LMFDB - Embedded newform 966.4.a.n.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$56.9958450655$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 267x^{3} + 1502x^{2} + 1857x + 198 $ x^5 - 2x^4 - 267x^3 + 1502x^2 + 1857x + 198
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-17.6344$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +14.7496 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +14.7496 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -29.4991 q^{10} +42.3277 q^{11} +12.0000 q^{12} +10.0659 q^{13} +14.0000 q^{14} +44.2487 q^{15} +16.0000 q^{16} +130.707 q^{17} -18.0000 q^{18} -139.943 q^{19} +58.9983 q^{20} -21.0000 q^{21} -84.6554 q^{22} +23.0000 q^{23} -24.0000 q^{24} +92.5498 q^{25} -20.1318 q^{26} +27.0000 q^{27} -28.0000 q^{28} +2.32129 q^{29} -88.4974 q^{30} +185.559 q^{31} -32.0000 q^{32} +126.983 q^{33} -261.414 q^{34} -103.247 q^{35} +36.0000 q^{36} -308.021 q^{37} +279.887 q^{38} +30.1978 q^{39} -117.997 q^{40} +472.360 q^{41} +42.0000 q^{42} +251.681 q^{43} +169.311 q^{44} +132.746 q^{45} -46.0000 q^{46} -526.215 q^{47} +48.0000 q^{48} +49.0000 q^{49} -185.100 q^{50} +392.121 q^{51} +40.2637 q^{52} +525.179 q^{53} -54.0000 q^{54} +624.315 q^{55} +56.0000 q^{56} -419.830 q^{57} -4.64258 q^{58} -384.942 q^{59} +176.995 q^{60} +720.848 q^{61} -371.119 q^{62} -63.0000 q^{63} +64.0000 q^{64} +148.468 q^{65} -253.966 q^{66} -110.487 q^{67} +522.829 q^{68} +69.0000 q^{69} +206.494 q^{70} +547.595 q^{71} -72.0000 q^{72} -516.277 q^{73} +616.042 q^{74} +277.649 q^{75} -559.774 q^{76} -296.294 q^{77} -60.3955 q^{78} -636.314 q^{79} +235.993 q^{80} +81.0000 q^{81} -944.721 q^{82} -372.514 q^{83} -84.0000 q^{84} +1927.87 q^{85} -503.362 q^{86} +6.96388 q^{87} -338.622 q^{88} -638.709 q^{89} -265.492 q^{90} -70.4614 q^{91} +92.0000 q^{92} +556.678 q^{93} +1052.43 q^{94} -2064.10 q^{95} -96.0000 q^{96} -481.847 q^{97} -98.0000 q^{98} +380.949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} - 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 - 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} - 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} + 18 q^{11} + 60 q^{12} - 22 q^{13} + 70 q^{14} + 80 q^{16} + 44 q^{17} - 90 q^{18} - 14 q^{19} - 105 q^{21} - 36 q^{22} + 115 q^{23} - 120 q^{24} + 43 q^{25} + 44 q^{26} + 135 q^{27} - 140 q^{28} - 39 q^{29} - 100 q^{31} - 160 q^{32} + 54 q^{33} - 88 q^{34} + 180 q^{36} + 255 q^{37} + 28 q^{38} - 66 q^{39} + 69 q^{41} + 210 q^{42} + 912 q^{43} + 72 q^{44} - 230 q^{46} - 319 q^{47} + 240 q^{48} + 245 q^{49} - 86 q^{50} + 132 q^{51} - 88 q^{52} + 745 q^{53} - 270 q^{54} + 2199 q^{55} + 280 q^{56} - 42 q^{57} + 78 q^{58} - 315 q^{59} + 1091 q^{61} + 200 q^{62} - 315 q^{63} + 320 q^{64} + 533 q^{65} - 108 q^{66} + 991 q^{67} + 176 q^{68} + 345 q^{69} + 923 q^{71} - 360 q^{72} + 1144 q^{73} - 510 q^{74} + 129 q^{75} - 56 q^{76} - 126 q^{77} + 132 q^{78} - 110 q^{79} + 405 q^{81} - 138 q^{82} + 218 q^{83} - 420 q^{84} + 2973 q^{85} - 1824 q^{86} - 117 q^{87} - 144 q^{88} - 13 q^{89} + 154 q^{91} + 460 q^{92} - 300 q^{93} + 638 q^{94} - 347 q^{95} - 480 q^{96} + 761 q^{97} - 490 q^{98} + 162 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 - 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 + 18 * q^11 + 60 * q^12 - 22 * q^13 + 70 * q^14 + 80 * q^16 + 44 * q^17 - 90 * q^18 - 14 * q^19 - 105 * q^21 - 36 * q^22 + 115 * q^23 - 120 * q^24 + 43 * q^25 + 44 * q^26 + 135 * q^27 - 140 * q^28 - 39 * q^29 - 100 * q^31 - 160 * q^32 + 54 * q^33 - 88 * q^34 + 180 * q^36 + 255 * q^37 + 28 * q^38 - 66 * q^39 + 69 * q^41 + 210 * q^42 + 912 * q^43 + 72 * q^44 - 230 * q^46 - 319 * q^47 + 240 * q^48 + 245 * q^49 - 86 * q^50 + 132 * q^51 - 88 * q^52 + 745 * q^53 - 270 * q^54 + 2199 * q^55 + 280 * q^56 - 42 * q^57 + 78 * q^58 - 315 * q^59 + 1091 * q^61 + 200 * q^62 - 315 * q^63 + 320 * q^64 + 533 * q^65 - 108 * q^66 + 991 * q^67 + 176 * q^68 + 345 * q^69 + 923 * q^71 - 360 * q^72 + 1144 * q^73 - 510 * q^74 + 129 * q^75 - 56 * q^76 - 126 * q^77 + 132 * q^78 - 110 * q^79 + 405 * q^81 - 138 * q^82 + 218 * q^83 - 420 * q^84 + 2973 * q^85 - 1824 * q^86 - 117 * q^87 - 144 * q^88 - 13 * q^89 + 154 * q^91 + 460 * q^92 - 300 * q^93 + 638 * q^94 - 347 * q^95 - 480 * q^96 + 761 * q^97 - 490 * q^98 + 162 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	14.7496	1.31924	0.659621	−	0.751599i	$-0.270717\pi$
$5$	14.7496	1.31924	0.659621	+	0.751599i	$0.270717\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−29.4991	−0.932845
$11$	42.3277	1.16021	0.580104	−	0.814543i	$-0.303012\pi$
$11$	42.3277	1.16021	0.580104	+	0.814543i	$0.303012\pi$
$12$	12.0000	0.288675
$13$	10.0659	0.214753	0.107376	−	0.994218i	$-0.465755\pi$
$13$	10.0659	0.214753	0.107376	+	0.994218i	$0.465755\pi$
$14$	14.0000	0.267261
$15$	44.2487	0.761664
$16$	16.0000	0.250000
$17$	130.707	1.86477	0.932386	−	0.361463i	$-0.117723\pi$
$17$	130.707	1.86477	0.932386	+	0.361463i	$0.117723\pi$
$18$	−18.0000	−0.235702
$19$	−139.943	−1.68975	−0.844874	−	0.534965i	$-0.820325\pi$
$19$	−139.943	−1.68975	−0.844874	+	0.534965i	$0.820325\pi$
$20$	58.9983	0.659621
$21$	−21.0000	−0.218218
$22$	−84.6554	−0.820390
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−24.0000	−0.204124
$25$	92.5498	0.740398
$26$	−20.1318	−0.151853
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	2.32129	0.0148639	0.00743195	−	0.999972i	$-0.497634\pi$
$29$	2.32129	0.0148639	0.00743195	+	0.999972i	$0.497634\pi$
$30$	−88.4974	−0.538578
$31$	185.559	1.07508	0.537540	−	0.843238i	$-0.319354\pi$
$31$	185.559	1.07508	0.537540	+	0.843238i	$0.319354\pi$
$32$	−32.0000	−0.176777
$33$	126.983	0.669846
$34$	−261.414	−1.31859
$35$	−103.247	−0.498626
$36$	36.0000	0.166667
$37$	−308.021	−1.36860	−0.684302	−	0.729199i	$-0.739893\pi$
$37$	−308.021	−1.36860	−0.684302	+	0.729199i	$0.739893\pi$
$38$	279.887	1.19483
$39$	30.1978	0.123987
$40$	−117.997	−0.466422
$41$	472.360	1.79928	0.899638	−	0.436637i	$-0.143830\pi$
$41$	472.360	1.79928	0.899638	+	0.436637i	$0.143830\pi$
$42$	42.0000	0.154303
