LMFDB - Embedded newform 4025.2.a.bc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 $ x^14 - 3x^13 - 18x^12 + 58x^11 + 111x^10 - 414x^9 - 244x^8 + 1330x^7 - 27x^6 - 1853x^5 + 539x^4 + 891x^3 - 218x^2 - 133*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.33696$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33696 q^{2} +0.00757499 q^{3} +3.46136 q^{4} -0.0177024 q^{6} +1.00000 q^{7} -3.41514 q^{8} -2.99994 q^{9} +O(q^{10})$	\(q-2.33696 q^{2} +0.00757499 q^{3} +3.46136 q^{4} -0.0177024 q^{6} +1.00000 q^{7} -3.41514 q^{8} -2.99994 q^{9} -4.99434 q^{11} +0.0262198 q^{12} -3.87824 q^{13} -2.33696 q^{14} +1.05832 q^{16} -0.475637 q^{17} +7.01073 q^{18} -1.54155 q^{19} +0.00757499 q^{21} +11.6715 q^{22} +1.00000 q^{23} -0.0258697 q^{24} +9.06327 q^{26} -0.0454495 q^{27} +3.46136 q^{28} -9.38110 q^{29} -11.0814 q^{31} +4.35705 q^{32} -0.0378321 q^{33} +1.11154 q^{34} -10.3839 q^{36} -4.42722 q^{37} +3.60253 q^{38} -0.0293776 q^{39} +3.21792 q^{41} -0.0177024 q^{42} +3.40274 q^{43} -17.2872 q^{44} -2.33696 q^{46} -8.07320 q^{47} +0.00801673 q^{48} +1.00000 q^{49} -0.00360295 q^{51} -13.4240 q^{52} -1.46842 q^{53} +0.106214 q^{54} -3.41514 q^{56} -0.0116772 q^{57} +21.9232 q^{58} -11.8954 q^{59} +8.24535 q^{61} +25.8968 q^{62} -2.99994 q^{63} -12.2989 q^{64} +0.0884119 q^{66} +4.54321 q^{67} -1.64635 q^{68} +0.00757499 q^{69} +11.0031 q^{71} +10.2452 q^{72} +13.6586 q^{73} +10.3462 q^{74} -5.33586 q^{76} -4.99434 q^{77} +0.0686542 q^{78} +13.1029 q^{79} +8.99948 q^{81} -7.52014 q^{82} +14.7630 q^{83} +0.0262198 q^{84} -7.95205 q^{86} -0.0710618 q^{87} +17.0564 q^{88} -6.08219 q^{89} -3.87824 q^{91} +3.46136 q^{92} -0.0839417 q^{93} +18.8667 q^{94} +0.0330047 q^{96} +3.91724 q^{97} -2.33696 q^{98} +14.9827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9	$ 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{11} + 17 q^{12} + 11 q^{13} + 3 q^{14} + 23 q^{16} + 3 q^{17} + 15 q^{18} - 2 q^{19} + 4 q^{21} + 23 q^{22} + 14 q^{23} - 12 q^{24} - 9 q^{26} + 25 q^{27} + 17 q^{28} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 6 q^{33} - 14 q^{34} + 13 q^{36} + 22 q^{37} + 20 q^{38} - 10 q^{39} - 17 q^{41} - 4 q^{42} + 18 q^{43} + 28 q^{44} + 3 q^{46} + 30 q^{47} + 8 q^{48} + 14 q^{49} + 4 q^{51} + 8 q^{52} + 11 q^{53} + 20 q^{54} + 3 q^{56} + 18 q^{57} + 38 q^{58} - 22 q^{59} - 8 q^{61} - 22 q^{62} + 18 q^{63} + 29 q^{64} - 9 q^{66} + 39 q^{67} + q^{68} + 4 q^{69} - 5 q^{71} - 24 q^{72} + 18 q^{73} + 35 q^{74} - 41 q^{76} + 5 q^{77} - 22 q^{78} + 10 q^{79} + 2 q^{81} - 8 q^{82} + 24 q^{83} + 17 q^{84} - 26 q^{86} + 5 q^{87} + 58 q^{88} + 25 q^{89} + 11 q^{91} + 17 q^{92} + 47 q^{93} - 2 q^{94} - 117 q^{96} + 43 q^{97} + 3 q^{98} + 55 q^{99}+O(q^{100}) $ 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9 + 5 * q^11 + 17 * q^12 + 11 * q^13 + 3 * q^14 + 23 * q^16 + 3 * q^17 + 15 * q^18 - 2 * q^19 + 4 * q^21 + 23 * q^22 + 14 * q^23 - 12 * q^24 - 9 * q^26 + 25 * q^27 + 17 * q^28 + 7 * q^29 - 3 * q^31 + 24 * q^32 + 6 * q^33 - 14 * q^34 + 13 * q^36 + 22 * q^37 + 20 * q^38 - 10 * q^39 - 17 * q^41 - 4 * q^42 + 18 * q^43 + 28 * q^44 + 3 * q^46 + 30 * q^47 + 8 * q^48 + 14 * q^49 + 4 * q^51 + 8 * q^52 + 11 * q^53 + 20 * q^54 + 3 * q^56 + 18 * q^57 + 38 * q^58 - 22 * q^59 - 8 * q^61 - 22 * q^62 + 18 * q^63 + 29 * q^64 - 9 * q^66 + 39 * q^67 + q^68 + 4 * q^69 - 5 * q^71 - 24 * q^72 + 18 * q^73 + 35 * q^74 - 41 * q^76 + 5 * q^77 - 22 * q^78 + 10 * q^79 + 2 * q^81 - 8 * q^82 + 24 * q^83 + 17 * q^84 - 26 * q^86 + 5 * q^87 + 58 * q^88 + 25 * q^89 + 11 * q^91 + 17 * q^92 + 47 * q^93 - 2 * q^94 - 117 * q^96 + 43 * q^97 + 3 * q^98 + 55 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.33696	−1.65248	−0.826239	−	0.563320i	$-0.809524\pi$
$2$	−2.33696	−1.65248	−0.826239	+	0.563320i	$0.809524\pi$
$3$	0.00757499	0.00437342	0.00218671	−	0.999998i	$-0.499304\pi$
$3$	0.00757499	0.00437342	0.00218671	+	0.999998i	$0.499304\pi$
$4$	3.46136	1.73068
$5$	0	0
$5$	0	0
$6$	−0.0177024	−0.00722699
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.41514	−1.20744
$9$	−2.99994	−0.999981
$10$	0	0
$11$	−4.99434	−1.50585	−0.752924	−	0.658107i	$-0.771357\pi$
$11$	−4.99434	−1.50585	−0.752924	+	0.658107i	$0.771357\pi$
$12$	0.0262198	0.00756901
$13$	−3.87824	−1.07563	−0.537815	−	0.843063i	$-0.680750\pi$
$13$	−3.87824	−1.07563	−0.537815	+	0.843063i	$0.680750\pi$
$14$	−2.33696	−0.624578
$15$	0	0
$16$	1.05832	0.264579
$17$	−0.475637	−0.115359	−0.0576794	−	0.998335i	$-0.518370\pi$
$17$	−0.475637	−0.115359	−0.0576794	+	0.998335i	$0.518370\pi$
$18$	7.01073	1.65245
$19$	−1.54155	−0.353655	−0.176828	−	0.984242i	$-0.556583\pi$
$19$	−1.54155	−0.353655	−0.176828	+	0.984242i	$0.556583\pi$
$20$	0	0
$21$	0.00757499	0.00165300
$22$	11.6715	2.48838
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.0258697	−0.00528063
$25$	0	0
$26$	9.06327	1.77745
$27$	−0.0454495	−0.00874677
$28$	3.46136	0.654136
$29$	−9.38110	−1.74203	−0.871013	−	0.491259i	$-0.836537\pi$
$29$	−9.38110	−1.74203	−0.871013	+	0.491259i	$0.836537\pi$
$30$	0	0
$31$	−11.0814	−1.99028	−0.995141	−	0.0984581i	$-0.968609\pi$
$31$	−11.0814	−1.99028	−0.995141	+	0.0984581i	$0.968609\pi$
$32$	4.35705	0.770226
$33$	−0.0378321	−0.00658572
$34$	1.11154	0.190628
$35$	0	0
$36$	−10.3839	−1.73065
$37$	−4.42722	−0.727830	−0.363915	−	0.931432i	$-0.618560\pi$
$37$	−4.42722	−0.727830	−0.363915	+	0.931432i	$0.618560\pi$
$38$	3.60253	0.584407
$39$	−0.0293776	−0.00470419
$40$	0	0
$41$	3.21792	0.502555	0.251278	−	0.967915i	$-0.419149\pi$
$41$	3.21792	0.502555	0.251278	+	0.967915i	$0.419149\pi$
$42$	−0.0177024	−0.00273154
$43$	3.40274	0.518912	0.259456	−	0.965755i	$-0.416457\pi$
$43$	3.40274	0.518912	0.259456	+	0.965755i	$0.416457\pi$
