LMFDB - Embedded newform 912.2.bo.d.529.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(289,912)] 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("912.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			529.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	912.529
Dual form			912.2.bo.d.481.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.613341 + 3.47843i) q^{5} +(1.85844 + 3.21891i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-2.64543 + 4.58202i) q^{11} +(0.213011 + 0.0775297i) q^{13} +(-0.613341 - 3.47843i) q^{15} +(-1.26604 - 1.06234i) q^{17} +(4.17752 + 1.24432i) q^{19} +(-2.84730 - 2.38917i) q^{21} +(-1.50727 - 8.54818i) q^{23} +(-7.02481 - 2.55682i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(0.0923963 - 0.0775297i) q^{29} +(1.56031 + 2.70253i) q^{31} +(0.918748 - 5.21048i) q^{33} +(-12.3366 + 4.49016i) q^{35} +5.12836 q^{37} -0.226682 q^{39} +(-6.67752 + 2.43042i) q^{41} +(0.929892 - 5.27368i) q^{43} +(1.76604 + 3.05888i) q^{45} +(1.92262 - 1.61327i) q^{47} +(-3.40760 + 5.90214i) q^{49} +(1.55303 + 0.565258i) q^{51} +(1.03074 + 5.84564i) q^{53} +(-14.3157 - 12.0123i) q^{55} +(-4.35117 + 0.259515i) q^{57} +(-0.167718 - 0.140732i) q^{59} +(-0.273318 - 1.55007i) q^{61} +(3.49273 + 1.27125i) q^{63} +(-0.400330 + 0.693392i) q^{65} +(-11.8589 + 9.95080i) q^{67} +(4.34002 + 7.51714i) q^{69} +(0.235300 - 1.33445i) q^{71} +(-2.27972 + 0.829748i) q^{73} +7.47565 q^{75} -19.6655 q^{77} +(-2.69207 + 0.979832i) q^{79} +(0.173648 - 0.984808i) q^{81} +(0.960637 + 1.66387i) q^{83} +(4.47178 - 3.75227i) q^{85} +(-0.0603074 + 0.104455i) q^{87} +(11.4226 + 4.15749i) q^{89} +(0.146307 + 0.829748i) q^{91} +(-2.39053 - 2.00589i) q^{93} +(-6.89053 + 13.7680i) q^{95} +(13.4081 + 11.2507i) q^{97} +(0.918748 + 5.21048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} + 9 q^{13} + 3 q^{15} - 3 q^{17} - 15 q^{21} - 27 q^{23} - 15 q^{25} - 3 q^{27} - 3 q^{29} + 15 q^{31} + 3 q^{33} - 12 q^{35} - 6 q^{37} + 12 q^{39} - 15 q^{41} - 3 q^{43} + 6 q^{45}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 + 9 * q^13 + 3 * q^15 - 3 * q^17 - 15 * q^21 - 27 * q^23 - 15 * q^25 - 3 * q^27 - 3 * q^29 + 15 * q^31 + 3 * q^33 - 12 * q^35 - 6 * q^37 + 12 * q^39 - 15 * q^41 - 3 * q^43 + 6 * q^45 - 15 * q^47 - 24 * q^49 - 3 * q^51 + 6 * q^53 - 27 * q^55 + 27 * q^59 - 15 * q^61 + 3 * q^63 + 12 * q^65 + 3 * q^67 + 6 * q^69 - 3 * q^71 + 12 * q^73 + 6 * q^75 - 42 * q^77 - 27 * q^79 - 3 * q^83 + 12 * q^85 - 6 * q^87 + 42 * q^89 + 42 * q^91 + 3 * q^93 - 24 * q^95 + 18 * q^97 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$		0			0
$5$	−0.613341	+	3.47843i	−0.274294	+	1.55560i	0.466900	+	0.884310i	$0.345371\pi$
$5$	−0.613341	+	3.47843i	−0.274294	+	1.55560i	−0.741194	+	0.671290i	$0.765740\pi$
$6$		0			0
$7$	1.85844	+	3.21891i	0.702425	+	1.21664i	0.967613	+	0.252438i	$0.0812325\pi$
$7$	1.85844	+	3.21891i	0.702425	+	1.21664i	−0.265188	+	0.964197i	$0.585434\pi$
$8$		0			0
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$		0			0
$11$	−2.64543	+	4.58202i	−0.797627	+	1.38153i	0.123531	+	0.992341i	$0.460578\pi$
$11$	−2.64543	+	4.58202i	−0.797627	+	1.38153i	−0.921158	+	0.389190i	$0.872755\pi$
$12$		0			0
$13$	0.213011	+	0.0775297i	0.0590786	+	0.0215029i	0.371390	−	0.928477i	$-0.378881\pi$
$13$	0.213011	+	0.0775297i	0.0590786	+	0.0215029i	−0.312312	+	0.949980i	$0.601103\pi$
$14$		0			0
$15$	−0.613341	−	3.47843i	−0.158364	−	0.898126i
$16$		0			0
$17$	−1.26604	−	1.06234i	−0.307061	−	0.257655i	0.476215	−	0.879329i	$-0.342008\pi$
$17$	−1.26604	−	1.06234i	−0.307061	−	0.257655i	−0.783276	+	0.621674i	$0.786453\pi$
$18$		0			0
$19$	4.17752	+	1.24432i	0.958388	+	0.285467i
$19$	4.17752	+	1.24432i	0.958388	+	0.285467i
$20$		0			0
$21$	−2.84730	−	2.38917i	−0.621331	−	0.521359i
$22$		0			0
$23$	−1.50727	−	8.54818i	−0.314288	−	1.78242i	−0.576182	−	0.817321i	$-0.695458\pi$
$23$	−1.50727	−	8.54818i	−0.314288	−	1.78242i	0.261894	−	0.965097i	$-0.415653\pi$
$24$		0			0
$25$	−7.02481	−	2.55682i	−1.40496	−	0.511365i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	0.0923963	−	0.0775297i	0.0171576	−	0.0143969i	−0.634169	−	0.773195i	$-0.718657\pi$
$29$	0.0923963	−	0.0775297i	0.0171576	−	0.0143969i	0.651326	+	0.758798i	$0.274213\pi$
$30$		0			0
$31$	1.56031	+	2.70253i	0.280239	+	0.485389i	0.971444	−	0.237271i	$-0.0762528\pi$
$31$	1.56031	+	2.70253i	0.280239	+	0.485389i	−0.691204	+	0.722660i	$0.742919\pi$
$32$		0			0
$33$	0.918748	−	5.21048i	0.159934	−	0.907028i
$34$		0			0
$35$	−12.3366	+	4.49016i	−2.08527	+	0.758976i
$36$		0			0
$37$	5.12836			0.843096			0.421548	−	0.906806i	$-0.361487\pi$
$37$	5.12836			0.843096			0.421548	+	0.906806i	$0.361487\pi$
$38$		0			0
$39$	−0.226682			−0.0362981
$40$		0			0
$41$	−6.67752	+	2.43042i	−1.04285	+	0.379568i	−0.805961	−	0.591968i	$-0.798351\pi$
$41$	−6.67752	+	2.43042i	−1.04285	+	0.379568i	−0.236892	+	0.971536i	$0.576129\pi$
$42$		0			0
$43$	0.929892	−	5.27368i	0.141807	−	0.804229i	−0.828068	−	0.560627i	$-0.810560\pi$
$43$	0.929892	−	5.27368i	0.141807	−	0.804229i	0.969875	−	0.243602i	$-0.0783289\pi$
$44$		0			0
$45$	1.76604	+	3.05888i	0.263266	+	0.455991i
$46$		0			0
$47$	1.92262	−	1.61327i	0.280443	−	0.235319i	−0.491706	−	0.870761i	$-0.663626\pi$
$47$	1.92262	−	1.61327i	0.280443	−	0.235319i	0.772149	+	0.635442i	$0.219182\pi$
$48$		0			0
$49$	−3.40760	+	5.90214i	−0.486801	+	0.843163i
$50$		0			0
$51$	1.55303	+	0.565258i	0.217468	+	0.0791519i
$52$		0			0
$53$	1.03074	+	5.84564i	0.141584	+	0.802961i	0.970047	+	0.242918i	$0.0781044\pi$
$53$	1.03074	+	5.84564i	0.141584	+	0.802961i	−0.828463	+	0.560043i	$0.810784\pi$
$54$		0			0
$55$	−14.3157	−	12.0123i	−1.93033	−	1.61974i
$56$		0			0
$57$	−4.35117	+	0.259515i	−0.576326	+	0.0343736i
$58$		0			0
$59$	−0.167718	−	0.140732i	−0.0218351	−	0.0183218i	0.631805	−	0.775128i	$-0.282314\pi$
$59$	−0.167718	−	0.140732i	−0.0218351	−	0.0183218i	−0.653640	+	0.756806i	$0.726759\pi$
$60$		0			0
$61$	−0.273318	−	1.55007i	−0.0349948	−	0.198466i	0.962298	−	0.271997i	$-0.0876841\pi$
$61$	−0.273318	−	1.55007i	−0.0349948	−	0.198466i	−0.997293	+	0.0735316i	$0.976573\pi$
$62$		0			0
$63$	3.49273	+	1.27125i	0.440042	+	0.160162i
$64$		0			0
$65$	−0.400330	+	0.693392i	−0.0496548	+	0.0860046i
$66$		0			0
$67$	−11.8589	+	9.95080i	−1.44880	+	1.21568i	−0.515343	+	0.856984i	$0.672336\pi$
$67$	−11.8589	+	9.95080i	−1.44880	+	1.21568i	−0.933453	+	0.358701i	$0.883220\pi$
$68$		0			0
$69$	4.34002	+	7.51714i	0.522477	+	0.904957i
$70$		0			0
$71$	0.235300	−	1.33445i	0.0279249	−	0.158370i	−0.967657	−	0.252271i	$-0.918823\pi$
$71$	0.235300	−	1.33445i	0.0279249	−	0.158370i	0.995582	+	0.0939008i	$0.0299337\pi$
$72$		0			0
$73$	−2.27972	+	0.829748i	−0.266820	+	0.0971147i	−0.471966	−	0.881617i	$-0.656455\pi$
$73$	−2.27972	+	0.829748i	−0.266820	+	0.0971147i	0.205145	+	0.978731i	$0.434233\pi$
