LMFDB - Embedded newform 4025.2.a.z.1.8

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:	$1$
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			1.8
Root			$-0.0822464$ 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)

$f(q)$	$=$	$q+0.0822464 q^{2} -1.69790 q^{3} -1.99324 q^{4} -0.139646 q^{6} -1.00000 q^{7} -0.328429 q^{8} -0.117136 q^{9} +O(q^{10})$	\(q+0.0822464 q^{2} -1.69790 q^{3} -1.99324 q^{4} -0.139646 q^{6} -1.00000 q^{7} -0.328429 q^{8} -0.117136 q^{9} -6.60175 q^{11} +3.38431 q^{12} +0.246024 q^{13} -0.0822464 q^{14} +3.95946 q^{16} +3.13258 q^{17} -0.00963397 q^{18} +3.09316 q^{19} +1.69790 q^{21} -0.542971 q^{22} -1.00000 q^{23} +0.557640 q^{24} +0.0202346 q^{26} +5.29258 q^{27} +1.99324 q^{28} +1.93958 q^{29} +11.0058 q^{31} +0.982510 q^{32} +11.2091 q^{33} +0.257644 q^{34} +0.233479 q^{36} +3.70320 q^{37} +0.254401 q^{38} -0.417725 q^{39} -1.36238 q^{41} +0.139646 q^{42} -8.92000 q^{43} +13.1589 q^{44} -0.0822464 q^{46} +3.34242 q^{47} -6.72277 q^{48} +1.00000 q^{49} -5.31881 q^{51} -0.490385 q^{52} -6.98280 q^{53} +0.435296 q^{54} +0.328429 q^{56} -5.25187 q^{57} +0.159524 q^{58} +10.4489 q^{59} -2.35009 q^{61} +0.905187 q^{62} +0.117136 q^{63} -7.83811 q^{64} +0.921910 q^{66} -9.34195 q^{67} -6.24397 q^{68} +1.69790 q^{69} -10.8504 q^{71} +0.0384707 q^{72} -11.5419 q^{73} +0.304574 q^{74} -6.16539 q^{76} +6.60175 q^{77} -0.0343564 q^{78} +8.34300 q^{79} -8.63487 q^{81} -0.112051 q^{82} +14.8750 q^{83} -3.38431 q^{84} -0.733638 q^{86} -3.29321 q^{87} +2.16821 q^{88} +15.2533 q^{89} -0.246024 q^{91} +1.99324 q^{92} -18.6867 q^{93} +0.274902 q^{94} -1.66820 q^{96} -7.03768 q^{97} +0.0822464 q^{98} +0.773300 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.0822464	0.0581570	0.0290785	−	0.999577i	$-0.490743\pi$
$2$	0.0822464	0.0581570	0.0290785	+	0.999577i	$0.490743\pi$
$3$	−1.69790	−0.980283	−0.490142	−	0.871643i	$-0.663055\pi$
$3$	−1.69790	−0.980283	−0.490142	+	0.871643i	$0.663055\pi$
$4$	−1.99324	−0.996618
$5$	0	0
$5$	0	0
$6$	−0.139646	−0.0570103
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.328429	−0.116117
$9$	−0.117136	−0.0390452
$10$	0	0
$11$	−6.60175	−1.99050	−0.995252	−	0.0973321i	$-0.968969\pi$
$11$	−6.60175	−1.99050	−0.995252	+	0.0973321i	$0.968969\pi$
$12$	3.38431	0.976967
$13$	0.246024	0.0682349	0.0341175	−	0.999418i	$-0.489138\pi$
$13$	0.246024	0.0682349	0.0341175	+	0.999418i	$0.489138\pi$
$14$	−0.0822464	−0.0219813
$15$	0	0
$16$	3.95946	0.989865
$17$	3.13258	0.759763	0.379881	−	0.925035i	$-0.375965\pi$
$17$	3.13258	0.759763	0.379881	+	0.925035i	$0.375965\pi$
$18$	−0.00963397	−0.00227075
$19$	3.09316	0.709619	0.354810	−	0.934939i	$-0.384546\pi$
$19$	3.09316	0.709619	0.354810	+	0.934939i	$0.384546\pi$
$20$	0	0
$21$	1.69790	0.370512
$22$	−0.542971	−0.115762
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.557640	0.113828
$25$	0	0
$26$	0.0202346	0.00396834
$27$	5.29258	1.01856
$28$	1.99324	0.376686
$29$	1.93958	0.360171	0.180086	−	0.983651i	$-0.442363\pi$
$29$	1.93958	0.360171	0.180086	+	0.983651i	$0.442363\pi$
$30$	0	0
$31$	11.0058	1.97670	0.988350	−	0.152199i	$-0.0486356\pi$
$31$	11.0058	1.97670	0.988350	+	0.152199i	$0.0486356\pi$
$32$	0.982510	0.173685
$33$	11.2091	1.95126
$34$	0.257644	0.0441855
$35$	0	0
$36$	0.233479	0.0389131
$37$	3.70320	0.608802	0.304401	−	0.952544i	$-0.401544\pi$
$37$	3.70320	0.608802	0.304401	+	0.952544i	$0.401544\pi$
$38$	0.254401	0.0412693
$39$	−0.417725	−0.0668895
$40$	0	0
$41$	−1.36238	−0.212767	−0.106384	−	0.994325i	$-0.533927\pi$
$41$	−1.36238	−0.212767	−0.106384	+	0.994325i	$0.533927\pi$
$42$	0.139646	0.0215479
$43$	−8.92000	−1.36029	−0.680144	−	0.733079i	$-0.738083\pi$
$43$	−8.92000	−1.36029	−0.680144	+	0.733079i	$0.738083\pi$
$44$	13.1589	1.98377
$45$	0	0
$46$	−0.0822464	−0.0121266
$47$	3.34242	0.487542	0.243771	−	0.969833i	$-0.421616\pi$
$47$	3.34242	0.487542	0.243771	+	0.969833i	$0.421616\pi$
$48$	−6.72277	−0.970348
$49$	1.00000	0.142857
$50$	0	0
$51$	−5.31881	−0.744783
$52$	−0.490385	−0.0680041
$53$	−6.98280	−0.959161	−0.479581	−	0.877498i	$-0.659211\pi$
$53$	−6.98280	−0.959161	−0.479581	+	0.877498i	$0.659211\pi$
$54$	0.435296	0.0592363
$55$	0	0
$56$	0.328429	0.0438882
$57$	−5.25187	−0.695627
$58$	0.159524	0.0209465
$59$	10.4489	1.36034	0.680168	−	0.733057i	$-0.261907\pi$
$59$	10.4489	1.36034	0.680168	+	0.733057i	$0.261907\pi$
$60$	0	0
$61$	−2.35009	−0.300898	−0.150449	−	0.988618i	$-0.548072\pi$
$61$	−2.35009	−0.300898	−0.150449	+	0.988618i	$0.548072\pi$
$62$	0.905187	0.114959
$63$	0.117136	0.0147577
$64$	−7.83811	−0.979764
$65$	0	0
$66$	0.921910	0.113479
$67$	−9.34195	−1.14130	−0.570650	−	0.821193i	$-0.693309\pi$
$67$	−9.34195	−1.14130	−0.570650	+	0.821193i	$0.693309\pi$
$68$	−6.24397	−0.757193
$69$	1.69790	0.204403
$70$	0	0
$71$	−10.8504	−1.28770	−0.643850	−	0.765151i	$-0.722664\pi$
$71$	−10.8504	−1.28770	−0.643850	+	0.765151i	$0.722664\pi$
$72$	0.0384707	0.00453382
$73$	−11.5419	−1.35087	−0.675436	−	0.737418i	$-0.736045\pi$
$73$	−11.5419	−1.35087	−0.675436	+	0.737418i	$0.736045\pi$
$74$	0.304574	0.0354061
$75$	0	0
$76$	−6.16539	−0.707219
$77$	6.60175	0.752340
$78$	−0.0343564	−0.00389009
$79$	8.34300	0.938660	0.469330	−	0.883023i	$-0.344495\pi$
