LMFDB - Embedded newform 1734.4.a.s.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1734,4,Mod(1,1734)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1734.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1734, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1734.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,4,6,8,9,12,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$102.309311950$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{569}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 142 $ x^2 - x - 142
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 102)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-11.4269$ of defining polynomial
Character	$\chi$	$=$	1734.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +16.4269 q^{5} +6.00000 q^{6} +6.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +32.8537 q^{10} +1.57314 q^{11} +12.0000 q^{12} -17.2806 q^{13} +12.0000 q^{14} +49.2806 q^{15} +16.0000 q^{16} +18.0000 q^{18} +145.842 q^{19} +65.7074 q^{20} +18.0000 q^{21} +3.14628 q^{22} -30.9880 q^{23} +24.0000 q^{24} +144.842 q^{25} -34.5612 q^{26} +27.0000 q^{27} +24.0000 q^{28} +59.7074 q^{29} +98.5612 q^{30} -30.0000 q^{31} +32.0000 q^{32} +4.71942 q^{33} +98.5612 q^{35} +36.0000 q^{36} -47.1223 q^{37} +291.683 q^{38} -51.8417 q^{39} +131.415 q^{40} -228.988 q^{41} +36.0000 q^{42} -376.086 q^{43} +6.29256 q^{44} +147.842 q^{45} -61.9760 q^{46} +456.806 q^{47} +48.0000 q^{48} -307.000 q^{49} +289.683 q^{50} -69.1223 q^{52} +563.122 q^{53} +54.0000 q^{54} +25.8417 q^{55} +48.0000 q^{56} +437.525 q^{57} +119.415 q^{58} +120.000 q^{59} +197.122 q^{60} +408.878 q^{61} -60.0000 q^{62} +54.0000 q^{63} +64.0000 q^{64} -283.866 q^{65} +9.43884 q^{66} +205.122 q^{67} -92.9641 q^{69} +197.122 q^{70} +895.391 q^{71} +72.0000 q^{72} +1067.05 q^{73} -94.2447 q^{74} +434.525 q^{75} +583.367 q^{76} +9.43884 q^{77} -103.683 q^{78} -1038.81 q^{79} +262.830 q^{80} +81.0000 q^{81} -457.976 q^{82} -1099.68 q^{83} +72.0000 q^{84} -752.173 q^{86} +179.122 q^{87} +12.5851 q^{88} -794.489 q^{89} +295.683 q^{90} -103.683 q^{91} -123.952 q^{92} -90.0000 q^{93} +913.612 q^{94} +2395.72 q^{95} +96.0000 q^{96} +1006.24 q^{97} -614.000 q^{98} +14.1583 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} + 9 q^{5} + 12 q^{6} + 12 q^{7} + 16 q^{8} + 18 q^{9} + 18 q^{10} + 27 q^{11} + 24 q^{12} + 37 q^{13} + 24 q^{14} + 27 q^{15} + 32 q^{16} + 36 q^{18} + 77 q^{19} + 36 q^{20}+ \cdots + 243 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 + 9 * q^5 + 12 * q^6 + 12 * q^7 + 16 * q^8 + 18 * q^9 + 18 * q^10 + 27 * q^11 + 24 * q^12 + 37 * q^13 + 24 * q^14 + 27 * q^15 + 32 * q^16 + 36 * q^18 + 77 * q^19 + 36 * q^20 + 36 * q^21 + 54 * q^22 + 105 * q^23 + 48 * q^24 + 75 * q^25 + 74 * q^26 + 54 * q^27 + 48 * q^28 + 24 * q^29 + 54 * q^30 - 60 * q^31 + 64 * q^32 + 81 * q^33 + 54 * q^35 + 72 * q^36 + 192 * q^37 + 154 * q^38 + 111 * q^39 + 72 * q^40 - 291 * q^41 + 72 * q^42 + 35 * q^43 + 108 * q^44 + 81 * q^45 + 210 * q^46 + 198 * q^47 + 96 * q^48 - 614 * q^49 + 150 * q^50 + 148 * q^52 + 840 * q^53 + 108 * q^54 - 163 * q^55 + 96 * q^56 + 231 * q^57 + 48 * q^58 + 240 * q^59 + 108 * q^60 + 1104 * q^61 - 120 * q^62 + 108 * q^63 + 128 * q^64 - 687 * q^65 + 162 * q^66 + 124 * q^67 + 315 * q^69 + 108 * q^70 + 1266 * q^71 + 144 * q^72 + 846 * q^73 + 384 * q^74 + 225 * q^75 + 308 * q^76 + 162 * q^77 + 222 * q^78 - 1362 * q^79 + 144 * q^80 + 162 * q^81 - 582 * q^82 - 1770 * q^83 + 144 * q^84 + 70 * q^86 + 72 * q^87 + 216 * q^88 - 444 * q^89 + 162 * q^90 + 222 * q^91 + 420 * q^92 - 180 * q^93 + 396 * q^94 + 2907 * q^95 + 192 * q^96 + 1440 * q^97 - 1228 * q^98 + 243 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	16.4269	1.46926	0.734632	−	0.678466i	$-0.237355\pi$
$5$	16.4269	1.46926	0.734632	+	0.678466i	$0.237355\pi$
$6$	6.00000	0.408248
$7$	6.00000	0.323970	0.161985	−	0.986793i	$-0.448210\pi$
$7$	6.00000	0.323970	0.161985	+	0.986793i	$0.448210\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	32.8537	1.03893
$11$	1.57314	0.0431199	0.0215600	−	0.999768i	$-0.493137\pi$
$11$	1.57314	0.0431199	0.0215600	+	0.999768i	$0.493137\pi$
$12$	12.0000	0.288675
$13$	−17.2806	−0.368675	−0.184337	−	0.982863i	$-0.559014\pi$
$13$	−17.2806	−0.368675	−0.184337	+	0.982863i	$0.559014\pi$
$14$	12.0000	0.229081
$15$	49.2806	0.848279
$16$	16.0000	0.250000
$17$	0	0
$17$	0	0
$18$	18.0000	0.235702
$19$	145.842	1.76097	0.880484	−	0.474076i	$-0.157218\pi$
$19$	145.842	1.76097	0.880484	+	0.474076i	$0.157218\pi$
$20$	65.7074	0.734632
$21$	18.0000	0.187044
$22$	3.14628	0.0304904
$23$	−30.9880	−0.280933	−0.140466	−	0.990085i	$-0.544860\pi$
$23$	−30.9880	−0.280933	−0.140466	+	0.990085i	$0.544860\pi$
$24$	24.0000	0.204124
$25$	144.842	1.15873
$26$	−34.5612	−0.260692
$27$	27.0000	0.192450
$28$	24.0000	0.161985
$29$	59.7074	0.382324	0.191162	−	0.981559i	$-0.438774\pi$
$29$	59.7074	0.382324	0.191162	+	0.981559i	$0.438774\pi$
$30$	98.5612	0.599824
$31$	−30.0000	−0.173812	−0.0869058	−	0.996217i	$-0.527698\pi$
$31$	−30.0000	−0.173812	−0.0869058	+	0.996217i	$0.527698\pi$
$32$	32.0000	0.176777
$33$	4.71942	0.0248953
$34$	0	0
$35$	98.5612	0.475996
$36$	36.0000	0.166667
$37$	−47.1223	−0.209375	−0.104687	−	0.994505i	$-0.533384\pi$
$37$	−47.1223	−0.209375	−0.104687	+	0.994505i	$0.533384\pi$
$38$	291.683	1.24519
$39$	−51.8417	−0.212854
$40$	131.415	0.519463
$41$	−228.988	−0.872242	−0.436121	−	0.899888i	$-0.643648\pi$
$41$	−228.988	−0.872242	−0.436121	+	0.899888i	$0.643648\pi$
$42$	36.0000	0.132260
$43$	−376.086	−1.33378	−0.666891	−	0.745155i	$-0.732375\pi$
$43$	−376.086	−1.33378	−0.666891	+	0.745155i	$0.732375\pi$
$44$	6.29256	0.0215600
$45$	147.842	0.489754
$46$	−61.9760	−0.198649
$47$	456.806	1.41770	0.708851	−	0.705358i	$-0.249214\pi$
$47$	456.806	1.41770	0.708851	+	0.705358i	$0.249214\pi$
$48$	48.0000	0.144338
