LMFDB - Embedded newform 336.4.bc.e.17.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{11} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.7
Root			$2.41164 - 1.78437i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.e.257.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.17709 - 3.09062i) q^{3} +(-4.27911 - 7.41164i) q^{5} +(6.41772 + 17.3728i) q^{7} +(7.89612 - 25.8196i) q^{9} +(53.8609 + 31.0966i) q^{11} +61.7061i q^{13} +(-40.7808 - 17.7340i) q^{15} +(13.3365 - 23.0995i) q^{17} +(58.6213 - 33.8450i) q^{19} +(80.5000 + 52.7328i) q^{21} +(45.8287 - 26.4592i) q^{23} +(25.8784 - 44.8227i) q^{25} +(-46.8158 - 132.255i) q^{27} -55.1116i q^{29} +(134.080 + 77.4108i) q^{31} +(321.089 - 36.5704i) q^{33} +(101.299 - 121.906i) q^{35} +(-157.940 - 273.560i) q^{37} +(190.710 + 257.752i) q^{39} +210.211 q^{41} -351.939 q^{43} +(-225.154 + 51.9617i) q^{45} +(-115.819 - 200.605i) q^{47} +(-260.626 + 222.987i) q^{49} +(-15.6841 - 137.707i) q^{51} +(232.890 + 134.459i) q^{53} -532.263i q^{55} +(140.264 - 322.550i) q^{57} +(-9.14155 + 15.8336i) q^{59} +(-72.3320 + 41.7609i) q^{61} +(499.233 - 28.5253i) q^{63} +(457.344 - 264.047i) q^{65} +(64.7354 - 112.125i) q^{67} +(109.655 - 252.162i) q^{69} +804.537i q^{71} +(370.377 + 213.837i) q^{73} +(-30.4336 - 267.208i) q^{75} +(-194.570 + 1135.28i) q^{77} +(609.284 + 1055.31i) q^{79} +(-604.302 - 407.749i) q^{81} +1371.18 q^{83} -228.274 q^{85} +(-170.329 - 230.206i) q^{87} +(-386.840 - 670.026i) q^{89} +(-1072.01 + 396.012i) q^{91} +(799.309 - 91.0371i) q^{93} +(-501.694 - 289.653i) q^{95} -848.768i q^{97} +(1228.19 - 1145.12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 80 q^{7} + 18 q^{9} + 342 q^{19} - 450 q^{21} - 194 q^{25} - 804 q^{31} + 1332 q^{33} - 962 q^{37} - 594 q^{39} - 1732 q^{43} - 2394 q^{45} + 820 q^{49} - 1638 q^{51} - 2664 q^{57} - 4620 q^{61}+ \cdots + 4284 q^{99}+O(q^{100}) $ 16 * q - 80 * q^7 + 18 * q^9 + 342 * q^19 - 450 * q^21 - 194 * q^25 - 804 * q^31 + 1332 * q^33 - 962 * q^37 - 594 * q^39 - 1732 * q^43 - 2394 * q^45 + 820 * q^49 - 1638 * q^51 - 2664 * q^57 - 4620 * q^61 + 2016 * q^63 + 706 * q^67 + 3294 * q^73 - 6174 * q^75 + 2656 * q^79 + 126 * q^81 + 5232 * q^85 - 1026 * q^87 - 4098 * q^91 + 2016 * q^93 + 4284 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.17709	−	3.09062i	0.803881	−	0.594790i
$3$	4.17709	−	3.09062i	0.803881	−	0.594790i
$4$		0			0
$5$	−4.27911	−	7.41164i	−0.382736	−	0.662917i	0.608717	−	0.793388i	$-0.291685\pi$
$5$	−4.27911	−	7.41164i	−0.382736	−	0.662917i	−0.991452	+	0.130470i	$0.958351\pi$
$6$		0			0
$7$	6.41772	+	17.3728i	0.346524	+	0.938041i
$7$	6.41772	+	17.3728i	0.346524	+	0.938041i
$8$		0			0
$9$	7.89612	−	25.8196i	0.292449	−	0.956281i
$10$		0			0
$11$	53.8609	+	31.0966i	1.47633	+	0.852361i	0.999643	−	0.0267105i	$-0.00850323\pi$
$11$	53.8609	+	31.0966i	1.47633	+	0.852361i	0.476690	+	0.879072i	$0.341837\pi$
$12$		0			0
$13$			61.7061i			1.31648i	0.752810	+	0.658238i	$0.228698\pi$
$13$			61.7061i			1.31648i	−0.752810	+	0.658238i	$0.771302\pi$
$14$		0			0
$15$	−40.7808	−	17.7340i	−0.701971	−	0.305259i
$16$		0			0
$17$	13.3365	−	23.0995i	0.190270	−	0.329557i	−0.755070	−	0.655644i	$-0.772397\pi$
$17$	13.3365	−	23.0995i	0.190270	−	0.329557i	0.945340	+	0.326088i	$0.105730\pi$
$18$		0			0
$19$	58.6213	−	33.8450i	0.707824	−	0.408662i	−0.102431	−	0.994740i	$-0.532662\pi$
$19$	58.6213	−	33.8450i	0.707824	−	0.408662i	0.810255	+	0.586078i	$0.199329\pi$
$20$		0			0
$21$	80.5000	+	52.7328i	0.836502	+	0.547964i
$22$		0			0
$23$	45.8287	−	26.4592i	0.415476	−	0.239875i	−0.277664	−	0.960678i	$-0.589560\pi$
$23$	45.8287	−	26.4592i	0.415476	−	0.239875i	0.693140	+	0.720803i	$0.256227\pi$
$24$		0			0
$25$	25.8784	−	44.8227i	0.207027	−	0.358581i
$26$		0			0
$27$	−46.8158	−	132.255i	−0.333693	−	0.942682i
$28$		0			0
$29$		−	55.1116i		−	0.352895i	−0.984310	−	0.176448i	$-0.943539\pi$
$29$		−	55.1116i		−	0.352895i	0.984310	−	0.176448i	$-0.0564606\pi$
$30$		0			0
$31$	134.080	+	77.4108i	0.776819	+	0.448497i	0.835302	−	0.549792i	$-0.185293\pi$
$31$	134.080	+	77.4108i	0.776819	+	0.448497i	−0.0584827	+	0.998288i	$0.518626\pi$
$32$		0			0
$33$	321.089	−	36.5704i	1.69377	−	0.192912i
$34$		0			0
$35$	101.299	−	121.906i	0.489217	−	0.588739i
$36$		0			0
$37$	−157.940	−	273.560i	−0.701761	−	1.21549i	−0.967848	−	0.251536i	$-0.919064\pi$
$37$	−157.940	−	273.560i	−0.701761	−	1.21549i	0.266087	−	0.963949i	$-0.414269\pi$
$38$		0			0
$39$	190.710	+	257.752i	0.783027	+	1.05829i
$40$		0			0
$41$	210.211			0.800719			0.400360	−	0.916358i	$-0.368885\pi$
$41$	210.211			0.800719			0.400360	+	0.916358i	$0.368885\pi$
$42$		0			0
$43$	−351.939			−1.24815			−0.624073	−	0.781366i	$-0.714523\pi$
$43$	−351.939			−1.24815			−0.624073	+	0.781366i	$0.714523\pi$
$44$		0			0
$45$	−225.154	+	51.9617i	−0.745866	+	0.172133i
$46$		0			0
$47$	−115.819	−	200.605i	−0.359446	−	0.622579i	0.628422	−	0.777872i	$-0.283701\pi$
$47$	−115.819	−	200.605i	−0.359446	−	0.622579i	−0.987868	+	0.155294i	$0.950368\pi$
$48$		0			0
$49$	−260.626	+	222.987i	−0.759842	+	0.650108i
$50$		0			0
$51$	−15.6841	−	137.707i	−0.0430630	−	0.378095i
$52$		0			0
$53$	232.890	+	134.459i	0.603583	+	0.348479i	0.770450	−	0.637500i	$-0.220032\pi$
$53$	232.890	+	134.459i	0.603583	+	0.348479i	−0.166867	+	0.985979i	$0.553365\pi$
$54$		0			0
$55$		−	532.263i		−	1.30492i
$56$		0			0
$57$	140.264	−	322.550i	0.325938	−	0.749522i
$58$		0			0
$59$	−9.14155	+	15.8336i	−0.0201717	+	0.0349384i	−0.875935	−	0.482429i	$-0.839755\pi$
$59$	−9.14155	+	15.8336i	−0.0201717	+	0.0349384i	0.855763	+	0.517367i	$0.173088\pi$
$60$		0			0
$61$	−72.3320	+	41.7609i	−0.151822	+	0.0876547i	−0.573987	−	0.818865i	$-0.694604\pi$
$61$	−72.3320	+	41.7609i	−0.151822	+	0.0876547i	0.422164	+	0.906519i	$0.361271\pi$
$62$		0			0
$63$	499.233	−	28.5253i	0.998372	−	0.0570452i
$64$		0			0
$65$	457.344	−	264.047i	0.872715	−	0.503862i
$66$		0			0
$67$	64.7354	−	112.125i	0.118040	−	0.204451i	−0.800951	−	0.598730i	$-0.795672\pi$
$67$	64.7354	−	112.125i	0.118040	−	0.204451i	0.918991	+	0.394279i	$0.129006\pi$
$68$		0			0
$69$	109.655	−	252.162i	0.191318	−	0.439952i
$70$		0			0
$71$			804.537i			1.34480i	0.740186	+	0.672402i	$0.234737\pi$
$71$			804.537i			1.34480i	−0.740186	+	0.672402i	$0.765263\pi$
$72$		0			0
$73$	370.377	+	213.837i	0.593826	+	0.342846i	0.766609	−	0.642114i	$-0.221943\pi$
$73$	370.377	+	213.837i	0.593826	+	0.342846i	−0.172783	+	0.984960i	$0.555276\pi$
$74$		0			0
$75$	−30.4336	−	267.208i	−0.0468556	−	0.411394i
$76$		0			0
$77$	−194.570	+	1135.28i	−0.287965	+	1.68022i
$78$		0			0
$79$	609.284	+	1055.31i	0.867718	+	1.50293i	0.864322	+	0.502938i	$0.167748\pi$
