LMFDB - Embedded newform 725.4.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,4,Mod(1,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("725.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	725.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:	$42.7763847542$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 36x^{5} + 95x^{4} + 249x^{3} - 970x^{2} + 810x - 171 $ x^7 - 2x^6 - 36x^5 + 95x^4 + 249x^3 - 970x^2 + 810x - 171
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 145)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-5.14097$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.21256 q^{2} -6.33996 q^{3} +19.1708 q^{4} +33.0474 q^{6} +6.37598 q^{7} -58.2287 q^{8} +13.1951 q^{9} +O(q^{10})$	\(q-5.21256 q^{2} -6.33996 q^{3} +19.1708 q^{4} +33.0474 q^{6} +6.37598 q^{7} -58.2287 q^{8} +13.1951 q^{9} -61.0073 q^{11} -121.542 q^{12} +58.3202 q^{13} -33.2352 q^{14} +150.154 q^{16} -56.1338 q^{17} -68.7802 q^{18} +68.4840 q^{19} -40.4234 q^{21} +318.005 q^{22} -82.7426 q^{23} +369.167 q^{24} -303.998 q^{26} +87.5227 q^{27} +122.233 q^{28} -29.0000 q^{29} +180.461 q^{31} -316.859 q^{32} +386.784 q^{33} +292.601 q^{34} +252.960 q^{36} -126.378 q^{37} -356.977 q^{38} -369.748 q^{39} +296.186 q^{41} +210.710 q^{42} -141.910 q^{43} -1169.56 q^{44} +431.301 q^{46} -207.501 q^{47} -951.971 q^{48} -302.347 q^{49} +355.886 q^{51} +1118.05 q^{52} -364.318 q^{53} -456.218 q^{54} -371.265 q^{56} -434.186 q^{57} +151.164 q^{58} -778.586 q^{59} -832.590 q^{61} -940.664 q^{62} +84.1314 q^{63} +450.413 q^{64} -2016.14 q^{66} +500.473 q^{67} -1076.13 q^{68} +524.585 q^{69} +1087.81 q^{71} -768.331 q^{72} -901.544 q^{73} +658.751 q^{74} +1312.90 q^{76} -388.981 q^{77} +1927.33 q^{78} -882.100 q^{79} -911.157 q^{81} -1543.89 q^{82} +1293.09 q^{83} -774.951 q^{84} +739.714 q^{86} +183.859 q^{87} +3552.38 q^{88} -48.0680 q^{89} +371.848 q^{91} -1586.25 q^{92} -1144.11 q^{93} +1081.61 q^{94} +2008.87 q^{96} +176.089 q^{97} +1576.00 q^{98} -804.996 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 6 q^{2} - q^{3} + 52 q^{4} + 3 q^{6} - 17 q^{7} - 138 q^{8} + 118 q^{9}+O(q^{10}) $ 7 * q - 6 * q^2 - q^3 + 52 * q^4 + 3 * q^6 - 17 * q^7 - 138 * q^8 + 118 * q^9	\( 7 q - 6 q^{2} - q^{3} + 52 q^{4} + 3 q^{6} - 17 q^{7} - 138 q^{8} + 118 q^{9} + 2 q^{11} + 77 q^{12} + 17 q^{13} + 361 q^{14} + 372 q^{16} - 95 q^{17} - 261 q^{18} + 94 q^{19} - 100 q^{21} - 190 q^{22} - 327 q^{23} - 117 q^{24} - 115 q^{26} + 236 q^{27} + 67 q^{28} - 203 q^{29} + 169 q^{31} - 890 q^{32} - 272 q^{33} + 377 q^{34} + 2443 q^{36} + 500 q^{37} - 282 q^{38} + 1129 q^{39} + 1208 q^{41} + 1892 q^{42} + 1517 q^{43} - 734 q^{44} - 1413 q^{46} - 1974 q^{47} + 2637 q^{48} + 794 q^{49} - 190 q^{51} + 2063 q^{52} + 255 q^{53} - 5052 q^{54} + 2057 q^{56} - 94 q^{57} + 174 q^{58} + 177 q^{59} - 705 q^{61} + 807 q^{62} - 200 q^{63} + 332 q^{64} - 2768 q^{66} + 744 q^{67} + 2323 q^{68} + 1551 q^{69} + 2024 q^{71} - 6897 q^{72} + 1405 q^{73} + 82 q^{74} - 18 q^{76} - 3402 q^{77} + 5311 q^{78} - 2157 q^{79} + 1099 q^{81} - 2266 q^{82} + 158 q^{83} - 4372 q^{84} + 3033 q^{86} + 29 q^{87} + 1250 q^{88} - 2244 q^{89} + 3376 q^{91} - 2599 q^{92} - 586 q^{93} + 2212 q^{94} - 5077 q^{96} + 727 q^{97} + 1567 q^{98} + 416 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 - q^3 + 52 * q^4 + 3 * q^6 - 17 * q^7 - 138 * q^8 + 118 * q^9 + 2 * q^11 + 77 * q^12 + 17 * q^13 + 361 * q^14 + 372 * q^16 - 95 * q^17 - 261 * q^18 + 94 * q^19 - 100 * q^21 - 190 * q^22 - 327 * q^23 - 117 * q^24 - 115 * q^26 + 236 * q^27 + 67 * q^28 - 203 * q^29 + 169 * q^31 - 890 * q^32 - 272 * q^33 + 377 * q^34 + 2443 * q^36 + 500 * q^37 - 282 * q^38 + 1129 * q^39 + 1208 * q^41 + 1892 * q^42 + 1517 * q^43 - 734 * q^44 - 1413 * q^46 - 1974 * q^47 + 2637 * q^48 + 794 * q^49 - 190 * q^51 + 2063 * q^52 + 255 * q^53 - 5052 * q^54 + 2057 * q^56 - 94 * q^57 + 174 * q^58 + 177 * q^59 - 705 * q^61 + 807 * q^62 - 200 * q^63 + 332 * q^64 - 2768 * q^66 + 744 * q^67 + 2323 * q^68 + 1551 * q^69 + 2024 * q^71 - 6897 * q^72 + 1405 * q^73 + 82 * q^74 - 18 * q^76 - 3402 * q^77 + 5311 * q^78 - 2157 * q^79 + 1099 * q^81 - 2266 * q^82 + 158 * q^83 - 4372 * q^84 + 3033 * q^86 + 29 * q^87 + 1250 * q^88 - 2244 * q^89 + 3376 * q^91 - 2599 * q^92 - 586 * q^93 + 2212 * q^94 - 5077 * q^96 + 727 * q^97 + 1567 * q^98 + 416 * 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 $

$2$	−5.21256	−1.84292	−0.921460	−	0.388473i	$-0.873003\pi$
$2$	−5.21256	−1.84292	−0.921460	+	0.388473i	$0.873003\pi$
$3$	−6.33996	−1.22013	−0.610063	−	0.792353i	$-0.708856\pi$
$3$	−6.33996	−1.22013	−0.610063	+	0.792353i	$0.708856\pi$
$4$	19.1708	2.39635
$5$	0	0
$5$	0	0
$6$	33.0474	2.24859
$7$	6.37598	0.344270	0.172135	−	0.985073i	$-0.444933\pi$
$7$	6.37598	0.344270	0.172135	+	0.985073i	$0.444933\pi$
$8$	−58.2287	−2.57337
$9$	13.1951	0.488706
$10$	0	0
$11$	−61.0073	−1.67222	−0.836109	−	0.548563i	$-0.815175\pi$
$11$	−61.0073	−1.67222	−0.836109	+	0.548563i	$0.815175\pi$
$12$	−121.542	−2.92385
$13$	58.3202	1.24424	0.622120	−	0.782922i	$-0.286272\pi$
$13$	58.3202	1.24424	0.622120	+	0.782922i	$0.286272\pi$
$14$	−33.2352	−0.634463
$15$	0	0
$16$	150.154	2.34616
$17$	−56.1338	−0.800850	−0.400425	−	0.916330i	$-0.631137\pi$
$17$	−56.1338	−0.800850	−0.400425	+	0.916330i	$0.631137\pi$
$18$	−68.7802	−0.900646
$19$	68.4840	0.826911	0.413455	−	0.910524i	$-0.364322\pi$
$19$	68.4840	0.826911	0.413455	+	0.910524i	$0.364322\pi$
$20$	0	0
$21$	−40.4234	−0.420053
$22$	318.005	3.08176
$23$	−82.7426	−0.750132	−0.375066	−	0.926998i	$-0.622380\pi$
$23$	−82.7426	−0.750132	−0.375066	+	0.926998i	$0.622380\pi$
$24$	369.167	3.13983
$25$	0	0
$26$	−303.998	−2.29303
$27$	87.5227	0.623843
