LMFDB - Embedded newform 459.3.i.a.305.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,3,Mod(152,459)] 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("459.152"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	459.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$12.5068441341$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			305.34
Character	$\chi$	$=$	459.305
Dual form			459.3.i.a.152.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.33588 + 1.92597i) q^{2} +(5.41875 + 9.38555i) q^{4} +(0.961073 + 1.66463i) q^{5} +(1.81586 + 1.04839i) q^{7} +26.3377i q^{8} +7.40400i q^{10} +(8.01476 - 13.8820i) q^{11} +(4.87777 + 8.44855i) q^{13} +(4.03833 + 6.99459i) q^{14} +(-29.0507 + 50.3174i) q^{16} +(-16.9068 - 1.77731i) q^{17} -4.56535 q^{19} +(-10.4156 + 18.0404i) q^{20} +(53.4727 - 30.8725i) q^{22} +(-10.8843 - 18.8521i) q^{23} +(10.6527 - 18.4510i) q^{25} +37.5778i q^{26} +22.7238i q^{28} +(-13.6294 + 23.6069i) q^{29} +(7.06013 - 4.07617i) q^{31} +(-102.583 + 59.2265i) q^{32} +(-52.9762 - 38.4910i) q^{34} +4.03030i q^{35} +59.8592i q^{37} +(-15.2295 - 8.79274i) q^{38} +(-43.8424 + 25.3125i) q^{40} +(-18.6406 - 32.2864i) q^{41} +(31.9800 - 55.3909i) q^{43} +173.720 q^{44} -83.8512i q^{46} +(49.9214 + 28.8221i) q^{47} +(-22.3018 - 38.6278i) q^{49} +(71.0722 - 41.0336i) q^{50} +(-52.8629 + 91.5612i) q^{52} -63.4712i q^{53} +30.8111 q^{55} +(-27.6121 + 47.8255i) q^{56} +(-90.9324 + 52.4999i) q^{58} +(-9.56077 + 5.51991i) q^{59} +(71.3234 + 41.1786i) q^{61} +31.4024 q^{62} -223.869 q^{64} +(-9.37578 + 16.2393i) q^{65} +(-15.9045 - 27.5475i) q^{67} +(-74.9330 - 168.311i) q^{68} +(-7.76225 + 13.4446i) q^{70} +108.385 q^{71} -9.85440i q^{73} +(-115.287 + 199.684i) q^{74} +(-24.7385 - 42.8483i) q^{76} +(29.1073 - 16.8051i) q^{77} +(-81.2952 - 46.9358i) q^{79} -111.679 q^{80} -143.605i q^{82} +(10.6690 + 6.15978i) q^{83} +(-13.2901 - 29.8517i) q^{85} +(213.363 - 123.185i) q^{86} +(365.620 + 211.091i) q^{88} +105.069i q^{89} +20.4551i q^{91} +(117.958 - 204.310i) q^{92} +(111.021 + 192.295i) q^{94} +(-4.38763 - 7.59960i) q^{95} +(-106.994 - 61.7732i) q^{97} -171.811i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	3.33588	+	1.92597i	1.66794	+	0.962987i	0.968745	+	0.248058i	$0.0797924\pi$
$2$	3.33588	+	1.92597i	1.66794	+	0.962987i	0.699197	+	0.714929i	$0.253541\pi$
$3$		0			0
$3$		0			0
$4$	5.41875	+	9.38555i	1.35469	+	2.34639i
$5$	0.961073	+	1.66463i	0.192215	+	0.332925i	0.945984	−	0.324214i	$-0.105100\pi$
$5$	0.961073	+	1.66463i	0.192215	+	0.332925i	−0.753769	+	0.657139i	$0.771766\pi$
$6$		0			0
$7$	1.81586	+	1.04839i	0.259408	+	0.149769i	0.624065	−	0.781373i	$-0.285480\pi$
$7$	1.81586	+	1.04839i	0.259408	+	0.149769i	−0.364656	+	0.931142i	$0.618814\pi$
$8$			26.3377i			3.29221i
$9$		0			0
$10$			7.40400i			0.740400i
$11$	8.01476	−	13.8820i	0.728615	−	1.26200i	−0.228854	−	0.973461i	$-0.573498\pi$
$11$	8.01476	−	13.8820i	0.728615	−	1.26200i	0.957469	−	0.288537i	$-0.0931689\pi$
$12$		0			0
$13$	4.87777	+	8.44855i	0.375213	+	0.649888i	0.990359	−	0.138525i	$-0.0442362\pi$
$13$	4.87777	+	8.44855i	0.375213	+	0.649888i	−0.615146	+	0.788413i	$0.710903\pi$
$14$	4.03833	+	6.99459i	0.288452	+	0.499613i
$15$		0			0
$16$	−29.0507	+	50.3174i	−1.81567	+	3.14483i
$17$	−16.9068	−	1.77731i	−0.994520	−	0.104547i
$17$	−16.9068	−	1.77731i	−0.994520	−	0.104547i
$18$		0			0
$19$	−4.56535			−0.240282			−0.120141	−	0.992757i	$-0.538335\pi$
$19$	−4.56535			−0.240282			−0.120141	+	0.992757i	$0.538335\pi$
$20$	−10.4156	+	18.0404i	−0.520781	+	0.902020i
$21$		0			0
$22$	53.4727	−	30.8725i	2.43058	−	1.40329i
$23$	−10.8843	−	18.8521i	−0.473229	−	0.819656i	0.526302	−	0.850298i	$-0.323578\pi$
$23$	−10.8843	−	18.8521i	−0.473229	−	0.819656i	−0.999530	+	0.0306416i	$0.990245\pi$
$24$		0			0
$25$	10.6527	−	18.4510i	0.426107	−	0.738039i
$26$			37.5778i			1.44530i
$27$		0			0
$28$			22.7238i			0.811563i
$29$	−13.6294	+	23.6069i	−0.469980	+	0.814030i	−0.999411	−	0.0343235i	$-0.989072\pi$
$29$	−13.6294	+	23.6069i	−0.469980	+	0.814030i	0.529430	+	0.848353i	$0.322406\pi$
$30$		0			0
$31$	7.06013	−	4.07617i	0.227746	−	0.131489i	−0.381786	−	0.924251i	$-0.624691\pi$
$31$	7.06013	−	4.07617i	0.227746	−	0.131489i	0.609532	+	0.792762i	$0.291357\pi$
$32$	−102.583	+	59.2265i	−3.20573	+	1.85083i
$33$		0			0
$34$	−52.9762	−	38.4910i	−1.55812	−	1.13209i
$35$			4.03030i			0.115151i
$36$		0			0
$37$			59.8592i			1.61782i	0.587934	+	0.808909i	$0.299941\pi$
$37$			59.8592i			1.61782i	−0.587934	+	0.808909i	$0.700059\pi$
$38$	−15.2295	−	8.79274i	−0.400776	−	0.231388i
$39$		0			0
$40$	−43.8424	+	25.3125i	−1.09606	+	0.632811i
$41$	−18.6406	−	32.2864i	−0.454648	−	0.787473i	0.544020	−	0.839072i	$-0.316901\pi$
$41$	−18.6406	−	32.2864i	−0.454648	−	0.787473i	−0.998668	+	0.0515992i	$0.983568\pi$
$42$		0			0
$43$	31.9800	−	55.3909i	0.743720	−	1.28816i	−0.207070	−	0.978326i	$-0.566393\pi$
$43$	31.9800	−	55.3909i	0.743720	−	1.28816i	0.950790	−	0.309835i	$-0.100274\pi$
$44$	173.720			3.94818
$45$		0			0
$46$		−	83.8512i		−	1.82285i
$47$	49.9214	+	28.8221i	1.06216	+	0.613237i	0.926028	−	0.377455i	$-0.123201\pi$
$47$	49.9214	+	28.8221i	1.06216	+	0.613237i	0.136129	+	0.990691i	$0.456534\pi$
$48$		0			0
$49$	−22.3018	−	38.6278i	−0.455138	−	0.788323i
$50$	71.0722	−	41.0336i	1.42144	−	0.820671i
$51$		0			0
$52$	−52.8629	+	91.5612i	−1.01659	+	1.76079i
$53$		−	63.4712i		−	1.19757i	−0.800910	−	0.598785i	$-0.795650\pi$
$53$		−	63.4712i		−	1.19757i	0.800910	−	0.598785i	$-0.204350\pi$
$54$		0			0
$55$	30.8111			0.560201
$56$	−27.6121	+	47.8255i	−0.493073	+	0.854027i
$57$		0			0
$58$	−90.9324	+	52.4999i	−1.56780	+	0.905170i
$59$	−9.56077	+	5.51991i	−0.162047	+	0.0935579i	−0.578830	−	0.815448i	$-0.696491\pi$
$59$	−9.56077	+	5.51991i	−0.162047	+	0.0935579i	0.416783	+	0.909006i	$0.363157\pi$
$60$		0			0
$61$	71.3234	+	41.1786i	1.16924	+	0.675059i	0.953500	−	0.301392i	$-0.0974514\pi$
$61$	71.3234	+	41.1786i	1.16924	+	0.675059i	0.215737	+	0.976452i	$0.430785\pi$
$62$	31.4024			0.506490
$63$		0			0
$64$	−223.869			−3.49795
$65$	−9.37578	+	16.2393i	−0.144243	+	0.249836i
$66$		0			0
$67$	−15.9045	−	27.5475i	−0.237381	−	0.411157i	0.722581	−	0.691287i	$-0.242956\pi$
$67$	−15.9045	−	27.5475i	−0.237381	−	0.411157i	−0.959962	+	0.280130i	$0.909622\pi$
$68$	−74.9330	−	168.311i	−1.10196	−	2.47516i
$69$		0			0
$70$	−7.76225	+	13.4446i	−0.110889	+	0.192066i
$71$	108.385			1.52655			0.763275	−	0.646074i	$-0.223590\pi$
$71$	108.385			1.52655			0.763275	+	0.646074i	$0.223590\pi$
$72$		0			0
$73$		−	9.85440i		−	0.134992i	−0.997720	−	0.0674959i	$-0.978499\pi$
$73$		−	9.85440i		−	0.134992i	0.997720	−	0.0674959i	$-0.0215009\pi$
$74$	−115.287	+	199.684i	−1.55794	+	2.69843i
$75$		0			0
$76$	−24.7385	−	42.8483i	−0.325506	−	0.563794i
$77$	29.1073	−	16.8051i	0.378017	−	0.218248i
$78$		0			0
$79$	−81.2952	−	46.9358i	−1.02905	−	0.594124i	−0.112340	−	0.993670i	$-0.535835\pi$
