LMFDB - Embedded newform 546.4.a.n.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(1,546)] 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("546.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-6,9,12,13] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.360321.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 153x - 224 $ x^3 - 153*x - 224
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$13.0450$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -4.85440 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +9.70880 q^{10} -37.3255 q^{11} +12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} -14.5632 q^{15} +16.0000 q^{16} +117.124 q^{17} -18.0000 q^{18} -94.5418 q^{19} -19.4176 q^{20} +21.0000 q^{21} +74.6510 q^{22} +217.595 q^{23} -24.0000 q^{24} -101.435 q^{25} +26.0000 q^{26} +27.0000 q^{27} +28.0000 q^{28} +82.8373 q^{29} +29.1264 q^{30} +19.5975 q^{31} -32.0000 q^{32} -111.977 q^{33} -234.248 q^{34} -33.9808 q^{35} +36.0000 q^{36} -197.266 q^{37} +189.084 q^{38} -39.0000 q^{39} +38.8352 q^{40} +248.347 q^{41} -42.0000 q^{42} +405.698 q^{43} -149.302 q^{44} -43.6896 q^{45} -435.191 q^{46} +448.039 q^{47} +48.0000 q^{48} +49.0000 q^{49} +202.870 q^{50} +351.373 q^{51} -52.0000 q^{52} +12.5181 q^{53} -54.0000 q^{54} +181.193 q^{55} -56.0000 q^{56} -283.626 q^{57} -165.675 q^{58} -293.178 q^{59} -58.2528 q^{60} -331.989 q^{61} -39.1950 q^{62} +63.0000 q^{63} +64.0000 q^{64} +63.1072 q^{65} +223.953 q^{66} +205.992 q^{67} +468.497 q^{68} +652.786 q^{69} +67.9616 q^{70} -703.002 q^{71} -72.0000 q^{72} +676.187 q^{73} +394.531 q^{74} -304.304 q^{75} -378.167 q^{76} -261.279 q^{77} +78.0000 q^{78} +541.152 q^{79} -77.6704 q^{80} +81.0000 q^{81} -496.694 q^{82} +516.308 q^{83} +84.0000 q^{84} -568.568 q^{85} -811.397 q^{86} +248.512 q^{87} +298.604 q^{88} +535.649 q^{89} +87.3792 q^{90} -91.0000 q^{91} +870.381 q^{92} +58.7925 q^{93} -896.077 q^{94} +458.944 q^{95} -96.0000 q^{96} +1589.02 q^{97} -98.0000 q^{98} -335.930 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} + 13 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} - 26 q^{10} + 17 q^{11} + 36 q^{12} - 39 q^{13} - 42 q^{14} + 39 q^{15} + 48 q^{16} + 89 q^{17} - 54 q^{18} + 89 q^{19}+ \cdots + 153 q^{99}+O(q^{100}) $ 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 + 13 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9 - 26 * q^10 + 17 * q^11 + 36 * q^12 - 39 * q^13 - 42 * q^14 + 39 * q^15 + 48 * q^16 + 89 * q^17 - 54 * q^18 + 89 * q^19 + 52 * q^20 + 63 * q^21 - 34 * q^22 + 289 * q^23 - 72 * q^24 + 86 * q^25 + 78 * q^26 + 81 * q^27 + 84 * q^28 + 125 * q^29 - 78 * q^30 - 208 * q^31 - 96 * q^32 + 51 * q^33 - 178 * q^34 + 91 * q^35 + 108 * q^36 + 213 * q^37 - 178 * q^38 - 117 * q^39 - 104 * q^40 + 530 * q^41 - 126 * q^42 - 75 * q^43 + 68 * q^44 + 117 * q^45 - 578 * q^46 + 298 * q^47 + 144 * q^48 + 147 * q^49 - 172 * q^50 + 267 * q^51 - 156 * q^52 + 710 * q^53 - 162 * q^54 - 87 * q^55 - 168 * q^56 + 267 * q^57 - 250 * q^58 - 250 * q^59 + 156 * q^60 - 511 * q^61 + 416 * q^62 + 189 * q^63 + 192 * q^64 - 169 * q^65 - 102 * q^66 - 522 * q^67 + 356 * q^68 + 867 * q^69 - 182 * q^70 + 282 * q^71 - 216 * q^72 - 701 * q^73 - 426 * q^74 + 258 * q^75 + 356 * q^76 + 119 * q^77 + 234 * q^78 + 1262 * q^79 + 208 * q^80 + 243 * q^81 - 1060 * q^82 + 1700 * q^83 + 252 * q^84 - 385 * q^85 + 150 * q^86 + 375 * q^87 - 136 * q^88 + 1628 * q^89 - 234 * q^90 - 273 * q^91 + 1156 * q^92 - 624 * q^93 - 596 * q^94 + 2775 * q^95 - 288 * q^96 + 1526 * q^97 - 294 * q^98 + 153 * 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
$5$	−4.85440	−0.434191	−0.217095	−	0.976150i	$-0.569658\pi$
$5$	−4.85440	−0.434191	−0.217095	+	0.976150i	$0.569658\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	9.70880	0.307019
$11$	−37.3255	−1.02310	−0.511548	−	0.859255i	$-0.670928\pi$
$11$	−37.3255	−1.02310	−0.511548	+	0.859255i	$0.670928\pi$
$12$	12.0000	0.288675
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−14.0000	−0.267261
$15$	−14.5632	−0.250680
$16$	16.0000	0.250000
$17$	117.124	1.67099	0.835494	−	0.549499i	$-0.185181\pi$
$17$	117.124	1.67099	0.835494	+	0.549499i	$0.185181\pi$
$18$	−18.0000	−0.235702
$19$	−94.5418	−1.14155	−0.570773	−	0.821108i	$-0.693356\pi$
$19$	−94.5418	−1.14155	−0.570773	+	0.821108i	$0.693356\pi$
$20$	−19.4176	−0.217095
$21$	21.0000	0.218218
$22$	74.6510	0.723438
$23$	217.595	1.97269	0.986343	−	0.164706i	$-0.0526674\pi$
$23$	217.595	1.97269	0.986343	+	0.164706i	$0.0526674\pi$
$24$	−24.0000	−0.204124
$25$	−101.435	−0.811479
$26$	26.0000	0.196116
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	82.8373	0.530431	0.265216	−	0.964189i	$-0.414557\pi$
$29$	82.8373	0.530431	0.265216	+	0.964189i	$0.414557\pi$
$30$	29.1264	0.177258
$31$	19.5975	0.113542	0.0567712	−	0.998387i	$-0.481919\pi$
$31$	19.5975	0.113542	0.0567712	+	0.998387i	$0.481919\pi$
$32$	−32.0000	−0.176777
$33$	−111.977	−0.590685
$34$	−234.248	−1.18157
$35$	−33.9808	−0.164109
$36$	36.0000	0.166667
$37$	−197.266	−0.876494	−0.438247	−	0.898855i	$-0.644401\pi$
$37$	−197.266	−0.876494	−0.438247	+	0.898855i	$0.644401\pi$
$38$	189.084	0.807195
$39$	−39.0000	−0.160128
$40$	38.8352	0.153510
$41$	248.347	0.945983	0.472991	−	0.881067i	$-0.343174\pi$
$41$	248.347	0.945983	0.472991	+	0.881067i	$0.343174\pi$
$42$	−42.0000	−0.154303
$43$	405.698	1.43880	0.719400	−	0.694596i	$-0.244417\pi$
$43$	405.698	1.43880	0.719400	+	0.694596i	$0.244417\pi$
$44$	−149.302	−0.511548
$45$	−43.6896	−0.144730
$46$	−435.191	−1.39490
$47$	448.039	1.39049	0.695246	−	0.718772i	$-0.255295\pi$
$47$	448.039	1.39049	0.695246	+	0.718772i	$0.255295\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	202.870	0.573802
$51$	351.373	0.964746
$52$	−52.0000	−0.138675
$53$	12.5181	0.0324433	0.0162216	−	0.999868i	$-0.494836\pi$
$53$	12.5181	0.0324433	0.0162216	+	0.999868i	$0.494836\pi$
