LMFDB - Embedded newform 6025.2.a.g.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:	$11$
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			1.11
Root			$-2.07008$ 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)

$f(q)$	$=$	$q+2.58701 q^{2} +2.62253 q^{3} +4.69261 q^{4} +6.78451 q^{6} +4.29833 q^{7} +6.96581 q^{8} +3.87767 q^{9} +O(q^{10})$	\(q+2.58701 q^{2} +2.62253 q^{3} +4.69261 q^{4} +6.78451 q^{6} +4.29833 q^{7} +6.96581 q^{8} +3.87767 q^{9} +0.392733 q^{11} +12.3065 q^{12} -3.86215 q^{13} +11.1198 q^{14} +8.63539 q^{16} -2.28113 q^{17} +10.0316 q^{18} -6.51433 q^{19} +11.2725 q^{21} +1.01600 q^{22} +3.95733 q^{23} +18.2681 q^{24} -9.99141 q^{26} +2.30173 q^{27} +20.1704 q^{28} -2.20828 q^{29} +0.970075 q^{31} +8.40821 q^{32} +1.02995 q^{33} -5.90130 q^{34} +18.1964 q^{36} -3.07546 q^{37} -16.8526 q^{38} -10.1286 q^{39} +8.48761 q^{41} +29.1621 q^{42} -4.56989 q^{43} +1.84294 q^{44} +10.2376 q^{46} -10.9885 q^{47} +22.6466 q^{48} +11.4757 q^{49} -5.98233 q^{51} -18.1236 q^{52} -0.970867 q^{53} +5.95460 q^{54} +29.9414 q^{56} -17.0840 q^{57} -5.71284 q^{58} +2.47906 q^{59} -8.72003 q^{61} +2.50959 q^{62} +16.6675 q^{63} +4.48133 q^{64} +2.66450 q^{66} +14.8157 q^{67} -10.7045 q^{68} +10.3782 q^{69} +7.87706 q^{71} +27.0112 q^{72} -5.53782 q^{73} -7.95625 q^{74} -30.5692 q^{76} +1.68810 q^{77} -26.2028 q^{78} +1.20590 q^{79} -5.59666 q^{81} +21.9575 q^{82} -10.3757 q^{83} +52.8976 q^{84} -11.8223 q^{86} -5.79128 q^{87} +2.73570 q^{88} -15.3272 q^{89} -16.6008 q^{91} +18.5702 q^{92} +2.54405 q^{93} -28.4273 q^{94} +22.0508 q^{96} +6.20641 q^{97} +29.6877 q^{98} +1.52289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.58701	1.82929	0.914646	−	0.404256i	$-0.132470\pi$
$2$	2.58701	1.82929	0.914646	+	0.404256i	$0.132470\pi$
$3$	2.62253	1.51412	0.757060	−	0.653346i	$-0.226635\pi$
$3$	2.62253	1.51412	0.757060	+	0.653346i	$0.226635\pi$
$4$	4.69261	2.34631
$5$	0	0
$5$	0	0
$6$	6.78451	2.76977
$7$	4.29833	1.62462	0.812309	−	0.583228i	$-0.198210\pi$
$7$	4.29833	1.62462	0.812309	+	0.583228i	$0.198210\pi$
$8$	6.96581	2.46279
$9$	3.87767	1.29256
$10$	0	0
$11$	0.392733	0.118413	0.0592067	−	0.998246i	$-0.481143\pi$
$11$	0.392733	0.118413	0.0592067	+	0.998246i	$0.481143\pi$
$12$	12.3065	3.55259
$13$	−3.86215	−1.07117	−0.535584	−	0.844482i	$-0.679908\pi$
$13$	−3.86215	−1.07117	−0.535584	+	0.844482i	$0.679908\pi$
$14$	11.1198	2.97190
$15$	0	0
$16$	8.63539	2.15885
$17$	−2.28113	−0.553255	−0.276627	−	0.960977i	$-0.589217\pi$
$17$	−2.28113	−0.553255	−0.276627	+	0.960977i	$0.589217\pi$
$18$	10.0316	2.36447
$19$	−6.51433	−1.49449	−0.747245	−	0.664549i	$-0.768624\pi$
$19$	−6.51433	−1.49449	−0.747245	+	0.664549i	$0.768624\pi$
$20$	0	0
$21$	11.2725	2.45987
$22$	1.01600	0.216613
$23$	3.95733	0.825159	0.412580	−	0.910921i	$-0.364628\pi$
$23$	3.95733	0.825159	0.412580	+	0.910921i	$0.364628\pi$
$24$	18.2681	3.72895
$25$	0	0
$26$	−9.99141	−1.95948
$27$	2.30173	0.442968
$28$	20.1704	3.81185
$29$	−2.20828	−0.410067	−0.205034	−	0.978755i	$-0.565730\pi$
$29$	−2.20828	−0.410067	−0.205034	+	0.978755i	$0.565730\pi$
$30$	0	0
$31$	0.970075	0.174231	0.0871153	−	0.996198i	$-0.472235\pi$
$31$	0.970075	0.174231	0.0871153	+	0.996198i	$0.472235\pi$
$32$	8.40821	1.48638
$33$	1.02995	0.179292
$34$	−5.90130	−1.01206
$35$	0	0
$36$	18.1964	3.03274
$37$	−3.07546	−0.505603	−0.252802	−	0.967518i	$-0.581352\pi$
$37$	−3.07546	−0.505603	−0.252802	+	0.967518i	$0.581352\pi$
$38$	−16.8526	−2.73386
$39$	−10.1286	−1.62188
$40$	0	0
$41$	8.48761	1.32554	0.662771	−	0.748822i	$-0.269380\pi$
$41$	8.48761	1.32554	0.662771	+	0.748822i	$0.269380\pi$
$42$	29.1621	4.49981
$43$	−4.56989	−0.696901	−0.348450	−	0.937327i	$-0.613292\pi$
$43$	−4.56989	−0.696901	−0.348450	+	0.937327i	$0.613292\pi$
$44$	1.84294	0.277834
$45$	0	0
$46$	10.2376	1.50946
$47$	−10.9885	−1.60284	−0.801419	−	0.598104i	$-0.795921\pi$
$47$	−10.9885	−1.60284	−0.801419	+	0.598104i	$0.795921\pi$
$48$	22.6466	3.26876
$49$	11.4757	1.63938
$50$	0	0
$51$	−5.98233	−0.837694
$52$	−18.1236	−2.51329
$53$	−0.970867	−0.133359	−0.0666794	−	0.997774i	$-0.521240\pi$
$53$	−0.970867	−0.133359	−0.0666794	+	0.997774i	$0.521240\pi$
$54$	5.95460	0.810318
$55$	0	0
$56$	29.9414	4.00109
$57$	−17.0840	−2.26284
$58$	−5.71284	−0.750132
$59$	2.47906	0.322746	0.161373	−	0.986893i	$-0.448408\pi$
$59$	2.47906	0.322746	0.161373	+	0.986893i	$0.448408\pi$
$60$	0	0
$61$	−8.72003	−1.11649	−0.558243	−	0.829678i	$-0.688524\pi$
$61$	−8.72003	−1.11649	−0.558243	+	0.829678i	$0.688524\pi$
$62$	2.50959	0.318718
$63$	16.6675	2.09991
$64$	4.48133	0.560166
$65$	0	0
$66$	2.66450	0.327977
$67$	14.8157	1.81003	0.905014	−	0.425381i	$-0.139860\pi$
$67$	14.8157	1.81003	0.905014	+	0.425381i	$0.139860\pi$
$68$	−10.7045	−1.29811
$69$	10.3782	1.24939
$70$	0	0
$71$	7.87706	0.934834	0.467417	−	0.884037i	$-0.345185\pi$
$71$	7.87706	0.934834	0.467417	+	0.884037i	$0.345185\pi$
$72$	27.0112	3.18330
$73$	−5.53782	−0.648153	−0.324076	−	0.946031i	$-0.605053\pi$
$73$	−5.53782	−0.648153	−0.324076	+	0.946031i	$0.605053\pi$
$74$	−7.95625	−0.924896
$75$	0	0
