LMFDB - Embedded newform 336.4.bl.e.31.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(31,336)] 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("336.31"); 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([3, 0, 0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bl (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-9,0,-21] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.419349987.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 17x^{4} - 24x^{3} + 289x^{2} - 204x + 144 $ x^6 + 17x^4 - 24x^3 + 289x^2 - 204x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Root			$0.364319 - 0.631019i$ of defining polynomial
Character	$\chi$	$=$	336.31
Dual form			336.4.bl.e.271.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 2.59808i) q^{3} +(10.5177 - 6.07241i) q^{5} +(-16.1550 + 9.05627i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-0.668197 - 0.385784i) q^{11} -61.4752i q^{13} +36.4344i q^{15} +(16.0704 + 9.27827i) q^{17} +(-40.2122 - 69.6496i) q^{19} +(0.703630 - 55.5563i) q^{21} +(-4.96500 + 2.86654i) q^{23} +(11.2482 - 19.4825i) q^{25} +27.0000 q^{27} -28.8053 q^{29} +(55.7304 - 96.5279i) q^{31} +(2.00459 - 1.15735i) q^{33} +(-114.920 + 193.351i) q^{35} +(-116.169 - 201.211i) q^{37} +(159.717 + 92.2128i) q^{39} -227.929i q^{41} -40.4244i q^{43} +(-94.6595 - 54.6517i) q^{45} +(-74.8596 - 129.661i) q^{47} +(178.968 - 292.608i) q^{49} +(-48.2113 + 27.8348i) q^{51} +(340.032 - 588.953i) q^{53} -9.37054 q^{55} +241.273 q^{57} +(171.650 - 297.307i) q^{59} +(292.887 - 169.098i) q^{61} +(143.284 + 85.1626i) q^{63} +(-373.302 - 646.578i) q^{65} +(730.648 + 421.840i) q^{67} -17.1993i q^{69} -912.430i q^{71} +(-256.835 - 148.284i) q^{73} +(33.7447 + 58.4476i) q^{75} +(14.2885 + 0.180966i) q^{77} +(-415.056 + 239.633i) q^{79} +(-40.5000 + 70.1481i) q^{81} -1210.95 q^{83} +225.366 q^{85} +(43.2080 - 74.8385i) q^{87} +(-866.187 + 500.093i) q^{89} +(556.736 + 993.131i) q^{91} +(167.191 + 289.584i) q^{93} +(-845.882 - 488.370i) q^{95} +258.680i q^{97} +6.94410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 21 q^{5} - 19 q^{7} - 27 q^{9} - 75 q^{11} + 162 q^{17} - 80 q^{19} - 93 q^{21} + 204 q^{23} + 228 q^{25} + 162 q^{27} + 642 q^{29} - 313 q^{31} + 225 q^{33} - 198 q^{35} + 36 q^{37} + 162 q^{39}+ \cdots - 4854 q^{95}+O(q^{100}) $ 6 * q - 9 * q^3 - 21 * q^5 - 19 * q^7 - 27 * q^9 - 75 * q^11 + 162 * q^17 - 80 * q^19 - 93 * q^21 + 204 * q^23 + 228 * q^25 + 162 * q^27 + 642 * q^29 - 313 * q^31 + 225 * q^33 - 198 * q^35 + 36 * q^37 + 162 * q^39 + 189 * q^45 + 84 * q^47 + 921 * q^49 - 486 * q^51 + 453 * q^53 + 1842 * q^55 + 480 * q^57 - 153 * q^59 - 576 * q^61 + 450 * q^63 - 1344 * q^65 - 762 * q^67 + 1746 * q^73 + 684 * q^75 + 1629 * q^77 - 579 * q^79 - 243 * q^81 + 1458 * q^83 + 1164 * q^85 - 963 * q^87 - 1302 * q^89 + 318 * q^91 - 939 * q^93 - 4854 * q^95

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$		0			0
$5$	10.5177	−	6.07241i	0.940733	−	0.543133i	0.0505431	−	0.998722i	$-0.483905\pi$
$5$	10.5177	−	6.07241i	0.940733	−	0.543133i	0.890190	+	0.455589i	$0.150571\pi$
$6$		0			0
$7$	−16.1550	+	9.05627i	−0.872288	+	0.488992i
$7$	−16.1550	+	9.05627i	−0.872288	+	0.488992i
$8$		0			0
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.668197	−	0.385784i	−0.0183154	−	0.0105744i	0.490814	−	0.871264i	$-0.336699\pi$
$11$	−0.668197	−	0.385784i	−0.0183154	−	0.0105744i	−0.509130	+	0.860690i	$0.670033\pi$
$12$		0			0
$13$		−	61.4752i		−	1.31155i	−0.754957	−	0.655775i	$-0.772342\pi$
$13$		−	61.4752i		−	1.31155i	0.754957	−	0.655775i	$-0.227658\pi$
$14$		0			0
$15$			36.4344i			0.627155i
$16$		0			0
$17$	16.0704	+	9.27827i	0.229274	+	0.132371i	0.610237	−	0.792219i	$-0.291074\pi$
$17$	16.0704	+	9.27827i	0.229274	+	0.132371i	−0.380963	+	0.924590i	$0.624408\pi$
$18$		0			0
$19$	−40.2122	−	69.6496i	−0.485543	−	0.840985i	0.514319	−	0.857599i	$-0.328045\pi$
$19$	−40.2122	−	69.6496i	−0.485543	−	0.840985i	−0.999862	+	0.0166137i	$0.994711\pi$
$20$		0			0
$21$	0.703630	−	55.5563i	0.00731165	−	0.577304i
$22$		0			0
$23$	−4.96500	+	2.86654i	−0.0450119	+	0.0259876i	−0.522337	−	0.852739i	$-0.674940\pi$
$23$	−4.96500	+	2.86654i	−0.0450119	+	0.0259876i	0.477325	+	0.878727i	$0.341606\pi$
$24$		0			0
$25$	11.2482	−	19.4825i	0.0899860	−	0.155860i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	−28.8053			−0.184449			−0.0922244	−	0.995738i	$-0.529398\pi$
$29$	−28.8053			−0.184449			−0.0922244	+	0.995738i	$0.529398\pi$
$30$		0			0
$31$	55.7304	−	96.5279i	0.322886	−	0.559255i	−0.658196	−	0.752847i	$-0.728680\pi$
$31$	55.7304	−	96.5279i	0.322886	−	0.559255i	0.981082	+	0.193591i	$0.0620135\pi$
$32$		0			0
$33$	2.00459	−	1.15735i	0.0105744	−	0.00610512i
$34$		0			0
$35$	−114.920	+	193.351i	−0.555003	+	0.933779i
$36$		0			0
$37$	−116.169	−	201.211i	−0.516164	−	0.894023i	−0.999824	−	0.0187665i	$-0.994026\pi$
$37$	−116.169	−	201.211i	−0.516164	−	0.894023i	0.483660	−	0.875256i	$-0.339307\pi$
$38$		0			0
$39$	159.717	+	92.2128i	0.655775	+	0.378612i
$40$		0			0
$41$		−	227.929i		−	0.868206i	−0.900863	−	0.434103i	$-0.857065\pi$
$41$		−	227.929i		−	0.868206i	0.900863	−	0.434103i	$-0.142935\pi$
$42$		0			0
$43$		−	40.4244i		−	0.143364i	−0.997428	−	0.0716821i	$-0.977163\pi$
$43$		−	40.4244i		−	0.143364i	0.997428	−	0.0716821i	$-0.0228367\pi$
$44$		0			0
$45$	−94.6595	−	54.6517i	−0.313578	−	0.181044i
$46$		0			0
$47$	−74.8596	−	129.661i	−0.232327	−	0.402403i	0.726165	−	0.687520i	$-0.241301\pi$
$47$	−74.8596	−	129.661i	−0.232327	−	0.402403i	−0.958493	+	0.285117i	$0.907967\pi$
$48$		0			0
$49$	178.968	−	292.608i	0.521773	−	0.853084i
$50$		0			0
$51$	−48.2113	+	27.8348i	−0.132371	+	0.0764246i
$52$		0			0
$53$	340.032	−	588.953i	0.881264	−	1.52639i	0.0313279	−	0.999509i	$-0.490026\pi$
$53$	340.032	−	588.953i	0.881264	−	1.52639i	0.849936	−	0.526885i	$-0.176640\pi$
$54$		0			0
$55$	−9.37054			−0.0229731
$56$		0			0
$57$	241.273			0.560657
$58$		0			0
$59$	171.650	−	297.307i	0.378762	−	0.656035i	−0.612120	−	0.790765i	$-0.709683\pi$
$59$	171.650	−	297.307i	0.378762	−	0.656035i	0.990882	+	0.134729i	$0.0430165\pi$
$60$		0			0
$61$	292.887	−	169.098i	0.614760	−	0.354932i	−0.160066	−	0.987106i	$-0.551171\pi$
$61$	292.887	−	169.098i	0.614760	−	0.354932i	0.774826	+	0.632174i	$0.217837\pi$
$62$		0			0
$63$	143.284	+	85.1626i	0.286541	+	0.170309i
$64$		0			0
$65$	−373.302	−	646.578i	−0.712345	−	1.23382i
$66$		0			0
$67$	730.648	+	421.840i	1.33228	+	0.769193i	0.985649	−	0.168808i	$-0.0539917\pi$
$67$	730.648	+	421.840i	1.33228	+	0.769193i	0.346633	+	0.938001i	$0.387325\pi$
