LMFDB - Embedded newform 2772.2.s.f.793.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2772,2,Mod(793,2772)] 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("2772.793"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2772, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2772 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2772.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,-2,0,4,0,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$22.1345314403$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 308)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.1
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	2772.793
Dual form			2772.2.s.f.2377.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71053 + 2.96273i) q^{5} +(-0.710533 - 2.54856i) q^{7} +(-0.500000 - 0.866025i) q^{11} +3.66019 q^{13} +(-0.880438 - 1.52496i) q^{17} +(-1.88044 + 3.25701i) q^{19} +(-0.619562 + 1.07311i) q^{23} +(-3.35185 - 5.80557i) q^{25} +2.89931 q^{29} +(-4.73229 - 8.19656i) q^{31} +(8.76608 + 2.25427i) q^{35} +(-1.42107 + 2.46136i) q^{37} -8.70370 q^{41} +12.0676 q^{43} +(2.11956 - 3.67119i) q^{47} +(-5.99028 + 3.62167i) q^{49} +(-0.112725 - 0.195246i) q^{53} +3.42107 q^{55} +(-3.27292 - 5.66886i) q^{59} +(5.12476 - 8.87635i) q^{61} +(-6.26088 + 10.8442i) q^{65} +(1.70370 + 2.95089i) q^{67} +4.23912 q^{71} +(-5.09097 - 8.81782i) q^{73} +(-1.85185 + 1.88962i) q^{77} +(3.67511 - 6.36547i) q^{79} +10.4887 q^{83} +6.02408 q^{85} +(3.63160 - 6.29012i) q^{89} +(-2.60069 - 9.32820i) q^{91} +(-6.43310 - 11.1425i) q^{95} +11.7472 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{5} + 4 q^{7} - 3 q^{11} + 6 q^{13} - 5 q^{17} - 11 q^{19} - 4 q^{23} - 11 q^{25} + 2 q^{29} - 19 q^{31} + 17 q^{35} + 8 q^{37} - 34 q^{41} + 20 q^{43} + 13 q^{47} - 12 q^{49} + 9 q^{53} + 4 q^{55}+ \cdots + 50 q^{97}+O(q^{100}) $ 6 * q - 2 * q^5 + 4 * q^7 - 3 * q^11 + 6 * q^13 - 5 * q^17 - 11 * q^19 - 4 * q^23 - 11 * q^25 + 2 * q^29 - 19 * q^31 + 17 * q^35 + 8 * q^37 - 34 * q^41 + 20 * q^43 + 13 * q^47 - 12 * q^49 + 9 * q^53 + 4 * q^55 + 6 * q^59 - 4 * q^61 - 37 * q^65 - 8 * q^67 + 26 * q^71 - 22 * q^73 - 2 * q^77 - 5 * q^79 - 6 * q^83 - 14 * q^85 - 3 * q^89 - 31 * q^91 + 3 * q^95 + 50 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2772\mathbb{Z}\right)^\times$.

$n$	$1387$	$1541$	$1585$	$2521$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.71053	+	2.96273i	−0.764974	+	1.32497i	0.175287	+	0.984517i	$0.443915\pi$
$5$	−1.71053	+	2.96273i	−0.764974	+	1.32497i	−0.940260	+	0.340456i	$0.889419\pi$
$6$		0			0
$7$	−0.710533	−	2.54856i	−0.268556	−	0.963264i
$7$	−0.710533	−	2.54856i	−0.268556	−	0.963264i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	3.66019			1.01515			0.507577	−	0.861606i	$-0.330541\pi$
$13$	3.66019			1.01515			0.507577	+	0.861606i	$0.330541\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.880438	−	1.52496i	−0.213538	−	0.369858i	0.739282	−	0.673396i	$-0.235165\pi$
$17$	−0.880438	−	1.52496i	−0.213538	−	0.369858i	−0.952819	+	0.303538i	$0.901832\pi$
$18$		0			0
$19$	−1.88044	+	3.25701i	−0.431402	+	0.747210i	−0.996994	−	0.0774746i	$-0.975314\pi$
$19$	−1.88044	+	3.25701i	−0.431402	+	0.747210i	0.565592	+	0.824685i	$0.308648\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.619562	+	1.07311i	−0.129188	+	0.223759i	−0.923362	−	0.383930i	$-0.874570\pi$
$23$	−0.619562	+	1.07311i	−0.129188	+	0.223759i	0.794175	+	0.607690i	$0.207904\pi$
$24$		0			0
$25$	−3.35185	−	5.80557i	−0.670370	−	1.16111i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.89931			0.538389			0.269194	−	0.963086i	$-0.413243\pi$
$29$	2.89931			0.538389			0.269194	+	0.963086i	$0.413243\pi$
$30$		0			0
$31$	−4.73229	−	8.19656i	−0.849944	−	1.47215i	−0.881258	−	0.472636i	$-0.843302\pi$
$31$	−4.73229	−	8.19656i	−0.849944	−	1.47215i	0.0313138	−	0.999510i	$-0.490031\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	8.76608	+	2.25427i	1.48174	+	0.381042i
$36$		0			0
$37$	−1.42107	+	2.46136i	−0.233622	+	0.404645i	−0.958871	−	0.283841i	$-0.908391\pi$
$37$	−1.42107	+	2.46136i	−0.233622	+	0.404645i	0.725249	+	0.688486i	$0.241724\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.70370			−1.35929			−0.679645	−	0.733542i	$-0.737866\pi$
$41$	−8.70370			−1.35929			−0.679645	+	0.733542i	$0.737866\pi$
$42$		0			0
$43$	12.0676			1.84029			0.920145	−	0.391579i	$-0.128071\pi$
$43$	12.0676			1.84029			0.920145	+	0.391579i	$0.128071\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.11956	−	3.67119i	0.309170	−	0.535498i	−0.669011	−	0.743252i	$-0.733282\pi$
$47$	2.11956	−	3.67119i	0.309170	−	0.535498i	0.978181	+	0.207754i	$0.0666155\pi$
$48$		0			0
$49$	−5.99028	+	3.62167i	−0.855755	+	0.517381i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.112725	−	0.195246i	−0.0154840	−	0.0268190i	0.858180	−	0.513350i	$-0.171596\pi$
$53$	−0.112725	−	0.195246i	−0.0154840	−	0.0268190i	−0.873664	+	0.486531i	$0.838262\pi$
$54$		0			0
$55$	3.42107			0.461297
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.27292	−	5.66886i	−0.426097	−	0.738022i	0.570425	−	0.821350i	$-0.306779\pi$
$59$	−3.27292	−	5.66886i	−0.426097	−	0.738022i	−0.996522	+	0.0833277i	$0.973445\pi$
$60$		0			0
$61$	5.12476	−	8.87635i	0.656159	−	1.13650i	−0.325443	−	0.945562i	$-0.605514\pi$
$61$	5.12476	−	8.87635i	0.656159	−	1.13650i	0.981602	−	0.190939i	$-0.0611532\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.26088	+	10.8442i	−0.776566	+	1.34505i
$66$		0			0
$67$	1.70370	+	2.95089i	0.208140	+	0.360509i	0.951129	−	0.308795i	$-0.0999258\pi$
$67$	1.70370	+	2.95089i	0.208140	+	0.360509i	−0.742989	+	0.669304i	$0.766592\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.23912			0.503091			0.251546	−	0.967845i	$-0.419061\pi$
$71$	4.23912			0.503091			0.251546	+	0.967845i	$0.419061\pi$
$72$		0			0
$73$	−5.09097	−	8.81782i	−0.595853	−	1.03205i	−0.993426	−	0.114477i	$-0.963481\pi$
