LMFDB - Embedded newform 952.2.q.e.681.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [952,2,Mod(137,952)] 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("952.137"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(952, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 952 = 2^{3} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	952.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.60175827243$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 17 x^{12} - 18 x^{11} + 102 x^{10} - 59 x^{9} + 462 x^{8} - 28 x^{7} + 1148 x^{6} + \cdots + 361 $ x^14 - 3x^13 + 17x^12 - 18x^11 + 102x^10 - 59x^9 + 462x^8 - 28x^7 + 1148x^6 - x^5 + 1982x^4 + 198x^3 + 1563x^2 - 532x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			681.3
Root			$-0.658657 - 1.14083i$ of defining polynomial
Character	$\chi$	$=$	952.681
Dual form			952.2.q.e.137.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.658657 - 1.14083i) q^{3} +(-0.533302 + 0.923707i) q^{5} +(-0.740531 + 2.54000i) q^{7} +(0.632341 - 1.09525i) q^{9} +(-0.756331 - 1.31000i) q^{11} -1.38743 q^{13} +1.40505 q^{15} +(-0.500000 - 0.866025i) q^{17} +(2.31887 - 4.01641i) q^{19} +(3.38546 - 0.828173i) q^{21} +(2.90976 - 5.03984i) q^{23} +(1.93118 + 3.34490i) q^{25} -5.61793 q^{27} +9.67008 q^{29} +(-0.886751 - 1.53590i) q^{31} +(-0.996326 + 1.72569i) q^{33} +(-1.95129 - 2.03862i) q^{35} +(4.46824 - 7.73921i) q^{37} +(0.913838 + 1.58281i) q^{39} +6.52095 q^{41} -7.24599 q^{43} +(0.674458 + 1.16820i) q^{45} +(2.40311 - 4.16231i) q^{47} +(-5.90323 - 3.76190i) q^{49} +(-0.658657 + 1.14083i) q^{51} +(-0.709445 - 1.22880i) q^{53} +1.61341 q^{55} -6.10937 q^{57} +(-0.520890 - 0.902208i) q^{59} +(6.92473 - 11.9940i) q^{61} +(2.31366 + 2.41721i) q^{63} +(0.739917 - 1.28157i) q^{65} +(-6.13093 - 10.6191i) q^{67} -7.66613 q^{69} -1.86001 q^{71} +(4.52897 + 7.84441i) q^{73} +(2.54397 - 4.40628i) q^{75} +(3.88750 - 0.950985i) q^{77} +(2.42267 - 4.19618i) q^{79} +(1.80327 + 3.12335i) q^{81} -8.41568 q^{83} +1.06660 q^{85} +(-6.36927 - 11.0319i) q^{87} +(-4.30313 + 7.45323i) q^{89} +(1.02743 - 3.52406i) q^{91} +(-1.16813 + 2.02326i) q^{93} +(2.47332 + 4.28392i) q^{95} -19.5711 q^{97} -1.91304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 4 q^{9} + 12 q^{11} + 4 q^{13} - 12 q^{15} - 7 q^{17} + 3 q^{19} + 18 q^{21} + 18 q^{23} - 15 q^{25} - 36 q^{27} + 10 q^{29} + 10 q^{31} - 21 q^{33} + 19 q^{35} - 11 q^{37}+ \cdots - 40 q^{99}+O(q^{100}) $ 14 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 4 * q^9 + 12 * q^11 + 4 * q^13 - 12 * q^15 - 7 * q^17 + 3 * q^19 + 18 * q^21 + 18 * q^23 - 15 * q^25 - 36 * q^27 + 10 * q^29 + 10 * q^31 - 21 * q^33 + 19 * q^35 - 11 * q^37 + 12 * q^39 - 30 * q^43 - 13 * q^45 - 15 * q^47 + 20 * q^49 + 3 * q^51 - 8 * q^53 - 18 * q^55 - 6 * q^57 - 9 * q^59 + 4 * q^61 + 41 * q^63 + 38 * q^65 + 30 * q^67 - 56 * q^69 - 54 * q^71 + 5 * q^73 + 2 * q^75 + 27 * q^77 - 3 * q^79 + 17 * q^81 - 24 * q^83 + 4 * q^85 - 19 * q^87 - 32 * q^89 - 11 * q^91 + 9 * q^93 + 42 * q^95 - 78 * q^97 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/952\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.658657	−	1.14083i	−0.380276	−	0.658657i	0.610826	−	0.791765i	$-0.290838\pi$
$3$	−0.658657	−	1.14083i	−0.380276	−	0.658657i	−0.991102	+	0.133108i	$0.957504\pi$
$4$		0			0
$5$	−0.533302	+	0.923707i	−0.238500	+	0.413094i	−0.960284	−	0.279024i	$-0.909989\pi$
$5$	−0.533302	+	0.923707i	−0.238500	+	0.413094i	0.721784	+	0.692118i	$0.243322\pi$
$6$		0			0
$7$	−0.740531	+	2.54000i	−0.279894	+	0.960031i
$7$	−0.740531	+	2.54000i	−0.279894	+	0.960031i
$8$		0			0
$9$	0.632341	−	1.09525i	0.210780	−	0.365082i
$10$		0			0
$11$	−0.756331	−	1.31000i	−0.228042	−	0.394981i	0.729185	−	0.684316i	$-0.239899\pi$
$11$	−0.756331	−	1.31000i	−0.228042	−	0.394981i	−0.957228	+	0.289335i	$0.906566\pi$
$12$		0			0
$13$	−1.38743			−0.384802			−0.192401	−	0.981316i	$-0.561628\pi$
$13$	−1.38743			−0.384802			−0.192401	+	0.981316i	$0.561628\pi$
$14$		0			0
$15$	1.40505			0.362783
$16$		0			0
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$		0			0
$19$	2.31887	−	4.01641i	0.531986	−	0.921427i	−0.467317	−	0.884090i	$-0.654779\pi$
$19$	2.31887	−	4.01641i	0.531986	−	0.921427i	0.999303	−	0.0373371i	$-0.0118875\pi$
$20$		0			0
$21$	3.38546	−	0.828173i	0.738768	−	0.180722i
$22$		0			0
$23$	2.90976	−	5.03984i	0.606726	−	1.05088i	−0.385050	−	0.922896i	$-0.625816\pi$
$23$	2.90976	−	5.03984i	0.606726	−	1.05088i	0.991776	−	0.127985i	$-0.0408508\pi$
$24$		0			0
$25$	1.93118	+	3.34490i	0.386235	+	0.668979i
$26$		0			0
$27$	−5.61793			−1.08117
$28$		0			0
$29$	9.67008			1.79569			0.897845	−	0.440312i	$-0.145132\pi$
$29$	9.67008			1.79569			0.897845	+	0.440312i	$0.145132\pi$
$30$		0			0
$31$	−0.886751	−	1.53590i	−0.159265	−	0.275855i	0.775339	−	0.631546i	$-0.217579\pi$
$31$	−0.886751	−	1.53590i	−0.159265	−	0.275855i	−0.934604	+	0.355690i	$0.884246\pi$
$32$		0			0
$33$	−0.996326	+	1.72569i	−0.173438	+	0.300404i
$34$		0			0
$35$	−1.95129	−	2.03862i	−0.329828	−	0.344590i
$36$		0			0
$37$	4.46824	−	7.73921i	0.734573	−	1.27232i	−0.220337	−	0.975424i	$-0.570716\pi$
$37$	4.46824	−	7.73921i	0.734573	−	1.27232i	0.954910	−	0.296895i	$-0.0959510\pi$
$38$		0			0
$39$	0.913838	+	1.58281i	0.146331	+	0.253453i
$40$		0			0
$41$	6.52095			1.01840			0.509201	−	0.860648i	$-0.329941\pi$
$41$	6.52095			1.01840			0.509201	+	0.860648i	$0.329941\pi$
$42$		0			0
$43$	−7.24599			−1.10500			−0.552501	−	0.833512i	$-0.686327\pi$
$43$	−7.24599			−1.10500			−0.552501	+	0.833512i	$0.686327\pi$
$44$		0			0
$45$	0.674458	+	1.16820i	0.100542	+	0.174144i
$46$		0			0
$47$	2.40311	−	4.16231i	0.350529	−	0.607135i	−0.635813	−	0.771843i	$-0.719335\pi$
$47$	2.40311	−	4.16231i	0.350529	−	0.607135i	0.986342	+	0.164709i	$0.0526684\pi$
$48$		0			0
$49$	−5.90323	−	3.76190i	−0.843318	−	0.537414i
$50$		0			0
$51$	−0.658657	+	1.14083i	−0.0922305	+	0.159748i
$52$		0			0
$53$	−0.709445	−	1.22880i	−0.0974498	−	0.168788i	0.813179	−	0.582014i	$-0.197735\pi$
$53$	−0.709445	−	1.22880i	−0.0974498	−	0.168788i	−0.910628	+	0.413226i	$0.864402\pi$
$54$		0			0
$55$	1.61341			0.217553
$56$		0			0
$57$	−6.10937			−0.809206
$58$		0			0
$59$	−0.520890	−	0.902208i	−0.0678141	−	0.117457i	0.830125	−	0.557578i	$-0.188269\pi$
$59$	−0.520890	−	0.902208i	−0.0678141	−	0.117457i	−0.897939	+	0.440120i	$0.854936\pi$
$60$		0			0
$61$	6.92473	−	11.9940i	0.886621	−	1.53567i	0.0427771	−	0.999085i	$-0.486379\pi$
$61$	6.92473	−	11.9940i	0.886621	−	1.53567i	0.843844	−	0.536588i	$-0.180287\pi$
