LMFDB - Embedded newform 546.4.a.n.1.3

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			1.3
Root			$-1.48548$ 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)

$f(q)$	$=$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.7180 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -41.4360 q^{10} -4.77607 q^{11} +12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} +62.1539 q^{15} +16.0000 q^{16} +4.36916 q^{17} -18.0000 q^{18} +120.503 q^{19} +82.8719 q^{20} +21.0000 q^{21} +9.55215 q^{22} +97.8632 q^{23} -24.0000 q^{24} +304.235 q^{25} +26.0000 q^{26} +27.0000 q^{27} +28.0000 q^{28} -162.421 q^{29} -124.308 q^{30} -140.814 q^{31} -32.0000 q^{32} -14.3282 q^{33} -8.73832 q^{34} +145.026 q^{35} +36.0000 q^{36} +331.624 q^{37} -241.006 q^{38} -39.0000 q^{39} -165.744 q^{40} -168.941 q^{41} -42.0000 q^{42} -488.182 q^{43} -19.1043 q^{44} +186.462 q^{45} -195.726 q^{46} +305.040 q^{47} +48.0000 q^{48} +49.0000 q^{49} -608.469 q^{50} +13.1075 q^{51} -52.0000 q^{52} +200.838 q^{53} -54.0000 q^{54} -98.9506 q^{55} -56.0000 q^{56} +361.508 q^{57} +324.842 q^{58} +247.331 q^{59} +248.616 q^{60} -535.385 q^{61} +281.628 q^{62} +63.0000 q^{63} +64.0000 q^{64} -269.334 q^{65} +28.6564 q^{66} -677.423 q^{67} +17.4766 q^{68} +293.590 q^{69} -290.052 q^{70} -183.364 q^{71} -72.0000 q^{72} -505.997 q^{73} -663.249 q^{74} +912.704 q^{75} +482.011 q^{76} -33.4325 q^{77} +78.0000 q^{78} +989.806 q^{79} +331.488 q^{80} +81.0000 q^{81} +337.882 q^{82} +787.139 q^{83} +84.0000 q^{84} +90.5202 q^{85} +976.364 q^{86} -487.263 q^{87} +38.2086 q^{88} +1034.29 q^{89} -372.924 q^{90} -91.0000 q^{91} +391.453 q^{92} -422.441 q^{93} -610.079 q^{94} +2496.57 q^{95} -96.0000 q^{96} +324.290 q^{97} -98.0000 q^{98} -42.9847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	20.7180	1.85307	0.926536	−	0.376205i	$-0.122771\pi$
$5$	20.7180	1.85307	0.926536	+	0.376205i	$0.122771\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−41.4360	−1.31032
$11$	−4.77607	−0.130913	−0.0654564	−	0.997855i	$-0.520850\pi$
$11$	−4.77607	−0.130913	−0.0654564	+	0.997855i	$0.520850\pi$
$12$	12.0000	0.288675
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−14.0000	−0.267261
$15$	62.1539	1.06987
$16$	16.0000	0.250000
$17$	4.36916	0.0623339	0.0311670	−	0.999514i	$-0.490078\pi$
$17$	4.36916	0.0623339	0.0311670	+	0.999514i	$0.490078\pi$
$18$	−18.0000	−0.235702
$19$	120.503	1.45501	0.727506	−	0.686101i	$-0.240679\pi$
$19$	120.503	1.45501	0.727506	+	0.686101i	$0.240679\pi$
$20$	82.8719	0.926536
$21$	21.0000	0.218218
$22$	9.55215	0.0925693
$23$	97.8632	0.887213	0.443606	−	0.896222i	$-0.353699\pi$
$23$	97.8632	0.887213	0.443606	+	0.896222i	$0.353699\pi$
$24$	−24.0000	−0.204124
$25$	304.235	2.43388
$26$	26.0000	0.196116
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	−162.421	−1.04003	−0.520014	−	0.854158i	$-0.674073\pi$
$29$	−162.421	−1.04003	−0.520014	+	0.854158i	$0.674073\pi$
$30$	−124.308	−0.756514
$31$	−140.814	−0.815836	−0.407918	−	0.913019i	$-0.633745\pi$
$31$	−140.814	−0.815836	−0.407918	+	0.913019i	$0.633745\pi$
$32$	−32.0000	−0.176777
$33$	−14.3282	−0.0755825
$34$	−8.73832	−0.0440768
$35$	145.026	0.700396
$36$	36.0000	0.166667
$37$	331.624	1.47348	0.736740	−	0.676177i	$-0.236364\pi$
$37$	331.624	1.47348	0.736740	+	0.676177i	$0.236364\pi$
$38$	−241.006	−1.02885
$39$	−39.0000	−0.160128
$40$	−165.744	−0.655160
$41$	−168.941	−0.643515	−0.321758	−	0.946822i	$-0.604274\pi$
$41$	−168.941	−0.643515	−0.321758	+	0.946822i	$0.604274\pi$
$42$	−42.0000	−0.154303
$43$	−488.182	−1.73133	−0.865664	−	0.500626i	$-0.833103\pi$
$43$	−488.182	−1.73133	−0.865664	+	0.500626i	$0.833103\pi$
$44$	−19.1043	−0.0654564
$45$	186.462	0.617691
$46$	−195.726	−0.627354
$47$	305.040	0.946694	0.473347	−	0.880876i	$-0.343046\pi$
$47$	305.040	0.946694	0.473347	+	0.880876i	$0.343046\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−608.469	−1.72101
$51$	13.1075	0.0359885
$52$	−52.0000	−0.138675
$53$	200.838	0.520513	0.260256	−	0.965540i	$-0.416193\pi$
$53$	200.838	0.520513	0.260256	+	0.965540i	$0.416193\pi$
$54$	−54.0000	−0.136083
$55$	−98.9506	−0.242591
$56$	−56.0000	−0.133631
$57$	361.508	0.840052
$58$	324.842	0.735411
$59$	247.331	0.545758	0.272879	−	0.962048i	$-0.412024\pi$
$59$	247.331	0.545758	0.272879	+	0.962048i	$0.412024\pi$
$60$	248.616	0.534936
$61$	−535.385	−1.12375	−0.561877	−	0.827220i	$-0.689921\pi$
$61$	−535.385	−1.12375	−0.561877	+	0.827220i	$0.689921\pi$
$62$	281.628	0.576883
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−269.334	−0.513950
$66$	28.6564	0.0534449
$67$	−677.423	−1.23523	−0.617615	−	0.786481i	$-0.711901\pi$
$67$	−677.423	−1.23523	−0.617615	+	0.786481i	$0.711901\pi$
$68$	17.4766	0.0311670
$69$	293.590	0.512232
$70$	−290.052	−0.495254
$71$	−183.364	−0.306498	−0.153249	−	0.988188i	$-0.548974\pi$
$71$	−183.364	−0.306498	−0.153249	+	0.988188i	$0.548974\pi$
$72$	−72.0000	−0.117851
$73$	−505.997	−0.811267	−0.405634	−	0.914036i	$-0.632949\pi$
$73$	−505.997	−0.811267	−0.405634	+	0.914036i	$0.632949\pi$
$74$	−663.249	−1.04191
$75$	912.704	1.40520
$76$	482.011	0.727506
$77$	−33.4325	−0.0494804
$78$	78.0000	0.113228
$79$	989.806	1.40964	0.704822	−	0.709384i	$-0.251027\pi$
$79$	989.806	1.40964	0.704822	+	0.709384i	$0.251027\pi$
$80$	331.488	0.463268
$81$	81.0000	0.111111
$82$	337.882	0.455034
$83$	787.139	1.04096	0.520480	−	0.853874i	$-0.325753\pi$
$83$	787.139	1.04096	0.520480	+	0.853874i	$0.325753\pi$
$84$	84.0000	0.109109
$85$	90.5202	0.115509
