LMFDB - Embedded newform 975.4.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,4,Mod(1,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("975.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	975.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:	$57.5268622556$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.3144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 16x - 8 $ x^3 - x^2 - 16*x - 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.20905$ of defining polynomial
Character	$\chi$	$=$	975.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.20905 q^{2} -3.00000 q^{3} +9.71610 q^{4} +12.6271 q^{6} +11.2543 q^{7} -7.22315 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.20905 q^{2} -3.00000 q^{3} +9.71610 q^{4} +12.6271 q^{6} +11.2543 q^{7} -7.22315 q^{8} +9.00000 q^{9} +25.8785 q^{11} -29.1483 q^{12} -13.0000 q^{13} -47.3699 q^{14} -47.3262 q^{16} +20.3276 q^{17} -37.8814 q^{18} +154.712 q^{19} -33.7629 q^{21} -108.924 q^{22} +180.418 q^{23} +21.6695 q^{24} +54.7176 q^{26} -27.0000 q^{27} +109.348 q^{28} -20.4522 q^{29} +266.424 q^{31} +256.984 q^{32} -77.6355 q^{33} -85.5599 q^{34} +87.4449 q^{36} -115.984 q^{37} -651.190 q^{38} +39.0000 q^{39} +391.184 q^{41} +142.110 q^{42} -151.407 q^{43} +251.438 q^{44} -759.390 q^{46} +467.365 q^{47} +141.979 q^{48} -216.341 q^{49} -60.9828 q^{51} -126.309 q^{52} -79.9842 q^{53} +113.644 q^{54} -81.2915 q^{56} -464.136 q^{57} +86.0843 q^{58} -873.710 q^{59} -187.068 q^{61} -1121.39 q^{62} +101.289 q^{63} -703.047 q^{64} +326.772 q^{66} +609.204 q^{67} +197.505 q^{68} -541.255 q^{69} +248.038 q^{71} -65.0084 q^{72} -852.765 q^{73} +488.181 q^{74} +1503.20 q^{76} +291.244 q^{77} -164.153 q^{78} -331.221 q^{79} +81.0000 q^{81} -1646.51 q^{82} +435.432 q^{83} -328.044 q^{84} +637.281 q^{86} +61.3566 q^{87} -186.924 q^{88} +259.233 q^{89} -146.306 q^{91} +1752.96 q^{92} -799.273 q^{93} -1967.16 q^{94} -770.951 q^{96} -1225.17 q^{97} +910.589 q^{98} +232.907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - 9 q^{3} + 10 q^{4} + 6 q^{6} - 30 q^{7} + 6 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - 9 * q^3 + 10 * q^4 + 6 * q^6 - 30 * q^7 + 6 * q^8 + 27 * q^9	$ 3 q - 2 q^{2} - 9 q^{3} + 10 q^{4} + 6 q^{6} - 30 q^{7} + 6 q^{8} + 27 q^{9} - 16 q^{11} - 30 q^{12} - 39 q^{13} - 176 q^{14} - 110 q^{16} + 146 q^{17} - 18 q^{18} + 94 q^{19} + 90 q^{21} + 56 q^{22} + 48 q^{23} - 18 q^{24} + 26 q^{26} - 81 q^{27} - 80 q^{28} - 2 q^{29} + 302 q^{31} - 154 q^{32} + 48 q^{33} + 164 q^{34} + 90 q^{36} - 374 q^{37} - 312 q^{38} + 117 q^{39} + 480 q^{41} + 528 q^{42} + 260 q^{43} + 712 q^{44} - 1104 q^{46} + 24 q^{47} + 330 q^{48} + 447 q^{49} - 438 q^{51} - 130 q^{52} + 678 q^{53} + 54 q^{54} + 96 q^{56} - 282 q^{57} + 628 q^{58} - 1788 q^{59} + 230 q^{61} - 1952 q^{62} - 270 q^{63} - 750 q^{64} - 168 q^{66} - 74 q^{67} + 460 q^{68} - 144 q^{69} - 948 q^{71} + 54 q^{72} + 222 q^{73} + 1724 q^{74} + 2392 q^{76} - 112 q^{77} - 78 q^{78} - 24 q^{79} + 243 q^{81} - 564 q^{82} + 796 q^{83} + 240 q^{84} + 1800 q^{86} + 6 q^{87} - 1608 q^{88} + 1436 q^{89} + 390 q^{91} + 1296 q^{92} - 906 q^{93} - 1920 q^{94} + 462 q^{96} - 3242 q^{97} + 5070 q^{98} - 144 q^{99}+O(q^{100}) $ 3 * q - 2 * q^2 - 9 * q^3 + 10 * q^4 + 6 * q^6 - 30 * q^7 + 6 * q^8 + 27 * q^9 - 16 * q^11 - 30 * q^12 - 39 * q^13 - 176 * q^14 - 110 * q^16 + 146 * q^17 - 18 * q^18 + 94 * q^19 + 90 * q^21 + 56 * q^22 + 48 * q^23 - 18 * q^24 + 26 * q^26 - 81 * q^27 - 80 * q^28 - 2 * q^29 + 302 * q^31 - 154 * q^32 + 48 * q^33 + 164 * q^34 + 90 * q^36 - 374 * q^37 - 312 * q^38 + 117 * q^39 + 480 * q^41 + 528 * q^42 + 260 * q^43 + 712 * q^44 - 1104 * q^46 + 24 * q^47 + 330 * q^48 + 447 * q^49 - 438 * q^51 - 130 * q^52 + 678 * q^53 + 54 * q^54 + 96 * q^56 - 282 * q^57 + 628 * q^58 - 1788 * q^59 + 230 * q^61 - 1952 * q^62 - 270 * q^63 - 750 * q^64 - 168 * q^66 - 74 * q^67 + 460 * q^68 - 144 * q^69 - 948 * q^71 + 54 * q^72 + 222 * q^73 + 1724 * q^74 + 2392 * q^76 - 112 * q^77 - 78 * q^78 - 24 * q^79 + 243 * q^81 - 564 * q^82 + 796 * q^83 + 240 * q^84 + 1800 * q^86 + 6 * q^87 - 1608 * q^88 + 1436 * q^89 + 390 * q^91 + 1296 * q^92 - 906 * q^93 - 1920 * q^94 + 462 * q^96 - 3242 * q^97 + 5070 * q^98 - 144 * 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 $

$2$	−4.20905	−1.48812	−0.744062	−	0.668111i	$-0.767103\pi$
$2$	−4.20905	−1.48812	−0.744062	+	0.668111i	$0.767103\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	9.71610	1.21451
$5$	0	0
$5$	0	0
$6$	12.6271	0.859169
$7$	11.2543	0.607675	0.303838	−	0.952724i	$-0.401732\pi$
$7$	11.2543	0.607675	0.303838	+	0.952724i	$0.401732\pi$
$8$	−7.22315	−0.319221
$9$	9.00000	0.333333
$10$	0	0
$11$	25.8785	0.709333	0.354666	−	0.934993i	$-0.384594\pi$
$11$	25.8785	0.709333	0.354666	+	0.934993i	$0.384594\pi$
$12$	−29.1483	−0.701199
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−47.3699	−0.904296
$15$	0	0
$16$	−47.3262	−0.739472
$17$	20.3276	0.290010	0.145005	−	0.989431i	$-0.453680\pi$
$17$	20.3276	0.290010	0.145005	+	0.989431i	$0.453680\pi$
$18$	−37.8814	−0.496041
$19$	154.712	1.86807	0.934035	−	0.357181i	$-0.116262\pi$
$19$	154.712	1.86807	0.934035	+	0.357181i	$0.116262\pi$
$20$	0	0
$21$	−33.7629	−0.350841
$22$	−108.924	−1.05558
$23$	180.418	1.63565	0.817823	−	0.575471i	$-0.195181\pi$
$23$	180.418	1.63565	0.817823	+	0.575471i	$0.195181\pi$
$24$	21.6695	0.184302
$25$	0	0
$26$	54.7176	0.412731
$27$	−27.0000	−0.192450
$28$	109.348	0.738029
$29$	−20.4522	−0.130961	−0.0654806	−	0.997854i	$-0.520858\pi$
$29$	−20.4522	−0.130961	−0.0654806	+	0.997854i	$0.520858\pi$
$30$	0	0
$31$	266.424	1.54359	0.771794	−	0.635873i	$-0.219360\pi$
$31$	266.424	1.54359	0.771794	+	0.635873i	$0.219360\pi$
$32$	256.984	1.41965
$33$	−77.6355	−0.409534
