LMFDB - Embedded newform 546.4.a.n.1.2

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			1.2
Root			$-11.5595$ 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)

$f(q)$	$=$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -2.86358 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +5.72716 q^{10} +59.1016 q^{11} +12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} -8.59075 q^{15} +16.0000 q^{16} -32.4934 q^{17} -18.0000 q^{18} +63.0391 q^{19} -11.4543 q^{20} +21.0000 q^{21} -118.203 q^{22} -26.4586 q^{23} -24.0000 q^{24} -116.800 q^{25} +26.0000 q^{26} +27.0000 q^{27} +28.0000 q^{28} +204.584 q^{29} +17.1815 q^{30} -86.7837 q^{31} -32.0000 q^{32} +177.305 q^{33} +64.9868 q^{34} -20.0451 q^{35} +36.0000 q^{36} +78.6412 q^{37} -126.078 q^{38} -39.0000 q^{39} +22.9087 q^{40} +450.594 q^{41} -42.0000 q^{42} +7.48375 q^{43} +236.406 q^{44} -25.7722 q^{45} +52.9171 q^{46} -455.078 q^{47} +48.0000 q^{48} +49.0000 q^{49} +233.600 q^{50} -97.4802 q^{51} -52.0000 q^{52} +496.644 q^{53} -54.0000 q^{54} -169.242 q^{55} -56.0000 q^{56} +189.117 q^{57} -409.167 q^{58} -204.153 q^{59} -34.3630 q^{60} +356.375 q^{61} +173.567 q^{62} +63.0000 q^{63} +64.0000 q^{64} +37.2266 q^{65} -354.609 q^{66} -50.5685 q^{67} -129.974 q^{68} -79.3757 q^{69} +40.0902 q^{70} +1168.37 q^{71} -72.0000 q^{72} -871.189 q^{73} -157.282 q^{74} -350.400 q^{75} +252.156 q^{76} +413.711 q^{77} +78.0000 q^{78} -268.958 q^{79} -45.8173 q^{80} +81.0000 q^{81} -901.188 q^{82} +396.553 q^{83} +84.0000 q^{84} +93.0475 q^{85} -14.9675 q^{86} +613.751 q^{87} -472.813 q^{88} +58.0564 q^{89} +51.5445 q^{90} -91.0000 q^{91} -105.834 q^{92} -260.351 q^{93} +910.156 q^{94} -180.518 q^{95} -96.0000 q^{96} -387.306 q^{97} -98.0000 q^{98} +531.914 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.86358	−0.256127	−0.128063	−	0.991766i	$-0.540876\pi$
$5$	−2.86358	−0.256127	−0.128063	+	0.991766i	$0.540876\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	5.72716	0.181109
$11$	59.1016	1.61998	0.809991	−	0.586443i	$-0.199472\pi$
$11$	59.1016	1.61998	0.809991	+	0.586443i	$0.199472\pi$
$12$	12.0000	0.288675
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−14.0000	−0.267261
$15$	−8.59075	−0.147875
$16$	16.0000	0.250000
$17$	−32.4934	−0.463577	−0.231788	−	0.972766i	$-0.574458\pi$
$17$	−32.4934	−0.463577	−0.231788	+	0.972766i	$0.574458\pi$
$18$	−18.0000	−0.235702
$19$	63.0391	0.761166	0.380583	−	0.924747i	$-0.375723\pi$
$19$	63.0391	0.761166	0.380583	+	0.924747i	$0.375723\pi$
$20$	−11.4543	−0.128063
$21$	21.0000	0.218218
$22$	−118.203	−1.14550
$23$	−26.4586	−0.239869	−0.119935	−	0.992782i	$-0.538268\pi$
$23$	−26.4586	−0.239869	−0.119935	+	0.992782i	$0.538268\pi$
$24$	−24.0000	−0.204124
$25$	−116.800	−0.934399
$26$	26.0000	0.196116
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	204.584	1.31001	0.655004	−	0.755626i	$-0.272667\pi$
$29$	204.584	1.31001	0.655004	+	0.755626i	$0.272667\pi$
$30$	17.1815	0.104563
$31$	−86.7837	−0.502800	−0.251400	−	0.967883i	$-0.580891\pi$
$31$	−86.7837	−0.502800	−0.251400	+	0.967883i	$0.580891\pi$
$32$	−32.0000	−0.176777
$33$	177.305	0.935297
$34$	64.9868	0.327798
$35$	−20.0451	−0.0968068
$36$	36.0000	0.166667
$37$	78.6412	0.349420	0.174710	−	0.984620i	$-0.444101\pi$
$37$	78.6412	0.349420	0.174710	+	0.984620i	$0.444101\pi$
$38$	−126.078	−0.538226
$39$	−39.0000	−0.160128
$40$	22.9087	0.0905544
$41$	450.594	1.71636	0.858182	−	0.513345i	$-0.171594\pi$
$41$	450.594	1.71636	0.858182	+	0.513345i	$0.171594\pi$
$42$	−42.0000	−0.154303
$43$	7.48375	0.0265410	0.0132705	−	0.999912i	$-0.495776\pi$
$43$	7.48375	0.0265410	0.0132705	+	0.999912i	$0.495776\pi$
$44$	236.406	0.809991
$45$	−25.7722	−0.0853755
$46$	52.9171	0.169613
$47$	−455.078	−1.41234	−0.706170	−	0.708042i	$-0.749579\pi$
$47$	−455.078	−1.41234	−0.706170	+	0.708042i	$0.749579\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	233.600	0.660720
$51$	−97.4802	−0.267646
$52$	−52.0000	−0.138675
$53$	496.644	1.28716	0.643579	−	0.765380i	$-0.277449\pi$
$53$	496.644	1.28716	0.643579	+	0.765380i	$0.277449\pi$
$54$	−54.0000	−0.136083
$55$	−169.242	−0.414920
$56$	−56.0000	−0.133631
$57$	189.117	0.439459
$58$	−409.167	−0.926315
$59$	−204.153	−0.450482	−0.225241	−	0.974303i	$-0.572317\pi$
$59$	−204.153	−0.450482	−0.225241	+	0.974303i	$0.572317\pi$
$60$	−34.3630	−0.0739374
$61$	356.375	0.748018	0.374009	−	0.927425i	$-0.377983\pi$
$61$	356.375	0.748018	0.374009	+	0.927425i	$0.377983\pi$
$62$	173.567	0.355533
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	37.2266	0.0710367
$66$	−354.609	−0.661355
$67$	−50.5685	−0.0922079	−0.0461039	−	0.998937i	$-0.514681\pi$
$67$	−50.5685	−0.0922079	−0.0461039	+	0.998937i	$0.514681\pi$
$68$	−129.974	−0.231788
$69$	−79.3757	−0.138489
$70$	40.0902	0.0684527
$71$	1168.37	1.95295	0.976476	−	0.215625i	$-0.0691788\pi$
$71$	1168.37	1.95295	0.976476	+	0.215625i	$0.0691788\pi$
$72$	−72.0000	−0.117851
$73$	−871.189	−1.39678	−0.698391	−	0.715717i	$-0.746100\pi$
$73$	−871.189	−1.39678	−0.698391	+	0.715717i	$0.746100\pi$
$74$	−157.282	−0.247077
$75$	−350.400	−0.539476
$76$	252.156	0.380583
$77$	413.711	0.612295
$78$	78.0000	0.113228
$79$	−268.958	−0.383040	−0.191520	−	0.981489i	$-0.561342\pi$
$79$	−268.958	−0.383040	−0.191520	+	0.981489i	$0.561342\pi$
$80$	−45.8173	−0.0640316
$81$	81.0000	0.111111
$82$	−901.188	−1.21365
$83$	396.553	0.524426	0.262213	−	0.965010i	$-0.415548\pi$
$83$	396.553	0.524426	0.262213	+	0.965010i	$0.415548\pi$
$84$	84.0000	0.109109
$85$	93.0475	0.118734
$86$	−14.9675	−0.0187673
