LMFDB - Embedded newform 952.2.q.d.137.2

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 = [14,0,0] 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} + 11 x^{12} - 6 x^{11} + 94 x^{10} - 39 x^{9} + 282 x^{8} - 47 x^{7} + 615 x^{6} - 134 x^{5} + \cdots + 16 $ x^14 + 11x^12 - 6x^11 + 94x^10 - 39x^9 + 282x^8 - 47x^7 + 615x^6 - 134x^5 + 348x^4 - 144x^3 + 168x^2 - 48x + 16
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			137.2
Root			$-0.759308 + 1.31516i$ of defining polynomial
Character	$\chi$	$=$	952.137
Dual form			952.2.q.d.681.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.759308 + 1.31516i) q^{3} +(0.399186 + 0.691411i) q^{5} +(1.00540 + 2.44728i) q^{7} +(0.346902 + 0.600853i) q^{9} +(2.82215 - 4.88810i) q^{11} +4.80031 q^{13} -1.21242 q^{15} +(0.500000 - 0.866025i) q^{17} +(2.53870 + 4.39716i) q^{19} +(-3.98197 - 0.535981i) q^{21} +(-2.09504 - 3.62871i) q^{23} +(2.18130 - 3.77812i) q^{25} -5.60947 q^{27} +1.85926 q^{29} +(-5.04506 + 8.73831i) q^{31} +(4.28576 + 7.42315i) q^{33} +(-1.29073 + 1.67206i) q^{35} +(3.05689 + 5.29469i) q^{37} +(-3.64491 + 6.31317i) q^{39} +6.24965 q^{41} -0.575750 q^{43} +(-0.276957 + 0.479704i) q^{45} +(-2.87068 - 4.97216i) q^{47} +(-4.97835 + 4.92097i) q^{49} +(0.759308 + 1.31516i) q^{51} +(-2.25167 + 3.90001i) q^{53} +4.50625 q^{55} -7.71062 q^{57} +(-3.98924 + 6.90957i) q^{59} +(-4.46706 - 7.73717i) q^{61} +(-1.12168 + 1.45306i) q^{63} +(1.91622 + 3.31898i) q^{65} +(-5.33937 + 9.24806i) q^{67} +6.36311 q^{69} +3.73942 q^{71} +(6.58929 - 11.4130i) q^{73} +(3.31256 + 5.73752i) q^{75} +(14.7999 + 1.99210i) q^{77} +(-2.57805 - 4.46532i) q^{79} +(3.21861 - 5.57480i) q^{81} +5.24724 q^{83} +0.798372 q^{85} +(-1.41175 + 2.44523i) q^{87} +(0.264175 + 0.457564i) q^{89} +(4.82621 + 11.7477i) q^{91} +(-7.66152 - 13.2701i) q^{93} +(-2.02683 + 3.51057i) q^{95} +5.53836 q^{97} +3.91604 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{5} - 7 q^{7} - q^{9} - 5 q^{11} + 22 q^{13} + 16 q^{15} + 7 q^{17} + 2 q^{19} - 13 q^{21} - 9 q^{23} - 2 q^{25} + 18 q^{27} + 18 q^{29} + 2 q^{31} - 2 q^{33} + 9 q^{35} - 8 q^{37} - q^{39}+ \cdots - 24 q^{99}+O(q^{100}) $ 14 * q + q^5 - 7 * q^7 - q^9 - 5 * q^11 + 22 * q^13 + 16 * q^15 + 7 * q^17 + 2 * q^19 - 13 * q^21 - 9 * q^23 - 2 * q^25 + 18 * q^27 + 18 * q^29 + 2 * q^31 - 2 * q^33 + 9 * q^35 - 8 * q^37 - q^39 + 12 * q^41 + 20 * q^43 + 10 * q^45 + q^47 - 21 * q^49 - 3 * q^53 + 22 * q^55 - 10 * q^57 + 4 * q^59 + 32 * q^61 + 13 * q^63 - 20 * q^65 - 31 * q^67 + 32 * q^69 + 6 * q^71 + 7 * q^73 + 19 * q^75 - 26 * q^77 - 8 * q^79 + q^81 + 48 * q^83 + 2 * q^85 + 3 * q^87 - 4 * q^89 - 15 * q^91 - 19 * q^93 - 23 * q^95 + 30 * q^97 - 24 * q^99

Character values

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

$n$	$239$	$409$	$477$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.759308	+	1.31516i	−0.438387	+	0.759308i	−0.997565	−	0.0697392i	$-0.977783\pi$
$3$	−0.759308	+	1.31516i	−0.438387	+	0.759308i	0.559179	+	0.829047i	$0.311117\pi$
$4$		0			0
$5$	0.399186	+	0.691411i	0.178521	+	0.309208i	0.941374	−	0.337364i	$-0.109535\pi$
$5$	0.399186	+	0.691411i	0.178521	+	0.309208i	−0.762853	+	0.646572i	$0.776202\pi$
$6$		0			0
$7$	1.00540	+	2.44728i	0.380004	+	0.924985i
$7$	1.00540	+	2.44728i	0.380004	+	0.924985i
$8$		0			0
$9$	0.346902	+	0.600853i	0.115634	+	0.200284i
$10$		0			0
$11$	2.82215	−	4.88810i	0.850909	−	1.47382i	−0.0294801	−	0.999565i	$-0.509385\pi$
$11$	2.82215	−	4.88810i	0.850909	−	1.47382i	0.880389	−	0.474252i	$-0.157282\pi$
$12$		0			0
$13$	4.80031			1.33137			0.665683	−	0.746235i	$-0.268140\pi$
$13$	4.80031			1.33137			0.665683	+	0.746235i	$0.268140\pi$
$14$		0			0
$15$	−1.21242			−0.313046
$16$		0			0
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$		0			0
$19$	2.53870	+	4.39716i	0.582418	+	1.00878i	0.995192	+	0.0979439i	$0.0312266\pi$
$19$	2.53870	+	4.39716i	0.582418	+	1.00878i	−0.412774	+	0.910833i	$0.635440\pi$
$20$		0			0
$21$	−3.98197	−	0.535981i	−0.868937	−	0.116961i
$22$		0			0
$23$	−2.09504	−	3.62871i	−0.436845	−	0.756638i	0.560599	−	0.828088i	$-0.310571\pi$
$23$	−2.09504	−	3.62871i	−0.436845	−	0.756638i	−0.997444	+	0.0714491i	$0.977238\pi$
$24$		0			0
$25$	2.18130	−	3.77812i	0.436260	−	0.755625i
$26$		0			0
$27$	−5.60947			−1.07954
$28$		0			0
$29$	1.85926			0.345256			0.172628	−	0.984987i	$-0.444774\pi$
$29$	1.85926			0.345256			0.172628	+	0.984987i	$0.444774\pi$
$30$		0			0
$31$	−5.04506	+	8.73831i	−0.906120	+	1.56945i	−0.0867140	+	0.996233i	$0.527637\pi$
$31$	−5.04506	+	8.73831i	−0.906120	+	1.56945i	−0.819406	+	0.573213i	$0.805697\pi$
$32$		0			0
$33$	4.28576	+	7.42315i	0.746054	+	1.29220i
$34$		0			0
$35$	−1.29073	+	1.67206i	−0.218174	+	0.282630i
$36$		0			0
$37$	3.05689	+	5.29469i	0.502550	+	0.870442i	0.999996	+	0.00294696i	$0.000938049\pi$
$37$	3.05689	+	5.29469i	0.502550	+	0.870442i	−0.497446	+	0.867495i	$0.665729\pi$
$38$		0			0
$39$	−3.64491	+	6.31317i	−0.583653	+	1.01092i
$40$		0			0
$41$	6.24965			0.976032			0.488016	−	0.872835i	$-0.337721\pi$
$41$	6.24965			0.976032			0.488016	+	0.872835i	$0.337721\pi$
$42$		0			0
$43$	−0.575750			−0.0878010			−0.0439005	−	0.999036i	$-0.513978\pi$
$43$	−0.575750			−0.0878010			−0.0439005	+	0.999036i	$0.513978\pi$
$44$		0			0
$45$	−0.276957	+	0.479704i	−0.0412864	+	0.0715101i
$46$		0			0
$47$	−2.87068	−	4.97216i	−0.418731	−	0.725264i	0.577081	−	0.816687i	$-0.304192\pi$
$47$	−2.87068	−	4.97216i	−0.418731	−	0.725264i	−0.995812	+	0.0914233i	$0.970858\pi$
$48$		0			0
$49$	−4.97835	+	4.92097i	−0.711194	+	0.702996i
$50$		0			0
$51$	0.759308	+	1.31516i	0.106324	+	0.184159i
$52$		0			0
$53$	−2.25167	+	3.90001i	−0.309291	+	0.535707i	−0.978207	−	0.207630i	$-0.933425\pi$
$53$	−2.25167	+	3.90001i	−0.309291	+	0.535707i	0.668917	+	0.743337i	$0.266758\pi$
$54$		0			0
$55$	4.50625			0.607622
$56$		0			0
$57$	−7.71062			−1.02130
$58$		0			0
$59$	−3.98924	+	6.90957i	−0.519355	+	0.899550i	0.480392	+	0.877054i	$0.340495\pi$
$59$	−3.98924	+	6.90957i	−0.519355	+	0.899550i	−0.999747	+	0.0224958i	$0.992839\pi$
$60$		0			0
$61$	−4.46706	−	7.73717i	−0.571948	−	0.990643i	−0.996366	−	0.0851766i	$-0.972855\pi$
$61$	−4.46706	−	7.73717i	−0.571948	−	0.990643i	0.424418	−	0.905466i	$-0.360479\pi$
$62$		0			0
$63$	−1.12168	+	1.45306i	−0.141318	+	0.183069i
$64$		0			0
$65$	1.91622	+	3.31898i	0.237677	+	0.411669i
$66$		0			0
$67$	−5.33937	+	9.24806i	−0.652308	+	1.12983i	0.330254	+	0.943892i	$0.392866\pi$
