LMFDB - Embedded newform 1900.2.l.b.493.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(493,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1900.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.l (of order $4$, degree $2$, 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:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 28 x^{10} - 64 x^{9} + 236 x^{8} - 420 x^{7} + 946 x^{6} - 1216 x^{5} + 1896 x^{4} + \cdots + 1370 $ x^12 - 4x^11 + 28x^10 - 64x^9 + 236x^8 - 420x^7 + 946x^6 - 1216x^5 + 1896x^4 - 1564x^3 + 2284x^2 - 1088*x + 1370
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.4
Root			$0.344446 + 1.84020i$ of defining polynomial
Character	$\chi$	$=$	1900.493
Dual form			1900.2.l.b.1557.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49576 - 1.49576i) q^{3} +(-0.311108 + 0.311108i) q^{7} -1.47457i q^{9} +O(q^{10})$	$q+(1.49576 - 1.49576i) q^{3} +(-0.311108 + 0.311108i) q^{7} -1.47457i q^{9} +2.90321 q^{11} +(2.84674 - 2.84674i) q^{13} +(2.52543 - 2.52543i) q^{17} +(-4.34250 - 0.377784i) q^{19} +0.930683i q^{21} +(4.11753 + 4.11753i) q^{23} +(2.28167 + 2.28167i) q^{27} +2.99151 q^{29} +0.930683i q^{31} +(4.34250 - 4.34250i) q^{33} +(-8.11992 - 8.11992i) q^{37} -8.51606i q^{39} -2.06083i q^{41} +(-2.11753 - 2.11753i) q^{43} +(2.73975 - 2.73975i) q^{47} +6.80642i q^{49} -7.55485i q^{51} +(0.565073 - 0.565073i) q^{53} +(-7.06039 + 5.93024i) q^{57} +9.32613 q^{59} +3.52543 q^{61} +(0.458751 + 0.458751i) q^{63} +(0.144771 + 0.144771i) q^{67} +12.3176 q^{69} -9.61568i q^{71} +(4.09679 + 4.09679i) q^{73} +(-0.903212 + 0.903212i) q^{77} +12.6072 q^{79} +11.2494 q^{81} +(-9.21432 - 9.21432i) q^{83} +(4.47457 - 4.47457i) q^{87} -7.55485 q^{89} +1.77129i q^{91} +(1.39207 + 1.39207i) q^{93} +(-12.0421 - 12.0421i) q^{97} -4.28100i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{7}+O(q^{10}) $ 12 * q - 4 * q^7	$ 12 q - 4 q^{7} + 8 q^{11} + 4 q^{17} - 4 q^{23} + 28 q^{43} - 20 q^{47} - 24 q^{57} + 16 q^{61} - 20 q^{63} + 76 q^{73} + 16 q^{77} + 4 q^{81} - 84 q^{83} + 80 q^{87} - 8 q^{93}+O(q^{100}) $ 12 * q - 4 * q^7 + 8 * q^11 + 4 * q^17 - 4 * q^23 + 28 * q^43 - 20 * q^47 - 24 * q^57 + 16 * q^61 - 20 * q^63 + 76 * q^73 + 16 * q^77 + 4 * q^81 - 84 * q^83 + 80 * q^87 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	1.49576	−	1.49576i	0.863575	−	0.863575i	−0.128176	−	0.991751i	$-0.540912\pi$
$3$	1.49576	−	1.49576i	0.863575	−	0.863575i	0.991751	+	0.128176i	$0.0409123\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.311108	+	0.311108i	−0.117588	+	0.117588i	−0.763452	−	0.645864i	$-0.776497\pi$
$7$	−0.311108	+	0.311108i	−0.117588	+	0.117588i	0.645864	+	0.763452i	$0.276497\pi$
$8$		0			0
$9$		−	1.47457i		−	0.491524i
$10$		0			0
$11$	2.90321			0.875351			0.437676	−	0.899133i	$-0.355802\pi$
$11$	2.90321			0.875351			0.437676	+	0.899133i	$0.355802\pi$
$12$		0			0
$13$	2.84674	−	2.84674i	0.789544	−	0.789544i	−0.191875	−	0.981419i	$-0.561457\pi$
$13$	2.84674	−	2.84674i	0.789544	−	0.789544i	0.981419	+	0.191875i	$0.0614570\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.52543	−	2.52543i	0.612506	−	0.612506i	−0.331092	−	0.943598i	$-0.607417\pi$
$17$	2.52543	−	2.52543i	0.612506	−	0.612506i	0.943598	+	0.331092i	$0.107417\pi$
$18$		0			0
$19$	−4.34250	−	0.377784i	−0.996237	−	0.0866697i
$19$	−4.34250	−	0.377784i	−0.996237	−	0.0866697i
$20$		0			0
$21$			0.930683i			0.203092i
$22$		0			0
$23$	4.11753	+	4.11753i	0.858565	+	0.858565i	0.991169	−	0.132604i	$-0.0423340\pi$
$23$	4.11753	+	4.11753i	0.858565	+	0.858565i	−0.132604	+	0.991169i	$0.542334\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.28167	+	2.28167i	0.439107	+	0.439107i
$28$		0			0
$29$	2.99151			0.555510			0.277755	−	0.960652i	$-0.410410\pi$
$29$	2.99151			0.555510			0.277755	+	0.960652i	$0.410410\pi$
$30$		0			0
$31$			0.930683i			0.167156i	0.996501	+	0.0835778i	$0.0266347\pi$
$31$			0.930683i			0.167156i	−0.996501	+	0.0835778i	$0.973365\pi$
$32$		0			0
$33$	4.34250	−	4.34250i	0.755932	−	0.755932i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−8.11992	−	8.11992i	−1.33491	−	1.33491i	−0.900919	−	0.433988i	$-0.857106\pi$
$37$	−8.11992	−	8.11992i	−1.33491	−	1.33491i	−0.433988	−	0.900919i	$-0.642894\pi$
$38$		0			0
$39$		−	8.51606i		−	1.36366i
$40$		0			0
$41$		−	2.06083i		−	0.321847i	−0.986967	−	0.160924i	$-0.948553\pi$
$41$		−	2.06083i		−	0.321847i	0.986967	−	0.160924i	$-0.0514473\pi$
$42$		0			0
$43$	−2.11753	−	2.11753i	−0.322921	−	0.322921i	0.526966	−	0.849886i	$-0.323330\pi$
$43$	−2.11753	−	2.11753i	−0.322921	−	0.322921i	−0.849886	+	0.526966i	$0.823330\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.73975	−	2.73975i	0.399633	−	0.399633i	−0.478470	−	0.878104i	$-0.658809\pi$
$47$	2.73975	−	2.73975i	0.399633	−	0.399633i	0.878104	+	0.478470i	$0.158809\pi$
$48$		0			0
$49$			6.80642i			0.972346i
$50$		0			0
$51$		−	7.55485i		−	1.05789i
$52$		0			0
$53$	0.565073	−	0.565073i	0.0776188	−	0.0776188i	−0.667232	−	0.744850i	$-0.732521\pi$
$53$	0.565073	−	0.565073i	0.0776188	−	0.0776188i	0.744850	+	0.667232i	$0.232521\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−7.06039	+	5.93024i	−0.935171	+	0.785480i
$58$		0			0
$59$	9.32613			1.21416			0.607080	−	0.794641i	$-0.292341\pi$
$59$	9.32613			1.21416			0.607080	+	0.794641i	$0.292341\pi$
$60$		0			0
$61$	3.52543			0.451385			0.225692	−	0.974199i	$-0.427536\pi$
$61$	3.52543			0.451385			0.225692	+	0.974199i	$0.427536\pi$
$62$		0			0
$63$	0.458751	+	0.458751i	0.0577972	+	0.0577972i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.144771	+	0.144771i	0.0176866	+	0.0176866i	0.715895	−	0.698208i	$-0.246019\pi$
$67$	0.144771	+	0.144771i	0.0176866	+	0.0176866i	−0.698208	+	0.715895i	$0.746019\pi$
$68$		0			0
$69$	12.3176			1.48287
$70$		0			0
$71$		−	9.61568i		−	1.14117i	−0.821238	−	0.570585i	$-0.806716\pi$
$71$		−	9.61568i		−	1.14117i	0.821238	−	0.570585i	$-0.193284\pi$
$72$		0			0