$86$	976.364	1.22423
$87$	−487.263	−0.600460
$88$	38.2086	0.0462847
$89$	1034.29	1.23185	0.615927	−	0.787803i	$-0.288782\pi$
$89$	1034.29	1.23185	0.615927	+	0.787803i	$0.288782\pi$
$90$	−372.924	−0.436773
$91$	−91.0000	−0.104828
$92$	391.453	0.443606
$93$	−422.441	−0.471023
$94$	−610.079	−0.669413
$95$	2496.57	2.69624
$96$	−96.0000	−0.102062
$97$	324.290	0.339450	0.169725	−	0.985491i	$-0.445712\pi$
$97$	324.290	0.339450	0.169725	+	0.985491i	$0.445712\pi$
$98$	−98.0000	−0.101015
$99$	−42.9847	−0.0436376
$100$	1216.94	1.21694
$101$	−966.966	−0.952641	−0.476321	−	0.879272i	$-0.658030\pi$
$101$	−966.966	−0.952641	−0.476321	+	0.879272i	$0.658030\pi$
$102$	−26.2150	−0.0254477
$103$	66.4516	0.0635696	0.0317848	−	0.999495i	$-0.489881\pi$
$103$	66.4516	0.0635696	0.0317848	+	0.999495i	$0.489881\pi$
$104$	104.000	0.0980581
$105$	435.078	0.404374
$106$	−401.675	−0.368058
$107$	−428.002	−0.386696	−0.193348	−	0.981130i	$-0.561935\pi$
$107$	−428.002	−0.386696	−0.193348	+	0.981130i	$0.561935\pi$
$108$	108.000	0.0962250
$109$	−588.563	−0.517194	−0.258597	−	0.965985i	$-0.583260\pi$
$109$	−588.563	−0.517194	−0.258597	+	0.965985i	$0.583260\pi$
$110$	197.901	0.171538
$111$	994.873	0.850714
$112$	112.000	0.0944911
$113$	329.616	0.274404	0.137202	−	0.990543i	$-0.456189\pi$
$113$	329.616	0.274404	0.137202	+	0.990543i	$0.456189\pi$
$114$	−723.017	−0.594006
$115$	2027.53	1.64407
$116$	−649.684	−0.520014
$117$	−117.000	−0.0924500
$118$	−494.661	−0.385909
$119$	30.5841	0.0235600
$120$	−497.232	−0.378257
$121$	−1308.19	−0.982862
$122$	1070.77	0.794615
$123$	−506.822	−0.371534
$124$	−563.255	−0.407918
$125$	3713.38	2.65708
$126$	−126.000	−0.0890871
$127$	−1255.49	−0.877219	−0.438609	−	0.898678i	$-0.644529\pi$
$127$	−1255.49	−0.877219	−0.438609	+	0.898678i	$0.644529\pi$
$128$	−128.000	−0.0883883
$129$	−1464.55	−0.999582
$130$	538.667	0.363417
$131$	2414.90	1.61062	0.805308	−	0.592857i	$-0.202000\pi$
$131$	2414.90	1.61062	0.805308	+	0.592857i	$0.202000\pi$
$132$	−57.3129	−0.0377913
$133$	843.519	0.549943
$134$	1354.85	0.873440
$135$	559.385	0.356624
$136$	−34.9533	−0.0220384
$137$	832.178	0.518962	0.259481	−	0.965748i	$-0.416449\pi$
$137$	832.178	0.518962	0.259481	+	0.965748i	$0.416449\pi$
$138$	−587.179	−0.362203
$139$	2186.57	1.33426	0.667130	−	0.744941i	$-0.267522\pi$
$139$	2186.57	1.33426	0.667130	+	0.744941i	$0.267522\pi$
$140$	580.103	0.350198
$141$	915.119	0.546574
$142$	366.729	0.216727
$143$	62.0890	0.0363087
$144$	144.000	0.0833333
$145$	−3365.03	−1.92725
$146$	1011.99	0.573653
$147$	147.000	0.0824786
$148$	1326.50	0.736740
$149$	−1149.68	−0.632118	−0.316059	−	0.948740i	$-0.602360\pi$
$149$	−1149.68	−0.632118	−0.316059	+	0.948740i	$0.602360\pi$
$150$	−1825.41	−0.993626
$151$	1959.00	1.05577	0.527885	−	0.849316i	$-0.322985\pi$
$151$	1959.00	1.05577	0.527885	+	0.849316i	$0.322985\pi$
$152$	−964.022	−0.514424
$153$	39.3224	0.0207780
$154$	66.8650	0.0349879
$155$	−2917.38	−1.51180
$156$	−156.000	−0.0800641
$157$	−2796.82	−1.42172	−0.710861	−	0.703332i	$-0.751695\pi$
$157$	−2796.82	−1.42172	−0.710861	+	0.703332i	$0.751695\pi$
$158$	−1979.61	−0.996769
$159$	602.513	0.300518
$160$	−662.975	−0.327580
$161$	685.043	0.335335
$162$	−162.000	−0.0785674
$163$	−2205.89	−1.05999	−0.529995	−	0.848000i	$-0.677806\pi$
$163$	−2205.89	−1.05999	−0.529995	+	0.848000i	$0.677806\pi$
$164$	−675.763	−0.321758
$165$	−296.852	−0.140060
$166$	−1574.28	−0.736070
$167$	1928.74	0.893716	0.446858	−	0.894605i	$-0.352543\pi$
$167$	1928.74	0.893716	0.446858	+	0.894605i	$0.352543\pi$
$168$	−168.000	−0.0771517
$169$	169.000	0.0769231
$170$	−181.040	−0.0816774
$171$	1084.52	0.485004
$172$	−1952.73	−0.865664
$173$	2857.91	1.25597	0.627985	−	0.778225i	$-0.283880\pi$
$173$	2857.91	1.25597	0.627985	+	0.778225i	$0.283880\pi$
$174$	974.525	0.424590
$175$	2129.64	0.919919
$176$	−76.4172	−0.0327282
$177$	741.992	0.315093
$178$	−2068.59	−0.871053
$179$	−3368.92	−1.40673	−0.703366	−	0.710828i	$-0.748320\pi$
$179$	−3368.92	−1.40673	−0.703366	+	0.710828i	$0.748320\pi$
$180$	745.847	0.308845
$181$	−785.583	−0.322607	−0.161304	−	0.986905i	$-0.551570\pi$
$181$	−785.583	−0.322607	−0.161304	+	0.986905i	$0.551570\pi$
$182$	182.000	0.0741249
$183$	−1606.16	−0.648800
$184$	−782.906	−0.313677
$185$	6870.59	2.73046
$186$	844.883	0.333064
$187$	−20.8674	−0.00816031
$188$	1220.16	0.473347
$189$	189.000	0.0727393
$190$	−4993.15	−1.90653
$191$	4263.49	1.61516	0.807580	−	0.589758i	$-0.200777\pi$
$191$	4263.49	1.61516	0.807580	+	0.589758i	$0.200777\pi$
$192$	192.000	0.0721688
$193$	−2953.69	−1.10161	−0.550806	−	0.834633i	$-0.685680\pi$
$193$	−2953.69	−1.10161	−0.550806	+	0.834633i	$0.685680\pi$
$194$	−648.580	−0.240027
$195$	−808.001	−0.296729
$196$	196.000	0.0714286
$197$	−3269.53	−1.18246	−0.591230	−	0.806503i	$-0.701357\pi$
$197$	−3269.53	−1.18246	−0.591230	+	0.806503i	$0.701357\pi$
$198$	85.9693	0.0308564
$199$	3465.50	1.23449	0.617244	−	0.786772i	$-0.288249\pi$
$199$	3465.50	1.23449	0.617244	+	0.786772i	$0.288249\pi$
$200$	−2433.88	−0.860506
$201$	−2032.27	−0.713160
$202$	1933.93	0.673619
$203$	−1136.95	−0.393093
$204$	52.4299	0.0179943
$205$	−3500.11	−1.19248
$206$	−132.903	−0.0449505
$207$	880.769	0.295738
$208$	−208.000	−0.0693375
$209$	−575.530	−0.190480
$210$	−870.155	−0.285935
$211$	−3533.52	−1.15288	−0.576440	−	0.817139i	$-0.695559\pi$
$211$	−3533.52	−1.15288	−0.576440	+	0.817139i	$0.695559\pi$
$212$	803.350	0.260256
$213$	−550.093	−0.176957
$214$	856.004	0.273436
$215$	−10114.1	−3.20828
