LMFDB - Embedded newform 1872.2.t.p.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1872,2,Mod(289,1872)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1872, 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("1872.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1872 = 2^{4} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1872.t (of order $3$, degree $2$, not 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:	$14.9479952584$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 10x^{2} + 100 $ x^4 + 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$1.58114 - 2.73861i$ of defining polynomial
Character	$\chi$	$=$	1872.289
Dual form			1872.2.t.p.1153.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16228 q^{5} +(-1.58114 + 2.73861i) q^{7} +O(q^{10})$	$q-2.16228 q^{5} +(-1.58114 + 2.73861i) q^{7} +(2.58114 + 4.47066i) q^{11} +(-3.08114 - 1.87259i) q^{13} +(1.50000 - 2.59808i) q^{17} +(0.581139 - 1.00656i) q^{19} +(0.418861 + 0.725489i) q^{23} -0.324555 q^{25} +(4.08114 + 7.06874i) q^{29} -6.32456 q^{31} +(3.41886 - 5.92164i) q^{35} +(-5.08114 - 8.80079i) q^{37} +(-1.50000 - 2.59808i) q^{41} +(1.41886 - 2.45754i) q^{43} -11.1623 q^{47} +(-1.50000 - 2.59808i) q^{49} +6.48683 q^{53} +(-5.58114 - 9.66682i) q^{55} +(5.16228 - 8.94133i) q^{59} +(3.08114 - 5.33669i) q^{61} +(6.66228 + 4.04905i) q^{65} +(-4.58114 - 7.93477i) q^{67} +(-0.418861 + 0.725489i) q^{71} -1.00000 q^{73} -16.3246 q^{77} +4.00000 q^{79} -15.4868 q^{83} +(-3.24342 + 5.61776i) q^{85} +(-6.00000 - 10.3923i) q^{89} +(10.0000 - 5.47723i) q^{91} +(-1.25658 + 2.17647i) q^{95} +(2.00000 - 3.46410i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5}+O(q^{10}) $ 4 * q + 4 * q^5	$ 4 q + 4 q^{5} + 4 q^{11} - 6 q^{13} + 6 q^{17} - 4 q^{19} + 8 q^{23} + 24 q^{25} + 10 q^{29} + 20 q^{35} - 14 q^{37} - 6 q^{41} + 12 q^{43} - 32 q^{47} - 6 q^{49} - 12 q^{53} - 16 q^{55} + 8 q^{59} + 6 q^{61} + 14 q^{65} - 12 q^{67} - 8 q^{71} - 4 q^{73} - 40 q^{77} + 16 q^{79} - 24 q^{83} + 6 q^{85} - 24 q^{89} + 40 q^{91} - 24 q^{95} + 8 q^{97}+O(q^{100}) $ 4 * q + 4 * q^5 + 4 * q^11 - 6 * q^13 + 6 * q^17 - 4 * q^19 + 8 * q^23 + 24 * q^25 + 10 * q^29 + 20 * q^35 - 14 * q^37 - 6 * q^41 + 12 * q^43 - 32 * q^47 - 6 * q^49 - 12 * q^53 - 16 * q^55 + 8 * q^59 + 6 * q^61 + 14 * q^65 - 12 * q^67 - 8 * q^71 - 4 * q^73 - 40 * q^77 + 16 * q^79 - 24 * q^83 + 6 * q^85 - 24 * q^89 + 40 * q^91 - 24 * q^95 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$5$	−2.16228			−0.967000			−0.483500	−	0.875344i	$-0.660635\pi$
$5$	−2.16228			−0.967000			−0.483500	+	0.875344i	$0.660635\pi$
$6$		0			0
$7$	−1.58114	+	2.73861i	−0.597614	+	1.03510i	0.395558	+	0.918441i	$0.370551\pi$
$7$	−1.58114	+	2.73861i	−0.597614	+	1.03510i	−0.993172	+	0.116657i	$0.962782\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.58114	+	4.47066i	0.778243	+	1.34796i	0.932954	+	0.359996i	$0.117222\pi$
$11$	2.58114	+	4.47066i	0.778243	+	1.34796i	−0.154711	+	0.987960i	$0.549445\pi$
$12$		0			0
$13$	−3.08114	−	1.87259i	−0.854554	−	0.519362i
$13$	−3.08114	−	1.87259i	−0.854554	−	0.519362i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	0.581139	−	1.00656i	0.133322	−	0.230921i	−0.791633	−	0.610997i	$-0.790769\pi$
$19$	0.581139	−	1.00656i	0.133322	−	0.230921i	0.924955	+	0.380076i	$0.124102\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.418861	+	0.725489i	0.0873386	+	0.151275i	0.906385	−	0.422452i	$-0.138830\pi$
$23$	0.418861	+	0.725489i	0.0873386	+	0.151275i	−0.819047	+	0.573727i	$0.805497\pi$
$24$		0			0
$25$	−0.324555			−0.0649111
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.08114	+	7.06874i	0.757848	+	1.31263i	0.943946	+	0.330101i	$0.107083\pi$
$29$	4.08114	+	7.06874i	0.757848	+	1.31263i	−0.186097	+	0.982531i	$0.559584\pi$
$30$		0			0
$31$	−6.32456			−1.13592			−0.567962	−	0.823055i	$-0.692268\pi$
$31$	−6.32456			−1.13592			−0.567962	+	0.823055i	$0.692268\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.41886	−	5.92164i	0.577893	−	1.00094i
$36$		0			0
$37$	−5.08114	−	8.80079i	−0.835334	−	1.44684i	−0.893758	−	0.448549i	$-0.851941\pi$
$37$	−5.08114	−	8.80079i	−0.835334	−	1.44684i	0.0584241	−	0.998292i	$-0.481392\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	1.41886	−	2.45754i	0.216374	−	0.374771i	−0.737323	−	0.675541i	$-0.763910\pi$
$43$	1.41886	−	2.45754i	0.216374	−	0.374771i	0.953697	+	0.300770i	$0.0972435\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−11.1623			−1.62819			−0.814093	−	0.580735i	$-0.802765\pi$
$47$	−11.1623			−1.62819			−0.814093	+	0.580735i	$0.802765\pi$
$48$		0			0
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.48683			0.891035			0.445518	−	0.895273i	$-0.353020\pi$
$53$	6.48683			0.891035			0.445518	+	0.895273i	$0.353020\pi$
$54$		0			0
$55$	−5.58114	−	9.66682i	−0.752561	−	1.30347i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.16228	−	8.94133i	0.672071	−	1.16406i	−0.305244	−	0.952274i	$-0.598738\pi$
$59$	5.16228	−	8.94133i	0.672071	−	1.16406i	0.977316	−	0.211788i	$-0.0679285\pi$
$60$		0			0
$61$	3.08114	−	5.33669i	0.394499	−	0.683293i	−0.598538	−	0.801095i	$-0.704251\pi$
$61$	3.08114	−	5.33669i	0.394499	−	0.683293i	0.993037	+	0.117802i	$0.0375847\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.66228	+	4.04905i	0.826354	+	0.502223i
$66$		0			0
$67$	−4.58114	−	7.93477i	−0.559675	−	0.969386i	−0.997523	−	0.0703369i	$-0.977593\pi$
$67$	−4.58114	−	7.93477i	−0.559675	−	0.969386i	0.437848	−	0.899049i	$-0.355741\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.418861	+	0.725489i	−0.0497097	+	0.0860997i	−0.889810	−	0.456332i	$-0.849163\pi$
