LMFDB - Embedded newform 425.2.d.b.101.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(101,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,2,0,2,0,0,0,6,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.93924352.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 17x^{4} + 73x^{2} + 67 $ x^6 + 17x^4 + 73x^2 + 67
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.5
Root			$2.21547i$ of defining polynomial
Character	$\chi$	$=$	425.101
Dual form			425.2.d.b.101.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.17009 q^{2} -2.21547i q^{3} +2.70928 q^{4} -4.80775i q^{6} +1.02091i q^{7} +1.53919 q^{8} -1.90829 q^{9} -4.98140i q^{11} -6.00231i q^{12} +3.87936 q^{13} +2.21547i q^{14} -2.07838 q^{16} +(1.63090 + 3.78684i) q^{17} -4.14116 q^{18} -4.04945 q^{19} +2.26180 q^{21} -10.8101i q^{22} +7.02322i q^{23} -3.41002i q^{24} +8.41855 q^{26} -2.41864i q^{27} +2.76593i q^{28} +0.644091i q^{29} +4.25729i q^{31} -7.58864 q^{32} -11.0361 q^{33} +(3.53919 + 8.21777i) q^{34} -5.17009 q^{36} +10.2596i q^{37} -8.78765 q^{38} -8.59460i q^{39} -5.82867i q^{41} +4.90829 q^{42} +5.86603 q^{43} -13.4960i q^{44} +15.2410i q^{46} -10.3402 q^{47} +4.60458i q^{48} +5.95774 q^{49} +(8.38962 - 3.61320i) q^{51} +10.5103 q^{52} +11.3896 q^{53} -5.24867i q^{54} +1.57138i q^{56} +8.97142i q^{57} +1.39773i q^{58} -0.447480 q^{59} +3.14275i q^{61} +9.23869i q^{62} -1.94820i q^{63} -12.3112 q^{64} -23.9493 q^{66} -5.07838 q^{67} +(4.41855 + 10.2596i) q^{68} +15.5597 q^{69} -3.41002i q^{71} -2.93722 q^{72} -3.78684i q^{73} +22.2642i q^{74} -10.9711 q^{76} +5.08557 q^{77} -18.6510i q^{78} +0.376821i q^{79} -11.0833 q^{81} -12.6487i q^{82} -3.57531 q^{83} +6.12783 q^{84} +12.7298 q^{86} +1.42696 q^{87} -7.66731i q^{88} -2.63090 q^{89} +3.96049i q^{91} +19.0278i q^{92} +9.43188 q^{93} -22.4391 q^{94} +16.8124i q^{96} -10.9037i q^{97} +12.9288 q^{98} +9.50596i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 2 q^{4} + 6 q^{8} - 16 q^{9} - 2 q^{13} - 6 q^{16} + 2 q^{17} + 16 q^{18} + 12 q^{19} - 2 q^{21} + 22 q^{26} - 6 q^{32} - 28 q^{33} + 18 q^{34} - 20 q^{36} - 32 q^{38} + 34 q^{42} + 8 q^{43}+ \cdots + 16 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^8 - 16 * q^9 - 2 * q^13 - 6 * q^16 + 2 * q^17 + 16 * q^18 + 12 * q^19 - 2 * q^21 + 22 * q^26 - 6 * q^32 - 28 * q^33 + 18 * q^34 - 20 * q^36 - 32 * q^38 + 34 * q^42 + 8 * q^43 - 40 * q^47 + 4 * q^49 - 8 * q^51 + 30 * q^52 + 10 * q^53 - 4 * q^59 - 22 * q^64 - 16 * q^66 - 24 * q^67 - 2 * q^68 + 24 * q^69 - 52 * q^72 - 36 * q^76 - 44 * q^77 + 34 * q^81 + 20 * q^83 - 6 * q^84 - 4 * q^86 + 76 * q^87 - 8 * q^89 + 30 * q^93 - 40 * q^94 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.17009			1.53448			0.767241	−	0.641358i	$-0.221629\pi$
$2$	2.17009			1.53448			0.767241	+	0.641358i	$0.221629\pi$
$3$		−	2.21547i		−	1.27910i	−0.768749	−	0.639550i	$-0.779121\pi$
$3$		−	2.21547i		−	1.27910i	0.768749	−	0.639550i	$-0.220879\pi$
$4$	2.70928			1.35464
$5$		0			0
$5$		0			0
$6$		−	4.80775i		−	1.96276i
$7$			1.02091i			0.385868i	0.981212	+	0.192934i	$0.0618004\pi$
$7$			1.02091i			0.385868i	−0.981212	+	0.192934i	$0.938200\pi$
$8$	1.53919			0.544185
$9$	−1.90829			−0.636097
$10$		0			0
$11$		−	4.98140i		−	1.50195i	−0.660332	−	0.750974i	$-0.729584\pi$
$11$		−	4.98140i		−	1.50195i	0.660332	−	0.750974i	$-0.270416\pi$
$12$		−	6.00231i		−	1.73272i
$13$	3.87936			1.07594			0.537971	−	0.842964i	$-0.319191\pi$
$13$	3.87936			1.07594			0.537971	+	0.842964i	$0.319191\pi$
$14$			2.21547i			0.592108i
$15$		0			0
$16$	−2.07838			−0.519594
$17$	1.63090	+	3.78684i	0.395551	+	0.918444i
$17$	1.63090	+	3.78684i	0.395551	+	0.918444i
$18$	−4.14116			−0.976080
$19$	−4.04945			−0.929007			−0.464504	−	0.885571i	$-0.653767\pi$
$19$	−4.04945			−0.929007			−0.464504	+	0.885571i	$0.653767\pi$
$20$		0			0
$21$	2.26180			0.493564
$22$		−	10.8101i		−	2.30471i
$23$			7.02322i			1.46444i	0.681067	+	0.732221i	$0.261516\pi$
$23$			7.02322i			1.46444i	−0.681067	+	0.732221i	$0.738484\pi$
$24$		−	3.41002i		−	0.696068i
$25$		0			0
$26$	8.41855			1.65101
$27$		−	2.41864i		−	0.465468i
$28$			2.76593i			0.522712i
$29$			0.644091i			0.119605i	0.998210	+	0.0598023i	$0.0190470\pi$
$29$			0.644091i			0.119605i	−0.998210	+	0.0598023i	$0.980953\pi$
$30$		0			0
$31$			4.25729i			0.764632i	0.924032	+	0.382316i	$0.124873\pi$
$31$			4.25729i			0.764632i	−0.924032	+	0.382316i	$0.875127\pi$
$32$	−7.58864			−1.34149
$33$	−11.0361			−1.92114
$34$	3.53919	+	8.21777i	0.606966	+	1.40934i
$35$		0			0
$36$	−5.17009			−0.861681
$37$			10.2596i			1.68667i	0.537390	+	0.843334i	$0.319410\pi$
$37$			10.2596i			1.68667i	−0.537390	+	0.843334i	$0.680590\pi$
$38$	−8.78765			−1.42555
$39$		−	8.59460i		−	1.37624i
$40$		0			0
$41$		−	5.82867i		−	0.910285i	−0.890419	−	0.455142i	$-0.849588\pi$
$41$		−	5.82867i		−	0.910285i	0.890419	−	0.455142i	$-0.150412\pi$
$42$	4.90829			0.757366
$43$	5.86603			0.894561			0.447281	−	0.894394i	$-0.352393\pi$
$43$	5.86603			0.894561			0.447281	+	0.894394i	$0.352393\pi$
$44$		−	13.4960i		−	2.03459i
$45$		0			0
$46$			15.2410i			2.24716i
$47$	−10.3402			−1.50827			−0.754135	−	0.656720i	$-0.771943\pi$
$47$	−10.3402			−1.50827			−0.754135	+	0.656720i	$0.771943\pi$
$48$			4.60458i			0.664613i
$49$	5.95774			0.851106
$50$		0			0
$51$	8.38962	−	3.61320i	1.17478	−	0.505949i
$52$	10.5103			1.45751
$53$	11.3896			1.56448			0.782242	−	0.622974i	$-0.214076\pi$
$53$	11.3896			1.56448			0.782242	+	0.622974i	$0.214076\pi$
$54$		−	5.24867i		−	0.714253i
$55$		0			0
$56$			1.57138i			0.209984i
$57$			8.97142i			1.18829i
$58$			1.39773i			0.183531i
$59$	−0.447480			−0.0582570			−0.0291285	−	0.999576i	$-0.509273\pi$
$59$	−0.447480			−0.0582570			−0.0291285	+	0.999576i	$0.509273\pi$
$60$		0			0
$61$			3.14275i			0.402388i	0.979551	+	0.201194i	$0.0644822\pi$
$61$			3.14275i			0.402388i	−0.979551	+	0.201194i	$0.935518\pi$
$62$			9.23869i			1.17331i
$63$		−	1.94820i		−	0.245450i
$64$	−12.3112			−1.53891
$65$		0			0
$66$	−23.9493			−2.94796
$67$	−5.07838			−0.620423			−0.310211	−	0.950668i	$-0.600400\pi$
$67$	−5.07838			−0.620423			−0.310211	+	0.950668i	$0.600400\pi$
