LMFDB - Embedded newform 1573.4.a.p.1.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,4,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1573.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1573.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:	$92.8100044390$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.33
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.77325 q^{2} +4.58517 q^{3} +14.7839 q^{4} -9.06658 q^{5} +21.8862 q^{6} -11.8931 q^{7} +32.3813 q^{8} -5.97621 q^{9} +O(q^{10})$	\(q+4.77325 q^{2} +4.58517 q^{3} +14.7839 q^{4} -9.06658 q^{5} +21.8862 q^{6} -11.8931 q^{7} +32.3813 q^{8} -5.97621 q^{9} -43.2770 q^{10} +67.7867 q^{12} -13.0000 q^{13} -56.7688 q^{14} -41.5718 q^{15} +36.2926 q^{16} +15.1695 q^{17} -28.5259 q^{18} -32.9390 q^{19} -134.039 q^{20} -54.5319 q^{21} +77.8610 q^{23} +148.474 q^{24} -42.7972 q^{25} -62.0522 q^{26} -151.202 q^{27} -175.827 q^{28} -91.3129 q^{29} -198.433 q^{30} -50.7299 q^{31} -85.8164 q^{32} +72.4080 q^{34} +107.830 q^{35} -88.3517 q^{36} -72.5347 q^{37} -157.226 q^{38} -59.6072 q^{39} -293.587 q^{40} +117.059 q^{41} -260.295 q^{42} -324.184 q^{43} +54.1837 q^{45} +371.650 q^{46} -333.390 q^{47} +166.408 q^{48} -201.554 q^{49} -204.282 q^{50} +69.5549 q^{51} -192.191 q^{52} +488.897 q^{53} -721.723 q^{54} -385.114 q^{56} -151.031 q^{57} -435.859 q^{58} +246.701 q^{59} -614.594 q^{60} -484.034 q^{61} -242.146 q^{62} +71.0757 q^{63} -699.964 q^{64} +117.865 q^{65} +493.429 q^{67} +224.265 q^{68} +357.006 q^{69} +514.698 q^{70} -881.321 q^{71} -193.517 q^{72} -132.429 q^{73} -346.226 q^{74} -196.233 q^{75} -486.967 q^{76} -284.520 q^{78} -448.552 q^{79} -329.050 q^{80} -531.927 q^{81} +558.750 q^{82} +970.880 q^{83} -806.195 q^{84} -137.536 q^{85} -1547.41 q^{86} -418.685 q^{87} -1496.56 q^{89} +258.632 q^{90} +154.610 q^{91} +1151.09 q^{92} -232.605 q^{93} -1591.35 q^{94} +298.644 q^{95} -393.483 q^{96} +632.256 q^{97} -962.067 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) $ 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9} + 18 q^{10} - 262 q^{12} - 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} + 209 q^{17} + 190 q^{18} + 107 q^{19} - 211 q^{20} + 68 q^{21} - 632 q^{23} - 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} + 931 q^{28} + 32 q^{29} + 300 q^{30} - 290 q^{31} - 876 q^{32} - 602 q^{34} - 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} + 377 q^{39} - 1159 q^{40} + 1121 q^{41} + 79 q^{42} - 349 q^{43} - 1024 q^{45} - 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} + 1322 q^{50} - 1414 q^{51} - 1261 q^{52} - 2608 q^{53} - 3131 q^{54} - 1675 q^{56} + 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} + 236 q^{61} - 1396 q^{62} - 1206 q^{63} + 1331 q^{64} + 364 q^{65} - 3213 q^{67} + 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} + 5074 q^{72} - 823 q^{73} - 2550 q^{74} - 3063 q^{75} - 2004 q^{76} + 468 q^{78} + 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} + 3843 q^{83} - 7191 q^{84} - 1582 q^{85} - 3542 q^{86} - 962 q^{87} - 3633 q^{89} + 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} + 6309 q^{94} - 1916 q^{95} + 2150 q^{96} + 1195 q^{97} + 1487 q^{98}+O(q^{100}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9 + 18 * q^10 - 262 * q^12 - 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 + 209 * q^17 + 190 * q^18 + 107 * q^19 - 211 * q^20 + 68 * q^21 - 632 * q^23 - 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 + 931 * q^28 + 32 * q^29 + 300 * q^30 - 290 * q^31 - 876 * q^32 - 602 * q^34 - 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 + 377 * q^39 - 1159 * q^40 + 1121 * q^41 + 79 * q^42 - 349 * q^43 - 1024 * q^45 - 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 + 1322 * q^50 - 1414 * q^51 - 1261 * q^52 - 2608 * q^53 - 3131 * q^54 - 1675 * q^56 + 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 + 236 * q^61 - 1396 * q^62 - 1206 * q^63 + 1331 * q^64 + 364 * q^65 - 3213 * q^67 + 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 + 5074 * q^72 - 823 * q^73 - 2550 * q^74 - 3063 * q^75 - 2004 * q^76 + 468 * q^78 + 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 + 3843 * q^83 - 7191 * q^84 - 1582 * q^85 - 3542 * q^86 - 962 * q^87 - 3633 * q^89 + 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 + 6309 * q^94 - 1916 * q^95 + 2150 * q^96 + 1195 * q^97 + 1487 * q^98

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 $

$2$	4.77325	1.68760	0.843799	−	0.536659i	$-0.180314\pi$
$2$	4.77325	1.68760	0.843799	+	0.536659i	$0.180314\pi$
$3$	4.58517	0.882417	0.441208	−	0.897405i	$-0.354550\pi$
$3$	4.58517	0.882417	0.441208	+	0.897405i	$0.354550\pi$
$4$	14.7839	1.84799
$5$	−9.06658	−0.810939	−0.405470	−	0.914109i	$-0.632892\pi$
$5$	−9.06658	−0.810939	−0.405470	+	0.914109i	$0.632892\pi$
$6$	21.8862	1.48916
$7$	−11.8931	−0.642167	−0.321084	−	0.947051i	$-0.604047\pi$
$7$	−11.8931	−0.642167	−0.321084	+	0.947051i	$0.604047\pi$
$8$	32.3813	1.43106
$9$	−5.97621	−0.221341
$10$	−43.2770	−1.36854
$11$	0	0
$11$	0	0
$12$	67.7867	1.63070
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−56.7688	−1.08372
$15$	−41.5718	−0.715586
$16$	36.2926	0.567072
$17$	15.1695	0.216421	0.108210	−	0.994128i	$-0.465488\pi$
$17$	15.1695	0.216421	0.108210	+	0.994128i	$0.465488\pi$
$18$	−28.5259	−0.373535
$19$	−32.9390	−0.397722	−0.198861	−	0.980028i	$-0.563724\pi$
$19$	−32.9390	−0.397722	−0.198861	+	0.980028i	$0.563724\pi$
$20$	−134.039	−1.49861
$21$	−54.5319	−0.566659
$22$	0	0
$23$	77.8610	0.705876	0.352938	−	0.935647i	$-0.385183\pi$
$23$	77.8610	0.705876	0.352938	+	0.935647i	$0.385183\pi$
$24$	148.474	1.26279
$25$	−42.7972	−0.342378
$26$	−62.0522	−0.468056
$27$	−151.202	−1.07773
$28$	−175.827	−1.18672
$29$	−91.3129	−0.584703	−0.292351	−	0.956311i	$-0.594438\pi$
$29$	−91.3129	−0.584703	−0.292351	+	0.956311i	$0.594438\pi$
$30$	−198.433	−1.20762
$31$	−50.7299	−0.293915	−0.146957	−	0.989143i	$-0.546948\pi$
