LMFDB - Embedded newform 840.2.dd.b.73.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(73,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.73"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dd (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.9
Character	$\chi$	$=$	840.73
Dual form			840.2.dd.b.817.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{3} +(-0.583460 + 2.15860i) q^{5} +(0.939373 - 2.47337i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-2.18212 + 3.77954i) q^{11} +(-2.79969 + 2.79969i) q^{13} +(-2.23606 - 0.00489121i) q^{15} +(-0.306752 + 0.0821940i) q^{17} +(-1.35172 - 2.34125i) q^{19} +(2.63222 + 0.267208i) q^{21} +(-0.783438 + 2.92383i) q^{23} +(-4.31915 - 2.51892i) q^{25} +(-0.707107 - 0.707107i) q^{27} +4.52748i q^{29} +(1.89712 + 1.09530i) q^{31} +(-4.21553 - 1.12955i) q^{33} +(4.79095 + 3.47085i) q^{35} +(-2.58561 - 0.692812i) q^{37} +(-3.42891 - 1.97968i) q^{39} +2.63418i q^{41} +(6.21198 + 6.21198i) q^{43} +(-0.574011 - 2.16114i) q^{45} +(1.62683 - 6.07142i) q^{47} +(-5.23516 - 4.64684i) q^{49} +(-0.158787 - 0.275026i) q^{51} +(-12.0435 + 3.22704i) q^{53} +(-6.88536 - 6.91554i) q^{55} +(1.91162 - 1.91162i) q^{57} +(-0.863327 + 1.49533i) q^{59} +(-8.84369 + 5.10591i) q^{61} +(0.423166 + 2.61169i) q^{63} +(-4.40992 - 7.67694i) q^{65} +(1.97779 + 7.38122i) q^{67} -3.02697 q^{69} +5.39235 q^{71} +(-4.04357 - 15.0908i) q^{73} +(1.31521 - 4.82392i) q^{75} +(7.29840 + 8.94759i) q^{77} +(-11.6020 + 6.69839i) q^{79} +(0.500000 - 0.866025i) q^{81} +(11.4560 - 11.4560i) q^{83} +(0.00155332 - 0.710113i) q^{85} +(-4.37321 + 1.17180i) q^{87} +(3.03332 + 5.25387i) q^{89} +(4.29473 + 9.55465i) q^{91} +(-0.566971 + 2.11597i) q^{93} +(5.84251 - 1.55181i) q^{95} +(7.89037 + 7.89037i) q^{97} -4.36424i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) $ 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$		0			0
$5$	−0.583460	+	2.15860i	−0.260931	+	0.965357i
$5$	−0.583460	+	2.15860i	−0.260931	+	0.965357i
$6$		0			0
$7$	0.939373	−	2.47337i	0.355049	−	0.934848i
$7$	0.939373	−	2.47337i	0.355049	−	0.934848i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	−2.18212	+	3.77954i	−0.657934	+	1.13957i	0.323216	+	0.946325i	$0.395236\pi$
$11$	−2.18212	+	3.77954i	−0.657934	+	1.13957i	−0.981150	+	0.193249i	$0.938097\pi$
$12$		0			0
$13$	−2.79969	+	2.79969i	−0.776495	+	0.776495i	−0.979233	−	0.202738i	$-0.935016\pi$
$13$	−2.79969	+	2.79969i	−0.776495	+	0.776495i	0.202738	+	0.979233i	$0.435016\pi$
$14$		0			0
$15$	−2.23606	−	0.00489121i	−0.577349	−	0.00126291i
$16$		0			0
$17$	−0.306752	+	0.0821940i	−0.0743983	+	0.0199350i	−0.295826	−	0.955242i	$-0.595595\pi$
$17$	−0.306752	+	0.0821940i	−0.0743983	+	0.0199350i	0.221428	+	0.975177i	$0.428928\pi$
$18$		0			0
$19$	−1.35172	−	2.34125i	−0.310106	−	0.537120i	0.668279	−	0.743911i	$-0.267031\pi$
$19$	−1.35172	−	2.34125i	−0.310106	−	0.537120i	−0.978385	+	0.206791i	$0.933698\pi$
$20$		0			0
$21$	2.63222	+	0.267208i	0.574398	+	0.0583096i
$22$		0			0
$23$	−0.783438	+	2.92383i	−0.163358	+	0.609661i	0.834886	+	0.550423i	$0.185534\pi$
$23$	−0.783438	+	2.92383i	−0.163358	+	0.609661i	−0.998244	+	0.0592377i	$0.981133\pi$
$24$		0			0
$25$	−4.31915	−	2.51892i	−0.863830	−	0.503784i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			4.52748i			0.840732i	0.907355	+	0.420366i	$0.138098\pi$
$29$			4.52748i			0.840732i	−0.907355	+	0.420366i	$0.861902\pi$
$30$		0			0
$31$	1.89712	+	1.09530i	0.340733	+	0.196722i	0.660596	−	0.750741i	$-0.270304\pi$
$31$	1.89712	+	1.09530i	0.340733	+	0.196722i	−0.319863	+	0.947464i	$0.603637\pi$
$32$		0			0
$33$	−4.21553	−	1.12955i	−0.733830	−	0.196629i
$34$		0			0
$35$	4.79095	+	3.47085i	0.809818	+	0.586681i
$36$		0			0
$37$	−2.58561	−	0.692812i	−0.425072	−	0.113898i	0.0399401	−	0.999202i	$-0.487283\pi$
$37$	−2.58561	−	0.692812i	−0.425072	−	0.113898i	−0.465012	+	0.885304i	$0.653950\pi$
$38$		0			0
$39$	−3.42891	−	1.97968i	−0.549065	−	0.317003i
$40$		0			0
$41$			2.63418i			0.411390i	0.978616	+	0.205695i	$0.0659454\pi$
$41$			2.63418i			0.411390i	−0.978616	+	0.205695i	$0.934055\pi$
$42$		0			0
$43$	6.21198	+	6.21198i	0.947319	+	0.947319i	0.998680	−	0.0513615i	$-0.0163561\pi$
$43$	6.21198	+	6.21198i	0.947319	+	0.947319i	−0.0513615	+	0.998680i	$0.516356\pi$
$44$		0			0
$45$	−0.574011	−	2.16114i	−0.0855685	−	0.322163i
$46$		0			0
$47$	1.62683	−	6.07142i	0.237298	−	0.885608i	−0.739802	−	0.672825i	$-0.765081\pi$
$47$	1.62683	−	6.07142i	0.237298	−	0.885608i	0.977100	−	0.212783i	$-0.0682526\pi$
$48$		0			0
$49$	−5.23516	−	4.64684i	−0.747880	−	0.663834i
$50$		0			0
$51$	−0.158787	−	0.275026i	−0.0222346	−	0.0385114i
$52$		0			0
$53$	−12.0435	+	3.22704i	−1.65430	+	0.443268i	−0.960812	−	0.277202i	$-0.910593\pi$
$53$	−12.0435	+	3.22704i	−1.65430	+	0.443268i	−0.693486	+	0.720470i	$0.743926\pi$
$54$		0			0
$55$	−6.88536	−	6.91554i	−0.928421	−	0.932492i
$56$		0			0
$57$	1.91162	−	1.91162i	0.253201	−	0.253201i
$58$		0			0
$59$	−0.863327	+	1.49533i	−0.112396	+	0.194675i	−0.916736	−	0.399494i	$-0.869186\pi$
$59$	−0.863327	+	1.49533i	−0.112396	+	0.194675i	0.804340	+	0.594169i	$0.202519\pi$
$60$		0			0
$61$	−8.84369	+	5.10591i	−1.13232	+	0.653745i	−0.944517	−	0.328462i	$-0.893470\pi$
$61$	−8.84369	+	5.10591i	−1.13232	+	0.653745i	−0.187802	+	0.982207i	$0.560136\pi$
$62$		0			0
$63$	0.423166	+	2.61169i	0.0533140	+	0.329042i
$64$		0			0
$65$	−4.40992	−	7.67694i	−0.546984	−	0.952208i
$66$		0			0
$67$	1.97779	+	7.38122i	0.241626	+	0.901759i	0.975049	+	0.221988i	$0.0712545\pi$
$67$	1.97779	+	7.38122i	0.241626	+	0.901759i	−0.733424	+	0.679772i	$0.762079\pi$
$68$		0			0
$69$	−3.02697			−0.364405
$70$		0			0
$71$	5.39235			0.639955			0.319977	−	0.947425i	$-0.396325\pi$
$71$	5.39235			0.639955			0.319977	+	0.947425i	$0.396325\pi$
$72$		0			0
$73$	−4.04357	−	15.0908i	−0.473264	−	1.76624i	−0.627922	−	0.778276i	$-0.716094\pi$
$73$	−4.04357	−	15.0908i	−0.473264	−	1.76624i	0.154658	−	0.987968i	$-0.450572\pi$
$74$		0			0
$75$	1.31521	−	4.82392i	0.151868	−	0.557018i
$76$		0			0
$77$	7.29840	+	8.94759i	0.831729	+	1.01967i
$78$		0			0
$79$	−11.6020	+	6.69839i	−1.30532	+	0.753628i	−0.981312	−	0.192425i	$-0.938365\pi$
$79$	−11.6020	+	6.69839i	−1.30532	+	0.753628i	−0.324011	+	0.946053i	$0.605031\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	11.4560	−	11.4560i	1.25746	−	1.25746i	0.305165	−	0.952299i	$-0.401288\pi$
$83$	11.4560	−	11.4560i	1.25746	−	1.25746i	0.952299	−	0.305165i	$-0.0987118\pi$
$84$		0			0
$85$	0.00155332	−	0.710113i	0.000168481	−	0.0770226i
$86$		0			0
$87$	−4.37321	+	1.17180i	−0.468858	+	0.125630i
$88$		0			0
$89$	3.03332	+	5.25387i	0.321532	+	0.556909i	0.980804	−	0.194995i	$-0.0624690\pi$
