LMFDB - Embedded newform 1600.2.l.i.1201.3

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1201.3
Root			$1.26868 - 0.624862i$ of defining polynomial
Character	$\chi$	$=$	1600.1201
Dual form			1600.2.l.i.401.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.720673 + 0.720673i) q^{3} +4.02840i q^{7} +1.96126i q^{9} +O(q^{10})$	$q+(-0.720673 + 0.720673i) q^{3} +4.02840i q^{7} +1.96126i q^{9} +(0.646837 + 0.646837i) q^{11} +(-4.91492 + 4.91492i) q^{13} +2.70862 q^{17} +(0.438397 - 0.438397i) q^{19} +(-2.90316 - 2.90316i) q^{21} -3.60080i q^{23} +(-3.57545 - 3.57545i) q^{27} +(2.00921 - 2.00921i) q^{29} -4.30994 q^{31} -0.932316 q^{33} +(0.743961 + 0.743961i) q^{37} -7.08410i q^{39} +0.603979i q^{41} +(-5.03010 - 5.03010i) q^{43} +10.8177 q^{47} -9.22800 q^{49} +(-1.95203 + 1.95203i) q^{51} +(-4.07420 - 4.07420i) q^{53} +0.631882i q^{57} +(-1.22845 - 1.22845i) q^{59} +(-6.98912 + 6.98912i) q^{61} -7.90074 q^{63} +(5.24219 - 5.24219i) q^{67} +(2.59500 + 2.59500i) q^{69} +13.7940i q^{71} -1.30876i q^{73} +(-2.60572 + 2.60572i) q^{77} -0.611127 q^{79} -0.730326 q^{81} +(1.29471 - 1.29471i) q^{83} +2.89597i q^{87} +10.9236i q^{89} +(-19.7993 - 19.7993i) q^{91} +(3.10606 - 3.10606i) q^{93} +12.7571 q^{97} +(-1.26862 + 1.26862i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 8 q^{11} + 8 q^{19} + 24 q^{27} - 16 q^{29} + 16 q^{37} + 8 q^{43} - 40 q^{47} - 16 q^{49} + 32 q^{51} - 16 q^{53} + 8 q^{59} + 16 q^{61} + 40 q^{63} + 40 q^{67} + 16 q^{69} - 16 q^{77} - 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} + 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^11 + 8 * q^19 + 24 * q^27 - 16 * q^29 + 16 * q^37 + 8 * q^43 - 40 * q^47 - 16 * q^49 + 32 * q^51 - 16 * q^53 + 8 * q^59 + 16 * q^61 + 40 * q^63 + 40 * q^67 + 16 * q^69 - 16 * q^77 - 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.720673	+	0.720673i	−0.416081	+	0.416081i	−0.883850	−	0.467770i	$-0.845058\pi$
$3$	−0.720673	+	0.720673i	−0.416081	+	0.416081i	0.467770	+	0.883850i	$0.345058\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			4.02840i			1.52259i	0.648405	+	0.761296i	$0.275437\pi$
$7$			4.02840i			1.52259i	−0.648405	+	0.761296i	$0.724563\pi$
$8$		0			0
$9$			1.96126i			0.653754i
$10$		0			0
$11$	0.646837	+	0.646837i	0.195029	+	0.195029i	0.797865	−	0.602836i	$-0.205963\pi$
$11$	0.646837	+	0.646837i	0.195029	+	0.195029i	−0.602836	+	0.797865i	$0.705963\pi$
$12$		0			0
$13$	−4.91492	+	4.91492i	−1.36315	+	1.36315i	−0.493286	+	0.869867i	$0.664204\pi$
$13$	−4.91492	+	4.91492i	−1.36315	+	1.36315i	−0.869867	+	0.493286i	$0.835796\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.70862			0.656938			0.328469	−	0.944515i	$-0.393467\pi$
$17$	2.70862			0.656938			0.328469	+	0.944515i	$0.393467\pi$
$18$		0			0
$19$	0.438397	−	0.438397i	0.100575	−	0.100575i	−0.655029	−	0.755604i	$-0.727344\pi$
$19$	0.438397	−	0.438397i	0.100575	−	0.100575i	0.755604	+	0.655029i	$0.227344\pi$
$20$		0			0
$21$	−2.90316	−	2.90316i	−0.633521	−	0.633521i
$22$		0			0
$23$		−	3.60080i		−	0.750819i	−0.926859	−	0.375410i	$-0.877502\pi$
$23$		−	3.60080i		−	0.750819i	0.926859	−	0.375410i	$-0.122498\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.57545	−	3.57545i	−0.688095	−	0.688095i
$28$		0			0
$29$	2.00921	−	2.00921i	0.373102	−	0.373102i	−0.495504	−	0.868606i	$-0.665017\pi$
$29$	2.00921	−	2.00921i	0.373102	−	0.373102i	0.868606	+	0.495504i	$0.165017\pi$
$30$		0			0
$31$	−4.30994			−0.774087			−0.387044	−	0.922061i	$-0.626504\pi$
$31$	−4.30994			−0.774087			−0.387044	+	0.922061i	$0.626504\pi$
$32$		0			0
$33$	−0.932316			−0.162295
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.743961	+	0.743961i	0.122306	+	0.122306i	0.765611	−	0.643304i	$-0.222437\pi$
$37$	0.743961	+	0.743961i	0.122306	+	0.122306i	−0.643304	+	0.765611i	$0.722437\pi$
$38$		0			0
$39$		−	7.08410i		−	1.13436i
$40$		0			0
$41$			0.603979i			0.0943256i	0.998887	+	0.0471628i	$0.0150180\pi$
$41$			0.603979i			0.0943256i	−0.998887	+	0.0471628i	$0.984982\pi$
$42$		0			0
$43$	−5.03010	−	5.03010i	−0.767083	−	0.767083i	0.210509	−	0.977592i	$-0.432488\pi$
$43$	−5.03010	−	5.03010i	−0.767083	−	0.767083i	−0.977592	+	0.210509i	$0.932488\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.8177			1.57793			0.788963	−	0.614440i	$-0.210618\pi$
$47$	10.8177			1.57793			0.788963	+	0.614440i	$0.210618\pi$
$48$		0			0
$49$	−9.22800			−1.31829
$50$		0			0
$51$	−1.95203	+	1.95203i	−0.273339	+	0.273339i
$52$		0			0
$53$	−4.07420	−	4.07420i	−0.559634	−	0.559634i	0.369569	−	0.929203i	$-0.379505\pi$
$53$	−4.07420	−	4.07420i	−0.559634	−	0.559634i	−0.929203	+	0.369569i	$0.879505\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			0.631882i			0.0836948i
$58$		0			0
$59$	−1.22845	−	1.22845i	−0.159931	−	0.159931i	0.622605	−	0.782536i	$-0.286074\pi$
$59$	−1.22845	−	1.22845i	−0.159931	−	0.159931i	−0.782536	+	0.622605i	$0.786074\pi$
$60$		0			0
$61$	−6.98912	+	6.98912i	−0.894865	+	0.894865i	−0.994976	−	0.100112i	$-0.968080\pi$
$61$	−6.98912	+	6.98912i	−0.894865	+	0.894865i	0.100112	+	0.994976i	$0.468080\pi$
$62$		0			0
$63$	−7.90074			−0.995400
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.24219	−	5.24219i	0.640435	−	0.640435i	−0.310227	−	0.950662i	$-0.600405\pi$
$67$	5.24219	−	5.24219i	0.640435	−	0.640435i	0.950662	+	0.310227i	$0.100405\pi$
$68$		0			0
$69$	2.59500	+	2.59500i	0.312401	+	0.312401i
$70$		0			0
$71$			13.7940i			1.63704i	0.574475	+	0.818522i	$0.305206\pi$
$71$			13.7940i			1.63704i	−0.574475	+	0.818522i	$0.694794\pi$
$72$		0			0
$73$		−	1.30876i		−	0.153179i	−0.997063	−	0.0765895i	$-0.975597\pi$
$73$		−	1.30876i		−	0.153179i	0.997063	−	0.0765895i	$-0.0244031\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.60572	+	2.60572i	−0.296949	+	0.296949i
$78$		0			0
$79$	−0.611127			−0.0687571			−0.0343786	−	0.999409i	$-0.510945\pi$
$79$	−0.611127			−0.0687571			−0.0343786	+	0.999409i	$0.510945\pi$
$80$		0			0
$81$	−0.730326			−0.0811473
$82$		0			0
