LMFDB - Embedded newform 2016.2.s.v.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2016,2,Mod(289,2016)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2016, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2016.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2016 = 2^{5} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2016.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$16.0978410475$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1156923.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 27x^2 - 18*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 672)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$0.500000 + 0.0585812i$ of defining polynomial
Character	$\chi$	$=$	2016.289
Dual form			2016.2.s.v.865.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37328 - 2.37860i) q^{5} +(2.64510 - 0.0585812i) q^{7} +O(q^{10})$	$q+(1.37328 - 2.37860i) q^{5} +(2.64510 - 0.0585812i) q^{7} +(-0.771819 - 1.33683i) q^{11} +6.03677 q^{13} +(3.74657 + 6.48925i) q^{17} +(-3.01839 + 5.22800i) q^{19} +(3.74657 - 6.48925i) q^{23} +(-1.27182 - 2.20285i) q^{25} -1.25343 q^{29} +(2.64510 + 4.58145i) q^{31} +(3.49314 - 6.37208i) q^{35} +(-2.47475 + 4.28639i) q^{37} +5.08727 q^{41} -3.45636 q^{43} +(-4.74657 + 8.22130i) q^{47} +(6.99314 - 0.309906i) q^{49} +(-1.91692 - 3.32021i) q^{53} -4.23970 q^{55} +(-2.77182 - 4.80093i) q^{59} +(7.29021 - 12.6270i) q^{61} +(8.29021 - 14.3591i) q^{65} +(-2.01839 - 3.49595i) q^{67} -5.49314 q^{71} +(-6.27182 - 10.8631i) q^{73} +(-2.11985 - 3.49084i) q^{77} +(-3.89853 + 6.75246i) q^{79} -6.52991 q^{83} +20.5804 q^{85} +(-4.74657 + 8.22130i) q^{89} +(15.9679 - 0.353641i) q^{91} +(8.29021 + 14.3591i) q^{95} +1.54364 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7}+O(q^{10}) $ 6 * q + 3 * q^7	$ 6 q + 3 q^{7} - 6 q^{13} + 6 q^{17} + 3 q^{19} + 6 q^{23} - 3 q^{25} - 24 q^{29} + 3 q^{31} - 12 q^{35} - 3 q^{37} + 12 q^{41} - 30 q^{43} - 12 q^{47} + 9 q^{49} + 6 q^{53} + 24 q^{55} - 12 q^{59} + 18 q^{61} + 24 q^{65} + 9 q^{67} - 33 q^{73} + 12 q^{77} - 27 q^{79} + 36 q^{83} + 72 q^{85} - 12 q^{89} + 51 q^{91} + 24 q^{95}+O(q^{100}) $ 6 * q + 3 * q^7 - 6 * q^13 + 6 * q^17 + 3 * q^19 + 6 * q^23 - 3 * q^25 - 24 * q^29 + 3 * q^31 - 12 * q^35 - 3 * q^37 + 12 * q^41 - 30 * q^43 - 12 * q^47 + 9 * q^49 + 6 * q^53 + 24 * q^55 - 12 * q^59 + 18 * q^61 + 24 * q^65 + 9 * q^67 - 33 * q^73 + 12 * q^77 - 27 * q^79 + 36 * q^83 + 72 * q^85 - 12 * q^89 + 51 * q^91 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$1765$	$1793$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.37328	−	2.37860i	0.614151	−	1.06374i	−0.376381	−	0.926465i	$-0.622832\pi$
$5$	1.37328	−	2.37860i	0.614151	−	1.06374i	0.990533	−	0.137277i	$-0.0438349\pi$
$6$		0			0
$7$	2.64510	−	0.0585812i	0.999755	−	0.0221416i
$7$	2.64510	−	0.0585812i	0.999755	−	0.0221416i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.771819	−	1.33683i	−0.232712	−	0.403069i	0.725893	−	0.687807i	$-0.241427\pi$
$11$	−0.771819	−	1.33683i	−0.232712	−	0.403069i	−0.958605	+	0.284738i	$0.908093\pi$
$12$		0			0
$13$	6.03677			1.67430			0.837150	−	0.546974i	$-0.184220\pi$
$13$	6.03677			1.67430			0.837150	+	0.546974i	$0.184220\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.74657	+	6.48925i	0.908676	+	1.57387i	0.815905	+	0.578186i	$0.196239\pi$
$17$	3.74657	+	6.48925i	0.908676	+	1.57387i	0.0927713	+	0.995687i	$0.470427\pi$
$18$		0			0
$19$	−3.01839	+	5.22800i	−0.692465	+	1.19939i	0.278562	+	0.960418i	$0.410142\pi$
$19$	−3.01839	+	5.22800i	−0.692465	+	1.19939i	−0.971028	+	0.238967i	$0.923191\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.74657	−	6.48925i	0.781213	−	1.35310i	−0.150022	−	0.988683i	$-0.547934\pi$
$23$	3.74657	−	6.48925i	0.781213	−	1.35310i	0.931235	−	0.364419i	$-0.118732\pi$
$24$		0			0
$25$	−1.27182	−	2.20285i	−0.254364	−	0.440571i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.25343			−0.232756			−0.116378	−	0.993205i	$-0.537128\pi$
$29$	−1.25343			−0.232756			−0.116378	+	0.993205i	$0.537128\pi$
$30$		0			0
$31$	2.64510	+	4.58145i	0.475074	+	0.822853i	0.999592	−	0.0285462i	$-0.00908778\pi$
$31$	2.64510	+	4.58145i	0.475074	+	0.822853i	−0.524518	+	0.851399i	$0.675754\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.49314	−	6.37208i	0.590448	−	1.07708i
$36$		0			0
$37$	−2.47475	+	4.28639i	−0.406846	+	0.704679i	−0.994534	−	0.104409i	$-0.966705\pi$
$37$	−2.47475	+	4.28639i	−0.406846	+	0.704679i	0.587688	+	0.809088i	$0.300038\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.08727			0.794499			0.397249	−	0.917711i	$-0.369965\pi$
$41$	5.08727			0.794499			0.397249	+	0.917711i	$0.369965\pi$
$42$		0			0
$43$	−3.45636			−0.527090			−0.263545	−	0.964647i	$-0.584892\pi$
$43$	−3.45636			−0.527090			−0.263545	+	0.964647i	$0.584892\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.74657	+	8.22130i	−0.692358	+	1.19920i	0.278705	+	0.960377i	$0.410095\pi$
$47$	−4.74657	+	8.22130i	−0.692358	+	1.19920i	−0.971063	+	0.238823i	$0.923239\pi$
$48$		0			0
$49$	6.99314	−	0.309906i	0.999019	−	0.0442723i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.91692	−	3.32021i	−0.263309	−	0.456065i	0.703810	−	0.710388i	$-0.251481\pi$
$53$	−1.91692	−	3.32021i	−0.263309	−	0.456065i	−0.967119	+	0.254323i	$0.918147\pi$
$54$		0			0
$55$	−4.23970			−0.571682
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.77182	−	4.80093i	−0.360860	−	0.625028i	0.627243	−	0.778824i	$-0.284183\pi$
$59$	−2.77182	−	4.80093i	−0.360860	−	0.625028i	−0.988103	+	0.153796i	$0.950850\pi$
$60$		0			0
$61$	7.29021	−	12.6270i	0.933415	−	1.61672i	0.155979	−	0.987760i	$-0.450147\pi$
$61$	7.29021	−	12.6270i	0.933415	−	1.61672i	0.777436	−	0.628962i	$-0.216520\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.29021	−	14.3591i	1.02827	−	1.78102i
$66$		0			0
$67$	−2.01839	−	3.49595i	−0.246585	−	0.427098i	0.715991	−	0.698110i	$-0.245975\pi$
$67$	−2.01839	−	3.49595i	−0.246585	−	0.427098i	−0.962576	+	0.271012i	$0.912642\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.49314			−0.651915			−0.325958	−	0.945384i	$-0.605687\pi$
