LMFDB - Embedded newform 1600.2.q.d.849.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1600.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			849.1
Root			$1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15831 + 1.15831i) q^{3} -4.31662 q^{7} +0.316625i q^{9} +O(q^{10})$	$q+(-1.15831 + 1.15831i) q^{3} -4.31662 q^{7} +0.316625i q^{9} +(0.158312 - 0.158312i) q^{11} +(-2.31662 + 2.31662i) q^{13} +5.31662i q^{17} +(3.15831 + 3.15831i) q^{19} +(5.00000 - 5.00000i) q^{21} +6.31662 q^{23} +(-3.84169 - 3.84169i) q^{27} +(-2.00000 - 2.00000i) q^{29} -4.31662 q^{31} +0.366750i q^{33} +(-7.31662 - 7.31662i) q^{37} -5.36675i q^{39} -5.00000i q^{41} +(-5.63325 - 5.63325i) q^{43} -8.00000i q^{47} +11.6332 q^{49} +(-6.15831 - 6.15831i) q^{51} +(3.31662 + 3.31662i) q^{53} -7.31662 q^{57} +(5.31662 - 5.31662i) q^{59} +(-3.63325 - 3.63325i) q^{61} -1.36675i q^{63} +(-5.84169 + 5.84169i) q^{67} +(-7.31662 + 7.31662i) q^{69} +4.63325i q^{71} +13.3166 q^{73} +(-0.683375 + 0.683375i) q^{77} -2.31662 q^{79} +7.94987 q^{81} +(-3.84169 + 3.84169i) q^{83} +4.63325 q^{87} -15.9499i q^{89} +(10.0000 - 10.0000i) q^{91} +(5.00000 - 5.00000i) q^{93} -6.63325i q^{97} +(0.0501256 + 0.0501256i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 - 4 * q^7	$ 4 q + 2 q^{3} - 4 q^{7} - 6 q^{11} + 4 q^{13} + 6 q^{19} + 20 q^{21} + 12 q^{23} - 22 q^{27} - 8 q^{29} - 4 q^{31} - 16 q^{37} + 4 q^{43} + 20 q^{49} - 18 q^{51} - 16 q^{57} + 8 q^{59} + 12 q^{61} - 30 q^{67} - 16 q^{69} + 40 q^{73} - 16 q^{77} + 4 q^{79} - 8 q^{81} - 22 q^{83} - 8 q^{87} + 40 q^{91} + 20 q^{93} + 40 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^7 - 6 * q^11 + 4 * q^13 + 6 * q^19 + 20 * q^21 + 12 * q^23 - 22 * q^27 - 8 * q^29 - 4 * q^31 - 16 * q^37 + 4 * q^43 + 20 * q^49 - 18 * q^51 - 16 * q^57 + 8 * q^59 + 12 * q^61 - 30 * q^67 - 16 * q^69 + 40 * q^73 - 16 * q^77 + 4 * q^79 - 8 * q^81 - 22 * q^83 - 8 * q^87 + 40 * q^91 + 20 * q^93 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.15831	+	1.15831i	−0.668752	+	0.668752i	−0.957427	−	0.288675i	$-0.906785\pi$
$3$	−1.15831	+	1.15831i	−0.668752	+	0.668752i	0.288675	+	0.957427i	$0.406785\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.31662			−1.63153			−0.815765	−	0.578383i	$-0.803684\pi$
$7$	−4.31662			−1.63153			−0.815765	+	0.578383i	$0.803684\pi$
$8$		0			0
$9$			0.316625i			0.105542i
$10$		0			0
$11$	0.158312	−	0.158312i	0.0477330	−	0.0477330i	−0.682837	−	0.730570i	$-0.739254\pi$
$11$	0.158312	−	0.158312i	0.0477330	−	0.0477330i	0.730570	+	0.682837i	$0.239254\pi$
$12$		0			0
$13$	−2.31662	+	2.31662i	−0.642516	+	0.642516i	−0.951173	−	0.308657i	$-0.900120\pi$
$13$	−2.31662	+	2.31662i	−0.642516	+	0.642516i	0.308657	+	0.951173i	$0.400120\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			5.31662i			1.28947i	0.764406	+	0.644735i	$0.223032\pi$
$17$			5.31662i			1.28947i	−0.764406	+	0.644735i	$0.776968\pi$
$18$		0			0
$19$	3.15831	+	3.15831i	0.724567	+	0.724567i	0.969532	−	0.244965i	$-0.0787766\pi$
$19$	3.15831	+	3.15831i	0.724567	+	0.724567i	−0.244965	+	0.969532i	$0.578777\pi$
$20$		0			0
$21$	5.00000	−	5.00000i	1.09109	−	1.09109i
$22$		0			0
$23$	6.31662			1.31711			0.658554	−	0.752534i	$-0.271169\pi$
$23$	6.31662			1.31711			0.658554	+	0.752534i	$0.271169\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.84169	−	3.84169i	−0.739333	−	0.739333i
$28$		0			0
$29$	−2.00000	−	2.00000i	−0.371391	−	0.371391i	0.496593	−	0.867984i	$-0.334584\pi$
$29$	−2.00000	−	2.00000i	−0.371391	−	0.371391i	−0.867984	+	0.496593i	$0.834584\pi$
$30$		0			0
$31$	−4.31662			−0.775289			−0.387644	−	0.921809i	$-0.626711\pi$
$31$	−4.31662			−0.775289			−0.387644	+	0.921809i	$0.626711\pi$
$32$		0			0
$33$			0.366750i			0.0638431i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.31662	−	7.31662i	−1.20285	−	1.20285i	−0.973297	−	0.229548i	$-0.926275\pi$
$37$	−7.31662	−	7.31662i	−1.20285	−	1.20285i	−0.229548	−	0.973297i	$-0.573725\pi$
$38$		0			0
$39$		−	5.36675i		−	0.859368i
$40$		0			0
$41$		−	5.00000i		−	0.780869i	−0.920631	−	0.390434i	$-0.872325\pi$
$41$		−	5.00000i		−	0.780869i	0.920631	−	0.390434i	$-0.127675\pi$
$42$		0			0
$43$	−5.63325	−	5.63325i	−0.859063	−	0.859063i	0.132165	−	0.991228i	$-0.457807\pi$
$43$	−5.63325	−	5.63325i	−0.859063	−	0.859063i	−0.991228	+	0.132165i	$0.957807\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	8.00000i		−	1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$		−	8.00000i		−	1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$		0			0
$49$	11.6332			1.66189
$50$		0			0
$51$	−6.15831	−	6.15831i	−0.862336	−	0.862336i
$52$		0			0
$53$	3.31662	+	3.31662i	0.455573	+	0.455573i	0.897199	−	0.441626i	$-0.145598\pi$
$53$	3.31662	+	3.31662i	0.455573	+	0.455573i	−0.441626	+	0.897199i	$0.645598\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−7.31662			−0.969111
$58$		0			0
$59$	5.31662	−	5.31662i	0.692166	−	0.692166i	−0.270542	−	0.962708i	$-0.587203\pi$
$59$	5.31662	−	5.31662i	0.692166	−	0.692166i	0.962708	+	0.270542i	$0.0872030\pi$
$60$		0			0
$61$	−3.63325	−	3.63325i	−0.465190	−	0.465190i	0.435162	−	0.900352i	$-0.356691\pi$
$61$	−3.63325	−	3.63325i	−0.465190	−	0.465190i	−0.900352	+	0.435162i	$0.856691\pi$
$62$		0			0
$63$		−	1.36675i		−	0.172194i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.84169	+	5.84169i	−0.713676	+	0.713676i	−0.967302	−	0.253626i	$-0.918377\pi$
$67$	−5.84169	+	5.84169i	−0.713676	+	0.713676i	0.253626	+	0.967302i	$0.418377\pi$
$68$		0			0
$69$	−7.31662	+	7.31662i	−0.880818	+	0.880818i
$70$		0			0
$71$			4.63325i			0.549866i	0.961463	+	0.274933i	$0.0886556\pi$
$71$			4.63325i			0.549866i	−0.961463	+	0.274933i	$0.911344\pi$
$72$		0			0
$73$	13.3166			1.55859			0.779297	−	0.626655i	$-0.215577\pi$
