LMFDB - Embedded newform 2214.2.i.b.901.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2214,2,Mod(901,2214)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2214.901"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2214, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2214 = 2 \cdot 3^{3} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2214.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$17.6788790075$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 738)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.12
Character	$\chi$	$=$	2214.901
Dual form			2214.2.i.b.1639.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.0761831 - 0.131953i) q^{5} +(-1.94692 + 1.12405i) q^{7} -1.00000 q^{8} +0.152366 q^{10} +(3.89096 - 2.24645i) q^{11} +(1.91844 + 1.10761i) q^{13} +(-1.94692 - 1.12405i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.10897i q^{17} +0.0605013i q^{19} +(0.0761831 + 0.131953i) q^{20} +(3.89096 + 2.24645i) q^{22} +(-0.0253272 + 0.0438680i) q^{23} +(2.48839 + 4.31002i) q^{25} +2.21523i q^{26} -2.24811i q^{28} +(4.83752 - 2.79295i) q^{29} +(0.00164427 - 0.00284796i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.69245 - 1.55449i) q^{34} +0.342536i q^{35} -0.348118 q^{37} +(-0.0523957 + 0.0302507i) q^{38} +(-0.0761831 + 0.131953i) q^{40} +(1.40311 + 6.24750i) q^{41} +(1.74162 + 3.01657i) q^{43} +4.49290i q^{44} -0.0506544 q^{46} +(8.96301 - 5.17479i) q^{47} +(-0.973004 + 1.68529i) q^{49} +(-2.48839 + 4.31002i) q^{50} +(-1.91844 + 1.10761i) q^{52} +0.876641i q^{53} -0.684565i q^{55} +(1.94692 - 1.12405i) q^{56} +(4.83752 + 2.79295i) q^{58} +(-2.14362 + 3.71286i) q^{59} +(2.86354 + 4.95981i) q^{61} +0.00328854 q^{62} +1.00000 q^{64} +(0.292306 - 0.168763i) q^{65} +(-1.29700 - 0.748824i) q^{67} +(2.69245 + 1.55449i) q^{68} +(-0.296645 + 0.171268i) q^{70} +1.94028i q^{71} +5.01815 q^{73} +(-0.174059 - 0.301479i) q^{74} +(-0.0523957 - 0.0302507i) q^{76} +(-5.05026 + 8.74731i) q^{77} +(-0.914489 + 0.527980i) q^{79} -0.152366 q^{80} +(-4.70894 + 4.33888i) q^{82} +(3.14751 + 5.45166i) q^{83} +(-0.410238 - 0.236851i) q^{85} +(-1.74162 + 3.01657i) q^{86} +(-3.89096 + 2.24645i) q^{88} -0.00331954i q^{89} -4.98007 q^{91} +(-0.0253272 - 0.0438680i) q^{92} +(8.96301 + 5.17479i) q^{94} +(0.00798333 + 0.00460918i) q^{95} +(3.02338 - 1.74555i) q^{97} -1.94601 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 4 q^{5} - 36 q^{8} - 8 q^{10} - 18 q^{16} - 4 q^{20} + 4 q^{23} - 26 q^{25} + 8 q^{31} + 18 q^{32} - 60 q^{37} + 4 q^{40} + 6 q^{41} + 6 q^{43} + 8 q^{46} + 38 q^{49} + 26 q^{50}+ \cdots + 76 q^{98}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 4 * q^5 - 36 * q^8 - 8 * q^10 - 18 * q^16 - 4 * q^20 + 4 * q^23 - 26 * q^25 + 8 * q^31 + 18 * q^32 - 60 * q^37 + 4 * q^40 + 6 * q^41 + 6 * q^43 + 8 * q^46 + 38 * q^49 + 26 * q^50 - 22 * q^59 - 46 * q^61 + 16 * q^62 + 36 * q^64 + 64 * q^73 - 30 * q^74 + 2 * q^77 + 8 * q^80 + 12 * q^82 - 68 * q^83 - 6 * q^86 + 36 * q^91 + 4 * q^92 + 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2214\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.0761831	−	0.131953i	0.0340701	−	0.0590111i	−0.848488	−	0.529215i	$-0.822486\pi$
$5$	0.0761831	−	0.131953i	0.0340701	−	0.0590111i	0.882558	+	0.470204i	$0.155820\pi$
$6$		0			0
$7$	−1.94692	+	1.12405i	−0.735866	+	0.424853i	−0.820564	−	0.571554i	$-0.806341\pi$
$7$	−1.94692	+	1.12405i	−0.735866	+	0.424853i	0.0846982	+	0.996407i	$0.473007\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.152366			0.0481824
$11$	3.89096	−	2.24645i	1.17317	−	0.677330i	0.218745	−	0.975782i	$-0.429804\pi$
$11$	3.89096	−	2.24645i	1.17317	−	0.677330i	0.954425	+	0.298452i	$0.0964704\pi$
$12$		0			0
$13$	1.91844	+	1.10761i	0.532081	+	0.307197i	0.741863	−	0.670551i	$-0.233942\pi$
$13$	1.91844	+	1.10761i	0.532081	+	0.307197i	−0.209783	+	0.977748i	$0.567276\pi$
$14$	−1.94692	−	1.12405i	−0.520336	−	0.300416i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	3.10897i		−	0.754037i	−0.926206	−	0.377018i	$-0.876949\pi$
$17$		−	3.10897i		−	0.754037i	0.926206	−	0.377018i	$-0.123051\pi$
$18$		0			0
$19$			0.0605013i			0.0138800i	0.999976	+	0.00693998i	$0.00220908\pi$
$19$			0.0605013i			0.0138800i	−0.999976	+	0.00693998i	$0.997791\pi$
$20$	0.0761831	+	0.131953i	0.0170351	+	0.0295056i
$21$		0			0
$22$	3.89096	+	2.24645i	0.829556	+	0.478944i
$23$	−0.0253272	+	0.0438680i	−0.00528109	+	0.00914711i	−0.868654	−	0.495419i	$-0.835014\pi$
$23$	−0.0253272	+	0.0438680i	−0.00528109	+	0.00914711i	0.863373	+	0.504567i	$0.168348\pi$
$24$		0			0
$25$	2.48839	+	4.31002i	0.497678	+	0.862004i
$26$			2.21523i			0.434442i
$27$		0			0
$28$		−	2.24811i		−	0.424853i
$29$	4.83752	−	2.79295i	0.898306	−	0.518637i	0.0216557	−	0.999765i	$-0.493106\pi$
$29$	4.83752	−	2.79295i	0.898306	−	0.518637i	0.876650	+	0.481128i	$0.159773\pi$
$30$		0			0
$31$	0.00164427	−	0.00284796i	0.000295319	−	0.000511508i	−0.865878	−	0.500256i	$-0.833239\pi$
$31$	0.00164427	−	0.00284796i	0.000295319	−	0.000511508i	0.866173	+	0.499744i	$0.166573\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	2.69245	−	1.55449i	0.461751	−	0.266592i
$35$			0.342536i			0.0578991i
$36$		0			0
$37$	−0.348118			−0.0572302			−0.0286151	−	0.999591i	$-0.509110\pi$
$37$	−0.348118			−0.0572302			−0.0286151	+	0.999591i	$0.509110\pi$
$38$	−0.0523957	+	0.0302507i	−0.00849970	+	0.00490731i
$39$		0			0
$40$	−0.0761831	+	0.131953i	−0.0120456	+	0.0208636i
$41$	1.40311	+	6.24750i	0.219129	+	0.975696i
$41$	1.40311	+	6.24750i	0.219129	+	0.975696i
$42$		0			0
$43$	1.74162	+	3.01657i	0.265594	+	0.460023i	0.967719	−	0.252031i	$-0.0810985\pi$
$43$	1.74162	+	3.01657i	0.265594	+	0.460023i	−0.702125	+	0.712054i	$0.747765\pi$
$44$			4.49290i			0.677330i
$45$		0			0
$46$	−0.0506544			−0.00746858
$47$	8.96301	−	5.17479i	1.30739	−	0.754821i	0.325729	−	0.945463i	$-0.394390\pi$
$47$	8.96301	−	5.17479i	1.30739	−	0.754821i	0.981660	+	0.190642i	$0.0610569\pi$
$48$		0			0
$49$	−0.973004	+	1.68529i	−0.139001	+	0.240756i
$50$	−2.48839	+	4.31002i	−0.351912	+	0.609529i
$51$		0			0
$52$	−1.91844	+	1.10761i	−0.266040	+	0.153598i
$53$			0.876641i			0.120416i	0.998186	+	0.0602080i	$0.0191764\pi$
$53$			0.876641i			0.120416i	−0.998186	+	0.0602080i	$0.980824\pi$
$54$		0			0
$55$		−	0.684565i		−	0.0923068i
$56$	1.94692	−	1.12405i	0.260168	−	0.150208i
$57$		0			0
$58$	4.83752	+	2.79295i	0.635198	+	0.366732i
$59$	−2.14362	+	3.71286i	−0.279075	+	0.483373i	−0.971155	−	0.238448i	$-0.923361\pi$
$59$	−2.14362	+	3.71286i	−0.279075	+	0.483373i	0.692080	+	0.721821i	$0.256695\pi$
$60$		0			0
$61$	2.86354	+	4.95981i	0.366639	+	0.635038i	0.989038	−	0.147663i	$-0.0471750\pi$
$61$	2.86354	+	4.95981i	0.366639	+	0.635038i	−0.622398	+	0.782701i	$0.713842\pi$
$62$	0.00328854			0.000417645
$63$		0			0
$64$	1.00000			0.125000
$65$	0.292306	−	0.168763i	0.0362561	−	0.0209325i
$66$		0			0
$67$	−1.29700	−	0.748824i	−0.158454	−	0.0914835i	0.418676	−	0.908136i	$-0.362494\pi$
$67$	−1.29700	−	0.748824i	−0.158454	−	0.0914835i	−0.577130	+	0.816652i	$0.695828\pi$
$68$	2.69245	+	1.55449i	0.326507	+	0.188509i
$69$		0			0
$70$	−0.296645	+	0.171268i	−0.0354558	+	0.0204704i
$71$			1.94028i			0.230269i	0.993350	+	0.115134i	$0.0367298\pi$
$71$			1.94028i			0.230269i	−0.993350	+	0.115134i	$0.963270\pi$
$72$		0			0