$68$		0			0
$69$		−	17.1993i		−	0.0300080i
$70$		0			0
$71$		−	912.430i		−	1.52515i	−0.646901	−	0.762574i	$-0.723935\pi$
$71$		−	912.430i		−	1.52515i	0.646901	−	0.762574i	$-0.276065\pi$
$72$		0			0
$73$	−256.835	−	148.284i	−0.411785	−	0.237744i	0.279771	−	0.960067i	$-0.409741\pi$
$73$	−256.835	−	148.284i	−0.411785	−	0.237744i	−0.691556	+	0.722323i	$0.743075\pi$
$74$		0			0
$75$	33.7447	+	58.4476i	0.0519534	+	0.0899860i
$76$		0			0
$77$	14.2885	+	0.180966i	0.0211471	+	0.000267831i
$78$		0			0
$79$	−415.056	+	239.633i	−0.591108	+	0.341276i	−0.765535	−	0.643394i	$-0.777526\pi$
$79$	−415.056	+	239.633i	−0.591108	+	0.341276i	0.174428	+	0.984670i	$0.444192\pi$
$80$		0			0
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−1210.95			−1.60144			−0.800720	−	0.599038i	$-0.795550\pi$
$83$	−1210.95			−1.60144			−0.800720	+	0.599038i	$0.795550\pi$
$84$		0			0
$85$	225.366			0.287580
$86$		0			0
$87$	43.2080	−	74.8385i	0.0532458	−	0.0922244i
$88$		0			0
$89$	−866.187	+	500.093i	−1.03164	+	0.595615i	−0.917453	−	0.397844i	$-0.869758\pi$
$89$	−866.187	+	500.093i	−1.03164	+	0.595615i	−0.114183	+	0.993460i	$0.536425\pi$
$90$		0			0
$91$	556.736	+	993.131i	0.641338	+	1.14405i
$92$		0			0
$93$	167.191	+	289.584i	0.186418	+	0.322886i
$94$		0			0
$95$	−845.882	−	488.370i	−0.913533	−	0.527429i
$96$		0			0
$97$			258.680i			0.270773i	0.990793	+	0.135386i	$0.0432276\pi$
$97$			258.680i			0.270773i	−0.990793	+	0.135386i	$0.956772\pi$
$98$		0			0
$99$			6.94410i			0.00704958i
$100$		0			0
$101$	1398.23	+	807.271i	1.37752	+	0.795311i	0.991860	−	0.127330i	$-0.0406407\pi$
$101$	1398.23	+	807.271i	1.37752	+	0.795311i	0.385659	+	0.922641i	$0.373974\pi$
$102$		0			0
$103$	346.878	+	600.810i	0.331834	+	0.574753i	0.982871	−	0.184293i	$-0.0589994\pi$
$103$	346.878	+	600.810i	0.331834	+	0.574753i	−0.651038	+	0.759045i	$0.725666\pi$
$104$		0			0
$105$	−329.960	−	588.598i	−0.306674	−	0.547060i
$106$		0			0
$107$	−1007.34	+	581.587i	−0.910123	+	0.525459i	−0.880471	−	0.474101i	$-0.842773\pi$
$107$	−1007.34	+	581.587i	−0.910123	+	0.525459i	−0.0296520	+	0.999560i	$0.509440\pi$
$108$		0			0
$109$	−853.188	+	1477.76i	−0.749730	+	1.29857i	0.198222	+	0.980157i	$0.436483\pi$
$109$	−853.188	+	1477.76i	−0.749730	+	1.29857i	−0.947952	+	0.318413i	$0.896850\pi$
$110$		0			0
$111$	697.014			0.596015
$112$		0			0
$113$	−359.545			−0.299320			−0.149660	−	0.988738i	$-0.547818\pi$
$113$	−359.545			−0.299320			−0.149660	+	0.988738i	$0.547818\pi$
$114$		0			0
$115$	−34.8137	+	60.2990i	−0.0282295	+	0.0488949i
$116$		0			0
$117$	−479.152	+	276.638i	−0.378612	+	0.218592i
$118$		0			0
$119$	−343.644	−	4.35231i	−0.264721	−	0.00335274i
$120$		0			0
$121$	−665.202	−	1152.16i	−0.499776	−	0.865638i
$122$		0			0
$123$	592.176	+	341.893i	0.434103	+	0.250630i
$124$		0			0
$125$			1244.89i			0.890768i
$126$		0			0
$127$		−	185.775i		−	0.129802i	−0.997892	−	0.0649009i	$-0.979327\pi$
$127$		−	185.775i		−	0.129802i	0.997892	−	0.0649009i	$-0.0206731\pi$
$128$		0			0
$129$	105.026	+	60.6366i	0.0716821	+	0.0413857i
$130$		0			0
$131$	−1468.22	−	2543.03i	−0.979230	−	1.69608i	−0.665204	−	0.746661i	$-0.731656\pi$
$131$	−1468.22	−	2543.03i	−0.979230	−	1.69608i	−0.314025	−	0.949415i	$-0.601678\pi$
$132$		0			0
$133$	1280.39	+	761.017i	0.834769	+	0.496155i
$134$		0			0
$135$	283.978	−	163.955i	0.181044	−	0.104526i
$136$		0			0
$137$	−190.339	+	329.678i	−0.118699	+	0.205593i	−0.919252	−	0.393669i	$-0.871206\pi$
$137$	−190.339	+	329.678i	−0.118699	+	0.205593i	0.800553	+	0.599262i	$0.204539\pi$
$138$		0			0
$139$	2618.74			1.59797			0.798987	−	0.601349i	$-0.205370\pi$
$139$	2618.74			1.59797			0.798987	+	0.601349i	$0.205370\pi$
$140$		0			0
$141$	449.157			0.268269
$142$		0			0
$143$	−23.7161	+	41.0775i	−0.0138688	+	0.0240215i
$144$		0			0
$145$	−302.966	+	174.918i	−0.173517	+	0.100180i
$146$		0			0
$147$	491.766	+	903.885i	0.275919	+	0.507151i
$148$		0			0
$149$	1387.26	+	2402.80i	0.762742	+	1.32111i	0.941432	+	0.337202i	$0.109481\pi$
$149$	1387.26	+	2402.80i	0.762742	+	1.32111i	−0.178691	+	0.983905i	$0.557186\pi$
$150$		0			0
$151$	−1142.90	−	659.854i	−0.615947	−	0.355617i	0.159343	−	0.987223i	$-0.449063\pi$
$151$	−1142.90	−	659.854i	−0.615947	−	0.355617i	−0.775289	+	0.631606i	$0.782396\pi$
$152$		0			0
$153$		−	167.009i		−	0.0882475i
$154$		0			0
$155$		−	1353.67i		−	0.701480i
$156$		0			0
$157$	1527.08	+	881.658i	0.776268	+	0.448178i	0.835106	−	0.550089i	$-0.185406\pi$
$157$	1527.08	+	881.658i	0.776268	+	0.448178i	−0.0588383	+	0.998268i	$0.518740\pi$
$158$		0			0
$159$	1020.10	+	1766.86i	0.508798	+	0.881264i
$160$		0			0
$161$	54.2494	−	91.2734i	0.0265556	−	0.0446792i
$162$		0			0
$163$	661.673	−	382.017i	0.317952	−	0.183570i	−0.332527	−	0.943094i	$-0.607901\pi$
$163$	661.673	−	382.017i	0.317952	−	0.183570i	0.650480	+	0.759524i	$0.274568\pi$
$164$		0			0
$165$	14.0558	−	24.3454i	0.00663178	−	0.0114866i
$166$		0			0
$167$	3031.09			1.40451			0.702253	−	0.711928i	$-0.252178\pi$
$167$	3031.09			1.40451			0.702253	+	0.711928i	$0.252178\pi$
$168$		0			0
$169$	−1582.20			−0.720163
$170$		0			0
$171$	−361.910	+	626.847i	−0.161848	+	0.280328i
$172$		0			0
$173$	−2130.08	+	1229.80i	−0.936110	+	0.540463i	−0.888739	−	0.458414i	$-0.848418\pi$
$173$	−2130.08	+	1229.80i	−0.936110	+	0.540463i	−0.0473709	+	0.998877i	$0.515084\pi$
$174$		0			0
$175$	−5.27640	+	416.607i	−0.00227919	+	0.179957i
$176$		0			0
$177$	514.951	+	891.921i	0.218678	+	0.378762i
$178$		0			0
$179$	−3578.02	−	2065.77i	−1.49405	−	0.862587i	−0.494069	−	0.869423i	$-0.664491\pi$
$179$	−3578.02	−	2065.77i	−1.49405	−	0.862587i	−0.999977	+	0.00683552i	$0.997824\pi$
$180$		0			0
$181$			3837.51i			1.57591i	0.615734	+	0.787954i	$0.288860\pi$
$181$			3837.51i			1.57591i	−0.615734	+	0.787954i	$0.711140\pi$
$182$		0			0
$183$			1014.59i			0.409840i
$184$		0			0
$185$	−2443.67	−	1410.85i	−0.971146	−	0.560691i
$186$		0			0
$187$	−7.15881	−	12.3994i	−0.00279949	−	0.00484885i
$188$		0			0
$189$	−436.185	+	244.519i	−0.167872	+	0.0941066i
$190$		0			0
$191$	−3453.28	+	1993.75i	−1.30822	+	0.755304i	−0.981800	−	0.189920i	$-0.939177\pi$
$191$	−3453.28	+	1993.75i	−1.30822	+	0.755304i	−0.326424	+	0.945223i	$0.605844\pi$
$192$		0			0
$193$	−1093.49	+	1893.98i	−0.407829	+	0.706381i	−0.994646	−	0.103339i	$-0.967048\pi$
$193$	−1093.49	+	1893.98i	−0.407829	+	0.706381i	0.586817	+	0.809720i	$0.300381\pi$
$194$		0			0
$195$	2239.81			0.822546
$196$		0			0
$197$	2046.43			0.740111			0.370056	−	0.929010i	$-0.379339\pi$