$87$	613.751	0.756333
$88$	−472.813	−0.572750
$89$	58.0564	0.0691457	0.0345728	−	0.999402i	$-0.488993\pi$
$89$	58.0564	0.0691457	0.0345728	+	0.999402i	$0.488993\pi$
$90$	51.5445	0.0603696
$91$	−91.0000	−0.104828
$92$	−105.834	−0.119935
$93$	−260.351	−0.290292
$94$	910.156	0.998675
$95$	−180.518	−0.194955
$96$	−96.0000	−0.102062
$97$	−387.306	−0.405412	−0.202706	−	0.979240i	$-0.564973\pi$
$97$	−387.306	−0.405412	−0.202706	+	0.979240i	$0.564973\pi$
$98$	−98.0000	−0.101015
$99$	531.914	0.539994
$100$	−467.200	−0.467200
$101$	1907.27	1.87901	0.939505	−	0.342535i	$-0.111285\pi$
$101$	1907.27	1.87901	0.939505	+	0.342535i	$0.111285\pi$
$102$	194.960	0.189255
$103$	849.245	0.812413	0.406207	−	0.913781i	$-0.366851\pi$
$103$	849.245	0.812413	0.406207	+	0.913781i	$0.366851\pi$
$104$	104.000	0.0980581
$105$	−60.1352	−0.0558914
$106$	−993.289	−0.910158
$107$	1921.47	1.73604	0.868019	−	0.496532i	$-0.165393\pi$
$107$	1921.47	1.73604	0.868019	+	0.496532i	$0.165393\pi$
$108$	108.000	0.0962250
$109$	1858.67	1.63329	0.816645	−	0.577140i	$-0.195831\pi$
$109$	1858.67	1.63329	0.816645	+	0.577140i	$0.195831\pi$
$110$	338.484	0.293393
$111$	235.924	0.201738
$112$	112.000	0.0944911
$113$	−58.7045	−0.0488713	−0.0244357	−	0.999701i	$-0.507779\pi$
$113$	−58.7045	−0.0488713	−0.0244357	+	0.999701i	$0.507779\pi$
$114$	−378.234	−0.310745
$115$	75.7663	0.0614369
$116$	818.334	0.655004
$117$	−117.000	−0.0924500
$118$	408.305	0.318539
$119$	−227.454	−0.175216
$120$	68.7260	0.0522816
$121$	2162.00	1.62434
$122$	−712.749	−0.528928
$123$	1351.78	0.990943
$124$	−347.135	−0.251400
$125$	692.414	0.495451
$126$	−126.000	−0.0890871
$127$	451.061	0.315159	0.157580	−	0.987506i	$-0.449631\pi$
$127$	451.061	0.315159	0.157580	+	0.987506i	$0.449631\pi$
$128$	−128.000	−0.0883883
$129$	22.4513	0.0153234
$130$	−74.4531	−0.0502306
$131$	−1363.92	−0.909667	−0.454834	−	0.890576i	$-0.650301\pi$
$131$	−1363.92	−0.909667	−0.454834	+	0.890576i	$0.650301\pi$
$132$	709.219	0.467648
$133$	441.274	0.287694
$134$	101.137	0.0652008
$135$	−77.3167	−0.0492916
$136$	259.947	0.163899
$137$	−2768.55	−1.72652	−0.863260	−	0.504759i	$-0.831581\pi$
$137$	−2768.55	−1.72652	−0.863260	+	0.504759i	$0.831581\pi$
$138$	158.751	0.0979262
$139$	1414.60	0.863199	0.431600	−	0.902065i	$-0.357949\pi$
$139$	1414.60	0.863199	0.431600	+	0.902065i	$0.357949\pi$
$140$	−80.1803	−0.0484034
$141$	−1365.23	−0.815415
$142$	−2336.73	−1.38095
$143$	−768.320	−0.449302
$144$	144.000	0.0833333
$145$	−585.842	−0.335528
$146$	1742.38	0.987673
$147$	147.000	0.0824786
$148$	314.565	0.174710
$149$	1893.06	1.04084	0.520420	−	0.853910i	$-0.325775\pi$
$149$	1893.06	1.04084	0.520420	+	0.853910i	$0.325775\pi$
$150$	700.799	0.381467
$151$	−2480.10	−1.33661	−0.668304	−	0.743888i	$-0.732979\pi$
$151$	−2480.10	−1.33661	−0.668304	+	0.743888i	$0.732979\pi$
$152$	−504.313	−0.269113
$153$	−292.441	−0.154526
$154$	−827.422	−0.432958
$155$	248.512	0.128780
$156$	−156.000	−0.0800641
$157$	3130.90	1.59155	0.795775	−	0.605593i	$-0.207064\pi$
$157$	3130.90	1.59155	0.795775	+	0.605593i	$0.207064\pi$
$158$	537.916	0.270850
$159$	1489.93	0.743141
$160$	91.6346	0.0452772
$161$	−185.210	−0.0906620
$162$	−162.000	−0.0785674
$163$	−1766.78	−0.848987	−0.424494	−	0.905431i	$-0.639548\pi$
$163$	−1766.78	−0.848987	−0.424494	+	0.905431i	$0.639548\pi$
$164$	1802.38	0.858182
$165$	−507.727	−0.239554
$166$	−793.106	−0.370825
$167$	2765.11	1.28126	0.640631	−	0.767849i	$-0.278673\pi$
$167$	2765.11	1.28126	0.640631	+	0.767849i	$0.278673\pi$
$168$	−168.000	−0.0771517
$169$	169.000	0.0769231
$170$	−186.095	−0.0839579
$171$	567.352	0.253722
$172$	29.9350	0.0132705
$173$	−1199.93	−0.527335	−0.263668	−	0.964614i	$-0.584932\pi$
$173$	−1199.93	−0.527335	−0.263668	+	0.964614i	$0.584932\pi$
$174$	−1227.50	−0.534808
$175$	−817.599	−0.353170
$176$	945.625	0.404995
$177$	−612.458	−0.260086
$178$	−116.113	−0.0488934
$179$	3064.58	1.27965	0.639825	−	0.768521i	$-0.279007\pi$
$179$	3064.58	1.27965	0.639825	+	0.768521i	$0.279007\pi$
$180$	−103.089	−0.0426878
$181$	−2317.74	−0.951803	−0.475901	−	0.879499i	$-0.657878\pi$
$181$	−2317.74	−0.951803	−0.475901	+	0.879499i	$0.657878\pi$
$182$	182.000	0.0741249
$183$	1069.12	0.431868
$184$	211.669	0.0848066
$185$	−225.196	−0.0894958
$186$	520.702	0.205267
$187$	−1920.41	−0.750986
$188$	−1820.31	−0.706170
$189$	189.000	0.0727393
$190$	361.035	0.137854
$191$	−756.591	−0.286623	−0.143311	−	0.989678i	$-0.545775\pi$
$191$	−756.591	−0.286623	−0.143311	+	0.989678i	$0.545775\pi$
$192$	192.000	0.0721688
$193$	54.2612	0.0202373	0.0101187	−	0.999949i	$-0.496779\pi$
$193$	54.2612	0.0202373	0.0101187	+	0.999949i	$0.496779\pi$
$194$	774.611	0.286669
$195$	111.680	0.0410131
$196$	196.000	0.0714286
$197$	−1717.75	−0.621242	−0.310621	−	0.950534i	$-0.600537\pi$
$197$	−1717.75	−0.621242	−0.310621	+	0.950534i	$0.600537\pi$
$198$	−1063.83	−0.381833
$199$	−2715.92	−0.967468	−0.483734	−	0.875215i	$-0.660720\pi$
$199$	−2715.92	−0.967468	−0.483734	+	0.875215i	$0.660720\pi$
$200$	934.399	0.330360
$201$	−151.706	−0.0532362
$202$	−3814.53	−1.32866
$203$	1432.08	0.495136
$204$	−389.921	−0.133823
$205$	−1290.31	−0.439606
$206$	−1698.49	−0.574463
$207$	−238.127	−0.0799564
$208$	−208.000	−0.0693375
$209$	3725.71	1.23307
$210$	120.270	0.0395212
$211$	−3121.69	−1.01851	−0.509256	−	0.860615i	$-0.670080\pi$
$211$	−3121.69	−1.01851	−0.509256	+	0.860615i	$0.670080\pi$
$212$	1986.58	0.643579
$213$	3505.10	1.12754
$214$	−3842.95	−1.22756
$215$	−21.4303	−0.00679785
$216$	−216.000	−0.0680414
$217$	−607.486	−0.190041