$73$	−5.09097	−	8.81782i	−0.595853	−	1.03205i	0.397573	−	0.917571i	$-0.369853\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.85185	+	1.88962i	−0.211038	+	0.215342i
$78$		0			0
$79$	3.67511	−	6.36547i	0.413482	−	0.716172i	−0.581786	−	0.813342i	$-0.697646\pi$
$79$	3.67511	−	6.36547i	0.413482	−	0.716172i	0.995268	+	0.0971704i	$0.0309792\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	10.4887			1.15128			0.575639	−	0.817704i	$-0.304753\pi$
$83$	10.4887			1.15128			0.575639	+	0.817704i	$0.304753\pi$
$84$		0			0
$85$	6.02408			0.653403
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.63160	−	6.29012i	0.384949	−	0.666751i	−0.606813	−	0.794844i	$-0.707552\pi$
$89$	3.63160	−	6.29012i	0.384949	−	0.666751i	0.991762	+	0.128094i	$0.0408858\pi$
$90$		0			0
$91$	−2.60069	−	9.32820i	−0.272626	−	0.977861i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.43310	−	11.1425i	−0.660023	−	1.14319i
$96$		0			0
$97$	11.7472			1.19275			0.596374	−	0.802707i	$-0.296608\pi$
$97$	11.7472			1.19275			0.596374	+	0.802707i	$0.296608\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.02696	+	10.4390i	0.599704	+	1.03872i	0.992864	+	0.119249i	$0.0380485\pi$
$101$	6.02696	+	10.4390i	0.599704	+	1.03872i	−0.393160	+	0.919470i	$0.628618\pi$
$102$		0			0
$103$	8.44802	−	14.6324i	0.832408	−	1.44177i	−0.0637149	−	0.997968i	$-0.520295\pi$
$103$	8.44802	−	14.6324i	0.832408	−	1.44177i	0.896123	−	0.443805i	$-0.146372\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.572097	−	0.990901i	0.0553067	−	0.0957940i	−0.837047	−	0.547132i	$-0.815720\pi$
$107$	0.572097	−	0.990901i	0.0553067	−	0.0957940i	0.892353	+	0.451338i	$0.149053\pi$
$108$		0			0
$109$	1.65335	+	2.86369i	0.158363	+	0.274292i	0.934278	−	0.356545i	$-0.116045\pi$
$109$	1.65335	+	2.86369i	0.158363	+	0.274292i	−0.775916	+	0.630836i	$0.782712\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	17.5322			1.64929			0.824643	−	0.565653i	$-0.191376\pi$
$113$	17.5322			1.64929			0.824643	+	0.565653i	$0.191376\pi$
$114$		0			0
$115$	−2.11956	−	3.67119i	−0.197650	−	0.342340i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.26088	+	3.32738i	−0.298924	+	0.305021i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.82846			0.521313
$126$		0			0
$127$	0.660190			0.0585824			0.0292912	−	0.999571i	$-0.490675\pi$
$127$	0.660190			0.0585824			0.0292912	+	0.999571i	$0.490675\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.85705	−	17.0729i	0.861214	−	1.49167i	−0.00954300	−	0.999954i	$-0.503038\pi$
$131$	9.85705	−	17.0729i	0.861214	−	1.49167i	0.870757	−	0.491713i	$-0.163629\pi$
$132$		0			0
$133$	9.63680	+	2.47819i	0.835617	+	0.214886i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.38727	+	2.40283i	0.118523	+	0.205288i	0.919183	−	0.393832i	$-0.128851\pi$
$137$	1.38727	+	2.40283i	0.118523	+	0.205288i	−0.800660	+	0.599119i	$0.795517\pi$
$138$		0			0
$139$	11.0000			0.933008			0.466504	−	0.884519i	$-0.345513\pi$
$139$	11.0000			0.933008			0.466504	+	0.884519i	$0.345513\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.83009	−	3.16982i	−0.153040	−	0.265073i
$144$		0			0
$145$	−4.95937	+	8.58988i	−0.411853	+	0.713351i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.39931	+	7.61983i	−0.360406	+	0.624241i	−0.988028	−	0.154277i	$-0.950695\pi$
$149$	−4.39931	+	7.61983i	−0.360406	+	0.624241i	0.627622	+	0.778518i	$0.284028\pi$
$150$		0			0
$151$	10.1940	+	17.6565i	0.829574	+	1.43687i	0.898372	+	0.439235i	$0.144750\pi$
$151$	10.1940	+	17.6565i	0.829574	+	1.43687i	−0.0687980	+	0.997631i	$0.521916\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	32.3789			2.60074
$156$		0			0
$157$	3.79630	+	6.57539i	0.302978	+	0.524773i	0.976809	−	0.214112i	$-0.0686858\pi$
$157$	3.79630	+	6.57539i	0.302978	+	0.524773i	−0.673831	+	0.738885i	$0.735352\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.17511	+	0.816506i	0.250233	+	0.0643497i
$162$		0			0
$163$	4.02175	−	6.96588i	0.315008	−	0.545610i	−0.664431	−	0.747349i	$-0.731326\pi$
$163$	4.02175	−	6.96588i	0.315008	−	0.545610i	0.979439	+	0.201740i	$0.0646594\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−15.7414			−1.21811			−0.609055	−	0.793128i	$-0.708451\pi$
$167$	−15.7414			−1.21811			−0.609055	+	0.793128i	$0.708451\pi$
$168$		0			0
$169$	0.396990			0.0305377
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.87360	+	3.24517i	−0.142447	+	0.246726i	−0.928418	−	0.371538i	$-0.878830\pi$
$173$	−1.87360	+	3.24517i	−0.142447	+	0.246726i	0.785970	+	0.618264i	$0.212164\pi$
$174$		0			0
$175$	−12.4142	+	12.6674i	−0.938428	+	0.957568i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.75116	−	9.96130i	−0.429862	−	0.744543i	0.566999	−	0.823719i	$-0.308104\pi$
$179$	−5.75116	−	9.96130i	−0.429862	−	0.744543i	−0.996861	+	0.0791759i	$0.974771\pi$
$180$		0			0
$181$	−5.79071			−0.430420			−0.215210	−	0.976568i	$-0.569044\pi$
$181$	−5.79071			−0.430420			−0.215210	+	0.976568i	$0.569044\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.86156	−	8.42048i	−0.357429	−	0.619086i
$186$		0			0
$187$	−0.880438	+	1.52496i	−0.0643840	+	0.111516i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.26088	−	16.0403i	0.670094	−	1.16064i	−0.307784	−	0.951456i	$-0.599587\pi$
$191$	9.26088	−	16.0403i	0.670094	−	1.16064i	0.977877	−	0.209180i	$-0.0670794\pi$
$192$		0			0
$193$	1.88727	+	3.26886i	0.135849	+	0.235297i	0.925921	−	0.377716i	$-0.123290\pi$
$193$	1.88727	+	3.26886i	0.135849	+	0.235297i	−0.790072	+	0.613013i	$0.789957\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.1683			−0.724459			−0.362230	−	0.932089i	$-0.617984\pi$
$197$	−10.1683			−0.724459			−0.362230	+	0.932089i	$0.617984\pi$
$198$		0			0
$199$	5.03899	+	8.72779i	0.357205	+	0.618697i	0.987493	−	0.157665i	$-0.0503965\pi$
$199$	5.03899	+	8.72779i	0.357205	+	0.618697i	−0.630288	+	0.776361i	$0.717063\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.06006	−	7.38906i	−0.144588	−	0.518611i
