LMFDB - Embedded newform 1026.2.h.g.505.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1026,2,Mod(505,1026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1026, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1026.505");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1026 = 2 \cdot 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1026.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.19265124738$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} + \cdots + 19683 $ x^18 + 4x^16 - 6x^15 + x^14 - 21x^13 - 12x^12 + 9x^10 + 135x^9 + 27x^8 - 324x^6 - 1701x^5 + 243x^4 - 4374x^3 + 8748x^2 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 342)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.7
Root			$-0.614525 - 1.61937i$ of defining polynomial
Character	$\chi$	$=$	1026.505
Dual form			1026.2.h.g.577.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.57955 q^{5} +(2.31561 - 4.01075i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.57955 q^{5} +(2.31561 - 4.01075i) q^{7} +1.00000 q^{8} +(-0.789777 - 1.36793i) q^{10} +(1.83826 - 3.18396i) q^{11} +(2.78676 - 4.82682i) q^{13} -4.63122 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.65387 + 6.32868i) q^{17} +(3.55454 + 2.52294i) q^{19} +(-0.789777 + 1.36793i) q^{20} -3.67652 q^{22} +(-1.05224 + 1.82254i) q^{23} -2.50501 q^{25} -5.57353 q^{26} +(2.31561 + 4.01075i) q^{28} -5.32452 q^{29} +(0.587415 + 1.01743i) q^{31} +(-0.500000 + 0.866025i) q^{32} +7.30773 q^{34} +(3.65763 - 6.33520i) q^{35} +1.16827 q^{37} +(0.407656 - 4.33979i) q^{38} +1.57955 q^{40} +4.49279 q^{41} +(-4.24734 - 7.35661i) q^{43} +(1.83826 + 3.18396i) q^{44} +2.10449 q^{46} +5.75562 q^{47} +(-7.22408 - 12.5125i) q^{49} +(1.25250 + 2.16940i) q^{50} +(2.78676 + 4.82682i) q^{52} +(-1.69773 - 2.94055i) q^{53} +(2.90363 - 5.02923i) q^{55} +(2.31561 - 4.01075i) q^{56} +(2.66226 + 4.61117i) q^{58} +1.98482 q^{59} +3.18599 q^{61} +(0.587415 - 1.01743i) q^{62} +1.00000 q^{64} +(4.40184 - 7.62422i) q^{65} +(-6.29213 + 10.8983i) q^{67} +(-3.65387 - 6.32868i) q^{68} -7.31525 q^{70} +(-4.03312 + 6.98558i) q^{71} +(7.45107 - 12.9056i) q^{73} +(-0.584135 - 1.01175i) q^{74} +(-3.96220 + 1.81686i) q^{76} +(-8.51338 - 14.7456i) q^{77} +(2.99319 + 5.18435i) q^{79} +(-0.789777 - 1.36793i) q^{80} +(-2.24640 - 3.89087i) q^{82} +(5.85781 - 10.1460i) q^{83} +(-5.77148 + 9.99650i) q^{85} +(-4.24734 + 7.35661i) q^{86} +(1.83826 - 3.18396i) q^{88} +(-3.00802 - 5.21004i) q^{89} +(-12.9061 - 22.3540i) q^{91} +(-1.05224 - 1.82254i) q^{92} +(-2.87781 - 4.98452i) q^{94} +(5.61459 + 3.98512i) q^{95} +(5.97017 + 10.3406i) q^{97} +(-7.22408 + 12.5125i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8}+O(q^{10}) $ 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8	$ 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8} - q^{11} + q^{13} - 10 q^{14} - 9 q^{16} + 5 q^{17} + 9 q^{19} + 2 q^{22} + 2 q^{23} + 18 q^{25} - 2 q^{26} + 5 q^{28} - 18 q^{29} + 4 q^{31} - 9 q^{32} - 10 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} + 2 q^{41} + 7 q^{43} - q^{44} - 4 q^{46} + 38 q^{47} + 6 q^{49} - 9 q^{50} + q^{52} + 10 q^{53} + 6 q^{55} + 5 q^{56} + 9 q^{58} - 10 q^{59} - 36 q^{61} + 4 q^{62} + 18 q^{64} + 45 q^{65} + 22 q^{67} + 5 q^{68} + 12 q^{70} - 11 q^{71} + 44 q^{73} - 10 q^{74} - 6 q^{76} + 2 q^{77} + 2 q^{79} - q^{82} + 7 q^{83} + 7 q^{86} - q^{88} - q^{89} - 25 q^{91} + 2 q^{92} - 19 q^{94} - 21 q^{95} + 6 q^{98}+O(q^{100}) $ 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8 - q^11 + q^13 - 10 * q^14 - 9 * q^16 + 5 * q^17 + 9 * q^19 + 2 * q^22 + 2 * q^23 + 18 * q^25 - 2 * q^26 + 5 * q^28 - 18 * q^29 + 4 * q^31 - 9 * q^32 - 10 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 + 2 * q^41 + 7 * q^43 - q^44 - 4 * q^46 + 38 * q^47 + 6 * q^49 - 9 * q^50 + q^52 + 10 * q^53 + 6 * q^55 + 5 * q^56 + 9 * q^58 - 10 * q^59 - 36 * q^61 + 4 * q^62 + 18 * q^64 + 45 * q^65 + 22 * q^67 + 5 * q^68 + 12 * q^70 - 11 * q^71 + 44 * q^73 - 10 * q^74 - 6 * q^76 + 2 * q^77 + 2 * q^79 - q^82 + 7 * q^83 + 7 * q^86 - q^88 - q^89 - 25 * q^91 + 2 * q^92 - 19 * q^94 - 21 * q^95 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1026\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$5$	1.57955			0.706398			0.353199	−	0.935548i	$-0.385094\pi$
$5$	1.57955			0.706398			0.353199	+	0.935548i	$0.385094\pi$
$6$		0			0
$7$	2.31561	−	4.01075i	0.875218	−	1.51592i	0.0186867	−	0.999825i	$-0.494051\pi$
$7$	2.31561	−	4.01075i	0.875218	−	1.51592i	0.856531	−	0.516096i	$-0.172615\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.789777	−	1.36793i	−0.249749	−	0.432579i
$11$	1.83826	−	3.18396i	0.554256	−	0.960000i	−0.443705	−	0.896173i	$-0.646336\pi$
$11$	1.83826	−	3.18396i	0.554256	−	0.960000i	0.997961	−	0.0638268i	$-0.0203305\pi$
$12$		0			0
$13$	2.78676	−	4.82682i	0.772909	−	1.33872i	−0.163053	−	0.986617i	$-0.552134\pi$
$13$	2.78676	−	4.82682i	0.772909	−	1.33872i	0.935962	−	0.352101i	$-0.114532\pi$
$14$	−4.63122			−1.23774
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.65387	+	6.32868i	−0.886193	+	1.53493i	−0.0418529	+	0.999124i	$0.513326\pi$
$17$	−3.65387	+	6.32868i	−0.886193	+	1.53493i	−0.844340	+	0.535808i	$0.820007\pi$
$18$		0			0
$19$	3.55454	+	2.52294i	0.815468	+	0.578802i
$19$	3.55454	+	2.52294i	0.815468	+	0.578802i
$20$	−0.789777	+	1.36793i	−0.176599	+	0.305879i
$21$		0			0
$22$	−3.67652			−0.783837
$23$	−1.05224	+	1.82254i	−0.219408	+	0.380025i	−0.954627	−	0.297804i	$-0.903746\pi$
$23$	−1.05224	+	1.82254i	−0.219408	+	0.380025i	0.735219	+	0.677829i	$0.237079\pi$
$24$		0			0
$25$	−2.50501			−0.501002
$26$	−5.57353			−1.09306
$27$		0			0
$28$	2.31561	+	4.01075i	0.437609	+	0.757961i
$29$	−5.32452			−0.988739			−0.494369	−	0.869252i	$-0.664601\pi$
$29$	−5.32452			−0.988739			−0.494369	+	0.869252i	$0.664601\pi$
$30$		0			0
$31$	0.587415	+	1.01743i	0.105503	+	0.182736i	0.913944	−	0.405841i	$-0.133021\pi$
$31$	0.587415	+	1.01743i	0.105503	+	0.182736i	−0.808441	+	0.588578i	$0.799688\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	7.30773			1.25327
$35$	3.65763	−	6.33520i	0.618252	−	1.07084i
$36$		0			0
$37$	1.16827			0.192062			0.0960312	−	0.995378i	$-0.469385\pi$
$37$	1.16827			0.192062			0.0960312	+	0.995378i	$0.469385\pi$
$38$	0.407656	−	4.33979i	0.0661305	−	0.704008i
$39$		0			0
$40$	1.57955			0.249749
$41$	4.49279			0.701656			0.350828	−	0.936440i	$-0.385900\pi$
$41$	4.49279			0.701656			0.350828	+	0.936440i	$0.385900\pi$
$42$		0			0
$43$	−4.24734	−	7.35661i	−0.647714	−	1.12187i	−0.983668	−	0.179995i	$-0.942392\pi$
$43$	−4.24734	−	7.35661i	−0.647714	−	1.12187i	0.335954	−	0.941878i	$-0.390941\pi$
$44$	1.83826	+	3.18396i	0.277128	+	0.480000i
$45$		0			0
$46$	2.10449			0.310289
$47$	5.75562			0.839544			0.419772	−	0.907630i	$-0.362110\pi$
$47$	5.75562			0.839544			0.419772	+	0.907630i	$0.362110\pi$
$48$		0			0
$49$	−7.22408	−	12.5125i	−1.03201	−	1.78750i
$50$	1.25250	+	2.16940i	0.177131	+	0.306800i
$51$		0			0
$52$	2.78676	+	4.82682i	0.386455	+	0.669359i
$53$	−1.69773	−	2.94055i	−0.233201	−	0.403916i	0.725547	−	0.688172i	$-0.241587\pi$
$53$	−1.69773	−	2.94055i	−0.233201	−	0.403916i	−0.958748	+	0.284256i	$0.908253\pi$
$54$		0			0
$55$	2.90363	−	5.02923i	0.391525	−	0.678142i
$56$	2.31561	−	4.01075i	0.309436	−	0.535959i
$57$		0			0
$58$	2.66226	+	4.61117i	0.349572	+	0.605476i
