LMFDB - Embedded newform 1274.2.m.c.589.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(491,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.491"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,2,6,0,-6,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			589.6
Root			$0.500000 + 3.15681i$ of defining polynomial
Character	$\chi$	$=$	1274.589
Dual form			1274.2.m.c.491.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(1.14539 - 1.98388i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.901839i q^{5} +(1.98388 - 1.14539i) q^{6} +1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +(0.450919 - 0.781015i) q^{10} +(-3.75609 - 2.16858i) q^{11} +2.29079 q^{12} +(0.426876 - 3.58019i) q^{13} +(-1.78914 - 1.03296i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.53296 - 4.38722i) q^{17} -2.24770i q^{18} +(-5.34544 + 3.08619i) q^{19} +(0.781015 - 0.450919i) q^{20} +(-2.16858 - 3.75609i) q^{22} +(4.22559 - 7.31893i) q^{23} +(1.98388 + 1.14539i) q^{24} +4.18669 q^{25} +(2.15978 - 2.88710i) q^{26} +1.72335 q^{27} +(1.09643 - 1.89907i) q^{29} +(-1.03296 - 1.78914i) q^{30} -0.873062i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-8.60441 + 4.96776i) q^{33} -5.06592i q^{34} +(1.12385 - 1.94657i) q^{36} +(0.124973 + 0.0721531i) q^{37} -6.17238 q^{38} +(-6.61373 - 4.94760i) q^{39} +0.901839 q^{40} +(3.46110 + 1.99827i) q^{41} +(3.85426 + 6.67577i) q^{43} -4.33716i q^{44} +(-1.75549 + 1.01353i) q^{45} +(7.31893 - 4.22559i) q^{46} +2.92115i q^{47} +(1.14539 + 1.98388i) q^{48} +(3.62578 + 2.09334i) q^{50} -11.6049 q^{51} +(3.31398 - 1.42041i) q^{52} +1.69699 q^{53} +(1.49246 + 0.861675i) q^{54} +(-1.95571 + 3.38739i) q^{55} +14.1396i q^{57} +(1.89907 - 1.09643i) q^{58} +(7.40394 - 4.27467i) q^{59} -2.06592i q^{60} +(4.16720 + 7.21780i) q^{61} +(0.436531 - 0.756094i) q^{62} -1.00000 q^{64} +(-3.22876 - 0.384973i) q^{65} -9.93552 q^{66} +(-8.99180 - 5.19142i) q^{67} +(2.53296 - 4.38722i) q^{68} +(-9.67992 - 16.7661i) q^{69} +(-2.83932 + 1.63928i) q^{71} +(1.94657 - 1.12385i) q^{72} -0.539023i q^{73} +(0.0721531 + 0.124973i) q^{74} +(4.79540 - 8.30588i) q^{75} +(-5.34544 - 3.08619i) q^{76} +(-3.25386 - 7.59161i) q^{78} +6.53349 q^{79} +(0.781015 + 0.450919i) q^{80} +(5.34547 - 9.25862i) q^{81} +(1.99827 + 3.46110i) q^{82} +13.2348i q^{83} +(-3.95656 + 2.28432i) q^{85} +7.70851i q^{86} +(-2.51168 - 4.35037i) q^{87} +(2.16858 - 3.75609i) q^{88} +(6.74790 + 3.89590i) q^{89} -2.02707 q^{90} +8.45117 q^{92} +(-1.73205 - 1.00000i) q^{93} +(-1.46057 + 2.52979i) q^{94} +(2.78325 + 4.82072i) q^{95} +2.29079i q^{96} +(-10.1378 + 5.85305i) q^{97} +9.74866i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} + 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} - 18 q^{11} + 4 q^{12} + 8 q^{13} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{22} - 6 q^{23} - 6 q^{24} - 24 q^{25} + 14 q^{26} - 40 q^{27}+ \cdots - 60 q^{97}+O(q^{100}) $ 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 - 18 * q^11 + 4 * q^12 + 8 * q^13 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^22 - 6 * q^23 - 6 * q^24 - 24 * q^25 + 14 * q^26 - 40 * q^27 - 10 * q^29 + 14 * q^30 - 12 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 - 54 * q^39 + 4 * q^40 + 24 * q^41 + 26 * q^43 - 72 * q^45 - 6 * q^46 + 2 * q^48 - 12 * q^50 - 36 * q^51 + 4 * q^52 + 36 * q^53 + 36 * q^54 + 6 * q^55 + 24 * q^58 - 6 * q^59 + 28 * q^61 + 2 * q^62 - 12 * q^64 - 34 * q^65 - 42 * q^67 + 4 * q^68 - 32 * q^69 + 48 * q^71 + 48 * q^75 - 12 * q^76 - 8 * q^78 + 44 * q^79 - 34 * q^81 - 6 * q^82 + 54 * q^85 - 2 * q^87 + 2 * q^88 - 12 * q^89 - 12 * q^90 - 12 * q^92 - 8 * q^94 + 32 * q^95 - 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.14539	−	1.98388i	0.661293	−	1.14539i	−0.318983	−	0.947760i	$-0.603341\pi$
$3$	1.14539	−	1.98388i	0.661293	−	1.14539i	0.980276	−	0.197633i	$-0.0633254\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	0.901839i		−	0.403315i	−0.979456	−	0.201657i	$-0.935367\pi$
$5$		−	0.901839i		−	0.403315i	0.979456	−	0.201657i	$-0.0646327\pi$
$6$	1.98388	−	1.14539i	0.809915	−	0.467605i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.12385	−	1.94657i	−0.374617	−	0.648856i
$10$	0.450919	−	0.781015i	0.142593	−	0.246979i
$11$	−3.75609	−	2.16858i	−1.13251	−	0.653852i	−0.187941	−	0.982180i	$-0.560181\pi$
$11$	−3.75609	−	2.16858i	−1.13251	−	0.653852i	−0.944564	+	0.328328i	$0.893515\pi$
$12$	2.29079			0.661293
$13$	0.426876	−	3.58019i	0.118394	−	0.992967i
$13$	0.426876	−	3.58019i	0.118394	−	0.992967i
$14$		0			0
$15$	−1.78914	−	1.03296i	−0.461954	−	0.266709i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.53296	−	4.38722i	−0.614333	−	1.06406i	−0.990501	−	0.137505i	$-0.956092\pi$
$17$	−2.53296	−	4.38722i	−0.614333	−	1.06406i	0.376168	−	0.926551i	$-0.377242\pi$
$18$		−	2.24770i		−	0.529789i
$19$	−5.34544	+	3.08619i	−1.22633	+	0.708021i	−0.966260	−	0.257570i	$-0.917078\pi$
$19$	−5.34544	+	3.08619i	−1.22633	+	0.708021i	−0.260068	+	0.965590i	$0.583745\pi$
$20$	0.781015	−	0.450919i	0.174640	−	0.100829i
$21$		0			0
$22$	−2.16858	−	3.75609i	−0.462343	−	0.800802i
$23$	4.22559	−	7.31893i	0.881096	−	1.52610i	0.0309711	−	0.999520i	$-0.490140\pi$
$23$	4.22559	−	7.31893i	0.881096	−	1.52610i	0.850124	−	0.526582i	$-0.176527\pi$
$24$	1.98388	+	1.14539i	0.404958	+	0.233802i
$25$	4.18669			0.837337
$26$	2.15978	−	2.88710i	0.423568	−	0.566207i
$27$	1.72335			0.331659
$28$		0			0
$29$	1.09643	−	1.89907i	0.203602	−	0.352649i	−0.746085	−	0.665851i	$-0.768069\pi$
$29$	1.09643	−	1.89907i	0.203602	−	0.352649i	0.949686	+	0.313203i	$0.101402\pi$
$30$	−1.03296	−	1.78914i	−0.188592	−	0.326651i
$31$		−	0.873062i		−	0.156807i	−0.996922	−	0.0784033i	$-0.975018\pi$
$31$		−	0.873062i		−	0.156807i	0.996922	−	0.0784033i	$-0.0249822\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−8.60441	+	4.96776i	−1.49784	+	0.864776i
$34$		−	5.06592i		−	0.868798i
$35$		0			0
$36$	1.12385	−	1.94657i	0.187309	−	0.324428i
$37$	0.124973	+	0.0721531i	0.0205454	+	0.0118619i	0.510238	−	0.860034i	$-0.329557\pi$
$37$	0.124973	+	0.0721531i	0.0205454	+	0.0118619i	−0.489692	+	0.871895i	$0.662891\pi$
$38$	−6.17238			−1.00129
$39$	−6.61373	−	4.94760i	−1.05904	−	0.792250i
$40$	0.901839			0.142593
$41$	3.46110	+	1.99827i	0.540533	+	0.312077i	0.745295	−	0.666735i	$-0.232309\pi$
$41$	3.46110	+	1.99827i	0.540533	+	0.312077i	−0.204762	+	0.978812i	$0.565642\pi$
$42$		0			0
$43$	3.85426	+	6.67577i	0.587768	+	1.01804i	0.994524	+	0.104508i	$0.0333267\pi$
$43$	3.85426	+	6.67577i	0.587768	+	1.01804i	−0.406756	+	0.913537i	$0.633340\pi$
$44$		−	4.33716i		−	0.653852i
$45$	−1.75549	+	1.01353i	−0.261693	+	0.151089i
$46$	7.31893	−	4.22559i	1.07912	−	0.623029i
$47$			2.92115i			0.426093i	0.977042	+	0.213047i	$0.0683387\pi$
$47$			2.92115i			0.426093i	−0.977042	+	0.213047i	$0.931661\pi$
$48$	1.14539	+	1.98388i	0.165323	+	0.286348i
$49$		0			0
$50$	3.62578	+	2.09334i	0.512762	+	0.296043i
$51$	−11.6049			−1.62502
$52$	3.31398	−	1.42041i	0.459566	−	0.196976i
$53$	1.69699			0.233099			0.116549	−	0.993185i	$-0.462817\pi$
$53$	1.69699			0.233099			0.116549	+	0.993185i	$0.462817\pi$
$54$	1.49246	+	0.861675i	0.203099	+	0.117259i
$55$	−1.95571	+	3.38739i	−0.263708	+	0.456756i
$56$		0			0
$57$			14.1396i			1.87284i
$58$	1.89907	−	1.09643i	0.249360	−	0.143968i
$59$	7.40394	−	4.27467i	0.963911	−	0.556514i	0.0665363	−	0.997784i	$-0.478805\pi$
$59$	7.40394	−	4.27467i	0.963911	−	0.556514i	0.897374	+	0.441270i	$0.145472\pi$
$60$		−	2.06592i		−	0.266709i
$61$	4.16720	+	7.21780i	0.533555	+	0.924145i	0.999232	+	0.0391900i	$0.0124777\pi$
$61$	4.16720	+	7.21780i	0.533555	+	0.924145i	−0.465676	+	0.884955i	$0.654189\pi$
$62$	0.436531	−	0.756094i	0.0554395	−	0.0960241i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.22876	−	0.384973i	−0.400478	−	0.0477501i
$66$	−9.93552			−1.22298
$67$	−8.99180	−	5.19142i	−1.09852	−	0.634233i	−0.162691	−	0.986677i	$-0.552017\pi$
$67$	−8.99180	−	5.19142i	−1.09852	−	0.634233i	−0.935833	+	0.352444i	$0.885351\pi$
$68$	2.53296	−	4.38722i	0.307167	−	0.532028i
$69$	−9.67992	−	16.7661i	−1.16532	−	2.01840i
$70$		0			0
$71$	−2.83932	+	1.63928i	−0.336965	+	0.194547i	−0.658929	−	0.752205i	$-0.728990\pi$