$49$	−307.000	−0.895044
$50$	289.683	0.819349
$51$	0	0
$52$	−69.1223	−0.184337
$53$	563.122	1.45945	0.729725	−	0.683741i	$-0.239648\pi$
$53$	563.122	1.45945	0.729725	+	0.683741i	$0.239648\pi$
$54$	54.0000	0.136083
$55$	25.8417	0.0633545
$56$	48.0000	0.114541
$57$	437.525	1.01670
$58$	119.415	0.270344
$59$	120.000	0.264791	0.132396	−	0.991197i	$-0.457733\pi$
$59$	120.000	0.264791	0.132396	+	0.991197i	$0.457733\pi$
$60$	197.122	0.424140
$61$	408.878	0.858220	0.429110	−	0.903252i	$-0.358827\pi$
$61$	408.878	0.858220	0.429110	+	0.903252i	$0.358827\pi$
$62$	−60.0000	−0.122903
$63$	54.0000	0.107990
$64$	64.0000	0.125000
$65$	−283.866	−0.541680
$66$	9.43884	0.0176036
$67$	205.122	0.374025	0.187013	−	0.982358i	$-0.440119\pi$
$67$	205.122	0.374025	0.187013	+	0.982358i	$0.440119\pi$
$68$	0	0
$69$	−92.9641	−0.162197
$70$	197.122	0.336580
$71$	895.391	1.49667	0.748333	−	0.663323i	$-0.230854\pi$
$71$	895.391	1.49667	0.748333	+	0.663323i	$0.230854\pi$
$72$	72.0000	0.117851
$73$	1067.05	1.71081	0.855403	−	0.517963i	$-0.173310\pi$
$73$	1067.05	1.71081	0.855403	+	0.517963i	$0.173310\pi$
$74$	−94.2447	−0.148050
$75$	434.525	0.668995
$76$	583.367	0.880484
$77$	9.43884	0.0139695
$78$	−103.683	−0.150511
$79$	−1038.81	−1.47943	−0.739714	−	0.672922i	$-0.765039\pi$
$79$	−1038.81	−1.47943	−0.739714	+	0.672922i	$0.765039\pi$
$80$	262.830	0.367316
$81$	81.0000	0.111111
$82$	−457.976	−0.616768
$83$	−1099.68	−1.45429	−0.727144	−	0.686485i	$-0.759153\pi$
$83$	−1099.68	−1.45429	−0.727144	+	0.686485i	$0.759153\pi$
$84$	72.0000	0.0935220
$85$	0	0
$86$	−752.173	−0.943126
$87$	179.122	0.220735
$88$	12.5851	0.0152452
$89$	−794.489	−0.946244	−0.473122	−	0.880997i	$-0.656873\pi$
$89$	−794.489	−0.946244	−0.473122	+	0.880997i	$0.656873\pi$
$90$	295.683	0.346309
$91$	−103.683	−0.119439
$92$	−123.952	−0.140466
$93$	−90.0000	−0.100350
$94$	913.612	1.00247
$95$	2395.72	2.58733
$96$	96.0000	0.102062
$97$	1006.24	1.05329	0.526643	−	0.850087i	$-0.323451\pi$
$97$	1006.24	1.05329	0.526643	+	0.850087i	$0.323451\pi$
$98$	−614.000	−0.632891
$99$	14.1583	0.0143733
$100$	579.367	0.579367
$101$	−394.173	−0.388333	−0.194167	−	0.980969i	$-0.562200\pi$
$101$	−394.173	−0.388333	−0.194167	+	0.980969i	$0.562200\pi$
$102$	0	0
$103$	748.892	0.716413	0.358207	−	0.933642i	$-0.383388\pi$
$103$	748.892	0.716413	0.358207	+	0.933642i	$0.383388\pi$
$104$	−138.245	−0.130346
$105$	295.683	0.274817
$106$	1126.24	1.03199
$107$	−1200.48	−1.08462	−0.542312	−	0.840177i	$-0.682451\pi$
$107$	−1200.48	−1.08462	−0.542312	+	0.840177i	$0.682451\pi$
$108$	108.000	0.0962250
$109$	1083.44	0.952061	0.476030	−	0.879429i	$-0.342075\pi$
$109$	1083.44	0.952061	0.476030	+	0.879429i	$0.342075\pi$
$110$	51.6835	0.0447984
$111$	−141.367	−0.120883
$112$	96.0000	0.0809924
$113$	−1027.06	−0.855024	−0.427512	−	0.904010i	$-0.640610\pi$
$113$	−1027.06	−0.855024	−0.427512	+	0.904010i	$0.640610\pi$
$114$	875.050	0.718912
$115$	−509.036	−0.412764
$116$	238.830	0.191162
$117$	−155.525	−0.122892
$118$	240.000	0.187236
$119$	0	0
$120$	394.245	0.299912
$121$	−1328.53	−0.998141
$122$	817.755	0.606853
$123$	−686.964	−0.503589
$124$	−120.000	−0.0869058
$125$	325.938	0.233222
$126$	108.000	0.0763604
$127$	−2291.63	−1.60117	−0.800586	−	0.599217i	$-0.795479\pi$
$127$	−2291.63	−1.60117	−0.800586	+	0.599217i	$0.795479\pi$
$128$	128.000	0.0883883
$129$	−1128.26	−0.770060
$130$	−567.731	−0.383026
$131$	−1935.04	−1.29057	−0.645287	−	0.763940i	$-0.723262\pi$
$131$	−1935.04	−1.29057	−0.645287	+	0.763940i	$0.723262\pi$
$132$	18.8777	0.0124477
$133$	875.050	0.570500
$134$	410.245	0.264476
$135$	443.525	0.282760
$136$	0	0
$137$	973.540	0.607118	0.303559	−	0.952813i	$-0.401825\pi$
$137$	973.540	0.607118	0.303559	+	0.952813i	$0.401825\pi$
$138$	−185.928	−0.114690
$139$	310.388	0.189401	0.0947007	−	0.995506i	$-0.469811\pi$
$139$	310.388	0.189401	0.0947007	+	0.995506i	$0.469811\pi$
$140$	394.245	0.237998
$141$	1370.42	0.818510
$142$	1790.78	1.05830
$143$	−27.1848	−0.0158972
$144$	144.000	0.0833333
$145$	980.806	0.561734
$146$	2134.10	1.20972
$147$	−921.000	−0.516754
$148$	−188.489	−0.104687
$149$	−2680.76	−1.47394	−0.736969	−	0.675927i	$-0.763743\pi$
$149$	−2680.76	−1.47394	−0.736969	+	0.675927i	$0.763743\pi$
$150$	869.050	0.473051
$151$	226.878	0.122272	0.0611359	−	0.998129i	$-0.480528\pi$
$151$	226.878	0.122272	0.0611359	+	0.998129i	$0.480528\pi$
$152$	1166.73	0.622596
$153$	0	0
$154$	18.8777	0.00987796
$155$	−492.806	−0.255375
$156$	−207.367	−0.106427
$157$	353.108	0.179497	0.0897486	−	0.995964i	$-0.471394\pi$
$157$	353.108	0.179497	0.0897486	+	0.995964i	$0.471394\pi$
$158$	−2077.61	−1.04611
$159$	1689.37	0.842613
$160$	525.660	0.259731
$161$	−185.928	−0.0910136
$162$	162.000	0.0785674
$163$	1070.70	0.514504	0.257252	−	0.966344i	$-0.417183\pi$
$163$	1070.70	0.514504	0.257252	+	0.966344i	$0.417183\pi$
$164$	−915.952	−0.436121
$165$	77.5252	0.0365778
$166$	−2199.37	−1.02834
$167$	−744.408	−0.344934	−0.172467	−	0.985015i	$-0.555174\pi$
$167$	−744.408	−0.344934	−0.172467	+	0.985015i	$0.555174\pi$
$168$	144.000	0.0661300
$169$	−1898.38	−0.864079
$170$	0	0
$171$	1312.58	0.586989
$172$	−1504.35	−0.666891
$173$	2870.53	1.26152	0.630758	−	0.775980i	$-0.282744\pi$
$173$	2870.53	1.26152	0.630758	+	0.775980i	$0.282744\pi$
$174$	358.245	0.156083
$175$	869.050	0.375395
$176$	25.1702	0.0107800
$177$	360.000	0.152877
$178$	−1588.98	−0.669095
$179$	1144.03	0.477702	0.238851	−	0.971056i	$-0.423229\pi$
$179$	1144.03	0.477702	0.238851	+	0.971056i	$0.423229\pi$
$180$	591.367	0.244877
$181$	−3516.07	−1.44391	−0.721955	−	0.691940i	$-0.756756\pi$
$181$	−3516.07	−1.44391	−0.721955	+	0.691940i	$0.756756\pi$
$182$	−207.367	−0.0844564
$183$	1226.63	0.495494
$184$	−247.904	−0.0993247
$185$	−774.072	−0.307626
$186$	−180.000	−0.0709583
$187$	0	0
$188$	1827.22	0.708851
$189$	162.000	0.0623480
$190$	4791.44	1.82952