$216$	−216.000	−0.0680414
$217$	−985.697	−0.308357
$218$	1177.13	0.365711
$219$	−1517.99	−0.468385
$220$	−395.802	−0.121295
$221$	−56.7991	−0.0172883
$222$	−1989.75	−0.601545
$223$	−3614.13	−1.08529	−0.542645	−	0.839962i	$-0.682577\pi$
$223$	−3614.13	−1.08529	−0.542645	+	0.839962i	$0.682577\pi$
$224$	−224.000	−0.0668153
$225$	2738.11	0.811293
$226$	−659.232	−0.194033
$227$	5575.95	1.63035	0.815173	−	0.579217i	$-0.196642\pi$
$227$	5575.95	1.63035	0.815173	+	0.579217i	$0.196642\pi$
$228$	1446.03	0.420026
$229$	−2466.11	−0.711639	−0.355819	−	0.934555i	$-0.615798\pi$
$229$	−2466.11	−0.711639	−0.355819	+	0.934555i	$0.615798\pi$
$230$	−4055.06	−1.16253
$231$	−100.298	−0.0285675
$232$	1299.37	0.367705
$233$	2555.70	0.718581	0.359290	−	0.933226i	$-0.383019\pi$
$233$	2555.70	0.718581	0.359290	+	0.933226i	$0.383019\pi$
$234$	234.000	0.0653720
$235$	6319.80	1.75429
$236$	989.322	0.272879
$237$	2969.42	0.813858
$238$	−61.1682	−0.0166594
$239$	−1321.35	−0.357619	−0.178809	−	0.983884i	$-0.557225\pi$
$239$	−1321.35	−0.357619	−0.178809	+	0.983884i	$0.557225\pi$
$240$	994.463	0.267468
$241$	−1708.80	−0.456737	−0.228369	−	0.973575i	$-0.573339\pi$
$241$	−1708.80	−0.456737	−0.228369	+	0.973575i	$0.573339\pi$
$242$	2616.38	0.694988
$243$	243.000	0.0641500
$244$	−2141.54	−0.561877
$245$	1015.18	0.264725
$246$	1013.64	0.262714
$247$	−1566.54	−0.403548
$248$	1126.51	0.288442
$249$	2361.42	0.600999
$250$	−7426.76	−1.87884
$251$	−611.446	−0.153762	−0.0768808	−	0.997040i	$-0.524496\pi$
$251$	−611.446	−0.153762	−0.0768808	+	0.997040i	$0.524496\pi$
$252$	252.000	0.0629941
$253$	−467.402	−0.116147
$254$	2510.98	0.620287
$255$	271.561	0.0666893
$256$	256.000	0.0625000
$257$	−1552.15	−0.376733	−0.188366	−	0.982099i	$-0.560319\pi$
$257$	−1552.15	−0.376733	−0.188366	+	0.982099i	$0.560319\pi$
$258$	2929.09	0.706811
$259$	2321.37	0.556923
$260$	−1077.33	−0.256975
$261$	−1461.79	−0.346676
$262$	−4829.80	−1.13888
$263$	−4710.85	−1.10450	−0.552250	−	0.833679i	$-0.686230\pi$
$263$	−4710.85	−1.10450	−0.552250	+	0.833679i	$0.686230\pi$
$264$	114.626	0.0267225
$265$	4160.95	0.964548
$266$	−1687.04	−0.388868
$267$	3102.88	0.711211
$268$	−2709.69	−0.617615
$269$	12.4875	0.00283040	0.00141520	−	0.999999i	$-0.499550\pi$
$269$	12.4875	0.00283040	0.00141520	+	0.999999i	$0.499550\pi$
$270$	−1118.77	−0.252171
$271$	−7813.28	−1.75138	−0.875688	−	0.482877i	$-0.839592\pi$
$271$	−7813.28	−1.75138	−0.875688	+	0.482877i	$0.839592\pi$
$272$	69.9066	0.0155835
$273$	−273.000	−0.0605228
$274$	−1664.36	−0.366961
$275$	−1453.05	−0.318626
$276$	1174.36	0.256116
$277$	8416.68	1.82566	0.912832	−	0.408335i	$-0.133890\pi$
$277$	8416.68	1.82566	0.912832	+	0.408335i	$0.133890\pi$
$278$	−4373.14	−0.943465
$279$	−1267.32	−0.271945
$280$	−1160.21	−0.247627
$281$	−4392.41	−0.932489	−0.466244	−	0.884656i	$-0.654393\pi$
$281$	−4392.41	−0.932489	−0.466244	+	0.884656i	$0.654393\pi$
$282$	−1830.24	−0.386486
$283$	−1833.24	−0.385070	−0.192535	−	0.981290i	$-0.561671\pi$
$283$	−1833.24	−0.385070	−0.192535	+	0.981290i	$0.561671\pi$
$284$	−733.457	−0.153249
$285$	7489.72	1.55668
$286$	−124.178	−0.0256741
$287$	−1182.59	−0.243226
$288$	−288.000	−0.0589256
$289$	−4893.91	−0.996114
$290$	6730.07	1.36277
$291$	972.870	0.195982
$292$	−2023.99	−0.405634
$293$	−8580.80	−1.71091	−0.855454	−	0.517879i	$-0.826722\pi$
$293$	−8580.80	−1.71091	−0.855454	+	0.517879i	$0.826722\pi$
$294$	−294.000	−0.0583212
$295$	5124.19	1.01133
$296$	−2653.00	−0.520954
$297$	−128.954	−0.0251942
$298$	2299.36	0.446975
$299$	−1272.22	−0.246069
$300$	3650.82	0.702600
$301$	−3417.28	−0.654380
$302$	−3918.00	−0.746542
$303$	−2900.90	−0.550008
$304$	1928.04	0.363753
$305$	−11092.1	−2.08240
$306$	−78.6449	−0.0146923
$307$	1026.30	0.190794	0.0953971	−	0.995439i	$-0.469588\pi$
$307$	1026.30	0.190794	0.0953971	+	0.995439i	$0.469588\pi$
$308$	−133.730	−0.0247402
$309$	199.355	0.0367019
$310$	5834.76	1.06901
$311$	−4690.73	−0.855263	−0.427631	−	0.903953i	$-0.640652\pi$
$311$	−4690.73	−0.855263	−0.427631	+	0.903953i	$0.640652\pi$
$312$	312.000	0.0566139
$313$	774.561	0.139875	0.0699374	−	0.997551i	$-0.477720\pi$
$313$	774.561	0.139875	0.0699374	+	0.997551i	$0.477720\pi$
$314$	5593.64	1.00531
$315$	1305.23	0.233465
$316$	3959.22	0.704822
$317$	−9791.97	−1.73493	−0.867463	−	0.497501i	$-0.834251\pi$
$317$	−9791.97	−1.73493	−0.867463	+	0.497501i	$0.834251\pi$
$318$	−1205.03	−0.212498
$319$	775.734	0.136153
$320$	1325.95	0.231634
$321$	−1284.01	−0.223259
$322$	−1370.09	−0.237118
$323$	526.496	0.0906966
$324$	324.000	0.0555556
$325$	−3955.05	−0.675036
$326$	4411.78	0.749527
$327$	−1765.69	−0.298602
$328$	1351.53	0.227517
$329$	2135.28	0.357817
$330$	593.704	0.0990373
$331$	1986.58	0.329887	0.164943	−	0.986303i	$-0.447256\pi$
$331$	1986.58	0.329887	0.164943	+	0.986303i	$0.447256\pi$
$332$	3148.56	0.520480
$333$	2984.62	0.491160
$334$	−3857.48	−0.631953
$335$	−14034.8	−2.28897
$336$	336.000	0.0545545
$337$	591.170	0.0955581	0.0477790	−	0.998858i	$-0.484786\pi$
$337$	591.170	0.0955581	0.0477790	+	0.998858i	$0.484786\pi$
$338$	−338.000	−0.0543928
$339$	988.848	0.158427
$340$	362.081	0.0577547
$341$	672.537	0.106803
$342$	−2169.05	−0.342950
$343$	343.000	0.0539949
$344$	3905.46	0.612117
$345$	6082.58	0.949204
$346$	−5715.82	−0.888105
$347$	10753.2	1.66358	0.831792	−	0.555087i	$-0.187315\pi$
$347$	10753.2	1.66358	0.831792	+	0.555087i	$0.187315\pi$
$348$	−1949.05	−0.300230
$349$	5368.78	0.823450	0.411725	−	0.911308i	$-0.364926\pi$
$349$	5368.78	0.823450	0.411725	+	0.911308i	$0.364926\pi$