$73$	13.3166			1.55859			0.779297	+	0.626655i	$0.215577\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.683375	+	0.683375i	−0.0778778	+	0.0778778i
$78$		0			0
$79$	−2.31662			−0.260641			−0.130320	−	0.991472i	$-0.541601\pi$
$79$	−2.31662			−0.260641			−0.130320	+	0.991472i	$0.541601\pi$
$80$		0			0
$81$	7.94987			0.883319
$82$		0			0
$83$	−3.84169	+	3.84169i	−0.421680	+	0.421680i	−0.885782	−	0.464102i	$-0.846377\pi$
$83$	−3.84169	+	3.84169i	−0.421680	+	0.421680i	0.464102	+	0.885782i	$0.346377\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.63325			0.496736
$88$		0			0
$89$		−	15.9499i		−	1.69068i	−0.534226	−	0.845342i	$-0.679397\pi$
$89$		−	15.9499i		−	1.69068i	0.534226	−	0.845342i	$-0.320603\pi$
$90$		0			0
$91$	10.0000	−	10.0000i	1.04828	−	1.04828i
$92$		0			0
$93$	5.00000	−	5.00000i	0.518476	−	0.518476i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	6.63325i		−	0.673504i	−0.941593	−	0.336752i	$-0.890672\pi$
$97$		−	6.63325i		−	0.673504i	0.941593	−	0.336752i	$-0.109328\pi$
$98$		0			0
$99$	0.0501256	+	0.0501256i	0.00503782	+	0.00503782i
$100$		0			0
$101$	−1.31662	+	1.31662i	−0.131009	+	0.131009i	−0.769571	−	0.638562i	$-0.779530\pi$
$101$	−1.31662	+	1.31662i	−0.131009	+	0.131009i	0.638562	+	0.769571i	$0.279530\pi$
$102$		0			0
$103$	8.63325			0.850659			0.425330	−	0.905038i	$-0.360158\pi$
$103$	8.63325			0.850659			0.425330	+	0.905038i	$0.360158\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.15831	−	6.15831i	−0.595347	−	0.595347i	0.343724	−	0.939071i	$-0.388311\pi$
$107$	−6.15831	−	6.15831i	−0.595347	−	0.595347i	−0.939071	+	0.343724i	$0.888311\pi$
$108$		0			0
$109$	−13.9499	−	13.9499i	−1.33616	−	1.33616i	−0.899750	−	0.436406i	$-0.856251\pi$
$109$	−13.9499	−	13.9499i	−1.33616	−	1.33616i	−0.436406	−	0.899750i	$-0.643749\pi$
$110$		0			0
$111$	16.9499			1.60881
$112$		0			0
$113$			15.6332i			1.47065i	0.677713	+	0.735326i	$0.262971\pi$
$113$			15.6332i			1.47065i	−0.677713	+	0.735326i	$0.737029\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.733501	−	0.733501i	−0.0678122	−	0.0678122i
$118$		0			0
$119$		−	22.9499i		−	2.10381i
$120$		0			0
$121$			10.9499i			0.995443i
$122$		0			0
$123$	5.79156	+	5.79156i	0.522208	+	0.522208i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	0.316625i		−	0.0280959i	−0.999901	−	0.0140480i	$-0.995528\pi$
$127$		−	0.316625i		−	0.0280959i	0.999901	−	0.0140480i	$-0.00447175\pi$
$128$		0			0
$129$	13.0501			1.14900
$130$		0			0
$131$	−1.00000	−	1.00000i	−0.0873704	−	0.0873704i	0.662071	−	0.749441i	$-0.269678\pi$
$131$	−1.00000	−	1.00000i	−0.0873704	−	0.0873704i	−0.749441	+	0.662071i	$0.769678\pi$
$132$		0			0
$133$	−13.6332	−	13.6332i	−1.18215	−	1.18215i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.63325			0.139538			0.0697690	−	0.997563i	$-0.477774\pi$
$137$	1.63325			0.139538			0.0697690	+	0.997563i	$0.477774\pi$
$138$		0			0
$139$	−5.84169	+	5.84169i	−0.495485	+	0.495485i	−0.910029	−	0.414544i	$-0.863941\pi$
$139$	−5.84169	+	5.84169i	−0.495485	+	0.495485i	0.414544	+	0.910029i	$0.363941\pi$
$140$		0			0
$141$	9.26650	+	9.26650i	0.780380	+	0.780380i
$142$		0			0
$143$			0.733501i			0.0613384i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−13.4749	+	13.4749i	−1.11139	+	1.11139i
$148$		0			0
$149$	−3.36675	+	3.36675i	−0.275815	+	0.275815i	−0.831436	−	0.555621i	$-0.812481\pi$
$149$	−3.36675	+	3.36675i	−0.275815	+	0.275815i	0.555621	+	0.831436i	$0.312481\pi$
$150$		0			0
$151$		−	2.31662i		−	0.188524i	−0.995547	−	0.0942621i	$-0.969951\pi$
$151$		−	2.31662i		−	0.188524i	0.995547	−	0.0942621i	$-0.0300492\pi$
$152$		0			0
$153$	−1.68338			−0.136093
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.68338	−	4.68338i	0.373774	−	0.373774i	−0.495076	−	0.868850i	$-0.664860\pi$
$157$	4.68338	−	4.68338i	0.373774	−	0.373774i	0.868850	+	0.495076i	$0.164860\pi$
$158$		0			0
$159$	−7.68338			−0.609331
$160$		0			0
$161$	−27.2665			−2.14890
$162$		0			0
$163$	−3.84169	+	3.84169i	−0.300904	+	0.300904i	−0.841368	−	0.540463i	$-0.818249\pi$
$163$	−3.84169	+	3.84169i	−0.300904	+	0.300904i	0.540463	+	0.841368i	$0.318249\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$		0			0
$169$			2.26650i			0.174346i
$170$		0			0
$171$	−1.00000	+	1.00000i	−0.0764719	+	0.0764719i
$172$		0			0
$173$	6.94987	−	6.94987i	0.528389	−	0.528389i	−0.391703	−	0.920092i	$-0.628114\pi$
$173$	6.94987	−	6.94987i	0.528389	−	0.528389i	0.920092	+	0.391703i	$0.128114\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			12.3166i			0.925774i
$178$		0			0
$179$	7.79156	+	7.79156i	0.582369	+	0.582369i	0.935554	−	0.353185i	$-0.114901\pi$
$179$	7.79156	+	7.79156i	0.582369	+	0.582369i	−0.353185	+	0.935554i	$0.614901\pi$
$180$		0			0
$181$	3.31662	−	3.31662i	0.246523	−	0.246523i	−0.573019	−	0.819542i	$-0.694228\pi$
$181$	3.31662	−	3.31662i	0.246523	−	0.246523i	0.819542	+	0.573019i	$0.194228\pi$
$182$		0			0
$183$	8.41688			0.622193
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.841688	+	0.841688i	0.0615503	+	0.0615503i
$188$		0			0
$189$	16.5831	+	16.5831i	1.20624	+	1.20624i
$190$		0			0
$191$	1.05013			0.0759844			0.0379922	−	0.999278i	$-0.487904\pi$
$191$	1.05013			0.0759844			0.0379922	+	0.999278i	$0.487904\pi$
$192$		0			0
$193$		−	11.3166i		−	0.814588i	−0.913297	−	0.407294i	$-0.866472\pi$
$193$		−	11.3166i		−	0.814588i	0.913297	−	0.407294i	$-0.133528\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−16.5831	−	16.5831i	−1.18150	−	1.18150i	−0.979356	−	0.202143i	$-0.935210\pi$
$197$	−16.5831	−	16.5831i	−1.18150	−	1.18150i	−0.202143	−	0.979356i	$-0.564790\pi$
$198$		0			0
$199$		−	0.633250i		−	0.0448899i	−0.999748	−	0.0224449i	$-0.992855\pi$
$199$		−	0.633250i		−	0.0448899i	0.999748	−	0.0224449i	$-0.00714505\pi$