$79$	8.34300	0.938660	0.469330	+	0.883023i	$0.344495\pi$
$80$	0	0
$81$	−8.63487	−0.959430
$82$	−0.112051	−0.0123739
$83$	14.8750	1.63274	0.816370	−	0.577529i	$-0.195983\pi$
$83$	14.8750	1.63274	0.816370	+	0.577529i	$0.195983\pi$
$84$	−3.38431	−0.369259
$85$	0	0
$86$	−0.733638	−0.0791102
$87$	−3.29321	−0.353070
$88$	2.16821	0.231132
$89$	15.2533	1.61684	0.808422	−	0.588604i	$-0.200322\pi$
$89$	15.2533	1.61684	0.808422	+	0.588604i	$0.200322\pi$
$90$	0	0
$91$	−0.246024	−0.0257904
$92$	1.99324	0.207809
$93$	−18.6867	−1.93773
$94$	0.274902	0.0283539
$95$	0	0
$96$	−1.66820	−0.170260
$97$	−7.03768	−0.714568	−0.357284	−	0.933996i	$-0.616297\pi$
$97$	−7.03768	−0.714568	−0.357284	+	0.933996i	$0.616297\pi$
$98$	0.0822464	0.00830814
$99$	0.773300	0.0777196
$100$	0	0
$101$	11.3084	1.12523	0.562616	−	0.826718i	$-0.309795\pi$
$101$	11.3084	1.12523	0.562616	+	0.826718i	$0.309795\pi$
$102$	−0.437453	−0.0433143
$103$	−18.6403	−1.83668	−0.918340	−	0.395792i	$-0.870470\pi$
$103$	−18.6403	−1.83668	−0.918340	+	0.395792i	$0.870470\pi$
$104$	−0.0808016	−0.00792325
$105$	0	0
$106$	−0.574310	−0.0557819
$107$	8.29183	0.801601	0.400801	−	0.916165i	$-0.368732\pi$
$107$	8.29183	0.801601	0.400801	+	0.916165i	$0.368732\pi$
$108$	−10.5494	−1.01511
$109$	15.7652	1.51004	0.755018	−	0.655704i	$-0.227628\pi$
$109$	15.7652	1.51004	0.755018	+	0.655704i	$0.227628\pi$
$110$	0	0
$111$	−6.28766	−0.596798
$112$	−3.95946	−0.374134
$113$	−9.08718	−0.854850	−0.427425	−	0.904051i	$-0.640579\pi$
$113$	−9.08718	−0.854850	−0.427425	+	0.904051i	$0.640579\pi$
$114$	−0.431948	−0.0404556
$115$	0	0
$116$	−3.86604	−0.358953
$117$	−0.0288182	−0.00266424
$118$	0.859387	0.0791130
$119$	−3.13258	−0.287163
$120$	0	0
$121$	32.5832	2.96211
$122$	−0.193286	−0.0174993
$123$	2.31318	0.208572
$124$	−21.9371	−1.97001
$125$	0	0
$126$	0.00963397	0.000858263 0
$127$	1.88462	0.167233	0.0836163	−	0.996498i	$-0.473353\pi$
$127$	1.88462	0.167233	0.0836163	+	0.996498i	$0.473353\pi$
$128$	−2.60968	−0.230665
$129$	15.1453	1.33347
$130$	0	0
$131$	−3.15585	−0.275728	−0.137864	−	0.990451i	$-0.544024\pi$
$131$	−3.15585	−0.275728	−0.137864	+	0.990451i	$0.544024\pi$
$132$	−22.3424	−1.94466
$133$	−3.09316	−0.268211
$134$	−0.768341	−0.0663746
$135$	0	0
$136$	−1.02883	−0.0882216
$137$	17.7862	1.51958	0.759790	−	0.650169i	$-0.225302\pi$
$137$	17.7862	1.51958	0.759790	+	0.650169i	$0.225302\pi$
$138$	0.139646	0.0118875
$139$	−14.7276	−1.24918	−0.624590	−	0.780953i	$-0.714734\pi$
$139$	−14.7276	−1.24918	−0.624590	+	0.780953i	$0.714734\pi$
$140$	0	0
$141$	−5.67509	−0.477929
$142$	−0.892403	−0.0748888
$143$	−1.62419	−0.135822
$144$	−0.463793	−0.0386494
$145$	0	0
$146$	−0.949276	−0.0785627
$147$	−1.69790	−0.140040
$148$	−7.38134	−0.606742
$149$	−17.3956	−1.42510	−0.712550	−	0.701622i	$-0.752460\pi$
$149$	−17.3956	−1.42510	−0.712550	+	0.701622i	$0.752460\pi$
$150$	0	0
$151$	−18.0339	−1.46758	−0.733789	−	0.679377i	$-0.762250\pi$
$151$	−18.0339	−1.46758	−0.733789	+	0.679377i	$0.762250\pi$
$152$	−1.01588	−0.0823990
$153$	−0.366937	−0.0296651
$154$	0.542971	0.0437538
$155$	0	0
$156$	0.832624	0.0666633
$157$	−0.261658	−0.0208826	−0.0104413	−	0.999945i	$-0.503324\pi$
$157$	−0.261658	−0.0208826	−0.0104413	+	0.999945i	$0.503324\pi$
$158$	0.686181	0.0545897
$159$	11.8561	0.940249
$160$	0	0
$161$	1.00000	0.0788110
$162$	−0.710187	−0.0557976
$163$	1.30151	0.101942	0.0509710	−	0.998700i	$-0.483768\pi$
$163$	1.30151	0.101942	0.0509710	+	0.998700i	$0.483768\pi$
$164$	2.71554	0.212048
$165$	0	0
$166$	1.22341	0.0949553
$167$	−8.41055	−0.650828	−0.325414	−	0.945572i	$-0.605504\pi$
$167$	−8.41055	−0.650828	−0.325414	+	0.945572i	$0.605504\pi$
$168$	−0.557640	−0.0430229
$169$	−12.9395	−0.995344
$170$	0	0
$171$	−0.362319	−0.0277072
$172$	17.7797	1.35569
$173$	15.2255	1.15758	0.578788	−	0.815478i	$-0.303526\pi$
$173$	15.2255	1.15758	0.578788	+	0.815478i	$0.303526\pi$
$174$	−0.270855	−0.0205335
$175$	0	0
$176$	−26.1394	−1.97033
$177$	−17.7412	−1.33351
$178$	1.25453	0.0940307
$179$	7.14026	0.533688	0.266844	−	0.963740i	$-0.414019\pi$
$179$	7.14026	0.533688	0.266844	+	0.963740i	$0.414019\pi$
$180$	0	0
$181$	0.600632	0.0446446	0.0223223	−	0.999751i	$-0.492894\pi$
$181$	0.600632	0.0446446	0.0223223	+	0.999751i	$0.492894\pi$
$182$	−0.0202346	−0.00149989
$183$	3.99021	0.294965
$184$	0.328429	0.0242121
$185$	0	0
$186$	−1.53692	−0.112692
$187$	−20.6805	−1.51231
$188$	−6.66222	−0.485893
$189$	−5.29258	−0.384979
$190$	0	0
$191$	−6.68037	−0.483375	−0.241687	−	0.970354i	$-0.577701\pi$
$191$	−6.68037	−0.483375	−0.241687	+	0.970354i	$0.577701\pi$
$192$	13.3083	0.960446
$193$	−15.2658	−1.09886	−0.549429	−	0.835541i	$-0.685155\pi$
$193$	−15.2658	−1.09886	−0.549429	+	0.835541i	$0.685155\pi$
$194$	−0.578824	−0.0415571
$195$	0	0
$196$	−1.99324	−0.142374
$197$	−6.38588	−0.454975	−0.227488	−	0.973781i	$-0.573051\pi$
$197$	−6.38588	−0.454975	−0.227488	+	0.973781i	$0.573051\pi$
$198$	0.0636011	0.00451994
$199$	−6.30168	−0.446715	−0.223357	−	0.974737i	$-0.571702\pi$
$199$	−6.30168	−0.446715	−0.223357	+	0.974737i	$0.571702\pi$
$200$	0	0
$201$	15.8617	1.11880
$202$	0.930079	0.0654401
$203$	−1.93958	−0.136132
$204$	10.6016	0.742264
$205$	0	0
$206$	−1.53309	−0.106816
$207$	0.117136	0.00814148
