LMFDB - Embedded newform 792.2.q.f.265.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(265,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.265"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,1,0,-4] 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:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 7x^{10} - 2x^{9} + 39x^{8} - 9x^{7} + 67x^{6} - 18x^{5} + 88x^{4} - 16x^{3} + 24x^{2} + 4x + 4 $ x^12 + 7x^10 - 2x^9 + 39x^8 - 9x^7 + 67x^6 - 18x^5 + 88x^4 - 16x^3 + 24x^2 + 4x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			265.5
Root			$-0.654157 - 1.13303i$ of defining polynomial
Character	$\chi$	$=$	792.265
Dual form			792.2.q.f.529.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23257 - 1.21686i) q^{3} +(-0.644157 + 1.11571i) q^{5} +(2.04089 + 3.53492i) q^{7} +(0.0384795 - 2.99975i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-0.317363 + 0.549690i) q^{13} +(0.563700 + 2.15905i) q^{15} +1.87510 q^{17} +6.37009 q^{19} +(6.81707 + 1.87357i) q^{21} +(-0.379815 + 0.657858i) q^{23} +(1.67012 + 2.89274i) q^{25} +(-3.60287 - 3.74424i) q^{27} +(2.34297 + 4.05813i) q^{29} +(-2.85825 + 4.95064i) q^{31} +(-1.67012 - 0.459008i) q^{33} -5.25861 q^{35} +3.77232 q^{37} +(0.277724 + 1.06372i) q^{39} +(3.52241 - 6.10099i) q^{41} +(-1.37077 - 2.37424i) q^{43} +(3.32208 + 1.97524i) q^{45} +(-1.76867 - 3.06343i) q^{47} +(-4.83045 + 8.36659i) q^{49} +(2.31120 - 2.28174i) q^{51} +2.90262 q^{53} +1.28831 q^{55} +(7.85161 - 7.75154i) q^{57} +(2.48116 - 4.29749i) q^{59} +(3.96207 + 6.86250i) q^{61} +(10.6824 - 5.98614i) q^{63} +(-0.408864 - 0.708173i) q^{65} +(4.45563 - 7.71737i) q^{67} +(0.332375 + 1.27304i) q^{69} -9.98378 q^{71} -9.27177 q^{73} +(5.57862 + 1.53320i) q^{75} +(2.04089 - 3.53492i) q^{77} +(-8.25154 - 14.2921i) q^{79} +(-8.99704 - 0.230858i) q^{81} +(-8.44755 - 14.6316i) q^{83} +(-1.20786 + 2.09207i) q^{85} +(7.82608 + 2.15088i) q^{87} -2.39069 q^{89} -2.59081 q^{91} +(2.50125 + 9.58014i) q^{93} +(-4.10334 + 7.10719i) q^{95} +(6.01708 + 10.4219i) q^{97} +(-2.61710 + 1.46655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{3} - 4 q^{5} - 5 q^{7} + 5 q^{9} - 6 q^{11} - 3 q^{13} - 7 q^{15} + 14 q^{17} + 10 q^{19} + 9 q^{21} - 8 q^{23} + 2 q^{25} - 11 q^{27} - 8 q^{29} - 4 q^{31} - 2 q^{33} + 16 q^{35} + 6 q^{37}+ \cdots - 7 q^{99}+O(q^{100}) $ 12 * q + q^3 - 4 * q^5 - 5 * q^7 + 5 * q^9 - 6 * q^11 - 3 * q^13 - 7 * q^15 + 14 * q^17 + 10 * q^19 + 9 * q^21 - 8 * q^23 + 2 * q^25 - 11 * q^27 - 8 * q^29 - 4 * q^31 - 2 * q^33 + 16 * q^35 + 6 * q^37 + 14 * q^39 - 5 * q^43 + 25 * q^45 - 17 * q^47 - 3 * q^49 - 15 * q^51 + 28 * q^53 + 8 * q^55 + 15 * q^57 - 4 * q^59 - q^61 + 15 * q^63 - 15 * q^65 + 4 * q^67 - 14 * q^69 + 14 * q^71 - 24 * q^73 + 38 * q^75 - 5 * q^77 - q^79 + 5 * q^81 - 22 * q^83 + 3 * q^85 - q^87 + 44 * q^89 + 22 * q^91 + 12 * q^93 - 24 * q^95 + 16 * q^97 - 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.23257	−	1.21686i	0.711627	−	0.702557i
$3$	1.23257	−	1.21686i	0.711627	−	0.702557i
$4$		0			0
$5$	−0.644157	+	1.11571i	−0.288076	+	0.498962i	−0.973350	−	0.229323i	$-0.926349\pi$
$5$	−0.644157	+	1.11571i	−0.288076	+	0.498962i	0.685275	+	0.728285i	$0.259682\pi$
$6$		0			0
$7$	2.04089	+	3.53492i	0.771383	+	1.33608i	0.936805	+	0.349852i	$0.113768\pi$
$7$	2.04089	+	3.53492i	0.771383	+	1.33608i	−0.165422	+	0.986223i	$0.552898\pi$
$8$		0			0
$9$	0.0384795	−	2.99975i	0.0128265	−	0.999918i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−0.317363	+	0.549690i	−0.0880208	+	0.152456i	−0.906674	−	0.421831i	$-0.861388\pi$
$13$	−0.317363	+	0.549690i	−0.0880208	+	0.152456i	0.818654	+	0.574288i	$0.194721\pi$
$14$		0			0
$15$	0.563700	+	2.15905i	0.145547	+	0.557465i
$16$		0			0
$17$	1.87510			0.454778			0.227389	−	0.973804i	$-0.426981\pi$
$17$	1.87510			0.454778			0.227389	+	0.973804i	$0.426981\pi$
$18$		0			0
$19$	6.37009			1.46140			0.730700	−	0.682699i	$-0.239194\pi$
$19$	6.37009			1.46140			0.730700	+	0.682699i	$0.239194\pi$
$20$		0			0
$21$	6.81707	+	1.87357i	1.48761	+	0.408846i
$22$		0			0
$23$	−0.379815	+	0.657858i	−0.0791968	+	0.137173i	−0.902904	−	0.429843i	$-0.858569\pi$
$23$	−0.379815	+	0.657858i	−0.0791968	+	0.137173i	0.823707	+	0.567016i	$0.191902\pi$
$24$		0			0
$25$	1.67012	+	2.89274i	0.334025	+	0.578548i
$26$		0			0
$27$	−3.60287	−	3.74424i	−0.693372	−	0.720580i
$28$		0			0
$29$	2.34297	+	4.05813i	0.435078	+	0.753577i	0.997302	−	0.0734081i	$-0.0233876\pi$
$29$	2.34297	+	4.05813i	0.435078	+	0.753577i	−0.562224	+	0.826985i	$0.690054\pi$
$30$		0			0
$31$	−2.85825	+	4.95064i	−0.513357	+	0.889161i	0.486523	+	0.873668i	$0.338265\pi$
$31$	−2.85825	+	4.95064i	−0.513357	+	0.889161i	−0.999880	+	0.0154929i	$0.995068\pi$
$32$		0			0
$33$	−1.67012	−	0.459008i	−0.290731	−	0.0799031i
$34$		0			0
$35$	−5.25861			−0.888868
$36$		0			0
$37$	3.77232			0.620166			0.310083	−	0.950709i	$-0.399643\pi$
$37$	3.77232			0.620166			0.310083	+	0.950709i	$0.399643\pi$
$38$		0			0
$39$	0.277724	+	1.06372i	0.0444714	+	0.170332i
$40$		0			0
$41$	3.52241	−	6.10099i	0.550108	−	0.952815i	−0.448158	−	0.893954i	$-0.647920\pi$
$41$	3.52241	−	6.10099i	0.550108	−	0.952815i	0.998266	−	0.0588606i	$-0.0187467\pi$
$42$		0			0
$43$	−1.37077	−	2.37424i	−0.209040	−	0.362067i	0.742373	−	0.669987i	$-0.233700\pi$
$43$	−1.37077	−	2.37424i	−0.209040	−	0.362067i	−0.951412	+	0.307920i	$0.900367\pi$
$44$		0			0
$45$	3.32208	+	1.97524i	0.495226	+	0.294452i
$46$		0			0
$47$	−1.76867	−	3.06343i	−0.257988	−	0.446848i	0.707715	−	0.706498i	$-0.249726\pi$
$47$	−1.76867	−	3.06343i	−0.257988	−	0.446848i	−0.965703	+	0.259650i	$0.916393\pi$
$48$		0			0
$49$	−4.83045	+	8.36659i	−0.690065	+	1.19523i
$50$		0			0
$51$	2.31120	−	2.28174i	0.323632	−	0.319508i
$52$		0			0
$53$	2.90262			0.398706			0.199353	−	0.979928i	$-0.436116\pi$
$53$	2.90262			0.398706			0.199353	+	0.979928i	$0.436116\pi$
$54$		0			0
$55$	1.28831			0.173716
$56$		0			0
$57$	7.85161	−	7.75154i	1.03997	−	1.02672i
$58$		0			0
$59$	2.48116	−	4.29749i	0.323019	−	0.559485i	−0.658090	−	0.752939i	$-0.728636\pi$
$59$	2.48116	−	4.29749i	0.323019	−	0.559485i	0.981109	+	0.193454i	$0.0619689\pi$
$60$		0			0
$61$	3.96207	+	6.86250i	0.507291	+	0.878653i	0.999964	+	0.00843895i	$0.00268623\pi$
$61$	3.96207	+	6.86250i	0.507291	+	0.878653i	−0.492674	+	0.870214i	$0.663980\pi$
$62$		0			0
$63$	10.6824	−	5.98614i	1.34586	−	0.754183i
$64$		0			0
$65$	−0.408864	−	0.708173i	−0.0507133	−	0.0878380i
$66$		0			0
$67$	4.45563	−	7.71737i	0.544341	−	0.942827i	−0.454307	−	0.890845i	$-0.650113\pi$
$67$	4.45563	−	7.71737i	0.544341	−	0.942827i	0.998648	−	0.0519815i	$-0.0165537\pi$