$73$	4.09679	+	4.09679i	0.479493	+	0.479493i	0.904969	−	0.425477i	$-0.139894\pi$
$73$	4.09679	+	4.09679i	0.479493	+	0.479493i	−0.425477	+	0.904969i	$0.639894\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.903212	+	0.903212i	−0.102931	+	0.102931i
$78$		0			0
$79$	12.6072			1.41842			0.709210	−	0.704998i	$-0.249052\pi$
$79$	12.6072			1.41842			0.709210	+	0.704998i	$0.249052\pi$
$80$		0			0
$81$	11.2494			1.24993
$82$		0			0
$83$	−9.21432	−	9.21432i	−1.01140	−	1.01140i	−0.999934	−	0.0114688i	$-0.996349\pi$
$83$	−9.21432	−	9.21432i	−1.01140	−	1.01140i	−0.0114688	−	0.999934i	$-0.503651\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.47457	−	4.47457i	0.479725	−	0.479725i
$88$		0			0
$89$	−7.55485			−0.800812			−0.400406	−	0.916338i	$-0.631131\pi$
$89$	−7.55485			−0.800812			−0.400406	+	0.916338i	$0.631131\pi$
$90$		0			0
$91$			1.77129i			0.185681i
$92$		0			0
$93$	1.39207	+	1.39207i	0.144351	+	0.144351i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−12.0421	−	12.0421i	−1.22269	−	1.22269i	−0.966671	−	0.256020i	$-0.917589\pi$
$97$	−12.0421	−	12.0421i	−1.22269	−	1.22269i	−0.256020	−	0.966671i	$-0.582411\pi$
$98$		0			0
$99$		−	4.28100i		−	0.430256i
$100$		0			0
$101$	−8.76986			−0.872634			−0.436317	−	0.899793i	$-0.643717\pi$
$101$	−8.76986			−0.872634			−0.436317	+	0.899793i	$0.643717\pi$
$102$		0			0
$103$	8.54022	−	8.54022i	0.841493	−	0.841493i	−0.147560	−	0.989053i	$-0.547142\pi$
$103$	8.54022	−	8.54022i	0.841493	−	0.841493i	0.989053	+	0.147560i	$0.0471419\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.77742	−	3.77742i	−0.365177	−	0.365177i	0.500538	−	0.865715i	$-0.333136\pi$
$107$	−3.77742	−	3.77742i	−0.365177	−	0.365177i	−0.865715	+	0.500538i	$0.833136\pi$
$108$		0			0
$109$	13.7373			1.31580			0.657899	−	0.753106i	$-0.271445\pi$
$109$	13.7373			1.31580			0.657899	+	0.753106i	$0.271445\pi$
$110$		0			0
$111$	−24.2908			−2.30558
$112$		0			0
$113$	−1.91606	+	1.91606i	−0.180248	+	0.180248i	−0.791464	−	0.611216i	$-0.790681\pi$
$113$	−1.91606	+	1.91606i	−0.180248	+	0.180248i	0.611216	+	0.791464i	$0.290681\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.19773	−	4.19773i	−0.388080	−	0.388080i
$118$		0			0
$119$			1.57136i			0.144046i
$120$		0			0
$121$	−2.57136			−0.233760
$122$		0			0
$123$	−3.08250	−	3.08250i	−0.277939	−	0.277939i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	5.12841	+	5.12841i	0.455073	+	0.455073i	0.897034	−	0.441961i	$-0.145717\pi$
$127$	5.12841	+	5.12841i	0.455073	+	0.455073i	−0.441961	+	0.897034i	$0.645717\pi$
$128$		0			0
$129$	−6.33462			−0.557732
$130$		0			0
$131$	−10.3684			−0.905893			−0.452946	−	0.891538i	$-0.649627\pi$
$131$	−10.3684			−0.905893			−0.452946	+	0.891538i	$0.649627\pi$
$132$		0			0
$133$	1.46852	−	1.23345i	0.127337	−	0.106954i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.99063	+	7.99063i	−0.682686	+	0.682686i	−0.960605	−	0.277919i	$-0.910355\pi$
$137$	−7.99063	+	7.99063i	−0.682686	+	0.682686i	0.277919	+	0.960605i	$0.410355\pi$
$138$		0			0
$139$			10.1891i			0.864231i	0.901818	+	0.432115i	$0.142233\pi$
$139$			10.1891i			0.864231i	−0.901818	+	0.432115i	$0.857767\pi$
$140$		0			0
$141$		−	8.19599i		−	0.690227i
$142$		0			0
$143$	8.26469	−	8.26469i	0.691128	−	0.691128i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	10.1807	+	10.1807i	0.839694	+	0.839694i
$148$		0			0
$149$			18.0874i			1.48178i	0.671627	+	0.740890i	$0.265596\pi$
$149$			18.0874i			1.48178i	−0.671627	+	0.740890i	$0.734404\pi$
$150$		0			0
$151$			13.5379i			1.10170i	0.834605	+	0.550848i	$0.185696\pi$
$151$			13.5379i			1.10170i	−0.834605	+	0.550848i	$0.814304\pi$
$152$		0			0
$153$	−3.72393	−	3.72393i	−0.301062	−	0.301062i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−15.1891	+	15.1891i	−1.21222	+	1.21222i	−0.241931	+	0.970293i	$0.577781\pi$
$157$	−15.1891	+	15.1891i	−1.21222	+	1.21222i	−0.970293	+	0.241931i	$0.922219\pi$
$158$		0			0
$159$		−	1.69042i		−	0.134059i
$160$		0			0
$161$	−2.56199			−0.201913
$162$		0			0
$163$	−5.44938	−	5.44938i	−0.426829	−	0.426829i	0.460718	−	0.887547i	$-0.347592\pi$
$163$	−5.44938	−	5.44938i	−0.426829	−	0.426829i	−0.887547	+	0.460718i	$0.847592\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.42644	+	2.42644i	0.187763	+	0.187763i	0.794729	−	0.606965i	$-0.207613\pi$
$167$	2.42644	+	2.42644i	0.187763	+	0.187763i	−0.606965	+	0.794729i	$0.707613\pi$
$168$		0			0
$169$		−	3.20787i		−	0.246759i
$170$		0			0
$171$	−0.557070	+	6.40333i	−0.0426002	+	0.489675i
$172$		0			0
$173$	−5.83825	+	5.83825i	−0.443874	+	0.443874i	−0.893312	−	0.449438i	$-0.851624\pi$
$173$	−5.83825	+	5.83825i	−0.443874	+	0.443874i	0.449438	+	0.893312i	$0.351624\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	13.9496	−	13.9496i	1.04852	−	1.04852i
$178$		0			0
$179$	−20.4516			−1.52862			−0.764311	−	0.644847i	$-0.776921\pi$
$179$	−20.4516			−1.52862			−0.764311	+	0.644847i	$0.776921\pi$
$180$		0			0
$181$		−	11.9660i		−	0.889429i	−0.895672	−	0.444715i	$-0.853305\pi$
$181$		−	11.9660i		−	0.889429i	0.895672	−	0.444715i	$-0.146695\pi$
$182$		0			0
$183$	5.27318	−	5.27318i	0.389805	−	0.389805i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	7.33185	−	7.33185i	0.536158	−	0.536158i
$188$		0			0
$189$	−1.41969			−0.103267
$190$		0			0
$191$	23.0923			1.67090			0.835452	−	0.549564i	$-0.185206\pi$
$191$	23.0923			1.67090			0.835452	+	0.549564i	$0.185206\pi$
$192$		0			0
$193$	2.42644	−	2.42644i	0.174659	−	0.174659i	−0.614364	−	0.789023i	$-0.710587\pi$
$193$	2.42644	−	2.42644i	0.174659	−	0.174659i	0.789023	+	0.614364i	$0.210587\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−13.0874	+	13.0874i	−0.932440	+	0.932440i	−0.997858	−	0.0654179i	$-0.979162\pi$
$197$	−13.0874	+	13.0874i	−0.932440	+	0.932440i	0.0654179	+	0.997858i	$0.479162\pi$
$198$		0			0
$199$		−	10.2953i		−	0.729814i	−0.931044	−	0.364907i	$-0.881101\pi$
$199$		−	10.2953i		−	0.729814i	0.931044	−	0.364907i	$-0.118899\pi$