$76$	−30.5692	−3.50653
$77$	1.68810	0.192377
$78$	−26.2028	−2.96688
$79$	1.20590	0.135675	0.0678373	−	0.997696i	$-0.478390\pi$
$79$	1.20590	0.135675	0.0678373	+	0.997696i	$0.478390\pi$
$80$	0	0
$81$	−5.59666	−0.621851
$82$	21.9575	2.42480
$83$	−10.3757	−1.13888	−0.569442	−	0.822031i	$-0.692841\pi$
$83$	−10.3757	−1.13888	−0.569442	+	0.822031i	$0.692841\pi$
$84$	52.8976	5.77160
$85$	0	0
$86$	−11.8223	−1.27483
$87$	−5.79128	−0.620891
$88$	2.73570	0.291627
$89$	−15.3272	−1.62468	−0.812339	−	0.583186i	$-0.801806\pi$
$89$	−15.3272	−1.62468	−0.812339	+	0.583186i	$0.801806\pi$
$90$	0	0
$91$	−16.6008	−1.74024
$92$	18.5702	1.93608
$93$	2.54405	0.263806
$94$	−28.4273	−2.93206
$95$	0	0
$96$	22.0508	2.25055
$97$	6.20641	0.630165	0.315083	−	0.949064i	$-0.397968\pi$
$97$	6.20641	0.630165	0.315083	+	0.949064i	$0.397968\pi$
$98$	29.6877	2.99891
$99$	1.52289	0.153056
$100$	0	0
$101$	6.33910	0.630764	0.315382	−	0.948965i	$-0.397867\pi$
$101$	6.33910	0.630764	0.315382	+	0.948965i	$0.397867\pi$
$102$	−15.4763	−1.53239
$103$	17.2615	1.70082	0.850412	−	0.526118i	$-0.176353\pi$
$103$	17.2615	1.70082	0.850412	+	0.526118i	$0.176353\pi$
$104$	−26.9030	−2.63806
$105$	0	0
$106$	−2.51164	−0.243952
$107$	−20.1199	−1.94507	−0.972533	−	0.232764i	$-0.925223\pi$
$107$	−20.1199	−1.94507	−0.972533	+	0.232764i	$0.925223\pi$
$108$	10.8011	1.03934
$109$	2.66248	0.255019	0.127510	−	0.991837i	$-0.459302\pi$
$109$	2.66248	0.255019	0.127510	+	0.991837i	$0.459302\pi$
$110$	0	0
$111$	−8.06550	−0.765544
$112$	37.1178	3.50730
$113$	18.1521	1.70761	0.853803	−	0.520596i	$-0.174290\pi$
$113$	18.1521	1.70761	0.853803	+	0.520596i	$0.174290\pi$
$114$	−44.1966	−4.13939
$115$	0	0
$116$	−10.3626	−0.962143
$117$	−14.9762	−1.38455
$118$	6.41335	0.590397
$119$	−9.80505	−0.898828
$120$	0	0
$121$	−10.8458	−0.985978
$122$	−22.5588	−2.04238
$123$	22.2590	2.00703
$124$	4.55218	0.408798
$125$	0	0
$126$	43.1191	3.84135
$127$	10.1820	0.903506	0.451753	−	0.892143i	$-0.350799\pi$
$127$	10.1820	0.903506	0.451753	+	0.892143i	$0.350799\pi$
$128$	−5.22319	−0.461669
$129$	−11.9847	−1.05519
$130$	0	0
$131$	12.2069	1.06652	0.533261	−	0.845951i	$-0.320966\pi$
$131$	12.2069	1.06652	0.533261	+	0.845951i	$0.320966\pi$
$132$	4.83318	0.420674
$133$	−28.0008	−2.42797
$134$	38.3284	3.31107
$135$	0	0
$136$	−15.8899	−1.36255
$137$	13.4160	1.14621	0.573105	−	0.819482i	$-0.305739\pi$
$137$	13.4160	1.14621	0.573105	+	0.819482i	$0.305739\pi$
$138$	26.8485	2.28550
$139$	−11.6854	−0.991147	−0.495573	−	0.868566i	$-0.665042\pi$
$139$	−11.6854	−0.991147	−0.495573	+	0.868566i	$0.665042\pi$
$140$	0	0
$141$	−28.8177	−2.42689
$142$	20.3780	1.71008
$143$	−1.51679	−0.126841
$144$	33.4853	2.79044
$145$	0	0
$146$	−14.3264	−1.18566
$147$	30.0953	2.48222
$148$	−14.4320	−1.18630
$149$	−11.5450	−0.945805	−0.472902	−	0.881115i	$-0.656794\pi$
$149$	−11.5450	−0.945805	−0.472902	+	0.881115i	$0.656794\pi$
$150$	0	0
$151$	7.09477	0.577364	0.288682	−	0.957425i	$-0.406783\pi$
$151$	7.09477	0.577364	0.288682	+	0.957425i	$0.406783\pi$
$152$	−45.3776	−3.68061
$153$	−8.84547	−0.715114
$154$	4.36712	0.351913
$155$	0	0
$156$	−47.5296	−3.80542
$157$	22.5748	1.80166	0.900831	−	0.434170i	$-0.142958\pi$
$157$	22.5748	1.80166	0.900831	+	0.434170i	$0.142958\pi$
$158$	3.11968	0.248188
$159$	−2.54613	−0.201921
$160$	0	0
$161$	17.0099	1.34057
$162$	−14.4786	−1.13755
$163$	17.8281	1.39640	0.698201	−	0.715902i	$-0.253984\pi$
$163$	17.8281	1.39640	0.698201	+	0.715902i	$0.253984\pi$
$164$	39.8291	3.11013
$165$	0	0
$166$	−26.8421	−2.08335
$167$	10.3380	0.799981	0.399990	−	0.916519i	$-0.369013\pi$
$167$	10.3380	0.799981	0.399990	+	0.916519i	$0.369013\pi$
$168$	78.5223	6.05813
$169$	1.91619	0.147399
$170$	0	0
$171$	−25.2605	−1.93171
$172$	−21.4447	−1.63514
$173$	−4.53402	−0.344715	−0.172358	−	0.985034i	$-0.555138\pi$
$173$	−4.53402	−0.344715	−0.172358	+	0.985034i	$0.555138\pi$
$174$	−14.9821	−1.13579
$175$	0	0
$176$	3.39140	0.255637
$177$	6.50142	0.488676
$178$	−39.6515	−2.97201
$179$	9.96262	0.744641	0.372321	−	0.928104i	$-0.378562\pi$
$179$	9.96262	0.744641	0.372321	+	0.928104i	$0.378562\pi$
$180$	0	0
$181$	−12.5806	−0.935111	−0.467555	−	0.883964i	$-0.654865\pi$
$181$	−12.5806	−0.935111	−0.467555	+	0.883964i	$0.654865\pi$
$182$	−42.9464	−3.18340
$183$	−22.8686	−1.69049
$184$	27.5660	2.03219
$185$	0	0
$186$	6.58148	0.482578
$187$	−0.895874	−0.0655128
$188$	−51.5648	−3.76075
$189$	9.89361	0.719654
$190$	0	0
$191$	−13.6635	−0.988658	−0.494329	−	0.869275i	$-0.664586\pi$
$191$	−13.6635	−0.988658	−0.494329	+	0.869275i	$0.664586\pi$
$192$	11.7524	0.848158
$193$	−22.7940	−1.64075	−0.820375	−	0.571826i	$-0.806235\pi$
$193$	−22.7940	−1.64075	−0.820375	+	0.571826i	$0.806235\pi$
$194$	16.0560	1.15276
$195$	0	0
$196$	53.8509	3.84649
$197$	−3.68078	−0.262245	−0.131123	−	0.991366i	$-0.541858\pi$
$197$	−3.68078	−0.262245	−0.131123	+	0.991366i	$0.541858\pi$
$198$	3.93973	0.279984
$199$	10.9051	0.773044	0.386522	−	0.922280i	$-0.373676\pi$
$199$	10.9051	0.773044	0.386522	+	0.922280i	$0.373676\pi$
$200$	0	0
$201$	38.8547	2.74060
$202$	16.3993	1.15385
$203$	−9.49192	−0.666202