$71$	−2.83932	+	1.63928i	−0.336965	+	0.194547i	0.321964	+	0.946752i	$0.395657\pi$
$72$	1.94657	−	1.12385i	0.229405	−	0.132447i
$73$		−	0.539023i		−	0.0630879i	−0.999502	−	0.0315439i	$-0.989958\pi$
$73$		−	0.539023i		−	0.0630879i	0.999502	−	0.0315439i	$-0.0100424\pi$
$74$	0.0721531	+	0.124973i	0.00838763	+	0.0145278i
$75$	4.79540	−	8.30588i	0.553725	−	0.959081i
$76$	−5.34544	−	3.08619i	−0.613164	−	0.354010i
$77$		0			0
$78$	−3.25386	−	7.59161i	−0.368427	−	0.859581i
$79$	6.53349			0.735075			0.367537	−	0.930009i	$-0.380201\pi$
$79$	6.53349			0.735075			0.367537	+	0.930009i	$0.380201\pi$
$80$	0.781015	+	0.450919i	0.0873202	+	0.0504143i
$81$	5.34547	−	9.25862i	0.593941	−	1.02874i
$82$	1.99827	+	3.46110i	0.220672	+	0.382215i
$83$			13.2348i			1.45271i	0.687319	+	0.726356i	$0.258788\pi$
$83$			13.2348i			1.45271i	−0.687319	+	0.726356i	$0.741212\pi$
$84$		0			0
$85$	−3.95656	+	2.28432i	−0.429149	+	0.247769i
$86$			7.70851i			0.831230i
$87$	−2.51168	−	4.35037i	−0.269281	−	0.466408i
$88$	2.16858	−	3.75609i	0.231172	−	0.400401i
$89$	6.74790	+	3.89590i	0.715276	+	0.412965i	0.813011	−	0.582248i	$-0.197827\pi$
$89$	6.74790	+	3.89590i	0.715276	+	0.412965i	−0.0977357	+	0.995212i	$0.531160\pi$
$90$	−2.02707			−0.213672
$91$		0			0
$92$	8.45117			0.881096
$93$	−1.73205	−	1.00000i	−0.179605	−	0.103695i
$94$	−1.46057	+	2.52979i	−0.150647	+	0.260928i
$95$	2.78325	+	4.82072i	0.285555	+	0.494596i
$96$			2.29079i			0.233802i
$97$	−10.1378	+	5.85305i	−1.02934	+	0.594287i	−0.916794	−	0.399360i	$-0.869232\pi$
$97$	−10.1378	+	5.85305i	−1.02934	+	0.594287i	−0.112541	+	0.993647i	$0.535899\pi$
$98$		0			0
$99$			9.74866i			0.979777i
$100$	2.09334	+	3.62578i	0.209334	+	0.362578i
$101$	5.37145	−	9.30362i	0.534479	−	0.925745i	−0.464709	−	0.885463i	$-0.653841\pi$
$101$	5.37145	−	9.30362i	0.534479	−	0.925745i	0.999188	−	0.0402814i	$-0.0128254\pi$
$102$	−10.0502	−	5.80247i	−0.995116	−	0.574530i
$103$	−4.81099			−0.474041			−0.237021	−	0.971505i	$-0.576171\pi$
$103$	−4.81099			−0.474041			−0.237021	+	0.971505i	$0.576171\pi$
$104$	3.58019	+	0.426876i	0.351067	+	0.0418586i
$105$		0			0
$106$	1.46963	+	0.848493i	0.142743	+	0.0824129i
$107$	−6.82652	+	11.8239i	−0.659944	+	1.14306i	0.320686	+	0.947186i	$0.396087\pi$
$107$	−6.82652	+	11.8239i	−0.659944	+	1.14306i	−0.980630	+	0.195871i	$0.937247\pi$
$108$	0.861675	+	1.49246i	0.0829147	+	0.143612i
$109$			5.11747i			0.490165i	0.969502	+	0.245082i	$0.0788150\pi$
$109$			5.11747i			0.490165i	−0.969502	+	0.245082i	$0.921185\pi$
$110$	−3.38739	+	1.95571i	−0.322975	+	0.186470i
$111$	0.286286	−	0.165287i	0.0271731	−	0.0156884i
$112$		0			0
$113$	−8.96603	−	15.5296i	−0.843453	−	1.46090i	−0.886958	−	0.461850i	$-0.847186\pi$
$113$	−8.96603	−	15.5296i	−0.843453	−	1.46090i	0.0435052	−	0.999053i	$-0.486147\pi$
$114$	−7.06980	+	12.2453i	−0.662148	+	1.14687i
$115$	−6.60049	−	3.81080i	−0.615499	−	0.355359i
$116$	2.19286			0.203602
$117$	−7.44884	+	3.19266i	−0.688645	+	0.295162i
$118$	8.54933			0.787030
$119$		0			0
$120$	1.03296	−	1.78914i	0.0942959	−	0.163325i
$121$	3.90550	+	6.76452i	0.355045	+	0.614956i
$122$			8.33440i			0.754561i
$123$	7.92864	−	4.57761i	0.714902	−	0.412749i
$124$	0.756094	−	0.436531i	0.0678993	−	0.0392017i
$125$		−	8.28491i		−	0.741025i
$126$		0			0
$127$	−9.75681	+	16.8993i	−0.865777	+	1.49957i	0.000496195		1.00000i	$0.499842\pi$
$127$	−9.75681	+	16.8993i	−0.865777	+	1.49957i	−0.866273	+	0.499570i	$0.833491\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	17.6586			1.55475
$130$	−2.60370	−	1.94777i	−0.228359	−	0.170831i
$131$	20.6496			1.80417			0.902083	−	0.431562i	$-0.142037\pi$
$131$	20.6496			1.80417			0.902083	+	0.431562i	$0.142037\pi$
$132$	−8.60441	−	4.96776i	−0.748918	−	0.432388i
$133$		0			0
$134$	−5.19142	−	8.99180i	−0.448470	−	0.776773i
$135$		−	1.55418i		−	0.133763i
$136$	4.38722	−	2.53296i	0.376201	−	0.217200i
$137$	2.76224	−	1.59478i	0.235994	−	0.136251i	−0.377340	−	0.926075i	$-0.623161\pi$
$137$	2.76224	−	1.59478i	0.235994	−	0.136251i	0.613334	+	0.789823i	$0.289828\pi$
$138$		−	19.3598i		−	1.64802i
$139$	−0.297855	−	0.515900i	−0.0252637	−	0.0437581i	0.853117	−	0.521719i	$-0.174709\pi$
$139$	−0.297855	−	0.515900i	−0.0252637	−	0.0437581i	−0.878381	+	0.477961i	$0.841376\pi$
$140$		0			0
$141$	5.79521	+	3.34587i	0.488045	+	0.281773i
$142$	−3.27856			−0.275131
$143$	−9.36733	+	12.5218i	−0.783335	+	1.04713i
$144$	2.24770			0.187309
$145$	−1.71266	−	0.988802i	−0.142228	−	0.0821155i
$146$	0.269511	−	0.466808i	0.0223049	−	0.0386333i
$147$		0			0
$148$			0.144306i			0.0118619i
$149$	9.70783	−	5.60482i	0.795297	−	0.459165i	−0.0465273	−	0.998917i	$-0.514815\pi$
$149$	9.70783	−	5.60482i	0.795297	−	0.459165i	0.841824	+	0.539752i	$0.181482\pi$
$150$	8.30588	−	4.79540i	0.678172	−	0.391543i
$151$		−	13.0731i		−	1.06387i	−0.846785	−	0.531935i	$-0.821465\pi$
$151$		−	13.0731i		−	1.06387i	0.846785	−	0.531935i	$-0.178535\pi$
$152$	−3.08619	−	5.34544i	−0.250323	−	0.433572i
$153$	−5.69334	+	9.86116i	−0.460280	+	0.797228i
$154$		0			0
$155$	−0.787362			−0.0632424
$156$	0.977882	−	8.20146i	0.0782932	−	0.656642i
$157$	−17.9245			−1.43053			−0.715266	−	0.698853i	$-0.753694\pi$
$157$	−17.9245			−1.43053			−0.715266	+	0.698853i	$0.753694\pi$
$158$	5.65817	+	3.26674i	0.450139	+	0.259888i
$159$	1.94372	−	3.36661i	0.154147	−	0.266990i
$160$	0.450919	+	0.781015i	0.0356483	+	0.0617447i
$161$		0			0
$162$	9.25862	−	5.34547i	0.727426	−	0.419980i
$163$	17.5958	−	10.1589i	1.37821	−	0.795710i	0.386266	−	0.922387i	$-0.373765\pi$
$163$	17.5958	−	10.1589i	1.37821	−	0.795710i	0.991944	+	0.126677i	$0.0404312\pi$
$164$			3.99654i			0.312077i
$165$	4.48012	+	7.75979i	0.348777	+	0.604099i
$166$	−6.61742	+	11.4617i	−0.513611	+	0.889601i
$167$	2.79770	+	1.61525i	0.216493	+	0.124992i	0.604325	−	0.796738i	$-0.293443\pi$
$167$	2.79770	+	1.61525i	0.216493	+	0.124992i	−0.387833	+	0.921730i	$0.626776\pi$
$168$		0			0
$169$	−12.6356	−	3.05660i	−0.971966	−	0.235123i
$170$	−4.56864			−0.350399
$171$	12.0150	+	6.93684i	0.918807	+	0.530474i
$172$	−3.85426	+	6.67577i	−0.293884	+	0.509022i
$173$	4.58522	+	7.94183i	0.348608	+	0.603806i	0.986002	−	0.166731i	$-0.0533212\pi$
$173$	4.58522	+	7.94183i	0.348608	+	0.603806i	−0.637395	+	0.770538i	$0.719988\pi$
$174$		−	5.02337i		−	0.380821i
$175$		0			0
$176$	3.75609	−	2.16858i	0.283126	−	0.163463i
$177$		−	19.5847i		−	1.47208i
$178$	3.89590	+	6.74790i	0.292010	+	0.505776i
$179$	−8.47747	+	14.6834i	−0.633636	+	1.09749i	0.353166	+	0.935561i	$0.385105\pi$
$179$	−8.47747	+	14.6834i	−0.633636	+	1.09749i	−0.986802	+	0.161929i	$0.948228\pi$
$180$	−1.75549	−	1.01353i	−0.130847	−	0.0755443i
$181$	2.65743			0.197525			0.0987626	−	0.995111i	$-0.468512\pi$
$181$	2.65743			0.197525			0.0987626	+	0.995111i	$0.468512\pi$
$182$		0			0
$183$	19.0923			1.41135
$184$	7.31893	+	4.22559i	0.539559	+	0.311514i
$185$	0.0650705	−	0.112705i	0.00478408	−	0.00828627i
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$			21.9717i			1.60673i
$188$	−2.52979	+	1.46057i	−0.184504	+	0.106523i
$189$		0			0
$190$			5.56649i			0.403836i
$191$	12.2430	+	21.2056i	0.885875	+	1.53438i	0.844708	+	0.535228i	$0.179774\pi$
$191$	12.2430	+	21.2056i	0.885875	+	1.53438i	0.0411671	+	0.999152i	$0.486892\pi$
$192$	−1.14539	+	1.98388i	−0.0826616	+	0.143174i
$193$	10.6009	+	6.12046i	0.763072	+	0.440560i	0.830398	−	0.557171i	$-0.188113\pi$
$193$	10.6009	+	6.12046i	0.763072	+	0.440560i	−0.0673254	+	0.997731i	$0.521447\pi$
$194$	−11.7061			−0.840449
$195$	−4.46194	+	5.96452i	−0.319526	+	0.427128i
$196$		0			0
$197$	4.72634	+	2.72876i	0.336738	+	0.194416i	0.658829	−	0.752293i	$-0.271052\pi$
$197$	4.72634	+	2.72876i	0.336738	+	0.194416i	−0.322091	+	0.946709i	$0.604386\pi$
$198$	−4.87433	+	8.44259i	−0.346404	+	0.599989i
$199$	6.40832	+	11.0995i	0.454274	+	0.786825i	0.998646	−	0.0520184i	$-0.0165654\pi$
$199$	6.40832	+	11.0995i	0.454274	+	0.786825i	−0.544372	+	0.838844i	$0.683232\pi$
$200$			4.18669i			0.296043i
$201$	−20.5983	+	11.8924i	−1.45289	+	0.838828i
$202$	9.30362	−	5.37145i	0.654600	−	0.377934i
$203$		0			0
$204$	−5.80247	−	10.0502i	−0.406254	−	0.703653i
$205$	1.80212	−	3.12136i	0.125865	−	0.218005i
