LMFDB - Embedded newform 925.2.b.g.149.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(149,925)] 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("925.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,-12,0,-4,0,0,-4,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.8689006034944.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} + 10x^{7} + 26x^{6} - 4x^{5} + 6x^{4} + 22x^{3} + 25x^{2} + 10x + 2 $ x^10 - 2x^9 + 2x^8 + 10x^7 + 26x^6 - 4x^5 + 6x^4 + 22x^3 + 25x^2 + 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.9
Root			$0.786830 + 0.786830i$ of defining polynomial
Character	$\chi$	$=$	925.149
Dual form			925.2.b.g.149.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.27092i q^{2} +0.518894i q^{3} -3.15709 q^{4} -1.17837 q^{6} -1.33546i q^{7} -2.62766i q^{8} +2.73075 q^{9} +5.55161 q^{11} -1.63819i q^{12} +2.96818i q^{13} +3.03272 q^{14} -0.346968 q^{16} -0.426340i q^{17} +6.20132i q^{18} +5.57456 q^{19} +0.692961 q^{21} +12.6073i q^{22} +3.50406i q^{23} +1.36348 q^{24} -6.74052 q^{26} +2.97365i q^{27} +4.21616i q^{28} -8.06544 q^{29} +4.57289 q^{31} -6.04326i q^{32} +2.88070i q^{33} +0.968185 q^{34} -8.62122 q^{36} -1.00000i q^{37} +12.6594i q^{38} -1.54017 q^{39} -6.87056 q^{41} +1.57366i q^{42} -7.35197i q^{43} -17.5269 q^{44} -7.95744 q^{46} +3.16383i q^{47} -0.180040i q^{48} +5.21655 q^{49} +0.221225 q^{51} -9.37082i q^{52} +6.51383i q^{53} -6.75293 q^{54} -3.50913 q^{56} +2.89261i q^{57} -18.3160i q^{58} -8.51080 q^{59} +3.31895 q^{61} +10.3847i q^{62} -3.64680i q^{63} +13.0298 q^{64} -6.54184 q^{66} +9.68410i q^{67} +1.34599i q^{68} -1.81823 q^{69} +7.81324 q^{71} -7.17548i q^{72} +0.762564i q^{73} +2.27092 q^{74} -17.5994 q^{76} -7.41394i q^{77} -3.49761i q^{78} -17.0722 q^{79} +6.64924 q^{81} -15.6025i q^{82} +2.74656i q^{83} -2.18774 q^{84} +16.6957 q^{86} -4.18511i q^{87} -14.5877i q^{88} -0.0865103 q^{89} +3.96388 q^{91} -11.0626i q^{92} +2.37285i q^{93} -7.18481 q^{94} +3.13581 q^{96} -17.8411i q^{97} +11.8464i q^{98} +15.1601 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9} + 14 q^{11} - 8 q^{14} + 16 q^{16} - 28 q^{19} - 18 q^{21} - 24 q^{24} - 40 q^{26} - 4 q^{29} + 16 q^{31} - 24 q^{34} - 72 q^{36} - 24 q^{39} - 18 q^{41} - 36 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) $ 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9 + 14 * q^11 - 8 * q^14 + 16 * q^16 - 28 * q^19 - 18 * q^21 - 24 * q^24 - 40 * q^26 - 4 * q^29 + 16 * q^31 - 24 * q^34 - 72 * q^36 - 24 * q^39 - 18 * q^41 - 36 * q^44 - 56 * q^46 - 4 * q^49 + 20 * q^51 + 24 * q^54 - 28 * q^56 - 24 * q^59 + 24 * q^61 - 24 * q^64 - 20 * q^66 + 60 * q^69 + 26 * q^71 + 36 * q^76 - 72 * q^79 + 42 * q^81 - 60 * q^84 - 16 * q^86 + 32 * q^89 - 8 * q^91 - 40 * q^94 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.27092i	1.60578i	0.596124	+	0.802892i	$0.296707\pi$
$2$	2.27092i	1.60578i	−0.596124	+	0.802892i	$0.703293\pi$
$3$	0.518894i	0.299584i	0.988718	+	0.149792i	$0.0478603\pi$
$3$	0.518894i	0.299584i	−0.988718	+	0.149792i	$0.952140\pi$
$4$	−3.15709	−1.57854
$5$	0	0
$5$	0	0
$6$	−1.17837	−0.481067
$7$	− 1.33546i	− 0.504755i	−0.967629	−	0.252378i	$-0.918787\pi$
$7$	− 1.33546i	− 0.504755i	0.967629	−	0.252378i	$-0.0812125\pi$
$8$	− 2.62766i	− 0.929018i
$9$	2.73075	0.910250
$10$	0	0
$11$	5.55161	1.67387	0.836937	−	0.547299i	$-0.184344\pi$
$11$	5.55161	1.67387	0.836937	+	0.547299i	$0.184344\pi$
$12$	− 1.63819i	− 0.472906i
$13$	2.96818i	0.823226i	0.911359	+	0.411613i	$0.135035\pi$
$13$	2.96818i	0.823226i	−0.911359	+	0.411613i	$0.864965\pi$
$14$	3.03272	0.810528
$15$	0	0
$16$	−0.346968	−0.0867420
$17$	− 0.426340i	− 0.103403i	−0.998663	−	0.0517013i	$-0.983536\pi$
$17$	− 0.426340i	− 0.103403i	0.998663	−	0.0517013i	$-0.0164644\pi$
$18$	6.20132i	1.46166i
$19$	5.57456	1.27889	0.639446	−	0.768836i	$-0.279164\pi$
$19$	5.57456	1.27889	0.639446	+	0.768836i	$0.279164\pi$
$20$	0	0
$21$	0.692961	0.151216
$22$	12.6073i	2.68788i
$23$	3.50406i	0.730646i	0.930881	+	0.365323i	$0.119042\pi$
$23$	3.50406i	0.730646i	−0.930881	+	0.365323i	$0.880958\pi$
$24$	1.36348	0.278319
$25$	0	0
$26$	−6.74052	−1.32192
$27$	2.97365i	0.572280i
$28$	4.21616i	0.796779i
$29$	−8.06544	−1.49771	−0.748857	−	0.662731i	$-0.769397\pi$
$29$	−8.06544	−1.49771	−0.748857	+	0.662731i	$0.769397\pi$
$30$	0	0
$31$	4.57289	0.821316	0.410658	−	0.911789i	$-0.365299\pi$
$31$	4.57289	0.821316	0.410658	+	0.911789i	$0.365299\pi$
$32$	− 6.04326i	− 1.06831i
$33$	2.88070i	0.501465i
$34$	0.968185	0.166042
$35$	0	0
$36$	−8.62122	−1.43687
$37$	− 1.00000i	− 0.164399i
$37$	− 1.00000i	− 0.164399i
$38$	12.6594i	2.05363i
$39$	−1.54017	−0.246625
$40$	0	0
$41$	−6.87056	−1.07300	−0.536501	−	0.843900i	$-0.680254\pi$
$41$	−6.87056	−1.07300	−0.536501	+	0.843900i	$0.680254\pi$
$42$	1.57366i	0.242821i
$43$	− 7.35197i	− 1.12116i	−0.828099	−	0.560582i	$-0.810577\pi$
$43$	− 7.35197i	− 1.12116i	0.828099	−	0.560582i	$-0.189423\pi$
$44$	−17.5269	−2.64229
$45$	0	0
$46$	−7.95744	−1.17326
$47$	3.16383i	0.461492i	0.973014	+	0.230746i	$0.0741166\pi$
$47$	3.16383i	0.461492i	−0.973014	+	0.230746i	$0.925883\pi$
$48$	− 0.180040i	− 0.0259865i
$49$	5.21655	0.745222
$50$	0	0
$51$	0.221225	0.0309777
$52$	− 9.37082i	− 1.29950i
$53$	6.51383i	0.894743i	0.894348	+	0.447371i	$0.147640\pi$
$53$	6.51383i	0.894743i	−0.894348	+	0.447371i	$0.852360\pi$
$54$	−6.75293	−0.918958
$55$	0	0
$56$	−3.50913	−0.468927
$57$	2.89261i	0.383135i
$58$	− 18.3160i	− 2.40501i
$59$	−8.51080	−1.10801	−0.554006	−	0.832513i	$-0.686901\pi$
$59$	−8.51080	−1.10801	−0.554006	+	0.832513i	$0.686901\pi$
$60$	0	0