$208$	0.974124	0.0675433
$209$	−20.4203	−1.41250
$210$	0	0
$211$	−8.29434	−0.571006	−0.285503	−	0.958378i	$-0.592161\pi$
$211$	−8.29434	−0.571006	−0.285503	+	0.958378i	$0.592161\pi$
$212$	13.9184	0.955917
$213$	18.4228	1.26231
$214$	0.681973	0.0466187
$215$	0	0
$216$	−1.73824	−0.118272
$217$	−11.0058	−0.747122
$218$	1.29663	0.0878191
$219$	19.5969	1.32424
$220$	0	0
$221$	0.770692	0.0518423
$222$	−0.517137	−0.0347080
$223$	−10.5347	−0.705455	−0.352728	−	0.935726i	$-0.614746\pi$
$223$	−10.5347	−0.705455	−0.352728	+	0.935726i	$0.614746\pi$
$224$	−0.982510	−0.0656467
$225$	0	0
$226$	−0.747388	−0.0497155
$227$	−25.8459	−1.71545	−0.857726	−	0.514107i	$-0.828123\pi$
$227$	−25.8459	−1.71545	−0.857726	+	0.514107i	$0.828123\pi$
$228$	10.4682	0.693275
$229$	12.2753	0.811173	0.405587	−	0.914057i	$-0.367067\pi$
$229$	12.2753	0.811173	0.405587	+	0.914057i	$0.367067\pi$
$230$	0	0
$231$	−11.2091	−0.737506
$232$	−0.637015	−0.0418221
$233$	5.01628	0.328628	0.164314	−	0.986408i	$-0.447459\pi$
$233$	5.01628	0.328628	0.164314	+	0.986408i	$0.447459\pi$
$234$	−0.00237019	−0.000154944 0
$235$	0	0
$236$	−20.8272	−1.35573
$237$	−14.1656	−0.920153
$238$	−0.257644	−0.0167006
$239$	−21.0757	−1.36328	−0.681638	−	0.731690i	$-0.738732\pi$
$239$	−21.0757	−1.36328	−0.681638	+	0.731690i	$0.738732\pi$
$240$	0	0
$241$	20.0468	1.29133	0.645664	−	0.763622i	$-0.276581\pi$
$241$	20.0468	1.29133	0.645664	+	0.763622i	$0.276581\pi$
$242$	2.67985	0.172267
$243$	−1.21660	−0.0780451
$244$	4.68428	0.299880
$245$	0	0
$246$	0.190251	0.0121299
$247$	0.760992	0.0484208
$248$	−3.61463	−0.229529
$249$	−25.2562	−1.60055
$250$	0	0
$251$	21.9579	1.38597	0.692987	−	0.720951i	$-0.256295\pi$
$251$	21.9579	1.38597	0.692987	+	0.720951i	$0.256295\pi$
$252$	−0.233479	−0.0147078
$253$	6.60175	0.415049
$254$	0.155003	0.00972574
$255$	0	0
$256$	15.4616	0.966349
$257$	0.625767	0.0390343	0.0195171	−	0.999810i	$-0.493787\pi$
$257$	0.625767	0.0390343	0.0195171	+	0.999810i	$0.493787\pi$
$258$	1.24564	0.0775504
$259$	−3.70320	−0.230105
$260$	0	0
$261$	−0.227194	−0.0140629
$262$	−0.259557	−0.0160355
$263$	−31.6637	−1.95247	−0.976233	−	0.216722i	$-0.930463\pi$
$263$	−31.6637	−1.95247	−0.976233	+	0.216722i	$0.930463\pi$
$264$	−3.68140	−0.226575
$265$	0	0
$266$	−0.254401	−0.0155983
$267$	−25.8985	−1.58496
$268$	18.6207	1.13744
$269$	21.6818	1.32196	0.660980	−	0.750403i	$-0.270141\pi$
$269$	21.6818	1.32196	0.660980	+	0.750403i	$0.270141\pi$
$270$	0	0
$271$	−0.699219	−0.0424746	−0.0212373	−	0.999774i	$-0.506761\pi$
$271$	−0.699219	−0.0424746	−0.0212373	+	0.999774i	$0.506761\pi$
$272$	12.4033	0.752062
$273$	0.417725	0.0252819
$274$	1.46285	0.0883742
$275$	0	0
$276$	−3.38431	−0.203712
$277$	18.6677	1.12163	0.560816	−	0.827940i	$-0.310487\pi$
$277$	18.6677	1.12163	0.560816	+	0.827940i	$0.310487\pi$
$278$	−1.21129	−0.0726486
$279$	−1.28917	−0.0771806
$280$	0	0
$281$	13.9288	0.830925	0.415462	−	0.909610i	$-0.363620\pi$
$281$	13.9288	0.830925	0.415462	+	0.909610i	$0.363620\pi$
$282$	−0.466756	−0.0277949
$283$	−13.6281	−0.810107	−0.405054	−	0.914293i	$-0.632747\pi$
$283$	−13.6281	−0.810107	−0.405054	+	0.914293i	$0.632747\pi$
$284$	21.6273	1.28335
$285$	0	0
$286$	−0.133584	−0.00789899
$287$	1.36238	0.0804185
$288$	−0.115087	−0.00678155
$289$	−7.18693	−0.422760
$290$	0	0
$291$	11.9493	0.700479
$292$	23.0056	1.34630
$293$	3.45057	0.201585	0.100792	−	0.994907i	$-0.467862\pi$
$293$	3.45057	0.201585	0.100792	+	0.994907i	$0.467862\pi$
$294$	−0.139646	−0.00814433
$295$	0	0
$296$	−1.21624	−0.0706924
$297$	−34.9403	−2.02744
$298$	−1.43072	−0.0828795
$299$	−0.246024	−0.0142280
$300$	0	0
$301$	8.92000	0.514140
$302$	−1.48322	−0.0853499
$303$	−19.2006	−1.10305
$304$	12.2472	0.702427
$305$	0	0
$306$	−0.0301792	−0.00172523
$307$	−16.4194	−0.937105	−0.468553	−	0.883436i	$-0.655224\pi$
$307$	−16.4194	−0.937105	−0.468553	+	0.883436i	$0.655224\pi$
$308$	−13.1589	−0.749795
$309$	31.6493	1.80047
$310$	0	0
$311$	−6.03494	−0.342210	−0.171105	−	0.985253i	$-0.554734\pi$
$311$	−6.03494	−0.342210	−0.171105	+	0.985253i	$0.554734\pi$
$312$	0.137193	0.00776703
$313$	24.1110	1.36283	0.681417	−	0.731895i	$-0.261364\pi$
$313$	24.1110	1.36283	0.681417	+	0.731895i	$0.261364\pi$
$314$	−0.0215204	−0.00121447
$315$	0	0
$316$	−16.6296	−0.935486
$317$	9.37979	0.526822	0.263411	−	0.964684i	$-0.415153\pi$
$317$	9.37979	0.526822	0.263411	+	0.964684i	$0.415153\pi$
$318$	0.975121	0.0546821
$319$	−12.8046	−0.716922
$320$	0	0
$321$	−14.0787	−0.785796
$322$	0.0822464	0.00458341
$323$	9.68957	0.539142
$324$	17.2113	0.956185
$325$	0	0
$326$	0.107044	0.00592864
$327$	−26.7678	−1.48026
$328$	0.447444	0.0247060
$329$	−3.34242	−0.184273
$330$	0	0
$331$	−23.4007	−1.28622	−0.643109	−	0.765774i	$-0.722356\pi$
$331$	−23.4007	−1.28622	−0.643109	+	0.765774i	$0.722356\pi$
$332$	−29.6493	−1.62722
$333$	−0.433776	−0.0237708
$334$	−0.691738	−0.0378502
$335$	0	0
$336$	6.72277	0.366757
$337$	−19.3173	−1.05228	−0.526141	−	0.850397i	$-0.676362\pi$
$337$	−19.3173	−1.05228	−0.526141	+	0.850397i	$0.676362\pi$
$338$	−1.06422	−0.0578862
$339$	15.4291	0.837995
$340$	0	0
$341$	−72.6576	−3.93463
$342$	−0.0297994	−0.00161137
$343$	−1.00000	−0.0539949
$344$	2.92959	0.157953
$345$	0	0
$346$	1.25225	0.0673211
