LMFDB - Embedded newform 1600.2.q.d.849.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(49,1600)]

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, 1, 2]))

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

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

chi := DirichletCharacter("1600.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.q (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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			849.2
Root			$-1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.d.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15831 - 2.15831i) q^{3} +2.31662 q^{7} -6.31662i q^{9} +O(q^{10})$	$q+(2.15831 - 2.15831i) q^{3} +2.31662 q^{7} -6.31662i q^{9} +(-3.15831 + 3.15831i) q^{11} +(4.31662 - 4.31662i) q^{13} -1.31662i q^{17} +(-0.158312 - 0.158312i) q^{19} +(5.00000 - 5.00000i) q^{21} -0.316625 q^{23} +(-7.15831 - 7.15831i) q^{27} +(-2.00000 - 2.00000i) q^{29} +2.31662 q^{31} +13.6332i q^{33} +(-0.683375 - 0.683375i) q^{37} -18.6332i q^{39} -5.00000i q^{41} +(7.63325 + 7.63325i) q^{43} -8.00000i q^{47} -1.63325 q^{49} +(-2.84169 - 2.84169i) q^{51} +(-3.31662 - 3.31662i) q^{53} -0.683375 q^{57} +(-1.31662 + 1.31662i) q^{59} +(9.63325 + 9.63325i) q^{61} -14.6332i q^{63} +(-9.15831 + 9.15831i) q^{67} +(-0.683375 + 0.683375i) q^{69} -8.63325i q^{71} +6.68338 q^{73} +(-7.31662 + 7.31662i) q^{77} +4.31662 q^{79} -11.9499 q^{81} +(-7.15831 + 7.15831i) q^{83} -8.63325 q^{87} +3.94987i q^{89} +(10.0000 - 10.0000i) q^{91} +(5.00000 - 5.00000i) q^{93} +6.63325i q^{97} +(19.9499 + 19.9499i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 - 4 * q^7	$ 4 q + 2 q^{3} - 4 q^{7} - 6 q^{11} + 4 q^{13} + 6 q^{19} + 20 q^{21} + 12 q^{23} - 22 q^{27} - 8 q^{29} - 4 q^{31} - 16 q^{37} + 4 q^{43} + 20 q^{49} - 18 q^{51} - 16 q^{57} + 8 q^{59} + 12 q^{61} - 30 q^{67} - 16 q^{69} + 40 q^{73} - 16 q^{77} + 4 q^{79} - 8 q^{81} - 22 q^{83} - 8 q^{87} + 40 q^{91} + 20 q^{93} + 40 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^7 - 6 * q^11 + 4 * q^13 + 6 * q^19 + 20 * q^21 + 12 * q^23 - 22 * q^27 - 8 * q^29 - 4 * q^31 - 16 * q^37 + 4 * q^43 + 20 * q^49 - 18 * q^51 - 16 * q^57 + 8 * q^59 + 12 * q^61 - 30 * q^67 - 16 * q^69 + 40 * q^73 - 16 * q^77 + 4 * q^79 - 8 * q^81 - 22 * q^83 - 8 * q^87 + 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	0.288675	−	0.957427i	$-0.406785\pi$
$3$	2.15831	−	2.15831i	1.24610	−	1.24610i	0.957427	−	0.288675i	$-0.0932147\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.31662			0.875602			0.437801	−	0.899072i	$-0.355757\pi$
$7$	2.31662			0.875602			0.437801	+	0.899072i	$0.355757\pi$
$8$		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	0.222220	−	0.974997i	$-0.428670\pi$
$13$	4.31662	−	4.31662i	1.19722	−	1.19722i	0.974997	−	0.222220i	$-0.0713302\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	1.31662i		−	0.319328i	−0.987171	−	0.159664i	$-0.948959\pi$
$17$		−	1.31662i		−	0.319328i	0.987171	−	0.159664i	$-0.0510411\pi$
$18$		0			0
$19$	−0.158312	−	0.158312i	−0.0363194	−	0.0363194i	0.688714	−	0.725033i	$-0.258176\pi$
$19$	−0.158312	−	0.158312i	−0.0363194	−	0.0363194i	−0.725033	+	0.688714i	$0.758176\pi$
$20$		0			0
$21$	5.00000	−	5.00000i	1.09109	−	1.09109i
$22$		0			0
$23$	−0.316625			−0.0660208			−0.0330104	−	0.999455i	$-0.510509\pi$
$23$	−0.316625			−0.0660208			−0.0330104	+	0.999455i	$0.510509\pi$
$24$		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	0.496593	−	0.867984i	$-0.334584\pi$
$29$	−2.00000	−	2.00000i	−0.371391	−	0.371391i	−0.867984	+	0.496593i	$0.834584\pi$
$30$		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
$33$			13.6332i			2.37324i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.683375	−	0.683375i	−0.112346	−	0.112346i	0.648699	−	0.761045i	$-0.275313\pi$
$37$	−0.683375	−	0.683375i	−0.112346	−	0.112346i	−0.761045	+	0.648699i	$0.775313\pi$