$68$	4.41855	+	10.2596i	0.535828	+	1.24416i
$69$	15.5597			1.87317
$70$		0			0
$71$		−	3.41002i		−	0.404695i	−0.979314	−	0.202348i	$-0.935143\pi$
$71$		−	3.41002i		−	0.404695i	0.979314	−	0.202348i	$-0.0648571\pi$
$72$	−2.93722			−0.346155
$73$		−	3.78684i		−	0.443216i	−0.975136	−	0.221608i	$-0.928869\pi$
$73$		−	3.78684i		−	0.443216i	0.975136	−	0.221608i	$-0.0711306\pi$
$74$			22.2642i			2.58816i
$75$		0			0
$76$	−10.9711			−1.25847
$77$	5.08557			0.579554
$78$		−	18.6510i		−	2.11181i
$79$			0.376821i			0.0423957i	0.999775	+	0.0211978i	$0.00674798\pi$
$79$			0.376821i			0.0423957i	−0.999775	+	0.0211978i	$0.993252\pi$
$80$		0			0
$81$	−11.0833			−1.23148
$82$		−	12.6487i		−	1.39682i
$83$	−3.57531			−0.392441			−0.196220	−	0.980560i	$-0.562867\pi$
$83$	−3.57531			−0.392441			−0.196220	+	0.980560i	$0.562867\pi$
$84$	6.12783			0.668601
$85$		0			0
$86$	12.7298			1.37269
$87$	1.42696			0.152986
$88$		−	7.66731i		−	0.817338i
$89$	−2.63090			−0.278875			−0.139437	−	0.990231i	$-0.544529\pi$
$89$	−2.63090			−0.278875			−0.139437	+	0.990231i	$0.544529\pi$
$90$		0			0
$91$			3.96049i			0.415172i
$92$			19.0278i			1.98379i
$93$	9.43188			0.978041
$94$	−22.4391			−2.31441
$95$		0			0
$96$			16.8124i			1.71591i
$97$		−	10.9037i		−	1.10710i	−0.832815	−	0.553551i	$-0.813272\pi$
$97$		−	10.9037i		−	1.10710i	0.832815	−	0.553551i	$-0.186728\pi$
$98$	12.9288			1.30601
$99$			9.50596i			0.955385i
$100$		0			0
$101$	−6.21953			−0.618867			−0.309433	−	0.950921i	$-0.600139\pi$
$101$	−6.21953			−0.618867			−0.309433	+	0.950921i	$0.600139\pi$
$102$	18.2062	−	7.84095i	1.80268	−	0.776370i
$103$	−10.4969			−1.03429			−0.517147	−	0.855897i	$-0.673006\pi$
$103$	−10.4969			−1.03429			−0.517147	+	0.855897i	$0.673006\pi$
$104$	5.97107			0.585512
$105$		0			0
$106$	24.7165			2.40068
$107$			5.15504i			0.498357i	0.968458	+	0.249178i	$0.0801605\pi$
$107$			5.15504i			0.498357i	−0.968458	+	0.249178i	$0.919839\pi$
$108$		−	6.55277i		−	0.630541i
$109$			6.92959i			0.663735i	0.943326	+	0.331867i	$0.107679\pi$
$109$			6.92959i			0.663735i	−0.943326	+	0.331867i	$0.892321\pi$
$110$		0			0
$111$	22.7298			2.15742
$112$		−	2.12184i		−	0.200495i
$113$		−	19.5783i		−	1.84177i	−0.389832	−	0.920886i	$-0.627467\pi$
$113$		−	19.5783i		−	1.84177i	0.389832	−	0.920886i	$-0.372533\pi$
$114$			19.4687i			1.82342i
$115$		0			0
$116$			1.74502i			0.162021i
$117$	−7.40295			−0.684403
$118$	−0.971071			−0.0893943
$119$	−3.86603	+	1.66500i	−0.354398	+	0.152631i
$120$		0			0
$121$	−13.8143			−1.25585
$122$			6.82004i			0.617458i
$123$	−12.9132			−1.16435
$124$			11.5342i			1.03580i
$125$		0			0
$126$		−	4.22776i		−	0.376638i
$127$	−2.20620			−0.195769			−0.0978845	−	0.995198i	$-0.531208\pi$
$127$	−2.20620			−0.195769			−0.0978845	+	0.995198i	$0.531208\pi$
$128$	−11.5392			−1.01993
$129$		−	12.9960i		−	1.14423i
$130$		0			0
$131$		−	19.2015i		−	1.67764i	−0.544408	−	0.838821i	$-0.683246\pi$
$131$		−	19.2015i		−	1.67764i	0.544408	−	0.838821i	$-0.316754\pi$
$132$	−29.8999			−2.60245
$133$		−	4.13413i		−	0.358474i
$134$	−11.0205			−0.952028
$135$		0			0
$136$	2.51026	+	5.82867i	0.215253	+	0.499804i
$137$	0.304056			0.0259772			0.0129886	−	0.999916i	$-0.495865\pi$
$137$	0.304056			0.0259772			0.0129886	+	0.999916i	$0.495865\pi$
$138$	33.7659			2.87435
$139$		−	18.9478i		−	1.60713i	−0.595215	−	0.803567i	$-0.702933\pi$
$139$		−	18.9478i		−	1.60713i	0.595215	−	0.803567i	$-0.297067\pi$
$140$		0			0
$141$			22.9083i			1.92923i
$142$		−	7.40004i		−	0.620998i
$143$		−	19.3246i		−	1.61601i
$144$	3.96615			0.330513
$145$		0			0
$146$		−	8.21777i		−	0.680108i
$147$		−	13.1992i		−	1.08865i
$148$			27.7961i			2.28482i
$149$	−19.4969			−1.59725			−0.798625	−	0.601829i	$-0.794439\pi$
$149$	−19.4969			−1.59725			−0.798625	+	0.601829i	$0.794439\pi$
$150$		0			0
$151$	−19.1773			−1.56062			−0.780312	−	0.625390i	$-0.784940\pi$
$151$	−19.1773			−1.56062			−0.780312	+	0.625390i	$0.784940\pi$
$152$	−6.23287			−0.505552
$153$	−3.11223	−	7.22640i	−0.251609	−	0.584220i
$154$	11.0361			0.889316
$155$		0			0
$156$		−	23.2851i		−	1.86430i
$157$	14.6248			1.16718			0.583591	−	0.812048i	$-0.301647\pi$
$157$	14.6248			1.16718			0.583591	+	0.812048i	$0.301647\pi$
$158$			0.817734i			0.0650554i
$159$		−	25.2333i		−	2.00113i
$160$		0			0
$161$	−7.17009			−0.565082
$162$	−24.0517			−1.88968
$163$			13.5760i			1.06335i	0.846947	+	0.531677i	$0.178438\pi$
$163$			13.5760i			1.06335i	−0.846947	+	0.531677i	$0.821562\pi$
$164$		−	15.7915i		−	1.23311i
$165$		0			0
$166$	−7.75872			−0.602194
$167$			2.59229i			0.200597i	0.994957	+	0.100299i	$0.0319798\pi$
$167$			2.59229i			0.200597i	−0.994957	+	0.100299i	$0.968020\pi$
$168$	3.48133			0.268590
$169$	2.04945			0.157650
$170$		0			0
$171$	7.72753			0.590939
$172$	15.8927			1.21181
$173$			11.0132i			0.837321i	0.908143	+	0.418661i	$0.137500\pi$
$173$			11.0132i			0.837321i	−0.908143	+	0.418661i	$0.862500\pi$
$174$	3.09663			0.234755
$175$		0			0
$176$			10.3532i			0.780404i
$177$			0.991377i			0.0745165i
$178$	−5.70928			−0.427928
$179$	24.9854			1.86750			0.933750	−	0.357926i	$-0.116516\pi$
$179$	24.9854			1.86750			0.933750	+	0.357926i	$0.116516\pi$
$180$		0			0
$181$		−	14.3432i		−	1.06612i	−0.846076	−	0.533062i	$-0.821041\pi$
$181$		−	14.3432i		−	1.06612i	0.846076	−	0.533062i	$-0.178959\pi$
$182$			8.59460i			0.637074i
$183$	6.96266			0.514695
$184$			10.8101i			0.796928i
$185$		0			0
$186$	20.4680			1.50079
$187$	18.8638	−	8.12415i	1.37946	−	0.594097i
$188$	−28.0144			−2.04316
$189$	2.46922			0.179609
$190$		0			0
$191$	5.39576			0.390424			0.195212	−	0.980761i	$-0.437461\pi$
$191$	5.39576			0.390424			0.195212	+	0.980761i	$0.437461\pi$
$192$			27.2751i			1.96841i
$193$			16.1387i			1.16169i	0.814013	+	0.580846i	$0.197278\pi$
$193$			16.1387i			1.16169i	−0.814013	+	0.580846i	$0.802722\pi$
$194$		−	23.6619i		−	1.69883i
$195$		0			0
$196$	16.1412			1.15294
$197$			9.26822i			0.660333i	0.943923	+	0.330167i	$0.107105\pi$
$197$			9.26822i			0.660333i	−0.943923	+	0.330167i	$0.892895\pi$
$198$			20.6287i			1.46602i
$199$			4.63411i			0.328503i	0.986418	+	0.164252i	$0.0525209\pi$
