LMFDB - Embedded newform 1568.2.i.y.961.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1568,2,Mod(961,1568)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1568, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1568.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.207360000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 $ x^8 + 6x^6 + 32x^4 + 24*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.4
Root			$-0.437016 - 0.756934i$ of defining polynomial
Character	$\chi$	$=$	1568.961
Dual form			1568.2.i.y.1537.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58114 + 2.73861i) q^{3} +(1.41421 - 2.44949i) q^{5} +(-3.50000 + 6.06218i) q^{9} +O(q^{10})$	$q+(1.58114 + 2.73861i) q^{3} +(1.41421 - 2.44949i) q^{5} +(-3.50000 + 6.06218i) q^{9} +(2.23607 + 3.87298i) q^{11} +8.94427 q^{15} +(2.12132 + 3.67423i) q^{17} +(1.58114 - 2.73861i) q^{19} +(4.47214 - 7.74597i) q^{23} +(-1.50000 - 2.59808i) q^{25} -12.6491 q^{27} -6.00000 q^{29} +(3.16228 + 5.47723i) q^{31} +(-7.07107 + 12.2474i) q^{33} +(-1.00000 + 1.73205i) q^{37} -1.41421 q^{41} +4.47214 q^{43} +(9.89949 + 17.1464i) q^{45} +(-3.16228 + 5.47723i) q^{47} +(-6.70820 + 11.6190i) q^{51} +(-3.00000 - 5.19615i) q^{53} +12.6491 q^{55} +10.0000 q^{57} +(1.58114 + 2.73861i) q^{59} +(-4.24264 + 7.34847i) q^{61} +28.2843 q^{69} -8.94427 q^{71} +(-3.53553 - 6.12372i) q^{73} +(4.74342 - 8.21584i) q^{75} +(4.47214 - 7.74597i) q^{79} +(-9.50000 - 16.4545i) q^{81} +9.48683 q^{83} +12.0000 q^{85} +(-9.48683 - 16.4317i) q^{87} +(4.94975 - 8.57321i) q^{89} +(-10.0000 + 17.3205i) q^{93} +(-4.47214 - 7.74597i) q^{95} -4.24264 q^{97} -31.3050 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 28 q^{9}+O(q^{10}) $ 8 * q - 28 * q^9	$ 8 q - 28 q^{9} - 12 q^{25} - 48 q^{29} - 8 q^{37} - 24 q^{53} + 80 q^{57} - 76 q^{81} + 96 q^{85} - 80 q^{93}+O(q^{100}) $ 8 * q - 28 * q^9 - 12 * q^25 - 48 * q^29 - 8 * q^37 - 24 * q^53 + 80 * q^57 - 76 * q^81 + 96 * q^85 - 80 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.58114	+	2.73861i	0.912871	+	1.58114i	0.809989	+	0.586445i	$0.199473\pi$
$3$	1.58114	+	2.73861i	0.912871	+	1.58114i	0.102882	+	0.994694i	$0.467194\pi$
$4$		0			0
$5$	1.41421	−	2.44949i	0.632456	−	1.09545i	−0.354593	−	0.935021i	$-0.615380\pi$
$5$	1.41421	−	2.44949i	0.632456	−	1.09545i	0.987048	−	0.160424i	$-0.0512862\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−3.50000	+	6.06218i	−1.16667	+	2.02073i
$10$		0			0
$11$	2.23607	+	3.87298i	0.674200	+	1.16775i	0.976702	+	0.214600i	$0.0688447\pi$
$11$	2.23607	+	3.87298i	0.674200	+	1.16775i	−0.302502	+	0.953149i	$0.597822\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	8.94427			2.30940
$16$		0			0
$17$	2.12132	+	3.67423i	0.514496	+	0.891133i	0.999859	+	0.0168199i	$0.00535420\pi$
$17$	2.12132	+	3.67423i	0.514496	+	0.891133i	−0.485363	+	0.874313i	$0.661312\pi$
$18$		0			0
$19$	1.58114	−	2.73861i	0.362738	−	0.628281i	−0.625672	−	0.780086i	$-0.715175\pi$
$19$	1.58114	−	2.73861i	0.362738	−	0.628281i	0.988410	+	0.151805i	$0.0485086\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.47214	−	7.74597i	0.932505	−	1.61515i	0.153481	−	0.988152i	$-0.450952\pi$
$23$	4.47214	−	7.74597i	0.932505	−	1.61515i	0.779024	−	0.626994i	$-0.215715\pi$
$24$		0			0
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$		0			0
$27$	−12.6491			−2.43432
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	3.16228	+	5.47723i	0.567962	+	0.983739i	0.996767	+	0.0803419i	$0.0256012\pi$
$31$	3.16228	+	5.47723i	0.567962	+	0.983739i	−0.428806	+	0.903397i	$0.641065\pi$
$32$		0			0
$33$	−7.07107	+	12.2474i	−1.23091	+	2.13201i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.41421			−0.220863			−0.110432	−	0.993884i	$-0.535223\pi$
$41$	−1.41421			−0.220863			−0.110432	+	0.993884i	$0.535223\pi$
$42$		0			0
$43$	4.47214			0.681994			0.340997	−	0.940064i	$-0.389235\pi$
$43$	4.47214			0.681994			0.340997	+	0.940064i	$0.389235\pi$
$44$		0			0
$45$	9.89949	+	17.1464i	1.47573	+	2.55604i
$46$		0			0
$47$	−3.16228	+	5.47723i	−0.461266	+	0.798935i	−0.999024	−	0.0441633i	$-0.985938\pi$
$47$	−3.16228	+	5.47723i	−0.461266	+	0.798935i	0.537759	+	0.843099i	$0.319271\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−6.70820	+	11.6190i	−0.939336	+	1.62698i
$52$		0			0
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$		0			0
$55$	12.6491			1.70561
$56$		0			0
$57$	10.0000			1.32453
$58$		0			0
$59$	1.58114	+	2.73861i	0.205847	+	0.356537i	0.950402	−	0.311024i	$-0.100672\pi$
$59$	1.58114	+	2.73861i	0.205847	+	0.356537i	−0.744555	+	0.667561i	$0.767338\pi$
$60$		0			0
$61$	−4.24264	+	7.34847i	−0.543214	+	0.940875i	0.455502	+	0.890235i	$0.349460\pi$
$61$	−4.24264	+	7.34847i	−0.543214	+	0.940875i	−0.998717	+	0.0506406i	$0.983874\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$		0			0
$69$	28.2843			3.40503
$70$		0			0
$71$	−8.94427			−1.06149			−0.530745	−	0.847532i	$-0.678088\pi$
$71$	−8.94427			−1.06149			−0.530745	+	0.847532i	$0.678088\pi$
$72$		0			0
$73$	−3.53553	−	6.12372i	−0.413803	−	0.716728i	0.581499	−	0.813547i	$-0.302466\pi$
$73$	−3.53553	−	6.12372i	−0.413803	−	0.716728i	−0.995302	+	0.0968194i	$0.969133\pi$
$74$		0			0
$75$	4.74342	−	8.21584i	0.547723	−	0.948683i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.47214	−	7.74597i	0.503155	−	0.871489i	−0.496839	−	0.867843i	$-0.665506\pi$
$79$	4.47214	−	7.74597i	0.503155	−	0.871489i	0.999993	−	0.00364646i	$-0.00116071\pi$
$80$		0			0
$81$	−9.50000	−	16.4545i	−1.05556	−	1.82828i