$67$	−5.33937	+	9.24806i	−0.652308	+	1.12983i	−0.982561	+	0.185938i	$0.940468\pi$
$68$		0			0
$69$	6.36311			0.766029
$70$		0			0
$71$	3.73942			0.443787			0.221894	−	0.975071i	$-0.428776\pi$
$71$	3.73942			0.443787			0.221894	+	0.975071i	$0.428776\pi$
$72$		0			0
$73$	6.58929	−	11.4130i	0.771218	−	1.33579i	−0.165678	−	0.986180i	$-0.552981\pi$
$73$	6.58929	−	11.4130i	0.771218	−	1.33579i	0.936896	−	0.349608i	$-0.113685\pi$
$74$		0			0
$75$	3.31256	+	5.73752i	0.382501	+	0.662512i
$76$		0			0
$77$	14.7999	+	1.99210i	1.68661	+	0.227021i
$78$		0			0
$79$	−2.57805	−	4.46532i	−0.290053	−	0.502387i	0.683769	−	0.729699i	$-0.260340\pi$
$79$	−2.57805	−	4.46532i	−0.290053	−	0.502387i	−0.973822	+	0.227312i	$0.927006\pi$
$80$		0			0
$81$	3.21861	−	5.57480i	0.357623	−	0.619422i
$82$		0			0
$83$	5.24724			0.575960			0.287980	−	0.957636i	$-0.407016\pi$
$83$	5.24724			0.575960			0.287980	+	0.957636i	$0.407016\pi$
$84$		0			0
$85$	0.798372			0.0865956
$86$		0			0
$87$	−1.41175	+	2.44523i	−0.151356	+	0.262156i
$88$		0			0
$89$	0.264175	+	0.457564i	0.0280025	+	0.0485017i	0.879687	−	0.475553i	$-0.157752\pi$
$89$	0.264175	+	0.457564i	0.0280025	+	0.0485017i	−0.851685	+	0.524055i	$0.824419\pi$
$90$		0			0
$91$	4.82621	+	11.7477i	0.505924	+	1.23149i
$92$		0			0
$93$	−7.66152	−	13.2701i	−0.794462	−	1.37605i
$94$		0			0
$95$	−2.02683	+	3.51057i	−0.207948	+	0.360177i
$96$		0			0
$97$	5.53836			0.562336			0.281168	−	0.959659i	$-0.409278\pi$
$97$	5.53836			0.562336			0.281168	+	0.959659i	$0.409278\pi$
$98$		0			0
$99$	3.91604			0.393577
$100$		0			0
$101$	−5.85708	+	10.1448i	−0.582801	+	1.00944i	0.412345	+	0.911028i	$0.364710\pi$
$101$	−5.85708	+	10.1448i	−0.582801	+	1.00944i	−0.995146	+	0.0984129i	$0.968623\pi$
$102$		0			0
$103$	2.27921	+	3.94770i	0.224577	+	0.388979i	0.956192	−	0.292739i	$-0.0945666\pi$
$103$	2.27921	+	3.94770i	0.224577	+	0.388979i	−0.731615	+	0.681718i	$0.761233\pi$
$104$		0			0
$105$	−1.21896	−	2.96713i	−0.118959	−	0.289563i
$106$		0			0
$107$	−8.82178	−	15.2798i	−0.852834	−	1.47715i	−0.878640	−	0.477485i	$-0.841549\pi$
$107$	−8.82178	−	15.2798i	−0.852834	−	1.47715i	0.0258062	−	0.999667i	$-0.491785\pi$
$108$		0			0
$109$	−6.71058	+	11.6231i	−0.642757	+	1.11329i	0.342058	+	0.939679i	$0.388876\pi$
$109$	−6.71058	+	11.6231i	−0.642757	+	1.11329i	−0.984815	+	0.173608i	$0.944457\pi$
$110$		0			0
$111$	−9.28449			−0.881245
$112$		0			0
$113$	−15.4940			−1.45755			−0.728775	−	0.684753i	$-0.759910\pi$
$113$	−15.4940			−1.45755			−0.728775	+	0.684753i	$0.759910\pi$
$114$		0			0
$115$	1.67262	−	2.89706i	0.155973	−	0.270152i
$116$		0			0
$117$	1.66524	+	2.88428i	0.153951	+	0.266652i
$118$		0			0
$119$	2.62210	+	0.352941i	0.240368	+	0.0323540i
$120$		0			0
$121$	−10.4290	−	18.0636i	−0.948092	−	1.64214i
$122$		0			0
$123$	−4.74541	+	8.21930i	−0.427879	+	0.741109i
$124$		0			0
$125$	7.47484			0.668570
$126$		0			0
$127$	1.46849			0.130308			0.0651539	−	0.997875i	$-0.479246\pi$
$127$	1.46849			0.130308			0.0651539	+	0.997875i	$0.479246\pi$
$128$		0			0
$129$	0.437172	−	0.757203i	0.0384908	−	0.0666680i
$130$		0			0
$131$	6.34953	+	10.9977i	0.554761	+	0.960875i	0.997922	+	0.0644328i	$0.0205238\pi$
$131$	6.34953	+	10.9977i	0.554761	+	0.960875i	−0.443161	+	0.896442i	$0.646143\pi$
$132$		0			0
$133$	−8.20868	+	10.6338i	−0.711782	+	0.922067i
$134$		0			0
$135$	−2.23922	−	3.87845i	−0.192722	−	0.333804i
$136$		0			0
$137$	6.11094	−	10.5845i	0.522093	−	0.904292i	−0.477576	−	0.878590i	$-0.658485\pi$
$137$	6.11094	−	10.5845i	0.522093	−	0.904292i	0.999670	−	0.0257018i	$-0.00818204\pi$
$138$		0			0
$139$	−6.86885			−0.582608			−0.291304	−	0.956631i	$-0.594089\pi$
$139$	−6.86885			−0.582608			−0.291304	+	0.956631i	$0.594089\pi$
$140$		0			0
$141$	8.71891			0.734265
$142$		0			0
$143$	13.5472	−	23.4644i	1.13287	−	1.96219i
$144$		0			0
$145$	0.742191	+	1.28551i	0.0616356	+	0.106756i
$146$		0			0
$147$	−2.69176	−	10.2839i	−0.222013	−	0.848199i
$148$		0			0
$149$	3.47149	+	6.01279i	0.284395	+	0.492587i	0.972462	−	0.233060i	$-0.0748739\pi$
$149$	3.47149	+	6.01279i	0.284395	+	0.492587i	−0.688067	+	0.725647i	$0.741541\pi$
$150$		0			0
$151$	6.87181	−	11.9023i	0.559220	−	0.968597i	−0.438342	−	0.898808i	$-0.644434\pi$
$151$	6.87181	−	11.9023i	0.559220	−	0.968597i	0.997562	−	0.0697890i	$-0.0222326\pi$
$152$		0			0
$153$	0.693805			0.0560908
$154$		0			0
$155$	−8.05568			−0.647048
$156$		0			0
$157$	1.94788	−	3.37384i	0.155458	−	0.269261i	−0.777768	−	0.628552i	$-0.783648\pi$
$157$	1.94788	−	3.37384i	0.155458	−	0.269261i	0.933226	+	0.359291i	$0.116981\pi$
$158$		0			0
$159$	−3.41942	−	5.92262i	−0.271178	−	0.469694i
$160$		0			0
$161$	6.77413	−	8.77543i	0.533876	−	0.691601i
$162$		0			0
$163$	−12.1831	−	21.1017i	−0.954254	−	1.65282i	−0.736067	−	0.676909i	$-0.763319\pi$
$163$	−12.1831	−	21.1017i	−0.954254	−	1.65282i	−0.218186	−	0.975907i	$-0.570014\pi$
$164$		0			0
$165$	−3.42163	+	5.92644i	−0.266373	+	0.461372i
$166$		0			0
$167$	14.5608			1.12675			0.563374	−	0.826202i	$-0.309503\pi$
$167$	14.5608			1.12675			0.563374	+	0.826202i	$0.309503\pi$
$168$		0			0
$169$	10.0429			0.772534
$170$		0			0
$171$	−1.76136	+	3.05077i	−0.134695	+	0.233298i
$172$		0			0
$173$	−6.99348	−	12.1131i	−0.531704	−	0.920939i	−0.999315	−	0.0370045i	$-0.988218\pi$
$173$	−6.99348	−	12.1131i	−0.531704	−	0.920939i	0.467611	−	0.883935i	$-0.345115\pi$
$174$		0			0
$175$	11.4392	+	1.53974i	0.864722	+	0.116393i
$176$		0			0
$177$	−6.05813	−	10.4930i	−0.455357	−	0.788701i
$178$		0			0
$179$	−11.4042	+	19.7526i	−0.852387	+	1.47638i	0.0266615	+	0.999645i	$0.491512\pi$
$179$	−11.4042	+	19.7526i	−0.852387	+	1.47638i	−0.879048	+	0.476733i	$0.841821\pi$
$180$		0			0
$181$	0.886797			0.0659151			0.0329575	−	0.999457i	$-0.489507\pi$
$181$	0.886797			0.0659151			0.0329575	+	0.999457i	$0.489507\pi$
$182$		0			0
$183$	13.5675			1.00294
$184$		0			0
$185$	−2.44054	+	4.22714i	−0.179432	+	0.310785i
$186$		0			0
$187$	−2.82215	−	4.88810i	−0.206376	−	0.357453i
$188$		0			0
$189$	−5.63974	−	13.7279i	−0.410231	−	0.998561i
$190$		0			0
$191$	−4.38853	−	7.60116i	−0.317543	−	0.550001i	0.662432	−	0.749122i	$-0.269525\pi$
$191$	−4.38853	−	7.60116i	−0.317543	−	0.550001i	−0.979975	+	0.199121i	$0.936191\pi$
$192$		0			0
$193$	8.61177	−	14.9160i	0.619889	−	1.07368i	−0.369617	−	0.929184i	$-0.620511\pi$
$193$	8.61177	−	14.9160i	0.619889	−	1.07368i	0.989506	−	0.144495i	$-0.0461556\pi$
$194$		0			0
$195$	−5.81999			−0.416778
$196$		0			0
$197$	20.3939			1.45300			0.726502	−	0.687164i	$-0.241145\pi$
