LMFDB - Embedded newform 6025.2.a.g.1.9

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2x^{10} - 11x^{9} + 15x^{8} + 43x^{7} - 28x^{6} - 62x^{5} + 14x^{4} + 31x^{3} + x^{2} - 5x - 1 $ x^11 - 2x^10 - 11x^9 + 15x^8 + 43x^7 - 28x^6 - 62x^5 + 14x^4 + 31x^3 + x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.54550$ of defining polynomial
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)

$f(q)$	$=$	$q+1.89846 q^{2} +0.0586609 q^{3} +1.60416 q^{4} +0.111366 q^{6} -2.85624 q^{7} -0.751482 q^{8} -2.99656 q^{9} +O(q^{10})$	\(q+1.89846 q^{2} +0.0586609 q^{3} +1.60416 q^{4} +0.111366 q^{6} -2.85624 q^{7} -0.751482 q^{8} -2.99656 q^{9} +1.30626 q^{11} +0.0941016 q^{12} -0.0326883 q^{13} -5.42247 q^{14} -4.63499 q^{16} +6.87716 q^{17} -5.68886 q^{18} -7.81086 q^{19} -0.167550 q^{21} +2.47988 q^{22} +1.89174 q^{23} -0.0440826 q^{24} -0.0620575 q^{26} -0.351763 q^{27} -4.58188 q^{28} +4.83672 q^{29} +1.83031 q^{31} -7.29639 q^{32} +0.0766261 q^{33} +13.0560 q^{34} -4.80697 q^{36} +10.4233 q^{37} -14.8286 q^{38} -0.00191752 q^{39} +0.425606 q^{41} -0.318087 q^{42} +4.54896 q^{43} +2.09545 q^{44} +3.59139 q^{46} -3.55753 q^{47} -0.271892 q^{48} +1.15811 q^{49} +0.403420 q^{51} -0.0524373 q^{52} +11.6903 q^{53} -0.667810 q^{54} +2.14641 q^{56} -0.458192 q^{57} +9.18233 q^{58} +10.6566 q^{59} +6.28395 q^{61} +3.47478 q^{62} +8.55889 q^{63} -4.58195 q^{64} +0.145472 q^{66} +13.1633 q^{67} +11.0321 q^{68} +0.110971 q^{69} +10.2138 q^{71} +2.25186 q^{72} +2.71664 q^{73} +19.7883 q^{74} -12.5299 q^{76} -3.73098 q^{77} -0.00364035 q^{78} -7.47865 q^{79} +8.96904 q^{81} +0.807997 q^{82} -4.99749 q^{83} -0.268777 q^{84} +8.63604 q^{86} +0.283726 q^{87} -0.981627 q^{88} -18.1176 q^{89} +0.0933656 q^{91} +3.03465 q^{92} +0.107368 q^{93} -6.75384 q^{94} -0.428013 q^{96} -17.0162 q^{97} +2.19863 q^{98} -3.91427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * 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 $

$2$	1.89846	1.34242	0.671208	−	0.741269i	$-0.265776\pi$
$2$	1.89846	1.34242	0.671208	+	0.741269i	$0.265776\pi$
$3$	0.0586609	0.0338679	0.0169339	−	0.999857i	$-0.494610\pi$
$3$	0.0586609	0.0338679	0.0169339	+	0.999857i	$0.494610\pi$
$4$	1.60416	0.802082
$5$	0	0
$5$	0	0
$6$	0.111366	0.0454648
$7$	−2.85624	−1.07956	−0.539779	−	0.841807i	$-0.681492\pi$
$7$	−2.85624	−1.07956	−0.539779	+	0.841807i	$0.681492\pi$
$8$	−0.751482	−0.265689
$9$	−2.99656	−0.998853
$10$	0	0
$11$	1.30626	0.393851	0.196925	−	0.980418i	$-0.436904\pi$
$11$	1.30626	0.393851	0.196925	+	0.980418i	$0.436904\pi$
$12$	0.0941016	0.0271648
$13$	−0.0326883	−0.00906609	−0.00453305	−	0.999990i	$-0.501443\pi$
$13$	−0.0326883	−0.00906609	−0.00453305	+	0.999990i	$0.501443\pi$
$14$	−5.42247	−1.44922
$15$	0	0
$16$	−4.63499	−1.15875
$17$	6.87716	1.66796	0.833979	−	0.551797i	$-0.186058\pi$
$17$	6.87716	1.66796	0.833979	+	0.551797i	$0.186058\pi$
$18$	−5.68886	−1.34088
$19$	−7.81086	−1.79193	−0.895967	−	0.444121i	$-0.853516\pi$
$19$	−7.81086	−1.79193	−0.895967	+	0.444121i	$0.853516\pi$
$20$	0	0
$21$	−0.167550	−0.0365623
$22$	2.47988	0.528712
$23$	1.89174	0.394454	0.197227	−	0.980358i	$-0.436806\pi$
$23$	1.89174	0.394454	0.197227	+	0.980358i	$0.436806\pi$
$24$	−0.0440826	−0.00899832
$25$	0	0
$26$	−0.0620575	−0.0121705
$27$	−0.351763	−0.0676969
$28$	−4.58188	−0.865893
$29$	4.83672	0.898156	0.449078	−	0.893493i	$-0.351753\pi$
$29$	4.83672	0.898156	0.449078	+	0.893493i	$0.351753\pi$
$30$	0	0
$31$	1.83031	0.328734	0.164367	−	0.986399i	$-0.447442\pi$
$31$	1.83031	0.328734	0.164367	+	0.986399i	$0.447442\pi$
$32$	−7.29639	−1.28983
$33$	0.0766261	0.0133389
$34$	13.0560	2.23909
$35$	0	0
$36$	−4.80697	−0.801162
$37$	10.4233	1.71359	0.856794	−	0.515659i	$-0.172453\pi$
$37$	10.4233	1.71359	0.856794	+	0.515659i	$0.172453\pi$
$38$	−14.8286	−2.40552
$39$	−0.00191752	−0.000307049 0
$40$	0	0
$41$	0.425606	0.0664685	0.0332342	−	0.999448i	$-0.489419\pi$
$41$	0.425606	0.0664685	0.0332342	+	0.999448i	$0.489419\pi$
$42$	−0.318087	−0.0490818
$43$	4.54896	0.693710	0.346855	−	0.937919i	$-0.387250\pi$
$43$	4.54896	0.693710	0.346855	+	0.937919i	$0.387250\pi$
$44$	2.09545	0.315900
$45$	0	0
$46$	3.59139	0.529522
$47$	−3.55753	−0.518919	−0.259459	−	0.965754i	$-0.583544\pi$
$47$	−3.55753	−0.518919	−0.259459	+	0.965754i	$0.583544\pi$
$48$	−0.271892	−0.0392443
$49$	1.15811	0.165444
$50$	0	0
$51$	0.403420	0.0564902
$52$	−0.0524373	−0.00727175
$53$	11.6903	1.60578	0.802890	−	0.596127i	$-0.203295\pi$
$53$	11.6903	1.60578	0.802890	+	0.596127i	$0.203295\pi$
$54$	−0.667810	−0.0908774
$55$	0	0
$56$	2.14641	0.286826
$57$	−0.458192	−0.0606890
$58$	9.18233	1.20570
$59$	10.6566	1.38738	0.693688	−	0.720275i	$-0.255985\pi$
$59$	10.6566	1.38738	0.693688	+	0.720275i	$0.255985\pi$
$60$	0	0
$61$	6.28395	0.804577	0.402289	−	0.915513i	$-0.368215\pi$
$61$	6.28395	0.804577	0.402289	+	0.915513i	$0.368215\pi$
$62$	3.47478	0.441297
$63$	8.55889	1.07832
$64$	−4.58195	−0.572744
$65$	0	0
$66$	0.145472	0.0179063
$67$	13.1633	1.60815	0.804076	−	0.594526i	$-0.202660\pi$
$67$	13.1633	1.60815	0.804076	+	0.594526i	$0.202660\pi$
$68$	11.0321	1.33784
$69$	0.110971	0.0133593
$70$	0	0
$71$	10.2138	1.21215	0.606075	−	0.795407i	$-0.292743\pi$