$38$		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	0.983578	+	0.180481i	$0.0577655\pi$
$43$	7.63325	+	7.63325i	1.16406	+	1.16406i	0.180481	+	0.983578i	$0.442234\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		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	$-0.354402\pi$
$53$	−3.31662	−	3.31662i	−0.455573	−	0.455573i	−0.897199	+	0.441626i	$0.854402\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.683375			−0.0905153
$58$		0			0
$59$	−1.31662	+	1.31662i	−0.171410	+	0.171410i	−0.787599	−	0.616189i	$-0.788676\pi$
$59$	−1.31662	+	1.31662i	−0.171410	+	0.171410i	0.616189	+	0.787599i	$0.288676\pi$
$60$		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
$63$		−	14.6332i		−	1.84362i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−9.15831	+	9.15831i	−1.11887	+	1.11887i	−0.126958	+	0.991908i	$0.540521\pi$
$67$	−9.15831	+	9.15831i	−1.11887	+	1.11887i	−0.991908	+	0.126958i	$0.959479\pi$
$68$		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
$73$	6.68338			0.782230			0.391115	−	0.920342i	$-0.372089\pi$
$73$	6.68338			0.782230			0.391115	+	0.920342i	$0.372089\pi$
$74$		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	$-0.421925\pi$
$79$	4.31662			0.485658			0.242829	+	0.970069i	$0.421925\pi$
$80$		0			0
$81$	−11.9499			−1.32776
$82$		0			0
$83$	−7.15831	+	7.15831i	−0.785727	+	0.785727i	−0.980791	−	0.195064i	$-0.937509\pi$
$83$	−7.15831	+	7.15831i	−0.785727	+	0.785727i	0.195064	+	0.980791i	$0.437509\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−8.63325			−0.925582
$88$		0			0
$89$			3.94987i			0.418686i	0.977842	+	0.209343i	$0.0671325\pi$
$89$			3.94987i			0.418686i	−0.977842	+	0.209343i	$0.932868\pi$
$90$		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
$97$			6.63325i			0.673504i	0.941593	+	0.336752i	$0.109328\pi$
$97$			6.63325i			0.673504i	−0.941593	+	0.336752i	$0.890672\pi$
$98$		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
$103$	−4.63325			−0.456528			−0.228264	−	0.973599i	$-0.573305\pi$
$103$	−4.63325			−0.456528			−0.228264	+	0.973599i	$0.573305\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.84169	−	2.84169i	−0.274716	−	0.274716i	0.556279	−	0.830995i	$-0.312229\pi$
$107$	−2.84169	−	2.84169i	−0.274716	−	0.274716i	−0.830995	+	0.556279i	$0.812229\pi$
$108$		0			0
$109$	5.94987	+	5.94987i	0.569895	+	0.569895i	0.932099	−	0.362204i	$-0.117976\pi$
$109$	5.94987	+	5.94987i	0.569895	+	0.569895i	−0.362204	+	0.932099i	$0.617976\pi$
$110$		0			0
$111$	−2.94987			−0.279990
$112$		0			0
$113$			2.36675i			0.222645i	0.993784	+	0.111323i	$0.0355087\pi$
$113$			2.36675i			0.222645i	−0.993784	+	0.111323i	$0.964491\pi$
$114$		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
$127$			6.31662i			0.560510i	0.959926	+	0.280255i	$0.0904190\pi$
$127$			6.31662i			0.560510i	−0.959926	+	0.280255i	$0.909581\pi$
$128$		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
$137$	−11.6332			−0.993896			−0.496948	−	0.867780i	$-0.665546\pi$
$137$	−11.6332			−0.993896			−0.496948	+	0.867780i	$0.665546\pi$
$138$		0			0
$139$	−9.15831	+	9.15831i	−0.776798	+	0.776798i	−0.979285	−	0.202487i	$-0.935098\pi$
$139$	−9.15831	+	9.15831i	−0.776798	+	0.776798i	0.202487	+	0.979285i	$0.435098\pi$
$140$		0			0
$141$	−17.2665	−	17.2665i	−1.45410	−	1.45410i
$142$		0			0
$143$			27.2665i			2.28014i
$144$		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	$0.663779\pi$
$149$	−16.6332	+	16.6332i	−1.36265	+	1.36265i	−0.870525	+	0.492124i	$0.836221\pi$
$150$		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
$153$	−8.31662			−0.672359
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.3166	−	11.3166i	0.903165	−	0.903165i	−0.0925436	−	0.995709i	$-0.529500\pi$
$157$	11.3166	−	11.3166i	0.903165	−	0.903165i	0.995709	+	0.0925436i	$0.0294998\pi$
$158$		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	−0.929501	−	0.368819i	$-0.879762\pi$
