LMFDB - Embedded newform 6025.2.a.n.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.35529 q^{2} +0.00323419 q^{3} -0.163197 q^{4} -0.00438325 q^{6} -1.75164 q^{7} +2.93175 q^{8} -2.99999 q^{9} +O(q^{10})$	\(q-1.35529 q^{2} +0.00323419 q^{3} -0.163197 q^{4} -0.00438325 q^{6} -1.75164 q^{7} +2.93175 q^{8} -2.99999 q^{9} +0.520685 q^{11} -0.000527809 q^{12} -6.40925 q^{13} +2.37398 q^{14} -3.64697 q^{16} +7.23117 q^{17} +4.06585 q^{18} +7.74003 q^{19} -0.00566514 q^{21} -0.705678 q^{22} +4.04638 q^{23} +0.00948184 q^{24} +8.68637 q^{26} -0.0194051 q^{27} +0.285862 q^{28} -7.52522 q^{29} -0.488538 q^{31} -0.920809 q^{32} +0.00168400 q^{33} -9.80032 q^{34} +0.489588 q^{36} +9.68508 q^{37} -10.4900 q^{38} -0.0207287 q^{39} -2.08005 q^{41} +0.00767789 q^{42} -3.81806 q^{43} -0.0849741 q^{44} -5.48400 q^{46} -0.613587 q^{47} -0.0117950 q^{48} -3.93176 q^{49} +0.0233870 q^{51} +1.04597 q^{52} -3.43235 q^{53} +0.0262995 q^{54} -5.13538 q^{56} +0.0250327 q^{57} +10.1988 q^{58} -14.0813 q^{59} +1.19998 q^{61} +0.662109 q^{62} +5.25490 q^{63} +8.54191 q^{64} -0.00228230 q^{66} -4.01251 q^{67} -1.18010 q^{68} +0.0130867 q^{69} +3.35739 q^{71} -8.79523 q^{72} -14.2716 q^{73} -13.1261 q^{74} -1.26315 q^{76} -0.912054 q^{77} +0.0280934 q^{78} -8.47034 q^{79} +8.99991 q^{81} +2.81907 q^{82} -13.5923 q^{83} +0.000924531 q^{84} +5.17457 q^{86} -0.0243380 q^{87} +1.52652 q^{88} +0.873363 q^{89} +11.2267 q^{91} -0.660355 q^{92} -0.00158002 q^{93} +0.831587 q^{94} -0.00297807 q^{96} +12.3555 q^{97} +5.32866 q^{98} -1.56205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	$ 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * 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 $

$2$	−1.35529	−0.958333	−0.479166	−	0.877724i	$-0.659061\pi$
$2$	−1.35529	−0.958333	−0.479166	+	0.877724i	$0.659061\pi$
$3$	0.00323419	0.00186726	0.000933630	−	1.00000i	$-0.499703\pi$
$3$	0.00323419	0.00186726	0.000933630		1.00000i	$0.499703\pi$
$4$	−0.163197	−0.0815983
$5$	0	0
$5$	0	0
$6$	−0.00438325	−0.00178946
$7$	−1.75164	−0.662058	−0.331029	−	0.943621i	$-0.607396\pi$
$7$	−1.75164	−0.662058	−0.331029	+	0.943621i	$0.607396\pi$
$8$	2.93175	1.03653
$9$	−2.99999	−0.999997
$10$	0	0
$11$	0.520685	0.156993	0.0784963	−	0.996914i	$-0.474988\pi$
$11$	0.520685	0.156993	0.0784963	+	0.996914i	$0.474988\pi$
$12$	−0.000527809 0	−0.000152365 0
$13$	−6.40925	−1.77761	−0.888803	−	0.458289i	$-0.848462\pi$
$13$	−6.40925	−1.77761	−0.888803	+	0.458289i	$0.848462\pi$
$14$	2.37398	0.634472
$15$	0	0
$16$	−3.64697	−0.911743
$17$	7.23117	1.75382	0.876909	−	0.480657i	$-0.159602\pi$
$17$	7.23117	1.75382	0.876909	+	0.480657i	$0.159602\pi$
$18$	4.06585	0.958329
$19$	7.74003	1.77569	0.887843	−	0.460147i	$-0.152203\pi$
$19$	7.74003	1.77569	0.887843	+	0.460147i	$0.152203\pi$
$20$	0	0
$21$	−0.00566514	−0.00123623
$22$	−0.705678	−0.150451
$23$	4.04638	0.843728	0.421864	−	0.906659i	$-0.361376\pi$
$23$	4.04638	0.843728	0.421864	+	0.906659i	$0.361376\pi$
$24$	0.00948184	0.00193547
$25$	0	0
$26$	8.68637	1.70354
$27$	−0.0194051	−0.00373451
$28$	0.285862	0.0540228
$29$	−7.52522	−1.39740	−0.698699	−	0.715416i	$-0.746237\pi$
$29$	−7.52522	−1.39740	−0.698699	+	0.715416i	$0.746237\pi$
$30$	0	0
$31$	−0.488538	−0.0877440	−0.0438720	−	0.999037i	$-0.513969\pi$
$31$	−0.488538	−0.0877440	−0.0438720	+	0.999037i	$0.513969\pi$
$32$	−0.920809	−0.162778
$33$	0.00168400	0.000293146 0
$34$	−9.80032	−1.68074
$35$	0	0
$36$	0.489588	0.0815981
$37$	9.68508	1.59222	0.796109	−	0.605153i	$-0.206888\pi$
$37$	9.68508	1.59222	0.796109	+	0.605153i	$0.206888\pi$
$38$	−10.4900	−1.70170
$39$	−0.0207287	−0.00331925
$40$	0	0
$41$	−2.08005	−0.324850	−0.162425	−	0.986721i	$-0.551932\pi$
$41$	−2.08005	−0.324850	−0.162425	+	0.986721i	$0.551932\pi$
$42$	0.00767789	0.00118472
$43$	−3.81806	−0.582249	−0.291124	−	0.956685i	$-0.594029\pi$
$43$	−3.81806	−0.582249	−0.291124	+	0.956685i	$0.594029\pi$
$44$	−0.0849741	−0.0128103
$45$	0	0
$46$	−5.48400	−0.808572
$47$	−0.613587	−0.0895009	−0.0447504	−	0.998998i	$-0.514249\pi$
$47$	−0.613587	−0.0895009	−0.0447504	+	0.998998i	$0.514249\pi$
$48$	−0.0117950	−0.00170246
$49$	−3.93176	−0.561679
$50$	0	0
$51$	0.0233870	0.00327483
$52$	1.04597	0.145050
$53$	−3.43235	−0.471469	−0.235734	−	0.971818i	$-0.575750\pi$
$53$	−3.43235	−0.471469	−0.235734	+	0.971818i	$0.575750\pi$
$54$	0.0262995	0.00357891
$55$	0	0
$56$	−5.13538	−0.686244
$57$	0.0250327	0.00331567
$58$	10.1988	1.33917
$59$	−14.0813	−1.83323	−0.916616	−	0.399768i	$-0.869091\pi$
$59$	−14.0813	−1.83323	−0.916616	+	0.399768i	$0.869091\pi$
$60$	0	0
$61$	1.19998	0.153642	0.0768208	−	0.997045i	$-0.475523\pi$
$61$	1.19998	0.153642	0.0768208	+	0.997045i	$0.475523\pi$
$62$	0.662109	0.0840880
$63$	5.25490	0.662056
$64$	8.54191	1.06774
$65$	0	0
$66$	−0.00228230	−0.000280931 0
$67$	−4.01251	−0.490206	−0.245103	−	0.969497i	$-0.578822\pi$
$67$	−4.01251	−0.490206	−0.245103	+	0.969497i	$0.578822\pi$
$68$	−1.18010	−0.143109
$69$	0.0130867	0.00157546
$70$	0	0
$71$	3.35739	0.398449	0.199224	−	0.979954i	$-0.436158\pi$
$71$	3.35739	0.398449	0.199224	+	0.979954i	$0.436158\pi$
$72$	−8.79523	−1.03653
$73$	−14.2716	−1.67037	−0.835185	−	0.549969i	$-0.814639\pi$
$73$	−14.2716	−1.67037	−0.835185	+	0.549969i	$0.814639\pi$
$74$	−13.1261	−1.52587
$75$	0	0
$76$	−1.26315	−0.144893
$77$	−0.912054	−0.103938
$78$	0.0280934	0.00318095
$79$	−8.47034	−0.952988	−0.476494	−	0.879178i	$-0.658093\pi$
$79$	−8.47034	−0.952988	−0.476494	+	0.879178i	$0.658093\pi$
$80$	0	0
$81$	8.99991	0.999990
