.947671 - 1.64141i) q^{17} +(-83.9968 - 48.4956i) q^{19} +(-86.5340 + 42.1054i) q^{21} +(-135.935 - 78.4822i) q^{23} +(-133.695 - 231.567i) q^{25} +(68.7652 - 122.288i) q^{27} -92.0138i q^{29} +(-67.3521 + 38.8857i) q^{31} +(16.4608 - 19.7685i) q^{33} +(150.796 - 334.440i) q^{35} +(-124.469 + 215.587i) q^{37} +(-31.8571 - 86.5074i) q^{39} -343.701 q^{41} +24.5859 q^{43} +(96.8547 + 525.996i) q^{45} +(-235.248 + 407.461i) q^{47} +(336.162 - 68.1462i) q^{49} +(-7.56826 - 6.30191i) q^{51} +(344.910 - 199.134i) q^{53} +98.0675i q^{55} +(-496.652 - 85.6379i) q^{57} +(335.568 + 581.220i) q^{59} +(-273.703 - 158.023i) q^{61} +(-346.336 + 360.691i) q^{63} +(304.352 + 175.718i) q^{65} +(-116.895 - 202.469i) q^{67} +(-803.750 - 138.591i) q^{69} +152.225i q^{71} +(539.897 - 311.709i) q^{73} +(-1067.71 - 889.059i) q^{75} +(-74.4305 + 53.5425i) q^{77} +(151.191 - 261.870i) q^{79} +(115.716 - 719.757i) q^{81} -856.438 q^{83} +37.5446 q^{85} +(-165.224 - 448.662i) q^{87} +(-453.577 + 785.618i) q^{89} +(32.8040 + 326.933i) q^{91} +(-258.586 + 310.548i) q^{93} +(1663.88 - 960.642i) q^{95} +70.3731i q^{97} +(44.7661 - 125.950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 80 q^{7} + 18 q^{9} + 342 q^{19} - 450 q^{21} - 194 q^{25} - 804 q^{31} + 1332 q^{33} - 962 q^{37} - 594 q^{39} - 1732 q^{43} - 2394 q^{45} + 820 q^{49} - 1638 q^{51} - 2664 q^{57} - 4620 q^{61}+ \cdots + 4284 q^{99}+O(q^{100}) \) 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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Groups

Database

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