$350$	−4259.29	−0.650481
$351$	−351.000	−0.0533761
$352$	152.834	0.0231423
$353$	8940.31	1.34800	0.674001	−	0.738731i	$-0.264574\pi$
$353$	8940.31	1.34800	0.674001	+	0.738731i	$0.264574\pi$
$354$	−1483.98	−0.222805
$355$	−3798.94	−0.567963
$356$	4137.18	0.615927
$357$	91.7524	0.0136024
$358$	6737.84	0.994709
$359$	−8280.74	−1.21738	−0.608692	−	0.793407i	$-0.708305\pi$
$359$	−8280.74	−1.21738	−0.608692	+	0.793407i	$0.708305\pi$
$360$	−1491.69	−0.218387
$361$	7661.92	1.11706
$362$	1571.17	0.228118
$363$	−3924.57	−0.567456
$364$	−364.000	−0.0524142
$365$	−10483.2	−1.50334
$366$	3212.31	0.458771
$367$	4595.69	0.653660	0.326830	−	0.945083i	$-0.394020\pi$
$367$	4595.69	0.653660	0.326830	+	0.945083i	$0.394020\pi$
$368$	1565.81	0.221803
$369$	−1520.47	−0.214505
$370$	−13741.2	−1.93073
$371$	1405.86	0.196735
$372$	−1689.77	−0.235512
$373$	−7309.76	−1.01470	−0.507352	−	0.861739i	$-0.669376\pi$
$373$	−7309.76	−1.01470	−0.507352	+	0.861739i	$0.669376\pi$
$374$	41.7349	0.00577021
$375$	11140.1	1.53407
$376$	−2440.32	−0.334707
$377$	2111.47	0.288452
$378$	−378.000	−0.0514344
$379$	4167.35	0.564809	0.282404	−	0.959295i	$-0.408868\pi$
$379$	4167.35	0.564809	0.282404	+	0.959295i	$0.408868\pi$
$380$	9986.30	1.34812
$381$	−3766.47	−0.506462
$382$	−8526.99	−1.14209
$383$	5265.63	0.702509	0.351255	−	0.936280i	$-0.385755\pi$
$383$	5265.63	0.702509	0.351255	+	0.936280i	$0.385755\pi$
$384$	−384.000	−0.0510310
$385$	−692.654	−0.0916907
$386$	5907.37	0.778957
$387$	−4393.64	−0.577109
$388$	1297.16	0.169725
$389$	−1642.30	−0.214056	−0.107028	−	0.994256i	$-0.534133\pi$
$389$	−1642.30	−0.214056	−0.107028	+	0.994256i	$0.534133\pi$
$390$	1616.00	0.209819
$391$	427.580	0.0553035
$392$	−392.000	−0.0505076
$393$	7244.69	0.929889
$394$	6539.06	0.836125
$395$	20506.8	2.61217
$396$	−171.939	−0.0218188
$397$	−12656.2	−1.60000	−0.799998	−	0.600002i	$-0.795166\pi$
$397$	−12656.2	−1.60000	−0.799998	+	0.600002i	$0.795166\pi$
$398$	−6931.01	−0.872915
$399$	2530.56	0.317510
$400$	4867.76	0.608469
$401$	6157.80	0.766848	0.383424	−	0.923572i	$-0.374745\pi$
$401$	6157.80	0.766848	0.383424	+	0.923572i	$0.374745\pi$
$402$	4064.54	0.504281
$403$	1830.58	0.226272
$404$	−3867.87	−0.476321
$405$	1678.16	0.205897
$406$	2273.89	0.277959
$407$	−1583.86	−0.192897
$408$	−104.860	−0.0127239
$409$	−5672.86	−0.685831	−0.342916	−	0.939366i	$-0.611414\pi$
$409$	−5672.86	−0.685831	−0.342916	+	0.939366i	$0.611414\pi$
$410$	7000.22	0.843211
$411$	2496.53	0.299623
$412$	265.806	0.0317848
$413$	1731.31	0.206277
$414$	−1761.54	−0.209118
$415$	16307.9	1.92898
$416$	416.000	0.0490290
$417$	6559.70	0.770336
$418$	1151.06	0.134689
$419$	4857.85	0.566399	0.283200	−	0.959061i	$-0.408604\pi$
$419$	4857.85	0.566399	0.283200	+	0.959061i	$0.408604\pi$
$420$	1740.31	0.202187
$421$	8200.60	0.949342	0.474671	−	0.880163i	$-0.342567\pi$
$421$	8200.60	0.949342	0.474671	+	0.880163i	$0.342567\pi$
$422$	7067.05	0.815210
$423$	2745.36	0.315565
$424$	−1606.70	−0.184029
$425$	1329.25	0.151713
$426$	1100.19	0.125127
$427$	−3747.70	−0.424739
$428$	−1712.01	−0.193348
$429$	186.267	0.0209628
$430$	20228.3	2.26859
$431$	−2797.33	−0.312628	−0.156314	−	0.987707i	$-0.549961\pi$
$431$	−2797.33	−0.312628	−0.156314	+	0.987707i	$0.549961\pi$
$432$	432.000	0.0481125
$433$	−7104.15	−0.788461	−0.394231	−	0.919012i	$-0.628989\pi$
$433$	−7104.15	−0.788461	−0.394231	+	0.919012i	$0.628989\pi$
$434$	1971.39	0.218041
$435$	−10095.1	−1.11270
$436$	−2354.25	−0.258597
$437$	11792.8	1.29091
$438$	3035.98	0.331198
$439$	4528.66	0.492349	0.246175	−	0.969226i	$-0.420826\pi$
$439$	4528.66	0.492349	0.246175	+	0.969226i	$0.420826\pi$
$440$	791.605	0.0857688
$441$	441.000	0.0476190
$442$	113.598	0.0122247
$443$	13450.5	1.44255	0.721276	−	0.692648i	$-0.243556\pi$
$443$	13450.5	1.44255	0.721276	+	0.692648i	$0.243556\pi$
$444$	3979.49	0.425357
$445$	21428.5	2.28272
$446$	7228.25	0.767416
$447$	−3449.04	−0.364953
$448$	448.000	0.0472456
$449$	−14582.1	−1.53268	−0.766339	−	0.642436i	$-0.777924\pi$
$449$	−14582.1	−1.53268	−0.766339	+	0.642436i	$0.777924\pi$
$450$	−5476.22	−0.573670
$451$	806.874	0.0842444
$452$	1318.46	0.137202
$453$	5877.00	0.609549
$454$	−11151.9	−1.15283
$455$	−1885.34	−0.194255
$456$	−2892.07	−0.297003
$457$	3508.45	0.359121	0.179561	−	0.983747i	$-0.442532\pi$
$457$	3508.45	0.359121	0.179561	+	0.983747i	$0.442532\pi$
$458$	4932.22	0.503204
$459$	117.967	0.0119962
$460$	8110.11	0.822035
$461$	5916.54	0.597746	0.298873	−	0.954293i	$-0.403389\pi$
$461$	5916.54	0.597746	0.298873	+	0.954293i	$0.403389\pi$
$462$	200.595	0.0202003
$463$	−2768.54	−0.277894	−0.138947	−	0.990300i	$-0.544372\pi$
$463$	−2768.54	−0.277894	−0.138947	+	0.990300i	$0.544372\pi$
$464$	−2598.73	−0.260007
$465$	−8752.13	−0.872840
$466$	−5111.39	−0.508113
$467$	−7346.67	−0.727972	−0.363986	−	0.931404i	$-0.618584\pi$
$467$	−7346.67	−0.727972	−0.363986	+	0.931404i	$0.618584\pi$
$468$	−468.000	−0.0462250
$469$	−4741.96	−0.466873
$470$	−12639.6	−1.24047
$471$	−8390.46	−0.820832
$472$	−1978.64	−0.192954
$473$	2331.59	0.226653
$474$	−5938.84	−0.575485
$475$	36661.1	3.54132
$476$	122.336	0.0117800
$477$	1807.54	0.173504
$478$	2642.69	0.252875
$479$	−16588.9	−1.58239	−0.791197	−	0.611561i	$-0.790542\pi$
$479$	−16588.9	−1.58239	−0.791197	+	0.611561i	$0.790542\pi$
$480$	−1988.93	−0.189128
$481$	−4311.12	−0.408670
$482$	3417.61	0.322962
$483$	2055.13	0.193606
$484$	−5232.76	−0.491431
$485$	6718.63	0.629026
$486$	−486.000	−0.0453609