$89$	3.03332	+	5.25387i	0.321532	+	0.556909i	−0.659273	+	0.751904i	$0.729136\pi$
$90$		0			0
$91$	4.29473	+	9.55465i	0.450210	+	1.00160i
$92$		0			0
$93$	−0.566971	+	2.11597i	−0.0587922	+	0.219415i
$94$		0			0
$95$	5.84251	−	1.55181i	0.599429	−	0.159212i
$96$		0			0
$97$	7.89037	+	7.89037i	0.801146	+	0.801146i	0.983275	−	0.182129i	$-0.0582987\pi$
$97$	7.89037	+	7.89037i	0.801146	+	0.801146i	−0.182129	+	0.983275i	$0.558299\pi$
$98$		0			0
$99$		−	4.36424i		−	0.438622i
$100$		0			0
$101$	−2.94262	−	1.69892i	−0.292801	−	0.169049i	0.346403	−	0.938086i	$-0.387403\pi$
$101$	−2.94262	−	1.69892i	−0.292801	−	0.169049i	−0.639205	+	0.769037i	$0.720736\pi$
$102$		0			0
$103$	14.9624	+	4.00916i	1.47429	+	0.395034i	0.904399	−	0.426687i	$-0.140319\pi$
$103$	14.9624	+	4.00916i	1.47429	+	0.395034i	0.569889	+	0.821722i	$0.306986\pi$
$104$		0			0
$105$	−2.11259	+	5.52602i	−0.206168	+	0.539285i
$106$		0			0
$107$	13.1754	+	3.53035i	1.27372	+	0.341291i	0.831454	−	0.555594i	$-0.187509\pi$
$107$	13.1754	+	3.53035i	1.27372	+	0.341291i	0.442263	+	0.896885i	$0.354176\pi$
$108$		0			0
$109$	−0.454868	−	0.262618i	−0.0435685	−	0.0251543i	0.478058	−	0.878329i	$-0.341341\pi$
$109$	−0.454868	−	0.262618i	−0.0435685	−	0.0251543i	−0.521626	+	0.853174i	$0.674674\pi$
$110$		0			0
$111$		−	2.67682i		−	0.254073i
$112$		0			0
$113$	12.2952	+	12.2952i	1.15664	+	1.15664i	0.985194	+	0.171445i	$0.0548436\pi$
$113$	12.2952	+	12.2952i	1.15664	+	1.15664i	0.171445	+	0.985194i	$0.445156\pi$
$114$		0			0
$115$	−5.85429	−	3.39707i	−0.545915	−	0.316779i
$116$		0			0
$117$	1.02476	−	3.82445i	0.0947390	−	0.353571i
$118$		0			0
$119$	−0.0848581	+	0.835923i	−0.00777893	+	0.0766290i
$120$		0			0
$121$	−4.02329	−	6.96854i	−0.365754	−	0.633504i
$122$		0			0
$123$	−2.54442	+	0.681776i	−0.229423	+	0.0614736i
$124$		0			0
$125$	7.95740	−	7.85365i	0.711732	−	0.702451i
$126$		0			0
$127$	6.07887	−	6.07887i	0.539413	−	0.539413i	−0.383944	−	0.923357i	$-0.625434\pi$
$127$	6.07887	−	6.07887i	0.539413	−	0.539413i	0.923357	+	0.383944i	$0.125434\pi$
$128$		0			0
$129$	−4.39254	+	7.60810i	−0.386741	+	0.669855i
$130$		0			0
$131$	−4.99501	+	2.88387i	−0.436416	+	0.251965i	−0.702076	−	0.712102i	$-0.747743\pi$
$131$	−4.99501	+	2.88387i	−0.436416	+	0.251965i	0.265660	+	0.964067i	$0.414410\pi$
$132$		0			0
$133$	−7.06056	+	1.14401i	−0.612228	+	0.0991979i
$134$		0			0
$135$	1.93893	−	1.11380i	0.166877	−	0.0958602i
$136$		0			0
$137$	4.91846	+	18.3559i	0.420212	+	1.56825i	0.774161	+	0.632989i	$0.218172\pi$
$137$	4.91846	+	18.3559i	0.420212	+	1.56825i	−0.353948	+	0.935265i	$0.615161\pi$
$138$		0			0
$139$	−0.316854			−0.0268752			−0.0134376	−	0.999910i	$-0.504277\pi$
$139$	−0.316854			−0.0268752			−0.0134376	+	0.999910i	$0.504277\pi$
$140$		0			0
$141$	6.28560			0.529343
$142$		0			0
$143$	−4.47229	−	16.6908i	−0.373992	−	1.39576i
$144$		0			0
$145$	−9.77305	−	2.64161i	−0.811607	−	0.219373i
$146$		0			0
$147$	3.13354	−	6.25946i	0.258450	−	0.516272i
$148$		0			0
$149$	−7.11870	+	4.10998i	−0.583187	+	0.336703i	−0.762399	−	0.647107i	$-0.775978\pi$
$149$	−7.11870	+	4.10998i	−0.583187	+	0.336703i	0.179212	+	0.983810i	$0.442645\pi$
$150$		0			0
$151$	4.68283	−	8.11090i	0.381083	−	0.660055i	−0.610134	−	0.792298i	$-0.708884\pi$
$151$	4.68283	−	8.11090i	0.381083	−	0.660055i	0.991217	+	0.132243i	$0.0422178\pi$
$152$		0			0
$153$	0.224558	−	0.224558i	0.0181544	−	0.0181544i
$154$		0			0
$155$	−3.47123	+	3.45607i	−0.278816	+	0.277598i
$156$		0			0
$157$	14.7926	−	3.96366i	1.18058	−	0.316334i	0.385421	−	0.922741i	$-0.374056\pi$
$157$	14.7926	−	3.96366i	1.18058	−	0.316334i	0.795155	+	0.606407i	$0.207390\pi$
$158$		0			0
$159$	−6.23416	−	10.7979i	−0.494401	−	0.856328i
$160$		0			0
$161$	6.49579	+	4.68430i	0.511940	+	0.369175i
$162$		0			0
$163$	4.76292	−	17.7755i	0.373061	−	1.39228i	−0.483097	−	0.875567i	$-0.660488\pi$
$163$	4.76292	−	17.7755i	0.373061	−	1.39228i	0.856158	−	0.516715i	$-0.172845\pi$
$164$		0			0
$165$	4.89784	−	8.44062i	0.381296	−	0.657101i
$166$		0			0
$167$	−7.47910	−	7.47910i	−0.578750	−	0.578750i	0.355809	−	0.934559i	$-0.384205\pi$
$167$	−7.47910	−	7.47910i	−0.578750	−	0.578750i	−0.934559	+	0.355809i	$0.884205\pi$
$168$		0			0
$169$		−	2.67657i		−	0.205890i
$170$		0			0
$171$	2.34125	+	1.35172i	0.179040	+	0.103369i
$172$		0			0
$173$	5.29635	+	1.41915i	0.402674	+	0.107896i	0.454471	−	0.890761i	$-0.349828\pi$
$173$	5.29635	+	1.41915i	0.402674	+	0.107896i	−0.0517971	+	0.998658i	$0.516495\pi$
$174$		0			0
$175$	−10.2875	+	8.31667i	−0.777663	+	0.628681i
$176$		0			0
$177$	−1.66782	−	0.446891i	−0.125361	−	0.0335904i
$178$		0			0
$179$	8.91592	+	5.14761i	0.666407	+	0.384750i	0.794714	−	0.606984i	$-0.207621\pi$
$179$	8.91592	+	5.14761i	0.666407	+	0.384750i	−0.128307	+	0.991735i	$0.540954\pi$
$180$		0			0
$181$		−	13.9242i		−	1.03498i	−0.855689	−	0.517490i	$-0.826866\pi$
$181$		−	13.9242i		−	1.03498i	0.855689	−	0.517490i	$-0.173134\pi$
$182$		0			0
$183$	−7.22085	−	7.22085i	−0.533780	−	0.533780i
$184$		0			0
$185$	3.00411	−	5.17708i	0.220866	−	0.380627i
$186$		0			0
$187$	0.358714	−	1.33874i	0.0262318	−	0.0978983i
$188$		0			0
$189$	−2.41318	+	1.08470i	−0.175533	+	0.0789005i
$190$		0			0
$191$	5.34601	+	9.25957i	0.386824	+	0.669999i	0.992020	−	0.126077i	$-0.0402387\pi$
$191$	5.34601	+	9.25957i	0.386824	+	0.669999i	−0.605196	+	0.796076i	$0.706905\pi$
$192$		0			0
$193$	4.16518	−	1.11606i	0.299816	−	0.0803356i	−0.105775	−	0.994390i	$-0.533732\pi$
$193$	4.16518	−	1.11606i	0.299816	−	0.0803356i	0.405591	+	0.914055i	$0.367066\pi$
$194$		0			0
$195$	6.27399	−	6.24660i	0.449289	−	0.447328i
$196$		0			0
$197$	−1.11483	+	1.11483i	−0.0794281	+	0.0794281i	−0.745705	−	0.666277i	$-0.767887\pi$
$197$	−1.11483	+	1.11483i	−0.0794281	+	0.0794281i	0.666277	+	0.745705i	$0.267887\pi$
$198$		0			0
$199$	−11.7514	+	20.3540i	−0.833034	+	1.44286i	0.0625877	+	0.998039i	$0.480065\pi$
$199$	−11.7514	+	20.3540i	−0.833034	+	1.44286i	−0.895621	+	0.444817i	$0.853269\pi$
$200$		0			0
$201$	−6.61782	+	3.82080i	−0.466785	+	0.269498i
$202$		0			0
$203$	11.1982	+	4.25299i	0.785957	+	0.298502i
$204$		0			0
$205$	−5.68615	−	1.53694i	−0.397138	−	0.107344i
$206$		0			0
$207$	−0.783438	−	2.92383i	−0.0544527	−	0.203220i
$208$		0			0
$209$	11.7985			0.816117
$210$		0			0
$211$	13.9609			0.961108			0.480554	−	0.876965i	$-0.340436\pi$
$211$	13.9609			0.961108			0.480554	+	0.876965i	$0.340436\pi$
$212$		0			0
$213$	1.39564	+	5.20861i	0.0956280	+	0.356888i
$214$		0			0
$215$	−17.0337	+	9.78477i	−1.16169	+	0.667316i
$216$		0			0
$217$	4.49120	−	3.66340i	0.304883	−	0.248688i
$218$		0			0
$219$	13.5300	−	7.81157i	0.914275	−	0.527857i
$220$		0			0
