LMFDB - Embedded newform 1638.2.j.t.1171.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1638.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.j (of order $3$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 14x^{8} + 63x^{6} + 110x^{4} + 73x^{2} + 12 $ x^10 + 14x^8 + 63x^6 + 110x^4 + 73x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.5
Root			$1.97525i$ of defining polynomial
Character	$\chi$	$=$	1638.1171
Dual form			1638.2.j.t.235.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.16142 - 3.74369i) q^{5} +(-2.22724 - 1.42807i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.16142 - 3.74369i) q^{5} +(-2.22724 - 1.42807i) q^{7} -1.00000 q^{8} +(-2.16142 - 3.74369i) q^{10} +(1.88293 + 3.26134i) q^{11} -1.00000 q^{13} +(-2.35037 + 1.21481i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.44876 - 2.50932i) q^{17} +(0.0658233 - 0.114009i) q^{19} -4.32284 q^{20} +3.76587 q^{22} +(3.03830 - 5.26249i) q^{23} +(-6.84348 - 11.8533i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(-0.123123 + 2.64288i) q^{28} -0.377892 q^{29} +(-1.77849 - 3.08043i) q^{31} +(0.500000 + 0.866025i) q^{32} -2.89751 q^{34} +(-10.1603 + 5.25145i) q^{35} +(3.83742 - 6.64661i) q^{37} +(-0.0658233 - 0.114009i) q^{38} +(-2.16142 + 3.74369i) q^{40} -6.56909 q^{41} +1.50751 q^{43} +(1.88293 - 3.26134i) q^{44} +(-3.03830 - 5.26249i) q^{46} +(-5.84757 + 10.1283i) q^{47} +(2.92123 + 6.36132i) q^{49} -13.6870 q^{50} +(0.500000 + 0.866025i) q^{52} +(-1.36393 - 2.36240i) q^{53} +16.2793 q^{55} +(2.22724 + 1.42807i) q^{56} +(-0.188946 + 0.327264i) q^{58} +(2.68206 + 4.64546i) q^{59} +(-6.22641 + 10.7845i) q^{61} -3.55697 q^{62} +1.00000 q^{64} +(-2.16142 + 3.74369i) q^{65} +(0.963338 + 1.66855i) q^{67} +(-1.44876 + 2.50932i) q^{68} +(-0.532241 + 11.4248i) q^{70} +2.77798 q^{71} +(3.80417 + 6.58901i) q^{73} +(-3.83742 - 6.64661i) q^{74} -0.131647 q^{76} +(0.463665 - 9.95276i) q^{77} +(0.0247324 - 0.0428378i) q^{79} +(2.16142 + 3.74369i) q^{80} +(-3.28454 + 5.68900i) q^{82} -4.30457 q^{83} -12.5255 q^{85} +(0.753754 - 1.30554i) q^{86} +(-1.88293 - 3.26134i) q^{88} +(-0.416190 + 0.720863i) q^{89} +(2.22724 + 1.42807i) q^{91} -6.07660 q^{92} +(5.84757 + 10.1283i) q^{94} +(-0.284544 - 0.492844i) q^{95} +11.4286 q^{97} +(6.96968 + 0.650799i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8}+O(q^{10}) $ 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8	$ 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8} + q^{10} + 9 q^{11} - 10 q^{13} - 6 q^{14} - 5 q^{16} - 8 q^{17} + 4 q^{19} + 2 q^{20} + 18 q^{22} + 6 q^{23} - 12 q^{25} - 5 q^{26} - 3 q^{28} - 14 q^{29} - 5 q^{31} + 5 q^{32} - 16 q^{34} - 8 q^{35} - 10 q^{37} - 4 q^{38} + q^{40} - 24 q^{41} + 8 q^{43} + 9 q^{44} - 6 q^{46} - 4 q^{47} - 5 q^{49} - 24 q^{50} + 5 q^{52} + 19 q^{53} - 2 q^{55} + 3 q^{56} - 7 q^{58} - 7 q^{59} + 4 q^{61} - 10 q^{62} + 10 q^{64} + q^{65} - 8 q^{68} + 11 q^{70} - 8 q^{71} - 6 q^{73} + 10 q^{74} - 8 q^{76} + 19 q^{77} - 9 q^{79} - q^{80} - 12 q^{82} - 34 q^{83} + 36 q^{85} + 4 q^{86} - 9 q^{88} + 10 q^{89} + 3 q^{91} - 12 q^{92} + 4 q^{94} + 18 q^{95} + 14 q^{97} + 5 q^{98}+O(q^{100}) $ 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8 + q^10 + 9 * q^11 - 10 * q^13 - 6 * q^14 - 5 * q^16 - 8 * q^17 + 4 * q^19 + 2 * q^20 + 18 * q^22 + 6 * q^23 - 12 * q^25 - 5 * q^26 - 3 * q^28 - 14 * q^29 - 5 * q^31 + 5 * q^32 - 16 * q^34 - 8 * q^35 - 10 * q^37 - 4 * q^38 + q^40 - 24 * q^41 + 8 * q^43 + 9 * q^44 - 6 * q^46 - 4 * q^47 - 5 * q^49 - 24 * q^50 + 5 * q^52 + 19 * q^53 - 2 * q^55 + 3 * q^56 - 7 * q^58 - 7 * q^59 + 4 * q^61 - 10 * q^62 + 10 * q^64 + q^65 - 8 * q^68 + 11 * q^70 - 8 * q^71 - 6 * q^73 + 10 * q^74 - 8 * q^76 + 19 * q^77 - 9 * q^79 - q^80 - 12 * q^82 - 34 * q^83 + 36 * q^85 + 4 * q^86 - 9 * q^88 + 10 * q^89 + 3 * q^91 - 12 * q^92 + 4 * q^94 + 18 * q^95 + 14 * q^97 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	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
$5$	2.16142	−	3.74369i	0.966617	−	1.67423i	0.261410	−	0.965228i	$-0.415813\pi$
$5$	2.16142	−	3.74369i	0.966617	−	1.67423i	0.705207	−	0.709001i	$-0.250854\pi$
$6$		0			0
$7$	−2.22724	−	1.42807i	−0.841819	−	0.539760i
$7$	−2.22724	−	1.42807i	−0.841819	−	0.539760i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.16142	−	3.74369i	−0.683501	−	1.18386i
$11$	1.88293	+	3.26134i	0.567726	+	0.983330i	0.996790	+	0.0800564i	$0.0255100\pi$
$11$	1.88293	+	3.26134i	0.567726	+	0.983330i	−0.429064	+	0.903274i	$0.641157\pi$
$12$		0			0
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−2.35037	+	1.21481i	−0.628162	+	0.324673i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.44876	−	2.50932i	−0.351375	−	0.608600i	0.635115	−	0.772417i	$-0.280953\pi$
$17$	−1.44876	−	2.50932i	−0.351375	−	0.608600i	−0.986491	+	0.163817i	$0.947619\pi$
$18$		0			0
$19$	0.0658233	−	0.114009i	0.0151009	−	0.0261555i	−0.858376	−	0.513021i	$-0.828526\pi$
$19$	0.0658233	−	0.114009i	0.0151009	−	0.0261555i	0.873477	+	0.486865i	$0.161860\pi$
$20$	−4.32284			−0.966617
$21$		0			0
$22$	3.76587			0.802886
$23$	3.03830	−	5.26249i	0.633529	−	1.09730i	−0.353296	−	0.935512i	$-0.614939\pi$
$23$	3.03830	−	5.26249i	0.633529	−	1.09730i	0.986825	−	0.161793i	$-0.0517276\pi$
$24$		0			0
$25$	−6.84348	−	11.8533i	−1.36870	−	2.37065i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$		0			0
$28$	−0.123123	+	2.64288i	−0.0232680	+	0.499458i
$29$	−0.377892			−0.0701729			−0.0350864	−	0.999384i	$-0.511171\pi$
$29$	−0.377892			−0.0701729			−0.0350864	+	0.999384i	$0.511171\pi$
$30$		0			0
$31$	−1.77849	−	3.08043i	−0.319426	−	0.553261i	0.660943	−	0.750436i	$-0.270157\pi$
$31$	−1.77849	−	3.08043i	−0.319426	−	0.553261i	−0.980368	+	0.197175i	$0.936823\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−2.89751			−0.496920
$35$	−10.1603	+	5.25145i	−1.71740	+	0.887657i
$36$		0			0
$37$	3.83742	−	6.64661i	0.630868	−	1.09270i	−0.356506	−	0.934293i	$-0.616032\pi$
$37$	3.83742	−	6.64661i	0.630868	−	1.09270i	0.987375	−	0.158403i	$-0.0506345\pi$
$38$	−0.0658233	−	0.114009i	−0.0106779	−	0.0184947i
$39$		0			0
$40$	−2.16142	+	3.74369i	−0.341751	+	0.591929i
$41$	−6.56909			−1.02592			−0.512960	−	0.858413i	$-0.671451\pi$
$41$	−6.56909			−1.02592			−0.512960	+	0.858413i	$0.671451\pi$
$42$		0			0
$43$	1.50751			0.229893			0.114946	−	0.993372i	$-0.463330\pi$
$43$	1.50751			0.229893			0.114946	+	0.993372i	$0.463330\pi$
$44$	1.88293	−	3.26134i	0.283863	−	0.491665i
$45$		0			0
$46$	−3.03830	−	5.26249i	−0.447973	−	0.775911i
$47$	−5.84757	+	10.1283i	−0.852956	+	1.47736i	0.0255718	+	0.999673i	$0.491859\pi$
$47$	−5.84757	+	10.1283i	−0.852956	+	1.47736i	−0.878528	+	0.477691i	$0.841474\pi$
$48$		0			0
$49$	2.92123	+	6.36132i	0.417319	+	0.908760i
$50$	−13.6870			−1.93563
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−1.36393	−	2.36240i	−0.187351	−	0.324501i	0.757016	−	0.653397i	$-0.226657\pi$
$53$	−1.36393	−	2.36240i	−0.187351	−	0.324501i	−0.944366	+	0.328896i	$0.893323\pi$
$54$		0			0
$55$	16.2793			2.19509
$56$	2.22724	+	1.42807i	0.297628	+	0.190834i
$57$		0			0
$58$	−0.188946	+	0.327264i	−0.0248099	+	0.0429719i
$59$	2.68206	+	4.64546i	0.349174	+	0.604788i	0.986103	−	0.166135i	$-0.0531288\pi$
$59$	2.68206	+	4.64546i	0.349174	+	0.604788i	−0.636929	+	0.770923i	$0.719795\pi$
$60$		0			0
$61$	−6.22641	+	10.7845i	−0.797211	+	1.38081i	0.124215	+	0.992255i	$0.460359\pi$
