LMFDB - Embedded newform 3525.2.a.y.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, 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("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.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:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 9x^{5} + 6x^{4} + 20x^{3} - 9x^{2} - 12x + 3 $ x^7 - x^6 - 9x^5 + 6x^4 + 20x^3 - 9x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.913267$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.913267 q^{2} +1.00000 q^{3} -1.16594 q^{4} +0.913267 q^{6} +2.03699 q^{7} -2.89135 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.913267 q^{2} +1.00000 q^{3} -1.16594 q^{4} +0.913267 q^{6} +2.03699 q^{7} -2.89135 q^{8} +1.00000 q^{9} -1.09181 q^{11} -1.16594 q^{12} -2.41055 q^{13} +1.86031 q^{14} -0.308690 q^{16} -3.31724 q^{17} +0.913267 q^{18} +4.97175 q^{19} +2.03699 q^{21} -0.997110 q^{22} -8.10054 q^{23} -2.89135 q^{24} -2.20148 q^{26} +1.00000 q^{27} -2.37501 q^{28} -7.37453 q^{29} -3.47270 q^{31} +5.50079 q^{32} -1.09181 q^{33} -3.02952 q^{34} -1.16594 q^{36} -2.18294 q^{37} +4.54054 q^{38} -2.41055 q^{39} -9.79861 q^{41} +1.86031 q^{42} +9.29991 q^{43} +1.27298 q^{44} -7.39796 q^{46} +1.00000 q^{47} -0.308690 q^{48} -2.85068 q^{49} -3.31724 q^{51} +2.81057 q^{52} -8.28822 q^{53} +0.913267 q^{54} -5.88965 q^{56} +4.97175 q^{57} -6.73492 q^{58} +12.8065 q^{59} -4.77390 q^{61} -3.17150 q^{62} +2.03699 q^{63} +5.64107 q^{64} -0.997110 q^{66} +12.8817 q^{67} +3.86771 q^{68} -8.10054 q^{69} -1.74938 q^{71} -2.89135 q^{72} -6.38143 q^{73} -1.99361 q^{74} -5.79678 q^{76} -2.22399 q^{77} -2.20148 q^{78} +12.4597 q^{79} +1.00000 q^{81} -8.94874 q^{82} -16.0648 q^{83} -2.37501 q^{84} +8.49330 q^{86} -7.37453 q^{87} +3.15679 q^{88} -9.67383 q^{89} -4.91027 q^{91} +9.44477 q^{92} -3.47270 q^{93} +0.913267 q^{94} +5.50079 q^{96} -19.4035 q^{97} -2.60343 q^{98} -1.09181 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9	$ 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9} - 8 q^{11} + 5 q^{12} - 5 q^{13} - 3 q^{14} + 9 q^{16} - 10 q^{17} - q^{18} + 7 q^{19} - 11 q^{21} - 20 q^{22} - 4 q^{23} - 6 q^{24} + 7 q^{27} - 2 q^{28} - 11 q^{29} + 3 q^{31} - 28 q^{32} - 8 q^{33} + 8 q^{34} + 5 q^{36} - 11 q^{37} + 2 q^{38} - 5 q^{39} - 20 q^{41} - 3 q^{42} - 18 q^{43} + q^{44} - 19 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} - 10 q^{51} - 29 q^{52} - 12 q^{53} - q^{54} - 47 q^{56} + 7 q^{57} + 19 q^{58} + 18 q^{59} - 4 q^{61} - 12 q^{62} - 11 q^{63} + 42 q^{64} - 20 q^{66} - 22 q^{67} - 44 q^{68} - 4 q^{69} - 14 q^{71} - 6 q^{72} - 30 q^{73} + 31 q^{74} - 2 q^{76} + 8 q^{77} - q^{79} + 7 q^{81} - 29 q^{82} - 54 q^{83} - 2 q^{84} - 29 q^{86} - 11 q^{87} + 22 q^{88} - 14 q^{89} + 20 q^{91} + 5 q^{92} + 3 q^{93} - q^{94} - 28 q^{96} - 24 q^{97} + 26 q^{98} - 8 q^{99}+O(q^{100}) $ 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9 - 8 * q^11 + 5 * q^12 - 5 * q^13 - 3 * q^14 + 9 * q^16 - 10 * q^17 - q^18 + 7 * q^19 - 11 * q^21 - 20 * q^22 - 4 * q^23 - 6 * q^24 + 7 * q^27 - 2 * q^28 - 11 * q^29 + 3 * q^31 - 28 * q^32 - 8 * q^33 + 8 * q^34 + 5 * q^36 - 11 * q^37 + 2 * q^38 - 5 * q^39 - 20 * q^41 - 3 * q^42 - 18 * q^43 + q^44 - 19 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 - 10 * q^51 - 29 * q^52 - 12 * q^53 - q^54 - 47 * q^56 + 7 * q^57 + 19 * q^58 + 18 * q^59 - 4 * q^61 - 12 * q^62 - 11 * q^63 + 42 * q^64 - 20 * q^66 - 22 * q^67 - 44 * q^68 - 4 * q^69 - 14 * q^71 - 6 * q^72 - 30 * q^73 + 31 * q^74 - 2 * q^76 + 8 * q^77 - q^79 + 7 * q^81 - 29 * q^82 - 54 * q^83 - 2 * q^84 - 29 * q^86 - 11 * q^87 + 22 * q^88 - 14 * q^89 + 20 * q^91 + 5 * q^92 + 3 * q^93 - q^94 - 28 * q^96 - 24 * q^97 + 26 * q^98 - 8 * 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 $

$2$	0.913267	0.645777	0.322889	−	0.946437i	$-0.395346\pi$
$2$	0.913267	0.645777	0.322889	+	0.946437i	$0.395346\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.16594	−0.582972
$5$	0	0
$5$	0	0
$6$	0.913267	0.372840
$7$	2.03699	0.769909	0.384955	−	0.922936i	$-0.374217\pi$
$7$	2.03699	0.769909	0.384955	+	0.922936i	$0.374217\pi$
$8$	−2.89135	−1.02225
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.09181	−0.329192	−0.164596	−	0.986361i	$-0.552632\pi$
$11$	−1.09181	−0.329192	−0.164596	+	0.986361i	$0.552632\pi$
$12$	−1.16594	−0.336579
$13$	−2.41055	−0.668567	−0.334284	−	0.942472i	$-0.608494\pi$
$13$	−2.41055	−0.668567	−0.334284	+	0.942472i	$0.608494\pi$
$14$	1.86031	0.497190
$15$	0	0
$16$	−0.308690	−0.0771724
$17$	−3.31724	−0.804548	−0.402274	−	0.915519i	$-0.631780\pi$
$17$	−3.31724	−0.804548	−0.402274	+	0.915519i	$0.631780\pi$
$18$	0.913267	0.215259
$19$	4.97175	1.14060	0.570299	−	0.821437i	$-0.306827\pi$
$19$	4.97175	1.14060	0.570299	+	0.821437i	$0.306827\pi$
$20$	0	0
$21$	2.03699	0.444507
$22$	−0.997110	−0.212585
$23$	−8.10054	−1.68908	−0.844540	−	0.535492i	$-0.820126\pi$
$23$	−8.10054	−1.68908	−0.844540	+	0.535492i	$0.820126\pi$
$24$	−2.89135	−0.590195
$25$	0	0
$26$	−2.20148	−0.431746
$27$	1.00000	0.192450
$28$	−2.37501	−0.448835
$29$	−7.37453	−1.36942	−0.684708	−	0.728817i	$-0.740070\pi$
$29$	−7.37453	−1.36942	−0.684708	+	0.728817i	$0.740070\pi$
$30$	0	0
$31$	−3.47270	−0.623716	−0.311858	−	0.950129i	$-0.600951\pi$
$31$	−3.47270	−0.623716	−0.311858	+	0.950129i	$0.600951\pi$
$32$	5.50079	0.972411
$33$	−1.09181	−0.190059
$34$	−3.02952	−0.519559
$35$	0	0
$36$	−1.16594	−0.194324
$37$	−2.18294	−0.358873	−0.179436	−	0.983770i	$-0.557427\pi$
$37$	−2.18294	−0.358873	−0.179436	+	0.983770i	$0.557427\pi$
$38$	4.54054	0.736572
$39$	−2.41055	−0.385998
$40$	0	0