$74$		0			0
$75$	7.47565			0.863214
$76$		0			0
$77$	−19.6655			−2.24109
$78$		0			0
$79$	−2.69207	+	0.979832i	−0.302881	+	0.110240i	−0.488990	−	0.872289i	$-0.662635\pi$
$79$	−2.69207	+	0.979832i	−0.302881	+	0.110240i	0.186109	+	0.982529i	$0.440412\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	0.960637	+	1.66387i	0.105444	+	0.182634i	0.913919	−	0.405896i	$-0.133040\pi$
$83$	0.960637	+	1.66387i	0.105444	+	0.182634i	−0.808476	+	0.588530i	$0.799707\pi$
$84$		0			0
$85$	4.47178	−	3.75227i	0.485033	−	0.406991i
$86$		0			0
$87$	−0.0603074	+	0.104455i	−0.00646563	+	0.0111988i
$88$		0			0
$89$	11.4226	+	4.15749i	1.21080	+	0.440693i	0.866980	−	0.498344i	$-0.166058\pi$
$89$	11.4226	+	4.15749i	1.21080	+	0.440693i	0.343816	+	0.939037i	$0.388280\pi$
$90$		0			0
$91$	0.146307	+	0.829748i	0.0153371	+	0.0869813i
$92$		0			0
$93$	−2.39053	−	2.00589i	−0.247886	−	0.208001i
$94$		0			0
$95$	−6.89053	+	13.7680i	−0.706953	+	1.41257i
$96$		0			0
$97$	13.4081	+	11.2507i	1.36138	+	1.14234i	0.975552	+	0.219767i	$0.0705296\pi$
$97$	13.4081	+	11.2507i	1.36138	+	1.14234i	0.385831	+	0.922570i	$0.373915\pi$
$98$		0			0
$99$	0.918748	+	5.21048i	0.0923377	+	0.523673i
$100$		0			0
$101$	−14.1099	−	5.13560i	−1.40399	−	0.511011i	−0.474631	−	0.880185i	$-0.657418\pi$
$101$	−14.1099	−	5.13560i	−1.40399	−	0.511011i	−0.929360	+	0.369174i	$0.879641\pi$
$102$		0			0
$103$	3.33022	−	5.76811i	0.328137	−	0.568349i	−0.654006	−	0.756490i	$-0.726913\pi$
$103$	3.33022	−	5.76811i	0.328137	−	0.568349i	0.982142	+	0.188141i	$0.0602461\pi$
$104$		0			0
$105$	10.0569	−	8.43874i	0.981453	−	0.823537i
$106$		0			0
$107$	4.04323	+	7.00309i	0.390874	+	0.677014i	0.992565	−	0.121715i	$-0.0388394\pi$
$107$	4.04323	+	7.00309i	0.390874	+	0.677014i	−0.601691	+	0.798729i	$0.705506\pi$
$108$		0			0
$109$	2.64796	−	15.0173i	0.253628	−	1.43840i	−0.545941	−	0.837823i	$-0.683828\pi$
$109$	2.64796	−	15.0173i	0.253628	−	1.43840i	0.799570	−	0.600573i	$-0.205061\pi$
$110$		0			0
$111$	−4.81908	+	1.75400i	−0.457407	+	0.166482i
$112$		0			0
$113$	0.815207			0.0766883			0.0383441	−	0.999265i	$-0.487792\pi$
$113$	0.815207			0.0766883			0.0383441	+	0.999265i	$0.487792\pi$
$114$		0			0
$115$	30.6587			2.85894
$116$		0			0
$117$	0.213011	−	0.0775297i	0.0196929	−	0.00716762i
$118$		0			0
$119$	1.06670	−	6.04958i	0.0977846	−	0.554564i
$120$		0			0
$121$	−8.49660	−	14.7165i	−0.772418	−	1.33787i
$122$		0			0
$123$	5.44356	−	4.56769i	0.490830	−	0.411855i
$124$		0			0
$125$	4.37211	−	7.57272i	0.391054	−	0.677325i
$126$		0			0
$127$	10.3969	+	3.78417i	0.922578	+	0.335791i	0.759264	−	0.650783i	$-0.225559\pi$
$127$	10.3969	+	3.78417i	0.922578	+	0.335791i	0.163314	+	0.986574i	$0.447782\pi$
$128$		0			0
$129$	0.929892	+	5.27368i	0.0818725	+	0.464322i
$130$		0			0
$131$	11.0307	+	9.25589i	0.963761	+	0.808691i	0.981561	−	0.191150i	$-0.0612218\pi$
$131$	11.0307	+	9.25589i	0.963761	+	0.808691i	−0.0178001	+	0.999842i	$0.505666\pi$
$132$		0			0
$133$	3.75830	+	15.7596i	0.325886	+	1.36653i
$134$		0			0
$135$	−2.70574	−	2.27038i	−0.232873	−	0.195403i
$136$		0			0
$137$	−0.0821293	−	0.465778i	−0.00701678	−	0.0397941i	0.981098	−	0.193510i	$-0.0619871\pi$
$137$	−0.0821293	−	0.465778i	−0.00701678	−	0.0397941i	−0.988115	+	0.153716i	$0.950876\pi$
$138$		0			0
$139$	−9.57057	−	3.48340i	−0.811766	−	0.295458i	−0.0974126	−	0.995244i	$-0.531057\pi$
$139$	−9.57057	−	3.48340i	−0.811766	−	0.295458i	−0.714353	+	0.699786i	$0.753279\pi$
$140$		0			0
$141$	−1.25490	+	2.17355i	−0.105682	+	0.183046i
$142$		0			0
$143$	−0.918748	+	0.770921i	−0.0768296	+	0.0644677i
$144$		0			0
$145$	0.213011	+	0.368946i	0.0176896	+	0.0306393i
$146$		0			0
$147$	1.18345	−	6.71167i	0.0976092	−	0.553569i
$148$		0			0
$149$	−4.58987	+	1.67058i	−0.376017	+	0.136859i	−0.523113	−	0.852263i	$-0.675229\pi$
$149$	−4.58987	+	1.67058i	−0.376017	+	0.136859i	0.147096	+	0.989122i	$0.453007\pi$
$150$		0			0
$151$	−9.04189			−0.735818			−0.367909	−	0.929862i	$-0.619926\pi$
$151$	−9.04189			−0.735818			−0.367909	+	0.929862i	$0.619926\pi$
$152$		0			0
$153$	−1.65270			−0.133613
$154$		0			0
$155$	−10.3576	+	3.76984i	−0.831940	+	0.302801i
$156$		0			0
$157$	0.0577812	−	0.327693i	0.00461144	−	0.0261528i	−0.982415	−	0.186709i	$-0.940218\pi$
$157$	0.0577812	−	0.327693i	0.00461144	−	0.0261528i	0.987027	+	0.160556i	$0.0513289\pi$
$158$		0			0
$159$	−2.96791	−	5.14057i	−0.235371	−	0.407674i
$160$		0			0
$161$	24.7147	−	20.7381i	1.94779	−	1.63439i
$162$		0			0
$163$	1.97044	−	3.41290i	0.154337	−	0.267319i	−0.778481	−	0.627669i	$-0.784009\pi$
$163$	1.97044	−	3.41290i	0.154337	−	0.267319i	0.932817	+	0.360350i	$0.117343\pi$
$164$		0			0
$165$	17.5608	+	6.39160i	1.36710	+	0.497585i
$166$		0			0
$167$	−1.04071	−	5.90214i	−0.0805323	−	0.456722i	−0.998232	−	0.0594456i	$-0.981067\pi$
$167$	−1.04071	−	5.90214i	−0.0805323	−	0.456722i	0.917699	−	0.397276i	$-0.130044\pi$
$168$		0			0
$169$	−9.91921	−	8.32321i	−0.763017	−	0.640247i
$170$		0			0
$171$	4.00000	−	1.73205i	0.305888	−	0.132453i
$172$		0			0
$173$	9.39306	+	7.88171i	0.714141	+	0.599235i	0.925758	−	0.378117i	$-0.123428\pi$
$173$	9.39306	+	7.88171i	0.714141	+	0.599235i	−0.211617	+	0.977353i	$0.567873\pi$
$174$		0			0
$175$	−4.82501	−	27.3640i	−0.364736	−	2.06852i
$176$		0			0
$177$	0.205737	+	0.0748822i	0.0154641	+	0.00562849i
$178$		0			0
$179$	4.03209	−	6.98378i	0.301372	−	0.521992i	−0.675075	−	0.737749i	$-0.735889\pi$
$179$	4.03209	−	6.98378i	0.301372	−	0.521992i	0.976447	+	0.215757i	$0.0692219\pi$
$180$		0			0
$181$	0.145430	−	0.122030i	0.0108097	−	0.00907042i	−0.637367	−	0.770561i	$-0.719976\pi$
$181$	0.145430	−	0.122030i	0.0108097	−	0.00907042i	0.648176	+	0.761490i	$0.275532\pi$
$182$		0			0
$183$	0.786989	+	1.36310i	0.0581759	+	0.100764i
$184$		0			0
$185$	−3.14543	+	17.8386i	−0.231257	+	1.31152i
$186$		0			0
$187$	8.21688	−	2.99070i	0.600878	−	0.218702i
$188$		0			0
$189$	−3.71688			−0.270363
$190$		0			0
$191$	−18.0378			−1.30517			−0.652584	−	0.757717i	$-0.726315\pi$
$191$	−18.0378			−1.30517			−0.652584	+	0.757717i	$0.726315\pi$
$192$		0			0
$193$	16.3871	−	5.96443i	1.17957	−	0.429329i	0.323521	−	0.946221i	$-0.395133\pi$
$193$	16.3871	−	5.96443i	1.17957	−	0.429329i	0.856050	+	0.516892i	$0.172911\pi$
$194$		0			0
$195$	0.139033	−	0.788496i	0.00995637	−	0.0564654i
$196$		0			0
$197$	5.24035	+	9.07656i	0.373360	+	0.646678i	0.990080	−	0.140504i	$-0.0448724\pi$
$197$	5.24035	+	9.07656i	0.373360	+	0.646678i	−0.616720	+	0.787182i	$0.711539\pi$
$198$		0			0
$199$	10.4593	−	8.77639i	0.741440	−	0.622142i	−0.191784	−	0.981437i	$-0.561427\pi$
$199$	10.4593	−	8.77639i	0.741440	−	0.622142i	0.933224	+	0.359295i	$0.116983\pi$
$200$		0			0
$201$	7.74035	−	13.4067i	0.545962	−	0.945635i
$202$		0			0
$203$	0.421274	+	0.153331i	0.0295677	+	0.0107617i
$204$		0			0
$205$	−4.35844	−	24.7179i	−0.304407	−	1.72638i
$206$		0			0
