LMFDB - Embedded newform 6017.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58820 q^{2} +0.659368 q^{3} +4.69880 q^{4} +0.894285 q^{5} -1.70658 q^{6} -1.01597 q^{7} -6.98504 q^{8} -2.56523 q^{9} +O(q^{10})$	\(q-2.58820 q^{2} +0.659368 q^{3} +4.69880 q^{4} +0.894285 q^{5} -1.70658 q^{6} -1.01597 q^{7} -6.98504 q^{8} -2.56523 q^{9} -2.31459 q^{10} -1.00000 q^{11} +3.09824 q^{12} -5.95469 q^{13} +2.62953 q^{14} +0.589663 q^{15} +8.68111 q^{16} -1.93269 q^{17} +6.63935 q^{18} -6.93846 q^{19} +4.20207 q^{20} -0.669897 q^{21} +2.58820 q^{22} -3.10040 q^{23} -4.60571 q^{24} -4.20025 q^{25} +15.4119 q^{26} -3.66954 q^{27} -4.77383 q^{28} +3.73242 q^{29} -1.52617 q^{30} -0.466224 q^{31} -8.49841 q^{32} -0.659368 q^{33} +5.00221 q^{34} -0.908565 q^{35} -12.0535 q^{36} -0.0454310 q^{37} +17.9582 q^{38} -3.92633 q^{39} -6.24662 q^{40} -4.03817 q^{41} +1.73383 q^{42} +5.37089 q^{43} -4.69880 q^{44} -2.29405 q^{45} +8.02448 q^{46} -2.95293 q^{47} +5.72405 q^{48} -5.96781 q^{49} +10.8711 q^{50} -1.27436 q^{51} -27.9799 q^{52} -6.33238 q^{53} +9.49751 q^{54} -0.894285 q^{55} +7.09658 q^{56} -4.57500 q^{57} -9.66027 q^{58} +2.90710 q^{59} +2.77071 q^{60} +7.41467 q^{61} +1.20668 q^{62} +2.60620 q^{63} +4.63339 q^{64} -5.32519 q^{65} +1.70658 q^{66} +13.9448 q^{67} -9.08134 q^{68} -2.04431 q^{69} +2.35155 q^{70} +0.747547 q^{71} +17.9183 q^{72} -2.02637 q^{73} +0.117585 q^{74} -2.76951 q^{75} -32.6024 q^{76} +1.01597 q^{77} +10.1621 q^{78} -14.9034 q^{79} +7.76339 q^{80} +5.27613 q^{81} +10.4516 q^{82} -17.7454 q^{83} -3.14771 q^{84} -1.72838 q^{85} -13.9010 q^{86} +2.46104 q^{87} +6.98504 q^{88} +2.65481 q^{89} +5.93747 q^{90} +6.04977 q^{91} -14.5682 q^{92} -0.307413 q^{93} +7.64279 q^{94} -6.20496 q^{95} -5.60358 q^{96} +12.9755 q^{97} +15.4459 q^{98} +2.56523 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.58820	−1.83014	−0.915068	−	0.403299i	$-0.867863\pi$
$2$	−2.58820	−1.83014	−0.915068	+	0.403299i	$0.867863\pi$
$3$	0.659368	0.380686	0.190343	−	0.981718i	$-0.439040\pi$
$3$	0.659368	0.380686	0.190343	+	0.981718i	$0.439040\pi$
$4$	4.69880	2.34940
$5$	0.894285	0.399936	0.199968	−	0.979802i	$-0.435916\pi$
$5$	0.894285	0.399936	0.199968	+	0.979802i	$0.435916\pi$
$6$	−1.70658	−0.696708
$7$	−1.01597	−0.384000	−0.192000	−	0.981395i	$-0.561497\pi$
$7$	−1.01597	−0.384000	−0.192000	+	0.981395i	$0.561497\pi$
$8$	−6.98504	−2.46959
$9$	−2.56523	−0.855078
$10$	−2.31459	−0.731938
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.09824	0.894384