$41$	−9.79861	−1.53029	−0.765143	−	0.643861i	$-0.777332\pi$
$41$	−9.79861	−1.53029	−0.765143	+	0.643861i	$0.777332\pi$
$42$	1.86031	0.287053
$43$	9.29991	1.41822	0.709112	−	0.705096i	$-0.249096\pi$
$43$	9.29991	1.41822	0.709112	+	0.705096i	$0.249096\pi$
$44$	1.27298	0.191909
$45$	0	0
$46$	−7.39796	−1.09077
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	−0.308690	−0.0445555
$49$	−2.85068	−0.407240
$50$	0	0
$51$	−3.31724	−0.464506
$52$	2.81057	0.389756
$53$	−8.28822	−1.13847	−0.569237	−	0.822173i	$-0.692761\pi$
$53$	−8.28822	−1.13847	−0.569237	+	0.822173i	$0.692761\pi$
$54$	0.913267	0.124280
$55$	0	0
$56$	−5.88965	−0.787037
$57$	4.97175	0.658524
$58$	−6.73492	−0.884338
$59$	12.8065	1.66727	0.833634	−	0.552318i	$-0.186257\pi$
$59$	12.8065	1.66727	0.833634	+	0.552318i	$0.186257\pi$
$60$	0	0
$61$	−4.77390	−0.611236	−0.305618	−	0.952154i	$-0.598863\pi$
$61$	−4.77390	−0.611236	−0.305618	+	0.952154i	$0.598863\pi$
$62$	−3.17150	−0.402781
$63$	2.03699	0.256636
$64$	5.64107	0.705133
$65$	0	0
$66$	−0.997110	−0.122736
$67$	12.8817	1.57375	0.786877	−	0.617110i	$-0.211697\pi$
$67$	12.8817	1.57375	0.786877	+	0.617110i	$0.211697\pi$
$68$	3.86771	0.469029
$69$	−8.10054	−0.975191
$70$	0	0
$71$	−1.74938	−0.207613	−0.103807	−	0.994598i	$-0.533102\pi$
$71$	−1.74938	−0.207613	−0.103807	+	0.994598i	$0.533102\pi$
$72$	−2.89135	−0.340749
$73$	−6.38143	−0.746890	−0.373445	−	0.927652i	$-0.621824\pi$
$73$	−6.38143	−0.746890	−0.373445	+	0.927652i	$0.621824\pi$
$74$	−1.99361	−0.231752
$75$	0	0
$76$	−5.79678	−0.664936
$77$	−2.22399	−0.253448
$78$	−2.20148	−0.249268
$79$	12.4597	1.40183	0.700913	−	0.713247i	$-0.252776\pi$
$79$	12.4597	1.40183	0.700913	+	0.713247i	$0.252776\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−8.94874	−0.988224
$83$	−16.0648	−1.76334	−0.881668	−	0.471871i	$-0.843579\pi$
$83$	−16.0648	−1.76334	−0.881668	+	0.471871i	$0.843579\pi$
$84$	−2.37501	−0.259135
$85$	0	0
$86$	8.49330	0.915857
$87$	−7.37453	−0.790633
$88$	3.15679	0.336515
$89$	−9.67383	−1.02542	−0.512712	−	0.858561i	$-0.671359\pi$
$89$	−9.67383	−1.02542	−0.512712	+	0.858561i	$0.671359\pi$
$90$	0	0
$91$	−4.91027	−0.514736
$92$	9.44477	0.984686
$93$	−3.47270	−0.360102
$94$	0.913267	0.0941963
$95$	0	0
$96$	5.50079	0.561422
$97$	−19.4035	−1.97013	−0.985064	−	0.172189i	$-0.944916\pi$
$97$	−19.4035	−1.97013	−0.985064	+	0.172189i	$0.944916\pi$
$98$	−2.60343	−0.262986
$99$	−1.09181	−0.109731
$100$	0	0
$101$	1.10842	0.110292	0.0551458	−	0.998478i	$-0.482438\pi$
$101$	1.10842	0.110292	0.0551458	+	0.998478i	$0.482438\pi$
$102$	−3.02952	−0.299968
$103$	5.62862	0.554604	0.277302	−	0.960783i	$-0.410560\pi$
$103$	5.62862	0.554604	0.277302	+	0.960783i	$0.410560\pi$
$104$	6.96976	0.683441
$105$	0	0
$106$	−7.56936	−0.735201
$107$	−3.63218	−0.351136	−0.175568	−	0.984467i	$-0.556176\pi$
$107$	−3.63218	−0.351136	−0.175568	+	0.984467i	$0.556176\pi$
$108$	−1.16594	−0.112193
$109$	−0.736387	−0.0705331	−0.0352665	−	0.999378i	$-0.511228\pi$
$109$	−0.736387	−0.0705331	−0.0352665	+	0.999378i	$0.511228\pi$
$110$	0	0
$111$	−2.18294	−0.207195
$112$	−0.628797	−0.0594157
$113$	1.80180	0.169499	0.0847493	−	0.996402i	$-0.472991\pi$
$113$	1.80180	0.169499	0.0847493	+	0.996402i	$0.472991\pi$
$114$	4.54054	0.425260
$115$	0	0
$116$	8.59829	0.798331
$117$	−2.41055	−0.222856
$118$	11.6958	1.07668
$119$	−6.75717	−0.619429
$120$	0	0
$121$	−9.80796	−0.891633
$122$	−4.35985	−0.394722
$123$	−9.79861	−0.883511
$124$	4.04897	0.363609
$125$	0	0
$126$	1.86031	0.165730
$127$	−21.3174	−1.89161	−0.945807	−	0.324729i	$-0.894727\pi$
$127$	−21.3174	−1.89161	−0.945807	+	0.324729i	$0.894727\pi$
$128$	−5.84977	−0.517052
$129$	9.29991	0.818812
$130$	0	0
$131$	−18.1461	−1.58544	−0.792718	−	0.609589i	$-0.791335\pi$
$131$	−18.1461	−1.58544	−0.792718	+	0.609589i	$0.791335\pi$
$132$	1.27298	0.110799
$133$	10.1274	0.878157
$134$	11.7645	1.01629
$135$	0	0
$136$	9.59130	0.822447
$137$	14.4382	1.23354	0.616771	−	0.787143i	$-0.288440\pi$
$137$	14.4382	1.23354	0.616771	+	0.787143i	$0.288440\pi$
$138$	−7.39796	−0.629756
$139$	−16.4018	−1.39118	−0.695592	−	0.718437i	$-0.744858\pi$
$139$	−16.4018	−1.39118	−0.695592	+	0.718437i	$0.744858\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	−1.59765	−0.134072
$143$	2.63186	0.220087
$144$	−0.308690	−0.0257241
$145$	0	0
$146$	−5.82795	−0.482325
$147$	−2.85068	−0.235120
$148$	2.54518	0.209213
$149$	−8.01143	−0.656322	−0.328161	−	0.944622i	$-0.606429\pi$
$149$	−8.01143	−0.656322	−0.328161	+	0.944622i	$0.606429\pi$
$150$	0	0
$151$	16.6431	1.35440	0.677199	−	0.735800i	$-0.263194\pi$
$151$	16.6431	1.35440	0.677199	+	0.735800i	$0.263194\pi$
$152$	−14.3751	−1.16597
$153$	−3.31724	−0.268183
$154$	−2.03110	−0.163671
$155$	0	0
$156$	2.81057	0.225026
$157$	2.79190	0.222818	0.111409	−	0.993775i	$-0.464464\pi$
$157$	2.79190	0.222818	0.111409	+	0.993775i	$0.464464\pi$
$158$	11.3790	0.905267
$159$	−8.28822	−0.657299
$160$	0	0
$161$	−16.5007	−1.30044
$162$	0.913267	0.0717530
$163$	−18.1033	−1.41796	−0.708982	−	0.705227i	$-0.750845\pi$
$163$	−18.1033	−1.41796	−0.708982	+	0.705227i	$0.750845\pi$
$164$	11.4246	0.892113
$165$	0	0
$166$	−14.6714	−1.13872
$167$	25.3801	1.96397	0.981986	−	0.188953i	$-0.0605095\pi$
$167$	25.3801	1.96397	0.981986	+	0.188953i	$0.0605095\pi$
$168$	−5.88965	−0.454396
$169$	−7.18923	−0.553018
$170$	0	0
$171$	4.97175	0.380199
$172$	−10.8432	−0.826784
$173$	−4.97224	−0.378033	−0.189016	−	0.981974i	$-0.560530\pi$
$173$	−4.97224	−0.378033	−0.189016	+	0.981974i	$0.560530\pi$
$174$	−6.73492	−0.510573
$175$	0	0
$176$	0.337029	0.0254045
$177$	12.8065	0.962597
$178$	−8.83479	−0.662196