$79$	−81.2952	−	46.9358i	−1.02905	−	0.594124i	−0.916713	+	0.399546i	$0.869168\pi$
$80$	−111.679			−1.39599
$81$		0			0
$82$		−	143.605i		−	1.75128i
$83$	10.6690	+	6.15978i	0.128543	+	0.0742142i	0.562893	−	0.826530i	$-0.309688\pi$
$83$	10.6690	+	6.15978i	0.128543	+	0.0742142i	−0.434350	+	0.900744i	$0.643022\pi$
$84$		0			0
$85$	−13.2901	−	29.8517i	−0.156355	−	0.351196i
$86$	213.363	−	123.185i	2.48097	−	1.43239i
$87$		0			0
$88$	365.620	+	211.091i	4.15477	+	2.39876i
$89$			105.069i			1.18056i	0.807200	+	0.590278i	$0.200982\pi$
$89$			105.069i			1.18056i	−0.807200	+	0.590278i	$0.799018\pi$
$90$		0			0
$91$			20.4551i			0.224782i
$92$	117.958	−	204.310i	1.28215	−	2.22076i
$93$		0			0
$94$	111.021	+	192.295i	1.18108	+	2.04569i
$95$	−4.38763	−	7.59960i	−0.0461856	−	0.0799958i
$96$		0			0
$97$	−106.994	−	61.7732i	−1.10303	−	0.636837i	−0.166018	−	0.986123i	$-0.553091\pi$
$97$	−106.994	−	61.7732i	−1.10303	−	0.636837i	−0.937016	+	0.349286i	$0.886424\pi$
$98$		−	171.811i		−	1.75317i
$99$		0			0
$100$	230.897			2.30897
$101$	118.803	+	68.5907i	1.17626	+	0.679116i	0.955147	−	0.296132i	$-0.0956967\pi$
$101$	118.803	+	68.5907i	1.17626	+	0.679116i	0.221116	+	0.975248i	$0.429030\pi$
$102$		0			0
$103$	−12.5477	−	21.7332i	−0.121822	−	0.211002i	0.798664	−	0.601777i	$-0.205540\pi$
$103$	−12.5477	−	21.7332i	−0.121822	−	0.211002i	−0.920486	+	0.390775i	$0.872207\pi$
$104$	−222.515	+	128.469i	−2.13957	+	1.23528i
$105$		0			0
$106$	122.244	−	211.733i	1.15324	−	1.99748i
$107$	−66.3062			−0.619684			−0.309842	−	0.950788i	$-0.600276\pi$
$107$	−66.3062			−0.619684			−0.309842	+	0.950788i	$0.600276\pi$
$108$		0			0
$109$		−	80.7042i		−	0.740405i	−0.928951	−	0.370203i	$-0.879288\pi$
$109$		−	80.7042i		−	0.740405i	0.928951	−	0.370203i	$-0.120712\pi$
$110$	102.782	+	59.3413i	0.934384	+	0.539467i
$111$		0			0
$112$	−105.504	+	60.9127i	−0.942000	+	0.543864i
$113$	3.56143	+	6.16858i	0.0315171	+	0.0545892i	0.881354	−	0.472457i	$-0.156633\pi$
$113$	3.56143	+	6.16858i	0.0315171	+	0.0545892i	−0.849837	+	0.527046i	$0.823299\pi$
$114$		0			0
$115$	20.9211	−	36.2365i	0.181923	−	0.315100i
$116$	−295.418			−2.54671
$117$		0			0
$118$	−42.5248			−0.360380
$119$	−28.8371	−	20.9522i	−0.242329	−	0.176069i
$120$		0			0
$121$	−67.9729	−	117.733i	−0.561760	−	0.972996i
$122$	158.618	+	274.734i	1.30015	+	2.25192i
$123$		0			0
$124$	76.5142	+	44.1755i	0.617050	+	0.356254i
$125$	89.0056			0.712045
$126$		0			0
$127$	−98.0581			−0.772111			−0.386055	−	0.922476i	$-0.626163\pi$
$127$	−98.0581			−0.772111			−0.386055	+	0.922476i	$0.626163\pi$
$128$	−336.468	−	194.260i	−2.62866	−	1.51765i
$129$		0			0
$130$	−62.5531	+	36.1150i	−0.481178	+	0.277808i
$131$	−40.8758	−	70.7990i	−0.312029	−	0.540451i	0.666772	−	0.745262i	$-0.267675\pi$
$131$	−40.8758	−	70.7990i	−0.312029	−	0.540451i	−0.978802	+	0.204811i	$0.934342\pi$
$132$		0			0
$133$	−8.29002	−	4.78625i	−0.0623310	−	0.0359868i
$134$		−	122.527i		−	0.914381i
$135$		0			0
$136$	46.8102	−	445.287i	0.344193	−	3.27417i
$137$	−196.073	−	113.203i	−1.43119	−	0.826298i	−0.433978	−	0.900924i	$-0.642890\pi$
$137$	−196.073	−	113.203i	−1.43119	−	0.826298i	−0.997212	+	0.0746261i	$0.976224\pi$
$138$		0			0
$139$	7.63297	−	4.40690i	0.0549134	−	0.0317043i	−0.472292	−	0.881442i	$-0.656573\pi$
$139$	7.63297	−	4.40690i	0.0549134	−	0.0317043i	0.527205	+	0.849738i	$0.323240\pi$
$140$	−37.8266	+	21.8392i	−0.270190	+	0.155994i
$141$		0			0
$142$	361.560	+	208.747i	2.54620	+	1.47005i
$143$	156.377			1.09354
$144$		0			0
$145$	−52.3955			−0.361348
$146$	18.9793	−	32.8731i	0.129995	−	0.225158i
$147$		0			0
$148$	−561.812	+	324.362i	−3.79603	+	2.19164i
$149$	−75.3329	+	43.4935i	−0.505590	+	0.291903i	−0.731019	−	0.682357i	$-0.760955\pi$
$149$	−75.3329	+	43.4935i	−0.505590	+	0.291903i	0.225429	+	0.974260i	$0.427622\pi$
$150$		0			0
$151$	31.4150	−	54.4124i	0.208047	−	0.360347i	−0.743053	−	0.669233i	$-0.766623\pi$
$151$	31.4150	−	54.4124i	0.208047	−	0.360347i	0.951099	+	0.308886i	$0.0999561\pi$
$152$		−	120.241i		−	0.791058i
$153$		0			0
$154$	129.465			0.840681
$155$	13.5706	+	7.83499i	0.0875523	+	0.0505483i
$156$		0			0
$157$	74.2135	+	128.541i	0.472697	+	0.818736i	0.999512	−	0.0312447i	$-0.00994711\pi$
$157$	74.2135	+	128.541i	0.472697	+	0.818736i	−0.526815	+	0.849980i	$0.676614\pi$
$158$	−180.794	−	313.145i	−1.14427	−	1.98193i
$159$		0			0
$160$	−197.180	−	113.842i	−1.23238	−	0.711512i
$161$		−	45.6436i		−	0.283501i
$162$		0			0
$163$			127.596i			0.782796i	0.920221	+	0.391398i	$0.128008\pi$
$163$			127.596i			0.782796i	−0.920221	+	0.391398i	$0.871992\pi$
$164$	202.017	−	349.904i	1.23181	−	2.13356i
$165$		0			0
$166$	23.7271	+	41.0966i	0.142935	+	0.247570i
$167$	18.9481	+	32.8191i	0.113462	+	0.196522i	0.917164	−	0.398510i	$-0.130473\pi$
$167$	18.9481	+	32.8191i	0.113462	+	0.196522i	−0.803702	+	0.595032i	$0.797139\pi$
$168$		0			0
$169$	36.9147	−	63.9381i	0.218430	−	0.378332i
$170$	13.1592	−	125.178i	0.0774070	−	0.736343i
$171$		0			0
$172$	693.166			4.03004
$173$	−129.833	+	224.877i	−0.750478	+	1.29987i	0.197113	+	0.980381i	$0.436843\pi$
$173$	−129.833	+	224.877i	−0.750478	+	1.29987i	−0.947591	+	0.319485i	$0.896490\pi$
$174$		0			0
$175$	38.6875	−	22.3362i	0.221071	−	0.127636i
$176$	465.670	+	806.563i	2.64585	+	4.58275i
$177$		0			0
$178$	−202.361	+	350.500i	−1.13686	+	1.96910i
$179$			245.745i			1.37288i	0.727188	+	0.686439i	$0.240827\pi$
$179$			245.745i			1.37288i	−0.727188	+	0.686439i	$0.759173\pi$
$180$		0			0
$181$		−	77.0628i		−	0.425761i	−0.977078	−	0.212881i	$-0.931715\pi$
$181$		−	77.0628i		−	0.425761i	0.977078	−	0.212881i	$-0.0682845\pi$
$182$	−39.3961	+	68.2360i	−0.216462	+	0.374923i
$183$		0			0
$184$	496.521	−	286.667i	2.69848	−	1.55797i
$185$	−99.6433	+	57.5291i	−0.538612	+	0.310968i
$186$		0			0
$187$	−160.177	+	220.456i	−0.856561	+	1.17891i
$188$			624.720i			3.32298i
$189$		0			0
$190$		−	33.8019i		−	0.177905i
$191$	30.8485	+	17.8104i	0.161511	+	0.0932482i	0.578577	−	0.815628i	$-0.303608\pi$
$191$	30.8485	+	17.8104i	0.161511	+	0.0932482i	−0.417066	+	0.908876i	$0.636942\pi$
$192$		0			0
$193$	155.857	−	89.9842i	0.807550	−	0.466239i	−0.0385544	−	0.999257i	$-0.512275\pi$
$193$	155.857	−	89.9842i	0.807550	−	0.466239i	0.846104	+	0.533017i	$0.178942\pi$
$194$	−237.947	−	412.137i	−1.22653	−	2.12442i
$195$		0			0
$196$	241.696	−	418.629i	1.23314	−	2.13586i
$197$	−248.804			−1.26297			−0.631483	−	0.775390i	$-0.717553\pi$
$197$	−248.804			−1.26297			−0.631483	+	0.775390i	$0.717553\pi$
$198$		0			0
$199$			197.747i			0.993705i	0.867835	+	0.496852i	$0.165511\pi$
$199$			197.747i			0.993705i	−0.867835	+	0.496852i	$0.834489\pi$
$200$	485.957	+	280.567i	2.42978	+	1.40284i
$201$		0			0
$202$	264.208	+	457.621i	1.30796	+	2.26545i
$203$	−49.4982	+	28.5778i	−0.243833	+	0.140777i
$204$		0			0
$205$	35.8299	−	62.0591i	0.174780	−	0.302727i
$206$		−	96.6661i		−	0.469253i
$207$		0			0
$208$	−566.811			−2.72505
$209$	−36.5902	+	63.3761i	−0.175073	+	0.303235i
$210$		0			0