$68$		0			0
$69$	0.332375	+	1.27304i	0.0400132	+	0.153256i
$70$		0			0
$71$	−9.98378			−1.18486			−0.592428	−	0.805623i	$-0.701831\pi$
$71$	−9.98378			−1.18486			−0.592428	+	0.805623i	$0.701831\pi$
$72$		0			0
$73$	−9.27177			−1.08518			−0.542589	−	0.839998i	$-0.682556\pi$
$73$	−9.27177			−1.08518			−0.542589	+	0.839998i	$0.682556\pi$
$74$		0			0
$75$	5.57862	+	1.53320i	0.644164	+	0.177039i
$76$		0			0
$77$	2.04089	−	3.53492i	0.232581	−	0.402842i
$78$		0			0
$79$	−8.25154	−	14.2921i	−0.928370	−	1.60798i	−0.786049	−	0.618164i	$-0.787877\pi$
$79$	−8.25154	−	14.2921i	−0.928370	−	1.60798i	−0.142321	−	0.989821i	$-0.545457\pi$
$80$		0			0
$81$	−8.99704	−	0.230858i	−0.999671	−	0.0256509i
$82$		0			0
$83$	−8.44755	−	14.6316i	−0.927240	−	1.60603i	−0.787919	−	0.615779i	$-0.788842\pi$
$83$	−8.44755	−	14.6316i	−0.927240	−	1.60603i	−0.139320	−	0.990247i	$-0.544492\pi$
$84$		0			0
$85$	−1.20786	+	2.09207i	−0.131011	+	0.226917i
$86$		0			0
$87$	7.82608	+	2.15088i	0.839044	+	0.230599i
$88$		0			0
$89$	−2.39069			−0.253412			−0.126706	−	0.991940i	$-0.540441\pi$
$89$	−2.39069			−0.253412			−0.126706	+	0.991940i	$0.540441\pi$
$90$		0			0
$91$	−2.59081			−0.271591
$92$		0			0
$93$	2.50125	+	9.58014i	0.259367	+	0.993414i
$94$		0			0
$95$	−4.10334	+	7.10719i	−0.420994	+	0.729183i
$96$		0			0
$97$	6.01708	+	10.4219i	0.610942	+	1.05818i	0.991082	+	0.133254i	$0.0425425\pi$
$97$	6.01708	+	10.4219i	0.610942	+	1.05818i	−0.380140	+	0.924929i	$0.624124\pi$
$98$		0			0
$99$	−2.61710	+	1.46655i	−0.263029	+	0.147394i
$100$		0			0
$101$	−3.51431	−	6.08696i	−0.349687	−	0.605675i	0.636507	−	0.771271i	$-0.280379\pi$
$101$	−3.51431	−	6.08696i	−0.349687	−	0.605675i	−0.986194	+	0.165596i	$0.947045\pi$
$102$		0			0
$103$	−4.04279	+	7.00232i	−0.398348	+	0.689960i	−0.993522	−	0.113637i	$-0.963750\pi$
$103$	−4.04279	+	7.00232i	−0.398348	+	0.689960i	0.595174	+	0.803597i	$0.297083\pi$
$104$		0			0
$105$	−6.48163	+	6.39902i	−0.632542	+	0.624480i
$106$		0			0
$107$	7.14038			0.690286			0.345143	−	0.938550i	$-0.387830\pi$
$107$	7.14038			0.690286			0.345143	+	0.938550i	$0.387830\pi$
$108$		0			0
$109$	−6.40838			−0.613812			−0.306906	−	0.951740i	$-0.599294\pi$
$109$	−6.40838			−0.613812			−0.306906	+	0.951740i	$0.599294\pi$
$110$		0			0
$111$	4.64967	−	4.59041i	0.441327	−	0.435702i
$112$		0			0
$113$	−6.42460	+	11.1277i	−0.604376	+	1.04681i	0.387774	+	0.921754i	$0.373244\pi$
$113$	−6.42460	+	11.1277i	−0.604376	+	1.04681i	−0.992150	+	0.125055i	$0.960089\pi$
$114$		0			0
$115$	−0.489321	−	0.847528i	−0.0456294	−	0.0790324i
$116$		0			0
$117$	1.63672	+	0.973164i	0.151315	+	0.0899690i
$118$		0			0
$119$	3.82686	+	6.62832i	0.350808	+	0.607618i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−3.08245	−	11.8062i	−0.277935	−	1.06453i
$124$		0			0
$125$	−10.7449			−0.961049
$126$		0			0
$127$	14.1597			1.25647			0.628235	−	0.778023i	$-0.283777\pi$
$127$	14.1597			1.25647			0.628235	+	0.778023i	$0.283777\pi$
$128$		0			0
$129$	−4.57869	−	1.25839i	−0.403132	−	0.110795i
$130$		0			0
$131$	−9.16523	+	15.8746i	−0.800770	+	1.38697i	0.118341	+	0.992973i	$0.462243\pi$
$131$	−9.16523	+	15.8746i	−0.800770	+	1.38697i	−0.919110	+	0.394001i	$0.871091\pi$
$132$		0			0
$133$	13.0006	+	22.5178i	1.12730	+	1.95254i
$134$		0			0
$135$	6.49831	−	1.60788i	0.559286	−	0.138385i
$136$		0			0
$137$	−1.71691	−	2.97377i	−0.146685	−	0.254066i	0.783315	−	0.621625i	$-0.213527\pi$
$137$	−1.71691	−	2.97377i	−0.146685	−	0.254066i	−0.930000	+	0.367558i	$0.880194\pi$
$138$		0			0
$139$	−2.74271	+	4.75051i	−0.232634	+	0.402933i	−0.958582	−	0.284816i	$-0.908068\pi$
$139$	−2.74271	+	4.75051i	−0.232634	+	0.402933i	0.725949	+	0.687749i	$0.241401\pi$
$140$		0			0
$141$	−5.90781	−	1.62367i	−0.497527	−	0.136738i
$142$		0			0
$143$	0.634727			0.0530785
$144$		0			0
$145$	−6.03695			−0.501341
$146$		0			0
$147$	4.22712	+	16.1904i	0.348647	+	1.33537i
$148$		0			0
$149$	1.27194	−	2.20307i	0.104202	−	0.180482i	−0.809210	−	0.587519i	$-0.800105\pi$
$149$	1.27194	−	2.20307i	0.104202	−	0.180482i	0.913412	+	0.407037i	$0.133438\pi$
$150$		0			0
$151$	−5.61804	−	9.73073i	−0.457190	−	0.791876i	0.541621	−	0.840623i	$-0.317811\pi$
$151$	−5.61804	−	9.73073i	−0.457190	−	0.791876i	−0.998811	+	0.0487467i	$0.984477\pi$
$152$		0			0
$153$	0.0721527	−	5.62483i	0.00583320	−	0.454741i
$154$		0			0
$155$	−3.68233	−	6.37798i	−0.295772	−	0.512291i
$156$		0			0
$157$	5.64620	−	9.77951i	0.450616	−	0.780490i	−0.547808	−	0.836604i	$-0.684538\pi$
$157$	5.64620	−	9.77951i	0.450616	−	0.780490i	0.998424	+	0.0561141i	$0.0178710\pi$
$158$		0			0
$159$	3.57770	−	3.53210i	0.283730	−	0.280114i
$160$		0			0
$161$	−3.10064			−0.244364
$162$		0			0
$163$	−14.8053			−1.15964			−0.579819	−	0.814745i	$-0.696877\pi$
$163$	−14.8053			−1.15964			−0.579819	+	0.814745i	$0.696877\pi$
$164$		0			0
$165$	1.58794	−	1.56770i	0.123621	−	0.122046i
$166$		0			0
$167$	−2.90539	+	5.03228i	−0.224826	+	0.389409i	−0.956267	−	0.292495i	$-0.905515\pi$
$167$	−2.90539	+	5.03228i	−0.224826	+	0.389409i	0.731442	+	0.681904i	$0.238848\pi$
$168$		0			0
$169$	6.29856	+	10.9094i	0.484505	+	0.839187i
$170$		0			0
$171$	0.245118	−	19.1087i	0.0187446	−	1.46128i
$172$		0			0
$173$	−11.7193	−	20.2984i	−0.891001	−	1.54326i	−0.838677	−	0.544630i	$-0.816670\pi$
$173$	−11.7193	−	20.2984i	−0.891001	−	1.54326i	−0.0523247	−	0.998630i	$-0.516663\pi$
$174$		0			0
$175$	−6.81707	+	11.8075i	−0.515322	+	0.892564i
$176$		0			0
$177$	−2.17125	−	8.31621i	−0.163201	−	0.625084i
$178$		0			0
$179$	−19.1537			−1.43162			−0.715808	−	0.698297i	$-0.753941\pi$
$179$	−19.1537			−1.43162			−0.715808	+	0.698297i	$0.753941\pi$
$180$		0			0
$181$	26.7543			1.98864			0.994318	−	0.106455i	$-0.0339499\pi$
$181$	26.7543			1.98864			0.994318	+	0.106455i	$0.0339499\pi$
$182$		0			0
$183$	13.2343	+	3.63724i	0.978306	+	0.268873i
$184$		0			0
$185$	−2.42997	+	4.20883i	−0.178655	+	0.309439i
$186$		0			0
$187$	−0.937549	−	1.62388i	−0.0685604	−	0.118750i
$188$		0			0
$189$	5.88256	−	20.3774i	0.427894	−	1.48224i
$190$		0			0
$191$	−11.7451	−	20.3431i	−0.849845	−	1.47198i	−0.881346	−	0.472472i	$-0.843362\pi$
$191$	−11.7451	−	20.3431i	−0.849845	−	1.47198i	0.0315007	−	0.999504i	$-0.489971\pi$
$192$		0			0
$193$	−7.55091	+	13.0786i	−0.543527	+	0.941416i	0.455171	+	0.890404i	$0.349578\pi$
$193$	−7.55091	+	13.0786i	−0.543527	+	0.941416i	−0.998698	+	0.0510120i	$0.983755\pi$
$194$		0			0
$195$	−1.36571	−	0.375344i	−0.0978002	−	0.0268789i
$196$		0			0
$197$	16.5092			1.17623			0.588116	−	0.808777i	$-0.299870\pi$
$197$	16.5092			1.17623			0.588116	+	0.808777i	$0.299870\pi$
$198$		0			0
