LMFDB - Embedded newform 2442.4.a.n.1.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2442,4,Mod(1,2442)] 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("2442.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2442, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 2442 = 2 \cdot 3 \cdot 11 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2442.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,-24,-36,48,-10] 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:	$144.082664234$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 849 x^{10} + 1205 x^{9} + 248360 x^{8} - 397682 x^{7} - 29936318 x^{6} + \cdots - 37088275010 $ x^12 - 2x^11 - 849x^10 + 1205x^9 + 248360x^8 - 397682x^7 - 29936318x^6 + 69190668x^5 + 1339839809x^4 - 4379648628x^3 - 15280838921x^2 + 65348896151*x - 37088275010
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$20.6786$ of defining polynomial
Character	$\chi$	$=$	2442.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +19.6786 q^{5} +6.00000 q^{6} -7.62338 q^{7} -8.00000 q^{8} +9.00000 q^{9} -39.3573 q^{10} +11.0000 q^{11} -12.0000 q^{12} -44.5633 q^{13} +15.2468 q^{14} -59.0359 q^{15} +16.0000 q^{16} -128.543 q^{17} -18.0000 q^{18} -59.7027 q^{19} +78.7145 q^{20} +22.8701 q^{21} -22.0000 q^{22} +129.457 q^{23} +24.0000 q^{24} +262.248 q^{25} +89.1267 q^{26} -27.0000 q^{27} -30.4935 q^{28} +176.065 q^{29} +118.072 q^{30} +82.8831 q^{31} -32.0000 q^{32} -33.0000 q^{33} +257.086 q^{34} -150.018 q^{35} +36.0000 q^{36} -37.0000 q^{37} +119.405 q^{38} +133.690 q^{39} -157.429 q^{40} +109.674 q^{41} -45.7403 q^{42} -189.963 q^{43} +44.0000 q^{44} +177.108 q^{45} -258.914 q^{46} +180.860 q^{47} -48.0000 q^{48} -284.884 q^{49} -524.497 q^{50} +385.629 q^{51} -178.253 q^{52} +126.628 q^{53} +54.0000 q^{54} +216.465 q^{55} +60.9870 q^{56} +179.108 q^{57} -352.131 q^{58} +71.2303 q^{59} -236.144 q^{60} +808.643 q^{61} -165.766 q^{62} -68.6104 q^{63} +64.0000 q^{64} -876.945 q^{65} +66.0000 q^{66} -988.947 q^{67} -514.172 q^{68} -388.371 q^{69} +300.035 q^{70} -122.744 q^{71} -72.0000 q^{72} -1011.42 q^{73} +74.0000 q^{74} -786.745 q^{75} -238.811 q^{76} -83.8571 q^{77} -267.380 q^{78} -64.1711 q^{79} +314.858 q^{80} +81.0000 q^{81} -219.347 q^{82} +877.672 q^{83} +91.4805 q^{84} -2529.55 q^{85} +379.925 q^{86} -528.196 q^{87} -88.0000 q^{88} +337.503 q^{89} -354.215 q^{90} +339.723 q^{91} +517.828 q^{92} -248.649 q^{93} -361.720 q^{94} -1174.87 q^{95} +96.0000 q^{96} -788.180 q^{97} +569.768 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{2} - 36 q^{3} + 48 q^{4} - 10 q^{5} + 72 q^{6} - 25 q^{7} - 96 q^{8} + 108 q^{9} + 20 q^{10} + 132 q^{11} - 144 q^{12} + 12 q^{13} + 50 q^{14} + 30 q^{15} + 192 q^{16} - 10 q^{17} - 216 q^{18}+ \cdots + 1188 q^{99}+O(q^{100}) $ 12 * q - 24 * q^2 - 36 * q^3 + 48 * q^4 - 10 * q^5 + 72 * q^6 - 25 * q^7 - 96 * q^8 + 108 * q^9 + 20 * q^10 + 132 * q^11 - 144 * q^12 + 12 * q^13 + 50 * q^14 + 30 * q^15 + 192 * q^16 - 10 * q^17 - 216 * q^18 - 9 * q^19 - 40 * q^20 + 75 * q^21 - 264 * q^22 - 201 * q^23 + 288 * q^24 + 210 * q^25 - 24 * q^26 - 324 * q^27 - 100 * q^28 - 84 * q^29 - 60 * q^30 + 10 * q^31 - 384 * q^32 - 396 * q^33 + 20 * q^34 - 565 * q^35 + 432 * q^36 - 444 * q^37 + 18 * q^38 - 36 * q^39 + 80 * q^40 + 215 * q^41 - 150 * q^42 - 434 * q^43 + 528 * q^44 - 90 * q^45 + 402 * q^46 - 256 * q^47 - 576 * q^48 + 519 * q^49 - 420 * q^50 + 30 * q^51 + 48 * q^52 - 448 * q^53 + 648 * q^54 - 110 * q^55 + 200 * q^56 + 27 * q^57 + 168 * q^58 - 588 * q^59 + 120 * q^60 + 735 * q^61 - 20 * q^62 - 225 * q^63 + 768 * q^64 - 859 * q^65 + 792 * q^66 - 288 * q^67 - 40 * q^68 + 603 * q^69 + 1130 * q^70 + 1019 * q^71 - 864 * q^72 - 309 * q^73 + 888 * q^74 - 630 * q^75 - 36 * q^76 - 275 * q^77 + 72 * q^78 + 1116 * q^79 - 160 * q^80 + 972 * q^81 - 430 * q^82 - 662 * q^83 + 300 * q^84 + 1093 * q^85 + 868 * q^86 + 252 * q^87 - 1056 * q^88 + 1603 * q^89 + 180 * q^90 + 1502 * q^91 - 804 * q^92 - 30 * q^93 + 512 * q^94 - 2017 * q^95 + 1152 * q^96 + 349 * q^97 - 1038 * q^98 + 1188 * 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
$5$	19.6786	1.76011	0.880055	−	0.474872i	$-0.157506\pi$
$5$	19.6786	1.76011	0.880055	+	0.474872i	$0.157506\pi$
$6$	6.00000	0.408248
$7$	−7.62338	−0.411624	−0.205812	−	0.978592i	$-0.565983\pi$
$7$	−7.62338	−0.411624	−0.205812	+	0.978592i	$0.565983\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−39.3573	−1.24459
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−12.0000	−0.288675
$13$	−44.5633	−0.950742	−0.475371	−	0.879785i	$-0.657686\pi$
$13$	−44.5633	−0.950742	−0.475371	+	0.879785i	$0.657686\pi$
$14$	15.2468	0.291062
$15$	−59.0359	−1.01620
$16$	16.0000	0.250000
$17$	−128.543	−1.83390	−0.916950	−	0.399003i	$-0.869356\pi$
$17$	−128.543	−1.83390	−0.916950	+	0.399003i	$0.869356\pi$
$18$	−18.0000	−0.235702
$19$	−59.7027	−0.720881	−0.360440	−	0.932782i	$-0.617374\pi$
$19$	−59.7027	−0.720881	−0.360440	+	0.932782i	$0.617374\pi$
$20$	78.7145	0.880055
$21$	22.8701	0.237651
$22$	−22.0000	−0.213201
$23$	129.457	1.17364	0.586818	−	0.809719i	$-0.300380\pi$
$23$	129.457	1.17364	0.586818	+	0.809719i	$0.300380\pi$
$24$	24.0000	0.204124
$25$	262.248	2.09799
$26$	89.1267	0.672276
$27$	−27.0000	−0.192450
$28$	−30.4935	−0.205812
$29$	176.065	1.12740	0.563698	−	0.825981i	$-0.309378\pi$
$29$	176.065	1.12740	0.563698	+	0.825981i	$0.309378\pi$
$30$	118.072	0.718562
$31$	82.8831	0.480201	0.240101	−	0.970748i	$-0.422820\pi$
$31$	82.8831	0.480201	0.240101	+	0.970748i	$0.422820\pi$
$32$	−32.0000	−0.176777
$33$	−33.0000	−0.174078
$34$	257.086	1.29676
$35$	−150.018	−0.724503
$36$	36.0000	0.166667
$37$	−37.0000	−0.164399
$37$	−37.0000	−0.164399
$38$	119.405	0.509740
$39$	133.690	0.548911
$40$	−157.429	−0.622293
$41$	109.674	0.417759	0.208880	−	0.977941i	$-0.433018\pi$
$41$	109.674	0.417759	0.208880	+	0.977941i	$0.433018\pi$
$42$	−45.7403	−0.168045
$43$	−189.963	−0.673699	−0.336849	−	0.941559i	$-0.609361\pi$