$13$	−5.95469	−1.65153	−0.825766	−	0.564012i	$-0.809257\pi$
$13$	−5.95469	−1.65153	−0.825766	+	0.564012i	$0.809257\pi$
$14$	2.62953	0.702772
$15$	0.589663	0.152250
$16$	8.68111	2.17028
$17$	−1.93269	−0.468747	−0.234374	−	0.972147i	$-0.575304\pi$
$17$	−1.93269	−0.468747	−0.234374	+	0.972147i	$0.575304\pi$
$18$	6.63935	1.56491
$19$	−6.93846	−1.59179	−0.795896	−	0.605433i	$-0.793000\pi$
$19$	−6.93846	−1.59179	−0.795896	+	0.605433i	$0.793000\pi$
$20$	4.20207	0.939611
$21$	−0.669897	−0.146183
$22$	2.58820	0.551807
$23$	−3.10040	−0.646479	−0.323239	−	0.946317i	$-0.604772\pi$
$23$	−3.10040	−0.646479	−0.323239	+	0.946317i	$0.604772\pi$
$24$	−4.60571	−0.940137
$25$	−4.20025	−0.840051
$26$	15.4119	3.02253
$27$	−3.66954	−0.706203
$28$	−4.77383	−0.902169
$29$	3.73242	0.693093	0.346547	−	0.938033i	$-0.387354\pi$
$29$	3.73242	0.693093	0.346547	+	0.938033i	$0.387354\pi$
$30$	−1.52617	−0.278639
$31$	−0.466224	−0.0837364	−0.0418682	−	0.999123i	$-0.513331\pi$
$31$	−0.466224	−0.0837364	−0.0418682	+	0.999123i	$0.513331\pi$
$32$	−8.49841	−1.50232
$33$	−0.659368	−0.114781
$34$	5.00221	0.857871
$35$	−0.908565	−0.153576
$36$	−12.0535	−2.00892
$37$	−0.0454310	−0.00746881	−0.00373440	−	0.999993i	$-0.501189\pi$
$37$	−0.0454310	−0.00746881	−0.00373440	+	0.999993i	$0.501189\pi$
$38$	17.9582	2.91320
$39$	−3.92633	−0.628716
$40$	−6.24662	−0.987677
$41$	−4.03817	−0.630657	−0.315328	−	0.948983i	$-0.602115\pi$
$41$	−4.03817	−0.630657	−0.315328	+	0.948983i	$0.602115\pi$
$42$	1.73383	0.267536
$43$	5.37089	0.819053	0.409527	−	0.912298i	$-0.365694\pi$
$43$	5.37089	0.819053	0.409527	+	0.912298i	$0.365694\pi$
$44$	−4.69880	−0.708371
$45$	−2.29405	−0.341977
$46$	8.02448	1.18314
$47$	−2.95293	−0.430729	−0.215365	−	0.976534i	$-0.569094\pi$
$47$	−2.95293	−0.430729	−0.215365	+	0.976534i	$0.569094\pi$
$48$	5.72405	0.826195
$49$	−5.96781	−0.852544
$50$	10.8711	1.53741
$51$	−1.27436	−0.178446
$52$	−27.9799	−3.88011
$53$	−6.33238	−0.869820	−0.434910	−	0.900474i	$-0.643220\pi$
$53$	−6.33238	−0.869820	−0.434910	+	0.900474i	$0.643220\pi$
$54$	9.49751	1.29245
$55$	−0.894285	−0.120585
$56$	7.09658	0.948320
$57$	−4.57500	−0.605974
$58$	−9.66027	−1.26846
$59$	2.90710	0.378472	0.189236	−	0.981932i	$-0.439399\pi$
$59$	2.90710	0.378472	0.189236	+	0.981932i	$0.439399\pi$
$60$	2.77071	0.357697
$61$	7.41467	0.949351	0.474675	−	0.880161i	$-0.342565\pi$
$61$	7.41467	0.949351	0.474675	+	0.880161i	$0.342565\pi$
$62$	1.20668	0.153249
$63$	2.60620	0.328350
$64$	4.63339	0.579173
$65$	−5.32519	−0.660508
$66$	1.70658	0.210065
$67$	13.9448	1.70363	0.851816	−	0.523840i	$-0.175501\pi$