$221$	0.628694	−	1.08893i	0.0422905	−	0.0732493i
$222$		0			0
$223$	19.7736	−	19.7736i	1.32414	−	1.32414i	0.413745	−	0.910393i	$-0.364220\pi$
$223$	19.7736	−	19.7736i	1.32414	−	1.32414i	0.910393	−	0.413745i	$-0.135780\pi$
$224$		0			0
$225$	4.99995	+	0.0218741i	0.333330	+	0.00145827i
$226$		0			0
$227$	−9.14875	+	2.45140i	−0.607224	+	0.162705i	−0.549313	−	0.835617i	$-0.685111\pi$
$227$	−9.14875	+	2.45140i	−0.607224	+	0.162705i	−0.0579110	+	0.998322i	$0.518444\pi$
$228$		0			0
$229$	0.927717	+	1.60685i	0.0613053	+	0.106184i	0.895049	−	0.445968i	$-0.147140\pi$
$229$	0.927717	+	1.60685i	0.0613053	+	0.106184i	−0.833744	+	0.552151i	$0.813807\pi$
$230$		0			0
$231$	−6.75375	+	9.36552i	−0.444364	+	0.616206i
$232$		0			0
$233$	7.12699	−	26.5983i	0.466905	−	1.74251i	−0.183591	−	0.983003i	$-0.558772\pi$
$233$	7.12699	−	26.5983i	0.466905	−	1.74251i	0.650496	−	0.759510i	$-0.274561\pi$
$234$		0			0
$235$	12.1566	+	7.05412i	0.793009	+	0.460160i
$236$		0			0
$237$	−9.47296	−	9.47296i	−0.615335	−	0.615335i
$238$		0			0
$239$			14.3815i			0.930260i	0.885242	+	0.465130i	$0.153992\pi$
$239$			14.3815i			0.930260i	−0.885242	+	0.465130i	$0.846008\pi$
$240$		0			0
$241$	5.73574	+	3.31153i	0.369471	+	0.213314i	0.673227	−	0.739435i	$-0.264908\pi$
$241$	5.73574	+	3.31153i	0.369471	+	0.213314i	−0.303756	+	0.952750i	$0.598241\pi$
$242$		0			0
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$		0			0
$245$	13.0852	−	8.58939i	0.835983	−	0.548756i
$246$		0			0
$247$	10.3392	+	2.77038i	0.657867	+	0.176275i
$248$		0			0
$249$	14.0307	+	8.10065i	0.889162	+	0.513358i
$250$		0			0
$251$			3.20820i			0.202500i	0.994861	+	0.101250i	$0.0322841\pi$
$251$			3.20820i			0.202500i	−0.994861	+	0.101250i	$0.967716\pi$
$252$		0			0
$253$	−9.34119	−	9.34119i	−0.587275	−	0.587275i
$254$		0			0
$255$	0.686319	−	0.182290i	0.0429789	−	0.0114155i
$256$		0			0
$257$	−4.06736	+	15.1796i	−0.253715	+	0.946877i	0.715086	+	0.699037i	$0.246388\pi$
$257$	−4.06736	+	15.1796i	−0.253715	+	0.946877i	−0.968801	+	0.247841i	$0.920279\pi$
$258$		0			0
$259$	−4.14244	+	5.74437i	−0.257398	+	0.356938i
$260$		0			0
$261$	−2.26374	−	3.92092i	−0.140122	−	0.242699i
$262$		0			0
$263$	−14.0606	+	3.76752i	−0.867011	+	0.232315i	−0.664795	−	0.747026i	$-0.731481\pi$
$263$	−14.0606	+	3.76752i	−0.867011	+	0.232315i	−0.202216	+	0.979341i	$0.564814\pi$
$264$		0			0
$265$	0.0609852	−	27.8799i	0.00374629	−	1.71265i
$266$		0			0
$267$	−4.28977	+	4.28977i	−0.262529	+	0.262529i
$268$		0			0
$269$	6.10002	−	10.5655i	0.371925	−	0.644193i	−0.617937	−	0.786228i	$-0.712031\pi$
$269$	6.10002	−	10.5655i	0.371925	−	0.644193i	0.989862	+	0.142035i	$0.0453646\pi$
$270$		0			0
$271$	−11.0842	+	6.39946i	−0.673317	+	0.388740i	−0.797332	−	0.603541i	$-0.793756\pi$
$271$	−11.0842	+	6.39946i	−0.673317	+	0.388740i	0.124015	+	0.992280i	$0.460423\pi$
$272$		0			0
$273$	−8.11752	+	6.62132i	−0.491295	+	0.400740i
$274$		0			0
$275$	18.9453	−	10.8278i	1.14244	−	0.652942i
$276$		0			0
$277$	5.42047	+	20.2295i	0.325685	+	1.21547i	0.913622	+	0.406565i	$0.133273\pi$
$277$	5.42047	+	20.2295i	0.325685	+	1.21547i	−0.587937	+	0.808906i	$0.700060\pi$
$278$		0			0
$279$	−2.19061			−0.131148
$280$		0			0
$281$	23.8868			1.42497			0.712483	−	0.701690i	$-0.247571\pi$
$281$	23.8868			1.42497			0.712483	+	0.701690i	$0.247571\pi$
$282$		0			0
$283$	1.67303	+	6.24382i	0.0994511	+	0.371157i	0.997657	−	0.0684190i	$-0.0217955\pi$
$283$	1.67303	+	6.24382i	0.0994511	+	0.371157i	−0.898206	+	0.439576i	$0.855129\pi$
$284$		0			0
$285$	3.01108	+	5.24179i	0.178361	+	0.310497i
$286$		0			0
$287$	6.51531	+	2.47448i	0.384586	+	0.146064i
$288$		0			0
$289$	−14.6351	+	8.44957i	−0.860888	+	0.497034i
$290$		0			0
$291$	−5.57934	+	9.66369i	−0.327066	+	0.566496i
$292$		0			0
$293$	−6.91665	+	6.91665i	−0.404075	+	0.404075i	−0.879666	−	0.475591i	$-0.842234\pi$
$293$	−6.91665	+	6.91665i	−0.404075	+	0.404075i	0.475591	+	0.879666i	$0.342234\pi$
$294$		0			0
$295$	−2.72410	−	2.73604i	−0.158603	−	0.159299i
$296$		0			0
$297$	4.21553	−	1.12955i	0.244610	−	0.0655430i
$298$		0			0
$299$	−5.99245	−	10.3792i	−0.346552	−	0.600246i
$300$		0			0
$301$	21.1999	−	9.52919i	1.22194	−	0.549253i
$302$		0			0
$303$	0.879426	−	3.28206i	0.0505217	−	0.188550i
$304$		0			0
$305$	−5.86170	−	22.0691i	−0.335640	−	1.26367i
$306$		0			0
$307$	7.31476	+	7.31476i	0.417475	+	0.417475i	0.884333	−	0.466857i	$-0.154614\pi$
$307$	7.31476	+	7.31476i	0.417475	+	0.417475i	−0.466857	+	0.884333i	$0.654614\pi$
$308$		0			0
$309$			15.4902i			0.881207i
$310$		0			0
$311$	−18.8693	−	10.8942i	−1.06998	−	0.617752i	−0.141803	−	0.989895i	$-0.545290\pi$
$311$	−18.8693	−	10.8942i	−1.06998	−	0.617752i	−0.928175	+	0.372143i	$0.878623\pi$
$312$		0			0
$313$	−22.7616	−	6.09895i	−1.28656	−	0.344733i	−0.450208	−	0.892924i	$-0.648650\pi$
$313$	−22.7616	−	6.09895i	−1.28656	−	0.344733i	−0.836353	+	0.548191i	$0.815317\pi$
$314$		0			0
$315$	−5.88451	−	0.610369i	−0.331555	−	0.0343904i
$316$		0			0
$317$	−21.3318	−	5.71583i	−1.19811	−	0.321033i	−0.396024	−	0.918240i	$-0.629610\pi$
$317$	−21.3318	−	5.71583i	−1.19811	−	0.321033i	−0.802087	+	0.597207i	$0.796277\pi$
$318$		0			0
$319$	−17.1118	−	9.87951i	−0.958077	−	0.553146i
$320$		0			0
$321$			13.6402i			0.761322i
$322$		0			0
$323$	0.607080	+	0.607080i	0.0337788	+	0.0337788i
$324$		0			0
$325$	19.1445	−	5.04009i	1.06195	−	0.279574i
$326$		0			0
$327$	0.135941	−	0.507340i	0.00751757	−	0.0280560i
$328$		0			0
$329$	−13.4887	−	9.72709i	−0.743656	−	0.536272i
$330$		0			0
$331$	0.440888	+	0.763640i	0.0242334	+	0.0419735i	0.877888	−	0.478866i	$-0.158952\pi$
$331$	0.440888	+	0.763640i	0.0242334	+	0.0419735i	−0.853654	+	0.520840i	$0.825619\pi$
$332$		0			0
$333$	2.58561	−	0.692812i	0.141691	−	0.0379659i
$334$		0			0
$335$	−17.0871	−	0.0373767i	−0.933568	−	0.00204211i
$336$		0			0
$337$	17.8218	−	17.8218i	0.970813	−	0.970813i	−0.0287728	−	0.999586i	$-0.509160\pi$
$337$	17.8218	−	17.8218i	0.970813	−	0.970813i	0.999586	+	0.0287728i	$0.00915993\pi$
$338$		0			0
$339$	−8.69405	+	15.0585i	−0.472196	+	0.817867i
$340$		0			0
$341$	−8.27950	+	4.78017i	−0.448360	+	0.258861i
$342$		0			0
$343$	−16.4111	+	8.58339i	−0.886118	+	0.463459i
$344$		0			0
$345$	1.76612	−	6.53404i	0.0950846	−	0.351781i
$346$		0			0
$347$	−5.76421	−	21.5123i	−0.309439	−	1.15484i	−0.929056	−	0.369938i	$-0.879379\pi$
$347$	−5.76421	−	21.5123i	−0.309439	−	1.15484i	0.619617	−	0.784904i	$-0.287288\pi$
$348$		0			0
$349$	1.52167			0.0814531			0.0407266	−	0.999170i	$-0.487033\pi$
$349$	1.52167			0.0814531			0.0407266	+	0.999170i	$0.487033\pi$
$350$		0			0
$351$	3.95937			0.211335
$352$		0			0
$353$	5.02235	+	18.7437i	0.267313	+	0.997625i	0.960819	+	0.277175i	$0.0893982\pi$