$43$	251.681	0.892581	0.446290	−	0.894888i	$-0.352745\pi$
$43$	251.681	0.892581	0.446290	+	0.894888i	$0.352745\pi$
$44$	169.311	0.580104
$45$	132.746	0.439747
$46$	−46.0000	−0.147442
$47$	−526.215	−1.63311	−0.816557	−	0.577265i	$-0.804120\pi$
$47$	−526.215	−1.63311	−0.816557	+	0.577265i	$0.804120\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−185.100	−0.523541
$51$	392.121	1.07663
$52$	40.2637	0.107376
$53$	525.179	1.36111	0.680556	−	0.732697i	$-0.261739\pi$
$53$	525.179	1.36111	0.680556	+	0.732697i	$0.261739\pi$
$54$	−54.0000	−0.136083
$55$	624.315	1.53059
$56$	56.0000	0.133631
$57$	−419.830	−0.975577
$58$	−4.64258	−0.0105104
$59$	−384.942	−0.849410	−0.424705	−	0.905332i	$-0.639622\pi$
$59$	−384.942	−0.849410	−0.424705	+	0.905332i	$0.639622\pi$
$60$	176.995	0.380832
$61$	720.848	1.51303	0.756517	−	0.653974i	$-0.226899\pi$
$61$	720.848	1.51303	0.756517	+	0.653974i	$0.226899\pi$
$62$	−371.119	−0.760196
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	148.468	0.283311
$66$	−253.966	−0.473653
$67$	−110.487	−0.201465	−0.100732	−	0.994914i	$-0.532119\pi$
$67$	−110.487	−0.201465	−0.100732	+	0.994914i	$0.532119\pi$
$68$	522.829	0.932386
$69$	69.0000	0.120386
$70$	206.494	0.352582
$71$	547.595	0.915318	0.457659	−	0.889128i	$-0.348688\pi$
$71$	547.595	0.915318	0.457659	+	0.889128i	$0.348688\pi$
$72$	−72.0000	−0.117851
$73$	−516.277	−0.827748	−0.413874	−	0.910334i	$-0.635825\pi$
$73$	−516.277	−0.827748	−0.413874	+	0.910334i	$0.635825\pi$
$74$	616.042	0.967749
$75$	277.649	0.427469
$76$	−559.774	−0.844874
$77$	−296.294	−0.438517
$78$	−60.3955	−0.0876724
$79$	−636.314	−0.906214	−0.453107	−	0.891456i	$-0.649684\pi$
$79$	−636.314	−0.906214	−0.453107	+	0.891456i	$0.649684\pi$
$80$	235.993	0.329810
$81$	81.0000	0.111111
$82$	−944.721	−1.27228
$83$	−372.514	−0.492635	−0.246318	−	0.969189i	$-0.579221\pi$
$83$	−372.514	−0.492635	−0.246318	+	0.969189i	$0.579221\pi$
$84$	−84.0000	−0.109109
$85$	1927.87	2.46009
$86$	−503.362	−0.631150
$87$	6.96388	0.00858168
$88$	−338.622	−0.410195
$89$	−638.709	−0.760708	−0.380354	−	0.924841i	$-0.624198\pi$
$89$	−638.709	−0.760708	−0.380354	+	0.924841i	$0.624198\pi$
$90$	−265.492	−0.310948
$91$	−70.4614	−0.0811689
$92$	92.0000	0.104257
$93$	556.678	0.620697
$94$	1052.43	1.15479
$95$	−2064.10	−2.22919
$96$	−96.0000	−0.102062
$97$	−481.847	−0.504373	−0.252186	−	0.967679i	$-0.581150\pi$
$97$	−481.847	−0.504373	−0.252186	+	0.967679i	$0.581150\pi$
$98$	−98.0000	−0.101015
$99$	380.949	0.386736
$100$	370.199	0.370199
$101$	−935.517	−0.921658	−0.460829	−	0.887489i	$-0.652448\pi$
$101$	−935.517	−0.921658	−0.460829	+	0.887489i	$0.652448\pi$
$102$	−784.243	−0.761290
$103$	1100.45	1.05272	0.526362	−	0.850261i	$-0.323556\pi$
$103$	1100.45	1.05272	0.526362	+	0.850261i	$0.323556\pi$
$104$	−80.5274	−0.0759265
$105$	−309.741	−0.287882
$106$	−1050.36	−0.962451
$107$	−912.358	−0.824308	−0.412154	−	0.911114i	$-0.635224\pi$
$107$	−912.358	−0.824308	−0.412154	+	0.911114i	$0.635224\pi$
$108$	108.000	0.0962250
$109$	−1372.38	−1.20596	−0.602982	−	0.797755i	$-0.706021\pi$
$109$	−1372.38	−1.20596	−0.602982	+	0.797755i	$0.706021\pi$
$110$	−1248.63	−1.08229
$111$	−924.063	−0.790164
$112$	−112.000	−0.0944911
$113$	1968.51	1.63877	0.819387	−	0.573240i	$-0.194314\pi$
$113$	1968.51	1.63877	0.819387	+	0.573240i	$0.194314\pi$
$114$	839.660	0.689837
$115$	339.240	0.275081
$116$	9.28517	0.00743195
$117$	90.5933	0.0715842
$118$	769.885	0.600624
$119$	−914.950	−0.704818
$120$	−353.990	−0.269289
$121$	460.634	0.346081
$122$	−1441.70	−1.06988
$123$	1417.08	1.03881
$124$	742.238	0.537540
$125$	−478.627	−0.342477
$126$	126.000	0.0890871
$127$	1613.25	1.12719	0.563594	−	0.826052i	$-0.309418\pi$
$127$	1613.25	1.12719	0.563594	+	0.826052i	$0.309418\pi$
$128$	−128.000	−0.0883883
$129$	755.042	0.515332
$130$	−296.936	−0.200331
$131$	2026.95	1.35188	0.675938	−	0.736959i	$-0.263739\pi$
$131$	2026.95	1.35188	0.675938	+	0.736959i	$0.263739\pi$
$132$	507.932	0.334923
$133$	979.604	0.638665
$134$	220.974	0.142457
$135$	398.238	0.253888
$136$	−1045.66	−0.659297
$137$	1230.43	0.767319	0.383659	−	0.923475i	$-0.374664\pi$
$137$	1230.43	0.767319	0.383659	+	0.923475i	$0.374664\pi$
$138$	−138.000	−0.0851257
$139$	658.467	0.401802	0.200901	−	0.979612i	$-0.435613\pi$
$139$	658.467	0.401802	0.200901	+	0.979612i	$0.435613\pi$
$140$	−412.988	−0.249313
$141$	−1578.65	−0.942879
$142$	−1095.19	−0.647228
$143$	426.067	0.249158
$144$	144.000	0.0833333
$145$	34.2381	0.0196091
$146$	1032.55	0.585307
$147$	147.000	0.0824786
$148$	−1232.08	−0.684302
$149$	2365.26	1.30047	0.650235	−	0.759733i	$-0.274671\pi$
$149$	2365.26	1.30047	0.650235	+	0.759733i	$0.274671\pi$
$150$	−555.299	−0.302266
$151$	426.016	0.229594	0.114797	−	0.993389i	$-0.463378\pi$
$151$	426.016	0.229594	0.114797	+	0.993389i	$0.463378\pi$
$152$	1119.55	0.597416
$153$	1176.36	0.621591
$154$	592.588	0.310078
$155$	2736.92	1.41829
$156$	120.791	0.0619937
$157$	1995.75	1.01451	0.507257	−	0.861795i	$-0.330660\pi$
$157$	1995.75	1.01451	0.507257	+	0.861795i	$0.330660\pi$
$158$	1272.63	0.640790
$159$	1575.54	0.785838
$160$	−471.986	−0.233211
$161$	−161.000	−0.0788110
$162$	−162.000	−0.0785674
$163$	−4023.83	−1.93356	−0.966781	−	0.255605i	$-0.917725\pi$
$163$	−4023.83	−1.93356	−0.966781	+	0.255605i	$0.917725\pi$
$164$	1889.44	0.899638
$165$	1872.95	0.883689
$166$	745.028	0.348346
$167$	−1110.52	−0.514580	−0.257290	−	0.966334i	$-0.582830\pi$
$167$	−1110.52	−0.514580	−0.257290	+	0.966334i	$0.582830\pi$
$168$	168.000	0.0771517
$169$	−2095.68	−0.953881
$170$	−3855.75	−1.73954
$171$	−1259.49	−0.563249
$172$	1006.72	0.446290
$173$	391.220	0.171930	0.0859650	−	0.996298i	$-0.472603\pi$
$173$	391.220	0.171930	0.0859650	+	0.996298i	$0.472603\pi$
$174$	−13.9278	−0.00606816
$175$	−647.848	−0.279844
$176$	677.243	0.290052
$177$	−1154.83	−0.490407
$178$	1277.42	0.537902
$179$	247.848	0.103492	0.0517458	−	0.998660i	$-0.483521\pi$
$179$	247.848	0.103492	0.0517458	+	0.998660i	$0.483521\pi$
$180$	530.984	0.219874
$181$	4777.15	1.96178	0.980891	−	0.194556i	$-0.0623266\pi$
$181$	4777.15	1.96178	0.980891	+	0.194556i	$0.0623266\pi$