$83$	1.29471	−	1.29471i	0.142113	−	0.142113i	−0.632471	−	0.774584i	$-0.717959\pi$
$83$	1.29471	−	1.29471i	0.142113	−	0.142113i	0.774584	+	0.632471i	$0.217959\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			2.89597i			0.310481i
$88$		0			0
$89$			10.9236i			1.15790i	0.815363	+	0.578950i	$0.196537\pi$
$89$			10.9236i			1.15790i	−0.815363	+	0.578950i	$0.803463\pi$
$90$		0			0
$91$	−19.7993	−	19.7993i	−2.07553	−	2.07553i
$92$		0			0
$93$	3.10606	−	3.10606i	0.322083	−	0.322083i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12.7571			1.29528			0.647642	−	0.761945i	$-0.275755\pi$
$97$	12.7571			1.29528			0.647642	+	0.761945i	$0.275755\pi$
$98$		0			0
$99$	−1.26862	+	1.26862i	−0.127501	+	0.127501i
$100$		0			0
$101$	−8.59804	−	8.59804i	−0.855537	−	0.855537i	0.135272	−	0.990809i	$-0.456809\pi$
$101$	−8.59804	−	8.59804i	−0.855537	−	0.855537i	−0.990809	+	0.135272i	$0.956809\pi$
$102$		0			0
$103$			12.0328i			1.18563i	0.805338	+	0.592815i	$0.201984\pi$
$103$			12.0328i			1.18563i	−0.805338	+	0.592815i	$0.798016\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.37309	−	2.37309i	−0.229415	−	0.229415i	0.583033	−	0.812448i	$-0.301866\pi$
$107$	−2.37309	−	2.37309i	−0.229415	−	0.229415i	−0.812448	+	0.583033i	$0.801866\pi$
$108$		0			0
$109$	−3.24479	+	3.24479i	−0.310794	+	0.310794i	−0.845217	−	0.534423i	$-0.820529\pi$
$109$	−3.24479	+	3.24479i	−0.310794	+	0.310794i	0.534423	+	0.845217i	$0.320529\pi$
$110$		0			0
$111$	−1.07230			−0.101779
$112$		0			0
$113$	−17.3173			−1.62907			−0.814536	−	0.580114i	$-0.803008\pi$
$113$	−17.3173			−1.62907			−0.814536	+	0.580114i	$0.803008\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−9.63944	−	9.63944i	−0.891166	−	0.891166i
$118$		0			0
$119$			10.9114i			1.00025i
$120$		0			0
$121$		−	10.1632i		−	0.923928i
$122$		0			0
$123$	−0.435271	−	0.435271i	−0.0392471	−	0.0392471i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−15.5438			−1.37929			−0.689645	−	0.724147i	$-0.742234\pi$
$127$	−15.5438			−1.37929			−0.689645	+	0.724147i	$0.742234\pi$
$128$		0			0
$129$	7.25011			0.638337
$130$		0			0
$131$	11.2770	−	11.2770i	0.985280	−	0.985280i	−0.0146129	−	0.999893i	$-0.504652\pi$
$131$	11.2770	−	11.2770i	0.985280	−	0.985280i	0.999893	+	0.0146129i	$0.00465160\pi$
$132$		0			0
$133$	1.76604	+	1.76604i	0.153135	+	0.153135i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			3.67273i			0.313782i	0.987616	+	0.156891i	$0.0501472\pi$
$137$			3.67273i			0.313782i	−0.987616	+	0.156891i	$0.949853\pi$
$138$		0			0
$139$	5.23552	+	5.23552i	0.444071	+	0.444071i	0.893378	−	0.449307i	$-0.148329\pi$
$139$	5.23552	+	5.23552i	0.444071	+	0.444071i	−0.449307	+	0.893378i	$0.648329\pi$
$140$		0			0
$141$	−7.79604	+	7.79604i	−0.656545	+	0.656545i
$142$		0			0
$143$	−6.35830			−0.531708
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.65037	−	6.65037i	0.548514	−	0.548514i
$148$		0			0
$149$	−3.29391	−	3.29391i	−0.269848	−	0.269848i	0.559191	−	0.829039i	$-0.311112\pi$
$149$	−3.29391	−	3.29391i	−0.269848	−	0.269848i	−0.829039	+	0.559191i	$0.811112\pi$
$150$		0			0
$151$			6.93206i			0.564123i	0.959396	+	0.282061i	$0.0910182\pi$
$151$			6.93206i			0.564123i	−0.959396	+	0.282061i	$0.908982\pi$
$152$		0			0
$153$			5.31232i			0.429475i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−5.65633	+	5.65633i	−0.451425	+	0.451425i	−0.895827	−	0.444403i	$-0.853416\pi$
$157$	−5.65633	+	5.65633i	−0.451425	+	0.451425i	0.444403	+	0.895827i	$0.353416\pi$
$158$		0			0
$159$	5.87233			0.465706
$160$		0			0
$161$	14.5055			1.14319
$162$		0			0
$163$	−10.9746	+	10.9746i	−0.859593	+	0.859593i	−0.991290	−	0.131697i	$-0.957957\pi$
$163$	−10.9746	+	10.9746i	−0.859593	+	0.859593i	0.131697	+	0.991290i	$0.457957\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			11.7686i			0.910685i	0.890316	+	0.455343i	$0.150483\pi$
$167$			11.7686i			0.910685i	−0.890316	+	0.455343i	$0.849517\pi$
$168$		0			0
$169$		−	35.3128i		−	2.71637i
$170$		0			0
$171$	0.859811	+	0.859811i	0.0657514	+	0.0657514i
$172$		0			0
$173$	1.40225	−	1.40225i	0.106611	−	0.106611i	−0.651789	−	0.758400i	$-0.725981\pi$
$173$	1.40225	−	1.40225i	0.106611	−	0.106611i	0.758400	+	0.651789i	$0.225981\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.77063			0.133088
$178$		0			0
$179$	−9.66131	+	9.66131i	−0.722120	+	0.722120i	−0.969037	−	0.246917i	$-0.920583\pi$
$179$	−9.66131	+	9.66131i	−0.722120	+	0.722120i	0.246917	+	0.969037i	$0.420583\pi$
$180$		0			0
$181$	0.294844	+	0.294844i	0.0219156	+	0.0219156i	0.717980	−	0.696064i	$-0.245067\pi$
$181$	0.294844	+	0.294844i	0.0219156	+	0.0219156i	−0.696064	+	0.717980i	$0.745067\pi$
$182$		0			0
$183$		−	10.0737i		−	0.744672i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.75204	+	1.75204i	0.128122	+	0.128122i
$188$		0			0
$189$	14.4033	−	14.4033i	1.04769	−	1.04769i
$190$		0			0
$191$	16.9352			1.22539			0.612694	−	0.790320i	$-0.290086\pi$
$191$	16.9352			1.22539			0.612694	+	0.790320i	$0.290086\pi$
$192$		0			0
$193$	16.5927			1.19437			0.597185	−	0.802103i	$-0.296286\pi$
$193$	16.5927			1.19437			0.597185	+	0.802103i	$0.296286\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.38392	+	2.38392i	0.169847	+	0.169847i	0.786912	−	0.617065i	$-0.211678\pi$
$197$	2.38392	+	2.38392i	0.169847	+	0.169847i	−0.617065	+	0.786912i	$0.711678\pi$
$198$		0			0
$199$		−	10.1411i		−	0.718883i	−0.933168	−	0.359442i	$-0.882967\pi$
$199$		−	10.1411i		−	0.718883i	0.933168	−	0.359442i	$-0.117033\pi$
$200$		0			0
$201$			7.55581i			0.532946i
$202$		0			0
$203$	8.09392	+	8.09392i	0.568082	+	0.568082i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	7.06211			0.490851
$208$		0			0
$209$	0.567143			0.0392301
$210$		0			0
$211$	2.81171	−	2.81171i	0.193566	−	0.193566i	−0.603669	−	0.797235i	$-0.706295\pi$
$211$	2.81171	−	2.81171i	0.193566	−	0.193566i	0.797235	+	0.603669i	$0.206295\pi$
$212$		0			0
$213$	−9.94095	−	9.94095i	−0.681143	−	0.681143i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	17.3621i		−	1.17862i
