LMFDB - Embedded newform 224.3.o.d.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(79,224)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("224.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} + \cdots + 4 $ x^12 - 3x^11 - 4x^10 + 3x^9 + 86x^8 - 163x^7 + 155x^6 - 166x^5 + 164x^4 - 116x^3 + 60x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.4
Root			$2.79733 - 1.03769i$ of defining polynomial
Character	$\chi$	$=$	224.79
Dual form			224.3.o.d.207.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.824388 + 1.42788i) q^{3} +(3.95004 + 2.28056i) q^{5} +(6.75545 - 1.83408i) q^{7} +(3.14077 - 5.43997i) q^{9} +O(q^{10})$	\(q+(0.824388 + 1.42788i) q^{3} +(3.95004 + 2.28056i) q^{5} +(6.75545 - 1.83408i) q^{7} +(3.14077 - 5.43997i) q^{9} +(-6.18983 - 10.7211i) q^{11} +18.3741i q^{13} +7.52026i q^{15} +(6.51422 + 11.2830i) q^{17} +(-1.51262 + 2.61993i) q^{19} +(8.18796 + 8.13400i) q^{21} +(26.2611 + 15.1619i) q^{23} +(-2.09812 - 3.63405i) q^{25} +25.1958 q^{27} -22.7701i q^{29} +(-19.5382 + 11.2804i) q^{31} +(10.2056 - 17.6767i) q^{33} +(30.8670 + 8.16151i) q^{35} +(11.9335 + 6.88983i) q^{37} +(-26.2361 + 15.1474i) q^{39} -60.5026 q^{41} -39.0188 q^{43} +(24.8123 - 14.3254i) q^{45} +(17.6115 + 10.1680i) q^{47} +(42.2723 - 24.7801i) q^{49} +(-10.7405 + 18.6031i) q^{51} +(4.12744 - 2.38298i) q^{53} -56.4650i q^{55} -4.98794 q^{57} +(5.86884 + 10.1651i) q^{59} +(-94.3137 - 54.4520i) q^{61} +(11.2400 - 42.5099i) q^{63} +(-41.9033 + 72.5786i) q^{65} +(-39.5997 - 68.5887i) q^{67} +49.9970i q^{69} -12.9952i q^{71} +(49.2909 + 85.3744i) q^{73} +(3.45933 - 5.99173i) q^{75} +(-61.4784 - 61.0732i) q^{77} +(-113.644 - 65.6123i) q^{79} +(-7.49577 - 12.9831i) q^{81} -28.3732 q^{83} +59.4242i q^{85} +(32.5130 - 18.7714i) q^{87} +(78.7090 - 136.328i) q^{89} +(33.6996 + 124.126i) q^{91} +(-32.2141 - 18.5988i) q^{93} +(-11.9498 + 6.89923i) q^{95} -39.6175 q^{97} -77.7633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 40 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 - 40 * q^9	$ 12 q + 6 q^{3} - 40 q^{9} - 30 q^{11} + 30 q^{17} - 78 q^{19} - 92 q^{25} - 156 q^{27} - 78 q^{33} + 222 q^{35} - 232 q^{41} + 200 q^{43} + 372 q^{49} - 10 q^{51} + 332 q^{57} + 110 q^{59} - 32 q^{65} - 434 q^{67} + 102 q^{73} + 60 q^{75} - 82 q^{81} + 536 q^{83} + 214 q^{89} + 8 q^{91} - 152 q^{97} - 504 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 40 * q^9 - 30 * q^11 + 30 * q^17 - 78 * q^19 - 92 * q^25 - 156 * q^27 - 78 * q^33 + 222 * q^35 - 232 * q^41 + 200 * q^43 + 372 * q^49 - 10 * q^51 + 332 * q^57 + 110 * q^59 - 32 * q^65 - 434 * q^67 + 102 * q^73 + 60 * q^75 - 82 * q^81 + 536 * q^83 + 214 * q^89 + 8 * q^91 - 152 * q^97 - 504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.824388	+	1.42788i	0.274796	+	0.475961i	0.970084	−	0.242771i	$-0.0780563\pi$
$3$	0.824388	+	1.42788i	0.274796	+	0.475961i	−0.695288	+	0.718732i	$0.744723\pi$
$4$		0			0
$5$	3.95004	+	2.28056i	0.790008	+	0.456111i	0.839965	−	0.542640i	$-0.182575\pi$
$5$	3.95004	+	2.28056i	0.790008	+	0.456111i	−0.0499573	+	0.998751i	$0.515909\pi$
$6$		0			0
$7$	6.75545	−	1.83408i	0.965065	−	0.262011i
$7$	6.75545	−	1.83408i	0.965065	−	0.262011i
$8$		0			0
$9$	3.14077	−	5.43997i	0.348974	−	0.604441i
$10$		0			0
$11$	−6.18983	−	10.7211i	−0.562712	−	0.974645i	−0.997259	−	0.0739960i	$-0.976425\pi$
$11$	−6.18983	−	10.7211i	−0.562712	−	0.974645i	0.434547	−	0.900649i	$-0.356909\pi$
$12$		0			0
$13$			18.3741i			1.41340i	0.707516	+	0.706698i	$0.249816\pi$
$13$			18.3741i			1.41340i	−0.707516	+	0.706698i	$0.750184\pi$
$14$		0			0
$15$			7.52026i			0.501350i
$16$		0			0
$17$	6.51422	+	11.2830i	0.383189	+	0.663703i	0.991516	−	0.129983i	$-0.0414924\pi$
$17$	6.51422	+	11.2830i	0.383189	+	0.663703i	−0.608327	+	0.793687i	$0.708159\pi$
$18$		0			0
$19$	−1.51262	+	2.61993i	−0.0796115	+	0.137891i	−0.903082	−	0.429467i	$-0.858701\pi$
$19$	−1.51262	+	2.61993i	−0.0796115	+	0.137891i	0.823471	+	0.567359i	$0.192035\pi$
$20$		0			0
$21$	8.18796	+	8.13400i	0.389903	+	0.387333i
$22$		0			0
$23$	26.2611	+	15.1619i	1.14179	+	0.659211i	0.946873	−	0.321609i	$-0.104224\pi$
$23$	26.2611	+	15.1619i	1.14179	+	0.659211i	0.194915	+	0.980820i	$0.437557\pi$
$24$		0			0
$25$	−2.09812	−	3.63405i	−0.0839248	−	0.145362i
$26$		0			0
$27$	25.1958			0.933179
$28$		0			0
$29$		−	22.7701i		−	0.785176i	−0.919714	−	0.392588i	$-0.871580\pi$
$29$		−	22.7701i		−	0.785176i	0.919714	−	0.392588i	$-0.128420\pi$
$30$		0			0
$31$	−19.5382	+	11.2804i	−0.630264	+	0.363883i	−0.780855	−	0.624713i	$-0.785216\pi$
$31$	−19.5382	+	11.2804i	−0.630264	+	0.363883i	0.150590	+	0.988596i	$0.451883\pi$
$32$		0			0
$33$	10.2056	−	17.6767i	0.309262	−	0.535657i
$34$		0			0
$35$	30.8670	+	8.16151i	0.881915	+	0.233186i
$36$		0			0
$37$	11.9335	+	6.88983i	0.322528	+	0.186212i	0.652519	−	0.757772i	$-0.273712\pi$
$37$	11.9335	+	6.88983i	0.322528	+	0.186212i	−0.329991	+	0.943984i	$0.607046\pi$
$38$		0			0
$39$	−26.2361	+	15.1474i	−0.672721	+	0.388395i
$40$		0			0
$41$	−60.5026			−1.47567			−0.737837	−	0.674979i	$-0.764153\pi$
$41$	−60.5026			−1.47567			−0.737837	+	0.674979i	$0.764153\pi$
$42$		0			0
$43$	−39.0188			−0.907414			−0.453707	−	0.891151i	$-0.649899\pi$
$43$	−39.0188			−0.907414			−0.453707	+	0.891151i	$0.649899\pi$
$44$		0			0
$45$	24.8123	−	14.3254i	0.551385	−	0.318342i
$46$		0			0
$47$	17.6115	+	10.1680i	0.374713	+	0.216341i	0.675516	−	0.737346i	$-0.263921\pi$
$47$	17.6115	+	10.1680i	0.374713	+	0.216341i	−0.300802	+	0.953686i	$0.597254\pi$
$48$		0			0
$49$	42.2723	−	24.7801i	0.862700	−	0.505716i
$50$		0			0
$51$	−10.7405	+	18.6031i	−0.210598	+	0.364766i
$52$		0			0
$53$	4.12744	−	2.38298i	0.0778762	−	0.0449619i	−0.460556	−	0.887631i	$-0.652350\pi$
$53$	4.12744	−	2.38298i	0.0778762	−	0.0449619i	0.538432	+	0.842669i	$0.319017\pi$
$54$		0			0
$55$		−	56.4650i		−	1.02664i
$56$		0			0
$57$	−4.98794			−0.0875077
$58$		0			0
$59$	5.86884	+	10.1651i	0.0994718	+	0.172290i	0.911466	−	0.411375i	$-0.134951\pi$
$59$	5.86884	+	10.1651i	0.0994718	+	0.172290i	−0.811994	+	0.583665i	$0.801618\pi$
$60$		0			0
$61$	−94.3137	−	54.4520i	−1.54613	−	0.892656i	−0.998432	−	0.0559779i	$-0.982172\pi$
$61$	−94.3137	−	54.4520i	−1.54613	−	0.892656i	−0.547694	−	0.836679i	$-0.684494\pi$
$62$		0			0
$63$	11.2400	−	42.5099i	0.178412	−	0.674760i
$64$		0			0
$65$	−41.9033	+	72.5786i	−0.644666	+	1.11659i
$66$		0			0
$67$	−39.5997	−	68.5887i	−0.591041	−	1.02371i	−0.994093	−	0.108535i	$-0.965384\pi$
$67$	−39.5997	−	68.5887i	−0.591041	−	1.02371i	0.403052	−	0.915177i	$-0.367949\pi$
$68$		0			0
$69$			49.9970i			0.724595i
$70$		0			0
$71$		−	12.9952i		−	0.183031i	−0.995804	−	0.0915157i	$-0.970829\pi$