$179$	18.3442	1.37111	0.685556	−	0.728020i	$-0.259559\pi$
$179$	18.3442	1.37111	0.685556	+	0.728020i	$0.259559\pi$
$180$	0	0
$181$	23.8079	1.76962	0.884812	−	0.465948i	$-0.154287\pi$
$181$	23.8079	1.76962	0.884812	+	0.465948i	$0.154287\pi$
$182$	−4.48439	−0.332405
$183$	−4.77390	−0.352897
$184$	23.4215	1.72666
$185$	0	0
$186$	−3.17150	−0.232546
$187$	3.62178	0.264851
$188$	−1.16594	−0.0850352
$189$	2.03699	0.148169
$190$	0	0
$191$	−0.999013	−0.0722861	−0.0361430	−	0.999347i	$-0.511507\pi$
$191$	−0.999013	−0.0722861	−0.0361430	+	0.999347i	$0.511507\pi$
$192$	5.64107	0.407109
$193$	−23.5875	−1.69786	−0.848932	−	0.528503i	$-0.822754\pi$
$193$	−23.5875	−1.69786	−0.848932	+	0.528503i	$0.822754\pi$
$194$	−17.7206	−1.27226
$195$	0	0
$196$	3.32373	0.237409
$197$	19.6365	1.39904	0.699520	−	0.714613i	$-0.253397\pi$
$197$	19.6365	1.39904	0.699520	+	0.714613i	$0.253397\pi$
$198$	−0.997110	−0.0708615
$199$	6.82369	0.483718	0.241859	−	0.970311i	$-0.422243\pi$
$199$	6.82369	0.483718	0.241859	+	0.970311i	$0.422243\pi$
$200$	0	0
$201$	12.8817	0.908607
$202$	1.01228	0.0712238
$203$	−15.0218	−1.05433
$204$	3.86771	0.270794
$205$	0	0
$206$	5.14043	0.358151
$207$	−8.10054	−0.563027
$208$	0.744113	0.0515949
$209$	−5.42818	−0.375475
$210$	0	0
$211$	15.6296	1.07598	0.537992	−	0.842950i	$-0.319183\pi$
$211$	15.6296	1.07598	0.537992	+	0.842950i	$0.319183\pi$
$212$	9.66360	0.663698
$213$	−1.74938	−0.119866
$214$	−3.31715	−0.226755
$215$	0	0
$216$	−2.89135	−0.196732
$217$	−7.07385	−0.480204
$218$	−0.672518	−0.0455487
$219$	−6.38143	−0.431217
$220$	0	0
$221$	7.99638	0.537895
$222$	−1.99361	−0.133802
$223$	4.31256	0.288790	0.144395	−	0.989520i	$-0.453876\pi$
$223$	4.31256	0.288790	0.144395	+	0.989520i	$0.453876\pi$
$224$	11.2050	0.748668
$225$	0	0
$226$	1.64552	0.109458
$227$	−20.5407	−1.36334	−0.681668	−	0.731662i	$-0.738745\pi$
$227$	−20.5407	−1.36334	−0.681668	+	0.731662i	$0.738745\pi$
$228$	−5.79678	−0.383901
$229$	28.0068	1.85074	0.925371	−	0.379063i	$-0.123754\pi$
$229$	28.0068	1.85074	0.925371	+	0.379063i	$0.123754\pi$
$230$	0	0
$231$	−2.22399	−0.146328
$232$	21.3224	1.39988
$233$	−9.47290	−0.620590	−0.310295	−	0.950640i	$-0.600428\pi$
$233$	−9.47290	−0.620590	−0.310295	+	0.950640i	$0.600428\pi$
$234$	−2.20148	−0.143915
$235$	0	0
$236$	−14.9317	−0.971970
$237$	12.4597	0.809344
$238$	−6.17110	−0.400013
$239$	4.90577	0.317328	0.158664	−	0.987333i	$-0.449281\pi$
$239$	4.90577	0.317328	0.158664	+	0.987333i	$0.449281\pi$
$240$	0	0
$241$	2.32047	0.149475	0.0747373	−	0.997203i	$-0.476188\pi$
$241$	2.32047	0.149475	0.0747373	+	0.997203i	$0.476188\pi$
$242$	−8.95729	−0.575796
$243$	1.00000	0.0641500
$244$	5.56610	0.356333
$245$	0	0
$246$	−8.94874	−0.570551
$247$	−11.9847	−0.762566
$248$	10.0408	0.637592
$249$	−16.0648	−1.01806
$250$	0	0
$251$	−2.61616	−0.165131	−0.0825653	−	0.996586i	$-0.526311\pi$
$251$	−2.61616	−0.165131	−0.0825653	+	0.996586i	$0.526311\pi$
$252$	−2.37501	−0.149612
$253$	8.84422	0.556031
$254$	−19.4685	−1.22156
$255$	0	0
$256$	−16.6245	−1.03903
$257$	3.93298	0.245333	0.122666	−	0.992448i	$-0.460856\pi$
$257$	3.93298	0.245333	0.122666	+	0.992448i	$0.460856\pi$
$258$	8.49330	0.528770
$259$	−4.44662	−0.276300
$260$	0	0
$261$	−7.37453	−0.456472
$262$	−16.5723	−1.02384
$263$	−17.9614	−1.10755	−0.553774	−	0.832667i	$-0.686813\pi$
$263$	−17.9614	−1.10755	−0.553774	+	0.832667i	$0.686813\pi$
$264$	3.15679	0.194287
$265$	0	0
$266$	9.24902	0.567094
$267$	−9.67383	−0.592029
$268$	−15.0194	−0.917454
$269$	2.38651	0.145508	0.0727541	−	0.997350i	$-0.476821\pi$
$269$	2.38651	0.145508	0.0727541	+	0.997350i	$0.476821\pi$
$270$	0	0
$271$	5.30119	0.322024	0.161012	−	0.986952i	$-0.448524\pi$
$271$	5.30119	0.322024	0.161012	+	0.986952i	$0.448524\pi$
$272$	1.02400	0.0620889
$273$	−4.91027	−0.297183
$274$	13.1860	0.796594
$275$	0	0
$276$	9.44477	0.568509
$277$	−23.4240	−1.40741	−0.703707	−	0.710490i	$-0.748473\pi$
$277$	−23.4240	−1.40741	−0.703707	+	0.710490i	$0.748473\pi$
$278$	−14.9792	−0.898395
$279$	−3.47270	−0.207905
$280$	0	0
$281$	3.14768	0.187775	0.0938875	−	0.995583i	$-0.470071\pi$
$281$	3.14768	0.187775	0.0938875	+	0.995583i	$0.470071\pi$
$282$	0.913267	0.0543843
$283$	0.635239	0.0377610	0.0188805	−	0.999822i	$-0.493990\pi$
$283$	0.635239	0.0377610	0.0188805	+	0.999822i	$0.493990\pi$
$284$	2.03968	0.121033
$285$	0	0
$286$	2.40359	0.142127
$287$	−19.9596	−1.17818
$288$	5.50079	0.324137
$289$	−5.99593	−0.352702
$290$	0	0
$291$	−19.4035	−1.13745
$292$	7.44039	0.435416
$293$	10.2585	0.599308	0.299654	−	0.954048i	$-0.403129\pi$
$293$	10.2585	0.599308	0.299654	+	0.954048i	$0.403129\pi$
$294$	−2.60343	−0.151835
$295$	0	0
$296$	6.31164	0.366857
$297$	−1.09181	−0.0633530
$298$	−7.31657	−0.423838
$299$	19.5268	1.12926
$300$	0	0
$301$	18.9438	1.09190
$302$	15.1996	0.874640
$303$	1.10842	0.0636769
$304$	−1.53473	−0.0880227
$305$	0	0
$306$	−3.02952	−0.173186
$307$	−2.23107	−0.127334	−0.0636668	−	0.997971i	$-0.520279\pi$
$307$	−2.23107	−0.127334	−0.0636668	+	0.997971i	$0.520279\pi$
$308$	2.59305	0.147753
$309$	5.62862	0.320201
$310$	0	0
$311$	10.9987	0.623678	0.311839	−	0.950135i	$-0.399055\pi$
$311$	10.9987	0.623678	0.311839	+	0.950135i	$0.399055\pi$
$312$	6.96976	0.394585
$313$	−8.03853	−0.454365	−0.227182	−	0.973852i	$-0.572951\pi$
$313$	−8.03853	−0.454365	−0.227182	+	0.973852i	$0.572951\pi$
$314$	2.54975	0.143891
$315$	0	0
$316$	−14.5273	−0.817224
$317$	−0.488878	−0.0274581	−0.0137291	−	0.999906i	$-0.504370\pi$
$317$	−0.488878	−0.0274581	−0.0137291	+	0.999906i	$0.504370\pi$
$318$	−7.56936	−0.424469
$319$	8.05155	0.450801
$320$	0	0
$321$	−3.63218	−0.202728
$322$	−15.0696	−0.839793