$54$	−54.0000	−0.136083
$55$	181.193	0.444219
$56$	−56.0000	−0.133631
$57$	−283.626	−0.659072
$58$	−165.675	−0.375072
$59$	−293.178	−0.646924	−0.323462	−	0.946241i	$-0.604847\pi$
$59$	−293.178	−0.646924	−0.323462	+	0.946241i	$0.604847\pi$
$60$	−58.2528	−0.125340
$61$	−331.989	−0.696834	−0.348417	−	0.937340i	$-0.613281\pi$
$61$	−331.989	−0.696834	−0.348417	+	0.937340i	$0.613281\pi$
$62$	−39.1950	−0.0802866
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	63.1072	0.120423
$66$	223.953	0.417677
$67$	205.992	0.375610	0.187805	−	0.982206i	$-0.439863\pi$
$67$	205.992	0.375610	0.187805	+	0.982206i	$0.439863\pi$
$68$	468.497	0.835494
$69$	652.786	1.13893
$70$	67.9616	0.116042
$71$	−703.002	−1.17509	−0.587543	−	0.809193i	$-0.699905\pi$
$71$	−703.002	−1.17509	−0.587543	+	0.809193i	$0.699905\pi$
$72$	−72.0000	−0.117851
$73$	676.187	1.08413	0.542066	−	0.840336i	$-0.317642\pi$
$73$	676.187	1.08413	0.542066	+	0.840336i	$0.317642\pi$
$74$	394.531	0.619775
$75$	−304.304	−0.468507
$76$	−378.167	−0.570773
$77$	−261.279	−0.386694
$78$	78.0000	0.113228
$79$	541.152	0.770688	0.385344	−	0.922773i	$-0.374083\pi$
$79$	541.152	0.770688	0.385344	+	0.922773i	$0.374083\pi$
$80$	−77.6704	−0.108548
$81$	81.0000	0.111111
$82$	−496.694	−0.668911
$83$	516.308	0.682798	0.341399	−	0.939919i	$-0.389099\pi$
$83$	516.308	0.682798	0.341399	+	0.939919i	$0.389099\pi$
$84$	84.0000	0.109109
$85$	−568.568	−0.725527
$86$	−811.397	−1.01739
$87$	248.512	0.306245
$88$	298.604	0.361719
$89$	535.649	0.637962	0.318981	−	0.947761i	$-0.396659\pi$
$89$	535.649	0.637962	0.318981	+	0.947761i	$0.396659\pi$
$90$	87.3792	0.102340
$91$	−91.0000	−0.104828
$92$	870.381	0.986343
$93$	58.7925	0.0655537
$94$	−896.077	−0.983227
$95$	458.944	0.495649
$96$	−96.0000	−0.102062
$97$	1589.02	1.66330	0.831650	−	0.555300i	$-0.187397\pi$
$97$	1589.02	1.66330	0.831650	+	0.555300i	$0.187397\pi$
$98$	−98.0000	−0.101015
$99$	−335.930	−0.341032
$100$	−405.739	−0.405739
$101$	11.7004	0.0115270	0.00576352	−	0.999983i	$-0.498165\pi$
$101$	11.7004	0.0115270	0.00576352	+	0.999983i	$0.498165\pi$
$102$	−702.745	−0.682178
$103$	−764.696	−0.731532	−0.365766	−	0.930707i	$-0.619193\pi$
$103$	−764.696	−0.731532	−0.365766	+	0.930707i	$0.619193\pi$
$104$	104.000	0.0980581
$105$	−101.942	−0.0947481
$106$	−25.0362	−0.0229409
$107$	592.527	0.535343	0.267672	−	0.963510i	$-0.413746\pi$
$107$	592.527	0.535343	0.267672	+	0.963510i	$0.413746\pi$
$108$	108.000	0.0962250
$109$	588.889	0.517480	0.258740	−	0.965947i	$-0.416693\pi$
$109$	588.889	0.517480	0.258740	+	0.965947i	$0.416693\pi$
$110$	−362.386	−0.314110
$111$	−591.797	−0.506044
$112$	112.000	0.0944911
$113$	1843.09	1.53436	0.767182	−	0.641429i	$-0.221658\pi$
$113$	1843.09	1.53436	0.767182	+	0.641429i	$0.221658\pi$
$114$	567.251	0.466034
$115$	−1056.29	−0.856521
$116$	331.349	0.265216
$117$	−117.000	−0.0924500
$118$	586.356	0.457444
$119$	819.870	0.631574
$120$	116.506	0.0886288
$121$	62.1930	0.0467265
$122$	663.979	0.492736
$123$	745.041	0.546163
$124$	78.3900	0.0567712
$125$	1099.20	0.786527
$126$	−126.000	−0.0890871
$127$	2122.43	1.48295	0.741477	−	0.670978i	$-0.234126\pi$
$127$	2122.43	1.48295	0.741477	+	0.670978i	$0.234126\pi$
$128$	−128.000	−0.0883883
$129$	1217.10	0.830692
$130$	−126.214	−0.0851518
$131$	1728.02	1.15250	0.576252	−	0.817272i	$-0.304515\pi$
$131$	1728.02	1.15250	0.576252	+	0.817272i	$0.304515\pi$
$132$	−447.906	−0.295343
$133$	−661.793	−0.431464
$134$	−411.983	−0.265597
$135$	−131.069	−0.0835600
$136$	−936.994	−0.590784
$137$	2629.37	1.63973	0.819863	−	0.572559i	$-0.194049\pi$
$137$	2629.37	1.63973	0.819863	+	0.572559i	$0.194049\pi$
$138$	−1305.57	−0.805345
$139$	−1705.17	−1.04051	−0.520253	−	0.854012i	$-0.674162\pi$
$139$	−1705.17	−1.04051	−0.520253	+	0.854012i	$0.674162\pi$
$140$	−135.923	−0.0820543
$141$	1344.12	0.802801
$142$	1406.00	0.830911
$143$	485.232	0.283756
$144$	144.000	0.0833333
$145$	−402.125	−0.230308
$146$	−1352.37	−0.766598
$147$	147.000	0.0824786
$148$	−789.063	−0.438247
$149$	62.6255	0.0344328	0.0172164	−	0.999852i	$-0.494520\pi$
$149$	62.6255	0.0344328	0.0172164	+	0.999852i	$0.494520\pi$
$150$	608.609	0.331285
$151$	556.100	0.299701	0.149850	−	0.988709i	$-0.452121\pi$
$151$	556.100	0.299701	0.149850	+	0.988709i	$0.452121\pi$
$152$	756.335	0.403598
$153$	1054.12	0.556996
$154$	522.557	0.273434
$155$	−95.1340	−0.0492990
$156$	−156.000	−0.0800641
$157$	−85.0851	−0.0432518	−0.0216259	−	0.999766i	$-0.506884\pi$
$157$	−85.0851	−0.0432518	−0.0216259	+	0.999766i	$0.506884\pi$
$158$	−1082.30	−0.544959
$159$	37.5543	0.0187311
$160$	155.341	0.0767548
$161$	1523.17	0.745605
$162$	−162.000	−0.0785674
$163$	−813.331	−0.390828	−0.195414	−	0.980721i	$-0.562605\pi$
$163$	−813.331	−0.390828	−0.195414	+	0.980721i	$0.562605\pi$
$164$	993.388	0.472991
$165$	543.579	0.256470
$166$	−1032.62	−0.482811
$167$	901.145	0.417561	0.208781	−	0.977963i	$-0.433051\pi$
$167$	901.145	0.417561	0.208781	+	0.977963i	$0.433051\pi$
$168$	−168.000	−0.0771517
$169$	169.000	0.0769231
$170$	1137.14	0.513025
$171$	−850.877	−0.380516
$172$	1622.79	0.719400
$173$	−2967.98	−1.30434	−0.652172	−	0.758071i	$-0.726142\pi$
$173$	−2967.98	−1.30434	−0.652172	+	0.758071i	$0.726142\pi$
$174$	−497.024	−0.216548
$175$	−710.044	−0.306710
$176$	−597.208	−0.255774
$177$	−879.534	−0.373502
$178$	−1071.30	−0.451108
$179$	−2399.66	−1.00200	−0.501002	−	0.865446i	$-0.667035\pi$
$179$	−2399.66	−1.00200	−0.501002	+	0.865446i	$0.667035\pi$
$180$	−174.758	−0.0723651
$181$	709.324	0.291291	0.145645	−	0.989337i	$-0.453474\pi$
$181$	709.324	0.291291	0.145645	+	0.989337i	$0.453474\pi$
$182$	182.000	0.0741249
$183$	−995.968	−0.402317
$184$	−1740.76	−0.697450
$185$	957.606	0.380566
$186$	−117.585	−0.0463535
$187$	−4371.72	−1.70958
$188$	1792.15	0.695246
$189$	189.000	0.0727393
$190$	−917.887	−0.350477
$191$	−4285.90	−1.62365	−0.811825	−	0.583901i	$-0.801525\pi$