$347$	−17.6122	−0.945474	−0.472737	−	0.881204i	$-0.656734\pi$
$347$	−17.6122	−0.945474	−0.472737	+	0.881204i	$0.656734\pi$
$348$	6.56415	0.351875
$349$	−15.3009	−0.819039	−0.409519	−	0.912301i	$-0.634304\pi$
$349$	−15.3009	−0.819039	−0.409519	+	0.912301i	$0.634304\pi$
$350$	0	0
$351$	1.30211	0.0695012
$352$	−6.48629	−0.345720
$353$	−17.2823	−0.919846	−0.459923	−	0.887959i	$-0.652123\pi$
$353$	−17.2823	−0.919846	−0.459923	+	0.887959i	$0.652123\pi$
$354$	−1.45915	−0.0775531
$355$	0	0
$356$	−30.4034	−1.61137
$357$	5.31881	0.281501
$358$	0.587261	0.0310377
$359$	14.7806	0.780092	0.390046	−	0.920795i	$-0.372459\pi$
$359$	14.7806	0.780092	0.390046	+	0.920795i	$0.372459\pi$
$360$	0	0
$361$	−9.43238	−0.496441
$362$	0.0493998	0.00259640
$363$	−55.3230	−2.90370
$364$	0.490385	0.0257031
$365$	0	0
$366$	0.328181	0.0171543
$367$	4.33697	0.226388	0.113194	−	0.993573i	$-0.463892\pi$
$367$	4.33697	0.226388	0.113194	+	0.993573i	$0.463892\pi$
$368$	−3.95946	−0.206401
$369$	0.159583	0.00830754
$370$	0	0
$371$	6.98280	0.362529
$372$	37.2471	1.93117
$373$	36.1147	1.86995	0.934974	−	0.354716i	$-0.115422\pi$
$373$	36.1147	1.86995	0.934974	+	0.354716i	$0.115422\pi$
$374$	−1.70090	−0.0879514
$375$	0	0
$376$	−1.09775	−0.0566120
$377$	0.477184	0.0245762
$378$	−0.435296	−0.0223892
$379$	−14.5940	−0.749642	−0.374821	−	0.927097i	$-0.622296\pi$
$379$	−14.5940	−0.749642	−0.374821	+	0.927097i	$0.622296\pi$
$380$	0	0
$381$	−3.19989	−0.163935
$382$	−0.549436	−0.0281116
$383$	−3.54230	−0.181003	−0.0905014	−	0.995896i	$-0.528847\pi$
$383$	−3.54230	−0.181003	−0.0905014	+	0.995896i	$0.528847\pi$
$384$	4.43097	0.226117
$385$	0	0
$386$	−1.25556	−0.0639062
$387$	1.04485	0.0531127
$388$	14.0278	0.712152
$389$	15.0209	0.761592	0.380796	−	0.924659i	$-0.375650\pi$
$389$	15.0209	0.761592	0.380796	+	0.924659i	$0.375650\pi$
$390$	0	0
$391$	−3.13258	−0.158421
$392$	−0.328429	−0.0165882
$393$	5.35831	0.270291
$394$	−0.525216	−0.0264600
$395$	0	0
$396$	−1.54137	−0.0774567
$397$	−23.7954	−1.19426	−0.597129	−	0.802146i	$-0.703692\pi$
$397$	−23.7954	−1.19426	−0.597129	+	0.802146i	$0.703692\pi$
$398$	−0.518291	−0.0259796
$399$	5.25187	0.262922
$400$	0	0
$401$	32.9473	1.64531	0.822656	−	0.568540i	$-0.192491\pi$
$401$	32.9473	1.64531	0.822656	+	0.568540i	$0.192491\pi$
$402$	1.30457	0.0650659
$403$	2.70770	0.134880
$404$	−22.5404	−1.12143
$405$	0	0
$406$	−0.159524	−0.00791702
$407$	−24.4476	−1.21182
$408$	1.74685	0.0864821
$409$	−36.0835	−1.78421	−0.892107	−	0.451823i	$-0.850774\pi$
$409$	−36.0835	−1.78421	−0.892107	+	0.451823i	$0.850774\pi$
$410$	0	0
$411$	−30.1992	−1.48962
$412$	37.1544	1.83047
$413$	−10.4489	−0.514158
$414$	0.00963397	0.000473484 0
$415$	0	0
$416$	0.241721	0.0118514
$417$	25.0060	1.22455
$418$	−1.67949	−0.0821467
$419$	26.9268	1.31546	0.657730	−	0.753254i	$-0.271517\pi$
$419$	26.9268	1.31546	0.657730	+	0.753254i	$0.271517\pi$
$420$	0	0
$421$	30.6345	1.49303	0.746517	−	0.665366i	$-0.231724\pi$
$421$	30.6345	1.49303	0.746517	+	0.665366i	$0.231724\pi$
$422$	−0.682179	−0.0332080
$423$	−0.391516	−0.0190361
$424$	2.29335	0.111375
$425$	0	0
$426$	1.51521	0.0734122
$427$	2.35009	0.113729
$428$	−16.5276	−0.798890
$429$	2.75772	0.133144
$430$	0	0
$431$	9.00563	0.433786	0.216893	−	0.976195i	$-0.430408\pi$
$431$	9.00563	0.433786	0.216893	+	0.976195i	$0.430408\pi$
$432$	20.9558	1.00823
$433$	−32.4600	−1.55993	−0.779963	−	0.625826i	$-0.784762\pi$
$433$	−32.4600	−1.55993	−0.779963	+	0.625826i	$0.784762\pi$
$434$	−0.905187	−0.0434504
$435$	0	0
$436$	−31.4238	−1.50493
$437$	−3.09316	−0.147966
$438$	1.61178	0.0770136
$439$	26.4667	1.26318	0.631592	−	0.775301i	$-0.282402\pi$
$439$	26.4667	1.26318	0.631592	+	0.775301i	$0.282402\pi$
$440$	0	0
$441$	−0.117136	−0.00557788
$442$	0.0633866	0.00301499
$443$	−22.9526	−1.09051	−0.545254	−	0.838271i	$-0.683567\pi$
$443$	−22.9526	−1.09051	−0.545254	+	0.838271i	$0.683567\pi$
$444$	12.5328	0.594779
$445$	0	0
$446$	−0.866440	−0.0410271
$447$	29.5359	1.39700
$448$	7.83811	0.370316
$449$	−17.2998	−0.816429	−0.408215	−	0.912886i	$-0.633848\pi$
$449$	−17.2998	−0.816429	−0.408215	+	0.912886i	$0.633848\pi$
$450$	0	0
$451$	8.99408	0.423514
$452$	18.1129	0.851959
$453$	30.6198	1.43864
$454$	−2.12573	−0.0997655
$455$	0	0
$456$	1.72487	0.0807744
$457$	−31.5304	−1.47493	−0.737465	−	0.675385i	$-0.763977\pi$
$457$	−31.5304	−1.47493	−0.737465	+	0.675385i	$0.763977\pi$
$458$	1.00960	0.0471754
$459$	16.5795	0.773863
$460$	0	0
$461$	13.1838	0.614032	0.307016	−	0.951704i	$-0.400670\pi$
$461$	13.1838	0.614032	0.307016	+	0.951704i	$0.400670\pi$
$462$	−0.921910	−0.0428911
$463$	−0.00217386	−0.000101028 0	−5.05140e−5	−	1.00000i	$-0.500016\pi$
$463$	−0.00217386	−0.000101028 0	−5.05140e−5		1.00000i	$0.500016\pi$
$464$	7.67969	0.356521
$465$	0	0
$466$	0.412571	0.0191120
$467$	6.12754	0.283549	0.141774	−	0.989899i	$-0.454719\pi$
$467$	6.12754	0.283549	0.141774	+	0.989899i	$0.454719\pi$
$468$	0.0574415	0.00265523
$469$	9.34195	0.431371
$470$	0	0
$471$	0.444268	0.0204708
$472$	−3.43174	−0.157958
$473$	58.8877	2.70766
$474$	−1.16507	−0.0535133
$475$	0	0
$476$	6.24397	0.286192
$477$	0.817934	0.0374506
$478$	−1.73340	−0.0792840
$479$	−12.7109	−0.580777	−0.290389	−	0.956909i	$-0.593785\pi$