$79$	609.284	+	1055.31i	0.867718	+	1.50293i	0.00339594	+	0.999994i	$0.498919\pi$
$80$		0			0
$81$	−604.302	−	407.749i	−0.828947	−	0.559327i
$82$		0			0
$83$	1371.18			1.81333			0.906663	−	0.421855i	$-0.138621\pi$
$83$	1371.18			1.81333			0.906663	+	0.421855i	$0.138621\pi$
$84$		0			0
$85$	−228.274			−0.291292
$86$		0			0
$87$	−170.329	−	230.206i	−0.209899	−	0.283686i
$88$		0			0
$89$	−386.840	−	670.026i	−0.460729	−	0.798007i	0.538268	−	0.842774i	$-0.319079\pi$
$89$	−386.840	−	670.026i	−0.460729	−	0.798007i	−0.998997	+	0.0447669i	$0.985745\pi$
$90$		0			0
$91$	−1072.01	+	396.012i	−1.23491	+	0.456191i
$92$		0			0
$93$	799.309	−	91.0371i	0.891231	−	0.101506i
$94$		0			0
$95$	−501.694	−	289.653i	−0.541819	−	0.312819i
$96$		0			0
$97$		−	848.768i		−	0.888447i	−0.895916	−	0.444223i	$-0.853480\pi$
$97$		−	848.768i		−	0.888447i	0.895916	−	0.444223i	$-0.146520\pi$
$98$		0			0
$99$	1228.19	−	1145.12i	1.24685	−	1.16252i
$100$		0			0
$101$	512.647	−	887.931i	0.505053	−	0.874777i	−0.494930	−	0.868933i	$-0.664806\pi$
$101$	512.647	−	887.931i	0.505053	−	0.874777i	0.999983	−	0.00584430i	$-0.00186031\pi$
$102$		0			0
$103$	−278.306	+	160.680i	−0.266236	+	0.153711i	−0.627176	−	0.778878i	$-0.715789\pi$
$103$	−278.306	+	160.680i	−0.266236	+	0.153711i	0.360940	+	0.932589i	$0.382456\pi$
$104$		0			0
$105$	46.3683	−	822.287i	0.0430960	−	0.764257i
$106$		0			0
$107$	−117.848	+	68.0393i	−0.106474	+	0.0614730i	−0.552292	−	0.833651i	$-0.686246\pi$
$107$	−117.848	+	68.0393i	−0.106474	+	0.0614730i	0.445817	+	0.895124i	$0.352913\pi$
$108$		0			0
$109$	−703.079	+	1217.77i	−0.617823	+	1.07010i	0.372059	+	0.928209i	$0.378652\pi$
$109$	−703.079	+	1217.77i	−0.617823	+	1.07010i	−0.989882	+	0.141892i	$0.954681\pi$
$110$		0			0
$111$	−1505.20	−	654.551i	−1.28709	−	0.559705i
$112$		0			0
$113$			467.285i			0.389013i	0.980901	+	0.194506i	$0.0623105\pi$
$113$			467.285i			0.389013i	−0.980901	+	0.194506i	$0.937690\pi$
$114$		0			0
$115$	−392.212	−	226.444i	−0.318035	−	0.183617i
$116$		0			0
$117$	1593.23	+	487.239i	1.25892	+	0.385002i
$118$		0			0
$119$	486.893	+	83.4460i	0.375071	+	0.0642814i
$120$		0			0
$121$	1268.50	+	2197.10i	0.953039	+	1.65071i
$122$		0			0
$123$	878.071	−	649.684i	0.643683	−	0.476260i
$124$		0			0
$125$	−1512.72			−1.08242
$126$		0			0
$127$	−259.166			−0.181081			−0.0905404	−	0.995893i	$-0.528859\pi$
$127$	−259.166			−0.181081			−0.0905404	+	0.995893i	$0.528859\pi$
$128$		0			0
$129$	−1470.08	+	1087.71i	−1.00336	+	0.742385i
$130$		0			0
$131$	−1323.92	−	2293.10i	−0.882991	−	1.52938i	−0.848000	−	0.529997i	$-0.822193\pi$
$131$	−1323.92	−	2293.10i	−0.882991	−	1.52938i	−0.0349910	−	0.999388i	$-0.511140\pi$
$132$		0			0
$133$	964.197	+	801.206i	0.628620	+	0.522356i
$134$		0			0
$135$	−779.894	+	912.914i	−0.497204	+	0.582008i
$136$		0			0
$137$	−405.314	−	234.008i	−0.252761	−	0.145932i	0.368267	−	0.929720i	$-0.379951\pi$
$137$	−405.314	−	234.008i	−0.252761	−	0.145932i	−0.621028	+	0.783788i	$0.713285\pi$
$138$		0			0
$139$			2923.27i			1.78380i	0.452229	+	0.891902i	$0.350629\pi$
$139$			2923.27i			1.78380i	−0.452229	+	0.891902i	$0.649371\pi$
$140$		0			0
$141$	−1103.78	−	479.990i	−0.659256	−	0.286684i
$142$		0			0
$143$	−1918.85	+	3323.54i	−1.12211	+	1.94356i
$144$		0			0
$145$	−408.467	+	235.829i	−0.233940	+	0.135066i
$146$		0			0
$147$	−399.489	+	1736.93i	−0.224145	+	0.974556i
$148$		0			0
$149$	−1570.24	+	906.580i	−0.863351	+	0.498456i	−0.865133	−	0.501543i	$-0.832766\pi$
$149$	−1570.24	+	906.580i	−0.863351	+	0.498456i	0.00178220	+	0.999998i	$0.499433\pi$
$150$		0			0
$151$	−827.154	+	1432.67i	−0.445780	+	0.772114i	−0.998106	−	0.0615140i	$-0.980407\pi$
$151$	−827.154	+	1432.67i	−0.445780	+	0.772114i	0.552326	+	0.833628i	$0.313740\pi$
$152$		0			0
$153$	−491.114	−	526.740i	−0.259505	−	0.278330i
$154$		0			0
$155$		−	1325.00i		−	0.686622i
$156$		0			0
$157$	−1200.29	−	692.988i	−0.610151	−	0.352271i	0.162874	−	0.986647i	$-0.447924\pi$
$157$	−1200.29	−	692.988i	−0.610151	−	0.352271i	−0.773024	+	0.634376i	$0.781257\pi$
$158$		0			0
$159$	1388.36	−	158.127i	0.692481	−	0.0788699i
$160$		0			0
$161$	753.785	+	626.363i	0.368985	+	0.306611i
$162$		0			0
$163$	−576.540	−	998.597i	−0.277044	−	0.479854i	0.693605	−	0.720356i	$-0.256021\pi$
$163$	−576.540	−	998.597i	−0.277044	−	0.479854i	−0.970649	+	0.240502i	$0.922688\pi$
$164$		0			0
$165$	−1645.02	−	2223.31i	−0.776151	−	1.04900i
$166$		0			0
$167$	303.672			0.140712			0.0703559	−	0.997522i	$-0.477586\pi$
$167$	303.672			0.140712			0.0703559	+	0.997522i	$0.477586\pi$
$168$		0			0
$169$	−1610.64			−0.733110
$170$		0			0
$171$	−410.984	−	1780.82i	−0.183794	−	0.796391i
$172$		0			0
$173$	−1308.97	−	2267.21i	−0.575256	−	0.996373i	−0.996014	−	0.0891996i	$-0.971569\pi$
$173$	−1308.97	−	2267.21i	−0.575256	−	0.996373i	0.420758	−	0.907173i	$-0.361764\pi$
$174$		0			0
$175$	944.774	+	161.920i	0.408104	+	0.0699428i
$176$		0			0
$177$	10.7507	+	94.3915i	0.00456537	+	0.0400842i
$178$		0			0
$179$	−2395.77	−	1383.20i	−1.00038	−	0.577569i	−0.0920191	−	0.995757i	$-0.529332\pi$
$179$	−2395.77	−	1383.20i	−1.00038	−	0.577569i	−0.908361	+	0.418188i	$0.862665\pi$
$180$		0			0
$181$			539.608i			0.221595i	0.993843	+	0.110798i	$0.0353405\pi$
$181$			539.608i			0.221595i	−0.993843	+	0.110798i	$0.964659\pi$
$182$		0			0
$183$	−173.070	+	397.990i	−0.0699109	+	0.160766i
$184$		0			0
$185$	−1351.68	+	2341.19i	−0.537178	+	0.930419i
$186$		0			0
$187$	1436.63	−	829.441i	0.561802	−	0.324357i
$188$		0			0
$189$	1997.18	−	1662.09i	0.768642	−	0.639679i
$190$		0			0
$191$	−2764.63	+	1596.16i	−1.04734	+	0.604680i	−0.921903	−	0.387422i	$-0.873366\pi$
$191$	−2764.63	+	1596.16i	−1.04734	+	0.604680i	−0.125434	+	0.992102i	$0.540032\pi$
$192$		0			0
$193$	−718.685	+	1244.80i	−0.268042	+	0.464262i	−0.968356	−	0.249573i	$-0.919710\pi$
$193$	−718.685	+	1244.80i	−0.268042	+	0.464262i	0.700314	+	0.713835i	$0.253043\pi$
$194$		0			0
$195$	1094.29	−	2516.42i	0.401867	−	0.924128i
$196$		0			0
$197$		−	2346.26i		−	0.848548i	−0.905534	−	0.424274i	$-0.860529\pi$
$197$		−	2346.26i		−	0.848548i	0.905534	−	0.424274i	$-0.139471\pi$
$198$		0			0
$199$	1586.15	+	915.766i	0.565022	+	0.326216i	0.755159	−	0.655542i	$-0.227560\pi$
$199$	1586.15	+	915.766i	0.565022	+	0.326216i	−0.190137	+	0.981758i	$0.560893\pi$
$200$		0			0
$201$	−76.1304	−	668.428i	−0.0267155	−	0.234564i
$202$		0			0
$203$	957.440	−	353.690i	0.331030	−	0.122287i
$204$		0			0
$205$	−899.518	−	1558.01i	−0.306464	−	0.530811i
$206$		0			0
$207$	−321.297	−	1392.20i	−0.107882	−	0.467463i
$208$		0			0
$209$	4209.86			1.39331
$210$		0			0
$211$	−4291.48			−1.40018			−0.700090	−	0.714055i	$-0.746857\pi$