$200$		0			0
$201$	0.433085			0.0305475
$202$		0			0
$203$	−0.930683	+	0.930683i	−0.0653211	+	0.0653211i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.07160	−	6.07160i	0.422005	−	0.422005i
$208$		0			0
$209$	−12.6072	−	1.09679i	−0.872057	−	0.0758664i
$210$		0			0
$211$			14.9576i			1.02972i	0.857274	+	0.514860i	$0.172156\pi$
$211$			14.9576i			1.02972i	−0.857274	+	0.514860i	$0.827844\pi$
$212$		0			0
$213$	−14.3827	−	14.3827i	−0.985487	−	0.985487i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.289543	−	0.289543i	−0.0196554	−	0.0196554i
$218$		0			0
$219$	12.2556			0.828156
$220$		0			0
$221$		−	14.3785i		−	0.967201i
$222$		0			0
$223$	3.55659	−	3.55659i	0.238167	−	0.238167i	−0.577924	−	0.816091i	$-0.696137\pi$
$223$	3.55659	−	3.55659i	0.238167	−	0.238167i	0.816091	+	0.577924i	$0.196137\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.83825	−	5.83825i	−0.387498	−	0.387498i	0.486296	−	0.873794i	$-0.338348\pi$
$227$	−5.83825	−	5.83825i	−0.387498	−	0.387498i	−0.873794	+	0.486296i	$0.838348\pi$
$228$		0			0
$229$			12.5763i			0.831064i	0.909579	+	0.415532i	$0.136405\pi$
$229$			12.5763i			0.831064i	−0.909579	+	0.415532i	$0.863595\pi$
$230$		0			0
$231$			2.70197i			0.177777i
$232$		0			0
$233$	8.74620	+	8.74620i	0.572983	+	0.572983i	0.932961	−	0.359978i	$-0.117216\pi$
$233$	8.74620	+	8.74620i	0.572983	+	0.572983i	−0.359978	+	0.932961i	$0.617216\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	18.8573	−	18.8573i	1.22491	−	1.22491i
$238$		0			0
$239$		−	17.0923i		−	1.10561i	−0.833310	−	0.552806i	$-0.813557\pi$
$239$		−	17.0923i		−	1.10561i	0.833310	−	0.552806i	$-0.186443\pi$
$240$		0			0
$241$			25.8555i			1.66550i	0.553649	+	0.832750i	$0.313235\pi$
$241$			25.8555i			1.66550i	−0.553649	+	0.832750i	$0.686765\pi$
$242$		0			0
$243$	9.98129	−	9.98129i	0.640300	−	0.640300i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.4374	+	11.2865i	−0.855002	+	0.718143i
$248$		0			0
$249$	−27.5647			−1.74685
$250$		0			0
$251$	5.37778			0.339443			0.169721	−	0.985492i	$-0.445713\pi$
$251$	5.37778			0.339443			0.169721	+	0.985492i	$0.445713\pi$
$252$		0			0
$253$	11.9541	+	11.9541i	0.751546	+	0.751546i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.48727	+	4.48727i	0.279908	+	0.279908i	0.833072	−	0.553164i	$-0.186580\pi$
$257$	4.48727	+	4.48727i	0.279908	+	0.279908i	−0.553164	+	0.833072i	$0.686580\pi$
$258$		0			0
$259$	5.05234			0.313937
$260$		0			0
$261$		−	4.41120i		−	0.273047i
$262$		0			0
$263$	11.8365	+	11.8365i	0.729872	+	0.729872i	0.970594	−	0.240722i	$-0.0773842\pi$
$263$	11.8365	+	11.8365i	0.729872	+	0.729872i	−0.240722	+	0.970594i	$0.577384\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−11.3002	+	11.3002i	−0.691562	+	0.691562i
$268$		0			0
$269$	−6.33462			−0.386229			−0.193114	−	0.981176i	$-0.561859\pi$
$269$	−6.33462			−0.386229			−0.193114	+	0.981176i	$0.561859\pi$
$270$		0			0
$271$	13.5669			0.824131			0.412066	−	0.911154i	$-0.364807\pi$
$271$	13.5669			0.824131			0.412066	+	0.911154i	$0.364807\pi$
$272$		0			0
$273$	2.64941	+	2.64941i	0.160350	+	0.160350i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	11.9032	−	11.9032i	0.715195	−	0.715195i	−0.252422	−	0.967617i	$-0.581227\pi$
$277$	11.9032	−	11.9032i	0.715195	−	0.715195i	0.967617	+	0.252422i	$0.0812273\pi$
$278$		0			0
$279$	1.37236			0.0821610
$280$		0			0
$281$		−	26.6961i		−	1.59256i	−0.604930	−	0.796279i	$-0.706799\pi$
$281$		−	26.6961i		−	1.59256i	0.604930	−	0.796279i	$-0.293201\pi$
$282$		0			0
$283$	13.1684	+	13.1684i	0.782779	+	0.782779i	0.980299	−	0.197520i	$-0.0632886\pi$
$283$	13.1684	+	13.1684i	0.782779	+	0.782779i	−0.197520	+	0.980299i	$0.563289\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.641140	+	0.641140i	0.0378453	+	0.0378453i
$288$		0			0
$289$			4.24443i			0.249672i
$290$		0			0
$291$	−36.0241			−2.11177
$292$		0			0
$293$	−22.7879	+	22.7879i	−1.33129	+	1.33129i	−0.427064	+	0.904221i	$0.640452\pi$
$293$	−22.7879	+	22.7879i	−1.33129	+	1.33129i	−0.904221	+	0.427064i	$0.859548\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	6.62416	+	6.62416i	0.384373	+	0.384373i
$298$		0			0
$299$	23.4431			1.35575
$300$		0			0
$301$	1.31756			0.0759430
$302$		0			0
$303$	−13.1176	+	13.1176i	−0.753585	+	0.753585i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	19.5756	+	19.5756i	1.11724	+	1.11724i	0.992145	+	0.125093i	$0.0399229\pi$
$307$	19.5756	+	19.5756i	1.11724	+	1.11724i	0.125093	+	0.992145i	$0.460077\pi$
$308$		0			0
$309$		−	25.5482i		−	1.45339i
$310$		0			0
$311$	30.1289			1.70845			0.854227	−	0.519901i	$-0.174031\pi$
$311$	30.1289			1.70845			0.854227	+	0.519901i	$0.174031\pi$
$312$		0			0
$313$	−11.5620	−	11.5620i	−0.653522	−	0.653522i	0.300317	−	0.953839i	$-0.402908\pi$
$313$	−11.5620	−	11.5620i	−0.653522	−	0.653522i	−0.953839	+	0.300317i	$0.902908\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.6011	−	10.6011i	−0.595414	−	0.595414i	0.343674	−	0.939089i	$-0.388328\pi$
$317$	−10.6011	−	10.6011i	−0.595414	−	0.595414i	−0.939089	+	0.343674i	$0.888328\pi$
$318$		0			0
$319$	8.68499			0.486266
$320$		0			0
$321$	−11.3002			−0.630716
$322$		0			0
$323$	−11.9207	+	10.0126i	−0.663287	+	0.557116i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	20.5477	−	20.5477i	1.13629	−	1.13629i
$328$		0			0
$329$			1.70471i			0.0939839i
$330$		0			0
$331$			26.7862i			1.47230i	0.676817	+	0.736151i	$0.263359\pi$
$331$			26.7862i			1.47230i	−0.676817	+	0.736151i	$0.736641\pi$
$332$		0			0
$333$	−11.9734	+	11.9734i	−0.656139	+	0.656139i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	10.0500	+	10.0500i	0.547458	+	0.547458i	0.925705	−	0.378247i	$-0.123473\pi$
$337$	10.0500	+	10.0500i	0.547458	+	0.547458i	−0.378247	+	0.925705i	$0.623473\pi$
$338$		0			0
$339$			5.73191i			0.311315i
$340$		0			0
$341$			2.70197i			0.146320i
$342$		0			0