$191$	−4153.61	−1.57353	−0.786766	−	0.617251i	$-0.788246\pi$
$191$	−4153.61	−1.57353	−0.786766	+	0.617251i	$0.788246\pi$
$192$	192.000	0.0721688
$193$	4090.91	1.52575	0.762875	−	0.646546i	$-0.223787\pi$
$193$	4090.91	1.52575	0.762875	+	0.646546i	$0.223787\pi$
$194$	2012.49	0.744785
$195$	−851.597	−0.312739
$196$	−1228.00	−0.447522
$197$	4823.75	1.74456	0.872278	−	0.489010i	$-0.162642\pi$
$197$	4823.75	1.74456	0.872278	+	0.489010i	$0.162642\pi$
$198$	28.3165	0.0101635
$199$	2985.74	1.06359	0.531793	−	0.846874i	$-0.321518\pi$
$199$	2985.74	1.06359	0.531793	+	0.846874i	$0.321518\pi$
$200$	1158.73	0.409674
$201$	615.367	0.215943
$202$	−788.346	−0.274593
$203$	358.245	0.123861
$204$	0	0
$205$	−3761.55	−1.28155
$206$	1497.78	0.506581
$207$	−278.892	−0.0936442
$208$	−276.489	−0.0921687
$209$	229.429	0.0759328
$210$	591.367	0.194325
$211$	4387.40	1.43147	0.715736	−	0.698370i	$-0.246091\pi$
$211$	4387.40	1.43147	0.715736	+	0.698370i	$0.246091\pi$
$212$	2252.49	0.729725
$213$	2686.17	0.864101
$214$	−2400.96	−0.766945
$215$	−6177.92	−1.95968
$216$	216.000	0.0680414
$217$	−180.000	−0.0563097
$218$	2166.88	0.673209
$219$	3201.15	0.987734
$220$	103.367	0.0316773
$221$	0	0
$222$	−282.734	−0.0854768
$223$	−918.791	−0.275905	−0.137952	−	0.990439i	$-0.544052\pi$
$223$	−918.791	−0.275905	−0.137952	+	0.990439i	$0.544052\pi$
$224$	192.000	0.0572703
$225$	1303.58	0.386245
$226$	−2054.12	−0.604593
$227$	−1754.31	−0.512942	−0.256471	−	0.966552i	$-0.582560\pi$
$227$	−1754.31	−0.512942	−0.256471	+	0.966552i	$0.582560\pi$
$228$	1750.10	0.508348
$229$	1859.18	0.536498	0.268249	−	0.963350i	$-0.413555\pi$
$229$	1859.18	0.536498	0.268249	+	0.963350i	$0.413555\pi$
$230$	−1018.07	−0.291868
$231$	28.3165	0.00806532
$232$	477.660	0.135172
$233$	−1537.43	−0.432276	−0.216138	−	0.976363i	$-0.569346\pi$
$233$	−1537.43	−0.432276	−0.216138	+	0.976363i	$0.569346\pi$
$234$	−311.050	−0.0868975
$235$	7503.89	2.08298
$236$	480.000	0.132396
$237$	−3116.42	−0.854148
$238$	0	0
$239$	−3904.69	−1.05679	−0.528396	−	0.848998i	$-0.677206\pi$
$239$	−3904.69	−1.05679	−0.528396	+	0.848998i	$0.677206\pi$
$240$	788.489	0.212070
$241$	−2369.64	−0.633369	−0.316685	−	0.948531i	$-0.602570\pi$
$241$	−2369.64	−0.633369	−0.316685	+	0.948531i	$0.602570\pi$
$242$	−2657.05	−0.705792
$243$	243.000	0.0641500
$244$	1635.51	0.429110
$245$	−5043.05	−1.31505
$246$	−1373.93	−0.356091
$247$	−2520.23	−0.649224
$248$	−240.000	−0.0614517
$249$	−3299.05	−0.839634
$250$	651.875	0.164913
$251$	7356.23	1.84989	0.924943	−	0.380107i	$-0.124113\pi$
$251$	7356.23	1.84989	0.924943	+	0.380107i	$0.124113\pi$
$252$	216.000	0.0539949
$253$	−48.7485	−0.0121138
$254$	−4583.25	−1.13220
$255$	0	0
$256$	256.000	0.0625000
$257$	−3415.32	−0.828957	−0.414479	−	0.910059i	$-0.636036\pi$
$257$	−3415.32	−0.828957	−0.414479	+	0.910059i	$0.636036\pi$
$258$	−2256.52	−0.544514
$259$	−282.734	−0.0678310
$260$	−1135.46	−0.270840
$261$	537.367	0.127441
$262$	−3870.08	−0.912574
$263$	3030.22	0.710460	0.355230	−	0.934779i	$-0.384402\pi$
$263$	3030.22	0.710460	0.355230	+	0.934779i	$0.384402\pi$
$264$	37.7553	0.00880182
$265$	9250.33	2.14431
$266$	1750.10	0.403404
$267$	−2383.47	−0.546314
$268$	820.489	0.187013
$269$	5449.58	1.23519	0.617596	−	0.786496i	$-0.288107\pi$
$269$	5449.58	1.23519	0.617596	+	0.786496i	$0.288107\pi$
$270$	887.050	0.199941
$271$	2628.14	0.589109	0.294554	−	0.955635i	$-0.404829\pi$
$271$	2628.14	0.589109	0.294554	+	0.955635i	$0.404829\pi$
$272$	0	0
$273$	−311.050	−0.0689584
$274$	1947.08	0.429297
$275$	227.856	0.0499645
$276$	−371.856	−0.0810983
$277$	−7133.14	−1.54725	−0.773626	−	0.633643i	$-0.781559\pi$
$277$	−7133.14	−1.54725	−0.773626	+	0.633643i	$0.781559\pi$
$278$	620.777	0.133927
$279$	−270.000	−0.0579372
$280$	788.489	0.168290
$281$	−6010.26	−1.27595	−0.637975	−	0.770057i	$-0.720228\pi$
$281$	−6010.26	−1.27595	−0.637975	+	0.770057i	$0.720228\pi$
$282$	2740.83	0.578774
$283$	−1226.19	−0.257559	−0.128780	−	0.991673i	$-0.541106\pi$
$283$	−1226.19	−0.257559	−0.128780	+	0.991673i	$0.541106\pi$
$284$	3581.56	0.748333
$285$	7187.17	1.49379
$286$	−54.3695	−0.0112410
$287$	−1373.93	−0.282580
$288$	288.000	0.0589256
$289$	0	0
$290$	1961.61	0.397206
$291$	3018.73	0.608114
$292$	4268.20	0.855403
$293$	8459.73	1.68677	0.843383	−	0.537312i	$-0.180560\pi$
$293$	8459.73	1.68677	0.843383	+	0.537312i	$0.180560\pi$
$294$	−1842.00	−0.365400
$295$	1971.22	0.389048
$296$	−376.979	−0.0740251
$297$	42.4748	0.00829844
$298$	−5361.53	−1.04223
$299$	535.491	0.103573
$300$	1738.10	0.334498
$301$	−2256.52	−0.432105
$302$	453.755	0.0864592
$303$	−1182.52	−0.224204
$304$	2333.47	0.440242
$305$	6716.58	1.26095
$306$	0	0
$307$	−3384.78	−0.629249	−0.314624	−	0.949216i	$-0.601879\pi$
$307$	−3384.78	−0.629249	−0.314624	+	0.949216i	$0.601879\pi$
$308$	37.7553	0.00698477
$309$	2246.68	0.413621
$310$	−985.612	−0.180577
$311$	861.003	0.156987	0.0784935	−	0.996915i	$-0.474989\pi$
$311$	861.003	0.156987	0.0784935	+	0.996915i	$0.474989\pi$
$312$	−414.734	−0.0752554
$313$	950.648	0.171674	0.0858368	−	0.996309i	$-0.472644\pi$
$313$	950.648	0.171674	0.0858368	+	0.996309i	$0.472644\pi$
$314$	706.216	0.126924
$315$	887.050	0.158665
$316$	−4155.22	−0.739714
$317$	−8401.18	−1.48851	−0.744254	−	0.667897i	$-0.767195\pi$
$317$	−8401.18	−1.48851	−0.744254	+	0.667897i	$0.767195\pi$
$318$	3378.73	0.595818
$319$	93.9281	0.0164858
$320$	1051.32	0.183658
$321$	−3601.44	−0.626208
$322$	−371.856	−0.0643563
$323$	0	0
$324$	324.000	0.0555556
$325$	−2502.95	−0.427196
$326$	2141.41	0.363809
$327$	3250.32	0.549673
$328$	−1831.90	−0.308384
$329$	2740.83	0.459292
$330$	155.050	0.0258644
$331$	−4128.20	−0.685518	−0.342759	−	0.939423i	$-0.611361\pi$
$331$	−4128.20	−0.685518	−0.342759	+	0.939423i	$0.611361\pi$
$332$	−4398.73	−0.727144
$333$	−424.101	−0.0697916
$334$	−1488.82	−0.243905
$335$	3369.52	0.549541
$336$	288.000	0.0467610