$28$	122.233	0.824994
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	0	0
$31$	180.461	1.04554	0.522770	−	0.852474i	$-0.324899\pi$
$31$	180.461	1.04554	0.522770	+	0.852474i	$0.324899\pi$
$32$	−316.859	−1.75041
$33$	386.784	2.04032
$34$	292.601	1.47590
$35$	0	0
$36$	252.960	1.17111
$37$	−126.378	−0.561523	−0.280761	−	0.959778i	$-0.590587\pi$
$37$	−126.378	−0.561523	−0.280761	+	0.959778i	$0.590587\pi$
$38$	−356.977	−1.52393
$39$	−369.748	−1.51813
$40$	0	0
$41$	296.186	1.12821	0.564104	−	0.825704i	$-0.309222\pi$
$41$	296.186	1.12821	0.564104	+	0.825704i	$0.309222\pi$
$42$	210.710	0.774124
$43$	−141.910	−0.503280	−0.251640	−	0.967821i	$-0.580970\pi$
$43$	−141.910	−0.503280	−0.251640	+	0.967821i	$0.580970\pi$
$44$	−1169.56	−4.00723
$45$	0	0
$46$	431.301	1.38243
$47$	−207.501	−0.643983	−0.321991	−	0.946743i	$-0.604352\pi$
$47$	−207.501	−0.643983	−0.321991	+	0.946743i	$0.604352\pi$
$48$	−951.971	−2.86261
$49$	−302.347	−0.881478
$50$	0	0
$51$	355.886	0.977137
$52$	1118.05	2.98164
$53$	−364.318	−0.944207	−0.472104	−	0.881543i	$-0.656505\pi$
$53$	−364.318	−0.944207	−0.472104	+	0.881543i	$0.656505\pi$
$54$	−456.218	−1.14969
$55$	0	0
$56$	−371.265	−0.885934
$57$	−434.186	−1.00894
$58$	151.164	0.342222
$59$	−778.586	−1.71802	−0.859010	−	0.511959i	$-0.828920\pi$
$59$	−778.586	−1.71802	−0.859010	+	0.511959i	$0.828920\pi$
$60$	0	0
$61$	−832.590	−1.74758	−0.873789	−	0.486306i	$-0.838344\pi$
$61$	−832.590	−1.74758	−0.873789	+	0.486306i	$0.838344\pi$
$62$	−940.664	−1.92685
$63$	84.1314	0.168247
$64$	450.413	0.879713
$65$	0	0
$66$	−2016.14	−3.76014
$67$	500.473	0.912574	0.456287	−	0.889833i	$-0.349179\pi$
$67$	500.473	0.912574	0.456287	+	0.889833i	$0.349179\pi$
$68$	−1076.13	−1.91912
$69$	524.585	0.915255
$70$	0	0
$71$	1087.81	1.81830	0.909151	−	0.416467i	$-0.136732\pi$
$71$	1087.81	1.81830	0.909151	+	0.416467i	$0.136732\pi$
$72$	−768.331	−1.25762
$73$	−901.544	−1.44545	−0.722724	−	0.691136i	$-0.757110\pi$
$73$	−901.544	−1.44545	−0.722724	+	0.691136i	$0.757110\pi$
$74$	658.751	1.03484
$75$	0	0
$76$	1312.90	1.98157
$77$	−388.981	−0.575695
$78$	1927.33	2.79779
$79$	−882.100	−1.25625	−0.628127	−	0.778111i	$-0.716178\pi$
$79$	−882.100	−1.25625	−0.628127	+	0.778111i	$0.716178\pi$
$80$	0	0
$81$	−911.157	−1.24987
$82$	−1543.89	−2.07920
$83$	1293.09	1.71007	0.855033	−	0.518573i	$-0.173537\pi$
$83$	1293.09	1.71007	0.855033	+	0.518573i	$0.173537\pi$
$84$	−774.951	−1.00660
$85$	0	0
$86$	739.714	0.927505
$87$	183.859	0.226572
$88$	3552.38	4.30323
$89$	−48.0680	−0.0572495	−0.0286247	−	0.999590i	$-0.509113\pi$
$89$	−48.0680	−0.0572495	−0.0286247	+	0.999590i	$0.509113\pi$
$90$	0	0
$91$	371.848	0.428355
$92$	−1586.25	−1.79758
$93$	−1144.11	−1.27569
$94$	1081.61	1.18681
$95$	0	0
$96$	2008.87	2.13572
$97$	176.089	0.184320	0.0921602	−	0.995744i	$-0.470623\pi$
$97$	176.089	0.184320	0.0921602	+	0.995744i	$0.470623\pi$
$98$	1576.00	1.62449
$99$	−804.996	−0.817223
$100$	0	0
$101$	432.965	0.426550	0.213275	−	0.976992i	$-0.431587\pi$
$101$	432.965	0.426550	0.213275	+	0.976992i	$0.431587\pi$
$102$	−1855.08	−1.80079
$103$	135.587	0.129707	0.0648533	−	0.997895i	$-0.479342\pi$
$103$	135.587	0.129707	0.0648533	+	0.997895i	$0.479342\pi$
$104$	−3395.91	−3.20189
$105$	0	0
$106$	1899.03	1.74010
$107$	753.450	0.680736	0.340368	−	0.940292i	$-0.389448\pi$
$107$	753.450	0.680736	0.340368	+	0.940292i	$0.389448\pi$
$108$	1677.88	1.49495
$109$	−382.704	−0.336297	−0.168149	−	0.985762i	$-0.553779\pi$
$109$	−382.704	−0.336297	−0.168149	+	0.985762i	$0.553779\pi$
$110$	0	0
$111$	801.228	0.685128
$112$	957.379	0.807713
$113$	−279.853	−0.232976	−0.116488	−	0.993192i	$-0.537164\pi$
$113$	−279.853	−0.232976	−0.116488	+	0.993192i	$0.537164\pi$
$114$	2263.22	1.85939
$115$	0	0
$116$	−555.954	−0.444992
$117$	769.539	0.608068
$118$	4058.43	3.16617
$119$	−357.908	−0.275709
$120$	0	0
$121$	2390.89	1.79631
$122$	4339.93	3.22065
$123$	−1877.81	−1.37656
$124$	3459.59	2.50548
$125$	0	0
$126$	−438.541	−0.310066
$127$	−2546.18	−1.77903	−0.889514	−	0.456908i	$-0.848957\pi$
$127$	−2546.18	−1.77903	−0.889514	+	0.456908i	$0.848957\pi$
$128$	187.061	0.129172
$129$	899.702	0.614065
$130$	0	0
$131$	−1545.63	−1.03085	−0.515427	−	0.856933i	$-0.672367\pi$
$131$	−1545.63	−1.03085	−0.515427	+	0.856933i	$0.672367\pi$
$132$	7414.97	4.88932
$133$	436.652	0.284681
$134$	−2608.75	−1.68180
$135$	0	0
$136$	3268.60	2.06088
$137$	−1328.80	−0.828667	−0.414334	−	0.910125i	$-0.635985\pi$
$137$	−1328.80	−0.828667	−0.414334	+	0.910125i	$0.635985\pi$
$138$	−2734.43	−1.68674
$139$	551.476	0.336515	0.168257	−	0.985743i	$-0.446186\pi$
$139$	551.476	0.336515	0.168257	+	0.985743i	$0.446186\pi$
$140$	0	0
$141$	1315.55	0.785740
$142$	−5670.28	−3.35098
$143$	−3557.96	−2.08064
$144$	1981.29	1.14658
$145$	0	0
$146$	4699.36	2.66385
$147$	1916.87	1.07551
$148$	−2422.76	−1.34561
$149$	1481.95	0.814806	0.407403	−	0.913249i	$-0.366435\pi$
$149$	1481.95	0.814806	0.407403	+	0.913249i	$0.366435\pi$
$150$	0	0
$151$	3075.77	1.65764	0.828818	−	0.559519i	$-0.189014\pi$
$151$	3075.77	1.65764	0.828818	+	0.559519i	$0.189014\pi$
$152$	−3987.73	−2.12795
$153$	−740.689	−0.391380
$154$	2027.59	1.06096
$155$	0	0
$156$	−7088.37	−3.63797
$157$	324.615	0.165013	0.0825066	−	0.996591i	$-0.473707\pi$
$157$	324.615	0.165013	0.0825066	+	0.996591i	$0.473707\pi$
$158$	4598.00	2.31517
$159$	2309.76	1.15205
$160$	0	0
$161$	−527.565	−0.258248
$162$	4749.46	2.30341
$163$	901.419	0.433157	0.216578	−	0.976265i	$-0.430510\pi$
$163$	901.419	0.433157	0.216578	+	0.976265i	$0.430510\pi$
$164$	5678.14	2.70359
$165$	0	0
$166$	−6740.34	−3.15152
$167$	2544.98	1.17926	0.589631	−	0.807673i	$-0.299273\pi$
$167$	2544.98	1.17926	0.589631	+	0.807673i	$0.299273\pi$
$168$	2353.80	1.08095