$59$	1.98482			0.258402			0.129201	−	0.991618i	$-0.458759\pi$
$59$	1.98482			0.258402			0.129201	+	0.991618i	$0.458759\pi$
$60$		0			0
$61$	3.18599			0.407925			0.203962	−	0.978979i	$-0.434618\pi$
$61$	3.18599			0.407925			0.203962	+	0.978979i	$0.434618\pi$
$62$	0.587415	−	1.01743i	0.0746018	−	0.129214i
$63$		0			0
$64$	1.00000			0.125000
$65$	4.40184	−	7.62422i	0.545981	−	0.945668i
$66$		0			0
$67$	−6.29213	+	10.8983i	−0.768706	+	1.33144i	0.169559	+	0.985520i	$0.445766\pi$
$67$	−6.29213	+	10.8983i	−0.768706	+	1.33144i	−0.938265	+	0.345918i	$0.887568\pi$
$68$	−3.65387	−	6.32868i	−0.443097	−	0.767466i
$69$		0			0
$70$	−7.31525			−0.874340
$71$	−4.03312	+	6.98558i	−0.478644	+	0.829035i	−0.999700	−	0.0244869i	$-0.992205\pi$
$71$	−4.03312	+	6.98558i	−0.478644	+	0.829035i	0.521056	+	0.853522i	$0.325538\pi$
$72$		0			0
$73$	7.45107	−	12.9056i	0.872082	−	1.51049i	0.0122430	−	0.999925i	$-0.496103\pi$
$73$	7.45107	−	12.9056i	0.872082	−	1.51049i	0.859839	−	0.510565i	$-0.170564\pi$
$74$	−0.584135	−	1.01175i	−0.0679043	−	0.117614i
$75$		0			0
$76$	−3.96220	+	1.81686i	−0.454496	+	0.208408i
$77$	−8.51338	−	14.7456i	−0.970189	−	1.68042i
$78$		0			0
$79$	2.99319	+	5.18435i	0.336760	+	0.583285i	0.983821	−	0.179153i	$-0.0573357\pi$
$79$	2.99319	+	5.18435i	0.336760	+	0.583285i	−0.647062	+	0.762438i	$0.724002\pi$
$80$	−0.789777	−	1.36793i	−0.0882997	−	0.152940i
$81$		0			0
$82$	−2.24640	−	3.89087i	−0.248073	−	0.429675i
$83$	5.85781	−	10.1460i	0.642978	−	1.11367i	−0.341787	−	0.939778i	$-0.611032\pi$
$83$	5.85781	−	10.1460i	0.642978	−	1.11367i	0.984765	−	0.173893i	$-0.0556346\pi$
$84$		0			0
$85$	−5.77148	+	9.99650i	−0.626005	+	1.08427i
$86$	−4.24734	+	7.35661i	−0.458003	+	0.793284i
$87$		0			0
$88$	1.83826	−	3.18396i	0.195959	−	0.339411i
$89$	−3.00802	−	5.21004i	−0.318849	−	0.552263i	0.661399	−	0.750034i	$-0.269963\pi$
$89$	−3.00802	−	5.21004i	−0.318849	−	0.552263i	−0.980248	+	0.197771i	$0.936630\pi$
$90$		0			0
$91$	−12.9061	−	22.3540i	−1.35293	−	2.34334i
$92$	−1.05224	−	1.82254i	−0.109704	−	0.190013i
$93$		0			0
$94$	−2.87781	−	4.98452i	−0.296824	−	0.514114i
$95$	5.61459	+	3.98512i	0.576045	+	0.408864i
$96$		0			0
$97$	5.97017	+	10.3406i	0.606179	+	1.04993i	0.991864	+	0.127303i	$0.0406320\pi$
$97$	5.97017	+	10.3406i	0.606179	+	1.04993i	−0.385684	+	0.922631i	$0.626035\pi$
$98$	−7.22408	+	12.5125i	−0.729742	+	1.26395i
$99$		0			0
$100$	1.25250	−	2.16940i	0.125250	−	0.216940i
$101$	−10.8932			−1.08392			−0.541959	−	0.840405i	$-0.682317\pi$
$101$	−10.8932			−1.08392			−0.541959	+	0.840405i	$0.682317\pi$
$102$		0			0
$103$	6.09893	+	10.5637i	0.600945	+	1.04087i	0.992678	+	0.120789i	$0.0385423\pi$
$103$	6.09893	+	10.5637i	0.600945	+	1.04087i	−0.391733	+	0.920079i	$0.628124\pi$
$104$	2.78676	−	4.82682i	0.273265	−	0.473308i
$105$		0			0
$106$	−1.69773	+	2.94055i	−0.164898	+	0.285612i
$107$	6.89925			0.666976			0.333488	−	0.942754i	$-0.391774\pi$
$107$	6.89925			0.666976			0.333488	+	0.942754i	$0.391774\pi$
$108$		0			0
$109$	−2.02428	+	3.50615i	−0.193890	+	0.335828i	−0.946536	−	0.322598i	$-0.895444\pi$
$109$	−2.02428	+	3.50615i	−0.193890	+	0.335828i	0.752646	+	0.658426i	$0.228777\pi$
$110$	−5.80726			−0.553701
$111$		0			0
$112$	−4.63122			−0.437609
$113$	0.671292	+	1.16271i	0.0631498	+	0.109379i	0.895872	−	0.444313i	$-0.146552\pi$
$113$	0.671292	+	1.16271i	0.0631498	+	0.109379i	−0.832722	+	0.553691i	$0.813219\pi$
$114$		0			0
$115$	−1.66207	+	2.87880i	−0.154989	+	0.268449i
$116$	2.66226	−	4.61117i	0.247185	−	0.428136i
$117$		0			0
$118$	−0.992410	−	1.71891i	−0.0913588	−	0.158238i
$119$	16.9218	+	29.3095i	1.55122	+	2.68680i
$120$		0			0
$121$	−1.25840	−	2.17961i	−0.114400	−	0.198146i
$122$	−1.59300	−	2.75915i	−0.144223	−	0.249802i
$123$		0			0
$124$	−1.17483			−0.105503
$125$	−11.8546			−1.06030
$126$		0			0
$127$	−3.95754	−	6.85466i	−0.351175	−	0.608253i	0.635281	−	0.772281i	$-0.280884\pi$
$127$	−3.95754	−	6.85466i	−0.351175	−	0.608253i	−0.986456	+	0.164029i	$0.947551\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−8.80369			−0.772134
$131$	1.39300			0.121707			0.0608537	−	0.998147i	$-0.480618\pi$
$131$	1.39300			0.121707			0.0608537	+	0.998147i	$0.480618\pi$
$132$		0			0
$133$	18.3498	−	8.41426i	1.59113	−	0.729609i
$134$	12.5843			1.08711
$135$		0			0
$136$	−3.65387	+	6.32868i	−0.313317	+	0.542680i
$137$	−2.40884			−0.205801			−0.102901	−	0.994692i	$-0.532812\pi$
$137$	−2.40884			−0.205801			−0.102901	+	0.994692i	$0.532812\pi$
$138$		0			0
$139$	4.23509	−	7.33539i	0.359216	−	0.622180i	−0.628614	−	0.777717i	$-0.716378\pi$
$139$	4.23509	−	7.33539i	0.359216	−	0.622180i	0.987830	+	0.155538i	$0.0497110\pi$
$140$	3.65763	+	6.33520i	0.309126	+	0.535422i
$141$		0			0
$142$	8.06625			0.676905
$143$	−10.2456	−	17.7459i	−0.856779	−	1.48399i
$144$		0			0
$145$	−8.41037			−0.698443
$146$	−14.9021			−1.23331
$147$		0			0
$148$	−0.584135	+	1.01175i	−0.0480156	+	0.0831655i
$149$	9.62256			0.788310			0.394155	−	0.919044i	$-0.371037\pi$
$149$	9.62256			0.788310			0.394155	+	0.919044i	$0.371037\pi$
$150$		0			0
$151$	−11.4046	+	19.7534i	−0.928094	+	1.60751i	−0.141587	+	0.989926i	$0.545220\pi$
$151$	−11.4046	+	19.7534i	−0.928094	+	1.60751i	−0.786507	+	0.617581i	$0.788113\pi$
$152$	3.55454	+	2.52294i	0.288312	+	0.204637i
$153$		0			0
$154$	−8.51338	+	14.7456i	−0.686027	+	1.18823i
$155$	0.927853	+	1.60709i	0.0745270	+	0.129085i
$156$		0			0
$157$	−4.37348			−0.349041			−0.174521	−	0.984654i	$-0.555838\pi$
$157$	−4.37348			−0.349041			−0.174521	+	0.984654i	$0.555838\pi$
$158$	2.99319	−	5.18435i	0.238125	−	0.412445i
$159$		0			0
$160$	−0.789777	+	1.36793i	−0.0624373	+	0.108145i
$161$	4.87316	+	8.44056i	0.384059	+	0.665210i
$162$		0			0
$163$	6.36953			0.498900			0.249450	−	0.968388i	$-0.419750\pi$
$163$	6.36953			0.498900			0.249450	+	0.968388i	$0.419750\pi$
$164$	−2.24640	+	3.89087i	−0.175414	+	0.303826i
$165$		0			0
$166$	−11.7156			−0.909308
$167$	−3.08570	+	5.34459i	−0.238779	+	0.413577i	−0.960364	−	0.278749i	$-0.910080\pi$
$167$	−3.08570	+	5.34459i	−0.238779	+	0.413577i	0.721585	+	0.692325i	$0.243414\pi$
$168$		0			0
$169$	−9.03210	−	15.6441i	−0.694777	−	1.20339i
$170$	11.5430			0.885305
$171$		0			0
$172$	8.49469			0.647714
$173$	−3.75669	−	6.50678i	−0.285616	−	0.494701i	0.687142	−	0.726523i	$-0.258865\pi$
$173$	−3.75669	−	6.50678i	−0.285616	−	0.494701i	−0.972758	+	0.231821i	$0.925532\pi$
$174$		0			0
$175$	−5.80062	+	10.0470i	−0.438486	+	0.759479i
$176$	−3.67652			−0.277128
$177$		0			0
$178$	−3.00802	+	5.21004i	−0.225460	+	0.390509i
$179$	−21.7463			−1.62540			−0.812698	−	0.582685i	$-0.802002\pi$
$179$	−21.7463			−1.62540			−0.812698	+	0.582685i	$0.802002\pi$
$180$		0			0
$181$	2.33180	+	4.03880i	0.173322	+	0.300202i	0.939579	−	0.342332i	$-0.111217\pi$
$181$	2.33180	+	4.03880i	0.173322	+	0.300202i	−0.766258	+	0.642534i	$0.777883\pi$
$182$	−12.9061	+	22.3540i	−0.956664	+	1.65699i
$183$		0			0
$184$	−1.05224	+	1.82254i	−0.0775723	+	0.134359i
$185$	1.84535			0.135673
$186$		0			0
$187$	13.4335	+	23.2675i	0.982356	+	1.70149i
$188$	−2.87781	+	4.98452i	−0.209886	+	0.363533i
$189$		0			0
$190$	0.643914	−	6.85494i	0.0467145	−	0.497310i
$191$	−2.83934	+	4.91788i	−0.205447	+	0.355845i	−0.950275	−	0.311411i	$-0.899198\pi$
$191$	−2.83934	+	4.91788i	−0.205447	+	0.355845i	0.744828	+	0.667257i	$0.232532\pi$
$192$		0			0
$193$	9.87222			0.710618			0.355309	−	0.934749i	$-0.384376\pi$
