LMFDB - Embedded newform 840.2.dd.b.313.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(73,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dd (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			313.7
Character	$\chi$	$=$	840.313
Dual form			840.2.dd.b.577.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{3} +(-2.22330 + 0.238577i) q^{5} +(-2.64040 - 0.168257i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-0.302014 - 0.523104i) q^{11} +(2.37412 - 2.37412i) q^{13} +(-2.20930 - 0.344985i) q^{15} +(0.730673 - 2.72691i) q^{17} +(3.87343 - 6.70898i) q^{19} +(-2.50688 - 0.845908i) q^{21} +(3.69567 - 0.990253i) q^{23} +(4.88616 - 1.06086i) q^{25} +(0.707107 + 0.707107i) q^{27} -1.06852i q^{29} +(1.47554 - 0.851906i) q^{31} +(-0.156334 - 0.583447i) q^{33} +(5.91054 - 0.255853i) q^{35} +(-0.716371 - 2.67353i) q^{37} +(2.90769 - 1.67875i) q^{39} -8.01044i q^{41} +(-8.31126 - 8.31126i) q^{43} +(-2.04473 - 0.905038i) q^{45} +(-9.12416 + 2.44481i) q^{47} +(6.94338 + 0.888529i) q^{49} +(1.41155 - 2.44488i) q^{51} +(-2.64249 + 9.86190i) q^{53} +(0.796271 + 1.09097i) q^{55} +(5.47786 - 5.47786i) q^{57} +(4.72374 + 8.18175i) q^{59} +(5.59172 + 3.22838i) q^{61} +(-2.20252 - 1.46591i) q^{63} +(-4.71197 + 5.84479i) q^{65} +(-3.06814 - 0.822105i) q^{67} +3.82604 q^{69} -16.5937 q^{71} +(11.5337 + 3.09044i) q^{73} +(4.99424 + 0.239919i) q^{75} +(0.709422 + 1.43202i) q^{77} +(-8.14616 - 4.70319i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.18915 - 2.18915i) q^{83} +(-0.973929 + 6.23707i) q^{85} +(0.276553 - 1.03211i) q^{87} +(-4.24238 + 7.34801i) q^{89} +(-6.66806 + 5.86914i) q^{91} +(1.64576 - 0.440979i) q^{93} +(-7.01121 + 15.8402i) q^{95} +(-4.19889 - 4.19889i) q^{97} -0.604029i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) $ 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$		0			0
$5$	−2.22330	+	0.238577i	−0.994292	+	0.106695i
$5$	−2.22330	+	0.238577i	−0.994292	+	0.106695i
$6$		0			0
$7$	−2.64040	−	0.168257i	−0.997976	−	0.0635951i
$7$	−2.64040	−	0.168257i	−0.997976	−	0.0635951i
$8$		0			0
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−0.302014	−	0.523104i	−0.0910608	−	0.157722i	0.816897	−	0.576784i	$-0.195692\pi$
$11$	−0.302014	−	0.523104i	−0.0910608	−	0.157722i	−0.907958	+	0.419062i	$0.862359\pi$
$12$		0			0
$13$	2.37412	−	2.37412i	0.658461	−	0.658461i	−0.296555	−	0.955016i	$-0.595838\pi$
$13$	2.37412	−	2.37412i	0.658461	−	0.658461i	0.955016	+	0.296555i	$0.0958377\pi$
$14$		0			0
$15$	−2.20930	−	0.344985i	−0.570438	−	0.0890748i
$16$		0			0
$17$	0.730673	−	2.72691i	0.177214	−	0.661372i	−0.818950	−	0.573865i	$-0.805443\pi$
$17$	0.730673	−	2.72691i	0.177214	−	0.661372i	0.996164	−	0.0875070i	$-0.0278900\pi$
$18$		0			0
$19$	3.87343	−	6.70898i	0.888627	−	1.53915i	0.0471270	−	0.998889i	$-0.484993\pi$
$19$	3.87343	−	6.70898i	0.888627	−	1.53915i	0.841500	−	0.540258i	$-0.181673\pi$
$20$		0			0
$21$	−2.50688	−	0.845908i	−0.547046	−	0.184592i
$22$		0			0
$23$	3.69567	−	0.990253i	0.770601	−	0.206482i	0.147964	−	0.988993i	$-0.452728\pi$
$23$	3.69567	−	0.990253i	0.770601	−	0.206482i	0.622637	+	0.782511i	$0.286061\pi$
$24$		0			0
$25$	4.88616	−	1.06086i	0.977232	−	0.212172i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	1.06852i		−	0.198419i	−0.995067	−	0.0992095i	$-0.968369\pi$
$29$		−	1.06852i		−	0.198419i	0.995067	−	0.0992095i	$-0.0316314\pi$
$30$		0			0
$31$	1.47554	−	0.851906i	0.265015	−	0.153007i	−0.361605	−	0.932331i	$-0.617771\pi$
$31$	1.47554	−	0.851906i	0.265015	−	0.153007i	0.626620	+	0.779325i	$0.284438\pi$
$32$		0			0
$33$	−0.156334	−	0.583447i	−0.0272143	−	0.101565i
$34$		0			0
$35$	5.91054	−	0.255853i	0.999064	−	0.0432471i
$36$		0			0
$37$	−0.716371	−	2.67353i	−0.117771	−	0.439526i	0.881709	−	0.471794i	$-0.156394\pi$
$37$	−0.716371	−	2.67353i	−0.117771	−	0.439526i	−0.999479	+	0.0322684i	$0.989727\pi$
$38$		0			0
$39$	2.90769	−	1.67875i	0.465602	−	0.268816i
$40$		0			0
$41$		−	8.01044i		−	1.25102i	−0.780216	−	0.625511i	$-0.784891\pi$
$41$		−	8.01044i		−	1.25102i	0.780216	−	0.625511i	$-0.215109\pi$
$42$		0			0
$43$	−8.31126	−	8.31126i	−1.26746	−	1.26746i	−0.947398	−	0.320058i	$-0.896298\pi$
$43$	−8.31126	−	8.31126i	−1.26746	−	1.26746i	−0.320058	−	0.947398i	$-0.603702\pi$
$44$		0			0
$45$	−2.04473	−	0.905038i	−0.304810	−	0.134915i
$46$		0			0
$47$	−9.12416	+	2.44481i	−1.33090	+	0.356612i	−0.853049	−	0.521831i	$-0.825249\pi$
$47$	−9.12416	+	2.44481i	−1.33090	+	0.356612i	−0.477846	+	0.878443i	$0.658582\pi$
$48$		0			0
$49$	6.94338	+	0.888529i	0.991911	+	0.126933i
$50$		0			0
$51$	1.41155	−	2.44488i	0.197657	−	0.342351i
$52$		0			0
$53$	−2.64249	+	9.86190i	−0.362974	+	1.35464i	0.507174	+	0.861844i	$0.330690\pi$
$53$	−2.64249	+	9.86190i	−0.362974	+	1.35464i	−0.870147	+	0.492792i	$0.835976\pi$
$54$		0			0
$55$	0.796271	+	1.09097i	0.107369	+	0.147106i
$56$		0			0
$57$	5.47786	−	5.47786i	0.725561	−	0.725561i
$58$		0			0
$59$	4.72374	+	8.18175i	0.614978	+	1.06517i	0.990388	+	0.138314i	$0.0441684\pi$
$59$	4.72374	+	8.18175i	0.614978	+	1.06517i	−0.375410	+	0.926859i	$0.622498\pi$
$60$		0			0
$61$	5.59172	+	3.22838i	0.715946	+	0.413351i	0.813259	−	0.581902i	$-0.197691\pi$
$61$	5.59172	+	3.22838i	0.715946	+	0.413351i	−0.0973129	+	0.995254i	$0.531025\pi$
$62$		0			0
$63$	−2.20252	−	1.46591i	−0.277492	−	0.184688i
$64$		0			0
$65$	−4.71197	+	5.84479i	−0.584448	+	0.724957i
$66$		0			0
$67$	−3.06814	−	0.822105i	−0.374833	−	0.100436i	0.0664841	−	0.997787i	$-0.478822\pi$
$67$	−3.06814	−	0.822105i	−0.374833	−	0.100436i	−0.441317	+	0.897351i	$0.645488\pi$
$68$		0			0
$69$	3.82604			0.460602
$70$		0			0
$71$	−16.5937			−1.96931			−0.984653	−	0.174521i	$-0.944162\pi$
$71$	−16.5937			−1.96931			−0.984653	+	0.174521i	$0.944162\pi$
$72$		0			0
$73$	11.5337	+	3.09044i	1.34991	+	0.361708i	0.860103	−	0.510121i	$-0.170399\pi$
$73$	11.5337	+	3.09044i	1.34991	+	0.361708i	0.489811	+	0.871829i	$0.337066\pi$
$74$		0			0
$75$	4.99424	+	0.239919i	0.576685	+	0.0277035i
$76$		0			0
$77$	0.709422	+	1.43202i	0.0808461	+	0.163194i
$78$		0			0
$79$	−8.14616	−	4.70319i	−0.916514	−	0.529150i	−0.0339928	−	0.999422i	$-0.510822\pi$
$79$	−8.14616	−	4.70319i	−0.916514	−	0.529150i	−0.882521	+	0.470272i	$0.844156\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	2.18915	−	2.18915i	0.240291	−	0.240291i	−0.576679	−	0.816970i	$-0.695652\pi$
$83$	2.18915	−	2.18915i	0.240291	−	0.240291i	0.816970	+	0.576679i	$0.195652\pi$
$84$		0			0
$85$	−0.973929	+	6.23707i	−0.105637	+	0.676505i
$86$		0			0
$87$	0.276553	−	1.03211i	0.0296496	−	0.110654i
$88$		0			0