$218$		0			0
$219$	0.943190	+	0.943190i	0.0637349	+	0.0637349i
$220$		0			0
$221$	−13.3127	+	13.3127i	−0.895507	+	0.895507i
$222$		0			0
$223$	14.0502			0.940871			0.470436	−	0.882434i	$-0.344097\pi$
$223$	14.0502			0.940871			0.470436	+	0.882434i	$0.344097\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.3495	+	13.3495i	−0.886037	+	0.886037i	−0.994140	−	0.108103i	$-0.965522\pi$
$227$	−13.3495	+	13.3495i	−0.886037	+	0.886037i	0.108103	+	0.994140i	$0.465522\pi$
$228$		0			0
$229$	8.78589	+	8.78589i	0.580588	+	0.580588i	0.935065	−	0.354477i	$-0.115341\pi$
$229$	8.78589	+	8.78589i	0.580588	+	0.580588i	−0.354477	+	0.935065i	$0.615341\pi$
$230$		0			0
$231$		−	3.75574i		−	0.247110i
$232$		0			0
$233$		−	15.1472i		−	0.992329i	−0.868229	−	0.496165i	$-0.834741\pi$
$233$		−	15.1472i		−	0.992329i	0.868229	−	0.496165i	$-0.165259\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.440423	−	0.440423i	0.0286085	−	0.0286085i
$238$		0			0
$239$	−17.9151			−1.15883			−0.579414	−	0.815033i	$-0.696719\pi$
$239$	−17.9151			−1.15883			−0.579414	+	0.815033i	$0.696719\pi$
$240$		0			0
$241$	25.6594			1.65287			0.826433	−	0.563035i	$-0.190366\pi$
$241$	25.6594			1.65287			0.826433	+	0.563035i	$0.190366\pi$
$242$		0			0
$243$	11.2527	−	11.2527i	0.721859	−	0.721859i
$244$		0			0
$245$		0			0
$246$		0			0
$247$			4.30937i			0.274199i
$248$		0			0
$249$			1.86613i			0.118261i
$250$		0			0
$251$	5.95195	+	5.95195i	0.375684	+	0.375684i	0.869542	−	0.493858i	$-0.164414\pi$
$251$	5.95195	+	5.95195i	0.375684	+	0.375684i	−0.493858	+	0.869542i	$0.664414\pi$
$252$		0			0
$253$	2.32913	−	2.32913i	0.146431	−	0.146431i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.17369			0.260348			0.130174	−	0.991491i	$-0.458446\pi$
$257$	4.17369			0.260348			0.130174	+	0.991491i	$0.458446\pi$
$258$		0			0
$259$	−2.99697	+	2.99697i	−0.186223	+	0.186223i
$260$		0			0
$261$	3.94059	+	3.94059i	0.243917	+	0.243917i
$262$		0			0
$263$			9.14469i			0.563885i	0.959431	+	0.281943i	$0.0909788\pi$
$263$			9.14469i			0.563885i	−0.959431	+	0.281943i	$0.909021\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−7.87234	−	7.87234i	−0.481780	−	0.481780i
$268$		0			0
$269$	−8.40029	+	8.40029i	−0.512175	+	0.512175i	−0.915192	−	0.403017i	$-0.867961\pi$
$269$	−8.40029	+	8.40029i	−0.512175	+	0.512175i	0.403017	+	0.915192i	$0.367961\pi$
$270$		0			0
$271$	−18.7794			−1.14077			−0.570383	−	0.821379i	$-0.693205\pi$
$271$	−18.7794			−1.14077			−0.570383	+	0.821379i	$0.693205\pi$
$272$		0			0
$273$	28.5376			1.72717
$274$		0			0
$275$		0			0
$276$		0			0
$277$	3.54167	+	3.54167i	0.212798	+	0.212798i	0.805455	−	0.592657i	$-0.201921\pi$
$277$	3.54167	+	3.54167i	0.212798	+	0.212798i	−0.592657	+	0.805455i	$0.701921\pi$
$278$		0			0
$279$		−	8.45291i		−	0.506062i
$280$		0			0
$281$		−	2.31811i		−	0.138287i	−0.997607	−	0.0691433i	$-0.977973\pi$
$281$		−	2.31811i		−	0.138287i	0.997607	−	0.0691433i	$-0.0220266\pi$
$282$		0			0
$283$	−1.63197	−	1.63197i	−0.0970108	−	0.0970108i	0.656936	−	0.753947i	$-0.271852\pi$
$283$	−1.63197	−	1.63197i	−0.0970108	−	0.0970108i	−0.753947	+	0.656936i	$0.771852\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.43307			−0.143619
$288$		0			0
$289$	−9.66335			−0.568433
$290$		0			0
$291$	−9.19367	+	9.19367i	−0.538943	+	0.538943i
$292$		0			0
$293$	11.5789	+	11.5789i	0.676444	+	0.676444i	0.959194	−	0.282750i	$-0.0912466\pi$
$293$	11.5789	+	11.5789i	0.676444	+	0.676444i	−0.282750	+	0.959194i	$0.591247\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	4.62546i		−	0.268397i
$298$		0			0
$299$	17.6976	+	17.6976i	1.02348	+	1.02348i
$300$		0			0
$301$	20.2632	−	20.2632i	1.16795	−	1.16795i
$302$		0			0
$303$	12.3927			0.711945
$304$		0			0
$305$		0			0
$306$		0			0
$307$	11.7116	−	11.7116i	0.668415	−	0.668415i	−0.288934	−	0.957349i	$-0.593301\pi$
$307$	11.7116	−	11.7116i	0.668415	−	0.668415i	0.957349	+	0.288934i	$0.0933008\pi$
$308$		0			0
$309$	−8.67174	−	8.67174i	−0.493318	−	0.493318i
$310$		0			0
$311$			11.2068i			0.635477i	0.948178	+	0.317739i	$0.102923\pi$
$311$			11.2068i			0.635477i	−0.948178	+	0.317739i	$0.897077\pi$
$312$		0			0
$313$			7.50635i			0.424284i	0.977239	+	0.212142i	$0.0680439\pi$
$313$			7.50635i			0.424284i	−0.977239	+	0.212142i	$0.931956\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.2854	+	16.2854i	−0.914680	+	0.914680i	−0.996636	−	0.0819564i	$-0.973883\pi$
$317$	−16.2854	+	16.2854i	−0.914680	+	0.914680i	0.0819564	+	0.996636i	$0.473883\pi$
$318$		0			0
$319$	2.59927			0.145531
$320$		0			0
$321$	3.42044			0.190910
$322$		0			0
$323$	1.18745	−	1.18745i	0.0660716	−	0.0660716i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	4.67686i		−	0.258631i
$328$		0			0
$329$			43.5781i			2.40254i
$330$		0			0
$331$	19.3846	+	19.3846i	1.06547	+	1.06547i	0.997701	+	0.0677707i	$0.0215886\pi$
$331$	19.3846	+	19.3846i	1.06547	+	1.06547i	0.0677707	+	0.997701i	$0.478411\pi$
$332$		0			0
$333$	−1.45910	+	1.45910i	−0.0799582	+	0.0799582i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.82991			0.426522			0.213261	−	0.976995i	$-0.431592\pi$
$337$	7.82991			0.426522			0.213261	+	0.976995i	$0.431592\pi$
$338$		0			0
$339$	12.4801	−	12.4801i	0.677825	−	0.677825i
$340$		0			0
$341$	−2.78783	−	2.78783i	−0.150969	−	0.150969i
$342$		0			0
$343$		−	8.97529i		−	0.484620i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.91753	+	8.91753i	0.478718	+	0.478718i	0.904721	−	0.426004i	$-0.140079\pi$
$347$	8.91753	+	8.91753i	0.478718	+	0.478718i	−0.426004	+	0.904721i	$0.640079\pi$
$348$		0			0
$349$	−6.69072	+	6.69072i	−0.358146	+	0.358146i	−0.863129	−	0.504983i	$-0.831499\pi$
$349$	−6.69072	+	6.69072i	−0.358146	+	0.358146i	0.504983	+	0.863129i	$0.331499\pi$
$350$		0			0
$351$	35.1461			1.87596
$352$		0			0
$353$	2.05215			0.109225			0.0546126	−	0.998508i	$-0.482608\pi$
$353$	2.05215			0.109225			0.0546126	+	0.998508i	$0.482608\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−7.86357	−	7.86357i	−0.416184	−	0.416184i