$43$	−189.963	−0.673699	−0.336849	+	0.941559i	$0.609361\pi$
$44$	44.0000	0.150756
$45$	177.108	0.586703
$46$	−258.914	−0.829886
$47$	180.860	0.561301	0.280650	−	0.959810i	$-0.409450\pi$
$47$	180.860	0.561301	0.280650	+	0.959810i	$0.409450\pi$
$48$	−48.0000	−0.144338
$49$	−284.884	−0.830566
$50$	−524.497	−1.48350
$51$	385.629	1.05880
$52$	−178.253	−0.475371
$53$	126.628	0.328183	0.164092	−	0.986445i	$-0.447531\pi$
$53$	126.628	0.328183	0.164092	+	0.986445i	$0.447531\pi$
$54$	54.0000	0.136083
$55$	216.465	0.530693
$56$	60.9870	0.145531
$57$	179.108	0.416201
$58$	−352.131	−0.797190
$59$	71.2303	0.157176	0.0785881	−	0.996907i	$-0.474959\pi$
$59$	71.2303	0.157176	0.0785881	+	0.996907i	$0.474959\pi$
$60$	−236.144	−0.508100
$61$	808.643	1.69731	0.848657	−	0.528944i	$-0.177412\pi$
$61$	808.643	1.69731	0.848657	+	0.528944i	$0.177412\pi$
$62$	−165.766	−0.339554
$63$	−68.6104	−0.137208
$64$	64.0000	0.125000
$65$	−876.945	−1.67341
$66$	66.0000	0.123091
$67$	−988.947	−1.80327	−0.901635	−	0.432498i	$-0.857632\pi$
$67$	−988.947	−1.80327	−0.901635	+	0.432498i	$0.857632\pi$
$68$	−514.172	−0.916950
$69$	−388.371	−0.677599
$70$	300.035	0.512301
$71$	−122.744	−0.205170	−0.102585	−	0.994724i	$-0.532711\pi$
$71$	−122.744	−0.205170	−0.102585	+	0.994724i	$0.532711\pi$
$72$	−72.0000	−0.117851
$73$	−1011.42	−1.62161	−0.810807	−	0.585314i	$-0.800971\pi$
$73$	−1011.42	−1.62161	−0.810807	+	0.585314i	$0.800971\pi$
$74$	74.0000	0.116248
$75$	−786.745	−1.21127
$76$	−238.811	−0.360440
$77$	−83.8571	−0.124109
$78$	−267.380	−0.388139
$79$	−64.1711	−0.0913900	−0.0456950	−	0.998955i	$-0.514550\pi$
$79$	−64.1711	−0.0913900	−0.0456950	+	0.998955i	$0.514550\pi$
$80$	314.858	0.440027
$81$	81.0000	0.111111
$82$	−219.347	−0.295401
$83$	877.672	1.16069	0.580344	−	0.814372i	$-0.302918\pi$
$83$	877.672	1.16069	0.580344	+	0.814372i	$0.302918\pi$
$84$	91.4805	0.118825
$85$	−2529.55	−3.22786
$86$	379.925	0.476377
$87$	−528.196	−0.650903
$88$	−88.0000	−0.106600
$89$	337.503	0.401969	0.200985	−	0.979594i	$-0.435586\pi$
$89$	337.503	0.401969	0.200985	+	0.979594i	$0.435586\pi$
$90$	−354.215	−0.414862
$91$	339.723	0.391348
$92$	517.828	0.586818
$93$	−248.649	−0.277244
$94$	−361.720	−0.396899
$95$	−1174.87	−1.26883
$96$	96.0000	0.102062
$97$	−788.180	−0.825027	−0.412513	−	0.910952i	$-0.635349\pi$
$97$	−788.180	−0.825027	−0.412513	+	0.910952i	$0.635349\pi$
$98$	569.768	0.587299
$99$	99.0000	0.100504
$100$	1048.99	1.04899
$101$	−650.997	−0.641352	−0.320676	−	0.947189i	$-0.603910\pi$
$101$	−650.997	−0.641352	−0.320676	+	0.947189i	$0.603910\pi$
$102$	−771.259	−0.748686
$103$	−1879.07	−1.79758	−0.898789	−	0.438382i	$-0.855552\pi$
$103$	−1879.07	−1.79758	−0.898789	+	0.438382i	$0.855552\pi$
$104$	356.507	0.336138
$105$	450.053	0.418292
$106$	−253.256	−0.232061
$107$	−1680.80	−1.51859	−0.759293	−	0.650749i	$-0.774455\pi$
$107$	−1680.80	−1.51859	−0.759293	+	0.650749i	$0.774455\pi$
$108$	−108.000	−0.0962250
$109$	2030.90	1.78464	0.892318	−	0.451408i	$-0.149078\pi$
$109$	2030.90	1.78464	0.892318	+	0.451408i	$0.149078\pi$
$110$	−432.930	−0.375257
$111$	111.000	0.0949158
$112$	−121.974	−0.102906
$113$	1615.98	1.34530	0.672648	−	0.739962i	$-0.265157\pi$
$113$	1615.98	1.34530	0.672648	+	0.739962i	$0.265157\pi$
$114$	−358.216	−0.294298
$115$	2547.54	2.06573
$116$	704.261	0.563698
$117$	−401.070	−0.316914
$118$	−142.461	−0.111140
$119$	979.932	0.754876
$120$	472.287	0.359281
$121$	121.000	0.0909091
$122$	−1617.29	−1.20018
$123$	−329.021	−0.241194
$124$	331.532	0.240101
$125$	2700.86	1.93258
$126$	137.221	0.0970206
$127$	−299.357	−0.209163	−0.104581	−	0.994516i	$-0.533350\pi$
$127$	−299.357	−0.209163	−0.104581	+	0.994516i	$0.533350\pi$
$128$	−128.000	−0.0883883
$129$	569.888	0.388960
$130$	1753.89	1.18328
$131$	−1839.11	−1.22659	−0.613295	−	0.789854i	$-0.710156\pi$
$131$	−1839.11	−1.22659	−0.613295	+	0.789854i	$0.710156\pi$
$132$	−132.000	−0.0870388
$133$	455.136	0.296732
$134$	1977.89	1.27510
$135$	−531.323	−0.338733
$136$	1028.34	0.648381
$137$	854.792	0.533064	0.266532	−	0.963826i	$-0.414122\pi$
$137$	854.792	0.533064	0.266532	+	0.963826i	$0.414122\pi$
$138$	776.742	0.479135
$139$	−2436.23	−1.48660	−0.743302	−	0.668956i	$-0.766742\pi$
$139$	−2436.23	−1.48660	−0.743302	+	0.668956i	$0.766742\pi$
$140$	−600.070	−0.362251
$141$	−542.580	−0.324067
$142$	245.488	0.145077
$143$	−490.197	−0.286659
$144$	144.000	0.0833333
$145$	3464.72	1.98434
$146$	2022.84	1.14665
$147$	854.652	0.479528
$148$	−148.000	−0.0821995
$149$	696.428	0.382910	0.191455	−	0.981501i	$-0.438679\pi$
$149$	696.428	0.382910	0.191455	+	0.981501i	$0.438679\pi$
$150$	1573.49	0.856500
$151$	−1773.95	−0.956039	−0.478019	−	0.878349i	$-0.658645\pi$
$151$	−1773.95	−0.956039	−0.478019	+	0.878349i	$0.658645\pi$
$152$	477.622	0.254870
$153$	−1156.89	−0.611300
$154$	167.714	0.0877584
$155$	1631.03	0.845207
$156$	534.760	0.274456
$157$	−1203.53	−0.611799	−0.305900	−	0.952064i	$-0.598957\pi$
$157$	−1203.53	−0.611799	−0.305900	+	0.952064i	$0.598957\pi$
$158$	128.342	0.0646225
$159$	−379.885	−0.189477
$160$	−629.716	−0.311146
$161$	−986.899	−0.483097
$162$	−162.000	−0.0785674
$163$	1265.56	0.608137	0.304068	−	0.952650i	$-0.401655\pi$
$163$	1265.56	0.608137	0.304068	+	0.952650i	$0.401655\pi$
$164$	438.694	0.208880
$165$	−649.395	−0.306396
$166$	−1755.34	−0.820730
$167$	1556.80	0.721372	0.360686	−	0.932687i	$-0.382543\pi$
$167$	1556.80	0.721372	0.360686	+	0.932687i	$0.382543\pi$
$168$	−182.961	−0.0840223
$169$	−211.110	−0.0960901
$170$	5059.10	2.28244
$171$	−537.324	−0.240294
$172$	−759.851	−0.336849
$173$	−2217.29	−0.974436	−0.487218	−	0.873280i	$-0.661988\pi$
$173$	−2217.29	−0.974436	−0.487218	+	0.873280i	$0.661988\pi$
$174$	1056.39	0.460258
$175$	−1999.22	−0.863581
$176$	176.000	0.0753778
$177$	−213.691	−0.0907457
$178$	−675.006	−0.284235
$179$	616.369	0.257372	0.128686	−	0.991685i	$-0.458924\pi$
$179$	616.369	0.257372	0.128686	+	0.991685i	$0.458924\pi$
$180$	708.431	0.293352