$89$	−4.24238	+	7.34801i	−0.449691	+	0.778887i	−0.998366	−	0.0571484i	$-0.981799\pi$
$89$	−4.24238	+	7.34801i	−0.449691	+	0.778887i	0.548675	+	0.836036i	$0.315133\pi$
$90$		0			0
$91$	−6.66806	+	5.86914i	−0.699003	+	0.615253i
$92$		0			0
$93$	1.64576	−	0.440979i	0.170657	−	0.0457274i
$94$		0			0
$95$	−7.01121	+	15.8402i	−0.719335	+	1.62517i
$96$		0			0
$97$	−4.19889	−	4.19889i	−0.426332	−	0.426332i	0.461045	−	0.887377i	$-0.347475\pi$
$97$	−4.19889	−	4.19889i	−0.426332	−	0.426332i	−0.887377	+	0.461045i	$0.847475\pi$
$98$		0			0
$99$		−	0.604029i		−	0.0607072i
$100$		0			0
$101$	11.0072	−	6.35500i	1.09526	−	0.632346i	0.160285	−	0.987071i	$-0.448759\pi$
$101$	11.0072	−	6.35500i	1.09526	−	0.632346i	0.934971	+	0.354724i	$0.115425\pi$
$102$		0			0
$103$	−1.20145	−	4.48387i	−0.118382	−	0.441809i	0.881135	−	0.472864i	$-0.156780\pi$
$103$	−1.20145	−	4.48387i	−0.118382	−	0.441809i	−0.999518	+	0.0310553i	$0.990113\pi$
$104$		0			0
$105$	5.77537	+	1.28263i	0.563618	+	0.125172i
$106$		0			0
$107$	−2.94573	−	10.9936i	−0.284774	−	1.06279i	−0.949004	−	0.315263i	$-0.897907\pi$
$107$	−2.94573	−	10.9936i	−0.284774	−	1.06279i	0.664230	−	0.747528i	$-0.268760\pi$
$108$		0			0
$109$	13.0939	−	7.55974i	1.25416	−	0.724092i	0.282230	−	0.959347i	$-0.408926\pi$
$109$	13.0939	−	7.55974i	1.25416	−	0.724092i	0.971934	+	0.235255i	$0.0755924\pi$
$110$		0			0
$111$		−	2.76784i		−	0.262712i
$112$		0			0
$113$	−0.101514	−	0.101514i	−0.00954961	−	0.00954961i	0.702316	−	0.711865i	$-0.252149\pi$
$113$	−0.101514	−	0.101514i	−0.00954961	−	0.00954961i	−0.711865	+	0.702316i	$0.752149\pi$
$114$		0			0
$115$	−7.98036	+	3.08334i	−0.744172	+	0.287523i
$116$		0			0
$117$	3.24310	−	0.868986i	0.299825	−	0.0803378i
$118$		0			0
$119$	−2.38809	+	7.07717i	−0.218915	+	0.648764i
$120$		0			0
$121$	5.31757	−	9.21031i	0.483416	−	0.837301i
$122$		0			0
$123$	2.07326	−	7.73749i	0.186939	−	0.697666i
$124$		0			0
$125$	−10.6103	+	3.52434i	−0.949016	+	0.315227i
$126$		0			0
$127$	−5.42109	+	5.42109i	−0.481044	+	0.481044i	−0.905465	−	0.424421i	$-0.860478\pi$
$127$	−5.42109	+	5.42109i	−0.481044	+	0.481044i	0.424421	+	0.905465i	$0.360478\pi$
$128$		0			0
$129$	−5.87695	−	10.1792i	−0.517437	−	0.896227i
$130$		0			0
$131$	9.07156	+	5.23747i	0.792586	+	0.457600i	0.840872	−	0.541234i	$-0.182043\pi$
$131$	9.07156	+	5.23747i	0.792586	+	0.457600i	−0.0482864	+	0.998834i	$0.515376\pi$
$132$		0			0
$133$	−11.3562	+	17.0626i	−0.984710	+	1.47952i
$134$		0			0
$135$	−1.74081	−	1.40341i	−0.149825	−	0.120787i
$136$		0			0
$137$	6.07172	+	1.62691i	0.518742	+	0.138996i	0.508685	−	0.860953i	$-0.330132\pi$
$137$	6.07172	+	1.62691i	0.518742	+	0.138996i	0.0100574	+	0.999949i	$0.496799\pi$
$138$		0			0
$139$	17.6135			1.49396			0.746978	−	0.664849i	$-0.231504\pi$
$139$	17.6135			1.49396			0.746978	+	0.664849i	$0.231504\pi$
$140$		0			0
$141$	−9.44602			−0.795499
$142$		0			0
$143$	−1.95893	−	0.524893i	−0.163814	−	0.0438937i
$144$		0			0
$145$	0.254925	+	2.37564i	0.0211703	+	0.197286i
$146$		0			0
$147$	6.47682	+	2.65533i	0.534199	+	0.219008i
$148$		0			0
$149$	6.00115	+	3.46476i	0.491633	+	0.283844i	0.725252	−	0.688484i	$-0.241723\pi$
$149$	6.00115	+	3.46476i	0.491633	+	0.283844i	−0.233619	+	0.972328i	$0.575057\pi$
$150$		0			0
$151$	−0.386607	−	0.669623i	−0.0314617	−	0.0544932i	0.849866	−	0.526999i	$-0.176683\pi$
$151$	−0.386607	−	0.669623i	−0.0314617	−	0.0544932i	−0.881328	+	0.472506i	$0.843350\pi$
$152$		0			0
$153$	1.99624	−	1.99624i	0.161386	−	0.161386i
$154$		0			0
$155$	−3.07734	+	2.24608i	−0.247178	+	0.180409i
$156$		0			0
$157$	4.15407	−	15.5032i	0.331531	−	1.23729i	−0.576050	−	0.817414i	$-0.695407\pi$
$157$	4.15407	−	15.5032i	0.331531	−	1.23729i	0.907581	−	0.419876i	$-0.137927\pi$
$158$		0			0
$159$	−5.10489	+	8.84194i	−0.404844	+	0.701211i
$160$		0			0
$161$	−9.92466	+	1.99284i	−0.782173	+	0.157058i
$162$		0			0
$163$	−6.42450	+	1.72144i	−0.503206	+	0.134834i	−0.501487	−	0.865165i	$-0.667214\pi$
$163$	−6.42450	+	1.72144i	−0.503206	+	0.134834i	−0.00171822	+	0.999999i	$0.500547\pi$
$164$		0			0
$165$	0.486776	+	1.25988i	0.0378954	+	0.0980817i
$166$		0			0
$167$	−12.6127	−	12.6127i	−0.976003	−	0.976003i	0.0237154	−	0.999719i	$-0.492450\pi$
$167$	−12.6127	−	12.6127i	−0.976003	−	0.976003i	−0.999719	+	0.0237154i	$0.992450\pi$
$168$		0			0
$169$			1.72715i			0.132858i
$170$		0			0
$171$	6.70898	−	3.87343i	0.513049	−	0.296209i
$172$		0			0
$173$	3.09676	+	11.5573i	0.235442	+	0.878683i	0.977949	+	0.208844i	$0.0669701\pi$
$173$	3.09676	+	11.5573i	0.235442	+	0.878683i	−0.742507	+	0.669839i	$0.766363\pi$
$174$		0			0
$175$	−13.0799	+	1.97896i	−0.988747	+	0.149595i
$176$		0			0
$177$	2.44519	+	9.12556i	0.183791	+	0.685919i
$178$		0			0
$179$	−3.98768	+	2.30229i	−0.298053	+	0.172081i	−0.641568	−	0.767066i	$-0.721716\pi$
$179$	−3.98768	+	2.30229i	−0.298053	+	0.172081i	0.343515	+	0.939147i	$0.388382\pi$
$180$		0			0
$181$		−	9.53754i		−	0.708919i	−0.935071	−	0.354460i	$-0.884665\pi$
$181$		−	9.53754i		−	0.708919i	0.935071	−	0.354460i	$-0.115335\pi$
$182$		0			0
$183$	4.56562	+	4.56562i	0.337500	+	0.337500i
$184$		0			0
$185$	2.23055	+	5.77316i	0.163994	+	0.424452i
$186$		0			0
$187$	−1.64713	+	0.441347i	−0.120450	+	0.0322745i
$188$		0			0
$189$	−1.74807	−	1.98602i	−0.127153	−	0.144461i
$190$		0			0
$191$	5.03567	−	8.72203i	0.364368	−	0.631104i	−0.624307	−	0.781179i	$-0.714618\pi$
$191$	5.03567	−	8.72203i	0.364368	−	0.631104i	0.988675	+	0.150076i	$0.0479517\pi$
$192$		0			0
$193$	−6.68382	+	24.9444i	−0.481112	+	1.79553i	0.115853	+	0.993266i	$0.463040\pi$
$193$	−6.68382	+	24.9444i	−0.481112	+	1.79553i	−0.596964	+	0.802268i	$0.703627\pi$
$194$		0			0
$195$	−6.06416	+	4.42609i	−0.434263	+	0.316959i
$196$		0			0
$197$	−1.44525	+	1.44525i	−0.102970	+	0.102970i	−0.756715	−	0.653745i	$-0.773197\pi$
$197$	−1.44525	+	1.44525i	−0.102970	+	0.102970i	0.653745	+	0.756715i	$0.273197\pi$
$198$		0			0
$199$	3.51710	+	6.09180i	0.249321	+	0.431836i	0.963338	−	0.268292i	$-0.0864594\pi$
$199$	3.51710	+	6.09180i	0.249321	+	0.431836i	−0.714017	+	0.700129i	$0.753126\pi$
$200$		0			0
$201$	−2.75082	−	1.58818i	−0.194028	−	0.112022i
$202$		0			0
$203$	−0.179786	+	2.82131i	−0.0126185	+	0.198017i
$204$		0			0
$205$	1.91111	+	17.8097i	0.133478	+	1.24388i
$206$		0			0
$207$	3.69567	+	0.990253i	0.256867	+	0.0688273i
$208$		0			0
$209$	−4.67933			−0.323676
$210$		0			0
$211$	12.1267			0.834835			0.417418	−	0.908715i	$-0.362935\pi$
$211$	12.1267			0.834835			0.417418	+	0.908715i	$0.362935\pi$
$212$		0			0
$213$	−16.0283	−	4.29476i	−1.09824	−	0.294272i
$214$		0			0
$215$	20.4613	+	16.4956i	1.39545	+	1.12499i
