LMFDB - Embedded newform 336.4.q.h.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.2
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	336.193
Dual form			336.4.q.h.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{3} +(6.41238 + 11.1066i) q^{5} +(-6.32475 - 17.4068i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{3} +(6.41238 + 11.1066i) q^{5} +(-6.32475 - 17.4068i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-18.4124 + 31.8912i) q^{11} +87.1238 q^{13} -38.4743 q^{15} +(-51.2990 + 88.8525i) q^{17} +(47.9124 + 82.9867i) q^{19} +(54.7114 + 9.67805i) q^{21} +(-48.0000 - 83.1384i) q^{23} +(-19.7371 + 34.1857i) q^{25} +27.0000 q^{27} -212.021 q^{29} +(-79.6238 + 137.912i) q^{31} +(-55.2371 - 95.6735i) q^{33} +(152.773 - 181.865i) q^{35} +(-64.3351 - 111.432i) q^{37} +(-130.686 + 226.354i) q^{39} -298.042 q^{41} +33.3297 q^{43} +(57.7114 - 99.9590i) q^{45} +(135.598 + 234.863i) q^{47} +(-262.995 + 220.188i) q^{49} +(-153.897 - 266.557i) q^{51} +(-224.134 + 388.212i) q^{53} -472.268 q^{55} -287.474 q^{57} +(-334.237 + 578.916i) q^{59} +(121.846 + 211.043i) q^{61} +(-107.211 + 127.627i) q^{63} +(558.670 + 967.645i) q^{65} +(-167.789 + 290.618i) q^{67} +288.000 q^{69} +339.608 q^{71} +(459.160 - 795.288i) q^{73} +(-59.2114 - 102.557i) q^{75} +(671.578 + 118.797i) q^{77} +(-68.1495 - 118.038i) q^{79} +(-40.5000 + 70.1481i) q^{81} -287.464 q^{83} -1315.79 q^{85} +(318.031 - 550.846i) q^{87} +(-80.9277 - 140.171i) q^{89} +(-551.036 - 1516.55i) q^{91} +(-238.871 - 413.737i) q^{93} +(-614.464 + 1064.28i) q^{95} +182.680 q^{97} +331.423 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 3 q^{5} + 20 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 + 3 * q^5 + 20 * q^7 - 18 * q^9	$ 4 q - 6 q^{3} + 3 q^{5} + 20 q^{7} - 18 q^{9} - 51 q^{11} + 122 q^{13} - 18 q^{15} - 24 q^{17} + 169 q^{19} + 15 q^{21} - 192 q^{23} - 11 q^{25} + 108 q^{27} - 78 q^{29} - 92 q^{31} - 153 q^{33} + 294 q^{35} + 173 q^{37} - 183 q^{39} + 348 q^{41} + 994 q^{43} + 27 q^{45} + 180 q^{47} - 146 q^{49} - 72 q^{51} - 285 q^{53} - 666 q^{55} - 1014 q^{57} - 1269 q^{59} - 328 q^{61} - 225 q^{63} + 1374 q^{65} - 875 q^{67} + 1152 q^{69} + 2808 q^{71} + 1361 q^{73} - 33 q^{75} + 897 q^{77} - 182 q^{79} - 162 q^{81} + 798 q^{83} - 4176 q^{85} + 117 q^{87} - 822 q^{89} - 1955 q^{91} - 276 q^{93} - 510 q^{95} + 1682 q^{97} + 918 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 + 3 * q^5 + 20 * q^7 - 18 * q^9 - 51 * q^11 + 122 * q^13 - 18 * q^15 - 24 * q^17 + 169 * q^19 + 15 * q^21 - 192 * q^23 - 11 * q^25 + 108 * q^27 - 78 * q^29 - 92 * q^31 - 153 * q^33 + 294 * q^35 + 173 * q^37 - 183 * q^39 + 348 * q^41 + 994 * q^43 + 27 * q^45 + 180 * q^47 - 146 * q^49 - 72 * q^51 - 285 * q^53 - 666 * q^55 - 1014 * q^57 - 1269 * q^59 - 328 * q^61 - 225 * q^63 + 1374 * q^65 - 875 * q^67 + 1152 * q^69 + 2808 * q^71 + 1361 * q^73 - 33 * q^75 + 897 * q^77 - 182 * q^79 - 162 * q^81 + 798 * q^83 - 4176 * q^85 + 117 * q^87 - 822 * q^89 - 1955 * q^91 - 276 * q^93 - 510 * q^95 + 1682 * q^97 + 918 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$		0			0
$5$	6.41238	+	11.1066i	0.573540	+	0.993401i	0.996199	+	0.0871118i	$0.0277637\pi$
$5$	6.41238	+	11.1066i	0.573540	+	0.993401i	−0.422658	+	0.906289i	$0.638903\pi$
$6$		0			0
$7$	−6.32475	−	17.4068i	−0.341504	−	0.939880i
$7$	−6.32475	−	17.4068i	−0.341504	−	0.939880i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	−18.4124	+	31.8912i	−0.504685	+	0.874141i	0.495300	+	0.868722i	$0.335058\pi$
$11$	−18.4124	+	31.8912i	−0.504685	+	0.874141i	−0.999985	+	0.00541879i	$0.998275\pi$
$12$		0			0
$13$	87.1238			1.85875			0.929376	−	0.369134i	$-0.120346\pi$
$13$	87.1238			1.85875			0.929376	+	0.369134i	$0.120346\pi$
$14$		0			0
$15$	−38.4743			−0.662267
$16$		0			0
$17$	−51.2990	+	88.8525i	−0.731873	+	1.26764i	0.224209	+	0.974541i	$0.428020\pi$
$17$	−51.2990	+	88.8525i	−0.731873	+	1.26764i	−0.956082	+	0.293100i	$0.905313\pi$
$18$		0			0
$19$	47.9124	+	82.9867i	0.578519	+	1.00202i	0.995650	+	0.0931772i	$0.0297023\pi$
$19$	47.9124	+	82.9867i	0.578519	+	1.00202i	−0.417131	+	0.908846i	$0.636964\pi$
$20$		0			0
$21$	54.7114	+	9.67805i	0.568524	+	0.100568i
$22$		0			0
$23$	−48.0000	−	83.1384i	−0.435161	−	0.753720i	0.562148	−	0.827037i	$-0.309975\pi$
$23$	−48.0000	−	83.1384i	−0.435161	−	0.753720i	−0.997309	+	0.0733164i	$0.976642\pi$
$24$		0			0
$25$	−19.7371	+	34.1857i	−0.157897	+	0.273486i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	−212.021			−1.35763			−0.678815	−	0.734309i	$-0.737506\pi$
$29$	−212.021			−1.35763			−0.678815	+	0.734309i	$0.737506\pi$
$30$		0			0
$31$	−79.6238	+	137.912i	−0.461318	+	0.799026i	−0.999027	−	0.0441046i	$-0.985956\pi$
$31$	−79.6238	+	137.912i	−0.461318	+	0.799026i	0.537709	+	0.843130i	$0.319290\pi$
$32$		0			0
$33$	−55.2371	−	95.6735i	−0.291380	−	0.504685i
$34$		0			0
$35$	152.773	−	181.865i	0.737811	−	0.878310i
$36$		0			0
$37$	−64.3351	−	111.432i	−0.285855	−	0.495115i	0.686961	−	0.726694i	$-0.258944\pi$
$37$	−64.3351	−	111.432i	−0.285855	−	0.495115i	−0.972816	+	0.231579i	$0.925611\pi$
$38$		0			0
$39$	−130.686	+	226.354i	−0.536576	+	0.929376i
$40$		0			0
$41$	−298.042			−1.13527			−0.567637	−	0.823279i	$-0.692142\pi$
$41$	−298.042			−1.13527			−0.567637	+	0.823279i	$0.692142\pi$
$42$		0			0
$43$	33.3297			0.118203			0.0591016	−	0.998252i	$-0.481176\pi$
$43$	33.3297			0.118203			0.0591016	+	0.998252i	$0.481176\pi$
$44$		0			0
$45$	57.7114	−	99.9590i	0.191180	−	0.331134i
$46$		0			0
$47$	135.598	+	234.863i	0.420830	+	0.728899i	0.996021	−	0.0891205i	$-0.0284056\pi$
$47$	135.598	+	234.863i	0.420830	+	0.728899i	−0.575191	+	0.818019i	$0.695072\pi$
$48$		0			0
$49$	−262.995	+	220.188i	−0.766749	+	0.641947i
$50$		0			0
$51$	−153.897	−	266.557i	−0.422547	−	0.731873i
$52$		0			0
$53$	−224.134	+	388.212i	−0.580890	+	1.00613i	0.414484	+	0.910057i	$0.363962\pi$
$53$	−224.134	+	388.212i	−0.580890	+	1.00613i	−0.995374	+	0.0960750i	$0.969371\pi$
$54$		0			0
$55$	−472.268			−1.15783
$56$		0			0
$57$	−287.474			−0.668016
$58$		0			0
$59$	−334.237	+	578.916i	−0.737525	+	1.27743i	0.216082	+	0.976375i	$0.430672\pi$
$59$	−334.237	+	578.916i	−0.737525	+	1.27743i	−0.953607	+	0.301055i	$0.902661\pi$
$60$		0			0
$61$	121.846	+	211.043i	0.255750	+	0.442971i	0.965099	−	0.261886i	$-0.0843444\pi$
$61$	121.846	+	211.043i	0.255750	+	0.442971i	−0.709349	+	0.704857i	$0.751011\pi$
$62$		0			0
$63$	−107.211	+	127.627i	−0.214403	+	0.255231i
$64$		0			0
$65$	558.670	+	967.645i	1.06607	+	1.84649i
$66$		0			0
$67$	−167.789	+	290.618i	−0.305950	+	0.529921i	−0.977472	−	0.211063i	$-0.932307\pi$
$67$	−167.789	+	290.618i	−0.305950	+	0.529921i	0.671522	+	0.740984i	$0.265641\pi$