$199$	3.87009			0.274344			0.137172	−	0.990547i	$-0.456199\pi$
$199$	3.87009			0.274344			0.137172	+	0.990547i	$0.456199\pi$
$200$		0			0
$201$	−3.89911	−	14.9341i	−0.275022	−	1.05337i
$202$		0			0
$203$	−9.56346	+	16.5644i	−0.671223	+	1.16259i
$204$		0			0
$205$	4.53797	+	7.85999i	0.316946	+	0.548966i
$206$		0			0
$207$	1.95880	+	1.16466i	0.136146	+	0.0809498i
$208$		0			0
$209$	−3.18505	−	5.51666i	−0.220314	−	0.381595i
$210$		0			0
$211$	−0.760845	+	1.31782i	−0.0523787	+	0.0907226i	−0.891026	−	0.453952i	$-0.850014\pi$
$211$	−0.760845	+	1.31782i	−0.0523787	+	0.0907226i	0.838647	+	0.544675i	$0.183347\pi$
$212$		0			0
$213$	−12.3058	+	12.1489i	−0.843176	+	0.832430i
$214$		0			0
$215$	3.53195			0.240877
$216$		0			0
$217$	−23.3335			−1.58398
$218$		0			0
$219$	−11.4281	+	11.2825i	−0.772242	+	0.762400i
$220$		0			0
$221$	−0.595087	+	1.03072i	−0.0400299	+	0.0693338i
$222$		0			0
$223$	−11.9980	−	20.7811i	−0.803443	−	1.39160i	−0.917337	−	0.398112i	$-0.869666\pi$
$223$	−11.9980	−	20.7811i	−0.803443	−	1.39160i	0.113894	−	0.993493i	$-0.463668\pi$
$224$		0			0
$225$	8.74177	−	4.89865i	0.582784	−	0.326576i
$226$		0			0
$227$	0.277631	+	0.480871i	0.0184270	+	0.0319165i	0.875092	−	0.483957i	$-0.160801\pi$
$227$	0.277631	+	0.480871i	0.0184270	+	0.0319165i	−0.856665	+	0.515873i	$0.827468\pi$
$228$		0			0
$229$	−0.0170395	+	0.0295133i	−0.00112600	+	0.00195030i	−0.866588	−	0.499025i	$-0.833692\pi$
$229$	−0.0170395	+	0.0295133i	−0.00112600	+	0.00195030i	0.865462	+	0.500975i	$0.167025\pi$
$230$		0			0
$231$	−1.78598	−	6.84054i	−0.117509	−	0.450075i
$232$		0			0
$233$	22.1134			1.44870			0.724348	−	0.689435i	$-0.242141\pi$
$233$	22.1134			1.44870			0.724348	+	0.689435i	$0.242141\pi$
$234$		0			0
$235$	4.55722			0.297280
$236$		0			0
$237$	−27.5622	−	7.57505i	−1.79035	−	0.492052i
$238$		0			0
$239$	−13.4984	+	23.3799i	−0.873138	+	1.51232i	−0.0144042	+	0.999896i	$0.504585\pi$
$239$	−13.4984	+	23.3799i	−0.873138	+	1.51232i	−0.858733	+	0.512423i	$0.828748\pi$
$240$		0			0
$241$	−5.55913	−	9.62869i	−0.358095	−	0.620238i	0.629548	−	0.776962i	$-0.283240\pi$
$241$	−5.55913	−	9.62869i	−0.358095	−	0.620238i	−0.987643	+	0.156723i	$0.949907\pi$
$242$		0			0
$243$	−11.3704	+	10.6636i	−0.729414	+	0.684072i
$244$		0			0
$245$	−6.22314	−	10.7788i	−0.397582	−	0.688632i
$246$		0			0
$247$	−2.02163	+	3.50157i	−0.128633	+	0.222800i
$248$		0			0
$249$	−28.2169	−	7.75499i	−1.78817	−	0.491453i
$250$		0			0
$251$	1.64637			0.103918			0.0519590	−	0.998649i	$-0.483453\pi$
$251$	1.64637			0.103918			0.0519590	+	0.998649i	$0.483453\pi$
$252$		0			0
$253$	0.759629			0.0477575
$254$		0			0
$255$	1.05699	+	4.04843i	0.0661915	+	0.253523i
$256$		0			0
$257$	0.0670884	−	0.116201i	0.00418486	−	0.00724839i	−0.863925	−	0.503620i	$-0.832001\pi$
$257$	0.0670884	−	0.116201i	0.00418486	−	0.00724839i	0.868110	+	0.496371i	$0.165335\pi$
$258$		0			0
$259$	7.69889	+	13.3349i	0.478386	+	0.828589i
$260$		0			0
$261$	12.2636	−	6.87216i	0.759095	−	0.425376i
$262$		0			0
$263$	−0.964401	−	1.67039i	−0.0594675	−	0.103001i	0.834759	−	0.550615i	$-0.185607\pi$
$263$	−0.964401	−	1.67039i	−0.0594675	−	0.103001i	−0.894226	+	0.447615i	$0.852274\pi$
$264$		0			0
$265$	−1.86974	+	3.23849i	−0.114858	+	0.198939i
$266$		0			0
$267$	−2.94670	+	2.90914i	−0.180335	+	0.178037i
$268$		0			0
$269$	22.2823			1.35858			0.679288	−	0.733872i	$-0.262289\pi$
$269$	22.2823			1.35858			0.679288	+	0.733872i	$0.262289\pi$
$270$		0			0
$271$	−20.0973			−1.22083			−0.610413	−	0.792084i	$-0.708996\pi$
$271$	−20.0973			−1.22083			−0.610413	+	0.792084i	$0.708996\pi$
$272$		0			0
$273$	−3.19337	+	3.15267i	−0.193272	+	0.190808i
$274$		0			0
$275$	1.67012	−	2.89274i	0.100712	−	0.174439i
$276$		0			0
$277$	−6.73459	−	11.6646i	−0.404642	−	0.700861i	0.589638	−	0.807668i	$-0.299271\pi$
$277$	−6.73459	−	11.6646i	−0.404642	−	0.700861i	−0.994280	+	0.106807i	$0.965937\pi$
$278$		0			0
$279$	14.7407	+	8.76455i	0.882503	+	0.524720i
$280$		0			0
$281$	−9.59736	−	16.6231i	−0.572530	−	0.991652i	−0.996305	−	0.0858841i	$-0.972629\pi$
$281$	−9.59736	−	16.6231i	−0.572530	−	0.991652i	0.423775	−	0.905768i	$-0.360705\pi$
$282$		0			0
$283$	15.0429	−	26.0551i	0.894207	−	1.54881i	0.0594245	−	0.998233i	$-0.481073\pi$
$283$	15.0429	−	26.0551i	0.894207	−	1.54881i	0.834783	−	0.550579i	$-0.185593\pi$
$284$		0			0
$285$	3.59082	+	13.7534i	0.212702	+	0.814678i
$286$		0			0
$287$	28.7554			1.69738
$288$		0			0
$289$	−13.4840			−0.793177
$290$		0			0
$291$	20.0985	+	5.52378i	1.17820	+	0.323810i
$292$		0			0
$293$	1.39483	−	2.41591i	0.0814866	−	0.141139i	−0.822402	−	0.568907i	$-0.807367\pi$
$293$	1.39483	−	2.41591i	0.0814866	−	0.141139i	0.903889	+	0.427768i	$0.140700\pi$
$294$		0			0
$295$	3.19651	+	5.53652i	0.186108	+	0.322348i
$296$		0			0
$297$	−1.44118	+	4.99229i	−0.0836256	+	0.289682i
$298$		0			0
$299$	−0.241079	−	0.417560i	−0.0139419	−	0.0241481i
$300$		0			0
$301$	5.59516	−	9.69110i	0.322500	−	0.558586i
$302$		0			0
$303$	−11.7387	−	3.22619i	−0.674368	−	0.185340i
$304$		0			0
$305$	−10.2088			−0.584553
$306$		0			0
$307$	12.0487			0.687658			0.343829	−	0.939032i	$-0.388276\pi$
$307$	12.0487			0.687658			0.343829	+	0.939032i	$0.388276\pi$
$308$		0			0
$309$	3.53784	+	13.5504i	0.201261	+	0.770856i
$310$		0			0
$311$	1.93673	−	3.35452i	0.109822	−	0.190217i	−0.805876	−	0.592084i	$-0.798305\pi$
$311$	1.93673	−	3.35452i	0.109822	−	0.190217i	0.915698	+	0.401867i	$0.131639\pi$
$312$		0			0
$313$	−4.73353	−	8.19872i	−0.267555	−	0.463419i	0.700675	−	0.713481i	$-0.252882\pi$
$313$	−4.73353	−	8.19872i	−0.267555	−	0.463419i	−0.968230	+	0.250062i	$0.919549\pi$
$314$		0			0
$315$	−0.202348	+	15.7745i	−0.0114010	+	0.888794i
$316$		0			0
$317$	5.78252	+	10.0156i	0.324779	+	0.562533i	0.981468	−	0.191629i	$-0.0613769\pi$
$317$	5.78252	+	10.0156i	0.324779	+	0.562533i	−0.656689	+	0.754162i	$0.728044\pi$
$318$		0			0
$319$	2.34297	−	4.05813i	0.131181	−	0.227212i
$320$		0			0
$321$	8.80105	−	8.68887i	0.491226	−	0.484966i
$322$		0			0
$323$	11.9445			0.664612
$324$		0			0
$325$	−2.12014			−0.117604
$326$		0			0
$327$	−7.89881	+	7.79813i	−0.436805	+	0.431238i
$328$		0			0
$329$	7.21934	−	12.5043i	0.398015	−	0.689382i
$330$		0			0
$331$	15.6072	+	27.0324i	0.857849	+	1.48584i	0.873977	+	0.485967i	$0.161533\pi$
$331$	15.6072	+	27.0324i	0.857849	+	1.48584i	−0.0161284	+	0.999870i	$0.505134\pi$
$332$		0			0
$333$	0.145157	−	11.3160i	0.00795455	−	0.620115i
$334$		0			0
$335$	5.74025	+	9.94240i	0.313623	+	0.543211i
$336$		0			0
$337$	5.08336	−	8.80463i	0.276908	−	0.479619i	−0.693707	−	0.720258i	$-0.744024\pi$
$337$	5.08336	−	8.80463i	0.276908	−	0.479619i	0.970615	+	0.240639i	$0.0773569\pi$