$479$	−12.7109	−0.580777	−0.290389	+	0.956909i	$0.593785\pi$
$480$	0	0
$481$	0.911077	0.0415415
$482$	1.64878	0.0750997
$483$	−1.69790	−0.0772571
$484$	−64.9459	−2.95209
$485$	0	0
$486$	−0.100061	−0.00453887
$487$	33.0640	1.49827	0.749137	−	0.662415i	$-0.230469\pi$
$487$	33.0640	1.49827	0.749137	+	0.662415i	$0.230469\pi$
$488$	0.771837	0.0349394
$489$	−2.20983	−0.0999320
$490$	0	0
$491$	−9.68268	−0.436973	−0.218487	−	0.975840i	$-0.570112\pi$
$491$	−9.68268	−0.436973	−0.218487	+	0.975840i	$0.570112\pi$
$492$	−4.61071	−0.207867
$493$	6.07590	0.273645
$494$	0.0625889	0.00281601
$495$	0	0
$496$	43.5770	1.95667
$497$	10.8504	0.486705
$498$	−2.07723	−0.0930830
$499$	−1.10739	−0.0495734	−0.0247867	−	0.999693i	$-0.507891\pi$
$499$	−1.10739	−0.0495734	−0.0247867	+	0.999693i	$0.507891\pi$
$500$	0	0
$501$	14.2803	0.637996
$502$	1.80596	0.0806040
$503$	18.6849	0.833120	0.416560	−	0.909108i	$-0.363236\pi$
$503$	18.6849	0.833120	0.416560	+	0.909108i	$0.363236\pi$
$504$	−0.0384707	−0.00171362
$505$	0	0
$506$	0.542971	0.0241380
$507$	21.9699	0.975719
$508$	−3.75648	−0.166667
$509$	−12.4158	−0.550322	−0.275161	−	0.961398i	$-0.588731\pi$
$509$	−12.4158	−0.550322	−0.275161	+	0.961398i	$0.588731\pi$
$510$	0	0
$511$	11.5419	0.510582
$512$	6.49101	0.286865
$513$	16.3708	0.722788
$514$	0.0514671	0.00227012
$515$	0	0
$516$	−30.1881	−1.32896
$517$	−22.0658	−0.970453
$518$	−0.304574	−0.0133822
$519$	−25.8514	−1.13475
$520$	0	0
$521$	0.401401	0.0175857	0.00879284	−	0.999961i	$-0.497201\pi$
$521$	0.401401	0.0175857	0.00879284	+	0.999961i	$0.497201\pi$
$522$	−0.0186859	−0.000817858 0
$523$	42.6625	1.86550	0.932750	−	0.360524i	$-0.117402\pi$
$523$	42.6625	1.86550	0.932750	+	0.360524i	$0.117402\pi$
$524$	6.29035	0.274795
$525$	0	0
$526$	−2.60422	−0.113550
$527$	34.4766	1.50182
$528$	44.3820	1.93148
$529$	1.00000	0.0434783
$530$	0	0
$531$	−1.22394	−0.0531145
$532$	6.16539	0.267304
$533$	−0.335178	−0.0145182
$534$	−2.13006	−0.0921767
$535$	0	0
$536$	3.06817	0.132525
$537$	−12.1234	−0.523165
$538$	1.78325	0.0768813
$539$	−6.60175	−0.284358
$540$	0	0
$541$	−6.31647	−0.271566	−0.135783	−	0.990739i	$-0.543355\pi$
$541$	−6.31647	−0.271566	−0.135783	+	0.990739i	$0.543355\pi$
$542$	−0.0575083	−0.00247019
$543$	−1.01981	−0.0437644
$544$	3.07779	0.131959
$545$	0	0
$546$	0.0343564	0.00147032
$547$	22.8214	0.975773	0.487886	−	0.872907i	$-0.337768\pi$
$547$	22.8214	0.975773	0.487886	+	0.872907i	$0.337768\pi$
$548$	−35.4521	−1.51444
$549$	0.275279	0.0117486
$550$	0	0
$551$	5.99943	0.255584
$552$	−0.557640	−0.0237347
$553$	−8.34300	−0.354780
$554$	1.53535	0.0652308
$555$	0	0
$556$	29.3556	1.24496
$557$	41.5536	1.76068	0.880340	−	0.474342i	$-0.157314\pi$
$557$	41.5536	1.76068	0.880340	+	0.474342i	$0.157314\pi$
$558$	−0.106030	−0.00448859
$559$	−2.19454	−0.0928191
$560$	0	0
$561$	35.1135	1.48249
$562$	1.14560	0.0483241
$563$	3.26920	0.137780	0.0688902	−	0.997624i	$-0.478054\pi$
$563$	3.26920	0.137780	0.0688902	+	0.997624i	$0.478054\pi$
$564$	11.3118	0.476312
$565$	0	0
$566$	−1.12086	−0.0471134
$567$	8.63487	0.362631
$568$	3.56358	0.149524
$569$	−28.9733	−1.21462	−0.607312	−	0.794464i	$-0.707752\pi$
$569$	−28.9733	−1.21462	−0.607312	+	0.794464i	$0.707752\pi$
$570$	0	0
$571$	−13.3000	−0.556586	−0.278293	−	0.960496i	$-0.589769\pi$
$571$	−13.3000	−0.556586	−0.278293	+	0.960496i	$0.589769\pi$
$572$	3.23740	0.135362
$573$	11.3426	0.473844
$574$	0.112051	0.00467690
$575$	0	0
$576$	0.918121	0.0382550
$577$	−4.55795	−0.189750	−0.0948749	−	0.995489i	$-0.530245\pi$
$577$	−4.55795	−0.189750	−0.0948749	+	0.995489i	$0.530245\pi$
$578$	−0.591099	−0.0245865
$579$	25.9198	1.07719
$580$	0	0
$581$	−14.8750	−0.617118
$582$	0.982785	0.0407378
$583$	46.0987	1.90921
$584$	3.79068	0.156860
$585$	0	0
$586$	0.283797	0.0117236
$587$	−26.2553	−1.08367	−0.541835	−	0.840485i	$-0.682270\pi$
$587$	−26.2553	−1.08367	−0.541835	+	0.840485i	$0.682270\pi$
$588$	3.38431	0.139567
$589$	34.0427	1.40270
$590$	0	0
$591$	10.8426	0.446005
$592$	14.6626	0.602631
$593$	−1.78889	−0.0734609	−0.0367305	−	0.999325i	$-0.511694\pi$
$593$	−1.78889	−0.0734609	−0.0367305	+	0.999325i	$0.511694\pi$
$594$	−2.87372	−0.117910
$595$	0	0
$596$	34.6734	1.42028
$597$	10.6996	0.437907
$598$	−0.0202346	−0.000827455 0
$599$	−28.6741	−1.17159	−0.585796	−	0.810459i	$-0.699218\pi$
$599$	−28.6741	−1.17159	−0.585796	+	0.810459i	$0.699218\pi$
$600$	0	0
$601$	14.2382	0.580788	0.290394	−	0.956907i	$-0.406214\pi$
$601$	14.2382	0.580788	0.290394	+	0.956907i	$0.406214\pi$
$602$	0.733638	0.0299008
$603$	1.09427	0.0445623
$604$	35.9458	1.46261
$605$	0	0
$606$	−1.57918	−0.0641499
$607$	−9.60343	−0.389791	−0.194896	−	0.980824i	$-0.562437\pi$
$607$	−9.60343	−0.389791	−0.194896	+	0.980824i	$0.562437\pi$
$608$	3.03906	0.123250
$609$	3.29321	0.133448
$610$	0	0
$611$	0.822316	0.0332673
$612$	0.731391	0.0295647
$613$	−7.96342	−0.321640	−0.160820	−	0.986984i	$-0.551414\pi$
$613$	−7.96342	−0.321640	−0.160820	+	0.986984i	$0.551414\pi$
$614$	−1.35044	−0.0544992
$615$	0	0
$616$	−2.16821	−0.0873596
$617$	19.6209	0.789909	0.394955	−	0.918701i	$-0.370760\pi$
$617$	19.6209	0.789909	0.394955	+	0.918701i	$0.370760\pi$
$618$	2.60304	0.104710
$619$	−6.67665	−0.268357	−0.134179	−	0.990957i	$-0.542840\pi$