$71$		−	12.9952i		−	0.183031i	0.995804	−	0.0915157i	$-0.0291712\pi$
$72$		0			0
$73$	49.2909	+	85.3744i	0.675218	+	1.16951i	0.976405	+	0.215947i	$0.0692839\pi$
$73$	49.2909	+	85.3744i	0.675218	+	1.16951i	−0.301187	+	0.953565i	$0.597383\pi$
$74$		0			0
$75$	3.45933	−	5.99173i	0.0461244	−	0.0798898i
$76$		0			0
$77$	−61.4784	−	61.0732i	−0.798421	−	0.793159i
$78$		0			0
$79$	−113.644	−	65.6123i	−1.43853	−	0.830535i	−0.440781	−	0.897615i	$-0.645299\pi$
$79$	−113.644	−	65.6123i	−1.43853	−	0.830535i	−0.997748	+	0.0670794i	$0.978632\pi$
$80$		0			0
$81$	−7.49577	−	12.9831i	−0.0925404	−	0.160285i
$82$		0			0
$83$	−28.3732			−0.341846			−0.170923	−	0.985284i	$-0.554675\pi$
$83$	−28.3732			−0.341846			−0.170923	+	0.985284i	$0.554675\pi$
$84$		0			0
$85$			59.4242i			0.699108i
$86$		0			0
$87$	32.5130	−	18.7714i	0.373713	−	0.215763i
$88$		0			0
$89$	78.7090	−	136.328i	0.884371	−	1.53178i	0.0379380	−	0.999280i	$-0.487921\pi$
$89$	78.7090	−	136.328i	0.884371	−	1.53178i	0.846433	−	0.532495i	$-0.178746\pi$
$90$		0			0
$91$	33.6996	+	124.126i	0.370325	+	1.36402i
$92$		0			0
$93$	−32.2141	−	18.5988i	−0.346388	−	0.199987i
$94$		0			0
$95$	−11.9498	+	6.89923i	−0.125788	+	0.0726235i
$96$		0			0
$97$	−39.6175			−0.408428			−0.204214	−	0.978926i	$-0.565464\pi$
$97$	−39.6175			−0.408428			−0.204214	+	0.978926i	$0.565464\pi$
$98$		0			0
$99$	−77.7633			−0.785488
$100$		0			0
$101$	37.7745	−	21.8091i	0.374005	−	0.215932i	−0.301202	−	0.953560i	$-0.597388\pi$
$101$	37.7745	−	21.8091i	0.374005	−	0.215932i	0.675207	+	0.737628i	$0.264054\pi$
$102$		0			0
$103$	−54.4748	−	31.4510i	−0.528881	−	0.305350i	0.211679	−	0.977339i	$-0.432107\pi$
$103$	−54.4748	−	31.4510i	−0.528881	−	0.305350i	−0.740561	+	0.671989i	$0.765440\pi$
$104$		0			0
$105$	13.7927	+	50.8027i	0.131359	+	0.483836i
$106$		0			0
$107$	22.1133	−	38.3014i	0.206667	−	0.357957i	−0.743996	−	0.668184i	$-0.767072\pi$
$107$	22.1133	−	38.3014i	0.206667	−	0.357957i	0.950663	+	0.310227i	$0.100405\pi$
$108$		0			0
$109$	7.63419	−	4.40760i	0.0700384	−	0.0404367i	−0.464572	−	0.885535i	$-0.653792\pi$
$109$	7.63419	−	4.40760i	0.0700384	−	0.0404367i	0.534610	+	0.845099i	$0.320458\pi$
$110$		0			0
$111$			22.7196i			0.204681i
$112$		0			0
$113$	−121.408			−1.07440			−0.537202	−	0.843454i	$-0.680519\pi$
$113$	−121.408			−1.07440			−0.537202	+	0.843454i	$0.680519\pi$
$114$		0			0
$115$	69.1550	+	119.780i	0.601347	+	1.04156i
$116$		0			0
$117$	99.9548	+	57.7089i	0.854314	+	0.493239i
$118$		0			0
$119$	64.7003	+	64.2739i	0.543700	+	0.540117i
$120$		0			0
$121$	−16.1279	+	27.9344i	−0.133289	+	0.230863i
$122$		0			0
$123$	−49.8776	−	86.3906i	−0.405509	−	0.702363i
$124$		0			0
$125$		−	133.167i		−	1.06534i
$126$		0			0
$127$			222.845i			1.75468i	0.479868	+	0.877341i	$0.340685\pi$
$127$			222.845i			1.75468i	−0.479868	+	0.877341i	$0.659315\pi$
$128$		0			0
$129$	−32.1666	−	55.7143i	−0.249354	−	0.431893i
$130$		0			0
$131$	118.527	−	205.294i	0.904785	−	1.56713i	0.0835786	−	0.996501i	$-0.473365\pi$
$131$	118.527	−	205.294i	0.904785	−	1.56713i	0.821206	−	0.570632i	$-0.193302\pi$
$132$		0			0
$133$	−5.41327	+	20.4731i	−0.0407013	+	0.153933i
$134$		0			0
$135$	99.5246	+	57.4605i	0.737219	+	0.425634i
$136$		0			0
$137$	4.83138	+	8.36820i	0.0352656	+	0.0610818i	0.883119	−	0.469148i	$-0.155439\pi$
$137$	4.83138	+	8.36820i	0.0352656	+	0.0610818i	−0.847854	+	0.530230i	$0.822106\pi$
$138$		0			0
$139$	63.0621			0.453684			0.226842	−	0.973932i	$-0.427160\pi$
$139$	63.0621			0.453684			0.226842	+	0.973932i	$0.427160\pi$
$140$		0			0
$141$			33.5296i			0.237798i
$142$		0			0
$143$	196.991	−	113.733i	1.37756	−	0.795334i
$144$		0			0
$145$	51.9285	−	89.9428i	0.358128	−	0.620295i
$146$		0			0
$147$	70.2318	+	39.9315i	0.477767	+	0.271643i
$148$		0			0
$149$	233.751	+	134.956i	1.56880	+	0.905746i	0.996309	+	0.0858343i	$0.0273556\pi$
$149$	233.751	+	134.956i	1.56880	+	0.905746i	0.572489	+	0.819912i	$0.305978\pi$
$150$		0			0
$151$	−93.6846	+	54.0888i	−0.620428	+	0.358204i	−0.777036	−	0.629457i	$-0.783277\pi$
$151$	−93.6846	+	54.0888i	−0.620428	+	0.358204i	0.156608	+	0.987661i	$0.449944\pi$
$152$		0			0
$153$	81.8386			0.534893
$154$		0			0
$155$	−102.902			−0.663885
$156$		0			0
$157$	−102.565	+	59.2159i	−0.653280	+	0.377171i	−0.789712	−	0.613478i	$-0.789770\pi$
$157$	−102.565	+	59.2159i	−0.653280	+	0.377171i	0.136432	+	0.990649i	$0.456437\pi$
$158$		0			0
$159$	6.80523	+	3.92900i	0.0428002	+	0.0247107i
$160$		0			0
$161$	205.214	+	54.2603i	1.27462	+	0.337021i
$162$		0			0
$163$	−41.0142	+	71.0387i	−0.251621	+	0.435820i	−0.963972	−	0.266003i	$-0.914297\pi$
$163$	−41.0142	+	71.0387i	−0.251621	+	0.435820i	0.712351	+	0.701823i	$0.247630\pi$
$164$		0			0
$165$	80.6254	−	46.5491i	0.488639	−	0.282116i
$166$		0			0
$167$			131.596i			0.788002i	0.919110	+	0.394001i	$0.128909\pi$
$167$			131.596i			0.788002i	−0.919110	+	0.394001i	$0.871091\pi$
$168$		0			0
$169$	−168.609			−0.997687
$170$		0			0
$171$	9.50157	+	16.4572i	0.0555648	+	0.0962410i
$172$		0			0
$173$	−95.3611	−	55.0568i	−0.551220	−	0.318247i	0.198394	−	0.980122i	$-0.436428\pi$
$173$	−95.3611	−	55.0568i	−0.551220	−	0.318247i	−0.749614	+	0.661875i	$0.769761\pi$
$174$		0			0
$175$	−20.8389	−	20.7015i	−0.119079	−	0.118295i
$176$		0			0
$177$	−9.67640	+	16.7600i	−0.0546689	+	0.0946893i
$178$		0			0
$179$	76.9263	+	133.240i	0.429756	+	0.744359i	0.996851	−	0.0792929i	$-0.0252662\pi$
$179$	76.9263	+	133.240i	0.429756	+	0.744359i	−0.567095	+	0.823652i	$0.691933\pi$
$180$		0			0
$181$			227.511i			1.25697i	0.777823	+	0.628484i	$0.216324\pi$
$181$			227.511i			1.25697i	−0.777823	+	0.628484i	$0.783676\pi$
$182$		0			0
$183$		−	179.558i		−	0.981194i
$184$		0			0
$185$	31.4253	+	54.4303i	0.169867	+	0.294218i
$186$		0			0
$187$	80.6438	−	139.679i	0.431250	−	0.746947i
$188$		0			0
$189$	170.209	−	46.2111i	0.900578	−	0.244503i
$190$		0			0
$191$	105.262	+	60.7728i	0.551107	+	0.318182i	0.749569	−	0.661927i	$-0.230261\pi$
$191$	105.262	+	60.7728i	0.551107	+	0.318182i	−0.198461	+	0.980109i	$0.563594\pi$
$192$		0			0
$193$	−42.7276	−	74.0064i	−0.221386	−	0.383453i	0.733843	−	0.679319i	$-0.237725\pi$
$193$	−42.7276	−	74.0064i	−0.221386	−	0.383453i	−0.955229	+	0.295867i	$0.904392\pi$
$194$		0			0
$195$	−138.178			−0.708606
$196$		0			0
$197$			214.100i			1.08680i	0.839474	+	0.543400i	$0.182863\pi$
$197$			214.100i			1.08680i	−0.839474	+	0.543400i	$0.817137\pi$
$198$		0			0
$199$	−214.968	+	124.112i	−1.08024	+	0.623677i	−0.930961	−	0.365118i	$-0.881029\pi$
$199$	−214.968	+	124.112i	−1.08024	+	0.623677i	−0.149279	+	0.988795i	$0.547695\pi$
$200$		0			0
$201$	65.2911	−	113.087i	0.324831	−	0.562624i
$202$		0			0