$204$		0			0
$205$	14.8880	−	25.7867i	1.03982	−	1.80102i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.76088			0.260145
$210$		0			0
$211$	−1.72313			−0.118625			−0.0593125	−	0.998239i	$-0.518891\pi$
$211$	−1.72313			−0.118625			−0.0593125	+	0.998239i	$0.518891\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−20.6420	+	35.7530i	−1.40777	+	2.43833i
$216$		0			0
$217$	−17.5270	+	17.8844i	−1.18981	+	1.21407i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.22257	−	5.58166i	−0.216774	−	0.375463i
$222$		0			0
$223$	−9.47825			−0.634710			−0.317355	−	0.948307i	$-0.602795\pi$
$223$	−9.47825			−0.634710			−0.317355	+	0.948307i	$0.602795\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.72094	−	16.8372i	−0.645201	−	1.11752i	−0.984255	−	0.176754i	$-0.943440\pi$
$227$	−9.72094	−	16.8372i	−0.645201	−	1.11752i	0.339054	−	0.940767i	$-0.389893\pi$
$228$		0			0
$229$	5.16019	−	8.93771i	0.340995	−	0.590621i	−0.643623	−	0.765343i	$-0.722569\pi$
$229$	5.16019	−	8.93771i	0.340995	−	0.590621i	0.984618	+	0.174722i	$0.0559028\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.557180	−	0.965064i	0.0365021	−	0.0632234i	−0.847197	−	0.531279i	$-0.821712\pi$
$233$	0.557180	−	0.965064i	0.0365021	−	0.0632234i	0.883699	+	0.468055i	$0.155045\pi$
$234$		0			0
$235$	7.25116	+	12.5594i	0.473014	+	0.819284i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	26.1053			1.68861			0.844307	−	0.535860i	$-0.180013\pi$
$239$	26.1053			1.68861			0.844307	+	0.535860i	$0.180013\pi$
$240$		0			0
$241$	−7.39768	−	12.8132i	−0.476526	−	0.825368i	0.523112	−	0.852264i	$-0.324771\pi$
$241$	−7.39768	−	12.8132i	−0.476526	−	0.825368i	−0.999638	+	0.0268962i	$0.991438\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.483448	−	23.9426i	−0.0308864	−	1.52964i
$246$		0			0
$247$	−6.88276	+	11.9213i	−0.437940	+	0.758534i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.96225			0.123856			0.0619281	−	0.998081i	$-0.480275\pi$
$251$	1.96225			0.123856			0.0619281	+	0.998081i	$0.480275\pi$
$252$		0			0
$253$	1.23912			0.0779030
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.25404	−	2.17206i	0.0782249	−	0.135489i	−0.824259	−	0.566213i	$-0.808408\pi$
$257$	1.25404	−	2.17206i	0.0782249	−	0.135489i	0.902484	+	0.430723i	$0.141741\pi$
$258$		0			0
$259$	7.28263	+	1.87279i	0.452521	+	0.116370i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.08414	−	3.60983i	−0.128513	−	0.222592i	0.794587	−	0.607150i	$-0.207687\pi$
$263$	−2.08414	−	3.60983i	−0.128513	−	0.222592i	−0.923101	+	0.384558i	$0.874354\pi$
$264$		0			0
$265$	0.771280			0.0473794
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.5744	−	18.3154i	−0.644734	−	1.11671i	−0.984363	−	0.176152i	$-0.943635\pi$
$269$	−10.5744	−	18.3154i	−0.644734	−	1.11671i	0.339629	−	0.940559i	$-0.389698\pi$
$270$		0			0
$271$	−6.63844	+	11.4981i	−0.403256	+	0.698460i	−0.994117	−	0.108313i	$-0.965455\pi$
$271$	−6.63844	+	11.4981i	−0.403256	+	0.698460i	0.590861	+	0.806774i	$0.298788\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.35185	+	5.80557i	−0.202124	+	0.350089i
$276$		0			0
$277$	4.75116	+	8.22925i	0.285470	+	0.494448i	0.972723	−	0.231970i	$-0.0745171\pi$
$277$	4.75116	+	8.22925i	0.285470	+	0.494448i	−0.687253	+	0.726418i	$0.741184\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−26.8766			−1.60332			−0.801662	−	0.597777i	$-0.796051\pi$
$281$	−26.8766			−1.60332			−0.801662	+	0.597777i	$0.796051\pi$
$282$		0			0
$283$	−0.154988	−	0.268447i	−0.00921309	−	0.0159575i	0.861382	−	0.507958i	$-0.169599\pi$
$283$	−0.154988	−	0.268447i	−0.00921309	−	0.0159575i	−0.870595	+	0.492000i	$0.836266\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.18427	+	22.1819i	0.365046	+	1.30935i
$288$		0			0
$289$	6.94966	−	12.0372i	0.408803	−	0.708068i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−31.2222			−1.82402			−0.912010	−	0.410169i	$-0.865470\pi$
$293$	−31.2222			−1.82402			−0.912010	+	0.410169i	$0.865470\pi$
$294$		0			0
$295$	22.3937			1.30381
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.26771	+	3.92779i	−0.131145	+	0.227150i
$300$		0			0
$301$	−8.57442	−	30.7549i	−0.494221	−	1.77268i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	17.5322	+	30.3666i	1.00389	+	1.73879i
$306$		0			0
$307$	7.50808			0.428509			0.214254	−	0.976778i	$-0.431268\pi$
$307$	7.50808			0.428509			0.214254	+	0.976778i	$0.431268\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.767713	−	1.32972i	−0.0435330	−	0.0754014i	0.843438	−	0.537227i	$-0.180528\pi$
$311$	−0.767713	−	1.32972i	−0.0435330	−	0.0754014i	−0.886971	+	0.461825i	$0.847195\pi$
$312$		0			0
$313$	6.42627	−	11.1306i	0.363234	−	0.629140i	−0.625257	−	0.780419i	$-0.715006\pi$
$313$	6.42627	−	11.1306i	0.363234	−	0.629140i	0.988491	+	0.151279i	$0.0483392\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.21574	−	2.10571i	0.0682825	−	0.118269i	−0.829863	−	0.557967i	$-0.811581\pi$
$317$	1.21574	−	2.10571i	0.0682825	−	0.118269i	0.898145	+	0.439699i	$0.144915\pi$
$318$		0			0
$319$	−1.44966	−	2.51088i	−0.0811652	−	0.140582i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.62244			0.368482
$324$		0			0
$325$	−12.2684	−	21.2495i	−0.680528	−	1.17871i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.8623	−	2.79332i	−0.598855	−	0.154001i
$330$		0			0
$331$	−5.20370	+	9.01307i	−0.286021	+	0.495403i	−0.972856	−	0.231410i	$-0.925666\pi$
$331$	−5.20370	+	9.01307i	−0.286021	+	0.495403i	0.686835	+	0.726813i	$0.258999\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.6569			−0.636886
$336$		0			0
$337$	−11.2164			−0.610998			−0.305499	−	0.952192i	$-0.598823\pi$
$337$	−11.2164			−0.610998			−0.305499	+	0.952192i	$0.598823\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.73229	+	8.19656i	−0.256268	+	0.443869i
$342$		0			0
$343$	13.4863	+	12.6933i	0.728193	+	0.685372i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.3788	−	23.1728i	−0.718212	−	1.24398i	−0.961708	−	0.274077i	$-0.911628\pi$