$62$		0			0
$63$	2.31366	+	2.41721i	0.291494	+	0.304540i
$64$		0			0
$65$	0.739917	−	1.28157i	0.0917754	−	0.158960i
$66$		0			0
$67$	−6.13093	−	10.6191i	−0.749013	−	1.29733i	−0.948296	−	0.317386i	$-0.897195\pi$
$67$	−6.13093	−	10.6191i	−0.749013	−	1.29733i	0.199284	−	0.979942i	$-0.436139\pi$
$68$		0			0
$69$	−7.66613			−0.922893
$70$		0			0
$71$	−1.86001			−0.220743			−0.110372	−	0.993890i	$-0.535204\pi$
$71$	−1.86001			−0.220743			−0.110372	+	0.993890i	$0.535204\pi$
$72$		0			0
$73$	4.52897	+	7.84441i	0.530076	+	0.918119i	0.999384	+	0.0350844i	$0.0111700\pi$
$73$	4.52897	+	7.84441i	0.530076	+	0.918119i	−0.469308	+	0.883034i	$0.655497\pi$
$74$		0			0
$75$	2.54397	−	4.40628i	0.293752	−	0.508794i
$76$		0			0
$77$	3.88750	−	0.950985i	0.443022	−	0.108375i
$78$		0			0
$79$	2.42267	−	4.19618i	0.272571	−	0.472107i	−0.696948	−	0.717121i	$-0.745459\pi$
$79$	2.42267	−	4.19618i	0.272571	−	0.472107i	0.969519	+	0.245014i	$0.0787926\pi$
$80$		0			0
$81$	1.80327	+	3.12335i	0.200363	+	0.347039i
$82$		0			0
$83$	−8.41568			−0.923741			−0.461871	−	0.886947i	$-0.652822\pi$
$83$	−8.41568			−0.923741			−0.461871	+	0.886947i	$0.652822\pi$
$84$		0			0
$85$	1.06660			0.115690
$86$		0			0
$87$	−6.36927	−	11.0319i	−0.682858	−	1.18274i
$88$		0			0
$89$	−4.30313	+	7.45323i	−0.456130	+	0.790041i	−0.998752	−	0.0499360i	$-0.984098\pi$
$89$	−4.30313	+	7.45323i	−0.456130	+	0.790041i	0.542622	+	0.839977i	$0.317432\pi$
$90$		0			0
$91$	1.02743	−	3.52406i	0.107704	−	0.369422i
$92$		0			0
$93$	−1.16813	+	2.02326i	−0.121130	+	0.209802i
$94$		0			0
$95$	2.47332	+	4.28392i	0.253757	+	0.439521i
$96$		0			0
$97$	−19.5711			−1.98714			−0.993572	−	0.113201i	$-0.963889\pi$
$97$	−19.5711			−1.98714			−0.993572	+	0.113201i	$0.963889\pi$
$98$		0			0
$99$	−1.91304			−0.192267
$100$		0			0
$101$	1.03706	+	1.79624i	0.103191	+	0.178732i	0.912998	−	0.407965i	$-0.133761\pi$
$101$	1.03706	+	1.79624i	0.103191	+	0.178732i	−0.809807	+	0.586697i	$0.800428\pi$
$102$		0			0
$103$	−3.04449	+	5.27321i	−0.299982	+	0.519585i	−0.976132	−	0.217180i	$-0.930314\pi$
$103$	−3.04449	+	5.27321i	−0.299982	+	0.519585i	0.676149	+	0.736765i	$0.263647\pi$
$104$		0			0
$105$	−1.04049	+	3.56884i	−0.101541	+	0.348283i
$106$		0			0
$107$	3.30821	−	5.72998i	0.319817	−	0.553939i	−0.660633	−	0.750709i	$-0.729712\pi$
$107$	3.30821	−	5.72998i	0.319817	−	0.553939i	0.980450	+	0.196770i	$0.0630454\pi$
$108$		0			0
$109$	5.54229	+	9.59953i	0.530855	+	0.919468i	0.999352	+	0.0360028i	$0.0114625\pi$
$109$	5.54229	+	9.59953i	0.530855	+	0.919468i	−0.468496	+	0.883465i	$0.655204\pi$
$110$		0			0
$111$	−11.7721			−1.11736
$112$		0			0
$113$	16.7578			1.57644			0.788222	−	0.615391i	$-0.211002\pi$
$113$	16.7578			1.57644			0.788222	+	0.615391i	$0.211002\pi$
$114$		0			0
$115$	3.10356	+	5.37552i	0.289408	+	0.501270i
$116$		0			0
$117$	−0.877326	+	1.51957i	−0.0811088	+	0.140485i
$118$		0			0
$119$	2.56997	−	0.628683i	0.235589	−	0.0576313i
$120$		0			0
$121$	4.35593	−	7.54469i	0.395993	−	0.685880i
$122$		0			0
$123$	−4.29507	−	7.43928i	−0.387274	−	0.670778i
$124$		0			0
$125$	−9.45263			−0.845469
$126$		0			0
$127$	9.42640			0.836458			0.418229	−	0.908342i	$-0.362651\pi$
$127$	9.42640			0.836458			0.418229	+	0.908342i	$0.362651\pi$
$128$		0			0
$129$	4.77262	+	8.26642i	0.420206	+	0.727818i
$130$		0			0
$131$	−3.03290	+	5.25313i	−0.264985	+	0.458968i	−0.967560	−	0.252642i	$-0.918700\pi$
$131$	−3.03290	+	5.25313i	−0.264985	+	0.458968i	0.702574	+	0.711610i	$0.252034\pi$
$132$		0			0
$133$	8.48449	+	8.86422i	0.735699	+	0.768625i
$134$		0			0
$135$	2.99605	−	5.18932i	0.257859	−	0.446625i
$136$		0			0
$137$	6.00410	+	10.3994i	0.512965	+	0.888481i	0.999887	+	0.0150356i	$0.00478617\pi$
$137$	6.00410	+	10.3994i	0.512965	+	0.888481i	−0.486922	+	0.873445i	$0.661880\pi$
$138$		0			0
$139$	17.7745			1.50762			0.753808	−	0.657095i	$-0.228215\pi$
$139$	17.7745			1.50762			0.753808	+	0.657095i	$0.228215\pi$
$140$		0			0
$141$	−6.33130			−0.533192
$142$		0			0
$143$	1.04935	+	1.81753i	0.0877513	+	0.151990i
$144$		0			0
$145$	−5.15708	+	8.93232i	−0.428272	+	0.741789i
$146$		0			0
$147$	−0.403477	+	9.21237i	−0.0332782	+	0.759824i
$148$		0			0
$149$	1.93128	−	3.34508i	0.158217	−	0.274039i	−0.776009	−	0.630722i	$-0.782759\pi$
$149$	1.93128	−	3.34508i	0.158217	−	0.274039i	0.934226	+	0.356683i	$0.116092\pi$
$150$		0			0
$151$	6.66153	+	11.5381i	0.542108	+	0.938958i	0.998783	+	0.0493243i	$0.0157068\pi$
$151$	6.66153	+	11.5381i	0.542108	+	0.938958i	−0.456675	+	0.889633i	$0.650960\pi$
$152$		0			0
$153$	−1.26468			−0.102243
$154$		0			0
$155$	1.89163			0.151939
$156$		0			0
$157$	−6.60875	−	11.4467i	−0.527436	−	0.913545i	−0.999489	−	0.0319752i	$-0.989820\pi$
$157$	−6.60875	−	11.4467i	−0.527436	−	0.913545i	0.472053	−	0.881570i	$-0.343513\pi$
$158$		0			0
$159$	−0.934563	+	1.61871i	−0.0741156	+	0.128372i
$160$		0			0
$161$	10.6465	+	11.1229i	0.839058	+	0.876611i
$162$		0			0
$163$	6.81807	−	11.8092i	0.534033	−	0.924971i	−0.465177	−	0.885218i	$-0.654009\pi$
$163$	6.81807	−	11.8092i	0.534033	−	0.924971i	0.999210	−	0.0397537i	$-0.0126573\pi$
$164$		0			0
$165$	−1.06269	−	1.84063i	−0.0827300	−	0.143293i
$166$		0			0
$167$	9.98605			0.772744			0.386372	−	0.922343i	$-0.373728\pi$
$167$	9.98605			0.772744			0.386372	+	0.922343i	$0.373728\pi$
$168$		0			0
$169$	−11.0751			−0.851927
$170$		0			0
$171$	−2.93264	−	5.07948i	−0.224264	−	0.388437i
$172$		0			0
$173$	−10.2631	+	17.7761i	−0.780286	+	1.35149i	0.151489	+	0.988459i	$0.451593\pi$
$173$	−10.2631	+	17.7761i	−0.780286	+	1.35149i	−0.931775	+	0.363036i	$0.881740\pi$
$174$		0			0
$175$	−9.92614	+	2.42820i	−0.750346	+	0.183554i
$176$		0			0
$177$	−0.686176	+	1.18849i	−0.0515761	+	0.0893325i
$178$		0			0
$179$	7.52684	+	13.0369i	0.562583	+	0.974422i	0.997270	+	0.0738403i	$0.0235255\pi$
$179$	7.52684	+	13.0369i	0.562583	+	0.974422i	−0.434687	+	0.900581i	$0.643141\pi$
$180$		0			0
$181$	−7.33791			−0.545422			−0.272711	−	0.962096i	$-0.587920\pi$
$181$	−7.33791			−0.545422			−0.272711	+	0.962096i	$0.587920\pi$
$182$		0			0
$183$	−18.2441			−1.34864
$184$		0			0
$185$	4.76584	+	8.25468i	0.350392	+	0.606896i
$186$		0			0
$187$	−0.756331	+	1.31000i	−0.0553084	+	0.0957970i
$188$		0			0
$189$	4.16025	−	14.2696i	0.302614	−	1.03796i
$190$		0			0
$191$	−1.69097	+	2.92885i	−0.122355	+	0.211924i	−0.920696	−	0.390281i	$-0.872378\pi$
$191$	−1.69097	+	2.92885i	−0.122355	+	0.211924i	0.798341	+	0.602205i	$0.205711\pi$
$192$		0			0
$193$	−9.73567	−	16.8627i	−0.700789	−	1.21380i	−0.968190	−	0.250216i	$-0.919498\pi$