$211$	79.4854	−	45.8909i	0.376708	−	0.217492i	−0.299677	−	0.954041i	$-0.596879\pi$
$211$	79.4854	−	45.8909i	0.376708	−	0.217492i	0.676385	+	0.736548i	$0.263546\pi$
$212$	595.712	−	343.935i	2.80996	−	1.62233i
$213$		0			0
$214$	−221.190	−	127.704i	−1.03360	−	0.596748i
$215$	122.940			0.571815
$216$		0			0
$217$	17.0936			0.0787723
$218$	155.434	−	269.220i	0.713001	−	1.23495i
$219$		0			0
$220$	166.958	+	289.179i	0.758898	+	1.31445i
$221$	−67.4520	−	151.508i	−0.305213	−	0.685554i
$222$		0			0
$223$	−120.868	+	209.350i	−0.542011	+	0.938790i	0.456778	+	0.889581i	$0.349003\pi$
$223$	−120.868	+	209.350i	−0.542011	+	0.938790i	−0.998789	+	0.0492090i	$0.984330\pi$
$224$	−248.369			−1.10879
$225$		0			0
$226$			27.4369i			0.121402i
$227$	−134.892	+	233.640i	−0.594238	+	1.02925i	0.399416	+	0.916770i	$0.369213\pi$
$227$	−134.892	+	233.640i	−0.594238	+	1.02925i	−0.993654	+	0.112480i	$0.964121\pi$
$228$		0			0
$229$	−177.933	−	308.190i	−0.777002	−	1.34581i	−0.933662	−	0.358154i	$-0.883406\pi$
$229$	−177.933	−	308.190i	−0.777002	−	1.34581i	0.156661	−	0.987653i	$-0.449927\pi$
$230$	139.581	−	80.5871i	0.606874	−	0.350379i
$231$		0			0
$232$	−621.751	−	358.968i	−2.67996	−	1.54728i
$233$	219.973			0.944089			0.472044	−	0.881575i	$-0.343516\pi$
$233$	219.973			0.944089			0.472044	+	0.881575i	$0.343516\pi$
$234$		0			0
$235$			110.801i			0.471492i
$236$	−103.615	−	59.8221i	−0.439046	−	0.253483i
$237$		0			0
$238$	−55.8438	−	125.434i	−0.234638	−	0.527032i
$239$	−138.734	+	80.0979i	−0.580475	+	0.335138i	−0.761322	−	0.648374i	$-0.775449\pi$
$239$	−138.734	+	80.0979i	−0.580475	+	0.335138i	0.180847	+	0.983511i	$0.442116\pi$
$240$		0			0
$241$	−9.30503	−	5.37226i	−0.0386101	−	0.0222915i	0.480571	−	0.876956i	$-0.340430\pi$
$241$	−9.30503	−	5.37226i	−0.0386101	−	0.0222915i	−0.519181	+	0.854664i	$0.673763\pi$
$242$		−	523.656i		−	2.16387i
$243$		0			0
$244$			892.547i			3.65798i
$245$	42.8672	−	74.2483i	0.174968	−	0.303054i
$246$		0			0
$247$	−22.2687	−	38.5706i	−0.0901568	−	0.156156i
$248$	107.357	+	185.948i	0.432891	+	0.749789i
$249$		0			0
$250$	296.912	+	171.423i	1.18765	+	0.685690i
$251$		−	186.042i		−	0.741202i	−0.928792	−	0.370601i	$-0.879152\pi$
$251$		−	186.042i		−	0.741202i	0.928792	−	0.370601i	$-0.120848\pi$
$252$		0			0
$253$	−348.939			−1.37921
$254$	−327.110	−	188.857i	−1.28784	−	0.743533i
$255$		0			0
$256$	−300.541	−	520.552i	−1.17399	−	2.03341i
$257$	−95.1663	+	54.9443i	−0.370297	+	0.213791i	−0.673588	−	0.739107i	$-0.735248\pi$
$257$	−95.1663	+	54.9443i	−0.370297	+	0.213791i	0.303291	+	0.952898i	$0.401914\pi$
$258$		0			0
$259$	−62.7556	+	108.696i	−0.242299	+	0.419675i
$260$	−203.220			−0.781616
$261$		0			0
$262$		−	314.903i		−	1.20192i
$263$	−74.0287	−	42.7405i	−0.281478	−	0.162511i	0.352614	−	0.935769i	$-0.385293\pi$
$263$	−74.0287	−	42.7405i	−0.281478	−	0.162511i	−0.634092	+	0.773257i	$0.718626\pi$
$264$		0			0
$265$	105.656	−	61.0004i	0.398701	−	0.230190i
$266$	−18.4364	−	31.9327i	−0.0693097	−	0.120048i
$267$		0			0
$268$	172.366	−	298.546i	0.643155	−	1.11398i
$269$	189.782			0.705509			0.352754	−	0.935716i	$-0.385245\pi$
$269$	189.782			0.705509			0.352754	+	0.935716i	$0.385245\pi$
$270$		0			0
$271$	−292.531			−1.07945			−0.539725	−	0.841842i	$-0.681472\pi$
$271$	−292.531			−1.07945			−0.539725	+	0.841842i	$0.681472\pi$
$272$	580.585	−	799.075i	2.13451	−	2.93778i
$273$		0			0
$274$	−436.051	−	755.263i	−1.59143	−	2.75643i
$275$	−170.757	−	295.761i	−0.620936	−	1.07549i
$276$		0			0
$277$	−113.202	−	65.3572i	−0.408672	−	0.235947i	0.281547	−	0.959547i	$-0.409152\pi$
$277$	−113.202	−	65.3572i	−0.408672	−	0.235947i	−0.690219	+	0.723601i	$0.742486\pi$
$278$	33.9503			0.122123
$279$		0			0
$280$	−106.149			−0.379103
$281$	−241.275	−	139.300i	−0.858629	−	0.495730i	0.00492381	−	0.999988i	$-0.498433\pi$
$281$	−241.275	−	139.300i	−0.858629	−	0.495730i	−0.863553	+	0.504258i	$0.831766\pi$
$282$		0			0
$283$	−378.741	+	218.666i	−1.33831	+	0.772672i	−0.986556	−	0.163421i	$-0.947747\pi$
$283$	−378.741	+	218.666i	−1.33831	+	0.772672i	−0.351752	+	0.936093i	$0.614414\pi$
$284$	587.311	+	1017.25i	2.06800	+	3.58188i
$285$		0			0
$286$	521.655	+	301.178i	1.82397	+	1.05307i
$287$		−	78.1700i		−	0.272369i
$288$		0			0
$289$	282.682	+	60.0973i	0.978140	+	0.207949i
$290$	−174.785	−	100.912i	−0.602708	−	0.347974i
$291$		0			0
$292$	92.4890	−	53.3985i	0.316743	−	0.182872i
$293$	−226.129	+	130.556i	−0.771771	+	0.445582i	−0.833506	−	0.552510i	$-0.813670\pi$
$293$	−226.129	+	130.556i	−0.771771	+	0.445582i	0.0617350	+	0.998093i	$0.480337\pi$
$294$		0			0
$295$	−18.3772	−	10.6101i	−0.0622956	−	0.0359664i
$296$	−1576.56			−5.32620
$297$		0			0
$298$	−335.069			−1.12439
$299$	106.182	−	183.912i	0.355123	−	0.615092i
$300$		0			0
$301$	116.142	−	67.0547i	0.385854	−	0.222773i
$302$	209.594	−	121.009i	0.694019	−	0.400692i
$303$		0			0
$304$	132.627	−	229.716i	0.436272	−	0.755646i
$305$			158.303i			0.519025i
$306$		0			0
$307$	235.917			0.768458			0.384229	−	0.923238i	$-0.374467\pi$
$307$	235.917			0.768458			0.384229	+	0.923238i	$0.374467\pi$
$308$	315.451	+	182.126i	1.02419	+	0.591317i
$309$		0			0
$310$	30.1800	+	52.2733i	0.0973548	+	0.168623i
$311$	192.749	+	333.851i	0.619772	+	1.07348i	0.989527	+	0.144347i	$0.0461081\pi$
$311$	192.749	+	333.851i	0.619772	+	1.07348i	−0.369756	+	0.929129i	$0.620559\pi$
$312$		0			0
$313$	−201.048	−	116.075i	−0.642325	−	0.370847i	0.143185	−	0.989696i	$-0.454266\pi$
$313$	−201.048	−	116.075i	−0.642325	−	0.370847i	−0.785510	+	0.618849i	$0.787599\pi$
$314$			571.733i			1.82081i
$315$		0			0
$316$		−	1017.33i		−	3.21941i
$317$	−197.964	+	342.883i	−0.624491	+	1.08165i	0.364148	+	0.931341i	$0.381360\pi$
$317$	−197.964	+	342.883i	−0.624491	+	1.08165i	−0.988639	+	0.150309i	$0.951973\pi$
$318$		0			0
$319$	218.473	+	378.407i	0.684869	+	1.18623i
$320$	−215.154	−	372.658i	−0.672357	−	1.16456i
$321$		0			0
$322$	87.9084	−	152.262i	0.273008	−	0.472863i
$323$	77.1856	+	8.11403i	0.238965	+	0.0251208i
$324$		0			0
$325$	207.845			0.639524
$326$	−245.746	+	425.645i	−0.753823	+	1.30566i
$327$		0			0
$328$	850.350	−	490.950i	2.59253	−	1.49680i
$329$	60.4334	+	104.674i	0.183688	+	0.318157i
$330$		0			0
$331$	−32.3946	+	56.1092i	−0.0978690	+	0.169514i	−0.910802	−	0.412843i	$-0.864536\pi$
$331$	−32.3946	+	56.1092i	−0.0978690	+	0.169514i	0.812933	+	0.582357i	$0.197869\pi$
$332$			133.513i			0.402148i
$333$		0			0
$334$			145.974i			0.437049i
$335$	30.5709	−	52.9503i	0.0912563	−	0.158061i
$336$		0			0
$337$	305.223	−	176.221i	0.905706	−	0.522910i	0.0266590	−	0.999645i	$-0.491513\pi$
$337$	305.223	−	176.221i	0.905706	−	0.522910i	0.879047	+	0.476735i	$0.158180\pi$
$338$	246.286	−	142.193i	0.728658	−	0.420691i
$339$		0			0
$340$	208.159	−	286.494i	0.612231	−	0.842630i
$341$		−	130.678i		−	0.383220i
$342$		0			0
$343$		−	196.265i		−	0.572202i
$344$	1458.87	+	842.279i	4.24090	+	2.44849i
$345$		0			0
$346$	−866.214	+	500.109i	−2.50351	+	1.44540i