$338$		0			0
$339$	5.62215	+	21.5336i	0.305353	+	1.16955i
$340$		0			0
$341$	5.71650			0.309566
$342$		0			0
$343$	−10.8612			−0.586450
$344$		0			0
$345$	−1.63445	−	0.449204i	−0.0879959	−	0.0241844i
$346$		0			0
$347$	17.4365	−	30.2010i	0.936043	−	1.62127i	0.163278	−	0.986580i	$-0.447793\pi$
$347$	17.4365	−	30.2010i	0.936043	−	1.62127i	0.772764	−	0.634693i	$-0.218874\pi$
$348$		0			0
$349$	−3.41880	−	5.92154i	−0.183004	−	0.316973i	0.759898	−	0.650042i	$-0.225249\pi$
$349$	−3.41880	−	5.92154i	−0.183004	−	0.316973i	−0.942902	+	0.333070i	$0.891916\pi$
$350$		0			0
$351$	3.20159	−	0.792172i	0.170888	−	0.0422830i
$352$		0			0
$353$	1.52878	+	2.64792i	0.0813686	+	0.140934i	0.903838	−	0.427875i	$-0.140738\pi$
$353$	1.52878	+	2.64792i	0.0813686	+	0.140934i	−0.822469	+	0.568809i	$0.807404\pi$
$354$		0			0
$355$	6.43112	−	11.1390i	0.341329	−	0.591198i
$356$		0			0
$357$	12.7827	+	3.51313i	0.676531	+	0.185934i
$358$		0			0
$359$	16.7183			0.882356			0.441178	−	0.897420i	$-0.354561\pi$
$359$	16.7183			0.882356			0.441178	+	0.897420i	$0.354561\pi$
$360$		0			0
$361$	21.5781			1.13569
$362$		0			0
$363$	0.437549	+	1.67587i	0.0229654	+	0.0879605i
$364$		0			0
$365$	5.97247	−	10.3446i	0.312614	−	0.541463i
$366$		0			0
$367$	−9.29762	−	16.1039i	−0.485332	−	0.840619i	0.514526	−	0.857475i	$-0.327968\pi$
$367$	−9.29762	−	16.1039i	−0.485332	−	0.840619i	−0.999858	+	0.0168556i	$0.994634\pi$
$368$		0			0
$369$	−18.1659	−	10.8011i	−0.945680	−	0.562284i
$370$		0			0
$371$	5.92393	+	10.2605i	0.307555	+	0.532701i
$372$		0			0
$373$	−6.83379	+	11.8365i	−0.353840	+	0.612869i	−0.986919	−	0.161218i	$-0.948458\pi$
$373$	−6.83379	+	11.8365i	−0.353840	+	0.612869i	0.633079	+	0.774088i	$0.281791\pi$
$374$		0			0
$375$	−13.2438	+	13.0750i	−0.683909	+	0.675192i
$376$		0			0
$377$	−2.97429			−0.153184
$378$		0			0
$379$	28.8290			1.48085			0.740424	−	0.672140i	$-0.234625\pi$
$379$	28.8290			1.48085			0.740424	+	0.672140i	$0.234625\pi$
$380$		0			0
$381$	17.4529	−	17.2305i	0.894139	−	0.882743i
$382$		0			0
$383$	−12.6392	+	21.8918i	−0.645834	+	1.11862i	0.338274	+	0.941048i	$0.390157\pi$
$383$	−12.6392	+	21.8918i	−0.645834	+	1.11862i	−0.984108	+	0.177570i	$0.943176\pi$
$384$		0			0
$385$	2.62931	+	4.55409i	0.134002	+	0.232098i
$386$		0			0
$387$	−7.17487	+	4.02060i	−0.364719	+	0.204379i
$388$		0			0
$389$	16.5668	+	28.6945i	0.839969	+	1.45487i	0.889920	+	0.456117i	$0.150760\pi$
$389$	16.5668	+	28.6945i	0.839969	+	1.45487i	−0.0499508	+	0.998752i	$0.515906\pi$
$390$		0			0
$391$	−0.712190	+	1.23355i	−0.0360170	+	0.0623832i
$392$		0			0
$393$	8.02047	+	30.7195i	0.404579	+	1.54959i
$394$		0			0
$395$	21.2611			1.06976
$396$		0			0
$397$	−29.8296			−1.49710			−0.748551	−	0.663077i	$-0.769250\pi$
$397$	−29.8296			−1.49710			−0.748551	+	0.663077i	$0.769250\pi$
$398$		0			0
$399$	43.4254	+	11.9348i	2.17399	+	0.597488i
$400$		0			0
$401$	−8.67440	+	15.0245i	−0.433179	+	0.750287i	−0.997145	−	0.0755103i	$-0.975941\pi$
$401$	−8.67440	+	15.0245i	−0.433179	+	0.750287i	0.563966	+	0.825798i	$0.309275\pi$
$402$		0			0
$403$	−1.81421	−	3.14230i	−0.0903722	−	0.156529i
$404$		0			0
$405$	6.05308	−	9.88940i	0.300780	−	0.491408i
$406$		0			0
$407$	−1.88616	−	3.26693i	−0.0934936	−	0.161936i
$408$		0			0
$409$	16.0594	−	27.8156i	0.794084	−	1.37539i	−0.129335	−	0.991601i	$-0.541284\pi$
$409$	16.0594	−	27.8156i	0.794084	−	1.37539i	0.923419	−	0.383793i	$-0.125382\pi$
$410$		0			0
$411$	−5.73489	−	1.57615i	−0.282881	−	0.0777457i
$412$		0			0
$413$	20.2551			0.996686
$414$		0			0
$415$	21.7662			1.06846
$416$		0			0
$417$	2.40014	+	9.19286i	0.117535	+	0.450176i
$418$		0			0
$419$	−16.0347	+	27.7729i	−0.783347	+	1.35680i	0.146635	+	0.989191i	$0.453156\pi$
$419$	−16.0347	+	27.7729i	−0.783347	+	1.35680i	−0.929982	+	0.367606i	$0.880178\pi$
$420$		0			0
$421$	−5.11232	−	8.85480i	−0.249159	−	0.431556i	0.714134	−	0.700009i	$-0.246821\pi$
$421$	−5.11232	−	8.85480i	−0.249159	−	0.431556i	−0.963293	+	0.268453i	$0.913488\pi$
$422$		0			0
$423$	−9.25760	+	5.18771i	−0.450120	+	0.252235i
$424$		0			0
$425$	3.13164	+	5.42417i	0.151907	+	0.263111i
$426$		0			0
$427$	−16.1723	+	28.0112i	−0.782631	+	1.35556i
$428$		0			0
$429$	0.782348	−	0.772377i	0.0377721	−	0.0372907i
$430$		0			0
$431$	−21.3465			−1.02822			−0.514112	−	0.857723i	$-0.671879\pi$
$431$	−21.3465			−1.02822			−0.514112	+	0.857723i	$0.671879\pi$
$432$		0			0
$433$	−15.0577			−0.723627			−0.361813	−	0.932251i	$-0.617842\pi$
$433$	−15.0577			−0.723627			−0.361813	+	0.932251i	$0.617842\pi$
$434$		0			0
$435$	−7.44099	+	7.34615i	−0.356768	+	0.352221i
$436$		0			0
$437$	−2.41945	+	4.19062i	−0.115738	+	0.200464i
$438$		0			0
$439$	0.826425	+	1.43141i	0.0394431	+	0.0683175i	0.885073	−	0.465452i	$-0.154108\pi$
$439$	0.826425	+	1.43141i	0.0394431	+	0.0683175i	−0.845630	+	0.533770i	$0.820775\pi$
$440$		0			0
$441$	24.9118	+	14.8121i	1.18628	+	0.705338i
$442$		0			0
$443$	0.615777	+	1.06656i	0.0292565	+	0.0506737i	0.880283	−	0.474449i	$-0.157353\pi$
$443$	0.615777	+	1.06656i	0.0292565	+	0.0506737i	−0.851026	+	0.525123i	$0.824019\pi$
$444$		0			0
$445$	1.53998	−	2.66732i	0.0730020	−	0.126443i
$446$		0			0
$447$	−1.11307	−	4.26323i	−0.0526466	−	0.201644i
$448$		0			0
$449$	37.7680			1.78238			0.891190	−	0.453630i	$-0.149871\pi$
$449$	37.7680			1.78238			0.891190	+	0.453630i	$0.149871\pi$
$450$		0			0
$451$	−7.04482			−0.331728
$452$		0			0
$453$	−18.7656	−	5.15746i	−0.881687	−	0.242318i
$454$		0			0
$455$	1.66889	−	2.89060i	0.0782388	−	0.135514i
$456$		0			0
$457$	−9.88076	−	17.1140i	−0.462202	−	0.800558i	0.536868	−	0.843666i	$-0.319607\pi$
$457$	−9.88076	−	17.1140i	−0.462202	−	0.800558i	−0.999070	+	0.0431083i	$0.986274\pi$
$458$		0			0
$459$	−6.75572	−	7.02082i	−0.315330	−	0.327704i
$460$		0			0
$461$	14.3931	+	24.9296i	0.670355	+	1.16109i	0.977804	+	0.209524i	$0.0671914\pi$
$461$	14.3931	+	24.9296i	0.670355	+	1.16109i	−0.307449	+	0.951565i	$0.599475\pi$
$462$		0			0
$463$	10.3909	−	17.9975i	0.482904	−	0.836415i	−0.516903	−	0.856044i	$-0.672915\pi$
$463$	10.3909	−	17.9975i	0.482904	−	0.836415i	0.999807	+	0.0196292i	$0.00624856\pi$
$464$		0			0
$465$	−12.2999	−	3.38044i	−0.570393	−	0.156764i
$466$		0			0
$467$	−14.6117			−0.676148			−0.338074	−	0.941120i	$-0.609775\pi$
$467$	−14.6117			−0.676148			−0.338074	+	0.941120i	$0.609775\pi$
$468$		0			0
$469$	36.3737			1.67958
$470$		0			0
$471$	−4.94098	−	18.9246i	−0.227668	−	0.872001i
$472$		0			0
$473$	−1.37077	+	2.37424i	−0.0630279	+	0.109167i
$474$		0			0
$475$	10.6388	+	18.4270i	0.488143	+	0.845489i
$476$		0			0
$477$	0.111691	−	8.70715i	0.00511399	−	0.398673i