$200$		0			0
$201$		−	13.5330i		−	0.954544i
$202$		0			0
$203$	8.63325	+	8.63325i	0.605935	+	0.605935i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			2.00000i			0.139010i
$208$		0			0
$209$	1.00000			0.0691714
$210$		0			0
$211$	4.79156	+	4.79156i	0.329865	+	0.329865i	0.852535	−	0.522670i	$-0.175064\pi$
$211$	4.79156	+	4.79156i	0.329865	+	0.329865i	−0.522670	+	0.852535i	$0.675064\pi$
$212$		0			0
$213$	−5.36675	−	5.36675i	−0.367724	−	0.367724i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	18.6332			1.26491
$218$		0			0
$219$	−15.4248	+	15.4248i	−1.04231	+	1.04231i
$220$		0			0
$221$	−12.3166	−	12.3166i	−0.828506	−	0.828506i
$222$		0			0
$223$		−	6.00000i		−	0.401790i	−0.979613	−	0.200895i	$-0.935615\pi$
$223$		−	6.00000i		−	0.401790i	0.979613	−	0.200895i	$-0.0643850\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.6332	−	17.6332i	1.17036	−	1.17036i	0.188236	−	0.982124i	$-0.439723\pi$
$227$	17.6332	−	17.6332i	1.17036	−	1.17036i	0.982124	−	0.188236i	$-0.0602770\pi$
$228$		0			0
$229$	2.00000	−	2.00000i	0.132164	−	0.132164i	−0.637930	−	0.770094i	$-0.720209\pi$
$229$	2.00000	−	2.00000i	0.132164	−	0.132164i	0.770094	+	0.637930i	$0.220209\pi$
$230$		0			0
$231$		−	1.58312i		−	0.104162i
$232$		0			0
$233$	−27.8997			−1.82777			−0.913887	−	0.405969i	$-0.866934\pi$
$233$	−27.8997			−1.82777			−0.913887	+	0.405969i	$0.866934\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.68338	−	2.68338i	0.174304	−	0.174304i
$238$		0			0
$239$	−5.36675			−0.347146			−0.173573	−	0.984821i	$-0.555531\pi$
$239$	−5.36675			−0.347146			−0.173573	+	0.984821i	$0.555531\pi$
$240$		0			0
$241$	−14.5831			−0.939382			−0.469691	−	0.882831i	$-0.655635\pi$
$241$	−14.5831			−0.939382			−0.469691	+	0.882831i	$0.655635\pi$
$242$		0			0
$243$	2.31662	−	2.31662i	0.148612	−	0.148612i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−14.6332			−0.931091
$248$		0			0
$249$		−	8.89975i		−	0.563999i
$250$		0			0
$251$	−14.1082	+	14.1082i	−0.890501	+	0.890501i	−0.994570	−	0.104069i	$-0.966814\pi$
$251$	−14.1082	+	14.1082i	−0.890501	+	0.890501i	0.104069	+	0.994570i	$0.466814\pi$
$252$		0			0
$253$	1.00000	−	1.00000i	0.0628695	−	0.0628695i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			3.36675i			0.210012i	0.994472	+	0.105006i	$0.0334862\pi$
$257$			3.36675i			0.210012i	−0.994472	+	0.105006i	$0.966514\pi$
$258$		0			0
$259$	31.5831	+	31.5831i	1.96248	+	1.96248i
$260$		0			0
$261$	0.633250	−	0.633250i	0.0391972	−	0.0391972i
$262$		0			0
$263$	−17.5831			−1.08422			−0.542111	−	0.840307i	$-0.682375\pi$
$263$	−17.5831			−1.08422			−0.542111	+	0.840307i	$0.682375\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	18.4749	+	18.4749i	1.13065	+	1.13065i
$268$		0			0
$269$	0.316625	+	0.316625i	0.0193050	+	0.0193050i	0.716693	−	0.697388i	$-0.245655\pi$
$269$	0.316625	+	0.316625i	0.0193050	+	0.0193050i	−0.697388	+	0.716693i	$0.745655\pi$
$270$		0			0
$271$	−18.9499			−1.15112			−0.575561	−	0.817759i	$-0.695216\pi$
$271$	−18.9499			−1.15112			−0.575561	+	0.817759i	$0.695216\pi$
$272$		0			0
$273$			23.1662i			1.40209i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	7.68338	+	7.68338i	0.461649	+	0.461649i	0.899196	−	0.437547i	$-0.144152\pi$
$277$	7.68338	+	7.68338i	0.461649	+	0.461649i	−0.437547	+	0.899196i	$0.644152\pi$
$278$		0			0
$279$		−	1.36675i		−	0.0818252i
$280$		0			0
$281$			19.2665i			1.14934i	0.818384	+	0.574671i	$0.194870\pi$
$281$			19.2665i			1.14934i	−0.818384	+	0.574671i	$0.805130\pi$
$282$		0			0
$283$	−7.15831	−	7.15831i	−0.425518	−	0.425518i	0.461581	−	0.887098i	$-0.347282\pi$
$283$	−7.15831	−	7.15831i	−0.425518	−	0.425518i	−0.887098	+	0.461581i	$0.847282\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			21.5831i			1.27401i
$288$		0			0
$289$	−11.2665			−0.662735
$290$		0			0
$291$	7.68338	+	7.68338i	0.450407	+	0.450407i
$292$		0			0
$293$	−8.26650	−	8.26650i	−0.482934	−	0.482934i	0.423133	−	0.906067i	$-0.360930\pi$
$293$	−8.26650	−	8.26650i	−0.482934	−	0.482934i	−0.906067	+	0.423133i	$0.860930\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.21637			−0.0705812
$298$		0			0
$299$	−14.6332	+	14.6332i	−0.846263	+	0.846263i
$300$		0			0
$301$	24.3166	+	24.3166i	1.40159	+	1.40159i
$302$		0			0
$303$		−	3.05013i		−	0.175225i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−10.8417	+	10.8417i	−0.618768	+	0.618768i	−0.945215	−	0.326448i	$-0.894148\pi$
$307$	−10.8417	+	10.8417i	−0.618768	+	0.618768i	0.326448	+	0.945215i	$0.394148\pi$
$308$		0			0
$309$	−10.0000	+	10.0000i	−0.568880	+	0.568880i
$310$		0			0
$311$		−	6.94987i		−	0.394091i	−0.980394	−	0.197046i	$-0.936865\pi$
$311$		−	6.94987i		−	0.394091i	0.980394	−	0.197046i	$-0.0631347\pi$
$312$		0			0
$313$	16.0000			0.904373			0.452187	−	0.891923i	$-0.350644\pi$
$313$	16.0000			0.904373			0.452187	+	0.891923i	$0.350644\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.94987	+	4.94987i	−0.278013	+	0.278013i	−0.832315	−	0.554303i	$-0.812985\pi$
$317$	−4.94987	+	4.94987i	−0.278013	+	0.278013i	0.554303	+	0.832315i	$0.312985\pi$
$318$		0			0
$319$	−0.633250			−0.0354552
$320$		0			0
$321$	14.2665			0.796278
$322$		0			0
$323$	−16.7916	+	16.7916i	−0.934308	+	0.934308i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	32.3166			1.78711
$328$		0			0
$329$			34.5330i			1.90387i
$330$		0			0
$331$	−2.15831	+	2.15831i	−0.118632	+	0.118632i	−0.763930	−	0.645299i	$-0.776733\pi$
$331$	−2.15831	+	2.15831i	−0.118632	+	0.118632i	0.645299	+	0.763930i	$0.276733\pi$
$332$		0			0
$333$	2.31662	−	2.31662i	0.126950	−	0.126950i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			16.8997i			0.920588i	0.887767	+	0.460294i	$0.152256\pi$
$337$			16.8997i			0.920588i	−0.887767	+	0.460294i	$0.847744\pi$