$163$	−7.15831	+	7.15831i	−0.560682	+	0.560682i	0.368819	+	0.929501i	$0.379762\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$		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	−0.999883	−	0.0153219i	$-0.995123\pi$
$173$	−12.9499	+	12.9499i	−0.984561	+	0.984561i	0.0153219	+	0.999883i	$0.495123\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			5.68338i			0.427189i
$178$		0			0
$179$	−8.79156	−	8.79156i	−0.657112	−	0.657112i	0.297584	−	0.954696i	$-0.403819\pi$
$179$	−8.79156	−	8.79156i	−0.657112	−	0.657112i	−0.954696	+	0.297584i	$0.903819\pi$
$180$		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
$183$	41.5831			3.07391
$184$		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
$193$		−	4.68338i		−	0.337117i	−0.985692	−	0.168558i	$-0.946089\pi$
$193$		−	4.68338i		−	0.337117i	0.985692	−	0.168558i	$-0.0539112\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.5831	+	16.5831i	1.18150	+	1.18150i	0.979356	+	0.202143i	$0.0647904\pi$
$197$	16.5831	+	16.5831i	1.18150	+	1.18150i	0.202143	+	0.979356i	$0.435210\pi$
$198$		0			0
$199$			12.6332i			0.895547i	0.894147	+	0.447774i	$0.147783\pi$
$199$			12.6332i			0.895547i	−0.894147	+	0.447774i	$0.852217\pi$
$200$		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
$207$			2.00000i			0.139010i
$208$		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
$217$	5.36675			0.364319
$218$		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
$223$		−	6.00000i		−	0.401790i	−0.979613	−	0.200895i	$-0.935615\pi$
$223$		−	6.00000i		−	0.401790i	0.979613	−	0.200895i	$-0.0643850\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.36675	−	4.36675i	0.289831	−	0.289831i	−0.547182	−	0.837014i	$-0.684300\pi$
$227$	4.36675	−	4.36675i	0.289831	−	0.289831i	0.837014	+	0.547182i	$0.184300\pi$
$228$		0			0
$229$	2.00000	−	2.00000i	0.132164	−	0.132164i	−0.637930	−	0.770094i	$-0.720209\pi$
$229$	2.00000	−	2.00000i	0.132164	−	0.132164i	0.770094	+	0.637930i	$0.220209\pi$
$230$		0			0
$231$			31.5831i			2.07802i
$232$		0			0
$233$	11.8997			0.779578			0.389789	−	0.920904i	$-0.372548\pi$
$233$	11.8997			0.779578			0.389789	+	0.920904i	$0.372548\pi$
$234$		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	$-0.705885\pi$
$239$	−18.6332			−1.20528			−0.602642	+	0.798011i	$0.705885\pi$
$240$		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
$247$	−1.36675			−0.0869642
$248$		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
$257$			16.6332i			1.03755i	0.854910	+	0.518777i	$0.173612\pi$
$257$			16.6332i			1.03755i	−0.854910	+	0.518777i	$0.826388\pi$
$258$		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
$263$	15.5831			0.960897			0.480448	−	0.877023i	$-0.340474\pi$
$263$	15.5831			0.960897			0.480448	+	0.877023i	$0.340474\pi$
$264$		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	0.487815	−	0.872947i	$-0.337794\pi$
$269$	−6.31662	−	6.31662i	−0.385131	−	0.385131i	−0.872947	+	0.487815i	$0.837794\pi$
$270$		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
$273$		−	43.1662i		−	2.61254i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	14.3166	+	14.3166i	0.860203	+	0.860203i	0.991361	−	0.131159i	$-0.0418698\pi$
$277$	14.3166	+	14.3166i	0.860203	+	0.860203i	−0.131159	+	0.991361i	$0.541870\pi$
$278$		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	$-0.301626\pi$
$283$	−3.84169	−	3.84169i	−0.228365	−	0.228365i	−0.812009	+	0.583645i	$0.801626\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	11.5831i		−	0.683730i
$288$		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	0.997578	+	0.0695627i	$0.0221604\pi$
$293$	18.2665	+	18.2665i	1.06714	+	1.06714i	0.0695627	+	0.997578i	$0.477840\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	45.2164			2.62372
$298$		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
$303$		−	22.9499i		−	1.31844i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−14.1583	+	14.1583i	−0.808058	+	0.808058i	−0.984340	−	0.176282i	$-0.943593\pi$