$204$	−28.0728	−1.96549
$205$	0	0
$206$	44.6556	3.11130
$207$	15.3452	1.06657
$208$	−33.3512	−2.31249
$209$	−2.55839	−0.176968
$210$	0	0
$211$	14.0951	0.970349	0.485174	−	0.874417i	$-0.338756\pi$
$211$	14.0951	0.970349	0.485174	+	0.874417i	$0.338756\pi$
$212$	−4.55590	−0.312901
$213$	20.6578	1.41545
$214$	−52.0504	−3.55809
$215$	0	0
$216$	16.0334	1.09094
$217$	4.16970	0.283058
$218$	6.88785	0.466504
$219$	−14.5231	−0.981380
$220$	0	0
$221$	8.81006	0.592628
$222$	−20.8655	−1.40040
$223$	−16.6721	−1.11645	−0.558224	−	0.829691i	$-0.688517\pi$
$223$	−16.6721	−1.11645	−0.558224	+	0.829691i	$0.688517\pi$
$224$	36.1413	2.41479
$225$	0	0
$226$	46.9596	3.12371
$227$	19.0910	1.26711	0.633556	−	0.773697i	$-0.281595\pi$
$227$	19.0910	1.26711	0.633556	+	0.773697i	$0.281595\pi$
$228$	−80.1688	−5.30931
$229$	−17.4855	−1.15547	−0.577736	−	0.816224i	$-0.696064\pi$
$229$	−17.4855	−1.15547	−0.577736	+	0.816224i	$0.696064\pi$
$230$	0	0
$231$	4.42709	0.291281
$232$	−15.3825	−1.00991
$233$	25.9768	1.70180	0.850898	−	0.525332i	$-0.176059\pi$
$233$	25.9768	1.70180	0.850898	+	0.525332i	$0.176059\pi$
$234$	−38.7434	−2.53274
$235$	0	0
$236$	11.6333	0.757262
$237$	3.16252	0.205428
$238$	−25.3658	−1.64422
$239$	−21.9518	−1.41995	−0.709973	−	0.704229i	$-0.751293\pi$
$239$	−21.9518	−1.41995	−0.709973	+	0.704229i	$0.751293\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−28.0581	−1.80364
$243$	−21.5826	−1.38453
$244$	−40.9197	−2.61962
$245$	0	0
$246$	57.5843	3.67144
$247$	25.1593	1.60085
$248$	6.75736	0.429093
$249$	−27.2107	−1.72441
$250$	0	0
$251$	−21.8198	−1.37725	−0.688626	−	0.725116i	$-0.741786\pi$
$251$	−21.8198	−1.37725	−0.688626	+	0.725116i	$0.741786\pi$
$252$	78.2143	4.92704
$253$	1.55417	0.0977100
$254$	26.3409	1.65278
$255$	0	0
$256$	−22.4751	−1.40469
$257$	14.1109	0.880212	0.440106	−	0.897946i	$-0.354941\pi$
$257$	14.1109	0.880212	0.440106	+	0.897946i	$0.354941\pi$
$258$	−31.0044	−1.93025
$259$	−13.2194	−0.821412
$260$	0	0
$261$	−8.56299	−0.530036
$262$	31.5793	1.95098
$263$	−22.9481	−1.41504	−0.707521	−	0.706692i	$-0.750187\pi$
$263$	−22.9481	−1.41504	−0.707521	+	0.706692i	$0.750187\pi$
$264$	7.17447	0.441558
$265$	0	0
$266$	−72.4382	−4.44147
$267$	−40.1960	−2.45996
$268$	69.5245	4.24688
$269$	−23.8837	−1.45621	−0.728106	−	0.685465i	$-0.759599\pi$
$269$	−23.8837	−1.45621	−0.728106	+	0.685465i	$0.759599\pi$
$270$	0	0
$271$	9.08280	0.551741	0.275870	−	0.961195i	$-0.411034\pi$
$271$	9.08280	0.551741	0.275870	+	0.961195i	$0.411034\pi$
$272$	−19.6984	−1.19439
$273$	−43.5361	−2.63493
$274$	34.7074	2.09675
$275$	0	0
$276$	48.7009	2.93145
$277$	3.96886	0.238466	0.119233	−	0.992866i	$-0.461957\pi$
$277$	3.96886	0.238466	0.119233	+	0.992866i	$0.461957\pi$
$278$	−30.2304	−1.81310
$279$	3.76163	0.225203
$280$	0	0
$281$	18.1150	1.08065	0.540324	−	0.841457i	$-0.318302\pi$
$281$	18.1150	1.08065	0.540324	+	0.841457i	$0.318302\pi$
$282$	−74.5516	−4.43948
$283$	6.95776	0.413596	0.206798	−	0.978384i	$-0.433696\pi$
$283$	6.95776	0.413596	0.206798	+	0.978384i	$0.433696\pi$
$284$	36.9640	2.19341
$285$	0	0
$286$	−3.92396	−0.232028
$287$	36.4826	2.15350
$288$	32.6043	1.92123
$289$	−11.7965	−0.693909
$290$	0	0
$291$	16.2765	0.954146
$292$	−25.9868	−1.52076
$293$	−22.1972	−1.29678	−0.648388	−	0.761310i	$-0.724556\pi$
$293$	−22.1972	−1.29678	−0.648388	+	0.761310i	$0.724556\pi$
$294$	77.8569	4.54071
$295$	0	0
$296$	−21.4231	−1.24519
$297$	0.903965	0.0524534
$298$	−29.8671	−1.73015
$299$	−15.2838	−0.883884
$300$	0	0
$301$	−19.6429	−1.13220
$302$	18.3542	1.05617
$303$	16.6245	0.955052
$304$	−56.2538	−3.22638
$305$	0	0
$306$	−22.8833	−1.30815
$307$	0.442232	0.0252395	0.0126197	−	0.999920i	$-0.495983\pi$
$307$	0.442232	0.0252395	0.0126197	+	0.999920i	$0.495983\pi$
$308$	7.92159	0.451374
$309$	45.2688	2.57525
$310$	0	0
$311$	18.1575	1.02962	0.514810	−	0.857304i	$-0.327863\pi$
$311$	18.1575	1.02962	0.514810	+	0.857304i	$0.327863\pi$
$312$	−70.5540	−3.99433
$313$	−18.3438	−1.03685	−0.518427	−	0.855122i	$-0.673482\pi$
$313$	−18.3438	−1.03685	−0.518427	+	0.855122i	$0.673482\pi$
$314$	58.4011	3.29576
$315$	0	0
$316$	5.65883	0.318334
$317$	21.2335	1.19259	0.596296	−	0.802765i	$-0.296638\pi$
$317$	21.2335	1.19259	0.596296	+	0.802765i	$0.296638\pi$
$318$	−6.58686	−0.369373
$319$	−0.867264	−0.0485575
$320$	0	0
$321$	−52.7652	−2.94506
$322$	44.0048	2.45229
$323$	14.8600	0.826834
$324$	−26.2630	−1.45905
$325$	0	0
$326$	46.1214	2.55443
$327$	6.98243	0.386129
$328$	59.1231	3.26453
$329$	−47.2322	−2.60400
$330$	0	0
$331$	26.3096	1.44610	0.723052	−	0.690794i	$-0.242739\pi$
$331$	26.3096	1.44610	0.723052	+	0.690794i	$0.242739\pi$
$332$	−48.6893	−2.67217
$333$	−11.9256	−0.653522
$334$	26.7446	1.46340
$335$	0	0
$336$	97.3427	5.31048
$337$	24.4944	1.33429	0.667147	−	0.744926i	$-0.267515\pi$
$337$	24.4944	1.33429	0.667147	+	0.744926i	$0.267515\pi$
$338$	4.95721	0.269636
$339$	47.6045	2.58552
$340$	0	0
$341$	0.380980	0.0206312
$342$	−65.3490	−3.53367
$343$	19.2380	1.03875
$344$	−31.8330	−1.71632
$345$	0	0
$346$	−11.7295	−0.630584
$347$	10.6167	0.569936	0.284968	−	0.958537i	$-0.408017\pi$