$338$		0			0
$339$	−18.1082	−	18.1082i	−0.983502	−	0.983502i
$340$		0			0
$341$	−0.683375	+	0.683375i	−0.0370068	+	0.0370068i
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.4248	−	15.4248i	−0.828047	−	0.828047i	0.159199	−	0.987246i	$-0.449109\pi$
$347$	−15.4248	−	15.4248i	−0.828047	−	0.828047i	−0.987246	+	0.159199i	$0.949109\pi$
$348$		0			0
$349$	2.26650	+	2.26650i	0.121323	+	0.121323i	0.765161	−	0.643838i	$-0.222659\pi$
$349$	2.26650	+	2.26650i	0.121323	+	0.121323i	−0.643838	+	0.765161i	$0.722659\pi$
$350$		0			0
$351$	17.7995			0.950067
$352$		0			0
$353$			6.73350i			0.358388i	0.983814	+	0.179194i	$0.0573490\pi$
$353$			6.73350i			0.358388i	−0.983814	+	0.179194i	$0.942651\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	26.5831	+	26.5831i	1.40693	+	1.40693i
$358$		0			0
$359$			16.3166i			0.861159i	0.902553	+	0.430579i	$0.141691\pi$
$359$			16.3166i			0.861159i	−0.902553	+	0.430579i	$0.858309\pi$
$360$		0			0
$361$			0.949874i			0.0499934i
$362$		0			0
$363$	−12.6834	−	12.6834i	−0.665705	−	0.665705i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	13.3668i		−	0.697739i	−0.937171	−	0.348869i	$-0.886566\pi$
$367$		−	13.3668i		−	0.697739i	0.937171	−	0.348869i	$-0.113434\pi$
$368$		0			0
$369$	1.58312			0.0824141
$370$		0			0
$371$	−14.3166	−	14.3166i	−0.743282	−	0.743282i
$372$		0			0
$373$	15.6332	+	15.6332i	0.809459	+	0.809459i	0.984552	−	0.175093i	$-0.0560226\pi$
$373$	15.6332	+	15.6332i	0.809459	+	0.809459i	−0.175093	+	0.984552i	$0.556023\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.26650			0.477249
$378$		0			0
$379$	18.4248	−	18.4248i	0.946419	−	0.946419i	−0.0522168	−	0.998636i	$-0.516629\pi$
$379$	18.4248	−	18.4248i	0.946419	−	0.946419i	0.998636	+	0.0522168i	$0.0166287\pi$
$380$		0			0
$381$	0.366750	+	0.366750i	0.0187892	+	0.0187892i
$382$		0			0
$383$		−	2.94987i		−	0.150732i	−0.997156	−	0.0753658i	$-0.975988\pi$
$383$		−	2.94987i		−	0.150732i	0.997156	−	0.0753658i	$-0.0240124\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.78363	−	1.78363i	0.0906668	−	0.0906668i
$388$		0			0
$389$	−22.2665	+	22.2665i	−1.12896	+	1.12896i	−0.138609	+	0.990347i	$0.544263\pi$
$389$	−22.2665	+	22.2665i	−1.12896	+	1.12896i	−0.990347	+	0.138609i	$0.955737\pi$
$390$		0			0
$391$			33.5831i			1.69837i
$392$		0			0
$393$	2.31662			0.116858
$394$		0			0
$395$		0			0
$396$		0			0
$397$	1.26650	−	1.26650i	0.0635638	−	0.0635638i	−0.674610	−	0.738174i	$-0.735688\pi$
$397$	1.26650	−	1.26650i	0.0635638	−	0.0635638i	0.738174	+	0.674610i	$0.235688\pi$
$398$		0			0
$399$	31.5831			1.58113
$400$		0			0
$401$	9.31662			0.465250			0.232625	−	0.972567i	$-0.425269\pi$
$401$	9.31662			0.465250			0.232625	+	0.972567i	$0.425269\pi$
$402$		0			0
$403$	10.0000	−	10.0000i	0.498135	−	0.498135i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.31662			−0.114831
$408$		0			0
$409$			6.36675i			0.314816i	0.987534	+	0.157408i	$0.0503137\pi$
$409$			6.36675i			0.314816i	−0.987534	+	0.157408i	$0.949686\pi$
$410$		0			0
$411$	−1.89181	+	1.89181i	−0.0933163	+	0.0933163i
$412$		0			0
$413$	−22.9499	+	22.9499i	−1.12929	+	1.12929i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	13.5330i		−	0.662714i
$418$		0			0
$419$	−21.4749	−	21.4749i	−1.04912	−	1.04912i	−0.998730	−	0.0503897i	$-0.983954\pi$
$419$	−21.4749	−	21.4749i	−1.04912	−	1.04912i	−0.0503897	−	0.998730i	$-0.516046\pi$
$420$		0			0
$421$	−8.63325	+	8.63325i	−0.420759	+	0.420759i	−0.885465	−	0.464706i	$-0.846160\pi$
$421$	−8.63325	+	8.63325i	−0.420759	+	0.420759i	0.464706	+	0.885465i	$0.346160\pi$
$422$		0			0
$423$	2.53300			0.123159
$424$		0			0
$425$		0			0
$426$		0			0
$427$	15.6834	+	15.6834i	0.758972	+	0.758972i
$428$		0			0
$429$	−0.849623	−	0.849623i	−0.0410202	−	0.0410202i
$430$		0			0
$431$	−8.94987			−0.431100			−0.215550	−	0.976493i	$-0.569154\pi$
$431$	−8.94987			−0.431100			−0.215550	+	0.976493i	$0.569154\pi$
$432$		0			0
$433$		−	20.5831i		−	0.989162i	−0.869132	−	0.494581i	$-0.835322\pi$
$433$		−	20.5831i		−	0.989162i	0.869132	−	0.494581i	$-0.164678\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	19.9499	+	19.9499i	0.954332	+	0.954332i
$438$		0			0
$439$			18.6332i			0.889316i	0.895700	+	0.444658i	$0.146675\pi$
$439$			18.6332i			0.889316i	−0.895700	+	0.444658i	$0.853325\pi$
$440$		0			0
$441$			3.68338i			0.175399i
$442$		0			0
$443$	−4.10819	−	4.10819i	−0.195186	−	0.195186i	0.602747	−	0.797933i	$-0.294073\pi$
$443$	−4.10819	−	4.10819i	−0.195186	−	0.195186i	−0.797933	+	0.602747i	$0.794073\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	7.79950i		−	0.368904i
$448$		0			0
$449$	−27.3166			−1.28915			−0.644576	−	0.764541i	$-0.722966\pi$
$449$	−27.3166			−1.28915			−0.644576	+	0.764541i	$0.722966\pi$
$450$		0			0
$451$	−0.791562	−	0.791562i	−0.0372732	−	0.0372732i
$452$		0			0
$453$	2.68338	+	2.68338i	0.126076	+	0.126076i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$		0			0
$459$	20.4248	−	20.4248i	0.953349	−	0.953349i
$460$		0			0
$461$	−26.3166	−	26.3166i	−1.22569	−	1.22569i	−0.965580	−	0.260108i	$-0.916242\pi$
$461$	−26.3166	−	26.3166i	−1.22569	−	1.22569i	−0.260108	−	0.965580i	$-0.583758\pi$
$462$		0			0
$463$		−	11.3668i		−	0.528258i	−0.964487	−	0.264129i	$-0.914916\pi$
$463$		−	11.3668i		−	0.528258i	0.964487	−	0.264129i	$-0.0850844\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.2665	−	12.2665i	0.567626	−	0.567626i	−0.363837	−	0.931463i	$-0.618533\pi$
$467$	12.2665	−	12.2665i	0.567626	−	0.567626i	0.931463	+	0.363837i	$0.118533\pi$
$468$		0			0
$469$	25.2164	−	25.2164i	1.16438	−	1.16438i
$470$		0			0
$471$			10.8496i			0.499924i
$472$		0			0
$473$	−1.78363			−0.0820112
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.05013	+	1.05013i	−0.0480819	+	0.0480819i