$207$	−6.64930	−	5.57943i	−0.462158	−	0.387797i
$208$		0			0
$209$	−16.7528	+	15.8497i	−1.15882	+	1.09635i
$210$		0			0
$211$	12.2023	+	10.2390i	0.840043	+	0.704880i	0.957573	−	0.288189i	$-0.0930532\pi$
$211$	12.2023	+	10.2390i	0.840043	+	0.704880i	−0.117530	+	0.993069i	$0.537498\pi$
$212$		0			0
$213$	0.235300	+	1.33445i	0.0161225	+	0.0914351i
$214$		0			0
$215$	17.7738	+	6.46913i	1.21216	+	0.441191i
$216$		0			0
$217$	−5.79948	+	10.0450i	−0.393694	+	0.681898i
$218$		0			0
$219$	1.85844	−	1.55942i	0.125582	−	0.105376i
$220$		0			0
$221$	−0.187319	−	0.324446i	−0.0126004	−	0.0218246i
$222$		0			0
$223$	−3.23261	+	18.3331i	−0.216472	+	1.22767i	0.661863	+	0.749625i	$0.269766\pi$
$223$	−3.23261	+	18.3331i	−0.216472	+	1.22767i	−0.878334	+	0.478047i	$0.841345\pi$
$224$		0			0
$225$	−7.02481	+	2.55682i	−0.468321	+	0.170455i
$226$		0			0
$227$	5.79292			0.384490			0.192245	−	0.981347i	$-0.438423\pi$
$227$	5.79292			0.384490			0.192245	+	0.981347i	$0.438423\pi$
$228$		0			0
$229$	−8.12836			−0.537137			−0.268568	−	0.963261i	$-0.586551\pi$
$229$	−8.12836			−0.537137			−0.268568	+	0.963261i	$0.586551\pi$
$230$		0			0
$231$	18.4795	−	6.72600i	1.21586	−	0.442538i
$232$		0			0
$233$	−2.95677	+	16.7687i	−0.193704	+	1.09855i	0.720548	+	0.693405i	$0.243890\pi$
$233$	−2.95677	+	16.7687i	−0.193704	+	1.09855i	−0.914252	+	0.405146i	$0.867221\pi$
$234$		0			0
$235$	4.43242	+	7.67717i	0.289139	+	0.500804i
$236$		0			0
$237$	2.19459	−	1.84148i	0.142554	−	0.119617i
$238$		0			0
$239$	−7.50980	+	13.0074i	−0.485769	+	0.841376i	−0.999866	−	0.0163558i	$-0.994794\pi$
$239$	−7.50980	+	13.0074i	−0.485769	+	0.841376i	0.514098	+	0.857732i	$0.328127\pi$
$240$		0			0
$241$	20.1596	+	7.33748i	1.29859	+	0.472649i	0.896538	−	0.442967i	$-0.146074\pi$
$241$	20.1596	+	7.33748i	1.29859	+	0.472649i	0.402054	+	0.915616i	$0.368296\pi$
$242$		0			0
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$		0			0
$245$	−18.4402	−	15.4731i	−1.17810	−	0.988542i
$246$		0			0
$247$	0.793386	+	0.588936i	0.0504819	+	0.0374731i
$248$		0			0
$249$	−1.47178	−	1.23497i	−0.0932704	−	0.0782631i
$250$		0			0
$251$	4.43969	+	25.1787i	0.280231	+	1.58927i	0.721839	+	0.692061i	$0.243297\pi$
$251$	4.43969	+	25.1787i	0.280231	+	1.58927i	−0.441608	+	0.897208i	$0.645592\pi$
$252$		0			0
$253$	43.1553	+	15.7072i	2.71315	+	0.987506i
$254$		0			0
$255$	−2.91875	+	5.05542i	−0.182779	+	0.316583i
$256$		0			0
$257$	2.13950	−	1.79525i	0.133458	−	0.111985i	−0.573615	−	0.819125i	$-0.694459\pi$
$257$	2.13950	−	1.79525i	0.133458	−	0.111985i	0.707073	+	0.707140i	$0.250015\pi$
$258$		0			0
$259$	9.53074	+	16.5077i	0.592212	+	1.02574i
$260$		0			0
$261$	0.0209445	−	0.118782i	0.00129643	−	0.00735244i
$262$		0			0
$263$	1.30066	−	0.473401i	0.0802021	−	0.0291912i	−0.301608	−	0.953432i	$-0.597523\pi$
$263$	1.30066	−	0.473401i	0.0802021	−	0.0291912i	0.381810	+	0.924241i	$0.375301\pi$
$264$		0			0
$265$	−20.9659			−1.28792
$266$		0			0
$267$	−12.1557			−0.743917
$268$		0			0
$269$	16.0471	−	5.84067i	0.978409	−	0.356112i	0.197188	−	0.980366i	$-0.436819\pi$
$269$	16.0471	−	5.84067i	0.978409	−	0.356112i	0.781221	+	0.624254i	$0.214597\pi$
$270$		0			0
$271$	4.46064	−	25.2975i	0.270964	−	1.53672i	−0.480531	−	0.876978i	$-0.659556\pi$
$271$	4.46064	−	25.2975i	0.270964	−	1.53672i	0.751496	−	0.659738i	$-0.229333\pi$
$272$		0			0
$273$	−0.421274	−	0.729669i	−0.0254967	−	0.0441615i
$274$		0			0
$275$	30.2991	−	25.4239i	1.82710	−	1.53312i
$276$		0			0
$277$	−11.1125	+	19.2474i	−0.667683	+	1.15646i	0.310867	+	0.950453i	$0.399381\pi$
$277$	−11.1125	+	19.2474i	−0.667683	+	1.15646i	−0.978550	+	0.206008i	$0.933953\pi$
$278$		0			0
$279$	2.93242	+	1.06731i	0.175559	+	0.0638984i
$280$		0			0
$281$	0.268104	+	1.52049i	0.0159937	+	0.0907050i	0.991760	−	0.128111i	$-0.0408915\pi$
$281$	0.268104	+	1.52049i	0.0159937	+	0.0907050i	−0.975766	+	0.218816i	$0.929780\pi$
$282$		0			0
$283$	−7.88326	−	6.61484i	−0.468611	−	0.393211i	0.377677	−	0.925938i	$-0.376723\pi$
$283$	−7.88326	−	6.61484i	−0.468611	−	0.393211i	−0.846288	+	0.532726i	$0.821168\pi$
$284$		0			0
$285$	1.76604	−	15.2944i	0.104611	−	0.905962i
$286$		0			0
$287$	−20.2331	−	16.9776i	−1.19432	−	1.00215i
$288$		0			0
$289$	−2.47771	−	14.0518i	−0.145748	−	0.826576i
$290$		0			0
$291$	−16.4474	−	5.98638i	−0.964166	−	0.350928i
$292$		0			0
$293$	14.2515	−	24.6843i	0.832581	−	1.44207i	−0.0634033	−	0.997988i	$-0.520195\pi$
$293$	14.2515	−	24.6843i	0.832581	−	1.44207i	0.895985	−	0.444085i	$-0.146471\pi$
$294$		0			0
$295$	0.592396	−	0.497079i	0.0344906	−	0.0289411i
$296$		0			0
$297$	−2.64543	−	4.58202i	−0.153503	−	0.265876i
$298$		0			0
$299$	0.341671	−	1.93771i	0.0197594	−	0.112061i
$300$		0			0
$301$	18.7037	−	6.80758i	1.07806	−	0.392382i
$302$		0			0
$303$	15.0155			0.862617
$304$		0			0
$305$	5.55943			0.318332
$306$		0			0
$307$	−24.0180	+	8.74184i	−1.37078	+	0.498923i	−0.919370	−	0.393394i	$-0.871301\pi$
$307$	−24.0180	+	8.74184i	−1.37078	+	0.498923i	−0.451410	+	0.892317i	$0.649079\pi$
$308$		0			0
$309$	−1.15657	+	6.55926i	−0.0657952	+	0.373143i
$310$		0			0
$311$	5.18732	+	8.98470i	0.294146	+	0.509476i	0.974786	−	0.223142i	$-0.0716315\pi$
$311$	5.18732	+	8.98470i	0.294146	+	0.509476i	−0.680640	+	0.732618i	$0.738298\pi$
$312$		0			0
$313$	−11.8250	+	9.92236i	−0.668389	+	0.560845i	−0.912588	−	0.408880i	$-0.865919\pi$
$313$	−11.8250	+	9.92236i	−0.668389	+	0.560845i	0.244199	+	0.969725i	$0.421475\pi$
$314$		0			0
$315$	−6.56418	+	11.3695i	−0.369850	+	0.640598i
$316$		0			0
$317$	−26.6844	−	9.71232i	−1.49874	−	0.545498i	−0.543009	−	0.839727i	$-0.682715\pi$
$317$	−26.6844	−	9.71232i	−1.49874	−	0.545498i	−0.955735	+	0.294229i	$0.904937\pi$
$318$		0			0
$319$	0.110815	+	0.628461i	0.00620443	+	0.0351870i
$320$		0			0
$321$	−6.19459	−	5.19788i	−0.345748	−	0.290117i
$322$		0			0
$323$	−3.96703	−	6.01330i	−0.220732	−	0.334589i
$324$		0			0
$325$	−1.29813	−	1.08926i	−0.0720075	−	0.0604215i
$326$		0			0
$327$	2.64796	+	15.0173i	0.146432	+	0.830459i
$328$		0			0
$329$	8.76604	+	3.19058i	0.483288	+	0.175902i
$330$		0			0
$331$	−12.9611	+	22.4493i	−0.712407	+	1.23392i	0.251545	+	0.967846i	$0.419062\pi$
$331$	−12.9611	+	22.4493i	−0.712407	+	1.23392i	−0.963951	+	0.266079i	$0.914272\pi$
$332$		0			0
$333$	3.92855	−	3.29644i	0.215283	−	0.180644i
$334$		0			0
$335$	−27.3396	−	47.3536i	−1.49372	−	2.58720i
$336$		0			0
$337$	−4.08260	+	23.1536i	−0.222393	+	1.26125i	0.645213	+	0.764003i	$0.276769\pi$
$337$	−4.08260	+	23.1536i	−0.222393	+	1.26125i	−0.867606	+	0.497252i	$0.834343\pi$
$338$		0			0
$339$	−0.766044	+	0.278817i	−0.0416058	+	0.0151433i
$340$		0			0
$341$	−16.5107			−0.894106
$342$		0			0
$343$	0.686852			0.0370865
$344$		0			0
$345$	−28.8097	+	10.4859i	−1.55106	+	0.564541i
$346$		0			0
$347$	0.417566	−	2.36813i	0.0224161	−	0.127128i	−0.971546	−	0.236850i	$-0.923885\pi$