$44$	−17.2872	−2.60615
$45$	0	0
$46$	−2.33696	−0.344565
$47$	−8.07320	−1.17760	−0.588799	−	0.808280i	$-0.700399\pi$
$47$	−8.07320	−1.17760	−0.588799	+	0.808280i	$0.700399\pi$
$48$	0.00801673	0.00115712
$49$	1.00000	0.142857
$50$	0	0
$51$	−0.00360295	−0.000504513 0
$52$	−13.4240	−1.86157
$53$	−1.46842	−0.201703	−0.100852	−	0.994901i	$-0.532157\pi$
$53$	−1.46842	−0.201703	−0.100852	+	0.994901i	$0.532157\pi$
$54$	0.106214	0.0144538
$55$	0	0
$56$	−3.41514	−0.456368
$57$	−0.0116772	−0.00154668
$58$	21.9232	2.87866
$59$	−11.8954	−1.54865	−0.774326	−	0.632787i	$-0.781911\pi$
$59$	−11.8954	−1.54865	−0.774326	+	0.632787i	$0.781911\pi$
$60$	0	0
$61$	8.24535	1.05571	0.527854	−	0.849335i	$-0.322997\pi$
$61$	8.24535	1.05571	0.527854	+	0.849335i	$0.322997\pi$
$62$	25.8968	3.28890
$63$	−2.99994	−0.377957
$64$	−12.2989	−1.53736
$65$	0	0
$66$	0.0884119	0.0108827
$67$	4.54321	0.555041	0.277521	−	0.960720i	$-0.410487\pi$
$67$	4.54321	0.555041	0.277521	+	0.960720i	$0.410487\pi$
$68$	−1.64635	−0.199650
$69$	0.00757499	0.000911922 0
$70$	0	0
$71$	11.0031	1.30583	0.652916	−	0.757430i	$-0.273545\pi$
$71$	11.0031	1.30583	0.652916	+	0.757430i	$0.273545\pi$
$72$	10.2452	1.20741
$73$	13.6586	1.59862	0.799308	−	0.600921i	$-0.205200\pi$
$73$	13.6586	1.59862	0.799308	+	0.600921i	$0.205200\pi$
$74$	10.3462	1.20272
$75$	0	0
$76$	−5.33586	−0.612065
$77$	−4.99434	−0.569157
$78$	0.0686542	0.00777356
$79$	13.1029	1.47419	0.737096	−	0.675788i	$-0.236197\pi$
$79$	13.1029	1.47419	0.737096	+	0.675788i	$0.236197\pi$
$80$	0	0
$81$	8.99948	0.999943
$82$	−7.52014	−0.830461
$83$	14.7630	1.62045	0.810225	−	0.586118i	$-0.199345\pi$
$83$	14.7630	1.62045	0.810225	+	0.586118i	$0.199345\pi$
$84$	0.0262198	0.00286082
$85$	0	0
$86$	−7.95205	−0.857491
$87$	−0.0710618	−0.00761862
$88$	17.0564	1.81822
$89$	−6.08219	−0.644710	−0.322355	−	0.946619i	$-0.604475\pi$
$89$	−6.08219	−0.644710	−0.322355	+	0.946619i	$0.604475\pi$
$90$	0	0
$91$	−3.87824	−0.406550
$92$	3.46136	0.360872
$93$	−0.0839417	−0.00870435
$94$	18.8667	1.94595
$95$	0	0
$96$	0.0330047	0.00336852
$97$	3.91724	0.397735	0.198867	−	0.980026i	$-0.436274\pi$
$97$	3.91724	0.397735	0.198867	+	0.980026i	$0.436274\pi$
$98$	−2.33696	−0.236068
$99$	14.9827	1.50582
$100$	0	0
$101$	2.79080	0.277695	0.138848	−	0.990314i	$-0.455660\pi$
$101$	2.79080	0.277695	0.138848	+	0.990314i	$0.455660\pi$
$102$	0.00841993	0.000833697 0
$103$	13.1299	1.29373	0.646863	−	0.762606i	$-0.276081\pi$
$103$	13.1299	1.29373	0.646863	+	0.762606i	$0.276081\pi$
$104$	13.2447	1.29875
$105$	0	0
$106$	3.43164	0.333310
$107$	−18.1208	−1.75181	−0.875903	−	0.482488i	$-0.839733\pi$
$107$	−18.1208	−1.75181	−0.875903	+	0.482488i	$0.839733\pi$
$108$	−0.157317	−0.0151379
$109$	−8.86577	−0.849186	−0.424593	−	0.905384i	$-0.639583\pi$
$109$	−8.86577	−0.849186	−0.424593	+	0.905384i	$0.639583\pi$
$110$	0	0
$111$	−0.0335361	−0.00318311
$112$	1.05832	0.100001
$113$	−5.71585	−0.537702	−0.268851	−	0.963182i	$-0.586644\pi$
$113$	−5.71585	−0.537702	−0.268851	+	0.963182i	$0.586644\pi$
$114$	0.0272891	0.00255586
$115$	0	0
$116$	−32.4714	−3.01489
$117$	11.6345	1.07561
$118$	27.7991	2.55911
$119$	−0.475637	−0.0436016
$120$	0	0
$121$	13.9434	1.26758
$122$	−19.2690	−1.74454
$123$	0.0243757	0.00219789
$124$	−38.3568	−3.44455
$125$	0	0
$126$	7.01073	0.624566
$127$	14.5563	1.29167	0.645833	−	0.763479i	$-0.276510\pi$
$127$	14.5563	1.29167	0.645833	+	0.763479i	$0.276510\pi$
$128$	20.0278	1.77023
$129$	0.0257757	0.00226942
$130$	0	0
$131$	−6.58099	−0.574984	−0.287492	−	0.957783i	$-0.592821\pi$
$131$	−6.58099	−0.574984	−0.287492	+	0.957783i	$0.592821\pi$
$132$	−0.130951	−0.0113978
$133$	−1.54155	−0.133669
$134$	−10.6173	−0.917193
$135$	0	0
$136$	1.62437	0.139288
$137$	−7.37371	−0.629978	−0.314989	−	0.949095i	$-0.602001\pi$
$137$	−7.37371	−0.629978	−0.314989	+	0.949095i	$0.602001\pi$
$138$	−0.0177024	−0.00150693
$139$	−11.7472	−0.996384	−0.498192	−	0.867067i	$-0.666003\pi$
$139$	−11.7472	−0.996384	−0.498192	+	0.867067i	$0.666003\pi$
$140$	0	0
$141$	−0.0611545	−0.00515014
$142$	−25.7138	−2.15786
$143$	19.3692	1.61974
$144$	−3.17488	−0.264574
$145$	0	0
$146$	−31.9195	−2.64168
$147$	0.00757499	0.000624775 0
$148$	−15.3242	−1.25964
$149$	0.282601	0.0231516	0.0115758	−	0.999933i	$-0.496315\pi$
$149$	0.282601	0.0231516	0.0115758	+	0.999933i	$0.496315\pi$
$150$	0	0
$151$	19.5423	1.59033	0.795166	−	0.606391i	$-0.207384\pi$
$151$	19.5423	1.59033	0.795166	+	0.606391i	$0.207384\pi$
$152$	5.26461	0.427016
$153$	1.42688	0.115357
$154$	11.6715	0.940520
$155$	0	0
$156$	−0.101687	−0.00814145
$157$	−23.7122	−1.89244	−0.946220	−	0.323523i	$-0.895133\pi$
$157$	−23.7122	−1.89244	−0.946220	+	0.323523i	$0.895133\pi$
$158$	−30.6209	−2.43607
$159$	−0.0111233	−0.000882134 0
$160$	0	0
$161$	1.00000	0.0788110
$162$	−21.0314	−1.65238
$163$	0.0532661	0.00417212	0.00208606	−	0.999998i	$-0.499336\pi$
$163$	0.0532661	0.00417212	0.00208606	+	0.999998i	$0.499336\pi$
$164$	11.1384	0.869763
$165$	0	0
$166$	−34.5005	−2.67776
$167$	6.63072	0.513101	0.256550	−	0.966531i	$-0.417414\pi$
$167$	6.63072	0.513101	0.256550	+	0.966531i	$0.417414\pi$
$168$	−0.0258697	−0.00199589
$169$	2.04074	0.156980
$170$	0	0
$171$	4.62455	0.353648
$172$	11.7781	0.898073
$173$	−6.76778	−0.514545	−0.257273	−	0.966339i	$-0.582824\pi$
$173$	−6.76778	−0.514545	−0.257273	+	0.966339i	$0.582824\pi$
$174$	0.166068	0.0125896
$175$	0	0
$176$	−5.28558	−0.398416
$177$	−0.0901077	−0.00677291
$178$	14.2138	1.06537
$179$	9.48534	0.708967	0.354484	−	0.935062i	$-0.384657\pi$
$179$	9.48534	0.708967	0.354484	+	0.935062i	$0.384657\pi$
$180$	0	0
$181$	18.0503	1.34167	0.670834	−	0.741607i	$-0.265936\pi$
$181$	18.0503	1.34167	0.670834	+	0.741607i	$0.265936\pi$