$34$	−85.5599	−0.431571
$35$	0	0
$36$	87.4449	0.404837
$37$	−115.984	−0.515340	−0.257670	−	0.966233i	$-0.582955\pi$
$37$	−115.984	−0.515340	−0.257670	+	0.966233i	$0.582955\pi$
$38$	−651.190	−2.77992
$39$	39.0000	0.160128
$40$	0	0
$41$	391.184	1.49006	0.745032	−	0.667029i	$-0.232434\pi$
$41$	391.184	1.49006	0.745032	+	0.667029i	$0.232434\pi$
$42$	142.110	0.522095
$43$	−151.407	−0.536963	−0.268482	−	0.963285i	$-0.586522\pi$
$43$	−151.407	−0.536963	−0.268482	+	0.963285i	$0.586522\pi$
$44$	251.438	0.861494
$45$	0	0
$46$	−759.390	−2.43404
$47$	467.365	1.45047	0.725236	−	0.688500i	$-0.241731\pi$
$47$	467.365	1.45047	0.725236	+	0.688500i	$0.241731\pi$
$48$	141.979	0.426934
$49$	−216.341	−0.630731
$50$	0	0
$51$	−60.9828	−0.167437
$52$	−126.309	−0.336845
$53$	−79.9842	−0.207296	−0.103648	−	0.994614i	$-0.533051\pi$
$53$	−79.9842	−0.207296	−0.103648	+	0.994614i	$0.533051\pi$
$54$	113.644	0.286390
$55$	0	0
$56$	−81.2915	−0.193983
$57$	−464.136	−1.07853
$58$	86.0843	0.194887
$59$	−873.710	−1.92792	−0.963960	−	0.266045i	$-0.914283\pi$
$59$	−873.710	−1.92792	−0.963960	+	0.266045i	$0.914283\pi$
$60$	0	0
$61$	−187.068	−0.392649	−0.196325	−	0.980539i	$-0.562901\pi$
$61$	−187.068	−0.392649	−0.196325	+	0.980539i	$0.562901\pi$
$62$	−1121.39	−2.29705
$63$	101.289	0.202558
$64$	−703.047	−1.37314
$65$	0	0
$66$	326.772	0.609437
$67$	609.204	1.11084	0.555418	−	0.831571i	$-0.312558\pi$
$67$	609.204	1.11084	0.555418	+	0.831571i	$0.312558\pi$
$68$	197.505	0.352221
$69$	−541.255	−0.944340
$70$	0	0
$71$	248.038	0.414601	0.207301	−	0.978277i	$-0.433532\pi$
$71$	248.038	0.414601	0.207301	+	0.978277i	$0.433532\pi$
$72$	−65.0084	−0.106407
$73$	−852.765	−1.36724	−0.683621	−	0.729838i	$-0.739596\pi$
$73$	−852.765	−1.36724	−0.683621	+	0.729838i	$0.739596\pi$
$74$	488.181	0.766890
$75$	0	0
$76$	1503.20	2.26880
$77$	291.244	0.431044
$78$	−164.153	−0.238291
$79$	−331.221	−0.471712	−0.235856	−	0.971788i	$-0.575789\pi$
$79$	−331.221	−0.471712	−0.235856	+	0.971788i	$0.575789\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−1646.51	−2.21740
$83$	435.432	0.575842	0.287921	−	0.957654i	$-0.407036\pi$
$83$	435.432	0.575842	0.287921	+	0.957654i	$0.407036\pi$
$84$	−328.044	−0.426101
$85$	0	0
$86$	637.281	0.799067
$87$	61.3566	0.0756105
$88$	−186.924	−0.226434
$89$	259.233	0.308749	0.154375	−	0.988012i	$-0.450664\pi$
$89$	259.233	0.308749	0.154375	+	0.988012i	$0.450664\pi$
$90$	0	0
$91$	−146.306	−0.168539
$92$	1752.96	1.98651
$93$	−799.273	−0.891191
$94$	−1967.16	−2.15848
$95$	0	0
$96$	−770.951	−0.819634
$97$	−1225.17	−1.28245	−0.641223	−	0.767355i	$-0.721572\pi$
$97$	−1225.17	−1.28245	−0.641223	+	0.767355i	$0.721572\pi$
$98$	910.589	0.938606
$99$	232.907	0.236444
$100$	0	0
$101$	645.416	0.635855	0.317927	−	0.948115i	$-0.397013\pi$
$101$	645.416	0.635855	0.317927	+	0.948115i	$0.397013\pi$
$102$	256.680	0.249167
$103$	511.137	0.488969	0.244484	−	0.969653i	$-0.421381\pi$
$103$	511.137	0.488969	0.244484	+	0.969653i	$0.421381\pi$
$104$	93.9010	0.0885360
$105$	0	0
$106$	336.657	0.308482
$107$	−608.195	−0.549499	−0.274750	−	0.961516i	$-0.588595\pi$
$107$	−608.195	−0.549499	−0.274750	+	0.961516i	$0.588595\pi$
$108$	−262.335	−0.233733
$109$	−1300.04	−1.14239	−0.571197	−	0.820813i	$-0.693521\pi$
$109$	−1300.04	−1.14239	−0.571197	+	0.820813i	$0.693521\pi$
$110$	0	0
$111$	347.951	0.297532
$112$	−532.623	−0.449359
$113$	−42.1953	−0.0351274	−0.0175637	−	0.999846i	$-0.505591\pi$
$113$	−42.1953	−0.0351274	−0.0175637	+	0.999846i	$0.505591\pi$
$114$	1953.57	1.60499
$115$	0	0
$116$	−198.716	−0.159054
$117$	−117.000	−0.0924500
$118$	3677.49	2.86899
$119$	228.773	0.176232
$120$	0	0
$121$	−661.303	−0.496847
$122$	787.378	0.584311
$123$	−1173.55	−0.860289
$124$	2588.61	1.87471
$125$	0	0
$126$	−426.329	−0.301432
$127$	311.018	0.217310	0.108655	−	0.994080i	$-0.465346\pi$
$127$	311.018	0.217310	0.108655	+	0.994080i	$0.465346\pi$
$128$	903.291	0.623753
$129$	454.222	0.310016
$130$	0	0
$131$	2000.98	1.33456	0.667278	−	0.744809i	$-0.267459\pi$
$131$	2000.98	1.33456	0.667278	+	0.744809i	$0.267459\pi$
$132$	−754.314	−0.497384
$133$	1741.17	1.13518
$134$	−2564.17	−1.65306
$135$	0	0
$136$	−146.829	−0.0925773
$137$	−1038.53	−0.647644	−0.323822	−	0.946118i	$-0.604968\pi$
$137$	−1038.53	−0.647644	−0.323822	+	0.946118i	$0.604968\pi$
$138$	2278.17	1.40529
$139$	−2858.46	−1.74426	−0.872128	−	0.489277i	$-0.837261\pi$
$139$	−2858.46	−1.74426	−0.872128	+	0.489277i	$0.837261\pi$
$140$	0	0
$141$	−1402.09	−0.837430
$142$	−1044.00	−0.616978
$143$	−336.421	−0.196734
$144$	−425.936	−0.246491
$145$	0	0
$146$	3589.33	2.03462
$147$	649.022	0.364153
$148$	−1126.91	−0.625887
$149$	743.479	0.408780	0.204390	−	0.978890i	$-0.434479\pi$
$149$	743.479	0.408780	0.204390	+	0.978890i	$0.434479\pi$
$150$	0	0
$151$	2277.24	1.22728	0.613640	−	0.789586i	$-0.289705\pi$
$151$	2277.24	1.22728	0.613640	+	0.789586i	$0.289705\pi$
$152$	−1117.51	−0.596328
$153$	182.948	0.0966700
$154$	−1225.86	−0.641447
$155$	0	0
$156$	378.928	0.194478
$157$	−3173.51	−1.61321	−0.806605	−	0.591091i	$-0.798697\pi$
$157$	−3173.51	−1.61321	−0.806605	+	0.591091i	$0.798697\pi$
$158$	1394.12	0.701966
$159$	239.953	0.119682
$160$	0	0
$161$	2030.48	0.993941
$162$	−340.933	−0.165347
$163$	2314.65	1.11225	0.556126	−	0.831098i	$-0.312287\pi$
$163$	2314.65	1.11225	0.556126	+	0.831098i	$0.312287\pi$
$164$	3800.78	1.80970
$165$	0	0
$166$	−1832.76	−0.856925
$167$	2665.65	1.23517	0.617587	−	0.786502i	$-0.288110\pi$
$167$	2665.65	1.23517	0.617587	+	0.786502i	$0.288110\pi$
$168$	243.874	0.111996
$169$	169.000	0.0769231
$170$	0	0
$171$	1392.41	0.622690
$172$	−1471.09	−0.652148
$173$	165.243	0.0726198	0.0363099	−	0.999341i	$-0.488440\pi$
$173$	165.243	0.0726198	0.0363099	+	0.999341i	$0.488440\pi$
$174$	−258.253	−0.112518
$175$	0	0
$176$	−1224.73	−0.524532
