LMFDB - Embedded newform 1368.2.e.e.379.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (of order $2$, degree $1$, 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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.319794774016000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + 2x^{8} + 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 + 2x^8 + 8x^4 - 32x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.6
Root			$0.491416 - 1.32609i$ of defining polynomial
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.e.379.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.491416 + 1.32609i) q^{2} +(-1.51702 - 1.30332i) q^{4} +2.08884i q^{5} -2.23607i q^{7} +(2.47381 - 1.37123i) q^{8} +O(q^{10})$	\(q+(-0.491416 + 1.32609i) q^{2} +(-1.51702 - 1.30332i) q^{4} +2.08884i q^{5} -2.23607i q^{7} +(2.47381 - 1.37123i) q^{8} +(-2.76999 - 1.02649i) q^{10} +0.602705 q^{11} +1.29574 q^{13} +(2.96522 + 1.09884i) q^{14} +(0.602705 + 3.95433i) q^{16} -2.20541 q^{17} +(-2.60270 + 3.49656i) q^{19} +(2.72243 - 3.16881i) q^{20} +(-0.296179 + 0.799240i) q^{22} -6.19040i q^{23} +0.636747 q^{25} +(-0.636747 + 1.71826i) q^{26} +(-2.91432 + 3.39216i) q^{28} +8.20902 q^{29} +4.94762 q^{31} +(-5.53997 - 1.14398i) q^{32} +(1.08377 - 2.92457i) q^{34} +4.67079 q^{35} +6.91328 q^{37} +(-3.35774 - 5.16968i) q^{38} +(2.86428 + 5.16739i) q^{40} +6.53862i q^{41} -0.191885 q^{43} +(-0.914316 - 0.785518i) q^{44} +(8.20902 + 3.04206i) q^{46} -0.223348i q^{47} +2.00000 q^{49} +(-0.312907 + 0.844383i) q^{50} +(-1.96566 - 1.68877i) q^{52} +4.83659 q^{53} +1.25895i q^{55} +(-3.06617 - 5.53160i) q^{56} +(-4.03404 + 10.8859i) q^{58} +5.60395i q^{59} +11.7743i q^{61} +(-2.43134 + 6.56098i) q^{62} +(4.23945 - 6.78432i) q^{64} +2.70659i q^{65} -6.23902i q^{67} +(3.34565 + 2.87436i) q^{68} +(-2.29530 + 6.19388i) q^{70} +12.4867 q^{71} -8.27349 q^{73} +(-3.39730 + 9.16762i) q^{74} +(8.50550 - 1.91219i) q^{76} -1.34769i q^{77} -15.4017 q^{79} +(-8.25997 + 1.25895i) q^{80} +(-8.67079 - 3.21318i) q^{82} -2.00000 q^{83} -4.60675i q^{85} +(0.0942954 - 0.254457i) q^{86} +(1.49098 - 0.826448i) q^{88} +7.44762i q^{89} -2.89736i q^{91} +(-8.06808 + 9.39097i) q^{92} +(0.296179 + 0.109757i) q^{94} +(-7.30375 - 5.43663i) q^{95} +17.6018i q^{97} +(-0.982832 + 2.65218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4}+O(q^{10}) $ 12 * q + 4 * q^4	$ 12 q + 4 q^{4} - 12 q^{17} - 24 q^{19} - 4 q^{20} - 44 q^{25} + 44 q^{26} - 20 q^{28} - 40 q^{35} - 4 q^{38} - 24 q^{43} + 4 q^{44} + 24 q^{49} - 4 q^{58} + 8 q^{62} - 8 q^{64} - 12 q^{68} + 4 q^{73} - 48 q^{74} - 12 q^{76} - 32 q^{80} - 8 q^{82} - 24 q^{83} - 8 q^{92}+O(q^{100}) $ 12 * q + 4 * q^4 - 12 * q^17 - 24 * q^19 - 4 * q^20 - 44 * q^25 + 44 * q^26 - 20 * q^28 - 40 * q^35 - 4 * q^38 - 24 * q^43 + 4 * q^44 + 24 * q^49 - 4 * q^58 + 8 * q^62 - 8 * q^64 - 12 * q^68 + 4 * q^73 - 48 * q^74 - 12 * q^76 - 32 * q^80 - 8 * q^82 - 24 * q^83 - 8 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.491416	+	1.32609i	−0.347483	+	0.937686i
$2$	−0.491416	+	1.32609i	−0.347483	+	0.937686i
$3$		0			0
$3$		0			0
$4$	−1.51702	−	1.30332i	−0.758510	−	0.651661i
$5$			2.08884i			0.934158i	0.884216	+	0.467079i	$0.154694\pi$
$5$			2.08884i			0.934158i	−0.884216	+	0.467079i	$0.845306\pi$
$6$		0			0
$7$		−	2.23607i		−	0.845154i	−0.906327	−	0.422577i	$-0.861126\pi$
$7$		−	2.23607i		−	0.845154i	0.906327	−	0.422577i	$-0.138874\pi$
$8$	2.47381	−	1.37123i	0.874623	−	0.484803i
$9$		0			0
$10$	−2.76999	−	1.02649i	−0.875947	−	0.324604i
$11$	0.602705			0.181722			0.0908612	−	0.995864i	$-0.471038\pi$
$11$	0.602705			0.181722			0.0908612	+	0.995864i	$0.471038\pi$
$12$		0			0
$13$	1.29574			0.359373			0.179687	−	0.983724i	$-0.442492\pi$
$13$	1.29574			0.359373			0.179687	+	0.983724i	$0.442492\pi$
$14$	2.96522	+	1.09884i	0.792489	+	0.293677i
$15$		0			0
$16$	0.602705	+	3.95433i	0.150676	+	0.988583i
$17$	−2.20541			−0.534890			−0.267445	−	0.963573i	$-0.586179\pi$
$17$	−2.20541			−0.534890			−0.267445	+	0.963573i	$0.586179\pi$
$18$		0			0
$19$	−2.60270	+	3.49656i	−0.597101	+	0.802166i
$19$	−2.60270	+	3.49656i	−0.597101	+	0.802166i
$20$	2.72243	−	3.16881i	0.608754	−	0.708568i
$21$		0			0
$22$	−0.296179	+	0.799240i	−0.0631455	+	0.170399i
$23$		−	6.19040i		−	1.29079i	−0.763850	−	0.645394i	$-0.776693\pi$
$23$		−	6.19040i		−	1.29079i	0.763850	−	0.645394i	$-0.223307\pi$
$24$		0			0
$25$	0.636747			0.127349
$26$	−0.636747	+	1.71826i	−0.124876	+	0.336979i
$27$		0			0
$28$	−2.91432	+	3.39216i	−0.550754	+	0.641058i
$29$	8.20902			1.52438			0.762188	−	0.647355i	$-0.224125\pi$
$29$	8.20902			1.52438			0.762188	+	0.647355i	$0.224125\pi$
$30$		0			0
$31$	4.94762			0.888618			0.444309	−	0.895874i	$-0.353449\pi$
$31$	4.94762			0.888618			0.444309	+	0.895874i	$0.353449\pi$
$32$	−5.53997	−	1.14398i	−0.979338	−	0.202229i
$33$		0			0
$34$	1.08377	−	2.92457i	0.185866	−	0.501559i
$35$	4.67079			0.789507
$36$		0			0
$37$	6.91328			1.13654			0.568268	−	0.822843i	$-0.307614\pi$
$37$	6.91328			1.13654			0.568268	+	0.822843i	$0.307614\pi$
$38$	−3.35774	−	5.16968i	−0.544697	−	0.838633i
$39$		0			0
$40$	2.86428	+	5.16739i	0.452883	+	0.817036i
$41$			6.53862i			1.02116i	0.859830	+	0.510580i	$0.170569\pi$
$41$			6.53862i			1.02116i	−0.859830	+	0.510580i	$0.829431\pi$
$42$		0			0
$43$	−0.191885			−0.0292622			−0.0146311	−	0.999893i	$-0.504657\pi$
$43$	−0.191885			−0.0292622			−0.0146311	+	0.999893i	$0.504657\pi$
$44$	−0.914316	−	0.785518i	−0.137838	−	0.118421i
$45$		0			0
$46$	8.20902	+	3.04206i	1.21035	+	0.448527i
$47$		−	0.223348i		−	0.0325786i	−0.999867	−	0.0162893i	$-0.994815\pi$
$47$		−	0.223348i		−	0.0325786i	0.999867	−	0.0162893i	$-0.00518528\pi$
$48$		0			0
$49$	2.00000			0.285714
$50$	−0.312907	+	0.844383i	−0.0442518	+	0.119414i
$51$		0			0
$52$	−1.96566	−	1.68877i	−0.272588	−	0.234190i
$53$	4.83659			0.664357			0.332178	−	0.943217i	$-0.392216\pi$
$53$	4.83659			0.664357			0.332178	+	0.943217i	$0.392216\pi$
$54$		0			0
$55$			1.25895i			0.169757i
$56$	−3.06617	−	5.53160i	−0.409734	−	0.739192i
$57$		0			0
$58$	−4.03404	+	10.8859i	−0.529696	+	1.42939i
$59$			5.60395i			0.729573i	0.931091	+	0.364786i	$0.118858\pi$
$59$			5.60395i			0.729573i	−0.931091	+	0.364786i	$0.881142\pi$
$60$		0			0
$61$			11.7743i			1.50754i	0.657138	+	0.753770i	$0.271767\pi$
$61$			11.7743i			1.50754i	−0.657138	+	0.753770i	$0.728233\pi$
$62$	−2.43134	+	6.56098i	−0.308780	+	0.833245i
$63$		0			0
$64$	4.23945	−	6.78432i	0.529931	−	0.848040i
$65$			2.70659i			0.335711i
$66$		0			0
$67$		−	6.23902i		−	0.762218i	−0.924530	−	0.381109i	$-0.875542\pi$
$67$		−	6.23902i		−	0.762218i	0.924530	−	0.381109i	$-0.124458\pi$
$68$	3.34565	+	2.87436i	0.405720	+	0.348567i
$69$		0			0
$70$	−2.29530	+	6.19388i	−0.274341	+	0.740310i