$337$	40.2293	0.00650276	0.00325138	−	0.999995i	$-0.498965\pi$
$337$	40.2293	0.00650276	0.00325138	+	0.999995i	$0.498965\pi$
$338$	−3796.76	−0.610996
$339$	−3081.18	−0.493648
$340$	0	0
$341$	−47.1942	−0.00749475
$342$	2625.15	0.415064
$343$	−3900.00	−0.613936
$344$	−3008.69	−0.471563
$345$	−1527.11	−0.238309
$346$	5741.06	0.892026
$347$	−1137.51	−0.175978	−0.0879892	−	0.996121i	$-0.528044\pi$
$347$	−1137.51	−0.175978	−0.0879892	+	0.996121i	$0.528044\pi$
$348$	716.489	0.110367
$349$	−625.741	−0.0959746	−0.0479873	−	0.998848i	$-0.515281\pi$
$349$	−625.741	−0.0959746	−0.0479873	+	0.998848i	$0.515281\pi$
$350$	1738.10	0.265444
$351$	−466.576	−0.0709515
$352$	50.3405	0.00762260
$353$	−6354.81	−0.958165	−0.479082	−	0.877770i	$-0.659031\pi$
$353$	−6354.81	−0.958165	−0.479082	+	0.877770i	$0.659031\pi$
$354$	720.000	0.108100
$355$	14708.5	2.19900
$356$	−3177.96	−0.473122
$357$	0	0
$358$	2288.06	0.337787
$359$	10466.9	1.53878	0.769388	−	0.638781i	$-0.220561\pi$
$359$	10466.9	1.53878	0.769388	+	0.638781i	$0.220561\pi$
$360$	1182.73	0.173154
$361$	14410.8	2.10101
$362$	−7032.14	−1.02100
$363$	−3985.58	−0.576277
$364$	−414.734	−0.0597197
$365$	17528.3	2.51362
$366$	2453.27	0.350367
$367$	8320.39	1.18344	0.591718	−	0.806145i	$-0.298450\pi$
$367$	8320.39	1.18344	0.591718	+	0.806145i	$0.298450\pi$
$368$	−495.808	−0.0702331
$369$	−2060.89	−0.290747
$370$	−1548.14	−0.217525
$371$	3378.73	0.472817
$372$	−360.000	−0.0501751
$373$	265.251	0.0368208	0.0184104	−	0.999831i	$-0.494139\pi$
$373$	265.251	0.0368208	0.0184104	+	0.999831i	$0.494139\pi$
$374$	0	0
$375$	977.813	0.134651
$376$	3654.45	0.501233
$377$	−1031.78	−0.140953
$378$	324.000	0.0440867
$379$	10168.5	1.37815	0.689077	−	0.724688i	$-0.258016\pi$
$379$	10168.5	1.37815	0.689077	+	0.724688i	$0.258016\pi$
$380$	9582.89	1.29366
$381$	−6874.88	−0.924438
$382$	−8307.22	−1.11266
$383$	1646.79	0.219705	0.109853	−	0.993948i	$-0.464962\pi$
$383$	1646.79	0.219705	0.109853	+	0.993948i	$0.464962\pi$
$384$	384.000	0.0510310
$385$	155.050	0.0205249
$386$	8181.81	1.07887
$387$	−3384.78	−0.444594
$388$	4024.98	0.526643
$389$	−6268.68	−0.817055	−0.408528	−	0.912746i	$-0.633958\pi$
$389$	−6268.68	−0.817055	−0.408528	+	0.912746i	$0.633958\pi$
$390$	−1703.19	−0.221140
$391$	0	0
$392$	−2456.00	−0.316446
$393$	−5805.12	−0.745114
$394$	9647.49	1.23359
$395$	−17064.3	−2.17367
$396$	56.6330	0.00718666
$397$	−13537.7	−1.71143	−0.855716	−	0.517446i	$-0.826883\pi$
$397$	−13537.7	−1.71143	−0.855716	+	0.517446i	$0.826883\pi$
$398$	5971.48	0.752069
$399$	2625.15	0.329378
$400$	2317.47	0.289683
$401$	−6490.51	−0.808281	−0.404141	−	0.914697i	$-0.632429\pi$
$401$	−6490.51	−0.808281	−0.404141	+	0.914697i	$0.632429\pi$
$402$	1230.73	0.152695
$403$	518.417	0.0640799
$404$	−1576.69	−0.194167
$405$	1330.58	0.163251
$406$	716.489	0.0875832
$407$	−74.1300	−0.00902822
$408$	0	0
$409$	−7733.80	−0.934992	−0.467496	−	0.883995i	$-0.654844\pi$
$409$	−7733.80	−0.934992	−0.467496	+	0.883995i	$0.654844\pi$
$410$	−7523.11	−0.906195
$411$	2920.62	0.350520
$412$	2995.57	0.358207
$413$	720.000	0.0857842
$414$	−557.784	−0.0662164
$415$	−18064.3	−2.13673
$416$	−552.979	−0.0651731
$417$	931.165	0.109351
$418$	458.859	0.0536926
$419$	8170.70	0.952660	0.476330	−	0.879267i	$-0.341967\pi$
$419$	8170.70	0.952660	0.476330	+	0.879267i	$0.341967\pi$
$420$	1182.73	0.137408
$421$	−13732.6	−1.58975	−0.794874	−	0.606774i	$-0.792463\pi$
$421$	−13732.6	−1.58975	−0.794874	+	0.606774i	$0.792463\pi$
$422$	8774.79	1.01220
$423$	4111.25	0.472567
$424$	4504.98	0.515993
$425$	0	0
$426$	5372.35	0.611012
$427$	2453.27	0.278037
$428$	−4801.92	−0.542312
$429$	−81.5543	−0.00917827
$430$	−12355.8	−1.38570
$431$	13075.7	1.46133	0.730667	−	0.682734i	$-0.239209\pi$
$431$	13075.7	1.46133	0.730667	+	0.682734i	$0.239209\pi$
$432$	432.000	0.0481125
$433$	−16873.0	−1.87266	−0.936331	−	0.351118i	$-0.885802\pi$
$433$	−16873.0	−1.87266	−0.936331	+	0.351118i	$0.885802\pi$
$434$	−360.000	−0.0398169
$435$	2942.42	0.324318
$436$	4333.76	0.476030
$437$	−4519.35	−0.494713
$438$	6402.30	0.698433
$439$	16207.3	1.76203	0.881014	−	0.473089i	$-0.156861\pi$
$439$	16207.3	1.76203	0.881014	+	0.473089i	$0.156861\pi$
$440$	206.734	0.0223992
$441$	−2763.00	−0.298348
$442$	0	0
$443$	8022.65	0.860423	0.430212	−	0.902728i	$-0.358439\pi$
$443$	8022.65	0.860423	0.430212	+	0.902728i	$0.358439\pi$
$444$	−565.468	−0.0604413
$445$	−13051.0	−1.39028
$446$	−1837.58	−0.195094
$447$	−8042.29	−0.850978
$448$	384.000	0.0404962
$449$	4730.44	0.497201	0.248600	−	0.968606i	$-0.420029\pi$
$449$	4730.44	0.497201	0.248600	+	0.968606i	$0.420029\pi$
$450$	2607.15	0.273116
$451$	−360.230	−0.0376110
$452$	−4108.24	−0.427512
$453$	680.633	0.0705937
$454$	−3508.62	−0.362705
$455$	−1703.19	−0.175488
$456$	3500.20	0.359456
$457$	−840.447	−0.0860273	−0.0430136	−	0.999074i	$-0.513696\pi$
$457$	−840.447	−0.0860273	−0.0430136	+	0.999074i	$0.513696\pi$
$458$	3718.36	0.379362
$459$	0	0
$460$	−2036.14	−0.206382
$461$	−6788.88	−0.685878	−0.342939	−	0.939358i	$-0.611422\pi$
$461$	−6788.88	−0.685878	−0.342939	+	0.939358i	$0.611422\pi$
$462$	56.6330	0.00570304
$463$	−11545.7	−1.15890	−0.579452	−	0.815006i	$-0.696733\pi$
$463$	−11545.7	−1.15890	−0.579452	+	0.815006i	$0.696733\pi$
$464$	955.319	0.0955810
$465$	−1478.42	−0.147441
$466$	−3074.86	−0.305665
$467$	−174.303	−0.0172715	−0.00863573	−	0.999963i	$-0.502749\pi$
$467$	−174.303	−0.0172715	−0.00863573	+	0.999963i	$0.502749\pi$
$468$	−622.101	−0.0614458
$469$	1230.73	0.121173
$470$	15007.8	1.47289
$471$	1059.32	0.103633
$472$	960.000	0.0936178
$473$	−591.636	−0.0575126
$474$	−6232.83	−0.603974
$475$	21124.0	2.04049
$476$	0	0
$477$	5068.10	0.486483
$478$	−7809.38	−0.747265
$479$	−16182.7	−1.54365	−0.771824	−	0.635837i	$-0.780655\pi$
$479$	−16182.7	−1.54365	−0.771824	+	0.635837i	$0.780655\pi$
$480$	1576.98	0.149956