$197$	20.3939			1.45300			0.726502	+	0.687164i	$0.241145\pi$
$198$		0			0
$199$	4.20788	−	7.28826i	0.298289	−	0.516651i	−0.677456	−	0.735563i	$-0.736918\pi$
$199$	4.20788	−	7.28826i	0.298289	−	0.516651i	0.975745	+	0.218912i	$0.0702509\pi$
$200$		0			0
$201$	−8.10845	−	14.0443i	−0.571926	−	0.990605i
$202$		0			0
$203$	1.86929	+	4.55013i	0.131199	+	0.319357i
$204$		0			0
$205$	2.49478	+	4.32108i	0.174243	+	0.301797i
$206$		0			0
$207$	1.45355	−	2.51762i	0.101028	−	0.174986i
$208$		0			0
$209$	28.6583			1.98234
$210$		0			0
$211$	−22.8992			−1.57644			−0.788222	−	0.615391i	$-0.788998\pi$
$211$	−22.8992			−1.57644			−0.788222	+	0.615391i	$0.788998\pi$
$212$		0			0
$213$	−2.83937	+	4.91793i	−0.194550	+	0.336971i
$214$		0			0
$215$	−0.229831	−	0.398080i	−0.0156744	−	0.0271488i
$216$		0			0
$217$	−26.4574	−	3.56122i	−1.79604	−	0.241751i
$218$		0			0
$219$	10.0066	+	17.3319i	0.676183	+	1.17118i
$220$		0			0
$221$	2.40015	−	4.15719i	0.161452	−	0.279643i
$222$		0			0
$223$	−9.97337			−0.667866			−0.333933	−	0.942597i	$-0.608376\pi$
$223$	−9.97337			−0.667866			−0.333933	+	0.942597i	$0.608376\pi$
$224$		0			0
$225$	3.02679			0.201786
$226$		0			0
$227$	11.7572	−	20.3641i	0.780353	−	1.35161i	−0.151384	−	0.988475i	$-0.548373\pi$
$227$	11.7572	−	20.3641i	0.780353	−	1.35161i	0.931736	−	0.363135i	$-0.118294\pi$
$228$		0			0
$229$	5.22090	+	9.04286i	0.345007	+	0.597569i	0.985355	−	0.170516i	$-0.0545433\pi$
$229$	5.22090	+	9.04286i	0.345007	+	0.597569i	−0.640348	+	0.768085i	$0.721210\pi$
$230$		0			0
$231$	−13.8576	+	17.9517i	−0.911765	+	1.18113i
$232$		0			0
$233$	−12.0454	−	20.8632i	−0.789118	−	1.36679i	−0.926508	−	0.376276i	$-0.877205\pi$
$233$	−12.0454	−	20.8632i	−0.789118	−	1.36679i	0.137390	−	0.990517i	$-0.456129\pi$
$234$		0			0
$235$	2.29187	−	3.96963i	0.149505	−	0.258950i
$236$		0			0
$237$	7.83014			0.508622
$238$		0			0
$239$	29.7263			1.92283			0.961417	−	0.275095i	$-0.0887093\pi$
$239$	29.7263			1.92283			0.961417	+	0.275095i	$0.0887093\pi$
$240$		0			0
$241$	−2.03223	+	3.51992i	−0.130907	+	0.226738i	−0.924027	−	0.382328i	$-0.875122\pi$
$241$	−2.03223	+	3.51992i	−0.130907	+	0.226738i	0.793119	+	0.609066i	$0.208456\pi$
$242$		0			0
$243$	−3.52637	−	6.10786i	−0.226217	−	0.391819i
$244$		0			0
$245$	−5.38970	−	1.47770i	−0.344336	−	0.0944070i
$246$		0			0
$247$	12.1865	+	21.1077i	0.775411	+	1.34305i
$248$		0			0
$249$	−3.98427	+	6.90096i	−0.252493	+	0.437331i
$250$		0			0
$251$	2.80048			0.176765			0.0883823	−	0.996087i	$-0.471830\pi$
$251$	2.80048			0.176765			0.0883823	+	0.996087i	$0.471830\pi$
$252$		0			0
$253$	−23.6500			−1.48686
$254$		0			0
$255$	−0.606211	+	1.04999i	−0.0379624	+	0.0657528i
$256$		0			0
$257$	−1.89829	−	3.28793i	−0.118412	−	0.205096i	0.800726	−	0.599030i	$-0.204447\pi$
$257$	−1.89829	−	3.28793i	−0.118412	−	0.205096i	−0.919139	+	0.393934i	$0.871114\pi$
$258$		0			0
$259$	−9.88420	+	12.8043i	−0.614175	+	0.795623i
$260$		0			0
$261$	0.644982	+	1.11714i	0.0399234	+	0.0691493i
$262$		0			0
$263$	3.61664	−	6.26420i	0.223012	−	0.386267i	−0.732709	−	0.680542i	$-0.761745\pi$
$263$	3.61664	−	6.26420i	0.223012	−	0.386267i	0.955721	+	0.294274i	$0.0950779\pi$
$264$		0			0
$265$	−3.59534			−0.220860
$266$		0			0
$267$	−0.802360			−0.0491036
$268$		0			0
$269$	−0.421685	+	0.730381i	−0.0257106	+	0.0445321i	−0.878594	−	0.477569i	$-0.841518\pi$
$269$	−0.421685	+	0.730381i	−0.0257106	+	0.0445321i	0.852884	+	0.522101i	$0.174852\pi$
$270$		0			0
$271$	−1.20606	−	2.08896i	−0.0732630	−	0.126895i	0.827067	−	0.562104i	$-0.190008\pi$
$271$	−1.20606	−	2.08896i	−0.0732630	−	0.126895i	−0.900330	+	0.435209i	$0.856675\pi$
$272$		0			0
$273$	−19.1147	−	2.57288i	−1.15687	−	0.155717i
$274$		0			0
$275$	−12.3119	−	21.3248i	−0.742435	−	1.28594i
$276$		0			0
$277$	−11.8650	+	20.5508i	−0.712900	+	1.23478i	0.250864	+	0.968022i	$0.419285\pi$
$277$	−11.8650	+	20.5508i	−0.712900	+	1.23478i	−0.963764	+	0.266757i	$0.914048\pi$
$278$		0			0
$279$	−7.00058			−0.419114
$280$		0			0
$281$	−2.87529			−0.171526			−0.0857629	−	0.996316i	$-0.527333\pi$
$281$	−2.87529			−0.171526			−0.0857629	+	0.996316i	$0.527333\pi$
$282$		0			0
$283$	13.1237	−	22.7309i	0.780123	−	1.35121i	−0.151747	−	0.988419i	$-0.548490\pi$
$283$	13.1237	−	22.7309i	0.780123	−	1.35121i	0.931870	−	0.362793i	$-0.118177\pi$
$284$		0			0
$285$	−3.07797	−	5.33121i	−0.182323	−	0.315794i
$286$		0			0
$287$	6.28338	+	15.2946i	0.370896	+	0.902815i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	−4.20532	+	7.28384i	−0.246520	+	0.426986i
$292$		0			0
$293$	−14.2126			−0.830311			−0.415156	−	0.909750i	$-0.636273\pi$
$293$	−14.2126			−0.830311			−0.415156	+	0.909750i	$0.636273\pi$
$294$		0			0
$295$	−6.36980			−0.370864
$296$		0			0
$297$	−15.8307	+	27.4197i	−0.918593	+	1.59105i
$298$		0			0
$299$	−10.0568	−	17.4189i	−0.581601	−	1.00736i
$300$		0			0
$301$	−0.578857	−	1.40902i	−0.0333648	−	0.0812146i
$302$		0			0
$303$	−8.89465	−	15.4060i	−0.510984	−	0.885051i
$304$		0			0
$305$	3.56637	−	6.17714i	0.204210	−	0.353702i
$306$		0			0
$307$	26.5976			1.51800			0.759002	−	0.651088i	$-0.225687\pi$
$307$	26.5976			1.51800			0.759002	+	0.651088i	$0.225687\pi$
$308$		0			0
$309$	−6.92248			−0.393806
$310$		0			0
$311$	−10.6272	+	18.4068i	−0.602611	+	1.04375i	0.389813	+	0.920894i	$0.372540\pi$
$311$	−10.6272	+	18.4068i	−0.602611	+	1.04375i	−0.992424	+	0.122859i	$0.960794\pi$
$312$		0			0
$313$	8.87844	+	15.3779i	0.501839	+	0.869211i	0.999998	+	0.00212502i	$0.000676414\pi$
$313$	8.87844	+	15.3779i	0.501839	+	0.869211i	−0.498159	+	0.867086i	$0.665990\pi$
$314$		0			0
$315$	−1.45242	−	0.195499i	−0.0818347	−	0.0110151i
$316$		0			0
$317$	−0.995267	−	1.72385i	−0.0558997	−	0.0968212i	0.836721	−	0.547629i	$-0.184469\pi$
$317$	−0.995267	−	1.72385i	−0.0558997	−	0.0968212i	−0.892621	+	0.450808i	$0.851136\pi$
$318$		0			0
$319$	5.24710	−	9.08825i	0.293781	−	0.508844i
$320$		0			0
$321$	26.7938			1.49548
$322$		0			0
$323$	5.07740			0.282514
$324$		0			0
$325$	10.4709	−	18.1362i	0.580822	−	1.00601i
$326$		0			0
$327$	−10.1908	−	17.6510i	−0.563552	−	0.976101i
$328$		0			0
$329$	9.28209	−	12.0243i	0.511738	−	0.662923i
$330$		0			0
$331$	7.69952	+	13.3360i	0.423204	+	0.733011i	0.996251	−	0.0865119i	$-0.0275721\pi$
$331$	7.69952	+	13.3360i	0.423204	+	0.733011i	−0.573047	+	0.819523i	$0.694239\pi$
$332$		0			0
$333$	−2.12089	+	3.67348i	−0.116224	+	0.201306i
$334$		0			0
$335$	−8.52561			−0.465804
$336$		0			0
$337$	−24.0830			−1.31188			−0.655942	−	0.754811i	$-0.727729\pi$