$197$	2046.43			0.740111			0.370056	+	0.929010i	$0.379339\pi$
$198$		0			0
$199$	−981.826	+	1700.57i	−0.349748	+	0.605781i	−0.986205	−	0.165531i	$-0.947066\pi$
$199$	−981.826	+	1700.57i	−0.349748	+	0.605781i	0.636457	+	0.771312i	$0.280399\pi$
$200$		0			0
$201$	−2191.94	+	1265.52i	−0.769193	+	0.444094i
$202$		0			0
$203$	465.350	−	260.869i	0.160893	−	0.0901941i
$204$		0			0
$205$	−1384.07	−	2397.29i	−0.471551	−	0.816751i
$206$		0			0
$207$	44.6850	+	25.7989i	0.0150040	+	0.00866255i
$208$		0			0
$209$			62.0529i			0.0205373i
$210$		0			0
$211$		−	3146.54i		−	1.02662i	−0.858203	−	0.513310i	$-0.828419\pi$
$211$		−	3146.54i		−	1.02662i	0.858203	−	0.513310i	$-0.171581\pi$
$212$		0			0
$213$	2370.56	+	1368.65i	0.762574	+	0.440272i
$214$		0			0
$215$	−245.473	−	425.172i	−0.0778658	−	0.134867i
$216$		0			0
$217$	−26.1424	+	2064.12i	−0.00817816	+	0.645721i
$218$		0			0
$219$	770.506	−	444.852i	0.237744	−	0.137262i
$220$		0			0
$221$	570.383	−	987.933i	0.173611	−	0.300704i
$222$		0			0
$223$	4563.97			1.37052			0.685261	−	0.728298i	$-0.259688\pi$
$223$	4563.97			1.37052			0.685261	+	0.728298i	$0.259688\pi$
$224$		0			0
$225$	−202.468			−0.0599906
$226$		0			0
$227$	−3077.57	+	5330.51i	−0.899848	+	1.55858i	−0.0721605	+	0.997393i	$0.522989\pi$
$227$	−3077.57	+	5330.51i	−0.899848	+	1.55858i	−0.827687	+	0.561189i	$0.810344\pi$
$228$		0			0
$229$	5214.27	−	3010.46i	1.50467	−	0.868720i	0.504681	−	0.863306i	$-0.331610\pi$
$229$	5214.27	−	3010.46i	1.50467	−	0.868720i	0.999985	−	0.00541399i	$-0.00172334\pi$
$230$		0			0
$231$	−21.9029	+	36.8511i	−0.00623854	+	0.0104962i
$232$		0			0
$233$	−423.782	−	734.012i	−0.119154	−	0.206381i	0.800279	−	0.599628i	$-0.204685\pi$
$233$	−423.782	−	734.012i	−0.119154	−	0.206381i	−0.919433	+	0.393247i	$0.871352\pi$
$234$		0			0
$235$	−1574.70	−	909.156i	−0.437116	−	0.252369i
$236$		0			0
$237$		−	1437.80i		−	0.394072i
$238$		0			0
$239$		−	7194.59i		−	1.94719i	−0.228276	−	0.973597i	$-0.573309\pi$
$239$		−	7194.59i		−	1.94719i	0.228276	−	0.973597i	$-0.426691\pi$
$240$		0			0
$241$	−1014.72	−	585.848i	−0.271219	−	0.156588i	0.358222	−	0.933636i	$-0.383383\pi$
$241$	−1014.72	−	585.848i	−0.271219	−	0.156588i	−0.629441	+	0.777048i	$0.716716\pi$
$242$		0			0
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	105.501	−	4164.33i	0.0275111	−	1.08592i
$246$		0			0
$247$	−4281.72	+	2472.05i	−1.10299	+	0.636814i
$248$		0			0
$249$	1816.43	−	3146.15i	0.462296	−	0.800720i
$250$		0			0
$251$	1267.79			0.318813			0.159406	−	0.987213i	$-0.449042\pi$
$251$	1267.79			0.318813			0.159406	+	0.987213i	$0.449042\pi$
$252$		0			0
$253$	4.42346			0.00109921
$254$		0			0
$255$	−338.049	+	585.517i	−0.0830173	+	0.143790i
$256$		0			0
$257$	1595.73	−	921.292i	0.387310	−	0.223613i	−0.293684	−	0.955903i	$-0.594881\pi$
$257$	1595.73	−	921.292i	0.387310	−	0.223613i	0.680994	+	0.732289i	$0.261548\pi$
$258$		0			0
$259$	3698.93	+	2198.50i	0.887414	+	0.527445i
$260$		0			0
$261$	129.624	+	224.515i	0.0307415	+	0.0532458i
$262$		0			0
$263$	−2960.32	−	1709.14i	−0.694073	−	0.400723i	0.111063	−	0.993813i	$-0.464574\pi$
$263$	−2960.32	−	1709.14i	−0.694073	−	0.400723i	−0.805136	+	0.593090i	$0.797908\pi$
$264$		0			0
$265$		−	8259.25i		−	1.91457i
$266$		0			0
$267$		−	3000.56i		−	0.687757i
$268$		0			0
$269$	−2646.61	−	1528.02i	−0.599876	−	0.346338i	0.169117	−	0.985596i	$-0.445908\pi$
$269$	−2646.61	−	1528.02i	−0.599876	−	0.346338i	−0.768993	+	0.639258i	$0.779242\pi$
$270$		0			0
$271$	1699.72	+	2944.01i	0.381000	+	0.659911i	0.991205	−	0.132332i	$-0.0422465\pi$
$271$	1699.72	+	2944.01i	0.381000	+	0.659911i	−0.610206	+	0.792243i	$0.708913\pi$
$272$		0			0
$273$	−3415.33	−	43.2558i	−0.757163	−	0.00958960i
$274$		0			0
$275$	−15.0321	+	8.67878i	−0.00329625	+	0.00190309i
$276$		0			0
$277$	579.502	−	1003.73i	0.125700	−	0.217719i	−0.796306	−	0.604894i	$-0.793216\pi$
$277$	579.502	−	1003.73i	0.125700	−	0.217719i	0.922006	+	0.387175i	$0.126549\pi$
$278$		0			0
$279$	−1003.15			−0.215257
$280$		0			0
$281$	1887.34			0.400673			0.200336	−	0.979727i	$-0.435797\pi$
$281$	1887.34			0.400673			0.200336	+	0.979727i	$0.435797\pi$
$282$		0			0
$283$	−3275.98	+	5674.16i	−0.688115	+	1.19185i	0.284331	+	0.958726i	$0.408228\pi$
$283$	−3275.98	+	5674.16i	−0.688115	+	1.19185i	−0.972447	+	0.233125i	$0.925105\pi$
$284$		0			0
$285$	2537.65	−	1465.11i	0.527429	−	0.304511i
$286$		0			0
$287$	2064.18	+	3682.19i	0.424546	+	0.757326i
$288$		0			0
$289$	−2284.33	−	3956.57i	−0.464956	−	0.805327i
$290$		0			0
$291$	−672.070	−	388.020i	−0.135386	−	0.0781654i
$292$		0			0
$293$		−	1482.10i		−	0.295513i	−0.989024	−	0.147757i	$-0.952795\pi$
$293$		−	1482.10i		−	0.295513i	0.989024	−	0.147757i	$-0.0472052\pi$
$294$		0			0
$295$		−	4169.32i		−	0.822872i
$296$		0			0
$297$	−18.0413	−	10.4162i	−0.00352479	−	0.00203504i
$298$		0			0
$299$	176.221	+	305.224i	0.0340841	+	0.0590354i
$300$		0			0
$301$	366.094	+	653.056i	0.0701040	+	0.125055i
$302$		0			0
$303$	−4194.70	+	2421.81i	−0.795311	+	0.459173i
$304$		0			0
$305$	2053.67	−	3557.06i	0.385550	−	0.667792i
$306$		0			0
$307$	5600.51			1.04117			0.520583	−	0.853811i	$-0.325715\pi$
$307$	5600.51			1.04117			0.520583	+	0.853811i	$0.325715\pi$
$308$		0			0
$309$	−2081.27			−0.383168
$310$		0			0
$311$	3244.84	−	5620.22i	0.591633	−	1.02474i	−0.402380	−	0.915473i	$-0.631817\pi$
$311$	3244.84	−	5620.22i	0.591633	−	1.02474i	0.994013	−	0.109266i	$-0.0348499\pi$
$312$		0			0
$313$	2424.16	−	1399.59i	0.437768	−	0.252745i	−0.264882	−	0.964281i	$-0.585333\pi$
$313$	2424.16	−	1399.59i	0.437768	−	0.252745i	0.702650	+	0.711535i	$0.252000\pi$
$314$		0			0
$315$	2024.16	+	25.6364i	0.362059	+	0.00458554i
$316$		0			0
$317$	3320.90	+	5751.97i	0.588393	+	1.01913i	0.994443	+	0.105275i	$0.0335724\pi$
$317$	3320.90	+	5751.97i	0.588393	+	1.01913i	−0.406050	+	0.913851i	$0.633094\pi$
$318$		0			0
$319$	19.2476	+	11.1126i	0.00337825	+	0.00195043i
$320$		0			0
$321$		−	3489.52i		−	0.606748i
$322$		0			0
$323$		−	1492.40i		−	0.257088i
$324$		0			0
$325$	−1197.69	−	691.488i	−0.204418	−	0.118021i
$326$		0			0
$327$	−2559.56	−	4433.29i	−0.432857	−	0.749730i
$328$		0			0
$329$	2383.60	+	1416.72i	0.399428	+	0.237405i
$330$		0			0
$331$	−2946.79	+	1701.33i	−0.489336	+	0.282518i	−0.724299	−	0.689486i	$-0.757836\pi$
$331$	−2946.79	+	1701.33i	−0.489336	+	0.282518i	0.234963	+	0.972004i	$0.424503\pi$
$332$		0			0
$333$	−1045.52	+	1810.90i	−0.172055	+	0.298008i
$334$		0			0
$335$	10246.3			1.67110
$336$		0			0
$337$	−4730.94			−0.764721			−0.382360	−	0.924013i	$-0.624889\pi$