$71$	12.4867			1.48190			0.740950	−	0.671560i	$-0.234376\pi$
$71$	12.4867			1.48190			0.740950	+	0.671560i	$0.234376\pi$
$72$		0			0
$73$	−8.27349			−0.968339			−0.484170	−	0.874974i	$-0.660878\pi$
$73$	−8.27349			−0.968339			−0.484170	+	0.874974i	$0.660878\pi$
$74$	−3.39730	+	9.16762i	−0.394928	+	1.06571i
$75$		0			0
$76$	8.50550	−	1.91219i	0.975648	−	0.219343i
$77$		−	1.34769i		−	0.153583i
$78$		0			0
$79$	−15.4017			−1.73283			−0.866416	−	0.499323i	$-0.833582\pi$
$79$	−15.4017			−1.73283			−0.866416	+	0.499323i	$0.833582\pi$
$80$	−8.25997	+	1.25895i	−0.923493	+	0.140755i
$81$		0			0
$82$	−8.67079	−	3.21318i	−0.957528	−	0.354837i
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$		0			0
$85$		−	4.60675i		−	0.499672i
$86$	0.0942954	−	0.254457i	0.0101681	−	0.0274388i
$87$		0			0
$88$	1.49098	−	0.826448i	0.158939	−	0.0880996i
$89$			7.44762i			0.789446i	0.918800	+	0.394723i	$0.129159\pi$
$89$			7.44762i			0.789446i	−0.918800	+	0.394723i	$0.870841\pi$
$90$		0			0
$91$		−	2.89736i		−	0.303726i
$92$	−8.06808	+	9.39097i	−0.841156	+	0.979076i
$93$		0			0
$94$	0.296179	+	0.109757i	0.0305485	+	0.0113205i
$95$	−7.30375	−	5.43663i	−0.749349	−	0.557787i
$96$		0			0
$97$			17.6018i			1.78719i	0.448870	+	0.893597i	$0.351827\pi$
$97$			17.6018i			1.78719i	−0.448870	+	0.893597i	$0.648173\pi$
$98$	−0.982832	+	2.65218i	−0.0992810	+	0.267910i
$99$		0			0
$100$	−0.965958	−	0.829886i	−0.0965958	−	0.0829886i
$101$			3.73098i			0.371247i	0.982621	+	0.185623i	$0.0594305\pi$
$101$			3.73098i			0.371247i	−0.982621	+	0.185623i	$0.940570\pi$
$102$		0			0
$103$	16.4180			1.61772			0.808859	−	0.588003i	$-0.200086\pi$
$103$	16.4180			1.61772			0.808859	+	0.588003i	$0.200086\pi$
$104$	3.20541	−	1.77676i	0.314316	−	0.174225i
$105$		0			0
$106$	−2.37678	+	6.41375i	−0.230853	+	0.622958i
$107$			6.51295i			0.629631i	0.949153	+	0.314815i	$0.101943\pi$
$107$			6.51295i			0.629631i	−0.949153	+	0.314815i	$0.898057\pi$
$108$		0			0
$109$	4.83659			0.463261			0.231631	−	0.972804i	$-0.425594\pi$
$109$	4.83659			0.463261			0.231631	+	0.972804i	$0.425594\pi$
$110$	−1.66948	−	0.618670i	−0.159179	−	0.0589879i
$111$		0			0
$112$	8.84216	−	1.34769i	0.835505	−	0.127345i
$113$		−	14.1309i		−	1.32933i	−0.747143	−	0.664663i	$-0.768575\pi$
$113$		−	14.1309i		−	1.32933i	0.747143	−	0.664663i	$-0.231425\pi$
$114$		0			0
$115$	12.9308			1.20580
$116$	−12.4533	−	10.6990i	−1.15626	−	0.993376i
$117$		0			0
$118$	−7.43134	−	2.75387i	−0.684110	−	0.253514i
$119$			4.93145i			0.452065i
$120$		0			0
$121$	−10.6367			−0.966977
$122$	−15.6137	−	5.78606i	−1.41360	−	0.523845i
$123$		0			0
$124$	−7.50564	−	6.44834i	−0.674026	−	0.579078i
$125$			11.7743i			1.05312i
$126$		0			0
$127$	−4.16667			−0.369732			−0.184866	−	0.982764i	$-0.559185\pi$
$127$	−4.16667			−0.369732			−0.184866	+	0.982764i	$0.559185\pi$
$128$	6.91328	+	8.95581i	0.611053	+	0.791589i
$129$		0			0
$130$	−3.58918	−	1.33006i	−0.314792	−	0.116654i
$131$	10.2600			0.896418			0.448209	−	0.893929i	$-0.352062\pi$
$131$	10.2600			0.896418			0.448209	+	0.893929i	$0.352062\pi$
$132$		0			0
$133$	7.81854	+	5.81983i	0.677954	+	0.504643i
$134$	8.27349	+	3.06595i	0.714721	+	0.264858i
$135$		0			0
$136$	−5.45576	+	3.02413i	−0.467828	+	0.259317i
$137$	17.1362			1.46404			0.732021	−	0.681282i	$-0.238577\pi$
$137$	17.1362			1.46404			0.732021	+	0.681282i	$0.238577\pi$
$138$		0			0
$139$	20.7389			1.75905			0.879524	−	0.475854i	$-0.157861\pi$
$139$	20.7389			1.75905			0.879524	+	0.475854i	$0.157861\pi$
$140$	−7.08568	−	6.08754i	−0.598850	−	0.514491i
$141$		0			0
$142$	−6.13617	+	16.5585i	−0.514936	+	1.38956i
$143$	0.780948			0.0653062
$144$		0			0
$145$			17.1473i			1.42401i
$146$	4.06573	−	10.9714i	0.336482	−	0.907998i
$147$		0			0
$148$	−10.4876	−	9.01023i	−0.862075	−	0.740636i
$149$		−	12.5154i		−	1.02530i	−0.858597	−	0.512651i	$-0.828663\pi$
$149$		−	12.5154i		−	1.02530i	0.858597	−	0.512651i	$-0.171337\pi$
$150$		0			0
$151$	−3.93133			−0.319927			−0.159963	−	0.987123i	$-0.551138\pi$
$151$	−3.93133			−0.319927			−0.159963	+	0.987123i	$0.551138\pi$
$152$	−1.64400	+	12.2187i	−0.133346	+	0.991070i
$153$		0			0
$154$	1.78716	+	0.662276i	0.144013	+	0.0533677i
$155$			10.3348i			0.830109i
$156$		0			0
$157$		−	1.77676i		−	0.141801i	−0.997483	−	0.0709003i	$-0.977413\pi$
$157$		−	1.77676i		−	0.141801i	0.997483	−	0.0709003i	$-0.0225872\pi$
$158$	7.56866	−	20.4241i	0.602131	−	1.62485i
$159$		0			0
$160$	2.38960	−	11.5721i	0.188914	−	0.914856i
$161$	−13.8422			−1.09091
$162$		0			0
$163$	9.68431			0.758534			0.379267	−	0.925287i	$-0.376176\pi$
$163$	9.68431			0.758534			0.379267	+	0.925287i	$0.376176\pi$
$164$	8.52193	−	9.91922i	0.665451	−	0.774561i
$165$		0			0
$166$	0.982832	−	2.65218i	0.0762825	−	0.205849i
$167$	−2.35614			−0.182323			−0.0911617	−	0.995836i	$-0.529058\pi$
$167$	−2.35614			−0.182323			−0.0911617	+	0.995836i	$0.529058\pi$
$168$		0			0
$169$	−11.3211			−0.870851
$170$	6.10896	+	2.26383i	0.468536	+	0.173628i
$171$		0			0
$172$	0.291094	+	0.250088i	0.0221957	+	0.0190690i
$173$	−16.9769			−1.29073			−0.645366	−	0.763873i	$-0.723295\pi$
$173$	−16.9769			−1.29073			−0.645366	+	0.763873i	$0.723295\pi$
$174$		0			0
$175$		−	1.42381i		−	0.107630i
$176$	0.363253	+	2.38330i	0.0273812	+	0.179648i
$177$		0			0
$178$	−9.87620	−	3.65988i	−0.740252	−	0.274319i
$179$		−	13.9504i		−	1.04270i	−0.853343	−	0.521350i	$-0.825429\pi$
$179$		−	13.9504i		−	1.04270i	0.853343	−	0.521350i	$-0.174571\pi$
$180$		0			0
$181$	−9.89523			−0.735507			−0.367753	−	0.929923i	$-0.619873\pi$
$181$	−9.89523			−0.735507			−0.367753	+	0.929923i	$0.619873\pi$
$182$	3.84216	+	1.42381i	0.284800	+	0.105540i
$183$		0			0
$184$	−8.48847	−	15.3139i	−0.625778	−	1.12895i
$185$			14.4407i			1.06170i
$186$		0			0
$187$	−1.32921			−0.0972016
$188$	−0.291094	+	0.338823i	−0.0212302	+	0.0247112i
$189$		0			0
$190$	10.7986	−	7.01377i	0.783416	−	0.508833i
$191$			16.8403i			1.21852i	0.792969	+	0.609261i	$0.208534\pi$
$191$			16.8403i			1.21852i	−0.792969	+	0.609261i	$0.791466\pi$
$192$		0			0
$193$			13.1706i			0.948040i	0.880514	+	0.474020i	$0.157198\pi$
$193$			13.1706i			0.948040i	−0.880514	+	0.474020i	$0.842802\pi$
$194$	−23.3416	−	8.64982i	−1.67583	−	0.621021i
$195$		0			0
$196$	−3.03404	−	2.60664i	−0.216717	−	0.186189i
$197$		−	22.8074i		−	1.62496i	−0.582990	−	0.812479i	$-0.698117\pi$
$197$		−	22.8074i		−	1.62496i	0.582990	−	0.812479i	$-0.301883\pi$
$198$		0			0
$199$		−	15.0636i		−	1.06783i	−0.845539	−	0.533914i	$-0.820721\pi$
$199$		−	15.0636i		−	1.06783i	0.845539	−	0.533914i	$-0.179279\pi$
$200$	1.57519	−	0.873127i	0.111383	−	0.0617394i
$201$		0			0
$202$	−4.94762	−	1.83347i	−0.348113	−	0.129002i
$203$		−	18.3559i		−	1.28833i
$204$		0			0
$205$	−13.6581			−0.953925