$218$	−3717.35	−1.15491
$219$	−2613.57	−0.806432
$220$	−676.969	−0.207460
$221$	422.414	0.128573
$222$	−471.847	−0.142650
$223$	154.775	0.0464776	0.0232388	−	0.999730i	$-0.492602\pi$
$223$	154.775	0.0464776	0.0232388	+	0.999730i	$0.492602\pi$
$224$	−224.000	−0.0668153
$225$	−1051.20	−0.311466
$226$	117.409	0.0345572
$227$	−3826.04	−1.11869	−0.559346	−	0.828934i	$-0.688948\pi$
$227$	−3826.04	−1.11869	−0.559346	+	0.828934i	$0.688948\pi$
$228$	756.469	0.219730
$229$	−6064.24	−1.74994	−0.874970	−	0.484176i	$-0.839119\pi$
$229$	−6064.24	−1.74994	−0.874970	+	0.484176i	$0.839119\pi$
$230$	−151.533	−0.0434424
$231$	1241.13	0.353509
$232$	−1636.67	−0.463158
$233$	249.377	0.0701168	0.0350584	−	0.999385i	$-0.488838\pi$
$233$	249.377	0.0701168	0.0350584	+	0.999385i	$0.488838\pi$
$234$	234.000	0.0653720
$235$	1303.15	0.361738
$236$	−816.611	−0.225241
$237$	−806.874	−0.221148
$238$	454.908	0.123896
$239$	−4299.56	−1.16366	−0.581832	−	0.813309i	$-0.697664\pi$
$239$	−4299.56	−1.16366	−0.581832	+	0.813309i	$0.697664\pi$
$240$	−137.452	−0.0369687
$241$	−2394.74	−0.640079	−0.320039	−	0.947404i	$-0.603696\pi$
$241$	−2394.74	−0.640079	−0.320039	+	0.947404i	$0.603696\pi$
$242$	−4323.99	−1.14858
$243$	243.000	0.0641500
$244$	1425.50	0.374009
$245$	−140.316	−0.0365895
$246$	−2703.56	−0.700703
$247$	−819.508	−0.211109
$248$	694.269	0.177767
$249$	1189.66	0.302777
$250$	−1384.83	−0.350337
$251$	6039.79	1.51884	0.759419	−	0.650602i	$-0.225483\pi$
$251$	6039.79	1.51884	0.759419	+	0.650602i	$0.225483\pi$
$252$	252.000	0.0629941
$253$	−1563.74	−0.388584
$254$	−902.122	−0.222851
$255$	279.143	0.0685513
$256$	256.000	0.0625000
$257$	−6079.81	−1.47567	−0.737837	−	0.674979i	$-0.764152\pi$
$257$	−6079.81	−1.47567	−0.737837	+	0.674979i	$0.764152\pi$
$258$	−44.9025	−0.0108353
$259$	550.489	0.132068
$260$	148.906	0.0355184
$261$	1841.25	0.436669
$262$	2727.84	0.643232
$263$	2350.79	0.551164	0.275582	−	0.961278i	$-0.411129\pi$
$263$	2350.79	0.551164	0.275582	+	0.961278i	$0.411129\pi$
$264$	−1418.44	−0.330677
$265$	−1422.18	−0.329675
$266$	−882.547	−0.203430
$267$	174.169	0.0399213
$268$	−202.274	−0.0461039
$269$	−980.274	−0.222187	−0.111094	−	0.993810i	$-0.535435\pi$
$269$	−980.274	−0.222187	−0.111094	+	0.993810i	$0.535435\pi$
$270$	154.633	0.0348544
$271$	−7039.12	−1.57784	−0.788922	−	0.614493i	$-0.789361\pi$
$271$	−7039.12	−1.57784	−0.788922	+	0.614493i	$0.789361\pi$
$272$	−519.894	−0.115894
$273$	−273.000	−0.0605228
$274$	5537.10	1.22083
$275$	−6903.06	−1.51371
$276$	−317.503	−0.0692443
$277$	4325.93	0.938339	0.469170	−	0.883108i	$-0.344553\pi$
$277$	4325.93	0.938339	0.469170	+	0.883108i	$0.344553\pi$
$278$	−2829.20	−0.610374
$279$	−781.053	−0.167600
$280$	160.361	0.0342264
$281$	−4145.13	−0.879992	−0.439996	−	0.898000i	$-0.645020\pi$
$281$	−4145.13	−0.879992	−0.439996	+	0.898000i	$0.645020\pi$
$282$	2730.47	0.576585
$283$	−6967.29	−1.46347	−0.731736	−	0.681588i	$-0.761290\pi$
$283$	−6967.29	−1.46347	−0.731736	+	0.681588i	$0.761290\pi$
$284$	4673.47	0.976476
$285$	−541.553	−0.112557
$286$	1536.64	0.317704
$287$	3154.16	0.648725
$288$	−288.000	−0.0589256
$289$	−3857.18	−0.785096
$290$	1171.68	0.237254
$291$	−1161.92	−0.234064
$292$	−3484.76	−0.698391
$293$	254.701	0.0507842	0.0253921	−	0.999678i	$-0.491917\pi$
$293$	254.701	0.0507842	0.0253921	+	0.999678i	$0.491917\pi$
$294$	−294.000	−0.0583212
$295$	584.608	0.115380
$296$	−629.130	−0.123539
$297$	1595.74	0.311766
$298$	−3786.11	−0.735985
$299$	343.961	0.0665277
$300$	−1401.60	−0.269738
$301$	52.3863	0.0100315
$302$	4960.20	0.945125
$303$	5721.80	1.08485
$304$	1008.63	0.190292
$305$	−1020.51	−0.191587
$306$	584.881	0.109266
$307$	6436.08	1.19650	0.598252	−	0.801308i	$-0.295862\pi$
$307$	6436.08	1.19650	0.598252	+	0.801308i	$0.295862\pi$
$308$	1654.84	0.306148
$309$	2547.73	0.469047
$310$	−497.024	−0.0910616
$311$	8299.35	1.51323	0.756613	−	0.653863i	$-0.226853\pi$
$311$	8299.35	1.51323	0.756613	+	0.653863i	$0.226853\pi$
$312$	312.000	0.0566139
$313$	−1008.05	−0.182040	−0.0910199	−	0.995849i	$-0.529013\pi$
$313$	−1008.05	−0.182040	−0.0910199	+	0.995849i	$0.529013\pi$
$314$	−6261.81	−1.12540
$315$	−180.406	−0.0322689
$316$	−1075.83	−0.191520
$317$	−52.2097	−0.00925045	−0.00462522	−	0.999989i	$-0.501472\pi$
$317$	−52.2097	−0.00925045	−0.00462522	+	0.999989i	$0.501472\pi$
$318$	−2979.87	−0.525480
$319$	12091.2	2.12219
$320$	−183.269	−0.0320158
$321$	5764.42	1.00230
$322$	370.420	0.0641077
$323$	−2048.35	−0.352859
$324$	324.000	0.0555556
$325$	1518.40	0.259156
$326$	3533.56	0.600325
$327$	5576.02	0.942981
$328$	−3604.75	−0.606826
$329$	−3185.55	−0.533814
$330$	1015.45	0.169391
$331$	975.175	0.161935	0.0809675	−	0.996717i	$-0.474199\pi$
$331$	975.175	0.161935	0.0809675	+	0.996717i	$0.474199\pi$
$332$	1586.21	0.262213
$333$	707.771	0.116473
$334$	−5530.23	−0.905989
$335$	144.807	0.0236169
$336$	336.000	0.0545545
$337$	−2306.96	−0.372902	−0.186451	−	0.982464i	$-0.559699\pi$
$337$	−2306.96	−0.372902	−0.186451	+	0.982464i	$0.559699\pi$
$338$	−338.000	−0.0543928
$339$	−176.114	−0.0282159
$340$	372.190	0.0593672
$341$	−5129.05	−0.814527
$342$	−1134.70	−0.179409
$343$	343.000	0.0539949
$344$	−59.8700	−0.00938365
$345$	227.299	0.0354706
$346$	2399.86	0.372882
$347$	−12759.0	−1.97389	−0.986947	−	0.161046i	$-0.948513\pi$
$347$	−12759.0	−1.97389	−0.986947	+	0.161046i	$0.948513\pi$
$348$	2455.00	0.378167
$349$	107.635	0.0165088	0.00825439	−	0.999966i	$-0.497373\pi$
$349$	107.635	0.0165088	0.00825439	+	0.999966i	$0.497373\pi$
$350$	1635.20	0.249729