$193$	−9.73567	−	16.8627i	−0.700789	−	1.21380i	0.267401	−	0.963585i	$-0.413835\pi$
$194$		0			0
$195$	−1.94941			−0.139600
$196$		0			0
$197$	21.4174			1.52593			0.762963	−	0.646442i	$-0.223744\pi$
$197$	21.4174			1.52593			0.762963	+	0.646442i	$0.223744\pi$
$198$		0			0
$199$	13.6722	+	23.6809i	0.969194	+	1.67869i	0.697898	+	0.716197i	$0.254119\pi$
$199$	13.6722	+	23.6809i	0.969194	+	1.67869i	0.271296	+	0.962496i	$0.412548\pi$
$200$		0			0
$201$	−8.07637	+	13.9887i	−0.569663	+	0.986686i
$202$		0			0
$203$	−7.16100	+	24.5620i	−0.502603	+	1.72392i
$204$		0			0
$205$	−3.47764	+	6.02345i	−0.242889	+	0.420696i
$206$		0			0
$207$	−3.67992	−	6.37380i	−0.255772	−	0.443010i
$208$		0			0
$209$	−7.01535			−0.485262
$210$		0			0
$211$	−17.1191			−1.17853			−0.589265	−	0.807940i	$-0.700583\pi$
$211$	−17.1191			−1.17853			−0.589265	+	0.807940i	$0.700583\pi$
$212$		0			0
$213$	1.22511	+	2.12196i	0.0839433	+	0.145394i
$214$		0			0
$215$	3.86430	−	6.69317i	0.263543	−	0.456470i
$216$		0			0
$217$	4.55785	−	1.11497i	0.309407	−	0.0756891i
$218$		0			0
$219$	5.96608	−	10.3336i	0.403150	−	0.698277i
$220$		0			0
$221$	0.693713	+	1.20155i	0.0466642	+	0.0808247i
$222$		0			0
$223$	−1.47921			−0.0990555			−0.0495277	−	0.998773i	$-0.515772\pi$
$223$	−1.47921			−0.0990555			−0.0495277	+	0.998773i	$0.515772\pi$
$224$		0			0
$225$	4.88465			0.325643
$226$		0			0
$227$	−0.405833	−	0.702924i	−0.0269361	−	0.0466547i	0.852243	−	0.523146i	$-0.175242\pi$
$227$	−0.405833	−	0.702924i	−0.0269361	−	0.0466547i	−0.879179	+	0.476491i	$0.841908\pi$
$228$		0			0
$229$	3.99803	−	6.92479i	0.264197	−	0.457603i	−0.703156	−	0.711036i	$-0.748226\pi$
$229$	3.99803	−	6.92479i	0.264197	−	0.457603i	0.967353	+	0.253433i	$0.0815596\pi$
$230$		0			0
$231$	−3.64544	−	3.80860i	−0.239852	−	0.250587i
$232$		0			0
$233$	−6.54149	+	11.3302i	−0.428547	+	0.742266i	−0.996744	−	0.0806266i	$-0.974308\pi$
$233$	−6.54149	+	11.3302i	−0.428547	+	0.742266i	0.568197	+	0.822893i	$0.307641\pi$
$234$		0			0
$235$	2.56317	+	4.43953i	0.167203	+	0.289603i
$236$		0			0
$237$	−6.38283			−0.414609
$238$		0			0
$239$	−24.5903			−1.59061			−0.795307	−	0.606206i	$-0.792691\pi$
$239$	−24.5903			−1.59061			−0.795307	+	0.606206i	$0.792691\pi$
$240$		0			0
$241$	−3.59007	−	6.21818i	−0.231256	−	0.400548i	0.726922	−	0.686720i	$-0.240950\pi$
$241$	−3.59007	−	6.21818i	−0.231256	−	0.400548i	−0.958178	+	0.286172i	$0.907617\pi$
$242$		0			0
$243$	−6.05142	+	10.4814i	−0.388199	+	0.672380i
$244$		0			0
$245$	6.62310	−	3.44662i	0.423134	−	0.220197i
$246$		0			0
$247$	−3.21726	+	5.57246i	−0.204710	+	0.354567i
$248$		0			0
$249$	5.54305	+	9.60085i	0.351277	+	0.608429i
$250$		0			0
$251$	−3.88964			−0.245512			−0.122756	−	0.992437i	$-0.539173\pi$
$251$	−3.88964			−0.245512			−0.122756	+	0.992437i	$0.539173\pi$
$252$		0			0
$253$	−8.80296			−0.553437
$254$		0			0
$255$	−0.702527	−	1.21681i	−0.0439940	−	0.0761998i
$256$		0			0
$257$	3.21510	−	5.56872i	0.200553	−	0.347367i	−0.748154	−	0.663525i	$-0.769060\pi$
$257$	3.21510	−	5.56872i	0.200553	−	0.347367i	0.948707	+	0.316158i	$0.102393\pi$
$258$		0			0
$259$	16.3488	+	17.0805i	1.01586	+	1.06133i
$260$		0			0
$261$	6.11479	−	10.5911i	0.378496	−	0.655574i
$262$		0			0
$263$	12.2689	+	21.2504i	0.756536	+	1.31036i	0.944607	+	0.328203i	$0.106443\pi$
$263$	12.2689	+	21.2504i	0.756536	+	1.31036i	−0.188071	+	0.982155i	$0.560224\pi$
$264$		0			0
$265$	1.51340			0.0929671
$266$		0			0
$267$	11.3371			0.693822
$268$		0			0
$269$	−6.05708	−	10.4912i	−0.369307	−	0.639658i	0.620150	−	0.784483i	$-0.287072\pi$
$269$	−6.05708	−	10.4912i	−0.369307	−	0.639658i	−0.989457	+	0.144825i	$0.953738\pi$
$270$		0			0
$271$	−2.64401	+	4.57955i	−0.160612	+	0.278188i	−0.935088	−	0.354415i	$-0.884680\pi$
$271$	−2.64401	+	4.57955i	−0.160612	+	0.278188i	0.774476	+	0.632603i	$0.218013\pi$
$272$		0			0
$273$	−4.69708	+	1.14903i	−0.284280	+	0.0695424i
$274$		0			0
$275$	2.92122	−	5.05970i	0.176156	−	0.305111i
$276$		0			0
$277$	−6.17834	−	10.7012i	−0.371221	−	0.642973i	0.618533	−	0.785759i	$-0.287727\pi$
$277$	−6.17834	−	10.7012i	−0.371221	−	0.642973i	−0.989754	+	0.142786i	$0.954394\pi$
$278$		0			0
$279$	−2.24292			−0.134280
$280$		0			0
$281$	−11.6504			−0.695006			−0.347503	−	0.937679i	$-0.612970\pi$
$281$	−11.6504			−0.695006			−0.347503	+	0.937679i	$0.612970\pi$
$282$		0			0
$283$	−14.4949	−	25.1059i	−0.861631	−	1.49239i	−0.870354	−	0.492426i	$-0.836110\pi$
$283$	−14.4949	−	25.1059i	−0.861631	−	1.49239i	0.00872345	−	0.999962i	$-0.497223\pi$
$284$		0			0
$285$	3.25814	−	5.64327i	0.192996	−	0.334278i
$286$		0			0
$287$	−4.82896	+	16.5632i	−0.285045	+	0.977697i
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	12.8906	+	22.3273i	0.755663	+	1.30885i
$292$		0			0
$293$	1.98538			0.115987			0.0579936	−	0.998317i	$-0.481530\pi$
$293$	1.98538			0.115987			0.0579936	+	0.998317i	$0.481530\pi$
$294$		0			0
$295$	1.11117			0.0646947
$296$		0			0
$297$	4.24901	+	7.35951i	0.246553	+	0.427042i
$298$		0			0
$299$	−4.03707	+	6.99241i	−0.233470	+	0.404381i
$300$		0			0
$301$	5.36588	−	18.4048i	0.309284	−	1.06084i
$302$		0			0
$303$	1.36613	−	2.36621i	0.0784822	−	0.135935i
$304$		0			0
$305$	7.38595	+	12.7928i	0.422918	+	0.732516i
$306$		0			0
$307$	−22.3558			−1.27591			−0.637956	−	0.770073i	$-0.720220\pi$
$307$	−22.3558			−1.27591			−0.637956	+	0.770073i	$0.720220\pi$
$308$		0			0
$309$	8.02110			0.456304
$310$		0			0
$311$	−7.46450	−	12.9289i	−0.423273	−	0.733131i	0.572984	−	0.819566i	$-0.305786\pi$
$311$	−7.46450	−	12.9289i	−0.423273	−	0.733131i	−0.996257	+	0.0864357i	$0.972452\pi$
$312$		0			0
$313$	−9.42498	+	16.3246i	−0.532732	+	0.922718i	0.466538	+	0.884501i	$0.345501\pi$
$313$	−9.42498	+	16.3246i	−0.532732	+	0.922718i	−0.999269	+	0.0382169i	$0.987832\pi$
$314$		0			0
$315$	−3.46668	+	0.848040i	−0.195325	+	0.0477817i
$316$		0			0
$317$	10.3571	−	17.9391i	0.581714	−	1.00756i	−0.413562	−	0.910476i	$-0.635716\pi$
$317$	10.3571	−	17.9391i	0.581714	−	1.00756i	0.995276	−	0.0970826i	$-0.0309511\pi$
$318$		0			0
$319$	−7.31379	−	12.6679i	−0.409493	−	0.709264i
$320$		0			0
$321$	−8.71590			−0.486474
$322$		0			0
$323$	−4.63775			−0.258051
$324$		0			0
$325$	−2.67936	−	4.64079i	−0.148624	−	0.257425i
$326$		0			0
$327$	7.30094	−	12.6456i	0.403743	−	0.699303i
$328$		0			0
$329$	8.79269	+	9.18622i	0.484757	+	0.506452i
$330$		0			0
$331$	17.3963	−	30.1312i	0.956186	−	1.65616i	0.224555	−	0.974462i	$-0.427907\pi$
$331$	17.3963	−	30.1312i	0.956186	−	1.65616i	0.731631	−	0.681701i	$-0.238759\pi$
$332$		0			0
$333$	−5.65090	−	9.78764i	−0.309667	−	0.536359i