$82$		0			0
$83$	9.48683			1.04132			0.520658	−	0.853766i	$-0.325687\pi$
$83$	9.48683			1.04132			0.520658	+	0.853766i	$0.325687\pi$
$84$		0			0
$85$	12.0000			1.30158
$86$		0			0
$87$	−9.48683	−	16.4317i	−1.01710	−	1.76166i
$88$		0			0
$89$	4.94975	−	8.57321i	0.524672	−	0.908759i	−0.474915	−	0.880032i	$-0.657521\pi$
$89$	4.94975	−	8.57321i	0.524672	−	0.908759i	0.999587	−	0.0287273i	$-0.00914543\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−10.0000	+	17.3205i	−1.03695	+	1.79605i
$94$		0			0
$95$	−4.47214	−	7.74597i	−0.458831	−	0.794719i
$96$		0			0
$97$	−4.24264			−0.430775			−0.215387	−	0.976529i	$-0.569101\pi$
$97$	−4.24264			−0.430775			−0.215387	+	0.976529i	$0.569101\pi$
$98$		0			0
$99$	−31.3050			−3.14627
$100$		0			0
$101$	4.24264	+	7.34847i	0.422159	+	0.731200i	0.996150	−	0.0876610i	$-0.0279392\pi$
$101$	4.24264	+	7.34847i	0.422159	+	0.731200i	−0.573992	+	0.818861i	$0.694606\pi$
$102$		0			0
$103$	−3.16228	+	5.47723i	−0.311588	+	0.539687i	−0.978706	−	0.205265i	$-0.934194\pi$
$103$	−3.16228	+	5.47723i	−0.311588	+	0.539687i	0.667118	+	0.744952i	$0.267528\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$		0			0
$111$	−6.32456			−0.600300
$112$		0			0
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$		0			0
$115$	−12.6491	−	21.9089i	−1.17954	−	2.04302i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.50000	+	7.79423i	−0.409091	+	0.708566i
$122$		0			0
$123$	−2.23607	−	3.87298i	−0.201619	−	0.349215i
$124$		0			0
$125$	5.65685			0.505964
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$	7.07107	+	12.2474i	0.622573	+	1.07833i
$130$		0			0
$131$	−7.90569	+	13.6931i	−0.690724	+	1.19637i	0.280877	+	0.959744i	$0.409375\pi$
$131$	−7.90569	+	13.6931i	−0.690724	+	1.19637i	−0.971601	+	0.236625i	$0.923959\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−17.8885	+	30.9839i	−1.53960	+	2.66667i
$136$		0			0
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	9.48683			0.804663			0.402331	−	0.915494i	$-0.368200\pi$
$139$	9.48683			0.804663			0.402331	+	0.915494i	$0.368200\pi$
$140$		0			0
$141$	−20.0000			−1.68430
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−8.48528	+	14.6969i	−0.704664	+	1.22051i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	−0.422744	−	0.906249i	$-0.638933\pi$
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	0.996207	−	0.0870170i	$-0.0277334\pi$
$150$		0			0
$151$	−8.94427	−	15.4919i	−0.727875	−	1.26072i	−0.957780	−	0.287503i	$-0.907175\pi$
$151$	−8.94427	−	15.4919i	−0.727875	−	1.26072i	0.229905	−	0.973213i	$-0.426158\pi$
$152$		0			0
$153$	−29.6985			−2.40098
$154$		0			0
$155$	17.8885			1.43684
$156$		0			0
$157$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$157$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$158$		0			0
$159$	9.48683	−	16.4317i	0.752355	−	1.30312i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	6.70820	−	11.6190i	0.525427	−	0.910066i	−0.474134	−	0.880453i	$-0.657239\pi$
$163$	6.70820	−	11.6190i	0.525427	−	0.910066i	0.999561	−	0.0296139i	$-0.00942777\pi$
$164$		0			0
$165$	20.0000	+	34.6410i	1.55700	+	2.69680i
$166$		0			0
$167$	6.32456			0.489409			0.244704	−	0.969598i	$-0.421309\pi$
$167$	6.32456			0.489409			0.244704	+	0.969598i	$0.421309\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$	11.0680	+	19.1703i	0.846389	+	1.46599i
$172$		0			0
$173$	2.82843	−	4.89898i	0.215041	−	0.372463i	−0.738244	−	0.674534i	$-0.764345\pi$
$173$	2.82843	−	4.89898i	0.215041	−	0.372463i	0.953285	+	0.302071i	$0.0976780\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.00000	+	8.66025i	−0.375823	+	0.650945i
$178$		0			0
$179$	−8.94427	−	15.4919i	−0.668526	−	1.15792i	−0.978316	−	0.207116i	$-0.933592\pi$
$179$	−8.94427	−	15.4919i	−0.668526	−	1.15792i	0.309790	−	0.950805i	$-0.399741\pi$
$180$		0			0
$181$	−22.6274			−1.68188			−0.840941	−	0.541126i	$-0.817998\pi$
$181$	−22.6274			−1.68188			−0.840941	+	0.541126i	$0.817998\pi$
$182$		0			0
$183$	−26.8328			−1.98354
$184$		0			0
$185$	2.82843	+	4.89898i	0.207950	+	0.360180i
$186$		0			0
$187$	−9.48683	+	16.4317i	−0.693746	+	1.20160i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.47214	−	7.74597i	0.323592	−	0.560478i	−0.657634	−	0.753338i	$-0.728443\pi$
$191$	4.47214	−	7.74597i	0.323592	−	0.560478i	0.981226	+	0.192859i	$0.0617760\pi$
$192$		0			0
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	−0.868255	−	0.496119i	$-0.834758\pi$
$193$	−12.0000	−	20.7846i	−0.863779	−	1.49611i	0.00447566	−	0.999990i	$-0.498575\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$		0			0
$199$	3.16228	+	5.47723i	0.224168	+	0.388270i	0.956069	−	0.293140i	$-0.0947003\pi$
$199$	3.16228	+	5.47723i	0.224168	+	0.388270i	−0.731902	+	0.681410i	$0.761367\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−2.00000	+	3.46410i	−0.139686	+	0.241943i
$206$		0			0
$207$	31.3050	+	54.2218i	2.17584	+	3.76867i
$208$		0			0
$209$	14.1421			0.978232
$210$		0			0
$211$	17.8885			1.23150			0.615749	−	0.787942i	$-0.288854\pi$
$211$	17.8885			1.23150			0.615749	+	0.787942i	$0.288854\pi$
$212$		0			0
$213$	−14.1421	−	24.4949i	−0.969003	−	1.67836i
$214$		0			0
$215$	6.32456	−	10.9545i	0.431331	−	0.747087i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	11.1803	−	19.3649i	0.755497	−	1.30856i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−25.2982			−1.69409			−0.847047	−	0.531518i	$-0.821622\pi$
$223$	−25.2982			−1.69409			−0.847047	+	0.531518i	$0.821622\pi$
$224$		0			0