$199$			4.63411i			0.328503i	−0.986418	+	0.164252i	$0.947479\pi$
$200$		0			0
$201$			11.2510i			0.793583i
$202$	−13.4969			−0.949641
$203$	−0.657560			−0.0461516
$204$	22.7298	−	9.78915i	1.59140	−	0.685378i
$205$		0			0
$206$	−22.7792			−1.58711
$207$		−	13.4023i		−	0.931528i
$208$	−8.06278			−0.559053
$209$			20.1719i			1.39532i
$210$		0			0
$211$			6.09593i			0.419661i	0.977738	+	0.209831i	$0.0672913\pi$
$211$			6.09593i			0.419661i	−0.977738	+	0.209831i	$0.932709\pi$
$212$	30.8576			2.11931
$213$	−7.55479			−0.517645
$214$			11.1869i			0.764720i
$215$		0			0
$216$		−	3.72275i		−	0.253301i
$217$	−4.34632			−0.295047
$218$			15.0378i			1.01849i
$219$	−8.38962			−0.566918
$220$		0			0
$221$	6.32684	+	14.6905i	0.425589	+	0.988192i
$222$	49.3256			3.31052
$223$	−17.7009			−1.18534			−0.592669	−	0.805446i	$-0.701926\pi$
$223$	−17.7009			−1.18534			−0.592669	+	0.805446i	$0.701926\pi$
$224$		−	7.74733i		−	0.517640i
$225$		0			0
$226$		−	42.4866i		−	2.82617i
$227$		−	25.5806i		−	1.69784i	−0.528518	−	0.848922i	$-0.677252\pi$
$227$		−	25.5806i		−	1.69784i	0.528518	−	0.848922i	$-0.322748\pi$
$228$			24.3060i			1.60971i
$229$	11.9867			0.792101			0.396051	−	0.918229i	$-0.370380\pi$
$229$	11.9867			0.792101			0.396051	+	0.918229i	$0.370380\pi$
$230$		0			0
$231$		−	11.2669i		−	0.741308i
$232$			0.991377i			0.0650871i
$233$			4.72774i			0.309724i	0.987936	+	0.154862i	$0.0494933\pi$
$233$			4.72774i			0.309724i	−0.987936	+	0.154862i	$0.950507\pi$
$234$	−16.0650			−1.05020
$235$		0			0
$236$	−1.21235			−0.0789171
$237$	0.834834			0.0542283
$238$	−8.38962	+	3.61320i	−0.543818	+	0.234209i
$239$	10.7649			0.696321			0.348161	−	0.937435i	$-0.386806\pi$
$239$	10.7649			0.696321			0.348161	+	0.937435i	$0.386806\pi$
$240$		0			0
$241$			21.6201i			1.39267i	0.717715	+	0.696337i	$0.245188\pi$
$241$			21.6201i			1.39267i	−0.717715	+	0.696337i	$0.754812\pi$
$242$	−29.9783			−1.92708
$243$			17.2987i			1.10971i
$244$			8.51458i			0.545090i
$245$		0			0
$246$	−28.0228			−1.78667
$247$	−15.7093			−0.999557
$248$			6.55277i			0.416101i
$249$			7.92097i			0.501971i
$250$		0			0
$251$	−0.837101			−0.0528374			−0.0264187	−	0.999651i	$-0.508410\pi$
$251$	−0.837101			−0.0528374			−0.0264187	+	0.999651i	$0.508410\pi$
$252$		−	5.27820i		−	0.332495i
$253$	34.9854			2.19952
$254$	−4.78765			−0.300404
$255$		0			0
$256$	−0.418551			−0.0261594
$257$	7.67316			0.478638			0.239319	−	0.970941i	$-0.423076\pi$
$257$	7.67316			0.478638			0.239319	+	0.970941i	$0.423076\pi$
$258$		−	28.2024i		−	1.75581i
$259$	−10.4741			−0.650832
$260$		0			0
$261$		−	1.22911i		−	0.0760802i
$262$		−	41.6689i		−	2.57431i
$263$	26.8371			1.65485			0.827423	−	0.561579i	$-0.189806\pi$
$263$	26.8371			1.65485			0.827423	+	0.561579i	$0.189806\pi$
$264$	−16.9867			−1.04546
$265$		0			0
$266$		−	8.97142i		−	0.550073i
$267$			5.82867i			0.356709i
$268$	−13.7587			−0.840448
$269$		−	20.5192i		−	1.25108i	−0.780193	−	0.625539i	$-0.784879\pi$
$269$		−	20.5192i		−	1.25108i	0.780193	−	0.625539i	$-0.215121\pi$
$270$		0			0
$271$	12.2062			0.741474			0.370737	−	0.928738i	$-0.379105\pi$
$271$	12.2062			0.741474			0.370737	+	0.928738i	$0.379105\pi$
$272$	−3.38962	−	7.87049i	−0.205526	−	0.477218i
$273$	8.77432			0.531046
$274$	0.659827			0.0398616
$275$		0			0
$276$	42.1555			2.53746
$277$		−	6.52324i		−	0.391943i	−0.980610	−	0.195972i	$-0.937214\pi$
$277$		−	6.52324i		−	0.391943i	0.980610	−	0.195972i	$-0.0627861\pi$
$278$		−	41.1184i		−	2.46612i
$279$		−	8.12415i		−	0.486380i
$280$		0			0
$281$	1.60811			0.0959319			0.0479659	−	0.998849i	$-0.484726\pi$
$281$	1.60811			0.0959319			0.0479659	+	0.998849i	$0.484726\pi$
$282$			49.7130i			2.96037i
$283$			2.18593i			0.129940i	0.997887	+	0.0649701i	$0.0206952\pi$
$283$			2.18593i			0.129940i	−0.997887	+	0.0649701i	$0.979305\pi$
$284$		−	9.23869i		−	0.548215i
$285$		0			0
$286$		−	41.9361i		−	2.47974i
$287$	5.95055			0.351250
$288$	14.4813			0.853321
$289$	−11.6803	+	12.3519i	−0.687079	+	0.726583i
$290$		0			0
$291$	−24.1568			−1.41609
$292$		−	10.2596i		−	0.600398i
$293$	−1.50307			−0.0878104			−0.0439052	−	0.999036i	$-0.513980\pi$
$293$	−1.50307			−0.0878104			−0.0439052	+	0.999036i	$0.513980\pi$
$294$		−	28.6433i		−	1.67051i
$295$		0			0
$296$			15.7915i			0.917860i
$297$	−12.0482			−0.699109
$298$	−42.3100			−2.45095
$299$			27.2456i			1.57565i
$300$		0			0
$301$			5.98870i			0.345183i
$302$	−41.6163			−2.39475
$303$			13.7792i			0.791593i
$304$	8.41628			0.482707
$305$		0			0
$306$	−6.75380	−	15.6819i	−0.386089	−	0.896475i
$307$	−0.340173			−0.0194147			−0.00970735	−	0.999953i	$-0.503090\pi$
$307$	−0.340173			−0.0194147			−0.00970735	+	0.999953i	$0.503090\pi$
$308$	13.7782			0.785086
$309$			23.2556i			1.32296i
$310$		0			0
$311$		−	23.1915i		−	1.31507i	−0.753424	−	0.657535i	$-0.771599\pi$
$311$		−	23.1915i		−	1.31507i	0.753424	−	0.657535i	$-0.228401\pi$
$312$		−	13.2287i		−	0.748928i
$313$		−	25.4070i		−	1.43609i	−0.695998	−	0.718043i	$-0.745038\pi$
$313$		−	25.4070i		−	1.43609i	0.695998	−	0.718043i	$-0.254962\pi$
$314$	31.7370			1.79102
$315$		0			0
$316$			1.02091i			0.0574308i
$317$		−	6.76956i		−	0.380216i	−0.981763	−	0.190108i	$-0.939116\pi$
$317$		−	6.76956i		−	0.380216i	0.981763	−	0.190108i	$-0.0608839\pi$
$318$		−	54.7585i		−	3.07070i
$319$	3.20847			0.179640
$320$		0			0
$321$	11.4208			0.637448
$322$	−15.5597			−0.867109
$323$	−6.60424	−	15.3346i	−0.367469	−	0.853241i
$324$	−30.0277			−1.66821
$325$		0			0
$326$			29.4611i			1.63170i
$327$	15.3523			0.848983
$328$		−	8.97142i		−	0.495364i
$329$		−	10.5564i		−	0.581993i
$330$		0			0
$331$	21.8888			1.20312			0.601559	−	0.798828i	$-0.294546\pi$
$331$	21.8888			1.20312			0.601559	+	0.798828i	$0.294546\pi$
$332$	−9.68649			−0.531615
$333$		−	19.5783i		−	1.07288i
$334$			5.62549i			0.307813i
$335$		0			0
$336$	−4.70086			−0.256453
$337$			29.7283i			1.61941i	0.586840	+	0.809703i	$0.300372\pi$
$337$			29.7283i			1.61941i	−0.586840	+	0.809703i	$0.699628\pi$
$338$	4.44748			0.241911
$339$	−43.3751			−2.35581
$340$		0			0
$341$	21.2072			1.14844
$342$	16.7694			0.906785
$343$			13.2287i			0.714283i