$334$		0			0
$335$	13.0786			0.714558
$336$		0			0
$337$	0.237639			0.0129450			0.00647250	−	0.999979i	$-0.497940\pi$
$337$	0.237639			0.0129450			0.00647250	+	0.999979i	$0.497940\pi$
$338$		0			0
$339$	−11.0377	−	19.1178i	−0.599484	−	1.03834i
$340$		0			0
$341$	−1.34136	+	2.32330i	−0.0726385	+	0.125814i
$342$		0			0
$343$	13.9268	−	12.2084i	0.751974	−	0.659192i
$344$		0			0
$345$	4.08836	−	7.08125i	0.220110	−	0.381242i
$346$		0			0
$347$	13.2691	+	22.9828i	0.712325	+	1.23378i	0.963982	+	0.265966i	$0.0856909\pi$
$347$	13.2691	+	22.9828i	0.712325	+	1.23378i	−0.251658	+	0.967816i	$0.580976\pi$
$348$		0			0
$349$	−3.16794			−0.169576			−0.0847880	−	0.996399i	$-0.527021\pi$
$349$	−3.16794			−0.169576			−0.0847880	+	0.996399i	$0.527021\pi$
$350$		0			0
$351$	7.79445			0.416037
$352$		0			0
$353$	−1.46566	−	2.53861i	−0.0780094	−	0.135116i	0.824382	−	0.566034i	$-0.191523\pi$
$353$	−1.46566	−	2.53861i	−0.0780094	−	0.135116i	−0.902391	+	0.430918i	$0.858190\pi$
$354$		0			0
$355$	0.991950	−	1.71811i	0.0526472	−	0.0911877i
$356$		0			0
$357$	−2.40995	−	2.51781i	−0.127548	−	0.133257i
$358$		0			0
$359$	3.89551	−	6.74722i	0.205597	−	0.356105i	−0.744726	−	0.667371i	$-0.767420\pi$
$359$	3.89551	−	6.74722i	0.205597	−	0.356105i	0.950323	+	0.311266i	$0.100753\pi$
$360$		0			0
$361$	−1.25436	−	2.17261i	−0.0660187	−	0.114348i
$362$		0			0
$363$	−11.4763			−0.602347
$364$		0			0
$365$	−9.66125			−0.505693
$366$		0			0
$367$	5.63892	+	9.76690i	0.294349	+	0.509828i	0.974833	−	0.222935i	$-0.0715638\pi$
$367$	5.63892	+	9.76690i	0.294349	+	0.509828i	−0.680484	+	0.732763i	$0.738230\pi$
$368$		0			0
$369$	4.12346	−	7.14205i	0.214659	−	0.371800i
$370$		0			0
$371$	3.64651	−	0.892032i	0.189317	−	0.0463120i
$372$		0			0
$373$	−13.6904	+	23.7124i	−0.708861	+	1.22778i	0.256418	+	0.966566i	$0.417458\pi$
$373$	−13.6904	+	23.7124i	−0.708861	+	1.22778i	−0.965280	+	0.261218i	$0.915876\pi$
$374$		0			0
$375$	6.22604	+	10.7838i	0.321512	+	0.556874i
$376$		0			0
$377$	−13.4165			−0.690986
$378$		0			0
$379$	1.43839			0.0738849			0.0369425	−	0.999317i	$-0.488238\pi$
$379$	1.43839			0.0738849			0.0369425	+	0.999317i	$0.488238\pi$
$380$		0			0
$381$	−6.20877	−	10.7539i	−0.318085	−	0.550939i
$382$		0			0
$383$	−15.6698	+	27.1409i	−0.800688	+	1.38683i	0.118475	+	0.992957i	$0.462199\pi$
$383$	−15.6698	+	27.1409i	−0.800688	+	1.38683i	−0.919164	+	0.393876i	$0.871134\pi$
$384$		0			0
$385$	−1.19478	+	4.09807i	−0.0608917	+	0.208857i
$386$		0			0
$387$	−4.58193	+	7.93614i	−0.232913	+	0.403417i
$388$		0			0
$389$	−1.57183	−	2.72249i	−0.0796950	−	0.138036i	0.823423	−	0.567428i	$-0.192061\pi$
$389$	−1.57183	−	2.72249i	−0.0796950	−	0.138036i	−0.903118	+	0.429392i	$0.858728\pi$
$390$		0			0
$391$	−5.81951			−0.294305
$392$		0			0
$393$	7.99056			0.403070
$394$		0			0
$395$	2.58403	+	4.47567i	0.130016	+	0.225195i
$396$		0			0
$397$	−7.60110	+	13.1655i	−0.381488	+	0.660757i	−0.991275	−	0.131808i	$-0.957922\pi$
$397$	−7.60110	+	13.1655i	−0.381488	+	0.660757i	0.609787	+	0.792566i	$0.291255\pi$
$398$		0			0
$399$	4.52418	−	15.5178i	0.226492	−	0.776863i
$400$		0			0
$401$	8.74437	−	15.1457i	0.436673	−	0.756340i	−0.560757	−	0.827980i	$-0.689490\pi$
$401$	8.74437	−	15.1457i	0.436673	−	0.756340i	0.997431	+	0.0716400i	$0.0228233\pi$
$402$		0			0
$403$	1.23030	+	2.13094i	0.0612857	+	0.106150i
$404$		0			0
$405$	−3.84675			−0.191146
$406$		0			0
$407$	−13.5179			−0.670056
$408$		0			0
$409$	−7.71289	−	13.3591i	−0.381378	−	0.660566i	0.609882	−	0.792493i	$-0.291217\pi$
$409$	−7.71289	−	13.3591i	−0.381378	−	0.660566i	−0.991259	+	0.131927i	$0.957884\pi$
$410$		0			0
$411$	7.90929	−	13.6993i	0.390136	−	0.675736i
$412$		0			0
$413$	2.67735	−	0.654949i	0.131744	−	0.0322279i
$414$		0			0
$415$	4.48810	−	7.77362i	0.220312	−	0.381592i
$416$		0			0
$417$	−11.7073	−	20.2777i	−0.573310	−	0.993002i
$418$		0			0
$419$	34.8605			1.70305			0.851525	−	0.524315i	$-0.175678\pi$
$419$	34.8605			1.70305			0.851525	+	0.524315i	$0.175678\pi$
$420$		0			0
$421$	0.607290			0.0295975			0.0147987	−	0.999890i	$-0.495289\pi$
$421$	0.607290			0.0295975			0.0147987	+	0.999890i	$0.495289\pi$
$422$		0			0
$423$	−3.03917	−	5.26399i	−0.147769	−	0.255944i
$424$		0			0
$425$	1.93118	−	3.34490i	0.0936759	−	0.162251i
$426$		0			0
$427$	25.3368	+	26.4708i	1.22613	+	1.28101i
$428$		0			0
$429$	1.38233	−	2.39426i	0.0667394	−	0.115596i
$430$		0			0
$431$	1.12361	+	1.94615i	0.0541224	+	0.0937428i	0.891817	−	0.452396i	$-0.149431\pi$
$431$	1.12361	+	1.94615i	0.0541224	+	0.0937428i	−0.837695	+	0.546139i	$0.816097\pi$
$432$		0			0
$433$	−10.7841			−0.518250			−0.259125	−	0.965844i	$-0.583434\pi$
$433$	−10.7841			−0.518250			−0.259125	+	0.965844i	$0.583434\pi$
$434$		0			0
$435$	13.5870			0.651446
$436$		0			0
$437$	−13.4947	−	23.3735i	−0.645540	−	1.11811i
$438$		0			0
$439$	9.32347	−	16.1487i	0.444985	−	0.770737i	−0.553066	−	0.833137i	$-0.686542\pi$
$439$	9.32347	−	16.1487i	0.444985	−	0.770737i	0.998051	+	0.0624007i	$0.0198757\pi$
$440$		0			0
$441$	−7.85306	+	4.08669i	−0.373955	+	0.194604i
$442$		0			0
$443$	−3.10496	+	5.37796i	−0.147521	+	0.255514i	−0.930311	−	0.366772i	$-0.880463\pi$
$443$	−3.10496	+	5.37796i	−0.147521	+	0.255514i	0.782789	+	0.622287i	$0.213796\pi$
$444$		0			0
$445$	−4.58973	−	7.94965i	−0.217574	−	0.376850i
$446$		0			0
$447$	−5.08821			−0.240664
$448$		0			0
$449$	26.2307			1.23790			0.618952	−	0.785428i	$-0.287557\pi$
$449$	26.2307			1.23790			0.618952	+	0.785428i	$0.287557\pi$
$450$		0			0
$451$	−4.93200	−	8.54247i	−0.232239	−	0.402249i
$452$		0			0
$453$	8.77533	−	15.1993i	0.412301	−	0.714126i
$454$		0			0
$455$	2.70727	+	2.82844i	0.126919	+	0.132599i
$456$		0			0
$457$	−5.67004	+	9.82081i	−0.265233	+	0.459398i	−0.967625	−	0.252393i	$-0.918782\pi$
$457$	−5.67004	+	9.82081i	−0.265233	+	0.459398i	0.702391	+	0.711791i	$0.252116\pi$
$458$		0			0
$459$	2.80896	+	4.86527i	0.131111	+	0.227091i
$460$		0			0
$461$	40.2862			1.87632			0.938159	−	0.346206i	$-0.112530\pi$
$461$	40.2862			1.87632			0.938159	+	0.346206i	$0.112530\pi$
$462$		0			0
$463$	−5.75634			−0.267520			−0.133760	−	0.991014i	$-0.542705\pi$
$463$	−5.75634			−0.267520			−0.133760	+	0.991014i	$0.542705\pi$
$464$		0			0
$465$	−1.24593	−	2.15802i	−0.0577788	−	0.100076i
$466$		0			0
$467$	5.09086	−	8.81763i	0.235577	−	0.408031i	−0.723863	−	0.689943i	$-0.757635\pi$
$467$	5.09086	−	8.81763i	0.235577	−	0.408031i	0.959440	+	0.281912i	$0.0909687\pi$
$468$		0			0
$469$	31.5127	−	7.70883i	1.45512	−	0.355961i
$470$		0			0
$471$	−8.70580	+	15.0789i	−0.401142	+	0.694799i