$347$	10.6167	0.569936	0.284968	+	0.958537i	$0.408017\pi$
$348$	−27.1763	−1.45680
$349$	3.73173	0.199755	0.0998774	−	0.995000i	$-0.468155\pi$
$349$	3.73173	0.199755	0.0998774	+	0.995000i	$0.468155\pi$
$350$	0	0
$351$	−8.88962	−0.474493
$352$	3.30218	0.176007
$353$	21.5973	1.14951	0.574754	−	0.818326i	$-0.305098\pi$
$353$	21.5973	1.14951	0.574754	+	0.818326i	$0.305098\pi$
$354$	16.8192	0.893931
$355$	0	0
$356$	−71.9245	−3.81199
$357$	−25.7141	−1.36093
$358$	25.7734	1.36217
$359$	0.342423	0.0180724	0.00903619	−	0.999959i	$-0.497124\pi$
$359$	0.342423	0.0180724	0.00903619	+	0.999959i	$0.497124\pi$
$360$	0	0
$361$	23.4365	1.23350
$362$	−32.5462	−1.71059
$363$	−28.4434	−1.49289
$364$	−77.9012	−4.08313
$365$	0	0
$366$	−59.1612	−3.09240
$367$	6.74979	0.352336	0.176168	−	0.984360i	$-0.443630\pi$
$367$	6.74979	0.352336	0.176168	+	0.984360i	$0.443630\pi$
$368$	34.1731	1.78139
$369$	32.9122	1.71334
$370$	0	0
$371$	−4.17311	−0.216657
$372$	11.9383	0.618969
$373$	20.0767	1.03953	0.519765	−	0.854309i	$-0.326019\pi$
$373$	20.0767	1.03953	0.519765	+	0.854309i	$0.326019\pi$
$374$	−2.31763	−0.119842
$375$	0	0
$376$	−76.5438	−3.94745
$377$	8.52870	0.439251
$378$	25.5948	1.31646
$379$	15.5218	0.797302	0.398651	−	0.917103i	$-0.369479\pi$
$379$	15.5218	0.797302	0.398651	+	0.917103i	$0.369479\pi$
$380$	0	0
$381$	26.7026	1.36802
$382$	−35.3476	−1.80854
$383$	−6.88079	−0.351592	−0.175796	−	0.984427i	$-0.556250\pi$
$383$	−6.88079	−0.351592	−0.175796	+	0.984427i	$0.556250\pi$
$384$	−13.6980	−0.699023
$385$	0	0
$386$	−58.9683	−3.00141
$387$	−17.7205	−0.900785
$388$	29.1243	1.47856
$389$	24.2174	1.22787	0.613935	−	0.789356i	$-0.289586\pi$
$389$	24.2174	1.22787	0.613935	+	0.789356i	$0.289586\pi$
$390$	0	0
$391$	−9.02717	−0.456523
$392$	79.9374	4.03745
$393$	32.0130	1.61484
$394$	−9.52222	−0.479723
$395$	0	0
$396$	7.14634	0.359117
$397$	15.0023	0.752945	0.376473	−	0.926428i	$-0.377137\pi$
$397$	15.0023	0.752945	0.376473	+	0.926428i	$0.377137\pi$
$398$	28.2117	1.41412
$399$	−73.4329	−3.67624
$400$	0	0
$401$	21.2639	1.06187	0.530935	−	0.847412i	$-0.321841\pi$
$401$	21.2639	1.06187	0.530935	+	0.847412i	$0.321841\pi$
$402$	100.517	5.01336
$403$	−3.74657	−0.186630
$404$	29.7469	1.47997
$405$	0	0
$406$	−24.5557	−1.21868
$407$	−1.20784	−0.0598702
$408$	−41.6718	−2.06306
$409$	4.22088	0.208709	0.104355	−	0.994540i	$-0.466722\pi$
$409$	4.22088	0.208709	0.104355	+	0.994540i	$0.466722\pi$
$410$	0	0
$411$	35.1840	1.73550
$412$	81.0014	3.99065
$413$	10.6558	0.524339
$414$	39.6982	1.95106
$415$	0	0
$416$	−32.4738	−1.59216
$417$	−30.6455	−1.50071
$418$	−6.61858	−0.323725
$419$	−27.1247	−1.32513	−0.662563	−	0.749006i	$-0.730531\pi$
$419$	−27.1247	−1.32513	−0.662563	+	0.749006i	$0.730531\pi$
$420$	0	0
$421$	15.8371	0.771855	0.385927	−	0.922529i	$-0.373882\pi$
$421$	15.8371	0.771855	0.385927	+	0.922529i	$0.373882\pi$
$422$	36.4642	1.77505
$423$	−42.6098	−2.07176
$424$	−6.76288	−0.328435
$425$	0	0
$426$	53.4420	2.58927
$427$	−37.4816	−1.81386
$428$	−94.4150	−4.56372
$429$	−3.97784	−0.192052
$430$	0	0
$431$	−24.6898	−1.18926	−0.594632	−	0.803998i	$-0.702702\pi$
$431$	−24.6898	−1.18926	−0.594632	+	0.803998i	$0.702702\pi$
$432$	19.8763	0.956301
$433$	7.59142	0.364820	0.182410	−	0.983223i	$-0.441610\pi$
$433$	7.59142	0.364820	0.182410	+	0.983223i	$0.441610\pi$
$434$	10.7871	0.517796
$435$	0	0
$436$	12.4940	0.598353
$437$	−25.7793	−1.23319
$438$	−37.5714	−1.79523
$439$	1.75383	0.0837055	0.0418528	−	0.999124i	$-0.486674\pi$
$439$	1.75383	0.0837055	0.0418528	+	0.999124i	$0.486674\pi$
$440$	0	0
$441$	44.4989	2.11900
$442$	22.7917	1.08409
$443$	−20.9752	−0.996562	−0.498281	−	0.867016i	$-0.666035\pi$
$443$	−20.9752	−0.996562	−0.498281	+	0.867016i	$0.666035\pi$
$444$	−37.8483	−1.79620
$445$	0	0
$446$	−43.1309	−2.04231
$447$	−30.2772	−1.43206
$448$	19.2622	0.910055
$449$	26.3840	1.24514	0.622570	−	0.782564i	$-0.286089\pi$
$449$	26.3840	1.24514	0.622570	+	0.782564i	$0.286089\pi$
$450$	0	0
$451$	3.33336	0.156962
$452$	85.1808	4.00657
$453$	18.6063	0.874198
$454$	49.3885	2.31792
$455$	0	0
$456$	−119.004	−5.57288
$457$	−26.3144	−1.23094	−0.615469	−	0.788161i	$-0.711033\pi$
$457$	−26.3144	−1.23094	−0.615469	+	0.788161i	$0.711033\pi$
$458$	−45.2350	−2.11369
$459$	−5.25054	−0.245074
$460$	0	0
$461$	−24.5160	−1.14182	−0.570912	−	0.821012i	$-0.693410\pi$
$461$	−24.5160	−1.14182	−0.570912	+	0.821012i	$0.693410\pi$
$462$	11.4529	0.532838
$463$	10.4600	0.486119	0.243060	−	0.970011i	$-0.421849\pi$
$463$	10.4600	0.486119	0.243060	+	0.970011i	$0.421849\pi$
$464$	−19.0694	−0.885273
$465$	0	0
$466$	67.2021	3.11308
$467$	13.1235	0.607284	0.303642	−	0.952786i	$-0.401797\pi$
$467$	13.1235	0.607284	0.303642	+	0.952786i	$0.401797\pi$
$468$	−70.2773	−3.24857
$469$	63.6829	2.94060
$470$	0	0
$471$	59.2030	2.72793
$472$	17.2687	0.794855
$473$	−1.79474	−0.0825224
$474$	8.18146	0.375787
$475$	0	0
$476$	−46.0113	−2.10893
$477$	−3.76471	−0.172374
$478$	−56.7896	−2.59750
$479$	−0.348871	−0.0159403	−0.00797016	−	0.999968i	$-0.502537\pi$
$479$	−0.348871	−0.0159403	−0.00797016	+	0.999968i	$0.502537\pi$