$337$	−4730.94			−0.764721			−0.382360	+	0.924013i	$0.624889\pi$
$338$		0			0
$339$	539.318	−	934.125i	0.0864062	−	0.149660i
$340$		0			0
$341$	−74.4777	+	42.9997i	−0.0118276	+	0.00682864i
$342$		0			0
$343$	−241.294	+	6347.86i	−0.0379843	+	0.999278i
$344$		0			0
$345$	−104.441	−	180.897i	−0.0162983	−	0.0282295i
$346$		0			0
$347$	2085.14	+	1203.85i	0.322582	+	0.186243i	0.652543	−	0.757752i	$-0.273702\pi$
$347$	2085.14	+	1203.85i	0.322582	+	0.186243i	−0.329961	+	0.943995i	$0.607036\pi$
$348$		0			0
$349$			208.381i			0.0319609i	0.999872	+	0.0159805i	$0.00508695\pi$
$349$			208.381i			0.0319609i	−0.999872	+	0.0159805i	$0.994913\pi$
$350$		0			0
$351$		−	1659.83i		−	0.252408i
$352$		0			0
$353$	−7738.53	−	4467.84i	−1.16680	−	0.673652i	−0.213876	−	0.976861i	$-0.568609\pi$
$353$	−7738.53	−	4467.84i	−1.16680	−	0.673652i	−0.952924	+	0.303208i	$0.901942\pi$
$354$		0			0
$355$	−5540.65	−	9596.68i	−0.828358	−	1.43476i
$356$		0			0
$357$	526.774	−	886.286i	0.0780948	−	0.131393i
$358$		0			0
$359$	−1743.42	+	1006.57i	−0.256307	+	0.147979i	−0.622649	−	0.782501i	$-0.713943\pi$
$359$	−1743.42	+	1006.57i	−0.256307	+	0.147979i	0.366342	+	0.930480i	$0.380610\pi$
$360$		0			0
$361$	195.452	−	338.533i	0.0284957	−	0.0493560i
$362$		0			0
$363$	3991.21			0.577092
$364$		0			0
$365$	−3601.76			−0.516506
$366$		0			0
$367$	5463.42	−	9462.92i	0.777080	−	1.34594i	−0.156539	−	0.987672i	$-0.550034\pi$
$367$	5463.42	−	9462.92i	0.777080	−	1.34594i	0.933618	−	0.358270i	$-0.116633\pi$
$368$		0			0
$369$	−1776.53	+	1025.68i	−0.250630	+	0.144701i
$370$		0			0
$371$	−159.505	+	12594.0i	−0.0223209	+	1.76239i
$372$		0			0
$373$	1569.77	+	2718.92i	0.217907	+	0.377427i	0.954168	−	0.299271i	$-0.0967436\pi$
$373$	1569.77	+	2718.92i	0.217907	+	0.377427i	−0.736261	+	0.676698i	$0.763410\pi$
$374$		0			0
$375$	−3234.31	−	1867.33i	−0.445384	−	0.257143i
$376$		0			0
$377$			1770.81i			0.241914i
$378$		0			0
$379$		−	7646.63i		−	1.03636i	−0.855271	−	0.518181i	$-0.826609\pi$
$379$		−	7646.63i		−	1.03636i	0.855271	−	0.518181i	$-0.173391\pi$
$380$		0			0
$381$	482.656	+	278.662i	0.0649009	+	0.0374705i
$382$		0			0
$383$	3396.30	+	5882.56i	0.453114	+	0.784817i	0.998578	−	0.0533178i	$-0.0169796\pi$
$383$	3396.30	+	5882.56i	0.453114	+	0.784817i	−0.545463	+	0.838135i	$0.683646\pi$
$384$		0			0
$385$	151.381	−	84.8621i	0.0200392	−	0.0112337i
$386$		0			0
$387$	−315.077	+	181.910i	−0.0413857	+	0.0238940i
$388$		0			0
$389$	5239.75	−	9075.51i	0.682945	−	1.18290i	−0.291133	−	0.956683i	$-0.594032\pi$
$389$	5239.75	−	9075.51i	0.682945	−	1.18290i	0.974078	−	0.226213i	$-0.0726345\pi$
$390$		0			0
$391$	−106.386			−0.0137601
$392$		0			0
$393$	8809.33			1.13072
$394$		0			0
$395$	−2910.30	+	5040.78i	−0.370716	+	0.642100i
$396$		0			0
$397$	4592.61	−	2651.54i	0.580595	−	0.335207i	−0.180775	−	0.983525i	$-0.557860\pi$
$397$	4592.61	−	2651.54i	0.580595	−	0.335207i	0.761370	+	0.648318i	$0.224527\pi$
$398$		0			0
$399$	−3897.77	+	2185.04i	−0.489054	+	0.274157i
$400$		0			0
$401$	−612.410	−	1060.72i	−0.0762650	−	0.132095i	0.825371	−	0.564591i	$-0.190966\pi$
$401$	−612.410	−	1060.72i	−0.0762650	−	0.132095i	−0.901636	+	0.432496i	$0.857633\pi$
$402$		0			0
$403$	−5934.07	−	3426.04i	−0.733491	−	0.423481i
$404$		0			0
$405$			983.730i			0.120696i
$406$		0			0
$407$			179.264i			0.0218325i
$408$		0			0
$409$	3918.04	+	2262.08i	0.473678	+	0.273478i	0.717778	−	0.696272i	$-0.245159\pi$
$409$	3918.04	+	2262.08i	0.473678	+	0.273478i	−0.244100	+	0.969750i	$0.578492\pi$
$410$		0			0
$411$	−571.018	−	989.033i	−0.0685310	−	0.118699i
$412$		0			0
$413$	−80.5189	+	6357.51i	−0.00959340	+	0.757463i
$414$		0			0
$415$	−12736.5	+	7353.41i	−1.50653	+	0.869795i
$416$		0			0
$417$	−3928.10	+	6803.67i	−0.461295	+	0.798987i
$418$		0			0
$419$	6684.96			0.779432			0.389716	−	0.920935i	$-0.372573\pi$
$419$	6684.96			0.779432			0.389716	+	0.920935i	$0.372573\pi$
$420$		0			0
$421$	1872.23			0.216739			0.108369	−	0.994111i	$-0.465437\pi$
$421$	1872.23			0.216739			0.108369	+	0.994111i	$0.465437\pi$
$422$		0			0
$423$	−673.736	+	1166.95i	−0.0774425	+	0.134134i
$424$		0			0
$425$	361.528	−	208.728i	0.0412628	−	0.0238231i
$426$		0			0
$427$	−3200.19	+	5384.25i	−0.362689	+	0.610216i
$428$		0			0
$429$	−71.1483	−	123.233i	−0.00800717	−	0.0138688i
$430$		0			0
$431$	10940.4	+	6316.43i	1.22269	+	0.705920i	0.965491	−	0.260438i	$-0.0838670\pi$
$431$	10940.4	+	6316.43i	1.22269	+	0.705920i	0.257199	+	0.966358i	$0.417200\pi$
$432$		0			0
$433$			1619.99i			0.179796i	0.995951	+	0.0898982i	$0.0286542\pi$
$433$			1619.99i			0.179796i	−0.995951	+	0.0898982i	$0.971346\pi$
$434$		0			0
$435$		−	1049.51i		−	0.115678i
$436$		0			0
$437$	399.308	+	230.540i	0.0437105	+	0.0252362i
$438$		0			0
$439$	−5281.36	−	9147.59i	−0.574181	−	0.994511i	−0.996130	−	0.0878917i	$-0.971987\pi$
$439$	−5281.36	−	9147.59i	−0.574181	−	0.994511i	0.421949	−	0.906620i	$-0.361346\pi$
$440$		0			0
$441$	−3086.01	−	78.1822i	−0.333226	−	0.00844209i
$442$		0			0
$443$	−7688.07	+	4438.71i	−0.824540	+	0.476048i	−0.851979	−	0.523575i	$-0.824598\pi$
$443$	−7688.07	+	4438.71i	−0.824540	+	0.476048i	0.0274398	+	0.999623i	$0.491265\pi$
$444$		0			0
$445$	−6073.54	+	10519.7i	−0.646996	+	1.12063i
$446$		0			0
$447$	−8323.54			−0.880738
$448$		0			0
$449$	−6745.07			−0.708952			−0.354476	−	0.935065i	$-0.615341\pi$
$449$	−6745.07			−0.708952			−0.354476	+	0.935065i	$0.615341\pi$
$450$		0			0
$451$	−87.9311	+	152.301i	−0.00918074	+	0.0159015i
$452$		0			0
$453$	3428.70	−	1979.56i	0.355617	−	0.205316i
$454$		0			0
$455$	11886.3	+	7064.75i	1.22470	+	0.727913i
$456$		0			0
$457$	8541.47	+	14794.3i	0.874295	+	1.51432i	0.857512	+	0.514465i	$0.172009\pi$
$457$	8541.47	+	14794.3i	0.874295	+	1.51432i	0.0167836	+	0.999859i	$0.494657\pi$
$458$		0			0
$459$	433.902	+	250.513i	0.0441237	+	0.0254749i
$460$		0			0
$461$			11025.8i			1.11394i	0.830534	+	0.556968i	$0.188036\pi$
$461$			11025.8i			1.11394i	−0.830534	+	0.556968i	$0.811964\pi$
$462$		0			0
$463$		−	10494.7i		−	1.05341i	−0.850048	−	0.526705i	$-0.823427\pi$
$463$		−	10494.7i		−	1.05341i	0.850048	−	0.526705i	$-0.176573\pi$
$464$		0			0
$465$	3516.94	+	2030.51i	0.350740	+	0.202500i
$466$		0			0
$467$	222.099	+	384.687i	0.0220075	+	0.0381181i	0.876819	−	0.480820i	$-0.159661\pi$
$467$	222.099	+	384.687i	0.0220075	+	0.0381181i	−0.854812	+	0.518938i	$0.826328\pi$
$468$		0			0
$469$	−15623.9	−	197.880i	−1.53826	−	0.0194824i
$470$		0			0
$471$	−4581.23	+	2644.97i	−0.448178	+	0.258756i
$472$		0			0
$473$	−15.5951	+	27.0114i	−0.00151599	+	0.00262577i