$225$	21.0000			1.40000
$226$		0			0
$227$	−7.90569	−	13.6931i	−0.524719	−	0.908841i	−0.999586	−	0.0287826i	$-0.990837\pi$
$227$	−7.90569	−	13.6931i	−0.524719	−	0.908841i	0.474866	−	0.880058i	$-0.342496\pi$
$228$		0			0
$229$	8.48528	−	14.6969i	0.560723	−	0.971201i	−0.436710	−	0.899602i	$-0.643857\pi$
$229$	8.48528	−	14.6969i	0.560723	−	0.971201i	0.997434	−	0.0715988i	$-0.0228101\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.00000	−	13.8564i	0.524097	−	0.907763i	−0.475509	−	0.879711i	$-0.657736\pi$
$233$	8.00000	−	13.8564i	0.524097	−	0.907763i	0.999606	−	0.0280525i	$-0.00893057\pi$
$234$		0			0
$235$	8.94427	+	15.4919i	0.583460	+	1.01058i
$236$		0			0
$237$	28.2843			1.83726
$238$		0			0
$239$	26.8328			1.73567			0.867835	−	0.496852i	$-0.165511\pi$
$239$	26.8328			1.73567			0.867835	+	0.496852i	$0.165511\pi$
$240$		0			0
$241$	−13.4350	−	23.2702i	−0.865426	−	1.49896i	−0.866623	−	0.498963i	$-0.833714\pi$
$241$	−13.4350	−	23.2702i	−0.865426	−	1.49896i	0.00119700	−	0.999999i	$-0.499619\pi$
$242$		0			0
$243$	11.0680	−	19.1703i	0.710011	−	1.22977i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	15.0000	+	25.9808i	0.950586	+	1.64646i
$250$		0			0
$251$	9.48683			0.598804			0.299402	−	0.954127i	$-0.403213\pi$
$251$	9.48683			0.598804			0.299402	+	0.954127i	$0.403213\pi$
$252$		0			0
$253$	40.0000			2.51478
$254$		0			0
$255$	18.9737	+	32.8634i	1.18818	+	2.05798i
$256$		0			0
$257$	12.0208	−	20.8207i	0.749838	−	1.29876i	−0.198062	−	0.980189i	$-0.563465\pi$
$257$	12.0208	−	20.8207i	0.749838	−	1.29876i	0.947900	−	0.318568i	$-0.103202\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	21.0000	−	36.3731i	1.29987	−	2.25144i
$262$		0			0
$263$	−4.47214	−	7.74597i	−0.275764	−	0.477637i	0.694564	−	0.719431i	$-0.255597\pi$
$263$	−4.47214	−	7.74597i	−0.275764	−	0.477637i	−0.970328	+	0.241794i	$0.922264\pi$
$264$		0			0
$265$	−16.9706			−1.04249
$266$		0			0
$267$	31.3050			1.91583
$268$		0			0
$269$	5.65685	+	9.79796i	0.344904	+	0.597392i	0.985336	−	0.170623i	$-0.0545780\pi$
$269$	5.65685	+	9.79796i	0.344904	+	0.597392i	−0.640432	+	0.768015i	$0.721245\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.70820	−	11.6190i	0.404520	−	0.700649i
$276$		0			0
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$		0			0
$279$	−44.2719			−2.65049
$280$		0			0
$281$	8.00000			0.477240			0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000			0.477240			0.238620	+	0.971113i	$0.423305\pi$
$282$		0			0
$283$	14.2302	+	24.6475i	0.845901	+	1.46514i	0.884837	+	0.465901i	$0.154270\pi$
$283$	14.2302	+	24.6475i	0.845901	+	1.46514i	−0.0389363	+	0.999242i	$0.512397\pi$
$284$		0			0
$285$	14.1421	−	24.4949i	0.837708	−	1.45095i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	−6.70820	−	11.6190i	−0.393242	−	0.681115i
$292$		0			0
$293$	8.48528			0.495715			0.247858	−	0.968796i	$-0.420273\pi$
$293$	8.48528			0.495715			0.247858	+	0.968796i	$0.420273\pi$
$294$		0			0
$295$	8.94427			0.520756
$296$		0			0
$297$	−28.2843	−	48.9898i	−1.64122	−	2.84268i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−13.4164	+	23.2379i	−0.770752	+	1.33498i
$304$		0			0
$305$	12.0000	+	20.7846i	0.687118	+	1.19012i
$306$		0			0
$307$	15.8114			0.902404			0.451202	−	0.892422i	$-0.350995\pi$
$307$	15.8114			0.902404			0.451202	+	0.892422i	$0.350995\pi$
$308$		0			0
$309$	−20.0000			−1.13776
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	−10.6066	+	18.3712i	−0.599521	+	1.03840i	0.393371	+	0.919380i	$0.371309\pi$
$313$	−10.6066	+	18.3712i	−0.599521	+	1.03840i	−0.992892	+	0.119020i	$0.962025\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	−0.892741	−	0.450570i	$-0.851221\pi$
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	0.836576	+	0.547852i	$0.184554\pi$
$318$		0			0
$319$	−13.4164	−	23.2379i	−0.751175	−	1.30107i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	13.4164			0.746509
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−15.8114	+	27.3861i	−0.874372	+	1.51446i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.70820	−	11.6190i	0.368716	−	0.638635i	−0.620649	−	0.784089i	$-0.713131\pi$
$331$	6.70820	−	11.6190i	0.368716	−	0.638635i	0.989365	+	0.145453i	$0.0464641\pi$
$332$		0			0
$333$	−7.00000	−	12.1244i	−0.383598	−	0.664411i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	6.32456	+	10.9545i	0.343503	+	0.594964i
$340$		0			0
$341$	−14.1421	+	24.4949i	−0.765840	+	1.32647i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	40.0000	−	69.2820i	2.15353	−	3.73002i
$346$		0			0
$347$	15.6525	+	27.1109i	0.840269	+	1.45539i	0.889667	+	0.456609i	$0.150936\pi$
$347$	15.6525	+	27.1109i	0.840269	+	1.45539i	−0.0493984	+	0.998779i	$0.515730\pi$
$348$		0			0
$349$	−11.3137			−0.605609			−0.302804	−	0.953053i	$-0.597923\pi$
$349$	−11.3137			−0.605609			−0.302804	+	0.953053i	$0.597923\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.707107	−	1.22474i	−0.0376355	−	0.0651866i	0.846594	−	0.532239i	$-0.178649\pi$
$353$	−0.707107	−	1.22474i	−0.0376355	−	0.0651866i	−0.884230	+	0.467052i	$0.845316\pi$
$354$		0			0
$355$	−12.6491	+	21.9089i	−0.671345	+	1.16280i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.94427	−	15.4919i	0.472061	−	0.817633i	−0.527428	−	0.849600i	$-0.676844\pi$
$359$	8.94427	−	15.4919i	0.472061	−	0.817633i	0.999489	+	0.0319666i	$0.0101770\pi$
$360$		0			0
$361$	4.50000	+	7.79423i	0.236842	+	0.410223i
$362$		0			0
$363$	−28.4605			−1.49379
$364$		0			0
$365$	−20.0000			−1.04685
$366$		0			0