$71$	10.2138	1.21215	0.606075	+	0.795407i	$0.292743\pi$
$72$	2.25186	0.265384
$73$	2.71664	0.317959	0.158979	−	0.987282i	$-0.449180\pi$
$73$	2.71664	0.317959	0.158979	+	0.987282i	$0.449180\pi$
$74$	19.7883	2.30035
$75$	0	0
$76$	−12.5299	−1.43728
$77$	−3.73098	−0.425185
$78$	−0.00364035	−0.000412188 0
$79$	−7.47865	−0.841414	−0.420707	−	0.907197i	$-0.638218\pi$
$79$	−7.47865	−0.841414	−0.420707	+	0.907197i	$0.638218\pi$
$80$	0	0
$81$	8.96904	0.996560
$82$	0.807997	0.0892284
$83$	−4.99749	−0.548546	−0.274273	−	0.961652i	$-0.588437\pi$
$83$	−4.99749	−0.548546	−0.274273	+	0.961652i	$0.588437\pi$
$84$	−0.268777	−0.0293260
$85$	0	0
$86$	8.63604	0.931248
$87$	0.283726	0.0304186
$88$	−0.981627	−0.104642
$89$	−18.1176	−1.92047	−0.960233	−	0.279200i	$-0.909931\pi$
$89$	−18.1176	−1.92047	−0.960233	+	0.279200i	$0.909931\pi$
$90$	0	0
$91$	0.0933656	0.00978737
$92$	3.03465	0.316384
$93$	0.107368	0.0111335
$94$	−6.75384	−0.696605
$95$	0	0
$96$	−0.428013	−0.0436838
$97$	−17.0162	−1.72773	−0.863866	−	0.503721i	$-0.831964\pi$
$97$	−17.0162	−1.72773	−0.863866	+	0.503721i	$0.831964\pi$
$98$	2.19863	0.222095
$99$	−3.91427	−0.393399
$100$	0	0
$101$	−15.5556	−1.54784	−0.773920	−	0.633283i	$-0.781707\pi$
$101$	−15.5556	−1.54784	−0.773920	+	0.633283i	$0.781707\pi$
$102$	0.765879	0.0758333
$103$	1.93630	0.190790	0.0953948	−	0.995440i	$-0.469589\pi$
$103$	1.93630	0.190790	0.0953948	+	0.995440i	$0.469589\pi$
$104$	0.0245646	0.00240876
$105$	0	0
$106$	22.1935	2.15563
$107$	16.6295	1.60764	0.803818	−	0.594876i	$-0.202799\pi$
$107$	16.6295	1.60764	0.803818	+	0.594876i	$0.202799\pi$
$108$	−0.564286	−0.0542984
$109$	−0.512734	−0.0491110	−0.0245555	−	0.999698i	$-0.507817\pi$
$109$	−0.512734	−0.0491110	−0.0245555	+	0.999698i	$0.507817\pi$
$110$	0	0
$111$	0.611443	0.0580356
$112$	13.2386	1.25093
$113$	−3.52571	−0.331671	−0.165836	−	0.986153i	$-0.553032\pi$
$113$	−3.52571	−0.331671	−0.165836	+	0.986153i	$0.553032\pi$
$114$	−0.869860	−0.0814699
$115$	0	0
$116$	7.75888	0.720394
$117$	0.0979523	0.00905570
$118$	20.2312	1.86244
$119$	−19.6428	−1.80066
$120$	0	0
$121$	−9.29370	−0.844882
$122$	11.9298	1.08008
$123$	0.0249664	0.00225115
$124$	2.93612	0.263671
$125$	0	0
$126$	16.2487	1.44755
$127$	7.92501	0.703231	0.351615	−	0.936145i	$-0.385632\pi$
$127$	7.92501	0.703231	0.351615	+	0.936145i	$0.385632\pi$
$128$	5.89411	0.520970
$129$	0.266846	0.0234945
$130$	0	0
$131$	17.4894	1.52806	0.764030	−	0.645181i	$-0.223218\pi$
$131$	17.4894	1.52806	0.764030	+	0.645181i	$0.223218\pi$
$132$	0.122921	0.0106989
$133$	22.3097	1.93450
$134$	24.9900	2.15881
$135$	0	0
$136$	−5.16806	−0.443158
$137$	−4.95710	−0.423514	−0.211757	−	0.977322i	$-0.567919\pi$
$137$	−4.95710	−0.423514	−0.211757	+	0.977322i	$0.567919\pi$
$138$	0.210674	0.0179338
$139$	6.93405	0.588138	0.294069	−	0.955784i	$-0.404990\pi$
$139$	6.93405	0.588138	0.294069	+	0.955784i	$0.404990\pi$
$140$	0	0
$141$	−0.208688	−0.0175747
$142$	19.3905	1.62721
$143$	−0.0426992	−0.00357069
$144$	13.8890	1.15742
$145$	0	0
$146$	5.15744	0.426833
$147$	0.0679357	0.00560324
$148$	16.7208	1.37444
$149$	−6.71478	−0.550097	−0.275048	−	0.961430i	$-0.588694\pi$
$149$	−6.71478	−0.550097	−0.275048	+	0.961430i	$0.588694\pi$
$150$	0	0
$151$	−5.07961	−0.413373	−0.206687	−	0.978407i	$-0.566268\pi$
$151$	−5.07961	−0.413373	−0.206687	+	0.978407i	$0.566268\pi$
$152$	5.86972	0.476097
$153$	−20.6078	−1.66604
$154$	−7.08313	−0.570775
$155$	0	0
$156$	−0.00307602	−0.000246279 0
$157$	14.1301	1.12771	0.563854	−	0.825875i	$-0.309318\pi$
$157$	14.1301	1.12771	0.563854	+	0.825875i	$0.309318\pi$
$158$	−14.1979	−1.12953
$159$	0.685761	0.0543843
$160$	0	0
$161$	−5.40325	−0.425836
$162$	17.0274	1.33780
$163$	15.2341	1.19323	0.596615	−	0.802527i	$-0.296512\pi$
$163$	15.2341	1.19323	0.596615	+	0.802527i	$0.296512\pi$
$164$	0.682741	0.0533131
$165$	0	0
$166$	−9.48755	−0.736377
$167$	8.25959	0.639146	0.319573	−	0.947562i	$-0.396461\pi$
$167$	8.25959	0.639146	0.319573	+	0.947562i	$0.396461\pi$
$168$	0.125910	0.00971420
$169$	−12.9989	−0.999918
$170$	0	0
$171$	23.4057	1.78988
$172$	7.29728	0.556412
$173$	−22.5364	−1.71341	−0.856704	−	0.515808i	$-0.827492\pi$
$173$	−22.5364	−1.71341	−0.856704	+	0.515808i	$0.827492\pi$
$174$	0.538643	0.0408345
$175$	0	0
$176$	−6.05448	−0.456373
$177$	0.625128	0.0469875
$178$	−34.3957	−2.57806
$179$	15.7940	1.18050	0.590248	−	0.807222i	$-0.299030\pi$
$179$	15.7940	1.18050	0.590248	+	0.807222i	$0.299030\pi$
$180$	0	0
$181$	−13.5927	−1.01034	−0.505170	−	0.863020i	$-0.668570\pi$
$181$	−13.5927	−1.01034	−0.505170	+	0.863020i	$0.668570\pi$
$182$	0.177251	0.0131387
$183$	0.368622	0.0272493
$184$	−1.42160	−0.104802
$185$	0	0
$186$	0.203834	0.0149458
$187$	8.98333	0.656926
$188$	−5.70686	−0.416215
$189$	1.00472	0.0730827
$190$	0	0
$191$	17.6417	1.27651	0.638254	−	0.769826i	$-0.279657\pi$
$191$	17.6417	1.27651	0.638254	+	0.769826i	$0.279657\pi$
$192$	−0.268781	−0.0193976
$193$	4.69247	0.337772	0.168886	−	0.985636i	$-0.445983\pi$
$193$	4.69247	0.337772	0.168886	+	0.985636i	$0.445983\pi$
$194$	−32.3046	−2.31934
$195$	0	0
$196$	1.85780	0.132700
$197$	5.72142	0.407634	0.203817	−	0.979009i	$-0.434665\pi$
$197$	5.72142	0.407634	0.203817	+	0.979009i	$0.434665\pi$
$198$	−7.43110	−0.528105