$487$	−20761.8	−1.93184	−0.965921	−	0.258836i	$-0.916661\pi$
$487$	−20761.8	−1.93184	−0.965921	+	0.258836i	$0.916661\pi$
$488$	4283.08	0.397307
$489$	−6617.67	−0.611986
$490$	−2030.36	−0.187189
$491$	6810.33	0.625959	0.312979	−	0.949760i	$-0.398673\pi$
$491$	6810.33	0.625959	0.312979	+	0.949760i	$0.398673\pi$
$492$	−2027.29	−0.185767
$493$	−709.643	−0.0648290
$494$	3133.07	0.285351
$495$	−890.556	−0.0808636
$496$	−2253.02	−0.203959
$497$	−1283.55	−0.115845
$498$	−4722.83	−0.424970
$499$	−16577.6	−1.48721	−0.743603	−	0.668622i	$-0.766885\pi$
$499$	−16577.6	−1.48721	−0.743603	+	0.668622i	$0.766885\pi$
$500$	14853.5	1.32854
$501$	5786.23	0.515987
$502$	1222.89	0.108726
$503$	7421.37	0.657857	0.328929	−	0.944355i	$-0.393312\pi$
$503$	7421.37	0.657857	0.328929	+	0.944355i	$0.393312\pi$
$504$	−504.000	−0.0445435
$505$	−20033.6	−1.76531
$506$	934.804	0.0821287
$507$	507.000	0.0444116
$508$	−5021.96	−0.438609
$509$	−9022.10	−0.785653	−0.392827	−	0.919613i	$-0.628503\pi$
$509$	−9022.10	−0.785653	−0.392827	+	0.919613i	$0.628503\pi$
$510$	−543.121	−0.0471565
$511$	−3541.98	−0.306630
$512$	−512.000	−0.0441942
$513$	3253.57	0.280017
$514$	3104.30	0.266390
$515$	1376.74	0.117799
$516$	−5858.19	−0.499791
$517$	−1456.89	−0.123934
$518$	−4642.74	−0.393804
$519$	8573.73	0.725135
$520$	2154.67	0.181709
$521$	11807.5	0.992892	0.496446	−	0.868068i	$-0.334638\pi$
$521$	11807.5	0.992892	0.496446	+	0.868068i	$0.334638\pi$
$522$	2923.58	0.245137
$523$	−22098.9	−1.84764	−0.923822	−	0.382823i	$-0.874952\pi$
$523$	−22098.9	−1.84764	−0.923822	+	0.382823i	$0.874952\pi$
$524$	9659.59	0.805308
$525$	6388.93	0.531116
$526$	9421.70	0.780999
$527$	−615.238	−0.0508543
$528$	−229.252	−0.0188956
$529$	−2589.79	−0.212854
$530$	−8321.90	−0.682038
$531$	2225.98	0.181919
$532$	3374.08	0.274971
$533$	2196.23	0.178479
$534$	−6205.77	−0.502902
$535$	−8867.34	−0.716576
$536$	5419.39	0.436720
$537$	−10106.8	−0.812177
$538$	−24.9750	−0.00200139
$539$	−234.028	−0.0187018
$540$	2237.54	0.178312
$541$	8059.75	0.640509	0.320255	−	0.947331i	$-0.396232\pi$
$541$	8059.75	0.640509	0.320255	+	0.947331i	$0.396232\pi$
$542$	15626.6	1.23841
$543$	−2356.75	−0.186257
$544$	−139.813	−0.0110192
$545$	−12193.8	−0.958397
$546$	546.000	0.0427960
$547$	951.002	0.0743362	0.0371681	−	0.999309i	$-0.488166\pi$
$547$	951.002	0.0743362	0.0371681	+	0.999309i	$0.488166\pi$
$548$	3328.71	0.259481
$549$	−4818.47	−0.374585
$550$	2906.10	0.225302
$551$	−19572.2	−1.51325
$552$	−2348.72	−0.181102
$553$	6928.64	0.532795
$554$	−16833.4	−1.29094
$555$	20611.8	1.57643
$556$	8746.27	0.667130
$557$	−18817.6	−1.43147	−0.715734	−	0.698373i	$-0.753908\pi$
$557$	−18817.6	−1.43147	−0.715734	+	0.698373i	$0.753908\pi$
$558$	2534.65	0.192294
$559$	6346.37	0.480184
$560$	2320.41	0.175099
$561$	−62.6023	−0.00471136
$562$	8784.83	0.659369
$563$	−10166.3	−0.761029	−0.380515	−	0.924775i	$-0.624253\pi$
$563$	−10166.3	−0.761029	−0.380515	+	0.924775i	$0.624253\pi$
$564$	3660.47	0.273287
$565$	6828.98	0.508491
$566$	3666.48	0.272285
$567$	567.000	0.0419961
$568$	1466.91	0.108363
$569$	5866.13	0.432199	0.216099	−	0.976371i	$-0.430666\pi$
$569$	5866.13	0.432199	0.216099	+	0.976371i	$0.430666\pi$
$570$	−14979.4	−1.10074
$571$	18588.0	1.36232	0.681158	−	0.732137i	$-0.261477\pi$
$571$	18588.0	1.36232	0.681158	+	0.732137i	$0.261477\pi$
$572$	248.356	0.0181543
$573$	12790.5	0.932513
$574$	2365.17	0.171987
$575$	29773.4	2.15937
$576$	576.000	0.0416667
$577$	−19543.0	−1.41003	−0.705015	−	0.709192i	$-0.749060\pi$
$577$	−19543.0	−1.41003	−0.705015	+	0.709192i	$0.749060\pi$
$578$	9787.82	0.704359
$579$	−8861.06	−0.636016
$580$	−13460.1	−0.963623
$581$	5509.97	0.393446
$582$	−1945.74	−0.138580
$583$	−959.215	−0.0681417
$584$	4047.98	0.286826
$585$	−2424.00	−0.171317
$586$	17161.6	1.20979
$587$	−21192.6	−1.49014	−0.745071	−	0.666986i	$-0.767584\pi$
$587$	−21192.6	−1.49014	−0.745071	+	0.666986i	$0.767584\pi$
$588$	588.000	0.0412393
$589$	−16968.5	−1.18705
$590$	−10248.4	−0.715117
$591$	−9808.59	−0.682693
$592$	5305.99	0.368370
$593$	−25022.1	−1.73277	−0.866385	−	0.499376i	$-0.833563\pi$
$593$	−25022.1	−1.73277	−0.866385	+	0.499376i	$0.833563\pi$
$594$	257.908	0.0178150
$595$	633.641	0.0436584
$596$	−4598.72	−0.316059
$597$	10396.5	0.712732
$598$	2544.44	0.173997
$599$	10114.9	0.689958	0.344979	−	0.938610i	$-0.387886\pi$
$599$	10114.9	0.689958	0.344979	+	0.938610i	$0.387886\pi$
$600$	−7301.63	−0.496813
$601$	−19577.8	−1.32877	−0.664387	−	0.747389i	$-0.731307\pi$
$601$	−19577.8	−1.32877	−0.664387	+	0.747389i	$0.731307\pi$
$602$	6834.55	0.462717
$603$	−6096.81	−0.411743
$604$	7836.01	0.527885
$605$	−27103.0	−1.82131
$606$	5801.80	0.388914
$607$	8913.63	0.596035	0.298017	−	0.954560i	$-0.403675\pi$
$607$	8913.63	0.596035	0.298017	+	0.954560i	$0.403675\pi$
$608$	−3856.09	−0.257212
$609$	−3410.84	−0.226953
$610$	22184.2	1.47248
$611$	−3965.51	−0.262566
$612$	157.290	0.0103890
$613$	−19205.1	−1.26539	−0.632696	−	0.774400i	$-0.718052\pi$
$613$	−19205.1	−1.26539	−0.632696	+	0.774400i	$0.718052\pi$
$614$	−2052.59	−0.134912
$615$	−10500.3	−0.688479
$616$	267.460	0.0174940
$617$	−23532.7	−1.53548	−0.767740	−	0.640762i	$-0.778619\pi$
$617$	−23532.7	−1.53548	−0.767740	+	0.640762i	$0.778619\pi$
$618$	−398.709	−0.0259522
$619$	3863.26	0.250852	0.125426	−	0.992103i	$-0.459970\pi$
$619$	3863.26	0.250852	0.125426	+	0.992103i	$0.459970\pi$
$620$	−11669.5	−0.755901
$621$	2642.31	0.170744
$622$	9381.46	0.604762
$623$	7240.06	0.465597
$624$	−624.000	−0.0400320
$625$	38904.4	2.48988