$343$	−4.29529	−	4.29529i	−0.231924	−	0.231924i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−18.0573	+	18.0573i	−0.969367	+	0.969367i	−0.999545	−	0.0301774i	$-0.990393\pi$
$347$	−18.0573	+	18.0573i	−0.969367	+	0.969367i	0.0301774	+	0.999545i	$0.490393\pi$
$348$		0			0
$349$		−	29.1941i		−	1.56272i	−0.624079	−	0.781361i	$-0.714526\pi$
$349$		−	29.1941i		−	1.56272i	0.624079	−	0.781361i	$-0.285474\pi$
$350$		0			0
$351$	12.9906			0.693389
$352$		0			0
$353$	8.89384	+	8.89384i	0.473372	+	0.473372i	0.903004	−	0.429632i	$-0.141357\pi$
$353$	8.89384	+	8.89384i	0.473372	+	0.473372i	−0.429632	+	0.903004i	$0.641357\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.35037	+	2.35037i	0.124395	+	0.124395i
$358$		0			0
$359$			27.9037i			1.47270i	0.676601	+	0.736350i	$0.263452\pi$
$359$			27.9037i			1.47270i	−0.676601	+	0.736350i	$0.736548\pi$
$360$		0			0
$361$	18.7146	+	3.28105i	0.984977	+	0.172687i
$362$		0			0
$363$	−3.84613	+	3.84613i	−0.201869	+	0.201869i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−1.89676	+	1.89676i	−0.0990100	+	0.0990100i	−0.754877	−	0.655867i	$-0.772303\pi$
$367$	−1.89676	+	1.89676i	−0.0990100	+	0.0990100i	0.655867	+	0.754877i	$0.272303\pi$
$368$		0			0
$369$	−3.03884			−0.158196
$370$		0			0
$371$			0.351597i			0.0182540i
$372$		0			0
$373$	−6.05909	+	6.05909i	−0.313728	+	0.313728i	−0.846352	−	0.532624i	$-0.821206\pi$
$373$	−6.05909	+	6.05909i	−0.313728	+	0.313728i	0.532624	+	0.846352i	$0.321206\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.51606	−	8.51606i	0.438599	−	0.438599i
$378$		0			0
$379$	−25.2144			−1.29518			−0.647588	−	0.761991i	$-0.724222\pi$
$379$	−25.2144			−1.29518			−0.647588	+	0.761991i	$0.724222\pi$
$380$		0			0
$381$	15.3417			0.785979
$382$		0			0
$383$	−11.3323	+	11.3323i	−0.579052	+	0.579052i	−0.934642	−	0.355590i	$-0.884280\pi$
$383$	−11.3323	+	11.3323i	−0.579052	+	0.579052i	0.355590	+	0.934642i	$0.384280\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.12245	+	3.12245i	−0.158723	+	0.158723i
$388$		0			0
$389$			19.1338i			0.970124i	0.874480	+	0.485062i	$0.161203\pi$
$389$			19.1338i			0.970124i	−0.874480	+	0.485062i	$0.838797\pi$
$390$		0			0
$391$	20.7971			1.05175
$392$		0			0
$393$	−15.5086	+	15.5086i	−0.782306	+	0.782306i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	6.71900	−	6.71900i	0.337217	−	0.337217i	−0.518102	−	0.855319i	$-0.673361\pi$
$397$	6.71900	−	6.71900i	0.337217	−	0.337217i	0.855319	+	0.518102i	$0.173361\pi$
$398$		0			0
$399$	0.351597	−	4.04149i	0.0176019	−	0.202327i
$400$		0			0
$401$		−	4.56334i		−	0.227882i	−0.993488	−	0.113941i	$-0.963653\pi$
$401$		−	4.56334i		−	0.227882i	0.993488	−	0.113941i	$-0.0363475\pi$
$402$		0			0
$403$	2.64941	+	2.64941i	0.131977	+	0.131977i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−23.5738	−	23.5738i	−1.16851	−	1.16851i
$408$		0			0
$409$	21.5817			1.06715			0.533574	−	0.845754i	$-0.320849\pi$
$409$	21.5817			1.06715			0.533574	+	0.845754i	$0.320849\pi$
$410$		0			0
$411$			23.9041i			1.17910i
$412$		0			0
$413$	−2.90143	+	2.90143i	−0.142770	+	0.142770i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	15.2405	+	15.2405i	0.746328	+	0.746328i
$418$		0			0
$419$		−	7.58120i		−	0.370366i	−0.982704	−	0.185183i	$-0.940712\pi$
$419$		−	7.58120i		−	0.370366i	0.982704	−	0.185183i	$-0.0592878\pi$
$420$		0			0
$421$		−	25.0149i		−	1.21915i	−0.792728	−	0.609576i	$-0.791340\pi$
$421$		−	25.0149i		−	1.21915i	0.792728	−	0.609576i	$-0.208660\pi$
$422$		0			0
$423$	−4.03996	−	4.03996i	−0.196429	−	0.196429i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.09679	+	1.09679i	−0.0530773	+	0.0530773i
$428$		0			0
$429$		−	24.7239i		−	1.19368i
$430$		0			0
$431$		−	21.2021i		−	1.02127i	−0.859798	−	0.510635i	$-0.829410\pi$
$431$		−	21.2021i		−	1.02127i	0.859798	−	0.510635i	$-0.170590\pi$
$432$		0			0
$433$	−19.0866	+	19.0866i	−0.917243	+	0.917243i	−0.996828	−	0.0795855i	$-0.974640\pi$
$433$	−19.0866	+	19.0866i	−0.917243	+	0.917243i	0.0795855	+	0.996828i	$0.474640\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−16.3248	−	19.4359i	−0.780922	−	0.929746i
$438$		0			0
$439$	−38.6622			−1.84524			−0.922622	−	0.385705i	$-0.873958\pi$
$439$	−38.6622			−1.84524			−0.922622	+	0.385705i	$0.873958\pi$
$440$		0			0
$441$	10.0366			0.477932
$442$		0			0
$443$	−0.725457	−	0.725457i	−0.0344675	−	0.0344675i	0.689663	−	0.724130i	$-0.257759\pi$
$443$	−0.725457	−	0.725457i	−0.0344675	−	0.0344675i	−0.724130	+	0.689663i	$0.757759\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	27.0544	+	27.0544i	1.27963	+	1.27963i
$448$		0			0
$449$	−41.0746			−1.93843			−0.969215	−	0.246216i	$-0.920813\pi$
$449$	−41.0746			−1.93843			−0.969215	+	0.246216i	$0.920813\pi$
$450$		0			0
$451$		−	5.98302i		−	0.281730i
$452$		0			0
$453$	20.2494	+	20.2494i	0.951398	+	0.951398i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.3684	+	15.3684i	−0.718904	+	0.718904i	−0.968381	−	0.249477i	$-0.919741\pi$
$457$	−15.3684	+	15.3684i	−0.718904	+	0.718904i	0.249477	+	0.968381i	$0.419741\pi$
$458$		0			0
$459$	11.5244			0.537912
$460$		0			0
$461$	−16.9304			−0.788528			−0.394264	−	0.918997i	$-0.629000\pi$
$461$	−16.9304			−0.788528			−0.394264	+	0.918997i	$0.629000\pi$
$462$		0			0
$463$	1.49532	+	1.49532i	0.0694932	+	0.0694932i	0.740999	−	0.671506i	$-0.234352\pi$
$463$	1.49532	+	1.49532i	0.0694932	+	0.0694932i	−0.671506	+	0.740999i	$0.734352\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.2192	−	20.2192i	0.935635	−	0.935635i	−0.0624153	−	0.998050i	$-0.519880\pi$
$467$	20.2192	−	20.2192i	0.935635	−	0.935635i	0.998050	+	0.0624153i	$0.0198803\pi$
$468$		0			0
$469$	−0.0900790			−0.00415946
$470$		0			0
$471$			45.4385i			2.09369i
$472$		0			0
$473$	−6.14764	−	6.14764i	−0.282669	−	0.282669i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.833241	−	0.833241i	−0.0381515	−	0.0381515i
$478$		0			0
$479$		−	11.2587i		−	0.514424i	−0.966355	−	0.257212i	$-0.917196\pi$
$479$		−	11.2587i		−	0.514424i	0.966355	−	0.257212i	$-0.0828039\pi$