$199$	−17.2694	−1.22420	−0.612099	−	0.790781i	$-0.709675\pi$
$199$	−17.2694	−1.22420	−0.612099	+	0.790781i	$0.709675\pi$
$200$	0	0
$201$	0.772170	0.0544647
$202$	−29.5317	−2.07785
$203$	−13.8148	−0.969611
$204$	0.647152	0.0453097
$205$	0	0
$206$	3.67600	0.256119
$207$	−5.66870	−0.394002
$208$	0.151510	0.0105053
$209$	−10.2030	−0.705754
$210$	0	0
$211$	17.1656	1.18173	0.590864	−	0.806771i	$-0.298787\pi$
$211$	17.1656	1.18173	0.590864	+	0.806771i	$0.298787\pi$
$212$	18.7531	1.28797
$213$	0.599148	0.0410530
$214$	31.5705	2.15812
$215$	0	0
$216$	0.264344	0.0179863
$217$	−5.22781	−0.354887
$218$	−0.973407	−0.0659275
$219$	0.159361	0.0107686
$220$	0	0
$221$	−0.224803	−0.0151219
$222$	1.16080	0.0779079
$223$	16.6760	1.11671	0.558353	−	0.829604i	$-0.311434\pi$
$223$	16.6760	1.11671	0.558353	+	0.829604i	$0.311434\pi$
$224$	20.8402	1.39245
$225$	0	0
$226$	−6.69344	−0.445241
$227$	19.6906	1.30691	0.653454	−	0.756966i	$-0.273319\pi$
$227$	19.6906	1.30691	0.653454	+	0.756966i	$0.273319\pi$
$228$	−0.735014	−0.0486775
$229$	26.8569	1.77476	0.887378	−	0.461043i	$-0.152525\pi$
$229$	26.8569	1.77476	0.887378	+	0.461043i	$0.152525\pi$
$230$	0	0
$231$	−0.218863	−0.0144001
$232$	−3.63470	−0.238630
$233$	−26.9529	−1.76574	−0.882870	−	0.469617i	$-0.844392\pi$
$233$	−26.9529	−1.76574	−0.882870	+	0.469617i	$0.844392\pi$
$234$	0.185959	0.0121565
$235$	0	0
$236$	17.0950	1.11279
$237$	−0.438704	−0.0284969
$238$	−37.2912	−2.41723
$239$	−29.2869	−1.89441	−0.947205	−	0.320628i	$-0.896106\pi$
$239$	−29.2869	−1.89441	−0.947205	+	0.320628i	$0.896106\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−17.6437	−1.13418
$243$	1.58142	0.101448
$244$	10.0805	0.645336
$245$	0	0
$246$	0.0473978	0.00302198
$247$	0.255323	0.0162458
$248$	−1.37545	−0.0873409
$249$	−0.293157	−0.0185781
$250$	0	0
$251$	23.4800	1.48204	0.741021	−	0.671481i	$-0.234342\pi$
$251$	23.4800	1.48204	0.741021	+	0.671481i	$0.234342\pi$
$252$	13.7299	0.864900
$253$	2.47109	0.155356
$254$	15.0453	0.944028
$255$	0	0
$256$	20.3537	1.27210
$257$	7.61520	0.475023	0.237512	−	0.971385i	$-0.423668\pi$
$257$	7.61520	0.475023	0.237512	+	0.971385i	$0.423668\pi$
$258$	0.506598	0.0315394
$259$	−29.7716	−1.84992
$260$	0	0
$261$	−14.4935	−0.897125
$262$	33.2031	2.05129
$263$	−26.2673	−1.61971	−0.809856	−	0.586628i	$-0.800455\pi$
$263$	−26.2673	−1.61971	−0.809856	+	0.586628i	$0.800455\pi$
$264$	−0.0575831	−0.00354400
$265$	0	0
$266$	42.3541	2.59690
$267$	−1.06280	−0.0650421
$268$	21.1161	1.28987
$269$	7.61455	0.464267	0.232134	−	0.972684i	$-0.425429\pi$
$269$	7.61455	0.464267	0.232134	+	0.972684i	$0.425429\pi$
$270$	0	0
$271$	−1.88212	−0.114331	−0.0571654	−	0.998365i	$-0.518206\pi$
$271$	−1.88212	−0.114331	−0.0571654	+	0.998365i	$0.518206\pi$
$272$	−31.8756	−1.93274
$273$	0.00547690	0.000331477 0
$274$	−9.41088	−0.568532
$275$	0	0
$276$	0.178015	0.0107153
$277$	−6.69720	−0.402395	−0.201198	−	0.979551i	$-0.564483\pi$
$277$	−6.69720	−0.402395	−0.201198	+	0.979551i	$0.564483\pi$
$278$	13.1640	0.789526
$279$	−5.48463	−0.328357
$280$	0	0
$281$	−7.36985	−0.439648	−0.219824	−	0.975540i	$-0.570548\pi$
$281$	−7.36985	−0.439648	−0.219824	+	0.975540i	$0.570548\pi$
$282$	−0.396186	−0.0235925
$283$	12.0845	0.718352	0.359176	−	0.933270i	$-0.383058\pi$
$283$	12.0845	0.718352	0.359176	+	0.933270i	$0.383058\pi$
$284$	16.3845	0.972243
$285$	0	0
$286$	−0.0810629	−0.00479335
$287$	−1.21563	−0.0717566
$288$	21.8641	1.28835
$289$	30.2954	1.78208
$290$	0	0
$291$	−0.998185	−0.0585146
$292$	4.35794	0.255029
$293$	1.92330	0.112360	0.0561802	−	0.998421i	$-0.482108\pi$
$293$	1.92330	0.112360	0.0561802	+	0.998421i	$0.482108\pi$
$294$	0.128973	0.00752189
$295$	0	0
$296$	−7.83296	−0.455281
$297$	−0.459493	−0.0266625
$298$	−12.7478	−0.738459
$299$	−0.0618375	−0.00357616
$300$	0	0
$301$	−12.9929	−0.748900
$302$	−9.64346	−0.554919
$303$	−0.912505	−0.0524221
$304$	36.2032	2.07640
$305$	0	0
$306$	−39.1232	−2.23652
$307$	25.5362	1.45743	0.728714	−	0.684818i	$-0.240118\pi$
$307$	25.5362	1.45743	0.728714	+	0.684818i	$0.240118\pi$
$308$	−5.98510	−0.341033
$309$	0.113585	0.00646164
$310$	0	0
$311$	−15.2461	−0.864526	−0.432263	−	0.901748i	$-0.642285\pi$
$311$	−15.2461	−0.864526	−0.432263	+	0.901748i	$0.642285\pi$
$312$	0.00144098	8.15796e−5 0
$313$	17.2249	0.973607	0.486804	−	0.873511i	$-0.338163\pi$
$313$	17.2249	0.973607	0.486804	+	0.873511i	$0.338163\pi$
$314$	26.8256	1.51385
$315$	0	0
$316$	−11.9970	−0.674882
$317$	−14.5284	−0.815994	−0.407997	−	0.912983i	$-0.633773\pi$
$317$	−14.5284	−0.815994	−0.407997	+	0.912983i	$0.633773\pi$
$318$	1.30189	0.0730064
$319$	6.31799	0.353739
$320$	0	0
$321$	0.975502	0.0544472
$322$	−10.2579	−0.571649
$323$	−53.7165	−2.98887
$324$	14.3878	0.799323
$325$	0	0
$326$	28.9215	1.60181
$327$	−0.0300774	−0.00166329
$328$	−0.319835	−0.0176599
$329$	10.1612	0.560203
$330$	0	0
$331$	−1.94049	−0.106659	−0.0533296	−	0.998577i	$-0.516983\pi$
$331$	−1.94049	−0.106659	−0.0533296	+	0.998577i	$0.516983\pi$
$332$	−8.01679	−0.439978
$333$	−31.2342	−1.71162
$334$	15.6805	0.858000
$335$	0	0
$336$	0.776590	0.0423665
$337$	−24.5332	−1.33641	−0.668205	−	0.743977i	$-0.732937\pi$
$337$	−24.5332	−1.33641	−0.668205	+	0.743977i	$0.732937\pi$
$338$	−24.6780	−1.34231
$339$	−0.206821	−0.0112330