$191$	−4285.90	−1.62365	−0.811825	+	0.583901i	$0.801525\pi$
$192$	192.000	0.0721688
$193$	−2644.57	−0.986324	−0.493162	−	0.869937i	$-0.664159\pi$
$193$	−2644.57	−0.986324	−0.493162	+	0.869937i	$0.664159\pi$
$194$	−3178.03	−1.17613
$195$	189.322	0.0695261
$196$	196.000	0.0714286
$197$	93.2818	0.0337363	0.0168681	−	0.999858i	$-0.494630\pi$
$197$	93.2818	0.0337363	0.0168681	+	0.999858i	$0.494630\pi$
$198$	671.859	0.241146
$199$	2311.41	0.823375	0.411687	−	0.911325i	$-0.364940\pi$
$199$	2311.41	0.823375	0.411687	+	0.911325i	$0.364940\pi$
$200$	811.479	0.286901
$201$	617.975	0.216859
$202$	−23.4007	−0.00815084
$203$	579.861	0.200484
$204$	1405.49	0.482373
$205$	−1205.58	−0.410737
$206$	1529.39	0.517271
$207$	1958.36	0.657562
$208$	−208.000	−0.0693375
$209$	3528.82	1.16791
$210$	203.885	0.0669971
$211$	222.218	0.0725029	0.0362514	−	0.999343i	$-0.488458\pi$
$211$	222.218	0.0725029	0.0362514	+	0.999343i	$0.488458\pi$
$212$	50.0724	0.0162216
$213$	−2109.01	−0.678436
$214$	−1185.05	−0.378545
$215$	−1969.42	−0.624714
$216$	−216.000	−0.0680414
$217$	137.182	0.0429150
$218$	−1177.78	−0.365914
$219$	2028.56	0.625924
$220$	724.771	0.222109
$221$	−1522.62	−0.463449
$222$	1183.59	0.357827
$223$	2509.35	0.753536	0.376768	−	0.926308i	$-0.377035\pi$
$223$	2509.35	0.753536	0.376768	+	0.926308i	$0.377035\pi$
$224$	−224.000	−0.0668153
$225$	−912.913	−0.270493
$226$	−3686.18	−1.08496
$227$	−1717.91	−0.502299	−0.251149	−	0.967948i	$-0.580809\pi$
$227$	−1717.91	−0.502299	−0.251149	+	0.967948i	$0.580809\pi$
$228$	−1134.50	−0.329536
$229$	−6571.65	−1.89636	−0.948180	−	0.317733i	$-0.897079\pi$
$229$	−6571.65	−1.89636	−0.948180	+	0.317733i	$0.897079\pi$
$230$	2112.59	0.605652
$231$	−783.836	−0.223258
$232$	−662.699	−0.187536
$233$	−6869.07	−1.93136	−0.965682	−	0.259726i	$-0.916368\pi$
$233$	−6869.07	−1.93136	−0.965682	+	0.259726i	$0.916368\pi$
$234$	234.000	0.0653720
$235$	−2174.96	−0.603739
$236$	−1172.71	−0.323462
$237$	1623.46	0.444957
$238$	−1639.74	−0.446590
$239$	590.909	0.159928	0.0799639	−	0.996798i	$-0.474520\pi$
$239$	590.909	0.159928	0.0799639	+	0.996798i	$0.474520\pi$
$240$	−233.011	−0.0626700
$241$	−1434.45	−0.383408	−0.191704	−	0.981453i	$-0.561401\pi$
$241$	−1434.45	−0.383408	−0.191704	+	0.981453i	$0.561401\pi$
$242$	−124.386	−0.0330406
$243$	243.000	0.0641500
$244$	−1327.96	−0.348417
$245$	−237.866	−0.0620272
$246$	−1490.08	−0.386196
$247$	1229.04	0.316608
$248$	−156.780	−0.0401433
$249$	1548.92	0.394213
$250$	−2198.41	−0.556159
$251$	−373.347	−0.0938864	−0.0469432	−	0.998898i	$-0.514948\pi$
$251$	−373.347	−0.0938864	−0.0469432	+	0.998898i	$0.514948\pi$
$252$	252.000	0.0629941
$253$	−8121.86	−2.01825
$254$	−4244.86	−1.04861
$255$	−1705.70	−0.418883
$256$	256.000	0.0625000
$257$	−6462.04	−1.56845	−0.784224	−	0.620478i	$-0.786939\pi$
$257$	−6462.04	−1.56845	−0.784224	+	0.620478i	$0.786939\pi$
$258$	−2434.19	−0.587388
$259$	−1380.86	−0.331284
$260$	252.429	0.0602114
$261$	745.536	0.176810
$262$	−3456.05	−0.814944
$263$	3456.05	0.810302	0.405151	−	0.914250i	$-0.367219\pi$
$263$	3456.05	0.810302	0.405151	+	0.914250i	$0.367219\pi$
$264$	895.812	0.208839
$265$	−60.7678	−0.0140866
$266$	1323.59	0.305091
$267$	1606.95	0.368328
$268$	823.967	0.187805
$269$	2397.79	0.543478	0.271739	−	0.962371i	$-0.412401\pi$
$269$	2397.79	0.543478	0.271739	+	0.962371i	$0.412401\pi$
$270$	262.137	0.0590859
$271$	3106.40	0.696311	0.348155	−	0.937437i	$-0.386808\pi$
$271$	3106.40	0.696311	0.348155	+	0.937437i	$0.386808\pi$
$272$	1873.99	0.417747
$273$	−273.000	−0.0605228
$274$	−5258.75	−1.15946
$275$	3786.11	0.830221
$276$	2611.14	0.569465
$277$	−2128.61	−0.461717	−0.230859	−	0.972987i	$-0.574153\pi$
$277$	−2128.61	−0.461717	−0.230859	+	0.972987i	$0.574153\pi$
$278$	3410.33	0.735749
$279$	176.377	0.0378475
$280$	271.846	0.0580212
$281$	−5702.46	−1.21061	−0.605303	−	0.795995i	$-0.706948\pi$
$281$	−5702.46	−1.21061	−0.605303	+	0.795995i	$0.706948\pi$
$282$	−2688.23	−0.567666
$283$	3188.53	0.669748	0.334874	−	0.942263i	$-0.391306\pi$
$283$	3188.53	0.669748	0.334874	+	0.942263i	$0.391306\pi$
$284$	−2812.01	−0.587543
$285$	1376.83	0.286163
$286$	−970.463	−0.200646
$287$	1738.43	0.357548
$288$	−288.000	−0.0589256
$289$	8805.09	1.79220
$290$	804.251	0.162853
$291$	4767.05	0.960307
$292$	2704.75	0.542066
$293$	2986.10	0.595392	0.297696	−	0.954661i	$-0.403782\pi$
$293$	2986.10	0.595392	0.297696	+	0.954661i	$0.403782\pi$
$294$	−294.000	−0.0583212
$295$	1423.20	0.280888
$296$	1578.13	0.309887
$297$	−1007.79	−0.196895
$298$	−125.251	−0.0243476
$299$	−2828.74	−0.547125
$300$	−1217.22	−0.234254
$301$	2839.89	0.543816
$302$	−1112.20	−0.211920
$303$	35.1011	0.00665513
$304$	−1512.67	−0.285387
$305$	1611.61	0.302559
$306$	−2108.24	−0.393856
$307$	−9398.38	−1.74721	−0.873605	−	0.486635i	$-0.838224\pi$
$307$	−9398.38	−1.74721	−0.873605	+	0.486635i	$0.838224\pi$
$308$	−1045.11	−0.193347
$309$	−2294.09	−0.422350
$310$	190.268	0.0348597
$311$	4101.38	0.747806	0.373903	−	0.927468i	$-0.378019\pi$
$311$	4101.38	0.747806	0.373903	+	0.927468i	$0.378019\pi$
$312$	312.000	0.0566139
$313$	1081.49	0.195302	0.0976509	−	0.995221i	$-0.468867\pi$
$313$	1081.49	0.195302	0.0976509	+	0.995221i	$0.468867\pi$
$314$	170.170	0.0305836
$315$	−305.827	−0.0547029
$316$	2164.61	0.385344
$317$	9170.18	1.62476	0.812379	−	0.583129i	$-0.198172\pi$
$317$	9170.18	1.62476	0.812379	+	0.583129i	$0.198172\pi$
$318$	−75.1086	−0.0132449
$319$	−3091.94	−0.542682
$320$	−310.681	−0.0542738
$321$	1777.58	0.309081
$322$	−3046.33	−0.527222
$323$	−11073.1	−1.90751
$324$	324.000	0.0555556
$325$	1318.65	0.225064
$326$	1626.66	0.276357
$327$	1766.67	0.298767
$328$	−1986.78	−0.334455
$329$	3136.27	0.525557
$330$	−1087.16	−0.181352
$331$	−5015.76	−0.832903	−0.416452	−	0.909158i	$-0.636727\pi$
$331$	−5015.76	−0.832903	−0.416452	+	0.909158i	$0.636727\pi$
$332$	2065.23	0.341399
$333$	−1775.39	−0.292165
$334$	−1802.29	−0.295260
$335$	−999.966	−0.163086