$61$	3.31895	0.424948	0.212474	−	0.977167i	$-0.431848\pi$
$61$	3.31895	0.424948	0.212474	+	0.977167i	$0.431848\pi$
$62$	10.3847i	1.31886i
$63$	− 3.64680i	− 0.459453i
$64$	13.0298	1.62873
$65$	0	0
$66$	−6.54184	−0.805245
$67$	9.68410i	1.18310i	0.806268	+	0.591550i	$0.201484\pi$
$67$	9.68410i	1.18310i	−0.806268	+	0.591550i	$0.798516\pi$
$68$	1.34599i	0.163226i
$69$	−1.81823	−0.218890
$70$	0	0
$71$	7.81324	0.927261	0.463630	−	0.886029i	$-0.346547\pi$
$71$	7.81324	0.927261	0.463630	+	0.886029i	$0.346547\pi$
$72$	− 7.17548i	− 0.845638i
$73$	0.762564i	0.0892514i	0.999004	+	0.0446257i	$0.0142095\pi$
$73$	0.762564i	0.0892514i	−0.999004	+	0.0446257i	$0.985790\pi$
$74$	2.27092	0.263989
$75$	0	0
$76$	−17.5994	−2.01879
$77$	− 7.41394i	− 0.844897i
$78$	− 3.49761i	− 0.396027i
$79$	−17.0722	−1.92077	−0.960385	−	0.278676i	$-0.910104\pi$
$79$	−17.0722	−1.92077	−0.960385	+	0.278676i	$0.910104\pi$
$80$	0	0
$81$	6.64924	0.738804
$82$	− 15.6025i	− 1.72301i
$83$	2.74656i	0.301474i	0.988574	+	0.150737i	$0.0481647\pi$
$83$	2.74656i	0.301474i	−0.988574	+	0.150737i	$0.951835\pi$
$84$	−2.18774	−0.238702
$85$	0	0
$86$	16.6957	1.80035
$87$	− 4.18511i	− 0.448691i
$88$	− 14.5877i	− 1.55506i
$89$	−0.0865103	−0.00917007	−0.00458503	−	0.999989i	$-0.501459\pi$
$89$	−0.0865103	−0.00917007	−0.00458503	+	0.999989i	$0.501459\pi$
$90$	0	0
$91$	3.96388	0.415528
$92$	− 11.0626i	− 1.15336i
$93$	2.37285i	0.246053i
$94$	−7.18481	−0.741057
$95$	0	0
$96$	3.13581	0.320047
$97$	− 17.8411i	− 1.81149i	−0.423822	−	0.905745i	$-0.639312\pi$
$97$	− 17.8411i	− 1.81149i	0.423822	−	0.905745i	$-0.360688\pi$
$98$	11.8464i	1.19667i
$99$	15.1601	1.52364
$100$	0	0
$101$	10.7584	1.07050	0.535250	−	0.844693i	$-0.320217\pi$
$101$	10.7584	1.07050	0.535250	+	0.844693i	$0.320217\pi$
$102$	0.502385i	0.0497436i
$103$	8.19451i	0.807429i	0.914885	+	0.403714i	$0.132281\pi$
$103$	8.19451i	0.807429i	−0.914885	+	0.403714i	$0.867719\pi$
$104$	7.79938	0.764792
$105$	0	0
$106$	−14.7924	−1.43676
$107$	− 5.61222i	− 0.542553i	−0.962501	−	0.271277i	$-0.912554\pi$
$107$	− 5.61222i	− 0.542553i	0.962501	−	0.271277i	$-0.0874458\pi$
$108$	− 9.38808i	− 0.903369i
$109$	0.377808	0.0361874	0.0180937	−	0.999836i	$-0.494240\pi$
$109$	0.377808	0.0361874	0.0180937	+	0.999836i	$0.494240\pi$
$110$	0	0
$111$	0.518894	0.0492512
$112$	0.463361i	0.0437835i
$113$	4.54935i	0.427967i	0.976837	+	0.213984i	$0.0686439\pi$
$113$	4.54935i	0.427967i	−0.976837	+	0.213984i	$0.931356\pi$
$114$	−6.56889	−0.615233
$115$	0	0
$116$	25.4633	2.36421
$117$	8.10537i	0.749341i
$118$	− 19.3274i	− 1.77923i
$119$	−0.569359	−0.0521930
$120$	0	0
$121$	19.8204	1.80186
$122$	7.53707i	0.682375i
$123$	− 3.56509i	− 0.321454i
$124$	−14.4370	−1.29648
$125$	0	0
$126$	8.28160	0.737783
$127$	12.7560i	1.13191i	0.824437	+	0.565954i	$0.191492\pi$
$127$	12.7560i	1.13191i	−0.824437	+	0.565954i	$0.808508\pi$
$128$	17.5032i	1.54708i
$129$	3.81489	0.335882
$130$	0	0
$131$	−14.4960	−1.26652	−0.633262	−	0.773938i	$-0.718284\pi$
$131$	−14.4960	−1.26652	−0.633262	+	0.773938i	$0.718284\pi$
$132$	− 9.09462i	− 0.791585i
$133$	− 7.44459i	− 0.645528i
$134$	−21.9918	−1.89980
$135$	0	0
$136$	−1.12028	−0.0960629
$137$	− 10.8425i	− 0.926341i	−0.886269	−	0.463170i	$-0.846712\pi$
$137$	− 10.8425i	− 0.926341i	0.886269	−	0.463170i	$-0.153288\pi$
$138$	− 4.12907i	− 0.351490i
$139$	−1.56615	−0.132839	−0.0664197	−	0.997792i	$-0.521158\pi$
$139$	−1.56615	−0.132839	−0.0664197	+	0.997792i	$0.521158\pi$
$140$	0	0
$141$	−1.64169	−0.138255
$142$	17.7433i	1.48898i
$143$	16.4782i	1.37798i
$144$	−0.947482	−0.0789569
$145$	0	0
$146$	−1.73172	−0.143319
$147$	2.70684i	0.223256i
$148$	3.15709i	0.259511i
$149$	8.09762	0.663383	0.331692	−	0.943388i	$-0.392381\pi$
$149$	8.09762	0.663383	0.331692	+	0.943388i	$0.392381\pi$
$150$	0	0
$151$	−12.0018	−0.976693	−0.488347	−	0.872650i	$-0.662400\pi$
$151$	−12.0018	−0.976693	−0.488347	+	0.872650i	$0.662400\pi$
$152$	− 14.6481i	− 1.18811i
$153$	− 1.16423i	− 0.0941222i
$154$	16.8365	1.35672
$155$	0	0
$156$	4.86246	0.389309
$157$	− 19.2732i	− 1.53817i	−0.639147	−	0.769084i	$-0.720713\pi$
$157$	− 19.2732i	− 1.53817i	0.639147	−	0.769084i	$-0.279287\pi$
$158$	− 38.7696i	− 3.08434i
$159$	−3.37999	−0.268050
$160$	0	0
$161$	4.67952	0.368798
$162$	15.0999i	1.18636i
$163$	0.995229i	0.0779524i	0.999240	+	0.0389762i	$0.0124096\pi$
$163$	0.995229i	0.0779524i	−0.999240	+	0.0389762i	$0.987590\pi$
$164$	21.6910	1.69378
$165$	0	0
$166$	−6.23723	−0.484103
$167$	− 24.2625i	− 1.87749i	−0.344615	−	0.938744i	$-0.611991\pi$
$167$	− 24.2625i	− 1.87749i	0.344615	−	0.938744i	$-0.388009\pi$
$168$	− 1.82086i	− 0.140483i
$169$	4.18988	0.322298
$170$	0	0
$171$	15.2227	1.16411
$172$	23.2108i	1.76981i
$173$	11.4556i	0.870950i	0.900201	+	0.435475i	$0.143420\pi$
$173$	11.4556i	0.870950i	−0.900201	+	0.435475i	$0.856580\pi$
$174$	9.50406	0.720501
$175$	0	0
$176$	−1.92623	−0.145195
$177$	− 4.41620i	− 0.331942i
$178$	− 0.196458i	− 0.0147252i
$179$	11.8233	0.883715	0.441858	−	0.897085i	$-0.354320\pi$
$179$	11.8233	0.883715	0.441858	+	0.897085i	$0.354320\pi$
$180$	0	0
$181$	−14.8035	−1.10034	−0.550168	−	0.835054i	$-0.685436\pi$
$181$	−14.8035	−1.10034	−0.550168	+	0.835054i	$0.685436\pi$
$182$	9.00167i	0.667248i
$183$	1.72218i	0.127307i
$184$	9.20747	0.678783
$185$	0	0
$186$	−5.38855	−0.395108
$187$	− 2.36687i	− 0.173083i
$188$	− 9.98849i	− 0.728485i
$189$	3.97118	0.288861
$190$	0	0
$191$	−7.71008	−0.557881	−0.278941	−	0.960308i	$-0.589983\pi$
$191$	−7.71008	−0.557881	−0.278941	+	0.960308i	$0.589983\pi$
$192$	6.76110i	0.487940i
$193$	− 26.0067i	− 1.87200i	−0.351997	−	0.936001i	$-0.614497\pi$