$472$		0			0
$473$	5.48037	+	9.49227i	0.251988	+	0.436455i
$474$		0			0
$475$	17.9126			0.821888
$476$		0			0
$477$	−1.79444			−0.0821620
$478$		0			0
$479$	−3.09337	−	5.35787i	−0.141340	−	0.244808i	0.786662	−	0.617384i	$-0.211808\pi$
$479$	−3.09337	−	5.35787i	−0.141340	−	0.244808i	−0.928001	+	0.372577i	$0.878474\pi$
$480$		0			0
$481$	−6.19934	+	10.7376i	−0.282666	+	0.489591i
$482$		0			0
$483$	5.67700	−	19.4720i	0.258313	−	0.886006i
$484$		0			0
$485$	10.4373	−	18.0780i	0.473934	−	0.820878i
$486$		0			0
$487$	−9.31247	−	16.1297i	−0.421988	−	0.730905i	0.574145	−	0.818753i	$-0.305334\pi$
$487$	−9.31247	−	16.1297i	−0.421988	−	0.730905i	−0.996134	+	0.0878479i	$0.972001\pi$
$488$		0			0
$489$	−17.9631			−0.812319
$490$		0			0
$491$	−24.1755			−1.09102			−0.545512	−	0.838103i	$-0.683665\pi$
$491$	−24.1755			−1.09102			−0.545512	+	0.838103i	$0.683665\pi$
$492$		0			0
$493$	−4.83504	−	8.37454i	−0.217759	−	0.377170i
$494$		0			0
$495$	1.02023	−	1.76709i	0.0458558	−	0.0794246i
$496$		0			0
$497$	1.37740	−	4.72444i	0.0617847	−	0.211920i
$498$		0			0
$499$	−7.14946	+	12.3832i	−0.320054	+	0.554350i	−0.980499	−	0.196525i	$-0.937034\pi$
$499$	−7.14946	+	12.3832i	−0.320054	+	0.554350i	0.660445	+	0.750874i	$0.270368\pi$
$500$		0			0
$501$	−6.57739	−	11.3924i	−0.293856	−	0.508973i
$502$		0			0
$503$	38.5611			1.71935			0.859676	−	0.510839i	$-0.170665\pi$
$503$	38.5611			1.71935			0.859676	+	0.510839i	$0.170665\pi$
$504$		0			0
$505$	−2.21226			−0.0984444
$506$		0			0
$507$	7.29466	+	12.6347i	0.323967	+	0.561128i
$508$		0			0
$509$	1.32765	−	2.29956i	0.0588471	−	0.101926i	−0.835101	−	0.550097i	$-0.814591\pi$
$509$	1.32765	−	2.29956i	0.0588471	−	0.101926i	0.893948	+	0.448170i	$0.147924\pi$
$510$		0			0
$511$	−23.2787	+	5.69458i	−1.02979	+	0.251913i
$512$		0			0
$513$	−13.0273	+	22.5639i	−0.575168	+	0.996220i
$514$		0			0
$515$	−3.24726	−	5.62443i	−0.143092	−	0.247842i
$516$		0			0
$517$	−7.27018			−0.319742
$518$		0			0
$519$	27.0394			1.18690
$520$		0			0
$521$	9.49867	+	16.4522i	0.416144	+	0.720783i	0.995548	−	0.0942576i	$-0.0300477\pi$
$521$	9.49867	+	16.4522i	0.416144	+	0.720783i	−0.579403	+	0.815041i	$0.696714\pi$
$522$		0			0
$523$	5.76616	−	9.98729i	0.252137	−	0.436714i	−0.711977	−	0.702203i	$-0.752200\pi$
$523$	5.76616	−	9.98729i	0.252137	−	0.436714i	0.964114	+	0.265489i	$0.0855334\pi$
$524$		0			0
$525$	9.30808	+	9.72467i	0.406238	+	0.424420i
$526$		0			0
$527$	−0.886751	+	1.53590i	−0.0386275	+	0.0669048i
$528$		0			0
$529$	−5.43335	−	9.41085i	−0.236233	−	0.409167i
$530$		0			0
$531$	−1.31752			−0.0571755
$532$		0			0
$533$	−9.04733			−0.391883
$534$		0			0
$535$	3.52855	+	6.11163i	0.152553	+	0.264229i
$536$		0			0
$537$	9.91522	−	17.1737i	0.427873	−	0.741098i
$538$		0			0
$539$	−0.463310	+	10.5785i	−0.0199562	+	0.455648i
$540$		0			0
$541$	6.66960	−	11.5521i	0.286749	−	0.496663i	−0.686283	−	0.727334i	$-0.740759\pi$
$541$	6.66960	−	11.5521i	0.286749	−	0.496663i	0.973032	+	0.230671i	$0.0740923\pi$
$542$		0			0
$543$	4.83317	+	8.37129i	0.207411	+	0.359246i
$544$		0			0
$545$	−11.8229			−0.506436
$546$		0			0
$547$	−4.90723			−0.209818			−0.104909	−	0.994482i	$-0.533455\pi$
$547$	−4.90723			−0.209818			−0.104909	+	0.994482i	$0.533455\pi$
$548$		0			0
$549$	−8.75758	−	15.1686i	−0.373765	−	0.647379i
$550$		0			0
$551$	22.4237	−	38.8390i	0.955282	−	1.65460i
$552$		0			0
$553$	8.86425	+	9.26098i	0.376946	+	0.393817i
$554$		0			0
$555$	6.27811	−	10.8740i	0.266491	−	0.461576i
$556$		0			0
$557$	−7.11057	−	12.3159i	−0.301284	−	0.521840i	0.675143	−	0.737687i	$-0.264082\pi$
$557$	−7.11057	−	12.3159i	−0.301284	−	0.521840i	−0.976427	+	0.215847i	$0.930749\pi$
$558$		0			0
$559$	10.0533			0.425208
$560$		0			0
$561$	1.99265			0.0841299
$562$		0			0
$563$	1.94926	+	3.37622i	0.0821517	+	0.142291i	0.904174	−	0.427164i	$-0.140487\pi$
$563$	1.94926	+	3.37622i	0.0821517	+	0.142291i	−0.822022	+	0.569455i	$0.807154\pi$
$564$		0			0
$565$	−8.93699	+	15.4793i	−0.375982	+	0.651220i
$566$		0			0
$567$	−9.26869	+	2.26737i	−0.389249	+	0.0952204i
$568$		0			0
$569$	18.4456	−	31.9487i	0.773279	−	1.33936i	−0.162478	−	0.986712i	$-0.551949\pi$
$569$	18.4456	−	31.9487i	0.773279	−	1.33936i	0.935757	−	0.352646i	$-0.114718\pi$
$570$		0			0
$571$	13.1072	+	22.7024i	0.548521	+	0.950066i	0.998376	+	0.0569649i	$0.0181423\pi$
$571$	13.1072	+	22.7024i	0.548521	+	0.950066i	−0.449855	+	0.893102i	$0.648524\pi$
$572$		0			0
$573$	4.45509			0.186114
$574$		0			0
$575$	22.4770			0.937356
$576$		0			0
$577$	4.03483	+	6.98853i	0.167972	+	0.290936i	0.937707	−	0.347428i	$-0.112945\pi$
$577$	4.03483	+	6.98853i	0.167972	+	0.290936i	−0.769735	+	0.638364i	$0.779611\pi$
$578$		0			0
$579$	−12.8249	+	22.2134i	−0.532986	+	0.923159i
$580$		0			0
$581$	6.23207	−	21.3759i	0.258550	−	0.886820i
$582$		0			0
$583$	−1.07315	+	1.85875i	−0.0444454	+	0.0769817i
$584$		0			0
$585$	−0.935760	−	1.62078i	−0.0386889	−	0.0670111i
$586$		0			0
$587$	−15.7307			−0.649276			−0.324638	−	0.945838i	$-0.605242\pi$
$587$	−15.7307			−0.649276			−0.324638	+	0.945838i	$0.605242\pi$
$588$		0			0
$589$	−8.22506			−0.338908
$590$		0			0
$591$	−14.1067	−	24.4336i	−0.580273	−	1.00506i
$592$		0			0
$593$	10.4944	−	18.1768i	0.430953	−	0.746433i	−0.566003	−	0.824403i	$-0.691511\pi$
$593$	10.4944	−	18.1768i	0.430953	−	0.746433i	0.996956	+	0.0779708i	$0.0248441\pi$
$594$		0			0
$595$	−0.789854	+	2.70918i	−0.0323808	+	0.111066i
$596$		0			0
$597$	18.0105	−	31.1952i	0.737122	−	1.27673i
$598$		0			0
$599$	15.3369	+	26.5644i	0.626651	+	1.08539i	0.988219	+	0.153045i	$0.0489080\pi$
$599$	15.3369	+	26.5644i	0.626651	+	1.08539i	−0.361568	+	0.932346i	$0.617759\pi$
$600$		0			0
$601$	−42.5012			−1.73366			−0.866829	−	0.498605i	$-0.833846\pi$
$601$	−42.5012			−1.73366			−0.866829	+	0.498605i	$0.833846\pi$
$602$		0			0
$603$	−15.5074			−0.631509
$604$		0			0
$605$	4.64605	+	8.04720i	0.188889	+	0.327165i
$606$		0			0
$607$	−7.52083	+	13.0265i	−0.305261	+	0.528728i	−0.977319	−	0.211771i	$-0.932077\pi$
$607$	−7.52083	+	13.0265i	−0.305261	+	0.528728i	0.672058	+	0.740498i	$0.265410\pi$
$608$		0			0
$609$	32.7377	−	8.00851i	1.32660	−	0.324521i
$610$		0			0
$611$	−3.33413	+	5.77489i	−0.134885	+	0.233627i
$612$		0			0
$613$	−10.8059	−	18.7164i	−0.436447	−	0.755949i	0.560965	−	0.827839i	$-0.310430\pi$
$613$	−10.8059	−	18.7164i	−0.436447	−	0.755949i	−0.997413	+	0.0718907i	$0.977097\pi$
$614$		0			0
$615$	9.16229			0.369459
$616$		0			0
$617$	−39.1713			−1.57698			−0.788489	−	0.615048i	$-0.789136\pi$