$177$	2621.13	1.11309
$178$	−1091.13	−0.459457
$179$	712.339	0.297446	0.148723	−	0.988879i	$-0.452484\pi$
$179$	712.339	0.297446	0.148723	+	0.988879i	$0.452484\pi$
$180$	0	0
$181$	2206.53	0.906133	0.453066	−	0.891477i	$-0.350330\pi$
$181$	2206.53	0.906133	0.453066	+	0.891477i	$0.350330\pi$
$182$	615.809	0.250806
$183$	561.204	0.226696
$184$	−1303.19	−0.522132
$185$	0	0
$186$	3364.18	1.32620
$187$	526.048	0.205714
$188$	4540.96	1.76162
$189$	−303.866	−0.116947
$190$	0	0
$191$	1470.64	0.557129	0.278565	−	0.960417i	$-0.410141\pi$
$191$	1470.64	0.557129	0.278565	+	0.960417i	$0.410141\pi$
$192$	2109.14	0.792782
$193$	−369.560	−0.137832	−0.0689158	−	0.997622i	$-0.521954\pi$
$193$	−369.560	−0.137832	−0.0689158	+	0.997622i	$0.521954\pi$
$194$	5156.80	1.90844
$195$	0	0
$196$	−2101.99	−0.766031
$197$	4273.41	1.54552	0.772761	−	0.634697i	$-0.218875\pi$
$197$	4273.41	1.54552	0.772761	+	0.634697i	$0.218875\pi$
$198$	−980.315	−0.351858
$199$	4154.31	1.47985	0.739927	−	0.672687i	$-0.234860\pi$
$199$	4154.31	1.47985	0.739927	+	0.672687i	$0.234860\pi$
$200$	0	0
$201$	−1827.61	−0.641342
$202$	−2716.59	−0.946230
$203$	−230.175	−0.0795819
$204$	−592.515	−0.203355
$205$	0	0
$206$	−2151.40	−0.727646
$207$	1623.77	0.545215
$208$	615.241	0.205093
$209$	4003.71	1.32508
$210$	0	0
$211$	1231.59	0.401830	0.200915	−	0.979609i	$-0.435608\pi$
$211$	1231.59	0.401830	0.200915	+	0.979609i	$0.435608\pi$
$212$	−777.134	−0.251763
$213$	−744.114	−0.239370
$214$	2559.92	0.817723
$215$	0	0
$216$	195.025	0.0614341
$217$	2998.42	0.938000
$218$	5471.92	1.70002
$219$	2558.30	0.789377
$220$	0	0
$221$	−264.259	−0.0804343
$222$	−1464.54	−0.442764
$223$	2187.24	0.656809	0.328404	−	0.944537i	$-0.393489\pi$
$223$	2187.24	0.656809	0.328404	+	0.944537i	$0.393489\pi$
$224$	2892.17	0.862684
$225$	0	0
$226$	177.602	0.0522739
$227$	−4138.67	−1.21010	−0.605051	−	0.796187i	$-0.706847\pi$
$227$	−4138.67	−1.21010	−0.605051	+	0.796187i	$0.706847\pi$
$228$	−4509.59	−1.30989
$229$	−835.354	−0.241056	−0.120528	−	0.992710i	$-0.538459\pi$
$229$	−835.354	−0.241056	−0.120528	+	0.992710i	$0.538459\pi$
$230$	0	0
$231$	−873.733	−0.248863
$232$	147.729	0.0418056
$233$	−3685.51	−1.03625	−0.518124	−	0.855305i	$-0.673370\pi$
$233$	−3685.51	−1.03625	−0.518124	+	0.855305i	$0.673370\pi$
$234$	492.459	0.137577
$235$	0	0
$236$	−8489.05	−2.34148
$237$	993.662	0.272343
$238$	−962.917	−0.262255
$239$	3026.21	0.819034	0.409517	−	0.912303i	$-0.365697\pi$
$239$	3026.21	0.819034	0.409517	+	0.912303i	$0.365697\pi$
$240$	0	0
$241$	3265.58	0.872839	0.436420	−	0.899743i	$-0.356246\pi$
$241$	3265.58	0.872839	0.436420	+	0.899743i	$0.356246\pi$
$242$	2783.46	0.739370
$243$	−243.000	−0.0641500
$244$	−1817.57	−0.476877
$245$	0	0
$246$	4939.53	1.28022
$247$	−2011.25	−0.518110
$248$	−1924.42	−0.492746
$249$	−1306.30	−0.332463
$250$	0	0
$251$	−6363.16	−1.60016	−0.800078	−	0.599897i	$-0.795208\pi$
$251$	−6363.16	−1.60016	−0.800078	+	0.599897i	$0.795208\pi$
$252$	984.131	0.246010
$253$	4668.96	1.16022
$254$	−1309.09	−0.323385
$255$	0	0
$256$	1822.38	0.444917
$257$	6085.36	1.47702	0.738511	−	0.674242i	$-0.235529\pi$
$257$	6085.36	1.47702	0.738511	+	0.674242i	$0.235529\pi$
$258$	−1911.84	−0.461342
$259$	−1305.31	−0.313159
$260$	0	0
$261$	−184.070	−0.0436538
$262$	−8422.24	−1.98598
$263$	−123.227	−0.0288916	−0.0144458	−	0.999896i	$-0.504598\pi$
$263$	−123.227	−0.0288916	−0.0144458	+	0.999896i	$0.504598\pi$
$264$	560.773	0.130732
$265$	0	0
$266$	−7328.69	−1.68929
$267$	−777.700	−0.178256
$268$	5919.08	1.34913
$269$	−1935.79	−0.438763	−0.219381	−	0.975639i	$-0.570404\pi$
$269$	−1935.79	−0.438763	−0.219381	+	0.975639i	$0.570404\pi$
$270$	0	0
$271$	−4612.69	−1.03395	−0.516976	−	0.856000i	$-0.672942\pi$
$271$	−4612.69	−1.03395	−0.516976	+	0.856000i	$0.672942\pi$
$272$	−962.028	−0.214454
$273$	438.918	0.0973059
$274$	4371.20	0.963774
$275$	0	0
$276$	−5258.89	−1.14691
$277$	5834.30	1.26552	0.632761	−	0.774347i	$-0.281922\pi$
$277$	5834.30	1.26552	0.632761	+	0.774347i	$0.281922\pi$
$278$	12031.4	2.59567
$279$	2397.82	0.514529
$280$	0	0
$281$	4691.91	0.996071	0.498036	−	0.867157i	$-0.334055\pi$
$281$	4691.91	0.996071	0.498036	+	0.867157i	$0.334055\pi$
$282$	5901.49	1.24620
$283$	−3465.60	−0.727945	−0.363973	−	0.931410i	$-0.618580\pi$
$283$	−3465.60	−0.727945	−0.363973	+	0.931410i	$0.618580\pi$
$284$	2409.96	0.503539
$285$	0	0
$286$	1416.01	0.292764
$287$	4402.50	0.905475
$288$	2312.85	0.473216
$289$	−4499.79	−0.915894
$290$	0	0
$291$	3675.51	0.740420
$292$	−8285.55	−1.66053
$293$	−2677.31	−0.533822	−0.266911	−	0.963721i	$-0.586003\pi$
$293$	−2677.31	−0.533822	−0.266911	+	0.963721i	$0.586003\pi$
$294$	−2731.77	−0.541904
$295$	0	0
$296$	837.767	0.164507
$297$	−698.720	−0.136511
$298$	−3129.34	−0.608315
$299$	−2345.44	−0.453646
$300$	0	0
$301$	−1703.98	−0.326299
$302$	−9585.02	−1.82634
$303$	−1936.25	−0.367111
$304$	−7321.93	−1.38139
$305$	0	0
$306$	−770.039	−0.143857
$307$	−471.915	−0.0877316	−0.0438658	−	0.999037i	$-0.513967\pi$
$307$	−471.915	−0.0877316	−0.0438658	+	0.999037i	$0.513967\pi$
$308$	2829.76	0.523508
$309$	−1533.41	−0.282306
$310$	0	0
$311$	−1518.52	−0.276872	−0.138436	−	0.990371i	$-0.544207\pi$
$311$	−1518.52	−0.276872	−0.138436	+	0.990371i	$0.544207\pi$
$312$	−281.703	−0.0511163
$313$	−4049.86	−0.731348	−0.365674	−	0.930743i	$-0.619161\pi$
$313$	−4049.86	−0.731348	−0.365674	+	0.930743i	$0.619161\pi$
$314$	13357.5	2.40066
$315$	0	0
$316$	−3218.17	−0.572900
$317$	−3253.96	−0.576532	−0.288266	−	0.957550i	$-0.593079\pi$
$317$	−3253.96	−0.576532	−0.288266	+	0.957550i	$0.593079\pi$
$318$	−1009.97	−0.178102
$319$	−529.272	−0.0928951
$320$	0	0
$321$	1824.59	0.317254
$322$	−8546.40	−1.47911
$323$	3144.92	0.541759
$324$	787.004	0.134946
$325$	0	0
$326$	−9742.46	−1.65517
$327$	3900.11	0.659561