$203$	−41.7621	−	153.822i	−0.205725	−	0.757746i
$204$		0			0
$205$	−238.988	−	137.980i	−1.16579	−	0.673071i
$206$		0			0
$207$	164.960	−	95.2398i	0.796909	−	0.460096i
$208$		0			0
$209$	37.4514			0.179193
$210$		0			0
$211$	−191.753			−0.908783			−0.454392	−	0.890802i	$-0.650143\pi$
$211$	−191.753			−0.908783			−0.454392	+	0.890802i	$0.650143\pi$
$212$		0			0
$213$	18.5557	−	10.7131i	0.0871157	−	0.0502963i
$214$		0			0
$215$	−154.126	−	88.9846i	−0.716864	−	0.413882i
$216$		0			0
$217$	−111.300	+	112.039i	−0.512905	+	0.516307i
$218$		0			0
$219$	−81.2697	+	140.763i	−0.371095	+	0.642755i
$220$		0			0
$221$	−207.315	+	119.693i	−0.938075	+	0.541598i
$222$		0			0
$223$		−	41.2269i		−	0.184874i	−0.995719	−	0.0924370i	$-0.970534\pi$
$223$		−	41.2269i		−	0.184874i	0.995719	−	0.0924370i	$-0.0294657\pi$
$224$		0			0
$225$	−26.3588			−0.117150
$226$		0			0
$227$	35.2219	+	61.0060i	0.155162	+	0.268749i	0.933118	−	0.359570i	$-0.117077\pi$
$227$	35.2219	+	61.0060i	0.155162	+	0.268749i	−0.777956	+	0.628319i	$0.783743\pi$
$228$		0			0
$229$	−81.8558	−	47.2595i	−0.357449	−	0.206373i	0.310512	−	0.950569i	$-0.399499\pi$
$229$	−81.8558	−	47.2595i	−0.357449	−	0.206373i	−0.667961	+	0.744196i	$0.732833\pi$
$230$		0			0
$231$	36.5233	−	138.132i	0.158110	−	0.597974i
$232$		0			0
$233$	68.1434	−	118.028i	0.292461	−	0.506557i	−0.681930	−	0.731417i	$-0.738859\pi$
$233$	68.1434	−	118.028i	0.292461	−	0.506557i	0.974391	+	0.224860i	$0.0721925\pi$
$234$		0			0
$235$	46.3775	+	80.3281i	0.197351	+	0.341822i
$236$		0			0
$237$		−	216.360i		−	0.912911i
$238$		0			0
$239$		−	173.230i		−	0.724813i	−0.932020	−	0.362406i	$-0.881955\pi$
$239$		−	173.230i		−	0.724813i	0.932020	−	0.362406i	$-0.118045\pi$
$240$		0			0
$241$	164.461	+	284.856i	0.682413	+	1.18197i	0.974242	+	0.225503i	$0.0724027\pi$
$241$	164.461	+	284.856i	0.682413	+	1.18197i	−0.291830	+	0.956470i	$0.594264\pi$
$242$		0			0
$243$	125.740	−	217.788i	0.517449	−	0.896248i
$244$		0			0
$245$	223.490	−	1.47783i	0.912203	−	0.00603196i
$246$		0			0
$247$	−48.1390	−	27.7931i	−0.194895	−	0.112523i
$248$		0			0
$249$	−23.3905	−	40.5136i	−0.0939379	−	0.162705i
$250$		0			0
$251$	−160.255			−0.638466			−0.319233	−	0.947676i	$-0.603425\pi$
$251$	−160.255			−0.638466			−0.319233	+	0.947676i	$0.603425\pi$
$252$		0			0
$253$		−	375.397i		−	1.48378i
$254$		0			0
$255$	−84.8507	+	48.9886i	−0.332748	+	0.192112i
$256$		0			0
$257$	−72.7208	+	125.956i	−0.282960	+	0.490102i	−0.972113	−	0.234515i	$-0.924650\pi$
$257$	−72.7208	+	125.956i	−0.282960	+	0.490102i	0.689152	+	0.724617i	$0.257983\pi$
$258$		0			0
$259$	93.2530	+	24.6569i	0.360050	+	0.0952004i
$260$		0			0
$261$	−123.869	−	71.5156i	−0.474593	−	0.274006i
$262$		0			0
$263$	175.617	−	101.392i	0.667745	−	0.385523i	−0.127477	−	0.991842i	$-0.540688\pi$
$263$	175.617	−	101.392i	0.667745	−	0.385523i	0.795222	+	0.606319i	$0.207355\pi$
$264$		0			0
$265$	21.7381			0.0820305
$266$		0			0
$267$	259.547			0.972087
$268$		0			0
$269$	191.662	−	110.656i	0.712497	−	0.411360i	−0.0994882	−	0.995039i	$-0.531721\pi$
$269$	191.662	−	110.656i	0.712497	−	0.411360i	0.811985	+	0.583679i	$0.198387\pi$
$270$		0			0
$271$	−101.651	−	58.6880i	−0.375095	−	0.216561i	0.300587	−	0.953754i	$-0.402817\pi$
$271$	−101.651	−	58.6880i	−0.375095	−	0.216561i	−0.675682	+	0.737193i	$0.736151\pi$
$272$		0			0
$273$	−149.455	+	150.447i	−0.547455	+	0.551087i
$274$		0			0
$275$	−25.9740	+	44.9883i	−0.0944509	+	0.163594i
$276$		0			0
$277$	−221.277	+	127.755i	−0.798835	+	0.461208i	−0.843064	−	0.537814i	$-0.819250\pi$
$277$	−221.277	+	127.755i	−0.798835	+	0.461208i	0.0442283	+	0.999021i	$0.485917\pi$
$278$		0			0
$279$			141.716i			0.507944i
$280$		0			0
$281$	−278.004			−0.989336			−0.494668	−	0.869082i	$-0.664710\pi$
$281$	−278.004			−0.989336			−0.494668	+	0.869082i	$0.664710\pi$
$282$		0			0
$283$	28.3448	+	49.0947i	0.100158	+	0.173479i	0.911750	−	0.410746i	$-0.134732\pi$
$283$	28.3448	+	49.0947i	0.100158	+	0.173479i	−0.811591	+	0.584225i	$0.801398\pi$
$284$		0			0
$285$	−19.7026	−	11.3753i	−0.0691318	−	0.0399133i
$286$		0			0
$287$	−408.723	+	110.967i	−1.42412	+	0.386643i
$288$		0			0
$289$	59.6300	−	103.282i	0.206332	−	0.357378i
$290$		0			0
$291$	−32.6602	−	56.5691i	−0.112234	−	0.194396i
$292$		0			0
$293$		−	287.871i		−	0.982493i	−0.871020	−	0.491247i	$-0.836541\pi$
$293$		−	287.871i		−	0.982493i	0.871020	−	0.491247i	$-0.163459\pi$
$294$		0			0
$295$			53.5369i			0.181481i
$296$		0			0
$297$	−155.958	−	270.127i	−0.525111	−	0.909518i
$298$		0			0
$299$	−278.586	+	482.525i	−0.931726	+	1.61380i
$300$		0			0
$301$	−263.590	+	71.5635i	−0.875713	+	0.237753i
$302$		0			0
$303$	62.2817	+	35.9584i	0.205550	+	0.118675i
$304$		0			0
$305$	−248.362	−	430.176i	−0.814302	−	1.41041i
$306$		0			0
$307$	−53.6483			−0.174750			−0.0873750	−	0.996175i	$-0.527848\pi$
$307$	−53.6483			−0.174750			−0.0873750	+	0.996175i	$0.527848\pi$
$308$		0			0
$309$		−	103.711i		−	0.335636i
$310$		0			0
$311$	−91.0263	+	52.5541i	−0.292689	+	0.168984i	−0.639154	−	0.769079i	$-0.720715\pi$
$311$	−91.0263	+	52.5541i	−0.292689	+	0.168984i	0.346465	+	0.938063i	$0.387382\pi$
$312$		0			0
$313$	−105.245	+	182.290i	−0.336246	+	0.582395i	−0.983723	−	0.179690i	$-0.942491\pi$
$313$	−105.245	+	182.290i	−0.336246	+	0.582395i	0.647477	+	0.762085i	$0.275824\pi$
$314$		0			0
$315$	141.345	−	142.282i	0.448713	−	0.451690i
$316$		0			0
$317$	54.4626	+	31.4440i	0.171806	+	0.0991925i	0.583437	−	0.812158i	$-0.301707\pi$
$317$	54.4626	+	31.4440i	0.171806	+	0.0991925i	−0.411631	+	0.911351i	$0.635041\pi$
$318$		0			0
$319$	−244.120	+	140.943i	−0.765268	+	0.441828i
$320$		0			0
$321$	72.9199			0.227165
$322$		0			0
$323$	−39.4141			−0.122025
$324$		0			0
$325$	66.7725	−	38.5511i	0.205454	−	0.118619i
$326$		0			0
$327$	12.5871	+	7.26715i	0.0384926	+	0.0222237i
$328$		0			0
$329$	137.623	+	36.3887i	0.418306	+	0.110604i
$330$		0			0
$331$	98.2893	−	170.242i	0.296947	−	0.514327i	−0.678489	−	0.734610i	$-0.737365\pi$
$331$	98.2893	−	170.242i	0.296947	−	0.514327i	0.975436	+	0.220284i	$0.0706983\pi$
$332$		0			0
$333$	74.9610	−	43.2787i	0.225108	−	0.129966i
$334$		0			0
$335$		−	361.238i		−	1.07832i
$336$		0			0
$337$	591.516			1.75524			0.877620	−	0.479358i	$-0.159130\pi$
$337$	591.516			1.75524			0.877620	+	0.479358i	$0.159130\pi$
$338$		0			0
$339$	−100.087	−	173.356i	−0.295242	−	0.511374i
$340$		0			0
$341$	241.876	+	139.647i	0.709314	+	0.409523i
$342$		0			0
$343$	240.120	−	244.931i	0.700059	−	0.714085i
$344$		0			0
$345$	−114.021	+	197.490i	−0.330496	+	0.572436i
$346$		0			0
$347$	123.770	+	214.376i	0.356685	+	0.617797i	0.987405	−	0.158214i	$-0.0505734\pi$