$193$	− 26.0067i	− 1.87200i	0.351997	−	0.936001i	$-0.385503\pi$
$194$	40.5158	2.90886
$195$	0	0
$196$	−16.4691	−1.17637
$197$	13.0887i	0.932530i	0.884645	+	0.466265i	$0.154401\pi$
$197$	13.0887i	0.932530i	−0.884645	+	0.466265i	$0.845599\pi$
$198$	34.4273i	2.44664i
$199$	−18.2990	−1.29718	−0.648590	−	0.761138i	$-0.724641\pi$
$199$	−18.2990	−1.29718	−0.648590	+	0.761138i	$0.724641\pi$
$200$	0	0
$201$	−5.02502	−0.354438
$202$	24.4315i	1.71899i
$203$	10.7710i	0.755979i
$204$	−0.698428	−0.0488997
$205$	0	0
$206$	−18.6091	−1.29656
$207$	9.56870i	0.665071i
$208$	− 1.02986i	− 0.0714083i
$209$	30.9478	2.14071
$210$	0	0
$211$	2.89163	0.199068	0.0995341	−	0.995034i	$-0.468265\pi$
$211$	2.89163	0.199068	0.0995341	+	0.995034i	$0.468265\pi$
$212$	− 20.5647i	− 1.41239i
$213$	4.05424i	0.277792i
$214$	12.7449	0.871224
$215$	0	0
$216$	7.81374	0.531658
$217$	− 6.10690i	− 0.414564i
$218$	0.857973i	0.0581092i
$219$	−0.395690	−0.0267383
$220$	0	0
$221$	1.26546	0.0851237
$222$	1.17837i	0.0790869i
$223$	− 25.8004i	− 1.72772i	−0.503728	−	0.863862i	$-0.668039\pi$
$223$	− 25.8004i	− 1.72772i	0.503728	−	0.863862i	$-0.331961\pi$
$224$	−8.07051	−0.539233
$225$	0	0
$226$	−10.3312	−0.687223
$227$	− 6.01093i	− 0.398960i	−0.979902	−	0.199480i	$-0.936075\pi$
$227$	− 6.01093i	− 0.398960i	0.979902	−	0.199480i	$-0.0639252\pi$
$228$	− 9.13222i	− 0.604796i
$229$	−5.22124	−0.345029	−0.172515	−	0.985007i	$-0.555189\pi$
$229$	−5.22124	−0.345029	−0.172515	+	0.985007i	$0.555189\pi$
$230$	0	0
$231$	3.84705	0.253117
$232$	21.1932i	1.39140i
$233$	15.2256i	0.997465i	0.866756	+	0.498733i	$0.166201\pi$
$233$	15.2256i	0.997465i	−0.866756	+	0.498733i	$0.833799\pi$
$234$	−18.4067	−1.20328
$235$	0	0
$236$	26.8693	1.74905
$237$	− 8.85865i	− 0.575431i
$238$	− 1.29297i	− 0.0838107i
$239$	12.1164	0.783745	0.391873	−	0.920019i	$-0.371827\pi$
$239$	12.1164	0.783745	0.391873	+	0.920019i	$0.371827\pi$
$240$	0	0
$241$	20.7909	1.33926	0.669628	−	0.742696i	$-0.266453\pi$
$241$	20.7909	1.33926	0.669628	+	0.742696i	$0.266453\pi$
$242$	45.0106i	2.89339i
$243$	12.3712i	0.793613i
$244$	−10.4782	−0.670799
$245$	0	0
$246$	8.09605	0.516185
$247$	16.5463i	1.05282i
$248$	− 12.0160i	− 0.763017i
$249$	−1.42517	−0.0903168
$250$	0	0
$251$	9.67062	0.610404	0.305202	−	0.952288i	$-0.401276\pi$
$251$	9.67062	0.610404	0.305202	+	0.952288i	$0.401276\pi$
$252$	11.5133i	0.725267i
$253$	19.4532i	1.22301i
$254$	−28.9678	−1.81760
$255$	0	0
$256$	−13.6888	−0.855550
$257$	31.6442i	1.97391i	0.160984	+	0.986957i	$0.448533\pi$
$257$	31.6442i	1.97391i	−0.160984	+	0.986957i	$0.551467\pi$
$258$	8.66332i	0.539355i
$259$	−1.33546	−0.0829813
$260$	0	0
$261$	−22.0247	−1.36329
$262$	− 32.9193i	− 2.03376i
$263$	− 14.3161i	− 0.882766i	−0.897319	−	0.441383i	$-0.854488\pi$
$263$	− 14.3161i	− 0.882766i	0.897319	−	0.441383i	$-0.145512\pi$
$264$	7.56950	0.465870
$265$	0	0
$266$	16.9061	1.03658
$267$	− 0.0448897i	− 0.00274720i
$268$	− 30.5736i	− 1.86758i
$269$	28.8212	1.75726	0.878631	−	0.477501i	$-0.158457\pi$
$269$	28.8212	1.75726	0.878631	+	0.477501i	$0.158457\pi$
$270$	0	0
$271$	10.4382	0.634078	0.317039	−	0.948412i	$-0.397311\pi$
$271$	10.4382	0.634078	0.317039	+	0.948412i	$0.397311\pi$
$272$	0.147926i	0.00896935i
$273$	2.05684i	0.124485i
$274$	24.6226	1.48750
$275$	0	0
$276$	5.74033	0.345527
$277$	16.2020i	0.973485i	0.873546	+	0.486742i	$0.161815\pi$
$277$	16.2020i	0.973485i	−0.873546	+	0.486742i	$0.838185\pi$
$278$	− 3.55661i	− 0.213311i
$279$	12.4874	0.747602
$280$	0	0
$281$	8.10953	0.483774	0.241887	−	0.970304i	$-0.422234\pi$
$281$	8.10953	0.483774	0.241887	+	0.970304i	$0.422234\pi$
$282$	− 3.72816i	− 0.222008i
$283$	0.429766i	0.0255470i	0.999918	+	0.0127735i	$0.00406603\pi$
$283$	0.429766i	0.0255470i	−0.999918	+	0.0127735i	$0.995934\pi$
$284$	−24.6671	−1.46372
$285$	0	0
$286$	−37.4207	−2.21274
$287$	9.17534i	0.541603i
$288$	− 16.5026i	− 0.972426i
$289$	16.8182	0.989308
$290$	0	0
$291$	9.25765	0.542693
$292$	− 2.40748i	− 0.140887i
$293$	− 14.3831i	− 0.840270i	−0.907462	−	0.420135i	$-0.861983\pi$
$293$	− 14.3831i	− 0.840270i	0.907462	−	0.420135i	$-0.138017\pi$
$294$	−6.14702	−0.358502
$295$	0	0
$296$	−2.62766	−0.152730
$297$	16.5086i	0.957924i
$298$	18.3891i	1.06525i
$299$	−10.4007	−0.601487
$300$	0	0
$301$	−9.81823	−0.565914
$302$	− 27.2552i	− 1.56836i
$303$	5.58247i	0.320705i
$304$	−1.93420	−0.110934
$305$	0	0
$306$	2.64387	0.151140
$307$	− 24.8429i	− 1.41786i	−0.705281	−	0.708928i	$-0.749179\pi$
$307$	− 24.8429i	− 1.41786i	0.705281	−	0.708928i	$-0.250821\pi$
$308$	23.4065i	1.33371i
$309$	−4.25208	−0.241892
$310$	0	0
$311$	−13.3533	−0.757198	−0.378599	−	0.925561i	$-0.623594\pi$
$311$	−13.3533	−0.757198	−0.378599	+	0.925561i	$0.623594\pi$
$312$	4.04705i	0.229119i
$313$	− 26.1131i	− 1.47600i	−0.674799	−	0.738001i	$-0.735770\pi$
$313$	− 26.1131i	− 1.47600i	0.674799	−	0.738001i	$-0.264230\pi$
$314$	43.7679	2.46997
$315$	0	0
$316$	53.8984	3.03202
$317$	27.5077i	1.54498i	0.635024	+	0.772492i	$0.280990\pi$
$317$	27.5077i	1.54498i	−0.635024	+	0.772492i	$0.719010\pi$
$318$	− 7.67568i	− 0.430431i
$319$	−44.7762	−2.50699
$320$	0	0
$321$	2.91215	0.162540
$322$	10.6268i	0.592210i
$323$	− 2.37666i	− 0.132241i
$324$	−20.9922	−1.16623
$325$	0	0
$326$	−2.26009	−0.125175
$327$	0.196042i	0.0108412i
$328$	18.0535i	0.996837i
$329$	4.22516	0.232940
$330$	0	0
$331$	−33.4582	−1.83903	−0.919516	−	0.393054i	$-0.871419\pi$
$331$	−33.4582	−1.83903	−0.919516	+	0.393054i	$0.871419\pi$
$332$	− 8.67114i	− 0.475891i
$333$	− 2.73075i	− 0.149644i
$334$	55.0982	3.01484
$335$	0	0
$336$	−0.240435	−0.0131168