$31$	−50.7299	−0.293915	−0.146957	+	0.989143i	$0.546948\pi$
$32$	−85.8164	−0.474073
$33$	0	0
$34$	72.4080	0.365231
$35$	107.830	0.520759
$36$	−88.3517	−0.409036
$37$	−72.5347	−0.322288	−0.161144	−	0.986931i	$-0.551518\pi$
$37$	−72.5347	−0.322288	−0.161144	+	0.986931i	$0.551518\pi$
$38$	−157.226	−0.671195
$39$	−59.6072	−0.244738
$40$	−293.587	−1.16051
$41$	117.059	0.445890	0.222945	−	0.974831i	$-0.428433\pi$
$41$	117.059	0.445890	0.222945	+	0.974831i	$0.428433\pi$
$42$	−260.295	−0.956293
$43$	−324.184	−1.14971	−0.574857	−	0.818254i	$-0.694942\pi$
$43$	−324.184	−1.14971	−0.574857	+	0.818254i	$0.694942\pi$
$44$	0	0
$45$	54.1837	0.179494
$46$	371.650	1.19124
$47$	−333.390	−1.03468	−0.517340	−	0.855780i	$-0.673078\pi$
$47$	−333.390	−1.03468	−0.517340	+	0.855780i	$0.673078\pi$
$48$	166.408	0.500394
$49$	−201.554	−0.587621
$50$	−204.282	−0.577796
$51$	69.5549	0.190973
$52$	−192.191	−0.512540
$53$	488.897	1.26708	0.633539	−	0.773711i	$-0.281602\pi$
$53$	488.897	1.26708	0.633539	+	0.773711i	$0.281602\pi$
$54$	−721.723	−1.81878
$55$	0	0
$56$	−385.114	−0.918982
$57$	−151.031	−0.350956
$58$	−435.859	−0.986743
$59$	246.701	0.544368	0.272184	−	0.962245i	$-0.412254\pi$
$59$	246.701	0.544368	0.272184	+	0.962245i	$0.412254\pi$
$60$	−614.594	−1.32239
$61$	−484.034	−1.01597	−0.507985	−	0.861366i	$-0.669609\pi$
$61$	−484.034	−1.01597	−0.507985	+	0.861366i	$0.669609\pi$
$62$	−242.146	−0.496010
$63$	71.0757	0.142138
$64$	−699.964	−1.36712
$65$	117.865	0.224914
$66$	0	0
$67$	493.429	0.899731	0.449865	−	0.893096i	$-0.351472\pi$
$67$	493.429	0.899731	0.449865	+	0.893096i	$0.351472\pi$
$68$	224.265	0.399943
$69$	357.006	0.622877
$70$	514.698	0.878832
$71$	−881.321	−1.47315	−0.736575	−	0.676356i	$-0.763558\pi$
$71$	−881.321	−1.47315	−0.736575	+	0.676356i	$0.763558\pi$
$72$	−193.517	−0.316753
$73$	−132.429	−0.212324	−0.106162	−	0.994349i	$-0.533856\pi$
$73$	−132.429	−0.212324	−0.106162	+	0.994349i	$0.533856\pi$
$74$	−346.226	−0.543892
$75$	−196.233	−0.302120
$76$	−486.967	−0.734986
$77$	0	0
$78$	−284.520	−0.413020
$79$	−448.552	−0.638810	−0.319405	−	0.947618i	$-0.603483\pi$
$79$	−448.552	−0.638810	−0.319405	+	0.947618i	$0.603483\pi$
$80$	−329.050	−0.459861
$81$	−531.927	−0.729667
$82$	558.750	0.752483
$83$	970.880	1.28395	0.641975	−	0.766725i	$-0.278115\pi$
$83$	970.880	1.28395	0.641975	+	0.766725i	$0.278115\pi$
$84$	−806.195	−1.04718
$85$	−137.536	−0.175504
$86$	−1547.41	−1.94025
$87$	−418.685	−0.515951
$88$	0	0
$89$	−1496.56	−1.78242	−0.891209	−	0.453593i	$-0.850142\pi$
$89$	−1496.56	−1.78242	−0.891209	+	0.453593i	$0.850142\pi$
$90$	258.632	0.302914
$91$	154.610	0.178105
$92$	1151.09	1.30445
$93$	−232.605	−0.259355
$94$	−1591.35	−1.74612
$95$	298.644	0.322528
$96$	−393.483	−0.418330
$97$	632.256	0.661813	0.330906	−	0.943664i	$-0.392646\pi$
$97$	632.256	0.661813	0.330906	+	0.943664i	$0.392646\pi$
$98$	−962.067	−0.991668
$99$	0	0
$100$	−632.710	−0.632710
$101$	1332.76	1.31302	0.656509	−	0.754318i	$-0.272032\pi$
$101$	1332.76	1.31302	0.656509	+	0.754318i	$0.272032\pi$
$102$	332.003	0.322286
$103$	−814.544	−0.779217	−0.389609	−	0.920981i	$-0.627390\pi$
$103$	−814.544	−0.779217	−0.389609	+	0.920981i	$0.627390\pi$
$104$	−420.957	−0.396906
$105$	494.418	0.459526
$106$	2333.63	2.13832
$107$	1713.59	1.54822	0.774110	−	0.633052i	$-0.218198\pi$
$107$	1713.59	1.54822	0.774110	+	0.633052i	$0.218198\pi$
$108$	−2235.35	−1.99164
$109$	219.748	0.193101	0.0965507	−	0.995328i	$-0.469219\pi$
$109$	219.748	0.193101	0.0965507	+	0.995328i	$0.469219\pi$
$110$	0	0
$111$	−332.584	−0.284392
$112$	−431.632	−0.364155
$113$	1079.25	0.898475	0.449237	−	0.893412i	$-0.351696\pi$
$113$	1079.25	0.898475	0.449237	+	0.893412i	$0.351696\pi$
$114$	−720.908	−0.592274
$115$	−705.933	−0.572423
$116$	−1349.96	−1.08052
$117$	77.6907	0.0613890
$118$	1177.56	0.918674
$119$	−180.413	−0.138978
$120$	−1346.15	−1.02405
$121$	0	0
$122$	−2310.41	−1.71455
$123$	536.734	0.393461
$124$	−749.985	−0.543151
$125$	1521.35	1.08859
$126$	339.262	0.239872
$127$	−705.940	−0.493245	−0.246622	−	0.969112i	$-0.579321\pi$
$127$	−705.940	−0.493245	−0.246622	+	0.969112i	$0.579321\pi$
$128$	−2654.57	−1.83307
$129$	−1486.44	−1.01453
$130$	562.601	0.379565
$131$	−941.040	−0.627626	−0.313813	−	0.949485i	$-0.601607\pi$
$131$	−941.040	−0.627626	−0.313813	+	0.949485i	$0.601607\pi$
$132$	0	0
$133$	391.747	0.255404
$134$	2355.26	1.51838
$135$	1370.88	0.873975
$136$	491.209	0.309712
$137$	−2346.40	−1.46326	−0.731629	−	0.681704i	$-0.761239\pi$
$137$	−2346.40	−1.46326	−0.731629	+	0.681704i	$0.761239\pi$
$138$	1704.08	1.05117
$139$	−2060.40	−1.25727	−0.628636	−	0.777700i	$-0.716386\pi$
$139$	−2060.40	−1.25727	−0.628636	+	0.777700i	$0.716386\pi$
$140$	1594.15	0.962356
$141$	−1528.65	−0.913018
$142$	−4206.77	−2.48608
$143$	0	0
$144$	−216.892	−0.125516
$145$	827.895	0.474158
$146$	−632.117	−0.358317
$147$	−924.159	−0.518526
$148$	−1072.35	−0.595584
$149$	399.175	0.219475	0.109737	−	0.993961i	$-0.464999\pi$
$149$	399.175	0.219475	0.109737	+	0.993961i	$0.464999\pi$
$150$	−936.667	−0.509857
$151$	501.795	0.270434	0.135217	−	0.990816i	$-0.456827\pi$
$151$	501.795	0.270434	0.135217	+	0.990816i	$0.456827\pi$
$152$	−1066.61	−0.569165
$153$	−90.6563	−0.0479028
$154$	0	0
$155$	459.946	0.238347
$156$	−881.228	−0.452274
$157$	2827.18	1.43716	0.718579	−	0.695446i	$-0.244793\pi$
$157$	2827.18	1.43716	0.718579	+	0.695446i	$0.244793\pi$
$158$	−2141.05	−1.07806
$159$	2241.68	1.11809
$160$	778.061	0.384445
$161$	−926.010	−0.453291
$162$	−2539.02	−1.23139
$163$	3648.17	1.75305	0.876523	−	0.481360i	$-0.159857\pi$
$163$	3648.17	1.75305	0.876523	+	0.481360i	$0.159857\pi$
$164$	1730.58	0.823999
$165$	0	0
$166$	4634.25	2.16679
$167$	1461.72	0.677313	0.338657	−	0.940910i	$-0.390027\pi$
$167$	1461.72	0.677313	0.338657	+	0.940910i	$0.390027\pi$
$168$	−1765.81	−0.810925
$169$	169.000	0.0769231
$170$	−656.492	−0.296180
$171$	196.850	0.0880322
$172$	−4792.71	−2.12466
$173$	3249.07	1.42788	0.713938	−	0.700209i	$-0.246910\pi$