$619$	−6.67665	−0.268357	−0.134179	+	0.990957i	$0.542840\pi$
$620$	0	0
$621$	−5.29258	−0.212384
$622$	−0.496352	−0.0199019
$623$	−15.2533	−0.611109
$624$	−1.65396	−0.0662116
$625$	0	0
$626$	1.98304	0.0792583
$627$	34.6716	1.38465
$628$	0.521545	0.0208119
$629$	11.6006	0.462545
$630$	0	0
$631$	−31.6619	−1.26044	−0.630220	−	0.776417i	$-0.717035\pi$
$631$	−31.6619	−1.26044	−0.630220	+	0.776417i	$0.717035\pi$
$632$	−2.74008	−0.108995
$633$	14.0830	0.559747
$634$	0.771454	0.0306384
$635$	0	0
$636$	−23.6320	−0.937069
$637$	0.246024	0.00974784
$638$	−1.05314	−0.0416940
$639$	1.27096	0.0502785
$640$	0	0
$641$	11.9889	0.473535	0.236767	−	0.971566i	$-0.423912\pi$
$641$	11.9889	0.473535	0.236767	+	0.971566i	$0.423912\pi$
$642$	−1.15792	−0.0456995
$643$	−5.87985	−0.231879	−0.115939	−	0.993256i	$-0.536988\pi$
$643$	−5.87985	−0.231879	−0.115939	+	0.993256i	$0.536988\pi$
$644$	−1.99324	−0.0785445
$645$	0	0
$646$	0.796932	0.0313549
$647$	−39.2723	−1.54395	−0.771977	−	0.635651i	$-0.780732\pi$
$647$	−39.2723	−1.54395	−0.771977	+	0.635651i	$0.780732\pi$
$648$	2.83594	0.111406
$649$	−68.9813	−2.70775
$650$	0	0
$651$	18.6867	0.732391
$652$	−2.59421	−0.101597
$653$	−5.15521	−0.201739	−0.100869	−	0.994900i	$-0.532162\pi$
$653$	−5.15521	−0.201739	−0.100869	+	0.994900i	$0.532162\pi$
$654$	−2.20155	−0.0860876
$655$	0	0
$656$	−5.39427	−0.210611
$657$	1.35196	0.0527450
$658$	−0.274902	−0.0107168
$659$	−7.88678	−0.307225	−0.153613	−	0.988131i	$-0.549091\pi$
$659$	−7.88678	−0.307225	−0.153613	+	0.988131i	$0.549091\pi$
$660$	0	0
$661$	−17.9076	−0.696524	−0.348262	−	0.937397i	$-0.613228\pi$
$661$	−17.9076	−0.696524	−0.348262	+	0.937397i	$0.613228\pi$
$662$	−1.92462	−0.0748026
$663$	−1.30856	−0.0508202
$664$	−4.88538	−0.189589
$665$	0	0
$666$	−0.0356765	−0.00138244
$667$	−1.93958	−0.0751009
$668$	16.7642	0.648627
$669$	17.8869	0.691546
$670$	0	0
$671$	15.5147	0.598938
$672$	1.66820	0.0643523
$673$	−13.0067	−0.501371	−0.250685	−	0.968069i	$-0.580656\pi$
$673$	−13.0067	−0.501371	−0.250685	+	0.968069i	$0.580656\pi$
$674$	−1.58878	−0.0611976
$675$	0	0
$676$	25.7914	0.991978
$677$	0.200917	0.00772187	0.00386093	−	0.999993i	$-0.498771\pi$
$677$	0.200917	0.00772187	0.00386093	+	0.999993i	$0.498771\pi$
$678$	1.26899	0.0487353
$679$	7.03768	0.270081
$680$	0	0
$681$	43.8837	1.68163
$682$	−5.97582	−0.228826
$683$	−39.3602	−1.50608	−0.753038	−	0.657977i	$-0.771412\pi$
$683$	−39.3602	−1.50608	−0.753038	+	0.657977i	$0.771412\pi$
$684$	0.722186	0.0276135
$685$	0	0
$686$	−0.0822464	−0.00314018
$687$	−20.8422	−0.795180
$688$	−35.3184	−1.34650
$689$	−1.71794	−0.0654483
$690$	0	0
$691$	−0.809781	−0.0308055	−0.0154028	−	0.999881i	$-0.504903\pi$
$691$	−0.809781	−0.0308055	−0.0154028	+	0.999881i	$0.504903\pi$
$692$	−30.3481	−1.15366
$693$	−0.773300	−0.0293752
$694$	−1.44854	−0.0549859
$695$	0	0
$696$	1.08159	0.0409975
$697$	−4.26776	−0.161653
$698$	−1.25844	−0.0476328
$699$	−8.51714	−0.322148
$700$	0	0
$701$	31.2805	1.18145	0.590723	−	0.806874i	$-0.298842\pi$
$701$	31.2805	1.18145	0.590723	+	0.806874i	$0.298842\pi$
$702$	0.107093	0.00404198
$703$	11.4546	0.432017
$704$	51.7453	1.95022
$705$	0	0
$706$	−1.42141	−0.0534954
$707$	−11.3084	−0.425298
$708$	35.3625	1.32900
$709$	−3.44403	−0.129343	−0.0646716	−	0.997907i	$-0.520600\pi$
$709$	−3.44403	−0.129343	−0.0646716	+	0.997907i	$0.520600\pi$
$710$	0	0
$711$	−0.977261	−0.0366502
$712$	−5.00962	−0.187743
$713$	−11.0058	−0.412170
$714$	0.437453	0.0163713
$715$	0	0
$716$	−14.2322	−0.531883
$717$	35.7845	1.33640
$718$	1.21565	0.0453678
$719$	−32.1023	−1.19721	−0.598607	−	0.801043i	$-0.704279\pi$
$719$	−32.1023	−1.19721	−0.598607	+	0.801043i	$0.704279\pi$
$720$	0	0
$721$	18.6403	0.694200
$722$	−0.775779	−0.0288715
$723$	−34.0375	−1.26587
$724$	−1.19720	−0.0444936
$725$	0	0
$726$	−4.55011	−0.168871
$727$	−17.2509	−0.639799	−0.319899	−	0.947452i	$-0.603649\pi$
$727$	−17.2509	−0.639799	−0.319899	+	0.947452i	$0.603649\pi$
$728$	0.0808016	0.00299471
$729$	27.9703	1.03594
$730$	0	0
$731$	−27.9426	−1.03350
$732$	−7.95343	−0.293967
$733$	−25.5277	−0.942886	−0.471443	−	0.881897i	$-0.656267\pi$
$733$	−25.5277	−0.942886	−0.471443	+	0.881897i	$0.656267\pi$
$734$	0.356700	0.0131660
$735$	0	0
$736$	−0.982510	−0.0362158
$737$	61.6732	2.27176
$738$	0.0131251	0.000483142 0
$739$	−2.19445	−0.0807240	−0.0403620	−	0.999185i	$-0.512851\pi$
$739$	−2.19445	−0.0807240	−0.0403620	+	0.999185i	$0.512851\pi$
$740$	0	0
$741$	−1.29209	−0.0474661
$742$	0.574310	0.0210836
$743$	20.2328	0.742271	0.371136	−	0.928579i	$-0.378969\pi$
$743$	20.2328	0.742271	0.371136	+	0.928579i	$0.378969\pi$
$744$	6.13727	0.225003
$745$	0	0
$746$	2.97030	0.108751
$747$	−1.74239	−0.0637506
$748$	41.2212	1.50720
$749$	−8.29183	−0.302977
$750$	0	0
$751$	−17.6486	−0.644008	−0.322004	−	0.946738i	$-0.604356\pi$
$751$	−17.6486	−0.644008	−0.322004	+	0.946738i	$0.604356\pi$
$752$	13.2342	0.482600
$753$	−37.2824	−1.35865
$754$	0.0392467	0.00142928
$755$	0	0
$756$	10.5494	0.383677
$757$	24.2728	0.882210	0.441105	−	0.897455i	$-0.354587\pi$
$757$	24.2728	0.882210	0.441105	+	0.897455i	$0.354587\pi$
$758$	−1.20030	−0.0435969
$759$	−11.2091	−0.406865
$760$	0	0
$761$	24.1023	0.873708	0.436854	−	0.899532i	$-0.356093\pi$