$216$		0			0
$217$	−4.03936	+	2.00110i	−0.274210	+	0.135843i
$218$		0			0
$219$	10.3408	+	5.97026i	0.698767	+	0.403433i
$220$		0			0
$221$	−4.73929	−	8.20869i	−0.318799	−	0.552177i
$222$		0			0
$223$	−4.88122	+	4.88122i	−0.326871	+	0.326871i	−0.851395	−	0.524525i	$-0.824243\pi$
$223$	−4.88122	+	4.88122i	−0.326871	+	0.326871i	0.524525	+	0.851395i	$0.324243\pi$
$224$		0			0
$225$	4.76197	+	1.52435i	0.317465	+	0.101623i
$226$		0			0
$227$	−2.56367	+	9.56773i	−0.170156	+	0.635033i	0.827170	+	0.561952i	$0.189950\pi$
$227$	−2.56367	+	9.56773i	−0.170156	+	0.635033i	−0.997326	+	0.0730802i	$0.976717\pi$
$228$		0			0
$229$	1.32546	−	2.29577i	0.0875889	−	0.151708i	−0.818903	−	0.573933i	$-0.805417\pi$
$229$	1.32546	−	2.29577i	0.0875889	−	0.151708i	0.906491	+	0.422224i	$0.138750\pi$
$230$		0			0
$231$	0.314615	+	1.56684i	0.0207002	+	0.103090i
$232$		0			0
$233$	−11.9524	+	3.20263i	−0.783026	+	0.209811i	−0.628118	−	0.778118i	$-0.716175\pi$
$233$	−11.9524	+	3.20263i	−0.783026	+	0.209811i	−0.154908	+	0.987929i	$0.549508\pi$
$234$		0			0
$235$	19.7025	−	7.61238i	1.28525	−	0.496577i
$236$		0			0
$237$	−6.65131	−	6.65131i	−0.432049	−	0.432049i
$238$		0			0
$239$			2.05152i			0.132702i	0.997796	+	0.0663508i	$0.0211356\pi$
$239$			2.05152i			0.132702i	−0.997796	+	0.0663508i	$0.978864\pi$
$240$		0			0
$241$	−12.7846	+	7.38119i	−0.823528	+	0.475464i	−0.851632	−	0.524141i	$-0.824386\pi$
$241$	−12.7846	+	7.38119i	−0.823528	+	0.475464i	0.0281037	+	0.999605i	$0.491053\pi$
$242$		0			0
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$		0			0
$245$	−15.6492	−	0.318936i	−0.999792	−	0.0203761i
$246$		0			0
$247$	−6.73192	−	25.1239i	−0.428342	−	1.59859i
$248$		0			0
$249$	2.68116	−	1.54797i	0.169911	−	0.0980984i
$250$		0			0
$251$			6.95633i			0.439079i	0.975604	+	0.219540i	$0.0704555\pi$
$251$			6.95633i			0.439079i	−0.975604	+	0.219540i	$0.929544\pi$
$252$		0			0
$253$	−1.63415	−	1.63415i	−0.102738	−	0.102738i
$254$		0			0
$255$	−2.55501	+	5.77247i	−0.160001	+	0.361486i
$256$		0			0
$257$	0.778496	−	0.208597i	0.0485613	−	0.0130120i	−0.234457	−	0.972127i	$-0.575331\pi$
$257$	0.778496	−	0.208597i	0.0485613	−	0.0130120i	0.283018	+	0.959115i	$0.408664\pi$
$258$		0			0
$259$	1.44166	+	7.17972i	0.0895805	+	0.446126i
$260$		0			0
$261$	0.534260	−	0.925365i	0.0330698	−	0.0572786i
$262$		0			0
$263$	−5.02671	+	18.7599i	−0.309960	+	1.15679i	0.618630	+	0.785682i	$0.287688\pi$
$263$	−5.02671	+	18.7599i	−0.309960	+	1.15679i	−0.928591	+	0.371106i	$0.878979\pi$
$264$		0			0
$265$	3.52223	−	22.5564i	0.216369	−	1.38563i
$266$		0			0
$267$	−5.99962	+	5.99962i	−0.367171	+	0.367171i
$268$		0			0
$269$	0.953541	+	1.65158i	0.0581384	+	0.100699i	0.893630	−	0.448805i	$-0.148150\pi$
$269$	0.953541	+	1.65158i	0.0581384	+	0.100699i	−0.835491	+	0.549504i	$0.814817\pi$
$270$		0			0
$271$	24.6547	+	14.2344i	1.49767	+	0.864680i	0.999996	−	0.00268518i	$-0.000854721\pi$
$271$	24.6547	+	14.2344i	1.49767	+	0.864680i	0.497673	+	0.867365i	$0.334188\pi$
$272$		0			0
$273$	−7.95990	+	3.94333i	−0.481755	+	0.238661i
$274$		0			0
$275$	−2.03063	−	2.23558i	−0.122452	−	0.134810i
$276$		0			0
$277$	−3.62872	−	0.972312i	−0.218029	−	0.0584206i	0.148151	−	0.988965i	$-0.452668\pi$
$277$	−3.62872	−	0.972312i	−0.218029	−	0.0584206i	−0.366180	+	0.930544i	$0.619334\pi$
$278$		0			0
$279$	1.70381			0.102005
$280$		0			0
$281$	−12.1025			−0.721976			−0.360988	−	0.932571i	$-0.617560\pi$
$281$	−12.1025			−0.721976			−0.360988	+	0.932571i	$0.617560\pi$
$282$		0			0
$283$	−11.5059	−	3.08300i	−0.683956	−	0.183266i	−0.0999229	−	0.994995i	$-0.531860\pi$
$283$	−11.5059	−	3.08300i	−0.683956	−	0.183266i	−0.584033	+	0.811730i	$0.698526\pi$
$284$		0			0
$285$	−10.8721	+	13.4858i	−0.644005	+	0.798833i
$286$		0			0
$287$	−1.34781	+	21.1507i	−0.0795588	+	1.24849i
$288$		0			0
$289$	7.82029	+	4.51505i	0.460017	+	0.265591i
$290$		0			0
$291$	−2.96906	−	5.14257i	−0.174049	−	0.301463i
$292$		0			0
$293$	7.09479	−	7.09479i	0.414482	−	0.414482i	−0.468815	−	0.883297i	$-0.655319\pi$
$293$	7.09479	−	7.09479i	0.414482	−	0.414482i	0.883297	+	0.468815i	$0.155319\pi$
$294$		0			0
$295$	−12.4543	−	17.0635i	−0.725116	−	0.993478i
$296$		0			0
$297$	0.156334	−	0.583447i	0.00907143	−	0.0338550i
$298$		0			0
$299$	6.42298	−	11.1249i	0.371451	−	0.643371i
$300$		0			0
$301$	20.5466	+	23.3435i	1.18429	+	1.34549i
$302$		0			0
$303$	12.2769	−	3.28959i	0.705291	−	0.188982i
$304$		0			0
$305$	−13.2023	−	5.84361i	−0.755962	−	0.334604i
$306$		0			0
$307$	−17.6262	−	17.6262i	−1.00598	−	1.00598i	−0.999982	−	0.00599819i	$-0.998091\pi$
$307$	−17.6262	−	17.6262i	−1.00598	−	1.00598i	−0.00599819	−	0.999982i	$-0.501909\pi$
$308$		0			0
$309$		−	4.64204i		−	0.264077i
$310$		0			0
$311$	22.3736	−	12.9174i	1.26869	−	0.732480i	0.293952	−	0.955820i	$-0.405029\pi$
$311$	22.3736	−	12.9174i	1.26869	−	0.732480i	0.974741	+	0.223340i	$0.0716960\pi$
$312$		0			0
$313$	1.20489	+	4.49672i	0.0681045	+	0.254170i	0.991581	−	0.129484i	$-0.0413322\pi$
$313$	1.20489	+	4.49672i	0.0681045	+	0.254170i	−0.923477	+	0.383654i	$0.874666\pi$
$314$		0			0
$315$	5.24661	+	2.73370i	0.295613	+	0.154026i
$316$		0			0
$317$	1.82503	+	6.81112i	0.102504	+	0.382551i	0.998050	−	0.0624184i	$-0.0198813\pi$
$317$	1.82503	+	6.81112i	0.102504	+	0.382551i	−0.895546	+	0.444969i	$0.853215\pi$
$318$		0			0
$319$	−0.558947	+	0.322708i	−0.0312950	+	0.0180682i
$320$		0			0
$321$		−	11.3814i		−	0.635249i
$322$		0			0
$323$	−15.4646	−	15.4646i	−0.860472	−	0.860472i
$324$		0			0
$325$	9.08171	−	14.1189i	0.503762	−	0.783177i
$326$		0			0
$327$	14.6043	−	3.91321i	0.807620	−	0.216401i
$328$		0			0
$329$	24.5027	−	4.92007i	1.35088	−	0.271252i
$330$		0			0
$331$	−6.23729	+	10.8033i	−0.342833	+	0.593803i	−0.984958	−	0.172797i	$-0.944720\pi$
$331$	−6.23729	+	10.8033i	−0.342833	+	0.593803i	0.642125	+	0.766600i	$0.278053\pi$
$332$		0			0
$333$	0.716371	−	2.67353i	0.0392569	−	0.146509i
$334$		0			0
$335$	7.01754	+	1.09580i	0.383409	+	0.0598700i
$336$		0			0
$337$	−13.6654	+	13.6654i	−0.744401	+	0.744401i	−0.973422	−	0.229021i	$-0.926448\pi$
$337$	−13.6654	+	13.6654i	−0.744401	+	0.744401i	0.229021	+	0.973422i	$0.426448\pi$
$338$		0			0
$339$	−0.0717811	−	0.124328i	−0.00389861	−	0.00675259i
$340$		0			0
$341$	−0.891271	−	0.514575i	−0.0482650	−	0.0278658i
$342$		0			0
$343$	−18.1838	−	3.51434i	−0.981831	−	0.189756i
$344$		0			0
$345$	−8.50646	+	0.912808i	−0.457972	+	0.0491439i
$346$		0			0
$347$	11.1600	+	2.99032i	0.599101	+	0.160529i	0.545609	−	0.838040i	$-0.316298\pi$
$347$	11.1600	+	2.99032i	0.599101	+	0.160529i	0.0534916	+	0.998568i	$0.482965\pi$