$173$	3249.07	1.42788	0.713938	+	0.700209i	$0.246910\pi$
$174$	−1998.49	−0.870719
$175$	508.992	0.219864
$176$	0	0
$177$	1131.17	0.480359
$178$	−7143.46	−3.00801
$179$	1160.00	0.484373	0.242187	−	0.970230i	$-0.422135\pi$
$179$	1160.00	0.484373	0.242187	+	0.970230i	$0.422135\pi$
$180$	801.047	0.331703
$181$	1271.67	0.522224	0.261112	−	0.965308i	$-0.415911\pi$
$181$	1271.67	0.522224	0.261112	+	0.965308i	$0.415911\pi$
$182$	737.994	0.300570
$183$	−2219.38	−0.896509
$184$	2521.24	1.01015
$185$	657.642	0.261356
$186$	−1110.28	−0.437687
$187$	0	0
$188$	−4928.81	−1.91208
$189$	1798.26	0.692084
$190$	1425.50	0.544298
$191$	−2345.38	−0.888510	−0.444255	−	0.895900i	$-0.646532\pi$
$191$	−2345.38	−0.888510	−0.444255	+	0.895900i	$0.646532\pi$
$192$	−3209.46	−1.20637
$193$	−1803.45	−0.672616	−0.336308	−	0.941752i	$-0.609178\pi$
$193$	−1803.45	−0.672616	−0.336308	+	0.941752i	$0.609178\pi$
$194$	3017.91	1.11687
$195$	540.433	0.198468
$196$	−2979.75	−1.08592
$197$	1652.94	0.597802	0.298901	−	0.954284i	$-0.403380\pi$
$197$	1652.94	0.597802	0.298901	+	0.954284i	$0.403380\pi$
$198$	0	0
$199$	−3746.42	−1.33456	−0.667278	−	0.744809i	$-0.732541\pi$
$199$	−3746.42	−1.33456	−0.667278	+	0.744809i	$0.732541\pi$
$200$	−1385.83	−0.489964
$201$	2262.46	0.793938
$202$	6361.61	2.21585
$203$	1085.99	0.375477
$204$	1028.29	0.352916
$205$	−1061.32	−0.361590
$206$	−3888.02	−1.31501
$207$	−465.314	−0.156239
$208$	−471.804	−0.157278
$209$	0	0
$210$	2359.98	0.775496
$211$	225.169	0.0734657	0.0367328	−	0.999325i	$-0.488305\pi$
$211$	225.169	0.0734657	0.0367328	+	0.999325i	$0.488305\pi$
$212$	7227.81	2.34155
$213$	−4041.01	−1.29993
$214$	8179.41	2.61277
$215$	2939.24	0.932347
$216$	−4896.10	−1.54230
$217$	603.336	0.188742
$218$	1048.91	0.325878
$219$	−607.210	−0.187358
$220$	0	0
$221$	−197.204	−0.0600243
$222$	−1587.51	−0.479939
$223$	−945.434	−0.283906	−0.141953	−	0.989873i	$-0.545338\pi$
$223$	−945.434	−0.283906	−0.141953	+	0.989873i	$0.545338\pi$
$224$	1020.62	0.304435
$225$	255.765	0.0757822
$226$	5151.55	1.51626
$227$	−1233.94	−0.360791	−0.180395	−	0.983594i	$-0.557738\pi$
$227$	−1233.94	−0.360791	−0.180395	+	0.983594i	$0.557738\pi$
$228$	−2232.83	−0.648563
$229$	−4662.97	−1.34558	−0.672790	−	0.739833i	$-0.734904\pi$
$229$	−4662.97	−1.34558	−0.672790	+	0.739833i	$0.734904\pi$
$230$	−3369.59	−0.966019
$231$	0	0
$232$	−2956.83	−0.836747
$233$	−2445.22	−0.687519	−0.343759	−	0.939058i	$-0.611700\pi$
$233$	−2445.22	−0.687519	−0.343759	+	0.939058i	$0.611700\pi$
$234$	370.837	0.103600
$235$	3022.71	0.839062
$236$	3647.20	1.00599
$237$	−2056.69	−0.563697
$238$	−861.156	−0.234540
$239$	5725.52	1.54959	0.774797	−	0.632210i	$-0.217852\pi$
$239$	5725.52	1.54959	0.774797	+	0.632210i	$0.217852\pi$
$240$	−1508.75	−0.405789
$241$	−2786.65	−0.744830	−0.372415	−	0.928066i	$-0.621470\pi$
$241$	−2786.65	−0.744830	−0.372415	+	0.928066i	$0.621470\pi$
$242$	0	0
$243$	1643.46	0.433861
$244$	−7155.91	−1.87750
$245$	1827.40	0.476525
$246$	2561.96	0.664004
$247$	428.207	0.110308
$248$	−1642.70	−0.420610
$249$	4451.65	1.13298
$250$	7261.76	1.83710
$251$	4592.35	1.15485	0.577423	−	0.816445i	$-0.304058\pi$
$251$	4592.35	1.15485	0.577423	+	0.816445i	$0.304058\pi$
$252$	1050.78	0.262669
$253$	0	0
$254$	−3369.63	−0.832399
$255$	−630.625	−0.154868
$256$	−7071.22	−1.72637
$257$	−3409.41	−0.827522	−0.413761	−	0.910385i	$-0.635785\pi$
$257$	−3409.41	−0.827522	−0.413761	+	0.910385i	$0.635785\pi$
$258$	−7095.15	−1.71211
$259$	862.664	0.206963
$260$	1742.51	0.415639
$261$	545.705	0.129419
$262$	−4491.82	−1.05918
$263$	−882.728	−0.206963	−0.103482	−	0.994631i	$-0.532998\pi$
$263$	−882.728	−0.206963	−0.103482	+	0.994631i	$0.532998\pi$
$264$	0	0
$265$	−4432.62	−1.02752
$266$	1869.90	0.431020
$267$	−6861.99	−1.57284
$268$	7294.81	1.66269
$269$	2805.83	0.635965	0.317982	−	0.948097i	$-0.396995\pi$
$269$	2805.83	0.635965	0.317982	+	0.948097i	$0.396995\pi$
$270$	6543.55	1.47492
$271$	6525.99	1.46282	0.731412	−	0.681935i	$-0.238862\pi$
$271$	6525.99	1.46282	0.731412	+	0.681935i	$0.238862\pi$
$272$	550.542	0.122726
$273$	708.915	0.157163
$274$	−11199.9	−2.46939
$275$	0	0
$276$	5277.95	1.15107
$277$	10.2630	0.00222616	0.00111308	−	0.999999i	$-0.499646\pi$
$277$	10.2630	0.00222616	0.00111308	+	0.999999i	$0.499646\pi$
$278$	−9834.79	−2.12177
$279$	303.172	0.0650553
$280$	3491.66	0.745239
$281$	1667.73	0.354052	0.177026	−	0.984206i	$-0.443352\pi$
$281$	1667.73	0.354052	0.177026	+	0.984206i	$0.443352\pi$
$282$	−7296.63	−1.54081
$283$	−1476.49	−0.310134	−0.155067	−	0.987904i	$-0.549559\pi$
$283$	−1476.49	−0.310134	−0.155067	+	0.987904i	$0.549559\pi$
$284$	−13029.4	−2.72236
$285$	1369.33	0.284604
$286$	0	0
$287$	−1392.19	−0.286336
$288$	512.857	0.104932
$289$	−4682.89	−0.953162
$290$	3951.75	0.800189
$291$	2899.00	0.583994
$292$	−1957.82	−0.392372
$293$	9585.67	1.91126	0.955632	−	0.294562i	$-0.0951738\pi$
$293$	9585.67	1.91126	0.955632	+	0.294562i	$0.0951738\pi$
$294$	−4411.24	−0.875064
$295$	−2236.73	−0.441449
$296$	−2348.77	−0.461214
$297$	0	0
$298$	1905.36	0.370385
$299$	−1012.19	−0.195775
$300$	−2901.08	−0.558314
$301$	3855.56	0.738308
$302$	2395.19	0.456384
$303$	6110.95	1.15863
$304$	−1195.44	−0.225537
$305$	4388.53	0.823890
$306$	−432.725	−0.0808407
$307$	6758.47	1.25644	0.628219	−	0.778037i	$-0.283784\pi$
$307$	6758.47	1.25644	0.628219	+	0.778037i	$0.283784\pi$
$308$	0	0
$309$	−3734.82	−0.687594
$310$	2195.44	0.402234
$311$	−6513.29	−1.18757	−0.593785	−	0.804623i	$-0.702367\pi$
$311$	−6513.29	−1.18757	−0.593785	+	0.804623i	$0.702367\pi$
$312$	−1930.16	−0.350236
$313$	56.2007	0.0101490	0.00507452	−	0.999987i	$-0.498385\pi$
$313$	56.2007	0.0101490	0.00507452	+	0.999987i	$0.498385\pi$
$314$	13494.8	2.42534
$315$	−644.413	−0.115265
$316$	−6631.35	−1.18051
$317$	−1302.94	−0.230853	−0.115426	−	0.993316i	$-0.536823\pi$
$317$	−1302.94	−0.230853	−0.115426	+	0.993316i	$0.536823\pi$
$318$	10700.1	1.88689
$319$	0	0
$320$	6346.28	1.10865
$321$	7857.12	1.36617
$322$	−4420.08	−0.764973
$323$	−499.669	−0.0860753