$71$	−0.418861	+	0.725489i	−0.0497097	+	0.0860997i	0.840100	+	0.542432i	$0.182496\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−16.3246			−1.86036
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−15.4868			−1.69990			−0.849950	−	0.526863i	$-0.823368\pi$
$83$	−15.4868			−1.69990			−0.849950	+	0.526863i	$0.823368\pi$
$84$		0			0
$85$	−3.24342	+	5.61776i	−0.351798	+	0.609332i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$90$		0			0
$91$	10.0000	−	5.47723i	1.04828	−	0.574169i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.25658	+	2.17647i	−0.128923	+	0.223301i
$96$		0			0
$97$	2.00000	−	3.46410i	0.203069	−	0.351726i	−0.746447	−	0.665445i	$-0.768242\pi$
$97$	2.00000	−	3.46410i	0.203069	−	0.351726i	0.949516	+	0.313719i	$0.101575\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.08114	−	12.2649i	−0.704600	−	1.22040i	−0.966836	−	0.255399i	$-0.917793\pi$
$101$	−7.08114	−	12.2649i	−0.704600	−	1.22040i	0.262236	−	0.965004i	$-0.415540\pi$
$102$		0			0
$103$	−15.8114			−1.55794			−0.778971	−	0.627060i	$-0.784258\pi$
$103$	−15.8114			−1.55794			−0.778971	+	0.627060i	$0.784258\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.90569	+	11.9610i	0.667599	+	1.15631i	0.978574	+	0.205897i	$0.0660111\pi$
$107$	6.90569	+	11.9610i	0.667599	+	1.15631i	−0.310975	+	0.950418i	$0.600656\pi$
$108$		0			0
$109$	−18.6491			−1.78626			−0.893130	−	0.449798i	$-0.851496\pi$
$109$	−18.6491			−1.78626			−0.893130	+	0.449798i	$0.851496\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.66228	+	16.7356i	−0.908951	+	1.57435i	−0.0934260	+	0.995626i	$0.529782\pi$
$113$	−9.66228	+	16.7356i	−0.908951	+	1.57435i	−0.815525	+	0.578722i	$0.803551\pi$
$114$		0			0
$115$	−0.905694	−	1.56871i	−0.0844564	−	0.146283i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.74342	+	8.21584i	0.434828	+	0.753145i
$120$		0			0
$121$	−7.82456	+	13.5525i	−0.711323	+	1.23205i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.5132			1.02977
$126$		0			0
$127$	−2.83772	−	4.91508i	−0.251807	−	0.436143i	0.712216	−	0.701960i	$-0.247692\pi$
$127$	−2.83772	−	4.91508i	−0.251807	−	0.436143i	−0.964023	+	0.265817i	$0.914358\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.64911			0.755676			0.377838	−	0.925872i	$-0.376668\pi$
$131$	8.64911			0.755676			0.377838	+	0.925872i	$0.376668\pi$
$132$		0			0
$133$	1.83772	+	3.18303i	0.159351	+	0.276004i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	3.16228	−	5.47723i	0.268221	−	0.464572i	−0.700182	−	0.713965i	$-0.746898\pi$
$139$	3.16228	−	5.47723i	0.268221	−	0.464572i	0.968402	+	0.249393i	$0.0802310\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.418861	−	18.6081i	0.0350269	−	1.55609i
$144$		0			0
$145$	−8.82456	−	15.2846i	−0.732839	−	1.26932i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.24342	−	16.0101i	0.757250	−	1.31160i	−0.186998	−	0.982360i	$-0.559876\pi$
$149$	9.24342	−	16.0101i	0.757250	−	1.31160i	0.944248	−	0.329235i	$-0.106791\pi$
$150$		0			0
$151$	−7.16228			−0.582858			−0.291429	−	0.956592i	$-0.594131\pi$
$151$	−7.16228			−0.582858			−0.291429	+	0.956592i	$0.594131\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	13.6754			1.09844
$156$		0			0
$157$	8.48683			0.677323			0.338662	−	0.940908i	$-0.390026\pi$
$157$	8.48683			0.677323			0.338662	+	0.940908i	$0.390026\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.64911			−0.208779
$162$		0			0
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	0.361619	+	0.932326i	$0.382224\pi$
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	−0.988227	+	0.152992i	$0.951109\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$		0			0
$169$	5.98683	+	11.5394i	0.460526	+	0.887646i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.32456	−	2.29420i	0.100704	−	0.174425i	−0.811271	−	0.584670i	$-0.801224\pi$
$173$	1.32456	−	2.29420i	0.100704	−	0.174425i	0.911975	+	0.410246i	$0.134557\pi$
$174$		0			0
$175$	0.513167	−	0.888831i	0.0387918	−	0.0671893i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.74342	−	3.01969i	−0.130309	−	0.225702i	0.793487	−	0.608588i	$-0.208264\pi$
$179$	−1.74342	−	3.01969i	−0.130309	−	0.225702i	−0.923796	+	0.382886i	$0.874930\pi$
$180$		0			0
$181$	10.1623			0.755356			0.377678	−	0.925937i	$-0.376723\pi$
$181$	10.1623			0.755356			0.377678	+	0.925937i	$0.376723\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.9868	+	19.0298i	0.807768	+	1.39910i
$186$		0			0
$187$	15.4868			1.13251
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.837722	−	1.45098i	0.0606155	−	0.104989i	−0.834125	−	0.551575i	$-0.814027\pi$
$191$	0.837722	−	1.45098i	0.0606155	−	0.104989i	0.894741	+	0.446586i	$0.147360\pi$
$192$		0			0
$193$	−8.98683	−	15.5657i	−0.646886	−	1.12044i	−0.983862	−	0.178927i	$-0.942737\pi$
$193$	−8.98683	−	15.5657i	−0.646886	−	1.12044i	0.336976	−	0.941513i	$-0.390596\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.48683	+	16.4317i	0.675909	+	1.17071i	0.976202	+	0.216862i	$0.0695820\pi$
$197$	9.48683	+	16.4317i	0.675909	+	1.17071i	−0.300293	+	0.953847i	$0.597085\pi$
$198$		0			0
$199$	−12.7434	+	22.0722i	−0.903357	+	1.56466i	−0.0802490	+	0.996775i	$0.525572\pi$
$199$	−12.7434	+	22.0722i	−0.903357	+	1.56466i	−0.823108	+	0.567885i	$0.807762\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−25.8114			−1.81160
$204$		0			0
$205$	3.24342	+	5.61776i	0.226530	+	0.392362i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.00000			0.415029
$210$		0			0
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	0.788935	−	0.614477i	$-0.210633\pi$
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	−0.926620	+	0.375999i	$0.877300\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.06797	+	5.31388i	−0.209234	+	0.362404i