$348$		0			0
$349$	34.3364			1.83799			0.918993	−	0.394274i	$-0.129004\pi$
$349$	34.3364			1.83799			0.918993	+	0.394274i	$0.129004\pi$
$350$		0			0
$351$	3.35751			0.179210
$352$		0			0
$353$	11.0254	+	2.95425i	0.586824	+	0.157239i	0.540001	−	0.841664i	$-0.318424\pi$
$353$	11.0254	+	2.95425i	0.586824	+	0.157239i	0.0468225	+	0.998903i	$0.485090\pi$
$354$		0			0
$355$	36.8928	−	3.95888i	1.95807	−	0.210115i
$356$		0			0
$357$	−4.13842	+	6.21794i	−0.219028	+	0.329088i
$358$		0			0
$359$	−5.61795	−	3.24352i	−0.296504	−	0.171187i	0.344367	−	0.938835i	$-0.388093\pi$
$359$	−5.61795	−	3.24352i	−0.296504	−	0.171187i	−0.640871	+	0.767648i	$0.721427\pi$
$360$		0			0
$361$	−20.5070	−	35.5191i	−1.07931	−	1.86943i
$362$		0			0
$363$	7.52019	−	7.52019i	0.394707	−	0.394707i
$364$		0			0
$365$	−26.3802	−	4.11931i	−1.38080	−	0.215614i
$366$		0			0
$367$	−3.49749	+	13.0528i	−0.182568	+	0.681352i	0.812570	+	0.582863i	$0.198068\pi$
$367$	−3.49749	+	13.0528i	−0.182568	+	0.681352i	−0.995138	+	0.0984890i	$0.968599\pi$
$368$		0			0
$369$	4.00522	−	6.93725i	0.208504	−	0.361139i
$370$		0			0
$371$	8.63654	−	25.5947i	0.448387	−	1.32881i
$372$		0			0
$373$	34.8881	−	9.34824i	1.80644	−	0.484034i	0.811485	−	0.584373i	$-0.198660\pi$
$373$	34.8881	−	9.34824i	1.80644	−	0.484034i	0.994953	+	0.100340i	$0.0319929\pi$
$374$		0			0
$375$	−11.1610	+	0.658100i	−0.576349	+	0.0339842i
$376$		0			0
$377$	−2.53679	−	2.53679i	−0.130651	−	0.130651i
$378$		0			0
$379$			11.0284i			0.566490i	0.959048	+	0.283245i	$0.0914110\pi$
$379$			11.0284i			0.566490i	−0.959048	+	0.283245i	$0.908589\pi$
$380$		0			0
$381$	−6.63945	+	3.83329i	−0.340149	+	0.196385i
$382$		0			0
$383$	−7.91637	−	29.5443i	−0.404508	−	1.50964i	−0.804962	−	0.593326i	$-0.797814\pi$
$383$	−7.91637	−	29.5443i	−0.404508	−	1.50964i	0.400454	−	0.916317i	$-0.368852\pi$
$384$		0			0
$385$	−1.91891	−	3.01456i	−0.0977966	−	0.153636i
$386$		0			0
$387$	−3.04213	−	11.3534i	−0.154640	−	0.577126i
$388$		0			0
$389$	4.14118	−	2.39091i	0.209966	−	0.121224i	−0.391329	−	0.920251i	$-0.627985\pi$
$389$	4.14118	−	2.39091i	0.209966	−	0.121224i	0.601296	+	0.799027i	$0.294651\pi$
$390$		0			0
$391$		−	10.8013i		−	0.546246i
$392$		0			0
$393$	7.40690	+	7.40690i	0.373628	+	0.373628i
$394$		0			0
$395$	19.2335	+	8.51312i	0.967740	+	0.428342i
$396$		0			0
$397$	−24.3101	+	6.51387i	−1.22009	+	0.326922i	−0.810713	−	0.585444i	$-0.800920\pi$
$397$	−24.3101	+	6.51387i	−1.22009	+	0.326922i	−0.409376	+	0.912366i	$0.634253\pi$
$398$		0			0
$399$	−15.3854	+	13.5420i	−0.770234	+	0.677950i
$400$		0			0
$401$	−12.6186	+	21.8561i	−0.630145	+	1.09144i	0.357377	+	0.933960i	$0.383671\pi$
$401$	−12.6186	+	21.8561i	−0.630145	+	1.09144i	−0.987522	+	0.157483i	$0.949662\pi$
$402$		0			0
$403$	1.48059	−	5.52563i	0.0737534	−	0.275251i
$404$		0			0
$405$	−1.31827	−	1.80615i	−0.0655052	−	0.0897483i
$406$		0			0
$407$	−1.18218	+	1.18218i	−0.0585986	+	0.0585986i
$408$		0			0
$409$	−8.17125	−	14.1530i	−0.404042	−	0.699822i	0.590167	−	0.807281i	$-0.299062\pi$
$409$	−8.17125	−	14.1530i	−0.404042	−	0.699822i	−0.994209	+	0.107459i	$0.965729\pi$
$410$		0			0
$411$	5.44375	+	3.14295i	0.268521	+	0.155030i
$412$		0			0
$413$	−11.0959	−	22.3979i	−0.545993	−	1.10213i
$414$		0			0
$415$	−4.34487	+	5.38944i	−0.213281	+	0.264557i
$416$		0			0
$417$	17.0133	+	4.55870i	0.833145	+	0.223241i
$418$		0			0
$419$	36.1342			1.76527			0.882635	−	0.470058i	$-0.155767\pi$
$419$	36.1342			1.76527			0.882635	+	0.470058i	$0.155767\pi$
$420$		0			0
$421$	−12.3536			−0.602076			−0.301038	−	0.953612i	$-0.597333\pi$
$421$	−12.3536			−0.602076			−0.301038	+	0.953612i	$0.597333\pi$
$422$		0			0
$423$	−9.12416	−	2.44481i	−0.443632	−	0.118871i
$424$		0			0
$425$	0.677316	−	14.0993i	0.0328547	−	0.683914i
$426$		0			0
$427$	−14.2211	−	9.46504i	−0.688209	−	0.458045i
$428$		0			0
$429$	−1.75633	−	1.01402i	−0.0847962	−	0.0489571i
$430$		0			0
$431$	0.758639	+	1.31400i	0.0365423	+	0.0632932i	0.883718	−	0.468019i	$-0.155032\pi$
$431$	0.758639	+	1.31400i	0.0365423	+	0.0632932i	−0.847176	+	0.531313i	$0.821699\pi$
$432$		0			0
$433$	−19.0028	+	19.0028i	−0.913217	+	0.913217i	−0.996524	−	0.0833072i	$-0.973452\pi$
$433$	−19.0028	+	19.0028i	−0.913217	+	0.913217i	0.0833072	+	0.996524i	$0.473452\pi$
$434$		0			0
$435$	−0.368623	+	2.36067i	−0.0176741	+	0.113186i
$436$		0			0
$437$	7.67136	−	28.6299i	0.366971	−	1.36955i
$438$		0			0
$439$	−5.53612	+	9.58883i	−0.264224	+	0.457650i	−0.967360	−	0.253406i	$-0.918449\pi$
$439$	−5.53612	+	9.58883i	−0.264224	+	0.457650i	0.703136	+	0.711056i	$0.251783\pi$
$440$		0			0
$441$	5.56888	+	4.24118i	0.265185	+	0.201961i
$442$		0			0
$443$	25.3574	−	6.79450i	1.20477	−	0.322816i	0.400060	−	0.916489i	$-0.368989\pi$
$443$	25.3574	−	6.79450i	1.20477	−	0.322816i	0.804707	+	0.593673i	$0.202323\pi$
$444$		0			0
$445$	7.67902	−	17.3490i	0.364020	−	0.822421i
$446$		0			0
$447$	4.89991	+	4.89991i	0.231758	+	0.231758i
$448$		0			0
$449$		−	33.7848i		−	1.59440i	−0.603714	−	0.797201i	$-0.706313\pi$
$449$		−	33.7848i		−	1.59440i	0.603714	−	0.797201i	$-0.293687\pi$
$450$		0			0
$451$	−4.19030	+	2.41927i	−0.197313	+	0.113919i
$452$		0			0
$453$	−0.200123	−	0.746868i	−0.00940258	−	0.0350909i
$454$		0			0
$455$	13.4249	−	14.6397i	0.629369	−	0.686322i
$456$		0			0
$457$	−1.58873	−	5.92921i	−0.0743175	−	0.277357i	0.918760	−	0.394816i	$-0.129192\pi$
$457$	−1.58873	−	5.92921i	−0.0743175	−	0.277357i	−0.993078	+	0.117459i	$0.962525\pi$
$458$		0			0
$459$	2.44488	−	1.41155i	0.114117	−	0.0658856i
$460$		0			0
$461$		−	33.4895i		−	1.55976i	−0.625928	−	0.779881i	$-0.715280\pi$
$461$		−	33.4895i		−	1.55976i	0.625928	−	0.779881i	$-0.284720\pi$
$462$		0			0
$463$	23.3606	+	23.3606i	1.08566	+	1.08566i	0.995970	+	0.0896875i	$0.0285868\pi$
$463$	23.3606	+	23.3606i	1.08566	+	1.08566i	0.0896875	+	0.995970i	$0.471413\pi$
$464$		0			0
$465$	−3.55381	+	1.37307i	−0.164804	+	0.0636746i
$466$		0			0
$467$	37.2684	−	9.98604i	1.72458	−	0.462099i	0.745655	−	0.666333i	$-0.232137\pi$
$467$	37.2684	−	9.98604i	1.72458	−	0.462099i	0.978922	+	0.204234i	$0.0654702\pi$
$468$		0			0
$469$	7.96277	+	2.68692i	0.367687	+	0.124070i
$470$		0			0
$471$	8.02505	−	13.8998i	0.369775	−	0.640469i
$472$		0			0
$473$	−1.83754	+	6.85778i	−0.0844900	+	0.315321i
$474$		0			0
$475$	11.8089	−	36.8904i	0.541831	−	1.69265i
$476$		0			0
$477$	−7.21941	+	7.21941i	−0.330554	+	0.330554i
$478$		0			0
$479$	−5.62243	−	9.73833i	−0.256895	−	0.444956i	0.708513	−	0.705697i	$-0.249366\pi$
$479$	−5.62243	−	9.73833i	−0.256895	−	0.444956i	−0.965409	+	0.260742i	$0.916033\pi$
$480$		0			0