$328$	−2825.58	−0.475660
$329$	5259.86	0.881415
$330$	0	0
$331$	−3422.45	−0.568322	−0.284161	−	0.958777i	$-0.591715\pi$
$331$	−3422.45	−0.568322	−0.284161	+	0.958777i	$0.591715\pi$
$332$	4230.71	0.699368
$333$	−1043.85	−0.171780
$334$	−11219.8	−1.83809
$335$	0	0
$336$	1597.87	0.259437
$337$	9301.67	1.50354	0.751772	−	0.659423i	$-0.229199\pi$
$337$	9301.67	1.50354	0.751772	+	0.659423i	$0.229199\pi$
$338$	−711.329	−0.114471
$339$	126.586	0.0202808
$340$	0	0
$341$	6894.66	1.09492
$342$	−5860.71	−0.926640
$343$	−6294.99	−0.990955
$344$	1093.64	0.171410
$345$	0	0
$346$	−695.518	−0.108067
$347$	−216.898	−0.0335554	−0.0167777	−	0.999859i	$-0.505341\pi$
$347$	−216.898	−0.0335554	−0.0167777	+	0.999859i	$0.505341\pi$
$348$	596.147	0.0918299
$349$	−4809.84	−0.737721	−0.368861	−	0.929485i	$-0.620252\pi$
$349$	−4809.84	−0.737721	−0.368861	+	0.929485i	$0.620252\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	6650.35	1.00700
$353$	2859.64	0.431170	0.215585	−	0.976485i	$-0.430834\pi$
$353$	2859.64	0.431170	0.215585	+	0.976485i	$0.430834\pi$
$354$	−11032.5	−1.65641
$355$	0	0
$356$	2518.74	0.374980
$357$	−686.319	−0.101747
$358$	−2998.27	−0.442636
$359$	3686.04	0.541899	0.270949	−	0.962594i	$-0.412662\pi$
$359$	3686.04	0.541899	0.270949	+	0.962594i	$0.412662\pi$
$360$	0	0
$361$	17076.8	2.48969
$362$	−9287.39	−1.34844
$363$	1983.91	0.286855
$364$	−1421.52	−0.204692
$365$	0	0
$366$	−2362.14	−0.337352
$367$	3470.59	0.493633	0.246816	−	0.969062i	$-0.420616\pi$
$367$	3470.59	0.493633	0.246816	+	0.969062i	$0.420616\pi$
$368$	−8538.52	−1.20951
$369$	3520.65	0.496688
$370$	0	0
$371$	−900.166	−0.125968
$372$	−7765.82	−1.08236
$373$	11963.4	1.66070	0.830352	−	0.557240i	$-0.188140\pi$
$373$	11963.4	1.66070	0.830352	+	0.557240i	$0.188140\pi$
$374$	−2214.16	−0.306127
$375$	0	0
$376$	−3375.85	−0.463021
$377$	265.879	0.0363221
$378$	1278.99	0.174032
$379$	345.604	0.0468403	0.0234202	−	0.999726i	$-0.492544\pi$
$379$	345.604	0.0468403	0.0234202	+	0.999726i	$0.492544\pi$
$380$	0	0
$381$	−933.055	−0.125464
$382$	−6189.99	−0.829078
$383$	3386.40	0.451793	0.225897	−	0.974151i	$-0.427469\pi$
$383$	3386.40	0.451793	0.225897	+	0.974151i	$0.427469\pi$
$384$	−2709.87	−0.360124
$385$	0	0
$386$	1555.49	0.205110
$387$	−1362.67	−0.178988
$388$	−11903.9	−1.55755
$389$	−1629.88	−0.212438	−0.106219	−	0.994343i	$-0.533874\pi$
$389$	−1629.88	−0.212438	−0.106219	+	0.994343i	$0.533874\pi$
$390$	0	0
$391$	3667.47	0.474353
$392$	1562.66	0.201343
$393$	−6002.95	−0.770506
$394$	−17987.0	−2.29993
$395$	0	0
$396$	2262.94	0.287165
$397$	−7938.94	−1.00364	−0.501819	−	0.864973i	$-0.667336\pi$
$397$	−7938.94	−1.00364	−0.501819	+	0.864973i	$0.667336\pi$
$398$	−17485.7	−2.20221
$399$	−5223.52	−0.655396
$400$	0	0
$401$	214.402	0.0267001	0.0133500	−	0.999911i	$-0.495750\pi$
$401$	214.402	0.0267001	0.0133500	+	0.999911i	$0.495750\pi$
$402$	7692.51	0.954396
$403$	−3463.52	−0.428114
$404$	6270.93	0.772253
$405$	0	0
$406$	968.819	0.118428
$407$	−3001.48	−0.365548
$408$	440.488	0.0534495
$409$	−4783.73	−0.578338	−0.289169	−	0.957278i	$-0.593379\pi$
$409$	−4783.73	−0.578338	−0.289169	+	0.957278i	$0.593379\pi$
$410$	0	0
$411$	3115.58	0.373917
$412$	4966.25	0.593859
$413$	−9832.99	−1.17155
$414$	−6834.51	−0.811347
$415$	0	0
$416$	−3340.79	−0.393739
$417$	8575.39	1.00705
$418$	−16851.8	−1.97189
$419$	−9903.67	−1.15472	−0.577358	−	0.816491i	$-0.695916\pi$
$419$	−9903.67	−1.15472	−0.577358	+	0.816491i	$0.695916\pi$
$420$	0	0
$421$	−12120.6	−1.40314	−0.701572	−	0.712598i	$-0.747518\pi$
$421$	−12120.6	−1.40314	−0.701572	+	0.712598i	$0.747518\pi$
$422$	−5183.82	−0.597973
$423$	4206.28	0.483491
$424$	577.738	0.0661732
$425$	0	0
$426$	3132.01	0.356213
$427$	−2105.32	−0.238603
$428$	−5909.28	−0.667374
$429$	1009.26	0.113584
$430$	0	0
$431$	−13672.6	−1.52805	−0.764023	−	0.645189i	$-0.776779\pi$
$431$	−13672.6	−1.52805	−0.764023	+	0.645189i	$0.776779\pi$
$432$	1277.81	0.142311
$433$	−7113.10	−0.789455	−0.394727	−	0.918798i	$-0.629161\pi$
$433$	−7113.10	−0.789455	−0.394727	+	0.918798i	$0.629161\pi$
$434$	−12620.5	−1.39586
$435$	0	0
$436$	−12631.3	−1.38745
$437$	27912.9	3.05550
$438$	−10768.0	−1.17469
$439$	−6022.04	−0.654707	−0.327353	−	0.944902i	$-0.606157\pi$
$439$	−6022.04	−0.654707	−0.327353	+	0.944902i	$0.606157\pi$
$440$	0	0
$441$	−1947.07	−0.210244
$442$	1112.28	0.119696
$443$	12994.4	1.39364	0.696821	−	0.717245i	$-0.254597\pi$
$443$	12994.4	1.39364	0.696821	+	0.717245i	$0.254597\pi$
$444$	3380.72	0.361356
$445$	0	0
$446$	−9206.20	−0.977413
$447$	−2230.44	−0.236009
$448$	−7912.30	−0.834422
$449$	10984.3	1.15452	0.577260	−	0.816560i	$-0.304122\pi$
$449$	10984.3	1.15452	0.577260	+	0.816560i	$0.304122\pi$
$450$	0	0
$451$	10123.2	1.05695
$452$	−409.973	−0.0426627
$453$	−6831.72	−0.708570
$454$	17419.9	1.80078
$455$	0	0
$456$	3352.52	0.344290
$457$	−9834.10	−1.00661	−0.503304	−	0.864109i	$-0.667882\pi$
$457$	−9834.10	−1.00661	−0.503304	+	0.864109i	$0.667882\pi$
$458$	3516.05	0.358721
$459$	−548.845	−0.0558124
$460$	0	0
$461$	3401.42	0.343644	0.171822	−	0.985128i	$-0.445035\pi$
$461$	3401.42	0.343644	0.171822	+	0.985128i	$0.445035\pi$
$462$	3677.59	0.370339
$463$	−1739.42	−0.174596	−0.0872979	−	0.996182i	$-0.527823\pi$
$463$	−1739.42	−0.174596	−0.0872979	+	0.996182i	$0.527823\pi$
$464$	967.925	0.0968422
$465$	0	0
$466$	15512.5	1.54207
$467$	7958.82	0.788630	0.394315	−	0.918975i	$-0.370982\pi$
$467$	7958.82	0.788630	0.394315	+	0.918975i	$0.370982\pi$
$468$	−1136.78	−0.112282
$469$	6856.16	0.675028
$470$	0	0
$471$	9520.54	0.931387
$472$	6310.94	0.615433
$473$	−3918.20	−0.380886
$474$	−4182.37	−0.405280
$475$	0	0
$476$	2222.78	0.214036
$477$	−719.858	−0.0690986
$478$	−12737.5	−1.21882
$479$	8431.98	0.804315	0.402158	−	0.915570i	$-0.368260\pi$
$479$	8431.98	0.804315	0.402158	+	0.915570i	$0.368260\pi$