$323$	−16.4925	−0.917666
$324$	−1.16594	−0.0647746
$325$	0	0
$326$	−16.5332	−0.915689
$327$	−0.736387	−0.0407223
$328$	28.3312	1.56433
$329$	2.03699	0.112303
$330$	0	0
$331$	15.3409	0.843211	0.421606	−	0.906779i	$-0.361467\pi$
$331$	15.3409	0.843211	0.421606	+	0.906779i	$0.361467\pi$
$332$	18.7306	1.02797
$333$	−2.18294	−0.119624
$334$	23.1788	1.26829
$335$	0	0
$336$	−0.628797	−0.0343037
$337$	−3.19856	−0.174236	−0.0871182	−	0.996198i	$-0.527766\pi$
$337$	−3.19856	−0.174236	−0.0871182	+	0.996198i	$0.527766\pi$
$338$	−6.56569	−0.357126
$339$	1.80180	0.0978601
$340$	0	0
$341$	3.79151	0.205322
$342$	4.54054	0.245524
$343$	−20.0657	−1.08345
$344$	−26.8893	−1.44977
$345$	0	0
$346$	−4.54099	−0.244125
$347$	−8.31509	−0.446377	−0.223189	−	0.974775i	$-0.571647\pi$
$347$	−8.31509	−0.446377	−0.223189	+	0.974775i	$0.571647\pi$
$348$	8.59829	0.460917
$349$	−5.72253	−0.306320	−0.153160	−	0.988201i	$-0.548945\pi$
$349$	−5.72253	−0.306320	−0.153160	+	0.988201i	$0.548945\pi$
$350$	0	0
$351$	−2.41055	−0.128666
$352$	−6.00579	−0.320110
$353$	12.5707	0.669071	0.334536	−	0.942383i	$-0.391421\pi$
$353$	12.5707	0.669071	0.334536	+	0.942383i	$0.391421\pi$
$354$	11.6958	0.621623
$355$	0	0
$356$	11.2791	0.597793
$357$	−6.75717	−0.357628
$358$	16.7532	0.885433
$359$	16.3546	0.863162	0.431581	−	0.902074i	$-0.357956\pi$
$359$	16.3546	0.863162	0.431581	+	0.902074i	$0.357956\pi$
$360$	0	0
$361$	5.71829	0.300963
$362$	21.7429	1.14278
$363$	−9.80796	−0.514784
$364$	5.72510	0.300077
$365$	0	0
$366$	−4.35985	−0.227893
$367$	5.92703	0.309388	0.154694	−	0.987962i	$-0.450561\pi$
$367$	5.92703	0.309388	0.154694	+	0.987962i	$0.450561\pi$
$368$	2.50055	0.130350
$369$	−9.79861	−0.510095
$370$	0	0
$371$	−16.8830	−0.876522
$372$	4.04897	0.209929
$373$	23.2147	1.20201	0.601006	−	0.799244i	$-0.294767\pi$
$373$	23.2147	1.20201	0.601006	+	0.799244i	$0.294767\pi$
$374$	3.30765	0.171035
$375$	0	0
$376$	−2.89135	−0.149110
$377$	17.7767	0.915547
$378$	1.86031	0.0956842
$379$	1.99305	0.102376	0.0511879	−	0.998689i	$-0.483699\pi$
$379$	1.99305	0.102376	0.0511879	+	0.998689i	$0.483699\pi$
$380$	0	0
$381$	−21.3174	−1.09212
$382$	−0.912366	−0.0466807
$383$	28.0007	1.43077	0.715383	−	0.698732i	$-0.246252\pi$
$383$	28.0007	1.43077	0.715383	+	0.698732i	$0.246252\pi$
$384$	−5.84977	−0.298520
$385$	0	0
$386$	−21.5417	−1.09644
$387$	9.29991	0.472741
$388$	22.6234	1.14853
$389$	−9.88992	−0.501439	−0.250719	−	0.968060i	$-0.580667\pi$
$389$	−9.88992	−0.501439	−0.250719	+	0.968060i	$0.580667\pi$
$390$	0	0
$391$	26.8714	1.35895
$392$	8.24232	0.416300
$393$	−18.1461	−0.915352
$394$	17.9333	0.903468
$395$	0	0
$396$	1.27298	0.0639698
$397$	−15.0105	−0.753355	−0.376677	−	0.926345i	$-0.622933\pi$
$397$	−15.0105	−0.753355	−0.376677	+	0.926345i	$0.622933\pi$
$398$	6.23185	0.312374
$399$	10.1274	0.507004
$400$	0	0
$401$	−6.46247	−0.322720	−0.161360	−	0.986896i	$-0.551588\pi$
$401$	−6.46247	−0.322720	−0.161360	+	0.986896i	$0.551588\pi$
$402$	11.7645	0.586758
$403$	8.37113	0.416996
$404$	−1.29235	−0.0642969
$405$	0	0
$406$	−13.7189	−0.680860
$407$	2.38334	0.118138
$408$	9.59130	0.474840
$409$	−10.5606	−0.522186	−0.261093	−	0.965314i	$-0.584083\pi$
$409$	−10.5606	−0.522186	−0.261093	+	0.965314i	$0.584083\pi$
$410$	0	0
$411$	14.4382	0.712186
$412$	−6.56265	−0.323318
$413$	26.0867	1.28364
$414$	−7.39796	−0.363590
$415$	0	0
$416$	−13.2599	−0.650122
$417$	−16.4018	−0.803200
$418$	−4.95738	−0.242473
$419$	12.1426	0.593207	0.296604	−	0.955001i	$-0.404146\pi$
$419$	12.1426	0.593207	0.296604	+	0.955001i	$0.404146\pi$
$420$	0	0
$421$	2.87964	0.140345	0.0701725	−	0.997535i	$-0.477645\pi$
$421$	2.87964	0.140345	0.0701725	+	0.997535i	$0.477645\pi$
$422$	14.2740	0.694846
$423$	1.00000	0.0486217
$424$	23.9642	1.16380
$425$	0	0
$426$	−1.59765	−0.0774064
$427$	−9.72439	−0.470596
$428$	4.23491	0.204702
$429$	2.63186	0.127067
$430$	0	0
$431$	23.1489	1.11504	0.557521	−	0.830163i	$-0.311753\pi$
$431$	23.1489	1.11504	0.557521	+	0.830163i	$0.311753\pi$
$432$	−0.308690	−0.0148518
$433$	−34.4235	−1.65429	−0.827144	−	0.561990i	$-0.810036\pi$
$433$	−34.4235	−1.65429	−0.827144	+	0.561990i	$0.810036\pi$
$434$	−6.46032	−0.310105
$435$	0	0
$436$	0.858586	0.0411188
$437$	−40.2739	−1.92656
$438$	−5.82795	−0.278470
$439$	28.6488	1.36733	0.683666	−	0.729795i	$-0.260385\pi$
$439$	28.6488	1.36733	0.683666	+	0.729795i	$0.260385\pi$
$440$	0	0
$441$	−2.85068	−0.135747
$442$	7.30283	0.347360
$443$	5.53724	0.263082	0.131541	−	0.991311i	$-0.458007\pi$
$443$	5.53724	0.263082	0.131541	+	0.991311i	$0.458007\pi$
$444$	2.54518	0.120789
$445$	0	0
$446$	3.93852	0.186494
$447$	−8.01143	−0.378928
$448$	11.4908	0.542889
$449$	−26.0042	−1.22721	−0.613606	−	0.789612i	$-0.710282\pi$
$449$	−26.0042	−1.22721	−0.613606	+	0.789612i	$0.710282\pi$
$450$	0	0
$451$	10.6982	0.503757
$452$	−2.10079	−0.0988129
$453$	16.6431	0.781962
$454$	−18.7592	−0.880411
$455$	0	0
$456$	−14.3751	−0.673175
$457$	18.8360	0.881111	0.440556	−	0.897725i	$-0.354781\pi$
$457$	18.8360	0.881111	0.440556	+	0.897725i	$0.354781\pi$
$458$	25.5777	1.19517
$459$	−3.31724	−0.154835
$460$	0	0
$461$	30.7115	1.43038	0.715188	−	0.698932i	$-0.246341\pi$
$461$	30.7115	1.43038	0.715188	+	0.698932i	$0.246341\pi$
$462$	−2.03110	−0.0944954
$463$	−2.48651	−0.115558	−0.0577789	−	0.998329i	$-0.518402\pi$
$463$	−2.48651	−0.115558	−0.0577789	+	0.998329i	$0.518402\pi$
$464$	2.27644	0.105681
$465$	0	0
$466$	−8.65129	−0.400763
$467$	41.7168	1.93042	0.965211	−	0.261471i	$-0.0842076\pi$
$467$	41.7168	1.93042	0.965211	+	0.261471i	$0.0842076\pi$
$468$	2.81057	0.129919
$469$	26.2399	1.21165
$470$	0	0