$351$	−351.000	−0.0533761
$352$	−1891.25	−0.286375
$353$	3367.88	0.507802	0.253901	−	0.967230i	$-0.418286\pi$
$353$	3367.88	0.507802	0.253901	+	0.967230i	$0.418286\pi$
$354$	1224.92	0.183908
$355$	−3345.71	−0.500203
$356$	232.226	0.0345728
$357$	−682.362	−0.101161
$358$	−6129.16	−0.904849
$359$	−8883.44	−1.30599	−0.652994	−	0.757363i	$-0.726487\pi$
$359$	−8883.44	−1.30599	−0.652994	+	0.757363i	$0.726487\pi$
$360$	206.178	0.0301848
$361$	−2885.07	−0.420626
$362$	4635.48	0.673026
$363$	6485.99	0.937813
$364$	−364.000	−0.0524142
$365$	2494.72	0.357753
$366$	−2138.25	−0.305377
$367$	768.610	0.109322	0.0546610	−	0.998505i	$-0.482592\pi$
$367$	768.610	0.109322	0.0546610	+	0.998505i	$0.482592\pi$
$368$	−423.337	−0.0599673
$369$	4055.34	0.572121
$370$	450.391	0.0632831
$371$	3476.51	0.486500
$372$	−1041.40	−0.145146
$373$	7584.20	1.05280	0.526401	−	0.850236i	$-0.323541\pi$
$373$	7584.20	1.05280	0.526401	+	0.850236i	$0.323541\pi$
$374$	3840.82	0.531027
$375$	2077.24	0.286049
$376$	3640.63	0.499338
$377$	−2659.59	−0.363331
$378$	−378.000	−0.0514344
$379$	−6686.65	−0.906254	−0.453127	−	0.891446i	$-0.649692\pi$
$379$	−6686.65	−0.906254	−0.453127	+	0.891446i	$0.649692\pi$
$380$	−722.070	−0.0974774
$381$	1353.18	0.181957
$382$	1513.18	0.202673
$383$	990.115	0.132095	0.0660477	−	0.997816i	$-0.478961\pi$
$383$	990.115	0.132095	0.0660477	+	0.997816i	$0.478961\pi$
$384$	−384.000	−0.0510310
$385$	−1184.70	−0.156825
$386$	−108.522	−0.0143100
$387$	67.3538	0.00884699
$388$	−1549.22	−0.202706
$389$	−612.101	−0.0797809	−0.0398905	−	0.999204i	$-0.512701\pi$
$389$	−612.101	−0.0797809	−0.0398905	+	0.999204i	$0.512701\pi$
$390$	−223.359	−0.0290006
$391$	859.729	0.111198
$392$	−392.000	−0.0505076
$393$	−4091.77	−0.525197
$394$	3435.50	0.439284
$395$	770.184	0.0981067
$396$	2127.66	0.269997
$397$	8640.65	1.09235	0.546173	−	0.837672i	$-0.316084\pi$
$397$	8640.65	1.09235	0.546173	+	0.837672i	$0.316084\pi$
$398$	5431.83	0.684103
$399$	1323.82	0.166100
$400$	−1868.80	−0.233600
$401$	2725.46	0.339408	0.169704	−	0.985495i	$-0.445719\pi$
$401$	2725.46	0.339408	0.169704	+	0.985495i	$0.445719\pi$
$402$	303.411	0.0376437
$403$	1128.19	0.139452
$404$	7629.06	0.939505
$405$	−231.950	−0.0284585
$406$	−2864.17	−0.350114
$407$	4647.82	0.566054
$408$	779.842	0.0946273
$409$	−5055.02	−0.611136	−0.305568	−	0.952170i	$-0.598846\pi$
$409$	−5055.02	−0.611136	−0.305568	+	0.952170i	$0.598846\pi$
$410$	2580.62	0.310849
$411$	−8305.66	−0.996807
$412$	3396.98	0.406207
$413$	−1429.07	−0.170266
$414$	476.254	0.0565377
$415$	−1135.56	−0.134319
$416$	416.000	0.0490290
$417$	4243.80	0.498368
$418$	−7451.42	−0.871916
$419$	4397.70	0.512749	0.256375	−	0.966577i	$-0.417472\pi$
$419$	4397.70	0.512749	0.256375	+	0.966577i	$0.417472\pi$
$420$	−240.541	−0.0279457
$421$	−1652.62	−0.191316	−0.0956580	−	0.995414i	$-0.530496\pi$
$421$	−1652.62	−0.191316	−0.0956580	+	0.995414i	$0.530496\pi$
$422$	6243.39	0.720197
$423$	−4095.70	−0.470780
$424$	−3973.15	−0.455079
$425$	3795.23	0.433166
$426$	−7010.20	−0.797290
$427$	2494.62	0.282724
$428$	7685.90	0.868019
$429$	−2304.96	−0.259405
$430$	42.8607	0.00480680
$431$	17441.4	1.94925	0.974623	−	0.223854i	$-0.0718639\pi$
$431$	17441.4	1.94925	0.974623	+	0.223854i	$0.0718639\pi$
$432$	432.000	0.0481125
$433$	2843.64	0.315605	0.157802	−	0.987471i	$-0.449559\pi$
$433$	2843.64	0.315605	0.157802	+	0.987471i	$0.449559\pi$
$434$	1214.97	0.134379
$435$	−1757.53	−0.193717
$436$	7434.70	0.816645
$437$	−1667.92	−0.182580
$438$	5227.14	0.570233
$439$	944.215	0.102654	0.0513268	−	0.998682i	$-0.483655\pi$
$439$	944.215	0.102654	0.0513268	+	0.998682i	$0.483655\pi$
$440$	1353.94	0.146696
$441$	441.000	0.0476190
$442$	−844.829	−0.0909149
$443$	4269.05	0.457853	0.228926	−	0.973444i	$-0.426478\pi$
$443$	4269.05	0.457853	0.228926	+	0.973444i	$0.426478\pi$
$444$	943.695	0.100869
$445$	−166.249	−0.0177101
$446$	−309.550	−0.0328646
$447$	5679.17	0.600929
$448$	448.000	0.0472456
$449$	−16165.6	−1.69911	−0.849557	−	0.527497i	$-0.823131\pi$
$449$	−16165.6	−1.69911	−0.849557	+	0.527497i	$0.823131\pi$
$450$	2102.40	0.220240
$451$	26630.8	2.78048
$452$	−234.818	−0.0244357
$453$	−7440.31	−0.771691
$454$	7652.07	0.791034
$455$	260.586	0.0268494
$456$	−1512.94	−0.155372
$457$	8138.49	0.833047	0.416524	−	0.909125i	$-0.363248\pi$
$457$	8138.49	0.833047	0.416524	+	0.909125i	$0.363248\pi$
$458$	12128.5	1.23740
$459$	−877.322	−0.0892154
$460$	303.065	0.0307184
$461$	−14793.7	−1.49460	−0.747299	−	0.664488i	$-0.768650\pi$
$461$	−14793.7	−1.49460	−0.747299	+	0.664488i	$0.768650\pi$
$462$	−2482.27	−0.249969
$463$	−2498.44	−0.250783	−0.125391	−	0.992107i	$-0.540019\pi$
$463$	−2498.44	−0.250783	−0.125391	+	0.992107i	$0.540019\pi$
$464$	3273.34	0.327502
$465$	745.536	0.0743515
$466$	−498.754	−0.0495801
$467$	−11002.2	−1.09019	−0.545096	−	0.838374i	$-0.683507\pi$
$467$	−11002.2	−1.09019	−0.545096	+	0.838374i	$0.683507\pi$
$468$	−468.000	−0.0462250
$469$	−353.980	−0.0348513
$470$	−2606.31	−0.255787
$471$	9392.71	0.918882
$472$	1633.22	0.159269
$473$	442.301	0.0429959
$474$	1613.75	0.156375
$475$	−7362.96	−0.711233
$476$	−909.815	−0.0876078
$477$	4469.80	0.429052
$478$	8599.12	0.822834
$479$	−8272.30	−0.789084	−0.394542	−	0.918878i	$-0.629097\pi$
$479$	−8272.30	−0.789084	−0.394542	+	0.918878i	$0.629097\pi$
$480$	274.904	0.0261408
$481$	−1022.34	−0.0969117
$482$	4789.49	0.452604
$483$	−555.630	−0.0523438
$484$	8647.98	0.812170
$485$	1109.08	0.103837
$486$	−486.000	−0.0453609
$487$	16565.9	1.54142	0.770710	−	0.637186i	$-0.219902\pi$