$193$	9.87222			0.710618			0.355309	+	0.934749i	$0.384376\pi$
$194$	5.97017	−	10.3406i	0.428634	−	0.742415i
$195$		0			0
$196$	14.4482			1.03201
$197$	25.0810			1.78695			0.893474	−	0.449114i	$-0.148260\pi$
$197$	25.0810			1.78695			0.893474	+	0.449114i	$0.148260\pi$
$198$		0			0
$199$	4.46649	+	7.73619i	0.316621	+	0.548404i	0.979781	−	0.200074i	$-0.0641183\pi$
$199$	4.46649	+	7.73619i	0.316621	+	0.548404i	−0.663160	+	0.748478i	$0.730785\pi$
$200$	−2.50501			−0.177131
$201$		0			0
$202$	5.44662	+	9.43383i	0.383223	+	0.663762i
$203$	−12.3295	+	21.3553i	−0.865361	+	1.49885i
$204$		0			0
$205$	7.09661			0.495648
$206$	6.09893	−	10.5637i	0.424932	−	0.736004i
$207$		0			0
$208$	−5.57353			−0.386455
$209$	14.5671	−	6.67971i	1.00763	−	0.462045i
$210$		0			0
$211$	6.32457			0.435401			0.217701	−	0.976016i	$-0.430144\pi$
$211$	6.32457			0.435401			0.217701	+	0.976016i	$0.430144\pi$
$212$	3.39546			0.233201
$213$		0			0
$214$	−3.44963	−	5.97493i	−0.235812	−	0.408438i
$215$	−6.70891	−	11.6202i	−0.457544	−	0.792489i
$216$		0			0
$217$	5.44089			0.369352
$218$	4.04855			0.274202
$219$		0			0
$220$	2.90363	+	5.02923i	0.195763	+	0.339071i
$221$	20.3649	+	35.2731i	1.36989	+	2.37272i
$222$		0			0
$223$	−0.878811	−	1.52215i	−0.0588496	−	0.101930i	0.835100	−	0.550099i	$-0.185410\pi$
$223$	−0.878811	−	1.52215i	−0.0588496	−	0.101930i	−0.893949	+	0.448168i	$0.852077\pi$
$224$	2.31561	+	4.01075i	0.154718	+	0.267980i
$225$		0			0
$226$	0.671292	−	1.16271i	0.0446537	−	0.0773424i
$227$	6.41556	−	11.1121i	0.425816	−	0.737535i	−0.570680	−	0.821172i	$-0.693320\pi$
$227$	6.41556	−	11.1121i	0.425816	−	0.737535i	0.996496	+	0.0836376i	$0.0266538\pi$
$228$		0			0
$229$	−0.207385	−	0.359201i	−0.0137044	−	0.0237367i	0.859092	−	0.511821i	$-0.171029\pi$
$229$	−0.207385	−	0.359201i	−0.0137044	−	0.0237367i	−0.872796	+	0.488085i	$0.837696\pi$
$230$	3.32415			0.219188
$231$		0			0
$232$	−5.32452			−0.349572
$233$	6.42184	−	11.1229i	0.420709	−	0.728689i	−0.575300	−	0.817942i	$-0.695115\pi$
$233$	6.42184	−	11.1229i	0.420709	−	0.728689i	0.996009	+	0.0892537i	$0.0284482\pi$
$234$		0			0
$235$	9.09132			0.593052
$236$	−0.992410	+	1.71891i	−0.0646004	+	0.111891i
$237$		0			0
$238$	16.9218	−	29.3095i	1.09688	−	1.89985i
$239$	−6.27082	−	10.8614i	−0.405626	−	0.702564i	0.588768	−	0.808302i	$-0.299613\pi$
$239$	−6.27082	−	10.8614i	−0.405626	−	0.702564i	−0.994394	+	0.105738i	$0.966280\pi$
$240$		0			0
$241$	−4.04956			−0.260855			−0.130427	−	0.991458i	$-0.541635\pi$
$241$	−4.04956			−0.260855			−0.130427	+	0.991458i	$0.541635\pi$
$242$	−1.25840	+	2.17961i	−0.0808928	+	0.140110i
$243$		0			0
$244$	−1.59300	+	2.75915i	−0.101981	+	0.176637i
$245$	−11.4108	−	19.7641i	−0.729011	−	1.26268i
$246$		0			0
$247$	22.0834	−	10.1263i	1.40513	−	0.644321i
$248$	0.587415	+	1.01743i	0.0373009	+	0.0646070i
$249$		0			0
$250$	5.92728	+	10.2664i	0.374874	+	0.649301i
$251$	9.59620	+	16.6211i	0.605707	+	1.04912i	0.991939	+	0.126714i	$0.0404430\pi$
$251$	9.59620	+	16.6211i	0.605707	+	1.04912i	−0.386232	+	0.922402i	$0.626224\pi$
$252$		0			0
$253$	3.86859	+	6.70059i	0.243216	+	0.421263i
$254$	−3.95754	+	6.85466i	−0.248318	+	0.430100i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.784594	+	1.35896i	−0.0489416	+	0.0847694i	−0.889458	−	0.457016i	$-0.848918\pi$
$257$	−0.784594	+	1.35896i	−0.0489416	+	0.0847694i	0.840517	+	0.541785i	$0.182251\pi$
$258$		0			0
$259$	2.70526	−	4.68564i	0.168096	−	0.291152i
$260$	4.40184	+	7.62422i	0.272991	+	0.472834i
$261$		0			0
$262$	−0.696502	−	1.20638i	−0.0430301	−	0.0745302i
$263$	13.9124	+	24.0970i	0.857876	+	1.48588i	0.873951	+	0.486014i	$0.161550\pi$
$263$	13.9124	+	24.0970i	0.857876	+	1.48588i	−0.0160751	+	0.999871i	$0.505117\pi$
$264$		0			0
$265$	−2.68165	−	4.64476i	−0.164733	−	0.285325i
$266$	−16.4619	−	11.6843i	−1.00934	−	0.716408i
$267$		0			0
$268$	−6.29213	−	10.8983i	−0.384353	−	0.665719i
$269$	−0.0554458	+	0.0960349i	−0.00338059	+	0.00585535i	−0.867711	−	0.497069i	$-0.834409\pi$
$269$	−0.0554458	+	0.0960349i	−0.00338059	+	0.00585535i	0.864330	+	0.502925i	$0.167743\pi$
$270$		0			0
$271$	−4.79718	+	8.30896i	−0.291408	+	0.504733i	−0.974143	−	0.225933i	$-0.927457\pi$
$271$	−4.79718	+	8.30896i	−0.291408	+	0.504733i	0.682735	+	0.730666i	$0.260790\pi$
$272$	7.30773			0.443097
$273$		0			0
$274$	1.20442	+	2.08612i	0.0727617	+	0.126027i
$275$	−4.60486	+	7.97585i	−0.277683	+	0.480962i
$276$		0			0
$277$	−7.63856	+	13.2304i	−0.458956	+	0.794936i	−0.998906	−	0.0467615i	$-0.985110\pi$
$277$	−7.63856	+	13.2304i	−0.458956	+	0.794936i	0.539950	+	0.841697i	$0.318443\pi$
$278$	−8.47018			−0.508007
$279$		0			0
$280$	3.65763	−	6.33520i	0.218585	−	0.378600i
$281$	−4.45297			−0.265642			−0.132821	−	0.991140i	$-0.542403\pi$
$281$	−4.45297			−0.265642			−0.132821	+	0.991140i	$0.542403\pi$
$282$		0			0
$283$	5.78180			0.343692			0.171846	−	0.985124i	$-0.445027\pi$
$283$	5.78180			0.343692			0.171846	+	0.985124i	$0.445027\pi$
$284$	−4.03312	−	6.98558i	−0.239322	−	0.414518i
$285$		0			0
$286$	−10.2456	+	17.7459i	−0.605834	+	1.04934i
$287$	10.4035	−	18.0195i	0.614102	−	1.06366i
$288$		0			0
$289$	−18.2015	−	31.5259i	−1.07068	−	1.85447i
$290$	4.20518	+	7.28359i	0.246937	+	0.427707i
$291$		0			0
$292$	7.45107	+	12.9056i	0.436041	+	0.755245i
$293$	9.50767	+	16.4678i	0.555444	+	0.962057i	0.997869	+	0.0652515i	$0.0207850\pi$
$293$	9.50767	+	16.4678i	0.555444	+	0.962057i	−0.442425	+	0.896806i	$0.645882\pi$
$294$		0			0
$295$	3.13513			0.182534
$296$	1.16827			0.0679043
$297$		0			0
$298$	−4.81128	−	8.33338i	−0.278710	−	0.482740i
$299$	5.86470	+	10.1580i	0.339164	+	0.587450i
$300$		0			0
$301$	−39.3407			−2.26756
$302$	22.8092			1.31252
$303$		0			0
$304$	0.407656	−	4.33979i	0.0233807	−	0.248904i
$305$	5.03245			0.288157
$306$		0			0
$307$	−12.2704	+	21.2529i	−0.700306	+	1.21297i	0.268053	+	0.963404i	$0.413620\pi$
$307$	−12.2704	+	21.2529i	−0.700306	+	1.21297i	−0.968359	+	0.249561i	$0.919714\pi$
$308$	17.0268			0.970189
$309$		0			0
$310$	0.927853	−	1.60709i	0.0526985	−	0.0912765i
$311$	−1.73597	−	3.00679i	−0.0984379	−	0.170500i	0.812600	−	0.582821i	$-0.198051\pi$
$311$	−1.73597	−	3.00679i	−0.0984379	−	0.170500i	−0.911038	+	0.412322i	$0.864718\pi$
$312$		0			0
$313$	4.12085			0.232924			0.116462	−	0.993195i	$-0.462845\pi$
$313$	4.12085			0.232924			0.116462	+	0.993195i	$0.462845\pi$
$314$	2.18674	+	3.78754i	0.123405	+	0.213743i
$315$		0			0
$316$	−5.98637			−0.336760
$317$	21.6390			1.21537			0.607683	−	0.794180i	$-0.292099\pi$
$317$	21.6390			1.21537			0.607683	+	0.794180i	$0.292099\pi$
$318$		0			0
$319$	−9.78785	+	16.9531i	−0.548014	+	0.949189i
$320$	1.57955			0.0882997
$321$		0			0
$322$	4.87316	−	8.44056i	0.271571	−	0.470374i
$323$	−28.9547	+	13.2771i	−1.61108	+	0.738758i
$324$		0			0
$325$	−6.98087	+	12.0912i	−0.387229	+	0.670700i
$326$	−3.18476	−	5.51617i	−0.176388	−	0.305512i
$327$		0			0
$328$	4.49279			0.248073
$329$	13.3278	−	23.0844i	0.734783	−	1.27268i
$330$		0			0
$331$	−8.48039	+	14.6885i	−0.466125	+	0.807352i	−0.999252	−	0.0386837i	$-0.987684\pi$
$331$	−8.48039	+	14.6885i	−0.466125	+	0.807352i	0.533127	+	0.846035i	$0.321017\pi$
$332$	5.85781	+	10.1460i	0.321489	+	0.556835i
$333$		0			0
$334$	6.17140			0.337684
$335$	−9.93876	+	17.2144i	−0.543012	+	0.940525i
$336$		0			0
$337$	−23.2326			−1.26556			−0.632779	−	0.774332i	$-0.718086\pi$