$324$	−7863.96	−1.34842
$325$	556.364	0.0949585
$326$	17413.6	2.95844
$327$	1007.58	0.170396
$328$	3790.51	0.638097
$329$	3965.04	0.664438
$330$	0	0
$331$	−5832.34	−0.968503	−0.484252	−	0.874929i	$-0.660908\pi$
$331$	−5832.34	−0.968503	−0.484252	+	0.874929i	$0.660908\pi$
$332$	14353.4	2.37273
$333$	433.483	0.0713354
$334$	6977.16	1.14303
$335$	−4473.71	−0.729627
$336$	−1979.11	−0.321337
$337$	10093.3	1.63150	0.815749	−	0.578406i	$-0.196325\pi$
$337$	10093.3	1.63150	0.815749	+	0.578406i	$0.196325\pi$
$338$	806.679	0.129815
$339$	4948.56	0.792829
$340$	−2033.32	−0.324329
$341$	0	0
$342$	939.615	0.148563
$343$	6476.44	1.01952
$344$	−10497.5	−1.64531
$345$	−3236.82	−0.505115
$346$	15508.6	2.40968
$347$	−11664.5	−1.80456	−0.902282	−	0.431146i	$-0.858109\pi$
$347$	−11664.5	−1.80456	−0.902282	+	0.431146i	$0.858109\pi$
$348$	−6189.80	−0.953472
$349$	−9533.46	−1.46222	−0.731109	−	0.682261i	$-0.760997\pi$
$349$	−9533.46	−1.46222	−0.731109	+	0.682261i	$0.760997\pi$
$350$	2429.55	0.371042
$351$	1965.62	0.298909
$352$	0	0
$353$	−10578.4	−1.59500	−0.797499	−	0.603321i	$-0.793844\pi$
$353$	−10578.4	−1.59500	−0.797499	+	0.603321i	$0.793844\pi$
$354$	5399.33	0.810653
$355$	7990.57	1.19463
$356$	−22125.0	−3.29389
$357$	−827.224	−0.122637
$358$	5536.99	0.817427
$359$	7869.83	1.15697	0.578487	−	0.815692i	$-0.303643\pi$
$359$	7869.83	1.15697	0.578487	+	0.815692i	$0.303643\pi$
$360$	1754.54	0.256867
$361$	−5774.02	−0.841817
$362$	6070.01	0.881305
$363$	0	0
$364$	2285.75	0.329136
$365$	1200.68	0.172182
$366$	−10593.6	−1.51295
$367$	−7239.25	−1.02966	−0.514831	−	0.857292i	$-0.672145\pi$
$367$	−7239.25	−1.02966	−0.514831	+	0.857292i	$0.672145\pi$
$368$	2825.78	0.400283
$369$	−699.567	−0.0986937
$370$	3139.09	0.441063
$371$	−5814.50	−0.813677
$372$	−3438.81	−0.479285
$373$	1489.27	0.206733	0.103366	−	0.994643i	$-0.467039\pi$
$373$	1489.27	0.206733	0.103366	+	0.994643i	$0.467039\pi$
$374$	0	0
$375$	6975.63	0.960587
$376$	−10795.6	−1.48069
$377$	1187.07	0.162167
$378$	8583.53	1.16796
$379$	−10526.0	−1.42661	−0.713306	−	0.700853i	$-0.752803\pi$
$379$	−10526.0	−1.42661	−0.713306	+	0.700853i	$0.752803\pi$
$380$	4415.12	0.596029
$381$	−3236.86	−0.435247
$382$	−11195.1	−1.49945
$383$	13890.7	1.85321	0.926607	−	0.376031i	$-0.122711\pi$
$383$	13890.7	1.85321	0.926607	+	0.376031i	$0.122711\pi$
$384$	−12171.7	−1.61753
$385$	0	0
$386$	−8608.30	−1.13511
$387$	1937.39	0.254479
$388$	9347.21	1.22302
$389$	3111.44	0.405543	0.202771	−	0.979226i	$-0.435005\pi$
$389$	3111.44	0.405543	0.202771	+	0.979226i	$0.435005\pi$
$390$	2579.62	0.334934
$391$	1181.12	0.152766
$392$	−6526.57	−0.840923
$393$	−4314.83	−0.553828
$394$	7889.89	1.00885
$395$	4066.83	0.518036
$396$	0	0
$397$	−7136.13	−0.902147	−0.451073	−	0.892487i	$-0.648959\pi$
$397$	−7136.13	−0.902147	−0.451073	+	0.892487i	$0.648959\pi$
$398$	−17882.6	−2.25219
$399$	1796.23	0.225373
$400$	−1553.22	−0.194153
$401$	−14665.5	−1.82633	−0.913167	−	0.407586i	$-0.866371\pi$
$401$	−14665.5	−1.82633	−0.913167	+	0.407586i	$0.866371\pi$
$402$	10799.3	1.33985
$403$	659.488	0.0815172
$404$	19703.4	2.42644
$405$	4822.76	0.591716
$406$	5183.72	0.633655
$407$	0	0
$408$	2252.28	0.273295
$409$	−5733.97	−0.693219	−0.346610	−	0.938010i	$-0.612667\pi$
$409$	−5733.97	−0.693219	−0.346610	+	0.938010i	$0.612667\pi$
$410$	−5065.95	−0.610218
$411$	−10758.6	−1.29120
$412$	−12042.1	−1.43998
$413$	−2934.04	−0.349575
$414$	−2221.06	−0.263669
$415$	−8802.56	−1.04121
$416$	1115.61	0.131484
$417$	−9447.28	−1.10944
$418$	0	0
$419$	−14210.7	−1.65690	−0.828448	−	0.560066i	$-0.810776\pi$
$419$	−14210.7	−1.65690	−0.828448	+	0.560066i	$0.810776\pi$
$420$	7309.43	0.849199
$421$	−13820.4	−1.59992	−0.799959	−	0.600055i	$-0.795146\pi$
$421$	−13820.4	−1.59992	−0.799959	+	0.600055i	$0.795146\pi$
$422$	1074.79	0.123981
$423$	1992.41	0.229017
$424$	15831.1	1.81327
$425$	−649.214	−0.0740976
$426$	−19288.7	−2.19376
$427$	5756.66	0.652423
$428$	25333.6	2.86109
$429$	0	0
$430$	14029.7	1.57343
$431$	−5076.09	−0.567300	−0.283650	−	0.958928i	$-0.591545\pi$
$431$	−5076.09	−0.567300	−0.283650	+	0.958928i	$0.591545\pi$
$432$	−5487.50	−0.611152
$433$	6801.79	0.754903	0.377452	−	0.926029i	$-0.376800\pi$
$433$	6801.79	0.754903	0.377452	+	0.926029i	$0.376800\pi$
$434$	2879.87	0.318521
$435$	3796.04	0.418405
$436$	3248.73	0.356849
$437$	−2564.66	−0.280742
$438$	−2898.36	−0.316185
$439$	−10759.7	−1.16978	−0.584890	−	0.811113i	$-0.698862\pi$
$439$	−10759.7	−1.16978	−0.584890	+	0.811113i	$0.698862\pi$
$440$	0	0
$441$	1204.53	0.130065
$442$	−941.304	−0.101297
$443$	9522.38	1.02127	0.510634	−	0.859798i	$-0.329411\pi$
$443$	9522.38	1.02127	0.510634	+	0.859798i	$0.329411\pi$
$444$	−4916.89	−0.525553
$445$	13568.7	1.44543
$446$	−4512.79	−0.479118
$447$	1830.29	0.193668
$448$	8324.75	0.877919
$449$	1190.40	0.125119	0.0625593	−	0.998041i	$-0.480074\pi$
$449$	1190.40	0.125119	0.0625593	+	0.998041i	$0.480074\pi$
$450$	1220.83	0.127890
$451$	0	0
$452$	15955.6	1.66037
$453$	2300.82	0.238635
$454$	−5889.90	−0.608870
$455$	−1401.79	−0.144432
$456$	−4890.57	−0.502241
$457$	17235.1	1.76416	0.882082	−	0.471096i	$-0.156142\pi$
$457$	17235.1	1.76416	0.882082	+	0.471096i	$0.156142\pi$
$458$	−22257.5	−2.27080
$459$	−2293.66	−0.233243
$460$	−10436.4	−1.05783
$461$	16519.2	1.66893	0.834463	−	0.551064i	$-0.185778\pi$
$461$	16519.2	1.66893	0.834463	+	0.551064i	$0.185778\pi$
$462$	0	0
$463$	−8199.50	−0.823030	−0.411515	−	0.911403i	$-0.635000\pi$
$463$	−8199.50	−0.823030	−0.411515	+	0.911403i	$0.635000\pi$
$464$	−3313.98	−0.331569
$465$	2108.93	0.210321
$466$	−11671.7	−1.16026
$467$	−15409.0	−1.52686	−0.763431	−	0.645889i	$-0.776487\pi$
$467$	−15409.0	−1.52686	−0.763431	+	0.645889i	$0.776487\pi$
$468$	1148.57	0.113446
$469$	−5868.41	−0.577778
$470$	14428.1	1.41600
$471$	12963.1	1.26817
$472$	7988.48	0.779025
$473$	0	0
$474$	−9817.07	−0.951294
$475$	1409.70	0.136171
$476$	−2667.21	−0.256830
$477$	−2921.75	−0.280456
$478$	27329.3	2.61509