$347$	−13.3788	−	23.1728i	−0.718212	−	1.24398i	0.243496	−	0.969902i	$-0.421706\pi$
$348$		0			0
$349$	−5.11436			−0.273765			−0.136883	−	0.990587i	$-0.543708\pi$
$349$	−5.11436			−0.273765			−0.136883	+	0.990587i	$0.543708\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.1505	−	17.5811i	−0.540255	−	0.935750i	−0.998889	−	0.0471242i	$-0.984994\pi$
$353$	−10.1505	−	17.5811i	−0.540255	−	0.935750i	0.458634	−	0.888625i	$-0.348339\pi$
$354$		0			0
$355$	−7.25116	+	12.5594i	−0.384852	+	0.666583i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.73392	−	8.19939i	0.249847	−	0.432747i	−0.713636	−	0.700516i	$-0.752953\pi$
$359$	4.73392	−	8.19939i	0.249847	−	0.432747i	0.963483	+	0.267769i	$0.0862864\pi$
$360$		0			0
$361$	2.42790	+	4.20525i	0.127784	+	0.221329i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	34.8331			1.82325
$366$		0			0
$367$	−10.7323	−	18.5889i	−0.560221	−	0.970331i	−0.997477	−	0.0709938i	$-0.977383\pi$
$367$	−10.7323	−	18.5889i	−0.560221	−	0.970331i	0.437256	−	0.899337i	$-0.355950\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.417500	+	0.426015i	−0.0216755	+	0.0221176i
$372$		0			0
$373$	−6.66827	+	11.5498i	−0.345270	+	0.598025i	−0.985403	−	0.170239i	$-0.945546\pi$
$373$	−6.66827	+	11.5498i	−0.345270	+	0.598025i	0.640133	+	0.768264i	$0.278879\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.6120			0.546548
$378$		0			0
$379$	−5.76088			−0.295916			−0.147958	−	0.988994i	$-0.547270\pi$
$379$	−5.76088			−0.295916			−0.147958	+	0.988994i	$0.547270\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.6150	+	25.3140i	−0.746794	+	1.29349i	0.202558	+	0.979270i	$0.435075\pi$
$383$	−14.6150	+	25.3140i	−0.746794	+	1.29349i	−0.949352	+	0.314215i	$0.898259\pi$
$384$		0			0
$385$	−2.43078	−	8.71878i	−0.123884	−	0.444350i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.2540	−	17.7605i	−0.519900	−	0.900494i	−0.999732	−	0.0231336i	$-0.992636\pi$
$389$	−10.2540	−	17.7605i	−0.519900	−	0.900494i	0.479832	−	0.877360i	$-0.340698\pi$
$390$		0			0
$391$	2.18194			0.110346
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.5728	+	21.7767i	0.632605	+	1.09570i
$396$		0			0
$397$	−5.78495	+	10.0198i	−0.290338	+	0.502881i	−0.973890	−	0.227022i	$-0.927101\pi$
$397$	−5.78495	+	10.0198i	−0.290338	+	0.502881i	0.683551	+	0.729903i	$0.260435\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.5933	−	21.8122i	0.628879	−	1.08925i	−0.358898	−	0.933377i	$-0.616847\pi$
$401$	12.5933	−	21.8122i	0.628879	−	1.08925i	0.987777	−	0.155874i	$-0.0498193\pi$
$402$		0			0
$403$	−17.3211	−	30.0010i	−0.862824	−	1.49445i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.84213			0.140879
$408$		0			0
$409$	−1.90383	−	3.29752i	−0.0941382	−	0.163052i	0.815110	−	0.579306i	$-0.196676\pi$
$409$	−1.90383	−	3.29752i	−0.0941382	−	0.163052i	−0.909249	+	0.416254i	$0.863343\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−12.1219	+	12.3691i	−0.596479	+	0.608645i
$414$		0			0
$415$	−17.9412	+	31.0750i	−0.880698	+	1.52541i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.08701			0.248517			0.124258	−	0.992250i	$-0.460345\pi$
$419$	5.08701			0.248517			0.124258	+	0.992250i	$0.460345\pi$
$420$		0			0
$421$	−16.9442			−0.825810			−0.412905	−	0.910774i	$-0.635486\pi$
$421$	−16.9442			−0.825810			−0.412905	+	0.910774i	$0.635486\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−5.90219	+	10.2229i	−0.286298	+	0.495883i
$426$		0			0
$427$	−26.2632	−	6.75381i	−1.27097	−	0.326840i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.22777	+	2.12657i	0.0591398	+	0.102433i	0.894079	−	0.447908i	$-0.147831\pi$
$431$	1.22777	+	2.12657i	0.0591398	+	0.102433i	−0.834940	+	0.550341i	$0.814498\pi$
$432$		0			0
$433$	−32.8629			−1.57929			−0.789646	−	0.613563i	$-0.789736\pi$
$433$	−32.8629			−1.57929			−0.789646	+	0.613563i	$0.789736\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.33009	−	4.03584i	−0.111464	−	0.193061i
$438$		0			0
$439$	0.0406283	−	0.0703702i	0.00193908	−	0.00335859i	−0.865054	−	0.501678i	$-0.832716\pi$
$439$	0.0406283	−	0.0703702i	0.00193908	−	0.00335859i	0.866993	+	0.498320i	$0.166049\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.86840	+	6.70027i	−0.183793	+	0.318339i	−0.943169	−	0.332313i	$-0.892171\pi$
$443$	−3.86840	+	6.70027i	−0.183793	+	0.318339i	0.759376	+	0.650652i	$0.225504\pi$
$444$		0			0
$445$	12.4239	+	21.5189i	0.588951	+	1.02009i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	21.1078			0.996140			0.498070	−	0.867137i	$-0.334042\pi$
$449$	21.1078			0.996140			0.498070	+	0.867137i	$0.334042\pi$
$450$		0			0
$451$	4.35185	+	7.53762i	0.204921	+	0.354933i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	32.0855	+	8.25107i	1.50419	+	0.386816i
$456$		0			0
$457$	8.35868	−	14.4777i	0.391003	−	0.677237i	−0.601579	−	0.798813i	$-0.705462\pi$
$457$	8.35868	−	14.4777i	0.391003	−	0.677237i	0.992582	+	0.121576i	$0.0387949\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.62571			0.262015			0.131008	−	0.991381i	$-0.458179\pi$
$461$	5.62571			0.262015			0.131008	+	0.991381i	$0.458179\pi$
$462$		0			0
$463$	24.3341			1.13090			0.565450	−	0.824783i	$-0.308703\pi$
$463$	24.3341			1.13090			0.565450	+	0.824783i	$0.308703\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.42395	+	16.3228i	−0.436088	+	0.755327i	−0.997384	−	0.0722885i	$-0.976970\pi$
$467$	−9.42395	+	16.3228i	−0.436088	+	0.755327i	0.561296	+	0.827615i	$0.310303\pi$
$468$		0			0
$469$	6.30998	−	6.43867i	0.291368	−	0.297310i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.03379	−	10.4508i	−0.277434	−	0.480530i
$474$		0			0
$475$	25.2118			1.15680
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.9383	+	25.8739i	0.682549	+	1.18221i	0.974200	+	0.225684i	$0.0724618\pi$
$479$	14.9383	+	25.8739i	0.682549	+	1.18221i	−0.291652	+	0.956525i	$0.594205\pi$
$480$		0			0