$71$	−5.49314			−0.651915			−0.325958	+	0.945384i	$0.605687\pi$
$72$		0			0
$73$	−6.27182	−	10.8631i	−0.734061	−	1.27143i	−0.955134	−	0.296173i	$-0.904289\pi$
$73$	−6.27182	−	10.8631i	−0.734061	−	1.27143i	0.221073	−	0.975257i	$-0.429044\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.11985	−	3.49084i	−0.241580	−	0.397818i
$78$		0			0
$79$	−3.89853	+	6.75246i	−0.438619	+	0.759711i	−0.997583	−	0.0694809i	$-0.977866\pi$
$79$	−3.89853	+	6.75246i	−0.438619	+	0.759711i	0.558964	+	0.829192i	$0.311199\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.52991			−0.716751			−0.358375	−	0.933578i	$-0.616669\pi$
$83$	−6.52991			−0.716751			−0.358375	+	0.933578i	$0.616669\pi$
$84$		0			0
$85$	20.5804			2.23226
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.74657	+	8.22130i	−0.503135	+	0.871456i	0.496858	+	0.867832i	$0.334487\pi$
$89$	−4.74657	+	8.22130i	−0.503135	+	0.871456i	−0.999993	+	0.00362404i	$0.998846\pi$
$90$		0			0
$91$	15.9679	−	0.353641i	1.67389	−	0.0370717i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.29021	+	14.3591i	0.850557	+	1.47321i
$96$		0			0
$97$	1.54364			0.156733			0.0783663	−	0.996925i	$-0.475030\pi$
$97$	1.54364			0.156733			0.0783663	+	0.996925i	$0.475030\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.29021	−	2.23470i	−0.128380	−	0.222361i	0.794669	−	0.607043i	$-0.207644\pi$
$101$	−1.29021	−	2.23470i	−0.128380	−	0.222361i	−0.923049	+	0.384682i	$0.874311\pi$
$102$		0			0
$103$	3.27182	−	5.66696i	0.322382	−	0.558382i	−0.658597	−	0.752496i	$-0.728850\pi$
$103$	3.27182	−	5.66696i	0.322382	−	0.558382i	0.980979	+	0.194114i	$0.0621832\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.26496	−	3.92302i	0.218961	−	0.379252i	−0.735529	−	0.677493i	$-0.763066\pi$
$107$	2.26496	−	3.92302i	0.218961	−	0.379252i	0.954491	+	0.298241i	$0.0963998\pi$
$108$		0			0
$109$	3.22132	+	5.57949i	0.308546	+	0.534418i	0.978045	−	0.208396i	$-0.0668242\pi$
$109$	3.22132	+	5.57949i	0.308546	+	0.534418i	−0.669498	+	0.742814i	$0.733491\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−8.00000			−0.752577			−0.376288	−	0.926503i	$-0.622800\pi$
$113$	−8.00000			−0.752577			−0.376288	+	0.926503i	$0.622800\pi$
$114$		0			0
$115$	−10.2902	−	17.8232i	−0.959567	−	1.66202i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.2902	+	16.9452i	0.943302	+	1.55337i
$120$		0			0
$121$	4.30859	−	7.46270i	0.391690	−	0.678427i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.74657			0.603431
$126$		0			0
$127$	−3.79707			−0.336935			−0.168468	−	0.985707i	$-0.553882\pi$
$127$	−3.79707			−0.336935			−0.168468	+	0.985707i	$0.553882\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.771819	+	1.33683i	−0.0674341	+	0.116799i	−0.897771	−	0.440462i	$-0.854815\pi$
$131$	−0.771819	+	1.33683i	−0.0674341	+	0.116799i	0.830337	+	0.557262i	$0.188148\pi$
$132$		0			0
$133$	−7.67768	+	14.0054i	−0.665739	+	1.21442i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.746568	+	1.29309i	0.0637836	+	0.110476i	0.896154	−	0.443744i	$-0.146350\pi$
$137$	0.746568	+	1.29309i	0.0637836	+	0.110476i	−0.832370	+	0.554220i	$0.813017\pi$
$138$		0			0
$139$	2.94950			0.250173			0.125087	−	0.992146i	$-0.460079\pi$
$139$	2.94950			0.250173			0.125087	+	0.992146i	$0.460079\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.65929	−	8.07013i	−0.389630	−	0.674858i
$144$		0			0
$145$	−1.72132	+	2.98141i	−0.142948	+	0.247593i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.746568	+	1.29309i	−0.0611613	+	0.105934i	−0.894985	−	0.446097i	$-0.852814\pi$
$149$	−0.746568	+	1.29309i	−0.0611613	+	0.105934i	0.833823	+	0.552031i	$0.186147\pi$
$150$		0			0
$151$	4.86642	+	8.42889i	0.396024	+	0.685933i	0.993231	−	0.116154i	$-0.0370565\pi$
$151$	4.86642	+	8.42889i	0.396024	+	0.685933i	−0.597208	+	0.802087i	$0.703723\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	14.5299			1.16707
$156$		0			0
$157$	−4.54364	−	7.86981i	−0.362622	−	0.628079i	0.625770	−	0.780008i	$-0.284785\pi$
$157$	−4.54364	−	7.86981i	−0.362622	−	0.628079i	−0.988391	+	0.151929i	$0.951452\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9.52991	−	17.3842i	0.751062	−	1.37007i
$162$		0			0
$163$	9.78334	−	16.9452i	0.766290	−	1.32725i	−0.173271	−	0.984874i	$-0.555434\pi$
$163$	9.78334	−	16.9452i	0.766290	−	1.32725i	0.939562	−	0.342380i	$-0.111233\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.8990			−0.920772			−0.460386	−	0.887719i	$-0.652289\pi$
$167$	−11.8990			−0.920772			−0.460386	+	0.887719i	$0.652289\pi$
$168$		0			0
$169$	23.4426			1.80328
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.29021	−	2.23470i	0.0980925	−	0.169901i	−0.812803	−	0.582539i	$-0.802059\pi$
$173$	1.29021	−	2.23470i	0.0980925	−	0.169901i	0.910895	+	0.412638i	$0.135393\pi$
$174$		0			0
$175$	−3.49314	−	5.75227i	−0.264056	−	0.434831i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.49314	+	2.58619i	0.111602	+	0.193301i	0.916416	−	0.400226i	$-0.131068\pi$
$179$	1.49314	+	2.58619i	0.111602	+	0.193301i	−0.804814	+	0.593527i	$0.797735\pi$
$180$		0			0
$181$	−10.5436			−0.783702			−0.391851	−	0.920029i	$-0.628165\pi$
$181$	−10.5436			−0.783702			−0.391851	+	0.920029i	$0.628165\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.79707	+	11.7729i	0.499730	+	0.865559i
$186$		0			0
$187$	5.78334	−	10.0170i	0.422920	−	0.732519i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.58041	+	14.8617i	−0.620857	+	1.07536i	0.368470	+	0.929640i	$0.379882\pi$
$191$	−8.58041	+	14.8617i	−0.620857	+	1.07536i	−0.989327	+	0.145716i	$0.953452\pi$
$192$		0			0
$193$	−5.44950	−	9.43881i	−0.392264	−	0.679420i	0.600484	−	0.799637i	$-0.294975\pi$
$193$	−5.44950	−	9.43881i	−0.392264	−	0.679420i	−0.992748	+	0.120216i	$0.961641\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.41959			−0.386130			−0.193065	−	0.981186i	$-0.561843\pi$
$197$	−5.41959			−0.386130			−0.193065	+	0.981186i	$0.561843\pi$
$198$		0			0
$199$	−11.4931	−	19.9067i	−0.814727	−	1.41115i	−0.909524	−	0.415652i	$-0.863554\pi$