$478$		0			0
$479$	19.9109	+	34.4867i	0.909753	+	1.57574i	0.814407	+	0.580294i	$0.197062\pi$
$479$	19.9109	+	34.4867i	0.909753	+	1.57574i	0.0953454	+	0.995444i	$0.469604\pi$
$480$		0			0
$481$	−1.19720	+	2.07361i	−0.0545875	+	0.0945483i
$482$		0			0
$483$	−3.82177	+	3.77306i	−0.173896	+	0.171680i
$484$		0			0
$485$	−15.5038			−0.703990
$486$		0			0
$487$	−12.6286			−0.572255			−0.286128	−	0.958192i	$-0.592368\pi$
$487$	−12.6286			−0.572255			−0.286128	+	0.958192i	$0.592368\pi$
$488$		0			0
$489$	−18.2486	+	18.0160i	−0.825230	+	0.814712i
$490$		0			0
$491$	19.9298	−	34.5194i	0.899419	−	1.55784i	0.0711813	−	0.997463i	$-0.477323\pi$
$491$	19.9298	−	34.5194i	0.899419	−	1.55784i	0.828238	−	0.560376i	$-0.189344\pi$
$492$		0			0
$493$	4.39329	+	7.60940i	0.197864	+	0.342710i
$494$		0			0
$495$	0.0495736	−	3.86462i	0.00222817	−	0.173702i
$496$		0			0
$497$	−20.3758	−	35.2919i	−0.913979	−	1.58306i
$498$		0			0
$499$	21.8613	−	37.8650i	0.978648	−	1.69507i	0.311320	−	0.950305i	$-0.399229\pi$
$499$	21.8613	−	37.8650i	0.978648	−	1.69507i	0.667328	−	0.744764i	$-0.267438\pi$
$500$		0			0
$501$	2.54250	+	9.73812i	0.113590	+	0.435067i
$502$		0			0
$503$	−5.68820			−0.253624			−0.126812	−	0.991927i	$-0.540475\pi$
$503$	−5.68820			−0.253624			−0.126812	+	0.991927i	$0.540475\pi$
$504$		0			0
$505$	9.05507			0.402945
$506$		0			0
$507$	21.0387	+	5.78218i	0.934363	+	0.256796i
$508$		0			0
$509$	−12.6383	+	21.8902i	−0.560183	+	0.970266i	0.437296	+	0.899317i	$0.355936\pi$
$509$	−12.6383	+	21.8902i	−0.560183	+	0.970266i	−0.997480	+	0.0709488i	$0.977397\pi$
$510$		0			0
$511$	−18.9226	−	32.7750i	−0.837088	−	1.44988i
$512$		0			0
$513$	−22.9506	−	23.8512i	−1.01329	−	1.05305i
$514$		0			0
$515$	−5.20839	−	9.02119i	−0.229509	−	0.397521i
$516$		0			0
$517$	−1.76867	+	3.06343i	−0.0777862	+	0.134730i
$518$		0			0
$519$	−39.1453	−	10.7585i	−1.71829	−	0.472246i
$520$		0			0
$521$	0.000322593	0		1.41331e−5	0		7.06653e−6	−	1.00000i	$-0.499998\pi$
$521$	0.000322593	0		1.41331e−5	0		7.06653e−6		1.00000i	$0.499998\pi$
$522$		0			0
$523$	35.9483			1.57191			0.785956	−	0.618283i	$-0.212171\pi$
$523$	35.9483			1.57191			0.785956	+	0.618283i	$0.212171\pi$
$524$		0			0
$525$	5.96560	+	22.8491i	0.260360	+	0.997216i
$526$		0			0
$527$	−5.35950	+	9.28293i	−0.233464	+	0.404371i
$528$		0			0
$529$	11.2115	+	19.4189i	0.487456	+	0.844298i
$530$		0			0
$531$	−12.7959	−	7.60822i	−0.555296	−	0.330169i
$532$		0			0
$533$	2.23577	+	3.87246i	0.0968418	+	0.167735i
$534$		0			0
$535$	−4.59952	+	7.96661i	−0.198855	+	0.344427i
$536$		0			0
$537$	−23.6084	+	23.3075i	−1.01878	+	1.00579i
$538$		0			0
$539$	9.66090			0.416125
$540$		0			0
$541$	−7.64007			−0.328472			−0.164236	−	0.986421i	$-0.552516\pi$
$541$	−7.64007			−0.328472			−0.164236	+	0.986421i	$0.552516\pi$
$542$		0			0
$543$	32.9767	−	32.5564i	1.41517	−	1.39713i
$544$		0			0
$545$	4.12800	−	7.14991i	0.176824	−	0.306269i
$546$		0			0
$547$	−16.1755	−	28.0167i	−0.691613	−	1.19791i	−0.971309	−	0.237820i	$-0.923567\pi$
$547$	−16.1755	−	28.0167i	−0.691613	−	1.19791i	0.279696	−	0.960089i	$-0.409766\pi$
$548$		0			0
$549$	20.7383	−	11.6212i	0.885087	−	0.495979i
$550$		0			0
$551$	14.9249	+	25.8507i	0.635822	+	1.10128i
$552$		0			0
$553$	33.6809	−	58.3371i	1.43226	−	2.48075i
$554$		0			0
$555$	2.12646	+	8.14464i	0.0902632	+	0.345721i
$556$		0			0
$557$	13.9455			0.590892			0.295446	−	0.955359i	$-0.404532\pi$
$557$	13.9455			0.590892			0.295446	+	0.955359i	$0.404532\pi$
$558$		0			0
$559$	1.74012			0.0735994
$560$		0			0
$561$	−3.13164	−	0.860685i	−0.132218	−	0.0363382i
$562$		0			0
$563$	3.16603	−	5.48372i	0.133432	−	0.231111i	−0.791565	−	0.611085i	$-0.790734\pi$
$563$	3.16603	−	5.48372i	0.133432	−	0.231111i	0.924997	+	0.379973i	$0.124067\pi$
$564$		0			0
$565$	−8.27691	−	14.3360i	−0.348212	−	0.603121i
$566$		0			0
$567$	−17.5459	−	32.2750i	−0.736858	−	1.35542i
$568$		0			0
$569$	4.02037	+	6.96348i	0.168542	+	0.291924i	0.937908	−	0.346885i	$-0.112761\pi$
$569$	4.02037	+	6.96348i	0.168542	+	0.291924i	−0.769365	+	0.638809i	$0.779427\pi$
$570$		0			0
$571$	2.90279	−	5.02778i	0.121478	−	0.210406i	−0.798873	−	0.601500i	$-0.794570\pi$
$571$	2.90279	−	5.02778i	0.121478	−	0.210406i	0.920351	+	0.391094i	$0.127903\pi$
$572$		0			0
$573$	−39.2315	−	10.7822i	−1.63892	−	0.450433i
$574$		0			0
$575$	−2.53735			−0.105815
$576$		0			0
$577$	−17.5466			−0.730476			−0.365238	−	0.930914i	$-0.619012\pi$
$577$	−17.5466			−0.730476			−0.365238	+	0.930914i	$0.619012\pi$
$578$		0			0
$579$	6.60779	+	25.3088i	0.274610	+	1.05180i
$580$		0			0
$581$	34.4810	−	59.7229i	1.43051	−	2.47772i
$582$		0			0
$583$	−1.45131	−	2.51374i	−0.0601072	−	0.104109i
$584$		0			0
$585$	−2.14008	+	1.19924i	−0.0884813	+	0.0495825i
$586$		0			0
$587$	−3.26482	−	5.65483i	−0.134753	−	0.233400i	0.790750	−	0.612139i	$-0.209691\pi$
$587$	−3.26482	−	5.65483i	−0.134753	−	0.233400i	−0.925503	+	0.378740i	$0.876358\pi$
$588$		0			0
$589$	−18.2073	+	31.5360i	−0.750220	+	1.29942i
$590$		0			0
$591$	20.3488	−	20.0895i	0.837038	−	0.826370i
$592$		0			0
$593$	−15.1772			−0.623252			−0.311626	−	0.950205i	$-0.600874\pi$
$593$	−15.1772			−0.623252			−0.311626	+	0.950205i	$0.600874\pi$
$594$		0			0
$595$	−9.86041			−0.404237
$596$		0			0
$597$	4.77018	−	4.70938i	0.195230	−	0.192742i
$598$		0			0
$599$	−11.8928	+	20.5989i	−0.485926	+	0.841649i	−0.999869	−	0.0161752i	$-0.994851\pi$
$599$	−11.8928	+	20.5989i	−0.485926	+	0.841649i	0.513943	+	0.857824i	$0.328184\pi$
$600$		0			0
$601$	10.0752	+	17.4507i	0.410975	+	0.711829i	0.994997	−	0.0999089i	$-0.0318551\pi$
$601$	10.0752	+	17.4507i	0.410975	+	0.711829i	−0.584022	+	0.811738i	$0.698522\pi$
$602$		0			0
$603$	−22.9788	−	13.6627i	−0.935767	−	0.556390i
$604$		0			0
$605$	−0.644157	−	1.11571i	−0.0261887	−	0.0453602i
$606$		0			0
$607$	1.05994	−	1.83587i	0.0430217	−	0.0745158i	−0.843713	−	0.536795i	$-0.819635\pi$
$607$	1.05994	−	1.83587i	0.0430217	−	0.0745158i	0.886734	+	0.462279i	$0.152968\pi$
$608$		0			0
$609$	8.36896	+	32.0543i	0.339127	+	1.29891i
$610$		0			0
$611$	2.24525			0.0908331
$612$		0			0
$613$	1.93317			0.0780800			0.0390400	−	0.999238i	$-0.487570\pi$
$613$	1.93317			0.0780800			0.0390400	+	0.999238i	$0.487570\pi$
$614$		0			0
$615$	15.1579	+	4.16593i	0.611227	+	0.167987i
$616$		0			0
$617$	−16.4960	+	28.5719i	−0.664105	+	1.15026i	0.315422	+	0.948951i	$0.397854\pi$
$617$	−16.4960	+	28.5719i	−0.664105	+	1.15026i	−0.979527	+	0.201312i	$0.935480\pi$
$618$		0			0
$619$	−9.79499	−	16.9654i	−0.393694	−	0.681898i	0.599240	−	0.800570i	$-0.295470\pi$