$347$	−261.090	−	452.222i	−0.752422	−	1.30323i	−0.946646	−	0.322276i	$-0.895552\pi$
$347$	−261.090	−	452.222i	−0.752422	−	1.30323i	0.194224	−	0.980957i	$-0.437781\pi$
$348$		0			0
$349$	−117.864	+	204.146i	−0.337718	+	0.584945i	−0.984003	−	0.178151i	$-0.942988\pi$
$349$	−117.864	+	204.146i	−0.337718	+	0.584945i	0.646285	+	0.763096i	$0.276322\pi$
$350$	172.076			0.491646
$351$		0			0
$352$			1898.75i			5.39417i
$353$	−588.207	−	339.601i	−1.66631	−	0.962043i	−0.969602	−	0.244686i	$-0.921315\pi$
$353$	−588.207	−	339.601i	−1.66631	−	0.962043i	−0.696705	−	0.717357i	$-0.745351\pi$
$354$		0			0
$355$	104.166	+	180.421i	0.293425	+	0.508227i
$356$	−986.135	+	569.345i	−2.77004	+	1.59928i
$357$		0			0
$358$	−473.298	+	819.777i	−1.32206	+	2.28988i
$359$		−	147.407i		−	0.410604i	−0.978699	−	0.205302i	$-0.934182\pi$
$359$		−	147.407i		−	0.410604i	0.978699	−	0.205302i	$-0.0658177\pi$
$360$		0			0
$361$	−340.158			−0.942265
$362$	148.421	−	257.073i	0.410002	−	0.710145i
$363$		0			0
$364$	−191.983	+	110.841i	−0.527425	+	0.304509i
$365$	16.4039	−	9.47079i	0.0449422	−	0.0259474i
$366$		0			0
$367$	86.7223	+	50.0691i	0.236301	+	0.136428i	0.613475	−	0.789714i	$-0.289771\pi$
$367$	86.7223	+	50.0691i	0.236301	+	0.136428i	−0.377175	+	0.926142i	$0.623104\pi$
$368$	1264.78			3.43691
$369$		0			0
$370$	−443.198			−1.19783
$371$	66.5423	−	115.255i	0.179359	−	0.310659i
$372$		0			0
$373$	−192.174	−	332.856i	−0.515213	−	0.892375i	−0.999844	−	0.0176561i	$-0.994380\pi$
$373$	−192.174	−	332.856i	−0.515213	−	0.892375i	0.484631	−	0.874718i	$-0.338954\pi$
$374$	−958.923	+	426.918i	−2.56397	+	1.14149i
$375$		0			0
$376$	−759.109	+	1314.81i	−2.01891	+	3.49685i
$377$	−265.925			−0.705371
$378$		0			0
$379$		−	169.020i		−	0.445963i	−0.974823	−	0.222982i	$-0.928421\pi$
$379$		−	169.020i		−	0.445963i	0.974823	−	0.222982i	$-0.0715790\pi$
$380$	47.5510	−	82.3607i	0.125134	−	0.216739i
$381$		0			0
$382$	68.6048	+	118.827i	0.179594	+	0.311065i
$383$	108.614	−	62.7085i	0.283588	−	0.163730i	−0.351459	−	0.936203i	$-0.614314\pi$
$383$	108.614	−	62.7085i	0.283588	−	0.163730i	0.635047	+	0.772474i	$0.280981\pi$
$384$		0			0
$385$	55.9485	+	32.3019i	0.145321	+	0.0839010i
$386$	693.229			1.79593
$387$		0			0
$388$		−	1338.93i		−	3.45086i
$389$	−140.793	−	81.2868i	−0.361936	−	0.208964i	0.307994	−	0.951388i	$-0.400342\pi$
$389$	−140.793	−	81.2868i	−0.361936	−	0.208964i	−0.669929	+	0.742425i	$0.733676\pi$
$390$		0			0
$391$	150.513	+	338.074i	0.384943	+	0.864639i
$392$	1017.37	−	587.378i	2.59533	−	1.49841i
$393$		0			0
$394$	−829.982	−	479.190i	−2.10655	−	1.21622i
$395$		−	180.435i		−	0.456797i
$396$		0			0
$397$			377.627i			0.951202i	0.879661	+	0.475601i	$0.157769\pi$
$397$			377.627i			0.951202i	−0.879661	+	0.475601i	$0.842231\pi$
$398$	−380.856	+	659.662i	−0.956925	+	1.65744i
$399$		0			0
$400$	618.936	+	1072.03i	1.54734	+	2.68007i
$401$	110.447	+	191.299i	0.275428	+	0.477055i	0.970243	−	0.242133i	$-0.0778471\pi$
$401$	110.447	+	191.299i	0.275428	+	0.477055i	−0.694815	+	0.719189i	$0.744514\pi$
$402$		0			0
$403$	68.8754	+	39.7653i	0.170907	+	0.0986731i
$404$			1486.70i			3.67996i
$405$		0			0
$406$	−220.160			−0.542267
$407$	830.965	+	479.758i	2.04168	+	1.17877i
$408$		0			0
$409$	56.8884	+	98.5336i	0.139091	+	0.240914i	0.927153	−	0.374683i	$-0.122248\pi$
$409$	56.8884	+	98.5336i	0.139091	+	0.240914i	−0.788061	+	0.615597i	$0.788915\pi$
$410$	239.049	−	138.015i	0.583045	−	0.336621i
$411$		0			0
$412$	135.986	−	235.534i	0.330062	−	0.571684i
$413$	−23.1480			−0.0560484
$414$		0			0
$415$			23.6800i			0.0570602i
$416$	−1000.76	−	577.787i	−2.40566	−	1.38891i
$417$		0			0
$418$	−244.121	+	140.944i	−0.584022	+	0.337185i
$419$	16.3853	+	28.3801i	0.0391056	+	0.0677329i	0.884916	−	0.465751i	$-0.154216\pi$
$419$	16.3853	+	28.3801i	0.0391056	+	0.0677329i	−0.845810	+	0.533484i	$0.820882\pi$
$420$		0			0
$421$	−28.3823	+	49.1596i	−0.0674164	+	0.116769i	−0.897763	−	0.440478i	$-0.854809\pi$
$421$	−28.3823	+	49.1596i	−0.0674164	+	0.116769i	0.830347	+	0.557247i	$0.188142\pi$
$422$	353.539			0.837769
$423$		0			0
$424$	1671.69			3.94265
$425$	−212.896	+	293.015i	−0.500932	+	0.689446i
$426$		0			0
$427$	86.3421	+	149.549i	0.202206	+	0.350232i
$428$	−359.297	−	622.321i	−0.839479	−	1.45402i
$429$		0			0
$430$	410.115	+	236.780i	0.953755	+	0.550651i
$431$	556.302			1.29072			0.645362	−	0.763877i	$-0.276707\pi$
$431$	556.302			1.29072			0.645362	+	0.763877i	$0.276707\pi$
$432$		0			0
$433$	471.902			1.08984			0.544921	−	0.838487i	$-0.316560\pi$
$433$	471.902			1.08984			0.544921	+	0.838487i	$0.316560\pi$
$434$	57.0223	+	32.9218i	0.131388	+	0.0758567i
$435$		0			0
$436$	757.454	−	437.316i	1.73728	−	1.00302i
$437$	49.6905	+	86.0664i	0.113708	+	0.196948i
$438$		0			0
$439$	79.8932	+	46.1264i	0.181989	+	0.105071i	0.588227	−	0.808696i	$-0.299826\pi$
$439$	79.8932	+	46.1264i	0.181989	+	0.105071i	−0.406238	+	0.913767i	$0.633160\pi$
$440$			811.493i			1.84430i
$441$		0			0
$442$	66.7874	−	635.323i	0.151103	−	1.43738i
$443$	−100.591	−	58.0764i	−0.227069	−	0.131098i	0.382150	−	0.924100i	$-0.375184\pi$
$443$	−100.591	−	58.0764i	−0.227069	−	0.131098i	−0.609219	+	0.793002i	$0.708517\pi$
$444$		0			0
$445$	−174.901	+	100.979i	−0.393037	+	0.226920i
$446$	−806.406	+	465.579i	−1.80808	+	1.04390i
$447$		0			0
$448$	−406.514	−	234.701i	−0.907397	−	0.523886i
$449$	489.480			1.09016			0.545078	−	0.838385i	$-0.316500\pi$
$449$	489.480			1.09016			0.545078	+	0.838385i	$0.316500\pi$
$450$		0			0
$451$	−597.599			−1.32505
$452$	−38.5971	+	66.8521i	−0.0853917	+	0.147903i
$453$		0			0
$454$	−899.968	+	519.597i	−1.98231	+	1.14449i
$455$	−34.0502	+	19.6589i	−0.0748355	+	0.0432063i
$456$		0			0
$457$	192.068	−	332.672i	0.420280	−	0.727947i	−0.575686	−	0.817671i	$-0.695265\pi$
$457$	192.068	−	332.672i	0.420280	−	0.727947i	0.995967	+	0.0897236i	$0.0285984\pi$
$458$		−	1370.78i		−	2.99297i
$459$		0			0
$460$	453.466			0.985795
$461$	175.353	+	101.240i	0.380375	+	0.219610i	0.677981	−	0.735079i	$-0.262855\pi$
$461$	175.353	+	101.240i	0.380375	+	0.219610i	−0.297606	+	0.954689i	$0.596188\pi$
$462$		0			0
$463$	52.1867	+	90.3901i	0.112714	+	0.195227i	0.916864	−	0.399200i	$-0.130712\pi$
$463$	52.1867	+	90.3901i	0.112714	+	0.195227i	−0.804149	+	0.594427i	$0.797379\pi$
$464$	−791.890	−	1371.59i	−1.70666	−	2.95602i
$465$		0			0
$466$	733.804	+	423.662i	1.57469	+	0.909145i
$467$			791.486i			1.69483i	0.530930	+	0.847416i	$0.321843\pi$
$467$			791.486i			1.69483i	−0.530930	+	0.847416i	$0.678157\pi$
$468$		0			0
$469$		−	66.6964i		−	0.142210i
$470$	−213.399	+	369.618i	−0.454041	+	0.786421i
$471$		0			0
$472$	−145.382	−	251.809i	−0.308013	−	0.533493i
$473$	−512.624	−	887.891i	−1.08377	−	1.87715i
$474$		0			0
$475$	−48.6332	+	84.2352i	−0.102386	+	0.177337i
$476$	40.3871	−	384.187i	0.0848468	−	0.807116i
$477$		0			0
$478$	−617.066			−1.29093
$479$	−11.1736	+	19.3533i	−0.0233270	+	0.0404035i	−0.877453	−	0.479662i	$-0.840759\pi$
