LMFDB - Embedded newform 1600.2.l.e.401.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.l (of order $4$, 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			401.2
Root			$-1.65831 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1600.401
Dual form			1600.2.l.e.1201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15831 + 2.15831i) q^{3} -2.31662i q^{7} +6.31662i q^{9} +O(q^{10})$	$q+(2.15831 + 2.15831i) q^{3} -2.31662i q^{7} +6.31662i q^{9} +(-3.15831 + 3.15831i) q^{11} +(4.31662 + 4.31662i) q^{13} -1.31662 q^{17} +(0.158312 + 0.158312i) q^{19} +(5.00000 - 5.00000i) q^{21} -0.316625i q^{23} +(-7.15831 + 7.15831i) q^{27} +(2.00000 + 2.00000i) q^{29} +2.31662 q^{31} -13.6332 q^{33} +(-0.683375 + 0.683375i) q^{37} +18.6332i q^{39} -5.00000i q^{41} +(-7.63325 + 7.63325i) q^{43} -8.00000 q^{47} +1.63325 q^{49} +(-2.84169 - 2.84169i) q^{51} +(3.31662 - 3.31662i) q^{53} +0.683375i q^{57} +(1.31662 - 1.31662i) q^{59} +(9.63325 + 9.63325i) q^{61} +14.6332 q^{63} +(9.15831 + 9.15831i) q^{67} +(0.683375 - 0.683375i) q^{69} -8.63325i q^{71} +6.68338i q^{73} +(7.31662 + 7.31662i) q^{77} -4.31662 q^{79} -11.9499 q^{81} +(-7.15831 - 7.15831i) q^{83} +8.63325i q^{87} -3.94987i q^{89} +(10.0000 - 10.0000i) q^{91} +(5.00000 + 5.00000i) q^{93} +6.63325 q^{97} +(-19.9499 - 19.9499i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3}+O(q^{10}) $ 4 * q + 2 * q^3	$ 4 q + 2 q^{3} - 6 q^{11} + 4 q^{13} + 8 q^{17} - 6 q^{19} + 20 q^{21} - 22 q^{27} + 8 q^{29} - 4 q^{31} - 28 q^{33} - 16 q^{37} - 4 q^{43} - 32 q^{47} - 20 q^{49} - 18 q^{51} - 8 q^{59} + 12 q^{61} + 32 q^{63} + 30 q^{67} + 16 q^{69} + 16 q^{77} - 4 q^{79} - 8 q^{81} - 22 q^{83} + 40 q^{91} + 20 q^{93} - 40 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 6 * q^11 + 4 * q^13 + 8 * q^17 - 6 * q^19 + 20 * q^21 - 22 * q^27 + 8 * q^29 - 4 * q^31 - 28 * q^33 - 16 * q^37 - 4 * q^43 - 32 * q^47 - 20 * q^49 - 18 * q^51 - 8 * q^59 + 12 * q^61 + 32 * q^63 + 30 * q^67 + 16 * q^69 + 16 * q^77 - 4 * q^79 - 8 * q^81 - 22 * q^83 + 40 * q^91 + 20 * q^93 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.15831	+	2.15831i	1.24610	+	1.24610i	0.957427	+	0.288675i	$0.0932147\pi$
$3$	2.15831	+	2.15831i	1.24610	+	1.24610i	0.288675	+	0.957427i	$0.406785\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	2.31662i		−	0.875602i	−0.899072	−	0.437801i	$-0.855757\pi$
$7$		−	2.31662i		−	0.875602i	0.899072	−	0.437801i	$-0.144243\pi$
$8$		0			0
$9$			6.31662i			2.10554i
$10$		0			0
$11$	−3.15831	+	3.15831i	−0.952267	+	0.952267i	−0.998912	−	0.0466445i	$-0.985147\pi$
$11$	−3.15831	+	3.15831i	−0.952267	+	0.952267i	0.0466445	+	0.998912i	$0.485147\pi$
$12$		0			0
$13$	4.31662	+	4.31662i	1.19722	+	1.19722i	0.974997	+	0.222220i	$0.0713302\pi$
$13$	4.31662	+	4.31662i	1.19722	+	1.19722i	0.222220	+	0.974997i	$0.428670\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.31662			−0.319328			−0.159664	−	0.987171i	$-0.551041\pi$
$17$	−1.31662			−0.319328			−0.159664	+	0.987171i	$0.551041\pi$
$18$		0			0
$19$	0.158312	+	0.158312i	0.0363194	+	0.0363194i	0.725033	−	0.688714i	$-0.241824\pi$
$19$	0.158312	+	0.158312i	0.0363194	+	0.0363194i	−0.688714	+	0.725033i	$0.741824\pi$
$20$		0			0
$21$	5.00000	−	5.00000i	1.09109	−	1.09109i
$22$		0			0
$23$		−	0.316625i		−	0.0660208i	−0.999455	−	0.0330104i	$-0.989491\pi$
$23$		−	0.316625i		−	0.0660208i	0.999455	−	0.0330104i	$-0.0105095\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−7.15831	+	7.15831i	−1.37762	+	1.37762i
$28$		0			0
$29$	2.00000	+	2.00000i	0.371391	+	0.371391i	0.867984	−	0.496593i	$-0.165416\pi$
$29$	2.00000	+	2.00000i	0.371391	+	0.371391i	−0.496593	+	0.867984i	$0.665416\pi$
$30$		0			0
$31$	2.31662			0.416078			0.208039	−	0.978121i	$-0.433292\pi$
$31$	2.31662			0.416078			0.208039	+	0.978121i	$0.433292\pi$
$32$		0			0
$33$	−13.6332			−2.37324
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.683375	+	0.683375i	−0.112346	+	0.112346i	−0.761045	−	0.648699i	$-0.775313\pi$
$37$	−0.683375	+	0.683375i	−0.112346	+	0.112346i	0.648699	+	0.761045i	$0.275313\pi$
$38$		0			0
$39$			18.6332i			2.98371i
$40$		0			0
$41$		−	5.00000i		−	0.780869i	−0.920631	−	0.390434i	$-0.872325\pi$
$41$		−	5.00000i		−	0.780869i	0.920631	−	0.390434i	$-0.127675\pi$
$42$		0			0
$43$	−7.63325	+	7.63325i	−1.16406	+	1.16406i	−0.180481	+	0.983578i	$0.557766\pi$
$43$	−7.63325	+	7.63325i	−1.16406	+	1.16406i	−0.983578	+	0.180481i	$0.942234\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$		0			0
$49$	1.63325			0.233321
$50$		0			0
$51$	−2.84169	−	2.84169i	−0.397916	−	0.397916i
$52$		0			0
$53$	3.31662	−	3.31662i	0.455573	−	0.455573i	−0.441626	−	0.897199i	$-0.645598\pi$
$53$	3.31662	−	3.31662i	0.455573	−	0.455573i	0.897199	+	0.441626i	$0.145598\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			0.683375i			0.0905153i
$58$		0			0
$59$	1.31662	−	1.31662i	0.171410	−	0.171410i	−0.616189	−	0.787599i	$-0.711324\pi$
$59$	1.31662	−	1.31662i	0.171410	−	0.171410i	0.787599	+	0.616189i	$0.211324\pi$
$60$		0			0
$61$	9.63325	+	9.63325i	1.23341	+	1.23341i	0.962645	+	0.270766i	$0.0872770\pi$
$61$	9.63325	+	9.63325i	1.23341	+	1.23341i	0.270766	+	0.962645i	$0.412723\pi$
$62$		0			0
$63$	14.6332			1.84362
$64$		0			0
$65$		0			0
$66$		0			0
$67$	9.15831	+	9.15831i	1.11887	+	1.11887i	0.991908	+	0.126958i	$0.0405213\pi$
$67$	9.15831	+	9.15831i	1.11887	+	1.11887i	0.126958	+	0.991908i	$0.459479\pi$
$68$		0			0
$69$	0.683375	−	0.683375i	0.0822687	−	0.0822687i
$70$		0			0
$71$		−	8.63325i		−	1.02458i	−0.858813	−	0.512289i	$-0.828798\pi$
$71$		−	8.63325i		−	1.02458i	0.858813	−	0.512289i	$-0.171202\pi$
$72$		0			0
$73$			6.68338i			0.782230i	0.920342	+	0.391115i	$0.127911\pi$
$73$			6.68338i			0.782230i	−0.920342	+	0.391115i	$0.872089\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.31662	+	7.31662i	0.833807	+	0.833807i
$78$		0			0