$61$	−6.22641	+	10.7845i	−0.797211	+	1.38081i	−0.921426	+	0.388554i	$0.872975\pi$
$62$	−3.55697			−0.451736
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.16142	+	3.74369i	−0.268091	+	0.464348i
$66$		0			0
$67$	0.963338	+	1.66855i	0.117690	+	0.203846i	0.918852	−	0.394602i	$-0.129118\pi$
$67$	0.963338	+	1.66855i	0.117690	+	0.203846i	−0.801162	+	0.598448i	$0.795784\pi$
$68$	−1.44876	+	2.50932i	−0.175688	+	0.304300i
$69$		0			0
$70$	−0.532241	+	11.4248i	−0.0636149	+	1.36552i
$71$	2.77798			0.329686			0.164843	−	0.986320i	$-0.447288\pi$
$71$	2.77798			0.329686			0.164843	+	0.986320i	$0.447288\pi$
$72$		0			0
$73$	3.80417	+	6.58901i	0.445244	+	0.771185i	0.998069	−	0.0621121i	$-0.0197836\pi$
$73$	3.80417	+	6.58901i	0.445244	+	0.771185i	−0.552825	+	0.833297i	$0.686450\pi$
$74$	−3.83742	−	6.64661i	−0.446091	−	0.772653i
$75$		0			0
$76$	−0.131647			−0.0151009
$77$	0.463665	−	9.95276i	0.0528395	−	1.13422i
$78$		0			0
$79$	0.0247324	−	0.0428378i	0.00278261	−	0.00481962i	−0.864631	−	0.502408i	$-0.832448\pi$
$79$	0.0247324	−	0.0428378i	0.00278261	−	0.00481962i	0.867413	+	0.497588i	$0.165781\pi$
$80$	2.16142	+	3.74369i	0.241654	+	0.418557i
$81$		0			0
$82$	−3.28454	+	5.68900i	−0.362717	+	0.628245i
$83$	−4.30457			−0.472488			−0.236244	−	0.971694i	$-0.575916\pi$
$83$	−4.30457			−0.472488			−0.236244	+	0.971694i	$0.575916\pi$
$84$		0			0
$85$	−12.5255			−1.35858
$86$	0.753754	−	1.30554i	0.0812794	−	0.140780i
$87$		0			0
$88$	−1.88293	−	3.26134i	−0.200721	−	0.347660i
$89$	−0.416190	+	0.720863i	−0.0441161	+	0.0764113i	−0.887240	−	0.461308i	$-0.847380\pi$
$89$	−0.416190	+	0.720863i	−0.0441161	+	0.0764113i	0.843124	+	0.537719i	$0.180714\pi$
$90$		0			0
$91$	2.22724	+	1.42807i	0.233479	+	0.149702i
$92$	−6.07660			−0.633529
$93$		0			0
$94$	5.84757	+	10.1283i	0.603131	+	1.04465i
$95$	−0.284544	−	0.492844i	−0.0291936	−	0.0505647i
$96$		0			0
$97$	11.4286			1.16040			0.580199	−	0.814475i	$-0.302975\pi$
$97$	11.4286			1.16040			0.580199	+	0.814475i	$0.302975\pi$
$98$	6.96968	+	0.650799i	0.704044	+	0.0657407i
$99$		0			0
$100$	−6.84348	+	11.8533i	−0.684348	+	1.18533i
$101$	−9.87572	−	17.1052i	−0.982671	−	1.70204i	−0.651861	−	0.758338i	$-0.726011\pi$
$101$	−9.87572	−	17.1052i	−0.982671	−	1.70204i	−0.330810	−	0.943697i	$-0.607322\pi$
$102$		0			0
$103$	7.46660	−	12.9325i	0.735706	−	1.27428i	−0.218707	−	0.975791i	$-0.570184\pi$
$103$	7.46660	−	12.9325i	0.735706	−	1.27428i	0.954413	−	0.298490i	$-0.0964829\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	−2.72786			−0.264954
$107$	−2.81976	+	4.88397i	−0.272597	+	0.472151i	−0.969526	−	0.244989i	$-0.921216\pi$
$107$	−2.81976	+	4.88397i	−0.272597	+	0.472151i	0.696929	+	0.717140i	$0.254549\pi$
$108$		0			0
$109$	−4.32284	−	7.48738i	−0.414053	−	0.717161i	0.581275	−	0.813707i	$-0.302554\pi$
$109$	−4.32284	−	7.48738i	−0.414053	−	0.717161i	−0.995329	+	0.0965458i	$0.969221\pi$
$110$	8.13963	−	14.0982i	0.776083	−	1.34421i
$111$		0			0
$112$	2.35037	−	1.21481i	0.222089	−	0.114789i
$113$	7.47669			0.703347			0.351674	−	0.936123i	$-0.385613\pi$
$113$	7.47669			0.703347			0.351674	+	0.936123i	$0.385613\pi$
$114$		0			0
$115$	−13.1341	−	22.7489i	−1.22476	−	2.12135i
$116$	0.188946	+	0.327264i	0.0175432	+	0.0303857i
$117$		0			0
$118$	5.36412			0.493807
$119$	−0.356750	+	7.65780i	−0.0327033	+	0.701989i
$120$		0			0
$121$	−1.59088	+	2.75549i	−0.144626	+	0.250499i
$122$	6.22641	+	10.7845i	0.563713	+	0.976380i
$123$		0			0
$124$	−1.77849	+	3.08043i	−0.159713	+	0.276631i
$125$	−37.5523			−3.35878
$126$		0			0
$127$	17.5275			1.55532			0.777658	−	0.628687i	$-0.216407\pi$
$127$	17.5275			1.55532			0.777658	+	0.628687i	$0.216407\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	2.16142	+	3.74369i	0.189569	+	0.328343i
$131$	−6.73051	+	11.6576i	−0.588047	+	1.01853i	0.406441	+	0.913677i	$0.366770\pi$
$131$	−6.73051	+	11.6576i	−0.588047	+	1.01853i	−0.994488	+	0.104851i	$0.966564\pi$
$132$		0			0
$133$	−0.309418	+	0.159926i	−0.0268299	+	0.0138674i
$134$	1.92668			0.166439
$135$		0			0
$136$	1.44876	+	2.50932i	0.124230	+	0.215173i
$137$	2.27243	+	3.93596i	0.194147	+	0.336272i	0.946620	−	0.322350i	$-0.104473\pi$
$137$	2.27243	+	3.93596i	0.194147	+	0.336272i	−0.752474	+	0.658622i	$0.771140\pi$
$138$		0			0
$139$	11.4116			0.967915			0.483958	−	0.875091i	$-0.339199\pi$
$139$	11.4116			0.967915			0.483958	+	0.875091i	$0.339199\pi$
$140$	9.62802	+	6.17332i	0.813716	+	0.521741i
$141$		0			0
$142$	1.38899	−	2.40580i	0.116562	−	0.201891i
$143$	−1.88293	−	3.26134i	−0.157459	−	0.272727i
$144$		0			0
$145$	−0.816784	+	1.41471i	−0.0678303	+	0.117485i
$146$	7.60833			0.629670
$147$		0			0
$148$	−7.67484			−0.630868
$149$	8.18615	−	14.1788i	0.670636	−	1.16158i	−0.307088	−	0.951681i	$-0.599355\pi$
$149$	8.18615	−	14.1788i	0.670636	−	1.16158i	0.977724	−	0.209894i	$-0.0673120\pi$
$150$		0			0
$151$	−2.89472	−	5.01381i	−0.235569	−	0.408018i	0.723869	−	0.689938i	$-0.242362\pi$
$151$	−2.89472	−	5.01381i	−0.235569	−	0.408018i	−0.959438	+	0.281920i	$0.909029\pi$
$152$	−0.0658233	+	0.114009i	−0.00533897	+	0.00924737i
$153$		0			0
$154$	−8.38751	−	5.37792i	−0.675885	−	0.433365i
$155$	−15.3762			−1.23505
$156$		0			0
$157$	−5.62407	−	9.74118i	−0.448850	−	0.777430i	0.549462	−	0.835519i	$-0.314833\pi$
$157$	−5.62407	−	9.74118i	−0.448850	−	0.777430i	−0.998311	+	0.0580884i	$0.981499\pi$
$158$	−0.0247324	−	0.0428378i	−0.00196760	−	0.00340799i
$159$		0			0
$160$	4.32284			0.341751
$161$	−14.2822	+	7.38194i	−1.12560	+	0.581778i
$162$		0			0
$163$	12.6252	−	21.8675i	0.988884	−	1.71280i	0.365676	−	0.930742i	$-0.380838\pi$
$163$	12.6252	−	21.8675i	0.988884	−	1.71280i	0.623209	−	0.782056i	$-0.285829\pi$
$164$	3.28454	+	5.68900i	0.256480	+	0.444236i
$165$		0			0
$166$	−2.15228	+	3.72787i	−0.167050	+	0.289339i
$167$	21.2416			1.64373			0.821863	−	0.569685i	$-0.192935\pi$
$167$	21.2416			1.64373			0.821863	+	0.569685i	$0.192935\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−6.26275	+	10.8474i	−0.480331	+	0.831958i
$171$		0			0
$172$	−0.753754	−	1.30554i	−0.0574732	−	0.0995465i
$173$	−3.97752	+	6.88926i	−0.302405	+	0.523781i	−0.976680	−	0.214699i	$-0.931123\pi$
$173$	−3.97752	+	6.88926i	−0.302405	+	0.523781i	0.674275	+	0.738480i	$0.264456\pi$
$174$		0			0
$175$	−1.68518	+	36.1731i	−0.127387	+	2.73443i
$176$	−3.76587			−0.283863
$177$		0			0
$178$	0.416190	+	0.720863i	0.0311948	+	0.0540309i
$179$	11.3228	+	19.6117i	0.846309	+	1.46585i	0.884480	+	0.466579i	$0.154514\pi$
$179$	11.3228	+	19.6117i	0.846309	+	1.46585i	−0.0381707	+	0.999271i	$0.512153\pi$
$180$		0			0
$181$	−9.93611			−0.738545			−0.369273	−	0.929321i	$-0.620393\pi$
$181$	−9.93611			−0.738545			−0.369273	+	0.929321i	$0.620393\pi$
$182$	2.35037	−	1.21481i	0.174221	−	0.0900481i
$183$		0			0
$184$	−3.03830	+	5.26249i	−0.223986	+	0.387956i
$185$	−16.5886	−	28.7322i	−1.21962	−	2.11244i
$186$		0			0
$187$	5.45583	−	9.44977i	0.398970	−	0.691036i
$188$	11.6951			0.852956
$189$		0			0
$190$	−0.569087			−0.0412859
$191$	11.8716	−	20.5623i	0.859001	−	1.48783i	−0.0138825	−	0.999904i	$-0.504419\pi$
$191$	11.8716	−	20.5623i	0.859001	−	1.48783i	0.872883	−	0.487929i	$-0.162248\pi$
$192$		0			0
$193$	−11.9720	−	20.7361i	−0.861764	−	1.49262i	−0.870225	−	0.492655i	$-0.836027\pi$
$193$	−11.9720	−	20.7361i	−0.861764	−	1.49262i	0.00846106	−	0.999964i	$-0.497307\pi$