$82$	2.81907	0.311314
$83$	−13.5923	−1.49195	−0.745973	−	0.665976i	$-0.768015\pi$
$83$	−13.5923	−1.49195	−0.745973	+	0.665976i	$0.768015\pi$
$84$	0.000924531 0	0.000100875 0
$85$	0	0
$86$	5.17457	0.557988
$87$	−0.0243380	−0.00260930
$88$	1.52652	0.162728
$89$	0.873363	0.0925763	0.0462881	−	0.998928i	$-0.485261\pi$
$89$	0.873363	0.0925763	0.0462881	+	0.998928i	$0.485261\pi$
$90$	0	0
$91$	11.2267	1.17688
$92$	−0.660355	−0.0688468
$93$	−0.00158002	−0.000163841 0
$94$	0.831587	0.0857716
$95$	0	0
$96$	−0.00297807	−0.000303948 0
$97$	12.3555	1.25451	0.627255	−	0.778814i	$-0.284178\pi$
$97$	12.3555	1.25451	0.627255	+	0.778814i	$0.284178\pi$
$98$	5.32866	0.538276
$99$	−1.56205	−0.156992
$100$	0	0
$101$	2.00318	0.199324	0.0996618	−	0.995021i	$-0.468224\pi$
$101$	2.00318	0.199324	0.0996618	+	0.995021i	$0.468224\pi$
$102$	−0.0316961	−0.00313838
$103$	18.4174	1.81472	0.907360	−	0.420354i	$-0.138094\pi$
$103$	18.4174	1.81472	0.907360	+	0.420354i	$0.138094\pi$
$104$	−18.7903	−1.84254
$105$	0	0
$106$	4.65181	0.451824
$107$	−11.5493	−1.11651	−0.558256	−	0.829669i	$-0.688529\pi$
$107$	−11.5493	−1.11651	−0.558256	+	0.829669i	$0.688529\pi$
$108$	0.00316685	0.000304730 0
$109$	−13.4270	−1.28607	−0.643037	−	0.765835i	$-0.722326\pi$
$109$	−13.4270	−1.28607	−0.643037	+	0.765835i	$0.722326\pi$
$110$	0	0
$111$	0.0313234	0.00297308
$112$	6.38819	0.603627
$113$	20.2940	1.90909	0.954547	−	0.298060i	$-0.0963394\pi$
$113$	20.2940	1.90909	0.954547	+	0.298060i	$0.0963394\pi$
$114$	−0.0339265	−0.00317751
$115$	0	0
$116$	1.22809	0.114025
$117$	19.2277	1.77760
$118$	19.0842	1.75685
$119$	−12.6664	−1.16113
$120$	0	0
$121$	−10.7289	−0.975353
$122$	−1.62632	−0.147240
$123$	−0.00672729	−0.000606579 0
$124$	0.0797278	0.00715977
$125$	0	0
$126$	−7.12190	−0.634470
$127$	1.30849	0.116109	0.0580547	−	0.998313i	$-0.481510\pi$
$127$	1.30849	0.116109	0.0580547	+	0.998313i	$0.481510\pi$
$128$	−9.73512	−0.860471
$129$	−0.0123483	−0.00108721
$130$	0	0
$131$	−16.4848	−1.44029	−0.720143	−	0.693825i	$-0.755924\pi$
$131$	−16.4848	−1.44029	−0.720143	+	0.693825i	$0.755924\pi$
$132$	−0.000274822 0	−2.39202e−5 0
$133$	−13.5578	−1.17561
$134$	5.43810	0.469780
$135$	0	0
$136$	21.2000	1.81789
$137$	18.6740	1.59542	0.797712	−	0.603039i	$-0.206044\pi$
$137$	18.6740	1.59542	0.797712	+	0.603039i	$0.206044\pi$
$138$	−0.0177363	−0.00150981
$139$	13.6395	1.15688	0.578442	−	0.815724i	$-0.303661\pi$
$139$	13.6395	1.15688	0.578442	+	0.815724i	$0.303661\pi$
$140$	0	0
$141$	−0.00198446	−0.000167121 0
$142$	−4.55023	−0.381847
$143$	−3.33720	−0.279071
$144$	10.9409	0.911740
$145$	0	0
$146$	19.3422	1.60077
$147$	−0.0127160	−0.00104880
$148$	−1.58057	−0.129922
$149$	−7.91223	−0.648195	−0.324097	−	0.946024i	$-0.605061\pi$
$149$	−7.91223	−0.648195	−0.324097	+	0.946024i	$0.605061\pi$
$150$	0	0
$151$	6.24467	0.508184	0.254092	−	0.967180i	$-0.418223\pi$
$151$	6.24467	0.508184	0.254092	+	0.967180i	$0.418223\pi$
$152$	22.6919	1.84055
$153$	−21.6934	−1.75381
$154$	1.23609	0.0996074
$155$	0	0
$156$	0.00338286	0.000270845 0
$157$	17.1395	1.36788	0.683942	−	0.729536i	$-0.260264\pi$
$157$	17.1395	1.36788	0.683942	+	0.729536i	$0.260264\pi$
$158$	11.4797	0.913279
$159$	−0.0111009	−0.000880355 0
$160$	0	0
$161$	−7.08780	−0.558597
$162$	−12.1975	−0.958323
$163$	2.91311	0.228172	0.114086	−	0.993471i	$-0.463606\pi$
$163$	2.91311	0.228172	0.114086	+	0.993471i	$0.463606\pi$
$164$	0.339458	0.0265072
$165$	0	0
$166$	18.4214	1.42978
$167$	20.3809	1.57712	0.788561	−	0.614957i	$-0.210827\pi$
$167$	20.3809	1.57712	0.788561	+	0.614957i	$0.210827\pi$
$168$	−0.0166088	−0.00128140
$169$	28.0785	2.15988
$170$	0	0
$171$	−23.2200	−1.77568
$172$	0.623095	0.0475105
$173$	15.0575	1.14480	0.572399	−	0.819975i	$-0.306013\pi$
$173$	15.0575	1.14480	0.572399	+	0.819975i	$0.306013\pi$
$174$	0.0329849	0.00250058
$175$	0	0
$176$	−1.89893	−0.143137
$177$	−0.0455417	−0.00342312
$178$	−1.18366	−0.0887189
$179$	−4.13509	−0.309071	−0.154536	−	0.987987i	$-0.549388\pi$
$179$	−4.13509	−0.309071	−0.154536	+	0.987987i	$0.549388\pi$
$180$	0	0
$181$	−6.54967	−0.486833	−0.243417	−	0.969922i	$-0.578268\pi$
$181$	−6.54967	−0.486833	−0.243417	+	0.969922i	$0.578268\pi$
$182$	−15.2154	−1.12784
$183$	0.00388096	0.000286889 0
$184$	11.8630	0.874550
$185$	0	0
$186$	0.00214139	0.000157014 0
$187$	3.76517	0.275336
$188$	0.100135	0.00730312
$189$	0.0339908	0.00247246
$190$	0	0
$191$	−3.35533	−0.242783	−0.121392	−	0.992605i	$-0.538736\pi$
$191$	−3.35533	−0.242783	−0.121392	+	0.992605i	$0.538736\pi$
$192$	0.0276261	0.00199375
$193$	15.7151	1.13120	0.565599	−	0.824680i	$-0.308645\pi$
$193$	15.7151	1.13120	0.565599	+	0.824680i	$0.308645\pi$
$194$	−16.7452	−1.20224
$195$	0	0
$196$	0.641649	0.0458321
$197$	8.52948	0.607700	0.303850	−	0.952720i	$-0.401728\pi$
$197$	8.52948	0.607700	0.303850	+	0.952720i	$0.401728\pi$
$198$	2.11703	0.150451
$199$	9.58489	0.679455	0.339727	−	0.940524i	$-0.389665\pi$
$199$	9.58489	0.679455	0.339727	+	0.940524i	$0.389665\pi$
$200$	0	0
$201$	−0.0129772	−0.000915341 0
$202$	−2.71488	−0.191018
$203$	13.1815	0.925158
$204$	−0.00381668	−0.000267221 0
$205$	0	0
$206$	−24.9609	−1.73911
$207$	−12.1391	−0.843725
$208$	23.3744	1.62072
$209$	4.03012	0.278769
$210$	0	0
$211$	5.20178	0.358105	0.179053	−	0.983840i	$-0.442697\pi$
$211$	5.20178	0.358105	0.179053	+	0.983840i	$0.442697\pi$
$212$	0.560147	0.0384711
$213$	0.0108584	0.000744007 0
$214$	15.6526	1.06999
$215$	0	0
$216$	−0.0568910	−0.00387094
$217$	0.855743	0.0580916
$218$	18.1975	1.23249
$219$	−0.0461572	−0.00311901