$216$		0			0
$217$	10.0000	−	17.3205i	0.678844	−	1.17579i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−9.48683	+	5.19615i	−0.638153	+	0.349531i
$222$		0			0
$223$	−7.16228	−	12.4054i	−0.479622	−	0.830729i	0.520105	−	0.854102i	$-0.325893\pi$
$223$	−7.16228	−	12.4054i	−0.479622	−	0.830729i	−0.999727	+	0.0233732i	$0.992559\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.74342	−	3.01969i	0.115715	−	0.200424i	−0.802351	−	0.596853i	$-0.796418\pi$
$227$	1.74342	−	3.01969i	0.115715	−	0.200424i	0.918065	+	0.396429i	$0.129751\pi$
$228$		0			0
$229$	9.67544			0.639371			0.319686	−	0.947524i	$-0.396423\pi$
$229$	9.67544			0.639371			0.319686	+	0.947524i	$0.396423\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.64911			0.566622			0.283311	−	0.959028i	$-0.408567\pi$
$233$	8.64911			0.566622			0.283311	+	0.959028i	$0.408567\pi$
$234$		0			0
$235$	24.1359			1.57446
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.51317			0.162563			0.0812816	−	0.996691i	$-0.474099\pi$
$239$	2.51317			0.162563			0.0812816	+	0.996691i	$0.474099\pi$
$240$		0			0
$241$	−0.337722	+	0.584952i	−0.0217546	+	0.0376801i	−0.876698	−	0.481042i	$-0.840259\pi$
$241$	−0.337722	+	0.584952i	−0.0217546	+	0.0376801i	0.854943	+	0.518722i	$0.173592\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.24342	+	5.61776i	0.207214	+	0.358906i
$246$		0			0
$247$	−3.67544	+	2.01312i	−0.233863	+	0.128092i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$		0			0
$253$	−2.16228	+	3.74517i	−0.135941	+	0.235457i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.98683	−	13.8336i	−0.498205	−	0.862916i	0.501793	−	0.864988i	$-0.332674\pi$
$257$	−7.98683	−	13.8336i	−0.498205	−	0.862916i	−0.999998	+	0.00207150i	$0.999341\pi$
$258$		0			0
$259$	32.1359			1.99683
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.7434	−	18.6081i	−0.662467	−	1.14743i	−0.979965	−	0.199168i	$-0.936176\pi$
$263$	−10.7434	−	18.6081i	−0.662467	−	1.14743i	0.317498	−	0.948259i	$-0.397157\pi$
$264$		0			0
$265$	−14.0263			−0.861631
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$		0			0
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	0.945944	−	0.324329i	$-0.105139\pi$
$271$	3.16228	+	5.47723i	0.192095	+	0.332718i	−0.753850	+	0.657047i	$0.771805\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.837722	−	1.45098i	−0.0505166	−	0.0874972i
$276$		0			0
$277$	10.4057	−	18.0232i	0.625218	−	1.08291i	−0.363281	−	0.931680i	$-0.618344\pi$
$277$	10.4057	−	18.0232i	0.625218	−	1.08291i	0.988499	−	0.151229i	$-0.0483231\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.3246			−0.794876			−0.397438	−	0.917629i	$-0.630101\pi$
$281$	−13.3246			−0.794876			−0.397438	+	0.917629i	$0.630101\pi$
$282$		0			0
$283$	−4.58114	−	7.93477i	−0.272320	−	0.471673i	0.697135	−	0.716940i	$-0.254458\pi$
$283$	−4.58114	−	7.93477i	−0.272320	−	0.471673i	−0.969456	+	0.245267i	$0.921124\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.48683			0.559990
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.08114	+	7.06874i	−0.238423	+	0.412960i	−0.960262	−	0.279101i	$-0.909964\pi$
$293$	−4.08114	+	7.06874i	−0.238423	+	0.412960i	0.721839	+	0.692061i	$0.243297\pi$
$294$		0			0
$295$	−11.1623	+	19.3336i	−0.649893	+	1.12565i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.0679718	−	3.01969i	0.00393091	−	0.174633i
$300$		0			0
$301$	4.48683	+	7.77142i	0.258617	+	0.447937i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.66228	+	11.5394i	−0.381481	+	0.660744i
$306$		0			0
$307$	7.48683			0.427296			0.213648	−	0.976911i	$-0.431465\pi$
$307$	7.48683			0.427296			0.213648	+	0.976911i	$0.431465\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.51317			−0.142509			−0.0712543	−	0.997458i	$-0.522700\pi$
$311$	−2.51317			−0.142509			−0.0712543	+	0.997458i	$0.522700\pi$
$312$		0			0
$313$	−4.00000			−0.226093			−0.113047	−	0.993590i	$-0.536061\pi$
$313$	−4.00000			−0.226093			−0.113047	+	0.993590i	$0.536061\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.48683			−0.364337			−0.182168	−	0.983267i	$-0.558312\pi$
$317$	−6.48683			−0.364337			−0.182168	+	0.983267i	$0.558312\pi$
$318$		0			0
$319$	−21.0680	+	36.4908i	−1.17958	+	2.04309i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.74342	−	3.01969i	−0.0970063	−	0.168020i
$324$		0			0
$325$	1.00000	+	0.607758i	0.0554700	+	0.0337124i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	17.6491	−	30.5692i	0.973027	−	1.68533i
$330$		0			0
$331$	13.4868	−	23.3599i	0.741303	−	1.28398i	−0.210599	−	0.977573i	$-0.567541\pi$
$331$	13.4868	−	23.3599i	0.741303	−	1.28398i	0.951902	−	0.306403i	$-0.0991253\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	9.90569	+	17.1572i	0.541206	+	0.937396i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−16.3246	−	28.2750i	−0.884024	−	1.53117i
$342$		0			0
$343$	−12.6491			−0.682988
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.74342	−	3.01969i	0.0935915	−	0.162105i	−0.815428	−	0.578858i	$-0.803499\pi$
$347$	1.74342	−	3.01969i	0.0935915	−	0.162105i	0.909020	+	0.416753i	$0.136832\pi$
$348$		0			0
$349$	15.3246	+	26.5429i	0.820305	+	1.42081i	0.905455	+	0.424441i	$0.139529\pi$
$349$	15.3246	+	26.5429i	0.820305	+	1.42081i	−0.0851508	+	0.996368i	$0.527137\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.33772	−	14.4414i	−0.443772	−	0.768636i	0.554194	−	0.832388i	$-0.313027\pi$
$353$	−8.33772	−	14.4414i	−0.443772	−	0.768636i	−0.997966	+	0.0637518i	$0.979693\pi$
$354$		0			0
$355$	0.905694	−	1.56871i	0.0480693	−	0.0832584i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	28.4605			1.50209			0.751044	−	0.660252i	$-0.229551\pi$