$481$	814.301	0.0771911
$482$	−4739.28	−0.447860
$483$	−557.784	−0.0525467
$484$	−5314.10	−0.499070
$485$	16529.4	1.54755
$486$	486.000	0.0453609
$487$	−17815.3	−1.65767	−0.828837	−	0.559491i	$-0.810997\pi$
$487$	−17815.3	−1.65767	−0.828837	+	0.559491i	$0.810997\pi$
$488$	3271.02	0.303427
$489$	3212.11	0.297049
$490$	−10086.1	−0.929884
$491$	−19445.2	−1.78727	−0.893635	−	0.448794i	$-0.851854\pi$
$491$	−19445.2	−1.78727	−0.893635	+	0.448794i	$0.851854\pi$
$492$	−2747.86	−0.251795
$493$	0	0
$494$	−5040.46	−0.459071
$495$	232.576	0.0211182
$496$	−480.000	−0.0434529
$497$	5372.35	0.484875
$498$	−6598.10	−0.593711
$499$	−9524.72	−0.854479	−0.427240	−	0.904138i	$-0.640514\pi$
$499$	−9524.72	−0.854479	−0.427240	+	0.904138i	$0.640514\pi$
$500$	1303.75	0.116611
$501$	−2233.22	−0.199148
$502$	14712.5	1.30807
$503$	−1592.37	−0.141154	−0.0705768	−	0.997506i	$-0.522484\pi$
$503$	−1592.37	−0.141154	−0.0705768	+	0.997506i	$0.522484\pi$
$504$	432.000	0.0381802
$505$	−6475.02	−0.570564
$506$	−97.4970	−0.00856575
$507$	−5695.14	−0.498876
$508$	−9166.50	−0.800586
$509$	−14893.7	−1.29696	−0.648480	−	0.761232i	$-0.724595\pi$
$509$	−14893.7	−1.29696	−0.648480	+	0.761232i	$0.724595\pi$
$510$	0	0
$511$	6402.30	0.554249
$512$	512.000	0.0441942
$513$	3937.73	0.338898
$514$	−6830.65	−0.586161
$515$	12301.9	1.05260
$516$	−4513.04	−0.385030
$517$	718.619	0.0611312
$518$	−565.468	−0.0479638
$519$	8611.58	0.728336
$520$	−2270.93	−0.191513
$521$	−4403.38	−0.370279	−0.185140	−	0.982712i	$-0.559274\pi$
$521$	−4403.38	−0.370279	−0.185140	+	0.982712i	$0.559274\pi$
$522$	1074.73	0.0901146
$523$	−6728.23	−0.562533	−0.281267	−	0.959630i	$-0.590755\pi$
$523$	−6728.23	−0.562533	−0.281267	+	0.959630i	$0.590755\pi$
$524$	−7740.16	−0.645287
$525$	2607.15	0.216734
$526$	6060.43	0.502371
$527$	0	0
$528$	75.5107	0.00622383
$529$	−11206.7	−0.921077
$530$	18500.7	1.51626
$531$	1080.00	0.0882637
$532$	3500.20	0.285250
$533$	3957.05	0.321574
$534$	−4766.94	−0.386302
$535$	−19720.1	−1.59360
$536$	1640.98	0.132238
$537$	3432.09	0.275802
$538$	10899.2	0.873413
$539$	−482.954	−0.0385942
$540$	1774.10	0.141380
$541$	−13624.4	−1.08273	−0.541366	−	0.840787i	$-0.682093\pi$
$541$	−13624.4	−1.08273	−0.541366	+	0.840787i	$0.682093\pi$
$542$	5256.29	0.416563
$543$	−10548.2	−0.833641
$544$	0	0
$545$	17797.5	1.39883
$546$	−622.101	−0.0487609
$547$	−3158.10	−0.246857	−0.123428	−	0.992353i	$-0.539389\pi$
$547$	−3158.10	−0.246857	−0.123428	+	0.992353i	$0.539389\pi$
$548$	3894.16	0.303559
$549$	3679.90	0.286073
$550$	455.713	0.0353303
$551$	8707.84	0.673260
$552$	−743.713	−0.0573451
$553$	−6232.83	−0.479290
$554$	−14266.3	−1.09407
$555$	−2322.22	−0.177608
$556$	1241.55	0.0947007
$557$	−5831.35	−0.443595	−0.221797	−	0.975093i	$-0.571192\pi$
$557$	−5831.35	−0.443595	−0.221797	+	0.975093i	$0.571192\pi$
$558$	−540.000	−0.0409678
$559$	6498.99	0.491732
$560$	1576.98	0.118999
$561$	0	0
$562$	−12020.5	−0.902233
$563$	12511.5	0.936587	0.468294	−	0.883573i	$-0.344869\pi$
$563$	12511.5	0.936587	0.468294	+	0.883573i	$0.344869\pi$
$564$	5481.67	0.409255
$565$	−16871.4	−1.25625
$566$	−2452.37	−0.182122
$567$	486.000	0.0359966
$568$	7163.13	0.529152
$569$	8469.14	0.623980	0.311990	−	0.950085i	$-0.399004\pi$
$569$	8469.14	0.623980	0.311990	+	0.950085i	$0.399004\pi$
$570$	14374.3	1.05627
$571$	5857.64	0.429308	0.214654	−	0.976690i	$-0.431138\pi$
$571$	5857.64	0.429308	0.214654	+	0.976690i	$0.431138\pi$
$572$	−108.739	−0.00794862
$573$	−12460.8	−0.908480
$574$	−2747.86	−0.199814
$575$	−4488.36	−0.325526
$576$	576.000	0.0416667
$577$	15537.9	1.12106	0.560528	−	0.828135i	$-0.310598\pi$
$577$	15537.9	1.12106	0.560528	+	0.828135i	$0.310598\pi$
$578$	0	0
$579$	12272.7	0.880893
$580$	3923.22	0.280867
$581$	−6598.10	−0.471145
$582$	6037.47	0.430002
$583$	885.870	0.0629314
$584$	8536.40	0.604861
$585$	−2554.79	−0.180560
$586$	16919.5	1.19272
$587$	−1491.54	−0.104876	−0.0524382	−	0.998624i	$-0.516699\pi$
$587$	−1491.54	−0.104876	−0.0524382	+	0.998624i	$0.516699\pi$
$588$	−3684.00	−0.258377
$589$	−4375.25	−0.306077
$590$	3942.45	0.275098
$591$	14471.2	1.00722
$592$	−753.957	−0.0523437
$593$	−14418.0	−0.998442	−0.499221	−	0.866475i	$-0.666380\pi$
$593$	−14418.0	−0.998442	−0.499221	+	0.866475i	$0.666380\pi$
$594$	84.9495	0.00586788
$595$	0	0
$596$	−10723.1	−0.736969
$597$	8957.22	0.614062
$598$	1070.98	0.0732370
$599$	3644.49	0.248597	0.124299	−	0.992245i	$-0.460332\pi$
$599$	3644.49	0.248597	0.124299	+	0.992245i	$0.460332\pi$
$600$	3476.20	0.236526
$601$	−6984.34	−0.474039	−0.237019	−	0.971505i	$-0.576171\pi$
$601$	−6984.34	−0.474039	−0.237019	+	0.971505i	$0.576171\pi$
$602$	−4513.04	−0.305544
$603$	1846.10	0.124675
$604$	907.511	0.0611359
$605$	−21823.5	−1.46653
$606$	−2365.04	−0.158536
$607$	−14362.8	−0.960407	−0.480204	−	0.877157i	$-0.659437\pi$
$607$	−14362.8	−0.960407	−0.480204	+	0.877157i	$0.659437\pi$
$608$	4666.94	0.311298
$609$	1074.73	0.0715114
$610$	13433.2	0.891627
$611$	−7893.87	−0.522671
$612$	0	0
$613$	−8703.81	−0.573481	−0.286740	−	0.958008i	$-0.592572\pi$
$613$	−8703.81	−0.573481	−0.286740	+	0.958008i	$0.592572\pi$
$614$	−6769.55	−0.444946
$615$	−11284.7	−0.739905
$616$	75.5107	0.00493898
$617$	26903.7	1.75543	0.877715	−	0.479182i	$-0.159067\pi$
$617$	26903.7	1.75543	0.877715	+	0.479182i	$0.159067\pi$
$618$	4493.35	0.292474
$619$	8641.76	0.561133	0.280567	−	0.959835i	$-0.409478\pi$
$619$	8641.76	0.561133	0.280567	+	0.959835i	$0.409478\pi$
$620$	−1971.22	−0.127687
$621$	−836.677	−0.0540655
$622$	1722.01	0.111007
$623$	−4766.94	−0.306554
$624$	−829.468	−0.0532136
$625$	−12751.1	−0.816070
$626$	1901.30	0.121392
$627$	688.288	0.0438398
$628$	1412.43	0.0897486
$629$	0	0
$630$	1774.10	0.112193
$631$	10472.0	0.660672	0.330336	−	0.943863i	$-0.392838\pi$
$631$	10472.0	0.660672	0.330336	+	0.943863i	$0.392838\pi$
$632$	−8310.45	−0.523057
$633$	13162.2	0.826461