$367$	−6.32456	−	10.9545i	−0.330139	−	0.571818i	0.652400	−	0.757875i	$-0.273762\pi$
$367$	−6.32456	−	10.9545i	−0.330139	−	0.571818i	−0.982539	+	0.186057i	$0.940429\pi$
$368$		0			0
$369$	4.94975	−	8.57321i	0.257674	−	0.446304i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	7.00000	−	12.1244i	0.362446	−	0.627775i	−0.625917	−	0.779890i	$-0.715275\pi$
$373$	7.00000	−	12.1244i	0.362446	−	0.627775i	0.988363	+	0.152115i	$0.0486083\pi$
$374$		0			0
$375$	8.94427	+	15.4919i	0.461880	+	0.800000i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−22.3607			−1.14859			−0.574295	−	0.818648i	$-0.694724\pi$
$379$	−22.3607			−1.14859			−0.574295	+	0.818648i	$0.694724\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	15.8114	−	27.3861i	0.807924	−	1.39937i	−0.106375	−	0.994326i	$-0.533924\pi$
$383$	15.8114	−	27.3861i	0.807924	−	1.39937i	0.914299	−	0.405040i	$-0.132742\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−15.6525	+	27.1109i	−0.795660	+	1.37812i
$388$		0			0
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	0.942578	+	0.333987i	$0.108394\pi$
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	−0.182047	+	0.983290i	$0.558272\pi$
$390$		0			0
$391$	37.9473			1.91908
$392$		0			0
$393$	−50.0000			−2.52217
$394$		0			0
$395$	−12.6491	−	21.9089i	−0.636446	−	1.10236i
$396$		0			0
$397$	−5.65685	+	9.79796i	−0.283909	+	0.491745i	−0.972344	−	0.233553i	$-0.924965\pi$
$397$	−5.65685	+	9.79796i	−0.283909	+	0.491745i	0.688435	+	0.725298i	$0.258298\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	0.199207	+	0.979957i	$0.436163\pi$
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−53.7401			−2.67037
$406$		0			0
$407$	−8.94427			−0.443351
$408$		0			0
$409$	−9.19239	−	15.9217i	−0.454534	−	0.787277i	0.544127	−	0.839003i	$-0.316861\pi$
$409$	−9.19239	−	15.9217i	−0.454534	−	0.787277i	−0.998661	+	0.0517263i	$0.983528\pi$
$410$		0			0
$411$	18.9737	−	32.8634i	0.935902	−	1.62103i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	13.4164	−	23.2379i	0.658586	−	1.14070i
$416$		0			0
$417$	15.0000	+	25.9808i	0.734553	+	1.27228i
$418$		0			0
$419$	3.16228			0.154487			0.0772437	−	0.997012i	$-0.475388\pi$
$419$	3.16228			0.154487			0.0772437	+	0.997012i	$0.475388\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$	−22.1359	−	38.3406i	−1.07629	−	1.86418i
$424$		0			0
$425$	6.36396	−	11.0227i	0.308697	−	0.534680i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.47214	−	7.74597i	−0.215415	−	0.373110i	0.737986	−	0.674816i	$-0.235777\pi$
$431$	−4.47214	−	7.74597i	−0.215415	−	0.373110i	−0.953401	+	0.301706i	$0.902444\pi$
$432$		0			0
$433$	−21.2132			−1.01944			−0.509721	−	0.860340i	$-0.670251\pi$
$433$	−21.2132			−1.01944			−0.509721	+	0.860340i	$0.670251\pi$
$434$		0			0
$435$	−53.6656			−2.57307
$436$		0			0
$437$	−14.1421	−	24.4949i	−0.676510	−	1.17175i
$438$		0			0
$439$	18.9737	−	32.8634i	0.905564	−	1.56848i	0.0854049	−	0.996346i	$-0.472782\pi$
$439$	18.9737	−	32.8634i	0.905564	−	1.56848i	0.820159	−	0.572136i	$-0.193885\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.94427	+	15.4919i	−0.424955	+	0.736044i	−0.996416	−	0.0845852i	$-0.973043\pi$
$443$	−8.94427	+	15.4919i	−0.424955	+	0.736044i	0.571461	+	0.820629i	$0.306377\pi$
$444$		0			0
$445$	−14.0000	−	24.2487i	−0.663664	−	1.14950i
$446$		0			0
$447$	44.2719			2.09399
$448$		0			0
$449$	14.0000			0.660701			0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000			0.660701			0.330350	+	0.943858i	$0.392833\pi$
$450$		0			0
$451$	−3.16228	−	5.47723i	−0.148906	−	0.257912i
$452$		0			0
$453$	28.2843	−	48.9898i	1.32891	−	2.30174i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	−0.944286	−	0.329125i	$-0.893246\pi$
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	0.757174	+	0.653213i	$0.226579\pi$
$458$		0			0
$459$	−26.8328	−	46.4758i	−1.25245	−	2.16930i
$460$		0			0
$461$	−5.65685			−0.263466			−0.131733	−	0.991285i	$-0.542054\pi$
$461$	−5.65685			−0.263466			−0.131733	+	0.991285i	$0.542054\pi$
$462$		0			0
$463$	−17.8885			−0.831351			−0.415676	−	0.909513i	$-0.636455\pi$
$463$	−17.8885			−0.831351			−0.415676	+	0.909513i	$0.636455\pi$
$464$		0			0
$465$	28.2843	+	48.9898i	1.31165	+	2.27185i
$466$		0			0
$467$	−17.3925	+	30.1247i	−0.804830	+	1.39401i	0.111575	+	0.993756i	$0.464410\pi$
$467$	−17.3925	+	30.1247i	−0.804830	+	1.39401i	−0.916406	+	0.400251i	$0.868923\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	10.0000	+	17.3205i	0.459800	+	0.796398i
$474$		0			0
$475$	−9.48683			−0.435286
$476$		0			0
$477$	42.0000			1.92305
$478$		0			0
$479$	9.48683	+	16.4317i	0.433464	+	0.750782i	0.997169	−	0.0751941i	$-0.0239576\pi$
$479$	9.48683	+	16.4317i	0.433464	+	0.750782i	−0.563704	+	0.825977i	$0.690624\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.00000	+	10.3923i	−0.272446	+	0.471890i
$486$		0			0
$487$	4.47214	+	7.74597i	0.202652	+	0.351003i	0.949382	−	0.314124i	$-0.101711\pi$
$487$	4.47214	+	7.74597i	0.202652	+	0.351003i	−0.746730	+	0.665127i	$0.768377\pi$
$488$		0			0
$489$	42.4264			1.91859
$490$		0			0
$491$	−35.7771			−1.61460			−0.807299	−	0.590143i	$-0.799071\pi$
$491$	−35.7771			−1.61460			−0.807299	+	0.590143i	$0.799071\pi$
$492$		0			0
$493$	−12.7279	−	22.0454i	−0.573237	−	0.992875i
$494$		0			0
$495$	−44.2719	+	76.6812i	−1.98987	+	3.44656i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−17.8885	+	30.9839i	−0.800801	+	1.38703i	0.118288	+	0.992979i	$0.462259\pi$