$480$	0	0
$481$	1507.79	0.142930
$482$	−13745.0	−1.29889
$483$	−6091.45	−0.573852
$484$	−6425.29	−0.603427
$485$	0	0
$486$	1022.80	0.0954632
$487$	11684.7	1.08723	0.543617	−	0.839334i	$-0.317055\pi$
$487$	11684.7	1.08723	0.543617	+	0.839334i	$0.317055\pi$
$488$	1351.22	0.125342
$489$	−6943.94	−0.642159
$490$	0	0
$491$	−3954.70	−0.363489	−0.181745	−	0.983346i	$-0.558174\pi$
$491$	−3954.70	−0.363489	−0.181745	+	0.983346i	$0.558174\pi$
$492$	−11402.3	−1.04483
$493$	−415.744	−0.0379801
$494$	8465.47	0.771011
$495$	0	0
$496$	−12608.8	−1.14144
$497$	2791.49	0.251943
$498$	5498.27	0.494746
$499$	−5690.37	−0.510493	−0.255246	−	0.966876i	$-0.582157\pi$
$499$	−5690.37	−0.510493	−0.255246	+	0.966876i	$0.582157\pi$
$500$	0	0
$501$	−7996.95	−0.713128
$502$	26782.8	2.38123
$503$	−10859.1	−0.962595	−0.481298	−	0.876557i	$-0.659834\pi$
$503$	−10859.1	−0.962595	−0.481298	+	0.876557i	$0.659834\pi$
$504$	−731.623	−0.0646609
$505$	0	0
$506$	−19651.9	−1.72655
$507$	−507.000	−0.0444116
$508$	3021.88	0.263926
$509$	−18558.6	−1.61610	−0.808049	−	0.589115i	$-0.799476\pi$
$509$	−18558.6	−1.61610	−0.808049	+	0.589115i	$0.799476\pi$
$510$	0	0
$511$	−9597.27	−0.830838
$512$	−14896.8	−1.28584
$513$	−4177.22	−0.359510
$514$	−25613.6	−2.19799
$515$	0	0
$516$	4413.27	0.376518
$517$	12094.7	1.02887
$518$	5494.13	0.466020
$519$	−495.730	−0.0419271
$520$	0	0
$521$	17297.5	1.45454	0.727271	−	0.686350i	$-0.240788\pi$
$521$	17297.5	1.45454	0.727271	+	0.686350i	$0.240788\pi$
$522$	774.759	0.0649622
$523$	5016.11	0.419386	0.209693	−	0.977767i	$-0.432753\pi$
$523$	5016.11	0.419386	0.209693	+	0.977767i	$0.432753\pi$
$524$	19441.8	1.62084
$525$	0	0
$526$	518.667	0.0429942
$527$	5415.77	0.447656
$528$	3674.19	0.302839
$529$	20383.8	1.67533
$530$	0	0
$531$	−7863.39	−0.642640
$532$	16917.4	1.37869
$533$	−5085.39	−0.413269
$534$	3273.38	0.265268
$535$	0	0
$536$	−4400.37	−0.354603
$537$	−2137.02	−0.171730
$538$	8147.83	0.652933
$539$	−5598.57	−0.447398
$540$	0	0
$541$	17642.3	1.40204	0.701018	−	0.713144i	$-0.252729\pi$
$541$	17642.3	1.40204	0.701018	+	0.713144i	$0.252729\pi$
$542$	19415.0	1.53865
$543$	−6619.59	−0.523156
$544$	5223.86	0.411712
$545$	0	0
$546$	−1847.43	−0.144803
$547$	18414.9	1.43943	0.719713	−	0.694271i	$-0.244273\pi$
$547$	18414.9	1.43943	0.719713	+	0.694271i	$0.244273\pi$
$548$	−10090.4	−0.786571
$549$	−1683.61	−0.130883
$550$	0	0
$551$	−3164.20	−0.244645
$552$	3909.57	0.301453
$553$	−3727.66	−0.286648
$554$	−24556.9	−1.88325
$555$	0	0
$556$	−27773.1	−2.11842
$557$	−8179.15	−0.622193	−0.311096	−	0.950378i	$-0.600696\pi$
$557$	−8179.15	−0.622193	−0.311096	+	0.950378i	$0.600696\pi$
$558$	−10092.5	−0.765683
$559$	1968.30	0.148927
$560$	0	0
$561$	−1578.14	−0.118769
$562$	−19748.5	−1.48228
$563$	1880.07	0.140738	0.0703690	−	0.997521i	$-0.477582\pi$
$563$	1880.07	0.140738	0.0703690	+	0.997521i	$0.477582\pi$
$564$	−13622.9	−1.01707
$565$	0	0
$566$	14586.9	1.08327
$567$	911.598	0.0675194
$568$	−1791.62	−0.132350
$569$	10118.3	0.745485	0.372743	−	0.927935i	$-0.378417\pi$
$569$	10118.3	0.745485	0.372743	+	0.927935i	$0.378417\pi$
$570$	0	0
$571$	23428.9	1.71711	0.858555	−	0.512721i	$-0.171362\pi$
$571$	23428.9	1.71711	0.858555	+	0.512721i	$0.171362\pi$
$572$	−3268.70	−0.238935
$573$	−4411.92	−0.321659
$574$	−18530.3	−1.34746
$575$	0	0
$576$	−6327.42	−0.457713
$577$	−20508.1	−1.47966	−0.739831	−	0.672793i	$-0.765094\pi$
$577$	−20508.1	−1.47966	−0.739831	+	0.672793i	$0.765094\pi$
$578$	18939.8	1.36296
$579$	1108.68	0.0795771
$580$	0	0
$581$	4900.49	0.349925
$582$	−15470.4	−1.10184
$583$	−2069.87	−0.147042
$584$	6159.65	0.436452
$585$	0	0
$586$	11268.9	0.794394
$587$	5968.43	0.419665	0.209833	−	0.977737i	$-0.432708\pi$
$587$	5968.43	0.419665	0.209833	+	0.977737i	$0.432708\pi$
$588$	6305.97	0.442268
$589$	41219.0	2.88353
$590$	0	0
$591$	−12820.2	−0.892308
$592$	5489.06	0.381080
$593$	14659.5	1.01517	0.507584	−	0.861602i	$-0.330539\pi$
$593$	14659.5	1.01517	0.507584	+	0.861602i	$0.330539\pi$
$594$	2940.95	0.203146
$595$	0	0
$596$	7223.72	0.496468
$597$	−12462.9	−0.854394
$598$	9872.07	0.675082
$599$	23635.9	1.61225	0.806125	−	0.591746i	$-0.201561\pi$
$599$	23635.9	1.61225	0.806125	+	0.591746i	$0.201561\pi$
$600$	0	0
$601$	−11527.0	−0.782356	−0.391178	−	0.920315i	$-0.627932\pi$
$601$	−11527.0	−0.782356	−0.391178	+	0.920315i	$0.627932\pi$
$602$	7172.15	0.485573
$603$	5482.83	0.370279
$604$	22125.9	1.49055
$605$	0	0
$606$	8149.77	0.546306
$607$	5098.56	0.340930	0.170465	−	0.985364i	$-0.445473\pi$
$607$	5098.56	0.340930	0.170465	+	0.985364i	$0.445473\pi$
$608$	39758.4	2.65200
$609$	690.525	0.0459466
$610$	0	0
$611$	−6075.74	−0.402288
$612$	1777.55	0.117407
$613$	−1516.39	−0.0999128	−0.0499564	−	0.998751i	$-0.515908\pi$
$613$	−1516.39	−0.0999128	−0.0499564	+	0.998751i	$0.515908\pi$
$614$	1986.31	0.130556
$615$	0	0
$616$	−2103.70	−0.137598
$617$	−18539.3	−1.20966	−0.604832	−	0.796353i	$-0.706760\pi$
$617$	−18539.3	−1.20966	−0.604832	+	0.796353i	$0.706760\pi$
$618$	6454.20	0.420107
$619$	25684.9	1.66779	0.833897	−	0.551920i	$-0.186105\pi$
$619$	25684.9	1.66779	0.833897	+	0.551920i	$0.186105\pi$
$620$	0	0
$621$	−4871.30	−0.314780
$622$	6391.51	0.412020
$623$	2917.49	0.187619
$624$	−1845.72	−0.118410
$625$	0	0
$626$	17046.1	1.08834
$627$	−12011.1	−0.765038
$628$	−30834.2	−1.95926
$629$	−2357.67	−0.149454
$630$	0	0
$631$	−22410.9	−1.41389	−0.706945	−	0.707269i	$-0.749927\pi$
$631$	−22410.9	−1.41389	−0.706945	+	0.707269i	$0.749927\pi$
$632$	2392.46	0.150580
$633$	−3694.77	−0.231997
$634$	13696.1	0.857950
$635$	0	0
$636$	2331.40	0.145356
$637$	2812.43	0.174933
$638$	2227.73	0.138239
$639$	2232.34	0.138200
$640$	0	0
$641$	6827.81	0.420721	0.210361	−	0.977624i	$-0.432536\pi$
$641$	6827.81	0.420721	0.210361	+	0.977624i	$0.432536\pi$