$487$	16565.9	1.54142	0.770710	+	0.637186i	$0.219902\pi$
$488$	−2851.00	−0.264464
$489$	−5300.34	−0.490163
$490$	280.631	0.0258727
$491$	−7325.26	−0.673288	−0.336644	−	0.941632i	$-0.609292\pi$
$491$	−7325.26	−0.673288	−0.336644	+	0.941632i	$0.609292\pi$
$492$	5407.13	0.495472
$493$	−6647.62	−0.607289
$494$	1639.02	0.149277
$495$	−1523.18	−0.138307
$496$	−1388.54	−0.125700
$497$	8178.57	0.738147
$498$	−2379.32	−0.214096
$499$	9451.91	0.847947	0.423974	−	0.905675i	$-0.360635\pi$
$499$	9451.91	0.847947	0.423974	+	0.905675i	$0.360635\pi$
$500$	2769.66	0.247726
$501$	8295.34	0.739737
$502$	−12079.6	−1.07398
$503$	−2665.87	−0.236312	−0.118156	−	0.992995i	$-0.537698\pi$
$503$	−2665.87	−0.236312	−0.118156	+	0.992995i	$0.537698\pi$
$504$	−504.000	−0.0445435
$505$	−5461.61	−0.481265
$506$	3127.49	0.274770
$507$	507.000	0.0444116
$508$	1804.24	0.157580
$509$	−19999.1	−1.74154	−0.870769	−	0.491692i	$-0.836378\pi$
$509$	−19999.1	−1.74154	−0.870769	+	0.491692i	$0.836378\pi$
$510$	−558.285	−0.0484731
$511$	−6098.33	−0.527934
$512$	−512.000	−0.0441942
$513$	1702.06	0.146486
$514$	12159.6	1.04346
$515$	−2431.88	−0.208081
$516$	89.8050	0.00766171
$517$	−26895.8	−2.28796
$518$	−1100.98	−0.0933864
$519$	−3599.79	−0.304457
$520$	−297.813	−0.0251153
$521$	12060.9	1.01420	0.507101	−	0.861887i	$-0.330717\pi$
$521$	12060.9	1.01420	0.507101	+	0.861887i	$0.330717\pi$
$522$	−3682.50	−0.308772
$523$	1686.86	0.141035	0.0705176	−	0.997511i	$-0.477535\pi$
$523$	1686.86	0.141035	0.0705176	+	0.997511i	$0.477535\pi$
$524$	−5455.69	−0.454834
$525$	−2452.80	−0.203903
$526$	−4701.59	−0.389732
$527$	2819.90	0.233087
$528$	2836.88	0.233824
$529$	−11466.9	−0.942463
$530$	2844.36	0.233116
$531$	−1837.37	−0.150161
$532$	1765.09	0.143847
$533$	−5857.72	−0.476034
$534$	−348.338	−0.0282286
$535$	−5502.30	−0.444645
$536$	404.548	0.0326004
$537$	9193.73	0.738806
$538$	1960.55	0.157110
$539$	2895.98	0.231426
$540$	−309.267	−0.0246458
$541$	167.625	0.0133212	0.00666058	−	0.999978i	$-0.497880\pi$
$541$	167.625	0.0133212	0.00666058	+	0.999978i	$0.497880\pi$
$542$	14078.2	1.11570
$543$	−6953.22	−0.549524
$544$	1039.79	0.0819496
$545$	−5322.47	−0.418329
$546$	546.000	0.0427960
$547$	14590.7	1.14050	0.570251	−	0.821471i	$-0.306846\pi$
$547$	14590.7	1.14050	0.570251	+	0.821471i	$0.306846\pi$
$548$	−11074.2	−0.863260
$549$	3207.37	0.249339
$550$	13806.1	1.07035
$551$	12896.8	0.997133
$552$	635.006	0.0489631
$553$	−1882.71	−0.144775
$554$	−8651.86	−0.663506
$555$	−675.587	−0.0516704
$556$	5658.40	0.431600
$557$	6039.39	0.459421	0.229710	−	0.973259i	$-0.426222\pi$
$557$	6039.39	0.459421	0.229710	+	0.973259i	$0.426222\pi$
$558$	1562.11	0.118511
$559$	−97.2888	−0.00736114
$560$	−320.721	−0.0242017
$561$	−5761.23	−0.433582
$562$	8290.26	0.622248
$563$	−3135.34	−0.234705	−0.117353	−	0.993090i	$-0.537441\pi$
$563$	−3135.34	−0.234705	−0.117353	+	0.993090i	$0.537441\pi$
$564$	−5460.94	−0.407707
$565$	168.105	0.0125172
$566$	13934.6	1.03483
$567$	567.000	0.0419961
$568$	−9346.93	−0.690473
$569$	−15935.0	−1.17404	−0.587021	−	0.809571i	$-0.699700\pi$
$569$	−15935.0	−1.17404	−0.587021	+	0.809571i	$0.699700\pi$
$570$	1083.11	0.0795900
$571$	20929.8	1.53395	0.766975	−	0.641677i	$-0.221761\pi$
$571$	20929.8	1.53395	0.766975	+	0.641677i	$0.221761\pi$
$572$	−3073.28	−0.224651
$573$	−2269.77	−0.165482
$574$	−6308.31	−0.458718
$575$	3090.36	0.224134
$576$	576.000	0.0416667
$577$	−8732.20	−0.630028	−0.315014	−	0.949087i	$-0.602009\pi$
$577$	−8732.20	−0.630028	−0.315014	+	0.949087i	$0.602009\pi$
$578$	7714.36	0.555147
$579$	162.784	0.0116840
$580$	−2343.37	−0.167764
$581$	2775.87	0.198214
$582$	2323.83	0.165509
$583$	29352.5	2.08517
$584$	6969.52	0.493837
$585$	335.039	0.0236789
$586$	−509.401	−0.0359099
$587$	−10812.9	−0.760302	−0.380151	−	0.924924i	$-0.624128\pi$
$587$	−10812.9	−0.760302	−0.380151	+	0.924924i	$0.624128\pi$
$588$	588.000	0.0412393
$589$	−5470.76	−0.382714
$590$	−1169.22	−0.0815862
$591$	−5153.25	−0.358674
$592$	1258.26	0.0873550
$593$	−20683.4	−1.43232	−0.716160	−	0.697936i	$-0.754102\pi$
$593$	−20683.4	−1.43232	−0.716160	+	0.697936i	$0.754102\pi$
$594$	−3191.49	−0.220452
$595$	651.333	0.0448774
$596$	7572.22	0.520420
$597$	−8147.75	−0.558568
$598$	−687.923	−0.0470422
$599$	−20659.9	−1.40925	−0.704625	−	0.709580i	$-0.748885\pi$
$599$	−20659.9	−1.40925	−0.704625	+	0.709580i	$0.748885\pi$
$600$	2803.20	0.190733
$601$	20635.6	1.40057	0.700286	−	0.713863i	$-0.253056\pi$
$601$	20635.6	1.40057	0.700286	+	0.713863i	$0.253056\pi$
$602$	−104.773	−0.00709337
$603$	−455.117	−0.0307360
$604$	−9920.41	−0.668304
$605$	−6191.05	−0.416037
$606$	−11443.6	−0.767103
$607$	−27628.5	−1.84746	−0.923730	−	0.383045i	$-0.874875\pi$
$607$	−27628.5	−1.84746	−0.923730	+	0.383045i	$0.874875\pi$
$608$	−2017.25	−0.134556
$609$	4296.25	0.285867
$610$	2041.02	0.135473
$611$	5916.02	0.391713
$612$	−1169.76	−0.0772628
$613$	7962.76	0.524654	0.262327	−	0.964979i	$-0.415510\pi$
$613$	7962.76	0.524654	0.262327	+	0.964979i	$0.415510\pi$
$614$	−12872.2	−0.846056
$615$	−3870.94	−0.253807
$616$	−3309.69	−0.216479
$617$	−12245.1	−0.798975	−0.399487	−	0.916739i	$-0.630812\pi$
$617$	−12245.1	−0.798975	−0.399487	+	0.916739i	$0.630812\pi$
$618$	−5095.47	−0.331666
$619$	7362.87	0.478092	0.239046	−	0.971008i	$-0.423165\pi$
$619$	7362.87	0.478092	0.239046	+	0.971008i	$0.423165\pi$
$620$	994.049	0.0643902
$621$	−714.381	−0.0461629
$622$	−16598.7	−1.07001
$623$	406.395	0.0261346
$624$	−624.000	−0.0400320
$625$	12617.2	0.807501
$626$	2016.10	0.128722
$627$	11177.1	0.711916