$220$	0	0
$221$	−46.3464	−3.11760
$222$	−0.0424522	−0.00284920
$223$	11.4604	0.767443	0.383722	−	0.923449i	$-0.374642\pi$
$223$	11.4604	0.767443	0.383722	+	0.923449i	$0.374642\pi$
$224$	1.61293	0.107768
$225$	0	0
$226$	−27.5041	−1.82955
$227$	−6.01180	−0.399017	−0.199508	−	0.979896i	$-0.563935\pi$
$227$	−6.01180	−0.399017	−0.199508	+	0.979896i	$0.563935\pi$
$228$	−0.00408526	−0.000270553 0
$229$	−17.8798	−1.18153	−0.590766	−	0.806843i	$-0.701174\pi$
$229$	−17.8798	−1.18153	−0.590766	+	0.806843i	$0.701174\pi$
$230$	0	0
$231$	−0.00294975	−0.000194080 0
$232$	−22.0621	−1.44845
$233$	−9.18126	−0.601485	−0.300742	−	0.953705i	$-0.597234\pi$
$233$	−9.18126	−0.601485	−0.300742	+	0.953705i	$0.597234\pi$
$234$	−26.0590	−1.70353
$235$	0	0
$236$	2.29803	0.149589
$237$	−0.0273947	−0.00177948
$238$	17.1666	1.11275
$239$	−1.99604	−0.129113	−0.0645566	−	0.997914i	$-0.520563\pi$
$239$	−1.99604	−0.129113	−0.0645566	+	0.997914i	$0.520563\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	14.5407	0.934713
$243$	0.0873227	0.00560175
$244$	−0.195833	−0.0125369
$245$	0	0
$246$	0.00911741	0.000581305 0
$247$	−49.6078	−3.15647
$248$	−1.43227	−0.0909494
$249$	−0.0439600	−0.00278585
$250$	0	0
$251$	11.9006	0.751159	0.375580	−	0.926790i	$-0.377444\pi$
$251$	11.9006	0.751159	0.375580	+	0.926790i	$0.377444\pi$
$252$	−0.857583	−0.0540226
$253$	2.10689	0.132459
$254$	−1.77337	−0.111271
$255$	0	0
$256$	−3.88993	−0.243121
$257$	−8.51417	−0.531099	−0.265550	−	0.964097i	$-0.585553\pi$
$257$	−8.51417	−0.531099	−0.265550	+	0.964097i	$0.585553\pi$
$258$	0.0167355	0.00104191
$259$	−16.9648	−1.05414
$260$	0	0
$261$	22.5756	1.39739
$262$	22.3417	1.38027
$263$	−25.7400	−1.58720	−0.793598	−	0.608442i	$-0.791795\pi$
$263$	−25.7400	−1.58720	−0.793598	+	0.608442i	$0.791795\pi$
$264$	0.00493706	0.000303855 0
$265$	0	0
$266$	18.3747	1.12662
$267$	0.00282462	0.000172864 0
$268$	0.654828	0.0400000
$269$	−9.22003	−0.562155	−0.281077	−	0.959685i	$-0.590692\pi$
$269$	−9.22003	−0.562155	−0.281077	+	0.959685i	$0.590692\pi$
$270$	0	0
$271$	8.84561	0.537332	0.268666	−	0.963233i	$-0.413417\pi$
$271$	8.84561	0.537332	0.268666	+	0.963233i	$0.413417\pi$
$272$	−26.3719	−1.59903
$273$	0.0363093	0.00219754
$274$	−25.3086	−1.52895
$275$	0	0
$276$	−0.00213571	−0.000128555 0
$277$	18.8524	1.13273	0.566366	−	0.824154i	$-0.308349\pi$
$277$	18.8524	1.13273	0.566366	+	0.824154i	$0.308349\pi$
$278$	−18.4854	−1.10868
$279$	1.46561	0.0877437
$280$	0	0
$281$	1.23045	0.0734025	0.0367012	−	0.999326i	$-0.488315\pi$
$281$	1.23045	0.0734025	0.0367012	+	0.999326i	$0.488315\pi$
$282$	0.00268951	0.000160158 0
$283$	−18.6579	−1.10910	−0.554549	−	0.832151i	$-0.687109\pi$
$283$	−18.6579	−1.10910	−0.554549	+	0.832151i	$0.687109\pi$
$284$	−0.547915	−0.0325128
$285$	0	0
$286$	4.52287	0.267443
$287$	3.64351	0.215069
$288$	2.76242	0.162777
$289$	35.2899	2.07588
$290$	0	0
$291$	0.0399600	0.00234250
$292$	2.32909	0.136299
$293$	29.7778	1.73964	0.869819	−	0.493371i	$-0.164235\pi$
$293$	29.7778	1.73964	0.869819	+	0.493371i	$0.164235\pi$
$294$	0.0172339	0.00100510
$295$	0	0
$296$	28.3943	1.65038
$297$	−0.0101040	−0.000586291 0
$298$	10.7233	0.621186
$299$	−25.9342	−1.49982
$300$	0	0
$301$	6.68787	0.385482
$302$	−8.46332	−0.487009
$303$	0.00647865	0.000372189 0
$304$	−28.2277	−1.61897
$305$	0	0
$306$	29.4009	1.68073
$307$	−10.1767	−0.580813	−0.290406	−	0.956903i	$-0.593790\pi$
$307$	−10.1767	−0.580813	−0.290406	+	0.956903i	$0.593790\pi$
$308$	0.148844	0.00848118
$309$	0.0595654	0.00338855
$310$	0	0
$311$	0.890634	0.0505032	0.0252516	−	0.999681i	$-0.491961\pi$
$311$	0.890634	0.0505032	0.0252516	+	0.999681i	$0.491961\pi$
$312$	−0.0607715	−0.00344051
$313$	13.4663	0.761163	0.380581	−	0.924747i	$-0.375724\pi$
$313$	13.4663	0.761163	0.380581	+	0.924747i	$0.375724\pi$
$314$	−23.2290	−1.31089
$315$	0	0
$316$	1.38233	0.0777622
$317$	24.8559	1.39604	0.698022	−	0.716076i	$-0.254064\pi$
$317$	24.8559	1.39604	0.698022	+	0.716076i	$0.254064\pi$
$318$	0.0150448	0.000843673 0
$319$	−3.91827	−0.219381
$320$	0	0
$321$	−0.0373526	−0.00208482
$322$	9.60600	0.535322
$323$	55.9695	3.11423
$324$	−1.46875	−0.0815975
$325$	0	0
$326$	−3.94810	−0.218665
$327$	−0.0434255	−0.00240144
$328$	−6.09820	−0.336717
$329$	1.07478	0.0592548
$330$	0	0
$331$	22.5504	1.23948	0.619742	−	0.784806i	$-0.287237\pi$
$331$	22.5504	1.23948	0.619742	+	0.784806i	$0.287237\pi$
$332$	2.21821	0.121740
$333$	−29.0551	−1.59221
$334$	−27.6220	−1.51141
$335$	0	0
$336$	0.0206606	0.00112713
$337$	−9.15637	−0.498779	−0.249390	−	0.968403i	$-0.580230\pi$
$337$	−9.15637	−0.498779	−0.249390	+	0.968403i	$0.580230\pi$
$338$	−38.0544	−2.06989
$339$	0.0656345	0.00356478
$340$	0	0
$341$	−0.254375	−0.0137752
$342$	31.4698	1.70169
$343$	19.1485	1.03392
$344$	−11.1936	−0.603519
$345$	0	0
$346$	−20.4072	−1.09710
$347$	−15.2016	−0.816067	−0.408033	−	0.912967i	$-0.633785\pi$
$347$	−15.2016	−0.816067	−0.408033	+	0.912967i	$0.633785\pi$
$348$	0.00397188	0.000212915 0
$349$	−8.78724	−0.470370	−0.235185	−	0.971951i	$-0.575570\pi$
$349$	−8.78724	−0.470370	−0.235185	+	0.971951i	$0.575570\pi$
$350$	0	0
$351$	0.124372	0.00663849
$352$	−0.479452	−0.0255549
$353$	−8.10726	−0.431506	−0.215753	−	0.976448i	$-0.569221\pi$
$353$	−8.10726	−0.431506	−0.215753	+	0.976448i	$0.569221\pi$
$354$	0.0617220	0.00328049
$355$	0	0
$356$	−0.142530	−0.00755407
$357$	−0.0409656	−0.00216813
$358$	5.60424	0.296193
$359$	11.2841	0.595554	0.297777	−	0.954635i	$-0.403755\pi$
$359$	11.2841	0.595554	0.297777	+	0.954635i	$0.403755\pi$