$480$	0	0
$481$	11.8779	0.541586
$482$	2.58701	0.117835
$483$	44.6090	2.02978
$484$	−50.8950	−2.31341
$485$	0	0
$486$	−55.8344	−2.53270
$487$	15.7693	0.714576	0.357288	−	0.933994i	$-0.383701\pi$
$487$	15.7693	0.714576	0.357288	+	0.933994i	$0.383701\pi$
$488$	−60.7421	−2.74967
$489$	46.7547	2.11432
$490$	0	0
$491$	−41.8057	−1.88667	−0.943333	−	0.331848i	$-0.892328\pi$
$491$	−41.8057	−1.88667	−0.943333	+	0.331848i	$0.892328\pi$
$492$	104.453	4.70911
$493$	5.03737	0.226872
$494$	65.0873	2.92842
$495$	0	0
$496$	8.37698	0.376137
$497$	33.8582	1.51875
$498$	−70.3943	−3.15444
$499$	−9.90463	−0.443392	−0.221696	−	0.975116i	$-0.571159\pi$
$499$	−9.90463	−0.443392	−0.221696	+	0.975116i	$0.571159\pi$
$500$	0	0
$501$	27.1118	1.21127
$502$	−56.4480	−2.51940
$503$	−4.86635	−0.216980	−0.108490	−	0.994098i	$-0.534602\pi$
$503$	−4.86635	−0.216980	−0.108490	+	0.994098i	$0.534602\pi$
$504$	116.103	5.17164
$505$	0	0
$506$	4.02066	0.178740
$507$	5.02528	0.223180
$508$	47.7802	2.11990
$509$	37.0006	1.64002	0.820011	−	0.572348i	$-0.193967\pi$
$509$	37.0006	1.64002	0.820011	+	0.572348i	$0.193967\pi$
$510$	0	0
$511$	−23.8034	−1.05300
$512$	−47.6969	−2.10792
$513$	−14.9942	−0.662011
$514$	36.5049	1.61016
$515$	0	0
$516$	−56.2394	−2.47580
$517$	−4.31554	−0.189797
$518$	−34.1986	−1.50260
$519$	−11.8906	−0.521940
$520$	0	0
$521$	1.70970	0.0749035	0.0374517	−	0.999298i	$-0.488076\pi$
$521$	1.70970	0.0749035	0.0374517	+	0.999298i	$0.488076\pi$
$522$	−22.1525	−0.969590
$523$	27.8507	1.21782	0.608912	−	0.793238i	$-0.291606\pi$
$523$	27.8507	1.21782	0.608912	+	0.793238i	$0.291606\pi$
$524$	57.2822	2.50239
$525$	0	0
$526$	−59.3670	−2.58852
$527$	−2.21286	−0.0963939
$528$	8.89407	0.387065
$529$	−7.33957	−0.319112
$530$	0	0
$531$	9.61299	0.417168
$532$	−131.397	−5.69677
$533$	−32.7804	−1.41988
$534$	−103.987	−4.49998
$535$	0	0
$536$	103.204	4.45772
$537$	26.1273	1.12748
$538$	−61.7872	−2.66384
$539$	4.50688	0.194125
$540$	0	0
$541$	22.5917	0.971294	0.485647	−	0.874155i	$-0.338584\pi$
$541$	22.5917	0.971294	0.485647	+	0.874155i	$0.338584\pi$
$542$	23.4973	1.00929
$543$	−32.9931	−1.41587
$544$	−19.1802	−0.822345
$545$	0	0
$546$	−112.628	−4.82005
$547$	−8.99990	−0.384808	−0.192404	−	0.981316i	$-0.561628\pi$
$547$	−8.99990	−0.384808	−0.192404	+	0.981316i	$0.561628\pi$
$548$	62.9563	2.68936
$549$	−33.8134	−1.44312
$550$	0	0
$551$	14.3855	0.612841
$552$	72.2927	3.07698
$553$	5.18337	0.220419
$554$	10.2675	0.436223
$555$	0	0
$556$	−54.8353	−2.32553
$557$	−20.8858	−0.884959	−0.442480	−	0.896779i	$-0.645901\pi$
$557$	−20.8858	−0.884959	−0.442480	+	0.896779i	$0.645901\pi$
$558$	9.73138	0.411962
$559$	17.6496	0.746498
$560$	0	0
$561$	−2.34946	−0.0991942
$562$	46.8636	1.97682
$563$	11.7929	0.497012	0.248506	−	0.968630i	$-0.420060\pi$
$563$	11.7929	0.497012	0.248506	+	0.968630i	$0.420060\pi$
$564$	−135.230	−5.69422
$565$	0	0
$566$	17.9998	0.756587
$567$	−24.0563	−1.01027
$568$	54.8701	2.30230
$569$	−22.5814	−0.946661	−0.473330	−	0.880885i	$-0.656948\pi$
$569$	−22.5814	−0.946661	−0.473330	+	0.880885i	$0.656948\pi$
$570$	0	0
$571$	−29.3013	−1.22622	−0.613110	−	0.789997i	$-0.710082\pi$
$571$	−29.3013	−1.22622	−0.613110	+	0.789997i	$0.710082\pi$
$572$	−7.11772	−0.297607
$573$	−35.8330	−1.49695
$574$	94.3808	3.93938
$575$	0	0
$576$	17.3771	0.724047
$577$	−19.6490	−0.817997	−0.408999	−	0.912535i	$-0.634122\pi$
$577$	−19.6490	−0.817997	−0.408999	+	0.912535i	$0.634122\pi$
$578$	−30.5175	−1.26936
$579$	−59.7781	−2.48429
$580$	0	0
$581$	−44.5984	−1.85025
$582$	42.1075	1.74541
$583$	−0.381292	−0.0157915
$584$	−38.5754	−1.59626
$585$	0	0
$586$	−57.4244	−2.37218
$587$	3.27853	0.135319	0.0676596	−	0.997708i	$-0.478447\pi$
$587$	3.27853	0.135319	0.0676596	+	0.997708i	$0.478447\pi$
$588$	141.226	5.82405
$589$	−6.31939	−0.260386
$590$	0	0
$591$	−9.65298	−0.397070
$592$	−26.5578	−1.09152
$593$	27.0287	1.10994	0.554968	−	0.831872i	$-0.312731\pi$
$593$	27.0287	1.10994	0.554968	+	0.831872i	$0.312731\pi$
$594$	2.33857	0.0959525
$595$	0	0
$596$	−54.1763	−2.21915
$597$	28.5991	1.17048
$598$	−39.5393	−1.61688
$599$	35.1311	1.43542	0.717710	−	0.696342i	$-0.245190\pi$
$599$	35.1311	1.43542	0.717710	+	0.696342i	$0.245190\pi$
$600$	0	0
$601$	−21.6912	−0.884803	−0.442401	−	0.896817i	$-0.645873\pi$
$601$	−21.6912	−0.884803	−0.442401	+	0.896817i	$0.645873\pi$
$602$	−50.8163	−2.07112
$603$	57.4506	2.33957
$604$	33.2930	1.35467
$605$	0	0
$606$	43.0077	1.74707
$607$	15.6513	0.635266	0.317633	−	0.948214i	$-0.397112\pi$
$607$	15.6513	0.635266	0.317633	+	0.948214i	$0.397112\pi$
$608$	−54.7739	−2.22137
$609$	−24.8929	−1.00871
$610$	0	0
$611$	42.4392	1.71691
$612$	−41.5084	−1.67788
$613$	31.7379	1.28188	0.640941	−	0.767590i	$-0.278544\pi$
$613$	31.7379	1.28188	0.640941	+	0.767590i	$0.278544\pi$
$614$	1.14406	0.0461704
$615$	0	0
$616$	11.7590	0.473783
$617$	−6.37933	−0.256822	−0.128411	−	0.991721i	$-0.540988\pi$
$617$	−6.37933	−0.256822	−0.128411	+	0.991721i	$0.540988\pi$
$618$	117.111	4.71088
$619$	−20.4880	−0.823483	−0.411742	−	0.911301i	$-0.635079\pi$
$619$	−20.4880	−0.823483	−0.411742	+	0.911301i	$0.635079\pi$