$480$		0			0
$481$	−46.2306			−2.10793
$482$		0			0
$483$	−3.83212	+	3.83212i	−0.174367	+	0.174367i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	15.4539	+	15.4539i	0.700284	+	0.700284i	0.964471	−	0.264187i	$-0.0851036\pi$
$487$	15.4539	+	15.4539i	0.700284	+	0.700284i	−0.264187	+	0.964471i	$0.585104\pi$
$488$		0			0
$489$	−16.3019			−0.737197
$490$		0			0
$491$	−20.9906			−0.947294			−0.473647	−	0.880715i	$-0.657063\pi$
$491$	−20.9906			−0.947294			−0.473647	+	0.880715i	$0.657063\pi$
$492$		0			0
$493$	7.55485	−	7.55485i	0.340253	−	0.340253i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.99151	+	2.99151i	0.134188	+	0.134188i
$498$		0			0
$499$			24.6780i			1.10474i	0.833599	+	0.552369i	$0.186276\pi$
$499$			24.6780i			1.10474i	−0.833599	+	0.552369i	$0.813724\pi$
$500$		0			0
$501$	7.25872			0.324296
$502$		0			0
$503$	15.0065	+	15.0065i	0.669105	+	0.669105i	0.957509	−	0.288404i	$-0.0931246\pi$
$503$	15.0065	+	15.0065i	0.669105	+	0.669105i	−0.288404	+	0.957509i	$0.593125\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−4.79819	−	4.79819i	−0.213095	−	0.213095i
$508$		0			0
$509$	34.6306			1.53497			0.767487	−	0.641065i	$-0.221507\pi$
$509$	34.6306			1.53497			0.767487	+	0.641065i	$0.221507\pi$
$510$		0			0
$511$	−2.54909			−0.112765
$512$		0			0
$513$	−9.04616	−	10.7701i	−0.399398	−	0.475512i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	7.95407	−	7.95407i	0.349819	−	0.349819i
$518$		0			0
$519$			17.4652i			0.766637i
$520$		0			0
$521$			39.0418i			1.71045i	0.518255	+	0.855226i	$0.326582\pi$
$521$			39.0418i			1.71045i	−0.518255	+	0.855226i	$0.673418\pi$
$522$		0			0
$523$	25.2904	−	25.2904i	1.10587	−	1.10587i	0.112187	−	0.993687i	$-0.464215\pi$
$523$	25.2904	−	25.2904i	1.10587	−	1.10587i	0.993687	−	0.112187i	$-0.0357855\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.35037	+	2.35037i	0.102384	+	0.102384i
$528$		0			0
$529$			10.9081i			0.474267i
$530$		0			0
$531$		−	13.7521i		−	0.596789i
$532$		0			0
$533$	−5.86665	−	5.86665i	−0.254113	−	0.254113i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−30.5906	+	30.5906i	−1.32008	+	1.32008i
$538$		0			0
$539$			19.7605i			0.851145i
$540$		0			0
$541$	−8.85283			−0.380613			−0.190307	−	0.981725i	$-0.560948\pi$
$541$	−8.85283			−0.380613			−0.190307	+	0.981725i	$0.560948\pi$
$542$		0			0
$543$	−17.8983	−	17.8983i	−0.768089	−	0.768089i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	11.9520	+	11.9520i	0.511032	+	0.511032i	0.914843	−	0.403810i	$-0.132314\pi$
$547$	11.9520	+	11.9520i	0.511032	+	0.511032i	−0.403810	+	0.914843i	$0.632314\pi$
$548$		0			0
$549$		−	5.19850i		−	0.221867i
$550$		0			0
$551$	−12.9906	−	1.13015i	−0.553420	−	0.0481459i
$552$		0			0
$553$	−3.92219	+	3.92219i	−0.166789	+	0.166789i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.8430	+	19.8430i	−0.840774	+	0.840774i	−0.988960	−	0.148185i	$-0.952657\pi$
$557$	−19.8430	+	19.8430i	−0.840774	+	0.840774i	0.148185	+	0.988960i	$0.452657\pi$
$558$		0			0
$559$	−12.0561			−0.509920
$560$		0			0
$561$		−	21.9333i		−	0.926026i
$562$		0			0
$563$	−10.4703	+	10.4703i	−0.441270	+	0.441270i	−0.892439	−	0.451169i	$-0.851007\pi$
$563$	−10.4703	+	10.4703i	−0.441270	+	0.441270i	0.451169	+	0.892439i	$0.351007\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−3.49976	+	3.49976i	−0.146976	+	0.146976i
$568$		0			0
$569$	−42.6744			−1.78901			−0.894503	−	0.447062i	$-0.852470\pi$
$569$	−42.6744			−1.78901			−0.894503	+	0.447062i	$0.852470\pi$
$570$		0			0
$571$	−23.2815			−0.974299			−0.487150	−	0.873319i	$-0.661963\pi$
$571$	−23.2815			−0.974299			−0.487150	+	0.873319i	$0.661963\pi$
$572$		0			0
$573$	34.5405	−	34.5405i	1.44295	−	1.44295i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	14.5526	−	14.5526i	0.605834	−	0.605834i	−0.336021	−	0.941855i	$-0.609081\pi$
$577$	14.5526	−	14.5526i	0.605834	−	0.605834i	0.941855	+	0.336021i	$0.109081\pi$
$578$		0			0
$579$		−	7.25872i		−	0.301662i
$580$		0			0
$581$	5.73329			0.237857
$582$		0			0
$583$	1.64053	−	1.64053i	0.0679437	−	0.0679437i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.20495	−	6.20495i	0.256106	−	0.256106i	−0.567362	−	0.823468i	$-0.692036\pi$
$587$	6.20495	−	6.20495i	0.256106	−	0.256106i	0.823468	+	0.567362i	$0.192036\pi$
$588$		0			0
$589$	0.351597	−	4.04149i	0.0144873	−	0.166527i
$590$		0			0
$591$			39.1512i			1.61046i
$592$		0			0
$593$	−32.5210	−	32.5210i	−1.33548	−	1.33548i	−0.900387	−	0.435089i	$-0.856717\pi$
$593$	−32.5210	−	32.5210i	−1.33548	−	1.33548i	−0.435089	−	0.900387i	$-0.643283\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−15.3992	−	15.3992i	−0.630249	−	0.630249i
$598$		0			0
$599$	20.8505			0.851929			0.425964	−	0.904740i	$-0.359935\pi$
$599$	20.8505			0.851929			0.425964	+	0.904740i	$0.359935\pi$
$600$		0			0
$601$		−	7.64493i		−	0.311843i	−0.987769	−	0.155922i	$-0.950165\pi$
$601$		−	7.64493i		−	0.311843i	0.987769	−	0.155922i	$-0.0498347\pi$
$602$		0			0
$603$	0.213476	−	0.213476i	0.00869341	−	0.00869341i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	16.0951	+	16.0951i	0.653279	+	0.653279i	0.953781	−	0.300502i	$-0.0971543\pi$
$607$	16.0951	+	16.0951i	0.653279	+	0.653279i	−0.300502	+	0.953781i	$0.597154\pi$
$608$		0			0
$609$			2.78415i			0.112819i
$610$		0			0
$611$		−	15.5987i		−	0.631056i
$612$		0			0
$613$	−9.69535	−	9.69535i	−0.391591	−	0.391591i	0.483663	−	0.875254i	$-0.339306\pi$
$613$	−9.69535	−	9.69535i	−0.391591	−	0.391591i	−0.875254	+	0.483663i	$0.839306\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	26.3319	−	26.3319i	1.06008	−	1.06008i	0.0620046	−	0.998076i	$-0.480251\pi$
$617$	26.3319	−	26.3319i	1.06008	−	1.06008i	0.998076	−	0.0620046i	$-0.0197493\pi$
$618$		0			0
$619$			38.0054i			1.52757i	0.645473	+	0.763783i	$0.276660\pi$
$619$			38.0054i			1.52757i	−0.645473	+	0.763783i	$0.723340\pi$
$620$		0			0
$621$			18.7897i			0.754004i
$622$		0			0