$347$	123.770	+	214.376i	0.356685	+	0.617797i	−0.630719	+	0.776011i	$0.717240\pi$
$348$		0			0
$349$			288.749i			0.827362i	0.910422	+	0.413681i	$0.135757\pi$
$349$			288.749i			0.827362i	−0.910422	+	0.413681i	$0.864243\pi$
$350$		0			0
$351$			462.952i			1.31895i
$352$		0			0
$353$	0.634830	+	1.09956i	0.00179839	+	0.00311490i	0.866923	−	0.498442i	$-0.166094\pi$
$353$	0.634830	+	1.09956i	0.00179839	+	0.00311490i	−0.865125	+	0.501557i	$0.832761\pi$
$354$		0			0
$355$	29.6364	−	51.3317i	0.0834827	−	0.144596i
$356$		0			0
$357$	−38.4374	+	145.371i	−0.107668	+	0.407202i
$358$		0			0
$359$	15.0707	+	8.70105i	0.0419796	+	0.0242369i	0.520843	−	0.853653i	$-0.325618\pi$
$359$	15.0707	+	8.70105i	0.0419796	+	0.0242369i	−0.478863	+	0.877889i	$0.658951\pi$
$360$		0			0
$361$	175.924	+	304.709i	0.487324	+	0.844070i
$362$		0			0
$363$	−53.1828			−0.146509
$364$		0			0
$365$			449.643i			1.23190i
$366$		0			0
$367$	459.021	−	265.016i	1.25074	−	0.722115i	0.279483	−	0.960151i	$-0.409837\pi$
$367$	459.021	−	265.016i	1.25074	−	0.722115i	0.971256	+	0.238036i	$0.0765036\pi$
$368$		0			0
$369$	−190.025	+	329.132i	−0.514972	+	0.891958i
$370$		0			0
$371$	23.5122	−	23.6682i	0.0633751	−	0.0637956i
$372$		0			0
$373$	−102.722	−	59.3066i	−0.275394	−	0.158999i	0.355942	−	0.934508i	$-0.384160\pi$
$373$	−102.722	−	59.3066i	−0.275394	−	0.158999i	−0.631337	+	0.775509i	$0.717493\pi$
$374$		0			0
$375$	190.147	−	109.782i	0.507059	−	0.292751i
$376$		0			0
$377$	418.381			1.10976
$378$		0			0
$379$	345.947			0.912790			0.456395	−	0.889777i	$-0.349140\pi$
$379$	345.947			0.912790			0.456395	+	0.889777i	$0.349140\pi$
$380$		0			0
$381$	−318.196	+	183.710i	−0.835160	+	0.482180i
$382$		0			0
$383$	350.630	+	202.436i	0.915483	+	0.528555i	0.882191	−	0.470891i	$-0.156068\pi$
$383$	350.630	+	202.436i	0.915483	+	0.528555i	0.0332920	+	0.999446i	$0.489401\pi$
$384$		0			0
$385$	−103.561	−	381.447i	−0.268990	−	0.990771i
$386$		0			0
$387$	−122.549	+	212.261i	−0.316664	+	0.548478i
$388$		0			0
$389$	116.391	−	67.1985i	0.299206	−	0.172747i	−0.342880	−	0.939379i	$-0.611402\pi$
$389$	116.391	−	67.1985i	0.299206	−	0.172747i	0.642086	+	0.766632i	$0.278069\pi$
$390$		0			0
$391$			395.070i			1.01041i
$392$		0			0
$393$	390.848			0.994525
$394$		0			0
$395$	−299.265	−	518.342i	−0.757633	−	1.31226i
$396$		0			0
$397$	530.424	+	306.240i	1.33608	+	0.771386i	0.986224	−	0.165417i	$-0.0528969\pi$
$397$	530.424	+	306.240i	1.33608	+	0.771386i	0.349857	+	0.936803i	$0.386230\pi$
$398$		0			0
$399$	−33.6958	+	9.14828i	−0.0844506	+	0.0229280i
$400$		0			0
$401$	63.1234	−	109.333i	0.157415	−	0.272651i	−0.776521	−	0.630092i	$-0.783017\pi$
$401$	63.1234	−	109.333i	0.157415	−	0.272651i	0.933936	+	0.357441i	$0.116351\pi$
$402$		0			0
$403$	−207.267	−	358.998i	−0.514311	−	0.890813i
$404$		0			0
$405$		−	68.3781i		−	0.168835i
$406$		0			0
$407$		−	170.588i		−	0.419134i
$408$		0			0
$409$	−171.259	−	296.630i	−0.418727	−	0.725257i	0.577084	−	0.816685i	$-0.304190\pi$
$409$	−171.259	−	296.630i	−0.418727	−	0.725257i	−0.995812	+	0.0914275i	$0.970857\pi$
$410$		0			0
$411$	−7.96587	+	13.7973i	−0.0193817	+	0.0335700i
$412$		0			0
$413$	58.2903	+	57.9061i	0.141139	+	0.140209i
$414$		0			0
$415$	−112.075	−	64.7068i	−0.270061	−	0.155920i
$416$		0			0
$417$	51.9876	+	90.0452i	0.124671	+	0.215936i
$418$		0			0
$419$	376.392			0.898311			0.449155	−	0.893454i	$-0.351725\pi$
$419$	376.392			0.898311			0.449155	+	0.893454i	$0.351725\pi$
$420$		0			0
$421$			111.135i			0.263978i	0.991251	+	0.131989i	$0.0421363\pi$
$421$			111.135i			0.263978i	−0.991251	+	0.131989i	$0.957864\pi$
$422$		0			0
$423$	110.627	−	63.8708i	0.261531	−	0.150995i
$424$		0			0
$425$	27.3352	−	47.3460i	0.0643181	−	0.111402i
$426$		0			0
$427$	−737.001	−	194.870i	−1.72600	−	0.456369i
$428$		0			0
$429$	324.794	+	187.520i	0.757096	+	0.437109i
$430$		0			0
$431$	35.7481	−	20.6392i	0.0829422	−	0.0478867i	−0.457955	−	0.888975i	$-0.651418\pi$
$431$	35.7481	−	20.6392i	0.0829422	−	0.0478867i	0.540898	+	0.841089i	$0.318085\pi$
$432$		0			0
$433$	−675.176			−1.55930			−0.779649	−	0.626217i	$-0.784603\pi$
$433$	−675.176			−1.55930			−0.779649	+	0.626217i	$0.784603\pi$
$434$		0			0
$435$	171.237			0.393648
$436$		0			0
$437$	−79.4461	+	45.8682i	−0.181799	+	0.104962i
$438$		0			0
$439$	459.215	+	265.128i	1.04605	+	0.603936i	0.921541	−	0.388282i	$-0.126931\pi$
$439$	459.215	+	265.128i	1.04605	+	0.603936i	0.124508	+	0.992219i	$0.460265\pi$
$440$		0			0
$441$	−2.03526	−	307.789i	−0.00461510	−	0.697933i
$442$		0			0
$443$	166.016	−	287.549i	0.374755	−	0.649094i	−0.615535	−	0.788109i	$-0.711060\pi$
$443$	166.016	−	287.549i	0.374755	−	0.649094i	0.990290	+	0.139015i	$0.0443935\pi$
$444$		0			0
$445$	621.808	−	359.001i	1.39732	−	0.806743i
$446$		0			0
$447$			445.025i			0.995582i
$448$		0			0
$449$	−19.4200			−0.0432517			−0.0216259	−	0.999766i	$-0.506884\pi$
$449$	−19.4200			−0.0432517			−0.0216259	+	0.999766i	$0.506884\pi$
$450$		0			0
$451$	374.501	+	648.654i	0.830379	+	1.43826i
$452$		0			0
$453$	−154.465	−	89.1804i	−0.340982	−	0.196866i
$454$		0			0
$455$	−149.961	+	567.155i	−0.329584	+	1.24650i
$456$		0			0
$457$	88.9796	−	154.117i	0.194704	−	0.337237i	−0.752100	−	0.659049i	$-0.770959\pi$
$457$	88.9796	−	154.117i	0.194704	−	0.337237i	0.946803	+	0.321813i	$0.104292\pi$
$458$		0			0
$459$	164.131	+	284.283i	0.357584	+	0.619354i
$460$		0			0
$461$			299.341i			0.649329i	0.945829	+	0.324664i	$0.105251\pi$
$461$			299.341i			0.649329i	−0.945829	+	0.324664i	$0.894749\pi$
$462$		0			0
$463$		−	505.213i		−	1.09117i	−0.838055	−	0.545586i	$-0.816307\pi$
$463$		−	505.213i		−	1.09117i	0.838055	−	0.545586i	$-0.183693\pi$
$464$		0			0
$465$	−84.8314	−	146.932i	−0.182433	−	0.315983i
$466$		0			0
$467$	−325.162	+	563.197i	−0.696278	+	1.20599i	0.273470	+	0.961881i	$0.411829\pi$
$467$	−325.162	+	563.197i	−0.696278	+	1.20599i	−0.969748	+	0.244108i	$0.921505\pi$
$468$		0			0
$469$	−393.311	−	390.719i	−0.838617	−	0.833089i
$470$		0			0
$471$	−169.107	−	97.6338i	−0.359037	−	0.207290i
$472$		0			0
$473$	241.520	+	418.324i	0.510612	+	0.884407i
$474$		0			0
$475$	12.6946			0.0267255
$476$		0			0
$477$		−	29.9375i		−	0.0627621i
$478$		0			0
$479$	−572.400	+	330.475i	−1.19499	+	0.689928i	−0.959434	−	0.281933i	$-0.909024\pi$
$479$	−572.400	+	330.475i	−1.19499	+	0.689928i	−0.235556	+	0.971861i	$0.575691\pi$
$480$		0			0
$481$	−126.595	+	219.269i	−0.263191	+	0.455860i
$482$		0			0
$483$	91.6985	+	337.753i	0.189852	+	0.699281i
$484$		0			0
$485$	−156.491	−	90.3500i	−0.322661	−	0.186289i
$486$		0			0
$487$	−334.373	+	193.050i	−0.686597	+	0.396407i	−0.802336	−	0.596873i	$-0.796410\pi$
$487$	−334.373	+	193.050i	−0.686597	+	0.396407i	0.115739	+	0.993280i	$0.463076\pi$