$617$	−39.1713			−1.57698			−0.788489	+	0.615048i	$0.789136\pi$
$618$		0			0
$619$	−7.49401	−	12.9800i	−0.301210	−	0.521710i	0.675201	−	0.737634i	$-0.264057\pi$
$619$	−7.49401	−	12.9800i	−0.301210	−	0.521710i	−0.976410	+	0.215924i	$0.930724\pi$
$620$		0			0
$621$	−16.3468	+	28.3135i	−0.655974	+	1.13618i
$622$		0			0
$623$	−15.7446	−	16.4493i	−0.630795	−	0.659027i
$624$		0			0
$625$	−4.61478	+	7.99303i	−0.184591	+	0.319721i
$626$		0			0
$627$	4.62071	+	8.00331i	0.184533	+	0.319621i
$628$		0			0
$629$	−8.93647			−0.356320
$630$		0			0
$631$	5.71290			0.227427			0.113713	−	0.993514i	$-0.463725\pi$
$631$	5.71290			0.227427			0.113713	+	0.993514i	$0.463725\pi$
$632$		0			0
$633$	11.2757	+	19.5300i	0.448167	+	0.776248i
$634$		0			0
$635$	−5.02712	+	8.70723i	−0.199495	+	0.345536i
$636$		0			0
$637$	8.19029	+	5.21936i	0.324511	+	0.206798i
$638$		0			0
$639$	−1.17616	+	2.03717i	−0.0465283	+	0.0805894i
$640$		0			0
$641$	−5.13372	−	8.89186i	−0.202770	−	0.351207i	0.746650	−	0.665217i	$-0.231661\pi$
$641$	−5.13372	−	8.89186i	−0.202770	−	0.351207i	−0.949420	+	0.314010i	$0.898328\pi$
$642$		0			0
$643$	−26.7479			−1.05483			−0.527417	−	0.849606i	$-0.676840\pi$
$643$	−26.7479			−1.05483			−0.527417	+	0.849606i	$0.676840\pi$
$644$		0			0
$645$	−10.1810			−0.400877
$646$		0			0
$647$	5.91752	+	10.2494i	0.232642	+	0.402947i	0.958585	−	0.284808i	$-0.0919298\pi$
$647$	5.91752	+	10.2494i	0.232642	+	0.402947i	−0.725943	+	0.687755i	$0.758596\pi$
$648$		0			0
$649$	−0.787931	+	1.36474i	−0.0309290	+	0.0535706i
$650$		0			0
$651$	−4.27405	−	4.46534i	−0.167513	−	0.175011i
$652$		0			0
$653$	−16.6634	+	28.8618i	−0.652088	+	1.12945i	0.330527	+	0.943797i	$0.392774\pi$
$653$	−16.6634	+	28.8618i	−0.652088	+	1.12945i	−0.982615	+	0.185654i	$0.940560\pi$
$654$		0			0
$655$	−3.23490	−	5.60301i	−0.126398	−	0.218928i
$656$		0			0
$657$	11.4554			0.446918
$658$		0			0
$659$	−5.18658			−0.202040			−0.101020	−	0.994884i	$-0.532211\pi$
$659$	−5.18658			−0.202040			−0.101020	+	0.994884i	$0.532211\pi$
$660$		0			0
$661$	−10.0280	−	17.3690i	−0.390044	−	0.675576i	0.602411	−	0.798186i	$-0.294207\pi$
$661$	−10.0280	−	17.3690i	−0.390044	−	0.675576i	−0.992455	+	0.122610i	$0.960874\pi$
$662$		0			0
$663$	0.913838	−	1.58281i	0.0354905	−	0.0614714i
$664$		0			0
$665$	−12.7127	+	3.10987i	−0.492979	+	0.120596i
$666$		0			0
$667$	28.1376	−	48.7357i	1.08949	−	1.88705i
$668$		0			0
$669$	0.974295	+	1.68753i	0.0376684	+	0.0652436i
$670$		0			0
$671$	−20.9496			−0.808749
$672$		0			0
$673$	−6.65916			−0.256692			−0.128346	−	0.991729i	$-0.540967\pi$
$673$	−6.65916			−0.256692			−0.128346	+	0.991729i	$0.540967\pi$
$674$		0			0
$675$	−10.8492	−	18.7914i	−0.417586	−	0.723281i
$676$		0			0
$677$	−8.51882	+	14.7550i	−0.327405	+	0.567082i	−0.981996	−	0.188901i	$-0.939507\pi$
$677$	−8.51882	+	14.7550i	−0.327405	+	0.567082i	0.654591	+	0.755983i	$0.272841\pi$
$678$		0			0
$679$	14.4930	−	49.7106i	0.556190	−	1.90772i
$680$		0			0
$681$	−0.534610	+	0.925972i	−0.0204863	+	0.0354833i
$682$		0			0
$683$	17.9906	+	31.1607i	0.688393	+	1.19233i	0.972358	+	0.233496i	$0.0750167\pi$
$683$	17.9906	+	31.1607i	0.688393	+	1.19233i	−0.283965	+	0.958835i	$0.591650\pi$
$684$		0			0
$685$	−12.8080			−0.489368
$686$		0			0
$687$	−10.5333			−0.401872
$688$		0			0
$689$	0.984302	+	1.70486i	0.0374989	+	0.0649500i
$690$		0			0
$691$	−3.32230	+	5.75440i	−0.126386	+	0.218908i	−0.922274	−	0.386537i	$-0.873671\pi$
$691$	−3.32230	+	5.75440i	−0.126386	+	0.218908i	0.795888	+	0.605444i	$0.207005\pi$
$692$		0			0
$693$	1.41666	−	4.85912i	0.0538146	−	0.184583i
$694$		0			0
$695$	−9.47920	+	16.4185i	−0.359567	+	0.622787i
$696$		0			0
$697$	−3.26048	−	5.64731i	−0.123499	−	0.213907i
$698$		0			0
$699$	17.2344			0.651865
$700$		0			0
$701$	2.82579			0.106728			0.0533642	−	0.998575i	$-0.483006\pi$
$701$	2.82579			0.106728			0.0533642	+	0.998575i	$0.483006\pi$
$702$		0			0
$703$	−20.7226	−	35.8925i	−0.781566	−	1.35371i
$704$		0			0
$705$	3.37650	−	5.84826i	0.127166	−	0.220258i
$706$		0			0
$707$	−5.33042	+	1.30396i	−0.200471	+	0.0490405i
$708$		0			0
$709$	12.8729	−	22.2964i	0.483450	−	0.837361i	−0.516369	−	0.856366i	$-0.672717\pi$
$709$	12.8729	−	22.2964i	0.483450	−	0.837361i	0.999819	+	0.0190055i	$0.00605001\pi$
$710$		0			0
$711$	−3.06390	−	5.30683i	−0.114905	−	0.199022i
$712$		0			0
$713$	−10.3209			−0.386521
$714$		0			0
$715$	−2.23849			−0.0837148
$716$		0			0
$717$	16.1966	+	28.0533i	0.604873	+	1.04767i
$718$		0			0
$719$	12.2553	−	21.2268i	0.457045	−	0.791626i	−0.541758	−	0.840535i	$-0.682241\pi$
$719$	12.2553	−	21.2268i	0.457045	−	0.791626i	0.998803	+	0.0489088i	$0.0155744\pi$
$720$		0			0
$721$	−11.1394	−	11.6380i	−0.414854	−	0.433421i
$722$		0			0
$723$	−4.72925	+	8.19129i	−0.175883	+	0.304638i
$724$		0			0
$725$	18.6746	+	32.3454i	0.693559	+	1.20128i
$726$		0			0
$727$	39.3988			1.46122			0.730610	−	0.682795i	$-0.239236\pi$
$727$	39.3988			1.46122			0.730610	+	0.682795i	$0.239236\pi$
$728$		0			0
$729$	26.7629			0.991217
$730$		0			0
$731$	3.62299	+	6.27521i	0.134001	+	0.232097i
$732$		0			0
$733$	−8.45491	+	14.6443i	−0.312289	+	0.540901i	−0.978858	−	0.204543i	$-0.934429\pi$
$733$	−8.45491	+	14.6443i	−0.312289	+	0.540901i	0.666568	+	0.745444i	$0.267762\pi$
$734$		0			0
$735$	−8.29436	−	5.28567i	−0.305942	−	0.194965i
$736$		0			0
$737$	−9.27403	+	16.0631i	−0.341613	+	0.591692i
$738$		0			0
$739$	14.8984	+	25.8048i	0.548047	+	0.949245i	0.998408	+	0.0563984i	$0.0179617\pi$
$739$	14.8984	+	25.8048i	0.548047	+	0.949245i	−0.450362	+	0.892846i	$0.648705\pi$
$740$		0			0
$741$	8.47630			0.311385
$742$		0			0
$743$	0.359789			0.0131994			0.00659968	−	0.999978i	$-0.497899\pi$
$743$	0.359789			0.0131994			0.00659968	+	0.999978i	$0.497899\pi$
$744$		0			0
$745$	2.05991	+	3.56787i	0.0754694	+	0.130717i
$746$		0			0
$747$	−5.32158	+	9.21725i	−0.194706	+	0.337242i
$748$		0			0
$749$	12.1043	+	12.6461i	0.442283	+	0.462078i
$750$		0			0
$751$	1.24776	−	2.16118i	0.0455314	−	0.0788628i	−0.842362	−	0.538913i	$-0.818835\pi$
$751$	1.24776	−	2.16118i	0.0455314	−	0.0788628i	0.887893	+	0.460050i	$0.152169\pi$
$752$		0			0
$753$	2.56194	+	4.43742i	0.0933624	+	0.161708i
$754$		0			0
$755$	−14.2104			−0.517171
$756$		0			0
$757$	−16.0052			−0.581720			−0.290860	−	0.956766i	$-0.593941\pi$
$757$	−16.0052			−0.581720			−0.290860	+	0.956766i	$0.593941\pi$
$758$		0			0
$759$	5.79813	+	10.0427i	0.210459	+	0.364525i
$760$		0			0
$761$	−16.6121	+	28.7730i	−0.602188	+	1.04302i	0.390301	+	0.920687i	$0.372371\pi$
$761$	−16.6121	+	28.7730i	−0.602188	+	1.04302i	−0.992489	+	0.122333i	$0.960962\pi$