$340$	0	0
$341$	2.39085	0.129472
$342$	44.4348	2.40276
$343$	16.6858	0.900951
$344$	−3.41846	−0.184311
$345$	0	0
$346$	−42.7845	−2.30011
$347$	−11.3199	−0.607687	−0.303843	−	0.952722i	$-0.598270\pi$
$347$	−11.3199	−0.607687	−0.303843	+	0.952722i	$0.598270\pi$
$348$	0.455143	0.0243982
$349$	4.50993	0.241411	0.120705	−	0.992688i	$-0.461484\pi$
$349$	4.50993	0.241411	0.120705	+	0.992688i	$0.461484\pi$
$350$	0	0
$351$	0.0114985	0.000613746 0
$352$	−9.53095	−0.508001
$353$	−6.36105	−0.338565	−0.169282	−	0.985568i	$-0.554145\pi$
$353$	−6.36105	−0.338565	−0.169282	+	0.985568i	$0.554145\pi$
$354$	1.18678	0.0630768
$355$	0	0
$356$	−29.0636	−1.54037
$357$	−1.15227	−0.0609844
$358$	29.9843	1.58472
$359$	13.8710	0.732086	0.366043	−	0.930598i	$-0.380712\pi$
$359$	13.8710	0.732086	0.366043	+	0.930598i	$0.380712\pi$
$360$	0	0
$361$	42.0095	2.21103
$362$	−25.8053	−1.35630
$363$	−0.545176	−0.0286143
$364$	0.149774	0.00785027
$365$	0	0
$366$	0.699815	0.0365799
$367$	5.54641	0.289520	0.144760	−	0.989467i	$-0.453759\pi$
$367$	5.54641	0.289520	0.144760	+	0.989467i	$0.453759\pi$
$368$	−8.76817	−0.457072
$369$	−1.27535	−0.0663922
$370$	0	0
$371$	−33.3902	−1.73353
$372$	0.172235	0.00892998
$373$	3.43469	0.177842	0.0889208	−	0.996039i	$-0.471658\pi$
$373$	3.43469	0.177842	0.0889208	+	0.996039i	$0.471658\pi$
$374$	17.0545	0.881869
$375$	0	0
$376$	2.67342	0.137871
$377$	−0.158104	−0.00814276
$378$	1.90743	0.0981074
$379$	13.3819	0.687380	0.343690	−	0.939083i	$-0.388323\pi$
$379$	13.3819	0.687380	0.343690	+	0.939083i	$0.388323\pi$
$380$	0	0
$381$	0.464888	0.0238169
$382$	33.4921	1.71361
$383$	−3.76773	−0.192522	−0.0962610	−	0.995356i	$-0.530688\pi$
$383$	−3.76773	−0.192522	−0.0962610	+	0.995356i	$0.530688\pi$
$384$	0.345753	0.0176442
$385$	0	0
$386$	8.90849	0.453430
$387$	−13.6312	−0.692915
$388$	−27.2967	−1.38578
$389$	5.36082	0.271804	0.135902	−	0.990722i	$-0.456607\pi$
$389$	5.36082	0.271804	0.135902	+	0.990722i	$0.456607\pi$
$390$	0	0
$391$	13.0098	0.657932
$392$	−0.870298	−0.0439567
$393$	1.02595	0.0517521
$394$	10.8619	0.547215
$395$	0	0
$396$	−6.27913	−0.315538
$397$	−10.3004	−0.516960	−0.258480	−	0.966017i	$-0.583222\pi$
$397$	−10.3004	−0.516960	−0.258480	+	0.966017i	$0.583222\pi$
$398$	−32.7854	−1.64338
$399$	1.30871	0.0655172
$400$	0	0
$401$	14.1315	0.705696	0.352848	−	0.935681i	$-0.385213\pi$
$401$	14.1315	0.705696	0.352848	+	0.935681i	$0.385213\pi$
$402$	1.46594	0.0731143
$403$	−0.0598297	−0.00298033
$404$	−24.9537	−1.24149
$405$	0	0
$406$	−26.2269	−1.30162
$407$	13.6156	0.674898
$408$	−0.303163	−0.0150088
$409$	34.9236	1.72686	0.863430	−	0.504469i	$-0.168312\pi$
$409$	34.9236	1.72686	0.863430	+	0.504469i	$0.168312\pi$
$410$	0	0
$411$	−0.290788	−0.0143435
$412$	3.10615	0.153029
$413$	−30.4379	−1.49775
$414$	−10.7618	−0.528914
$415$	0	0
$416$	0.238506	0.0116937
$417$	0.406757	0.0199190
$418$	−19.3700	−0.947416
$419$	−25.6966	−1.25536	−0.627681	−	0.778470i	$-0.715996\pi$
$419$	−25.6966	−1.25536	−0.627681	+	0.778470i	$0.715996\pi$
$420$	0	0
$421$	4.35851	0.212421	0.106210	−	0.994344i	$-0.466128\pi$
$421$	4.35851	0.212421	0.106210	+	0.994344i	$0.466128\pi$
$422$	32.5882	1.58637
$423$	10.6603	0.518324
$424$	−8.78501	−0.426638
$425$	0	0
$426$	1.13746	0.0551102
$427$	−17.9485	−0.868587
$428$	26.6764	1.28945
$429$	−0.00250477	−0.000120932 0
$430$	0	0
$431$	−29.4052	−1.41640	−0.708199	−	0.706013i	$-0.750492\pi$
$431$	−29.4052	−1.41640	−0.708199	+	0.706013i	$0.750492\pi$
$432$	1.63042	0.0784436
$433$	−35.6211	−1.71184	−0.855920	−	0.517109i	$-0.827008\pi$
$433$	−35.6211	−1.71184	−0.855920	+	0.517109i	$0.827008\pi$
$434$	−9.92480	−0.476406
$435$	0	0
$436$	−0.822510	−0.0393911
$437$	−14.7761	−0.706835
$438$	0.302540	0.0144559
$439$	−23.6123	−1.12695	−0.563477	−	0.826132i	$-0.690537\pi$
$439$	−23.6123	−1.12695	−0.563477	+	0.826132i	$0.690537\pi$
$440$	0	0
$441$	−3.47034	−0.165254
$442$	−0.426779	−0.0202998
$443$	31.3676	1.49032	0.745159	−	0.666887i	$-0.232373\pi$
$443$	31.3676	1.49032	0.745159	+	0.666887i	$0.232373\pi$
$444$	0.980854	0.0465493
$445$	0	0
$446$	31.6587	1.49908
$447$	−0.393895	−0.0186306
$448$	13.0872	0.618310
$449$	−18.2826	−0.862811	−0.431406	−	0.902158i	$-0.641982\pi$
$449$	−18.2826	−0.862811	−0.431406	+	0.902158i	$0.641982\pi$
$450$	0	0
$451$	0.555950	0.0261787
$452$	−5.65582	−0.266027
$453$	−0.297975	−0.0140001
$454$	37.3818	1.75441
$455$	0	0
$456$	0.344323	0.0161244
$457$	19.2842	0.902076	0.451038	−	0.892505i	$-0.351054\pi$
$457$	19.2842	0.902076	0.451038	+	0.892505i	$0.351054\pi$
$458$	50.9869	2.38246
$459$	−2.41913	−0.112916
$460$	0	0
$461$	−6.49999	−0.302735	−0.151367	−	0.988478i	$-0.548368\pi$
$461$	−6.49999	−0.302735	−0.151367	+	0.988478i	$0.548368\pi$
$462$	−0.415502	−0.0193309
$463$	14.8910	0.692041	0.346021	−	0.938227i	$-0.387533\pi$
$463$	14.8910	0.692041	0.346021	+	0.938227i	$0.387533\pi$
$464$	−22.4181	−1.04073
$465$	0	0
$466$	−51.1690	−2.37036
$467$	28.1955	1.30473	0.652366	−	0.757904i	$-0.273777\pi$
$467$	28.1955	1.30473	0.652366	+	0.757904i	$0.273777\pi$
$468$	0.157132	0.00726341
$469$	−37.5975	−1.73609
$470$	0	0
$471$	0.828886	0.0381931
$472$	−8.00827	−0.368611
$473$	5.94211	0.273218
$474$	−0.832863	−0.0382547
$475$	0	0