$79$	−4.31662			−0.485658			−0.242829	−	0.970069i	$-0.578075\pi$
$79$	−4.31662			−0.485658			−0.242829	+	0.970069i	$0.578075\pi$
$80$		0			0
$81$	−11.9499			−1.32776
$82$		0			0
$83$	−7.15831	−	7.15831i	−0.785727	−	0.785727i	0.195064	−	0.980791i	$-0.437509\pi$
$83$	−7.15831	−	7.15831i	−0.785727	−	0.785727i	−0.980791	+	0.195064i	$0.937509\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			8.63325i			0.925582i
$88$		0			0
$89$		−	3.94987i		−	0.418686i	−0.977842	−	0.209343i	$-0.932868\pi$
$89$		−	3.94987i		−	0.418686i	0.977842	−	0.209343i	$-0.0671325\pi$
$90$		0			0
$91$	10.0000	−	10.0000i	1.04828	−	1.04828i
$92$		0			0
$93$	5.00000	+	5.00000i	0.518476	+	0.518476i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.63325			0.673504			0.336752	−	0.941593i	$-0.390672\pi$
$97$	6.63325			0.673504			0.336752	+	0.941593i	$0.390672\pi$
$98$		0			0
$99$	−19.9499	−	19.9499i	−2.00504	−	2.00504i
$100$		0			0
$101$	5.31662	−	5.31662i	0.529024	−	0.529024i	−0.391257	−	0.920281i	$-0.627960\pi$
$101$	5.31662	−	5.31662i	0.529024	−	0.529024i	0.920281	+	0.391257i	$0.127960\pi$
$102$		0			0
$103$		−	4.63325i		−	0.456528i	−0.973599	−	0.228264i	$-0.926695\pi$
$103$		−	4.63325i		−	0.456528i	0.973599	−	0.228264i	$-0.0733049\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.84169	+	2.84169i	−0.274716	+	0.274716i	−0.830995	−	0.556279i	$-0.812229\pi$
$107$	−2.84169	+	2.84169i	−0.274716	+	0.274716i	0.556279	+	0.830995i	$0.312229\pi$
$108$		0			0
$109$	−5.94987	−	5.94987i	−0.569895	−	0.569895i	0.362204	−	0.932099i	$-0.382024\pi$
$109$	−5.94987	−	5.94987i	−0.569895	−	0.569895i	−0.932099	+	0.362204i	$0.882024\pi$
$110$		0			0
$111$	−2.94987			−0.279990
$112$		0			0
$113$	−2.36675			−0.222645			−0.111323	−	0.993784i	$-0.535509\pi$
$113$	−2.36675			−0.222645			−0.111323	+	0.993784i	$0.535509\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−27.2665	+	27.2665i	−2.52079	+	2.52079i
$118$		0			0
$119$			3.05013i			0.279605i
$120$		0			0
$121$		−	8.94987i		−	0.813625i
$122$		0			0
$123$	10.7916	−	10.7916i	0.973042	−	0.973042i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	6.31662			0.560510			0.280255	−	0.959926i	$-0.409581\pi$
$127$	6.31662			0.560510			0.280255	+	0.959926i	$0.409581\pi$
$128$		0			0
$129$	−32.9499			−2.90107
$130$		0			0
$131$	−1.00000	−	1.00000i	−0.0873704	−	0.0873704i	0.662071	−	0.749441i	$-0.269678\pi$
$131$	−1.00000	−	1.00000i	−0.0873704	−	0.0873704i	−0.749441	+	0.662071i	$0.769678\pi$
$132$		0			0
$133$	0.366750	−	0.366750i	0.0318013	−	0.0318013i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			11.6332i			0.993896i	0.867780	+	0.496948i	$0.165546\pi$
$137$			11.6332i			0.993896i	−0.867780	+	0.496948i	$0.834454\pi$
$138$		0			0
$139$	9.15831	−	9.15831i	0.776798	−	0.776798i	−0.202487	−	0.979285i	$-0.564902\pi$
$139$	9.15831	−	9.15831i	0.776798	−	0.776798i	0.979285	+	0.202487i	$0.0649024\pi$
$140$		0			0
$141$	−17.2665	−	17.2665i	−1.45410	−	1.45410i
$142$		0			0
$143$	−27.2665			−2.28014
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.52506	+	3.52506i	0.290742	+	0.290742i
$148$		0			0
$149$	16.6332	−	16.6332i	1.36265	−	1.36265i	0.492124	−	0.870525i	$-0.336221\pi$
$149$	16.6332	−	16.6332i	1.36265	−	1.36265i	0.870525	−	0.492124i	$-0.163779\pi$
$150$		0			0
$151$			4.31662i			0.351282i	0.984454	+	0.175641i	$0.0561998\pi$
$151$			4.31662i			0.351282i	−0.984454	+	0.175641i	$0.943800\pi$
$152$		0			0
$153$		−	8.31662i		−	0.672359i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−11.3166	−	11.3166i	−0.903165	−	0.903165i	0.0925436	−	0.995709i	$-0.470500\pi$
$157$	−11.3166	−	11.3166i	−0.903165	−	0.903165i	−0.995709	+	0.0925436i	$0.970500\pi$
$158$		0			0
$159$	14.3166			1.13538
$160$		0			0
$161$	−0.733501			−0.0578080
$162$		0			0
$163$	−7.15831	−	7.15831i	−0.560682	−	0.560682i	0.368819	−	0.929501i	$-0.379762\pi$
$163$	−7.15831	−	7.15831i	−0.560682	−	0.560682i	−0.929501	+	0.368819i	$0.879762\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	18.0000i		−	1.39288i	−0.717614	−	0.696441i	$-0.754766\pi$
$167$		−	18.0000i		−	1.39288i	0.717614	−	0.696441i	$-0.245234\pi$
$168$		0			0
$169$			24.2665i			1.86665i
$170$		0			0
$171$	−1.00000	+	1.00000i	−0.0764719	+	0.0764719i
$172$		0			0
$173$	−12.9499	−	12.9499i	−0.984561	−	0.984561i	0.0153219	−	0.999883i	$-0.495123\pi$
$173$	−12.9499	−	12.9499i	−0.984561	−	0.984561i	−0.999883	+	0.0153219i	$0.995123\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.68338			0.427189
$178$		0			0
$179$	8.79156	+	8.79156i	0.657112	+	0.657112i	0.954696	−	0.297584i	$-0.0961807\pi$
$179$	8.79156	+	8.79156i	0.657112	+	0.657112i	−0.297584	+	0.954696i	$0.596181\pi$
$180$		0			0
$181$	−3.31662	+	3.31662i	−0.246523	+	0.246523i	−0.819542	−	0.573019i	$-0.805772\pi$
$181$	−3.31662	+	3.31662i	−0.246523	+	0.246523i	0.573019	+	0.819542i	$0.305772\pi$
$182$		0			0
$183$			41.5831i			3.07391i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.15831	−	4.15831i	0.304086	−	0.304086i
$188$		0			0
$189$	16.5831	+	16.5831i	1.20624	+	1.20624i
$190$		0			0
$191$	20.9499			1.51588			0.757940	−	0.652324i	$-0.226206\pi$
$191$	20.9499			1.51588			0.757940	+	0.652324i	$0.226206\pi$
$192$		0			0
$193$	4.68338			0.337117			0.168558	−	0.985692i	$-0.446089\pi$
$193$	4.68338			0.337117			0.168558	+	0.985692i	$0.446089\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.5831	−	16.5831i	1.18150	−	1.18150i	0.202143	−	0.979356i	$-0.435210\pi$
$197$	16.5831	−	16.5831i	1.18150	−	1.18150i	0.979356	−	0.202143i	$-0.0647904\pi$
$198$		0			0
$199$		−	12.6332i		−	0.895547i	−0.894147	−	0.447774i	$-0.852217\pi$
$199$		−	12.6332i		−	0.895547i	0.894147	−	0.447774i	$-0.147783\pi$
$200$		0			0
$201$			39.5330i			2.78844i
$202$		0			0
$203$	4.63325	−	4.63325i	0.325190	−	0.325190i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.00000			0.139010
$208$		0			0
$209$	−1.00000			−0.0691714
$210$		0			0