$199$	−11.4931	−	19.9067i	−0.814727	−	1.41115i	0.0947970	−	0.995497i	$-0.469780\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.31546	+	0.0734275i	−0.232699	+	0.00515360i
$204$		0			0
$205$	6.98627	−	12.1006i	0.487942	−	0.845141i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.31859			0.644580
$210$		0			0
$211$	−3.08727			−0.212537			−0.106268	−	0.994337i	$-0.533890\pi$
$211$	−3.08727			−0.212537			−0.106268	+	0.994337i	$0.533890\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.74657	+	8.22130i	−0.323713	+	0.560688i
$216$		0			0
$217$	7.26496	+	11.9635i	0.493177	+	0.812132i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	22.6172	+	39.1741i	1.52140	+	2.63514i
$222$		0			0
$223$	22.7466			1.52322			0.761611	−	0.648034i	$-0.224409\pi$
$223$	22.7466			1.52322			0.761611	+	0.648034i	$0.224409\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.3017	−	19.5752i	−0.750122	−	1.29925i	−0.947763	−	0.318975i	$-0.896661\pi$
$227$	−11.3017	−	19.5752i	−0.750122	−	1.29925i	0.197641	−	0.980274i	$-0.436672\pi$
$228$		0			0
$229$	5.67768	−	9.83403i	0.375192	−	0.649851i	−0.615164	−	0.788399i	$-0.710910\pi$
$229$	5.67768	−	9.83403i	0.375192	−	0.649851i	0.990356	+	0.138548i	$0.0442435\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.70979	−	2.96145i	0.112012	−	0.194011i	−0.804569	−	0.593859i	$-0.797604\pi$
$233$	1.70979	−	2.96145i	0.112012	−	0.194011i	0.916582	+	0.399848i	$0.130937\pi$
$234$		0			0
$235$	13.0368	+	22.5804i	0.850425	+	1.47298i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.49314			−0.484691			−0.242345	−	0.970190i	$-0.577917\pi$
$239$	−7.49314			−0.484691			−0.242345	+	0.970190i	$0.577917\pi$
$240$		0			0
$241$	9.30173	+	16.1111i	0.599177	+	1.03781i	0.992943	+	0.118594i	$0.0378388\pi$
$241$	9.30173	+	16.1111i	0.599177	+	1.03781i	−0.393766	+	0.919211i	$0.628828\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.86642	−	17.0594i	0.566455	−	1.08989i
$246$		0			0
$247$	−18.2213	+	31.5602i	−1.15939	+	2.00813i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	24.5299			1.54831			0.774157	−	0.632994i	$-0.218174\pi$
$251$	24.5299			1.54831			0.774157	+	0.632994i	$0.218174\pi$
$252$		0			0
$253$	−11.5667			−0.727191
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.74657	+	15.1495i	−0.545596	+	0.945000i	0.452973	+	0.891524i	$0.350363\pi$
$257$	−8.74657	+	15.1495i	−0.545596	+	0.945000i	−0.998569	+	0.0534758i	$0.982970\pi$
$258$		0			0
$259$	−6.29487	+	11.4829i	−0.391144	+	0.713514i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.74657	+	11.6854i	0.416011	+	0.720553i	0.995534	−	0.0944035i	$-0.0300944\pi$
$263$	6.74657	+	11.6854i	0.416011	+	0.720553i	−0.579523	+	0.814956i	$0.696761\pi$
$264$		0			0
$265$	−10.5299			−0.646847
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.17035	+	5.49121i	0.193300	+	0.334805i	0.946342	−	0.323167i	$-0.104748\pi$
$269$	3.17035	+	5.49121i	0.193300	+	0.334805i	−0.753042	+	0.657972i	$0.771414\pi$
$270$		0			0
$271$	−10.1199	+	17.5281i	−0.614737	+	1.06476i	0.375693	+	0.926744i	$0.377405\pi$
$271$	−10.1199	+	17.5281i	−0.614737	+	1.06476i	−0.990431	+	0.138012i	$0.955929\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.96323	+	3.40041i	−0.118387	+	0.205052i
$276$		0			0
$277$	1.27182	+	2.20285i	0.0764162	+	0.132357i	0.901701	−	0.432360i	$-0.142319\pi$
$277$	1.27182	+	2.20285i	0.0764162	+	0.132357i	−0.825285	+	0.564716i	$0.808986\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−26.5804			−1.58565			−0.792827	−	0.609447i	$-0.791392\pi$
$281$	−26.5804			−1.58565			−0.792827	+	0.609447i	$0.791392\pi$
$282$		0			0
$283$	−10.2718	−	17.7913i	−0.610596	−	1.05758i	−0.991140	−	0.132821i	$-0.957597\pi$
$283$	−10.2718	−	17.7913i	−0.610596	−	1.05758i	0.380544	−	0.924763i	$-0.375737\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	13.4564	−	0.298018i	0.794304	−	0.0175915i
$288$		0			0
$289$	−19.5735	+	33.9024i	−1.15139	+	1.99426i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.25343			−0.306909			−0.153454	−	0.988156i	$-0.549040\pi$
$293$	−5.25343			−0.306909			−0.153454	+	0.988156i	$0.549040\pi$
$294$		0			0
$295$	−15.2260			−0.886491
$296$		0			0
$297$		0			0
$298$		0			0
$299$	22.6172	−	39.1741i	1.30799	−	2.26550i
$300$		0			0
$301$	−9.14243	+	0.202478i	−0.526961	+	0.0116706i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−20.0230	−	34.6809i	−1.14652	−	1.98582i
$306$		0			0
$307$	−14.8485			−0.847449			−0.423724	−	0.905791i	$-0.639277\pi$
$307$	−14.8485			−0.847449			−0.423724	+	0.905791i	$0.639277\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.949499	+	1.64458i	0.0538412	+	0.0932556i	0.891690	−	0.452647i	$-0.149520\pi$
$311$	0.949499	+	1.64458i	0.0538412	+	0.0932556i	−0.837849	+	0.545903i	$0.816187\pi$
$312$		0			0
$313$	0.0436371	−	0.0755817i	0.00246652	−	0.00427213i	−0.864790	−	0.502135i	$-0.832548\pi$
$313$	0.0436371	−	0.0755817i	0.00246652	−	0.00427213i	0.867256	+	0.497862i	$0.165882\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.11985	−	7.13579i	0.231394	−	0.400786i	−0.726825	−	0.686823i	$-0.759005\pi$
$317$	4.11985	−	7.13579i	0.231394	−	0.400786i	0.958219	+	0.286037i	$0.0923380\pi$
$318$		0			0
$319$	0.967422	+	1.67562i	0.0541652	+	0.0938169i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−45.2344			−2.51691
$324$		0			0
$325$	−7.67768	−	13.2981i	−0.425881	−	0.737648i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−12.0735	+	22.0242i	−0.665636	+	1.21424i
$330$		0			0
$331$	−2.76496	+	4.78904i	−0.151976	+	0.263230i	−0.931954	−	0.362577i	$-0.881897\pi$
$331$	−2.76496	+	4.78904i	−0.151976	+	0.263230i	0.779978	+	0.625807i	$0.215230\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.0873			−0.605763
$336$		0			0
$337$	7.17455			0.390823			0.195411	−	0.980721i	$-0.437396\pi$
$337$	7.17455			0.390823			0.195411	+	0.980721i	$0.437396\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.08308	−	7.07210i	0.221111	−	0.382976i
$342$		0			0