$307$	−14.1583	+	14.1583i	−0.808058	+	0.808058i	0.176282	+	0.984340i	$0.443593\pi$
$308$		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
$313$	16.0000			0.904373			0.452187	−	0.891923i	$-0.350644\pi$
$313$	16.0000			0.904373			0.452187	+	0.891923i	$0.350644\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.9499	−	14.9499i	0.839669	−	0.839669i	−0.149147	−	0.988815i	$-0.547653\pi$
$317$	14.9499	−	14.9499i	0.839669	−	0.839669i	0.988815	+	0.149147i	$0.0476526\pi$
$318$		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
$327$	25.6834			1.42029
$328$		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
$337$		−	22.8997i		−	1.24743i	−0.781652	−	0.623714i	$-0.785623\pi$
$337$		−	22.8997i		−	1.24743i	0.781652	−	0.623714i	$-0.214377\pi$
$338$		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
$343$	−20.0000			−1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.4248	+	14.4248i	0.774364	+	0.774364i	0.978866	−	0.204502i	$-0.0655574\pi$
$347$	14.4248	+	14.4248i	0.774364	+	0.774364i	−0.204502	+	0.978866i	$0.565557\pi$
$348$		0			0
$349$	−24.2665	−	24.2665i	−1.29896	−	1.29896i	−0.929082	−	0.369874i	$-0.879401\pi$
$349$	−24.2665	−	24.2665i	−1.29896	−	1.29896i	−0.369874	−	0.929082i	$-0.620599\pi$
$350$		0			0
$351$	−61.7995			−3.29861
$352$		0			0
$353$			33.2665i			1.77060i	0.465023	+	0.885299i	$0.346046\pi$
$353$			33.2665i			1.77060i	−0.465023	+	0.885299i	$0.653954\pi$
$354$		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	$0.0822514\pi$
$359$			9.68338i			0.511069i	−0.966800	+	0.255534i	$0.917749\pi$
$360$		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
$367$		−	26.6332i		−	1.39024i	−0.718892	−	0.695122i	$-0.755350\pi$
$367$		−	26.6332i		−	1.39024i	0.718892	−	0.695122i	$-0.244650\pi$
$368$		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	$-0.222383\pi$
$373$	2.36675	+	2.36675i	0.122546	+	0.122546i	−0.643174	+	0.765720i	$0.722383\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.2665			−0.889270
$378$		0			0
$379$	−11.4248	+	11.4248i	−0.586853	+	0.586853i	−0.936778	−	0.349925i	$-0.886207\pi$
$379$	−11.4248	+	11.4248i	−0.586853	+	0.586853i	0.349925	+	0.936778i	$0.386207\pi$
$380$		0			0
$381$	13.6332	+	13.6332i	0.698453	+	0.698453i
$382$		0			0
$383$			16.9499i			0.866098i	0.901370	+	0.433049i	$0.142562\pi$
$383$			16.9499i			0.866098i	−0.901370	+	0.433049i	$0.857438\pi$
$384$		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	−0.590626	−	0.806946i	$-0.701119\pi$
$389$	4.26650	−	4.26650i	0.216320	−	0.216320i	0.806946	+	0.590626i	$0.201119\pi$
$390$		0			0
$391$			0.416876i			0.0210823i
$392$		0			0
$393$	−4.31662			−0.217745
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−25.2665	+	25.2665i	−1.26809	+	1.26809i	−0.321015	+	0.947074i	$0.604024\pi$
$397$	−25.2665	+	25.2665i	−1.26809	+	1.26809i	−0.947074	+	0.321015i	$0.895976\pi$
$398$		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
$407$	4.31662			0.213967
$408$		0			0
$409$			19.6332i			0.970802i	0.874292	+	0.485401i	$0.161326\pi$
$409$			19.6332i			0.970802i	−0.874292	+	0.485401i	$0.838674\pi$
$410$		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
$417$			39.5330i			1.93594i
$418$		0			0
$419$	−11.5251	−	11.5251i	−0.563036	−	0.563036i	0.367132	−	0.930169i	$-0.380340\pi$
$419$	−11.5251	−	11.5251i	−0.563036	−	0.563036i	−0.930169	+	0.367132i	$0.880340\pi$
$420$		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
$423$	−50.5330			−2.45700
$424$		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
$433$			12.5831i			0.604706i	0.953196	+	0.302353i	$0.0977722\pi$
$433$			12.5831i			0.604706i	−0.953196	+	0.302353i	$0.902228\pi$
$434$		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	$0.0408784\pi$
$439$			5.36675i			0.256141i	−0.991765	+	0.128071i	$0.959122\pi$
$440$		0			0
$441$			10.3166i			0.491268i
$442$		0			0