$476$	−31.5103	−1.44427
$477$	−35.0305	−1.60394
$478$	−55.6001	−2.54309
$479$	0.415031	0.0189633	0.00948163	−	0.999955i	$-0.496982\pi$
$479$	0.415031	0.0189633	0.00948163	+	0.999955i	$0.496982\pi$
$480$	0	0
$481$	−0.340721	−0.0155356
$482$	1.89846	0.0864726
$483$	−0.316959	−0.0144222
$484$	−14.9086	−0.677664
$485$	0	0
$486$	3.00227	0.136186
$487$	22.1210	1.00240	0.501199	−	0.865332i	$-0.332893\pi$
$487$	22.1210	1.00240	0.501199	+	0.865332i	$0.332893\pi$
$488$	−4.72227	−0.213767
$489$	0.893648	0.0404122
$490$	0	0
$491$	30.2068	1.36321	0.681606	−	0.731719i	$-0.261282\pi$
$491$	30.2068	1.36321	0.681606	+	0.731719i	$0.261282\pi$
$492$	0.0400502	0.00180560
$493$	33.2629	1.49809
$494$	0.484722	0.0218087
$495$	0	0
$496$	−8.48347	−0.380919
$497$	−29.1730	−1.30859
$498$	−0.556548	−0.0249395
$499$	−0.812872	−0.0363892	−0.0181946	−	0.999834i	$-0.505792\pi$
$499$	−0.812872	−0.0363892	−0.0181946	+	0.999834i	$0.505792\pi$
$500$	0	0
$501$	0.484515	0.0216465
$502$	44.5759	1.98952
$503$	11.1197	0.495804	0.247902	−	0.968785i	$-0.420259\pi$
$503$	11.1197	0.495804	0.247902	+	0.968785i	$0.420259\pi$
$504$	−6.43185	−0.286497
$505$	0	0
$506$	4.69127	0.208552
$507$	−0.762529	−0.0338651
$508$	12.7130	0.564048
$509$	−24.8929	−1.10336	−0.551680	−	0.834056i	$-0.686013\pi$
$509$	−24.8929	−1.10336	−0.551680	+	0.834056i	$0.686013\pi$
$510$	0	0
$511$	−7.75938	−0.343255
$512$	26.8525	1.18672
$513$	2.74757	0.121308
$514$	14.4572	0.637679
$515$	0	0
$516$	0.428065	0.0188445
$517$	−4.64704	−0.204377
$518$	−56.5203	−2.48336
$519$	−1.32200	−0.0580295
$520$	0	0
$521$	8.74317	0.383045	0.191523	−	0.981488i	$-0.438657\pi$
$521$	8.74317	0.383045	0.191523	+	0.981488i	$0.438657\pi$
$522$	−27.5154	−1.20432
$523$	14.3144	0.625927	0.312964	−	0.949765i	$-0.398678\pi$
$523$	14.3144	0.625927	0.312964	+	0.949765i	$0.398678\pi$
$524$	28.0559	1.22563
$525$	0	0
$526$	−49.8675	−2.17433
$527$	12.5873	0.548313
$528$	−0.355161	−0.0154564
$529$	−19.4213	−0.844406
$530$	0	0
$531$	−31.9333	−1.38579
$532$	35.7884	1.55162
$533$	−0.0139123	−0.000602610 0
$534$	−2.01768	−0.0873136
$535$	0	0
$536$	−9.89198	−0.427268
$537$	0.926488	0.0399809
$538$	14.4559	0.623240
$539$	1.51279	0.0651604
$540$	0	0
$541$	7.09802	0.305168	0.152584	−	0.988291i	$-0.451241\pi$
$541$	7.09802	0.305168	0.152584	+	0.988291i	$0.451241\pi$
$542$	−3.57314	−0.153479
$543$	−0.797362	−0.0342181
$544$	−50.1785	−2.15138
$545$	0	0
$546$	0.0103977	0.000444981 0
$547$	−31.4468	−1.34457	−0.672284	−	0.740294i	$-0.734686\pi$
$547$	−31.4468	−1.34457	−0.672284	+	0.740294i	$0.734686\pi$
$548$	−7.95200	−0.339693
$549$	−18.8302	−0.803654
$550$	0	0
$551$	−37.7789	−1.60944
$552$	−0.0833926	−0.00354942
$553$	21.3608	0.908354
$554$	−12.7144	−0.540182
$555$	0	0
$556$	11.1233	0.471735
$557$	13.3707	0.566534	0.283267	−	0.959041i	$-0.408582\pi$
$557$	13.3707	0.566534	0.283267	+	0.959041i	$0.408582\pi$
$558$	−10.4124	−0.440791
$559$	−0.148698	−0.00628924
$560$	0	0
$561$	0.526970	0.0222487
$562$	−13.9914	−0.590191
$563$	18.0026	0.758719	0.379359	−	0.925249i	$-0.376144\pi$
$563$	18.0026	0.758719	0.379359	+	0.925249i	$0.376144\pi$
$564$	−0.334769	−0.0140963
$565$	0	0
$566$	22.9421	0.964327
$567$	−25.6177	−1.07584
$568$	−7.67546	−0.322055
$569$	29.0989	1.21989	0.609944	−	0.792444i	$-0.291192\pi$
$569$	29.0989	1.21989	0.609944	+	0.792444i	$0.291192\pi$
$570$	0	0
$571$	−41.1140	−1.72057	−0.860284	−	0.509816i	$-0.829714\pi$
$571$	−41.1140	−1.72057	−0.860284	+	0.509816i	$0.829714\pi$
$572$	−0.0684965	−0.00286398
$573$	1.03488	0.0432326
$574$	−2.30783	−0.0963272
$575$	0	0
$576$	13.7301	0.572087
$577$	1.38506	0.0576610	0.0288305	−	0.999584i	$-0.490822\pi$
$577$	1.38506	0.0576610	0.0288305	+	0.999584i	$0.490822\pi$
$578$	57.5147	2.39229
$579$	0.275265	0.0114396
$580$	0	0
$581$	14.2740	0.592187
$582$	−1.89502	−0.0785510
$583$	15.2705	0.632438
$584$	−2.04151	−0.0844782
$585$	0	0
$586$	3.65131	0.150834
$587$	−20.8434	−0.860298	−0.430149	−	0.902758i	$-0.641539\pi$
$587$	−20.8434	−0.860298	−0.430149	+	0.902758i	$0.641539\pi$
$588$	0.108980	0.00449426
$589$	−14.2963	−0.589069
$590$	0	0
$591$	0.335623	0.0138057
$592$	−48.3121	−1.98561
$593$	−21.7517	−0.893235	−0.446617	−	0.894725i	$-0.647371\pi$
$593$	−21.7517	−0.893235	−0.446617	+	0.894725i	$0.647371\pi$
$594$	−0.872330	−0.0357921
$595$	0	0
$596$	−10.7716	−0.441222
$597$	−1.01304	−0.0414610
$598$	−0.117396	−0.00480069
$599$	24.9777	1.02056	0.510281	−	0.860008i	$-0.329541\pi$
$599$	24.9777	1.02056	0.510281	+	0.860008i	$0.329541\pi$
$600$	0	0
$601$	35.2249	1.43685	0.718427	−	0.695602i	$-0.244862\pi$
$601$	35.2249	1.43685	0.718427	+	0.695602i	$0.244862\pi$
$602$	−24.6666	−1.00534
$603$	−39.4446	−1.60631
$604$	−8.14853	−0.331559
$605$	0	0
$606$	−1.73236	−0.0703722
$607$	−2.52767	−0.102595	−0.0512974	−	0.998683i	$-0.516336\pi$
$607$	−2.52767	−0.102595	−0.0512974	+	0.998683i	$0.516336\pi$
$608$	56.9910	2.31129
$609$	−0.810390	−0.0328386
$610$	0	0
$611$	0.116289	0.00470457
$612$	−33.0583	−1.33630
$613$	15.4658	0.624656	0.312328	−	0.949974i	$-0.398891\pi$
$613$	15.4658	0.624656	0.312328	+	0.949974i	$0.398891\pi$
$614$	48.4795	1.95647
$615$	0	0
$616$	2.80376	0.112967
$617$	30.6973	1.23583	0.617913	−	0.786247i	$-0.287978\pi$