$343$	18.4794	−	1.22940i	0.997794	−	0.0663814i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.0368	−	20.8483i	−0.646168	−	1.11920i	−0.984030	−	0.178000i	$-0.943037\pi$
$347$	−12.0368	−	20.8483i	−0.646168	−	1.11920i	0.337863	−	0.941195i	$-0.390296\pi$
$348$		0			0
$349$	−31.1608			−1.66800			−0.834000	−	0.551764i	$-0.813955\pi$
$349$	−31.1608			−1.66800			−0.834000	+	0.551764i	$0.813955\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.08727	−	8.81142i	−0.270768	−	0.468984i	0.698290	−	0.715814i	$-0.253944\pi$
$353$	−5.08727	−	8.81142i	−0.270768	−	0.468984i	−0.969059	+	0.246830i	$0.920611\pi$
$354$		0			0
$355$	−7.54364	+	13.0660i	−0.400375	+	0.693469i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	16.1240	−	27.9277i	0.850995	−	1.47397i	−0.0293169	−	0.999570i	$-0.509333\pi$
$359$	16.1240	−	27.9277i	0.850995	−	1.47397i	0.880312	−	0.474396i	$-0.157333\pi$
$360$		0			0
$361$	−8.72132	−	15.1058i	−0.459017	−	0.795040i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−34.4520			−1.80330
$366$		0			0
$367$	1.93531	+	3.35205i	0.101022	+	0.174976i	0.912106	−	0.409954i	$-0.134455\pi$
$367$	1.93531	+	3.35205i	0.101022	+	0.174976i	−0.811084	+	0.584930i	$0.801122\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−5.26496	−	8.66999i	−0.273343	−	0.450123i
$372$		0			0
$373$	−17.3454	+	30.0431i	−0.898109	+	1.55557i	−0.0682000	+	0.997672i	$0.521726\pi$
$373$	−17.3454	+	30.0431i	−0.898109	+	1.55557i	−0.829909	+	0.557899i	$0.811608\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.56668			−0.389704
$378$		0			0
$379$	−13.4564			−0.691207			−0.345603	−	0.938381i	$-0.612326\pi$
$379$	−13.4564			−0.691207			−0.345603	+	0.938381i	$0.612326\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.08727	+	3.61527i	−0.106655	+	0.184731i	−0.914413	−	0.404782i	$-0.867347\pi$
$383$	−2.08727	+	3.61527i	−0.106655	+	0.184731i	0.807758	+	0.589514i	$0.200681\pi$
$384$		0			0
$385$	−11.2145	+	0.248367i	−0.571542	+	0.0126579i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.32698	−	16.1548i	−0.472897	−	0.819081i	0.526622	−	0.850099i	$-0.323458\pi$
$389$	−9.32698	−	16.1548i	−0.472897	−	0.819081i	−0.999519	+	0.0310185i	$0.990125\pi$
$390$		0			0
$391$	56.1471			2.83948
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.7076	+	18.5461i	0.538757	+	0.933155i
$396$		0			0
$397$	0.728181	−	1.26125i	0.0365464	−	0.0633002i	−0.847174	−	0.531316i	$-0.821698\pi$
$397$	0.728181	−	1.26125i	0.0365464	−	0.0633002i	0.883720	+	0.468016i	$0.155031\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.6172	+	25.3177i	−0.729947	+	1.26431i	0.226958	+	0.973905i	$0.427122\pi$
$401$	−14.6172	+	25.3177i	−0.729947	+	1.26431i	−0.956905	+	0.290401i	$0.906211\pi$
$402$		0			0
$403$	15.9679	+	27.6572i	0.795417	+	1.37770i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.64023			0.378712
$408$		0			0
$409$	−13.0299	−	22.5685i	−0.644288	−	1.11594i	−0.984466	−	0.175578i	$-0.943821\pi$
$409$	−13.0299	−	22.5685i	−0.644288	−	1.11594i	0.340178	−	0.940361i	$-0.389513\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−7.61299	−	12.5366i	−0.374611	−	0.616885i
$414$		0			0
$415$	−8.96742	+	15.5320i	−0.440193	+	0.762437i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	32.8853			1.60655			0.803275	−	0.595608i	$-0.203089\pi$
$419$	32.8853			1.60655			0.803275	+	0.595608i	$0.203089\pi$
$420$		0			0
$421$	−17.1976			−0.838160			−0.419080	−	0.907949i	$-0.637647\pi$
$421$	−17.1976			−0.838160			−0.419080	+	0.907949i	$0.637647\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.52991	−	16.5063i	0.462269	−	0.800673i
$426$		0			0
$427$	18.5436	−	33.8268i	0.897389	−	1.63699i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.49314	−	2.58619i	−0.0719219	−	0.124572i	0.827822	−	0.560991i	$-0.189580\pi$
$431$	−1.49314	−	2.58619i	−0.0719219	−	0.124572i	−0.899744	+	0.436419i	$0.856247\pi$
$432$		0			0
$433$	18.4426			0.886297			0.443148	−	0.896448i	$-0.353862\pi$
$433$	18.4426			0.886297			0.443148	+	0.896448i	$0.353862\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	22.6172	+	39.1741i	1.08193	+	1.87395i
$438$		0			0
$439$	0.286010	−	0.495384i	0.0136505	−	0.0236434i	−0.859119	−	0.511775i	$-0.828988\pi$
$439$	0.286010	−	0.495384i	0.0136505	−	0.0236434i	0.872770	+	0.488132i	$0.162321\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.2650	+	31.6358i	−0.867794	+	1.50306i	−0.00354850	+	0.999994i	$0.501130\pi$
$443$	−18.2650	+	31.6358i	−0.867794	+	1.50306i	−0.864246	+	0.503070i	$0.832204\pi$
$444$		0			0
$445$	13.0368	+	22.5804i	0.618002	+	1.07041i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	22.5530			1.06434			0.532170	−	0.846638i	$-0.321377\pi$
$449$	22.5530			1.06434			0.532170	+	0.846638i	$0.321377\pi$
$450$		0			0
$451$	−3.92645	−	6.80082i	−0.184889	−	0.320238i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	21.0873	−	38.4668i	0.988587	−	1.80335i
$456$		0			0
$457$	−10.1172	+	17.5235i	−0.473262	+	0.819714i	−0.999532	−	0.0306040i	$-0.990257\pi$
$457$	−10.1172	+	17.5235i	−0.473262	+	0.819714i	0.526270	+	0.850318i	$0.323590\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−25.4931			−1.18733			−0.593667	−	0.804711i	$-0.702320\pi$
$461$	−25.4931			−1.18733			−0.593667	+	0.804711i	$0.702320\pi$
$462$		0			0
$463$	7.70446			0.358057			0.179028	−	0.983844i	$-0.442705\pi$
$463$	7.70446			0.358057			0.179028	+	0.983844i	$0.442705\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.0735	+	31.3043i	−0.836344	+	1.44859i	0.0565874	+	0.998398i	$0.481978\pi$
$467$	−18.0735	+	31.3043i	−0.836344	+	1.44859i	−0.892931	+	0.450193i	$0.851355\pi$
$468$		0			0
$469$	−5.54364	−	9.12890i	−0.255981	−	0.421534i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.66769	+	4.62057i	0.122660	+	0.212454i
$474$		0			0
$475$	15.3554			0.704552
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.2902	−	23.0193i	−0.607245	−	1.05178i	−0.991692	−	0.128632i	$-0.958941\pi$
$479$	−13.2902	−	23.0193i	−0.607245	−	1.05178i	0.384447	−	0.923147i	$-0.374392\pi$
$480$		0			0
$481$	−14.9395	+	25.8760i	−0.681183	+	1.17984i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.11985	−	3.67169i	0.0962575	−	0.166723i