$488$		0			0
$489$	−135.246			−0.276578
$490$		0			0
$491$	898.359			1.82965			0.914826	−	0.403848i	$-0.132328\pi$
$491$	898.359			1.82965			0.914826	+	0.403848i	$0.132328\pi$
$492$		0			0
$493$	256.914	−	148.329i	0.521124	−	0.300871i
$494$		0			0
$495$	−307.168	−	177.344i	−0.620542	−	0.358270i
$496$		0			0
$497$	−23.8343	−	87.7887i	−0.0479563	−	0.176637i
$498$		0			0
$499$	395.588	−	685.178i	0.792761	−	1.37310i	−0.131490	−	0.991318i	$-0.541976\pi$
$499$	395.588	−	685.178i	0.792761	−	1.37310i	0.924251	−	0.381785i	$-0.124691\pi$
$500$		0			0
$501$	−187.904	+	108.486i	−0.375058	+	0.216540i
$502$		0			0
$503$		−	798.990i		−	1.58845i	−0.607624	−	0.794225i	$-0.707877\pi$
$503$		−	798.990i		−	1.58845i	0.607624	−	0.794225i	$-0.292123\pi$
$504$		0			0
$505$	198.948			0.393956
$506$		0			0
$507$	−138.999	−	240.754i	−0.274160	−	0.474860i
$508$		0			0
$509$	−477.272	−	275.553i	−0.937666	−	0.541362i	−0.0484379	−	0.998826i	$-0.515424\pi$
$509$	−477.272	−	275.553i	−0.937666	−	0.541362i	−0.889228	+	0.457465i	$0.848758\pi$
$510$		0			0
$511$	489.566	+	486.339i	0.958055	+	0.951741i
$512$		0			0
$513$	−38.1117	+	66.0114i	−0.0742918	+	0.128677i
$514$		0			0
$515$	−143.452	−	248.466i	−0.278547	−	0.482458i
$516$		0			0
$517$		−	251.753i		−	0.486950i
$518$		0			0
$519$		−	181.553i		−	0.349812i
$520$		0			0
$521$	−71.3914	−	123.654i	−0.137028	−	0.237339i	0.789343	−	0.613953i	$-0.210422\pi$
$521$	−71.3914	−	123.654i	−0.137028	−	0.237339i	−0.926370	+	0.376614i	$0.877088\pi$
$522$		0			0
$523$	−416.255	+	720.976i	−0.795900	+	1.37854i	0.126367	+	0.991984i	$0.459668\pi$
$523$	−416.255	+	720.976i	−0.795900	+	1.37854i	−0.922266	+	0.386555i	$0.873665\pi$
$524$		0			0
$525$	12.3800	−	46.8216i	0.0235810	−	0.0891839i
$526$		0			0
$527$	−254.552	−	146.966i	−0.483021	−	0.278872i
$528$		0			0
$529$	195.264	+	338.207i	0.369119	+	0.639333i
$530$		0			0
$531$	73.7306			0.138852
$532$		0			0
$533$		−	1111.68i		−	2.08571i
$534$		0			0
$535$	174.697	−	100.862i	0.326537	−	0.188526i
$536$		0			0
$537$	−126.834	+	219.683i	−0.236191	+	0.409094i
$538$		0			0
$539$	−527.328	−	299.821i	−0.978345	−	0.556255i
$540$		0			0
$541$	533.874	+	308.232i	0.986829	+	0.569746i	0.904325	−	0.426845i	$-0.140375\pi$
$541$	533.874	+	308.232i	0.986829	+	0.569746i	0.0825038	+	0.996591i	$0.473708\pi$
$542$		0			0
$543$	−324.859	+	187.557i	−0.598267	+	0.345410i
$544$		0			0
$545$	40.2071			0.0737746
$546$		0			0
$547$	−577.704			−1.05613			−0.528065	−	0.849204i	$-0.677082\pi$
$547$	−577.704			−1.05613			−0.528065	+	0.849204i	$0.677082\pi$
$548$		0			0
$549$	−592.435	+	342.043i	−1.07912	+	0.623028i
$550$		0			0
$551$	59.6562	+	34.4425i	0.108269	+	0.0625091i
$552$		0			0
$553$	−888.053	−	234.809i	−1.60588	−	0.424610i
$554$		0			0
$555$	−51.8133	+	89.7433i	−0.0933573	+	0.161700i
$556$		0			0
$557$	−445.752	+	257.355i	−0.800273	+	0.462038i	−0.843566	−	0.537025i	$-0.819548\pi$
$557$	−445.752	+	257.355i	−0.800273	+	0.462038i	0.0432939	+	0.999062i	$0.486215\pi$
$558$		0			0
$559$		−	716.937i		−	1.28253i
$560$		0			0
$561$	265.927			0.474023
$562$		0			0
$563$	−304.360	−	527.166i	−0.540603	−	0.936352i	−0.998869	−	0.0475374i	$-0.984863\pi$
$563$	−304.360	−	527.166i	−0.540603	−	0.936352i	0.458266	−	0.888815i	$-0.348471\pi$
$564$		0			0
$565$	−479.565	−	276.877i	−0.848788	−	0.490048i
$566$		0			0
$567$	−74.4493	−	73.9586i	−0.131304	−	0.130438i
$568$		0			0
$569$	−93.1872	+	161.405i	−0.163774	+	0.283664i	−0.936219	−	0.351417i	$-0.885700\pi$
$569$	−93.1872	+	161.405i	−0.163774	+	0.283664i	0.772445	+	0.635081i	$0.219033\pi$
$570$		0			0
$571$	91.8878	+	159.154i	0.160924	+	0.278729i	0.935200	−	0.354119i	$-0.115219\pi$
$571$	91.8878	+	159.154i	0.160924	+	0.278729i	−0.774276	+	0.632848i	$0.781886\pi$
$572$		0			0
$573$			200.401i			0.349741i
$574$		0			0
$575$		−	127.246i		−	0.221297i
$576$		0			0
$577$	−67.2281	−	116.442i	−0.116513	−	0.201807i	0.801870	−	0.597498i	$-0.203838\pi$
$577$	−67.2281	−	116.442i	−0.116513	−	0.201807i	−0.918384	+	0.395691i	$0.870505\pi$
$578$		0			0
$579$	70.4482	−	122.020i	0.121672	−	0.210743i
$580$		0			0
$581$	−191.674	+	52.0387i	−0.329904	+	0.0895675i
$582$		0			0
$583$	−51.0963	−	29.5005i	−0.0876437	−	0.0506011i
$584$		0			0
$585$	263.217	+	455.905i	0.449944	+	0.779325i
$586$		0			0
$587$	921.405			1.56968			0.784842	−	0.619696i	$-0.212744\pi$
$587$	921.405			1.56968			0.784842	+	0.619696i	$0.212744\pi$
$588$		0			0
$589$		−	68.2517i		−	0.115877i
$590$		0			0
$591$	−305.709	+	176.501i	−0.517274	+	0.298648i
$592$		0			0
$593$	−48.1873	+	83.4628i	−0.0812602	+	0.140747i	−0.903791	−	0.427973i	$-0.859228\pi$
$593$	−48.1873	+	83.4628i	−0.0812602	+	0.140747i	0.822531	+	0.568720i	$0.192561\pi$
$594$		0			0
$595$	108.989	+	401.437i	0.183174	+	0.674684i
$596$		0			0
$597$	−354.434	−	204.632i	−0.593692	−	0.342768i
$598$		0			0
$599$	144.711	−	83.5489i	0.241587	−	0.139481i	−0.374319	−	0.927300i	$-0.622123\pi$
$599$	144.711	−	83.5489i	0.241587	−	0.139481i	0.615906	+	0.787820i	$0.288790\pi$
$600$		0			0
$601$	88.4635			0.147194			0.0735969	−	0.997288i	$-0.476552\pi$
$601$	88.4635			0.147194			0.0735969	+	0.997288i	$0.476552\pi$
$602$		0			0
$603$	−497.494			−0.825032
$604$		0			0
$605$	−127.412	+	73.5614i	−0.210598	+	0.121589i
$606$		0			0
$607$	−48.1243	−	27.7846i	−0.0792822	−	0.0457736i	0.459835	−	0.888004i	$-0.347909\pi$
$607$	−48.1243	−	27.7846i	−0.0792822	−	0.0457736i	−0.539117	+	0.842231i	$0.681242\pi$
$608$		0			0
$609$	185.212	−	186.441i	0.304125	−	0.306142i
$610$		0			0
$611$	−186.829	+	323.597i	−0.305775	+	0.529618i
$612$		0			0
$613$	752.678	−	434.559i	1.22786	−	0.708905i	0.261278	−	0.965264i	$-0.415856\pi$
$613$	752.678	−	434.559i	1.22786	−	0.708905i	0.966582	+	0.256359i	$0.0825229\pi$
$614$		0			0
$615$		−	454.995i		−	0.739829i
$616$		0			0
$617$	−249.359			−0.404147			−0.202074	−	0.979370i	$-0.564768\pi$
$617$	−249.359			−0.404147			−0.202074	+	0.979370i	$0.564768\pi$
$618$		0			0
$619$	−248.837	−	430.998i	−0.401998	−	0.696280i	0.591969	−	0.805961i	$-0.298351\pi$
$619$	−248.837	−	430.998i	−0.401998	−	0.696280i	−0.993967	+	0.109680i	$0.965017\pi$
$620$		0			0
$621$	661.671	+	382.016i	1.06549	+	0.615162i
$622$		0			0
$623$	281.679	−	1065.32i	0.452133	−	1.70998i
$624$		0			0
$625$	251.243	−	435.165i	0.401988	−	0.696264i
$626$		0			0
$627$	30.8745	+	53.4762i	0.0492416	+	0.0852890i
$628$		0			0
$629$			179.527i			0.285417i
$630$		0			0
$631$			172.763i			0.273792i	0.990585	+	0.136896i	$0.0437126\pi$
$631$			172.763i			0.273792i	−0.990585	+	0.136896i	$0.956287\pi$
$632$		0			0
$633$	−158.079	−	273.801i	−0.249730	−	0.432545i
$634$		0			0