$617$	30.6973	1.23583	0.617913	+	0.786247i	$0.287978\pi$
$618$	0.215637	0.00867421
$619$	23.3333	0.937843	0.468921	−	0.883240i	$-0.344643\pi$
$619$	23.3333	0.937843	0.468921	+	0.883240i	$0.344643\pi$
$620$	0	0
$621$	−0.665443	−0.0267033
$622$	−28.9441	−1.16055
$623$	51.7483	2.07325
$624$	0.00888769	0.000355792 0
$625$	0	0
$626$	32.7008	1.30699
$627$	−0.598515	−0.0239024
$628$	22.6670	0.904514
$629$	71.6831	2.85819
$630$	0	0
$631$	10.9076	0.434226	0.217113	−	0.976146i	$-0.430336\pi$
$631$	10.9076	0.434226	0.217113	+	0.976146i	$0.430336\pi$
$632$	5.62007	0.223554
$633$	1.00695	0.0400226
$634$	−27.5816	−1.09540
$635$	0	0
$636$	1.10007	0.0436207
$637$	−0.0378566	−0.00149993
$638$	11.9945	0.474865
$639$	−30.6061	−1.21076
$640$	0	0
$641$	−14.8286	−0.585694	−0.292847	−	0.956159i	$-0.594603\pi$
$641$	−14.8286	−0.585694	−0.292847	+	0.956159i	$0.594603\pi$
$642$	1.85195	0.0730908
$643$	−23.5754	−0.929723	−0.464862	−	0.885383i	$-0.653896\pi$
$643$	−23.5754	−0.929723	−0.464862	+	0.885383i	$0.653896\pi$
$644$	−8.66770	−0.341555
$645$	0	0
$646$	−101.979	−4.01231
$647$	16.0518	0.631063	0.315531	−	0.948915i	$-0.397817\pi$
$647$	16.0518	0.631063	0.315531	+	0.948915i	$0.397817\pi$
$648$	−6.74007	−0.264775
$649$	13.9203	0.546419
$650$	0	0
$651$	−0.306668	−0.0120193
$652$	24.4381	0.957068
$653$	−23.5284	−0.920737	−0.460369	−	0.887728i	$-0.652283\pi$
$653$	−23.5284	−0.920737	−0.460369	+	0.887728i	$0.652283\pi$
$654$	−0.0571009	−0.00223282
$655$	0	0
$656$	−1.97268	−0.0770201
$657$	−8.14058	−0.317594
$658$	19.2906	0.752025
$659$	−18.1185	−0.705797	−0.352898	−	0.935662i	$-0.614804\pi$
$659$	−18.1185	−0.705797	−0.352898	+	0.935662i	$0.614804\pi$
$660$	0	0
$661$	21.6080	0.840455	0.420227	−	0.907419i	$-0.361950\pi$
$661$	21.6080	0.840455	0.420227	+	0.907419i	$0.361950\pi$
$662$	−3.68396	−0.143181
$663$	−0.0131871	−0.000512145 0
$664$	3.75552	0.145743
$665$	0	0
$666$	−59.2969	−2.29771
$667$	9.14979	0.354281
$668$	13.2497	0.512647
$669$	0.978227	0.0378204
$670$	0	0
$671$	8.20844	0.316883
$672$	1.22251	0.0471592
$673$	−2.71054	−0.104484	−0.0522419	−	0.998634i	$-0.516637\pi$
$673$	−2.71054	−0.104484	−0.0522419	+	0.998634i	$0.516637\pi$
$674$	−46.5754	−1.79402
$675$	0	0
$676$	−20.8524	−0.802016
$677$	−29.4284	−1.13103	−0.565513	−	0.824739i	$-0.691322\pi$
$677$	−29.4284	−1.13103	−0.565513	+	0.824739i	$0.691322\pi$
$678$	−0.392643	−0.0150794
$679$	48.6023	1.86519
$680$	0	0
$681$	1.15507	0.0442622
$682$	4.53895	0.173805
$683$	−29.4065	−1.12521	−0.562604	−	0.826727i	$-0.690200\pi$
$683$	−29.4065	−1.12521	−0.562604	+	0.826727i	$0.690200\pi$
$684$	37.5465	1.43563
$685$	0	0
$686$	31.6775	1.20945
$687$	1.57545	0.0601072
$688$	−21.0844	−0.803835
$689$	−0.382134	−0.0145582
$690$	0	0
$691$	−10.3045	−0.392003	−0.196001	−	0.980604i	$-0.562796\pi$
$691$	−10.3045	−0.392003	−0.196001	+	0.980604i	$0.562796\pi$
$692$	−36.1520	−1.37429
$693$	11.1801	0.424697
$694$	−21.4905	−0.815769
$695$	0	0
$696$	−0.213215	−0.00808189
$697$	2.92696	0.110867
$698$	8.56193	0.324074
$699$	−1.58108	−0.0598019
$700$	0	0
$701$	−40.6631	−1.53582	−0.767911	−	0.640556i	$-0.778704\pi$
$701$	−40.6631	−1.53582	−0.767911	+	0.640556i	$0.778704\pi$
$702$	0.0218295	0.000823903 0
$703$	−81.4153	−3.07064
$704$	−5.98520	−0.225576
$705$	0	0
$706$	−12.0762	−0.454495
$707$	44.4306	1.67098
$708$	1.00281	0.0376878
$709$	41.5598	1.56081	0.780405	−	0.625274i	$-0.215013\pi$
$709$	41.5598	1.56081	0.780405	+	0.625274i	$0.215013\pi$
$710$	0	0
$711$	22.4102	0.840448
$712$	13.6151	0.510247
$713$	3.46246	0.129670
$714$	−2.18753	−0.0818664
$715$	0	0
$716$	25.3361	0.946855
$717$	−1.71799	−0.0641597
$718$	26.3337	0.982764
$719$	18.9487	0.706668	0.353334	−	0.935497i	$-0.385048\pi$
$719$	18.9487	0.706668	0.353334	+	0.935497i	$0.385048\pi$
$720$	0	0
$721$	−5.53055	−0.205968
$722$	79.7535	2.96812
$723$	0.0586609	0.00218162
$724$	−21.8050	−0.810376
$725$	0	0
$726$	−1.03500	−0.0384124
$727$	−40.0259	−1.48448	−0.742240	−	0.670135i	$-0.766236\pi$
$727$	−40.0259	−1.48448	−0.742240	+	0.670135i	$0.766236\pi$
$728$	−0.0701625	−0.00260040
$729$	−26.8144	−0.993124
$730$	0	0
$731$	31.2840	1.15708
$732$	0.591330	0.0218562
$733$	37.8081	1.39647	0.698236	−	0.715867i	$-0.253969\pi$
$733$	37.8081	1.39647	0.698236	+	0.715867i	$0.253969\pi$
$734$	10.5297	0.388657
$735$	0	0
$736$	−13.8028	−0.508779
$737$	17.1946	0.633372
$738$	−2.42121	−0.0891260
$739$	16.6037	0.610779	0.305389	−	0.952228i	$-0.401213\pi$
$739$	16.6037	0.610779	0.305389	+	0.952228i	$0.401213\pi$
$740$	0	0
$741$	0.0149775	0.000550212 0
$742$	−63.3900	−2.32712
$743$	−15.1837	−0.557037	−0.278518	−	0.960431i	$-0.589843\pi$
$743$	−15.1837	−0.557037	−0.278518	+	0.960431i	$0.589843\pi$
$744$	−0.0806848	−0.00295805
$745$	0	0
$746$	6.52064	0.238738
$747$	14.9753	0.547916
$748$	14.4107	0.526908
$749$	−47.4979	−1.73553
$750$	0	0
$751$	14.1466	0.516217	0.258108	−	0.966116i	$-0.416901\pi$
$751$	14.1466	0.516217	0.258108	+	0.966116i	$0.416901\pi$
$752$	16.4891	0.601296
$753$	1.37736	0.0501936
$754$	−0.300154	−0.0109310
$755$	0	0
$756$	1.61174	0.0586183
$757$	−38.6301	−1.40403	−0.702017	−	0.712160i	$-0.747717\pi$
$757$	−38.6301	−1.40403	−0.702017	+	0.712160i	$0.747717\pi$
$758$	25.4050	0.922750
$759$	0.144956	0.00526158
$760$	0	0