$481$	−5.20137	+	9.00904i	−0.237162	+	0.410777i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−20.0940	+	34.8038i	−0.912421	+	1.58036i
$486$		0			0
$487$	6.21574	+	10.7660i	0.281662	+	0.487853i	0.971794	−	0.235831i	$-0.0757810\pi$
$487$	6.21574	+	10.7660i	0.281662	+	0.487853i	−0.690132	+	0.723683i	$0.742448\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10.0917			−0.455430			−0.227715	−	0.973728i	$-0.573125\pi$
$491$	−10.0917			−0.455430			−0.227715	+	0.973728i	$0.573125\pi$
$492$		0			0
$493$	−2.55267	−	4.42135i	−0.114966	−	0.199128i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.01204	−	10.8036i	−0.135108	−	0.484610i
$498$		0			0
$499$	7.74269	−	13.4107i	0.346610	−	0.600347i	−0.639035	−	0.769178i	$-0.720666\pi$
$499$	7.74269	−	13.4107i	0.346610	−	0.600347i	0.985645	+	0.168831i	$0.0539993\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.99673			0.178205			0.0891027	−	0.996022i	$-0.471600\pi$
$503$	3.99673			0.178205			0.0891027	+	0.996022i	$0.471600\pi$
$504$		0			0
$505$	−41.2372			−1.83503
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.891788	+	1.54462i	−0.0395278	+	0.0684642i	−0.885112	−	0.465377i	$-0.845919\pi$
$509$	−0.891788	+	1.54462i	−0.0395278	+	0.0684642i	0.845585	+	0.533841i	$0.179252\pi$
$510$		0			0
$511$	−18.8554	+	19.2400i	−0.834114	+	0.851127i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	28.9012	+	50.0584i	1.27354	+	2.20584i
$516$		0			0
$517$	−4.23912			−0.186436
$518$		0			0
$519$		0			0
$520$		0			0
$521$	16.5865	+	28.7286i	0.726666	+	1.25862i	0.958285	+	0.285816i	$0.0922645\pi$
$521$	16.5865	+	28.7286i	0.726666	+	1.25862i	−0.231619	+	0.972807i	$0.574402\pi$
$522$		0			0
$523$	12.6219	−	21.8617i	0.551916	−	0.955947i	−0.446220	−	0.894923i	$-0.647230\pi$
$523$	12.6219	−	21.8617i	0.551916	−	0.955947i	0.998136	−	0.0610240i	$-0.0194366\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.33297	+	14.4331i	−0.362990	+	0.628717i
$528$		0			0
$529$	10.7323	+	18.5889i	0.466621	+	0.808212i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−31.8572			−1.37989
$534$		0			0
$535$	1.95718	+	3.38994i	0.0846163	+	0.146560i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.13160	+	3.37690i	0.264107	+	0.145454i
$540$		0			0
$541$	3.97141	−	6.87868i	0.170744	−	0.295738i	−0.767936	−	0.640527i	$-0.778716\pi$
$541$	3.97141	−	6.87868i	0.170744	−	0.295738i	0.938680	+	0.344789i	$0.112049\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11.3125			−0.484573
$546$		0			0
$547$	17.2495			0.737537			0.368768	−	0.929521i	$-0.379780\pi$
$547$	17.2495			0.737537			0.368768	+	0.929521i	$0.379780\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.45198	+	9.44311i	−0.232262	+	0.402290i
$552$		0			0
$553$	−18.8341	−	4.84334i	−0.800905	−	0.205960i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.62928	+	9.75019i	0.238520	+	0.413129i	0.960290	−	0.279004i	$-0.0900044\pi$
$557$	5.62928	+	9.75019i	0.238520	+	0.413129i	−0.721770	+	0.692133i	$0.756671\pi$
$558$		0			0
$559$	44.1696			1.86818
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.16143	−	8.93987i	−0.217528	−	0.376770i	0.736523	−	0.676412i	$-0.236466\pi$
$563$	−5.16143	−	8.93987i	−0.217528	−	0.376770i	−0.954052	+	0.299642i	$0.903133\pi$
$564$		0			0
$565$	−29.9893	+	51.9431i	−1.26166	+	2.18526i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.57605	−	9.65801i	0.233760	−	0.404885i	−0.725151	−	0.688590i	$-0.758230\pi$
$569$	5.57605	−	9.65801i	0.233760	−	0.404885i	0.958912	+	0.283705i	$0.0915635\pi$
$570$		0			0
$571$	−4.28783	−	7.42674i	−0.179440	−	0.310800i	0.762249	−	0.647284i	$-0.224095\pi$
$571$	−4.28783	−	7.42674i	−0.179440	−	0.310800i	−0.941689	+	0.336485i	$0.890762\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.30671			0.346414
$576$		0			0
$577$	−21.7902	−	37.7417i	−0.907136	−	1.57121i	−0.818024	−	0.575184i	$-0.804930\pi$
$577$	−21.7902	−	37.7417i	−0.907136	−	1.57121i	−0.0891120	−	0.996022i	$-0.528403\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.45254	−	26.7309i	−0.309183	−	1.10899i
$582$		0			0
$583$	−0.112725	+	0.195246i	−0.00466860	+	0.00808625i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	44.4315			1.83388			0.916942	−	0.399022i	$-0.130650\pi$
$587$	44.4315			1.83388			0.916942	+	0.399022i	$0.130650\pi$
$588$		0			0
$589$	35.5951			1.46667
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.51724	+	4.35999i	−0.103371	+	0.179043i	−0.913071	−	0.407800i	$-0.866296\pi$
$593$	−2.51724	+	4.35999i	−0.103371	+	0.179043i	0.809701	+	0.586843i	$0.199629\pi$
$594$		0			0
$595$	−4.28031	−	15.3527i	−0.175475	−	0.629399i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.36784	−	5.83328i	−0.137606	−	0.238341i	0.788984	−	0.614414i	$-0.210608\pi$
$599$	−3.36784	−	5.83328i	−0.137606	−	0.238341i	−0.926590	+	0.376073i	$0.877274\pi$
$600$		0			0
$601$	−30.4854			−1.24352			−0.621762	−	0.783206i	$-0.713583\pi$
$601$	−30.4854			−1.24352			−0.621762	+	0.783206i	$0.713583\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.71053	−	2.96273i	−0.0695431	−	0.120452i
$606$		0			0
$607$	−13.6586	+	23.6573i	−0.554384	+	0.960221i	0.443568	+	0.896241i	$0.353713\pi$
$607$	−13.6586	+	23.6573i	−0.554384	+	0.960221i	−0.997951	+	0.0639797i	$0.979621\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.75800	−	13.4372i	0.313855	−	0.543613i
$612$		0			0
$613$	17.1248	+	29.6610i	0.691663	+	1.19799i	0.971293	+	0.237887i	$0.0764548\pi$
$613$	17.1248	+	29.6610i	0.691663	+	1.19799i	−0.279630	+	0.960108i	$0.590212\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.13052			−0.367581			−0.183790	−	0.982965i	$-0.558837\pi$
$617$	−9.13052			−0.367581			−0.183790	+	0.982965i	$0.558837\pi$
$618$		0			0
$619$	3.66019	+	6.33963i	0.147115	+	0.254811i	0.930160	−	0.367154i	$-0.119668\pi$
$619$	3.66019	+	6.33963i	0.147115	+	0.254811i	−0.783045	+	0.621965i	$0.786334\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18.6111	−	4.78600i	−0.745638	−	0.191747i