$337$	−24.0830			−1.31188			−0.655942	+	0.754811i	$0.727729\pi$
$338$		0			0
$339$	11.7647	−	20.3770i	0.638970	−	1.10673i
$340$		0			0
$341$	28.4758	+	49.3216i	1.54205	+	2.67091i
$342$		0			0
$343$	−17.0482	−	7.23590i	−0.920517	−	0.390702i
$344$		0			0
$345$	2.54007	+	4.39953i	0.136753	+	0.236862i
$346$		0			0
$347$	9.19663	−	15.9290i	0.493701	−	0.855115i	−0.506273	−	0.862373i	$-0.668977\pi$
$347$	9.19663	−	15.9290i	0.493701	−	0.855115i	0.999974	+	0.00725830i	$0.00231041\pi$
$348$		0			0
$349$	22.6309			1.21140			0.605701	−	0.795692i	$-0.292893\pi$
$349$	22.6309			1.21140			0.605701	+	0.795692i	$0.292893\pi$
$350$		0			0
$351$	−26.9272			−1.43727
$352$		0			0
$353$	−2.75923	+	4.77913i	−0.146859	+	0.254367i	−0.930065	−	0.367395i	$-0.880250\pi$
$353$	−2.75923	+	4.77913i	−0.146859	+	0.254367i	0.783206	+	0.621762i	$0.213583\pi$
$354$		0			0
$355$	1.49272	+	2.58547i	0.0792256	+	0.137223i
$356$		0			0
$357$	−2.45516	+	3.18050i	−0.129941	+	0.168330i
$358$		0			0
$359$	−9.33341	−	16.1659i	−0.492599	−	0.853206i	0.507365	−	0.861731i	$-0.330620\pi$
$359$	−9.33341	−	16.1659i	−0.492599	−	0.853206i	−0.999964	+	0.00852545i	$0.997286\pi$
$360$		0			0
$361$	−3.39000	+	5.87166i	−0.178421	+	0.309035i
$362$		0			0
$363$	31.6753			1.66252
$364$		0			0
$365$	10.5214			0.550716
$366$		0			0
$367$	−12.8238	+	22.2115i	−0.669398	+	1.15943i	0.308674	+	0.951168i	$0.400115\pi$
$367$	−12.8238	+	22.2115i	−0.669398	+	1.15943i	−0.978073	+	0.208264i	$0.933219\pi$
$368$		0			0
$369$	2.16802	+	3.75512i	0.112863	+	0.195484i
$370$		0			0
$371$	−11.8082	−	1.58941i	−0.613053	−	0.0825182i
$372$		0			0
$373$	2.52018	+	4.36508i	0.130490	+	0.226015i	0.923866	−	0.382717i	$-0.125012\pi$
$373$	2.52018	+	4.36508i	0.130490	+	0.226015i	−0.793376	+	0.608732i	$0.791678\pi$
$374$		0			0
$375$	−5.67571	+	9.83061i	−0.293092	+	0.507651i
$376$		0			0
$377$	8.92502			0.459662
$378$		0			0
$379$	22.9762			1.18021			0.590105	−	0.807326i	$-0.299086\pi$
$379$	22.9762			1.18021			0.590105	+	0.807326i	$0.299086\pi$
$380$		0			0
$381$	−1.11504	+	1.93130i	−0.0571252	+	0.0989438i
$382$		0			0
$383$	14.4673	+	25.0581i	0.739245	+	1.28041i	0.952836	+	0.303487i	$0.0981510\pi$
$383$	14.4673	+	25.0581i	0.739245	+	1.28041i	−0.213590	+	0.976923i	$0.568516\pi$
$384$		0			0
$385$	4.53057	+	11.0280i	0.230899	+	0.562041i
$386$		0			0
$387$	−0.199729	−	0.345941i	−0.0101528	−	0.0175852i
$388$		0			0
$389$	−3.75696	+	6.50725i	−0.190486	+	0.329931i	−0.945411	−	0.325880i	$-0.894340\pi$
$389$	−3.75696	+	6.50725i	−0.190486	+	0.329931i	0.754926	+	0.655810i	$0.227673\pi$
$390$		0			0
$391$	−4.19007			−0.211901
$392$		0			0
$393$	−19.2850			−0.972800
$394$		0			0
$395$	2.05825	−	3.56499i	0.103562	−	0.179374i
$396$		0			0
$397$	13.0530	+	22.6084i	0.655109	+	1.13468i	0.981866	+	0.189574i	$0.0607108\pi$
$397$	13.0530	+	22.6084i	0.655109	+	1.13468i	−0.326757	+	0.945108i	$0.605956\pi$
$398$		0			0
$399$	−7.75224	−	18.8701i	−0.388097	−	0.944684i
$400$		0			0
$401$	−3.36153	−	5.82234i	−0.167867	−	0.290754i	0.769803	−	0.638282i	$-0.220354\pi$
$401$	−3.36153	−	5.82234i	−0.167867	−	0.290754i	−0.937670	+	0.347528i	$0.887021\pi$
$402$		0			0
$403$	−24.2179	+	41.9466i	−1.20638	+	2.08951i
$404$		0			0
$405$	5.13930			0.255374
$406$		0			0
$407$	34.5080			1.71050
$408$		0			0
$409$	−2.44865	+	4.24119i	−0.121078	+	0.209714i	−0.920193	−	0.391465i	$-0.871969\pi$
$409$	−2.44865	+	4.24119i	−0.121078	+	0.209714i	0.799115	+	0.601178i	$0.205302\pi$
$410$		0			0
$411$	9.28018	+	16.0737i	0.457757	+	0.792859i
$412$		0			0
$413$	−20.9204	−	2.81593i	−1.02943	−	0.138563i
$414$		0			0
$415$	2.09463	+	3.62800i	0.102821	+	0.178091i
$416$		0			0
$417$	5.21557	−	9.03364i	0.255408	−	0.442379i
$418$		0			0
$419$	−4.81341			−0.235151			−0.117575	−	0.993064i	$-0.537512\pi$
$419$	−4.81341			−0.235151			−0.117575	+	0.993064i	$0.537512\pi$
$420$		0			0
$421$	−0.402770			−0.0196298			−0.00981490	−	0.999952i	$-0.503124\pi$
$421$	−0.402770			−0.0196298			−0.00981490	+	0.999952i	$0.503124\pi$
$422$		0			0
$423$	1.99169	−	3.44971i	0.0968392	−	0.167730i
$424$		0			0
$425$	−2.18130	−	3.77812i	−0.105809	−	0.183266i
$426$		0			0
$427$	14.4439	−	18.7111i	0.698987	−	0.905492i
$428$		0			0
$429$	20.5729	+	35.6334i	0.993271	+	1.72040i
$430$		0			0
$431$	−4.03202	+	6.98366i	−0.194215	+	0.336391i	−0.946643	−	0.322284i	$-0.895549\pi$
$431$	−4.03202	+	6.98366i	−0.194215	+	0.336391i	0.752428	+	0.658675i	$0.228883\pi$
$432$		0			0
$433$	−31.8869			−1.53238			−0.766192	−	0.642611i	$-0.777851\pi$
$433$	−31.8869			−1.53238			−0.766192	+	0.642611i	$0.777851\pi$
$434$		0			0
$435$	−2.25421			−0.108081
$436$		0			0
$437$	10.6373	−	18.4244i	0.508853	−	0.881359i
$438$		0			0
$439$	−9.48183	−	16.4230i	−0.452543	−	0.783828i	0.546000	−	0.837785i	$-0.316150\pi$
$439$	−9.48183	−	16.4230i	−0.452543	−	0.783828i	−0.998543	+	0.0539573i	$0.982817\pi$
$440$		0			0
$441$	−4.68378	−	1.28416i	−0.223037	−	0.0611505i
$442$		0			0
$443$	−5.46078	−	9.45835i	−0.259449	−	0.449380i	0.706645	−	0.707568i	$-0.250208\pi$
$443$	−5.46078	−	9.45835i	−0.259449	−	0.449380i	−0.966095	+	0.258189i	$0.916874\pi$
$444$		0			0
$445$	−0.210910	+	0.365307i	−0.00999808	+	0.0173172i
$446$		0			0
$447$	−10.5437			−0.498700
$448$		0			0
$449$	3.09341			0.145987			0.0729936	−	0.997332i	$-0.476745\pi$
$449$	3.09341			0.145987			0.0729936	+	0.997332i	$0.476745\pi$
$450$		0			0
$451$	17.6374	−	30.5489i	0.830514	−	1.43849i
$452$		0			0
$453$	10.4356	+	18.0751i	0.490309	+	0.849240i
$454$		0			0
$455$	−6.19592	+	8.02641i	−0.290469	+	0.376284i
$456$		0			0
$457$	−0.524616	−	0.908661i	−0.0245405	−	0.0425054i	0.853494	−	0.521102i	$-0.174479\pi$
$457$	−0.524616	−	0.908661i	−0.0245405	−	0.0425054i	−0.878035	+	0.478597i	$0.841146\pi$
$458$		0			0
$459$	−2.80474	+	4.85795i	−0.130914	+	0.226749i
$460$		0			0
$461$	−29.5804			−1.37770			−0.688848	−	0.724906i	$-0.741883\pi$
$461$	−29.5804			−1.37770			−0.688848	+	0.724906i	$0.741883\pi$
$462$		0			0
$463$	1.85379			0.0861529			0.0430764	−	0.999072i	$-0.486284\pi$
$463$	1.85379			0.0861529			0.0430764	+	0.999072i	$0.486284\pi$
$464$		0			0
$465$	6.11674	−	10.5945i	0.283657	−	0.491309i
$466$		0			0
$467$	−15.9179	−	27.5706i	−0.736591	−	1.27581i	−0.954022	−	0.299737i	$-0.903101\pi$
$467$	−15.9179	−	27.5706i	−0.736591	−	1.27581i	0.217431	−	0.976076i	$-0.430232\pi$
$468$		0			0
$469$	−28.0008	−	3.76896i	−1.29296	−	0.174035i
$470$		0			0
$471$	2.95809	+	5.12356i	0.136302	+	0.236081i
$472$		0			0