$211$	−4291.48			−1.40018			−0.700090	+	0.714055i	$0.746857\pi$
$212$		0			0
$213$	2486.52	+	3360.62i	0.799876	+	1.08106i
$214$		0			0
$215$	1505.99	+	2608.45i	0.477709	+	0.827417i
$216$		0			0
$217$	−484.356	+	2826.13i	−0.151522	+	0.884103i
$218$		0			0
$219$	2207.98	−	251.478i	0.681287	−	0.0775949i
$220$		0			0
$221$	1425.38	+	822.945i	0.433853	+	0.250485i
$222$		0			0
$223$		−	1170.88i		−	0.351604i	−0.984426	−	0.175802i	$-0.943748\pi$
$223$		−	1170.88i		−	0.351604i	0.984426	−	0.175802i	$-0.0562519\pi$
$224$		0			0
$225$	−952.964	−	1022.09i	−0.282360	−	0.302843i
$226$		0			0
$227$	1063.49	−	1842.02i	0.310954	−	0.538588i	−0.667615	−	0.744506i	$-0.732685\pi$
$227$	1063.49	−	1842.02i	0.310954	−	0.538588i	0.978569	+	0.205919i	$0.0660182\pi$
$228$		0			0
$229$	−1124.19	+	649.049i	−0.324403	+	0.187294i	−0.653354	−	0.757053i	$-0.726638\pi$
$229$	−1124.19	+	649.049i	−0.324403	+	0.187294i	0.328950	+	0.944347i	$0.393305\pi$
$230$		0			0
$231$	2695.99	+	5343.51i	0.767892	+	1.52198i
$232$		0			0
$233$	−3641.17	+	2102.23i	−1.02378	+	0.591081i	−0.915197	−	0.403007i	$-0.867965\pi$
$233$	−3641.17	+	2102.23i	−1.02378	+	0.591081i	−0.108585	+	0.994087i	$0.534632\pi$
$234$		0			0
$235$	−991.207	+	1716.82i	−0.275145	+	0.476566i
$236$		0			0
$237$	5806.59	+	2525.06i	1.59147	+	0.692068i
$238$		0			0
$239$		−	3816.77i		−	1.03300i	−0.856288	−	0.516498i	$-0.827235\pi$
$239$		−	3816.77i		−	1.03300i	0.856288	−	0.516498i	$-0.172765\pi$
$240$		0			0
$241$	−1417.67	−	818.491i	−0.378921	−	0.218770i	0.298428	−	0.954432i	$-0.403538\pi$
$241$	−1417.67	−	818.491i	−0.378921	−	0.218770i	−0.677349	+	0.735662i	$0.736871\pi$
$242$		0			0
$243$	−3784.42	+	164.465i	−0.999057	+	0.0434174i
$244$		0			0
$245$	2767.95	+	977.479i	0.721786	+	0.254893i
$246$		0			0
$247$	2088.44	+	3617.29i	0.537994	+	0.931833i
$248$		0			0
$249$	5727.52	−	4237.78i	1.45770	−	1.07855i
$250$		0			0
$251$	5269.47			1.32512			0.662562	−	0.749007i	$-0.269469\pi$
$251$	5269.47			1.32512			0.662562	+	0.749007i	$0.269469\pi$
$252$		0			0
$253$	3291.16			0.817841
$254$		0			0
$255$	−953.521	+	705.509i	−0.234164	+	0.173257i
$256$		0			0
$257$	−570.595	−	988.300i	−0.138493	−	0.239877i	0.788433	−	0.615120i	$-0.210893\pi$
$257$	−570.595	−	988.300i	−0.138493	−	0.239877i	−0.926926	+	0.375243i	$0.877559\pi$
$258$		0			0
$259$	3738.88	−	4499.48i	0.896998	−	1.07948i
$260$		0			0
$261$	−1422.96	−	435.168i	−0.337467	−	0.103204i
$262$		0			0
$263$	1978.91	+	1142.53i	0.463974	+	0.267875i	0.713714	−	0.700438i	$-0.247012\pi$
$263$	1978.91	+	1142.53i	0.463974	+	0.267875i	−0.249740	+	0.968313i	$0.580345\pi$
$264$		0			0
$265$		−	2301.46i		−	0.533501i
$266$		0			0
$267$	−3686.66	−	1603.18i	−0.845018	−	0.367465i
$268$		0			0
$269$	937.191	−	1623.26i	0.212422	−	0.367926i	−0.740050	−	0.672552i	$-0.765198\pi$
$269$	937.191	−	1623.26i	0.212422	−	0.367926i	0.952472	+	0.304626i	$0.0985315\pi$
$270$		0			0
$271$	−2841.71	+	1640.66i	−0.636980	+	0.367760i	−0.783450	−	0.621455i	$-0.786542\pi$
$271$	−2841.71	+	1640.66i	−0.636980	+	0.367760i	0.146471	+	0.989215i	$0.453209\pi$
$272$		0			0
$273$	−3253.94	+	4967.34i	−0.721382	+	1.10123i
$274$		0			0
$275$	2787.66	−	1609.46i	0.611282	−	0.352924i
$276$		0			0
$277$	265.374	−	459.642i	0.0575625	−	0.0997011i	−0.835808	−	0.549022i	$-0.815000\pi$
$277$	265.374	−	459.642i	0.0575625	−	0.0997011i	0.893371	+	0.449320i	$0.148334\pi$
$278$		0			0
$279$	3057.42	−	2850.63i	0.656069	−	0.611695i
$280$		0			0
$281$		−	5216.62i		−	1.10747i	−0.832695	−	0.553733i	$-0.813203\pi$
$281$		−	5216.62i		−	1.10747i	0.832695	−	0.553733i	$-0.186797\pi$
$282$		0			0
$283$	907.832	+	524.137i	0.190689	+	0.110094i	0.592305	−	0.805714i	$-0.298218\pi$
$283$	907.832	+	524.137i	0.190689	+	0.110094i	−0.401616	+	0.915808i	$0.631551\pi$
$284$		0			0
$285$	−2990.83	+	340.640i	−0.621619	+	0.0707991i
$286$		0			0
$287$	1349.08	+	3651.95i	0.277469	+	0.751108i
$288$		0			0
$289$	2100.77	+	3638.65i	0.427595	+	0.740616i
$290$		0			0
$291$	−2623.22	−	3545.38i	−0.528439	−	0.714205i
$292$		0			0
$293$	6408.45			1.27777			0.638884	−	0.769303i	$-0.279397\pi$
$293$	6408.45			1.27777			0.638884	+	0.769303i	$0.279397\pi$
$294$		0			0
$295$	156.471			0.0308817
$296$		0			0
$297$	1591.13	−	8579.16i	0.310864	−	1.67614i
$298$		0			0
$299$	1632.69	+	2827.91i	0.315790	+	0.546964i
$300$		0			0
$301$	−2258.65	−	6114.16i	−0.432512	−	1.17081i
$302$		0			0
$303$	−602.886	−	5293.37i	−0.114307	−	1.00362i
$304$		0			0
$305$	619.034	+	357.399i	0.116216	+	0.0670971i
$306$		0			0
$307$		−	3717.93i		−	0.691184i	−0.938385	−	0.345592i	$-0.887678\pi$
$307$		−	3717.93i		−	0.691184i	0.938385	−	0.345592i	$-0.112322\pi$
$308$		0			0
$309$	−665.907	+	1531.31i	−0.122596	+	0.281920i
$310$		0			0
$311$	−202.816	+	351.287i	−0.0369795	+	0.0640503i	−0.883923	−	0.467633i	$-0.845107\pi$
$311$	−202.816	+	351.287i	−0.0369795	+	0.0640503i	0.846943	+	0.531683i	$0.178440\pi$
$312$		0			0
$313$	−2640.01	+	1524.21i	−0.476748	+	0.275251i	−0.719060	−	0.694948i	$-0.755427\pi$
$313$	−2640.01	+	1524.21i	−0.476748	+	0.275251i	0.242312	+	0.970198i	$0.422094\pi$
$314$		0			0
$315$	−2347.69	−	3578.07i	−0.419929	−	0.640005i
$316$		0			0
$317$	−5714.50	+	3299.27i	−1.01249	+	0.584559i	−0.911919	−	0.410371i	$-0.865399\pi$
$317$	−5714.50	+	3299.27i	−1.01249	+	0.584559i	−0.100568	+	0.994930i	$0.532066\pi$
$318$		0			0
$319$	1713.78	−	2968.36i	0.300794	−	0.520991i
$320$		0			0
$321$	−281.976	+	648.428i	−0.0490292	+	0.112747i
$322$		0			0
$323$		−	1805.50i		−	0.311024i
$324$		0			0
$325$	2765.83	+	1596.85i	0.472064	+	0.272546i
$326$		0			0
$327$	826.838	+	7259.67i	0.139830	+	1.22771i
$328$		0			0
$329$	2741.76	−	3299.52i	0.459448	−	0.552914i
$330$		0			0
$331$	−184.027	−	318.744i	−0.0305591	−	0.0529298i	0.850341	−	0.526231i	$-0.176395\pi$
$331$	−184.027	−	318.744i	−0.0305591	−	0.0529298i	−0.880900	+	0.473302i	$0.843062\pi$
$332$		0			0
$333$	−8310.31	+	1917.88i	−1.36757	+	0.315613i
$334$		0			0
$335$	−1108.04			−0.180712
$336$		0			0
$337$	6514.00			1.05294			0.526469	−	0.850194i	$-0.323516\pi$
$337$	6514.00			1.05294			0.526469	+	0.850194i	$0.323516\pi$
$338$		0			0
$339$	1444.20	+	1951.89i	0.231381	+	0.312720i
$340$		0			0
$341$	4814.43	+	8338.83i	0.764562	+	1.32426i
$342$		0			0
$343$	−5546.52	−	3096.72i	−0.873131	−	0.487485i
$344$		0			0
$345$	−2338.16	+	266.304i	−0.364876	+	0.0415574i
$346$		0			0
$347$	2098.92	+	1211.81i	0.324715	+	0.187474i	0.653492	−	0.756933i	$-0.273303\pi$
$347$	2098.92	+	1211.81i	0.324715	+	0.187474i	−0.328777	+	0.944407i	$0.606637\pi$
$348$		0			0
$349$		−	10490.9i		−	1.60907i	−0.593903	−	0.804536i	$-0.702414\pi$
$349$		−	10490.9i		−	1.60907i	0.593903	−	0.804536i	$-0.297586\pi$
$350$		0			0