$619$	−9.79499	−	16.9654i	−0.393694	−	0.681898i	−0.992934	+	0.118672i	$0.962136\pi$
$620$		0			0
$621$	3.83160	−	0.948057i	0.153757	−	0.0380442i
$622$		0			0
$623$	−4.87913	−	8.45090i	−0.195478	−	0.338578i
$624$		0			0
$625$	−1.42924	+	2.47551i	−0.0571695	+	0.0990206i
$626$		0			0
$627$	−10.6388	−	2.92392i	−0.424874	−	0.116770i
$628$		0			0
$629$	7.07347			0.282038
$630$		0			0
$631$	−30.0742			−1.19723			−0.598617	−	0.801036i	$-0.704283\pi$
$631$	−30.0742			−1.19723			−0.598617	+	0.801036i	$0.704283\pi$
$632$		0			0
$633$	0.665813	+	2.55016i	0.0264637	+	0.101360i
$634$		0			0
$635$	−9.12108	+	15.7982i	−0.361959	+	0.626931i
$636$		0			0
$637$	−3.06602	−	5.31050i	−0.121480	−	0.210410i
$638$		0			0
$639$	−0.384170	+	29.9489i	−0.0151975	+	1.18476i
$640$		0			0
$641$	−15.9042	−	27.5469i	−0.628179	−	1.08804i	−0.987917	−	0.154985i	$-0.950467\pi$
$641$	−15.9042	−	27.5469i	−0.628179	−	1.08804i	0.359738	−	0.933053i	$-0.382866\pi$
$642$		0			0
$643$	−13.7948	+	23.8934i	−0.544016	+	0.942263i	0.454652	+	0.890669i	$0.349763\pi$
$643$	−13.7948	+	23.8934i	−0.544016	+	0.942263i	−0.998668	+	0.0515939i	$0.983570\pi$
$644$		0			0
$645$	4.35340	−	4.29791i	0.171415	−	0.169230i
$646$		0			0
$647$	29.7962			1.17141			0.585704	−	0.810525i	$-0.300818\pi$
$647$	29.7962			1.17141			0.585704	+	0.810525i	$0.300818\pi$
$648$		0			0
$649$	−4.96231			−0.194788
$650$		0			0
$651$	−28.7603	+	28.3937i	−1.12720	+	1.11284i
$652$		0			0
$653$	−16.4258	+	28.4503i	−0.642792	+	1.11335i	0.342015	+	0.939694i	$0.388891\pi$
$653$	−16.4258	+	28.4503i	−0.642792	+	1.11335i	−0.984807	+	0.173653i	$0.944443\pi$
$654$		0			0
$655$	−11.8077	−	20.4515i	−0.461365	−	0.799107i
$656$		0			0
$657$	−0.356772	+	27.8130i	−0.0139190	+	1.08509i
$658$		0			0
$659$	−5.06773	−	8.77757i	−0.197411	−	0.341926i	0.750277	−	0.661123i	$-0.229920\pi$
$659$	−5.06773	−	8.77757i	−0.197411	−	0.341926i	−0.947688	+	0.319198i	$0.896587\pi$
$660$		0			0
$661$	−4.28181	+	7.41631i	−0.166543	+	0.288461i	−0.937202	−	0.348787i	$-0.886594\pi$
$661$	−4.28181	+	7.41631i	−0.166543	+	0.288461i	0.770659	+	0.637248i	$0.219927\pi$
$662$		0			0
$663$	0.520759	+	1.99458i	0.0202246	+	0.0774631i
$664$		0			0
$665$	−33.4978			−1.29899
$666$		0			0
$667$	−3.55957			−0.137827
$668$		0			0
$669$	−40.0762	−	11.0143i	−1.54943	−	0.425839i
$670$		0			0
$671$	3.96207	−	6.86250i	0.152954	−	0.264924i
$672$		0			0
$673$	0.573061	+	0.992570i	0.0220899	+	0.0382608i	0.876859	−	0.480748i	$-0.159635\pi$
$673$	0.573061	+	0.992570i	0.0220899	+	0.0382608i	−0.854769	+	0.519008i	$0.826301\pi$
$674$		0			0
$675$	4.81389	−	16.6755i	0.185287	−	0.641840i
$676$		0			0
$677$	3.24461	+	5.61982i	0.124700	+	0.215987i	0.921616	−	0.388104i	$-0.126870\pi$
$677$	3.24461	+	5.61982i	0.124700	+	0.215987i	−0.796915	+	0.604091i	$0.793536\pi$
$678$		0			0
$679$	−24.5604	+	42.5398i	−0.942541	+	1.63253i
$680$		0			0
$681$	0.927355	+	0.254870i	0.0355363	+	0.00976663i
$682$		0			0
$683$	28.2950			1.08268			0.541339	−	0.840805i	$-0.317918\pi$
$683$	28.2950			1.08268			0.541339	+	0.840805i	$0.317918\pi$
$684$		0			0
$685$	4.42383			0.169026
$686$		0			0
$687$	0.0149112	+	0.0571122i	0.000568900	+	0.00217897i
$688$		0			0
$689$	−0.921186	+	1.59554i	−0.0350944	+	0.0607853i
$690$		0			0
$691$	20.1532	+	34.9063i	0.766663	+	1.32790i	0.939363	+	0.342924i	$0.111417\pi$
$691$	20.1532	+	34.9063i	0.766663	+	1.32790i	−0.172700	+	0.984974i	$0.555249\pi$
$692$		0			0
$693$	−10.5254	−	6.25818i	−0.399825	−	0.237729i
$694$		0			0
$695$	−3.53347	−	6.12015i	−0.134032	−	0.232151i
$696$		0			0
$697$	6.60486	−	11.4400i	0.250177	−	0.433319i
$698$		0			0
$699$	27.2564	−	26.9090i	1.03093	−	1.01779i
$700$		0			0
$701$	32.4271			1.22475			0.612377	−	0.790566i	$-0.290213\pi$
$701$	32.4271			1.22475			0.612377	+	0.790566i	$0.290213\pi$
$702$		0			0
$703$	24.0300			0.906310
$704$		0			0
$705$	5.61711	−	5.54552i	0.211553	−	0.208856i
$706$		0			0
$707$	14.3446	−	24.8456i	0.539485	−	0.934415i
$708$		0			0
$709$	−15.6889	−	27.1739i	−0.589208	−	1.02054i	−0.994336	−	0.106278i	$-0.966107\pi$
$709$	−15.6889	−	27.1739i	−0.589208	−	1.02054i	0.405128	−	0.914260i	$-0.367227\pi$
$710$		0			0
$711$	−43.1902	+	24.2026i	−1.61976	+	0.907669i
$712$		0			0
$713$	−2.17121	−	3.76065i	−0.0813125	−	0.140837i
$714$		0			0
$715$	−0.408864	+	0.708173i	−0.0152906	+	0.0264842i
$716$		0			0
$717$	11.8124	+	45.2432i	0.441142	+	1.68964i
$718$		0			0
$719$	−13.4457			−0.501440			−0.250720	−	0.968060i	$-0.580667\pi$
$719$	−13.4457			−0.501440			−0.250720	+	0.968060i	$0.580667\pi$
$720$		0			0
$721$	−33.0036			−1.22912
$722$		0			0
$723$	−18.5688	−	5.10337i	−0.690583	−	0.189796i
$724$		0			0
$725$	−7.82608	+	13.5552i	−0.290653	+	0.503426i
$726$		0			0
$727$	−14.6638	−	25.3985i	−0.543851	−	0.941978i	−0.998678	−	0.0513984i	$-0.983632\pi$
$727$	−14.6638	−	25.3985i	−0.543851	−	0.941978i	0.454827	−	0.890580i	$-0.349701\pi$
$728$		0			0
$729$	−1.03872	+	26.9800i	−0.0384710	+	0.999260i
$730$		0			0
$731$	−2.57032	−	4.45192i	−0.0950667	−	0.164660i
$732$		0			0
$733$	8.16123	−	14.1357i	0.301442	−	0.522113i	−0.675021	−	0.737799i	$-0.735865\pi$
$733$	8.16123	−	14.1357i	0.301442	−	0.522113i	0.976463	+	0.215686i	$0.0691987\pi$
$734$		0			0
$735$	−20.7868	−	5.71295i	−0.766733	−	0.210725i
$736$		0			0
$737$	−8.91125			−0.328250
$738$		0			0
$739$	−11.9475			−0.439494			−0.219747	−	0.975557i	$-0.570523\pi$
$739$	−11.9475			−0.439494			−0.219747	+	0.975557i	$0.570523\pi$
$740$		0			0
$741$	1.76913	+	6.77600i	0.0649905	+	0.248923i
$742$		0			0
$743$	12.3295	−	21.3553i	0.452324	−	0.783449i	−0.546206	−	0.837651i	$-0.683928\pi$
$743$	12.3295	−	21.3553i	0.452324	−	0.783449i	0.998530	+	0.0542023i	$0.0172616\pi$
$744$		0			0
$745$	1.63866	+	2.83825i	0.0600359	+	0.103985i
$746$		0			0
$747$	−44.2162	+	24.7776i	−1.61779	+	0.906564i
$748$		0			0
$749$	14.5727	+	25.2407i	0.532475	+	0.922274i
$750$		0			0
$751$	7.67002	−	13.2849i	0.279883	−	0.484772i	−0.691472	−	0.722403i	$-0.743038\pi$
$751$	7.67002	−	13.2849i	0.279883	−	0.484772i	0.971355	+	0.237631i	$0.0763710\pi$
$752$		0			0
$753$	2.02928	−	2.00341i	0.0739509	−	0.0730084i
$754$		0			0
$755$	14.4756			0.526821
$756$		0			0
$757$	−6.66820			−0.242360			−0.121180	−	0.992631i	$-0.538668\pi$
$757$	−6.66820			−0.242360			−0.121180	+	0.992631i	$0.538668\pi$
$758$		0			0
$759$	0.936300	−	0.924366i	0.0339855	−	0.0335524i
$760$		0			0
$761$	2.89929	−	5.02171i	0.105099	−	0.182037i	−0.808680	−	0.588249i	$-0.799817\pi$
$761$	2.89929	−	5.02171i	0.105099	−	0.182037i	0.913779	+	0.406212i	$0.133151\pi$
$762$		0			0
$763$	−13.0788	−	22.6531i	−0.473484	−	0.820098i
$764$		0			0
$765$	6.22922	+	3.70378i	0.225218	+	0.133910i