$194$	5.71430	−	9.89746i	0.410263	−	0.710596i
$195$		0			0
$196$	4.04845	−	5.71052i	0.289175	−	0.407894i
$197$	15.2813			1.08875			0.544373	−	0.838843i	$-0.316768\pi$
$197$	15.2813			1.08875			0.544373	+	0.838843i	$0.316768\pi$
$198$		0			0
$199$	0.804166	+	1.39286i	0.0570058	+	0.0987370i	0.893120	−	0.449818i	$-0.148511\pi$
$199$	0.804166	+	1.39286i	0.0570058	+	0.0987370i	−0.836114	+	0.548555i	$0.815178\pi$
$200$	6.84348	+	11.8533i	0.483907	+	0.838152i
$201$		0			0
$202$	−19.7514			−1.38971
$203$	0.841659	+	0.539657i	0.0590728	+	0.0378765i
$204$		0			0
$205$	−14.1986	+	24.5926i	−0.991671	+	1.71762i
$206$	−7.46660	−	12.9325i	−0.520223	−	0.901052i
$207$		0			0
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	0.495764			0.0342927
$210$		0			0
$211$	−10.2622			−0.706479			−0.353240	−	0.935533i	$-0.614920\pi$
$211$	−10.2622			−0.706479			−0.353240	+	0.935533i	$0.614920\pi$
$212$	−1.36393	+	2.36240i	−0.0936753	+	0.162250i
$213$		0			0
$214$	2.81976	+	4.88397i	0.192755	+	0.333861i
$215$	3.25836	−	5.64364i	0.222218	−	0.384893i
$216$		0			0
$217$	−0.437945	+	9.40067i	−0.0297296	+	0.638159i
$218$	−8.64568			−0.585560
$219$		0			0
$220$	−8.13963	−	14.0982i	−0.548773	−	0.950504i
$221$	1.44876	+	2.50932i	0.0974540	+	0.168795i
$222$		0			0
$223$	14.5452			0.974021			0.487010	−	0.873396i	$-0.338087\pi$
$223$	14.5452			0.974021			0.487010	+	0.873396i	$0.338087\pi$
$224$	0.123123	−	2.64288i	0.00822649	−	0.176585i
$225$		0			0
$226$	3.73834	−	6.47500i	0.248671	−	0.430711i
$227$	−8.98180	−	15.5569i	−0.596143	−	1.03255i	−0.993385	−	0.114835i	$-0.963366\pi$
$227$	−8.98180	−	15.5569i	−0.596143	−	1.03255i	0.397242	−	0.917714i	$-0.369967\pi$
$228$		0			0
$229$	11.5962	−	20.0852i	0.766300	−	1.32727i	−0.173257	−	0.984877i	$-0.555429\pi$
$229$	11.5962	−	20.0852i	0.766300	−	1.32727i	0.939557	−	0.342393i	$-0.111238\pi$
$230$	−26.2682			−1.73207
$231$		0			0
$232$	0.377892			0.0248099
$233$	−8.76192	+	15.1761i	−0.574012	+	0.994219i	0.422136	+	0.906533i	$0.361281\pi$
$233$	−8.76192	+	15.1761i	−0.574012	+	0.994219i	−0.996148	+	0.0876860i	$0.972053\pi$
$234$		0			0
$235$	25.2781	+	43.7830i	1.64896	+	2.85609i
$236$	2.68206	−	4.64546i	0.174587	−	0.302394i
$237$		0			0
$238$	6.45347	+	4.13785i	0.418317	+	0.268217i
$239$	−4.22717			−0.273433			−0.136716	−	0.990610i	$-0.543655\pi$
$239$	−4.22717			−0.273433			−0.136716	+	0.990610i	$0.543655\pi$
$240$		0			0
$241$	−10.9988	−	19.0506i	−0.708498	−	1.22715i	−0.965414	−	0.260721i	$-0.916040\pi$
$241$	−10.9988	−	19.0506i	−0.708498	−	1.22715i	0.256917	−	0.966434i	$-0.417293\pi$
$242$	1.59088	+	2.75549i	0.102266	+	0.177130i
$243$		0			0
$244$	12.4528			0.797211
$245$	30.1288	+	2.81330i	1.92486	+	0.179735i
$246$		0			0
$247$	−0.0658233	+	0.114009i	−0.00418824	+	0.00725424i
$248$	1.77849	+	3.08043i	0.112934	+	0.195607i
$249$		0			0
$250$	−18.7762	+	32.5213i	−1.18751	+	2.05683i
$251$	10.2610			0.647667			0.323834	−	0.946114i	$-0.395028\pi$
$251$	10.2610			0.647667			0.323834	+	0.946114i	$0.395028\pi$
$252$		0			0
$253$	22.8837			1.43868
$254$	8.76376	−	15.1793i	0.549887	−	0.952433i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.51962	+	7.82822i	−0.281926	+	0.488311i	−0.971859	−	0.235563i	$-0.924307\pi$
$257$	−4.51962	+	7.82822i	−0.281926	+	0.488311i	0.689933	+	0.723873i	$0.257640\pi$
$258$		0			0
$259$	−18.0387	+	9.32352i	−1.12087	+	0.579335i
$260$	4.32284			0.268091
$261$		0			0
$262$	6.73051	+	11.6576i	0.415812	+	0.720208i
$263$	14.1391	+	24.4897i	0.871856	+	1.51010i	0.860075	+	0.510168i	$0.170417\pi$
$263$	14.1391	+	24.4897i	0.871856	+	1.51010i	0.0117806	+	0.999931i	$0.496250\pi$
$264$		0			0
$265$	−11.7921			−0.724385
$266$	−0.0162087	+	0.347927i	−0.000993820	+	0.0213328i
$267$		0			0
$268$	0.963338	−	1.66855i	0.0588452	−	0.101923i
$269$	9.12215	+	15.8000i	0.556187	+	0.963345i	0.997810	+	0.0661439i	$0.0210696\pi$
$269$	9.12215	+	15.8000i	0.556187	+	0.963345i	−0.441623	+	0.897201i	$0.645597\pi$
$270$		0			0
$271$	1.80601	−	3.12810i	0.109707	−	0.190019i	−0.805944	−	0.591991i	$-0.798342\pi$
$271$	1.80601	−	3.12810i	0.109707	−	0.190019i	0.915652	+	0.401973i	$0.131675\pi$
$272$	2.89751			0.175688
$273$		0			0
$274$	4.54486			0.274565
$275$	25.7716	−	44.6378i	1.55409	−	2.69176i
$276$		0			0
$277$	11.2738	+	19.5269i	0.677380	+	1.17326i	0.975767	+	0.218811i	$0.0702180\pi$
$277$	11.2738	+	19.5269i	0.677380	+	1.17326i	−0.298387	+	0.954445i	$0.596449\pi$
$278$	5.70578	−	9.88269i	0.342210	−	0.592725i
$279$		0			0
$280$	10.1603	−	5.25145i	0.607192	−	0.313834i
$281$	−22.3104			−1.33093			−0.665465	−	0.746429i	$-0.731767\pi$
$281$	−22.3104			−1.33093			−0.665465	+	0.746429i	$0.731767\pi$
$282$		0			0
$283$	−3.25129	−	5.63140i	−0.193269	−	0.334752i	0.753063	−	0.657949i	$-0.228576\pi$
$283$	−3.25129	−	5.63140i	−0.193269	−	0.334752i	−0.946332	+	0.323197i	$0.895242\pi$
$284$	−1.38899	−	2.40580i	−0.0824215	−	0.142758i
$285$		0			0
$286$	−3.76587			−0.222680
$287$	14.6310	+	9.38112i	0.863638	+	0.553750i
$288$		0			0
$289$	4.30220	−	7.45164i	0.253071	−	0.438331i
$290$	0.816784	+	1.41471i	0.0479632	+	0.0830748i
$291$		0			0
$292$	3.80417	−	6.58901i	0.222622	−	0.385593i
$293$	16.6333			0.971727			0.485863	−	0.874035i	$-0.338505\pi$
$293$	16.6333			0.971727			0.485863	+	0.874035i	$0.338505\pi$
$294$		0			0
$295$	23.1882			1.35007
$296$	−3.83742	+	6.64661i	−0.223046	+	0.386326i
$297$		0			0
$298$	−8.18615	−	14.1788i	−0.474211	−	0.821358i
$299$	−3.03830	+	5.26249i	−0.175709	+	0.304337i
$300$		0			0
$301$	−3.35759	−	2.15283i	−0.193528	−	0.124087i
$302$	−5.78944			−0.333145
$303$		0			0
$304$	0.0658233	+	0.114009i	0.00377522	+	0.00653888i
$305$	26.9158	+	46.6195i	1.54119	+	2.66943i
$306$		0			0
$307$	−15.6051			−0.890628			−0.445314	−	0.895375i	$-0.646908\pi$
$307$	−15.6051			−0.890628			−0.445314	+	0.895375i	$0.646908\pi$
$308$	−8.85117	+	4.57483i	−0.504342	+	0.260675i
$309$		0			0
$310$	−7.68812	+	13.3162i	−0.436656	+	0.756310i
$311$	−9.98528	−	17.2950i	−0.566213	−	0.980710i	−0.996936	−	0.0782255i	$-0.975075\pi$
$311$	−9.98528	−	17.2950i	−0.566213	−	0.980710i	0.430723	−	0.902484i	$-0.358259\pi$
$312$		0			0
$313$	5.77439	−	10.0015i	0.326388	−	0.565320i	−0.655404	−	0.755278i	$-0.727502\pi$
$313$	5.77439	−	10.0015i	0.326388	−	0.565320i	0.981792	+	0.189958i	$0.0608351\pi$
$314$	−11.2481			−0.634769
$315$		0			0
$316$	−0.0494648			−0.00278261
$317$	9.65895	−	16.7298i	0.542501	−	0.939639i	−0.456259	−	0.889847i	$-0.650811\pi$
$317$	9.65895	−	16.7298i	0.542501	−	0.939639i	0.998760	−	0.0497920i	$-0.0158558\pi$
$318$		0			0
$319$	−0.711546	−	1.23243i	−0.0398390	−	0.0690031i
$320$	2.16142	−	3.74369i	0.120827	−	0.209279i
$321$		0			0
$322$	−0.748168	+	16.0597i	−0.0416938	+	0.894974i
$323$	−0.381448			−0.0212243
$324$		0			0
$325$	6.84348	+	11.8533i	0.379608	+	0.657500i
$326$	−12.6252	−	21.8675i	−0.699247	−	1.21113i
$327$		0			0
$328$	6.56909			0.362717
$329$	27.4879	−	14.2074i	1.51546	−	0.783282i
$330$		0			0
$331$	−2.19529	+	3.80235i	−0.120664	+	0.208996i	−0.920030	−	0.391849i	$-0.871836\pi$
$331$	−2.19529	+	3.80235i	−0.120664	+	0.208996i	0.799366	+	0.600845i	$0.205169\pi$
$332$	2.15228	+	3.72787i	0.118122	+	0.204593i
$333$		0			0
$334$	10.6208	−	18.3958i	0.581145	−	1.00657i
$335$	8.32872			0.455046
$336$		0			0
$337$	10.0052			0.545015			0.272508	−	0.962154i	$-0.412147\pi$
$337$	10.0052			0.545015			0.272508	+	0.962154i	$0.412147\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$		0			0