$486$		0			0
$487$	−20.2118	−	35.0078i	−0.915883	−	1.58636i	−0.805603	−	0.592456i	$-0.798158\pi$
$487$	−20.2118	−	35.0078i	−0.915883	−	1.58636i	−0.110281	−	0.993900i	$-0.535175\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	14.6309			0.660284			0.330142	−	0.943931i	$-0.392903\pi$
$491$	14.6309			0.660284			0.330142	+	0.943931i	$0.392903\pi$
$492$		0			0
$493$	−4.69607	−	8.13383i	−0.211500	−	0.366329i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.5299	+	0.321794i	−0.651756	+	0.0144344i
$498$		0			0
$499$	−18.0552	+	31.2725i	−0.808260	+	1.39995i	0.105808	+	0.994387i	$0.466257\pi$
$499$	−18.0552	+	31.2725i	−0.808260	+	1.39995i	−0.914068	+	0.405561i	$0.867076\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	19.4931			0.869156			0.434578	−	0.900634i	$-0.356898\pi$
$503$	19.4931			0.869156			0.434578	+	0.900634i	$0.356898\pi$
$504$		0			0
$505$	−7.08727			−0.315380
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−11.9537	+	20.7044i	−0.529838	+	0.917707i	0.469556	+	0.882903i	$0.344414\pi$
$509$	−11.9537	+	20.7044i	−0.529838	+	0.917707i	−0.999394	+	0.0348040i	$0.988919\pi$
$510$		0			0
$511$	−17.2260	−	28.3666i	−0.762032	−	1.25487i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.98627	−	15.5647i	−0.395982	−	0.685862i
$516$		0			0
$517$	14.6540			0.644480
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−3.54364	−	6.13776i	−0.155250	−	0.268900i	0.777900	−	0.628388i	$-0.216285\pi$
$521$	−3.54364	−	6.13776i	−0.155250	−	0.268900i	−0.933150	+	0.359488i	$0.882952\pi$
$522$		0			0
$523$	−14.3737	+	24.8961i	−0.628520	+	1.08863i	0.359329	+	0.933211i	$0.383006\pi$
$523$	−14.3737	+	24.8961i	−0.628520	+	1.08863i	−0.987849	+	0.155418i	$0.950328\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−19.8201	+	34.3294i	−0.863378	+	1.49541i
$528$		0			0
$529$	−16.5735	−	28.7062i	−0.720589	−	1.24810i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	30.7107			1.33023
$534$		0			0
$535$	−6.22085	−	10.7748i	−0.268951	−	0.465837i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.81172	−	9.10944i	−0.250329	−	0.392371i
$540$		0			0
$541$	3.51152	−	6.08214i	0.150972	−	0.261491i	−0.780613	−	0.625015i	$-0.785093\pi$
$541$	3.51152	−	6.08214i	0.150972	−	0.261491i	0.931585	+	0.363523i	$0.118426\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	17.6951			0.757976
$546$		0			0
$547$	−5.59414			−0.239188			−0.119594	−	0.992823i	$-0.538159\pi$
$547$	−5.59414			−0.239188			−0.119594	+	0.992823i	$0.538159\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.78334	−	6.55294i	0.161176	−	0.279165i
$552$		0			0
$553$	−9.91646	+	18.0893i	−0.421691	+	0.769237i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.3228	+	24.8078i	0.606876	+	1.05114i	0.991752	+	0.128172i	$0.0409108\pi$
$557$	14.3228	+	24.8078i	0.606876	+	1.05114i	−0.384876	+	0.922968i	$0.625756\pi$
$558$		0			0
$559$	−20.8653			−0.882507
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.94637	+	17.2276i	0.419189	+	0.726057i	0.995858	−	0.0909207i	$-0.0289810\pi$
$563$	9.94637	+	17.2276i	0.419189	+	0.726057i	−0.576669	+	0.816978i	$0.695648\pi$
$564$		0			0
$565$	−10.9863	+	19.0288i	−0.462196	+	0.800547i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.8201	−	30.8653i	0.747058	−	1.29394i	−0.202169	−	0.979351i	$-0.564799\pi$
$569$	17.8201	−	30.8653i	0.747058	−	1.29394i	0.949227	−	0.314592i	$-0.101868\pi$
$570$		0			0
$571$	−13.8385	−	23.9690i	−0.579123	−	1.00307i	−0.995580	−	0.0939155i	$-0.970062\pi$
$571$	−13.8385	−	23.9690i	−0.579123	−	1.00307i	0.416457	−	0.909155i	$-0.363272\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−19.0598			−0.794849
$576$		0			0
$577$	3.00686	+	5.20804i	0.125177	+	0.216814i	0.921802	−	0.387660i	$-0.126717\pi$
$577$	3.00686	+	5.20804i	0.125177	+	0.216814i	−0.796625	+	0.604474i	$0.793383\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−17.2723	+	0.382530i	−0.716575	+	0.0158700i
$582$		0			0
$583$	−2.95903	+	5.12519i	−0.122551	+	0.212264i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.5436			0.641555			0.320777	−	0.947155i	$-0.396056\pi$
$587$	15.5436			0.641555			0.320777	+	0.947155i	$0.396056\pi$
$588$		0			0
$589$	−31.9358			−1.31589
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−24.3270	+	42.1356i	−0.998989	+	1.73030i	−0.460568	+	0.887624i	$0.652354\pi$
$593$	−24.3270	+	42.1356i	−0.998989	+	1.73030i	−0.538421	+	0.842676i	$0.680979\pi$
$594$		0			0
$595$	54.4373	−	1.20562i	2.23171	−	0.0494258i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.4564	+	18.1110i	0.427235	+	0.739993i	0.996626	−	0.0820735i	$-0.0261542\pi$
$599$	10.4564	+	18.1110i	0.427235	+	0.739993i	−0.569391	+	0.822067i	$0.692821\pi$
$600$		0			0
$601$	−7.98627			−0.325767			−0.162883	−	0.986645i	$-0.552079\pi$
$601$	−7.98627			−0.325767			−0.162883	+	0.986645i	$0.552079\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−11.8338	−	20.4968i	−0.481114	−	0.833314i
$606$		0			0
$607$	1.35490	−	2.34675i	0.0549936	−	0.0952517i	−0.837218	−	0.546869i	$-0.815819\pi$
$607$	1.35490	−	2.34675i	0.0549936	−	0.0952517i	0.892212	+	0.451618i	$0.149153\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−28.6540	+	49.6301i	−1.15922	+	2.00782i
$612$		0			0
$613$	8.25343	+	14.2954i	0.333353	+	0.577384i	0.983167	−	0.182709i	$-0.0584866\pi$
$613$	8.25343	+	14.2954i	0.333353	+	0.577384i	−0.649814	+	0.760093i	$0.725153\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	23.1608			0.932420			0.466210	−	0.884674i	$-0.345619\pi$
$617$	23.1608			0.932420			0.466210	+	0.884674i	$0.345619\pi$
$618$		0			0
$619$	−14.7145	−	25.4862i	−0.591424	−	1.02438i	−0.994041	−	0.109008i	$-0.965233\pi$
$619$	−14.7145	−	25.4862i	−0.591424	−	1.02438i	0.402617	−	0.915369i	$-0.368101\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−12.0735	+	22.0242i	−0.483716	+	0.882382i
$624$		0			0
$625$	15.6240	−	27.0616i	0.624962	−	1.08247i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−37.0873			−1.47877
$630$		0			0