$474$		0			0
$475$	−1809.27			−0.174768
$476$		0			0
$477$	−6120.58			−0.587510
$478$		0			0
$479$	3577.53	−	6196.46i	0.341256	−	0.591072i	−0.643411	−	0.765521i	$-0.722481\pi$
$479$	3577.53	−	6196.46i	0.341256	−	0.591072i	0.984666	+	0.174449i	$0.0558145\pi$
$480$		0			0
$481$	−12369.5	+	7141.51i	−1.17256	+	0.676975i
$482$		0			0
$483$	155.761	+	277.854i	0.0146737	+	0.0261756i
$484$		0			0
$485$	1570.81	+	2720.72i	0.147066	+	0.254725i
$486$		0			0
$487$	−6789.38	−	3919.85i	−0.631737	−	0.364734i	0.149687	−	0.988733i	$-0.452173\pi$
$487$	−6789.38	−	3919.85i	−0.631737	−	0.364734i	−0.781425	+	0.624000i	$0.785507\pi$
$488$		0			0
$489$			2292.10i			0.211968i
$490$		0			0
$491$		−	5561.90i		−	0.511211i	−0.966781	−	0.255606i	$-0.917725\pi$
$491$		−	5561.90i		−	0.511211i	0.966781	−	0.255606i	$-0.0822749\pi$
$492$		0			0
$493$	−462.914	−	267.264i	−0.0422893	−	0.0244157i
$494$		0			0
$495$	42.1674	+	73.0361i	0.00382886	+	0.00663178i
$496$		0			0
$497$	8263.21	+	14740.3i	0.745786	+	1.33037i
$498$		0			0
$499$	4928.49	−	2845.47i	0.442143	−	0.255272i	−0.262363	−	0.964969i	$-0.584502\pi$
$499$	4928.49	−	2845.47i	0.442143	−	0.255272i	0.704506	+	0.709698i	$0.251168\pi$
$500$		0			0
$501$	−4546.63	+	7874.99i	−0.405446	+	0.702253i
$502$		0			0
$503$	16635.5			1.47463			0.737314	−	0.675550i	$-0.236094\pi$
$503$	16635.5			1.47463			0.737314	+	0.675550i	$0.236094\pi$
$504$		0			0
$505$	19608.3			1.72784
$506$		0			0
$507$	2373.30	−	4110.67i	0.207893	−	0.360081i
$508$		0			0
$509$	−9535.07	+	5505.08i	−0.830323	+	0.479387i	−0.853963	−	0.520333i	$-0.825808\pi$
$509$	−9535.07	+	5505.08i	−0.830323	+	0.479387i	0.0236400	+	0.999721i	$0.492474\pi$
$510$		0			0
$511$	5492.07	+	69.5580i	0.475450	+	0.00602166i
$512$		0			0
$513$	−1085.73	−	1880.54i	−0.0934428	−	0.161848i
$514$		0			0
$515$	7296.72	+	4212.76i	0.624334	+	0.360459i
$516$		0			0
$517$			115.518i			0.00982687i
$518$		0			0
$519$		−	7378.81i		−	0.624073i
$520$		0			0
$521$	6052.88	+	3494.63i	0.508985	+	0.293863i	0.732416	−	0.680857i	$-0.238392\pi$
$521$	6052.88	+	3494.63i	0.508985	+	0.293863i	−0.223431	+	0.974720i	$0.571726\pi$
$522$		0			0
$523$	5071.85	+	8784.70i	0.424047	+	0.734471i	0.996331	−	0.0855846i	$-0.0272758\pi$
$523$	5071.85	+	8784.70i	0.424047	+	0.734471i	−0.572284	+	0.820056i	$0.693942\pi$
$524$		0			0
$525$	−1074.46	−	638.620i	−0.0893208	−	0.0530888i
$526$		0			0
$527$	1791.22	−	1034.16i	0.148059	−	0.0854817i
$528$		0			0
$529$	−6067.07	+	10508.5i	−0.498649	+	0.863686i
$530$		0			0
$531$	−3089.70			−0.252508
$532$		0			0
$533$	−14011.9			−1.13870
$534$		0			0
$535$	−7063.27	+	12233.9i	−0.570788	+	0.988634i
$536$		0			0
$537$	10734.1	−	6197.32i	0.862587	−	0.498015i
$538$		0			0
$539$	−232.469	+	126.477i	−0.0185773	+	0.0101071i
$540$		0			0
$541$	−5267.98	−	9124.42i	−0.418648	−	0.725119i	0.577156	−	0.816634i	$-0.304162\pi$
$541$	−5267.98	−	9124.42i	−0.418648	−	0.725119i	−0.995804	+	0.0915149i	$0.970829\pi$
$542$		0			0
$543$	−9970.13	−	5756.26i	−0.787954	−	0.454926i
$544$		0			0
$545$			20723.6i			1.62881i
$546$		0			0
$547$		−	15181.0i		−	1.18664i	−0.804966	−	0.593321i	$-0.797816\pi$
$547$		−	15181.0i		−	1.18664i	0.804966	−	0.593321i	$-0.202184\pi$
$548$		0			0
$549$	−2635.98	−	1521.89i	−0.204920	−	0.118311i
$550$		0			0
$551$	1158.33	+	2006.28i	0.0895579	+	0.155119i
$552$		0			0
$553$	4535.06	−	7630.13i	0.348735	−	0.586738i
$554$		0			0
$555$	7331.00	−	4232.55i	0.560691	−	0.323715i
$556$		0			0
$557$	5980.73	−	10358.9i	0.454958	−	0.788011i	−0.543727	−	0.839262i	$-0.682987\pi$
$557$	5980.73	−	10358.9i	0.454958	−	0.788011i	0.998686	+	0.0512509i	$0.0163208\pi$
$558$		0			0
$559$	−2485.10			−0.188029
$560$		0			0
$561$	42.9528			0.00323257
$562$		0			0
$563$	−10321.5	+	17877.3i	−0.772645	+	1.33826i	0.163464	+	0.986549i	$0.447733\pi$
$563$	−10321.5	+	17877.3i	−0.772645	+	1.33826i	−0.936109	+	0.351711i	$0.885600\pi$
$564$		0			0
$565$	−3781.59	+	2183.30i	−0.281580	+	0.162570i
$566$		0			0
$567$	18.9980	−	1500.02i	0.00140713	−	0.111102i
$568$		0			0
$569$	335.607	+	581.289i	0.0247265	+	0.0428276i	0.878124	−	0.478433i	$-0.158795\pi$
$569$	335.607	+	581.289i	0.0247265	+	0.0428276i	−0.853397	+	0.521261i	$0.825462\pi$
$570$		0			0
$571$	12166.9	+	7024.54i	0.891711	+	0.514830i	0.874502	−	0.485022i	$-0.161188\pi$
$571$	12166.9	+	7024.54i	0.891711	+	0.514830i	0.0172093	+	0.999852i	$0.494522\pi$
$572$		0			0
$573$		−	11962.5i		−	0.872149i
$574$		0			0
$575$			128.974i			0.00935409i
$576$		0			0
$577$	9665.49	+	5580.37i	0.697365	+	0.402624i	0.806365	−	0.591418i	$-0.201432\pi$
$577$	9665.49	+	5580.37i	0.697365	+	0.402624i	−0.109000	+	0.994042i	$0.534765\pi$
$578$		0			0
$579$	−3280.47	−	5681.94i	−0.235460	−	0.407829i
$580$		0			0
$581$	19563.0	−	10966.7i	1.39692	−	0.783092i
$582$		0			0
$583$	−454.417	+	262.358i	−0.0322813	+	0.0186376i
$584$		0			0
$585$	−3359.72	+	5819.21i	−0.237448	+	0.411273i
$586$		0			0
$587$	−337.441			−0.0237269			−0.0118635	−	0.999930i	$-0.503776\pi$
$587$	−337.441			−0.0237269			−0.0118635	+	0.999930i	$0.503776\pi$
$588$		0			0
$589$	−8964.17			−0.627101
$590$		0			0
$591$	−3069.64	+	5316.78i	−0.213652	+	0.370056i
$592$		0			0
$593$	−7282.42	+	4204.51i	−0.504306	+	0.291161i	−0.730490	−	0.682923i	$-0.760708\pi$
$593$	−7282.42	+	4204.51i	−0.504306	+	0.291161i	0.226184	+	0.974085i	$0.427375\pi$
$594$		0			0
$595$	−3640.78	+	2040.97i	−0.250853	+	0.140625i
$596$		0			0
$597$	−2945.48	−	5101.72i	−0.201927	−	0.349748i
$598$		0			0
$599$	−4933.96	−	2848.62i	−0.336554	−	0.194310i	0.322193	−	0.946674i	$-0.395580\pi$
$599$	−4933.96	−	2848.62i	−0.336554	−	0.194310i	−0.658747	+	0.752364i	$0.728913\pi$
$600$		0			0
$601$		−	17264.3i		−	1.17176i	−0.810398	−	0.585880i	$-0.800749\pi$
$601$		−	17264.3i		−	1.17176i	0.810398	−	0.585880i	$-0.199251\pi$
$602$		0			0
$603$		−	7593.12i		−	0.512795i
$604$		0			0
$605$	−13992.8	−	8078.76i	−0.940312	−	0.542890i
$606$		0			0
$607$	4217.42	+	7304.79i	0.282010	+	0.488455i	0.971880	−	0.235478i	$-0.0756656\pi$
$607$	4217.42	+	7304.79i	0.282010	+	0.488455i	−0.689870	+	0.723933i	$0.742332\pi$
$608$		0			0
$609$	−20.2683	+	1600.32i	−0.00134863	+	0.106483i
$610$		0			0
$611$	−7970.91	+	4602.01i	−0.527771	+	0.304709i
$612$		0			0
$613$	12924.6	−	22386.0i	0.851579	−	1.47498i	−0.0282034	−	0.999602i	$-0.508979\pi$
$613$	12924.6	−	22386.0i	0.851579	−	1.47498i	0.879783	−	0.475376i	$-0.157688\pi$
$614$		0			0
$615$	8304.45			0.544500
$616$		0			0
$617$	18654.5			1.21718			0.608591	−	0.793484i	$-0.291735\pi$