$206$	−4.16644	−	2.40550i	−0.290290	−	0.167599i
$207$	−18.9957			−1.32029
$208$	2.88710	+	2.15978i	0.200184	+	0.149754i
$209$	26.7706			1.85176
$210$		0			0
$211$	9.65552	−	16.7239i	0.664713	−	1.15132i	−0.314649	−	0.949208i	$-0.601887\pi$
$211$	9.65552	−	16.7239i	0.664713	−	1.15132i	0.979363	−	0.202110i	$-0.0647797\pi$
$212$	0.848493	+	1.46963i	0.0582747	+	0.100935i
$213$			7.51048i			0.514610i
$214$	−11.8239	+	6.82652i	−0.808263	+	0.466651i
$215$	6.02046	−	3.47592i	0.410592	−	0.237056i
$216$			1.72335i			0.117259i
$217$		0			0
$218$	−2.55874	+	4.43186i	−0.173299	+	0.300163i
$219$	−1.06936	−	0.617393i	−0.0722604	−	0.0417196i
$220$	−3.91142			−0.263708
$221$	−16.7883	+	7.19569i	−1.12931	+	0.484034i
$222$	0.330575			0.0221867
$223$	9.21079	+	5.31785i	0.616800	+	0.356110i	0.775622	−	0.631197i	$-0.217436\pi$
$223$	9.21079	+	5.31785i	0.616800	+	0.356110i	−0.158822	+	0.987307i	$0.550770\pi$
$224$		0			0
$225$	−4.70522	−	8.14967i	−0.313681	−	0.543312i
$226$		−	17.9321i		−	1.19282i
$227$	−19.6776	+	11.3609i	−1.30605	+	0.754047i	−0.981434	−	0.191800i	$-0.938567\pi$
$227$	−19.6776	+	11.3609i	−1.30605	+	0.754047i	−0.324613	+	0.945847i	$0.605234\pi$
$228$	−12.2453	+	7.06980i	−0.810962	+	0.468209i
$229$		−	20.3094i		−	1.34208i	−0.741420	−	0.671042i	$-0.765847\pi$
$229$		−	20.3094i		−	1.34208i	0.741420	−	0.671042i	$-0.234153\pi$
$230$	−3.81080	−	6.60049i	−0.251277	−	0.435224i
$231$		0			0
$232$	1.89907	+	1.09643i	0.124680	+	0.0719841i
$233$	10.6446			0.697352			0.348676	−	0.937243i	$-0.386631\pi$
$233$	10.6446			0.697352			0.348676	+	0.937243i	$0.386631\pi$
$234$	−8.04721	−	0.959491i	−0.526063	−	0.0627239i
$235$	2.63441			0.171850
$236$	7.40394	+	4.27467i	0.481955	+	0.278257i
$237$	7.48341	−	12.9617i	0.486100	−	0.841950i
$238$		0			0
$239$		−	0.311564i		−	0.0201534i	−0.999949	−	0.0100767i	$-0.996792\pi$
$239$		−	0.311564i		−	0.0201534i	0.999949	−	0.0100767i	$-0.00320757\pi$
$240$	1.78914	−	1.03296i	0.115488	−	0.0666773i
$241$	21.9100	−	12.6498i	1.41135	−	0.814843i	0.415833	−	0.909441i	$-0.363490\pi$
$241$	21.9100	−	12.6498i	1.41135	−	0.814843i	0.995516	+	0.0945983i	$0.0301567\pi$
$242$			7.81099i			0.502110i
$243$	−9.66031	−	16.7321i	−0.619709	−	1.07337i
$244$	−4.16720	+	7.21780i	−0.266778	+	0.462073i
$245$		0			0
$246$	9.15521			0.583715
$247$	8.76732	+	20.4551i	0.557851	+	1.30153i
$248$	0.873062			0.0554395
$249$	26.2563	+	15.1591i	1.66393	+	0.960669i
$250$	4.14246	−	7.17494i	0.261992	−	0.453783i
$251$	−4.02015	−	6.96311i	−0.253750	−	0.439507i	0.710805	−	0.703389i	$-0.248331\pi$
$251$	−4.02015	−	6.96311i	−0.253750	−	0.439507i	−0.964555	+	0.263881i	$0.914997\pi$
$252$		0			0
$253$	−31.7434	+	18.3271i	−1.99569	+	1.15221i
$254$	−16.8993	+	9.75681i	−1.06036	+	0.612197i
$255$			10.4658i			0.655393i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.46634	−	14.6641i	0.528116	−	0.914723i	−0.471347	−	0.881948i	$-0.656232\pi$
$257$	8.46634	−	14.6641i	0.528116	−	0.914723i	0.999463	−	0.0327753i	$-0.0104346\pi$
$258$	15.2928	+	8.82928i	0.952085	+	0.549687i
$259$		0			0
$260$	−1.28098	−	2.98867i	−0.0794431	−	0.185350i
$261$	−4.92890			−0.305091
$262$	17.8831	+	10.3248i	1.10482	+	0.637869i
$263$	−5.16045	+	8.93817i	−0.318207	+	0.551151i	−0.980114	−	0.198435i	$-0.936414\pi$
$263$	−5.16045	+	8.93817i	−0.318207	+	0.551151i	0.661907	+	0.749586i	$0.269747\pi$
$264$	−4.96776	−	8.60441i	−0.305744	−	0.529565i
$265$		−	1.53041i		−	0.0940122i
$266$		0			0
$267$	15.4580	−	8.92468i	0.946014	−	0.546181i
$268$		−	10.3828i		−	0.634233i
$269$	−3.06999	−	5.31738i	−0.187181	−	0.324207i	0.757128	−	0.653266i	$-0.226602\pi$
$269$	−3.06999	−	5.31738i	−0.187181	−	0.324207i	−0.944309	+	0.329059i	$0.893268\pi$
$270$	0.777092	−	1.34596i	0.0472923	−	0.0819127i
$271$	−9.24673	−	5.33860i	−0.561699	−	0.324297i	0.192128	−	0.981370i	$-0.438461\pi$
$271$	−9.24673	−	5.33860i	−0.561699	−	0.324297i	−0.753827	+	0.657073i	$0.771794\pi$
$272$	5.06592			0.307167
$273$		0			0
$274$	3.18956			0.192689
$275$	−15.7256	−	9.07917i	−0.948289	−	0.547495i
$276$	9.67992	−	16.7661i	0.582662	−	1.00920i
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	0.981084	+	0.193585i	$0.0620114\pi$
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	−0.322892	+	0.946436i	$0.604655\pi$
$278$		−	0.595710i		−	0.0357283i
$279$	−1.69948	+	0.981193i	−0.101745	+	0.0587425i
$280$		0			0
$281$		−	25.7719i		−	1.53743i	−0.639594	−	0.768713i	$-0.720898\pi$
$281$		−	25.7719i		−	1.53743i	0.639594	−	0.768713i	$-0.279102\pi$
$282$	3.34587	+	5.79521i	0.199243	+	0.345100i
$283$	5.66344	−	9.80937i	0.336657	−	0.583107i	−0.647145	−	0.762367i	$-0.724037\pi$
$283$	5.66344	−	9.80937i	0.336657	−	0.583107i	0.983802	+	0.179260i	$0.0573704\pi$
$284$	−2.83932	−	1.63928i	−0.168482	−	0.0972733i
$285$	12.7516			0.755342
$286$	−14.3733	+	6.16055i	−0.849908	+	0.364281i
$287$		0			0
$288$	1.94657	+	1.12385i	0.114703	+	0.0662236i
$289$	−4.33177	+	7.50285i	−0.254810	+	0.441344i
$290$	−0.988802	−	1.71266i	−0.0580645	−	0.100571i
$291$			26.8162i			1.57199i
$292$	0.466808	−	0.269511i	0.0273178	−	0.0157720i
$293$	−20.5646	+	11.8730i	−1.20140	+	0.693626i	−0.960865	−	0.277016i	$-0.910655\pi$
$293$	−20.5646	+	11.8730i	−1.20140	+	0.693626i	−0.240530	+	0.970642i	$0.577321\pi$
$294$		0			0
$295$	−3.85506	−	6.67716i	−0.224450	−	0.388759i
$296$	−0.0721531	+	0.124973i	−0.00419382	+	0.00726390i
$297$	−6.47306	−	3.73723i	−0.375605	−	0.216856i
$298$	11.2096			0.649357
$299$	−24.3994	−	18.2527i	−1.41105	−	1.05558i
$300$	9.59081			0.553725
$301$		0			0
$302$	6.53653	−	11.3216i	0.376135	−	0.651485i
$303$	−12.3048	−	21.3126i	−0.706894	−	1.22438i
$304$		−	6.17238i		−	0.354010i
$305$	6.50930	−	3.75814i	0.372721	−	0.215191i
$306$	−9.86116	+	5.69334i	−0.563725	+	0.325467i
$307$			6.68810i			0.381710i	0.981618	+	0.190855i	$0.0611261\pi$
$307$			6.68810i			0.381710i	−0.981618	+	0.190855i	$0.938874\pi$
$308$		0			0
$309$	−5.51048	+	9.54443i	−0.313480	+	0.542964i
$310$	−0.681875	−	0.393681i	−0.0387279	−	0.0223596i
$311$	−9.18724			−0.520961			−0.260480	−	0.965479i	$-0.583881\pi$
$311$	−9.18724			−0.520961			−0.260480	+	0.965479i	$0.583881\pi$
$312$	4.94760	−	6.61373i	0.280103	−	0.374429i
$313$	17.1631			0.970118			0.485059	−	0.874481i	$-0.338798\pi$
$313$	17.1631			0.970118			0.485059	+	0.874481i	$0.338798\pi$
$314$	−15.5231	−	8.96225i	−0.876018	−	0.505769i
$315$		0			0
$316$	3.26674	+	5.65817i	0.183769	+	0.318297i
$317$		−	3.76247i		−	0.211322i	−0.994402	−	0.105661i	$-0.966304\pi$
$317$		−	3.76247i		−	0.211322i	0.994402	−	0.105661i	$-0.0336958\pi$
$318$	3.36661	−	1.94372i	0.188790	−	0.108998i
$319$	−8.23658	+	4.75539i	−0.461160	+	0.266251i
$320$			0.901839i			0.0504143i
$321$	15.6381	+	27.0860i	0.872833	+	1.51179i
$322$		0			0
$323$	27.0796	+	15.6344i	1.50675	+	0.869921i
$324$	10.6909			0.593941
$325$	1.78720	−	14.9891i	0.0991358	−	0.831448i
$326$	20.3179			1.12530
$327$	10.1524	+	5.86152i	0.561432	+	0.324143i
$328$	−1.99827	+	3.46110i	−0.110336	+	0.191107i
$329$		0			0
$330$			8.96024i			0.493245i
$331$	−27.9083	+	16.1129i	−1.53398	+	0.885643i	−0.534806	+	0.844975i	$0.679615\pi$
$331$	−27.9083	+	16.1129i	−1.53398	+	0.885643i	−0.999173	+	0.0406683i	$0.987051\pi$
$332$	−11.4617	+	6.61742i	−0.629043	+	0.363178i
$333$		−	0.324358i		−	0.0177747i
$334$	1.61525	+	2.79770i	0.0883827	+	0.153083i
$335$	−4.68182	+	8.10916i	−0.255795	+	0.443051i
$336$		0			0
$337$	−3.01703			−0.164348			−0.0821740	−	0.996618i	$-0.526186\pi$
$337$	−3.01703			−0.164348			−0.0821740	+	0.996618i	$0.526186\pi$
$338$	−9.41441	−	8.96487i	−0.512077	−	0.487624i
$339$	−41.0785			−2.23108
$340$	−3.95656	−	2.28432i	−0.214575	−	0.123885i
$341$	−1.89331	+	3.27931i	−0.102528	+	0.177584i
$342$	6.93684	+	12.0150i	0.375101	+	0.649695i
$343$		0			0
$344$	−6.67577	+	3.85426i	−0.359933	+	0.207808i
$345$	−15.1203	+	8.72972i	−0.814051	+	0.469993i
$346$			9.17044i			0.493006i
$347$	−0.234270	−	0.405768i	−0.0125763	−	0.0217828i	0.859669	−	0.510852i	$-0.170670\pi$
$347$	−0.234270	−	0.405768i	−0.0125763	−	0.0217828i	−0.872245	+	0.489069i	$0.837337\pi$
$348$	2.51168	−	4.35037i	0.134640	−	0.233204i
$349$	27.9044	+	16.1106i	1.49369	+	0.862380i	0.999974	−	0.00724565i	$-0.00230638\pi$