$478$		0			0
$479$	−36.2164			−1.65477			−0.827384	−	0.561636i	$-0.810172\pi$
$479$	−36.2164			−1.65477			−0.827384	+	0.561636i	$0.810172\pi$
$480$		0			0
$481$	33.8997			1.54570
$482$		0			0
$483$	31.5831	−	31.5831i	1.43708	−	1.43708i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	14.2164			0.644205			0.322103	−	0.946705i	$-0.395610\pi$
$487$	14.2164			0.644205			0.322103	+	0.946705i	$0.395610\pi$
$488$		0			0
$489$		−	8.89975i		−	0.402461i
$490$		0			0
$491$	−16.3668	+	16.3668i	−0.738621	+	0.738621i	−0.972311	−	0.233690i	$-0.924920\pi$
$491$	−16.3668	+	16.3668i	−0.738621	+	0.738621i	0.233690	+	0.972311i	$0.424920\pi$
$492$		0			0
$493$	10.6332	−	10.6332i	0.478897	−	0.478897i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	20.0000i		−	0.897123i
$498$		0			0
$499$	−16.8997	−	16.8997i	−0.756537	−	0.756537i	0.219154	−	0.975690i	$-0.429670\pi$
$499$	−16.8997	−	16.8997i	−0.756537	−	0.756537i	−0.975690	+	0.219154i	$0.929670\pi$
$500$		0			0
$501$	−20.8496	+	20.8496i	−0.931492	+	0.931492i
$502$		0			0
$503$	7.89975			0.352232			0.176116	−	0.984369i	$-0.443647\pi$
$503$	7.89975			0.352232			0.176116	+	0.984369i	$0.443647\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.62531	−	2.62531i	−0.116594	−	0.116594i
$508$		0			0
$509$	−6.26650	−	6.26650i	−0.277758	−	0.277758i	0.554456	−	0.832213i	$-0.312927\pi$
$509$	−6.26650	−	6.26650i	−0.277758	−	0.277758i	−0.832213	+	0.554456i	$0.812927\pi$
$510$		0			0
$511$	−57.4829			−2.54289
$512$		0			0
$513$		−	24.2665i		−	1.07139i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.26650	−	1.26650i	−0.0557006	−	0.0557006i
$518$		0			0
$519$			16.1003i			0.706723i
$520$		0			0
$521$			0.366750i			0.0160676i	0.999968	+	0.00803381i	$0.00255727\pi$
$521$			0.366750i			0.0160676i	−0.999968	+	0.00803381i	$0.997443\pi$
$522$		0			0
$523$	2.47494	+	2.47494i	0.108221	+	0.108221i	0.759144	−	0.650923i	$-0.225618\pi$
$523$	2.47494	+	2.47494i	0.108221	+	0.108221i	−0.650923	+	0.759144i	$0.725618\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	22.9499i		−	0.999712i
$528$		0			0
$529$	16.8997			0.734772
$530$		0			0
$531$	1.68338	+	1.68338i	0.0730523	+	0.0730523i
$532$		0			0
$533$	11.5831	+	11.5831i	0.501721	+	0.501721i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−18.0501			−0.778920
$538$		0			0
$539$	1.84169	−	1.84169i	0.0793271	−	0.0793271i
$540$		0			0
$541$	18.3166	+	18.3166i	0.787493	+	0.787493i	0.981083	−	0.193589i	$-0.0620130\pi$
$541$	18.3166	+	18.3166i	0.787493	+	0.787493i	−0.193589	+	0.981083i	$0.562013\pi$
$542$		0			0
$543$			7.68338i			0.329725i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	20.7414	−	20.7414i	0.886840	−	0.886840i	−0.107378	−	0.994218i	$-0.534246\pi$
$547$	20.7414	−	20.7414i	0.886840	−	0.886840i	0.994218	+	0.107378i	$0.0342456\pi$
$548$		0			0
$549$	1.15038	−	1.15038i	0.0490969	−	0.0490969i
$550$		0			0
$551$		−	12.6332i		−	0.538195i
$552$		0			0
$553$	10.0000			0.425243
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.6834	−	19.6834i	0.834011	−	0.834011i	−0.154051	−	0.988063i	$-0.549232\pi$
$557$	19.6834	−	19.6834i	0.834011	−	0.834011i	0.988063	+	0.154051i	$0.0492322\pi$
$558$		0			0
$559$	26.1003			1.10392
$560$		0			0
$561$	−1.94987			−0.0823238
$562$		0			0
$563$	−1.94987	+	1.94987i	−0.0821774	+	0.0821774i	−0.747001	−	0.664823i	$-0.768507\pi$
$563$	−1.94987	+	1.94987i	−0.0821774	+	0.0821774i	0.664823	+	0.747001i	$0.268507\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−34.3166			−1.44116
$568$		0			0
$569$		−	9.00000i		−	0.377300i	−0.982044	−	0.188650i	$-0.939589\pi$
$569$		−	9.00000i		−	0.377300i	0.982044	−	0.188650i	$-0.0604111\pi$
$570$		0			0
$571$	28.2665	−	28.2665i	1.18292	−	1.18292i	0.203931	−	0.978985i	$-0.434628\pi$
$571$	28.2665	−	28.2665i	1.18292	−	1.18292i	0.978985	−	0.203931i	$-0.0653718\pi$
$572$		0			0
$573$	−1.21637	+	1.21637i	−0.0508147	+	0.0508147i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	2.36675i		−	0.0985291i	−0.998786	−	0.0492646i	$-0.984312\pi$
$577$		−	2.36675i		−	0.0985291i	0.998786	−	0.0492646i	$-0.0156877\pi$
$578$		0			0
$579$	13.1082	+	13.1082i	0.544758	+	0.544758i
$580$		0			0
$581$	16.5831	−	16.5831i	0.687984	−	0.687984i
$582$		0			0
$583$	1.05013			0.0434918
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.4248	+	20.4248i	0.843022	+	0.843022i	0.989251	−	0.146229i	$-0.0467135\pi$
$587$	20.4248	+	20.4248i	0.843022	+	0.843022i	−0.146229	+	0.989251i	$0.546714\pi$
$588$		0			0
$589$	−13.6332	−	13.6332i	−0.561748	−	0.561748i
$590$		0			0
$591$	38.4169			1.58026
$592$		0			0
$593$		−	17.5330i		−	0.719994i	−0.932953	−	0.359997i	$-0.882778\pi$
$593$		−	17.5330i		−	0.719994i	0.932953	−	0.359997i	$-0.117222\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.733501	+	0.733501i	0.0300202	+	0.0300202i
$598$		0			0
$599$			10.2164i			0.417430i	0.977977	+	0.208715i	$0.0669281\pi$
$599$			10.2164i			0.417430i	−0.977977	+	0.208715i	$0.933072\pi$
$600$		0			0
$601$		−	41.9499i		−	1.71117i	−0.517661	−	0.855586i	$-0.673197\pi$
$601$		−	41.9499i		−	1.71117i	0.517661	−	0.855586i	$-0.326803\pi$
$602$		0			0
$603$	−1.84962	−	1.84962i	−0.0753225	−	0.0753225i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			45.1662i			1.83324i	0.399758	+	0.916621i	$0.369094\pi$
$607$			45.1662i			1.83324i	−0.399758	+	0.916621i	$0.630906\pi$
$608$		0			0
$609$	−20.0000			−0.810441
$610$		0			0
$611$	18.5330	+	18.5330i	0.749765	+	0.749765i
$612$		0			0
$613$	10.2665	+	10.2665i	0.414660	+	0.414660i	0.883358	−	0.468698i	$-0.155277\pi$
$613$	10.2665	+	10.2665i	0.414660	+	0.414660i	−0.468698	+	0.883358i	$0.655277\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−27.2665			−1.09771			−0.548854	−	0.835918i	$-0.684936\pi$