$628$	12523.6	0.795775
$629$	−2555.32	−0.161983
$630$	360.811	0.0228176
$631$	19949.4	1.25859	0.629297	−	0.777165i	$-0.283343\pi$
$631$	19949.4	1.25859	0.629297	+	0.777165i	$0.283343\pi$
$632$	2151.66	0.135425
$633$	−9365.08	−0.588039
$634$	104.419	0.00654105
$635$	−1291.65	−0.0807206
$636$	5959.73	0.371570
$637$	−637.000	−0.0396214
$638$	−24182.4	−1.50061
$639$	10515.3	0.650984
$640$	366.539	0.0226386
$641$	11730.9	0.722843	0.361422	−	0.932402i	$-0.382292\pi$
$641$	11730.9	0.722843	0.361422	+	0.932402i	$0.382292\pi$
$642$	−11528.8	−0.708734
$643$	−846.190	−0.0518981	−0.0259491	−	0.999663i	$-0.508261\pi$
$643$	−846.190	−0.0518981	−0.0259491	+	0.999663i	$0.508261\pi$
$644$	−740.840	−0.0453310
$645$	−64.2910	−0.00392474
$646$	4096.71	0.249509
$647$	−25203.4	−1.53145	−0.765725	−	0.643168i	$-0.777620\pi$
$647$	−25203.4	−1.53145	−0.765725	+	0.643168i	$0.777620\pi$
$648$	−648.000	−0.0392837
$649$	−12065.7	−0.729772
$650$	−3036.80	−0.183251
$651$	−1822.46	−0.109720
$652$	−7067.12	−0.424494
$653$	−7684.53	−0.460519	−0.230259	−	0.973129i	$-0.573957\pi$
$653$	−7684.53	−0.460519	−0.230259	+	0.973129i	$0.573957\pi$
$654$	−11152.0	−0.666788
$655$	3905.70	0.232990
$656$	7209.50	0.429091
$657$	−7840.71	−0.465594
$658$	6371.10	0.377464
$659$	14728.2	0.870608	0.435304	−	0.900283i	$-0.356641\pi$
$659$	14728.2	0.870608	0.435304	+	0.900283i	$0.356641\pi$
$660$	−2030.91	−0.119777
$661$	−22425.8	−1.31961	−0.659806	−	0.751436i	$-0.729362\pi$
$661$	−22425.8	−1.31961	−0.659806	+	0.751436i	$0.729362\pi$
$662$	−1950.35	−0.114505
$663$	1267.24	0.0742317
$664$	−3172.42	−0.185412
$665$	−1263.62	−0.0736860
$666$	−1415.54	−0.0823591
$667$	−5412.99	−0.314230
$668$	11060.5	0.640631
$669$	464.325	0.0268339
$670$	−289.614	−0.0166997
$671$	21062.3	1.21177
$672$	−672.000	−0.0385758
$673$	7433.61	0.425772	0.212886	−	0.977077i	$-0.431714\pi$
$673$	7433.61	0.425772	0.212886	+	0.977077i	$0.431714\pi$
$674$	4613.91	0.263681
$675$	−3153.60	−0.179825
$676$	676.000	0.0384615
$677$	−7865.75	−0.446537	−0.223268	−	0.974757i	$-0.571673\pi$
$677$	−7865.75	−0.446537	−0.223268	+	0.974757i	$0.571673\pi$
$678$	352.227	0.0199516
$679$	−2711.14	−0.153231
$680$	−744.380	−0.0419789
$681$	−11478.1	−0.645877
$682$	10258.1	0.575958
$683$	26540.5	1.48689	0.743444	−	0.668799i	$-0.233191\pi$
$683$	26540.5	1.48689	0.743444	+	0.668799i	$0.233191\pi$
$684$	2269.41	0.126861
$685$	7927.98	0.442208
$686$	−686.000	−0.0381802
$687$	−18192.7	−1.01033
$688$	119.740	0.00663524
$689$	−6456.38	−0.356993
$690$	−454.598	−0.0250815
$691$	−7542.99	−0.415266	−0.207633	−	0.978207i	$-0.566576\pi$
$691$	−7542.99	−0.415266	−0.207633	+	0.978207i	$0.566576\pi$
$692$	−4799.72	−0.263668
$693$	3723.40	0.204098
$694$	25518.1	1.39575
$695$	−4050.82	−0.221088
$696$	−4910.01	−0.267404
$697$	−14641.3	−0.795667
$698$	−215.270	−0.0116735
$699$	748.131	0.0404820
$700$	−3270.40	−0.176585
$701$	10176.9	0.548326	0.274163	−	0.961683i	$-0.411599\pi$
$701$	10176.9	0.548326	0.274163	+	0.961683i	$0.411599\pi$
$702$	702.000	0.0377426
$703$	4957.47	0.265967
$704$	3782.50	0.202498
$705$	3909.46	0.208849
$706$	−6735.76	−0.359070
$707$	13350.9	0.710199
$708$	−2449.83	−0.130043
$709$	31494.4	1.66826	0.834132	−	0.551565i	$-0.185969\pi$
$709$	31494.4	1.66826	0.834132	+	0.551565i	$0.185969\pi$
$710$	6691.43	0.353697
$711$	−2420.62	−0.127680
$712$	−464.451	−0.0244467
$713$	2296.17	0.120606
$714$	1364.72	0.0715315
$715$	2200.15	0.115078
$716$	12258.3	0.639825
$717$	−12898.7	−0.671841
$718$	17766.9	0.923473
$719$	11064.9	0.573922	0.286961	−	0.957942i	$-0.407355\pi$
$719$	11064.9	0.573922	0.286961	+	0.957942i	$0.407355\pi$
$720$	−412.356	−0.0213439
$721$	5944.71	0.307063
$722$	5770.15	0.297428
$723$	−7184.23	−0.369550
$724$	−9270.96	−0.475901
$725$	−23895.3	−1.22407
$726$	−12972.0	−0.663134
$727$	−8659.09	−0.441744	−0.220872	−	0.975303i	$-0.570890\pi$
$727$	−8659.09	−0.441744	−0.220872	+	0.975303i	$0.570890\pi$
$728$	728.000	0.0370625
$729$	729.000	0.0370370
$730$	−4989.45	−0.252969
$731$	−243.173	−0.0123038
$732$	4276.49	0.215934
$733$	−26632.1	−1.34199	−0.670996	−	0.741461i	$-0.734133\pi$
$733$	−26632.1	−1.34199	−0.670996	+	0.741461i	$0.734133\pi$
$734$	−1537.22	−0.0773023
$735$	−420.947	−0.0211250
$736$	846.674	0.0424033
$737$	−2988.68	−0.149375
$738$	−8110.69	−0.404551
$739$	−14666.9	−0.730083	−0.365042	−	0.930991i	$-0.618945\pi$
$739$	−14666.9	−0.730083	−0.365042	+	0.930991i	$0.618945\pi$
$740$	−900.783	−0.0447479
$741$	−2458.52	−0.121884
$742$	−6953.02	−0.344007
$743$	9564.26	0.472246	0.236123	−	0.971723i	$-0.424123\pi$
$743$	9564.26	0.472246	0.236123	+	0.971723i	$0.424123\pi$
$744$	2082.81	0.102634
$745$	−5420.92	−0.266587
$746$	−15168.4	−0.744444
$747$	3568.98	0.174809
$748$	−7681.65	−0.375493
$749$	13450.3	0.656160
$750$	−4154.48	−0.202267
$751$	−40644.5	−1.97488	−0.987442	−	0.157981i	$-0.949501\pi$
$751$	−40644.5	−1.97488	−0.987442	+	0.157981i	$0.949501\pi$
$752$	−7281.25	−0.353085
$753$	18119.4	0.876902
$754$	5319.17	0.256914
$755$	7101.98	0.342341
$756$	756.000	0.0363696
$757$	12926.9	0.620657	0.310328	−	0.950629i	$-0.399561\pi$
$757$	12926.9	0.620657	0.310328	+	0.950629i	$0.399561\pi$
$758$	13373.3	0.640818
$759$	−4691.23	−0.224349
$760$	1444.14	0.0689270
$761$	−3944.97	−0.187917	−0.0939586	−	0.995576i	$-0.529952\pi$
$761$	−3944.97	−0.187917	−0.0939586	+	0.995576i	$0.529952\pi$
$762$	−2706.37	−0.128663
$763$	13010.7	0.617326
$764$	−3026.36	−0.143311
$765$	837.428	0.0395781
$766$	−1980.23	−0.0934055
$767$	2653.98	0.124941
$768$	768.000	0.0360844