$68$		0			0
$69$	288.000			0.502480
$70$		0			0
$71$	339.608			0.567663			0.283831	−	0.958874i	$-0.408394\pi$
$71$	339.608			0.567663			0.283831	+	0.958874i	$0.408394\pi$
$72$		0			0
$73$	459.160	−	795.288i	0.736173	−	1.27509i	−0.218034	−	0.975941i	$-0.569964\pi$
$73$	459.160	−	795.288i	0.736173	−	1.27509i	0.954207	−	0.299147i	$-0.0967022\pi$
$74$		0			0
$75$	−59.2114	−	102.557i	−0.0911619	−	0.157897i
$76$		0			0
$77$	671.578	+	118.797i	0.993940	+	0.175821i
$78$		0			0
$79$	−68.1495	−	118.038i	−0.0970559	−	0.168106i	0.813409	−	0.581692i	$-0.197609\pi$
$79$	−68.1495	−	118.038i	−0.0970559	−	0.168106i	−0.910465	+	0.413587i	$0.864276\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−287.464			−0.380160			−0.190080	−	0.981769i	$-0.560875\pi$
$83$	−287.464			−0.380160			−0.190080	+	0.981769i	$0.560875\pi$
$84$		0			0
$85$	−1315.79			−1.67903
$86$		0			0
$87$	318.031	−	550.846i	0.391914	−	0.678815i
$88$		0			0
$89$	−80.9277	−	140.171i	−0.0963856	−	0.166945i	0.813800	−	0.581144i	$-0.197395\pi$
$89$	−80.9277	−	140.171i	−0.0963856	−	0.166945i	−0.910186	+	0.414200i	$0.864062\pi$
$90$		0			0
$91$	−551.036	−	1516.55i	−0.634772	−	1.74700i
$92$		0			0
$93$	−238.871	−	413.737i	−0.266342	−	0.461318i
$94$		0			0
$95$	−614.464	+	1064.28i	−0.663607	+	1.14940i
$96$		0			0
$97$	182.680			0.191220			0.0956101	−	0.995419i	$-0.469520\pi$
$97$	182.680			0.191220			0.0956101	+	0.995419i	$0.469520\pi$
$98$		0			0
$99$	331.423			0.336457
$100$		0			0
$101$	766.051	−	1326.84i	0.754703	−	1.30718i	−0.190819	−	0.981625i	$-0.561114\pi$
$101$	766.051	−	1326.84i	0.754703	−	1.30718i	0.945522	−	0.325558i	$-0.105552\pi$
$102$		0			0
$103$	243.954	+	422.541i	0.233374	+	0.404215i	0.958799	−	0.284086i	$-0.0916901\pi$
$103$	243.954	+	422.541i	0.233374	+	0.404215i	−0.725425	+	0.688301i	$0.758357\pi$
$104$		0			0
$105$	243.340	+	669.715i	0.226167	+	0.622452i
$106$		0			0
$107$	246.176	+	426.389i	0.222418	+	0.385239i	0.955542	−	0.294856i	$-0.0952718\pi$
$107$	246.176	+	426.389i	0.222418	+	0.385239i	−0.733124	+	0.680095i	$0.761938\pi$
$108$		0			0
$109$	−424.036	+	734.452i	−0.372617	+	0.645392i	−0.989967	−	0.141296i	$-0.954873\pi$
$109$	−424.036	+	734.452i	−0.372617	+	0.645392i	0.617350	+	0.786689i	$0.288206\pi$
$110$		0			0
$111$	386.011			0.330077
$112$		0			0
$113$	−736.350			−0.613009			−0.306505	−	0.951869i	$-0.599159\pi$
$113$	−736.350			−0.613009			−0.306505	+	0.951869i	$0.599159\pi$
$114$		0			0
$115$	615.588	−	1066.23i	0.499164	−	0.864578i
$116$		0			0
$117$	−392.057	−	679.062i	−0.309792	−	0.536576i
$118$		0			0
$119$	1871.09	+	330.983i	1.44137	+	0.254968i
$120$		0			0
$121$	−12.5312	−	21.7046i	−0.00941485	−	0.0163070i
$122$		0			0
$123$	447.062	−	774.335i	0.327726	−	0.567637i
$124$		0			0
$125$	1096.85			0.784839
$126$		0			0
$127$	2511.37			1.75471			0.877355	−	0.479841i	$-0.159306\pi$
$127$	2511.37			1.75471			0.877355	+	0.479841i	$0.159306\pi$
$128$		0			0
$129$	−49.9946	+	86.5931i	−0.0341223	+	0.0591016i
$130$		0			0
$131$	−339.711	−	588.397i	−0.226570	−	0.392431i	0.730219	−	0.683213i	$-0.239418\pi$
$131$	−339.711	−	588.397i	−0.226570	−	0.392431i	−0.956789	+	0.290782i	$0.906085\pi$
$132$		0			0
$133$	1141.50	−	1358.87i	0.744215	−	0.885934i
$134$		0			0
$135$	173.134	+	299.877i	0.110378	+	0.191180i
$136$		0			0
$137$	82.2683	−	142.493i	0.0513040	−	0.0888612i	−0.839233	−	0.543772i	$-0.816996\pi$
$137$	82.2683	−	142.493i	0.0513040	−	0.0888612i	0.890537	+	0.454911i	$0.150329\pi$
$138$		0			0
$139$	521.991			0.318523			0.159261	−	0.987236i	$-0.449089\pi$
$139$	521.991			0.318523			0.159261	+	0.987236i	$0.449089\pi$
$140$		0			0
$141$	−813.588			−0.485932
$142$		0			0
$143$	−1604.16	+	2778.48i	−0.938085	+	1.62481i
$144$		0			0
$145$	−1359.56	−	2354.82i	−0.778656	−	1.34867i
$146$		0			0
$147$	−177.572	−	1013.56i	−0.0996318	−	0.568689i
$148$		0			0
$149$	1206.06	+	2088.96i	0.663117	+	1.14855i	0.979792	+	0.200019i	$0.0641003\pi$
$149$	1206.06	+	2088.96i	0.663117	+	1.14855i	−0.316675	+	0.948534i	$0.602566\pi$
$150$		0			0
$151$	−787.289	+	1363.62i	−0.424296	+	0.734902i	−0.996354	−	0.0853111i	$-0.972812\pi$
$151$	−787.289	+	1363.62i	−0.424296	+	0.734902i	0.572059	+	0.820213i	$0.306145\pi$
$152$		0			0
$153$	923.382			0.487915
$154$		0			0
$155$	−2042.31			−1.05834
$156$		0			0
$157$	−1039.37	+	1800.24i	−0.528349	+	0.915128i	0.471104	+	0.882078i	$0.343856\pi$
$157$	−1039.37	+	1800.24i	−0.528349	+	0.915128i	−0.999454	+	0.0330505i	$0.989478\pi$
$158$		0			0
$159$	−672.402	−	1164.64i	−0.335377	−	0.580890i
$160$		0			0
$161$	−1143.59	+	1361.36i	−0.559797	+	0.666398i
$162$		0			0
$163$	−1589.71	−	2753.46i	−0.763901	−	1.32312i	−0.940826	−	0.338891i	$-0.889948\pi$
$163$	−1589.71	−	2753.46i	−0.763901	−	1.32312i	0.176924	−	0.984224i	$-0.443385\pi$
$164$		0			0
$165$	708.402	−	1226.99i	0.334237	−	0.578915i
$166$		0			0
$167$	2979.28			1.38050			0.690250	−	0.723571i	$-0.257500\pi$
$167$	2979.28			1.38050			0.690250	+	0.723571i	$0.257500\pi$
$168$		0			0
$169$	5393.55			2.45496
$170$		0			0
$171$	431.211	−	746.880i	0.192840	−	0.334008i
$172$		0			0
$173$	−8.18518	−	14.1772i	−0.00359716	−	0.00623046i	0.864221	−	0.503112i	$-0.167812\pi$
$173$	−8.18518	−	14.1772i	−0.00359716	−	0.00623046i	−0.867818	+	0.496882i	$0.834478\pi$
$174$		0			0
$175$	719.897	+	127.345i	0.310966	+	0.0550077i
$176$		0			0
$177$	−1002.71	−	1736.75i	−0.425810	−	0.737525i
$178$		0			0
$179$	1349.15	−	2336.79i	0.563351	−	0.975753i	−0.433850	−	0.900985i	$-0.642845\pi$
$179$	1349.15	−	2336.79i	0.563351	−	0.975753i	0.997201	−	0.0747677i	$-0.0238215\pi$
$180$		0			0
$181$	31.3297			0.0128659			0.00643293	−	0.999979i	$-0.497952\pi$
$181$	31.3297			0.0128659			0.00643293	+	0.999979i	$0.497952\pi$
$182$		0			0
$183$	−731.073			−0.295314
$184$		0			0
$185$	825.082	−	1429.08i	0.327899	−	0.567937i
$186$		0			0
$187$	−1889.07	−	3271.97i	−0.738731	−	1.27952i
$188$		0			0
$189$	−170.768	−	469.984i	−0.0657226	−	0.180880i
$190$		0			0
$191$	−772.587	−	1338.16i	−0.292683	−	0.506942i	0.681760	−	0.731576i	$-0.261215\pi$
$191$	−772.587	−	1338.16i	−0.292683	−	0.506942i	−0.974443	+	0.224634i	$0.927881\pi$
$192$		0			0
$193$	915.099	−	1585.00i	0.341297	−	0.591143i	−0.643377	−	0.765549i	$-0.722467\pi$
$193$	915.099	−	1585.00i	0.341297	−	0.591143i	0.984674	+	0.174406i	$0.0558006\pi$
$194$		0			0
$195$	−3352.02			−1.23099
$196$		0			0
$197$	4728.45			1.71009			0.855047	−	0.518551i	$-0.173528\pi$
$197$	4728.45			1.71009			0.855047	+	0.518551i	$0.173528\pi$
$198$		0			0
$199$	−164.125	+	284.272i	−0.0584648	+	0.101264i	−0.893776	−	0.448513i	$-0.851954\pi$
$199$	−164.125	+	284.272i	−0.0584648	+	0.101264i	0.835312	+	0.549777i	$0.185287\pi$