$360$	0	0
$361$	40.9081	2.15306
$362$	8.87668	0.466548
$363$	−0.0346992	−0.00182124
$364$	−1.83216	−0.0960313
$365$	0	0
$366$	−0.00525982	−0.000274935 0
$367$	−27.4137	−1.43098	−0.715491	−	0.698621i	$-0.753797\pi$
$367$	−27.4137	−1.43098	−0.715491	+	0.698621i	$0.753797\pi$
$368$	−14.7570	−0.769263
$369$	6.24014	0.324849
$370$	0	0
$371$	6.01224	0.312140
$372$	0.000257855 0	1.33691e−5 0
$373$	−10.6742	−0.552687	−0.276343	−	0.961059i	$-0.589123\pi$
$373$	−10.6742	−0.552687	−0.276343	+	0.961059i	$0.589123\pi$
$374$	−5.10288	−0.263864
$375$	0	0
$376$	−1.79889	−0.0927704
$377$	48.2310	2.48402
$378$	−0.0460672	−0.00236944
$379$	5.37779	0.276238	0.138119	−	0.990416i	$-0.455894\pi$
$379$	5.37779	0.276238	0.138119	+	0.990416i	$0.455894\pi$
$380$	0	0
$381$	0.00423189	0.000216806 0
$382$	4.54743	0.232667
$383$	10.7652	0.550075	0.275038	−	0.961433i	$-0.411310\pi$
$383$	10.7652	0.550075	0.275038	+	0.961433i	$0.411310\pi$
$384$	−0.0314852	−0.00160672
$385$	0	0
$386$	−21.2985	−1.08406
$387$	11.4541	0.582247
$388$	−2.01638	−0.102366
$389$	9.96227	0.505107	0.252554	−	0.967583i	$-0.418730\pi$
$389$	9.96227	0.505107	0.252554	+	0.967583i	$0.418730\pi$
$390$	0	0
$391$	29.2601	1.47974
$392$	−11.5269	−0.582198
$393$	−0.0533151	−0.00268939
$394$	−11.5599	−0.582379
$395$	0	0
$396$	0.254922	0.0128103
$397$	−5.60492	−0.281303	−0.140651	−	0.990059i	$-0.544920\pi$
$397$	−5.60492	−0.281303	−0.140651	+	0.990059i	$0.544920\pi$
$398$	−12.9903	−0.651144
$399$	−0.0438483	−0.00219516
$400$	0	0
$401$	13.2631	0.662328	0.331164	−	0.943573i	$-0.392559\pi$
$401$	13.2631	0.662328	0.331164	+	0.943573i	$0.392559\pi$
$402$	0.0175878	0.000877201 0
$403$	3.13116	0.155974
$404$	−0.326912	−0.0162645
$405$	0	0
$406$	−17.8647	−0.886609
$407$	5.04288	0.249966
$408$	0.0685648	0.00339447
$409$	−4.23470	−0.209393	−0.104696	−	0.994504i	$-0.533387\pi$
$409$	−4.23470	−0.209393	−0.104696	+	0.994504i	$0.533387\pi$
$410$	0	0
$411$	0.0603951	0.00297907
$412$	−3.00566	−0.148078
$413$	24.6654	1.21371
$414$	16.4520	0.808569
$415$	0	0
$416$	5.90170	0.289354
$417$	0.0441126	0.00216020
$418$	−5.46197	−0.267154
$419$	−12.9637	−0.633319	−0.316660	−	0.948539i	$-0.602561\pi$
$419$	−12.9637	−0.633319	−0.316660	+	0.948539i	$0.602561\pi$
$420$	0	0
$421$	23.9785	1.16864	0.584321	−	0.811523i	$-0.301361\pi$
$421$	23.9785	1.16864	0.584321	+	0.811523i	$0.301361\pi$
$422$	−7.04990	−0.343184
$423$	1.84075	0.0895006
$424$	−10.0628	−0.488692
$425$	0	0
$426$	−0.0147163	−0.000713007 0
$427$	−2.10193	−0.101720
$428$	1.88481	0.0911055
$429$	−0.0107931	−0.000521098 0
$430$	0	0
$431$	34.8077	1.67663	0.838314	−	0.545188i	$-0.183542\pi$
$431$	34.8077	1.67663	0.838314	+	0.545188i	$0.183542\pi$
$432$	0.0707699	0.00340492
$433$	−4.84552	−0.232861	−0.116430	−	0.993199i	$-0.537145\pi$
$433$	−4.84552	−0.232861	−0.116430	+	0.993199i	$0.537145\pi$
$434$	−1.15978	−0.0556711
$435$	0	0
$436$	2.19124	0.104942
$437$	31.3191	1.49820
$438$	0.0625563	0.00298905
$439$	26.6850	1.27361	0.636803	−	0.771027i	$-0.280257\pi$
$439$	26.6850	1.27361	0.636803	+	0.771027i	$0.280257\pi$
$440$	0	0
$441$	11.7952	0.561677
$442$	62.8127	2.98769
$443$	15.2700	0.725499	0.362749	−	0.931887i	$-0.381838\pi$
$443$	15.2700	0.725499	0.362749	+	0.931887i	$0.381838\pi$
$444$	−0.00511187	−0.000242599 0
$445$	0	0
$446$	−15.5321	−0.735466
$447$	−0.0255896	−0.00121035
$448$	−14.9624	−0.706905
$449$	1.48785	0.0702161	0.0351081	−	0.999384i	$-0.488822\pi$
$449$	1.48785	0.0702161	0.0351081	+	0.999384i	$0.488822\pi$
$450$	0	0
$451$	−1.08305	−0.0509990
$452$	−3.31191	−0.155779
$453$	0.0201964	0.000948911 0
$454$	8.14771	0.382391
$455$	0	0
$456$	0.0733898	0.00343679
$457$	−15.7506	−0.736783	−0.368391	−	0.929671i	$-0.620091\pi$
$457$	−15.7506	−0.736783	−0.368391	+	0.929671i	$0.620091\pi$
$458$	24.2323	1.13230
$459$	−0.140322	−0.00654965
$460$	0	0
$461$	−18.5850	−0.865589	−0.432795	−	0.901493i	$-0.642472\pi$
$461$	−18.5850	−0.865589	−0.432795	+	0.901493i	$0.642472\pi$
$462$	0.00399776	0.000185993 0
$463$	11.4924	0.534095	0.267047	−	0.963683i	$-0.413952\pi$
$463$	11.4924	0.534095	0.267047	+	0.963683i	$0.413952\pi$
$464$	27.4443	1.27407
$465$	0	0
$466$	12.4433	0.576422
$467$	36.9736	1.71094	0.855468	−	0.517855i	$-0.173270\pi$
$467$	36.9736	1.71094	0.855468	+	0.517855i	$0.173270\pi$
$468$	−3.13789	−0.145049
$469$	7.02847	0.324544
$470$	0	0
$471$	0.0554325	0.00255420
$472$	−41.2830	−1.90020
$473$	−1.98801	−0.0914087
$474$	0.0371277	0.00170533
$475$	0	0
$476$	2.06712	0.0947462
$477$	10.2970	0.471467
$478$	2.70521	0.123733
$479$	19.2946	0.881593	0.440796	−	0.897607i	$-0.354696\pi$
$479$	19.2946	0.881593	0.440796	+	0.897607i	$0.354696\pi$
$480$	0	0
$481$	−62.0741	−2.83034
$482$	−1.35529	−0.0617316
$483$	−0.0229233	−0.00104305
$484$	1.75092	0.0795872
$485$	0	0
$486$	−0.118347	−0.00536834
$487$	−1.55804	−0.0706017	−0.0353008	−	0.999377i	$-0.511239\pi$
$487$	−1.55804	−0.0706017	−0.0353008	+	0.999377i	$0.511239\pi$
$488$	3.51804	0.159254
$489$	0.00942154	0.000426057 0
$490$	0	0
$491$	−16.3159	−0.736328	−0.368164	−	0.929761i	$-0.620014\pi$
$491$	−16.3159	−0.736328	−0.368164	+	0.929761i	$0.620014\pi$
$492$	0.00109787	4.94958e−5 0
$493$	−54.4162	−2.45078
$494$	67.2328	3.02495
$495$	0	0
$496$	1.78169	0.0800000
$497$	−5.88094	−0.263796
$498$	0.0595784	0.00266977
$499$	21.2210	0.949984	0.474992	−	0.879990i	$-0.342451\pi$
$499$	21.2210	0.949984	0.474992	+	0.879990i	$0.342451\pi$
$500$	0	0
$501$	0.0659157	0.00294489
$502$	−16.1287	−0.719860
$503$	−13.1299	−0.585432	−0.292716	−	0.956199i	$-0.594559\pi$