$620$	0	0
$621$	9.10870	0.365519
$622$	46.9737	1.88347
$623$	−65.8813	−2.63948
$624$	−87.4645	−3.50138
$625$	0	0
$626$	−47.4556	−1.89671
$627$	−6.70946	−0.267950
$628$	105.935	4.22725
$629$	7.01553	0.279727
$630$	0	0
$631$	34.1846	1.36087	0.680434	−	0.732809i	$-0.261791\pi$
$631$	34.1846	1.36087	0.680434	+	0.732809i	$0.261791\pi$
$632$	8.40009	0.334138
$633$	36.9649	1.46922
$634$	54.9312	2.18160
$635$	0	0
$636$	−11.9480	−0.473769
$637$	−44.3208	−1.75605
$638$	−2.24362	−0.0888257
$639$	30.5447	1.20833
$640$	0	0
$641$	40.8997	1.61544	0.807721	−	0.589565i	$-0.200701\pi$
$641$	40.8997	1.61544	0.807721	+	0.589565i	$0.200701\pi$
$642$	−136.504	−5.38738
$643$	−8.39595	−0.331104	−0.165552	−	0.986201i	$-0.552941\pi$
$643$	−8.39595	−0.331104	−0.165552	+	0.986201i	$0.552941\pi$
$644$	79.8209	3.14539
$645$	0	0
$646$	38.4430	1.51252
$647$	8.33727	0.327772	0.163886	−	0.986479i	$-0.447597\pi$
$647$	8.33727	0.327772	0.163886	+	0.986479i	$0.447597\pi$
$648$	−38.9853	−1.53149
$649$	0.973609	0.0382175
$650$	0	0
$651$	10.9352	0.428584
$652$	83.6603	3.27639
$653$	22.0468	0.862759	0.431379	−	0.902171i	$-0.358027\pi$
$653$	22.0468	0.862759	0.431379	+	0.902171i	$0.358027\pi$
$654$	18.0636	0.706343
$655$	0	0
$656$	73.2939	2.86164
$657$	−21.4739	−0.837775
$658$	−122.190	−4.76347
$659$	7.05259	0.274730	0.137365	−	0.990521i	$-0.456137\pi$
$659$	7.05259	0.274730	0.137365	+	0.990521i	$0.456137\pi$
$660$	0	0
$661$	−0.213425	−0.00830127	−0.00415063	−	0.999991i	$-0.501321\pi$
$661$	−0.213425	−0.00830127	−0.00415063	+	0.999991i	$0.501321\pi$
$662$	68.0630	2.64535
$663$	23.1047	0.897310
$664$	−72.2754	−2.80483
$665$	0	0
$666$	−30.8518	−1.19548
$667$	−8.73888	−0.338371
$668$	48.5124	1.87700
$669$	−43.7231	−1.69043
$670$	0	0
$671$	−3.42464	−0.132207
$672$	94.7817	3.65628
$673$	−27.4723	−1.05898	−0.529489	−	0.848317i	$-0.677616\pi$
$673$	−27.4723	−1.05898	−0.529489	+	0.848317i	$0.677616\pi$
$674$	63.3672	2.44081
$675$	0	0
$676$	8.99195	0.345844
$677$	44.4995	1.71026	0.855128	−	0.518417i	$-0.173479\pi$
$677$	44.4995	1.71026	0.855128	+	0.518417i	$0.173479\pi$
$678$	123.153	4.72967
$679$	26.6772	1.02378
$680$	0	0
$681$	50.0667	1.91856
$682$	0.985599	0.0377405
$683$	36.8604	1.41042	0.705211	−	0.708997i	$-0.250852\pi$
$683$	36.8604	1.41042	0.705211	+	0.708997i	$0.250852\pi$
$684$	−118.538	−4.53240
$685$	0	0
$686$	49.7688	1.90018
$687$	−45.8562	−1.74952
$688$	−39.4628	−1.50450
$689$	3.74963	0.142850
$690$	0	0
$691$	−34.6351	−1.31758	−0.658791	−	0.752326i	$-0.728932\pi$
$691$	−34.6351	−1.31758	−0.658791	+	0.752326i	$0.728932\pi$
$692$	−21.2764	−0.808807
$693$	6.54589	0.248658
$694$	27.4656	1.04258
$695$	0	0
$696$	−40.3410	−1.52912
$697$	−19.3613	−0.733362
$698$	9.65401	0.365410
$699$	68.1249	2.57672
$700$	0	0
$701$	−1.17164	−0.0442521	−0.0221260	−	0.999755i	$-0.507044\pi$
$701$	−1.17164	−0.0442521	−0.0221260	+	0.999755i	$0.507044\pi$
$702$	−22.9975	−0.867986
$703$	20.0346	0.755619
$704$	1.75996	0.0663312
$705$	0	0
$706$	55.8724	2.10279
$707$	27.2476	1.02475
$708$	30.5086	1.14658
$709$	−42.7315	−1.60481	−0.802407	−	0.596777i	$-0.796448\pi$
$709$	−42.7315	−1.60481	−0.802407	+	0.596777i	$0.796448\pi$
$710$	0	0
$711$	4.67610	0.175367
$712$	−106.766	−4.00123
$713$	3.83890	0.143768
$714$	−66.5225	−2.48954
$715$	0	0
$716$	46.7507	1.74716
$717$	−57.5694	−2.14997
$718$	0.885850	0.0330596
$719$	−41.9975	−1.56624	−0.783122	−	0.621868i	$-0.786374\pi$
$719$	−41.9975	−1.56624	−0.783122	+	0.621868i	$0.786374\pi$
$720$	0	0
$721$	74.1956	2.76319
$722$	60.6304	2.25643
$723$	2.62253	0.0975330
$724$	−59.0360	−2.19406
$725$	0	0
$726$	−73.5832	−2.73093
$727$	−12.9516	−0.480350	−0.240175	−	0.970730i	$-0.577205\pi$
$727$	−12.9516	−0.480350	−0.240175	+	0.970730i	$0.577205\pi$
$728$	−115.638	−4.28583
$729$	−39.8111	−1.47449
$730$	0	0
$731$	10.4245	0.385564
$732$	−107.313	−3.96641
$733$	−10.9185	−0.403283	−0.201641	−	0.979459i	$-0.564628\pi$
$733$	−10.9185	−0.403283	−0.201641	+	0.979459i	$0.564628\pi$
$734$	17.4618	0.644525
$735$	0	0
$736$	33.2740	1.22650
$737$	5.81862	0.214332
$738$	85.1441	3.13420
$739$	−41.7541	−1.53595	−0.767975	−	0.640480i	$-0.778735\pi$
$739$	−41.7541	−1.53595	−0.767975	+	0.640480i	$0.778735\pi$
$740$	0	0
$741$	65.9811	2.42388
$742$	−10.7959	−0.396329
$743$	−26.5560	−0.974246	−0.487123	−	0.873333i	$-0.661954\pi$
$743$	−26.5560	−0.974246	−0.487123	+	0.873333i	$0.661954\pi$
$744$	17.7214	0.649698
$745$	0	0
$746$	51.9385	1.90160
$747$	−40.2337	−1.47207
$748$	−4.20399	−0.153713
$749$	−86.4822	−3.15999
$750$	0	0
$751$	−39.8014	−1.45237	−0.726187	−	0.687497i	$-0.758710\pi$
$751$	−39.8014	−1.45237	−0.726187	+	0.687497i	$0.758710\pi$
$752$	−94.8900	−3.46028
$753$	−57.2231	−2.08533
$754$	22.0638	0.803517
$755$	0	0
$756$	46.4269	1.68853
$757$	−2.82083	−0.102525	−0.0512623	−	0.998685i	$-0.516324\pi$
$757$	−2.82083	−0.102525	−0.0512623	+	0.998685i	$0.516324\pi$
$758$	40.1551	1.45850
$759$	4.07587	0.147945
$760$	0	0
$761$	−32.9918	−1.19595	−0.597975	−	0.801515i	$-0.704028\pi$
$761$	−32.9918	−1.19595	−0.597975	+	0.801515i	$0.704028\pi$
$762$	69.0799	2.50250