$337$	− 23.0022i	− 1.25301i	−0.779418	−	0.626504i	$-0.784485\pi$
$337$	− 23.0022i	− 1.25301i	0.779418	−	0.626504i	$-0.215515\pi$
$338$	9.51489i	0.517542i
$339$	−2.36063	−0.128212
$340$	0	0
$341$	25.3869	1.37478
$342$	34.5697i	1.86931i
$343$	− 16.3147i	− 0.880910i
$344$	−19.3185	−1.04158
$345$	0	0
$346$	−26.0147	−1.39856
$347$	− 21.1611i	− 1.13599i	−0.823033	−	0.567993i	$-0.807720\pi$
$347$	− 21.1611i	− 1.13599i	0.823033	−	0.567993i	$-0.192280\pi$
$348$	13.2128i	0.708278i
$349$	15.9769	0.855224	0.427612	−	0.903962i	$-0.359355\pi$
$349$	15.9769	0.855224	0.427612	+	0.903962i	$0.359355\pi$
$350$	0	0
$351$	−8.82635	−0.471116
$352$	− 33.5498i	− 1.78821i
$353$	− 18.8153i	− 1.00144i	−0.865611	−	0.500718i	$-0.833069\pi$
$353$	− 18.8153i	− 1.00144i	0.865611	−	0.500718i	$-0.166931\pi$
$354$	10.0289	0.533028
$355$	0	0
$356$	0.273121	0.0144754
$357$	− 0.295437i	− 0.0156362i
$358$	26.8498i	1.41906i
$359$	−33.7385	−1.78065	−0.890326	−	0.455324i	$-0.849523\pi$
$359$	−33.7385	−1.78065	−0.890326	+	0.455324i	$0.849523\pi$
$360$	0	0
$361$	12.0758	0.635567
$362$	− 33.6176i	− 1.76690i
$363$	10.2847i	0.539806i
$364$	−12.5143	−0.655929
$365$	0	0
$366$	−3.91094	−0.204428
$367$	− 18.0331i	− 0.941320i	−0.882315	−	0.470660i	$-0.844016\pi$
$367$	− 18.0331i	− 0.941320i	0.882315	−	0.470660i	$-0.155984\pi$
$368$	− 1.21580i	− 0.0633777i
$369$	−18.7618	−0.976699
$370$	0	0
$371$	8.69893	0.451626
$372$	− 7.49129i	− 0.388405i
$373$	− 27.0210i	− 1.39909i	−0.714587	−	0.699547i	$-0.753385\pi$
$373$	− 27.0210i	− 1.39909i	0.714587	−	0.699547i	$-0.246615\pi$
$374$	5.37499	0.277934
$375$	0	0
$376$	8.31346	0.428734
$377$	− 23.9397i	− 1.23296i
$378$	9.01825i	0.463849i
$379$	34.0246	1.74772	0.873862	−	0.486173i	$-0.161608\pi$
$379$	34.0246	1.74772	0.873862	+	0.486173i	$0.161608\pi$
$380$	0	0
$381$	−6.61899	−0.339101
$382$	− 17.5090i	− 0.895838i
$383$	− 2.74649i	− 0.140339i	−0.997535	−	0.0701696i	$-0.977646\pi$
$383$	− 2.74649i	− 0.140339i	0.997535	−	0.0701696i	$-0.0223540\pi$
$384$	−9.08232	−0.463480
$385$	0	0
$386$	59.0592	3.00603
$387$	− 20.0764i	− 1.02054i
$388$	56.3260i	2.85952i
$389$	−2.23432	−0.113285	−0.0566423	−	0.998395i	$-0.518039\pi$
$389$	−2.23432	−0.113285	−0.0566423	+	0.998395i	$0.518039\pi$
$390$	0	0
$391$	1.49392	0.0755507
$392$	− 13.7073i	− 0.692325i
$393$	− 7.52190i	− 0.379430i
$394$	−29.7234	−1.49744
$395$	0	0
$396$	−47.8617	−2.40514
$397$	5.74533i	0.288350i	0.989552	+	0.144175i	$0.0460528\pi$
$397$	5.74533i	0.288350i	−0.989552	+	0.144175i	$0.953947\pi$
$398$	− 41.5555i	− 2.08299i
$399$	3.86295	0.193390
$400$	0	0
$401$	−16.4458	−0.821264	−0.410632	−	0.911801i	$-0.634692\pi$
$401$	−16.4458	−0.821264	−0.410632	+	0.911801i	$0.634692\pi$
$402$	− 11.4114i	− 0.569150i
$403$	13.5732i	0.676129i
$404$	−33.9652	−1.68983
$405$	0	0
$406$	−24.4602	−1.21394
$407$	− 5.55161i	− 0.275183i
$408$	− 0.581304i	− 0.0287789i
$409$	−32.5835	−1.61115	−0.805575	−	0.592494i	$-0.798144\pi$
$409$	−32.5835	−1.61115	−0.805575	+	0.592494i	$0.798144\pi$
$410$	0	0
$411$	5.62613	0.277517
$412$	− 25.8708i	− 1.27456i
$413$	11.3658i	0.559275i
$414$	−21.7298	−1.06796
$415$	0	0
$416$	17.9375	0.879458
$417$	− 0.812667i	− 0.0397965i
$418$	70.2801i	3.43751i
$419$	−26.6150	−1.30023	−0.650115	−	0.759836i	$-0.725279\pi$
$419$	−26.6150	−1.30023	−0.650115	+	0.759836i	$0.725279\pi$
$420$	0	0
$421$	−13.6775	−0.666600	−0.333300	−	0.942821i	$-0.608162\pi$
$421$	−13.6775	−0.666600	−0.333300	+	0.942821i	$0.608162\pi$
$422$	6.56667i	0.319661i
$423$	8.63962i	0.420073i
$424$	17.1161	0.831232
$425$	0	0
$426$	−9.20687	−0.446074
$427$	− 4.43231i	− 0.214495i
$428$	17.7183i	0.856445i
$429$	−8.55045	−0.412820
$430$	0	0
$431$	11.2668	0.542704	0.271352	−	0.962480i	$-0.412529\pi$
$431$	11.2668	0.542704	0.271352	+	0.962480i	$0.412529\pi$
$432$	− 1.03176i	− 0.0496407i
$433$	− 19.9228i	− 0.957427i	−0.877971	−	0.478714i	$-0.841103\pi$
$433$	− 19.9228i	− 0.957427i	0.877971	−	0.478714i	$-0.158897\pi$
$434$	13.8683	0.665700
$435$	0	0
$436$	−1.19277	−0.0571235
$437$	19.5336i	0.934418i
$438$	− 0.898581i	− 0.0429359i
$439$	−18.4321	−0.879717	−0.439859	−	0.898067i	$-0.644971\pi$
$439$	−18.4321	−0.879717	−0.439859	+	0.898067i	$0.644971\pi$
$440$	0	0
$441$	14.2451	0.678338
$442$	2.87375i	0.136690i
$443$	22.1719i	1.05342i	0.850045	+	0.526710i	$0.176575\pi$
$443$	22.1719i	1.05342i	−0.850045	+	0.526710i	$0.823425\pi$
$444$	−1.63819	−0.0777453
$445$	0	0
$446$	58.5908	2.77435
$447$	4.20181i	0.198739i
$448$	− 17.4008i	− 0.822109i
$449$	4.70999	0.222278	0.111139	−	0.993805i	$-0.464550\pi$
$449$	4.70999	0.222278	0.111139	+	0.993805i	$0.464550\pi$
$450$	0	0
$451$	−38.1427	−1.79607
$452$	− 14.3627i	− 0.675565i
$453$	− 6.22767i	− 0.292601i
$454$	13.6504	0.640643
$455$	0	0
$456$	7.60079	0.355940
$457$	− 12.9225i	− 0.604488i	−0.953231	−	0.302244i	$-0.902264\pi$
$457$	− 12.9225i	− 0.604488i	0.953231	−	0.302244i	$-0.0977357\pi$
$458$	− 11.8570i	− 0.554043i
$459$	1.26779	0.0591752
$460$	0	0
$461$	−11.7403	−0.546802	−0.273401	−	0.961900i	$-0.588149\pi$
$461$	−11.7403	−0.546802	−0.273401	+	0.961900i	$0.588149\pi$
$462$	8.73635i	0.406452i
$463$	− 0.377012i	− 0.0175212i	−0.999962	−	0.00876061i	$-0.997211\pi$
$463$	− 0.377012i	− 0.0175212i	0.999962	−	0.00876061i	$-0.00278862\pi$
$464$	2.79845	0.129915
$465$	0	0
$466$	−34.5763	−1.60171
$467$	− 7.22290i	− 0.334236i	−0.985937	−	0.167118i	$-0.946554\pi$
$467$	− 7.22290i	− 0.334236i	0.985937	−	0.167118i	$-0.0534461\pi$
$468$	− 25.5894i	− 1.18287i
$469$	12.9327	0.597176
$470$	0	0
$471$	10.0007	0.460810
$472$	22.3635i	1.02936i
$473$	− 40.8153i	− 1.87669i
$474$	20.1173	0.924019
$475$	0	0
$476$	1.79752	0.0823890