$359$	28.4605			1.50209			0.751044	+	0.660252i	$0.229551\pi$
$360$		0			0
$361$	8.82456	+	15.2846i	0.464450	+	0.804451i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.16228			0.113179
$366$		0			0
$367$	−3.25658	−	5.64057i	−0.169992	−	0.294435i	0.768425	−	0.639940i	$-0.221041\pi$
$367$	−3.25658	−	5.64057i	−0.169992	−	0.294435i	−0.938417	+	0.345505i	$0.887708\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−10.2566	+	17.7649i	−0.532495	+	0.922309i
$372$		0			0
$373$	−1.24342	+	2.15366i	−0.0643817	+	0.111512i	−0.896420	−	0.443207i	$-0.853841\pi$
$373$	−1.24342	+	2.15366i	−0.0643817	+	0.111512i	0.832038	+	0.554719i	$0.187174\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.662278	−	29.4221i	0.0341090	−	1.51531i
$378$		0			0
$379$	15.1623	+	26.2618i	0.778834	+	1.34898i	0.932614	+	0.360875i	$0.117522\pi$
$379$	15.1623	+	26.2618i	0.778834	+	1.34898i	−0.153780	+	0.988105i	$0.549145\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.48683	+	6.03937i	−0.178169	+	0.308597i	−0.941253	−	0.337701i	$-0.890351\pi$
$383$	−3.48683	+	6.03937i	−0.178169	+	0.308597i	0.763085	+	0.646299i	$0.223684\pi$
$384$		0			0
$385$	35.2982			1.79896
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.48683			−0.328895			−0.164448	−	0.986386i	$-0.552584\pi$
$389$	−6.48683			−0.328895			−0.164448	+	0.986386i	$0.552584\pi$
$390$		0			0
$391$	2.51317			0.127096
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.64911			−0.435184
$396$		0			0
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	0.330075	+	0.943955i	$0.392926\pi$
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	−0.982526	+	0.186124i	$0.940407\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	19.4868	+	11.8433i	0.970708	+	0.589956i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	26.2302	−	45.4321i	1.30019	−	2.25199i
$408$		0			0
$409$	−13.6623	+	23.6638i	−0.675556	+	1.17010i	0.300750	+	0.953703i	$0.402763\pi$
$409$	−13.6623	+	23.6638i	−0.675556	+	1.17010i	−0.976306	+	0.216395i	$0.930570\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.3246	+	28.2750i	0.803279	+	1.39132i
$414$		0			0
$415$	33.4868			1.64380
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.48683	+	6.03937i	0.170343	+	0.295043i	0.938540	−	0.345171i	$-0.112179\pi$
$419$	3.48683	+	6.03937i	0.170343	+	0.295043i	−0.768197	+	0.640214i	$0.778846\pi$
$420$		0			0
$421$	−30.1623			−1.47002			−0.735010	−	0.678057i	$-0.762822\pi$
$421$	−30.1623			−1.47002			−0.735010	+	0.678057i	$0.762822\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.486833	+	0.843219i	−0.0236149	+	0.0409022i
$426$		0			0
$427$	9.74342	+	16.8761i	0.471517	+	0.816691i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4.74342	+	8.21584i	0.228482	+	0.395743i	0.957359	−	0.288903i	$-0.0932904\pi$
$431$	4.74342	+	8.21584i	0.228482	+	0.395743i	−0.728876	+	0.684646i	$0.759957\pi$
$432$		0			0
$433$	−1.66228	+	2.87915i	−0.0798840	+	0.138363i	−0.903200	−	0.429221i	$-0.858788\pi$
$433$	−1.66228	+	2.87915i	−0.0798840	+	0.138363i	0.823316	+	0.567584i	$0.192122\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.973666			0.0465768
$438$		0			0
$439$	−3.25658	−	5.64057i	−0.155428	−	0.269210i	0.777787	−	0.628528i	$-0.216342\pi$
$439$	−3.25658	−	5.64057i	−0.155428	−	0.269210i	−0.933215	+	0.359319i	$0.883009\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	12.9737	+	22.4710i	0.615011	+	1.06523i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−16.3246	+	28.2750i	−0.770403	+	1.33438i	0.166939	+	0.985967i	$0.446612\pi$
$449$	−16.3246	+	28.2750i	−0.770403	+	1.33438i	−0.937342	+	0.348411i	$0.886722\pi$
$450$		0			0
$451$	7.74342	−	13.4120i	0.364623	−	0.631546i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−21.6228	+	11.8433i	−1.01369	+	0.555222i
$456$		0			0
$457$	−4.66228	−	8.07530i	−0.218092	−	0.377747i	0.736133	−	0.676837i	$-0.236650\pi$
$457$	−4.66228	−	8.07530i	−0.218092	−	0.377747i	−0.954225	+	0.299091i	$0.903317\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.243416	−	0.421610i	0.0113370	−	0.0196363i	−0.860301	−	0.509786i	$-0.829725\pi$
$461$	0.243416	−	0.421610i	0.0113370	−	0.0196363i	0.871638	+	0.490150i	$0.163058\pi$
$462$		0			0
$463$	−8.83772			−0.410724			−0.205362	−	0.978686i	$-0.565837\pi$
$463$	−8.83772			−0.410724			−0.205362	+	0.978686i	$0.565837\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−37.8114			−1.74970			−0.874851	−	0.484392i	$-0.839041\pi$
$467$	−37.8114			−1.74970			−0.874851	+	0.484392i	$0.839041\pi$
$468$		0			0
$469$	28.9737			1.33788
$470$		0			0
$471$		0			0
$472$		0			0
$473$	14.6491			0.673567
$474$		0			0
$475$	−0.188612	+	0.326685i	−0.00865410	+	0.0149893i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$		0			0
$481$	−0.824555	+	36.6313i	−0.0375965	+	1.67025i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.32456	+	7.49035i	−0.196368	+	0.340119i
$486$		0			0
$487$	2.74342	−	4.75174i	0.124316	−	0.215322i	−0.797149	−	0.603782i	$-0.793660\pi$
$487$	2.74342	−	4.75174i	0.124316	−	0.215322i	0.921465	+	0.388460i	$0.126993\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.9057	−	22.3533i	−0.582426	−	1.00879i	−0.995191	−	0.0979536i	$-0.968770\pi$
$491$	−12.9057	−	22.3533i	−0.582426	−	1.00879i	0.412765	−	0.910837i	$-0.364563\pi$
$492$		0			0
$493$	24.4868			1.10283
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.32456	−	2.29420i	−0.0594144	−	0.102909i
$498$		0			0
$499$	12.6491			0.566252			0.283126	−	0.959083i	$-0.408629\pi$
$499$	12.6491			0.566252			0.283126	+	0.959083i	$0.408629\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−15.9057	+	27.5495i	−0.709200	+	1.22837i	0.255954	+	0.966689i	$0.417610\pi$