$353$	5.02235	+	18.7437i	0.267313	+	0.997625i	−0.693506	+	0.720450i	$0.743935\pi$
$354$		0			0
$355$	−3.14622	+	11.6400i	−0.166984	+	0.617785i
$356$		0			0
$357$	−0.829403	+	0.134386i	−0.0438966	+	0.00711247i
$358$		0			0
$359$	−26.7834	+	15.4634i	−1.41357	+	0.816126i	−0.995723	−	0.0923909i	$-0.970549\pi$
$359$	−26.7834	+	15.4634i	−1.41357	+	0.816126i	−0.417849	+	0.908517i	$0.637216\pi$
$360$		0			0
$361$	5.84570	−	10.1250i	0.307668	−	0.532897i
$362$		0			0
$363$	5.68979	−	5.68979i	0.298637	−	0.298637i
$364$		0			0
$365$	34.9343	+	0.0764161i	1.82855	+	0.00399980i
$366$		0			0
$367$	−11.9942	+	3.21383i	−0.626091	+	0.167761i	−0.557895	−	0.829911i	$-0.688391\pi$
$367$	−11.9942	+	3.21383i	−0.626091	+	0.167761i	−0.0681957	+	0.997672i	$0.521724\pi$
$368$		0			0
$369$	−1.31709	−	2.28127i	−0.0685649	−	0.118758i
$370$		0			0
$371$	−3.33164	+	32.8194i	−0.172970	+	1.70390i
$372$		0			0
$373$	1.57261	−	5.86906i	0.0814266	−	0.303888i	−0.913187	−	0.407541i	$-0.866386\pi$
$373$	1.57261	−	5.86906i	0.0814266	−	0.303888i	0.994614	+	0.103653i	$0.0330530\pi$
$374$		0			0
$375$	9.64557	+	5.65359i	0.498095	+	0.291950i
$376$		0			0
$377$	−12.6756	−	12.6756i	−0.652825	−	0.652825i
$378$		0			0
$379$		−	12.2273i		−	0.628072i	−0.949411	−	0.314036i	$-0.898319\pi$
$379$		−	12.2273i		−	0.628072i	0.949411	−	0.314036i	$-0.101681\pi$
$380$		0			0
$381$	7.44507	+	4.29841i	0.381423	+	0.220214i
$382$		0			0
$383$	−11.9425	−	3.19999i	−0.610234	−	0.163512i	−0.0595499	−	0.998225i	$-0.518967\pi$
$383$	−11.9425	−	3.19999i	−0.610234	−	0.163512i	−0.550684	+	0.834714i	$0.685633\pi$
$384$		0			0
$385$	−23.5726	+	10.5338i	−1.20137	+	0.536852i
$386$		0			0
$387$	−8.48573	−	2.27374i	−0.431354	−	0.115581i
$388$		0			0
$389$	−25.2993	−	14.6065i	−1.28272	−	0.740581i	−0.305378	−	0.952231i	$-0.598783\pi$
$389$	−25.2993	−	14.6065i	−1.28272	−	0.740581i	−0.977345	+	0.211651i	$0.932116\pi$
$390$		0			0
$391$		−	0.961285i		−	0.0486143i
$392$		0			0
$393$	−4.07841	−	4.07841i	−0.205729	−	0.205729i
$394$		0			0
$395$	−7.68990	−	28.9523i	−0.386921	−	1.45675i
$396$		0			0
$397$	−9.54692	+	35.6296i	−0.479146	+	1.78820i	0.125939	+	0.992038i	$0.459805\pi$
$397$	−9.54692	+	35.6296i	−0.479146	+	1.78820i	−0.605086	+	0.796160i	$0.706861\pi$
$398$		0			0
$399$	−2.93243	−	6.52388i	−0.146805	−	0.326603i
$400$		0			0
$401$	17.7131	+	30.6799i	0.884549	+	1.53208i	0.846230	+	0.532818i	$0.178867\pi$
$401$	17.7131	+	30.6799i	0.884549	+	1.53208i	0.0383185	+	0.999266i	$0.487800\pi$
$402$		0			0
$403$	−8.37788	+	2.24485i	−0.417332	+	0.111824i
$404$		0			0
$405$	1.57768	+	1.58459i	0.0783954	+	0.0787391i
$406$		0			0
$407$	8.26062	−	8.26062i	0.409464	−	0.409464i
$408$		0			0
$409$	−13.9895	+	24.2306i	−0.691737	+	1.19812i	0.279531	+	0.960137i	$0.409821\pi$
$409$	−13.9895	+	24.2306i	−0.691737	+	1.19812i	−0.971268	+	0.237988i	$0.923512\pi$
$410$		0			0
$411$	−16.4575	+	9.50174i	−0.811788	+	0.468686i
$412$		0			0
$413$	2.88752	+	3.54000i	0.142085	+	0.174192i
$414$		0			0
$415$	18.0449	+	31.4132i	0.885791	+	1.54201i
$416$		0			0
$417$	−0.0820080	−	0.306058i	−0.00401595	−	0.0149877i
$418$		0			0
$419$	−6.49494			−0.317299			−0.158649	−	0.987335i	$-0.550714\pi$
$419$	−6.49494			−0.317299			−0.158649	+	0.987335i	$0.550714\pi$
$420$		0			0
$421$	−16.6014			−0.809103			−0.404551	−	0.914515i	$-0.632572\pi$
$421$	−16.6014			−0.809103			−0.404551	+	0.914515i	$0.632572\pi$
$422$		0			0
$423$	1.62683	+	6.07142i	0.0790993	+	0.295203i
$424$		0			0
$425$	1.53195	+	0.417676i	0.0743104	+	0.0202603i
$426$		0			0
$427$	4.32130	+	26.6701i	0.209122	+	1.29066i
$428$		0			0
$429$	14.9646	−	8.63981i	0.722497	−	0.417134i
$430$		0			0
$431$	2.13950	−	3.70572i	0.103056	−	0.178498i	−0.809886	−	0.586587i	$-0.800471\pi$
$431$	2.13950	−	3.70572i	0.103056	−	0.178498i	0.912942	+	0.408089i	$0.133805\pi$
$432$		0			0
$433$	11.5948	−	11.5948i	0.557208	−	0.557208i	−0.371303	−	0.928512i	$-0.621089\pi$
$433$	11.5948	−	11.5948i	0.557208	−	0.557208i	0.928512	+	0.371303i	$0.121089\pi$
$434$		0			0
$435$	0.0221449	−	10.1237i	0.00106177	−	0.485396i
$436$		0			0
$437$	7.90441	−	2.11798i	0.378119	−	0.101317i
$438$		0			0
$439$	−13.9971	−	24.2437i	−0.668046	−	1.15709i	−0.978450	−	0.206484i	$-0.933798\pi$
$439$	−13.9971	−	24.2437i	−0.668046	−	1.15709i	0.310404	−	0.950605i	$-0.399536\pi$
$440$		0			0
$441$	6.85720	+	1.40670i	0.326533	+	0.0669858i
$442$		0			0
$443$	−2.35732	+	8.79765i	−0.112000	+	0.417989i	−0.999045	−	0.0436936i	$-0.986087\pi$
$443$	−2.35732	+	8.79765i	−0.112000	+	0.417989i	0.887045	+	0.461683i	$0.152754\pi$
$444$		0			0
$445$	−13.1108	+	3.48232i	−0.621514	+	0.165078i
$446$		0			0
$447$	−5.81239	−	5.81239i	−0.274917	−	0.274917i
$448$		0			0
$449$			26.7133i			1.26068i	0.776319	+	0.630340i	$0.217084\pi$
$449$			26.7133i			1.26068i	−0.776319	+	0.630340i	$0.782916\pi$
$450$		0			0
$451$	−9.95599	−	5.74809i	−0.468809	−	0.270667i
$452$		0			0
$453$	9.04653	+	2.42401i	0.425043	+	0.113890i
$454$		0			0
$455$	−23.1305	+	3.69588i	−1.08438	+	0.173265i
$456$		0			0
$457$	−3.39673	−	0.910151i	−0.158892	−	0.0425751i	0.178496	−	0.983941i	$-0.442877\pi$
$457$	−3.39673	−	0.910151i	−0.158892	−	0.0425751i	−0.337388	+	0.941366i	$0.609544\pi$
$458$		0			0
$459$	0.275026	+	0.158787i	0.0128371	+	0.00741152i
$460$		0			0
$461$			2.72235i			0.126793i	0.997988	+	0.0633963i	$0.0201932\pi$
$461$			2.72235i			0.126793i	−0.997988	+	0.0633963i	$0.979807\pi$
$462$		0			0
$463$	26.6530	+	26.6530i	1.23867	+	1.23867i	0.960544	+	0.278128i	$0.0897140\pi$
$463$	26.6530	+	26.6530i	1.23867	+	1.23867i	0.278128	+	0.960544i	$0.410286\pi$
$464$		0			0
$465$	−4.23673	−	2.45845i	−0.196474	−	0.114008i
$466$		0			0
$467$	11.0524	−	41.2480i	0.511442	−	1.90873i	0.106717	−	0.994289i	$-0.465966\pi$
$467$	11.0524	−	41.2480i	0.511442	−	1.90873i	0.404725	−	0.914438i	$-0.367367\pi$
$468$		0			0
$469$	20.1144	+	2.04190i	0.928797	+	0.0942860i
$470$		0			0
$471$	7.65720	+	13.2627i	0.352825	+	0.611111i
$472$		0			0
$473$	−37.0337	+	9.92316i	−1.70281	+	0.456267i
$474$		0			0
$475$	−0.0591354	+	13.5171i	−0.00271332	+	0.620206i
$476$		0			0
$477$	8.81643	−	8.81643i	0.403677	−	0.403677i
$478$		0			0
$479$	12.8201	−	22.2051i	0.585766	−	1.01458i	−0.409013	−	0.912528i	$-0.634127\pi$
$479$	12.8201	−	22.2051i	0.585766	−	1.01458i	0.994779	−	0.102048i	$-0.0325397\pi$
$480$		0			0
$481$	9.17858	−	5.29926i	0.418507	−	0.241625i
$482$		0			0
$483$	−2.84346	+	7.48684i	−0.129382	+	0.340663i
$484$		0			0
$485$	−21.6359	+	12.4285i	−0.982436	+	0.564348i
$486$		0			0
$487$	6.31034	+	23.5505i	0.285949	+	1.06717i	0.948143	+	0.317843i	$0.102959\pi$
$487$	6.31034	+	23.5505i	0.285949	+	1.06717i	−0.662195	+	0.749332i	$0.730375\pi$