$182$	140.923	0.0573950
$183$	2162.54	0.873551
$184$	−184.000	−0.0737210
$185$	−4543.18	−1.80552
$186$	−1113.36	−0.438899
$187$	5532.53	2.16352
$188$	−2104.86	−0.816557
$189$	−189.000	−0.0727393
$190$	4128.21	1.57627
$191$	−4316.61	−1.63528	−0.817641	−	0.575728i	$-0.804719\pi$
$191$	−4316.61	−1.63528	−0.817641	+	0.575728i	$0.804719\pi$
$192$	192.000	0.0721688
$193$	1079.24	0.402513	0.201257	−	0.979539i	$-0.435497\pi$
$193$	1079.24	0.402513	0.201257	+	0.979539i	$0.435497\pi$
$194$	963.694	0.356645
$195$	445.404	0.163569
$196$	196.000	0.0714286
$197$	2858.01	1.03363	0.516814	−	0.856098i	$-0.327118\pi$
$197$	2858.01	1.03363	0.516814	+	0.856098i	$0.327118\pi$
$198$	−761.898	−0.273463
$199$	−1262.83	−0.449848	−0.224924	−	0.974376i	$-0.572213\pi$
$199$	−1262.83	−0.449848	−0.224924	+	0.974376i	$0.572213\pi$
$200$	−740.398	−0.261770
$201$	−331.461	−0.116316
$202$	1871.03	0.651710
$203$	−16.2490	−0.00561803
$204$	1568.49	0.538314
$205$	6967.11	2.37368
$206$	−2200.90	−0.744388
$207$	207.000	0.0695048
$208$	161.055	0.0536881
$209$	−5923.48	−1.96046
$210$	619.482	0.203563
$211$	4634.84	1.51221	0.756103	−	0.654452i	$-0.227101\pi$
$211$	4634.84	1.51221	0.756103	+	0.654452i	$0.227101\pi$
$212$	2100.72	0.680556
$213$	1642.79	0.528459
$214$	1824.72	0.582874
$215$	3712.18	1.17753
$216$	−216.000	−0.0680414
$217$	−1298.92	−0.406342
$218$	2744.76	0.852745
$219$	−1548.83	−0.477901
$220$	2497.26	0.765297
$221$	1315.69	0.400465
$222$	1848.13	0.558730
$223$	6210.03	1.86482	0.932408	−	0.361406i	$-0.117703\pi$
$223$	6210.03	1.86482	0.932408	+	0.361406i	$0.117703\pi$
$224$	224.000	0.0668153
$225$	832.948	0.246799
$226$	−3937.01	−1.15879
$227$	3524.50	1.03052	0.515262	−	0.857033i	$-0.327694\pi$
$227$	3524.50	1.03052	0.515262	+	0.857033i	$0.327694\pi$
$228$	−1679.32	−0.487788
$229$	3779.20	1.09055	0.545276	−	0.838257i	$-0.316425\pi$
$229$	3779.20	1.09055	0.545276	+	0.838257i	$0.316425\pi$
$230$	−678.480	−0.194512
$231$	−888.882	−0.253178
$232$	−18.5703	−0.00525518
$233$	−3731.19	−1.04909	−0.524546	−	0.851382i	$-0.675765\pi$
$233$	−3731.19	−1.04909	−0.524546	+	0.851382i	$0.675765\pi$
$234$	−181.187	−0.0506177
$235$	−7761.45	−2.15447
$236$	−1539.77	−0.424705
$237$	−1908.94	−0.523203
$238$	1829.90	0.498381
$239$	−2058.01	−0.556993	−0.278496	−	0.960437i	$-0.589836\pi$
$239$	−2058.01	−0.556993	−0.278496	+	0.960437i	$0.589836\pi$
$240$	707.979	0.190416
$241$	−1871.63	−0.500259	−0.250130	−	0.968212i	$-0.580473\pi$
$241$	−1871.63	−0.500259	−0.250130	+	0.968212i	$0.580473\pi$
$242$	−921.267	−0.244716
$243$	243.000	0.0641500
$244$	2883.39	0.756517
$245$	722.729	0.188463
$246$	−2834.16	−0.734551
$247$	−1408.66	−0.362878
$248$	−1484.48	−0.380098
$249$	−1117.54	−0.284423
$250$	957.254	0.242168
$251$	2134.03	0.536648	0.268324	−	0.963329i	$-0.413530\pi$
$251$	2134.03	0.536648	0.268324	+	0.963329i	$0.413530\pi$
$252$	−252.000	−0.0629941
$253$	973.537	0.241920
$254$	−3226.50	−0.797042
$255$	5783.62	1.42033
$256$	256.000	0.0625000
$257$	−1163.45	−0.282390	−0.141195	−	0.989982i	$-0.545094\pi$
$257$	−1163.45	−0.282390	−0.141195	+	0.989982i	$0.545094\pi$
$258$	−1510.08	−0.364394
$259$	2156.15	0.517284
$260$	593.872	0.141655
$261$	20.8916	0.00495463
$262$	−4053.90	−0.955920
$263$	−1293.93	−0.303373	−0.151686	−	0.988429i	$-0.548470\pi$
$263$	−1293.93	−0.303373	−0.151686	+	0.988429i	$0.548470\pi$
$264$	−1015.86	−0.236826
$265$	7746.16	1.79563
$266$	−1959.21	−0.451604
$267$	−1916.13	−0.439195
$268$	−441.948	−0.100732
$269$	4078.04	0.924321	0.462161	−	0.886796i	$-0.347074\pi$
$269$	4078.04	0.924321	0.462161	+	0.886796i	$0.347074\pi$
$270$	−796.477	−0.179526
$271$	−6404.96	−1.43570	−0.717848	−	0.696200i	$-0.754873\pi$
$271$	−6404.96	−1.43570	−0.717848	+	0.696200i	$0.754873\pi$
$272$	2091.31	0.466193
$273$	−211.384	−0.0468629
$274$	−2460.86	−0.542576
$275$	3917.42	0.859015
$276$	276.000	0.0601929
$277$	7500.20	1.62687	0.813435	−	0.581655i	$-0.197595\pi$
$277$	7500.20	1.62687	0.813435	+	0.581655i	$0.197595\pi$
$278$	−1316.93	−0.284117
$279$	1670.03	0.358360
$280$	825.976	0.176291
$281$	−6836.93	−1.45145	−0.725724	−	0.687986i	$-0.758495\pi$
$281$	−6836.93	−1.45145	−0.725724	+	0.687986i	$0.758495\pi$
$282$	3157.29	0.666716
$283$	413.086	0.0867683	0.0433841	−	0.999058i	$-0.486186\pi$
$283$	413.086	0.0867683	0.0433841	+	0.999058i	$0.486186\pi$
$284$	2190.38	0.457659
$285$	−6192.31	−1.28702
$286$	−852.134	−0.176181
$287$	−3306.52	−0.680062
$288$	−288.000	−0.0589256
$289$	12171.4	2.47738
$290$	−68.4761	−0.0138657
$291$	−1445.54	−0.291200
$292$	−2065.11	−0.413874
$293$	−7266.73	−1.44890	−0.724449	−	0.689328i	$-0.757906\pi$
$293$	−7266.73	−1.44890	−0.724449	+	0.689328i	$0.757906\pi$
$294$	−294.000	−0.0583212
$295$	−5677.73	−1.12058
$296$	2464.17	0.483875
$297$	1142.85	0.223282
$298$	−4730.53	−0.919571
$299$	231.516	0.0447790
$300$	1110.60	0.213735
$301$	−1761.77	−0.337364
$302$	−852.032	−0.162347
$303$	−2806.55	−0.532119
$304$	−2239.09	−0.422437
$305$	10632.2	1.99606
$306$	−2352.73	−0.439531
$307$	818.170	0.152102	0.0760512	−	0.997104i	$-0.475769\pi$
$307$	818.170	0.152102	0.0760512	+	0.997104i	$0.475769\pi$
$308$	−1185.18	−0.219259
$309$	3301.35	0.607790
$310$	−5473.84	−1.00288
$311$	5832.78	1.06349	0.531747	−	0.846903i	$-0.321536\pi$
$311$	5832.78	1.06349	0.531747	+	0.846903i	$0.321536\pi$
$312$	−241.582	−0.0438362
$313$	−3736.04	−0.674676	−0.337338	−	0.941384i	$-0.609526\pi$
$313$	−3736.04	−0.674676	−0.337338	+	0.941384i	$0.609526\pi$
$314$	−3991.51	−0.717369
$315$	−929.223	−0.166209
$316$	−2545.26	−0.453107
$317$	−9381.15	−1.66214	−0.831069	−	0.556169i	$-0.812271\pi$
$317$	−9381.15	−1.66214	−0.831069	+	0.556169i	$0.812271\pi$
$318$	−3151.07	−0.555671
$319$	98.2549	0.0172452
$320$	943.972	0.164905
$321$	−2737.07	−0.475915
$322$	322.000	0.0557278
$323$	−18291.6	−3.15100
$324$	324.000	0.0555556
$325$	931.599	0.159002
$326$	8047.66	1.36724
$327$	−4117.14	−0.696264
$328$	−3778.88	−0.636140
$329$	3683.51	0.617259
$330$	−3745.89	−0.624862
$331$	−9579.97	−1.59082	−0.795412	−	0.606069i	$-0.792746\pi$
$331$	−9579.97	−1.59082	−0.795412	+	0.606069i	$0.792746\pi$
