LMFDB - Embedded newform 441.2.o.e.146.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(146,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(441, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("441.146"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.18
Character	$\chi$	$=$	441.146
Dual form			441.2.o.e.293.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.58658 + 0.916012i) q^{2} +(1.44264 + 0.958541i) q^{3} +(0.678156 + 1.17460i) q^{4} +(-0.322784 - 0.559079i) q^{5} +(1.41082 + 2.84227i) q^{6} -1.17925i q^{8} +(1.16240 + 2.76565i) q^{9} -1.18270i q^{10} +(4.60375 + 2.65797i) q^{11} +(-0.147571 + 2.34456i) q^{12} +(-4.44045 + 2.56370i) q^{13} +(0.0702397 - 1.11595i) q^{15} +(2.43652 - 4.22018i) q^{16} -1.62986 q^{17} +(-0.689134 + 5.45270i) q^{18} -2.41378i q^{19} +(0.437796 - 0.758285i) q^{20} +(4.86947 + 8.43418i) q^{22} +(-1.27442 + 0.735784i) q^{23} +(1.13036 - 1.70123i) q^{24} +(2.29162 - 3.96920i) q^{25} -9.39351 q^{26} +(-0.974073 + 5.10404i) q^{27} +(-6.43846 - 3.71724i) q^{29} +(1.13366 - 1.70620i) q^{30} +(4.90799 - 2.83363i) q^{31} +(5.68894 - 3.28451i) q^{32} +(4.09375 + 8.24737i) q^{33} +(-2.58590 - 1.49297i) q^{34} +(-2.46025 + 3.24090i) q^{36} -7.99471 q^{37} +(2.21105 - 3.82965i) q^{38} +(-8.86336 - 0.557875i) q^{39} +(-0.659294 + 0.380644i) q^{40} +(-5.99052 - 10.3759i) q^{41} +(-1.51281 + 2.62026i) q^{43} +7.21009i q^{44} +(1.17101 - 1.54258i) q^{45} -2.69595 q^{46} +(1.54176 - 2.67041i) q^{47} +(7.56023 - 3.75268i) q^{48} +(7.27168 - 4.19830i) q^{50} +(-2.35130 - 1.56229i) q^{51} +(-6.02264 - 3.47717i) q^{52} -2.36199i q^{53} +(-6.22080 + 7.20569i) q^{54} -3.43181i q^{55} +(2.31371 - 3.48220i) q^{57} +(-6.81008 - 11.7954i) q^{58} +(-1.47918 - 2.56202i) q^{59} +(1.35843 - 0.674284i) q^{60} +(9.18018 + 5.30018i) q^{61} +10.3825 q^{62} +2.28853 q^{64} +(2.86662 + 1.65504i) q^{65} +(-1.05962 + 16.8350i) q^{66} +(5.07747 + 8.79444i) q^{67} +(-1.10530 - 1.91444i) q^{68} +(-2.54380 - 0.160111i) q^{69} -4.76597i q^{71} +(3.26140 - 1.37076i) q^{72} +11.8055i q^{73} +(-12.6842 - 7.32325i) q^{74} +(7.11062 - 3.52950i) q^{75} +(2.83523 - 1.63692i) q^{76} +(-13.5514 - 9.00406i) q^{78} +(-3.48104 + 6.02934i) q^{79} -3.14588 q^{80} +(-6.29766 + 6.42958i) q^{81} -21.9496i q^{82} +(-3.51618 + 6.09021i) q^{83} +(0.526093 + 0.911221i) q^{85} +(-4.80038 + 2.77150i) q^{86} +(-5.72522 - 11.5342i) q^{87} +(3.13442 - 5.42898i) q^{88} -4.32674 q^{89} +(3.27093 - 1.37476i) q^{90} +(-1.72850 - 0.997953i) q^{92} +(9.79659 + 0.616613i) q^{93} +(4.89226 - 2.82455i) q^{94} +(-1.34949 + 0.779129i) q^{95} +(11.3554 + 0.714729i) q^{96} +(14.3946 + 8.31075i) q^{97} +(-1.99965 + 15.8220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64}+ \cdots - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.58658	+	0.916012i	1.12188	+	0.647718i	0.941880	−	0.335948i	$-0.109057\pi$
$2$	1.58658	+	0.916012i	1.12188	+	0.647718i	0.180001	+	0.983667i	$0.442390\pi$
$3$	1.44264	+	0.958541i	0.832906	+	0.553414i
$3$	1.44264	+	0.958541i	0.832906	+	0.553414i
$4$	0.678156	+	1.17460i	0.339078	+	0.587300i
$5$	−0.322784	−	0.559079i	−0.144353	−	0.250028i	0.784778	−	0.619777i	$-0.212777\pi$
$5$	−0.322784	−	0.559079i	−0.144353	−	0.250028i	−0.929132	+	0.369749i	$0.879444\pi$
$6$	1.41082	+	2.84227i	0.575966	+	1.16035i
$7$		0			0
$7$		0			0
$8$		−	1.17925i		−	0.416928i
$9$	1.16240	+	2.76565i	0.387466	+	0.921884i
$10$		−	1.18270i		−	0.374002i
$11$	4.60375	+	2.65797i	1.38808	+	0.801410i	0.993099	−	0.117279i	$-0.0374171\pi$
$11$	4.60375	+	2.65797i	1.38808	+	0.801410i	0.394983	+	0.918688i	$0.370750\pi$
$12$	−0.147571	+	2.34456i	−0.0426000	+	0.676817i
$13$	−4.44045	+	2.56370i	−1.23156	+	0.711041i	−0.967355	−	0.253425i	$-0.918443\pi$
$13$	−4.44045	+	2.56370i	−1.23156	+	0.711041i	−0.264205	+	0.964467i	$0.585110\pi$
$14$		0			0
$15$	0.0702397	−	1.11595i	0.0181358	−	0.288137i
$16$	2.43652	−	4.22018i	0.609130	−	1.05504i
$17$	−1.62986			−0.395299			−0.197650	−	0.980273i	$-0.563331\pi$
$17$	−1.62986			−0.395299			−0.197650	+	0.980273i	$0.563331\pi$
$18$	−0.689134	+	5.45270i	−0.162430	+	1.28521i
$19$		−	2.41378i		−	0.553759i	−0.960905	−	0.276879i	$-0.910700\pi$
$19$		−	2.41378i		−	0.553759i	0.960905	−	0.276879i	$-0.0893002\pi$
$20$	0.437796	−	0.758285i	0.0978942	−	0.169558i
$21$		0			0
$22$	4.86947	+	8.43418i	1.03818	+	1.79817i
$23$	−1.27442	+	0.735784i	−0.265734	+	0.153422i	−0.626947	−	0.779062i	$-0.715696\pi$
$23$	−1.27442	+	0.735784i	−0.265734	+	0.153422i	0.361213	+	0.932483i	$0.382363\pi$
$24$	1.13036	−	1.70123i	0.230734	−	0.347262i
$25$	2.29162	−	3.96920i	0.458324	−	0.793841i
$26$	−9.39351			−1.84222
$27$	−0.974073	+	5.10404i	−0.187461	+	0.982272i
$28$		0			0
$29$	−6.43846	−	3.71724i	−1.19559	−	0.690275i	−0.236022	−	0.971748i	$-0.575844\pi$
$29$	−6.43846	−	3.71724i	−1.19559	−	0.690275i	−0.959569	+	0.281473i	$0.909177\pi$
$30$	1.13366	−	1.70620i	0.206978	−	0.311508i
$31$	4.90799	−	2.83363i	0.881501	−	0.508935i	0.0103477	−	0.999946i	$-0.496706\pi$
$31$	4.90799	−	2.83363i	0.881501	−	0.508935i	0.871153	+	0.491012i	$0.163373\pi$
$32$	5.68894	−	3.28451i	1.00567	−	0.580625i
$33$	4.09375	+	8.24737i	0.712631	+	1.43568i
$34$	−2.58590	−	1.49297i	−0.443479	−	0.256043i
$35$		0			0
$36$	−2.46025	+	3.24090i	−0.410042	+	0.540150i
$37$	−7.99471			−1.31432			−0.657161	−	0.753750i	$-0.728243\pi$
$37$	−7.99471			−1.31432			−0.657161	+	0.753750i	$0.728243\pi$
$38$	2.21105	−	3.82965i	0.358680	−	0.621251i
$39$	−8.86336	−	0.557875i	−1.41927	−	0.0893315i
$40$	−0.659294	+	0.380644i	−0.104244	+	0.0601851i
$41$	−5.99052	−	10.3759i	−0.935562	−	1.62044i	−0.773628	−	0.633640i	$-0.781560\pi$
$41$	−5.99052	−	10.3759i	−0.935562	−	1.62044i	−0.161934	−	0.986802i	$-0.551773\pi$
$42$		0			0
$43$	−1.51281	+	2.62026i	−0.230701	+	0.399586i	−0.958015	−	0.286719i	$-0.907435\pi$
$43$	−1.51281	+	2.62026i	−0.230701	+	0.399586i	0.727314	+	0.686305i	$0.240769\pi$
$44$			7.21009i			1.08696i
$45$	1.17101	−	1.54258i	0.174564	−	0.229954i
$46$	−2.69595			−0.397496
$47$	1.54176	−	2.67041i	0.224889	−	0.389520i	−0.731397	−	0.681952i	$-0.761131\pi$
$47$	1.54176	−	2.67041i	0.224889	−	0.389520i	0.956286	+	0.292432i	$0.0944646\pi$
$48$	7.56023	−	3.75268i	1.09122	−	0.541652i
$49$		0			0
$50$	7.27168	−	4.19830i	1.02837	−	0.593730i
$51$	−2.35130	−	1.56229i	−0.329247	−	0.218764i
$52$	−6.02264	−	3.47717i	−0.835190	−	0.482197i
$53$		−	2.36199i		−	0.324444i	−0.986754	−	0.162222i	$-0.948134\pi$
$53$		−	2.36199i		−	0.324444i	0.986754	−	0.162222i	$-0.0518661\pi$
$54$	−6.22080	+	7.20569i	−0.846544	+	0.980571i
$55$		−	3.43181i		−	0.462745i
$56$		0			0
$57$	2.31371	−	3.48220i	0.306458	−	0.461229i
$58$	−6.81008	−	11.7954i	−0.894207	−	1.54881i
$59$	−1.47918	−	2.56202i	−0.192573	−	0.333546i	0.753529	−	0.657414i	$-0.228350\pi$
$59$	−1.47918	−	2.56202i	−0.192573	−	0.333546i	−0.946102	+	0.323868i	$0.895017\pi$
$60$	1.35843	−	0.674284i	0.175372	−	0.0870497i
$61$	9.18018	+	5.30018i	1.17540	+	0.678618i	0.954946	−	0.296779i	$-0.0959124\pi$
$61$	9.18018	+	5.30018i	1.17540	+	0.678618i	0.220455	+	0.975397i	$0.429246\pi$
$62$	10.3825			1.31859
$63$		0			0
$64$	2.28853			0.286066
$65$	2.86662	+	1.65504i	0.355560	+	0.205283i
$66$	−1.05962	+	16.8350i	−0.130431	+	2.07225i
$67$	5.07747	+	8.79444i	0.620312	+	1.07441i	0.989428	+	0.145028i	$0.0463273\pi$
$67$	5.07747	+	8.79444i	0.620312	+	1.07441i	−0.369116	+	0.929383i	$0.620339\pi$
$68$	−1.10530	−	1.91444i	−0.134037	−	0.232159i
$69$	−2.54380	−	0.160111i	−0.306237	−	0.0192751i
$70$		0			0
$71$		−	4.76597i		−	0.565617i	−0.959176	−	0.282808i	$-0.908734\pi$
$71$		−	4.76597i		−	0.565617i	0.959176	−	0.282808i	$-0.0912661\pi$
$72$	3.26140	−	1.37076i	0.384360	−	0.161546i
$73$			11.8055i			1.38173i	0.722982	+	0.690867i	$0.242771\pi$
$73$			11.8055i			1.38173i	−0.722982	+	0.690867i	$0.757229\pi$
$74$	−12.6842	−	7.32325i	−1.47451	−	0.851311i
$75$	7.11062	−	3.52950i	0.821064	−	0.407552i
$76$	2.83523	−	1.63692i	0.325223	−	0.187767i
$77$		0			0
$78$	−13.5514	−	9.00406i	−1.53440	−	1.01951i
$79$	−3.48104	+	6.02934i	−0.391648	+	0.678354i	−0.992667	−	0.120881i	$-0.961428\pi$
$79$	−3.48104	+	6.02934i	−0.391648	+	0.678354i	0.601019	+	0.799235i	$0.294762\pi$
$80$	−3.14588			−0.351720