$200$		0			0
$201$	−503.366	−	871.855i	−0.176640	−	0.305950i
$202$		0			0
$203$	1340.98	+	3690.61i	0.463637	+	1.27601i
$204$		0			0
$205$	−1911.15	−	3310.22i	−0.651126	−	1.12778i
$206$		0			0
$207$	−432.000	+	748.246i	−0.145054	+	0.251240i
$208$		0			0
$209$	−3528.72			−1.16788
$210$		0			0
$211$	4935.76			1.61039			0.805193	−	0.593013i	$-0.202062\pi$
$211$	4935.76			1.61039			0.805193	+	0.593013i	$0.202062\pi$
$212$		0			0
$213$	−509.412	+	882.327i	−0.163870	+	0.283831i
$214$		0			0
$215$	213.723	+	370.179i	0.0677943	+	0.117423i
$216$		0			0
$217$	2904.22	+	513.735i	0.908530	+	0.160712i
$218$		0			0
$219$	1377.48	+	2385.86i	0.425029	+	0.736173i
$220$		0			0
$221$	−4469.36	+	7741.16i	−1.36037	+	2.35623i
$222$		0			0
$223$	−3446.00			−1.03480			−0.517402	−	0.855742i	$-0.673101\pi$
$223$	−3446.00			−1.03480			−0.517402	+	0.855742i	$0.673101\pi$
$224$		0			0
$225$	355.268			0.105265
$226$		0			0
$227$	2862.37	−	4957.77i	0.836927	−	1.44960i	−0.0555255	−	0.998457i	$-0.517683\pi$
$227$	2862.37	−	4957.77i	0.836927	−	1.44960i	0.892452	−	0.451142i	$-0.148983\pi$
$228$		0			0
$229$	−1508.57	−	2612.93i	−0.435325	−	0.754004i	0.561997	−	0.827139i	$-0.310033\pi$
$229$	−1508.57	−	2612.93i	−0.435325	−	0.754004i	−0.997322	+	0.0731345i	$0.976700\pi$
$230$		0			0
$231$	−1316.01	+	1566.61i	−0.374836	+	0.446215i
$232$		0			0
$233$	−190.856	−	330.573i	−0.0536627	−	0.0929466i	0.837946	−	0.545753i	$-0.183756\pi$
$233$	−190.856	−	330.573i	−0.0536627	−	0.0929466i	−0.891609	+	0.452806i	$0.850423\pi$
$234$		0			0
$235$	−1739.01	+	3012.06i	−0.482726	+	0.836106i
$236$		0			0
$237$	408.897			0.112071
$238$		0			0
$239$	1377.38			0.372785			0.186392	−	0.982475i	$-0.440320\pi$
$239$	1377.38			0.372785			0.186392	+	0.982475i	$0.440320\pi$
$240$		0			0
$241$	−2903.36	+	5028.77i	−0.776025	+	1.34411i	0.158192	+	0.987408i	$0.449434\pi$
$241$	−2903.36	+	5028.77i	−0.776025	+	1.34411i	−0.934217	+	0.356706i	$0.883900\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−4131.95	−	1509.04i	−1.07747	−	0.393507i
$246$		0			0
$247$	4174.31	+	7230.11i	1.07532	+	1.86251i
$248$		0			0
$249$	431.196	−	746.854i	0.109743	−	0.190080i
$250$		0			0
$251$	4348.52			1.09353			0.546765	−	0.837286i	$-0.315859\pi$
$251$	4348.52			1.09353			0.546765	+	0.837286i	$0.315859\pi$
$252$		0			0
$253$	3535.18			0.878477
$254$		0			0
$255$	1973.69	−	3418.53i	0.484695	−	0.839517i
$256$		0			0
$257$	2345.56	+	4062.62i	0.569307	+	0.986068i	0.996635	+	0.0819713i	$0.0261216\pi$
$257$	2345.56	+	4062.62i	0.569307	+	0.986068i	−0.427328	+	0.904097i	$0.640545\pi$
$258$		0			0
$259$	−1532.77	+	1824.65i	−0.367728	+	0.437753i
$260$		0			0
$261$	954.094	+	1652.54i	0.226272	+	0.391914i
$262$		0			0
$263$	−3790.81	+	6565.87i	−0.888788	+	1.53943i	−0.0474778	+	0.998872i	$0.515118\pi$
$263$	−3790.81	+	6565.87i	−0.888788	+	1.53943i	−0.841310	+	0.540553i	$0.818215\pi$
$264$		0			0
$265$	−5748.93			−1.33266
$266$		0			0
$267$	485.566			0.111297
$268$		0			0
$269$	1800.95	−	3119.33i	0.408200	−	0.707023i	−0.586488	−	0.809958i	$-0.699490\pi$
$269$	1800.95	−	3119.33i	0.408200	−	0.707023i	0.994688	+	0.102935i	$0.0328233\pi$
$270$		0			0
$271$	−1918.13	−	3322.31i	−0.429957	−	0.744707i	0.566912	−	0.823778i	$-0.308138\pi$
$271$	−1918.13	−	3322.31i	−0.429957	−	0.744707i	−0.996869	+	0.0790710i	$0.974805\pi$
$272$		0			0
$273$	4766.66	+	843.188i	1.05675	+	0.186931i
$274$		0			0
$275$	−726.815	−	1258.88i	−0.159377	−	0.276048i
$276$		0			0
$277$	−2701.52	+	4679.17i	−0.585988	+	1.01496i	0.408763	+	0.912640i	$0.365960\pi$
$277$	−2701.52	+	4679.17i	−0.585988	+	1.01496i	−0.994751	+	0.102321i	$0.967373\pi$
$278$		0			0
$279$	1433.23			0.307545
$280$		0			0
$281$	150.842			0.0320230			0.0160115	−	0.999872i	$-0.494903\pi$
$281$	150.842			0.0320230			0.0160115	+	0.999872i	$0.494903\pi$
$282$		0			0
$283$	908.571	−	1573.69i	0.190844	−	0.330552i	−0.754686	−	0.656086i	$-0.772211\pi$
$283$	908.571	−	1573.69i	0.190844	−	0.330552i	0.945530	+	0.325534i	$0.105544\pi$
$284$		0			0
$285$	−1843.39	−	3192.85i	−0.383134	−	0.663607i
$286$		0			0
$287$	1885.04	+	5187.96i	0.387701	+	1.06702i
$288$		0			0
$289$	−2806.68	−	4861.31i	−0.571275	−	0.989478i
$290$		0			0
$291$	−274.020	+	474.617i	−0.0552005	+	0.0956101i
$292$		0			0
$293$	−2817.59			−0.561792			−0.280896	−	0.959738i	$-0.590632\pi$
$293$	−2817.59			−0.561792			−0.280896	+	0.959738i	$0.590632\pi$
$294$		0			0
$295$	−8573.02			−1.69200
$296$		0			0
$297$	−497.134	+	861.062i	−0.0971268	+	0.168228i
$298$		0			0
$299$	−4181.94	−	7243.33i	−0.808856	−	1.40098i
$300$		0			0
$301$	−210.802	−	580.165i	−0.0403669	−	0.111097i
$302$		0			0
$303$	2298.15	+	3980.52i	0.435728	+	0.754703i
$304$		0			0
$305$	−1562.64	+	2706.57i	−0.293365	+	0.508124i
$306$		0			0
$307$	−8589.21			−1.59678			−0.798391	−	0.602139i	$-0.794315\pi$
$307$	−8589.21			−1.59678			−0.798391	+	0.602139i	$0.794315\pi$
$308$		0			0
$309$	−1463.72			−0.269477
$310$		0			0
$311$	−2999.15	+	5194.67i	−0.546836	+	0.947147i	0.451653	+	0.892194i	$0.350834\pi$
$311$	−2999.15	+	5194.67i	−0.546836	+	0.947147i	−0.998489	+	0.0549538i	$0.982499\pi$
$312$		0			0
$313$	2481.64	+	4298.32i	0.448148	+	0.776216i	0.998266	−	0.0588717i	$-0.0187503\pi$
$313$	2481.64	+	4298.32i	0.448148	+	0.776216i	−0.550117	+	0.835087i	$0.685417\pi$
$314$		0			0
$315$	−2104.98	−	372.356i	−0.376515	−	0.0666028i
$316$		0			0
$317$	1952.30	+	3381.49i	0.345906	+	0.599127i	0.985518	−	0.169571i	$-0.0542383\pi$
$317$	1952.30	+	3381.49i	0.345906	+	0.599127i	−0.639612	+	0.768698i	$0.720905\pi$
$318$		0			0
$319$	3903.81	−	6761.59i	0.685176	−	1.18676i
$320$		0			0
$321$	−1477.05			−0.256826
$322$		0			0
$323$	−9831.43			−1.69361
$324$		0			0
$325$	−1719.57	+	2978.39i	−0.293491	+	0.508342i
$326$		0			0
$327$	−1272.11	−	2203.36i	−0.215131	−	0.372617i
$328$		0			0
$329$	3230.59	−	3845.78i	0.541362	−	0.644452i
$330$		0			0
$331$	−1224.86	−	2121.52i	−0.203397	−	0.352295i	0.746224	−	0.665695i	$-0.231865\pi$
$331$	−1224.86	−	2121.52i	−0.203397	−	0.352295i	−0.949621	+	0.313401i	$0.898532\pi$
$332$		0			0
$333$	−579.016	+	1002.89i	−0.0952850	+	0.165038i
$334$		0			0
$335$	−4303.69			−0.701898
$336$		0			0
$337$	−1770.59			−0.286203			−0.143101	−	0.989708i	$-0.545707\pi$
$337$	−1770.59			−0.286203			−0.143101	+	0.989708i	$0.545707\pi$
$338$		0			0
$339$	1104.53	−	1913.09i	0.176960	−	0.306505i
$340$		0			0
$341$	−2932.13	−	5078.59i	−0.465641	−	0.806513i
$342$		0			0
$343$	5496.15	+	3185.28i	0.865201	+	0.501425i
$344$		0			0
$345$	1846.76	+	3198.69i	0.288193	+	0.499164i
$346$		0			0
$347$	−2017.36	+	3494.17i	−0.312097	+	0.540567i	−0.978816	−	0.204741i	$-0.934365\pi$