$499$	−17.8885	+	30.9839i	−0.800801	+	1.38703i	−0.919089	+	0.394049i	$0.871074\pi$
$500$		0			0
$501$	10.0000	+	17.3205i	0.446767	+	0.773823i
$502$		0			0
$503$	37.9473			1.69199			0.845994	−	0.533192i	$-0.179008\pi$
$503$	37.9473			1.69199			0.845994	+	0.533192i	$0.179008\pi$
$504$		0			0
$505$	24.0000			1.06799
$506$		0			0
$507$	−20.5548	−	35.6020i	−0.912871	−	1.58114i
$508$		0			0
$509$	−5.65685	+	9.79796i	−0.250736	+	0.434287i	−0.963729	−	0.266884i	$-0.914006\pi$
$509$	−5.65685	+	9.79796i	−0.250736	+	0.434287i	0.712993	+	0.701171i	$0.247339\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−20.0000	+	34.6410i	−0.883022	+	1.52944i
$514$		0			0
$515$	8.94427	+	15.4919i	0.394132	+	0.682656i
$516$		0			0
$517$	−28.2843			−1.24394
$518$		0			0
$519$	17.8885			0.785220
$520$		0			0
$521$	−0.707107	−	1.22474i	−0.0309789	−	0.0536570i	0.850120	−	0.526589i	$-0.176529\pi$
$521$	−0.707107	−	1.22474i	−0.0309789	−	0.0536570i	−0.881099	+	0.472931i	$0.843196\pi$
$522$		0			0
$523$	−1.58114	+	2.73861i	−0.0691384	+	0.119751i	−0.898522	−	0.438928i	$-0.855358\pi$
$523$	−1.58114	+	2.73861i	−0.0691384	+	0.119751i	0.829384	+	0.558679i	$0.188692\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.4164	+	23.2379i	−0.584428	+	1.01226i
$528$		0			0
$529$	−28.5000	−	49.3634i	−1.23913	−	2.14624i
$530$		0			0
$531$	−22.1359			−0.960618
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	28.2843	−	48.9898i	1.22056	−	2.11407i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$		0			0
$543$	−35.7771	−	61.9677i	−1.53534	−	2.65929i
$544$		0			0
$545$	28.2843			1.21157
$546$		0			0
$547$	13.4164			0.573644			0.286822	−	0.957984i	$-0.407401\pi$
$547$	13.4164			0.573644			0.286822	+	0.957984i	$0.407401\pi$
$548$		0			0
$549$	−29.6985	−	51.4393i	−1.26750	−	2.19538i
$550$		0			0
$551$	−9.48683	+	16.4317i	−0.404153	+	0.700013i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−8.94427	+	15.4919i	−0.379663	+	0.657596i
$556$		0			0
$557$	11.0000	+	19.0526i	0.466085	+	0.807283i	0.999250	−	0.0387286i	$-0.0123308\pi$
$557$	11.0000	+	19.0526i	0.466085	+	0.807283i	−0.533165	+	0.846011i	$0.678997\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−60.0000			−2.53320
$562$		0			0
$563$	14.2302	+	24.6475i	0.599734	+	1.03877i	0.992860	+	0.119285i	$0.0380601\pi$
$563$	14.2302	+	24.6475i	0.599734	+	1.03877i	−0.393127	+	0.919484i	$0.628607\pi$
$564$		0			0
$565$	5.65685	−	9.79796i	0.237986	−	0.412203i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	2.23607	+	3.87298i	0.0935765	+	0.162079i	0.909014	−	0.416766i	$-0.136837\pi$
$571$	2.23607	+	3.87298i	0.0935765	+	0.162079i	−0.815437	+	0.578846i	$0.803503\pi$
$572$		0			0
$573$	28.2843			1.18159
$574$		0			0
$575$	−26.8328			−1.11901
$576$		0			0
$577$	17.6777	+	30.6186i	0.735931	+	1.27467i	0.954314	+	0.298807i	$0.0965886\pi$
$577$	17.6777	+	30.6186i	0.735931	+	1.27467i	−0.218383	+	0.975863i	$0.570078\pi$
$578$		0			0
$579$	37.9473	−	65.7267i	1.57704	−	2.73151i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	13.4164	−	23.2379i	0.555651	−	0.962415i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.16228			−0.130521			−0.0652606	−	0.997868i	$-0.520788\pi$
$587$	−3.16228			−0.130521			−0.0652606	+	0.997868i	$0.520788\pi$
$588$		0			0
$589$	20.0000			0.824086
$590$		0			0
$591$	−34.7851	−	60.2495i	−1.43087	−	2.47833i
$592$		0			0
$593$	−3.53553	+	6.12372i	−0.145187	+	0.251471i	−0.929443	−	0.368967i	$-0.879712\pi$
$593$	−3.53553	+	6.12372i	−0.145187	+	0.251471i	0.784256	+	0.620438i	$0.213045\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.0000	+	17.3205i	−0.409273	+	0.708881i
$598$		0			0
$599$	−17.8885	−	30.9839i	−0.730906	−	1.26597i	−0.956496	−	0.291744i	$-0.905764\pi$
$599$	−17.8885	−	30.9839i	−0.730906	−	1.26597i	0.225590	−	0.974222i	$-0.427569\pi$
$600$		0			0
$601$	−12.7279			−0.519183			−0.259591	−	0.965719i	$-0.583588\pi$
$601$	−12.7279			−0.519183			−0.259591	+	0.965719i	$0.583588\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	12.7279	+	22.0454i	0.517464	+	0.896273i
$606$		0			0
$607$	6.32456	−	10.9545i	0.256706	−	0.444627i	−0.708652	−	0.705559i	$-0.750696\pi$
$607$	6.32456	−	10.9545i	0.256706	−	0.444627i	0.965357	+	0.260931i	$0.0840295\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	−0.999574	−	0.0291886i	$-0.990708\pi$
$613$	−13.0000	−	22.5167i	−0.525065	−	0.909439i	0.474509	−	0.880251i	$-0.342626\pi$
$614$		0			0
$615$	−12.6491			−0.510061
$616$		0			0
$617$	22.0000			0.885687			0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000			0.885687			0.442843	+	0.896599i	$0.353970\pi$
$618$		0			0
$619$	−7.90569	−	13.6931i	−0.317757	−	0.550371i	0.662263	−	0.749271i	$-0.269596\pi$
$619$	−7.90569	−	13.6931i	−0.317757	−	0.550371i	−0.980020	+	0.198901i	$0.936263\pi$
$620$		0			0
$621$	−56.5685	+	97.9796i	−2.27002	+	3.93179i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.5000	−	26.8468i	0.620000	−	1.07387i
$626$		0			0
$627$	22.3607	+	38.7298i	0.893000	+	1.54672i
$628$		0			0
$629$	−8.48528			−0.338330
$630$		0			0
$631$	8.94427			0.356066			0.178033	−	0.984025i	$-0.443027\pi$
$631$	8.94427			0.356066			0.178033	+	0.984025i	$0.443027\pi$
$632$		0			0
$633$	28.2843	+	48.9898i	1.12420	+	1.94717i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	31.3050	−	54.2218i	1.23840	−	2.14498i
$640$		0			0
$641$	11.0000	+	19.0526i	0.434474	+	0.752531i	0.997253	−	0.0740768i	$-0.0236010\pi$
$641$	11.0000	+	19.0526i	0.434474	+	0.752531i	−0.562779	+	0.826608i	$0.690268\pi$
$642$		0			0