$488$		0			0
$489$	18.4025			0.832190
$490$		0			0
$491$	7.86333			0.354867			0.177434	−	0.984133i	$-0.443221\pi$
$491$	7.86333			0.354867			0.177434	+	0.984133i	$0.443221\pi$
$492$		0			0
$493$	−0.372132	−	1.38881i	−0.0167600	−	0.0625491i
$494$		0			0
$495$	9.42067	+	2.54636i	0.423427	+	0.114450i
$496$		0			0
$497$	5.06543	−	13.3373i	0.227216	−	0.598260i
$498$		0			0
$499$	2.03266	−	1.17356i	0.0909945	−	0.0525357i	−0.453812	−	0.891097i	$-0.649936\pi$
$499$	2.03266	−	1.17356i	0.0909945	−	0.0525357i	0.544807	+	0.838562i	$0.316603\pi$
$500$		0			0
$501$	5.28852	−	9.15998i	0.236274	−	0.409238i
$502$		0			0
$503$	−14.5260	+	14.5260i	−0.647682	+	0.647682i	−0.952432	−	0.304750i	$-0.901427\pi$
$503$	−14.5260	+	14.5260i	−0.647682	+	0.647682i	0.304750	+	0.952432i	$0.401427\pi$
$504$		0			0
$505$	5.38420	−	5.36070i	0.239594	−	0.238548i
$506$		0			0
$507$	2.58537	−	0.692748i	0.114820	−	0.0307660i
$508$		0			0
$509$	8.29178	+	14.3618i	0.367527	+	0.636575i	0.989178	−	0.146719i	$-0.0468714\pi$
$509$	8.29178	+	14.3618i	0.367527	+	0.636575i	−0.621652	+	0.783294i	$0.713538\pi$
$510$		0			0
$511$	−41.1236	−	4.17463i	−1.81920	−	0.184675i
$512$		0			0
$513$	−0.699702	+	2.61132i	−0.0308926	+	0.115293i
$514$		0			0
$515$	−17.3842	+	29.9587i	−0.766037	+	1.32014i
$516$		0			0
$517$	19.3972	+	19.3972i	0.853090	+	0.853090i
$518$		0			0
$519$			5.48319i			0.240685i
$520$		0			0
$521$	−28.8215	−	16.6401i	−1.26269	−	0.729015i	−0.289097	−	0.957300i	$-0.593355\pi$
$521$	−28.8215	−	16.6401i	−1.26269	−	0.729015i	−0.973594	+	0.228285i	$0.926688\pi$
$522$		0			0
$523$	22.7287	+	6.09013i	0.993855	+	0.266303i	0.718869	−	0.695146i	$-0.244660\pi$
$523$	22.7287	+	6.09013i	0.993855	+	0.266303i	0.274986	+	0.961448i	$0.411327\pi$
$524$		0			0
$525$	−10.6959	−	7.78447i	−0.466807	−	0.339742i
$526$		0			0
$527$	−0.671974	−	0.180055i	−0.0292716	−	0.00784331i
$528$		0			0
$529$	11.9836	+	6.91872i	0.521025	+	0.300814i
$530$		0			0
$531$		−	1.72665i		−	0.0749304i
$532$		0			0
$533$	−7.37489	−	7.37489i	−0.319442	−	0.319442i
$534$		0			0
$535$	−15.3080	+	26.3807i	−0.661821	+	1.14054i
$536$		0			0
$537$	−2.66460	+	9.94441i	−0.114986	+	0.429133i
$538$		0			0
$539$	28.9867	−	9.64654i	1.24854	−	0.415506i
$540$		0			0
$541$	7.54153	+	13.0623i	0.324236	+	0.561592i	0.981357	−	0.192192i	$-0.0615596\pi$
$541$	7.54153	+	13.0623i	0.324236	+	0.561592i	−0.657122	+	0.753784i	$0.728226\pi$
$542$		0			0
$543$	13.4498	−	3.60386i	0.577185	−	0.154656i
$544$		0			0
$545$	0.832287	−	0.828654i	0.0356513	−	0.0354956i
$546$		0			0
$547$	−24.4516	+	24.4516i	−1.04547	+	1.04547i	−0.0465590	+	0.998916i	$0.514826\pi$
$547$	−24.4516	+	24.4516i	−1.04547	+	1.04547i	−0.998916	+	0.0465590i	$0.985174\pi$
$548$		0			0
$549$	5.10591	−	8.84369i	0.217915	−	0.377440i
$550$		0			0
$551$	10.6000	−	6.11989i	0.451574	−	0.260716i
$552$		0			0
$553$	5.66907	+	34.9883i	0.241073	+	1.48785i
$554$		0			0
$555$	5.77820	+	1.56182i	0.245271	+	0.0662955i
$556$		0			0
$557$	−4.92576	−	18.3832i	−0.208711	−	0.778920i	−0.988286	−	0.152612i	$-0.951232\pi$
$557$	−4.92576	−	18.3832i	−0.208711	−	0.778920i	0.779575	−	0.626309i	$-0.215435\pi$
$558$		0			0
$559$	−34.7833			−1.47118
$560$		0			0
$561$	1.38596			0.0585155
$562$		0			0
$563$	−5.33699	−	19.9179i	−0.224927	−	0.839441i	−0.982434	−	0.186613i	$-0.940249\pi$
$563$	−5.33699	−	19.9179i	−0.224927	−	0.839441i	0.757506	−	0.652828i	$-0.226418\pi$
$564$		0			0
$565$	−33.7143	+	19.3668i	−1.41837	+	0.814766i
$566$		0			0
$567$	−1.67232	−	2.05021i	−0.0702308	−	0.0861006i
$568$		0			0
$569$	−5.59023	+	3.22752i	−0.234354	+	0.135305i	−0.612579	−	0.790409i	$-0.709868\pi$
$569$	−5.59023	+	3.22752i	−0.234354	+	0.135305i	0.378225	+	0.925714i	$0.376535\pi$
$570$		0			0
$571$	23.4901	−	40.6860i	0.983028	−	1.70265i	0.332638	−	0.943055i	$-0.392061\pi$
$571$	23.4901	−	40.6860i	0.983028	−	1.70265i	0.650390	−	0.759600i	$-0.274605\pi$
$572$		0			0
$573$	−7.56041	+	7.56041i	−0.315841	+	0.315841i
$574$		0			0
$575$	10.7487	−	10.6550i	0.448251	−	0.444346i
$576$		0			0
$577$	13.4042	−	3.59166i	0.558026	−	0.149523i	0.0312266	−	0.999512i	$-0.490059\pi$
$577$	13.4042	−	3.59166i	0.558026	−	0.149523i	0.526799	+	0.849990i	$0.323392\pi$
$578$		0			0
$579$	2.15606	+	3.73440i	0.0896027	+	0.155196i
$580$		0			0
$581$	−17.5736	−	39.0966i	−0.729076	−	1.62200i
$582$		0			0
$583$	14.0836	−	52.5606i	0.583282	−	2.17684i
$584$		0			0
$585$	7.65758	+	4.44347i	0.316602	+	0.183715i
$586$		0			0
$587$	−25.6597	−	25.6597i	−1.05909	−	1.05909i	−0.998141	−	0.0609461i	$-0.980588\pi$
$587$	−25.6597	−	25.6597i	−1.05909	−	1.05909i	−0.0609461	−	0.998141i	$-0.519412\pi$
$588$		0			0
$589$		−	5.92219i		−	0.244019i
$590$		0			0
$591$	−1.36538	−	0.788301i	−0.0561641	−	0.0324264i
$592$		0			0
$593$	−3.09944	−	0.830494i	−0.127279	−	0.0341043i	0.194617	−	0.980879i	$-0.437654\pi$
$593$	−3.09944	−	0.830494i	−0.127279	−	0.0341043i	−0.321896	+	0.946775i	$0.604320\pi$
$594$		0			0
$595$	−1.75492	−	0.670903i	−0.0719446	−	0.0275043i
$596$		0			0
$597$	−22.7019	−	6.08297i	−0.929128	−	0.248959i
$598$		0			0
$599$	−35.6333	−	20.5729i	−1.45594	−	0.840586i	−0.457130	−	0.889400i	$-0.651123\pi$
$599$	−35.6333	−	20.5729i	−1.45594	−	0.840586i	−0.998808	+	0.0488140i	$0.984456\pi$
$600$		0			0
$601$		−	35.6457i		−	1.45402i	−0.686628	−	0.727009i	$-0.740910\pi$
$601$		−	35.6457i		−	1.45402i	0.686628	−	0.727009i	$-0.259090\pi$
$602$		0			0
$603$	−5.40343	−	5.40343i	−0.220045	−	0.220045i
$604$		0			0
$605$	17.3898	−	4.61882i	0.706994	−	0.187782i
$606$		0			0
$607$	8.36776	−	31.2289i	0.339637	−	1.26754i	−0.559117	−	0.829088i	$-0.688860\pi$
$607$	8.36776	−	31.2289i	0.339637	−	1.26754i	0.898754	−	0.438453i	$-0.144473\pi$
$608$		0			0
$609$	−1.20978	+	11.9173i	−0.0490227	+	0.482915i
$610$		0			0
$611$	12.4435	+	21.5527i	0.503410	+	0.871931i
$612$		0			0
$613$	9.43387	−	2.52780i	0.381030	−	0.102097i	−0.0632197	−	0.998000i	$-0.520137\pi$
$613$	9.43387	−	2.52780i	0.381030	−	0.102097i	0.444250	+	0.895903i	$0.353470\pi$
$614$		0			0
$615$	0.0128843	−	5.89019i	0.000519546	−	0.237515i
$616$		0			0
$617$	−9.23419	+	9.23419i	−0.371754	+	0.371754i	−0.868116	−	0.496362i	$-0.834669\pi$
$617$	−9.23419	+	9.23419i	−0.371754	+	0.371754i	0.496362	+	0.868116i	$0.334669\pi$
$618$		0			0
$619$	12.1118	−	20.9783i	0.486815	−	0.843188i	−0.513070	−	0.858347i	$-0.671492\pi$
$619$	12.1118	−	20.9783i	0.486815	−	0.843188i	0.999885	+	0.0151586i	$0.00482531\pi$
$620$		0			0
$621$	2.62144	−	1.51349i	0.105195	−	0.0607341i
$622$		0			0
$623$	15.8442	−	2.56720i	0.634785	−	0.102853i
$624$		0			0
$625$	12.3101	+	21.7592i	0.492404	+	0.870367i
$626$		0			0
$627$	3.05367	+	11.3964i	0.121952	+	0.455130i
$628$		0			0