$503$	−13.1299	−0.585432	−0.292716	+	0.956199i	$0.594559\pi$
$504$	15.4061	0.686241
$505$	0	0
$506$	−2.85544	−0.126940
$507$	0.0908111	0.00403306
$508$	−0.213540	−0.00947433
$509$	21.1618	0.937979	0.468989	−	0.883204i	$-0.344618\pi$
$509$	21.1618	0.937979	0.468989	+	0.883204i	$0.344618\pi$
$510$	0	0
$511$	24.9988	1.10588
$512$	24.7422	1.09346
$513$	−0.150196	−0.00663132
$514$	11.5391	0.508970
$515$	0	0
$516$	0.00201521	8.87145e−5 0
$517$	−0.319486	−0.0140510
$518$	22.9922	1.01022
$519$	0.0486987	0.00213764
$520$	0	0
$521$	45.1138	1.97647	0.988236	−	0.152939i	$-0.0488739\pi$
$521$	45.1138	1.97647	0.988236	+	0.152939i	$0.0488739\pi$
$522$	−30.5964	−1.33917
$523$	35.7214	1.56199	0.780994	−	0.624539i	$-0.214713\pi$
$523$	35.7214	1.56199	0.780994	+	0.624539i	$0.214713\pi$
$524$	2.69027	0.117525
$525$	0	0
$526$	34.8851	1.52106
$527$	−3.53270	−0.153887
$528$	−0.00614149	−0.000267274 0
$529$	−6.62683	−0.288123
$530$	0	0
$531$	42.2438	1.83323
$532$	2.21258	0.0959275
$533$	13.3316	0.577455
$534$	−0.00382817	−0.000165661 0
$535$	0	0
$536$	−11.7637	−0.508113
$537$	−0.0133737	−0.000577116 0
$538$	12.4958	0.538731
$539$	−2.04721	−0.0881795
$540$	0	0
$541$	8.43247	0.362540	0.181270	−	0.983433i	$-0.441979\pi$
$541$	8.43247	0.362540	0.181270	+	0.983433i	$0.441979\pi$
$542$	−11.9883	−0.514943
$543$	−0.0211829	−0.000909044 0
$544$	−6.65853	−0.285482
$545$	0	0
$546$	−0.0492095	−0.00210597
$547$	−17.1023	−0.731243	−0.365622	−	0.930764i	$-0.619144\pi$
$547$	−17.1023	−0.731243	−0.365622	+	0.930764i	$0.619144\pi$
$548$	−3.04753	−0.130184
$549$	−3.59993	−0.153641
$550$	0	0
$551$	−58.2454	−2.48134
$552$	0.0383671	0.00163301
$553$	14.8370	0.630933
$554$	−25.5504	−1.08553
$555$	0	0
$556$	−2.22591	−0.0943998
$557$	−8.96982	−0.380063	−0.190032	−	0.981778i	$-0.560859\pi$
$557$	−8.96982	−0.380063	−0.190032	+	0.981778i	$0.560859\pi$
$558$	−1.98632	−0.0840877
$559$	24.4709	1.03501
$560$	0	0
$561$	0.0121773	0.000514124 0
$562$	−1.66761	−0.0703440
$563$	−39.1815	−1.65131	−0.825653	−	0.564179i	$-0.809193\pi$
$563$	−39.1815	−1.65131	−0.825653	+	0.564179i	$0.809193\pi$
$564$	0.000323857 0	1.36368e−5 0
$565$	0	0
$566$	25.2868	1.06288
$567$	−15.7646	−0.662051
$568$	9.84303	0.413005
$569$	−9.01889	−0.378092	−0.189046	−	0.981968i	$-0.560539\pi$
$569$	−9.01889	−0.378092	−0.189046	+	0.981968i	$0.560539\pi$
$570$	0	0
$571$	4.89738	0.204949	0.102474	−	0.994736i	$-0.467324\pi$
$571$	4.89738	0.204949	0.102474	+	0.994736i	$0.467324\pi$
$572$	0.544620	0.0227717
$573$	−0.0108518	−0.000453339 0
$574$	−4.93800	−0.206108
$575$	0	0
$576$	−25.6256	−1.06773
$577$	−33.2405	−1.38382	−0.691911	−	0.721983i	$-0.743231\pi$
$577$	−33.2405	−1.38382	−0.691911	+	0.721983i	$0.743231\pi$
$578$	−47.8279	−1.98938
$579$	0.0508257	0.00211224
$580$	0	0
$581$	23.8088	0.987755
$582$	−0.0541573	−0.00224489
$583$	−1.78717	−0.0740171
$584$	−41.8409	−1.73139
$585$	0	0
$586$	−40.3575	−1.66715
$587$	4.64656	0.191784	0.0958921	−	0.995392i	$-0.469430\pi$
$587$	4.64656	0.191784	0.0958921	+	0.995392i	$0.469430\pi$
$588$	0.00207522	8.55804e−5 0
$589$	−3.78130	−0.155806
$590$	0	0
$591$	0.0275860	0.00113473
$592$	−35.3212	−1.45169
$593$	27.6666	1.13613	0.568065	−	0.822984i	$-0.307692\pi$
$593$	27.6666	1.13613	0.568065	+	0.822984i	$0.307692\pi$
$594$	0.0136938	0.000561862 0
$595$	0	0
$596$	1.29125	0.0528916
$597$	0.0309993	0.00126872
$598$	35.1483	1.43732
$599$	32.3511	1.32183	0.660916	−	0.750460i	$-0.270168\pi$
$599$	32.3511	1.32183	0.660916	+	0.750460i	$0.270168\pi$
$600$	0	0
$601$	−6.23850	−0.254474	−0.127237	−	0.991872i	$-0.540611\pi$
$601$	−6.23850	−0.254474	−0.127237	+	0.991872i	$0.540611\pi$
$602$	−9.06398	−0.369420
$603$	12.0375	0.490204
$604$	−1.01911	−0.0414670
$605$	0	0
$606$	−0.00878043	−0.000356681 0
$607$	35.7865	1.45253	0.726265	−	0.687415i	$-0.241255\pi$
$607$	35.7865	1.45253	0.726265	+	0.687415i	$0.241255\pi$
$608$	−7.12709	−0.289042
$609$	0.0426314	0.00172751
$610$	0	0
$611$	3.93263	0.159097
$612$	3.54030	0.143108
$613$	10.2898	0.415599	0.207800	−	0.978171i	$-0.433370\pi$
$613$	10.2898	0.415599	0.207800	+	0.978171i	$0.433370\pi$
$614$	13.7923	0.556612
$615$	0	0
$616$	−2.67392	−0.107735
$617$	−30.5405	−1.22951	−0.614757	−	0.788717i	$-0.710746\pi$
$617$	−30.5405	−1.22951	−0.614757	+	0.788717i	$0.710746\pi$
$618$	−0.0807282	−0.00324736
$619$	−39.5706	−1.59048	−0.795239	−	0.606296i	$-0.792655\pi$
$619$	−39.5706	−1.59048	−0.795239	+	0.606296i	$0.792655\pi$
$620$	0	0
$621$	−0.0785203	−0.00315091
$622$	−1.20706	−0.0483989
$623$	−1.52982	−0.0612909
$624$	0.0755971	0.00302631
$625$	0	0
$626$	−18.2508	−0.729447
$627$	0.0130342	0.000520535 0
$628$	−2.79712	−0.111617
$629$	70.0345	2.79246
$630$	0	0
$631$	−29.7732	−1.18525	−0.592627	−	0.805477i	$-0.701909\pi$
$631$	−29.7732	−1.18525	−0.592627	+	0.805477i	$0.701909\pi$
$632$	−24.8329	−0.987801
$633$	0.0168235	0.000668675 0
$634$	−33.6868	−1.33787
$635$	0	0
$636$	0.00181162	7.18355e−5 0
$637$	25.1996	0.998445
$638$	5.31038	0.210240
$639$	−10.0721	−0.398447
$640$	0	0
$641$	−36.0859	−1.42531	−0.712654	−	0.701516i	$-0.752507\pi$
$641$	−36.0859	−1.42531	−0.712654	+	0.701516i	$0.752507\pi$
$642$	0.0506235	0.00199795
$643$	−17.0539	−0.672540	−0.336270	−	0.941766i	$-0.609165\pi$
$643$	−17.0539	−0.672540	−0.336270	+	0.941766i	$0.609165\pi$
$644$	1.15671	0.0455806
$645$	0	0
$646$	−75.8548	−2.98447
$647$	37.1032	1.45868	0.729338	−	0.684153i	$-0.239828\pi$
$647$	37.1032	1.45868	0.729338	+	0.684153i	$0.239828\pi$
$648$	26.3855	1.03652
$649$	−7.33194	−0.287804