$182$	9.06327	0.671815
$183$	0.0624585	0.00461706
$184$	−3.41514	−0.251768
$185$	0	0
$186$	0.196168	0.0143837
$187$	2.37549	0.173713
$188$	−27.9443	−2.03805
$189$	−0.0454495	−0.00330597
$190$	0	0
$191$	−23.6976	−1.71470	−0.857349	−	0.514735i	$-0.827890\pi$
$191$	−23.6976	−1.71470	−0.857349	+	0.514735i	$0.827890\pi$
$192$	−0.0931639	−0.00672352
$193$	14.5036	1.04399	0.521995	−	0.852948i	$-0.325188\pi$
$193$	14.5036	1.04399	0.521995	+	0.852948i	$0.325188\pi$
$194$	−9.15441	−0.657248
$195$	0	0
$196$	3.46136	0.247240
$197$	2.63536	0.187762	0.0938809	−	0.995583i	$-0.470073\pi$
$197$	2.63536	0.187762	0.0938809	+	0.995583i	$0.470073\pi$
$198$	−35.0140	−2.48833
$199$	−19.5257	−1.38414	−0.692070	−	0.721830i	$-0.743301\pi$
$199$	−19.5257	−1.38414	−0.692070	+	0.721830i	$0.743301\pi$
$200$	0	0
$201$	0.0344148	0.00242743
$202$	−6.52198	−0.458885
$203$	−9.38110	−0.658424
$204$	−0.0124711	−0.000873152 0
$205$	0	0
$206$	−30.6840	−2.13785
$207$	−2.99994	−0.208510
$208$	−4.10440	−0.284589
$209$	7.69900	0.532551
$210$	0	0
$211$	−10.5337	−0.725168	−0.362584	−	0.931951i	$-0.618105\pi$
$211$	−10.5337	−0.725168	−0.362584	+	0.931951i	$0.618105\pi$
$212$	−5.08274	−0.349084
$213$	0.0833487	0.00571096
$214$	42.3476	2.89482
$215$	0	0
$216$	0.155217	0.0105612
$217$	−11.0814	−0.752256
$218$	20.7189	1.40326
$219$	0.103464	0.00699143
$220$	0	0
$221$	1.84463	0.124083
$222$	0.0783725	0.00526002
$223$	15.2356	1.02025	0.510127	−	0.860099i	$-0.329598\pi$
$223$	15.2356	1.02025	0.510127	+	0.860099i	$0.329598\pi$
$224$	4.35705	0.291118
$225$	0	0
$226$	13.3577	0.888540
$227$	−27.4434	−1.82148	−0.910740	−	0.412980i	$-0.864488\pi$
$227$	−27.4434	−1.82148	−0.910740	+	0.412980i	$0.864488\pi$
$228$	−0.0404191	−0.00267682
$229$	29.8273	1.97105	0.985523	−	0.169540i	$-0.0542283\pi$
$229$	29.8273	1.97105	0.985523	+	0.169540i	$0.0542283\pi$
$230$	0	0
$231$	−0.0378321	−0.00248917
$232$	32.0378	2.10339
$233$	−22.9219	−1.50166	−0.750832	−	0.660494i	$-0.770347\pi$
$233$	−22.9219	−1.50166	−0.750832	+	0.660494i	$0.770347\pi$
$234$	−27.1893	−1.77742
$235$	0	0
$236$	−41.1744	−2.68022
$237$	0.0992544	0.00644727
$238$	1.11154	0.0720506
$239$	15.2760	0.988122	0.494061	−	0.869427i	$-0.335512\pi$
$239$	15.2760	0.988122	0.494061	+	0.869427i	$0.335512\pi$
$240$	0	0
$241$	5.89087	0.379464	0.189732	−	0.981836i	$-0.439238\pi$
$241$	5.89087	0.379464	0.189732	+	0.981836i	$0.439238\pi$
$242$	−32.5851	−2.09465
$243$	0.204520	0.0131199
$244$	28.5402	1.82710
$245$	0	0
$246$	−0.0569650	−0.00363196
$247$	5.97849	0.380402
$248$	37.8447	2.40314
$249$	0.111830	0.00708692
$250$	0	0
$251$	4.08671	0.257951	0.128975	−	0.991648i	$-0.458831\pi$
$251$	4.08671	0.257951	0.128975	+	0.991648i	$0.458831\pi$
$252$	−10.3839	−0.654124
$253$	−4.99434	−0.313991
$254$	−34.0175	−2.13445
$255$	0	0
$256$	−22.2064	−1.38790
$257$	19.2722	1.20216	0.601082	−	0.799187i	$-0.294736\pi$
$257$	19.2722	1.20216	0.601082	+	0.799187i	$0.294736\pi$
$258$	−0.0602367	−0.00375017
$259$	−4.42722	−0.275094
$260$	0	0
$261$	28.1428	1.74199
$262$	15.3795	0.950148
$263$	−25.2660	−1.55797	−0.778984	−	0.627044i	$-0.784264\pi$
$263$	−25.2660	−1.55797	−0.778984	+	0.627044i	$0.784264\pi$
$264$	0.129202	0.00795183
$265$	0	0
$266$	3.60253	0.220885
$267$	−0.0460725	−0.00281959
$268$	15.7257	0.960600
$269$	7.84347	0.478225	0.239112	−	0.970992i	$-0.423144\pi$
$269$	7.84347	0.478225	0.239112	+	0.970992i	$0.423144\pi$
$270$	0	0
$271$	−19.5068	−1.18495	−0.592477	−	0.805588i	$-0.701850\pi$
$271$	−19.5068	−1.18495	−0.592477	+	0.805588i	$0.701850\pi$
$272$	−0.503374	−0.0305215
$273$	−0.0293776	−0.00177802
$274$	17.2320	1.04103
$275$	0	0
$276$	0.0262198	0.00157825
$277$	24.9162	1.49707	0.748534	−	0.663097i	$-0.230758\pi$
$277$	24.9162	1.49707	0.748534	+	0.663097i	$0.230758\pi$
$278$	27.4527	1.64650
$279$	33.2436	1.99024
$280$	0	0
$281$	−2.78384	−0.166070	−0.0830349	−	0.996547i	$-0.526461\pi$
$281$	−2.78384	−0.166070	−0.0830349	+	0.996547i	$0.526461\pi$
$282$	0.142915	0.00851048
$283$	−12.1104	−0.719891	−0.359946	−	0.932973i	$-0.617205\pi$
$283$	−12.1104	−0.719891	−0.359946	+	0.932973i	$0.617205\pi$
$284$	38.0859	2.25998
$285$	0	0
$286$	−45.2650	−2.67658
$287$	3.21792	0.189948
$288$	−13.0709	−0.770211
$289$	−16.7738	−0.986692
$290$	0	0
$291$	0.0296730	0.00173946
$292$	47.2773	2.76670
$293$	−0.650821	−0.0380214	−0.0190107	−	0.999819i	$-0.506052\pi$
$293$	−0.650821	−0.0380214	−0.0190107	+	0.999819i	$0.506052\pi$
$294$	−0.0177024	−0.00103243
$295$	0	0
$296$	15.1196	0.878808
$297$	0.226990	0.0131713
$298$	−0.660427	−0.0382575
$299$	−3.87824	−0.224284
$300$	0	0
$301$	3.40274	0.196130
$302$	−45.6696	−2.62799
$303$	0.0211403	0.00121448
$304$	−1.63144	−0.0935697
$305$	0	0
$306$	−3.33456	−0.190624
$307$	22.5537	1.28721	0.643603	−	0.765359i	$-0.277439\pi$
$307$	22.5537	1.28721	0.643603	+	0.765359i	$0.277439\pi$
$308$	−17.2872	−0.985031
$309$	0.0994587	0.00565801
$310$	0	0
$311$	25.7851	1.46214	0.731069	−	0.682303i	$-0.239022\pi$
$311$	25.7851	1.46214	0.731069	+	0.682303i	$0.239022\pi$
$312$	0.100329	0.00568000
$313$	5.58377	0.315613	0.157807	−	0.987470i	$-0.449558\pi$
$313$	5.58377	0.315613	0.157807	+	0.987470i	$0.449558\pi$
$314$	55.4144	3.12722
$315$	0	0
$316$	45.3539	2.55136
$317$	−4.35295	−0.244486	−0.122243	−	0.992500i	$-0.539009\pi$
$317$	−4.35295	−0.244486	−0.122243	+	0.992500i	$0.539009\pi$
$318$	0.0259946	0.00145771
$319$	46.8524	2.62323
$320$	0	0
$321$	−0.137265	−0.00766139
$322$	−2.33696	−0.130233
$323$	0.733217	0.0407973
$324$	31.1505	1.73058
$325$	0	0
$326$	−0.124480	−0.00689434
$327$	−0.0671581	−0.00371385
$328$	−10.9897	−0.606803
$329$	−8.07320	−0.445090
$330$	0	0
$331$	−10.7648	−0.591685	−0.295842	−	0.955237i	$-0.595600\pi$