$358$		0			0
$359$			9.52634i			0.502781i	0.967886	+	0.251391i	$0.0808879\pi$
$359$			9.52634i			0.502781i	−0.967886	+	0.251391i	$0.919112\pi$
$360$		0			0
$361$			18.6156i			0.979769i
$362$		0			0
$363$	7.32435	+	7.32435i	0.384429	+	0.384429i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−3.39736			−0.177341			−0.0886703	−	0.996061i	$-0.528262\pi$
$367$	−3.39736			−0.177341			−0.0886703	+	0.996061i	$0.528262\pi$
$368$		0			0
$369$	−1.18456			−0.0616657
$370$		0			0
$371$	16.4125	−	16.4125i	0.852094	−	0.852094i
$372$		0			0
$373$	22.4895	+	22.4895i	1.16446	+	1.16446i	0.983488	+	0.180971i	$0.0579241\pi$
$373$	22.4895	+	22.4895i	1.16446	+	1.16446i	0.180971	+	0.983488i	$0.442076\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			19.7502i			1.01719i
$378$		0			0
$379$	−14.9819	−	14.9819i	−0.769567	−	0.769567i	0.208463	−	0.978030i	$-0.433154\pi$
$379$	−14.9819	−	14.9819i	−0.769567	−	0.769567i	−0.978030	+	0.208463i	$0.933154\pi$
$380$		0			0
$381$	11.2020	−	11.2020i	0.573896	−	0.573896i
$382$		0			0
$383$	26.1197			1.33466			0.667328	−	0.744764i	$-0.267438\pi$
$383$	26.1197			1.33466			0.667328	+	0.744764i	$0.267438\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	9.86534	−	9.86534i	0.501483	−	0.501483i
$388$		0			0
$389$	−2.08395	−	2.08395i	−0.105660	−	0.105660i	0.652300	−	0.757961i	$-0.273804\pi$
$389$	−2.08395	−	2.08395i	−0.105660	−	0.105660i	−0.757961	+	0.652300i	$0.773804\pi$
$390$		0			0
$391$		−	9.75322i		−	0.493241i
$392$		0			0
$393$			16.2541i			0.819912i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.43282	+	1.43282i	−0.0719114	+	0.0719114i	−0.742148	−	0.670236i	$-0.766193\pi$
$397$	−1.43282	+	1.43282i	−0.0719114	+	0.0719114i	0.670236	+	0.742148i	$0.266193\pi$
$398$		0			0
$399$	−2.54547			−0.127433
$400$		0			0
$401$	−29.9853			−1.49739			−0.748697	−	0.662912i	$-0.769320\pi$
$401$	−29.9853			−1.49739			−0.748697	+	0.662912i	$0.769320\pi$
$402$		0			0
$403$	21.1830	−	21.1830i	1.05520	−	1.05520i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			0.962443i			0.0477065i
$408$		0			0
$409$			4.17833i			0.206605i	0.994650	+	0.103302i	$0.0329410\pi$
$409$			4.17833i			0.206605i	−0.994650	+	0.103302i	$0.967059\pi$
$410$		0			0
$411$	−2.64684	−	2.64684i	−0.130559	−	0.130559i
$412$		0			0
$413$	4.94870	−	4.94870i	0.243510	−	0.243510i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−7.54620			−0.369539
$418$		0			0
$419$	24.4667	−	24.4667i	1.19528	−	1.19528i	0.219712	−	0.975565i	$-0.429488\pi$
$419$	24.4667	−	24.4667i	1.19528	−	1.19528i	0.975565	−	0.219712i	$-0.0705119\pi$
$420$		0			0
$421$	25.6017	+	25.6017i	1.24775	+	1.24775i	0.956711	+	0.291039i	$0.0940008\pi$
$421$	25.6017	+	25.6017i	1.24775	+	1.24775i	0.291039	+	0.956711i	$0.405999\pi$
$422$		0			0
$423$			21.2164i			1.03158i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−28.1550	−	28.1550i	−1.36251	−	1.36251i
$428$		0			0
$429$	4.58226	−	4.58226i	0.221233	−	0.221233i
$430$		0			0
$431$	−17.6126			−0.848367			−0.424184	−	0.905576i	$-0.639439\pi$
$431$	−17.6126			−0.848367			−0.424184	+	0.905576i	$0.639439\pi$
$432$		0			0
$433$	−27.0568			−1.30027			−0.650133	−	0.759820i	$-0.725287\pi$
$433$	−27.0568			−1.30027			−0.650133	+	0.759820i	$0.725287\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.57858	−	1.57858i	−0.0755138	−	0.0755138i
$438$		0			0
$439$		−	22.9965i		−	1.09756i	−0.835967	−	0.548780i	$-0.815092\pi$
$439$		−	22.9965i		−	1.09756i	0.835967	−	0.548780i	$-0.184908\pi$
$440$		0			0
$441$		−	18.0985i		−	0.861834i
$442$		0			0
$443$	−13.7715	−	13.7715i	−0.654303	−	0.654303i	0.299723	−	0.954026i	$-0.403106\pi$
$443$	−13.7715	−	13.7715i	−0.654303	−	0.654303i	−0.954026	+	0.299723i	$0.903106\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	4.74766			0.224557
$448$		0			0
$449$	6.88838			0.325083			0.162541	−	0.986702i	$-0.448031\pi$
$449$	6.88838			0.325083			0.162541	+	0.986702i	$0.448031\pi$
$450$		0			0
$451$	−0.390676	+	0.390676i	−0.0183962	+	0.0183962i
$452$		0			0
$453$	−4.99575	−	4.99575i	−0.234721	−	0.234721i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			2.52622i			0.118171i	0.998253	+	0.0590857i	$0.0188185\pi$
$457$			2.52622i			0.118171i	−0.998253	+	0.0590857i	$0.981181\pi$
$458$		0			0
$459$	−9.68454	−	9.68454i	−0.452036	−	0.452036i
$460$		0			0
$461$	9.23502	−	9.23502i	0.430118	−	0.430118i	−0.458550	−	0.888668i	$-0.651631\pi$
$461$	9.23502	−	9.23502i	0.430118	−	0.430118i	0.888668	+	0.458550i	$0.151631\pi$
$462$		0			0
$463$	−11.2676			−0.523652			−0.261826	−	0.965115i	$-0.584325\pi$
$463$	−11.2676			−0.523652			−0.261826	+	0.965115i	$0.584325\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−25.8291	+	25.8291i	−1.19523	+	1.19523i	−0.219650	+	0.975579i	$0.570492\pi$
$467$	−25.8291	+	25.8291i	−1.19523	+	1.19523i	−0.975579	+	0.219650i	$0.929508\pi$
$468$		0			0
$469$	21.1176	+	21.1176i	0.975122	+	0.975122i
$470$		0			0
$471$		−	8.15273i		−	0.375658i
$472$		0			0
$473$		−	6.50731i		−	0.299206i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	7.99056	−	7.99056i	0.365863	−	0.365863i
$478$		0			0
$479$	15.7261			0.718545			0.359273	−	0.933233i	$-0.383025\pi$
$479$	15.7261			0.718545			0.359273	+	0.933233i	$0.383025\pi$
$480$		0			0
$481$	−7.31301			−0.333445
$482$		0			0
$483$	−10.4537	+	10.4537i	−0.475660	+	0.475660i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	35.3717i		−	1.60284i	−0.598100	−	0.801422i	$-0.704077\pi$
$487$		−	35.3717i		−	1.60284i	0.598100	−	0.801422i	$-0.295923\pi$
$488$		0			0
$489$		−	15.8181i		−	0.715320i
$490$		0			0
$491$	−7.95703	−	7.95703i	−0.359096	−	0.359096i	0.504384	−	0.863480i	$-0.331720\pi$
$491$	−7.95703	−	7.95703i	−0.359096	−	0.359096i	−0.863480	+	0.504384i	$0.831720\pi$
$492$		0			0
$493$	5.44221	−	5.44221i	0.245105	−	0.245105i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−55.5677			−2.49255
$498$		0			0
$499$	−11.5864	+	11.5864i	−0.518677	+	0.518677i	−0.917171	−	0.398494i	$-0.869533\pi$