$73$	5.01815			0.587330			0.293665	−	0.955908i	$-0.405125\pi$
$73$	5.01815			0.587330			0.293665	+	0.955908i	$0.405125\pi$
$74$	−0.174059	−	0.301479i	−0.0202339	−	0.0350462i
$75$		0			0
$76$	−0.0523957	−	0.0302507i	−0.00601020	−	0.00346999i
$77$	−5.05026	+	8.74731i	−0.575531	+	0.996848i
$78$		0			0
$79$	−0.914489	+	0.527980i	−0.102888	+	0.0594024i	−0.550561	−	0.834795i	$-0.685586\pi$
$79$	−0.914489	+	0.527980i	−0.102888	+	0.0594024i	0.447673	+	0.894197i	$0.352253\pi$
$80$	−0.152366			−0.0170351
$81$		0			0
$82$	−4.70894	+	4.33888i	−0.520015	+	0.479149i
$83$	3.14751	+	5.45166i	0.345485	+	0.598397i	0.985442	−	0.170014i	$-0.0543812\pi$
$83$	3.14751	+	5.45166i	0.345485	+	0.598397i	−0.639957	+	0.768411i	$0.721048\pi$
$84$		0			0
$85$	−0.410238	−	0.236851i	−0.0444966	−	0.0256901i
$86$	−1.74162	+	3.01657i	−0.187804	+	0.325285i
$87$		0			0
$88$	−3.89096	+	2.24645i	−0.414778	+	0.239472i
$89$		−	0.00331954i		−	0.000351871i	−1.00000		0.000175935i	$-0.999944\pi$
$89$		−	0.00331954i		−	0.000351871i	1.00000		0.000175935i	$-5.60020e-5\pi$
$90$		0			0
$91$	−4.98007			−0.522054
$92$	−0.0253272	−	0.0438680i	−0.00264054	−	0.00457356i
$93$		0			0
$94$	8.96301	+	5.17479i	0.924463	+	0.533739i
$95$	0.00798333	+	0.00460918i	0.000819072	+	0.000472892i
$96$		0			0
$97$	3.02338	−	1.74555i	0.306978	−	0.177234i	−0.338595	−	0.940932i	$-0.609952\pi$
$97$	3.02338	−	1.74555i	0.306978	−	0.177234i	0.645573	+	0.763698i	$0.276618\pi$
$98$	−1.94601			−0.196577
$99$		0			0
$100$	−4.97678			−0.497678
$101$	−1.42966	+	0.825415i	−0.142257	+	0.0821319i	−0.569439	−	0.822034i	$-0.692840\pi$
$101$	−1.42966	+	0.825415i	−0.142257	+	0.0821319i	0.427182	+	0.904165i	$0.359506\pi$
$102$		0			0
$103$	−4.52054	+	7.82980i	−0.445422	+	0.771493i	−0.998082	−	0.0619136i	$-0.980280\pi$
$103$	−4.52054	+	7.82980i	−0.445422	+	0.771493i	0.552660	+	0.833407i	$0.313613\pi$
$104$	−1.91844	−	1.10761i	−0.188119	−	0.108610i
$105$		0			0
$106$	−0.759193	+	0.438321i	−0.0737394	+	0.0425735i
$107$	18.3510			1.77406			0.887030	−	0.461711i	$-0.152764\pi$
$107$	18.3510			1.77406			0.887030	+	0.461711i	$0.152764\pi$
$108$		0			0
$109$			11.5501i			1.10630i	0.833081	+	0.553151i	$0.186575\pi$
$109$			11.5501i			1.10630i	−0.833081	+	0.553151i	$0.813425\pi$
$110$	0.592851	−	0.342283i	0.0565261	−	0.0326354i
$111$		0			0
$112$	1.94692	+	1.12405i	0.183967	+	0.106213i
$113$	−7.94827	+	13.7668i	−0.747710	+	1.29507i	0.201208	+	0.979549i	$0.435513\pi$
$113$	−7.94827	+	13.7668i	−0.747710	+	1.29507i	−0.948918	+	0.315523i	$0.897820\pi$
$114$		0			0
$115$	0.00385901	+	0.00668400i	0.000359854	+	0.000623286i
$116$			5.58589i			0.518637i
$117$		0			0
$118$	−4.28724			−0.394672
$119$	3.49465	+	6.05292i	0.320354	+	0.554870i
$120$		0			0
$121$	4.59306	−	7.95542i	0.417551	−	0.723220i
$122$	−2.86354	+	4.95981i	−0.259253	+	0.449040i
$123$		0			0
$124$	0.00164427	+	0.00284796i	0.000147660	+	0.000255754i
$125$	1.52012			0.135964
$126$		0			0
$127$	−17.4982			−1.55271			−0.776356	−	0.630295i	$-0.782934\pi$
$127$	−17.4982			−1.55271			−0.776356	+	0.630295i	$0.782934\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	0.292306	+	0.168763i	0.0256369	+	0.0148015i
$131$	8.70047	−	15.0696i	0.760163	−	1.31664i	−0.182603	−	0.983187i	$-0.558452\pi$
$131$	8.70047	−	15.0696i	0.760163	−	1.31664i	0.942766	−	0.333455i	$-0.108214\pi$
$132$		0			0
$133$	−0.0680068	−	0.117791i	−0.00589694	−	0.0102138i
$134$		−	1.49765i		−	0.129377i
$135$		0			0
$136$			3.10897i			0.266592i
$137$	12.0713	−	6.96940i	1.03132	−	0.595436i	0.113961	−	0.993485i	$-0.463646\pi$
$137$	12.0713	−	6.96940i	1.03132	−	0.595436i	0.917364	+	0.398050i	$0.130313\pi$
$138$		0			0
$139$	2.48118	−	4.29753i	0.210451	−	0.364512i	−0.741405	−	0.671058i	$-0.765840\pi$
$139$	2.48118	−	4.29753i	0.210451	−	0.364512i	0.951856	+	0.306546i	$0.0991734\pi$
$140$	−0.296645	−	0.171268i	−0.0250710	−	0.0144748i
$141$		0			0
$142$	−1.68033	+	0.970139i	−0.141010	+	0.0814122i
$143$	9.95279			0.832294
$144$		0			0
$145$		−	0.851101i		−	0.0706801i
$146$	2.50908	+	4.34585i	0.207653	+	0.359665i
$147$		0			0
$148$	0.174059	−	0.301479i	0.0143076	−	0.0247814i
$149$	8.57976	+	4.95353i	0.702882	+	0.405809i	0.808420	−	0.588606i	$-0.200323\pi$
$149$	8.57976	+	4.95353i	0.702882	+	0.405809i	−0.105538	+	0.994415i	$0.533657\pi$
$150$		0			0
$151$	6.77557	−	3.91188i	0.551388	−	0.318344i	−0.198294	−	0.980143i	$-0.563540\pi$
$151$	6.77557	−	3.91188i	0.551388	−	0.318344i	0.749682	+	0.661799i	$0.230207\pi$
$152$		−	0.0605013i		−	0.00490731i
$153$		0			0
$154$	−10.1005			−0.813923
$155$	−0.000250531	0	0.000433932i	−2.01231e−5	0	3.48543e-5i
$156$		0			0
$157$	13.7927	+	7.96323i	1.10078	+	0.635535i	0.936426	−	0.350866i	$-0.114113\pi$
$157$	13.7927	+	7.96323i	1.10078	+	0.635535i	0.164354	+	0.986402i	$0.447446\pi$
$158$	−0.914489	−	0.527980i	−0.0727528	−	0.0420039i
$159$		0			0
$160$	−0.0761831	−	0.131953i	−0.00602280	−	0.0104318i
$161$		−	0.113877i		−	0.00897473i
$162$		0			0
$163$	−4.13724			−0.324054			−0.162027	−	0.986786i	$-0.551803\pi$
$163$	−4.13724			−0.324054			−0.162027	+	0.986786i	$0.551803\pi$
$164$	−6.11205	−	1.90862i	−0.477271	−	0.149038i
$165$		0			0
$166$	−3.14751	+	5.45166i	−0.244295	+	0.423130i
$167$	0.0737849	+	0.0425997i	0.00570965	+	0.00329647i	0.502852	−	0.864372i	$-0.332284\pi$
$167$	0.0737849	+	0.0425997i	0.00570965	+	0.00329647i	−0.497142	+	0.867669i	$0.665617\pi$
$168$		0			0
$169$	−4.04638	−	7.00854i	−0.311260	−	0.539118i
$170$		−	0.473702i		−	0.0363313i
$171$		0			0
$172$	−3.48324			−0.265594
$173$	−9.30221	−	16.1119i	−0.707234	−	1.22497i	−0.965879	−	0.258993i	$-0.916609\pi$
$173$	−9.30221	−	16.1119i	−0.707234	−	1.22497i	0.258645	−	0.965972i	$-0.416724\pi$
$174$		0			0
$175$	−9.68940	−	5.59418i	−0.732450	−	0.422880i
$176$	−3.89096	−	2.24645i	−0.293292	−	0.169332i
$177$		0			0
$178$	0.00287481	−	0.00165977i	0.000215476	−	0.000124405i
$179$			11.0168i			0.823435i	0.911311	+	0.411718i	$0.135071\pi$
$179$			11.0168i			0.823435i	−0.911311	+	0.411718i	$0.864929\pi$
$180$		0			0
$181$		−	2.81886i		−	0.209524i	−0.994497	−	0.104762i	$-0.966592\pi$
$181$		−	2.81886i		−	0.209524i	0.994497	−	0.104762i	$-0.0334081\pi$
$182$	−2.49004	−	4.31287i	−0.184574	−	0.319691i
$183$		0			0
$184$	0.0253272	−	0.0438680i	0.00186715	−	0.00323399i
$185$	−0.0265207	+	0.0459352i	−0.00194984	+	0.00337722i
$186$		0			0
$187$	−6.98415	−	12.0969i	−0.510731	−	0.884613i
$188$			10.3496i			0.754821i
$189$		0			0
$190$			0.00921835i			0.000668770i
$191$	15.8790	−	9.16777i	1.14897	−	0.663356i	0.200332	−	0.979728i	$-0.435798\pi$
$191$	15.8790	−	9.16777i	1.14897	−	0.663356i	0.948635	+	0.316372i	$0.102465\pi$
$192$		0			0
$193$	−19.3630	−	11.1792i	−1.39378	−	0.804697i	−0.400045	−	0.916496i	$-0.631005\pi$
$193$	−19.3630	−	11.1792i	−1.39378	−	0.804697i	−0.993731	+	0.111799i	$0.964339\pi$
$194$	3.02338	+	1.74555i	0.217066	+	0.125323i
$195$		0			0
$196$	−0.973004	−	1.68529i	−0.0695003	−	0.120378i
$197$	1.75385			0.124957			0.0624783	−	0.998046i	$-0.480100\pi$
$197$	1.75385			0.124957			0.0624783	+	0.998046i	$0.480100\pi$
$198$		0			0
$199$		−	10.1027i		−	0.716158i	−0.933691	−	0.358079i	$-0.883432\pi$
$199$		−	10.1027i		−	0.716158i	0.933691	−	0.358079i	$-0.116568\pi$
$200$	−2.48839	−	4.31002i	−0.175956	−	0.304765i
$201$		0			0
$202$	−1.42966	−	0.825415i	−0.100591	−	0.0580760i