$623$	2.35037	−	2.35037i	0.0941657	−	0.0941657i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−20.4978	+	17.2168i	−0.818604	+	0.687571i
$628$		0			0
$629$	−41.0125			−1.63528
$630$		0			0
$631$	25.0968			0.999087			0.499544	−	0.866289i	$-0.333501\pi$
$631$	25.0968			0.999087			0.499544	+	0.866289i	$0.333501\pi$
$632$		0			0
$633$	22.3729	+	22.3729i	0.889241	+	0.889241i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	19.3761	+	19.3761i	0.767710	+	0.767710i
$638$		0			0
$639$	−14.1790			−0.560913
$640$		0			0
$641$			10.1667i			0.401562i	0.979636	+	0.200781i	$0.0643480\pi$
$641$			10.1667i			0.401562i	−0.979636	+	0.200781i	$0.935652\pi$
$642$		0			0
$643$	−31.1082	−	31.1082i	−1.22679	−	1.22679i	−0.965173	−	0.261614i	$-0.915745\pi$
$643$	−31.1082	−	31.1082i	−1.22679	−	1.22679i	−0.261614	−	0.965173i	$-0.584255\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−24.6336	+	24.6336i	−0.968446	+	0.968446i	−0.999517	−	0.0310708i	$-0.990108\pi$
$647$	−24.6336	+	24.6336i	−0.968446	+	0.968446i	0.0310708	+	0.999517i	$0.490108\pi$
$648$		0			0
$649$	27.0757			1.06282
$650$		0			0
$651$	−0.866170			−0.0339479
$652$		0			0
$653$	−4.09234	−	4.09234i	−0.160146	−	0.160146i	0.622486	−	0.782631i	$-0.286123\pi$
$653$	−4.09234	−	4.09234i	−0.160146	−	0.160146i	−0.782631	+	0.622486i	$0.786123\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.04101	−	6.04101i	0.235682	−	0.235682i
$658$		0			0
$659$	−9.90522			−0.385853			−0.192926	−	0.981213i	$-0.561798\pi$
$659$	−9.90522			−0.385853			−0.192926	+	0.981213i	$0.561798\pi$
$660$		0			0
$661$		−	22.1328i		−	0.860866i	−0.902623	−	0.430433i	$-0.858361\pi$
$661$		−	22.1328i		−	0.860866i	0.902623	−	0.430433i	$-0.141639\pi$
$662$		0			0
$663$	−21.5067	−	21.5067i	−0.835251	−	0.835251i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	12.3176	+	12.3176i	0.476941	+	0.476941i
$668$		0			0
$669$		−	10.6396i		−	0.411349i
$670$		0			0
$671$	10.2351			0.395120
$672$		0			0
$673$	−27.1304	+	27.1304i	−1.04580	+	1.04580i	−0.0469019	+	0.998899i	$0.514935\pi$
$673$	−27.1304	+	27.1304i	−1.04580	+	1.04580i	−0.998899	+	0.0469019i	$0.985065\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.5677	−	21.5677i	−0.828915	−	0.828915i	0.158452	−	0.987367i	$-0.449350\pi$
$677$	−21.5677	−	21.5677i	−0.828915	−	0.828915i	−0.987367	+	0.158452i	$0.949350\pi$
$678$		0			0
$679$	7.49279			0.287547
$680$		0			0
$681$	−17.4652			−0.669268
$682$		0			0
$683$	18.0872	−	18.0872i	0.692087	−	0.692087i	−0.270604	−	0.962691i	$-0.587223\pi$
$683$	18.0872	−	18.0872i	0.692087	−	0.692087i	0.962691	+	0.270604i	$0.0872233\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	18.8111	+	18.8111i	0.717686	+	0.717686i
$688$		0			0
$689$		−	3.21723i		−	0.122567i
$690$		0			0
$691$	9.09679			0.346058			0.173029	−	0.984917i	$-0.444645\pi$
$691$	9.09679			0.346058			0.173029	+	0.984917i	$0.444645\pi$
$692$		0			0
$693$	1.33185	+	1.33185i	0.0505929	+	0.0505929i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−5.20448	−	5.20448i	−0.197134	−	0.197134i
$698$		0			0
$699$	26.1644			0.989627
$700$		0			0
$701$	−14.0687			−0.531367			−0.265683	−	0.964060i	$-0.585598\pi$
$701$	−14.0687			−0.531367			−0.265683	+	0.964060i	$0.585598\pi$
$702$		0			0
$703$	32.1932	+	38.3283i	1.21419	+	1.44558i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.72837	−	2.72837i	0.102611	−	0.102611i
$708$		0			0
$709$			40.6035i			1.52490i	0.647050	+	0.762448i	$0.276003\pi$
$709$			40.6035i			1.52490i	−0.647050	+	0.762448i	$0.723997\pi$
$710$		0			0
$711$		−	18.5902i		−	0.697187i
$712$		0			0
$713$	−3.83212	+	3.83212i	−0.143514	+	0.143514i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−25.5660	−	25.5660i	−0.954779	−	0.954779i
$718$		0			0
$719$		−	33.5067i		−	1.24959i	−0.780789	−	0.624794i	$-0.785183\pi$
$719$		−	33.5067i		−	1.24959i	0.780789	−	0.624794i	$-0.214817\pi$
$720$		0			0
$721$			5.31386i			0.197898i
$722$		0			0
$723$	38.6735	+	38.6735i	1.43828	+	1.43828i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−2.59210	+	2.59210i	−0.0961358	+	0.0961358i	−0.753539	−	0.657403i	$-0.771655\pi$
$727$	−2.59210	+	2.59210i	−0.0961358	+	0.0961358i	0.657403	+	0.753539i	$0.271655\pi$
$728$		0			0
$729$			3.88892i			0.144034i
$730$		0			0
$731$	−10.6953			−0.395582
$732$		0			0
$733$	−15.1334	−	15.1334i	−0.558963	−	0.558963i	0.370049	−	0.929012i	$-0.379341\pi$
$733$	−15.1334	−	15.1334i	−0.558963	−	0.558963i	−0.929012	+	0.370049i	$0.879341\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.420302	+	0.420302i	0.0154820	+	0.0154820i
$738$		0			0
$739$		−	13.4291i		−	0.493998i	−0.969016	−	0.246999i	$-0.920556\pi$
$739$		−	13.4291i		−	0.493998i	0.969016	−	0.246999i	$-0.0794444\pi$
$740$		0			0
$741$	−3.21723	+	36.9810i	−0.118188	+	1.35853i
$742$		0			0
$743$	−23.7186	+	23.7186i	−0.870152	+	0.870152i	−0.992489	−	0.122337i	$-0.960961\pi$
$743$	−23.7186	+	23.7186i	−0.870152	+	0.870152i	0.122337	+	0.992489i	$0.460961\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−13.5872	+	13.5872i	−0.497129	+	0.497129i
$748$		0			0
$749$	2.35037			0.0858807
$750$		0			0
$751$		−	20.3615i		−	0.743002i	−0.928433	−	0.371501i	$-0.878843\pi$
$751$		−	20.3615i		−	0.743002i	0.928433	−	0.371501i	$-0.121157\pi$
$752$		0			0
$753$	8.04385	−	8.04385i	0.293134	−	0.293134i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	3.67799	−	3.67799i	0.133679	−	0.133679i	−0.637101	−	0.770780i	$-0.719867\pi$
$757$	3.67799	−	3.67799i	0.133679	−	0.133679i	0.770780	+	0.637101i	$0.219867\pi$
$758$		0			0
$759$	35.7607			1.29803
$760$		0			0
$761$	−15.9126			−0.576831			−0.288415	−	0.957505i	$-0.593128\pi$
$761$	−15.9126			−0.576831			−0.288415	+	0.957505i	$0.593128\pi$
$762$		0			0
$763$	−4.27379	+	4.27379i	−0.154722	+	0.154722i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	26.5491	−	26.5491i	0.958632	−	0.958632i
$768$		0			0
$769$		−	27.0277i		−	0.974643i	−0.873223	−	0.487321i	$-0.837974\pi$