$631$	35.7054			1.42141			0.710705	−	0.703491i	$-0.248376\pi$
$631$	35.7054			1.42141			0.710705	+	0.703491i	$0.248376\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.21445	+	9.03170i	−0.206929	+	0.358412i
$636$		0			0
$637$	42.2160	−	1.87083i	1.67266	−	0.0741252i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.68141	−	2.91229i	−0.0664118	−	0.115029i	0.830908	−	0.556410i	$-0.187822\pi$
$641$	−1.68141	−	2.91229i	−0.0664118	−	0.115029i	−0.897319	+	0.441382i	$0.854488\pi$
$642$		0			0
$643$	−10.2113			−0.402695			−0.201348	−	0.979520i	$-0.564532\pi$
$643$	−10.2113			−0.402695			−0.201348	+	0.979520i	$0.564532\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.2765	+	17.7994i	0.404010	+	0.699766i	0.994206	−	0.107494i	$-0.0342827\pi$
$647$	10.2765	+	17.7994i	0.404010	+	0.699766i	−0.590196	+	0.807260i	$0.700949\pi$
$648$		0			0
$649$	−4.27868	+	7.41089i	−0.167953	+	0.290903i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.67722	+	9.83323i	−0.222167	+	0.384804i	−0.955466	−	0.295102i	$-0.904646\pi$
$653$	−5.67722	+	9.83323i	−0.222167	+	0.384804i	0.733299	+	0.679906i	$0.237980\pi$
$654$		0			0
$655$	2.11985	+	3.67169i	0.0828295	+	0.143465i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.2344			0.827174			0.413587	−	0.910465i	$-0.364276\pi$
$659$	21.2344			0.827174			0.413587	+	0.910465i	$0.364276\pi$
$660$		0			0
$661$	14.4610	+	25.0472i	0.562469	+	0.974224i	0.997280	+	0.0737028i	$0.0234816\pi$
$661$	14.4610	+	25.0472i	0.562469	+	0.974224i	−0.434812	+	0.900521i	$0.643185\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	22.7696	+	37.4955i	0.882968	+	1.45401i
$666$		0			0
$667$	−4.69607	+	8.13383i	−0.181832	+	0.314943i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−22.5069			−0.868868
$672$		0			0
$673$	−34.2618			−1.32070			−0.660348	−	0.750960i	$-0.729591\pi$
$673$	−34.2618			−1.32070			−0.660348	+	0.750960i	$0.729591\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.3733	−	30.0914i	0.667710	−	1.15651i	−0.310833	−	0.950464i	$-0.600608\pi$
$677$	17.3733	−	30.0914i	0.667710	−	1.15651i	0.978543	−	0.206042i	$-0.0660585\pi$
$678$		0			0
$679$	4.08308	−	0.0904281i	0.156694	−	0.00347031i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.140907	−	0.244058i	−0.00539166	−	0.00933863i	0.863317	−	0.504662i	$-0.168383\pi$
$683$	−0.140907	−	0.244058i	−0.00539166	−	0.00933863i	−0.868709	+	0.495323i	$0.835050\pi$
$684$		0			0
$685$	4.10100			0.156691
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−11.5720	−	20.0433i	−0.440859	−	0.763590i
$690$		0			0
$691$	17.2076	−	29.8044i	0.654608	−	1.13381i	−0.327384	−	0.944891i	$-0.606167\pi$
$691$	17.2076	−	29.8044i	0.654608	−	1.13381i	0.981992	−	0.188922i	$-0.0604995\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.05050	−	7.01567i	0.153644	−	0.266120i
$696$		0			0
$697$	19.0598	+	33.0126i	0.721942	+	1.25044i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	0.498472			0.0188270			0.00941352	−	0.999956i	$-0.497004\pi$
$701$	0.498472			0.0188270			0.00941352	+	0.999956i	$0.497004\pi$
$702$		0			0
$703$	−14.9395	−	25.8760i	−0.563454	−	0.975931i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.54364	−	5.83543i	−0.133272	−	0.219464i
$708$		0			0
$709$	2.08727	−	3.61527i	0.0783892	−	0.135774i	−0.824166	−	0.566348i	$-0.808356\pi$
$709$	2.08727	−	3.61527i	0.0783892	−	0.135774i	0.902555	+	0.430574i	$0.141689\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	39.6402			1.48454
$714$		0			0
$715$	−25.5941			−0.957166
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.493136	−	0.854137i	0.0183909	−	0.0318540i	−0.856683	−	0.515842i	$-0.827479\pi$
$719$	0.493136	−	0.854137i	0.0183909	−	0.0318540i	0.875074	+	0.483988i	$0.160812\pi$
$720$		0			0
$721$	8.32232	−	15.1813i	0.309939	−	0.565383i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.59414	+	2.76113i	0.0592048	+	0.102546i
$726$		0			0
$727$	34.9304			1.29550			0.647749	−	0.761854i	$-0.275711\pi$
$727$	34.9304			1.29550			0.647749	+	0.761854i	$0.275711\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.9495	−	22.4292i	−0.478955	−	0.829574i
$732$		0			0
$733$	−2.56202	+	4.43756i	−0.0946305	+	0.163905i	−0.909454	−	0.415804i	$-0.863500\pi$
$733$	−2.56202	+	4.43756i	−0.0946305	+	0.163905i	0.814824	+	0.579709i	$0.196834\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.11566	+	5.39648i	−0.114767	+	0.198782i
$738$		0			0
$739$	−8.46102	−	14.6549i	−0.311244	−	0.539090i	0.667388	−	0.744710i	$-0.267412\pi$
$739$	−8.46102	−	14.6549i	−0.311244	−	0.539090i	−0.978632	+	0.205620i	$0.934079\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	6.81172			0.249898			0.124949	−	0.992163i	$-0.460123\pi$
$743$	6.81172			0.249898			0.124949	+	0.992163i	$0.460123\pi$
$744$		0			0
$745$	2.05050	+	3.55157i	0.0751245	+	0.130120i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	5.76122	−	10.5095i	0.210511	−	0.384008i
$750$		0			0
$751$	−13.0877	+	22.6686i	−0.477578	+	0.827190i	−0.999670	−	0.0256996i	$-0.991819\pi$
$751$	−13.0877	+	22.6686i	−0.477578	+	0.827190i	0.522091	+	0.852890i	$0.325152\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	26.7319			0.972874
$756$		0			0
$757$	49.7138			1.80688			0.903439	−	0.428717i	$-0.141034\pi$
$757$	49.7138			1.80688			0.903439	+	0.428717i	$0.141034\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.32698	+	10.9586i	−0.229353	+	0.397251i	−0.957616	−	0.288046i	$-0.906994\pi$
$761$	−6.32698	+	10.9586i	−0.229353	+	0.397251i	0.728264	+	0.685297i	$0.240328\pi$
$762$		0			0
$763$	8.84757	+	14.5696i	0.320304	+	0.527455i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.7328	−	28.9821i	−0.604188	−	1.04648i
$768$		0			0
$769$	−20.2344			−0.729670			−0.364835	−	0.931072i	$-0.618875\pi$
$769$	−20.2344			−0.729670			−0.364835	+	0.931072i	$0.618875\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−9.87062	−	17.0964i	−0.355021	−	0.614915i	0.632100	−	0.774887i	$-0.282193\pi$
$773$	−9.87062	−	17.0964i	−0.355021	−	0.614915i	−0.987122	+	0.159972i	$0.948860\pi$
$774$		0			0