$203$	−6.27885	+	10.8753i	−0.440689	+	0.763295i
$204$		0			0
$205$	0.931270	+	0.290809i	0.0650427	+	0.0203110i
$206$	−9.04108			−0.629922
$207$		0			0
$208$		−	2.21523i		−	0.153598i
$209$	0.135913	+	0.235408i	0.00940131	+	0.0162835i
$210$		0			0
$211$	−0.747210	−	0.431402i	−0.0514401	−	0.0296989i	0.474059	−	0.880493i	$-0.342788\pi$
$211$	−0.747210	−	0.431402i	−0.0514401	−	0.0296989i	−0.525499	+	0.850794i	$0.676122\pi$
$212$	−0.759193	−	0.438321i	−0.0521416	−	0.0301040i
$213$		0			0
$214$	9.17551	+	15.8925i	0.627225	+	1.08639i
$215$	0.530727			0.0361953
$216$		0			0
$217$			0.00739299i			0.000501869i
$218$	−10.0027	+	5.77507i	−0.677469	+	0.391137i
$219$		0			0
$220$	0.592851	+	0.342283i	0.0399700	+	0.0230767i
$221$	3.44354	−	5.96439i	0.231638	−	0.401208i
$222$		0			0
$223$	−11.3675	−	19.6891i	−0.761225	−	1.31848i	−0.942219	−	0.334996i	$-0.891265\pi$
$223$	−11.3675	−	19.6891i	−0.761225	−	1.31848i	0.180994	−	0.983484i	$-0.442068\pi$
$224$			2.24811i			0.150208i
$225$		0			0
$226$	−15.8965			−1.05742
$227$	−8.80325	+	5.08256i	−0.584292	+	0.337341i	−0.762837	−	0.646590i	$-0.776194\pi$
$227$	−8.80325	+	5.08256i	−0.584292	+	0.337341i	0.178545	+	0.983932i	$0.442861\pi$
$228$		0			0
$229$	13.9895	+	8.07682i	0.924449	+	0.533731i	0.885052	−	0.465493i	$-0.154123\pi$
$229$	13.9895	+	8.07682i	0.924449	+	0.533731i	0.0393975	+	0.999224i	$0.487456\pi$
$230$	−0.00385901	+	0.00668400i	−0.000254455	+	0.000440730i
$231$		0			0
$232$	−4.83752	+	2.79295i	−0.317599	+	0.183366i
$233$			2.68759i			0.176070i	0.996117	+	0.0880351i	$0.0280588\pi$
$233$			2.68759i			0.176070i	−0.996117	+	0.0880351i	$0.971941\pi$
$234$		0			0
$235$		−	1.57693i		−	0.102867i
$236$	−2.14362	−	3.71286i	−0.139538	−	0.241686i
$237$		0			0
$238$	−3.49465	+	6.05292i	−0.226525	+	0.392352i
$239$	−23.5174	−	13.5778i	−1.52121	−	0.878274i	−0.999686	−	0.0250396i	$-0.992029\pi$
$239$	−23.5174	−	13.5778i	−1.52121	−	0.878274i	−0.521528	−	0.853234i	$-0.674638\pi$
$240$		0			0
$241$	12.1315	+	21.0123i	0.781457	+	1.35352i	0.931093	+	0.364783i	$0.118857\pi$
$241$	12.1315	+	21.0123i	0.781457	+	1.35352i	−0.149635	+	0.988741i	$0.547810\pi$
$242$	9.18613			0.590507
$243$		0			0
$244$	−5.72709			−0.366639
$245$	0.148253	+	0.256782i	0.00947153	+	0.0164052i
$246$		0			0
$247$	−0.0670121	+	0.116068i	−0.00426388	+	0.00738526i
$248$	−0.00164427	+	0.00284796i	−0.000104411	+	0.000180845i
$249$		0			0
$250$	0.760062	+	1.31647i	0.0480705	+	0.0832606i
$251$	26.5027			1.67284			0.836418	−	0.548092i	$-0.184646\pi$
$251$	26.5027			1.67284			0.836418	+	0.548092i	$0.184646\pi$
$252$		0			0
$253$			0.227585i			0.0143081i
$254$	−8.74909	−	15.1539i	−0.548967	−	0.950838i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.08716	+	1.20502i	0.130193	+	0.0751672i	0.563682	−	0.825992i	$-0.309384\pi$
$257$	2.08716	+	1.20502i	0.130193	+	0.0751672i	−0.433489	+	0.901159i	$0.642718\pi$
$258$		0			0
$259$	0.677757	−	0.391303i	0.0421138	−	0.0243144i
$260$			0.337526i			0.0209325i
$261$		0			0
$262$	17.4009			1.07503
$263$	−7.28003	+	4.20313i	−0.448906	+	0.259176i	−0.707368	−	0.706845i	$-0.750118\pi$
$263$	−7.28003	+	4.20313i	−0.448906	+	0.259176i	0.258462	+	0.966021i	$0.416784\pi$
$264$		0			0
$265$	0.115675	+	0.0667852i	0.00710588	+	0.00410258i
$266$	0.0680068	−	0.117791i	0.00416976	−	0.00722224i
$267$		0			0
$268$	1.29700	−	0.748824i	0.0792270	−	0.0457417i
$269$	7.61355			0.464206			0.232103	−	0.972691i	$-0.425439\pi$
$269$	7.61355			0.464206			0.232103	+	0.972691i	$0.425439\pi$
$270$		0			0
$271$	12.9827			0.788643			0.394321	−	0.918973i	$-0.370980\pi$
$271$	12.9827			0.788643			0.394321	+	0.918973i	$0.370980\pi$
$272$	−2.69245	+	1.55449i	−0.163254	+	0.0942546i
$273$		0			0
$274$	12.0713	+	6.96940i	0.729257	+	0.421037i
$275$	19.3645	+	11.1801i	1.16772	+	0.674185i
$276$		0			0
$277$	−5.19938	−	9.00560i	−0.312401	−	0.541094i	0.666481	−	0.745522i	$-0.267800\pi$
$277$	−5.19938	−	9.00560i	−0.312401	−	0.541094i	−0.978882	+	0.204428i	$0.934466\pi$
$278$	4.96236			0.297623
$279$		0			0
$280$		−	0.342536i		−	0.0204704i
$281$	−0.455533	+	0.263002i	−0.0271748	+	0.0156894i	−0.513526	−	0.858074i	$-0.671661\pi$
$281$	−0.455533	+	0.263002i	−0.0271748	+	0.0156894i	0.486351	+	0.873763i	$0.338328\pi$
$282$		0			0
$283$	−0.117657	+	0.203788i	−0.00699397	+	0.0121139i	−0.869501	−	0.493931i	$-0.835560\pi$
$283$	−0.117657	+	0.203788i	−0.00699397	+	0.0121139i	0.862507	+	0.506045i	$0.168893\pi$
$284$	−1.68033	−	0.970139i	−0.0997092	−	0.0575671i
$285$		0			0
$286$	4.97640	+	8.61937i	0.294260	+	0.509674i
$287$	−9.75428	−	10.5862i	−0.575777	−	0.624884i
$288$		0			0
$289$	7.33429			0.431429
$290$	0.737075	−	0.425550i	0.0432825	−	0.0249892i
$291$		0			0
$292$	−2.50908	+	4.34585i	−0.146833	+	0.254321i
$293$	−26.9416	−	15.5548i	−1.57395	−	0.908719i	−0.995678	−	0.0928735i	$-0.970395\pi$
$293$	−26.9416	−	15.5548i	−1.57395	−	0.908719i	−0.578270	−	0.815846i	$-0.696272\pi$
$294$		0			0
$295$	0.326615	+	0.565714i	0.0190163	+	0.0329371i
$296$	0.348118			0.0202339
$297$		0			0
$298$			9.90706i			0.573900i
$299$	−0.0971776	+	0.0561055i	−0.00561993	+	0.00324467i
$300$		0			0
$301$	−6.78158	−	3.91535i	−0.390884	−	0.225677i
$302$	6.77557	+	3.91188i	0.389890	+	0.225103i
$303$		0			0
$304$	0.0523957	−	0.0302507i	0.00300510	−	0.00173499i
$305$	0.872615			0.0499658
$306$		0			0
$307$	22.9910			1.31216			0.656082	−	0.754689i	$-0.272212\pi$
$307$	22.9910			1.31216			0.656082	+	0.754689i	$0.272212\pi$
$308$	−5.05026	−	8.74731i	−0.287765	−	0.498424i
$309$		0			0
$310$	0.000250531	0	0.000433932i	1.42292e−5	0	2.46457e-5i
$311$	−19.4064	−	11.2043i	−1.10043	−	0.635336i	−0.164099	−	0.986444i	$-0.552472\pi$
$311$	−19.4064	−	11.2043i	−1.10043	−	0.635336i	−0.936335	+	0.351108i	$0.885805\pi$
$312$		0			0
$313$	−18.2668	+	10.5463i	−1.03250	+	0.596113i	−0.917699	−	0.397276i	$-0.869956\pi$
$313$	−18.2668	+	10.5463i	−1.03250	+	0.596113i	−0.114799	+	0.993389i	$0.536622\pi$
$314$			15.9265i			0.898782i
$315$		0			0
$316$		−	1.05596i		−	0.0594024i
$317$	−4.43915	+	2.56295i	−0.249328	+	0.143949i	−0.619456	−	0.785031i	$-0.712647\pi$
$317$	−4.43915	+	2.56295i	−0.249328	+	0.143949i	0.370129	+	0.928980i	$0.379314\pi$
$318$		0			0
$319$	12.5484	−	21.7345i	0.702577	−	1.21690i
$320$	0.0761831	−	0.131953i	0.00425876	−	0.00737639i
$321$		0			0
$322$	0.0986200	−	0.0569383i	0.00549588	−	0.00317305i
$323$	0.188097			0.0104660
$324$		0			0
$325$			11.0247i			0.611541i
$326$	−2.06862	−	3.58296i	−0.114570	−	0.198442i
$327$		0			0
$328$	−1.40311	−	6.24750i	−0.0774739	−	0.344961i
$329$	−11.6335	+	20.1498i	−0.641375	+	1.11089i
$330$		0			0
$331$	−19.3235	+	11.1564i	−1.06212	+	0.613213i	−0.926017	−	0.377482i	$-0.876790\pi$
$331$	−19.3235	+	11.1564i	−1.06212	+	0.613213i	−0.136099	+	0.990695i	$0.543457\pi$
$332$	−6.29503			−0.345485
$333$		0			0
$334$			0.0851994i			0.00466191i
$335$	−0.197619	+	0.114095i	−0.0107971	+	0.00623370i
$336$		0			0
$337$	−5.65749	+	9.79906i	−0.308183	+	0.533789i	−0.977965	−	0.208769i	$-0.933054\pi$
$337$	−5.65749	+	9.79906i	−0.308183	+	0.533789i	0.669782	+	0.742558i	$0.266388\pi$
$338$	4.04638	−	7.00854i	0.220094	−	0.381214i
$339$		0			0
$340$	0.410238	−	0.236851i	0.0222483	−	0.0128451i
$341$		−	0.0147751i		−	0.000800115i
$342$		0			0
$343$		−	20.1116i		−	1.08592i
$344$	−1.74162	−	3.01657i	−0.0939018	−	0.162643i