$650$	0	0
$651$	0.00276764	0.000108472 0
$652$	−0.475410	−0.0186185
$653$	12.9348	0.506177	0.253088	−	0.967443i	$-0.418554\pi$
$653$	12.9348	0.506177	0.253088	+	0.967443i	$0.418554\pi$
$654$	0.0588540	0.00230137
$655$	0	0
$656$	7.58590	0.296180
$657$	42.8148	1.67036
$658$	−1.45664	−0.0567858
$659$	36.3765	1.41703	0.708514	−	0.705697i	$-0.249366\pi$
$659$	36.3765	1.41703	0.708514	+	0.705697i	$0.249366\pi$
$660$	0	0
$661$	43.5387	1.69346	0.846730	−	0.532023i	$-0.178568\pi$
$661$	43.5387	1.69346	0.846730	+	0.532023i	$0.178568\pi$
$662$	−30.5623	−1.18784
$663$	−0.149893	−0.00582136
$664$	−39.8492	−1.54645
$665$	0	0
$666$	39.3781	1.52587
$667$	−30.4499	−1.17902
$668$	−3.32609	−0.128690
$669$	0.0370650	0.00143302
$670$	0	0
$671$	0.624812	0.0241206
$672$	0.00521651	0.000201231 0
$673$	0.620436	0.0239160	0.0119580	−	0.999929i	$-0.496194\pi$
$673$	0.620436	0.0239160	0.0119580	+	0.999929i	$0.496194\pi$
$674$	12.4095	0.477996
$675$	0	0
$676$	−4.58232	−0.176243
$677$	24.8458	0.954903	0.477452	−	0.878658i	$-0.341561\pi$
$677$	24.8458	0.954903	0.477452	+	0.878658i	$0.341561\pi$
$678$	−0.0889536	−0.00341624
$679$	−21.6424	−0.830559
$680$	0	0
$681$	−0.0194433	−0.000745068 0
$682$	0.344751	0.0132012
$683$	−2.75069	−0.105252	−0.0526261	−	0.998614i	$-0.516759\pi$
$683$	−2.75069	−0.105252	−0.0526261	+	0.998614i	$0.516759\pi$
$684$	3.78943	0.144892
$685$	0	0
$686$	−25.9517	−0.990841
$687$	−0.0578267	−0.00220623
$688$	13.9244	0.530861
$689$	21.9988	0.838086
$690$	0	0
$691$	−43.0138	−1.63632	−0.818161	−	0.574989i	$-0.805007\pi$
$691$	−43.0138	−1.63632	−0.818161	+	0.574989i	$0.805007\pi$
$692$	−2.45733	−0.0934137
$693$	2.73615	0.103938
$694$	20.6026	0.782063
$695$	0	0
$696$	−0.0713529	−0.00270463
$697$	−15.0412	−0.569727
$698$	11.9092	0.450771
$699$	−0.0296939	−0.00112313
$700$	0	0
$701$	−2.06921	−0.0781529	−0.0390765	−	0.999236i	$-0.512442\pi$
$701$	−2.06921	−0.0781529	−0.0390765	+	0.999236i	$0.512442\pi$
$702$	−0.168560	−0.00636189
$703$	74.9629	2.82728
$704$	4.44765	0.167627
$705$	0	0
$706$	10.9877	0.413526
$707$	−3.50885	−0.131964
$708$	0.00743225	0.000279321 0
$709$	−25.9506	−0.974594	−0.487297	−	0.873236i	$-0.662017\pi$
$709$	−25.9506	−0.974594	−0.487297	+	0.873236i	$0.662017\pi$
$710$	0	0
$711$	25.4109	0.952984
$712$	2.56048	0.0959582
$713$	−1.97681	−0.0740321
$714$	0.0555201	0.00207779
$715$	0	0
$716$	0.674833	0.0252197
$717$	−0.00645557	−0.000241088 0
$718$	−15.2932	−0.570739
$719$	26.5866	0.991512	0.495756	−	0.868462i	$-0.334891\pi$
$719$	26.5866	0.991512	0.495756	+	0.868462i	$0.334891\pi$
$720$	0	0
$721$	−32.2607	−1.20145
$722$	−55.4422	−2.06335
$723$	0.00323419	0.000120281 0
$724$	1.06888	0.0397248
$725$	0	0
$726$	0.0470274	0.00174535
$727$	−23.3030	−0.864259	−0.432130	−	0.901811i	$-0.642238\pi$
$727$	−23.3030	−0.864259	−0.432130	+	0.901811i	$0.642238\pi$
$728$	32.9139	1.21987
$729$	−26.9994	−0.999979
$730$	0	0
$731$	−27.6091	−1.02116
$732$	−0.000633360 0	−2.34097e−5 0
$733$	−4.54039	−0.167703	−0.0838515	−	0.996478i	$-0.526722\pi$
$733$	−4.54039	−0.167703	−0.0838515	+	0.996478i	$0.526722\pi$
$734$	37.1534	1.37136
$735$	0	0
$736$	−3.72594	−0.137340
$737$	−2.08925	−0.0769586
$738$	−8.45718	−0.311313
$739$	9.10395	0.334894	0.167447	−	0.985881i	$-0.446448\pi$
$739$	9.10395	0.334894	0.167447	+	0.985881i	$0.446448\pi$
$740$	0	0
$741$	−0.160441	−0.00589395
$742$	−8.14831	−0.299134
$743$	6.48352	0.237857	0.118929	−	0.992903i	$-0.462054\pi$
$743$	6.48352	0.237857	0.118929	+	0.992903i	$0.462054\pi$
$744$	−0.00463224	−0.000169826 0
$745$	0	0
$746$	14.4665	0.529658
$747$	40.7767	1.49194
$748$	−0.614463	−0.0224670
$749$	20.2302	0.739196
$750$	0	0
$751$	28.2400	1.03049	0.515246	−	0.857042i	$-0.327700\pi$
$751$	28.2400	1.03049	0.515246	+	0.857042i	$0.327700\pi$
$752$	2.23774	0.0816018
$753$	0.0384888	0.00140261
$754$	−65.3669	−2.38052
$755$	0	0
$756$	−0.00554718	−0.000201749 0
$757$	−34.7400	−1.26265	−0.631323	−	0.775520i	$-0.717488\pi$
$757$	−34.7400	−1.26265	−0.631323	+	0.775520i	$0.717488\pi$
$758$	−7.28845	−0.264728
$759$	0.00681408	0.000247335 0
$760$	0	0
$761$	20.7359	0.751674	0.375837	−	0.926686i	$-0.377355\pi$
$761$	20.7359	0.751674	0.375837	+	0.926686i	$0.377355\pi$
$762$	−0.00573542	−0.000207773 0
$763$	23.5193	0.851456
$764$	0.547579	0.0198107
$765$	0	0
$766$	−14.5899	−0.527155
$767$	90.2507	3.25877
$768$	−0.0125808	−0.000453970 0
$769$	−8.82762	−0.318332	−0.159166	−	0.987252i	$-0.550881\pi$
$769$	−8.82762	−0.318332	−0.159166	+	0.987252i	$0.550881\pi$
$770$	0	0
$771$	−0.0275364	−0.000991700 0
$772$	−2.56466	−0.0923040
$773$	17.5441	0.631017	0.315508	−	0.948923i	$-0.397825\pi$
$773$	17.5441	0.631017	0.315508	+	0.948923i	$0.397825\pi$
$774$	−15.5237	−0.557986
$775$	0	0
$776$	36.2233	1.30034
$777$	−0.0548673	−0.00196835
$778$	−13.5017	−0.484061
$779$	−16.0997	−0.576831
$780$	0	0
$781$	1.74814	0.0625535
$782$	−39.6558	−1.41809
$783$	0.146028	0.00521860
$784$	14.3390	0.512107
$785$	0	0
$786$	0.0722572	0.00257733
$787$	27.0121	0.962878	0.481439	−	0.876480i	$-0.340114\pi$
$787$	27.0121	0.962878	0.481439	+	0.876480i	$0.340114\pi$
$788$	−1.39198	−0.0495873
$789$	−0.0832480	−0.00296371
$790$	0	0
$791$	−35.5477	−1.26393
$792$	−4.57955	−0.162727
$793$	−7.69097	−0.273114
$794$	7.59628	0.269582
$795$	0	0
$796$	−1.56422	−0.0554424
$797$	−17.0166	−0.602757	−0.301379	−	0.953505i	$-0.597447\pi$
$797$	−17.0166	−0.602757	−0.301379	+	0.953505i	$0.597447\pi$
$798$	0.0594271	0.00210370
$799$	−4.43696	−0.156968
$800$	0	0
$801$	−2.62008	−0.0925760
$802$	−17.9753	−0.634730