$479$	−11.1736	+	19.3533i	−0.0233270	+	0.0404035i	0.854126	+	0.520066i	$0.174093\pi$
$480$		0			0
$481$	−505.724	+	291.980i	−1.05140	+	0.607026i
$482$	−20.6937	−	35.8425i	−0.0429329	−	0.0743620i
$483$		0			0
$484$	736.657	−	1275.93i	1.52202	−	2.63621i
$485$		−	237.474i		−	0.489637i
$486$		0			0
$487$			186.736i			0.383441i	0.981450	+	0.191721i	$0.0614067\pi$
$487$			186.736i			0.383441i	−0.981450	+	0.191721i	$0.938593\pi$
$488$	−1084.55	+	1878.50i	−2.22244	+	3.84938i
$489$		0			0
$490$	286.000	−	165.122i	0.583674	−	0.336985i
$491$	403.887	−	233.184i	0.822581	−	0.474917i	−0.0287247	−	0.999587i	$-0.509145\pi$
$491$	403.887	−	233.184i	0.822581	−	0.474917i	0.851306	+	0.524670i	$0.175811\pi$
$492$		0			0
$493$	272.387	−	374.894i	0.552510	−	0.760434i
$494$		−	171.556i		−	0.347279i
$495$		0			0
$496$			473.663i			0.954966i
$497$	196.812	+	113.629i	0.395999	+	0.228630i
$498$		0			0
$499$	261.353	−	150.892i	0.523753	−	0.302389i	−0.214716	−	0.976677i	$-0.568883\pi$
$499$	261.353	−	150.892i	0.523753	−	0.302389i	0.738469	+	0.674288i	$0.235549\pi$
$500$	482.299	+	835.367i	0.964599	+	1.67073i
$501$		0			0
$502$	358.312	−	620.614i	0.713768	−	1.23628i
$503$	181.984			0.361798			0.180899	−	0.983502i	$-0.442099\pi$
$503$	181.984			0.361798			0.180899	+	0.983502i	$0.442099\pi$
$504$		0			0
$505$			263.683i			0.522144i
$506$	−1164.02	−	672.048i	−2.30044	−	1.32816i
$507$		0			0
$508$	−531.352	−	920.329i	−1.04597	−	1.81167i
$509$	100.063	−	57.7716i	0.196588	−	0.113500i	−0.398475	−	0.917179i	$-0.630460\pi$
$509$	100.063	−	57.7716i	0.196588	−	0.113500i	0.595063	+	0.803679i	$0.297127\pi$
$510$		0			0
$511$	10.3312	−	17.8942i	0.0202176	−	0.0350180i
$512$		−	761.256i		−	1.48683i
$513$		0			0
$514$	−423.285			−0.823512
$515$	24.1185	−	41.7744i	0.0468320	−	0.0811154i
$516$		0			0
$517$	800.216	−	462.005i	1.54781	−	0.893627i
$518$	−418.691	+	241.731i	−0.808283	+	0.466662i
$519$		0			0
$520$	−427.707	−	246.937i	−0.822513	−	0.474878i
$521$	−561.330			−1.07741			−0.538704	−	0.842495i	$-0.681086\pi$
$521$	−561.330			−1.07741			−0.538704	+	0.842495i	$0.681086\pi$
$522$		0			0
$523$	387.856			0.741599			0.370799	−	0.928713i	$-0.379084\pi$
$523$	387.856			0.741599			0.370799	+	0.928713i	$0.379084\pi$
$524$	442.992	−	767.285i	0.845405	−	1.46428i
$525$		0			0
$526$	−164.634	−	285.155i	−0.312993	−	0.542119i
$527$	−126.609	+	56.3671i	−0.240245	+	0.106958i
$528$		0			0
$529$	27.5656	−	47.7451i	0.0521089	−	0.0902553i
$530$	469.941			0.886681
$531$		0			0
$532$		−	103.742i		−	0.195004i
$533$	181.849	−	314.971i	0.341180	−	0.590940i
$534$		0			0
$535$	−63.7251	−	110.375i	−0.119112	−	0.206309i
$536$	725.538	−	418.889i	1.35362	−	0.781510i
$537$		0			0
$538$	633.090	+	365.515i	1.17675	+	0.679396i
$539$	−714.974			−1.32648
$540$		0			0
$541$			602.045i			1.11284i	0.830902	+	0.556419i	$0.187825\pi$
$541$			602.045i			1.11284i	−0.830902	+	0.556419i	$0.812175\pi$
$542$	−975.849	−	563.407i	−1.80046	−	1.03950i
$543$		0			0
$544$	1839.62	−	819.011i	3.38166	−	1.50553i
$545$	134.342	−	77.5626i	0.246500	−	0.142317i
$546$		0			0
$547$	34.8771	+	20.1363i	0.0637608	+	0.0368123i	0.531541	−	0.847032i	$-0.321613\pi$
$547$	34.8771	+	20.1363i	0.0637608	+	0.0368123i	−0.467781	+	0.883845i	$0.654946\pi$
$548$		−	2453.67i		−	4.47750i
$549$		0			0
$550$		−	1315.50i		−	2.39181i
$551$	62.2231	−	107.774i	0.112928	−	0.195596i
$552$		0			0
$553$	−98.4137	−	170.457i	−0.177963	−	0.308241i
$554$	−251.753	−	436.048i	−0.454427	−	0.787091i
$555$		0			0
$556$	82.7223	+	47.7598i	0.148781	+	0.0858988i
$557$		−	986.424i		−	1.77096i	−0.464680	−	0.885479i	$-0.653830\pi$
$557$		−	986.424i		−	1.77096i	0.464680	−	0.885479i	$-0.346170\pi$
$558$		0			0
$559$	623.964			1.11621
$560$	−202.794	−	117.083i	−0.362132	−	0.209077i
$561$		0			0
$562$	−536.577	−	929.378i	−0.954763	−	1.65370i
$563$	592.060	−	341.826i	1.05162	−	0.607151i	0.128514	−	0.991708i	$-0.458979\pi$
$563$	592.060	−	341.826i	1.05162	−	0.607151i	0.923101	+	0.384557i	$0.125646\pi$
$564$		0			0
$565$	−6.84559	+	11.8569i	−0.0121161	+	0.0209857i
$566$	−1684.58			−2.97629
$567$		0			0
$568$			2854.61i			5.02573i
$569$	479.317	+	276.734i	0.842385	+	0.486351i	0.858074	−	0.513526i	$-0.171661\pi$
$569$	479.317	+	276.734i	0.842385	+	0.486351i	−0.0156891	+	0.999877i	$0.504994\pi$
$570$		0			0
$571$	10.9653	−	6.33080i	0.0192036	−	0.0110872i	−0.490367	−	0.871516i	$-0.663137\pi$
$571$	10.9653	−	6.33080i	0.0192036	−	0.0110872i	0.509571	+	0.860429i	$0.329804\pi$
$572$	847.367	+	1467.68i	1.48141	+	2.56588i
$573$		0			0
$574$	150.553	−	260.766i	0.262288	−	0.454296i
$575$	−463.786			−0.806585
$576$		0			0
$577$	−363.680			−0.630294			−0.315147	−	0.949043i	$-0.602054\pi$
$577$	−363.680			−0.630294			−0.315147	+	0.949043i	$0.602054\pi$
$578$	827.250	+	744.916i	1.43123	+	1.28878i
$579$		0			0
$580$	−283.918	−	491.761i	−0.489514	−	0.847863i
$581$	12.9156	+	22.3705i	0.0222300	+	0.0385035i
$582$		0			0
$583$	−881.106	−	508.707i	−1.51133	−	0.872567i
$584$	259.542			0.444422
$585$		0			0
$586$	−1005.79			−1.71636
$587$	233.131	+	134.598i	0.397157	+	0.229299i	0.685257	−	0.728302i	$-0.259690\pi$
$587$	233.131	+	134.598i	0.397157	+	0.229299i	−0.288099	+	0.957601i	$0.593023\pi$
$588$		0			0
$589$	−32.2320	+	18.6091i	−0.0547232	+	0.0315945i
$590$	−40.8695	−	70.7880i	−0.0692703	−	0.119980i
$591$		0			0
$592$	−3011.96	−	1738.96i	−5.08777	−	2.93742i
$593$			531.551i			0.896376i	0.893939	+	0.448188i	$0.147931\pi$
$593$			531.551i			0.896376i	−0.893939	+	0.448188i	$0.852069\pi$
$594$		0			0
$595$	7.16308	−	68.1396i	0.0120388	−	0.114520i
$596$	−816.421	−	471.361i	−1.36983	−	0.790874i
$597$		0			0
$598$	708.421	−	409.007i	1.18465	−	0.683958i
$599$	203.598	−	117.548i	0.339897	−	0.196240i	−0.320330	−	0.947306i	$-0.603794\pi$
$599$	203.598	−	117.548i	0.339897	−	0.196240i	0.660226	+	0.751067i	$0.270460\pi$
$600$		0			0
$601$	−853.915	−	493.008i	−1.42082	−	0.820313i	−0.424454	−	0.905450i	$-0.639534\pi$
$601$	−853.915	−	493.008i	−1.42082	−	0.820313i	−0.996369	+	0.0851370i	$0.972867\pi$
$602$	516.582			0.858110
$603$		0			0
$604$	680.921			1.12735
$605$	130.654	−	226.299i	0.215957	−	0.374048i
$606$		0			0
$607$	181.598	−	104.846i	0.299173	−	0.172728i	−0.342898	−	0.939373i	$-0.611409\pi$
$607$	181.598	−	104.846i	0.299173	−	0.172728i	0.642072	+	0.766645i	$0.278075\pi$
$608$	468.329	−	270.390i	0.770277	−	0.444720i
$609$		0			0
$610$	−304.887	+	528.079i	−0.499814	+	0.865703i
$611$			562.351i			0.920378i
$612$		0			0
$613$	635.527			1.03675			0.518374	−	0.855154i	$-0.326538\pi$
$613$	635.527			1.03675			0.518374	+	0.855154i	$0.326538\pi$
$614$	786.990	+	454.369i	1.28174	+	0.740015i
$615$		0			0
$616$	442.609	+	766.620i	0.718520	+	1.24451i
$617$	93.9470	+	162.721i	0.152264	+	0.263729i	0.932059	−	0.362305i	$-0.118010\pi$
$617$	93.9470	+	162.721i	0.152264	+	0.263729i	−0.779795	+	0.626035i	$0.784677\pi$
$618$		0			0
$619$	737.742	+	425.936i	1.19183	+	0.688103i	0.958721	−	0.284348i	$-0.0917770\pi$
$619$	737.742	+	425.936i	1.19183	+	0.688103i	0.233108	+	0.972451i	$0.425110\pi$