$169$	1204.25	0.548132
$170$	0	0
$171$	903.651	0.404116
$172$	−2720.53	−1.20604
$173$	−2230.16	−0.980093	−0.490046	−	0.871696i	$-0.663020\pi$
$173$	−2230.16	−0.980093	−0.490046	+	0.871696i	$0.663020\pi$
$174$	−958.376	−0.417553
$175$	0	0
$176$	−9160.50	−3.92329
$177$	4936.20	2.09620
$178$	250.558	0.105506
$179$	2904.03	1.21261	0.606305	−	0.795232i	$-0.292651\pi$
$179$	2904.03	1.21261	0.606305	+	0.795232i	$0.292651\pi$
$180$	0	0
$181$	−2585.86	−1.06191	−0.530955	−	0.847400i	$-0.678167\pi$
$181$	−2585.86	−1.06191	−0.530955	+	0.847400i	$0.678167\pi$
$182$	−1938.28	−0.789423
$183$	5278.59	2.13226
$184$	4817.99	1.93037
$185$	0	0
$186$	5963.77	2.35099
$187$	3424.57	1.33920
$188$	−3977.97	−1.54321
$189$	558.043	0.214770
$190$	0	0
$191$	2468.97	0.935333	0.467666	−	0.883905i	$-0.345095\pi$
$191$	2468.97	0.935333	0.467666	+	0.883905i	$0.345095\pi$
$192$	−2855.60	−1.07336
$193$	4371.20	1.63029	0.815145	−	0.579258i	$-0.196657\pi$
$193$	4371.20	1.63029	0.815145	+	0.579258i	$0.196657\pi$
$194$	−917.873	−0.339688
$195$	0	0
$196$	−5796.24	−2.11233
$197$	1498.89	0.542089	0.271045	−	0.962567i	$-0.412631\pi$
$197$	1498.89	0.542089	0.271045	+	0.962567i	$0.412631\pi$
$198$	4196.09	1.50608
$199$	−4496.34	−1.60169	−0.800847	−	0.598869i	$-0.795617\pi$
$199$	−4496.34	−1.60169	−0.800847	+	0.598869i	$0.795617\pi$
$200$	0	0
$201$	−3172.98	−1.11346
$202$	−2256.86	−0.786098
$203$	−184.903	−0.0639294
$204$	6822.63	2.34157
$205$	0	0
$206$	−706.756	−0.239039
$207$	−1091.79	−0.366594
$208$	8757.02	2.91918
$209$	−4178.02	−1.38278
$210$	0	0
$211$	4691.38	1.53065	0.765327	−	0.643641i	$-0.222577\pi$
$211$	4691.38	1.53065	0.765327	+	0.643641i	$0.222577\pi$
$212$	−6984.29	−2.26265
$213$	−6896.68	−2.21856
$214$	−3927.41	−1.25454
$215$	0	0
$216$	−5096.33	−1.60538
$217$	1150.61	0.359948
$218$	1994.87	0.619769
$219$	5715.75	1.76363
$220$	0	0
$221$	−3273.73	−0.996449
$222$	−4176.45	−1.26264
$223$	−2929.52	−0.879709	−0.439854	−	0.898069i	$-0.644970\pi$
$223$	−2929.52	−0.879709	−0.439854	+	0.898069i	$0.644970\pi$
$224$	−2020.28	−0.602615
$225$	0	0
$226$	1458.75	0.429357
$227$	815.482	0.238438	0.119219	−	0.992868i	$-0.461961\pi$
$227$	815.482	0.238438	0.119219	+	0.992868i	$0.461961\pi$
$228$	−8323.70	−2.41777
$229$	−5075.40	−1.46459	−0.732297	−	0.680985i	$-0.761552\pi$
$229$	−5075.40	−1.46459	−0.732297	+	0.680985i	$0.761552\pi$
$230$	0	0
$231$	2466.12	0.702420
$232$	1688.63	0.477863
$233$	1015.87	0.285629	0.142815	−	0.989749i	$-0.454385\pi$
$233$	1015.87	0.285629	0.142815	+	0.989749i	$0.454385\pi$
$234$	−4011.27	−1.12062
$235$	0	0
$236$	−14926.1	−4.11698
$237$	5592.48	1.53279
$238$	1865.62	0.508109
$239$	−1966.75	−0.532294	−0.266147	−	0.963932i	$-0.585751\pi$
$239$	−1966.75	−0.532294	−0.266147	+	0.963932i	$0.585751\pi$
$240$	0	0
$241$	4490.20	1.20016	0.600082	−	0.799939i	$-0.295135\pi$
$241$	4490.20	1.20016	0.600082	+	0.799939i	$0.295135\pi$
$242$	−12462.7	−3.31046
$243$	3413.58	0.901159
$244$	−15961.4	−4.18781
$245$	0	0
$246$	9788.20	2.53688
$247$	3994.00	1.02888
$248$	−10508.0	−2.69056
$249$	−8198.16	−2.08650
$250$	0	0
$251$	5919.15	1.48850	0.744250	−	0.667902i	$-0.232807\pi$
$251$	5919.15	1.48850	0.744250	+	0.667902i	$0.232807\pi$
$252$	1612.87	0.403180
$253$	5047.91	1.25438
$254$	13272.1	3.27861
$255$	0	0
$256$	−4578.37	−1.11777
$257$	−752.906	−0.182743	−0.0913716	−	0.995817i	$-0.529125\pi$
$257$	−752.906	−0.182743	−0.0913716	+	0.995817i	$0.529125\pi$
$258$	−4689.76	−1.13167
$259$	−805.780	−0.193316
$260$	0	0
$261$	−382.657	−0.0907505
$262$	8056.67	1.89978
$263$	169.736	0.0397961	0.0198981	−	0.999802i	$-0.493666\pi$
$263$	169.736	0.0397961	0.0198981	+	0.999802i	$0.493666\pi$
$264$	−22521.9	−5.25048
$265$	0	0
$266$	−2276.08	−0.524644
$267$	304.749	0.0698515
$268$	9594.48	2.18685
$269$	6630.15	1.50278	0.751389	−	0.659860i	$-0.229384\pi$
$269$	6630.15	1.50278	0.751389	+	0.659860i	$0.229384\pi$
$270$	0	0
$271$	−478.527	−0.107264	−0.0536318	−	0.998561i	$-0.517080\pi$
$271$	−478.527	−0.107264	−0.0536318	+	0.998561i	$0.517080\pi$
$272$	−8428.72	−1.87892
$273$	−2357.50	−0.522647
$274$	6926.48	1.52717
$275$	0	0
$276$	10056.7	2.19327
$277$	6220.41	1.34927	0.674636	−	0.738150i	$-0.264301\pi$
$277$	6220.41	1.34927	0.674636	+	0.738150i	$0.264301\pi$
$278$	−2874.60	−0.620170
$279$	2381.19	0.510962
$280$	0	0
$281$	−4153.25	−0.881716	−0.440858	−	0.897577i	$-0.645326\pi$
$281$	−4153.25	−0.881716	−0.440858	+	0.897577i	$0.645326\pi$
$282$	−6857.39	−1.44806
$283$	3561.31	0.748049	0.374024	−	0.927419i	$-0.377978\pi$
$283$	3561.31	0.748049	0.374024	+	0.927419i	$0.377978\pi$
$284$	20854.2	4.35729
$285$	0	0
$286$	18546.1	3.83445
$287$	1888.48	0.388409
$288$	−4180.97	−0.855438
$289$	−1762.00	−0.358639
$290$	0	0
$291$	−1116.39	−0.224894
$292$	−17283.4	−3.46381
$293$	1062.29	0.211808	0.105904	−	0.994376i	$-0.466226\pi$
$293$	1062.29	0.211808	0.105904	+	0.994376i	$0.466226\pi$
$294$	−9991.79	−1.98209
$295$	0	0
$296$	7358.80	1.44500
$297$	−5339.52	−1.04320
$298$	−7724.76	−1.50162
$299$	−4825.57	−0.933344
$300$	0	0
$301$	−904.813	−0.173264
$302$	−16032.7	−3.05489
$303$	−2744.98	−0.520445
$304$	10283.2	1.94006
$305$	0	0
$306$	3860.89	0.721283
$307$	−680.667	−0.126540	−0.0632699	−	0.997996i	$-0.520153\pi$
$307$	−680.667	−0.126540	−0.0632699	+	0.997996i	$0.520153\pi$
$308$	−7457.09	−1.37957
$309$	−859.615	−0.158258
$310$	0	0
$311$	829.406	0.151226	0.0756130	−	0.997137i	$-0.475909\pi$
$311$	829.406	0.151226	0.0756130	+	0.997137i	$0.475909\pi$
$312$	21529.9	3.90670
$313$	10589.7	1.91236	0.956178	−	0.292786i	$-0.0945825\pi$
$313$	10589.7	1.91236	0.956178	+	0.292786i	$0.0945825\pi$
$314$	−1692.08	−0.304106
$315$	0	0
$316$	−16910.6	−3.01043
$317$	−6086.97	−1.07848	−0.539241	−	0.842152i	$-0.681289\pi$