$626$	−1549.12	−0.0989064
$627$	−1726.59	−0.109973
$628$	−11187.3	−0.710861
$629$	1448.92	0.0918478
$630$	−2610.47	−0.165085
$631$	18861.6	1.18996	0.594982	−	0.803739i	$-0.297159\pi$
$631$	18861.6	1.18996	0.594982	+	0.803739i	$0.297159\pi$
$632$	−7918.45	−0.498384
$633$	−10600.6	−0.665616
$634$	19583.9	1.22678
$635$	−26011.2	−1.62555
$636$	2410.05	0.150259
$637$	−637.000	−0.0396214
$638$	−1551.47	−0.0962746
$639$	−1650.28	−0.102166
$640$	−2651.90	−0.163790
$641$	2199.27	0.135516	0.0677582	−	0.997702i	$-0.478415\pi$
$641$	2199.27	0.135516	0.0677582	+	0.997702i	$0.478415\pi$
$642$	2568.01	0.157868
$643$	1133.04	0.0694910	0.0347455	−	0.999396i	$-0.488938\pi$
$643$	1133.04	0.0694910	0.0347455	+	0.999396i	$0.488938\pi$
$644$	2740.17	0.167667
$645$	−30342.4	−1.85230
$646$	−1052.99	−0.0641322
$647$	−17693.8	−1.07514	−0.537571	−	0.843218i	$-0.680658\pi$
$647$	−17693.8	−1.07514	−0.537571	+	0.843218i	$0.680658\pi$
$648$	−648.000	−0.0392837
$649$	−1181.27	−0.0714466
$650$	7910.10	0.477323
$651$	−2957.09	−0.178030
$652$	−8823.55	−0.529995
$653$	20208.7	1.21107	0.605533	−	0.795820i	$-0.292960\pi$
$653$	20208.7	1.21107	0.605533	+	0.795820i	$0.292960\pi$
$654$	3531.38	0.211143
$655$	50031.8	2.98459
$656$	−2703.05	−0.160879
$657$	−4553.98	−0.270422
$658$	−4270.55	−0.253014
$659$	14194.4	0.839051	0.419526	−	0.907744i	$-0.362196\pi$
$659$	14194.4	0.839051	0.419526	+	0.907744i	$0.362196\pi$
$660$	−1187.41	−0.0700300
$661$	1698.75	0.0999600	0.0499800	−	0.998750i	$-0.484084\pi$
$661$	1698.75	0.0999600	0.0499800	+	0.998750i	$0.484084\pi$
$662$	−3973.17	−0.233265
$663$	−170.397	−0.00998142
$664$	−6297.11	−0.368035
$665$	17476.0	1.01908
$666$	−5969.24	−0.347302
$667$	−15895.0	−0.922726
$668$	7714.97	0.446858
$669$	−10842.4	−0.626593
$670$	28069.7	1.61855
$671$	2557.04	0.147114
$672$	−672.000	−0.0385758
$673$	−33390.7	−1.91251	−0.956253	−	0.292542i	$-0.905499\pi$
$673$	−33390.7	−1.91251	−0.956253	+	0.292542i	$0.905499\pi$
$674$	−1182.34	−0.0675698
$675$	8214.34	0.468400
$676$	676.000	0.0384615
$677$	−7417.34	−0.421081	−0.210540	−	0.977585i	$-0.567522\pi$
$677$	−7417.34	−0.421081	−0.210540	+	0.977585i	$0.567522\pi$
$678$	−1977.70	−0.112025
$679$	2270.03	0.128300
$680$	−724.161	−0.0408387
$681$	16727.8	0.941281
$682$	−1345.07	−0.0755214
$683$	−11589.1	−0.649261	−0.324631	−	0.945841i	$-0.605240\pi$
$683$	−11589.1	−0.649261	−0.324631	+	0.945841i	$0.605240\pi$
$684$	4338.10	0.242502
$685$	17241.1	0.961674
$686$	−686.000	−0.0381802
$687$	−7398.33	−0.410865
$688$	−7810.91	−0.432832
$689$	−2610.89	−0.144364
$690$	−12165.2	−0.671189
$691$	29229.5	1.60918	0.804588	−	0.593833i	$-0.202386\pi$
$691$	29229.5	1.60918	0.804588	+	0.593833i	$0.202386\pi$
$692$	11431.6	0.627985
$693$	−300.893	−0.0164935
$694$	−21506.5	−1.17633
$695$	45301.3	2.47248
$696$	3898.10	0.212295
$697$	−738.129	−0.0401128
$698$	−10737.6	−0.582267
$699$	7667.09	0.414873
$700$	8518.57	0.459960
$701$	−15437.4	−0.831761	−0.415880	−	0.909419i	$-0.636527\pi$
$701$	−15437.4	−0.831761	−0.415880	+	0.909419i	$0.636527\pi$
$702$	702.000	0.0377426
$703$	39961.7	2.14393
$704$	−305.669	−0.0163641
$705$	18959.4	1.01284
$706$	−17880.6	−0.953181
$707$	−6768.76	−0.360064
$708$	2967.97	0.157547
$709$	5732.22	0.303636	0.151818	−	0.988408i	$-0.451487\pi$
$709$	5732.22	0.303636	0.151818	+	0.988408i	$0.451487\pi$
$710$	7597.88	0.401610
$711$	8908.25	0.469881
$712$	−8274.36	−0.435526
$713$	−13780.5	−0.723820
$714$	−183.505	−0.00961834
$715$	1286.36	0.0672826
$716$	−13475.7	−0.703366
$717$	−3964.04	−0.206471
$718$	16561.5	0.860820
$719$	9149.31	0.474564	0.237282	−	0.971441i	$-0.423743\pi$
$719$	9149.31	0.474564	0.237282	+	0.971441i	$0.423743\pi$
$720$	2983.39	0.154423
$721$	465.161	0.0240270
$722$	−15323.8	−0.789881
$723$	−5126.41	−0.263697
$724$	−3142.33	−0.161304
$725$	−49414.1	−2.53130
$726$	7849.13	0.401252
$727$	1378.45	0.0703217	0.0351608	−	0.999382i	$-0.488806\pi$
$727$	1378.45	0.0703217	0.0351608	+	0.999382i	$0.488806\pi$
$728$	728.000	0.0370625
$729$	729.000	0.0370370
$730$	20966.5	1.06302
$731$	−2132.95	−0.107920
$732$	−6424.62	−0.324400
$733$	19871.4	1.00132	0.500659	−	0.865644i	$-0.333091\pi$
$733$	19871.4	1.00132	0.500659	+	0.865644i	$0.333091\pi$
$734$	−9191.38	−0.462207
$735$	3045.54	0.152839
$736$	−3131.62	−0.156839
$737$	3235.42	0.161707
$738$	3040.93	0.151678
$739$	36445.0	1.81414	0.907070	−	0.420979i	$-0.138313\pi$
$739$	36445.0	1.81414	0.907070	+	0.420979i	$0.138313\pi$
$740$	27482.4	1.36523
$741$	−4699.61	−0.232988
$742$	−2811.73	−0.139113
$743$	−6926.69	−0.342013	−0.171006	−	0.985270i	$-0.554702\pi$
$743$	−6926.69	−0.342013	−0.171006	+	0.985270i	$0.554702\pi$
$744$	3379.53	0.166532
$745$	−23819.1	−1.17136
$746$	14619.5	0.717505
$747$	7084.25	0.346987
$748$	−83.4697	−0.00408015
$749$	−2996.01	−0.146157
$750$	−22280.3	−1.08475
$751$	−21315.0	−1.03568	−0.517841	−	0.855477i	$-0.673264\pi$
$751$	−21315.0	−1.03568	−0.517841	+	0.855477i	$0.673264\pi$
$752$	4880.63	0.236673
$753$	−1834.34	−0.0887743
$754$	−4222.94	−0.203966
$755$	40586.6	1.95642
$756$	756.000	0.0363696
$757$	17209.0	0.826253	0.413126	−	0.910674i	$-0.364437\pi$
$757$	17209.0	0.826253	0.413126	+	0.910674i	$0.364437\pi$
$758$	−8334.71	−0.399380
$759$	−1402.21	−0.0670578
$760$	−19972.6	−0.953266
$761$	13206.4	0.629083	0.314541	−	0.949244i	$-0.398149\pi$
$761$	13206.4	0.629083	0.314541	+	0.949244i	$0.398149\pi$
$762$	7532.94	0.358123
$763$	−4119.94	−0.195481
$764$	17054.0	0.807580
$765$	814.682	0.0385031
$766$	−10531.3	−0.496749