$769$	−10642.5	−0.499063	−0.249532	−	0.968367i	$-0.580277\pi$
$769$	−10642.5	−0.499063	−0.249532	+	0.968367i	$0.580277\pi$
$770$	2369.39	0.110892
$771$	−18239.4	−0.851980
$772$	217.045	0.0101187
$773$	12182.3	0.566841	0.283420	−	0.958996i	$-0.408531\pi$
$773$	12182.3	0.566841	0.283420	+	0.958996i	$0.408531\pi$
$774$	−134.708	−0.00625576
$775$	10136.3	0.469816
$776$	3098.44	0.143335
$777$	1651.47	0.0762497
$778$	1224.20	0.0564136
$779$	28405.0	1.30644
$780$	446.719	0.0205065
$781$	69052.3	3.16375
$782$	−1719.46	−0.0786287
$783$	5523.76	0.252111
$784$	784.000	0.0357143
$785$	−8965.60	−0.407638
$786$	8183.53	0.371370
$787$	6325.80	0.286519	0.143260	−	0.989685i	$-0.454242\pi$
$787$	6325.80	0.286519	0.143260	+	0.989685i	$0.454242\pi$
$788$	−6871.00	−0.310621
$789$	7052.38	0.318215
$790$	−1540.37	−0.0693719
$791$	−410.932	−0.0184716
$792$	−4255.31	−0.190917
$793$	−4632.87	−0.207463
$794$	−17281.3	−0.772406
$795$	−4266.55	−0.190338
$796$	−10863.7	−0.483734
$797$	−25890.7	−1.15069	−0.575343	−	0.817912i	$-0.695131\pi$
$797$	−25890.7	−1.15069	−0.575343	+	0.817912i	$0.695131\pi$
$798$	−2647.64	−0.117450
$799$	14787.0	0.654728
$800$	3737.60	0.165180
$801$	522.508	0.0230486
$802$	−5450.91	−0.239998
$803$	−51488.7	−2.26276
$804$	−606.822	−0.0266181
$805$	530.364	0.0232210
$806$	−2256.38	−0.0986072
$807$	−2940.82	−0.128280
$808$	−15258.1	−0.664331
$809$	−13464.8	−0.585164	−0.292582	−	0.956240i	$-0.594514\pi$
$809$	−13464.8	−0.585164	−0.292582	+	0.956240i	$0.594514\pi$
$810$	463.900	0.0201232
$811$	−23175.9	−1.00347	−0.501735	−	0.865021i	$-0.667305\pi$
$811$	−23175.9	−1.00347	−0.501735	+	0.865021i	$0.667305\pi$
$812$	5728.34	0.247568
$813$	−21117.4	−0.910969
$814$	−9295.64	−0.400261
$815$	5059.32	0.217448
$816$	−1559.68	−0.0669116
$817$	471.769	0.0202021
$818$	10110.0	0.432138
$819$	−819.000	−0.0349428
$820$	−5161.25	−0.219803
$821$	7846.85	0.333565	0.166783	−	0.985994i	$-0.446662\pi$
$821$	7846.85	0.333565	0.166783	+	0.985994i	$0.446662\pi$
$822$	16611.3	0.704849
$823$	44364.2	1.87903	0.939514	−	0.342512i	$-0.111278\pi$
$823$	44364.2	1.87903	0.939514	+	0.342512i	$0.111278\pi$
$824$	−6793.96	−0.287231
$825$	−20709.2	−0.873940
$826$	2858.14	0.120396
$827$	−4465.76	−0.187775	−0.0938873	−	0.995583i	$-0.529929\pi$
$827$	−4465.76	−0.187775	−0.0938873	+	0.995583i	$0.529929\pi$
$828$	−952.508	−0.0399782
$829$	13452.2	0.563588	0.281794	−	0.959475i	$-0.409071\pi$
$829$	13452.2	0.563588	0.281794	+	0.959475i	$0.409071\pi$
$830$	2271.12	0.0949781
$831$	12977.8	0.541750
$832$	−832.000	−0.0346688
$833$	−1592.18	−0.0662253
$834$	−8487.59	−0.352400
$835$	−7918.13	−0.328165
$836$	14902.8	0.616537
$837$	−2343.16	−0.0967639
$838$	−8795.41	−0.362568
$839$	29035.3	1.19477	0.597385	−	0.801955i	$-0.296207\pi$
$839$	29035.3	1.19477	0.597385	+	0.801955i	$0.296207\pi$
$840$	481.082	0.0197606
$841$	17465.4	0.716119
$842$	3305.25	0.135281
$843$	−12435.4	−0.508063
$844$	−12486.8	−0.509256
$845$	−483.945	−0.0197020
$846$	8191.41	0.332892
$847$	15134.0	0.613943
$848$	7946.31	0.321789
$849$	−20901.9	−0.844936
$850$	−7590.45	−0.306295
$851$	−2080.73	−0.0838151
$852$	14020.4	0.563769
$853$	−38972.4	−1.56435	−0.782175	−	0.623059i	$-0.785890\pi$
$853$	−38972.4	−1.56435	−0.782175	+	0.623059i	$0.785890\pi$
$854$	−4989.24	−0.199916
$855$	−1624.66	−0.0649850
$856$	−15371.8	−0.613782
$857$	−12383.2	−0.493584	−0.246792	−	0.969068i	$-0.579376\pi$
$857$	−12383.2	−0.493584	−0.246792	+	0.969068i	$0.579376\pi$
$858$	4609.92	0.183427
$859$	2245.56	0.0891940	0.0445970	−	0.999005i	$-0.485800\pi$
$859$	2245.56	0.0891940	0.0445970	+	0.999005i	$0.485800\pi$
$860$	−85.7213	−0.00339892
$861$	9462.47	0.374541
$862$	−34882.9	−1.37832
$863$	27218.6	1.07362	0.536810	−	0.843703i	$-0.319629\pi$
$863$	27218.6	1.07362	0.536810	+	0.843703i	$0.319629\pi$
$864$	−864.000	−0.0340207
$865$	3436.10	0.135065
$866$	−5687.29	−0.223166
$867$	−11571.5	−0.453276
$868$	−2429.94	−0.0950203
$869$	−15895.8	−0.620517
$870$	3515.05	0.136979
$871$	657.391	0.0255739
$872$	−14869.4	−0.577455
$873$	−3485.75	−0.135137
$874$	3335.85	0.129104
$875$	4846.90	0.187263
$876$	−10454.3	−0.403216
$877$	2859.06	0.110084	0.0550419	−	0.998484i	$-0.482471\pi$
$877$	2859.06	0.110084	0.0550419	+	0.998484i	$0.482471\pi$
$878$	−1888.43	−0.0725870
$879$	764.102	0.0293203
$880$	−2707.88	−0.103730
$881$	−7926.56	−0.303124	−0.151562	−	0.988448i	$-0.548430\pi$
$881$	−7926.56	−0.303124	−0.151562	+	0.988448i	$0.548430\pi$
$882$	−882.000	−0.0336718
$883$	47708.7	1.81826	0.909130	−	0.416512i	$-0.136748\pi$
$883$	47708.7	1.81826	0.909130	+	0.416512i	$0.136748\pi$
$884$	1689.66	0.0642866
$885$	1753.82	0.0666148
$886$	−8538.11	−0.323751
$887$	−9008.31	−0.341003	−0.170501	−	0.985357i	$-0.554539\pi$
$887$	−9008.31	−0.341003	−0.170501	+	0.985357i	$0.554539\pi$
$888$	−1887.39	−0.0713251
$889$	3157.43	0.119119
$890$	332.499	0.0125229
$891$	4787.23	0.179998
$892$	619.101	0.0232388
$893$	−28687.7	−1.07503
$894$	−11358.3	−0.424921
$895$	−8775.67	−0.327752
$896$	−896.000	−0.0334077
$897$	1031.88	0.0384098
$898$	32331.2	1.20145
$899$	−17754.5	−0.658672
$900$	−4204.80	−0.155733
$901$	−16137.7	−0.596697
$902$	−53261.6	−1.96609
$903$	157.159	0.00579171
$904$	469.636	0.0172786
$905$	6637.04	0.243782
$906$	14880.6	0.545668
$907$	−2196.17	−0.0803998	−0.0401999	−	0.999192i	$-0.512799\pi$
$907$	−2196.17	−0.0803998	−0.0401999	+	0.999192i	$0.512799\pi$
$908$	−15304.1	−0.559346
$909$	17165.4	0.626337
$910$	−521.172	−0.0189854
$911$	53137.6	1.93252	0.966262	−	0.257562i	$-0.0829192\pi$
$911$	53137.6	1.93252	0.966262	+	0.257562i	$0.0829192\pi$