$317$	−6086.97	−1.07848	−0.539241	+	0.842152i	$0.681289\pi$
$318$	−12039.8	−2.12314
$319$	1769.21	0.310523
$320$	0	0
$321$	−4776.84	−0.830583
$322$	2749.97	0.475931
$323$	−3844.27	−0.662231
$324$	−17467.6	−2.99514
$325$	0	0
$326$	−4698.70	−0.798273
$327$	2426.33	0.410325
$328$	−17246.5	−2.90330
$329$	−1323.02	−0.221704
$330$	0	0
$331$	5241.06	0.870316	0.435158	−	0.900354i	$-0.356693\pi$
$331$	5241.06	0.870316	0.435158	+	0.900354i	$0.356693\pi$
$332$	24789.7	4.09792
$333$	−1667.56	−0.274420
$334$	−13265.9	−2.17328
$335$	0	0
$336$	−6069.74	−0.985511
$337$	6647.79	1.07457	0.537283	−	0.843402i	$-0.319451\pi$
$337$	6647.79	1.07457	0.537283	+	0.843402i	$0.319451\pi$
$338$	−6277.21	−1.01016
$339$	1774.26	0.284261
$340$	0	0
$341$	−11009.4	−1.74837
$342$	−4710.34	−0.744754
$343$	−4114.72	−0.647737
$344$	8263.22	1.29512
$345$	0	0
$346$	11624.9	1.80623
$347$	4066.40	0.629094	0.314547	−	0.949242i	$-0.398147\pi$
$347$	4066.40	0.629094	0.314547	+	0.949242i	$0.398147\pi$
$348$	3524.73	0.542946
$349$	−4087.38	−0.626912	−0.313456	−	0.949603i	$-0.601487\pi$
$349$	−4087.38	−0.626912	−0.313456	+	0.949603i	$0.601487\pi$
$350$	0	0
$351$	5104.34	0.776209
$352$	19330.7	2.92707
$353$	1812.11	0.273226	0.136613	−	0.990625i	$-0.456378\pi$
$353$	1812.11	0.273226	0.136613	+	0.990625i	$0.456378\pi$
$354$	−25730.3	−3.86313
$355$	0	0
$356$	−921.504	−0.137190
$357$	2269.12	0.336399
$358$	−15137.4	−2.23474
$359$	12501.8	1.83793	0.918967	−	0.394333i	$-0.129025\pi$
$359$	12501.8	1.83793	0.918967	+	0.394333i	$0.129025\pi$
$360$	0	0
$361$	−2168.94	−0.316218
$362$	13479.0	1.95702
$363$	−15158.2	−2.19173
$364$	7128.64	1.02649
$365$	0	0
$366$	−27515.0	−3.92959
$367$	5366.63	0.763312	0.381656	−	0.924304i	$-0.375354\pi$
$367$	5366.63	0.763312	0.381656	+	0.924304i	$0.375354\pi$
$368$	−12424.1	−1.75993
$369$	3908.20	0.551363
$370$	0	0
$371$	−2322.89	−0.325063
$372$	−21933.6	−3.05700
$373$	−1807.46	−0.250903	−0.125451	−	0.992100i	$-0.540038\pi$
$373$	−1807.46	−0.250903	−0.125451	+	0.992100i	$0.540038\pi$
$374$	−17850.8	−2.46803
$375$	0	0
$376$	12082.5	1.65721
$377$	−1691.29	−0.231049
$378$	−2908.83	−0.395805
$379$	6151.37	0.833706	0.416853	−	0.908974i	$-0.363133\pi$
$379$	6151.37	0.833706	0.416853	+	0.908974i	$0.363133\pi$
$380$	0	0
$381$	16142.6	2.17064
$382$	−12869.7	−1.72374
$383$	1284.92	0.171426	0.0857130	−	0.996320i	$-0.472683\pi$
$383$	1284.92	0.171426	0.0857130	+	0.996320i	$0.472683\pi$
$384$	−1185.96	−0.157606
$385$	0	0
$386$	−22785.2	−3.00449
$387$	−1872.51	−0.245956
$388$	3375.76	0.441697
$389$	7789.62	1.01529	0.507647	−	0.861565i	$-0.330515\pi$
$389$	7789.62	1.01529	0.507647	+	0.861565i	$0.330515\pi$
$390$	0	0
$391$	4644.66	0.600743
$392$	17605.3	2.26837
$393$	9799.20	1.25777
$394$	−7813.07	−0.999027
$395$	0	0
$396$	−15432.4	−1.95836
$397$	7666.16	0.969152	0.484576	−	0.874749i	$-0.338974\pi$
$397$	7666.16	0.969152	0.484576	+	0.874749i	$0.338974\pi$
$398$	23437.5	2.95179
$399$	−2768.36	−0.347346
$400$	0	0
$401$	2382.60	0.296711	0.148356	−	0.988934i	$-0.452602\pi$
$401$	2382.60	0.296711	0.148356	+	0.988934i	$0.452602\pi$
$402$	16539.3	2.05201
$403$	10524.5	1.30090
$404$	8300.29	1.02217
$405$	0	0
$406$	963.820	0.117817
$407$	7709.95	0.938988
$408$	−20722.8	−2.51453
$409$	2636.65	0.318763	0.159381	−	0.987217i	$-0.449050\pi$
$409$	2636.65	0.318763	0.159381	+	0.987217i	$0.449050\pi$
$410$	0	0
$411$	8424.56	1.01108
$412$	2599.31	0.310823
$413$	−4964.24	−0.591463
$414$	5691.05	0.675604
$415$	0	0
$416$	−18479.3	−2.17793
$417$	−3496.33	−0.410591
$418$	21778.2	2.54834
$419$	−6602.97	−0.769871	−0.384936	−	0.922943i	$-0.625776\pi$
$419$	−6602.97	−0.769871	−0.384936	+	0.922943i	$0.625776\pi$
$420$	0	0
$421$	15883.7	1.83878	0.919390	−	0.393347i	$-0.128683\pi$
$421$	15883.7	1.83878	0.919390	+	0.393347i	$0.128683\pi$
$422$	−24454.1	−2.82087
$423$	−2738.00	−0.314718
$424$	21213.8	2.42979
$425$	0	0
$426$	35949.4	4.08862
$427$	−5308.57	−0.601639
$428$	14444.3	1.63128
$429$	22557.3	2.53864
$430$	0	0
$431$	−1219.60	−0.136301	−0.0681507	−	0.997675i	$-0.521710\pi$
$431$	−1219.60	−0.136301	−0.0681507	+	0.997675i	$0.521710\pi$
$432$	13141.9	1.46363
$433$	11053.2	1.22675	0.613377	−	0.789790i	$-0.289811\pi$
$433$	11053.2	1.22675	0.613377	+	0.789790i	$0.289811\pi$
$434$	−5997.65	−0.663356
$435$	0	0
$436$	−7336.76	−0.805888
$437$	−5666.55	−0.620292
$438$	−29793.7	−3.25023
$439$	2683.07	0.291699	0.145850	−	0.989307i	$-0.453408\pi$
$439$	2683.07	0.291699	0.145850	+	0.989307i	$0.453408\pi$
$440$	0	0
$441$	−3989.49	−0.430784
$442$	17064.6	1.83638
$443$	−8012.04	−0.859285	−0.429643	−	0.902999i	$-0.641360\pi$
$443$	−8012.04	−0.859285	−0.429643	+	0.902999i	$0.641360\pi$
$444$	15360.2	1.64181
$445$	0	0
$446$	15270.3	1.62123
$447$	−9395.50	−0.994165
$448$	2871.82	0.302859
$449$	−1841.49	−0.193553	−0.0967765	−	0.995306i	$-0.530853\pi$
$449$	−1841.49	−0.193553	−0.0967765	+	0.995306i	$0.530853\pi$
$450$	0	0
$451$	−18069.5	−1.88661
$452$	−5365.01	−0.558294
$453$	−19500.3	−2.02252
$454$	−4250.75	−0.439422
$455$	0	0
$456$	25282.1	2.59636
$457$	5983.60	0.612475	0.306238	−	0.951955i	$-0.400930\pi$
$457$	5983.60	0.612475	0.306238	+	0.951955i	$0.400930\pi$
$458$	26455.9	2.69913
$459$	−4912.98	−0.499604
$460$	0	0
$461$	−1961.26	−0.198146	−0.0990728	−	0.995080i	$-0.531588\pi$
$461$	−1961.26	−0.198146	−0.0990728	+	0.995080i	$0.531588\pi$
$462$	−12854.8	−1.29450
$463$	−10864.9	−1.09057	−0.545286	−	0.838250i	$-0.683579\pi$
$463$	−10864.9	−1.09057	−0.545286	+	0.838250i	$0.683579\pi$
$464$	−4354.47	−0.435671
$465$	0	0
$466$	−5295.27	−0.526392
$467$	−8762.37	−0.868253	−0.434126	−	0.900852i	$-0.642943\pi$
$467$	−8762.37	−0.868253	−0.434126	+	0.900852i	$0.642943\pi$
$468$	14752.7	1.45715
$469$	3191.00	0.314172
$470$	0	0