$336$	336.000	0.0545545
$337$	−11257.2	−1.81964	−0.909821	−	0.415000i	$-0.863781\pi$
$337$	−11257.2	−1.81964	−0.909821	+	0.415000i	$0.863781\pi$
$338$	−338.000	−0.0543928
$339$	5529.27	0.885866
$340$	−2274.27	−0.362764
$341$	−731.486	−0.116165
$342$	1701.75	0.269065
$343$	343.000	0.0539949
$344$	−3245.59	−0.508693
$345$	−3168.88	−0.494513
$346$	5935.96	0.922310
$347$	7961.81	1.23174	0.615868	−	0.787850i	$-0.288806\pi$
$347$	7961.81	1.23174	0.615868	+	0.787850i	$0.288806\pi$
$348$	994.048	0.153122
$349$	−4918.41	−0.754375	−0.377187	−	0.926137i	$-0.623109\pi$
$349$	−4918.41	−0.754375	−0.377187	+	0.926137i	$0.623109\pi$
$350$	1420.09	0.216877
$351$	−351.000	−0.0533761
$352$	1194.42	0.180860
$353$	−8048.19	−1.21349	−0.606745	−	0.794897i	$-0.707525\pi$
$353$	−8048.19	−1.21349	−0.606745	+	0.794897i	$0.707525\pi$
$354$	1759.07	0.264106
$355$	3412.65	0.510211
$356$	2142.59	0.318981
$357$	2459.61	0.364640
$358$	4799.32	0.708524
$359$	−737.826	−0.108471	−0.0542353	−	0.998528i	$-0.517272\pi$
$359$	−737.826	−0.108471	−0.0542353	+	0.998528i	$0.517272\pi$
$360$	349.517	0.0511698
$361$	2079.16	0.303129
$362$	−1418.65	−0.205974
$363$	186.579	0.0269776
$364$	−364.000	−0.0524142
$365$	−3282.48	−0.470720
$366$	1991.94	0.284481
$367$	343.699	0.0488854	0.0244427	−	0.999701i	$-0.492219\pi$
$367$	343.699	0.0488854	0.0244427	+	0.999701i	$0.492219\pi$
$368$	3481.53	0.493171
$369$	2235.12	0.315328
$370$	−1915.21	−0.269100
$371$	87.6267	0.0122624
$372$	235.170	0.0327769
$373$	6601.55	0.916396	0.458198	−	0.888850i	$-0.348495\pi$
$373$	6601.55	0.916396	0.458198	+	0.888850i	$0.348495\pi$
$374$	8743.44	1.20886
$375$	3297.61	0.454102
$376$	−3584.31	−0.491613
$377$	−1076.89	−0.147115
$378$	−378.000	−0.0514344
$379$	−2104.70	−0.285254	−0.142627	−	0.989776i	$-0.545555\pi$
$379$	−2104.70	−0.285254	−0.142627	+	0.989776i	$0.545555\pi$
$380$	1835.77	0.247824
$381$	6367.29	0.856184
$382$	8571.80	1.14809
$383$	−5072.74	−0.676776	−0.338388	−	0.941007i	$-0.609882\pi$
$383$	−5072.74	−0.676776	−0.338388	+	0.941007i	$0.609882\pi$
$384$	−384.000	−0.0510310
$385$	1268.35	0.167899
$386$	5289.15	0.697437
$387$	3651.29	0.479600
$388$	6356.06	0.831650
$389$	4260.40	0.555298	0.277649	−	0.960683i	$-0.410445\pi$
$389$	4260.40	0.555298	0.277649	+	0.960683i	$0.410445\pi$
$390$	−378.643	−0.0491624
$391$	25485.7	3.29633
$392$	−392.000	−0.0505076
$393$	5184.07	0.665399
$394$	−186.564	−0.0238552
$395$	−2626.97	−0.334625
$396$	−1343.72	−0.170516
$397$	−5954.40	−0.752753	−0.376376	−	0.926467i	$-0.622830\pi$
$397$	−5954.40	−0.752753	−0.376376	+	0.926467i	$0.622830\pi$
$398$	−4622.82	−0.582214
$399$	−1985.38	−0.249106
$400$	−1622.96	−0.202870
$401$	144.743	0.0180252	0.00901262	−	0.999959i	$-0.497131\pi$
$401$	144.743	0.0180252	0.00901262	+	0.999959i	$0.497131\pi$
$402$	−1235.95	−0.153342
$403$	−254.767	−0.0314910
$404$	46.8015	0.00576352
$405$	−393.206	−0.0482434
$406$	−1159.72	−0.141764
$407$	7363.04	0.896738
$408$	−2810.98	−0.341089
$409$	1360.88	0.164526	0.0822630	−	0.996611i	$-0.473785\pi$
$409$	1360.88	0.164526	0.0822630	+	0.996611i	$0.473785\pi$
$410$	2411.15	0.290435
$411$	7888.12	0.946697
$412$	−3058.79	−0.365766
$413$	−2052.25	−0.244514
$414$	−3916.72	−0.464966
$415$	−2506.37	−0.296464
$416$	416.000	0.0490290
$417$	−5115.50	−0.600736
$418$	−7057.64	−0.825839
$419$	−15750.6	−1.83643	−0.918216	−	0.396081i	$-0.870370\pi$
$419$	−15750.6	−1.83643	−0.918216	+	0.396081i	$0.870370\pi$
$420$	−407.769	−0.0473741
$421$	16454.0	1.90480	0.952399	−	0.304854i	$-0.0986078\pi$
$421$	16454.0	1.90480	0.952399	+	0.304854i	$0.0986078\pi$
$422$	−444.436	−0.0512673
$423$	4032.35	0.463498
$424$	−100.145	−0.0114704
$425$	−11880.5	−1.35597
$426$	4218.01	0.479726
$427$	−2323.93	−0.263378
$428$	2370.11	0.267672
$429$	1455.69	0.163827
$430$	3938.84	0.441739
$431$	−2792.11	−0.312045	−0.156022	−	0.987754i	$-0.549867\pi$
$431$	−2792.11	−0.312045	−0.156022	+	0.987754i	$0.549867\pi$
$432$	432.000	0.0481125
$433$	832.508	0.0923967	0.0461983	−	0.998932i	$-0.485289\pi$
$433$	832.508	0.0923967	0.0461983	+	0.998932i	$0.485289\pi$
$434$	−274.365	−0.0303455
$435$	−1206.38	−0.132969
$436$	2355.56	0.258740
$437$	−20571.9	−2.25191
$438$	−4057.12	−0.442595
$439$	−12645.9	−1.37484	−0.687420	−	0.726260i	$-0.741257\pi$
$439$	−12645.9	−1.37484	−0.687420	+	0.726260i	$0.741257\pi$
$440$	−1449.54	−0.157055
$441$	441.000	0.0476190
$442$	3045.23	0.327708
$443$	15610.5	1.67421	0.837107	−	0.547039i	$-0.184245\pi$
$443$	15610.5	1.67421	0.837107	+	0.547039i	$0.184245\pi$
$444$	−2367.19	−0.253022
$445$	−2600.25	−0.276997
$446$	−5018.70	−0.532831
$447$	187.877	0.0198798
$448$	448.000	0.0472456
$449$	7424.72	0.780388	0.390194	−	0.920733i	$-0.372408\pi$
$449$	7424.72	0.780388	0.390194	+	0.920733i	$0.372408\pi$
$450$	1825.83	0.191267
$451$	−9269.68	−0.967832
$452$	7372.35	0.767182
$453$	1668.30	0.173032
$454$	3435.82	0.355179
$455$	441.750	0.0455155
$456$	2269.00	0.233017
$457$	−11630.9	−1.19053	−0.595265	−	0.803529i	$-0.702953\pi$
$457$	−11630.9	−1.19053	−0.595265	+	0.803529i	$0.702953\pi$
$458$	13143.3	1.34093
$459$	3162.35	0.321582
$460$	−4225.18	−0.428261
$461$	8200.13	0.828456	0.414228	−	0.910173i	$-0.364052\pi$
$461$	8200.13	0.828456	0.414228	+	0.910173i	$0.364052\pi$
$462$	1567.67	0.157867
$463$	−15254.0	−1.53113	−0.765566	−	0.643357i	$-0.777541\pi$
$463$	−15254.0	−1.53113	−0.765566	+	0.643357i	$0.777541\pi$
$464$	1325.40	0.132608
$465$	−285.402	−0.0284628
$466$	13738.1	1.36568
$467$	14907.8	1.47720	0.738600	−	0.674144i	$-0.235487\pi$
$467$	14907.8	1.47720	0.738600	+	0.674144i	$0.235487\pi$
$468$	−468.000	−0.0462250
$469$	1441.94	0.141967
$470$	4349.92	0.426908
$471$	−255.255	−0.0249714
$472$	2345.42	0.228722
$473$	−15142.9	−1.47203
$474$	−3246.91	−0.314632
$475$	9589.83	0.926341
$476$	3279.48	0.315787
$477$	112.663	0.0108144
$478$	−1181.82	−0.113086
$479$	18190.2	1.73514	0.867570	−	0.497315i	$-0.165681\pi$