$211$	−11.7916	−	11.7916i	−0.811765	−	0.811765i	0.173134	−	0.984898i	$-0.444611\pi$
$211$	−11.7916	−	11.7916i	−0.811765	−	0.811765i	−0.984898	+	0.173134i	$0.944611\pi$
$212$		0			0
$213$	18.6332	−	18.6332i	1.27673	−	1.27673i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	5.36675i		−	0.364319i
$218$		0			0
$219$	−14.4248	+	14.4248i	−0.974738	+	0.974738i
$220$		0			0
$221$	−5.68338	−	5.68338i	−0.382305	−	0.382305i
$222$		0			0
$223$	6.00000			0.401790			0.200895	−	0.979613i	$-0.435615\pi$
$223$	6.00000			0.401790			0.200895	+	0.979613i	$0.435615\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.36675	−	4.36675i	−0.289831	−	0.289831i	0.547182	−	0.837014i	$-0.315700\pi$
$227$	−4.36675	−	4.36675i	−0.289831	−	0.289831i	−0.837014	+	0.547182i	$0.815700\pi$
$228$		0			0
$229$	−2.00000	+	2.00000i	−0.132164	+	0.132164i	−0.770094	−	0.637930i	$-0.779791\pi$
$229$	−2.00000	+	2.00000i	−0.132164	+	0.132164i	0.637930	+	0.770094i	$0.279791\pi$
$230$		0			0
$231$			31.5831i			2.07802i
$232$		0			0
$233$			11.8997i			0.779578i	0.920904	+	0.389789i	$0.127452\pi$
$233$			11.8997i			0.779578i	−0.920904	+	0.389789i	$0.872548\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−9.31662	−	9.31662i	−0.605180	−	0.605180i
$238$		0			0
$239$	18.6332			1.20528			0.602642	−	0.798011i	$-0.294115\pi$
$239$	18.6332			1.20528			0.602642	+	0.798011i	$0.294115\pi$
$240$		0			0
$241$	18.5831			1.19704			0.598522	−	0.801106i	$-0.295755\pi$
$241$	18.5831			1.19704			0.598522	+	0.801106i	$0.295755\pi$
$242$		0			0
$243$	−4.31662	−	4.31662i	−0.276912	−	0.276912i
$244$		0			0
$245$		0			0
$246$		0			0
$247$			1.36675i			0.0869642i
$248$		0			0
$249$		−	30.8997i		−	1.95819i
$250$		0			0
$251$	9.10819	−	9.10819i	0.574904	−	0.574904i	−0.358591	−	0.933495i	$-0.616743\pi$
$251$	9.10819	−	9.10819i	0.574904	−	0.574904i	0.933495	+	0.358591i	$0.116743\pi$
$252$		0			0
$253$	1.00000	+	1.00000i	0.0628695	+	0.0628695i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	16.6332			1.03755			0.518777	−	0.854910i	$-0.326388\pi$
$257$	16.6332			1.03755			0.518777	+	0.854910i	$0.326388\pi$
$258$		0			0
$259$	1.58312	+	1.58312i	0.0983705	+	0.0983705i
$260$		0			0
$261$	−12.6332	+	12.6332i	−0.781979	+	0.781979i
$262$		0			0
$263$			15.5831i			0.960897i	0.877023	+	0.480448i	$0.159526\pi$
$263$			15.5831i			0.960897i	−0.877023	+	0.480448i	$0.840474\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	8.52506	−	8.52506i	0.521725	−	0.521725i
$268$		0			0
$269$	6.31662	+	6.31662i	0.385131	+	0.385131i	0.872947	−	0.487815i	$-0.162206\pi$
$269$	6.31662	+	6.31662i	0.385131	+	0.385131i	−0.487815	+	0.872947i	$0.662206\pi$
$270$		0			0
$271$	0.949874			0.0577008			0.0288504	−	0.999584i	$-0.490815\pi$
$271$	0.949874			0.0577008			0.0288504	+	0.999584i	$0.490815\pi$
$272$		0			0
$273$	43.1662			2.61254
$274$		0			0
$275$		0			0
$276$		0			0
$277$	14.3166	−	14.3166i	0.860203	−	0.860203i	−0.131159	−	0.991361i	$-0.541870\pi$
$277$	14.3166	−	14.3166i	0.860203	−	0.860203i	0.991361	+	0.131159i	$0.0418698\pi$
$278$		0			0
$279$			14.6332i			0.876070i
$280$		0			0
$281$		−	7.26650i		−	0.433483i	−0.976229	−	0.216741i	$-0.930457\pi$
$281$		−	7.26650i		−	0.433483i	0.976229	−	0.216741i	$-0.0695429\pi$
$282$		0			0
$283$	3.84169	−	3.84169i	0.228365	−	0.228365i	−0.583645	−	0.812009i	$-0.698374\pi$
$283$	3.84169	−	3.84169i	0.228365	−	0.228365i	0.812009	+	0.583645i	$0.198374\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.5831			−0.683730
$288$		0			0
$289$	−15.2665			−0.898029
$290$		0			0
$291$	14.3166	+	14.3166i	0.839255	+	0.839255i
$292$		0			0
$293$	−18.2665	+	18.2665i	−1.06714	+	1.06714i	−0.0695627	+	0.997578i	$0.522160\pi$
$293$	−18.2665	+	18.2665i	−1.06714	+	1.06714i	−0.997578	+	0.0695627i	$0.977840\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	45.2164i		−	2.62372i
$298$		0			0
$299$	1.36675	−	1.36675i	0.0790412	−	0.0790412i
$300$		0			0
$301$	17.6834	+	17.6834i	1.01925	+	1.01925i
$302$		0			0
$303$	22.9499			1.31844
$304$		0			0
$305$		0			0
$306$		0			0
$307$	14.1583	+	14.1583i	0.808058	+	0.808058i	0.984340	−	0.176282i	$-0.0564071\pi$
$307$	14.1583	+	14.1583i	0.808058	+	0.808058i	−0.176282	+	0.984340i	$0.556407\pi$
$308$		0			0
$309$	10.0000	−	10.0000i	0.568880	−	0.568880i
$310$		0			0
$311$			12.9499i			0.734320i	0.930158	+	0.367160i	$0.119670\pi$
$311$			12.9499i			0.734320i	−0.930158	+	0.367160i	$0.880330\pi$
$312$		0			0
$313$			16.0000i			0.904373i	0.891923	+	0.452187i	$0.149356\pi$
$313$			16.0000i			0.904373i	−0.891923	+	0.452187i	$0.850644\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.9499	−	14.9499i	−0.839669	−	0.839669i	0.149147	−	0.988815i	$-0.452347\pi$
$317$	−14.9499	−	14.9499i	−0.839669	−	0.839669i	−0.988815	+	0.149147i	$0.952347\pi$
$318$		0			0
$319$	−12.6332			−0.707326
$320$		0			0
$321$	−12.2665			−0.684649
$322$		0			0
$323$	−0.208438	−	0.208438i	−0.0115978	−	0.0115978i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	25.6834i		−	1.42029i
$328$		0			0
$329$			18.5330i			1.02176i
$330$		0			0
$331$	1.15831	−	1.15831i	0.0636666	−	0.0636666i	−0.674557	−	0.738223i	$-0.735665\pi$
$331$	1.15831	−	1.15831i	0.0636666	−	0.0636666i	0.738223	+	0.674557i	$0.235665\pi$
$332$		0			0
$333$	−4.31662	−	4.31662i	−0.236550	−	0.236550i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−22.8997			−1.24743			−0.623714	−	0.781652i	$-0.714377\pi$
$337$	−22.8997			−1.24743			−0.623714	+	0.781652i	$0.714377\pi$
$338$		0			0
$339$	−5.10819	−	5.10819i	−0.277439	−	0.277439i
$340$		0			0
$341$	−7.31662	+	7.31662i	−0.396217	+	0.396217i
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.4248	−	14.4248i	0.774364	−	0.774364i	−0.204502	−	0.978866i	$-0.565557\pi$
$347$	14.4248	−	14.4248i	0.774364	−	0.774364i	0.978866	+	0.204502i	$0.0655574\pi$
$348$		0			0
$349$	24.2665	+	24.2665i	1.29896	+	1.29896i	0.929082	+	0.369874i	$0.120599\pi$