$345$		0			0
$346$	9.30221	−	16.1119i	0.500090	−	0.866181i
$347$	−8.32356	−	4.80561i	−0.446832	−	0.257979i	0.259659	−	0.965700i	$-0.416390\pi$
$347$	−8.32356	−	4.80561i	−0.446832	−	0.257979i	−0.706491	+	0.707722i	$0.749723\pi$
$348$		0			0
$349$	10.4020	+	18.0167i	0.556804	+	0.964414i	0.997761	+	0.0668850i	$0.0213061\pi$
$349$	10.4020	+	18.0167i	0.556804	+	0.964414i	−0.440956	+	0.897529i	$0.645361\pi$
$350$		−	11.1884i		−	0.598043i
$351$		0			0
$352$		−	4.49290i		−	0.239472i
$353$	10.2974	+	17.8356i	0.548076	+	0.949296i	0.998406	+	0.0564335i	$0.0179729\pi$
$353$	10.2974	+	17.8356i	0.548076	+	0.949296i	−0.450330	+	0.892862i	$0.648694\pi$
$354$		0			0
$355$	0.256025	+	0.147816i	0.0135884	+	0.00784527i
$356$	0.00287481	+	0.00165977i	0.000152364	+	8.79677e-5i
$357$		0			0
$358$	−9.54084	+	5.50841i	−0.504249	+	0.291128i
$359$	−34.3488			−1.81286			−0.906430	−	0.422357i	$-0.861203\pi$
$359$	−34.3488			−1.81286			−0.906430	+	0.422357i	$0.861203\pi$
$360$		0			0
$361$	18.9963			0.999807
$362$	2.44120	−	1.40943i	0.128307	−	0.0740779i
$363$		0			0
$364$	2.49004	−	4.31287i	0.130513	−	0.226056i
$365$	0.382298	−	0.662160i	0.0200104	−	0.0346590i
$366$		0			0
$367$	−18.5511	−	32.1314i	−0.968359	−	1.67725i	−0.700306	−	0.713843i	$-0.746953\pi$
$367$	−18.5511	−	32.1314i	−0.968359	−	1.67725i	−0.268053	−	0.963404i	$-0.586380\pi$
$368$	0.0506544			0.00264054
$369$		0			0
$370$	−0.0530414			−0.00275749
$371$	−0.985392	−	1.70675i	−0.0511590	−	0.0886100i
$372$		0			0
$373$	−14.4749	+	25.0713i	−0.749483	+	1.29814i	0.198588	+	0.980083i	$0.436365\pi$
$373$	−14.4749	+	25.0713i	−0.749483	+	1.29814i	−0.948071	+	0.318060i	$0.896969\pi$
$374$	6.98415	−	12.0969i	0.361142	−	0.625516i
$375$		0			0
$376$	−8.96301	+	5.17479i	−0.462232	+	0.266870i
$377$	12.3740			0.637295
$378$		0			0
$379$	15.9088			0.817181			0.408591	−	0.912718i	$-0.366020\pi$
$379$	15.9088			0.817181			0.408591	+	0.912718i	$0.366020\pi$
$380$	−0.00798333	+	0.00460918i	−0.000409536	+	0.000236446i
$381$		0			0
$382$	15.8790	+	9.16777i	0.812442	+	0.469064i
$383$	−30.4846	−	17.6003i	−1.55769	−	0.899333i	−0.997477	−	0.0709852i	$-0.977386\pi$
$383$	−30.4846	−	17.6003i	−1.55769	−	0.899333i	−0.560214	−	0.828348i	$-0.689281\pi$
$384$		0			0
$385$	0.769489	+	1.33279i	0.0392168	+	0.0679254i
$386$		−	22.3584i		−	1.13801i
$387$		0			0
$388$			3.49110i			0.177234i
$389$	−7.23140	−	12.5251i	−0.366646	−	0.635050i	0.622393	−	0.782705i	$-0.286161\pi$
$389$	−7.23140	−	12.5251i	−0.366646	−	0.635050i	−0.989039	+	0.147655i	$0.952827\pi$
$390$		0			0
$391$	0.136384	+	0.0787416i	0.00689726	+	0.00398213i
$392$	0.973004	−	1.68529i	0.0491441	−	0.0851201i
$393$		0			0
$394$	0.876924	+	1.51888i	0.0441788	+	0.0765199i
$395$			0.160893i			0.00809539i
$396$		0			0
$397$		−	20.6165i		−	1.03471i	−0.855770	−	0.517356i	$-0.826916\pi$
$397$		−	20.6165i		−	1.03471i	0.855770	−	0.517356i	$-0.173084\pi$
$398$	8.74915	−	5.05133i	0.438555	−	0.253200i
$399$		0			0
$400$	2.48839	−	4.31002i	0.124420	−	0.215501i
$401$	1.07622	−	1.86407i	0.0537438	−	0.0930870i	−0.837902	−	0.545821i	$-0.816218\pi$
$401$	1.07622	−	1.86407i	0.0537438	−	0.0930870i	0.891646	+	0.452734i	$0.149551\pi$
$402$		0			0
$403$	0.00630888	−	0.00364243i	0.000314267	−	0.000181442i
$404$		−	1.65083i		−	0.0821319i
$405$		0			0
$406$	−12.5577			−0.623228
$407$	−1.35451	+	0.782029i	−0.0671408	+	0.0387637i
$408$		0			0
$409$	7.42636	−	12.8628i	0.367210	−	0.636026i	−0.621918	−	0.783082i	$-0.713646\pi$
$409$	7.42636	−	12.8628i	0.367210	−	0.636026i	0.989128	+	0.147056i	$0.0469798\pi$
$410$	0.213787	+	0.951908i	0.0105582	+	0.0470114i
$411$		0			0
$412$	−4.52054	−	7.82980i	−0.222711	−	0.385747i
$413$		−	9.63818i		−	0.474264i
$414$		0			0
$415$	0.959149			0.0470828
$416$	1.91844	−	1.10761i	0.0940594	−	0.0543052i
$417$		0			0
$418$	−0.135913	+	0.235408i	−0.00664773	+	0.0115142i
$419$	16.6809	−	28.8921i	0.814913	−	1.41147i	−0.0944767	−	0.995527i	$-0.530118\pi$
$419$	16.6809	−	28.8921i	0.814913	−	1.41147i	0.909390	−	0.415944i	$-0.136549\pi$
$420$		0			0
$421$	5.14435	−	2.97009i	0.250720	−	0.144753i	−0.369374	−	0.929281i	$-0.620428\pi$
$421$	5.14435	−	2.97009i	0.250720	−	0.144753i	0.620094	+	0.784527i	$0.287094\pi$
$422$		−	0.862804i		−	0.0420006i
$423$		0			0
$424$		−	0.876641i		−	0.0425735i
$425$	13.3997	−	7.73634i	0.649983	−	0.375268i
$426$		0			0
$427$	−11.1502	−	6.43756i	−0.539595	−	0.311535i
$428$	−9.17551	+	15.8925i	−0.443515	+	0.768191i
$429$		0			0
$430$	0.265364	+	0.459623i	0.0127970	+	0.0221650i
$431$	−1.21900			−0.0587171			−0.0293585	−	0.999569i	$-0.509346\pi$
$431$	−1.21900			−0.0587171			−0.0293585	+	0.999569i	$0.509346\pi$
$432$		0			0
$433$	−19.0267			−0.914365			−0.457182	−	0.889373i	$-0.651141\pi$
$433$	−19.0267			−0.914365			−0.457182	+	0.889373i	$0.651141\pi$
$434$	−0.00640252	+	0.00369649i	−0.000307331	+	0.000177437i
$435$		0			0
$436$	−10.0027	−	5.77507i	−0.479043	−	0.276576i
$437$	−0.00265407	−	0.00153233i	−0.000126962	−	7.33013e-5i
$438$		0			0
$439$	25.0111	−	14.4402i	1.19372	−	0.689192i	0.234568	−	0.972100i	$-0.424632\pi$
$439$	25.0111	−	14.4402i	1.19372	−	0.689192i	0.959147	+	0.282908i	$0.0912991\pi$
$440$			0.684565i			0.0326354i
$441$		0			0
$442$	6.88708			0.327585
$443$	−9.41162	−	16.3014i	−0.447160	−	0.774503i	0.551040	−	0.834479i	$-0.314231\pi$
$443$	−9.41162	−	16.3014i	−0.447160	−	0.774503i	−0.998200	+	0.0599755i	$0.980898\pi$
$444$		0			0
$445$	−0.000438023	0	0.000252893i	−2.07643e−5	0	1.19883e-5i
$446$	11.3675	−	19.6891i	0.538267	−	0.932306i
$447$		0			0
$448$	−1.94692	+	1.12405i	−0.0919833	+	0.0531066i
$449$	−31.1337			−1.46929			−0.734645	−	0.678452i	$-0.762651\pi$
$449$	−31.1337			−1.46929			−0.734645	+	0.678452i	$0.762651\pi$
$450$		0			0
$451$	19.4941	+	21.1568i	0.917944	+	0.996234i
$452$	−7.94827	−	13.7668i	−0.373855	−	0.647536i
$453$		0			0
$454$	−8.80325	−	5.08256i	−0.413157	−	0.238536i
$455$	−0.379397	+	0.657135i	−0.0177864	+	0.0308070i
$456$		0			0
$457$	25.2256	−	14.5640i	1.18000	−	0.681276i	0.223988	−	0.974592i	$-0.428092\pi$
$457$	25.2256	−	14.5640i	1.18000	−	0.681276i	0.956015	+	0.293316i	$0.0947589\pi$
$458$			16.1536i			0.754810i
$459$		0			0
$460$	−0.00771802			−0.000359854
$461$	−11.9827	−	20.7547i	−0.558091	−	0.966641i	−0.997656	−	0.0684307i	$-0.978201\pi$
$461$	−11.9827	−	20.7547i	−0.558091	−	0.966641i	0.439565	−	0.898211i	$-0.355133\pi$
$462$		0			0
$463$	−7.25914	−	4.19107i	−0.337361	−	0.194775i	0.321744	−	0.946827i	$-0.395731\pi$
$463$	−7.25914	−	4.19107i	−0.337361	−	0.194775i	−0.659104	+	0.752051i	$0.729064\pi$
$464$	−4.83752	−	2.79295i	−0.224576	−	0.129659i
$465$		0			0
$466$	−2.32752	+	1.34380i	−0.107820	+	0.0622502i
$467$	23.9715			1.10927			0.554635	−	0.832094i	$-0.312858\pi$
$467$	23.9715			1.10927			0.554635	+	0.832094i	$0.312858\pi$
$468$		0			0
$469$	3.36688			0.155468
$470$	1.36566	−	0.788463i	0.0629931	−	0.0363691i
$471$		0			0
$472$	2.14362	−	3.71286i	0.0986681	−	0.170898i
$473$	13.5531	+	7.82491i	0.623174	+	0.359790i
$474$		0			0
$475$	−0.260762	+	0.150551i	−0.0119646	+	0.00690776i
$476$	−6.98931			−0.320354
$477$		0			0
$478$		−	27.1556i		−	1.24207i
$479$	10.1348	−	5.85131i	0.463069	−	0.267353i	−0.250265	−	0.968177i	$-0.580518\pi$
$479$	10.1348	−	5.85131i	0.463069	−	0.267353i	0.713334	+	0.700824i	$0.247184\pi$
$480$		0			0