$499$	−11.5864	+	11.5864i	−0.518677	+	0.518677i	0.398494	+	0.917171i	$0.369533\pi$
$500$		0			0
$501$	−8.48135	−	8.48135i	−0.378919	−	0.378919i
$502$		0			0
$503$		−	23.5051i		−	1.04804i	−0.851706	−	0.524020i	$-0.824432\pi$
$503$		−	23.5051i		−	1.04804i	0.851706	−	0.524020i	$-0.175568\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	25.4490	+	25.4490i	1.13023	+	1.13023i
$508$		0			0
$509$	−3.08381	+	3.08381i	−0.136687	+	0.136687i	−0.772140	−	0.635452i	$-0.780814\pi$
$509$	−3.08381	+	3.08381i	−0.136687	+	0.136687i	0.635452	+	0.772140i	$0.280814\pi$
$510$		0			0
$511$	5.27222			0.233229
$512$		0			0
$513$	−3.13493			−0.138411
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.99730	+	6.99730i	0.307741	+	0.307741i
$518$		0			0
$519$			2.02113i			0.0887178i
$520$		0			0
$521$		−	11.5762i		−	0.507161i	−0.967314	−	0.253580i	$-0.918392\pi$
$521$		−	11.5762i		−	0.507161i	0.967314	−	0.253580i	$-0.0816083\pi$
$522$		0			0
$523$	3.97900	+	3.97900i	0.173990	+	0.173990i	0.788730	−	0.614740i	$-0.210739\pi$
$523$	3.97900	+	3.97900i	0.173990	+	0.173990i	−0.614740	+	0.788730i	$0.710739\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.6740			−0.508527
$528$		0			0
$529$	10.0342			0.436271
$530$		0			0
$531$	2.40932	−	2.40932i	0.104555	−	0.104555i
$532$		0			0
$533$	−2.96851	−	2.96851i	−0.128580	−	0.128580i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		−	13.9253i		−	0.600921i
$538$		0			0
$539$	−5.96902	−	5.96902i	−0.257104	−	0.257104i
$540$		0			0
$541$	17.2148	−	17.2148i	0.740123	−	0.740123i	−0.232478	−	0.972602i	$-0.574684\pi$
$541$	17.2148	−	17.2148i	0.740123	−	0.740123i	0.972602	+	0.232478i	$0.0746835\pi$
$542$		0			0
$543$	−0.424973			−0.0182373
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−20.3610	+	20.3610i	−0.870573	+	0.870573i	−0.992535	−	0.121962i	$-0.961081\pi$
$547$	−20.3610	+	20.3610i	−0.870573	+	0.870573i	0.121962	+	0.992535i	$0.461081\pi$
$548$		0			0
$549$	−13.7075	−	13.7075i	−0.585021	−	0.585021i
$550$		0			0
$551$		−	1.76167i		−	0.0750495i
$552$		0			0
$553$		−	2.46186i		−	0.104689i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.7029	−	22.7029i	0.961954	−	0.961954i	−0.0373478	−	0.999302i	$-0.511891\pi$
$557$	22.7029	−	22.7029i	0.961954	−	0.961954i	0.999302	+	0.0373478i	$0.0118910\pi$
$558$		0			0
$559$	49.4451			2.09130
$560$		0			0
$561$	−2.52529			−0.106618
$562$		0			0
$563$	15.4153	−	15.4153i	0.649676	−	0.649676i	−0.303238	−	0.952915i	$-0.598068\pi$
$563$	15.4153	−	15.4153i	0.649676	−	0.649676i	0.952915	+	0.303238i	$0.0980678\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	2.94204i		−	0.123554i
$568$		0			0
$569$		−	22.6529i		−	0.949660i	−0.880078	−	0.474830i	$-0.842510\pi$
$569$		−	22.6529i		−	0.949660i	0.880078	−	0.474830i	$-0.157490\pi$
$570$		0			0
$571$	13.4941	+	13.4941i	0.564710	+	0.564710i	0.930642	−	0.365931i	$-0.119250\pi$
$571$	13.4941	+	13.4941i	0.564710	+	0.564710i	−0.365931	+	0.930642i	$0.619250\pi$
$572$		0			0
$573$	−12.2047	+	12.2047i	−0.509860	+	0.509860i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−6.08684			−0.253398			−0.126699	−	0.991941i	$-0.540438\pi$
$577$	−6.08684			−0.253398			−0.126699	+	0.991941i	$0.540438\pi$
$578$		0			0
$579$	−11.9579	+	11.9579i	−0.496955	+	0.496955i
$580$		0			0
$581$	5.21561	+	5.21561i	0.216380	+	0.216380i
$582$		0			0
$583$		−	5.27068i		−	0.218289i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.4418	+	21.4418i	0.884999	+	0.884999i	0.994038	−	0.109039i	$-0.0347772\pi$
$587$	21.4418	+	21.4418i	0.884999	+	0.884999i	−0.109039	+	0.994038i	$0.534777\pi$
$588$		0			0
$589$	−1.88946	+	1.88946i	−0.0778540	+	0.0778540i
$590$		0			0
$591$	−3.43605			−0.141340
$592$		0			0
$593$	28.2005			1.15806			0.579028	−	0.815308i	$-0.303432\pi$
$593$	28.2005			1.15806			0.579028	+	0.815308i	$0.303432\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.30841	+	7.30841i	0.299113	+	0.299113i
$598$		0			0
$599$			38.0516i			1.55475i	0.629039	+	0.777374i	$0.283449\pi$
$599$			38.0516i			1.55475i	−0.629039	+	0.777374i	$0.716551\pi$
$600$		0			0
$601$			19.0716i			0.777947i	0.921249	+	0.388974i	$0.127170\pi$
$601$			19.0716i			0.777947i	−0.921249	+	0.388974i	$0.872830\pi$
$602$		0			0
$603$	10.2813	+	10.2813i	0.418687	+	0.418687i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	5.73433			0.232749			0.116375	−	0.993205i	$-0.462873\pi$
$607$	5.73433			0.232749			0.116375	+	0.993205i	$0.462873\pi$
$608$		0			0
$609$	−11.6661			−0.472736
$610$		0			0
$611$	−53.1682	+	53.1682i	−2.15096	+	2.15096i
$612$		0			0
$613$	−5.36917	−	5.36917i	−0.216859	−	0.216859i	0.590315	−	0.807173i	$-0.299004\pi$
$613$	−5.36917	−	5.36917i	−0.216859	−	0.216859i	−0.807173	+	0.590315i	$0.799004\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			28.2915i			1.13897i	0.822000	+	0.569487i	$0.192858\pi$
$617$			28.2915i			1.13897i	−0.822000	+	0.569487i	$0.807142\pi$
$618$		0			0
$619$	−18.9669	−	18.9669i	−0.762345	−	0.762345i	0.214401	−	0.976746i	$-0.431220\pi$
$619$	−18.9669	−	18.9669i	−0.762345	−	0.762345i	−0.976746	+	0.214401i	$0.931220\pi$
$620$		0			0
$621$	−12.8745	+	12.8745i	−0.516635	+	0.516635i
$622$		0			0
$623$	−44.0046			−1.76301
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.408725	+	0.408725i	−0.0163229	+	0.0163229i
$628$		0			0
$629$	2.01511	+	2.01511i	0.0803477	+	0.0803477i
$630$		0			0
$631$		−	41.7662i		−	1.66269i	−0.555758	−	0.831344i	$-0.687572\pi$
$631$		−	41.7662i		−	1.66269i	0.555758	−	0.831344i	$-0.312428\pi$
$632$		0			0
$633$			4.05265i			0.161078i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	45.3549	−	45.3549i	1.79703	−	1.79703i
$638$		0			0
$639$	−27.0536			−1.07022
$640$		0			0
$641$	−2.85195			−0.112645			−0.0563227	−	0.998413i	$-0.517938\pi$
$641$	−2.85195			−0.112645			−0.0563227	+	0.998413i	$0.517938\pi$
$642$		0			0
$643$	−31.8921	+	31.8921i	−1.25770	+	1.25770i	−0.305516	+	0.952187i	$0.598829\pi$