$331$	−10.7648	−0.591685	−0.295842	+	0.955237i	$0.595600\pi$
$332$	51.1002	2.80449
$333$	13.2814	0.727816
$334$	−15.4957	−0.847888
$335$	0	0
$336$	0.00801673	0.000437349 0
$337$	−0.415084	−0.0226111	−0.0113055	−	0.999936i	$-0.503599\pi$
$337$	−0.415084	−0.0226111	−0.0113055	+	0.999936i	$0.503599\pi$
$338$	−4.76911	−0.259405
$339$	−0.0432975	−0.00235160
$340$	0	0
$341$	55.3443	2.99706
$342$	−10.8074	−0.584396
$343$	1.00000	0.0539949
$344$	−11.6208	−0.626554
$345$	0	0
$346$	15.8160	0.850274
$347$	−4.09489	−0.219825	−0.109913	−	0.993941i	$-0.535057\pi$
$347$	−4.09489	−0.219825	−0.109913	+	0.993941i	$0.535057\pi$
$348$	−0.245971	−0.0131854
$349$	−4.93152	−0.263978	−0.131989	−	0.991251i	$-0.542136\pi$
$349$	−4.93152	−0.263978	−0.131989	+	0.991251i	$0.542136\pi$
$350$	0	0
$351$	0.176264	0.00940828
$352$	−21.7606	−1.15984
$353$	14.1977	0.755667	0.377833	−	0.925874i	$-0.376669\pi$
$353$	14.1977	0.755667	0.377833	+	0.925874i	$0.376669\pi$
$354$	0.210578	0.0111921
$355$	0	0
$356$	−21.0527	−1.11579
$357$	−0.00360295	−0.000190688 0
$358$	−22.1668	−1.17155
$359$	−24.5208	−1.29416	−0.647078	−	0.762424i	$-0.724009\pi$
$359$	−24.5208	−1.29416	−0.647078	+	0.762424i	$0.724009\pi$
$360$	0	0
$361$	−16.6236	−0.874928
$362$	−42.1828	−2.21708
$363$	0.105621	0.00554367
$364$	−13.4240	−0.703609
$365$	0	0
$366$	−0.145963	−0.00762959
$367$	−16.4023	−0.856191	−0.428096	−	0.903733i	$-0.640815\pi$
$367$	−16.4023	−0.856191	−0.428096	+	0.903733i	$0.640815\pi$
$368$	1.05832	0.0551685
$369$	−9.65358	−0.502546
$370$	0	0
$371$	−1.46842	−0.0762367
$372$	−0.290553	−0.0150645
$373$	−3.44368	−0.178307	−0.0891535	−	0.996018i	$-0.528416\pi$
$373$	−3.44368	−0.178307	−0.0891535	+	0.996018i	$0.528416\pi$
$374$	−5.55142	−0.287057
$375$	0	0
$376$	27.5712	1.42187
$377$	36.3822	1.87378
$378$	0.106214	0.00546304
$379$	−3.28827	−0.168907	−0.0844536	−	0.996427i	$-0.526914\pi$
$379$	−3.28827	−0.168907	−0.0844536	+	0.996427i	$0.526914\pi$
$380$	0	0
$381$	0.110264	0.00564900
$382$	55.3803	2.83350
$383$	−18.1838	−0.929151	−0.464576	−	0.885533i	$-0.653793\pi$
$383$	−18.1838	−0.929151	−0.464576	+	0.885533i	$0.653793\pi$
$384$	0.151711	0.00774195
$385$	0	0
$386$	−33.8942	−1.72517
$387$	−10.2080	−0.518903
$388$	13.5590	0.688353
$389$	−27.9376	−1.41649	−0.708246	−	0.705966i	$-0.750513\pi$
$389$	−27.9376	−1.41649	−0.708246	+	0.705966i	$0.750513\pi$
$390$	0	0
$391$	−0.475637	−0.0240540
$392$	−3.41514	−0.172491
$393$	−0.0498510	−0.00251465
$394$	−6.15872	−0.310272
$395$	0	0
$396$	51.8607	2.60610
$397$	−20.5903	−1.03340	−0.516699	−	0.856167i	$-0.672839\pi$
$397$	−20.5903	−1.03340	−0.516699	+	0.856167i	$0.672839\pi$
$398$	45.6307	2.28726
$399$	−0.0116772	−0.000584592 0
$400$	0	0
$401$	0.448572	0.0224006	0.0112003	−	0.999937i	$-0.496435\pi$
$401$	0.448572	0.0224006	0.0112003	+	0.999937i	$0.496435\pi$
$402$	−0.0804258	−0.00401127
$403$	42.9764	2.14081
$404$	9.65998	0.480602
$405$	0	0
$406$	21.9232	1.08803
$407$	22.1110	1.09600
$408$	0.0123046	0.000609168 0
$409$	−6.40103	−0.316511	−0.158255	−	0.987398i	$-0.550587\pi$
$409$	−6.40103	−0.316511	−0.158255	+	0.987398i	$0.550587\pi$
$410$	0	0
$411$	−0.0558558	−0.00275516
$412$	45.4473	2.23903
$413$	−11.8954	−0.585335
$414$	7.01073	0.344559
$415$	0	0
$416$	−16.8977	−0.828478
$417$	−0.0889850	−0.00435761
$418$	−17.9922	−0.880029
$419$	−8.49010	−0.414768	−0.207384	−	0.978260i	$-0.566495\pi$
$419$	−8.49010	−0.414768	−0.207384	+	0.978260i	$0.566495\pi$
$420$	0	0
$421$	−25.3915	−1.23751	−0.618753	−	0.785585i	$-0.712362\pi$
$421$	−25.3915	−1.23751	−0.618753	+	0.785585i	$0.712362\pi$
$422$	24.6167	1.19832
$423$	24.2192	1.17758
$424$	5.01487	0.243544
$425$	0	0
$426$	−0.194782	−0.00943723
$427$	8.24535	0.399020
$428$	−62.7227	−3.03182
$429$	0.146722	0.00708379
$430$	0	0
$431$	19.3251	0.930857	0.465428	−	0.885086i	$-0.345900\pi$
$431$	19.3251	0.930857	0.465428	+	0.885086i	$0.345900\pi$
$432$	−0.0480999	−0.00231421
$433$	35.6715	1.71426	0.857132	−	0.515097i	$-0.172244\pi$
$433$	35.6715	1.71426	0.857132	+	0.515097i	$0.172244\pi$
$434$	25.8968	1.24309
$435$	0	0
$436$	−30.6876	−1.46967
$437$	−1.54155	−0.0737422
$438$	−0.241790	−0.0115532
$439$	−18.2969	−0.873261	−0.436631	−	0.899641i	$-0.643828\pi$
$439$	−18.2969	−0.873261	−0.436631	+	0.899641i	$0.643828\pi$
$440$	0	0
$441$	−2.99994	−0.142854
$442$	−4.31083	−0.205045
$443$	−4.02535	−0.191250	−0.0956251	−	0.995417i	$-0.530485\pi$
$443$	−4.02535	−0.191250	−0.0956251	+	0.995417i	$0.530485\pi$
$444$	−0.116081	−0.00550895
$445$	0	0
$446$	−35.6050	−1.68595
$447$	0.00214070	0.000101252 0
$448$	−12.2989	−0.581067
$449$	29.7863	1.40570	0.702851	−	0.711337i	$-0.251910\pi$
$449$	29.7863	1.40570	0.702851	+	0.711337i	$0.251910\pi$
$450$	0	0
$451$	−16.0714	−0.756772
$452$	−19.7846	−0.930591
$453$	0.148033	0.00695520
$454$	64.1339	3.00996
$455$	0	0
$456$	0.0398794	0.00186752
$457$	−19.5513	−0.914572	−0.457286	−	0.889320i	$-0.651178\pi$
$457$	−19.5513	−0.914572	−0.457286	+	0.889320i	$0.651178\pi$
$458$	−69.7052	−3.25711
$459$	0.0216175	0.00100902
$460$	0	0
$461$	0.191900	0.00893768	0.00446884	−	0.999990i	$-0.498578\pi$
$461$	0.191900	0.00893768	0.00446884	+	0.999990i	$0.498578\pi$
$462$	0.0884119	0.00411329
$463$	26.2178	1.21845	0.609223	−	0.792999i	$-0.291481\pi$
$463$	26.2178	1.21845	0.609223	+	0.792999i	$0.291481\pi$
$464$	−9.92816	−0.460903
$465$	0	0
$466$	53.5675	2.48147
$467$	41.2187	1.90737	0.953687	−	0.300799i	$-0.0972535\pi$
$467$	41.2187	1.90737	0.953687	+	0.300799i	$0.0972535\pi$
$468$	40.2712	1.86154
$469$	4.54321	0.209786
$470$	0	0
$471$	−0.179620	−0.00827645
$472$	40.6246	1.86990
$473$	−16.9944	−0.781404
$474$	−0.231953	−0.0106540
$475$	0	0
$476$	−1.64635	−0.0754604
$477$	4.40518	0.201699