$443$	19.1082	+	19.1082i	0.907857	+	0.907857i	0.996099	−	0.0882417i	$-0.0281248\pi$
$443$	19.1082	+	19.1082i	0.907857	+	0.907857i	−0.0882417	+	0.996099i	$0.528125\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			71.7995i			3.39600i
$448$		0			0
$449$	−20.6834			−0.976109			−0.488054	−	0.872813i	$-0.662293\pi$
$449$	−20.6834			−0.976109			−0.488054	+	0.872813i	$0.662293\pi$
$450$		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
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$		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
$463$		−	24.6332i		−	1.14480i	−0.819973	−	0.572402i	$-0.806012\pi$
$463$		−	24.6332i		−	1.14480i	0.819973	−	0.572402i	$-0.193988\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.2665	+	14.2665i	−0.660175	+	0.660175i	−0.955421	−	0.295246i	$-0.904598\pi$
$467$	−14.2665	+	14.2665i	−0.660175	+	0.660175i	0.295246	+	0.955421i	$0.404598\pi$
$468$		0			0
$469$	−21.2164	+	21.2164i	−0.979681	+	0.979681i
$470$		0			0
$471$		−	48.8496i		−	2.25087i
$472$		0			0
$473$	−48.2164			−2.21699
$474$		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	$-0.425015\pi$
$479$	10.2164			0.466798			0.233399	+	0.972381i	$0.425015\pi$
$480$		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
$487$	−32.2164			−1.45986			−0.729932	−	0.683520i	$-0.760448\pi$
$487$	−32.2164			−1.45986			−0.729932	+	0.683520i	$0.760448\pi$
$488$		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
$497$		−	20.0000i		−	0.897123i
$498$		0			0
$499$	22.8997	+	22.8997i	1.02513	+	1.02513i	0.999676	+	0.0254576i	$0.00810429\pi$
$499$	22.8997	+	22.8997i	1.02513	+	1.02513i	0.0254576	+	0.999676i	$0.491896\pi$
$500$		0			0
$501$	38.8496	−	38.8496i	1.73567	−	1.73567i
$502$		0			0
$503$	−31.8997			−1.42234			−0.711170	−	0.703020i	$-0.751834\pi$
$503$	−31.8997			−1.42234			−0.711170	+	0.703020i	$0.751834\pi$
$504$		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	0.995285	−	0.0969887i	$-0.0309211\pi$
$509$	20.2665	+	20.2665i	0.898297	+	0.898297i	−0.0969887	+	0.995285i	$0.530921\pi$
$510$		0			0
$511$	15.4829			0.684922
$512$		0			0
$513$			2.26650i			0.100068i
$514$		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	$-0.324240\pi$
$523$	−7.47494	−	7.47494i	−0.326856	−	0.326856i	−0.851390	+	0.524534i	$0.824240\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	3.05013i		−	0.132866i
$528$		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
$537$	−37.9499			−1.63766
$538$		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
$543$			14.3166i			0.614385i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−15.7414	+	15.7414i	−0.673055	+	0.673055i	−0.958419	−	0.285364i	$-0.907886\pi$
$547$	−15.7414	+	15.7414i	−0.673055	+	0.673055i	0.285364	+	0.958419i	$0.407886\pi$
$548$		0			0
$549$	60.8496	−	60.8496i	2.59700	−	2.59700i
$550$		0			0
$551$			0.633250i			0.0269773i
$552$		0			0
$553$	10.0000			0.425243
$554$		0			0
$555$		0			0
$556$		0			0
$557$	26.3166	−	26.3166i	1.11507	−	1.11507i	0.122617	−	0.992454i	$-0.460871\pi$
$557$	26.3166	−	26.3166i	1.11507	−	1.11507i	0.992454	−	0.122617i	$-0.0391287\pi$
$558$		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	−0.219186	−	0.975683i	$-0.570340\pi$
$563$	17.9499	−	17.9499i	0.756497	−	0.756497i	0.975683	+	0.219186i	$0.0703402\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−27.6834			−1.16259
$568$		0			0
$569$		−	9.00000i		−	0.377300i	−0.982044	−	0.188650i	$-0.939589\pi$
$569$		−	9.00000i		−	0.377300i	0.982044	−	0.188650i	$-0.0604111\pi$
$570$		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
$577$		−	15.6332i		−	0.650821i	−0.945573	−	0.325410i	$-0.894498\pi$
$577$		−	15.6332i		−	0.650821i	0.945573	−	0.325410i	$-0.105502\pi$
$578$		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
$583$	20.9499			0.867655
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.42481	−	9.42481i	−0.389004	−	0.389004i	0.485328	−	0.874332i	$-0.338700\pi$