$471$	2.79190	0.128644
$472$	−37.0282	−1.70436
$473$	−10.1537	−0.466867
$474$	11.3790	0.522656
$475$	0	0
$476$	7.87848	0.361110
$477$	−8.28822	−0.379492
$478$	4.48028	0.204923
$479$	−6.88676	−0.314664	−0.157332	−	0.987546i	$-0.550289\pi$
$479$	−6.88676	−0.314664	−0.157332	+	0.987546i	$0.550289\pi$
$480$	0	0
$481$	5.26209	0.239931
$482$	2.11921	0.0965273
$483$	−16.5007	−0.750808
$484$	11.4355	0.519797
$485$	0	0
$486$	0.913267	0.0414266
$487$	8.73216	0.395692	0.197846	−	0.980233i	$-0.436605\pi$
$487$	8.73216	0.395692	0.197846	+	0.980233i	$0.436605\pi$
$488$	13.8030	0.624834
$489$	−18.1033	−0.818662
$490$	0	0
$491$	42.1105	1.90042	0.950209	−	0.311613i	$-0.100869\pi$
$491$	42.1105	1.90042	0.950209	+	0.311613i	$0.100869\pi$
$492$	11.4246	0.515062
$493$	24.4631	1.10176
$494$	−10.9452	−0.492448
$495$	0	0
$496$	1.07199	0.0481336
$497$	−3.56347	−0.159843
$498$	−14.6714	−0.657442
$499$	3.94933	0.176796	0.0883982	−	0.996085i	$-0.471825\pi$
$499$	3.94933	0.176796	0.0883982	+	0.996085i	$0.471825\pi$
$500$	0	0
$501$	25.3801	1.13390
$502$	−2.38925	−0.106638
$503$	2.40095	0.107053	0.0535266	−	0.998566i	$-0.482954\pi$
$503$	2.40095	0.107053	0.0535266	+	0.998566i	$0.482954\pi$
$504$	−5.88965	−0.262346
$505$	0	0
$506$	8.07713	0.359072
$507$	−7.18923	−0.319285
$508$	24.8549	1.10276
$509$	4.24488	0.188151	0.0940756	−	0.995565i	$-0.470010\pi$
$509$	4.24488	0.188151	0.0940756	+	0.995565i	$0.470010\pi$
$510$	0	0
$511$	−12.9989	−0.575037
$512$	−3.48310	−0.153933
$513$	4.97175	0.219508
$514$	3.59186	0.158430
$515$	0	0
$516$	−10.8432	−0.477344
$517$	−1.09181	−0.0480175
$518$	−4.06095	−0.178428
$519$	−4.97224	−0.218257
$520$	0	0
$521$	−29.9427	−1.31182	−0.655908	−	0.754841i	$-0.727714\pi$
$521$	−29.9427	−1.31182	−0.655908	+	0.754841i	$0.727714\pi$
$522$	−6.73492	−0.294779
$523$	−25.8544	−1.13054	−0.565268	−	0.824908i	$-0.691227\pi$
$523$	−25.8544	−1.13054	−0.565268	+	0.824908i	$0.691227\pi$
$524$	21.1574	0.924264
$525$	0	0
$526$	−16.4036	−0.715230
$527$	11.5198	0.501809
$528$	0.337029	0.0146673
$529$	42.6188	1.85299
$530$	0	0
$531$	12.8065	0.555756
$532$	−11.8080	−0.511940
$533$	23.6201	1.02310
$534$	−8.83479	−0.382319
$535$	0	0
$536$	−37.2456	−1.60877
$537$	18.3442	0.791612
$538$	2.17952	0.0939659
$539$	3.11239	0.134060
$540$	0	0
$541$	−34.1608	−1.46869	−0.734345	−	0.678777i	$-0.762510\pi$
$541$	−34.1608	−1.46869	−0.734345	+	0.678777i	$0.762510\pi$
$542$	4.84140	0.207956
$543$	23.8079	1.02169
$544$	−18.2474	−0.782352
$545$	0	0
$546$	−4.48439	−0.191914
$547$	−11.6882	−0.499750	−0.249875	−	0.968278i	$-0.580390\pi$
$547$	−11.6882	−0.499750	−0.249875	+	0.968278i	$0.580390\pi$
$548$	−16.8342	−0.719120
$549$	−4.77390	−0.203745
$550$	0	0
$551$	−36.6643	−1.56195
$552$	23.4215	0.996886
$553$	25.3802	1.07928
$554$	−21.3924	−0.908877
$555$	0	0
$556$	19.1236	0.811021
$557$	8.26827	0.350338	0.175169	−	0.984538i	$-0.443953\pi$
$557$	8.26827	0.350338	0.175169	+	0.984538i	$0.443953\pi$
$558$	−3.17150	−0.134260
$559$	−22.4179	−0.948178
$560$	0	0
$561$	3.62178	0.152912
$562$	2.87468	0.121261
$563$	16.1069	0.678827	0.339413	−	0.940637i	$-0.389771\pi$
$563$	16.1069	0.678827	0.339413	+	0.940637i	$0.389771\pi$
$564$	−1.16594	−0.0490951
$565$	0	0
$566$	0.580143	0.0243852
$567$	2.03699	0.0855455
$568$	5.05807	0.212232
$569$	−21.2188	−0.889538	−0.444769	−	0.895645i	$-0.646714\pi$
$569$	−21.2188	−0.889538	−0.444769	+	0.895645i	$0.646714\pi$
$570$	0	0
$571$	34.2996	1.43539	0.717697	−	0.696356i	$-0.245196\pi$
$571$	34.2996	1.43539	0.717697	+	0.696356i	$0.245196\pi$
$572$	−3.06859	−0.128304
$573$	−0.999013	−0.0417344
$574$	−18.2285	−0.760842
$575$	0	0
$576$	5.64107	0.235044
$577$	−1.61588	−0.0672699	−0.0336349	−	0.999434i	$-0.510708\pi$
$577$	−1.61588	−0.0672699	−0.0336349	+	0.999434i	$0.510708\pi$
$578$	−5.47589	−0.227767
$579$	−23.5875	−0.980262
$580$	0	0
$581$	−32.7237	−1.35761
$582$	−17.7206	−0.734542
$583$	9.04912	0.374776
$584$	18.4510	0.763506
$585$	0	0
$586$	9.36876	0.387020
$587$	−14.1258	−0.583035	−0.291517	−	0.956565i	$-0.594160\pi$
$587$	−14.1258	−0.583035	−0.291517	+	0.956565i	$0.594160\pi$
$588$	3.32373	0.137068
$589$	−17.2654	−0.711408
$590$	0	0
$591$	19.6365	0.807736
$592$	0.673851	0.0276951
$593$	−33.8071	−1.38829	−0.694146	−	0.719834i	$-0.744218\pi$
$593$	−33.8071	−1.38829	−0.694146	+	0.719834i	$0.744218\pi$
$594$	−0.997110	−0.0409119
$595$	0	0
$596$	9.34087	0.382617
$597$	6.82369	0.279275
$598$	17.8332	0.729253
$599$	−14.5929	−0.596249	−0.298125	−	0.954527i	$-0.596361\pi$
$599$	−14.5929	−0.596249	−0.298125	+	0.954527i	$0.596361\pi$
$600$	0	0
$601$	36.2690	1.47944	0.739722	−	0.672913i	$-0.234957\pi$
$601$	36.2690	1.47944	0.739722	+	0.672913i	$0.234957\pi$
$602$	17.3008	0.705126
$603$	12.8817	0.524585
$604$	−19.4049	−0.789576
$605$	0	0
$606$	1.01228	0.0411211
$607$	−44.5100	−1.80661	−0.903303	−	0.429004i	$-0.858865\pi$
$607$	−44.5100	−1.80661	−0.903303	+	0.429004i	$0.858865\pi$
$608$	27.3485	1.10913
$609$	−15.0218	−0.608716
$610$	0	0
$611$	−2.41055	−0.0975206
$612$	3.86771	0.156343
$613$	48.2341	1.94816	0.974078	−	0.226212i	$-0.0726341\pi$
$613$	48.2341	1.94816	0.974078	+	0.226212i	$0.0726341\pi$
$614$	−2.03756	−0.0822292
$615$	0	0
$616$	6.43035	0.259086
$617$	−25.6611	−1.03308	−0.516539	−	0.856264i	$-0.672780\pi$
$617$	−25.6611	−1.03308	−0.516539	+	0.856264i	$0.672780\pi$
$618$	5.14043	0.206778
$619$	10.7544	0.432255	0.216127	−	0.976365i	$-0.430657\pi$
$619$	10.7544	0.432255	0.216127	+	0.976365i	$0.430657\pi$
$620$	0	0
$621$	−8.10054	−0.325064
$622$	10.0447	0.402757
$623$	−19.7055	−0.789483
$624$	0.744113	0.0297884
$625$	0	0
$626$	−7.34133	−0.293418
$627$	−5.42818	−0.216781