$477$	17.7876i	0.814439i
$478$	27.5154i	1.25853i
$479$	−29.5805	−1.35157	−0.675783	−	0.737101i	$-0.736194\pi$
$479$	−29.5805	−1.35157	−0.675783	+	0.737101i	$0.736194\pi$
$480$	0	0
$481$	2.96818	0.135338
$482$	47.2144i	2.15056i
$483$	2.42817i	0.110486i
$484$	−62.5748	−2.84431
$485$	0	0
$486$	−28.0940	−1.27437
$487$	3.98732i	0.180683i	0.995911	+	0.0903413i	$0.0287958\pi$
$487$	3.98732i	0.180683i	−0.995911	+	0.0903413i	$0.971204\pi$
$488$	− 8.72106i	− 0.394784i
$489$	−0.516419	−0.0233533
$490$	0	0
$491$	4.67346	0.210910	0.105455	−	0.994424i	$-0.466370\pi$
$491$	4.67346	0.210910	0.105455	+	0.994424i	$0.466370\pi$
$492$	11.2553i	0.507429i
$493$	3.43862i	0.154868i
$494$	−37.5754	−1.69060
$495$	0	0
$496$	−1.58665	−0.0712426
$497$	− 10.4342i	− 0.468040i
$498$	− 3.23646i	− 0.145029i
$499$	−2.75874	−0.123498	−0.0617491	−	0.998092i	$-0.519668\pi$
$499$	−2.75874	−0.123498	−0.0617491	+	0.998092i	$0.519668\pi$
$500$	0	0
$501$	12.5897	0.562465
$502$	21.9612i	0.980177i
$503$	− 5.38439i	− 0.240078i	−0.992769	−	0.120039i	$-0.961698\pi$
$503$	− 5.38439i	− 0.240078i	0.992769	−	0.120039i	$-0.0383020\pi$
$504$	−9.58254	−0.426840
$505$	0	0
$506$	−44.1766	−1.96389
$507$	2.17410i	0.0965553i
$508$	− 40.2717i	− 1.78677i
$509$	−16.0712	−0.712342	−0.356171	−	0.934421i	$-0.615918\pi$
$509$	−16.0712	−0.712342	−0.356171	+	0.934421i	$0.615918\pi$
$510$	0	0
$511$	1.01837	0.0450501
$512$	3.92024i	0.173252i
$513$	16.5768i	0.731884i
$514$	−71.8616	−3.16968
$515$	0	0
$516$	−12.0440	−0.530205
$517$	17.5644i	0.772479i
$518$	− 3.03272i	− 0.133250i
$519$	−5.94422	−0.260922
$520$	0	0
$521$	−26.9444	−1.18045	−0.590227	−	0.807237i	$-0.700962\pi$
$521$	−26.9444	−1.18045	−0.590227	+	0.807237i	$0.700962\pi$
$522$	− 50.0164i	− 2.18916i
$523$	− 8.47473i	− 0.370574i	−0.982684	−	0.185287i	$-0.940679\pi$
$523$	− 8.47473i	− 0.370574i	0.982684	−	0.185287i	$-0.0593215\pi$
$524$	45.7652	1.99926
$525$	0	0
$526$	32.5107	1.41753
$527$	− 1.94961i	− 0.0849262i
$528$	− 0.999510i	− 0.0434981i
$529$	10.7216	0.466156
$530$	0	0
$531$	−23.2408	−1.00857
$532$	23.5032i	1.01899i
$533$	− 20.3931i	− 0.883323i
$534$	0.101941	0.00441142
$535$	0	0
$536$	25.4465	1.09912
$537$	6.13504i	0.264747i
$538$	65.4508i	2.82178i
$539$	28.9603	1.24741
$540$	0	0
$541$	18.8254	0.809368	0.404684	−	0.914457i	$-0.367382\pi$
$541$	18.8254	0.809368	0.404684	+	0.914457i	$0.367382\pi$
$542$	23.7045i	1.01819i
$543$	− 7.68145i	− 0.329643i
$544$	−2.57648	−0.110466
$545$	0	0
$546$	−4.67091	−0.199897
$547$	17.8907i	0.764953i	0.923965	+	0.382476i	$0.124929\pi$
$547$	17.8907i	0.764953i	−0.923965	+	0.382476i	$0.875071\pi$
$548$	34.2309i	1.46227i
$549$	9.06321	0.386809
$550$	0	0
$551$	−44.9613	−1.91542
$552$	4.77770i	0.203352i
$553$	22.7992i	0.969519i
$554$	−36.7935	−1.56321
$555$	0	0
$556$	4.94448	0.209693
$557$	− 19.5753i	− 0.829433i	−0.909951	−	0.414717i	$-0.863881\pi$
$557$	− 19.5753i	− 0.829433i	0.909951	−	0.414717i	$-0.136119\pi$
$558$	28.3580i	1.20049i
$559$	21.8220	0.922972
$560$	0	0
$561$	1.22816	0.0518528
$562$	18.4161i	0.776837i
$563$	− 20.0503i	− 0.845018i	−0.906359	−	0.422509i	$-0.861150\pi$
$563$	− 20.0503i	− 0.845018i	0.906359	−	0.422509i	$-0.138850\pi$
$564$	5.18297	0.218242
$565$	0	0
$566$	−0.975966	−0.0410229
$567$	− 8.87977i	− 0.372915i
$568$	− 20.5305i	− 0.861442i
$569$	34.7651	1.45743	0.728715	−	0.684817i	$-0.240118\pi$
$569$	34.7651	1.45743	0.728715	+	0.684817i	$0.240118\pi$
$570$	0	0
$571$	1.04707	0.0438184	0.0219092	−	0.999760i	$-0.493026\pi$
$571$	1.04707	0.0438184	0.0219092	+	0.999760i	$0.493026\pi$
$572$	− 52.0232i	− 2.17520i
$573$	− 4.00071i	− 0.167132i
$574$	−20.8365	−0.869698
$575$	0	0
$576$	35.5812	1.48255
$577$	− 28.6481i	− 1.19264i	−0.802749	−	0.596318i	$-0.796630\pi$
$577$	− 28.6481i	− 1.19264i	0.802749	−	0.596318i	$-0.203370\pi$
$578$	38.1929i	1.58862i
$579$	13.4947	0.560821
$580$	0	0
$581$	3.66791	0.152171
$582$	21.0234i	0.871448i
$583$	36.1622i	1.49769i
$584$	2.00376	0.0829161
$585$	0	0
$586$	32.6629	1.34929
$587$	− 26.6924i	− 1.10171i	−0.834600	−	0.550857i	$-0.814301\pi$
$587$	− 26.6924i	− 1.10171i	0.834600	−	0.550857i	$-0.185699\pi$
$588$	− 8.54573i	− 0.352420i
$589$	25.4919	1.05037
$590$	0	0
$591$	−6.79164	−0.279371
$592$	0.346968i	0.0142603i
$593$	10.0943i	0.414521i	0.978286	+	0.207261i	$0.0664548\pi$
$593$	10.0943i	0.414521i	−0.978286	+	0.207261i	$0.933545\pi$
$594$	−37.4897	−1.53822
$595$	0	0
$596$	−25.5649	−1.04718
$597$	− 9.49523i	− 0.388614i
$598$	− 23.6192i	− 0.965859i
$599$	9.37239	0.382946	0.191473	−	0.981498i	$-0.438674\pi$
$599$	9.37239	0.382946	0.191473	+	0.981498i	$0.438674\pi$
$600$	0	0
$601$	−41.6868	−1.70044	−0.850220	−	0.526427i	$-0.823531\pi$
$601$	−41.6868	−1.70044	−0.850220	+	0.526427i	$0.823531\pi$
$602$	− 22.2964i	− 0.908735i
$603$	26.4448i	1.07692i
$604$	37.8908	1.54175
$605$	0	0
$606$	−12.6774	−0.514982
$607$	20.4257i	0.829052i	0.910037	+	0.414526i	$0.136053\pi$
$607$	20.4257i	0.829052i	−0.910037	+	0.414526i	$0.863947\pi$
$608$	− 33.6885i	− 1.36625i
$609$	−5.58903	−0.226479
$610$	0	0
$611$	−9.39083	−0.379912
$612$	3.67557i	0.148576i
$613$	− 39.0819i	− 1.57850i	−0.614070	−	0.789251i	$-0.710469\pi$
$613$	− 39.0819i	− 1.57850i	0.614070	−	0.789251i	$-0.289531\pi$
$614$	56.4162	2.27677
$615$	0	0
$616$	−19.4813	−0.784924
$617$	24.7773i	0.997495i	0.866747	+	0.498747i	$0.166206\pi$
$617$	24.7773i	0.997495i	−0.866747	+	0.498747i	$0.833794\pi$
$618$	− 9.65615i	− 0.388427i
$619$	−27.7629	−1.11589	−0.557943	−	0.829879i	$-0.688409\pi$
$619$	−27.7629	−1.11589	−0.557943	+	0.829879i	$0.688409\pi$
$620$	0	0
$621$	−10.4198	−0.418134
$622$	− 30.3244i	− 1.21590i