$181$	−2737.88	−1.12434	−0.562168	−	0.827023i	$-0.690033\pi$
$181$	−2737.88	−1.12434	−0.562168	+	0.827023i	$0.690033\pi$
$182$	−679.446	−0.276725
$183$	−2425.93	−0.979945
$184$	−1035.66	−0.414943
$185$	−728.109	−0.289360
$186$	497.299	0.196041
$187$	−1413.97	−0.552941
$188$	723.440	0.280650
$189$	205.831	0.0792170
$190$	2349.73	0.897198
$191$	1036.43	0.392637	0.196319	−	0.980540i	$-0.437101\pi$
$191$	1036.43	0.392637	0.196319	+	0.980540i	$0.437101\pi$
$192$	−192.000	−0.0721688
$193$	−910.755	−0.339676	−0.169838	−	0.985472i	$-0.554325\pi$
$193$	−910.755	−0.339676	−0.169838	+	0.985472i	$0.554325\pi$
$194$	1576.36	0.583382
$195$	2630.84	0.966144
$196$	−1139.54	−0.415283
$197$	−3935.82	−1.42343	−0.711715	−	0.702468i	$-0.752081\pi$
$197$	−3935.82	−1.42343	−0.711715	+	0.702468i	$0.752081\pi$
$198$	−198.000	−0.0710669
$199$	531.843	0.189454	0.0947270	−	0.995503i	$-0.469802\pi$
$199$	531.843	0.189454	0.0947270	+	0.995503i	$0.469802\pi$
$200$	−2097.99	−0.741750
$201$	2966.84	1.04112
$202$	1301.99	0.453505
$203$	−1342.21	−0.464063
$204$	1542.52	0.529401
$205$	2158.23	0.735303
$206$	3758.14	1.27108
$207$	1165.11	0.391212
$208$	−713.013	−0.237685
$209$	−656.730	−0.217354
$210$	−900.105	−0.295777
$211$	1083.96	0.353662	0.176831	−	0.984241i	$-0.443415\pi$
$211$	1083.96	0.353662	0.176831	+	0.984241i	$0.443415\pi$
$212$	506.513	0.164092
$213$	368.232	0.118455
$214$	3361.59	1.07380
$215$	−3738.20	−1.18578
$216$	216.000	0.0680414
$217$	−631.849	−0.197662
$218$	−4061.81	−1.26193
$219$	3034.26	0.936239
$220$	865.860	0.265347
$221$	5728.31	1.74356
$222$	−222.000	−0.0671156
$223$	3608.94	1.08373	0.541867	−	0.840464i	$-0.317718\pi$
$223$	3608.94	1.08373	0.541867	+	0.840464i	$0.317718\pi$
$224$	243.948	0.0727655
$225$	2360.24	0.699329
$226$	−3231.96	−0.951268
$227$	605.777	0.177123	0.0885613	−	0.996071i	$-0.471773\pi$
$227$	605.777	0.177123	0.0885613	+	0.996071i	$0.471773\pi$
$228$	716.432	0.208100
$229$	208.354	0.0601241	0.0300621	−	0.999548i	$-0.490430\pi$
$229$	208.354	0.0601241	0.0300621	+	0.999548i	$0.490430\pi$
$230$	−5095.07	−1.46069
$231$	251.571	0.0716545
$232$	−1408.52	−0.398595
$233$	−2814.81	−0.791436	−0.395718	−	0.918372i	$-0.629504\pi$
$233$	−2814.81	−0.791436	−0.395718	+	0.918372i	$0.629504\pi$
$234$	802.140	0.224092
$235$	3559.07	0.987951
$236$	284.921	0.0785881
$237$	192.513	0.0527640
$238$	−1959.86	−0.533778
$239$	−3270.08	−0.885038	−0.442519	−	0.896759i	$-0.645915\pi$
$239$	−3270.08	−0.885038	−0.442519	+	0.896759i	$0.645915\pi$
$240$	−944.574	−0.254050
$241$	−2870.78	−0.767317	−0.383658	−	0.923475i	$-0.625336\pi$
$241$	−2870.78	−0.767317	−0.383658	+	0.923475i	$0.625336\pi$
$242$	−242.000	−0.0642824
$243$	−243.000	−0.0641500
$244$	3234.57	0.848657
$245$	−5606.13	−1.46189
$246$	658.042	0.170550
$247$	2660.55	0.685372
$248$	−663.065	−0.169777
$249$	−2633.02	−0.670123
$250$	−5401.72	−1.36654
$251$	−2446.26	−0.615167	−0.307583	−	0.951521i	$-0.599520\pi$
$251$	−2446.26	−0.615167	−0.307583	+	0.951521i	$0.599520\pi$
$252$	−274.442	−0.0686039
$253$	1424.03	0.353865
$254$	598.714	0.147900
$255$	7588.66	1.86361
$256$	256.000	0.0625000
$257$	5897.70	1.43147	0.715736	−	0.698371i	$-0.246091\pi$
$257$	5897.70	1.43147	0.715736	+	0.698371i	$0.246091\pi$
$258$	−1139.78	−0.275036
$259$	282.065	0.0676705
$260$	−3507.78	−0.836705
$261$	1584.59	0.375799
$262$	3678.21	0.867331
$263$	−3942.53	−0.924360	−0.462180	−	0.886786i	$-0.652933\pi$
$263$	−3942.53	−0.924360	−0.462180	+	0.886786i	$0.652933\pi$
$264$	264.000	0.0615457
$265$	2491.87	0.577639
$266$	−910.272	−0.209821
$267$	−1012.51	−0.232077
$268$	−3955.79	−0.901635
$269$	−1688.86	−0.382794	−0.191397	−	0.981513i	$-0.561302\pi$
$269$	−1688.86	−0.382794	−0.191397	+	0.981513i	$0.561302\pi$
$270$	1062.65	0.239521
$271$	4918.72	1.10255	0.551274	−	0.834324i	$-0.314142\pi$
$271$	4918.72	1.10255	0.551274	+	0.834324i	$0.314142\pi$
$272$	−2056.69	−0.458475
$273$	−1019.17	−0.225945
$274$	−1709.58	−0.376933
$275$	2884.73	0.632567
$276$	−1553.48	−0.338800
$277$	−8139.00	−1.76543	−0.882717	−	0.469906i	$-0.844288\pi$
$277$	−8139.00	−1.76543	−0.882717	+	0.469906i	$0.844288\pi$
$278$	4872.45	1.05119
$279$	745.948	0.160067
$280$	1200.14	0.256150
$281$	3013.65	0.639785	0.319892	−	0.947454i	$-0.396353\pi$
$281$	3013.65	0.639785	0.319892	+	0.947454i	$0.396353\pi$
$282$	1085.16	0.229150
$283$	439.255	0.0922650	0.0461325	−	0.998935i	$-0.485310\pi$
$283$	439.255	0.0922650	0.0461325	+	0.998935i	$0.485310\pi$
$284$	−490.977	−0.102585
$285$	3524.60	0.732559
$286$	980.393	0.202699
$287$	−836.083	−0.171960
$288$	−288.000	−0.0589256
$289$	11610.3	2.36319
$290$	−6929.45	−1.40314
$291$	2364.54	0.476329
$292$	−4045.68	−0.810807
$293$	12.5754	0.00250738	0.00125369	−	0.999999i	$-0.499601\pi$
$293$	12.5754	0.00250738	0.00125369	+	0.999999i	$0.499601\pi$
$294$	−1709.30	−0.339077
$295$	1401.71	0.276647
$296$	296.000	0.0581238
$297$	−297.000	−0.0580259
$298$	−1392.86	−0.270758
$299$	−5769.03	−1.11583
$300$	−3146.98	−0.605637
$301$	1448.16	0.277310
$302$	3547.90	0.676022
$303$	1952.99	0.370285
$304$	−955.243	−0.180220
$305$	15913.0	2.98746
$306$	2313.78	0.432254
$307$	7167.37	1.33245	0.666227	−	0.745749i	$-0.267908\pi$
$307$	7167.37	1.33245	0.666227	+	0.745749i	$0.267908\pi$
$308$	−335.429	−0.0620546
$309$	5637.22	1.03783
$310$	−3262.05	−0.597652
$311$	−5266.79	−0.960297	−0.480149	−	0.877187i	$-0.659417\pi$
$311$	−5266.79	−0.960297	−0.480149	+	0.877187i	$0.659417\pi$
$312$	−1069.52	−0.194069
$313$	−1484.46	−0.268071	−0.134036	−	0.990976i	$-0.542794\pi$
$313$	−1484.46	−0.268071	−0.134036	+	0.990976i	$0.542794\pi$
$314$	2407.07	0.432607
$315$	−1350.16	−0.241501
$316$	−256.684	−0.0456950
$317$	−1932.38	−0.342377	−0.171189	−	0.985238i	$-0.554761\pi$
$317$	−1932.38	−0.342377	−0.171189	+	0.985238i	$0.554761\pi$
$318$	759.769	0.133980
$319$	1936.72	0.339923
$320$	1259.43	0.220014
$321$	5042.39	0.876756
$322$	1973.80	0.341601
$323$	7674.37	1.32202
$324$	324.000	0.0555556
$325$	−11686.7	−1.99464