$479$	18190.2	1.73514	0.867570	+	0.497315i	$0.165681\pi$
$480$	466.022	0.0443144
$481$	2564.45	0.243096
$482$	2868.91	0.271110
$483$	4569.50	0.430475
$484$	248.772	0.0233633
$485$	−7713.71	−0.722189
$486$	−486.000	−0.0453609
$487$	10247.9	0.953549	0.476774	−	0.879026i	$-0.341806\pi$
$487$	10247.9	0.953549	0.476774	+	0.879026i	$0.341806\pi$
$488$	2655.91	0.246368
$489$	−2439.99	−0.225645
$490$	475.731	0.0438599
$491$	−13915.1	−1.27898	−0.639489	−	0.768800i	$-0.720854\pi$
$491$	−13915.1	−1.27898	−0.639489	+	0.768800i	$0.720854\pi$
$492$	2980.16	0.273082
$493$	9702.26	0.886344
$494$	−2458.09	−0.223876
$495$	1630.74	0.148073
$496$	313.560	0.0283856
$497$	−4921.02	−0.444140
$498$	−3097.85	−0.278751
$499$	8085.70	0.725382	0.362691	−	0.931910i	$-0.381858\pi$
$499$	8085.70	0.725382	0.362691	+	0.931910i	$0.381858\pi$
$500$	4396.82	0.393263
$501$	2703.44	0.241079
$502$	746.695	0.0663877
$503$	16846.5	1.49334	0.746668	−	0.665196i	$-0.231652\pi$
$503$	16846.5	1.49334	0.746668	+	0.665196i	$0.231652\pi$
$504$	−504.000	−0.0445435
$505$	−56.7982	−0.00500493
$506$	16243.7	1.42712
$507$	507.000	0.0444116
$508$	8489.72	0.741477
$509$	−14103.8	−1.22818	−0.614088	−	0.789237i	$-0.710476\pi$
$509$	−14103.8	−1.22818	−0.614088	+	0.789237i	$0.710476\pi$
$510$	3411.41	0.296195
$511$	4733.31	0.409764
$512$	−512.000	−0.0441942
$513$	−2552.63	−0.219691
$514$	12924.1	1.10906
$515$	3712.14	0.317624
$516$	4868.38	0.415346
$517$	−16723.3	−1.42261
$518$	2761.72	0.234253
$519$	−8903.94	−0.753063
$520$	−504.857	−0.0425759
$521$	−19125.4	−1.60826	−0.804128	−	0.594457i	$-0.797367\pi$
$521$	−19125.4	−1.60826	−0.804128	+	0.594457i	$0.797367\pi$
$522$	−1491.07	−0.125024
$523$	5324.03	0.445132	0.222566	−	0.974918i	$-0.428557\pi$
$523$	5324.03	0.445132	0.222566	+	0.974918i	$0.428557\pi$
$524$	6912.09	0.576252
$525$	−2130.13	−0.177079
$526$	−6912.11	−0.572970
$527$	2295.34	0.189728
$528$	−1791.62	−0.147671
$529$	35180.7	2.89149
$530$	121.536	0.00996070
$531$	−2638.60	−0.215641
$532$	−2647.17	−0.215732
$533$	−3228.51	−0.262368
$534$	−3213.89	−0.260447
$535$	−2876.36	−0.232441
$536$	−1647.93	−0.132798
$537$	−7198.97	−0.578508
$538$	−4795.57	−0.384297
$539$	−1828.95	−0.146157
$540$	−524.275	−0.0417800
$541$	5559.63	0.441825	0.220912	−	0.975294i	$-0.429097\pi$
$541$	5559.63	0.441825	0.220912	+	0.975294i	$0.429097\pi$
$542$	−6212.80	−0.492366
$543$	2127.97	0.168177
$544$	−3747.98	−0.295392
$545$	−2858.70	−0.224685
$546$	546.000	0.0427960
$547$	17982.3	1.40561	0.702803	−	0.711385i	$-0.251932\pi$
$547$	17982.3	1.40561	0.702803	+	0.711385i	$0.251932\pi$
$548$	10517.5	0.819863
$549$	−2987.90	−0.232278
$550$	−7572.21	−0.587055
$551$	−7831.59	−0.605512
$552$	−5222.29	−0.402673
$553$	3788.06	0.291293
$554$	4257.22	0.326483
$555$	2872.82	0.219720
$556$	−6820.67	−0.520253
$557$	−6167.80	−0.469188	−0.234594	−	0.972093i	$-0.575376\pi$
$557$	−6167.80	−0.469188	−0.234594	+	0.972093i	$0.575376\pi$
$558$	−352.755	−0.0267622
$559$	−5274.08	−0.399051
$560$	−543.693	−0.0410272
$561$	−13115.2	−0.987028
$562$	11404.9	0.856027
$563$	13596.7	1.01782	0.508909	−	0.860821i	$-0.330049\pi$
$563$	13596.7	1.01782	0.508909	+	0.860821i	$0.330049\pi$
$564$	5376.46	0.401401
$565$	−8947.09	−0.666207
$566$	−6377.07	−0.473583
$567$	567.000	0.0419961
$568$	5624.02	0.415455
$569$	−27041.1	−1.99231	−0.996154	−	0.0876247i	$-0.972072\pi$
$569$	−27041.1	−1.99231	−0.996154	+	0.0876247i	$0.972072\pi$
$570$	−2753.66	−0.202348
$571$	8298.22	0.608178	0.304089	−	0.952644i	$-0.401648\pi$
$571$	8298.22	0.608178	0.304089	+	0.952644i	$0.401648\pi$
$572$	1940.93	0.141878
$573$	−12857.7	−0.937414
$574$	−3476.86	−0.252824
$575$	−22071.7	−1.60079
$576$	576.000	0.0416667
$577$	−4866.75	−0.351136	−0.175568	−	0.984467i	$-0.556176\pi$
$577$	−4866.75	−0.351136	−0.175568	+	0.984467i	$0.556176\pi$
$578$	−17610.2	−1.26728
$579$	−7933.72	−0.569455
$580$	−1608.50	−0.115154
$581$	3614.16	0.258073
$582$	−9534.09	−0.679039
$583$	−467.244	−0.0331926
$584$	−5409.49	−0.383299
$585$	567.965	0.0401409
$586$	−5972.20	−0.421006
$587$	14245.5	1.00166	0.500832	−	0.865545i	$-0.333027\pi$
$587$	14245.5	1.00166	0.500832	+	0.865545i	$0.333027\pi$
$588$	588.000	0.0412393
$589$	−1852.78	−0.129614
$590$	−2846.40	−0.198618
$591$	279.845	0.0194777
$592$	−3156.25	−0.219124
$593$	5901.47	0.408675	0.204337	−	0.978901i	$-0.434496\pi$
$593$	5901.47	0.408675	0.204337	+	0.978901i	$0.434496\pi$
$594$	2015.58	0.139226
$595$	−3979.97	−0.274224
$596$	250.502	0.0172164
$597$	6934.23	0.475376
$598$	5657.48	0.386875
$599$	7847.97	0.535324	0.267662	−	0.963513i	$-0.413749\pi$
$599$	7847.97	0.535324	0.267662	+	0.963513i	$0.413749\pi$
$600$	2434.44	0.165642
$601$	−20973.8	−1.42353	−0.711764	−	0.702418i	$-0.752104\pi$
$601$	−20973.8	−1.42353	−0.711764	+	0.702418i	$0.752104\pi$
$602$	−5679.78	−0.384536
$603$	1853.93	0.125203
$604$	2224.40	0.149850
$605$	−301.910	−0.0202882
$606$	−70.2022	−0.00470589
$607$	−20786.1	−1.38992	−0.694960	−	0.719048i	$-0.744578\pi$
$607$	−20786.1	−1.38992	−0.694960	+	0.719048i	$0.744578\pi$
$608$	3025.34	0.201799
$609$	1739.58	0.115750
$610$	−3223.22	−0.213941
$611$	−5824.50	−0.385653
$612$	4216.47	0.278498
$613$	24969.3	1.64519	0.822594	−	0.568629i	$-0.192526\pi$
$613$	24969.3	1.64519	0.822594	+	0.568629i	$0.192526\pi$
$614$	18796.8	1.23546
$615$	−3616.73	−0.237139
$616$	2090.23	0.136717
$617$	−1619.24	−0.105653	−0.0528267	−	0.998604i	$-0.516823\pi$
$617$	−1619.24	−0.105653	−0.0528267	+	0.998604i	$0.516823\pi$
$618$	4588.18	0.298647
$619$	−3389.13	−0.220066	−0.110033	−	0.993928i	$-0.535096\pi$
$619$	−3389.13	−0.220066	−0.110033	+	0.993928i	$0.535096\pi$
$620$	−380.536	−0.0246495
$621$	5875.07	0.379644
$622$	−8202.75	−0.528779
$623$	3749.54	0.241127
$624$	−624.000	−0.0400320
$625$	7343.37	0.469976
$626$	−2162.98	−0.138099
$627$	10586.5	0.674295
$628$	−340.340	−0.0216259
$629$	−23104.6	−1.46461
$630$	611.654	0.0386808