$349$	27.9044	+	16.1106i	1.49369	+	0.862380i	0.493712	+	0.869625i	$0.335640\pi$
$350$		0			0
$351$	0.735656	−	6.16992i	0.0392664	−	0.329326i
$352$	4.33716			0.231172
$353$	11.3583	+	6.55771i	0.604540	+	0.349031i	0.770826	−	0.637046i	$-0.219844\pi$
$353$	11.3583	+	6.55771i	0.604540	+	0.349031i	−0.166285	+	0.986078i	$0.553177\pi$
$354$	9.79235	−	16.9608i	0.520457	−	0.901459i
$355$	1.47837	+	2.56060i	0.0784635	+	0.135903i
$356$			7.79180i			0.412965i
$357$		0			0
$358$	−14.6834	+	8.47747i	−0.776043	+	0.448048i
$359$			4.37981i			0.231157i	0.993298	+	0.115579i	$0.0368722\pi$
$359$			4.37981i			0.231157i	−0.993298	+	0.115579i	$0.963128\pi$
$360$	−1.01353	−	1.75549i	−0.0534179	−	0.0925225i
$361$	9.54914	−	16.5396i	0.502586	−	0.870505i
$362$	2.30140	+	1.32871i	0.120959	+	0.0698357i
$363$	17.8933			0.939156
$364$		0			0
$365$	−0.486112			−0.0254443
$366$	16.5344	+	9.54617i	0.864269	+	0.498986i
$367$	12.9094	−	22.3597i	0.673865	−	1.16717i	−0.302934	−	0.953011i	$-0.597966\pi$
$367$	12.9094	−	22.3597i	0.673865	−	1.16717i	0.976799	−	0.214157i	$-0.0687004\pi$
$368$	4.22559	+	7.31893i	0.220274	+	0.381526i
$369$		−	8.98303i		−	0.467638i
$370$	0.112705	−	0.0650705i	0.00585928	−	0.00338285i
$371$		0			0
$372$		−	2.00000i		−	0.103695i
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	−0.924138	−	0.382059i	$-0.875215\pi$
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	0.131196	−	0.991356i	$-0.458118\pi$
$374$	−10.9859	+	19.0281i	−0.568065	+	0.983918i
$375$	−16.4363	−	9.48948i	−0.848765	−	0.490035i
$376$	−2.92115			−0.150647
$377$	−6.33100	−	4.73609i	−0.326063	−	0.243921i
$378$		0			0
$379$	−33.0409	−	19.0762i	−1.69720	−	0.979877i	−0.948400	−	0.317076i	$-0.897299\pi$
$379$	−33.0409	−	19.0762i	−1.69720	−	0.979877i	−0.748796	−	0.662801i	$-0.769368\pi$
$380$	−2.78325	+	4.82072i	−0.142778	+	0.247298i
$381$	22.3508	+	38.7127i	1.14507	+	1.98331i
$382$			24.4861i			1.25282i
$383$	27.6783	−	15.9801i	1.41430	−	0.816544i	0.418507	−	0.908214i	$-0.362554\pi$
$383$	27.6783	−	15.9801i	1.41430	−	0.816544i	0.995790	+	0.0916693i	$0.0292203\pi$
$384$	−1.98388	+	1.14539i	−0.101239	+	0.0584506i
$385$		0			0
$386$	6.12046	+	10.6009i	0.311523	+	0.539574i
$387$	8.66323	−	15.0051i	0.440377	−	0.762754i
$388$	−10.1378	−	5.85305i	−0.514668	−	0.297144i
$389$	5.24585			0.265975			0.132988	−	0.991118i	$-0.457543\pi$
$389$	5.24585			0.265975			0.132988	+	0.991118i	$0.457543\pi$
$390$	−6.84641	+	2.93446i	−0.346681	+	0.148592i
$391$	−42.8130			−2.16514
$392$		0			0
$393$	23.6520	−	40.9664i	1.19308	−	2.06648i
$394$	2.72876	+	4.72634i	0.137473	+	0.238110i
$395$		−	5.89215i		−	0.296466i
$396$	−8.44259	+	4.87433i	−0.424256	+	0.244944i
$397$	−21.2432	+	12.2648i	−1.06617	+	0.615552i	−0.927132	−	0.374736i	$-0.877734\pi$
$397$	−21.2432	+	12.2648i	−1.06617	+	0.615552i	−0.139035	+	0.990287i	$0.544400\pi$
$398$			12.8166i			0.642440i
$399$		0			0
$400$	−2.09334	+	3.62578i	−0.104667	+	0.181289i
$401$	3.69916	+	2.13571i	0.184727	+	0.106652i	0.589512	−	0.807760i	$-0.299320\pi$
$401$	3.69916	+	2.13571i	0.184727	+	0.106652i	−0.404784	+	0.914412i	$0.632653\pi$
$402$	−23.7849			−1.18628
$403$	−3.12573	−	0.372689i	−0.155704	−	0.0185650i
$404$	10.7429			0.534479
$405$	−8.34979	−	4.82075i	−0.414904	−	0.239545i
$406$		0			0
$407$	−0.312940	−	0.542028i	−0.0155119	−	0.0268673i
$408$		−	11.6049i		−	0.574530i
$409$	1.39990	−	0.808235i	0.0692208	−	0.0399646i	−0.464990	−	0.885316i	$-0.653942\pi$
$409$	1.39990	−	0.808235i	0.0692208	−	0.0399646i	0.534211	+	0.845351i	$0.320609\pi$
$410$	3.12136	−	1.80212i	0.154153	−	0.0890001i
$411$		−	7.30661i		−	0.360408i
$412$	−2.40550	−	4.16644i	−0.118510	−	0.205266i
$413$		0			0
$414$	−16.4508	−	9.49787i	−0.808512	−	0.466795i
$415$	11.9357			0.585900
$416$	1.42041	+	3.31398i	0.0696414	+	0.162481i
$417$	−1.36464			−0.0668269
$418$	23.1840	+	13.3853i	1.13397	+	0.654697i
$419$	−13.0156	+	22.5437i	−0.635854	+	1.10133i	0.350480	+	0.936570i	$0.386018\pi$
$419$	−13.0156	+	22.5437i	−0.635854	+	1.10133i	−0.986334	+	0.164761i	$0.947315\pi$
$420$		0			0
$421$			37.5391i			1.82954i	0.403971	+	0.914772i	$0.367630\pi$
$421$			37.5391i			1.82954i	−0.403971	+	0.914772i	$0.632370\pi$
$422$	16.7239	−	9.65552i	0.814104	−	0.470023i
$423$	5.68622	−	3.28294i	0.276473	−	0.159622i
$424$			1.69699i			0.0824129i
$425$	−10.6047	−	18.3679i	−0.514404	−	0.890974i
$426$	−3.75524	+	6.50427i	−0.181942	+	0.315133i
$427$		0			0
$428$	−13.6530			−0.659944
$429$	14.1125	+	32.9261i	0.681359	+	1.58969i
$430$	6.95183			0.335247
$431$	18.6662	+	10.7769i	0.899118	+	0.519106i	0.876914	−	0.480647i	$-0.159598\pi$
$431$	18.6662	+	10.7769i	0.899118	+	0.519106i	0.0222041	+	0.999753i	$0.492932\pi$
$432$	−0.861675	+	1.49246i	−0.0414573	+	0.0718062i
$433$	−1.59958	−	2.77056i	−0.0768710	−	0.133145i	0.825027	−	0.565093i	$-0.191160\pi$
$433$	−1.59958	−	2.77056i	−0.0768710	−	0.133145i	−0.901898	+	0.431948i	$0.857826\pi$
$434$		0			0
$435$	−3.92333	+	2.26513i	−0.188109	+	0.108605i
$436$	−4.43186	+	2.55874i	−0.212248	+	0.122541i
$437$			52.1638i			2.49534i
$438$	−0.617393	−	1.06936i	−0.0295002	−	0.0510958i
$439$	−13.3114	+	23.0560i	−0.635317	+	1.10040i	0.351131	+	0.936326i	$0.385797\pi$
$439$	−13.3114	+	23.0560i	−0.635317	+	1.10040i	−0.986448	+	0.164075i	$0.947536\pi$
$440$	−3.38739	−	1.95571i	−0.161488	−	0.0932349i
$441$		0			0
$442$	−18.1370	−	2.16252i	−0.862688	−	0.102861i
$443$	9.09867			0.432291			0.216145	−	0.976361i	$-0.430652\pi$
$443$	9.09867			0.432291			0.216145	+	0.976361i	$0.430652\pi$
$444$	0.286286	+	0.165287i	0.0135865	+	0.00784420i
$445$	3.51347	−	6.08551i	0.166555	−	0.288481i
$446$	5.31785	+	9.21079i	0.251808	+	0.436144i
$447$		−	25.6789i		−	1.21457i
$448$		0			0
$449$	6.08550	−	3.51346i	0.287192	−	0.165811i	−0.349483	−	0.936943i	$-0.613643\pi$
$449$	6.08550	−	3.51346i	0.287192	−	0.165811i	0.636675	+	0.771132i	$0.280309\pi$
$450$		−	9.41043i		−	0.443612i
$451$	−8.66681	−	15.0114i	−0.408104	−	0.706858i
$452$	8.96603	−	15.5296i	0.421726	−	0.730452i
$453$	−25.9354	−	14.9738i	−1.21855	−	0.703531i
$454$	−22.7217			−1.06638
$455$		0			0
$456$	−14.1396			−0.662148
$457$	−16.5853	−	9.57556i	−0.775830	−	0.447926i	0.0591204	−	0.998251i	$-0.481170\pi$
$457$	−16.5853	−	9.57556i	−0.775830	−	0.447926i	−0.834950	+	0.550325i	$0.814504\pi$
$458$	10.1547	−	17.5885i	0.474498	−	0.821855i
$459$	−4.36518	−	7.56071i	−0.203749	−	0.352904i
$460$		−	7.62159i		−	0.355359i
$461$	2.82026	−	1.62828i	0.131353	−	0.0758365i	−0.432884	−	0.901450i	$-0.642504\pi$
$461$	2.82026	−	1.62828i	0.131353	−	0.0758365i	0.564236	+	0.825613i	$0.309171\pi$
$462$		0			0
$463$			21.2761i			0.988786i	0.869238	+	0.494393i	$0.164610\pi$
$463$			21.2761i			0.988786i	−0.869238	+	0.494393i	$0.835390\pi$
$464$	1.09643	+	1.89907i	0.0509004	+	0.0881621i
$465$	−0.901839	+	1.56203i	−0.0418218	+	0.0724374i
$466$	9.21851	+	5.32231i	0.427039	+	0.246551i
$467$	3.33171			0.154173			0.0770866	−	0.997024i	$-0.475438\pi$
$467$	3.33171			0.154173			0.0770866	+	0.997024i	$0.475438\pi$
$468$	−6.48935	−	4.85455i	−0.299970	−	0.224402i
$469$		0			0
$470$	2.28146	+	1.31720i	0.105236	+	0.0607580i
$471$	−20.5306	+	35.5601i	−0.946001	+	1.63852i
$472$	4.27467	+	7.40394i	0.196757	+	0.340794i
$473$		−	33.4331i		−	1.53725i
$474$	12.9617	−	7.48341i	0.595348	−	0.343725i
$475$	−22.3797	+	12.9209i	−1.02685	+	0.592852i
$476$		0			0
$477$	−1.90716	−	3.30330i	−0.0873229	−	0.151248i
$478$	0.155782	−	0.269822i	0.00712530	−	0.0123414i
$479$	0.160402	+	0.0926079i	0.00732894	+	0.00423136i	0.503660	−	0.863902i	$-0.331986\pi$
$479$	0.160402	+	0.0926079i	0.00732894	+	0.00423136i	−0.496331	+	0.868133i	$0.665320\pi$
$480$	2.06592			0.0942959
$481$	0.311670	−	0.416627i	0.0142109	−	0.0189965i
$482$	25.2995			1.15236
$483$		0			0
$484$	−3.90550	+	6.76452i	−0.177523	+	0.307478i
$485$	5.27851	+	9.14264i	0.239685	+	0.415146i
$486$		−	19.3206i		−	0.876401i
$487$	−27.0466	+	15.6154i	−1.22560	+	0.707601i	−0.966106	−	0.258144i	$-0.916889\pi$
$487$	−27.0466	+	15.6154i	−1.22560	+	0.707601i	−0.259494	+	0.965745i	$0.583556\pi$
$488$	−7.21780	+	4.16720i	−0.326735	+	0.188640i
$489$		−	46.5440i		−	2.10479i
$490$		0			0
$491$	13.4236	−	23.2504i	0.605799	−	1.04927i	−0.386126	−	0.922446i	$-0.626187\pi$