$326$	−2531.12	−0.430018
$327$	−6092.71	−1.03036
$328$	−877.389	−0.147700
$329$	−1378.76	−0.231045
$330$	1298.79	0.216655
$331$	−5496.59	−0.912749	−0.456375	−	0.889788i	$-0.650852\pi$
$331$	−5496.59	−0.912749	−0.456375	+	0.889788i	$0.650852\pi$
$332$	3510.69	0.580344
$333$	−333.000	−0.0547997
$334$	−3113.61	−0.510087
$335$	−19461.1	−3.17395
$336$	365.922	0.0594127
$337$	−4874.51	−0.787928	−0.393964	−	0.919126i	$-0.628896\pi$
$337$	−4874.51	−0.787928	−0.393964	+	0.919126i	$0.628896\pi$
$338$	422.220	0.0679459
$339$	−4847.94	−0.776707
$340$	−10118.2	−1.61393
$341$	911.714	0.144786
$342$	1074.65	0.169913
$343$	4786.60	0.753504
$344$	1519.70	0.238188
$345$	−7642.61	−1.19265
$346$	4434.58	0.689031
$347$	−4328.38	−0.669624	−0.334812	−	0.942285i	$-0.608673\pi$
$347$	−4328.38	−0.669624	−0.334812	+	0.942285i	$0.608673\pi$
$348$	−2112.78	−0.325451
$349$	2008.31	0.308030	0.154015	−	0.988068i	$-0.450780\pi$
$349$	2008.31	0.308030	0.154015	+	0.988068i	$0.450780\pi$
$350$	3998.44	0.610644
$351$	1203.21	0.182970
$352$	−352.000	−0.0533002
$353$	11928.1	1.79849	0.899247	−	0.437441i	$-0.144115\pi$
$353$	11928.1	1.79849	0.899247	+	0.437441i	$0.144115\pi$
$354$	427.382	0.0641669
$355$	−2415.44	−0.361121
$356$	1350.01	0.200985
$357$	−2939.80	−0.435828
$358$	−1232.74	−0.181990
$359$	−12349.1	−1.81549	−0.907744	−	0.419524i	$-0.862197\pi$
$359$	−12349.1	−1.81549	−0.907744	+	0.419524i	$0.862197\pi$
$360$	−1416.86	−0.207431
$361$	−3294.59	−0.480331
$362$	5475.76	0.795026
$363$	−363.000	−0.0524864
$364$	1358.89	0.195674
$365$	−19903.4	−2.85422
$366$	4851.86	0.692925
$367$	−10206.3	−1.45167	−0.725835	−	0.687869i	$-0.758546\pi$
$367$	−10206.3	−1.45167	−0.725835	+	0.687869i	$0.758546\pi$
$368$	2071.31	0.293409
$369$	987.062	0.139253
$370$	1456.22	0.204609
$371$	−965.334	−0.135088
$372$	−994.597	−0.138622
$373$	3585.24	0.497686	0.248843	−	0.968544i	$-0.419950\pi$
$373$	3585.24	0.497686	0.248843	+	0.968544i	$0.419950\pi$
$374$	2827.95	0.390989
$375$	−8102.58	−1.11577
$376$	−1446.88	−0.198450
$377$	−7846.06	−1.07186
$378$	−411.662	−0.0560149
$379$	−1892.67	−0.256516	−0.128258	−	0.991741i	$-0.540939\pi$
$379$	−1892.67	−0.256516	−0.128258	+	0.991741i	$0.540939\pi$
$380$	−4699.47	−0.634415
$381$	898.071	0.120760
$382$	−2072.87	−0.277637
$383$	−5467.33	−0.729419	−0.364710	−	0.931121i	$-0.618832\pi$
$383$	−5467.33	−0.729419	−0.364710	+	0.931121i	$0.618832\pi$
$384$	384.000	0.0510310
$385$	−1650.19	−0.218446
$386$	1821.51	0.240187
$387$	−1709.66	−0.224566
$388$	−3152.72	−0.412513
$389$	−10091.5	−1.31532	−0.657661	−	0.753314i	$-0.728454\pi$
$389$	−10091.5	−1.31532	−0.657661	+	0.753314i	$0.728454\pi$
$390$	−5261.67	−0.683167
$391$	−16640.8	−2.15233
$392$	2279.07	0.293649
$393$	5517.32	0.708173
$394$	7871.65	1.00652
$395$	−1262.80	−0.160856
$396$	396.000	0.0502519
$397$	−5008.53	−0.633176	−0.316588	−	0.948563i	$-0.602537\pi$
$397$	−5008.53	−0.633176	−0.316588	+	0.948563i	$0.602537\pi$
$398$	−1063.69	−0.133964
$399$	−1365.41	−0.171318
$400$	4195.97	0.524497
$401$	−9436.86	−1.17520	−0.587599	−	0.809153i	$-0.699927\pi$
$401$	−9436.86	−1.17520	−0.587599	+	0.809153i	$0.699927\pi$
$402$	−5933.68	−0.736182
$403$	−3693.55	−0.456547
$404$	−2603.99	−0.320676
$405$	1593.97	0.195568
$406$	2684.42	0.328142
$407$	−407.000	−0.0495682
$408$	−3085.03	−0.374343
$409$	7545.40	0.912215	0.456108	−	0.889925i	$-0.349243\pi$
$409$	7545.40	0.912215	0.456108	+	0.889925i	$0.349243\pi$
$410$	−4316.45	−0.519937
$411$	−2564.38	−0.307765
$412$	−7516.29	−0.898789
$413$	−543.015	−0.0646974
$414$	−2330.23	−0.276629
$415$	17271.4	2.04294
$416$	1426.03	0.168069
$417$	7308.68	0.858292
$418$	1313.46	0.153692
$419$	−4840.78	−0.564409	−0.282204	−	0.959354i	$-0.591066\pi$
$419$	−4840.78	−0.564409	−0.282204	+	0.959354i	$0.591066\pi$
$420$	1800.21	0.209146
$421$	5644.79	0.653469	0.326735	−	0.945116i	$-0.394052\pi$
$421$	5644.79	0.653469	0.326735	+	0.945116i	$0.394052\pi$
$422$	−2167.92	−0.250077
$423$	1627.74	0.187100
$424$	−1013.03	−0.116030
$425$	−33710.2	−3.84750
$426$	−736.465	−0.0837602
$427$	−6164.59	−0.698654
$428$	−6723.19	−0.759293
$429$	1470.59	0.165503
$430$	7476.41	0.838476
$431$	−13712.7	−1.53252	−0.766260	−	0.642530i	$-0.777885\pi$
$431$	−13712.7	−1.53252	−0.766260	+	0.642530i	$0.777885\pi$
$432$	−432.000	−0.0481125
$433$	853.426	0.0947183	0.0473591	−	0.998878i	$-0.484919\pi$
$433$	853.426	0.0947183	0.0473591	+	0.998878i	$0.484919\pi$
$434$	1263.70	0.139768
$435$	−10394.2	−1.14566
$436$	8123.61	0.892318
$437$	−7728.93	−0.846052
$438$	−6068.52	−0.662021
$439$	9836.18	1.06937	0.534687	−	0.845050i	$-0.320430\pi$
$439$	9836.18	1.06937	0.534687	+	0.845050i	$0.320430\pi$
$440$	−1731.72	−0.187628
$441$	−2563.96	−0.276855
$442$	−11456.6	−1.23289
$443$	10273.2	1.10180	0.550899	−	0.834572i	$-0.314285\pi$
$443$	10273.2	1.10180	0.550899	+	0.834572i	$0.314285\pi$
$444$	444.000	0.0474579
$445$	6641.60	0.707510
$446$	−7217.88	−0.766315
$447$	−2089.28	−0.221073
$448$	−487.896	−0.0514529
$449$	−12358.0	−1.29891	−0.649456	−	0.760399i	$-0.725003\pi$
$449$	−12358.0	−1.29891	−0.649456	+	0.760399i	$0.725003\pi$
$450$	−4720.47	−0.494500
$451$	1206.41	0.125959
$452$	6463.91	0.672648
$453$	5321.85	0.551969
$454$	−1211.55	−0.125245
$455$	6685.28	0.688815
$456$	−1432.86	−0.147149
$457$	4803.00	0.491630	0.245815	−	0.969317i	$-0.420944\pi$
$457$	4803.00	0.491630	0.245815	+	0.969317i	$0.420944\pi$
$458$	−416.708	−0.0425142
$459$	3470.66	0.352934
$460$	10190.1	1.03286
$461$	11574.5	1.16936	0.584682	−	0.811263i	$-0.301219\pi$
$461$	11574.5	1.16936	0.584682	+	0.811263i	$0.301219\pi$
$462$	−503.143	−0.0506674
$463$	−12838.1	−1.28864	−0.644318	−	0.764758i	$-0.722858\pi$
$463$	−12838.1	−1.28864	−0.644318	+	0.764758i	$0.722858\pi$
$464$	2817.04	0.281849
$465$	−4893.08	−0.487981
$466$	5629.62	0.559629
$467$	−13745.1	−1.36199	−0.680994	−	0.732289i	$-0.738452\pi$
$467$	−13745.1	−1.36199	−0.680994	+	0.732289i	$0.738452\pi$
$468$	−1604.28	−0.158457
$469$	7539.11	0.742269