$332$	−1490.06	−0.246318
$333$	−2772.19	−0.456201
$334$	2221.05	0.363863
$335$	−1629.64	−0.265781
$336$	−336.000	−0.0545545
$337$	1213.74	0.196192	0.0980961	−	0.995177i	$-0.468725\pi$
$337$	1213.74	0.196192	0.0980961	+	0.995177i	$0.468725\pi$
$338$	4191.35	0.674496
$339$	5905.52	0.946147
$340$	7711.50	1.23004
$341$	7854.30	1.24731
$342$	2518.98	0.398277
$343$	−343.000	−0.0539949
$344$	−2013.45	−0.315575
$345$	1017.72	0.158818
$346$	−782.440	−0.121573
$347$	5376.82	0.831823	0.415912	−	0.909405i	$-0.363463\pi$
$347$	5376.82	0.831823	0.415912	+	0.909405i	$0.363463\pi$
$348$	27.8555	0.00429084
$349$	777.446	0.119243	0.0596214	−	0.998221i	$-0.481011\pi$
$349$	777.446	0.119243	0.0596214	+	0.998221i	$0.481011\pi$
$350$	1295.70	0.197880
$351$	271.780	0.0413292
$352$	−1354.49	−0.205098
$353$	10586.4	1.59620	0.798099	−	0.602527i	$-0.205839\pi$
$353$	10586.4	1.59620	0.798099	+	0.602527i	$0.205839\pi$
$354$	2309.65	0.346770
$355$	8076.79	1.20753
$356$	−2554.84	−0.380354
$357$	−2744.85	−0.406927
$358$	−495.695	−0.0731796
$359$	−4419.64	−0.649749	−0.324874	−	0.945757i	$-0.605322\pi$
$359$	−4419.64	−0.649749	−0.324874	+	0.945757i	$0.605322\pi$
$360$	−1061.97	−0.155474
$361$	12725.2	1.85525
$362$	−9554.30	−1.38719
$363$	1381.90	0.199810
$364$	−281.846	−0.0405844
$365$	−7614.86	−1.09200
$366$	−4325.09	−0.617694
$367$	−4134.26	−0.588029	−0.294014	−	0.955801i	$-0.594991\pi$
$367$	−4134.26	−0.588029	−0.294014	+	0.955801i	$0.594991\pi$
$368$	368.000	0.0521286
$369$	4251.24	0.599759
$370$	9086.35	1.27669
$371$	−3676.25	−0.514452
$372$	2226.71	0.310349
$373$	−1365.08	−0.189494	−0.0947470	−	0.995501i	$-0.530204\pi$
$373$	−1365.08	−0.189494	−0.0947470	+	0.995501i	$0.530204\pi$
$374$	−11065.1	−1.52984
$375$	−1435.88	−0.197729
$376$	4209.72	0.577393
$377$	23.3659	0.00319206
$378$	378.000	0.0514344
$379$	−1871.13	−0.253598	−0.126799	−	0.991928i	$-0.540470\pi$
$379$	−1871.13	−0.253598	−0.126799	+	0.991928i	$0.540470\pi$
$380$	−8256.42	−1.11459
$381$	4839.75	0.650782
$382$	8633.22	1.15632
$383$	3753.99	0.500835	0.250417	−	0.968138i	$-0.419432\pi$
$383$	3753.99	0.500835	0.250417	+	0.968138i	$0.419432\pi$
$384$	−384.000	−0.0510310
$385$	−4370.21	−0.578510
$386$	−2158.47	−0.284620
$387$	2265.13	0.297527
$388$	−1927.39	−0.252186
$389$	−7589.56	−0.989218	−0.494609	−	0.869116i	$-0.664689\pi$
$389$	−7589.56	−0.989218	−0.494609	+	0.869116i	$0.664689\pi$
$390$	−890.808	−0.115661
$391$	3006.26	0.388832
$392$	−392.000	−0.0505076
$393$	6080.86	0.780505
$394$	−5716.02	−0.730886
$395$	−9385.36	−1.19552
$396$	1523.80	0.193368
$397$	−8594.50	−1.08651	−0.543256	−	0.839567i	$-0.682809\pi$
$397$	−8594.50	−1.08651	−0.543256	+	0.839567i	$0.682809\pi$
$398$	2525.67	0.318091
$399$	2938.81	0.368733
$400$	1480.80	0.185100
$401$	2139.65	0.266456	0.133228	−	0.991085i	$-0.457466\pi$
$401$	2139.65	0.266456	0.133228	+	0.991085i	$0.457466\pi$
$402$	662.922	0.0822476
$403$	1867.83	0.230876
$404$	−3742.07	−0.460829
$405$	1194.72	0.146582
$406$	32.4981	0.00397254
$407$	−13037.8	−1.58786
$408$	−3136.97	−0.380645
$409$	−4352.18	−0.526165	−0.263083	−	0.964773i	$-0.584739\pi$
$409$	−4352.18	−0.526165	−0.263083	+	0.964773i	$0.584739\pi$
$410$	−13934.2	−1.67844
$411$	3691.29	0.443012
$412$	4401.80	0.526362
$413$	2694.60	0.321047
$414$	−414.000	−0.0491473
$415$	−5494.42	−0.649905
$416$	−322.109	−0.0379633
$417$	1975.40	0.231980
$418$	11847.0	1.38625
$419$	−13645.6	−1.59100	−0.795501	−	0.605953i	$-0.792792\pi$
$419$	−13645.6	−1.59100	−0.795501	+	0.605953i	$0.792792\pi$
$420$	−1238.96	−0.143941
$421$	−9808.90	−1.13553	−0.567763	−	0.823192i	$-0.692191\pi$
$421$	−9808.90	−1.13553	−0.567763	+	0.823192i	$0.692191\pi$
$422$	−9269.68	−1.06929
$423$	−4735.94	−0.544371
$424$	−4201.43	−0.481225
$425$	12096.9	1.38067
$426$	−3285.57	−0.373677
$427$	−5045.94	−0.571873
$428$	−3649.43	−0.412154
$429$	1278.20	0.143851
$430$	−7424.37	−0.832639
$431$	3927.66	0.438953	0.219476	−	0.975618i	$-0.429565\pi$
$431$	3927.66	0.438953	0.219476	+	0.975618i	$0.429565\pi$
$432$	432.000	0.0481125
$433$	−11978.7	−1.32947	−0.664734	−	0.747080i	$-0.731455\pi$
$433$	−11978.7	−1.32947	−0.664734	+	0.747080i	$0.731455\pi$
$434$	2597.83	0.287327
$435$	102.714	0.0113213
$436$	−5489.52	−0.602982
$437$	−3218.70	−0.352337
$438$	3097.66	0.337927
$439$	16065.6	1.74662	0.873312	−	0.487162i	$-0.161968\pi$
$439$	16065.6	1.74662	0.873312	+	0.487162i	$0.161968\pi$
$440$	−4994.52	−0.541147
$441$	441.000	0.0476190
$442$	−2631.37	−0.283171
$443$	−954.723	−0.102393	−0.0511967	−	0.998689i	$-0.516304\pi$
$443$	−954.723	−0.102393	−0.0511967	+	0.998689i	$0.516304\pi$
$444$	−3696.25	−0.395082
$445$	−9420.68	−1.00356
$446$	−12420.1	−1.31862
$447$	7095.79	0.750826
$448$	−448.000	−0.0472456
$449$	−141.057	−0.0148261	−0.00741304	−	0.999973i	$-0.502360\pi$
$449$	−141.057	−0.0148261	−0.00741304	+	0.999973i	$0.502360\pi$
$450$	−1665.90	−0.174514
$451$	19993.9	2.08753
$452$	7874.03	0.819387
$453$	1278.05	0.132556
$454$	−7048.99	−0.728691
$455$	−1039.28	−0.107081
$456$	3358.64	0.344918
$457$	−16657.1	−1.70500	−0.852501	−	0.522725i	$-0.824915\pi$
$457$	−16657.1	−1.70500	−0.852501	+	0.522725i	$0.824915\pi$
$458$	−7558.39	−0.771137
$459$	3529.09	0.358876
$460$	1356.96	0.137540
$461$	15347.3	1.55053	0.775264	−	0.631637i	$-0.217617\pi$
$461$	15347.3	1.55053	0.775264	+	0.631637i	$0.217617\pi$
$462$	1777.76	0.179024
$463$	−2427.10	−0.243622	−0.121811	−	0.992553i	$-0.538870\pi$
$463$	−2427.10	−0.243622	−0.121811	+	0.992553i	$0.538870\pi$
$464$	37.1407	0.00371597
$465$	8210.76	0.818850
$466$	7462.38	0.741820
$467$	−9582.71	−0.949539	−0.474770	−	0.880110i	$-0.657469\pi$
$467$	−9582.71	−0.949539	−0.474770	+	0.880110i	$0.657469\pi$
$468$	362.373	0.0357921
$469$	773.409	0.0761465
$470$	15522.9	1.52344
$471$	5987.26	0.585729
$472$	3079.54	0.300312
$473$	10653.1	1.03558
$474$	3817.88	0.369960
$475$	−12951.7	−1.25109
$476$	−3659.80	−0.352409
$477$	4726.61	0.453704
$478$	4116.01	0.393853
$479$	−6317.04	−0.602574	−0.301287	−	0.953534i	$-0.597416\pi$
$479$	−6317.04	−0.602574	−0.301287	+	0.953534i	$0.597416\pi$
$480$	−1415.96	−0.134645