$767$	−3215.30	−0.151366
$768$	768.000	0.0360844
$769$	−28023.4	−1.31411	−0.657055	−	0.753843i	$-0.728198\pi$
$769$	−28023.4	−1.31411	−0.657055	+	0.753843i	$0.728198\pi$
$770$	1385.31	0.0648351
$771$	−4656.44	−0.217507
$772$	−11814.7	−0.550806
$773$	−26004.0	−1.20996	−0.604980	−	0.796241i	$-0.706819\pi$
$773$	−26004.0	−1.20996	−0.604980	+	0.796241i	$0.706819\pi$
$774$	8787.28	0.408078
$775$	−42840.5	−1.98564
$776$	−2594.32	−0.120014
$777$	6964.11	0.321540
$778$	3284.60	0.151361
$779$	−20357.8	−0.936322
$780$	−3232.00	−0.148365
$781$	875.762	0.0401245
$782$	−855.160	−0.0391055
$783$	−4385.36	−0.200153
$784$	784.000	0.0357143
$785$	−57944.4	−2.63455
$786$	−14489.4	−0.657531
$787$	13013.4	0.589427	0.294713	−	0.955586i	$-0.404776\pi$
$787$	13013.4	0.589427	0.294713	+	0.955586i	$0.404776\pi$
$788$	−13078.1	−0.591230
$789$	−14132.5	−0.637683
$790$	−41013.6	−1.84709
$791$	2307.31	0.103715
$792$	343.877	0.0154282
$793$	6960.01	0.311674
$794$	25312.5	1.13137
$795$	12482.8	0.556882
$796$	13862.0	0.617244
$797$	221.082	0.00982578	0.00491289	−	0.999988i	$-0.498436\pi$
$797$	221.082	0.00982578	0.00491289	+	0.999988i	$0.498436\pi$
$798$	−5061.12	−0.224513
$799$	1332.77	0.0590111
$800$	−9735.51	−0.430253
$801$	9308.65	0.410618
$802$	−12315.6	−0.542243
$803$	2416.68	0.106205
$804$	−8129.08	−0.356580
$805$	14192.7	0.621400
$806$	−3661.16	−0.159999
$807$	37.4625	0.00163413
$808$	7735.73	0.336809
$809$	30683.2	1.33345	0.666726	−	0.745303i	$-0.267695\pi$
$809$	30683.2	1.33345	0.666726	+	0.745303i	$0.267695\pi$
$810$	−3356.31	−0.145591
$811$	−9920.45	−0.429537	−0.214768	−	0.976665i	$-0.568900\pi$
$811$	−9920.45	−0.429537	−0.214768	+	0.976665i	$0.568900\pi$
$812$	−4547.78	−0.196547
$813$	−23439.8	−1.01116
$814$	3167.73	0.136399
$815$	−45701.6	−1.96424
$816$	209.720	0.00899713
$817$	−58827.3	−2.51910
$818$	11345.7	0.484956
$819$	−819.000	−0.0349428
$820$	−14000.4	−0.596240
$821$	14724.4	0.625926	0.312963	−	0.949765i	$-0.398678\pi$
$821$	14724.4	0.625926	0.312963	+	0.949765i	$0.398678\pi$
$822$	−4993.07	−0.211865
$823$	−20738.3	−0.878364	−0.439182	−	0.898398i	$-0.644732\pi$
$823$	−20738.3	−0.878364	−0.439182	+	0.898398i	$0.644732\pi$
$824$	−531.612	−0.0224752
$825$	−4359.14	−0.183959
$826$	−3462.63	−0.145860
$827$	43370.0	1.82361	0.911803	−	0.410628i	$-0.134691\pi$
$827$	43370.0	1.82361	0.911803	+	0.410628i	$0.134691\pi$
$828$	3523.08	0.147869
$829$	−19816.5	−0.830225	−0.415113	−	0.909770i	$-0.636258\pi$
$829$	−19816.5	−0.830225	−0.415113	+	0.909770i	$0.636258\pi$
$830$	−32615.9	−1.36399
$831$	25250.0	1.05405
$832$	−832.000	−0.0346688
$833$	214.089	0.00890485
$834$	−13119.4	−0.544710
$835$	39959.6	1.65612
$836$	−2302.12	−0.0952398
$837$	−3801.97	−0.157008
$838$	−9715.69	−0.400505
$839$	18050.1	0.742741	0.371370	−	0.928485i	$-0.378888\pi$
$839$	18050.1	0.742741	0.371370	+	0.928485i	$0.378888\pi$
$840$	−3480.62	−0.142968
$841$	1991.54	0.0816575
$842$	−16401.2	−0.671286
$843$	−13177.2	−0.538373
$844$	−14134.1	−0.576440
$845$	3501.34	0.142544
$846$	−5490.71	−0.223138
$847$	−9157.32	−0.371487
$848$	3213.40	0.130128
$849$	−5499.72	−0.222320
$850$	−2658.50	−0.107277
$851$	32453.8	1.30729
$852$	−2200.37	−0.0884783
$853$	45732.3	1.83569	0.917846	−	0.396938i	$-0.129927\pi$
$853$	45732.3	1.83569	0.917846	+	0.396938i	$0.129927\pi$
$854$	7495.39	0.300336
$855$	22469.2	0.898748
$856$	3424.02	0.136718
$857$	−39858.1	−1.58871	−0.794356	−	0.607453i	$-0.792191\pi$
$857$	−39858.1	−1.58871	−0.794356	+	0.607453i	$0.792191\pi$
$858$	−372.534	−0.0148230
$859$	−16129.4	−0.640660	−0.320330	−	0.947306i	$-0.603794\pi$
$859$	−16129.4	−0.640660	−0.320330	+	0.947306i	$0.603794\pi$
$860$	−40456.6	−1.60414
$861$	−3547.76	−0.140427
$862$	5594.66	0.221061
$863$	−3507.71	−0.138359	−0.0691794	−	0.997604i	$-0.522038\pi$
$863$	−3507.71	−0.138359	−0.0691794	+	0.997604i	$0.522038\pi$
$864$	−864.000	−0.0340207
$865$	59210.1	2.32740
$866$	14208.3	0.557526
$867$	−14681.7	−0.575107
$868$	−3942.79	−0.154178
$869$	−4727.39	−0.184540
$870$	20190.2	0.786795
$871$	8806.50	0.342591
$872$	4708.50	0.182856
$873$	2918.61	0.113150
$874$	−23585.6	−0.912808
$875$	25993.7	1.00428
$876$	−6071.97	−0.234193
$877$	−39422.3	−1.51790	−0.758949	−	0.651150i	$-0.774287\pi$
$877$	−39422.3	−1.51790	−0.758949	+	0.651150i	$0.774287\pi$
$878$	−9057.32	−0.348143
$879$	−25742.4	−0.987793
$880$	−1583.21	−0.0606477
$881$	4291.98	0.164132	0.0820662	−	0.996627i	$-0.473848\pi$
$881$	4291.98	0.164132	0.0820662	+	0.996627i	$0.473848\pi$
$882$	−882.000	−0.0336718
$883$	28323.0	1.07944	0.539720	−	0.841844i	$-0.318530\pi$
$883$	28323.0	1.07944	0.539720	+	0.841844i	$0.318530\pi$
$884$	−227.196	−0.00864416
$885$	15372.6	0.583891
$886$	−26900.9	−1.02004
$887$	21374.1	0.809100	0.404550	−	0.914516i	$-0.367428\pi$
$887$	21374.1	0.809100	0.404550	+	0.914516i	$0.367428\pi$
$888$	−7958.99	−0.300773
$889$	−8788.43	−0.331558
$890$	−42857.0	−1.61412
$891$	−386.862	−0.0145459
$892$	−14456.5	−0.542645
$893$	36758.1	1.37745
$894$	6898.09	0.258061
$895$	−69797.2	−2.60678
$896$	−896.000	−0.0334077
$897$	−3816.67	−0.142068
$898$	29164.2	1.08377
$899$	22871.1	0.848492
$900$	10952.4	0.405646
$901$	877.492	0.0324456
$902$	−1613.75	−0.0595698
$903$	−10251.8	−0.377807
$904$	−2636.93	−0.0970165
$905$	−16275.7	−0.597815
$906$	−11754.0	−0.431016
$907$	7756.25	0.283949	0.141975	−	0.989870i	$-0.454655\pi$
$907$	7756.25	0.283949	0.141975	+	0.989870i	$0.454655\pi$
$908$	22303.8	0.815173
$909$	−8702.70	−0.317547
$910$	3770.67	0.137359