$481$	−8.04802	−	4.64653i	−0.366958	−	0.211863i
$482$		0			0
$483$	−10.1023	−	0.643758i	−0.459669	−	0.0292920i
$484$		0			0
$485$	10.3372	+	8.33364i	0.469386	+	0.378411i
$486$		0			0
$487$	−0.900588	−	0.241312i	−0.0408096	−	0.0109349i	0.238357	−	0.971178i	$-0.423391\pi$
$487$	−0.900588	−	0.241312i	−0.0408096	−	0.0109349i	−0.279166	+	0.960243i	$0.590058\pi$
$488$		0			0
$489$	−6.65113			−0.300774
$490$		0			0
$491$	−23.2545			−1.04946			−0.524730	−	0.851269i	$-0.675834\pi$
$491$	−23.2545			−1.04946			−0.524730	+	0.851269i	$0.675834\pi$
$492$		0			0
$493$	−2.91375	−	0.780738i	−0.131229	−	0.0351627i
$494$		0			0
$495$	0.144108	+	1.34294i	0.00647716	+	0.0603606i
$496$		0			0
$497$	43.8139	+	2.79200i	1.96532	+	0.125238i
$498$		0			0
$499$	6.19486	+	3.57661i	0.277320	+	0.160111i	0.632210	−	0.774797i	$-0.282148\pi$
$499$	6.19486	+	3.57661i	0.277320	+	0.160111i	−0.354889	+	0.934908i	$0.615481\pi$
$500$		0			0
$501$	−8.91856	−	15.4474i	−0.398452	−	0.690139i
$502$		0			0
$503$	5.58976	−	5.58976i	0.249235	−	0.249235i	−0.571422	−	0.820657i	$-0.693608\pi$
$503$	5.58976	−	5.58976i	0.249235	−	0.249235i	0.820657	+	0.571422i	$0.193608\pi$
$504$		0			0
$505$	−22.9562	+	16.7552i	−1.02154	+	0.745595i
$506$		0			0
$507$	−0.447020	+	1.66830i	−0.0198529	+	0.0740919i
$508$		0			0
$509$	−9.05283	+	15.6800i	−0.401260	+	0.695002i	−0.993878	−	0.110481i	$-0.964761\pi$
$509$	−9.05283	+	15.6800i	−0.401260	+	0.695002i	0.592619	+	0.805483i	$0.298094\pi$
$510$		0			0
$511$	−29.9335	−	10.1006i	−1.32418	−	0.446824i
$512$		0			0
$513$	7.48290	−	2.00504i	0.330378	−	0.0885245i
$514$		0			0
$515$	3.74094	+	9.68237i	0.164845	+	0.426656i
$516$		0			0
$517$	4.03452	+	4.03452i	0.177438	+	0.177438i
$518$		0			0
$519$			11.9650i			0.525204i
$520$		0			0
$521$	31.1728	−	17.9976i	1.36570	−	0.788490i	0.375328	−	0.926892i	$-0.377530\pi$
$521$	31.1728	−	17.9976i	1.36570	−	0.788490i	0.990376	+	0.138402i	$0.0441966\pi$
$522$		0			0
$523$	1.90751	+	7.11893i	0.0834096	+	0.311289i	0.995008	−	0.0997924i	$-0.0318179\pi$
$523$	1.90751	+	7.11893i	0.0834096	+	0.311289i	−0.911599	+	0.411081i	$0.865151\pi$
$524$		0			0
$525$	−13.1464	−	1.47380i	−0.573756	−	0.0643217i
$526$		0			0
$527$	−1.24493	−	4.64614i	−0.0542299	−	0.202389i
$528$		0			0
$529$	−7.24117	+	4.18069i	−0.314834	+	0.181769i
$530$		0			0
$531$			9.44747i			0.409985i
$532$		0			0
$533$	−19.0177	−	19.0177i	−0.823749	−	0.823749i
$534$		0			0
$535$	9.17207	+	23.7393i	0.396543	+	1.02634i
$536$		0			0
$537$	−4.44768	+	1.19175i	−0.191932	+	0.0514279i
$538$		0			0
$539$	−1.63221	−	3.90046i	−0.0703041	−	0.168005i
$540$		0			0
$541$	−16.0310	+	27.7665i	−0.689227	+	1.19378i	0.282861	+	0.959161i	$0.408717\pi$
$541$	−16.0310	+	27.7665i	−0.689227	+	1.19378i	−0.972088	+	0.234616i	$0.924617\pi$
$542$		0			0
$543$	2.46850	−	9.21255i	0.105933	−	0.395348i
$544$		0			0
$545$	−27.3080	+	19.9315i	−1.16975	+	0.853772i
$546$		0			0
$547$	−12.2782	+	12.2782i	−0.524977	+	0.524977i	−0.919071	−	0.394093i	$-0.871059\pi$
$547$	−12.2782	+	12.2782i	−0.524977	+	0.524977i	0.394093	+	0.919071i	$0.371059\pi$
$548$		0			0
$549$	3.22838	+	5.59172i	0.137784	+	0.238649i
$550$		0			0
$551$	−7.16868	−	4.13884i	−0.305396	−	0.176320i
$552$		0			0
$553$	20.7177	+	13.7889i	0.881008	+	0.586364i
$554$		0			0
$555$	0.660345	+	6.15376i	0.0280301	+	0.261213i
$556$		0			0
$557$	16.1612	+	4.33039i	0.684773	+	0.183484i	0.584400	−	0.811465i	$-0.301330\pi$
$557$	16.1612	+	4.33039i	0.684773	+	0.183484i	0.100373	+	0.994950i	$0.467996\pi$
$558$		0			0
$559$	−39.4638			−1.66914
$560$		0			0
$561$	−1.70524			−0.0719951
$562$		0			0
$563$	21.3252	+	5.71407i	0.898750	+	0.240819i	0.678479	−	0.734619i	$-0.262639\pi$
$563$	21.3252	+	5.71407i	0.898750	+	0.240819i	0.220271	+	0.975439i	$0.429306\pi$
$564$		0			0
$565$	0.249915	+	0.201477i	0.0105140	+	0.00847620i
$566$		0			0
$567$	−1.17448	−	2.37078i	−0.0493237	−	0.0995633i
$568$		0			0
$569$	−10.0101	−	5.77933i	−0.419645	−	0.242282i	0.275281	−	0.961364i	$-0.411229\pi$
$569$	−10.0101	−	5.77933i	−0.419645	−	0.242282i	−0.694925	+	0.719082i	$0.744563\pi$
$570$		0			0
$571$	17.0517	+	29.5344i	0.713592	+	1.23598i	0.963500	+	0.267708i	$0.0862664\pi$
$571$	17.0517	+	29.5344i	0.713592	+	1.23598i	−0.249908	+	0.968270i	$0.580400\pi$
$572$		0			0
$573$	7.12151	−	7.12151i	0.297505	−	0.297505i
$574$		0			0
$575$	17.0071	−	8.75913i	0.709247	−	0.365281i
$576$		0			0
$577$	−3.66029	+	13.6604i	−0.152380	+	0.568689i	0.846936	+	0.531695i	$0.178445\pi$
$577$	−3.66029	+	13.6604i	−0.152380	+	0.568689i	−0.999316	+	0.0369936i	$0.988222\pi$
$578$		0			0
$579$	−12.9121	+	22.3645i	−0.536611	+	0.929437i
$580$		0			0
$581$	−6.14858	+	5.41190i	−0.255086	+	0.224523i
$582$		0			0
$583$	5.95687	−	1.59614i	0.246708	−	0.0661053i
$584$		0			0
$585$	−7.00308	+	2.70575i	−0.289542	+	0.111869i
$586$		0			0
$587$	2.03863	+	2.03863i	0.0841434	+	0.0841434i	0.747926	−	0.663782i	$-0.231050\pi$
$587$	2.03863	+	2.03863i	0.0841434	+	0.0841434i	−0.663782	+	0.747926i	$0.731050\pi$
$588$		0			0
$589$		−	13.1992i		−	0.543864i
$590$		0			0
$591$	−1.77007	+	1.02195i	−0.0728109	+	0.0420374i
$592$		0			0
$593$	−12.4687	−	46.5338i	−0.512028	−	1.91091i	−0.397837	−	0.917456i	$-0.630239\pi$
$593$	−12.4687	−	46.5338i	−0.512028	−	1.91091i	−0.114191	−	0.993459i	$-0.536428\pi$
$594$		0			0
$595$	3.62099	−	16.3045i	0.148446	−	0.668417i
$596$		0			0
$597$	1.82059	+	6.79452i	0.0745116	+	0.278081i
$598$		0			0
$599$	−17.5251	+	10.1181i	−0.716057	+	0.413416i	−0.813300	−	0.581845i	$-0.802331\pi$
$599$	−17.5251	+	10.1181i	−0.716057	+	0.413416i	0.0972425	+	0.995261i	$0.468998\pi$
$600$		0			0
$601$			37.9071i			1.54626i	0.634245	+	0.773132i	$0.281311\pi$
$601$			37.9071i			1.54626i	−0.634245	+	0.773132i	$0.718689\pi$
$602$		0			0
$603$	−2.24603	−	2.24603i	−0.0914655	−	0.0914655i
$604$		0			0
$605$	−9.62521	+	21.7460i	−0.391321	+	0.884099i
$606$		0			0
$607$	−7.03741	+	1.88567i	−0.285640	+	0.0765369i	−0.398794	−	0.917041i	$-0.630571\pi$
$607$	−7.03741	+	1.88567i	−0.285640	+	0.0765369i	0.113154	+	0.993577i	$0.463904\pi$
$608$		0			0
$609$	−0.903869	+	2.67865i	−0.0366266	+	0.108544i
$610$		0			0
$611$	−15.8575	+	27.4661i	−0.641527	+	1.11116i
$612$		0			0
$613$	−7.40759	+	27.6455i	−0.299190	+	1.11659i	0.638643	+	0.769503i	$0.279496\pi$
$613$	−7.40759	+	27.6455i	−0.299190	+	1.11659i	−0.937833	+	0.347088i	$0.887170\pi$
$614$		0			0
$615$	−2.76349	+	17.6974i	−0.111434	+	0.713629i
$616$		0			0
$617$	27.7306	−	27.7306i	1.11639	−	1.11639i	0.124125	−	0.992267i	$-0.460388\pi$
$617$	27.7306	−	27.7306i	1.11639	−	1.11639i	0.992267	−	0.124125i	$-0.0396123\pi$