$503$	−15.9057	+	27.5495i	−0.709200	+	1.22837i	−0.965154	+	0.261681i	$0.915723\pi$
$504$		0			0
$505$	15.3114	+	26.5201i	0.681348	+	1.18013i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.9189	+	18.9120i	0.483970	+	0.838261i	0.999830	−	0.0184120i	$-0.00586104\pi$
$509$	10.9189	+	18.9120i	0.483970	+	0.838261i	−0.515860	+	0.856673i	$0.672528\pi$
$510$		0			0
$511$	1.58114	−	2.73861i	0.0699455	−	0.121149i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	34.1886			1.50653
$516$		0			0
$517$	−28.8114	−	49.9028i	−1.26712	−	2.19472i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−27.0000			−1.18289			−0.591446	−	0.806345i	$-0.701443\pi$
$521$	−27.0000			−1.18289			−0.591446	+	0.806345i	$0.701443\pi$
$522$		0			0
$523$	0.581139	+	1.00656i	0.0254114	+	0.0440139i	0.878451	−	0.477832i	$-0.158577\pi$
$523$	0.581139	+	1.00656i	0.0254114	+	0.0440139i	−0.853040	+	0.521845i	$0.825244\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9.48683	+	16.4317i	−0.413253	+	0.715775i
$528$		0			0
$529$	11.1491	−	19.3108i	0.484744	−	0.839601i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.243416	+	10.8139i	−0.0105435	+	0.468403i
$534$		0			0
$535$	−14.9320	−	25.8630i	−0.645568	−	1.11816i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.74342	−	13.4120i	0.333533	−	0.577695i
$540$		0			0
$541$	−34.4868			−1.48270			−0.741352	−	0.671116i	$-0.765815\pi$
$541$	−34.4868			−1.48270			−0.741352	+	0.671116i	$0.765815\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	40.3246			1.72731
$546$		0			0
$547$	2.18861			0.0935783			0.0467891	−	0.998905i	$-0.485101\pi$
$547$	2.18861			0.0935783			0.0467891	+	0.998905i	$0.485101\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.48683			0.404153
$552$		0			0
$553$	−6.32456	+	10.9545i	−0.268947	+	0.465831i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.243416	−	0.421610i	−0.0103139	−	0.0178642i	0.860822	−	0.508905i	$-0.169950\pi$
$557$	−0.243416	−	0.421610i	−0.0103139	−	0.0178642i	−0.871136	+	0.491041i	$0.836616\pi$
$558$		0			0
$559$	−8.97367	+	4.91508i	−0.379546	+	0.207886i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.67544	−	13.2943i	0.323481	−	0.560286i	−0.657722	−	0.753260i	$-0.728480\pi$
$563$	7.67544	−	13.2943i	0.323481	−	0.560286i	0.981204	+	0.192974i	$0.0618133\pi$
$564$		0			0
$565$	20.8925	−	36.1869i	0.878955	−	1.52240i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.6491	+	20.1769i	0.488356	+	0.845858i	0.999910	−	0.0133934i	$-0.00426338\pi$
$569$	11.6491	+	20.1769i	0.488356	+	0.845858i	−0.511554	+	0.859251i	$0.670930\pi$
$570$		0			0
$571$	−8.13594			−0.340479			−0.170239	−	0.985403i	$-0.554454\pi$
$571$	−8.13594			−0.340479			−0.170239	+	0.985403i	$0.554454\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−0.135944	−	0.235461i	−0.00566924	−	0.00981941i
$576$		0			0
$577$	25.6491			1.06779			0.533893	−	0.845552i	$-0.320728\pi$
$577$	25.6491			1.06779			0.533893	+	0.845552i	$0.320728\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	24.4868	−	42.4124i	1.01589	−	1.75956i
$582$		0			0
$583$	16.7434	+	29.0004i	0.693441	+	1.20108i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.67544	+	2.90196i	0.0691530	+	0.119777i	0.898529	−	0.438915i	$-0.144637\pi$
$587$	1.67544	+	2.90196i	0.0691530	+	0.119777i	−0.829376	+	0.558691i	$0.811304\pi$
$588$		0			0
$589$	−3.67544	+	6.36606i	−0.151444	+	0.262309i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.3246			0.547174			0.273587	−	0.961847i	$-0.411790\pi$
$593$	13.3246			0.547174			0.273587	+	0.961847i	$0.411790\pi$
$594$		0			0
$595$	−10.2566	−	17.7649i	−0.420479	−	0.728291i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−39.6228			−1.61894			−0.809471	−	0.587159i	$-0.800246\pi$
$599$	−39.6228			−1.61894			−0.809471	+	0.587159i	$0.800246\pi$
$600$		0			0
$601$	−8.14911	−	14.1147i	−0.332409	−	0.575750i	0.650575	−	0.759442i	$-0.274528\pi$
$601$	−8.14911	−	14.1147i	−0.332409	−	0.575750i	−0.982984	+	0.183693i	$0.941195\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	16.9189	−	29.3043i	0.687850	−	1.19139i
$606$		0			0
$607$	−16.6491	+	28.8371i	−0.675767	+	1.17046i	0.300478	+	0.953789i	$0.402854\pi$
$607$	−16.6491	+	28.8371i	−0.675767	+	1.17046i	−0.976244	+	0.216673i	$0.930479\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	34.3925	+	20.9023i	1.39137	+	0.845618i
$612$		0			0
$613$	−0.756584	−	1.31044i	−0.0305581	−	0.0529282i	0.850342	−	0.526231i	$-0.176395\pi$
$613$	−0.756584	−	1.31044i	−0.0305581	−	0.0529282i	−0.880900	+	0.473302i	$0.843062\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.3114	+	31.7163i	−0.737189	+	1.27685i	0.216568	+	0.976268i	$0.430514\pi$
$617$	−18.3114	+	31.7163i	−0.737189	+	1.27685i	−0.953756	+	0.300581i	$0.902820\pi$
$618$		0			0
$619$	0.649111			0.0260900			0.0130450	−	0.999915i	$-0.495848\pi$
$619$	0.649111			0.0260900			0.0130450	+	0.999915i	$0.495848\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	37.9473			1.52033
$624$		0			0
$625$	−23.2719			−0.930875
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−30.4868			−1.21559
$630$		0			0
$631$	12.6491	−	21.9089i	0.503553	−	0.872180i	−0.496438	−	0.868072i	$-0.665359\pi$
$631$	12.6491	−	21.9089i	0.503553	−	0.872180i	0.999992	−	0.00410769i	$-0.00130752\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.13594	+	10.6278i	0.243497	+	0.421750i
$636$		0			0
$637$	−0.243416	+	10.8139i	−0.00964451	+	0.428463i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−20.8246	+	36.0692i	−0.822520	+	1.42465i	0.0812791	+	0.996691i	$0.474099\pi$
$641$	−20.8246	+	36.0692i	−0.822520	+	1.42465i	−0.903800	+	0.427956i	$0.859234\pi$