$620$			169.823i			0.273909i
$621$		0			0
$622$			1484.92i			2.38733i
$623$	−110.153	+	190.791i	−0.176811	+	0.306246i
$624$		0			0
$625$	−180.776	−	313.113i	−0.289242	−	0.500981i
$626$	−447.115	−	774.426i	−0.714241	−	1.23710i
$627$		0			0
$628$	−804.289	+	1393.07i	−1.28071	+	2.21826i
$629$	106.388	−	1012.03i	0.169139	−	1.60895i
$630$		0			0
$631$	593.612			0.940748			0.470374	−	0.882467i	$-0.344119\pi$
$631$	593.612			0.940748			0.470374	+	0.882467i	$0.344119\pi$
$632$	1236.18	−	2141.13i	1.95598	−	3.38786i
$633$		0			0
$634$	−1320.77	+	762.546i	−2.08323	+	1.20275i
$635$	−94.2409	−	163.230i	−0.148411	−	0.257055i
$636$		0			0
$637$	217.566	−	376.835i	0.341548	−	0.591578i
$638$			1683.10i			2.63808i
$639$		0			0
$640$		−	746.791i		−	1.16686i
$641$	194.586	−	337.034i	0.303567	−	0.525793i	−0.673374	−	0.739302i	$-0.735156\pi$
$641$	194.586	−	337.034i	0.303567	−	0.525793i	0.976941	+	0.213508i	$0.0684891\pi$
$642$		0			0
$643$	676.406	−	390.523i	1.05195	−	0.607346i	0.128758	−	0.991676i	$-0.458901\pi$
$643$	676.406	−	390.523i	1.05195	−	0.607346i	0.923196	+	0.384330i	$0.125568\pi$
$644$	428.391	−	247.331i	0.665203	−	0.384055i
$645$		0			0
$646$	241.855	+	175.725i	0.374388	+	0.272020i
$647$			621.675i			0.960858i	0.877033	+	0.480429i	$0.159519\pi$
$647$			621.675i			0.960858i	−0.877033	+	0.480429i	$0.840481\pi$
$648$		0			0
$649$			176.963i			0.272671i
$650$	693.348	+	400.305i	1.06669	+	0.615853i
$651$		0			0
$652$	−1197.56	+	691.410i	−1.83674	+	1.06044i
$653$	354.528	+	614.060i	0.542921	+	0.940367i	0.998735	+	0.0502918i	$0.0160151\pi$
$653$	354.528	+	614.060i	0.542921	+	0.940367i	−0.455813	+	0.890075i	$0.650652\pi$
$654$		0			0
$655$	78.5693	−	136.086i	0.119953	−	0.207765i
$656$	2166.09			3.30196
$657$		0			0
$658$			465.572i			0.707557i
$659$	772.563	+	446.040i	1.17233	+	0.676843i	0.954227	−	0.299083i	$-0.0966809\pi$
$659$	772.563	+	446.040i	1.17233	+	0.676843i	0.218100	+	0.975926i	$0.430014\pi$
$660$		0			0
$661$	29.8378	+	51.6805i	0.0451403	+	0.0781853i	0.887713	−	0.460398i	$-0.152293\pi$
$661$	29.8378	+	51.6805i	0.0451403	+	0.0781853i	−0.842572	+	0.538583i	$0.818960\pi$
$662$	−216.130	+	124.782i	−0.326480	+	0.188493i
$663$		0			0
$664$	−162.234	+	280.998i	−0.244329	+	0.423190i
$665$		−	18.3997i		−	0.0276687i
$666$		0			0
$667$	593.385			0.889633
$668$	−205.351	+	355.678i	−0.307411	+	0.532451i
$669$		0			0
$670$	203.962	−	117.757i	0.304420	−	0.175757i
$671$	1143.28	−	660.074i	1.70385	−	0.983716i
$672$		0			0
$673$	421.512	+	243.360i	0.626317	+	0.361605i	0.779325	−	0.626621i	$-0.215562\pi$
$673$	421.512	+	243.360i	0.626317	+	0.361605i	−0.153007	+	0.988225i	$0.548896\pi$
$674$	1357.58			2.01422
$675$		0			0
$676$	800.126			1.18362
$677$	386.478	−	669.399i	0.570868	−	0.988773i	−0.425609	−	0.904907i	$-0.639940\pi$
$677$	386.478	−	669.399i	0.570868	−	0.988773i	0.996477	−	0.0838654i	$-0.0267266\pi$
$678$		0			0
$679$	−129.524	−	224.343i	−0.190757	−	0.330402i
$680$	786.225	−	350.032i	1.15621	−	0.514753i
$681$		0			0
$682$	251.683	−	435.927i	0.369036	−	0.639190i
$683$	267.933			0.392288			0.196144	−	0.980575i	$-0.437158\pi$
$683$	267.933			0.392288			0.196144	+	0.980575i	$0.437158\pi$
$684$		0			0
$685$		−	435.184i		−	0.635305i
$686$	378.002	−	654.718i	0.551023	−	0.954400i
$687$		0			0
$688$	1858.08	+	3218.29i	2.70070	+	4.67775i
$689$	536.239	−	309.598i	0.778286	−	0.449344i
$690$		0			0
$691$	302.043	+	174.385i	0.437110	+	0.252366i	0.702371	−	0.711811i	$-0.252125\pi$
$691$	302.043	+	174.385i	0.437110	+	0.252366i	−0.265261	+	0.964177i	$0.585458\pi$
$692$	−2814.12			−4.06665
$693$		0			0
$694$		−	2011.41i		−	2.89829i
$695$	14.6717	+	8.47069i	0.0211103	+	0.0121880i
$696$		0			0
$697$	257.770	+	578.991i	0.369828	+	0.830690i
$698$	−786.359	+	454.004i	−1.12659	+	0.650436i
$699$		0			0
$700$	419.276	+	242.069i	0.598965	+	0.345813i
$701$			26.4726i			0.0377641i	0.999822	+	0.0188821i	$0.00601070\pi$
$701$			26.4726i			0.0377641i	−0.999822	+	0.0188821i	$0.993989\pi$
$702$		0			0
$703$		−	273.278i		−	0.388732i
$704$	−1794.26	+	3107.74i	−2.54866	+	4.41441i
$705$		0			0
$706$	−1308.13	−	2265.74i	−1.85287	−	3.20927i
$707$	143.819	+	249.102i	0.203421	+	0.352336i
$708$		0			0
$709$	−487.401	−	281.401i	−0.687448	−	0.396899i	0.115207	−	0.993341i	$-0.463247\pi$
$709$	−487.401	−	281.401i	−0.687448	−	0.396899i	−0.802655	+	0.596443i	$0.796580\pi$
$710$			802.483i			1.13026i
$711$		0			0
$712$	−2767.29			−3.88664
$713$	−153.689	−	88.7322i	−0.215552	−	0.124449i
$714$		0			0
$715$	150.289	+	260.309i	0.210195	+	0.364068i
$716$	−2306.45	+	1331.63i	−3.22130	+	1.85982i
$717$		0			0
$718$	283.902	−	491.732i	0.395406	−	0.684864i
$719$	−298.002			−0.414467			−0.207234	−	0.978291i	$-0.566446\pi$
$719$	−298.002			−0.414467			−0.207234	+	0.978291i	$0.566446\pi$
$720$		0			0
$721$		−	52.6193i		−	0.0729809i
$722$	−1134.73	−	655.135i	−1.57164	−	0.907389i
$723$		0			0
$724$	723.277	−	417.584i	0.999001	−	0.576773i
$725$	290.380	+	502.953i	0.400524	+	0.693728i
$726$		0			0
$727$	−590.193	+	1022.24i	−0.811819	+	1.40611i	0.0997704	+	0.995010i	$0.468189\pi$
$727$	−590.193	+	1022.24i	−0.811819	+	1.40611i	−0.911590	+	0.411102i	$0.865144\pi$
$728$	−538.742			−0.740030
$729$		0			0
$730$	72.9620			0.0999479
$731$	−639.127	+	879.647i	−0.874319	+	1.20335i
$732$		0			0
$733$	−130.429	−	225.909i	−0.177938	−	0.308198i	0.763236	−	0.646120i	$-0.223609\pi$
$733$	−130.429	−	225.909i	−0.177938	−	0.308198i	−0.941174	+	0.337922i	$0.890276\pi$
$734$	192.864	+	334.050i	0.262757	+	0.455109i
$735$		0			0
$736$	2233.09	+	1289.27i	3.03409	+	1.75173i
$737$	−509.885			−0.691838
$738$		0			0
$739$	−761.457			−1.03039			−0.515194	−	0.857074i	$-0.672280\pi$
$739$	−761.457			−1.03039			−0.515194	+	0.857074i	$0.672280\pi$
$740$	−1079.88	−	623.472i	−1.45930	−	0.842529i
$741$		0			0
$742$	443.955	−	256.317i	0.598322	−	0.345441i
$743$	350.832	+	607.658i	0.472183	+	0.817844i	0.999493	−	0.0318282i	$-0.0101329\pi$
$743$	350.832	+	607.658i	0.472183	+	0.817844i	−0.527311	+	0.849673i	$0.676800\pi$
$744$		0			0
$745$	−144.801	−	83.6008i	−0.194363	−	0.112216i
$746$		−	1480.49i		−	1.98457i
$747$		0			0
$748$	−2937.06	−	308.754i	−3.92655	−	0.412773i
$749$	−120.403	−	69.5145i	−0.160751	−	0.0928097i
$750$		0			0
$751$	−1236.19	+	713.715i	−1.64606	+	0.950353i	−0.667442	+	0.744662i	$0.732611\pi$
$751$	−1236.19	+	713.715i	−1.64606	+	0.950353i	−0.978617	+	0.205691i	$0.934056\pi$
$752$	−2900.51	+	1674.61i	−3.85705	+	2.22687i
$753$		0			0
$754$	−887.095	−	512.165i	−1.17652	−	0.679263i
$755$	120.768			0.159958
$756$		0			0
$757$	668.338			0.882878			0.441439	−	0.897291i	$-0.354468\pi$
$757$	668.338			0.882878			0.441439	+	0.897291i	$0.354468\pi$
$758$	325.528	−	563.832i	0.429457	−	0.743841i
$759$		0			0
$760$	200.156	−	115.560i	0.263363	−	0.152053i
$761$	−177.215	+	102.315i	−0.232872	+	0.134449i	−0.611896	−	0.790938i	$-0.709593\pi$
$761$	−177.215	+	102.315i	−0.232872	+	0.134449i	0.379024	+	0.925387i	$0.376260\pi$