$629$	0.850086			0.0338952
$630$		0			0
$631$	−14.1379			−0.562819			−0.281410	−	0.959588i	$-0.590802\pi$
$631$	−14.1379			−0.562819			−0.281410	+	0.959588i	$0.590802\pi$
$632$		0			0
$633$	3.61335	+	13.4852i	0.143618	+	0.535988i
$634$		0			0
$635$	9.57511	+	16.6687i	0.379977	+	0.661476i
$636$		0			0
$637$	27.6666	−	1.64711i	1.09619	−	0.0652609i
$638$		0			0
$639$	−4.66992	+	2.69618i	−0.184739	+	0.106659i
$640$		0			0
$641$	−16.8927	+	29.2590i	−0.667222	+	1.15566i	0.311456	+	0.950260i	$0.399183\pi$
$641$	−16.8927	+	29.2590i	−0.667222	+	1.15566i	−0.978678	+	0.205401i	$0.934150\pi$
$642$		0			0
$643$	−5.54153	+	5.54153i	−0.218537	+	0.218537i	−0.807882	−	0.589345i	$-0.799386\pi$
$643$	−5.54153	+	5.54153i	−0.218537	+	0.218537i	0.589345	+	0.807882i	$0.299386\pi$
$644$		0			0
$645$	−13.8600	−	13.9208i	−0.545737	−	0.548130i
$646$		0			0
$647$	2.44295	−	0.654586i	0.0960422	−	0.0257344i	−0.210478	−	0.977599i	$-0.567502\pi$
$647$	2.44295	−	0.654586i	0.0960422	−	0.0257344i	0.306520	+	0.951864i	$0.400835\pi$
$648$		0			0
$649$	−3.76776	−	6.52596i	−0.147898	−	0.256166i
$650$		0			0
$651$	4.70098	+	3.39001i	0.184246	+	0.132865i
$652$		0			0
$653$	−2.47246	+	9.22736i	−0.0967550	+	0.361094i	−0.997280	−	0.0737104i	$-0.976516\pi$
$653$	−2.47246	+	9.22736i	−0.0967550	+	0.361094i	0.900525	+	0.434805i	$0.143183\pi$
$654$		0			0
$655$	−3.31075	−	12.4649i	−0.129362	−	0.487043i
$656$		0			0
$657$	11.0472	+	11.0472i	0.430994	+	0.430994i
$658$		0			0
$659$			25.7019i			1.00120i	0.865678	+	0.500602i	$0.166888\pi$
$659$			25.7019i			1.00120i	−0.865678	+	0.500602i	$0.833112\pi$
$660$		0			0
$661$	−4.00560	−	2.31264i	−0.155800	−	0.0899511i	0.420073	−	0.907490i	$-0.362004\pi$
$661$	−4.00560	−	2.31264i	−0.155800	−	0.0899511i	−0.575873	+	0.817539i	$0.695338\pi$
$662$		0			0
$663$	1.21454	+	0.325436i	0.0471690	+	0.0126389i
$664$		0			0
$665$	1.65010	−	15.9084i	0.0639880	−	0.616903i
$666$		0			0
$667$	−13.2376	−	3.54700i	−0.512562	−	0.137341i
$668$		0			0
$669$	24.2176	+	13.9820i	0.936307	+	0.540577i
$670$		0			0
$671$		−	44.5668i		−	1.72048i
$672$		0			0
$673$	−19.3062	−	19.3062i	−0.744198	−	0.744198i	0.229185	−	0.973383i	$-0.426394\pi$
$673$	−19.3062	−	19.3062i	−0.744198	−	0.744198i	−0.973383	+	0.229185i	$0.926394\pi$
$674$		0			0
$675$	1.27295	+	4.83524i	0.0489960	+	0.186109i
$676$		0			0
$677$	3.07047	−	11.4592i	0.118008	−	0.440411i	−0.881487	−	0.472209i	$-0.843457\pi$
$677$	3.07047	−	11.4592i	0.118008	−	0.440411i	0.999494	+	0.0317981i	$0.0101234\pi$
$678$		0			0
$679$	26.9278	−	12.1038i	1.03340	−	0.464503i
$680$		0			0
$681$	−4.73574	−	8.20255i	−0.181474	−	0.314322i
$682$		0			0
$683$	−42.4276	+	11.3685i	−1.62345	+	0.435002i	−0.952012	−	0.306060i	$-0.900989\pi$
$683$	−42.4276	+	11.3685i	−1.62345	+	0.435002i	−0.671437	+	0.741062i	$0.734322\pi$
$684$		0			0
$685$	−42.4930	−	0.0929501i	−1.62357	−	0.00355144i
$686$		0			0
$687$	−1.31199	+	1.31199i	−0.0500555	+	0.0500555i
$688$		0			0
$689$	24.6833	−	42.7528i	0.940359	−	1.62875i
$690$		0			0
$691$	7.97994	−	4.60722i	0.303571	−	0.175267i	−0.340475	−	0.940254i	$-0.610588\pi$
$691$	7.97994	−	4.60722i	0.303571	−	0.175267i	0.644046	+	0.764987i	$0.277254\pi$
$692$		0			0
$693$	−10.7944	−	4.09965i	−0.410045	−	0.155733i
$694$		0			0
$695$	0.184872	−	0.683963i	0.00701259	−	0.0259442i
$696$		0			0
$697$	−0.216514	−	0.808040i	−0.00820104	−	0.0306067i
$698$		0			0
$699$	27.5366			1.04153
$700$		0			0
$701$	16.6053			0.627174			0.313587	−	0.949559i	$-0.398469\pi$
$701$	16.6053			0.627174			0.313587	+	0.949559i	$0.398469\pi$
$702$		0			0
$703$	1.87298	+	6.99005i	0.0706407	+	0.263635i
$704$		0			0
$705$	−3.66739	+	13.5681i	−0.138122	+	0.511005i
$706$		0			0
$707$	−6.96628	+	5.68228i	−0.261994	+	0.213704i
$708$		0			0
$709$	27.6385	−	15.9571i	1.03799	−	0.599282i	0.118725	−	0.992927i	$-0.462119\pi$
$709$	27.6385	−	15.9571i	1.03799	−	0.599282i	0.919262	+	0.393645i	$0.128786\pi$
$710$		0			0
$711$	6.69839	−	11.6020i	0.251209	−	0.435107i
$712$		0			0
$713$	−4.68876	+	4.68876i	−0.175596	+	0.175596i
$714$		0			0
$715$	38.6383	+	0.0845183i	1.44499	+	0.00316081i
$716$		0			0
$717$	−13.8914	+	3.72220i	−0.518785	+	0.139008i
$718$		0			0
$719$	8.63741	+	14.9604i	0.322121	+	0.557930i	0.980925	−	0.194384i	$-0.0622709\pi$
$719$	8.63741	+	14.9604i	0.322121	+	0.557930i	−0.658804	+	0.752314i	$0.728938\pi$
$720$		0			0
$721$	23.9714	−	33.2415i	0.892742	−	1.23798i
$722$		0			0
$723$	−1.71417	+	6.39738i	−0.0637508	+	0.237921i
$724$		0			0
$725$	11.4044	−	19.5549i	0.423547	−	0.726250i
$726$		0			0
$727$	30.3766	+	30.3766i	1.12661	+	1.12661i	0.990725	+	0.135880i	$0.0433861\pi$
$727$	30.3766	+	30.3766i	1.12661	+	1.12661i	0.135880	+	0.990725i	$0.456614\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−2.41613	−	1.39495i	−0.0893637	−	0.0515941i
$732$		0			0
$733$	34.0692	+	9.12882i	1.25838	+	0.337181i	0.825566	−	0.564305i	$-0.190856\pi$
$733$	34.0692	+	9.12882i	1.25838	+	0.337181i	0.432809	+	0.901486i	$0.357522\pi$
$734$		0			0
$735$	11.6834	+	10.4162i	0.430949	+	0.384208i
$736$		0			0
$737$	−32.2134	−	8.63155i	−1.18660	−	0.317947i
$738$		0			0
$739$	25.1311	+	14.5095i	0.924463	+	0.533739i	0.885056	−	0.465484i	$-0.154120\pi$
$739$	25.1311	+	14.5095i	0.924463	+	0.533739i	0.0394067	+	0.999223i	$0.487453\pi$
$740$		0			0
$741$			10.7039i			0.393218i
$742$		0			0
$743$	6.98196	+	6.98196i	0.256143	+	0.256143i	0.823483	−	0.567340i	$-0.192028\pi$
$743$	6.98196	+	6.98196i	0.256143	+	0.256143i	−0.567340	+	0.823483i	$0.692028\pi$
$744$		0			0
$745$	−4.71835	−	17.7645i	−0.172867	−	0.650840i
$746$		0			0
$747$	−4.19321	+	15.6493i	−0.153421	+	0.572576i
$748$		0			0
$749$	21.1085	−	29.2715i	0.771288	−	1.06956i
$750$		0			0
$751$	−2.61368	−	4.52703i	−0.0953745	−	0.165194i	0.814390	−	0.580317i	$-0.197072\pi$
$751$	−2.61368	−	4.52703i	−0.0953745	−	0.165194i	−0.909765	+	0.415124i	$0.863738\pi$
$752$		0			0
$753$	−3.09888	+	0.830342i	−0.112929	+	0.0302594i
$754$		0			0
$755$	14.7760	+	14.8408i	0.537753	+	0.540111i
$756$		0			0
$757$	−33.4817	+	33.4817i	−1.21691	+	1.21691i	−0.248207	+	0.968707i	$0.579841\pi$
$757$	−33.4817	+	33.4817i	−1.21691	+	1.21691i	−0.968707	+	0.248207i	$0.920159\pi$
$758$		0			0
$759$	6.60522	−	11.4406i	0.239754	−	0.415266i
$760$		0			0
$761$	−45.5767	+	26.3137i	−1.65215	+	0.953872i	−0.675970	+	0.736929i	$0.736275\pi$
$761$	−45.5767	+	26.3137i	−1.65215	+	0.953872i	−0.976184	+	0.216942i	$0.930392\pi$
$762$		0			0
$763$	−1.07684	+	0.878363i	−0.0389844	+	0.0317989i
$764$		0			0
$765$	0.353711	+	0.615753i	0.0127885	+	0.0222626i
$766$		0			0
$767$	−1.76940	−	6.60351i	−0.0638895	−	0.238439i
$768$		0			0
$769$	34.1069			1.22993			0.614963	−	0.788556i	$-0.289171\pi$