$761$	36.2446	1.31386	0.656932	−	0.753950i	$-0.271854\pi$
$761$	36.2446	1.31386	0.656932	+	0.753950i	$0.271854\pi$
$762$	0.882573	0.0319722
$763$	1.46449	0.0530182
$764$	28.3002	1.02386
$765$	0	0
$766$	−7.15290	−0.258445
$767$	−0.348347	−0.0125781
$768$	1.19396	0.0430834
$769$	17.9179	0.646136	0.323068	−	0.946376i	$-0.395286\pi$
$769$	17.9179	0.646136	0.323068	+	0.946376i	$0.395286\pi$
$770$	0	0
$771$	0.446714	0.0160880
$772$	7.52749	0.270920
$773$	38.6326	1.38952	0.694760	−	0.719242i	$-0.255511\pi$
$773$	38.6326	1.38952	0.694760	+	0.719242i	$0.255511\pi$
$774$	−25.8784	−0.930180
$775$	0	0
$776$	12.7874	0.459040
$777$	−1.74643	−0.0626527
$778$	10.1773	0.364875
$779$	−3.32435	−0.119107
$780$	0	0
$781$	13.3418	0.477406
$782$	24.6986	0.883219
$783$	−1.70138	−0.0608023
$784$	−5.36782	−0.191708
$785$	0	0
$786$	1.94772	0.0694729
$787$	−3.70780	−0.132169	−0.0660844	−	0.997814i	$-0.521051\pi$
$787$	−3.70780	−0.132169	−0.0660844	+	0.997814i	$0.521051\pi$
$788$	9.17809	0.326956
$789$	−1.54086	−0.0548562
$790$	0	0
$791$	10.0703	0.358058
$792$	2.94150	0.104522
$793$	−0.205411	−0.00729437
$794$	−19.5549	−0.693976
$795$	0	0
$796$	−27.7030	−0.981906
$797$	−17.1467	−0.607366	−0.303683	−	0.952773i	$-0.598216\pi$
$797$	−17.1467	−0.607366	−0.303683	+	0.952773i	$0.598216\pi$
$798$	2.48453	0.0879514
$799$	−24.4657	−0.865535
$800$	0	0
$801$	54.2906	1.91826
$802$	26.8282	0.947337
$803$	3.54863	0.125228
$804$	1.23869	0.0436851
$805$	0	0
$806$	−0.113584	−0.00400084
$807$	0.446676	0.0157237
$808$	11.6898	0.411244
$809$	37.6942	1.32526	0.662628	−	0.748948i	$-0.269441\pi$
$809$	37.6942	1.32526	0.662628	+	0.748948i	$0.269441\pi$
$810$	0	0
$811$	−49.5861	−1.74120	−0.870602	−	0.491988i	$-0.836271\pi$
$811$	−49.5861	−1.74120	−0.870602	+	0.491988i	$0.836271\pi$
$812$	−22.1612	−0.777707
$813$	−0.110407	−0.00387214
$814$	25.8486	0.905994
$815$	0	0
$816$	−1.86985	−0.0654578
$817$	−35.5313	−1.24308
$818$	66.3011	2.31817
$819$	−0.279775	−0.00977614
$820$	0	0
$821$	26.3990	0.921330	0.460665	−	0.887574i	$-0.347611\pi$
$821$	26.3990	0.921330	0.460665	+	0.887574i	$0.347611\pi$
$822$	−0.552050	−0.0192550
$823$	−11.0567	−0.385413	−0.192707	−	0.981256i	$-0.561727\pi$
$823$	−11.0567	−0.385413	−0.192707	+	0.981256i	$0.561727\pi$
$824$	−1.45510	−0.0506907
$825$	0	0
$826$	−57.7853	−2.01061
$827$	10.3426	0.359647	0.179823	−	0.983699i	$-0.442447\pi$
$827$	10.3426	0.359647	0.179823	+	0.983699i	$0.442447\pi$
$828$	−9.09351	−0.316021
$829$	−28.3073	−0.983155	−0.491577	−	0.870834i	$-0.663579\pi$
$829$	−28.3073	−0.983155	−0.491577	+	0.870834i	$0.663579\pi$
$830$	0	0
$831$	−0.392863	−0.0136283
$832$	0.149776	0.00519255
$833$	7.96451	0.275954
$834$	0.772214	0.0267396
$835$	0	0
$836$	−16.3672	−0.566073
$837$	−0.643836	−0.0222542
$838$	−48.7841	−1.68522
$839$	27.9634	0.965403	0.482701	−	0.875785i	$-0.339656\pi$
$839$	27.9634	0.965403	0.482701	+	0.875785i	$0.339656\pi$
$840$	0	0
$841$	−5.60618	−0.193316
$842$	8.27447	0.285157
$843$	−0.432322	−0.0148900
$844$	27.5364	0.947842
$845$	0	0
$846$	20.2383	0.695806
$847$	26.5450	0.912098
$848$	−54.1842	−1.86069
$849$	0.708890	0.0243290
$850$	0	0
$851$	19.7182	0.675932
$852$	0.961131	0.0329278
$853$	42.3785	1.45101	0.725505	−	0.688216i	$-0.241606\pi$
$853$	42.3785	1.45101	0.725505	+	0.688216i	$0.241606\pi$
$854$	−34.0745	−1.16601
$855$	0	0
$856$	−12.4968	−0.427131
$857$	−51.3511	−1.75412	−0.877060	−	0.480380i	$-0.840499\pi$
$857$	−51.3511	−1.75412	−0.877060	+	0.480380i	$0.840499\pi$
$858$	−0.00475522	−0.000162341 0
$859$	−19.3983	−0.661863	−0.330931	−	0.943655i	$-0.607363\pi$
$859$	−19.3983	−0.661863	−0.330931	+	0.943655i	$0.607363\pi$
$860$	0	0
$861$	−0.0713101	−0.00243024
$862$	−55.8246	−1.90139
$863$	32.8754	1.11909	0.559545	−	0.828800i	$-0.310976\pi$
$863$	32.8754	1.11909	0.559545	+	0.828800i	$0.310976\pi$
$864$	2.56660	0.0873176
$865$	0	0
$866$	−67.6253	−2.29800
$867$	1.77715	0.0603553
$868$	−8.38626	−0.284648
$869$	−9.76902	−0.331391
$870$	0	0
$871$	−0.430285	−0.0145797
$872$	0.385311	0.0130483
$873$	50.9900	1.72575
$874$	−28.0518	−0.948867
$875$	0	0
$876$	0.255640	0.00863729
$877$	−44.8961	−1.51603	−0.758016	−	0.652236i	$-0.773831\pi$
$877$	−44.8961	−1.51603	−0.758016	+	0.652236i	$0.773831\pi$
$878$	−44.8271	−1.51284
$879$	0.112822	0.00380541
$880$	0	0
$881$	−2.38516	−0.0803581	−0.0401791	−	0.999192i	$-0.512793\pi$
$881$	−2.38516	−0.0803581	−0.0401791	+	0.999192i	$0.512793\pi$
$882$	−6.58832	−0.221840
$883$	1.17033	0.0393847	0.0196923	−	0.999806i	$-0.493731\pi$
$883$	1.17033	0.0393847	0.0196923	+	0.999806i	$0.493731\pi$
$884$	−0.360620	−0.0121290
$885$	0	0
$886$	59.5502	2.00063
$887$	−9.47952	−0.318291	−0.159146	−	0.987255i	$-0.550874\pi$
$887$	−9.47952	−0.318291	−0.159146	+	0.987255i	$0.550874\pi$
$888$	−0.459488	−0.0154194
$889$	−22.6357	−0.759178
$890$	0	0
$891$	11.7159	0.392496
$892$	26.7510	0.895689
$893$	27.7873	0.929868
$894$	−0.747795	−0.0250100
$895$	0	0
$896$	−16.8350	−0.562418
$897$	−0.00362744	−0.000121117 0
$898$	−34.7089	−1.15825
$899$	8.85270	0.295254
$900$	0	0
$901$	80.3958	2.67837
$902$	1.05545	0.0351427
$903$	−0.762177	−0.0253637
$904$	2.64951	0.0881214
$905$	0	0
$906$	−0.565694	−0.0187939
$907$	54.3964	1.80620	0.903102	−	0.429426i	$-0.141284\pi$