$642$		0			0
$643$	10.0000	−	17.3205i	0.394362	−	0.683054i	−0.598658	−	0.801005i	$-0.704299\pi$
$643$	10.0000	−	17.3205i	0.394362	−	0.683054i	0.993019	+	0.117951i	$0.0376325\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.67544	−	13.2943i	−0.301753	−	0.522651i	0.674780	−	0.738019i	$-0.264238\pi$
$647$	−7.67544	−	13.2943i	−0.301753	−	0.522651i	−0.976533	+	0.215367i	$0.930905\pi$
$648$		0			0
$649$	53.2982			2.09214
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	−0.994623	−	0.103558i	$-0.966977\pi$
$653$	−15.0000	−	25.9808i	−0.586995	−	1.01671i	0.407628	−	0.913148i	$-0.366356\pi$
$654$		0			0
$655$	−18.7018			−0.730739
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−21.4868	+	37.2163i	−0.837008	+	1.44974i	0.0553767	+	0.998466i	$0.482364\pi$
$659$	−21.4868	+	37.2163i	−0.837008	+	1.44974i	−0.892385	+	0.451275i	$0.850969\pi$
$660$		0			0
$661$	−3.75658	−	6.50659i	−0.146114	−	0.253077i	0.783674	−	0.621172i	$-0.213343\pi$
$661$	−3.75658	−	6.50659i	−0.146114	−	0.253077i	−0.929788	+	0.368095i	$0.880010\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.97367	−	6.88259i	−0.154092	−	0.266895i
$666$		0			0
$667$	−3.41886	+	5.92164i	−0.132379	+	0.229287i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	31.8114			1.22807
$672$		0			0
$673$	−13.6623	−	23.6638i	−0.526642	−	0.912171i	−0.999518	−	0.0310419i	$-0.990117\pi$
$673$	−13.6623	−	23.6638i	−0.526642	−	0.912171i	0.472876	−	0.881129i	$-0.343216\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$		0			0
$679$	6.32456	+	10.9545i	0.242714	+	0.420393i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	13.8114	−	23.9220i	0.528478	−	0.915351i	−0.470971	−	0.882149i	$-0.656096\pi$
$683$	13.8114	−	23.9220i	0.528478	−	0.915351i	0.999449	−	0.0332020i	$-0.0105705\pi$
$684$		0			0
$685$	−3.24342	+	5.61776i	−0.123925	+	0.214644i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−19.9868	−	12.1472i	−0.761438	−	0.462770i
$690$		0			0
$691$	1.41886	+	2.45754i	0.0539760	+	0.0934892i	0.891751	−	0.452527i	$-0.149477\pi$
$691$	1.41886	+	2.45754i	0.0539760	+	0.0934892i	−0.837775	+	0.546016i	$0.816144\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.83772	+	11.8433i	−0.259370	+	0.449241i
$696$		0			0
$697$	−9.00000			−0.340899
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	−11.8114			−0.445475
$704$		0			0
$705$		0			0
$706$		0			0
$707$	44.7851			1.68432
$708$		0			0
$709$	5.73025	−	9.92508i	0.215204	−	0.372744i	−0.738132	−	0.674657i	$-0.764292\pi$
$709$	5.73025	−	9.92508i	0.215204	−	0.372744i	0.953336	+	0.301912i	$0.0976250\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.64911	−	4.58839i	−0.0992100	−	0.171837i
$714$		0			0
$715$	−0.905694	+	40.2360i	−0.0338710	+	1.50474i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12.8377	+	22.2356i	−0.478766	+	0.829247i	−0.999704	−	0.0243475i	$-0.992249\pi$
$719$	−12.8377	+	22.2356i	−0.478766	+	0.829247i	0.520937	+	0.853595i	$0.325583\pi$
$720$		0			0
$721$	25.0000	−	43.3013i	0.931049	−	1.61262i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.32456	−	2.29420i	−0.0491927	−	0.0852043i
$726$		0			0
$727$	15.1623			0.562338			0.281169	−	0.959658i	$-0.409278\pi$
$727$	15.1623			0.562338			0.281169	+	0.959658i	$0.409278\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.25658	−	7.37262i	−0.157435	−	0.272686i
$732$		0			0
$733$	−35.4605			−1.30976			−0.654882	−	0.755731i	$-0.727282\pi$
$733$	−35.4605			−1.30976			−0.654882	+	0.755731i	$0.727282\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	23.6491	−	40.9615i	0.871126	−	1.50883i
$738$		0			0
$739$	11.8114	+	20.4579i	0.434489	+	0.752557i	0.997254	−	0.0740601i	$-0.0235957\pi$
$739$	11.8114	+	20.4579i	0.434489	+	0.752557i	−0.562765	+	0.826617i	$0.690262\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.16228	−	8.94133i	−0.189386	−	0.328025i	0.755660	−	0.654964i	$-0.227316\pi$
$743$	−5.16228	−	8.94133i	−0.189386	−	0.328025i	−0.945046	+	0.326939i	$0.893983\pi$
$744$		0			0
$745$	−19.9868	+	34.6182i	−0.732261	+	1.26831i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−43.6754			−1.59587
$750$		0			0
$751$	−15.3925	−	26.6606i	−0.561681	−	0.972861i	−0.997350	−	0.0727534i	$-0.976821\pi$
$751$	−15.3925	−	26.6606i	−0.561681	−	0.972861i	0.435669	−	0.900107i	$-0.356512\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	15.4868			0.563624
$756$		0			0
$757$	0.675445	+	1.16990i	0.0245495	+	0.0425209i	0.878039	−	0.478589i	$-0.158852\pi$
$757$	0.675445	+	1.16990i	0.0245495	+	0.0425209i	−0.853490	+	0.521110i	$0.825518\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$		0			0
$763$	29.4868	−	51.0727i	1.06750	−	1.84896i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−32.6491	+	17.8827i	−1.17889	+	0.645705i
$768$		0			0
$769$	−14.3246	−	24.8109i	−0.516557	−	0.894702i	−0.999815	−	0.0192247i	$-0.993880\pi$
$769$	−14.3246	−	24.8109i	−0.516557	−	0.894702i	0.483259	−	0.875478i	$-0.339453\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.32456	−	2.29420i	0.0476409	−	0.0825165i	−0.841222	−	0.540691i	$-0.818163\pi$
$773$	1.32456	−	2.29420i	0.0476409	−	0.0825165i	0.888863	+	0.458174i	$0.151496\pi$
$774$		0			0
$775$	2.05267			0.0737340
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.48683			−0.124929
$780$		0			0
$781$	−4.32456			−0.154745
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−18.3509			−0.654971
$786$		0			0
$787$	−23.4868	+	40.6804i	−0.837215	+	1.45010i	0.0549988	+	0.998486i	$0.482484\pi$
$787$	−23.4868	+	40.6804i	−0.837215	+	1.45010i	−0.892214	+	0.451613i	$0.850849\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−30.5548	−	52.9225i	−1.08640	−	1.88171i
$792$		0			0