$634$	−16802.4	−1.05253
$635$	−37644.2	−2.35254
$636$	6757.47	0.421307
$637$	5305.14	0.329980
$638$	187.856	0.0116572
$639$	8058.52	0.498889
$640$	2102.64	0.129866
$641$	−9806.52	−0.604266	−0.302133	−	0.953266i	$-0.597699\pi$
$641$	−9806.52	−0.604266	−0.302133	+	0.953266i	$0.597699\pi$
$642$	−7202.88	−0.442796
$643$	−13782.6	−0.845307	−0.422653	−	0.906291i	$-0.638901\pi$
$643$	−13782.6	−0.845307	−0.422653	+	0.906291i	$0.638901\pi$
$644$	−743.713	−0.0455068
$645$	−18533.8	−1.13142
$646$	0	0
$647$	13972.3	0.849005	0.424502	−	0.905427i	$-0.360449\pi$
$647$	13972.3	0.849005	0.424502	+	0.905427i	$0.360449\pi$
$648$	648.000	0.0392837
$649$	188.777	0.0114178
$650$	−5005.90	−0.302073
$651$	−540.000	−0.0325104
$652$	4282.82	0.257252
$653$	−469.753	−0.0281514	−0.0140757	−	0.999901i	$-0.504481\pi$
$653$	−469.753	−0.0281514	−0.0140757	+	0.999901i	$0.504481\pi$
$654$	6500.63	0.388677
$655$	−31786.6	−1.89619
$656$	−3663.81	−0.218060
$657$	9603.45	0.570269
$658$	5481.67	0.324769
$659$	6126.73	0.362160	0.181080	−	0.983468i	$-0.442041\pi$
$659$	6126.73	0.362160	0.181080	+	0.983468i	$0.442041\pi$
$660$	310.101	0.0182889
$661$	19862.7	1.16879	0.584393	−	0.811471i	$-0.301333\pi$
$661$	19862.7	1.16879	0.584393	+	0.811471i	$0.301333\pi$
$662$	−8256.40	−0.484734
$663$	0	0
$664$	−8797.47	−0.514169
$665$	14374.3	0.838215
$666$	−848.202	−0.0493501
$667$	−1850.22	−0.107407
$668$	−2977.63	−0.172467
$669$	−2756.37	−0.159294
$670$	6739.03	0.388584
$671$	643.222	0.0370064
$672$	576.000	0.0330650
$673$	−29895.9	−1.71234	−0.856169	−	0.516697i	$-0.827162\pi$
$673$	−29895.9	−1.71234	−0.856169	+	0.516697i	$0.827162\pi$
$674$	80.4586	0.00459815
$675$	3910.73	0.222998
$676$	−7593.53	−0.432039
$677$	−3689.27	−0.209439	−0.104719	−	0.994502i	$-0.533394\pi$
$677$	−3689.27	−0.209439	−0.104719	+	0.994502i	$0.533394\pi$
$678$	−6162.36	−0.349062
$679$	6037.47	0.341232
$680$	0	0
$681$	−5262.94	−0.296147
$682$	−94.3884	−0.00529959
$683$	−14206.2	−0.795879	−0.397940	−	0.917412i	$-0.630275\pi$
$683$	−14206.2	−0.795879	−0.397940	+	0.917412i	$0.630275\pi$
$684$	5250.30	0.293495
$685$	15992.2	0.892016
$686$	−7800.00	−0.434119
$687$	5577.54	0.309747
$688$	−6017.38	−0.333446
$689$	−9731.08	−0.538062
$690$	−3054.22	−0.168510
$691$	36094.2	1.98710	0.993550	−	0.113391i	$-0.0361714\pi$
$691$	36094.2	1.98710	0.993550	+	0.113391i	$0.0361714\pi$
$692$	11482.1	0.630758
$693$	84.9495	0.00465652
$694$	−2275.01	−0.124436
$695$	5098.71	0.278281
$696$	1432.98	0.0780415
$697$	0	0
$698$	−1251.48	−0.0678643
$699$	−4612.29	−0.249575
$700$	3476.20	0.187697
$701$	17089.4	0.920767	0.460383	−	0.887720i	$-0.347712\pi$
$701$	17089.4	0.920767	0.460383	+	0.887720i	$0.347712\pi$
$702$	−933.151	−0.0501703
$703$	−6872.40	−0.368702
$704$	100.681	0.00538999
$705$	22511.7	1.20261
$706$	−12709.6	−0.677525
$707$	−2365.04	−0.125808
$708$	1440.00	0.0764386
$709$	17325.6	0.917737	0.458868	−	0.888504i	$-0.348255\pi$
$709$	17325.6	0.917737	0.458868	+	0.888504i	$0.348255\pi$
$710$	29416.9	1.55493
$711$	−9349.25	−0.493143
$712$	−6355.91	−0.334548
$713$	929.641	0.0488293
$714$	0	0
$715$	−446.560	−0.0233572
$716$	4576.12	0.238851
$717$	−11714.1	−0.610140
$718$	20933.8	1.08808
$719$	−3861.73	−0.200304	−0.100152	−	0.994972i	$-0.531933\pi$
$719$	−3861.73	−0.200304	−0.100152	+	0.994972i	$0.531933\pi$
$720$	2365.47	0.122439
$721$	4493.35	0.232096
$722$	28821.6	1.48564
$723$	−7108.92	−0.365676
$724$	−14064.3	−0.721955
$725$	8648.13	0.443012
$726$	−7971.15	−0.407489
$727$	3016.23	0.153873	0.0769366	−	0.997036i	$-0.475486\pi$
$727$	3016.23	0.153873	0.0769366	+	0.997036i	$0.475486\pi$
$728$	−829.468	−0.0422282
$729$	729.000	0.0370370
$730$	35056.6	1.77740
$731$	0	0
$732$	4906.53	0.247747
$733$	6778.92	0.341590	0.170795	−	0.985307i	$-0.445366\pi$
$733$	6778.92	0.341590	0.170795	+	0.985307i	$0.445366\pi$
$734$	16640.8	0.836815
$735$	−15129.1	−0.759247
$736$	−991.617	−0.0496623
$737$	322.686	0.0161279
$738$	−4121.78	−0.205589
$739$	−25629.9	−1.27579	−0.637896	−	0.770123i	$-0.720195\pi$
$739$	−25629.9	−1.27579	−0.637896	+	0.770123i	$0.720195\pi$
$740$	−3096.29	−0.153813
$741$	−7560.69	−0.374830
$742$	6757.47	0.334332
$743$	−8981.07	−0.443450	−0.221725	−	0.975109i	$-0.571169\pi$
$743$	−8981.07	−0.443450	−0.221725	+	0.975109i	$0.571169\pi$
$744$	−720.000	−0.0354791
$745$	−44036.5	−2.16560
$746$	530.501	0.0260362
$747$	−9897.15	−0.484763
$748$	0	0
$749$	−7202.88	−0.351385
$750$	1955.63	0.0952125
$751$	−4198.37	−0.203996	−0.101998	−	0.994785i	$-0.532523\pi$
$751$	−4198.37	−0.203996	−0.101998	+	0.994785i	$0.532523\pi$
$752$	7308.89	0.354425
$753$	22068.7	1.06803
$754$	−2063.56	−0.0996689
$755$	3726.89	0.179649
$756$	648.000	0.0311740
$757$	−11693.1	−0.561418	−0.280709	−	0.959793i	$-0.590570\pi$
$757$	−11693.1	−0.561418	−0.280709	+	0.959793i	$0.590570\pi$
$758$	20337.0	0.974502
$759$	−146.245	−0.00699390
$760$	19165.8	0.914758
$761$	13505.6	0.643333	0.321667	−	0.946853i	$-0.395757\pi$
$761$	13505.6	0.643333	0.321667	+	0.946853i	$0.395757\pi$
$762$	−13749.8	−0.653676
$763$	6500.63	0.308439
$764$	−16614.4	−0.786766
$765$	0	0
$766$	3293.58	0.155355
$767$	−2073.67	−0.0976217
$768$	768.000	0.0360844
$769$	15256.1	0.715407	0.357704	−	0.933835i	$-0.383560\pi$
$769$	15256.1	0.715407	0.357704	+	0.933835i	$0.383560\pi$
$770$	310.101	0.0145133
$771$	−10246.0	−0.478599
$772$	16363.6	0.762875
$773$	16038.3	0.746256	0.373128	−	0.927780i	$-0.378285\pi$
$773$	16038.3	0.746256	0.373128	+	0.927780i	$0.378285\pi$
$774$	−6769.56	−0.314375
$775$	−4345.25	−0.201401
$776$	8049.96	0.372393
$777$	−848.202	−0.0391623
$778$	−12537.4	−0.577745
$779$	−33396.0	−1.53599
$780$	−3406.39	−0.156370
$781$	1408.57	0.0645362
$782$	0	0
$783$	1612.10	0.0735783
$784$	−4912.00	−0.223761
$785$	5800.45	0.263729
$786$	−11610.2	−0.526875
$787$	26105.8	1.18243	0.591215	−	0.806514i	$-0.298648\pi$
$787$	26105.8	1.18243	0.591215	+	0.806514i	$0.298648\pi$