$491$	13.4236	−	23.2504i	0.605799	−	1.04927i	0.991925	−	0.126829i	$-0.0404798\pi$
$492$	7.92864	+	4.57761i	0.357451	+	0.206374i
$493$	−11.1088			−0.500317
$494$	−2.63484	+	22.0983i	−0.118547	+	0.994250i
$495$	8.79172			0.395158
$496$	0.756094	+	0.436531i	0.0339496	+	0.0196008i
$497$		0			0
$498$	15.1591	+	26.2563i	0.679295	+	1.17657i
$499$		−	15.2869i		−	0.684337i	−0.939639	−	0.342168i	$-0.888839\pi$
$499$		−	15.2869i		−	0.684337i	0.939639	−	0.342168i	$-0.111161\pi$
$500$	7.17494	−	4.14246i	0.320873	−	0.185256i
$501$	6.40893	−	3.70020i	0.286330	−	0.165313i
$502$		−	8.04030i		−	0.358856i
$503$	−13.0551	−	22.6121i	−0.582097	−	1.00822i	−0.995230	−	0.0975513i	$-0.968899\pi$
$503$	−13.0551	−	22.6121i	−0.582097	−	1.00822i	0.413133	−	0.910671i	$-0.364434\pi$
$504$		0			0
$505$	−8.39036	−	4.84418i	−0.373366	−	0.215563i
$506$	−36.6541			−1.62947
$507$	−20.5366	+	21.5664i	−0.912062	+	0.957798i
$508$	−19.5136			−0.865777
$509$	−14.7459	−	8.51357i	−0.653602	−	0.377357i	0.136233	−	0.990677i	$-0.456500\pi$
$509$	−14.7459	−	8.51357i	−0.653602	−	0.377357i	−0.789835	+	0.613320i	$0.789834\pi$
$510$	−5.23289	+	9.06364i	−0.231716	+	0.401345i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−9.21206	+	5.31858i	−0.406722	+	0.234821i
$514$	14.6641	−	8.46634i	0.646807	−	0.373434i
$515$			4.33874i			0.191188i
$516$	8.82928	+	15.2928i	0.388687	+	0.673226i
$517$	6.33475	−	10.9721i	0.278602	−	0.482553i
$518$		0			0
$519$	21.0075			0.922128
$520$	0.384973	−	3.22876i	0.0168822	−	0.141590i
$521$	18.7760			0.822593			0.411297	−	0.911502i	$-0.365076\pi$
$521$	18.7760			0.822593			0.411297	+	0.911502i	$0.365076\pi$
$522$	−4.26855	−	2.46445i	−0.186829	−	0.107866i
$523$	−1.51624	+	2.62620i	−0.0663004	+	0.114836i	−0.897270	−	0.441482i	$-0.854453\pi$
$523$	−1.51624	+	2.62620i	−0.0663004	+	0.114836i	0.830970	+	0.556318i	$0.187786\pi$
$524$	10.3248	+	17.8831i	0.451042	+	0.781227i
$525$		0			0
$526$	−8.93817	+	5.16045i	−0.389723	+	0.225006i
$527$	−3.83031	+	2.21143i	−0.166851	+	0.0963315i
$528$		−	9.93552i		−	0.432388i
$529$	−24.2111	−	41.9349i	−1.05266	−	1.82326i
$530$	0.765204	−	1.32537i	0.0332383	−	0.0575705i
$531$	−16.6419	−	9.60818i	−0.722195	−	0.416960i
$532$		0			0
$533$	8.63164	−	11.5384i	0.373878	−	0.499783i
$534$	17.8494			0.772417
$535$	10.6632	+	6.15642i	0.461011	+	0.266165i
$536$	5.19142	−	8.99180i	0.224235	−	0.388387i
$537$	19.4201	+	33.6366i	0.838038	+	1.45153i
$538$		−	6.13999i		−	0.264714i
$539$		0			0
$540$	1.34596	−	0.777092i	0.0579210	−	0.0334407i
$541$			6.11845i			0.263053i	0.991313	+	0.131526i	$0.0419878\pi$
$541$			6.11845i			0.263053i	−0.991313	+	0.131526i	$0.958012\pi$
$542$	−5.33860	−	9.24673i	−0.229313	−	0.397181i
$543$	3.04380	−	5.27202i	0.130622	−	0.226244i
$544$	4.38722	+	2.53296i	0.188100	+	0.108600i
$545$	4.61513			0.197691
$546$		0			0
$547$	−37.4754			−1.60233			−0.801166	−	0.598442i	$-0.795786\pi$
$547$	−37.4754			−1.60233			−0.801166	+	0.598442i	$0.795786\pi$
$548$	2.76224	+	1.59478i	0.117997	+	0.0681257i
$549$	9.36663	−	16.2235i	0.399758	−	0.692402i
$550$	−9.07917	−	15.7256i	−0.387137	−	0.670541i
$551$			13.5352i			0.576617i
$552$	16.7661	−	9.67992i	0.713613	−	0.412005i
$553$		0			0
$554$			21.9090i			0.930823i
$555$	−0.149063	−	0.258184i	−0.00632736	−	0.0109593i
$556$	0.297855	−	0.515900i	0.0126319	−	0.0218790i
$557$	−7.69941	−	4.44526i	−0.326234	−	0.188352i	0.327934	−	0.944701i	$-0.393648\pi$
$557$	−7.69941	−	4.44526i	−0.326234	−	0.188352i	−0.654168	+	0.756349i	$0.726981\pi$
$558$	−1.96239			−0.0830744
$559$	25.5458	−	10.9493i	1.08047	−	0.463104i
$560$		0			0
$561$	43.5893	+	25.1663i	1.84034	+	1.06252i
$562$	12.8860	−	22.3192i	0.543562	−	0.941477i
$563$	−8.89598	−	15.4083i	−0.374921	−	0.649382i	0.615394	−	0.788219i	$-0.288997\pi$
$563$	−8.89598	−	15.4083i	−0.374921	−	0.649382i	−0.990315	+	0.138838i	$0.955663\pi$
$564$			6.69173i			0.281773i
$565$	−14.0052	+	8.08591i	−0.589204	+	0.340177i
$566$	9.80937	−	5.66344i	0.412319	−	0.238052i
$567$		0			0
$568$	−1.63928	−	2.83932i	−0.0687826	−	0.119135i
$569$	5.58684	−	9.67669i	0.234212	−	0.405668i	−0.724831	−	0.688927i	$-0.758082\pi$
$569$	5.58684	−	9.67669i	0.234212	−	0.405668i	0.959044	+	0.283259i	$0.0914155\pi$
$570$	11.0432	+	6.37582i	0.462551	+	0.267054i
$571$	−16.7239			−0.699873			−0.349936	−	0.936773i	$-0.613797\pi$
$571$	−16.7239			−0.699873			−0.349936	+	0.936773i	$0.613797\pi$
$572$	−15.5279	−	1.85143i	−0.649253	−	0.0774122i
$573$	56.0924			2.34329
$574$		0			0
$575$	17.6912	−	30.6421i	0.737774	−	1.27786i
$576$	1.12385	+	1.94657i	0.0468272	+	0.0811070i
$577$		−	0.798887i		−	0.0332581i	−0.999862	−	0.0166291i	$-0.994707\pi$
$577$		−	0.798887i		−	0.0332581i	0.999862	−	0.0166291i	$-0.00529344\pi$
$578$	−7.50285	+	4.33177i	−0.312078	+	0.180178i
$579$	24.2845	−	14.0207i	1.00923	−	0.582679i
$580$		−	1.97760i		−	0.0821155i
$581$		0			0
$582$	−13.4081	+	23.2235i	−0.555783	+	0.962645i
$583$	−6.37404	−	3.68005i	−0.263986	−	0.152412i
$584$	0.539023			0.0223049
$585$	2.87927	+	6.71765i	0.119043	+	0.277741i
$586$	−23.7459			−0.980935
$587$	−6.94921	−	4.01213i	−0.286825	−	0.165598i	0.349684	−	0.936868i	$-0.386289\pi$
$587$	−6.94921	−	4.01213i	−0.286825	−	0.165598i	−0.636509	+	0.771269i	$0.719622\pi$
$588$		0			0
$589$	2.69444	+	4.66690i	0.111022	+	0.192296i
$590$		−	7.71012i		−	0.317421i
$591$	10.8270	−	6.25100i	0.445365	−	0.257132i
$592$	−0.124973	+	0.0721531i	−0.00513635	+	0.00296548i
$593$			4.93120i			0.202500i	0.994861	+	0.101250i	$0.0322842\pi$
$593$			4.93120i			0.202500i	−0.994861	+	0.101250i	$0.967716\pi$
$594$	−3.73723	−	6.47306i	−0.153340	−	0.265593i
$595$		0			0
$596$	9.70783	+	5.60482i	0.397648	+	0.229582i
$597$	29.3602			1.20163
$598$	−12.0041	−	28.0070i	−0.490886	−	1.14529i
$599$	−17.8249			−0.728306			−0.364153	−	0.931339i	$-0.618642\pi$
$599$	−17.8249			−0.728306			−0.364153	+	0.931339i	$0.618642\pi$
$600$	8.30588	+	4.79540i	0.339086	+	0.195772i
$601$	−0.0809165	+	0.140152i	−0.00330065	+	0.00571690i	−0.867671	−	0.497139i	$-0.834384\pi$
$601$	−0.0809165	+	0.140152i	−0.00330065	+	0.00571690i	0.864370	+	0.502856i	$0.167717\pi$
$602$		0			0
$603$			23.3375i			0.950378i
$604$	11.3216	−	6.53653i	0.460670	−	0.265968i
$605$	6.10050	−	3.52213i	0.248021	−	0.143195i
$606$		−	24.6097i		−	0.999700i
$607$	3.09423	+	5.35937i	0.125591	+	0.217530i	0.921964	−	0.387276i	$-0.126584\pi$
$607$	3.09423	+	5.35937i	0.125591	+	0.217530i	−0.796373	+	0.604806i	$0.793251\pi$
$608$	3.08619	−	5.34544i	0.125162	−	0.216786i
$609$		0			0
$610$	7.51629			0.304326
$611$	10.4583	+	1.24697i	0.423097	+	0.0504469i
$612$	−11.3867			−0.460280
$613$	32.2269	+	18.6062i	1.30163	+	0.751497i	0.980684	−	0.195600i	$-0.0626654\pi$
$613$	32.2269	+	18.6062i	1.30163	+	0.751497i	0.320947	+	0.947097i	$0.395999\pi$
$614$	−3.34405	+	5.79207i	−0.134955	+	0.233749i
$615$	−4.12826	−	7.15036i	−0.166468	−	0.288330i
$616$		0			0
$617$	−5.78536	+	3.34018i	−0.232910	+	0.134471i	−0.611914	−	0.790924i	$-0.709600\pi$
$617$	−5.78536	+	3.34018i	−0.232910	+	0.134471i	0.379004	+	0.925395i	$0.376267\pi$
$618$	−9.54443	+	5.51048i	−0.383933	+	0.221664i
$619$			23.7344i			0.953965i	0.878913	+	0.476982i	$0.158269\pi$
$619$			23.7344i			0.953965i	−0.878913	+	0.476982i	$0.841731\pi$
$620$	−0.393681	−	0.681875i	−0.0158106	−	0.0273848i
$621$	7.28216	−	12.6131i	0.292223	−	0.506145i
$622$	−7.95639	−	4.59362i	−0.319022	−	0.184187i
$623$		0			0
$624$	7.59161	−	3.25386i	0.303908	−	0.130259i
$625$	13.4618			0.538471
$626$	14.8637	+	8.58157i	0.594074	+	0.342989i
$627$	30.6629	−	53.1097i	1.22456	−	2.12100i
$628$	−8.96225	−	15.5231i	−0.357633	−	0.619438i
$629$		−	0.731044i		−	0.0291486i
$630$		0			0
$631$	19.9348	−	11.5093i	0.793590	−	0.458180i	−0.0476346	−	0.998865i	$-0.515168\pi$
$631$	19.9348	−	11.5093i	0.793590	−	0.458180i	0.841225	+	0.540685i	$0.181835\pi$
$632$			6.53349i			0.259888i
$633$	−22.1187	−	38.3108i	−0.879141	−	1.52272i
$634$	1.88124	−	3.25840i	0.0747135	−	0.129408i
$635$	15.2404	+	8.79907i	0.604798	+	0.349181i
$636$	3.88743			0.154147
$637$		0			0
$638$	−9.51078			−0.376536
$639$	6.38194	+	3.68461i	0.252466	+	0.145761i
$640$	−0.450919	+	0.781015i	−0.0178242	+	0.0308723i
$641$	6.32539	+	10.9559i	0.249838	+	0.432732i	0.963481	−	0.267778i	$-0.0862893\pi$