$617$	−27.2665			−1.09771			−0.548854	+	0.835918i	$0.684936\pi$
$618$		0			0
$619$	−21.6332	+	21.6332i	−0.869514	+	0.869514i	−0.992418	−	0.122905i	$-0.960779\pi$
$619$	−21.6332	+	21.6332i	−0.869514	+	0.869514i	0.122905	+	0.992418i	$0.460779\pi$
$620$		0			0
$621$	−24.2665	−	24.2665i	−0.973781	−	0.973781i
$622$		0			0
$623$			68.8496i			2.75840i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.15831	+	1.15831i	−0.0462585	+	0.0462585i
$628$		0			0
$629$	38.8997	−	38.8997i	1.55103	−	1.55103i
$630$		0			0
$631$		−	17.6834i		−	0.703964i	−0.936007	−	0.351982i	$-0.885508\pi$
$631$		−	17.6834i		−	0.703964i	0.936007	−	0.351982i	$-0.114492\pi$
$632$		0			0
$633$	−11.1003			−0.441195
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−26.9499	+	26.9499i	−1.06779	+	1.06779i
$638$		0			0
$639$	−1.46700			−0.0580337
$640$		0			0
$641$	15.8997			0.628002			0.314001	−	0.949423i	$-0.398330\pi$
$641$	15.8997			0.628002			0.314001	+	0.949423i	$0.398330\pi$
$642$		0			0
$643$	−24.2665	+	24.2665i	−0.956977	+	0.956977i	−0.999112	−	0.0421346i	$-0.986584\pi$
$643$	−24.2665	+	24.2665i	−0.956977	+	0.956977i	0.0421346	+	0.999112i	$0.486584\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−45.1662			−1.77567			−0.887834	−	0.460163i	$-0.847791\pi$
$647$	−45.1662			−1.77567			−0.887834	+	0.460163i	$0.847791\pi$
$648$		0			0
$649$		−	1.68338i		−	0.0660783i
$650$		0			0
$651$	−21.5831	+	21.5831i	−0.845909	+	0.845909i
$652$		0			0
$653$	−29.6332	+	29.6332i	−1.15964	+	1.15964i	−0.175085	+	0.984553i	$0.556020\pi$
$653$	−29.6332	+	29.6332i	−1.15964	+	1.15964i	−0.984553	+	0.175085i	$0.943980\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			4.21637i			0.164496i
$658$		0			0
$659$	−21.8417	−	21.8417i	−0.850831	−	0.850831i	0.139404	−	0.990236i	$-0.455481\pi$
$659$	−21.8417	−	21.8417i	−0.850831	−	0.850831i	−0.990236	+	0.139404i	$0.955481\pi$
$660$		0			0
$661$	−2.41688	+	2.41688i	−0.0940056	+	0.0940056i	−0.752546	−	0.658540i	$-0.771174\pi$
$661$	−2.41688	+	2.41688i	−0.0940056	+	0.0940056i	0.658540	+	0.752546i	$0.271174\pi$
$662$		0			0
$663$	28.5330			1.10813
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−12.6332	−	12.6332i	−0.489161	−	0.489161i
$668$		0			0
$669$	6.94987	+	6.94987i	0.268698	+	0.268698i
$670$		0			0
$671$	−1.15038			−0.0444098
$672$		0			0
$673$		−	29.3668i		−	1.13201i	−0.824404	−	0.566003i	$-0.808489\pi$
$673$		−	29.3668i		−	1.13201i	0.824404	−	0.566003i	$-0.191511\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−24.6332	−	24.6332i	−0.946733	−	0.946733i	0.0519186	−	0.998651i	$-0.483466\pi$
$677$	−24.6332	−	24.6332i	−0.946733	−	0.946733i	−0.998651	+	0.0519186i	$0.983466\pi$
$678$		0			0
$679$			28.6332i			1.09884i
$680$		0			0
$681$			40.8496i			1.56536i
$682$		0			0
$683$	−4.47494	−	4.47494i	−0.171229	−	0.171229i	0.616290	−	0.787519i	$-0.288635\pi$
$683$	−4.47494	−	4.47494i	−0.171229	−	0.171229i	−0.787519	+	0.616290i	$0.788635\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			4.63325i			0.176769i
$688$		0			0
$689$	−15.3668			−0.585427
$690$		0			0
$691$	22.8417	+	22.8417i	0.868939	+	0.868939i	0.992355	−	0.123416i	$-0.0393850\pi$
$691$	22.8417	+	22.8417i	0.868939	+	0.868939i	−0.123416	+	0.992355i	$0.539385\pi$
$692$		0			0
$693$	−0.216374	−	0.216374i	−0.00821935	−	0.00821935i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	26.5831			1.00691
$698$		0			0
$699$	32.3166	−	32.3166i	1.22233	−	1.22233i
$700$		0			0
$701$	5.26650	+	5.26650i	0.198913	+	0.198913i	0.799534	−	0.600621i	$-0.205080\pi$
$701$	5.26650	+	5.26650i	0.198913	+	0.198913i	−0.600621	+	0.799534i	$0.705080\pi$
$702$		0			0
$703$		−	46.2164i		−	1.74308i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.68338	−	5.68338i	0.213745	−	0.213745i
$708$		0			0
$709$	22.0000	−	22.0000i	0.826227	−	0.826227i	−0.160765	−	0.986993i	$-0.551396\pi$
$709$	22.0000	−	22.0000i	0.826227	−	0.826227i	0.986993	+	0.160765i	$0.0513962\pi$
$710$		0			0
$711$		−	0.733501i		−	0.0275084i
$712$		0			0
$713$	−27.2665			−1.02114
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6.21637	−	6.21637i	0.232155	−	0.232155i
$718$		0			0
$719$	−16.9499			−0.632124			−0.316062	−	0.948739i	$-0.602361\pi$
$719$	−16.9499			−0.632124			−0.316062	+	0.948739i	$0.602361\pi$
$720$		0			0
$721$	−37.2665			−1.38788
$722$		0			0
$723$	16.8918	−	16.8918i	0.628213	−	0.628213i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−50.5330			−1.87417			−0.937083	−	0.349108i	$-0.886485\pi$
$727$	−50.5330			−1.87417			−0.937083	+	0.349108i	$0.886485\pi$
$728$		0			0
$729$			29.2164i			1.08209i
$730$		0			0
$731$	29.9499	−	29.9499i	1.10774	−	1.10774i
$732$		0			0
$733$	−12.3166	+	12.3166i	−0.454925	+	0.454925i	−0.896985	−	0.442060i	$-0.854248\pi$
$733$	−12.3166	+	12.3166i	−0.454925	+	0.454925i	0.442060	+	0.896985i	$0.354248\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			1.84962i			0.0681317i
$738$		0			0
$739$	−27.6332	−	27.6332i	−1.01651	−	1.01651i	−0.999861	−	0.0166440i	$-0.994702\pi$
$739$	−27.6332	−	27.6332i	−1.01651	−	1.01651i	−0.0166440	−	0.999861i	$-0.505298\pi$
$740$		0			0
$741$	16.9499	−	16.9499i	0.622669	−	0.622669i
$742$		0			0
$743$	−13.6834			−0.501994			−0.250997	−	0.967988i	$-0.580758\pi$
$743$	−13.6834			−0.501994			−0.250997	+	0.967988i	$0.580758\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.21637	−	1.21637i	−0.0445048	−	0.0445048i
$748$		0			0
$749$	26.5831	+	26.5831i	0.971326	+	0.971326i
$750$		0			0
$751$	50.4327			1.84032			0.920159	−	0.391546i	$-0.128060\pi$
$751$	50.4327			1.84032			0.920159	+	0.391546i	$0.128060\pi$
$752$		0			0
$753$		−	32.6834i		−	1.19105i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−27.6834	−	27.6834i	−1.00617	−	1.00617i	−0.999981	−	0.00618854i	$-0.998030\pi$