$763$	11.4442	0.414309
$764$	−64.1176	−2.31969
$765$	0	0
$766$	−17.8007	−0.643164
$767$	−9.57450	−0.345715
$768$	−58.9417	−2.12687
$769$	0.243111	0.00876681	0.00438341	−	0.999990i	$-0.498605\pi$
$769$	0.243111	0.00876681	0.00438341	+	0.999990i	$0.498605\pi$
$770$	0	0
$771$	37.0062	1.33275
$772$	−106.964	−3.84970
$773$	5.21480	0.187563	0.0937817	−	0.995593i	$-0.470104\pi$
$773$	5.21480	0.187563	0.0937817	+	0.995593i	$0.470104\pi$
$774$	−45.8432	−1.64780
$775$	0	0
$776$	43.2327	1.55196
$777$	−34.6682	−1.24372
$778$	62.6506	2.24613
$779$	−55.2911	−1.98101
$780$	0	0
$781$	3.09358	0.110697
$782$	−23.3534	−0.835114
$783$	−5.08286	−0.181647
$784$	99.0970	3.53918
$785$	0	0
$786$	82.8178	2.95401
$787$	−22.2230	−0.792163	−0.396082	−	0.918215i	$-0.629630\pi$
$787$	−22.2230	−0.792163	−0.396082	+	0.918215i	$0.629630\pi$
$788$	−17.2725	−0.615307
$789$	−60.1822	−2.14254
$790$	0	0
$791$	78.0238	2.77421
$792$	10.6082	0.376945
$793$	33.6781	1.19594
$794$	38.8111	1.37736
$795$	0	0
$796$	51.1736	1.81380
$797$	0.864482	0.0306215	0.0153108	−	0.999883i	$-0.495126\pi$
$797$	0.864482	0.0306215	0.0153108	+	0.999883i	$0.495126\pi$
$798$	−189.972	−6.72492
$799$	25.0662	0.886777
$800$	0	0
$801$	−59.4338	−2.09999
$802$	55.0100	1.94247
$803$	−2.17488	−0.0767500
$804$	182.330	6.43029
$805$	0	0
$806$	−9.69241	−0.341401
$807$	−62.6356	−2.20488
$808$	44.1570	1.55344
$809$	45.0997	1.58562	0.792810	−	0.609468i	$-0.208617\pi$
$809$	45.0997	1.58562	0.792810	+	0.609468i	$0.208617\pi$
$810$	0	0
$811$	−28.1179	−0.987354	−0.493677	−	0.869645i	$-0.664347\pi$
$811$	−28.1179	−0.987354	−0.493677	+	0.869645i	$0.664347\pi$
$812$	−44.5419	−1.56312
$813$	23.8199	0.835401
$814$	−3.12468	−0.109520
$815$	0	0
$816$	−51.6598	−1.80845
$817$	29.7697	1.04151
$818$	10.9195	0.381790
$819$	−64.3725	−2.24936
$820$	0	0
$821$	−30.3753	−1.06011	−0.530053	−	0.847964i	$-0.677828\pi$
$821$	−30.3753	−1.06011	−0.530053	+	0.847964i	$0.677828\pi$
$822$	91.0213	3.17473
$823$	−55.5506	−1.93637	−0.968185	−	0.250234i	$-0.919492\pi$
$823$	−55.5506	−1.93637	−0.968185	+	0.250234i	$0.919492\pi$
$824$	120.240	4.18877
$825$	0	0
$826$	27.5667	0.959169
$827$	1.95094	0.0678408	0.0339204	−	0.999425i	$-0.489201\pi$
$827$	1.95094	0.0678408	0.0339204	+	0.999425i	$0.489201\pi$
$828$	72.0092	2.50249
$829$	20.8527	0.724244	0.362122	−	0.932131i	$-0.382052\pi$
$829$	20.8527	0.724244	0.362122	+	0.932131i	$0.382052\pi$
$830$	0	0
$831$	10.4085	0.361066
$832$	−17.3075	−0.600031
$833$	−26.1775	−0.906996
$834$	−79.2801	−2.74524
$835$	0	0
$836$	−12.0055	−0.415220
$837$	2.23285	0.0771786
$838$	−70.1717	−2.42404
$839$	−28.1542	−0.971992	−0.485996	−	0.873961i	$-0.661543\pi$
$839$	−28.1542	−0.971992	−0.485996	+	0.873961i	$0.661543\pi$
$840$	0	0
$841$	−24.1235	−0.831845
$842$	40.9708	1.41195
$843$	47.5071	1.63623
$844$	66.1430	2.27674
$845$	0	0
$846$	−110.232	−3.78985
$847$	−46.6187	−1.60184
$848$	−8.38382	−0.287902
$849$	18.2469	0.626233
$850$	0	0
$851$	−12.1706	−0.417203
$852$	96.9392	3.32108
$853$	−37.0256	−1.26773	−0.633866	−	0.773443i	$-0.718533\pi$
$853$	−37.0256	−1.26773	−0.633866	+	0.773443i	$0.718533\pi$
$854$	−96.9652	−3.31808
$855$	0	0
$856$	−140.152	−4.79029
$857$	−13.2564	−0.452831	−0.226415	−	0.974031i	$-0.572701\pi$
$857$	−13.2564	−0.452831	−0.226415	+	0.974031i	$0.572701\pi$
$858$	−10.2907	−0.351319
$859$	−56.4702	−1.92674	−0.963370	−	0.268176i	$-0.913579\pi$
$859$	−56.4702	−1.92674	−0.963370	+	0.268176i	$0.913579\pi$
$860$	0	0
$861$	95.6767	3.26065
$862$	−63.8727	−2.17551
$863$	0.366270	0.0124680	0.00623398	−	0.999981i	$-0.498016\pi$
$863$	0.366270	0.0124680	0.00623398	+	0.999981i	$0.498016\pi$
$864$	19.3534	0.658417
$865$	0	0
$866$	19.6391	0.667363
$867$	−30.9366	−1.05066
$868$	19.5668	0.664141
$869$	0.473597	0.0160657
$870$	0	0
$871$	−57.2205	−1.93884
$872$	18.5463	0.628058
$873$	24.0664	0.814526
$874$	−66.6913	−2.25587
$875$	0	0
$876$	−68.1513	−2.30262
$877$	−15.2141	−0.513745	−0.256872	−	0.966445i	$-0.582692\pi$
$877$	−15.2141	−0.513745	−0.256872	+	0.966445i	$0.582692\pi$
$878$	4.53716	0.153122
$879$	−58.2129	−1.96347
$880$	0	0
$881$	−30.1389	−1.01541	−0.507703	−	0.861532i	$-0.669505\pi$
$881$	−30.1389	−1.01541	−0.507703	+	0.861532i	$0.669505\pi$
$882$	115.119	3.87626
$883$	7.14871	0.240573	0.120287	−	0.992739i	$-0.461619\pi$
$883$	7.14871	0.240573	0.120287	+	0.992739i	$0.461619\pi$
$884$	41.3422	1.39049
$885$	0	0
$886$	−54.2630	−1.82300
$887$	−40.8402	−1.37128	−0.685639	−	0.727942i	$-0.740477\pi$
$887$	−40.8402	−1.37128	−0.685639	+	0.727942i	$0.740477\pi$
$888$	−56.1828	−1.88537
$889$	43.7656	1.46785
$890$	0	0
$891$	−2.19799	−0.0736356
$892$	−78.2358	−2.61953
$893$	71.5827	2.39542
$894$	−78.3273	−2.61966
$895$	0	0
$896$	−22.4510	−0.750036
$897$	−40.0822	−1.33831
$898$	68.2558	2.27772
$899$	−2.14220	−0.0714462
$900$	0	0
$901$	2.21467	0.0737814
$902$	8.62344	0.287129
$903$	−51.5141	−1.71428
$904$	126.444	4.20547
$905$	0	0
$906$	48.1345	1.59916
$907$	−31.0528	−1.03109	−0.515545	−	0.856862i	$-0.672411\pi$
$907$	−31.0528	−1.03109	−0.515545	+	0.856862i	$0.672411\pi$
$908$	89.5865	2.97303