$762$		0			0
$763$	−28.4871	+	6.96869i	−1.03130	+	0.252283i
$764$		0			0
$765$	0.674458	−	1.16820i	0.0243851	−	0.0422362i
$766$		0			0
$767$	0.722696	+	1.25175i	0.0260950	+	0.0451979i
$768$		0			0
$769$	−9.74167			−0.351294			−0.175647	−	0.984453i	$-0.556202\pi$
$769$	−9.74167			−0.351294			−0.175647	+	0.984453i	$0.556202\pi$
$770$		0			0
$771$	−8.47060			−0.305061
$772$		0			0
$773$	−1.88424	−	3.26359i	−0.0677713	−	0.117383i	0.830149	−	0.557542i	$-0.188255\pi$
$773$	−1.88424	−	3.26359i	−0.0677713	−	0.117383i	−0.897920	+	0.440159i	$0.854922\pi$
$774$		0			0
$775$	3.42495	−	5.93218i	0.123028	−	0.213090i
$776$		0			0
$777$	8.71764	−	29.9013i	0.312743	−	1.07270i
$778$		0			0
$779$	15.1213	−	26.1908i	0.541775	−	0.938383i
$780$		0			0
$781$	1.40679	+	2.43663i	0.0503388	+	0.0871894i
$782$		0			0
$783$	−54.3258			−1.94145
$784$		0			0
$785$	14.0978			0.503174
$786$		0			0
$787$	2.93842	+	5.08950i	0.104743	+	0.181421i	0.913633	−	0.406539i	$-0.133265\pi$
$787$	2.93842	+	5.08950i	0.104743	+	0.181421i	−0.808890	+	0.587960i	$0.799931\pi$
$788$		0			0
$789$	16.1621	−	27.9935i	0.575385	−	0.996596i
$790$		0			0
$791$	−12.4097	+	42.5649i	−0.441238	+	1.51343i
$792$		0			0
$793$	−9.60755	+	16.6408i	−0.341174	+	0.590931i
$794$		0			0
$795$	−0.996809	−	1.72652i	−0.0353532	−	0.0612335i
$796$		0			0
$797$	51.1852			1.81307			0.906536	−	0.422128i	$-0.138717\pi$
$797$	51.1852			1.81307			0.906536	+	0.422128i	$0.138717\pi$
$798$		0			0
$799$	−4.80622			−0.170032
$800$		0			0
$801$	5.44208	+	9.42597i	0.192287	+	0.333050i
$802$		0			0
$803$	6.85081	−	11.8659i	0.241760	−	0.418740i
$804$		0			0
$805$	−15.9521	+	3.90231i	−0.562238	+	0.137538i
$806$		0			0
$807$	−7.97909	+	13.8202i	−0.280877	+	0.486493i
$808$		0			0
$809$	−16.7943	−	29.0885i	−0.590455	−	1.02270i	−0.994171	−	0.107814i	$-0.965615\pi$
$809$	−16.7943	−	29.0885i	−0.590455	−	1.02270i	0.403716	−	0.914884i	$-0.367718\pi$
$810$		0			0
$811$	13.2015			0.463569			0.231784	−	0.972767i	$-0.425544\pi$
$811$	13.2015			0.463569			0.231784	+	0.972767i	$0.425544\pi$
$812$		0			0
$813$	6.96597			0.244307
$814$		0			0
$815$	7.27219	+	12.5958i	0.254734	+	0.441211i
$816$		0			0
$817$	−16.8025	+	29.1028i	−0.587846	+	1.01818i
$818$		0			0
$819$	−3.21003	−	3.35370i	−0.112168	−	0.117188i
$820$		0			0
$821$	−25.0124	+	43.3227i	−0.872937	+	1.51197i	−0.0139936	+	0.999902i	$0.504454\pi$
$821$	−25.0124	+	43.3227i	−0.872937	+	1.51197i	−0.858944	+	0.512070i	$0.828879\pi$
$822$		0			0
$823$	−0.458951	−	0.794927i	−0.0159980	−	0.0277094i	0.857916	−	0.513791i	$-0.171759\pi$
$823$	−0.458951	−	0.794927i	−0.0159980	−	0.0277094i	−0.873914	+	0.486081i	$0.838426\pi$
$824$		0			0
$825$	−7.69633			−0.267952
$826$		0			0
$827$	28.9682			1.00732			0.503661	−	0.863901i	$-0.331986\pi$
$827$	28.9682			1.00732			0.503661	+	0.863901i	$0.331986\pi$
$828$		0			0
$829$	14.0128	+	24.2708i	0.486683	+	0.842960i	0.999883	−	0.0153095i	$-0.00487336\pi$
$829$	14.0128	+	24.2708i	0.486683	+	0.842960i	−0.513200	+	0.858269i	$0.671540\pi$
$830$		0			0
$831$	−8.13882	+	14.0969i	−0.282333	+	0.489014i
$832$		0			0
$833$	−0.306287	+	6.99330i	−0.0106122	+	0.242303i
$834$		0			0
$835$	−5.32559	+	9.22418i	−0.184299	+	0.319216i
$836$		0			0
$837$	4.98171	+	8.62857i	0.172193	+	0.298247i
$838$		0			0
$839$	−23.9213			−0.825854			−0.412927	−	0.910764i	$-0.635494\pi$
$839$	−23.9213			−0.825854			−0.412927	+	0.910764i	$0.635494\pi$
$840$		0			0
$841$	64.5105			2.22450
$842$		0			0
$843$	7.67364	+	13.2911i	0.264294	+	0.457771i
$844$		0			0
$845$	5.90635	−	10.2301i	0.203185	−	0.351926i
$846$		0			0
$847$	15.9378	+	16.6511i	0.547630	+	0.572140i
$848$		0			0
$849$	−19.0943	+	33.0723i	−0.655315	+	1.13504i
$850$		0			0
$851$	−26.0029	−	45.0384i	−0.891369	−	1.54390i
$852$		0			0
$853$	9.31907			0.319079			0.159540	−	0.987192i	$-0.448999\pi$
$853$	9.31907			0.319079			0.159540	+	0.987192i	$0.448999\pi$
$854$		0			0
$855$	6.25593			0.213948
$856$		0			0
$857$	6.62222	+	11.4700i	0.226211	+	0.391808i	0.956682	−	0.291135i	$-0.0940329\pi$
$857$	6.62222	+	11.4700i	0.226211	+	0.391808i	−0.730471	+	0.682943i	$0.760700\pi$
$858$		0			0
$859$	16.7311	−	28.9792i	0.570859	−	0.988757i	−0.425619	−	0.904902i	$-0.639944\pi$
$859$	16.7311	−	28.9792i	0.570859	−	0.988757i	0.996478	−	0.0838543i	$-0.0267230\pi$
$860$		0			0
$861$	22.0764	−	5.40048i	0.752363	−	0.184048i
$862$		0			0
$863$	−19.5309	+	33.8285i	−0.664839	+	1.15153i	0.314491	+	0.949261i	$0.398166\pi$
$863$	−19.5309	+	33.8285i	−0.664839	+	1.15153i	−0.979329	+	0.202274i	$0.935167\pi$
$864$		0			0
$865$	−10.9466	−	18.9601i	−0.372196	−	0.644663i
$866$		0			0
$867$	1.31731			0.0447384
$868$		0			0
$869$	−7.32935			−0.248631
$870$		0			0
$871$	8.50621	+	14.7332i	0.288222	+	0.499215i
$872$		0			0
$873$	−12.3756	+	21.4352i	−0.418851	+	0.725471i
$874$		0			0
$875$	6.99996	−	24.0097i	0.236642	−	0.811676i
$876$		0			0
$877$	−14.7339	+	25.5199i	−0.497529	+	0.861746i	−0.999996	−	0.00285076i	$-0.999093\pi$
$877$	−14.7339	+	25.5199i	−0.497529	+	0.861746i	0.502467	+	0.864597i	$0.332426\pi$
$878$		0			0
$879$	−1.30769	−	2.26498i	−0.0441072	−	0.0763958i
$880$		0			0
$881$	33.8065			1.13897			0.569485	−	0.822001i	$-0.307143\pi$
$881$	33.8065			1.13897			0.569485	+	0.822001i	$0.307143\pi$
$882$		0			0
$883$	−18.5091			−0.622879			−0.311440	−	0.950266i	$-0.600811\pi$
$883$	−18.5091			−0.622879			−0.311440	+	0.950266i	$0.600811\pi$
$884$		0			0
$885$	−0.731879	−	1.26765i	−0.0246018	−	0.0426116i
$886$		0			0
$887$	27.1872	−	47.0896i	0.912856	−	1.58111i	0.102846	−	0.994697i	$-0.467205\pi$
$887$	27.1872	−	47.0896i	0.912856	−	1.58111i	0.810010	−	0.586416i	$-0.199461\pi$
$888$		0			0
$889$	−6.98054	+	23.9431i	−0.234120	+	0.803025i
$890$		0			0
$891$	2.72773	−	4.72457i	0.0913825	−	0.158279i
$892$		0			0
$893$	−11.1450	−	19.3037i	−0.372954	−	0.645974i
$894$		0			0
$895$	−16.0563			−0.536704
$896$		0			0
$897$	10.6362			0.355132
$898$		0			0
$899$	−8.57496	−	14.8523i	−0.285991	−	0.495351i
$900$		0			0
$901$	−0.709445	+	1.22880i	−0.0236350	+	0.0409371i
$902$		0			0
$903$	−24.5310	+	6.00093i	−0.816341	+	0.199699i
$904$		0			0
$905$	3.91332	−	6.77807i	0.130083	−	0.225311i
$906$		0			0
$907$	26.8719	+	46.5434i	0.892266	+	1.54545i	0.837152	+	0.546970i	$0.184219\pi$
$907$	26.8719	+	46.5434i	0.892266	+	1.54545i	0.0551133	+	0.998480i	$0.482448\pi$
$908$		0			0
$909$	2.62310			0.0870026
$910$		0			0
$911$	−8.53540			−0.282790			−0.141395	−	0.989953i	$-0.545159\pi$
$911$	−8.53540			−0.282790			−0.141395	+	0.989953i	$0.545159\pi$
$912$		0			0