$617$	18654.5			1.21718			0.608591	+	0.793484i	$0.291735\pi$
$618$		0			0
$619$	4075.65	−	7059.23i	0.264643	−	0.458376i	−0.702827	−	0.711361i	$-0.748079\pi$
$619$	4075.65	−	7059.23i	0.264643	−	0.458376i	0.967470	+	0.252985i	$0.0814125\pi$
$620$		0			0
$621$	−134.055	+	77.3967i	−0.00866255	+	0.00500133i
$622$		0			0
$623$	9464.27	−	15923.4i	0.608632	−	1.02401i
$624$		0			0
$625$	8965.48	+	15528.7i	0.573791	+	0.993835i
$626$		0			0
$627$	−161.218	−	93.0793i	−0.0102686	−	0.00592860i
$628$		0			0
$629$		−	4311.39i		−	0.273301i
$630$		0			0
$631$			29638.3i			1.86986i	0.354833	+	0.934930i	$0.384538\pi$
$631$			29638.3i			1.86986i	−0.354833	+	0.934930i	$0.615462\pi$
$632$		0			0
$633$	8174.95	+	4719.81i	0.513310	+	0.296360i
$634$		0			0
$635$	−1128.10	−	1953.92i	−0.0704996	−	0.122109i
$636$		0			0
$637$	−17988.1	−	11002.1i	−1.11886	−	0.684331i
$638$		0			0
$639$	−7111.69	+	4105.94i	−0.440272	+	0.254191i
$640$		0			0
$641$	6414.94	−	11111.0i	0.395281	−	0.684646i	−0.597856	−	0.801603i	$-0.703981\pi$
$641$	6414.94	−	11111.0i	0.395281	−	0.684646i	0.993137	+	0.116957i	$0.0373140\pi$
$642$		0			0
$643$	22280.4			1.36649			0.683245	−	0.730189i	$-0.260568\pi$
$643$	22280.4			1.36649			0.683245	+	0.730189i	$0.260568\pi$
$644$		0			0
$645$	1472.84			0.0899116
$646$		0			0
$647$	3349.69	−	5801.84i	0.203540	−	0.352541i	−0.746127	−	0.665804i	$-0.768089\pi$
$647$	3349.69	−	5801.84i	0.203540	−	0.352541i	0.949666	+	0.313263i	$0.101422\pi$
$648$		0			0
$649$	−229.392	+	132.440i	−0.0138743	+	0.00801034i
$650$		0			0
$651$	−5323.52	−	3164.10i	−0.320500	−	0.190493i
$652$		0			0
$653$	−10547.7	−	18269.2i	−0.632104	−	1.09484i	−0.987121	−	0.159977i	$-0.948858\pi$
$653$	−10547.7	−	18269.2i	−0.632104	−	1.09484i	0.355017	−	0.934860i	$-0.384475\pi$
$654$		0			0
$655$	−30884.7	−	17831.3i	−1.84239	−	1.06370i
$656$		0			0
$657$			2669.11i			0.158496i
$658$		0			0
$659$			435.480i			0.0257418i	0.999917	+	0.0128709i	$0.00409705\pi$
$659$			435.480i			0.0257418i	−0.999917	+	0.0128709i	$0.995903\pi$
$660$		0			0
$661$	9260.55	+	5346.58i	0.544922	+	0.314611i	0.747071	−	0.664744i	$-0.231459\pi$
$661$	9260.55	+	5346.58i	0.544922	+	0.314611i	−0.202149	+	0.979355i	$0.564793\pi$
$662$		0			0
$663$	1711.15	+	2963.80i	0.100235	+	0.173611i
$664$		0			0
$665$	18088.0	+	229.088i	1.05477	+	0.0133589i
$666$		0			0
$667$	143.019	−	82.5718i	0.00830240	−	0.00479339i
$668$		0			0
$669$	−6845.96	+	11857.6i	−0.395635	+	0.685261i
$670$		0			0
$671$	−260.942			−0.0150127
$672$		0			0
$673$	−2981.24			−0.170755			−0.0853777	−	0.996349i	$-0.527210\pi$
$673$	−2981.24			−0.170755			−0.0853777	+	0.996349i	$0.527210\pi$
$674$		0			0
$675$	303.703	−	526.028i	0.0173178	−	0.0299953i
$676$		0			0
$677$	6443.27	−	3720.03i	0.365783	−	0.211185i	−0.305832	−	0.952086i	$-0.598934\pi$
$677$	6443.27	−	3720.03i	0.365783	−	0.211185i	0.671615	+	0.740901i	$0.265601\pi$
$678$		0			0
$679$	−2342.67	−	4178.97i	−0.132406	−	0.236192i
$680$		0			0
$681$	−9232.71	−	15991.5i	−0.519527	−	0.899848i
$682$		0			0
$683$	−16424.1	−	9482.49i	−0.920135	−	0.531240i	−0.0364572	−	0.999335i	$-0.511607\pi$
$683$	−16424.1	−	9482.49i	−0.920135	−	0.531240i	−0.883678	+	0.468095i	$0.844941\pi$
$684$		0			0
$685$			4623.27i			0.257878i
$686$		0			0
$687$			18062.8i			1.00311i
$688$		0			0
$689$	−36206.0	−	20903.5i	−2.00194	−	1.15582i
$690$		0			0
$691$	−5065.46	−	8773.63i	−0.278870	−	0.483017i	0.692234	−	0.721673i	$-0.256626\pi$
$691$	−5065.46	−	8773.63i	−0.278870	−	0.483017i	−0.971104	+	0.238656i	$0.923293\pi$
$692$		0			0
$693$	−62.8877	−	112.182i	−0.00344719	−	0.00614927i
$694$		0			0
$695$	27543.1	−	15902.0i	1.50327	−	0.867911i
$696$		0			0
$697$	2114.78	−	3662.91i	0.114926	−	0.199057i
$698$		0			0
$699$	2542.69			0.137587
$700$		0			0
$701$	−19406.6			−1.04562			−0.522808	−	0.852450i	$-0.675116\pi$
$701$	−19406.6			−1.04562			−0.522808	+	0.852450i	$0.675116\pi$
$702$		0			0
$703$	−9342.84	+	16182.3i	−0.501240	+	0.868173i
$704$		0			0
$705$	4724.11	−	2727.47i	0.252369	−	0.145705i
$706$		0			0
$707$	−29899.3	−	378.680i	−1.59050	−	0.0201439i
$708$		0			0
$709$	−12317.6	−	21334.8i	−0.652466	−	1.13010i	−0.982523	−	0.186143i	$-0.940401\pi$
$709$	−12317.6	−	21334.8i	−0.652466	−	1.13010i	0.330057	−	0.943961i	$-0.392932\pi$
$710$		0			0
$711$	3735.51	+	2156.70i	0.197036	+	0.113759i
$712$		0			0
$713$			639.015i			0.0335642i
$714$		0			0
$715$			576.056i			0.0301304i
$716$		0			0
$717$	18692.1	+	10791.9i	0.973597	+	0.562106i
$718$		0			0
$719$	1156.13	+	2002.48i	0.0599672	+	0.103866i	0.894450	−	0.447167i	$-0.147567\pi$
$719$	1156.13	+	2002.48i	0.0599672	+	0.103866i	−0.834483	+	0.551033i	$0.814234\pi$
$720$		0			0
$721$	−11044.9	−	6564.66i	−0.570504	−	0.339086i
$722$		0			0
$723$	3044.16	−	1757.54i	0.156588	−	0.0904063i
$724$		0			0
$725$	−324.010	+	561.201i	−0.0165978	+	0.0287482i
$726$		0			0
$727$	125.782			0.00641675			0.00320838	−	0.999995i	$-0.498979\pi$
$727$	125.782			0.00641675			0.00320838	+	0.999995i	$0.498979\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	375.068	−	649.637i	0.0189773	−	0.0328696i
$732$		0			0
$733$	−15549.8	+	8977.69i	−0.783554	+	0.452385i	−0.837688	−	0.546148i	$-0.816093\pi$
$733$	−15549.8	+	8977.69i	−0.783554	+	0.452385i	0.0541342	+	0.998534i	$0.482760\pi$
$734$		0			0
$735$	10661.0	+	6520.60i	0.535017	+	0.327233i
$736$		0			0
$737$	−325.478	−	563.744i	−0.0162675	−	0.0281761i
$738$		0			0
$739$	21422.9	+	12368.5i	1.06638	+	0.615673i	0.927189	−	0.374593i	$-0.122217\pi$
$739$	21422.9	+	12368.5i	1.06638	+	0.615673i	0.139188	+	0.990266i	$0.455551\pi$
$740$		0			0
$741$		−	14832.3i		−	0.735329i
$742$		0			0
$743$			30155.3i			1.48895i	0.667650	+	0.744475i	$0.267300\pi$
$743$			30155.3i			1.48895i	−0.667650	+	0.744475i	$0.732700\pi$
$744$		0			0
$745$	29181.5	+	16848.0i	1.43507	+	0.828540i
$746$		0			0
$747$	5449.30	+	9438.46i	0.266907	+	0.462296i
$748$		0			0
$749$	11006.5	−	18518.3i	0.536943	−	0.903395i
$750$		0			0
$751$	776.708	−	448.433i	0.0377397	−	0.0217890i	−0.481011	−	0.876714i	$-0.659730\pi$
$751$	776.708	−	448.433i	0.0377397	−	0.0217890i	0.518751	+	0.854925i	$0.326397\pi$
$752$		0			0
$753$	−1901.68	+	3293.81i	−0.0920333	+	0.159406i
$754$		0			0
$755$	−16027.6			−0.772588
$756$		0			0
$757$	37636.5			1.80703			0.903514	−	0.428559i	$-0.140978\pi$
$757$	37636.5			1.80703			0.903514	+	0.428559i	$0.140978\pi$
$758$		0			0
$759$	−6.63520	+	11.4925i	−0.000317315	+	0.000549606i
$760$		0			0
$761$	12562.6	−	7253.04i	0.598417	−	0.345496i	−0.170002	−	0.985444i	$-0.554377\pi$