$481$	−3100.51	−0.293911
$482$	3743.26	0.353737
$483$	−483.000	−0.0455016
$484$	1842.53	0.173040
$485$	−7107.04	−0.665390
$486$	−486.000	−0.0453609
$487$	−1264.34	−0.117645	−0.0588223	−	0.998268i	$-0.518735\pi$
$487$	−1264.34	−0.117645	−0.0588223	+	0.998268i	$0.518735\pi$
$488$	−5766.78	−0.534939
$489$	−12071.5	−1.11634
$490$	−1445.46	−0.133264
$491$	5723.94	0.526106	0.263053	−	0.964781i	$-0.415271\pi$
$491$	5723.94	0.526106	0.263053	+	0.964781i	$0.415271\pi$
$492$	5668.33	0.519406
$493$	303.409	0.0277178
$494$	2817.32	0.256593
$495$	5618.84	0.510198
$496$	2968.95	0.268770
$497$	−3833.17	−0.345958
$498$	2235.08	0.201117
$499$	−5075.35	−0.455318	−0.227659	−	0.973741i	$-0.573107\pi$
$499$	−5075.35	−0.455318	−0.227659	+	0.973741i	$0.573107\pi$
$500$	−1914.51	−0.171239
$501$	−3331.57	−0.297093
$502$	−4268.06	−0.379468
$503$	−10914.5	−0.967498	−0.483749	−	0.875207i	$-0.660725\pi$
$503$	−10914.5	−0.967498	−0.483749	+	0.875207i	$0.660725\pi$
$504$	504.000	0.0445435
$505$	−13798.5	−1.21589
$506$	−1947.07	−0.171063
$507$	−6287.03	−0.550724
$508$	6453.00	0.563594
$509$	−21289.7	−1.85393	−0.926965	−	0.375147i	$-0.877592\pi$
$509$	−21289.7	−1.85393	−0.926965	+	0.375147i	$0.877592\pi$
$510$	−11567.2	−1.00433
$511$	3613.94	0.312860
$512$	−512.000	−0.0441942
$513$	−3778.47	−0.325192
$514$	2326.90	0.199680
$515$	16231.2	1.38880
$516$	3020.17	0.257666
$517$	−22273.5	−1.89475
$518$	−4312.29	−0.365775
$519$	1173.66	0.0992639
$520$	−1187.74	−0.100165
$521$	13107.4	1.10220	0.551101	−	0.834438i	$-0.314208\pi$
$521$	13107.4	1.10220	0.551101	+	0.834438i	$0.314208\pi$
$522$	−41.7833	−0.00350345
$523$	−623.676	−0.0521442	−0.0260721	−	0.999660i	$-0.508300\pi$
$523$	−623.676	−0.0521442	−0.0260721	+	0.999660i	$0.508300\pi$
$524$	8107.81	0.675938
$525$	−1943.55	−0.161568
$526$	2587.85	0.214517
$527$	24253.9	2.00478
$528$	2031.73	0.167461
$529$	529.000	0.0434783
$530$	−15492.3	−1.26971
$531$	−3464.48	−0.283137
$532$	3918.41	0.319332
$533$	4754.74	0.386399
$534$	3832.25	0.310558
$535$	−13456.9	−1.08746
$536$	883.896	0.0712285
$537$	743.543	0.0597509
$538$	−8156.08	−0.653594
$539$	2074.06	0.165744
$540$	1592.95	0.126944
$541$	3942.45	0.313307	0.156653	−	0.987654i	$-0.449929\pi$
$541$	3942.45	0.313307	0.156653	+	0.987654i	$0.449929\pi$
$542$	12809.9	1.01519
$543$	14331.4	1.13264
$544$	−4182.63	−0.329648
$545$	−20242.0	−1.59096
$546$	422.769	0.0331370
$547$	4364.16	0.341130	0.170565	−	0.985346i	$-0.445441\pi$
$547$	4364.16	0.341130	0.170565	+	0.985346i	$0.445441\pi$
$548$	4921.72	0.383659
$549$	6487.63	0.504345
$550$	−7834.84	−0.607416
$551$	−324.849	−0.0251162
$552$	−552.000	−0.0425628
$553$	4454.20	0.342517
$554$	−15000.4	−1.15037
$555$	−13629.5	−1.04242
$556$	2633.87	0.200901
$557$	−7477.20	−0.568796	−0.284398	−	0.958706i	$-0.591794\pi$
$557$	−7477.20	−0.568796	−0.284398	+	0.958706i	$0.591794\pi$
$558$	−3340.07	−0.253399
$559$	2533.40	0.191684
$560$	−1651.95	−0.124657
$561$	16597.6	1.24911
$562$	13673.9	1.02633
$563$	−20768.5	−1.55469	−0.777343	−	0.629077i	$-0.783433\pi$
$563$	−20768.5	−1.55469	−0.777343	+	0.629077i	$0.783433\pi$
$564$	−6314.58	−0.471439
$565$	29034.6	2.16194
$566$	−826.172	−0.0613544
$567$	−567.000	−0.0419961
$568$	−4380.76	−0.323614
$569$	−391.730	−0.0288615	−0.0144307	−	0.999896i	$-0.504594\pi$
$569$	−391.730	−0.0288615	−0.0144307	+	0.999896i	$0.504594\pi$
$570$	12384.6	0.910061
$571$	−17909.2	−1.31257	−0.656285	−	0.754513i	$-0.727873\pi$
$571$	−17909.2	−1.31257	−0.656285	+	0.754513i	$0.727873\pi$
$572$	1704.27	0.124579
$573$	−12949.8	−0.944130
$574$	6613.05	0.480877
$575$	2128.64	0.154384
$576$	576.000	0.0416667
$577$	−25507.2	−1.84034	−0.920172	−	0.391514i	$-0.871951\pi$
$577$	−25507.2	−1.84034	−0.920172	+	0.391514i	$0.871951\pi$
$578$	−24342.7	−1.75177
$579$	3237.71	0.232391
$580$	136.952	0.00980454
$581$	2607.60	0.186199
$582$	2891.08	0.205909
$583$	22229.6	1.57917
$584$	4130.21	0.292653
$585$	1336.21	0.0944368
$586$	14533.5	1.02453
$587$	−14300.1	−1.00550	−0.502751	−	0.864431i	$-0.667679\pi$
$587$	−14300.1	−1.00550	−0.502751	+	0.864431i	$0.667679\pi$
$588$	588.000	0.0412393
$589$	−25967.8	−1.81661
$590$	11355.5	0.792368
$591$	8574.03	0.596766
$592$	−4928.34	−0.342151
$593$	−13679.9	−0.947327	−0.473663	−	0.880706i	$-0.657069\pi$
$593$	−13679.9	−0.947327	−0.473663	+	0.880706i	$0.657069\pi$
$594$	−2285.70	−0.157884
$595$	−13495.1	−0.929825
$596$	9461.06	0.650235
$597$	−3788.50	−0.259720
$598$	−463.032	−0.0316635
$599$	17442.0	1.18975	0.594876	−	0.803818i	$-0.297201\pi$
$599$	17442.0	1.18975	0.594876	+	0.803818i	$0.297201\pi$
$600$	−2221.19	−0.151133
$601$	−2846.22	−0.193177	−0.0965887	−	0.995324i	$-0.530793\pi$
$601$	−2846.22	−0.193177	−0.0965887	+	0.995324i	$0.530793\pi$
$602$	3523.53	0.238552
$603$	−994.383	−0.0671549
$604$	1704.06	0.114797
$605$	6794.15	0.456564
$606$	5613.10	0.376265
$607$	−25186.7	−1.68418	−0.842090	−	0.539337i	$-0.818675\pi$
$607$	−25186.7	−1.68418	−0.842090	+	0.539337i	$0.818675\pi$
$608$	4478.19	0.298708
$609$	−48.7471	−0.00324357
$610$	−21264.4	−1.41143
$611$	−5296.84	−0.350715
$612$	4705.46	0.310795
$613$	−12637.0	−0.832633	−0.416316	−	0.909220i	$-0.636679\pi$
$613$	−12637.0	−0.832633	−0.416316	+	0.909220i	$0.636679\pi$
$614$	−1636.34	−0.107553
$615$	20901.3	1.37044
$616$	2370.35	0.155039
$617$	18041.9	1.17721	0.588606	−	0.808420i	$-0.299677\pi$
$617$	18041.9	1.17721	0.588606	+	0.808420i	$0.299677\pi$
$618$	−6602.70	−0.429773
$619$	7378.97	0.479137	0.239569	−	0.970879i	$-0.422994\pi$
$619$	7378.97	0.479137	0.239569	+	0.970879i	$0.422994\pi$
$620$	10947.7	0.709145
$621$	621.000	0.0401286
$622$	−11665.6	−0.752003
$623$	4470.96	0.287521
$624$	483.164	0.0309969
$625$	−18628.3	−1.19221
$626$	7472.08	0.477068
$627$	−17770.4	−1.13187
$628$	7983.02	0.507257
$629$	−40260.5	−2.55214
$630$	1858.45	0.117527
$631$	−16993.1	−1.07208	−0.536041	−	0.844192i	$-0.680081\pi$
$631$	−16993.1	−1.07208	−0.536041	+	0.844192i	$0.680081\pi$
$632$	5090.51	0.320395
$633$	13904.5	0.873073
$634$	18762.3	1.17531
$635$	23794.8	1.48703
$636$	6302.15	0.392919
$637$	493.230	0.0306789