$67$	13.9448	1.70363	0.851816	+	0.523840i	$0.175501\pi$
$68$	−9.08134	−1.10127
$69$	−2.04431	−0.246106
$70$	2.35155	0.281064
$71$	0.747547	0.0887176	0.0443588	−	0.999016i	$-0.485876\pi$
$71$	0.747547	0.0887176	0.0443588	+	0.999016i	$0.485876\pi$
$72$	17.9183	2.11169
$73$	−2.02637	−0.237169	−0.118584	−	0.992944i	$-0.537836\pi$
$73$	−2.02637	−0.237169	−0.118584	+	0.992944i	$0.537836\pi$
$74$	0.117585	0.0136689
$75$	−2.76951	−0.319796
$76$	−32.6024	−3.73976
$77$	1.01597	0.115780
$78$	10.1621	1.15064
$79$	−14.9034	−1.67676	−0.838380	−	0.545086i	$-0.816497\pi$
$79$	−14.9034	−1.67676	−0.838380	+	0.545086i	$0.816497\pi$
$80$	7.76339	0.867974
$81$	5.27613	0.586236
$82$	10.4516	1.15419
$83$	−17.7454	−1.94781	−0.973905	−	0.226958i	$-0.927122\pi$
$83$	−17.7454	−1.94781	−0.973905	+	0.226958i	$0.927122\pi$
$84$	−3.14771	−0.343443
$85$	−1.72838	−0.187469
$86$	−13.9010	−1.49898
$87$	2.46104	0.263851
$88$	6.98504	0.744608
$89$	2.65481	0.281409	0.140705	−	0.990052i	$-0.455063\pi$
$89$	2.65481	0.281409	0.140705	+	0.990052i	$0.455063\pi$
$90$	5.93747	0.625864
$91$	6.04977	0.634188
$92$	−14.5682	−1.51884
$93$	−0.307413	−0.0318773
$94$	7.64279	0.788293
$95$	−6.20496	−0.636616
$96$	−5.60358	−0.571913
$97$	12.9755	1.31746	0.658731	−	0.752378i	$-0.271093\pi$
$97$	12.9755	1.31746	0.658731	+	0.752378i	$0.271093\pi$
$98$	15.4459	1.56027
$99$	2.56523	0.257816
$100$	−19.7361	−1.97361
$101$	−15.2697	−1.51939	−0.759696	−	0.650279i	$-0.774652\pi$
$101$	−15.2697	−1.51939	−0.759696	+	0.650279i	$0.774652\pi$
$102$	3.29829	0.326580
$103$	15.2768	1.50527	0.752633	−	0.658440i	$-0.228783\pi$
$103$	15.2768	1.50527	0.752633	+	0.658440i	$0.228783\pi$
$104$	41.5937	4.07860
$105$	−0.599079	−0.0584641
$106$	16.3895	1.59189
$107$	15.3004	1.47915	0.739575	−	0.673074i	$-0.235027\pi$
$107$	15.3004	1.47915	0.739575	+	0.673074i	$0.235027\pi$
$108$	−17.2424	−1.65915
$109$	0.832398	0.0797292	0.0398646	−	0.999205i	$-0.487307\pi$
$109$	0.832398	0.0797292	0.0398646	+	0.999205i	$0.487307\pi$
$110$	2.31459	0.220688
$111$	−0.0299557	−0.00284327
$112$	−8.81973	−0.833386
$113$	10.2226	0.961660	0.480830	−	0.876814i	$-0.340335\pi$
$113$	10.2226	0.961660	0.480830	+	0.876814i	$0.340335\pi$
$114$	11.8410	1.10901
$115$	−2.77264	−0.258550
$116$	17.5379	1.62835
$117$	15.2752	1.41219
$118$	−7.52417	−0.692656
$119$	1.96355	0.179999
$120$	−4.11882	−0.375995
$121$	1.00000	0.0909091
$122$	−19.1907	−1.73744
$123$	−2.66264	−0.240082
$124$	−2.19069	−0.196730
$125$	−8.22765	−0.735903
$126$	−6.74536	−0.600925