$473$	−1.62485	+	2.81432i	−0.0747107	+	0.129403i
$474$		0			0
$475$	22.1507			1.01634
$476$		0			0
$477$	−3.12444			−0.143058
$478$		0			0
$479$	18.7418	−	32.4617i	0.856334	−	1.48321i	−0.0190675	−	0.999818i	$-0.506070\pi$
$479$	18.7418	−	32.4617i	0.856334	−	1.48321i	0.875402	−	0.483396i	$-0.160597\pi$
$480$		0			0
$481$	14.6740	+	25.4161i	0.669078	+	1.15888i
$482$		0			0
$483$	6.39745	+	15.5723i	0.291094	+	0.708565i
$484$		0			0
$485$	2.21084	+	3.82928i	0.100389	+	0.173879i
$486$		0			0
$487$	−15.5422	+	26.9198i	−0.704283	+	1.21985i	0.262667	+	0.964887i	$0.415398\pi$
$487$	−15.5422	+	26.9198i	−0.704283	+	1.21985i	−0.966950	+	0.254967i	$0.917935\pi$
$488$		0			0
$489$	37.0029			1.67333
$490$		0			0
$491$	37.0322			1.67124			0.835621	−	0.549306i	$-0.185108\pi$
$491$	37.0322			1.67124			0.835621	+	0.549306i	$0.185108\pi$
$492$		0			0
$493$	0.929630	−	1.61017i	0.0418684	−	0.0725183i
$494$		0			0
$495$	1.56323	+	2.70759i	0.0702619	+	0.121697i
$496$		0			0
$497$	3.75960	+	9.15140i	0.168641	+	0.410496i
$498$		0			0
$499$	−3.81702	−	6.61128i	−0.170873	−	0.295961i	0.767852	−	0.640627i	$-0.221326\pi$
$499$	−3.81702	−	6.61128i	−0.170873	−	0.295961i	−0.938725	+	0.344666i	$0.887992\pi$
$500$		0			0
$501$	−11.0561	+	19.1498i	−0.493952	+	0.855549i
$502$		0			0
$503$	0.908307			0.0404994			0.0202497	−	0.999795i	$-0.493554\pi$
$503$	0.908307			0.0404994			0.0202497	+	0.999795i	$0.493554\pi$
$504$		0			0
$505$	−9.35226			−0.416170
$506$		0			0
$507$	−7.62568	+	13.2081i	−0.338669	+	0.586591i
$508$		0			0
$509$	3.54117	+	6.13349i	0.156960	+	0.271862i	0.933771	−	0.357871i	$-0.116497\pi$
$509$	3.54117	+	6.13349i	0.156960	+	0.271862i	−0.776811	+	0.629734i	$0.783164\pi$
$510$		0			0
$511$	34.5556	+	4.65125i	1.52865	+	0.205759i
$512$		0			0
$513$	−14.2408	−	24.6657i	−0.628745	−	1.08902i
$514$		0			0
$515$	−1.81966	+	3.15174i	−0.0801836	+	0.138882i
$516$		0			0
$517$	−32.4059			−1.42521
$518$		0			0
$519$	21.2408			0.932369
$520$		0			0
$521$	8.46355	−	14.6593i	0.370795	−	0.642235i	−0.618893	−	0.785475i	$-0.712419\pi$
$521$	8.46355	−	14.6593i	0.370795	−	0.642235i	0.989688	+	0.143240i	$0.0457520\pi$
$522$		0			0
$523$	4.31166	+	7.46801i	0.188536	+	0.326553i	0.944762	−	0.327756i	$-0.106293\pi$
$523$	4.31166	+	7.46801i	0.188536	+	0.326553i	−0.756227	+	0.654310i	$0.772959\pi$
$524$		0			0
$525$	−10.7109	+	13.8752i	−0.467461	+	0.605565i
$526$		0			0
$527$	5.04506	+	8.73831i	0.219766	+	0.380647i
$528$		0			0
$529$	2.72164	−	4.71402i	0.118332	−	0.204957i
$530$		0			0
$531$	−5.53552			−0.240221
$532$		0			0
$533$	30.0002			1.29946
$534$		0			0
$535$	7.04307	−	12.1989i	0.304498	−	0.527407i
$536$		0			0
$537$	−17.3185	−	29.9966i	−0.747350	−	1.29445i
$538$		0			0
$539$	10.0046	+	38.2224i	0.430927	+	1.64636i
$540$		0			0
$541$	22.3060	+	38.6351i	0.959009	+	1.66105i	0.724914	+	0.688839i	$0.241879\pi$
$541$	22.3060	+	38.6351i	0.959009	+	1.66105i	0.234095	+	0.972214i	$0.424787\pi$
$542$		0			0
$543$	−0.673352	+	1.16628i	−0.0288963	+	0.0500499i
$544$		0			0
$545$	−10.7151			−0.458983
$546$		0			0
$547$	34.2732			1.46542			0.732709	−	0.680543i	$-0.238256\pi$
$547$	34.2732			1.46542			0.732709	+	0.680543i	$0.238256\pi$
$548$		0			0
$549$	3.09927	−	5.36809i	0.132273	−	0.229104i
$550$		0			0
$551$	4.72011	+	8.17546i	0.201083	+	0.348286i
$552$		0			0
$553$	8.33591	−	10.7986i	0.354479	−	0.459204i
$554$		0			0
$555$	−3.70624	−	6.41940i	−0.157321	−	0.272488i
$556$		0			0
$557$	−11.4631	+	19.8547i	−0.485707	+	0.841269i	−0.999865	−	0.0164266i	$-0.994771\pi$
$557$	−11.4631	+	19.8547i	−0.485707	+	0.841269i	0.514158	+	0.857695i	$0.328104\pi$
$558$		0			0
$559$	−2.76378			−0.116895
$560$		0			0
$561$	8.57151			0.361890
$562$		0			0
$563$	−6.64813	+	11.5149i	−0.280185	+	0.485295i	−0.971430	−	0.237326i	$-0.923729\pi$
$563$	−6.64813	+	11.5149i	−0.280185	+	0.485295i	0.691245	+	0.722620i	$0.257063\pi$
$564$		0			0
$565$	−6.18498	−	10.7127i	−0.260204	−	0.450686i
$566$		0			0
$567$	16.8791	+	2.27196i	0.708854	+	0.0954132i
$568$		0			0
$569$	−7.98356	−	13.8279i	−0.334688	−	0.579697i	0.648737	−	0.761013i	$-0.275298\pi$
$569$	−7.98356	−	13.8279i	−0.334688	−	0.579697i	−0.983425	+	0.181316i	$0.941964\pi$
$570$		0			0
$571$	11.2969	−	19.5667i	0.472759	−	0.818842i	−0.526755	−	0.850017i	$-0.676592\pi$
$571$	11.2969	−	19.5667i	0.472759	−	0.818842i	0.999514	+	0.0311751i	$0.00992495\pi$
$572$		0			0
$573$	13.3290			0.556827
$574$		0			0
$575$	−18.2796			−0.762313
$576$		0			0
$577$	−18.5524	+	32.1337i	−0.772346	+	1.33774i	0.163928	+	0.986472i	$0.447583\pi$
$577$	−18.5524	+	32.1337i	−0.772346	+	1.33774i	−0.936274	+	0.351270i	$0.885750\pi$
$578$		0			0
$579$	13.0780	+	22.6517i	0.543502	+	0.941373i
$580$		0			0
$581$	5.27556	+	12.8415i	0.218867	+	0.532754i
$582$		0			0
$583$	12.7091	+	22.0128i	0.526357	+	0.911676i
$584$		0			0
$585$	−1.32948	+	2.30273i	−0.0549672	+	0.0952060i
$586$		0			0
$587$	−14.9886			−0.618646			−0.309323	−	0.950957i	$-0.600102\pi$
$587$	−14.9886			−0.618646			−0.309323	+	0.950957i	$0.600102\pi$
$588$		0			0
$589$	−51.2316			−2.11096
$590$		0			0
$591$	−15.4852	+	26.8212i	−0.636978	+	1.10328i
$592$		0			0
$593$	−21.2759	−	36.8510i	−0.873697	−	1.51329i	−0.858144	−	0.513408i	$-0.828383\pi$
$593$	−21.2759	−	36.8510i	−0.873697	−	1.51329i	−0.0155526	−	0.999879i	$-0.504951\pi$
$594$		0			0
$595$	0.802681	+	1.95384i	0.0329067	+	0.0800996i
$596$		0			0
$597$	6.39015	+	11.0681i	0.261531	+	0.452986i
$598$		0			0
$599$	2.69666	−	4.67076i	0.110183	−	0.190842i	−0.805661	−	0.592377i	$-0.798190\pi$
$599$	2.69666	−	4.67076i	0.110183	−	0.190842i	0.915844	+	0.401535i	$0.131523\pi$
$600$		0			0
$601$	−39.2266			−1.60009			−0.800044	−	0.599942i	$-0.795191\pi$
$601$	−39.2266			−1.60009			−0.800044	+	0.599942i	$0.795191\pi$
$602$		0			0
$603$	−7.40896			−0.301716
$604$		0			0
$605$	8.32624	−	14.4215i	0.338510	−	0.586316i
$606$		0			0
$607$	1.85618	+	3.21500i	0.0753401	+	0.130493i	0.901234	−	0.433333i	$-0.142662\pi$
$607$	1.85618	+	3.21500i	0.0753401	+	0.130493i	−0.825894	+	0.563825i	$0.809329\pi$
$608$		0			0
$609$	−7.40352	−	0.996529i	−0.300006	−	0.0403814i
$610$		0			0
$611$	−13.7801	−	23.8679i	−0.557484	−	0.965591i
$612$		0			0
$613$	9.32919	−	16.1586i	0.376803	−	0.652641i	−0.613792	−	0.789467i	$-0.710357\pi$
$613$	9.32919	−	16.1586i	0.376803	−	0.652641i	0.990595	+	0.136826i	$0.0436902\pi$
$614$		0			0
$615$	−7.57721			−0.305543
$616$		0			0
$617$	0.327324			0.0131776			0.00658878	−	0.999978i	$-0.497903\pi$