$349$	24.2665	+	24.2665i	1.29896	+	1.29896i	0.369874	+	0.929082i	$0.379401\pi$
$350$		0			0
$351$	−61.7995			−3.29861
$352$		0			0
$353$	−33.2665			−1.77060			−0.885299	−	0.465023i	$-0.846046\pi$
$353$	−33.2665			−1.77060			−0.885299	+	0.465023i	$0.846046\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−6.58312	+	6.58312i	−0.348416	+	0.348416i
$358$		0			0
$359$		−	9.68338i		−	0.511069i	−0.966800	−	0.255534i	$-0.917749\pi$
$359$		−	9.68338i		−	0.511069i	0.966800	−	0.255534i	$-0.0822514\pi$
$360$		0			0
$361$		−	18.9499i		−	0.997362i
$362$		0			0
$363$	19.3166	−	19.3166i	1.01386	−	1.01386i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−26.6332			−1.39024			−0.695122	−	0.718892i	$-0.744650\pi$
$367$	−26.6332			−1.39024			−0.695122	+	0.718892i	$0.744650\pi$
$368$		0			0
$369$	31.5831			1.64415
$370$		0			0
$371$	−7.68338	−	7.68338i	−0.398901	−	0.398901i
$372$		0			0
$373$	−2.36675	+	2.36675i	−0.122546	+	0.122546i	−0.765720	−	0.643174i	$-0.777617\pi$
$373$	−2.36675	+	2.36675i	−0.122546	+	0.122546i	0.643174	+	0.765720i	$0.277617\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			17.2665i			0.889270i
$378$		0			0
$379$	11.4248	−	11.4248i	0.586853	−	0.586853i	−0.349925	−	0.936778i	$-0.613793\pi$
$379$	11.4248	−	11.4248i	0.586853	−	0.586853i	0.936778	+	0.349925i	$0.113793\pi$
$380$		0			0
$381$	13.6332	+	13.6332i	0.698453	+	0.698453i
$382$		0			0
$383$	−16.9499			−0.866098			−0.433049	−	0.901370i	$-0.642562\pi$
$383$	−16.9499			−0.866098			−0.433049	+	0.901370i	$0.642562\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−48.2164	−	48.2164i	−2.45098	−	2.45098i
$388$		0			0
$389$	−4.26650	+	4.26650i	−0.216320	+	0.216320i	−0.806946	−	0.590626i	$-0.798881\pi$
$389$	−4.26650	+	4.26650i	−0.216320	+	0.216320i	0.590626	+	0.806946i	$0.298881\pi$
$390$		0			0
$391$			0.416876i			0.0210823i
$392$		0			0
$393$		−	4.31662i		−	0.217745i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	25.2665	+	25.2665i	1.26809	+	1.26809i	0.947074	+	0.321015i	$0.104024\pi$
$397$	25.2665	+	25.2665i	1.26809	+	1.26809i	0.321015	+	0.947074i	$0.395976\pi$
$398$		0			0
$399$	1.58312			0.0792553
$400$		0			0
$401$	2.68338			0.134001			0.0670007	−	0.997753i	$-0.478657\pi$
$401$	2.68338			0.134001			0.0670007	+	0.997753i	$0.478657\pi$
$402$		0			0
$403$	10.0000	+	10.0000i	0.498135	+	0.498135i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	4.31662i		−	0.213967i
$408$		0			0
$409$		−	19.6332i		−	0.970802i	−0.874292	−	0.485401i	$-0.838674\pi$
$409$		−	19.6332i		−	0.970802i	0.874292	−	0.485401i	$-0.161326\pi$
$410$		0			0
$411$	−25.1082	+	25.1082i	−1.23850	+	1.23850i
$412$		0			0
$413$	−3.05013	−	3.05013i	−0.150087	−	0.150087i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	39.5330			1.93594
$418$		0			0
$419$	11.5251	+	11.5251i	0.563036	+	0.563036i	0.930169	−	0.367132i	$-0.119660\pi$
$419$	11.5251	+	11.5251i	0.563036	+	0.563036i	−0.367132	+	0.930169i	$0.619660\pi$
$420$		0			0
$421$	4.63325	−	4.63325i	0.225811	−	0.225811i	−0.585129	−	0.810940i	$-0.698956\pi$
$421$	4.63325	−	4.63325i	0.225811	−	0.225811i	0.810940	+	0.585129i	$0.198956\pi$
$422$		0			0
$423$		−	50.5330i		−	2.45700i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	22.3166	−	22.3166i	1.07998	−	1.07998i
$428$		0			0
$429$	−58.8496	−	58.8496i	−2.84129	−	2.84129i
$430$		0			0
$431$	10.9499			0.527437			0.263718	−	0.964600i	$-0.415051\pi$
$431$	10.9499			0.527437			0.263718	+	0.964600i	$0.415051\pi$
$432$		0			0
$433$	−12.5831			−0.604706			−0.302353	−	0.953196i	$-0.597772\pi$
$433$	−12.5831			−0.604706			−0.302353	+	0.953196i	$0.597772\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.0501256	−	0.0501256i	0.00239783	−	0.00239783i
$438$		0			0
$439$		−	5.36675i		−	0.256141i	−0.991765	−	0.128071i	$-0.959122\pi$
$439$		−	5.36675i		−	0.256141i	0.991765	−	0.128071i	$-0.0408784\pi$
$440$		0			0
$441$			10.3166i			0.491268i
$442$		0			0
$443$	−19.1082	+	19.1082i	−0.907857	+	0.907857i	−0.996099	−	0.0882417i	$-0.971875\pi$
$443$	−19.1082	+	19.1082i	−0.907857	+	0.907857i	0.0882417	+	0.996099i	$0.471875\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	71.7995			3.39600
$448$		0			0
$449$	20.6834			0.976109			0.488054	−	0.872813i	$-0.337707\pi$
$449$	20.6834			0.976109			0.488054	+	0.872813i	$0.337707\pi$
$450$		0			0
$451$	15.7916	+	15.7916i	0.743596	+	0.743596i
$452$		0			0
$453$	−9.31662	+	9.31662i	−0.437733	+	0.437733i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	17.0000i		−	0.795226i	−0.917553	−	0.397613i	$-0.869839\pi$
$457$		−	17.0000i		−	0.795226i	0.917553	−	0.397613i	$-0.130161\pi$
$458$		0			0
$459$	9.42481	−	9.42481i	0.439913	−	0.439913i
$460$		0			0
$461$	−19.6834	−	19.6834i	−0.916746	−	0.916746i	0.0800451	−	0.996791i	$-0.474494\pi$
$461$	−19.6834	−	19.6834i	−0.916746	−	0.916746i	−0.996791	+	0.0800451i	$0.974494\pi$
$462$		0			0
$463$	24.6332			1.14480			0.572402	−	0.819973i	$-0.306012\pi$
$463$	24.6332			1.14480			0.572402	+	0.819973i	$0.306012\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.2665	+	14.2665i	0.660175	+	0.660175i	0.955421	−	0.295246i	$-0.0954017\pi$
$467$	14.2665	+	14.2665i	0.660175	+	0.660175i	−0.295246	+	0.955421i	$0.595402\pi$
$468$		0			0
$469$	21.2164	−	21.2164i	0.979681	−	0.979681i
$470$		0			0
$471$		−	48.8496i		−	2.25087i
$472$		0			0
$473$		−	48.2164i		−	2.21699i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	20.9499	+	20.9499i	0.959229	+	0.959229i
$478$		0			0
$479$	−10.2164			−0.466798			−0.233399	−	0.972381i	$-0.574985\pi$
$479$	−10.2164			−0.466798			−0.233399	+	0.972381i	$0.574985\pi$
$480$		0			0
$481$	−5.89975			−0.269005
$482$		0			0
$483$	−1.58312	−	1.58312i	−0.0720346	−	0.0720346i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			32.2164i			1.45986i	0.683520	+	0.729932i	$0.260448\pi$
$487$			32.2164i			1.45986i	−0.683520	+	0.729932i	$0.739552\pi$
$488$		0			0