$344$	9.02893			0.486807
$345$		0			0
$346$			23.8997i			1.28485i
$347$		−	22.0474i		−	1.18357i	−0.806097	−	0.591784i	$-0.798424\pi$
$347$		−	22.0474i		−	1.18357i	0.806097	−	0.591784i	$-0.201576\pi$
$348$	3.86603			0.207241
$349$	−15.0761			−0.807006			−0.403503	−	0.914978i	$-0.632207\pi$
$349$	−15.0761			−0.807006			−0.403503	+	0.914978i	$0.632207\pi$
$350$		0			0
$351$		−	9.38280i		−	0.500817i
$352$			37.8020i			2.01485i
$353$	−14.1194			−0.751501			−0.375750	−	0.926721i	$-0.622615\pi$
$353$	−14.1194			−0.751501			−0.375750	+	0.926721i	$0.622615\pi$
$354$			2.15137i			0.114344i
$355$		0			0
$356$	−7.12783			−0.377774
$357$	3.68876	+	8.56506i	0.195230	+	0.453311i
$358$	54.2206			2.86565
$359$	23.8082			1.25655			0.628274	−	0.777992i	$-0.283762\pi$
$359$	23.8082			1.25655			0.628274	+	0.777992i	$0.283762\pi$
$360$		0			0
$361$	−2.60197			−0.136946
$362$		−	31.1261i		−	1.63595i
$363$			30.6052i			1.60635i
$364$			10.7300i			0.562407i
$365$		0			0
$366$	15.1096			0.789790
$367$			3.77323i			0.196961i	0.995139	+	0.0984806i	$0.0313982\pi$
$367$			3.77323i			0.196961i	−0.995139	+	0.0984806i	$0.968602\pi$
$368$		−	14.5969i		−	0.760916i
$369$			11.1228i			0.579029i
$370$		0			0
$371$			11.6278i			0.603685i
$372$	25.5536			1.32489
$373$	−1.54760			−0.0801317			−0.0400658	−	0.999197i	$-0.512757\pi$
$373$	−1.54760			−0.0801317			−0.0400658	+	0.999197i	$0.512757\pi$
$374$	40.9360	−	17.6301i	2.11675	−	0.911631i
$375$		0			0
$376$	−15.9155			−0.820778
$377$			2.49866i			0.128688i
$378$	5.35842			0.275608
$379$			13.4824i			0.692543i	0.938134	+	0.346271i	$0.112552\pi$
$379$			13.4824i			0.692543i	−0.938134	+	0.346271i	$0.887448\pi$
$380$		0			0
$381$			4.88777i			0.250408i
$382$	11.7093			0.599099
$383$	4.44748			0.227256			0.113628	−	0.993523i	$-0.463753\pi$
$383$	4.44748			0.227256			0.113628	+	0.993523i	$0.463753\pi$
$384$			25.5647i			1.30459i
$385$		0			0
$386$			35.0225i			1.78260i
$387$	−11.1941			−0.569028
$388$		−	29.5411i		−	1.49972i
$389$	−25.4680			−1.29128			−0.645639	−	0.763642i	$-0.723409\pi$
$389$	−25.4680			−1.29128			−0.645639	+	0.763642i	$0.723409\pi$
$390$		0			0
$391$	−26.5958	+	11.4542i	−1.34501	+	0.579261i
$392$	9.17009			0.463159
$393$	−42.5402			−2.14587
$394$			20.1128i			1.01327i
$395$		0			0
$396$			25.7543i			1.29420i
$397$			14.3937i			0.722400i	0.932488	+	0.361200i	$0.117633\pi$
$397$			14.3937i			0.722400i	−0.932488	+	0.361200i	$0.882367\pi$
$398$			10.0564i			0.504083i
$399$	−9.15902			−0.458525
$400$		0			0
$401$			0.456838i			0.0228134i	0.999935	+	0.0114067i	$0.00363094\pi$
$401$			0.456838i			0.0228134i	−0.999935	+	0.0114067i	$0.996369\pi$
$402$			24.4156i			1.21774i
$403$			16.5156i			0.822699i
$404$	−16.8504			−0.838340
$405$		0			0
$406$	−1.42696			−0.0708189
$407$	51.1071			2.53329
$408$	12.9132	−	5.56140i	0.639299	−	0.275330i
$409$	26.7770			1.32404			0.662018	−	0.749488i	$-0.269700\pi$
$409$	26.7770			1.32404			0.662018	+	0.749488i	$0.269700\pi$
$410$		0			0
$411$		−	0.673625i		−	0.0332275i
$412$	−28.4391			−1.40109
$413$		−	0.456838i		−	0.0224795i
$414$		−	29.0843i		−	1.42941i
$415$		0			0
$416$	−29.4391			−1.44337
$417$	−41.9783			−2.05568
$418$			43.7748i			2.14109i
$419$			16.2914i			0.795889i	0.917409	+	0.397944i	$0.130276\pi$
$419$			16.2914i			0.795889i	−0.917409	+	0.397944i	$0.869724\pi$
$420$		0			0
$421$	−6.21953			−0.303122			−0.151561	−	0.988448i	$-0.548430\pi$
$421$	−6.21953			−0.303122			−0.151561	+	0.988448i	$0.548430\pi$
$422$			13.2287i			0.643963i
$423$	19.7321			0.959406
$424$	17.5308			0.851370
$425$		0			0
$426$	−16.3945			−0.794318
$427$	−3.20847			−0.155269
$428$			13.9664i			0.675093i
$429$	−42.8131			−2.06704
$430$		0			0
$431$		−	24.4292i		−	1.17671i	−0.808602	−	0.588357i	$-0.799775\pi$
$431$		−	24.4292i		−	1.17671i	0.808602	−	0.588357i	$-0.200225\pi$
$432$			5.02686i			0.241855i
$433$	−6.85989			−0.329665			−0.164833	−	0.986322i	$-0.552708\pi$
$433$	−6.85989			−0.329665			−0.164833	+	0.986322i	$0.552708\pi$
$434$	−9.43188			−0.452745
$435$		0			0
$436$			18.7742i			0.899120i
$437$		−	28.4402i		−	1.36048i
$438$	−18.2062			−0.869926
$439$			13.0255i			0.621675i	0.950463	+	0.310837i	$0.100609\pi$
$439$			13.0255i			0.621675i	−0.950463	+	0.310837i	$0.899391\pi$
$440$		0			0
$441$	−11.3691			−0.541386
$442$	13.7298	+	31.8797i	0.653060	+	1.51636i
$443$	−2.71542			−0.129013			−0.0645067	−	0.997917i	$-0.520547\pi$
$443$	−2.71542			−0.129013			−0.0645067	+	0.997917i	$0.520547\pi$
$444$	61.5813			2.92252
$445$		0			0
$446$	−38.4124			−1.81888
$447$			43.1948i			2.04304i
$448$		−	12.5687i		−	0.593815i
$449$			20.5697i			0.970743i	0.874308	+	0.485372i	$0.161316\pi$
$449$			20.5697i			0.970743i	−0.874308	+	0.485372i	$0.838684\pi$
$450$		0			0
$451$	−29.0349			−1.36720
$452$		−	53.0430i		−	2.49493i
$453$			42.4866i			1.99619i
$454$		−	55.5121i		−	2.60531i
$455$		0			0
$456$			13.8087i			0.646652i
$457$	−15.0338			−0.703254			−0.351627	−	0.936140i	$-0.614371\pi$
$457$	−15.0338			−0.703254			−0.351627	+	0.936140i	$0.614371\pi$
$458$	26.0121			1.21547
$459$	9.15902	−	3.94456i	0.427507	−	0.184116i
$460$		0			0
$461$	−12.7382			−0.593277			−0.296639	−	0.954990i	$-0.595866\pi$
$461$	−12.7382			−0.593277			−0.296639	+	0.954990i	$0.595866\pi$
$462$		−	24.4501i		−	1.13752i
$463$	−5.68261			−0.264093			−0.132047	−	0.991243i	$-0.542155\pi$
$463$	−5.68261			−0.264093			−0.132047	+	0.991243i	$0.542155\pi$
$464$		−	1.33866i		−	0.0621459i
$465$		0			0
$466$			10.2596i			0.475267i
$467$	23.9155			1.10668			0.553338	−	0.832957i	$-0.313354\pi$
$467$	23.9155			1.10668			0.553338	+	0.832957i	$0.313354\pi$
$468$	−20.0566			−0.927118
$469$		−	5.18457i		−	0.239401i
$470$		0			0
$471$		−	32.4007i		−	1.49294i
$472$	−0.688756			−0.0317026
$473$		−	29.2210i		−	1.34358i
$474$	1.81166			0.0832124
$475$		0			0
$476$	−10.4741	+	4.51095i	−0.480082	+	0.206759i
$477$	−21.7347			−0.995164
$478$	23.3607			1.06849
$479$		−	11.6142i		−	0.530666i	−0.964157	−	0.265333i	$-0.914518\pi$
$479$		−	11.6142i		−	0.530666i	0.964157	−	0.265333i	$-0.0854818\pi$
$480$		0			0
$481$			39.8007i			1.81476i
$482$			46.9175i			2.13704i