$81$	−6.29766	+	6.42958i	−0.699740	+	0.714397i
$82$		−	21.9496i		−	2.42392i
$83$	−3.51618	+	6.09021i	−0.385951	+	0.668487i	−0.991901	−	0.127016i	$-0.959460\pi$
$83$	−3.51618	+	6.09021i	−0.385951	+	0.668487i	0.605949	+	0.795503i	$0.292793\pi$
$84$		0			0
$85$	0.526093	+	0.911221i	0.0570628	+	0.0988357i
$86$	−4.80038	+	2.77150i	−0.517638	+	0.298859i
$87$	−5.72522	−	11.5342i	−0.613808	−	1.23659i
$88$	3.13442	−	5.42898i	0.334130	−	0.578731i
$89$	−4.32674			−0.458633			−0.229317	−	0.973352i	$-0.573649\pi$
$89$	−4.32674			−0.458633			−0.229317	+	0.973352i	$0.573649\pi$
$90$	3.27093	−	1.37476i	0.344786	−	0.144913i
$91$		0			0
$92$	−1.72850	−	0.997953i	−0.180209	−	0.104044i
$93$	9.79659	+	0.616613i	1.01586	+	0.0639398i
$94$	4.89226	−	2.82455i	0.504598	−	0.291330i
$95$	−1.34949	+	0.779129i	−0.138455	+	0.0799370i
$96$	11.3554	+	0.714729i	1.15896	+	0.0729467i
$97$	14.3946	+	8.31075i	1.46156	+	0.843829i	0.999083	−	0.0428048i	$-0.0136294\pi$
$97$	14.3946	+	8.31075i	1.46156	+	0.843829i	0.462472	+	0.886634i	$0.346963\pi$
$98$		0			0
$99$	−1.99965	+	15.8220i	−0.200972	+	1.59017i
$100$	6.21631			0.621631
$101$	−2.32577	+	4.02835i	−0.231423	+	0.400836i	−0.958227	−	0.286009i	$-0.907671\pi$
$101$	−2.32577	+	4.02835i	−0.231423	+	0.400836i	0.726804	+	0.686845i	$0.241005\pi$
$102$	−2.29944	−	4.63251i	−0.227679	−	0.458687i
$103$	8.92382	−	5.15217i	0.879290	−	0.507658i	0.00886554	−	0.999961i	$-0.497178\pi$
$103$	8.92382	−	5.15217i	0.879290	−	0.507658i	0.870424	+	0.492303i	$0.163845\pi$
$104$	3.02324	+	5.23641i	0.296453	+	0.513472i
$105$		0			0
$106$	2.16361	−	3.74749i	0.210149	−	0.363988i
$107$			0.308550i			0.0298287i	0.999889	+	0.0149143i	$0.00474756\pi$
$107$			0.308550i			0.0298287i	−0.999889	+	0.0149143i	$0.995252\pi$
$108$	−6.65578	+	2.31719i	−0.640453	+	0.222971i
$109$	−6.28845			−0.602324			−0.301162	−	0.953573i	$-0.597375\pi$
$109$	−6.28845			−0.602324			−0.301162	+	0.953573i	$0.597375\pi$
$110$	3.14358	−	5.44484i	0.299728	−	0.519145i
$111$	−11.5335	−	7.66326i	−1.09471	−	0.727365i
$112$		0			0
$113$	7.72869	−	4.46216i	0.727054	−	0.419765i	−0.0902895	−	0.995916i	$-0.528779\pi$
$113$	7.72869	−	4.46216i	0.727054	−	0.419765i	0.817343	+	0.576151i	$0.195446\pi$
$114$	6.86062	−	3.40541i	0.642556	−	0.318946i
$115$	0.822722	+	0.474999i	0.0767192	+	0.0442939i
$116$		−	10.0835i		−	0.936228i
$117$	−12.2519	−	9.30071i	−1.13269	−	0.859851i
$118$		−	5.41979i		−	0.498932i
$119$		0			0
$120$	−1.31598	−	0.0828302i	−0.120132	−	0.00756133i
$121$	8.62966	+	14.9470i	0.784515	+	1.35882i
$122$	9.71006	+	16.8183i	0.879107	+	1.52266i
$123$	1.30357	−	20.7108i	0.117539	−	1.86743i
$124$	6.65676	+	3.84328i	0.597795	+	0.345137i
$125$	−6.18664			−0.553350
$126$		0			0
$127$	−2.49989			−0.221829			−0.110915	−	0.993830i	$-0.535378\pi$
$127$	−2.49989			−0.221829			−0.110915	+	0.993830i	$0.535378\pi$
$128$	−7.74695	−	4.47270i	−0.684740	−	0.395335i
$129$	−4.69406	+	2.32999i	−0.413289	+	0.205144i
$130$	3.03208	+	5.25171i	0.265931	+	0.460605i
$131$	−1.26725	−	2.19494i	−0.110720	−	0.191773i	0.805341	−	0.592812i	$-0.201982\pi$
$131$	−1.26725	−	2.19494i	−0.110720	−	0.191773i	−0.916061	+	0.401039i	$0.868649\pi$
$132$	−6.91116	+	10.4015i	−0.601540	+	0.905337i
$133$		0			0
$134$			18.6041i			1.60715i
$135$	3.16797	−	1.10292i	0.272656	−	0.0949241i
$136$			1.92202i			0.164812i
$137$	1.05041	+	0.606456i	0.0897429	+	0.0518131i	0.544200	−	0.838956i	$-0.316833\pi$
$137$	1.05041	+	0.606456i	0.0897429	+	0.0518131i	−0.454457	+	0.890769i	$0.650167\pi$
$138$	−3.88927	−	2.58418i	−0.331077	−	0.219980i
$139$	6.11754	−	3.53196i	0.518883	−	0.299577i	−0.217594	−	0.976039i	$-0.569821\pi$
$139$	6.11754	−	3.53196i	0.518883	−	0.299577i	0.736478	+	0.676462i	$0.236488\pi$
$140$		0			0
$141$	4.78390	−	2.37459i	0.402877	−	0.199977i
$142$	4.36569	−	7.56159i	0.366360	−	0.634555i
$143$	−27.2570			−2.27934
$144$	14.5038	+	1.83304i	1.20865	+	0.152753i
$145$			4.79947i			0.398574i
$146$	−10.8140	+	18.7304i	−0.894974	+	1.55014i
$147$		0			0
$148$	−5.42166	−	9.39060i	−0.445658	−	0.771902i
$149$	6.00270	−	3.46566i	0.491760	−	0.283918i	−0.233544	−	0.972346i	$-0.575032\pi$
$149$	6.00270	−	3.46566i	0.491760	−	0.283918i	0.725304	+	0.688428i	$0.241699\pi$
$150$	14.5146	+	0.913575i	1.18511	+	0.0745931i
$151$	−3.15939	+	5.47223i	−0.257108	+	0.445323i	−0.965466	−	0.260530i	$-0.916103\pi$
$151$	−3.15939	+	5.47223i	−0.257108	+	0.445323i	0.708358	+	0.705853i	$0.249436\pi$
$152$	−2.84645			−0.230878
$153$	−1.89455	−	4.50763i	−0.153165	−	0.364420i
$154$		0			0
$155$	−3.16844	−	1.82930i	−0.254495	−	0.146933i
$156$	−5.35546	−	10.7892i	−0.428780	−	0.863831i
$157$	−1.72363	+	0.995139i	−0.137561	+	0.0794208i	−0.567201	−	0.823579i	$-0.691974\pi$
$157$	−1.72363	+	0.995139i	−0.137561	+	0.0794208i	0.429640	+	0.903000i	$0.358640\pi$
$158$	−11.0459	+	6.37735i	−0.878765	+	0.507355i
$159$	2.26407	−	3.40749i	0.179552	−	0.270232i
$160$	−3.67260	−	2.12038i	−0.290345	−	0.167631i
$161$		0			0
$162$	−15.8813	+	4.43230i	−1.24775	+	0.348234i
$163$	−5.98729			−0.468961			−0.234480	−	0.972121i	$-0.575339\pi$
$163$	−5.98729			−0.468961			−0.234480	+	0.972121i	$0.575339\pi$
$164$	8.12502	−	14.0729i	0.634457	−	1.09891i
$165$	3.28953	−	4.95085i	0.256090	−	0.385423i
$166$	−11.1574	+	6.44173i	−0.865983	+	0.499976i
$167$	0.697990	+	1.20895i	0.0540121	+	0.0935516i	0.891767	−	0.452494i	$-0.149466\pi$
$167$	0.697990	+	1.20895i	0.0540121	+	0.0935516i	−0.837755	+	0.546046i	$0.816132\pi$
$168$		0			0
$169$	6.64508	−	11.5096i	0.511160	−	0.885355i
$170$			1.92763i			0.147843i
$171$	6.67567	−	2.80577i	0.510501	−	0.214563i
$172$	−4.10368			−0.312903
$173$	−3.80506	+	6.59055i	−0.289293	+	0.501071i	−0.973641	−	0.228085i	$-0.926754\pi$
$173$	−3.80506	+	6.59055i	−0.289293	+	0.501071i	0.684348	+	0.729156i	$0.260087\pi$
$174$	1.48191	−	23.5442i	0.112343	−	1.78488i
$175$		0			0
$176$	22.4343	−	12.9524i	1.69105	−	0.976326i
$177$	0.321878	−	5.11391i	0.0241938	−	0.384385i
$178$	−6.86471	−	3.96334i	−0.514532	−	0.297065i
$179$			9.24786i			0.691218i	0.938379	+	0.345609i	$0.112328\pi$
$179$			9.24786i			0.691218i	−0.938379	+	0.345609i	$0.887672\pi$
$180$	2.60605	+	0.329362i	0.194243	+	0.0245492i
$181$		−	11.9634i		−	0.889234i	−0.895721	−	0.444617i	$-0.853340\pi$
$181$		−	11.9634i		−	0.889234i	0.895721	−	0.444617i	$-0.146660\pi$
$182$		0			0
$183$	8.16322	+	16.4458i	0.603443	+	1.21571i
$184$	0.867674	+	1.50286i	0.0639658	+	0.110792i
$185$	2.58057	+	4.46967i	0.189727	+	0.328617i
$186$	14.9782	+	9.95210i	1.09826	+	0.729723i
$187$	−7.50347	−	4.33213i	−0.548708	−	0.316797i
$188$	4.18223			0.305020
$189$		0			0
$190$	−2.85477			−0.207107
$191$	−17.5586	−	10.1375i	−1.27050	−	0.733521i	−0.295415	−	0.955369i	$-0.595458\pi$
$191$	−17.5586	−	10.1375i	−1.27050	−	0.733521i	−0.975081	+	0.221847i	$0.928791\pi$
$192$	3.30152	+	2.19365i	0.238266	+	0.158313i
$193$	8.44583	+	14.6286i	0.607944	+	1.05299i	0.991579	+	0.129505i	$0.0413389\pi$
$193$	8.44583	+	14.6286i	0.607944	+	1.05299i	−0.383634	+	0.923485i	$0.625328\pi$
$194$	15.2255	+	26.3713i	1.09313	+	1.89335i
$195$	2.54906	+	5.13539i	0.182542	+	0.367753i
$196$		0			0
$197$			18.7102i			1.33305i	0.745484	+	0.666524i	$0.232219\pi$
$197$			18.7102i			1.33305i	−0.745484	+	0.666524i	$0.767781\pi$
$198$	−17.6657	+	23.2711i	−1.25545	+	1.65381i
$199$		−	18.0446i		−	1.27915i	−0.768729	−	0.639574i	$-0.779111\pi$
$199$		−	18.0446i		−	1.27915i	0.768729	−	0.639574i	$-0.220889\pi$
$200$	−4.68069	−	2.70240i	−0.330975	−	0.191088i
$201$	−1.10489	+	17.5541i	−0.0779327	+	1.23817i
$202$	−7.38004	+	4.26087i	−0.519258	+	0.299794i
$203$		0			0
$204$	0.240520	−	3.82131i	0.0168397	−	0.267545i
$205$	−3.86729	+	6.69834i	−0.270103	+	0.467833i
$206$	18.8778			1.31528
$207$	−3.51630	−	2.66931i	−0.244400	−	0.185530i
$208$			24.9860i			1.73247i
$209$	6.41576	−	11.1124i	0.443788	−	0.768663i
$210$		0			0
$211$	−4.03491	−	6.98868i	−0.277775	−	0.481120i	0.693057	−	0.720883i	$-0.256264\pi$
$211$	−4.03491	−	6.98868i	−0.277775	−	0.481120i	−0.970831	+	0.239763i	$0.922930\pi$
$212$	2.77440	−	1.60180i	0.190546	−	0.110012i
$213$	4.56838	−	6.87556i	0.313020	−	0.471106i
$214$	−0.282636	+	0.489540i	−0.0193206	+	0.0334642i
$215$	1.95324			0.133210