$479$	−13545.8	−1.29211	−0.646057	−	0.763289i	$-0.723583\pi$
$479$	−13545.8	−1.29211	−0.646057	+	0.763289i	$0.723583\pi$
$480$	3567.54	0.339240
$481$	942.952	0.0893865
$482$	−13301.4	−1.25697
$483$	−4245.91	−0.399991
$484$	0	0
$485$	−5732.39	−0.536690
$486$	7844.66	0.732183
$487$	−13442.1	−1.25076	−0.625378	−	0.780322i	$-0.715055\pi$
$487$	−13442.1	−1.25076	−0.625378	+	0.780322i	$0.715055\pi$
$488$	−15673.6	−1.45392
$489$	16727.5	1.54692
$490$	8722.66	0.804182
$491$	2915.13	0.267939	0.133969	−	0.990985i	$-0.457228\pi$
$491$	2915.13	0.267939	0.133969	+	0.990985i	$0.457228\pi$
$492$	7935.02	0.727111
$493$	−1385.17	−0.126542
$494$	2043.94	0.186156
$495$	0	0
$496$	−1841.12	−0.166671
$497$	10481.6	0.946009
$498$	21248.8	1.91201
$499$	−3327.50	−0.298516	−0.149258	−	0.988798i	$-0.547688\pi$
$499$	−3327.50	−0.298516	−0.149258	+	0.988798i	$0.547688\pi$
$500$	22491.4	2.01170
$501$	6702.24	0.597673
$502$	21920.4	1.94892
$503$	6084.35	0.539339	0.269670	−	0.962953i	$-0.413085\pi$
$503$	6084.35	0.539339	0.269670	+	0.962953i	$0.413085\pi$
$504$	2301.52	0.203409
$505$	−12083.6	−1.06478
$506$	0	0
$507$	774.894	0.0678782
$508$	−10436.6	−0.911510
$509$	−2352.04	−0.204818	−0.102409	−	0.994742i	$-0.532655\pi$
$509$	−2352.04	−0.204818	−0.102409	+	0.994742i	$0.532655\pi$
$510$	−3010.13	−0.261354
$511$	1574.99	0.136348
$512$	−12516.1	−1.08035
$513$	4980.42	0.428638
$514$	−16274.0	−1.39653
$515$	7385.12	0.631898
$516$	−21975.4	−1.87483
$517$	0	0
$518$	4117.71	0.349270
$519$	14897.6	1.25998
$520$	3816.63	0.321866
$521$	7671.28	0.645077	0.322538	−	0.946556i	$-0.395464\pi$
$521$	7671.28	0.645077	0.322538	+	0.946556i	$0.395464\pi$
$522$	2604.79	0.218407
$523$	−12733.8	−1.06464	−0.532321	−	0.846542i	$-0.678680\pi$
$523$	−12733.8	−1.06464	−0.532321	+	0.846542i	$0.678680\pi$
$524$	−13912.2	−1.15985
$525$	2333.81	0.194011
$526$	−4213.48	−0.349271
$527$	−769.548	−0.0636092
$528$	0	0
$529$	−6104.66	−0.501739
$530$	−21158.0	−1.73405
$531$	−1474.34	−0.120491
$532$	5791.55	0.471984
$533$	−1521.76	−0.123668
$534$	−32754.0	−2.65431
$535$	−15536.4	−1.25551
$536$	15977.9	1.28757
$537$	5318.82	0.427419
$538$	13392.9	1.07325
$539$	0	0
$540$	20267.0	1.61509
$541$	5992.02	0.476187	0.238093	−	0.971242i	$-0.423478\pi$
$541$	5992.02	0.476187	0.238093	+	0.971242i	$0.423478\pi$
$542$	31150.2	2.46866
$543$	5830.83	0.460820
$544$	−1301.80	−0.102599
$545$	−1992.36	−0.156593
$546$	3383.83	0.265228
$547$	3837.04	0.299927	0.149963	−	0.988692i	$-0.452084\pi$
$547$	3837.04	0.299927	0.149963	+	0.988692i	$0.452084\pi$
$548$	−34688.9	−2.70408
$549$	2892.69	0.224876
$550$	0	0
$551$	3007.75	0.232549
$552$	11560.3	0.891376
$553$	5334.67	0.410223
$554$	48.9881	0.00375686
$555$	3015.40	0.230624
$556$	−30460.7	−2.32342
$557$	−22543.6	−1.71490	−0.857452	−	0.514563i	$-0.827954\pi$
$557$	−22543.6	−1.71490	−0.857452	+	0.514563i	$0.827954\pi$
$558$	1447.12	0.109787
$559$	4214.40	0.318873
$560$	3913.42	0.295308
$561$	0	0
$562$	7960.51	0.597498
$563$	−17443.9	−1.30581	−0.652907	−	0.757438i	$-0.726451\pi$
$563$	−17443.9	−1.30581	−0.652907	+	0.757438i	$0.726451\pi$
$564$	−22599.4	−1.68725
$565$	−9785.13	−0.728608
$566$	−7047.63	−0.523382
$567$	6326.27	0.468569
$568$	−28538.3	−2.10817
$569$	12215.4	0.899995	0.449997	−	0.893030i	$-0.351425\pi$
$569$	12215.4	0.899995	0.449997	+	0.893030i	$0.351425\pi$
$570$	6536.16	0.480298
$571$	15055.4	1.10341	0.551706	−	0.834039i	$-0.313977\pi$
$571$	15055.4	1.10341	0.551706	+	0.834039i	$0.313977\pi$
$572$	0	0
$573$	−10753.9	−0.784036
$574$	−6645.27	−0.483220
$575$	−3332.24	−0.241676
$576$	4183.13	0.302599
$577$	−7621.88	−0.549919	−0.274959	−	0.961456i	$-0.588664\pi$
$577$	−7621.88	−0.549919	−0.274959	+	0.961456i	$0.588664\pi$
$578$	−22352.6	−1.60855
$579$	−8269.11	−0.593528
$580$	12239.5	0.876239
$581$	−11546.8	−0.824511
$582$	13837.6	0.985548
$583$	0	0
$584$	−4288.22	−0.303849
$585$	−704.389	−0.0497827
$586$	45754.8	3.22545
$587$	7182.51	0.505032	0.252516	−	0.967593i	$-0.418742\pi$
$587$	7182.51	0.505032	0.252516	+	0.967593i	$0.418742\pi$
$588$	−13662.7	−0.958231
$589$	1670.99	0.116896
$590$	−10676.5	−0.744989
$591$	7579.01	0.527511
$592$	−2632.48	−0.182760
$593$	6280.73	0.434939	0.217470	−	0.976067i	$-0.430220\pi$
$593$	6280.73	0.434939	0.217470	+	0.976067i	$0.430220\pi$
$594$	0	0
$595$	1635.73	0.112703
$596$	5901.37	0.405586
$597$	−17178.0	−1.17763
$598$	−4831.45	−0.330389
$599$	−10192.7	−0.695261	−0.347631	−	0.937632i	$-0.613014\pi$
$599$	−10192.7	−0.695261	−0.347631	+	0.937632i	$0.613014\pi$
$600$	−6354.26	−0.432353
$601$	16378.7	1.11165	0.555825	−	0.831300i	$-0.312403\pi$
$601$	16378.7	1.11165	0.555825	+	0.831300i	$0.312403\pi$
$602$	18403.6	1.24597
$603$	−2948.84	−0.199147
$604$	7418.49	0.499759
$605$	0	0
$606$	29169.1	1.95530
$607$	−2478.17	−0.165709	−0.0828547	−	0.996562i	$-0.526404\pi$
$607$	−2478.17	−0.165709	−0.0828547	+	0.996562i	$0.526404\pi$
$608$	2826.71	0.188549
$609$	4979.47	0.331327
$610$	20947.5	1.39039
$611$	4334.07	0.286968
$612$	−1340.25	−0.0885238
$613$	−8550.12	−0.563354	−0.281677	−	0.959509i	$-0.590891\pi$
$613$	−8550.12	−0.563354	−0.281677	+	0.959509i	$0.590891\pi$
$614$	32259.9	2.12036
$615$	−4866.34	−0.319073
$616$	0	0
$617$	−4958.66	−0.323547	−0.161773	−	0.986828i	$-0.551721\pi$
$617$	−4958.66	−0.323547	−0.161773	+	0.986828i	$0.551721\pi$
$618$	−17827.2	−1.16038
$619$	16883.4	1.09629	0.548144	−	0.836384i	$-0.315335\pi$
$619$	16883.4	1.09629	0.548144	+	0.836384i	$0.315335\pi$
$620$	6799.80	0.440462
$621$	−11772.7	−0.760745
$622$	−31089.5	−2.00414
$623$	17798.8	1.14461
$624$	−2163.30	−0.138784
$625$	−8443.75	−0.540400
$626$	268.260	0.0171275
$627$	0	0
$628$	41796.8	2.65585
$629$	−1100.32	−0.0697497
$630$	−3075.94	−0.194521
$631$	−473.439	−0.0298689	−0.0149345	−	0.999888i	$-0.504754\pi$
$631$	−473.439	−0.0298689	−0.0149345	+	0.999888i	$0.504754\pi$
$632$	−14524.7	−0.914178
$633$	1032.44	0.0648273
$634$	−6219.25	−0.389587
$635$	6400.46	0.399991
$636$	33140.7	2.06622
$637$	2620.20	0.162977
$638$	0	0
$639$	5266.96	0.326068