$483$			15.8851i			0.722796i
$484$	−37.4268			−1.70122
$485$		0			0
$486$			37.5398i			1.70284i
$487$			7.96411i			0.360888i	0.983585	+	0.180444i	$0.0577535\pi$
$487$			7.96411i			0.360888i	−0.983585	+	0.180444i	$0.942246\pi$
$488$			4.83729i			0.218974i
$489$	30.0772			1.36014
$490$		0			0
$491$	36.2557			1.63619			0.818097	−	0.575080i	$-0.195029\pi$
$491$	36.2557			1.63619			0.818097	+	0.575080i	$0.195029\pi$
$492$	−34.9854			−1.57727
$493$	−2.43907	+	1.05045i	−0.109850	+	0.0473097i
$494$	−34.0905			−1.53380
$495$		0			0
$496$		−	8.84826i		−	0.397298i
$497$	3.48133			0.156159
$498$			17.1892i			0.770266i
$499$			20.1583i			0.902409i	0.892420	+	0.451205i	$0.149006\pi$
$499$			20.1583i			0.902409i	−0.892420	+	0.451205i	$0.850994\pi$
$500$		0			0
$501$	5.74313			0.256584
$502$	−1.81658			−0.0810780
$503$			19.2151i			0.856759i	0.903599	+	0.428379i	$0.140915\pi$
$503$			19.2151i			0.856759i	−0.903599	+	0.428379i	$0.859085\pi$
$504$		−	2.99864i		−	0.133570i
$505$		0			0
$506$	75.9214			3.37512
$507$		−	4.54048i		−	0.201650i
$508$	−5.97721			−0.265196
$509$	1.52813			0.0677330			0.0338665	−	0.999426i	$-0.489218\pi$
$509$	1.52813			0.0677330			0.0338665	+	0.999426i	$0.489218\pi$
$510$		0			0
$511$	3.86603			0.171023
$512$	22.1701			0.979789
$513$			9.79417i			0.432423i
$514$	16.6514			0.734462
$515$		0			0
$516$		−	35.2097i		−	1.55002i
$517$			51.5085i			2.26534i
$518$	−22.7298			−0.998690
$519$	24.3995			1.07102
$520$		0			0
$521$			9.96279i			0.436478i	0.975895	+	0.218239i	$0.0700312\pi$
$521$			9.96279i			0.436478i	−0.975895	+	0.218239i	$0.929969\pi$
$522$		−	2.66728i		−	0.116744i
$523$	−31.2618			−1.36698			−0.683491	−	0.729959i	$-0.739539\pi$
$523$	−31.2618			−1.36698			−0.683491	+	0.729959i	$0.739539\pi$
$524$		−	52.0221i		−	2.27260i
$525$		0			0
$526$	58.2388			2.53933
$527$	−16.1217	+	6.94320i	−0.702272	+	0.302451i
$528$	22.9372			0.998214
$529$	−26.3256			−1.14459
$530$		0			0
$531$	0.853922			0.0370571
$532$		−	11.2005i		−	0.485603i
$533$		−	22.6115i		−	0.979413i
$534$			12.6487i			0.547363i
$535$		0			0
$536$	−7.81658			−0.337625
$537$		−	55.3544i		−	2.38872i
$538$		−	44.5284i		−	1.91976i
$539$		−	29.6779i		−	1.27832i
$540$		0			0
$541$			29.1433i			1.25297i	0.779434	+	0.626485i	$0.215507\pi$
$541$			29.1433i			1.25297i	−0.779434	+	0.626485i	$0.784493\pi$
$542$	26.4885			1.13778
$543$	−31.7770			−1.36368
$544$	−12.3763	−	28.7370i	−0.530629	−	1.23209i
$545$		0			0
$546$	19.0410			0.814881
$547$			18.5069i			0.791298i	0.918402	+	0.395649i	$0.129480\pi$
$547$			18.5069i			0.791298i	−0.918402	+	0.395649i	$0.870520\pi$
$548$	0.823770			0.0351897
$549$		−	5.99729i		−	0.255958i
$550$		0			0
$551$		−	2.60821i		−	0.111114i
$552$	23.9493			1.01935
$553$	−0.384701			−0.0163591
$554$		−	14.1560i		−	0.601430i
$555$		0			0
$556$		−	51.3349i		−	2.17708i
$557$	1.44029			0.0610271			0.0305136	−	0.999534i	$-0.490286\pi$
$557$	1.44029			0.0610271			0.0305136	+	0.999534i	$0.490286\pi$
$558$		−	17.6301i		−	0.746342i
$559$	22.7565			0.962496
$560$		0			0
$561$	−17.9988	−	41.7920i	−0.759909	−	1.76446i
$562$	3.48974			0.147206
$563$	−2.47414			−0.104273			−0.0521363	−	0.998640i	$-0.516603\pi$
$563$	−2.47414			−0.104273			−0.0521363	+	0.998640i	$0.516603\pi$
$564$			62.0649i			2.61340i
$565$		0			0
$566$			4.74366i			0.199391i
$567$		−	11.3151i		−	0.475188i
$568$		−	5.24867i		−	0.220229i
$569$	15.3919			0.645262			0.322631	−	0.946525i	$-0.395433\pi$
$569$	15.3919			0.645262			0.322631	+	0.946525i	$0.395433\pi$
$570$		0			0
$571$		−	17.8974i		−	0.748982i	−0.927231	−	0.374491i	$-0.877817\pi$
$571$		−	17.8974i		−	0.748982i	0.927231	−	0.374491i	$-0.122183\pi$
$572$		−	52.3558i		−	2.18910i
$573$		−	11.9541i		−	0.499391i
$574$	12.9132			0.538987
$575$		0			0
$576$	23.4934			0.978893
$577$	−44.1894			−1.83963			−0.919814	−	0.392355i	$-0.871661\pi$
$577$	−44.1894			−1.83963			−0.919814	+	0.392355i	$0.871661\pi$
$578$	−25.3474	+	26.8047i	−1.05431	+	1.11493i
$579$	35.7548			1.48592
$580$		0			0
$581$		−	3.65007i		−	0.151430i
$582$	−52.4222			−2.17297
$583$		−	56.7362i		−	2.34977i
$584$		−	5.82867i		−	0.241192i
$585$		0			0
$586$	−3.26180			−0.134744
$587$	−3.04718			−0.125771			−0.0628853	−	0.998021i	$-0.520030\pi$
$587$	−3.04718			−0.125771			−0.0628853	+	0.998021i	$0.520030\pi$
$588$		−	35.7602i		−	1.47473i
$589$		−	17.2397i		−	0.710348i
$590$		0			0
$591$	20.5334			0.844633
$592$		−	21.3233i		−	0.876383i
$593$	9.68876			0.397870			0.198935	−	0.980013i	$-0.436252\pi$
$593$	9.68876			0.397870			0.198935	+	0.980013i	$0.436252\pi$
$594$	−26.1457			−1.07277
$595$		0			0
$596$	−52.8225			−2.16370
$597$	10.2667			0.420189
$598$			59.1253i			2.41781i
$599$	−33.2846			−1.35997			−0.679986	−	0.733225i	$-0.738014\pi$
$599$	−33.2846			−1.35997			−0.679986	+	0.733225i	$0.738014\pi$
$600$		0			0
$601$		−	13.1055i		−	0.534586i	−0.963615	−	0.267293i	$-0.913871\pi$
$601$		−	13.1055i		−	0.534586i	0.963615	−	0.267293i	$-0.0861292\pi$
$602$			12.9960i			0.529677i
$603$	9.69102			0.394649
$604$	−51.9565			−2.11408
$605$		0			0
$606$			29.9020i			1.21469i
$607$		−	8.34094i		−	0.338548i	−0.985569	−	0.169274i	$-0.945858\pi$
$607$		−	8.34094i		−	0.338548i	0.985569	−	0.169274i	$-0.0541423\pi$
$608$	30.7298			1.24626
$609$			1.45680i			0.0590326i
$610$		0			0
$611$	−40.1133			−1.62281
$612$	−8.43188	−	19.5783i	−0.340839	−	0.791406i
$613$	32.6430			1.31844			0.659219	−	0.751951i	$-0.270887\pi$
$613$	32.6430			1.31844			0.659219	+	0.751951i	$0.270887\pi$
$614$	−0.738205			−0.0297915
$615$		0			0
$616$	7.82765			0.315385
$617$		−	31.5324i		−	1.26945i	−0.772739	−	0.634724i	$-0.781114\pi$
$617$		−	31.5324i		−	1.26945i	0.772739	−	0.634724i	$-0.218886\pi$
$618$			50.4666i			2.03007i
$619$			42.1234i			1.69308i	0.532323	+	0.846541i	$0.321319\pi$
$619$			42.1234i			1.69308i	−0.532323	+	0.846541i	$0.678681\pi$
$620$		0			0
$621$	16.9867			0.681652
$622$		−	50.3276i		−	2.01795i
$623$		−	2.68591i		−	0.107609i
$624$			17.8628i			0.715085i
$625$		0			0
$626$		−	55.1353i		−	2.20365i
$627$	44.6902			1.78475
$628$	39.6225			1.58111
$629$	−38.8515	+	16.7324i	−1.54911	+	0.667163i
$630$		0			0