$481$	−0.667845	−	0.385580i	−0.0304511	−	0.0175810i
$482$	−12.1315	+	21.0123i	−0.552574	+	0.957086i
$483$		0			0
$484$	4.59306	+	7.95542i	0.208776	+	0.361610i
$485$		−	0.531925i		−	0.0241535i
$486$		0			0
$487$	22.9890			1.04173			0.520865	−	0.853639i	$-0.325610\pi$
$487$	22.9890			1.04173			0.520865	+	0.853639i	$0.325610\pi$
$488$	−2.86354	−	4.95981i	−0.129627	−	0.224520i
$489$		0			0
$490$	−0.148253	+	0.256782i	−0.00669738	+	0.0116002i
$491$	4.35559	−	7.54411i	0.196565	−	0.340461i	−0.750847	−	0.660476i	$-0.770355\pi$
$491$	4.35559	−	7.54411i	0.196565	−	0.340461i	0.947412	+	0.320015i	$0.103688\pi$
$492$		0			0
$493$	−8.68319	−	15.0397i	−0.391071	−	0.677356i
$494$	−0.134024			−0.00603004
$495$		0			0
$496$	−0.00328854			−0.000147660
$497$	−2.18098	−	3.77756i	−0.0978302	−	0.169447i
$498$		0			0
$499$	−24.1741	−	13.9569i	−1.08218	−	0.624798i	−0.150698	−	0.988580i	$-0.548152\pi$
$499$	−24.1741	−	13.9569i	−1.08218	−	0.624798i	−0.931484	+	0.363781i	$0.881486\pi$
$500$	−0.760062	+	1.31647i	−0.0339910	+	0.0588742i
$501$		0			0
$502$	13.2514	+	22.9520i	0.591437	+	1.02440i
$503$			10.0849i			0.449666i	0.974397	+	0.224833i	$0.0721836\pi$
$503$			10.0849i			0.449666i	−0.974397	+	0.224833i	$0.927816\pi$
$504$		0			0
$505$			0.251531i			0.0111930i
$506$	−0.197094	+	0.113793i	−0.00876192	+	0.00505869i
$507$		0			0
$508$	8.74909	−	15.1539i	0.388178	−	0.672344i
$509$	10.5634	+	6.09879i	0.468215	+	0.270324i	0.715492	−	0.698621i	$-0.246202\pi$
$509$	10.5634	+	6.09879i	0.468215	+	0.270324i	−0.247277	+	0.968945i	$0.579536\pi$
$510$		0			0
$511$	−9.76993	+	5.64067i	−0.432196	+	0.249529i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			2.41004i			0.106302i
$515$	0.688777	+	1.19300i	0.0303511	+	0.0525697i
$516$		0			0
$517$	23.2498	−	40.2699i	1.02253	−	1.77107i
$518$	0.677757	+	0.391303i	0.0297790	+	0.0171929i
$519$		0			0
$520$	−0.292306	+	0.168763i	−0.0128185	+	0.00740074i
$521$			18.7938i			0.823370i	0.911326	+	0.411685i	$0.135060\pi$
$521$			18.7938i			0.823370i	−0.911326	+	0.411685i	$0.864940\pi$
$522$		0			0
$523$	−20.8411			−0.911316			−0.455658	−	0.890155i	$-0.650596\pi$
$523$	−20.8411			−0.911316			−0.455658	+	0.890155i	$0.650596\pi$
$524$	8.70047	+	15.0696i	0.380082	+	0.658321i
$525$		0			0
$526$	−7.28003	−	4.20313i	−0.317424	−	0.183265i
$527$	−0.00885422	−	0.00511199i	−0.000385696	−	0.000222682i
$528$		0			0
$529$	11.4987	+	19.9164i	0.499944	+	0.865929i
$530$			0.133570i			0.00580193i
$531$		0			0
$532$	0.136014			0.00589694
$533$	−4.22803	+	13.5396i	−0.183136	+	0.586465i
$534$		0			0
$535$	1.39804	−	2.42147i	0.0604424	−	0.104689i
$536$	1.29700	+	0.748824i	0.0560220	+	0.0323443i
$537$		0			0
$538$	3.80678	+	6.59353i	0.164122	+	0.284267i
$539$			8.74322i			0.376597i
$540$		0			0
$541$	2.31546			0.0995496			0.0497748	−	0.998760i	$-0.484150\pi$
$541$	2.31546			0.0995496			0.0497748	+	0.998760i	$0.484150\pi$
$542$	6.49135	+	11.2433i	0.278827	+	0.482943i
$543$		0			0
$544$	−2.69245	−	1.55449i	−0.115438	−	0.0666481i
$545$	1.52407	+	0.879925i	0.0652842	+	0.0376918i
$546$		0			0
$547$	31.2092	−	18.0186i	1.33441	−	0.770421i	0.348437	−	0.937332i	$-0.386713\pi$
$547$	31.2092	−	18.0186i	1.33441	−	0.770421i	0.985972	+	0.166911i	$0.0533792\pi$
$548$			13.9388i			0.595436i
$549$		0			0
$550$			22.3602i			0.953441i
$551$	0.168977	+	0.292677i	0.00719866	+	0.0124684i
$552$		0			0
$553$	1.18696	−	2.05587i	0.0504746	−	0.0874245i
$554$	5.19938	−	9.00560i	0.220901	−	0.382611i
$555$		0			0
$556$	2.48118	+	4.29753i	0.105225	+	0.182256i
$557$			5.07788i			0.215157i	0.994197	+	0.107578i	$0.0343096\pi$
$557$			5.07788i			0.215157i	−0.994197	+	0.107578i	$0.965690\pi$
$558$		0			0
$559$			7.71616i			0.326359i
$560$	0.296645	−	0.171268i	0.0125355	−	0.00723739i
$561$		0			0
$562$	−0.455533	−	0.263002i	−0.0192155	−	0.0110941i
$563$	1.13978	+	0.658050i	0.0480358	+	0.0277335i	0.523826	−	0.851826i	$-0.324504\pi$
$563$	1.13978	+	0.658050i	0.0480358	+	0.0277335i	−0.475790	+	0.879559i	$0.657838\pi$
$564$		0			0
$565$	1.21105	+	2.09759i	0.0509491	+	0.0882465i
$566$	−0.235314			−0.00989097
$567$		0			0
$568$		−	1.94028i		−	0.0814122i
$569$	−10.4013	−	18.0157i	−0.436047	−	0.755256i	0.561333	−	0.827590i	$-0.310289\pi$
$569$	−10.4013	−	18.0157i	−0.436047	−	0.755256i	−0.997380	+	0.0723342i	$0.976955\pi$
$570$		0			0
$571$	−33.5087	−	19.3463i	−1.40230	−	0.809616i	−0.407669	−	0.913130i	$-0.633658\pi$
$571$	−33.5087	−	19.3463i	−1.40230	−	0.809616i	−0.994628	+	0.103514i	$0.966991\pi$
$572$	−4.97640	+	8.61937i	−0.208074	+	0.360394i
$573$		0			0
$574$	4.29079	−	13.7406i	0.179094	−	0.573520i
$575$	−0.252096			−0.0105131
$576$		0			0
$577$		−	10.4317i		−	0.434279i	−0.976141	−	0.217139i	$-0.930327\pi$
$577$		−	10.4317i		−	0.434279i	0.976141	−	0.217139i	$-0.0696726\pi$
$578$	3.66714	+	6.35168i	0.152533	+	0.264195i
$579$		0			0
$580$	0.737075	+	0.425550i	0.0306054	+	0.0176700i
$581$	−12.2559	−	7.07595i	−0.508461	−	0.293560i
$582$		0			0
$583$	1.96933	+	3.41098i	0.0815613	+	0.141268i
$584$	−5.01815			−0.207653
$585$		0			0
$586$		−	31.1095i		−	1.28512i
$587$	−30.2978	+	17.4925i	−1.25052	+	0.721991i	−0.971214	−	0.238210i	$-0.923439\pi$
$587$	−30.2978	+	17.4925i	−1.25052	+	0.721991i	−0.279311	+	0.960201i	$0.590106\pi$
$588$		0			0
$589$	0.000172305	0	9.94805e-5i	7.09971e−6	0	4.09902e-6i
$590$	−0.326615	+	0.565714i	−0.0134465	+	0.0232901i
$591$		0			0
$592$	0.174059	+	0.301479i	0.00715378	+	0.0123907i
$593$			22.5454i			0.925829i	0.886403	+	0.462914i	$0.153196\pi$
$593$			22.5454i			0.925829i	−0.886403	+	0.462914i	$0.846804\pi$
$594$		0			0
$595$	1.06493			0.0436580
$596$	−8.57976	+	4.95353i	−0.351441	+	0.202904i
$597$		0			0
$598$	−0.0971776	−	0.0561055i	−0.00397389	−	0.00229433i
$599$	−13.5814	+	23.5236i	−0.554920	+	0.961150i	0.442990	+	0.896527i	$0.353918\pi$
$599$	−13.5814	+	23.5236i	−0.554920	+	0.961150i	−0.997910	+	0.0646232i	$0.979415\pi$
$600$		0			0
$601$	28.8178	−	16.6379i	1.17550	−	0.678676i	0.220531	−	0.975380i	$-0.429221\pi$
$601$	28.8178	−	16.6379i	1.17550	−	0.678676i	0.954969	+	0.296704i	$0.0958876\pi$
$602$		−	7.83069i		−	0.319155i
$603$		0			0
$604$			7.82375i			0.318344i
$605$	−0.699827	−	1.21214i	−0.0284520	−	0.0492804i
$606$		0			0
$607$	−11.6925	+	20.2520i	−0.474583	+	0.822002i	−0.999576	−	0.0291043i	$-0.990735\pi$
$607$	−11.6925	+	20.2520i	−0.474583	+	0.822002i	0.524993	+	0.851106i	$0.324068\pi$
$608$	0.0523957	+	0.0302507i	0.00212493	+	0.00122683i
$609$		0			0
$610$	0.436307	+	0.755706i	0.0176656	+	0.0305977i
$611$	22.9267			0.927515
$612$		0			0
$613$	−2.50447			−0.101155			−0.0505774	−	0.998720i	$-0.516106\pi$
$613$	−2.50447			−0.101155			−0.0505774	+	0.998720i	$0.516106\pi$
$614$	11.4955	+	19.9108i	0.463920	+	0.803533i
$615$		0			0
$616$	5.05026	−	8.74731i	0.203481	−	0.352439i
$617$	−4.37348	+	7.57509i	−0.176070	+	0.304962i	−0.940531	−	0.339708i	$-0.889672\pi$
$617$	−4.37348	+	7.57509i	−0.176070	+	0.304962i	0.764461	+	0.644670i	$0.223005\pi$
$618$		0			0
$619$	−6.04371	−	10.4680i	−0.242917	−	0.420745i	0.718627	−	0.695396i	$-0.244771\pi$
$619$	−6.04371	−	10.4680i	−0.242917	−	0.420745i	−0.961544	+	0.274651i	$0.911438\pi$
$620$	0.000501062	0		2.01231e−5	0
$621$		0			0
$622$		−	22.4086i		−	0.898501i
$623$	0.00373134	+	0.00646288i	0.000149493	+	0.000258930i
$624$		0			0
$625$	−12.3262	+	21.3495i	−0.493046	+	0.853981i