$793$	−19.4868	+	10.6734i	−0.691998	+	0.379023i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.48683	+	16.4317i	−0.336041	+	0.582040i	−0.983684	−	0.179904i	$-0.942421\pi$
$797$	−9.48683	+	16.4317i	−0.336041	+	0.582040i	0.647643	+	0.761944i	$0.275755\pi$
$798$		0			0
$799$	−16.7434	+	29.0004i	−0.592339	+	1.02596i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.58114	−	4.47066i	−0.0910864	−	0.157766i
$804$		0			0
$805$	5.72811			0.201889
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.50000	−	2.59808i	−0.0527372	−	0.0913435i	0.838452	−	0.544976i	$-0.183461\pi$
$809$	−1.50000	−	2.59808i	−0.0527372	−	0.0913435i	−0.891189	+	0.453632i	$0.850128\pi$
$810$		0			0
$811$	−38.9737			−1.36855			−0.684275	−	0.729224i	$-0.739881\pi$
$811$	−38.9737			−1.36855			−0.684275	+	0.729224i	$0.739881\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	17.2982	−	29.9614i	0.605930	−	1.04950i
$816$		0			0
$817$	−1.64911	−	2.85634i	−0.0576951	−	0.0999308i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.32456	+	12.6865i	0.255629	+	0.442762i	0.965066	−	0.262007i	$-0.0843842\pi$
$821$	7.32456	+	12.6865i	0.255629	+	0.442762i	−0.709437	+	0.704768i	$0.751051\pi$
$822$		0			0
$823$	1.35089	−	2.33981i	0.0470890	−	0.0815606i	−0.841520	−	0.540226i	$-0.818339\pi$
$823$	1.35089	−	2.33981i	0.0470890	−	0.0815606i	0.888609	+	0.458665i	$0.151672\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−30.9737			−1.07706			−0.538530	−	0.842606i	$-0.681020\pi$
$827$	−30.9737			−1.07706			−0.538530	+	0.842606i	$0.681020\pi$
$828$		0			0
$829$	−2.91886	−	5.05562i	−0.101376	−	0.175589i	0.810876	−	0.585218i	$-0.198991\pi$
$829$	−2.91886	−	5.05562i	−0.101376	−	0.175589i	−0.912252	+	0.409630i	$0.865658\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−9.00000			−0.311832
$834$		0			0
$835$	−12.9737	−	22.4710i	−0.448972	−	0.777643i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−10.3246	+	17.8827i	−0.356443	+	0.617378i	−0.987364	−	0.158470i	$-0.949344\pi$
$839$	−10.3246	+	17.8827i	−0.356443	+	0.617378i	0.630921	+	0.775847i	$0.282677\pi$
$840$		0			0
$841$	−18.8114	+	32.5823i	−0.648669	+	1.12353i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−12.9452	−	24.9514i	−0.445328	−	0.858354i
$846$		0			0
$847$	−24.7434	−	42.8569i	−0.850194	−	1.47258i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.25658	−	7.37262i	0.145914	−	0.252730i
$852$		0			0
$853$	10.8641			0.371978			0.185989	−	0.982552i	$-0.440451\pi$
$853$	10.8641			0.371978			0.185989	+	0.982552i	$0.440451\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.350889			−0.0119862			−0.00599308	−	0.999982i	$-0.501908\pi$
$857$	−0.350889			−0.0119862			−0.00599308	+	0.999982i	$0.501908\pi$
$858$		0			0
$859$	−47.4868			−1.62023			−0.810115	−	0.586271i	$-0.800595\pi$
$859$	−47.4868			−1.62023			−0.810115	+	0.586271i	$0.800595\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.1886			−0.551067			−0.275533	−	0.961292i	$-0.588854\pi$
$863$	−16.1886			−0.551067			−0.275533	+	0.961292i	$0.588854\pi$
$864$		0			0
$865$	−2.86406	+	4.96069i	−0.0973808	+	0.168669i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.3246	+	17.8827i	0.350237	+	0.606628i
$870$		0			0
$871$	−0.743416	+	33.0267i	−0.0251897	+	1.11907i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−18.2039	+	31.5301i	−0.615405	+	1.06591i
$876$		0			0
$877$	0.432028	−	0.748295i	0.0145886	−	0.0252681i	−0.858639	−	0.512581i	$-0.828689\pi$
$877$	0.432028	−	0.748295i	0.0145886	−	0.0252681i	0.873228	+	0.487313i	$0.162023\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13.9868	+	24.2259i	0.471228	+	0.816191i	0.999458	−	0.0329099i	$-0.0104774\pi$
$881$	13.9868	+	24.2259i	0.471228	+	0.816191i	−0.528230	+	0.849101i	$0.677144\pi$
$882$		0			0
$883$	36.6491			1.23334			0.616670	−	0.787221i	$-0.288481\pi$
$883$	36.6491			1.23334			0.616670	+	0.787221i	$0.288481\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.8377	+	22.2356i	0.431049	+	0.746598i	0.996964	−	0.0778654i	$-0.0248104\pi$
$887$	12.8377	+	22.2356i	0.431049	+	0.746598i	−0.565915	+	0.824463i	$0.691477\pi$
$888$		0			0
$889$	17.9473			0.601934
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.48683	+	11.2355i	−0.217074	+	0.375982i
$894$		0			0
$895$	3.76975	+	6.52940i	0.126009	+	0.218254i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−25.8114	−	44.7066i	−0.860858	−	1.49105i
$900$		0			0
$901$	9.73025	−	16.8533i	0.324162	−	0.561464i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.9737			−0.730429
$906$		0			0
$907$	−26.1359	−	45.2688i	−0.867830	−	1.50313i	−0.864210	−	0.503132i	$-0.832181\pi$
$907$	−26.1359	−	45.2688i	−0.867830	−	1.50313i	−0.00362007	−	0.999993i	$-0.501152\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−25.9473			−0.859673			−0.429837	−	0.902907i	$-0.641429\pi$
$911$	−25.9473			−0.859673			−0.429837	+	0.902907i	$0.641429\pi$
$912$		0			0
$913$	−39.9737	−	69.2364i	−1.32294	−	2.29139i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.6754	+	23.6866i	−0.451603	+	0.782199i
$918$		0			0
$919$	14.3246	−	24.8109i	0.472523	−	0.818435i	−0.526982	−	0.849876i	$-0.676677\pi$
$919$	14.3246	−	24.8109i	0.472523	−	0.818435i	0.999506	+	0.0314417i	$0.0100099\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.64911	−	1.45098i	0.0871965	−	0.0477595i
$924$		0			0
$925$	1.64911	+	2.85634i	0.0542224	+	0.0939160i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	23.4737	−	40.6576i	0.770146	−	1.33393i	−0.167337	−	0.985900i	$-0.553517\pi$
$929$	23.4737	−	40.6576i	0.770146	−	1.33393i	0.937483	−	0.348032i	$-0.113150\pi$
$930$		0			0
$931$	−3.48683			−0.114276