$470$	−7118.15	−0.698587
$471$	3610.60	0.353222
$472$	−569.842	−0.0555702
$473$	−2089.59	−0.203128
$474$	−385.026	−0.0373098
$475$	−15656.9	−1.51240
$476$	3919.73	0.377438
$477$	1139.65	0.109394
$478$	6540.16	0.625816
$479$	−9500.67	−0.906256	−0.453128	−	0.891445i	$-0.649692\pi$
$479$	−9500.67	−0.906256	−0.453128	+	0.891445i	$0.649692\pi$
$480$	1889.15	0.179640
$481$	1648.84	0.156301
$482$	5741.56	0.542575
$483$	2960.70	0.278916
$484$	484.000	0.0454545
$485$	−15510.3	−1.45214
$486$	486.000	0.0453609
$487$	−10163.7	−0.945710	−0.472855	−	0.881140i	$-0.656777\pi$
$487$	−10163.7	−0.945710	−0.472855	+	0.881140i	$0.656777\pi$
$488$	−6469.15	−0.600091
$489$	−3796.68	−0.351108
$490$	11212.3	1.03371
$491$	−9197.61	−0.845382	−0.422691	−	0.906274i	$-0.638914\pi$
$491$	−9197.61	−0.845382	−0.422691	+	0.906274i	$0.638914\pi$
$492$	−1316.08	−0.120597
$493$	−22632.0	−2.06753
$494$	−5321.10	−0.484631
$495$	1948.18	0.176898
$496$	1326.13	0.120050
$497$	935.725	0.0844527
$498$	5266.03	0.473849
$499$	12568.2	1.12751	0.563756	−	0.825941i	$-0.309356\pi$
$499$	12568.2	1.12751	0.563756	+	0.825941i	$0.309356\pi$
$500$	10803.4	0.966289
$501$	−4670.41	−0.416484
$502$	4892.53	0.434989
$503$	15386.9	1.36395	0.681974	−	0.731376i	$-0.261122\pi$
$503$	15386.9	1.36395	0.681974	+	0.731376i	$0.261122\pi$
$504$	548.883	0.0485103
$505$	−12810.7	−1.12885
$506$	−2848.05	−0.250220
$507$	633.330	0.0554776
$508$	−1197.43	−0.104581
$509$	−896.573	−0.0780745	−0.0390372	−	0.999238i	$-0.512429\pi$
$509$	−896.573	−0.0780745	−0.0390372	+	0.999238i	$0.512429\pi$
$510$	−15177.3	−1.31777
$511$	7710.44	0.667494
$512$	−512.000	−0.0441942
$513$	1611.97	0.138734
$514$	−11795.4	−1.01220
$515$	−36977.6	−3.16393
$516$	2279.55	0.194480
$517$	1989.46	0.169239
$518$	−564.130	−0.0478503
$519$	6651.87	0.562591
$520$	7015.56	0.591640
$521$	11113.4	0.934526	0.467263	−	0.884118i	$-0.345240\pi$
$521$	11113.4	0.934526	0.467263	+	0.884118i	$0.345240\pi$
$522$	−3169.18	−0.265730
$523$	3046.49	0.254711	0.127355	−	0.991857i	$-0.459351\pi$
$523$	3046.49	0.254711	0.127355	+	0.991857i	$0.459351\pi$
$524$	−7356.42	−0.613295
$525$	5997.65	0.498589
$526$	7885.06	0.653621
$527$	−10654.0	−0.880641
$528$	−528.000	−0.0435194
$529$	4592.11	0.377423
$530$	−4983.74	−0.408452
$531$	641.073	0.0523921
$532$	1820.54	0.148366
$533$	−4887.42	−0.397181
$534$	2025.02	0.164103
$535$	−33075.8	−2.67288
$536$	7911.58	0.637552
$537$	−1849.11	−0.148594
$538$	3377.72	0.270676
$539$	−3133.73	−0.250425
$540$	−2125.29	−0.169367
$541$	−4054.27	−0.322194	−0.161097	−	0.986939i	$-0.551503\pi$
$541$	−4054.27	−0.322194	−0.161097	+	0.986939i	$0.551503\pi$
$542$	−9837.43	−0.779620
$543$	8213.64	0.649136
$544$	4113.38	0.324191
$545$	39965.4	3.14115
$546$	2038.34	0.159767
$547$	−17601.1	−1.37581	−0.687906	−	0.725799i	$-0.741470\pi$
$547$	−17601.1	−1.37581	−0.687906	+	0.725799i	$0.741470\pi$
$548$	3419.17	0.266532
$549$	7277.79	0.565771
$550$	−5769.46	−0.447292
$551$	−10511.6	−0.812719
$552$	3106.97	0.239568
$553$	489.200	0.0376183
$554$	16278.0	1.24835
$555$	2184.33	0.167062
$556$	−9744.91	−0.743302
$557$	18422.1	1.40138	0.700691	−	0.713465i	$-0.252875\pi$
$557$	18422.1	1.40138	0.700691	+	0.713465i	$0.252875\pi$
$558$	−1491.90	−0.113185
$559$	8465.37	0.640513
$560$	−2400.28	−0.181126
$561$	4241.92	0.319241
$562$	−6027.31	−0.452396
$563$	−16043.3	−1.20096	−0.600482	−	0.799638i	$-0.705025\pi$
$563$	−16043.3	−1.20096	−0.600482	+	0.799638i	$0.705025\pi$
$564$	−2170.32	−0.162034
$565$	31800.2	2.36787
$566$	−878.510	−0.0652412
$567$	−617.493	−0.0457360
$568$	981.953	0.0725385
$569$	13106.4	0.965641	0.482821	−	0.875719i	$-0.339612\pi$
$569$	13106.4	0.965641	0.482821	+	0.875719i	$0.339612\pi$
$570$	−7049.20	−0.517998
$571$	−16227.9	−1.18934	−0.594671	−	0.803969i	$-0.702718\pi$
$571$	−16227.9	−1.18934	−0.594671	+	0.803969i	$0.702718\pi$
$572$	−1960.79	−0.143330
$573$	−3109.30	−0.226689
$574$	1672.17	0.121594
$575$	33949.9	2.46227
$576$	576.000	0.0416667
$577$	9933.42	0.716696	0.358348	−	0.933588i	$-0.383340\pi$
$577$	9933.42	0.716696	0.358348	+	0.933588i	$0.383340\pi$
$578$	−23220.7	−1.67102
$579$	2732.26	0.196112
$580$	13858.9	0.992171
$581$	−6690.82	−0.477766
$582$	−4729.08	−0.336816
$583$	1392.91	0.0989510
$584$	8091.36	0.573327
$585$	−7892.51	−0.557803
$586$	−25.1508	−0.00177299
$587$	−24494.9	−1.72234	−0.861170	−	0.508317i	$-0.830268\pi$
$587$	−24494.9	−1.72234	−0.861170	+	0.508317i	$0.830268\pi$
$588$	3418.61	0.239764
$589$	−4948.34	−0.346168
$590$	−2803.43	−0.195619
$591$	11807.5	0.821818
$592$	−592.000	−0.0410997
$593$	13342.9	0.923989	0.461994	−	0.886883i	$-0.347134\pi$
$593$	13342.9	0.923989	0.461994	+	0.886883i	$0.347134\pi$
$594$	594.000	0.0410305
$595$	19283.7	1.32866
$596$	2785.71	0.191455
$597$	−1595.53	−0.109381
$598$	11538.1	0.789008
$599$	−2082.93	−0.142081	−0.0710403	−	0.997473i	$-0.522632\pi$
$599$	−2082.93	−0.142081	−0.0710403	+	0.997473i	$0.522632\pi$
$600$	6293.96	0.428250
$601$	15572.9	1.05696	0.528478	−	0.848947i	$-0.322763\pi$
$601$	15572.9	1.05696	0.528478	+	0.848947i	$0.322763\pi$
$602$	−2896.31	−0.196088
$603$	−8900.52	−0.601090
$604$	−7095.79	−0.478019
$605$	2381.11	0.160010
$606$	−3905.98	−0.261831
$607$	−18666.2	−1.24817	−0.624085	−	0.781357i	$-0.714528\pi$
$607$	−18666.2	−1.24817	−0.624085	+	0.781357i	$0.714528\pi$
$608$	1910.49	0.127435
$609$	4026.64	0.267927
$610$	−31826.0	−2.11245
$611$	−8059.72	−0.533652
$612$	−4627.55	−0.305650
$613$	6576.58	0.433320	0.216660	−	0.976247i	$-0.430484\pi$
$613$	6576.58	0.433320	0.216660	+	0.976247i	$0.430484\pi$
$614$	−14334.7	−0.942188
$615$	−6474.68	−0.424527
$616$	670.857	0.0438792
$617$	−21150.1	−1.38001	−0.690007	−	0.723802i	$-0.742393\pi$
$617$	−21150.1	−1.38001	−0.690007	+	0.723802i	$0.742393\pi$
$618$	−11274.4	−0.733858
$619$	21259.4	1.38043	0.690217	−	0.723602i	$-0.257515\pi$
$619$	21259.4	1.38043	0.690217	+	0.723602i	$0.257515\pi$
$620$	6524.10	0.422604
$621$	−3495.34	−0.225866
$622$	10533.6	0.679033
$623$	−2572.91	−0.165460