$626$	−18.2668	−	10.5463i	−0.730086	−	0.421515i
$627$		0			0
$628$	−13.7927	+	7.96323i	−0.550390	+	0.317768i
$629$			1.08229i			0.0431537i
$630$		0			0
$631$	35.0019			1.39341			0.696703	−	0.717360i	$-0.254650\pi$
$631$	35.0019			1.39341			0.696703	+	0.717360i	$0.254650\pi$
$632$	0.914489	−	0.527980i	0.0363764	−	0.0210019i
$633$		0			0
$634$	−4.43915	−	2.56295i	−0.176301	−	0.101788i
$635$	−1.33306	+	2.30894i	−0.0529011	+	0.0916273i
$636$		0			0
$637$	−3.73331	+	2.15543i	−0.147919	+	0.0854011i
$638$	25.0968			0.993594
$639$		0			0
$640$	0.152366			0.00602280
$641$	17.8871	−	10.3271i	0.706496	−	0.407896i	−0.103266	−	0.994654i	$-0.532929\pi$
$641$	17.8871	−	10.3271i	0.706496	−	0.407896i	0.809762	+	0.586758i	$0.199596\pi$
$642$		0			0
$643$	−6.59943	−	3.81018i	−0.260256	−	0.150259i	0.364195	−	0.931323i	$-0.381344\pi$
$643$	−6.59943	−	3.81018i	−0.260256	−	0.150259i	−0.624451	+	0.781064i	$0.714677\pi$
$644$	0.0986200	+	0.0569383i	0.00388617	+	0.00224368i
$645$		0			0
$646$	0.0940485	+	0.162897i	0.00370029	+	0.00640909i
$647$	19.1667			0.753519			0.376760	−	0.926311i	$-0.377038\pi$
$647$	19.1667			0.753519			0.376760	+	0.926311i	$0.377038\pi$
$648$		0			0
$649$			19.2621i			0.756105i
$650$	−9.54768	+	5.51236i	−0.374491	+	0.216212i
$651$		0			0
$652$	2.06862	−	3.58296i	0.0810135	−	0.140320i
$653$	3.52182	+	2.03333i	0.137820	+	0.0795702i	0.567324	−	0.823494i	$-0.307979\pi$
$653$	3.52182	+	2.03333i	0.137820	+	0.0795702i	−0.429505	+	0.903065i	$0.641312\pi$
$654$		0			0
$655$	−1.32566	−	2.29610i	−0.0517977	−	0.0897162i
$656$	4.70894	−	4.33888i	0.183853	−	0.169405i
$657$		0			0
$658$	−23.2670			−0.907042
$659$	−2.48203	+	1.43300i	−0.0966863	+	0.0558218i	−0.547564	−	0.836764i	$-0.684445\pi$
$659$	−2.48203	+	1.43300i	−0.0966863	+	0.0558218i	0.450877	+	0.892586i	$0.351111\pi$
$660$		0			0
$661$	−20.8742	+	36.1552i	−0.811912	+	1.40627i	0.0996118	+	0.995026i	$0.468240\pi$
$661$	−20.8742	+	36.1552i	−0.811912	+	1.40627i	−0.911524	+	0.411247i	$0.865093\pi$
$662$	−19.3235	−	11.1564i	−0.751030	−	0.433607i
$663$		0			0
$664$	−3.14751	−	5.45166i	−0.122147	−	0.211565i
$665$	−0.0207239			−0.000803637
$666$		0			0
$667$			0.282950i			0.0109559i
$668$	−0.0737849	+	0.0425997i	−0.00285482	+	0.00164823i
$669$		0			0
$670$	−0.197619	−	0.114095i	−0.00763469	−	0.00440789i
$671$	22.2839	+	12.8656i	0.860260	+	0.496671i
$672$		0			0
$673$	−4.77694	+	2.75797i	−0.184138	+	0.106312i	−0.589235	−	0.807962i	$-0.700571\pi$
$673$	−4.77694	+	2.75797i	−0.184138	+	0.106312i	0.405098	+	0.914273i	$0.367238\pi$
$674$	−11.3150			−0.435837
$675$		0			0
$676$	8.09276			0.311260
$677$	−4.69237	−	8.12742i	−0.180342	−	0.312362i	0.761655	−	0.647983i	$-0.224387\pi$
$677$	−4.69237	−	8.12742i	−0.180342	−	0.312362i	−0.941997	+	0.335621i	$0.891054\pi$
$678$		0			0
$679$	−3.92419	+	6.79689i	−0.150596	+	0.260841i
$680$	0.410238	+	0.236851i	0.0157319	+	0.00908282i
$681$		0			0
$682$	0.0127956	−	0.00738753i	0.000489968	−	0.000282883i
$683$			23.2267i			0.888745i	0.895842	+	0.444372i	$0.146573\pi$
$683$			23.2267i			0.888745i	−0.895842	+	0.444372i	$0.853427\pi$
$684$		0			0
$685$		−	2.12380i		−	0.0811462i
$686$	17.4172	−	10.0558i	0.664990	−	0.383932i
$687$		0			0
$688$	1.74162	−	3.01657i	0.0663986	−	0.115006i
$689$	−0.970980	+	1.68179i	−0.0369914	+	0.0640710i
$690$		0			0
$691$	−11.8142	+	6.82090i	−0.449431	+	0.259479i	−0.707590	−	0.706623i	$-0.750218\pi$
$691$	−11.8142	+	6.82090i	−0.449431	+	0.259479i	0.258159	+	0.966103i	$0.416884\pi$
$692$	18.6044			0.707234
$693$		0			0
$694$		−	9.61122i		−	0.364837i
$695$	−0.378048	−	0.654798i	−0.0143402	−	0.0248379i
$696$		0			0
$697$	19.4233	−	4.36223i	0.735710	−	0.165231i
$698$	−10.4020	+	18.0167i	−0.393720	+	0.681943i
$699$		0			0
$700$	9.68940	−	5.59418i	0.366225	−	0.211440i
$701$	7.54613			0.285013			0.142507	−	0.989794i	$-0.454484\pi$
$701$	7.54613			0.285013			0.142507	+	0.989794i	$0.454484\pi$
$702$		0			0
$703$		−	0.0210616i		−	0.000794353i
$704$	3.89096	−	2.24645i	0.146646	−	0.0846662i
$705$		0			0
$706$	−10.2974	+	17.8356i	−0.387548	+	0.671253i
$707$	1.85562	−	3.21403i	0.0697879	−	0.120876i
$708$		0			0
$709$	23.4317	−	13.5283i	0.879997	−	0.508067i	0.00933984	−	0.999956i	$-0.497027\pi$
$709$	23.4317	−	13.5283i	0.879997	−	0.508067i	0.870658	+	0.491890i	$0.163694\pi$
$710$			0.295633i			0.0110949i
$711$		0			0
$712$			0.00331954i			0.000124405i
$713$	8.32895e−5	0	0.000144262i	3.11922e−6	0	5.40264e-6i
$714$		0			0
$715$	0.758234	−	1.31330i	0.0283564	−	0.0491146i
$716$	−9.54084	−	5.50841i	−0.356558	−	0.205859i
$717$		0			0
$718$	−17.1744	−	29.7469i	−0.640943	−	1.11015i
$719$		−	21.8641i		−	0.815395i	−0.913117	−	0.407698i	$-0.866332\pi$
$719$		−	21.8641i		−	0.815395i	0.913117	−	0.407698i	$-0.133668\pi$
$720$		0			0
$721$		−	20.3253i		−	0.756955i
$722$	9.49817	+	16.4513i	0.353485	+	0.612254i
$723$		0			0
$724$	2.44120	+	1.40943i	0.0907266	+	0.0523810i
$725$	24.0753	+	13.8999i	0.894135	+	0.516229i
$726$		0			0
$727$	−37.3725	+	21.5770i	−1.38607	+	0.800247i	−0.992869	−	0.119207i	$-0.961965\pi$
$727$	−37.3725	+	21.5770i	−1.38607	+	0.800247i	−0.393198	+	0.919454i	$0.628631\pi$
$728$	4.98007			0.184574
$729$		0			0
$730$	0.764596			0.0282990
$731$	9.37844	−	5.41464i	0.346874	−	0.200268i
$732$		0			0
$733$	1.20158	−	2.08120i	0.0443815	−	0.0768710i	−0.842981	−	0.537943i	$-0.819202\pi$
$733$	1.20158	−	2.08120i	0.0443815	−	0.0768710i	0.887363	+	0.461072i	$0.152535\pi$
$734$	18.5511	−	32.1314i	0.684733	−	1.18599i
$735$		0			0
$736$	0.0253272	+	0.0438680i	0.000933573	+	0.00161700i
$737$	−6.72878			−0.247858
$738$		0			0
$739$	−5.19796			−0.191210			−0.0956050	−	0.995419i	$-0.530479\pi$
$739$	−5.19796			−0.191210			−0.0956050	+	0.995419i	$0.530479\pi$
$740$	−0.0265207	−	0.0459352i	−0.000974920	−	0.00168861i
$741$		0			0
$742$	0.985392	−	1.70675i	0.0361749	−	0.0626567i
$743$	10.6340	−	18.4187i	0.390125	−	0.675716i	−0.602341	−	0.798239i	$-0.705765\pi$
$743$	10.6340	−	18.4187i	0.390125	−	0.675716i	0.992466	+	0.122523i	$0.0390985\pi$
$744$		0			0
$745$	1.30727	−	0.754750i	0.0478945	−	0.0276519i
$746$	−28.9498			−1.05993
$747$		0			0
$748$	13.9683			0.510731
$749$	−35.7280	+	20.6275i	−1.30547	+	0.753714i
$750$		0			0
$751$	11.9325	+	6.88921i	0.435422	+	0.251391i	0.701654	−	0.712518i	$-0.252445\pi$
$751$	11.9325	+	6.88921i	0.435422	+	0.251391i	−0.266232	+	0.963909i	$0.585779\pi$
$752$	−8.96301	−	5.17479i	−0.326847	−	0.188705i
$753$		0			0
$754$	6.18701	+	10.7162i	0.225318	+	0.390262i
$755$		−	1.19207i		−	0.0433841i
$756$		0			0
$757$			28.8018i			1.04682i	0.852081	+	0.523410i	$0.175341\pi$
$757$			28.8018i			1.04682i	−0.852081	+	0.523410i	$0.824659\pi$
$758$	7.95441	+	13.7774i	0.288917	+	0.500419i
$759$		0			0
$760$	−0.00798333	−	0.00460918i	−0.000289586	−	0.000167192i
$761$	16.8740	−	29.2266i	0.611681	−	1.05946i	−0.379276	−	0.925284i	$-0.623827\pi$
$761$	16.8740	−	29.2266i	0.611681	−	1.05946i	0.990957	−	0.134179i	$-0.0428398\pi$
$762$		0			0
$763$	−12.9830	−	22.4872i	−0.470015	−	0.814091i
$764$			18.3355i			0.663356i
$765$		0			0
$766$		−	35.2006i		−	1.27185i
$767$	−8.22483	+	4.74861i	−0.296981	+	0.171462i
$768$		0			0
$769$	6.64402	−	11.5078i	0.239589	−	0.414981i	−0.721007	−	0.692928i	$-0.756321\pi$
$769$	6.64402	−	11.5078i	0.239589	−	0.414981i	0.960596	+	0.277947i	$0.0896539\pi$