$628$	−3.25520	−0.129897
$629$	7.24133	0.288731
$630$	0	0
$631$	44.2477	1.76147	0.880737	−	0.473606i	$-0.157048\pi$
$631$	44.2477	1.76147	0.880737	+	0.473606i	$0.157048\pi$
$632$	−36.0254	−1.43301
$633$	15.6296	0.621220
$634$	−0.446476	−0.0177318
$635$	0	0
$636$	9.66360	0.383187
$637$	6.87172	0.272267
$638$	7.35322	0.291117
$639$	−1.74938	−0.0692044
$640$	0	0
$641$	9.35579	0.369532	0.184766	−	0.982783i	$-0.440847\pi$
$641$	9.35579	0.369532	0.184766	+	0.982783i	$0.440847\pi$
$642$	−3.31715	−0.130917
$643$	18.1081	0.714115	0.357057	−	0.934082i	$-0.383780\pi$
$643$	18.1081	0.714115	0.357057	+	0.934082i	$0.383780\pi$
$644$	19.2389	0.758119
$645$	0	0
$646$	−15.0620	−0.592608
$647$	−20.8586	−0.820035	−0.410018	−	0.912078i	$-0.634477\pi$
$647$	−20.8586	−0.820035	−0.410018	+	0.912078i	$0.634477\pi$
$648$	−2.89135	−0.113583
$649$	−13.9822	−0.548851
$650$	0	0
$651$	−7.07385	−0.277246
$652$	21.1075	0.826633
$653$	21.1738	0.828595	0.414297	−	0.910142i	$-0.364027\pi$
$653$	21.1738	0.828595	0.414297	+	0.910142i	$0.364027\pi$
$654$	−0.672518	−0.0262975
$655$	0	0
$656$	3.02473	0.118096
$657$	−6.38143	−0.248963
$658$	1.86031	0.0725226
$659$	−34.7351	−1.35309	−0.676544	−	0.736403i	$-0.736523\pi$
$659$	−34.7351	−1.35309	−0.676544	+	0.736403i	$0.736523\pi$
$660$	0	0
$661$	−23.1649	−0.901008	−0.450504	−	0.892774i	$-0.648756\pi$
$661$	−23.1649	−0.901008	−0.450504	+	0.892774i	$0.648756\pi$
$662$	14.0103	0.544527
$663$	7.99638	0.310554
$664$	46.4488	1.80256
$665$	0	0
$666$	−1.99361	−0.0772507
$667$	59.7377	2.31305
$668$	−29.5918	−1.14494
$669$	4.31256	0.166733
$670$	0	0
$671$	5.21217	0.201214
$672$	11.2050	0.432244
$673$	5.64609	0.217641	0.108820	−	0.994061i	$-0.465293\pi$
$673$	5.64609	0.217641	0.108820	+	0.994061i	$0.465293\pi$
$674$	−2.92114	−0.112518
$675$	0	0
$676$	8.38223	0.322394
$677$	9.03594	0.347279	0.173640	−	0.984809i	$-0.444447\pi$
$677$	9.03594	0.347279	0.173640	+	0.984809i	$0.444447\pi$
$678$	1.64552	0.0631958
$679$	−39.5247	−1.51682
$680$	0	0
$681$	−20.5407	−0.787122
$682$	3.46266	0.132592
$683$	−50.2971	−1.92456	−0.962282	−	0.272054i	$-0.912297\pi$
$683$	−50.2971	−1.92456	−0.962282	+	0.272054i	$0.912297\pi$
$684$	−5.79678	−0.221645
$685$	0	0
$686$	−18.3254	−0.699665
$687$	28.0068	1.06853
$688$	−2.87079	−0.109448
$689$	19.9792	0.761147
$690$	0	0
$691$	26.8350	1.02085	0.510425	−	0.859922i	$-0.329488\pi$
$691$	26.8350	1.02085	0.510425	+	0.859922i	$0.329488\pi$
$692$	5.79735	0.220382
$693$	−2.22399	−0.0844826
$694$	−7.59390	−0.288260
$695$	0	0
$696$	21.3224	0.808222
$697$	32.5043	1.23119
$698$	−5.22620	−0.197814
$699$	−9.47290	−0.358298
$700$	0	0
$701$	2.64516	0.0999062	0.0499531	−	0.998752i	$-0.484093\pi$
$701$	2.64516	0.0999062	0.0499531	+	0.998752i	$0.484093\pi$
$702$	−2.20148	−0.0830895
$703$	−10.8530	−0.409330
$704$	−6.15895	−0.232124
$705$	0	0
$706$	11.4804	0.432071
$707$	2.25783	0.0849145
$708$	−14.9317	−0.561167
$709$	−2.68535	−0.100850	−0.0504252	−	0.998728i	$-0.516058\pi$
$709$	−2.68535	−0.100850	−0.0504252	+	0.998728i	$0.516058\pi$
$710$	0	0
$711$	12.4597	0.467275
$712$	27.9705	1.04824
$713$	28.1308	1.05351
$714$	−6.17110	−0.230948
$715$	0	0
$716$	−21.3883	−0.799320
$717$	4.90577	0.183209
$718$	14.9361	0.557410
$719$	−49.8759	−1.86006	−0.930028	−	0.367487i	$-0.880218\pi$
$719$	−49.8759	−1.86006	−0.930028	+	0.367487i	$0.880218\pi$
$720$	0	0
$721$	11.4654	0.426995
$722$	5.22233	0.194355
$723$	2.32047	0.0862992
$724$	−27.7586	−1.03164
$725$	0	0
$726$	−8.95729	−0.332436
$727$	32.3750	1.20072	0.600362	−	0.799729i	$-0.295023\pi$
$727$	32.3750	1.20072	0.600362	+	0.799729i	$0.295023\pi$
$728$	14.1973	0.526188
$729$	1.00000	0.0370370
$730$	0	0
$731$	−30.8500	−1.14103
$732$	5.56610	0.205729
$733$	25.9723	0.959308	0.479654	−	0.877458i	$-0.340762\pi$
$733$	25.9723	0.959308	0.479654	+	0.877458i	$0.340762\pi$
$734$	5.41296	0.199796
$735$	0	0
$736$	−44.5594	−1.64248
$737$	−14.0643	−0.518067
$738$	−8.94874	−0.329408
$739$	45.1960	1.66256	0.831280	−	0.555853i	$-0.187608\pi$
$739$	45.1960	1.66256	0.831280	+	0.555853i	$0.187608\pi$
$740$	0	0
$741$	−11.9847	−0.440268
$742$	−15.4187	−0.566038
$743$	−39.2875	−1.44132	−0.720660	−	0.693289i	$-0.756161\pi$
$743$	−39.2875	−1.44132	−0.720660	+	0.693289i	$0.756161\pi$
$744$	10.0408	0.368114
$745$	0	0
$746$	21.2012	0.776232
$747$	−16.0648	−0.587779
$748$	−4.22279	−0.154400
$749$	−7.39870	−0.270343
$750$	0	0
$751$	51.5161	1.87985	0.939924	−	0.341384i	$-0.110896\pi$
$751$	51.5161	1.87985	0.939924	+	0.341384i	$0.110896\pi$
$752$	−0.308690	−0.0112568
$753$	−2.61616	−0.0953382
$754$	16.2349	0.591240
$755$	0	0
$756$	−2.37501	−0.0863784
$757$	−22.3984	−0.814083	−0.407042	−	0.913410i	$-0.633440\pi$
$757$	−22.3984	−0.814083	−0.407042	+	0.913410i	$0.633440\pi$
$758$	1.82018	0.0661120
$759$	8.84422	0.321025
$760$	0	0
$761$	28.2089	1.02257	0.511287	−	0.859410i	$-0.329169\pi$
$761$	28.2089	1.02257	0.511287	+	0.859410i	$0.329169\pi$
$762$	−19.4685	−0.705269
$763$	−1.50001	−0.0543041
$764$	1.16479	0.0421407
$765$	0	0
$766$	25.5721	0.923956
$767$	−30.8708	−1.11468
$768$	−16.6245	−0.599886
$769$	28.5201	1.02846	0.514230	−	0.857652i	$-0.328078\pi$
$769$	28.5201	1.02846	0.514230	+	0.857652i	$0.328078\pi$
$770$	0	0
$771$	3.93298	0.141643
$772$	27.5017	0.989806
$773$	−34.4606	−1.23946	−0.619731	−	0.784814i	$-0.712758\pi$
$773$	−34.4606	−1.23946	−0.619731	+	0.784814i	$0.712758\pi$
$774$	8.49330	0.305286
$775$	0	0
$776$	56.1024	2.01396
$777$	−4.44662	−0.159522
$778$	−9.03214	−0.323818
$779$	−48.7162	−1.74544
$780$	0	0
$781$	1.90998	0.0683445
$782$	24.5408	0.877577
$783$	−7.37453	−0.263544
$784$	0.879975	0.0314277
$785$	0	0