$775$	6.72818	−	11.6536i	0.241683	−	0.418608i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−15.3554	+	26.5963i	−0.550163	+	0.952910i
$780$		0			0
$781$	4.23970	+	7.34338i	0.151709	+	0.262767i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−24.9588			−0.890818
$786$		0			0
$787$	−8.45636	−	14.6469i	−0.301437	−	0.522104i	0.675025	−	0.737795i	$-0.264133\pi$
$787$	−8.45636	−	14.6469i	−0.301437	−	0.522104i	−0.976462	+	0.215691i	$0.930800\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−21.1608	+	0.468649i	−0.752392	+	0.0166633i
$792$		0			0
$793$	44.0093	−	76.2264i	1.56282	−	2.70688i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.48475			−0.123436			−0.0617180	−	0.998094i	$-0.519658\pi$
$797$	−3.48475			−0.123436			−0.0617180	+	0.998094i	$0.519658\pi$
$798$		0			0
$799$	−71.1334			−2.51652
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.68141	+	16.7687i	−0.341650	+	0.591754i
$804$		0			0
$805$	−28.2628	−	46.5413i	−0.996131	−	1.64036i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.59414	−	16.6175i	−0.337312	−	0.584241i	0.646614	−	0.762817i	$-0.276184\pi$
$809$	−9.59414	−	16.6175i	−0.337312	−	0.584241i	−0.983926	+	0.178576i	$0.942851\pi$
$810$		0			0
$811$	48.8285			1.71460			0.857300	−	0.514817i	$-0.172140\pi$
$811$	48.8285			1.71460			0.857300	+	0.514817i	$0.172140\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−26.8706	−	46.5413i	−0.941237	−	1.63027i
$816$		0			0
$817$	10.4326	−	18.0699i	0.364992	−	0.632184i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.2723	+	22.9883i	−0.463206	+	0.802296i	−0.999119	−	0.0419773i	$-0.986634\pi$
$821$	−13.2723	+	22.9883i	−0.463206	+	0.802296i	0.535913	+	0.844273i	$0.319968\pi$
$822$		0			0
$823$	8.47941	+	14.6868i	0.295574	+	0.511949i	0.975118	−	0.221686i	$-0.0711559\pi$
$823$	8.47941	+	14.6868i	0.295574	+	0.511949i	−0.679545	+	0.733634i	$0.737823\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	42.4289			1.47540			0.737699	−	0.675130i	$-0.235912\pi$
$827$	42.4289			1.47540			0.737699	+	0.675130i	$0.235912\pi$
$828$		0			0
$829$	15.9679	+	27.6572i	0.554588	+	0.960574i	0.997935	+	0.0642243i	$0.0204573\pi$
$829$	15.9679	+	27.6572i	0.554588	+	0.960574i	−0.443348	+	0.896350i	$0.646209\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	28.2113	+	44.2191i	0.977464	+	1.53210i
$834$		0			0
$835$	−16.3407	+	28.3029i	−0.565493	+	0.979463i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	49.5392			1.71028			0.855142	−	0.518394i	$-0.173470\pi$
$839$	49.5392			1.71028			0.855142	+	0.518394i	$0.173470\pi$
$840$		0			0
$841$	−27.4289			−0.945824
$842$		0			0
$843$		0			0
$844$		0			0
$845$	32.1934	−	55.7606i	1.10749	−	1.91822i
$846$		0			0
$847$	10.9595	−	19.9920i	0.376573	−	0.686934i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	18.5436	+	32.1185i	0.635668	+	1.10101i
$852$		0			0
$853$	11.4564			0.392258			0.196129	−	0.980578i	$-0.437163\pi$
$853$	11.4564			0.392258			0.196129	+	0.980578i	$0.437163\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.1240	−	27.9277i	−0.550787	−	0.953991i	−0.998218	−	0.0596726i	$-0.980994\pi$
$857$	−16.1240	−	27.9277i	−0.550787	−	0.953991i	0.447431	−	0.894318i	$-0.352339\pi$
$858$		0			0
$859$	−1.54364	+	2.67366i	−0.0526682	+	0.0912240i	−0.891158	−	0.453694i	$-0.850106\pi$
$859$	−1.54364	+	2.67366i	−0.0526682	+	0.0912240i	0.838489	+	0.544918i	$0.183439\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.07355	−	15.7158i	0.308867	−	0.534974i	−0.669248	−	0.743039i	$-0.733383\pi$
$863$	9.07355	−	15.7158i	0.308867	−	0.534974i	0.978115	+	0.208066i	$0.0667168\pi$
$864$		0			0
$865$	−3.54364	−	6.13776i	−0.120487	−	0.208690i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.0358			0.408288
$870$		0			0
$871$	−12.1845	−	21.1042i	−0.412858	−	0.715090i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	17.8454	−	0.395222i	0.603283	−	0.0133609i
$876$		0			0
$877$	−4.44264	+	7.69487i	−0.150017	+	0.259837i	−0.931234	−	0.364423i	$-0.881266\pi$
$877$	−4.44264	+	7.69487i	−0.150017	+	0.259837i	0.781216	+	0.624260i	$0.214600\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	41.5667			1.40042			0.700209	−	0.713938i	$-0.253090\pi$
$881$	41.5667			1.40042			0.700209	+	0.713938i	$0.253090\pi$
$882$		0			0
$883$	28.7182			0.966444			0.483222	−	0.875498i	$-0.339466\pi$
$883$	28.7182			0.966444			0.483222	+	0.875498i	$0.339466\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.9074	−	36.2127i	0.702001	−	1.21590i	−0.265761	−	0.964039i	$-0.585623\pi$
$887$	20.9074	−	36.2127i	0.702001	−	1.21590i	0.967763	−	0.251863i	$-0.0810433\pi$
$888$		0			0
$889$	−10.0436	+	0.222437i	−0.336853	+	0.00746029i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−28.6540	−	49.6301i	−0.958868	−	1.66081i
$894$		0			0
$895$	8.20200			0.274163
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.31546	−	5.74254i	−0.110577	−	0.191524i
$900$		0			0
$901$	14.3638	−	24.8787i	0.478526	−	0.828831i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−14.4794	+	25.0791i	−0.481312	+	0.833657i
$906$		0			0
$907$	28.5851	+	49.5108i	0.949152	+	1.64398i	0.747217	+	0.664580i	$0.231389\pi$
$907$	28.5851	+	49.5108i	0.949152	+	1.64398i	0.201935	+	0.979399i	$0.435277\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	24.4059			0.808602			0.404301	−	0.914626i	$-0.367515\pi$
$911$	24.4059			0.808602			0.404301	+	0.914626i	$0.367515\pi$
$912$		0			0
$913$	5.03991	+	8.72937i	0.166797	+	0.288900i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.96323	+	3.58126i	−0.0648314	+	0.118264i
$918$		0			0
$919$	−23.8522	+	41.3133i	−0.786812	+	1.36280i	0.141098	+	0.989996i	$0.454937\pi$
$919$	−23.8522	+	41.3133i	−0.786812	+	1.36280i	−0.927910	+	0.372803i	$0.878397\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−33.1608			−1.09150
$924$		0			0
$925$	12.5897			0.413948
$926$		0			0
$927$		0			0
$928$		0			0
$929$	19.6172	−	33.9780i	0.643619	−	1.11478i	−0.341000	−	0.940063i	$-0.610766\pi$
$929$	19.6172	−	33.9780i	0.643619	−	1.11478i	0.984619	−	0.174717i	$-0.0559012\pi$
$930$		0			0