$347$	−2017.36	+	3494.17i	−0.312097	+	0.540567i	0.666719	+	0.745309i	$0.267698\pi$
$348$		0			0
$349$	6791.53			1.04167			0.520834	−	0.853658i	$-0.325621\pi$
$349$	6791.53			1.04167			0.520834	+	0.853658i	$0.325621\pi$
$350$		0			0
$351$	2352.34			0.357717
$352$		0			0
$353$	5078.40	−	8796.05i	0.765712	−	1.32625i	−0.174158	−	0.984718i	$-0.555720\pi$
$353$	5078.40	−	8796.05i	0.765712	−	1.32625i	0.939870	−	0.341534i	$-0.110946\pi$
$354$		0			0
$355$	2177.69	+	3771.88i	0.325577	+	0.563917i
$356$		0			0
$357$	−3666.56	+	4364.77i	−0.543571	+	0.647081i
$358$		0			0
$359$	−6421.36	−	11122.1i	−0.944029	−	1.63511i	−0.757683	−	0.652623i	$-0.773669\pi$
$359$	−6421.36	−	11122.1i	−0.944029	−	1.63511i	−0.186347	−	0.982484i	$-0.559665\pi$
$360$		0			0
$361$	−1161.69	+	2012.11i	−0.169367	+	0.293353i
$362$		0			0
$363$	75.1870			0.0108713
$364$		0			0
$365$	11777.2			1.68890
$366$		0			0
$367$	−957.408	+	1658.28i	−0.136175	+	0.235862i	−0.926046	−	0.377411i	$-0.876814\pi$
$367$	−957.408	+	1658.28i	−0.136175	+	0.235862i	0.789871	+	0.613274i	$0.210148\pi$
$368$		0			0
$369$	1341.19	+	2323.00i	0.189212	+	0.327726i
$370$		0			0
$371$	8175.13	+	1446.12i	1.14402	+	0.202369i
$372$		0			0
$373$	−2857.43	−	4949.21i	−0.396654	−	0.687026i	0.596656	−	0.802497i	$-0.296496\pi$
$373$	−2857.43	−	4949.21i	−0.396654	−	0.687026i	−0.993311	+	0.115471i	$0.963162\pi$
$374$		0			0
$375$	−1645.27	+	2849.69i	−0.226564	+	0.392420i
$376$		0			0
$377$	−18472.0			−2.52350
$378$		0			0
$379$	11570.3			1.56815			0.784075	−	0.620666i	$-0.213138\pi$
$379$	11570.3			1.56815			0.784075	+	0.620666i	$0.213138\pi$
$380$		0			0
$381$	−3767.06	+	6524.74i	−0.506541	+	0.877355i
$382$		0			0
$383$	3059.01	+	5298.36i	0.408115	+	0.706876i	0.994679	−	0.103027i	$-0.0328528\pi$
$383$	3059.01	+	5298.36i	0.408115	+	0.706876i	−0.586563	+	0.809903i	$0.699519\pi$
$384$		0			0
$385$	2986.98	+	8220.69i	0.395404	+	1.08822i
$386$		0			0
$387$	−149.984	−	259.779i	−0.0197005	−	0.0341223i
$388$		0			0
$389$	1629.23	−	2821.91i	0.212353	−	0.367806i	−0.740098	−	0.672499i	$-0.765221\pi$
$389$	1629.23	−	2821.91i	0.212353	−	0.367806i	0.952450	+	0.304694i	$0.0985541\pi$
$390$		0			0
$391$	9849.41			1.27393
$392$		0			0
$393$	2038.27			0.261621
$394$		0			0
$395$	874.000	−	1513.81i	0.111331	−	0.192831i
$396$		0			0
$397$	−361.963	−	626.938i	−0.0457592	−	0.0792572i	0.842239	−	0.539105i	$-0.181237\pi$
$397$	−361.963	−	626.938i	−0.0457592	−	0.0792572i	−0.887998	+	0.459848i	$0.847904\pi$
$398$		0			0
$399$	1818.20	+	5004.01i	0.228130	+	0.627855i
$400$		0			0
$401$	−5514.91	−	9552.11i	−0.686787	−	1.18955i	−0.972872	−	0.231346i	$-0.925687\pi$
$401$	−5514.91	−	9552.11i	−0.686787	−	1.18955i	0.286085	−	0.958204i	$-0.407646\pi$
$402$		0			0
$403$	−6937.12	+	12015.4i	−0.857475	+	1.48519i
$404$		0			0
$405$	−1038.80			−0.127453
$406$		0			0
$407$	4738.25			0.577067
$408$		0			0
$409$	−1341.78	+	2324.03i	−0.162217	+	0.280968i	−0.935663	−	0.352894i	$-0.885198\pi$
$409$	−1341.78	+	2324.03i	−0.162217	+	0.280968i	0.773447	+	0.633861i	$0.218531\pi$
$410$		0			0
$411$	246.805	+	427.479i	0.0296204	+	0.0513040i
$412$		0			0
$413$	12191.1	+	2156.51i	1.45250	+	0.256937i
$414$		0			0
$415$	−1843.33	−	3192.74i	−0.218037	−	0.377652i
$416$		0			0
$417$	−782.986	+	1356.17i	−0.0919497	+	0.159261i
$418$		0			0
$419$	−10024.9			−1.16885			−0.584427	−	0.811446i	$-0.698681\pi$
$419$	−10024.9			−1.16885			−0.584427	+	0.811446i	$0.698681\pi$
$420$		0			0
$421$	−5560.68			−0.643731			−0.321866	−	0.946785i	$-0.604310\pi$
$421$	−5560.68			−0.643731			−0.321866	+	0.946785i	$0.604310\pi$
$422$		0			0
$423$	1220.38	−	2113.76i	0.140277	−	0.242966i
$424$		0			0
$425$	−2024.99	−	3507.39i	−0.231121	−	0.400313i
$426$		0			0
$427$	2902.94	−	3455.74i	0.329000	−	0.391651i
$428$		0			0
$429$	−4812.47	−	8335.44i	−0.541604	−	0.938085i
$430$		0			0
$431$	5763.11	−	9982.00i	0.644081	−	1.11558i	−0.340431	−	0.940269i	$-0.610573\pi$
$431$	5763.11	−	9982.00i	0.644081	−	1.11558i	0.984513	−	0.175312i	$-0.0560936\pi$
$432$		0			0
$433$	2228.79			0.247365			0.123683	−	0.992322i	$-0.460530\pi$
$433$	2228.79			0.247365			0.123683	+	0.992322i	$0.460530\pi$
$434$		0			0
$435$	8157.34			0.899114
$436$		0			0
$437$	4599.59	−	7966.72i	0.503497	−	0.872082i
$438$		0			0
$439$	2304.63	+	3991.74i	0.250556	+	0.433975i	0.963679	−	0.267063i	$-0.0860533\pi$
$439$	2304.63	+	3991.74i	0.250556	+	0.433975i	−0.713123	+	0.701039i	$0.752720\pi$
$440$		0			0
$441$	2899.67	+	1059.00i	0.313106	+	0.114350i
$442$		0			0
$443$	531.662	+	920.865i	0.0570203	+	0.0987621i	0.893127	−	0.449805i	$-0.148507\pi$
$443$	531.662	+	920.865i	0.0570203	+	0.0987621i	−0.836106	+	0.548568i	$0.815173\pi$
$444$		0			0
$445$	1037.88	−	1797.66i	0.110562	−	0.191499i
$446$		0			0
$447$	−7236.37			−0.765702
$448$		0			0
$449$	−12265.9			−1.28923			−0.644613	−	0.764509i	$-0.722982\pi$
$449$	−12265.9			−1.28923			−0.644613	+	0.764509i	$0.722982\pi$
$450$		0			0
$451$	5487.65	−	9504.89i	0.572957	−	0.992390i
$452$		0			0
$453$	−2361.87	−	4090.87i	−0.244967	−	0.424296i
$454$		0			0
$455$	13310.2	−	15844.8i	1.37141	−	1.63256i
$456$		0			0
$457$	8895.59	+	15407.6i	0.910543	+	1.57711i	0.813299	+	0.581846i	$0.197669\pi$
$457$	8895.59	+	15407.6i	0.910543	+	1.57711i	0.0972436	+	0.995261i	$0.468997\pi$
$458$		0			0
$459$	−1385.07	+	2399.02i	−0.140849	+	0.243958i
$460$		0			0
$461$	15368.9			1.55272			0.776358	−	0.630293i	$-0.217065\pi$
$461$	15368.9			1.55272			0.776358	+	0.630293i	$0.217065\pi$
$462$		0			0
$463$	4104.98			0.412040			0.206020	−	0.978548i	$-0.433949\pi$
$463$	4104.98			0.412040			0.206020	+	0.978548i	$0.433949\pi$
$464$		0			0
$465$	3063.46	−	5306.08i	0.305516	−	0.529169i
$466$		0			0
$467$	1903.68	+	3297.27i	0.188634	+	0.326723i	0.944795	−	0.327662i	$-0.106261\pi$
$467$	1903.68	+	3297.27i	0.188634	+	0.326723i	−0.756161	+	0.654385i	$0.772927\pi$
$468$		0			0
$469$	6119.96	+	1082.58i	0.602545	+	0.106586i
$470$		0			0
$471$	−3118.11	−	5400.73i	−0.305043	−	0.528349i
$472$		0			0
$473$	−613.679	+	1062.92i	−0.0596554	+	0.103326i
$474$		0			0
$475$	−3782.61			−0.365385
$476$		0			0
$477$	4034.41			0.387260
$478$		0			0
$479$	4937.33	−	8551.70i	0.470965	−	0.815735i	−0.528484	−	0.848943i	$-0.677239\pi$
$479$	4937.33	−	8551.70i	0.470965	−	0.815735i	0.999448	+	0.0332085i	$0.0105725\pi$
$480$		0			0
$481$	−5605.12	−	9708.35i	−0.531334	−	0.920297i
$482$		0			0
$483$	−1821.53	−	5013.17i	−0.171599	−	0.472271i
$484$		0			0
$485$	1171.41	+	2028.95i	0.109673	+	0.189958i
$486$		0			0
$487$	−3381.86	+	5857.56i	−0.314675	+	0.545033i	−0.979368	−	0.202083i	$-0.935229\pi$
$487$	−3381.86	+	5857.56i	−0.314675	+	0.545033i	0.664693	+	0.747116i	$0.268562\pi$
$488$		0			0
$489$	9538.28			0.882077