$631$	14492.0	0.914293	0.457147	−	0.889391i	$-0.348871\pi$
$631$	14492.0	0.914293	0.457147	+	0.889391i	$0.348871\pi$
$632$	−4329.22	−0.272479
$633$	666.653	0.0418595
$634$	−18340.4	−1.14888
$635$	−10303.1	−0.643885
$636$	150.217	0.00936556
$637$	−637.000	−0.0396214
$638$	6183.89	0.383734
$639$	−6327.02	−0.391695
$640$	621.363	0.0383774
$641$	5611.83	0.345794	0.172897	−	0.984940i	$-0.444687\pi$
$641$	5611.83	0.345794	0.172897	+	0.984940i	$0.444687\pi$
$642$	−3555.16	−0.218553
$643$	−2387.85	−0.146450	−0.0732252	−	0.997315i	$-0.523329\pi$
$643$	−2387.85	−0.146450	−0.0732252	+	0.997315i	$0.523329\pi$
$644$	6092.67	0.372803
$645$	−5908.26	−0.360679
$646$	22146.3	1.34881
$647$	−18302.7	−1.11214	−0.556070	−	0.831135i	$-0.687691\pi$
$647$	−18302.7	−1.11214	−0.556070	+	0.831135i	$0.687691\pi$
$648$	−648.000	−0.0392837
$649$	10943.0	0.661866
$650$	−2637.31	−0.159144
$651$	411.547	0.0247770
$652$	−3253.33	−0.195414
$653$	14142.9	0.847554	0.423777	−	0.905767i	$-0.360704\pi$
$653$	14142.9	0.847554	0.423777	+	0.905767i	$0.360704\pi$
$654$	−3533.33	−0.211260
$655$	−8388.51	−0.500407
$656$	3973.55	0.236496
$657$	6085.68	0.361378
$658$	−6272.54	−0.371625
$659$	−15772.6	−0.932343	−0.466172	−	0.884694i	$-0.654367\pi$
$659$	−15772.6	−0.932343	−0.466172	+	0.884694i	$0.654367\pi$
$660$	2174.31	0.128235
$661$	−27618.9	−1.62519	−0.812595	−	0.582828i	$-0.801946\pi$
$661$	−27618.9	−1.62519	−0.812595	+	0.582828i	$0.801946\pi$
$662$	10031.5	0.588952
$663$	−4567.85	−0.267572
$664$	−4130.47	−0.241405
$665$	3212.61	0.187338
$666$	3550.78	0.206592
$667$	18025.0	1.04637
$668$	3604.58	0.208781
$669$	7528.05	0.435054
$670$	1999.93	0.115320
$671$	12391.7	0.712928
$672$	−672.000	−0.0385758
$673$	9200.07	0.526949	0.263475	−	0.964666i	$-0.415132\pi$
$673$	9200.07	0.526949	0.263475	+	0.964666i	$0.415132\pi$
$674$	22514.4	1.28668
$675$	−2738.74	−0.156169
$676$	676.000	0.0384615
$677$	−32034.9	−1.81861	−0.909307	−	0.416127i	$-0.863387\pi$
$677$	−32034.9	−1.81861	−0.909307	+	0.416127i	$0.863387\pi$
$678$	−11058.5	−0.626402
$679$	11123.1	0.628668
$680$	4548.54	0.256513
$681$	−5153.74	−0.290002
$682$	1462.97	0.0821409
$683$	−8728.38	−0.488993	−0.244497	−	0.969650i	$-0.578623\pi$
$683$	−8728.38	−0.488993	−0.244497	+	0.969650i	$0.578623\pi$
$684$	−3403.51	−0.190258
$685$	−12764.0	−0.711954
$686$	−686.000	−0.0381802
$687$	−19714.9	−1.09486
$688$	6491.17	0.359700
$689$	−162.735	−0.00899814
$690$	6337.77	0.349673
$691$	−20218.5	−1.11309	−0.556546	−	0.830817i	$-0.687874\pi$
$691$	−20218.5	−1.11309	−0.556546	+	0.830817i	$0.687874\pi$
$692$	−11871.9	−0.652172
$693$	−2351.51	−0.128898
$694$	−15923.6	−0.870969
$695$	8277.56	0.451778
$696$	−1988.10	−0.108274
$697$	29087.5	1.58073
$698$	9836.83	0.533423
$699$	−20607.2	−1.11507
$700$	−2840.17	−0.153355
$701$	31990.5	1.72363	0.861816	−	0.507221i	$-0.169327\pi$
$701$	31990.5	1.72363	0.861816	+	0.507221i	$0.169327\pi$
$702$	702.000	0.0377426
$703$	18649.9	1.00056
$704$	−2388.83	−0.127887
$705$	−6524.87	−0.348569
$706$	16096.4	0.858067
$707$	81.9026	0.00435681
$708$	−3518.13	−0.186751
$709$	21247.3	1.12547	0.562737	−	0.826636i	$-0.309749\pi$
$709$	21247.3	1.12547	0.562737	+	0.826636i	$0.309749\pi$
$710$	−6825.31	−0.360774
$711$	4870.37	0.256896
$712$	−4285.19	−0.225554
$713$	4264.32	0.223983
$714$	−4919.22	−0.257839
$715$	−2355.51	−0.123204
$716$	−9598.63	−0.501002
$717$	1772.73	0.0923343
$718$	1475.65	0.0767003
$719$	−3028.18	−0.157068	−0.0785341	−	0.996911i	$-0.525024\pi$
$719$	−3028.18	−0.157068	−0.0785341	+	0.996911i	$0.525024\pi$
$720$	−699.033	−0.0361825
$721$	−5352.87	−0.276493
$722$	−4158.32	−0.214344
$723$	−4303.36	−0.221361
$724$	2837.30	0.145645
$725$	−8402.59	−0.430434
$726$	−373.158	−0.0190760
$727$	10195.6	0.520131	0.260066	−	0.965591i	$-0.416256\pi$
$727$	10195.6	0.520131	0.260066	+	0.965591i	$0.416256\pi$
$728$	728.000	0.0370625
$729$	729.000	0.0370370
$730$	6564.96	0.332849
$731$	47517.1	2.40422
$732$	−3983.87	−0.201159
$733$	−15183.3	−0.765085	−0.382542	−	0.923938i	$-0.624951\pi$
$733$	−15183.3	−0.765085	−0.382542	+	0.923938i	$0.624951\pi$
$734$	−687.398	−0.0345672
$735$	−713.597	−0.0358114
$736$	−6963.05	−0.348725
$737$	−7688.74	−0.384286
$738$	−4470.25	−0.222970
$739$	7083.95	0.352621	0.176311	−	0.984335i	$-0.443584\pi$
$739$	7083.95	0.352621	0.176311	+	0.984335i	$0.443584\pi$
$740$	3830.43	0.190283
$741$	3687.13	0.182794
$742$	−175.253	−0.00867083
$743$	19458.4	0.960781	0.480391	−	0.877055i	$-0.340495\pi$
$743$	19458.4	0.960781	0.480391	+	0.877055i	$0.340495\pi$
$744$	−470.340	−0.0231767
$745$	−304.009	−0.0149504
$746$	−13203.1	−0.647990
$747$	4646.77	0.227599
$748$	−17486.9	−0.854791
$749$	4147.69	0.202341
$750$	−6595.23	−0.321098
$751$	16575.5	0.805392	0.402696	−	0.915334i	$-0.368073\pi$
$751$	16575.5	0.805392	0.402696	+	0.915334i	$0.368073\pi$
$752$	7168.62	0.347623
$753$	−1120.04	−0.0542053
$754$	2153.77	0.104026
$755$	−2699.53	−0.130127
$756$	756.000	0.0363696
$757$	4318.02	0.207320	0.103660	−	0.994613i	$-0.466945\pi$
$757$	4318.02	0.207320	0.103660	+	0.994613i	$0.466945\pi$
$758$	4209.41	0.201705
$759$	−24365.6	−1.16524
$760$	−3671.55	−0.175238
$761$	−3407.44	−0.162312	−0.0811562	−	0.996701i	$-0.525861\pi$
$761$	−3407.44	−0.162312	−0.0811562	+	0.996701i	$0.525861\pi$
$762$	−12734.6	−0.605413
$763$	4122.22	0.195589
$764$	−17143.6	−0.811825
$765$	−5117.11	−0.241842
$766$	10145.5	0.478553
$767$	3811.31	0.179424
$768$	768.000	0.0360844
$769$	−34681.1	−1.62631	−0.813154	−	0.582049i	$-0.802251\pi$
$769$	−34681.1	−1.62631	−0.813154	+	0.582049i	$0.802251\pi$
$770$	−2536.70	−0.118722
$771$	−19386.1	−0.905544
$772$	−10578.3	−0.493162
$773$	16220.7	0.754744	0.377372	−	0.926062i	$-0.376828\pi$
$773$	16220.7	0.754744	0.377372	+	0.926062i	$0.376828\pi$
$774$	−7302.57	−0.339129
$775$	−1987.87	−0.0921372
$776$	−12712.1	−0.588065
$777$	−4142.58	−0.191267
$778$	−8520.80	−0.392655
$779$	−23479.2	−1.07988