$931$	−19.4878	+	37.4955i	−0.638687	+	1.22887i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−15.8843	−	27.5125i	−0.519474	−	0.899755i
$936$		0			0
$937$	15.3491			0.501433			0.250717	−	0.968061i	$-0.419334\pi$
$937$	15.3491			0.501433			0.250717	+	0.968061i	$0.419334\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−6.08308	−	10.5362i	−0.198303	−	0.343470i	0.749676	−	0.661806i	$-0.230210\pi$
$941$	−6.08308	−	10.5362i	−0.198303	−	0.343470i	−0.947978	+	0.318335i	$0.896876\pi$
$942$		0			0
$943$	19.0598	−	33.0126i	0.620673	−	1.07504i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.52991	+	16.5063i	−0.309680	+	0.536382i	−0.978292	−	0.207229i	$-0.933555\pi$
$947$	−9.52991	+	16.5063i	−0.309680	+	0.536382i	0.668612	+	0.743611i	$0.266889\pi$
$948$		0			0
$949$	−37.8615	−	65.5781i	−1.22904	−	2.12876i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−17.1334			−0.555004			−0.277502	−	0.960725i	$-0.589507\pi$
$953$	−17.1334			−0.555004			−0.277502	+	0.960725i	$0.589507\pi$
$954$		0			0
$955$	23.5667	+	40.8187i	0.762600	+	1.32086i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.05050	+	3.37663i	0.0662141	+	0.109037i
$960$		0			0
$961$	1.50686	−	2.60996i	0.0486085	−	0.0841924i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−29.9348			−0.963637
$966$		0			0
$967$	26.7833			0.861294			0.430647	−	0.902520i	$-0.358285\pi$
$967$	26.7833			0.861294			0.430647	+	0.902520i	$0.358285\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.75809	−	9.97331i	0.184786	−	0.320059i	−0.758718	−	0.651419i	$-0.774174\pi$
$971$	5.75809	−	9.97331i	0.184786	−	0.320059i	0.943504	+	0.331360i	$0.107507\pi$
$972$		0			0
$973$	7.80173	−	0.172785i	0.250112	−	0.00553924i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.6677	+	18.4770i	0.341289	+	0.591131i	0.984672	−	0.174414i	$-0.0558030\pi$
$977$	10.6677	+	18.4770i	0.341289	+	0.591131i	−0.643383	+	0.765544i	$0.722470\pi$
$978$		0			0
$979$	14.6540			0.468343
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−25.1976	−	43.6435i	−0.803678	−	1.39201i	−0.917180	−	0.398474i	$-0.869540\pi$
$983$	−25.1976	−	43.6435i	−0.803678	−	1.39201i	0.113501	−	0.993538i	$-0.463793\pi$
$984$		0			0
$985$	−7.44264	+	12.8910i	−0.237142	+	0.410742i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−12.9495	+	22.4292i	−0.411770	+	0.713207i
$990$		0			0
$991$	−6.34117	−	10.9832i	−0.201434	−	0.348894i	0.747557	−	0.664198i	$-0.231227\pi$
$991$	−6.34117	−	10.9832i	−0.201434	−	0.348894i	−0.948991	+	0.315304i	$0.897893\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−63.1334			−2.00146
$996$		0			0
$997$	20.1708	+	34.9369i	0.638816	+	1.10646i	0.985693	+	0.168551i	$0.0539089\pi$
$997$	20.1708	+	34.9369i	0.638816	+	1.10646i	−0.346877	+	0.937911i	$0.612758\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2016.2.s.v.289.3		6
3.2	odd	2		672.2.q.l.289.1	yes	6
4.3	odd	2		2016.2.s.u.289.3		6
7.4	even	3	inner	2016.2.s.v.865.3		6
12.11	even	2		672.2.q.k.289.1	yes	6
21.2	odd	6		4704.2.a.bs.1.3		3
21.5	even	6		4704.2.a.bv.1.1		3
21.11	odd	6		672.2.q.l.193.1	yes	6
24.5	odd	2		1344.2.q.y.961.3		6
24.11	even	2		1344.2.q.z.961.3		6
28.11	odd	6		2016.2.s.u.865.3		6
84.11	even	6		672.2.q.k.193.1	✓	6
84.23	even	6		4704.2.a.bu.1.3		3
84.47	odd	6		4704.2.a.bt.1.1		3
168.5	even	6		9408.2.a.eg.1.3		3
168.11	even	6		1344.2.q.z.193.3		6
168.53	odd	6		1344.2.q.y.193.3		6
168.107	even	6		9408.2.a.eh.1.1		3
168.131	odd	6		9408.2.a.ei.1.3		3
168.149	odd	6		9408.2.a.ej.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.q.k.193.1	✓	6	84.11	even	6
672.2.q.k.289.1	yes	6	12.11	even	2
672.2.q.l.193.1	yes	6	21.11	odd	6
672.2.q.l.289.1	yes	6	3.2	odd	2
1344.2.q.y.193.3		6	168.53	odd	6
1344.2.q.y.961.3		6	24.5	odd	2
1344.2.q.z.193.3		6	168.11	even	6
1344.2.q.z.961.3		6	24.11	even	2
2016.2.s.u.289.3		6	4.3	odd	2
2016.2.s.u.865.3		6	28.11	odd	6
2016.2.s.v.289.3		6	1.1	even	1	trivial
2016.2.s.v.865.3		6	7.4	even	3	inner
4704.2.a.bs.1.3		3	21.2	odd	6
4704.2.a.bt.1.1		3	84.47	odd	6
4704.2.a.bu.1.3		3	84.23	even	6
4704.2.a.bv.1.1		3	21.5	even	6
9408.2.a.eg.1.3		3	168.5	even	6
9408.2.a.eh.1.1		3	168.107	even	6
9408.2.a.ei.1.3		3	168.131	odd	6
9408.2.a.ej.1.1		3	168.149	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2016.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37328 - 2.37860i) q^{5} +(2.64510 - 0.0585812i) q^{7} +O(q^{10})\)	\(q+(1.37328 - 2.37860i) q^{5} +(2.64510 - 0.0585812i) q^{7} +(-0.771819 - 1.33683i) q^{11} +6.03677 q^{13} +(3.74657 + 6.48925i) q^{17} +(-3.01839 + 5.22800i) q^{19} +(3.74657 - 6.48925i) q^{23} +(-1.27182 - 2.20285i) q^{25} -1.25343 q^{29} +(2.64510 + 4.58145i) q^{31} +(3.49314 - 6.37208i) q^{35} +(-2.47475 + 4.28639i) q^{37} +5.08727 q^{41} -3.45636 q^{43} +(-4.74657 + 8.22130i) q^{47} +(6.99314 - 0.309906i) q^{49} +(-1.91692 - 3.32021i) q^{53} -4.23970 q^{55} +(-2.77182 - 4.80093i) q^{59} +(7.29021 - 12.6270i) q^{61} +(8.29021 - 14.3591i) q^{65} +(-2.01839 - 3.49595i) q^{67} -5.49314 q^{71} +(-6.27182 - 10.8631i) q^{73} +(-2.11985 - 3.49084i) q^{77} +(-3.89853 + 6.75246i) q^{79} -6.52991 q^{83} +20.5804 q^{85} +(-4.74657 + 8.22130i) q^{89} +(15.9679 - 0.353641i) q^{91} +(8.29021 + 14.3591i) q^{95} +1.54364 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7}+O(q^{10}) \) 6 * q + 3 * q^7	\( 6 q + 3 q^{7} - 6 q^{13} + 6 q^{17} + 3 q^{19} + 6 q^{23} - 3 q^{25} - 24 q^{29} + 3 q^{31} - 12 q^{35} - 3 q^{37} + 12 q^{41} - 30 q^{43} - 12 q^{47} + 9 q^{49} + 6 q^{53} + 24 q^{55} - 12 q^{59} + 18 q^{61} + 24 q^{65} + 9 q^{67} - 33 q^{73} + 12 q^{77} - 27 q^{79} + 36 q^{83} + 72 q^{85} - 12 q^{89} + 51 q^{91} + 24 q^{95}+O(q^{100}) \) 6 * q + 3 * q^7 - 6 * q^13 + 6 * q^17 + 3 * q^19 + 6 * q^23 - 3 * q^25 - 24 * q^29 + 3 * q^31 - 12 * q^35 - 3 * q^37 + 12 * q^41 - 30 * q^43 - 12 * q^47 + 9 * q^49 + 6 * q^53 + 24 * q^55 - 12 * q^59 + 18 * q^61 + 24 * q^65 + 9 * q^67 - 33 * q^73 + 12 * q^77 - 27 * q^79 + 36 * q^83 + 72 * q^85 - 12 * q^89 + 51 * q^91 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more