$471$	−2058.04	−0.201337
$472$	45336.0	4.42110
$473$	8657.53	0.841594
$474$	−29151.2	−2.82480
$475$	0	0
$476$	−6861.39	−0.660696
$477$	−4807.21	−0.461440
$478$	10251.8	0.980975
$479$	19725.6	1.88160	0.940798	−	0.338969i	$-0.110078\pi$
$479$	19725.6	1.88160	0.940798	+	0.338969i	$0.110078\pi$
$480$	0	0
$481$	−7370.36	−0.698669
$482$	−23405.5	−2.21181
$483$	3344.74	0.315095
$484$	45835.4	4.30460
$485$	0	0
$486$	−17793.5	−1.66076
$487$	−7534.19	−0.701041	−0.350520	−	0.936555i	$-0.613995\pi$
$487$	−7534.19	−0.701041	−0.350520	+	0.936555i	$0.613995\pi$
$488$	48480.6	4.49716
$489$	−5714.96	−0.528506
$490$	0	0
$491$	19428.1	1.78570	0.892849	−	0.450356i	$-0.148703\pi$
$491$	19428.1	1.78570	0.892849	+	0.450356i	$0.148703\pi$
$492$	−35999.2	−3.29872
$493$	1627.88	0.148714
$494$	−20819.0	−1.89613
$495$	0	0
$496$	27096.9	2.45300
$497$	6935.86	0.625987
$498$	42733.4	3.84524
$499$	−10255.2	−0.920011	−0.460005	−	0.887916i	$-0.652153\pi$
$499$	−10255.2	−0.920011	−0.460005	+	0.887916i	$0.652153\pi$
$500$	0	0
$501$	−16135.1	−1.43885
$502$	−30853.9	−2.74318
$503$	−7473.22	−0.662454	−0.331227	−	0.943551i	$-0.607463\pi$
$503$	−7473.22	−0.662454	−0.331227	+	0.943551i	$0.607463\pi$
$504$	−4898.86	−0.432962
$505$	0	0
$506$	−26312.5	−2.31173
$507$	−7634.87	−0.668789
$508$	−48812.3	−4.26318
$509$	8947.08	0.779121	0.389560	−	0.921001i	$-0.372627\pi$
$509$	8947.08	0.779121	0.389560	+	0.921001i	$0.372627\pi$
$510$	0	0
$511$	−5748.22	−0.497625
$512$	22368.6	1.93078
$513$	5993.90	0.515862
$514$	3924.57	0.336781
$515$	0	0
$516$	17248.0	1.47152
$517$	12659.1	1.07688
$518$	4200.18	0.356265
$519$	14139.1	1.19584
$520$	0	0
$521$	−10606.3	−0.891879	−0.445940	−	0.895063i	$-0.647130\pi$
$521$	−10606.3	−0.891879	−0.445940	+	0.895063i	$0.647130\pi$
$522$	1994.62	0.167246
$523$	20727.8	1.73301	0.866503	−	0.499172i	$-0.166362\pi$
$523$	20727.8	1.73301	0.866503	+	0.499172i	$0.166362\pi$
$524$	−29630.9	−2.47029
$525$	0	0
$526$	−884.760	−0.0733410
$527$	−10130.0	−0.837320
$528$	58077.2	4.78690
$529$	−5320.66	−0.437302
$530$	0	0
$531$	−10273.5	−0.839607
$532$	8370.99	0.682196
$533$	17273.7	1.40376
$534$	−1588.53	−0.128731
$535$	0	0
$536$	−29141.9	−2.34839
$537$	−18411.4	−1.47954
$538$	−34560.1	−2.76950
$539$	18445.4	1.47402
$540$	0	0
$541$	−4680.36	−0.371949	−0.185974	−	0.982555i	$-0.559544\pi$
$541$	−4680.36	−0.371949	−0.185974	+	0.982555i	$0.559544\pi$
$542$	2494.35	0.197678
$543$	16394.3	1.29566
$544$	17786.5	1.40182
$545$	0	0
$546$	12288.6	0.963196
$547$	−8552.59	−0.668524	−0.334262	−	0.942480i	$-0.608487\pi$
$547$	−8552.59	−0.668524	−0.334262	+	0.942480i	$0.608487\pi$
$548$	−25474.3	−1.98578
$549$	−10986.1	−0.854052
$550$	0	0
$551$	−1986.04	−0.153553
$552$	−30545.9	−2.35529
$553$	−5624.25	−0.432491
$554$	−32424.3	−2.48660
$555$	0	0
$556$	10572.3	0.806409
$557$	−10564.2	−0.803629	−0.401814	−	0.915721i	$-0.631620\pi$
$557$	−10564.2	−0.803629	−0.401814	+	0.915721i	$0.631620\pi$
$558$	−12412.1	−0.941662
$559$	−8276.21	−0.626201
$560$	0	0
$561$	−21711.6	−1.63399
$562$	21649.1	1.62493
$563$	−16624.5	−1.24447	−0.622236	−	0.782829i	$-0.713776\pi$
$563$	−16624.5	−1.24447	−0.622236	+	0.782829i	$0.713776\pi$
$564$	25220.2	1.88291
$565$	0	0
$566$	−18563.5	−1.37859
$567$	−5809.52	−0.430294
$568$	−63341.8	−4.67916
$569$	−9400.24	−0.692581	−0.346290	−	0.938127i	$-0.612559\pi$
$569$	−9400.24	−0.692581	−0.346290	+	0.938127i	$0.612559\pi$
$570$	0	0
$571$	8882.86	0.651026	0.325513	−	0.945537i	$-0.394463\pi$
$571$	8882.86	0.651026	0.325513	+	0.945537i	$0.394463\pi$
$572$	−68209.0	−4.98595
$573$	−15653.2	−1.14122
$574$	−9843.81	−0.715806
$575$	0	0
$576$	5943.23	0.429921
$577$	−17503.7	−1.26289	−0.631447	−	0.775419i	$-0.717539\pi$
$577$	−17503.7	−1.26289	−0.631447	+	0.775419i	$0.717539\pi$
$578$	9184.51	0.660944
$579$	−27713.2	−1.98916
$580$	0	0
$581$	8244.74	0.588725
$582$	5819.28	0.414462
$583$	22226.1	1.57892
$584$	52495.7	3.71967
$585$	0	0
$586$	−5537.26	−0.390345
$587$	9109.83	0.640550	0.320275	−	0.947325i	$-0.396225\pi$
$587$	9109.83	0.640550	0.320275	+	0.947325i	$0.396225\pi$
$588$	36747.9	2.57731
$589$	12358.7	0.864568
$590$	0	0
$591$	−9502.91	−0.661417
$592$	−18976.1	−1.31742
$593$	−15168.7	−1.05043	−0.525213	−	0.850971i	$-0.676014\pi$
$593$	−15168.7	−1.05043	−0.525213	+	0.850971i	$0.676014\pi$
$594$	27832.6	1.92254
$595$	0	0
$596$	28410.2	1.95256
$597$	28506.6	1.95427
$598$	25153.6	1.72008
$599$	9963.96	0.679660	0.339830	−	0.940487i	$-0.389630\pi$
$599$	9963.96	0.679660	0.339830	+	0.940487i	$0.389630\pi$
$600$	0	0
$601$	−15546.7	−1.05518	−0.527589	−	0.849499i	$-0.676904\pi$
$601$	−15546.7	−1.05518	−0.527589	+	0.849499i	$0.676904\pi$
$602$	4716.40	0.319312
$603$	6603.77	0.445981
$604$	58965.1	3.97228
$605$	0	0
$606$	14308.4	0.959138
$607$	13532.0	0.904856	0.452428	−	0.891801i	$-0.350558\pi$
$607$	13532.0	0.904856	0.452428	+	0.891801i	$0.350558\pi$
$608$	−21699.7	−1.44744
$609$	1172.28	0.0780019
$610$	0	0
$611$	−12101.5	−0.801269
$612$	−14199.6	−0.937886
$613$	−3618.68	−0.238429	−0.119215	−	0.992868i	$-0.538038\pi$
$613$	−3618.68	−0.238429	−0.119215	+	0.992868i	$0.538038\pi$
$614$	3548.02	0.233203
$615$	0	0
$616$	22649.9	1.48148
$617$	17669.4	1.15291	0.576455	−	0.817129i	$-0.304436\pi$
$617$	17669.4	1.15291	0.576455	+	0.817129i	$0.304436\pi$
$618$	4480.80	0.291657
$619$	−20897.7	−1.35695	−0.678474	−	0.734624i	$-0.737358\pi$
$619$	−20897.7	−1.35695	−0.678474	+	0.734624i	$0.737358\pi$
$620$	0	0
$621$	−7241.86	−0.467964
$622$	−4323.33	−0.278697
$623$	−306.481	−0.0197093
$624$	−55519.1	−3.56177
$625$	0	0
$626$	−55199.7	−3.52432
$627$	26488.5	1.68716
$628$	6223.14	0.395430
$629$	7094.05	0.449695
$630$	0	0
$631$	−10549.0	−0.665529	−0.332765	−	0.943010i	$-0.607981\pi$
$631$	−10549.0	−0.665529	−0.332765	+	0.943010i	$0.607981\pi$