$216$	6.01894	+	1.14868i	0.409537	+	0.0781576i
$217$		0			0
$218$	−9.97713	−	5.76030i	−0.675736	−	0.390137i
$219$	−11.3161	+	17.0311i	−0.764671	+	1.15085i
$220$	4.03101	−	2.32730i	0.271770	−	0.156907i
$221$	7.23732	−	4.17847i	0.486835	−	0.281074i
$222$	−11.2791	−	22.7232i	−0.757005	−	1.52508i
$223$	20.2450	+	11.6884i	1.35570	+	0.782716i	0.989041	−	0.147638i	$-0.0471671\pi$
$223$	20.2450	+	11.6884i	1.35570	+	0.782716i	0.366662	+	0.930354i	$0.380500\pi$
$224$		0			0
$225$	13.6412	+	1.72403i	0.909414	+	0.114935i
$226$	16.3496			1.08756
$227$	7.22154	−	12.5081i	0.479310	−	0.830190i	−0.520408	−	0.853918i	$-0.674220\pi$
$227$	7.22154	−	12.5081i	0.479310	−	0.830190i	0.999718	+	0.0237280i	$0.00755356\pi$
$228$	5.65925	+	0.356203i	0.374793	+	0.0235901i
$229$	−11.3568	+	6.55685i	−0.750479	+	0.433289i	−0.825867	−	0.563865i	$-0.809314\pi$
$229$	−11.3568	+	6.55685i	−0.750479	+	0.433289i	0.0753881	+	0.997154i	$0.475980\pi$
$230$	0.870209	+	1.50725i	0.0573799	+	0.0993849i
$231$		0			0
$232$	−4.38357	+	7.59256i	−0.287795	+	0.498476i
$233$		−	8.45202i		−	0.553710i	−0.960912	−	0.276855i	$-0.910708\pi$
$233$		−	8.45202i		−	0.553710i	0.960912	−	0.276855i	$-0.0892922\pi$
$234$	−10.9190	−	25.9792i	−0.713797	−	1.69831i
$235$	−1.99063			−0.129854
$236$	2.00623	−	3.47489i	0.130594	−	0.226196i
$237$	−10.8013	+	5.36143i	−0.701617	+	0.348262i
$238$		0			0
$239$	−24.2111	+	13.9783i	−1.56608	+	0.904179i	−0.569466	+	0.822015i	$0.692850\pi$
$239$	−24.2111	+	13.9783i	−1.56608	+	0.904179i	−0.996619	+	0.0821642i	$0.973817\pi$
$240$	−4.53836	−	3.01546i	−0.292950	−	0.194647i
$241$	19.4058	+	11.2039i	1.25004	+	0.721710i	0.971117	−	0.238605i	$-0.0766900\pi$
$241$	19.4058	+	11.2039i	1.25004	+	0.721710i	0.278921	+	0.960314i	$0.410023\pi$
$242$			31.6195i			2.03258i
$243$	−15.2482	+	3.23897i	−0.978176	+	0.207780i
$244$			14.3774i			0.920418i
$245$		0			0
$246$	21.0396	−	31.6652i	1.34143	−	2.01890i
$247$	6.18819	+	10.7183i	0.393745	+	0.681987i
$248$	−3.34156	−	5.78775i	−0.212189	−	0.367523i
$249$	−10.9103	+	5.41555i	−0.691412	+	0.343197i
$250$	−9.81559	−	5.66703i	−0.620792	−	0.358415i
$251$	6.39587			0.403704			0.201852	−	0.979416i	$-0.435304\pi$
$251$	6.39587			0.403704			0.201852	+	0.979416i	$0.435304\pi$
$252$		0			0
$253$	−7.82278			−0.491814
$254$	−3.96627	−	2.28993i	−0.248866	−	0.143683i
$255$	−0.114481	+	1.81884i	−0.00716907	+	0.113900i
$256$	−10.4826	−	18.1565i	−0.655165	−	1.13478i
$257$	1.65705	+	2.87009i	0.103364	+	0.179031i	0.913069	−	0.407806i	$-0.133706\pi$
$257$	1.65705	+	2.87009i	0.103364	+	0.179031i	−0.809705	+	0.586837i	$0.800373\pi$
$258$	−9.58180	−	0.603094i	−0.596537	−	0.0375470i
$259$		0			0
$260$			4.48950i			0.278427i
$261$	2.79655	−	22.1274i	0.173102	−	1.36965i
$262$		−	4.64326i		−	0.286862i
$263$	19.6502	+	11.3451i	1.21169	+	0.699567i	0.963126	−	0.269050i	$-0.0867096\pi$
$263$	19.6502	+	11.3451i	1.21169	+	0.699567i	0.248559	+	0.968617i	$0.420043\pi$
$264$	9.72573	−	4.82757i	0.598577	−	0.297116i
$265$	−1.32054	+	0.762413i	−0.0811200	+	0.0468347i
$266$		0			0
$267$	−6.24191	−	4.14736i	−0.381999	−	0.253814i
$268$	−6.88664	+	11.9280i	−0.420668	+	0.728619i
$269$	2.76100			0.168341			0.0841707	−	0.996451i	$-0.473176\pi$
$269$	2.76100			0.168341			0.0841707	+	0.996451i	$0.473176\pi$
$270$	6.03653	+	1.15203i	0.367371	+	0.0701105i
$271$			6.08922i			0.369894i	0.982749	+	0.184947i	$0.0592113\pi$
$271$			6.08922i			0.369894i	−0.982749	+	0.184947i	$0.940789\pi$
$272$	−3.97119	+	6.87830i	−0.240789	+	0.417058i
$273$		0			0
$274$	1.11104	+	1.92438i	0.0671205	+	0.116256i
$275$	21.1001	−	12.1821i	1.27238	−	0.734611i
$276$	−1.53702	−	3.09652i	−0.0925180	−	0.186389i
$277$	4.71684	−	8.16980i	0.283407	−	0.490876i	−0.688814	−	0.724938i	$-0.741869\pi$
$277$	4.71684	−	8.16980i	0.283407	−	0.490876i	0.972222	+	0.234062i	$0.0752019\pi$
$278$	12.9413			0.776167
$279$	13.5419	+	10.2800i	0.810730	+	0.615446i
$280$		0			0
$281$	4.57153	+	2.63938i	0.272715	+	0.157452i	0.630121	−	0.776497i	$-0.283005\pi$
$281$	4.57153	+	2.63938i	0.272715	+	0.157452i	−0.357406	+	0.933949i	$0.616339\pi$
$282$	9.76520	+	0.614638i	0.581509	+	0.0366011i
$283$	−17.0346	+	9.83496i	−1.01260	+	0.584628i	−0.911953	−	0.410294i	$-0.865426\pi$
$283$	−17.0346	+	9.83496i	−1.01260	+	0.584628i	−0.100651	+	0.994922i	$0.532093\pi$
$284$	5.59811	−	3.23207i	0.332187	−	0.191788i
$285$	−2.69365	−	0.169543i	−0.159558	−	0.0100429i
$286$	−43.2453	−	24.9677i	−2.55715	−	1.47637i
$287$		0			0
$288$	15.6966	+	11.9157i	0.924933	+	0.702141i
$289$	−14.3436			−0.843738
$290$	−4.39637	+	7.61474i	−0.258164	+	0.447153i
$291$	12.8000	+	25.7873i	0.750352	+	1.51168i
$292$	−13.8668	+	8.00600i	−0.811493	+	0.468516i
$293$	−9.11647	−	15.7902i	−0.532590	−	0.922473i	−0.999276	−	0.0380495i	$-0.987886\pi$
$293$	−9.11647	−	15.7902i	−0.532590	−	0.922473i	0.466686	−	0.884423i	$-0.345448\pi$
$294$		0			0
$295$	−0.954912	+	1.65396i	−0.0555971	+	0.0962970i
$296$			9.42778i			0.547979i
$297$	−18.0508	+	20.9086i	−1.04741	+	1.21324i
$298$	12.6983			0.735595
$299$	3.77265	−	6.53443i	0.218178	−	0.377896i
$300$	8.96787	+	5.95858i	0.517760	+	0.344019i
$301$		0			0
$302$	−10.0253	+	5.78808i	−0.576888	+	0.333067i
$303$	−7.21658	+	3.58210i	−0.414582	+	0.205786i
$304$	−10.1866	−	5.88122i	−0.584240	−	0.337311i
$305$		−	6.84326i		−	0.391844i
$306$	1.12319	−	8.88714i	0.0642086	−	0.508044i
$307$			26.0447i			1.48645i	0.669042	+	0.743224i	$0.266704\pi$
$307$			26.0447i			1.48645i	−0.669042	+	0.743224i	$0.733296\pi$
$308$		0			0
$309$	17.8124	+	1.12114i	1.01331	+	0.0637795i
$310$	−3.35132	−	5.80466i	−0.190342	−	0.329683i
$311$	14.1433	+	24.4969i	0.801992	+	1.38909i	0.918303	+	0.395878i	$0.129560\pi$
$311$	14.1433	+	24.4969i	0.801992	+	1.38909i	−0.116311	+	0.993213i	$0.537107\pi$
$312$	−0.657875	+	10.4521i	−0.0372448	+	0.591736i
$313$	−4.82891	−	2.78797i	−0.272946	−	0.157586i	0.357280	−	0.933998i	$-0.383704\pi$
$313$	−4.82891	−	2.78797i	−0.272946	−	0.157586i	−0.630226	+	0.776412i	$0.717038\pi$
$314$	−3.64624			−0.205769
$315$		0			0
$316$	−9.44276			−0.531197
$317$	29.0708	+	16.7841i	1.63278	+	0.942686i	0.983230	+	0.182367i	$0.0583760\pi$
$317$	29.0708	+	16.7841i	1.63278	+	0.942686i	0.649550	+	0.760319i	$0.274957\pi$
$318$	6.71342	−	3.33235i	0.376470	−	0.186869i
$319$	−19.7607	−	34.2265i	−1.10639	−	1.91632i
$320$	−0.738701	−	1.27947i	−0.0412947	−	0.0715244i
$321$	−0.295758	+	0.445126i	−0.0165076	+	0.0248445i
$322$		0			0
$323$			3.93412i			0.218901i
$324$	−11.8230	−	3.03698i	−0.656832	−	0.168721i
$325$			23.5001i			1.30355i
$326$	−9.49931	−	5.48443i	−0.526118	−	0.303755i
$327$	−9.07195	−	6.02774i	−0.501680	−	0.333335i
$328$	−12.2358	+	7.06433i	−0.675608	+	0.390063i
$329$		0			0
$330$	9.75414	−	4.84167i	0.536948	−	0.266525i
$331$	15.1867	−	26.3042i	0.834739	−	1.44581i	−0.0595042	−	0.998228i	$-0.518952\pi$
$331$	15.1867	−	26.3042i	0.834739	−	1.44581i	0.894243	−	0.447582i	$-0.147715\pi$
$332$	−9.53809			−0.523470
$333$	−9.29304	−	22.1106i	−0.509255	−	1.21165i
$334$			2.55747i			0.139938i
$335$	3.27785	−	5.67741i	0.179088	−	0.310190i
$336$		0			0
$337$	1.86121	+	3.22371i	0.101387	+	0.175607i	0.912256	−	0.409620i	$-0.134339\pi$
$337$	1.86121	+	3.22371i	0.101387	+	0.175607i	−0.810870	+	0.585227i	$0.801005\pi$
$338$	21.0859	−	12.1739i	1.14692	−	0.662175i
$339$	15.4268	+	0.970991i	0.837871	+	0.0527370i
$340$	−0.713547	+	1.23590i	−0.0386975	+	0.0670261i
$341$	30.1268			1.63146
$342$	13.1616	+	1.66342i	0.711698	+	0.0899472i
$343$		0			0
$344$	3.08995	+	1.78398i	0.166599	+	0.0961858i
$345$	0.731583	+	1.47386i	0.0393871	+	0.0793501i
$346$	−12.0741	+	6.97096i	−0.649105	+	0.374761i
$347$	6.18028	−	3.56818i	0.331775	−	0.191550i	−0.324854	−	0.945764i	$-0.605315\pi$
$347$	6.18028	−	3.56818i	0.331775	−	0.191550i	0.656629	+	0.754214i	$0.271982\pi$
$348$	9.66544	−	14.5468i	0.518122	−	0.779790i
$349$	−13.2087	−	7.62607i	−0.707047	−	0.408214i	0.102920	−	0.994690i	$-0.467182\pi$
$349$	−13.2087	−	7.62607i	−0.707047	−	0.408214i	−0.809967	+	0.586476i	$0.800515\pi$
$350$		0			0
$351$	−8.75987	−	25.1615i	−0.467567	−	1.34302i
$352$	34.9206			1.86127
$353$	17.2359	−	29.8534i	0.917373	−	1.58894i	0.113985	−	0.993482i	$-0.463638\pi$