$761$	12562.6	−	7253.04i	0.598417	−	0.345496i	0.768418	+	0.639948i	$0.221044\pi$
$762$		0			0
$763$	400.219	−	31600.0i	0.0189894	−	1.49934i
$764$		0			0
$765$	−1014.15	−	1756.55i	−0.0479301	−	0.0830173i
$766$		0			0
$767$	−18277.0	−	10552.2i	−0.860423	−	0.496765i
$768$		0			0
$769$		−	38539.5i		−	1.80724i	−0.428331	−	0.903622i	$-0.640898\pi$
$769$		−	38539.5i		−	1.80724i	0.428331	−	0.903622i	$-0.359102\pi$
$770$		0			0
$771$			5527.75i			0.258207i
$772$		0			0
$773$	−17334.9	−	10008.3i	−0.806590	−	0.465685i	0.0391804	−	0.999232i	$-0.487525\pi$
$773$	−17334.9	−	10008.3i	−0.806590	−	0.465685i	−0.845770	+	0.533547i	$0.820859\pi$
$774$		0			0
$775$	−1253.74	−	2171.54i	−0.0581105	−	0.100650i
$776$		0			0
$777$	−11260.3	+	6312.35i	−0.519897	+	0.291447i
$778$		0			0
$779$	−15875.1	+	9165.52i	−0.730149	+	0.421552i
$780$		0			0
$781$	−352.001	+	609.683i	−0.0161275	+	0.0279336i
$782$		0			0
$783$	−777.744			−0.0354972
$784$		0			0
$785$	21415.1			0.973681
$786$		0			0
$787$	2826.82	−	4896.20i	0.128037	−	0.221767i	−0.794879	−	0.606768i	$-0.792466\pi$
$787$	2826.82	−	4896.20i	0.128037	−	0.221767i	0.922916	+	0.385001i	$0.125799\pi$
$788$		0			0
$789$	8880.96	−	5127.42i	0.400723	−	0.231358i
$790$		0			0
$791$	5808.45	−	3256.14i	0.261093	−	0.146365i
$792$		0			0
$793$	−10395.4	−	18005.3i	−0.465511	−	0.806288i
$794$		0			0
$795$	21458.2	+	12388.9i	0.957287	+	0.552690i
$796$		0			0
$797$			31124.0i			1.38327i	0.722246	+	0.691636i	$0.243110\pi$
$797$			31124.0i			1.38327i	−0.722246	+	0.691636i	$0.756890\pi$
$798$		0			0
$799$		−	2778.27i		−	0.123014i
$800$		0			0
$801$	7795.68	+	4500.84i	0.343879	+	0.198538i
$802$		0			0
$803$	114.411	+	198.166i	0.00502799	+	0.00870874i
$804$		0			0
$805$	16.3306	−	1289.41i	0.000715005	−	0.0564544i
$806$		0			0
$807$	7939.83	−	4584.06i	0.346338	−	0.199959i
$808$		0			0
$809$	19799.6	−	34294.0i	0.860468	−	1.49037i	−0.0110106	−	0.999939i	$-0.503505\pi$
$809$	19799.6	−	34294.0i	0.860468	−	1.49037i	0.871478	−	0.490434i	$-0.163162\pi$
$810$		0			0
$811$	−13128.8			−0.568453			−0.284226	−	0.958757i	$-0.591737\pi$
$811$	−13128.8			−0.568453			−0.284226	+	0.958757i	$0.591737\pi$
$812$		0			0
$813$	−10198.3			−0.439941
$814$		0			0
$815$	4639.53	−	8035.90i	0.199406	−	0.345381i
$816$		0			0
$817$	−2815.54	+	1625.55i	−0.120567	+	0.0696095i
$818$		0			0
$819$	5235.38	−	8808.42i	0.223369	−	0.375813i
$820$		0			0
$821$	3713.99	+	6432.82i	0.157880	+	0.273455i	0.934104	−	0.357001i	$-0.116201\pi$
$821$	3713.99	+	6432.82i	0.157880	+	0.273455i	−0.776224	+	0.630457i	$0.782868\pi$
$822$		0			0
$823$	3281.61	+	1894.64i	0.138991	+	0.0802465i	0.567883	−	0.823109i	$-0.307763\pi$
$823$	3281.61	+	1894.64i	0.138991	+	0.0802465i	−0.428892	+	0.903356i	$0.641096\pi$
$824$		0			0
$825$		−	52.0727i		−	0.00219750i
$826$		0			0
$827$		−	24254.8i		−	1.01986i	−0.860216	−	0.509930i	$-0.829671\pi$
$827$		−	24254.8i		−	1.01986i	0.860216	−	0.509930i	$-0.170329\pi$
$828$		0			0
$829$	−3719.17	−	2147.26i	−0.155817	−	0.0899608i	0.420064	−	0.907494i	$-0.362008\pi$
$829$	−3719.17	−	2147.26i	−0.155817	−	0.0899608i	−0.575881	+	0.817534i	$0.695341\pi$
$830$		0			0
$831$	1738.51	+	3011.18i	0.0725729	+	0.125700i
$832$		0			0
$833$	5590.99	−	3041.82i	0.232553	−	0.126522i
$834$		0			0
$835$	31880.1	−	18406.0i	1.32127	−	0.762833i
$836$		0			0
$837$	1504.72	−	2606.25i	0.0621395	−	0.107629i
$838$		0			0
$839$	−30994.8			−1.27540			−0.637699	−	0.770285i	$-0.720114\pi$
$839$	−30994.8			−1.27540			−0.637699	+	0.770285i	$0.720114\pi$
$840$		0			0
$841$	−23559.3			−0.965979
$842$		0			0
$843$	−2831.00	+	4903.44i	−0.115664	+	0.200336i
$844$		0			0
$845$	−16641.1	+	9607.74i	−0.677481	+	0.391144i
$846$		0			0
$847$	21180.7	+	12589.0i	0.859239	+	0.510699i
$848$		0			0
$849$	−9827.93	−	17022.5i	−0.397284	−	0.688115i
$850$		0			0
$851$	1153.56	+	666.008i	0.0464671	+	0.0268278i
$852$		0			0
$853$		−	5644.76i		−	0.226580i	−0.993562	−	0.113290i	$-0.963861\pi$
$853$		−	5644.76i		−	0.226580i	0.993562	−	0.113290i	$-0.0361390\pi$
$854$		0			0
$855$			8790.66i			0.351619i
$856$		0			0
$857$	−8690.47	−	5017.45i	−0.346395	−	0.199991i	0.316701	−	0.948525i	$-0.397425\pi$
$857$	−8690.47	−	5017.45i	−0.346395	−	0.199991i	−0.663096	+	0.748534i	$0.730758\pi$
$858$		0			0
$859$	14845.4	+	25713.0i	0.589662	+	1.02132i	0.994277	+	0.106837i	$0.0340723\pi$
$859$	14845.4	+	25713.0i	0.589662	+	1.02132i	−0.404615	+	0.914487i	$0.632594\pi$
$860$		0			0
$861$	−12662.9	−	160.377i	−0.501219	−	0.00634802i
$862$		0			0
$863$	20415.6	−	11786.9i	0.805278	−	0.464927i	−0.0400357	−	0.999198i	$-0.512747\pi$
$863$	20415.6	−	11786.9i	0.805278	−	0.464927i	0.845313	+	0.534271i	$0.179414\pi$
$864$		0			0
$865$	−14935.7	+	25869.4i	−0.587086	+	1.01686i
$866$		0			0
$867$	13706.0			0.536885
$868$		0			0
$869$	369.786			0.0144351
$870$		0			0
$871$	25932.7	−	44916.7i	1.00884	−	1.74735i
$872$		0			0
$873$	2016.21	−	1164.06i	0.0781654	−	0.0451288i
$874$		0			0
$875$	−11274.0	−	20111.1i	−0.435579	−	0.777006i
$876$		0			0
$877$	15462.2	+	26781.3i	0.595350	+	1.03118i	0.993497	+	0.113855i	$0.0363198\pi$
$877$	15462.2	+	26781.3i	0.595350	+	1.03118i	−0.398148	+	0.917321i	$0.630347\pi$
$878$		0			0
$879$	3850.62	+	2223.15i	0.147757	+	0.0853073i
$880$		0			0
$881$			44143.8i			1.68813i	0.536241	+	0.844065i	$0.319844\pi$
$881$			44143.8i			1.68813i	−0.536241	+	0.844065i	$0.680156\pi$
$882$		0			0
$883$			36026.0i			1.37301i	0.727123	+	0.686507i	$0.240857\pi$
$883$			36026.0i			1.37301i	−0.727123	+	0.686507i	$0.759143\pi$
$884$		0			0
$885$	10832.2	+	6253.98i	0.411436	+	0.237543i
$886$		0			0
$887$	−7688.11	−	13316.2i	−0.291028	−	0.504075i	0.683025	−	0.730395i	$-0.260664\pi$
$887$	−7688.11	−	13316.2i	−0.291028	−	0.504075i	−0.974053	+	0.226320i	$0.927330\pi$
$888$		0			0
$889$	1682.42	+	3001.19i	0.0634721	+	0.113225i
$890$		0			0
$891$	54.1239	−	31.2485i	0.00203504	−	0.00117493i
$892$		0			0
$893$	−6020.54	+	10427.9i	−0.225610	+	0.390768i
$894$		0			0
$895$	−50176.9			−1.87400
$896$		0			0
$897$	−1057.33			−0.0393569
$898$		0			0
$899$	−1605.33	+	2780.52i	−0.0595560	+	0.103154i
$900$		0			0
$901$	10928.9	−	6309.82i	0.404101	−	0.233308i
$902$		0			0
$903$	−2245.83	−	28.4438i	−0.0827647	−	0.00104823i
$904$		0			0
$905$	23302.9	+	40361.8i	0.855927	+	1.48251i
$906$		0			0
$907$	41406.8	+	23906.2i	1.51587	+	0.875186i	0.999827	+	0.0186205i	$0.00592743\pi$
$907$	41406.8	+	23906.2i	1.51587	+	0.875186i	0.516039	+	0.856565i	$0.327406\pi$
$908$		0			0
$909$		−	14530.9i		−	0.530208i
$910$		0			0
$911$		−	23686.8i		−	0.861446i	−0.902484	−	0.430723i	$-0.858259\pi$