$913$	6.36505	+	11.0246i	0.210652	+	0.364860i
$914$		0			0
$915$	9.72962	−	16.8522i	0.321651	−	0.557117i
$916$		0			0
$917$	−11.0970	−	11.5937i	−0.366456	−	0.382857i
$918$		0			0
$919$	−12.3543	+	21.3983i	−0.407532	+	0.705866i	−0.994613	−	0.103663i	$-0.966944\pi$
$919$	−12.3543	+	21.3983i	−0.407532	+	0.705866i	0.587081	+	0.809528i	$0.300277\pi$
$920$		0			0
$921$	14.7248	+	25.5041i	0.485199	+	0.840389i
$922$		0			0
$923$	2.58063			0.0849425
$924$		0			0
$925$	34.5158			1.13487
$926$		0			0
$927$	3.85031	+	6.66893i	0.126461	+	0.219036i
$928$		0			0
$929$	−15.2393	+	26.3953i	−0.499986	+	0.866001i	−1.00000		1.63042e-5i	$-0.999995\pi$
$929$	−15.2393	+	26.3953i	−0.499986	+	0.866001i	0.500014	+	0.866017i	$0.333328\pi$
$930$		0			0
$931$	−28.7982	+	14.9864i	−0.943822	+	0.491159i
$932$		0			0
$933$	−9.83310	+	17.0314i	−0.321921	+	0.557584i
$934$		0			0
$935$	−0.806706	−	1.39726i	−0.0263821	−	0.0456952i
$936$		0			0
$937$	56.4625			1.84455			0.922275	−	0.386535i	$-0.126328\pi$
$937$	56.4625			1.84455			0.922275	+	0.386535i	$0.126328\pi$
$938$		0			0
$939$	24.8313			0.810340
$940$		0			0
$941$	1.54767	+	2.68064i	0.0504525	+	0.0873863i	0.890149	−	0.455670i	$-0.150600\pi$
$941$	1.54767	+	2.68064i	0.0504525	+	0.0873863i	−0.839696	+	0.543056i	$0.817267\pi$
$942$		0			0
$943$	18.9744	−	32.8646i	0.617891	−	1.07022i
$944$		0			0
$945$	10.9622	+	11.4528i	0.356601	+	0.372561i
$946$		0			0
$947$	−17.1065	+	29.6294i	−0.555888	+	0.962826i	0.441946	+	0.897042i	$0.354288\pi$
$947$	−17.1065	+	29.6294i	−0.555888	+	0.962826i	−0.997834	+	0.0657840i	$0.979045\pi$
$948$		0			0
$949$	−6.28361	−	10.8835i	−0.203975	−	0.353294i
$950$		0			0
$951$	−27.2872			−0.884848
$952$		0			0
$953$	−48.5260			−1.57191			−0.785956	−	0.618283i	$-0.787829\pi$
$953$	−48.5260			−1.57191			−0.785956	+	0.618283i	$0.787829\pi$
$954$		0			0
$955$	−1.80360	−	3.12393i	−0.0583631	−	0.101088i
$956$		0			0
$957$	−9.63456	+	16.6875i	−0.311441	+	0.539432i
$958$		0			0
$959$	−30.8607	+	7.54935i	−0.996545	+	0.243781i
$960$		0			0
$961$	13.9273	−	24.1229i	0.449269	−	0.778157i
$962$		0			0
$963$	−4.18383	−	7.24661i	−0.134822	−	0.233519i
$964$		0			0
$965$	20.7682			0.668552
$966$		0			0
$967$	−47.8714			−1.53944			−0.769720	−	0.638382i	$-0.779604\pi$
$967$	−47.8714			−1.53944			−0.769720	+	0.638382i	$0.779604\pi$
$968$		0			0
$969$	3.05469	+	5.29087i	0.0981307	+	0.169967i
$970$		0			0
$971$	−24.3670	+	42.2049i	−0.781974	+	1.35442i	0.148816	+	0.988865i	$0.452454\pi$
$971$	−24.3670	+	42.2049i	−0.781974	+	1.35442i	−0.930790	+	0.365554i	$0.880879\pi$
$972$		0			0
$973$	−13.1626	+	45.1474i	−0.421973	+	1.44736i
$974$		0			0
$975$	−3.52957	+	6.11339i	−0.113037	+	0.195785i
$976$		0			0
$977$	30.2903	+	52.4644i	0.969073	+	1.67848i	0.698249	+	0.715855i	$0.253963\pi$
$977$	30.2903	+	52.4644i	0.969073	+	1.67848i	0.270823	+	0.962629i	$0.412704\pi$
$978$		0			0
$979$	13.0184			0.416068
$980$		0			0
$981$	14.0185			0.447575
$982$		0			0
$983$	−17.0037	−	29.4512i	−0.542333	−	0.939348i	−0.998770	−	0.0495921i	$-0.984208\pi$
$983$	−17.0037	−	29.4512i	−0.542333	−	0.939348i	0.456437	−	0.889756i	$-0.349125\pi$
$984$		0			0
$985$	−11.4220	+	19.7834i	−0.363934	+	0.630352i
$986$		0			0
$987$	4.68852	−	16.0815i	0.149237	−	0.511880i
$988$		0			0
$989$	−21.0840	+	36.5186i	−0.670434	+	1.16123i
$990$		0			0
$991$	11.6475	+	20.1741i	0.369995	+	0.640850i	0.989564	−	0.144092i	$-0.0460261\pi$
$991$	11.6475	+	20.1741i	0.369995	+	0.640850i	−0.619569	+	0.784942i	$0.712693\pi$
$992$		0			0
$993$	−45.8327			−1.45446
$994$		0			0
$995$	−29.1656			−0.924611
$996$		0			0
$997$	23.1570	+	40.1091i	0.733389	+	1.27027i	0.955426	+	0.295229i	$0.0953960\pi$
$997$	23.1570	+	40.1091i	0.733389	+	1.27027i	−0.222037	+	0.975038i	$0.571271\pi$
$998$		0			0
$999$	−25.1022	+	43.4783i	−0.794199	+	1.37559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.q.e.681.3	yes	14
7.2	even	3		6664.2.a.v.1.5		7
7.4	even	3	inner	952.2.q.e.137.3	✓	14
7.5	odd	6		6664.2.a.y.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.q.e.137.3	✓	14	7.4	even	3	inner
952.2.q.e.681.3	yes	14	1.1	even	1	trivial
6664.2.a.v.1.5		7	7.2	even	3
6664.2.a.y.1.3		7	7.5	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:	\( N \)	\(=\)	\( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	952.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.658657 - 1.14083i) q^{3} +(-0.533302 + 0.923707i) q^{5} +(-0.740531 + 2.54000i) q^{7} +(0.632341 - 1.09525i) q^{9} +(-0.756331 - 1.31000i) q^{11} -1.38743 q^{13} +1.40505 q^{15} +(-0.500000 - 0.866025i) q^{17} +(2.31887 - 4.01641i) q^{19} +(3.38546 - 0.828173i) q^{21} +(2.90976 - 5.03984i) q^{23} +(1.93118 + 3.34490i) q^{25} -5.61793 q^{27} +9.67008 q^{29} +(-0.886751 - 1.53590i) q^{31} +(-0.996326 + 1.72569i) q^{33} +(-1.95129 - 2.03862i) q^{35} +(4.46824 - 7.73921i) q^{37} +(0.913838 + 1.58281i) q^{39} +6.52095 q^{41} -7.24599 q^{43} +(0.674458 + 1.16820i) q^{45} +(2.40311 - 4.16231i) q^{47} +(-5.90323 - 3.76190i) q^{49} +(-0.658657 + 1.14083i) q^{51} +(-0.709445 - 1.22880i) q^{53} +1.61341 q^{55} -6.10937 q^{57} +(-0.520890 - 0.902208i) q^{59} +(6.92473 - 11.9940i) q^{61} +(2.31366 + 2.41721i) q^{63} +(0.739917 - 1.28157i) q^{65} +(-6.13093 - 10.6191i) q^{67} -7.66613 q^{69} -1.86001 q^{71} +(4.52897 + 7.84441i) q^{73} +(2.54397 - 4.40628i) q^{75} +(3.88750 - 0.950985i) q^{77} +(2.42267 - 4.19618i) q^{79} +(1.80327 + 3.12335i) q^{81} -8.41568 q^{83} +1.06660 q^{85} +(-6.36927 - 11.0319i) q^{87} +(-4.30313 + 7.45323i) q^{89} +(1.02743 - 3.52406i) q^{91} +(-1.16813 + 2.02326i) q^{93} +(2.47332 + 4.28392i) q^{95} -19.5711 q^{97} -1.91304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 4 q^{9} + 12 q^{11} + 4 q^{13} - 12 q^{15} - 7 q^{17} + 3 q^{19} + 18 q^{21} + 18 q^{23} - 15 q^{25} - 36 q^{27} + 10 q^{29} + 10 q^{31} - 21 q^{33} + 19 q^{35} - 11 q^{37}+ \cdots - 40 q^{99}+O(q^{100}) \) 14 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 4 * q^9 + 12 * q^11 + 4 * q^13 - 12 * q^15 - 7 * q^17 + 3 * q^19 + 18 * q^21 + 18 * q^23 - 15 * q^25 - 36 * q^27 + 10 * q^29 + 10 * q^31 - 21 * q^33 + 19 * q^35 - 11 * q^37 + 12 * q^39 - 30 * q^43 - 13 * q^45 - 15 * q^47 + 20 * q^49 + 3 * q^51 - 8 * q^53 - 18 * q^55 - 6 * q^57 - 9 * q^59 + 4 * q^61 + 41 * q^63 + 38 * q^65 + 30 * q^67 - 56 * q^69 - 54 * q^71 + 5 * q^73 + 2 * q^75 + 27 * q^77 - 3 * q^79 + 17 * q^81 - 24 * q^83 + 4 * q^85 - 19 * q^87 - 32 * q^89 - 11 * q^91 + 9 * q^93 + 42 * q^95 - 78 * q^97 - 40 * q^99

Introduction

L-functions

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