$353$	17.2359	−	29.8534i	0.917373	−	1.58894i	0.803389	−	0.595455i	$-0.203028\pi$
$354$	5.19509	−	7.81878i	0.276116	−	0.415563i
$355$	−2.66455	+	1.53838i	−0.141420	+	0.0816487i
$356$	−2.93420	−	5.08219i	−0.155512	−	0.269355i
$357$		0			0
$358$	−8.47115	+	14.6725i	−0.447714	+	0.775464i
$359$		−	6.62557i		−	0.349684i	−0.984596	−	0.174842i	$-0.944059\pi$
$359$		−	6.62557i		−	0.349684i	0.984596	−	0.174842i	$-0.0559415\pi$
$360$	−1.81909	−	1.38092i	−0.0958745	−	0.0727808i
$361$	13.1737			0.693351
$362$	10.9586	−	18.9809i	0.575973	−	0.997614i
$363$	−1.87786	+	29.8350i	−0.0985622	+	1.56593i
$364$		0			0
$365$	6.60022	−	3.81064i	0.345472	−	0.199458i
$366$	−2.11296	+	33.5702i	−0.110446	+	1.75474i
$367$	2.68222	+	1.54858i	0.140011	+	0.0808352i	0.568369	−	0.822774i	$-0.307575\pi$
$367$	2.68222	+	1.54858i	0.140011	+	0.0808352i	−0.428358	+	0.903609i	$0.640908\pi$
$368$			7.17101i			0.373815i
$369$	21.7327	−	28.6286i	1.13136	−	1.49035i
$370$			9.45532i			0.491559i
$371$		0			0
$372$	5.91934	+	11.9252i	0.306904	+	0.618295i
$373$	−4.84999	−	8.40043i	−0.251123	−	0.434958i	0.712712	−	0.701457i	$-0.247467\pi$
$373$	−4.84999	−	8.40043i	−0.251123	−	0.434958i	−0.963835	+	0.266499i	$0.914133\pi$
$374$	−7.93657	−	13.7465i	−0.410390	−	0.710816i
$375$	−8.92507	−	5.93015i	−0.460888	−	0.306231i
$376$	−3.14909	−	1.81813i	−0.162402	−	0.0937628i
$377$	38.1195			1.96326
$378$		0			0
$379$	7.76103			0.398657			0.199329	−	0.979933i	$-0.436124\pi$
$379$	7.76103			0.398657			0.199329	+	0.979933i	$0.436124\pi$
$380$	−1.83033	−	1.05674i	−0.0938941	−	0.0542098i
$381$	−3.60643	−	2.39624i	−0.184763	−	0.122763i
$382$	−18.5721	−	32.1678i	−0.950231	−	1.64585i
$383$	−12.3063	−	21.3152i	−0.628825	−	1.08916i	−0.987788	−	0.155804i	$-0.950203\pi$
$383$	−12.3063	−	21.3152i	−0.628825	−	1.08916i	0.358963	−	0.933352i	$-0.383130\pi$
$384$	−6.88876	−	13.8783i	−0.351541	−	0.708222i
$385$		0			0
$386$			30.9459i			1.57511i
$387$	−9.00521	−	1.13811i	−0.457761	−	0.0578536i
$388$			22.5440i			1.14450i
$389$	5.56578	+	3.21340i	0.282196	+	0.162926i	0.634417	−	0.772991i	$-0.281240\pi$
$389$	5.56578	+	3.21340i	0.282196	+	0.162926i	−0.352221	+	0.935917i	$0.614573\pi$
$390$	−0.659797	+	10.4827i	−0.0334101	+	0.530811i
$391$	2.07712	−	1.19923i	0.105044	−	0.0606474i
$392$		0			0
$393$	0.275761	−	4.38121i	0.0139103	−	0.221003i
$394$	−17.1388	+	29.6852i	−0.863439	+	1.49552i
$395$	4.49450			0.226143
$396$	−19.9406	+	8.38099i	−1.00205	+	0.421161i
$397$			13.2600i			0.665498i	0.943015	+	0.332749i	$0.107976\pi$
$397$			13.2600i			0.665498i	−0.943015	+	0.332749i	$0.892024\pi$
$398$	16.5291	−	28.6292i	0.828528	−	1.43505i
$399$		0			0
$400$	−11.1672	−	19.3421i	−0.558358	−	0.967105i
$401$	−13.6877	+	7.90259i	−0.683530	+	0.394636i	−0.801184	−	0.598418i	$-0.795796\pi$
$401$	−13.6877	+	7.90259i	−0.683530	+	0.394636i	0.117653	+	0.993055i	$0.462463\pi$
$402$	−17.8328	+	26.8389i	−0.889419	+	1.33860i
$403$	−14.5291	+	25.1652i	−0.723747	+	1.25357i
$404$	−6.30894			−0.313882
$405$	5.62742	+	1.44552i	0.279629	+	0.0718286i
$406$		0			0
$407$	−36.8056	−	21.2497i	−1.82439	−	1.05331i
$408$	−1.84233	+	2.77277i	−0.0912090	+	0.137273i
$409$	−4.69257	+	2.70926i	−0.232033	+	0.133964i	−0.611509	−	0.791237i	$-0.709437\pi$
$409$	−4.69257	+	2.70926i	−0.232033	+	0.133964i	0.379477	+	0.925201i	$0.376104\pi$
$410$	−12.2715	+	7.08497i	−0.606048	+	0.349902i
$411$	0.934051	+	1.88176i	0.0460733	+	0.0928204i
$412$	12.1035	+	6.98795i	0.596296	+	0.344271i
$413$		0			0
$414$	−3.13376	−	7.45605i	−0.154016	−	0.366445i
$415$	4.53987			0.222854
$416$	−16.8410	+	29.1694i	−0.825697	+	1.43015i
$417$	12.2109	+	0.768575i	0.597971	+	0.0376373i
$418$	20.3582	−	11.7538i	0.995754	−	0.574899i
$419$	−12.2469	−	21.2123i	−0.598302	−	1.03629i	−0.993072	−	0.117509i	$-0.962509\pi$
$419$	−12.2469	−	21.2123i	−0.598302	−	1.03629i	0.394770	−	0.918780i	$-0.370824\pi$
$420$		0			0
$421$	5.99347	−	10.3810i	0.292104	−	0.505939i	−0.682203	−	0.731163i	$-0.738978\pi$
$421$	5.99347	−	10.3810i	0.292104	−	0.505939i	0.974307	+	0.225224i	$0.0723113\pi$
$422$		−	14.7841i		−	0.719680i
$423$	9.17758	+	1.15990i	0.446229	+	0.0563962i
$424$	−2.78538			−0.135270
$425$	−3.73502	+	6.46925i	−0.181175	+	0.313805i
$426$	13.5462	−	6.72394i	0.656315	−	0.325776i
$427$		0			0
$428$	−0.362424	+	0.209245i	−0.0175184	+	0.0101143i
$429$	−39.3219	−	26.1269i	−1.89848	−	1.26142i
$430$	3.09897	+	1.78919i	0.149446	+	0.0862825i
$431$		−	30.8219i		−	1.48464i	−0.670046	−	0.742320i	$-0.733726\pi$
$431$		−	30.8219i		−	1.48464i	0.670046	−	0.742320i	$-0.266274\pi$
$432$	19.1666	+	16.5469i	0.922153	+	0.796111i
$433$		−	6.06173i		−	0.291308i	−0.989336	−	0.145654i	$-0.953471\pi$
$433$		−	6.06173i		−	0.291308i	0.989336	−	0.145654i	$-0.0465287\pi$
$434$		0			0
$435$	−4.60049	+	6.92389i	−0.220577	+	0.331975i
$436$	−4.26455	−	7.38642i	−0.204235	−	0.353745i
$437$	1.77602	+	3.07616i	0.0849585	+	0.147152i
$438$	−33.5546	+	16.6555i	−1.60330	+	0.795831i
$439$	−23.5081	−	13.5724i	−1.12198	−	0.647776i	−0.180075	−	0.983653i	$-0.557634\pi$
$439$	−23.5081	−	13.5724i	−1.12198	−	0.647776i	−0.941906	+	0.335877i	$0.890967\pi$
$440$	−4.04697			−0.192932
$441$		0			0
$442$	15.3101			0.728228
$443$	−4.63465	−	2.67582i	−0.220199	−	0.127132i	0.385843	−	0.922564i	$-0.373910\pi$
$443$	−4.63465	−	2.67582i	−0.220199	−	0.127132i	−0.606042	+	0.795432i	$0.707244\pi$
$444$	1.17978	−	18.7441i	0.0559901	−	0.889556i
$445$	1.39660	+	2.41899i	0.0662053	+	0.114671i
$446$	21.4135	+	37.0893i	1.01396	+	1.75623i
$447$	11.9817	+	0.754147i	0.566714	+	0.0356699i
$448$		0			0
$449$		−	34.2418i		−	1.61597i	−0.589204	−	0.807985i	$-0.700558\pi$
$449$		−	34.2418i		−	1.61597i	0.589204	−	0.807985i	$-0.299442\pi$
$450$	20.0636	+	15.2308i	0.945809	+	0.717988i
$451$		−	63.6906i		−	2.99907i
$452$	10.4825	+	6.05208i	0.493056	+	0.284666i
$453$	−9.80321	+	4.86603i	−0.460595	+	0.228626i
$454$	22.9151	−	13.2300i	1.07546	−	0.620916i
$455$		0			0
$456$	−4.10640	−	2.72844i	−0.192300	−	0.127771i
$457$	7.93019	−	13.7355i	0.370958	−	0.642519i	−0.618755	−	0.785584i	$-0.712363\pi$
$457$	7.93019	−	13.7355i	0.370958	−	0.642519i	0.989713	+	0.143065i	$0.0456959\pi$
$458$	−24.0246			−1.12260
$459$	1.58760	−	8.31887i	0.0741030	−	0.388292i
$460$			1.28849i			0.0600763i
$461$	−6.50676	+	11.2700i	−0.303050	+	0.524898i	−0.976825	−	0.214038i	$-0.931338\pi$
$461$	−6.50676	+	11.2700i	−0.303050	+	0.524898i	0.673775	+	0.738936i	$0.264672\pi$
$462$		0			0
$463$	−6.01941	−	10.4259i	−0.279746	−	0.484534i	0.691576	−	0.722304i	$-0.256917\pi$
$463$	−6.01941	−	10.4259i	−0.279746	−	0.484534i	−0.971321	+	0.237770i	$0.923583\pi$
$464$	−31.3749	+	18.1143i	−1.45654	+	0.840935i
$465$	−2.81745	−	5.67610i	−0.130656	−	0.263223i
$466$	7.74215	−	13.4098i	0.358648	−	0.621197i
$467$	−20.3457			−0.941486			−0.470743	−	0.882270i	$-0.656014\pi$
$467$	−20.3457			−0.941486			−0.470743	+	0.882270i	$0.656014\pi$
$468$	2.61594	−	20.6984i	0.120922	−	0.956783i
$469$		0			0
$470$	−3.15829	−	1.82344i	−0.145681	−	0.0841090i
$471$	−3.44045	−	0.216548i	−0.158528	−	0.00997800i
$472$	−3.02126	+	1.74433i	−0.139065	+	0.0802891i
$473$	−13.9292	+	8.04201i	−0.640464	+	0.369772i
$474$	−22.0482	−	1.38775i	−1.01271	−	0.0637414i
$475$	−9.58078	−	5.53146i	−0.439596	−	0.253801i
$476$		0			0
$477$	6.53244	−	2.74557i	0.299100	−	0.125711i
$478$	−51.2171			−2.34261
$479$	−12.1492	+	21.0430i	−0.555109	+	0.961477i	0.442786	+	0.896627i	$0.353990\pi$
$479$	−12.1492	+	21.0430i	−0.555109	+	0.961477i	−0.997895	+	0.0648499i	$0.979343\pi$
$480$	−3.26576	−	6.57927i	−0.149061	−	0.300301i
$481$	35.5001	−	20.4960i	1.61867	−	0.934538i
$482$	20.5259	+	35.5519i	0.934929	+	1.61934i
$483$		0			0
$484$	−11.7045	+	20.2728i	−0.532023	+	0.921491i
$485$		−	10.7303i		−	0.487239i
$486$	−27.1595	−	8.82869i	−1.23198	−	0.400477i
$487$	−27.3091			−1.23749			−0.618747	−	0.785590i	$-0.712359\pi$
$487$	−27.3091			−1.23749			−0.618747	+	0.785590i	$0.712359\pi$
$488$	6.25025	−	10.8257i	0.282935	−	0.490058i
$489$	−8.63748	−	5.73907i	−0.390601	−	0.259530i
$490$		0			0
$491$	−13.2899	+	7.67290i	−0.599763	+	0.346273i	−0.768948	−	0.639311i	$-0.779220\pi$
$491$	−13.2899	+	7.67290i	−0.599763	+	0.346273i	0.169185	+	0.985584i	$0.445886\pi$
$492$	25.2109	−	12.5140i	1.13660	−	0.564173i