$489$		−	30.8997i		−	1.39733i
$490$		0			0
$491$	−29.6332	+	29.6332i	−1.33733	+	1.33733i	−0.438693	+	0.898637i	$0.644558\pi$
$491$	−29.6332	+	29.6332i	−1.33733	+	1.33733i	−0.898637	+	0.438693i	$0.855442\pi$
$492$		0			0
$493$	−2.63325	−	2.63325i	−0.118596	−	0.118596i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−20.0000			−0.897123
$498$		0			0
$499$	−22.8997	−	22.8997i	−1.02513	−	1.02513i	−0.999676	−	0.0254576i	$-0.991896\pi$
$499$	−22.8997	−	22.8997i	−1.02513	−	1.02513i	−0.0254576	−	0.999676i	$-0.508104\pi$
$500$		0			0
$501$	38.8496	−	38.8496i	1.73567	−	1.73567i
$502$		0			0
$503$		−	31.8997i		−	1.42234i	−0.703020	−	0.711170i	$-0.748166\pi$
$503$		−	31.8997i		−	1.42234i	0.703020	−	0.711170i	$-0.251834\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−52.3747	+	52.3747i	−2.32604	+	2.32604i
$508$		0			0
$509$	−20.2665	−	20.2665i	−0.898297	−	0.898297i	0.0969887	−	0.995285i	$-0.469079\pi$
$509$	−20.2665	−	20.2665i	−0.898297	−	0.898297i	−0.995285	+	0.0969887i	$0.969079\pi$
$510$		0			0
$511$	15.4829			0.684922
$512$		0			0
$513$	−2.26650			−0.100068
$514$		0			0
$515$		0			0
$516$		0			0
$517$	25.2665	−	25.2665i	1.11122	−	1.11122i
$518$		0			0
$519$		−	55.8997i		−	2.45373i
$520$		0			0
$521$			13.6332i			0.597284i	0.954365	+	0.298642i	$0.0965336\pi$
$521$			13.6332i			0.597284i	−0.954365	+	0.298642i	$0.903466\pi$
$522$		0			0
$523$	7.47494	−	7.47494i	0.326856	−	0.326856i	−0.524534	−	0.851390i	$-0.675760\pi$
$523$	7.47494	−	7.47494i	0.326856	−	0.326856i	0.851390	+	0.524534i	$0.175760\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.05013			−0.132866
$528$		0			0
$529$	22.8997			0.995641
$530$		0			0
$531$	8.31662	+	8.31662i	0.360911	+	0.360911i
$532$		0			0
$533$	21.5831	−	21.5831i	0.934869	−	0.934869i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			37.9499i			1.63766i
$538$		0			0
$539$	−5.15831	+	5.15831i	−0.222184	+	0.222184i
$540$		0			0
$541$	11.6834	+	11.6834i	0.502308	+	0.502308i	0.912154	−	0.409847i	$-0.134418\pi$
$541$	11.6834	+	11.6834i	0.502308	+	0.502308i	−0.409847	+	0.912154i	$0.634418\pi$
$542$		0			0
$543$	−14.3166			−0.614385
$544$		0			0
$545$		0			0
$546$		0			0
$547$	15.7414	+	15.7414i	0.673055	+	0.673055i	0.958419	−	0.285364i	$-0.0921145\pi$
$547$	15.7414	+	15.7414i	0.673055	+	0.673055i	−0.285364	+	0.958419i	$0.592114\pi$
$548$		0			0
$549$	−60.8496	+	60.8496i	−2.59700	+	2.59700i
$550$		0			0
$551$			0.633250i			0.0269773i
$552$		0			0
$553$			10.0000i			0.425243i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−26.3166	−	26.3166i	−1.11507	−	1.11507i	−0.992454	−	0.122617i	$-0.960871\pi$
$557$	−26.3166	−	26.3166i	−1.11507	−	1.11507i	−0.122617	−	0.992454i	$-0.539129\pi$
$558$		0			0
$559$	−65.8997			−2.78726
$560$		0			0
$561$	17.9499			0.757844
$562$		0			0
$563$	17.9499	+	17.9499i	0.756497	+	0.756497i	0.975683	−	0.219186i	$-0.0703402\pi$
$563$	17.9499	+	17.9499i	0.756497	+	0.756497i	−0.219186	+	0.975683i	$0.570340\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			27.6834i			1.16259i
$568$		0			0
$569$			9.00000i			0.377300i	0.982044	+	0.188650i	$0.0604111\pi$
$569$			9.00000i			0.377300i	−0.982044	+	0.188650i	$0.939589\pi$
$570$		0			0
$571$	1.73350	−	1.73350i	0.0725448	−	0.0725448i	−0.669903	−	0.742448i	$-0.733665\pi$
$571$	1.73350	−	1.73350i	0.0725448	−	0.0725448i	0.742448	+	0.669903i	$0.233665\pi$
$572$		0			0
$573$	45.2164	+	45.2164i	1.88894	+	1.88894i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−15.6332			−0.650821			−0.325410	−	0.945573i	$-0.605502\pi$
$577$	−15.6332			−0.650821			−0.325410	+	0.945573i	$0.605502\pi$
$578$		0			0
$579$	10.1082	+	10.1082i	0.420082	+	0.420082i
$580$		0			0
$581$	−16.5831	+	16.5831i	−0.687984	+	0.687984i
$582$		0			0
$583$			20.9499i			0.867655i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.42481	+	9.42481i	−0.389004	+	0.389004i	−0.874332	−	0.485328i	$-0.838700\pi$
$587$	−9.42481	+	9.42481i	−0.389004	+	0.389004i	0.485328	+	0.874332i	$0.338700\pi$
$588$		0			0
$589$	0.366750	+	0.366750i	0.0151117	+	0.0151117i
$590$		0			0
$591$	71.5831			2.94454
$592$		0			0
$593$	−35.5330			−1.45917			−0.729583	−	0.683893i	$-0.760286\pi$
$593$	−35.5330			−1.45917			−0.729583	+	0.683893i	$0.760286\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	27.2665	−	27.2665i	1.11594	−	1.11594i
$598$		0			0
$599$			36.2164i			1.47976i	0.672738	+	0.739880i	$0.265118\pi$
$599$			36.2164i			1.47976i	−0.672738	+	0.739880i	$0.734882\pi$
$600$		0			0
$601$		−	22.0501i		−	0.899443i	−0.893169	−	0.449722i	$-0.851523\pi$
$601$		−	22.0501i		−	0.899443i	0.893169	−	0.449722i	$-0.148477\pi$
$602$		0			0
$603$	−57.8496	+	57.8496i	−2.35582	+	2.35582i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−21.1662			−0.859112			−0.429556	−	0.903040i	$-0.641330\pi$
$607$	−21.1662			−0.859112			−0.429556	+	0.903040i	$0.641330\pi$
$608$		0			0
$609$	20.0000			0.810441
$610$		0			0
$611$	−34.5330	−	34.5330i	−1.39706	−	1.39706i
$612$		0			0
$613$	16.2665	−	16.2665i	0.656998	−	0.656998i	−0.297671	−	0.954669i	$-0.596210\pi$
$613$	16.2665	−	16.2665i	0.656998	−	0.656998i	0.954669	+	0.297671i	$0.0962098\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			0.733501i			0.0295296i	0.999891	+	0.0147648i	$0.00469996\pi$
$617$			0.733501i			0.0295296i	−0.999891	+	0.0147648i	$0.995300\pi$
$618$		0			0
$619$	8.36675	−	8.36675i	0.336288	−	0.336288i	−0.518680	−	0.854968i	$-0.673576\pi$
$619$	8.36675	−	8.36675i	0.336288	−	0.336288i	0.854968	+	0.518680i	$0.173576\pi$
$620$		0			0
$621$	2.26650	+	2.26650i	0.0909515	+	0.0909515i
$622$		0			0
$623$	−9.15038			−0.366602
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.15831	−	2.15831i	−0.0861947	−	0.0861947i
$628$		0			0
$629$	0.899749	−	0.899749i	0.0358753	−	0.0358753i
$630$		0			0
$631$		−	24.3166i		−	0.968030i	−0.875060	−	0.484015i	$-0.839178\pi$