$643$	−31.8921	+	31.8921i	−1.25770	+	1.25770i	−0.952187	+	0.305516i	$0.901171\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			7.83402i			0.307987i	0.988072	+	0.153994i	$0.0492135\pi$
$647$			7.83402i			0.307987i	−0.988072	+	0.153994i	$0.950786\pi$
$648$		0			0
$649$		−	1.58922i		−	0.0623823i
$650$		0			0
$651$	12.5124	+	12.5124i	0.490401	+	0.490401i
$652$		0			0
$653$	12.6822	−	12.6822i	0.496292	−	0.496292i	−0.413989	−	0.910282i	$-0.635865\pi$
$653$	12.6822	−	12.6822i	0.496292	−	0.496292i	0.910282	+	0.413989i	$0.135865\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.56682			0.100141
$658$		0			0
$659$	−12.9694	+	12.9694i	−0.505217	+	0.505217i	−0.913055	−	0.407837i	$-0.866283\pi$
$659$	−12.9694	+	12.9694i	−0.505217	+	0.505217i	0.407837	+	0.913055i	$0.366283\pi$
$660$		0			0
$661$	−6.85796	−	6.85796i	−0.266744	−	0.266744i	0.561043	−	0.827787i	$-0.310400\pi$
$661$	−6.85796	−	6.85796i	−0.266744	−	0.266744i	−0.827787	+	0.561043i	$0.810400\pi$
$662$		0			0
$663$		−	19.1882i		−	0.745206i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.23478	−	7.23478i	−0.280132	−	0.280132i
$668$		0			0
$669$	−10.1256	+	10.1256i	−0.391478	+	0.391478i
$670$		0			0
$671$	−9.04164			−0.349049
$672$		0			0
$673$	−23.1277			−0.891508			−0.445754	−	0.895155i	$-0.647064\pi$
$673$	−23.1277			−0.891508			−0.445754	+	0.895155i	$0.647064\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.2521	+	20.2521i	0.778352	+	0.778352i	0.979550	−	0.201199i	$-0.0644837\pi$
$677$	20.2521	+	20.2521i	0.778352	+	0.778352i	−0.201199	+	0.979550i	$0.564484\pi$
$678$		0			0
$679$			51.3905i			1.97219i
$680$		0			0
$681$		−	19.2412i		−	0.737326i
$682$		0			0
$683$	26.2957	+	26.2957i	1.00618	+	1.00618i	0.999981	+	0.00619708i	$0.00197260\pi$
$683$	26.2957	+	26.2957i	1.00618	+	1.00618i	0.00619708	+	0.999981i	$0.498027\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−12.6635			−0.483143
$688$		0			0
$689$	40.0487			1.52573
$690$		0			0
$691$	4.91230	−	4.91230i	0.186873	−	0.186873i	−0.607470	−	0.794343i	$-0.707815\pi$
$691$	4.91230	−	4.91230i	0.186873	−	0.186873i	0.794343	+	0.607470i	$0.207815\pi$
$692$		0			0
$693$	−5.11049	−	5.11049i	−0.194132	−	0.194132i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			1.63595i			0.0619661i
$698$		0			0
$699$	10.9162	+	10.9162i	0.412889	+	0.412889i
$700$		0			0
$701$	−12.3598	+	12.3598i	−0.466824	+	0.466824i	−0.900884	−	0.434060i	$-0.857081\pi$
$701$	−12.3598	+	12.3598i	−0.466824	+	0.466824i	0.434060	+	0.900884i	$0.357081\pi$
$702$		0			0
$703$	0.652300			0.0246020
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34.6363	−	34.6363i	1.30263	−	1.30263i
$708$		0			0
$709$	−26.6076	−	26.6076i	−0.999270	−	0.999270i	0.000729493	−	1.00000i	$-0.499768\pi$
$709$	−26.6076	−	26.6076i	−0.999270	−	0.999270i	−1.00000		0.000729493i	$0.999768\pi$
$710$		0			0
$711$		−	1.19858i		−	0.0449502i
$712$		0			0
$713$			15.5192i			0.581200i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	12.9109	−	12.9109i	0.482166	−	0.482166i
$718$		0			0
$719$	−50.9765			−1.90110			−0.950551	−	0.310570i	$-0.899480\pi$
$719$	−50.9765			−1.90110			−0.950551	+	0.310570i	$0.899480\pi$
$720$		0			0
$721$	−48.4731			−1.80523
$722$		0			0
$723$	−18.4920	+	18.4920i	−0.687726	+	0.687726i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	13.2824i		−	0.492616i	−0.969192	−	0.246308i	$-0.920782\pi$
$727$		−	13.2824i		−	0.492616i	0.969192	−	0.246308i	$-0.0792175\pi$
$728$		0			0
$729$			14.0280i			0.519556i
$730$		0			0
$731$	−13.6246	−	13.6246i	−0.503926	−	0.503926i
$732$		0			0
$733$	−21.3075	+	21.3075i	−0.787012	+	0.787012i	−0.981003	−	0.193991i	$-0.937857\pi$
$733$	−21.3075	+	21.3075i	−0.787012	+	0.787012i	0.193991	+	0.981003i	$0.437857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.78168			0.249807
$738$		0			0
$739$	−5.83841	+	5.83841i	−0.214769	+	0.214769i	−0.806290	−	0.591521i	$-0.798528\pi$
$739$	−5.83841	+	5.83841i	−0.214769	+	0.214769i	0.591521	+	0.806290i	$0.298528\pi$
$740$		0			0
$741$	−3.10565	−	3.10565i	−0.114089	−	0.114089i
$742$		0			0
$743$			3.25778i			0.119516i	0.998213	+	0.0597582i	$0.0190330\pi$
$743$			3.25778i			0.119516i	−0.998213	+	0.0597582i	$0.980967\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.53926	+	2.53926i	0.0929068	+	0.0929068i
$748$		0			0
$749$	9.55975	−	9.55975i	0.349306	−	0.349306i
$750$		0			0
$751$	−20.7322			−0.756530			−0.378265	−	0.925697i	$-0.623479\pi$
$751$	−20.7322			−0.756530			−0.378265	+	0.925697i	$0.623479\pi$
$752$		0			0
$753$	−8.57882			−0.312630
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−23.3278	−	23.3278i	−0.847862	−	0.847862i	0.142004	−	0.989866i	$-0.454645\pi$
$757$	−23.3278	−	23.3278i	−0.847862	−	0.847862i	−0.989866	+	0.142004i	$0.954645\pi$
$758$		0			0
$759$			3.35709i			0.121854i
$760$		0			0
$761$			24.0242i			0.870878i	0.900218	+	0.435439i	$0.143407\pi$
$761$			24.0242i			0.870878i	−0.900218	+	0.435439i	$0.856593\pi$
$762$		0			0
$763$	−13.0713	−	13.0713i	−0.473213	−	0.473213i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.0755			0.436021
$768$		0			0
$769$	−2.70862			−0.0976754			−0.0488377	−	0.998807i	$-0.515552\pi$
$769$	−2.70862			−0.0976754			−0.0488377	+	0.998807i	$0.515552\pi$
$770$		0			0
$771$	−3.00787	+	3.00787i	−0.108326	+	0.108326i
$772$		0			0
$773$	−22.9473	−	22.9473i	−0.825358	−	0.825358i	0.161513	−	0.986871i	$-0.448363\pi$
$773$	−22.9473	−	22.9473i	−0.825358	−	0.825358i	−0.986871	+	0.161513i	$0.948363\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	4.31967i		−	0.154967i
$778$		0			0
$779$	0.264783	+	0.264783i	0.00948682	+	0.00948682i
$780$		0			0
$781$	−8.92246	+	8.92246i	−0.319271	+	0.319271i
$782$		0			0
$783$	−14.3677			−0.513459
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−14.0592	+	14.0592i	−0.501157	+	0.501157i	−0.911797	−	0.410641i	$-0.865305\pi$
$787$	−14.0592	+	14.0592i	−0.501157	+	0.501157i	0.410641	+	0.911797i	$0.365305\pi$
$788$		0			0
$789$	−6.59033	−	6.59033i	−0.234622	−	0.234622i
$790$		0			0
$791$		−	69.7609i		−	2.48041i
$792$		0			0