$762$		0			0
$763$	84.6091	−	146.547i	0.110890	−	0.192067i
$764$			386.041i			0.505289i
$765$		0			0
$766$	483.099			0.630678
$767$	−93.2705	−	53.8498i	−0.121604	−	0.0702083i
$768$		0			0
$769$	−312.900	−	541.959i	−0.406892	−	0.704758i	0.587647	−	0.809117i	$-0.300054\pi$
$769$	−312.900	−	541.959i	−0.406892	−	0.704758i	−0.994540	+	0.104359i	$0.966721\pi$
$770$	124.425	+	215.511i	0.161591	+	0.279884i
$771$		0			0
$772$	1689.10	+	975.204i	2.18796	+	1.26322i
$773$		−	925.923i		−	1.19783i	−0.800812	−	0.598915i	$-0.795599\pi$
$773$		−	925.923i		−	1.19783i	0.800812	−	0.598915i	$-0.204401\pi$
$774$		0			0
$775$		−	173.689i		−	0.224114i
$776$	1626.96	−	2817.99i	2.09660	−	3.63142i
$777$		0			0
$778$	−313.113	−	542.327i	−0.402458	−	0.697079i
$779$	85.1006	+	147.399i	0.109243	+	0.189215i
$780$		0			0
$781$	868.680	−	1504.60i	1.11227	−	1.92650i
$782$	−149.029	+	1417.66i	−0.190575	+	1.81286i
$783$		0			0
$784$	2591.53			3.30553
$785$	−142.649	+	247.075i	−0.181719	+	0.314746i
$786$		0			0
$787$	938.824	−	542.030i	1.19292	−	0.688730i	0.233949	−	0.972249i	$-0.424835\pi$
$787$	938.824	−	542.030i	1.19292	−	0.688730i	0.958967	+	0.283519i	$0.0915019\pi$
$788$	−1348.21	−	2335.16i	−1.71092	−	2.96341i
$789$		0			0
$790$	347.513	−	601.910i	0.439890	−	0.761911i
$791$			14.9350i			0.0188812i
$792$		0			0
$793$			803.439i			1.01316i
$794$	−727.300	+	1259.72i	−0.915995	+	1.58655i
$795$		0			0
$796$	−1855.97	+	1071.54i	−2.33162	+	1.34616i
$797$	−347.182	+	200.446i	−0.435611	+	0.251500i	−0.701734	−	0.712439i	$-0.747591\pi$
$797$	−347.182	+	200.446i	−0.435611	+	0.251500i	0.266123	+	0.963939i	$0.414257\pi$
$798$		0			0
$799$	−792.787	−	576.016i	−0.992224	−	0.720922i
$800$			2523.68i			3.15460i
$801$		0			0
$802$			850.870i			1.06093i
$803$	−136.799	−	78.9807i	−0.170359	−	0.0983570i
$804$		0			0
$805$	75.9796	−	43.8668i	0.0943846	−	0.0544930i
$806$	153.174	+	265.305i	0.190042	+	0.329162i
$807$		0			0
$808$	−1806.52	+	3128.99i	−2.23579	+	3.87251i
$809$	1350.56			1.66942			0.834712	−	0.550686i	$-0.185634\pi$
$809$	1350.56			1.66942			0.834712	+	0.550686i	$0.185634\pi$
$810$		0			0
$811$		−	1313.82i		−	1.62000i	−0.586429	−	0.810000i	$-0.699467\pi$
$811$		−	1313.82i		−	1.62000i	0.586429	−	0.810000i	$-0.300533\pi$
$812$	−536.437	−	309.712i	−0.660637	−	0.381419i
$813$		0			0
$814$	1848.00	+	3200.83i	2.27027	+	3.93223i
$815$	−212.399	+	122.629i	−0.260613	+	0.150465i
$816$		0			0
$817$	−146.000	+	252.879i	−0.178702	+	0.309521i
$818$			438.262i			0.535773i
$819$		0			0
$820$	776.612			0.947088
$821$	−117.459	+	203.444i	−0.143068	+	0.247800i	−0.928650	−	0.370956i	$-0.879030\pi$
$821$	−117.459	+	203.444i	−0.143068	+	0.247800i	0.785583	+	0.618757i	$0.212363\pi$
$822$		0			0
$823$	−436.903	+	252.246i	−0.530867	+	0.306496i	−0.741369	−	0.671097i	$-0.765823\pi$
$823$	−436.903	+	252.246i	−0.530867	+	0.306496i	0.210503	+	0.977593i	$0.432490\pi$
$824$	572.404	−	330.477i	0.694664	−	0.401065i
$825$		0			0
$826$	−77.2190	−	44.5824i	−0.0934855	−	0.0539739i
$827$	−1619.10			−1.95779			−0.978897	−	0.204354i	$-0.934491\pi$
$827$	−1619.10			−1.95779			−0.978897	+	0.204354i	$0.934491\pi$
$828$		0			0
$829$	949.863			1.14579			0.572897	−	0.819627i	$-0.305819\pi$
$829$	949.863			1.14579			0.572897	+	0.819627i	$0.305819\pi$
$830$	−45.6070	+	78.9936i	−0.0549482	+	0.0951731i
$831$		0			0
$832$	−1091.98	−	1891.37i	−1.31248	−	2.27328i
$833$	308.399	+	692.711i	0.370227	+	0.831586i
$834$		0			0
$835$	−36.4211	+	63.0831i	−0.0436180	+	0.0755487i
$836$	−793.093			−0.948676
$837$		0			0
$838$			126.230i			0.150633i
$839$	236.894	−	410.312i	0.282352	−	0.489049i	−0.689611	−	0.724180i	$-0.742219\pi$
$839$	236.894	−	410.312i	0.282352	−	0.489049i	0.971964	+	0.235131i	$0.0755519\pi$
$840$		0			0
$841$	48.9772	+	84.8310i	0.0582369	+	0.100869i
$842$	−189.360	+	109.327i	−0.224893	+	0.129842i
$843$		0			0
$844$	861.423	+	497.343i	1.02064	+	0.589269i
$845$	141.911			0.167942
$846$		0			0
$847$		−	285.047i		−	0.336537i
$848$	3193.70	+	1843.88i	3.76616	+	2.17439i
$849$		0			0
$850$	−1274.54	+	567.431i	−1.49945	+	0.667566i
$851$	1128.47	−	651.524i	1.32605	−	0.765598i
$852$		0			0
$853$	−1465.59	−	846.158i	−1.71816	−	0.991979i	−0.922282	−	0.386519i	$-0.873677\pi$
$853$	−1465.59	−	846.158i	−1.71816	−	0.991979i	−0.795876	−	0.605460i	$-0.792989\pi$
$854$			665.171i			0.778888i
$855$		0			0
$856$		−	1746.35i		−	2.04013i
$857$	723.424	−	1253.01i	0.844135	−	1.46208i	−0.0422354	−	0.999108i	$-0.513448\pi$
$857$	723.424	−	1253.01i	0.844135	−	1.46208i	0.886370	−	0.462977i	$-0.153219\pi$
$858$		0			0
$859$	770.329	+	1334.25i	0.896774	+	1.55326i	0.831593	+	0.555385i	$0.187429\pi$
$859$	770.329	+	1334.25i	0.896774	+	1.55326i	0.0651810	+	0.997873i	$0.479238\pi$
$860$	666.183	+	1153.86i	0.774631	+	1.34170i
$861$		0			0
$862$	1855.76	+	1071.42i	2.15285	+	1.24295i
$863$			544.316i			0.630725i	0.948971	+	0.315362i	$0.102126\pi$
$863$			544.316i			0.630725i	−0.948971	+	0.315362i	$0.897874\pi$
$864$		0			0
$865$	−499.115			−0.577011
$866$	1574.21	+	908.870i	1.81779	+	1.04950i
$867$		0			0
$868$	92.6259	+	160.433i	0.106712	+	0.184830i
$869$	−1303.12	+	752.359i	−1.49957	+	0.865776i
$870$		0			0
$871$	155.158	−	268.741i	0.178137	−	0.308543i
$872$	2125.56			2.43757
$873$		0			0
$874$			382.810i			0.437998i
$875$	161.621	+	93.3122i	0.184710	+	0.106643i
$876$		0			0
$877$	607.579	−	350.786i	0.692793	−	0.399984i	−0.111865	−	0.993723i	$-0.535682\pi$
$877$	607.579	−	350.786i	0.692793	−	0.399984i	0.804657	+	0.593739i	$0.202349\pi$
$878$	177.676	+	307.744i	0.202365	+	0.350506i
$879$		0			0
$880$	−895.085	+	1550.33i	−1.01714	+	1.76174i
$881$	4.84762			0.00550241			0.00275121	−	0.999996i	$-0.499124\pi$
$881$	4.84762			0.00550241			0.00275121	+	0.999996i	$0.499124\pi$
$882$		0			0
$883$	−123.439			−0.139795			−0.0698976	−	0.997554i	$-0.522267\pi$
$883$	−123.439			−0.139795			−0.0698976	+	0.997554i	$0.522267\pi$
$884$	1056.48	−	1454.06i	1.19511	−	1.64486i
$885$		0			0
$886$	−223.707	−	387.473i	−0.252491	−	0.437328i
$887$	217.673	+	377.021i	0.245403	+	0.425051i	0.962245	−	0.272185i	$-0.0877462\pi$
$887$	217.673	+	377.021i	0.245403	+	0.425051i	−0.716841	+	0.697236i	$0.754413\pi$
$888$		0			0
$889$	−178.059	−	102.803i	−0.200292	−	0.115639i
$890$	−777.935			−0.874084
$891$		0			0
$892$	−2619.82			−2.93702
$893$	−227.908	−	131.583i	−0.255217	−	0.147349i
$894$		0			0
$895$	−409.074	+	236.179i	−0.457066	+	0.263887i
$896$	−407.318	−	705.496i	−0.454596	−	0.787384i
$897$		0			0
$898$	1632.85	+	942.726i	1.81832	+	1.04981i
$899$			222.224i			0.247190i
$900$		0			0
$901$	−112.808	+	1073.10i	−0.125203	+	1.19101i
$902$	−1993.52	−	1150.96i	−2.21011	−	1.27601i
$903$		0			0
$904$	−162.466	+	93.8000i	−0.179719	+	0.103761i
$905$	128.281	−	74.0629i	0.141747	−	0.0818375i
$906$		0			0
$907$	788.571	+	455.282i	0.869428	+	0.501964i	0.867158	−	0.498033i	$-0.165944\pi$
$907$	788.571	+	455.282i	0.869428	+	0.501964i	0.00226956	+	0.999997i	$0.499278\pi$