$638$	−196.510	−0.0121942
$639$	4928.36	0.305106
$640$	−1887.94	−0.116606
$641$	−8921.59	−0.549738	−0.274869	−	0.961482i	$-0.588634\pi$
$641$	−8921.59	−0.549738	−0.274869	+	0.961482i	$0.588634\pi$
$642$	5474.15	0.336523
$643$	−9392.87	−0.576079	−0.288039	−	0.957619i	$-0.593003\pi$
$643$	−9392.87	−0.576079	−0.288039	+	0.957619i	$0.593003\pi$
$644$	−644.000	−0.0394055
$645$	11136.6	0.679847
$646$	36583.2	2.22809
$647$	−18165.8	−1.10382	−0.551908	−	0.833905i	$-0.686100\pi$
$647$	−18165.8	−1.10382	−0.551908	+	0.833905i	$0.686100\pi$
$648$	−648.000	−0.0392837
$649$	−16293.7	−0.985492
$650$	−1863.20	−0.112432
$651$	−3896.75	−0.234602
$652$	−16095.3	−0.966781
$653$	−16400.9	−0.982873	−0.491437	−	0.870913i	$-0.663528\pi$
$653$	−16400.9	−0.982873	−0.491437	+	0.870913i	$0.663528\pi$
$654$	8234.27	0.492333
$655$	29896.7	1.78345
$656$	7557.77	0.449819
$657$	−4646.49	−0.275916
$658$	−7367.01	−0.436468
$659$	27218.7	1.60894	0.804470	−	0.593993i	$-0.202449\pi$
$659$	27218.7	1.60894	0.804470	+	0.593993i	$0.202449\pi$
$660$	7491.78	0.441844
$661$	−9573.25	−0.563323	−0.281661	−	0.959514i	$-0.590885\pi$
$661$	−9573.25	−0.563323	−0.281661	+	0.959514i	$0.590885\pi$
$662$	19159.9	1.12488
$663$	3947.06	0.231208
$664$	2980.11	0.174173
$665$	14448.7	0.842553
$666$	5544.38	0.322583
$667$	53.3897	0.00309934
$668$	−4442.09	−0.257290
$669$	18630.1	1.07665
$670$	3259.27	0.187935
$671$	30511.8	1.75543
$672$	672.000	0.0385758
$673$	−1542.19	−0.0883312	−0.0441656	−	0.999024i	$-0.514063\pi$
$673$	−1542.19	−0.0883312	−0.0441656	+	0.999024i	$0.514063\pi$
$674$	−2427.48	−0.138729
$675$	2498.84	0.142490
$676$	−8382.71	−0.476941
$677$	22855.3	1.29749	0.648745	−	0.761006i	$-0.275294\pi$
$677$	22855.3	1.29749	0.648745	+	0.761006i	$0.275294\pi$
$678$	−11811.0	−0.669027
$679$	3372.93	0.190635
$680$	−15423.0	−0.869772
$681$	10573.5	0.594974
$682$	−15708.6	−0.881985
$683$	−25808.4	−1.44587	−0.722935	−	0.690916i	$-0.757207\pi$
$683$	−25808.4	−1.44587	−0.722935	+	0.690916i	$0.757207\pi$
$684$	−5037.96	−0.281625
$685$	18148.3	1.01228
$686$	686.000	0.0381802
$687$	11337.6	0.629630
$688$	4026.89	0.223145
$689$	5286.41	0.292302
$690$	−2035.44	−0.112301
$691$	−2206.28	−0.121463	−0.0607314	−	0.998154i	$-0.519343\pi$
$691$	−2206.28	−0.121463	−0.0607314	+	0.998154i	$0.519343\pi$
$692$	1564.88	0.0859650
$693$	−2666.64	−0.146172
$694$	−10753.6	−0.588188
$695$	9712.10	0.530074
$696$	−55.7110	−0.00303408
$697$	61740.9	3.35524
$698$	−1554.89	−0.0843174
$699$	−11193.6	−0.605694
$700$	−2591.39	−0.139922
$701$	−11620.7	−0.626117	−0.313059	−	0.949734i	$-0.601354\pi$
$701$	−11620.7	−0.626117	−0.313059	+	0.949734i	$0.601354\pi$
$702$	−543.560	−0.0292241
$703$	43105.5	2.31260
$704$	2708.97	0.145026
$705$	−23284.3	−1.24388
$706$	−21172.8	−1.12868
$707$	6548.62	0.348354
$708$	−4619.31	−0.245204
$709$	23105.6	1.22390	0.611952	−	0.790895i	$-0.290385\pi$
$709$	23105.6	1.22390	0.611952	+	0.790895i	$0.290385\pi$
$710$	−16153.6	−0.853850
$711$	−5726.83	−0.302071
$712$	5109.67	0.268951
$713$	4267.87	0.224170
$714$	5489.70	0.287741
$715$	6284.31	0.328699
$716$	991.391	0.0517458
$717$	−6174.02	−0.321580
$718$	8839.28	0.459442
$719$	2800.22	0.145244	0.0726220	−	0.997360i	$-0.476863\pi$
$719$	2800.22	0.145244	0.0726220	+	0.997360i	$0.476863\pi$
$720$	2123.94	0.109937
$721$	−7703.15	−0.397892
$722$	−25450.3	−1.31186
$723$	−5614.90	−0.288825
$724$	19108.6	0.980891
$725$	214.835	0.0110052
$726$	−2763.80	−0.141287
$727$	14537.6	0.741638	0.370819	−	0.928705i	$-0.379077\pi$
$727$	14537.6	0.741638	0.370819	+	0.928705i	$0.379077\pi$
$728$	563.691	0.0286975
$729$	729.000	0.0370370
$730$	15229.7	0.772161
$731$	32896.5	1.66446
$732$	8650.18	0.436776
$733$	24269.9	1.22296	0.611481	−	0.791259i	$-0.290574\pi$
$733$	24269.9	1.22296	0.611481	+	0.791259i	$0.290574\pi$
$734$	8268.52	0.415799
$735$	2168.19	0.108809
$736$	−736.000	−0.0368605
$737$	−4676.66	−0.233741
$738$	−8502.49	−0.424093
$739$	−377.866	−0.0188092	−0.00940461	−	0.999956i	$-0.502994\pi$
$739$	−377.866	−0.0188092	−0.00940461	+	0.999956i	$0.502994\pi$
$740$	−18172.7	−0.902760
$741$	−4225.98	−0.209508
$742$	7352.51	0.363772
$743$	17021.4	0.840450	0.420225	−	0.907420i	$-0.361951\pi$
$743$	17021.4	0.840450	0.420225	+	0.907420i	$0.361951\pi$
$744$	−4453.43	−0.219450
$745$	34886.6	1.71563
$746$	2730.16	0.133993
$747$	−3352.63	−0.164212
$748$	22130.1	1.08176
$749$	6386.51	0.311559
$750$	2871.76	0.139816
$751$	−2387.81	−0.116022	−0.0580109	−	0.998316i	$-0.518476\pi$
$751$	−2387.81	−0.116022	−0.0580109	+	0.998316i	$0.518476\pi$
$752$	−8419.44	−0.408279
$753$	6402.09	0.309834
$754$	−46.7319	−0.00225713
$755$	6283.55	0.302890
$756$	−756.000	−0.0363696
$757$	17647.6	0.847310	0.423655	−	0.905824i	$-0.360747\pi$
$757$	17647.6	0.847310	0.423655	+	0.905824i	$0.360747\pi$
$758$	3742.27	0.179321
$759$	2920.61	0.139673
$760$	16512.8	0.788136
$761$	40185.0	1.91420	0.957100	−	0.289758i	$-0.0935748\pi$
$761$	40185.0	1.91420	0.957100	+	0.289758i	$0.0935748\pi$
$762$	−9679.50	−0.460173
$763$	9606.65	0.455812
$764$	−17266.4	−0.817641
$765$	17350.9	0.820029
$766$	−7507.97	−0.354144
$767$	−3874.80	−0.182413
$768$	768.000	0.0360844
$769$	9523.15	0.446572	0.223286	−	0.974753i	$-0.428322\pi$
$769$	9523.15	0.446572	0.223286	+	0.974753i	$0.428322\pi$
$770$	8740.41	0.409068
$771$	−3490.35	−0.163038
$772$	4316.94	0.201257
$773$	17405.5	0.809876	0.404938	−	0.914344i	$-0.367293\pi$
$773$	17405.5	0.809876	0.404938	+	0.914344i	$0.367293\pi$
$774$	−4530.25	−0.210383
$775$	17173.5	0.795987
$776$	3854.78	0.178323
$777$	6468.44	0.298654
$778$	15179.1	0.699483
$779$	−66103.7	−3.04032
$780$	1781.62	0.0817847
$781$	23178.4	1.06196
$782$	−6012.53	−0.274946
$783$	62.6749	0.00286056
$784$	784.000	0.0357143
$785$	29436.5	1.33839
$786$	−12161.7	−0.551901
$787$	−22143.5	−1.00296	−0.501481	−	0.865169i	$-0.667211\pi$
$787$	−22143.5	−1.00296	−0.501481	+	0.865169i	$0.667211\pi$
$788$	11432.0	0.516814
$789$	−3881.78	−0.175152
$790$	18770.7	0.845357
$791$	−13779.5	−0.619399
$792$	−3047.59	−0.136732
$793$	7256.00	0.324928
$794$	17189.0	0.768280
$795$	23238.5	1.03671
$796$	−5051.33	−0.224924