$347$	0.417566	−	2.36813i	0.0224161	−	0.127128i	0.993962	+	0.109722i	$0.0349961\pi$
$348$		0			0
$349$	−2.59879	−	4.50124i	−0.139110	−	0.240946i	0.788050	−	0.615611i	$-0.211091\pi$
$349$	−2.59879	−	4.50124i	−0.139110	−	0.240946i	−0.927160	+	0.374665i	$0.877758\pi$
$350$		0			0
$351$	−0.173648	+	0.145708i	−0.00926865	+	0.00777732i
$352$		0			0
$353$	−4.13816	+	7.16750i	−0.220252	+	0.381487i	−0.954884	−	0.296978i	$-0.904021\pi$
$353$	−4.13816	+	7.16750i	−0.220252	+	0.381487i	0.734633	+	0.678465i	$0.237355\pi$
$354$		0			0
$355$	4.49747	+	1.63695i	0.238701	+	0.0868801i
$356$		0			0
$357$	1.06670	+	6.04958i	0.0564560	+	0.320178i
$358$		0			0
$359$	1.75877	+	1.47578i	0.0928244	+	0.0778889i	0.688019	−	0.725693i	$-0.258481\pi$
$359$	1.75877	+	1.47578i	0.0928244	+	0.0778889i	−0.595195	+	0.803582i	$0.702925\pi$
$360$		0			0
$361$	15.9033	+	10.3964i	0.837017	+	0.547177i
$362$		0			0
$363$	13.0175	+	10.9230i	0.683244	+	0.573310i
$364$		0			0
$365$	−1.48798	−	8.43874i	−0.0778843	−	0.441704i
$366$		0			0
$367$	28.0638	+	10.2144i	1.46492	+	0.533186i	0.946715	−	0.322072i	$-0.104379\pi$
$367$	28.0638	+	10.2144i	1.46492	+	0.533186i	0.518202	+	0.855258i	$0.326602\pi$
$368$		0			0
$369$	−3.55303	+	6.15403i	−0.184964	+	0.320366i
$370$		0			0
$371$	−16.9010	+	14.1817i	−0.877459	+	0.736275i
$372$		0			0
$373$	9.92649	+	17.1932i	0.513974	+	0.890229i	0.999869	+	0.0162118i	$0.00516060\pi$
$373$	9.92649	+	17.1932i	0.513974	+	0.890229i	−0.485894	+	0.874017i	$0.661506\pi$
$374$		0			0
$375$	−1.51842	+	8.61138i	−0.0784108	+	0.444690i
$376$		0			0
$377$	0.0256923	−	0.00935122i	0.00132322	−	0.000481612i
$378$		0			0
$379$	−25.8256			−1.32657			−0.663287	−	0.748365i	$-0.730839\pi$
$379$	−25.8256			−1.32657			−0.663287	+	0.748365i	$0.730839\pi$
$380$		0			0
$381$	−11.0642			−0.566835
$382$		0			0
$383$	18.9201	−	6.88635i	0.966772	−	0.351876i	0.190088	−	0.981767i	$-0.439123\pi$
$383$	18.9201	−	6.88635i	0.966772	−	0.351876i	0.776684	+	0.629891i	$0.216900\pi$
$384$		0			0
$385$	12.0617	−	68.4050i	0.614719	−	3.48624i
$386$		0			0
$387$	−2.67752	−	4.63760i	−0.136106	−	0.235742i
$388$		0			0
$389$	8.68139	−	7.28455i	0.440164	−	0.369341i	−0.395607	−	0.918420i	$-0.629466\pi$
$389$	8.68139	−	7.28455i	0.440164	−	0.369341i	0.835771	+	0.549079i	$0.185021\pi$
$390$		0			0
$391$	−7.17277	+	12.4236i	−0.362743	+	0.628289i
$392$		0			0
$393$	−13.5312	−	4.92496i	−0.682559	−	0.248431i
$394$		0			0
$395$	−1.75712	−	9.96513i	−0.0884104	−	0.501400i
$396$		0			0
$397$	10.0307	+	8.41679i	0.503429	+	0.422427i	0.858810	−	0.512295i	$-0.171204\pi$
$397$	10.0307	+	8.41679i	0.503429	+	0.422427i	−0.355381	+	0.934722i	$0.615649\pi$
$398$		0			0
$399$	−8.92174	−	13.5237i	−0.446646	−	0.677034i
$400$		0			0
$401$	16.2554	+	13.6399i	0.811754	+	0.681143i	0.951026	−	0.309112i	$-0.100032\pi$
$401$	16.2554	+	13.6399i	0.811754	+	0.681143i	−0.139272	+	0.990254i	$0.544476\pi$
$402$		0			0
$403$	0.122836	+	0.696639i	0.00611891	+	0.0347021i
$404$		0			0
$405$	3.31908	+	1.20805i	0.164926	+	0.0600283i
$406$		0			0
$407$	−13.5667	+	23.4982i	−0.672477	+	1.16476i
$408$		0			0
$409$	−22.2763	+	18.6920i	−1.10149	+	0.924262i	−0.997525	−	0.0703185i	$-0.977598\pi$
$409$	−22.2763	+	18.6920i	−1.10149	+	0.924262i	−0.103968	+	0.994581i	$0.533154\pi$
$410$		0			0
$411$	0.236482	+	0.409598i	0.0116648	+	0.0202040i
$412$		0			0
$413$	0.141311	−	0.801414i	0.00695345	−	0.0394350i
$414$		0			0
$415$	−6.37686	+	2.32099i	−0.313028	+	0.113933i
$416$		0			0
$417$	10.1848			0.498751
$418$		0			0
$419$	−40.4962			−1.97837			−0.989184	−	0.146679i	$-0.953141\pi$
$419$	−40.4962			−1.97837			−0.989184	+	0.146679i	$0.953141\pi$
$420$		0			0
$421$	−29.3491	+	10.6822i	−1.43039	+	0.520619i	−0.937043	−	0.349215i	$-0.886448\pi$
$421$	−29.3491	+	10.6822i	−1.43039	+	0.520619i	−0.493345	+	0.869834i	$0.664226\pi$
$422$		0			0
$423$	0.435822	−	2.47167i	0.0211904	−	0.120177i
$424$		0			0
$425$	6.17752	+	10.6998i	0.299654	+	0.519015i
$426$		0			0
$427$	4.48158	−	3.76049i	0.216879	−	0.181983i
$428$		0			0
$429$	0.599670	−	1.03866i	0.0289524	−	0.0501469i
$430$		0			0
$431$	24.4513	+	8.89955i	1.17778	+	0.428676i	0.855417	−	0.517941i	$-0.173301\pi$
$431$	24.4513	+	8.89955i	1.17778	+	0.428676i	0.322361	+	0.946617i	$0.395523\pi$
$432$		0			0
$433$	−4.69965	−	26.6530i	−0.225851	−	1.28086i	−0.861053	−	0.508516i	$-0.830194\pi$
$433$	−4.69965	−	26.6530i	−0.225851	−	1.28086i	0.635202	−	0.772346i	$-0.280917\pi$
$434$		0			0
$435$	−0.326352	−	0.273842i	−0.0156474	−	0.0131297i
$436$		0			0
$437$	4.34002	−	37.5857i	0.207611	−	1.79797i
$438$		0			0
$439$	2.25284	+	1.89036i	0.107522	+	0.0902219i	0.694964	−	0.719045i	$-0.255420\pi$
$439$	2.25284	+	1.89036i	0.107522	+	0.0902219i	−0.587442	+	0.809267i	$0.699865\pi$
$440$		0			0
$441$	1.18345	+	6.71167i	0.0563547	+	0.319603i
$442$		0			0
$443$	25.9402	+	9.44145i	1.23245	+	0.448577i	0.874437	−	0.485138i	$-0.161231\pi$
$443$	25.9402	+	9.44145i	1.23245	+	0.448577i	0.358017	+	0.933715i	$0.383453\pi$
$444$		0			0
$445$	−21.4675	+	37.1828i	−1.01766	+	1.76263i
$446$		0			0
$447$	3.74170	−	3.13966i	0.176976	−	0.148501i
$448$		0			0
$449$	−8.46110	−	14.6551i	−0.399304	−	0.691615i	0.594336	−	0.804217i	$-0.297415\pi$
$449$	−8.46110	−	14.6551i	−0.399304	−	0.691615i	−0.993640	+	0.112602i	$0.964082\pi$
$450$		0			0
$451$	6.52869	−	37.0260i	0.307424	−	1.74349i
$452$		0			0
$453$	8.49660	−	3.09251i	0.399205	−	0.145299i
$454$		0			0
$455$	−2.97596			−0.139515
$456$		0			0
$457$	9.19160			0.429965			0.214982	−	0.976618i	$-0.431031\pi$
$457$	9.19160			0.429965			0.214982	+	0.976618i	$0.431031\pi$
$458$		0			0
$459$	1.55303	−	0.565258i	0.0724894	−	0.0263840i
$460$		0			0
$461$	−2.68210	+	15.2110i	−0.124918	+	0.708445i	0.856438	+	0.516249i	$0.172672\pi$
$461$	−2.68210	+	15.2110i	−0.124918	+	0.708445i	−0.981357	+	0.192196i	$0.938439\pi$
$462$		0			0
$463$	14.9907	+	25.9646i	0.696675	+	1.20668i	0.969613	+	0.244645i	$0.0786715\pi$
$463$	14.9907	+	25.9646i	0.696675	+	1.20668i	−0.272937	+	0.962032i	$0.587995\pi$
$464$		0			0
$465$	8.44356	−	7.08499i	0.391561	−	0.328559i
$466$		0			0
$467$	14.4427	−	25.0155i	0.668328	−	1.15758i	−0.310044	−	0.950722i	$-0.600344\pi$
$467$	14.4427	−	25.0155i	0.668328	−	1.15758i	0.978372	−	0.206855i	$-0.0663230\pi$
$468$		0			0
$469$	−54.0699	−	19.6798i	−2.49671	−	0.908730i
$470$		0			0
$471$	0.0577812	+	0.327693i	0.00266242	+	0.0150993i
$472$		0			0
$473$	21.7041	+	18.2119i	0.997958	+	0.837386i
$474$		0			0
$475$	−26.1648	−	19.4223i	−1.20052	−	0.891157i
$476$		0			0
$477$	4.54710	+	3.81547i	0.208198	+	0.174699i
$478$		0			0
$479$	−2.37211	−	13.4529i	−0.108385	−	0.614679i	−0.989814	−	0.142364i	$-0.954530\pi$
$479$	−2.37211	−	13.4529i	−0.108385	−	0.614679i	0.881430	−	0.472315i	$-0.156582\pi$
$480$		0			0
$481$	1.09240	+	0.397600i	0.0498090	+	0.0181290i
$482$		0			0
$483$	−16.1313	+	27.9403i	−0.734002	+	1.27133i
$484$		0			0