$340$	6.26275	+	10.8474i	0.339645	+	0.588283i
$341$	6.69755	−	11.6005i	0.362692	−	0.628202i
$342$		0			0
$343$	2.57812	−	18.3399i	0.139205	−	0.990264i
$344$	−1.50751			−0.0812794
$345$		0			0
$346$	3.97752	+	6.88926i	0.213833	+	0.370369i
$347$	−6.16026	−	10.6699i	−0.330700	−	0.572790i	0.651949	−	0.758263i	$-0.273952\pi$
$347$	−6.16026	−	10.6699i	−0.330700	−	0.572790i	−0.982649	+	0.185473i	$0.940618\pi$
$348$		0			0
$349$	8.19868			0.438865			0.219433	−	0.975628i	$-0.429579\pi$
$349$	8.19868			0.438865			0.219433	+	0.975628i	$0.429579\pi$
$350$	30.4842	+	19.5459i	1.62945	+	1.04477i
$351$		0			0
$352$	−1.88293	+	3.26134i	−0.100361	+	0.173830i
$353$	14.2236	+	24.6360i	0.757047	+	1.31124i	0.944350	+	0.328942i	$0.106692\pi$
$353$	14.2236	+	24.6360i	0.757047	+	1.31124i	−0.187303	+	0.982302i	$0.559975\pi$
$354$		0			0
$355$	6.00439	−	10.3999i	0.318680	−	0.551970i
$356$	0.832380			0.0441161
$357$		0			0
$358$	22.6457			1.19686
$359$	−5.05683	+	8.75869i	−0.266889	+	0.462266i	−0.968057	−	0.250731i	$-0.919329\pi$
$359$	−5.05683	+	8.75869i	−0.266889	+	0.462266i	0.701168	+	0.712997i	$0.252662\pi$
$360$		0			0
$361$	9.49133	+	16.4395i	0.499544	+	0.865235i
$362$	−4.96805	+	8.60492i	−0.261115	+	0.452265i
$363$		0			0
$364$	0.123123	−	2.64288i	0.00645339	−	0.138525i
$365$	32.8896			1.72152
$366$		0			0
$367$	14.4396	+	25.0100i	0.753739	+	1.30551i	0.945999	+	0.324170i	$0.105085\pi$
$367$	14.4396	+	25.0100i	0.753739	+	1.30551i	−0.192260	+	0.981344i	$0.561582\pi$
$368$	3.03830	+	5.26249i	0.158382	+	0.274326i
$369$		0			0
$370$	−33.1771			−1.72480
$371$	−0.335863	+	7.20943i	−0.0174371	+	0.374295i
$372$		0			0
$373$	−11.7210	+	20.3013i	−0.606889	+	1.05116i	0.384861	+	0.922974i	$0.374249\pi$
$373$	−11.7210	+	20.3013i	−0.606889	+	1.05116i	−0.991750	+	0.128188i	$0.959084\pi$
$374$	−5.45583	−	9.44977i	−0.282114	−	0.488636i
$375$		0			0
$376$	5.84757	−	10.1283i	0.301566	−	0.522327i
$377$	0.377892			0.0194624
$378$		0			0
$379$	−15.8899			−0.816209			−0.408105	−	0.912935i	$-0.633810\pi$
$379$	−15.8899			−0.816209			−0.408105	+	0.912935i	$0.633810\pi$
$380$	−0.284544	+	0.492844i	−0.0145968	+	0.0252824i
$381$		0			0
$382$	−11.8716	−	20.5623i	−0.607405	−	1.05206i
$383$	−6.69461	+	11.5954i	−0.342079	+	0.592497i	−0.984819	−	0.173587i	$-0.944464\pi$
$383$	−6.69461	+	11.5954i	−0.342079	+	0.592497i	0.642740	+	0.766084i	$0.277798\pi$
$384$		0			0
$385$	−36.2579	−	23.2479i	−1.84787	−	1.18482i
$386$	−23.9440			−1.21872
$387$		0			0
$388$	−5.71430	−	9.89746i	−0.290100	−	0.502467i
$389$	−5.30239	−	9.18401i	−0.268842	−	0.465648i	0.699721	−	0.714416i	$-0.253308\pi$
$389$	−5.30239	−	9.18401i	−0.268842	−	0.465648i	−0.968563	+	0.248768i	$0.919974\pi$
$390$		0			0
$391$	−17.6070			−0.890426
$392$	−2.92123	−	6.36132i	−0.147544	−	0.321295i
$393$		0			0
$394$	7.64064	−	13.2340i	0.384930	−	0.666718i
$395$	−0.106914	−	0.185181i	−0.00537944	−	0.00931746i
$396$		0			0
$397$	−2.41210	+	4.17787i	−0.121060	+	0.209681i	−0.920186	−	0.391482i	$-0.871963\pi$
$397$	−2.41210	+	4.17787i	−0.121060	+	0.209681i	0.799126	+	0.601163i	$0.205296\pi$
$398$	1.60833			0.0806184
$399$		0			0
$400$	13.6870			0.684348
$401$	−2.68463	+	4.64992i	−0.134064	+	0.232206i	−0.925240	−	0.379383i	$-0.876136\pi$
$401$	−2.68463	+	4.64992i	−0.134064	+	0.232206i	0.791175	+	0.611589i	$0.209470\pi$
$402$		0			0
$403$	1.77849	+	3.08043i	0.0885927	+	0.153447i
$404$	−9.87572	+	17.1052i	−0.491335	+	0.851018i
$405$		0			0
$406$	0.888186	−	0.459069i	0.0440799	−	0.0227832i
$407$	28.9025			1.43264
$408$		0			0
$409$	−15.5290	−	26.8970i	−0.767859	−	1.32997i	−0.938722	−	0.344675i	$-0.887989\pi$
$409$	−15.5290	−	26.8970i	−0.767859	−	1.32997i	0.170863	−	0.985295i	$-0.445344\pi$
$410$	14.1986	+	24.5926i	0.701217	+	1.21454i
$411$		0			0
$412$	−14.9332			−0.735706
$413$	0.660446	−	14.1767i	0.0324984	−	0.697592i
$414$		0			0
$415$	−9.30398	+	16.1150i	−0.456715	+	0.791053i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$		0			0
$418$	0.247882	−	0.429344i	0.0121243	−	0.0209999i
$419$	−3.97577			−0.194229			−0.0971146	−	0.995273i	$-0.530961\pi$
$419$	−3.97577			−0.194229			−0.0971146	+	0.995273i	$0.530961\pi$
$420$		0			0
$421$	16.7383			0.815776			0.407888	−	0.913032i	$-0.366265\pi$
$421$	16.7383			0.815776			0.407888	+	0.913032i	$0.366265\pi$
$422$	−5.13110	+	8.88733i	−0.249778	+	0.432628i
$423$		0			0
$424$	1.36393	+	2.36240i	0.0662384	+	0.114728i
$425$	−19.8291	+	34.3450i	−0.961852	+	1.66598i
$426$		0			0
$427$	29.2687	−	15.1279i	1.41641	−	0.732089i
$428$	5.63952			0.272597
$429$		0			0
$430$	−3.25836	−	5.64364i	−0.157132	−	0.272161i
$431$	−1.43335	−	2.48263i	−0.0690419	−	0.119584i	0.829438	−	0.558599i	$-0.188661\pi$
$431$	−1.43335	−	2.48263i	−0.0690419	−	0.119584i	−0.898480	+	0.439015i	$0.855328\pi$
$432$		0			0
$433$	−39.9780			−1.92122			−0.960611	−	0.277896i	$-0.910363\pi$
$433$	−39.9780			−1.92122			−0.960611	+	0.277896i	$0.910363\pi$
$434$	7.92225	+	5.07961i	0.380280	+	0.243829i
$435$		0			0
$436$	−4.32284	+	7.48738i	−0.207027	+	0.358581i
$437$	−0.399982	−	0.692788i	−0.0191337	−	0.0331406i
$438$		0			0
$439$	7.93138	−	13.7376i	0.378544	−	0.655658i	−0.612306	−	0.790621i	$-0.709758\pi$
$439$	7.93138	−	13.7376i	0.378544	−	0.655658i	0.990851	+	0.134963i	$0.0430914\pi$
$440$	−16.2793			−0.776083
$441$		0			0
$442$	2.89751			0.137821
$443$	18.0121	−	31.1978i	0.855779	−	1.48225i	−0.0201406	−	0.999797i	$-0.506411\pi$
$443$	18.0121	−	31.1978i	0.855779	−	1.48225i	0.875920	−	0.482456i	$-0.160255\pi$
$444$		0			0
$445$	1.79912	+	3.11617i	0.0852867	+	0.147721i
$446$	7.27261	−	12.5965i	0.344368	−	0.596463i
$447$		0			0
$448$	−2.22724	−	1.42807i	−0.105227	−	0.0674700i
$449$	26.3576			1.24389			0.621946	−	0.783060i	$-0.286342\pi$
$449$	26.3576			1.24389			0.621946	+	0.783060i	$0.286342\pi$
$450$		0			0
$451$	−12.3692	−	21.4240i	−0.582441	−	1.00882i
$452$	−3.73834	−	6.47500i	−0.175837	−	0.304558i
$453$		0			0
$454$	−17.9636			−0.843073
$455$	10.1603	−	5.25145i	0.476321	−	0.246192i
$456$		0			0
$457$	18.4195	−	31.9036i	0.861629	−	1.49239i	−0.00872626	−	0.999962i	$-0.502778\pi$
$457$	18.4195	−	31.9036i	0.861629	−	1.49239i	0.870356	−	0.492424i	$-0.163889\pi$
$458$	−11.5962	−	20.0852i	−0.541856	−	0.938522i
$459$		0			0
$460$	−13.1341	+	22.7489i	−0.612380	+	1.06067i
$461$	−19.9659			−0.929905			−0.464952	−	0.885336i	$-0.653929\pi$
$461$	−19.9659			−0.929905			−0.464952	+	0.885336i	$0.653929\pi$
$462$		0			0
$463$	−13.1611			−0.611648			−0.305824	−	0.952088i	$-0.598932\pi$
$463$	−13.1611			−0.611648			−0.305824	+	0.952088i	$0.598932\pi$
$464$	0.188946	−	0.327264i	0.00877161	−	0.0151929i
$465$		0			0
$466$	8.76192	+	15.1761i	0.405888	+	0.703019i
$467$	−13.9514	+	24.1645i	−0.645592	+	1.11820i	0.338572	+	0.940940i	$0.390056\pi$
$467$	−13.9514	+	24.1645i	−0.645592	+	1.11820i	−0.984164	+	0.177258i	$0.943277\pi$
$468$		0			0
$469$	0.237218	−	5.09198i	0.0109537	−	0.235126i
$470$	50.5563			2.33199
$471$		0			0
$472$	−2.68206	−	4.64546i	−0.123452	−	0.213825i
$473$	2.83854	+	4.91649i	0.130516	+	0.226061i
$474$		0			0
$475$	−1.80184			−0.0826741
$476$	6.81022	−	3.51994i	0.312146	−	0.161336i
$477$		0			0
$478$	−2.11358	+	3.66083i	−0.0966731	+	0.167443i
$479$	−1.46559	−	2.53847i	−0.0669644	−	0.115986i	0.830599	−	0.556871i	$-0.187998\pi$
$479$	−1.46559	−	2.53847i	−0.0669644	−	0.115986i	−0.897564	+	0.440885i	$0.854665\pi$