$641$	6.32539	+	10.9559i	0.249838	+	0.432732i	−0.713643	+	0.700510i	$0.752956\pi$
$642$			31.2762i			1.23437i
$643$	13.1971	−	7.61938i	0.520445	−	0.300479i	−0.216672	−	0.976244i	$-0.569520\pi$
$643$	13.1971	−	7.61938i	0.520445	−	0.300479i	0.737117	+	0.675766i	$0.236187\pi$
$644$		0			0
$645$		−	15.9252i		−	0.627053i
$646$	15.6344	+	27.0796i	0.615127	+	1.06543i
$647$	14.6821	−	25.4301i	0.577213	−	0.999762i	−0.418585	−	0.908178i	$-0.637474\pi$
$647$	14.6821	−	25.4301i	0.577213	−	0.999762i	0.995797	−	0.0915840i	$-0.0291930\pi$
$648$	9.25862	+	5.34547i	0.363713	+	0.209990i
$649$	−37.0799			−1.45551
$650$	9.04233	−	12.0874i	0.354669	−	0.474106i
$651$		0			0
$652$	17.5958	+	10.1589i	0.689105	+	0.397855i
$653$	14.5106	−	25.1330i	0.567842	−	0.983532i	−0.428937	−	0.903335i	$-0.641112\pi$
$653$	14.5106	−	25.1330i	0.567842	−	0.983532i	0.996779	−	0.0801974i	$-0.0255551\pi$
$654$	5.86152	+	10.1524i	0.229204	+	0.396992i
$655$		−	18.6226i		−	0.727647i
$656$	−3.46110	+	1.99827i	−0.135133	+	0.0780192i
$657$	−1.04925	+	0.605782i	−0.0409350	+	0.0236338i
$658$		0			0
$659$	−3.98651	−	6.90484i	−0.155293	−	0.268975i	0.777873	−	0.628422i	$-0.216299\pi$
$659$	−3.98651	−	6.90484i	−0.155293	−	0.268975i	−0.933166	+	0.359447i	$0.882965\pi$
$660$	−4.48012	+	7.75979i	−0.174388	+	0.302049i
$661$	−3.40668	−	1.96685i	−0.132505	−	0.0765015i	0.432282	−	0.901738i	$-0.357708\pi$
$661$	−3.40668	−	1.96685i	−0.132505	−	0.0765015i	−0.564787	+	0.825237i	$0.691042\pi$
$662$	−32.2257			−1.25249
$663$	−4.95387	+	41.5479i	−0.192392	+	1.61359i
$664$	−13.2348			−0.513611
$665$		0			0
$666$	0.162179	−	0.280902i	0.00628430	−	0.0108847i
$667$	−9.26611	−	16.0494i	−0.358785	−	0.621434i
$668$			3.23051i			0.124992i
$669$	21.1000	−	12.1821i	0.815772	−	0.470986i
$670$	−8.10916	+	4.68182i	−0.313284	+	0.180875i
$671$		−	36.1477i		−	1.39547i
$672$		0			0
$673$	18.1599	−	31.4539i	0.700014	−	1.21246i	−0.268447	−	0.963295i	$-0.586510\pi$
$673$	18.1599	−	31.4539i	0.700014	−	1.21246i	0.968461	−	0.249166i	$-0.0801563\pi$
$674$	−2.61282	−	1.50851i	−0.100642	−	0.0581058i
$675$	7.21513			0.277710
$676$	−3.67069	−	12.4710i	−0.141180	−	0.479654i
$677$	21.1068			0.811201			0.405600	−	0.914051i	$-0.367062\pi$
$677$	21.1068			0.811201			0.405600	+	0.914051i	$0.367062\pi$
$678$	−35.5750	−	20.5393i	−1.36625	−	0.788805i
$679$		0			0
$680$	−2.28432	−	3.95656i	−0.0875997	−	0.151727i
$681$			52.0506i			1.99458i
$682$	−3.27931	+	1.89331i	−0.125571	+	0.0724985i
$683$	−22.8854	+	13.2129i	−0.875685	+	0.505577i	−0.869233	−	0.494402i	$-0.835387\pi$
$683$	−22.8854	+	13.2129i	−0.875685	+	0.505577i	−0.00645161	+	0.999979i	$0.502054\pi$
$684$			13.8737i			0.530474i
$685$	−1.43824	−	2.49110i	−0.0549522	−	0.0951799i
$686$		0			0
$687$	−40.2914	−	23.2623i	−1.53721	−	0.887511i
$688$	−7.70851			−0.293884
$689$	0.724402	−	6.07553i	0.0275975	−	0.231459i
$690$	−17.4594			−0.664670
$691$	−0.675291	−	0.389880i	−0.0256893	−	0.0148317i	0.487100	−	0.873346i	$-0.338055\pi$
$691$	−0.675291	−	0.389880i	−0.0256893	−	0.0148317i	−0.512790	+	0.858514i	$0.671388\pi$
$692$	−4.58522	+	7.94183i	−0.174304	+	0.301903i
$693$		0			0
$694$		−	0.468540i		−	0.0177855i
$695$	−0.465259	+	0.268617i	−0.0176483	+	0.0101892i
$696$	4.35037	−	2.51168i	0.164900	−	0.0952052i
$697$		−	20.2461i		−	0.766877i
$698$	16.1106	+	27.9044i	0.609795	+	1.05620i
$699$	12.1923	−	21.1176i	0.461154	−	0.798742i
$700$		0			0
$701$	21.5491			0.813899			0.406950	−	0.913451i	$-0.366592\pi$
$701$	21.5491			0.813899			0.406950	+	0.913451i	$0.366592\pi$
$702$	3.72206	−	4.97548i	0.140480	−	0.187787i
$703$	−0.890713			−0.0335939
$704$	3.75609	+	2.16858i	0.141563	+	0.0817315i
$705$	3.01743	−	5.22634i	0.113643	−	0.196835i
$706$	6.55771	+	11.3583i	0.246803	+	0.427474i
$707$		0			0
$708$	16.9608	−	9.79235i	0.637428	−	0.368019i
$709$	−3.92952	+	2.26871i	−0.147576	+	0.0852031i	−0.571970	−	0.820275i	$-0.693821\pi$
$709$	−3.92952	+	2.26871i	−0.147576	+	0.0852031i	0.424394	+	0.905478i	$0.360487\pi$
$710$			2.95673i			0.110964i
$711$	−7.34267	−	12.7179i	−0.275372	−	0.476958i
$712$	−3.89590	+	6.74790i	−0.146005	+	0.252888i
$713$	−6.38988	−	3.68920i	−0.239303	−	0.138162i
$714$		0			0
$715$	11.2927	+	8.44782i	0.422322	+	0.315931i
$716$	−16.9549			−0.633636
$717$	−0.618106	−	0.356863i	−0.0230836	−	0.0133273i
$718$	−2.18990	+	3.79302i	−0.0817265	+	0.141554i
$719$	7.30036	+	12.6446i	0.272258	+	0.471564i	0.969440	−	0.245330i	$-0.0788964\pi$
$719$	7.30036	+	12.6446i	0.272258	+	0.471564i	−0.697182	+	0.716894i	$0.745563\pi$
$720$		−	2.02707i		−	0.0755443i
$721$		0			0
$722$	16.5396	−	9.54914i	0.615540	−	0.355382i
$723$		−	57.9558i		−	2.15540i
$724$	1.32871	+	2.30140i	0.0493813	+	0.0855309i
$725$	4.59040	−	7.95081i	0.170483	−	0.295286i
$726$	15.4961	+	8.94666i	0.575113	+	0.332042i
$727$	−30.6315			−1.13606			−0.568030	−	0.823008i	$-0.692294\pi$
$727$	−30.6315			−1.13606			−0.568030	+	0.823008i	$0.692294\pi$
$728$		0			0
$729$	−12.1866			−0.451355
$730$	−0.420985	−	0.243056i	−0.0155814	−	0.00899590i
$731$	19.5254	−	33.8189i	0.722171	−	1.25084i
$732$	9.54617	+	16.5344i	0.352837	+	0.611131i
$733$		−	17.7195i		−	0.654484i	−0.944941	−	0.327242i	$-0.893881\pi$
$733$		−	17.7195i		−	0.654484i	0.944941	−	0.327242i	$-0.106119\pi$
$734$	22.3597	−	12.9094i	0.825313	−	0.476495i
$735$		0			0
$736$			8.45117i			0.311514i
$737$	22.5160	+	38.9989i	0.829389	+	1.43654i
$738$	4.49151	−	7.77953i	0.165335	−	0.286368i
$739$	−9.05014	−	5.22510i	−0.332915	−	0.192208i	0.324220	−	0.945982i	$-0.394898\pi$
$739$	−9.05014	−	5.22510i	−0.332915	−	0.192208i	−0.657134	+	0.753773i	$0.728232\pi$
$740$	0.130141			0.00478408
$741$	50.6225	+	6.03586i	1.85966	+	0.221733i
$742$		0			0
$743$	42.0103	+	24.2547i	1.54121	+	0.889818i	0.998763	+	0.0497278i	$0.0158354\pi$
$743$	42.0103	+	24.2547i	1.54121	+	0.889818i	0.542447	+	0.840090i	$0.317498\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$	−5.05464	−	8.75490i	−0.185188	−	0.320755i
$746$		−	30.6285i		−	1.12139i
$747$	25.7625	−	14.8740i	0.942601	−	0.544211i
$748$	−19.0281	+	10.9859i	−0.695735	+	0.401683i
$749$		0			0
$750$	−9.48948	−	16.4363i	−0.346507	−	0.600168i
$751$	15.7278	−	27.2413i	0.573914	−	0.994049i	−0.422244	−	0.906482i	$-0.638758\pi$
$751$	15.7278	−	27.2413i	0.573914	−	0.994049i	0.996159	−	0.0875667i	$-0.0279091\pi$
$752$	−2.52979	−	1.46057i	−0.0922519	−	0.0532617i
$753$	−18.4186			−0.671212
$754$	−3.11476	−	7.26708i	−0.113433	−	0.264651i
$755$	−11.7898			−0.429075
$756$		0			0
$757$	−24.3442	+	42.1654i	−0.884805	+	1.53253i	−0.0388676	+	0.999244i	$0.512375\pi$
$757$	−24.3442	+	42.1654i	−0.884805	+	1.53253i	−0.845937	+	0.533283i	$0.820958\pi$
$758$	−19.0762	−	33.0409i	−0.692877	−	1.20010i
$759$			83.9668i			3.04780i
$760$	−4.82072	+	2.78325i	−0.174866	+	0.100959i
$761$	40.3350	−	23.2874i	1.46214	−	0.844169i	0.463033	−	0.886341i	$-0.346761\pi$
$761$	40.3350	−	23.2874i	1.46214	−	0.844169i	0.999110	+	0.0421718i	$0.0134277\pi$
$762$			44.7016i			1.61937i
$763$		0			0
$764$	−12.2430	+	21.2056i	−0.442937	+	0.767190i
$765$	8.89318	+	5.13448i	0.321534	+	0.185637i
$766$	31.9602			1.15477
$767$	−12.1436	−	28.3323i	−0.438479	−	1.02302i
$768$	−2.29079			−0.0826616
$769$	24.1069	+	13.9181i	0.869315	+	0.501899i	0.867121	−	0.498098i	$-0.165968\pi$
$769$	24.1069	+	13.9181i	0.869315	+	0.501899i	0.00219468	+	0.999998i	$0.499301\pi$
$770$		0			0
$771$	−19.3946	−	33.5924i	−0.698479	−	1.20980i
$772$			12.2409i			0.440560i
$773$	−24.6578	+	14.2362i	−0.886880	+	0.512040i	−0.872921	−	0.487862i	$-0.837777\pi$
$773$	−24.6578	+	14.2362i	−0.886880	+	0.512040i	−0.0139594	+	0.999903i	$0.504444\pi$
$774$	15.0051	−	8.66323i	0.539349	−	0.311393i
$775$		−	3.65524i		−	0.131300i
$776$	−5.85305	−	10.1378i	−0.210112	−	0.363925i
$777$		0			0
$778$	4.54304	+	2.62292i	0.162876	+	0.0940364i
$779$	−24.6681			−0.883828
$780$	−7.39639	−	0.881892i	−0.264833	−	0.0315768i
$781$	14.2196			0.508819
$782$	−37.0771	−	21.4065i	−1.32587	−	0.765494i
$783$	1.88953	−	3.27276i	0.0675263	−	0.116959i
$784$		0			0
$785$			16.1650i			0.576954i
$786$	40.9664	−	23.6520i	1.46122	−	0.843637i
$787$	−13.1046	+	7.56594i	−0.467128	+	0.269697i	−0.715037	−	0.699087i	$-0.753590\pi$