$337$	−23.2326			−1.26556			−0.632779	+	0.774332i	$0.718086\pi$
$338$	−9.03210	+	15.6441i	−0.491282	+	0.850925i
$339$		0			0
$340$	−5.77148	−	9.99650i	−0.313002	−	0.542136i
$341$	4.31928			0.233902
$342$		0			0
$343$	−34.4940			−1.86250
$344$	−4.24734	−	7.35661i	−0.229001	−	0.396642i
$345$		0			0
$346$	−3.75669	+	6.50678i	−0.201961	+	0.349807i
$347$	−16.4030			−0.880559			−0.440280	−	0.897861i	$-0.645121\pi$
$347$	−16.4030			−0.880559			−0.440280	+	0.897861i	$0.645121\pi$
$348$		0			0
$349$	1.92719	−	3.33798i	0.103160	−	0.178678i	−0.809825	−	0.586671i	$-0.800438\pi$
$349$	1.92719	−	3.33798i	0.103160	−	0.178678i	0.912985	+	0.407993i	$0.133771\pi$
$350$	11.6012			0.620112
$351$		0			0
$352$	1.83826	+	3.18396i	0.0979796	+	0.169706i
$353$	4.42315	−	7.66112i	0.235421	−	0.407760i	−0.723974	−	0.689827i	$-0.757687\pi$
$353$	4.42315	−	7.66112i	0.235421	−	0.407760i	0.959395	+	0.282067i	$0.0910199\pi$
$354$		0			0
$355$	−6.37054	+	11.0341i	−0.338113	+	0.585629i
$356$	6.01603			0.318849
$357$		0			0
$358$	10.8732	+	18.8329i	0.574664	+	0.995348i
$359$	11.0150	−	19.0785i	0.581349	−	1.00693i	−0.413971	−	0.910290i	$-0.635858\pi$
$359$	11.0150	−	19.0785i	0.581349	−	1.00693i	0.995320	−	0.0966358i	$-0.0308082\pi$
$360$		0			0
$361$	6.26957	+	17.9358i	0.329977	+	0.943989i
$362$	2.33180	−	4.03880i	0.122557	−	0.212275i
$363$		0			0
$364$	25.8122			1.35293
$365$	11.7694	−	20.3851i	0.616037	−	1.06701i
$366$		0			0
$367$	12.3653			0.645463			0.322731	−	0.946491i	$-0.395399\pi$
$367$	12.3653			0.645463			0.322731	+	0.946491i	$0.395399\pi$
$368$	2.10449			0.109704
$369$		0			0
$370$	−0.922673	−	1.59812i	−0.0479675	−	0.0830821i
$371$	−15.7251			−0.816406
$372$		0			0
$373$	3.36121	+	5.82178i	0.174037	+	0.301440i	0.939827	−	0.341649i	$-0.110986\pi$
$373$	3.36121	+	5.82178i	0.174037	+	0.301440i	−0.765791	+	0.643090i	$0.777652\pi$
$374$	13.4335	−	23.2675i	0.694630	−	1.20314i
$375$		0			0
$376$	5.75562			0.296824
$377$	−14.8382	+	25.7005i	−0.764205	+	1.32364i
$378$		0			0
$379$	26.1451			1.34298			0.671491	−	0.741013i	$-0.265654\pi$
$379$	26.1451			1.34298			0.671491	+	0.741013i	$0.265654\pi$
$380$	−6.25851	+	2.86982i	−0.321055	+	0.147219i
$381$		0			0
$382$	5.67868			0.290546
$383$	−13.7394			−0.702052			−0.351026	−	0.936366i	$-0.614167\pi$
$383$	−13.7394			−0.702052			−0.351026	+	0.936366i	$0.614167\pi$
$384$		0			0
$385$	−13.4473	−	23.2915i	−0.685340	−	1.18704i
$386$	−4.93611	−	8.54959i	−0.251241	−	0.435163i
$387$		0			0
$388$	−11.9403			−0.606179
$389$	−30.4005			−1.54137			−0.770683	−	0.637219i	$-0.780085\pi$
$389$	−30.4005			−1.54137			−0.770683	+	0.637219i	$0.780085\pi$
$390$		0			0
$391$	−7.68951	−	13.3186i	−0.388875	−	0.673552i
$392$	−7.22408	−	12.5125i	−0.364871	−	0.631975i
$393$		0			0
$394$	−12.5405	−	21.7208i	−0.631782	−	1.09428i
$395$	4.72790	+	8.18896i	0.237886	+	0.412031i
$396$		0			0
$397$	9.16006	−	15.8657i	0.459730	−	0.796277i	−0.539216	−	0.842168i	$-0.681279\pi$
$397$	9.16006	−	15.8657i	0.459730	−	0.796277i	0.998946	+	0.0458910i	$0.0146127\pi$
$398$	4.46649	−	7.73619i	0.223885	−	0.387780i
$399$		0			0
$400$	1.25250	+	2.16940i	0.0626252	+	0.108470i
$401$	−34.6046			−1.72807			−0.864035	−	0.503431i	$-0.832071\pi$
$401$	−34.6046			−1.72807			−0.864035	+	0.503431i	$0.832071\pi$
$402$		0			0
$403$	6.54794			0.326176
$404$	5.44662	−	9.43383i	0.270980	−	0.469350i
$405$		0			0
$406$	24.6590			1.22381
$407$	2.14758	−	3.71972i	0.106452	−	0.184380i
$408$		0			0
$409$	2.50569	−	4.33998i	0.123898	−	0.214598i	−0.797403	−	0.603447i	$-0.793794\pi$
$409$	2.50569	−	4.33998i	0.123898	−	0.214598i	0.921302	+	0.388848i	$0.127127\pi$
$410$	−3.54830	−	6.14584i	−0.175238	−	0.303521i
$411$		0			0
$412$	−12.1979			−0.600945
$413$	4.59607	−	7.96062i	0.226158	−	0.391717i
$414$		0			0
$415$	9.25272	−	16.0262i	0.454198	−	0.786695i
$416$	2.78676	+	4.82682i	0.136632	+	0.236654i
$417$		0			0
$418$	−13.0684	−	9.27563i	−0.639194	−	0.453686i
$419$	14.5553	+	25.2106i	0.711074	+	1.23162i	0.964454	+	0.264250i	$0.0851244\pi$
$419$	14.5553	+	25.2106i	0.711074	+	1.23162i	−0.253380	+	0.967367i	$0.581542\pi$
$420$		0			0
$421$	1.71985	+	2.97887i	0.0838204	+	0.145181i	0.904888	−	0.425650i	$-0.139954\pi$
$421$	1.71985	+	2.97887i	0.0838204	+	0.145181i	−0.821068	+	0.570831i	$0.806621\pi$
$422$	−3.16229	−	5.47724i	−0.153938	−	0.266628i
$423$		0			0
$424$	−1.69773	−	2.94055i	−0.0824490	−	0.142806i
$425$	9.15297	−	15.8534i	0.443984	−	0.769004i
$426$		0			0
$427$	7.37751	−	12.7782i	0.357023	−	0.618382i
$428$	−3.44963	+	5.97493i	−0.166744	+	0.288809i
$429$		0			0
$430$	−6.70891	+	11.6202i	−0.323532	+	0.560374i
$431$	4.96062	+	8.59205i	0.238945	+	0.413865i	0.960412	−	0.278584i	$-0.0898652\pi$
$431$	4.96062	+	8.59205i	0.238945	+	0.413865i	−0.721467	+	0.692449i	$0.756532\pi$
$432$		0			0
$433$	0.263521	+	0.456432i	0.0126640	+	0.0219347i	0.872288	−	0.488993i	$-0.162635\pi$
$433$	0.263521	+	0.456432i	0.0126640	+	0.0219347i	−0.859624	+	0.510927i	$0.829302\pi$
$434$	−2.72044	−	4.71195i	−0.130586	−	0.226181i
$435$		0			0
$436$	−2.02428	−	3.50615i	−0.0969452	−	0.167914i
$437$	−8.33839	+	3.82355i	−0.398879	+	0.182905i
$438$		0			0
$439$	8.17519	+	14.1598i	0.390180	+	0.675812i	0.992473	−	0.122463i	$-0.0390793\pi$
$439$	8.17519	+	14.1598i	0.390180	+	0.675812i	−0.602293	+	0.798275i	$0.705746\pi$
$440$	2.90363	−	5.02923i	0.138425	−	0.239759i
$441$		0			0
$442$	20.3649	−	35.2731i	0.968661	−	1.67777i
$443$	−5.78636			−0.274918			−0.137459	−	0.990507i	$-0.543894\pi$
$443$	−5.78636			−0.274918			−0.137459	+	0.990507i	$0.543894\pi$
$444$		0			0
$445$	−4.75133	−	8.22954i	−0.225234	−	0.390117i
$446$	−0.878811	+	1.52215i	−0.0416129	+	0.0720757i
$447$		0			0
$448$	2.31561	−	4.01075i	0.109402	−	0.189490i
$449$	10.4180			0.491658			0.245829	−	0.969313i	$-0.420940\pi$
$449$	10.4180			0.491658			0.245829	+	0.969313i	$0.420940\pi$
$450$		0			0
$451$	8.25892	−	14.3049i	0.388897	−	0.673590i
$452$	−1.34258			−0.0631498
$453$		0			0
$454$	−12.8311			−0.602194
$455$	−20.3859	−	35.3094i	−0.955705	−	1.65533i
$456$		0			0
$457$	−10.3149	+	17.8659i	−0.482510	+	0.835733i	−0.999798	−	0.0200789i	$-0.993608\pi$
$457$	−10.3149	+	17.8659i	−0.482510	+	0.835733i	0.517288	+	0.855811i	$0.326942\pi$
$458$	−0.207385	+	0.359201i	−0.00969047	+	0.0167844i
$459$		0			0
$460$	−1.66207	−	2.87880i	−0.0774946	−	0.134225i
$461$	−7.65320	−	13.2557i	−0.356445	−	0.617381i	0.630919	−	0.775849i	$-0.282678\pi$
$461$	−7.65320	−	13.2557i	−0.356445	−	0.617381i	−0.987364	+	0.158468i	$0.949345\pi$
$462$		0			0
$463$	4.73547	+	8.20208i	0.220076	+	0.381183i	0.954831	−	0.297150i	$-0.0960361\pi$
$463$	4.73547	+	8.20208i	0.220076	+	0.381183i	−0.734755	+	0.678333i	$0.762703\pi$
$464$	2.66226	+	4.61117i	0.123592	+	0.214068i
$465$		0			0
$466$	−12.8437			−0.594972
$467$	15.0904			0.698299			0.349149	−	0.937067i	$-0.386471\pi$
$467$	15.0904			0.698299			0.349149	+	0.937067i	$0.386471\pi$
$468$		0			0
$469$	29.1402	+	50.4723i	1.34557	+	2.33060i
$470$	−4.54566	−	7.87331i	−0.209676	−	0.363169i
$471$		0			0
$472$	1.98482			0.0913588
$473$	−31.2309			−1.43600
$474$		0			0
$475$	−8.90417	−	6.31998i	−0.408551	−	0.289981i
$476$	−33.8437			−1.55122
$477$		0			0
$478$	−6.27082	+	10.8614i	−0.286821	+	0.496788i
$479$	−27.7856			−1.26956			−0.634779	−	0.772694i	$-0.718909\pi$
$479$	−27.7856			−1.26956			−0.634779	+	0.772694i	$0.718909\pi$