$797$	−19969.2	−0.887509	−0.443755	−	0.896148i	$-0.646354\pi$
$797$	−19969.2	−0.887509	−0.443755	+	0.896148i	$0.646354\pi$
$798$	−5877.62	−0.260734
$799$	−68780.1	−3.04539
$800$	−2961.59	−0.130885
$801$	−5748.38	−0.253569
$802$	−4279.30	−0.188413
$803$	−21852.8	−0.960360
$804$	−1325.84	−0.0581578
$805$	−2374.68	−0.103971
$806$	−3735.65	−0.163254
$807$	12234.1	0.533657
$808$	7484.14	0.325855
$809$	1148.60	0.0499168	0.0249584	−	0.999688i	$-0.492055\pi$
$809$	1148.60	0.0499168	0.0249584	+	0.999688i	$0.492055\pi$
$810$	−2389.43	−0.103649
$811$	27397.0	1.18624	0.593120	−	0.805114i	$-0.297896\pi$
$811$	27397.0	1.18624	0.593120	+	0.805114i	$0.297896\pi$
$812$	−64.9962	−0.00280901
$813$	−19214.9	−0.828899
$814$	26075.6	1.12279
$815$	−59349.8	−2.55084
$816$	6273.94	0.269157
$817$	−35221.1	−1.50824
$818$	8704.36	0.372055
$819$	−634.153	−0.0270563
$820$	27868.5	1.18684
$821$	16675.6	0.708870	0.354435	−	0.935081i	$-0.384673\pi$
$821$	16675.6	0.708870	0.354435	+	0.935081i	$0.384673\pi$
$822$	−7382.57	−0.313256
$823$	−16191.0	−0.685764	−0.342882	−	0.939379i	$-0.611403\pi$
$823$	−16191.0	−0.685764	−0.342882	+	0.939379i	$0.611403\pi$
$824$	−8803.60	−0.372194
$825$	11752.3	0.495953
$826$	−5389.19	−0.227014
$827$	10865.6	0.456874	0.228437	−	0.973559i	$-0.426638\pi$
$827$	10865.6	0.456874	0.228437	+	0.973559i	$0.426638\pi$
$828$	828.000	0.0347524
$829$	−19722.5	−0.826284	−0.413142	−	0.910667i	$-0.635569\pi$
$829$	−19722.5	−0.826284	−0.413142	+	0.910667i	$0.635569\pi$
$830$	10988.8	0.459552
$831$	22500.6	0.939274
$832$	644.219	0.0268441
$833$	6404.65	0.266396
$834$	−3950.80	−0.164035
$835$	−16379.7	−0.678855
$836$	−23693.9	−0.980229
$837$	5010.10	0.206899
$838$	27291.1	1.12501
$839$	5398.08	0.222125	0.111062	−	0.993813i	$-0.464575\pi$
$839$	5398.08	0.222125	0.111062	+	0.993813i	$0.464575\pi$
$840$	2477.93	0.101782
$841$	−24383.6	−0.999779
$842$	19617.8	0.802939
$843$	−20510.8	−0.837994
$844$	18539.4	0.756103
$845$	−30910.3	−1.25840
$846$	9471.87	0.384929
$847$	−3224.44	−0.130806
$848$	8402.86	0.340278
$849$	1239.26	0.0500957
$850$	−24193.8	−0.976284
$851$	−7084.48	−0.285374
$852$	6571.14	0.264230
$853$	−32431.9	−1.30181	−0.650906	−	0.759158i	$-0.725611\pi$
$853$	−32431.9	−1.30181	−0.650906	+	0.759158i	$0.725611\pi$
$854$	10091.9	0.404376
$855$	−18576.9	−0.743062
$856$	7298.87	0.291437
$857$	6007.90	0.239470	0.119735	−	0.992806i	$-0.461795\pi$
$857$	6007.90	0.239470	0.119735	+	0.992806i	$0.461795\pi$
$858$	−2556.40	−0.101718
$859$	26225.0	1.04166	0.520829	−	0.853661i	$-0.325623\pi$
$859$	26225.0	1.04166	0.520829	+	0.853661i	$0.325623\pi$
$860$	14848.7	0.588765
$861$	−9919.57	−0.392634
$862$	−7855.32	−0.310387
$863$	−24202.3	−0.954640	−0.477320	−	0.878730i	$-0.658392\pi$
$863$	−24202.3	−0.954640	−0.477320	+	0.878730i	$0.658392\pi$
$864$	−864.000	−0.0340207
$865$	5770.32	0.226817
$866$	23957.4	0.940076
$867$	36514.1	1.43031
$868$	−5195.66	−0.203171
$869$	−26933.7	−1.05140
$870$	−205.428	−0.00800537
$871$	−1112.15	−0.0432651
$872$	10979.0	0.426373
$873$	−4336.62	−0.168124
$874$	6437.40	0.249140
$875$	3350.39	0.129444
$876$	−6195.32	−0.238950
$877$	−13075.6	−0.503458	−0.251729	−	0.967798i	$-0.580999\pi$
$877$	−13075.6	−0.503458	−0.251729	+	0.967798i	$0.580999\pi$
$878$	−32131.1	−1.23505
$879$	−21800.2	−0.836522
$880$	9989.04	0.382648
$881$	−25765.5	−0.985315	−0.492658	−	0.870223i	$-0.663975\pi$
$881$	−25765.5	−0.985315	−0.492658	+	0.870223i	$0.663975\pi$
$882$	−882.000	−0.0336718
$883$	−39963.4	−1.52308	−0.761539	−	0.648120i	$-0.775556\pi$
$883$	−39963.4	−1.52308	−0.761539	+	0.648120i	$0.775556\pi$
$884$	5262.75	0.200232
$885$	−17033.2	−0.646966
$886$	1909.45	0.0724030
$887$	−9454.40	−0.357889	−0.178945	−	0.983859i	$-0.557268\pi$
$887$	−9454.40	−0.357889	−0.178945	+	0.983859i	$0.557268\pi$
$888$	7392.50	0.279365
$889$	−11292.8	−0.426037
$890$	18841.4	0.709622
$891$	3428.54	0.128912
$892$	24840.1	0.932408
$893$	73640.3	2.75955
$894$	−14191.6	−0.530914
$895$	3655.65	0.136530
$896$	896.000	0.0334077
$897$	694.548	0.0258532
$898$	282.115	0.0104836
$899$	430.738	0.0159799
$900$	3331.79	0.123400
$901$	68644.6	2.53816
$902$	−39987.9	−1.47611
$903$	−5285.30	−0.194777
$904$	−15748.1	−0.579394
$905$	70460.9	2.58807
$906$	−2556.10	−0.0937314
$907$	−25983.6	−0.951237	−0.475618	−	0.879652i	$-0.657776\pi$
$907$	−25983.6	−0.951237	−0.475618	+	0.879652i	$0.657776\pi$
$908$	14098.0	0.515262
$909$	−8419.65	−0.307219
$910$	2078.55	0.0757179
$911$	3785.55	0.137674	0.0688368	−	0.997628i	$-0.478071\pi$
$911$	3785.55	0.137674	0.0688368	+	0.997628i	$0.478071\pi$
$912$	−6717.28	−0.243894
$913$	−15767.7	−0.571559
$914$	33314.2	1.20562
$915$	31896.6	1.15242
$916$	15116.8	0.545276
$917$	−14188.7	−0.510961
$918$	−7058.19	−0.253763
$919$	12541.4	0.450165	0.225083	−	0.974340i	$-0.427735\pi$
$919$	12541.4	0.450165	0.225083	+	0.974340i	$0.427735\pi$
$920$	−2713.92	−0.0972558
$921$	2454.51	0.0878164
$922$	−30694.5	−1.09639
$923$	5512.05	0.196567
$924$	−3555.53	−0.126589
$925$	−28507.3	−1.01331
$926$	4854.20	0.172267
$927$	9904.05	0.350908
$928$	−74.2813	−0.00262759
$929$	−29821.8	−1.05320	−0.526599	−	0.850114i	$-0.676533\pi$
$929$	−29821.8	−1.05320	−0.526599	+	0.850114i	$0.676533\pi$
$930$	−16421.5	−0.579014
$931$	−6857.23	−0.241393
$932$	−14924.8	−0.524546
$933$	17498.3	0.614008
$934$	19165.4	0.671426
$935$	81602.5	2.85421
$936$	−724.746	−0.0253088
$937$	24422.1	0.851479	0.425740	−	0.904846i	$-0.360014\pi$
$937$	24422.1	0.851479	0.425740	+	0.904846i	$0.360014\pi$
$938$	−1546.82	−0.0538437
$939$	−11208.1	−0.389524
$940$	−31045.8	−1.07724
$941$	28588.2	0.990381	0.495190	−	0.868785i	$-0.335098\pi$
$941$	28588.2	0.990381	0.495190	+	0.868785i	$0.335098\pi$
$942$	−11974.5	−0.414173
$943$	10864.3	0.375175
$944$	−6159.08	−0.212353
$945$	−2787.67	−0.0959607
$946$	−21306.1	−0.732265
$947$	15050.8	0.516459	0.258229	−	0.966084i	$-0.416861\pi$
$947$	15050.8	0.516459	0.258229	+	0.966084i	$0.416861\pi$
$948$	−7635.77	−0.261601
$949$	−5196.80	−0.177761
$950$	25903.5	0.884652
$951$	−28143.5	−0.959636
$952$	7319.60	0.249191