$623$	0.115531i	0.00462864i
$624$	0.534391	0.0213928
$625$	0	0
$626$	59.3009	2.37014
$627$	16.0586i	0.641320i
$628$	60.8472i	2.42807i
$629$	−0.426340	−0.0169993
$630$	0	0
$631$	20.6678	0.822772	0.411386	−	0.911461i	$-0.365045\pi$
$631$	20.6678	0.822772	0.411386	+	0.911461i	$0.365045\pi$
$632$	44.8599i	1.78443i
$633$	1.50045i	0.0596376i
$634$	−62.4678	−2.48091
$635$	0	0
$636$	10.6709	0.423129
$637$	15.4837i	0.613486i
$638$	− 101.683i	− 4.02568i
$639$	21.3360	0.844039
$640$	0	0
$641$	−23.3208	−0.921116	−0.460558	−	0.887630i	$-0.652351\pi$
$641$	−23.3208	−0.921116	−0.460558	+	0.887630i	$0.652351\pi$
$642$	6.61326i	0.261004i
$643$	− 8.04242i	− 0.317162i	−0.987346	−	0.158581i	$-0.949308\pi$
$643$	− 8.04242i	− 0.317162i	0.987346	−	0.158581i	$-0.0506919\pi$
$644$	−14.7737	−0.582163
$645$	0	0
$646$	5.39721	0.212350
$647$	49.3437i	1.93990i	0.243305	+	0.969950i	$0.421768\pi$
$647$	49.3437i	1.93990i	−0.243305	+	0.969950i	$0.578232\pi$
$648$	− 17.4719i	− 0.686362i
$649$	−47.2487	−1.85467
$650$	0	0
$651$	3.16884	0.124196
$652$	− 3.14203i	− 0.123051i
$653$	− 24.9760i	− 0.977385i	−0.872456	−	0.488693i	$-0.837474\pi$
$653$	− 24.9760i	− 0.977385i	0.872456	−	0.488693i	$-0.162526\pi$
$654$	−0.445197	−0.0174086
$655$	0	0
$656$	2.38386	0.0930743
$657$	2.08237i	0.0812410i
$658$	9.59501i	0.374052i
$659$	32.3446	1.25997	0.629983	−	0.776609i	$-0.283062\pi$
$659$	32.3446	1.25997	0.629983	+	0.776609i	$0.283062\pi$
$660$	0	0
$661$	−1.85884	−0.0723006	−0.0361503	−	0.999346i	$-0.511510\pi$
$661$	−1.85884	−0.0723006	−0.0361503	+	0.999346i	$0.511510\pi$
$662$	− 75.9811i	− 2.95309i
$663$	0.656637i	0.0255017i
$664$	7.21703	0.280075
$665$	0	0
$666$	6.20132	0.240296
$667$	− 28.2618i	− 1.09430i
$668$	76.5988i	2.96370i
$669$	13.3877	0.517598
$670$	0	0
$671$	18.4255	0.711309
$672$	− 4.18774i	− 0.161546i
$673$	44.3587i	1.70990i	0.518709	+	0.854951i	$0.326413\pi$
$673$	44.3587i	1.70990i	−0.518709	+	0.854951i	$0.673587\pi$
$674$	52.2362	2.01206
$675$	0	0
$676$	−13.2278	−0.508762
$677$	8.33112i	0.320191i	0.987102	+	0.160096i	$0.0511802\pi$
$677$	8.33112i	0.320191i	−0.987102	+	0.160096i	$0.948820\pi$
$678$	− 5.36081i	− 0.205881i
$679$	−23.8260	−0.914360
$680$	0	0
$681$	3.11904	0.119522
$682$	57.6518i	2.20760i
$683$	24.2726i	0.928764i	0.885635	+	0.464382i	$0.153723\pi$
$683$	24.2726i	0.928764i	−0.885635	+	0.464382i	$0.846277\pi$
$684$	−48.0595	−1.83760
$685$	0	0
$686$	37.0494	1.41455
$687$	− 2.70927i	− 0.103365i
$688$	2.55090i	0.0972520i
$689$	−19.3342	−0.736576
$690$	0	0
$691$	29.0133	1.10372	0.551858	−	0.833938i	$-0.313919\pi$
$691$	29.0133	1.10372	0.551858	+	0.833938i	$0.313919\pi$
$692$	− 36.1662i	− 1.37483i
$693$	− 20.2456i	− 0.769067i
$694$	48.0552	1.82415
$695$	0	0
$696$	−10.9970	−0.416842
$697$	2.92919i	0.110951i
$698$	36.2823i	1.37330i
$699$	−7.90050	−0.298824
$700$	0	0
$701$	33.0887	1.24974	0.624871	−	0.780728i	$-0.285151\pi$
$701$	33.0887	1.24974	0.624871	+	0.780728i	$0.285151\pi$
$702$	− 20.0440i	− 0.756510i
$703$	− 5.57456i	− 0.210249i
$704$	72.3366	2.72629
$705$	0	0
$706$	42.7280	1.60809
$707$	− 14.3674i	− 0.540341i
$708$	13.9423i	0.523985i
$709$	31.3446	1.17717	0.588586	−	0.808434i	$-0.299685\pi$
$709$	31.3446	1.17717	0.588586	+	0.808434i	$0.299685\pi$
$710$	0	0
$711$	−46.6198	−1.74838
$712$	0.227319i	0.00851916i
$713$	16.0237i	0.600091i
$714$	0.670914	0.0251083
$715$	0	0
$716$	−37.3272	−1.39498
$717$	6.28713i	0.234797i
$718$	− 76.6176i	− 2.85934i
$719$	19.2288	0.717114	0.358557	−	0.933508i	$-0.383269\pi$
$719$	19.2288	0.717114	0.358557	+	0.933508i	$0.383269\pi$
$720$	0	0
$721$	10.9434	0.407554
$722$	27.4231i	1.02058i
$723$	10.7883i	0.401219i
$724$	46.7360	1.73693
$725$	0	0
$726$	−23.3557	−0.866813
$727$	51.4657i	1.90876i	0.298599	+	0.954379i	$0.403481\pi$
$727$	51.4657i	1.90876i	−0.298599	+	0.954379i	$0.596519\pi$
$728$	− 10.4157i	− 0.386033i
$729$	13.5284	0.501051
$730$	0	0
$731$	−3.13444	−0.115931
$732$	− 5.43708i	− 0.200960i
$733$	− 8.23113i	− 0.304024i	−0.988379	−	0.152012i	$-0.951425\pi$
$733$	− 8.23113i	− 0.304024i	0.988379	−	0.152012i	$-0.0485752\pi$
$734$	40.9518	1.51156
$735$	0	0
$736$	21.1759	0.780554
$737$	53.7624i	1.98036i
$738$	− 42.6065i	− 1.56837i
$739$	11.7725	0.433057	0.216528	−	0.976276i	$-0.430527\pi$
$739$	11.7725	0.433057	0.216528	+	0.976276i	$0.430527\pi$
$740$	0	0
$741$	−8.58580	−0.315407
$742$	19.7546i	0.725214i
$743$	29.3902i	1.07822i	0.842234	+	0.539112i	$0.181240\pi$
$743$	29.3902i	1.07822i	−0.842234	+	0.539112i	$0.818760\pi$
$744$	6.23503	0.228587
$745$	0	0
$746$	61.3625	2.24664
$747$	7.50017i	0.274417i
$748$	7.47243i	0.273219i
$749$	−7.49487	−0.273857
$750$	0	0
$751$	−9.66463	−0.352667	−0.176334	−	0.984330i	$-0.556424\pi$
$751$	−9.66463	−0.352667	−0.176334	+	0.984330i	$0.556424\pi$
$752$	− 1.09775i	− 0.0400307i
$753$	5.01803i	0.182867i
$754$	54.3652	1.97986
$755$	0	0
$756$	−12.5374	−0.455980
$757$	3.21095i	0.116704i	0.998296	+	0.0583520i	$0.0185846\pi$
$757$	3.21095i	0.116704i	−0.998296	+	0.0583520i	$0.981415\pi$
$758$	77.2672i	2.80647i
$759$	−10.0941	−0.366394
$760$	0	0
$761$	−3.78248	−0.137115	−0.0685574	−	0.997647i	$-0.521840\pi$
$761$	−3.78248	−0.137115	−0.0685574	+	0.997647i	$0.521840\pi$
$762$	− 15.0312i	− 0.544524i
$763$	− 0.504546i	− 0.0182658i
$764$	24.3414	0.880641
$765$	0	0
$766$	6.23707	0.225354
$767$	− 25.2616i	− 0.912144i
$768$	− 7.10304i	− 0.256309i
$769$	−7.39888	−0.266810	−0.133405	−	0.991062i	$-0.542591\pi$
$769$	−7.39888	−0.266810	−0.133405	+	0.991062i	$0.542591\pi$
$770$	0	0
$771$	−16.4200	−0.591352
$772$	82.1054i	2.95504i
$773$	12.8663i	0.462769i	0.972862	+	0.231385i	$0.0743256\pi$