$631$		−	24.3166i		−	0.968030i	0.875060	−	0.484015i	$-0.160822\pi$
$632$		0			0
$633$		−	50.8997i		−	2.02308i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	7.05013	+	7.05013i	0.279336	+	0.279336i
$638$		0			0
$639$	54.5330			2.15729
$640$		0			0
$641$	−23.8997			−0.943983			−0.471992	−	0.881603i	$-0.656465\pi$
$641$	−23.8997			−0.943983			−0.471992	+	0.881603i	$0.656465\pi$
$642$		0			0
$643$	2.26650	+	2.26650i	0.0893820	+	0.0893820i	0.750384	−	0.661002i	$-0.229869\pi$
$643$	2.26650	+	2.26650i	0.0893820	+	0.0893820i	−0.661002	+	0.750384i	$0.729869\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	21.1662i		−	0.832131i	−0.909335	−	0.416066i	$-0.863409\pi$
$647$		−	21.1662i		−	0.832131i	0.909335	−	0.416066i	$-0.136591\pi$
$648$		0			0
$649$			8.31662i			0.326456i
$650$		0			0
$651$	11.5831	−	11.5831i	0.453978	−	0.453978i
$652$		0			0
$653$	−16.3668	−	16.3668i	−0.640480	−	0.640480i	0.310193	−	0.950674i	$-0.399606\pi$
$653$	−16.3668	−	16.3668i	−0.640480	−	0.640480i	−0.950674	+	0.310193i	$0.899606\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−42.2164			−1.64702
$658$		0			0
$659$	25.1583	+	25.1583i	0.980029	+	0.980029i	0.999804	−	0.0197757i	$-0.00629522\pi$
$659$	25.1583	+	25.1583i	0.980029	+	0.980029i	−0.0197757	+	0.999804i	$0.506295\pi$
$660$		0			0
$661$	−35.5831	+	35.5831i	−1.38402	+	1.38402i	−0.546684	+	0.837339i	$0.684110\pi$
$661$	−35.5831	+	35.5831i	−1.38402	+	1.38402i	−0.837339	+	0.546684i	$0.815890\pi$
$662$		0			0
$663$		−	24.5330i		−	0.952783i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.633250	−	0.633250i	0.0245195	−	0.0245195i
$668$		0			0
$669$	12.9499	+	12.9499i	0.500671	+	0.500671i
$670$		0			0
$671$	−60.8496			−2.34907
$672$		0			0
$673$	42.6332			1.64339			0.821696	−	0.569927i	$-0.193028\pi$
$673$	42.6332			1.64339			0.821696	+	0.569927i	$0.193028\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.3668	+	11.3668i	−0.436860	+	0.436860i	−0.890954	−	0.454094i	$-0.849963\pi$
$677$	−11.3668	+	11.3668i	−0.436860	+	0.436860i	0.454094	+	0.890954i	$0.349963\pi$
$678$		0			0
$679$		−	15.3668i		−	0.589722i
$680$		0			0
$681$		−	18.8496i		−	0.722319i
$682$		0			0
$683$	−5.47494	+	5.47494i	−0.209493	+	0.209493i	−0.804052	−	0.594559i	$-0.797327\pi$
$683$	−5.47494	+	5.47494i	−0.209493	+	0.209493i	0.594559	+	0.804052i	$0.297327\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.63325			−0.329379
$688$		0			0
$689$	28.6332			1.09084
$690$		0			0
$691$	26.1583	+	26.1583i	0.995109	+	0.995109i	0.999988	−	0.00487900i	$-0.00155304\pi$
$691$	26.1583	+	26.1583i	0.995109	+	0.995109i	−0.00487900	+	0.999988i	$0.501553\pi$
$692$		0			0
$693$	−46.2164	+	46.2164i	−1.75561	+	1.75561i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			6.58312i			0.249354i
$698$		0			0
$699$	−25.6834	+	25.6834i	−0.971434	+	0.971434i
$700$		0			0
$701$	−21.2665	−	21.2665i	−0.803225	−	0.803225i	0.180374	−	0.983598i	$-0.442269\pi$
$701$	−21.2665	−	21.2665i	−0.803225	−	0.803225i	−0.983598	+	0.180374i	$0.942269\pi$
$702$		0			0
$703$	−0.216374			−0.00816068
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−12.3166	−	12.3166i	−0.463214	−	0.463214i
$708$		0			0
$709$	−22.0000	+	22.0000i	−0.826227	+	0.826227i	−0.986993	−	0.160765i	$-0.948604\pi$
$709$	−22.0000	+	22.0000i	−0.826227	+	0.826227i	0.160765	+	0.986993i	$0.448604\pi$
$710$		0			0
$711$		−	27.2665i		−	1.02257i
$712$		0			0
$713$		−	0.733501i		−	0.0274698i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	40.2164	+	40.2164i	1.50191	+	1.50191i
$718$		0			0
$719$	−2.94987			−0.110012			−0.0550059	−	0.998486i	$-0.517518\pi$
$719$	−2.94987			−0.110012			−0.0550059	+	0.998486i	$0.517518\pi$
$720$		0			0
$721$	−10.7335			−0.399736
$722$		0			0
$723$	40.1082	+	40.1082i	1.49164	+	1.49164i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	2.53300i		−	0.0939437i	−0.998896	−	0.0469719i	$-0.985043\pi$
$727$		−	2.53300i		−	0.0939437i	0.998896	−	0.0469719i	$-0.0149571\pi$
$728$		0			0
$729$			17.2164i			0.637643i
$730$		0			0
$731$	10.0501	−	10.0501i	0.371717	−	0.371717i
$732$		0			0
$733$	−5.68338	−	5.68338i	−0.209920	−	0.209920i	0.594313	−	0.804234i	$-0.297424\pi$
$733$	−5.68338	−	5.68338i	−0.209920	−	0.209920i	−0.804234	+	0.594313i	$0.797424\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−57.8496			−2.13092
$738$		0			0
$739$	14.3668	+	14.3668i	0.528489	+	0.528489i	0.920122	−	0.391632i	$-0.128089\pi$
$739$	14.3668	+	14.3668i	0.528489	+	0.528489i	−0.391632	+	0.920122i	$0.628089\pi$
$740$		0			0
$741$	−2.94987	+	2.94987i	−0.108366	+	0.108366i
$742$		0			0
$743$		−	20.3166i		−	0.745345i	−0.927963	−	0.372672i	$-0.878442\pi$
$743$		−	20.3166i		−	0.745345i	0.927963	−	0.372672i	$-0.121558\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	45.2164	−	45.2164i	1.65438	−	1.65438i
$748$		0			0
$749$	6.58312	+	6.58312i	0.240542	+	0.240542i
$750$		0			0
$751$	−42.4327			−1.54839			−0.774196	−	0.632945i	$-0.781846\pi$
$751$	−42.4327			−1.54839			−0.774196	+	0.632945i	$0.781846\pi$
$752$		0			0
$753$	39.3166			1.43278
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−34.3166	+	34.3166i	−1.24726	+	1.24726i	−0.290333	+	0.956926i	$0.593766\pi$
$757$	−34.3166	+	34.3166i	−1.24726	+	1.24726i	−0.956926	+	0.290333i	$0.906234\pi$
$758$		0			0
$759$			4.31662i			0.156684i
$760$		0			0
$761$		−	32.2665i		−	1.16966i	−0.811156	−	0.584830i	$-0.801161\pi$
$761$		−	32.2665i		−	1.16966i	0.811156	−	0.584830i	$-0.198839\pi$
$762$		0			0
$763$	−13.7836	+	13.7836i	−0.499001	+	0.499001i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	11.3668			0.410430
$768$		0			0
$769$	−32.4829			−1.17136			−0.585681	−	0.810542i	$-0.699173\pi$
$769$	−32.4829			−1.17136			−0.585681	+	0.810542i	$0.699173\pi$
$770$		0			0
$771$	35.8997	+	35.8997i	1.29290	+	1.29290i
$772$		0			0
$773$	−17.3668	+	17.3668i	−0.624639	+	0.624639i	−0.946714	−	0.322075i	$-0.895620\pi$