$907$	54.3964	1.80620	0.903102	+	0.429426i	$0.141284\pi$
$908$	31.5869	1.04825
$909$	46.6133	1.54607
$910$	0	0
$911$	−33.3073	−1.10352	−0.551760	−	0.834003i	$-0.686043\pi$
$911$	−33.3073	−1.10352	−0.551760	+	0.834003i	$0.686043\pi$
$912$	2.12371	0.0703231
$913$	−6.52800	−0.216045
$914$	36.6103	1.21096
$915$	0	0
$916$	43.0829	1.42350
$917$	−49.9540	−1.64963
$918$	−4.59264	−0.151580
$919$	42.6183	1.40585	0.702924	−	0.711265i	$-0.251877\pi$
$919$	42.6183	1.40585	0.702924	+	0.711265i	$0.251877\pi$
$920$	0	0
$921$	1.49798	0.0493600
$922$	−12.3400	−0.406396
$923$	−0.333870	−0.0109895
$924$	−0.351091	−0.0115501
$925$	0	0
$926$	28.2699	0.929007
$927$	−5.80225	−0.190571
$928$	−35.2906	−1.15847
$929$	−23.7308	−0.778584	−0.389292	−	0.921114i	$-0.627280\pi$
$929$	−23.7308	−0.778584	−0.389292	+	0.921114i	$0.627280\pi$
$930$	0	0
$931$	−9.04583	−0.296465
$932$	−43.2368	−1.41627
$933$	−0.894348	−0.0292796
$934$	53.5281	1.75149
$935$	0	0
$936$	−0.0736094	−0.00240600
$937$	−2.73291	−0.0892803	−0.0446402	−	0.999003i	$-0.514214\pi$
$937$	−2.73291	−0.0892803	−0.0446402	+	0.999003i	$0.514214\pi$
$938$	−71.3776	−2.33056
$939$	1.01043	0.0329740
$940$	0	0
$941$	13.4573	0.438694	0.219347	−	0.975647i	$-0.429607\pi$
$941$	13.4573	0.438694	0.219347	+	0.975647i	$0.429607\pi$
$942$	1.57361	0.0512710
$943$	0.805134	0.0262188
$944$	−49.3934	−1.60762
$945$	0	0
$946$	11.2809	0.366773
$947$	20.9231	0.679910	0.339955	−	0.940442i	$-0.389588\pi$
$947$	20.9231	0.679910	0.339955	+	0.940442i	$0.389588\pi$
$948$	−0.703753	−0.0228568
$949$	−0.0888023	−0.00288265
$950$	0	0
$951$	−0.852246	−0.0276360
$952$	14.7612	0.478414
$953$	−5.85313	−0.189601	−0.0948007	−	0.995496i	$-0.530221\pi$
$953$	−5.85313	−0.189601	−0.0948007	+	0.995496i	$0.530221\pi$
$954$	−66.5042	−2.15315
$955$	0	0
$956$	−46.9809	−1.51947
$957$	0.370619	0.0119804
$958$	0.787922	0.0254566
$959$	14.1587	0.457208
$960$	0	0
$961$	−27.6500	−0.891934
$962$	−0.646847	−0.0208552
$963$	−49.8313	−1.60579
$964$	1.60416	0.0516666
$965$	0	0
$966$	−0.601736	−0.0193605
$967$	−24.2896	−0.781102	−0.390551	−	0.920581i	$-0.627715\pi$
$967$	−24.2896	−0.781102	−0.390551	+	0.920581i	$0.627715\pi$
$968$	6.98404	0.224476
$969$	−3.15106	−0.101227
$970$	0	0
$971$	−31.0666	−0.996974	−0.498487	−	0.866897i	$-0.666111\pi$
$971$	−31.0666	−0.996974	−0.498487	+	0.866897i	$0.666111\pi$
$972$	2.53686	0.0813698
$973$	−19.8053	−0.634929
$974$	41.9959	1.34563
$975$	0	0
$976$	−29.1260	−0.932301
$977$	15.3572	0.491319	0.245660	−	0.969356i	$-0.420995\pi$
$977$	15.3572	0.491319	0.245660	+	0.969356i	$0.420995\pi$
$978$	1.69656	0.0542500
$979$	−23.6663	−0.756377
$980$	0	0
$981$	1.53644	0.0490547
$982$	57.3465	1.83000
$983$	−16.8346	−0.536939	−0.268470	−	0.963288i	$-0.586518\pi$
$983$	−16.8346	−0.536939	−0.268470	+	0.963288i	$0.586518\pi$
$984$	−0.0187618	−0.000598105 0
$985$	0	0
$986$	63.1484	2.01105
$987$	0.596062	0.0189729
$988$	0.409580	0.0130305
$989$	8.60543	0.273637
$990$	0	0
$991$	35.8777	1.13969	0.569847	−	0.821751i	$-0.307002\pi$
$991$	35.8777	1.13969	0.569847	+	0.821751i	$0.307002\pi$
$992$	−13.3547	−0.424011
$993$	−0.113831	−0.00361232
$994$	−55.3838	−1.75667
$995$	0	0
$996$	−0.470272	−0.0149011
$997$	7.32399	0.231953	0.115977	−	0.993252i	$-0.463000\pi$
$997$	7.32399	0.231953	0.115977	+	0.993252i	$0.463000\pi$
$998$	−1.54321	−0.0488494
$999$	−3.66655	−0.116005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.g.1.9		11
5.4	even	2		1205.2.a.b.1.3	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.3	✓	11	5.4	even	2
6025.2.a.g.1.9		11	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)

\(f(q)\)	\(=\)	\(q+1.89846 q^{2} +0.0586609 q^{3} +1.60416 q^{4} +0.111366 q^{6} -2.85624 q^{7} -0.751482 q^{8} -2.99656 q^{9} +O(q^{10})\)	\(q+1.89846 q^{2} +0.0586609 q^{3} +1.60416 q^{4} +0.111366 q^{6} -2.85624 q^{7} -0.751482 q^{8} -2.99656 q^{9} +1.30626 q^{11} +0.0941016 q^{12} -0.0326883 q^{13} -5.42247 q^{14} -4.63499 q^{16} +6.87716 q^{17} -5.68886 q^{18} -7.81086 q^{19} -0.167550 q^{21} +2.47988 q^{22} +1.89174 q^{23} -0.0440826 q^{24} -0.0620575 q^{26} -0.351763 q^{27} -4.58188 q^{28} +4.83672 q^{29} +1.83031 q^{31} -7.29639 q^{32} +0.0766261 q^{33} +13.0560 q^{34} -4.80697 q^{36} +10.4233 q^{37} -14.8286 q^{38} -0.00191752 q^{39} +0.425606 q^{41} -0.318087 q^{42} +4.54896 q^{43} +2.09545 q^{44} +3.59139 q^{46} -3.55753 q^{47} -0.271892 q^{48} +1.15811 q^{49} +0.403420 q^{51} -0.0524373 q^{52} +11.6903 q^{53} -0.667810 q^{54} +2.14641 q^{56} -0.458192 q^{57} +9.18233 q^{58} +10.6566 q^{59} +6.28395 q^{61} +3.47478 q^{62} +8.55889 q^{63} -4.58195 q^{64} +0.145472 q^{66} +13.1633 q^{67} +11.0321 q^{68} +0.110971 q^{69} +10.2138 q^{71} +2.25186 q^{72} +2.71664 q^{73} +19.7883 q^{74} -12.5299 q^{76} -3.73098 q^{77} -0.00364035 q^{78} -7.47865 q^{79} +8.96904 q^{81} +0.807997 q^{82} -4.99749 q^{83} -0.268777 q^{84} +8.63604 q^{86} +0.283726 q^{87} -0.981627 q^{88} -18.1176 q^{89} +0.0933656 q^{91} +3.03465 q^{92} +0.107368 q^{93} -6.75384 q^{94} -0.428013 q^{96} -17.0162 q^{97} +2.19863 q^{98} -3.91427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

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Database

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