$757$	−27.6834	−	27.6834i	−1.00617	−	1.00617i	−0.00618854	−	0.999981i	$-0.501970\pi$
$758$		0			0
$759$			2.31662i			0.0840882i
$760$		0			0
$761$		−	5.73350i		−	0.207839i	−0.994586	−	0.103920i	$-0.966862\pi$
$761$		−	5.73350i		−	0.207839i	0.994586	−	0.103920i	$-0.0331385\pi$
$762$		0			0
$763$	60.2164	+	60.2164i	2.17998	+	2.17998i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			24.6332i			0.889455i
$768$		0			0
$769$	−40.4829			−1.45985			−0.729925	−	0.683527i	$-0.760445\pi$
$769$	−40.4829			−1.45985			−0.729925	+	0.683527i	$0.760445\pi$
$770$		0			0
$771$	−3.89975	−	3.89975i	−0.140446	−	0.140446i
$772$		0			0
$773$	30.6332	+	30.6332i	1.10180	+	1.10180i	0.994193	+	0.107608i	$0.0343191\pi$
$773$	30.6332	+	30.6332i	1.10180	+	1.10180i	0.107608	+	0.994193i	$0.465681\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−73.1662			−2.62482
$778$		0			0
$779$	15.7916	−	15.7916i	0.565791	−	0.565791i
$780$		0			0
$781$	0.733501	+	0.733501i	0.0262467	+	0.0262467i
$782$		0			0
$783$			15.3668i			0.549163i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.00000	+	7.00000i	−0.249523	+	0.249523i	−0.820775	−	0.571252i	$-0.806458\pi$
$787$	−7.00000	+	7.00000i	−0.249523	+	0.249523i	0.571252	+	0.820775i	$0.306458\pi$
$788$		0			0
$789$	20.3668	−	20.3668i	0.725076	−	0.725076i
$790$		0			0
$791$		−	67.4829i		−	2.39941i
$792$		0			0
$793$	16.8338			0.597784
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.36675	−	2.36675i	0.0838346	−	0.0838346i	−0.663946	−	0.747781i	$-0.731120\pi$
$797$	2.36675	−	2.36675i	0.0838346	−	0.0838346i	0.747781	+	0.663946i	$0.231120\pi$
$798$		0			0
$799$	42.5330			1.50471
$800$		0			0
$801$	5.05013			0.178437
$802$		0			0
$803$	2.10819	−	2.10819i	0.0743963	−	0.0743963i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.733501			−0.0258205
$808$		0			0
$809$			14.5330i			0.510953i	0.966815	+	0.255477i	$0.0822323\pi$
$809$			14.5330i			0.510953i	−0.966815	+	0.255477i	$0.917768\pi$
$810$		0			0
$811$	24.3668	−	24.3668i	0.855632	−	0.855632i	−0.135188	−	0.990820i	$-0.543164\pi$
$811$	24.3668	−	24.3668i	0.855632	−	0.855632i	0.990820	+	0.135188i	$0.0431637\pi$
$812$		0			0
$813$	21.9499	−	21.9499i	0.769816	−	0.769816i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		−	35.5831i		−	1.24490i
$818$		0			0
$819$	3.16625	+	3.16625i	0.110638	+	0.110638i
$820$		0			0
$821$	−28.2665	+	28.2665i	−0.986508	+	0.986508i	−0.999910	−	0.0134026i	$-0.995734\pi$
$821$	−28.2665	+	28.2665i	−0.986508	+	0.986508i	0.0134026	+	0.999910i	$0.495734\pi$
$822$		0			0
$823$	−29.8997			−1.04224			−0.521120	−	0.853484i	$-0.674486\pi$
$823$	−29.8997			−1.04224			−0.521120	+	0.853484i	$0.674486\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−11.1583	−	11.1583i	−0.388013	−	0.388013i	0.485965	−	0.873978i	$-0.338468\pi$
$827$	−11.1583	−	11.1583i	−0.388013	−	0.388013i	−0.873978	+	0.485965i	$0.838468\pi$
$828$		0			0
$829$	27.2665	+	27.2665i	0.947005	+	0.947005i	0.998665	−	0.0516601i	$-0.0164512\pi$
$829$	27.2665	+	27.2665i	0.947005	+	0.947005i	−0.0516601	+	0.998665i	$0.516451\pi$
$830$		0			0
$831$	−17.7995			−0.617458
$832$		0			0
$833$			61.8496i			2.14296i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	16.5831	+	16.5831i	0.573197	+	0.573197i
$838$		0			0
$839$		−	10.6332i		−	0.367101i	−0.983010	−	0.183550i	$-0.941241\pi$
$839$		−	10.6332i		−	0.367101i	0.983010	−	0.183550i	$-0.0587590\pi$
$840$		0			0
$841$		−	21.0000i		−	0.724138i
$842$		0			0
$843$	−22.3166	−	22.3166i	−0.768625	−	0.768625i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	47.2665i		−	1.62410i
$848$		0			0
$849$	16.5831			0.569131
$850$		0			0
$851$	−46.2164	−	46.2164i	−1.58428	−	1.58428i
$852$		0			0
$853$	−33.6332	−	33.6332i	−1.15158	−	1.15158i	−0.986236	−	0.165345i	$-0.947126\pi$
$853$	−33.6332	−	33.6332i	−1.15158	−	1.15158i	−0.165345	−	0.986236i	$-0.552874\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.36675			−0.285803			−0.142901	−	0.989737i	$-0.545643\pi$
$857$	−8.36675			−0.285803			−0.142901	+	0.989737i	$0.545643\pi$
$858$		0			0
$859$	−7.42481	+	7.42481i	−0.253331	+	0.253331i	−0.822335	−	0.569004i	$-0.807329\pi$
$859$	−7.42481	+	7.42481i	−0.253331	+	0.253331i	0.569004	+	0.822335i	$0.307329\pi$
$860$		0			0
$861$	−25.0000	−	25.0000i	−0.851998	−	0.851998i
$862$		0			0
$863$			32.5330i			1.10744i	0.832704	+	0.553718i	$0.186791\pi$
$863$			32.5330i			1.10744i	−0.832704	+	0.553718i	$0.813209\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	13.0501	−	13.0501i	0.443206	−	0.443206i
$868$		0			0
$869$	−0.366750	+	0.366750i	−0.0124412	+	0.0124412i
$870$		0			0
$871$		−	27.0660i		−	0.917096i
$872$		0			0
$873$	2.10025			0.0710827
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−39.5831	+	39.5831i	−1.33663	+	1.33663i	−0.437322	+	0.899305i	$0.644073\pi$
$877$	−39.5831	+	39.5831i	−1.33663	+	1.33663i	−0.899305	+	0.437322i	$0.855927\pi$
$878$		0			0
$879$	19.1504			0.645926
$880$		0			0
$881$	−1.89975			−0.0640042			−0.0320021	−	0.999488i	$-0.510188\pi$
$881$	−1.89975			−0.0640042			−0.0320021	+	0.999488i	$0.510188\pi$
$882$		0			0
$883$	18.8417	−	18.8417i	0.634073	−	0.634073i	−0.315014	−	0.949087i	$-0.602009\pi$
$883$	18.8417	−	18.8417i	0.634073	−	0.634073i	0.949087	+	0.315014i	$0.102009\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.53300			0.219357			0.109678	−	0.993967i	$-0.465018\pi$
$887$	6.53300			0.219357			0.109678	+	0.993967i	$0.465018\pi$
$888$		0			0
$889$			1.36675i			0.0458393i
$890$		0			0
$891$	1.25856	−	1.25856i	0.0421635	−	0.0421635i
$892$		0			0
$893$	25.2665	−	25.2665i	0.845511	−	0.845511i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	33.8997i		−	1.13188i
$898$		0			0
$899$	8.63325	+	8.63325i	0.287935	+	0.287935i
$900$		0			0