$493$	10.4938	+	6.05859i	0.472616	+	0.272865i
$494$			22.6738i			1.02014i
$495$	9.49119	−	3.98913i	0.426597	−	0.179298i
$496$		−	27.6168i		−	1.24003i
$497$		0			0
$498$	−22.2708	−	1.40176i	−0.997976	−	0.0628143i
$499$	5.15504	+	8.92879i	0.230771	+	0.399707i	0.958035	−	0.286650i	$-0.0925418\pi$
$499$	5.15504	+	8.92879i	0.230771	+	0.399707i	−0.727264	+	0.686358i	$0.759208\pi$
$500$	−4.19551	−	7.26683i	−0.187629	−	0.324982i
$501$	−0.151886	+	2.41313i	−0.00678579	+	0.107811i
$502$	10.1476	+	5.85869i	0.452907	+	0.261486i
$503$	−24.6770			−1.10029			−0.550146	−	0.835068i	$-0.685428\pi$
$503$	−24.6770			−1.10029			−0.550146	+	0.835068i	$0.685428\pi$
$504$		0			0
$505$	3.00289			0.133627
$506$	−12.4115	−	7.16576i	−0.551757	−	0.318557i
$507$	20.6189	−	10.2346i	0.915716	−	0.454535i
$508$	−1.69531	−	2.93637i	−0.0752174	−	0.130280i
$509$	−2.58601	−	4.47911i	−0.114623	−	0.198533i	0.803006	−	0.595971i	$-0.203233\pi$
$509$	−2.58601	−	4.47911i	−0.114623	−	0.198533i	−0.917629	+	0.397438i	$0.869899\pi$
$510$	−1.84771	+	2.78087i	−0.0818181	+	0.123139i
$511$		0			0
$512$		−	20.5181i		−	0.906778i
$513$	12.3200	+	2.35120i	0.543942	+	0.103808i
$514$			6.07150i			0.267802i
$515$	−5.76093	−	3.32608i	−0.253857	−	0.146564i
$516$	−5.92012	−	3.93354i	−0.260619	−	0.173165i
$517$	14.1958	−	8.19594i	0.624330	−	0.360457i
$518$		0			0
$519$	−11.8066	+	5.86047i	−0.518254	+	0.257246i
$520$	1.95171	−	3.38046i	0.0855882	−	0.148243i
$521$	38.3328			1.67939			0.839696	−	0.543058i	$-0.182733\pi$
$521$	38.3328			1.67939			0.839696	+	0.543058i	$0.182733\pi$
$522$	24.7060	−	32.5453i	1.08135	−	1.42447i
$523$			27.3050i			1.19396i	0.802255	+	0.596982i	$0.203634\pi$
$523$			27.3050i			1.19396i	−0.802255	+	0.596982i	$0.796366\pi$
$524$	1.71878	−	2.97702i	0.0750855	−	0.130052i
$525$		0			0
$526$	20.7844	+	35.9997i	0.906245	+	1.56966i
$527$	−7.99934	+	4.61842i	−0.348457	+	0.201182i
$528$	44.7799	+	2.81852i	1.94879	+	0.122660i
$529$	−10.4172	+	18.0432i	−0.452924	+	0.784487i
$530$	−2.79352			−0.121343
$531$	5.36625	−	7.06898i	0.232875	−	0.306768i
$532$		0			0
$533$	53.2012	+	30.7158i	2.30440	+	1.33045i
$534$	−6.10425	−	12.2978i	−0.264157	−	0.532177i
$535$	0.172504	−	0.0995952i	0.00745799	−	0.00430588i
$536$	10.3709	−	5.98762i	0.447953	−	0.258626i
$537$	−8.86446	+	13.3413i	−0.382530	+	0.575720i
$538$	4.38055	+	2.52911i	0.188859	+	0.109038i
$539$		0			0
$540$	3.44387	+	2.97315i	0.148201	+	0.127944i
$541$	19.5610			0.840995			0.420498	−	0.907294i	$-0.361856\pi$
$541$	19.5610			0.840995			0.420498	+	0.907294i	$0.361856\pi$
$542$	−5.57779	+	9.66102i	−0.239587	+	0.414977i
$543$	11.4674	−	17.2589i	0.492114	−	0.740648i
$544$	−9.27219	+	5.35330i	−0.397542	+	0.229521i
$545$	2.02981	+	3.51574i	0.0869476	+	0.150598i
$546$		0			0
$547$	12.6246	−	21.8665i	0.539790	−	0.934944i	−0.459125	−	0.888372i	$-0.651837\pi$
$547$	12.6246	−	21.8665i	0.539790	−	0.934944i	0.998915	−	0.0465723i	$-0.0148298\pi$
$548$			1.64509i			0.0702747i
$549$	−3.98743	+	31.5501i	−0.170179	+	1.34653i
$550$	44.6359			1.90328
$551$	−8.97260	+	15.5410i	−0.382246	+	0.662069i
$552$	−0.188811	+	2.99978i	−0.00803632	+	0.127679i
$553$		0			0
$554$	14.9673	−	8.64136i	0.635898	−	0.367136i
$555$	−0.561546	+	8.92169i	−0.0238363	+	0.378705i
$556$	8.29730	+	4.79045i	0.351884	+	0.203160i
$557$		−	33.2789i		−	1.41007i	−0.709171	−	0.705036i	$-0.750931\pi$
$557$		−	33.2789i		−	1.41007i	0.709171	−	0.705036i	$-0.249069\pi$
$558$	12.0687	+	28.7145i	0.510907	+	1.21558i
$559$		−	15.5135i		−	0.656152i
$560$		0			0
$561$	−6.67225	−	13.4421i	−0.281703	−	0.567525i
$562$	4.83540	+	8.37516i	0.203969	+	0.353285i
$563$	−15.2587	−	26.4289i	−0.643079	−	1.11385i	−0.984742	−	0.174023i	$-0.944323\pi$
$563$	−15.2587	−	26.4289i	−0.643079	−	1.11385i	0.341663	−	0.939823i	$-0.389010\pi$
$564$	6.03343	+	4.00883i	0.254053	+	0.168802i
$565$	−4.98940	−	2.88063i	−0.209905	−	0.121189i
$566$	−36.0358			−1.51470
$567$		0			0
$568$	−5.62028			−0.235822
$569$	13.4044	+	7.73906i	0.561943	+	0.324438i	0.753925	−	0.656960i	$-0.228158\pi$
$569$	13.4044	+	7.73906i	0.561943	+	0.324438i	−0.191982	+	0.981398i	$0.561491\pi$
$570$	−4.11839	−	2.73641i	−0.172500	−	0.114616i
$571$	12.2042	+	21.1384i	0.510731	+	0.884613i	0.999923	+	0.0124362i	$0.00395868\pi$
$571$	12.2042	+	21.1384i	0.510731	+	0.884613i	−0.489191	+	0.872177i	$0.662708\pi$
$572$	−18.4845	−	32.0160i	−0.772875	−	1.33866i
$573$	−15.6135	−	31.4553i	−0.652264	−	1.31407i
$574$		0			0
$575$			6.74455i			0.281267i
$576$	2.66018	+	6.32928i	0.110841	+	0.263720i
$577$		−	14.6533i		−	0.610024i	−0.952349	−	0.305012i	$-0.901340\pi$
$577$		−	14.6533i		−	0.610024i	0.952349	−	0.305012i	$-0.0986605\pi$
$578$	−22.7572	−	13.1389i	−0.946574	−	0.546505i
$579$	−1.83786	+	29.1994i	−0.0763789	+	1.21349i
$580$	−5.63746	+	3.25479i	−0.234083	+	0.135148i
$581$		0			0
$582$	−3.31316	+	52.6385i	−0.137335	+	2.18194i
$583$	6.27811	−	10.8740i	0.260013	−	0.450355i
$584$	13.9217			0.576084
$585$	−1.24512	+	9.85188i	−0.0514794	+	0.407325i
$586$		−	33.4032i		−	1.37987i
$587$	−11.6129	+	20.1141i	−0.479314	+	0.830197i	−0.999719	−	0.0237232i	$-0.992448\pi$
$587$	−11.6129	+	20.1141i	−0.479314	+	0.830197i	0.520404	+	0.853920i	$0.325781\pi$
$588$		0			0
$589$	−6.83975	−	11.8468i	−0.281827	−	0.488139i
$590$	−3.03009	+	1.74942i	−0.124747	+	0.0720225i
$591$	−17.9345	+	26.9920i	−0.737727	+	1.11030i
$592$	−19.4793	+	33.7391i	−0.800594	+	1.38667i
$593$	−11.1121			−0.456319			−0.228160	−	0.973624i	$-0.573271\pi$
$593$	−11.1121			−0.456319			−0.228160	+	0.973624i	$0.573271\pi$
$594$	−47.7916	+	16.6385i	−1.96091	+	0.682684i
$595$		0			0
$596$	8.14153	+	4.70051i	0.333490	+	0.192541i
$597$	17.2965	−	26.0318i	0.707899	−	1.06541i
$598$	11.9712	−	6.91159i	0.489540	−	0.282636i
$599$	−13.5581	+	7.82776i	−0.553968	+	0.319833i	−0.750721	−	0.660620i	$-0.770294\pi$
$599$	−13.5581	+	7.82776i	−0.553968	+	0.319833i	0.196753	+	0.980453i	$0.436960\pi$
$600$	−4.16217	−	8.38521i	−0.169920	−	0.342325i
$601$	30.5665	+	17.6476i	1.24684	+	0.719861i	0.970477	−	0.241194i	$-0.0775390\pi$
$601$	30.5665	+	17.6476i	1.24684	+	0.719861i	0.276358	+	0.961055i	$0.410872\pi$
$602$		0			0
$603$	−18.4203	+	24.2652i	−0.750133	+	0.988154i
$604$	−8.57024			−0.348718
$605$	5.57104	−	9.64932i	0.226495	−	0.392301i
$606$	−14.7309	−	0.927189i	−0.598403	−	0.0376645i
$607$	33.6062	−	19.4025i	1.36403	−	0.787524i	0.373874	−	0.927479i	$-0.378029\pi$
$607$	33.6062	−	19.4025i	1.36403	−	0.787524i	0.990158	+	0.139955i	$0.0446959\pi$
$608$	−7.92809	−	13.7318i	−0.321526	−	0.556900i
$609$		0			0
$610$	6.26850	−	10.8574i	0.253804	−	0.439602i
$611$			15.8105i			0.639623i
$612$	4.00987	−	5.28221i	0.162089	−	0.213521i
$613$	31.7572			1.28266			0.641330	−	0.767265i	$-0.278383\pi$
$613$	31.7572			1.28266			0.641330	+	0.767265i	$0.278383\pi$
$614$	−23.8572	+	41.3220i	−0.962800	+	1.66762i
$615$	−11.9997	+	5.95632i	−0.483876	+	0.240182i
$616$		0			0
$617$	1.25518	−	0.724680i	0.0505317	−	0.0291745i	−0.474521	−	0.880244i	$-0.657379\pi$
$617$	1.25518	−	0.724680i	0.0505317	−	0.0291745i	0.525053	+	0.851070i	$0.324045\pi$
$618$	27.2338	+	18.0951i	1.09550	+	0.727893i
$619$	−25.2590	−	14.5833i	−1.01524	−	0.586152i	−0.102522	−	0.994731i	$-0.532691\pi$
$619$	−25.2590	−	14.5833i	−1.01524	−	0.586152i	−0.912723	+	0.408579i	$0.866024\pi$
$620$		−	4.96220i		−	0.199287i
$621$	−2.51409	−	7.22137i	−0.100887	−	0.289783i
$622$			51.8217i			2.07786i
$623$		0			0
$624$	−23.9501	+	36.0457i	−0.958771	+	1.44298i
$625$	−9.46116	−	16.3872i	−0.378446	−	0.655488i
$626$	−5.10764	−	8.84668i	−0.204142	−	0.353585i
$627$	19.9073	−	9.88142i	0.795022	−	0.394626i
$628$	−2.33778	−	1.34972i	−0.0932877	−	0.0538597i
$629$	13.0303			0.519551
$630$		0			0
$631$	11.7428			0.467473			0.233736	−	0.972300i	$-0.424905\pi$
$631$	11.7428			0.467473			0.233736	+	0.972300i	$0.424905\pi$
$632$	7.11011	+	4.10503i	0.282825	+	0.163289i
$633$	0.878020	−	13.9497i	0.0348982	−	0.554453i
$634$	30.7488	+	53.2585i	1.22119	+	2.11516i
$635$	0.806924	+	1.39763i	0.0320218	+	0.0554634i
$636$	5.53783	+	0.348560i	0.219589	+	0.0138213i
$637$		0			0
$638$		−	72.4041i		−	2.86651i
$639$	13.1810	−	5.53996i	0.521433	−	0.219157i
$640$			5.77487i			0.228272i