$642$	−7679.77	−0.472113
$643$	23264.3	1.42684	0.713418	−	0.700738i	$-0.247146\pi$
$643$	23264.3	1.42684	0.713418	+	0.700738i	$0.247146\pi$
$644$	19728.4	1.20715
$645$	0	0
$646$	−13237.1	−0.806204
$647$	−14745.9	−0.896014	−0.448007	−	0.894030i	$-0.647866\pi$
$647$	−14745.9	−0.896014	−0.448007	+	0.894030i	$0.647866\pi$
$648$	−585.075	−0.0354690
$649$	−22610.3	−1.36754
$650$	0	0
$651$	−8995.26	−0.541554
$652$	22489.3	1.35084
$653$	−10909.0	−0.653755	−0.326878	−	0.945067i	$-0.605997\pi$
$653$	−10909.0	−0.653755	−0.326878	+	0.945067i	$0.605997\pi$
$654$	−16415.8	−0.981509
$655$	0	0
$656$	−18513.2	−1.10186
$657$	−7674.89	−0.455747
$658$	−22139.0	−1.31166
$659$	−4182.99	−0.247263	−0.123631	−	0.992328i	$-0.539454\pi$
$659$	−4182.99	−0.247263	−0.123631	+	0.992328i	$0.539454\pi$
$660$	0	0
$661$	2224.23	0.130881	0.0654406	−	0.997856i	$-0.479155\pi$
$661$	2224.23	0.130881	0.0654406	+	0.997856i	$0.479155\pi$
$662$	14405.2	0.845734
$663$	792.776	0.0464387
$664$	−3145.19	−0.183821
$665$	0	0
$666$	4393.63	0.255630
$667$	−3689.95	−0.214206
$668$	25899.7	1.50013
$669$	−6561.72	−0.379209
$670$	0	0
$671$	−4841.04	−0.278519
$672$	−8676.51	−0.498071
$673$	24152.5	1.38337	0.691687	−	0.722197i	$-0.256868\pi$
$673$	24152.5	1.38337	0.691687	+	0.722197i	$0.256868\pi$
$674$	−39151.2	−2.23746
$675$	0	0
$676$	1642.02	0.0934240
$677$	15310.7	0.869187	0.434593	−	0.900627i	$-0.356892\pi$
$677$	15310.7	0.869187	0.434593	+	0.900627i	$0.356892\pi$
$678$	−532.806	−0.0301804
$679$	−13788.4	−0.779310
$680$	0	0
$681$	12416.0	0.698652
$682$	−29020.0	−1.62937
$683$	−11399.6	−0.638646	−0.319323	−	0.947646i	$-0.603455\pi$
$683$	−11399.6	−0.638646	−0.319323	+	0.947646i	$0.603455\pi$
$684$	13528.8	0.756265
$685$	0	0
$686$	26495.9	1.47466
$687$	2506.06	0.139174
$688$	7165.54	0.397069
$689$	1039.79	0.0574935
$690$	0	0
$691$	−3323.23	−0.182955	−0.0914773	−	0.995807i	$-0.529159\pi$
$691$	−3323.23	−0.182955	−0.0914773	+	0.995807i	$0.529159\pi$
$692$	1605.52	0.0881976
$693$	2621.20	0.143681
$694$	912.936	0.0499345
$695$	0	0
$696$	−443.188	−0.0241365
$697$	7951.82	0.432133
$698$	20244.8	1.09782
$699$	11056.5	0.598279
$700$	0	0
$701$	−12670.4	−0.682673	−0.341336	−	0.939941i	$-0.610880\pi$
$701$	−12670.4	−0.682673	−0.341336	+	0.939941i	$0.610880\pi$
$702$	−1477.38	−0.0794302
$703$	−17944.0	−0.962692
$704$	−18193.8	−0.974012
$705$	0	0
$706$	−12036.4	−0.641635
$707$	7263.71	0.386393
$708$	25467.2	1.35186
$709$	13075.2	0.692594	0.346297	−	0.938125i	$-0.387439\pi$
$709$	13075.2	0.692594	0.346297	+	0.938125i	$0.387439\pi$
$710$	0	0
$711$	−2980.99	−0.157237
$712$	−1872.48	−0.0985592
$713$	48067.8	2.52476
$714$	2888.75	0.151413
$715$	0	0
$716$	6921.16	0.361251
$717$	−9078.62	−0.472869
$718$	−15514.7	−0.806412
$719$	−2988.41	−0.155005	−0.0775026	−	0.996992i	$-0.524695\pi$
$719$	−2988.41	−0.155005	−0.0775026	+	0.996992i	$0.524695\pi$
$720$	0	0
$721$	5752.48	0.297134
$722$	−71877.0	−3.70496
$723$	−9796.73	−0.503934
$724$	21438.9	1.10051
$725$	0	0
$726$	−8350.37	−0.426875
$727$	5507.46	0.280963	0.140482	−	0.990083i	$-0.455135\pi$
$727$	5507.46	0.280963	0.140482	+	0.990083i	$0.455135\pi$
$728$	1056.79	0.0538011
$729$	729.000	0.0370370
$730$	0	0
$731$	−3077.75	−0.155725
$732$	5452.71	0.275325
$733$	36585.2	1.84353	0.921764	−	0.387751i	$-0.126748\pi$
$733$	36585.2	1.84353	0.921764	+	0.387751i	$0.126748\pi$
$734$	−14607.9	−0.734587
$735$	0	0
$736$	46364.6	2.32204
$737$	15765.3	0.787953
$738$	−14818.6	−0.739133
$739$	6425.89	0.319865	0.159933	−	0.987128i	$-0.448872\pi$
$739$	6425.89	0.319865	0.159933	+	0.987128i	$0.448872\pi$
$740$	0	0
$741$	6033.76	0.299131
$742$	3788.84	0.187457
$743$	−20411.0	−1.00782	−0.503908	−	0.863757i	$-0.668105\pi$
$743$	−20411.0	−1.00782	−0.503908	+	0.863757i	$0.668105\pi$
$744$	5773.27	0.284487
$745$	0	0
$746$	−50354.6	−2.47133
$747$	3918.89	0.191947
$748$	5111.13	0.249842
$749$	−6844.81	−0.333917
$750$	0	0
$751$	−24259.5	−1.17875	−0.589375	−	0.807860i	$-0.700626\pi$
$751$	−24259.5	−1.17875	−0.589375	+	0.807860i	$0.700626\pi$
$752$	−22118.6	−1.07258
$753$	19089.5	0.923850
$754$	−1119.10	−0.0540518
$755$	0	0
$756$	−2952.39	−0.142034
$757$	−9295.39	−0.446297	−0.223148	−	0.974785i	$-0.571633\pi$
$757$	−9295.39	−0.446297	−0.223148	+	0.974785i	$0.571633\pi$
$758$	−1454.66	−0.0697042
$759$	−14006.9	−0.669851
$760$	0	0
$761$	−21974.7	−1.04676	−0.523378	−	0.852101i	$-0.675328\pi$
$761$	−21974.7	−1.04676	−0.523378	+	0.852101i	$0.675328\pi$
$762$	3927.27	0.186706
$763$	−14631.0	−0.694204
$764$	14288.9	0.676641
$765$	0	0
$766$	−14253.5	−0.672324
$767$	11358.2	0.534709
$768$	−5467.13	−0.256873
$769$	22987.4	1.07795	0.538977	−	0.842320i	$-0.318811\pi$
$769$	22987.4	1.07795	0.538977	+	0.842320i	$0.318811\pi$
$770$	0	0
$771$	−18256.1	−0.852759
$772$	−3590.68	−0.167398
$773$	−31970.9	−1.48760	−0.743799	−	0.668404i	$-0.766978\pi$
$773$	−31970.9	−1.48760	−0.743799	+	0.668404i	$0.766978\pi$
$774$	5735.53	0.266356
$775$	0	0
$776$	8849.59	0.409384
$777$	3915.94	0.180803
$778$	6860.25	0.316133
$779$	60520.8	2.78354
$780$	0	0
$781$	6418.85	0.294090
$782$	−15436.6	−0.705896
$783$	552.209	0.0252035
$784$	10238.6	0.466408
$785$	0	0
$786$	25266.7	1.14661
$787$	−6087.26	−0.275715	−0.137857	−	0.990452i	$-0.544022\pi$
$787$	−6087.26	−0.275715	−0.137857	+	0.990452i	$0.544022\pi$
$788$	41520.9	1.87706
$789$	369.680	0.0166805
$790$	0	0
$791$	−474.878	−0.0213460
$792$	−1682.32	−0.0754780
$793$	2431.88	0.108901
$794$	33415.4	1.49354
$795$	0	0
$796$	40363.6	1.79730
$797$	−23080.0	−1.02577	−0.512883	−	0.858458i	$-0.671423\pi$
$797$	−23080.0	−1.02577	−0.512883	+	0.858458i	$0.671423\pi$
$798$	21986.1	0.975311
$799$	9500.41	0.420651
$800$	0	0
$801$	2333.10	0.102916
$802$	−902.429	−0.0397330
$803$	−22068.3	−0.969829
$804$	−17757.3	−0.778918
$805$	0	0
$806$	14578.1	0.637087