$478$	−35.6993	−1.63285
$479$	−4.54688	−0.207752	−0.103876	−	0.994590i	$-0.533125\pi$
$479$	−4.54688	−0.207752	−0.103876	+	0.994590i	$0.533125\pi$
$480$	0	0
$481$	17.1698	0.782876
$482$	−13.7667	−0.627056
$483$	0.00757499	0.000344674 0
$484$	48.2632	2.19378
$485$	0	0
$486$	−0.477953	−0.0216804
$487$	9.38327	0.425197	0.212598	−	0.977140i	$-0.431807\pi$
$487$	9.38327	0.425197	0.212598	+	0.977140i	$0.431807\pi$
$488$	−28.1591	−1.27470
$489$	0.000403490 0	1.82465e−5 0
$490$	0	0
$491$	24.4624	1.10397	0.551987	−	0.833853i	$-0.313870\pi$
$491$	24.4624	1.10397	0.551987	+	0.833853i	$0.313870\pi$
$492$	0.0843733	0.00380384
$493$	4.46200	0.200958
$494$	−13.9715	−0.628606
$495$	0	0
$496$	−11.7276	−0.526587
$497$	11.0031	0.493558
$498$	−0.261341	−0.0117110
$499$	9.26057	0.414560	0.207280	−	0.978282i	$-0.433539\pi$
$499$	9.26057	0.414560	0.207280	+	0.978282i	$0.433539\pi$
$500$	0	0
$501$	0.0502277	0.00224401
$502$	−9.55045	−0.426258
$503$	5.76022	0.256836	0.128418	−	0.991720i	$-0.459010\pi$
$503$	5.76022	0.256836	0.128418	+	0.991720i	$0.459010\pi$
$504$	10.2452	0.456359
$505$	0	0
$506$	11.6715	0.518863
$507$	0.0154586	0.000686539 0
$508$	50.3848	2.23546
$509$	10.7526	0.476600	0.238300	−	0.971192i	$-0.423410\pi$
$509$	10.7526	0.476600	0.238300	+	0.971192i	$0.423410\pi$
$510$	0	0
$511$	13.6586	0.604220
$512$	11.8397	0.523247
$513$	0.0700626	0.00309334
$514$	−45.0382	−1.98655
$515$	0	0
$516$	0.0892191	0.00392765
$517$	40.3203	1.77328
$518$	10.3462	0.454586
$519$	−0.0512659	−0.00225032
$520$	0	0
$521$	1.29984	0.0569470	0.0284735	−	0.999595i	$-0.490935\pi$
$521$	1.29984	0.0569470	0.0284735	+	0.999595i	$0.490935\pi$
$522$	−65.7684	−2.87861
$523$	−4.59165	−0.200779	−0.100390	−	0.994948i	$-0.532009\pi$
$523$	−4.59165	−0.200779	−0.100390	+	0.994948i	$0.532009\pi$
$524$	−22.7792	−0.995114
$525$	0	0
$526$	59.0455	2.57451
$527$	5.27073	0.229597
$528$	−0.0400382	−0.00174244
$529$	1.00000	0.0434783
$530$	0	0
$531$	35.6856	1.54862
$532$	−5.33586	−0.231339
$533$	−12.4799	−0.540563
$534$	0.107669	0.00465931
$535$	0	0
$536$	−15.5157	−0.670177
$537$	0.0718514	0.00310062
$538$	−18.3298	−0.790256
$539$	−4.99434	−0.215121
$540$	0	0
$541$	34.9259	1.50158	0.750791	−	0.660540i	$-0.229673\pi$
$541$	34.9259	1.50158	0.750791	+	0.660540i	$0.229673\pi$
$542$	45.5865	1.95811
$543$	0.136731	0.00586769
$544$	−2.07238	−0.0888524
$545$	0	0
$546$	0.0686542	0.00293813
$547$	27.0941	1.15846	0.579229	−	0.815165i	$-0.303354\pi$
$547$	27.0941	1.15846	0.579229	+	0.815165i	$0.303354\pi$
$548$	−25.5231	−1.09029
$549$	−24.7356	−1.05569
$550$	0	0
$551$	14.4614	0.616077
$552$	−0.0258697	−0.00110109
$553$	13.1029	0.557192
$554$	−58.2280	−2.47387
$555$	0	0
$556$	−40.6613	−1.72442
$557$	23.9676	1.01554	0.507770	−	0.861492i	$-0.330470\pi$
$557$	23.9676	1.01554	0.507770	+	0.861492i	$0.330470\pi$
$558$	−77.6889	−3.28883
$559$	−13.1966	−0.558158
$560$	0	0
$561$	0.0179943	0.000759721 0
$562$	6.50571	0.274427
$563$	33.5325	1.41323	0.706613	−	0.707601i	$-0.250222\pi$
$563$	33.5325	1.41323	0.706613	+	0.707601i	$0.250222\pi$
$564$	−0.211678	−0.00891325
$565$	0	0
$566$	28.3016	1.18960
$567$	8.99948	0.377943
$568$	−37.5773	−1.57671
$569$	−8.02616	−0.336474	−0.168237	−	0.985747i	$-0.553807\pi$
$569$	−8.02616	−0.336474	−0.168237	+	0.985747i	$0.553807\pi$
$570$	0	0
$571$	9.76773	0.408767	0.204383	−	0.978891i	$-0.434481\pi$
$571$	9.76773	0.408767	0.204383	+	0.978891i	$0.434481\pi$
$572$	67.0440	2.80325
$573$	−0.179509	−0.00749911
$574$	−7.52014	−0.313885
$575$	0	0
$576$	36.8959	1.53733
$577$	4.38607	0.182595	0.0912973	−	0.995824i	$-0.470899\pi$
$577$	4.38607	0.182595	0.0912973	+	0.995824i	$0.470899\pi$
$578$	39.1996	1.63049
$579$	0.109865	0.00456581
$580$	0	0
$581$	14.7630	0.612473
$582$	−0.0693446	−0.00287442
$583$	7.33379	0.303735
$584$	−46.6460	−1.93023
$585$	0	0
$586$	1.52094	0.0628295
$587$	−18.7391	−0.773445	−0.386723	−	0.922196i	$-0.626393\pi$
$587$	−18.7391	−0.773445	−0.386723	+	0.922196i	$0.626393\pi$
$588$	0.0262198	0.00108129
$589$	17.0825	0.703874
$590$	0	0
$591$	0.0199628	0.000821162 0
$592$	−4.68539	−0.192568
$593$	−22.0316	−0.904731	−0.452366	−	0.891833i	$-0.649420\pi$
$593$	−22.0316	−0.904731	−0.452366	+	0.891833i	$0.649420\pi$
$594$	−0.530466	−0.0217653
$595$	0	0
$596$	0.978186	0.0400681
$597$	−0.147907	−0.00605343
$598$	9.06327	0.370625
$599$	0.514129	0.0210067	0.0105034	−	0.999945i	$-0.496657\pi$
$599$	0.514129	0.0210067	0.0105034	+	0.999945i	$0.496657\pi$
$600$	0	0
$601$	−37.8191	−1.54267	−0.771337	−	0.636427i	$-0.780412\pi$
$601$	−37.8191	−1.54267	−0.771337	+	0.636427i	$0.780412\pi$
$602$	−7.95205	−0.324101
$603$	−13.6294	−0.555030
$604$	67.6431	2.75236
$605$	0	0
$606$	−0.0494040	−0.00200690
$607$	−41.2268	−1.67334	−0.836672	−	0.547704i	$-0.815502\pi$
$607$	−41.2268	−1.67334	−0.836672	+	0.547704i	$0.815502\pi$
$608$	−6.71660	−0.272394
$609$	−0.0710618	−0.00287957
$610$	0	0
$611$	31.3098	1.26666
$612$	4.93896	0.199646
$613$	0.810033	0.0327169	0.0163585	−	0.999866i	$-0.494793\pi$
$613$	0.810033	0.0327169	0.0163585	+	0.999866i	$0.494793\pi$
$614$	−52.7069	−2.12708
$615$	0	0
$616$	17.0564	0.687221
$617$	21.8594	0.880025	0.440012	−	0.897992i	$-0.354974\pi$
$617$	21.8594	0.880025	0.440012	+	0.897992i	$0.354974\pi$
$618$	−0.232431	−0.00934974
$619$	−1.80602	−0.0725901	−0.0362950	−	0.999341i	$-0.511556\pi$
$619$	−1.80602	−0.0725901	−0.0362950	+	0.999341i	$0.511556\pi$
$620$	0	0
$621$	−0.0454495	−0.00182383
$622$	−60.2586	−2.41615
$623$	−6.08219	−0.243678
$624$	−0.0310908	−0.00124463
$625$	0	0
$626$	−13.0490	−0.521544
$627$	0.0583199	0.00232907
$628$	−82.0766	−3.27521
$629$	2.10575	0.0839616
$630$	0	0
$631$	42.9474	1.70971	0.854854	−	0.518869i	$-0.173647\pi$