$480$		0			0
$481$	−3.83742	+	6.64661i	−0.174971	+	0.303059i
$482$	−21.9977			−1.00197
$483$		0			0
$484$	3.18176			0.144626
$485$	24.7020	−	42.7851i	1.12166	−	1.94277i
$486$		0			0
$487$	−8.01669	−	13.8853i	−0.363271	−	0.629203i	0.625226	−	0.780444i	$-0.285007\pi$
$487$	−8.01669	−	13.8853i	−0.363271	−	0.629203i	−0.988497	+	0.151240i	$0.951673\pi$
$488$	6.22641	−	10.7845i	0.281856	−	0.488190i
$489$		0			0
$490$	17.5008	−	24.6857i	0.790606	−	1.11519i
$491$	14.3670			0.648375			0.324187	−	0.945993i	$-0.394909\pi$
$491$	14.3670			0.648375			0.324187	+	0.945993i	$0.394909\pi$
$492$		0			0
$493$	0.547474	+	0.948253i	0.0246570	+	0.0427072i
$494$	0.0658233	+	0.114009i	0.00296153	+	0.00512952i
$495$		0			0
$496$	3.55697			0.159713
$497$	−6.18724	−	3.96715i	−0.277536	−	0.177951i
$498$		0			0
$499$	10.5765	−	18.3190i	0.473467	−	0.820069i	−0.526072	−	0.850440i	$-0.676336\pi$
$499$	10.5765	−	18.3190i	0.473467	−	0.820069i	0.999539	+	0.0303712i	$0.00966894\pi$
$500$	18.7762	+	32.5213i	0.839696	+	1.45440i
$501$		0			0
$502$	5.13049	−	8.88627i	0.228985	−	0.396614i
$503$	−26.5967			−1.18589			−0.592943	−	0.805244i	$-0.702034\pi$
$503$	−26.5967			−1.18589			−0.592943	+	0.805244i	$0.702034\pi$
$504$		0			0
$505$	−85.3823			−3.79946
$506$	11.4418	−	19.8178i	0.508651	−	0.881010i
$507$		0			0
$508$	−8.76376	−	15.1793i	−0.388829	−	0.673472i
$509$	4.42620	−	7.66640i	0.196188	−	0.339807i	−0.751101	−	0.660187i	$-0.770477\pi$
$509$	4.42620	−	7.66640i	0.196188	−	0.339807i	0.947289	+	0.320379i	$0.103810\pi$
$510$		0			0
$511$	0.936760	−	20.1079i	0.0414398	−	0.889523i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	4.51962	+	7.82822i	0.199352	+	0.345288i
$515$	−32.2769	−	55.9053i	−1.42229	−	2.46348i
$516$		0			0
$517$	−44.0424			−1.93698
$518$	−0.944949	+	20.2837i	−0.0415187	+	0.891216i
$519$		0			0
$520$	2.16142	−	3.74369i	0.0947846	−	0.164172i
$521$	−0.263293	−	0.456037i	−0.0115351	−	0.0199793i	0.860200	−	0.509956i	$-0.170338\pi$
$521$	−0.263293	−	0.456037i	−0.0115351	−	0.0199793i	−0.871735	+	0.489977i	$0.837005\pi$
$522$		0			0
$523$	4.40147	−	7.62357i	0.192463	−	0.333355i	−0.753603	−	0.657330i	$-0.771686\pi$
$523$	4.40147	−	7.62357i	0.192463	−	0.333355i	0.946066	+	0.323975i	$0.105019\pi$
$524$	13.4610			0.588047
$525$		0			0
$526$	28.2782			1.23299
$527$	−5.15319	+	8.92559i	−0.224477	+	0.388805i
$528$		0			0
$529$	−6.96251	−	12.0594i	−0.302718	−	0.524322i
$530$	−5.89606	+	10.2123i	−0.256109	+	0.443593i
$531$		0			0
$532$	0.293209	+	0.188001i	0.0127122	+	0.00815086i
$533$	6.56909			0.284539
$534$		0			0
$535$	12.1894	+	21.1126i	0.526993	+	0.912779i
$536$	−0.963338	−	1.66855i	−0.0416099	−	0.0720704i
$537$		0			0
$538$	18.2443			0.786568
$539$	−15.2459	+	21.5051i	−0.656689	+	0.926289i
$540$		0			0
$541$	3.32854	−	5.76519i	0.143105	−	0.247865i	−0.785559	−	0.618786i	$-0.787625\pi$
$541$	3.32854	−	5.76519i	0.143105	−	0.247865i	0.928664	+	0.370921i	$0.120958\pi$
$542$	−1.80601	−	3.12810i	−0.0775749	−	0.134364i
$543$		0			0
$544$	1.44876	−	2.50932i	0.0621150	−	0.107586i
$545$	−37.3739			−1.60092
$546$		0			0
$547$	−6.52029			−0.278788			−0.139394	−	0.990237i	$-0.544515\pi$
$547$	−6.52029			−0.278788			−0.139394	+	0.990237i	$0.544515\pi$
$548$	2.27243	−	3.93596i	0.0970734	−	0.168136i
$549$		0			0
$550$	−25.7716	−	44.6378i	−1.09891	−	1.90336i
$551$	−0.0248741	+	0.0430832i	−0.00105967	+	0.00183541i
$552$		0			0
$553$	−0.116260	+	0.0600905i	−0.00494389	+	0.00255531i
$554$	22.5477			0.957960
$555$		0			0
$556$	−5.70578	−	9.88269i	−0.241979	−	0.419120i
$557$	10.3888	+	17.9940i	0.440190	+	0.762431i	0.997703	−	0.0677370i	$-0.0215779\pi$
$557$	10.3888	+	17.9940i	0.440190	+	0.762431i	−0.557514	+	0.830168i	$0.688245\pi$
$558$		0			0
$559$	−1.50751			−0.0637608
$560$	0.532241	−	11.4248i	0.0224913	−	0.482785i
$561$		0			0
$562$	−11.1552	+	19.3214i	−0.470555	+	0.815025i
$563$	14.6242	+	25.3299i	0.616338	+	1.06753i	0.990148	+	0.140023i	$0.0447176\pi$
$563$	14.6242	+	25.3299i	0.616338	+	1.06753i	−0.373811	+	0.927505i	$0.621949\pi$
$564$		0			0
$565$	16.1603	−	27.9904i	0.679867	−	1.17756i
$566$	−6.50258			−0.273324
$567$		0			0
$568$	−2.77798			−0.116562
$569$	−12.9702	+	22.4650i	−0.543737	+	0.941781i	0.454948	+	0.890518i	$0.349658\pi$
$569$	−12.9702	+	22.4650i	−0.543737	+	0.941781i	−0.998685	+	0.0512627i	$0.983675\pi$
$570$		0			0
$571$	12.8560	+	22.2672i	0.538005	+	0.931852i	0.999011	+	0.0444552i	$0.0141552\pi$
$571$	12.8560	+	22.2672i	0.538005	+	0.931852i	−0.461006	+	0.887397i	$0.652511\pi$
$572$	−1.88293	+	3.26134i	−0.0787294	+	0.136363i
$573$		0			0
$574$	15.4398	−	7.98023i	0.644443	−	0.333088i
$575$	−83.1701			−3.46843
$576$		0			0
$577$	8.28106	+	14.3432i	0.344745	+	0.597116i	0.985307	−	0.170790i	$-0.0546320\pi$
$577$	8.28106	+	14.3432i	0.344745	+	0.597116i	−0.640562	+	0.767906i	$0.721299\pi$
$578$	−4.30220	−	7.45164i	−0.178948	−	0.309947i
$579$		0			0
$580$	1.63357			0.0678303
$581$	9.58733	+	6.14723i	0.397749	+	0.255030i
$582$		0			0
$583$	5.13639	−	8.89649i	0.212728	−	0.368455i
$584$	−3.80417	−	6.58901i	−0.157418	−	0.272655i
$585$		0			0
$586$	8.31664	−	14.4048i	0.343557	−	0.595059i
$587$	20.2537			0.835961			0.417980	−	0.908456i	$-0.362738\pi$
$587$	20.2537			0.835961			0.417980	+	0.908456i	$0.362738\pi$
$588$		0			0
$589$	−0.468263			−0.0192945
$590$	11.5941	−	20.0816i	0.477322	−	0.826746i
$591$		0			0
$592$	3.83742	+	6.64661i	0.157717	+	0.273174i
$593$	−9.07602	+	15.7201i	−0.372707	+	0.645548i	−0.989981	−	0.141200i	$-0.954904\pi$
$593$	−9.07602	+	15.7201i	−0.372707	+	0.645548i	0.617274	+	0.786749i	$0.288237\pi$
$594$		0			0
$595$	27.8973	+	17.8873i	1.14368	+	0.733307i
$596$	−16.3723			−0.670636
$597$		0			0
$598$	3.03830	+	5.26249i	0.124245	+	0.215199i
$599$	16.2999	+	28.2323i	0.665997	+	1.15354i	0.979014	+	0.203793i	$0.0653270\pi$
$599$	16.2999	+	28.2323i	0.665997	+	1.15354i	−0.313017	+	0.949748i	$0.601340\pi$
$600$		0			0
$601$	29.2357			1.19255			0.596275	−	0.802780i	$-0.296647\pi$
$601$	29.2357			1.19255			0.596275	+	0.802780i	$0.296647\pi$
$602$	−3.54320	+	1.83134i	−0.144410	+	0.0746400i
$603$		0			0
$604$	−2.89472	+	5.01381i	−0.117785	+	0.204009i
$605$	6.87713	+	11.9115i	0.279595	+	0.484273i
$606$		0			0
$607$	9.36882	−	16.2273i	0.380269	−	0.658645i	−0.610832	−	0.791760i	$-0.709165\pi$
$607$	9.36882	−	16.2273i	0.380269	−	0.658645i	0.991101	+	0.133116i	$0.0424981\pi$
$608$	0.131647			0.00533897
$609$		0			0
$610$	53.8316			2.17958
$611$	5.84757	−	10.1283i	0.236568	−	0.409747i
$612$		0			0
$613$	14.1496	+	24.5079i	0.571498	+	0.989864i	0.996412	+	0.0846306i	$0.0269710\pi$
$613$	14.1496	+	24.5079i	0.571498	+	0.989864i	−0.424914	+	0.905234i	$0.639696\pi$
$614$	−7.80253	+	13.5144i	−0.314884	+	0.545396i
$615$		0			0
$616$	−0.463665	+	9.95276i	−0.0186816	+	0.401008i
$617$	−6.69414			−0.269496			−0.134748	−	0.990880i	$-0.543022\pi$
$617$	−6.69414			−0.269496			−0.134748	+	0.990880i	$0.543022\pi$
$618$		0			0
$619$	16.2195	+	28.0930i	0.651917	+	1.12915i	0.982657	+	0.185432i	$0.0593685\pi$
$619$	16.2195	+	28.0930i	0.651917	+	1.12915i	−0.330740	+	0.943722i	$0.607298\pi$
$620$	7.68812	+	13.3162i	0.308762	+	0.534792i
$621$		0			0
$622$	−19.9706			−0.800746
$623$	1.95640	−	1.01119i	0.0783815	−	0.0405124i
$624$		0			0
$625$	−46.9490	+	81.3181i	−1.87796	+	3.25272i
$626$	−5.77439	−	10.0015i	−0.230791	−	0.399742i
$627$		0			0