$766$		0			0
$767$	1.57486	+	2.72773i	0.0568648	+	0.0984927i
$768$		0			0
$769$	9.82077	−	17.0101i	0.354146	−	0.613399i	−0.632825	−	0.774294i	$-0.718105\pi$
$769$	9.82077	−	17.0101i	0.354146	−	0.613399i	0.986971	+	0.160896i	$0.0514383\pi$
$770$		0			0
$771$	−0.0587089	−	0.224863i	−0.00211435	−	0.00809825i
$772$		0			0
$773$	−11.8012			−0.424460			−0.212230	−	0.977220i	$-0.568073\pi$
$773$	−11.8012			−0.424460			−0.212230	+	0.977220i	$0.568073\pi$
$774$		0			0
$775$	−19.0945			−0.685896
$776$		0			0
$777$	25.7162	+	7.06771i	0.922563	+	0.253553i
$778$		0			0
$779$	22.4381	−	38.8639i	0.803927	−	1.39244i
$780$		0			0
$781$	4.99189	+	8.64621i	0.178624	+	0.309386i
$782$		0			0
$783$	6.75326	−	23.3935i	0.241342	−	0.836017i
$784$		0			0
$785$	7.27408	+	12.5991i	0.259623	+	0.449680i
$786$		0			0
$787$	−24.9599	+	43.2318i	−0.889723	+	1.54105i	−0.0495208	+	0.998773i	$0.515769\pi$
$787$	−24.9599	+	43.2318i	−0.889723	+	1.54105i	−0.840202	+	0.542273i	$0.817564\pi$
$788$		0			0
$789$	−3.22134	−	0.885336i	−0.114683	−	0.0315188i
$790$		0			0
$791$	−52.4476			−1.86482
$792$		0			0
$793$	−5.02966			−0.178608
$794$		0			0
$795$	1.63621	+	6.26691i	0.0580304	+	0.222264i
$796$		0			0
$797$	6.81649	−	11.8065i	0.241452	−	0.418208i	−0.719676	−	0.694310i	$-0.755710\pi$
$797$	6.81649	−	11.8065i	0.241452	−	0.418208i	0.961128	+	0.276102i	$0.0890429\pi$
$798$		0			0
$799$	−3.31644	−	5.74424i	−0.117327	−	0.203217i
$800$		0			0
$801$	−0.0919924	+	7.17147i	−0.00325039	+	0.253392i
$802$		0			0
$803$	4.63588	+	8.02958i	0.163597	+	0.283358i
$804$		0			0
$805$	1.99730	−	3.45942i	0.0703955	−	0.121929i
$806$		0			0
$807$	27.4646	−	27.1145i	0.966799	−	0.954477i
$808$		0			0
$809$	47.6700			1.67599			0.837994	−	0.545679i	$-0.183728\pi$
$809$	47.6700			1.67599			0.837994	+	0.545679i	$0.183728\pi$
$810$		0			0
$811$	14.9369			0.524506			0.262253	−	0.964999i	$-0.415535\pi$
$811$	14.9369			0.524506			0.262253	+	0.964999i	$0.415535\pi$
$812$		0			0
$813$	−24.7714	+	24.4557i	−0.868773	+	0.857700i
$814$		0			0
$815$	9.53692	−	16.5184i	0.334064	−	0.578615i
$816$		0			0
$817$	−8.73190	−	15.1241i	−0.305491	−	0.529125i
$818$		0			0
$819$	−0.0996931	+	7.77180i	−0.00348356	+	0.271569i
$820$		0			0
$821$	−5.96878	−	10.3382i	−0.208312	−	0.360807i	0.742871	−	0.669435i	$-0.233464\pi$
$821$	−5.96878	−	10.3382i	−0.208312	−	0.360807i	−0.951183	+	0.308628i	$0.900130\pi$
$822$		0			0
$823$	2.11763	−	3.66783i	0.0738158	−	0.127853i	−0.826755	−	0.562562i	$-0.809816\pi$
$823$	2.11763	−	3.66783i	0.0738158	−	0.127853i	0.900571	+	0.434710i	$0.143149\pi$
$824$		0			0
$825$	−1.46152	−	5.59783i	−0.0508836	−	0.194891i
$826$		0			0
$827$	−6.16070			−0.214228			−0.107114	−	0.994247i	$-0.534161\pi$
$827$	−6.16070			−0.214228			−0.107114	+	0.994247i	$0.534161\pi$
$828$		0			0
$829$	−27.3809			−0.950979			−0.475490	−	0.879721i	$-0.657729\pi$
$829$	−27.3809			−0.950979			−0.475490	+	0.879721i	$0.657729\pi$
$830$		0			0
$831$	−22.4952	−	6.18246i	−0.780349	−	0.214467i
$832$		0			0
$833$	−9.05757	+	15.6882i	−0.313826	+	0.543563i
$834$		0			0
$835$	−3.74305	−	6.48315i	−0.129534	−	0.224359i
$836$		0			0
$837$	28.8343	−	7.13449i	0.996659	−	0.246604i
$838$		0			0
$839$	20.6604	+	35.7848i	0.713275	+	1.23543i	0.963621	+	0.267271i	$0.0861220\pi$
$839$	20.6604	+	35.7848i	0.713275	+	1.23543i	−0.250347	+	0.968156i	$0.580545\pi$
$840$		0			0
$841$	3.52103	−	6.09860i	0.121415	−	0.210297i
$842$		0			0
$843$	−32.0575	−	8.81053i	−1.10412	−	0.303451i
$844$		0			0
$845$	−16.2291			−0.558296
$846$		0			0
$847$	−4.08178			−0.140252
$848$		0			0
$849$	−13.1640	−	50.4200i	−0.451787	−	1.73041i
$850$		0			0
$851$	−1.43278	+	2.48165i	−0.0491152	+	0.0850700i
$852$		0			0
$853$	−1.73415	−	3.00363i	−0.0593761	−	0.102842i	0.834809	−	0.550539i	$-0.185578\pi$
$853$	−1.73415	−	3.00363i	−0.0593761	−	0.102842i	−0.894186	+	0.447697i	$0.852244\pi$
$854$		0			0
$855$	21.1619	+	12.5825i	0.723723	+	0.430312i
$856$		0			0
$857$	−0.121222	−	0.209963i	−0.00414088	−	0.00717221i	0.863948	−	0.503582i	$-0.167985\pi$
$857$	−0.121222	−	0.209963i	−0.00414088	−	0.00717221i	−0.868088	+	0.496410i	$0.834651\pi$
$858$		0			0
$859$	−7.71054	+	13.3550i	−0.263080	+	0.455668i	−0.967059	−	0.254553i	$-0.918072\pi$
$859$	−7.71054	+	13.3550i	−0.263080	+	0.455668i	0.703979	+	0.710221i	$0.251405\pi$
$860$		0			0
$861$	35.4431	−	34.9914i	1.20790	−	1.19250i
$862$		0			0
$863$	37.8799			1.28945			0.644724	−	0.764416i	$-0.276972\pi$
$863$	37.8799			1.28945			0.644724	+	0.764416i	$0.276972\pi$
$864$		0			0
$865$	30.1963			1.02670
$866$		0			0
$867$	−16.6200	+	16.4082i	−0.564446	+	0.557252i
$868$		0			0
$869$	−8.25154	+	14.2921i	−0.279914	+	0.484826i
$870$		0			0
$871$	2.82810	+	4.89842i	0.0958267	+	0.165977i
$872$		0			0
$873$	31.4946	−	17.6487i	1.06593	−	0.597319i
$874$		0			0
$875$	−21.9291	−	37.9822i	−0.741337	−	1.28403i
$876$		0			0
$877$	6.64174	−	11.5038i	0.224275	−	0.388456i	−0.731826	−	0.681491i	$-0.761332\pi$
$877$	6.64174	−	11.5038i	0.224275	−	0.388456i	0.956102	+	0.293035i	$0.0946651\pi$
$878$		0			0
$879$	−1.22061	−	4.67510i	−0.0411701	−	0.157687i
$880$		0			0
$881$	2.85831			0.0962990			0.0481495	−	0.998840i	$-0.484668\pi$
$881$	2.85831			0.0962990			0.0481495	+	0.998840i	$0.484668\pi$
$882$		0			0
$883$	1.05489			0.0354999			0.0177499	−	0.999842i	$-0.494350\pi$
$883$	1.05489			0.0354999			0.0177499	+	0.999842i	$0.494350\pi$
$884$		0			0
$885$	10.6771	+	2.93445i	0.358908	+	0.0986404i
$886$		0			0
$887$	−0.0206451	+	0.0357584i	−0.000693196	+	0.00120065i	−0.866372	−	0.499400i	$-0.833554\pi$
$887$	−0.0206451	+	0.0357584i	−0.000693196	+	0.00120065i	0.865679	+	0.500600i	$0.166887\pi$
$888$		0			0
$889$	28.8984	+	50.0535i	0.969221	+	1.67874i
$890$		0			0
$891$	4.29859	+	7.90709i	0.144008	+	0.264898i
$892$		0			0
$893$	−11.2666	−	19.5144i	−0.377023	−	0.653023i
$894$		0			0
$895$	12.3380	−	21.3701i	0.412414	−	0.714322i
$896$		0			0
$897$	−0.805262	−	0.221314i	−0.0268869	−	0.00738946i
$898$		0			0
$899$	−26.7871			−0.893401
$900$		0			0
$901$	5.44270			0.181323
$902$		0			0
$903$	−4.89631	−	18.7536i	−0.162939	−	0.624079i
$904$		0			0
$905$	−17.2340	+	29.8502i	−0.572878	+	0.992253i
$906$		0			0
$907$	13.7674	+	23.8458i	0.457139	+	0.791788i	0.998808	−	0.0488037i	$-0.0155409\pi$
$907$	13.7674	+	23.8458i	0.457139	+	0.791788i	−0.541669	+	0.840592i	$0.682208\pi$
$908$		0			0
$909$	−18.3946	+	10.3078i	−0.610111	+	0.341889i
$910$		0			0
$911$	−1.66761	−	2.88838i	−0.0552503	−	0.0956963i	0.837077	−	0.547084i	$-0.184262\pi$
$911$	−1.66761	−	2.88838i	−0.0552503	−	0.0956963i	−0.892328	+	0.451388i	$0.850929\pi$
$912$		0			0