$631$	42.9474	1.70971	0.854854	+	0.518869i	$0.173647\pi$
$632$	−44.7483	−1.77999
$633$	−0.0797925	−0.00317147
$634$	10.1726	0.404007
$635$	0	0
$636$	−0.0385018	−0.00152669
$637$	−3.87824	−0.153661
$638$	−109.492	−4.33483
$639$	−33.0088	−1.30581
$640$	0	0
$641$	40.7586	1.60987	0.804933	−	0.593365i	$-0.202201\pi$
$641$	40.7586	1.60987	0.804933	+	0.593365i	$0.202201\pi$
$642$	0.320782	0.0126603
$643$	40.0053	1.57765	0.788827	−	0.614615i	$-0.210689\pi$
$643$	40.0053	1.57765	0.788827	+	0.614615i	$0.210689\pi$
$644$	3.46136	0.136397
$645$	0	0
$646$	−1.71350	−0.0674166
$647$	12.2909	0.483207	0.241604	−	0.970375i	$-0.422327\pi$
$647$	12.2909	0.483207	0.241604	+	0.970375i	$0.422327\pi$
$648$	−30.7345	−1.20737
$649$	59.4097	2.33203
$650$	0	0
$651$	−0.0839417	−0.00328993
$652$	0.184373	0.00722061
$653$	18.1745	0.711221	0.355611	−	0.934634i	$-0.384273\pi$
$653$	18.1745	0.711221	0.355611	+	0.934634i	$0.384273\pi$
$654$	0.156946	0.00613706
$655$	0	0
$656$	3.40558	0.132965
$657$	−40.9750	−1.59859
$658$	18.8667	0.735502
$659$	4.72077	0.183895	0.0919476	−	0.995764i	$-0.470691\pi$
$659$	4.72077	0.183895	0.0919476	+	0.995764i	$0.470691\pi$
$660$	0	0
$661$	−32.3257	−1.25732	−0.628662	−	0.777679i	$-0.716397\pi$
$661$	−32.3257	−1.25732	−0.628662	+	0.777679i	$0.716397\pi$
$662$	25.1568	0.977746
$663$	0.0139731	0.000542670 0
$664$	−50.4178	−1.95659
$665$	0	0
$666$	−31.0380	−1.20270
$667$	−9.38110	−0.363238
$668$	22.9514	0.888014
$669$	0.115410	0.00446200
$670$	0	0
$671$	−41.1800	−1.58974
$672$	0.0330047	0.00127318
$673$	−24.3701	−0.939398	−0.469699	−	0.882827i	$-0.655637\pi$
$673$	−24.3701	−0.939398	−0.469699	+	0.882827i	$0.655637\pi$
$674$	0.970033	0.0373643
$675$	0	0
$676$	7.06373	0.271682
$677$	4.98060	0.191420	0.0957101	−	0.995409i	$-0.469488\pi$
$677$	4.98060	0.191420	0.0957101	+	0.995409i	$0.469488\pi$
$678$	0.101184	0.00388596
$679$	3.91724	0.150330
$680$	0	0
$681$	−0.207883	−0.00796611
$682$	−129.337	−4.95258
$683$	46.8124	1.79122	0.895612	−	0.444835i	$-0.146738\pi$
$683$	46.8124	1.79122	0.895612	+	0.444835i	$0.146738\pi$
$684$	16.0073	0.612053
$685$	0	0
$686$	−2.33696	−0.0892254
$687$	0.225942	0.00862022
$688$	3.60117	0.137293
$689$	5.69489	0.216958
$690$	0	0
$691$	−33.7972	−1.28571	−0.642853	−	0.765990i	$-0.722249\pi$
$691$	−33.7972	−1.28571	−0.642853	+	0.765990i	$0.722249\pi$
$692$	−23.4258	−0.890514
$693$	14.9827	0.569147
$694$	9.56957	0.363256
$695$	0	0
$696$	0.242686	0.00919900
$697$	−1.53056	−0.0579742
$698$	11.5248	0.436218
$699$	−0.173633	−0.00656741
$700$	0	0
$701$	3.84137	0.145087	0.0725433	−	0.997365i	$-0.476888\pi$
$701$	3.84137	0.145087	0.0725433	+	0.997365i	$0.476888\pi$
$702$	−0.411922	−0.0155470
$703$	6.82476	0.257401
$704$	61.4247	2.31503
$705$	0	0
$706$	−33.1794	−1.24872
$707$	2.79080	0.104959
$708$	−0.311896	−0.0117218
$709$	−16.3215	−0.612966	−0.306483	−	0.951876i	$-0.599152\pi$
$709$	−16.3215	−0.612966	−0.306483	+	0.951876i	$0.599152\pi$
$710$	0	0
$711$	−39.3080	−1.47416
$712$	20.7715	0.778447
$713$	−11.0814	−0.415003
$714$	0.00841993	0.000315108 0
$715$	0	0
$716$	32.8322	1.22700
$717$	0.115716	0.00432148
$718$	57.3039	2.13856
$719$	22.4621	0.837694	0.418847	−	0.908057i	$-0.362434\pi$
$719$	22.4621	0.837694	0.418847	+	0.908057i	$0.362434\pi$
$720$	0	0
$721$	13.1299	0.488982
$722$	38.8487	1.44580
$723$	0.0446233	0.00165956
$724$	62.4787	2.32200
$725$	0	0
$726$	−0.246832	−0.00916079
$727$	22.6321	0.839378	0.419689	−	0.907668i	$-0.362139\pi$
$727$	22.6321	0.839378	0.419689	+	0.907668i	$0.362139\pi$
$728$	13.2447	0.490883
$729$	−26.9969	−0.999885
$730$	0	0
$731$	−1.61847	−0.0598612
$732$	0.216192	0.00799067
$733$	39.9481	1.47552	0.737758	−	0.675065i	$-0.235884\pi$
$733$	39.9481	1.47552	0.737758	+	0.675065i	$0.235884\pi$
$734$	38.3314	1.41484
$735$	0	0
$736$	4.35705	0.160603
$737$	−22.6903	−0.835808
$738$	22.5600	0.830445
$739$	−30.1882	−1.11049	−0.555246	−	0.831686i	$-0.687376\pi$
$739$	−30.1882	−1.11049	−0.555246	+	0.831686i	$0.687376\pi$
$740$	0	0
$741$	0.0452870	0.00166366
$742$	3.43164	0.125979
$743$	−31.0282	−1.13831	−0.569156	−	0.822229i	$-0.692730\pi$
$743$	−31.0282	−1.13831	−0.569156	+	0.822229i	$0.692730\pi$
$744$	0.286673	0.0105099
$745$	0	0
$746$	8.04773	0.294648
$747$	−44.2882	−1.62042
$748$	8.22244	0.300642
$749$	−18.1208	−0.662120
$750$	0	0
$751$	39.9950	1.45944	0.729720	−	0.683746i	$-0.239651\pi$
$751$	39.9950	1.45944	0.729720	+	0.683746i	$0.239651\pi$
$752$	−8.54400	−0.311567
$753$	0.0309568	0.00112813
$754$	−85.0235	−3.09637
$755$	0	0
$756$	−0.157317	−0.00572158
$757$	−35.1223	−1.27654	−0.638270	−	0.769812i	$-0.720350\pi$
$757$	−35.1223	−1.27654	−0.638270	+	0.769812i	$0.720350\pi$
$758$	7.68455	0.279115
$759$	−0.0378321	−0.00137322
$760$	0	0
$761$	5.62354	0.203853	0.101927	−	0.994792i	$-0.467499\pi$
$761$	5.62354	0.203853	0.101927	+	0.994792i	$0.467499\pi$
$762$	−0.257682	−0.00933485
$763$	−8.86577	−0.320962
$764$	−82.0261	−2.96760
$765$	0	0
$766$	42.4949	1.53540
$767$	46.1333	1.66578
$768$	−0.168213	−0.00606988
$769$	−29.0696	−1.04828	−0.524138	−	0.851634i	$-0.675612\pi$
$769$	−29.0696	−1.04828	−0.524138	+	0.851634i	$0.675612\pi$
$770$	0	0
$771$	0.145986	0.00525758
$772$	50.2022	1.80682
$773$	−32.3579	−1.16383	−0.581917	−	0.813248i	$-0.697697\pi$
$773$	−32.3579	−1.16383	−0.581917	+	0.813248i	$0.697697\pi$
$774$	23.8557	0.857475
$775$	0	0
$776$	−13.3779	−0.480240
$777$	−0.0335361	−0.00120310
$778$	65.2889	2.34072
$779$	−4.96058	−0.177731
$780$	0	0
$781$	−54.9533	−1.96639
$782$	1.11154	0.0397487
$783$	0.426367	0.0152371
$784$	1.05832	0.0377970
$785$	0	0
$786$	0.116500	0.00415540
$787$	12.6066	0.449378	0.224689	−	0.974431i	$-0.427863\pi$
$787$	12.6066	0.449378	0.224689	+	0.974431i	$0.427863\pi$