$793$		−	68.7019i		−	2.43967i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−35.4258	+	35.4258i	−1.25485	+	1.25485i	−0.301326	+	0.953521i	$0.597429\pi$
$797$	−35.4258	+	35.4258i	−1.25485	+	1.25485i	−0.953521	+	0.301326i	$0.902571\pi$
$798$		0			0
$799$	29.3011			1.03660
$800$		0			0
$801$	−21.4240			−0.756981
$802$		0			0
$803$	0.846556	−	0.846556i	0.0298743	−	0.0298743i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	12.1077i		−	0.426212i
$808$		0			0
$809$			16.9217i			0.594935i	0.954732	+	0.297467i	$0.0961420\pi$
$809$			16.9217i			0.594935i	−0.954732	+	0.297467i	$0.903858\pi$
$810$		0			0
$811$	20.4270	+	20.4270i	0.717288	+	0.717288i	0.968049	−	0.250761i	$-0.0806807\pi$
$811$	20.4270	+	20.4270i	0.717288	+	0.717288i	−0.250761	+	0.968049i	$0.580681\pi$
$812$		0			0
$813$	13.5338	−	13.5338i	0.474651	−	0.474651i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−4.41036			−0.154299
$818$		0			0
$819$	38.8315	−	38.8315i	1.35688	−	1.35688i
$820$		0			0
$821$	32.4563	+	32.4563i	1.13273	+	1.13273i	0.989721	+	0.143013i	$0.0456792\pi$
$821$	32.4563	+	32.4563i	1.13273	+	1.13273i	0.143013	+	0.989721i	$0.454321\pi$
$822$		0			0
$823$			6.50705i			0.226821i	0.993548	+	0.113411i	$0.0361776\pi$
$823$			6.50705i			0.226821i	−0.993548	+	0.113411i	$0.963822\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27.0528	+	27.0528i	0.940718	+	0.940718i	0.998339	−	0.0576204i	$-0.0183513\pi$
$827$	27.0528	+	27.0528i	0.940718	+	0.940718i	−0.0576204	+	0.998339i	$0.518351\pi$
$828$		0			0
$829$	−8.54216	+	8.54216i	−0.296682	+	0.296682i	−0.839713	−	0.543031i	$-0.817277\pi$
$829$	−8.54216	+	8.54216i	−0.296682	+	0.296682i	0.543031	+	0.839713i	$0.317277\pi$
$830$		0			0
$831$	−5.10477			−0.177083
$832$		0			0
$833$	−24.9952			−0.866032
$834$		0			0
$835$		0			0
$836$		0			0
$837$	15.4099	+	15.4099i	0.532646	+	0.532646i
$838$		0			0
$839$		−	24.4138i		−	0.842860i	−0.906861	−	0.421430i	$-0.861528\pi$
$839$		−	24.4138i		−	0.842860i	0.906861	−	0.421430i	$-0.138472\pi$
$840$		0			0
$841$			20.9261i			0.721590i
$842$		0			0
$843$	1.67060	+	1.67060i	0.0575384	+	0.0575384i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	40.9414			1.40676
$848$		0			0
$849$	2.35224			0.0807287
$850$		0			0
$851$	2.67885	−	2.67885i	0.0918299	−	0.0918299i
$852$		0			0
$853$	−8.23270	−	8.23270i	−0.281882	−	0.281882i	0.551977	−	0.833859i	$-0.313874\pi$
$853$	−8.23270	−	8.23270i	−0.281882	−	0.281882i	−0.833859	+	0.551977i	$0.813874\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			4.73909i			0.161884i	0.996719	+	0.0809421i	$0.0257929\pi$
$857$			4.73909i			0.161884i	−0.996719	+	0.0809421i	$0.974207\pi$
$858$		0			0
$859$	9.65120	+	9.65120i	0.329295	+	0.329295i	0.852318	−	0.523024i	$-0.175196\pi$
$859$	9.65120	+	9.65120i	0.329295	+	0.329295i	−0.523024	+	0.852318i	$0.675196\pi$
$860$		0			0
$861$	1.75345	−	1.75345i	0.0597573	−	0.0597573i
$862$		0			0
$863$	−3.80368			−0.129479			−0.0647393	−	0.997902i	$-0.520622\pi$
$863$	−3.80368			−0.129479			−0.0647393	+	0.997902i	$0.520622\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	6.96412	−	6.96412i	0.236514	−	0.236514i
$868$		0			0
$869$	−0.395300	−	0.395300i	−0.0134096	−	0.0134096i
$870$		0			0
$871$			51.5299i			1.74602i
$872$		0			0
$873$			25.0199i			0.846796i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.38917	+	2.38917i	−0.0806765	+	0.0806765i	−0.746294	−	0.665617i	$-0.768168\pi$
$877$	−2.38917	+	2.38917i	−0.0806765	+	0.0806765i	0.665617	+	0.746294i	$0.268168\pi$
$878$		0			0
$879$	−16.6891			−0.562911
$880$		0			0
$881$	−23.6195			−0.795762			−0.397881	−	0.917437i	$-0.630254\pi$
$881$	−23.6195			−0.795762			−0.397881	+	0.917437i	$0.630254\pi$
$882$		0			0
$883$	−9.64752	+	9.64752i	−0.324665	+	0.324665i	−0.850553	−	0.525889i	$-0.823733\pi$
$883$	−9.64752	+	9.64752i	−0.324665	+	0.324665i	0.525889	+	0.850553i	$0.323733\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			8.91140i			0.299215i	0.988745	+	0.149608i	$0.0478011\pi$
$887$			8.91140i			0.299215i	−0.988745	+	0.149608i	$0.952199\pi$
$888$		0			0
$889$		−	62.6167i		−	2.10010i
$890$		0			0
$891$	−0.472402	−	0.472402i	−0.0158261	−	0.0158261i
$892$		0			0
$893$	4.74246	−	4.74246i	0.158700	−	0.158700i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−25.5084			−0.851702
$898$		0			0
$899$	−8.65959	+	8.65959i	−0.288813	+	0.288813i
$900$		0			0
$901$	−11.0355	−	11.0355i	−0.367645	−	0.367645i
$902$		0			0
$903$			29.2064i			0.971927i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	23.4874	+	23.4874i	0.779886	+	0.779886i	0.979811	−	0.199925i	$-0.0640699\pi$
$907$	23.4874	+	23.4874i	0.779886	+	0.779886i	−0.199925	+	0.979811i	$0.564070\pi$
$908$		0			0
$909$	16.8630	−	16.8630i	0.559310	−	0.559310i
$910$		0			0
$911$	1.77171			0.0586993			0.0293497	−	0.999569i	$-0.490656\pi$
$911$	1.77171			0.0586993			0.0293497	+	0.999569i	$0.490656\pi$
$912$		0			0
$913$	1.67493			0.0554322
$914$		0			0
$915$		0			0
$916$		0			0
$917$	45.4285	+	45.4285i	1.50018	+	1.50018i
$918$		0			0
$919$		−	46.2001i		−	1.52400i	−0.647576	−	0.762001i	$-0.724217\pi$
$919$		−	46.2001i		−	1.52400i	0.647576	−	0.762001i	$-0.275783\pi$
$920$		0			0
$921$			16.8804i			0.556229i
$922$		0			0
$923$	−67.7963	−	67.7963i	−2.23154	−	2.23154i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−23.5995			−0.775110
$928$		0			0
$929$	−35.5011			−1.16475			−0.582376	−	0.812920i	$-0.697877\pi$
$929$	−35.5011			−1.16475			−0.582376	+	0.812920i	$0.697877\pi$
$930$		0			0
$931$	−4.04553	+	4.04553i	−0.132587	+	0.132587i
$932$		0			0
$933$	−8.07641	−	8.07641i	−0.264410	−	0.264410i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			10.0385i			0.327945i	0.986465	+	0.163972i	$0.0524308\pi$
$937$			10.0385i			0.327945i	−0.986465	+	0.163972i	$0.947569\pi$
$938$		0			0
$939$	−5.40962	−	5.40962i	−0.176536	−	0.176536i
$940$		0			0
$941$	42.3367	−	42.3367i	1.38014	−	1.38014i	0.535777	−	0.844359i	$-0.320019\pi$
$941$	42.3367	−	42.3367i	1.38014	−	1.38014i	0.844359	−	0.535777i	$-0.179981\pi$