$641$	−10.0267	−	5.78891i	−0.396030	−	0.228648i	0.288740	−	0.957408i	$-0.406764\pi$
$641$	−10.0267	−	5.78891i	−0.396030	−	0.228648i	−0.684770	+	0.728760i	$0.740097\pi$
$642$	−0.876985	+	0.435310i	−0.0346118	+	0.0171803i
$643$	−13.1240	+	7.57712i	−0.517558	+	0.298812i	−0.735935	−	0.677052i	$-0.763257\pi$
$643$	−13.1240	+	7.57712i	−0.517558	+	0.298812i	0.218377	+	0.975865i	$0.429924\pi$
$644$		0			0
$645$	2.81782	+	1.87226i	0.110951	+	0.0737203i
$646$	−3.60370	+	6.24180i	−0.141786	+	0.245580i
$647$	−12.4411			−0.489111			−0.244556	−	0.969635i	$-0.578642\pi$
$647$	−12.4411			−0.489111			−0.244556	+	0.969635i	$0.578642\pi$
$648$	7.58209	+	7.42653i	0.297853	+	0.291742i
$649$		−	15.7265i		−	0.617319i
$650$	−21.5264	+	37.2847i	−0.844333	+	1.46243i
$651$		0			0
$652$	−4.06032	−	7.03268i	−0.159014	−	0.275421i
$653$	−3.97013	+	2.29216i	−0.155363	+	0.0896990i	−0.575666	−	0.817685i	$-0.695257\pi$
$653$	−3.97013	+	2.29216i	−0.155363	+	0.0896990i	0.420303	+	0.907384i	$0.361924\pi$
$654$	−8.87188	−	17.8735i	−0.346918	−	0.698909i
$655$	−0.818096	+	1.41698i	−0.0319656	+	0.0553661i
$656$	−58.3841			−2.27952
$657$	−32.6500	+	13.7227i	−1.27380	+	0.535375i
$658$		0			0
$659$	15.6110	+	9.01301i	0.608118	+	0.351097i	0.772228	−	0.635345i	$-0.219142\pi$
$659$	15.6110	+	9.01301i	0.608118	+	0.351097i	−0.164111	+	0.986442i	$0.552475\pi$
$660$	8.04609	+	0.506434i	0.313194	+	0.0197129i
$661$	0.554932	−	0.320390i	0.0215844	−	0.0124617i	−0.489169	−	0.872189i	$-0.662700\pi$
$661$	0.554932	−	0.320390i	0.0215844	−	0.0124617i	0.510753	+	0.859727i	$0.329367\pi$
$662$	48.1899	−	27.8225i	1.87296	−	1.08135i
$663$	14.4461	+	0.909258i	0.561038	+	0.0353127i
$664$	7.18189	+	4.14647i	0.278711	+	0.160914i
$665$		0			0
$666$	5.50943	−	43.5927i	0.213486	−	1.68918i
$667$	10.9404			0.423612
$668$	−0.946692	+	1.63972i	−0.0366286	+	0.0634426i
$669$	18.0023	+	36.2678i	0.696008	+	1.40219i
$670$	10.4012	−	6.00511i	0.401832	−	0.231998i
$671$	28.1755	+	48.8014i	1.08770	+	1.88396i
$672$		0			0
$673$	−11.0695	+	19.1729i	−0.426697	+	0.739061i	−0.996577	−	0.0826667i	$-0.973656\pi$
$673$	−11.0695	+	19.1729i	−0.426697	+	0.739061i	0.569880	+	0.821728i	$0.306990\pi$
$674$			6.81956i			0.262680i
$675$	18.0268	+	15.5628i	0.693850	+	0.599013i
$676$	18.0256			0.693292
$677$	10.0160	−	17.3482i	0.384947	−	0.666747i	−0.606815	−	0.794843i	$-0.707553\pi$
$677$	10.0160	−	17.3482i	0.384947	−	0.666747i	0.991762	+	0.128096i	$0.0408865\pi$
$678$	23.5865	+	15.6717i	0.905833	+	0.601869i
$679$		0			0
$680$	1.07456	−	0.620397i	0.0412074	−	0.0237911i
$681$	22.4075	−	11.1225i	0.858659	−	0.426213i
$682$	47.7986	+	27.5966i	1.83030	+	1.05673i
$683$			20.9366i			0.801116i	0.916271	+	0.400558i	$0.131184\pi$
$683$			20.9366i			0.801116i	−0.916271	+	0.400558i	$0.868816\pi$
$684$	7.82281	+	5.93850i	0.299113	+	0.227064i
$685$		−	0.783018i		−	0.0299176i
$686$		0			0
$687$	−22.6688	−	1.42681i	−0.864867	−	0.0544361i
$688$	7.37198	+	12.7686i	0.281054	+	0.486800i
$689$	6.05543	+	10.4883i	0.230693	+	0.399573i
$690$	−0.189362	+	3.00854i	−0.00720890	+	0.114533i
$691$	−1.33430	−	0.770358i	−0.0507591	−	0.0293058i	0.474406	−	0.880306i	$-0.342663\pi$
$691$	−1.33430	−	0.770358i	−0.0507591	−	0.0293058i	−0.525165	+	0.851001i	$0.675996\pi$
$692$	−10.3217			−0.392372
$693$		0			0
$694$	13.0740			0.496282
$695$	−3.94929	−	2.28012i	−0.149805	−	0.0864900i
$696$	−13.6017	+	6.75147i	−0.515570	+	0.255914i
$697$	9.76372	+	16.9113i	0.369827	+	0.640560i
$698$	−13.9711	−	24.1987i	−0.528815	−	0.915935i
$699$	8.10161	−	12.1932i	0.306431	−	0.461189i
$700$		0			0
$701$			31.6641i			1.19593i	0.801520	+	0.597967i	$0.204025\pi$
$701$			31.6641i			1.19593i	−0.801520	+	0.597967i	$0.795975\pi$
$702$	9.14996	−	47.9448i	0.345343	−	1.80956i
$703$			19.2975i			0.727818i
$704$	10.5358	+	6.08286i	0.397083	+	0.229256i
$705$	−2.87175	−	1.90810i	−0.108156	−	0.0718631i
$706$	54.6922	−	31.5766i	2.05837	−	1.18840i
$707$		0			0
$708$	6.22509	−	3.08995i	0.233953	−	0.116127i
$709$	−11.1762	+	19.3578i	−0.419732	+	0.726996i	−0.995912	−	0.0903259i	$-0.971209\pi$
$709$	−11.1762	+	19.3578i	−0.419732	+	0.726996i	0.576181	+	0.817322i	$0.304542\pi$
$710$	−5.63670			−0.211542
$711$	−20.7214	−	2.61886i	−0.777114	−	0.0982148i
$712$			5.10231i			0.191217i
$713$	−4.16988	+	7.22244i	−0.156163	+	0.270482i
$714$		0			0
$715$	8.79812	+	15.2388i	0.329031	+	0.569898i
$716$	−10.8625	+	6.27149i	−0.405952	+	0.234377i
$717$	−48.3265	−	3.04175i	−1.80479	−	0.113596i
$718$	6.06910	−	10.5120i	0.226497	−	0.392304i
$719$	38.9087			1.45105			0.725525	−	0.688195i	$-0.241597\pi$
$719$	38.9087			1.45105			0.725525	+	0.688195i	$0.241597\pi$
$720$	−3.65677	−	8.70041i	−0.136280	−	0.324245i
$721$		0			0
$722$	20.9011	+	12.0672i	0.777858	+	0.449096i
$723$	17.2561	+	34.7645i	0.641760	+	1.29290i
$724$	14.0522	−	8.11306i	0.522247	−	0.301520i
$725$	−29.5090	+	17.0370i	−1.09594	+	0.632739i
$726$	−30.3086	+	45.6154i	−1.12486	+	1.69295i
$727$	−11.4647	−	6.61915i	−0.425202	−	0.245491i	0.272098	−	0.962269i	$-0.412282\pi$
$727$	−11.4647	−	6.61915i	−0.425202	−	0.245491i	−0.697301	+	0.716779i	$0.745616\pi$
$728$		0			0
$729$	−25.1024	−	9.94341i	−0.929717	−	0.368274i
$730$	13.9624			0.516771
$731$	2.46567	−	4.27066i	0.0911960	−	0.157956i
$732$	−13.7813	+	20.7413i	−0.509372	+	0.766622i
$733$	−28.1222	+	16.2364i	−1.03872	+	0.599704i	−0.919470	−	0.393161i	$-0.871382\pi$
$733$	−28.1222	+	16.2364i	−1.03872	+	0.599704i	−0.119248	+	0.992865i	$0.538048\pi$
$734$	2.83703	+	4.91389i	0.104717	+	0.181375i
$735$		0			0
$736$	−4.83338	+	8.37167i	−0.178161	+	0.308584i
$737$			53.9832i			1.98850i
$738$	60.7048	−	25.5141i	2.23458	−	0.939188i
$739$	−13.8393			−0.509087			−0.254543	−	0.967061i	$-0.581925\pi$
$739$	−13.8393			−0.509087			−0.254543	+	0.967061i	$0.581925\pi$
$740$	−3.50005	+	6.06227i	−0.128665	+	0.222854i
$741$	−1.34659	+	21.3942i	−0.0494681	+	0.785936i
$742$		0			0
$743$	31.8593	−	18.3940i	1.16880	−	0.674810i	0.215406	−	0.976525i	$-0.430892\pi$
$743$	31.8593	−	18.3940i	1.16880	−	0.674810i	0.953398	+	0.301715i	$0.0975591\pi$
$744$	0.727143	−	11.5526i	0.0266583	−	0.423541i
$745$	−3.87515	−	2.23732i	−0.141975	−	0.0819690i
$746$		−	17.7706i		−	0.650628i
$747$	−20.9306	−	2.64529i	−0.765811	−	0.0967862i
$748$		−	11.7514i		−	0.429675i
$749$		0			0
$750$	−8.72824	−	17.5841i	−0.318710	−	0.642081i
$751$	1.82952	+	3.16883i	0.0667602	+	0.115632i	0.897473	−	0.441068i	$-0.145400\pi$
$751$	1.82952	+	3.16883i	0.0667602	+	0.115632i	−0.830713	+	0.556701i	$0.812067\pi$
$752$	−7.51308	−	13.0130i	−0.273974	−	0.474537i
$753$	9.22691	+	6.13070i	0.336247	+	0.223415i
$754$	60.4797	+	34.9180i	2.20254	+	1.27164i
$755$	4.07921			0.148458
$756$		0			0
$757$	13.8901			0.504842			0.252421	−	0.967617i	$-0.418773\pi$
$757$	13.8901			0.504842			0.252421	+	0.967617i	$0.418773\pi$
$758$	12.3135	+	7.10920i	0.447246	+	0.258218i
$759$	−11.2854	−	7.49846i	−0.409635	−	0.272177i
$760$	0.918790	+	1.59139i	0.0333280	+	0.0577258i
$761$	−6.82083	−	11.8140i	−0.247255	−	0.428258i	0.715508	−	0.698604i	$-0.246195\pi$
$761$	−6.82083	−	11.8140i	−0.247255	−	0.428258i	−0.962763	+	0.270346i	$0.912862\pi$
$762$	−3.52689	−	7.10536i	−0.127766	−	0.257400i
$763$		0			0
$764$		−	27.4991i		−	0.994884i
$765$	−1.90859	+	2.51419i	−0.0690052	+	0.0909008i
$766$		−	45.0910i		−	1.62920i
$767$	13.1365	+	7.58434i	0.474330	+	0.273855i
$768$	2.28108	−	36.2412i	0.0823114	−	1.30774i
$769$	−22.9328	+	13.2402i	−0.826976	+	0.477455i	−0.852816	−	0.522211i	$-0.825107\pi$
$769$	−22.9328	+	13.2402i	−0.826976	+	0.477455i	0.0258399	+	0.999666i	$0.491774\pi$
$770$		0			0
$771$	−0.360583	+	5.72884i	−0.0129861	+	0.206319i
$772$	−11.4552	+	19.8410i	−0.412281	+	0.714092i
$773$	26.2218			0.943132			0.471566	−	0.881831i	$-0.343689\pi$
$773$	26.2218			0.943132			0.471566	+	0.881831i	$0.343689\pi$
$774$	−13.2450	−	10.0546i	−0.476080	−	0.361405i
$775$		−	25.9744i		−	0.933028i
$776$	9.80047	−	16.9749i	0.351816	−	0.609364i
$777$		0			0
$778$	5.88703	+	10.1966i	0.211060	+	0.365567i
$779$	−25.0451	+	14.4598i	−0.897334	+	0.518076i
$780$	−4.30337	+	6.47672i	−0.154086	+	0.231904i
$781$	12.6678	−	21.9413i	0.453291	−	0.785123i
$782$	4.39402			0.157130
$783$	25.2445	−	29.2412i	0.902164	−	1.04500i