$618$		0			0
$619$	−10.8629	−	18.8152i	−0.436619	−	0.756246i	0.560808	−	0.827946i	$-0.310491\pi$
$619$	−10.8629	−	18.8152i	−0.436619	−	0.756246i	−0.997426	+	0.0717005i	$0.977157\pi$
$620$		0			0
$621$	3.31345	+	1.91302i	0.132964	+	0.0767669i
$622$		0			0
$623$	12.4379	−	18.6878i	0.498314	−	0.748713i
$624$		0			0
$625$	22.7491	−	10.3671i	0.909966	−	0.414683i
$626$		0			0
$627$	−4.51989	−	1.21110i	−0.180507	−	0.0483667i
$628$		0			0
$629$	−7.81391			−0.311561
$630$		0			0
$631$	15.9568			0.635232			0.317616	−	0.948219i	$-0.397118\pi$
$631$	15.9568			0.635232			0.317616	+	0.948219i	$0.397118\pi$
$632$		0			0
$633$	11.7135	+	3.13862i	0.465569	+	0.124749i
$634$		0			0
$635$	10.7594	−	13.3461i	0.426973	−	0.529623i
$636$		0			0
$637$	18.5939	−	14.3749i	0.736715	−	0.569555i
$638$		0			0
$639$	−14.3705	−	8.29684i	−0.568490	−	0.328218i
$640$		0			0
$641$	17.4091	+	30.1535i	0.687619	+	1.19099i	0.972606	+	0.232459i	$0.0746772\pi$
$641$	17.4091	+	30.1535i	0.687619	+	1.19099i	−0.284988	+	0.958531i	$0.591989\pi$
$642$		0			0
$643$	11.9683	−	11.9683i	0.471982	−	0.471982i	−0.430573	−	0.902556i	$-0.641689\pi$
$643$	11.9683	−	11.9683i	0.471982	−	0.471982i	0.902556	+	0.430573i	$0.141689\pi$
$644$		0			0
$645$	15.4948	+	21.2293i	0.610106	+	0.835903i
$646$		0			0
$647$	−10.8040	+	40.3209i	−0.424747	+	1.58518i	0.339727	+	0.940524i	$0.389665\pi$
$647$	−10.8040	+	40.3209i	−0.424747	+	1.58518i	−0.764474	+	0.644654i	$0.777001\pi$
$648$		0			0
$649$	2.85327	−	4.94201i	0.112001	−	0.193991i
$650$		0			0
$651$	−4.41964	+	0.887449i	−0.173219	+	0.0347819i
$652$		0			0
$653$	−11.1520	+	2.98817i	−0.436411	+	0.116936i	−0.470334	−	0.882488i	$-0.655867\pi$
$653$	−11.1520	+	2.98817i	−0.436411	+	0.116936i	0.0339230	+	0.999424i	$0.489200\pi$
$654$		0			0
$655$	−21.4184	−	9.48021i	−0.836885	−	0.370422i
$656$		0			0
$657$	8.44323	+	8.44323i	0.329402	+	0.329402i
$658$		0			0
$659$		−	44.8565i		−	1.74736i	−0.486501	−	0.873680i	$-0.661727\pi$
$659$		−	44.8565i		−	1.74736i	0.486501	−	0.873680i	$-0.338273\pi$
$660$		0			0
$661$	28.9348	−	16.7055i	1.12543	−	0.649769i	0.182650	−	0.983178i	$-0.441532\pi$
$661$	28.9348	−	16.7055i	1.12543	−	0.649769i	0.942782	+	0.333409i	$0.108199\pi$
$662$		0			0
$663$	−2.45324	−	9.15561i	−0.0952759	−	0.355574i
$664$		0			0
$665$	21.1776	−	40.6448i	0.821232	−	1.57614i
$666$		0			0
$667$	−1.05810	−	3.94890i	−0.0409700	−	0.152902i
$668$		0			0
$669$	−5.97825	+	3.45154i	−0.231133	+	0.133444i
$670$		0			0
$671$		−	3.90007i		−	0.150560i
$672$		0			0
$673$	−10.0958	−	10.0958i	−0.389166	−	0.389166i	0.485224	−	0.874390i	$-0.338738\pi$
$673$	−10.0958	−	10.0958i	−0.389166	−	0.389166i	−0.874390	+	0.485224i	$0.838738\pi$
$674$		0			0
$675$	4.20518	+	2.70490i	0.161857	+	0.104112i
$676$		0			0
$677$	−5.48757	+	1.47039i	−0.210905	+	0.0565117i	−0.362724	−	0.931896i	$-0.618153\pi$
$677$	−5.48757	+	1.47039i	−0.210905	+	0.0565117i	0.151820	+	0.988408i	$0.451487\pi$
$678$		0			0
$679$	10.3802	+	11.7932i	0.398357	+	0.452582i
$680$		0			0
$681$	−4.95262	+	8.57819i	−0.189785	+	0.328717i
$682$		0			0
$683$	−4.45782	+	16.6368i	−0.170574	+	0.636590i	0.826689	+	0.562658i	$0.190221\pi$
$683$	−4.45782	+	16.6368i	−0.170574	+	0.636590i	−0.997263	+	0.0739318i	$0.976445\pi$
$684$		0			0
$685$	−13.8874	−	2.16855i	−0.530611	−	0.0828559i
$686$		0			0
$687$	1.87448	−	1.87448i	0.0715161	−	0.0715161i
$688$		0			0
$689$	17.1397	+	29.6869i	0.652971	+	1.13098i
$690$		0			0
$691$	14.4106	+	8.31995i	0.548204	+	0.316506i	0.748397	−	0.663251i	$-0.230824\pi$
$691$	14.4106	+	8.31995i	0.548204	+	0.316506i	−0.200193	+	0.979756i	$0.564157\pi$
$692$		0			0
$693$	−0.101632	+	1.59487i	−0.00386068	+	0.0605843i
$694$		0			0
$695$	−39.1601	+	4.20218i	−1.48543	+	0.159398i
$696$		0			0
$697$	−21.8437	−	5.85301i	−0.827391	−	0.221699i
$698$		0			0
$699$	−12.3740			−0.468028
$700$		0			0
$701$	7.31937			0.276449			0.138224	−	0.990401i	$-0.455860\pi$
$701$	7.31937			0.276449			0.138224	+	0.990401i	$0.455860\pi$
$702$		0			0
$703$	−20.7115	−	5.54963i	−0.781149	−	0.209308i
$704$		0			0
$705$	21.0014	−	2.25361i	0.790958	−	0.0848758i
$706$		0			0
$707$	−30.1326	+	14.9277i	−1.13325	+	0.561413i
$708$		0			0
$709$	−12.6343	−	7.29441i	−0.474491	−	0.273947i	0.243627	−	0.969869i	$-0.421663\pi$
$709$	−12.6343	−	7.29441i	−0.474491	−	0.273947i	−0.718118	+	0.695922i	$0.754996\pi$
$710$		0			0
$711$	−4.70319	−	8.14616i	−0.176383	−	0.305505i
$712$		0			0
$713$	4.60953	−	4.60953i	0.172628	−	0.172628i
$714$		0			0
$715$	4.48052	+	0.699641i	0.167562	+	0.0261651i
$716$		0			0
$717$	−0.530971	+	1.98161i	−0.0198295	+	0.0740047i
$718$		0			0
$719$	−0.356285	+	0.617104i	−0.0132872	+	0.0230141i	−0.872593	−	0.488449i	$-0.837563\pi$
$719$	−0.356285	+	0.617104i	−0.0132872	+	0.0230141i	0.859305	+	0.511463i	$0.170896\pi$
$720$		0			0
$721$	2.41786	+	12.0413i	0.0900458	+	0.448443i
$722$		0			0
$723$	−14.2594	+	3.82078i	−0.530311	+	0.142096i
$724$		0			0
$725$	−1.13355	−	5.22096i	−0.0420990	−	0.193901i
$726$		0			0
$727$	17.3663	+	17.3663i	0.644081	+	0.644081i	0.951556	−	0.307475i	$-0.0994841\pi$
$727$	17.3663	+	17.3663i	0.644081	+	0.644081i	−0.307475	+	0.951556i	$0.599484\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−28.7369	+	16.5912i	−1.06287	+	0.613649i
$732$		0			0
$733$	7.08303	+	26.4342i	0.261618	+	0.976370i	0.964288	+	0.264855i	$0.0853240\pi$
$733$	7.08303	+	26.4342i	0.261618	+	0.976370i	−0.702671	+	0.711515i	$0.748009\pi$
$734$		0			0
$735$	−15.0334	−	4.35839i	−0.554517	−	0.160761i
$736$		0			0
$737$	0.496575	+	1.85324i	0.0182916	+	0.0682651i
$738$		0			0
$739$	25.0384	−	14.4559i	0.921053	−	0.531770i	0.0370818	−	0.999312i	$-0.488194\pi$
$739$	25.0384	−	14.4559i	0.921053	−	0.531770i	0.883971	+	0.467542i	$0.154860\pi$
$740$		0			0
$741$		−	26.0102i		−	0.955507i
$742$		0			0
$743$	−7.60634	−	7.60634i	−0.279050	−	0.279050i	0.553680	−	0.832730i	$-0.313223\pi$
$743$	−7.60634	−	7.60634i	−0.279050	−	0.279050i	−0.832730	+	0.553680i	$0.813223\pi$
$744$		0			0
$745$	−14.1690	−	6.27148i	−0.519111	−	0.229769i
$746$		0			0
$747$	2.99044	−	0.801286i	0.109415	−	0.0293175i
$748$		0			0
$749$	5.92814	+	29.5231i	0.216609	+	1.07875i
$750$		0			0
$751$	0.742022	−	1.28522i	0.0270768	−	0.0468983i	−0.852169	−	0.523266i	$-0.824713\pi$
$751$	0.742022	−	1.28522i	0.0270768	−	0.0468983i	0.879246	+	0.476368i	$0.158047\pi$
$752$		0			0
$753$	−1.80043	+	6.71929i	−0.0656113	+	0.244865i
$754$		0			0
$755$	1.01930	+	1.39654i	0.0370962	+	0.0508253i
$756$		0			0
$757$	35.7985	−	35.7985i	1.30112	−	1.30112i	0.373483	−	0.927637i	$-0.378163\pi$