$127$	4.59672	0.407893	0.203946	−	0.978982i	$-0.434623\pi$
$127$	4.59672	0.407893	0.203946	+	0.978982i	$0.434623\pi$
$128$	5.00467	0.442355
$129$	3.54139	0.311802
$130$	13.7827	1.20882
$131$	−18.4785	−1.61447	−0.807236	−	0.590229i	$-0.799038\pi$
$131$	−18.4785	−1.61447	−0.807236	+	0.590229i	$0.799038\pi$
$132$	−3.09824	−0.269667
$133$	7.04925	0.611248
$134$	−36.0921	−3.11788
$135$	−3.28161	−0.282436
$136$	13.4999	1.15761
$137$	9.75632	0.833539	0.416769	−	0.909012i	$-0.363162\pi$
$137$	9.75632	0.833539	0.416769	+	0.909012i	$0.363162\pi$
$138$	5.29108	0.450407
$139$	−10.1814	−0.863573	−0.431787	−	0.901976i	$-0.642117\pi$
$139$	−10.1814	−0.863573	−0.431787	+	0.901976i	$0.642117\pi$
$140$	−4.26916	−0.360810
$141$	−1.94707	−0.163973
$142$	−1.93481	−0.162365
$143$	5.95469	0.497956
$144$	−22.2691	−1.85576
$145$	3.33785	0.277193
$146$	5.24466	0.434052
$147$	−3.93498	−0.324552
$148$	−0.213471	−0.0175472
$149$	−3.12311	−0.255855	−0.127928	−	0.991784i	$-0.540833\pi$
$149$	−3.12311	−0.255855	−0.127928	+	0.991784i	$0.540833\pi$
$150$	7.16806	0.585270
$151$	−4.64398	−0.377922	−0.188961	−	0.981985i	$-0.560512\pi$
$151$	−4.64398	−0.377922	−0.188961	+	0.981985i	$0.560512\pi$
$152$	48.4654	3.93107
$153$	4.95781	0.400815
$154$	−2.62953	−0.211894
$155$	−0.416938	−0.0334892
$156$	−18.4490	−1.47710
$157$	17.6047	1.40501	0.702505	−	0.711678i	$-0.252065\pi$
$157$	17.6047	1.40501	0.702505	+	0.711678i	$0.252065\pi$
$158$	38.5730	3.06870
$159$	−4.17537	−0.331128
$160$	−7.60000	−0.600833
$161$	3.14991	0.248248
$162$	−13.6557	−1.07289
$163$	16.5054	1.29280	0.646401	−	0.762998i	$-0.276273\pi$
$163$	16.5054	1.29280	0.646401	+	0.762998i	$0.276273\pi$
$164$	−18.9746	−1.48166
$165$	−0.589663	−0.0459052
$166$	45.9287	3.56476
$167$	5.87225	0.454409	0.227204	−	0.973847i	$-0.427041\pi$
$167$	5.87225	0.454409	0.227204	+	0.973847i	$0.427041\pi$
$168$	4.67926	0.361012
$169$	22.4583	1.72756
$170$	4.47340	0.343094
$171$	17.7988	1.36111
$172$	25.2367	1.92428
$173$	20.9482	1.59266	0.796332	−	0.604859i	$-0.206771\pi$
$173$	20.9482	1.59266	0.796332	+	0.604859i	$0.206771\pi$
$174$	−6.36967	−0.482884
$175$	4.26732	0.322579
$176$	−8.68111	−0.654364
$177$	1.91685	0.144079
$178$	−6.87119	−0.515017
$179$	0.709018	0.0529945	0.0264972	−	0.999649i	$-0.491565\pi$
$179$	0.709018	0.0529945	0.0264972	+	0.999649i	$0.491565\pi$
$180$	−10.7793	−0.803440
$181$	24.2144	1.79985	0.899923	−	0.436049i	$-0.143623\pi$
$181$	24.2144	1.79985	0.899923	+	0.436049i	$0.143623\pi$
$182$	−15.6580	−1.16065
$183$	4.88899	0.361405
$184$	21.6564	1.59653