$912$	3025.88	0.109865
$913$	23436.9	0.849560
$914$	−16277.0	−0.589053
$915$	−3061.52	−0.110613
$916$	−24257.0	−0.874970
$917$	−9547.45	−0.343822
$918$	1754.64	0.0630848
$919$	−33583.2	−1.20545	−0.602725	−	0.797949i	$-0.705918\pi$
$919$	−33583.2	−1.20545	−0.602725	+	0.797949i	$0.705918\pi$
$920$	−606.130	−0.0217212
$921$	19308.2	0.690802
$922$	29587.3	1.05684
$923$	−15188.8	−0.541652
$924$	4964.53	0.176754
$925$	−9185.29	−0.326498
$926$	4996.88	0.177330
$927$	7643.20	0.270804
$928$	−6546.67	−0.231579
$929$	18564.4	0.655627	0.327814	−	0.944742i	$-0.393688\pi$
$929$	18564.4	0.655627	0.327814	+	0.944742i	$0.393688\pi$
$930$	−1491.07	−0.0525744
$931$	3088.91	0.108738
$932$	997.507	0.0350584
$933$	24898.1	0.873661
$934$	22004.3	0.770882
$935$	5499.26	0.192348
$936$	936.000	0.0326860
$937$	14666.3	0.511341	0.255671	−	0.966764i	$-0.417704\pi$
$937$	14666.3	0.511341	0.255671	+	0.966764i	$0.417704\pi$
$938$	707.959	0.0246436
$939$	−3024.16	−0.105101
$940$	5212.62	0.180869
$941$	−28244.6	−0.978478	−0.489239	−	0.872150i	$-0.662726\pi$
$941$	−28244.6	−0.978478	−0.489239	+	0.872150i	$0.662726\pi$
$942$	−18785.4	−0.649748
$943$	−11922.1	−0.411703
$944$	−3266.44	−0.112620
$945$	−541.217	−0.0186305
$946$	−884.603	−0.0304027
$947$	−38462.1	−1.31980	−0.659899	−	0.751354i	$-0.729401\pi$
$947$	−38462.1	−1.31980	−0.659899	+	0.751354i	$0.729401\pi$
$948$	−3227.50	−0.110574
$949$	11325.5	0.387397
$950$	14725.9	0.502918
$951$	−156.629	−0.00534075
$952$	1819.63	0.0619481
$953$	16450.0	0.559146	0.279573	−	0.960124i	$-0.409807\pi$
$953$	16450.0	0.559146	0.279573	+	0.960124i	$0.409807\pi$
$954$	−8939.60	−0.303386
$955$	2166.56	0.0734117
$956$	−17198.2	−0.581832
$957$	36273.6	1.22525
$958$	16544.6	0.557966
$959$	−19379.9	−0.652563
$960$	−549.808	−0.0184843
$961$	−22259.6	−0.747192
$962$	2044.67	0.0685269
$963$	17293.3	0.578679
$964$	−9578.97	−0.320039
$965$	−155.381	−0.00518332
$966$	1111.26	0.0370126
$967$	−6346.84	−0.211066	−0.105533	−	0.994416i	$-0.533655\pi$
$967$	−6346.84	−0.211066	−0.105533	+	0.994416i	$0.533655\pi$
$968$	−17296.0	−0.574291
$969$	−6145.06	−0.203723
$970$	−2218.16	−0.0734236
$971$	22198.7	0.733665	0.366833	−	0.930287i	$-0.380442\pi$
$971$	22198.7	0.733665	0.366833	+	0.930287i	$0.380442\pi$
$972$	972.000	0.0320750
$973$	9902.19	0.326259
$974$	−33131.7	−1.08995
$975$	4555.20	0.149624
$976$	5701.99	0.187004
$977$	−19311.9	−0.632388	−0.316194	−	0.948695i	$-0.602405\pi$
$977$	−19311.9	−0.632388	−0.316194	+	0.948695i	$0.602405\pi$
$978$	10600.7	0.346598
$979$	3431.23	0.112015
$980$	−561.262	−0.0182948
$981$	16728.1	0.544430
$982$	14650.5	0.476086
$983$	58447.9	1.89644	0.948220	−	0.317615i	$-0.102882\pi$
$983$	58447.9	1.89644	0.948220	+	0.317615i	$0.102882\pi$
$984$	−10814.3	−0.350351
$985$	4918.92	0.159117
$986$	13295.2	0.429418
$987$	−9556.64	−0.308198
$988$	−3278.03	−0.105555
$989$	−198.009	−0.00636636
$990$	3046.36	0.0977977
$991$	−30133.5	−0.965914	−0.482957	−	0.875644i	$-0.660437\pi$
$991$	−30133.5	−0.965914	−0.482957	+	0.875644i	$0.660437\pi$
$992$	2777.08	0.0888834
$993$	2925.52	0.0934932
$994$	−16357.1	−0.521949
$995$	7777.25	0.247794
$996$	4758.63	0.151389
$997$	12814.7	0.407065	0.203533	−	0.979068i	$-0.434758\pi$
$997$	12814.7	0.407065	0.203533	+	0.979068i	$0.434758\pi$
$998$	−18903.8	−0.599589
$999$	2123.31	0.0672459

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.a.n.1.2	✓	3
3.2	odd	2		1638.4.a.ba.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.a.n.1.2	✓	3	1.1	even	1	trivial
1638.4.a.ba.1.2		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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -2.86358 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +5.72716 q^{10} +59.1016 q^{11} +12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} -8.59075 q^{15} +16.0000 q^{16} -32.4934 q^{17} -18.0000 q^{18} +63.0391 q^{19} -11.4543 q^{20} +21.0000 q^{21} -118.203 q^{22} -26.4586 q^{23} -24.0000 q^{24} -116.800 q^{25} +26.0000 q^{26} +27.0000 q^{27} +28.0000 q^{28} +204.584 q^{29} +17.1815 q^{30} -86.7837 q^{31} -32.0000 q^{32} +177.305 q^{33} +64.9868 q^{34} -20.0451 q^{35} +36.0000 q^{36} +78.6412 q^{37} -126.078 q^{38} -39.0000 q^{39} +22.9087 q^{40} +450.594 q^{41} -42.0000 q^{42} +7.48375 q^{43} +236.406 q^{44} -25.7722 q^{45} +52.9171 q^{46} -455.078 q^{47} +48.0000 q^{48} +49.0000 q^{49} +233.600 q^{50} -97.4802 q^{51} -52.0000 q^{52} +496.644 q^{53} -54.0000 q^{54} -169.242 q^{55} -56.0000 q^{56} +189.117 q^{57} -409.167 q^{58} -204.153 q^{59} -34.3630 q^{60} +356.375 q^{61} +173.567 q^{62} +63.0000 q^{63} +64.0000 q^{64} +37.2266 q^{65} -354.609 q^{66} -50.5685 q^{67} -129.974 q^{68} -79.3757 q^{69} +40.0902 q^{70} +1168.37 q^{71} -72.0000 q^{72} -871.189 q^{73} -157.282 q^{74} -350.400 q^{75} +252.156 q^{76} +413.711 q^{77} +78.0000 q^{78} -268.958 q^{79} -45.8173 q^{80} +81.0000 q^{81} -901.188 q^{82} +396.553 q^{83} +84.0000 q^{84} +93.0475 q^{85} -14.9675 q^{86} +613.751 q^{87} -472.813 q^{88} +58.0564 q^{89} +51.5445 q^{90} -91.0000 q^{91} -105.834 q^{92} -260.351 q^{93} +910.156 q^{94} -180.518 q^{95} -96.0000 q^{96} -387.306 q^{97} -98.0000 q^{98} +531.914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} + 13 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} - 26 q^{10} + 17 q^{11} + 36 q^{12} - 39 q^{13} - 42 q^{14} + 39 q^{15} + 48 q^{16} + 89 q^{17} - 54 q^{18} + 89 q^{19}+ \cdots + 153 q^{99}+O(q^{100}) \) 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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