$485$	−47.3585	+	39.7385i	−2.15044	+	1.80443i
$486$		0			0
$487$	−3.08899	−	5.35029i	−0.139976	−	0.242445i	0.787512	−	0.616300i	$-0.211369\pi$
$487$	−3.08899	−	5.35029i	−0.139976	−	0.242445i	−0.927487	+	0.373855i	$0.878036\pi$
$488$		0			0
$489$	−0.684326	+	3.88100i	−0.0309463	+	0.175505i
$490$		0			0
$491$	3.85591	−	1.40344i	0.174015	−	0.0633363i	−0.253543	−	0.967324i	$-0.581596\pi$
$491$	3.85591	−	1.40344i	0.174015	−	0.0633363i	0.427558	+	0.903988i	$0.359374\pi$
$492$		0			0
$493$	−0.199340			−0.00897784
$494$		0			0
$495$	−18.6878			−0.839953
$496$		0			0
$497$	4.73277	−	1.72259i	0.212294	−	0.0772687i
$498$		0			0
$499$	−4.61540	+	26.1752i	−0.206614	+	1.17176i	0.688266	+	0.725458i	$0.258372\pi$
$499$	−4.61540	+	26.1752i	−0.206614	+	1.17176i	−0.894880	+	0.446306i	$0.852739\pi$
$500$		0			0
$501$	2.99660	+	5.19026i	0.133878	+	0.231884i
$502$		0			0
$503$	19.8746	−	16.6768i	0.886166	−	0.743582i	−0.0812712	−	0.996692i	$-0.525898\pi$
$503$	19.8746	−	16.6768i	0.886166	−	0.743582i	0.967437	+	0.253110i	$0.0814535\pi$
$504$		0			0
$505$	26.5180	−	45.9305i	1.18004	−	2.04388i
$506$		0			0
$507$	12.1677	+	4.42869i	0.540387	+	0.196685i
$508$		0			0
$509$	−4.37551	−	24.8148i	−0.193941	−	1.09990i	−0.913918	−	0.405898i	$-0.866959\pi$
$509$	−4.37551	−	24.8148i	−0.193941	−	1.09990i	0.719977	−	0.693998i	$-0.244152\pi$
$510$		0			0
$511$	−6.90760	−	5.79617i	−0.305574	−	0.256407i
$512$		0			0
$513$	−3.16637	+	2.99568i	−0.139799	+	0.132262i
$514$		0			0
$515$	18.0214	+	15.1218i	0.794118	+	0.666344i
$516$		0			0
$517$	2.30587	+	13.0773i	0.101412	+	0.575137i
$518$		0			0
$519$	−11.5223	−	4.19377i	−0.505772	−	0.184086i
$520$		0			0
$521$	1.38800	−	2.40409i	0.0608095	−	0.105325i	−0.834018	−	0.551737i	$-0.813965\pi$
$521$	1.38800	−	2.40409i	0.0608095	−	0.105325i	0.894827	+	0.446412i	$0.147298\pi$
$522$		0			0
$523$	−8.60678	+	7.22195i	−0.376348	+	0.315794i	−0.811267	−	0.584676i	$-0.801222\pi$
$523$	−8.60678	+	7.22195i	−0.376348	+	0.315794i	0.434919	+	0.900470i	$0.356777\pi$
$524$		0			0
$525$	13.8931	+	24.0635i	0.606343	+	1.05022i
$526$		0			0
$527$	0.895582	−	5.07910i	0.0390122	−	0.221249i
$528$		0			0
$529$	−49.1865	+	17.9024i	−2.13854	+	0.778366i
$530$		0			0
$531$	−0.218941			−0.00950122
$532$		0			0
$533$	−1.61081			−0.0697721
$534$		0			0
$535$	−26.8396	+	9.76882i	−1.16038	+	0.422343i
$536$		0			0
$537$	−1.40033	+	7.94166i	−0.0604287	+	0.342708i
$538$		0			0
$539$	−18.0292	−	31.2274i	−0.776571	−	1.34506i
$540$		0			0
$541$	−16.8628	+	14.1496i	−0.724987	+	0.608337i	−0.928760	−	0.370682i	$-0.879124\pi$
$541$	−16.8628	+	14.1496i	−0.724987	+	0.608337i	0.203773	+	0.979018i	$0.434680\pi$
$542$		0			0
$543$	−0.0949225	+	0.164411i	−0.00407351	+	0.00705553i
$544$		0			0
$545$	50.6125	+	18.4215i	2.16800	+	0.789088i
$546$		0			0
$547$	−5.93107	−	33.6368i	−0.253594	−	1.43821i	−0.799655	−	0.600460i	$-0.794984\pi$
$547$	−5.93107	−	33.6368i	−0.253594	−	1.43821i	0.546061	−	0.837746i	$-0.316127\pi$
$548$		0			0
$549$	−1.20574	−	1.01173i	−0.0514596	−	0.0431797i
$550$		0			0
$551$	0.482459	−	0.208911i	0.0205534	−	0.00889990i
$552$		0			0
$553$	−8.15704	−	6.84457i	−0.346873	−	0.291061i
$554$		0			0
$555$	−3.14543	−	17.8386i	−0.133516	−	0.757207i
$556$		0			0
$557$	35.5774	+	12.9491i	1.50746	+	0.548672i	0.957981	−	0.286832i	$-0.0926023\pi$
$557$	35.5774	+	12.9491i	1.50746	+	0.548672i	0.549484	+	0.835504i	$0.314824\pi$
$558$		0			0
$559$	0.606944	−	1.05126i	0.0256710	−	0.0444635i
$560$		0			0
$561$	−6.69846	+	5.62068i	−0.282809	+	0.237305i
$562$		0			0
$563$	5.86231	+	10.1538i	0.247067	+	0.427933i	0.962711	−	0.270533i	$-0.0871999\pi$
$563$	5.86231	+	10.1538i	0.247067	+	0.427933i	−0.715644	+	0.698465i	$0.753867\pi$
$564$		0			0
$565$	−0.500000	+	2.83564i	−0.0210352	+	0.119296i
$566$		0			0
$567$	3.49273	−	1.27125i	0.146681	−	0.0533874i
$568$		0			0
$569$	14.8972			0.624524			0.312262	−	0.949996i	$-0.398913\pi$
$569$	14.8972			0.624524			0.312262	+	0.949996i	$0.398913\pi$
$570$		0			0
$571$	−12.9409			−0.541559			−0.270779	−	0.962641i	$-0.587281\pi$
$571$	−12.9409			−0.541559			−0.270779	+	0.962641i	$0.587281\pi$
$572$		0			0
$573$	16.9500	−	6.16928i	0.708095	−	0.257725i
$574$		0			0
$575$	−11.2679	+	63.9032i	−0.469902	+	2.66495i
$576$		0			0
$577$	−11.3657	−	19.6860i	−0.473161	−	0.819539i	0.526367	−	0.850257i	$-0.323554\pi$
$577$	−11.3657	−	19.6860i	−0.473161	−	0.819539i	−0.999528	+	0.0307187i	$0.990220\pi$
$578$		0			0
$579$	−13.3589	+	11.2095i	−0.555177	+	0.465849i
$580$		0			0
$581$	−3.57057	+	6.18442i	−0.148132	+	0.256573i
$582$		0			0
$583$	−29.5116	−	10.7413i	−1.22225	−	0.444861i
$584$		0			0
$585$	0.139033	+	0.788496i	0.00574831	+	0.0326003i
$586$		0			0
$587$	8.08899	+	6.78747i	0.333868	+	0.280149i	0.794274	−	0.607560i	$-0.207852\pi$
$587$	8.08899	+	6.78747i	0.333868	+	0.280149i	−0.460405	+	0.887709i	$0.652296\pi$
$588$		0			0
$589$	3.15539	+	13.2314i	0.130016	+	0.545190i
$590$		0			0
$591$	−8.02869	−	6.73687i	−0.330256	−	0.277118i
$592$		0			0
$593$	−1.86808	−	10.5944i	−0.0767128	−	0.435060i	−0.998839	−	0.0481709i	$-0.984661\pi$
$593$	−1.86808	−	10.5944i	−0.0767128	−	0.435060i	0.922126	−	0.386889i	$-0.126450\pi$
$594$		0			0
$595$	20.3888	+	7.42091i	0.835858	+	0.304228i
$596$		0			0
$597$	−6.82682	+	11.8244i	−0.279403	+	0.483940i
$598$		0			0
$599$	18.7153	−	15.7040i	0.764686	−	0.641648i	−0.174656	−	0.984630i	$-0.555881\pi$
$599$	18.7153	−	15.7040i	0.764686	−	0.641648i	0.939342	+	0.342982i	$0.111437\pi$
$600$		0			0
$601$	13.2057	+	22.8730i	0.538673	+	0.933009i	0.998976	+	0.0452473i	$0.0144076\pi$
$601$	13.2057	+	22.8730i	0.538673	+	0.933009i	−0.460303	+	0.887762i	$0.652259\pi$
$602$		0			0
$603$	−2.68820	+	15.2455i	−0.109472	+	0.620845i
$604$		0			0
$605$	56.4017	−	20.5286i	2.29306	−	0.834604i
$606$		0			0
$607$	16.3618			0.664107			0.332053	−	0.943261i	$-0.392259\pi$
$607$	16.3618			0.664107			0.332053	+	0.943261i	$0.392259\pi$
$608$		0			0
$609$	−0.448311			−0.0181665
$610$		0			0
$611$	0.534615	−	0.194584i	0.0216282	−	0.00787203i
$612$		0			0
$613$	1.03162	−	5.85062i	0.0416668	−	0.236304i	−0.956861	−	0.290546i	$-0.906163\pi$
$613$	1.03162	−	5.85062i	0.0416668	−	0.236304i	0.998528	+	0.0542418i	$0.0172742\pi$
$614$		0			0
$615$	12.5496	+	21.7366i	0.506050	+	0.876504i
$616$		0			0
$617$	−26.1438	+	21.9373i	−1.05251	+	0.883162i	−0.993355	−	0.115087i	$-0.963285\pi$
$617$	−26.1438	+	21.9373i	−1.05251	+	0.883162i	−0.0591558	+	0.998249i	$0.518841\pi$
$618$		0			0
$619$	16.1506	−	27.9737i	0.649149	−	1.12436i	−0.334177	−	0.942510i	$-0.608458\pi$
$619$	16.1506	−	27.9737i	0.649149	−	1.12436i	0.983326	−	0.181849i	$-0.0582083\pi$
$620$		0			0
$621$	8.15657	+	2.96875i	0.327312	+	0.119132i
$622$		0			0
$623$	7.84565	+	44.4949i	0.314329	+	1.78265i
$624$		0			0
$625$	−4.97384	−	4.17355i	−0.198954	−	0.166942i
$626$		0			0
$627$	10.3216	−	20.6237i	0.412205	−	0.823629i