$640$	24067.9	1.48651
$641$	−31090.9	−1.91579	−0.957893	−	0.287127i	$-0.907300\pi$
$641$	−31090.9	−1.91579	−0.957893	+	0.287127i	$0.907300\pi$
$642$	37504.0	2.30555
$643$	19604.9	1.20240	0.601199	−	0.799099i	$-0.294690\pi$
$643$	19604.9	1.20240	0.601199	+	0.799099i	$0.294690\pi$
$644$	−13690.0	−0.837676
$645$	13476.9	0.822719
$646$	−2385.04	−0.145261
$647$	30449.9	1.85025	0.925123	−	0.379667i	$-0.123961\pi$
$647$	30449.9	1.85025	0.925123	+	0.379667i	$0.123961\pi$
$648$	−17224.5	−1.04420
$649$	0	0
$650$	2655.66	0.160252
$651$	2766.40	0.166549
$652$	53934.2	3.23961
$653$	−30937.8	−1.85404	−0.927020	−	0.375012i	$-0.877639\pi$
$653$	−30937.8	−1.85404	−0.927020	+	0.375012i	$0.877639\pi$
$654$	4809.44	0.287560
$655$	8532.01	0.508966
$656$	4248.36	0.252852
$657$	791.423	0.0469960
$658$	18926.1	1.12130
$659$	−31012.0	−1.83317	−0.916584	−	0.399842i	$-0.869065\pi$
$659$	−31012.0	−1.83317	−0.916584	+	0.399842i	$0.869065\pi$
$660$	0	0
$661$	6859.42	0.403632	0.201816	−	0.979423i	$-0.435316\pi$
$661$	6859.42	0.403632	0.201816	+	0.979423i	$0.435316\pi$
$662$	−27839.2	−1.63444
$663$	−904.214	−0.0529665
$664$	31438.3	1.83741
$665$	−3551.80	−0.207117
$666$	2069.12	0.120386
$667$	−7109.72	−0.412728
$668$	21609.9	1.25167
$669$	−4334.98	−0.250523
$670$	−21354.1	−1.23132
$671$	0	0
$672$	4679.74	0.268638
$673$	13973.4	0.800349	0.400175	−	0.916439i	$-0.368950\pi$
$673$	13973.4	0.800349	0.400175	+	0.916439i	$0.368950\pi$
$674$	48177.6	2.75331
$675$	6471.00	0.368991
$676$	2498.48	0.142153
$677$	−17009.0	−0.965598	−0.482799	−	0.875731i	$-0.660380\pi$
$677$	−17009.0	−0.965598	−0.482799	+	0.875731i	$0.660380\pi$
$678$	23620.7	1.33798
$679$	−7519.48	−0.424995
$680$	−4453.58	−0.251157
$681$	−5657.83	−0.318368
$682$	0	0
$683$	11464.8	0.642298	0.321149	−	0.947029i	$-0.395931\pi$
$683$	11464.8	0.642298	0.321149	+	0.947029i	$0.395931\pi$
$684$	2910.21	0.162682
$685$	21273.8	1.18661
$686$	30913.7	1.72054
$687$	−21380.5	−1.18736
$688$	−11765.5	−0.651970
$689$	−6355.66	−0.351424
$690$	−15450.2	−0.852431
$691$	5067.06	0.278958	0.139479	−	0.990225i	$-0.455457\pi$
$691$	5067.06	0.278958	0.139479	+	0.990225i	$0.455457\pi$
$692$	48034.0	2.63870
$693$	0	0
$694$	−55677.6	−3.04538
$695$	18680.8	1.01957
$696$	−13557.6	−0.738359
$697$	1775.73	0.0964998
$698$	−45505.6	−2.46764
$699$	−11211.8	−0.606678
$700$	7524.89	0.406306
$701$	−34685.3	−1.86883	−0.934413	−	0.356191i	$-0.884075\pi$
$701$	−34685.3	−1.86883	−0.934413	+	0.356191i	$0.884075\pi$
$702$	9382.39	0.504438
$703$	2389.22	0.128181
$704$	0	0
$705$	13859.6	0.740402
$706$	−50493.6	−2.69171
$707$	−15850.7	−0.843178
$708$	16723.0	0.887698
$709$	11799.7	0.625031	0.312516	−	0.949913i	$-0.398828\pi$
$709$	11799.7	0.625031	0.312516	+	0.949913i	$0.398828\pi$
$710$	38141.0	2.01606
$711$	2680.64	0.141395
$712$	−48460.6	−2.55075
$713$	−3949.88	−0.207467
$714$	−3948.55	−0.206962
$715$	0	0
$716$	17149.4	0.895116
$717$	26252.5	1.36739
$718$	37564.6	1.95251
$719$	−710.761	−0.0368664	−0.0184332	−	0.999830i	$-0.505868\pi$
$719$	−710.761	−0.0368664	−0.0184332	+	0.999830i	$0.505868\pi$
$720$	1966.47	0.101786
$721$	9687.45	0.500388
$722$	−27560.9	−1.42065
$723$	−12777.3	−0.657250
$724$	18800.3	0.965065
$725$	3907.94	0.200189
$726$	0	0
$727$	10823.4	0.552159	0.276079	−	0.961135i	$-0.410965\pi$
$727$	10823.4	0.552159	0.276079	+	0.961135i	$0.410965\pi$
$728$	5006.48	0.254880
$729$	21897.6	1.11251
$730$	5731.13	0.290574
$731$	−4917.73	−0.248822
$732$	−32811.1	−1.65674
$733$	−13712.5	−0.690972	−0.345486	−	0.938424i	$-0.612286\pi$
$733$	−13712.5	−0.690972	−0.345486	+	0.938424i	$0.612286\pi$
$734$	−34554.7	−1.73765
$735$	8378.96	0.420493
$736$	−6681.76	−0.334637
$737$	0	0
$738$	−3339.21	−0.166555
$739$	28709.5	1.42909	0.714544	−	0.699590i	$-0.246634\pi$
$739$	28709.5	1.42909	0.714544	+	0.699590i	$0.246634\pi$
$740$	9722.51	0.482982
$741$	1963.40	0.0973378
$742$	−27754.1	−1.37316
$743$	−26232.5	−1.29526	−0.647629	−	0.761956i	$-0.724239\pi$
$743$	−26232.5	−1.29526	−0.647629	+	0.761956i	$0.724239\pi$
$744$	−7532.05	−0.371154
$745$	−3619.15	−0.177980
$746$	7108.65	0.348882
$747$	−5802.18	−0.284191
$748$	0	0
$749$	−20380.0	−0.994216
$750$	33296.4	1.62108
$751$	21560.4	1.04760	0.523801	−	0.851841i	$-0.324513\pi$
$751$	21560.4	1.04760	0.523801	+	0.851841i	$0.324513\pi$
$752$	−12099.6	−0.586738
$753$	21056.7	1.01906
$754$	5666.17	0.273673
$755$	−4549.57	−0.219305
$756$	26585.3	1.27896
$757$	−15876.4	−0.762271	−0.381135	−	0.924519i	$-0.624467\pi$
$757$	−15876.4	−0.762271	−0.381135	+	0.924519i	$0.624467\pi$
$758$	−50243.3	−2.40755
$759$	0	0
$760$	9670.46	0.461559
$761$	−15532.1	−0.739865	−0.369933	−	0.929059i	$-0.620619\pi$
$761$	−15532.1	−0.739865	−0.369933	+	0.929059i	$0.620619\pi$
$762$	−15450.3	−0.734522
$763$	−2613.49	−0.124003
$764$	−34673.8	−1.64196
$765$	821.942	0.0388463
$766$	66303.7	3.12748
$767$	−3207.11	−0.150980
$768$	−32422.7	−1.52338
$769$	−31012.1	−1.45426	−0.727130	−	0.686500i	$-0.759146\pi$
$769$	−31012.1	−1.45426	−0.727130	+	0.686500i	$0.759146\pi$
$770$	0	0
$771$	−15632.7	−0.730220
$772$	−26662.0	−1.24299
$773$	−11624.1	−0.540869	−0.270434	−	0.962738i	$-0.587167\pi$
$773$	−11624.1	−0.540869	−0.270434	+	0.962738i	$0.587167\pi$
$774$	9247.66	0.429458
$775$	2171.10	0.100630
$776$	20473.2	0.947096
$777$	3955.46	0.182627
$778$	14851.7	0.684393
$779$	−3855.79	−0.177340
$780$	7989.72	0.366766
$781$	0	0
$782$	5637.76	0.257808
$783$	13806.7	0.630153
$784$	−7314.92	−0.333223
$785$	−25632.9	−1.16545
$786$	−20595.7	−0.934638
$787$	30975.4	1.40299	0.701496	−	0.712673i	$-0.252516\pi$
$787$	30975.4	1.40299	0.701496	+	0.712673i	$0.252516\pi$
$788$	24436.9	1.10473
$789$	−4047.46	−0.182628
$790$	19412.0	0.874237
$791$	−12835.7	−0.576971
$792$	0	0
$793$	6292.44	0.281779
$794$	−34062.5	−1.52246
$795$	−20324.3	−0.906704
$796$	−55386.7	−2.46624
$797$	−37851.8	−1.68228	−0.841142	−	0.540814i	$-0.818116\pi$
$797$	−37851.8	−1.68228	−0.841142	+	0.540814i	$0.818116\pi$
$798$	8573.83	0.380339
$799$	−5057.37	−0.223926