$206$	−8.06808	+	21.7718i	−0.562130	+	1.51691i
$207$		0			0
$208$	0.780948	+	5.12378i	0.0541490	+	0.355270i
$209$	−1.56866	+	2.10739i	−0.108507	+	0.145771i
$210$		0			0
$211$		−	10.1285i		−	0.697277i	−0.937257	−	0.348639i	$-0.886644\pi$
$211$		−	10.1285i		−	0.697277i	0.937257	−	0.348639i	$-0.113356\pi$
$212$	−7.33721	−	6.30364i	−0.503922	−	0.432935i
$213$		0			0
$214$	−8.63675	−	3.20057i	−0.590396	−	0.218786i
$215$		−	0.400818i		−	0.0273355i
$216$		0			0
$217$		−	11.0632i		−	0.751019i
$218$	−2.37678	+	6.41375i	−0.160976	+	0.434394i
$219$		0			0
$220$	1.64082	−	1.90986i	0.110624	−	0.128763i
$221$	−2.85764			−0.192225
$222$		0			0
$223$	7.53909			0.504855			0.252428	−	0.967616i	$-0.418771\pi$
$223$	7.53909			0.504855			0.252428	+	0.967616i	$0.418771\pi$
$224$	−2.55802	+	12.3878i	−0.170915	+	0.827692i
$225$		0			0
$226$	18.7389	+	6.94417i	1.24649	+	0.461919i
$227$			16.2127i			1.07607i	0.842922	+	0.538036i	$0.180834\pi$
$227$			16.2127i			1.07607i	−0.842922	+	0.538036i	$0.819166\pi$
$228$		0			0
$229$		−	24.4495i		−	1.61567i	−0.589409	−	0.807835i	$-0.700639\pi$
$229$		−	24.4495i		−	1.61567i	0.589409	−	0.807835i	$-0.299361\pi$
$230$	−6.35438	+	17.1473i	−0.418995	+	1.13066i
$231$		0			0
$232$	20.3075	−	11.2565i	1.33326	−	0.739023i
$233$	0.774073			0.0507112			0.0253556	−	0.999678i	$-0.491928\pi$
$233$	0.774073			0.0507112			0.0253556	+	0.999678i	$0.491928\pi$
$234$		0			0
$235$	0.466538			0.0304336
$236$	7.30375	−	8.50131i	0.475434	−	0.553388i
$237$		0			0
$238$	−6.53953	−	2.42339i	−0.423895	−	0.157085i
$239$		−	1.20046i		−	0.0776514i	−0.999246	−	0.0388257i	$-0.987638\pi$
$239$		−	1.20046i		−	0.0776514i	0.999246	−	0.0388257i	$-0.0123617\pi$
$240$		0			0
$241$		−	16.7862i		−	1.08129i	−0.841250	−	0.540647i	$-0.818180\pi$
$241$		−	16.7862i		−	1.08129i	0.841250	−	0.540647i	$-0.181820\pi$
$242$	5.22707	−	14.1053i	0.336009	−	0.906721i
$243$		0			0
$244$	15.3457	−	17.8618i	0.982405	−	1.14348i
$245$			4.17768i			0.266902i
$246$		0			0
$247$	−3.37243	+	4.53063i	−0.214582	+	0.288277i
$248$	12.2395	−	6.78432i	0.777206	−	0.430805i
$249$		0			0
$250$	−15.6137	−	5.78606i	−0.987498	−	0.365943i
$251$	23.2178			1.46549			0.732747	−	0.680502i	$-0.238238\pi$
$251$	23.2178			1.46549			0.732747	+	0.680502i	$0.238238\pi$
$252$		0			0
$253$		−	3.73098i		−	0.234565i
$254$	2.04757	−	5.52537i	0.128476	−	0.346693i
$255$		0			0
$256$	−15.2735	+	4.76659i	−0.954593	+	0.297912i
$257$		−	3.97673i		−	0.248062i	−0.992278	−	0.124031i	$-0.960418\pi$
$257$		−	3.97673i		−	0.248062i	0.992278	−	0.124031i	$-0.0395821\pi$
$258$		0			0
$259$		−	15.4586i		−	0.960548i
$260$	3.52756	−	4.10596i	0.218770	−	0.254641i
$261$		0			0
$262$	−5.04191	+	13.6056i	−0.311490	+	0.840558i
$263$		−	14.3809i		−	0.886765i	−0.896333	−	0.443382i	$-0.853778\pi$
$263$		−	14.3809i		−	0.886765i	0.896333	−	0.443382i	$-0.146222\pi$
$264$		0			0
$265$			10.1029i			0.620614i
$266$	−11.5598	+	7.50813i	−0.708774	+	0.460353i
$267$		0			0
$268$	−8.13145	+	9.46473i	−0.496707	+	0.578150i
$269$	9.28271			0.565977			0.282988	−	0.959123i	$-0.408674\pi$
$269$	9.28271			0.565977			0.282988	+	0.959123i	$0.408674\pi$
$270$		0			0
$271$			10.8148i			0.656951i	0.944513	+	0.328475i	$0.106535\pi$
$271$			10.8148i			0.656951i	−0.944513	+	0.328475i	$0.893465\pi$
$272$	−1.32921	−	8.72092i	−0.0805953	−	0.528784i
$273$		0			0
$274$	−8.42098	+	22.7241i	−0.508730	+	1.37281i
$275$	0.383770			0.0231422
$276$		0			0
$277$			14.0229i			0.842557i	0.906931	+	0.421279i	$0.138419\pi$
$277$			14.0229i			0.842557i	−0.906931	+	0.421279i	$0.861581\pi$
$278$	−10.1914	+	27.5016i	−0.611240	+	1.64944i
$279$		0			0
$280$	11.5546	−	6.40473i	0.690521	−	0.382756i
$281$			30.6277i			1.82710i	0.406730	+	0.913548i	$0.366669\pi$
$281$			30.6277i			1.82710i	−0.406730	+	0.913548i	$0.633331\pi$
$282$		0			0
$283$	−9.49243			−0.564266			−0.282133	−	0.959375i	$-0.591042\pi$
$283$	−9.49243			−0.564266			−0.282133	+	0.959375i	$0.591042\pi$
$284$	−18.9426	−	16.2742i	−1.12404	−	0.965696i
$285$		0			0
$286$	−0.383770	+	1.03561i	−0.0226928	+	0.0612367i
$287$	14.6208			0.863039
$288$		0			0
$289$	−12.1362			−0.713892
$290$	−22.7389	−	8.42647i	−1.33527	−	0.494819i
$291$		0			0
$292$	12.5511	+	10.7830i	0.734495	+	0.631029i
$293$	9.93934			0.580663			0.290331	−	0.956926i	$-0.406235\pi$
$293$	9.93934			0.580663			0.290331	+	0.956926i	$0.406235\pi$
$294$		0			0
$295$	−11.7058			−0.681536
$296$	17.1021	−	9.47970i	0.994041	−	0.550996i
$297$		0			0
$298$	16.5965	+	6.15027i	0.961412	+	0.356276i
$299$		−	8.02114i		−	0.463875i
$300$		0			0
$301$			0.429068i			0.0247311i
$302$	1.93192	−	5.21329i	0.111169	−	0.299991i
$303$		0			0
$304$	−15.3952	−	8.18457i	−0.882977	−	0.469417i
$305$	−24.5946			−1.40828
$306$		0			0
$307$		−	16.9668i		−	0.968344i	−0.874973	−	0.484172i	$-0.839121\pi$
$307$		−	16.9668i		−	0.968344i	0.874973	−	0.484172i	$-0.160879\pi$
$308$	−1.75647	+	2.04447i	−0.100084	+	0.116495i
$309$		0			0
$310$	−13.7048	−	5.07867i	−0.778382	−	0.288449i
$311$		−	34.3174i		−	1.94596i	−0.230884	−	0.972981i	$-0.574162\pi$
$311$		−	34.3174i		−	1.94596i	0.230884	−	0.972981i	$-0.425838\pi$
$312$		0			0
$313$	13.5675			0.766881			0.383440	−	0.923566i	$-0.374739\pi$
$313$	13.5675			0.766881			0.383440	+	0.923566i	$0.374739\pi$
$314$	2.35614	+	0.873127i	0.132965	+	0.0492734i
$315$		0			0
$316$	23.3648	+	20.0734i	1.31437	+	1.12922i
$317$	2.07669			0.116638			0.0583192	−	0.998298i	$-0.481426\pi$
$317$	2.07669			0.116638			0.0583192	+	0.998298i	$0.481426\pi$
$318$		0			0
$319$	4.94762			0.277013
$320$	14.1714	+	8.85554i	0.792204	+	0.495040i
$321$		0			0
$322$	6.80226	−	18.3559i	0.379075	−	1.02294i
$323$	5.74003	−	7.71135i	0.319384	−	0.429071i
$324$		0			0
$325$	0.825058			0.0457660
$326$	−4.75903	+	12.8423i	−0.263578	+	0.711267i
$327$		0			0
$328$	8.96596	+	16.1753i	0.495062	+	0.893131i
$329$	−0.499421			−0.0275339
$330$		0			0
$331$			20.1739i			1.10886i	0.832231	+	0.554429i	$0.187063\pi$
$331$			20.1739i			1.10886i	−0.832231	+	0.554429i	$0.812937\pi$
$332$	3.03404	+	2.60664i	0.166515	+	0.143058i
$333$		0			0
$334$	1.15784	−	3.12445i	0.0633544	−	0.170962i
$335$	13.0323			0.712032
$336$		0			0
$337$		−	1.79760i		−	0.0979213i	−0.998801	−	0.0489606i	$-0.984409\pi$
$337$		−	1.79760i		−	0.0979213i	0.998801	−	0.0489606i	$-0.0155909\pi$
$338$	5.56335	−	15.0127i	0.302606	−	0.816585i
$339$		0			0
$340$	−6.00408	+	6.98853i	−0.325617	+	0.379006i
$341$	2.98195			0.161482
$342$		0			0
$343$		−	20.1246i		−	1.08663i
$344$	−0.474687	+	0.263119i	−0.0255934	+	0.0141864i
$345$		0			0
$346$	8.34274	−	22.5129i	0.448508	−	1.21030i
$347$	21.9853			1.18023			0.590117	−	0.807318i	$-0.299082\pi$
$347$	21.9853			1.18023			0.590117	+	0.807318i	$0.299082\pi$
$348$		0			0