$490$		0			0
$491$	5574.29			0.512351			0.256175	−	0.966630i	$-0.417538\pi$
$491$	5574.29			0.512351			0.256175	+	0.966630i	$0.417538\pi$
$492$		0			0
$493$	10876.5	−	18838.6i	0.993612	−	1.72099i
$494$		0			0
$495$	2125.21	+	3680.97i	0.192972	+	0.334237i
$496$		0			0
$497$	−2147.94	−	5911.50i	−0.193859	−	0.533535i
$498$		0			0
$499$	2893.73	+	5012.09i	0.259601	+	0.449643i	0.966135	−	0.258037i	$-0.0830755\pi$
$499$	2893.73	+	5012.09i	0.259601	+	0.449643i	−0.706534	+	0.707679i	$0.749742\pi$
$500$		0			0
$501$	−4468.92	+	7740.39i	−0.398516	+	0.690250i
$502$		0			0
$503$	−8296.10			−0.735397			−0.367699	−	0.929945i	$-0.619854\pi$
$503$	−8296.10			−0.735397			−0.367699	+	0.929945i	$0.619854\pi$
$504$		0			0
$505$	19648.8			1.73141
$506$		0			0
$507$	−8090.32	+	14012.9i	−0.708686	+	1.22748i
$508$		0			0
$509$	4880.19	+	8452.74i	0.424972	+	0.736073i	0.996418	−	0.0845670i	$-0.0269507\pi$
$509$	4880.19	+	8452.74i	0.424972	+	0.736073i	−0.571446	+	0.820640i	$0.693617\pi$
$510$		0			0
$511$	−16747.5	−	2962.51i	−1.44984	−	0.256466i
$512$		0			0
$513$	1293.63	+	2240.64i	0.111336	+	0.192840i
$514$		0			0
$515$	−3128.65	+	5418.98i	−0.267699	+	0.463667i
$516$		0			0
$517$	−9986.73			−0.849547
$518$		0			0
$519$	49.1111			0.00415364
$520$		0			0
$521$	3268.99	−	5662.06i	0.274889	−	0.476121i	−0.695218	−	0.718799i	$-0.744692\pi$
$521$	3268.99	−	5662.06i	0.274889	−	0.476121i	0.970107	+	0.242677i	$0.0780256\pi$
$522$		0			0
$523$	−5171.92	−	8958.02i	−0.432413	−	0.748962i	0.564667	−	0.825319i	$-0.309004\pi$
$523$	−5171.92	−	8958.02i	−0.432413	−	0.748962i	−0.997081	+	0.0763570i	$0.975671\pi$
$524$		0			0
$525$	−1410.70	+	1679.33i	−0.117272	+	0.139604i
$526$		0			0
$527$	−8169.24	−	14149.5i	−0.675252	−	1.16957i
$528$		0			0
$529$	1475.50	−	2555.64i	0.121271	−	0.210047i
$530$		0			0
$531$	6016.27			0.491683
$532$		0			0
$533$	−25966.5			−2.11020
$534$		0			0
$535$	−3157.14	+	5468.33i	−0.255131	+	0.441900i
$536$		0			0
$537$	4047.44	+	7010.37i	0.325251	+	0.563351i
$538$		0			0
$539$	−2179.68	−	12441.4i	−0.174184	−	0.994228i
$540$		0			0
$541$	3421.60	+	5926.38i	0.271915	+	0.470970i	0.969352	−	0.245676i	$-0.0790098\pi$
$541$	3421.60	+	5926.38i	0.271915	+	0.470970i	−0.697437	+	0.716646i	$0.745676\pi$
$542$		0			0
$543$	−46.9946	+	81.3970i	−0.00371405	+	0.00643293i
$544$		0			0
$545$	−10876.3			−0.854844
$546$		0			0
$547$	18402.1			1.43842			0.719211	−	0.694791i	$-0.244503\pi$
$547$	18402.1			1.43842			0.719211	+	0.694791i	$0.244503\pi$
$548$		0			0
$549$	1096.61	−	1899.38i	0.0852498	−	0.147657i
$550$		0			0
$551$	−10158.4	−	17594.9i	−0.785414	−	1.36038i
$552$		0			0
$553$	−1623.64	+	1932.83i	−0.124854	+	0.148630i
$554$		0			0
$555$	2475.25	+	4287.25i	0.189312	+	0.327899i
$556$		0			0
$557$	−323.239	+	559.866i	−0.0245890	+	0.0425894i	−0.878058	−	0.478554i	$-0.841161\pi$
$557$	−323.239	+	559.866i	−0.0245890	+	0.0425894i	0.853469	+	0.521144i	$0.174494\pi$
$558$		0			0
$559$	2903.81			0.219710
$560$		0			0
$561$	11334.4			0.853013
$562$		0			0
$563$	3087.40	−	5347.53i	0.231116	−	0.400305i	−0.727021	−	0.686616i	$-0.759096\pi$
$563$	3087.40	−	5347.53i	0.231116	−	0.400305i	0.958137	+	0.286311i	$0.0924289\pi$
$564$		0			0
$565$	−4721.76	−	8178.32i	−0.351585	−	0.608964i
$566$		0			0
$567$	1477.21	+	261.307i	0.109412	+	0.0193543i
$568$		0			0
$569$	3418.59	+	5921.17i	0.251871	+	0.436253i	0.964041	−	0.265754i	$-0.0856208\pi$
$569$	3418.59	+	5921.17i	0.251871	+	0.436253i	−0.712170	+	0.702007i	$0.752287\pi$
$570$		0			0
$571$	−2942.77	+	5097.03i	−0.215676	+	0.373562i	−0.953482	−	0.301451i	$-0.902529\pi$
$571$	−2942.77	+	5097.03i	−0.215676	+	0.373562i	0.737805	+	0.675014i	$0.235862\pi$
$572$		0			0
$573$	4635.52			0.337961
$574$		0			0
$575$	3789.53			0.274842
$576$		0			0
$577$	6001.62	−	10395.1i	0.433017	−	0.750007i	−0.564115	−	0.825696i	$-0.690782\pi$
$577$	6001.62	−	10395.1i	0.433017	−	0.750007i	0.997131	+	0.0756896i	$0.0241158\pi$
$578$		0			0
$579$	2745.30	+	4754.99i	0.197048	+	0.341297i
$580$		0			0
$581$	1818.14	+	5003.84i	0.129826	+	0.357305i
$582$		0			0
$583$	−8253.68	−	14295.8i	−0.586334	−	1.01556i
$584$		0			0
$585$	5028.03	−	8708.81i	0.355357	−	0.615496i
$586$		0			0
$587$	12719.4			0.894358			0.447179	−	0.894445i	$-0.352429\pi$
$587$	12719.4			0.894358			0.447179	+	0.894445i	$0.352429\pi$
$588$		0			0
$589$	−15259.9			−1.06752
$590$		0			0
$591$	−7092.68	+	12284.9i	−0.493661	+	0.855047i
$592$		0			0
$593$	−9580.20	−	16593.4i	−0.663426	−	1.14909i	−0.979709	−	0.200423i	$-0.935768\pi$
$593$	−9580.20	−	16593.4i	−0.663426	−	1.14909i	0.316283	−	0.948665i	$-0.397565\pi$
$594$		0			0
$595$	8322.07	+	22903.8i	0.573398	+	1.57809i
$596$		0			0
$597$	−492.374	−	852.817i	−0.0337547	−	0.0584648i
$598$		0			0
$599$	533.983	−	924.885i	0.0364240	−	0.0630881i	−0.847239	−	0.531212i	$-0.821737\pi$
$599$	533.983	−	924.885i	0.0364240	−	0.0630881i	0.883663	+	0.468124i	$0.155070\pi$
$600$		0			0
$601$	7554.96			0.512768			0.256384	−	0.966575i	$-0.417469\pi$
$601$	7554.96			0.512768			0.256384	+	0.966575i	$0.417469\pi$
$602$		0			0
$603$	3020.20			0.203967
$604$		0			0
$605$	160.709	−	278.356i	0.0107996	−	0.0187054i
$606$		0			0
$607$	−5888.71	−	10199.5i	−0.393765	−	0.682020i	0.599178	−	0.800616i	$-0.295494\pi$
$607$	−5888.71	−	10199.5i	−0.393765	−	0.682020i	−0.992943	+	0.118595i	$0.962161\pi$
$608$		0			0
$609$	−11599.9	−	2051.95i	−0.771845	−	0.136534i
$610$		0			0
$611$	11813.8	+	20462.1i	0.782219	+	1.35484i
$612$		0			0
$613$	−13426.5	+	23255.3i	−0.884649	+	1.53226i	−0.0385337	+	0.999257i	$0.512269\pi$
$613$	−13426.5	+	23255.3i	−0.884649	+	1.53226i	−0.846115	+	0.533000i	$0.821065\pi$
$614$		0			0
$615$	11466.9			0.751855
$616$		0			0
$617$	−6816.72			−0.444782			−0.222391	−	0.974958i	$-0.571386\pi$
$617$	−6816.72			−0.444782			−0.222391	+	0.974958i	$0.571386\pi$
$618$		0			0
$619$	−8356.74	+	14474.3i	−0.542627	+	0.939857i	0.456126	+	0.889915i	$0.349237\pi$
$619$	−8356.74	+	14474.3i	−0.542627	+	0.939857i	−0.998752	+	0.0499414i	$0.984097\pi$
$620$		0			0
$621$	−1296.00	−	2244.74i	−0.0837467	−	0.145054i
$622$		0			0
$623$	−1928.08	+	2295.24i	−0.123992	+	0.147603i
$624$		0			0
$625$	9500.53	+	16455.4i	0.608034	+	1.05315i
$626$		0			0
$627$	5293.08	−	9167.89i	0.337138	−	0.583940i
$628$		0			0
$629$	13201.3			0.836838
$630$		0			0
$631$	−592.225			−0.0373631			−0.0186815	−	0.999825i	$-0.505947\pi$
$631$	−592.225			−0.0373631			−0.0186815	+	0.999825i	$0.505947\pi$
$632$		0			0
$633$	−7403.63	+	12823.5i	−0.464878	+	0.805193i
$634$		0			0
$635$	16103.9	+	27892.7i	1.00640	+	1.74313i
$636$		0			0
$637$	−22913.1	+	19183.6i	−1.42520	+	1.19322i
$638$		0			0
$639$	−1528.24	−	2646.98i	−0.0946104	−	0.163870i