$635$	−508.210	+	880.245i	−0.800330	+	1.38621i
$636$		0			0
$637$	455.312	+	776.717i	0.714776	+	1.21934i
$638$		0			0
$639$	−70.6937	−	40.8150i	−0.110632	−	0.0638732i
$640$		0			0
$641$	213.949	+	370.570i	0.333774	+	0.578113i	0.983248	−	0.182270i	$-0.0583446\pi$
$641$	213.949	+	370.570i	0.333774	+	0.578113i	−0.649475	+	0.760383i	$0.725011\pi$
$642$		0			0
$643$	15.9463			0.0247998			0.0123999	−	0.999923i	$-0.496053\pi$
$643$	15.9463			0.0247998			0.0123999	+	0.999923i	$0.496053\pi$
$644$		0			0
$645$		−	293.431i		−	0.454932i
$646$		0			0
$647$	−450.510	+	260.102i	−0.696306	+	0.402012i	−0.805970	−	0.591956i	$-0.798356\pi$
$647$	−450.510	+	260.102i	−0.696306	+	0.402012i	0.109664	+	0.993969i	$0.465022\pi$
$648$		0			0
$649$	72.6542	−	125.841i	0.111948	−	0.193899i
$650$		0			0
$651$	−251.733	−	66.5603i	−0.386686	−	0.102243i
$652$		0			0
$653$	−367.687	−	212.284i	−0.563074	−	0.325091i	0.191305	−	0.981531i	$-0.438728\pi$
$653$	−367.687	−	212.284i	−0.563074	−	0.325091i	−0.754378	+	0.656440i	$0.772061\pi$
$654$		0			0
$655$	936.371	−	540.614i	1.42957	−	0.825365i
$656$		0			0
$657$	619.246			0.942535
$658$		0			0
$659$	−304.044			−0.461372			−0.230686	−	0.973028i	$-0.574097\pi$
$659$	−304.044			−0.461372			−0.230686	+	0.973028i	$0.574097\pi$
$660$		0			0
$661$	155.112	−	89.5542i	0.234663	−	0.135483i	−0.378058	−	0.925782i	$-0.623408\pi$
$661$	155.112	−	89.5542i	0.234663	−	0.135483i	0.612722	+	0.790299i	$0.290075\pi$
$662$		0			0
$663$	−341.815	−	197.347i	−0.515559	−	0.297658i
$664$		0			0
$665$	−68.0727	+	68.5243i	−0.102365	+	0.103044i
$666$		0			0
$667$	345.237	−	597.968i	0.517597	−	0.896504i
$668$		0			0
$669$	58.8671	−	33.9870i	0.0879927	−	0.0508026i
$670$		0			0
$671$			1348.20i			2.00923i
$672$		0			0
$673$	544.352			0.808844			0.404422	−	0.914573i	$-0.367473\pi$
$673$	544.352			0.808844			0.404422	+	0.914573i	$0.367473\pi$
$674$		0			0
$675$	−52.8639	−	91.5629i	−0.0783168	−	0.135649i
$676$		0			0
$677$	−471.416	−	272.172i	−0.696330	−	0.402027i	0.109649	−	0.993970i	$-0.465027\pi$
$677$	−471.416	−	272.172i	−0.696330	−	0.402027i	−0.805979	+	0.591944i	$0.798361\pi$
$678$		0			0
$679$	−267.634	+	72.6616i	−0.394159	+	0.107013i
$680$		0			0
$681$	−58.0730	+	100.585i	−0.0852760	+	0.147702i
$682$		0			0
$683$	443.494	+	768.154i	0.649332	+	1.12468i	0.983283	+	0.182086i	$0.0582848\pi$
$683$	443.494	+	768.154i	0.649332	+	1.12468i	−0.333951	+	0.942591i	$0.608382\pi$
$684$		0			0
$685$			44.0730i			0.0643401i
$686$		0			0
$687$		−	155.841i		−	0.226842i
$688$		0			0
$689$	43.7852	+	75.8382i	0.0635489	+	0.110070i
$690$		0			0
$691$	589.242	−	1020.60i	0.852738	−	1.47698i	−0.0259906	−	0.999662i	$-0.508274\pi$
$691$	589.242	−	1020.60i	0.852738	−	1.47698i	0.878728	−	0.477323i	$-0.158393\pi$
$692$		0			0
$693$	−525.326	+	142.624i	−0.758046	+	0.205807i
$694$		0			0
$695$	249.098	+	143.817i	0.358414	+	0.206930i
$696$		0			0
$697$	−394.127	−	682.648i	−0.565462	−	0.979409i
$698$		0			0
$699$	224.706			0.321468
$700$		0			0
$701$			901.601i			1.28616i	0.765797	+	0.643082i	$0.222345\pi$
$701$			901.601i			1.28616i	−0.765797	+	0.643082i	$0.777655\pi$
$702$		0			0
$703$	−36.1018	+	20.8434i	−0.0513539	+	0.0296492i
$704$		0			0
$705$	−76.4661	+	132.443i	−0.108463	+	0.187863i
$706$		0			0
$707$	215.184	−	216.612i	0.304363	−	0.306382i
$708$		0			0
$709$	−288.215	−	166.401i	−0.406510	−	0.234698i	0.282779	−	0.959185i	$-0.408744\pi$
$709$	−288.215	−	166.401i	−0.406510	−	0.234698i	−0.689289	+	0.724487i	$0.742077\pi$
$710$		0			0
$711$	−713.858	+	412.146i	−1.00402	+	0.579671i
$712$		0			0
$713$	−684.126			−0.959504
$714$		0			0
$715$	1037.50			1.45104
$716$		0			0
$717$	247.352	−	142.809i	0.344982	−	0.199176i
$718$		0			0
$719$	1026.20	+	592.475i	1.42726	+	0.824027i	0.996904	−	0.0786341i	$-0.0250559\pi$
$719$	1026.20	+	592.475i	1.42726	+	0.824027i	0.430353	+	0.902661i	$0.358389\pi$
$720$		0			0
$721$	−425.685	−	112.555i	−0.590410	−	0.156109i
$722$		0			0
$723$	−271.160	+	469.663i	−0.375049	+	0.649603i
$724$		0			0
$725$	−82.7477	+	47.7744i	−0.114135	+	0.0658957i
$726$		0			0
$727$		−	19.9398i		−	0.0274275i	−0.999906	−	0.0137138i	$-0.995635\pi$
$727$		−	19.9398i		−	0.0274275i	0.999906	−	0.0137138i	$-0.00436536\pi$
$728$		0			0
$729$	279.711			0.383691
$730$		0			0
$731$	−254.177	−	440.247i	−0.347711	−	0.602254i
$732$		0			0
$733$	898.325	+	518.648i	1.22555	+	0.707569i	0.966095	−	0.258188i	$-0.0831252\pi$
$733$	898.325	+	518.648i	1.22555	+	0.707569i	0.259450	+	0.965756i	$0.416459\pi$
$734$		0			0
$735$	186.352	+	317.899i	0.253541	+	0.432515i
$736$		0			0
$737$	−490.231	+	849.105i	−0.665171	+	1.15211i
$738$		0			0
$739$	−209.986	−	363.706i	−0.284148	−	0.492160i	0.688254	−	0.725470i	$-0.258378\pi$
$739$	−209.986	−	363.706i	−0.284148	−	0.492160i	−0.972402	+	0.233310i	$0.925044\pi$
$740$		0			0
$741$		−	91.6491i		−	0.123683i
$742$		0			0
$743$			1241.67i			1.67116i	0.549370	+	0.835579i	$0.314868\pi$
$743$			1241.67i			1.67116i	−0.549370	+	0.835579i	$0.685132\pi$
$744$		0			0
$745$	615.551	+	1066.17i	0.826243	+	1.43109i
$746$		0			0
$747$	−89.1137	+	154.349i	−0.119295	+	0.206626i
$748$		0			0
$749$	79.1379	−	299.301i	0.105658	−	0.399601i
$750$		0			0
$751$	561.008	+	323.898i	0.747015	+	0.431289i	0.824614	−	0.565695i	$-0.191392\pi$
$751$	561.008	+	323.898i	0.747015	+	0.431289i	−0.0775992	+	0.996985i	$0.524725\pi$
$752$		0			0
$753$	−132.112	−	228.825i	−0.175448	−	0.303885i
$754$		0			0
$755$	−493.411			−0.653524
$756$		0			0
$757$		−	105.310i		−	0.139116i	−0.997578	−	0.0695578i	$-0.977841\pi$
$757$		−	105.310i		−	0.139116i	0.997578	−	0.0695578i	$-0.0221588\pi$
$758$		0			0
$759$	536.023	−	309.473i	0.706223	−	0.407738i
$760$		0			0
$761$	210.942	−	365.362i	0.277190	−	0.480108i	−0.693495	−	0.720461i	$-0.743930\pi$
$761$	210.942	−	365.362i	0.277190	−	0.480108i	0.970685	+	0.240354i	$0.0772634\pi$
$762$		0			0
$763$	43.4885	−	43.7770i	0.0569967	−	0.0573749i
$764$		0			0
$765$	323.266	+	186.638i	0.422570	+	0.243971i
$766$		0			0
$767$	−186.775	+	107.835i	−0.243514	+	0.140593i
$768$		0			0
$769$	−189.767			−0.246772			−0.123386	−	0.992359i	$-0.539375\pi$
$769$	−189.767			−0.246772			−0.123386	+	0.992359i	$0.539375\pi$
$770$		0			0
$771$	−239.801			−0.311025
$772$		0			0
$773$	729.875	−	421.394i	0.944211	−	0.545141i	0.0529334	−	0.998598i	$-0.483143\pi$
$773$	729.875	−	421.394i	0.944211	−	0.545141i	0.891278	+	0.453457i	$0.149810\pi$
$774$		0			0
$775$	81.9870	+	47.3352i	0.105790	+	0.0610777i
$776$		0			0
$777$	41.6695	+	153.481i	0.0536287	+	0.197530i
$778$		0			0
$779$	91.5174	−	158.513i	0.117481	−	0.203482i
$780$		0			0
$781$	−139.323	+	80.4382i	−0.178391	+	0.102994i
$782$		0			0
$783$		−	573.712i		−	0.732710i