$349$		−	6.85543i		−	0.366963i	−0.983023	−	0.183481i	$-0.941263\pi$
$349$		−	6.85543i		−	0.366963i	0.983023	−	0.183481i	$-0.0587367\pi$
$350$	1.88810	+	0.699682i	0.100923	+	0.0373996i
$351$		0			0
$352$	−3.33897	−	0.689483i	−0.177968	−	0.0367496i
$353$	−12.2940			−0.654344			−0.327172	−	0.944965i	$-0.606096\pi$
$353$	−12.2940			−0.654344			−0.327172	+	0.944965i	$0.606096\pi$
$354$		0			0
$355$			26.0827i			1.38433i
$356$	9.70664	−	11.2982i	0.514451	−	0.598803i
$357$		0			0
$358$	18.4994	+	6.85543i	0.977725	+	0.362321i
$359$			14.7691i			0.779484i	0.920924	+	0.389742i	$0.127436\pi$
$359$			14.7691i			0.779484i	−0.920924	+	0.389742i	$0.872564\pi$
$360$		0			0
$361$	−5.45185	−	18.2010i	−0.286940	−	0.957949i
$362$	4.86267	−	13.1220i	0.255576	−	0.689674i
$363$		0			0
$364$	−3.77619	+	4.39536i	−0.197926	+	0.230379i
$365$		−	17.2820i		−	0.904582i
$366$		0			0
$367$		−	21.9240i		−	1.14442i	−0.820106	−	0.572212i	$-0.806085\pi$
$367$		−	21.9240i		−	1.14442i	0.820106	−	0.572212i	$-0.193915\pi$
$368$	24.4789	−	3.73098i	1.27605	−	0.194491i
$369$		0			0
$370$	−19.1497	−	7.09641i	−0.995545	−	0.368925i
$371$		−	10.8149i		−	0.561484i
$372$		0			0
$373$	34.6907			1.79622			0.898109	−	0.439774i	$-0.144941\pi$
$373$	34.6907			1.79622			0.898109	+	0.439774i	$0.144941\pi$
$374$	0.653196	−	1.76265i	0.0337759	−	0.0911446i
$375$		0			0
$376$	−0.306261	−	0.552519i	−0.0157942	−	0.0284940i
$377$	10.6367			0.547820
$378$		0			0
$379$		−	33.2666i		−	1.70879i	−0.519622	−	0.854396i	$-0.673927\pi$
$379$		−	33.2666i		−	1.70879i	0.519622	−	0.854396i	$-0.326073\pi$
$380$	3.99426	+	17.7666i	0.204901	+	0.911409i
$381$		0			0
$382$	−22.3318	−	8.27560i	−1.14259	−	0.423417i
$383$	−33.6303			−1.71843			−0.859214	−	0.511616i	$-0.829047\pi$
$383$	−33.6303			−1.71843			−0.859214	+	0.511616i	$0.829047\pi$
$384$		0			0
$385$	2.81511			0.143471
$386$	−17.4654	−	6.47224i	−0.888964	−	0.329428i
$387$		0			0
$388$	22.9408	−	26.7023i	1.16464	−	1.35561i
$389$			18.2006i			0.922808i	0.887190	+	0.461404i	$0.152654\pi$
$389$			18.2006i			0.922808i	−0.887190	+	0.461404i	$0.847346\pi$
$390$		0			0
$391$			13.6524i			0.690430i
$392$	4.94762	−	2.74246i	0.249892	−	0.138515i
$393$		0			0
$394$	30.2446	+	11.2079i	1.52370	+	0.564646i
$395$		−	32.1718i		−	1.61874i
$396$		0			0
$397$			11.1854i			0.561377i	0.959799	+	0.280688i	$0.0905627\pi$
$397$			11.1854i			0.561377i	−0.959799	+	0.280688i	$0.909437\pi$
$398$	19.9756	+	7.40247i	1.00129	+	0.371053i
$399$		0			0
$400$	0.383770	+	2.51791i	0.0191885	+	0.125895i
$401$		−	22.8703i		−	1.14209i	−0.820919	−	0.571044i	$-0.806538\pi$
$401$		−	22.8703i		−	1.14209i	0.820919	−	0.571044i	$-0.193462\pi$
$402$		0			0
$403$	6.41082			0.319346
$404$	4.86267	−	5.65998i	0.241927	−	0.281595i
$405$		0			0
$406$	24.3416	+	9.02039i	1.20805	+	0.447675i
$407$	4.16667			0.206534
$408$		0			0
$409$			1.65290i			0.0817304i	0.999165	+	0.0408652i	$0.0130114\pi$
$409$			1.65290i			0.0817304i	−0.999165	+	0.0408652i	$0.986989\pi$
$410$	6.71182	−	18.1119i	0.331473	−	0.894483i
$411$		0			0
$412$	−24.9065	−	21.3980i	−1.22706	−	1.05420i
$413$	12.5308			0.616601
$414$		0			0
$415$		−	4.17768i		−	0.205074i
$416$	−7.17836	−	1.48230i	−0.351948	−	0.0726758i
$417$		0			0
$418$	−2.02372	−	3.11579i	−0.0989836	−	0.152398i
$419$	−23.8615			−1.16571			−0.582856	−	0.812576i	$-0.698065\pi$
$419$	−23.8615			−1.16571			−0.582856	+	0.812576i	$0.698065\pi$
$420$		0			0
$421$	6.17644			0.301021			0.150511	−	0.988608i	$-0.451908\pi$
$421$	6.17644			0.301021			0.150511	+	0.988608i	$0.451908\pi$
$422$	13.4313	+	4.97732i	0.653827	+	0.242292i
$423$		0			0
$424$	11.9648	−	6.63208i	0.581062	−	0.322082i
$425$	−1.40429			−0.0681180
$426$		0			0
$427$	26.3281			1.27410
$428$	8.48847	−	9.88028i	0.410306	−	0.477581i
$429$		0			0
$430$	0.531519	+	0.196968i	0.0256321	+	0.00949864i
$431$	−20.9083			−1.00712			−0.503558	−	0.863962i	$-0.667976\pi$
$431$	−20.9083			−1.00712			−0.503558	+	0.863962i	$0.667976\pi$
$432$		0			0
$433$		−	1.41484i		−	0.0679927i	−0.999422	−	0.0339964i	$-0.989177\pi$
$433$		−	1.41484i		−	0.0679927i	0.999422	−	0.0339964i	$-0.0108235\pi$
$434$	14.6708	+	5.43663i	0.704220	+	0.260967i
$435$		0			0
$436$	−7.33721	−	6.30364i	−0.351389	−	0.301889i
$437$	21.6451	+	16.1118i	1.03543	+	0.770731i
$438$		0			0
$439$	−13.5912			−0.648673			−0.324337	−	0.945942i	$-0.605141\pi$
$439$	−13.5912			−0.648673			−0.324337	+	0.945942i	$0.605141\pi$
$440$	1.72632	+	3.11441i	0.0822989	+	0.148474i
$441$		0			0
$442$	1.40429	−	3.78948i	0.0667951	−	0.180247i
$443$	−19.1907			−0.911779			−0.455889	−	0.890036i	$-0.650679\pi$
$443$	−19.1907			−0.911779			−0.455889	+	0.890036i	$0.650679\pi$
$444$		0			0
$445$	−15.5569			−0.737467
$446$	−3.70483	+	9.99751i	−0.175429	+	0.473396i
$447$		0			0
$448$	−15.1702	−	9.47970i	−0.716725	−	0.447874i
$449$		−	14.5341i		−	0.685906i	−0.939353	−	0.342953i	$-0.888573\pi$
$449$		−	14.5341i		−	0.685906i	0.939353	−	0.342953i	$-0.111427\pi$
$450$		0			0
$451$			3.94086i			0.185568i
$452$	−18.4172	+	21.4369i	−0.866270	+	1.00831i
$453$		0			0
$454$	−21.4994	−	7.96716i	−1.00902	−	0.373917i
$455$	6.05212			0.283728
$456$		0			0
$457$	−9.61507			−0.449774			−0.224887	−	0.974385i	$-0.572201\pi$
$457$	−9.61507			−0.449774			−0.224887	+	0.974385i	$0.572201\pi$
$458$	32.4222	+	12.0149i	1.51499	+	0.561419i
$459$		0			0
$460$	−19.6162	−	16.8529i	−0.914611	−	0.785772i
$461$			18.6473i			0.868492i	0.900794	+	0.434246i	$0.142985\pi$
$461$			18.6473i			0.868492i	−0.900794	+	0.434246i	$0.857015\pi$
$462$		0			0
$463$		−	26.6447i		−	1.23829i	−0.785279	−	0.619143i	$-0.787480\pi$
$463$		−	26.6447i		−	1.23829i	0.785279	−	0.619143i	$-0.212520\pi$
$464$	4.94762	+	32.4612i	0.229687	+	1.50697i
$465$		0			0
$466$	−0.380392	+	1.02649i	−0.0176213	+	0.0475512i
$467$	−20.1919			−0.934369			−0.467185	−	0.884160i	$-0.654732\pi$
$467$	−20.1919			−0.934369			−0.467185	+	0.884160i	$0.654732\pi$
$468$		0			0
$469$	−13.9509			−0.644192
$470$	−0.229264	+	0.618670i	−0.0105752	+	0.0285371i
$471$		0			0
$472$	7.68431	+	13.8631i	0.353699	+	0.638101i
$473$	−0.115650			−0.00531760
$474$		0			0
$475$	−1.65726	+	2.22642i	−0.0760405	+	0.102155i
$476$	6.42726	−	7.48111i	0.294593	−	0.342896i
$477$		0			0
$478$	1.59192	+	0.589926i	0.0728126	+	0.0269826i
$479$		−	5.80220i		−	0.265109i	−0.991176	−	0.132555i	$-0.957682\pi$
$479$		−	5.80220i		−	0.265109i	0.991176	−	0.132555i	$-0.0423180\pi$
$480$		0			0
$481$	8.95781			0.408441
$482$	22.2600	+	8.24900i	1.01391	+	0.375732i
$483$		0			0
$484$	16.1362	+	13.8631i	0.733462	+	0.630141i
$485$	−36.7674			−1.66952
$486$		0			0
$487$	−3.70928			−0.168083			−0.0840417	−	0.996462i	$-0.526783\pi$
$487$	−3.70928			−0.168083			−0.0840417	+	0.996462i	$0.526783\pi$
$488$	16.1452	+	29.1273i	0.730860	+	1.31853i
$489$		0			0