$807$	5807.37	0.253320
$808$	−4661.94	−0.202978
$809$	−32377.8	−1.40710	−0.703550	−	0.710646i	$-0.748403\pi$
$809$	−32377.8	−1.40710	−0.703550	+	0.710646i	$0.748403\pi$
$810$	0	0
$811$	26352.8	1.14103	0.570513	−	0.821288i	$-0.306744\pi$
$811$	26352.8	1.14103	0.570513	+	0.821288i	$0.306744\pi$
$812$	−2236.40	−0.0966532
$813$	13838.1	0.596952
$814$	12633.4	0.543980
$815$	0	0
$816$	2886.08	0.123815
$817$	−23424.5	−1.00308
$818$	20135.0	0.860638
$819$	−1316.75	−0.0561796
$820$	0	0
$821$	35355.3	1.50294	0.751468	−	0.659770i	$-0.229346\pi$
$821$	35355.3	1.50294	0.751468	+	0.659770i	$0.229346\pi$
$822$	−13113.6	−0.556435
$823$	12663.3	0.536347	0.268173	−	0.963371i	$-0.413580\pi$
$823$	12663.3	0.536347	0.268173	+	0.963371i	$0.413580\pi$
$824$	−3692.02	−0.156089
$825$	0	0
$826$	41387.6	1.74341
$827$	16295.2	0.685176	0.342588	−	0.939486i	$-0.388697\pi$
$827$	16295.2	0.685176	0.342588	+	0.939486i	$0.388697\pi$
$828$	15776.7	0.662170
$829$	13638.9	0.571411	0.285705	−	0.958318i	$-0.407772\pi$
$829$	13638.9	0.571411	0.285705	+	0.958318i	$0.407772\pi$
$830$	0	0
$831$	−17502.9	−0.730649
$832$	9139.61	0.380840
$833$	−4397.69	−0.182918
$834$	−36094.2	−1.49861
$835$	0	0
$836$	38900.5	1.60933
$837$	−7193.46	−0.297064
$838$	41685.0	1.71836
$839$	−1890.31	−0.0777838	−0.0388919	−	0.999243i	$-0.512383\pi$
$839$	−1890.31	−0.0777838	−0.0388919	+	0.999243i	$0.512383\pi$
$840$	0	0
$841$	−23970.7	−0.982849
$842$	51016.4	2.08805
$843$	−14075.7	−0.575082
$844$	11966.3	0.488028
$845$	0	0
$846$	−17704.5	−0.719494
$847$	−7442.50	−0.301921
$848$	3785.35	0.153289
$849$	10396.8	0.420279
$850$	0	0
$851$	−20925.6	−0.842914
$852$	−7229.89	−0.290718
$853$	−1620.21	−0.0650351	−0.0325175	−	0.999471i	$-0.510352\pi$
$853$	−1620.21	−0.0650351	−0.0325175	+	0.999471i	$0.510352\pi$
$854$	8861.39	0.355071
$855$	0	0
$856$	4393.08	0.175412
$857$	14508.4	0.578292	0.289146	−	0.957285i	$-0.406629\pi$
$857$	14508.4	0.578292	0.289146	+	0.957285i	$0.406629\pi$
$858$	−4248.03	−0.169027
$859$	29639.8	1.17730	0.588648	−	0.808389i	$-0.299660\pi$
$859$	29639.8	1.17730	0.588648	+	0.808389i	$0.299660\pi$
$860$	0	0
$861$	−13207.5	−0.522776
$862$	57548.8	2.27392
$863$	−21528.8	−0.849186	−0.424593	−	0.905384i	$-0.639583\pi$
$863$	−21528.8	−0.849186	−0.424593	+	0.905384i	$0.639583\pi$
$864$	−6938.56	−0.273211
$865$	0	0
$866$	29939.4	1.17481
$867$	13499.4	0.528792
$868$	29132.9	1.13921
$869$	−8571.50	−0.334601
$870$	0	0
$871$	−7919.65	−0.308091
$872$	9390.36	0.364676
$873$	−11026.5	−0.427482
$874$	−117487.	−4.54696
$875$	0	0
$876$	24856.7	0.958708
$877$	−14865.3	−0.572366	−0.286183	−	0.958175i	$-0.592387\pi$
$877$	−14865.3	−0.572366	−0.286183	+	0.958175i	$0.592387\pi$
$878$	25347.1	0.974285
$879$	8031.92	0.308202
$880$	0	0
$881$	−21336.0	−0.815921	−0.407961	−	0.913000i	$-0.633760\pi$
$881$	−21336.0	−0.815921	−0.407961	+	0.913000i	$0.633760\pi$
$882$	8195.30	0.312869
$883$	−37538.2	−1.43065	−0.715323	−	0.698794i	$-0.753720\pi$
$883$	−37538.2	−1.43065	−0.715323	+	0.698794i	$0.753720\pi$
$884$	−2567.57	−0.0976884
$885$	0	0
$886$	−54694.1	−2.07391
$887$	−34575.0	−1.30881	−0.654406	−	0.756144i	$-0.727081\pi$
$887$	−34575.0	−1.30881	−0.654406	+	0.756144i	$0.727081\pi$
$888$	−2513.30	−0.0949784
$889$	3500.29	0.132054
$890$	0	0
$891$	2096.16	0.0788148
$892$	21251.4	0.797703
$893$	72306.9	2.70958
$894$	9388.02	0.351211
$895$	0	0
$896$	10165.9	0.379039
$897$	7036.32	0.261913
$898$	−46233.3	−1.71807
$899$	−5448.96	−0.202150
$900$	0	0
$901$	−1625.89	−0.0601178
$902$	−42609.2	−1.57287
$903$	5111.95	0.188389
$904$	304.783	0.0112134
$905$	0	0
$906$	28755.0	1.05444
$907$	10424.8	0.381641	0.190820	−	0.981625i	$-0.438885\pi$
$907$	10424.8	0.381641	0.190820	+	0.981625i	$0.438885\pi$
$908$	−40211.7	−1.46968
$909$	5808.75	0.211952
$910$	0	0
$911$	10961.8	0.398661	0.199331	−	0.979932i	$-0.436123\pi$
$911$	10961.8	0.398661	0.199331	+	0.979932i	$0.436123\pi$
$912$	21965.8	0.797543
$913$	11268.3	0.408464
$914$	41392.2	1.49796
$915$	0	0
$916$	−8116.38	−0.292765
$917$	22519.7	0.810976
$918$	2310.12	0.0830558
$919$	−10779.2	−0.386914	−0.193457	−	0.981109i	$-0.561970\pi$
$919$	−10779.2	−0.386914	−0.193457	+	0.981109i	$0.561970\pi$
$920$	0	0
$921$	1415.74	0.0506519
$922$	−14316.7	−0.511384
$923$	−3224.49	−0.114990
$924$	−8489.28	−0.302248
$925$	0	0
$926$	7321.32	0.259820
$927$	4600.23	0.162990
$928$	−5255.88	−0.185919
$929$	5429.07	0.191735	0.0958675	−	0.995394i	$-0.469437\pi$
$929$	5429.07	0.191735	0.0958675	+	0.995394i	$0.469437\pi$
$930$	0	0
$931$	−33470.5	−1.17825
$932$	−35808.8	−1.25854
$933$	4555.55	0.159852
$934$	−33499.1	−1.17358
$935$	0	0
$936$	845.109	0.0295120
$937$	21300.1	0.742631	0.371315	−	0.928507i	$-0.378907\pi$
$937$	21300.1	0.742631	0.371315	+	0.928507i	$0.378907\pi$
$938$	−28857.9	−1.00453
$939$	12149.6	0.422244
$940$	0	0
$941$	26851.2	0.930207	0.465103	−	0.885256i	$-0.346017\pi$
$941$	26851.2	0.930207	0.465103	+	0.885256i	$0.346017\pi$
$942$	−40072.4	−1.38602
$943$	70576.7	2.43722
$944$	41349.4	1.42564
$945$	0	0
$946$	16491.9	0.566805
$947$	8021.68	0.275258	0.137629	−	0.990484i	$-0.456052\pi$
$947$	8021.68	0.275258	0.137629	+	0.990484i	$0.456052\pi$
$948$	9654.52	0.330764
$949$	11085.9	0.379204
$950$	0	0
$951$	9761.88	0.332861
$952$	−1652.46	−0.0562569
$953$	−35715.0	−1.21398	−0.606990	−	0.794709i	$-0.707623\pi$
$953$	−35715.0	−1.21398	−0.606990	+	0.794709i	$0.707623\pi$
$954$	3029.92	0.102827
$955$	0	0
$956$	29402.9	0.994726
$957$	1587.82	0.0536330
$958$	−35490.6	−1.19692
$959$	−11687.9	−0.393557
$960$	0	0
$961$	41190.9	1.38266
$962$	−6346.35	−0.212697
$963$	−5473.76	−0.183166
$964$	31728.7	1.06007
$965$	0	0
$966$	25639.2	0.853963
$967$	−53338.8	−1.77380	−0.886898	−	0.461965i	$-0.847145\pi$
$967$	−53338.8	−1.77380	−0.886898	+	0.461965i	$0.847145\pi$
$968$	4776.69	0.158604