$784$		0			0
$785$	−540.181			−0.688128
$786$		0			0
$787$	747.098	+	1294.01i	0.949298	+	1.64423i	0.746907	+	0.664928i	$0.231538\pi$
$787$	747.098	+	1294.01i	0.949298	+	1.64423i	0.202391	+	0.979305i	$0.435129\pi$
$788$		0			0
$789$	289.553	+	167.173i	0.366987	+	0.211880i
$790$		0			0
$791$	−820.164	+	222.671i	−1.03687	+	0.281506i
$792$		0			0
$793$	1000.51	−	1732.93i	1.26168	−	2.18529i
$794$		0			0
$795$	17.9206	+	31.0394i	0.0225417	+	0.0390433i
$796$		0			0
$797$			292.040i			0.366424i	0.983073	+	0.183212i	$0.0586494\pi$
$797$			292.040i			0.366424i	−0.983073	+	0.183212i	$0.941351\pi$
$798$		0			0
$799$			264.947i			0.331598i
$800$		0			0
$801$	−494.414	−	856.349i	−0.617245	−	1.06910i
$802$		0			0
$803$	610.205	−	1056.91i	0.759906	−	1.31620i
$804$		0			0
$805$	686.859	+	682.332i	0.853241	+	0.847617i
$806$		0			0
$807$	316.007	+	182.447i	0.391582	+	0.226080i
$808$		0			0
$809$	−78.4531	−	135.885i	−0.0969754	−	0.167966i	0.813456	−	0.581627i	$-0.197583\pi$
$809$	−78.4531	−	135.885i	−0.0969754	−	0.167966i	−0.910431	+	0.413660i	$0.864250\pi$
$810$		0			0
$811$	−1183.00			−1.45869			−0.729347	−	0.684144i	$-0.760176\pi$
$811$	−1183.00			−1.45869			−0.729347	+	0.684144i	$0.760176\pi$
$812$		0			0
$813$		−	193.527i		−	0.238040i
$814$		0			0
$815$	−324.015	+	187.070i	−0.397565	+	0.229534i
$816$		0			0
$817$	59.0206	−	102.227i	0.0722406	−	0.125124i
$818$		0			0
$819$	781.083	+	206.525i	0.953703	+	0.252167i
$820$		0			0
$821$	160.574	+	92.7074i	0.195583	+	0.112920i	0.594594	−	0.804026i	$-0.297313\pi$
$821$	160.574	+	92.7074i	0.195583	+	0.112920i	−0.399010	+	0.916946i	$0.630646\pi$
$822$		0			0
$823$	564.922	−	326.158i	0.686418	−	0.396304i	−0.115850	−	0.993267i	$-0.536959\pi$
$823$	564.922	−	326.158i	0.686418	−	0.396304i	0.802269	+	0.596963i	$0.203626\pi$
$824$		0			0
$825$	−85.6506			−0.103819
$826$		0			0
$827$	829.430			1.00294			0.501469	−	0.865176i	$-0.332793\pi$
$827$	829.430			1.00294			0.501469	+	0.865176i	$0.332793\pi$
$828$		0			0
$829$	653.961	−	377.565i	0.788856	−	0.455446i	−0.0507039	−	0.998714i	$-0.516146\pi$
$829$	653.961	−	377.565i	0.788856	−	0.455446i	0.839560	+	0.543268i	$0.182813\pi$
$830$		0			0
$831$	−364.837	−	210.639i	−0.439034	−	0.253476i
$832$		0			0
$833$	554.963	+	315.534i	0.666222	+	0.378792i
$834$		0			0
$835$	−300.113	+	519.811i	−0.359417	+	0.622528i
$836$		0			0
$837$	−492.281	+	284.219i	−0.588150	+	0.339568i
$838$		0			0
$839$			88.6147i			0.105619i	0.998605	+	0.0528097i	$0.0168177\pi$
$839$			88.6147i			0.105619i	−0.998605	+	0.0528097i	$0.983182\pi$
$840$		0			0
$841$	322.522			0.383499
$842$		0			0
$843$	−229.183	−	396.956i	−0.271866	−	0.470885i
$844$		0			0
$845$	−666.013	−	384.523i	−0.788181	−	0.455056i
$846$		0			0
$847$	−57.7177	+	218.290i	−0.0681437	+	0.257721i
$848$		0			0
$849$	−46.7343	+	80.9461i	−0.0550462	+	0.0953429i
$850$		0			0
$851$	208.925	+	361.869i	0.245506	+	0.425228i
$852$		0			0
$853$		−	367.466i		−	0.430792i	−0.976527	−	0.215396i	$-0.930896\pi$
$853$		−	367.466i		−	0.430792i	0.976527	−	0.215396i	$-0.0691042\pi$
$854$		0			0
$855$			86.6755i			0.101375i
$856$		0			0
$857$	82.6698	+	143.188i	0.0964642	+	0.167081i	0.910219	−	0.414128i	$-0.135913\pi$
$857$	82.6698	+	143.188i	0.0964642	+	0.167081i	−0.813755	+	0.581209i	$0.802580\pi$
$858$		0			0
$859$	−325.486	+	563.758i	−0.378913	+	0.656296i	−0.990904	−	0.134568i	$-0.957035\pi$
$859$	−325.486	+	563.758i	−0.378913	+	0.656296i	0.611992	+	0.790864i	$0.290369\pi$
$860$		0			0
$861$	−495.393	−	492.128i	−0.575370	−	0.571577i
$862$		0			0
$863$	−118.417	−	68.3679i	−0.137215	−	0.0792212i	0.429821	−	0.902914i	$-0.358577\pi$
$863$	−118.417	−	68.3679i	−0.137215	−	0.0792212i	−0.567036	+	0.823693i	$0.691910\pi$
$864$		0			0
$865$	−251.120	−	434.953i	−0.290312	−	0.502836i
$866$		0			0
$867$	196.633			0.226797
$868$		0			0
$869$			1624.51i			1.86941i
$870$		0			0
$871$	1260.26	−	727.611i	1.44691	−	0.835374i
$872$		0			0
$873$	−124.429	+	215.518i	−0.142531	+	0.246871i
$874$		0			0
$875$	−244.239	−	899.606i	−0.279131	−	1.02812i
$876$		0			0
$877$	152.855	+	88.2509i	0.174293	+	0.100628i	0.584609	−	0.811315i	$-0.301248\pi$
$877$	152.855	+	88.2509i	0.174293	+	0.100628i	−0.410316	+	0.911944i	$0.634581\pi$
$878$		0			0
$879$	411.045	−	237.317i	0.467628	−	0.269985i
$880$		0			0
$881$	734.879			0.834142			0.417071	−	0.908874i	$-0.363057\pi$
$881$	734.879			0.834142			0.417071	+	0.908874i	$0.363057\pi$
$882$		0			0
$883$	−872.637			−0.988264			−0.494132	−	0.869387i	$-0.664514\pi$
$883$	−872.637			−0.988264			−0.494132	+	0.869387i	$0.664514\pi$
$884$		0			0
$885$	−76.4443	+	44.1352i	−0.0863778	+	0.0498702i
$886$		0			0
$887$	−20.8696	−	12.0490i	−0.0235282	−	0.0135840i	0.488190	−	0.872738i	$-0.337657\pi$
$887$	−20.8696	−	12.0490i	−0.0235282	−	0.0135840i	−0.511718	+	0.859153i	$0.670991\pi$
$888$		0			0
$889$	408.714	+	1505.42i	0.459746	+	1.69338i
$890$		0			0
$891$	−92.7951	+	160.726i	−0.104147	+	0.180388i
$892$		0			0
$893$	−53.2790	+	30.7607i	−0.0596630	+	0.0344464i
$894$		0			0
$895$			701.740i			0.784067i
$896$		0			0
$897$	−918.652			−1.02414
$898$		0			0
$899$	256.855	+	444.887i	0.285712	+	0.494868i
$900$		0			0
$901$	53.7741	+	31.0465i	0.0596827	+	0.0344578i
$902$		0			0
$903$	−319.485	−	317.379i	−0.353803	−	0.351472i
$904$		0			0
$905$	−518.852	+	898.678i	−0.573317	+	0.993014i
$906$		0			0
$907$	−706.653	−	1223.96i	−0.779110	−	1.34946i	−0.932455	−	0.361285i	$-0.882338\pi$
$907$	−706.653	−	1223.96i	−0.779110	−	1.34946i	0.153345	−	0.988173i	$-0.450995\pi$
$908$		0			0
$909$		−	273.990i		−	0.301419i
$910$		0			0
$911$		−	1778.28i		−	1.95201i	−0.217746	−	0.976005i	$-0.569871\pi$
$911$		−	1778.28i		−	1.95201i	0.217746	−	0.976005i	$-0.430129\pi$
$912$		0			0
$913$	175.625	+	304.192i	0.192361	+	0.333179i
$914$		0			0
$915$	409.493	−	709.263i	0.447534	−	0.775151i
$916$		0			0
$917$	424.176	−	1604.24i	0.462569	−	1.74945i
$918$		0			0
$919$	−774.089	−	446.921i	−0.842317	−	0.486312i	0.0157340	−	0.999876i	$-0.494991\pi$
$919$	−774.089	−	446.921i	−0.842317	−	0.486312i	−0.858051	+	0.513564i	$0.828325\pi$
$920$		0			0
$921$	−44.2270	−	76.6034i	−0.0480206	−	0.0831742i
$922$		0			0
$923$	238.776			0.258696
$924$		0			0
$925$		−	57.8228i		−	0.0625111i
$926$		0			0
$927$	−342.185	+	197.561i	−0.369132	+	0.213118i
$928$		0			0
$929$	364.730	−	631.731i	0.392605	−	0.680012i	−0.600187	−	0.799859i	$-0.704907\pi$
$929$	364.730	−	631.731i	0.392605	−	0.680012i	0.992792	+	0.119848i	$0.0382406\pi$
$930$		0			0
$931$	0.980197	+	148.233i	0.00105284	+	0.159220i
$932$		0			0
$933$	−150.082	−	86.6499i	−0.160860	−	0.0928724i
$934$		0			0
$935$	637.092	−	367.825i	0.681382	−	0.393396i
$936$		0			0