$617$	0.327324			0.0131776			0.00658878	+	0.999978i	$0.497903\pi$
$618$		0			0
$619$	−5.83076	+	10.0992i	−0.234358	+	0.405920i	−0.959086	−	0.283115i	$-0.908632\pi$
$619$	−5.83076	+	10.0992i	−0.234358	+	0.405920i	0.724728	+	0.689035i	$0.241965\pi$
$620$		0			0
$621$	11.7521	+	20.3551i	0.471594	+	0.816824i
$622$		0			0
$623$	−0.854187	+	1.10654i	−0.0342223	+	0.0443327i
$624$		0			0
$625$	−7.92265	−	13.7224i	−0.316906	−	0.548897i
$626$		0			0
$627$	−21.7605	+	37.6903i	−0.869031	+	1.50521i
$628$		0			0
$629$	6.11378			0.243773
$630$		0			0
$631$	10.1776			0.405162			0.202581	−	0.979266i	$-0.435067\pi$
$631$	10.1776			0.405162			0.202581	+	0.979266i	$0.435067\pi$
$632$		0			0
$633$	17.3875	−	30.1161i	0.691092	−	1.19701i
$634$		0			0
$635$	0.586203	+	1.01533i	0.0232627	+	0.0402922i
$636$		0			0
$637$	−23.8976	+	23.6222i	−0.946858	+	0.935945i
$638$		0			0
$639$	1.29721	+	2.24684i	0.0513170	+	0.0888836i
$640$		0			0
$641$	8.45887	−	14.6512i	0.334105	−	0.578687i	−0.649207	−	0.760612i	$-0.724899\pi$
$641$	8.45887	−	14.6512i	0.334105	−	0.578687i	0.983313	+	0.181924i	$0.0582326\pi$
$642$		0			0
$643$	−17.1979			−0.678220			−0.339110	−	0.940747i	$-0.610126\pi$
$643$	−17.1979			−0.678220			−0.339110	+	0.940747i	$0.610126\pi$
$644$		0			0
$645$	0.698051			0.0274857
$646$		0			0
$647$	15.4467	−	26.7545i	0.607273	−	1.05183i	−0.384415	−	0.923161i	$-0.625597\pi$
$647$	15.4467	−	26.7545i	0.607273	−	1.05183i	0.991688	−	0.128667i	$-0.0410700\pi$
$648$		0			0
$649$	22.5165	+	38.9997i	0.883848	+	1.53087i
$650$		0			0
$651$	24.7729	−	32.0916i	0.970925	−	1.25777i
$652$		0			0
$653$	−3.56998	−	6.18339i	−0.139704	−	0.241975i	0.787680	−	0.616084i	$-0.211282\pi$
$653$	−3.56998	−	6.18339i	−0.139704	−	0.241975i	−0.927385	+	0.374109i	$0.877949\pi$
$654$		0			0
$655$	−5.06929	+	8.78027i	−0.198074	+	0.343074i
$656$		0			0
$657$	9.14336			0.356716
$658$		0			0
$659$	31.5442			1.22879			0.614394	−	0.789000i	$-0.289401\pi$
$659$	31.5442			1.22879			0.614394	+	0.789000i	$0.289401\pi$
$660$		0			0
$661$	20.7244	−	35.8958i	0.806088	−	1.39618i	−0.109467	−	0.993990i	$-0.534914\pi$
$661$	20.7244	−	35.8958i	0.806088	−	1.39618i	0.915554	−	0.402194i	$-0.131752\pi$
$662$		0			0
$663$	3.64491	+	6.31317i	0.141557	+	0.245183i
$664$		0			0
$665$	−10.6291	−	1.43070i	−0.412179	−	0.0554802i
$666$		0			0
$667$	−3.89522	−	6.74672i	−0.150823	−	0.261234i
$668$		0			0
$669$	7.57286	−	13.1166i	0.292784	−	0.507116i
$670$		0			0
$671$	−50.4267			−1.94670
$672$		0			0
$673$	−34.7524			−1.33961			−0.669804	−	0.742538i	$-0.733622\pi$
$673$	−34.7524			−1.33961			−0.669804	+	0.742538i	$0.733622\pi$
$674$		0			0
$675$	−12.2359	+	21.1933i	−0.470962	+	0.815730i
$676$		0			0
$677$	−2.63952	−	4.57178i	−0.101445	−	0.175708i	0.810835	−	0.585274i	$-0.199013\pi$
$677$	−2.63952	−	4.57178i	−0.101445	−	0.175708i	−0.912280	+	0.409567i	$0.865680\pi$
$678$		0			0
$679$	5.56825	+	13.5539i	0.213690	+	0.520152i
$680$		0			0
$681$	17.8547	+	30.9252i	0.684193	+	1.18506i
$682$		0			0
$683$	−14.1289	+	24.4720i	−0.540627	+	0.936394i	0.458241	+	0.888828i	$0.348480\pi$
$683$	−14.1289	+	24.4720i	−0.540627	+	0.936394i	−0.998868	+	0.0475659i	$0.984854\pi$
$684$		0			0
$685$	9.75762			0.372819
$686$		0			0
$687$	−15.8571			−0.604985
$688$		0			0
$689$	−10.8087	+	18.7212i	−0.411779	+	0.713222i
$690$		0			0
$691$	−17.1436	−	29.6935i	−0.652172	−	1.12960i	−0.982595	−	0.185762i	$-0.940525\pi$
$691$	−17.1436	−	29.6935i	−0.652172	−	1.12960i	0.330423	−	0.943833i	$-0.392809\pi$
$692$		0			0
$693$	3.93717	+	9.58364i	0.149561	+	0.364052i
$694$		0			0
$695$	−2.74195	−	4.74920i	−0.104008	−	0.180147i
$696$		0			0
$697$	3.12483	−	5.41236i	0.118361	−	0.205008i
$698$		0			0
$699$	36.5846			1.38376
$700$		0			0
$701$	30.1766			1.13975			0.569877	−	0.821730i	$-0.306991\pi$
$701$	30.1766			1.13975			0.569877	+	0.821730i	$0.306991\pi$
$702$		0			0
$703$	−15.5211	+	26.8833i	−0.585388	+	1.01392i
$704$		0			0
$705$	3.48047	+	6.02835i	0.131082	+	0.227041i
$706$		0			0
$707$	−30.7157	−	4.13440i	−1.15518	−	0.155490i
$708$		0			0
$709$	−18.5958	−	32.2089i	−0.698380	−	1.20963i	−0.969028	−	0.246951i	$-0.920571\pi$
$709$	−18.5958	−	32.2089i	−0.698380	−	1.20963i	0.270648	−	0.962678i	$-0.412762\pi$
$710$		0			0
$711$	1.78867	−	3.09806i	0.0670802	−	0.116186i
$712$		0			0
$713$	42.2784			1.58334
$714$		0			0
$715$	21.6314			0.808967
$716$		0			0
$717$	−22.5714	+	39.0948i	−0.842945	+	1.46002i
$718$		0			0
$719$	−12.7382	−	22.0631i	−0.475053	−	0.822816i	0.524539	−	0.851387i	$-0.324238\pi$
$719$	−12.7382	−	22.0631i	−0.475053	−	0.822816i	−0.999592	+	0.0285707i	$0.990904\pi$
$720$		0			0
$721$	−7.36963	+	9.54687i	−0.274459	+	0.355544i
$722$		0			0
$723$	−3.08617	−	5.34540i	−0.114776	−	0.198798i
$724$		0			0
$725$	4.05561	−	7.02452i	0.150621	−	0.260884i
$726$		0			0
$727$	29.7250			1.10244			0.551220	−	0.834360i	$-0.314162\pi$
$727$	29.7250			1.10244			0.551220	+	0.834360i	$0.314162\pi$
$728$		0			0
$729$	30.0221			1.11193
$730$		0			0
$731$	−0.287875	+	0.498614i	−0.0106474	+	0.0184419i
$732$		0			0
$733$	−16.1043	−	27.8934i	−0.594824	−	1.03027i	−0.993572	−	0.113205i	$-0.963888\pi$
$733$	−16.1043	−	27.8934i	−0.594824	−	1.03027i	0.398747	−	0.917061i	$-0.369445\pi$
$734$		0			0
$735$	6.03586	−	5.96629i	0.222636	−	0.220070i
$736$		0			0
$737$	30.1370	+	52.1988i	1.11011	+	1.92277i
$738$		0			0
$739$	6.37001	−	11.0332i	0.234325	−	0.405862i	−0.724752	−	0.689010i	$-0.758045\pi$
$739$	6.37001	−	11.0332i	0.234325	−	0.405862i	0.959076	+	0.283148i	$0.0913788\pi$
$740$		0			0
$741$	−37.0134			−1.35972
$742$		0			0
$743$	−37.8141			−1.38727			−0.693633	−	0.720328i	$-0.743991\pi$
$743$	−37.8141			−1.38727			−0.693633	+	0.720328i	$0.743991\pi$
$744$		0			0
$745$	−2.77154	+	4.80045i	−0.101541	+	0.175875i
$746$		0			0
$747$	1.82028	+	3.15282i	0.0666006	+	0.115356i
$748$		0			0
$749$	28.5245	−	36.9516i	1.04226	−	1.35018i
$750$		0			0
$751$	−14.1488	−	24.5064i	−0.516296	−	0.894252i	−0.999821	−	0.0189209i	$-0.993977\pi$
$751$	−14.1488	−	24.5064i	−0.516296	−	0.894252i	0.483525	−	0.875331i	$-0.339356\pi$
$752$		0			0
$753$	−2.12643	+	3.68308i	−0.0774913	+	0.134219i
$754$		0			0
$755$	10.9725			0.399331
$756$		0			0
$757$	−27.2325			−0.989782			−0.494891	−	0.868955i	$-0.664792\pi$
$757$	−27.2325			−0.989782			−0.494891	+	0.868955i	$0.664792\pi$
$758$		0			0
$759$	17.9576	−	31.1035i	0.651821	−	1.12899i
$760$		0			0
$761$	−6.04326	−	10.4672i	−0.219068	−	0.379437i	0.735455	−	0.677573i	$-0.236968\pi$