$788$	9.12195	0.324956
$789$	−0.191390	−0.00681365
$790$	0	0
$791$	−5.71585	−0.203232
$792$	−51.1682	−1.81818
$793$	−31.9774	−1.13555
$794$	48.1187	1.70767
$795$	0	0
$796$	−67.5856	−2.39551
$797$	−31.7455	−1.12448	−0.562242	−	0.826973i	$-0.690061\pi$
$797$	−31.7455	−1.12448	−0.562242	+	0.826973i	$0.690061\pi$
$798$	0.0272891	0.000966025 0
$799$	3.83991	0.135846
$800$	0	0
$801$	18.2462	0.644698
$802$	−1.04829	−0.0370165
$803$	−68.2155	−2.40727
$804$	0.119122	0.00420111
$805$	0	0
$806$	−100.434	−3.53764
$807$	0.0594142	0.00209148
$808$	−9.53099	−0.335299
$809$	−21.5831	−0.758821	−0.379411	−	0.925228i	$-0.623873\pi$
$809$	−21.5831	−0.758821	−0.379411	+	0.925228i	$0.623873\pi$
$810$	0	0
$811$	−6.27428	−0.220320	−0.110160	−	0.993914i	$-0.535136\pi$
$811$	−6.27428	−0.220320	−0.110160	+	0.993914i	$0.535136\pi$
$812$	−32.4714	−1.13952
$813$	−0.147764	−0.00518230
$814$	−51.6724	−1.81112
$815$	0	0
$816$	−0.00381305	−0.000133484 0
$817$	−5.24548	−0.183516
$818$	14.9589	0.523027
$819$	11.6345	0.406542
$820$	0	0
$821$	−50.7376	−1.77075	−0.885377	−	0.464874i	$-0.846100\pi$
$821$	−50.7376	−1.77075	−0.885377	+	0.464874i	$0.846100\pi$
$822$	0.130533	0.00455285
$823$	−20.6689	−0.720473	−0.360236	−	0.932861i	$-0.617304\pi$
$823$	−20.6689	−0.720473	−0.360236	+	0.932861i	$0.617304\pi$
$824$	−44.8404	−1.56209
$825$	0	0
$826$	27.7991	0.967253
$827$	9.51670	0.330928	0.165464	−	0.986216i	$-0.447088\pi$
$827$	9.51670	0.330928	0.165464	+	0.986216i	$0.447088\pi$
$828$	−10.3839	−0.360865
$829$	43.2509	1.50217	0.751083	−	0.660208i	$-0.229532\pi$
$829$	43.2509	1.50217	0.751083	+	0.660208i	$0.229532\pi$
$830$	0	0
$831$	0.188740	0.00654731
$832$	47.6980	1.65363
$833$	−0.475637	−0.0164798
$834$	0.207954	0.00720086
$835$	0	0
$836$	26.6491	0.921677
$837$	0.503645	0.0174085
$838$	19.8410	0.685396
$839$	12.6656	0.437264	0.218632	−	0.975807i	$-0.429841\pi$
$839$	12.6656	0.437264	0.218632	+	0.975807i	$0.429841\pi$
$840$	0	0
$841$	59.0051	2.03466
$842$	59.3389	2.04495
$843$	−0.0210876	−0.000726294 0
$844$	−36.4609	−1.25504
$845$	0	0
$846$	−56.5991	−1.94592
$847$	13.9434	0.479101
$848$	−1.55405	−0.0533664
$849$	−0.0917365	−0.00314839
$850$	0	0
$851$	−4.42722	−0.151763
$852$	0.288500	0.00988385
$853$	5.14537	0.176174	0.0880871	−	0.996113i	$-0.471925\pi$
$853$	5.14537	0.176174	0.0880871	+	0.996113i	$0.471925\pi$
$854$	−19.2690	−0.659372
$855$	0	0
$856$	61.8852	2.11519
$857$	−13.1648	−0.449702	−0.224851	−	0.974393i	$-0.572190\pi$
$857$	−13.1648	−0.449702	−0.224851	+	0.974393i	$0.572190\pi$
$858$	−0.342882	−0.0117058
$859$	−27.8506	−0.950249	−0.475124	−	0.879919i	$-0.657597\pi$
$859$	−27.8506	−0.950249	−0.475124	+	0.879919i	$0.657597\pi$
$860$	0	0
$861$	0.0243757	0.000830723 0
$862$	−45.1619	−1.53822
$863$	36.4254	1.23994	0.619968	−	0.784627i	$-0.287146\pi$
$863$	36.4254	1.23994	0.619968	+	0.784627i	$0.287146\pi$
$864$	−0.198026	−0.00673698
$865$	0	0
$866$	−83.3628	−2.83278
$867$	−0.127061	−0.00431522
$868$	−38.3568	−1.30192
$869$	−65.4403	−2.21991
$870$	0	0
$871$	−17.6196	−0.597019
$872$	30.2779	1.02534
$873$	−11.7515	−0.397727
$874$	3.60253	0.121857
$875$	0	0
$876$	0.358125	0.0120999
$877$	−32.5408	−1.09882	−0.549412	−	0.835551i	$-0.685148\pi$
$877$	−32.5408	−1.09882	−0.549412	+	0.835551i	$0.685148\pi$
$878$	42.7589	1.44304
$879$	−0.00492997	−0.000166284 0
$880$	0	0
$881$	−22.7388	−0.766088	−0.383044	−	0.923730i	$-0.625124\pi$
$881$	−22.7388	−0.766088	−0.383044	+	0.923730i	$0.625124\pi$
$882$	7.01073	0.236064
$883$	−13.1029	−0.440946	−0.220473	−	0.975393i	$-0.570760\pi$
$883$	−13.1029	−0.440946	−0.220473	+	0.975393i	$0.570760\pi$
$884$	6.38495	0.214749
$885$	0	0
$886$	9.40707	0.316037
$887$	−16.4374	−0.551914	−0.275957	−	0.961170i	$-0.588995\pi$
$887$	−16.4374	−0.551914	−0.275957	+	0.961170i	$0.588995\pi$
$888$	0.114531	0.00384340
$889$	14.5563	0.488204
$890$	0	0
$891$	−44.9464	−1.50576
$892$	52.7361	1.76574
$893$	12.4452	0.416464
$894$	−0.00500273	−0.000167316 0
$895$	0	0
$896$	20.0278	0.669083
$897$	−0.0293776	−0.000980891 0
$898$	−69.6093	−2.32289
$899$	103.956	3.46713
$900$	0	0
$901$	0.698436	0.0232683
$902$	37.5581	1.25055
$903$	0.0257757	0.000857762 0
$904$	19.5205	0.649241
$905$	0	0
$906$	−0.345947	−0.0114933
$907$	−49.2654	−1.63583	−0.817916	−	0.575338i	$-0.804871\pi$
$907$	−49.2654	−1.63583	−0.817916	+	0.575338i	$0.804871\pi$
$908$	−94.9915	−3.15240
$909$	−8.37225	−0.277690
$910$	0	0
$911$	7.82158	0.259140	0.129570	−	0.991570i	$-0.458640\pi$
$911$	7.82158	0.259140	0.129570	+	0.991570i	$0.458640\pi$
$912$	−0.0123582	−0.000409220 0
$913$	−73.7314	−2.44015
$914$	45.6906	1.51131
$915$	0	0
$916$	103.243	3.41126
$917$	−6.58099	−0.217323
$918$	−0.0505191	−0.00166738
$919$	47.8000	1.57678	0.788388	−	0.615178i	$-0.210916\pi$
$919$	47.8000	1.57678	0.788388	+	0.615178i	$0.210916\pi$
$920$	0	0
$921$	0.170844	0.00562950
$922$	−0.448462	−0.0147693
$923$	−42.6728	−1.40459
$924$	−0.130951	−0.00430796
$925$	0	0
$926$	−61.2699	−2.01345
$927$	−39.3889	−1.29370
$928$	−40.8740	−1.34175
$929$	−22.2564	−0.730210	−0.365105	−	0.930966i	$-0.618967\pi$
$929$	−22.2564	−0.730210	−0.365105	+	0.930966i	$0.618967\pi$
$930$	0	0
$931$	−1.54155	−0.0505222
$932$	−79.3410	−2.59890
$933$	0.195322	0.00639455
$934$	−96.3263	−3.15189
$935$	0	0
$936$	−39.7335	−1.29873
$937$	−3.52344	−0.115106	−0.0575529	−	0.998342i	$-0.518330\pi$
$937$	−3.52344	−0.115106	−0.0575529	+	0.998342i	$0.518330\pi$
$938$	−10.6173	−0.346666
$939$	0.0422970	0.00138031
$940$	0	0
$941$	−21.9747	−0.716355	−0.358178	−	0.933653i	$-0.616602\pi$
$941$	−21.9747	−0.716355	−0.358178	+	0.933653i	$0.616602\pi$
$942$	0.419764	0.0136766
$943$	3.21792	0.104790
$944$	−12.5891	−0.409740
$945$	0	0
$946$	39.7152	1.29125