$640$		0			0
$641$	−3481.96	+	6030.92i	−0.214554	+	0.371618i	−0.953134	−	0.302547i	$-0.902163\pi$
$641$	−3481.96	+	6030.92i	−0.214554	+	0.371618i	0.738581	+	0.674165i	$0.235496\pi$
$642$		0			0
$643$	−5466.06			−0.335242			−0.167621	−	0.985852i	$-0.553608\pi$
$643$	−5466.06			−0.335242			−0.167621	+	0.985852i	$0.553608\pi$
$644$		0			0
$645$	−1282.34			−0.0782821
$646$		0			0
$647$	−618.633	+	1071.50i	−0.0375904	+	0.0651085i	−0.884209	−	0.467092i	$-0.845302\pi$
$647$	−618.633	+	1071.50i	−0.0375904	+	0.0651085i	0.846618	+	0.532201i	$0.178635\pi$
$648$		0			0
$649$	−12308.2	−	21318.4i	−0.744436	−	1.28940i
$650$		0			0
$651$	−5691.05	+	6774.78i	−0.342626	+	0.407872i
$652$		0			0
$653$	−13575.9	−	23514.2i	−0.813578	−	1.40916i	−0.910344	−	0.413852i	$-0.864183\pi$
$653$	−13575.9	−	23514.2i	−0.813578	−	1.40916i	0.0967657	−	0.995307i	$-0.469150\pi$
$654$		0			0
$655$	4356.71	−	7546.05i	0.259895	−	0.450151i
$656$		0			0
$657$	−8264.88			−0.490782
$658$		0			0
$659$	−5900.66			−0.348797			−0.174398	−	0.984675i	$-0.555798\pi$
$659$	−5900.66			−0.348797			−0.174398	+	0.984675i	$0.555798\pi$
$660$		0			0
$661$	−1809.49	+	3134.13i	−0.106477	+	0.184423i	−0.914341	−	0.404946i	$-0.867290\pi$
$661$	−1809.49	+	3134.13i	−0.106477	+	0.184423i	0.807864	+	0.589369i	$0.200624\pi$
$662$		0			0
$663$	−13408.1	−	23223.5i	−0.785410	−	1.36037i
$664$		0			0
$665$	22412.1	+	3964.54i	1.30692	+	0.231186i
$666$		0			0
$667$	10177.0	+	17627.1i	0.590787	+	1.02327i
$668$		0			0
$669$	5169.00	−	8952.98i	0.298722	−	0.517402i
$670$		0			0
$671$	−8973.86			−0.516292
$672$		0			0
$673$	−13952.5			−0.799151			−0.399576	−	0.916700i	$-0.630842\pi$
$673$	−13952.5			−0.799151			−0.399576	+	0.916700i	$0.630842\pi$
$674$		0			0
$675$	−532.902	+	923.014i	−0.0303873	+	0.0526323i
$676$		0			0
$677$	14459.4	+	25044.5i	0.820859	+	1.42177i	0.905044	+	0.425319i	$0.139838\pi$
$677$	14459.4	+	25044.5i	0.820859	+	1.42177i	−0.0841848	+	0.996450i	$0.526829\pi$
$678$		0			0
$679$	−1155.41	−	3179.88i	−0.0653026	−	0.179724i
$680$		0			0
$681$	8587.12	+	14873.3i	0.483200	+	0.836927i
$682$		0			0
$683$	−5565.06	+	9638.97i	−0.311773	+	0.540007i	−0.978746	−	0.205075i	$-0.934256\pi$
$683$	−5565.06	+	9638.97i	−0.311773	+	0.540007i	0.666973	+	0.745082i	$0.267590\pi$
$684$		0			0
$685$	2110.14			0.117700
$686$		0			0
$687$	9051.44			0.502670
$688$		0			0
$689$	−19527.4	+	33822.5i	−1.07973	+	1.87015i
$690$		0			0
$691$	−7012.64	−	12146.2i	−0.386069	−	0.668690i	0.605848	−	0.795580i	$-0.292834\pi$
$691$	−7012.64	−	12146.2i	−0.386069	−	0.668690i	−0.991917	+	0.126890i	$0.959501\pi$
$692$		0			0
$693$	−2096.17	−	5769.02i	−0.114902	−	0.316229i
$694$		0			0
$695$	3347.20	+	5797.52i	0.182686	+	0.316421i
$696$		0			0
$697$	15289.2	−	26481.7i	0.830877	−	1.43912i
$698$		0			0
$699$	1145.14			0.0619644
$700$		0			0
$701$	30366.7			1.63614			0.818070	−	0.575119i	$-0.195044\pi$
$701$	30366.7			1.63614			0.818070	+	0.575119i	$0.195044\pi$
$702$		0			0
$703$	6164.90	−	10677.9i	0.330745	−	0.572867i
$704$		0			0
$705$	−5217.03	−	9036.17i	−0.278702	−	0.482726i
$706$		0			0
$707$	−27941.2	−	4942.59i	−1.48633	−	0.262921i
$708$		0			0
$709$	−8445.48	−	14628.0i	−0.447358	−	0.774847i	0.550855	−	0.834601i	$-0.314302\pi$
$709$	−8445.48	−	14628.0i	−0.447358	−	0.774847i	−0.998213	+	0.0597542i	$0.980968\pi$
$710$		0			0
$711$	−613.346	+	1062.35i	−0.0323520	+	0.0560353i
$712$		0			0
$713$	15287.8			0.802989
$714$		0			0
$715$	−41145.8			−2.15212
$716$		0			0
$717$	−2066.08	+	3578.55i	−0.107614	+	0.186392i
$718$		0			0
$719$	5503.61	+	9532.54i	0.285466	+	0.494442i	0.972722	−	0.231973i	$-0.0745182\pi$
$719$	5503.61	+	9532.54i	0.285466	+	0.494442i	−0.687256	+	0.726415i	$0.741185\pi$
$720$		0			0
$721$	5812.14	−	6918.93i	0.300216	−	0.357385i
$722$		0			0
$723$	−8710.09	−	15086.3i	−0.448038	−	0.776025i
$724$		0			0
$725$	4184.68	−	7248.08i	0.214366	−	0.371292i
$726$		0			0
$727$	14618.0			0.745737			0.372869	−	0.927884i	$-0.378374\pi$
$727$	14618.0			0.745737			0.372869	+	0.927884i	$0.378374\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−1709.78	+	2961.43i	−0.0865096	+	0.149839i
$732$		0			0
$733$	14261.1	+	24701.0i	0.718617	+	1.24468i	0.961548	+	0.274638i	$0.0885581\pi$
$733$	14261.1	+	24701.0i	0.718617	+	1.24468i	−0.242930	+	0.970044i	$0.578109\pi$
$734$		0			0
$735$	10118.5	−	8471.56i	0.507793	−	0.425140i
$736$		0			0
$737$	−6178.77	−	10702.0i	−0.308817	−	0.534887i
$738$		0			0
$739$	10119.7	−	17527.9i	0.503735	−	0.872495i	−0.496256	−	0.868176i	$-0.665292\pi$
$739$	10119.7	−	17527.9i	0.503735	−	0.872495i	0.999991	−	0.00431822i	$-0.00137454\pi$
$740$		0			0
$741$	−25045.8			−1.24168
$742$		0			0
$743$	−13977.6			−0.690159			−0.345079	−	0.938573i	$-0.612148\pi$
$743$	−13977.6			−0.690159			−0.345079	+	0.938573i	$0.612148\pi$
$744$		0			0
$745$	−15467.4	+	26790.4i	−0.760649	+	1.31748i
$746$		0			0
$747$	1293.59	+	2240.56i	0.0633601	+	0.109743i
$748$		0			0
$749$	5865.07	−	6981.94i	0.286122	−	0.340607i
$750$		0			0
$751$	7513.90	+	13014.5i	0.365095	+	0.632363i	0.988791	−	0.149304i	$-0.0477032\pi$
$751$	7513.90	+	13014.5i	0.365095	+	0.632363i	−0.623697	+	0.781667i	$0.714370\pi$
$752$		0			0
$753$	−6522.78	+	11297.8i	−0.315675	+	0.546765i
$754$		0			0
$755$	−20193.6			−0.973403
$756$		0			0
$757$	20769.4			0.997196			0.498598	−	0.866833i	$-0.333848\pi$
$757$	20769.4			0.997196			0.498598	+	0.866833i	$0.333848\pi$
$758$		0			0
$759$	−5302.76	+	9184.66i	−0.253594	+	0.439238i
$760$		0			0
$761$	−5605.57	−	9709.13i	−0.267019	−	0.462491i	0.701071	−	0.713091i	$-0.252705\pi$
$761$	−5605.57	−	9709.13i	−0.267019	−	0.462491i	−0.968091	+	0.250600i	$0.919372\pi$
$762$		0			0
$763$	15466.4	+	2735.89i	0.733842	+	0.129811i
$764$		0			0
$765$	5921.07	+	10255.6i	0.279839	+	0.484695i
$766$		0			0
$767$	−29120.0	+	50437.3i	−1.37088	+	2.37443i
$768$		0			0
$769$	4305.86			0.201916			0.100958	−	0.994891i	$-0.467809\pi$
$769$	4305.86			0.201916			0.100958	+	0.994891i	$0.467809\pi$
$770$		0			0
$771$	−14073.3			−0.657379
$772$		0			0
$773$	−8320.24	+	14411.1i	−0.387139	+	0.670544i	−0.992063	−	0.125739i	$-0.959870\pi$
$773$	−8320.24	+	14411.1i	−0.387139	+	0.670544i	0.604925	+	0.796283i	$0.293203\pi$
$774$		0			0
$775$	−3143.09	−	5443.99i	−0.145681	−	0.252328i
$776$		0			0
$777$	−2441.42	−	6719.22i	−0.112723	−	0.310233i
$778$		0			0
$779$	−14279.9	−	24733.5i	−0.656778	−	1.13757i
$780$		0			0
$781$	−6252.99	+	10830.5i	−0.286491	+	0.496217i
$782$		0			0
$783$	−5724.56			−0.261276
$784$		0			0
$785$	−26659.4			−1.21212
$786$		0			0
$787$	−4883.53	+	8458.51i	−0.221193	+	0.383118i	−0.955171	−	0.296056i	$-0.904328\pi$