$761$	−6.04326	−	10.4672i	−0.219068	−	0.379437i	−0.954523	+	0.298136i	$0.903635\pi$
$762$		0			0
$763$	−35.1917	−	4.73687i	−1.27402	−	0.171486i
$764$		0			0
$765$	0.276957	+	0.479704i	0.0100134	+	0.0173437i
$766$		0			0
$767$	−19.1496	+	33.1681i	−0.691452	+	1.19763i
$768$		0			0
$769$	−1.76850			−0.0637739			−0.0318870	−	0.999491i	$-0.510152\pi$
$769$	−1.76850			−0.0637739			−0.0318870	+	0.999491i	$0.510152\pi$
$770$		0			0
$771$	5.76555			0.207641
$772$		0			0
$773$	−3.95620	+	6.85234i	−0.142295	+	0.246462i	−0.928360	−	0.371681i	$-0.878781\pi$
$773$	−3.95620	+	6.85234i	−0.142295	+	0.246462i	0.786066	+	0.618143i	$0.212115\pi$
$774$		0			0
$775$	22.0096	+	38.1218i	0.790608	+	1.36937i
$776$		0			0
$777$	−9.33460	−	22.7217i	−0.334877	−	0.815138i
$778$		0			0
$779$	15.8660	+	27.4807i	0.568458	+	0.984599i
$780$		0			0
$781$	10.5532	−	18.2786i	0.377623	−	0.654061i
$782$		0			0
$783$	−10.4295			−0.372719
$784$		0			0
$785$	3.11027			0.111010
$786$		0			0
$787$	−7.92246	+	13.7221i	−0.282405	+	0.489140i	−0.971977	−	0.235078i	$-0.924466\pi$
$787$	−7.92246	+	13.7221i	−0.282405	+	0.489140i	0.689572	+	0.724218i	$0.257799\pi$
$788$		0			0
$789$	5.49229	+	9.51292i	0.195531	+	0.338669i
$790$		0			0
$791$	−15.5776	−	37.9181i	−0.553875	−	1.34821i
$792$		0			0
$793$	−21.4432	−	37.1408i	−0.761472	−	1.31891i
$794$		0			0
$795$	2.72997	−	4.72845i	0.0968222	−	0.167701i
$796$		0			0
$797$	7.19960			0.255023			0.127511	−	0.991837i	$-0.459301\pi$
$797$	7.19960			0.255023			0.127511	+	0.991837i	$0.459301\pi$
$798$		0			0
$799$	−5.74135			−0.203114
$800$		0			0
$801$	−0.183286	+	0.317460i	−0.00647608	+	0.0112169i
$802$		0			0
$803$	−37.1919	−	64.4182i	−1.31247	−	2.27327i
$804$		0			0
$805$	8.77157	+	1.18067i	0.309157	+	0.0416132i
$806$		0			0
$807$	−0.640378	−	1.10917i	−0.0225424	−	0.0390446i
$808$		0			0
$809$	16.1351	−	27.9468i	0.567280	−	0.982558i	−0.429554	−	0.903041i	$-0.641329\pi$
$809$	16.1351	−	27.9468i	0.567280	−	0.982558i	0.996834	−	0.0795164i	$-0.0253376\pi$
$810$		0			0
$811$	−9.81258			−0.344566			−0.172283	−	0.985047i	$-0.555114\pi$
$811$	−9.81258			−0.344566			−0.172283	+	0.985047i	$0.555114\pi$
$812$		0			0
$813$	3.66309			0.128470
$814$		0			0
$815$	9.72664	−	16.8470i	0.340710	−	0.590126i
$816$		0			0
$817$	−1.46166	−	2.53166i	−0.0511369	−	0.0885717i
$818$		0			0
$819$	−5.38441	+	6.97515i	−0.188146	+	0.243731i
$820$		0			0
$821$	2.13697	+	3.70134i	0.0745808	+	0.129178i	0.900904	−	0.434019i	$-0.142905\pi$
$821$	2.13697	+	3.70134i	0.0745808	+	0.129178i	−0.826323	+	0.563196i	$0.809571\pi$
$822$		0			0
$823$	0.448191	−	0.776290i	0.0156230	−	0.0270598i	−0.858108	−	0.513469i	$-0.828360\pi$
$823$	0.448191	−	0.776290i	0.0156230	−	0.0270598i	0.873731	+	0.486409i	$0.161694\pi$
$824$		0			0
$825$	37.3941			1.30190
$826$		0			0
$827$	−19.0211			−0.661428			−0.330714	−	0.943731i	$-0.607290\pi$
$827$	−19.0211			−0.661428			−0.330714	+	0.943731i	$0.607290\pi$
$828$		0			0
$829$	−4.26122	+	7.38065i	−0.147998	+	0.256341i	−0.930488	−	0.366323i	$-0.880616\pi$
$829$	−4.26122	+	7.38065i	−0.147998	+	0.256341i	0.782489	+	0.622664i	$0.213950\pi$
$830$		0			0
$831$	−18.0184	−	31.2088i	−0.625052	−	1.08262i
$832$		0			0
$833$	1.77251	+	6.77187i	0.0614139	+	0.234631i
$834$		0			0
$835$	5.81247	+	10.0675i	0.201149	+	0.348400i
$836$		0			0
$837$	28.3001	−	49.0173i	0.978196	−	1.69429i
$838$		0			0
$839$	−16.8692			−0.582389			−0.291195	−	0.956664i	$-0.594053\pi$
$839$	−16.8692			−0.582389			−0.291195	+	0.956664i	$0.594053\pi$
$840$		0			0
$841$	−25.5432			−0.880798
$842$		0			0
$843$	2.18323	−	3.78147i	0.0751946	−	0.130241i
$844$		0			0
$845$	4.00900	+	6.94380i	0.137914	+	0.238874i
$846$		0			0
$847$	33.7213	−	43.6838i	1.15868	−	1.50099i
$848$		0			0
$849$	19.9299	+	34.5195i	0.683991	+	1.18471i
$850$		0			0
$851$	12.8086	−	22.1852i	0.439073	−	0.760497i
$852$		0			0
$853$	14.8586			0.508750			0.254375	−	0.967106i	$-0.418130\pi$
$853$	14.8586			0.508750			0.254375	+	0.967106i	$0.418130\pi$
$854$		0			0
$855$	−2.81245			−0.0961837
$856$		0			0
$857$	−0.854275	+	1.47965i	−0.0291815	+	0.0505438i	−0.880247	−	0.474515i	$-0.842623\pi$
$857$	−0.854275	+	1.47965i	−0.0291815	+	0.0505438i	0.851066	+	0.525059i	$0.175957\pi$
$858$		0			0
$859$	−0.374650	−	0.648912i	−0.0127829	−	0.0221406i	0.859563	−	0.511029i	$-0.170736\pi$
$859$	−0.374650	−	0.648912i	−0.0127829	−	0.0221406i	−0.872346	+	0.488889i	$0.837402\pi$
$860$		0			0
$861$	−24.8859	−	3.34970i	−0.848110	−	0.114157i
$862$		0			0
$863$	11.5038	+	19.9251i	0.391593	+	0.678259i	0.992660	−	0.120940i	$-0.0385907\pi$
$863$	11.5038	+	19.9251i	0.391593	+	0.678259i	−0.601067	+	0.799199i	$0.705257\pi$
$864$		0			0
$865$	5.58340	−	9.67073i	0.189841	−	0.328815i
$866$		0			0
$867$	1.51862			0.0515749
$868$		0			0
$869$	−29.1026			−0.987236
$870$		0			0
$871$	−25.6306	+	44.3935i	−0.868460	+	1.50422i
$872$		0			0
$873$	1.92127	+	3.32774i	0.0650252	+	0.112627i
$874$		0			0
$875$	7.51518	+	18.2930i	0.254060	+	0.618417i
$876$		0			0
$877$	−24.1514	−	41.8314i	−0.815534	−	1.41255i	−0.908944	−	0.416918i	$-0.863110\pi$
$877$	−24.1514	−	41.8314i	−0.815534	−	1.41255i	0.0934102	−	0.995628i	$-0.470223\pi$
$878$		0			0
$879$	10.7918	−	18.6919i	0.363998	−	0.630462i
$880$		0			0
$881$	−52.2783			−1.76130			−0.880650	−	0.473767i	$-0.842894\pi$
$881$	−52.2783			−1.76130			−0.880650	+	0.473767i	$0.842894\pi$
$882$		0			0
$883$	11.5340			0.388149			0.194075	−	0.980987i	$-0.437830\pi$
$883$	11.5340			0.388149			0.194075	+	0.980987i	$0.437830\pi$
$884$		0			0
$885$	4.83664	−	8.37731i	0.162582	−	0.281600i
$886$		0			0
$887$	−12.3853	−	21.4520i	−0.415859	−	0.720288i	0.579660	−	0.814859i	$-0.303186\pi$
$887$	−12.3853	−	21.4520i	−0.415859	−	0.720288i	−0.995518	+	0.0945706i	$0.969852\pi$
$888$		0			0
$889$	1.47642	+	3.59382i	0.0495175	+	0.120533i
$890$		0			0
$891$	−18.1668	−	31.4658i	−0.608610	−	1.05414i
$892$		0			0
$893$	14.5756	−	25.2456i	0.487753	−	0.844813i
$894$		0			0
$895$	−18.2095			−0.608677
$896$		0			0
$897$	30.5449			1.01986
$898$		0			0
$899$	−9.38009	+	16.2468i	−0.312843	+	0.541861i
$900$		0			0
$901$	2.25167	+	3.90001i	0.0750140	+	0.129928i
$902$		0			0
$903$	2.29262	+	0.308591i	0.0762936	+	0.0102693i
$904$		0			0
$905$	0.353997	+	0.613141i	0.0117673	+	0.0203815i
$906$		0			0
$907$	5.83019	−	10.0982i	0.193588	−	0.335305i	−0.752848	−	0.658194i	$-0.771321\pi$
$907$	5.83019	−	10.0982i	0.193588	−	0.335305i	0.946437	+	0.322889i	$0.104654\pi$
$908$		0			0
$909$	−8.12734			−0.269567
$910$		0			0