$769$		−	27.0277i		−	0.974643i	0.873223	−	0.487321i	$-0.162026\pi$
$770$		0			0
$771$	13.4237			0.483443
$772$		0			0
$773$	8.89182	−	8.89182i	0.319817	−	0.319817i	−0.528880	−	0.848697i	$-0.677388\pi$
$773$	8.89182	−	8.89182i	0.319817	−	0.319817i	0.848697	+	0.528880i	$0.177388\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	7.55707	−	7.55707i	0.271108	−	0.271108i
$778$		0			0
$779$	−0.778549	+	8.94914i	−0.0278944	+	0.320636i
$780$		0			0
$781$		−	27.9163i		−	0.998925i
$782$		0			0
$783$	6.82564	+	6.82564i	0.243928	+	0.243928i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−20.9266	−	20.9266i	−0.745952	−	0.745952i	0.227764	−	0.973716i	$-0.426858\pi$
$787$	−20.9266	−	20.9266i	−0.745952	−	0.745952i	−0.973716	+	0.227764i	$0.926858\pi$
$788$		0			0
$789$	35.4091			1.26060
$790$		0			0
$791$		−	1.19220i		−	0.0423898i
$792$		0			0
$793$	10.0360	−	10.0360i	0.356388	−	0.356388i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−35.3951	−	35.3951i	−1.25376	−	1.25376i	−0.954021	−	0.299738i	$-0.903101\pi$
$797$	−35.3951	−	35.3951i	−1.25376	−	1.25376i	−0.299738	−	0.954021i	$-0.596899\pi$
$798$		0			0
$799$		−	13.8381i		−	0.489556i
$800$		0			0
$801$			11.1402i			0.393619i
$802$		0			0
$803$	11.8938	+	11.8938i	0.419725	+	0.419725i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−9.47505	+	9.47505i	−0.333538	+	0.333538i
$808$		0			0
$809$		−	18.3555i		−	0.645345i	−0.946511	−	0.322673i	$-0.895419\pi$
$809$		−	18.3555i		−	0.645345i	0.946511	−	0.322673i	$-0.104581\pi$
$810$		0			0
$811$			1.77129i			0.0621983i	0.999516	+	0.0310991i	$0.00990076\pi$
$811$			1.77129i			0.0621983i	−0.999516	+	0.0310991i	$0.990099\pi$
$812$		0			0
$813$	20.2928	−	20.2928i	0.711699	−	0.711699i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	8.39540	+	9.99534i	0.293718	+	0.349693i
$818$		0			0
$819$	2.61189			0.0912668
$820$		0			0
$821$	18.7654			0.654917			0.327459	−	0.944865i	$-0.393808\pi$
$821$	18.7654			0.654917			0.327459	+	0.944865i	$0.393808\pi$
$822$		0			0
$823$	25.6844	+	25.6844i	0.895304	+	0.895304i	0.995016	−	0.0997127i	$-0.0317924\pi$
$823$	25.6844	+	25.6844i	0.895304	+	0.895304i	−0.0997127	+	0.995016i	$0.531792\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−19.7063	−	19.7063i	−0.685257	−	0.685257i	0.275923	−	0.961180i	$-0.411017\pi$
$827$	−19.7063	−	19.7063i	−0.685257	−	0.685257i	−0.961180	+	0.275923i	$0.911017\pi$
$828$		0			0
$829$	14.1790			0.492457			0.246229	−	0.969212i	$-0.420809\pi$
$829$	14.1790			0.492457			0.246229	+	0.969212i	$0.420809\pi$
$830$		0			0
$831$		−	35.6086i		−	1.23525i
$832$		0			0
$833$	17.1891	+	17.1891i	0.595568	+	0.595568i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.12351	+	2.12351i	−0.0733992	+	0.0733992i
$838$		0			0
$839$	19.0319			0.657054			0.328527	−	0.944495i	$-0.393448\pi$
$839$	19.0319			0.657054			0.328527	+	0.944495i	$0.393448\pi$
$840$		0			0
$841$	−20.0509			−0.691409
$842$		0			0
$843$	−39.9309	−	39.9309i	−1.37529	−	1.37529i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.799970	−	0.799970i	0.0274873	−	0.0274873i
$848$		0			0
$849$	39.3934			1.35198
$850$		0			0
$851$		−	66.8681i		−	2.29221i
$852$		0			0
$853$	11.9906	+	11.9906i	0.410551	+	0.410551i	0.881931	−	0.471379i	$-0.156244\pi$
$853$	11.9906	+	11.9906i	0.410551	+	0.410551i	−0.471379	+	0.881931i	$0.656244\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.5107	−	26.5107i	−0.905587	−	0.905587i	0.0903251	−	0.995912i	$-0.471209\pi$
$857$	−26.5107	−	26.5107i	−0.905587	−	0.905587i	−0.995912	+	0.0903251i	$0.971209\pi$
$858$		0			0
$859$		−	44.9719i		−	1.53442i	−0.641395	−	0.767211i	$-0.721644\pi$
$859$		−	44.9719i		−	1.53442i	0.641395	−	0.767211i	$-0.278356\pi$
$860$		0			0
$861$	1.91798			0.0653645
$862$		0			0
$863$	29.4121	−	29.4121i	1.00120	−	1.00120i	0.00120035	−	0.999999i	$-0.499618\pi$
$863$	29.4121	−	29.4121i	1.00120	−	1.00120i	0.999999	−	0.00120035i	$-0.000382082\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	6.34863	+	6.34863i	0.215611	+	0.215611i
$868$		0			0
$869$	36.6013			1.24162
$870$		0			0
$871$	0.824253			0.0279287
$872$		0			0
$873$	−17.7570	+	17.7570i	−0.600982	+	0.600982i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.98977	+	6.98977i	0.236028	+	0.236028i	0.815203	−	0.579175i	$-0.196625\pi$
$877$	6.98977	+	6.98977i	0.236028	+	0.236028i	−0.579175	+	0.815203i	$0.696625\pi$
$878$		0			0
$879$			68.1704i			2.29933i
$880$		0			0
$881$	15.5254			0.523065			0.261532	−	0.965195i	$-0.415772\pi$
$881$	15.5254			0.523065			0.261532	+	0.965195i	$0.415772\pi$
$882$		0			0
$883$	−3.40790	−	3.40790i	−0.114685	−	0.114685i	0.647435	−	0.762120i	$-0.275842\pi$
$883$	−3.40790	−	3.40790i	−0.114685	−	0.114685i	−0.762120	+	0.647435i	$0.775842\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.4077	−	23.4077i	−0.785954	−	0.785954i	0.194874	−	0.980828i	$-0.437570\pi$
$887$	−23.4077	−	23.4077i	−0.785954	−	0.785954i	−0.980828	+	0.194874i	$0.937570\pi$
$888$		0			0
$889$	−3.19098			−0.107022
$890$		0			0
$891$	32.6593			1.09413
$892$		0			0
$893$	−12.9324	+	10.8623i	−0.432766	+	0.363493i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	35.0651	−	35.0651i	1.17079	−	1.17079i
$898$		0			0
$899$			2.78415i			0.0928566i
$900$		0			0
$901$		−	2.85410i		−	0.0950840i
$902$		0			0
$903$	1.97075	−	1.97075i	0.0655825	−	0.0655825i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	22.0781	+	22.0781i	0.733091	+	0.733091i	0.971231	−	0.238140i	$-0.0765376\pi$
$907$	22.0781	+	22.0781i	0.733091	+	0.733091i	−0.238140	+	0.971231i	$0.576538\pi$
$908$		0			0
$909$			12.9318i			0.428920i
$910$		0			0
$911$		−	4.67272i		−	0.154814i	−0.997000	−	0.0774071i	$-0.975336\pi$
$911$		−	4.67272i		−	0.154814i	0.997000	−	0.0774071i	$-0.0246641\pi$
$912$		0			0
$913$	−26.7511	−	26.7511i	−0.885333	−	0.885333i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.22570	−	3.22570i	0.106522	−	0.106522i
$918$		0			0