$800$	3672.70	0.162312
$801$	8943.76	0.394522
$802$	−70002.0	−3.08212
$803$	0	0
$804$	33448.0	1.46719
$805$	8395.74	0.367591
$806$	3147.90	0.137568
$807$	12865.2	0.561186
$808$	43156.6	1.87901
$809$	−19791.9	−0.860132	−0.430066	−	0.902797i	$-0.641510\pi$
$809$	−19791.9	−0.860132	−0.430066	+	0.902797i	$0.641510\pi$
$810$	23020.2	0.998578
$811$	−2693.15	−0.116608	−0.0583042	−	0.998299i	$-0.518569\pi$
$811$	−2693.15	−0.116608	−0.0583042	+	0.998299i	$0.518569\pi$
$812$	16055.2	0.693877
$813$	29922.8	1.29082
$814$	0	0
$815$	−33076.4	−1.42161
$816$	2524.33	0.108296
$817$	10678.3	0.457266
$818$	−27369.7	−1.16988
$819$	−923.984	−0.0394220
$820$	−15690.5	−0.668213
$821$	3105.45	0.132011	0.0660055	−	0.997819i	$-0.478975\pi$
$821$	3105.45	0.132011	0.0660055	+	0.997819i	$0.478975\pi$
$822$	−51353.6	−2.17903
$823$	−42198.7	−1.78731	−0.893654	−	0.448756i	$-0.851867\pi$
$823$	−42198.7	−1.78731	−0.893654	+	0.448756i	$0.851867\pi$
$824$	−26376.0	−1.11511
$825$	0	0
$826$	−14004.9	−0.589943
$827$	36205.4	1.52235	0.761175	−	0.648546i	$-0.224623\pi$
$827$	36205.4	1.52235	0.761175	+	0.648546i	$0.224623\pi$
$828$	−6879.15	−0.288728
$829$	11988.2	0.502251	0.251126	−	0.967954i	$-0.419199\pi$
$829$	11988.2	0.502251	0.251126	+	0.967954i	$0.419199\pi$
$830$	−42016.8	−1.75714
$831$	47.0578	0.00196440
$832$	9099.54	0.379170
$833$	−3057.48	−0.127173
$834$	−45094.2	−1.87228
$835$	−13252.8	−0.549260
$836$	0	0
$837$	7670.43	0.316761
$838$	−67831.3	−2.79617
$839$	11022.7	0.453573	0.226786	−	0.973945i	$-0.427178\pi$
$839$	11022.7	0.453573	0.226786	+	0.973945i	$0.427178\pi$
$840$	16009.9	0.657611
$841$	−16051.0	−0.658123
$842$	−65968.3	−2.70002
$843$	7646.84	0.312421
$844$	3328.87	0.135764
$845$	−1532.25	−0.0623799
$846$	9510.26	0.386489
$847$	0	0
$848$	17743.3	0.718525
$849$	−6769.94	−0.273668
$850$	−3098.86	−0.125047
$851$	−5647.63	−0.227495
$852$	−59741.9	−2.40226
$853$	27784.7	1.11527	0.557637	−	0.830085i	$-0.311708\pi$
$853$	27784.7	1.11527	0.557637	+	0.830085i	$0.311708\pi$
$854$	27478.0	1.10103
$855$	−1784.76	−0.0713887
$856$	55488.4	2.21560
$857$	29633.9	1.18118	0.590592	−	0.806970i	$-0.298894\pi$
$857$	29633.9	1.18118	0.590592	+	0.806970i	$0.298894\pi$
$858$	0	0
$859$	−24852.1	−0.987126	−0.493563	−	0.869710i	$-0.664306\pi$
$859$	−24852.1	−0.987126	−0.493563	+	0.869710i	$0.664306\pi$
$860$	43453.5	1.72297
$861$	−6383.43	−0.252668
$862$	−24229.4	−0.957375
$863$	43483.0	1.71515	0.857577	−	0.514356i	$-0.171969\pi$
$863$	43483.0	1.71515	0.857577	+	0.514356i	$0.171969\pi$
$864$	12975.6	0.510924
$865$	−29458.0	−1.15792
$866$	32466.6	1.27397
$867$	−21471.8	−0.841086
$868$	8919.66	0.348794
$869$	0	0
$870$	18119.5	0.706100
$871$	−6414.58	−0.249540
$872$	7115.72	0.276340
$873$	−3778.49	−0.146486
$874$	−12241.8	−0.473780
$875$	−18093.5	−0.699055
$876$	−8976.93	−0.346236
$877$	18488.9	0.711887	0.355943	−	0.934508i	$-0.384160\pi$
$877$	18488.9	0.711887	0.355943	+	0.934508i	$0.384160\pi$
$878$	−51358.8	−1.97412
$879$	43951.9	1.68653
$880$	0	0
$881$	14831.7	0.567189	0.283594	−	0.958944i	$-0.408473\pi$
$881$	14831.7	0.567189	0.283594	+	0.958944i	$0.408473\pi$
$882$	5749.51	0.219497
$883$	4167.10	0.158816	0.0794078	−	0.996842i	$-0.474697\pi$
$883$	4167.10	0.158816	0.0794078	+	0.996842i	$0.474697\pi$
$884$	−2915.45	−0.110924
$885$	−10255.8	−0.389542
$886$	45452.7	1.72349
$887$	33695.1	1.27550	0.637752	−	0.770242i	$-0.279865\pi$
$887$	33695.1	1.27550	0.637752	+	0.770242i	$0.279865\pi$
$888$	−10769.5	−0.406983
$889$	8395.82	0.316746
$890$	64766.7	2.43931
$891$	0	0
$892$	−13977.2	−0.524654
$893$	10981.5	0.411515
$894$	8736.41	0.326834
$895$	−10517.3	−0.392797
$896$	31571.1	1.17714
$897$	−4641.08	−0.172755
$898$	5682.05	0.211150
$899$	4632.29	0.171853
$900$	3781.21	0.140045
$901$	7416.34	0.274222
$902$	0	0
$903$	17678.4	0.651496
$904$	34947.6	1.28577
$905$	−11529.7	−0.423492
$906$	10982.4	0.402721
$907$	−4805.35	−0.175920	−0.0879598	−	0.996124i	$-0.528035\pi$
$907$	−4805.35	−0.175920	−0.0879598	+	0.996124i	$0.528035\pi$
$908$	−18242.5	−0.666737
$909$	−7964.87	−0.290625
$910$	−6691.08	−0.243744
$911$	−31.3854	−0.00114143	−0.000570716	−	1.00000i	$-0.500182\pi$
$911$	−31.3854	−0.00114143	−0.000570716		1.00000i	$0.500182\pi$
$912$	−5481.30	−0.199018
$913$	0	0
$914$	82267.3	2.97720
$915$	20122.1	0.727014
$916$	−68937.0	−2.48662
$917$	11191.9	0.403041
$918$	−10948.2	−0.393621
$919$	2340.98	0.0840281	0.0420141	−	0.999117i	$-0.486623\pi$
$919$	2340.98	0.0840281	0.0420141	+	0.999117i	$0.486623\pi$
$920$	−22859.0	−0.819173
$921$	30988.8	1.10870
$922$	78850.2	2.81648
$923$	11457.2	0.408578
$924$	0	0
$925$	3104.28	0.110344
$926$	−39138.3	−1.38894
$927$	4867.88	0.172473
$928$	7836.15	0.277192
$929$	−2330.64	−0.0823097	−0.0411548	−	0.999153i	$-0.513104\pi$
$929$	−2330.64	−0.0823097	−0.0411548	+	0.999153i	$0.513104\pi$
$930$	10066.5	0.354938
$931$	6638.98	0.233710
$932$	−36149.9	−1.27053
$933$	−29864.5	−1.04793
$934$	−73551.1	−2.57673
$935$	0	0
$936$	2515.72	0.0878515
$937$	−16298.7	−0.568254	−0.284127	−	0.958787i	$-0.591704\pi$
$937$	−16298.7	−0.568254	−0.284127	+	0.958787i	$0.591704\pi$
$938$	−28011.4	−0.975057
$939$	257.690	0.00895568
$940$	44687.4	1.55058
$941$	24321.1	0.842557	0.421278	−	0.906931i	$-0.361582\pi$
$941$	24321.1	0.842557	0.421278	+	0.906931i	$0.361582\pi$
$942$	61876.2	2.14016
$943$	9114.31	0.314743
$944$	8953.42	0.308696
$945$	−16304.0	−0.561238
$946$	0	0
$947$	39588.2	1.35844	0.679221	−	0.733934i	$-0.262318\pi$
$947$	39588.2	1.35844	0.679221	+	0.733934i	$0.262318\pi$
$948$	−30405.9	−1.04170
$949$	1721.58	0.0588881
$950$	6728.83	0.229802
$951$	−5974.20	−0.203708
$952$	−5842.00	−0.198887
$953$	25081.1	0.852526	0.426263	−	0.904599i	$-0.359830\pi$
$953$	25081.1	0.852526	0.426263	+	0.904599i	$0.359830\pi$
$954$	−13946.2	−0.473298
$955$	21264.5	0.720528
$956$	84645.5	2.86363
$957$	0	0
$958$	−64657.4	−2.18057
$959$	27906.0	0.939656
$960$	29098.8	0.978290
$961$	−27217.5	−0.913614
$962$	4500.94	0.150848
$963$	−10240.8	−0.342684