$953$	6981.72	0.237314	0.118657	−	0.992935i	$-0.462141\pi$
$953$	6981.72	0.237314	0.118657	+	0.992935i	$0.462141\pi$
$954$	−9453.22	−0.320817
$955$	−63668.1	−2.15733
$956$	−8232.02	−0.278496
$957$	294.765	0.00995652
$958$	12634.1	0.426084
$959$	−8613.00	−0.290019
$960$	2831.92	0.0952081
$961$	4641.31	0.155796
$962$	6201.03	0.207827
$963$	−8211.22	−0.274769
$964$	−7486.53	−0.250130
$965$	15918.3	0.531012
$966$	966.000	0.0321745
$967$	34491.9	1.14704	0.573519	−	0.819192i	$-0.305578\pi$
$967$	34491.9	1.14704	0.573519	+	0.819192i	$0.305578\pi$
$968$	−3685.07	−0.122358
$969$	−54874.8	−1.81923
$970$	14214.1	0.470501
$971$	−22939.4	−0.758145	−0.379073	−	0.925367i	$-0.623757\pi$
$971$	−22939.4	−0.758145	−0.379073	+	0.925367i	$0.623757\pi$
$972$	972.000	0.0320750
$973$	−4609.27	−0.151867
$974$	2528.69	0.0831873
$975$	2794.80	0.0918001
$976$	11533.6	0.378259
$977$	−2817.71	−0.0922686	−0.0461343	−	0.998935i	$-0.514690\pi$
$977$	−2817.71	−0.0922686	−0.0461343	+	0.998935i	$0.514690\pi$
$978$	24143.0	0.789374
$979$	−27035.1	−0.882579
$980$	2890.92	0.0942315
$981$	−12351.4	−0.401988
$982$	−11447.9	−0.372013
$983$	−39793.8	−1.29118	−0.645588	−	0.763686i	$-0.723388\pi$
$983$	−39793.8	−1.29118	−0.645588	+	0.763686i	$0.723388\pi$
$984$	−11336.7	−0.367276
$985$	42154.4	1.36361
$986$	−606.819	−0.0195994
$987$	11050.5	0.356375
$988$	−5634.64	−0.181439
$989$	5788.66	0.186116
$990$	−11237.7	−0.360764
$991$	−35456.0	−1.13653	−0.568263	−	0.822847i	$-0.692384\pi$
$991$	−35456.0	−1.13653	−0.568263	+	0.822847i	$0.692384\pi$
$992$	−5937.90	−0.190049
$993$	−28739.9	−0.918463
$994$	7666.33	0.244629
$995$	−18626.2	−0.593459
$996$	−4470.17	−0.142212
$997$	14345.1	0.455680	0.227840	−	0.973699i	$-0.426834\pi$
$997$	14345.1	0.455680	0.227840	+	0.973699i	$0.426834\pi$
$998$	10150.7	0.321959
$999$	−8316.57	−0.263388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.n.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.n.1.5	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +14.7496 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +14.7496 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -29.4991 q^{10} +42.3277 q^{11} +12.0000 q^{12} +10.0659 q^{13} +14.0000 q^{14} +44.2487 q^{15} +16.0000 q^{16} +130.707 q^{17} -18.0000 q^{18} -139.943 q^{19} +58.9983 q^{20} -21.0000 q^{21} -84.6554 q^{22} +23.0000 q^{23} -24.0000 q^{24} +92.5498 q^{25} -20.1318 q^{26} +27.0000 q^{27} -28.0000 q^{28} +2.32129 q^{29} -88.4974 q^{30} +185.559 q^{31} -32.0000 q^{32} +126.983 q^{33} -261.414 q^{34} -103.247 q^{35} +36.0000 q^{36} -308.021 q^{37} +279.887 q^{38} +30.1978 q^{39} -117.997 q^{40} +472.360 q^{41} +42.0000 q^{42} +251.681 q^{43} +169.311 q^{44} +132.746 q^{45} -46.0000 q^{46} -526.215 q^{47} +48.0000 q^{48} +49.0000 q^{49} -185.100 q^{50} +392.121 q^{51} +40.2637 q^{52} +525.179 q^{53} -54.0000 q^{54} +624.315 q^{55} +56.0000 q^{56} -419.830 q^{57} -4.64258 q^{58} -384.942 q^{59} +176.995 q^{60} +720.848 q^{61} -371.119 q^{62} -63.0000 q^{63} +64.0000 q^{64} +148.468 q^{65} -253.966 q^{66} -110.487 q^{67} +522.829 q^{68} +69.0000 q^{69} +206.494 q^{70} +547.595 q^{71} -72.0000 q^{72} -516.277 q^{73} +616.042 q^{74} +277.649 q^{75} -559.774 q^{76} -296.294 q^{77} -60.3955 q^{78} -636.314 q^{79} +235.993 q^{80} +81.0000 q^{81} -944.721 q^{82} -372.514 q^{83} -84.0000 q^{84} +1927.87 q^{85} -503.362 q^{86} +6.96388 q^{87} -338.622 q^{88} -638.709 q^{89} -265.492 q^{90} -70.4614 q^{91} +92.0000 q^{92} +556.678 q^{93} +1052.43 q^{94} -2064.10 q^{95} -96.0000 q^{96} -481.847 q^{97} -98.0000 q^{98} +380.949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} - 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 - 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} + 15 q^{3} + 20 q^{4} - 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} + 18 q^{11} + 60 q^{12} - 22 q^{13} + 70 q^{14} + 80 q^{16} + 44 q^{17} - 90 q^{18} - 14 q^{19} - 105 q^{21} - 36 q^{22} + 115 q^{23} - 120 q^{24} + 43 q^{25} + 44 q^{26} + 135 q^{27} - 140 q^{28} - 39 q^{29} - 100 q^{31} - 160 q^{32} + 54 q^{33} - 88 q^{34} + 180 q^{36} + 255 q^{37} + 28 q^{38} - 66 q^{39} + 69 q^{41} + 210 q^{42} + 912 q^{43} + 72 q^{44} - 230 q^{46} - 319 q^{47} + 240 q^{48} + 245 q^{49} - 86 q^{50} + 132 q^{51} - 88 q^{52} + 745 q^{53} - 270 q^{54} + 2199 q^{55} + 280 q^{56} - 42 q^{57} + 78 q^{58} - 315 q^{59} + 1091 q^{61} + 200 q^{62} - 315 q^{63} + 320 q^{64} + 533 q^{65} - 108 q^{66} + 991 q^{67} + 176 q^{68} + 345 q^{69} + 923 q^{71} - 360 q^{72} + 1144 q^{73} - 510 q^{74} + 129 q^{75} - 56 q^{76} - 126 q^{77} + 132 q^{78} - 110 q^{79} + 405 q^{81} - 138 q^{82} + 218 q^{83} - 420 q^{84} + 2973 q^{85} - 1824 q^{86} - 117 q^{87} - 144 q^{88} - 13 q^{89} + 154 q^{91} + 460 q^{92} - 300 q^{93} + 638 q^{94} - 347 q^{95} - 480 q^{96} + 761 q^{97} - 490 q^{98} + 162 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 + 15 * q^3 + 20 * q^4 - 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 + 18 * q^11 + 60 * q^12 - 22 * q^13 + 70 * q^14 + 80 * q^16 + 44 * q^17 - 90 * q^18 - 14 * q^19 - 105 * q^21 - 36 * q^22 + 115 * q^23 - 120 * q^24 + 43 * q^25 + 44 * q^26 + 135 * q^27 - 140 * q^28 - 39 * q^29 - 100 * q^31 - 160 * q^32 + 54 * q^33 - 88 * q^34 + 180 * q^36 + 255 * q^37 + 28 * q^38 - 66 * q^39 + 69 * q^41 + 210 * q^42 + 912 * q^43 + 72 * q^44 - 230 * q^46 - 319 * q^47 + 240 * q^48 + 245 * q^49 - 86 * q^50 + 132 * q^51 - 88 * q^52 + 745 * q^53 - 270 * q^54 + 2199 * q^55 + 280 * q^56 - 42 * q^57 + 78 * q^58 - 315 * q^59 + 1091 * q^61 + 200 * q^62 - 315 * q^63 + 320 * q^64 + 533 * q^65 - 108 * q^66 + 991 * q^67 + 176 * q^68 + 345 * q^69 + 923 * q^71 - 360 * q^72 + 1144 * q^73 - 510 * q^74 + 129 * q^75 - 56 * q^76 - 126 * q^77 + 132 * q^78 - 110 * q^79 + 405 * q^81 - 138 * q^82 + 218 * q^83 - 420 * q^84 + 2973 * q^85 - 1824 * q^86 - 117 * q^87 - 144 * q^88 - 13 * q^89 + 154 * q^91 + 460 * q^92 - 300 * q^93 + 638 * q^94 - 347 * q^95 - 480 * q^96 + 761 * q^97 - 490 * q^98 + 162 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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