$587$	−9.42481	−	9.42481i	−0.389004	−	0.389004i	−0.874332	+	0.485328i	$0.838700\pi$
$588$		0			0
$589$	−0.366750	−	0.366750i	−0.0151117	−	0.0151117i
$590$		0			0
$591$	71.5831			2.94454
$592$		0			0
$593$			35.5330i			1.45917i	0.683893	+	0.729583i	$0.260286\pi$
$593$			35.5330i			1.45917i	−0.683893	+	0.729583i	$0.739714\pi$
$594$		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	$-0.734882\pi$
$599$		−	36.2164i		−	1.47976i	0.672738	−	0.739880i	$-0.265118\pi$
$600$		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
$607$		−	21.1662i		−	0.859112i	−0.903040	−	0.429556i	$-0.858670\pi$
$607$		−	21.1662i		−	0.859112i	0.903040	−	0.429556i	$-0.141330\pi$
$608$		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	$-0.403790\pi$
$613$	−16.2665	−	16.2665i	−0.656998	−	0.656998i	−0.954669	+	0.297671i	$0.903790\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.733501			−0.0295296			−0.0147648	−	0.999891i	$-0.504700\pi$
$617$	−0.733501			−0.0295296			−0.0147648	+	0.999891i	$0.504700\pi$
$618$		0			0
$619$	−8.36675	+	8.36675i	−0.336288	+	0.336288i	−0.854968	−	0.518680i	$-0.826424\pi$
$619$	−8.36675	+	8.36675i	−0.336288	+	0.336288i	0.518680	+	0.854968i	$0.326424\pi$
$620$		0			0
$621$	2.26650	+	2.26650i	0.0909515	+	0.0909515i
$622$		0			0
$623$			9.15038i			0.366602i
$624$		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
$633$	−50.8997			−2.02308
$634$		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	−0.661002	−	0.750384i	$-0.729869\pi$
$643$	2.26650	−	2.26650i	0.0893820	−	0.0893820i	0.750384	+	0.661002i	$0.229869\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.1662			0.832131			0.416066	−	0.909335i	$-0.363409\pi$
$647$	21.1662			0.832131			0.416066	+	0.909335i	$0.363409\pi$
$648$		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	−0.950674	−	0.310193i	$-0.899606\pi$
$653$	−16.3668	+	16.3668i	−0.640480	+	0.640480i	0.310193	+	0.950674i	$0.399606\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	42.2164i		−	1.64702i
$658$		0			0
$659$	−25.1583	−	25.1583i	−0.980029	−	0.980029i	0.0197757	−	0.999804i	$-0.493705\pi$
$659$	−25.1583	−	25.1583i	−0.980029	−	0.980029i	−0.999804	+	0.0197757i	$0.993705\pi$
$660$		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
$663$	−24.5330			−0.952783
$664$		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
$673$		−	42.6332i		−	1.64339i	−0.569927	−	0.821696i	$-0.693028\pi$
$673$		−	42.6332i		−	1.64339i	0.569927	−	0.821696i	$-0.306972\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.3668	−	11.3668i	−0.436860	−	0.436860i	0.454094	−	0.890954i	$-0.349963\pi$
$677$	−11.3668	−	11.3668i	−0.436860	−	0.436860i	−0.890954	+	0.454094i	$0.849963\pi$
$678$		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	$-0.202673\pi$
$683$	5.47494	+	5.47494i	0.209493	+	0.209493i	−0.594559	+	0.804052i	$0.702673\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	8.63325i		−	0.329379i
$688$		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
$697$	−6.58312			−0.249354
$698$		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
$703$			0.216374i			0.00816068i
$704$		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	−0.160765	−	0.986993i	$-0.551396\pi$
$709$	22.0000	−	22.0000i	0.826227	−	0.826227i	0.986993	+	0.160765i	$0.0513962\pi$
$710$		0			0
$711$		−	27.2665i		−	1.02257i
$712$		0			0
$713$	−0.733501			−0.0274698
$714$		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	$-0.482482\pi$
$719$	2.94987			0.110012			0.0550059	+	0.998486i	$0.482482\pi$
$720$		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
$727$	2.53300			0.0939437			0.0469719	−	0.998896i	$-0.485043\pi$
$727$	2.53300			0.0939437			0.0469719	+	0.998896i	$0.485043\pi$
$728$		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	−0.804234	−	0.594313i	$-0.797424\pi$
$733$	−5.68338	+	5.68338i	−0.209920	+	0.209920i	0.594313	+	0.804234i	$0.297424\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	57.8496i		−	2.13092i