$351$	8160.92	−	2888.82i	1.24102	−	0.439298i
$352$		0			0
$353$	−4005.42	+	6937.60i	−0.603930	+	1.04604i	0.388290	+	0.921537i	$0.373066\pi$
$353$	−4005.42	+	6937.60i	−0.603930	+	1.04604i	−0.992220	+	0.124500i	$0.960267\pi$
$354$		0			0
$355$	5962.94	−	3442.71i	0.891494	−	0.514704i
$356$		0			0
$357$	2291.69	−	1156.24i	0.339746	−	0.171414i
$358$		0			0
$359$	−9906.07	+	5719.27i	−1.45633	+	0.840813i	−0.998828	−	0.0483961i	$-0.984589\pi$
$359$	−9906.07	+	5719.27i	−1.45633	+	0.840813i	−0.457502	+	0.889209i	$0.651256\pi$
$360$		0			0
$361$	−1138.53	+	1971.99i	−0.165990	+	0.287504i
$362$		0			0
$363$	12089.0	+	5257.03i	1.74796	+	0.760118i
$364$		0			0
$365$		−	3660.13i		−	0.524877i
$366$		0			0
$367$	1259.42	+	727.126i	0.179131	+	0.103421i	0.586884	−	0.809671i	$-0.300354\pi$
$367$	1259.42	+	727.126i	0.179131	+	0.103421i	−0.407753	+	0.913092i	$0.633688\pi$
$368$		0			0
$369$	1659.85	−	5427.57i	0.234170	−	0.765713i
$370$		0			0
$371$	−841.305	+	4908.87i	−0.117731	+	0.686942i
$372$		0			0
$373$	−3990.41	−	6911.59i	−0.553929	−	0.959433i	−0.997986	−	0.0634346i	$-0.979795\pi$
$373$	−3990.41	−	6911.59i	−0.553929	−	0.959433i	0.444057	−	0.895999i	$-0.353539\pi$
$374$		0			0
$375$	−6318.78	+	4675.26i	−0.870135	+	0.643811i
$376$		0			0
$377$	3400.72			0.464578
$378$		0			0
$379$	−5818.85			−0.788639			−0.394320	−	0.918973i	$-0.629020\pi$
$379$	−5818.85			−0.788639			−0.394320	+	0.918973i	$0.629020\pi$
$380$		0			0
$381$	−1082.56	+	800.983i	−0.145567	+	0.107705i
$382$		0			0
$383$	−618.611	−	1071.47i	−0.0825314	−	0.142949i	0.821805	−	0.569769i	$-0.192967\pi$
$383$	−618.611	−	1071.47i	−0.0825314	−	0.142949i	−0.904337	+	0.426820i	$0.859634\pi$
$384$		0			0
$385$	9246.88	−	3415.91i	1.22406	−	0.452185i
$386$		0			0
$387$	−2778.96	+	9086.93i	−0.365019	+	1.19358i
$388$		0			0
$389$	−2602.51	−	1502.56i	−0.339209	−	0.195842i	0.320713	−	0.947176i	$-0.396077\pi$
$389$	−2602.51	−	1502.56i	−0.339209	−	0.195842i	−0.659922	+	0.751334i	$0.729411\pi$
$390$		0			0
$391$		−	1411.50i		−	0.182564i
$392$		0			0
$393$	−12617.3	−	5486.75i	−1.61948	−	0.704249i
$394$		0			0
$395$	5214.39	−	9031.58i	0.664213	−	1.15045i
$396$		0			0
$397$	−5552.29	+	3205.62i	−0.701918	+	0.405253i	−0.808061	−	0.589098i	$-0.799483\pi$
$397$	−5552.29	+	3205.62i	−0.701918	+	0.405253i	0.106143	+	0.994351i	$0.466150\pi$
$398$		0			0
$399$	6503.76	+	366.743i	0.816028	+	0.0460153i
$400$		0			0
$401$	2993.97	−	1728.57i	0.372848	−	0.215264i	−0.301854	−	0.953354i	$-0.597606\pi$
$401$	2993.97	−	1728.57i	0.372848	−	0.215264i	0.674702	+	0.738090i	$0.264272\pi$
$402$		0			0
$403$	−4776.72	+	8273.52i	−0.590435	+	1.02266i
$404$		0			0
$405$	−436.213	+	6223.68i	−0.0535200	+	0.763598i
$406$		0			0
$407$		−	19645.6i		−	2.39261i
$408$		0			0
$409$	13285.6	+	7670.42i	1.60618	+	0.927329i	0.990214	+	0.139558i	$0.0445681\pi$
$409$	13285.6	+	7670.42i	1.60618	+	0.927329i	0.615968	+	0.787772i	$0.288765\pi$
$410$		0			0
$411$	−2416.26	+	275.199i	−0.289989	+	0.0330282i
$412$		0			0
$413$	−333.742	−	57.1983i	−0.0397636	−	0.00681487i
$414$		0			0
$415$	−5867.42	−	10162.7i	−0.694024	−	1.20209i
$416$		0			0
$417$	9034.73	+	12210.8i	1.06099	+	1.43397i
$418$		0			0
$419$	−2968.51			−0.346112			−0.173056	−	0.984912i	$-0.555364\pi$
$419$	−2968.51			−0.346112			−0.173056	+	0.984912i	$0.555364\pi$
$420$		0			0
$421$	−8733.67			−1.01105			−0.505526	−	0.862811i	$-0.668702\pi$
$421$	−8733.67			−1.01105			−0.505526	+	0.862811i	$0.668702\pi$
$422$		0			0
$423$	−6094.05	+	1406.40i	−0.700480	+	0.161659i
$424$		0			0
$425$	−690.255	−	1195.56i	−0.0787819	−	0.136454i
$426$		0			0
$427$	−1189.71	−	988.597i	−0.134834	−	0.112041i
$428$		0			0
$429$	2256.61	+	19813.2i	0.253964	+	2.22981i
$430$		0			0
$431$	−51.3171	−	29.6279i	−0.00573517	−	0.00331120i	0.497130	−	0.867676i	$-0.334387\pi$
$431$	−51.3171	−	29.6279i	−0.00573517	−	0.00331120i	−0.502865	+	0.864365i	$0.667721\pi$
$432$		0			0
$433$		−	3034.66i		−	0.336805i	−0.985718	−	0.168403i	$-0.946139\pi$
$433$		−	3034.66i		−	0.336805i	0.985718	−	0.168403i	$-0.0538609\pi$
$434$		0			0
$435$	−977.347	+	2247.49i	−0.107725	+	0.247722i
$436$		0			0
$437$	1791.03	−	3102.15i	0.196056	−	0.339578i
$438$		0			0
$439$	2155.72	−	1244.61i	0.234367	−	0.135312i	−0.378218	−	0.925716i	$-0.623463\pi$
$439$	2155.72	−	1244.61i	0.234367	−	0.135312i	0.612585	+	0.790405i	$0.290130\pi$
$440$		0			0
$441$	3699.50	+	8489.98i	0.399471	+	0.916746i
$442$		0			0
$443$	−13052.4	+	7535.83i	−1.39986	+	0.808212i	−0.994378	−	0.105889i	$-0.966231\pi$
$443$	−13052.4	+	7535.83i	−1.39986	+	0.808212i	−0.405487	+	0.914101i	$0.632898\pi$
$444$		0			0
$445$	−3310.66	+	5734.23i	−0.352675	+	0.610851i
$446$		0			0
$447$	−3757.15	+	8639.89i	−0.397555	+	0.914212i
$448$		0			0
$449$		−	5352.96i		−	0.562632i	−0.959615	−	0.281316i	$-0.909229\pi$
$449$		−	5352.96i		−	0.562632i	0.959615	−	0.281316i	$-0.0907709\pi$
$450$		0			0
$451$	11322.2	+	6536.86i	1.18213	+	0.682502i
$452$		0			0
$453$	972.754	+	8540.82i	0.100892	+	0.885834i
$454$		0			0
$455$	7522.33	+	6250.74i	0.775060	+	0.644042i
$456$		0			0
$457$	−1063.05	−	1841.25i	−0.108812	−	0.188468i	0.806477	−	0.591265i	$-0.201371\pi$
$457$	−1063.05	−	1841.25i	−0.108812	−	0.188468i	−0.915289	+	0.402797i	$0.868038\pi$
$458$		0			0
$459$	−3679.38	−	682.394i	−0.374159	−	0.0693931i
$460$		0			0
$461$	987.346			0.0997512			0.0498756	−	0.998755i	$-0.484118\pi$
$461$	987.346			0.0997512			0.0498756	+	0.998755i	$0.484118\pi$
$462$		0			0
$463$	17023.3			1.70872			0.854362	−	0.519678i	$-0.173948\pi$
$463$	17023.3			1.70872			0.854362	+	0.519678i	$0.173948\pi$
$464$		0			0
$465$	−4095.07	−	5534.64i	−0.408396	−	0.551963i
$466$		0			0
$467$	−6858.57	−	11879.4i	−0.679608	−	1.17712i	−0.975099	−	0.221770i	$-0.928817\pi$
$467$	−6858.57	−	11879.4i	−0.679608	−	1.17712i	0.295491	−	0.955345i	$-0.404517\pi$
$468$		0			0
$469$	2363.37	+	405.046i	0.232687	+	0.0398791i
$470$		0			0
$471$	−7155.48	+	814.971i	−0.700015	+	0.0797280i
$472$		0			0
$473$	−18955.8	−	10944.1i	−1.84268	−	1.06387i
$474$		0			0
$475$		−	3503.42i		−	0.338416i
$476$		0			0
$477$	5310.61	−	4951.42i	0.509761	−	0.475283i
$478$		0			0
$479$	−974.841	+	1688.47i	−0.0929887	+	0.161061i	−0.908767	−	0.417303i	$-0.862975\pi$
$479$	−974.841	+	1688.47i	−0.0929887	+	0.161061i	0.815779	+	0.578364i	$0.196309\pi$
$480$		0			0
$481$	16880.3	−	9745.85i	1.60016	−	0.923851i
$482$		0			0
$483$	5084.48	+	286.711i	0.478989	+	0.0270099i
$484$		0			0
$485$	−6290.76	+	3631.97i	−0.588967	+	0.340040i
$486$		0			0
$487$	1269.48	−	2198.80i	0.118122	−	0.204594i	−0.800901	−	0.598796i	$-0.795646\pi$
$487$	1269.48	−	2198.80i	0.118122	−	0.204594i	0.919023	+	0.394203i	$0.128979\pi$