$632$	51363.5	3.23280
$633$	−29743.2	−1.86759
$634$	31728.7	1.98755
$635$	0	0
$636$	44280.1	2.76072
$637$	−17632.9	−1.09677
$638$	−9222.13	−0.572269
$639$	14353.7	0.888615
$640$	0	0
$641$	−3620.31	−0.223079	−0.111540	−	0.993760i	$-0.535578\pi$
$641$	−3620.31	−0.223079	−0.111540	+	0.993760i	$0.535578\pi$
$642$	24899.6	1.53070
$643$	−7456.81	−0.457337	−0.228669	−	0.973504i	$-0.573437\pi$
$643$	−7456.81	−0.457337	−0.228669	+	0.973504i	$0.573437\pi$
$644$	−10113.9	−0.618854
$645$	0	0
$646$	20038.5	1.22044
$647$	23585.7	1.43315	0.716576	−	0.697509i	$-0.245708\pi$
$647$	23585.7	1.43315	0.716576	+	0.697509i	$0.245708\pi$
$648$	53055.5	3.21638
$649$	47499.4	2.87290
$650$	0	0
$651$	−7294.85	−0.439182
$652$	17280.9	1.03800
$653$	11910.8	0.713791	0.356895	−	0.934144i	$-0.383835\pi$
$653$	11910.8	0.713791	0.356895	+	0.934144i	$0.383835\pi$
$654$	−12647.4	−0.756196
$655$	0	0
$656$	44473.6	2.64696
$657$	−11895.9	−0.706400
$658$	6896.35	0.408583
$659$	2497.06	0.147605	0.0738024	−	0.997273i	$-0.476487\pi$
$659$	2497.06	0.147605	0.0738024	+	0.997273i	$0.476487\pi$
$660$	0	0
$661$	19274.6	1.13418	0.567091	−	0.823655i	$-0.308069\pi$
$661$	19274.6	1.13418	0.567091	+	0.823655i	$0.308069\pi$
$662$	−27319.3	−1.60392
$663$	20755.3	1.21579
$664$	−75295.2	−4.40063
$665$	0	0
$666$	8692.27	0.505733
$667$	2399.54	0.139296
$668$	48789.4	2.82593
$669$	18573.0	1.07336
$670$	0	0
$671$	50794.1	2.92233
$672$	12808.5	0.735266
$673$	10560.6	0.604875	0.302438	−	0.953169i	$-0.402200\pi$
$673$	10560.6	0.604875	0.302438	+	0.953169i	$0.402200\pi$
$674$	−34652.1	−1.98034
$675$	0	0
$676$	23086.4	1.31352
$677$	3316.76	0.188292	0.0941459	−	0.995558i	$-0.469988\pi$
$677$	3316.76	0.188292	0.0941459	+	0.995558i	$0.469988\pi$
$678$	−9248.42	−0.523869
$679$	1122.74	0.0634561
$680$	0	0
$681$	−5170.12	−0.290924
$682$	57387.4	3.22211
$683$	−28395.1	−1.59079	−0.795393	−	0.606094i	$-0.792735\pi$
$683$	−28395.1	−1.59079	−0.795393	+	0.606094i	$0.792735\pi$
$684$	17323.7	0.968406
$685$	0	0
$686$	21448.2	1.19373
$687$	32177.9	1.78699
$688$	−21308.3	−1.18077
$689$	−21247.1	−1.17482
$690$	0	0
$691$	13485.0	0.742391	0.371196	−	0.928555i	$-0.378948\pi$
$691$	13485.0	0.742391	0.371196	+	0.928555i	$0.378948\pi$
$692$	−42754.0	−2.34865
$693$	−5132.63	−0.281346
$694$	−21196.4	−1.15937
$695$	0	0
$696$	−10705.9	−0.583052
$697$	−16626.1	−0.903526
$698$	21305.7	1.15535
$699$	−6440.55	−0.348503
$700$	0	0
$701$	−14838.8	−0.799505	−0.399753	−	0.916623i	$-0.630904\pi$
$701$	−14838.8	−0.799505	−0.399753	+	0.916623i	$0.630904\pi$
$702$	−26606.7	−1.43049
$703$	−8654.84	−0.464329
$704$	−27478.5	−1.47107
$705$	0	0
$706$	−9445.72	−0.503533
$707$	2760.57	0.146849
$708$	94631.0	5.02324
$709$	10329.0	0.547130	0.273565	−	0.961853i	$-0.411797\pi$
$709$	10329.0	0.547130	0.273565	+	0.961853i	$0.411797\pi$
$710$	0	0
$711$	−11639.4	−0.613939
$712$	2798.94	0.147324
$713$	−14931.8	−0.784293
$714$	−11827.9	−0.619957
$715$	0	0
$716$	55672.7	2.90584
$717$	12469.1	0.649465
$718$	−65166.3	−3.38717
$719$	15242.7	0.790624	0.395312	−	0.918547i	$-0.370637\pi$
$719$	15242.7	0.790624	0.395312	+	0.918547i	$0.370637\pi$
$720$	0	0
$721$	864.499	0.0446541
$722$	11305.8	0.582765
$723$	−28467.7	−1.46435
$724$	−49573.2	−2.54471
$725$	0	0
$726$	79012.9	4.03918
$727$	25276.3	1.28947	0.644735	−	0.764406i	$-0.276968\pi$
$727$	25276.3	1.28947	0.644735	+	0.764406i	$0.276968\pi$
$728$	−21652.2	−1.10231
$729$	2959.25	0.150346
$730$	0	0
$731$	7965.94	0.403052
$732$	101195.	5.10966
$733$	−2020.15	−0.101795	−0.0508977	−	0.998704i	$-0.516208\pi$
$733$	−2020.15	−0.101795	−0.0508977	+	0.998704i	$0.516208\pi$
$734$	−27973.9	−1.40672
$735$	0	0
$736$	26217.7	1.31304
$737$	−30532.5	−1.52602
$738$	−20371.7	−1.01612
$739$	−13269.9	−0.660540	−0.330270	−	0.943886i	$-0.607140\pi$
$739$	−13269.9	−0.660540	−0.330270	+	0.943886i	$0.607140\pi$
$740$	0	0
$741$	−25321.8	−1.25536
$742$	12108.2	0.599064
$743$	19031.0	0.939675	0.469837	−	0.882753i	$-0.344313\pi$
$743$	19031.0	0.939675	0.469837	+	0.882753i	$0.344313\pi$
$744$	66620.3	3.28282
$745$	0	0
$746$	9421.50	0.462394
$747$	17062.5	0.835720
$748$	65651.9	3.20919
$749$	4803.98	0.234357
$750$	0	0
$751$	38291.2	1.86054	0.930271	−	0.366872i	$-0.119571\pi$
$751$	38291.2	1.86054	0.930271	+	0.366872i	$0.119571\pi$
$752$	−31157.2	−1.51089
$753$	−37527.1	−1.81616
$754$	8815.94	0.425806
$755$	0	0
$756$	10698.1	0.514666
$757$	−17281.3	−0.829723	−0.414861	−	0.909885i	$-0.636170\pi$
$757$	−17281.3	−0.829723	−0.414861	+	0.909885i	$0.636170\pi$
$758$	−32064.4	−1.53645
$759$	−32003.5	−1.53051
$760$	0	0
$761$	−4698.24	−0.223799	−0.111899	−	0.993720i	$-0.535693\pi$
$761$	−4698.24	−0.223799	−0.111899	+	0.993720i	$0.535693\pi$
$762$	−84144.6	−4.00031
$763$	−2440.11	−0.115777
$764$	47332.3	2.24139
$765$	0	0
$766$	−6697.71	−0.315924
$767$	−45407.3	−2.13763
$768$	29026.7	1.36382
$769$	10247.2	0.480523	0.240262	−	0.970708i	$-0.422767\pi$
$769$	10247.2	0.480523	0.240262	+	0.970708i	$0.422767\pi$
$770$	0	0
$771$	4773.40	0.222970
$772$	83799.5	3.90675
$773$	−8085.14	−0.376200	−0.188100	−	0.982150i	$-0.560233\pi$
$773$	−8085.14	−0.376200	−0.188100	+	0.982150i	$0.560233\pi$
$774$	9760.58	0.453277
$775$	0	0
$776$	−10253.4	−0.474324
$777$	5108.61	0.235869
$778$	−40603.9	−1.87110
$779$	20284.0	0.932928
$780$	0	0
$781$	−66364.4	−3.04060
$782$	−24210.6	−1.10712
$783$	−2538.16	−0.115845
$784$	−45398.6	−2.06809
$785$	0	0
$786$	−51079.0	−2.31797
$787$	−18275.2	−0.827754	−0.413877	−	0.910333i	$-0.635826\pi$
$787$	−18275.2	−0.827754	−0.413877	+	0.910333i	$0.635826\pi$
$788$	28735.0	1.29904
$789$	−1076.12	−0.0485562
$790$	0	0
$791$	−1784.34	−0.0802069
$792$	46873.8	2.10302
$793$	−48556.8	−2.17440
$794$	−39960.3	−1.78607