$628$		0			0
$629$	−6.49273	−	5.44804i	−0.258882	−	0.217228i
$630$		0			0
$631$	−3.13058	−	17.7544i	−0.124626	−	0.706791i	−0.981529	−	0.191313i	$-0.938725\pi$
$631$	−3.13058	−	17.7544i	−0.124626	−	0.706791i	0.856903	−	0.515478i	$-0.172386\pi$
$632$		0			0
$633$	−14.9684	−	5.44804i	−0.594940	−	0.216540i
$634$		0			0
$635$	−19.5398	+	33.8440i	−0.775414	+	1.34306i
$636$		0			0
$637$	−1.18345	+	0.993031i	−0.0468899	+	0.0393453i
$638$		0			0
$639$	−0.677519	−	1.17350i	−0.0268022	−	0.0464228i
$640$		0			0
$641$	0.449493	−	2.54920i	0.0177539	−	0.100687i	−0.974643	−	0.223765i	$-0.928165\pi$
$641$	0.449493	−	2.54920i	0.0177539	−	0.100687i	0.992397	+	0.123077i	$0.0392764\pi$
$642$		0			0
$643$	15.2160	−	5.53817i	0.600061	−	0.218404i	−0.0240880	−	0.999710i	$-0.507668\pi$
$643$	15.2160	−	5.53817i	0.600061	−	0.218404i	0.624149	+	0.781306i	$0.285446\pi$
$644$		0			0
$645$	−18.9145			−0.744756
$646$		0			0
$647$	−0.477407			−0.0187688			−0.00938439	−	0.999956i	$-0.502987\pi$
$647$	−0.477407			−0.0187688			−0.00938439	+	0.999956i	$0.502987\pi$
$648$		0			0
$649$	1.08853	−	0.396191i	0.0427284	−	0.0155519i
$650$		0			0
$651$	2.01414	−	11.4227i	0.0789403	−	0.447693i
$652$		0			0
$653$	−8.05097	−	13.9447i	−0.315059	−	0.545698i	0.664391	−	0.747385i	$-0.268691\pi$
$653$	−8.05097	−	13.9447i	−0.315059	−	0.545698i	−0.979450	+	0.201687i	$0.935358\pi$
$654$		0			0
$655$	−38.9616	+	32.6926i	−1.52235	+	1.27741i
$656$		0			0
$657$	−1.21301	+	2.10100i	−0.0473241	+	0.0819677i
$658$		0			0
$659$	−13.6630	−	4.97291i	−0.532234	−	0.193717i	0.0619017	−	0.998082i	$-0.480283\pi$
$659$	−13.6630	−	4.97291i	−0.532234	−	0.193717i	−0.594135	+	0.804365i	$0.702506\pi$
$660$		0			0
$661$	−2.52915	−	14.3435i	−0.0983726	−	0.557899i	−0.993662	−	0.112413i	$-0.964142\pi$
$661$	−2.52915	−	14.3435i	−0.0983726	−	0.557899i	0.895289	−	0.445486i	$-0.146969\pi$
$662$		0			0
$663$	0.286989	+	0.240812i	0.0111457	+	0.00935238i
$664$		0			0
$665$	−57.1237	+	3.40700i	−2.21516	+	0.132118i
$666$		0			0
$667$	−0.802004	−	0.672961i	−0.0310537	−	0.0260572i
$668$		0			0
$669$	−3.23261	−	18.3331i	−0.124980	−	0.708797i
$670$		0			0
$671$	7.82547	+	2.84824i	0.302099	+	0.109955i
$672$		0			0
$673$	−12.4324	+	21.5336i	−0.479235	+	0.830059i	−0.999716	−	0.0238142i	$-0.992419\pi$
$673$	−12.4324	+	21.5336i	−0.479235	+	0.830059i	0.520482	+	0.853873i	$0.325752\pi$
$674$		0			0
$675$	5.72668	−	4.80526i	0.220420	−	0.184954i
$676$		0			0
$677$	−23.2271	−	40.2306i	−0.892692	−	1.54619i	−0.836636	−	0.547760i	$-0.815481\pi$
$677$	−23.2271	−	40.2306i	−0.892692	−	1.54619i	−0.0560563	−	0.998428i	$-0.517853\pi$
$678$		0			0
$679$	−11.2970	+	64.0682i	−0.433537	+	2.45871i
$680$		0			0
$681$	−5.44356	+	1.98129i	−0.208598	+	0.0759234i
$682$		0			0
$683$	26.0000			0.994862			0.497431	−	0.867503i	$-0.334277\pi$
$683$	26.0000			0.994862			0.497431	+	0.867503i	$0.334277\pi$
$684$		0			0
$685$	1.67055			0.0638284
$686$		0			0
$687$	7.63816	−	2.78006i	0.291414	−	0.106066i
$688$		0			0
$689$	−0.233651	+	1.32510i	−0.00890139	+	0.0504823i
$690$		0			0
$691$	−8.03478	−	13.9166i	−0.305657	−	0.529414i	0.671750	−	0.740778i	$-0.265543\pi$
$691$	−8.03478	−	13.9166i	−0.305657	−	0.529414i	−0.977407	+	0.211364i	$0.932210\pi$
$692$		0			0
$693$	−15.0646	+	12.6407i	−0.572259	+	0.480182i
$694$		0			0
$695$	17.9868	−	31.1540i	0.682278	−	1.18174i
$696$		0			0
$697$	11.0360	+	4.01676i	0.418017	+	0.152146i
$698$		0			0
$699$	−2.95677	−	16.7687i	−0.111835	−	0.634249i
$700$		0			0
$701$	−7.59240	−	6.37078i	−0.286761	−	0.240621i	0.488048	−	0.872817i	$-0.337709\pi$
$701$	−7.59240	−	6.37078i	−0.286761	−	0.240621i	−0.774808	+	0.632196i	$0.782154\pi$
$702$		0			0
$703$	21.4238	+	6.38133i	0.808014	+	0.240676i
$704$		0			0
$705$	−6.79086	−	5.69821i	−0.255759	−	0.214607i
$706$		0			0
$707$	−9.69144	−	54.9629i	−0.364484	−	2.06709i
$708$		0			0
$709$	25.8148	+	9.39582i	0.969495	+	0.352867i	0.777747	−	0.628577i	$-0.216362\pi$
$709$	25.8148	+	9.39582i	0.969495	+	0.352867i	0.191748	+	0.981444i	$0.438584\pi$
$710$		0			0
$711$	−1.43242	+	2.48102i	−0.0537199	+	0.0930456i
$712$		0			0
$713$	20.7499	−	17.4112i	0.777090	−	0.652056i
$714$		0			0
$715$	−2.11809	−	3.66864i	−0.0792120	−	0.137199i
$716$		0			0
$717$	2.60813	−	14.7914i	0.0974023	−	0.552396i
$718$		0			0
$719$	11.5239	−	4.19437i	0.429770	−	0.156424i	−0.118072	−	0.993005i	$-0.537671\pi$
$719$	11.5239	−	4.19437i	0.429770	−	0.156424i	0.547843	+	0.836581i	$0.315449\pi$
$720$		0			0
$721$	24.7561			0.921965
$722$		0			0
$723$	−21.4534			−0.797859
$724$		0			0
$725$	−0.847296	+	0.308391i	−0.0314678	+	0.0114533i
$726$		0			0
$727$	−4.90719	+	27.8301i	−0.181998	+	1.03216i	0.747755	+	0.663975i	$0.231132\pi$
$727$	−4.90719	+	27.8301i	−0.181998	+	1.03216i	−0.929752	+	0.368185i	$0.879979\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	−6.77972	+	5.68886i	−0.250757	+	0.210410i
$732$		0			0
$733$	11.2883	−	19.5520i	0.416944	−	0.722168i	−0.578686	−	0.815550i	$-0.696434\pi$
$733$	11.2883	−	19.5520i	0.416944	−	0.722168i	0.995630	+	0.0933819i	$0.0297677\pi$
$734$		0			0
$735$	22.6202	+	8.23308i	0.834359	+	0.303682i
$736$		0			0
$737$	−14.2229	−	80.6619i	−0.523906	−	2.97122i
$738$		0			0
$739$	−20.2986	−	17.0325i	−0.746696	−	0.626552i	0.187931	−	0.982182i	$-0.439822\pi$
$739$	−20.2986	−	17.0325i	−0.746696	−	0.626552i	−0.934627	+	0.355630i	$0.884266\pi$
$740$		0			0
$741$	−0.946967	−	0.282065i	−0.0347877	−	0.0103619i
$742$		0			0
$743$	21.1536	+	17.7500i	0.776052	+	0.651185i	0.942251	−	0.334907i	$-0.108705\pi$
$743$	21.1536	+	17.7500i	0.776052	+	0.651185i	−0.166199	+	0.986092i	$0.553150\pi$
$744$		0			0
$745$	−2.99582	−	16.9902i	−0.109759	−	0.622472i
$746$		0			0
$747$	1.80541	+	0.657115i	0.0660564	+	0.0240426i
$748$		0			0
$749$	−15.0282	+	26.0296i	−0.549119	+	0.951102i
$750$		0			0
$751$	−0.988140	+	0.829148i	−0.0360578	+	0.0302561i	−0.660638	−	0.750704i	$-0.729714\pi$
$751$	−0.988140	+	0.829148i	−0.0360578	+	0.0302561i	0.624581	+	0.780960i	$0.285270\pi$
$752$		0			0
$753$	−12.7836	−	22.1418i	−0.465860	−	0.806893i
$754$		0			0
$755$	5.54576	−	31.4516i	0.201831	−	1.14464i
$756$		0			0
$757$	24.3259	−	8.85392i	0.884141	−	0.321801i	0.140262	−	0.990114i	$-0.455206\pi$
$757$	24.3259	−	8.85392i	0.884141	−	0.321801i	0.743880	+	0.668313i	$0.232983\pi$
$758$		0			0
$759$	−45.9249			−1.66697
$760$		0			0
$761$	11.3396			0.411059			0.205529	−	0.978651i	$-0.434108\pi$
$761$	11.3396			0.411059			0.205529	+	0.978651i	$0.434108\pi$
$762$		0			0
$763$	53.2605	−	19.3852i	1.92816	−	0.701792i
$764$		0			0
$765$	1.01367	−	5.74881i	0.0366493	−	0.207849i
$766$		0			0
$767$	−0.0248149	−	0.0429807i	−0.000896015	−	0.00155194i
$768$		0			0
$769$	16.4283	−	13.7850i	0.592420	−	0.497099i	−0.296579	−	0.955008i	$-0.595846\pi$
$769$	16.4283	−	13.7850i	0.592420	−	0.497099i	0.888999	+	0.457909i	$0.151401\pi$
$770$		0			0