$769$	34.1069			1.22993			0.614963	+	0.788556i	$0.289171\pi$
$770$		0			0
$771$	−15.7151			−0.565965
$772$		0			0
$773$	−0.603106	−	2.25082i	−0.0216922	−	0.0809564i	0.954231	−	0.299070i	$-0.0966764\pi$
$773$	−0.603106	−	2.25082i	−0.0216922	−	0.0809564i	−0.975923	+	0.218113i	$0.930010\pi$
$774$		0			0
$775$	−5.43497	−	9.50948i	−0.195230	−	0.341591i
$776$		0			0
$777$	−6.62078	−	2.51453i	−0.237519	−	0.0902084i
$778$		0			0
$779$	6.16727	−	3.56067i	0.220965	−	0.127574i
$780$		0			0
$781$	−11.7668	+	20.3806i	−0.421048	+	0.729276i
$782$		0			0
$783$	3.20141	−	3.20141i	0.114409	−	0.114409i
$784$		0			0
$785$	−0.0749060	+	34.2439i	−0.00267351	+	1.22222i
$786$		0			0
$787$	23.1456	−	6.20186i	0.825053	−	0.221072i	0.178499	−	0.983940i	$-0.442876\pi$
$787$	23.1456	−	6.20186i	0.825053	−	0.221072i	0.646554	+	0.762868i	$0.276209\pi$
$788$		0			0
$789$	−7.27828	−	12.6064i	−0.259114	−	0.448798i
$790$		0			0
$791$	41.9605	−	18.8609i	1.49194	−	0.670617i
$792$		0			0
$793$	10.4647	−	39.0546i	0.371611	−	1.38687i
$794$		0			0
$795$	26.9457	−	7.15695i	0.955667	−	0.253831i
$796$		0			0
$797$	4.27731	+	4.27731i	0.151510	+	0.151510i	0.778792	−	0.627282i	$-0.215833\pi$
$797$	4.27731	+	4.27731i	0.151510	+	0.151510i	−0.627282	+	0.778792i	$0.715833\pi$
$798$		0			0
$799$			1.99614i			0.0706182i
$800$		0			0
$801$	−5.25387	−	3.03332i	−0.185636	−	0.107177i
$802$		0			0
$803$	65.8598	+	17.6471i	2.32414	+	0.622752i
$804$		0			0
$805$	−13.9016	+	11.2887i	−0.489967	+	0.397876i
$806$		0			0
$807$	11.7843	+	3.15760i	0.414828	+	0.111153i
$808$		0			0
$809$	24.3656	+	14.0675i	0.856649	+	0.494587i	0.862889	−	0.505394i	$-0.168653\pi$
$809$	24.3656	+	14.0675i	0.856649	+	0.494587i	−0.00623939	+	0.999981i	$0.501986\pi$
$810$		0			0
$811$			14.6408i			0.514108i	0.966397	+	0.257054i	$0.0827518\pi$
$811$			14.6408i			0.514108i	−0.966397	+	0.257054i	$0.917248\pi$
$812$		0			0
$813$	−9.05021	−	9.05021i	−0.317405	−	0.317405i
$814$		0			0
$815$	35.5912	+	20.6525i	1.24671	+	0.723427i
$816$		0			0
$817$	6.14694	−	22.9407i	0.215054	−	0.802593i
$818$		0			0
$819$	−8.49667	−	6.12720i	−0.296898	−	0.214102i
$820$		0			0
$821$	−19.0342	−	32.9682i	−0.664298	−	1.15060i	−0.979475	−	0.201565i	$-0.935397\pi$
$821$	−19.0342	−	32.9682i	−0.664298	−	1.15060i	0.315178	−	0.949033i	$-0.397936\pi$
$822$		0			0
$823$	27.2459	−	7.30051i	0.949731	−	0.254480i	0.249483	−	0.968379i	$-0.419739\pi$
$823$	27.2459	−	7.30051i	0.949731	−	0.254480i	0.700248	+	0.713900i	$0.253073\pi$
$824$		0			0
$825$	15.3623	+	15.4973i	0.534845	+	0.539546i
$826$		0			0
$827$	−13.2575	+	13.2575i	−0.461008	+	0.461008i	−0.898986	−	0.437977i	$-0.855695\pi$
$827$	−13.2575	+	13.2575i	−0.461008	+	0.461008i	0.437977	+	0.898986i	$0.355695\pi$
$828$		0			0
$829$	−23.4677	+	40.6472i	−0.815067	+	1.41174i	0.0942131	+	0.995552i	$0.469967\pi$
$829$	−23.4677	+	40.6472i	−0.815067	+	1.41174i	−0.909280	+	0.416185i	$0.863367\pi$
$830$		0			0
$831$	−18.1373	+	10.4715i	−0.629174	+	0.363254i
$832$		0			0
$833$	1.98784	+	0.995129i	0.0688745	+	0.0344792i
$834$		0			0
$835$	20.5082	−	11.7807i	0.709714	−	0.407686i
$836$		0			0
$837$	−0.566971	−	2.11597i	−0.0195974	−	0.0731385i
$838$		0			0
$839$	37.4760			1.29382			0.646908	−	0.762568i	$-0.276062\pi$
$839$	37.4760			1.29382			0.646908	+	0.762568i	$0.276062\pi$
$840$		0			0
$841$	8.50190			0.293169
$842$		0			0
$843$	6.18235	+	23.0728i	0.212931	+	0.794671i
$844$		0			0
$845$	5.77766	+	1.56167i	0.198758	+	0.0537232i
$846$		0			0
$847$	−21.0152	+	3.40504i	−0.722090	+	0.116999i
$848$		0			0
$849$	−5.59806	+	3.23204i	−0.192125	+	0.110923i
$850$		0			0
$851$	4.05133	−	7.01711i	0.138878	−	0.240544i
$852$		0			0
$853$	−3.02250	+	3.02250i	−0.103488	+	0.103488i	−0.756955	−	0.653467i	$-0.773314\pi$
$853$	−3.02250	+	3.02250i	−0.103488	+	0.103488i	0.653467	+	0.756955i	$0.273314\pi$
$854$		0			0
$855$	−4.28386	+	4.26516i	−0.146505	+	0.145865i
$856$		0			0
$857$	12.7393	−	3.41348i	0.435166	−	0.116602i	−0.0345842	−	0.999402i	$-0.511011\pi$
$857$	12.7393	−	3.41348i	0.435166	−	0.116602i	0.469750	+	0.882799i	$0.344344\pi$
$858$		0			0
$859$	−3.65300	−	6.32718i	−0.124639	−	0.215881i	0.796953	−	0.604041i	$-0.206444\pi$
$859$	−3.65300	−	6.32718i	−0.124639	−	0.215881i	−0.921592	+	0.388161i	$0.873111\pi$
$860$		0			0
$861$	−0.703874	+	6.93375i	−0.0239879	+	0.236301i
$862$		0			0
$863$	−4.24474	+	15.8416i	−0.144493	+	0.539254i	0.855285	+	0.518158i	$0.173382\pi$
$863$	−4.24474	+	15.8416i	−0.144493	+	0.539254i	−0.999777	+	0.0210958i	$0.993284\pi$
$864$		0			0
$865$	−6.15360	+	10.6047i	−0.209229	+	0.360571i
$866$		0			0
$867$	−11.9495	−	11.9495i	−0.405826	−	0.405826i
$868$		0			0
$869$		−	58.4668i		−	1.98335i
$870$		0			0
$871$	−26.2024	−	15.1279i	−0.887833	−	0.512591i
$872$		0			0
$873$	−10.7785	−	2.88808i	−0.364795	−	0.0977466i
$874$		0			0
$875$	−11.9500	−	27.0591i	−0.403985	−	0.914766i
$876$		0			0
$877$	−4.78568	−	1.28232i	−0.161601	−	0.0433008i	0.177111	−	0.984191i	$-0.443325\pi$
$877$	−4.78568	−	1.28232i	−0.161601	−	0.0433008i	−0.338712	+	0.940890i	$0.609991\pi$
$878$		0			0
$879$	−8.47113	−	4.89081i	−0.285724	−	0.164963i
$880$		0			0
$881$			31.5578i			1.06321i	0.846993	+	0.531605i	$0.178411\pi$
$881$			31.5578i			1.06321i	−0.846993	+	0.531605i	$0.821589\pi$
$882$		0			0
$883$	−4.81686	−	4.81686i	−0.162100	−	0.162100i	0.621396	−	0.783496i	$-0.286566\pi$
$883$	−4.81686	−	4.81686i	−0.162100	−	0.162100i	−0.783496	+	0.621396i	$0.786566\pi$
$884$		0			0
$885$	1.93777	−	3.33942i	0.0651373	−	0.112253i
$886$		0			0
$887$	4.31598	−	16.1074i	0.144916	−	0.540835i	−0.854843	−	0.518887i	$-0.826346\pi$
$887$	4.31598	−	16.1074i	0.144916	−	0.540835i	0.999759	−	0.0219480i	$-0.00698684\pi$
$888$		0			0
$889$	−9.32500	−	20.7457i	−0.312751	−	0.695787i
$890$		0			0
$891$	2.18212	+	3.77954i	0.0731037	+	0.126619i
$892$		0			0
$893$	−16.4137	+	4.39805i	−0.549265	+	0.147175i
$894$		0			0
$895$	−16.3137	+	16.2425i	−0.545308	+	0.542927i
$896$		0			0
$897$	8.47460	−	8.47460i	0.282959	−	0.282959i
$898$		0			0
$899$	−4.95897	+	8.58919i	−0.165391	+	0.286466i
$900$		0			0
$901$	3.42912	−	1.97980i	0.114240	−	0.0659567i
$902$		0			0
$903$	14.6914	+	18.0112i	0.488900	+	0.599376i
$904$		0			0
$905$	30.0569	+	8.12424i	0.999126	+	0.270059i
$906$		0			0
$907$	−3.00183	−	11.2030i	−0.0996741	−	0.371989i	0.898013	−	0.439970i	$-0.145011\pi$
$907$	−3.00183	−	11.2030i	−0.0996741	−	0.371989i	−0.997687	+	0.0679811i	$0.978344\pi$
$908$		0			0
$909$	3.39784			0.112699
$910$		0			0
$911$	−18.0104			−0.596712			−0.298356	−	0.954455i	$-0.596438\pi$
$911$	−18.0104			−0.596712			−0.298356	+	0.954455i	$0.596438\pi$
$912$		0			0
$913$	18.3001	+	68.2971i	0.605646	+	2.26030i
$914$		0			0