$185$	−0.0406283	−0.00298705
$186$	0.795649	0.0583398
$187$	1.93269	0.141333
$188$	−13.8752	−1.01195
$189$	3.72813	0.271182
$190$	16.0597	1.16509
$191$	−2.98815	−0.216215	−0.108107	−	0.994139i	$-0.534479\pi$
$191$	−2.98815	−0.216215	−0.108107	+	0.994139i	$0.534479\pi$
$192$	3.05511	0.220483
$193$	−13.8218	−0.994918	−0.497459	−	0.867488i	$-0.665733\pi$
$193$	−13.8218	−0.994918	−0.497459	+	0.867488i	$0.665733\pi$
$194$	−33.5832	−2.41114
$195$	−3.51126	−0.251446
$196$	−28.0415	−2.00297
$197$	10.0169	0.713676	0.356838	−	0.934166i	$-0.383855\pi$
$197$	10.0169	0.713676	0.356838	+	0.934166i	$0.383855\pi$
$198$	−6.63935	−0.471838
$199$	−7.02361	−0.497891	−0.248945	−	0.968518i	$-0.580084\pi$
$199$	−7.02361	−0.497891	−0.248945	+	0.968518i	$0.580084\pi$
$200$	29.3389	2.07458
$201$	9.19478	0.648550
$202$	39.5211	2.78069
$203$	−3.79202	−0.266148
$204$	−5.98794	−0.419240
$205$	−3.61128	−0.252223
$206$	−39.5394	−2.75484
$207$	7.95326	0.552790
$208$	−51.6933	−3.58429
$209$	6.93846	0.479943
$210$	1.55054	0.106997
$211$	16.5777	1.14126	0.570629	−	0.821208i	$-0.306699\pi$
$211$	16.5777	1.14126	0.570629	+	0.821208i	$0.306699\pi$
$212$	−29.7546	−2.04355
$213$	0.492909	0.0337736
$214$	−39.6007	−2.70705
$215$	4.80311	0.327569
$216$	25.6319	1.74403
$217$	0.473669	0.0321547
$218$	−2.15441	−0.145915
$219$	−1.33613	−0.0902870
$220$	−4.20207	−0.283303
$221$	11.5086	0.774151
$222$	0.0775316	0.00520358
$223$	−10.7221	−0.718004	−0.359002	−	0.933337i	$-0.616883\pi$
$223$	−10.7221	−0.718004	−0.359002	+	0.933337i	$0.616883\pi$
$224$	8.63411	0.576891
$225$	10.7746	0.718309
$226$	−26.4581	−1.75997
$227$	4.48160	0.297454	0.148727	−	0.988878i	$-0.452482\pi$
$227$	4.48160	0.297454	0.148727	+	0.988878i	$0.452482\pi$
$228$	−21.4970	−1.42367
$229$	6.36200	0.420413	0.210207	−	0.977657i	$-0.432586\pi$
$229$	6.36200	0.420413	0.210207	+	0.977657i	$0.432586\pi$
$230$	7.17617	0.473183
$231$	0.669897	0.0440760
$232$	−26.0711	−1.71165
$233$	−16.5218	−1.08238	−0.541189	−	0.840901i	$-0.682026\pi$
$233$	−16.5218	−1.08238	−0.541189	+	0.840901i	$0.682026\pi$
$234$	−39.5352	−2.58450
$235$	−2.64076	−0.172264
$236$	13.6599	0.889183
$237$	−9.82681	−0.638320
$238$	−5.08208	−0.329422
$239$	0.366383	0.0236994	0.0118497	−	0.999930i	$-0.496228\pi$
$239$	0.366383	0.0236994	0.0118497	+	0.999930i	$0.496228\pi$
$240$	5.11893	0.330426
$241$	12.5426	0.807938	0.403969	−	0.914773i	$-0.367630\pi$
$241$	12.5426	0.807938	0.403969	+	0.914773i	$0.367630\pi$
$242$	−2.58820	−0.166376
$243$	14.4875	0.929375
$244$	34.8400	2.23040