$787$	−13.1046	+	7.56594i	−0.467128	+	0.269697i	0.247908	+	0.968783i	$0.420257\pi$
$788$			5.45751i			0.194416i
$789$	11.8215	+	20.4754i	0.420856	+	0.728945i
$790$	2.94608	−	5.10275i	0.104817	−	0.181548i
$791$		0			0
$792$	−9.74866			−0.346404
$793$	27.6200	−	11.8383i	0.980815	−	0.420389i
$794$	−24.5296			−0.870522
$795$	−3.03614	−	1.75292i	−0.107681	−	0.0621696i
$796$	−6.40832	+	11.0995i	−0.227137	+	0.393413i
$797$	−6.97234	−	12.0764i	−0.246973	−	0.427770i	0.715712	−	0.698396i	$-0.246103\pi$
$797$	−6.97234	−	12.0764i	−0.246973	−	0.427770i	−0.962684	+	0.270626i	$0.912769\pi$
$798$		0			0
$799$	12.8157	−	7.39916i	0.453387	−	0.261763i
$800$	−3.62578	+	2.09334i	−0.128191	+	0.0740109i
$801$		−	17.5137i		−	0.618815i
$802$	2.13571	+	3.69916i	0.0754147	+	0.130622i
$803$	−1.16892	+	2.02462i	−0.0412501	+	0.0714473i
$804$	−20.5983	−	11.8924i	−0.726446	−	0.419414i
$805$		0			0
$806$	−2.52062	−	1.88562i	−0.0887850	−	0.0664183i
$807$	−14.0654			−0.495125
$808$	9.30362	+	5.37145i	0.327300	+	0.188967i
$809$	10.8714	−	18.8299i	0.382220	−	0.662024i	−0.609159	−	0.793048i	$-0.708493\pi$
$809$	10.8714	−	18.8299i	0.382220	−	0.662024i	0.991379	+	0.131024i	$0.0418264\pi$
$810$	−4.82075	−	8.34979i	−0.169384	−	0.293382i
$811$		−	21.1256i		−	0.741819i	−0.928669	−	0.370910i	$-0.879046\pi$
$811$		−	21.1256i		−	0.741819i	0.928669	−	0.370910i	$-0.120954\pi$
$812$		0			0
$813$	−21.1823	+	12.2296i	−0.742895	+	0.428911i
$814$		−	0.625880i		−	0.0219371i
$815$	−9.16173	−	15.8686i	−0.320921	−	0.555852i
$816$	5.80247	−	10.0502i	0.203127	−	0.351827i
$817$	−41.2054	−	23.7899i	−1.44159	−	0.832304i
$818$	1.61647			0.0565185
$819$		0			0
$820$	3.60423			0.125865
$821$	−14.0933	−	8.13678i	−0.491860	−	0.283976i	0.233486	−	0.972360i	$-0.424987\pi$
$821$	−14.0933	−	8.13678i	−0.491860	−	0.283976i	−0.725346	+	0.688385i	$0.758320\pi$
$822$	3.65330	−	6.32771i	0.127424	−	0.220704i
$823$	9.32713	+	16.1551i	0.325123	+	0.563130i	0.981537	−	0.191271i	$-0.0612609\pi$
$823$	9.32713	+	16.1551i	0.325123	+	0.563130i	−0.656414	+	0.754401i	$0.727928\pi$
$824$		−	4.81099i		−	0.167599i
$825$	−36.0240	+	20.7985i	−1.25419	+	0.724109i
$826$		0			0
$827$			47.3361i			1.64604i	0.568015	+	0.823018i	$0.307712\pi$
$827$			47.3361i			1.64604i	−0.568015	+	0.823018i	$0.692288\pi$
$828$	−9.49787	−	16.4508i	−0.330074	−	0.571704i
$829$	−0.460988	+	0.798454i	−0.0160108	+	0.0277315i	−0.873920	−	0.486070i	$-0.838430\pi$
$829$	−0.460988	+	0.798454i	−0.0160108	+	0.0277315i	0.857909	+	0.513802i	$0.171763\pi$
$830$	10.3366	+	5.96784i	0.358789	+	0.207147i
$831$	50.1888			1.74103
$832$	−0.426876	+	3.58019i	−0.0147993	+	0.124121i
$833$		0			0
$834$	−1.18182	−	0.682322i	−0.0409230	−	0.0236269i
$835$	1.45670	−	2.52307i	0.0504111	−	0.0873146i
$836$	13.3853	+	23.1840i	0.462941	+	0.801837i
$837$		−	1.50459i		−	0.0520063i
$838$	−22.5437	+	13.0156i	−0.778758	+	0.449616i
$839$	14.3894	−	8.30775i	0.496779	−	0.286815i	−0.230604	−	0.973048i	$-0.574070\pi$
$839$	14.3894	−	8.30775i	0.496779	−	0.286815i	0.727382	+	0.686232i	$0.240737\pi$
$840$		0			0
$841$	12.0957	+	20.9503i	0.417093	+	0.722426i
$842$	−18.7696	+	32.5098i	−0.646841	+	1.12036i
$843$	−51.1284	−	29.5190i	−1.76096	−	1.01669i
$844$	19.3110			0.664713
$845$	−2.75656	+	11.3952i	−0.0948284	+	0.392008i
$846$	6.56588			0.225740
$847$		0			0
$848$	−0.848493	+	1.46963i	−0.0291374	+	0.0504674i
$849$	−12.9737	−	22.4712i	−0.445258	−	0.771209i
$850$		−	21.2094i		−	0.727477i
$851$	1.05617	−	0.609779i	0.0362050	−	0.0209029i
$852$	−6.50427	+	3.75524i	−0.222832	+	0.128652i
$853$			26.3277i			0.901445i	0.892664	+	0.450722i	$0.148834\pi$
$853$			26.3277i			0.901445i	−0.892664	+	0.450722i	$0.851166\pi$
$854$		0			0
$855$	6.25591	−	10.8356i	0.213948	−	0.370568i
$856$	−11.8239	−	6.82652i	−0.404132	−	0.233325i
$857$	−14.1058			−0.481845			−0.240923	−	0.970544i	$-0.577450\pi$
$857$	−14.1058			−0.481845			−0.240923	+	0.970544i	$0.577450\pi$
$858$	−4.24123	+	35.5711i	−0.144793	+	1.21438i
$859$	−23.4719			−0.800850			−0.400425	−	0.916329i	$-0.631138\pi$
$859$	−23.4719			−0.800850			−0.400425	+	0.916329i	$0.631138\pi$
$860$	6.02046	+	3.47592i	0.205296	+	0.118528i
$861$		0			0
$862$	10.7769	+	18.6662i	0.367063	+	0.635772i
$863$			11.9484i			0.406727i	0.979103	+	0.203364i	$0.0651874\pi$
$863$			11.9484i			0.406727i	−0.979103	+	0.203364i	$0.934813\pi$
$864$	−1.49246	+	0.861675i	−0.0507747	+	0.0293148i
$865$	7.16225	−	4.13513i	0.243524	−	0.140599i
$866$		−	3.19917i		−	0.108712i
$867$	9.92317	+	17.1874i	0.337009	+	0.583716i
$868$		0			0
$869$	−24.5404	−	14.1684i	−0.832476	−	0.480630i
$870$	−4.53027			−0.153591
$871$	−22.4247	+	29.9763i	−0.759831	+	1.01571i
$872$	−5.11747			−0.173299
$873$	22.7867	+	13.1559i	0.771214	+	0.445261i
$874$	−26.0819	+	45.1752i	−0.882234	+	1.52807i
$875$		0			0
$876$		−	1.23479i		−	0.0417196i
$877$	−28.3486	+	16.3671i	−0.957264	+	0.552677i	−0.895330	−	0.445403i	$-0.853060\pi$
$877$	−28.3486	+	16.3671i	−0.957264	+	0.552677i	−0.0619342	+	0.998080i	$0.519727\pi$
$878$	−23.0560	+	13.3114i	−0.778101	+	0.449237i
$879$			54.3969i			1.83476i
$880$	−1.95571	−	3.38739i	−0.0659270	−	0.114189i
$881$	5.29540	−	9.17190i	0.178407	−	0.309009i	−0.762928	−	0.646483i	$-0.776239\pi$
$881$	5.29540	−	9.17190i	0.178407	−	0.309009i	0.941335	+	0.337474i	$0.109572\pi$
$882$		0			0
$883$	−38.6713			−1.30139			−0.650696	−	0.759338i	$-0.725523\pi$
$883$	−38.6713			−1.30139			−0.650696	+	0.759338i	$0.725523\pi$
$884$	−14.6258	−	10.9413i	−0.491919	−	0.367995i
$885$	−17.6622			−0.593710
$886$	7.87968	+	4.54933i	0.264723	+	0.152838i
$887$	2.36082	−	4.08906i	0.0792685	−	0.137297i	−0.823666	−	0.567075i	$-0.808075\pi$
$887$	2.36082	−	4.08906i	0.0792685	−	0.137297i	0.902935	+	0.429778i	$0.141408\pi$
$888$	0.165287	+	0.286286i	0.00554668	+	0.00960714i
$889$		0			0
$890$	6.08551	−	3.51347i	0.203987	−	0.117772i
$891$	−40.1562	+	23.1842i	−1.34528	+	0.776699i
$892$			10.6357i			0.356110i
$893$	−9.01522	−	15.6148i	−0.301683	−	0.522530i
$894$	12.8394	−	22.2386i	0.429415	−	0.743769i
$895$	13.2421	+	7.64531i	0.442634	+	0.255555i
$896$		0			0
$897$	−64.1580	+	27.4989i	−2.14217	+	0.918162i
$898$	7.02693			0.234492
$899$	−1.65801	−	0.957251i	−0.0552976	−	0.0319261i
$900$	4.70522	−	8.14967i	0.156841	−	0.271656i
$901$	−4.29840	−	7.44504i	−0.143200	−	0.248030i
$902$		−	17.3336i		−	0.577147i
$903$		0			0
$904$	15.5296	−	8.96603i	0.516507	−	0.298206i
$905$		−	2.39657i		−	0.0796648i
$906$	−14.9738	−	25.9354i	−0.497471	−	0.861646i
$907$	−20.9654	+	36.3132i	−0.696146	+	1.20576i	0.273646	+	0.961830i	$0.411770\pi$
$907$	−20.9654	+	36.3132i	−0.696146	+	1.20576i	−0.969793	+	0.243930i	$0.921563\pi$
$908$	−19.6776	−	11.3609i	−0.653023	−	0.377023i
$909$	−24.1468			−0.800900
$910$		0			0
$911$	−54.1425			−1.79382			−0.896910	−	0.442213i	$-0.854194\pi$
$911$	−54.1425			−1.79382			−0.896910	+	0.442213i	$0.854194\pi$
$912$	−12.2453	−	7.06980i	−0.405481	−	0.234105i
$913$	28.7008	−	49.7113i	0.949859	−	1.64520i
$914$	−9.57556	−	16.5853i	−0.316731	−	0.548595i
$915$		−	17.2182i		−	0.569216i
$916$	17.5885	−	10.1547i	0.581139	−	0.335521i
$917$		0			0
$918$		−	8.73035i		−	0.288145i
$919$	12.9117	+	22.3636i	0.425916	+	0.737708i	0.996506	−	0.0835271i	$-0.0266185\pi$
$919$	12.9117	+	22.3636i	0.425916	+	0.737708i	−0.570589	+	0.821236i	$0.693285\pi$
$920$	3.81080	−	6.60049i	0.125638	−	0.217612i
$921$	13.2684	+	7.66051i	0.437208	+	0.252422i
$922$	3.25656			0.107249
$923$	4.65690	+	10.8651i	0.153284	+	0.357628i
$924$		0			0
$925$	0.523222	+	0.302083i	0.0172034	+	0.00993241i
$926$	−10.6381	+	18.4257i	−0.349589	+	0.605506i
$927$	5.40684	+	9.36493i	0.177584	+	0.307585i
$928$			2.19286i			0.0719841i
$929$	−13.8843	+	8.01610i	−0.455529	+	0.263000i	−0.710162	−	0.704038i	$-0.751379\pi$
$929$	−13.8843	+	8.01610i	−0.455529	+	0.263000i	0.254633	+	0.967038i	$0.418045\pi$
$930$	−1.56203	+	0.901839i	−0.0512210	+	0.0295725i
$931$		0			0
$932$	5.32231	+	9.21851i	0.174338	+	0.301962i
$933$	−10.5230	+	18.2264i	−0.344508	+	0.596705i
$934$	2.88535	+	1.66586i	0.0944115	+	0.0545085i
$935$	19.8150			0.648018
$936$	−3.19266	−	7.44884i	−0.104355	−	0.243473i
$937$	−47.0232			−1.53618			−0.768091	−	0.640340i	$-0.778793\pi$
$937$	−47.0232			−1.53618			−0.768091	+	0.640340i	$0.778793\pi$