$937$	637.240			0.680085			0.340042	−	0.940410i	$-0.389559\pi$
$937$	637.240			0.680085			0.340042	+	0.940410i	$0.389559\pi$
$938$		0			0
$939$	−347.051			−0.369596
$940$		0			0
$941$	−1518.64	+	876.787i	−1.61386	+	0.931761i	−0.625393	+	0.780310i	$0.715061\pi$
$941$	−1518.64	+	876.787i	−1.61386	+	0.931761i	−0.988465	+	0.151451i	$0.951605\pi$
$942$		0			0
$943$	−1588.87	−	917.332i	−1.68491	−	0.972780i
$944$		0			0
$945$	777.721	+	205.636i	0.822985	+	0.217604i
$946$		0			0
$947$	−436.996	+	756.900i	−0.461453	+	0.799261i	−0.999034	−	0.0439519i	$-0.986005\pi$
$947$	−436.996	+	756.900i	−0.461453	+	0.799261i	0.537580	+	0.843213i	$0.319339\pi$
$948$		0			0
$949$	−1568.68	+	905.679i	−1.65298	+	0.954351i
$950$		0			0
$951$			103.688i			0.109031i
$952$		0			0
$953$	−880.208			−0.923618			−0.461809	−	0.886979i	$-0.652800\pi$
$953$	−880.208			−0.923618			−0.461809	+	0.886979i	$0.652800\pi$
$954$		0			0
$955$	277.191	+	480.110i	0.290253	+	0.502733i
$956$		0			0
$957$	−402.500	−	232.383i	−0.420585	−	0.242825i
$958$		0			0
$959$	47.9861	+	47.6699i	0.0500377	+	0.0497079i
$960$		0			0
$961$	−226.006	+	391.454i	−0.235178	+	0.407340i
$962$		0			0
$963$	−138.906	−	240.592i	−0.144243	−	0.249836i
$964$		0			0
$965$		−	389.771i		−	0.403908i
$966$		0			0
$967$		−	259.016i		−	0.267855i	−0.990991	−	0.133928i	$-0.957241\pi$
$967$		−	259.016i		−	0.267855i	0.990991	−	0.133928i	$-0.0427590\pi$
$968$		0			0
$969$	−32.4925	−	56.2787i	−0.0335320	−	0.0580792i
$970$		0			0
$971$	−216.325	+	374.686i	−0.222786	+	0.385877i	−0.955653	−	0.294495i	$-0.904848\pi$
$971$	−216.325	+	374.686i	−0.222786	+	0.385877i	0.732867	+	0.680372i	$0.238182\pi$
$972$		0			0
$973$	426.013	−	115.661i	0.437835	−	0.118870i
$974$		0			0
$975$	110.093	+	63.5622i	0.112916	+	0.0651920i
$976$		0			0
$977$	−407.755	−	706.252i	−0.417354	−	0.722878i	0.578319	−	0.815811i	$-0.303709\pi$
$977$	−407.755	−	706.252i	−0.417354	−	0.722878i	−0.995672	+	0.0929330i	$0.970376\pi$
$978$		0			0
$979$	−1948.78			−1.99058
$980$		0			0
$981$		−	55.3730i		−	0.0564455i
$982$		0			0
$983$	−120.735	+	69.7061i	−0.122822	+	0.0709116i	−0.560153	−	0.828389i	$-0.689257\pi$
$983$	−120.735	+	69.7061i	−0.122822	+	0.0709116i	0.437330	+	0.899301i	$0.355924\pi$
$984$		0			0
$985$	−488.267	+	845.702i	−0.495702	+	0.858581i
$986$		0			0
$987$	61.4958	+	226.507i	0.0623058	+	0.229491i
$988$		0			0
$989$	−1024.68	−	591.598i	−1.03607	−	0.598178i
$990$		0			0
$991$	−1341.28	+	774.390i	−1.35346	+	0.781423i	−0.988733	−	0.149690i	$-0.952172\pi$
$991$	−1341.28	+	774.390i	−1.35346	+	0.781423i	−0.364731	+	0.931113i	$0.618839\pi$
$992$		0			0
$993$	324.114			0.326399
$994$		0			0
$995$	−1132.18			−1.13786
$996$		0			0
$997$	−1110.67	+	641.248i	−1.11402	+	0.643178i	−0.939867	−	0.341541i	$-0.889051\pi$
$997$	−1110.67	+	641.248i	−1.11402	+	0.643178i	−0.174150	+	0.984719i	$0.555718\pi$
$998$		0			0
$999$	300.676	+	173.595i	0.300977	+	0.173769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.o.d.79.4		12
4.3	odd	2		56.3.k.d.51.5	yes	12
7.2	even	3		1568.3.g.j.687.3		6
7.4	even	3	inner	224.3.o.d.207.3		12
7.5	odd	6		1568.3.g.l.687.4		6
8.3	odd	2	inner	224.3.o.d.79.3		12
8.5	even	2		56.3.k.d.51.4	yes	12
28.3	even	6		392.3.k.l.67.4		12
28.11	odd	6		56.3.k.d.11.4	✓	12
28.19	even	6		392.3.g.i.99.1		6
28.23	odd	6		392.3.g.j.99.1		6
28.27	even	2		392.3.k.l.275.5		12
56.5	odd	6		392.3.g.i.99.2		6
56.11	odd	6	inner	224.3.o.d.207.4		12
56.13	odd	2		392.3.k.l.275.4		12
56.19	even	6		1568.3.g.l.687.3		6
56.37	even	6		392.3.g.j.99.2		6
56.45	odd	6		392.3.k.l.67.5		12
56.51	odd	6		1568.3.g.j.687.4		6
56.53	even	6		56.3.k.d.11.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.4	✓	12	28.11	odd	6
56.3.k.d.11.5	yes	12	56.53	even	6
56.3.k.d.51.4	yes	12	8.5	even	2
56.3.k.d.51.5	yes	12	4.3	odd	2
224.3.o.d.79.3		12	8.3	odd	2	inner
224.3.o.d.79.4		12	1.1	even	1	trivial
224.3.o.d.207.3		12	7.4	even	3	inner
224.3.o.d.207.4		12	56.11	odd	6	inner
392.3.g.i.99.1		6	28.19	even	6
392.3.g.i.99.2		6	56.5	odd	6
392.3.g.j.99.1		6	28.23	odd	6
392.3.g.j.99.2		6	56.37	even	6
392.3.k.l.67.4		12	28.3	even	6
392.3.k.l.67.5		12	56.45	odd	6
392.3.k.l.275.4		12	56.13	odd	2
392.3.k.l.275.5		12	28.27	even	2
1568.3.g.j.687.3		6	7.2	even	3
1568.3.g.j.687.4		6	56.51	odd	6
1568.3.g.l.687.3		6	56.19	even	6
1568.3.g.l.687.4		6	7.5	odd	6

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.824388 + 1.42788i) q^{3} +(3.95004 + 2.28056i) q^{5} +(6.75545 - 1.83408i) q^{7} +(3.14077 - 5.43997i) q^{9} +O(q^{10})\)	\(q+(0.824388 + 1.42788i) q^{3} +(3.95004 + 2.28056i) q^{5} +(6.75545 - 1.83408i) q^{7} +(3.14077 - 5.43997i) q^{9} +(-6.18983 - 10.7211i) q^{11} +18.3741i q^{13} +7.52026i q^{15} +(6.51422 + 11.2830i) q^{17} +(-1.51262 + 2.61993i) q^{19} +(8.18796 + 8.13400i) q^{21} +(26.2611 + 15.1619i) q^{23} +(-2.09812 - 3.63405i) q^{25} +25.1958 q^{27} -22.7701i q^{29} +(-19.5382 + 11.2804i) q^{31} +(10.2056 - 17.6767i) q^{33} +(30.8670 + 8.16151i) q^{35} +(11.9335 + 6.88983i) q^{37} +(-26.2361 + 15.1474i) q^{39} -60.5026 q^{41} -39.0188 q^{43} +(24.8123 - 14.3254i) q^{45} +(17.6115 + 10.1680i) q^{47} +(42.2723 - 24.7801i) q^{49} +(-10.7405 + 18.6031i) q^{51} +(4.12744 - 2.38298i) q^{53} -56.4650i q^{55} -4.98794 q^{57} +(5.86884 + 10.1651i) q^{59} +(-94.3137 - 54.4520i) q^{61} +(11.2400 - 42.5099i) q^{63} +(-41.9033 + 72.5786i) q^{65} +(-39.5997 - 68.5887i) q^{67} +49.9970i q^{69} -12.9952i q^{71} +(49.2909 + 85.3744i) q^{73} +(3.45933 - 5.99173i) q^{75} +(-61.4784 - 61.0732i) q^{77} +(-113.644 - 65.6123i) q^{79} +(-7.49577 - 12.9831i) q^{81} -28.3732 q^{83} +59.4242i q^{85} +(32.5130 - 18.7714i) q^{87} +(78.7090 - 136.328i) q^{89} +(33.6996 + 124.126i) q^{91} +(-32.2141 - 18.5988i) q^{93} +(-11.9498 + 6.89923i) q^{95} -39.6175 q^{97} -77.7633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 40 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 - 40 * q^9	\( 12 q + 6 q^{3} - 40 q^{9} - 30 q^{11} + 30 q^{17} - 78 q^{19} - 92 q^{25} - 156 q^{27} - 78 q^{33} + 222 q^{35} - 232 q^{41} + 200 q^{43} + 372 q^{49} - 10 q^{51} + 332 q^{57} + 110 q^{59} - 32 q^{65} - 434 q^{67} + 102 q^{73} + 60 q^{75} - 82 q^{81} + 536 q^{83} + 214 q^{89} + 8 q^{91} - 152 q^{97} - 504 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 40 * q^9 - 30 * q^11 + 30 * q^17 - 78 * q^19 - 92 * q^25 - 156 * q^27 - 78 * q^33 + 222 * q^35 - 232 * q^41 + 200 * q^43 + 372 * q^49 - 10 * q^51 + 332 * q^57 + 110 * q^59 - 32 * q^65 - 434 * q^67 + 102 * q^73 + 60 * q^75 - 82 * q^81 + 536 * q^83 + 214 * q^89 + 8 * q^91 - 152 * q^97 - 504 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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