$490$	−5.53997	−	2.05298i	−0.250270	−	0.0927441i
$491$	9.68431			0.437047			0.218523	−	0.975832i	$-0.429876\pi$
$491$	9.68431			0.437047			0.218523	+	0.975832i	$0.429876\pi$
$492$		0			0
$493$	−18.1043			−0.815374
$494$	−4.35075	−	6.69856i	−0.195750	−	0.301382i
$495$		0			0
$496$	2.98195	+	19.5645i	0.133894	+	0.878473i
$497$		−	27.9211i		−	1.25243i
$498$		0			0
$499$	28.0804			1.25705			0.628527	−	0.777788i	$-0.283658\pi$
$499$	28.0804			1.25705			0.628527	+	0.777788i	$0.283658\pi$
$500$	15.3457	−	17.8618i	0.686278	−	0.798804i
$501$		0			0
$502$	−11.4096	+	30.7888i	−0.509235	+	1.37417i
$503$			22.9011i			1.02111i	0.859845	+	0.510555i	$0.170560\pi$
$503$			22.9011i			1.02111i	−0.859845	+	0.510555i	$0.829440\pi$
$504$		0			0
$505$	−7.79343			−0.346803
$506$	4.94762	+	1.83347i	0.219948	+	0.0815075i
$507$		0			0
$508$	6.32092	+	5.43051i	0.280446	+	0.240940i
$509$	−38.0190			−1.68516			−0.842582	−	0.538568i	$-0.818965\pi$
$509$	−38.0190			−1.68516			−0.842582	+	0.538568i	$0.818965\pi$
$510$		0			0
$511$			18.5001i			0.818396i
$512$	1.18472	−	22.5964i	0.0523575	−	0.998628i
$513$		0			0
$514$	5.27349	+	1.95423i	0.232604	+	0.0861973i
$515$			34.2947i			1.51120i
$516$		0			0
$517$		−	0.134613i		−	0.00592026i
$518$	20.4994	+	7.59658i	0.900693	+	0.333775i
$519$		0			0
$520$	3.71136	+	6.69559i	0.162754	+	0.293621i
$521$			35.7095i			1.56446i	0.622989	+	0.782231i	$0.285918\pi$
$521$			35.7095i			1.56446i	−0.622989	+	0.782231i	$0.714082\pi$
$522$		0			0
$523$			15.3754i			0.672319i	0.941805	+	0.336160i	$0.109128\pi$
$523$			15.3754i			0.672319i	−0.941805	+	0.336160i	$0.890872\pi$
$524$	−15.5646	−	13.3720i	−0.679942	−	0.584160i
$525$		0			0
$526$	19.0704	+	7.06701i	0.831507	+	0.308136i
$527$	−10.9115			−0.475313
$528$		0			0
$529$	−15.3211			−0.666133
$530$	−13.3973	−	4.96471i	−0.581941	−	0.215653i
$531$		0			0
$532$	−4.27579	−	19.0189i	−0.185379	−	0.824573i
$533$			8.47235i			0.366978i
$534$		0			0
$535$	−13.6045			−0.588174
$536$	−8.55514	−	15.4341i	−0.369526	−	0.666653i
$537$		0			0
$538$	−4.56167	+	12.3097i	−0.196668	+	0.530709i
$539$	1.20541			0.0519207
$540$		0			0
$541$			19.8352i			0.852780i	0.904539	+	0.426390i	$0.140215\pi$
$541$			19.8352i			0.852780i	−0.904539	+	0.426390i	$0.859785\pi$
$542$	−14.3413	−	5.31455i	−0.616014	−	0.228280i
$543$		0			0
$544$	12.2179	+	2.52295i	0.523839	+	0.108171i
$545$			10.1029i			0.432759i
$546$		0			0
$547$		−	15.7838i		−	0.674868i	−0.941349	−	0.337434i	$-0.890441\pi$
$547$		−	15.7838i		−	0.674868i	0.941349	−	0.337434i	$-0.109559\pi$
$548$	−25.9959	−	22.3339i	−1.11049	−	0.954059i
$549$		0			0
$550$	−0.188591	+	0.508913i	−0.00804154	+	0.0217001i
$551$	−21.3657	+	28.7033i	−0.910207	+	1.22280i
$552$		0			0
$553$			34.4394i			1.46451i
$554$	−18.5957	−	6.89110i	−0.790054	−	0.292775i
$555$		0			0
$556$	−31.4613	−	27.0294i	−1.33426	−	1.14630i
$557$			0.429068i			0.0181802i	0.999959	+	0.00909011i	$0.00289351\pi$
$557$			0.429068i			0.0181802i	−0.999959	+	0.00909011i	$0.997106\pi$
$558$		0			0
$559$	−0.248633			−0.0105161
$560$	2.81511	+	18.4699i	0.118960	+	0.780494i
$561$		0			0
$562$	−40.6151	−	15.0509i	−1.71324	−	0.634886i
$563$			8.17604i			0.344579i	0.985046	+	0.172290i	$0.0551165\pi$
$563$			8.17604i			0.344579i	−0.985046	+	0.172290i	$0.944884\pi$
$564$		0			0
$565$	29.5173			1.24180
$566$	4.66473	−	12.5878i	0.196073	−	0.529105i
$567$		0			0
$568$	30.8897	−	17.1222i	1.29610	−	0.718430i
$569$		−	33.8822i		−	1.42041i	−0.703993	−	0.710207i	$-0.748601\pi$
$569$		−	33.8822i		−	1.42041i	0.703993	−	0.710207i	$-0.251399\pi$
$570$		0			0
$571$	−34.1362			−1.42855			−0.714277	−	0.699863i	$-0.753244\pi$
$571$	−34.1362			−1.42855			−0.714277	+	0.699863i	$0.753244\pi$
$572$	−1.18472	−	1.01783i	−0.0495354	−	0.0425575i
$573$		0			0
$574$	−7.18489	+	19.3885i	−0.299892	+	0.809259i
$575$		−	3.94172i		−	0.164381i
$576$		0			0
$577$	−5.41082			−0.225255			−0.112628	−	0.993637i	$-0.535927\pi$
$577$	−5.41082			−0.225255			−0.112628	+	0.993637i	$0.535927\pi$
$578$	5.96391	−	16.0936i	0.248066	−	0.669407i
$579$		0			0
$580$	22.3485	−	26.0129i	0.927970	−	1.08012i
$581$			4.47214i			0.185535i
$582$		0			0
$583$	2.91504			0.120729
$584$	−20.4670	+	11.3449i	−0.846932	+	0.469454i
$585$		0			0
$586$	−4.88435	+	13.1804i	−0.201771	+	0.544479i
$587$	−43.7648			−1.80637			−0.903183	−	0.429257i	$-0.858776\pi$
$587$	−43.7648			−1.80637			−0.903183	+	0.429257i	$0.858776\pi$
$588$		0			0
$589$	−12.8772	+	17.2996i	−0.530595	+	0.712819i
$590$	5.75240	−	15.5229i	0.236822	−	0.639067i
$591$		0			0
$592$	4.16667	+	27.3374i	0.171249	+	1.12356i
$593$	−3.93192			−0.161464			−0.0807322	−	0.996736i	$-0.525726\pi$
$593$	−3.93192			−0.161464			−0.0807322	+	0.996736i	$0.525726\pi$
$594$		0			0
$595$	−10.3010			−0.422300
$596$	−16.3116	+	18.9861i	−0.668150	+	0.777703i
$597$		0			0
$598$	10.6367	+	3.94172i	0.434969	+	0.161189i
$599$	−18.7742			−0.767092			−0.383546	−	0.923522i	$-0.625297\pi$
$599$	−18.7742			−0.767092			−0.383546	+	0.923522i	$0.625297\pi$
$600$		0			0
$601$			27.3529i			1.11575i	0.829926	+	0.557874i	$0.188383\pi$
$601$			27.3529i			1.11575i	−0.829926	+	0.557874i	$0.811617\pi$
$602$	−0.568983	−	0.210851i	−0.0231900	−	0.00859365i
$603$		0			0
$604$	5.96391	+	5.12378i	0.242668	+	0.208484i
$605$		−	22.2185i		−	0.903309i
$606$		0			0
$607$	−33.8391			−1.37349			−0.686743	−	0.726901i	$-0.740960\pi$
$607$	−33.8391			−1.37349			−0.686743	+	0.726901i	$0.740960\pi$
$608$	18.4189	−	16.3934i	0.746986	−	0.664840i
$609$		0			0
$610$	12.0862	−	32.6146i	0.489354	−	1.32052i
$611$		−	0.289400i		−	0.0117079i
$612$		0			0
$613$			15.7997i			0.638144i	0.947730	+	0.319072i	$0.103371\pi$
$613$			15.7997i			0.638144i	−0.947730	+	0.319072i	$0.896629\pi$
$614$	22.4994	+	8.33773i	0.908003	+	0.336484i
$615$		0			0
$616$	−1.84799	−	3.33392i	−0.0744578	−	0.134328i
$617$	31.4983			1.26807			0.634036	−	0.773303i	$-0.281397\pi$
$617$	31.4983			1.26807			0.634036	+	0.773303i	$0.281397\pi$
$618$		0			0
$619$	−8.04103			−0.323196			−0.161598	−	0.986857i	$-0.551665\pi$
$619$	−8.04103			−0.323196			−0.161598	+	0.986857i	$0.551665\pi$
$620$	13.4695	−	15.6781i	0.540950	−	0.629647i
$621$		0			0
$622$	45.5079	+	16.8641i	1.82470	+	0.676190i
$623$	16.6534			0.667203
$624$		0			0
$625$	−21.4108			−0.856433
$626$	−6.66729	+	17.9917i	−0.266478	+	0.719093i
$627$		0			0
$628$	−2.31569	+	2.69538i	−0.0924060	+	0.107557i
$629$	−15.2466			−0.607922
$630$		0			0
$631$			30.6449i			1.21996i	0.792419	+	0.609978i	$0.208822\pi$
$631$			30.6449i			1.21996i	−0.792419	+	0.609978i	$0.791178\pi$
$632$	−38.1010	+	21.1194i	−1.51558	+	0.840083i
$633$		0			0
$634$	−1.02052	+	2.75387i	−0.0405299	+	0.109370i
$635$		−	8.70350i		−	0.345388i
$636$		0			0
$637$	2.59148			0.102678
$638$	−2.43134	+	6.56098i	−0.0962575	+	0.259752i