$908$	−2923.78			−3.22003
$909$		0			0
$910$	−151.450			−0.166428
$911$	230.613	−	399.434i	0.253143	−	0.438456i	−0.711247	−	0.702943i	$-0.751869\pi$
$911$	230.613	−	399.434i	0.253143	−	0.438456i	0.964389	+	0.264486i	$0.0852024\pi$
$912$		0			0
$913$	171.020	−	98.7383i	0.187316	−	0.108147i
$914$	1281.43	−	739.837i	1.40201	−	0.809449i
$915$		0			0
$916$	1928.35	−	3340.01i	2.10519	−	3.64630i
$917$		−	171.415i		−	0.186930i
$918$		0			0
$919$	−888.394			−0.966696			−0.483348	−	0.875428i	$-0.660579\pi$
$919$	−888.394			−0.966696			−0.483348	+	0.875428i	$0.660579\pi$
$920$	954.386	+	551.015i	1.03738	+	0.598929i
$921$		0			0
$922$	389.971	+	675.450i	0.422962	+	0.732592i
$923$	528.677	+	915.696i	0.572781	+	0.992086i
$924$		0			0
$925$	1104.46	+	637.661i	1.19401	+	0.689364i
$926$			402.041i			0.434170i
$927$		0			0
$928$		−	3228.89i		−	3.47941i
$929$	146.755	−	254.186i	0.157971	−	0.273613i	−0.776166	−	0.630528i	$-0.782838\pi$
$929$	146.755	−	254.186i	0.157971	−	0.273613i	0.934137	+	0.356915i	$0.116172\pi$
$930$		0			0
$931$	101.815	+	176.349i	0.109361	+	0.189419i
$932$	1191.98	+	2064.57i	1.27895	+	2.21520i
$933$		0			0
$934$	−1524.38	+	2640.31i	−1.63210	+	2.82688i
$935$	−520.918	−	54.7607i	−0.557132	−	0.0585676i
$936$		0			0
$937$	−1540.93			−1.64453			−0.822266	−	0.569104i	$-0.807290\pi$
$937$	−1540.93			−1.64453			−0.822266	+	0.569104i	$0.807290\pi$
$938$	128.456	−	222.492i	0.136946	−	0.237198i
$939$		0			0
$940$	−1039.92	+	600.401i	−1.10630	+	0.638724i
$941$	−62.8561	−	108.870i	−0.0667971	−	0.115696i	0.830693	−	0.556731i	$-0.187945\pi$
$941$	−62.8561	−	108.870i	−0.0667971	−	0.115696i	−0.897490	+	0.441035i	$0.854611\pi$
$942$		0			0
$943$	−405.777	+	702.827i	−0.430305	+	0.745310i
$944$		−	641.430i		−	0.679481i
$945$		0			0
$946$		−	3949.20i		−	4.17463i
$947$	105.533	−	182.789i	0.111440	−	0.193019i	−0.804911	−	0.593395i	$-0.797787\pi$
$947$	105.533	−	182.789i	0.111440	−	0.193019i	0.916351	+	0.400376i	$0.131121\pi$
$948$		0			0
$949$	83.2553	−	48.0675i	0.0877295	−	0.0506507i
$950$	−324.469	+	187.333i	−0.341547	+	0.197192i
$951$		0			0
$952$	551.833	−	759.503i	0.579657	−	0.797797i
$953$			252.571i			0.265028i	0.991181	+	0.132514i	$0.0423049\pi$
$953$			252.571i			0.265028i	−0.991181	+	0.132514i	$0.957695\pi$
$954$		0			0
$955$			68.4684i			0.0716947i
$956$	−1503.53	−	868.061i	−1.57273	−	0.908014i
$957$		0			0
$958$	−74.5479	+	43.0402i	−0.0778162	+	0.0449272i
$959$	−237.360	−	411.120i	−0.247508	−	0.428697i
$960$		0			0
$961$	−447.270	+	774.694i	−0.465421	+	0.806133i
$962$	−2249.38			−2.33823
$963$		0			0
$964$		−	116.444i		−	0.120792i
$965$	299.580	+	172.963i	0.310446	+	0.179236i
$966$		0			0
$967$	−171.788	−	297.546i	−0.177651	−	0.307700i	0.763425	−	0.645897i	$-0.223516\pi$
$967$	−171.788	−	297.546i	−0.177651	−	0.307700i	−0.941075	+	0.338197i	$0.890183\pi$
$968$	3100.80	−	1790.25i	3.20331	−	1.84943i
$969$		0			0
$970$	457.369	−	792.186i	0.471514	−	0.816687i
$971$		−	1446.79i		−	1.49000i	−0.667063	−	0.745001i	$-0.732449\pi$
$971$		−	1446.79i		−	1.49000i	0.667063	−	0.745001i	$-0.267551\pi$
$972$		0			0
$973$	18.4805			0.0189933
$974$	−359.648	+	622.929i	−0.369249	+	0.639558i
$975$		0			0
$976$	−4144.00	+	2392.54i	−4.24590	+	2.45137i
$977$	−1014.73	+	585.856i	−1.03862	+	0.599648i	−0.919442	−	0.393225i	$-0.871359\pi$
$977$	−1014.73	+	585.856i	−1.03862	+	0.599648i	−0.119178	+	0.992873i	$0.538026\pi$
$978$		0			0
$979$	1458.57	+	842.107i	1.48986	+	0.860171i
$980$	929.148			0.948110
$981$		0			0
$982$	1796.43			1.82936
$983$	546.711	−	946.930i	0.556165	−	0.963307i	−0.441646	−	0.897189i	$-0.645605\pi$
$983$	546.711	−	946.930i	0.556165	−	0.963307i	0.997812	−	0.0661175i	$-0.0210612\pi$
$984$		0			0
$985$	−239.119	−	414.166i	−0.242760	−	0.420473i
$986$	1630.69	−	725.992i	1.65384	−	0.736300i
$987$		0			0
$988$	241.337	−	418.009i	0.244269	−	0.423086i
$989$	−1392.31			−1.40780
$990$		0			0
$991$			1036.20i			1.04561i	0.852451	+	0.522806i	$0.175115\pi$
$991$			1036.20i			1.04561i	−0.852451	+	0.522806i	$0.824885\pi$
$992$	−482.835	+	836.294i	−0.486729	+	0.843038i
$993$		0			0
$994$	437.694	+	758.108i	0.440336	+	0.762684i
$995$	−329.175	+	190.049i	−0.330829	+	0.191004i
$996$		0			0
$997$	−1505.65	−	869.289i	−1.51018	−	0.871905i	−0.999929	−	0.0118815i	$-0.996218\pi$
$997$	−1505.65	−	869.289i	−1.51018	−	0.871905i	−0.510254	−	0.860024i	$-0.670449\pi$
$998$	1162.46			1.16479
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.3.i.a.305.34		68
3.2	odd	2		153.3.i.a.101.2	yes	68
9.4	even	3		153.3.i.a.50.1	✓	68
9.5	odd	6	inner	459.3.i.a.152.33		68
17.16	even	2	inner	459.3.i.a.305.33		68
51.50	odd	2		153.3.i.a.101.1	yes	68
153.50	odd	6	inner	459.3.i.a.152.34		68
153.67	even	6		153.3.i.a.50.2	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.1	✓	68	9.4	even	3
153.3.i.a.50.2	yes	68	153.67	even	6
153.3.i.a.101.1	yes	68	51.50	odd	2
153.3.i.a.101.2	yes	68	3.2	odd	2
459.3.i.a.152.33		68	9.5	odd	6	inner
459.3.i.a.152.34		68	153.50	odd	6	inner
459.3.i.a.305.33		68	17.16	even	2	inner
459.3.i.a.305.34		68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	459.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.33588 + 1.92597i) q^{2} +(5.41875 + 9.38555i) q^{4} +(0.961073 + 1.66463i) q^{5} +(1.81586 + 1.04839i) q^{7} +26.3377i q^{8} +7.40400i q^{10} +(8.01476 - 13.8820i) q^{11} +(4.87777 + 8.44855i) q^{13} +(4.03833 + 6.99459i) q^{14} +(-29.0507 + 50.3174i) q^{16} +(-16.9068 - 1.77731i) q^{17} -4.56535 q^{19} +(-10.4156 + 18.0404i) q^{20} +(53.4727 - 30.8725i) q^{22} +(-10.8843 - 18.8521i) q^{23} +(10.6527 - 18.4510i) q^{25} +37.5778i q^{26} +22.7238i q^{28} +(-13.6294 + 23.6069i) q^{29} +(7.06013 - 4.07617i) q^{31} +(-102.583 + 59.2265i) q^{32} +(-52.9762 - 38.4910i) q^{34} +4.03030i q^{35} +59.8592i q^{37} +(-15.2295 - 8.79274i) q^{38} +(-43.8424 + 25.3125i) q^{40} +(-18.6406 - 32.2864i) q^{41} +(31.9800 - 55.3909i) q^{43} +173.720 q^{44} -83.8512i q^{46} +(49.9214 + 28.8221i) q^{47} +(-22.3018 - 38.6278i) q^{49} +(71.0722 - 41.0336i) q^{50} +(-52.8629 + 91.5612i) q^{52} -63.4712i q^{53} +30.8111 q^{55} +(-27.6121 + 47.8255i) q^{56} +(-90.9324 + 52.4999i) q^{58} +(-9.56077 + 5.51991i) q^{59} +(71.3234 + 41.1786i) q^{61} +31.4024 q^{62} -223.869 q^{64} +(-9.37578 + 16.2393i) q^{65} +(-15.9045 - 27.5475i) q^{67} +(-74.9330 - 168.311i) q^{68} +(-7.76225 + 13.4446i) q^{70} +108.385 q^{71} -9.85440i q^{73} +(-115.287 + 199.684i) q^{74} +(-24.7385 - 42.8483i) q^{76} +(29.1073 - 16.8051i) q^{77} +(-81.2952 - 46.9358i) q^{79} -111.679 q^{80} -143.605i q^{82} +(10.6690 + 6.15978i) q^{83} +(-13.2901 - 29.8517i) q^{85} +(213.363 - 123.185i) q^{86} +(365.620 + 211.091i) q^{88} +105.069i q^{89} +20.4551i q^{91} +(117.958 - 204.310i) q^{92} +(111.021 + 192.295i) q^{94} +(-4.38763 - 7.59960i) q^{95} +(-106.994 - 61.7732i) q^{97} -171.811i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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