$911$	31045.3	1.12906	0.564531	−	0.825412i	$-0.309057\pi$
$911$	31045.3	1.12906	0.564531	+	0.825412i	$0.309057\pi$
$912$	5784.13	0.210013
$913$	−3759.43	−0.136275
$914$	−7016.90	−0.253937
$915$	−33276.3	−1.20227
$916$	−9864.44	−0.355819
$917$	16904.3	0.608755
$918$	−235.935	−0.00848257
$919$	9125.50	0.327554	0.163777	−	0.986497i	$-0.447632\pi$
$919$	9125.50	0.327554	0.163777	+	0.986497i	$0.447632\pi$
$920$	−16220.2	−0.581266
$921$	3078.89	0.110155
$922$	−11833.1	−0.422670
$923$	2383.74	0.0850072
$924$	−401.190	−0.0142838
$925$	100892.	3.58627
$926$	5537.08	0.196501
$927$	598.064	0.0211899
$928$	5197.47	0.183853
$929$	31370.0	1.10787	0.553937	−	0.832558i	$-0.313125\pi$
$929$	31370.0	1.10787	0.553937	+	0.832558i	$0.313125\pi$
$930$	17504.3	0.617191
$931$	5904.64	0.207859
$932$	10222.8	0.359290
$933$	−14072.2	−0.493786
$934$	14693.3	0.514754
$935$	−432.331	−0.0151216
$936$	936.000	0.0326860
$937$	12356.6	0.430815	0.215408	−	0.976524i	$-0.430892\pi$
$937$	12356.6	0.430815	0.215408	+	0.976524i	$0.430892\pi$
$938$	9483.93	0.330129
$939$	2323.68	0.0807567
$940$	25279.2	0.877146
$941$	−10165.5	−0.352163	−0.176081	−	0.984376i	$-0.556342\pi$
$941$	−10165.5	−0.352163	−0.176081	+	0.984376i	$0.556342\pi$
$942$	16780.9	0.580416
$943$	−16533.1	−0.570935
$944$	3957.29	0.136439
$945$	3915.70	0.134791
$946$	−4663.19	−0.160268
$947$	2723.10	0.0934412	0.0467206	−	0.998908i	$-0.485123\pi$
$947$	2723.10	0.0934412	0.0467206	+	0.998908i	$0.485123\pi$
$948$	11877.7	0.406929
$949$	6577.97	0.225005
$950$	−73322.2	−2.50409
$951$	−29375.9	−1.00166
$952$	−244.673	−0.00832972
$953$	46944.0	1.59566	0.797831	−	0.602882i	$-0.205981\pi$
$953$	46944.0	1.59566	0.797831	+	0.602882i	$0.205981\pi$
$954$	−3615.08	−0.122686
$955$	88331.0	2.99301
$956$	−5285.39	−0.178809
$957$	2327.20	0.0786079
$958$	33177.8	1.11892
$959$	5825.25	0.196149
$960$	3977.85	0.133734
$961$	−9962.47	−0.334412
$962$	8622.24	0.288973
$963$	−3852.02	−0.128899
$964$	−6835.21	−0.228369
$965$	−61194.4	−2.04137
$966$	−4110.26	−0.136900
$967$	29887.9	0.993931	0.496965	−	0.867770i	$-0.334448\pi$
$967$	29887.9	0.993931	0.496965	+	0.867770i	$0.334448\pi$
$968$	10465.5	0.347494
$969$	1579.49	0.0523637
$970$	−13437.3	−0.444788
$971$	−9988.34	−0.330115	−0.165057	−	0.986284i	$-0.552781\pi$
$971$	−9988.34	−0.330115	−0.165057	+	0.986284i	$0.552781\pi$
$972$	972.000	0.0320750
$973$	15306.0	0.504303
$974$	41523.6	1.36602
$975$	−11865.2	−0.389732
$976$	−8566.16	−0.280939
$977$	−40337.6	−1.32090	−0.660448	−	0.750872i	$-0.729634\pi$
$977$	−40337.6	−1.32090	−0.660448	+	0.750872i	$0.729634\pi$
$978$	13235.3	0.432739
$979$	−4939.87	−0.161265
$980$	4060.72	0.132362
$981$	−5297.07	−0.172398
$982$	−13620.7	−0.442620
$983$	19688.9	0.638840	0.319420	−	0.947613i	$-0.396512\pi$
$983$	19688.9	0.638840	0.319420	+	0.947613i	$0.396512\pi$
$984$	4054.58	0.131357
$985$	−67738.1	−2.19118
$986$	1419.29	0.0458410
$987$	6405.83	0.206585
$988$	−6266.14	−0.201774
$989$	−47775.1	−1.53606
$990$	1781.11	0.0571792
$991$	39692.6	1.27233	0.636163	−	0.771554i	$-0.280520\pi$
$991$	39692.6	1.27233	0.636163	+	0.771554i	$0.280520\pi$
$992$	4506.04	0.144221
$993$	5959.75	0.190460
$994$	2567.10	0.0819150
$995$	71798.3	2.28760
$996$	9445.67	0.300499
$997$	−58088.8	−1.84523	−0.922613	−	0.385727i	$-0.873951\pi$
$997$	−58088.8	−1.84523	−0.922613	+	0.385727i	$0.873951\pi$
$998$	33155.2	1.05161
$999$	8953.86	0.283571

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.a.n.1.3	✓	3	1.1	even	1	trivial
1638.4.a.ba.1.1		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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.7180 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -41.4360 q^{10} -4.77607 q^{11} +12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} +62.1539 q^{15} +16.0000 q^{16} +4.36916 q^{17} -18.0000 q^{18} +120.503 q^{19} +82.8719 q^{20} +21.0000 q^{21} +9.55215 q^{22} +97.8632 q^{23} -24.0000 q^{24} +304.235 q^{25} +26.0000 q^{26} +27.0000 q^{27} +28.0000 q^{28} -162.421 q^{29} -124.308 q^{30} -140.814 q^{31} -32.0000 q^{32} -14.3282 q^{33} -8.73832 q^{34} +145.026 q^{35} +36.0000 q^{36} +331.624 q^{37} -241.006 q^{38} -39.0000 q^{39} -165.744 q^{40} -168.941 q^{41} -42.0000 q^{42} -488.182 q^{43} -19.1043 q^{44} +186.462 q^{45} -195.726 q^{46} +305.040 q^{47} +48.0000 q^{48} +49.0000 q^{49} -608.469 q^{50} +13.1075 q^{51} -52.0000 q^{52} +200.838 q^{53} -54.0000 q^{54} -98.9506 q^{55} -56.0000 q^{56} +361.508 q^{57} +324.842 q^{58} +247.331 q^{59} +248.616 q^{60} -535.385 q^{61} +281.628 q^{62} +63.0000 q^{63} +64.0000 q^{64} -269.334 q^{65} +28.6564 q^{66} -677.423 q^{67} +17.4766 q^{68} +293.590 q^{69} -290.052 q^{70} -183.364 q^{71} -72.0000 q^{72} -505.997 q^{73} -663.249 q^{74} +912.704 q^{75} +482.011 q^{76} -33.4325 q^{77} +78.0000 q^{78} +989.806 q^{79} +331.488 q^{80} +81.0000 q^{81} +337.882 q^{82} +787.139 q^{83} +84.0000 q^{84} +90.5202 q^{85} +976.364 q^{86} -487.263 q^{87} +38.2086 q^{88} +1034.29 q^{89} -372.924 q^{90} -91.0000 q^{91} +391.453 q^{92} -422.441 q^{93} -610.079 q^{94} +2496.57 q^{95} -96.0000 q^{96} +324.290 q^{97} -98.0000 q^{98} -42.9847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} + 13 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} - 26 q^{10} + 17 q^{11} + 36 q^{12} - 39 q^{13} - 42 q^{14} + 39 q^{15} + 48 q^{16} + 89 q^{17} - 54 q^{18} + 89 q^{19}+ \cdots + 153 q^{99}+O(q^{100}) \) 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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