$624$	2139.04	0.137228
$625$	20368.2	1.30356
$626$	2968.91	0.189555
$627$	1970.19	0.125489
$628$	−4814.14	−0.305900
$629$	4756.10	0.301491
$630$	2700.32	0.170767
$631$	2631.83	0.166040	0.0830202	−	0.996548i	$-0.473543\pi$
$631$	2631.83	0.166040	0.0830202	+	0.996548i	$0.473543\pi$
$632$	513.369	0.0323112
$633$	−3251.87	−0.204187
$634$	3864.77	0.242097
$635$	−5890.94	−0.368149
$636$	−1519.54	−0.0947384
$637$	12695.4	0.789654
$638$	−3873.44	−0.240362
$639$	−1104.70	−0.0683899
$640$	−2518.86	−0.155573
$641$	13428.3	0.827436	0.413718	−	0.910405i	$-0.364230\pi$
$641$	13428.3	0.827436	0.413718	+	0.910405i	$0.364230\pi$
$642$	−10084.8	−0.619960
$643$	−24625.7	−1.51033	−0.755167	−	0.655532i	$-0.772444\pi$
$643$	−24625.7	−1.51033	−0.755167	+	0.655532i	$0.772444\pi$
$644$	−3947.60	−0.241548
$645$	11214.6	0.684612
$646$	−15348.7	−0.934811
$647$	−5842.98	−0.355041	−0.177520	−	0.984117i	$-0.556808\pi$
$647$	−5842.98	−0.355041	−0.177520	+	0.984117i	$0.556808\pi$
$648$	−648.000	−0.0392837
$649$	783.533	0.0473904
$650$	23373.3	1.41043
$651$	1895.55	0.114120
$652$	5062.24	0.304068
$653$	16490.4	0.988240	0.494120	−	0.869394i	$-0.335490\pi$
$653$	16490.4	0.988240	0.494120	+	0.869394i	$0.335490\pi$
$654$	12185.4	0.728574
$655$	−36191.1	−2.15893
$656$	1754.78	0.104440
$657$	−9102.78	−0.540538
$658$	2757.53	0.163373
$659$	−2850.53	−0.168499	−0.0842495	−	0.996445i	$-0.526849\pi$
$659$	−2850.53	−0.168499	−0.0842495	+	0.996445i	$0.526849\pi$
$660$	−2597.58	−0.153198
$661$	3529.11	0.207665	0.103833	−	0.994595i	$-0.466889\pi$
$661$	3529.11	0.207665	0.103833	+	0.994595i	$0.466889\pi$
$662$	10993.2	0.645411
$663$	−17184.9	−1.00665
$664$	−7021.38	−0.410365
$665$	8956.45	0.522280
$666$	666.000	0.0387492
$667$	22792.9	1.32315
$668$	6227.21	0.360686
$669$	−10826.8	−0.625694
$670$	38922.2	2.24432
$671$	8895.07	0.511759
$672$	−731.844	−0.0420112
$673$	−13791.6	−0.789936	−0.394968	−	0.918695i	$-0.629244\pi$
$673$	−13791.6	−0.789936	−0.394968	+	0.918695i	$0.629244\pi$
$674$	9749.03	0.557149
$675$	−7080.71	−0.403758
$676$	−844.439	−0.0480450
$677$	−19272.6	−1.09410	−0.547050	−	0.837100i	$-0.684249\pi$
$677$	−19272.6	−1.09410	−0.547050	+	0.837100i	$0.684249\pi$
$678$	9695.87	0.549215
$679$	6008.60	0.339600
$680$	20236.4	1.14122
$681$	−1817.33	−0.102262
$682$	−1823.43	−0.102379
$683$	−15061.0	−0.843769	−0.421884	−	0.906650i	$-0.638631\pi$
$683$	−15061.0	−0.843769	−0.421884	+	0.906650i	$0.638631\pi$
$684$	−2149.30	−0.120147
$685$	16821.1	0.938252
$686$	−9573.19	−0.532808
$687$	−625.062	−0.0347127
$688$	−3039.40	−0.168425
$689$	−5642.97	−0.312018
$690$	15285.2	0.843331
$691$	28229.4	1.55412	0.777059	−	0.629428i	$-0.216711\pi$
$691$	28229.4	1.55412	0.777059	+	0.629428i	$0.216711\pi$
$692$	−8869.16	−0.487218
$693$	−754.714	−0.0413697
$694$	8656.76	0.473496
$695$	−47941.6	−2.61659
$696$	4225.57	0.230129
$697$	−14097.8	−0.766129
$698$	−4016.63	−0.217810
$699$	8444.44	0.456936
$700$	−7996.87	−0.431790
$701$	−12949.8	−0.697729	−0.348865	−	0.937173i	$-0.613433\pi$
$701$	−12949.8	−0.697729	−0.348865	+	0.937173i	$0.613433\pi$
$702$	−2406.42	−0.129380
$703$	2209.00	0.118512
$704$	704.000	0.0376889
$705$	−10677.2	−0.570394
$706$	−23856.2	−1.27173
$707$	4962.79	0.263996
$708$	−854.764	−0.0453729
$709$	4907.28	0.259939	0.129969	−	0.991518i	$-0.458512\pi$
$709$	4907.28	0.259939	0.129969	+	0.991518i	$0.458512\pi$
$710$	4830.87	0.255351
$711$	−577.540	−0.0304633
$712$	−2700.03	−0.142118
$713$	10729.8	0.563582
$714$	5879.59	0.308177
$715$	−9646.40	−0.504552
$716$	2465.48	0.128686
$717$	9810.25	0.510977
$718$	24698.2	1.28374
$719$	261.021	0.0135389	0.00676943	−	0.999977i	$-0.497845\pi$
$719$	261.021	0.0135389	0.00676943	+	0.999977i	$0.497845\pi$
$720$	2833.72	0.146676
$721$	14324.9	0.739925
$722$	6589.18	0.339645
$723$	8612.34	0.443010
$724$	−10951.5	−0.562168
$725$	46172.8	2.36526
$726$	726.000	0.0371135
$727$	20347.7	1.03804	0.519019	−	0.854763i	$-0.326298\pi$
$727$	20347.7	1.03804	0.519019	+	0.854763i	$0.326298\pi$
$728$	−2717.78	−0.138362
$729$	729.000	0.0370370
$730$	39806.7	2.01824
$731$	24418.4	1.23550
$732$	−9703.72	−0.489972
$733$	21666.5	1.09177	0.545887	−	0.837859i	$-0.316193\pi$
$733$	21666.5	1.09177	0.545887	+	0.837859i	$0.316193\pi$
$734$	20412.5	1.02649
$735$	16818.4	0.844021
$736$	−4142.62	−0.207472
$737$	−10878.4	−0.543706
$738$	−1974.12	−0.0984668
$739$	−14740.0	−0.733719	−0.366859	−	0.930276i	$-0.619567\pi$
$739$	−14740.0	−0.733719	−0.366859	+	0.930276i	$0.619567\pi$
$740$	−2912.44	−0.144680
$741$	−7981.65	−0.395699
$742$	1930.67	0.0955217
$743$	−17530.5	−0.865588	−0.432794	−	0.901493i	$-0.642472\pi$
$743$	−17530.5	−0.865588	−0.432794	+	0.901493i	$0.642472\pi$
$744$	1989.19	0.0980207
$745$	13704.7	0.673963
$746$	−7170.49	−0.351917
$747$	7899.05	0.386896
$748$	−5655.90	−0.276471
$749$	12813.3	0.625086
$750$	16205.2	0.788971
$751$	−24646.5	−1.19755	−0.598777	−	0.800916i	$-0.704347\pi$
$751$	−24646.5	−1.19755	−0.598777	+	0.800916i	$0.704347\pi$
$752$	2893.76	0.140325
$753$	7338.79	0.355167
$754$	15692.1	0.757922
$755$	−34908.9	−1.68273
$756$	823.325	0.0396085
$757$	15563.6	0.747251	0.373625	−	0.927580i	$-0.378115\pi$
$757$	15563.6	0.747251	0.373625	+	0.927580i	$0.378115\pi$
$758$	3785.33	0.181384
$759$	−4272.08	−0.204304
$760$	9398.94	0.448599
$761$	−31578.1	−1.50421	−0.752107	−	0.659041i	$-0.770962\pi$
$761$	−31578.1	−1.50421	−0.752107	+	0.659041i	$0.770962\pi$
$762$	−1796.14	−0.0853903
$763$	−15482.3	−0.734598
$764$	4145.74	0.196319
$765$	−22766.0	−1.07595
$766$	10934.7	0.515777
$767$	−3174.26	−0.149434
$768$	−768.000	−0.0360844
$769$	6887.27	0.322967	0.161483	−	0.986875i	$-0.448372\pi$
$769$	6887.27	0.322967	0.161483	+	0.986875i	$0.448372\pi$
$770$	3300.39	0.154465
$771$	−17693.1	−0.826461
$772$	−3643.02	−0.169838
$773$	−1973.37	−0.0918203	−0.0459102	−	0.998946i	$-0.514619\pi$
$773$	−1973.37	−0.0918203	−0.0459102	+	0.998946i	$0.514619\pi$
$774$	3419.33	0.158792
$775$	21736.0	1.00746
$776$	6305.44	0.291691