$911$	−15.4049			−0.510389			−0.255194	−	0.966890i	$-0.582139\pi$
$911$	−15.4049			−0.510389			−0.255194	+	0.966890i	$0.582139\pi$
$912$		0			0
$913$	14.8085	−	25.6490i	0.490089	−	0.848859i
$914$		0			0
$915$	5.41595	+	9.38071i	0.179046	+	0.310117i
$916$		0			0
$917$	−20.5307	+	26.5962i	−0.677983	+	0.878282i
$918$		0			0
$919$	22.4714	+	38.9216i	0.741264	+	1.28391i	0.951920	+	0.306346i	$0.0991066\pi$
$919$	22.4714	+	38.9216i	0.741264	+	1.28391i	−0.210656	+	0.977560i	$0.567560\pi$
$920$		0			0
$921$	−20.1958	+	34.9801i	−0.665473	+	1.15263i
$922$		0			0
$923$	17.9504			0.590843
$924$		0			0
$925$	26.6720			0.876970
$926$		0			0
$927$	−1.58133	+	2.73894i	−0.0519375	+	0.0899585i
$928$		0			0
$929$	17.5270	+	30.3577i	0.575042	+	0.996002i	0.996037	+	0.0889394i	$0.0283477\pi$
$929$	17.5270	+	30.3577i	0.575042	+	0.996002i	−0.420995	+	0.907063i	$0.638319\pi$
$930$		0			0
$931$	−34.2769	−	9.39774i	−1.12338	−	0.307998i
$932$		0			0
$933$	−16.1386	−	27.9528i	−0.528353	−	0.915135i
$934$		0			0
$935$	2.25312	−	3.90252i	0.0736850	−	0.127626i
$936$		0			0
$937$	9.30499			0.303981			0.151990	−	0.988382i	$-0.451432\pi$
$937$	9.30499			0.303981			0.151990	+	0.988382i	$0.451432\pi$
$938$		0			0
$939$	−26.9659			−0.879999
$940$		0			0
$941$	5.18398	−	8.97892i	0.168993	−	0.292705i	−0.769073	−	0.639161i	$-0.779282\pi$
$941$	5.18398	−	8.97892i	0.168993	−	0.292705i	0.938066	+	0.346456i	$0.112615\pi$
$942$		0			0
$943$	−13.0933	−	22.6782i	−0.426375	−	0.738503i
$944$		0			0
$945$	7.24034	−	9.37939i	0.235528	−	0.305111i
$946$		0			0
$947$	−5.72785	−	9.92092i	−0.186130	−	0.322387i	0.757827	−	0.652456i	$-0.226261\pi$
$947$	−5.72785	−	9.92092i	−0.186130	−	0.322387i	−0.943957	+	0.330069i	$0.892928\pi$
$948$		0			0
$949$	31.6306	−	54.7858i	1.02677	−	1.77842i
$950$		0			0
$951$	3.02286			0.0980228
$952$		0			0
$953$	25.4052			0.822956			0.411478	−	0.911420i	$-0.365013\pi$
$953$	25.4052			0.822956			0.411478	+	0.911420i	$0.365013\pi$
$954$		0			0
$955$	3.50368	−	6.06856i	0.113377	−	0.196374i
$956$		0			0
$957$	7.96834	+	13.8016i	0.257580	+	0.446141i
$958$		0			0
$959$	32.0471	+	4.31360i	1.03485	+	0.139293i
$960$		0			0
$961$	−35.4053	−	61.3239i	−1.14211	−	1.97819i
$962$		0			0
$963$	6.12060	−	10.6012i	0.197233	−	0.341618i
$964$		0			0
$965$	13.7508			0.442654
$966$		0			0
$967$	29.5141			0.949108			0.474554	−	0.880226i	$-0.342609\pi$
$967$	29.5141			0.949108			0.474554	+	0.880226i	$0.342609\pi$
$968$		0			0
$969$	−3.85531	+	6.67760i	−0.123850	+	0.214515i
$970$		0			0
$971$	5.34427	+	9.25655i	0.171506	+	0.297057i	0.938947	−	0.344063i	$-0.111803\pi$
$971$	5.34427	+	9.25655i	0.171506	+	0.297057i	−0.767441	+	0.641120i	$0.778470\pi$
$972$		0			0
$973$	−6.90592	−	16.8100i	−0.221394	−	0.538904i
$974$		0			0
$975$	15.9013	+	27.5419i	0.509249	+	0.882045i
$976$		0			0
$977$	26.0881	−	45.1858i	0.834631	−	1.44562i	−0.0597000	−	0.998216i	$-0.519014\pi$
$977$	26.0881	−	45.1858i	0.834631	−	1.44562i	0.894331	−	0.447407i	$-0.147652\pi$
$978$		0			0
$979$	2.98216			0.0953102
$980$		0			0
$981$	−9.31166			−0.297298
$982$		0			0
$983$	10.0349	−	17.3809i	0.320063	−	0.554365i	−0.660438	−	0.750881i	$-0.729629\pi$
$983$	10.0349	−	17.3809i	0.320063	−	0.554365i	0.980501	+	0.196515i	$0.0629626\pi$
$984$		0			0
$985$	8.14096	+	14.1006i	0.259393	+	0.449281i
$986$		0			0
$987$	8.76596	+	21.3376i	0.279024	+	0.679184i
$988$		0			0
$989$	1.20622	+	2.08923i	0.0383555	+	0.0664336i
$990$		0			0
$991$	22.6282	−	39.1932i	0.718809	−	1.24501i	−0.242663	−	0.970111i	$-0.578021\pi$
$991$	22.6282	−	39.1932i	0.718809	−	1.24501i	0.961472	−	0.274903i	$-0.0886457\pi$
$992$		0			0
$993$	−23.3852			−0.742108
$994$		0			0
$995$	6.71891			0.213004
$996$		0			0
$997$	−13.2262	+	22.9085i	−0.418878	+	0.725518i	−0.995827	−	0.0912621i	$-0.970910\pi$
$997$	−13.2262	+	22.9085i	−0.418878	+	0.725518i	0.576949	+	0.816780i	$0.304243\pi$
$998$		0			0
$999$	−17.1476	−	29.7004i	−0.542524	−	0.939680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	952.2.q.d.137.2	✓	14
7.2	even	3	inner	952.2.q.d.681.2	yes	14
7.3	odd	6		6664.2.a.x.1.2		7
7.4	even	3		6664.2.a.w.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
952.2.q.d.137.2	✓	14	1.1	even	1	trivial
952.2.q.d.681.2	yes	14	7.2	even	3	inner
6664.2.a.w.1.6		7	7.4	even	3
6664.2.a.x.1.2		7	7.3	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)

\(f(q)\)	\(=\)	\(q+(-0.759308 + 1.31516i) q^{3} +(0.399186 + 0.691411i) q^{5} +(1.00540 + 2.44728i) q^{7} +(0.346902 + 0.600853i) q^{9} +(2.82215 - 4.88810i) q^{11} +4.80031 q^{13} -1.21242 q^{15} +(0.500000 - 0.866025i) q^{17} +(2.53870 + 4.39716i) q^{19} +(-3.98197 - 0.535981i) q^{21} +(-2.09504 - 3.62871i) q^{23} +(2.18130 - 3.77812i) q^{25} -5.60947 q^{27} +1.85926 q^{29} +(-5.04506 + 8.73831i) q^{31} +(4.28576 + 7.42315i) q^{33} +(-1.29073 + 1.67206i) q^{35} +(3.05689 + 5.29469i) q^{37} +(-3.64491 + 6.31317i) q^{39} +6.24965 q^{41} -0.575750 q^{43} +(-0.276957 + 0.479704i) q^{45} +(-2.87068 - 4.97216i) q^{47} +(-4.97835 + 4.92097i) q^{49} +(0.759308 + 1.31516i) q^{51} +(-2.25167 + 3.90001i) q^{53} +4.50625 q^{55} -7.71062 q^{57} +(-3.98924 + 6.90957i) q^{59} +(-4.46706 - 7.73717i) q^{61} +(-1.12168 + 1.45306i) q^{63} +(1.91622 + 3.31898i) q^{65} +(-5.33937 + 9.24806i) q^{67} +6.36311 q^{69} +3.73942 q^{71} +(6.58929 - 11.4130i) q^{73} +(3.31256 + 5.73752i) q^{75} +(14.7999 + 1.99210i) q^{77} +(-2.57805 - 4.46532i) q^{79} +(3.21861 - 5.57480i) q^{81} +5.24724 q^{83} +0.798372 q^{85} +(-1.41175 + 2.44523i) q^{87} +(0.264175 + 0.457564i) q^{89} +(4.82621 + 11.7477i) q^{91} +(-7.66152 - 13.2701i) q^{93} +(-2.02683 + 3.51057i) q^{95} +5.53836 q^{97} +3.91604 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{5} - 7 q^{7} - q^{9} - 5 q^{11} + 22 q^{13} + 16 q^{15} + 7 q^{17} + 2 q^{19} - 13 q^{21} - 9 q^{23} - 2 q^{25} + 18 q^{27} + 18 q^{29} + 2 q^{31} - 2 q^{33} + 9 q^{35} - 8 q^{37} - q^{39}+ \cdots - 24 q^{99}+O(q^{100}) \) 14 * q + q^5 - 7 * q^7 - q^9 - 5 * q^11 + 22 * q^13 + 16 * q^15 + 7 * q^17 + 2 * q^19 - 13 * q^21 - 9 * q^23 - 2 * q^25 + 18 * q^27 + 18 * q^29 + 2 * q^31 - 2 * q^33 + 9 * q^35 - 8 * q^37 - q^39 + 12 * q^41 + 20 * q^43 + 10 * q^45 + q^47 - 21 * q^49 - 3 * q^53 + 22 * q^55 - 10 * q^57 + 4 * q^59 + 32 * q^61 + 13 * q^63 - 20 * q^65 - 31 * q^67 + 32 * q^69 + 6 * q^71 + 7 * q^73 + 19 * q^75 - 26 * q^77 - 8 * q^79 + q^81 + 48 * q^83 + 2 * q^85 + 3 * q^87 - 4 * q^89 - 15 * q^91 - 19 * q^93 - 23 * q^95 + 30 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more