$938$		0			0
$939$	19.6586	−	34.0496i	0.641533	−	1.11117i
$940$	1.31720	+	2.28146i	0.0429624	+	0.0744131i
$941$			52.8569i			1.72308i	0.507686	+	0.861542i	$0.330501\pi$
$941$			52.8569i			1.72308i	−0.507686	+	0.861542i	$0.669499\pi$
$942$	−35.5601	+	20.5306i	−1.15861	+	0.668923i
$943$	29.2504	−	16.8877i	0.952523	−	0.549939i
$944$			8.54933i			0.278257i
$945$		0			0
$946$	16.7165	−	28.9539i	0.543502	−	0.941372i
$947$	−33.4029	−	19.2852i	−1.08545	−	0.626684i	−0.153088	−	0.988213i	$-0.548922\pi$
$947$	−33.4029	−	19.2852i	−1.08545	−	0.626684i	−0.932361	+	0.361528i	$0.882255\pi$
$948$	14.9668			0.486100
$949$	−1.92981	−	0.230096i	−0.0626441	−	0.00746923i
$950$	−25.8418			−0.838419
$951$	−7.46430	−	4.30951i	−0.242046	−	0.139746i
$952$		0			0
$953$	13.6505	+	23.6433i	0.442182	+	0.765882i	0.997851	−	0.0655217i	$-0.0208711\pi$
$953$	13.6505	+	23.6433i	0.442182	+	0.765882i	−0.555669	+	0.831404i	$0.687538\pi$
$954$		−	3.81432i		−	0.123493i
$955$	19.1240	−	11.0412i	0.618838	−	0.357286i
$956$	0.269822	−	0.155782i	0.00872668	−	0.00503835i
$957$			21.7872i			0.704279i
$958$	0.0926079	+	0.160402i	0.00299203	+	0.00518234i
$959$		0			0
$960$	1.78914	+	1.03296i	0.0577442	+	0.0333386i
$961$	30.2378			0.975412
$962$	0.478227	−	0.204974i	0.0154187	−	0.00660863i
$963$	30.6880			0.988906
$964$	21.9100	+	12.6498i	0.705674	+	0.407421i
$965$	5.51966	−	9.56034i	0.177684	−	0.307758i
$966$		0			0
$967$		−	25.2494i		−	0.811966i	−0.913881	−	0.405983i	$-0.866929\pi$
$967$		−	25.2494i		−	0.811966i	0.913881	−	0.405983i	$-0.133071\pi$
$968$	−6.76452	+	3.90550i	−0.217420	+	0.125527i
$969$	62.0335	−	35.8151i	1.99280	−	1.15055i
$970$			10.5570i			0.338965i
$971$	−3.28682	−	5.69294i	−0.105479	−	0.182695i	0.808455	−	0.588558i	$-0.200304\pi$
$971$	−3.28682	−	5.69294i	−0.105479	−	0.182695i	−0.913934	+	0.405863i	$0.866971\pi$
$972$	9.66031	−	16.7321i	0.309854	−	0.536684i
$973$		0			0
$974$	−31.2308			−1.00070
$975$	−27.6896	−	20.7140i	−0.886777	−	0.663380i
$976$	−8.33440			−0.266778
$977$	12.0773	+	6.97285i	0.386388	+	0.223081i	0.680594	−	0.732661i	$-0.261722\pi$
$977$	12.0773	+	6.97285i	0.386388	+	0.223081i	−0.294206	+	0.955742i	$0.595055\pi$
$978$	23.2720	−	40.3083i	0.744156	−	1.28892i
$979$	−16.8972	−	29.2667i	−0.540036	−	0.935369i
$980$		0			0
$981$	9.96151	−	5.75128i	0.318047	−	0.183624i
$982$	23.2504	−	13.4236i	0.741949	−	0.428365i
$983$		−	47.1390i		−	1.50350i	−0.659449	−	0.751750i	$-0.729210\pi$
$983$		−	47.1390i		−	1.50350i	0.659449	−	0.751750i	$-0.270790\pi$
$984$	4.57761	+	7.92864i	0.145929	+	0.252756i
$985$	2.46090	−	4.26240i	0.0784107	−	0.135811i
$986$	−9.62054	−	5.55442i	−0.306380	−	0.176889i
$987$		0			0
$988$	−13.3310	+	17.8203i	−0.424115	+	0.566939i
$989$	65.1459			2.07152
$990$	7.61385	+	4.39586i	0.241984	+	0.139710i
$991$	−4.70805	+	8.15458i	−0.149556	+	0.259039i	−0.931063	−	0.364857i	$-0.881118\pi$
$991$	−4.70805	+	8.15458i	−0.149556	+	0.259039i	0.781507	+	0.623896i	$0.214451\pi$
$992$	0.436531	+	0.756094i	0.0138599	+	0.0240060i
$993$			73.8223i			2.34268i
$994$		0			0
$995$	10.0100	−	5.77927i	0.317338	−	0.183215i
$996$			30.3182i			0.960669i
$997$	20.2607	+	35.0926i	0.641664	+	1.11139i	0.985061	+	0.172204i	$0.0550888\pi$
$997$	20.2607	+	35.0926i	0.641664	+	1.11139i	−0.343398	+	0.939190i	$0.611578\pi$
$998$	7.64346	−	13.2389i	0.241950	−	0.419069i
$999$	0.215372	+	0.124345i	0.00681407	+	0.00393410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.m.c.589.6		12
7.2	even	3		1274.2.o.e.459.3		12
7.3	odd	6		1274.2.v.e.667.3		12
7.4	even	3		1274.2.v.d.667.1		12
7.5	odd	6		1274.2.o.d.459.1		12
7.6	odd	2		182.2.m.b.43.4	✓	12
13.10	even	6	inner	1274.2.m.c.491.6		12
21.20	even	2		1638.2.bj.g.1135.2		12
28.27	even	2		1456.2.cc.d.225.5		12
91.6	even	12		2366.2.a.bf.1.5		6
91.10	odd	6		1274.2.o.d.569.4		12
91.20	even	12		2366.2.a.bh.1.5		6
91.23	even	6		1274.2.v.d.361.1		12
91.48	odd	6		2366.2.d.r.337.5		12
91.62	odd	6		182.2.m.b.127.4	yes	12
91.69	odd	6		2366.2.d.r.337.11		12
91.75	odd	6		1274.2.v.e.361.3		12
91.88	even	6		1274.2.o.e.569.6		12
273.62	even	6		1638.2.bj.g.127.2		12
364.335	even	6		1456.2.cc.d.673.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.4	✓	12	7.6	odd	2
182.2.m.b.127.4	yes	12	91.62	odd	6
1274.2.m.c.491.6		12	13.10	even	6	inner
1274.2.m.c.589.6		12	1.1	even	1	trivial
1274.2.o.d.459.1		12	7.5	odd	6
1274.2.o.d.569.4		12	91.10	odd	6
1274.2.o.e.459.3		12	7.2	even	3
1274.2.o.e.569.6		12	91.88	even	6
1274.2.v.d.361.1		12	91.23	even	6
1274.2.v.d.667.1		12	7.4	even	3
1274.2.v.e.361.3		12	91.75	odd	6
1274.2.v.e.667.3		12	7.3	odd	6
1456.2.cc.d.225.5		12	28.27	even	2
1456.2.cc.d.673.5		12	364.335	even	6
1638.2.bj.g.127.2		12	273.62	even	6
1638.2.bj.g.1135.2		12	21.20	even	2
2366.2.a.bf.1.5		6	91.6	even	12
2366.2.a.bh.1.5		6	91.20	even	12
2366.2.d.r.337.5		12	91.48	odd	6
2366.2.d.r.337.11		12	91.69	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.14539 - 1.98388i) q^{3} +(0.500000 + 0.866025i) q^{4} -0.901839i q^{5} +(1.98388 - 1.14539i) q^{6} +1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +(0.450919 - 0.781015i) q^{10} +(-3.75609 - 2.16858i) q^{11} +2.29079 q^{12} +(0.426876 - 3.58019i) q^{13} +(-1.78914 - 1.03296i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.53296 - 4.38722i) q^{17} -2.24770i q^{18} +(-5.34544 + 3.08619i) q^{19} +(0.781015 - 0.450919i) q^{20} +(-2.16858 - 3.75609i) q^{22} +(4.22559 - 7.31893i) q^{23} +(1.98388 + 1.14539i) q^{24} +4.18669 q^{25} +(2.15978 - 2.88710i) q^{26} +1.72335 q^{27} +(1.09643 - 1.89907i) q^{29} +(-1.03296 - 1.78914i) q^{30} -0.873062i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-8.60441 + 4.96776i) q^{33} -5.06592i q^{34} +(1.12385 - 1.94657i) q^{36} +(0.124973 + 0.0721531i) q^{37} -6.17238 q^{38} +(-6.61373 - 4.94760i) q^{39} +0.901839 q^{40} +(3.46110 + 1.99827i) q^{41} +(3.85426 + 6.67577i) q^{43} -4.33716i q^{44} +(-1.75549 + 1.01353i) q^{45} +(7.31893 - 4.22559i) q^{46} +2.92115i q^{47} +(1.14539 + 1.98388i) q^{48} +(3.62578 + 2.09334i) q^{50} -11.6049 q^{51} +(3.31398 - 1.42041i) q^{52} +1.69699 q^{53} +(1.49246 + 0.861675i) q^{54} +(-1.95571 + 3.38739i) q^{55} +14.1396i q^{57} +(1.89907 - 1.09643i) q^{58} +(7.40394 - 4.27467i) q^{59} -2.06592i q^{60} +(4.16720 + 7.21780i) q^{61} +(0.436531 - 0.756094i) q^{62} -1.00000 q^{64} +(-3.22876 - 0.384973i) q^{65} -9.93552 q^{66} +(-8.99180 - 5.19142i) q^{67} +(2.53296 - 4.38722i) q^{68} +(-9.67992 - 16.7661i) q^{69} +(-2.83932 + 1.63928i) q^{71} +(1.94657 - 1.12385i) q^{72} -0.539023i q^{73} +(0.0721531 + 0.124973i) q^{74} +(4.79540 - 8.30588i) q^{75} +(-5.34544 - 3.08619i) q^{76} +(-3.25386 - 7.59161i) q^{78} +6.53349 q^{79} +(0.781015 + 0.450919i) q^{80} +(5.34547 - 9.25862i) q^{81} +(1.99827 + 3.46110i) q^{82} +13.2348i q^{83} +(-3.95656 + 2.28432i) q^{85} +7.70851i q^{86} +(-2.51168 - 4.35037i) q^{87} +(2.16858 - 3.75609i) q^{88} +(6.74790 + 3.89590i) q^{89} -2.02707 q^{90} +8.45117 q^{92} +(-1.73205 - 1.00000i) q^{93} +(-1.46057 + 2.52979i) q^{94} +(2.78325 + 4.82072i) q^{95} +2.29079i q^{96} +(-10.1378 + 5.85305i) q^{97} +9.74866i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} + 6 q^{4} - 6 q^{6} - 6 q^{9} + 2 q^{10} - 18 q^{11} + 4 q^{12} + 8 q^{13} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{22} - 6 q^{23} - 6 q^{24} - 24 q^{25} + 14 q^{26} - 40 q^{27}+ \cdots - 60 q^{97}+O(q^{100}) \) 12 * q + 2 * q^3 + 6 * q^4 - 6 * q^6 - 6 * q^9 + 2 * q^10 - 18 * q^11 + 4 * q^12 + 8 * q^13 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^22 - 6 * q^23 - 6 * q^24 - 24 * q^25 + 14 * q^26 - 40 * q^27 - 10 * q^29 + 14 * q^30 - 12 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 - 54 * q^39 + 4 * q^40 + 24 * q^41 + 26 * q^43 - 72 * q^45 - 6 * q^46 + 2 * q^48 - 12 * q^50 - 36 * q^51 + 4 * q^52 + 36 * q^53 + 36 * q^54 + 6 * q^55 + 24 * q^58 - 6 * q^59 + 28 * q^61 + 2 * q^62 - 12 * q^64 - 34 * q^65 - 42 * q^67 + 4 * q^68 - 32 * q^69 + 48 * q^71 + 48 * q^75 - 12 * q^76 - 8 * q^78 + 44 * q^79 - 34 * q^81 - 6 * q^82 + 54 * q^85 - 2 * q^87 + 2 * q^88 - 12 * q^89 - 12 * q^90 - 12 * q^92 - 8 * q^94 + 32 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more