$643$	−3.16228			−0.124708			−0.0623540	−	0.998054i	$-0.519861\pi$
$643$	−3.16228			−0.124708			−0.0623540	+	0.998054i	$0.519861\pi$
$644$		0			0
$645$	40.0000			1.57500
$646$		0			0
$647$	15.8114	+	27.3861i	0.621610	+	1.07666i	0.989186	+	0.146666i	$0.0468544\pi$
$647$	15.8114	+	27.3861i	0.621610	+	1.07666i	−0.367576	+	0.929993i	$0.619812\pi$
$648$		0			0
$649$	−7.07107	+	12.2474i	−0.277564	+	0.480754i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.0000	−	22.5167i	0.508729	−	0.881145i	−0.491220	−	0.871036i	$-0.663449\pi$
$653$	13.0000	−	22.5167i	0.508729	−	0.881145i	0.999949	−	0.0101092i	$-0.00321793\pi$
$654$		0			0
$655$	22.3607	+	38.7298i	0.873704	+	1.51330i
$656$		0			0
$657$	49.4975			1.93108
$658$		0			0
$659$	−4.47214			−0.174210			−0.0871048	−	0.996199i	$-0.527762\pi$
$659$	−4.47214			−0.174210			−0.0871048	+	0.996199i	$0.527762\pi$
$660$		0			0
$661$	4.24264	+	7.34847i	0.165020	+	0.285822i	0.936662	−	0.350234i	$-0.113898\pi$
$661$	4.24264	+	7.34847i	0.165020	+	0.285822i	−0.771643	+	0.636056i	$0.780565\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−26.8328	+	46.4758i	−1.03897	+	1.79955i
$668$		0			0
$669$	−40.0000	−	69.2820i	−1.54649	−	2.67860i
$670$		0			0
$671$	−37.9473			−1.46494
$672$		0			0
$673$	−36.0000			−1.38770			−0.693849	−	0.720121i	$-0.744086\pi$
$673$	−36.0000			−1.38770			−0.693849	+	0.720121i	$0.744086\pi$
$674$		0			0
$675$	18.9737	+	32.8634i	0.730297	+	1.26491i
$676$		0			0
$677$	−14.1421	+	24.4949i	−0.543526	+	0.941415i	0.455172	+	0.890404i	$0.349578\pi$
$677$	−14.1421	+	24.4949i	−0.543526	+	0.941415i	−0.998698	+	0.0510117i	$0.983755\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	25.0000	−	43.3013i	0.958002	−	1.65931i
$682$		0			0
$683$	8.94427	+	15.4919i	0.342243	+	0.592782i	0.984849	−	0.173415i	$-0.0554800\pi$
$683$	8.94427	+	15.4919i	0.342243	+	0.592782i	−0.642606	+	0.766197i	$0.722147\pi$
$684$		0			0
$685$	−33.9411			−1.29682
$686$		0			0
$687$	53.6656			2.04747
$688$		0			0
$689$		0			0
$690$		0			0
$691$	4.74342	−	8.21584i	0.180448	−	0.312545i	−0.761585	−	0.648065i	$-0.775579\pi$
$691$	4.74342	−	8.21584i	0.180448	−	0.312545i	0.942033	+	0.335520i	$0.108912\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	13.4164	−	23.2379i	0.508913	−	0.881464i
$696$		0			0
$697$	−3.00000	−	5.19615i	−0.113633	−	0.196818i
$698$		0			0
$699$	50.5964			1.91373
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	3.16228	+	5.47723i	0.119268	+	0.206577i
$704$		0			0
$705$	−28.2843	+	48.9898i	−1.06525	+	1.84506i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	0.347325	+	0.937745i	$0.387090\pi$
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	−0.985773	+	0.168080i	$0.946243\pi$
$710$		0			0
$711$	31.3050	+	54.2218i	1.17403	+	2.03348i
$712$		0			0
$713$	56.5685			2.11851
$714$		0			0
$715$		0			0
$716$		0			0
$717$	42.4264	+	73.4847i	1.58444	+	2.74434i
$718$		0			0
$719$	−3.16228	+	5.47723i	−0.117933	+	0.204266i	−0.918948	−	0.394378i	$-0.870960\pi$
$719$	−3.16228	+	5.47723i	−0.117933	+	0.204266i	0.801015	+	0.598644i	$0.204293\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	42.4853	−	73.5867i	1.58004	−	2.73672i
$724$		0			0
$725$	9.00000	+	15.5885i	0.334252	+	0.578941i
$726$		0			0
$727$	−18.9737			−0.703694			−0.351847	−	0.936057i	$-0.614446\pi$
$727$	−18.9737			−0.703694			−0.351847	+	0.936057i	$0.614446\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	9.48683	+	16.4317i	0.350883	+	0.607748i
$732$		0			0
$733$	−7.07107	+	12.2474i	−0.261176	+	0.452370i	−0.966555	−	0.256461i	$-0.917444\pi$
$733$	−7.07107	+	12.2474i	−0.261176	+	0.452370i	0.705379	+	0.708831i	$0.250777\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−2.23607	−	3.87298i	−0.0822551	−	0.142470i	0.821963	−	0.569541i	$-0.192879\pi$
$739$	−2.23607	−	3.87298i	−0.0822551	−	0.142470i	−0.904218	+	0.427071i	$0.859546\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	17.8885			0.656267			0.328134	−	0.944631i	$-0.393580\pi$
$743$	17.8885			0.656267			0.328134	+	0.944631i	$0.393580\pi$
$744$		0			0
$745$	−19.7990	−	34.2929i	−0.725379	−	1.25639i
$746$		0			0
$747$	−33.2039	+	57.5109i	−1.21487	+	2.10421i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−22.3607	+	38.7298i	−0.815953	+	1.41327i	0.0926889	+	0.995695i	$0.470454\pi$
$751$	−22.3607	+	38.7298i	−0.815953	+	1.41327i	−0.908642	+	0.417577i	$0.862880\pi$
$752$		0			0
$753$	15.0000	+	25.9808i	0.546630	+	0.946792i
$754$		0			0
$755$	−50.5964			−1.84139
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$		0			0
$759$	63.2456	+	109.545i	2.29567	+	3.97621i
$760$		0			0
$761$	13.4350	−	23.2702i	0.487019	−	0.843542i	−0.512869	−	0.858467i	$-0.671417\pi$
$761$	13.4350	−	23.2702i	0.487019	−	0.843542i	0.999889	+	0.0149244i	$0.00475076\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−42.0000	+	72.7461i	−1.51851	+	2.63014i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−46.6690			−1.68293			−0.841464	−	0.540312i	$-0.818306\pi$
$769$	−46.6690			−1.68293			−0.841464	+	0.540312i	$0.818306\pi$
$770$		0			0
$771$	76.0263			2.73802
$772$		0			0
$773$	7.07107	+	12.2474i	0.254329	+	0.440510i	0.964713	−	0.263304i	$-0.0848122\pi$
$773$	7.07107	+	12.2474i	0.254329	+	0.440510i	−0.710384	+	0.703814i	$0.751479\pi$
$774$		0			0
$775$	9.48683	−	16.4317i	0.340777	−	0.590243i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.23607	+	3.87298i	−0.0801154	+	0.138764i
$780$		0			0
$781$	−20.0000	−	34.6410i	−0.715656	−	1.23955i
$782$		0			0
$783$	75.8947			2.71225