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−33.4868			−1.09514
$936$		0			0
$937$	−36.2982			−1.18581			−0.592906	−	0.805272i	$-0.702019\pi$
$937$	−36.2982			−1.18581			−0.592906	+	0.805272i	$0.702019\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	52.5964			1.71460			0.857298	−	0.514821i	$-0.172142\pi$
$941$	52.5964			1.71460			0.857298	+	0.514821i	$0.172142\pi$
$942$		0			0
$943$	1.25658	−	2.17647i	0.0409200	−	0.0708755i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.48683	−	16.4317i	−0.308281	−	0.533958i	0.669706	−	0.742627i	$-0.266420\pi$
$947$	−9.48683	−	16.4317i	−0.308281	−	0.533958i	−0.977986	+	0.208669i	$0.933087\pi$
$948$		0			0
$949$	3.08114	+	1.87259i	0.100018	+	0.0607868i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−11.6491	+	20.1769i	−0.377352	+	0.653592i	−0.990676	−	0.136239i	$-0.956499\pi$
$953$	−11.6491	+	20.1769i	−0.377352	+	0.653592i	0.613324	+	0.789831i	$0.289832\pi$
$954$		0			0
$955$	−1.81139	+	3.13742i	−0.0586151	+	0.101524i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.74342	+	8.21584i	0.153173	+	0.265303i
$960$		0			0
$961$	9.00000			0.290323
$962$		0			0
$963$		0			0
$964$		0			0
$965$	19.4320	+	33.6573i	0.625539	+	1.08347i
$966$		0			0
$967$	−53.4868			−1.72002			−0.860010	−	0.510277i	$-0.829543\pi$
$967$	−53.4868			−1.72002			−0.860010	+	0.510277i	$0.829543\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.48683	−	16.4317i	0.304447	−	0.527318i	−0.672691	−	0.739923i	$-0.734862\pi$
$971$	9.48683	−	16.4317i	0.304447	−	0.527318i	0.977138	+	0.212606i	$0.0681950\pi$
$972$		0			0
$973$	10.0000	+	17.3205i	0.320585	+	0.555270i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	0.647737	−	0.761864i	$-0.275715\pi$
$977$	−10.5000	−	18.1865i	−0.335925	−	0.581839i	−0.983662	+	0.180025i	$0.942382\pi$
$978$		0			0
$979$	30.9737	−	53.6480i	0.989923	−	1.71460i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	39.6228			1.26377			0.631885	−	0.775062i	$-0.282281\pi$
$983$	39.6228			1.26377			0.631885	+	0.775062i	$0.282281\pi$
$984$		0			0
$985$	−20.5132	−	35.5298i	−0.653604	−	1.13208i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.37722			0.0755913
$990$		0			0
$991$	−21.3925	−	37.0529i	−0.679556	−	1.17703i	−0.975115	−	0.221701i	$-0.928839\pi$
$991$	−21.3925	−	37.0529i	−0.679556	−	1.17703i	0.295559	−	0.955325i	$-0.404494\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	27.5548	−	47.7263i	0.873546	−	1.51303i
$996$		0			0
$997$	1.26975	−	2.19927i	0.0402134	−	0.0696517i	−0.845218	−	0.534421i	$-0.820530\pi$
$997$	1.26975	−	2.19927i	0.0402134	−	0.0696517i	0.885432	+	0.464770i	$0.153863\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1872.2.t.p.289.1		4
3.2	odd	2		1872.2.t.n.289.2		4
4.3	odd	2		234.2.h.d.55.1	✓	4
12.11	even	2		234.2.h.e.55.2	yes	4
13.9	even	3	inner	1872.2.t.p.1153.1		4
39.35	odd	6		1872.2.t.n.1153.2		4
52.3	odd	6		3042.2.a.w.1.1		2
52.11	even	12		3042.2.b.k.1351.3		4
52.15	even	12		3042.2.b.k.1351.2		4
52.23	odd	6		3042.2.a.q.1.2		2
52.35	odd	6		234.2.h.d.217.1	yes	4
156.11	odd	12		3042.2.b.j.1351.2		4
156.23	even	6		3042.2.a.x.1.1		2
156.35	even	6		234.2.h.e.217.2	yes	4
156.107	even	6		3042.2.a.r.1.2		2
156.119	odd	12		3042.2.b.j.1351.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.h.d.55.1	✓	4	4.3	odd	2
234.2.h.d.217.1	yes	4	52.35	odd	6
234.2.h.e.55.2	yes	4	12.11	even	2
234.2.h.e.217.2	yes	4	156.35	even	6
1872.2.t.n.289.2		4	3.2	odd	2
1872.2.t.n.1153.2		4	39.35	odd	6
1872.2.t.p.289.1		4	1.1	even	1	trivial
1872.2.t.p.1153.1		4	13.9	even	3	inner
3042.2.a.q.1.2		2	52.23	odd	6
3042.2.a.r.1.2		2	156.107	even	6
3042.2.a.w.1.1		2	52.3	odd	6
3042.2.a.x.1.1		2	156.23	even	6
3042.2.b.j.1351.2		4	156.11	odd	12
3042.2.b.j.1351.3		4	156.119	odd	12
3042.2.b.k.1351.2		4	52.15	even	12
3042.2.b.k.1351.3		4	52.11	even	12

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:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.16228 q^{5} +(-1.58114 + 2.73861i) q^{7} +O(q^{10})\)	\(q-2.16228 q^{5} +(-1.58114 + 2.73861i) q^{7} +(2.58114 + 4.47066i) q^{11} +(-3.08114 - 1.87259i) q^{13} +(1.50000 - 2.59808i) q^{17} +(0.581139 - 1.00656i) q^{19} +(0.418861 + 0.725489i) q^{23} -0.324555 q^{25} +(4.08114 + 7.06874i) q^{29} -6.32456 q^{31} +(3.41886 - 5.92164i) q^{35} +(-5.08114 - 8.80079i) q^{37} +(-1.50000 - 2.59808i) q^{41} +(1.41886 - 2.45754i) q^{43} -11.1623 q^{47} +(-1.50000 - 2.59808i) q^{49} +6.48683 q^{53} +(-5.58114 - 9.66682i) q^{55} +(5.16228 - 8.94133i) q^{59} +(3.08114 - 5.33669i) q^{61} +(6.66228 + 4.04905i) q^{65} +(-4.58114 - 7.93477i) q^{67} +(-0.418861 + 0.725489i) q^{71} -1.00000 q^{73} -16.3246 q^{77} +4.00000 q^{79} -15.4868 q^{83} +(-3.24342 + 5.61776i) q^{85} +(-6.00000 - 10.3923i) q^{89} +(10.0000 - 5.47723i) q^{91} +(-1.25658 + 2.17647i) q^{95} +(2.00000 - 3.46410i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5}+O(q^{10}) \) 4 * q + 4 * q^5	\( 4 q + 4 q^{5} + 4 q^{11} - 6 q^{13} + 6 q^{17} - 4 q^{19} + 8 q^{23} + 24 q^{25} + 10 q^{29} + 20 q^{35} - 14 q^{37} - 6 q^{41} + 12 q^{43} - 32 q^{47} - 6 q^{49} - 12 q^{53} - 16 q^{55} + 8 q^{59} + 6 q^{61} + 14 q^{65} - 12 q^{67} - 8 q^{71} - 4 q^{73} - 40 q^{77} + 16 q^{79} - 24 q^{83} + 6 q^{85} - 24 q^{89} + 40 q^{91} - 24 q^{95} + 8 q^{97}+O(q^{100}) \) 4 * q + 4 * q^5 + 4 * q^11 - 6 * q^13 + 6 * q^17 - 4 * q^19 + 8 * q^23 + 24 * q^25 + 10 * q^29 + 20 * q^35 - 14 * q^37 - 6 * q^41 + 12 * q^43 - 32 * q^47 - 6 * q^49 - 12 * q^53 - 16 * q^55 + 8 * q^59 + 6 * q^61 + 14 * q^65 - 12 * q^67 - 8 * q^71 - 4 * q^73 - 40 * q^77 + 16 * q^79 - 24 * q^83 + 6 * q^85 - 24 * q^89 + 40 * q^91 - 24 * q^95 + 8 * q^97

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