$639$		0			0
$640$	−18.7073	+	14.4407i	−0.739469	+	0.570820i
$641$		−	6.08412i		−	0.240308i	−0.992755	−	0.120154i	$-0.961661\pi$
$641$		−	6.08412i		−	0.240308i	0.992755	−	0.120154i	$-0.0383389\pi$
$642$		0			0
$643$	6.98648			0.275520			0.137760	−	0.990466i	$-0.456010\pi$
$643$	6.98648			0.275520			0.137760	+	0.990466i	$0.456010\pi$
$644$	20.9988	+	18.0408i	0.827470	+	0.710906i
$645$		0			0
$646$	7.40518	+	11.4013i	0.291353	+	0.448577i
$647$		−	42.0486i		−	1.65310i	−0.562862	−	0.826551i	$-0.690300\pi$
$647$		−	42.0486i		−	1.65310i	0.562862	−	0.826551i	$-0.309700\pi$
$648$		0			0
$649$			3.37753i			0.132580i
$650$	−0.405446	+	1.09410i	−0.0159029	+	0.0429141i
$651$		0			0
$652$	−14.6913	−	12.6218i	−0.575356	−	0.494307i
$653$			15.7745i			0.617303i	0.951175	+	0.308651i	$0.0998777\pi$
$653$			15.7745i			0.617303i	−0.951175	+	0.308651i	$0.900122\pi$
$654$		0			0
$655$			21.4314i			0.837395i
$656$	−25.8559	+	3.94086i	−1.00950	+	0.153865i
$657$		0			0
$658$	0.245423	−	0.662276i	0.00956759	−	0.0258182i
$659$		−	4.40556i		−	0.171616i	−0.996312	−	0.0858080i	$-0.972653\pi$
$659$		−	4.40556i		−	0.171616i	0.996312	−	0.0858080i	$-0.0273472\pi$
$660$		0			0
$661$	−24.2366			−0.942694			−0.471347	−	0.881948i	$-0.656232\pi$
$661$	−24.2366			−0.942694			−0.471347	+	0.881948i	$0.656232\pi$
$662$	−26.7524	−	9.91378i	−1.03976	−	0.385310i
$663$		0			0
$664$	−4.94762	+	2.74246i	−0.192005	+	0.106428i
$665$	−12.1567	+	16.3317i	−0.471416	+	0.633316i
$666$		0			0
$667$		−	50.8171i		−	1.96765i
$668$	3.57431	+	3.07081i	0.138294	+	0.118813i
$669$		0			0
$670$	−6.40429	+	17.2820i	−0.247419	+	0.667662i
$671$			7.09641i			0.273954i
$672$		0			0
$673$		−	37.6208i		−	1.45018i	−0.688656	−	0.725088i	$-0.741799\pi$
$673$		−	37.6208i		−	1.45018i	0.688656	−	0.725088i	$-0.258201\pi$
$674$	2.38377	+	0.883367i	0.0918194	+	0.0340260i
$675$		0			0
$676$	17.1743	+	14.7550i	0.660549	+	0.567499i
$677$	29.2511			1.12421			0.562106	−	0.827065i	$-0.309991\pi$
$677$	29.2511			1.12421			0.562106	+	0.827065i	$0.309991\pi$
$678$		0			0
$679$	39.3589			1.51046
$680$	−6.31692	−	11.3962i	−0.242243	−	0.437025i
$681$		0			0
$682$	−1.46538	+	3.95433i	−0.0561123	+	0.151419i
$683$			14.2243i			0.544278i	0.962258	+	0.272139i	$0.0877310\pi$
$683$			14.2243i			0.544278i	−0.962258	+	0.272139i	$0.912269\pi$
$684$		0			0
$685$			35.7947i			1.36765i
$686$	26.6870	+	9.88955i	1.01891	+	0.377585i
$687$		0			0
$688$	−0.115650	−	0.758778i	−0.00440912	−	0.0289281i
$689$	6.26696			0.238752
$690$		0			0
$691$	−27.0135			−1.02764			−0.513821	−	0.857897i	$-0.671771\pi$
$691$	−27.0135			−1.02764			−0.513821	+	0.857897i	$0.671771\pi$
$692$	25.7544	+	22.1264i	0.979034	+	0.841120i
$693$		0			0
$694$	−10.8039	+	29.1545i	−0.410112	+	1.10669i
$695$			43.3202i			1.64323i
$696$		0			0
$697$		−	14.4203i		−	0.546209i
$698$	9.09091	+	3.36887i	0.344096	+	0.127514i
$699$		0			0
$700$	−1.85568	+	2.15995i	−0.0701382	+	0.0816384i
$701$			45.2033i			1.70731i	0.520843	+	0.853653i	$0.325618\pi$
$701$			45.2033i			1.70731i	−0.520843	+	0.853653i	$0.674382\pi$
$702$		0			0
$703$	−17.9932	+	24.1727i	−0.678627	+	0.911690i
$704$	2.55514	−	4.08895i	0.0963004	−	0.154108i
$705$		0			0
$706$	6.04147	−	16.3029i	0.227374	−	0.613569i
$707$	8.34274			0.313761
$708$		0			0
$709$			14.1576i			0.531698i	0.964015	+	0.265849i	$0.0856523\pi$
$709$			14.1576i			0.531698i	−0.964015	+	0.265849i	$0.914348\pi$
$710$	−34.5880	−	12.8175i	−1.29807	−	0.481031i
$711$		0			0
$712$	10.2124	+	18.4240i	0.382726	+	0.690468i
$713$		−	30.6277i		−	1.14702i
$714$		0			0
$715$			1.63128i			0.0610063i
$716$	−18.1818	+	21.1630i	−0.679486	+	0.790898i
$717$		0			0
$718$	−19.5851	−	7.25777i	−0.730911	−	0.270858i
$719$		−	5.67260i		−	0.211552i	−0.994390	−	0.105776i	$-0.966267\pi$
$719$		−	5.67260i		−	0.211552i	0.994390	−	0.105776i	$-0.0337327\pi$
$720$		0			0
$721$		−	36.7118i		−	1.36722i
$722$	26.8153	+	1.71463i	0.997962	+	0.0638120i
$723$		0			0
$724$	15.0113	+	12.8967i	0.557890	+	0.479301i
$725$	5.22707			0.194128
$726$		0			0
$727$		−	26.1143i		−	0.968526i	−0.874923	−	0.484263i	$-0.839088\pi$
$727$		−	26.1143i		−	0.968526i	0.874923	−	0.484263i	$-0.160912\pi$
$728$	−3.97295	−	7.16751i	−0.147247	−	0.265646i
$729$		0			0
$730$	22.9175	+	8.49265i	0.848214	+	0.314327i
$731$	0.423186			0.0156521
$732$		0			0
$733$		−	22.3959i		−	0.827213i	−0.910456	−	0.413606i	$-0.864269\pi$
$733$		−	22.3959i		−	0.827213i	0.910456	−	0.413606i	$-0.135731\pi$
$734$	29.0732	+	10.7738i	1.07311	+	0.397668i
$735$		0			0
$736$	−7.08171	+	34.2947i	−0.261035	+	1.26412i
$737$		−	3.76029i		−	0.138512i
$738$		0			0
$739$	−8.39614			−0.308857			−0.154428	−	0.988004i	$-0.549354\pi$
$739$	−8.39614			−0.308857			−0.154428	+	0.988004i	$0.549354\pi$
$740$	18.8209	−	21.9069i	0.691871	−	0.805314i
$741$		0			0
$742$	14.3416	+	5.31464i	0.526496	+	0.195106i
$743$	37.7837			1.38615			0.693075	−	0.720866i	$-0.256256\pi$
$743$	37.7837			1.38615			0.693075	+	0.720866i	$0.256256\pi$
$744$		0			0
$745$	26.1427			0.957794
$746$	−17.0476	+	46.0030i	−0.624156	+	1.68429i
$747$		0			0
$748$	2.01644	+	1.73239i	0.0737284	+	0.0633425i
$749$	14.5634			0.532135
$750$		0			0
$751$	43.2902			1.57968			0.789841	−	0.613312i	$-0.210163\pi$
$751$	43.2902			1.57968			0.789841	+	0.613312i	$0.210163\pi$
$752$	0.883191	−	0.134613i	0.0322067	−	0.00490882i
$753$		0			0
$754$	−5.22707	+	14.1053i	−0.190359	+	0.513684i
$755$		−	8.21191i		−	0.298862i
$756$		0			0
$757$		−	31.9115i		−	1.15984i	−0.814672	−	0.579921i	$-0.803083\pi$
$757$		−	31.9115i		−	1.15984i	0.814672	−	0.579921i	$-0.196917\pi$
$758$	44.1145	+	16.3477i	1.60231	+	0.593777i
$759$		0			0
$760$	−25.5230	−	3.43406i	−0.925815	−	0.124566i
$761$	−12.3826			−0.448869			−0.224435	−	0.974489i	$-0.572054\pi$
$761$	−12.3826			−0.448869			−0.224435	+	0.974489i	$0.572054\pi$
$762$		0			0
$763$		−	10.8149i		−	0.391527i
$764$	21.9484	−	25.5471i	0.794064	−	0.924262i
$765$		0			0
$766$	16.5265	−	44.5968i	0.597126	−	1.61135i
$767$			7.26126i			0.262189i
$768$		0			0
$769$	−15.9308			−0.574478			−0.287239	−	0.957859i	$-0.592737\pi$
$769$	−15.9308			−0.574478			−0.287239	+	0.957859i	$0.592737\pi$
$770$	−1.38339	+	3.73308i	−0.0498539	+	0.134531i
$771$		0			0
$772$	17.1655	−	19.9801i	0.617801	−	0.719099i
$773$	13.8707			0.498893			0.249447	−	0.968389i	$-0.419751\pi$
$773$	13.8707			0.498893			0.249447	+	0.968389i	$0.419751\pi$
$774$		0			0
$775$	3.15038			0.113165
$776$	24.1362	+	43.5435i	0.866438	+	1.56312i
$777$		0			0
$778$	−24.1356	−	8.94408i	−0.865305	−	0.320661i
$779$	−22.8627	−	17.0181i	−0.819140	−	0.609737i
$780$		0			0
$781$	7.52580			0.269294
$782$	−18.1043	−	6.70899i	−0.647407	−	0.239913i
$783$		0			0
$784$	1.20541	+	7.90867i	0.0430504	+	0.282452i