$913$	−8.44755	+	14.6316i	−0.279573	+	0.484235i
$914$		0			0
$915$	−12.5831	+	12.4227i	−0.415983	+	0.410682i
$916$		0			0
$917$	−74.8208			−2.47080
$918$		0			0
$919$	30.4941			1.00591			0.502953	−	0.864314i	$-0.332247\pi$
$919$	30.4941			1.00591			0.502953	+	0.864314i	$0.332247\pi$
$920$		0			0
$921$	14.8510	−	14.6617i	0.489356	−	0.483119i
$922$		0			0
$923$	3.16849	−	5.48798i	0.104292	−	0.180639i
$924$		0			0
$925$	6.30025	+	10.9123i	0.207151	+	0.358796i
$926$		0			0
$927$	20.8497	+	12.3968i	0.684793	+	0.407165i
$928$		0			0
$929$	12.2327	+	21.1877i	0.401342	+	0.695145i	0.993888	−	0.110391i	$-0.0352104\pi$
$929$	12.2327	+	21.1877i	0.401342	+	0.695145i	−0.592546	+	0.805537i	$0.701877\pi$
$930$		0			0
$931$	−30.7704	+	53.2959i	−1.00846	+	1.74670i
$932$		0			0
$933$	−1.69483	−	6.49143i	−0.0554862	−	0.212520i
$934$		0			0
$935$	2.41571			0.0790023
$936$		0			0
$937$	18.2256			0.595405			0.297703	−	0.954659i	$-0.403780\pi$
$937$	18.2256			0.595405			0.297703	+	0.954659i	$0.403780\pi$
$938$		0			0
$939$	−15.8112	−	4.34546i	−0.515978	−	0.141809i
$940$		0			0
$941$	−9.44290	+	16.3556i	−0.307830	+	0.533177i	−0.977887	−	0.209132i	$-0.932936\pi$
$941$	−9.44290	+	16.3556i	−0.307830	+	0.533177i	0.670058	+	0.742309i	$0.266269\pi$
$942$		0			0
$943$	2.67573	+	4.63449i	0.0871336	+	0.150920i
$944$		0			0
$945$	18.9461	+	19.6895i	0.616316	+	0.640500i
$946$		0			0
$947$	−28.4732	−	49.3171i	−0.925256	−	1.60259i	−0.791149	−	0.611624i	$-0.790517\pi$
$947$	−28.4732	−	49.3171i	−0.925256	−	1.60259i	−0.134108	−	0.990967i	$-0.542817\pi$
$948$		0			0
$949$	2.94252	−	5.09659i	0.0955182	−	0.165442i
$950$		0			0
$951$	19.3150	+	5.30845i	0.626333	+	0.172138i
$952$		0			0
$953$	−17.9737			−0.582224			−0.291112	−	0.956689i	$-0.594025\pi$
$953$	−17.9737			−0.582224			−0.291112	+	0.956689i	$0.594025\pi$
$954$		0			0
$955$	30.2627			0.979280
$956$		0			0
$957$	−2.05032	−	7.85303i	−0.0662775	−	0.253852i
$958$		0			0
$959$	7.00803	−	12.1383i	0.226301	−	0.391965i
$960$		0			0
$961$	−0.839208	−	1.45355i	−0.0270712	−	0.0468887i
$962$		0			0
$963$	0.274758	−	21.4194i	0.00885395	−	0.690229i
$964$		0			0
$965$	−9.72795	−	16.8493i	−0.313154	−	0.542398i
$966$		0			0
$967$	−27.7266	+	48.0239i	−0.891627	+	1.54434i	−0.0537033	+	0.998557i	$0.517103\pi$
$967$	−27.7266	+	48.0239i	−0.891627	+	1.54434i	−0.837924	+	0.545787i	$0.816231\pi$
$968$		0			0
$969$	14.7225	−	14.5349i	0.472956	−	0.466928i
$970$		0			0
$971$	−57.3995			−1.84204			−0.921019	−	0.389517i	$-0.872642\pi$
$971$	−57.3995			−1.84204			−0.921019	+	0.389517i	$0.872642\pi$
$972$		0			0
$973$	−22.3902			−0.717798
$974$		0			0
$975$	−2.61324	+	2.57993i	−0.0836905	+	0.0826238i
$976$		0			0
$977$	3.31468	−	5.74120i	0.106046	−	0.183677i	−0.808119	−	0.589019i	$-0.799514\pi$
$977$	3.31468	−	5.74120i	0.106046	−	0.183677i	0.914165	+	0.405342i	$0.132848\pi$
$978$		0			0
$979$	1.19534	+	2.07040i	0.0382034	+	0.0661702i
$980$		0			0
$981$	−0.246591	+	19.2236i	−0.00787304	+	0.613761i
$982$		0			0
$983$	9.17287	+	15.8879i	0.292569	+	0.506745i	0.974416	−	0.224750i	$-0.0721565\pi$
$983$	9.17287	+	15.8879i	0.292569	+	0.506745i	−0.681847	+	0.731495i	$0.738823\pi$
$984$		0			0
$985$	−10.6345	+	18.4195i	−0.338844	+	0.586895i
$986$		0			0
$987$	−6.31762	−	24.1974i	−0.201092	−	0.770211i
$988$		0			0
$989$	2.08255			0.0662211
$990$		0			0
$991$	−32.4397			−1.03048			−0.515240	−	0.857046i	$-0.672297\pi$
$991$	−32.4397			−1.03048			−0.515240	+	0.857046i	$0.672297\pi$
$992$		0			0
$993$	52.1318	+	14.3277i	1.65435	+	0.454674i
$994$		0			0
$995$	−2.49295	+	4.31791i	−0.0790318	+	0.136887i
$996$		0			0
$997$	13.0761	+	22.6484i	0.414123	+	0.717282i	0.995336	−	0.0964694i	$-0.0307550\pi$
$997$	13.0761	+	22.6484i	0.414123	+	0.717282i	−0.581213	+	0.813752i	$0.697422\pi$
$998$		0			0
$999$	−13.5912	−	14.1245i	−0.430006	−	0.446879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.q.f.265.5	✓	12
3.2	odd	2		2376.2.q.f.793.3		12
9.2	odd	6		2376.2.q.f.1585.3		12
9.4	even	3		7128.2.a.ba.1.3		6
9.5	odd	6		7128.2.a.w.1.4		6
9.7	even	3	inner	792.2.q.f.529.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
792.2.q.f.265.5	✓	12	1.1	even	1	trivial
792.2.q.f.529.5	yes	12	9.7	even	3	inner
2376.2.q.f.793.3		12	3.2	odd	2
2376.2.q.f.1585.3		12	9.2	odd	6
7128.2.a.w.1.4		6	9.5	odd	6
7128.2.a.ba.1.3		6	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23257 - 1.21686i) q^{3} +(-0.644157 + 1.11571i) q^{5} +(2.04089 + 3.53492i) q^{7} +(0.0384795 - 2.99975i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-0.317363 + 0.549690i) q^{13} +(0.563700 + 2.15905i) q^{15} +1.87510 q^{17} +6.37009 q^{19} +(6.81707 + 1.87357i) q^{21} +(-0.379815 + 0.657858i) q^{23} +(1.67012 + 2.89274i) q^{25} +(-3.60287 - 3.74424i) q^{27} +(2.34297 + 4.05813i) q^{29} +(-2.85825 + 4.95064i) q^{31} +(-1.67012 - 0.459008i) q^{33} -5.25861 q^{35} +3.77232 q^{37} +(0.277724 + 1.06372i) q^{39} +(3.52241 - 6.10099i) q^{41} +(-1.37077 - 2.37424i) q^{43} +(3.32208 + 1.97524i) q^{45} +(-1.76867 - 3.06343i) q^{47} +(-4.83045 + 8.36659i) q^{49} +(2.31120 - 2.28174i) q^{51} +2.90262 q^{53} +1.28831 q^{55} +(7.85161 - 7.75154i) q^{57} +(2.48116 - 4.29749i) q^{59} +(3.96207 + 6.86250i) q^{61} +(10.6824 - 5.98614i) q^{63} +(-0.408864 - 0.708173i) q^{65} +(4.45563 - 7.71737i) q^{67} +(0.332375 + 1.27304i) q^{69} -9.98378 q^{71} -9.27177 q^{73} +(5.57862 + 1.53320i) q^{75} +(2.04089 - 3.53492i) q^{77} +(-8.25154 - 14.2921i) q^{79} +(-8.99704 - 0.230858i) q^{81} +(-8.44755 - 14.6316i) q^{83} +(-1.20786 + 2.09207i) q^{85} +(7.82608 + 2.15088i) q^{87} -2.39069 q^{89} -2.59081 q^{91} +(2.50125 + 9.58014i) q^{93} +(-4.10334 + 7.10719i) q^{95} +(6.01708 + 10.4219i) q^{97} +(-2.61710 + 1.46655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{3} - 4 q^{5} - 5 q^{7} + 5 q^{9} - 6 q^{11} - 3 q^{13} - 7 q^{15} + 14 q^{17} + 10 q^{19} + 9 q^{21} - 8 q^{23} + 2 q^{25} - 11 q^{27} - 8 q^{29} - 4 q^{31} - 2 q^{33} + 16 q^{35} + 6 q^{37}+ \cdots - 7 q^{99}+O(q^{100}) \) 12 * q + q^3 - 4 * q^5 - 5 * q^7 + 5 * q^9 - 6 * q^11 - 3 * q^13 - 7 * q^15 + 14 * q^17 + 10 * q^19 + 9 * q^21 - 8 * q^23 + 2 * q^25 - 11 * q^27 - 8 * q^29 - 4 * q^31 - 2 * q^33 + 16 * q^35 + 6 * q^37 + 14 * q^39 - 5 * q^43 + 25 * q^45 - 17 * q^47 - 3 * q^49 - 15 * q^51 + 28 * q^53 + 8 * q^55 + 15 * q^57 - 4 * q^59 - q^61 + 15 * q^63 - 15 * q^65 + 4 * q^67 - 14 * q^69 + 14 * q^71 - 24 * q^73 + 38 * q^75 - 5 * q^77 - q^79 + 5 * q^81 - 22 * q^83 + 3 * q^85 - q^87 + 44 * q^89 + 22 * q^91 + 12 * q^93 - 24 * q^95 + 16 * q^97 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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