$777$	−846.195	−0.0390696
$778$	20183.0	0.930074
$779$	−6547.81	−0.301155
$780$	10523.3	0.483072
$781$	−1350.19	−0.0618610
$782$	33281.6	1.52193
$783$	−4753.76	−0.216968
$784$	−4558.15	−0.207642
$785$	−23683.9	−1.07683
$786$	−11034.6	−0.500754
$787$	24591.4	1.11384	0.556918	−	0.830568i	$-0.311984\pi$
$787$	24591.4	1.11384	0.556918	+	0.830568i	$0.311984\pi$
$788$	−15743.3	−0.711715
$789$	11827.6	0.533680
$790$	2525.60	0.113743
$791$	−12319.2	−0.553756
$792$	−792.000	−0.0355335
$793$	−36035.8	−1.61371
$794$	10017.1	0.447723
$795$	−7475.61	−0.333500
$796$	2127.37	0.0947270
$797$	32687.9	1.45278	0.726388	−	0.687284i	$-0.241197\pi$
$797$	32687.9	1.45278	0.726388	+	0.687284i	$0.241197\pi$
$798$	2730.82	0.121140
$799$	−23248.3	−1.02937
$800$	−8391.95	−0.370875
$801$	3037.53	0.133990
$802$	18873.7	0.830990
$803$	−11125.6	−0.488935
$804$	11867.4	0.520559
$805$	−19420.8	−0.850303
$806$	7387.09	0.322828
$807$	5066.58	0.221006
$808$	5207.97	0.226752
$809$	36034.6	1.56602	0.783010	−	0.622009i	$-0.213683\pi$
$809$	36034.6	1.56602	0.783010	+	0.622009i	$0.213683\pi$
$810$	−3187.94	−0.138287
$811$	29746.7	1.28798	0.643988	−	0.765035i	$-0.277279\pi$
$811$	29746.7	1.28798	0.643988	+	0.765035i	$0.277279\pi$
$812$	−5368.85	−0.232032
$813$	−14756.1	−0.636557
$814$	814.000	0.0350500
$815$	24904.5	1.07039
$816$	6170.07	0.264701
$817$	11341.3	0.485656
$818$	−15090.8	−0.645034
$819$	3057.51	0.130449
$820$	8632.90	0.367651
$821$	16006.4	0.680421	0.340211	−	0.940349i	$-0.389502\pi$
$821$	16006.4	0.680421	0.340211	+	0.940349i	$0.389502\pi$
$822$	5128.75	0.217623
$823$	3807.17	0.161251	0.0806255	−	0.996744i	$-0.474308\pi$
$823$	3807.17	0.161251	0.0806255	+	0.996744i	$0.474308\pi$
$824$	15032.6	0.635540
$825$	−8654.20	−0.365213
$826$	1086.03	0.0457480
$827$	−26132.1	−1.09879	−0.549396	−	0.835562i	$-0.685142\pi$
$827$	−26132.1	−1.09879	−0.549396	+	0.835562i	$0.685142\pi$
$828$	4660.45	0.195606
$829$	19673.3	0.824222	0.412111	−	0.911134i	$-0.364792\pi$
$829$	19673.3	0.824222	0.412111	+	0.911134i	$0.364792\pi$
$830$	−34542.8	−1.44457
$831$	24417.0	1.01927
$832$	−2852.05	−0.118843
$833$	36619.9	1.52317
$834$	−14617.4	−0.606904
$835$	30635.8	1.26969
$836$	−2626.92	−0.108677
$837$	−2237.84	−0.0924148
$838$	9681.55	0.399097
$839$	−18550.6	−0.763336	−0.381668	−	0.924300i	$-0.624650\pi$
$839$	−18550.6	−0.763336	−0.381668	+	0.924300i	$0.624650\pi$
$840$	−3600.42	−0.147889
$841$	6609.99	0.271023
$842$	−11289.6	−0.462072
$843$	−9040.96	−0.369380
$844$	4335.83	0.176831
$845$	−4154.35	−0.169129
$846$	−3255.48	−0.132300
$847$	−922.428	−0.0374203
$848$	2026.05	0.0820459
$849$	−1317.76	−0.0532692
$850$	67420.4	2.72059
$851$	−4789.91	−0.192945
$852$	1472.93	0.0592274
$853$	−7325.39	−0.294041	−0.147020	−	0.989133i	$-0.546968\pi$
$853$	−7325.39	−0.294041	−0.147020	+	0.989133i	$0.546968\pi$
$854$	12329.2	0.494023
$855$	−10573.8	−0.422943
$856$	13446.4	0.536901
$857$	359.529	0.0143305	0.00716526	−	0.999974i	$-0.497719\pi$
$857$	359.529	0.0143305	0.00716526	+	0.999974i	$0.497719\pi$
$858$	−2941.18	−0.117028
$859$	−11820.7	−0.469521	−0.234760	−	0.972053i	$-0.575431\pi$
$859$	−11820.7	−0.469521	−0.234760	+	0.972053i	$0.575431\pi$
$860$	−14952.8	−0.592892
$861$	2508.25	0.0992809
$862$	27425.4	1.08366
$863$	−12468.0	−0.491791	−0.245896	−	0.969296i	$-0.579082\pi$
$863$	−12468.0	−0.491791	−0.245896	+	0.969296i	$0.579082\pi$
$864$	864.000	0.0340207
$865$	−43633.2	−1.71512
$866$	−1706.85	−0.0669759
$867$	−34831.0	−1.36439
$868$	−2527.40	−0.0988311
$869$	−705.882	−0.0275551
$870$	20788.3	0.810104
$871$	44070.8	1.71444
$872$	−16247.2	−0.630964
$873$	−7093.62	−0.275009
$874$	15457.9	0.598249
$875$	−20589.7	−0.795495
$876$	12137.0	0.468119
$877$	41133.6	1.58379	0.791895	−	0.610657i	$-0.209094\pi$
$877$	41133.6	1.58379	0.791895	+	0.610657i	$0.209094\pi$
$878$	−19672.4	−0.756162
$879$	−37.7262	−0.00144764
$880$	3463.44	0.132673
$881$	14973.3	0.572602	0.286301	−	0.958140i	$-0.407574\pi$
$881$	14973.3	0.572602	0.286301	+	0.958140i	$0.407574\pi$
$882$	5127.91	0.195766
$883$	−6806.20	−0.259396	−0.129698	−	0.991554i	$-0.541401\pi$
$883$	−6806.20	−0.259396	−0.129698	+	0.991554i	$0.541401\pi$
$884$	22913.2	0.871782
$885$	−4205.14	−0.159722
$886$	−20546.5	−0.779089
$887$	34169.6	1.29346	0.646732	−	0.762717i	$-0.276135\pi$
$887$	34169.6	1.29346	0.646732	+	0.762717i	$0.276135\pi$
$888$	−888.000	−0.0335578
$889$	2282.11	0.0860962
$890$	−13283.2	−0.500285
$891$	891.000	0.0335013
$892$	14435.8	0.541867
$893$	−10797.8	−0.404631
$894$	4178.57	0.156322
$895$	12129.3	0.453003
$896$	975.792	0.0363827
$897$	17307.1	0.644222
$898$	24716.1	0.918469
$899$	14592.8	0.541377
$900$	9440.94	0.349664
$901$	−16277.2	−0.601855
$902$	−2412.82	−0.0890666
$903$	−4344.47	−0.160105
$904$	−12927.8	−0.475634
$905$	−53877.7	−1.97896
$906$	−10643.7	−0.390301
$907$	−7416.61	−0.271515	−0.135758	−	0.990742i	$-0.543347\pi$
$907$	−7416.61	−0.271515	−0.135758	+	0.990742i	$0.543347\pi$
$908$	2423.11	0.0885613
$909$	−5858.97	−0.213784
$910$	−13370.6	−0.487066
$911$	11599.0	0.421837	0.210919	−	0.977504i	$-0.432355\pi$
$911$	11599.0	0.421837	0.210919	+	0.977504i	$0.432355\pi$
$912$	2865.73	0.104050
$913$	9654.39	0.349960
$914$	−9606.00	−0.347635
$915$	−47739.0	−1.72481
$916$	833.416	0.0300621
$917$	14020.2	0.504894
$918$	−6941.33	−0.249562
$919$	−21110.5	−0.757750	−0.378875	−	0.925448i	$-0.623689\pi$
$919$	−21110.5	−0.757750	−0.378875	+	0.925448i	$0.623689\pi$
$920$	−20380.3	−0.730346
$921$	−21502.1	−0.769293
$922$	−23148.9	−0.826865
$923$	5469.89	0.195063
$924$	1006.29	0.0358272
$925$	−9703.19	−0.344907
$926$	25676.2	0.911203
$927$	−16911.7	−0.599193
$928$	−5634.09	−0.199297
$929$	−26121.8	−0.922527	−0.461263	−	0.887263i	$-0.652604\pi$
$929$	−26121.8	−0.922527	−0.461263	+	0.887263i	$0.652604\pi$
$930$	9786.15	0.345054
$931$	17008.4	0.598739
$932$	−11259.2	−0.395718
$933$	15800.4	0.554428
$934$	27490.2	0.963070
$935$	−27825.1	−0.973238
$936$	3208.56	0.112046