$780$	757.286	0.0347631
$781$	26239.9	1.20223
$782$	−50971.4	−2.33086
$783$	2236.61	0.102082
$784$	784.000	0.0357143
$785$	413.037	0.0187795
$786$	−10368.1	−0.470508
$787$	−5286.23	−0.239433	−0.119717	−	0.992808i	$-0.538199\pi$
$787$	−5286.23	−0.239433	−0.119717	+	0.992808i	$0.538199\pi$
$788$	373.127	0.0168681
$789$	10368.2	0.467828
$790$	5253.93	0.236616
$791$	12901.6	0.579935
$792$	2687.44	0.120573
$793$	4315.86	0.193267
$794$	11908.8	0.532277
$795$	−182.304	−0.00813288
$796$	9245.64	0.411687
$797$	821.656	0.0365176	0.0182588	−	0.999833i	$-0.494188\pi$
$797$	821.656	0.0365176	0.0182588	+	0.999833i	$0.494188\pi$
$798$	3970.76	0.176144
$799$	52476.2	2.32350
$800$	3245.91	0.143450
$801$	4820.84	0.212654
$802$	−289.486	−0.0127458
$803$	−25239.0	−1.10917
$804$	2471.90	0.108429
$805$	−7394.06	−0.323735
$806$	509.535	0.0222675
$807$	7193.36	0.313777
$808$	−93.6030	−0.00407542
$809$	22619.6	0.983021	0.491511	−	0.870872i	$-0.336445\pi$
$809$	22619.6	0.983021	0.491511	+	0.870872i	$0.336445\pi$
$810$	786.412	0.0341132
$811$	13429.3	0.581464	0.290732	−	0.956805i	$-0.406101\pi$
$811$	13429.3	0.581464	0.290732	+	0.956805i	$0.406101\pi$
$812$	2319.45	0.100242
$813$	9319.20	0.402015
$814$	−14726.1	−0.634090
$815$	3948.23	0.169694
$816$	5621.96	0.241186
$817$	−38355.5	−1.64246
$818$	−2721.76	−0.116337
$819$	−819.000	−0.0349428
$820$	−4822.30	−0.205368
$821$	−28625.2	−1.21684	−0.608421	−	0.793614i	$-0.708197\pi$
$821$	−28625.2	−1.21684	−0.608421	+	0.793614i	$0.708197\pi$
$822$	−15776.2	−0.669416
$823$	−21209.9	−0.898335	−0.449167	−	0.893448i	$-0.648279\pi$
$823$	−21209.9	−0.898335	−0.449167	+	0.893448i	$0.648279\pi$
$824$	6117.57	0.258636
$825$	11358.3	0.479328
$826$	4104.49	0.172898
$827$	5648.78	0.237518	0.118759	−	0.992923i	$-0.462108\pi$
$827$	5648.78	0.237518	0.118759	+	0.992923i	$0.462108\pi$
$828$	7833.43	0.328781
$829$	1853.34	0.0776466	0.0388233	−	0.999246i	$-0.487639\pi$
$829$	1853.34	0.0776466	0.0388233	+	0.999246i	$0.487639\pi$
$830$	5012.73	0.209632
$831$	−6385.82	−0.266573
$832$	−832.000	−0.0346688
$833$	5739.09	0.238713
$834$	10231.0	0.424785
$835$	−4374.52	−0.181301
$836$	14115.3	0.583956
$837$	529.132	0.0218512
$838$	31501.1	1.29855
$839$	5780.54	0.237862	0.118931	−	0.992903i	$-0.462053\pi$
$839$	5780.54	0.237862	0.118931	+	0.992903i	$0.462053\pi$
$840$	815.539	0.0334985
$841$	−17527.0	−0.718643
$842$	−32908.0	−1.34690
$843$	−17107.4	−0.698943
$844$	888.871	0.0362514
$845$	−820.393	−0.0333993
$846$	−8064.70	−0.327742
$847$	435.351	0.0176610
$848$	200.290	0.00811082
$849$	9565.60	0.386679
$850$	23761.0	0.958816
$851$	−42924.1	−1.72905
$852$	−8436.03	−0.339218
$853$	−30035.9	−1.20564	−0.602819	−	0.797878i	$-0.705956\pi$
$853$	−30035.9	−1.20564	−0.602819	+	0.797878i	$0.705956\pi$
$854$	4647.85	0.186237
$855$	4130.49	0.165216
$856$	−4740.22	−0.189272
$857$	−32056.8	−1.27776	−0.638879	−	0.769308i	$-0.720601\pi$
$857$	−32056.8	−1.27776	−0.638879	+	0.769308i	$0.720601\pi$
$858$	−2911.39	−0.115843
$859$	31491.8	1.25086	0.625429	−	0.780281i	$-0.284924\pi$
$859$	31491.8	1.25086	0.625429	+	0.780281i	$0.284924\pi$
$860$	−7877.69	−0.312357
$861$	5215.29	0.206430
$862$	5584.23	0.220649
$863$	10925.1	0.430931	0.215466	−	0.976511i	$-0.430873\pi$
$863$	10925.1	0.430931	0.215466	+	0.976511i	$0.430873\pi$
$864$	−864.000	−0.0340207
$865$	14407.8	0.566334
$866$	−1665.02	−0.0653343
$867$	26415.3	1.03473
$868$	548.730	0.0214575
$869$	−20198.8	−0.788488
$870$	2412.75	0.0940229
$871$	−2677.89	−0.104176
$872$	−4711.11	−0.182957
$873$	14301.1	0.554433
$874$	41143.7	1.59234
$875$	7694.43	0.297279
$876$	8114.24	0.312962
$877$	−17702.7	−0.681618	−0.340809	−	0.940133i	$-0.610701\pi$
$877$	−17702.7	−0.681618	−0.340809	+	0.940133i	$0.610701\pi$
$878$	25291.8	0.972159
$879$	8958.31	0.343750
$880$	2899.09	0.111055
$881$	−19496.4	−0.745575	−0.372787	−	0.927917i	$-0.621598\pi$
$881$	−19496.4	−0.745575	−0.372787	+	0.927917i	$0.621598\pi$
$882$	−882.000	−0.0336718
$883$	−15666.7	−0.597085	−0.298543	−	0.954396i	$-0.596501\pi$
$883$	−15666.7	−0.597085	−0.298543	+	0.954396i	$0.596501\pi$
$884$	−6090.46	−0.231724
$885$	4269.61	0.162171
$886$	−31221.0	−1.18385
$887$	2274.22	0.0860889	0.0430445	−	0.999073i	$-0.486294\pi$
$887$	2274.22	0.0860889	0.0430445	+	0.999073i	$0.486294\pi$
$888$	4734.38	0.178914
$889$	14857.0	0.560504
$890$	5200.50	0.195867
$891$	−3023.37	−0.113677
$892$	10037.4	0.376768
$893$	−42358.4	−1.58731
$894$	−375.753	−0.0140571
$895$	11648.9	0.435061
$896$	−896.000	−0.0334077
$897$	−8486.22	−0.315882
$898$	−14849.4	−0.551818
$899$	1623.40	0.0602264
$900$	−3651.65	−0.135246
$901$	1466.17	0.0542123
$902$	18539.4	0.684360
$903$	8519.67	0.313972
$904$	−14744.7	−0.542480
$905$	−3443.34	−0.126476
$906$	−3336.60	−0.122352
$907$	−30324.1	−1.11014	−0.555069	−	0.831804i	$-0.687308\pi$
$907$	−30324.1	−1.11014	−0.555069	+	0.831804i	$0.687308\pi$
$908$	−6871.65	−0.251149
$909$	105.303	0.00384234
$910$	−883.500	−0.0321843
$911$	46908.1	1.70596	0.852982	−	0.521940i	$-0.174791\pi$
$911$	46908.1	1.70596	0.852982	+	0.521940i	$0.174791\pi$
$912$	−4538.01	−0.164768
$913$	−19271.5	−0.698568
$914$	23261.9	0.841832
$915$	4834.82	0.174682
$916$	−26286.6	−0.948180
$917$	12096.2	0.435606
$918$	−6324.71	−0.227393
$919$	−4708.28	−0.169001	−0.0845005	−	0.996423i	$-0.526929\pi$
$919$	−4708.28	−0.169001	−0.0845005	+	0.996423i	$0.526929\pi$
$920$	8450.36	0.302826
$921$	−28195.1	−1.00875
$922$	−16400.3	−0.585807
$923$	9139.03	0.325910
$924$	−3135.34	−0.111629
$925$	20009.6	0.711256
$926$	30508.0	1.08267
$927$	−6882.27	−0.243844
$928$	−2650.79	−0.0937679
$929$	−7004.36	−0.247369	−0.123684	−	0.992322i	$-0.539471\pi$
$929$	−7004.36	−0.247369	−0.123684	+	0.992322i	$0.539471\pi$
$930$	570.804	0.0201262
$931$	−4632.55	−0.163078
$932$	−27476.3	−0.965682
$933$	12304.1	0.431746
$934$	−29815.7	−1.04454
$935$	21222.1	0.742285
$936$	936.000	0.0326860