$628$	−5.62407	+	9.74118i	−0.224425	+	0.388715i
$629$	−22.2380			−0.886686
$630$		0			0
$631$	43.9306			1.74885			0.874425	−	0.485161i	$-0.161239\pi$
$631$	43.9306			1.74885			0.874425	+	0.485161i	$0.161239\pi$
$632$	−0.0247324	+	0.0428378i	−0.000983802	+	0.00170399i
$633$		0			0
$634$	−9.65895	−	16.7298i	−0.383606	−	0.664425i
$635$	37.8844	−	65.6176i	1.50340	−	2.60396i
$636$		0			0
$637$	−2.92123	−	6.36132i	−0.115743	−	0.252045i
$638$	−1.42309			−0.0563408
$639$		0			0
$640$	−2.16142	−	3.74369i	−0.0854377	−	0.147982i
$641$	1.20415	+	2.08564i	0.0475610	+	0.0823780i	0.888826	−	0.458245i	$-0.151522\pi$
$641$	1.20415	+	2.08564i	0.0475610	+	0.0823780i	−0.841265	+	0.540623i	$0.818188\pi$
$642$		0			0
$643$	−27.3453			−1.07839			−0.539197	−	0.842180i	$-0.681272\pi$
$643$	−27.3453			−1.07839			−0.539197	+	0.842180i	$0.681272\pi$
$644$	13.5341	+	8.67780i	0.533317	+	0.341953i
$645$		0			0
$646$	−0.190724	+	0.330344i	−0.00750393	+	0.0129972i
$647$	4.11229	+	7.12269i	0.161671	+	0.280022i	0.935468	−	0.353412i	$-0.114978\pi$
$647$	4.11229	+	7.12269i	0.161671	+	0.280022i	−0.773797	+	0.633433i	$0.781645\pi$
$648$		0			0
$649$	−10.1003	+	17.4942i	−0.396471	+	0.686707i
$650$	13.6870			0.536847
$651$		0			0
$652$	−25.2505			−0.988884
$653$	6.94528	−	12.0296i	0.271790	−	0.470754i	−0.697530	−	0.716555i	$-0.745718\pi$
$653$	6.94528	−	12.0296i	0.271790	−	0.470754i	0.969320	+	0.245801i	$0.0790511\pi$
$654$		0			0
$655$	29.0949	+	50.3939i	1.13683	+	1.96905i
$656$	3.28454	−	5.68900i	0.128240	−	0.222118i
$657$		0			0
$658$	1.43994	−	30.9089i	0.0561347	−	1.20496i
$659$	−33.1346			−1.29074			−0.645371	−	0.763869i	$-0.723297\pi$
$659$	−33.1346			−1.29074			−0.645371	+	0.763869i	$0.723297\pi$
$660$		0			0
$661$	18.7611	+	32.4952i	0.729723	+	1.26392i	0.957000	+	0.290087i	$0.0936842\pi$
$661$	18.7611	+	32.4952i	0.729723	+	1.26392i	−0.227277	+	0.973830i	$0.572982\pi$
$662$	2.19529	+	3.80235i	0.0853223	+	0.147783i
$663$		0			0
$664$	4.30457			0.167050
$665$	−0.0700677	+	1.50403i	−0.00271711	+	0.0583239i
$666$		0			0
$667$	−1.14815	+	1.98865i	−0.0444565	+	0.0770010i
$668$	−10.6208	−	18.3958i	−0.410931	−	0.711754i
$669$		0			0
$670$	4.16436	−	7.21288i	0.160883	−	0.278658i
$671$	−46.8957			−1.81039
$672$		0			0
$673$	40.3089			1.55380			0.776898	−	0.629627i	$-0.216792\pi$
$673$	40.3089			1.55380			0.776898	+	0.629627i	$0.216792\pi$
$674$	5.00258	−	8.66471i	0.192692	−	0.333752i
$675$		0			0
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−2.22985	+	3.86222i	−0.0857002	+	0.148437i	−0.905689	−	0.423942i	$-0.860646\pi$
$677$	−2.22985	+	3.86222i	−0.0857002	+	0.148437i	0.819989	+	0.572379i	$0.193979\pi$
$678$		0			0
$679$	−25.4543	−	16.3208i	−0.976846	−	0.626336i
$680$	12.5255			0.480331
$681$		0			0
$682$	−6.69755	−	11.6005i	−0.256462	−	0.444206i
$683$	−8.02923	−	13.9070i	−0.307230	−	0.532138i	0.670525	−	0.741887i	$-0.266069\pi$
$683$	−8.02923	−	13.9070i	−0.307230	−	0.532138i	−0.977755	+	0.209749i	$0.932735\pi$
$684$		0			0
$685$	19.6467			0.750662
$686$	−14.5938	−	11.4027i	−0.557194	−	0.435356i
$687$		0			0
$688$	−0.753754	+	1.30554i	−0.0287366	+	0.0497733i
$689$	1.36393	+	2.36240i	0.0519617	+	0.0900003i
$690$		0			0
$691$	−22.4358	+	38.8600i	−0.853499	+	1.47830i	0.0245322	+	0.999699i	$0.492190\pi$
$691$	−22.4358	+	38.8600i	−0.853499	+	1.47830i	−0.878031	+	0.478604i	$0.841143\pi$
$692$	7.95503			0.302405
$693$		0			0
$694$	−12.3205			−0.467681
$695$	24.6652	−	42.7213i	0.935603	−	1.62051i
$696$		0			0
$697$	9.51701	+	16.4840i	0.360483	+	0.624374i
$698$	4.09934	−	7.10026i	0.155162	−	0.268749i
$699$		0			0
$700$	32.1694	−	16.6271i	1.21589	−	0.628446i
$701$	8.85377			0.334402			0.167201	−	0.985923i	$-0.446527\pi$
$701$	8.85377			0.334402			0.167201	+	0.985923i	$0.446527\pi$
$702$		0			0
$703$	−0.505184	−	0.875004i	−0.0190534	−	0.0330014i
$704$	1.88293	+	3.26134i	0.0709658	+	0.122916i
$705$		0			0
$706$	28.4473			1.07063
$707$	−2.43185	+	52.2008i	−0.0914593	+	1.96321i
$708$		0			0
$709$	−25.8201	+	44.7217i	−0.969694	+	1.67956i	−0.273257	+	0.961941i	$0.588101\pi$
$709$	−25.8201	+	44.7217i	−0.969694	+	1.67956i	−0.696437	+	0.717618i	$0.745232\pi$
$710$	−6.00439	−	10.3999i	−0.225341	−	0.390302i
$711$		0			0
$712$	0.416190	−	0.720863i	0.0155974	−	0.0270155i
$713$	−21.6143			−0.809461
$714$		0			0
$715$	−16.2793			−0.608810
$716$	11.3228	−	19.6117i	0.423154	−	0.732925i
$717$		0			0
$718$	5.05683	+	8.75869i	0.188719	+	0.326871i
$719$	−1.01539	+	1.75870i	−0.0378675	+	0.0655885i	−0.884338	−	0.466847i	$-0.845390\pi$
$719$	−1.01539	+	1.75870i	−0.0378675	+	0.0655885i	0.846471	+	0.532436i	$0.178723\pi$
$720$		0			0
$721$	−35.0985	+	18.1411i	−1.30714	+	0.675609i
$722$	18.9827			0.706462
$723$		0			0
$724$	4.96805	+	8.60492i	0.184636	+	0.319799i
$725$	2.58610	+	4.47925i	0.0960453	+	0.166355i
$726$		0			0
$727$	4.75679			0.176420			0.0882098	−	0.996102i	$-0.471885\pi$
$727$	4.75679			0.176420			0.0882098	+	0.996102i	$0.471885\pi$
$728$	−2.22724	−	1.42807i	−0.0825472	−	0.0529278i
$729$		0			0
$730$	16.4448	−	28.4832i	0.608650	−	1.05421i
$731$	−2.18401	−	3.78282i	−0.0807787	−	0.139913i
$732$		0			0
$733$	21.8849	−	37.9057i	0.808336	−	1.40008i	−0.105680	−	0.994400i	$-0.533702\pi$
$733$	21.8849	−	37.9057i	0.808336	−	1.40008i	0.914016	−	0.405678i	$-0.132965\pi$
$734$	28.8791			1.06595
$735$		0			0
$736$	6.07660			0.223986
$737$	−3.62780	+	6.28354i	−0.133632	+	0.231457i
$738$		0			0
$739$	12.4857	+	21.6259i	0.459294	+	0.795521i	0.998924	−	0.0463814i	$-0.0147690\pi$
$739$	12.4857	+	21.6259i	0.459294	+	0.795521i	−0.539629	+	0.841903i	$0.681436\pi$
$740$	−16.5886	+	28.7322i	−0.609808	+	1.05622i
$741$		0			0
$742$	6.07562	+	3.89558i	0.223043	+	0.143011i
$743$	−7.77364			−0.285187			−0.142594	−	0.989781i	$-0.545544\pi$
$743$	−7.77364			−0.285187			−0.142594	+	0.989781i	$0.545544\pi$
$744$		0			0
$745$	−35.3874	−	61.2928i	−1.29650	−	2.24560i
$746$	11.7210	+	20.3013i	0.429135	+	0.743284i
$747$		0			0
$748$	−10.9117			−0.398970
$749$	13.2550	−	6.85098i	0.484325	−	0.250329i
$750$		0			0
$751$	−26.8940	+	46.5819i	−0.981378	+	1.69980i	−0.324335	+	0.945942i	$0.605141\pi$
$751$	−26.8940	+	46.5819i	−0.981378	+	1.69980i	−0.657042	+	0.753854i	$0.728193\pi$
$752$	−5.84757	−	10.1283i	−0.213239	−	0.369341i
$753$		0			0
$754$	0.188946	−	0.327264i	0.00688101	−	0.0119183i
$755$	−25.0268			−0.910820
$756$		0			0
$757$	−20.9996			−0.763243			−0.381621	−	0.924319i	$-0.624634\pi$
$757$	−20.9996			−0.763243			−0.381621	+	0.924319i	$0.624634\pi$
$758$	−7.94495	+	13.7611i	−0.288574	+	0.499824i
$759$		0			0
$760$	0.284544	+	0.492844i	0.0103215	+	0.0178773i
$761$	15.1116	−	26.1741i	0.547796	−	0.948811i	−0.450629	−	0.892711i	$-0.648800\pi$
$761$	15.1116	−	26.1741i	0.547796	−	0.948811i	0.998425	−	0.0560996i	$-0.0178664\pi$
$762$		0			0
$763$	−1.06448	+	22.8495i	−0.0385368	+	0.827209i
$764$	−23.7433			−0.859001
$765$		0			0
$766$	6.69461	+	11.5954i	0.241886	+	0.418959i
$767$	−2.68206	−	4.64546i	−0.0968435	−	0.167738i
$768$		0			0
$769$	26.1031			0.941303			0.470652	−	0.882319i	$-0.344019\pi$
$769$	26.1031			0.941303			0.470652	+	0.882319i	$0.344019\pi$
$770$	−38.2622	+	19.7763i	−1.37887	+	0.712688i
$771$		0			0
$772$	−11.9720	+	20.7361i	−0.430882	+	0.746309i
$773$	6.72662	+	11.6509i	0.241940	+	0.419052i	0.961267	−	0.275620i	$-0.0888830\pi$
$773$	6.72662	+	11.6509i	0.241940	+	0.419052i	−0.719327	+	0.694672i	$0.755550\pi$