$937$	−6932.22	−0.241692	−0.120846	−	0.992671i	$-0.538561\pi$
$937$	−6932.22	−0.241692	−0.120846	+	0.992671i	$0.538561\pi$
$938$	−15078.2	−0.524863
$939$	4453.37	0.154771
$940$	14236.3	0.493975
$941$	−25606.7	−0.887093	−0.443546	−	0.896251i	$-0.646280\pi$
$941$	−25606.7	−0.887093	−0.443546	+	0.896251i	$0.646280\pi$
$942$	−7221.20	−0.249766
$943$	14198.0	0.490298
$944$	1139.68	0.0392940
$945$	4050.47	0.139431
$946$	4179.18	0.143633
$947$	50905.3	1.74678	0.873390	−	0.487021i	$-0.161917\pi$
$947$	50905.3	1.74678	0.873390	+	0.487021i	$0.161917\pi$
$948$	770.053	0.0263820
$949$	45072.2	1.54174
$950$	31313.9	1.06943
$951$	5797.15	0.197671
$952$	−7839.46	−0.266889
$953$	−26708.4	−0.907837	−0.453919	−	0.891043i	$-0.649974\pi$
$953$	−26708.4	−0.907837	−0.453919	+	0.891043i	$0.649974\pi$
$954$	−2279.31	−0.0773536
$955$	20395.6	0.691085
$956$	−13080.3	−0.442519
$957$	−5810.15	−0.196255
$958$	19001.3	0.640820
$959$	−6516.40	−0.219422
$960$	−3778.30	−0.127025
$961$	−22921.4	−0.769407
$962$	−3297.69	−0.110521
$963$	−15127.2	−0.506195
$964$	−11483.1	−0.383658
$965$	−17922.4	−0.597868
$966$	−5921.39	−0.197223
$967$	11436.7	0.380330	0.190165	−	0.981752i	$-0.439098\pi$
$967$	11436.7	0.380330	0.190165	+	0.981752i	$0.439098\pi$
$968$	−968.000	−0.0321412
$969$	−23023.1	−0.763270
$970$	31020.6	1.02682
$971$	38157.4	1.26110	0.630551	−	0.776148i	$-0.282829\pi$
$971$	38157.4	1.26110	0.630551	+	0.776148i	$0.282829\pi$
$972$	−972.000	−0.0320750
$973$	18572.3	0.611922
$974$	20327.4	0.668718
$975$	35060.0	1.15161
$976$	12938.3	0.424328
$977$	8159.41	0.267188	0.133594	−	0.991036i	$-0.457348\pi$
$977$	8159.41	0.267188	0.133594	+	0.991036i	$0.457348\pi$
$978$	7593.36	0.248271
$979$	3712.53	0.121198
$980$	−22424.5	−0.730944
$981$	18278.1	0.594879
$982$	18395.2	0.597775
$983$	22858.6	0.741685	0.370842	−	0.928696i	$-0.379069\pi$
$983$	22858.6	0.741685	0.370842	+	0.928696i	$0.379069\pi$
$984$	2632.17	0.0852748
$985$	−77451.6	−2.50539
$986$	45264.0	1.46197
$987$	4136.29	0.133394
$988$	10642.2	0.342686
$989$	−24592.0	−0.790677
$990$	−3896.37	−0.125086
$991$	−42120.6	−1.35016	−0.675078	−	0.737746i	$-0.735890\pi$
$991$	−42120.6	−1.35016	−0.675078	+	0.737746i	$0.735890\pi$
$992$	−2652.26	−0.0848884
$993$	16489.8	0.526976
$994$	−1871.45	−0.0597171
$995$	10465.9	0.333460
$996$	−10532.1	−0.335062
$997$	43308.1	1.37571	0.687855	−	0.725848i	$-0.258553\pi$
$997$	43308.1	1.37571	0.687855	+	0.725848i	$0.258553\pi$
$998$	−25136.3	−0.797271
$999$	999.000	0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2442.4.a.n.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2442.4.a.n.1.12	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2442 = 2 \cdot 3 \cdot 11 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2442.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +19.6786 q^{5} +6.00000 q^{6} -7.62338 q^{7} -8.00000 q^{8} +9.00000 q^{9} -39.3573 q^{10} +11.0000 q^{11} -12.0000 q^{12} -44.5633 q^{13} +15.2468 q^{14} -59.0359 q^{15} +16.0000 q^{16} -128.543 q^{17} -18.0000 q^{18} -59.7027 q^{19} +78.7145 q^{20} +22.8701 q^{21} -22.0000 q^{22} +129.457 q^{23} +24.0000 q^{24} +262.248 q^{25} +89.1267 q^{26} -27.0000 q^{27} -30.4935 q^{28} +176.065 q^{29} +118.072 q^{30} +82.8831 q^{31} -32.0000 q^{32} -33.0000 q^{33} +257.086 q^{34} -150.018 q^{35} +36.0000 q^{36} -37.0000 q^{37} +119.405 q^{38} +133.690 q^{39} -157.429 q^{40} +109.674 q^{41} -45.7403 q^{42} -189.963 q^{43} +44.0000 q^{44} +177.108 q^{45} -258.914 q^{46} +180.860 q^{47} -48.0000 q^{48} -284.884 q^{49} -524.497 q^{50} +385.629 q^{51} -178.253 q^{52} +126.628 q^{53} +54.0000 q^{54} +216.465 q^{55} +60.9870 q^{56} +179.108 q^{57} -352.131 q^{58} +71.2303 q^{59} -236.144 q^{60} +808.643 q^{61} -165.766 q^{62} -68.6104 q^{63} +64.0000 q^{64} -876.945 q^{65} +66.0000 q^{66} -988.947 q^{67} -514.172 q^{68} -388.371 q^{69} +300.035 q^{70} -122.744 q^{71} -72.0000 q^{72} -1011.42 q^{73} +74.0000 q^{74} -786.745 q^{75} -238.811 q^{76} -83.8571 q^{77} -267.380 q^{78} -64.1711 q^{79} +314.858 q^{80} +81.0000 q^{81} -219.347 q^{82} +877.672 q^{83} +91.4805 q^{84} -2529.55 q^{85} +379.925 q^{86} -528.196 q^{87} -88.0000 q^{88} +337.503 q^{89} -354.215 q^{90} +339.723 q^{91} +517.828 q^{92} -248.649 q^{93} -361.720 q^{94} -1174.87 q^{95} +96.0000 q^{96} -788.180 q^{97} +569.768 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{2} - 36 q^{3} + 48 q^{4} - 10 q^{5} + 72 q^{6} - 25 q^{7} - 96 q^{8} + 108 q^{9} + 20 q^{10} + 132 q^{11} - 144 q^{12} + 12 q^{13} + 50 q^{14} + 30 q^{15} + 192 q^{16} - 10 q^{17} - 216 q^{18}+ \cdots + 1188 q^{99}+O(q^{100}) \) 12 * q - 24 * q^2 - 36 * q^3 + 48 * q^4 - 10 * q^5 + 72 * q^6 - 25 * q^7 - 96 * q^8 + 108 * q^9 + 20 * q^10 + 132 * q^11 - 144 * q^12 + 12 * q^13 + 50 * q^14 + 30 * q^15 + 192 * q^16 - 10 * q^17 - 216 * q^18 - 9 * q^19 - 40 * q^20 + 75 * q^21 - 264 * q^22 - 201 * q^23 + 288 * q^24 + 210 * q^25 - 24 * q^26 - 324 * q^27 - 100 * q^28 - 84 * q^29 - 60 * q^30 + 10 * q^31 - 384 * q^32 - 396 * q^33 + 20 * q^34 - 565 * q^35 + 432 * q^36 - 444 * q^37 + 18 * q^38 - 36 * q^39 + 80 * q^40 + 215 * q^41 - 150 * q^42 - 434 * q^43 + 528 * q^44 - 90 * q^45 + 402 * q^46 - 256 * q^47 - 576 * q^48 + 519 * q^49 - 420 * q^50 + 30 * q^51 + 48 * q^52 - 448 * q^53 + 648 * q^54 - 110 * q^55 + 200 * q^56 + 27 * q^57 + 168 * q^58 - 588 * q^59 + 120 * q^60 + 735 * q^61 - 20 * q^62 - 225 * q^63 + 768 * q^64 - 859 * q^65 + 792 * q^66 - 288 * q^67 - 40 * q^68 + 603 * q^69 + 1130 * q^70 + 1019 * q^71 - 864 * q^72 - 309 * q^73 + 888 * q^74 - 630 * q^75 - 36 * q^76 - 275 * q^77 + 72 * q^78 + 1116 * q^79 - 160 * q^80 + 972 * q^81 - 430 * q^82 - 662 * q^83 + 300 * q^84 + 1093 * q^85 + 868 * q^86 + 252 * q^87 - 1056 * q^88 + 1603 * q^89 + 180 * q^90 + 1502 * q^91 - 804 * q^92 - 30 * q^93 + 512 * q^94 - 2017 * q^95 + 1152 * q^96 + 349 * q^97 - 1038 * q^98 + 1188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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