$757$	35.7985	−	35.7985i	1.30112	−	1.30112i	0.927637	−	0.373483i	$-0.121837\pi$
$758$		0			0
$759$	−1.15552	−	2.00142i	−0.0419427	−	0.0726469i
$760$		0			0
$761$	25.8513	+	14.9252i	0.937108	+	0.541039i	0.889052	−	0.457805i	$-0.151364\pi$
$761$	25.8513	+	14.9252i	0.937108	+	0.541039i	0.0480552	+	0.998845i	$0.484698\pi$
$762$		0			0
$763$	−35.8449	+	17.7576i	−1.29767	+	0.642868i
$764$		0			0
$765$	−3.96198	+	4.91449i	−0.143246	+	0.177684i
$766$		0			0
$767$	30.6391	+	8.20972i	1.10631	+	0.296436i
$768$		0			0
$769$	−53.8150			−1.94062			−0.970309	−	0.241870i	$-0.922239\pi$
$769$	−53.8150			−1.94062			−0.970309	+	0.241870i	$0.922239\pi$
$770$		0			0
$771$	0.805959			0.0290259
$772$		0			0
$773$	49.2130	+	13.1866i	1.77007	+	0.474288i	0.988716	−	0.149802i	$-0.0478637\pi$
$773$	49.2130	+	13.1866i	1.77007	+	0.474288i	0.781352	+	0.624090i	$0.214530\pi$
$774$		0			0
$775$	6.30599	−	5.72789i	0.226518	−	0.205752i
$776$		0			0
$777$	−0.465709	+	7.30820i	−0.0167072	+	0.262180i
$778$		0			0
$779$	−53.7419	−	31.0279i	−1.92550	−	1.11169i
$780$		0			0
$781$	5.01153	+	8.68022i	0.179327	+	0.310603i
$782$		0			0
$783$	0.755557	−	0.755557i	0.0270014	−	0.0270014i
$784$		0			0
$785$	−5.53705	+	35.4594i	−0.197626	+	1.26560i
$786$		0			0
$787$	8.57757	−	32.0119i	0.305757	−	1.14110i	−0.626534	−	0.779394i	$-0.715527\pi$
$787$	8.57757	−	32.0119i	0.305757	−	1.14110i	0.932292	−	0.361708i	$-0.117806\pi$
$788$		0			0
$789$	−9.71086	+	16.8197i	−0.345716	+	0.598797i
$790$		0			0
$791$	0.250956	+	0.285117i	0.00892297	+	0.0101376i
$792$		0			0
$793$	20.9399	−	5.61083i	0.743598	−	0.199247i
$794$		0			0
$795$	9.24024	−	20.8762i	0.327718	−	0.740403i
$796$		0			0
$797$	27.6409	+	27.6409i	0.979091	+	0.979091i	0.999786	−	0.0206950i	$-0.00658790\pi$
$797$	27.6409	+	27.6409i	0.979091	+	0.979091i	−0.0206950	+	0.999786i	$0.506588\pi$
$798$		0			0
$799$			26.6671i			0.943414i
$800$		0			0
$801$	−7.34801	+	4.24238i	−0.259629	+	0.149897i
$802$		0			0
$803$	−1.86671	−	6.96667i	−0.0658748	−	0.245848i
$804$		0			0
$805$	21.5901	−	6.79848i	0.760951	−	0.239615i
$806$		0			0
$807$	0.493589	+	1.84210i	0.0173752	+	0.0648450i
$808$		0			0
$809$	−38.8681	+	22.4405i	−1.36653	+	0.788966i	−0.990483	−	0.137635i	$-0.956050\pi$
$809$	−38.8681	+	22.4405i	−1.36653	+	0.788966i	−0.376046	+	0.926601i	$0.622717\pi$
$810$		0			0
$811$			34.9982i			1.22895i	0.788935	+	0.614476i	$0.210633\pi$
$811$			34.9982i			1.22895i	−0.788935	+	0.614476i	$0.789367\pi$
$812$		0			0
$813$	20.1305	+	20.1305i	0.706008	+	0.706008i
$814$		0			0
$815$	13.8729	−	5.36002i	0.485947	−	0.187753i
$816$		0			0
$817$	−87.9533	+	23.5670i	−3.07710	+	0.824505i
$818$		0			0
$819$	−8.70928	+	1.74879i	−0.304327	+	0.0611078i
$820$		0			0
$821$	2.14361	−	3.71284i	0.0748124	−	0.129579i	−0.826192	−	0.563388i	$-0.809498\pi$
$821$	2.14361	−	3.71284i	0.0748124	−	0.129579i	0.901005	+	0.433809i	$0.142831\pi$
$822$		0			0
$823$	−1.08857	+	4.06259i	−0.0379450	+	0.141613i	−0.982300	−	0.187316i	$-0.940021\pi$
$823$	−1.08857	+	4.06259i	−0.0379450	+	0.141613i	0.944355	+	0.328929i	$0.106688\pi$
$824$		0			0
$825$	−1.38283	−	2.68497i	−0.0481440	−	0.0934786i
$826$		0			0
$827$	−23.7840	+	23.7840i	−0.827050	+	0.827050i	−0.987108	−	0.160058i	$-0.948832\pi$
$827$	−23.7840	+	23.7840i	−0.827050	+	0.827050i	0.160058	+	0.987108i	$0.448832\pi$
$828$		0			0
$829$	−24.1909	−	41.8998i	−0.840184	−	1.45524i	−0.889739	−	0.456469i	$-0.849114\pi$
$829$	−24.1909	−	41.8998i	−0.840184	−	1.45524i	0.0495557	−	0.998771i	$-0.484219\pi$
$830$		0			0
$831$	−3.25342	−	1.87836i	−0.112860	−	0.0651597i
$832$		0			0
$833$	7.49627	−	18.2847i	0.259731	−	0.633528i
$834$		0			0
$835$	31.0511	+	25.0328i	1.07457	+	0.866297i
$836$		0			0
$837$	1.64576	+	0.440979i	0.0568856	+	0.0152425i
$838$		0			0
$839$	−36.1266			−1.24723			−0.623614	−	0.781733i	$-0.714336\pi$
$839$	−36.1266			−1.24723			−0.623614	+	0.781733i	$0.714336\pi$
$840$		0			0
$841$	27.8583			0.960630
$842$		0			0
$843$	−11.6901	−	3.13236i	−0.402630	−	0.107884i
$844$		0			0
$845$	−0.412060	−	3.83999i	−0.0141753	−	0.132100i
$846$		0			0
$847$	−15.5902	+	23.4241i	−0.535686	+	0.804863i
$848$		0			0
$849$	−10.3159	−	5.95591i	−0.354042	−	0.204406i
$850$		0			0
$851$	−5.29495	−	9.17112i	−0.181508	−	0.314382i
$852$		0			0
$853$	−2.72229	+	2.72229i	−0.0932093	+	0.0932093i	−0.752174	−	0.658965i	$-0.770995\pi$
$853$	−2.72229	+	2.72229i	−0.0932093	+	0.0932093i	0.658965	+	0.752174i	$0.270995\pi$
$854$		0			0
$855$	−13.9920	+	10.2124i	−0.478516	+	0.349258i
$856$		0			0
$857$	5.78929	−	21.6059i	0.197758	−	0.738045i	−0.793777	−	0.608209i	$-0.791888\pi$
$857$	5.78929	−	21.6059i	0.197758	−	0.738045i	0.991536	−	0.129836i	$-0.0414450\pi$
$858$		0			0
$859$	−25.0354	+	43.3625i	−0.854196	+	1.47951i	0.0231938	+	0.999731i	$0.492617\pi$
$859$	−25.0354	+	43.3625i	−0.854196	+	1.47951i	−0.877389	+	0.479779i	$0.840717\pi$
$860$		0			0
$861$	−6.77610	+	20.0812i	−0.230929	+	0.684366i
$862$		0			0
$863$	49.6316	−	13.2988i	1.68948	−	0.452695i	0.719224	−	0.694778i	$-0.244497\pi$
$863$	49.6316	−	13.2988i	1.68948	−	0.452695i	0.970256	+	0.242083i	$0.0778307\pi$
$864$		0			0
$865$	−9.64234	−	24.9565i	−0.327850	−	0.848547i
$866$		0			0
$867$	6.38524	+	6.38524i	0.216854	+	0.216854i
$868$		0			0
$869$			5.68172i			0.192739i
$870$		0			0
$871$	−9.23588	+	5.33234i	−0.312946	+	0.180679i
$872$		0			0
$873$	−1.53690	−	5.73579i	−0.0520162	−	0.194127i
$874$		0			0
$875$	28.6085	−	7.52040i	0.967142	−	0.254236i
$876$		0			0
$877$	−1.34505	−	5.01978i	−0.0454190	−	0.169506i	0.939491	−	0.342574i	$-0.111299\pi$
$877$	−1.34505	−	5.01978i	−0.0454190	−	0.169506i	−0.984910	+	0.173068i	$0.944632\pi$
$878$		0			0
$879$	8.68930	−	5.01677i	0.293083	−	0.169211i
$880$		0			0
$881$			26.3865i			0.888984i	0.895783	+	0.444492i	$0.146616\pi$
$881$			26.3865i			0.888984i	−0.895783	+	0.444492i	$0.853384\pi$
$882$		0			0
$883$	29.7015	+	29.7015i	0.999536	+	0.999536i	1.00000		0.000464000i	$-0.000147696\pi$
$883$	29.7015	+	29.7015i	0.999536	+	0.999536i	−0.000464000		1.00000i	$0.500148\pi$
$884$		0			0
$885$	−7.61354	−	19.7055i	−0.255926	−	0.662394i
$886$		0			0
$887$	−14.1320	+	3.78666i	−0.474506	+	0.127143i	−0.488143	−	0.872764i	$-0.662326\pi$
$887$	−14.1320	+	3.78666i	−0.474506	+	0.127143i	0.0136373	+	0.999907i	$0.495659\pi$
$888$		0			0
$889$	15.2260	−	13.4017i	0.510662	−	0.449478i
$890$		0			0
$891$	0.302014	−	0.523104i	0.0101179	−	0.0175247i
$892$		0			0
$893$	−18.9396	+	70.6836i	−0.633790	+	2.36534i
$894$		0			0
$895$	8.31656	−	6.07006i	0.277992	−	0.202900i
$896$		0			0
$897$	9.08347	−	9.08347i	0.303288	−	0.303288i
$898$		0			0
$899$	−0.910277	−	1.57665i	−0.0303595	−	0.0525841i