$911$		−	23686.8i		−	0.861446i	0.902484	−	0.430723i	$-0.141741\pi$
$912$		0			0
$913$	809.156	+	467.167i	0.0293310	+	0.0169342i
$914$		0			0
$915$	6161.01	+	10671.2i	0.222597	+	0.385550i
$916$		0			0
$917$	46749.5	+	27786.1i	1.68354	+	1.00063i
$918$		0			0
$919$	−1741.06	+	1005.20i	−0.0624943	+	0.0360811i	−0.530922	−	0.847421i	$-0.678154\pi$
$919$	−1741.06	+	1005.20i	−0.0624943	+	0.0360811i	0.468427	+	0.883502i	$0.344821\pi$
$920$		0			0
$921$	−8400.77	+	14550.6i	−0.300559	+	0.520583i
$922$		0			0
$923$	−56091.8			−2.00031
$924$		0			0
$925$	−5226.79			−0.185790
$926$		0			0
$927$	3121.90	−	5407.29i	0.110611	−	0.191584i
$928$		0			0
$929$	−43408.4	+	25061.9i	−1.53303	+	0.885095i	−0.533810	+	0.845605i	$0.679240\pi$
$929$	−43408.4	+	25061.9i	−1.53303	+	0.885095i	−0.999220	+	0.0394904i	$0.987427\pi$
$930$		0			0
$931$	−27576.7	−	698.640i	−0.970775	−	0.0245940i
$932$		0			0
$933$	9734.51	+	16860.7i	0.341580	+	0.591633i
$934$		0			0
$935$	−150.589	−	86.9424i	−0.00526714	−	0.00304098i
$936$		0			0
$937$			24059.4i			0.838833i	0.907794	+	0.419416i	$0.137765\pi$
$937$			24059.4i			0.838833i	−0.907794	+	0.419416i	$0.862235\pi$
$938$		0			0
$939$			8397.52i			0.291845i
$940$		0			0
$941$	−28425.4	−	16411.4i	−0.984740	−	0.568540i	−0.0810424	−	0.996711i	$-0.525825\pi$
$941$	−28425.4	−	16411.4i	−0.984740	−	0.568540i	−0.903698	+	0.428171i	$0.859158\pi$
$942$		0			0
$943$	653.367	+	1131.67i	0.0225626	+	0.0390796i
$944$		0			0
$945$	−3102.85	+	5220.48i	−0.106810	+	0.179706i
$946$		0			0
$947$	−7552.82	+	4360.62i	−0.259170	+	0.149632i	−0.623956	−	0.781460i	$-0.714475\pi$
$947$	−7552.82	+	4360.62i	−0.259170	+	0.149632i	0.364786	+	0.931091i	$0.381142\pi$
$948$		0			0
$949$	−9115.78	+	15789.0i	−0.311813	+	0.540076i
$950$		0			0
$951$	−19925.4			−0.679417
$952$		0			0
$953$	−31310.6			−1.06427			−0.532136	−	0.846659i	$-0.678610\pi$
$953$	−31310.6			−1.06427			−0.532136	+	0.846659i	$0.678610\pi$
$954$		0			0
$955$	−24213.8	+	41939.5i	−0.820460	+	1.42108i
$956$		0			0
$957$	−57.7429	+	33.3379i	−0.00195043	+	0.00112608i
$958$		0			0
$959$	89.2857	−	7049.71i	0.00300645	−	0.237379i
$960$		0			0
$961$	8683.75	+	15040.7i	0.291489	+	0.504874i
$962$		0			0
$963$	9066.05	+	5234.29i	0.303374	+	0.175153i
$964$		0			0
$965$			26560.4i			0.886022i
$966$		0			0
$967$			48965.2i			1.62835i	0.580620	+	0.814175i	$0.302810\pi$
$967$			48965.2i			1.62835i	−0.580620	+	0.814175i	$0.697190\pi$
$968$		0			0
$969$	3877.37	+	2238.60i	0.128544	+	0.0742148i
$970$		0			0
$971$	−13889.1	−	24056.5i	−0.459033	−	0.795068i	0.539877	−	0.841744i	$-0.318471\pi$
$971$	−13889.1	−	24056.5i	−0.459033	−	0.795068i	−0.998910	+	0.0466754i	$0.985137\pi$
$972$		0			0
$973$	−42305.7	+	23716.0i	−1.39389	+	0.781397i
$974$		0			0
$975$	3593.08	−	2074.46i	0.118021	−	0.0681395i
$976$		0			0
$977$	10030.4	−	17373.1i	0.328454	−	0.568899i	−0.653751	−	0.756709i	$-0.726806\pi$
$977$	10030.4	−	17373.1i	0.328454	−	0.568899i	0.982205	+	0.187810i	$0.0601391\pi$
$978$		0			0
$979$	771.711			0.0251930
$980$		0			0
$981$	15357.4			0.499820
$982$		0			0
$983$	23717.3	−	41079.6i	0.769548	−	1.33290i	−0.168260	−	0.985743i	$-0.553815\pi$
$983$	23717.3	−	41079.6i	0.769548	−	1.33290i	0.937808	−	0.347154i	$-0.112852\pi$
$984$		0			0
$985$	21523.7	−	12426.7i	0.696247	−	0.401979i
$986$		0			0
$987$	−7256.14	+	4067.69i	−0.234008	+	0.131181i
$988$		0			0
$989$	115.878	+	200.707i	0.00372570	+	0.00645310i
$990$		0			0
$991$	35138.6	+	20287.3i	1.12635	+	0.650300i	0.943015	−	0.332750i	$-0.107976\pi$
$991$	35138.6	+	20287.3i	1.12635	+	0.650300i	0.183338	+	0.983050i	$0.441310\pi$
$992$		0			0
$993$		−	10208.0i		−	0.326224i
$994$		0			0
$995$			23848.2i			0.759838i
$996$		0			0
$997$	30411.0	+	17557.8i	0.966024	+	0.557734i	0.898022	−	0.439951i	$-0.145004\pi$
$997$	30411.0	+	17557.8i	0.966024	+	0.557734i	0.0680022	+	0.997685i	$0.478337\pi$
$998$		0			0
$999$	−3136.56	−	5432.69i	−0.0993359	−	0.172055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bl.e.31.3	✓	6
4.3	odd	2		336.4.bl.g.31.3	yes	6
7.5	odd	6		336.4.bl.g.271.3	yes	6
28.19	even	6	inner	336.4.bl.e.271.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.4.bl.e.31.3	✓	6	1.1	even	1	trivial
336.4.bl.e.271.3	yes	6	28.19	even	6	inner
336.4.bl.g.31.3	yes	6	4.3	odd	2
336.4.bl.g.271.3	yes	6	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +(10.5177 - 6.07241i) q^{5} +(-16.1550 + 9.05627i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(-0.668197 - 0.385784i) q^{11} -61.4752i q^{13} +36.4344i q^{15} +(16.0704 + 9.27827i) q^{17} +(-40.2122 - 69.6496i) q^{19} +(0.703630 - 55.5563i) q^{21} +(-4.96500 + 2.86654i) q^{23} +(11.2482 - 19.4825i) q^{25} +27.0000 q^{27} -28.8053 q^{29} +(55.7304 - 96.5279i) q^{31} +(2.00459 - 1.15735i) q^{33} +(-114.920 + 193.351i) q^{35} +(-116.169 - 201.211i) q^{37} +(159.717 + 92.2128i) q^{39} -227.929i q^{41} -40.4244i q^{43} +(-94.6595 - 54.6517i) q^{45} +(-74.8596 - 129.661i) q^{47} +(178.968 - 292.608i) q^{49} +(-48.2113 + 27.8348i) q^{51} +(340.032 - 588.953i) q^{53} -9.37054 q^{55} +241.273 q^{57} +(171.650 - 297.307i) q^{59} +(292.887 - 169.098i) q^{61} +(143.284 + 85.1626i) q^{63} +(-373.302 - 646.578i) q^{65} +(730.648 + 421.840i) q^{67} -17.1993i q^{69} -912.430i q^{71} +(-256.835 - 148.284i) q^{73} +(33.7447 + 58.4476i) q^{75} +(14.2885 + 0.180966i) q^{77} +(-415.056 + 239.633i) q^{79} +(-40.5000 + 70.1481i) q^{81} -1210.95 q^{83} +225.366 q^{85} +(43.2080 - 74.8385i) q^{87} +(-866.187 + 500.093i) q^{89} +(556.736 + 993.131i) q^{91} +(167.191 + 289.584i) q^{93} +(-845.882 - 488.370i) q^{95} +258.680i q^{97} +6.94410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 21 q^{5} - 19 q^{7} - 27 q^{9} - 75 q^{11} + 162 q^{17} - 80 q^{19} - 93 q^{21} + 204 q^{23} + 228 q^{25} + 162 q^{27} + 642 q^{29} - 313 q^{31} + 225 q^{33} - 198 q^{35} + 36 q^{37} + 162 q^{39}+ \cdots - 4854 q^{95}+O(q^{100}) \) 6 * q - 9 * q^3 - 21 * q^5 - 19 * q^7 - 27 * q^9 - 75 * q^11 + 162 * q^17 - 80 * q^19 - 93 * q^21 + 204 * q^23 + 228 * q^25 + 162 * q^27 + 642 * q^29 - 313 * q^31 + 225 * q^33 - 198 * q^35 + 36 * q^37 + 162 * q^39 + 189 * q^45 + 84 * q^47 + 921 * q^49 - 486 * q^51 + 453 * q^53 + 1842 * q^55 + 480 * q^57 - 153 * q^59 - 576 * q^61 + 450 * q^63 - 1344 * q^65 - 762 * q^67 + 1746 * q^73 + 684 * q^75 + 1629 * q^77 - 579 * q^79 - 243 * q^81 + 1458 * q^83 + 1164 * q^85 - 963 * q^87 - 1302 * q^89 + 318 * q^91 - 939 * q^93 - 4854 * q^95

Introduction

L-functions

Modular forms

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