$803$	−7.43104	−0.262236
$804$	0.00211784	7.46903e−5 0
$805$	0	0
$806$	−4.24363	−0.149475
$807$	−0.0298193	−0.00104969
$808$	5.87282	0.206605
$809$	49.8144	1.75138	0.875690	−	0.482873i	$-0.160407\pi$
$809$	49.8144	1.75138	0.875690	+	0.482873i	$0.160407\pi$
$810$	0	0
$811$	−38.1758	−1.34053	−0.670267	−	0.742120i	$-0.733821\pi$
$811$	−38.1758	−1.34053	−0.670267	+	0.742120i	$0.733821\pi$
$812$	−2.15117	−0.0754914
$813$	0.0286084	0.00100334
$814$	−6.83455	−0.239551
$815$	0	0
$816$	−0.0852917	−0.00298581
$817$	−29.5519	−1.03389
$818$	5.73924	0.200668
$819$	−33.6800	−1.17687
$820$	0	0
$821$	3.94490	0.137678	0.0688390	−	0.997628i	$-0.478071\pi$
$821$	3.94490	0.137678	0.0688390	+	0.997628i	$0.478071\pi$
$822$	−0.0818527	−0.00285494
$823$	5.79068	0.201850	0.100925	−	0.994894i	$-0.467820\pi$
$823$	5.79068	0.201850	0.100925	+	0.994894i	$0.467820\pi$
$824$	53.9953	1.88101
$825$	0	0
$826$	−33.4287	−1.16313
$827$	−7.31807	−0.254474	−0.127237	−	0.991872i	$-0.540611\pi$
$827$	−7.31807	−0.254474	−0.127237	+	0.991872i	$0.540611\pi$
$828$	1.98106	0.0688466
$829$	7.19485	0.249888	0.124944	−	0.992164i	$-0.460125\pi$
$829$	7.19485	0.249888	0.124944	+	0.992164i	$0.460125\pi$
$830$	0	0
$831$	0.0609723	0.00211511
$832$	−54.7472	−1.89802
$833$	−28.4312	−0.985083
$834$	−0.0597852	−0.00207019
$835$	0	0
$836$	−0.657703	−0.0227471
$837$	0.00948013	0.000327681 0
$838$	17.5696	0.606930
$839$	−21.3479	−0.737010	−0.368505	−	0.929626i	$-0.620130\pi$
$839$	−21.3479	−0.737010	−0.368505	+	0.929626i	$0.620130\pi$
$840$	0	0
$841$	27.6289	0.952721
$842$	−32.4978	−1.11995
$843$	0.00397951	0.000137061 0
$844$	−0.848913	−0.0292208
$845$	0	0
$846$	−2.49475	−0.0857713
$847$	18.7932	0.645740
$848$	12.5177	0.429859
$849$	−0.0603432	−0.00207097
$850$	0	0
$851$	39.1895	1.34340
$852$	−0.00177206	−6.07098e−5 0
$853$	−13.1633	−0.450702	−0.225351	−	0.974278i	$-0.572353\pi$
$853$	−13.1633	−0.450702	−0.225351	+	0.974278i	$0.572353\pi$
$854$	2.84872	0.0974813
$855$	0	0
$856$	−33.8597	−1.15730
$857$	29.5441	1.00921	0.504604	−	0.863351i	$-0.331639\pi$
$857$	29.5441	1.00921	0.504604	+	0.863351i	$0.331639\pi$
$858$	0.0146278	0.000499385 0
$859$	20.6602	0.704918	0.352459	−	0.935827i	$-0.385346\pi$
$859$	20.6602	0.704918	0.352459	+	0.935827i	$0.385346\pi$
$860$	0	0
$861$	0.0117838	0.000401590 0
$862$	−47.1744	−1.60677
$863$	−55.8835	−1.90230	−0.951148	−	0.308736i	$-0.900094\pi$
$863$	−55.8835	−1.90230	−0.951148	+	0.308736i	$0.900094\pi$
$864$	0.0178684	0.000607895 0
$865$	0	0
$866$	6.56707	0.223158
$867$	0.114134	0.00387620
$868$	−0.139654	−0.00474018
$869$	−4.41038	−0.149612
$870$	0	0
$871$	25.7172	0.871392
$872$	−39.3647	−1.33306
$873$	−37.0664	−1.25451
$874$	−42.4464	−1.43577
$875$	0	0
$876$	0.00753270	0.000254506 0
$877$	−29.1533	−0.984439	−0.492219	−	0.870471i	$-0.663814\pi$
$877$	−29.1533	−0.984439	−0.492219	+	0.870471i	$0.663814\pi$
$878$	−36.1658	−1.22054
$879$	0.0963071	0.00324836
$880$	0	0
$881$	26.2379	0.883976	0.441988	−	0.897021i	$-0.354273\pi$
$881$	26.2379	0.883976	0.441988	+	0.897021i	$0.354273\pi$
$882$	−15.9859	−0.538274
$883$	39.9021	1.34281	0.671407	−	0.741089i	$-0.265690\pi$
$883$	39.9021	1.34281	0.671407	+	0.741089i	$0.265690\pi$
$884$	7.56358	0.254391
$885$	0	0
$886$	−20.6952	−0.695269
$887$	48.5726	1.63091	0.815454	−	0.578822i	$-0.196488\pi$
$887$	48.5726	1.63091	0.815454	+	0.578822i	$0.196488\pi$
$888$	0.0918324	0.00308169
$889$	−2.29200	−0.0768711
$890$	0	0
$891$	4.68612	0.156991
$892$	−1.87029	−0.0626221
$893$	−4.74918	−0.158925
$894$	0.0346813	0.00115992
$895$	0	0
$896$	17.0524	0.569682
$897$	−0.0838762	−0.00280055
$898$	−2.01647	−0.0672904
$899$	3.67636	0.122613
$900$	0	0
$901$	−24.8199	−0.826870
$902$	1.46785	0.0488740
$903$	0.0216298	0.000719796 0
$904$	59.4969	1.97884
$905$	0	0
$906$	−0.0273720	−0.000909373 0
$907$	37.5879	1.24809	0.624043	−	0.781390i	$-0.285489\pi$
$907$	37.5879	1.24809	0.624043	+	0.781390i	$0.285489\pi$
$908$	0.981105	0.0325591
$909$	−6.00951	−0.199323
$910$	0	0
$911$	−7.66887	−0.254081	−0.127040	−	0.991898i	$-0.540548\pi$
$911$	−7.66887	−0.254081	−0.127040	+	0.991898i	$0.540548\pi$
$912$	−0.0912937	−0.00302304
$913$	−7.07730	−0.234224
$914$	21.3466	0.706083
$915$	0	0
$916$	2.91793	0.0964110
$917$	28.8755	0.953553
$918$	0.190176	0.00627675
$919$	35.0798	1.15717	0.578587	−	0.815621i	$-0.303604\pi$
$919$	35.0798	1.15717	0.578587	+	0.815621i	$0.303604\pi$
$920$	0	0
$921$	−0.0329132	−0.00108453
$922$	25.1880	0.829522
$923$	−21.5183	−0.708285
$924$	0.000481390 0	1.58366e−5 0
$925$	0	0
$926$	−15.5754	−0.511841
$927$	−55.2520	−1.81471
$928$	6.92929	0.227465
$929$	9.34233	0.306512	0.153256	−	0.988187i	$-0.451024\pi$
$929$	9.34233	0.306512	0.153256	+	0.988187i	$0.451024\pi$
$930$	0	0
$931$	−30.4319	−0.997366
$932$	1.49835	0.0490802
$933$	0.00288048	9.43026e−5 0
$934$	−50.1099	−1.63965
$935$	0	0
$936$	56.3708	1.84254
$937$	42.7479	1.39651	0.698257	−	0.715847i	$-0.253959\pi$
$937$	42.7479	1.39651	0.698257	+	0.715847i	$0.253959\pi$
$938$	−9.52559	−0.311022
$939$	0.0435527	0.00142129
$940$	0	0
$941$	14.3514	0.467843	0.233922	−	0.972255i	$-0.424844\pi$
$941$	14.3514	0.467843	0.233922	+	0.972255i	$0.424844\pi$
$942$	−0.0751270	−0.00244777
$943$	−8.41668	−0.274085
$944$	51.3542	1.67144
$945$	0	0
$946$	2.69432	0.0876000
$947$	53.6096	1.74208	0.871038	−	0.491215i	$-0.163447\pi$
$947$	53.6096	1.74208	0.871038	+	0.491215i	$0.163447\pi$
$948$	0.00447072	0.000145202 0
$949$	91.4705	2.96926
$950$	0	0
$951$	0.0803885	0.00260678
$952$	−37.1348	−1.20355