$245$	−5.33692	−0.340964
$246$	6.89146	0.439383
$247$	41.3164	2.62890
$248$	3.25660	0.206794
$249$	−11.7007	−0.741504
$250$	21.2948	1.34680
$251$	−7.65751	−0.483338	−0.241669	−	0.970359i	$-0.577695\pi$
$251$	−7.65751	−0.483338	−0.241669	+	0.970359i	$0.577695\pi$
$252$	12.2460	0.771425
$253$	3.10040	0.194921
$254$	−11.8972	−0.746500
$255$	−1.13964	−0.0713669
$256$	−22.2199	−1.38874
$257$	−18.9529	−1.18225	−0.591124	−	0.806581i	$-0.701316\pi$
$257$	−18.9529	−1.18225	−0.591124	+	0.806581i	$0.701316\pi$
$258$	−9.16585	−0.570641
$259$	0.0461564	0.00286802
$260$	−25.0220	−1.55180
$261$	−9.57454	−0.592649
$262$	47.8261	2.95470
$263$	−25.4119	−1.56696	−0.783482	−	0.621414i	$-0.786558\pi$
$263$	−25.4119	−1.56696	−0.783482	+	0.621414i	$0.786558\pi$
$264$	4.60571	0.283462
$265$	−5.66296	−0.347873
$266$	−18.2449	−1.11867
$267$	1.75050	0.107129
$268$	65.5240	4.00251
$269$	−1.21371	−0.0740013	−0.0370007	−	0.999315i	$-0.511780\pi$
$269$	−1.21371	−0.0740013	−0.0370007	+	0.999315i	$0.511780\pi$
$270$	8.49348	0.516897
$271$	13.4345	0.816085	0.408043	−	0.912963i	$-0.366211\pi$
$271$	13.4345	0.816085	0.408043	+	0.912963i	$0.366211\pi$
$272$	−16.7779	−1.01731
$273$	3.98903	0.241427
$274$	−25.2513	−1.52549
$275$	4.20025	0.253285
$276$	−9.60579	−0.578200
$277$	5.84528	0.351209	0.175604	−	0.984461i	$-0.443812\pi$
$277$	5.84528	0.351209	0.175604	+	0.984461i	$0.443812\pi$
$278$	26.3515	1.58046
$279$	1.19597	0.0716011
$280$	6.34636	0.379268
$281$	−17.0189	−1.01526	−0.507631	−	0.861575i	$-0.669479\pi$
$281$	−17.0189	−1.01526	−0.507631	+	0.861575i	$0.669479\pi$
$282$	5.03941	0.300092
$283$	10.6829	0.635031	0.317516	−	0.948253i	$-0.397151\pi$
$283$	10.6829	0.635031	0.317516	+	0.948253i	$0.397151\pi$
$284$	3.51258	0.208433
$285$	−4.09135	−0.242351
$286$	−15.4119	−0.911327
$287$	4.10265	0.242172
$288$	21.8004	1.28460
$289$	−13.2647	−0.780276
$290$	−8.63904	−0.507302
$291$	8.55563	0.501540
$292$	−9.52152	−0.557205
$293$	−29.8956	−1.74652	−0.873260	−	0.487255i	$-0.837998\pi$
$293$	−29.8956	−1.74652	−0.873260	+	0.487255i	$0.837998\pi$
$294$	10.1845	0.593974
$295$	2.59978	0.151365
$296$	0.317337	0.0184449
$297$	3.66954	0.212928
$298$	8.08325	0.468250
$299$	18.4619	1.06768
$300$	−13.0134	−0.751328
$301$	−5.45665	−0.314516
$302$	12.0196	0.691648
$303$	−10.0683	−0.578412
$304$	−60.2336	−3.45463
$305$	6.63083	0.379680
$306$	−12.8318	−0.733547
$307$	−9.25755	−0.528356	−0.264178	−	0.964474i	$-0.585101\pi$
$307$	−9.25755	−0.528356	−0.264178	+	0.964474i	$0.585101\pi$
$308$	4.77383	0.272014
$309$	10.0730	0.573034