$795$	0	0
$796$	−86198.6	−3.83822
$797$	−9583.07	−0.425910	−0.212955	−	0.977062i	$-0.568309\pi$
$797$	−9583.07	−0.425910	−0.212955	+	0.977062i	$0.568309\pi$
$798$	14430.2	0.640132
$799$	11647.8	0.515734
$800$	0	0
$801$	−634.261	−0.0279782
$802$	−12419.5	−0.546816
$803$	55000.8	2.41711
$804$	−60828.6	−2.66823
$805$	0	0
$806$	−54859.7	−2.39746
$807$	−42034.8	−1.83358
$808$	−25211.0	−1.09767
$809$	−23688.5	−1.02947	−0.514735	−	0.857349i	$-0.672110\pi$
$809$	−23688.5	−1.02947	−0.514735	+	0.857349i	$0.672110\pi$
$810$	0	0
$811$	−37691.0	−1.63195	−0.815974	−	0.578088i	$-0.803799\pi$
$811$	−37691.0	−1.63195	−0.815974	+	0.578088i	$0.803799\pi$
$812$	−3544.75	−0.153197
$813$	3033.84	0.130875
$814$	−40188.6	−1.73048
$815$	0	0
$816$	53437.7	2.29252
$817$	−9718.55	−0.416168
$818$	−13743.7	−0.587454
$819$	4906.56	0.209340
$820$	0	0
$821$	35720.0	1.51844	0.759218	−	0.650836i	$-0.225582\pi$
$821$	35720.0	1.51844	0.759218	+	0.650836i	$0.225582\pi$
$822$	−43913.6	−1.86334
$823$	−2501.23	−0.105939	−0.0529693	−	0.998596i	$-0.516869\pi$
$823$	−2501.23	−0.105939	−0.0529693	+	0.998596i	$0.516869\pi$
$824$	−7895.05	−0.333783
$825$	0	0
$826$	25876.4	1.09002
$827$	21356.3	0.897983	0.448991	−	0.893536i	$-0.351783\pi$
$827$	21356.3	0.897983	0.448991	+	0.893536i	$0.351783\pi$
$828$	−20930.6	−0.878489
$829$	−21251.7	−0.890353	−0.445176	−	0.895443i	$-0.646859\pi$
$829$	−21251.7	−0.890353	−0.445176	+	0.895443i	$0.646859\pi$
$830$	0	0
$831$	−39437.2	−1.64628
$832$	26268.2	1.09457
$833$	16971.9	0.705932
$834$	18224.9	0.756685
$835$	0	0
$836$	−80096.2	−3.31362
$837$	15794.4	0.652252
$838$	34418.4	1.41881
$839$	−18259.4	−0.751354	−0.375677	−	0.926751i	$-0.622590\pi$
$839$	−18259.4	−0.751354	−0.375677	+	0.926751i	$0.622590\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	−82795.1	−3.38873
$843$	26331.4	1.07580
$844$	89937.7	3.66799
$845$	0	0
$846$	14272.0	0.580001
$847$	15244.3	0.618417
$848$	−54703.9	−2.21526
$849$	−22578.5	−0.912713
$850$	0	0
$851$	10456.8	0.421216
$852$	−132215.	−5.31645
$853$	28424.6	1.14096	0.570481	−	0.821311i	$-0.306757\pi$
$853$	28424.6	1.14096	0.570481	+	0.821311i	$0.306757\pi$
$854$	27671.3	1.10877
$855$	0	0
$856$	−43872.4	−1.75178
$857$	9320.80	0.371520	0.185760	−	0.982595i	$-0.440525\pi$
$857$	9320.80	0.371520	0.185760	+	0.982595i	$0.440525\pi$
$858$	−117581.	−4.67851
$859$	21132.4	0.839380	0.419690	−	0.907668i	$-0.362139\pi$
$859$	21132.4	0.839380	0.419690	+	0.907668i	$0.362139\pi$
$860$	0	0
$861$	−11972.9	−0.473907
$862$	6357.23	0.251193
$863$	−21301.0	−0.840203	−0.420102	−	0.907477i	$-0.638006\pi$
$863$	−21301.0	−0.840203	−0.420102	+	0.907477i	$0.638006\pi$
$864$	−27732.3	−1.09198
$865$	0	0
$866$	−57615.7	−2.26081
$867$	11171.0	0.437585
$868$	22058.2	0.862564
$869$	53814.6	2.10073
$870$	0	0
$871$	29187.7	1.13546
$872$	22284.4	0.865417
$873$	2323.50	0.0900785
$874$	29537.2	1.14315
$875$	0	0
$876$	109576.	4.22628
$877$	−11419.6	−0.439697	−0.219848	−	0.975534i	$-0.570556\pi$
$877$	−11419.6	−0.439697	−0.219848	+	0.975534i	$0.570556\pi$
$878$	−13985.7	−0.537578
$879$	−6734.88	−0.258432
$880$	0	0
$881$	15004.2	0.573784	0.286892	−	0.957963i	$-0.407378\pi$
$881$	15004.2	0.573784	0.286892	+	0.957963i	$0.407378\pi$
$882$	20795.5	0.793900
$883$	4234.36	0.161379	0.0806894	−	0.996739i	$-0.474288\pi$
$883$	4234.36	0.161379	0.0806894	+	0.996739i	$0.474288\pi$
$884$	−62760.2	−2.38784
$885$	0	0
$886$	41763.3	1.58359
$887$	−50237.9	−1.90172	−0.950860	−	0.309622i	$-0.899798\pi$
$887$	−50237.9	−1.90172	−0.950860	+	0.309622i	$0.899798\pi$
$888$	−46654.5	−1.76309
$889$	−16234.4	−0.612467
$890$	0	0
$891$	55587.2	2.09006
$892$	−56161.3	−2.10809
$893$	−14210.5	−0.532516
$894$	48974.6	1.83217
$895$	0	0
$896$	1192.70	0.0444702
$897$	30593.9	1.13880
$898$	9598.89	0.356703
$899$	−5233.37	−0.194152
$900$	0	0
$901$	20450.6	0.756168
$902$	94188.6	3.47687
$903$	5736.48	0.211404
$904$	16295.5	0.599534
$905$	0	0
$906$	101646.	3.72735
$907$	31312.6	1.14633	0.573164	−	0.819441i	$-0.305716\pi$
$907$	31312.6	1.14633	0.573164	+	0.819441i	$0.305716\pi$
$908$	15633.5	0.571382
$909$	5713.00	0.208458
$910$	0	0
$911$	872.220	0.0317211	0.0158606	−	0.999874i	$-0.494951\pi$
$911$	872.220	0.0317211	0.0158606	+	0.999874i	$0.494951\pi$
$912$	−65194.8	−2.36712
$913$	−78888.2	−2.85960
$914$	−31189.9	−1.12874
$915$	0	0
$916$	−97299.7	−3.50969
$917$	−9854.87	−0.354893
$918$	25609.2	0.920731
$919$	−26902.3	−0.965641	−0.482820	−	0.875719i	$-0.660388\pi$
$919$	−26902.3	−0.965641	−0.482820	+	0.875719i	$0.660388\pi$
$920$	0	0
$921$	4315.40	0.154394
$922$	10223.2	0.365166
$923$	63441.3	2.26240
$924$	47277.7	1.68325
$925$	0	0
$926$	56634.0	2.00984
$927$	1789.08	0.0633884
$928$	9188.90	0.325044
$929$	−45849.6	−1.61924	−0.809621	−	0.586952i	$-0.800328\pi$
$929$	−45849.6	−1.61924	−0.809621	+	0.586952i	$0.800328\pi$
$930$	0	0
$931$	−20705.9	−0.728904
$932$	19475.0	0.684469
$933$	−5258.40	−0.184515
$934$	45674.4	1.60012
$935$	0	0
$936$	−44809.2	−1.56478
$937$	−22736.8	−0.792722	−0.396361	−	0.918095i	$-0.629727\pi$
$937$	−22736.8	−0.792722	−0.396361	+	0.918095i	$0.629727\pi$
$938$	−16633.3	−0.578994
$939$	−67138.5	−2.33331
$940$	0	0
$941$	−46907.0	−1.62500	−0.812500	−	0.582961i	$-0.801894\pi$
$941$	−46907.0	−1.62500	−0.812500	+	0.582961i	$0.801894\pi$
$942$	10727.7	0.371048
$943$	−24507.2	−0.846305
$944$	−116908.	−4.03075
$945$	0	0
$946$	−45128.0	−1.55099
$947$	−14219.4	−0.487928	−0.243964	−	0.969784i	$-0.578448\pi$
$947$	−14219.4	−0.487928	−0.243964	+	0.969784i	$0.578448\pi$
$948$	107212.	3.67310
$949$	−52578.2	−1.79848
$950$	0	0
$951$	38591.2	1.31588
$952$	20840.5	0.709501
$953$	50695.8	1.72319	0.861594	−	0.507597i	$-0.169466\pi$
$953$	50695.8	1.72319	0.861594	+	0.507597i	$0.169466\pi$