$964$	−41197.6	−1.37644
$965$	16351.1	0.545451
$966$	−20266.8	−0.675024
$967$	14890.4	0.495185	0.247593	−	0.968864i	$-0.420361\pi$
$967$	14890.4	0.495185	0.247593	+	0.968864i	$0.420361\pi$
$968$	0	0
$969$	−2291.07	−0.0759543
$970$	−27362.1	−0.905717
$971$	−11633.6	−0.384492	−0.192246	−	0.981347i	$-0.561577\pi$
$971$	−11633.6	−0.384492	−0.192246	+	0.981347i	$0.561577\pi$
$972$	24296.8	0.801770
$973$	24504.5	0.807379
$974$	−64162.3	−2.11077
$975$	2551.02	0.0837929
$976$	−17566.8	−0.576128
$977$	−33160.5	−1.08587	−0.542936	−	0.839774i	$-0.682688\pi$
$977$	−33160.5	−1.08587	−0.542936	+	0.839774i	$0.682688\pi$
$978$	79844.4	2.61057
$979$	0	0
$980$	27016.2	0.880612
$981$	−1313.26	−0.0427412
$982$	13914.6	0.452173
$983$	−8985.92	−0.291563	−0.145781	−	0.989317i	$-0.546570\pi$
$983$	−8985.92	−0.291563	−0.145781	+	0.989317i	$0.546570\pi$
$984$	17380.1	0.563067
$985$	−14986.5	−0.484781
$986$	−6611.78	−0.213552
$987$	18180.4	0.586311
$988$	6330.57	0.203848
$989$	−25241.3	−0.811555
$990$	0	0
$991$	22624.0	0.725202	0.362601	−	0.931944i	$-0.381889\pi$
$991$	22624.0	0.725202	0.362601	+	0.931944i	$0.381889\pi$
$992$	4353.46	0.139337
$993$	−26742.3	−0.854623
$994$	50031.5	1.59648
$995$	33967.2	1.08224
$996$	65812.8	2.09373
$997$	−27806.8	−0.883299	−0.441649	−	0.897188i	$-0.645606\pi$
$997$	−27806.8	−0.883299	−0.441649	+	0.897188i	$0.645606\pi$
$998$	−15883.0	−0.503775
$999$	10967.4	0.347339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.4.a.p.1.33		34
11.7	odd	10		143.4.h.a.27.1	✓	68
11.8	odd	10		143.4.h.a.53.1	yes	68
11.10	odd	2		1573.4.a.o.1.2		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.h.a.27.1	✓	68	11.7	odd	10
143.4.h.a.53.1	yes	68	11.8	odd	10
1573.4.a.o.1.2		34	11.10	odd	2
1573.4.a.p.1.33		34	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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q+4.77325 q^{2} +4.58517 q^{3} +14.7839 q^{4} -9.06658 q^{5} +21.8862 q^{6} -11.8931 q^{7} +32.3813 q^{8} -5.97621 q^{9} +O(q^{10})\)	\(q+4.77325 q^{2} +4.58517 q^{3} +14.7839 q^{4} -9.06658 q^{5} +21.8862 q^{6} -11.8931 q^{7} +32.3813 q^{8} -5.97621 q^{9} -43.2770 q^{10} +67.7867 q^{12} -13.0000 q^{13} -56.7688 q^{14} -41.5718 q^{15} +36.2926 q^{16} +15.1695 q^{17} -28.5259 q^{18} -32.9390 q^{19} -134.039 q^{20} -54.5319 q^{21} +77.8610 q^{23} +148.474 q^{24} -42.7972 q^{25} -62.0522 q^{26} -151.202 q^{27} -175.827 q^{28} -91.3129 q^{29} -198.433 q^{30} -50.7299 q^{31} -85.8164 q^{32} +72.4080 q^{34} +107.830 q^{35} -88.3517 q^{36} -72.5347 q^{37} -157.226 q^{38} -59.6072 q^{39} -293.587 q^{40} +117.059 q^{41} -260.295 q^{42} -324.184 q^{43} +54.1837 q^{45} +371.650 q^{46} -333.390 q^{47} +166.408 q^{48} -201.554 q^{49} -204.282 q^{50} +69.5549 q^{51} -192.191 q^{52} +488.897 q^{53} -721.723 q^{54} -385.114 q^{56} -151.031 q^{57} -435.859 q^{58} +246.701 q^{59} -614.594 q^{60} -484.034 q^{61} -242.146 q^{62} +71.0757 q^{63} -699.964 q^{64} +117.865 q^{65} +493.429 q^{67} +224.265 q^{68} +357.006 q^{69} +514.698 q^{70} -881.321 q^{71} -193.517 q^{72} -132.429 q^{73} -346.226 q^{74} -196.233 q^{75} -486.967 q^{76} -284.520 q^{78} -448.552 q^{79} -329.050 q^{80} -531.927 q^{81} +558.750 q^{82} +970.880 q^{83} -806.195 q^{84} -137.536 q^{85} -1547.41 q^{86} -418.685 q^{87} -1496.56 q^{89} +258.632 q^{90} +154.610 q^{91} +1151.09 q^{92} -232.605 q^{93} -1591.35 q^{94} +298.644 q^{95} -393.483 q^{96} +632.256 q^{97} -962.067 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9	\( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9} + 18 q^{10} - 262 q^{12} - 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} + 209 q^{17} + 190 q^{18} + 107 q^{19} - 211 q^{20} + 68 q^{21} - 632 q^{23} - 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} + 931 q^{28} + 32 q^{29} + 300 q^{30} - 290 q^{31} - 876 q^{32} - 602 q^{34} - 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} + 377 q^{39} - 1159 q^{40} + 1121 q^{41} + 79 q^{42} - 349 q^{43} - 1024 q^{45} - 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} + 1322 q^{50} - 1414 q^{51} - 1261 q^{52} - 2608 q^{53} - 3131 q^{54} - 1675 q^{56} + 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} + 236 q^{61} - 1396 q^{62} - 1206 q^{63} + 1331 q^{64} + 364 q^{65} - 3213 q^{67} + 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} + 5074 q^{72} - 823 q^{73} - 2550 q^{74} - 3063 q^{75} - 2004 q^{76} + 468 q^{78} + 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} + 3843 q^{83} - 7191 q^{84} - 1582 q^{85} - 3542 q^{86} - 962 q^{87} - 3633 q^{89} + 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} + 6309 q^{94} - 1916 q^{95} + 2150 q^{96} + 1195 q^{97} + 1487 q^{98}+O(q^{100}) \) 34 * q + 3 * q^2 - 29 * q^3 + 97 * q^4 - 28 * q^5 - 36 * q^6 + 36 * q^7 + 57 * q^8 + 265 * q^9 + 18 * q^10 - 262 * q^12 - 442 * q^13 - 231 * q^14 - 196 * q^15 + 225 * q^16 + 209 * q^17 + 190 * q^18 + 107 * q^19 - 211 * q^20 + 68 * q^21 - 632 * q^23 - 152 * q^24 + 296 * q^25 - 39 * q^26 - 920 * q^27 + 931 * q^28 + 32 * q^29 + 300 * q^30 - 290 * q^31 - 876 * q^32 - 602 * q^34 - 104 * q^35 - 611 * q^36 - 656 * q^37 - 1361 * q^38 + 377 * q^39 - 1159 * q^40 + 1121 * q^41 + 79 * q^42 - 349 * q^43 - 1024 * q^45 - 490 * q^46 - 1608 * q^47 - 1827 * q^48 + 808 * q^49 + 1322 * q^50 - 1414 * q^51 - 1261 * q^52 - 2608 * q^53 - 3131 * q^54 - 1675 * q^56 + 2150 * q^57 - 1673 * q^58 - 2011 * q^59 - 201 * q^60 + 236 * q^61 - 1396 * q^62 - 1206 * q^63 + 1331 * q^64 + 364 * q^65 - 3213 * q^67 + 1321 * q^68 - 162 * q^69 + 174 * q^70 - 3756 * q^71 + 5074 * q^72 - 823 * q^73 - 2550 * q^74 - 3063 * q^75 - 2004 * q^76 + 468 * q^78 + 2120 * q^79 - 5005 * q^80 + 710 * q^81 - 2534 * q^82 + 3843 * q^83 - 7191 * q^84 - 1582 * q^85 - 3542 * q^86 - 962 * q^87 - 3633 * q^89 + 995 * q^90 - 468 * q^91 - 2072 * q^92 - 508 * q^93 + 6309 * q^94 - 1916 * q^95 + 2150 * q^96 + 1195 * q^97 + 1487 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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