$787$	−4883.53	+	8458.51i	−0.221193	+	0.383118i	0.733977	+	0.679174i	$0.237662\pi$
$788$		0			0
$789$	−11372.4	−	19697.6i	−0.513142	−	0.888788i
$790$		0			0
$791$	4657.23	+	12817.5i	0.209345	+	0.576155i
$792$		0			0
$793$	10615.6	+	18386.8i	0.475375	+	0.823374i
$794$		0			0
$795$	8623.39	−	14936.2i	0.384705	−	0.666328i
$796$		0			0
$797$	23118.5			1.02748			0.513738	−	0.857947i	$-0.328260\pi$
$797$	23118.5			1.02748			0.513738	+	0.857947i	$0.328260\pi$
$798$		0			0
$799$	−27824.2			−1.23198
$800$		0			0
$801$	−728.350	+	1261.54i	−0.0321285	+	0.0556483i
$802$		0			0
$803$	16908.4	+	29286.3i	0.743071	+	1.28704i
$804$		0			0
$805$	−22453.1	−	3971.79i	−0.983066	−	0.173897i
$806$		0			0
$807$	5402.84	+	9358.00i	0.235674	+	0.408200i
$808$		0			0
$809$	−5230.33	+	9059.20i	−0.227304	+	0.393701i	−0.957008	−	0.290061i	$-0.906324\pi$
$809$	−5230.33	+	9059.20i	−0.227304	+	0.393701i	0.729705	+	0.683763i	$0.239658\pi$
$810$		0			0
$811$	9167.55			0.396937			0.198469	−	0.980107i	$-0.436403\pi$
$811$	9167.55			0.396937			0.198469	+	0.980107i	$0.436403\pi$
$812$		0			0
$813$	11508.8			0.496472
$814$		0			0
$815$	20387.7	−	35312.5i	0.876256	−	1.51772i
$816$		0			0
$817$	1596.91	+	2765.92i	0.0683827	+	0.118442i
$818$		0			0
$819$	−9340.66	+	11119.4i	−0.398521	+	0.474410i
$820$		0			0
$821$	−14413.7	−	24965.2i	−0.612717	−	1.06126i	−0.990780	−	0.135477i	$-0.956743\pi$
$821$	−14413.7	−	24965.2i	−0.612717	−	1.06126i	0.378064	−	0.925780i	$-0.376590\pi$
$822$		0			0
$823$	21397.2	−	37061.0i	0.906268	−	1.56970i	0.0870618	−	0.996203i	$-0.472252\pi$
$823$	21397.2	−	37061.0i	0.906268	−	1.56970i	0.819206	−	0.573499i	$-0.194414\pi$
$824$		0			0
$825$	4360.89			0.184032
$826$		0			0
$827$	6028.87			0.253500			0.126750	−	0.991935i	$-0.459545\pi$
$827$	6028.87			0.253500			0.126750	+	0.991935i	$0.459545\pi$
$828$		0			0
$829$	9703.71	−	16807.3i	0.406542	−	0.704152i	−0.587957	−	0.808892i	$-0.700068\pi$
$829$	9703.71	−	16807.3i	0.406542	−	0.704152i	0.994500	+	0.104740i	$0.0334010\pi$
$830$		0			0
$831$	−8104.57	−	14037.5i	−0.338320	−	0.585988i
$832$		0			0
$833$	−6072.84	−	34663.2i	−0.252595	−	1.44179i
$834$		0			0
$835$	19104.3	+	33089.5i	0.791773	+	1.37139i
$836$		0			0
$837$	−2149.84	+	3723.63i	−0.0887806	+	0.153773i
$838$		0			0
$839$	10599.5			0.436156			0.218078	−	0.975931i	$-0.430021\pi$
$839$	10599.5			0.436156			0.218078	+	0.975931i	$0.430021\pi$
$840$		0			0
$841$	20563.8			0.843159
$842$		0			0
$843$	−226.263	+	391.899i	−0.00924425	+	0.0160115i
$844$		0			0
$845$	34585.5	+	59903.8i	1.40802	+	2.43876i
$846$		0			0
$847$	−298.552	+	355.404i	−0.0121114	+	0.0144177i
$848$		0			0
$849$	2725.71	+	4721.07i	0.110184	+	0.190844i
$850$		0			0
$851$	−6176.17	+	10697.4i	−0.248786	+	0.430909i
$852$		0			0
$853$	−34766.1			−1.39551			−0.697754	−	0.716338i	$-0.745817\pi$
$853$	−34766.1			−1.39551			−0.697754	+	0.716338i	$0.745817\pi$
$854$		0			0
$855$	11060.4			0.442405
$856$		0			0
$857$	−15002.0	+	25984.2i	−0.597968	+	1.03571i	0.395153	+	0.918615i	$0.370692\pi$
$857$	−15002.0	+	25984.2i	−0.597968	+	1.03571i	−0.993121	+	0.117096i	$0.962642\pi$
$858$		0			0
$859$	−13065.3	−	22629.8i	−0.518955	−	0.898857i	−0.999757	−	0.0220275i	$-0.992988\pi$
$859$	−13065.3	−	22629.8i	−0.518955	−	0.898857i	0.480802	−	0.876829i	$-0.340345\pi$
$860$		0			0
$861$	−16306.3	−	2884.46i	−0.645431	−	0.114172i
$862$		0			0
$863$	22334.2	+	38683.9i	0.880955	+	1.52586i	0.850281	+	0.526329i	$0.176432\pi$
$863$	22334.2	+	38683.9i	0.880955	+	1.52586i	0.0306737	+	0.999529i	$0.490235\pi$
$864$		0			0
$865$	104.973	−	181.818i	0.00412623	−	0.00714684i
$866$		0			0
$867$	16840.1			0.659652
$868$		0			0
$869$	5019.18			0.195931
$870$		0			0
$871$	−14618.4	+	25319.8i	−0.568685	+	0.984992i
$872$		0			0
$873$	−822.061	−	1423.85i	−0.0318700	−	0.0552005i
$874$		0			0
$875$	−6937.28	−	19092.6i	−0.268026	−	0.737655i
$876$		0			0
$877$	−1839.28	−	3185.72i	−0.0708187	−	0.122662i	0.828442	−	0.560075i	$-0.189228\pi$
$877$	−1839.28	−	3185.72i	−0.0708187	−	0.122662i	−0.899260	+	0.437414i	$0.855895\pi$
$878$		0			0
$879$	4226.38	−	7320.30i	0.162175	−	0.280896i
$880$		0			0
$881$	−33443.6			−1.27894			−0.639468	−	0.768817i	$-0.720846\pi$
$881$	−33443.6			−1.27894			−0.639468	+	0.768817i	$0.720846\pi$
$882$		0			0
$883$	21095.4			0.803983			0.401991	−	0.915644i	$-0.368318\pi$
$883$	21095.4			0.803983			0.401991	+	0.915644i	$0.368318\pi$
$884$		0			0
$885$	12859.5	−	22273.3i	0.488439	−	0.846001i
$886$		0			0
$887$	7226.65	+	12516.9i	0.273560	+	0.473819i	0.969771	−	0.244018i	$-0.0784656\pi$
$887$	7226.65	+	12516.9i	0.273560	+	0.473819i	−0.696211	+	0.717837i	$0.745132\pi$
$888$		0			0
$889$	−15883.8	−	43715.0i	−0.599242	−	1.64922i
$890$		0			0
$891$	−1491.40	−	2583.18i	−0.0560762	−	0.0971268i
$892$		0			0
$893$	−12993.6	+	22505.7i	−0.486916	+	0.843363i
$894$		0			0
$895$	34604.9			1.29242
$896$		0			0
$897$	25091.6			0.933986
$898$		0			0
$899$	16881.9	−	29240.3i	0.626299	−	1.08478i
$900$		0			0
$901$	−22995.7	−	39829.8i	−0.850276	−	1.47272i
$902$		0			0
$903$	1823.51	+	322.567i	0.0672013	+	0.0118874i
$904$		0			0
$905$	200.898	+	347.965i	0.00737909	+	0.0127810i
$906$		0			0
$907$	−2602.04	+	4506.87i	−0.0952584	+	0.164992i	−0.909716	−	0.415230i	$-0.863701\pi$
$907$	−2602.04	+	4506.87i	−0.0952584	+	0.164992i	0.814458	+	0.580223i	$0.197034\pi$
$908$		0			0
$909$	−13788.9			−0.503135
$910$		0			0
$911$	−31584.8			−1.14868			−0.574342	−	0.818616i	$-0.694742\pi$
$911$	−31584.8			−1.14868			−0.574342	+	0.818616i	$0.694742\pi$
$912$		0			0
$913$	5292.90	−	9167.57i	0.191861	−	0.332314i
$914$		0			0
$915$	−4687.92	−	8119.71i	−0.169375	−	0.293365i
$916$		0			0
$917$	−8093.54	+	9634.76i	−0.291464	+	0.346966i
$918$		0			0
$919$	−23315.3	−	40383.3i	−0.836889	−	1.44953i	−0.892483	−	0.451081i	$-0.851039\pi$
$919$	−23315.3	−	40383.3i	−0.836889	−	1.44953i	0.0555943	−	0.998453i	$-0.482295\pi$
$920$		0			0
$921$	12883.8	−	22315.4i	0.460951	−	0.798391i
$922$		0			0
$923$	29587.9			1.05514
$924$		0			0
$925$	5079.16			0.180543
$926$		0			0
$927$	2195.59	−	3802.87i	0.0777912	−	0.134738i
$928$		0			0
$929$	19246.3	+	33335.6i	0.679711	+	1.17729i	0.975068	+	0.221907i	$0.0712280\pi$
$929$	19246.3	+	33335.6i	0.679711	+	1.17729i	−0.295357	+	0.955387i	$0.595439\pi$
$930$		0			0
$931$	−30873.4	−	11275.4i	−1.08682	−	0.396923i
$932$		0			0
$933$	−8997.44	−	15584.0i	−0.315716	−	0.546836i
$934$		0			0
$935$	24226.9	−	41962.2i	0.847384	−	1.46771i
$936$		0			0
$937$	39893.8			1.39090			0.695450	−	0.718574i	$-0.255205\pi$
$937$	39893.8			1.39090			0.695450	+	0.718574i	$0.255205\pi$
$938$		0			0
$939$	−14889.8			−0.517477
$940$		0			0
$941$	16315.4	−	28259.0i	0.565213	−	0.978977i	−0.431817	−	0.901961i	$-0.642127\pi$