$785$	3.71136			0.132464
$786$		0			0
$787$			39.2994i			1.40087i	0.713715	+	0.700436i	$0.247011\pi$
$787$			39.2994i			1.40087i	−0.713715	+	0.700436i	$0.752989\pi$
$788$	−29.7253	+	34.5993i	−1.05892	+	1.23255i
$789$		0			0
$790$	42.6626	+	15.8097i	1.51787	+	0.562485i
$791$	−31.5977			−1.12349
$792$		0			0
$793$			15.2564i			0.541770i
$794$	−14.8328	−	5.49666i	−0.526395	−	0.195069i
$795$		0			0
$796$	−19.6327	+	22.8517i	−0.695862	+	0.809959i
$797$	−40.0155			−1.41742			−0.708711	−	0.705499i	$-0.750723\pi$
$797$	−40.0155			−1.41742			−0.708711	+	0.705499i	$0.750723\pi$
$798$		0			0
$799$			0.492573i			0.0174260i
$800$	−3.52756	−	0.728427i	−0.124718	−	0.0257538i
$801$		0			0
$802$	30.3281	+	11.2388i	1.07092	+	0.396857i
$803$	−4.98648			−0.175969
$804$		0			0
$805$		−	28.9141i		−	1.01909i
$806$	−3.15038	+	8.50131i	−0.110967	+	0.299446i
$807$		0			0
$808$	5.11604	+	9.22974i	0.179982	+	0.324701i
$809$	−13.2723			−0.466630			−0.233315	−	0.972401i	$-0.574957\pi$
$809$	−13.2723			−0.466630			−0.233315	+	0.972401i	$0.574957\pi$
$810$		0			0
$811$			36.2317i			1.27227i	0.771579	+	0.636133i	$0.219467\pi$
$811$			36.2317i			1.27227i	−0.771579	+	0.636133i	$0.780533\pi$
$812$	−23.9237	+	27.8463i	−0.839556	+	0.977214i
$813$		0			0
$814$	−2.04757	+	5.52537i	−0.0717672	+	0.193664i
$815$			20.2290i			0.708590i
$816$		0			0
$817$	0.499421	−	0.670938i	0.0174725	−	0.0234731i
$818$	−2.19189	−	0.812259i	−0.0766375	−	0.0284000i
$819$		0			0
$820$	20.7197	+	17.8009i	0.723562	+	0.621636i
$821$		−	7.95152i		−	0.277510i	−0.990327	−	0.138755i	$-0.955690\pi$
$821$		−	7.95152i		−	0.277510i	0.990327	−	0.138755i	$-0.0443101\pi$
$822$		0			0
$823$			41.1653i			1.43493i	0.696594	+	0.717465i	$0.254698\pi$
$823$			41.1653i			1.43493i	−0.696594	+	0.717465i	$0.745302\pi$
$824$	40.6151	−	22.5129i	1.41489	−	0.784275i
$825$		0			0
$826$	−6.15784	+	16.6170i	−0.214259	+	0.578178i
$827$			17.1575i			0.596626i	0.954468	+	0.298313i	$0.0964239\pi$
$827$			17.1575i			0.596626i	−0.954468	+	0.298313i	$0.903576\pi$
$828$		0			0
$829$	6.56691			0.228078			0.114039	−	0.993476i	$-0.463621\pi$
$829$	6.56691			0.228078			0.114039	+	0.993476i	$0.463621\pi$
$830$	5.53997	+	2.05298i	0.192295	+	0.0712599i
$831$		0			0
$832$	5.49322	−	8.79071i	0.190443	−	0.304763i
$833$	−4.41082			−0.152826
$834$		0			0
$835$		−	4.92159i		−	0.170319i
$836$	5.12631	−	1.15249i	0.177297	−	0.0398596i
$837$		0			0
$838$	11.7259	−	31.6425i	0.405065	−	1.09307i
$839$	2.12080			0.0732180			0.0366090	−	0.999330i	$-0.488344\pi$
$839$	2.12080			0.0732180			0.0366090	+	0.999330i	$0.488344\pi$
$840$		0			0
$841$	38.3880			1.32372
$842$	−3.03520	+	8.19051i	−0.104600	+	0.282263i
$843$		0			0
$844$	−13.2007	+	15.3652i	−0.454388	+	0.528892i
$845$		−	23.6479i		−	0.813512i
$846$		0			0
$847$			23.7845i			0.817245i
$848$	2.91504	+	19.1255i	0.100103	+	0.656772i
$849$		0			0
$850$	0.690089	−	1.86221i	0.0236699	−	0.0638733i
$851$		−	42.7960i		−	1.46703i
$852$		0			0
$853$			4.74136i			0.162341i	0.996700	+	0.0811706i	$0.0258658\pi$
$853$			4.74136i			0.162341i	−0.996700	+	0.0811706i	$0.974134\pi$
$854$	−12.9380	+	34.9133i	−0.442730	+	1.19471i
$855$		0			0
$856$	8.93076	+	16.1118i	0.305247	+	0.550690i
$857$			0.619596i			0.0211650i	0.999944	+	0.0105825i	$0.00336858\pi$
$857$			0.619596i			0.0211650i	−0.999944	+	0.0105825i	$0.996631\pi$
$858$		0			0
$859$	−6.94544			−0.236975			−0.118488	−	0.992956i	$-0.537805\pi$
$859$	−6.94544			−0.236975			−0.118488	+	0.992956i	$0.537805\pi$
$860$	−0.522394	+	0.608049i	−0.0178135	+	0.0207343i
$861$		0			0
$862$	10.2747	−	27.7262i	0.349956	−	0.944358i
$863$	−2.60477			−0.0886674			−0.0443337	−	0.999017i	$-0.514116\pi$
$863$	−2.60477			−0.0886674			−0.0443337	+	0.999017i	$0.514116\pi$
$864$		0			0
$865$		−	35.4621i		−	1.20575i
$866$	1.87620	+	0.695273i	0.0637558	+	0.0236263i
$867$		0			0
$868$	−14.4189	+	16.7831i	−0.489410	+	0.569656i
$869$	−9.28271			−0.314894
$870$		0			0
$871$		−	8.08414i		−	0.273921i
$872$	11.9648	−	6.63208i	0.405179	−	0.224591i
$873$		0			0
$874$	−32.0024	+	20.7857i	−1.08250	+	0.703088i
$875$	26.3281			0.890051
$876$		0			0
$877$	34.1318			1.15255			0.576275	−	0.817256i	$-0.304506\pi$
$877$	34.1318			1.15255			0.576275	+	0.817256i	$0.304506\pi$
$878$	6.67894	−	18.0232i	0.225403	−	0.608252i
$879$		0			0
$880$	−4.97832	+	0.758778i	−0.167819	+	0.0255784i
$881$	−19.1849			−0.646355			−0.323178	−	0.946338i	$-0.604751\pi$
$881$	−19.1849			−0.646355			−0.323178	+	0.946338i	$0.604751\pi$
$882$		0			0
$883$	−31.1497			−1.04827			−0.524135	−	0.851635i	$-0.675611\pi$
$883$	−31.1497			−1.04827			−0.524135	+	0.851635i	$0.675611\pi$
$884$	4.33509	+	3.72442i	0.145805	+	0.125266i
$885$		0			0
$886$	9.43063	−	25.4486i	0.316828	−	0.854962i
$887$	16.1960			0.543808			0.271904	−	0.962324i	$-0.412347\pi$
$887$	16.1960			0.543808			0.271904	+	0.962324i	$0.412347\pi$
$888$		0			0
$889$			9.31695i			0.312481i
$890$	7.64490	−	20.6298i	0.256258	−	0.691512i
$891$		0			0
$892$	−11.4370	−	9.82587i	−0.382938	−	0.328994i
$893$	0.780948	+	0.581308i	0.0261334	+	0.0194527i
$894$		0			0
$895$	29.1401			0.974046
$896$	20.0258	−	15.4586i	0.669015	−	0.516434i
$897$		0			0
$898$	19.2735	+	7.14228i	0.643165	+	0.238341i
$899$	40.6151			1.35459
$900$		0			0
$901$	−10.6667			−0.355358
$902$	−5.22593	−	1.93660i	−0.174004	−	0.0644817i
$903$		0			0
$904$	−19.3768	−	34.9572i	−0.644462	−	1.16266i
$905$		−	20.6696i		−	0.687079i
$906$		0			0
$907$			50.5945i			1.67996i	0.542615	+	0.839982i	$0.317434\pi$
$907$			50.5945i			1.67996i	−0.542615	+	0.839982i	$0.682566\pi$
$908$	21.1303	−	24.5949i	0.701234	−	0.816212i
$909$		0			0
$910$	−2.97411	+	8.02565i	−0.0985908	+	0.266048i
$911$	12.8236			0.424864			0.212432	−	0.977176i	$-0.431862\pi$
$911$	12.8236			0.424864			0.212432	+	0.977176i	$0.431862\pi$
$912$		0			0
$913$	−1.20541			−0.0398932
$914$	4.72500	−	12.7504i	0.156289	−	0.421747i
$915$		0			0
$916$	−31.8656	+	37.0904i	−1.05287	+	1.22550i
$917$		−	22.9420i		−	0.757611i
$918$		0			0
$919$			20.9469i			0.690974i	0.938423	+	0.345487i	$0.112286\pi$
$919$			20.9469i			0.690974i	−0.938423	+	0.345487i	$0.887714\pi$
$920$	31.9882	−	17.7311i	1.05462	−	0.584576i
$921$		0			0
$922$	−24.7280	−	9.16359i	−0.814373	−	0.301787i
$923$	16.1795			0.532555
$924$		0			0
$925$	4.40201			0.144737
$926$	35.3333	+	13.0936i	1.16112	+	0.430284i
$927$		0			0
$928$	−45.4777	−	9.39097i	−1.49288	−	0.308274i
$929$	−23.9783			−0.786703			−0.393352	−	0.919388i	$-0.628684\pi$
$929$	−23.9783			−0.786703			−0.393352	+	0.919388i	$0.628684\pi$
$930$		0			0
$931$	−5.20541	+	6.99312i	−0.170600	+	0.229190i
$932$	−1.17428	−	1.00887i	−0.0384650	−	0.0330465i
$933$		0			0
$934$	9.92261	−	26.7762i	0.324678	−	0.876145i
$935$		−	2.77651i		−	0.0908016i
$936$		0			0