$480$		0			0
$481$	3.25569	−	5.63903i	0.148447	−	0.257117i
$482$	2.02478	+	3.50702i	0.0922261	+	0.159740i
$483$		0			0
$484$	2.51679			0.114400
$485$	9.43021	+	16.3336i	0.428204	+	0.741671i
$486$		0			0
$487$	26.0008			1.17821			0.589105	−	0.808057i	$-0.299480\pi$
$487$	26.0008			1.17821			0.589105	+	0.808057i	$0.299480\pi$
$488$	3.18599			0.144223
$489$		0			0
$490$	−11.4108	+	19.7641i	−0.515488	+	0.892852i
$491$	32.9529			1.48714			0.743572	−	0.668656i	$-0.233130\pi$
$491$	32.9529			1.48714			0.743572	+	0.668656i	$0.233130\pi$
$492$		0			0
$493$	19.4551	−	33.6972i	0.876213	−	1.51765i
$494$	−19.8113	−	14.0617i	−0.891355	−	0.632664i
$495$		0			0
$496$	0.587415	−	1.01743i	0.0263757	−	0.0456841i
$497$	18.6783	+	32.3517i	0.837835	+	1.45117i
$498$		0			0
$499$	4.08509			0.182874			0.0914368	−	0.995811i	$-0.470854\pi$
$499$	4.08509			0.182874			0.0914368	+	0.995811i	$0.470854\pi$
$500$	5.92728	−	10.2664i	0.265076	−	0.459125i
$501$		0			0
$502$	9.59620	−	16.6211i	0.428300	−	0.741837i
$503$	−4.15278	−	7.19283i	−0.185163	−	0.320712i	0.758468	−	0.651710i	$-0.225948\pi$
$503$	−4.15278	−	7.19283i	−0.185163	−	0.320712i	−0.943632	+	0.330998i	$0.892615\pi$
$504$		0			0
$505$	−17.2065			−0.765678
$506$	3.86859	−	6.70059i	0.171980	−	0.297878i
$507$		0			0
$508$	7.91508			0.351175
$509$	−7.38166	+	12.7854i	−0.327186	+	0.566704i	−0.981952	−	0.189128i	$-0.939434\pi$
$509$	−7.38166	+	12.7854i	−0.327186	+	0.566704i	0.654766	+	0.755832i	$0.272767\pi$
$510$		0			0
$511$	−34.5075	−	59.7688i	−1.52652	−	2.64402i
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.56919			0.0692139
$515$	9.63358	+	16.6859i	0.424506	+	0.735267i
$516$		0			0
$517$	10.5803	−	18.3257i	0.465322	−	0.805962i
$518$	−5.41051			−0.237724
$519$		0			0
$520$	4.40184	−	7.62422i	0.193034	−	0.334344i
$521$	−31.7044			−1.38899			−0.694497	−	0.719495i	$-0.744373\pi$
$521$	−31.7044			−1.38899			−0.694497	+	0.719495i	$0.744373\pi$
$522$		0			0
$523$	14.4395	+	25.0100i	0.631396	+	1.09361i	0.987267	+	0.159075i	$0.0508511\pi$
$523$	14.4395	+	25.0100i	0.631396	+	1.09361i	−0.355870	+	0.934535i	$0.615816\pi$
$524$	−0.696502	+	1.20638i	−0.0304268	+	0.0527008i
$525$		0			0
$526$	13.9124	−	24.0970i	0.606610	−	1.05068i
$527$	−8.58534			−0.373983
$528$		0			0
$529$	9.28557	+	16.0831i	0.403720	+	0.699264i
$530$	−2.68165	+	4.64476i	−0.116484	+	0.201756i
$531$		0			0
$532$	−1.88794	+	20.0985i	−0.0818527	+	0.871382i
$533$	12.5203	−	21.6859i	0.542316	−	0.939320i
$534$		0			0
$535$	10.8977			0.471151
$536$	−6.29213	+	10.8983i	−0.271779	+	0.470734i
$537$		0			0
$538$	0.110892			0.00478087
$539$	−53.1189			−2.28799
$540$		0			0
$541$	−14.3701	−	24.8898i	−0.617820	−	1.07010i	−0.989883	−	0.141888i	$-0.954683\pi$
$541$	−14.3701	−	24.8898i	−0.617820	−	1.07010i	0.372063	−	0.928208i	$-0.378651\pi$
$542$	9.59436			0.412113
$543$		0			0
$544$	−3.65387	−	6.32868i	−0.156658	−	0.271340i
$545$	−3.19745	+	5.53815i	−0.136964	+	0.237228i
$546$		0			0
$547$	6.24240			0.266906			0.133453	−	0.991055i	$-0.457393\pi$
$547$	6.24240			0.266906			0.133453	+	0.991055i	$0.457393\pi$
$548$	1.20442	−	2.08612i	0.0514503	−	0.0891145i
$549$		0			0
$550$	9.20972			0.392704
$551$	−18.9262	−	13.4334i	−0.806285	−	0.572284i
$552$		0			0
$553$	27.7242			1.17895
$554$	15.2771			0.649062
$555$		0			0
$556$	4.23509	+	7.33539i	0.179608	+	0.311090i
$557$	−6.56478	−	11.3705i	−0.278159	−	0.481785i	0.692769	−	0.721160i	$-0.256391\pi$
$557$	−6.56478	−	11.3705i	−0.278159	−	0.481785i	−0.970927	+	0.239375i	$0.923057\pi$
$558$		0			0
$559$	−47.3454			−2.00250
$560$	−7.31525			−0.309126
$561$		0			0
$562$	2.22648	+	3.85638i	0.0939185	+	0.162672i
$563$	6.22302	+	10.7786i	0.262269	+	0.454264i	0.966845	−	0.255366i	$-0.0821958\pi$
$563$	6.22302	+	10.7786i	0.262269	+	0.454264i	−0.704575	+	0.709629i	$0.748863\pi$
$564$		0			0
$565$	1.06034	+	1.83657i	0.0446089	+	0.0772649i
$566$	−2.89090	−	5.00718i	−0.121514	−	0.210468i
$567$		0			0
$568$	−4.03312	+	6.98558i	−0.169226	+	0.293108i
$569$	17.5284	−	30.3601i	0.734830	−	1.27276i	−0.219968	−	0.975507i	$-0.570595\pi$
$569$	17.5284	−	30.3601i	0.734830	−	1.27276i	0.954798	−	0.297255i	$-0.0960712\pi$
$570$		0			0
$571$	−3.38933	−	5.87049i	−0.141839	−	0.245672i	0.786350	−	0.617781i	$-0.211968\pi$
$571$	−3.38933	−	5.87049i	−0.141839	−	0.245672i	−0.928189	+	0.372109i	$0.878635\pi$
$572$	20.4912			0.856779
$573$		0			0
$574$	−20.8071			−0.868471
$575$	2.63588	−	4.56547i	0.109924	−	0.190393i
$576$		0			0
$577$	−40.8352			−1.69999			−0.849997	−	0.526788i	$-0.823396\pi$
$577$	−40.8352			−1.69999			−0.849997	+	0.526788i	$0.823396\pi$
$578$	−18.2015	+	31.5259i	−0.757082	+	1.31131i
$579$		0			0
$580$	4.20518	−	7.28359i	0.174611	−	0.302435i
$581$	−27.1288	−	46.9884i	−1.12549	−	1.94941i
$582$		0			0
$583$	−12.4835			−0.517012
$584$	7.45107	−	12.9056i	0.308328	−	0.534039i
$585$		0			0
$586$	9.50767	−	16.4678i	0.392758	−	0.680277i
$587$	6.10104	+	10.5673i	0.251817	+	0.436159i	0.964026	−	0.265808i	$-0.0856387\pi$
$587$	6.10104	+	10.5673i	0.251817	+	0.436159i	−0.712209	+	0.701967i	$0.752305\pi$
$588$		0			0
$589$	−0.478926	+	5.09852i	−0.0197338	+	0.210081i
$590$	−1.56757	−	2.71510i	−0.0645357	−	0.111779i
$591$		0			0
$592$	−0.584135	−	1.01175i	−0.0240078	−	0.0415827i
$593$	−5.17093	−	8.95632i	−0.212345	−	0.367792i	0.740103	−	0.672493i	$-0.234777\pi$
$593$	−5.17093	−	8.95632i	−0.212345	−	0.367792i	−0.952448	+	0.304702i	$0.901443\pi$
$594$		0			0
$595$	26.7290	+	46.2959i	1.09578	+	1.89795i
$596$	−4.81128	+	8.33338i	−0.197078	+	0.341348i
$597$		0			0
$598$	5.86470	−	10.1580i	0.239826	−	0.415390i
$599$	6.57091	−	11.3811i	0.268480	−	0.465021i	−0.699989	−	0.714153i	$-0.746812\pi$
$599$	6.57091	−	11.3811i	0.268480	−	0.465021i	0.968470	+	0.249132i	$0.0801453\pi$
$600$		0			0
$601$	−4.17421	+	7.22994i	−0.170269	+	0.294915i	−0.938514	−	0.345241i	$-0.887797\pi$
$601$	−4.17421	+	7.22994i	−0.170269	+	0.294915i	0.768245	+	0.640156i	$0.221130\pi$
$602$	19.6704	+	34.0701i	0.801704	+	1.38859i
$603$		0			0
$604$	−11.4046	−	19.7534i	−0.464047	−	0.803753i
$605$	−1.98770	−	3.44281i	−0.0808117	−	0.139970i
$606$		0			0
$607$	2.44638	+	4.23725i	0.0992953	+	0.171985i	0.911393	−	0.411537i	$-0.135008\pi$
$607$	2.44638	+	4.23725i	0.0992953	+	0.171985i	−0.812098	+	0.583521i	$0.801674\pi$
$608$	−3.96220	+	1.81686i	−0.160688	+	0.0736833i
$609$		0			0
$610$	−2.51622	−	4.35823i	−0.101879	−	0.176459i
$611$	16.0396	−	27.7813i	0.648891	−	1.12391i
$612$		0			0
$613$	−5.76017	+	9.97691i	−0.232651	+	0.402964i	−0.958587	−	0.284798i	$-0.908073\pi$
$613$	−5.76017	+	9.97691i	−0.232651	+	0.402964i	0.725936	+	0.687762i	$0.241407\pi$
$614$	24.5407			0.990382
$615$		0			0
$616$	−8.51338	−	14.7456i	−0.343014	−	0.594117i
$617$	−10.4427	+	18.0872i	−0.420406	+	0.728165i	−0.995979	−	0.0895856i	$-0.971446\pi$
$617$	−10.4427	+	18.0872i	−0.420406	+	0.728165i	0.575573	+	0.817750i	$0.304779\pi$
$618$		0			0
$619$	22.7753	−	39.4479i	0.915415	−	1.58555i	0.109124	−	0.994028i	$-0.465196\pi$
$619$	22.7753	−	39.4479i	0.915415	−	1.58555i	0.806292	−	0.591518i	$-0.201471\pi$
$620$	−1.85571			−0.0745270
$621$		0			0
$622$	−1.73597	+	3.00679i	−0.0696061	+	0.120561i
$623$	−27.8616			−1.11625
$624$		0			0
$625$	−6.19988			−0.247995
$626$	−2.06042	−	3.56876i	−0.0823511	−	0.142636i
$627$		0			0
$628$	2.18674	−	3.78754i	0.0872603	−	0.151139i
$629$	−4.26870	+	7.39361i	−0.170204	+	0.294803i