$773$	−17.3668	+	17.3668i	−0.624639	+	0.624639i	0.322075	+	0.946714i	$0.395620\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			6.83375i			0.245159i
$778$		0			0
$779$	0.791562	−	0.791562i	0.0283607	−	0.0283607i
$780$		0			0
$781$	27.2665	+	27.2665i	0.975672	+	0.975672i
$782$		0			0
$783$	−28.6332			−1.02327
$784$		0			0
$785$		0			0
$786$		0			0
$787$	7.00000	+	7.00000i	0.249523	+	0.249523i	0.820775	−	0.571252i	$-0.193542\pi$
$787$	7.00000	+	7.00000i	0.249523	+	0.249523i	−0.571252	+	0.820775i	$0.693542\pi$
$788$		0			0
$789$	−33.6332	+	33.6332i	−1.19738	+	1.19738i
$790$		0			0
$791$			5.48287i			0.194949i
$792$		0			0
$793$			83.1662i			2.95332i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.6332	−	15.6332i	−0.553758	−	0.553758i	0.373765	−	0.927523i	$-0.378067\pi$
$797$	−15.6332	−	15.6332i	−0.553758	−	0.553758i	−0.927523	+	0.373765i	$0.878067\pi$
$798$		0			0
$799$	10.5330			0.372631
$800$		0			0
$801$	24.9499			0.881560
$802$		0			0
$803$	−21.1082	−	21.1082i	−0.744892	−	0.744892i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			27.2665i			0.959826i
$808$		0			0
$809$			38.5330i			1.35475i	0.735639	+	0.677374i	$0.236882\pi$
$809$			38.5330i			1.35475i	−0.735639	+	0.677374i	$0.763118\pi$
$810$		0			0
$811$	37.6332	−	37.6332i	1.32148	−	1.32148i	0.408905	−	0.912577i	$-0.365911\pi$
$811$	37.6332	−	37.6332i	1.32148	−	1.32148i	0.912577	−	0.408905i	$-0.134089\pi$
$812$		0			0
$813$	2.05013	+	2.05013i	0.0719010	+	0.0719010i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.41688			−0.0845558
$818$		0			0
$819$	63.1662	+	63.1662i	2.20721	+	2.20721i
$820$		0			0
$821$	−1.73350	+	1.73350i	−0.0604996	+	0.0604996i	−0.736709	−	0.676210i	$-0.763621\pi$
$821$	−1.73350	+	1.73350i	−0.0604996	+	0.0604996i	0.676210	+	0.736709i	$0.263621\pi$
$822$		0			0
$823$			9.89975i			0.345084i	0.985002	+	0.172542i	$0.0551980\pi$
$823$			9.89975i			0.345084i	−0.985002	+	0.172542i	$0.944802\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.84169	+	7.84169i	−0.272682	+	0.272682i	−0.830179	−	0.557497i	$-0.811762\pi$
$827$	−7.84169	+	7.84169i	−0.272682	+	0.272682i	0.557497	+	0.830179i	$0.311762\pi$
$828$		0			0
$829$	−0.733501	−	0.733501i	−0.0254755	−	0.0254755i	0.694254	−	0.719730i	$-0.255734\pi$
$829$	−0.733501	−	0.733501i	−0.0254755	−	0.0254755i	−0.719730	+	0.694254i	$0.755734\pi$
$830$		0			0
$831$	61.7995			2.14380
$832$		0			0
$833$	−2.15038			−0.0745061
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−16.5831	+	16.5831i	−0.573197	+	0.573197i
$838$		0			0
$839$		−	2.63325i		−	0.0909099i	−0.998966	−	0.0454549i	$-0.985526\pi$
$839$		−	2.63325i		−	0.0909099i	0.998966	−	0.0454549i	$-0.0144737\pi$
$840$		0			0
$841$		−	21.0000i		−	0.724138i
$842$		0			0
$843$	15.6834	−	15.6834i	0.540164	−	0.540164i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−20.7335			−0.712412
$848$		0			0
$849$	16.5831			0.569131
$850$		0			0
$851$	0.216374	+	0.216374i	0.00741719	+	0.00741719i
$852$		0			0
$853$	20.3668	−	20.3668i	0.697344	−	0.697344i	−0.266493	−	0.963837i	$-0.585865\pi$
$853$	20.3668	−	20.3668i	0.697344	−	0.697344i	0.963837	+	0.266493i	$0.0858648\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			21.6332i			0.738978i	0.929235	+	0.369489i	$0.120467\pi$
$857$			21.6332i			0.738978i	−0.929235	+	0.369489i	$0.879533\pi$
$858$		0			0
$859$	−22.4248	+	22.4248i	−0.765125	+	0.765125i	−0.977244	−	0.212119i	$-0.931964\pi$
$859$	−22.4248	+	22.4248i	−0.765125	+	0.765125i	0.212119	+	0.977244i	$0.431964\pi$
$860$		0			0
$861$	−25.0000	−	25.0000i	−0.851998	−	0.851998i
$862$		0			0
$863$	20.5330			0.698951			0.349476	−	0.936945i	$-0.386360\pi$
$863$	20.5330			0.698951			0.349476	+	0.936945i	$0.386360\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−32.9499	−	32.9499i	−1.11904	−	1.11904i
$868$		0			0
$869$	13.6332	−	13.6332i	0.462476	−	0.462476i
$870$		0			0
$871$			79.0660i			2.67905i
$872$		0			0
$873$			41.8997i			1.41809i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.41688	+	6.41688i	0.216683	+	0.216683i	0.807099	−	0.590416i	$-0.201036\pi$
$877$	6.41688	+	6.41688i	0.216683	+	0.216683i	−0.590416	+	0.807099i	$0.701036\pi$
$878$		0			0
$879$	−78.8496			−2.65953
$880$		0			0
$881$	37.8997			1.27687			0.638437	−	0.769674i	$-0.279581\pi$
$881$	37.8997			1.27687			0.638437	+	0.769674i	$0.279581\pi$
$882$		0			0
$883$	22.1583	+	22.1583i	0.745687	+	0.745687i	0.973666	−	0.227979i	$-0.0732119\pi$
$883$	22.1583	+	22.1583i	0.745687	+	0.745687i	−0.227979	+	0.973666i	$0.573212\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			46.5330i			1.56243i	0.624265	+	0.781213i	$0.285399\pi$
$887$			46.5330i			1.56243i	−0.624265	+	0.781213i	$0.714601\pi$
$888$		0			0
$889$		−	14.6332i		−	0.490783i
$890$		0			0
$891$	37.7414	−	37.7414i	1.26439	−	1.26439i
$892$		0			0
$893$	−1.26650	−	1.26650i	−0.0423818	−	0.0423818i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	5.89975			0.196987
$898$		0			0
$899$	4.63325	+	4.63325i	0.154528	+	0.154528i
$900$		0			0
$901$	−4.36675	+	4.36675i	−0.145478	+	0.145478i
$902$		0			0
$903$			76.3325i			2.54019i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	13.6332	−	13.6332i	0.452685	−	0.452685i	−0.443560	−	0.896245i	$-0.646285\pi$
$907$	13.6332	−	13.6332i	0.452685	−	0.452685i	0.896245	+	0.443560i	$0.146285\pi$
$908$		0			0
$909$	33.5831	+	33.5831i	1.11388	+	1.11388i
$910$		0			0
$911$	41.1662			1.36390			0.681949	−	0.731399i	$-0.261132\pi$
$911$	41.1662			1.36390			0.681949	+	0.731399i	$0.261132\pi$
$912$		0			0
$913$	45.2164			1.49644
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.31662	+	2.31662i	−0.0765017	+	0.0765017i
$918$		0			0
$919$			4.41688i			0.145699i	0.997343	+	0.0728496i	$0.0232093\pi$
$919$			4.41688i			0.145699i	−0.997343	+	0.0728496i	$0.976791\pi$
$920$		0			0
$921$			61.1161i			2.01384i
$922$		0			0
$923$	37.2665	−	37.2665i	1.22664	−	1.22664i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	29.2665			0.961238