$488$		0			0
$489$	−5494.55	−	2389.36i	−0.508123	−	0.220962i
$490$		0			0
$491$			17119.1i			1.57347i	0.617289	+	0.786737i	$0.288231\pi$
$491$			17119.1i			1.57347i	−0.617289	+	0.786737i	$0.711769\pi$
$492$		0			0
$493$	−1273.05	−	734.997i	−0.116299	−	0.0671452i
$494$		0			0
$495$	−13742.8	−	4202.82i	−1.24787	−	0.381621i
$496$		0			0
$497$	−13977.0	+	5163.29i	−1.26148	+	0.466007i
$498$		0			0
$499$	454.423	+	787.084i	0.0407671	+	0.0706107i	0.885689	−	0.464279i	$-0.153687\pi$
$499$	454.423	+	787.084i	0.0407671	+	0.0706107i	−0.844922	+	0.534890i	$0.820353\pi$
$500$		0			0
$501$	1268.47	−	938.536i	0.113116	−	0.0836940i
$502$		0			0
$503$	13477.7			1.19471			0.597356	−	0.801976i	$-0.296218\pi$
$503$	13477.7			1.19471			0.597356	+	0.801976i	$0.296218\pi$
$504$		0			0
$505$	−8774.71			−0.773207
$506$		0			0
$507$	−6727.80	+	4977.89i	−0.589333	+	0.436047i
$508$		0			0
$509$	−7065.77	−	12238.3i	−0.615294	−	1.06572i	−0.990333	−	0.138711i	$-0.955704\pi$
$509$	−7065.77	−	12238.3i	−0.615294	−	1.06572i	0.375039	−	0.927009i	$-0.377629\pi$
$510$		0			0
$511$	−1337.97	+	7806.81i	−0.115828	+	0.675837i
$512$		0			0
$513$	−7220.56	−	6168.46i	−0.621434	−	0.530885i
$514$		0			0
$515$	2381.80	+	1375.14i	0.203796	+	0.117662i
$516$		0			0
$517$		−	14406.3i		−	1.22551i
$518$		0			0
$519$	−12474.8	−	5424.78i	−1.05507	−	0.458808i
$520$		0			0
$521$	−5532.79	+	9583.08i	−0.465251	+	0.805839i	−0.999213	−	0.0396697i	$-0.987369\pi$
$521$	−5532.79	+	9583.08i	−0.465251	+	0.805839i	0.533961	+	0.845509i	$0.320703\pi$
$522$		0			0
$523$	5211.30	−	3008.74i	0.435706	−	0.251555i	−0.266069	−	0.963954i	$-0.585725\pi$
$523$	5211.30	−	3008.74i	0.435706	−	0.251555i	0.701774	+	0.712399i	$0.252391\pi$
$524$		0			0
$525$	4446.83	−	2243.58i	0.369668	−	0.186511i
$526$		0			0
$527$	3576.31	−	2064.78i	0.295610	−	0.170671i
$528$		0			0
$529$	−4683.32	+	8111.75i	−0.384920	+	0.666701i
$530$		0			0
$531$	336.635	+	361.055i	0.0275117	+	0.0295075i
$532$		0			0
$533$			12971.3i			1.05413i
$534$		0			0
$535$	1008.57	+	582.296i	0.0815030	+	0.0470558i
$536$		0			0
$537$	−14282.3	+	1626.67i	−1.14772	+	0.130719i
$538$		0			0
$539$	−20971.7	+	3905.69i	−1.67591	+	0.312115i
$540$		0			0
$541$	−3477.08	−	6022.47i	−0.276324	−	0.478607i	0.694145	−	0.719836i	$-0.255783\pi$
$541$	−3477.08	−	6022.47i	−0.276324	−	0.478607i	−0.970468	+	0.241229i	$0.922450\pi$
$542$		0			0
$543$	1667.72	+	2253.99i	0.131803	+	0.178136i
$544$		0			0
$545$	12034.2			0.945852
$546$		0			0
$547$	−14101.3			−1.10224			−0.551122	−	0.834424i	$-0.685800\pi$
$547$	−14101.3			−1.10224			−0.551122	+	0.834424i	$0.685800\pi$
$548$		0			0
$549$	507.107	+	2197.33i	0.0394222	+	0.170819i
$550$		0			0
$551$	−1865.25	−	3230.71i	−0.144215	−	0.249788i
$552$		0			0
$553$	−14423.4	+	17357.6i	−1.10913	+	1.33476i
$554$		0			0
$555$	1589.61	+	13956.9i	0.121577	+	1.06745i
$556$		0			0
$557$	−7314.84	−	4223.22i	−0.556445	−	0.321263i	0.195273	−	0.980749i	$-0.437441\pi$
$557$	−7314.84	−	4223.22i	−0.556445	−	0.321263i	−0.751717	+	0.659486i	$0.770774\pi$
$558$		0			0
$559$		−	21716.8i		−	1.64315i
$560$		0			0
$561$	3437.46	−	7904.74i	0.258698	−	0.594899i
$562$		0			0
$563$	−10951.1	+	18967.8i	−0.819774	+	1.41989i	0.0860755	+	0.996289i	$0.472567\pi$
$563$	−10951.1	+	18967.8i	−0.819774	+	1.41989i	−0.905849	+	0.423601i	$0.860766\pi$
$564$		0			0
$565$	3463.35	−	1999.56i	0.257883	−	0.148889i
$566$		0			0
$567$	3205.49	−	13115.2i	0.237422	−	0.971407i
$568$		0			0
$569$	8724.86	−	5037.30i	0.642821	−	0.371133i	−0.142879	−	0.989740i	$-0.545636\pi$
$569$	8724.86	−	5037.30i	0.642821	−	0.371133i	0.785700	+	0.618607i	$0.212303\pi$
$570$		0			0
$571$	9133.47	−	15819.6i	0.669394	−	1.15942i	−0.308680	−	0.951166i	$-0.599887\pi$
$571$	9133.47	−	15819.6i	0.669394	−	1.15942i	0.978074	−	0.208258i	$-0.0667795\pi$
$572$		0			0
$573$	−6614.97	+	15211.7i	−0.482276	+	1.10904i
$574$		0			0
$575$		−	2738.89i		−	0.198642i
$576$		0			0
$577$	3379.83	+	1951.34i	0.243855	+	0.140789i	0.616947	−	0.787005i	$-0.288369\pi$
$577$	3379.83	+	1951.34i	0.243855	+	0.140789i	−0.373093	+	0.927794i	$0.621703\pi$
$578$		0			0
$579$	845.191	+	7420.81i	0.0606648	+	0.532640i
$580$		0			0
$581$	8799.82	+	23821.1i	0.628361	+	1.70097i
$582$		0			0
$583$	8362.44	+	14484.2i	0.594060	+	1.02894i
$584$		0			0
$585$	−3206.35	−	13893.4i	−0.226609	−	0.981915i
$586$		0			0
$587$	3318.05			0.233306			0.116653	−	0.993173i	$-0.462783\pi$
$587$	3318.05			0.233306			0.116653	+	0.993173i	$0.462783\pi$
$588$		0			0
$589$	10479.9			0.733135
$590$		0			0
$591$	−7251.39	−	9800.53i	−0.504708	−	0.682132i
$592$		0			0
$593$	12126.5	+	21003.6i	0.839754	+	1.45450i	0.890101	+	0.455764i	$0.150634\pi$
$593$	12126.5	+	21003.6i	0.839754	+	1.45450i	−0.0503470	+	0.998732i	$0.516033\pi$
$594$		0			0
$595$	−1465.00	−	3965.75i	−0.100940	−	0.273244i
$596$		0			0
$597$	9455.78	−	1076.96i	0.648240	−	0.0738311i
$598$		0			0
$599$	−9619.77	−	5553.97i	−0.656182	−	0.378847i	0.134639	−	0.990895i	$-0.457013\pi$
$599$	−9619.77	−	5553.97i	−0.656182	−	0.378847i	−0.790821	+	0.612048i	$0.790346\pi$
$600$		0			0
$601$			13367.3i			0.907258i	0.891191	+	0.453629i	$0.149871\pi$
$601$			13367.3i			0.907258i	−0.891191	+	0.453629i	$0.850129\pi$
$602$		0			0
$603$	−2383.86	−	2556.79i	−0.160992	−	0.172671i
$604$		0			0
$605$	10856.1	−	18803.3i	0.729524	−	1.26357i
$606$		0			0
$607$	−10180.8	+	5877.90i	−0.680769	+	0.393042i	−0.800145	−	0.599807i	$-0.795244\pi$
$607$	−10180.8	+	5877.90i	−0.680769	+	0.393042i	0.119376	+	0.992849i	$0.461911\pi$
$608$		0			0
$609$	2906.19	−	4436.48i	0.193374	−	0.295198i
$610$		0			0
$611$	12378.5	−	7146.75i	0.819610	−	0.473202i
$612$		0			0
$613$	11860.0	−	20542.2i	0.781439	−	1.35349i	−0.149664	−	0.988737i	$-0.547819\pi$
$613$	11860.0	−	20542.2i	0.781439	−	1.35349i	0.931103	−	0.364755i	$-0.118847\pi$
$614$		0			0
$615$	−8572.59	−	3727.88i	−0.562082	−	0.244427i
$616$		0			0
$617$		−	9294.78i		−	0.606473i	−0.952915	−	0.303237i	$-0.901933\pi$
$617$		−	9294.78i		−	0.606473i	0.952915	−	0.303237i	$-0.0980672\pi$
$618$		0			0
$619$	11638.1	+	6719.28i	0.755696	+	0.436301i	0.827748	−	0.561100i	$-0.189622\pi$
$619$	11638.1	+	6719.28i	0.755696	+	0.436301i	−0.0720523	+	0.997401i	$0.522955\pi$
$620$		0			0
$621$	−5644.86	−	4822.35i	−0.364767	−	0.311617i
$622$		0			0
$623$	9157.58	−	11020.5i	0.588909	−	0.708712i
$624$		0			0
$625$	3238.32	+	5608.94i	0.207253	+	0.358972i
$626$		0			0
$627$	17584.9	−	13011.1i	1.12006	−	0.828728i
$628$		0			0
$629$	−8425.47			−0.534095
$630$		0			0
$631$	−11635.5			−0.734076			−0.367038	−	0.930206i	$-0.619628\pi$
$631$	−11635.5			−0.734076			−0.367038	+	0.930206i	$0.619628\pi$
$632$		0			0
$633$	−17925.9	+	13263.4i	−1.12558	+	0.832813i