$630$		0			0
$631$	19.0978	+	33.0784i	0.760272	+	1.31683i	0.942710	+	0.333612i	$0.108268\pi$
$631$	19.0978	+	33.0784i	0.760272	+	1.31683i	−0.182439	+	0.983217i	$0.558399\pi$
$632$	2.99319	+	5.18435i	0.119063	+	0.206222i
$633$		0			0
$634$	−10.8195	−	18.7399i	−0.429697	−	0.744257i
$635$	−6.25115	−	10.8273i	−0.248069	−	0.429669i
$636$		0			0
$637$	−80.5272			−3.19060
$638$	19.5757			0.775010
$639$		0			0
$640$	−0.789777	−	1.36793i	−0.0312187	−	0.0540723i
$641$	−17.7856	−	30.8056i	−0.702491	−	1.21675i	−0.967590	−	0.252528i	$-0.918738\pi$
$641$	−17.7856	−	30.8056i	−0.702491	−	1.21675i	0.265099	−	0.964221i	$-0.414595\pi$
$642$		0			0
$643$	8.68472			0.342492			0.171246	−	0.985228i	$-0.445221\pi$
$643$	8.68472			0.342492			0.171246	+	0.985228i	$0.445221\pi$
$644$	−9.74632			−0.384059
$645$		0			0
$646$	25.9757	+	18.4370i	1.02200	+	0.725392i
$647$	−8.66501			−0.340657			−0.170328	−	0.985387i	$-0.554483\pi$
$647$	−8.66501			−0.340657			−0.170328	+	0.985387i	$0.554483\pi$
$648$		0			0
$649$	3.64862	−	6.31959i	0.143221	−	0.248066i
$650$	13.9617			0.547624
$651$		0			0
$652$	−3.18476	+	5.51617i	−0.124725	+	0.216030i
$653$	−22.1970	−	38.4463i	−0.868635	−	1.50452i	−0.863392	−	0.504533i	$-0.831665\pi$
$653$	−22.1970	−	38.4463i	−0.868635	−	1.50452i	−0.00524262	−	0.999986i	$-0.501669\pi$
$654$		0			0
$655$	2.20033			0.0859738
$656$	−2.24640	−	3.89087i	−0.0877070	−	0.151913i
$657$		0			0
$658$	−26.6555			−1.03914
$659$	9.04193			0.352224			0.176112	−	0.984370i	$-0.443648\pi$
$659$	9.04193			0.352224			0.176112	+	0.984370i	$0.443648\pi$
$660$		0			0
$661$	−3.69025	+	6.39170i	−0.143534	+	0.248608i	−0.928825	−	0.370519i	$-0.879180\pi$
$661$	−3.69025	+	6.39170i	−0.143534	+	0.248608i	0.785291	+	0.619127i	$0.212513\pi$
$662$	16.9608			0.659200
$663$		0			0
$664$	5.85781	−	10.1460i	0.227327	−	0.393742i
$665$	28.9845	−	13.2908i	1.12397	−	0.515394i
$666$		0			0
$667$	5.60269	−	9.70414i	0.216937	−	0.375746i
$668$	−3.08570	−	5.34459i	−0.119389	−	0.206788i
$669$		0			0
$670$	19.8775			0.767936
$671$	5.85668	−	10.1441i	0.226095	−	0.391607i
$672$		0			0
$673$	10.3428	−	17.9142i	0.398685	−	0.690544i	−0.594879	−	0.803816i	$-0.702800\pi$
$673$	10.3428	−	17.9142i	0.398685	−	0.690544i	0.993564	+	0.113272i	$0.0361332\pi$
$674$	11.6163	+	20.1200i	0.447442	+	0.774993i
$675$		0			0
$676$	18.0642			0.694777
$677$	−13.9362	+	24.1381i	−0.535610	+	0.927704i	0.463524	+	0.886085i	$0.346585\pi$
$677$	−13.9362	+	24.1381i	−0.535610	+	0.927704i	−0.999134	+	0.0416191i	$0.986748\pi$
$678$		0			0
$679$	55.2983			2.12216
$680$	−5.77148	+	9.99650i	−0.221326	+	0.383348i
$681$		0			0
$682$	−2.15964	−	3.74061i	−0.0826970	−	0.143235i
$683$	22.0360			0.843183			0.421591	−	0.906786i	$-0.361472\pi$
$683$	22.0360			0.843183			0.421591	+	0.906786i	$0.361472\pi$
$684$		0			0
$685$	−3.80489			−0.145378
$686$	17.2470	+	29.8727i	0.658494	+	1.14055i
$687$		0			0
$688$	−4.24734	+	7.35661i	−0.161928	+	0.280468i
$689$	−18.9247			−0.720973
$690$		0			0
$691$	11.6097	−	20.1087i	0.441656	−	0.764970i	−0.556157	−	0.831077i	$-0.687725\pi$
$691$	11.6097	−	20.1087i	0.441656	−	0.764970i	0.997813	+	0.0661073i	$0.0210580\pi$
$692$	7.51338			0.285616
$693$		0			0
$694$	8.20150	+	14.2054i	0.311325	+	0.539230i
$695$	6.68955	−	11.5866i	0.253749	−	0.439506i
$696$		0			0
$697$	−16.4161	+	28.4335i	−0.621803	+	1.07699i
$698$	−3.85437			−0.145890
$699$		0			0
$700$	−5.80062	−	10.0470i	−0.219243	−	0.379740i
$701$	0.439487	−	0.761215i	0.0165992	−	0.0287507i	−0.857606	−	0.514306i	$-0.828049\pi$
$701$	0.439487	−	0.761215i	0.0165992	−	0.0287507i	0.874206	+	0.485556i	$0.161383\pi$
$702$		0			0
$703$	4.15267	+	2.94747i	0.156621	+	0.111166i
$704$	1.83826	−	3.18396i	0.0692820	−	0.120000i
$705$		0			0
$706$	−8.84630			−0.332935
$707$	−25.2245	+	43.6901i	−0.948664	+	1.64313i
$708$		0			0
$709$	−11.1131			−0.417363			−0.208682	−	0.977984i	$-0.566917\pi$
$709$	−11.1131			−0.417363			−0.208682	+	0.977984i	$0.566917\pi$
$710$	12.7411			0.478164
$711$		0			0
$712$	−3.00802	−	5.21004i	−0.112730	−	0.195254i
$713$	−2.47241			−0.0925925
$714$		0			0
$715$	−16.1835	−	28.0306i	−0.605227	−	1.04828i
$716$	10.8732	−	18.8329i	0.406349	−	0.703817i
$717$		0			0
$718$	−22.0300			−0.822152
$719$	2.95842	−	5.12414i	0.110331	−	0.191098i	−0.805573	−	0.592497i	$-0.798142\pi$
$719$	2.95842	−	5.12414i	0.110331	−	0.191098i	0.915904	+	0.401398i	$0.131476\pi$
$720$		0			0
$721$	56.4909			2.10383
$722$	12.3981	−	14.3975i	0.461408	−	0.535820i
$723$		0			0
$724$	−4.66361			−0.173322
$725$	13.3380			0.495360
$726$		0			0
$727$	−20.0288	−	34.6909i	−0.742828	−	1.28662i	−0.951203	−	0.308566i	$-0.900151\pi$
$727$	−20.0288	−	34.6909i	−0.742828	−	1.28662i	0.208375	−	0.978049i	$-0.433183\pi$
$728$	−12.9061	−	22.3540i	−0.478332	−	0.828495i
$729$		0			0
$730$	−23.5387			−0.871208
$731$	62.0769			2.29600
$732$		0			0
$733$	17.5793	+	30.4482i	0.649306	+	1.12463i	0.983289	+	0.182052i	$0.0582738\pi$
$733$	17.5793	+	30.4482i	0.649306	+	1.12463i	−0.333983	+	0.942579i	$0.608393\pi$
$734$	−6.18264	−	10.7087i	−0.228205	−	0.395264i
$735$		0			0
$736$	−1.05224	−	1.82254i	−0.0387862	−	0.0671796i
$737$	23.1331	+	40.0678i	0.852120	+	1.47592i
$738$		0			0
$739$	6.34630	−	10.9921i	0.233453	−	0.404352i	−0.725369	−	0.688360i	$-0.758331\pi$
$739$	6.34630	−	10.9921i	0.233453	−	0.404352i	0.958822	+	0.284008i	$0.0916643\pi$
$740$	−0.922673	+	1.59812i	−0.0339181	+	0.0587479i
$741$		0			0
$742$	7.86255	+	13.6183i	0.288643	+	0.499945i
$743$	5.78991			0.212411			0.106206	−	0.994344i	$-0.466130\pi$
$743$	5.78991			0.212411			0.106206	+	0.994344i	$0.466130\pi$
$744$		0			0
$745$	15.1993			0.556861
$746$	3.36121	−	5.82178i	0.123062	−	0.213150i
$747$		0			0
$748$	−26.8670			−0.982356
$749$	15.9760	−	27.6712i	0.583749	−	1.01108i
$750$		0			0
$751$	1.63799	−	2.83708i	0.0597712	−	0.103527i	−0.834591	−	0.550869i	$-0.814296\pi$
$751$	1.63799	−	2.83708i	0.0597712	−	0.103527i	0.894363	+	0.447343i	$0.147630\pi$
$752$	−2.87781	−	4.98452i	−0.104943	−	0.181767i
$753$		0			0
$754$	29.6764			1.08075
$755$	−18.0142	+	31.2015i	−0.655604	+	1.13554i
$756$		0			0
$757$	−25.2937	+	43.8099i	−0.919314	+	1.59230i	−0.118854	+	0.992912i	$0.537922\pi$
$757$	−25.2937	+	43.8099i	−0.919314	+	1.59230i	−0.800460	+	0.599386i	$0.795411\pi$
$758$	−13.0725	−	22.6423i	−0.474816	−	0.822405i
$759$		0			0
$760$	5.61459	+	3.98512i	0.203663	+	0.144555i
$761$	17.8934	+	30.9923i	0.648636	+	1.12347i	0.983449	+	0.181186i	$0.0579935\pi$
$761$	17.8934	+	30.9923i	0.648636	+	1.12347i	−0.334813	+	0.942285i	$0.608673\pi$
$762$		0			0
$763$	9.37486	+	16.2377i	0.339393	+	0.587845i
$764$	−2.83934	−	4.91788i	−0.102724	−	0.177923i
$765$		0			0
$766$	6.86972	+	11.8987i	0.248213	+	0.429917i
$767$	5.53123	−	9.58037i	0.199721	−	0.345927i
$768$		0			0
$769$	18.6819	−	32.3580i	0.673687	−	1.16686i	−0.303163	−	0.952939i	$-0.598043\pi$
$769$	18.6819	−	32.3580i	0.673687	−	1.16686i	0.976851	−	0.213922i	$-0.0686239\pi$
$770$	−13.4473	+	23.2915i	−0.484608	+	0.839366i
$771$		0			0
$772$	−4.93611	+	8.54959i	−0.177654	+	0.307706i
$773$	9.33015	+	16.1603i	0.335582	+	0.581245i	0.983596	−	0.180383i	$-0.0577337\pi$
$773$	9.33015	+	16.1603i	0.335582	+	0.581245i	−0.648014	+	0.761628i	$0.724400\pi$
$774$		0			0
$775$	−1.47148	−	2.54868i	−0.0528571	−	0.0915512i
$776$	5.97017	+	10.3406i	0.214317	+	0.371208i
$777$		0			0