$624$		0			0
$625$	6.78947	−	11.7597i	0.271579	−	0.470388i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.00465			0.199548
$630$		0			0
$631$	12.7199			0.506370			0.253185	−	0.967418i	$-0.418522\pi$
$631$	12.7199			0.506370			0.253185	+	0.967418i	$0.418522\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.12928	+	1.95596i	−0.0448140	+	0.0776201i
$636$		0			0
$637$	−21.9256	+	13.2560i	−0.868723	+	0.525222i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.08250	−	7.07110i	−0.161249	−	0.279292i	0.774068	−	0.633103i	$-0.218219\pi$
$641$	−4.08250	−	7.07110i	−0.161249	−	0.279292i	−0.935317	+	0.353811i	$0.884886\pi$
$642$		0			0
$643$	8.39123			0.330918			0.165459	−	0.986217i	$-0.447089\pi$
$643$	8.39123			0.330918			0.165459	+	0.986217i	$0.447089\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.2599	+	35.0912i	0.796500	+	1.37958i	0.921882	+	0.387470i	$0.126651\pi$
$647$	20.2599	+	35.0912i	0.796500	+	1.37958i	−0.125382	+	0.992109i	$0.540016\pi$
$648$		0			0
$649$	−3.27292	+	5.66886i	−0.128473	+	0.222522i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.35185	−	12.7338i	0.287700	−	0.498311i	−0.685560	−	0.728016i	$-0.740443\pi$
$653$	7.35185	−	12.7338i	0.287700	−	0.498311i	0.973260	+	0.229705i	$0.0737760\pi$
$654$		0			0
$655$	33.7216	+	58.4076i	1.31761	+	2.28217i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.2873			−0.751326			−0.375663	−	0.926756i	$-0.622585\pi$
$659$	−19.2873			−0.751326			−0.375663	+	0.926756i	$0.622585\pi$
$660$		0			0
$661$	9.90615	+	17.1580i	0.385305	+	0.667367i	0.991811	−	0.127711i	$-0.0407631\pi$
$661$	9.90615	+	17.1580i	0.385305	+	0.667367i	−0.606507	+	0.795078i	$0.707430\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−23.8263	+	24.3122i	−0.923943	+	0.942788i
$666$		0			0
$667$	−1.79630	+	3.11129i	−0.0695531	+	0.120470i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.2495			−0.395679
$672$		0			0
$673$	−1.11901			−0.0431345			−0.0215673	−	0.999767i	$-0.506866\pi$
$673$	−1.11901			−0.0431345			−0.0215673	+	0.999767i	$0.506866\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.7571	−	37.6843i	0.836191	−	1.44833i	−0.0568653	−	0.998382i	$-0.518111\pi$
$677$	21.7571	−	37.6843i	0.836191	−	1.44833i	0.893057	−	0.449944i	$-0.148556\pi$
$678$		0			0
$679$	−8.34678	−	29.9384i	−0.320320	−	1.14893i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.54746	−	13.0726i	−0.288796	−	0.500209i	0.684727	−	0.728800i	$-0.259922\pi$
$683$	−7.54746	−	13.0726i	−0.288796	−	0.500209i	−0.973523	+	0.228591i	$0.926588\pi$
$684$		0			0
$685$	−9.49192			−0.362668
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.412595	−	0.714636i	−0.0157186	−	0.0272255i
$690$		0			0
$691$	−1.07085	+	1.85477i	−0.0407372	+	0.0705588i	−0.885675	−	0.464306i	$-0.846304\pi$
$691$	−1.07085	+	1.85477i	−0.0407372	+	0.0705588i	0.844938	+	0.534864i	$0.179637\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−18.8159	+	32.5900i	−0.713726	+	1.23621i
$696$		0			0
$697$	7.66307	+	13.2728i	0.290259	+	0.502744i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.1910			0.384908			0.192454	−	0.981306i	$-0.438355\pi$
$701$	10.1910			0.384908			0.192454	+	0.981306i	$0.438355\pi$
$702$		0			0
$703$	−5.34446	−	9.25687i	−0.201570	−	0.349129i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	22.3220	−	22.7773i	0.839506	−	0.856628i
$708$		0			0
$709$	−0.172784	+	0.299270i	−0.00648903	+	0.0112393i	−0.869252	−	0.494370i	$-0.835399\pi$
$709$	−0.172784	+	0.299270i	−0.00648903	+	0.0112393i	0.862763	+	0.505609i	$0.168732\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	11.7278			0.439209
$714$		0			0
$715$	12.5218			0.468287
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.4383	+	23.2758i	−0.501164	+	0.868042i	0.498835	+	0.866697i	$0.333761\pi$
$719$	−13.4383	+	23.2758i	−0.501164	+	0.868042i	−0.999999	+	0.00134491i	$0.999572\pi$
$720$		0			0
$721$	−43.2941	−	11.1335i	−1.61236	−	0.414632i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.71806	−	16.8322i	−0.360920	−	0.625131i
$726$		0			0
$727$	−46.1261			−1.71072			−0.855362	−	0.518031i	$-0.826665\pi$
$727$	−46.1261			−1.71072			−0.855362	+	0.518031i	$0.826665\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−10.6248	−	18.4026i	−0.392971	−	0.680646i
$732$		0			0
$733$	−15.4698	+	26.7944i	−0.571389	+	0.989675i	0.425034	+	0.905177i	$0.360262\pi$
$733$	−15.4698	+	26.7944i	−0.571389	+	0.989675i	−0.996424	+	0.0844979i	$0.973071\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.70370	−	2.95089i	0.0627565	−	0.108697i
$738$		0			0
$739$	−20.1150	−	34.8403i	−0.739944	−	1.28162i	−0.952520	−	0.304476i	$-0.901519\pi$
$739$	−20.1150	−	34.8403i	−0.739944	−	1.28162i	0.212576	−	0.977145i	$-0.431815\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−37.3710			−1.37101			−0.685505	−	0.728068i	$-0.740418\pi$
$743$	−37.3710			−1.37101			−0.685505	+	0.728068i	$0.740418\pi$
$744$		0			0
$745$	−15.0503	−	26.0680i	−0.551402	−	0.955056i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.93186	−	0.753953i	−0.107128	−	0.0275489i
$750$		0			0
$751$	−19.8698	+	34.4155i	−0.725058	+	1.25584i	0.233891	+	0.972263i	$0.424854\pi$
$751$	−19.8698	+	34.4155i	−0.725058	+	1.25584i	−0.958950	+	0.283575i	$0.908479\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−69.7486			−2.53841
$756$		0			0
$757$	6.60628			0.240109			0.120055	−	0.992767i	$-0.461693\pi$
$757$	6.60628			0.240109			0.120055	+	0.992767i	$0.461693\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.518875	−	0.898718i	0.0188092	−	0.0325785i	−0.856468	−	0.516201i	$-0.827346\pi$
$761$	0.518875	−	0.898718i	0.0188092	−	0.0325785i	0.875277	+	0.483622i	$0.160679\pi$
$762$		0			0
$763$	6.12352	−	6.24841i	0.221686	−	0.226208i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.9795	−	20.7491i	−0.432554	−	0.749206i
$768$		0			0
$769$	6.03199			0.217519			0.108760	−	0.994068i	$-0.465312\pi$