$774$		0			0
$775$	−24.3421	+	42.1617i	−0.874393	+	1.51449i
$776$	−11.4286			−0.410263
$777$		0			0
$778$	−10.6048			−0.380200
$779$	−0.432399	+	0.748937i	−0.0154923	+	0.0268335i
$780$		0			0
$781$	5.23076	+	9.05994i	0.187171	+	0.324190i
$782$	−8.80351	+	15.2481i	−0.314813	+	0.545272i
$783$		0			0
$784$	−6.96968	−	0.650799i	−0.248917	−	0.0232428i
$785$	−48.6239			−1.73546
$786$		0			0
$787$	17.8585	+	30.9319i	0.636588	+	1.10260i	0.986176	+	0.165700i	$0.0529882\pi$
$787$	17.8585	+	30.9319i	0.636588	+	1.10260i	−0.349588	+	0.936903i	$0.613678\pi$
$788$	−7.64064	−	13.2340i	−0.272187	−	0.471441i
$789$		0			0
$790$	−0.213828			−0.00760767
$791$	−16.6524	−	10.6772i	−0.592091	−	0.379639i
$792$		0			0
$793$	6.22641	−	10.7845i	0.221106	−	0.382968i
$794$	2.41210	+	4.17787i	0.0856021	+	0.148267i
$795$		0			0
$796$	0.804166	−	1.39286i	0.0285029	−	0.0493685i
$797$	−24.5486			−0.869555			−0.434777	−	0.900538i	$-0.643173\pi$
$797$	−24.5486			−0.869555			−0.434777	+	0.900538i	$0.643173\pi$
$798$		0			0
$799$	33.8869			1.19883
$800$	6.84348	−	11.8533i	0.241954	−	0.419076i
$801$		0			0
$802$	2.68463	+	4.64992i	0.0947977	+	0.164194i
$803$	−14.3260	+	24.8133i	−0.505553	+	0.875644i
$804$		0			0
$805$	−3.23421	+	69.4237i	−0.113991	+	2.44686i
$806$	3.55697			0.125289
$807$		0			0
$808$	9.87572	+	17.1052i	0.347427	+	0.601761i
$809$	23.5522	+	40.7936i	0.828051	+	1.43423i	0.899565	+	0.436786i	$0.143883\pi$
$809$	23.5522	+	40.7936i	0.828051	+	1.43423i	−0.0715146	+	0.997440i	$0.522783\pi$
$810$		0			0
$811$	−39.0782			−1.37222			−0.686111	−	0.727497i	$-0.740683\pi$
$811$	−39.0782			−1.37222			−0.686111	+	0.727497i	$0.740683\pi$
$812$	0.0465272	−	0.998726i	0.00163278	−	0.0350484i
$813$		0			0
$814$	14.4512	−	25.0303i	0.506515	−	0.877310i
$815$	−54.5769	−	94.5299i	−1.91174	−	3.31124i
$816$		0			0
$817$	0.0992292	−	0.171870i	0.00347159	−	0.00601297i
$818$	−31.0580			−1.08592
$819$		0			0
$820$	28.3971			0.991671
$821$	−3.78324	+	6.55277i	−0.132036	+	0.228693i	−0.924461	−	0.381276i	$-0.875485\pi$
$821$	−3.78324	+	6.55277i	−0.132036	+	0.228693i	0.792425	+	0.609969i	$0.208818\pi$
$822$		0			0
$823$	−15.5143	−	26.8716i	−0.540796	−	0.936685i	−0.998859	−	0.0477657i	$-0.984790\pi$
$823$	−15.5143	−	26.8716i	−0.540796	−	0.936685i	0.458063	−	0.888920i	$-0.348543\pi$
$824$	−7.46660	+	12.9325i	−0.260111	+	0.450526i
$825$		0			0
$826$	−11.9472	−	7.66033i	−0.415696	−	0.266537i
$827$	−38.2677			−1.33070			−0.665348	−	0.746533i	$-0.731717\pi$
$827$	−38.2677			−1.33070			−0.665348	+	0.746533i	$0.731717\pi$
$828$		0			0
$829$	0.833940	+	1.44443i	0.0289639	+	0.0501670i	0.880144	−	0.474707i	$-0.157446\pi$
$829$	0.833940	+	1.44443i	0.0289639	+	0.0501670i	−0.851180	+	0.524874i	$0.824113\pi$
$830$	9.30398	+	16.1150i	0.322946	+	0.559359i
$831$		0			0
$832$	−1.00000			−0.0346688
$833$	11.7304	−	16.5463i	0.406436	−	0.573296i
$834$		0			0
$835$	45.9121	−	79.5220i	1.58885	−	2.75197i
$836$	−0.247882	−	0.429344i	−0.00857317	−	0.0148492i
$837$		0			0
$838$	−1.98789	+	3.44312i	−0.0686704	+	0.118941i
$839$	40.4545			1.39664			0.698322	−	0.715784i	$-0.253930\pi$
$839$	40.4545			1.39664			0.698322	+	0.715784i	$0.253930\pi$
$840$		0			0
$841$	−28.8572			−0.995076
$842$	8.36916	−	14.4958i	0.288420	−	0.499559i
$843$		0			0
$844$	5.13110	+	8.88733i	0.176620	+	0.305915i
$845$	2.16142	−	3.74369i	0.0743551	−	0.128787i
$846$		0			0
$847$	7.47831	−	3.86525i	0.256958	−	0.132812i
$848$	2.72786			0.0936753
$849$		0			0
$850$	19.8291	+	34.3450i	0.680132	+	1.17802i
$851$	−23.3185	−	40.3888i	−0.799347	−	1.38451i
$852$		0			0
$853$	3.00738			0.102971			0.0514854	−	0.998674i	$-0.483604\pi$
$853$	3.00738			0.102971			0.0514854	+	0.998674i	$0.483604\pi$
$854$	1.53323	−	32.9114i	0.0524660	−	1.12620i
$855$		0			0
$856$	2.81976	−	4.88397i	0.0963775	−	0.166931i
$857$	10.2883	+	17.8199i	0.351442	+	0.608716i	0.986502	−	0.163747i	$-0.0523580\pi$
$857$	10.2883	+	17.8199i	0.351442	+	0.608716i	−0.635060	+	0.772463i	$0.719025\pi$
$858$		0			0
$859$	5.61717	−	9.72923i	0.191656	−	0.331957i	−0.754143	−	0.656710i	$-0.771948\pi$
$859$	5.61717	−	9.72923i	0.191656	−	0.331957i	0.945799	+	0.324753i	$0.105281\pi$
$860$	−6.51672			−0.222218
$861$		0			0
$862$	−2.86669			−0.0976399
$863$	−16.2269	+	28.1058i	−0.552370	+	0.956732i	0.445733	+	0.895166i	$0.352943\pi$
$863$	−16.2269	+	28.1058i	−0.552370	+	0.956732i	−0.998103	+	0.0615664i	$0.980390\pi$
$864$		0			0
$865$	17.1942	+	29.7812i	0.584619	+	1.01259i
$866$	−19.9890	+	34.6220i	−0.679255	+	1.17650i
$867$		0			0
$868$	8.36019	−	4.32106i	0.283763	−	0.146666i
$869$	0.186278			0.00631904
$870$		0			0
$871$	−0.963338	−	1.66855i	−0.0326415	−	0.0565367i
$872$	4.32284	+	7.48738i	0.146390	+	0.253555i
$873$		0			0
$874$	−0.799963			−0.0270592
$875$	83.6382	+	53.6274i	2.82749	+	1.81294i
$876$		0			0
$877$	4.65341	−	8.05994i	0.157134	−	0.272165i	−0.776700	−	0.629871i	$-0.783108\pi$
$877$	4.65341	−	8.05994i	0.157134	−	0.272165i	0.933834	+	0.357706i	$0.116441\pi$
$878$	−7.93138	−	13.7376i	−0.267671	−	0.463620i
$879$		0			0
$880$	−8.13963	+	14.0982i	−0.274387	+	0.475252i
$881$	−29.6765			−0.999827			−0.499914	−	0.866075i	$-0.666635\pi$
$881$	−29.6765			−0.999827			−0.499914	+	0.866075i	$0.666635\pi$
$882$		0			0
$883$	52.7454			1.77503			0.887513	−	0.460783i	$-0.152431\pi$
$883$	52.7454			1.77503			0.887513	+	0.460783i	$0.152431\pi$
$884$	1.44876	−	2.50932i	0.0487270	−	0.0843976i
$885$		0			0
$886$	−18.0121	−	31.1978i	−0.605127	−	1.04811i
$887$	−19.9467	+	34.5487i	−0.669745	+	1.16003i	0.308231	+	0.951312i	$0.400263\pi$
$887$	−19.9467	+	34.5487i	−0.669745	+	1.16003i	−0.977975	+	0.208720i	$0.933070\pi$
$888$		0			0
$889$	−39.0381	−	25.0305i	−1.30930	−	0.839497i
$890$	3.59825			0.120614
$891$		0			0
$892$	−7.27261	−	12.5965i	−0.243505	−	0.421763i
$893$	0.769813	+	1.33336i	0.0257608	+	0.0446190i
$894$		0			0
$895$	97.8937			3.27223
$896$	−2.35037	+	1.21481i	−0.0785202	+	0.0405841i
$897$		0			0
$898$	13.1788	−	22.8263i	0.439782	−	0.761725i
$899$	0.672077	+	1.16407i	0.0224150	+	0.0388239i
$900$		0			0
$901$	−3.95201	+	6.84509i	−0.131661	+	0.228043i
$902$	−24.7383			−0.823696
$903$		0			0
$904$	−7.47669			−0.248671
$905$	−21.4761	+	37.1977i	−0.713890	+	1.23649i
$906$		0			0
$907$	7.35377	+	12.7371i	0.244178	+	0.422929i	0.961900	−	0.273401i	$-0.0881485\pi$
$907$	7.35377	+	12.7371i	0.244178	+	0.422929i	−0.717722	+	0.696330i	$0.754815\pi$
$908$	−8.98180	+	15.5569i	−0.298071	+	0.516275i
$909$		0			0
$910$	0.532241	−	11.4248i	0.0176436	−	0.378728i
$911$	38.0850			1.26181			0.630907	−	0.775859i	$-0.282683\pi$
$911$	38.0850			1.26181			0.630907	+	0.775859i	$0.282683\pi$
$912$		0			0
$913$	−8.10522	−	14.0387i	−0.268244	−	0.464612i
$914$	−18.4195	−	31.9036i	−0.609264	−	1.05528i
$915$		0			0
$916$	−23.1924			−0.766300
$917$	31.6383	−	16.3526i	1.04479	−	0.540012i
$918$		0			0
$919$	−9.55858	+	16.5560i	−0.315309	+	0.546131i	−0.979503	−	0.201429i	$-0.935441\pi$
$919$	−9.55858	+	16.5560i	−0.315309	+	0.546131i	0.664194	+	0.747560i	$0.268775\pi$
$920$	13.1341	+	22.7489i	0.433018	+	0.750009i
$921$		0			0
$922$	−9.98295	+	17.2910i	−0.328771	+	0.569448i
$923$	−2.77798			−0.0914384
$924$		0			0
$925$	−105.045			−3.45387
$926$	−6.58055	+	11.3978i	−0.216250	+	0.374556i
$927$		0			0
$928$	−0.188946	−	0.327264i	−0.00620246	−	0.0107430i
$929$	15.5674	−	26.9636i	0.510751	−	0.884646i	−0.489172	−	0.872188i	$-0.662701\pi$