$954$	25057.9	0.850397
$955$	0	0
$956$	−37704.1	−1.27556
$957$	−11216.7	−0.378877
$958$	−102821.	−3.46763
$959$	−8472.42	−0.285286
$960$	0	0
$961$	2775.13	0.0931533
$962$	38418.5	1.28759
$963$	9941.82	0.332680
$964$	86080.9	2.87602
$965$	0	0
$966$	−17434.7	−0.580695
$967$	15022.8	0.499586	0.249793	−	0.968299i	$-0.419638\pi$
$967$	15022.8	0.499586	0.249793	+	0.968299i	$0.419638\pi$
$968$	−139218.	−4.62257
$969$	24372.5	0.808006
$970$	0	0
$971$	15417.1	0.509534	0.254767	−	0.967003i	$-0.418001\pi$
$971$	15417.1	0.509534	0.254767	+	0.967003i	$0.418001\pi$
$972$	65441.3	2.15950
$973$	3516.20	0.115852
$974$	39272.5	1.29196
$975$	0	0
$976$	−125017.	−4.10009
$977$	−35120.3	−1.15005	−0.575024	−	0.818136i	$-0.695007\pi$
$977$	−35120.3	−1.15005	−0.575024	+	0.818136i	$0.695007\pi$
$978$	29789.6	0.973994
$979$	2932.50	0.0957336
$980$	0	0
$981$	−5049.81	−0.164351
$982$	−101270.	−3.29090
$983$	−2757.23	−0.0894628	−0.0447314	−	0.998999i	$-0.514243\pi$
$983$	−2757.23	−0.0894628	−0.0447314	+	0.998999i	$0.514243\pi$
$984$	109342.	3.54239
$985$	0	0
$986$	−8485.43	−0.274068
$987$	8387.92	0.270507
$988$	76568.3	2.46555
$989$	11742.0	0.377526
$990$	0	0
$991$	14086.1	0.451525	0.225762	−	0.974182i	$-0.427513\pi$
$991$	14086.1	0.451525	0.225762	+	0.974182i	$0.427513\pi$
$992$	−57180.6	−1.83013
$993$	−33228.1	−1.06189
$994$	−36153.6	−1.15364
$995$	0	0
$996$	−157166.	−4.99998
$997$	20962.8	0.665897	0.332948	−	0.942945i	$-0.391957\pi$
$997$	20962.8	0.665897	0.332948	+	0.942945i	$0.391957\pi$
$998$	53455.9	1.69551
$999$	−11060.9	−0.350302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.4.a.f.1.2		7
5.4	even	2		145.4.a.d.1.6	✓	7
15.14	odd	2		1305.4.a.l.1.2		7
20.19	odd	2		2320.4.a.s.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.4.a.d.1.6	✓	7	5.4	even	2
725.4.a.f.1.2		7	1.1	even	1	trivial
1305.4.a.l.1.2		7	15.14	odd	2
2320.4.a.s.1.2		7	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q-5.21256 q^{2} -6.33996 q^{3} +19.1708 q^{4} +33.0474 q^{6} +6.37598 q^{7} -58.2287 q^{8} +13.1951 q^{9} +O(q^{10})\)	\(q-5.21256 q^{2} -6.33996 q^{3} +19.1708 q^{4} +33.0474 q^{6} +6.37598 q^{7} -58.2287 q^{8} +13.1951 q^{9} -61.0073 q^{11} -121.542 q^{12} +58.3202 q^{13} -33.2352 q^{14} +150.154 q^{16} -56.1338 q^{17} -68.7802 q^{18} +68.4840 q^{19} -40.4234 q^{21} +318.005 q^{22} -82.7426 q^{23} +369.167 q^{24} -303.998 q^{26} +87.5227 q^{27} +122.233 q^{28} -29.0000 q^{29} +180.461 q^{31} -316.859 q^{32} +386.784 q^{33} +292.601 q^{34} +252.960 q^{36} -126.378 q^{37} -356.977 q^{38} -369.748 q^{39} +296.186 q^{41} +210.710 q^{42} -141.910 q^{43} -1169.56 q^{44} +431.301 q^{46} -207.501 q^{47} -951.971 q^{48} -302.347 q^{49} +355.886 q^{51} +1118.05 q^{52} -364.318 q^{53} -456.218 q^{54} -371.265 q^{56} -434.186 q^{57} +151.164 q^{58} -778.586 q^{59} -832.590 q^{61} -940.664 q^{62} +84.1314 q^{63} +450.413 q^{64} -2016.14 q^{66} +500.473 q^{67} -1076.13 q^{68} +524.585 q^{69} +1087.81 q^{71} -768.331 q^{72} -901.544 q^{73} +658.751 q^{74} +1312.90 q^{76} -388.981 q^{77} +1927.33 q^{78} -882.100 q^{79} -911.157 q^{81} -1543.89 q^{82} +1293.09 q^{83} -774.951 q^{84} +739.714 q^{86} +183.859 q^{87} +3552.38 q^{88} -48.0680 q^{89} +371.848 q^{91} -1586.25 q^{92} -1144.11 q^{93} +1081.61 q^{94} +2008.87 q^{96} +176.089 q^{97} +1576.00 q^{98} -804.996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 6 q^{2} - q^{3} + 52 q^{4} + 3 q^{6} - 17 q^{7} - 138 q^{8} + 118 q^{9}+O(q^{10}) \) 7 * q - 6 * q^2 - q^3 + 52 * q^4 + 3 * q^6 - 17 * q^7 - 138 * q^8 + 118 * q^9	\( 7 q - 6 q^{2} - q^{3} + 52 q^{4} + 3 q^{6} - 17 q^{7} - 138 q^{8} + 118 q^{9} + 2 q^{11} + 77 q^{12} + 17 q^{13} + 361 q^{14} + 372 q^{16} - 95 q^{17} - 261 q^{18} + 94 q^{19} - 100 q^{21} - 190 q^{22} - 327 q^{23} - 117 q^{24} - 115 q^{26} + 236 q^{27} + 67 q^{28} - 203 q^{29} + 169 q^{31} - 890 q^{32} - 272 q^{33} + 377 q^{34} + 2443 q^{36} + 500 q^{37} - 282 q^{38} + 1129 q^{39} + 1208 q^{41} + 1892 q^{42} + 1517 q^{43} - 734 q^{44} - 1413 q^{46} - 1974 q^{47} + 2637 q^{48} + 794 q^{49} - 190 q^{51} + 2063 q^{52} + 255 q^{53} - 5052 q^{54} + 2057 q^{56} - 94 q^{57} + 174 q^{58} + 177 q^{59} - 705 q^{61} + 807 q^{62} - 200 q^{63} + 332 q^{64} - 2768 q^{66} + 744 q^{67} + 2323 q^{68} + 1551 q^{69} + 2024 q^{71} - 6897 q^{72} + 1405 q^{73} + 82 q^{74} - 18 q^{76} - 3402 q^{77} + 5311 q^{78} - 2157 q^{79} + 1099 q^{81} - 2266 q^{82} + 158 q^{83} - 4372 q^{84} + 3033 q^{86} + 29 q^{87} + 1250 q^{88} - 2244 q^{89} + 3376 q^{91} - 2599 q^{92} - 586 q^{93} + 2212 q^{94} - 5077 q^{96} + 727 q^{97} + 1567 q^{98} + 416 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 - q^3 + 52 * q^4 + 3 * q^6 - 17 * q^7 - 138 * q^8 + 118 * q^9 + 2 * q^11 + 77 * q^12 + 17 * q^13 + 361 * q^14 + 372 * q^16 - 95 * q^17 - 261 * q^18 + 94 * q^19 - 100 * q^21 - 190 * q^22 - 327 * q^23 - 117 * q^24 - 115 * q^26 + 236 * q^27 + 67 * q^28 - 203 * q^29 + 169 * q^31 - 890 * q^32 - 272 * q^33 + 377 * q^34 + 2443 * q^36 + 500 * q^37 - 282 * q^38 + 1129 * q^39 + 1208 * q^41 + 1892 * q^42 + 1517 * q^43 - 734 * q^44 - 1413 * q^46 - 1974 * q^47 + 2637 * q^48 + 794 * q^49 - 190 * q^51 + 2063 * q^52 + 255 * q^53 - 5052 * q^54 + 2057 * q^56 - 94 * q^57 + 174 * q^58 + 177 * q^59 - 705 * q^61 + 807 * q^62 - 200 * q^63 + 332 * q^64 - 2768 * q^66 + 744 * q^67 + 2323 * q^68 + 1551 * q^69 + 2024 * q^71 - 6897 * q^72 + 1405 * q^73 + 82 * q^74 - 18 * q^76 - 3402 * q^77 + 5311 * q^78 - 2157 * q^79 + 1099 * q^81 - 2266 * q^82 + 158 * q^83 - 4372 * q^84 + 3033 * q^86 + 29 * q^87 + 1250 * q^88 - 2244 * q^89 + 3376 * q^91 - 2599 * q^92 - 586 * q^93 + 2212 * q^94 - 5077 * q^96 + 727 * q^97 + 1567 * q^98 + 416 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more