$941$	16315.4	−	28259.0i	0.565213	−	0.978977i	0.997030	−	0.0770161i	$-0.0245393\pi$
$942$		0			0
$943$	14306.0	+	24778.7i	0.494027	+	0.855680i
$944$		0			0
$945$	4124.88	−	4910.36i	0.141992	−	0.169031i
$946$		0			0
$947$	15014.7	+	26006.1i	0.515217	+	0.892382i	0.999844	+	0.0176614i	$0.00562208\pi$
$947$	15014.7	+	26006.1i	0.515217	+	0.892382i	−0.484627	+	0.874721i	$0.661045\pi$
$948$		0			0
$949$	40003.7	−	69288.5i	1.36836	−	2.37007i
$950$		0			0
$951$	−11713.8			−0.399418
$952$		0			0
$953$	−34963.6			−1.18844			−0.594220	−	0.804303i	$-0.702539\pi$
$953$	−34963.6			−1.18844			−0.594220	+	0.804303i	$0.702539\pi$
$954$		0			0
$955$	9908.24	−	17161.6i	0.335731	−	0.581503i
$956$		0			0
$957$	11711.4	+	20284.8i	0.395587	+	0.685176i
$958$		0			0
$959$	−3000.67	−	530.798i	−0.101039	−	0.0178732i
$960$		0			0
$961$	2215.61	+	3837.56i	0.0743719	+	0.128816i
$962$		0			0
$963$	2215.58	−	3837.50i	0.0741393	−	0.128413i
$964$		0			0
$965$	23471.8			0.782990
$966$		0			0
$967$	−20520.5			−0.682414			−0.341207	−	0.939988i	$-0.610836\pi$
$967$	−20520.5			−0.682414			−0.341207	+	0.939988i	$0.610836\pi$
$968$		0			0
$969$	14747.1	−	25542.8i	0.488902	−	0.846804i
$970$		0			0
$971$	19887.6	+	34446.4i	0.657286	+	1.13845i	0.981315	+	0.192406i	$0.0616290\pi$
$971$	19887.6	+	34446.4i	0.657286	+	1.13845i	−0.324029	+	0.946047i	$0.605038\pi$
$972$		0			0
$973$	−3301.46	−	9086.20i	−0.108777	−	0.299373i
$974$		0			0
$975$	−5158.72	−	8935.16i	−0.169447	−	0.293491i
$976$		0			0
$977$	3586.02	−	6211.17i	0.117428	−	0.203391i	−0.801320	−	0.598236i	$-0.795868\pi$
$977$	3586.02	−	6211.17i	0.117428	−	0.203391i	0.918748	+	0.394845i	$0.129202\pi$
$978$		0			0
$979$	5960.29			0.194578
$980$		0			0
$981$	7632.65			0.248412
$982$		0			0
$983$	24174.1	−	41870.8i	0.784369	−	1.35857i	−0.145006	−	0.989431i	$-0.546320\pi$
$983$	24174.1	−	41870.8i	0.784369	−	1.35857i	0.929375	−	0.369137i	$-0.120347\pi$
$984$		0			0
$985$	30320.6	+	52516.9i	0.980807	+	1.69881i
$986$		0			0
$987$	5145.74	+	14162.0i	0.165948	+	0.456718i
$988$		0			0
$989$	−1599.83	−	2770.98i	−0.0514373	−	0.0890921i
$990$		0			0
$991$	18472.3	−	31994.9i	0.592121	−	1.02558i	−0.401826	−	0.915716i	$-0.631624\pi$
$991$	18472.3	−	31994.9i	0.592121	−	1.02558i	0.993946	−	0.109867i	$-0.0350425\pi$
$992$		0			0
$993$	7349.18			0.234863
$994$		0			0
$995$	−4209.72			−0.134128
$996$		0			0
$997$	−28294.8	+	49008.0i	−0.898802	+	1.55677i	−0.0697741	+	0.997563i	$0.522228\pi$
$997$	−28294.8	+	49008.0i	−0.898802	+	1.55677i	−0.829028	+	0.559208i	$0.811105\pi$
$998$		0			0
$999$	−1737.05	−	3008.66i	−0.0550128	−	0.0952850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.h.193.2		4
4.3	odd	2		84.4.i.b.25.2	✓	4
7.2	even	3	inner	336.4.q.h.289.2		4
7.3	odd	6		2352.4.a.bp.1.2		2
7.4	even	3		2352.4.a.cb.1.1		2
12.11	even	2		252.4.k.d.109.1		4
28.3	even	6		588.4.a.h.1.2		2
28.11	odd	6		588.4.a.g.1.1		2
28.19	even	6		588.4.i.i.373.1		4
28.23	odd	6		84.4.i.b.37.2	yes	4
28.27	even	2		588.4.i.i.361.1		4
84.11	even	6		1764.4.a.x.1.2		2
84.23	even	6		252.4.k.d.37.1		4
84.47	odd	6		1764.4.k.z.1549.2		4
84.59	odd	6		1764.4.a.p.1.1		2
84.83	odd	2		1764.4.k.z.361.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.i.b.25.2	✓	4	4.3	odd	2
84.4.i.b.37.2	yes	4	28.23	odd	6
252.4.k.d.37.1		4	84.23	even	6
252.4.k.d.109.1		4	12.11	even	2
336.4.q.h.193.2		4	1.1	even	1	trivial
336.4.q.h.289.2		4	7.2	even	3	inner
588.4.a.g.1.1		2	28.11	odd	6
588.4.a.h.1.2		2	28.3	even	6
588.4.i.i.361.1		4	28.27	even	2
588.4.i.i.373.1		4	28.19	even	6
1764.4.a.p.1.1		2	84.59	odd	6
1764.4.a.x.1.2		2	84.11	even	6
1764.4.k.z.361.2		4	84.83	odd	2
1764.4.k.z.1549.2		4	84.47	odd	6
2352.4.a.bp.1.2		2	7.3	odd	6
2352.4.a.cb.1.1		2	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +(6.41238 + 11.1066i) q^{5} +(-6.32475 - 17.4068i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{3} +(6.41238 + 11.1066i) q^{5} +(-6.32475 - 17.4068i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-18.4124 + 31.8912i) q^{11} +87.1238 q^{13} -38.4743 q^{15} +(-51.2990 + 88.8525i) q^{17} +(47.9124 + 82.9867i) q^{19} +(54.7114 + 9.67805i) q^{21} +(-48.0000 - 83.1384i) q^{23} +(-19.7371 + 34.1857i) q^{25} +27.0000 q^{27} -212.021 q^{29} +(-79.6238 + 137.912i) q^{31} +(-55.2371 - 95.6735i) q^{33} +(152.773 - 181.865i) q^{35} +(-64.3351 - 111.432i) q^{37} +(-130.686 + 226.354i) q^{39} -298.042 q^{41} +33.3297 q^{43} +(57.7114 - 99.9590i) q^{45} +(135.598 + 234.863i) q^{47} +(-262.995 + 220.188i) q^{49} +(-153.897 - 266.557i) q^{51} +(-224.134 + 388.212i) q^{53} -472.268 q^{55} -287.474 q^{57} +(-334.237 + 578.916i) q^{59} +(121.846 + 211.043i) q^{61} +(-107.211 + 127.627i) q^{63} +(558.670 + 967.645i) q^{65} +(-167.789 + 290.618i) q^{67} +288.000 q^{69} +339.608 q^{71} +(459.160 - 795.288i) q^{73} +(-59.2114 - 102.557i) q^{75} +(671.578 + 118.797i) q^{77} +(-68.1495 - 118.038i) q^{79} +(-40.5000 + 70.1481i) q^{81} -287.464 q^{83} -1315.79 q^{85} +(318.031 - 550.846i) q^{87} +(-80.9277 - 140.171i) q^{89} +(-551.036 - 1516.55i) q^{91} +(-238.871 - 413.737i) q^{93} +(-614.464 + 1064.28i) q^{95} +182.680 q^{97} +331.423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 3 q^{5} + 20 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 + 3 * q^5 + 20 * q^7 - 18 * q^9	\( 4 q - 6 q^{3} + 3 q^{5} + 20 q^{7} - 18 q^{9} - 51 q^{11} + 122 q^{13} - 18 q^{15} - 24 q^{17} + 169 q^{19} + 15 q^{21} - 192 q^{23} - 11 q^{25} + 108 q^{27} - 78 q^{29} - 92 q^{31} - 153 q^{33} + 294 q^{35} + 173 q^{37} - 183 q^{39} + 348 q^{41} + 994 q^{43} + 27 q^{45} + 180 q^{47} - 146 q^{49} - 72 q^{51} - 285 q^{53} - 666 q^{55} - 1014 q^{57} - 1269 q^{59} - 328 q^{61} - 225 q^{63} + 1374 q^{65} - 875 q^{67} + 1152 q^{69} + 2808 q^{71} + 1361 q^{73} - 33 q^{75} + 897 q^{77} - 182 q^{79} - 162 q^{81} + 798 q^{83} - 4176 q^{85} + 117 q^{87} - 822 q^{89} - 1955 q^{91} - 276 q^{93} - 510 q^{95} + 1682 q^{97} + 918 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 + 3 * q^5 + 20 * q^7 - 18 * q^9 - 51 * q^11 + 122 * q^13 - 18 * q^15 - 24 * q^17 + 169 * q^19 + 15 * q^21 - 192 * q^23 - 11 * q^25 + 108 * q^27 - 78 * q^29 - 92 * q^31 - 153 * q^33 + 294 * q^35 + 173 * q^37 - 183 * q^39 + 348 * q^41 + 994 * q^43 + 27 * q^45 + 180 * q^47 - 146 * q^49 - 72 * q^51 - 285 * q^53 - 666 * q^55 - 1014 * q^57 - 1269 * q^59 - 328 * q^61 - 225 * q^63 + 1374 * q^65 - 875 * q^67 + 1152 * q^69 + 2808 * q^71 + 1361 * q^73 - 33 * q^75 + 897 * q^77 - 182 * q^79 - 162 * q^81 + 798 * q^83 - 4176 * q^85 + 117 * q^87 - 822 * q^89 - 1955 * q^91 - 276 * q^93 - 510 * q^95 + 1682 * q^97 + 918 * q^99

Introduction

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