$761$	24.1023	0.873708	0.436854	+	0.899532i	$0.356093\pi$
$762$	−0.263179	−0.00953398
$763$	−15.7652	−0.570740
$764$	13.3156	0.481740
$765$	0	0
$766$	−0.291341	−0.0105266
$767$	2.57069	0.0928224
$768$	−26.2522	−0.947296
$769$	−12.1040	−0.436483	−0.218241	−	0.975895i	$-0.570032\pi$
$769$	−12.1040	−0.436483	−0.218241	+	0.975895i	$0.570032\pi$
$770$	0	0
$771$	−1.06249	−0.0382646
$772$	30.4284	1.09514
$773$	18.7858	0.675677	0.337838	−	0.941204i	$-0.390304\pi$
$773$	18.7858	0.675677	0.337838	+	0.941204i	$0.390304\pi$
$774$	0.0859351	0.00308887
$775$	0	0
$776$	2.31138	0.0829737
$777$	6.28766	0.225568
$778$	1.23542	0.0442919
$779$	−4.21405	−0.150984
$780$	0	0
$781$	71.6314	2.56317
$782$	−0.257644	−0.00921332
$783$	10.2654	0.366855
$784$	3.95946	0.141409
$785$	0	0
$786$	0.440702	0.0157193
$787$	8.47883	0.302238	0.151119	−	0.988516i	$-0.451712\pi$
$787$	8.47883	0.302238	0.151119	+	0.988516i	$0.451712\pi$
$788$	12.7286	0.453437
$789$	53.7618	1.91397
$790$	0	0
$791$	9.08718	0.323103
$792$	−0.253974	−0.00902458
$793$	−0.578179	−0.0205317
$794$	−1.95709	−0.0694544
$795$	0	0
$796$	12.5607	0.445204
$797$	−13.4259	−0.475570	−0.237785	−	0.971318i	$-0.576421\pi$
$797$	−13.4259	−0.475570	−0.237785	+	0.971318i	$0.576421\pi$
$798$	0.431948	0.0152908
$799$	10.4704	0.370416
$800$	0	0
$801$	−1.78670	−0.0631299
$802$	2.70980	0.0956864
$803$	76.1965	2.68892
$804$	−31.6161	−1.11501
$805$	0	0
$806$	0.222698	0.00784421
$807$	−36.8135	−1.29590
$808$	−3.71402	−0.130659
$809$	−9.82391	−0.345390	−0.172695	−	0.984975i	$-0.555248\pi$
$809$	−9.82391	−0.345390	−0.172695	+	0.984975i	$0.555248\pi$
$810$	0	0
$811$	47.1994	1.65740	0.828698	−	0.559697i	$-0.189082\pi$
$811$	47.1994	1.65740	0.828698	+	0.559697i	$0.189082\pi$
$812$	3.86604	0.135671
$813$	1.18720	0.0416371
$814$	−2.01073	−0.0704759
$815$	0	0
$816$	−21.0596	−0.737234
$817$	−27.5910	−0.965286
$818$	−2.96774	−0.103765
$819$	0.0288182	0.00100699
$820$	0	0
$821$	4.98377	0.173935	0.0869674	−	0.996211i	$-0.472282\pi$
$821$	4.98377	0.173935	0.0869674	+	0.996211i	$0.472282\pi$
$822$	−2.48378	−0.0866317
$823$	−45.2197	−1.57626	−0.788130	−	0.615508i	$-0.788951\pi$
$823$	−45.2197	−1.57626	−0.788130	+	0.615508i	$0.788951\pi$
$824$	6.12201	0.213270
$825$	0	0
$826$	−0.859387	−0.0299019
$827$	20.5669	0.715180	0.357590	−	0.933879i	$-0.383599\pi$
$827$	20.5669	0.715180	0.357590	+	0.933879i	$0.383599\pi$
$828$	−0.233479	−0.00811395
$829$	−17.7978	−0.618142	−0.309071	−	0.951039i	$-0.600018\pi$
$829$	−17.7978	−0.618142	−0.309071	+	0.951039i	$0.600018\pi$
$830$	0	0
$831$	−31.6959	−1.09952
$832$	−1.92837	−0.0668541
$833$	3.13258	0.108538
$834$	2.05666	0.0712162
$835$	0	0
$836$	40.7024	1.40772
$837$	58.2491	2.01338
$838$	2.21463	0.0765032
$839$	19.0475	0.657591	0.328796	−	0.944401i	$-0.393357\pi$
$839$	19.0475	0.657591	0.328796	+	0.944401i	$0.393357\pi$
$840$	0	0
$841$	−25.2380	−0.870277
$842$	2.51958	0.0868304
$843$	−23.6498	−0.814541
$844$	16.5326	0.569075
$845$	0	0
$846$	−0.0322008	−0.00110708
$847$	−32.5832	−1.11957
$848$	−27.6481	−0.949440
$849$	23.1392	0.794135
$850$	0	0
$851$	−3.70320	−0.126944
$852$	−36.7210	−1.25804
$853$	44.7021	1.53057	0.765285	−	0.643691i	$-0.222598\pi$
$853$	44.7021	1.53057	0.765285	+	0.643691i	$0.222598\pi$
$854$	0.193286	0.00661412
$855$	0	0
$856$	−2.72328	−0.0930797
$857$	9.33908	0.319017	0.159508	−	0.987197i	$-0.449009\pi$
$857$	9.33908	0.319017	0.159508	+	0.987197i	$0.449009\pi$
$858$	0.226812	0.00774324
$859$	−18.5401	−0.632580	−0.316290	−	0.948662i	$-0.602437\pi$
$859$	−18.5401	−0.632580	−0.316290	+	0.948662i	$0.602437\pi$
$860$	0	0
$861$	−2.31318	−0.0788329
$862$	0.740680	0.0252277
$863$	45.6312	1.55330	0.776651	−	0.629931i	$-0.216917\pi$
$863$	45.6312	1.55330	0.776651	+	0.629931i	$0.216917\pi$
$864$	5.20002	0.176908
$865$	0	0
$866$	−2.66971	−0.0907206
$867$	12.2027	0.414425
$868$	21.9371	0.744595
$869$	−55.0784	−1.86841
$870$	0	0
$871$	−2.29835	−0.0778765
$872$	−5.17776	−0.175341
$873$	0.824363	0.0279005
$874$	−0.254401	−0.00860524
$875$	0	0
$876$	−39.0613	−1.31976
$877$	1.38573	0.0467927	0.0233964	−	0.999726i	$-0.492552\pi$
$877$	1.38573	0.0467927	0.0233964	+	0.999726i	$0.492552\pi$
$878$	2.17679	0.0734630
$879$	−5.85873	−0.197610
$880$	0	0
$881$	−38.9570	−1.31249	−0.656247	−	0.754546i	$-0.727857\pi$
$881$	−38.9570	−1.31249	−0.656247	+	0.754546i	$0.727857\pi$
$882$	−0.00963397	−0.000324393 0
$883$	39.1069	1.31605	0.658026	−	0.752996i	$-0.271392\pi$
$883$	39.1069	1.31605	0.658026	+	0.752996i	$0.271392\pi$
$884$	−1.53617	−0.0516670
$885$	0	0
$886$	−1.88776	−0.0634207
$887$	−52.8859	−1.77573	−0.887867	−	0.460101i	$-0.847813\pi$
$887$	−52.8859	−1.77573	−0.887867	+	0.460101i	$0.847813\pi$
$888$	2.06505	0.0692985
$889$	−1.88462	−0.0632080
$890$	0	0
$891$	57.0053	1.90975
$892$	20.9981	0.703069
$893$	10.3386	0.345969
$894$	2.42922	0.0812453
$895$	0	0
$896$	2.60968	0.0871831
$897$	0.417725	0.0139474
$898$	−1.42285	−0.0474811
$899$	21.3466	0.711950
$900$	0	0
$901$	−21.8742	−0.728735
$902$	0.739730	0.0246303
$903$	−15.1453	−0.504003
$904$	2.98450	0.0992629
$905$	0	0
$906$	2.51837	0.0836671
$907$	−18.2844	−0.607122	−0.303561	−	0.952812i	$-0.598176\pi$
$907$	−18.2844	−0.607122	−0.303561	+	0.952812i	$0.598176\pi$