$919$		−	16.5303i		−	0.545286i	−0.962115	−	0.272643i	$-0.912102\pi$
$919$		−	16.5303i		−	0.545286i	0.962115	−	0.272643i	$-0.0878978\pi$
$920$		0			0
$921$	58.5606			1.92964
$922$		0			0
$923$	−27.3733	−	27.3733i	−0.901004	−	0.901004i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−12.5932	−	12.5932i	−0.413614	−	0.413614i
$928$		0			0
$929$		−	33.1655i		−	1.08812i	−0.839045	−	0.544062i	$-0.816886\pi$
$929$		−	33.1655i		−	1.08812i	0.839045	−	0.544062i	$-0.183114\pi$
$930$		0			0
$931$	2.57136	−	29.5569i	0.0842729	−	0.968687i
$932$		0			0
$933$	45.0655	−	45.0655i	1.47538	−	1.47538i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−32.6686	+	32.6686i	−1.06724	+	1.06724i	−0.0696672	+	0.997570i	$0.522194\pi$
$937$	−32.6686	+	32.6686i	−1.06724	+	1.06724i	−0.997570	+	0.0696672i	$0.977806\pi$
$938$		0			0
$939$	−34.5878			−1.12873
$940$		0			0
$941$		−	3.86014i		−	0.125837i	−0.998019	−	0.0629185i	$-0.979959\pi$
$941$		−	3.86014i		−	0.125837i	0.998019	−	0.0629185i	$-0.0200408\pi$
$942$		0			0
$943$	8.48553	−	8.48553i	0.276327	−	0.276327i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−36.1733	+	36.1733i	−1.17547	+	1.17547i	−0.194590	+	0.980885i	$0.562338\pi$
$947$	−36.1733	+	36.1733i	−1.17547	+	1.17547i	−0.980885	+	0.194590i	$0.937662\pi$
$948$		0			0
$949$	23.3250			0.757161
$950$		0			0
$951$	−31.7132			−1.02837
$952$		0			0
$953$	−13.5239	+	13.5239i	−0.438081	+	0.438081i	−0.891366	−	0.453285i	$-0.850252\pi$
$953$	−13.5239	+	13.5239i	−0.438081	+	0.438081i	0.453285	+	0.891366i	$0.350252\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	12.9906	−	12.9906i	0.419927	−	0.419927i
$958$		0			0
$959$		−	4.97190i		−	0.160551i
$960$		0			0
$961$	30.1338			0.972059
$962$		0			0
$963$	−5.57008	+	5.57008i	−0.179493	+	0.179493i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	21.0163	−	21.0163i	0.675839	−	0.675839i	−0.283217	−	0.959056i	$-0.591402\pi$
$967$	21.0163	−	21.0163i	0.675839	−	0.675839i	0.959056	+	0.283217i	$0.0914017\pi$
$968$		0			0
$969$	−2.85410	+	32.8069i	−0.0916870	+	1.05391i
$970$		0			0
$971$			29.4261i			0.944329i	0.881510	+	0.472164i	$0.156527\pi$
$971$			29.4261i			0.944329i	−0.881510	+	0.472164i	$0.843473\pi$
$972$		0			0
$973$	−3.16992	−	3.16992i	−0.101623	−	0.101623i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.4917	+	10.4917i	0.335658	+	0.335658i	0.854730	−	0.519072i	$-0.173722\pi$
$977$	10.4917	+	10.4917i	0.335658	+	0.335658i	−0.519072	+	0.854730i	$0.673722\pi$
$978$		0			0
$979$	−21.9333			−0.700992
$980$		0			0
$981$		−	20.2567i		−	0.646747i
$982$		0			0
$983$	−4.06697	+	4.06697i	−0.129716	+	0.129716i	−0.768984	−	0.639268i	$-0.779237\pi$
$983$	−4.06697	+	4.06697i	−0.129716	+	0.129716i	0.639268	+	0.768984i	$0.279237\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.54984	+	2.54984i	0.0811622	+	0.0811622i
$988$		0			0
$989$		−	17.4380i		−	0.554496i
$990$		0			0
$991$			16.8189i			0.534271i	0.963659	+	0.267135i	$0.0860771\pi$
$991$			16.8189i			0.534271i	−0.963659	+	0.267135i	$0.913923\pi$
$992$		0			0
$993$	40.0656	+	40.0656i	1.27144	+	1.27144i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−17.1847	+	17.1847i	−0.544244	+	0.544244i	−0.924770	−	0.380526i	$-0.875743\pi$
$997$	−17.1847	+	17.1847i	−0.544244	+	0.544244i	0.380526	+	0.924770i	$0.375743\pi$
$998$		0			0
$999$		−	37.0539i		−	1.17233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.l.b.493.4		12
5.2	odd	4	inner	1900.2.l.b.1557.3		12
5.3	odd	4		380.2.l.b.37.4	yes	12
5.4	even	2		380.2.l.b.113.3	yes	12
15.8	even	4		3420.2.bb.d.37.4		12
15.14	odd	2		3420.2.bb.d.2773.3		12
19.18	odd	2	inner	1900.2.l.b.493.3		12
95.18	even	4		380.2.l.b.37.3	✓	12
95.37	even	4	inner	1900.2.l.b.1557.4		12
95.94	odd	2		380.2.l.b.113.4	yes	12
285.113	odd	4		3420.2.bb.d.37.3		12
285.284	even	2		3420.2.bb.d.2773.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.l.b.37.3	✓	12	95.18	even	4
380.2.l.b.37.4	yes	12	5.3	odd	4
380.2.l.b.113.3	yes	12	5.4	even	2
380.2.l.b.113.4	yes	12	95.94	odd	2
1900.2.l.b.493.3		12	19.18	odd	2	inner
1900.2.l.b.493.4		12	1.1	even	1	trivial
1900.2.l.b.1557.3		12	5.2	odd	4	inner
1900.2.l.b.1557.4		12	95.37	even	4	inner
3420.2.bb.d.37.3		12	285.113	odd	4
3420.2.bb.d.37.4		12	15.8	even	4
3420.2.bb.d.2773.3		12	15.14	odd	2
3420.2.bb.d.2773.4		12	285.284	even	2

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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.49576 - 1.49576i) q^{3} +(-0.311108 + 0.311108i) q^{7} -1.47457i q^{9} +O(q^{10})\)	\(q+(1.49576 - 1.49576i) q^{3} +(-0.311108 + 0.311108i) q^{7} -1.47457i q^{9} +2.90321 q^{11} +(2.84674 - 2.84674i) q^{13} +(2.52543 - 2.52543i) q^{17} +(-4.34250 - 0.377784i) q^{19} +0.930683i q^{21} +(4.11753 + 4.11753i) q^{23} +(2.28167 + 2.28167i) q^{27} +2.99151 q^{29} +0.930683i q^{31} +(4.34250 - 4.34250i) q^{33} +(-8.11992 - 8.11992i) q^{37} -8.51606i q^{39} -2.06083i q^{41} +(-2.11753 - 2.11753i) q^{43} +(2.73975 - 2.73975i) q^{47} +6.80642i q^{49} -7.55485i q^{51} +(0.565073 - 0.565073i) q^{53} +(-7.06039 + 5.93024i) q^{57} +9.32613 q^{59} +3.52543 q^{61} +(0.458751 + 0.458751i) q^{63} +(0.144771 + 0.144771i) q^{67} +12.3176 q^{69} -9.61568i q^{71} +(4.09679 + 4.09679i) q^{73} +(-0.903212 + 0.903212i) q^{77} +12.6072 q^{79} +11.2494 q^{81} +(-9.21432 - 9.21432i) q^{83} +(4.47457 - 4.47457i) q^{87} -7.55485 q^{89} +1.77129i q^{91} +(1.39207 + 1.39207i) q^{93} +(-12.0421 - 12.0421i) q^{97} -4.28100i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{7}+O(q^{10}) \) 12 * q - 4 * q^7	\( 12 q - 4 q^{7} + 8 q^{11} + 4 q^{17} - 4 q^{23} + 28 q^{43} - 20 q^{47} - 24 q^{57} + 16 q^{61} - 20 q^{63} + 76 q^{73} + 16 q^{77} + 4 q^{81} - 84 q^{83} + 80 q^{87} - 8 q^{93}+O(q^{100}) \) 12 * q - 4 * q^7 + 8 * q^11 + 4 * q^17 - 4 * q^23 + 28 * q^43 - 20 * q^47 - 24 * q^57 + 16 * q^61 - 20 * q^63 + 76 * q^73 + 16 * q^77 + 4 * q^81 - 84 * q^83 + 80 * q^87 - 8 * q^93

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