$784$		0			0
$785$	1.11272	+	0.642430i	0.0397148	+	0.0229293i
$786$	4.45076	−	6.69854i	0.158753	−	0.238929i
$787$	25.1554	−	14.5235i	0.896694	−	0.517706i	0.0205676	−	0.999788i	$-0.493453\pi$
$787$	25.1554	−	14.5235i	0.896694	−	0.517706i	0.876126	+	0.482082i	$0.160119\pi$
$788$	−21.9770	+	12.6884i	−0.782899	+	0.452007i
$789$	17.4734	+	35.2024i	0.622070	+	1.25324i
$790$	7.13088	+	4.11702i	0.253705	+	0.146477i
$791$		0			0
$792$	18.6581	+	2.35809i	0.662987	+	0.0837909i
$793$	−54.3522			−1.93010
$794$	−12.1463	+	21.0380i	−0.431055	+	0.746610i
$795$	−2.63586	−	0.165905i	−0.0934844	−	0.00588406i
$796$	21.1952	−	12.2371i	0.751245	−	0.433731i
$797$	−15.8184	−	27.3983i	−0.560317	−	0.970498i	−0.997469	−	0.0711097i	$-0.977346\pi$
$797$	−15.8184	−	27.3983i	−0.560317	−	0.970498i	0.437151	−	0.899388i	$-0.355987\pi$
$798$		0			0
$799$	−2.51286	+	4.35240i	−0.0888986	+	0.153977i
$800$		−	30.1074i		−	1.06446i
$801$	−5.02939	−	11.9662i	−0.177705	−	0.422807i
$802$	−28.9555			−1.02245
$803$	−31.3788	+	54.3497i	−1.10733	+	1.91796i
$804$	−21.3684	+	10.6066i	−0.753605	+	0.374068i
$805$		0			0
$806$	−46.1032	+	26.6177i	−1.62392	+	0.937569i
$807$	3.98313	+	2.64654i	0.140213	+	0.0931625i
$808$	4.75044	+	2.74267i	0.167120	+	0.0964868i
$809$		−	39.8909i		−	1.40249i	−0.712920	−	0.701245i	$-0.752628\pi$
$809$		−	39.8909i		−	1.40249i	0.712920	−	0.701245i	$-0.247372\pi$
$810$	7.60424	+	7.44822i	0.267186	+	0.261704i
$811$		−	28.9516i		−	1.01663i	−0.861172	−	0.508314i	$-0.830269\pi$
$811$		−	28.9516i		−	1.01663i	0.861172	−	0.508314i	$-0.169731\pi$
$812$		0			0
$813$	−5.83676	+	8.78452i	−0.204704	+	0.308087i
$814$	−38.9300	−	67.4288i	−1.36450	−	2.36338i
$815$	1.93260	+	3.34737i	0.0676961	+	0.117253i
$816$	−12.3221	+	6.11634i	−0.431360	+	0.214115i
$817$	6.32473	+	3.65158i	0.221274	+	0.127753i
$818$	−9.92684			−0.347084
$819$		0			0
$820$	−10.4905			−0.366344
$821$	0.359377	+	0.207486i	0.0125423	+	0.00724132i	0.506258	−	0.862382i	$-0.331028\pi$
$821$	0.359377	+	0.207486i	0.0125423	+	0.00724132i	−0.493716	+	0.869623i	$0.664362\pi$
$822$	−0.241769	+	3.84116i	−0.00843267	+	0.133976i
$823$	6.54814	+	11.3417i	0.228254	+	0.395347i	0.957291	−	0.289127i	$-0.0933650\pi$
$823$	6.54814	+	11.3417i	0.228254	+	0.395347i	−0.729037	+	0.684475i	$0.760032\pi$
$824$	−6.07570	−	10.5234i	−0.211657	−	0.366601i
$825$	42.1168	+	2.65090i	1.46632	+	0.0922926i
$826$		0			0
$827$		−	35.2637i		−	1.22624i	−0.789990	−	0.613120i	$-0.789914\pi$
$827$		−	35.2637i		−	1.22624i	0.789990	−	0.613120i	$-0.210086\pi$
$828$	0.750779	−	5.94046i	0.0260914	−	0.206445i
$829$			33.5052i			1.16368i	0.813302	+	0.581842i	$0.197668\pi$
$829$			33.5052i			1.16368i	−0.813302	+	0.581842i	$0.802332\pi$
$830$	7.20287	+	4.15858i	0.250015	+	0.144346i
$831$	14.6358	−	7.26477i	0.507709	−	0.252012i
$832$	−10.1621	+	5.86710i	−0.352308	+	0.203405i
$833$		0			0
$834$	18.6696	+	12.4048i	0.646474	+	0.429542i
$835$	0.450600	−	0.780462i	0.0155937	−	0.0270090i
$836$	17.4036			0.601914
$837$	9.68220	+	27.8107i	0.334666	+	0.961279i
$838$		−	44.8733i		−	1.55012i
$839$	22.4984	−	38.9684i	0.776731	−	1.34534i	−0.157085	−	0.987585i	$-0.550210\pi$
$839$	22.4984	−	38.9684i	0.776731	−	1.34534i	0.933816	−	0.357753i	$-0.116457\pi$
$840$		0			0
$841$	13.1358	+	22.7519i	0.452959	+	0.784548i
$842$	19.0182	−	10.9802i	0.655412	−	0.378402i
$843$	4.06511	+	8.18966i	0.140010	+	0.282067i
$844$	5.47260	−	9.47882i	0.188375	−	0.326275i
$845$	−8.57970			−0.295151
$846$	13.4985	+	10.2470i	0.464087	+	0.352301i
$847$		0			0
$848$	−9.96802	−	5.75504i	−0.342303	−	0.197629i
$849$	−34.0020	−	2.14014i	−1.16695	−	0.0734495i
$850$	−11.8518	+	6.84265i	−0.406514	+	0.234701i
$851$	10.1886	−	5.88238i	0.349260	−	0.201645i
$852$	11.1741	+	0.703317i	0.382819	+	0.0240953i
$853$	−15.8457	−	9.14854i	−0.542548	−	0.313240i	0.203563	−	0.979062i	$-0.434748\pi$
$853$	−15.8457	−	9.14854i	−0.542548	−	0.313240i	−0.746111	+	0.665822i	$0.768081\pi$
$854$		0			0
$855$	−3.72345	−	2.82657i	−0.127339	−	0.0966665i
$856$	0.363859			0.0124364
$857$	−5.28926	+	9.16126i	−0.180678	+	0.312943i	−0.942111	−	0.335300i	$-0.891162\pi$
$857$	−5.28926	+	9.16126i	−0.180678	+	0.312943i	0.761434	+	0.648243i	$0.224496\pi$
$858$	−38.4547	−	77.4717i	−1.31282	−	2.64484i
$859$	−28.2972	+	16.3374i	−0.965488	+	0.557425i	−0.897858	−	0.440286i	$-0.854877\pi$
$859$	−28.2972	+	16.3374i	−0.965488	+	0.557425i	−0.0676303	+	0.997710i	$0.521544\pi$
$860$	1.32460	+	2.29428i	0.0451686	+	0.0782343i
$861$		0			0
$862$	28.2332	−	48.9014i	0.961628	−	1.66559i
$863$		−	9.35166i		−	0.318334i	−0.987252	−	0.159167i	$-0.949119\pi$
$863$		−	9.35166i		−	0.318334i	0.987252	−	0.159167i	$-0.0508809\pi$
$864$	11.2228	+	32.2359i	0.381808	+	1.09669i
$865$	4.91285			0.167042
$866$	5.55262	−	9.61742i	0.188686	−	0.326813i
$867$	−20.6925	−	13.7489i	−0.702755	−	0.466937i
$868$		0			0
$869$	−32.0517	+	18.5050i	−1.08728	+	0.627741i
$870$	−13.6414	+	6.77120i	−0.462487	+	0.229565i
$871$	−45.0925	−	26.0342i	−1.52790	−	0.882135i
$872$			7.41567i			0.251126i
$873$	−6.25234	+	49.4710i	−0.211610	+	1.67434i
$874$			6.50742i			0.220117i
$875$		0			0
$876$	−27.6788	−	1.74215i	−0.935181	−	0.0588618i
$877$	−0.619077	−	1.07227i	−0.0209048	−	0.0362081i	0.855384	−	0.517995i	$-0.173321\pi$
$877$	−0.619077	−	1.07227i	−0.0209048	−	0.0362081i	−0.876289	+	0.481787i	$0.839988\pi$
$878$	−24.8650	−	43.0674i	−0.839153	−	1.45346i
$879$	1.98379	−	31.5180i	0.0669117	−	1.06308i
$880$	−14.4828	−	8.36167i	−0.488217	−	0.281872i
$881$	−37.3480			−1.25828			−0.629142	−	0.777290i	$-0.716594\pi$
$881$	−37.3480			−1.25828			−0.629142	+	0.777290i	$0.716594\pi$
$882$		0			0
$883$	3.90708			0.131484			0.0657419	−	0.997837i	$-0.479059\pi$
$883$	3.90708			0.131484			0.0657419	+	0.997837i	$0.479059\pi$
$884$	9.81607	+	5.66731i	0.330150	+	0.190612i
$885$	−2.96297	+	1.47073i	−0.0995993	+	0.0494382i
$886$	−4.90216	−	8.49079i	−0.164691	−	0.285254i
$887$	−7.25578	−	12.5674i	−0.243625	−	0.421972i	0.718119	−	0.695920i	$-0.245003\pi$
$887$	−7.25578	−	12.5674i	−0.243625	−	0.421972i	−0.961744	+	0.273949i	$0.911670\pi$
$888$	−9.03691	+	13.6009i	−0.303259	+	0.456415i
$889$		0			0
$890$			5.11722i			0.171530i
$891$	−46.0825	+	12.8611i	−1.54382	+	0.430864i
$892$			31.7063i			1.06161i
$893$	−6.44579	−	3.72148i	−0.215700	−	0.124534i
$894$	18.3191	+	12.1719i	0.612682	+	0.407089i
$895$	5.17028	−	2.98506i	0.172823	−	0.0997797i
$896$		0			0
$897$	11.7061	−	5.81056i	0.390855	−	0.194009i
$898$	31.3659	−	54.3273i	1.04669	−	1.81293i
$899$	−42.1331			−1.40522
$900$	7.22582	+	17.1921i	0.240861	+	0.573071i
$901$			3.84972i			0.128253i
$902$	58.3414	−	101.050i	1.94256	−	3.36460i
$903$		0			0
$904$	−5.26201	−	9.11407i	−0.175012	−	0.303129i
$905$	−6.68849	+	3.86160i	−0.222333	+	0.128364i
$906$	−20.0109	−	1.25952i	−0.664818	−	0.0418447i
$907$	9.60695	−	16.6397i	0.318993	−	0.552513i	−0.661285	−	0.750135i	$-0.729989\pi$
$907$	9.60695	−	16.6397i	0.318993	−	0.552513i	0.980278	+	0.197622i	$0.0633219\pi$
$908$	19.5893			0.650094
$909$	−13.8445	−	1.74972i	−0.459193	−	0.0580346i
$910$		0			0
$911$	10.1252	+	5.84579i	0.335463	+	0.193680i	0.658264	−	0.752787i	$-0.271291\pi$
$911$	10.1252	+	5.84579i	0.335463	+	0.193680i	−0.322801	+	0.946467i	$0.604624\pi$
$912$	−9.05813	−	18.2487i	−0.299945	−	0.604275i
$913$	−32.3752	+	18.6919i	−1.07146	+	0.618610i
$914$	25.1637	−	14.5283i	0.832342	−	0.480553i
$915$	6.55954	−	9.87233i	0.216852	−	0.326369i
$916$	−15.4034	−	8.89314i	−0.508942	−	0.293838i
$917$		0			0
$918$	10.1390	−	11.7443i	0.334638	−	0.387619i
$919$	39.9860			1.31902			0.659508	−	0.751698i	$-0.270765\pi$
$919$	39.9860			1.31902			0.659508	+	0.751698i	$0.270765\pi$
$920$	0.560143	−	0.970196i	0.0184674	−	0.0319864i
$921$	−24.9649	+	37.5730i	−0.822621	+	1.23807i
$922$	−20.6470	+	11.9205i	−0.679972	+	0.392582i
$923$	12.2185	+	21.1631i	0.402177	+	0.696591i
$924$		0			0
$925$	−18.3209	+	31.7326i	−0.602386	+	1.04336i
$926$		−	22.0554i		−	0.724786i
$927$	24.6221	+	18.6913i	0.808697	+	0.613903i
$928$	−48.8373			−1.60316
$929$	6.38359	−	11.0567i	0.209439	−	0.362759i	−0.742099	−	0.670290i	$-0.766170\pi$
$929$	6.38359	−	11.0567i	0.209439	−	0.362759i	0.951538	+	0.307532i	$0.0995030\pi$