$631$	16.7031			0.664941			0.332471	−	0.943114i	$-0.392118\pi$
$631$	16.7031			0.664941			0.332471	+	0.943114i	$0.392118\pi$
$632$			0.579999i			0.0230711i
$633$	13.5053			0.536789
$634$		−	14.6905i		−	0.583436i
$635$		0			0
$636$		−	68.3640i		−	2.71081i
$637$	23.1122			0.915740
$638$	6.96266			0.275654
$639$			6.50731i			0.257425i
$640$		0			0
$641$		−	16.3260i		−	0.644838i	−0.946597	−	0.322419i	$-0.895504\pi$
$641$		−	16.3260i		−	0.644838i	0.946597	−	0.322419i	$-0.104496\pi$
$642$	24.7842			0.978153
$643$			28.0633i			1.10671i	0.832945	+	0.553355i	$0.186653\pi$
$643$			28.0633i			1.10671i	−0.832945	+	0.553355i	$0.813347\pi$
$644$	−19.4257			−0.765481
$645$		0			0
$646$	−14.3318	−	33.2775i	−0.563876	−	1.30928i
$647$	−39.7815			−1.56397			−0.781986	−	0.623296i	$-0.785793\pi$
$647$	−39.7815			−1.56397			−0.781986	+	0.623296i	$0.785793\pi$
$648$	−17.0593			−0.670152
$649$			2.22908i			0.0874989i
$650$		0			0
$651$			9.62912i			0.377395i
$652$			36.7811i			1.44046i
$653$			35.7761i			1.40003i	0.714129	+	0.700014i	$0.246823\pi$
$653$			35.7761i			1.40003i	−0.714129	+	0.700014i	$0.753177\pi$
$654$	33.3158			1.30275
$655$		0			0
$656$			12.1142i			0.472979i
$657$			7.22640i			0.281929i
$658$		−	22.9083i		−	0.893059i
$659$	−5.18568			−0.202006			−0.101003	−	0.994886i	$-0.532205\pi$
$659$	−5.18568			−0.202006			−0.101003	+	0.994886i	$0.532205\pi$
$660$		0			0
$661$	31.4079			1.22162			0.610812	−	0.791775i	$-0.290843\pi$
$661$	31.4079			1.22162			0.610812	+	0.791775i	$0.290843\pi$
$662$	47.5006			1.84616
$663$	32.5464	−	14.0169i	1.26400	−	0.544372i
$664$	−5.50307			−0.213561
$665$		0			0
$666$		−	42.4866i		−	1.64632i
$667$	−4.52359			−0.175154
$668$			7.02322i			0.271737i
$669$			39.2157i			1.51617i
$670$		0			0
$671$	15.6553			0.604366
$672$	−17.1639			−0.662113
$673$		−	17.8838i		−	0.689368i	−0.938719	−	0.344684i	$-0.887986\pi$
$673$		−	17.8838i		−	0.689368i	0.938719	−	0.344684i	$-0.112014\pi$
$674$			64.5131i			2.48495i
$675$		0			0
$676$	5.55252			0.213558
$677$		−	3.30278i		−	0.126936i	−0.997984	−	0.0634682i	$-0.979784\pi$
$677$		−	3.30278i		−	0.126936i	0.997984	−	0.0634682i	$-0.0202161\pi$
$678$	−94.1276			−3.61495
$679$	11.1317			0.427196
$680$		0			0
$681$	−56.6730			−2.17171
$682$	46.0216			1.76226
$683$		−	10.8742i		−	0.416088i	−0.978119	−	0.208044i	$-0.933290\pi$
$683$		−	10.8742i		−	0.416088i	0.978119	−	0.208044i	$-0.0667097\pi$
$684$	20.9360			0.800508
$685$		0			0
$686$			28.7074i			1.09606i
$687$		−	26.5561i		−	1.01318i
$688$	−12.1918			−0.464809
$689$	44.1845			1.68329
$690$		0			0
$691$			3.41002i			0.129723i	0.997894	+	0.0648617i	$0.0206606\pi$
$691$			3.41002i			0.129723i	−0.997894	+	0.0648617i	$0.979339\pi$
$692$			29.8379i			1.13427i
$693$	−9.70474			−0.368653
$694$		−	47.8448i		−	1.81616i
$695$		0			0
$696$	2.19636			0.0832529
$697$	22.0722	−	9.50596i	0.836046	−	0.360064i
$698$	−32.7165			−1.23834
$699$	10.4741			0.396168
$700$		0			0
$701$	−2.68422			−0.101382			−0.0506908	−	0.998714i	$-0.516142\pi$
$701$	−2.68422			−0.101382			−0.0506908	+	0.998714i	$0.516142\pi$
$702$		−	20.3615i		−	0.768494i
$703$		−	41.5457i		−	1.56693i
$704$			61.3272i			2.31136i
$705$		0			0
$706$	−30.6404			−1.15316
$707$		−	6.34959i		−	0.238801i
$708$			2.68591i			0.100943i
$709$		−	46.9766i		−	1.76424i	−0.471021	−	0.882122i	$-0.656115\pi$
$709$		−	46.9766i		−	1.76424i	0.471021	−	0.882122i	$-0.343885\pi$
$710$		0			0
$711$		−	0.719084i		−	0.0269678i
$712$	−4.04945			−0.151759
$713$	−29.8999			−1.11976
$714$	8.00492	+	18.5869i	0.299577	+	0.695598i
$715$		0			0
$716$	67.6925			2.52979
$717$		−	23.8492i		−	0.890665i
$718$	51.6658			1.92815
$719$		−	37.4252i		−	1.39572i	−0.716232	−	0.697862i	$-0.754135\pi$
$719$		−	37.4252i		−	1.39572i	0.716232	−	0.697862i	$-0.245865\pi$
$720$		0			0
$721$		−	10.7164i		−	0.399101i
$722$	−5.64650			−0.210141
$723$	47.8987			1.78137
$724$		−	38.8598i		−	1.44421i
$725$		0			0
$726$			66.4158i			2.46492i
$727$	37.8537			1.40392			0.701959	−	0.712218i	$-0.252309\pi$
$727$	37.8537			1.40392			0.701959	+	0.712218i	$0.252309\pi$
$728$			6.09593i			0.225930i
$729$	5.07489			0.187959
$730$		0			0
$731$	9.56690	+	22.2137i	0.353844	+	0.821605i
$732$	18.8638			0.697225
$733$	−36.0205			−1.33045			−0.665224	−	0.746644i	$-0.731664\pi$
$733$	−36.0205			−1.33045			−0.665224	+	0.746644i	$0.731664\pi$
$734$			8.18824i			0.302233i
$735$		0			0
$736$		−	53.2967i		−	1.96454i
$737$			25.2974i			0.931842i
$738$			24.1374i			0.888511i
$739$	19.0349			0.700210			0.350105	−	0.936710i	$-0.386146\pi$
$739$	19.0349			0.700210			0.350105	+	0.936710i	$0.386146\pi$
$740$		0			0
$741$			34.8034i			1.27853i
$742$			25.2333i			0.926344i
$743$			10.8901i			0.399518i	0.979845	+	0.199759i	$0.0640160\pi$
$743$			10.8901i			0.399518i	−0.979845	+	0.199759i	$0.935984\pi$
$744$	14.5174			0.532235
$745$		0			0
$746$	−3.35842			−0.122961
$747$	6.82273			0.249630
$748$	51.1071	−	22.0106i	1.86866	−	0.804786i
$749$	−5.26284			−0.192300
$750$		0			0
$751$			1.59232i			0.0581047i	0.999578	+	0.0290524i	$0.00924895\pi$
$751$			1.59232i			0.0581047i	−0.999578	+	0.0290524i	$0.990751\pi$
$752$	21.4908			0.783688
$753$			1.85457i			0.0675843i
$754$			5.42231i			0.197469i
$755$		0			0
$756$	6.68980			0.243306
$757$	−7.42696			−0.269937			−0.134969	−	0.990850i	$-0.543093\pi$
$757$	−7.42696			−0.269937			−0.134969	+	0.990850i	$0.543093\pi$
$758$			29.2579i			1.06269i
$759$		−	77.5091i		−	2.81340i
$760$		0			0
$761$	42.3679			1.53583			0.767917	−	0.640549i	$-0.221293\pi$
$761$	42.3679			1.53583			0.767917	+	0.640549i	$0.221293\pi$
$762$			10.6069i			0.384247i
$763$	−7.07450			−0.256114
$764$	14.6186			0.528883
$765$		0			0
$766$	9.65142			0.348720
$767$	−1.73594			−0.0626811
$768$			0.927285i			0.0334605i
$769$	−3.40522			−0.122795			−0.0613977	−	0.998113i	$-0.519556\pi$
$769$	−3.40522			−0.122795			−0.0613977	+	0.998113i	$0.519556\pi$
$770$		0			0
$771$		−	16.9996i		−	0.612226i
$772$			43.7243i			1.57367i
$773$	49.7058			1.78779			0.893896	−	0.448274i	$-0.147961\pi$
$773$	49.7058			1.78779			0.893896	+	0.448274i	$0.147961\pi$
$774$	−24.2922			−0.873163
$775$		0			0