$786$	−16.5723	−0.591113
$787$	−22.8212	−0.813488	−0.406744	−	0.913542i	$-0.633336\pi$
$787$	−22.8212	−0.813488	−0.406744	+	0.913542i	$0.633336\pi$
$788$	−22.8950	−0.815601
$789$	−17.9614	−0.639443
$790$	0	0
$791$	3.67024	0.130499
$792$	3.15679	0.112172
$793$	11.5078	0.408652
$794$	−13.7086	−0.486499
$795$	0	0
$796$	−7.95603	−0.281994
$797$	2.74900	0.0973745	0.0486872	−	0.998814i	$-0.484496\pi$
$797$	2.74900	0.0973745	0.0486872	+	0.998814i	$0.484496\pi$
$798$	9.24902	0.327412
$799$	−3.31724	−0.117355
$800$	0	0
$801$	−9.67383	−0.341808
$802$	−5.90196	−0.208406
$803$	6.96728	0.245870
$804$	−15.0194	−0.529692
$805$	0	0
$806$	7.64508	0.269286
$807$	2.38651	0.0840092
$808$	−3.20482	−0.112745
$809$	−10.9075	−0.383489	−0.191744	−	0.981445i	$-0.561414\pi$
$809$	−10.9075	−0.383489	−0.191744	+	0.981445i	$0.561414\pi$
$810$	0	0
$811$	−37.6352	−1.32155	−0.660775	−	0.750584i	$-0.729772\pi$
$811$	−37.6352	−1.32155	−0.660775	+	0.750584i	$0.729772\pi$
$812$	17.5146	0.614642
$813$	5.30119	0.185921
$814$	2.17663	0.0762908
$815$	0	0
$816$	1.02400	0.0358471
$817$	46.2368	1.61762
$818$	−9.64461	−0.337216
$819$	−4.91027	−0.171579
$820$	0	0
$821$	15.8845	0.554374	0.277187	−	0.960816i	$-0.410598\pi$
$821$	15.8845	0.554374	0.277187	+	0.960816i	$0.410598\pi$
$822$	13.1860	0.459914
$823$	10.5900	0.369144	0.184572	−	0.982819i	$-0.440910\pi$
$823$	10.5900	0.369144	0.184572	+	0.982819i	$0.440910\pi$
$824$	−16.2743	−0.566942
$825$	0	0
$826$	23.8242	0.828948
$827$	−22.2314	−0.773062	−0.386531	−	0.922276i	$-0.626327\pi$
$827$	−22.2314	−0.773062	−0.386531	+	0.922276i	$0.626327\pi$
$828$	9.44477	0.328229
$829$	−47.0279	−1.63335	−0.816674	−	0.577100i	$-0.804184\pi$
$829$	−47.0279	−1.63335	−0.816674	+	0.577100i	$0.804184\pi$
$830$	0	0
$831$	−23.4240	−0.812571
$832$	−13.5981	−0.471429
$833$	9.45638	0.327644
$834$	−14.9792	−0.518689
$835$	0	0
$836$	6.32895	0.218891
$837$	−3.47270	−0.120034
$838$	11.0895	0.383080
$839$	−6.10911	−0.210910	−0.105455	−	0.994424i	$-0.533630\pi$
$839$	−6.10911	−0.210910	−0.105455	+	0.994424i	$0.533630\pi$
$840$	0	0
$841$	25.3837	0.875301
$842$	2.62988	0.0906317
$843$	3.14768	0.108412
$844$	−18.2232	−0.627268
$845$	0	0
$846$	0.913267	0.0313988
$847$	−19.9787	−0.686476
$848$	2.55849	0.0878588
$849$	0.635239	0.0218014
$850$	0	0
$851$	17.6830	0.606165
$852$	2.03968	0.0698782
$853$	8.18044	0.280093	0.140047	−	0.990145i	$-0.455275\pi$
$853$	8.18044	0.280093	0.140047	+	0.990145i	$0.455275\pi$
$854$	−8.88096	−0.303900
$855$	0	0
$856$	10.5019	0.358947
$857$	34.5271	1.17942	0.589712	−	0.807614i	$-0.299241\pi$
$857$	34.5271	1.17942	0.589712	+	0.807614i	$0.299241\pi$
$858$	2.40359	0.0820571
$859$	18.7039	0.638167	0.319084	−	0.947727i	$-0.396625\pi$
$859$	18.7039	0.638167	0.319084	+	0.947727i	$0.396625\pi$
$860$	0	0
$861$	−19.9596	−0.680223
$862$	21.1411	0.720069
$863$	−25.4759	−0.867209	−0.433604	−	0.901103i	$-0.642758\pi$
$863$	−25.4759	−0.867209	−0.433604	+	0.901103i	$0.642758\pi$
$864$	5.50079	0.187141
$865$	0	0
$866$	−31.4379	−1.06830
$867$	−5.99593	−0.203633
$868$	8.24771	0.279946
$869$	−13.6036	−0.461469
$870$	0	0
$871$	−31.0521	−1.05216
$872$	2.12915	0.0721022
$873$	−19.4035	−0.656709
$874$	−36.7808	−1.24413
$875$	0	0
$876$	7.44039	0.251387
$877$	−39.7428	−1.34202	−0.671010	−	0.741448i	$-0.734139\pi$
$877$	−39.7428	−1.34202	−0.671010	+	0.741448i	$0.734139\pi$
$878$	26.1640	0.882992
$879$	10.2585	0.346011
$880$	0	0
$881$	−14.4943	−0.488324	−0.244162	−	0.969734i	$-0.578513\pi$
$881$	−14.4943	−0.488324	−0.244162	+	0.969734i	$0.578513\pi$
$882$	−2.60343	−0.0876621
$883$	−18.7687	−0.631618	−0.315809	−	0.948823i	$-0.602276\pi$
$883$	−18.7687	−0.631618	−0.315809	+	0.948823i	$0.602276\pi$
$884$	−9.32333	−0.313577
$885$	0	0
$886$	5.05698	0.169893
$887$	−7.49125	−0.251532	−0.125766	−	0.992060i	$-0.540139\pi$
$887$	−7.49125	−0.251532	−0.125766	+	0.992060i	$0.540139\pi$
$888$	6.31164	0.211805
$889$	−43.4233	−1.45637
$890$	0	0
$891$	−1.09181	−0.0365769
$892$	−5.02820	−0.168357
$893$	4.97175	0.166373
$894$	−7.31657	−0.244703
$895$	0	0
$896$	−11.9159	−0.398083
$897$	19.5268	0.651981
$898$	−23.7487	−0.792506
$899$	25.6096	0.854126
$900$	0	0
$901$	27.4940	0.915958
$902$	9.77029	0.325315
$903$	18.9438	0.630411
$904$	−5.20963	−0.173270
$905$	0	0
$906$	15.1996	0.504973
$907$	13.0411	0.433023	0.216511	−	0.976280i	$-0.430532\pi$
$907$	13.0411	0.433023	0.216511	+	0.976280i	$0.430532\pi$
$908$	23.9493	0.794786
$909$	1.10842	0.0367639
$910$	0	0
$911$	−2.46579	−0.0816952	−0.0408476	−	0.999165i	$-0.513006\pi$
$911$	−2.46579	−0.0816952	−0.0408476	+	0.999165i	$0.513006\pi$
$912$	−1.53473	−0.0508199
$913$	17.5396	0.580475
$914$	17.2023	0.569002
$915$	0	0
$916$	−32.6543	−1.07893
$917$	−36.9635	−1.22064
$918$	−3.02952	−0.0999892
$919$	9.22107	0.304175	0.152087	−	0.988367i	$-0.451400\pi$
$919$	9.22107	0.304175	0.152087	+	0.988367i	$0.451400\pi$
$920$	0	0
$921$	−2.23107	−0.0735161
$922$	28.0478	0.923704
$923$	4.21697	0.138803
$924$	2.59305	0.0853051
$925$	0	0
$926$	−2.27085	−0.0746246
$927$	5.62862	0.184868
$928$	−40.5657	−1.33164
$929$	−21.0330	−0.690069	−0.345034	−	0.938590i	$-0.612133\pi$
$929$	−21.0330	−0.690069	−0.345034	+	0.938590i	$0.612133\pi$
$930$	0	0
$931$	−14.1729	−0.464497
$932$	11.0449	0.361786
$933$	10.9987	0.360081
$934$	38.0986	1.24662
$935$	0	0
$936$	6.96976	0.227814
$937$	−25.0112	−0.817079	−0.408539	−	0.912741i	$-0.633962\pi$
$937$	−25.0112	−0.817079	−0.408539	+	0.912741i	$0.633962\pi$
$938$	23.9641	0.782455
$939$	−8.03853	−0.262328
$940$	0	0
$941$	36.7705	1.19868	0.599342	−	0.800493i	$-0.295429\pi$
$941$	36.7705	1.19868	0.599342	+	0.800493i	$0.295429\pi$