$771$	−1.39646	+	2.41874i	−0.0502923	+	0.0871087i
$772$		0			0
$773$	−3.99108	−	1.45263i	−0.143549	−	0.0522476i	0.269246	−	0.963071i	$-0.413225\pi$
$773$	−3.99108	−	1.45263i	−0.143549	−	0.0522476i	−0.412796	+	0.910824i	$0.635448\pi$
$774$		0			0
$775$	−4.05097	−	22.9742i	−0.145515	−	0.825258i
$776$		0			0
$777$	−14.6019	−	12.2525i	−0.523842	−	0.439556i
$778$		0			0
$779$	−30.9197	+	1.84413i	−1.10781	+	0.0660728i
$780$		0			0
$781$	5.49201	+	4.60834i	0.196520	+	0.164900i
$782$		0			0
$783$	0.0209445	+	0.118782i	0.000748497	+	0.00424493i
$784$		0			0
$785$	1.10442	+	0.401975i	0.0394184	+	0.0143471i
$786$		0			0
$787$	−5.41013	+	9.37062i	−0.192850	+	0.334027i	−0.946194	−	0.323601i	$-0.895107\pi$
$787$	−5.41013	+	9.37062i	−0.192850	+	0.334027i	0.753343	+	0.657627i	$0.228440\pi$
$788$		0			0
$789$	−1.06031	+	0.889704i	−0.0377479	+	0.0316743i
$790$		0			0
$791$	1.51501	+	2.62408i	0.0538677	+	0.0933016i
$792$		0			0
$793$	0.0619563	−	0.351371i	0.00220013	−	0.0124776i
$794$		0			0
$795$	19.7015	−	7.17074i	0.698739	−	0.254320i
$796$		0			0
$797$	22.0327			0.780439			0.390219	−	0.920722i	$-0.372399\pi$
$797$	22.0327			0.780439			0.390219	+	0.920722i	$0.372399\pi$
$798$		0			0
$799$	−4.14796			−0.146744
$800$		0			0
$801$	11.4226	−	4.15749i	0.403598	−	0.146898i
$802$		0			0
$803$	2.22890	−	12.6407i	0.0786563	−	0.446082i
$804$		0			0
$805$	56.9774	+	98.6877i	2.00819	+	3.47828i
$806$		0			0
$807$	−13.0817	+	10.9769i	−0.460498	+	0.386404i
$808$		0			0
$809$	−3.34343	+	5.79098i	−0.117549	+	0.203600i	−0.918796	−	0.394733i	$-0.870837\pi$
$809$	−3.34343	+	5.79098i	−0.117549	+	0.203600i	0.801247	+	0.598334i	$0.204170\pi$
$810$		0			0
$811$	23.9530	+	8.71816i	0.841102	+	0.306136i	0.726407	−	0.687265i	$-0.241189\pi$
$811$	23.9530	+	8.71816i	0.841102	+	0.306136i	0.114695	+	0.993401i	$0.463411\pi$
$812$		0			0
$813$	4.46064	+	25.2975i	0.156441	+	0.887223i
$814$		0			0
$815$	10.6630	+	8.94729i	0.373508	+	0.313410i
$816$		0			0
$817$	10.4468	−	20.8738i	0.365487	−	0.730282i
$818$		0			0
$819$	0.645430	+	0.541580i	0.0225531	+	0.0189243i
$820$		0			0
$821$	−7.34348	−	41.6470i	−0.256289	−	1.45349i	−0.792741	−	0.609558i	$-0.791347\pi$
$821$	−7.34348	−	41.6470i	−0.256289	−	1.45349i	0.536452	−	0.843931i	$-0.319764\pi$
$822$		0			0
$823$	−0.506397	−	0.184313i	−0.0176519	−	0.00642476i	0.333179	−	0.942864i	$-0.391879\pi$
$823$	−0.506397	−	0.184313i	−0.0176519	−	0.00642476i	−0.350831	+	0.936439i	$0.614101\pi$
$824$		0			0
$825$	−19.7763	+	34.2536i	−0.688523	+	1.19256i
$826$		0			0
$827$	12.2745	−	10.2995i	0.426826	−	0.358150i	−0.403926	−	0.914791i	$-0.632355\pi$
$827$	12.2745	−	10.2995i	0.426826	−	0.358150i	0.830753	+	0.556642i	$0.187910\pi$
$828$		0			0
$829$	10.0517	+	17.4100i	0.349110	+	0.604676i	0.986092	−	0.166203i	$-0.0531508\pi$
$829$	10.0517	+	17.4100i	0.349110	+	0.604676i	−0.636982	+	0.770879i	$0.719817\pi$
$830$		0			0
$831$	3.85932	−	21.8873i	0.133878	−	0.759261i
$832$		0			0
$833$	10.5842	−	3.85235i	0.366722	−	0.133476i
$834$		0			0
$835$	21.1685			0.732566
$836$		0			0
$837$	−3.12061			−0.107864
$838$		0			0
$839$	29.1031	−	10.5927i	1.00475	−	0.365700i	0.213337	−	0.976979i	$-0.431567\pi$
$839$	29.1031	−	10.5927i	1.00475	−	0.365700i	0.791415	+	0.611279i	$0.209345\pi$
$840$		0			0
$841$	−5.03327	+	28.5451i	−0.173561	+	0.984314i
$842$		0			0
$843$	−0.771974	−	1.33710i	−0.0265882	−	0.0460521i
$844$		0			0
$845$	35.0355	−	29.3983i	1.20526	−	1.01133i
$846$		0			0
$847$	31.5808	−	54.6996i	1.08513	−	1.87950i
$848$		0			0
$849$	9.67024	+	3.51968i	0.331882	+	0.120795i
$850$		0			0
$851$	−7.72984	−	43.8381i	−0.264975	−	1.50275i
$852$		0			0
$853$	−16.3209	−	13.6949i	−0.558817	−	0.468903i	0.319097	−	0.947722i	$-0.396620\pi$
$853$	−16.3209	−	13.6949i	−0.558817	−	0.468903i	−0.877913	+	0.478819i	$0.841065\pi$
$854$		0			0
$855$	3.57145	+	14.9761i	0.122141	+	0.512170i
$856$		0			0
$857$	42.5551	+	35.7080i	1.45366	+	1.21976i	0.929857	+	0.367920i	$0.119930\pi$
$857$	42.5551	+	35.7080i	1.45366	+	1.21976i	0.523799	+	0.851842i	$0.324514\pi$
$858$		0			0
$859$	4.11902	+	23.3601i	0.140539	+	0.797038i	0.970841	+	0.239724i	$0.0770569\pi$
$859$	4.11902	+	23.3601i	0.140539	+	0.797038i	−0.830302	+	0.557314i	$0.811832\pi$
$860$		0			0
$861$	24.8195	+	9.03358i	0.845848	+	0.307863i
$862$		0			0
$863$	10.5410	−	18.2576i	0.358820	−	0.621495i	−0.628944	−	0.777451i	$-0.716512\pi$
$863$	10.5410	−	18.2576i	0.358820	−	0.621495i	0.987764	+	0.155956i	$0.0498458\pi$
$864$		0			0
$865$	−33.1771	+	27.8389i	−1.12806	+	0.946551i
$866$		0			0
$867$	7.13429	+	12.3569i	0.242293	+	0.419664i
$868$		0			0
$869$	2.63206	−	14.9272i	0.0892866	−	0.506370i
$870$		0			0
$871$	−3.29756	+	1.20021i	−0.111734	+	0.0406677i
$872$		0			0
$873$	17.5030			0.592387
$874$		0			0
$875$	32.5012			1.09874
$876$		0			0
$877$	48.1134	−	17.5118i	1.62467	−	0.591333i	0.640409	−	0.768034i	$-0.278765\pi$
$877$	48.1134	−	17.5118i	1.62467	−	0.591333i	0.984265	+	0.176701i	$0.0565425\pi$
$878$		0			0
$879$	−4.94949	+	28.0700i	−0.166942	+	0.946777i
$880$		0			0
$881$	17.0804	+	29.5841i	0.575452	+	0.996713i	0.995992	+	0.0894388i	$0.0285074\pi$
$881$	17.0804	+	29.5841i	0.575452	+	0.996713i	−0.420540	+	0.907274i	$0.638159\pi$
$882$		0			0
$883$	−21.5403	+	18.0745i	−0.724889	+	0.608254i	−0.928733	−	0.370750i	$-0.879101\pi$
$883$	−21.5403	+	18.0745i	−0.724889	+	0.608254i	0.203844	+	0.979003i	$0.434656\pi$
$884$		0			0
$885$	−0.386659	+	0.669713i	−0.0129974	+	0.0225122i
$886$		0			0
$887$	−33.4298	−	12.1674i	−1.12246	−	0.408543i	−0.286912	−	0.957957i	$-0.592629\pi$
$887$	−33.4298	−	12.1674i	−1.12246	−	0.408543i	−0.835550	+	0.549414i	$0.814851\pi$
$888$		0			0
$889$	7.14115	+	40.4995i	0.239506	+	1.35831i
$890$		0			0
$891$	4.05303	+	3.40090i	0.135782	+	0.113934i
$892$		0			0
$893$	10.0392	−	4.34710i	0.335949	−	0.145470i
$894$		0			0
$895$	21.8195	+	18.3088i	0.729347	+	0.611995i
$896$		0			0
$897$	0.341671	+	1.93771i	0.0114081	+	0.0646984i
$898$		0			0
$899$	0.353693	+	0.128734i	0.0117963	+	0.00429351i
$900$		0			0
$901$	4.90508	−	8.49584i	0.163412	−	0.283038i
$902$		0			0
$903$	−15.2474	+	12.7941i	−0.507401	+	0.425760i
$904$		0			0
$905$	0.335275	+	0.580713i	0.0111449	+	0.0193035i
$906$		0			0
$907$	1.61422	−	9.15469i	0.0535992	−	0.303976i	−0.946209	−	0.323556i	$-0.895122\pi$
$907$	1.61422	−	9.15469i	0.0535992	−	0.303976i	0.999808	+	0.0195795i	$0.00623275\pi$
$908$		0			0
$909$	−14.1099	+	5.13560i	−0.467997	+	0.170337i
$910$		0			0
$911$	−3.79055			−0.125587			−0.0627933	−	0.998027i	$-0.520001\pi$
$911$	−3.79055			−0.125587			−0.0627933	+	0.998027i	$0.520001\pi$
$912$		0			0
$913$	−10.1652			−0.336419
$914$		0			0
$915$	−5.22416	+	1.90144i	−0.172705	+	0.0628596i
$916$		0			0
$917$	−9.29394	+	52.7085i	−0.306913	+	1.74059i
$918$		0			0
$919$	−2.21554	−	3.83742i	−0.0730838	−	0.126585i	0.827168	−	0.561955i	$-0.189951\pi$