$776$		−	16.7828i		−	0.602469i
$777$			23.2051i			0.832479i
$778$	−55.2678			−1.98145
$779$			23.6029i			0.845661i
$780$		0			0
$781$	−16.9867			−0.607831
$782$	−57.7152	+	24.8565i	−2.06389	+	0.888867i
$783$	1.55783			0.0556722
$784$	−12.3824			−0.442230
$785$		0			0
$786$	−92.3160			−3.29280
$787$		−	3.96049i		−	0.141176i	−0.997506	−	0.0705880i	$-0.977512\pi$
$787$		−	3.96049i		−	0.141176i	0.997506	−	0.0705880i	$-0.0224876\pi$
$788$			25.1102i			0.894512i
$789$		−	59.4567i		−	2.11671i
$790$		0			0
$791$	19.9877			0.710681
$792$			14.6315i			0.519906i
$793$			12.1919i			0.432946i
$794$			31.2356i			1.10851i
$795$		0			0
$796$			12.5551i			0.445003i
$797$	−16.3652			−0.579686			−0.289843	−	0.957074i	$-0.593603\pi$
$797$	−16.3652			−0.579686			−0.289843	+	0.957074i	$0.593603\pi$
$798$	−19.8759			−0.703598
$799$	−16.8638	−	39.1566i	−0.596597	−	1.38526i
$800$		0			0
$801$	5.02052			0.177391
$802$			0.991377i			0.0350067i
$803$	−18.8638			−0.665688
$804$			30.4820i			1.07502i
$805$		0			0
$806$			35.8402i			1.26242i
$807$	−45.4596			−1.60025
$808$	−9.57304			−0.336778
$809$		−	32.7111i		−	1.15006i	−0.818132	−	0.575030i	$-0.804990\pi$
$809$		−	32.7111i		−	1.15006i	0.818132	−	0.575030i	$-0.195010\pi$
$810$		0			0
$811$			41.1343i			1.44442i	0.691673	+	0.722211i	$0.256874\pi$
$811$			41.1343i			1.44442i	−0.691673	+	0.722211i	$0.743126\pi$
$812$	−1.78151			−0.0625187
$813$		−	27.0424i		−	0.948420i
$814$	110.907			3.88728
$815$		0			0
$816$	−17.4368	+	7.50959i	−0.610410	+	0.262888i
$817$	−23.7542			−0.831054
$818$	58.1084			2.03171
$819$		−	7.55776i		−	0.264089i
$820$		0			0
$821$		−	30.1347i		−	1.05171i	−0.850575	−	0.525854i	$-0.823746\pi$
$821$		−	30.1347i		−	1.05171i	0.850575	−	0.525854i	$-0.176254\pi$
$822$		−	1.46182i		−	0.0509870i
$823$			26.6151i			0.927745i	0.885902	+	0.463873i	$0.153540\pi$
$823$			26.6151i			0.927745i	−0.885902	+	0.463873i	$0.846460\pi$
$824$	−16.1568			−0.562847
$825$		0			0
$826$		−	0.991377i		−	0.0344944i
$827$			4.04050i			0.140502i	0.997529	+	0.0702510i	$0.0223800\pi$
$827$			4.04050i			0.140502i	−0.997529	+	0.0702510i	$0.977620\pi$
$828$		−	36.3107i		−	1.26188i
$829$	−6.14220			−0.213327			−0.106664	−	0.994295i	$-0.534017\pi$
$829$	−6.14220			−0.213327			−0.106664	+	0.994295i	$0.534017\pi$
$830$		0			0
$831$	−14.4520			−0.501335
$832$	−47.7598			−1.65577
$833$	9.71646	+	22.5610i	0.336655	+	0.781693i
$834$	−91.0965			−3.15441
$835$		0			0
$836$			54.6513i			1.89015i
$837$	10.2969			0.355912
$838$			35.3538i			1.22128i
$839$		−	15.0242i		−	0.518693i	−0.965784	−	0.259347i	$-0.916493\pi$
$839$		−	15.0242i		−	0.518693i	0.965784	−	0.259347i	$-0.0835072\pi$
$840$		0			0
$841$	28.5851			0.985695
$842$	−13.4969			−0.465135
$843$		−	3.56272i		−	0.122706i
$844$			16.5156i			0.568489i
$845$		0			0
$846$	42.8203			1.47219
$847$		−	14.1032i		−	0.484591i
$848$	−23.6719			−0.812898
$849$	4.84286			0.166206
$850$		0			0
$851$	−72.0554			−2.47003
$852$	−20.4680			−0.701222
$853$		−	45.3326i		−	1.55216i	−0.630636	−	0.776079i	$-0.717206\pi$
$853$		−	45.3326i		−	1.55216i	0.630636	−	0.776079i	$-0.282794\pi$
$854$	−6.96266			−0.238257
$855$		0			0
$856$			7.93458i			0.271198i
$857$		−	1.39773i		−	0.0477456i	−0.999715	−	0.0238728i	$-0.992400\pi$
$857$		−	1.39773i		−	0.0477456i	0.999715	−	0.0238728i	$-0.00759968\pi$
$858$	−92.9081			−3.17183
$859$	−45.9976			−1.56942			−0.784708	−	0.619865i	$-0.787187\pi$
$859$	−45.9976			−1.56942			−0.784708	+	0.619865i	$0.787187\pi$
$860$		0			0
$861$		−	13.1832i		−	0.449284i
$862$		−	53.0135i		−	1.80565i
$863$	−28.7670			−0.979239			−0.489619	−	0.871936i	$-0.662864\pi$
$863$	−28.7670			−0.979239			−0.489619	+	0.871936i	$0.662864\pi$
$864$			18.3542i			0.624423i
$865$		0			0
$866$	−14.8865			−0.505866
$867$	27.3652	+	25.8774i	0.929372	+	0.878843i
$868$	−11.7754			−0.399682
$869$	1.87709			0.0636761
$870$		0			0
$871$	−19.7009			−0.667538
$872$			10.6660i			0.361195i
$873$			20.8074i			0.704224i
$874$		−	61.7176i		−	2.08763i
$875$		0			0
$876$	−22.7298			−0.767969
$877$			38.1652i			1.28875i	0.764710	+	0.644374i	$0.222882\pi$
$877$			38.1652i			1.28875i	−0.764710	+	0.644374i	$0.777118\pi$
$878$			28.2665i			0.953949i
$879$			3.33000i			0.112318i
$880$		0			0
$881$			15.2569i			0.514019i	0.966409	+	0.257009i	$0.0827371\pi$
$881$			15.2569i			0.514019i	−0.966409	+	0.257009i	$0.917263\pi$
$882$	−24.6719			−0.830747
$883$	15.2123			0.511936			0.255968	−	0.966685i	$-0.417606\pi$
$883$	15.2123			0.511936			0.255968	+	0.966685i	$0.417606\pi$
$884$	17.1412	+	39.8007i	0.576520	+	1.33864i
$885$		0			0
$886$	−5.89269			−0.197969
$887$			32.2911i			1.08423i	0.840305	+	0.542115i	$0.182376\pi$
$887$			32.2911i			1.08423i	−0.840305	+	0.542115i	$0.817624\pi$
$888$	34.9854			1.17403
$889$		−	2.25234i		−	0.0755410i
$890$		0			0
$891$			55.2103i			1.84961i
$892$	−47.9565			−1.60570
$893$	41.8720			1.40119
$894$			93.7364i			3.13502i
$895$		0			0
$896$		−	11.7805i		−	0.393559i
$897$	60.3617			2.01542
$898$			44.6380i			1.48959i
$899$	−2.74208			−0.0914535
$900$		0			0
$901$	18.5753	+	43.1307i	0.618833	+	1.43689i
$902$	−63.0082			−2.09794
$903$	13.2678			0.441523
$904$		−	30.1347i		−	1.00227i
$905$		0			0
$906$			92.1996i			3.06313i
$907$		−	42.3425i		−	1.40596i	−0.711210	−	0.702980i	$-0.751852\pi$
$907$		−	42.3425i		−	1.40596i	0.711210	−	0.702980i	$-0.248148\pi$
$908$		−	69.3049i		−	2.29996i
$909$	11.8687			0.393659
$910$		0			0
$911$		−	1.71548i		−	0.0568365i	−0.999596	−	0.0284183i	$-0.990953\pi$
$911$		−	1.71548i		−	0.0568365i	0.999596	−	0.0284183i	$-0.00904703\pi$
$912$		−	18.6460i		−	0.617431i
$913$			17.8100i			0.589426i
$914$	−32.6248			−1.07913
$915$		0			0
$916$	32.4752			1.07301
$917$	19.6030			0.647349
$918$	19.8759	−	8.56004i	0.656002	−	0.282523i
$919$	42.1894			1.39170			0.695850	−	0.718187i	$-0.255028\pi$
$919$	42.1894			1.39170			0.695850	+	0.718187i	$0.255028\pi$
$920$		0			0
$921$			0.753642i			0.0248333i
$922$	−27.6430			−0.910374
$923$		−	13.2287i		−	0.435428i
$924$		−	30.5251i		−	1.00420i
$925$		0			0
$926$	−12.3318			−0.405247
$927$	20.0312			0.657911
$928$		−	4.88777i		−	0.160449i