$942$	2.54975	0.0830754
$943$	79.3740	2.58477
$944$	−3.95324	−0.128667
$945$	0	0
$946$	−9.27303	−0.301492
$947$	−27.6088	−0.897167	−0.448583	−	0.893741i	$-0.648071\pi$
$947$	−27.6088	−0.897167	−0.448583	+	0.893741i	$0.648071\pi$
$948$	−14.5273	−0.471825
$949$	15.3828	0.499346
$950$	0	0
$951$	−0.488878	−0.0158529
$952$	19.5374	0.633210
$953$	15.8746	0.514229	0.257114	−	0.966381i	$-0.417228\pi$
$953$	15.8746	0.514229	0.257114	+	0.966381i	$0.417228\pi$
$954$	−7.56936	−0.245067
$955$	0	0
$956$	−5.71985	−0.184993
$957$	8.05155	0.260270
$958$	−6.28945	−0.203203
$959$	29.4105	0.949715
$960$	0	0
$961$	−18.9403	−0.610979
$962$	4.80570	0.154942
$963$	−3.63218	−0.117045
$964$	−2.70554	−0.0871394
$965$	0	0
$966$	−15.0696	−0.484855
$967$	38.5084	1.23835	0.619173	−	0.785255i	$-0.287468\pi$
$967$	38.5084	1.23835	0.619173	+	0.785255i	$0.287468\pi$
$968$	28.3583	0.911469
$969$	−16.4925	−0.529815
$970$	0	0
$971$	−11.6414	−0.373589	−0.186794	−	0.982399i	$-0.559810\pi$
$971$	−11.6414	−0.373589	−0.186794	+	0.982399i	$0.559810\pi$
$972$	−1.16594	−0.0373976
$973$	−33.4103	−1.07109
$974$	7.97479	0.255529
$975$	0	0
$976$	1.47365	0.0471705
$977$	−50.2756	−1.60846	−0.804229	−	0.594320i	$-0.797421\pi$
$977$	−50.2756	−1.60846	−0.804229	+	0.594320i	$0.797421\pi$
$978$	−16.5332	−0.528673
$979$	10.5619	0.337561
$980$	0	0
$981$	−0.736387	−0.0235110
$982$	38.4581	1.22725
$983$	23.6134	0.753151	0.376575	−	0.926386i	$-0.377102\pi$
$983$	23.6134	0.753151	0.376575	+	0.926386i	$0.377102\pi$
$984$	28.3312	0.903166
$985$	0	0
$986$	22.3413	0.711493
$987$	2.03699	0.0648380
$988$	13.9734	0.444555
$989$	−75.3343	−2.39549
$990$	0	0
$991$	−59.5975	−1.89318	−0.946588	−	0.322446i	$-0.895495\pi$
$991$	−59.5975	−1.89318	−0.946588	+	0.322446i	$0.895495\pi$
$992$	−19.1026	−0.606508
$993$	15.3409	0.486828
$994$	−3.25440	−0.103223
$995$	0	0
$996$	18.7306	0.593501
$997$	−53.0303	−1.67949	−0.839743	−	0.542984i	$-0.817295\pi$
$997$	−53.0303	−1.67949	−0.839743	+	0.542984i	$0.817295\pi$
$998$	3.60680	0.114171
$999$	−2.18294	−0.0690651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.y.1.5	✓	7
5.4	even	2		3525.2.a.bb.1.3	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3525.2.a.y.1.5	✓	7	1.1	even	1	trivial
3525.2.a.bb.1.3	yes	7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q+0.913267 q^{2} +1.00000 q^{3} -1.16594 q^{4} +0.913267 q^{6} +2.03699 q^{7} -2.89135 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.913267 q^{2} +1.00000 q^{3} -1.16594 q^{4} +0.913267 q^{6} +2.03699 q^{7} -2.89135 q^{8} +1.00000 q^{9} -1.09181 q^{11} -1.16594 q^{12} -2.41055 q^{13} +1.86031 q^{14} -0.308690 q^{16} -3.31724 q^{17} +0.913267 q^{18} +4.97175 q^{19} +2.03699 q^{21} -0.997110 q^{22} -8.10054 q^{23} -2.89135 q^{24} -2.20148 q^{26} +1.00000 q^{27} -2.37501 q^{28} -7.37453 q^{29} -3.47270 q^{31} +5.50079 q^{32} -1.09181 q^{33} -3.02952 q^{34} -1.16594 q^{36} -2.18294 q^{37} +4.54054 q^{38} -2.41055 q^{39} -9.79861 q^{41} +1.86031 q^{42} +9.29991 q^{43} +1.27298 q^{44} -7.39796 q^{46} +1.00000 q^{47} -0.308690 q^{48} -2.85068 q^{49} -3.31724 q^{51} +2.81057 q^{52} -8.28822 q^{53} +0.913267 q^{54} -5.88965 q^{56} +4.97175 q^{57} -6.73492 q^{58} +12.8065 q^{59} -4.77390 q^{61} -3.17150 q^{62} +2.03699 q^{63} +5.64107 q^{64} -0.997110 q^{66} +12.8817 q^{67} +3.86771 q^{68} -8.10054 q^{69} -1.74938 q^{71} -2.89135 q^{72} -6.38143 q^{73} -1.99361 q^{74} -5.79678 q^{76} -2.22399 q^{77} -2.20148 q^{78} +12.4597 q^{79} +1.00000 q^{81} -8.94874 q^{82} -16.0648 q^{83} -2.37501 q^{84} +8.49330 q^{86} -7.37453 q^{87} +3.15679 q^{88} -9.67383 q^{89} -4.91027 q^{91} +9.44477 q^{92} -3.47270 q^{93} +0.913267 q^{94} +5.50079 q^{96} -19.4035 q^{97} -2.60343 q^{98} -1.09181 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 5 q^{4} - q^{6} - 11 q^{7} - 6 q^{8} + 7 q^{9} - 8 q^{11} + 5 q^{12} - 5 q^{13} - 3 q^{14} + 9 q^{16} - 10 q^{17} - q^{18} + 7 q^{19} - 11 q^{21} - 20 q^{22} - 4 q^{23} - 6 q^{24} + 7 q^{27} - 2 q^{28} - 11 q^{29} + 3 q^{31} - 28 q^{32} - 8 q^{33} + 8 q^{34} + 5 q^{36} - 11 q^{37} + 2 q^{38} - 5 q^{39} - 20 q^{41} - 3 q^{42} - 18 q^{43} + q^{44} - 19 q^{46} + 7 q^{47} + 9 q^{48} + 14 q^{49} - 10 q^{51} - 29 q^{52} - 12 q^{53} - q^{54} - 47 q^{56} + 7 q^{57} + 19 q^{58} + 18 q^{59} - 4 q^{61} - 12 q^{62} - 11 q^{63} + 42 q^{64} - 20 q^{66} - 22 q^{67} - 44 q^{68} - 4 q^{69} - 14 q^{71} - 6 q^{72} - 30 q^{73} + 31 q^{74} - 2 q^{76} + 8 q^{77} - q^{79} + 7 q^{81} - 29 q^{82} - 54 q^{83} - 2 q^{84} - 29 q^{86} - 11 q^{87} + 22 q^{88} - 14 q^{89} + 20 q^{91} + 5 q^{92} + 3 q^{93} - q^{94} - 28 q^{96} - 24 q^{97} + 26 q^{98} - 8 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 5 * q^4 - q^6 - 11 * q^7 - 6 * q^8 + 7 * q^9 - 8 * q^11 + 5 * q^12 - 5 * q^13 - 3 * q^14 + 9 * q^16 - 10 * q^17 - q^18 + 7 * q^19 - 11 * q^21 - 20 * q^22 - 4 * q^23 - 6 * q^24 + 7 * q^27 - 2 * q^28 - 11 * q^29 + 3 * q^31 - 28 * q^32 - 8 * q^33 + 8 * q^34 + 5 * q^36 - 11 * q^37 + 2 * q^38 - 5 * q^39 - 20 * q^41 - 3 * q^42 - 18 * q^43 + q^44 - 19 * q^46 + 7 * q^47 + 9 * q^48 + 14 * q^49 - 10 * q^51 - 29 * q^52 - 12 * q^53 - q^54 - 47 * q^56 + 7 * q^57 + 19 * q^58 + 18 * q^59 - 4 * q^61 - 12 * q^62 - 11 * q^63 + 42 * q^64 - 20 * q^66 - 22 * q^67 - 44 * q^68 - 4 * q^69 - 14 * q^71 - 6 * q^72 - 30 * q^73 + 31 * q^74 - 2 * q^76 + 8 * q^77 - q^79 + 7 * q^81 - 29 * q^82 - 54 * q^83 - 2 * q^84 - 29 * q^86 - 11 * q^87 + 22 * q^88 - 14 * q^89 + 20 * q^91 + 5 * q^92 + 3 * q^93 - q^94 - 28 * q^96 - 24 * q^97 + 26 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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