$947$	8.71337	0.283146	0.141573	−	0.989928i	$-0.454784\pi$
$947$	8.71337	0.283146	0.141573	+	0.989928i	$0.454784\pi$
$948$	0.343556	0.0111582
$949$	−52.9712	−1.71952
$950$	0	0
$951$	−0.0329736	−0.00106924
$952$	1.62437	0.0526461
$953$	22.0600	0.714594	0.357297	−	0.933991i	$-0.383698\pi$
$953$	22.0600	0.714594	0.357297	+	0.933991i	$0.383698\pi$
$954$	−10.2947	−0.333304
$955$	0	0
$956$	52.8758	1.71013
$957$	0.354906	0.0114725
$958$	10.6259	0.343306
$959$	−7.37371	−0.238109
$960$	0	0
$961$	91.7979	2.96122
$962$	−40.1251	−1.29368
$963$	54.3614	1.75177
$964$	20.3904	0.656732
$965$	0	0
$966$	−0.0177024	−0.000569566 0
$967$	14.8633	0.477973	0.238986	−	0.971023i	$-0.423185\pi$
$967$	14.8633	0.477973	0.238986	+	0.971023i	$0.423185\pi$
$968$	−47.6187	−1.53052
$969$	0.00555411	0.000178424 0
$970$	0	0
$971$	−32.4718	−1.04207	−0.521036	−	0.853535i	$-0.674454\pi$
$971$	−32.4718	−1.04207	−0.521036	+	0.853535i	$0.674454\pi$
$972$	0.707917	0.0227064
$973$	−11.7472	−0.376598
$974$	−21.9283	−0.702628
$975$	0	0
$976$	8.72618	0.279318
$977$	17.9922	0.575622	0.287811	−	0.957687i	$-0.407072\pi$
$977$	17.9922	0.575622	0.287811	+	0.957687i	$0.407072\pi$
$978$	−0.000942939 0	−3.01519e−5 0
$979$	30.3765	0.970836
$980$	0	0
$981$	26.5968	0.849170
$982$	−57.1677	−1.82429
$983$	7.91109	0.252325	0.126162	−	0.992010i	$-0.459734\pi$
$983$	7.91109	0.252325	0.126162	+	0.992010i	$0.459734\pi$
$984$	−0.0832467	−0.00265381
$985$	0	0
$986$	−10.4275	−0.332079
$987$	−0.0611545	−0.00194657
$988$	20.6937	0.658355
$989$	3.40274	0.108201
$990$	0	0
$991$	23.8214	0.756712	0.378356	−	0.925660i	$-0.376490\pi$
$991$	23.8214	0.756712	0.378356	+	0.925660i	$0.376490\pi$
$992$	−48.2824	−1.53297
$993$	−0.0815430	−0.00258769
$994$	−25.7138	−0.815594
$995$	0	0
$996$	0.387083	0.0122652
$997$	3.86775	0.122493	0.0612464	−	0.998123i	$-0.480492\pi$
$997$	3.86775	0.122493	0.0612464	+	0.998123i	$0.480492\pi$
$998$	−21.6415	−0.685051
$999$	0.201215	0.00636616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bc.1.2	yes	14
5.4	even	2		4025.2.a.z.1.13	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.13	✓	14	5.4	even	2
4025.2.a.bc.1.2	yes	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33696 q^{2} +0.00757499 q^{3} +3.46136 q^{4} -0.0177024 q^{6} +1.00000 q^{7} -3.41514 q^{8} -2.99994 q^{9} +O(q^{10})\)	\(q-2.33696 q^{2} +0.00757499 q^{3} +3.46136 q^{4} -0.0177024 q^{6} +1.00000 q^{7} -3.41514 q^{8} -2.99994 q^{9} -4.99434 q^{11} +0.0262198 q^{12} -3.87824 q^{13} -2.33696 q^{14} +1.05832 q^{16} -0.475637 q^{17} +7.01073 q^{18} -1.54155 q^{19} +0.00757499 q^{21} +11.6715 q^{22} +1.00000 q^{23} -0.0258697 q^{24} +9.06327 q^{26} -0.0454495 q^{27} +3.46136 q^{28} -9.38110 q^{29} -11.0814 q^{31} +4.35705 q^{32} -0.0378321 q^{33} +1.11154 q^{34} -10.3839 q^{36} -4.42722 q^{37} +3.60253 q^{38} -0.0293776 q^{39} +3.21792 q^{41} -0.0177024 q^{42} +3.40274 q^{43} -17.2872 q^{44} -2.33696 q^{46} -8.07320 q^{47} +0.00801673 q^{48} +1.00000 q^{49} -0.00360295 q^{51} -13.4240 q^{52} -1.46842 q^{53} +0.106214 q^{54} -3.41514 q^{56} -0.0116772 q^{57} +21.9232 q^{58} -11.8954 q^{59} +8.24535 q^{61} +25.8968 q^{62} -2.99994 q^{63} -12.2989 q^{64} +0.0884119 q^{66} +4.54321 q^{67} -1.64635 q^{68} +0.00757499 q^{69} +11.0031 q^{71} +10.2452 q^{72} +13.6586 q^{73} +10.3462 q^{74} -5.33586 q^{76} -4.99434 q^{77} +0.0686542 q^{78} +13.1029 q^{79} +8.99948 q^{81} -7.52014 q^{82} +14.7630 q^{83} +0.0262198 q^{84} -7.95205 q^{86} -0.0710618 q^{87} +17.0564 q^{88} -6.08219 q^{89} -3.87824 q^{91} +3.46136 q^{92} -0.0839417 q^{93} +18.8667 q^{94} +0.0330047 q^{96} +3.91724 q^{97} -2.33696 q^{98} +14.9827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9	\( 14 q + 3 q^{2} + 4 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 3 q^{8} + 18 q^{9} + 5 q^{11} + 17 q^{12} + 11 q^{13} + 3 q^{14} + 23 q^{16} + 3 q^{17} + 15 q^{18} - 2 q^{19} + 4 q^{21} + 23 q^{22} + 14 q^{23} - 12 q^{24} - 9 q^{26} + 25 q^{27} + 17 q^{28} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 6 q^{33} - 14 q^{34} + 13 q^{36} + 22 q^{37} + 20 q^{38} - 10 q^{39} - 17 q^{41} - 4 q^{42} + 18 q^{43} + 28 q^{44} + 3 q^{46} + 30 q^{47} + 8 q^{48} + 14 q^{49} + 4 q^{51} + 8 q^{52} + 11 q^{53} + 20 q^{54} + 3 q^{56} + 18 q^{57} + 38 q^{58} - 22 q^{59} - 8 q^{61} - 22 q^{62} + 18 q^{63} + 29 q^{64} - 9 q^{66} + 39 q^{67} + q^{68} + 4 q^{69} - 5 q^{71} - 24 q^{72} + 18 q^{73} + 35 q^{74} - 41 q^{76} + 5 q^{77} - 22 q^{78} + 10 q^{79} + 2 q^{81} - 8 q^{82} + 24 q^{83} + 17 q^{84} - 26 q^{86} + 5 q^{87} + 58 q^{88} + 25 q^{89} + 11 q^{91} + 17 q^{92} + 47 q^{93} - 2 q^{94} - 117 q^{96} + 43 q^{97} + 3 q^{98} + 55 q^{99}+O(q^{100}) \) 14 * q + 3 * q^2 + 4 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 3 * q^8 + 18 * q^9 + 5 * q^11 + 17 * q^12 + 11 * q^13 + 3 * q^14 + 23 * q^16 + 3 * q^17 + 15 * q^18 - 2 * q^19 + 4 * q^21 + 23 * q^22 + 14 * q^23 - 12 * q^24 - 9 * q^26 + 25 * q^27 + 17 * q^28 + 7 * q^29 - 3 * q^31 + 24 * q^32 + 6 * q^33 - 14 * q^34 + 13 * q^36 + 22 * q^37 + 20 * q^38 - 10 * q^39 - 17 * q^41 - 4 * q^42 + 18 * q^43 + 28 * q^44 + 3 * q^46 + 30 * q^47 + 8 * q^48 + 14 * q^49 + 4 * q^51 + 8 * q^52 + 11 * q^53 + 20 * q^54 + 3 * q^56 + 18 * q^57 + 38 * q^58 - 22 * q^59 - 8 * q^61 - 22 * q^62 + 18 * q^63 + 29 * q^64 - 9 * q^66 + 39 * q^67 + q^68 + 4 * q^69 - 5 * q^71 - 24 * q^72 + 18 * q^73 + 35 * q^74 - 41 * q^76 + 5 * q^77 - 22 * q^78 + 10 * q^79 + 2 * q^81 - 8 * q^82 + 24 * q^83 + 17 * q^84 - 26 * q^86 + 5 * q^87 + 58 * q^88 + 25 * q^89 + 11 * q^91 + 17 * q^92 + 47 * q^93 - 2 * q^94 - 117 * q^96 + 43 * q^97 + 3 * q^98 + 55 * q^99

Introduction

L-functions

Modular forms

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