$929$			25.6952i			0.843032i	0.906821	+	0.421516i	$0.138502\pi$
$929$			25.6952i			0.843032i	−0.906821	+	0.421516i	$0.861498\pi$
$930$		0			0
$931$	−24.1256			−0.790683
$932$			12.8087i			0.419564i
$933$	−51.3800			−1.68211
$934$	51.8987			1.69818
$935$		0			0
$936$	−11.3945			−0.372442
$937$	7.46186			0.243768			0.121884	−	0.992544i	$-0.461106\pi$
$937$	7.46186			0.243768			0.121884	+	0.992544i	$0.461106\pi$
$938$		−	11.2510i		−	0.367357i
$939$	−56.2883			−1.83690
$940$		0			0
$941$		−	23.5252i		−	0.766899i	−0.923562	−	0.383449i	$-0.874736\pi$
$941$		−	23.5252i		−	0.766899i	0.923562	−	0.383449i	$-0.125264\pi$
$942$		−	70.3122i		−	2.29090i
$943$	40.9360			1.33306
$944$	0.930033			0.0302700
$945$		0			0
$946$		−	63.4122i		−	2.06171i
$947$			2.59229i			0.0842380i	0.999113	+	0.0421190i	$0.0134109\pi$
$947$			2.59229i			0.0842380i	−0.999113	+	0.0421190i	$0.986589\pi$
$948$	2.26180			0.0734597
$949$		−	14.6905i		−	0.476875i
$950$		0			0
$951$	−14.9977			−0.486335
$952$	−5.95055	+	2.56275i	−0.192858	+	0.0830593i
$953$	−22.0712			−0.714956			−0.357478	−	0.933922i	$-0.616363\pi$
$953$	−22.0712			−0.714956			−0.357478	+	0.933922i	$0.616363\pi$
$954$	−47.1662			−1.52706
$955$		0			0
$956$	29.1650			0.943263
$957$		−	7.10826i		−	0.229777i
$958$		−	25.2038i		−	0.814297i
$959$			0.310414i			0.0100238i
$960$		0			0
$961$	12.8755			0.415338
$962$			86.3709i			2.78471i
$963$		−	9.83732i		−	0.317003i
$964$			58.5749i			1.88657i
$965$		0			0
$966$			34.4720i			1.10912i
$967$	−6.20167			−0.199432			−0.0997161	−	0.995016i	$-0.531793\pi$
$967$	−6.20167			−0.199432			−0.0997161	+	0.995016i	$0.531793\pi$
$968$	−21.2628			−0.683414
$969$	−33.9733	+	14.6315i	−1.09138	+	0.470030i
$970$		0			0
$971$	21.8888			0.702446			0.351223	−	0.936292i	$-0.385766\pi$
$971$	21.8888			0.702446			0.351223	+	0.936292i	$0.385766\pi$
$972$			46.8671i			1.50326i
$973$	19.3440			0.620142
$974$			17.2828i			0.553777i
$975$		0			0
$976$		−	6.53182i		−	0.209079i
$977$	48.5090			1.55194			0.775971	−	0.630769i	$-0.217260\pi$
$977$	48.5090			1.55194			0.775971	+	0.630769i	$0.217260\pi$
$978$	65.2700			2.08711
$979$			13.1055i			0.418855i
$980$		0			0
$981$		−	13.2237i		−	0.422200i
$982$	78.6779			2.51071
$983$		−	20.2247i		−	0.645068i	−0.946558	−	0.322534i	$-0.895465\pi$
$983$		−	20.2247i		−	0.645068i	0.946558	−	0.322534i	$-0.104535\pi$
$984$	−19.8759			−0.633620
$985$		0			0
$986$	−5.29299	+	2.27956i	−0.168563	+	0.0725959i
$987$	−23.3874			−0.744428
$988$	−42.5608			−1.35404
$989$			41.1984i			1.31003i
$990$		0			0
$991$		−	10.6205i		−	0.337371i	−0.985670	−	0.168686i	$-0.946048\pi$
$991$		−	10.6205i		−	0.337371i	0.985670	−	0.168686i	$-0.0539522\pi$
$992$		−	32.3070i		−	1.02575i
$993$		−	48.4939i		−	1.53891i
$994$	7.55479			0.239623
$995$		0			0
$996$			21.4601i			0.679989i
$997$		−	38.4302i		−	1.21710i	−0.793517	−	0.608548i	$-0.791752\pi$
$997$		−	38.4302i		−	1.21710i	0.793517	−	0.608548i	$-0.208248\pi$
$998$			43.7453i			1.38473i
$999$	24.8143			0.785090

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.d.b.101.5	yes	6
5.2	odd	4		425.2.c.c.424.11		12
5.3	odd	4		425.2.c.c.424.2		12
5.4	even	2		425.2.d.a.101.2	yes	6
17.4	even	4		7225.2.a.ba.1.1		6
17.13	even	4		7225.2.a.ba.1.2		6
17.16	even	2	inner	425.2.d.b.101.6	yes	6
85.4	even	4		7225.2.a.bg.1.6		6
85.33	odd	4		425.2.c.c.424.1		12
85.64	even	4		7225.2.a.bg.1.5		6
85.67	odd	4		425.2.c.c.424.12		12
85.84	even	2		425.2.d.a.101.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.c.c.424.1		12	85.33	odd	4
425.2.c.c.424.2		12	5.3	odd	4
425.2.c.c.424.11		12	5.2	odd	4
425.2.c.c.424.12		12	85.67	odd	4
425.2.d.a.101.1	✓	6	85.84	even	2
425.2.d.a.101.2	yes	6	5.4	even	2
425.2.d.b.101.5	yes	6	1.1	even	1	trivial
425.2.d.b.101.6	yes	6	17.16	even	2	inner
7225.2.a.ba.1.1		6	17.4	even	4
7225.2.a.ba.1.2		6	17.13	even	4
7225.2.a.bg.1.5		6	85.64	even	4
7225.2.a.bg.1.6		6	85.4	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.17009 q^{2} -2.21547i q^{3} +2.70928 q^{4} -4.80775i q^{6} +1.02091i q^{7} +1.53919 q^{8} -1.90829 q^{9} -4.98140i q^{11} -6.00231i q^{12} +3.87936 q^{13} +2.21547i q^{14} -2.07838 q^{16} +(1.63090 + 3.78684i) q^{17} -4.14116 q^{18} -4.04945 q^{19} +2.26180 q^{21} -10.8101i q^{22} +7.02322i q^{23} -3.41002i q^{24} +8.41855 q^{26} -2.41864i q^{27} +2.76593i q^{28} +0.644091i q^{29} +4.25729i q^{31} -7.58864 q^{32} -11.0361 q^{33} +(3.53919 + 8.21777i) q^{34} -5.17009 q^{36} +10.2596i q^{37} -8.78765 q^{38} -8.59460i q^{39} -5.82867i q^{41} +4.90829 q^{42} +5.86603 q^{43} -13.4960i q^{44} +15.2410i q^{46} -10.3402 q^{47} +4.60458i q^{48} +5.95774 q^{49} +(8.38962 - 3.61320i) q^{51} +10.5103 q^{52} +11.3896 q^{53} -5.24867i q^{54} +1.57138i q^{56} +8.97142i q^{57} +1.39773i q^{58} -0.447480 q^{59} +3.14275i q^{61} +9.23869i q^{62} -1.94820i q^{63} -12.3112 q^{64} -23.9493 q^{66} -5.07838 q^{67} +(4.41855 + 10.2596i) q^{68} +15.5597 q^{69} -3.41002i q^{71} -2.93722 q^{72} -3.78684i q^{73} +22.2642i q^{74} -10.9711 q^{76} +5.08557 q^{77} -18.6510i q^{78} +0.376821i q^{79} -11.0833 q^{81} -12.6487i q^{82} -3.57531 q^{83} +6.12783 q^{84} +12.7298 q^{86} +1.42696 q^{87} -7.66731i q^{88} -2.63090 q^{89} +3.96049i q^{91} +19.0278i q^{92} +9.43188 q^{93} -22.4391 q^{94} +16.8124i q^{96} -10.9037i q^{97} +12.9288 q^{98} +9.50596i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 2 q^{4} + 6 q^{8} - 16 q^{9} - 2 q^{13} - 6 q^{16} + 2 q^{17} + 16 q^{18} + 12 q^{19} - 2 q^{21} + 22 q^{26} - 6 q^{32} - 28 q^{33} + 18 q^{34} - 20 q^{36} - 32 q^{38} + 34 q^{42} + 8 q^{43}+ \cdots + 16 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^8 - 16 * q^9 - 2 * q^13 - 6 * q^16 + 2 * q^17 + 16 * q^18 + 12 * q^19 - 2 * q^21 + 22 * q^26 - 6 * q^32 - 28 * q^33 + 18 * q^34 - 20 * q^36 - 32 * q^38 + 34 * q^42 + 8 * q^43 - 40 * q^47 + 4 * q^49 - 8 * q^51 + 30 * q^52 + 10 * q^53 - 4 * q^59 - 22 * q^64 - 16 * q^66 - 24 * q^67 - 2 * q^68 + 24 * q^69 - 52 * q^72 - 36 * q^76 - 44 * q^77 + 34 * q^81 + 20 * q^83 - 6 * q^84 - 4 * q^86 + 76 * q^87 - 8 * q^89 + 30 * q^93 - 40 * q^94 + 16 * q^98

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