$908$	51.5169	1.70965
$909$	−1.32462	−0.0439349
$910$	0	0
$911$	−18.9986	−0.629451	−0.314725	−	0.949183i	$-0.601912\pi$
$911$	−18.9986	−0.629451	−0.314725	+	0.949183i	$0.601912\pi$
$912$	−20.7946	−0.688577
$913$	−98.2009	−3.24998
$914$	−2.59326	−0.0857775
$915$	0	0
$916$	−24.4675	−0.808430
$917$	3.15585	0.104215
$918$	1.36360	0.0450055
$919$	−22.7119	−0.749196	−0.374598	−	0.927187i	$-0.622219\pi$
$919$	−22.7119	−0.749196	−0.374598	+	0.927187i	$0.622219\pi$
$920$	0	0
$921$	27.8785	0.918629
$922$	1.08432	0.0357102
$923$	−2.66945	−0.0878661
$924$	22.3424	0.735011
$925$	0	0
$926$	−0.000178792 0	−5.87548e−6 0
$927$	2.18344	0.0717135
$928$	1.90566	0.0625563
$929$	3.95786	0.129853	0.0649266	−	0.997890i	$-0.479319\pi$
$929$	3.95786	0.129853	0.0649266	+	0.997890i	$0.479319\pi$
$930$	0	0
$931$	3.09316	0.101374
$932$	−9.99863	−0.327516
$933$	10.2467	0.335462
$934$	0.503968	0.0164903
$935$	0	0
$936$	0.00946474	0.000309365 0
$937$	28.9014	0.944166	0.472083	−	0.881554i	$-0.343502\pi$
$937$	28.9014	0.944166	0.472083	+	0.881554i	$0.343502\pi$
$938$	0.768341	0.0250872
$939$	−40.9381	−1.33596
$940$	0	0
$941$	−15.2403	−0.496818	−0.248409	−	0.968655i	$-0.579908\pi$
$941$	−15.2403	−0.496818	−0.248409	+	0.968655i	$0.579908\pi$
$942$	0.0365395	0.00119052
$943$	1.36238	0.0443651
$944$	41.3721	1.34655
$945$	0	0
$946$	4.84330	0.157469
$947$	−40.6538	−1.32107	−0.660535	−	0.750795i	$-0.729671\pi$
$947$	−40.6538	−1.32107	−0.660535	+	0.750795i	$0.729671\pi$
$948$	28.2353	0.917041
$949$	−2.83958	−0.0921766
$950$	0	0
$951$	−15.9259	−0.516434
$952$	1.02883	0.0333446
$953$	−44.0243	−1.42609	−0.713043	−	0.701120i	$-0.752684\pi$
$953$	−44.0243	−1.42609	−0.713043	+	0.701120i	$0.752684\pi$
$954$	0.0672721	0.00217801
$955$	0	0
$956$	42.0089	1.35866
$957$	21.7410	0.702787
$958$	−1.04543	−0.0337762
$959$	−17.7862	−0.574347
$960$	0	0
$961$	90.1276	2.90734
$962$	0.0749328	0.00241593
$963$	−0.971268	−0.0312987
$964$	−39.9580	−1.28696
$965$	0	0
$966$	−0.139646	−0.00449304
$967$	−43.6146	−1.40255	−0.701276	−	0.712890i	$-0.747386\pi$
$967$	−43.6146	−1.40255	−0.701276	+	0.712890i	$0.747386\pi$
$968$	−10.7013	−0.343952
$969$	−16.4519	−0.528512
$970$	0	0
$971$	14.4375	0.463321	0.231661	−	0.972797i	$-0.425584\pi$
$971$	14.4375	0.463321	0.231661	+	0.972797i	$0.425584\pi$
$972$	2.42498	0.0777811
$973$	14.7276	0.472146
$974$	2.71940	0.0871351
$975$	0	0
$976$	−9.30507	−0.297848
$977$	−35.6431	−1.14032	−0.570162	−	0.821532i	$-0.693120\pi$
$977$	−35.6431	−1.14032	−0.570162	+	0.821532i	$0.693120\pi$
$978$	−0.181751	−0.00581174
$979$	−100.698	−3.21833
$980$	0	0
$981$	−1.84667	−0.0589596
$982$	−0.796365	−0.0254130
$983$	−13.6965	−0.436849	−0.218425	−	0.975854i	$-0.570092\pi$
$983$	−13.6965	−0.436849	−0.218425	+	0.975854i	$0.570092\pi$
$984$	−0.759716	−0.0242189
$985$	0	0
$986$	0.499721	0.0159143
$987$	5.67509	0.180640
$988$	−1.51684	−0.0482570
$989$	8.92000	0.283640
$990$	0	0
$991$	32.4192	1.02983	0.514915	−	0.857241i	$-0.327823\pi$
$991$	32.4192	1.02983	0.514915	+	0.857241i	$0.327823\pi$
$992$	10.8133	0.343323
$993$	39.7320	1.26086
$994$	0.892403	0.0283053
$995$	0	0
$996$	50.3416	1.59513
$997$	−17.2696	−0.546935	−0.273467	−	0.961881i	$-0.588171\pi$
$997$	−17.2696	−0.546935	−0.273467	+	0.961881i	$0.588171\pi$
$998$	−0.0910785	−0.00288304
$999$	19.5995	0.620100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.z.1.8	✓	14
5.4	even	2		4025.2.a.bc.1.7	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.z.1.8	✓	14	1.1	even	1	trivial
4025.2.a.bc.1.7	yes	14	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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0822464 q^{2} -1.69790 q^{3} -1.99324 q^{4} -0.139646 q^{6} -1.00000 q^{7} -0.328429 q^{8} -0.117136 q^{9} +O(q^{10})\)	\(q+0.0822464 q^{2} -1.69790 q^{3} -1.99324 q^{4} -0.139646 q^{6} -1.00000 q^{7} -0.328429 q^{8} -0.117136 q^{9} -6.60175 q^{11} +3.38431 q^{12} +0.246024 q^{13} -0.0822464 q^{14} +3.95946 q^{16} +3.13258 q^{17} -0.00963397 q^{18} +3.09316 q^{19} +1.69790 q^{21} -0.542971 q^{22} -1.00000 q^{23} +0.557640 q^{24} +0.0202346 q^{26} +5.29258 q^{27} +1.99324 q^{28} +1.93958 q^{29} +11.0058 q^{31} +0.982510 q^{32} +11.2091 q^{33} +0.257644 q^{34} +0.233479 q^{36} +3.70320 q^{37} +0.254401 q^{38} -0.417725 q^{39} -1.36238 q^{41} +0.139646 q^{42} -8.92000 q^{43} +13.1589 q^{44} -0.0822464 q^{46} +3.34242 q^{47} -6.72277 q^{48} +1.00000 q^{49} -5.31881 q^{51} -0.490385 q^{52} -6.98280 q^{53} +0.435296 q^{54} +0.328429 q^{56} -5.25187 q^{57} +0.159524 q^{58} +10.4489 q^{59} -2.35009 q^{61} +0.905187 q^{62} +0.117136 q^{63} -7.83811 q^{64} +0.921910 q^{66} -9.34195 q^{67} -6.24397 q^{68} +1.69790 q^{69} -10.8504 q^{71} +0.0384707 q^{72} -11.5419 q^{73} +0.304574 q^{74} -6.16539 q^{76} +6.60175 q^{77} -0.0343564 q^{78} +8.34300 q^{79} -8.63487 q^{81} -0.112051 q^{82} +14.8750 q^{83} -3.38431 q^{84} -0.733638 q^{86} -3.29321 q^{87} +2.16821 q^{88} +15.2533 q^{89} -0.246024 q^{91} +1.99324 q^{92} -18.6867 q^{93} +0.274902 q^{94} -1.66820 q^{96} -7.03768 q^{97} +0.0822464 q^{98} +0.773300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 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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