$788$	19295.0	0.872278
$789$	9090.65	0.410185
$790$	−34128.6	−1.53702
$791$	−6162.36	−0.277002
$792$	113.266	0.00508173
$793$	−7065.64	−0.316404
$794$	−27075.4	−1.21016
$795$	27751.0	1.23802
$796$	11943.0	0.531793
$797$	−5988.53	−0.266154	−0.133077	−	0.991106i	$-0.542486\pi$
$797$	−5988.53	−0.266154	−0.133077	+	0.991106i	$0.542486\pi$
$798$	5250.30	0.232906
$799$	0	0
$800$	4634.94	0.204837
$801$	−7150.40	−0.315415
$802$	−12981.0	−0.571541
$803$	1678.62	0.0737698
$804$	2461.47	0.107972
$805$	−3054.22	−0.133723
$806$	1036.83	0.0453114
$807$	16348.7	0.713138
$808$	−3153.38	−0.137297
$809$	44380.7	1.92873	0.964365	−	0.264577i	$-0.0852323\pi$
$809$	44380.7	1.92873	0.964365	+	0.264577i	$0.0852323\pi$
$810$	2661.15	0.115436
$811$	−33546.5	−1.45250	−0.726249	−	0.687432i	$-0.758738\pi$
$811$	−33546.5	−1.45250	−0.726249	+	0.687432i	$0.758738\pi$
$812$	1432.98	0.0619307
$813$	7884.43	0.340122
$814$	−148.260	−0.00638392
$815$	17588.3	0.755941
$816$	0	0
$817$	−54849.1	−2.34875
$818$	−15467.6	−0.661139
$819$	−933.151	−0.0398131
$820$	−15046.2	−0.640776
$821$	13701.7	0.582451	0.291226	−	0.956654i	$-0.405937\pi$
$821$	13701.7	0.582451	0.291226	+	0.956654i	$0.405937\pi$
$822$	5841.24	0.247855
$823$	−4440.76	−0.188087	−0.0940433	−	0.995568i	$-0.529979\pi$
$823$	−4440.76	−0.188087	−0.0940433	+	0.995568i	$0.529979\pi$
$824$	5991.14	0.253290
$825$	683.569	0.0288470
$826$	1440.00	0.0606586
$827$	−8705.42	−0.366043	−0.183021	−	0.983109i	$-0.558588\pi$
$827$	−8705.42	−0.366043	−0.183021	+	0.983109i	$0.558588\pi$
$828$	−1115.57	−0.0468221
$829$	5755.30	0.241121	0.120561	−	0.992706i	$-0.461531\pi$
$829$	5755.30	0.241121	0.120561	+	0.992706i	$0.461531\pi$
$830$	−36128.7	−1.51090
$831$	−21399.4	−0.893306
$832$	−1105.96	−0.0460843
$833$	0	0
$834$	1862.33	0.0773228
$835$	−12228.3	−0.506799
$836$	917.718	0.0379664
$837$	−810.000	−0.0334501
$838$	16341.4	0.673633
$839$	−29272.2	−1.20451	−0.602257	−	0.798302i	$-0.705732\pi$
$839$	−29272.2	−1.20451	−0.602257	+	0.798302i	$0.705732\pi$
$840$	2365.47	0.0971624
$841$	−20824.0	−0.853828
$842$	−27465.1	−1.12412
$843$	−18030.8	−0.736670
$844$	17549.6	0.715736
$845$	−31184.4	−1.26956
$846$	8222.50	0.334155
$847$	−7971.15	−0.323367
$848$	9009.96	0.364862
$849$	−3678.56	−0.148702
$850$	0	0
$851$	1460.23	0.0588202
$852$	10744.7	0.432051
$853$	45569.0	1.82913	0.914567	−	0.404434i	$-0.132531\pi$
$853$	45569.0	1.82913	0.914567	+	0.404434i	$0.132531\pi$
$854$	4906.53	0.196602
$855$	21561.5	0.862442
$856$	−9603.84	−0.383473
$857$	−33462.5	−1.33379	−0.666895	−	0.745151i	$-0.732377\pi$
$857$	−33462.5	−1.33379	−0.666895	+	0.745151i	$0.732377\pi$
$858$	−163.109	−0.00649002
$859$	−7859.19	−0.312168	−0.156084	−	0.987744i	$-0.549887\pi$
$859$	−7859.19	−0.312168	−0.156084	+	0.987744i	$0.549887\pi$
$860$	−24711.7	−0.979839
$861$	−4121.78	−0.163148
$862$	26151.4	1.03332
$863$	−17613.4	−0.694746	−0.347373	−	0.937727i	$-0.612926\pi$
$863$	−17613.4	−0.694746	−0.347373	+	0.937727i	$0.612926\pi$
$864$	864.000	0.0340207
$865$	47153.8	1.85350
$866$	−33745.9	−1.32417
$867$	0	0
$868$	−720.000	−0.0281548
$869$	−1634.19	−0.0637928
$870$	5884.83	0.229327
$871$	−3544.63	−0.137894
$872$	8667.51	0.336604
$873$	9056.20	0.351095
$874$	−9038.69	−0.349815
$875$	1955.63	0.0755568
$876$	12804.6	0.493867
$877$	−38660.0	−1.48855	−0.744274	−	0.667874i	$-0.767204\pi$
$877$	−38660.0	−1.48855	−0.744274	+	0.667874i	$0.767204\pi$
$878$	32414.5	1.24594
$879$	25379.2	0.973855
$880$	413.468	0.0158386
$881$	−15647.5	−0.598384	−0.299192	−	0.954193i	$-0.596717\pi$
$881$	−15647.5	−0.598384	−0.299192	+	0.954193i	$0.596717\pi$
$882$	−5526.00	−0.210964
$883$	−12759.6	−0.486291	−0.243145	−	0.969990i	$-0.578179\pi$
$883$	−12759.6	−0.486291	−0.243145	+	0.969990i	$0.578179\pi$
$884$	0	0
$885$	5913.67	0.224617
$886$	16045.3	0.608411
$887$	−18022.4	−0.682225	−0.341113	−	0.940022i	$-0.610804\pi$
$887$	−18022.4	−0.682225	−0.341113	+	0.940022i	$0.610804\pi$
$888$	−1130.94	−0.0427384
$889$	−13749.8	−0.518731
$890$	−26101.9	−0.983077
$891$	127.424	0.00479111
$892$	−3675.17	−0.137952
$893$	66621.4	2.49653
$894$	−16084.6	−0.601732
$895$	18792.8	0.701871
$896$	768.000	0.0286351
$897$	1606.47	0.0597977
$898$	9460.88	0.351574
$899$	−1791.22	−0.0664523
$900$	5214.30	0.193122
$901$	0	0
$902$	−720.460	−0.0265950
$903$	−6769.56	−0.249476
$904$	−8216.48	−0.302296
$905$	−57758.0	−2.12148
$906$	1361.27	0.0499173
$907$	51434.0	1.88295	0.941477	−	0.337078i	$-0.109439\pi$
$907$	51434.0	1.88295	0.941477	+	0.337078i	$0.109439\pi$
$908$	−7017.25	−0.256471
$909$	−3547.56	−0.129444
$910$	−3406.39	−0.124089
$911$	7890.19	0.286953	0.143476	−	0.989654i	$-0.454172\pi$
$911$	7890.19	0.286953	0.143476	+	0.989654i	$0.454172\pi$
$912$	7000.40	0.254174
$913$	−1729.96	−0.0627088
$914$	−1680.89	−0.0608305
$915$	20149.7	0.728010
$916$	7436.72	0.268249
$917$	−11610.2	−0.418107
$918$	0	0
$919$	−46068.0	−1.65358	−0.826792	−	0.562507i	$-0.809837\pi$
$919$	−46068.0	−1.65358	−0.826792	+	0.562507i	$0.809837\pi$
$920$	−4072.29	−0.145934
$921$	−10154.3	−0.363297
$922$	−13577.8	−0.484989
$923$	−15472.9	−0.551783
$924$	113.266	0.00403266
$925$	−6825.28	−0.242610
$926$	−23091.3	−0.819469
$927$	6740.03	0.238804
$928$	1910.64	0.0675860
$929$	28007.0	0.989106	0.494553	−	0.869147i	$-0.335332\pi$
$929$	28007.0	0.989106	0.494553	+	0.869147i	$0.335332\pi$
$930$	−2956.83	−0.104256
$931$	−44773.4	−1.57614
$932$	−6149.72	−0.216138
$933$	2583.01	0.0906365
$934$	−348.606	−0.0122128
$935$	0	0
$936$	−1244.20	−0.0434487
$937$	−42032.8	−1.46548	−0.732738	−	0.680511i	$-0.761758\pi$
$937$	−42032.8	−1.46548	−0.732738	+	0.680511i	$0.761758\pi$
$938$	2461.47	0.0856821
$939$	2851.95	0.0991158
$940$	30015.5	1.04149
$941$	−31863.4	−1.10384	−0.551922	−	0.833896i	$-0.686105\pi$
$941$	−31863.4	−1.10384	−0.551922	+	0.833896i	$0.686105\pi$
$942$	2118.65	0.0732794
$943$	7095.89	0.245041