$738$		0			0
$739$	−14.3668	−	14.3668i	−0.528489	−	0.528489i	0.391632	−	0.920122i	$-0.371911\pi$
$739$	−14.3668	−	14.3668i	−0.528489	−	0.528489i	−0.920122	+	0.391632i	$0.871911\pi$
$740$		0			0
$741$	−2.94987	+	2.94987i	−0.108366	+	0.108366i
$742$		0			0
$743$	−20.3166			−0.745345			−0.372672	−	0.927963i	$-0.621558\pi$
$743$	−20.3166			−0.745345			−0.372672	+	0.927963i	$0.621558\pi$
$744$		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
$753$		−	39.3166i		−	1.43278i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−34.3166	−	34.3166i	−1.24726	−	1.24726i	−0.956926	−	0.290333i	$-0.906234\pi$
$757$	−34.3166	−	34.3166i	−1.24726	−	1.24726i	−0.290333	−	0.956926i	$-0.593766\pi$
$758$		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
$767$			11.3668i			0.410430i
$768$		0			0
$769$	32.4829			1.17136			0.585681	−	0.810542i	$-0.300827\pi$
$769$	32.4829			1.17136			0.585681	+	0.810542i	$0.300827\pi$
$770$		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	$-0.104380\pi$
$773$	17.3668	+	17.3668i	0.624639	+	0.624639i	−0.322075	+	0.946714i	$0.604380\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−6.83375			−0.245159
$778$		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
$783$			28.6332i			1.02327i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.00000	+	7.00000i	−0.249523	+	0.249523i	−0.820775	−	0.571252i	$-0.806458\pi$
$787$	−7.00000	+	7.00000i	−0.249523	+	0.249523i	0.571252	+	0.820775i	$0.306458\pi$
$788$		0			0
$789$	33.6332	−	33.6332i	1.19738	−	1.19738i
$790$		0			0
$791$			5.48287i			0.194949i
$792$		0			0
$793$	83.1662			2.95332
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.6332	−	15.6332i	0.553758	−	0.553758i	−0.373765	−	0.927523i	$-0.621933\pi$
$797$	15.6332	−	15.6332i	0.553758	−	0.553758i	0.927523	+	0.373765i	$0.121933\pi$
$798$		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
$807$	−27.2665			−0.959826
$808$		0			0
$809$		−	38.5330i		−	1.35475i	−0.735639	−	0.677374i	$-0.763118\pi$
$809$		−	38.5330i		−	1.35475i	0.735639	−	0.677374i	$-0.236882\pi$
$810$		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
$817$		−	2.41688i		−	0.0845558i
$818$		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
$823$	9.89975			0.345084			0.172542	−	0.985002i	$-0.444802\pi$
$823$	9.89975			0.345084			0.172542	+	0.985002i	$0.444802\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−7.84169	−	7.84169i	−0.272682	−	0.272682i	0.557497	−	0.830179i	$-0.311762\pi$
$827$	−7.84169	−	7.84169i	−0.272682	−	0.272682i	−0.830179	+	0.557497i	$0.811762\pi$
$828$		0			0
$829$	0.733501	+	0.733501i	0.0254755	+	0.0254755i	0.719730	−	0.694254i	$-0.244266\pi$
$829$	0.733501	+	0.733501i	0.0254755	+	0.0254755i	−0.694254	+	0.719730i	$0.744266\pi$
$830$		0			0
$831$	61.7995			2.14380
$832$		0			0
$833$			2.15038i			0.0745061i
$834$		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	$0.0144737\pi$
$839$			2.63325i			0.0909099i	−0.998966	+	0.0454549i	$0.985526\pi$
$840$		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
$847$		−	20.7335i		−	0.712412i
$848$		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	$-0.414135\pi$
$853$	−20.3668	−	20.3668i	−0.697344	−	0.697344i	−0.963837	+	0.266493i	$0.914135\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21.6332			−0.738978			−0.369489	−	0.929235i	$-0.620467\pi$
$857$	−21.6332			−0.738978			−0.369489	+	0.929235i	$0.620467\pi$
$858$		0			0
$859$	22.4248	−	22.4248i	0.765125	−	0.765125i	−0.212119	−	0.977244i	$-0.568036\pi$
$859$	22.4248	−	22.4248i	0.765125	−	0.765125i	0.977244	+	0.212119i	$0.0680365\pi$
$860$		0			0
$861$	−25.0000	−	25.0000i	−0.851998	−	0.851998i
$862$		0			0
$863$		−	20.5330i		−	0.698951i	−0.936945	−	0.349476i	$-0.886360\pi$
$863$		−	20.5330i		−	0.698951i	0.936945	−	0.349476i	$-0.113640\pi$
$864$		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
$873$	41.8997			1.41809