$953$	−9.87157	−0.319772	−0.159886	−	0.987136i	$-0.551113\pi$
$953$	−9.87157	−0.319772	−0.159886	+	0.987136i	$0.551113\pi$
$954$	−13.9554	−0.451823
$955$	0	0
$956$	0.325747	0.0105354
$957$	−0.0126724	−0.000409641 0
$958$	−26.1497	−0.844859
$959$	−32.7101	−1.05626
$960$	0	0
$961$	−30.7613	−0.992301
$962$	84.1283	2.71240
$963$	34.6477	1.11651
$964$	−0.163197	−0.00525621
$965$	0	0
$966$	0.0310676	0.000999584 0
$967$	27.0564	0.870075	0.435038	−	0.900412i	$-0.356735\pi$
$967$	27.0564	0.870075	0.435038	+	0.900412i	$0.356735\pi$
$968$	−31.4544	−1.01098
$969$	0.181016	0.00581507
$970$	0	0
$971$	40.8922	1.31229	0.656147	−	0.754634i	$-0.272185\pi$
$971$	40.8922	1.31229	0.656147	+	0.754634i	$0.272185\pi$
$972$	−0.0142508	−0.000457094 0
$973$	−23.8914	−0.765924
$974$	2.11160	0.0676599
$975$	0	0
$976$	−4.37629	−0.140082
$977$	−24.8089	−0.793707	−0.396853	−	0.917882i	$-0.629898\pi$
$977$	−24.8089	−0.793707	−0.396853	+	0.917882i	$0.629898\pi$
$978$	−0.0127689	−0.000408304 0
$979$	0.454747	0.0145338
$980$	0	0
$981$	40.2809	1.28607
$982$	22.1128	0.705647
$983$	27.6155	0.880797	0.440399	−	0.897802i	$-0.354837\pi$
$983$	27.6155	0.880797	0.440399	+	0.897802i	$0.354837\pi$
$984$	−0.0197227	−0.000628738 0
$985$	0	0
$986$	73.7495	2.34866
$987$	0.00347605	0.000110644 0
$988$	8.09583	0.257563
$989$	−15.4493	−0.491260
$990$	0	0
$991$	−14.2011	−0.451112	−0.225556	−	0.974230i	$-0.572420\pi$
$991$	−14.2011	−0.451112	−0.225556	+	0.974230i	$0.572420\pi$
$992$	0.449850	0.0142828
$993$	0.0729323	0.00231444
$994$	7.97036	0.252804
$995$	0	0
$996$	0.00717412	0.000227321 0
$997$	−17.0452	−0.539828	−0.269914	−	0.962884i	$-0.586995\pi$
$997$	−17.0452	−0.539828	−0.269914	+	0.962884i	$0.586995\pi$
$998$	−28.7606	−0.910401
$999$	−0.187940	−0.00594616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.n.1.11	yes	40
5.4	even	2		6025.2.a.m.1.30	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.30	✓	40	5.4	even	2
6025.2.a.n.1.11	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.35529 q^{2} +0.00323419 q^{3} -0.163197 q^{4} -0.00438325 q^{6} -1.75164 q^{7} +2.93175 q^{8} -2.99999 q^{9} +O(q^{10})\)	\(q-1.35529 q^{2} +0.00323419 q^{3} -0.163197 q^{4} -0.00438325 q^{6} -1.75164 q^{7} +2.93175 q^{8} -2.99999 q^{9} +0.520685 q^{11} -0.000527809 q^{12} -6.40925 q^{13} +2.37398 q^{14} -3.64697 q^{16} +7.23117 q^{17} +4.06585 q^{18} +7.74003 q^{19} -0.00566514 q^{21} -0.705678 q^{22} +4.04638 q^{23} +0.00948184 q^{24} +8.68637 q^{26} -0.0194051 q^{27} +0.285862 q^{28} -7.52522 q^{29} -0.488538 q^{31} -0.920809 q^{32} +0.00168400 q^{33} -9.80032 q^{34} +0.489588 q^{36} +9.68508 q^{37} -10.4900 q^{38} -0.0207287 q^{39} -2.08005 q^{41} +0.00767789 q^{42} -3.81806 q^{43} -0.0849741 q^{44} -5.48400 q^{46} -0.613587 q^{47} -0.0117950 q^{48} -3.93176 q^{49} +0.0233870 q^{51} +1.04597 q^{52} -3.43235 q^{53} +0.0262995 q^{54} -5.13538 q^{56} +0.0250327 q^{57} +10.1988 q^{58} -14.0813 q^{59} +1.19998 q^{61} +0.662109 q^{62} +5.25490 q^{63} +8.54191 q^{64} -0.00228230 q^{66} -4.01251 q^{67} -1.18010 q^{68} +0.0130867 q^{69} +3.35739 q^{71} -8.79523 q^{72} -14.2716 q^{73} -13.1261 q^{74} -1.26315 q^{76} -0.912054 q^{77} +0.0280934 q^{78} -8.47034 q^{79} +8.99991 q^{81} +2.81907 q^{82} -13.5923 q^{83} +0.000924531 q^{84} +5.17457 q^{86} -0.0243380 q^{87} +1.52652 q^{88} +0.873363 q^{89} +11.2267 q^{91} -0.660355 q^{92} -0.00158002 q^{93} +0.831587 q^{94} -0.00297807 q^{96} +12.3555 q^{97} +5.32866 q^{98} -1.56205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9	\( 40 q + 9 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 20 q^{7} + 27 q^{8} + 38 q^{9} + q^{11} + 26 q^{12} + 11 q^{13} - q^{14} + 43 q^{16} + 20 q^{17} + 18 q^{18} + 2 q^{21} + 23 q^{22} + 79 q^{23} - 2 q^{24} + 2 q^{26} + 26 q^{27} + 30 q^{28} + 2 q^{29} + q^{31} + 68 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 16 q^{37} + 45 q^{38} - 2 q^{39} - 2 q^{41} + 19 q^{42} + 25 q^{43} + 3 q^{44} + 14 q^{46} + 88 q^{47} + 75 q^{48} + 40 q^{49} - 10 q^{51} + 18 q^{52} + 34 q^{53} + 4 q^{54} - 15 q^{56} + 51 q^{57} + 53 q^{58} + q^{59} + 9 q^{61} + 39 q^{62} + 110 q^{63} + 17 q^{64} + 26 q^{66} + 30 q^{67} + 44 q^{68} - 7 q^{69} + 5 q^{71} + 18 q^{72} + 23 q^{73} - 18 q^{74} + 43 q^{76} + 30 q^{77} + 46 q^{78} + 5 q^{79} + 44 q^{81} + 5 q^{82} + 65 q^{83} - 65 q^{84} + 40 q^{86} + 33 q^{87} + 71 q^{88} - 9 q^{89} + q^{91} + 117 q^{92} + 68 q^{93} - 72 q^{94} + 83 q^{96} - 8 q^{97} + 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q + 9 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 20 * q^7 + 27 * q^8 + 38 * q^9 + q^11 + 26 * q^12 + 11 * q^13 - q^14 + 43 * q^16 + 20 * q^17 + 18 * q^18 + 2 * q^21 + 23 * q^22 + 79 * q^23 - 2 * q^24 + 2 * q^26 + 26 * q^27 + 30 * q^28 + 2 * q^29 + q^31 + 68 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 16 * q^37 + 45 * q^38 - 2 * q^39 - 2 * q^41 + 19 * q^42 + 25 * q^43 + 3 * q^44 + 14 * q^46 + 88 * q^47 + 75 * q^48 + 40 * q^49 - 10 * q^51 + 18 * q^52 + 34 * q^53 + 4 * q^54 - 15 * q^56 + 51 * q^57 + 53 * q^58 + q^59 + 9 * q^61 + 39 * q^62 + 110 * q^63 + 17 * q^64 + 26 * q^66 + 30 * q^67 + 44 * q^68 - 7 * q^69 + 5 * q^71 + 18 * q^72 + 23 * q^73 - 18 * q^74 + 43 * q^76 + 30 * q^77 + 46 * q^78 + 5 * q^79 + 44 * q^81 + 5 * q^82 + 65 * q^83 - 65 * q^84 + 40 * q^86 + 33 * q^87 + 71 * q^88 - 9 * q^89 + q^91 + 117 * q^92 + 68 * q^93 - 72 * q^94 + 83 * q^96 - 8 * q^97 + 76 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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