$930$	0.729267	−	11.5864i	0.0239136	−	0.379933i
$931$		0			0
$932$	9.92775	−	5.73179i	0.325194	−	0.187751i
$933$	−3.07766	+	48.8970i	−0.100758	+	1.60082i
$934$	−32.2801	−	18.6369i	−1.05624	−	0.609818i
$935$			5.59337i			0.182923i
$936$	−10.9679	+	14.4480i	−0.358496	+	0.472249i
$937$		−	11.9436i		−	0.390179i	−0.980785	−	0.195090i	$-0.937500\pi$
$937$		−	11.9436i		−	0.390179i	0.980785	−	0.195090i	$-0.0624997\pi$
$938$		0			0
$939$	−4.29398	−	8.65074i	−0.140129	−	0.282306i
$940$	−1.34996	−	2.33819i	−0.0440307	−	0.0762634i
$941$	−12.5159	−	21.6781i	−0.408006	−	0.706686i	0.586661	−	0.809833i	$-0.300442\pi$
$941$	−12.5159	−	21.6781i	−0.408006	−	0.706686i	−0.994666	+	0.103146i	$0.967109\pi$
$942$	−5.26019	−	3.49507i	−0.171386	−	0.113875i
$943$	15.2688	+	8.81546i	0.497221	+	0.287071i
$944$	−14.4162			−0.469208
$945$		0			0
$946$	−29.4663			−0.958032
$947$	−28.3671	−	16.3777i	−0.921806	−	0.532205i	−0.0375955	−	0.999293i	$-0.511970\pi$
$947$	−28.3671	−	16.3777i	−0.921806	−	0.532205i	−0.884211	+	0.467088i	$0.845303\pi$
$948$	−13.6225	−	9.05127i	−0.442437	−	0.293972i
$949$	−30.2658	−	52.4219i	−0.982470	−	1.70169i
$950$	−10.1338	−	17.5522i	−0.328783	−	0.569469i
$951$	25.8504	+	52.0789i	0.838258	+	1.68877i
$952$		0			0
$953$		−	6.77705i		−	0.219530i	−0.993958	−	0.109765i	$-0.964990\pi$
$953$		−	6.77705i		−	0.219530i	0.993958	−	0.109765i	$-0.0350099\pi$
$954$	12.8792	+	1.62773i	0.416980	+	0.0526996i
$955$			13.0889i			0.423545i
$956$	−32.8378	−	18.9589i	−1.06205	−	0.613175i
$957$	4.30004	−	68.3178i	0.139000	−	2.20840i
$958$	−38.5512	+	22.2575i	−1.24553	+	0.719109i
$959$		0			0
$960$	0.160746	−	2.55388i	0.00518804	−	0.0824262i
$961$	0.558897	−	0.968037i	0.0180289	−	0.0312270i
$962$	75.0984			2.42127
$963$	−0.853343	+	0.358658i	−0.0274986	+	0.0115576i
$964$			30.3921i			0.978863i
$965$	5.45236	−	9.44377i	0.175518	−	0.304006i
$966$		0			0
$967$	20.7901	+	36.0096i	0.668566	+	1.15799i	0.978305	+	0.207169i	$0.0664249\pi$
$967$	20.7901	+	36.0096i	0.668566	+	1.15799i	−0.309739	+	0.950822i	$0.600242\pi$
$968$	17.6263	−	10.1765i	0.566530	−	0.327086i
$969$	−3.77102	+	5.67551i	−0.121143	+	0.182324i
$970$	9.82910	−	17.0245i	0.315593	−	0.546624i
$971$	41.2514			1.32382			0.661910	−	0.749583i	$-0.269746\pi$
$971$	41.2514			1.32382			0.661910	+	0.749583i	$0.269746\pi$
$972$	−14.1452	−	15.7141i	−0.453707	−	0.504029i
$973$		0			0
$974$	−43.3281	−	25.0155i	−1.38832	−	0.801547i
$975$	−22.5258	+	33.9021i	−0.721403	+	1.08573i
$976$	44.7354	−	25.8280i	1.43195	−	0.826734i
$977$	3.96507	−	2.28924i	0.126854	−	0.0732391i	−0.435230	−	0.900319i	$-0.643333\pi$
$977$	3.96507	−	2.28924i	0.126854	−	0.0732391i	0.562084	+	0.827080i	$0.310000\pi$
$978$	−8.44700	−	17.0175i	−0.270105	−	0.544160i
$979$	−19.9192	−	11.5004i	−0.636621	−	0.367553i
$980$		0			0
$981$	−7.30968	−	17.3917i	−0.233380	−	0.555273i
$982$	−28.1139			−0.897150
$983$	−12.2401	+	21.2004i	−0.390397	+	0.676188i	−0.992502	−	0.122229i	$-0.960996\pi$
$983$	−12.2401	+	21.2004i	−0.390397	+	0.676188i	0.602105	+	0.798417i	$0.294329\pi$
$984$	−24.4232	−	1.53724i	−0.778584	−	0.0490054i
$985$	10.4605	−	6.03936i	0.333299	−	0.192430i
$986$	11.0995	+	19.2249i	0.353480	+	0.612245i
$987$		0			0
$988$	−8.39312	+	14.5373i	−0.267021	+	0.462494i
$989$		−	4.45240i		−	0.141578i
$990$	18.7126	+	2.36497i	0.594726	+	0.0751638i
$991$	−42.1854			−1.34006			−0.670032	−	0.742332i	$-0.733720\pi$
$991$	−42.1854			−1.34006			−0.670032	+	0.742332i	$0.733720\pi$
$992$	18.6142	−	32.2407i	0.591001	−	1.02364i
$993$	47.1226	−	23.3903i	1.49539	−	0.742268i
$994$		0			0
$995$	−10.0884	+	5.82452i	−0.319822	+	0.184650i
$996$	−13.7600	−	9.14265i	−0.436002	−	0.289696i
$997$	−8.38168	−	4.83917i	−0.265451	−	0.153258i	0.361368	−	0.932423i	$-0.382310\pi$
$997$	−8.38168	−	4.83917i	−0.265451	−	0.153258i	−0.626818	+	0.779165i	$0.715643\pi$
$998$			18.8883i			0.597899i
$999$	7.78744	−	40.8053i	0.246384	−	1.29102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.e.146.18	yes	48
3.2	odd	2		1323.2.o.e.440.7		48
7.2	even	3		441.2.i.d.227.7		48
7.3	odd	6		441.2.s.d.362.7		48
7.4	even	3		441.2.s.d.362.8		48
7.5	odd	6		441.2.i.d.227.8		48
7.6	odd	2	inner	441.2.o.e.146.17	✓	48
9.4	even	3		1323.2.o.e.881.8		48
9.5	odd	6	inner	441.2.o.e.293.17	yes	48
21.2	odd	6		1323.2.i.d.521.15		48
21.5	even	6		1323.2.i.d.521.17		48
21.11	odd	6		1323.2.s.d.656.17		48
21.17	even	6		1323.2.s.d.656.18		48
21.20	even	2		1323.2.o.e.440.8		48
63.4	even	3		1323.2.i.d.1097.17		48
63.5	even	6		441.2.s.d.374.8		48
63.13	odd	6		1323.2.o.e.881.7		48
63.23	odd	6		441.2.s.d.374.7		48
63.31	odd	6		1323.2.i.d.1097.15		48
63.32	odd	6		441.2.i.d.68.18		48
63.40	odd	6		1323.2.s.d.962.17		48
63.41	even	6	inner	441.2.o.e.293.18	yes	48
63.58	even	3		1323.2.s.d.962.18		48
63.59	even	6		441.2.i.d.68.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.17		48	63.59	even	6
441.2.i.d.68.18		48	63.32	odd	6
441.2.i.d.227.7		48	7.2	even	3
441.2.i.d.227.8		48	7.5	odd	6
441.2.o.e.146.17	✓	48	7.6	odd	2	inner
441.2.o.e.146.18	yes	48	1.1	even	1	trivial
441.2.o.e.293.17	yes	48	9.5	odd	6	inner
441.2.o.e.293.18	yes	48	63.41	even	6	inner
441.2.s.d.362.7		48	7.3	odd	6
441.2.s.d.362.8		48	7.4	even	3
441.2.s.d.374.7		48	63.23	odd	6
441.2.s.d.374.8		48	63.5	even	6
1323.2.i.d.521.15		48	21.2	odd	6
1323.2.i.d.521.17		48	21.5	even	6
1323.2.i.d.1097.15		48	63.31	odd	6
1323.2.i.d.1097.17		48	63.4	even	3
1323.2.o.e.440.7		48	3.2	odd	2
1323.2.o.e.440.8		48	21.20	even	2
1323.2.o.e.881.7		48	63.13	odd	6
1323.2.o.e.881.8		48	9.4	even	3
1323.2.s.d.656.17		48	21.11	odd	6
1323.2.s.d.656.18		48	21.17	even	6
1323.2.s.d.962.17		48	63.40	odd	6
1323.2.s.d.962.18		48	63.58	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58658 + 0.916012i) q^{2} +(1.44264 + 0.958541i) q^{3} +(0.678156 + 1.17460i) q^{4} +(-0.322784 - 0.559079i) q^{5} +(1.41082 + 2.84227i) q^{6} -1.17925i q^{8} +(1.16240 + 2.76565i) q^{9} -1.18270i q^{10} +(4.60375 + 2.65797i) q^{11} +(-0.147571 + 2.34456i) q^{12} +(-4.44045 + 2.56370i) q^{13} +(0.0702397 - 1.11595i) q^{15} +(2.43652 - 4.22018i) q^{16} -1.62986 q^{17} +(-0.689134 + 5.45270i) q^{18} -2.41378i q^{19} +(0.437796 - 0.758285i) q^{20} +(4.86947 + 8.43418i) q^{22} +(-1.27442 + 0.735784i) q^{23} +(1.13036 - 1.70123i) q^{24} +(2.29162 - 3.96920i) q^{25} -9.39351 q^{26} +(-0.974073 + 5.10404i) q^{27} +(-6.43846 - 3.71724i) q^{29} +(1.13366 - 1.70620i) q^{30} +(4.90799 - 2.83363i) q^{31} +(5.68894 - 3.28451i) q^{32} +(4.09375 + 8.24737i) q^{33} +(-2.58590 - 1.49297i) q^{34} +(-2.46025 + 3.24090i) q^{36} -7.99471 q^{37} +(2.21105 - 3.82965i) q^{38} +(-8.86336 - 0.557875i) q^{39} +(-0.659294 + 0.380644i) q^{40} +(-5.99052 - 10.3759i) q^{41} +(-1.51281 + 2.62026i) q^{43} +7.21009i q^{44} +(1.17101 - 1.54258i) q^{45} -2.69595 q^{46} +(1.54176 - 2.67041i) q^{47} +(7.56023 - 3.75268i) q^{48} +(7.27168 - 4.19830i) q^{50} +(-2.35130 - 1.56229i) q^{51} +(-6.02264 - 3.47717i) q^{52} -2.36199i q^{53} +(-6.22080 + 7.20569i) q^{54} -3.43181i q^{55} +(2.31371 - 3.48220i) q^{57} +(-6.81008 - 11.7954i) q^{58} +(-1.47918 - 2.56202i) q^{59} +(1.35843 - 0.674284i) q^{60} +(9.18018 + 5.30018i) q^{61} +10.3825 q^{62} +2.28853 q^{64} +(2.86662 + 1.65504i) q^{65} +(-1.05962 + 16.8350i) q^{66} +(5.07747 + 8.79444i) q^{67} +(-1.10530 - 1.91444i) q^{68} +(-2.54380 - 0.160111i) q^{69} -4.76597i q^{71} +(3.26140 - 1.37076i) q^{72} +11.8055i q^{73} +(-12.6842 - 7.32325i) q^{74} +(7.11062 - 3.52950i) q^{75} +(2.83523 - 1.63692i) q^{76} +(-13.5514 - 9.00406i) q^{78} +(-3.48104 + 6.02934i) q^{79} -3.14588 q^{80} +(-6.29766 + 6.42958i) q^{81} -21.9496i q^{82} +(-3.51618 + 6.09021i) q^{83} +(0.526093 + 0.911221i) q^{85} +(-4.80038 + 2.77150i) q^{86} +(-5.72522 - 11.5342i) q^{87} +(3.13442 - 5.42898i) q^{88} -4.32674 q^{89} +(3.27093 - 1.37476i) q^{90} +(-1.72850 - 0.997953i) q^{92} +(9.79659 + 0.616613i) q^{93} +(4.89226 - 2.82455i) q^{94} +(-1.34949 + 0.779129i) q^{95} +(11.3554 + 0.714729i) q^{96} +(14.3946 + 8.31075i) q^{97} +(-1.99965 + 15.8220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64}+ \cdots - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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