$784$		0			0
$785$		0			0
$786$		0			0
$787$	7.90569	+	13.6931i	0.281808	+	0.488105i	0.971830	−	0.235683i	$-0.0757327\pi$
$787$	7.90569	+	13.6931i	0.281808	+	0.488105i	−0.690022	+	0.723788i	$0.742399\pi$
$788$		0			0
$789$	14.1421	−	24.4949i	0.503473	−	0.872041i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−26.8328	−	46.4758i	−0.951662	−	1.64833i
$796$		0			0
$797$	45.2548			1.60301			0.801504	−	0.597989i	$-0.204033\pi$
$797$	45.2548			1.60301			0.801504	+	0.597989i	$0.204033\pi$
$798$		0			0
$799$	−26.8328			−0.949277
$800$		0			0
$801$	34.6482	+	60.0125i	1.22424	+	2.12044i
$802$		0			0
$803$	15.8114	−	27.3861i	0.557972	−	0.966435i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−17.8885	+	30.9839i	−0.629707	+	1.09068i
$808$		0			0
$809$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$809$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$810$		0			0
$811$	−41.1096			−1.44355			−0.721777	−	0.692126i	$-0.756674\pi$
$811$	−41.1096			−1.44355			−0.721777	+	0.692126i	$0.756674\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−18.9737	−	32.8634i	−0.664619	−	1.15115i
$816$		0			0
$817$	7.07107	−	12.2474i	0.247385	−	0.428484i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	−0.765487	−	0.643451i	$-0.777502\pi$
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	0.939989	+	0.341206i	$0.110835\pi$
$822$		0			0
$823$	−8.94427	−	15.4919i	−0.311778	−	0.540015i	0.666970	−	0.745085i	$-0.267591\pi$
$823$	−8.94427	−	15.4919i	−0.311778	−	0.540015i	−0.978747	+	0.205070i	$0.934258\pi$
$824$		0			0
$825$	42.4264			1.47710
$826$		0			0
$827$	17.8885			0.622046			0.311023	−	0.950402i	$-0.399328\pi$
$827$	17.8885			0.622046			0.311023	+	0.950402i	$0.399328\pi$
$828$		0			0
$829$	−15.5563	−	26.9444i	−0.540294	−	0.935817i	−0.998887	−	0.0471706i	$-0.984980\pi$
$829$	−15.5563	−	26.9444i	−0.540294	−	0.935817i	0.458593	−	0.888647i	$-0.348354\pi$
$830$		0			0
$831$	34.7851	−	60.2495i	1.20668	−	2.09003i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.94427	−	15.4919i	0.309529	−	0.536120i
$836$		0			0
$837$	−40.0000	−	69.2820i	−1.38260	−	2.39474i
$838$		0			0
$839$	−56.9210			−1.96513			−0.982566	−	0.185917i	$-0.940475\pi$
$839$	−56.9210			−1.96513			−0.982566	+	0.185917i	$0.940475\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	12.6491	+	21.9089i	0.435659	+	0.754583i
$844$		0			0
$845$	−18.3848	+	31.8434i	−0.632456	+	1.09545i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−45.0000	+	77.9423i	−1.54440	+	2.67497i
$850$		0			0
$851$	8.94427	+	15.4919i	0.306606	+	0.531057i
$852$		0			0
$853$	33.9411			1.16212			0.581061	−	0.813860i	$-0.302638\pi$
$853$	33.9411			1.16212			0.581061	+	0.813860i	$0.302638\pi$
$854$		0			0
$855$	62.6099			2.14121
$856$		0			0
$857$	−24.7487	−	42.8661i	−0.845401	−	1.46428i	−0.885273	−	0.465072i	$-0.846028\pi$
$857$	−24.7487	−	42.8661i	−0.845401	−	1.46428i	0.0398720	−	0.999205i	$-0.487305\pi$
$858$		0			0
$859$	−1.58114	+	2.73861i	−0.0539478	+	0.0934403i	−0.891738	−	0.452552i	$-0.850514\pi$
$859$	−1.58114	+	2.73861i	−0.0539478	+	0.0934403i	0.837790	+	0.545992i	$0.183847\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−13.4164	+	23.2379i	−0.456700	+	0.791027i	−0.998784	−	0.0492968i	$-0.984302\pi$
$863$	−13.4164	+	23.2379i	−0.456700	+	0.791027i	0.542084	+	0.840324i	$0.317635\pi$
$864$		0			0
$865$	−8.00000	−	13.8564i	−0.272008	−	0.471132i
$866$		0			0
$867$	−3.16228			−0.107397
$868$		0			0
$869$	40.0000			1.35691
$870$		0			0
$871$		0			0
$872$		0			0
$873$	14.8492	−	25.7196i	0.502571	−	0.870478i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	0.256064	+	0.966660i	$0.417574\pi$
$877$	−21.0000	+	36.3731i	−0.709120	+	1.22823i	−0.965184	+	0.261571i	$0.915759\pi$
$878$		0			0
$879$	13.4164	+	23.2379i	0.452524	+	0.783795i
$880$		0			0
$881$	26.8701			0.905275			0.452638	−	0.891695i	$-0.350483\pi$
$881$	26.8701			0.905275			0.452638	+	0.891695i	$0.350483\pi$
$882$		0			0
$883$	53.6656			1.80599			0.902996	−	0.429649i	$-0.141363\pi$
$883$	53.6656			1.80599			0.902996	+	0.429649i	$0.141363\pi$
$884$		0			0
$885$	14.1421	+	24.4949i	0.475383	+	0.823387i
$886$		0			0
$887$	−9.48683	+	16.4317i	−0.318537	+	0.551722i	−0.980183	−	0.198094i	$-0.936525\pi$
$887$	−9.48683	+	16.4317i	−0.318537	+	0.551722i	0.661646	+	0.749816i	$0.269858\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	42.4853	−	73.5867i	1.42331	−	2.46525i
$892$		0			0
$893$	10.0000	+	17.3205i	0.334637	+	0.579609i
$894$		0			0
$895$	−50.5964			−1.69125
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18.9737	−	32.8634i	−0.632807	−	1.09605i
$900$		0			0
$901$	12.7279	−	22.0454i	0.424029	−	0.734439i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−32.0000	+	55.4256i	−1.06372	+	1.84241i
$906$		0			0
$907$	8.94427	+	15.4919i	0.296990	+	0.514401i	0.975446	−	0.220240i	$-0.0706840\pi$
$907$	8.94427	+	15.4919i	0.296990	+	0.514401i	−0.678456	+	0.734641i	$0.737351\pi$
$908$		0			0
$909$	−59.3970			−1.97007
$910$		0			0
$911$	−53.6656			−1.77802			−0.889011	−	0.457886i	$-0.848607\pi$
$911$	−53.6656			−1.77802			−0.889011	+	0.457886i	$0.848607\pi$
$912$		0			0
$913$	21.2132	+	36.7423i	0.702055	+	1.21599i
$914$		0			0
$915$	−37.9473	+	65.7267i	−1.25450	+	2.17286i
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$919$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$920$		0			0
$921$	25.0000	+	43.3013i	0.823778	+	1.42683i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	6.00000			0.197279