$909$	24.5810	0.815299
$910$	0	0
$911$	41.1039	1.36183	0.680916	−	0.732362i	$-0.261582\pi$
$911$	41.1039	1.36183	0.680916	+	0.732362i	$0.261582\pi$
$912$	−147.527	−4.88512
$913$	−4.07489	−0.134859
$914$	−68.0757	−2.25174
$915$	0	0
$916$	−82.0525	−2.71109
$917$	52.4693	1.73269
$918$	−13.5832	−0.448312
$919$	−42.8124	−1.41225	−0.706125	−	0.708087i	$-0.749558\pi$
$919$	−42.8124	−1.41225	−0.706125	+	0.708087i	$0.749558\pi$
$920$	0	0
$921$	1.15977	0.0382156
$922$	−63.4231	−2.08873
$923$	−30.4224	−1.00136
$924$	20.7746	0.683435
$925$	0	0
$926$	27.0602	0.889254
$927$	66.9344	2.19841
$928$	−18.5677	−0.609514
$929$	9.39377	0.308200	0.154100	−	0.988055i	$-0.450752\pi$
$929$	9.39377	0.308200	0.154100	+	0.988055i	$0.450752\pi$
$930$	0	0
$931$	−74.7563	−2.45004
$932$	121.899	3.99293
$933$	47.6187	1.55897
$934$	33.9507	1.11090
$935$	0	0
$936$	−104.321	−3.40984
$937$	11.8593	0.387425	0.193713	−	0.981058i	$-0.437947\pi$
$937$	11.8593	0.387425	0.193713	+	0.981058i	$0.437947\pi$
$938$	164.748	5.37922
$939$	−48.1073	−1.56992
$940$	0	0
$941$	9.22870	0.300847	0.150424	−	0.988622i	$-0.451936\pi$
$941$	9.22870	0.300847	0.150424	+	0.988622i	$0.451936\pi$
$942$	153.159	4.99018
$943$	33.5882	1.09378
$944$	21.4077	0.696760
$945$	0	0
$946$	−4.64302	−0.150958
$947$	9.63658	0.313147	0.156573	−	0.987666i	$-0.449955\pi$
$947$	9.63658	0.313147	0.156573	+	0.987666i	$0.449955\pi$
$948$	14.8405	0.481996
$949$	21.3879	0.694280
$950$	0	0
$951$	55.6855	1.80573
$952$	−68.3002	−2.21362
$953$	1.81806	0.0588929	0.0294464	−	0.999566i	$-0.490626\pi$
$953$	1.81806	0.0588929	0.0294464	+	0.999566i	$0.490626\pi$
$954$	−9.73933	−0.315322
$955$	0	0
$956$	−103.012	−3.33163
$957$	−2.27443	−0.0735218
$958$	−0.902532	−0.0291595
$959$	57.6666	1.86215
$960$	0	0
$961$	−30.0590	−0.969644
$962$	30.7282	0.990718
$963$	−78.0185	−2.51411
$964$	4.69261	0.151139
$965$	0	0
$966$	115.404	3.71306
$967$	−3.53944	−0.113821	−0.0569104	−	0.998379i	$-0.518125\pi$
$967$	−3.53944	−0.113821	−0.0569104	+	0.998379i	$0.518125\pi$
$968$	−75.5496	−2.42825
$969$	38.9709	1.25193
$970$	0	0
$971$	23.3662	0.749858	0.374929	−	0.927054i	$-0.377667\pi$
$971$	23.3662	0.749858	0.374929	+	0.927054i	$0.377667\pi$
$972$	−101.279	−3.24852
$973$	−50.2280	−1.61023
$974$	40.7954	1.30717
$975$	0	0
$976$	−75.3009	−2.41032
$977$	−4.90755	−0.157006	−0.0785031	−	0.996914i	$-0.525014\pi$
$977$	−4.90755	−0.157006	−0.0785031	+	0.996914i	$0.525014\pi$
$978$	120.955	3.86771
$979$	−6.01949	−0.192384
$980$	0	0
$981$	10.3242	0.329627
$982$	−108.152	−3.45126
$983$	−3.60795	−0.115076	−0.0575379	−	0.998343i	$-0.518325\pi$
$983$	−3.60795	−0.115076	−0.0575379	+	0.998343i	$0.518325\pi$
$984$	155.052	4.94289
$985$	0	0
$986$	13.0317	0.415014
$987$	−123.868	−3.94276
$988$	118.063	3.75608
$989$	−18.0845	−0.575054
$990$	0	0
$991$	52.9546	1.68216	0.841080	−	0.540911i	$-0.181920\pi$
$991$	52.9546	1.68216	0.841080	+	0.540911i	$0.181920\pi$
$992$	8.15659	0.258972
$993$	68.9976	2.18957
$994$	87.5915	2.77823
$995$	0	0
$996$	−127.689	−4.04599
$997$	−33.1318	−1.04929	−0.524647	−	0.851320i	$-0.675803\pi$
$997$	−33.1318	−1.04929	−0.524647	+	0.851320i	$0.675803\pi$
$998$	−25.6234	−0.811094
$999$	−7.07889	−0.223966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.g.1.11		11
5.4	even	2		1205.2.a.b.1.1	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.1	✓	11	5.4	even	2
6025.2.a.g.1.11		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)

\(f(q)\)	\(=\)	\(q+2.58701 q^{2} +2.62253 q^{3} +4.69261 q^{4} +6.78451 q^{6} +4.29833 q^{7} +6.96581 q^{8} +3.87767 q^{9} +O(q^{10})\)	\(q+2.58701 q^{2} +2.62253 q^{3} +4.69261 q^{4} +6.78451 q^{6} +4.29833 q^{7} +6.96581 q^{8} +3.87767 q^{9} +0.392733 q^{11} +12.3065 q^{12} -3.86215 q^{13} +11.1198 q^{14} +8.63539 q^{16} -2.28113 q^{17} +10.0316 q^{18} -6.51433 q^{19} +11.2725 q^{21} +1.01600 q^{22} +3.95733 q^{23} +18.2681 q^{24} -9.99141 q^{26} +2.30173 q^{27} +20.1704 q^{28} -2.20828 q^{29} +0.970075 q^{31} +8.40821 q^{32} +1.02995 q^{33} -5.90130 q^{34} +18.1964 q^{36} -3.07546 q^{37} -16.8526 q^{38} -10.1286 q^{39} +8.48761 q^{41} +29.1621 q^{42} -4.56989 q^{43} +1.84294 q^{44} +10.2376 q^{46} -10.9885 q^{47} +22.6466 q^{48} +11.4757 q^{49} -5.98233 q^{51} -18.1236 q^{52} -0.970867 q^{53} +5.95460 q^{54} +29.9414 q^{56} -17.0840 q^{57} -5.71284 q^{58} +2.47906 q^{59} -8.72003 q^{61} +2.50959 q^{62} +16.6675 q^{63} +4.48133 q^{64} +2.66450 q^{66} +14.8157 q^{67} -10.7045 q^{68} +10.3782 q^{69} +7.87706 q^{71} +27.0112 q^{72} -5.53782 q^{73} -7.95625 q^{74} -30.5692 q^{76} +1.68810 q^{77} -26.2028 q^{78} +1.20590 q^{79} -5.59666 q^{81} +21.9575 q^{82} -10.3757 q^{83} +52.8976 q^{84} -11.8223 q^{86} -5.79128 q^{87} +2.73570 q^{88} -15.3272 q^{89} -16.6008 q^{91} +18.5702 q^{92} +2.54405 q^{93} -28.4273 q^{94} +22.0508 q^{96} +6.20641 q^{97} +29.6877 q^{98} +1.52289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 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

Varieties

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Database

Properties

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