$778$	15.2002	+	26.3276i	0.544955	+	0.943889i
$779$	15.9698	+	11.3350i	0.572178	+	0.406120i
$780$		0			0
$781$	14.8279	+	25.6826i	0.530583	+	0.918996i
$782$	−7.68951	+	13.3186i	−0.274976	+	0.476273i
$783$		0			0
$784$	−7.22408	+	12.5125i	−0.258003	+	0.446874i
$785$	−6.90814			−0.246562
$786$		0			0
$787$	15.7775	+	27.3274i	0.562406	+	0.974116i	0.997286	+	0.0736276i	$0.0234576\pi$
$787$	15.7775	+	27.3274i	0.562406	+	0.974116i	−0.434880	+	0.900489i	$0.643209\pi$
$788$	−12.5405	+	21.7208i	−0.446737	+	0.773771i
$789$		0			0
$790$	4.72790	−	8.18896i	0.168211	−	0.291350i
$791$	6.21780			0.221079
$792$		0			0
$793$	8.87861	−	15.3782i	0.315289	−	0.546096i
$794$	−18.3201			−0.650157
$795$		0			0
$796$	−8.93298			−0.316621
$797$	16.9685	+	29.3903i	0.601055	+	1.04106i	0.992662	+	0.120926i	$0.0385862\pi$
$797$	16.9685	+	29.3903i	0.601055	+	1.04106i	−0.391606	+	0.920133i	$0.628080\pi$
$798$		0			0
$799$	−21.0303	+	36.4255i	−0.743998	+	1.28864i
$800$	1.25250	−	2.16940i	0.0442827	−	0.0766999i
$801$		0			0
$802$	17.3023	+	29.9685i	0.610965	+	1.05822i
$803$	−27.3940	−	47.4478i	−0.966714	−	1.67440i
$804$		0			0
$805$	7.69742	+	13.3323i	0.271298	+	0.469903i
$806$	−3.27397	−	5.67069i	−0.115321	−	0.199741i
$807$		0			0
$808$	−10.8932			−0.383223
$809$	−41.0728			−1.44404			−0.722021	−	0.691871i	$-0.756787\pi$
$809$	−41.0728			−1.44404			−0.722021	+	0.691871i	$0.756787\pi$
$810$		0			0
$811$	−21.7934	−	37.7472i	−0.765269	−	1.32549i	−0.940104	−	0.340887i	$-0.889273\pi$
$811$	−21.7934	−	37.7472i	−0.765269	−	1.32549i	0.174835	−	0.984598i	$-0.444061\pi$
$812$	−12.3295	−	21.3553i	−0.432681	−	0.749425i
$813$		0			0
$814$	−4.29517			−0.150546
$815$	10.0610			0.352422
$816$		0			0
$817$	3.46291	−	36.8652i	0.121152	−	1.28975i
$818$	−5.01138			−0.175219
$819$		0			0
$820$	−3.54830	+	6.14584i	−0.123912	+	0.214622i
$821$	22.2616			0.776935			0.388467	−	0.921462i	$-0.373005\pi$
$821$	22.2616			0.776935			0.388467	+	0.921462i	$0.373005\pi$
$822$		0			0
$823$	0.707725	−	1.22581i	0.0246697	−	0.0427292i	−0.853427	−	0.521212i	$-0.825480\pi$
$823$	0.707725	−	1.22581i	0.0246697	−	0.0427292i	0.878097	+	0.478483i	$0.158813\pi$
$824$	6.09893	+	10.5637i	0.212466	+	0.368002i
$825$		0			0
$826$	−9.19213			−0.319835
$827$	27.8318	+	48.2061i	0.967807	+	1.67629i	0.701876	+	0.712300i	$0.252346\pi$
$827$	27.8318	+	48.2061i	0.967807	+	1.67629i	0.265932	+	0.963992i	$0.414320\pi$
$828$		0			0
$829$	−35.2830			−1.22543			−0.612714	−	0.790305i	$-0.709922\pi$
$829$	−35.2830			−1.22543			−0.612714	+	0.790305i	$0.709922\pi$
$830$	−18.5054			−0.642333
$831$		0			0
$832$	2.78676	−	4.82682i	0.0966136	−	0.167340i
$833$	105.583			3.65825
$834$		0			0
$835$	−4.87403	+	8.44206i	−0.168673	+	0.292150i
$836$	−1.49875	+	15.9553i	−0.0518355	+	0.551827i
$837$		0			0
$838$	14.5553	−	25.2106i	0.502805	−	0.870885i
$839$	15.4460	+	26.7532i	0.533255	+	0.923624i	0.999246	+	0.0388347i	$0.0123646\pi$
$839$	15.4460	+	26.7532i	0.533255	+	0.923624i	−0.465991	+	0.884789i	$0.654302\pi$
$840$		0			0
$841$	−0.649476			−0.0223957
$842$	1.71985	−	2.97887i	0.0592700	−	0.102659i
$843$		0			0
$844$	−3.16229	+	5.47724i	−0.108850	+	0.188534i
$845$	−14.2667	−	24.7106i	−0.490789	−	0.850072i
$846$		0			0
$847$	−11.6558			−0.400498
$848$	−1.69773	+	2.94055i	−0.0583003	+	0.100979i
$849$		0			0
$850$	−18.3059			−0.627889
$851$	−1.22930	+	2.12922i	−0.0421400	+	0.0729886i
$852$		0			0
$853$	17.4963	+	30.3045i	0.599062	+	1.03761i	0.992960	+	0.118452i	$0.0377931\pi$
$853$	17.4963	+	30.3045i	0.599062	+	1.03761i	−0.393898	+	0.919154i	$0.628874\pi$
$854$	−14.7550			−0.504906
$855$		0			0
$856$	6.89925			0.235812
$857$	6.27992	+	10.8771i	0.214518	+	0.371556i	0.953123	−	0.302582i	$-0.0978486\pi$
$857$	6.27992	+	10.8771i	0.214518	+	0.371556i	−0.738605	+	0.674138i	$0.764515\pi$
$858$		0			0
$859$	−5.41813	+	9.38447i	−0.184864	+	0.320194i	−0.943531	−	0.331285i	$-0.892518\pi$
$859$	−5.41813	+	9.38447i	−0.184864	+	0.320194i	0.758667	+	0.651479i	$0.225851\pi$
$860$	13.4178			0.457544
$861$		0			0
$862$	4.96062	−	8.59205i	0.168959	−	0.292646i
$863$	−53.4590			−1.81977			−0.909883	−	0.414866i	$-0.863829\pi$
$863$	−53.4590			−1.81977			−0.909883	+	0.414866i	$0.863829\pi$
$864$		0			0
$865$	−5.93390	−	10.2778i	−0.201759	−	0.349456i
$866$	0.263521	−	0.456432i	0.00895482	−	0.0155102i
$867$		0			0
$868$	−2.72044	+	4.71195i	−0.0923379	+	0.159934i
$869$	22.0090			0.746604
$870$		0			0
$871$	35.0694	+	60.7419i	1.18828	+	2.05816i
$872$	−2.02428	+	3.50615i	−0.0685506	+	0.118733i
$873$		0			0
$874$	7.48049	+	5.30948i	0.253031	+	0.179596i
$875$	−27.4505	+	47.5457i	−0.927997	+	1.60734i
$876$		0			0
$877$	2.18593			0.0738137			0.0369068	−	0.999319i	$-0.488250\pi$
$877$	2.18593			0.0738137			0.0369068	+	0.999319i	$0.488250\pi$
$878$	8.17519	−	14.1598i	0.275899	−	0.477871i
$879$		0			0
$880$	−5.80726			−0.195763
$881$	−29.8678			−1.00627			−0.503135	−	0.864208i	$-0.667820\pi$
$881$	−29.8678			−1.00627			−0.503135	+	0.864208i	$0.667820\pi$
$882$		0			0
$883$	3.18840	+	5.52247i	0.107298	+	0.185846i	0.914675	−	0.404191i	$-0.132447\pi$
$883$	3.18840	+	5.52247i	0.107298	+	0.185846i	−0.807377	+	0.590036i	$0.799113\pi$
$884$	−40.7299			−1.36989
$885$		0			0
$886$	2.89318	+	5.01113i	0.0971982	+	0.168352i
$887$	−12.5079	+	21.6644i	−0.419976	+	0.727419i	−0.995937	−	0.0900580i	$-0.971295\pi$
$887$	−12.5079	+	21.6644i	−0.419976	+	0.727419i	0.575961	+	0.817477i	$0.304628\pi$
$888$		0			0
$889$	−36.6564			−1.22942
$890$	−4.75133	+	8.22954i	−0.159265	+	0.275855i
$891$		0			0
$892$	1.75762			0.0588496
$893$	20.4586	+	14.5211i	0.684621	+	0.485929i
$894$		0			0
$895$	−34.3495			−1.14818
$896$	−4.63122			−0.154718
$897$		0			0
$898$	−5.20902	−	9.02229i	−0.173827	−	0.301078i
$899$	−3.12770	−	5.41734i	−0.104315	−	0.180678i
$900$		0			0
$901$	24.8131			0.826644
$902$	−16.5178			−0.549984
$903$		0			0
$904$	0.671292	+	1.16271i	0.0223268	+	0.0386712i
$905$	3.68321	+	6.37951i	0.122434	+	0.212062i
$906$		0			0
$907$	6.06572	+	10.5061i	0.201409	+	0.348851i	0.948983	−	0.315328i	$-0.102115\pi$
$907$	6.06572	+	10.5061i	0.201409	+	0.348851i	−0.747574	+	0.664179i	$0.768781\pi$
$908$	6.41556	+	11.1121i	0.212908	+	0.368767i
$909$		0			0
$910$	−20.3859	+	35.3094i	−0.675785	+	1.17049i
$911$	5.82232	−	10.0846i	0.192902	−	0.334116i	−0.753309	−	0.657667i	$-0.771543\pi$
$911$	5.82232	−	10.0846i	0.192902	−	0.334116i	0.946211	+	0.323551i	$0.104877\pi$
$912$		0			0
$913$	−21.5363	−	37.3020i	−0.712749	−	1.23452i
$914$	20.6298			0.682373
$915$		0			0
$916$	0.414770			0.0137044
$917$	3.22565	−	5.58699i	0.106520	−	0.184499i
$918$		0			0
$919$	−49.1168			−1.62021			−0.810107	−	0.586282i	$-0.800591\pi$
$919$	−49.1168			−1.62021			−0.810107	+	0.586282i	$0.800591\pi$
$920$	−1.66207	+	2.87880i	−0.0547969	+	0.0949111i
$921$		0			0
$922$	−7.65320	+	13.2557i	−0.252045	+	0.436554i
$923$	22.4787	+	38.9343i	0.739896	+	1.28154i
$924$		0			0
$925$	−2.92653			−0.0962237
$926$	4.73547	−	8.20208i	0.155617	−	0.269537i
$927$		0			0
$928$	2.66226	−	4.61117i	0.0873930	−	0.151369i
$929$	19.3012	+	33.4307i	0.633253	+	1.09683i	0.986882	+	0.161441i	$0.0516140\pi$
$929$	19.3012	+	33.4307i	0.633253	+	1.09683i	−0.353630	+	0.935386i	$0.615053\pi$
$930$		0			0
$931$	5.88988	−	62.7020i	0.193033	−	2.05498i
$932$	6.42184	+	11.1229i	0.210354	+	0.364344i
$933$		0			0
$934$	−7.54518	−	13.0686i	−0.246886	−	0.427619i