$926$		0			0
$927$	−22.1359	−	38.3406i	−0.727040	−	1.25927i
$928$		0			0
$929$	2.12132	−	3.67423i	0.0695983	−	0.120548i	−0.829126	−	0.559061i	$-0.811162\pi$
$929$	2.12132	−	3.67423i	0.0695983	−	0.120548i	0.898725	+	0.438514i	$0.144495\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	26.8328	+	46.4758i	0.877527	+	1.51992i
$936$		0			0
$937$	−38.1838			−1.24741			−0.623705	−	0.781660i	$-0.714373\pi$
$937$	−38.1838			−1.24741			−0.623705	+	0.781660i	$0.714373\pi$
$938$		0			0
$939$	−67.0820			−2.18914
$940$		0			0
$941$	24.0416	+	41.6413i	0.783735	+	1.35747i	0.929752	+	0.368186i	$0.120021\pi$
$941$	24.0416	+	41.6413i	0.783735	+	1.35747i	−0.146017	+	0.989282i	$0.546646\pi$
$942$		0			0
$943$	−6.32456	+	10.9545i	−0.205956	+	0.356726i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.23607	−	3.87298i	0.0726624	−	0.125855i	−0.827405	−	0.561606i	$-0.810184\pi$
$947$	2.23607	−	3.87298i	0.0726624	−	0.125855i	0.900067	+	0.435751i	$0.143517\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−6.32456			−0.205088
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	−12.6491	−	21.9089i	−0.409316	−	0.708955i
$956$		0			0
$957$	42.4264	−	73.4847i	1.37145	−	2.37542i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−4.50000	+	7.79423i	−0.145161	+	0.251427i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−67.8823			−2.18521
$966$		0			0
$967$	8.94427			0.287628			0.143814	−	0.989605i	$-0.454063\pi$
$967$	8.94427			0.287628			0.143814	+	0.989605i	$0.454063\pi$
$968$		0			0
$969$	21.2132	+	36.7423i	0.681466	+	1.18033i
$970$		0			0
$971$	14.2302	−	24.6475i	0.456670	−	0.790976i	−0.542112	−	0.840306i	$-0.682375\pi$
$971$	14.2302	−	24.6475i	0.456670	−	0.790976i	0.998783	+	0.0493298i	$0.0157085\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	0.945899	−	0.324462i	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		0			0
$979$	44.2719			1.41494
$980$		0			0
$981$	−70.0000			−2.23493
$982$		0			0
$983$	−3.16228	−	5.47723i	−0.100861	−	0.174696i	0.811179	−	0.584798i	$-0.198826\pi$
$983$	−3.16228	−	5.47723i	−0.100861	−	0.174696i	−0.912040	+	0.410102i	$0.865493\pi$
$984$		0			0
$985$	−31.1127	+	53.8888i	−0.991333	+	1.71704i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	20.0000	−	34.6410i	0.635963	−	1.10152i
$990$		0			0
$991$	−26.8328	−	46.4758i	−0.852372	−	1.47635i	−0.879061	−	0.476709i	$-0.841830\pi$
$991$	−26.8328	−	46.4758i	−0.852372	−	1.47635i	0.0266889	−	0.999644i	$-0.491504\pi$
$992$		0			0
$993$	42.4264			1.34636
$994$		0			0
$995$	17.8885			0.567105
$996$		0			0
$997$	−26.8701	−	46.5403i	−0.850983	−	1.47395i	−0.880322	−	0.474377i	$-0.842673\pi$
$997$	−26.8701	−	46.5403i	−0.850983	−	1.47395i	0.0293387	−	0.999570i	$-0.490660\pi$
$998$		0			0
$999$	12.6491	−	21.9089i	0.400200	−	0.693167i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.i.y.961.4		8
4.3	odd	2	inner	1568.2.i.y.961.2		8
7.2	even	3		1568.2.a.x.1.1	✓	4
7.3	odd	6	inner	1568.2.i.y.1537.1		8
7.4	even	3	inner	1568.2.i.y.1537.4		8
7.5	odd	6		1568.2.a.x.1.4	yes	4
7.6	odd	2	inner	1568.2.i.y.961.1		8
28.3	even	6	inner	1568.2.i.y.1537.3		8
28.11	odd	6	inner	1568.2.i.y.1537.2		8
28.19	even	6		1568.2.a.x.1.2	yes	4
28.23	odd	6		1568.2.a.x.1.3	yes	4
28.27	even	2	inner	1568.2.i.y.961.3		8
56.5	odd	6		3136.2.a.bz.1.1		4
56.19	even	6		3136.2.a.bz.1.3		4
56.37	even	6		3136.2.a.bz.1.4		4
56.51	odd	6		3136.2.a.bz.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1568.2.a.x.1.1	✓	4	7.2	even	3
1568.2.a.x.1.2	yes	4	28.19	even	6
1568.2.a.x.1.3	yes	4	28.23	odd	6
1568.2.a.x.1.4	yes	4	7.5	odd	6
1568.2.i.y.961.1		8	7.6	odd	2	inner
1568.2.i.y.961.2		8	4.3	odd	2	inner
1568.2.i.y.961.3		8	28.27	even	2	inner
1568.2.i.y.961.4		8	1.1	even	1	trivial
1568.2.i.y.1537.1		8	7.3	odd	6	inner
1568.2.i.y.1537.2		8	28.11	odd	6	inner
1568.2.i.y.1537.3		8	28.3	even	6	inner
1568.2.i.y.1537.4		8	7.4	even	3	inner
3136.2.a.bz.1.1		4	56.5	odd	6
3136.2.a.bz.1.2		4	56.51	odd	6
3136.2.a.bz.1.3		4	56.19	even	6
3136.2.a.bz.1.4		4	56.37	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.58114 + 2.73861i) q^{3} +(1.41421 - 2.44949i) q^{5} +(-3.50000 + 6.06218i) q^{9} +O(q^{10})\)	\(q+(1.58114 + 2.73861i) q^{3} +(1.41421 - 2.44949i) q^{5} +(-3.50000 + 6.06218i) q^{9} +(2.23607 + 3.87298i) q^{11} +8.94427 q^{15} +(2.12132 + 3.67423i) q^{17} +(1.58114 - 2.73861i) q^{19} +(4.47214 - 7.74597i) q^{23} +(-1.50000 - 2.59808i) q^{25} -12.6491 q^{27} -6.00000 q^{29} +(3.16228 + 5.47723i) q^{31} +(-7.07107 + 12.2474i) q^{33} +(-1.00000 + 1.73205i) q^{37} -1.41421 q^{41} +4.47214 q^{43} +(9.89949 + 17.1464i) q^{45} +(-3.16228 + 5.47723i) q^{47} +(-6.70820 + 11.6190i) q^{51} +(-3.00000 - 5.19615i) q^{53} +12.6491 q^{55} +10.0000 q^{57} +(1.58114 + 2.73861i) q^{59} +(-4.24264 + 7.34847i) q^{61} +28.2843 q^{69} -8.94427 q^{71} +(-3.53553 - 6.12372i) q^{73} +(4.74342 - 8.21584i) q^{75} +(4.47214 - 7.74597i) q^{79} +(-9.50000 - 16.4545i) q^{81} +9.48683 q^{83} +12.0000 q^{85} +(-9.48683 - 16.4317i) q^{87} +(4.94975 - 8.57321i) q^{89} +(-10.0000 + 17.3205i) q^{93} +(-4.47214 - 7.74597i) q^{95} -4.24264 q^{97} -31.3050 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 28 q^{9}+O(q^{10}) \) 8 * q - 28 * q^9	\( 8 q - 28 q^{9} - 12 q^{25} - 48 q^{29} - 8 q^{37} - 24 q^{53} + 80 q^{57} - 76 q^{81} + 96 q^{85} - 80 q^{93}+O(q^{100}) \) 8 * q - 28 * q^9 - 12 * q^25 - 48 * q^29 - 8 * q^37 - 24 * q^53 + 80 * q^57 - 76 * q^81 + 96 * q^85 - 80 * q^93

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