$773$	12.8663i	0.462769i	−0.972862	+	0.231385i	$0.925674\pi$
$774$	45.5919	1.63877
$775$	0	0
$776$	−46.8804	−1.68291
$777$	− 0.692961i	− 0.0248598i
$778$	− 5.07397i	− 0.181911i
$779$	−38.3004	−1.37225
$780$	0	0
$781$	43.3761	1.55212
$782$	3.39257i	0.121318i
$783$	− 23.9838i	− 0.857111i
$784$	−1.80998	−0.0646420
$785$	0	0
$786$	17.0817	0.609282
$787$	− 3.19598i	− 0.113924i	−0.998376	−	0.0569621i	$-0.981859\pi$
$787$	− 3.19598i	− 0.113924i	0.998376	−	0.0569621i	$-0.0181414\pi$
$788$	− 41.3221i	− 1.47204i
$789$	7.42852	0.264462
$790$	0	0
$791$	6.07546	0.216019
$792$	− 39.8355i	− 1.41549i
$793$	9.85125i	0.349828i
$794$	−13.0472	−0.463027
$795$	0	0
$796$	57.7715	2.04766
$797$	− 33.4964i	− 1.18650i	−0.805017	−	0.593252i	$-0.797844\pi$
$797$	− 33.4964i	− 1.18650i	0.805017	−	0.593252i	$-0.202156\pi$
$798$	8.77247i	0.310542i
$799$	1.34887	0.0477195
$800$	0	0
$801$	−0.236238	−0.00834705
$802$	− 37.3471i	− 1.31877i
$803$	4.23346i	0.149396i
$804$	15.8644	0.559495
$805$	0	0
$806$	−30.8237	−1.08572
$807$	14.9552i	0.526447i
$808$	− 28.2694i	− 0.994514i
$809$	−3.02505	−0.106355	−0.0531775	−	0.998585i	$-0.516935\pi$
$809$	−3.02505	−0.106355	−0.0531775	+	0.998585i	$0.516935\pi$
$810$	0	0
$811$	−15.5601	−0.546388	−0.273194	−	0.961959i	$-0.588080\pi$
$811$	−15.5601	−0.546388	−0.273194	+	0.961959i	$0.588080\pi$
$812$	− 34.0052i	− 1.19335i
$813$	5.41635i	0.189960i
$814$	12.6073	0.441885
$815$	0	0
$816$	−0.0767581	−0.00268707
$817$	− 40.9840i	− 1.43385i
$818$	− 73.9946i	− 2.58716i
$819$	10.8244	0.378234
$820$	0	0
$821$	−21.2585	−0.741928	−0.370964	−	0.928647i	$-0.620973\pi$
$821$	−21.2585	−0.741928	−0.370964	+	0.928647i	$0.620973\pi$
$822$	12.7765i	0.445632i
$823$	21.0705i	0.734472i	0.930128	+	0.367236i	$0.119696\pi$
$823$	21.0705i	0.734472i	−0.930128	+	0.367236i	$0.880304\pi$
$824$	21.5324	0.750116
$825$	0	0
$826$	−25.8109	−0.898075
$827$	− 11.8965i	− 0.413683i	−0.978374	−	0.206841i	$-0.933682\pi$
$827$	− 11.8965i	− 0.413683i	0.978374	−	0.206841i	$-0.0663184\pi$
$828$	− 30.2092i	− 1.04984i
$829$	−3.76808	−0.130871	−0.0654355	−	0.997857i	$-0.520844\pi$
$829$	−3.76808	−0.130871	−0.0654355	+	0.997857i	$0.520844\pi$
$830$	0	0
$831$	−8.40713	−0.291640
$832$	38.6749i	1.34081i
$833$	− 2.22403i	− 0.0770579i
$834$	1.84550	0.0639046
$835$	0	0
$836$	−97.7050	−3.37920
$837$	13.5982i	0.470022i
$838$	− 60.4407i	− 2.08789i
$839$	−27.0741	−0.934703	−0.467352	−	0.884071i	$-0.654792\pi$
$839$	−27.0741	−0.934703	−0.467352	+	0.884071i	$0.654792\pi$
$840$	0	0
$841$	36.0513	1.24315
$842$	− 31.0605i	− 1.07042i
$843$	4.20799i	0.144931i
$844$	−9.12914	−0.314238
$845$	0	0
$846$	−19.6199	−0.674547
$847$	− 26.4693i	− 0.909496i
$848$	− 2.26009i	− 0.0776118i
$849$	−0.223003	−0.00765345
$850$	0	0
$851$	3.50406	0.120118
$852$	− 12.7996i	− 0.438507i
$853$	5.26211i	0.180171i	0.995934	+	0.0900857i	$0.0287141\pi$
$853$	5.26211i	0.180171i	−0.995934	+	0.0900857i	$0.971286\pi$
$854$	10.0654	0.344432
$855$	0	0
$856$	−14.7470	−0.504042
$857$	43.5043i	1.48608i	0.669247	+	0.743040i	$0.266617\pi$
$857$	43.5043i	1.48608i	−0.669247	+	0.743040i	$0.733383\pi$
$858$	− 19.4174i	− 0.662899i
$859$	−12.2666	−0.418530	−0.209265	−	0.977859i	$-0.567107\pi$
$859$	−12.2666	−0.418530	−0.209265	+	0.977859i	$0.567107\pi$
$860$	0	0
$861$	−4.76103	−0.162255
$862$	25.5861i	0.871466i
$863$	25.5488i	0.869692i	0.900505	+	0.434846i	$0.143197\pi$
$863$	25.5488i	0.869692i	−0.900505	+	0.434846i	$0.856803\pi$
$864$	17.9705	0.611370
$865$	0	0
$866$	45.2431	1.53742
$867$	8.72688i	0.296380i
$868$	19.2800i	0.654407i
$869$	−94.7781	−3.21513
$870$	0	0
$871$	−28.7442	−0.973960
$872$	− 0.992751i	− 0.0336188i
$873$	− 48.7196i	− 1.64891i
$874$	−44.3593	−1.50047
$875$	0	0
$876$	1.24923	0.0422075
$877$	− 5.42848i	− 0.183307i	−0.995791	−	0.0916534i	$-0.970785\pi$
$877$	− 5.42848i	− 0.183307i	0.995791	−	0.0916534i	$-0.0292152\pi$
$878$	− 41.8579i	− 1.41264i
$879$	7.46331	0.251731
$880$	0	0
$881$	−1.60640	−0.0541211	−0.0270606	−	0.999634i	$-0.508615\pi$
$881$	−1.60640	−0.0541211	−0.0270606	+	0.999634i	$0.508615\pi$
$882$	32.3495i	1.08926i
$883$	27.0365i	0.909850i	0.890530	+	0.454925i	$0.150334\pi$
$883$	27.0365i	0.909850i	−0.890530	+	0.454925i	$0.849666\pi$
$884$	−3.99516	−0.134372
$885$	0	0
$886$	−50.3508	−1.69157
$887$	5.22338i	0.175384i	0.996148	+	0.0876919i	$0.0279491\pi$
$887$	5.22338i	0.175384i	−0.996148	+	0.0876919i	$0.972051\pi$
$888$	− 1.36348i	− 0.0457553i
$889$	17.0350	0.571337
$890$	0	0
$891$	36.9140	1.23667
$892$	81.4543i	2.72729i
$893$	17.6370i	0.590199i
$894$	−9.54198	−0.319132
$895$	0	0
$896$	23.3748	0.780897
$897$	− 5.39686i	− 0.180196i
$898$	10.6960i	0.356931i
$899$	−36.8824	−1.23010
$900$	0	0
$901$	2.77710	0.0925187
$902$	− 86.6191i	− 2.88410i
$903$	− 5.09462i	− 0.169538i
$904$	11.9541	0.397589
$905$	0	0
$906$	14.1425	0.469855
$907$	35.8601i	1.19071i	0.803461	+	0.595357i	$0.202989\pi$
$907$	35.8601i	1.19071i	−0.803461	+	0.595357i	$0.797011\pi$
$908$	18.9771i	0.629776i
$909$	29.3785	0.974423
$910$	0	0
$911$	−37.2761	−1.23501	−0.617506	−	0.786566i	$-0.711857\pi$
$911$	−37.2761	−1.23501	−0.617506	+	0.786566i	$0.711857\pi$
$912$	− 1.00364i	− 0.0332339i
$913$	15.2478i	0.504630i
$914$	29.3459	0.970677
$915$	0	0
$916$	16.4839	0.544644
$917$	19.3588i	0.639285i
$918$	2.87904i	0.0950226i
$919$	−20.7180	−0.683423	−0.341712	−	0.939805i	$-0.611007\pi$
$919$	−20.7180	−0.683423	−0.341712	+	0.939805i	$0.611007\pi$
$920$	0	0
$921$	12.8908	0.424767
$922$	− 26.6614i	− 0.878046i
$923$	23.1911i	0.763345i
$924$	−12.1455	−0.399557
$925$	0	0
$926$	0.856165	0.0281353
$927$	22.3771i	0.734962i
$928$	48.7415i	1.60002i