$969$	−9434.77	−0.312785
$970$	0	0
$971$	23112.9	0.763882	0.381941	−	0.924187i	$-0.375256\pi$
$971$	23112.9	0.763882	0.381941	+	0.924187i	$0.375256\pi$
$972$	−2361.01	−0.0779110
$973$	−32170.0	−1.05994
$974$	−49181.3	−1.61794
$975$	0	0
$976$	8853.22	0.290353
$977$	52874.6	1.73143	0.865715	−	0.500538i	$-0.166864\pi$
$977$	52874.6	1.73143	0.865715	+	0.500538i	$0.166864\pi$
$978$	29227.4	0.955612
$979$	6708.57	0.219006
$980$	0	0
$981$	−11700.3	−0.380798
$982$	16645.5	0.540917
$983$	−45173.1	−1.46572	−0.732858	−	0.680381i	$-0.761814\pi$
$983$	−45173.1	−1.46572	−0.732858	+	0.680381i	$0.761814\pi$
$984$	8476.73	0.274622
$985$	0	0
$986$	1749.89	0.0565190
$987$	−15779.6	−0.508885
$988$	−19541.6	−0.629251
$989$	−27316.7	−0.878281
$990$	0	0
$991$	60485.6	1.93884	0.969418	−	0.245414i	$-0.0789239\pi$
$991$	60485.6	1.93884	0.969418	+	0.245414i	$0.0789239\pi$
$992$	68466.7	2.19135
$993$	10267.3	0.328121
$994$	−11749.5	−0.374922
$995$	0	0
$996$	−12692.1	−0.403780
$997$	18108.1	0.575214	0.287607	−	0.957749i	$-0.407140\pi$
$997$	18108.1	0.575214	0.287607	+	0.957749i	$0.407140\pi$
$998$	23951.1	0.759677
$999$	3131.56	0.0991773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.4.a.l.1.1		3
5.4	even	2		39.4.a.c.1.3	✓	3
15.14	odd	2		117.4.a.f.1.1		3
20.19	odd	2		624.4.a.t.1.1		3
35.34	odd	2		1911.4.a.k.1.3		3
40.19	odd	2		2496.4.a.bp.1.3		3
40.29	even	2		2496.4.a.bl.1.3		3
60.59	even	2		1872.4.a.bk.1.3		3
65.34	odd	4		507.4.b.g.337.6		6
65.44	odd	4		507.4.b.g.337.1		6
65.64	even	2		507.4.a.h.1.1		3
195.194	odd	2		1521.4.a.u.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.a.c.1.3	✓	3	5.4	even	2
117.4.a.f.1.1		3	15.14	odd	2
507.4.a.h.1.1		3	65.64	even	2
507.4.b.g.337.1		6	65.44	odd	4
507.4.b.g.337.6		6	65.34	odd	4
624.4.a.t.1.1		3	20.19	odd	2
975.4.a.l.1.1		3	1.1	even	1	trivial
1521.4.a.u.1.3		3	195.194	odd	2
1872.4.a.bk.1.3		3	60.59	even	2
1911.4.a.k.1.3		3	35.34	odd	2
2496.4.a.bl.1.3		3	40.29	even	2
2496.4.a.bp.1.3		3	40.19	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	975.a (trivial)

\(f(q)\)	\(=\)	\(q-4.20905 q^{2} -3.00000 q^{3} +9.71610 q^{4} +12.6271 q^{6} +11.2543 q^{7} -7.22315 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.20905 q^{2} -3.00000 q^{3} +9.71610 q^{4} +12.6271 q^{6} +11.2543 q^{7} -7.22315 q^{8} +9.00000 q^{9} +25.8785 q^{11} -29.1483 q^{12} -13.0000 q^{13} -47.3699 q^{14} -47.3262 q^{16} +20.3276 q^{17} -37.8814 q^{18} +154.712 q^{19} -33.7629 q^{21} -108.924 q^{22} +180.418 q^{23} +21.6695 q^{24} +54.7176 q^{26} -27.0000 q^{27} +109.348 q^{28} -20.4522 q^{29} +266.424 q^{31} +256.984 q^{32} -77.6355 q^{33} -85.5599 q^{34} +87.4449 q^{36} -115.984 q^{37} -651.190 q^{38} +39.0000 q^{39} +391.184 q^{41} +142.110 q^{42} -151.407 q^{43} +251.438 q^{44} -759.390 q^{46} +467.365 q^{47} +141.979 q^{48} -216.341 q^{49} -60.9828 q^{51} -126.309 q^{52} -79.9842 q^{53} +113.644 q^{54} -81.2915 q^{56} -464.136 q^{57} +86.0843 q^{58} -873.710 q^{59} -187.068 q^{61} -1121.39 q^{62} +101.289 q^{63} -703.047 q^{64} +326.772 q^{66} +609.204 q^{67} +197.505 q^{68} -541.255 q^{69} +248.038 q^{71} -65.0084 q^{72} -852.765 q^{73} +488.181 q^{74} +1503.20 q^{76} +291.244 q^{77} -164.153 q^{78} -331.221 q^{79} +81.0000 q^{81} -1646.51 q^{82} +435.432 q^{83} -328.044 q^{84} +637.281 q^{86} +61.3566 q^{87} -186.924 q^{88} +259.233 q^{89} -146.306 q^{91} +1752.96 q^{92} -799.273 q^{93} -1967.16 q^{94} -770.951 q^{96} -1225.17 q^{97} +910.589 q^{98} +232.907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - 9 q^{3} + 10 q^{4} + 6 q^{6} - 30 q^{7} + 6 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - 9 * q^3 + 10 * q^4 + 6 * q^6 - 30 * q^7 + 6 * q^8 + 27 * q^9	\( 3 q - 2 q^{2} - 9 q^{3} + 10 q^{4} + 6 q^{6} - 30 q^{7} + 6 q^{8} + 27 q^{9} - 16 q^{11} - 30 q^{12} - 39 q^{13} - 176 q^{14} - 110 q^{16} + 146 q^{17} - 18 q^{18} + 94 q^{19} + 90 q^{21} + 56 q^{22} + 48 q^{23} - 18 q^{24} + 26 q^{26} - 81 q^{27} - 80 q^{28} - 2 q^{29} + 302 q^{31} - 154 q^{32} + 48 q^{33} + 164 q^{34} + 90 q^{36} - 374 q^{37} - 312 q^{38} + 117 q^{39} + 480 q^{41} + 528 q^{42} + 260 q^{43} + 712 q^{44} - 1104 q^{46} + 24 q^{47} + 330 q^{48} + 447 q^{49} - 438 q^{51} - 130 q^{52} + 678 q^{53} + 54 q^{54} + 96 q^{56} - 282 q^{57} + 628 q^{58} - 1788 q^{59} + 230 q^{61} - 1952 q^{62} - 270 q^{63} - 750 q^{64} - 168 q^{66} - 74 q^{67} + 460 q^{68} - 144 q^{69} - 948 q^{71} + 54 q^{72} + 222 q^{73} + 1724 q^{74} + 2392 q^{76} - 112 q^{77} - 78 q^{78} - 24 q^{79} + 243 q^{81} - 564 q^{82} + 796 q^{83} + 240 q^{84} + 1800 q^{86} + 6 q^{87} - 1608 q^{88} + 1436 q^{89} + 390 q^{91} + 1296 q^{92} - 906 q^{93} - 1920 q^{94} + 462 q^{96} - 3242 q^{97} + 5070 q^{98} - 144 q^{99}+O(q^{100}) \) 3 * q - 2 * q^2 - 9 * q^3 + 10 * q^4 + 6 * q^6 - 30 * q^7 + 6 * q^8 + 27 * q^9 - 16 * q^11 - 30 * q^12 - 39 * q^13 - 176 * q^14 - 110 * q^16 + 146 * q^17 - 18 * q^18 + 94 * q^19 + 90 * q^21 + 56 * q^22 + 48 * q^23 - 18 * q^24 + 26 * q^26 - 81 * q^27 - 80 * q^28 - 2 * q^29 + 302 * q^31 - 154 * q^32 + 48 * q^33 + 164 * q^34 + 90 * q^36 - 374 * q^37 - 312 * q^38 + 117 * q^39 + 480 * q^41 + 528 * q^42 + 260 * q^43 + 712 * q^44 - 1104 * q^46 + 24 * q^47 + 330 * q^48 + 447 * q^49 - 438 * q^51 - 130 * q^52 + 678 * q^53 + 54 * q^54 + 96 * q^56 - 282 * q^57 + 628 * q^58 - 1788 * q^59 + 230 * q^61 - 1952 * q^62 - 270 * q^63 - 750 * q^64 - 168 * q^66 - 74 * q^67 + 460 * q^68 - 144 * q^69 - 948 * q^71 + 54 * q^72 + 222 * q^73 + 1724 * q^74 + 2392 * q^76 - 112 * q^77 - 78 * q^78 - 24 * q^79 + 243 * q^81 - 564 * q^82 + 796 * q^83 + 240 * q^84 + 1800 * q^86 + 6 * q^87 - 1608 * q^88 + 1436 * q^89 + 390 * q^91 + 1296 * q^92 - 906 * q^93 - 1920 * q^94 + 462 * q^96 - 3242 * q^97 + 5070 * q^98 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more