$900$		0			0
$901$	24.9617	+	14.4116i	0.831595	+	0.480121i
$902$		0			0
$903$	13.8048	+	27.8659i	0.459394	+	0.927319i
$904$		0			0
$905$	2.27544	+	21.2048i	0.0756382	+	0.704873i
$906$		0			0
$907$	−13.4776	−	3.61132i	−0.447517	−	0.119912i	0.0280201	−	0.999607i	$-0.491080\pi$
$907$	−13.4776	−	3.61132i	−0.447517	−	0.119912i	−0.475538	+	0.879695i	$0.657746\pi$
$908$		0			0
$909$	12.7100			0.421564
$910$		0			0
$911$	−41.6320			−1.37933			−0.689665	−	0.724128i	$-0.742242\pi$
$911$	−41.6320			−1.37933			−0.689665	+	0.724128i	$0.742242\pi$
$912$		0			0
$913$	−1.80631	−	0.484000i	−0.0597802	−	0.0160181i
$914$		0			0
$915$	−11.2400	−	9.06150i	−0.371583	−	0.299564i
$916$		0			0
$917$	−23.0713	−	15.3553i	−0.761880	−	0.507078i
$918$		0			0
$919$	1.45630	+	0.840796i	0.0480390	+	0.0277353i	0.523827	−	0.851825i	$-0.324504\pi$
$919$	1.45630	+	0.840796i	0.0480390	+	0.0277353i	−0.475788	+	0.879560i	$0.657837\pi$
$920$		0			0
$921$	−12.4636	−	21.5876i	−0.410690	−	0.711335i
$922$		0			0
$923$	−39.3953	+	39.3953i	−1.29671	+	1.29671i
$924$		0			0
$925$	−6.33655	−	12.3033i	−0.208344	−	0.404531i
$926$		0			0
$927$	1.20145	−	4.48387i	0.0394608	−	0.147270i
$928$		0			0
$929$	3.75511	−	6.50405i	0.123201	−	0.213391i	−0.797827	−	0.602886i	$-0.794017\pi$
$929$	3.75511	−	6.50405i	0.123201	−	0.213391i	0.921028	+	0.389495i	$0.127351\pi$
$930$		0			0
$931$	32.8558	−	43.1414i	1.07681	−	1.41390i
$932$		0			0
$933$	24.9546	−	6.68655i	0.816975	−	0.218908i
$934$		0			0
$935$	3.55678	−	1.37422i	0.116319	−	0.0449417i
$936$		0			0
$937$	10.6515	+	10.6515i	0.347970	+	0.347970i	0.859353	−	0.511383i	$-0.170867\pi$
$937$	10.6515	+	10.6515i	0.347970	+	0.347970i	−0.511383	+	0.859353i	$0.670867\pi$
$938$		0			0
$939$			4.65535i			0.151921i
$940$		0			0
$941$	−33.1391	+	19.1328i	−1.08030	+	0.623713i	−0.930978	−	0.365075i	$-0.881043\pi$
$941$	−33.1391	+	19.1328i	−1.08030	+	0.623713i	−0.149325	+	0.988788i	$0.547710\pi$
$942$		0			0
$943$	−7.93237	−	29.6040i	−0.258313	−	0.964039i
$944$		0			0
$945$	4.36030	+	3.99847i	0.141841	+	0.130070i
$946$		0			0
$947$	−12.2266	−	45.6304i	−0.397312	−	1.48279i	−0.817807	−	0.575493i	$-0.804810\pi$
$947$	−12.2266	−	45.6304i	−0.397312	−	1.48279i	0.420495	−	0.907295i	$-0.361856\pi$
$948$		0			0
$949$	34.7193	−	20.0452i	1.12704	−	0.650695i
$950$		0			0
$951$			7.05139i			0.228657i
$952$		0			0
$953$	35.7556	+	35.7556i	1.15824	+	1.15824i	0.984855	+	0.173382i	$0.0554696\pi$
$953$	35.7556	+	35.7556i	1.15824	+	1.15824i	0.173382	+	0.984855i	$0.444530\pi$
$954$		0			0
$955$	−9.11494	+	20.5931i	−0.294952	+	0.666378i
$956$		0			0
$957$	−0.623424	+	0.167046i	−0.0201524	+	0.00539983i
$958$		0			0
$959$	−15.7580	−	5.31730i	−0.508852	−	0.171705i
$960$		0			0
$961$	−14.0485	+	24.3327i	−0.453178	+	0.784927i
$962$		0			0
$963$	2.94573	−	10.9936i	0.0949247	−	0.354264i
$964$		0			0
$965$	8.90900	−	57.0535i	0.286791	−	1.83662i
$966$		0			0
$967$	34.1802	−	34.1802i	1.09916	−	1.09916i	0.104653	−	0.994509i	$-0.466627\pi$
$967$	34.1802	−	34.1802i	1.09916	−	1.09916i	0.994509	−	0.104653i	$-0.0333732\pi$
$968$		0			0
$969$	−10.9351	−	18.9402i	−0.351286	−	0.608445i
$970$		0			0
$971$	−8.38453	−	4.84081i	−0.269072	−	0.155349i	0.359394	−	0.933186i	$-0.382984\pi$
$971$	−8.38453	−	4.84081i	−0.269072	−	0.155349i	−0.628466	+	0.777837i	$0.716317\pi$
$972$		0			0
$973$	−46.5065	−	2.96359i	−1.49093	−	0.0950082i
$974$		0			0
$975$	12.4265	−	11.2873i	0.397966	−	0.361483i
$976$		0			0
$977$	29.1940	+	7.82252i	0.934000	+	0.250264i	0.693559	−	0.720399i	$-0.256042\pi$
$977$	29.1940	+	7.82252i	0.934000	+	0.250264i	0.240440	+	0.970664i	$0.422708\pi$
$978$		0			0
$979$	5.12503			0.163797
$980$		0			0
$981$	15.1195			0.482728
$982$		0			0
$983$	−10.3935	−	2.78494i	−0.331503	−	0.0888259i	0.0892286	−	0.996011i	$-0.471560\pi$
$983$	−10.3935	−	2.78494i	−0.331503	−	0.0888259i	−0.420731	+	0.907185i	$0.638226\pi$
$984$		0			0
$985$	2.86844	−	3.55805i	0.0913960	−	0.113369i
$986$		0			0
$987$	24.9412	+	1.58936i	0.793888	+	0.0505898i
$988$		0			0
$989$	−38.9460	−	22.4855i	−1.23841	−	0.714997i
$990$		0			0
$991$	13.9909	+	24.2329i	0.444434	+	0.769783i	0.998013	−	0.0630142i	$-0.0200713\pi$
$991$	13.9909	+	24.2329i	0.444434	+	0.769783i	−0.553578	+	0.832797i	$0.686738\pi$
$992$		0			0
$993$	−8.82086	+	8.82086i	−0.279922	+	0.279922i
$994$		0			0
$995$	−9.27295	−	12.7048i	−0.293972	−	0.402770i
$996$		0			0
$997$	−9.87854	+	36.8672i	−0.312856	+	1.16760i	0.613112	+	0.789996i	$0.289917\pi$
$997$	−9.87854	+	36.8672i	−0.312856	+	1.16760i	−0.925969	+	0.377600i	$0.876749\pi$
$998$		0			0
$999$	1.38392	−	2.39702i	0.0437854	−	0.0758385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dd.b.313.7	yes	48
5.2	odd	4		840.2.dd.a.817.8	yes	48
7.3	odd	6		840.2.dd.a.73.8	✓	48
35.17	even	12	inner	840.2.dd.b.577.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dd.a.73.8	✓	48	7.3	odd	6
840.2.dd.a.817.8	yes	48	5.2	odd	4
840.2.dd.b.313.7	yes	48	1.1	even	1	trivial
840.2.dd.b.577.7	yes	48	35.17	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{3} +(-2.22330 + 0.238577i) q^{5} +(-2.64040 - 0.168257i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-0.302014 - 0.523104i) q^{11} +(2.37412 - 2.37412i) q^{13} +(-2.20930 - 0.344985i) q^{15} +(0.730673 - 2.72691i) q^{17} +(3.87343 - 6.70898i) q^{19} +(-2.50688 - 0.845908i) q^{21} +(3.69567 - 0.990253i) q^{23} +(4.88616 - 1.06086i) q^{25} +(0.707107 + 0.707107i) q^{27} -1.06852i q^{29} +(1.47554 - 0.851906i) q^{31} +(-0.156334 - 0.583447i) q^{33} +(5.91054 - 0.255853i) q^{35} +(-0.716371 - 2.67353i) q^{37} +(2.90769 - 1.67875i) q^{39} -8.01044i q^{41} +(-8.31126 - 8.31126i) q^{43} +(-2.04473 - 0.905038i) q^{45} +(-9.12416 + 2.44481i) q^{47} +(6.94338 + 0.888529i) q^{49} +(1.41155 - 2.44488i) q^{51} +(-2.64249 + 9.86190i) q^{53} +(0.796271 + 1.09097i) q^{55} +(5.47786 - 5.47786i) q^{57} +(4.72374 + 8.18175i) q^{59} +(5.59172 + 3.22838i) q^{61} +(-2.20252 - 1.46591i) q^{63} +(-4.71197 + 5.84479i) q^{65} +(-3.06814 - 0.822105i) q^{67} +3.82604 q^{69} -16.5937 q^{71} +(11.5337 + 3.09044i) q^{73} +(4.99424 + 0.239919i) q^{75} +(0.709422 + 1.43202i) q^{77} +(-8.14616 - 4.70319i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.18915 - 2.18915i) q^{83} +(-0.973929 + 6.23707i) q^{85} +(0.276553 - 1.03211i) q^{87} +(-4.24238 + 7.34801i) q^{89} +(-6.66806 + 5.86914i) q^{91} +(1.64576 - 0.440979i) q^{93} +(-7.01121 + 15.8402i) q^{95} +(-4.19889 - 4.19889i) q^{97} -0.604029i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) \) 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more