$937$	−55088.9	−1.92068	−0.960340	−	0.278833i	$-0.910053\pi$
$937$	−55088.9	−1.92068	−0.960340	+	0.278833i	$0.910053\pi$
$938$	−2883.88	−0.100386
$939$	3244.47	0.112758
$940$	−8699.83	−0.301869
$941$	10906.1	0.377820	0.188910	−	0.981994i	$-0.439505\pi$
$941$	10906.1	0.377820	0.188910	+	0.981994i	$0.439505\pi$
$942$	510.510	0.0176575
$943$	54039.2	1.86613
$944$	−4690.85	−0.161731
$945$	−917.481	−0.0315827
$946$	30285.8	1.04088
$947$	30964.0	1.06251	0.531253	−	0.847213i	$-0.321721\pi$
$947$	30964.0	1.06251	0.531253	+	0.847213i	$0.321721\pi$
$948$	6493.82	0.222478
$949$	−8790.43	−0.300684
$950$	−19179.7	−0.655022
$951$	27510.5	0.938055
$952$	−6558.96	−0.223295
$953$	−12393.9	−0.421279	−0.210640	−	0.977564i	$-0.567555\pi$
$953$	−12393.9	−0.421279	−0.210640	+	0.977564i	$0.567555\pi$
$954$	−225.326	−0.00764695
$955$	20805.5	0.704973
$956$	2363.64	0.0799639
$957$	−9275.83	−0.313318
$958$	−36380.4	−1.22693
$959$	18405.6	0.619758
$960$	−932.044	−0.0313350
$961$	−29406.9	−0.987108
$962$	−5128.91	−0.171895
$963$	5332.74	0.178448
$964$	−5737.82	−0.191704
$965$	12837.8	0.428253
$966$	−9139.00	−0.304392
$967$	56827.9	1.88983	0.944913	−	0.327321i	$-0.106146\pi$
$967$	56827.9	1.88983	0.944913	+	0.327321i	$0.106146\pi$
$968$	−497.544	−0.0165203
$969$	−33219.4	−1.10130
$970$	15427.4	0.510665
$971$	42021.7	1.38882	0.694408	−	0.719582i	$-0.255666\pi$
$971$	42021.7	1.38882	0.694408	+	0.719582i	$0.255666\pi$
$972$	972.000	0.0320750
$973$	−11936.2	−0.393274
$974$	−20495.9	−0.674261
$975$	3955.96	0.129941
$976$	−5311.83	−0.174208
$977$	−43195.5	−1.41448	−0.707239	−	0.706974i	$-0.750060\pi$
$977$	−43195.5	−1.41448	−0.707239	+	0.706974i	$0.750060\pi$
$978$	4879.99	0.159555
$979$	−19993.4	−0.652697
$980$	−951.462	−0.0310136
$981$	5300.00	0.172493
$982$	27830.1	0.904374
$983$	−27575.9	−0.894745	−0.447372	−	0.894348i	$-0.647640\pi$
$983$	−27575.9	−0.894745	−0.447372	+	0.894348i	$0.647640\pi$
$984$	−5960.33	−0.193098
$985$	−452.827	−0.0146480
$986$	−19404.5	−0.626740
$987$	9408.81	0.303430
$988$	4916.18	0.158304
$989$	88278.1	2.83830
$990$	−3261.47	−0.104703
$991$	55914.9	1.79233	0.896163	−	0.443724i	$-0.146343\pi$
$991$	55914.9	1.79233	0.896163	+	0.443724i	$0.146343\pi$
$992$	−627.120	−0.0200716
$993$	−15047.3	−0.480877
$994$	9842.03	0.314055
$995$	−11220.5	−0.357502
$996$	6195.70	0.197107
$997$	−4719.87	−0.149930	−0.0749648	−	0.997186i	$-0.523884\pi$
$997$	−4719.87	−0.149930	−0.0749648	+	0.997186i	$0.523884\pi$
$998$	−16171.4	−0.512922
$999$	−5326.17	−0.168681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.a.n.1.1	✓	3
3.2	odd	2		1638.4.a.ba.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.a.n.1.1	✓	3	1.1	even	1	trivial
1638.4.a.ba.1.3		3	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -4.85440 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +9.70880 q^{10} -37.3255 q^{11} +12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} -14.5632 q^{15} +16.0000 q^{16} +117.124 q^{17} -18.0000 q^{18} -94.5418 q^{19} -19.4176 q^{20} +21.0000 q^{21} +74.6510 q^{22} +217.595 q^{23} -24.0000 q^{24} -101.435 q^{25} +26.0000 q^{26} +27.0000 q^{27} +28.0000 q^{28} +82.8373 q^{29} +29.1264 q^{30} +19.5975 q^{31} -32.0000 q^{32} -111.977 q^{33} -234.248 q^{34} -33.9808 q^{35} +36.0000 q^{36} -197.266 q^{37} +189.084 q^{38} -39.0000 q^{39} +38.8352 q^{40} +248.347 q^{41} -42.0000 q^{42} +405.698 q^{43} -149.302 q^{44} -43.6896 q^{45} -435.191 q^{46} +448.039 q^{47} +48.0000 q^{48} +49.0000 q^{49} +202.870 q^{50} +351.373 q^{51} -52.0000 q^{52} +12.5181 q^{53} -54.0000 q^{54} +181.193 q^{55} -56.0000 q^{56} -283.626 q^{57} -165.675 q^{58} -293.178 q^{59} -58.2528 q^{60} -331.989 q^{61} -39.1950 q^{62} +63.0000 q^{63} +64.0000 q^{64} +63.1072 q^{65} +223.953 q^{66} +205.992 q^{67} +468.497 q^{68} +652.786 q^{69} +67.9616 q^{70} -703.002 q^{71} -72.0000 q^{72} +676.187 q^{73} +394.531 q^{74} -304.304 q^{75} -378.167 q^{76} -261.279 q^{77} +78.0000 q^{78} +541.152 q^{79} -77.6704 q^{80} +81.0000 q^{81} -496.694 q^{82} +516.308 q^{83} +84.0000 q^{84} -568.568 q^{85} -811.397 q^{86} +248.512 q^{87} +298.604 q^{88} +535.649 q^{89} +87.3792 q^{90} -91.0000 q^{91} +870.381 q^{92} +58.7925 q^{93} -896.077 q^{94} +458.944 q^{95} -96.0000 q^{96} +1589.02 q^{97} -98.0000 q^{98} -335.930 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} + 13 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} - 26 q^{10} + 17 q^{11} + 36 q^{12} - 39 q^{13} - 42 q^{14} + 39 q^{15} + 48 q^{16} + 89 q^{17} - 54 q^{18} + 89 q^{19}+ \cdots + 153 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 + 13 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9 - 26 * q^10 + 17 * q^11 + 36 * q^12 - 39 * q^13 - 42 * q^14 + 39 * q^15 + 48 * q^16 + 89 * q^17 - 54 * q^18 + 89 * q^19 + 52 * q^20 + 63 * q^21 - 34 * q^22 + 289 * q^23 - 72 * q^24 + 86 * q^25 + 78 * q^26 + 81 * q^27 + 84 * q^28 + 125 * q^29 - 78 * q^30 - 208 * q^31 - 96 * q^32 + 51 * q^33 - 178 * q^34 + 91 * q^35 + 108 * q^36 + 213 * q^37 - 178 * q^38 - 117 * q^39 - 104 * q^40 + 530 * q^41 - 126 * q^42 - 75 * q^43 + 68 * q^44 + 117 * q^45 - 578 * q^46 + 298 * q^47 + 144 * q^48 + 147 * q^49 - 172 * q^50 + 267 * q^51 - 156 * q^52 + 710 * q^53 - 162 * q^54 - 87 * q^55 - 168 * q^56 + 267 * q^57 - 250 * q^58 - 250 * q^59 + 156 * q^60 - 511 * q^61 + 416 * q^62 + 189 * q^63 + 192 * q^64 - 169 * q^65 - 102 * q^66 - 522 * q^67 + 356 * q^68 + 867 * q^69 - 182 * q^70 + 282 * q^71 - 216 * q^72 - 701 * q^73 - 426 * q^74 + 258 * q^75 + 356 * q^76 + 119 * q^77 + 234 * q^78 + 1262 * q^79 + 208 * q^80 + 243 * q^81 - 1060 * q^82 + 1700 * q^83 + 252 * q^84 - 385 * q^85 + 150 * q^86 + 375 * q^87 - 136 * q^88 + 1628 * q^89 - 234 * q^90 - 273 * q^91 + 1156 * q^92 - 624 * q^93 - 596 * q^94 + 2775 * q^95 - 288 * q^96 + 1526 * q^97 - 294 * q^98 + 153 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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