$769$	6.03199			0.217519			0.108760	+	0.994068i	$0.465312\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.45034	+	12.9044i	0.267970	+	0.464138i	0.968338	−	0.249645i	$-0.0803138\pi$
$773$	7.45034	+	12.9044i	0.267970	+	0.464138i	−0.700367	+	0.713783i	$0.746980\pi$
$774$		0			0
$775$	−31.7238	+	54.9473i	−1.13955	+	1.97376i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.3668	−	28.3481i	0.586400	−	1.01567i
$780$		0			0
$781$	−2.11956	−	3.67119i	−0.0758439	−	0.131365i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−25.9748			−0.927081
$786$		0			0
$787$	−0.490285	−	0.849198i	−0.0174768	−	0.0302706i	0.857155	−	0.515059i	$-0.172230\pi$
$787$	−0.490285	−	0.849198i	−0.0174768	−	0.0302706i	−0.874632	+	0.484788i	$0.838897\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.4572	−	44.6817i	−0.442926	−	1.58870i
$792$		0			0
$793$	18.7576	−	32.4891i	0.666102	−	1.15372i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	37.2873			1.32078			0.660392	−	0.750921i	$-0.270390\pi$
$797$	37.2873			1.32078			0.660392	+	0.750921i	$0.270390\pi$
$798$		0			0
$799$	−7.46457			−0.264078
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.09097	+	8.81782i	−0.179656	+	0.311174i
$804$		0			0
$805$	−7.85021	+	8.01033i	−0.276684	+	0.282327i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	13.4234	+	23.2500i	0.471941	+	0.817426i	0.999485	−	0.0321019i	$-0.0102201\pi$
$809$	13.4234	+	23.2500i	0.471941	+	0.817426i	−0.527543	+	0.849528i	$0.676887\pi$
$810$		0			0
$811$	31.0572			1.09057			0.545283	−	0.838252i	$-0.316422\pi$
$811$	31.0572			1.09057			0.545283	+	0.838252i	$0.316422\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	13.7587	+	23.8307i	0.481946	+	0.834755i
$816$		0			0
$817$	−22.6923	+	39.3043i	−0.793905	+	1.37508i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.92231	+	17.1859i	−0.346291	+	0.599794i	−0.985587	−	0.169167i	$-0.945892\pi$
$821$	−9.92231	+	17.1859i	−0.346291	+	0.599794i	0.639296	+	0.768960i	$0.279226\pi$
$822$		0			0
$823$	−9.29179	−	16.0939i	−0.323891	−	0.560996i	0.657396	−	0.753545i	$-0.271658\pi$
$823$	−9.29179	−	16.0939i	−0.323891	−	0.560996i	−0.981287	+	0.192549i	$0.938325\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.25744			−0.252366			−0.126183	−	0.992007i	$-0.540273\pi$
$827$	−7.25744			−0.252366			−0.126183	+	0.992007i	$0.540273\pi$
$828$		0			0
$829$	21.4893	+	37.2206i	0.746356	+	1.29273i	0.949559	+	0.313589i	$0.101531\pi$
$829$	21.4893	+	37.2206i	0.746356	+	1.29273i	−0.203203	+	0.979137i	$0.565135\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	10.7970	+	5.94631i	0.374094	+	0.206028i
$834$		0			0
$835$	26.9263	−	46.6377i	0.931822	−	1.61396i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−35.1650			−1.21403			−0.607015	−	0.794690i	$-0.707633\pi$
$839$	−35.1650			−1.21403			−0.607015	+	0.794690i	$0.707633\pi$
$840$		0			0
$841$	−20.5940			−0.710137
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.679065	+	1.17617i	−0.0233605	+	0.0404616i
$846$		0			0
$847$	2.56238	+	0.658939i	0.0880445	+	0.0226414i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.76088	−	3.04993i	−0.0603621	−	0.104550i
$852$		0			0
$853$	−40.5587			−1.38870			−0.694352	−	0.719635i	$-0.744309\pi$
$853$	−40.5587			−1.38870			−0.694352	+	0.719635i	$0.744309\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21.0978	−	36.5425i	−0.720687	−	1.24827i	−0.960725	−	0.277504i	$-0.910493\pi$
$857$	−21.0978	−	36.5425i	−0.720687	−	1.24827i	0.240037	−	0.970764i	$-0.422840\pi$
$858$		0			0
$859$	−26.5715	+	46.0233i	−0.906609	+	1.57029i	−0.0878670	+	0.996132i	$0.528005\pi$
$859$	−26.5715	+	46.0233i	−0.906609	+	1.57029i	−0.818742	+	0.574161i	$0.805328\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.9932	−	27.7010i	0.544414	−	0.942952i	−0.454230	−	0.890884i	$-0.650086\pi$
$863$	15.9932	−	27.7010i	0.544414	−	0.942952i	0.998644	−	0.0520676i	$-0.0165811\pi$
$864$		0			0
$865$	−6.40972	−	11.1020i	−0.217937	−	0.377478i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.35021			−0.249339
$870$		0			0
$871$	6.23585	+	10.8008i	0.211294	+	0.365972i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.14132	−	14.8542i	−0.140002	−	0.502162i
$876$		0			0
$877$	−9.84609	+	17.0539i	−0.332479	+	0.575870i	−0.982997	−	0.183620i	$-0.941218\pi$
$877$	−9.84609	+	17.0539i	−0.332479	+	0.575870i	0.650518	+	0.759491i	$0.274552\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	42.3333			1.42624			0.713122	−	0.701040i	$-0.247281\pi$
$881$	42.3333			1.42624			0.713122	+	0.701040i	$0.247281\pi$
$882$		0			0
$883$	22.5023			0.757263			0.378632	−	0.925547i	$-0.376395\pi$
$883$	22.5023			0.757263			0.378632	+	0.925547i	$0.376395\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.9286	+	22.3930i	−0.434100	+	0.751883i	−0.997222	−	0.0744911i	$-0.976267\pi$
$887$	−12.9286	+	22.3930i	−0.434100	+	0.751883i	0.563122	+	0.826374i	$0.309600\pi$
$888$		0			0
$889$	−0.469087	−	1.68253i	−0.0157327	−	0.0564303i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.97141	+	13.8069i	0.266753	+	0.462030i
$894$		0			0
$895$	39.3502			1.31533
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13.7204	−	23.7644i	−0.457600	−	0.792587i
$900$		0			0
$901$	−0.198495	+	0.343803i	−0.00661283	+	0.0114538i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.90520	−	17.1563i	0.329260	−	0.570295i
$906$		0			0
$907$	−7.29071	−	12.6279i	−0.242084	−	0.419302i	0.719224	−	0.694779i	$-0.244498\pi$
$907$	−7.29071	−	12.6279i	−0.242084	−	0.419302i	−0.961308	+	0.275477i	$0.911164\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	8.63860			0.286210			0.143105	−	0.989708i	$-0.454291\pi$
$911$	8.63860			0.286210			0.143105	+	0.989708i	$0.454291\pi$
$912$		0			0
$913$	−5.24433	−	9.08344i	−0.173562	−	0.300618i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−50.5150	−	12.9904i	−1.66815	−	0.428980i
$918$		0			0