$634$		0			0
$635$	1109.00	+	1920.84i	0.0693060	+	0.120042i
$636$		0			0
$637$	−13759.7	−	16082.2i	−0.855851	−	1.00031i
$638$		0			0
$639$	20772.8	+	6352.73i	1.28601	+	0.393286i
$640$		0			0
$641$	21346.3	+	12324.3i	1.31533	+	0.759409i	0.982974	−	0.183744i	$-0.0588218\pi$
$641$	21346.3	+	12324.3i	1.31533	+	0.759409i	0.332360	+	0.943153i	$0.392155\pi$
$642$		0			0
$643$			5268.28i			0.323111i	0.986864	+	0.161556i	$0.0516511\pi$
$643$			5268.28i			0.323111i	−0.986864	+	0.161556i	$0.948349\pi$
$644$		0			0
$645$	14352.4	+	6241.28i	0.876161	+	0.381008i
$646$		0			0
$647$	9235.29	−	15996.0i	0.561169	−	0.971974i	−0.436225	−	0.899837i	$-0.643685\pi$
$647$	9235.29	−	15996.0i	0.561169	−	0.971974i	0.997395	−	0.0721365i	$-0.0229817\pi$
$648$		0			0
$649$	−984.743	+	568.542i	−0.0595602	+	0.0343871i
$650$		0			0
$651$	6711.31	+	13302.0i	0.404050	+	0.800837i
$652$		0			0
$653$	11414.2	−	6589.99i	0.684030	−	0.394925i	−0.117341	−	0.993092i	$-0.537437\pi$
$653$	11414.2	−	6589.99i	0.684030	−	0.394925i	0.801372	+	0.598166i	$0.204104\pi$
$654$		0			0
$655$	−11330.4	+	19624.9i	−0.675904	+	1.17070i
$656$		0			0
$657$	8445.72	−	7874.49i	0.501521	−	0.467600i
$658$		0			0
$659$			10701.0i			0.632549i	0.948668	+	0.316275i	$0.102432\pi$
$659$			10701.0i			0.632549i	−0.948668	+	0.316275i	$0.897568\pi$
$660$		0			0
$661$	−11215.0	−	6475.01i	−0.659931	−	0.381011i	0.132320	−	0.991207i	$-0.457758\pi$
$661$	−11215.0	−	6475.01i	−0.659931	−	0.381011i	−0.792251	+	0.610196i	$0.791091\pi$
$662$		0			0
$663$	8497.36	−	967.804i	0.497753	−	0.0566914i
$664$		0			0
$665$	1812.35	−	10574.7i	0.105684	−	0.616647i
$666$		0			0
$667$	−1458.21	−	2525.69i	−0.0846508	−	0.146619i
$668$		0			0
$669$	−3618.74	−	4890.86i	−0.209131	−	0.282648i
$670$		0			0
$671$	−5194.48			−0.298854
$672$		0			0
$673$	3025.28			0.173278			0.0866389	−	0.996240i	$-0.472387\pi$
$673$	3025.28			0.173278			0.0866389	+	0.996240i	$0.472387\pi$
$674$		0			0
$675$	−7139.52	−	1324.13i	−0.407111	−	0.0755047i
$676$		0			0
$677$	−1368.23	−	2369.84i	−0.0776739	−	0.134535i	0.824572	−	0.565757i	$-0.191416\pi$
$677$	−1368.23	−	2369.84i	−0.0776739	−	0.134535i	−0.902246	+	0.431222i	$0.858083\pi$
$678$		0			0
$679$	14745.4	−	5447.15i	0.833399	−	0.307868i
$680$		0			0
$681$	−1250.69	−	10981.2i	−0.0703770	−	0.617913i
$682$		0			0
$683$	−7977.54	−	4605.84i	−0.446928	−	0.258034i	0.259604	−	0.965715i	$-0.416408\pi$
$683$	−7977.54	−	4605.84i	−0.446928	−	0.258034i	−0.706532	+	0.707681i	$0.749741\pi$
$684$		0			0
$685$			4005.39i			0.223413i
$686$		0			0
$687$	−2689.86	+	6185.57i	−0.149381	+	0.343514i
$688$		0			0
$689$	−8296.95	+	14370.7i	−0.458764	+	0.794603i
$690$		0			0
$691$	−2228.30	+	1286.51i	−0.122675	+	0.0708264i	−0.560082	−	0.828437i	$-0.689230\pi$
$691$	−2228.30	+	1286.51i	−0.122675	+	0.0708264i	0.437407	+	0.899264i	$0.355897\pi$
$692$		0			0
$693$	27776.1	+	13988.0i	1.52255	+	0.766755i
$694$		0			0
$695$	21666.2	−	12509.0i	1.18251	−	0.682725i
$696$		0			0
$697$	2803.49	−	4855.79i	0.152353	−	0.263882i
$698$		0			0
$699$	−8712.29	+	20034.7i	−0.471430	+	1.08409i
$700$		0			0
$701$		−	18596.9i		−	1.00199i	−0.865450	−	0.500996i	$-0.832967\pi$
$701$		−	18596.9i		−	1.00199i	0.865450	−	0.500996i	$-0.167033\pi$
$702$		0			0
$703$	−18517.3	−	10691.0i	−0.993446	−	0.573566i
$704$		0			0
$705$	1165.68	+	10234.8i	0.0622726	+	0.546756i
$706$		0			0
$707$	18715.8	+	3207.61i	0.995590	+	0.170629i
$708$		0			0
$709$	12000.1	+	20784.8i	0.635647	+	1.10097i	0.986378	+	0.164496i	$0.0525998\pi$
$709$	12000.1	+	20784.8i	0.635647	+	1.10097i	−0.350731	+	0.936476i	$0.614067\pi$
$710$		0			0
$711$	32058.7	−	7398.59i	1.69099	−	0.390252i
$712$		0			0
$713$	8192.92			0.430333
$714$		0			0
$715$	32843.9			1.71789
$716$		0			0
$717$	−11796.2	−	15943.0i	−0.614416	−	0.830406i
$718$		0			0
$719$	8305.93	+	14386.3i	0.430819	+	0.746200i	0.996944	−	0.0781192i	$-0.0248915\pi$
$719$	8305.93	+	14386.3i	0.430819	+	0.746200i	−0.566125	+	0.824319i	$0.691558\pi$
$720$		0			0
$721$	−4577.54	−	3803.74i	−0.236445	−	0.196475i
$722$		0			0
$723$	−8451.37	+	962.565i	−0.434730	+	0.0495134i
$724$		0			0
$725$	−2470.25	−	1426.20i	−0.126542	−	0.0730589i
$726$		0			0
$727$		−	31798.3i		−	1.62219i	−0.584912	−	0.811097i	$-0.698871\pi$
$727$		−	31798.3i		−	1.62219i	0.584912	−	0.811097i	$-0.301129\pi$
$728$		0			0
$729$	−15299.6	+	12383.2i	−0.777299	+	0.629132i
$730$		0			0
$731$	−4693.65	+	8129.64i	−0.237484	+	0.411334i
$732$		0			0
$733$	29412.4	−	16981.3i	1.48209	−	0.855686i	0.482298	−	0.876007i	$-0.339802\pi$
$733$	29412.4	−	16981.3i	1.48209	−	0.855686i	0.999794	+	0.0203212i	$0.00646890\pi$
$734$		0			0
$735$	14583.0	−	4471.66i	0.731838	−	0.224408i
$736$		0			0
$737$	6973.40	−	4026.10i	0.348533	−	0.201225i
$738$		0			0
$739$	−14447.3	+	25023.5i	−0.719153	+	1.24561i	0.242183	+	0.970231i	$0.422137\pi$
$739$	−14447.3	+	25023.5i	−0.719153	+	1.24561i	−0.961336	+	0.275379i	$0.911197\pi$
$740$		0			0
$741$	19903.3	+	8655.16i	0.986729	+	0.429089i
$742$		0			0
$743$		−	8565.28i		−	0.422920i	−0.977387	−	0.211460i	$-0.932178\pi$
$743$		−	8565.28i		−	0.422920i	0.977387	−	0.211460i	$-0.0678218\pi$
$744$		0			0
$745$	13438.5	+	7758.72i	0.660870	+	0.381553i
$746$		0			0
$747$	10827.0	−	35403.2i	0.530306	−	1.73405i
$748$		0			0
$749$	−1938.34	−	1610.68i	−0.0945601	−	0.0785754i
$750$		0			0
$751$	−7333.06	−	12701.2i	−0.356308	−	0.617144i	0.631033	−	0.775756i	$-0.282631\pi$
$751$	−7333.06	−	12701.2i	−0.356308	−	0.617144i	−0.987341	+	0.158613i	$0.949298\pi$
$752$		0			0
$753$	22011.0	−	16285.9i	1.06524	−	0.788171i
$754$		0			0
$755$	14157.9			0.682464
$756$		0			0
$757$	−19962.2			−0.958439			−0.479220	−	0.877695i	$-0.659080\pi$
$757$	−19962.2			−0.958439			−0.479220	+	0.877695i	$0.659080\pi$
$758$		0			0
$759$	13747.5	−	10171.7i	0.657447	−	0.486444i
$760$		0			0
$761$	−19166.3	−	33197.0i	−0.912980	−	1.58133i	−0.809833	−	0.586661i	$-0.800442\pi$
$761$	−19166.3	−	33197.0i	−0.912980	−	1.58133i	−0.103147	−	0.994666i	$-0.532891\pi$
$762$		0			0
$763$	−25668.2	−	4399.13i	−1.21789	−	0.208728i
$764$		0			0
$765$	−1802.48	+	5893.94i	−0.0851880	+	0.278557i
$766$		0			0
$767$	−977.032	−	564.089i	−0.0459955	−	0.0265555i
$768$		0			0
$769$		−	1797.33i		−	0.0842826i	−0.999112	−	0.0421413i	$-0.986582\pi$
$769$		−	1797.33i		−	0.0842826i	0.999112	−	0.0421413i	$-0.0134180\pi$
$770$		0			0
$771$	−5437.89	−	2364.72i	−0.254009	−	0.110458i
$772$		0			0
$773$	5866.15	−	10160.5i	0.272951	−	0.472765i	−0.696665	−	0.717396i	$-0.745334\pi$
$773$	5866.15	−	10160.5i	0.272951	−	0.472765i	0.969616	+	0.244632i	$0.0786671\pi$
$774$		0			0
$775$	6939.52	−	4006.53i	0.321645	−	0.185702i
$776$		0			0