$919$	−2.21554	−	3.83742i	−0.0730838	−	0.126585i	−0.900251	+	0.435370i	$0.856617\pi$
$920$		0			0
$921$	19.5797	−	16.4293i	0.645172	−	0.541363i
$922$		0			0
$923$	0.153581	−	0.266010i	0.00505518	−	0.00875583i
$924$		0			0
$925$	−36.0257	−	13.1123i	−1.18452	−	0.431130i
$926$		0			0
$927$	−1.15657	−	6.55926i	−0.0379869	−	0.215434i
$928$		0			0
$929$	23.3384	+	19.5833i	0.765709	+	0.642506i	0.939606	−	0.342258i	$-0.111192\pi$
$929$	23.3384	+	19.5833i	0.765709	+	0.642506i	−0.173897	+	0.984764i	$0.555636\pi$
$930$		0			0
$931$	−21.5795	+	20.4162i	−0.707239	+	0.669112i
$932$		0			0
$933$	−7.94743	−	6.66869i	−0.260187	−	0.218323i
$934$		0			0
$935$	5.36319	+	30.4162i	0.175395	+	0.994715i
$936$		0			0
$937$	1.34477	+	0.489456i	0.0439317	+	0.0159898i	0.363893	−	0.931441i	$-0.381448\pi$
$937$	1.34477	+	0.489456i	0.0439317	+	0.0159898i	−0.319961	+	0.947431i	$0.603670\pi$
$938$		0			0
$939$	7.71823	−	13.3684i	0.251875	−	0.436260i
$940$		0			0
$941$	3.47384	−	2.91490i	0.113244	−	0.0950230i	−0.584407	−	0.811460i	$-0.698673\pi$
$941$	3.47384	−	2.91490i	0.113244	−	0.0950230i	0.697651	+	0.716437i	$0.254229\pi$
$942$		0			0
$943$	30.8405	+	53.4173i	1.00430	+	1.73951i
$944$		0			0
$945$	2.27972	−	12.9289i	0.0741591	−	0.420577i
$946$		0			0
$947$	0.388881	−	0.141541i	0.0126369	−	0.00459946i	−0.335694	−	0.941971i	$-0.608971\pi$
$947$	0.388881	−	0.141541i	0.0126369	−	0.00459946i	0.348331	+	0.937372i	$0.386749\pi$
$948$		0			0
$949$	−0.549935			−0.0178516
$950$		0			0
$951$	28.3969			0.920833
$952$		0			0
$953$	−13.3678	+	4.86549i	−0.433027	+	0.157609i	−0.549331	−	0.835605i	$-0.685117\pi$
$953$	−13.3678	+	4.86549i	−0.433027	+	0.157609i	0.116304	+	0.993214i	$0.462895\pi$
$954$		0			0
$955$	11.0633	−	62.7431i	0.358000	−	2.03032i
$956$		0			0
$957$	−0.319078	−	0.552659i	−0.0103143	−	0.0178649i
$958$		0			0
$959$	1.34667	−	1.12999i	0.0434862	−	0.0364892i
$960$		0			0
$961$	10.6309	−	18.4132i	0.342932	−	0.593975i
$962$		0			0
$963$	7.59879	+	2.76573i	0.244868	+	0.0891245i
$964$		0			0
$965$	10.6959	+	60.6597i	0.344314	+	1.95270i
$966$		0			0
$967$	43.5376	+	36.5324i	1.40008	+	1.17480i	0.961066	+	0.276320i	$0.0891150\pi$
$967$	43.5376	+	36.5324i	1.40008	+	1.17480i	0.439009	+	0.898482i	$0.355329\pi$
$968$		0			0
$969$	5.78446	+	4.29385i	0.185824	+	0.137938i
$970$		0			0
$971$	6.94356	+	5.82634i	0.222830	+	0.186976i	0.747368	−	0.664411i	$-0.231317\pi$
$971$	6.94356	+	5.82634i	0.222830	+	0.186976i	−0.524538	+	0.851387i	$0.675762\pi$
$972$		0			0
$973$	−6.57357	−	37.2806i	−0.210739	−	1.19516i
$974$		0			0
$975$	1.59240	+	0.579585i	0.0509975	+	0.0185616i
$976$		0			0
$977$	1.32635	−	2.29731i	0.0424338	−	0.0734974i	−0.844028	−	0.536298i	$-0.819822\pi$
$977$	1.32635	−	2.29731i	0.0424338	−	0.0734974i	0.886462	+	0.462801i	$0.153156\pi$
$978$		0			0
$979$	−49.2674	+	41.3403i	−1.57459	+	1.32124i
$980$		0			0
$981$	−7.62449	−	13.2060i	−0.243431	−	0.421635i
$982$		0			0
$983$	9.34183	−	52.9802i	0.297958	−	1.68980i	−0.356972	−	0.934115i	$-0.616191\pi$
$983$	9.34183	−	52.9802i	0.297958	−	1.68980i	0.654930	−	0.755690i	$-0.272698\pi$
$984$		0			0
$985$	−34.7863	+	12.6612i	−1.10838	+	0.403418i
$986$		0			0
$987$	−9.32863			−0.296934
$988$		0			0
$989$	−46.4820			−1.47804
$990$		0			0
$991$	50.3598	−	18.3295i	1.59973	−	0.582255i	0.620360	−	0.784317i	$-0.286986\pi$
$991$	50.3598	−	18.3295i	1.59973	−	0.582255i	0.979373	+	0.202062i	$0.0647642\pi$
$992$		0			0
$993$	4.50134	−	25.5284i	0.142846	−	0.810119i
$994$		0			0
$995$	24.1129	+	41.7648i	0.764431	+	1.32403i
$996$		0			0
$997$	13.8938	−	11.6583i	0.440020	−	0.369221i	−0.395697	−	0.918381i	$-0.629497\pi$
$997$	13.8938	−	11.6583i	0.440020	−	0.369221i	0.835717	+	0.549160i	$0.185052\pi$
$998$		0			0
$999$	−2.56418	+	4.44129i	−0.0811270	+	0.140516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.d.529.1		6
4.3	odd	2		114.2.i.c.73.1	yes	6
12.11	even	2		342.2.u.b.73.1		6
19.6	even	9	inner	912.2.bo.d.481.1		6
76.43	odd	18		2166.2.a.r.1.1		3
76.63	odd	18		114.2.i.c.25.1	✓	6
76.71	even	18		2166.2.a.p.1.1		3
228.71	odd	18		6498.2.a.bu.1.3		3
228.119	even	18		6498.2.a.bp.1.3		3
228.215	even	18		342.2.u.b.253.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.c.25.1	✓	6	76.63	odd	18
114.2.i.c.73.1	yes	6	4.3	odd	2
342.2.u.b.73.1		6	12.11	even	2
342.2.u.b.253.1		6	228.215	even	18
912.2.bo.d.481.1		6	19.6	even	9	inner
912.2.bo.d.529.1		6	1.1	even	1	trivial
2166.2.a.p.1.1		3	76.71	even	18
2166.2.a.r.1.1		3	76.43	odd	18
6498.2.a.bp.1.3		3	228.119	even	18
6498.2.a.bu.1.3		3	228.71	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.613341 + 3.47843i) q^{5} +(1.85844 + 3.21891i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-2.64543 + 4.58202i) q^{11} +(0.213011 + 0.0775297i) q^{13} +(-0.613341 - 3.47843i) q^{15} +(-1.26604 - 1.06234i) q^{17} +(4.17752 + 1.24432i) q^{19} +(-2.84730 - 2.38917i) q^{21} +(-1.50727 - 8.54818i) q^{23} +(-7.02481 - 2.55682i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(0.0923963 - 0.0775297i) q^{29} +(1.56031 + 2.70253i) q^{31} +(0.918748 - 5.21048i) q^{33} +(-12.3366 + 4.49016i) q^{35} +5.12836 q^{37} -0.226682 q^{39} +(-6.67752 + 2.43042i) q^{41} +(0.929892 - 5.27368i) q^{43} +(1.76604 + 3.05888i) q^{45} +(1.92262 - 1.61327i) q^{47} +(-3.40760 + 5.90214i) q^{49} +(1.55303 + 0.565258i) q^{51} +(1.03074 + 5.84564i) q^{53} +(-14.3157 - 12.0123i) q^{55} +(-4.35117 + 0.259515i) q^{57} +(-0.167718 - 0.140732i) q^{59} +(-0.273318 - 1.55007i) q^{61} +(3.49273 + 1.27125i) q^{63} +(-0.400330 + 0.693392i) q^{65} +(-11.8589 + 9.95080i) q^{67} +(4.34002 + 7.51714i) q^{69} +(0.235300 - 1.33445i) q^{71} +(-2.27972 + 0.829748i) q^{73} +7.47565 q^{75} -19.6655 q^{77} +(-2.69207 + 0.979832i) q^{79} +(0.173648 - 0.984808i) q^{81} +(0.960637 + 1.66387i) q^{83} +(4.47178 - 3.75227i) q^{85} +(-0.0603074 + 0.104455i) q^{87} +(11.4226 + 4.15749i) q^{89} +(0.146307 + 0.829748i) q^{91} +(-2.39053 - 2.00589i) q^{93} +(-6.89053 + 13.7680i) q^{95} +(13.4081 + 11.2507i) q^{97} +(0.918748 + 5.21048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} + 9 q^{13} + 3 q^{15} - 3 q^{17} - 15 q^{21} - 27 q^{23} - 15 q^{25} - 3 q^{27} - 3 q^{29} + 15 q^{31} + 3 q^{33} - 12 q^{35} - 6 q^{37} + 12 q^{39} - 15 q^{41} - 3 q^{43} + 6 q^{45}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 + 9 * q^13 + 3 * q^15 - 3 * q^17 - 15 * q^21 - 27 * q^23 - 15 * q^25 - 3 * q^27 - 3 * q^29 + 15 * q^31 + 3 * q^33 - 12 * q^35 - 6 * q^37 + 12 * q^39 - 15 * q^41 - 3 * q^43 + 6 * q^45 - 15 * q^47 - 24 * q^49 - 3 * q^51 + 6 * q^53 - 27 * q^55 + 27 * q^59 - 15 * q^61 + 3 * q^63 + 12 * q^65 + 3 * q^67 + 6 * q^69 - 3 * q^71 + 12 * q^73 + 6 * q^75 - 42 * q^77 - 27 * q^79 - 3 * q^83 + 12 * q^85 - 6 * q^87 + 42 * q^89 + 42 * q^91 + 3 * q^93 - 24 * q^95 + 18 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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