$919$	15.5241	−	26.8885i	0.512092	−	0.886969i	−0.487810	−	0.872950i	$-0.662204\pi$
$919$	15.5241	−	26.8885i	0.512092	−	0.886969i	0.999902	−	0.0140194i	$-0.00446267\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	15.5160			0.510715
$924$		0			0
$925$	19.0528			0.626452
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.96333	−	6.86469i	0.130033	−	0.225223i	−0.793656	−	0.608366i	$-0.791825\pi$
$929$	3.96333	−	6.86469i	0.130033	−	0.225223i	0.923689	+	0.383143i	$0.125158\pi$
$930$		0			0
$931$	−0.531469	−	26.3208i	−0.0174182	−	0.862628i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.01204	−	5.21700i	−0.0985042	−	0.170614i
$936$		0			0
$937$	−9.42571			−0.307925			−0.153962	−	0.988077i	$-0.549203\pi$
$937$	−9.42571			−0.307925			−0.153962	+	0.988077i	$0.549203\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−23.1826	−	40.1535i	−0.755732	−	1.30897i	−0.945009	−	0.327043i	$-0.893948\pi$
$941$	−23.1826	−	40.1535i	−0.755732	−	1.30897i	0.189277	−	0.981924i	$-0.439385\pi$
$942$		0			0
$943$	5.39248	−	9.34004i	0.175603	−	0.304154i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.06075	−	3.56932i	0.0669653	−	0.115987i	−0.830599	−	0.556871i	$-0.812002\pi$
$947$	2.06075	−	3.56932i	0.0669653	−	0.115987i	0.897564	+	0.440884i	$0.145335\pi$
$948$		0			0
$949$	−18.6339	−	32.2749i	−0.604883	−	1.04769i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−37.6446			−1.21943			−0.609714	−	0.792621i	$-0.708716\pi$
$953$	−37.6446			−1.21943			−0.609714	+	0.792621i	$0.708716\pi$
$954$		0			0
$955$	31.6821	+	54.8750i	1.02521	+	1.77571i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.13805	−	5.24284i	0.165916	−	0.169300i
$960$		0			0
$961$	−29.2891	+	50.7302i	−0.944809	+	1.63646i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.9130			−0.415684
$966$		0			0
$967$	−1.22545			−0.0394078			−0.0197039	−	0.999806i	$-0.506272\pi$
$967$	−1.22545			−0.0394078			−0.0197039	+	0.999806i	$0.506272\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−16.6814	+	28.8930i	−0.535331	+	0.927221i	0.463816	+	0.885932i	$0.346480\pi$
$971$	−16.6814	+	28.8930i	−0.535331	+	0.927221i	−0.999147	+	0.0412893i	$0.986853\pi$
$972$		0			0
$973$	−7.81587	−	28.0341i	−0.250565	−	0.898733i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.1460	+	31.4297i	0.580541	+	1.00553i	0.995415	+	0.0956474i	$0.0304921\pi$
$977$	18.1460	+	31.4297i	0.580541	+	1.00553i	−0.414875	+	0.909879i	$0.636175\pi$
$978$		0			0
$979$	−7.26320			−0.232133
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−0.574975	−	0.995887i	−0.0183389	−	0.0317639i	0.856710	−	0.515798i	$-0.172504\pi$
$983$	−0.574975	−	0.995887i	−0.0183389	−	0.0317639i	−0.875049	+	0.484034i	$0.839171\pi$
$984$		0			0
$985$	17.3932	−	30.1258i	0.554192	−	0.959889i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.47661	+	12.9499i	−0.237742	+	0.411782i
$990$		0			0
$991$	−12.7603	−	22.1015i	−0.405345	−	0.702078i	0.589017	−	0.808121i	$-0.299515\pi$
$991$	−12.7603	−	22.1015i	−0.405345	−	0.702078i	−0.994362	+	0.106043i	$0.966182\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−34.4775			−1.09301
$996$		0			0
$997$	4.27059	+	7.39688i	0.135251	+	0.234262i	0.925693	−	0.378275i	$-0.123483\pi$
$997$	4.27059	+	7.39688i	0.135251	+	0.234262i	−0.790442	+	0.612536i	$0.790149\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2772.2.s.f.793.1		6
3.2	odd	2		308.2.i.a.177.1	✓	6
7.4	even	3	inner	2772.2.s.f.2377.1		6
12.11	even	2		1232.2.q.l.177.3		6
21.2	odd	6		2156.2.a.i.1.3		3
21.5	even	6		2156.2.a.h.1.1		3
21.11	odd	6		308.2.i.a.221.1	yes	6
21.17	even	6		2156.2.i.l.1145.3		6
21.20	even	2		2156.2.i.l.177.3		6
84.11	even	6		1232.2.q.l.529.3		6
84.23	even	6		8624.2.a.ci.1.1		3
84.47	odd	6		8624.2.a.cn.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.i.a.177.1	✓	6	3.2	odd	2
308.2.i.a.221.1	yes	6	21.11	odd	6
1232.2.q.l.177.3		6	12.11	even	2
1232.2.q.l.529.3		6	84.11	even	6
2156.2.a.h.1.1		3	21.5	even	6
2156.2.a.i.1.3		3	21.2	odd	6
2156.2.i.l.177.3		6	21.20	even	2
2156.2.i.l.1145.3		6	21.17	even	6
2772.2.s.f.793.1		6	1.1	even	1	trivial
2772.2.s.f.2377.1		6	7.4	even	3	inner
8624.2.a.ci.1.1		3	84.23	even	6
8624.2.a.cn.1.3		3	84.47	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:	\( N \)	\(=\)	\( 2772 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2772.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71053 + 2.96273i) q^{5} +(-0.710533 - 2.54856i) q^{7} +(-0.500000 - 0.866025i) q^{11} +3.66019 q^{13} +(-0.880438 - 1.52496i) q^{17} +(-1.88044 + 3.25701i) q^{19} +(-0.619562 + 1.07311i) q^{23} +(-3.35185 - 5.80557i) q^{25} +2.89931 q^{29} +(-4.73229 - 8.19656i) q^{31} +(8.76608 + 2.25427i) q^{35} +(-1.42107 + 2.46136i) q^{37} -8.70370 q^{41} +12.0676 q^{43} +(2.11956 - 3.67119i) q^{47} +(-5.99028 + 3.62167i) q^{49} +(-0.112725 - 0.195246i) q^{53} +3.42107 q^{55} +(-3.27292 - 5.66886i) q^{59} +(5.12476 - 8.87635i) q^{61} +(-6.26088 + 10.8442i) q^{65} +(1.70370 + 2.95089i) q^{67} +4.23912 q^{71} +(-5.09097 - 8.81782i) q^{73} +(-1.85185 + 1.88962i) q^{77} +(3.67511 - 6.36547i) q^{79} +10.4887 q^{83} +6.02408 q^{85} +(3.63160 - 6.29012i) q^{89} +(-2.60069 - 9.32820i) q^{91} +(-6.43310 - 11.1425i) q^{95} +11.7472 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{5} + 4 q^{7} - 3 q^{11} + 6 q^{13} - 5 q^{17} - 11 q^{19} - 4 q^{23} - 11 q^{25} + 2 q^{29} - 19 q^{31} + 17 q^{35} + 8 q^{37} - 34 q^{41} + 20 q^{43} + 13 q^{47} - 12 q^{49} + 9 q^{53} + 4 q^{55}+ \cdots + 50 q^{97}+O(q^{100}) \) 6 * q - 2 * q^5 + 4 * q^7 - 3 * q^11 + 6 * q^13 - 5 * q^17 - 11 * q^19 - 4 * q^23 - 11 * q^25 + 2 * q^29 - 19 * q^31 + 17 * q^35 + 8 * q^37 - 34 * q^41 + 20 * q^43 + 13 * q^47 - 12 * q^49 + 9 * q^53 + 4 * q^55 + 6 * q^59 - 4 * q^61 - 37 * q^65 - 8 * q^67 + 26 * q^71 - 22 * q^73 - 2 * q^77 - 5 * q^79 - 6 * q^83 - 14 * q^85 - 3 * q^89 - 31 * q^91 + 3 * q^95 + 50 * q^97

Introduction

L-functions

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