$777$	1711.43	−	30350.2i	0.0790182	−	1.40130i
$778$		0			0
$779$	12322.9	−	7114.61i	0.566768	−	0.327224i
$780$		0			0
$781$	−25018.4	+	43333.1i	−1.14626	+	1.98538i
$782$		0			0
$783$	−7288.76	+	2580.09i	−0.332668	+	0.117759i
$784$		0			0
$785$			11861.5i			0.539306i
$786$		0			0
$787$	−13313.4	−	7686.49i	−0.603013	−	0.348150i	0.167213	−	0.985921i	$-0.446523\pi$
$787$	−13313.4	−	7686.49i	−0.603013	−	0.348150i	−0.770226	+	0.637771i	$0.779857\pi$
$788$		0			0
$789$	11797.2	−	1343.64i	0.532309	−	0.0606272i
$790$		0			0
$791$	−8118.02	+	2998.90i	−0.364910	+	0.134802i
$792$		0			0
$793$	−2576.90	−	4463.32i	−0.115395	−	0.199871i
$794$		0			0
$795$	−7112.95	−	9613.42i	−0.317321	−	0.428871i
$796$		0			0
$797$	−33773.5			−1.50103			−0.750513	−	0.660856i	$-0.770193\pi$
$797$	−33773.5			−1.50103			−0.750513	+	0.660856i	$0.770193\pi$
$798$		0			0
$799$	−6178.50			−0.273567
$800$		0			0
$801$	−20354.3	+	4697.43i	−0.897859	+	0.207211i
$802$		0			0
$803$	13299.2	+	23034.9i	0.584457	+	1.01231i
$804$		0			0
$805$	1416.85	−	8267.06i	0.0620340	−	0.361957i
$806$		0			0
$807$	−1102.16	−	9677.01i	−0.0480766	−	0.422115i
$808$		0			0
$809$	30723.2	+	17738.1i	1.33519	+	0.770874i	0.986090	−	0.166210i	$-0.0531530\pi$
$809$	30723.2	+	17738.1i	1.33519	+	0.770874i	0.349103	+	0.937084i	$0.386486\pi$
$810$		0			0
$811$			31038.0i			1.34389i	0.740603	+	0.671943i	$0.234540\pi$
$811$			31038.0i			1.34389i	−0.740603	+	0.671943i	$0.765460\pi$
$812$		0			0
$813$	−6799.40	+	15635.8i	−0.293315	+	0.674505i
$814$		0			0
$815$	−4934.16	+	8546.22i	−0.212069	+	0.367314i
$816$		0			0
$817$	−20631.1	+	11911.4i	−0.883467	+	0.510070i
$818$		0			0
$819$	1760.19	+	30805.7i	0.0750987	+	1.31433i
$820$		0			0
$821$	−4221.32	+	2437.18i	−0.179446	+	0.103603i	−0.587032	−	0.809563i	$-0.699704\pi$
$821$	−4221.32	+	2437.18i	−0.179446	+	0.103603i	0.407586	+	0.913167i	$0.366371\pi$
$822$		0			0
$823$	−11051.1	+	19141.0i	−0.468064	+	0.810710i	−0.999334	−	0.0364924i	$-0.988382\pi$
$823$	−11051.1	+	19141.0i	−0.468064	+	0.810710i	0.531270	+	0.847202i	$0.321715\pi$
$824$		0			0
$825$	6670.09	−	15338.5i	0.281482	−	0.647293i
$826$		0			0
$827$			18204.1i			0.765439i	0.923865	+	0.382719i	$0.125012\pi$
$827$			18204.1i			0.765439i	−0.923865	+	0.382719i	$0.874988\pi$
$828$		0			0
$829$	−27346.1	−	15788.3i	−1.14568	−	0.661458i	−0.197848	−	0.980233i	$-0.563395\pi$
$829$	−27346.1	−	15788.3i	−1.14568	−	0.661458i	−0.947830	+	0.318775i	$0.896729\pi$
$830$		0			0
$831$	−312.087	−	2740.14i	−0.0130279	−	0.114385i
$832$		0			0
$833$	1675.05	+	8994.21i	0.0696724	+	0.374107i
$834$		0			0
$835$	−1299.45	−	2250.71i	−0.0538554	−	0.0932803i
$836$		0			0
$837$	3960.91	−	21356.7i	0.163571	−	0.881953i
$838$		0			0
$839$	−19529.4			−0.803612			−0.401806	−	0.915725i	$-0.631617\pi$
$839$	−19529.4			−0.803612			−0.401806	+	0.915725i	$0.631617\pi$
$840$		0			0
$841$	21351.7			0.875465
$842$		0			0
$843$	−16122.6	−	21790.3i	−0.658709	−	0.890270i
$844$		0			0
$845$	6892.13	+	11937.5i	0.280587	+	0.485992i
$846$		0			0
$847$	−30028.8	+	36137.6i	−1.21818	+	1.46600i
$848$		0			0
$849$	5412.01	−	616.399i	0.218775	−	0.0249172i
$850$		0			0
$851$	−14476.3	−	8357.92i	−0.583129	−	0.336670i
$852$		0			0
$853$		−	20178.9i		−	0.809979i	−0.914321	−	0.404989i	$-0.867275\pi$
$853$		−	20178.9i		−	0.809979i	0.914321	−	0.404989i	$-0.132725\pi$
$854$		0			0
$855$	−11440.2	+	10666.4i	−0.457597	+	0.426647i
$856$		0			0
$857$	7058.30	−	12225.3i	0.281338	−	0.487292i	−0.690376	−	0.723450i	$-0.742555\pi$
$857$	7058.30	−	12225.3i	0.281338	−	0.487292i	0.971715	+	0.236158i	$0.0758884\pi$
$858$		0			0
$859$	16476.7	−	9512.82i	0.654456	−	0.377850i	−0.135706	−	0.990749i	$-0.543330\pi$
$859$	16476.7	−	9512.82i	0.654456	−	0.377850i	0.790161	+	0.612899i	$0.209997\pi$
$860$		0			0
$861$	16922.0	+	11085.0i	0.669803	+	0.438766i
$862$		0			0
$863$	−9357.24	+	5402.41i	−0.369090	+	0.213094i	−0.673061	−	0.739587i	$-0.735021\pi$
$863$	−9357.24	+	5402.41i	−0.369090	+	0.213094i	0.303971	+	0.952681i	$0.401687\pi$
$864$		0			0
$865$	−11202.5	+	19403.3i	−0.440342	+	0.762694i
$866$		0			0
$867$	20020.8	+	8706.25i	0.784247	+	0.341038i
$868$		0			0
$869$			75786.5i			2.95844i
$870$		0			0
$871$	6918.79	+	3994.57i	0.269155	+	0.155397i
$872$		0			0
$873$	−21914.8	−	6701.98i	−0.849605	−	0.259825i
$874$		0			0
$875$	−9708.24	−	26280.2i	−0.375084	−	1.01535i
$876$		0			0
$877$	−1795.88	−	3110.55i	−0.0691476	−	0.119767i	0.829379	−	0.558687i	$-0.188695\pi$
$877$	−1795.88	−	3110.55i	−0.0691476	−	0.119767i	−0.898526	+	0.438920i	$0.855361\pi$
$878$		0			0
$879$	26768.7	−	19806.1i	1.02717	−	0.760004i
$880$		0			0
$881$	−47633.6			−1.82158			−0.910792	−	0.412865i	$-0.864528\pi$
$881$	−47633.6			−1.82158			−0.910792	+	0.412865i	$0.864528\pi$
$882$		0			0
$883$	42383.1			1.61530			0.807648	−	0.589665i	$-0.200740\pi$
$883$	42383.1			1.61530			0.807648	+	0.589665i	$0.200740\pi$
$884$		0			0
$885$	653.593	−	483.592i	0.0248252	−	0.0183681i
$886$		0			0
$887$	−8634.30	−	14955.0i	−0.326845	−	0.566112i	0.655039	−	0.755595i	$-0.272652\pi$
$887$	−8634.30	−	14955.0i	−0.326845	−	0.566112i	−0.981884	+	0.189483i	$0.939319\pi$
$888$		0			0
$889$	−1663.25	−	4502.43i	−0.0627488	−	0.169861i
$890$		0			0
$891$	−19868.6	−	40753.5i	−0.747053	−	1.53232i
$892$		0			0
$893$	−13578.9	−	7839.81i	−0.508849	−	0.293784i
$894$		0			0
$895$			23675.4i			0.884225i
$896$		0			0
$897$	15559.9	+	6766.39i	0.579186	+	0.251865i
$898$		0			0
$899$	4266.23	−	7389.33i	0.158272	−	0.274136i
$900$		0			0
$901$	6211.89	−	3586.44i	0.229687	−	0.132610i
$902$		0			0
$903$	−28331.1	−	18558.8i	−1.04408	−	0.683939i
$904$		0			0
$905$	3999.38	−	2309.04i	0.146899	−	0.0848124i
$906$		0			0
$907$	2270.97	−	3933.44i	0.0831383	−	0.144000i	−0.821458	−	0.570269i	$-0.806839\pi$
$907$	2270.97	−	3933.44i	0.0831383	−	0.144000i	0.904596	+	0.426269i	$0.140172\pi$
$908$		0			0
$909$	−18878.1	−	20247.6i	−0.688831	−	0.738800i
$910$		0			0
$911$		−	11585.4i		−	0.421342i	−0.977557	−	0.210671i	$-0.932435\pi$
$911$		−	11585.4i		−	0.421342i	0.977557	−	0.210671i	$-0.0675648\pi$
$912$		0			0
$913$	73852.7	+	42638.9i	2.67707	+	1.54561i
$914$		0			0
$915$	3690.34	−	420.310i	0.133332	−	0.0151858i
$916$		0			0
$917$	31341.0	−	37716.7i	1.12865	−	1.35825i
$918$		0			0
$919$	−2666.17	−	4617.93i	−0.0957004	−	0.165758i	0.814200	−	0.580584i	$-0.197176\pi$
$919$	−2666.17	−	4617.93i	−0.0957004	−	0.165758i	−0.909901	+	0.414826i	$0.863842\pi$
$920$		0			0
$921$	−11490.7	−	15530.1i	−0.411109	−	0.555629i
$922$		0			0
$923$	−49644.9			−1.77040
$924$		0			0
$925$	−16348.9			−0.581134
$926$		0			0
$927$	1951.15	+	8454.49i	0.0691308	+	0.299549i
$928$		0			0
$929$	−4965.04	−	8599.69i	−0.175347	−	0.303710i	0.764934	−	0.644108i	$-0.222771\pi$