$944$	1920.00	0.0661978
$945$	2661.15	0.0916056
$946$	−1183.27	−0.0406676
$947$	42612.1	1.46220	0.731102	−	0.682269i	$-0.239007\pi$
$947$	42612.1	1.46220	0.731102	+	0.682269i	$0.239007\pi$
$948$	−12465.7	−0.427074
$949$	−18439.3	−0.630731
$950$	42247.9	1.44285
$951$	−25203.5	−0.859390
$952$	0	0
$953$	−6529.28	−0.221935	−0.110968	−	0.993824i	$-0.535395\pi$
$953$	−6529.28	−0.221935	−0.110968	+	0.993824i	$0.535395\pi$
$954$	10136.2	0.343995
$955$	−68230.8	−2.31193
$956$	−15618.8	−0.528396
$957$	281.784	0.00951807
$958$	−32365.4	−1.09152
$959$	5841.24	0.196688
$960$	3153.96	0.106035
$961$	−28891.0	−0.969790
$962$	1628.60	0.0545824
$963$	−10804.3	−0.361541
$964$	−9478.56	−0.316685
$965$	67200.8	2.24173
$966$	−1115.57	−0.0371561
$967$	−21784.1	−0.724436	−0.362218	−	0.932093i	$-0.617980\pi$
$967$	−21784.1	−0.724436	−0.362218	+	0.932093i	$0.617980\pi$
$968$	−10628.2	−0.352896
$969$	0	0
$970$	33058.9	1.09429
$971$	293.579	0.00970279	0.00485140	−	0.999988i	$-0.498456\pi$
$971$	293.579	0.00970279	0.00485140	+	0.999988i	$0.498456\pi$
$972$	972.000	0.0320750
$973$	1862.33	0.0613603
$974$	−35630.5	−1.17215
$975$	−7508.85	−0.246642
$976$	6542.04	0.214555
$977$	−42000.5	−1.37535	−0.687673	−	0.726020i	$-0.741368\pi$
$977$	−42000.5	−1.37535	−0.687673	+	0.726020i	$0.741368\pi$
$978$	6424.23	0.210045
$979$	−1249.84	−0.0408020
$980$	−20172.2	−0.657527
$981$	9750.95	0.317354
$982$	−38890.4	−1.26379
$983$	−4754.22	−0.154258	−0.0771292	−	0.997021i	$-0.524575\pi$
$983$	−4754.22	−0.154258	−0.0771292	+	0.997021i	$0.524575\pi$
$984$	−5495.71	−0.178046
$985$	79239.0	2.56321
$986$	0	0
$987$	8222.50	0.265172
$988$	−10080.9	−0.324612
$989$	11654.2	0.374703
$990$	465.151	0.0149328
$991$	44080.5	1.41298	0.706491	−	0.707722i	$-0.250277\pi$
$991$	44080.5	1.41298	0.706491	+	0.707722i	$0.250277\pi$
$992$	−960.000	−0.0307258
$993$	−12384.6	−0.395784
$994$	10744.7	0.342858
$995$	49046.4	1.56269
$996$	−13196.2	−0.419817
$997$	6073.28	0.192922	0.0964608	−	0.995337i	$-0.469248\pi$
$997$	6073.28	0.192922	0.0964608	+	0.995337i	$0.469248\pi$
$998$	−19049.4	−0.604208
$999$	−1272.30	−0.0402942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.4.a.s.1.2		2
17.4	even	4		102.4.b.a.67.1	✓	4
17.13	even	4		102.4.b.a.67.4	yes	4
17.16	even	2		1734.4.a.m.1.1		2
51.38	odd	4		306.4.b.e.271.4		4
51.47	odd	4		306.4.b.e.271.1		4
68.47	odd	4		816.4.c.b.577.2		4
68.55	odd	4		816.4.c.b.577.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.4.b.a.67.1	✓	4	17.4	even	4
102.4.b.a.67.4	yes	4	17.13	even	4
306.4.b.e.271.1		4	51.47	odd	4
306.4.b.e.271.4		4	51.38	odd	4
816.4.c.b.577.2		4	68.47	odd	4
816.4.c.b.577.3		4	68.55	odd	4
1734.4.a.m.1.1		2	17.16	even	2
1734.4.a.s.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1734.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +16.4269 q^{5} +6.00000 q^{6} +6.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +32.8537 q^{10} +1.57314 q^{11} +12.0000 q^{12} -17.2806 q^{13} +12.0000 q^{14} +49.2806 q^{15} +16.0000 q^{16} +18.0000 q^{18} +145.842 q^{19} +65.7074 q^{20} +18.0000 q^{21} +3.14628 q^{22} -30.9880 q^{23} +24.0000 q^{24} +144.842 q^{25} -34.5612 q^{26} +27.0000 q^{27} +24.0000 q^{28} +59.7074 q^{29} +98.5612 q^{30} -30.0000 q^{31} +32.0000 q^{32} +4.71942 q^{33} +98.5612 q^{35} +36.0000 q^{36} -47.1223 q^{37} +291.683 q^{38} -51.8417 q^{39} +131.415 q^{40} -228.988 q^{41} +36.0000 q^{42} -376.086 q^{43} +6.29256 q^{44} +147.842 q^{45} -61.9760 q^{46} +456.806 q^{47} +48.0000 q^{48} -307.000 q^{49} +289.683 q^{50} -69.1223 q^{52} +563.122 q^{53} +54.0000 q^{54} +25.8417 q^{55} +48.0000 q^{56} +437.525 q^{57} +119.415 q^{58} +120.000 q^{59} +197.122 q^{60} +408.878 q^{61} -60.0000 q^{62} +54.0000 q^{63} +64.0000 q^{64} -283.866 q^{65} +9.43884 q^{66} +205.122 q^{67} -92.9641 q^{69} +197.122 q^{70} +895.391 q^{71} +72.0000 q^{72} +1067.05 q^{73} -94.2447 q^{74} +434.525 q^{75} +583.367 q^{76} +9.43884 q^{77} -103.683 q^{78} -1038.81 q^{79} +262.830 q^{80} +81.0000 q^{81} -457.976 q^{82} -1099.68 q^{83} +72.0000 q^{84} -752.173 q^{86} +179.122 q^{87} +12.5851 q^{88} -794.489 q^{89} +295.683 q^{90} -103.683 q^{91} -123.952 q^{92} -90.0000 q^{93} +913.612 q^{94} +2395.72 q^{95} +96.0000 q^{96} +1006.24 q^{97} -614.000 q^{98} +14.1583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} + 6 q^{3} + 8 q^{4} + 9 q^{5} + 12 q^{6} + 12 q^{7} + 16 q^{8} + 18 q^{9} + 18 q^{10} + 27 q^{11} + 24 q^{12} + 37 q^{13} + 24 q^{14} + 27 q^{15} + 32 q^{16} + 36 q^{18} + 77 q^{19} + 36 q^{20}+ \cdots + 243 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 + 6 * q^3 + 8 * q^4 + 9 * q^5 + 12 * q^6 + 12 * q^7 + 16 * q^8 + 18 * q^9 + 18 * q^10 + 27 * q^11 + 24 * q^12 + 37 * q^13 + 24 * q^14 + 27 * q^15 + 32 * q^16 + 36 * q^18 + 77 * q^19 + 36 * q^20 + 36 * q^21 + 54 * q^22 + 105 * q^23 + 48 * q^24 + 75 * q^25 + 74 * q^26 + 54 * q^27 + 48 * q^28 + 24 * q^29 + 54 * q^30 - 60 * q^31 + 64 * q^32 + 81 * q^33 + 54 * q^35 + 72 * q^36 + 192 * q^37 + 154 * q^38 + 111 * q^39 + 72 * q^40 - 291 * q^41 + 72 * q^42 + 35 * q^43 + 108 * q^44 + 81 * q^45 + 210 * q^46 + 198 * q^47 + 96 * q^48 - 614 * q^49 + 150 * q^50 + 148 * q^52 + 840 * q^53 + 108 * q^54 - 163 * q^55 + 96 * q^56 + 231 * q^57 + 48 * q^58 + 240 * q^59 + 108 * q^60 + 1104 * q^61 - 120 * q^62 + 108 * q^63 + 128 * q^64 - 687 * q^65 + 162 * q^66 + 124 * q^67 + 315 * q^69 + 108 * q^70 + 1266 * q^71 + 144 * q^72 + 846 * q^73 + 384 * q^74 + 225 * q^75 + 308 * q^76 + 162 * q^77 + 222 * q^78 - 1362 * q^79 + 144 * q^80 + 162 * q^81 - 582 * q^82 - 1770 * q^83 + 144 * q^84 + 70 * q^86 + 72 * q^87 + 216 * q^88 - 444 * q^89 + 162 * q^90 + 222 * q^91 + 420 * q^92 - 180 * q^93 + 396 * q^94 + 2907 * q^95 + 192 * q^96 + 1440 * q^97 - 1228 * q^98 + 243 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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