$901$	−17.6332	+	17.6332i	−0.587449	+	0.587449i
$902$		0			0
$903$	−56.3325			−1.87463
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.366750	+	0.366750i	0.0121777	+	0.0121777i	0.713169	−	0.700992i	$-0.247259\pi$
$907$	0.366750	+	0.366750i	0.0121777	+	0.0121777i	−0.700992	+	0.713169i	$0.747259\pi$
$908$		0			0
$909$	−0.416876	−	0.416876i	−0.0138269	−	0.0138269i
$910$		0			0
$911$	−25.1662			−0.833795			−0.416897	−	0.908954i	$-0.636883\pi$
$911$	−25.1662			−0.833795			−0.416897	+	0.908954i	$0.636883\pi$
$912$		0			0
$913$			1.21637i			0.0402561i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.31662	+	4.31662i	0.142548	+	0.142548i
$918$		0			0
$919$		−	37.5831i		−	1.23975i	−0.784699	−	0.619876i	$-0.787183\pi$
$919$		−	37.5831i		−	1.23975i	0.784699	−	0.619876i	$-0.212817\pi$
$920$		0			0
$921$		−	25.1161i		−	0.827604i
$922$		0			0
$923$	−10.7335	−	10.7335i	−0.353297	−	0.353297i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			2.73350i			0.0897799i
$928$		0			0
$929$	20.0000			0.656179			0.328089	−	0.944647i	$-0.393595\pi$
$929$	20.0000			0.656179			0.328089	+	0.944647i	$0.393595\pi$
$930$		0			0
$931$	36.7414	+	36.7414i	1.20415	+	1.20415i
$932$		0			0
$933$	8.05013	+	8.05013i	0.263549	+	0.263549i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−16.0501			−0.524335			−0.262167	−	0.965022i	$-0.584437\pi$
$937$	−16.0501			−0.524335			−0.262167	+	0.965022i	$0.584437\pi$
$938$		0			0
$939$	−18.5330	+	18.5330i	−0.604802	+	0.604802i
$940$		0			0
$941$	−10.9499	−	10.9499i	−0.356956	−	0.356956i	0.505734	−	0.862690i	$-0.331222\pi$
$941$	−10.9499	−	10.9499i	−0.356956	−	0.356956i	−0.862690	+	0.505734i	$0.831222\pi$
$942$		0			0
$943$		−	31.5831i		−	1.02849i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−38.5831	+	38.5831i	−1.25378	+	1.25378i	−0.299772	+	0.954011i	$0.596911\pi$
$947$	−38.5831	+	38.5831i	−1.25378	+	1.25378i	−0.954011	+	0.299772i	$0.903089\pi$
$948$		0			0
$949$	−30.8496	+	30.8496i	−1.00142	+	1.00142i
$950$		0			0
$951$		−	11.4670i		−	0.371843i
$952$		0			0
$953$	15.6332			0.506411			0.253205	−	0.967413i	$-0.418515\pi$
$953$	15.6332			0.506411			0.253205	+	0.967413i	$0.418515\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.733501	−	0.733501i	0.0237107	−	0.0237107i
$958$		0			0
$959$	−7.05013			−0.227660
$960$		0			0
$961$	−12.3668			−0.398927
$962$		0			0
$963$	1.94987	−	1.94987i	0.0628338	−	0.0628338i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	13.3668			0.429846			0.214923	−	0.976631i	$-0.431050\pi$
$967$	13.3668			0.429846			0.214923	+	0.976631i	$0.431050\pi$
$968$		0			0
$969$		−	38.8997i		−	1.24964i
$970$		0			0
$971$	−27.5251	+	27.5251i	−0.883321	+	0.883321i	−0.993871	−	0.110549i	$-0.964739\pi$
$971$	−27.5251	+	27.5251i	−0.883321	+	0.883321i	0.110549	+	0.993871i	$0.464739\pi$
$972$		0			0
$973$	25.2164	−	25.2164i	0.808400	−	0.808400i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	56.3826i		−	1.80384i	−0.431903	−	0.901920i	$-0.642158\pi$
$977$		−	56.3826i		−	1.80384i	0.431903	−	0.901920i	$-0.357842\pi$
$978$		0			0
$979$	−2.52506	−	2.52506i	−0.0807014	−	0.0807014i
$980$		0			0
$981$	4.41688	−	4.41688i	0.141020	−	0.141020i
$982$		0			0
$983$	21.6834			0.691592			0.345796	−	0.938310i	$-0.387609\pi$
$983$	21.6834			0.691592			0.345796	+	0.938310i	$0.387609\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−40.0000	−	40.0000i	−1.27321	−	1.27321i
$988$		0			0
$989$	−35.5831	−	35.5831i	−1.13148	−	1.13148i
$990$		0			0
$991$	23.4829			0.745958			0.372979	−	0.927840i	$-0.378336\pi$
$991$	23.4829			0.745958			0.372979	+	0.927840i	$0.378336\pi$
$992$		0			0
$993$		−	5.00000i		−	0.158670i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	16.9499	+	16.9499i	0.536808	+	0.536808i	0.922590	−	0.385782i	$-0.126068\pi$
$997$	16.9499	+	16.9499i	0.536808	+	0.536808i	−0.385782	+	0.922590i	$0.626068\pi$
$998$		0			0
$999$			56.2164i			1.77861i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.15831 + 1.15831i) q^{3} -4.31662 q^{7} +0.316625i q^{9} +O(q^{10})\)	\(q+(-1.15831 + 1.15831i) q^{3} -4.31662 q^{7} +0.316625i q^{9} +(0.158312 - 0.158312i) q^{11} +(-2.31662 + 2.31662i) q^{13} +5.31662i q^{17} +(3.15831 + 3.15831i) q^{19} +(5.00000 - 5.00000i) q^{21} +6.31662 q^{23} +(-3.84169 - 3.84169i) q^{27} +(-2.00000 - 2.00000i) q^{29} -4.31662 q^{31} +0.366750i q^{33} +(-7.31662 - 7.31662i) q^{37} -5.36675i q^{39} -5.00000i q^{41} +(-5.63325 - 5.63325i) q^{43} -8.00000i q^{47} +11.6332 q^{49} +(-6.15831 - 6.15831i) q^{51} +(3.31662 + 3.31662i) q^{53} -7.31662 q^{57} +(5.31662 - 5.31662i) q^{59} +(-3.63325 - 3.63325i) q^{61} -1.36675i q^{63} +(-5.84169 + 5.84169i) q^{67} +(-7.31662 + 7.31662i) q^{69} +4.63325i q^{71} +13.3166 q^{73} +(-0.683375 + 0.683375i) q^{77} -2.31662 q^{79} +7.94987 q^{81} +(-3.84169 + 3.84169i) q^{83} +4.63325 q^{87} -15.9499i q^{89} +(10.0000 - 10.0000i) q^{91} +(5.00000 - 5.00000i) q^{93} -6.63325i q^{97} +(0.0501256 + 0.0501256i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 - 4 * q^7	\( 4 q + 2 q^{3} - 4 q^{7} - 6 q^{11} + 4 q^{13} + 6 q^{19} + 20 q^{21} + 12 q^{23} - 22 q^{27} - 8 q^{29} - 4 q^{31} - 16 q^{37} + 4 q^{43} + 20 q^{49} - 18 q^{51} - 16 q^{57} + 8 q^{59} + 12 q^{61} - 30 q^{67} - 16 q^{69} + 40 q^{73} - 16 q^{77} + 4 q^{79} - 8 q^{81} - 22 q^{83} - 8 q^{87} + 40 q^{91} + 20 q^{93} + 40 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^7 - 6 * q^11 + 4 * q^13 + 6 * q^19 + 20 * q^21 + 12 * q^23 - 22 * q^27 - 8 * q^29 - 4 * q^31 - 16 * q^37 + 4 * q^43 + 20 * q^49 - 18 * q^51 - 16 * q^57 + 8 * q^59 + 12 * q^61 - 30 * q^67 - 16 * q^69 + 40 * q^73 - 16 * q^77 + 4 * q^79 - 8 * q^81 - 22 * q^83 - 8 * q^87 + 40 * q^91 + 20 * q^93 + 40 * q^99

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