$929$	−4965.04	−	8599.69i	−0.175347	−	0.303710i	−0.940281	+	0.340398i	$0.889438\pi$
$930$		0			0
$931$	−7731.23	+	21892.7i	−0.272160	+	0.770680i
$932$		0			0
$933$	238.516	+	2094.18i	0.00836942	+	0.0734839i
$934$		0			0
$935$	−12295.0	−	7098.54i	−0.430044	−	0.248286i
$936$		0			0
$937$			28533.5i			0.994821i	0.867515	+	0.497411i	$0.165716\pi$
$937$			28533.5i			0.994821i	−0.867515	+	0.497411i	$0.834284\pi$
$938$		0			0
$939$	−6316.79	+	14526.0i	−0.219532	+	0.504834i
$940$		0			0
$941$	2850.92	−	4937.95i	0.0987646	−	0.171065i	−0.812409	−	0.583088i	$-0.801844\pi$
$941$	2850.92	−	4937.95i	0.0987646	−	0.171065i	0.911174	+	0.412023i	$0.135178\pi$
$942$		0			0
$943$	9633.71	−	5562.03i	0.332680	−	0.192073i
$944$		0			0
$945$	−20865.0	−	7690.09i	−0.718241	−	0.264718i
$946$		0			0
$947$	14842.2	−	8569.15i	0.509299	−	0.294044i	−0.223246	−	0.974762i	$-0.571665\pi$
$947$	14842.2	−	8569.15i	0.509299	−	0.294044i	0.732546	+	0.680718i	$0.238332\pi$
$948$		0			0
$949$	−13195.0	+	22854.5i	−0.451348	+	0.781758i
$950$		0			0
$951$	−13673.2	+	31442.7i	−0.466228	+	1.07213i
$952$		0			0
$953$		−	48616.8i		−	1.65252i	−0.563287	−	0.826261i	$-0.690464\pi$
$953$		−	48616.8i		−	1.65252i	0.563287	−	0.826261i	$-0.309536\pi$
$954$		0			0
$955$	23660.3	+	13660.3i	0.801706	+	0.462865i
$956$		0			0
$957$	−2015.45	−	17695.7i	−0.0680776	−	0.597724i
$958$		0			0
$959$	1464.18	−	8543.21i	0.0493021	−	0.287669i
$960$		0			0
$961$	−2910.62	−	5041.35i	−0.0977015	−	0.169224i
$962$		0			0
$963$	826.208	+	3580.02i	0.0276471	+	0.119797i
$964$		0			0
$965$	12301.3			0.410356
$966$		0			0
$967$	14811.1			0.492547			0.246273	−	0.969200i	$-0.420794\pi$
$967$	14811.1			0.492547			0.246273	+	0.969200i	$0.420794\pi$
$968$		0			0
$969$	−5580.12	−	7541.73i	−0.184994	−	0.250026i
$970$		0			0
$971$	1364.94	+	2364.14i	0.0451111	+	0.0781348i	0.887699	−	0.460424i	$-0.152302\pi$
$971$	1364.94	+	2364.14i	0.0451111	+	0.0781348i	−0.842588	+	0.538558i	$0.818969\pi$
$972$		0			0
$973$	−50785.3	+	18760.7i	−1.67328	+	0.618131i
$974$		0			0
$975$	16488.4	−	1877.94i	0.541591	−	0.0616843i
$976$		0			0
$977$	49381.0	+	28510.2i	1.61703	+	0.933593i	0.987683	+	0.156470i	$0.0500114\pi$
$977$	49381.0	+	28510.2i	1.61703	+	0.933593i	0.629348	+	0.777123i	$0.283322\pi$
$978$		0			0
$979$		−	48117.6i		−	1.57083i
$980$		0			0
$981$	25890.7	+	27768.9i	0.842636	+	0.903763i
$982$		0			0
$983$	−26554.1	+	45993.0i	−0.861591	+	1.49232i	0.00880172	+	0.999961i	$0.497198\pi$
$983$	−26554.1	+	45993.0i	−0.861591	+	1.49232i	−0.870393	+	0.492358i	$0.836135\pi$
$984$		0			0
$985$	−17389.6	+	10039.9i	−0.562517	+	0.324770i
$986$		0			0
$987$	1255.01	−	22256.1i	0.0404736	−	0.717752i
$988$		0			0
$989$	−16128.9	+	9312.03i	−0.518574	+	0.299399i
$990$		0			0
$991$	−9561.35	+	16560.7i	−0.306485	+	0.530847i	−0.977591	−	0.210514i	$-0.932486\pi$
$991$	−9561.35	+	16560.7i	−0.306485	+	0.530847i	0.671106	+	0.741361i	$0.265820\pi$
$992$		0			0
$993$	−1753.82	−	762.665i	−0.0560480	−	0.0243731i
$994$		0			0
$995$		−	15674.7i		−	0.499417i
$996$		0			0
$997$	18152.4	+	10480.3i	0.576623	+	0.332914i	0.759790	−	0.650168i	$-0.225302\pi$
$997$	18152.4	+	10480.3i	0.576623	+	0.332914i	−0.183167	+	0.983082i	$0.558635\pi$
$998$		0			0
$999$	−28785.5	+	33695.2i	−0.911644	+	1.06714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.e.17.7		16
3.2	odd	2	inner	336.4.bc.e.17.4		16
4.3	odd	2		42.4.f.a.17.1	yes	16
7.5	odd	6	inner	336.4.bc.e.257.4		16
12.11	even	2		42.4.f.a.17.7	yes	16
21.5	even	6	inner	336.4.bc.e.257.7		16
28.3	even	6		294.4.d.a.293.1		16
28.11	odd	6		294.4.d.a.293.8		16
28.19	even	6		42.4.f.a.5.7	yes	16
28.23	odd	6		294.4.f.a.215.6		16
28.27	even	2		294.4.f.a.227.4		16
84.11	even	6		294.4.d.a.293.9		16
84.23	even	6		294.4.f.a.215.4		16
84.47	odd	6		42.4.f.a.5.1	✓	16
84.59	odd	6		294.4.d.a.293.16		16
84.83	odd	2		294.4.f.a.227.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.1	✓	16	84.47	odd	6
42.4.f.a.5.7	yes	16	28.19	even	6
42.4.f.a.17.1	yes	16	4.3	odd	2
42.4.f.a.17.7	yes	16	12.11	even	2
294.4.d.a.293.1		16	28.3	even	6
294.4.d.a.293.8		16	28.11	odd	6
294.4.d.a.293.9		16	84.11	even	6
294.4.d.a.293.16		16	84.59	odd	6
294.4.f.a.215.4		16	84.23	even	6
294.4.f.a.215.6		16	28.23	odd	6
294.4.f.a.227.4		16	28.27	even	2
294.4.f.a.227.6		16	84.83	odd	2
336.4.bc.e.17.4		16	3.2	odd	2	inner
336.4.bc.e.17.7		16	1.1	even	1	trivial
336.4.bc.e.257.4		16	7.5	odd	6	inner
336.4.bc.e.257.7		16	21.5	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4.17709 - 3.09062i) q^{3} +(-4.27911 - 7.41164i) q^{5} +(6.41772 + 17.3728i) q^{7} +(7.89612 - 25.8196i) q^{9} +(53.8609 + 31.0966i) q^{11} +61.7061i q^{13} +(-40.7808 - 17.7340i) q^{15} +(13.3365 - 23.0995i) q^{17} +(58.6213 - 33.8450i) q^{19} +(80.5000 + 52.7328i) q^{21} +(45.8287 - 26.4592i) q^{23} +(25.8784 - 44.8227i) q^{25} +(-46.8158 - 132.255i) q^{27} -55.1116i q^{29} +(134.080 + 77.4108i) q^{31} +(321.089 - 36.5704i) q^{33} +(101.299 - 121.906i) q^{35} +(-157.940 - 273.560i) q^{37} +(190.710 + 257.752i) q^{39} +210.211 q^{41} -351.939 q^{43} +(-225.154 + 51.9617i) q^{45} +(-115.819 - 200.605i) q^{47} +(-260.626 + 222.987i) q^{49} +(-15.6841 - 137.707i) q^{51} +(232.890 + 134.459i) q^{53} -532.263i q^{55} +(140.264 - 322.550i) q^{57} +(-9.14155 + 15.8336i) q^{59} +(-72.3320 + 41.7609i) q^{61} +(499.233 - 28.5253i) q^{63} +(457.344 - 264.047i) q^{65} +(64.7354 - 112.125i) q^{67} +(109.655 - 252.162i) q^{69} +804.537i q^{71} +(370.377 + 213.837i) q^{73} +(-30.4336 - 267.208i) q^{75} +(-194.570 + 1135.28i) q^{77} +(609.284 + 1055.31i) q^{79} +(-604.302 - 407.749i) q^{81} +1371.18 q^{83} -228.274 q^{85} +(-170.329 - 230.206i) q^{87} +(-386.840 - 670.026i) q^{89} +(-1072.01 + 396.012i) q^{91} +(799.309 - 91.0371i) q^{93} +(-501.694 - 289.653i) q^{95} -848.768i q^{97} +(1228.19 - 1145.12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 80 q^{7} + 18 q^{9} + 342 q^{19} - 450 q^{21} - 194 q^{25} - 804 q^{31} + 1332 q^{33} - 962 q^{37} - 594 q^{39} - 1732 q^{43} - 2394 q^{45} + 820 q^{49} - 1638 q^{51} - 2664 q^{57} - 4620 q^{61}+ \cdots + 4284 q^{99}+O(q^{100}) \) 16 * q - 80 * q^7 + 18 * q^9 + 342 * q^19 - 450 * q^21 - 194 * q^25 - 804 * q^31 + 1332 * q^33 - 962 * q^37 - 594 * q^39 - 1732 * q^43 - 2394 * q^45 + 820 * q^49 - 1638 * q^51 - 2664 * q^57 - 4620 * q^61 + 2016 * q^63 + 706 * q^67 + 3294 * q^73 - 6174 * q^75 + 2656 * q^79 + 126 * q^81 + 5232 * q^85 - 1026 * q^87 - 4098 * q^91 + 2016 * q^93 + 4284 * q^99

Introduction

L-functions

Modular forms

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Database

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