$770$	−0.769489	+	1.33279i	−0.0277304	+	0.0480305i
$771$		0			0
$772$	19.3630	−	11.1792i	0.696888	−	0.402348i
$773$		−	33.2399i		−	1.19556i	−0.801661	−	0.597779i	$-0.796050\pi$
$773$		−	33.2399i		−	1.19556i	0.801661	−	0.597779i	$-0.203950\pi$
$774$		0			0
$775$	0.0163663			0.000587896
$776$	−3.02338	+	1.74555i	−0.108533	+	0.0626616i
$777$		0			0
$778$	7.23140	−	12.5251i	0.259258	−	0.449048i
$779$	−0.377982	+	0.0848901i	−0.0135426	+	0.00304150i
$780$		0			0
$781$	4.35873	+	7.54955i	0.155968	+	0.270144i
$782$			0.157483i			0.00563159i
$783$		0			0
$784$	1.94601			0.0695003
$785$	2.10154	−	1.21333i	0.0750073	−	0.0433055i
$786$		0			0
$787$	−27.0243	+	46.8074i	−0.963311	+	1.66850i	−0.249226	+	0.968445i	$0.580176\pi$
$787$	−27.0243	+	46.8074i	−0.963311	+	1.66850i	−0.714085	+	0.700059i	$0.753157\pi$
$788$	−0.876924	+	1.51888i	−0.0312391	+	0.0541078i
$789$		0			0
$790$	−0.139337	+	0.0804463i	−0.00495739	+	0.00286215i
$791$		−	35.7371i		−	1.27067i
$792$		0			0
$793$			12.6868i			0.450522i
$794$	17.8544	−	10.3083i	0.633630	−	0.365826i
$795$		0			0
$796$	8.74915	+	5.05133i	0.310106	+	0.179040i
$797$	−7.72987	+	13.3885i	−0.273806	+	0.474246i	−0.969833	−	0.243770i	$-0.921616\pi$
$797$	−7.72987	+	13.3885i	−0.273806	+	0.474246i	0.696027	+	0.718015i	$0.254949\pi$
$798$		0			0
$799$	−16.0883	−	27.8657i	−0.569163	−	0.985819i
$800$	4.97678			0.175956
$801$		0			0
$802$	2.15244			0.0760052
$803$	19.5254	−	11.2730i	0.689038	−	0.397816i
$804$		0			0
$805$	−0.0150264	−	0.00867547i	−0.000529609	−	0.000305770i
$806$	0.00630888	+	0.00364243i	0.000222221	+	0.000128299i
$807$		0			0
$808$	1.42966	−	0.825415i	0.0502953	−	0.0290380i
$809$			50.5603i			1.77761i	0.458290	+	0.888803i	$0.348462\pi$
$809$			50.5603i			1.77761i	−0.458290	+	0.888803i	$0.651538\pi$
$810$		0			0
$811$	6.13463			0.215416			0.107708	−	0.994183i	$-0.465649\pi$
$811$	6.13463			0.215416			0.107708	+	0.994183i	$0.465649\pi$
$812$	−6.27885	−	10.8753i	−0.220344	−	0.381648i
$813$		0			0
$814$	−1.35451	−	0.782029i	−0.0474757	−	0.0274101i
$815$	−0.315188	+	0.545922i	−0.0110406	+	0.0191228i
$816$		0			0
$817$	−0.182507	+	0.105370i	−0.00638510	+	0.00368644i
$818$	14.8527			0.519313
$819$		0			0
$820$	−0.717483	+	0.661098i	−0.0250556	+	0.0230866i
$821$	4.37657	+	7.58045i	0.152743	+	0.264559i	0.932235	−	0.361853i	$-0.117856\pi$
$821$	4.37657	+	7.58045i	0.152743	+	0.264559i	−0.779492	+	0.626413i	$0.784523\pi$
$822$		0			0
$823$	−26.3734	−	15.2267i	−0.919319	−	0.530769i	−0.0359014	−	0.999355i	$-0.511430\pi$
$823$	−26.3734	−	15.2267i	−0.919319	−	0.530769i	−0.883418	+	0.468586i	$0.844764\pi$
$824$	4.52054	−	7.82980i	0.157480	−	0.272764i
$825$		0			0
$826$	8.34691	−	4.81909i	0.290426	−	0.167678i
$827$		−	23.8217i		−	0.828361i	−0.910195	−	0.414181i	$-0.864068\pi$
$827$		−	23.8217i		−	0.828361i	0.910195	−	0.414181i	$-0.135932\pi$
$828$		0			0
$829$	−34.0006			−1.18089			−0.590445	−	0.807078i	$-0.701048\pi$
$829$	−34.0006			−1.18089			−0.590445	+	0.807078i	$0.701048\pi$
$830$	0.479575	+	0.830648i	0.0166463	+	0.0288322i
$831$		0			0
$832$	1.91844	+	1.10761i	0.0665101	+	0.0383996i
$833$	5.23953	+	3.02504i	0.181539	+	0.104812i
$834$		0			0
$835$	0.0112423	−	0.00649075i	0.000389056	−	0.000224622i
$836$	−0.271826			−0.00940131
$837$		0			0
$838$	33.3617			1.15246
$839$	−23.8762	+	13.7849i	−0.824298	+	0.475909i	−0.851896	−	0.523710i	$-0.824547\pi$
$839$	−23.8762	+	13.7849i	−0.824298	+	0.475909i	0.0275982	+	0.999619i	$0.491214\pi$
$840$		0			0
$841$	1.10110	−	1.90716i	0.0379689	−	0.0657641i
$842$	5.14435	+	2.97009i	0.177286	+	0.102356i
$843$		0			0
$844$	0.747210	−	0.431402i	0.0257200	−	0.0148495i
$845$	−1.23306			−0.0424187
$846$		0			0
$847$			20.6514i			0.709591i
$848$	0.759193	−	0.438321i	0.0260708	−	0.0150520i
$849$		0			0
$850$	13.3997	+	7.73634i	0.459607	+	0.265354i
$851$	0.00881685	−	0.0152712i	0.000302238	−	0.000523491i
$852$		0			0
$853$	−12.3422	−	21.3773i	−0.422589	−	0.731946i	0.573603	−	0.819134i	$-0.305545\pi$
$853$	−12.3422	−	21.3773i	−0.422589	−	0.731946i	−0.996192	+	0.0871877i	$0.972212\pi$
$854$		−	12.8751i		−	0.440578i
$855$		0			0
$856$	−18.3510			−0.627225
$857$	12.6375	+	21.8889i	0.431690	+	0.747709i	0.997019	−	0.0771563i	$-0.0245841\pi$
$857$	12.6375	+	21.8889i	0.431690	+	0.747709i	−0.565329	+	0.824866i	$0.691251\pi$
$858$		0			0
$859$	−4.48560	+	7.76928i	−0.153047	+	0.265085i	−0.932346	−	0.361567i	$-0.882242\pi$
$859$	−4.48560	+	7.76928i	−0.153047	+	0.265085i	0.779299	+	0.626652i	$0.215575\pi$
$860$	−0.265364	+	0.459623i	−0.00904883	+	0.0156730i
$861$		0			0
$862$	−0.609499	−	1.05568i	−0.0207596	−	0.0359567i
$863$	15.5313			0.528690			0.264345	−	0.964428i	$-0.414844\pi$
$863$	15.5313			0.528690			0.264345	+	0.964428i	$0.414844\pi$
$864$		0			0
$865$	−2.83468			−0.0963821
$866$	−9.51335	−	16.4776i	−0.323277	−	0.559932i
$867$		0			0
$868$	−0.00640252	−	0.00369649i	−0.000217316	−	0.000125467i
$869$	−2.37216	+	4.10870i	−0.0804701	+	0.139378i
$870$		0			0
$871$	−1.65882	−	2.87316i	−0.0562069	−	0.0973531i
$872$		−	11.5501i		−	0.391137i
$873$		0			0
$874$		−	0.00306466i		−	0.000103664i
$875$	−2.95956	+	1.70870i	−0.100051	+	0.0577647i
$876$		0			0
$877$	−22.1024	+	38.2825i	−0.746345	+	1.29271i	0.203219	+	0.979133i	$0.434860\pi$
$877$	−22.1024	+	38.2825i	−0.746345	+	1.29271i	−0.949564	+	0.313574i	$0.898474\pi$
$878$	25.0111	+	14.4402i	0.844084	+	0.487332i
$879$		0			0
$880$	−0.592851	+	0.342283i	−0.0199850	+	0.0115383i
$881$	−18.7461			−0.631574			−0.315787	−	0.948830i	$-0.602268\pi$
$881$	−18.7461			−0.631574			−0.315787	+	0.948830i	$0.602268\pi$
$882$		0			0
$883$			10.3327i			0.347724i	0.984770	+	0.173862i	$0.0556247\pi$
$883$			10.3327i			0.347724i	−0.984770	+	0.173862i	$0.944375\pi$
$884$	3.44354	+	5.96439i	0.115819	+	0.200604i
$885$		0			0
$886$	9.41162	−	16.3014i	0.316190	−	0.547656i
$887$	−27.9654	−	16.1458i	−0.938986	−	0.542124i	−0.0493435	−	0.998782i	$-0.515713\pi$
$887$	−27.9654	−	16.1458i	−0.938986	−	0.542124i	−0.889642	+	0.456658i	$0.849046\pi$
$888$		0			0
$889$	34.0675	−	19.6689i	1.14259	−	0.659674i
$890$		0	0.000505786i		0	1.69540e-5i
$891$		0			0
$892$	22.7350			0.761225
$893$	0.313082	+	0.542274i	0.0104769	+	0.0181465i
$894$		0			0
$895$	1.45370	+	0.839295i	0.0485919	+	0.0280545i
$896$	−1.94692	−	1.12405i	−0.0650420	−	0.0375520i
$897$		0			0
$898$	−15.5668	−	26.9626i	−0.519472	−	0.899753i
$899$		−	0.0183694i		−	0.000612654i
$900$		0			0
$901$	2.72545			0.0907980
$902$	−8.57524	+	27.4608i	−0.285524	+	0.914345i
$903$		0			0
$904$	7.94827	−	13.7668i	0.264355	−	0.457877i
$905$	−0.371957	−	0.214749i	−0.0123643	−	0.00713851i
$906$		0			0
$907$	7.00150	+	12.1269i	0.232481	+	0.402669i	0.958538	−	0.284966i	$-0.0919824\pi$
$907$	7.00150	+	12.1269i	0.232481	+	0.402669i	−0.726057	+	0.687635i	$0.758649\pi$
$908$		−	10.1651i		−	0.337341i
$909$		0			0
$910$	−0.758794			−0.0251538
$911$	−21.2207	−	36.7553i	−0.703073	−	1.21776i	−0.967383	−	0.253320i	$-0.918478\pi$
$911$	−21.2207	−	36.7553i	−0.703073	−	1.21776i	0.264310	−	0.964438i	$-0.414856\pi$
$912$		0			0
$913$	24.4937	+	14.1415i	0.810624	+	0.468014i
$914$	25.2256	+	14.5640i	0.834389	+	0.481735i
$915$		0			0
$916$	−13.9895	+	8.07682i	−0.462225	+	0.266866i
$917$			39.1192i			1.29183i
$918$		0			0
$919$			24.0226i			0.792432i	0.918157	+	0.396216i	$0.129677\pi$