$942$		0			0
$943$	2.17481			0.0708215
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−36.3384	+	36.3384i	−1.18084	+	1.18084i	−0.201313	+	0.979527i	$0.564521\pi$
$947$	−36.3384	+	36.3384i	−1.18084	+	1.18084i	−0.979527	+	0.201313i	$0.935479\pi$
$948$		0			0
$949$	6.43246	+	6.43246i	0.208807	+	0.208807i
$950$		0			0
$951$		−	23.4729i		−	0.761161i
$952$		0			0
$953$			32.7338i			1.06035i	0.847888	+	0.530176i	$0.177874\pi$
$953$			32.7338i			1.06035i	−0.847888	+	0.530176i	$0.822126\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.87322	+	1.87322i	−0.0605527	+	0.0605527i
$958$		0			0
$959$	−14.7952			−0.477762
$960$		0			0
$961$	−12.4244			−0.400789
$962$		0			0
$963$	4.65424	−	4.65424i	0.149981	−	0.149981i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	49.7169i		−	1.59879i	−0.600807	−	0.799394i	$-0.705154\pi$
$967$		−	49.7169i		−	1.59879i	0.600807	−	0.799394i	$-0.294846\pi$
$968$		0			0
$969$			1.71153i			0.0549823i
$970$		0			0
$971$	24.7937	+	24.7937i	0.795667	+	0.795667i	0.982409	−	0.186742i	$-0.0597928\pi$
$971$	24.7937	+	24.7937i	0.795667	+	0.795667i	−0.186742	+	0.982409i	$0.559793\pi$
$972$		0			0
$973$	−21.0908	+	21.0908i	−0.676139	+	0.676139i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	49.4546			1.58219			0.791096	−	0.611692i	$-0.209511\pi$
$977$	49.4546			1.58219			0.791096	+	0.611692i	$0.209511\pi$
$978$		0			0
$979$	−7.06579	+	7.06579i	−0.225824	+	0.225824i
$980$		0			0
$981$	−6.36387	−	6.36387i	−0.203183	−	0.203183i
$982$		0			0
$983$			23.9656i			0.764383i	0.924083	+	0.382191i	$0.124830\pi$
$983$			23.9656i			0.764383i	−0.924083	+	0.382191i	$0.875170\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−31.4056	−	31.4056i	−0.999650	−	0.999650i
$988$		0			0
$989$	−18.1124	+	18.1124i	−0.575940	+	0.575940i
$990$		0			0
$991$	−28.8345			−0.915957			−0.457978	−	0.888963i	$-0.651426\pi$
$991$	−28.8345			−0.915957			−0.457978	+	0.888963i	$0.651426\pi$
$992$		0			0
$993$	−27.9399			−0.886645
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−6.03212	−	6.03212i	−0.191039	−	0.191039i	0.605106	−	0.796145i	$-0.293131\pi$
$997$	−6.03212	−	6.03212i	−0.191039	−	0.191039i	−0.796145	+	0.605106i	$0.793131\pi$
$998$		0			0
$999$		−	5.31998i		−	0.168317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.l.i.1201.3		16
4.3	odd	2		400.2.l.h.101.8		16
5.2	odd	4		1600.2.q.g.49.6		16
5.3	odd	4		1600.2.q.h.49.3		16
5.4	even	2		320.2.l.a.241.6		16
15.14	odd	2		2880.2.t.c.2161.1		16
16.3	odd	4		400.2.l.h.301.8		16
16.13	even	4	inner	1600.2.l.i.401.3		16
20.3	even	4		400.2.q.g.149.5		16
20.7	even	4		400.2.q.h.149.4		16
20.19	odd	2		80.2.l.a.21.1	✓	16
40.19	odd	2		640.2.l.b.481.6		16
40.29	even	2		640.2.l.a.481.3		16
60.59	even	2		720.2.t.c.181.8		16
80.3	even	4		400.2.q.h.349.4		16
80.13	odd	4		1600.2.q.g.849.6		16
80.19	odd	4		80.2.l.a.61.1	yes	16
80.29	even	4		320.2.l.a.81.6		16
80.59	odd	4		640.2.l.b.161.6		16
80.67	even	4		400.2.q.g.349.5		16
80.69	even	4		640.2.l.a.161.3		16
80.77	odd	4		1600.2.q.h.849.3		16
160.19	odd	8		5120.2.a.v.1.5		8
160.29	even	8		5120.2.a.u.1.5		8
160.99	odd	8		5120.2.a.s.1.4		8
160.109	even	8		5120.2.a.t.1.4		8
240.29	odd	4		2880.2.t.c.721.4		16
240.179	even	4		720.2.t.c.541.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.1	✓	16	20.19	odd	2
80.2.l.a.61.1	yes	16	80.19	odd	4
320.2.l.a.81.6		16	80.29	even	4
320.2.l.a.241.6		16	5.4	even	2
400.2.l.h.101.8		16	4.3	odd	2
400.2.l.h.301.8		16	16.3	odd	4
400.2.q.g.149.5		16	20.3	even	4
400.2.q.g.349.5		16	80.67	even	4
400.2.q.h.149.4		16	20.7	even	4
400.2.q.h.349.4		16	80.3	even	4
640.2.l.a.161.3		16	80.69	even	4
640.2.l.a.481.3		16	40.29	even	2
640.2.l.b.161.6		16	80.59	odd	4
640.2.l.b.481.6		16	40.19	odd	2
720.2.t.c.181.8		16	60.59	even	2
720.2.t.c.541.8		16	240.179	even	4
1600.2.l.i.401.3		16	16.13	even	4	inner
1600.2.l.i.1201.3		16	1.1	even	1	trivial
1600.2.q.g.49.6		16	5.2	odd	4
1600.2.q.g.849.6		16	80.13	odd	4
1600.2.q.h.49.3		16	5.3	odd	4
1600.2.q.h.849.3		16	80.77	odd	4
2880.2.t.c.721.4		16	240.29	odd	4
2880.2.t.c.2161.1		16	15.14	odd	2
5120.2.a.s.1.4		8	160.99	odd	8
5120.2.a.t.1.4		8	160.109	even	8
5120.2.a.u.1.5		8	160.29	even	8
5120.2.a.v.1.5		8	160.19	odd	8

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)

\(f(q)\)	\(=\)	\(q+(-0.720673 + 0.720673i) q^{3} +4.02840i q^{7} +1.96126i q^{9} +O(q^{10})\)	\(q+(-0.720673 + 0.720673i) q^{3} +4.02840i q^{7} +1.96126i q^{9} +(0.646837 + 0.646837i) q^{11} +(-4.91492 + 4.91492i) q^{13} +2.70862 q^{17} +(0.438397 - 0.438397i) q^{19} +(-2.90316 - 2.90316i) q^{21} -3.60080i q^{23} +(-3.57545 - 3.57545i) q^{27} +(2.00921 - 2.00921i) q^{29} -4.30994 q^{31} -0.932316 q^{33} +(0.743961 + 0.743961i) q^{37} -7.08410i q^{39} +0.603979i q^{41} +(-5.03010 - 5.03010i) q^{43} +10.8177 q^{47} -9.22800 q^{49} +(-1.95203 + 1.95203i) q^{51} +(-4.07420 - 4.07420i) q^{53} +0.631882i q^{57} +(-1.22845 - 1.22845i) q^{59} +(-6.98912 + 6.98912i) q^{61} -7.90074 q^{63} +(5.24219 - 5.24219i) q^{67} +(2.59500 + 2.59500i) q^{69} +13.7940i q^{71} -1.30876i q^{73} +(-2.60572 + 2.60572i) q^{77} -0.611127 q^{79} -0.730326 q^{81} +(1.29471 - 1.29471i) q^{83} +2.89597i q^{87} +10.9236i q^{89} +(-19.7993 - 19.7993i) q^{91} +(3.10606 - 3.10606i) q^{93} +12.7571 q^{97} +(-1.26862 + 1.26862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 8 q^{11} + 8 q^{19} + 24 q^{27} - 16 q^{29} + 16 q^{37} + 8 q^{43} - 40 q^{47} - 16 q^{49} + 32 q^{51} - 16 q^{53} + 8 q^{59} + 16 q^{61} + 40 q^{63} + 40 q^{67} + 16 q^{69} - 16 q^{77} - 16 q^{79} - 16 q^{81} + 40 q^{83} - 32 q^{91} + 48 q^{93} + 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^11 + 8 * q^19 + 24 * q^27 - 16 * q^29 + 16 * q^37 + 8 * q^43 - 40 * q^47 - 16 * q^49 + 32 * q^51 - 16 * q^53 + 8 * q^59 + 16 * q^61 + 40 * q^63 + 40 * q^67 + 16 * q^69 - 16 * q^77 - 16 * q^79 - 16 * q^81 + 40 * q^83 - 32 * q^91 + 48 * q^93 + 8 * q^99

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