$928$		0			0
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	0.258564	+	0.258564i	0.00847408	+	0.00847408i
$932$		0			0
$933$	−27.9499	+	27.9499i	−0.915038	+	0.915038i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			35.9499i			1.17443i	0.809431	+	0.587216i	$0.199776\pi$
$937$			35.9499i			1.17443i	−0.809431	+	0.587216i	$0.800224\pi$
$938$		0			0
$939$	−34.5330	+	34.5330i	−1.12694	+	1.12694i
$940$		0			0
$941$	8.94987	+	8.94987i	0.291758	+	0.291758i	0.837774	−	0.546017i	$-0.183856\pi$
$941$	8.94987	+	8.94987i	0.291758	+	0.291758i	−0.546017	+	0.837774i	$0.683856\pi$
$942$		0			0
$943$	−1.58312			−0.0515536
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.41688	+	5.41688i	0.176025	+	0.176025i	0.789620	−	0.613596i	$-0.210277\pi$
$947$	5.41688	+	5.41688i	0.176025	+	0.176025i	−0.613596	+	0.789620i	$0.710277\pi$
$948$		0			0
$949$	−28.8496	+	28.8496i	−0.936498	+	0.936498i
$950$		0			0
$951$		−	64.5330i		−	2.09263i
$952$		0			0
$953$			2.36675i			0.0766666i	0.999265	+	0.0383333i	$0.0122049\pi$
$953$			2.36675i			0.0766666i	−0.999265	+	0.0383333i	$0.987795\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−27.2665	−	27.2665i	−0.881401	−	0.881401i
$958$		0			0
$959$	26.9499			0.870257
$960$		0			0
$961$	−25.6332			−0.826879
$962$		0			0
$963$	−17.9499	−	17.9499i	−0.578427	−	0.578427i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	26.6332i		−	0.856468i	−0.903668	−	0.428234i	$-0.859136\pi$
$967$		−	26.6332i		−	0.856468i	0.903668	−	0.428234i	$-0.140864\pi$
$968$		0			0
$969$		−	0.899749i		−	0.0289041i
$970$		0			0
$971$	−37.4749	+	37.4749i	−1.20263	+	1.20263i	−0.229264	+	0.973364i	$0.573632\pi$
$971$	−37.4749	+	37.4749i	−1.20263	+	1.20263i	−0.973364	+	0.229264i	$0.926368\pi$
$972$		0			0
$973$	−21.2164	−	21.2164i	−0.680166	−	0.680166i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	56.3826			1.80384			0.901920	−	0.431903i	$-0.142158\pi$
$977$	56.3826			1.80384			0.901920	+	0.431903i	$0.142158\pi$
$978$		0			0
$979$	12.4749	+	12.4749i	0.398701	+	0.398701i
$980$		0			0
$981$	37.5831	−	37.5831i	1.19994	−	1.19994i
$982$		0			0
$983$			28.3166i			0.903160i	0.892231	+	0.451580i	$0.149139\pi$
$983$			28.3166i			0.903160i	−0.892231	+	0.451580i	$0.850861\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−40.0000	+	40.0000i	−1.27321	+	1.27321i
$988$		0			0
$989$	2.41688	+	2.41688i	0.0768522	+	0.0768522i
$990$		0			0
$991$	−49.4829			−1.57188			−0.785938	−	0.618306i	$-0.787819\pi$
$991$	−49.4829			−1.57188			−0.785938	+	0.618306i	$0.787819\pi$
$992$		0			0
$993$	5.00000			0.158670
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.94987	+	2.94987i	−0.0934235	+	0.0934235i	−0.752274	−	0.658850i	$-0.771043\pi$
$997$	−2.94987	+	2.94987i	−0.0934235	+	0.0934235i	0.658850	+	0.752274i	$0.271043\pi$
$998$		0			0
$999$		−	9.78363i		−	0.309540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.l.e.401.2		4
4.3	odd	2		400.2.l.d.301.1	yes	4
5.2	odd	4		1600.2.q.d.849.2		4
5.3	odd	4		1600.2.q.c.849.1		4
5.4	even	2		1600.2.l.d.401.1		4
16.5	even	4	inner	1600.2.l.e.1201.2		4
16.11	odd	4		400.2.l.d.101.1	✓	4
20.3	even	4		400.2.q.c.349.2		4
20.7	even	4		400.2.q.d.349.1		4
20.19	odd	2		400.2.l.e.301.2	yes	4
80.27	even	4		400.2.q.c.149.2		4
80.37	odd	4		1600.2.q.c.49.1		4
80.43	even	4		400.2.q.d.149.1		4
80.53	odd	4		1600.2.q.d.49.2		4
80.59	odd	4		400.2.l.e.101.2	yes	4
80.69	even	4		1600.2.l.d.1201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.d.101.1	✓	4	16.11	odd	4
400.2.l.d.301.1	yes	4	4.3	odd	2
400.2.l.e.101.2	yes	4	80.59	odd	4
400.2.l.e.301.2	yes	4	20.19	odd	2
400.2.q.c.149.2		4	80.27	even	4
400.2.q.c.349.2		4	20.3	even	4
400.2.q.d.149.1		4	80.43	even	4
400.2.q.d.349.1		4	20.7	even	4
1600.2.l.d.401.1		4	5.4	even	2
1600.2.l.d.1201.1		4	80.69	even	4
1600.2.l.e.401.2		4	1.1	even	1	trivial
1600.2.l.e.1201.2		4	16.5	even	4	inner
1600.2.q.c.49.1		4	80.37	odd	4
1600.2.q.c.849.1		4	5.3	odd	4
1600.2.q.d.49.2		4	80.53	odd	4
1600.2.q.d.849.2		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.15831 + 2.15831i) q^{3} -2.31662i q^{7} +6.31662i q^{9} +O(q^{10})\)	\(q+(2.15831 + 2.15831i) q^{3} -2.31662i q^{7} +6.31662i q^{9} +(-3.15831 + 3.15831i) q^{11} +(4.31662 + 4.31662i) q^{13} -1.31662 q^{17} +(0.158312 + 0.158312i) q^{19} +(5.00000 - 5.00000i) q^{21} -0.316625i q^{23} +(-7.15831 + 7.15831i) q^{27} +(2.00000 + 2.00000i) q^{29} +2.31662 q^{31} -13.6332 q^{33} +(-0.683375 + 0.683375i) q^{37} +18.6332i q^{39} -5.00000i q^{41} +(-7.63325 + 7.63325i) q^{43} -8.00000 q^{47} +1.63325 q^{49} +(-2.84169 - 2.84169i) q^{51} +(3.31662 - 3.31662i) q^{53} +0.683375i q^{57} +(1.31662 - 1.31662i) q^{59} +(9.63325 + 9.63325i) q^{61} +14.6332 q^{63} +(9.15831 + 9.15831i) q^{67} +(0.683375 - 0.683375i) q^{69} -8.63325i q^{71} +6.68338i q^{73} +(7.31662 + 7.31662i) q^{77} -4.31662 q^{79} -11.9499 q^{81} +(-7.15831 - 7.15831i) q^{83} +8.63325i q^{87} -3.94987i q^{89} +(10.0000 - 10.0000i) q^{91} +(5.00000 + 5.00000i) q^{93} +6.63325 q^{97} +(-19.9499 - 19.9499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3}+O(q^{10}) \) 4 * q + 2 * q^3	\( 4 q + 2 q^{3} - 6 q^{11} + 4 q^{13} + 8 q^{17} - 6 q^{19} + 20 q^{21} - 22 q^{27} + 8 q^{29} - 4 q^{31} - 28 q^{33} - 16 q^{37} - 4 q^{43} - 32 q^{47} - 20 q^{49} - 18 q^{51} - 8 q^{59} + 12 q^{61} + 32 q^{63} + 30 q^{67} + 16 q^{69} + 16 q^{77} - 4 q^{79} - 8 q^{81} - 22 q^{83} + 40 q^{91} + 20 q^{93} - 40 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 6 * q^11 + 4 * q^13 + 8 * q^17 - 6 * q^19 + 20 * q^21 - 22 * q^27 + 8 * q^29 - 4 * q^31 - 28 * q^33 - 16 * q^37 - 4 * q^43 - 32 * q^47 - 20 * q^49 - 18 * q^51 - 8 * q^59 + 12 * q^61 + 32 * q^63 + 30 * q^67 + 16 * q^69 + 16 * q^77 - 4 * q^79 - 8 * q^81 - 22 * q^83 + 40 * q^91 + 20 * q^93 - 40 * q^99

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