$919$			24.0226i			0.792432i	−0.918157	+	0.396216i	$0.870323\pi$
$920$	−0.00385901	−	0.00668400i	−0.000127228	−	0.000220365i
$921$		0			0
$922$	11.9827	−	20.7547i	0.394630	−	0.683519i
$923$	−2.14908	+	3.72231i	−0.0707378	+	0.122521i
$924$		0			0
$925$	−0.866254	−	1.50040i	−0.0284823	−	0.0493327i
$926$		−	8.38213i		−	0.275454i
$927$		0			0
$928$		−	5.58589i		−	0.183366i
$929$	35.2695	−	20.3629i	1.15716	−	0.668084i	0.206535	−	0.978439i	$-0.433781\pi$
$929$	35.2695	−	20.3629i	1.15716	−	0.668084i	0.950621	+	0.310355i	$0.100448\pi$
$930$		0			0
$931$	−0.101962	−	0.0588680i	−0.00334168	−	0.00192932i
$932$	−2.32752	−	1.34380i	−0.0762406	−	0.0440175i
$933$		0			0
$934$	11.9858	+	20.7599i	0.392186	+	0.679286i
$935$	−2.12830			−0.0696027
$936$		0			0
$937$		−	30.1667i		−	0.985505i	−0.870170	−	0.492752i	$-0.835991\pi$
$937$		−	30.1667i		−	0.985505i	0.870170	−	0.492752i	$-0.164009\pi$
$938$	1.68344	+	2.91580i	0.0549662	+	0.0952043i
$939$		0			0
$940$	1.36566	+	0.788463i	0.0445429	+	0.0257168i
$941$	−11.2157	+	19.4261i	−0.365620	+	0.633272i	−0.988875	−	0.148746i	$-0.952476\pi$
$941$	−11.2157	+	19.4261i	−0.365620	+	0.633272i	0.623256	+	0.782018i	$0.285810\pi$
$942$		0			0
$943$	−0.309602	−	0.0966801i	−0.0100820	−	0.00314834i
$944$	4.28724			0.139538
$945$		0			0
$946$			15.6498i			0.508820i
$947$	−1.60522	−	2.78033i	−0.0521628	−	0.0903486i	0.838765	−	0.544494i	$-0.183278\pi$
$947$	−1.60522	−	2.78033i	−0.0521628	−	0.0903486i	−0.890928	+	0.454145i	$0.849945\pi$
$948$		0			0
$949$	9.62704	+	5.55817i	0.312507	+	0.180426i
$950$	−0.260762	−	0.150551i	−0.00846024	−	0.00488452i
$951$		0			0
$952$	−3.49465	−	6.05292i	−0.113262	−	0.196176i
$953$	−58.6410			−1.89957			−0.949784	−	0.312905i	$-0.898698\pi$
$953$	−58.6410			−1.89957			−0.949784	+	0.312905i	$0.898698\pi$
$954$		0			0
$955$		−	2.79371i		−	0.0904025i
$956$	23.5174	−	13.5778i	0.760607	−	0.439137i
$957$		0			0
$958$	10.1348	+	5.85131i	0.327439	+	0.189047i
$959$	−15.6680	+	27.1377i	−0.505945	+	0.876322i
$960$		0			0
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$		−	0.771161i		−	0.0248632i
$963$		0			0
$964$	−24.2630			−0.781457
$965$	−2.95026	+	1.70333i	−0.0949722	+	0.0548322i
$966$		0			0
$967$	8.04704	+	4.64596i	0.258775	+	0.149404i	0.623776	−	0.781603i	$-0.285598\pi$
$967$	8.04704	+	4.64596i	0.258775	+	0.149404i	−0.365000	+	0.931007i	$0.618931\pi$
$968$	−4.59306	+	7.95542i	−0.147627	+	0.255697i
$969$		0			0
$970$	0.460661	−	0.265963i	0.0147909	−	0.00853955i
$971$		−	48.0170i		−	1.54094i	−0.637478	−	0.770469i	$-0.720022\pi$
$971$		−	48.0170i		−	1.54094i	0.637478	−	0.770469i	$-0.279978\pi$
$972$		0			0
$973$			11.1559i			0.357642i
$974$	11.4945	+	19.9090i	0.368307	+	0.637926i
$975$		0			0
$976$	2.86354	−	4.95981i	0.0916598	−	0.158759i
$977$	−36.3768	−	21.0021i	−1.16380	−	0.671918i	−0.211585	−	0.977360i	$-0.567863\pi$
$977$	−36.3768	−	21.0021i	−1.16380	−	0.671918i	−0.952211	+	0.305442i	$0.901196\pi$
$978$		0			0
$979$	−0.00745718	−	0.0129162i	−0.000238332	−	0.000412804i
$980$	−0.296506			−0.00947153
$981$		0			0
$982$	8.71119			0.277985
$983$	−6.83770	−	11.8433i	−0.218089	−	0.377741i	0.736135	−	0.676835i	$-0.236649\pi$
$983$	−6.83770	−	11.8433i	−0.218089	−	0.377741i	−0.954224	+	0.299094i	$0.903316\pi$
$984$		0			0
$985$	0.133614	−	0.231425i	0.00425728	−	0.00737383i
$986$	8.68319	−	15.0397i	0.276529	−	0.478963i
$987$		0			0
$988$	−0.0670121	−	0.116068i	−0.00213194	−	0.00369263i
$989$	−0.176441			−0.00561051
$990$		0			0
$991$			45.7751i			1.45410i	0.686587	+	0.727048i	$0.259108\pi$
$991$			45.7751i			1.45410i	−0.686587	+	0.727048i	$0.740892\pi$
$992$	−0.00164427	−	0.00284796i	−5.22056e−5	−	9.04227e-5i
$993$		0			0
$994$	2.18098	−	3.77756i	0.0691764	−	0.119817i
$995$	−1.33307	−	0.769651i	−0.0422613	−	0.0243996i
$996$		0			0
$997$	−36.9732	+	21.3465i	−1.17095	+	0.676050i	−0.953904	−	0.300111i	$-0.902976\pi$
$997$	−36.9732	+	21.3465i	−1.17095	+	0.676050i	−0.217049	+	0.976161i	$0.569643\pi$
$998$		−	27.9139i		−	0.883598i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2214.2.i.b.901.12		36
3.2	odd	2		738.2.i.b.409.11	yes	36
9.2	odd	6		738.2.i.b.655.8	yes	36
9.7	even	3	inner	2214.2.i.b.1639.11		36
41.40	even	2	inner	2214.2.i.b.901.11		36
123.122	odd	2		738.2.i.b.409.8	✓	36
369.245	odd	6		738.2.i.b.655.11	yes	36
369.286	even	6	inner	2214.2.i.b.1639.12		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.i.b.409.8	✓	36	123.122	odd	2
738.2.i.b.409.11	yes	36	3.2	odd	2
738.2.i.b.655.8	yes	36	9.2	odd	6
738.2.i.b.655.11	yes	36	369.245	odd	6
2214.2.i.b.901.11		36	41.40	even	2	inner
2214.2.i.b.901.12		36	1.1	even	1	trivial
2214.2.i.b.1639.11		36	9.7	even	3	inner
2214.2.i.b.1639.12		36	369.286	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2214 = 2 \cdot 3^{3} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2214.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.0761831 - 0.131953i) q^{5} +(-1.94692 + 1.12405i) q^{7} -1.00000 q^{8} +0.152366 q^{10} +(3.89096 - 2.24645i) q^{11} +(1.91844 + 1.10761i) q^{13} +(-1.94692 - 1.12405i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.10897i q^{17} +0.0605013i q^{19} +(0.0761831 + 0.131953i) q^{20} +(3.89096 + 2.24645i) q^{22} +(-0.0253272 + 0.0438680i) q^{23} +(2.48839 + 4.31002i) q^{25} +2.21523i q^{26} -2.24811i q^{28} +(4.83752 - 2.79295i) q^{29} +(0.00164427 - 0.00284796i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.69245 - 1.55449i) q^{34} +0.342536i q^{35} -0.348118 q^{37} +(-0.0523957 + 0.0302507i) q^{38} +(-0.0761831 + 0.131953i) q^{40} +(1.40311 + 6.24750i) q^{41} +(1.74162 + 3.01657i) q^{43} +4.49290i q^{44} -0.0506544 q^{46} +(8.96301 - 5.17479i) q^{47} +(-0.973004 + 1.68529i) q^{49} +(-2.48839 + 4.31002i) q^{50} +(-1.91844 + 1.10761i) q^{52} +0.876641i q^{53} -0.684565i q^{55} +(1.94692 - 1.12405i) q^{56} +(4.83752 + 2.79295i) q^{58} +(-2.14362 + 3.71286i) q^{59} +(2.86354 + 4.95981i) q^{61} +0.00328854 q^{62} +1.00000 q^{64} +(0.292306 - 0.168763i) q^{65} +(-1.29700 - 0.748824i) q^{67} +(2.69245 + 1.55449i) q^{68} +(-0.296645 + 0.171268i) q^{70} +1.94028i q^{71} +5.01815 q^{73} +(-0.174059 - 0.301479i) q^{74} +(-0.0523957 - 0.0302507i) q^{76} +(-5.05026 + 8.74731i) q^{77} +(-0.914489 + 0.527980i) q^{79} -0.152366 q^{80} +(-4.70894 + 4.33888i) q^{82} +(3.14751 + 5.45166i) q^{83} +(-0.410238 - 0.236851i) q^{85} +(-1.74162 + 3.01657i) q^{86} +(-3.89096 + 2.24645i) q^{88} -0.00331954i q^{89} -4.98007 q^{91} +(-0.0253272 - 0.0438680i) q^{92} +(8.96301 + 5.17479i) q^{94} +(0.00798333 + 0.00460918i) q^{95} +(3.02338 - 1.74555i) q^{97} -1.94601 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 4 q^{5} - 36 q^{8} - 8 q^{10} - 18 q^{16} - 4 q^{20} + 4 q^{23} - 26 q^{25} + 8 q^{31} + 18 q^{32} - 60 q^{37} + 4 q^{40} + 6 q^{41} + 6 q^{43} + 8 q^{46} + 38 q^{49} + 26 q^{50}+ \cdots + 76 q^{98}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 4 * q^5 - 36 * q^8 - 8 * q^10 - 18 * q^16 - 4 * q^20 + 4 * q^23 - 26 * q^25 + 8 * q^31 + 18 * q^32 - 60 * q^37 + 4 * q^40 + 6 * q^41 + 6 * q^43 + 8 * q^46 + 38 * q^49 + 26 * q^50 - 22 * q^59 - 46 * q^61 + 16 * q^62 + 36 * q^64 + 64 * q^73 - 30 * q^74 + 2 * q^77 + 8 * q^80 + 12 * q^82 - 68 * q^83 - 6 * q^86 + 36 * q^91 + 4 * q^92 + 76 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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