$929$	15.5674	−	26.9636i	0.510751	−	0.884646i	0.999922	−	0.0124586i	$-0.00396581\pi$
$930$		0			0
$931$	0.917535	+	0.0856755i	0.0300710	+	0.00280790i
$932$	17.5238			0.574012
$933$		0			0
$934$	13.9514	+	24.1645i	0.456503	+	0.790686i
$935$	−23.5847	−	40.8499i	−0.771302	−	1.33593i
$936$		0			0
$937$	22.0441			0.720150			0.360075	−	0.932923i	$-0.382751\pi$
$937$	22.0441			0.720150			0.360075	+	0.932923i	$0.382751\pi$
$938$	−4.29118	−	2.75143i	−0.140112	−	0.0898373i
$939$		0			0
$940$	25.2781	−	43.7830i	0.824482	−	1.42804i
$941$	−19.8142	−	34.3192i	−0.645924	−	1.11877i	−0.984087	−	0.177685i	$-0.943139\pi$
$941$	−19.8142	−	34.3192i	−0.645924	−	1.11877i	0.338164	−	0.941087i	$-0.390194\pi$
$942$		0			0
$943$	−19.9588	+	34.5697i	−0.649949	+	1.12575i
$944$	−5.36412			−0.174587
$945$		0			0
$946$	5.67708			0.184578
$947$	−12.1471	+	21.0395i	−0.394729	+	0.683690i	−0.993067	−	0.117554i	$-0.962495\pi$
$947$	−12.1471	+	21.0395i	−0.394729	+	0.683690i	0.598338	+	0.801244i	$0.295828\pi$
$948$		0			0
$949$	−3.80417	−	6.58901i	−0.123488	−	0.213888i
$950$	−0.900921	+	1.56044i	−0.0292297	+	0.0506274i
$951$		0			0
$952$	0.356750	−	7.65780i	0.0115623	−	0.248191i
$953$	−27.0783			−0.877151			−0.438575	−	0.898694i	$-0.644517\pi$
$953$	−27.0783			−0.877151			−0.438575	+	0.898694i	$0.644517\pi$
$954$		0			0
$955$	−51.3192	−	88.8874i	−1.66065	−	2.87633i
$956$	2.11358	+	3.66083i	0.0683582	+	0.118400i
$957$		0			0
$958$	−2.93117			−0.0947019
$959$	0.559576	−	12.0115i	0.0180697	−	0.387873i
$960$		0			0
$961$	9.17397	−	15.8898i	0.295935	−	0.512574i
$962$	3.83742	+	6.64661i	0.123723	+	0.214295i
$963$		0			0
$964$	−10.9988	+	19.0506i	−0.354249	+	0.613577i
$965$	−103.506			−3.33198
$966$		0			0
$967$	−13.4255			−0.431736			−0.215868	−	0.976423i	$-0.569258\pi$
$967$	−13.4255			−0.431736			−0.215868	+	0.976423i	$0.569258\pi$
$968$	1.59088	−	2.75549i	0.0511329	−	0.0885648i
$969$		0			0
$970$	−24.7020	−	42.7851i	−0.793134	−	1.37375i
$971$	−3.38054	+	5.85526i	−0.108487	+	0.187904i	−0.915157	−	0.403097i	$-0.867934\pi$
$971$	−3.38054	+	5.85526i	−0.108487	+	0.187904i	0.806671	+	0.591001i	$0.201267\pi$
$972$		0			0
$973$	−25.4163	−	16.2965i	−0.814809	−	0.522442i
$974$	−16.0334			−0.513742
$975$		0			0
$976$	−6.22641	−	10.7845i	−0.199303	−	0.345202i
$977$	15.1172	+	26.1838i	0.483643	+	0.837694i	0.999824	−	0.0187859i	$-0.00598010\pi$
$977$	15.1172	+	26.1838i	0.483643	+	0.837694i	−0.516181	+	0.856480i	$0.672647\pi$
$978$		0			0
$979$	−3.13464			−0.100183
$980$	−12.6280	−	27.4990i	−0.403387	−	0.878423i
$981$		0			0
$982$	7.18351	−	12.4422i	0.229235	−	0.397047i
$983$	−16.7048	−	28.9335i	−0.532799	−	0.922836i	−0.999266	−	0.0382971i	$-0.987807\pi$
$983$	−16.7048	−	28.9335i	−0.532799	−	0.922836i	0.466467	−	0.884539i	$-0.345527\pi$
$984$		0			0
$985$	33.0293	−	57.2084i	1.05240	−	1.82281i
$986$	1.09495			0.0348703
$987$		0			0
$988$	0.131647			0.00418824
$989$	4.58026	−	7.93324i	0.145644	−	0.252262i
$990$		0			0
$991$	−6.10170	−	10.5685i	−0.193827	−	0.335718i	0.752688	−	0.658377i	$-0.228757\pi$
$991$	−6.10170	−	10.5685i	−0.193827	−	0.335718i	−0.946515	+	0.322659i	$0.895423\pi$
$992$	1.77849	−	3.08043i	0.0564670	−	0.0978037i
$993$		0			0
$994$	−6.52928	+	3.37473i	−0.207096	+	0.107040i
$995$	6.95257			0.220411
$996$		0			0
$997$	−17.4432	−	30.2126i	−0.552433	−	0.956842i	−0.998098	−	0.0616426i	$-0.980366\pi$
$997$	−17.4432	−	30.2126i	−0.552433	−	0.956842i	0.445665	−	0.895200i	$-0.352967\pi$
$998$	−10.5765	−	18.3190i	−0.334792	−	0.579876i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.j.t.1171.5	yes	10
3.2	odd	2		1638.2.j.s.1171.1	yes	10
7.4	even	3	inner	1638.2.j.t.235.5	yes	10
21.11	odd	6		1638.2.j.s.235.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.j.s.235.1	✓	10	21.11	odd	6
1638.2.j.s.1171.1	yes	10	3.2	odd	2
1638.2.j.t.235.5	yes	10	7.4	even	3	inner
1638.2.j.t.1171.5	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.16142 - 3.74369i) q^{5} +(-2.22724 - 1.42807i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.16142 - 3.74369i) q^{5} +(-2.22724 - 1.42807i) q^{7} -1.00000 q^{8} +(-2.16142 - 3.74369i) q^{10} +(1.88293 + 3.26134i) q^{11} -1.00000 q^{13} +(-2.35037 + 1.21481i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.44876 - 2.50932i) q^{17} +(0.0658233 - 0.114009i) q^{19} -4.32284 q^{20} +3.76587 q^{22} +(3.03830 - 5.26249i) q^{23} +(-6.84348 - 11.8533i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(-0.123123 + 2.64288i) q^{28} -0.377892 q^{29} +(-1.77849 - 3.08043i) q^{31} +(0.500000 + 0.866025i) q^{32} -2.89751 q^{34} +(-10.1603 + 5.25145i) q^{35} +(3.83742 - 6.64661i) q^{37} +(-0.0658233 - 0.114009i) q^{38} +(-2.16142 + 3.74369i) q^{40} -6.56909 q^{41} +1.50751 q^{43} +(1.88293 - 3.26134i) q^{44} +(-3.03830 - 5.26249i) q^{46} +(-5.84757 + 10.1283i) q^{47} +(2.92123 + 6.36132i) q^{49} -13.6870 q^{50} +(0.500000 + 0.866025i) q^{52} +(-1.36393 - 2.36240i) q^{53} +16.2793 q^{55} +(2.22724 + 1.42807i) q^{56} +(-0.188946 + 0.327264i) q^{58} +(2.68206 + 4.64546i) q^{59} +(-6.22641 + 10.7845i) q^{61} -3.55697 q^{62} +1.00000 q^{64} +(-2.16142 + 3.74369i) q^{65} +(0.963338 + 1.66855i) q^{67} +(-1.44876 + 2.50932i) q^{68} +(-0.532241 + 11.4248i) q^{70} +2.77798 q^{71} +(3.80417 + 6.58901i) q^{73} +(-3.83742 - 6.64661i) q^{74} -0.131647 q^{76} +(0.463665 - 9.95276i) q^{77} +(0.0247324 - 0.0428378i) q^{79} +(2.16142 + 3.74369i) q^{80} +(-3.28454 + 5.68900i) q^{82} -4.30457 q^{83} -12.5255 q^{85} +(0.753754 - 1.30554i) q^{86} +(-1.88293 - 3.26134i) q^{88} +(-0.416190 + 0.720863i) q^{89} +(2.22724 + 1.42807i) q^{91} -6.07660 q^{92} +(5.84757 + 10.1283i) q^{94} +(-0.284544 - 0.492844i) q^{95} +11.4286 q^{97} +(6.96968 + 0.650799i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8}+O(q^{10}) \) 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8	\( 10 q + 5 q^{2} - 5 q^{4} - q^{5} - 3 q^{7} - 10 q^{8} + q^{10} + 9 q^{11} - 10 q^{13} - 6 q^{14} - 5 q^{16} - 8 q^{17} + 4 q^{19} + 2 q^{20} + 18 q^{22} + 6 q^{23} - 12 q^{25} - 5 q^{26} - 3 q^{28} - 14 q^{29} - 5 q^{31} + 5 q^{32} - 16 q^{34} - 8 q^{35} - 10 q^{37} - 4 q^{38} + q^{40} - 24 q^{41} + 8 q^{43} + 9 q^{44} - 6 q^{46} - 4 q^{47} - 5 q^{49} - 24 q^{50} + 5 q^{52} + 19 q^{53} - 2 q^{55} + 3 q^{56} - 7 q^{58} - 7 q^{59} + 4 q^{61} - 10 q^{62} + 10 q^{64} + q^{65} - 8 q^{68} + 11 q^{70} - 8 q^{71} - 6 q^{73} + 10 q^{74} - 8 q^{76} + 19 q^{77} - 9 q^{79} - q^{80} - 12 q^{82} - 34 q^{83} + 36 q^{85} + 4 q^{86} - 9 q^{88} + 10 q^{89} + 3 q^{91} - 12 q^{92} + 4 q^{94} + 18 q^{95} + 14 q^{97} + 5 q^{98}+O(q^{100}) \) 10 * q + 5 * q^2 - 5 * q^4 - q^5 - 3 * q^7 - 10 * q^8 + q^10 + 9 * q^11 - 10 * q^13 - 6 * q^14 - 5 * q^16 - 8 * q^17 + 4 * q^19 + 2 * q^20 + 18 * q^22 + 6 * q^23 - 12 * q^25 - 5 * q^26 - 3 * q^28 - 14 * q^29 - 5 * q^31 + 5 * q^32 - 16 * q^34 - 8 * q^35 - 10 * q^37 - 4 * q^38 + q^40 - 24 * q^41 + 8 * q^43 + 9 * q^44 - 6 * q^46 - 4 * q^47 - 5 * q^49 - 24 * q^50 + 5 * q^52 + 19 * q^53 - 2 * q^55 + 3 * q^56 - 7 * q^58 - 7 * q^59 + 4 * q^61 - 10 * q^62 + 10 * q^64 + q^65 - 8 * q^68 + 11 * q^70 - 8 * q^71 - 6 * q^73 + 10 * q^74 - 8 * q^76 + 19 * q^77 - 9 * q^79 - q^80 - 12 * q^82 - 34 * q^83 + 36 * q^85 + 4 * q^86 - 9 * q^88 + 10 * q^89 + 3 * q^91 - 12 * q^92 + 4 * q^94 + 18 * q^95 + 14 * q^97 + 5 * q^98

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