$929$	−4.73148	−0.155235	−0.0776173	−	0.996983i	$-0.524731\pi$
$929$	−4.73148	−0.155235	−0.0776173	+	0.996983i	$0.524731\pi$
$930$	0	0
$931$	29.0800	0.953059
$932$	− 48.0687i	− 1.57454i
$933$	− 6.92897i	− 0.226844i
$934$	16.4026	0.536711
$935$	0	0
$936$	21.2981	0.696152
$937$	− 9.43501i	− 0.308228i	−0.988053	−	0.154114i	$-0.950748\pi$
$937$	− 9.43501i	− 0.308228i	0.988053	−	0.154114i	$-0.0492524\pi$
$938$	29.3691i	0.958937i
$939$	13.5500	0.442186
$940$	0	0
$941$	41.6919	1.35912	0.679559	−	0.733621i	$-0.262171\pi$
$941$	41.6919	1.35912	0.679559	+	0.733621i	$0.262171\pi$
$942$	22.7109i	0.739962i
$943$	− 24.0748i	− 0.783985i
$944$	2.95297	0.0961111
$945$	0	0
$946$	92.6883	3.01356
$947$	40.4822i	1.31550i	0.753238	+	0.657748i	$0.228491\pi$
$947$	40.4822i	1.31550i	−0.753238	+	0.657748i	$0.771509\pi$
$948$	27.9676i	0.908344i
$949$	−2.26343	−0.0734741
$950$	0	0
$951$	−14.2736	−0.462852
$952$	1.49608i	0.0484882i
$953$	− 57.3835i	− 1.85883i	−0.369033	−	0.929416i	$-0.620311\pi$
$953$	− 57.3835i	− 1.85883i	0.369033	−	0.929416i	$-0.379689\pi$
$954$	−40.3943	−1.30781
$955$	0	0
$956$	−38.2526	−1.23718
$957$	− 23.2341i	− 0.751052i
$958$	− 67.1749i	− 2.17032i
$959$	−14.4797	−0.467575
$960$	0	0
$961$	−10.0887	−0.325440
$962$	6.74052i	0.217323i
$963$	− 15.3256i	− 0.493859i
$964$	−65.6386	−2.11408
$965$	0	0
$966$	−5.51419	−0.177416
$967$	− 5.51447i	− 0.177333i	−0.996061	−	0.0886667i	$-0.971739\pi$
$967$	− 5.51447i	− 0.177333i	0.996061	−	0.0886667i	$-0.0282606\pi$
$968$	− 52.0813i	− 1.67396i
$969$	1.23323	0.0396172
$970$	0	0
$971$	−29.5277	−0.947590	−0.473795	−	0.880635i	$-0.657116\pi$
$971$	−29.5277	−0.947590	−0.473795	+	0.880635i	$0.657116\pi$
$972$	− 39.0570i	− 1.25275i
$973$	2.09153i	0.0670514i
$974$	−9.05489	−0.290137
$975$	0	0
$976$	−1.15157	−0.0368608
$977$	45.5206i	1.45633i	0.685401	+	0.728166i	$0.259627\pi$
$977$	45.5206i	1.45633i	−0.685401	+	0.728166i	$0.740373\pi$
$978$	− 1.17275i	− 0.0375003i
$979$	−0.480272	−0.0153495
$980$	0	0
$981$	1.03170	0.0329396
$982$	10.6131i	0.338677i
$983$	11.2739i	0.359582i	0.983705	+	0.179791i	$0.0575421\pi$
$983$	11.2739i	0.359582i	−0.983705	+	0.179791i	$0.942458\pi$
$984$	−9.36785	−0.298636
$985$	0	0
$986$	−7.80883	−0.248684
$987$	2.19241i	0.0697852i
$988$	− 52.2383i	− 1.66192i
$989$	25.7617	0.819175
$990$	0	0
$991$	−12.4139	−0.394341	−0.197170	−	0.980369i	$-0.563175\pi$
$991$	−12.4139	−0.394341	−0.197170	+	0.980369i	$0.563175\pi$
$992$	− 27.6352i	− 0.877417i
$993$	− 17.3613i	− 0.550944i
$994$	23.6954	0.751571
$995$	0	0
$996$	4.49940	0.142569
$997$	− 38.6932i	− 1.22543i	−0.790306	−	0.612713i	$-0.790078\pi$
$997$	− 38.6932i	− 1.22543i	0.790306	−	0.612713i	$-0.209922\pi$
$998$	− 6.26488i	− 0.198311i
$999$	2.97365	0.0940822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.b.g.149.9		10
5.2	odd	4		925.2.a.h.1.1		5
5.3	odd	4		185.2.a.d.1.5	✓	5
5.4	even	2	inner	925.2.b.g.149.2		10
15.2	even	4		8325.2.a.cc.1.5		5
15.8	even	4		1665.2.a.q.1.1		5
20.3	even	4		2960.2.a.ba.1.3		5
35.13	even	4		9065.2.a.j.1.5		5
185.73	odd	4		6845.2.a.g.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.d.1.5	✓	5	5.3	odd	4
925.2.a.h.1.1		5	5.2	odd	4
925.2.b.g.149.2		10	5.4	even	2	inner
925.2.b.g.149.9		10	1.1	even	1	trivial
1665.2.a.q.1.1		5	15.8	even	4
2960.2.a.ba.1.3		5	20.3	even	4
6845.2.a.g.1.1		5	185.73	odd	4
8325.2.a.cc.1.5		5	15.2	even	4
9065.2.a.j.1.5		5	35.13	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.27092i q^{2} +0.518894i q^{3} -3.15709 q^{4} -1.17837 q^{6} -1.33546i q^{7} -2.62766i q^{8} +2.73075 q^{9} +5.55161 q^{11} -1.63819i q^{12} +2.96818i q^{13} +3.03272 q^{14} -0.346968 q^{16} -0.426340i q^{17} +6.20132i q^{18} +5.57456 q^{19} +0.692961 q^{21} +12.6073i q^{22} +3.50406i q^{23} +1.36348 q^{24} -6.74052 q^{26} +2.97365i q^{27} +4.21616i q^{28} -8.06544 q^{29} +4.57289 q^{31} -6.04326i q^{32} +2.88070i q^{33} +0.968185 q^{34} -8.62122 q^{36} -1.00000i q^{37} +12.6594i q^{38} -1.54017 q^{39} -6.87056 q^{41} +1.57366i q^{42} -7.35197i q^{43} -17.5269 q^{44} -7.95744 q^{46} +3.16383i q^{47} -0.180040i q^{48} +5.21655 q^{49} +0.221225 q^{51} -9.37082i q^{52} +6.51383i q^{53} -6.75293 q^{54} -3.50913 q^{56} +2.89261i q^{57} -18.3160i q^{58} -8.51080 q^{59} +3.31895 q^{61} +10.3847i q^{62} -3.64680i q^{63} +13.0298 q^{64} -6.54184 q^{66} +9.68410i q^{67} +1.34599i q^{68} -1.81823 q^{69} +7.81324 q^{71} -7.17548i q^{72} +0.762564i q^{73} +2.27092 q^{74} -17.5994 q^{76} -7.41394i q^{77} -3.49761i q^{78} -17.0722 q^{79} +6.64924 q^{81} -15.6025i q^{82} +2.74656i q^{83} -2.18774 q^{84} +16.6957 q^{86} -4.18511i q^{87} -14.5877i q^{88} -0.0865103 q^{89} +3.96388 q^{91} -11.0626i q^{92} +2.37285i q^{93} -7.18481 q^{94} +3.13581 q^{96} -17.8411i q^{97} +11.8464i q^{98} +15.1601 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9} + 14 q^{11} - 8 q^{14} + 16 q^{16} - 28 q^{19} - 18 q^{21} - 24 q^{24} - 40 q^{26} - 4 q^{29} + 16 q^{31} - 24 q^{34} - 72 q^{36} - 24 q^{39} - 18 q^{41} - 36 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) \) 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9 + 14 * q^11 - 8 * q^14 + 16 * q^16 - 28 * q^19 - 18 * q^21 - 24 * q^24 - 40 * q^26 - 4 * q^29 + 16 * q^31 - 24 * q^34 - 72 * q^36 - 24 * q^39 - 18 * q^41 - 36 * q^44 - 56 * q^46 - 4 * q^49 + 20 * q^51 + 24 * q^54 - 28 * q^56 - 24 * q^59 + 24 * q^61 - 24 * q^64 - 20 * q^66 + 60 * q^69 + 26 * q^71 + 36 * q^76 - 72 * q^79 + 42 * q^81 - 60 * q^84 - 16 * q^86 + 32 * q^89 - 8 * q^91 - 40 * q^94 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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