$935$	21.2190	+	36.7523i	0.693934	+	1.20193i
$936$		0			0
$937$	14.3272	+	24.8154i	0.468049	+	0.810685i	0.999333	−	0.0365089i	$-0.0116237\pi$
$937$	14.3272	+	24.8154i	0.468049	+	0.810685i	−0.531284	+	0.847194i	$0.678290\pi$
$938$	29.1402	−	50.4723i	0.951462	−	1.64798i
$939$		0			0
$940$	−4.54566	+	7.87331i	−0.148263	+	0.256799i
$941$	30.1051	−	52.1435i	0.981398	−	1.69983i	0.324434	−	0.945908i	$-0.394826\pi$
$941$	30.1051	−	52.1435i	0.981398	−	1.69983i	0.656963	−	0.753922i	$-0.271841\pi$
$942$		0			0
$943$	−4.72751	+	8.18828i	−0.153949	+	0.266647i
$944$	−0.992410	−	1.71891i	−0.0323002	−	0.0559456i
$945$		0			0
$946$	15.6154	+	27.0467i	0.507702	+	0.879365i
$947$	−11.3315	−	19.6267i	−0.368223	−	0.637781i	0.621065	−	0.783759i	$-0.286700\pi$
$947$	−11.3315	−	19.6267i	−0.368223	−	0.637781i	−0.989288	+	0.145979i	$0.953367\pi$
$948$		0			0
$949$	−41.5287	−	71.9299i	−1.34808	−	2.33494i
$950$	−1.02118	+	10.8712i	−0.0331315	+	0.352709i
$951$		0			0
$952$	16.9218	+	29.3095i	0.548440	+	0.949926i
$953$	−0.368894	+	0.638943i	−0.0119496	+	0.0206974i	−0.871938	−	0.489616i	$-0.837137\pi$
$953$	−0.368894	+	0.638943i	−0.0119496	+	0.0206974i	0.859989	+	0.510313i	$0.170470\pi$
$954$		0			0
$955$	−4.48489	+	7.76806i	−0.145128	+	0.251368i
$956$	12.5416			0.405626
$957$		0			0
$958$	13.8928	+	24.0631i	0.448857	+	0.777443i
$959$	−5.57793	+	9.66126i	−0.180121	+	0.311978i
$960$		0			0
$961$	14.8099	−	25.6515i	0.477738	−	0.827467i
$962$	−6.51139			−0.209935
$963$		0			0
$964$	2.02478	−	3.50702i	0.0652137	−	0.112953i
$965$	15.5937			0.501979
$966$		0			0
$967$	43.0984			1.38595			0.692975	−	0.720962i	$-0.256300\pi$
$967$	43.0984			1.38595			0.692975	+	0.720962i	$0.256300\pi$
$968$	−1.25840	−	2.17961i	−0.0404464	−	0.0700552i
$969$		0			0
$970$	9.43021	−	16.3336i	0.302786	−	0.524441i
$971$	15.9702	−	27.6611i	0.512507	−	0.887687i	−0.487388	−	0.873185i	$-0.662050\pi$
$971$	15.9702	−	27.6611i	0.512507	−	0.887687i	0.999895	−	0.0145021i	$-0.00461632\pi$
$972$		0			0
$973$	−19.6136	−	33.9718i	−0.628783	−	1.08908i
$974$	−13.0004	−	22.5174i	−0.416560	−	0.721503i
$975$		0			0
$976$	−1.59300	−	2.75915i	−0.0509906	−	0.0883183i
$977$	2.30771	+	3.99708i	0.0738303	+	0.127878i	0.900577	−	0.434697i	$-0.143144\pi$
$977$	2.30771	+	3.99708i	0.0738303	+	0.127878i	−0.826747	+	0.562574i	$0.809811\pi$
$978$		0			0
$979$	−22.1181			−0.706896
$980$	22.8216			0.729011
$981$		0			0
$982$	−16.4765	−	28.5381i	−0.525785	−	0.910686i
$983$	12.7271	+	22.0440i	0.405932	+	0.703094i	0.994429	−	0.105405i	$-0.0336137\pi$
$983$	12.7271	+	22.0440i	0.405932	+	0.703094i	−0.588498	+	0.808499i	$0.700280\pi$
$984$		0			0
$985$	39.6168			1.26230
$986$	−38.9102			−1.23915
$987$		0			0
$988$	−2.27208	+	24.1880i	−0.0722845	+	0.769522i
$989$	17.8769			0.568454
$990$		0			0
$991$	2.51258	−	4.35191i	0.0798147	−	0.138243i	−0.823355	−	0.567526i	$-0.807900\pi$
$991$	2.51258	−	4.35191i	0.0798147	−	0.138243i	0.903170	+	0.429283i	$0.141234\pi$
$992$	−1.17483			−0.0373009
$993$		0			0
$994$	18.6783	−	32.3517i	0.592439	−	1.02613i
$995$	7.05506	+	12.2197i	0.223661	+	0.387392i
$996$		0			0
$997$	−51.3469			−1.62617			−0.813086	−	0.582143i	$-0.802214\pi$
$997$	−51.3469			−1.62617			−0.813086	+	0.582143i	$0.802214\pi$
$998$	−2.04254	−	3.53779i	−0.0646556	−	0.111987i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1026.2.h.g.505.7		18
3.2	odd	2		342.2.h.g.277.1	yes	18
9.4	even	3		1026.2.f.g.847.3		18
9.5	odd	6		342.2.f.g.49.7	yes	18
19.7	even	3		1026.2.f.g.235.3		18
57.26	odd	6		342.2.f.g.7.7	✓	18
171.121	even	3	inner	1026.2.h.g.577.7		18
171.140	odd	6		342.2.h.g.121.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.7	✓	18	57.26	odd	6
342.2.f.g.49.7	yes	18	9.5	odd	6
342.2.h.g.121.1	yes	18	171.140	odd	6
342.2.h.g.277.1	yes	18	3.2	odd	2
1026.2.f.g.235.3		18	19.7	even	3
1026.2.f.g.847.3		18	9.4	even	3
1026.2.h.g.505.7		18	1.1	even	1	trivial
1026.2.h.g.577.7		18	171.121	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1026 = 2 \cdot 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1026.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.57955 q^{5} +(2.31561 - 4.01075i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.57955 q^{5} +(2.31561 - 4.01075i) q^{7} +1.00000 q^{8} +(-0.789777 - 1.36793i) q^{10} +(1.83826 - 3.18396i) q^{11} +(2.78676 - 4.82682i) q^{13} -4.63122 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.65387 + 6.32868i) q^{17} +(3.55454 + 2.52294i) q^{19} +(-0.789777 + 1.36793i) q^{20} -3.67652 q^{22} +(-1.05224 + 1.82254i) q^{23} -2.50501 q^{25} -5.57353 q^{26} +(2.31561 + 4.01075i) q^{28} -5.32452 q^{29} +(0.587415 + 1.01743i) q^{31} +(-0.500000 + 0.866025i) q^{32} +7.30773 q^{34} +(3.65763 - 6.33520i) q^{35} +1.16827 q^{37} +(0.407656 - 4.33979i) q^{38} +1.57955 q^{40} +4.49279 q^{41} +(-4.24734 - 7.35661i) q^{43} +(1.83826 + 3.18396i) q^{44} +2.10449 q^{46} +5.75562 q^{47} +(-7.22408 - 12.5125i) q^{49} +(1.25250 + 2.16940i) q^{50} +(2.78676 + 4.82682i) q^{52} +(-1.69773 - 2.94055i) q^{53} +(2.90363 - 5.02923i) q^{55} +(2.31561 - 4.01075i) q^{56} +(2.66226 + 4.61117i) q^{58} +1.98482 q^{59} +3.18599 q^{61} +(0.587415 - 1.01743i) q^{62} +1.00000 q^{64} +(4.40184 - 7.62422i) q^{65} +(-6.29213 + 10.8983i) q^{67} +(-3.65387 - 6.32868i) q^{68} -7.31525 q^{70} +(-4.03312 + 6.98558i) q^{71} +(7.45107 - 12.9056i) q^{73} +(-0.584135 - 1.01175i) q^{74} +(-3.96220 + 1.81686i) q^{76} +(-8.51338 - 14.7456i) q^{77} +(2.99319 + 5.18435i) q^{79} +(-0.789777 - 1.36793i) q^{80} +(-2.24640 - 3.89087i) q^{82} +(5.85781 - 10.1460i) q^{83} +(-5.77148 + 9.99650i) q^{85} +(-4.24734 + 7.35661i) q^{86} +(1.83826 - 3.18396i) q^{88} +(-3.00802 - 5.21004i) q^{89} +(-12.9061 - 22.3540i) q^{91} +(-1.05224 - 1.82254i) q^{92} +(-2.87781 - 4.98452i) q^{94} +(5.61459 + 3.98512i) q^{95} +(5.97017 + 10.3406i) q^{97} +(-7.22408 + 12.5125i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8}+O(q^{10}) \) 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8	\( 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8} - q^{11} + q^{13} - 10 q^{14} - 9 q^{16} + 5 q^{17} + 9 q^{19} + 2 q^{22} + 2 q^{23} + 18 q^{25} - 2 q^{26} + 5 q^{28} - 18 q^{29} + 4 q^{31} - 9 q^{32} - 10 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} + 2 q^{41} + 7 q^{43} - q^{44} - 4 q^{46} + 38 q^{47} + 6 q^{49} - 9 q^{50} + q^{52} + 10 q^{53} + 6 q^{55} + 5 q^{56} + 9 q^{58} - 10 q^{59} - 36 q^{61} + 4 q^{62} + 18 q^{64} + 45 q^{65} + 22 q^{67} + 5 q^{68} + 12 q^{70} - 11 q^{71} + 44 q^{73} - 10 q^{74} - 6 q^{76} + 2 q^{77} + 2 q^{79} - q^{82} + 7 q^{83} + 7 q^{86} - q^{88} - q^{89} - 25 q^{91} + 2 q^{92} - 19 q^{94} - 21 q^{95} + 6 q^{98}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8 - q^11 + q^13 - 10 * q^14 - 9 * q^16 + 5 * q^17 + 9 * q^19 + 2 * q^22 + 2 * q^23 + 18 * q^25 - 2 * q^26 + 5 * q^28 - 18 * q^29 + 4 * q^31 - 9 * q^32 - 10 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 + 2 * q^41 + 7 * q^43 - q^44 - 4 * q^46 + 38 * q^47 + 6 * q^49 - 9 * q^50 + q^52 + 10 * q^53 + 6 * q^55 + 5 * q^56 + 9 * q^58 - 10 * q^59 - 36 * q^61 + 4 * q^62 + 18 * q^64 + 45 * q^65 + 22 * q^67 + 5 * q^68 + 12 * q^70 - 11 * q^71 + 44 * q^73 - 10 * q^74 - 6 * q^76 + 2 * q^77 + 2 * q^79 - q^82 + 7 * q^83 + 7 * q^86 - q^88 - q^89 - 25 * q^91 + 2 * q^92 - 19 * q^94 - 21 * q^95 + 6 * q^98

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