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.41688	+	6.41688i	−0.216683	+	0.216683i	−0.807099	−	0.590416i	$-0.798964\pi$
$877$	−6.41688	+	6.41688i	−0.216683	+	0.216683i	0.590416	+	0.807099i	$0.298964\pi$
$878$		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	−0.227979	−	0.973666i	$-0.573212\pi$
$883$	22.1583	−	22.1583i	0.745687	−	0.745687i	0.973666	+	0.227979i	$0.0732119\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−46.5330			−1.56243			−0.781213	−	0.624265i	$-0.785399\pi$
$887$	−46.5330			−1.56243			−0.781213	+	0.624265i	$0.785399\pi$
$888$		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
$897$			5.89975i			0.196987i
$898$		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
$903$	76.3325			2.54019
$904$		0			0
$905$		0			0
$906$		0			0
$907$	13.6332	+	13.6332i	0.452685	+	0.452685i	0.896245	−	0.443560i	$-0.146285\pi$
$907$	13.6332	+	13.6332i	0.452685	+	0.452685i	−0.443560	+	0.896245i	$0.646285\pi$
$908$		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
$913$		−	45.2164i		−	1.49644i
$914$		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	$-0.976791\pi$
$919$		−	4.41688i		−	0.145699i	0.997343	−	0.0728496i	$-0.0232093\pi$
$920$		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
$927$			29.2665i			0.961238i
$928$		0			0
$929$	20.0000			0.656179			0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000			0.656179			0.328089	+	0.944647i	$0.393595\pi$
$930$		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
$937$	−35.9499			−1.17443			−0.587216	−	0.809431i	$-0.699776\pi$
$937$	−35.9499			−1.17443			−0.587216	+	0.809431i	$0.699776\pi$
$938$		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
$943$			1.58312i			0.0515536i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.41688	+	5.41688i	−0.176025	+	0.176025i	−0.789620	−	0.613596i	$-0.789723\pi$
$947$	−5.41688	+	5.41688i	−0.176025	+	0.176025i	0.613596	+	0.789620i	$0.289723\pi$
$948$		0			0
$949$	28.8496	−	28.8496i	0.936498	−	0.936498i
$950$		0			0
$951$		−	64.5330i		−	2.09263i
$952$		0			0
$953$	2.36675			0.0766666			0.0383333	−	0.999265i	$-0.487795\pi$
$953$	2.36675			0.0766666			0.0383333	+	0.999265i	$0.487795\pi$
$954$		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
$967$	26.6332			0.856468			0.428234	−	0.903668i	$-0.359136\pi$
$967$	26.6332			0.856468			0.428234	+	0.903668i	$0.359136\pi$
$968$		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
$977$			56.3826i			1.80384i	0.431903	+	0.901920i	$0.357842\pi$
$977$			56.3826i			1.80384i	−0.431903	+	0.901920i	$0.642158\pi$
$978$		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
$983$	28.3166			0.903160			0.451580	−	0.892231i	$-0.350861\pi$
$983$	28.3166			0.903160			0.451580	+	0.892231i	$0.350861\pi$
$984$		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
$993$		−	5.00000i		−	0.158670i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.94987	−	2.94987i	−0.0934235	−	0.0934235i	0.658850	−	0.752274i	$-0.271043\pi$
$997$	−2.94987	−	2.94987i	−0.0934235	−	0.0934235i	−0.752274	+	0.658850i	$0.771043\pi$
$998$		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.q.d.849.2		4
4.3	odd	2		400.2.q.d.349.1		4
5.2	odd	4		1600.2.l.d.401.1		4
5.3	odd	4		1600.2.l.e.401.2		4
5.4	even	2		1600.2.q.c.849.1		4
16.5	even	4		1600.2.q.c.49.1		4
16.11	odd	4		400.2.q.c.149.2		4
20.3	even	4		400.2.l.d.301.1	yes	4
20.7	even	4		400.2.l.e.301.2	yes	4
20.19	odd	2		400.2.q.c.349.2		4
80.27	even	4		400.2.l.e.101.2	yes	4
80.37	odd	4		1600.2.l.d.1201.1		4
80.43	even	4		400.2.l.d.101.1	✓	4
80.53	odd	4		1600.2.l.e.1201.2		4
80.59	odd	4		400.2.q.d.149.1		4
80.69	even	4	inner	1600.2.q.d.49.2		4

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

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.q (of order \(4\), degree \(2\), not minimal)

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

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