$937$	4.13733			0.135161			0.0675803	−	0.997714i	$-0.478472\pi$
$937$	4.13733			0.135161			0.0675803	+	0.997714i	$0.478472\pi$
$938$	6.85568	−	18.5001i	0.223846	−	0.604049i
$939$		0			0
$940$	−0.707747	−	0.608049i	−0.0230842	−	0.0198324i
$941$	3.88722			0.126720			0.0633598	−	0.997991i	$-0.479818\pi$
$941$	3.88722			0.126720			0.0633598	+	0.997991i	$0.479818\pi$
$942$		0			0
$943$	40.4767			1.31810
$944$	−22.1599	+	3.37753i	−0.721243	+	0.109929i
$945$		0			0
$946$	0.0568323	−	0.153362i	0.00184778	−	0.00498624i
$947$	−49.8475			−1.61983			−0.809914	−	0.586549i	$-0.800486\pi$
$947$	−49.8475			−1.61983			−0.809914	+	0.586549i	$0.800486\pi$
$948$		0			0
$949$	−10.7203			−0.347995
$950$	−2.13803	−	3.29178i	−0.0693668	−	0.106799i
$951$		0			0
$952$	6.76215	+	12.1995i	0.219163	+	0.395386i
$953$			7.37588i			0.238928i	0.992839	+	0.119464i	$0.0381176\pi$
$953$			7.37588i			0.238928i	−0.992839	+	0.119464i	$0.961882\pi$
$954$		0			0
$955$	−35.1767			−1.13829
$956$	−1.56459	+	1.82113i	−0.0506024	+	0.0588994i
$957$		0			0
$958$	7.69423	+	2.85129i	0.248589	+	0.0921211i
$959$		−	38.3176i		−	1.23734i
$960$		0			0
$961$	−6.52110			−0.210358
$962$	−4.40201	+	11.8788i	−0.141926	+	0.382989i
$963$		0			0
$964$	−21.8778	+	25.4650i	−0.704637	+	0.820172i
$965$	−27.5113			−0.885619
$966$		0			0
$967$		−	38.1528i		−	1.22691i	−0.789729	−	0.613455i	$-0.789779\pi$
$967$		−	38.1528i		−	1.22691i	0.789729	−	0.613455i	$-0.210221\pi$
$968$	−26.3133	+	14.5854i	−0.845740	+	0.468794i
$969$		0			0
$970$	18.0681	−	48.7568i	0.580131	−	1.56549i
$971$		−	21.2378i		−	0.681554i	−0.940144	−	0.340777i	$-0.889310\pi$
$971$		−	21.2378i		−	0.681554i	0.940144	−	0.340777i	$-0.110690\pi$
$972$		0			0
$973$		−	46.3735i		−	1.48667i
$974$	1.82280	−	4.91883i	0.0584062	−	0.157610i
$975$		0			0
$976$	−46.5594	+	7.09641i	−1.49033	+	0.227150i
$977$			10.4436i			0.334121i	0.985947	+	0.167060i	$0.0534275\pi$
$977$			10.4436i			0.334121i	−0.985947	+	0.167060i	$0.946573\pi$
$978$		0			0
$979$			4.48872i			0.143460i
$980$	5.44486	−	6.33763i	0.173930	−	0.202448i
$981$		0			0
$982$	−4.75903	+	12.8423i	−0.151867	+	0.409813i
$983$	25.3103			0.807272			0.403636	−	0.914920i	$-0.367746\pi$
$983$	25.3103			0.807272			0.403636	+	0.914920i	$0.367746\pi$
$984$		0			0
$985$	47.6410			1.51797
$986$	8.89672	−	24.0078i	0.283329	−	0.764565i
$987$		0			0
$988$	11.0209	−	2.47770i	0.350622	−	0.0788262i
$989$			1.18785i			0.0377713i
$990$		0			0
$991$	−52.6132			−1.67131			−0.835657	−	0.549251i	$-0.814913\pi$
$991$	−52.6132			−1.67131			−0.835657	+	0.549251i	$0.814913\pi$
$992$	−27.4097	−	5.65998i	−0.870258	−	0.179705i
$993$		0			0
$994$	37.0259	+	13.7209i	1.17439	+	0.435200i
$995$	31.4654			0.997520
$996$		0			0
$997$		−	0.312083i		−	0.00988376i	−0.999988	−	0.00494188i	$-0.998427\pi$
$997$		−	0.312083i		−	0.00988376i	0.999988	−	0.00494188i	$-0.00157305\pi$
$998$	−13.7992	+	37.2372i	−0.436805	+	1.17872i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.e.379.6		12
3.2	odd	2		152.2.b.c.75.7	yes	12
4.3	odd	2		5472.2.e.e.5167.8		12
8.3	odd	2	inner	1368.2.e.e.379.8		12
8.5	even	2		5472.2.e.e.5167.5		12
12.11	even	2		608.2.b.c.303.5		12
19.18	odd	2	inner	1368.2.e.e.379.7		12
24.5	odd	2		608.2.b.c.303.6		12
24.11	even	2		152.2.b.c.75.5	✓	12
57.56	even	2		152.2.b.c.75.6	yes	12
76.75	even	2		5472.2.e.e.5167.7		12
152.37	odd	2		5472.2.e.e.5167.6		12
152.75	even	2	inner	1368.2.e.e.379.5		12
228.227	odd	2		608.2.b.c.303.7		12
456.227	odd	2		152.2.b.c.75.8	yes	12
456.341	even	2		608.2.b.c.303.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.b.c.75.5	✓	12	24.11	even	2
152.2.b.c.75.6	yes	12	57.56	even	2
152.2.b.c.75.7	yes	12	3.2	odd	2
152.2.b.c.75.8	yes	12	456.227	odd	2
608.2.b.c.303.5		12	12.11	even	2
608.2.b.c.303.6		12	24.5	odd	2
608.2.b.c.303.7		12	228.227	odd	2
608.2.b.c.303.8		12	456.341	even	2
1368.2.e.e.379.5		12	152.75	even	2	inner
1368.2.e.e.379.6		12	1.1	even	1	trivial
1368.2.e.e.379.7		12	19.18	odd	2	inner
1368.2.e.e.379.8		12	8.3	odd	2	inner
5472.2.e.e.5167.5		12	8.5	even	2
5472.2.e.e.5167.6		12	152.37	odd	2
5472.2.e.e.5167.7		12	76.75	even	2
5472.2.e.e.5167.8		12	4.3	odd	2

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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.491416 + 1.32609i) q^{2} +(-1.51702 - 1.30332i) q^{4} +2.08884i q^{5} -2.23607i q^{7} +(2.47381 - 1.37123i) q^{8} +O(q^{10})\)	\(q+(-0.491416 + 1.32609i) q^{2} +(-1.51702 - 1.30332i) q^{4} +2.08884i q^{5} -2.23607i q^{7} +(2.47381 - 1.37123i) q^{8} +(-2.76999 - 1.02649i) q^{10} +0.602705 q^{11} +1.29574 q^{13} +(2.96522 + 1.09884i) q^{14} +(0.602705 + 3.95433i) q^{16} -2.20541 q^{17} +(-2.60270 + 3.49656i) q^{19} +(2.72243 - 3.16881i) q^{20} +(-0.296179 + 0.799240i) q^{22} -6.19040i q^{23} +0.636747 q^{25} +(-0.636747 + 1.71826i) q^{26} +(-2.91432 + 3.39216i) q^{28} +8.20902 q^{29} +4.94762 q^{31} +(-5.53997 - 1.14398i) q^{32} +(1.08377 - 2.92457i) q^{34} +4.67079 q^{35} +6.91328 q^{37} +(-3.35774 - 5.16968i) q^{38} +(2.86428 + 5.16739i) q^{40} +6.53862i q^{41} -0.191885 q^{43} +(-0.914316 - 0.785518i) q^{44} +(8.20902 + 3.04206i) q^{46} -0.223348i q^{47} +2.00000 q^{49} +(-0.312907 + 0.844383i) q^{50} +(-1.96566 - 1.68877i) q^{52} +4.83659 q^{53} +1.25895i q^{55} +(-3.06617 - 5.53160i) q^{56} +(-4.03404 + 10.8859i) q^{58} +5.60395i q^{59} +11.7743i q^{61} +(-2.43134 + 6.56098i) q^{62} +(4.23945 - 6.78432i) q^{64} +2.70659i q^{65} -6.23902i q^{67} +(3.34565 + 2.87436i) q^{68} +(-2.29530 + 6.19388i) q^{70} +12.4867 q^{71} -8.27349 q^{73} +(-3.39730 + 9.16762i) q^{74} +(8.50550 - 1.91219i) q^{76} -1.34769i q^{77} -15.4017 q^{79} +(-8.25997 + 1.25895i) q^{80} +(-8.67079 - 3.21318i) q^{82} -2.00000 q^{83} -4.60675i q^{85} +(0.0942954 - 0.254457i) q^{86} +(1.49098 - 0.826448i) q^{88} +7.44762i q^{89} -2.89736i q^{91} +(-8.06808 + 9.39097i) q^{92} +(0.296179 + 0.109757i) q^{94} +(-7.30375 - 5.43663i) q^{95} +17.6018i q^{97} +(-0.982832 + 2.65218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4}+O(q^{10}) \) 12 * q + 4 * q^4	\( 12 q + 4 q^{4} - 12 q^{17} - 24 q^{19} - 4 q^{20} - 44 q^{25} + 44 q^{26} - 20 q^{28} - 40 q^{35} - 4 q^{38} - 24 q^{43} + 4 q^{44} + 24 q^{49} - 4 q^{58} + 8 q^{62} - 8 q^{64} - 12 q^{68} + 4 q^{73} - 48 q^{74} - 12 q^{76} - 32 q^{80} - 8 q^{82} - 24 q^{83} - 8 q^{92}+O(q^{100}) \) 12 * q + 4 * q^4 - 12 * q^17 - 24 * q^19 - 4 * q^20 - 44 * q^25 + 44 * q^26 - 20 * q^28 - 40 * q^35 - 4 * q^38 - 24 * q^43 + 4 * q^44 + 24 * q^49 - 4 * q^58 + 8 * q^62 - 8 * q^64 - 12 * q^68 + 4 * q^73 - 48 * q^74 - 12 * q^76 - 32 * q^80 - 8 * q^82 - 24 * q^83 - 8 * q^92

Introduction

L-functions

Modular forms

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Database

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