$915$	19.8000	−	11.3739i	0.654569	−	0.376009i
$916$		0			0
$917$	2.44071	+	15.0636i	0.0805995	+	0.497443i
$918$		0			0
$919$	28.7287	−	16.5865i	0.947672	−	0.547139i	0.0553148	−	0.998469i	$-0.482384\pi$
$919$	28.7287	−	16.5865i	0.947672	−	0.547139i	0.892357	+	0.451330i	$0.149050\pi$
$920$		0			0
$921$	−5.17232	+	8.95872i	−0.170434	+	0.295200i
$922$		0			0
$923$	−15.0969	+	15.0969i	−0.496922	+	0.496922i
$924$		0			0
$925$	9.42250	+	9.50531i	0.309810	+	0.312533i
$926$		0			0
$927$	−14.9624	+	4.00916i	−0.491429	+	0.131678i
$928$		0			0
$929$	−28.5132	−	49.3864i	−0.935489	−	1.62032i	−0.773759	−	0.633480i	$-0.781626\pi$
$929$	−28.5132	−	49.3864i	−0.935489	−	1.62032i	−0.161730	−	0.986835i	$-0.551707\pi$
$930$		0			0
$931$	−3.80294	+	18.5380i	−0.124636	+	0.607560i
$932$		0			0
$933$	5.63924	−	21.0459i	0.184620	−	0.689013i
$934$		0			0
$935$	2.68051	+	1.55542i	0.0876621	+	0.0508678i
$936$		0			0
$937$	−18.4132	−	18.4132i	−0.601534	−	0.601534i	0.339186	−	0.940719i	$-0.389848\pi$
$937$	−18.4132	−	18.4132i	−0.601534	−	0.601534i	−0.940719	+	0.339186i	$0.889848\pi$
$938$		0			0
$939$		−	23.5645i		−	0.769000i
$940$		0			0
$941$	2.15419	+	1.24372i	0.0702245	+	0.0405441i	0.534701	−	0.845041i	$-0.320424\pi$
$941$	2.15419	+	1.24372i	0.0702245	+	0.0405441i	−0.464477	+	0.885585i	$0.653758\pi$
$942$		0			0
$943$	−7.70189	−	2.06372i	−0.250808	−	0.0672038i
$944$		0			0
$945$	−0.933452	−	5.84197i	−0.0303652	−	0.190039i
$946$		0			0
$947$	−49.1124	−	13.1596i	−1.59594	−	0.427630i	−0.652126	−	0.758111i	$-0.726123\pi$
$947$	−49.1124	−	13.1596i	−1.59594	−	0.427630i	−0.943813	+	0.330481i	$0.892789\pi$
$948$		0			0
$949$	53.5704	+	30.9289i	1.73897	+	1.00399i
$950$		0			0
$951$		−	22.0843i		−	0.716131i
$952$		0			0
$953$	−9.31188	−	9.31188i	−0.301641	−	0.301641i	0.540014	−	0.841656i	$-0.318419\pi$
$953$	−9.31188	−	9.31188i	−0.301641	−	0.301641i	−0.841656	+	0.540014i	$0.818419\pi$
$954$		0			0
$955$	−23.1069	+	6.13734i	−0.747723	+	0.198600i
$956$		0			0
$957$	5.11401	−	19.0857i	0.165312	−	0.616954i
$958$		0			0
$959$	50.0214	+	5.07788i	1.61527	+	0.163973i
$960$		0			0
$961$	−13.1006	−	22.6909i	−0.422601	−	0.731966i
$962$		0			0
$963$	−13.1754	+	3.53035i	−0.424572	+	0.113764i
$964$		0			0
$965$	−0.0210915	+	9.64216i	−0.000678959	+	0.310392i
$966$		0			0
$967$	18.4525	−	18.4525i	0.593394	−	0.593394i	−0.345153	−	0.938547i	$-0.612173\pi$
$967$	18.4525	−	18.4525i	0.593394	−	0.593394i	0.938547	+	0.345153i	$0.112173\pi$
$968$		0			0
$969$	−0.429270	+	0.743518i	−0.0137901	+	0.0238852i
$970$		0			0
$971$	29.7627	−	17.1835i	0.955131	−	0.551445i	0.0604600	−	0.998171i	$-0.480743\pi$
$971$	29.7627	−	17.1835i	0.955131	−	0.551445i	0.894671	+	0.446725i	$0.147410\pi$
$972$		0			0
$973$	−0.297644	+	0.783700i	−0.00954204	+	0.0251243i
$974$		0			0
$975$	9.82331	+	17.1877i	0.314598	+	0.550447i
$976$		0			0
$977$	4.64414	+	17.3322i	0.148579	+	0.554505i	0.999570	+	0.0293246i	$0.00933566\pi$
$977$	4.64414	+	17.3322i	0.148579	+	0.554505i	−0.850991	+	0.525181i	$0.823998\pi$
$978$		0			0
$979$	−26.4763			−0.846186
$980$		0			0
$981$	0.525237			0.0167695
$982$		0			0
$983$	−7.55607	−	28.1996i	−0.241001	−	0.899428i	−0.975351	−	0.220658i	$-0.929180\pi$
$983$	−7.55607	−	28.1996i	−0.241001	−	0.899428i	0.734350	−	0.678771i	$-0.237487\pi$
$984$		0			0
$985$	−1.75601	−	3.05693i	−0.0559512	−	0.0974017i
$986$		0			0
$987$	5.90452	−	15.5466i	0.187943	−	0.494855i
$988$		0			0
$989$	−23.0295	+	13.2961i	−0.732295	+	0.422791i
$990$		0			0
$991$	17.3733	−	30.0914i	0.551880	−	0.955885i	−0.446258	−	0.894904i	$-0.647244\pi$
$991$	17.3733	−	30.0914i	0.551880	−	0.955885i	0.998139	−	0.0609809i	$-0.0194229\pi$
$992$		0			0
$993$	−0.623510	+	0.623510i	−0.0197865	+	0.0197865i
$994$		0			0
$995$	−37.0798	−	37.2423i	−1.17551	−	1.18066i
$996$		0			0
$997$	−30.4690	+	8.16415i	−0.964964	+	0.258561i	−0.706700	−	0.707513i	$-0.749817\pi$
$997$	−30.4690	+	8.16415i	−0.964964	+	0.258561i	−0.258264	+	0.966074i	$0.583150\pi$
$998$		0			0
$999$	1.33841	+	2.31820i	0.0423454	+	0.0733445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dd.b.73.9	yes	48
5.2	odd	4		840.2.dd.a.577.7	yes	48
7.5	odd	6		840.2.dd.a.313.7	✓	48
35.12	even	12	inner	840.2.dd.b.817.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dd.a.313.7	✓	48	7.5	odd	6
840.2.dd.a.577.7	yes	48	5.2	odd	4
840.2.dd.b.73.9	yes	48	1.1	even	1	trivial
840.2.dd.b.817.9	yes	48	35.12	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{3} +(-0.583460 + 2.15860i) q^{5} +(0.939373 - 2.47337i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-2.18212 + 3.77954i) q^{11} +(-2.79969 + 2.79969i) q^{13} +(-2.23606 - 0.00489121i) q^{15} +(-0.306752 + 0.0821940i) q^{17} +(-1.35172 - 2.34125i) q^{19} +(2.63222 + 0.267208i) q^{21} +(-0.783438 + 2.92383i) q^{23} +(-4.31915 - 2.51892i) q^{25} +(-0.707107 - 0.707107i) q^{27} +4.52748i q^{29} +(1.89712 + 1.09530i) q^{31} +(-4.21553 - 1.12955i) q^{33} +(4.79095 + 3.47085i) q^{35} +(-2.58561 - 0.692812i) q^{37} +(-3.42891 - 1.97968i) q^{39} +2.63418i q^{41} +(6.21198 + 6.21198i) q^{43} +(-0.574011 - 2.16114i) q^{45} +(1.62683 - 6.07142i) q^{47} +(-5.23516 - 4.64684i) q^{49} +(-0.158787 - 0.275026i) q^{51} +(-12.0435 + 3.22704i) q^{53} +(-6.88536 - 6.91554i) q^{55} +(1.91162 - 1.91162i) q^{57} +(-0.863327 + 1.49533i) q^{59} +(-8.84369 + 5.10591i) q^{61} +(0.423166 + 2.61169i) q^{63} +(-4.40992 - 7.67694i) q^{65} +(1.97779 + 7.38122i) q^{67} -3.02697 q^{69} +5.39235 q^{71} +(-4.04357 - 15.0908i) q^{73} +(1.31521 - 4.82392i) q^{75} +(7.29840 + 8.94759i) q^{77} +(-11.6020 + 6.69839i) q^{79} +(0.500000 - 0.866025i) q^{81} +(11.4560 - 11.4560i) q^{83} +(0.00155332 - 0.710113i) q^{85} +(-4.37321 + 1.17180i) q^{87} +(3.03332 + 5.25387i) q^{89} +(4.29473 + 9.55465i) q^{91} +(-0.566971 + 2.11597i) q^{93} +(5.84251 - 1.55181i) q^{95} +(7.89037 + 7.89037i) q^{97} -4.36424i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 4 q^{11} - 16 q^{13} - 4 q^{15} + 4 q^{17} - 8 q^{19} + 48 q^{23} - 20 q^{25} + 24 q^{33} - 4 q^{37} + 12 q^{39} + 16 q^{43} + 4 q^{45} - 12 q^{47} + 12 q^{49} - 52 q^{53} + 56 q^{55} + 8 q^{57}+ \cdots - 44 q^{97}+O(q^{100}) \) 48 * q + 4 * q^7 - 4 * q^11 - 16 * q^13 - 4 * q^15 + 4 * q^17 - 8 * q^19 + 48 * q^23 - 20 * q^25 + 24 * q^33 - 4 * q^37 + 12 * q^39 + 16 * q^43 + 4 * q^45 - 12 * q^47 + 12 * q^49 - 52 * q^53 + 56 * q^55 + 8 * q^57 - 8 * q^59 + 12 * q^65 + 68 * q^67 + 8 * q^69 + 16 * q^71 + 52 * q^73 + 24 * q^75 + 16 * q^77 - 108 * q^79 + 24 * q^81 - 64 * q^83 + 32 * q^85 - 8 * q^87 - 64 * q^89 + 48 * q^91 + 48 * q^93 - 84 * q^95 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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