$310$	1.07912	0.0612899
$311$	−5.21518	−0.295726	−0.147863	−	0.989008i	$-0.547239\pi$
$311$	−5.21518	−0.295726	−0.147863	+	0.989008i	$0.547239\pi$
$312$	27.4256	1.55267
$313$	−29.0895	−1.64424	−0.822119	−	0.569315i	$-0.807208\pi$
$313$	−29.0895	−1.64424	−0.822119	+	0.569315i	$0.807208\pi$
$314$	−45.5646	−2.57136
$315$	2.33068	0.131319
$316$	−70.0280	−3.93938
$317$	−7.96289	−0.447241	−0.223620	−	0.974676i	$-0.571788\pi$
$317$	−7.96289	−0.447241	−0.223620	+	0.974676i	$0.571788\pi$
$318$	10.8067	0.606010
$319$	−3.73242	−0.208976
$320$	4.14357	0.231633
$321$	10.0886	0.563092
$322$	−8.15261	−0.454327
$323$	13.4099	0.746148
$324$	24.7915	1.37730
$325$	25.0112	1.38737
$326$	−42.7193	−2.36601
$327$	0.548856	0.0303518
$328$	28.2068	1.55746
$329$	3.00008	0.165400
$330$	1.52617	0.0840128
$331$	−2.56567	−0.141022	−0.0705109	−	0.997511i	$-0.522463\pi$
$331$	−2.56567	−0.141022	−0.0705109	+	0.997511i	$0.522463\pi$
$332$	−83.3820	−4.57618
$333$	0.116541	0.00638641
$334$	−15.1986	−0.831630
$335$	12.4707	0.681345
$336$	−5.81545	−0.317259
$337$	−10.7956	−0.588076	−0.294038	−	0.955794i	$-0.594999\pi$
$337$	−10.7956	−0.588076	−0.294038	+	0.955794i	$0.594999\pi$
$338$	−58.1266	−3.16167
$339$	6.74044	0.366091
$340$	−8.12131	−0.440440
$341$	0.466224	0.0252475
$342$	−46.0669	−2.49101
$343$	13.1749	0.711377
$344$	−37.5159	−2.02272
$345$	−1.82819	−0.0984266
$346$	−54.2183	−2.91479
$347$	−11.0685	−0.594187	−0.297093	−	0.954848i	$-0.596017\pi$
$347$	−11.0685	−0.594187	−0.297093	+	0.954848i	$0.596017\pi$
$348$	11.5639	0.619892
$349$	3.56392	0.190772	0.0953862	−	0.995440i	$-0.469591\pi$
$349$	3.56392	0.190772	0.0953862	+	0.995440i	$0.469591\pi$
$350$	−11.0447	−0.590364
$351$	21.8509	1.16632
$352$	8.49841	0.452967
$353$	17.3600	0.923981	0.461991	−	0.886885i	$-0.347135\pi$
$353$	17.3600	0.923981	0.461991	+	0.886885i	$0.347135\pi$
$354$	−4.96120	−0.263685
$355$	0.668521	0.0354814
$356$	12.4744	0.661143
$357$	1.29471	0.0685231
$358$	−1.83508	−0.0969871
$359$	14.2074	0.749839	0.374920	−	0.927057i	$-0.377670\pi$
$359$	14.2074	0.749839	0.374920	+	0.927057i	$0.377670\pi$
$360$	16.0240	0.844541
$361$	29.1423	1.53380
$362$	−62.6719	−3.29396
$363$	0.659368	0.0346078
$364$	28.4267	1.48996
$365$	−1.81215	−0.0948525
$366$	−12.6537	−0.661420
$367$	14.2266	0.742625	0.371313	−	0.928508i	$-0.378908\pi$
$367$	14.2266	0.742625	0.371313	+	0.928508i	$0.378908\pi$
$368$	−26.9150	−1.40304
$369$	10.3589	0.539261
$370$	0.105154	0.00546671
$371$	6.43350	0.334011
$372$	−1.44447	−0.0748925
$373$	9.75438	0.505063	0.252531	−	0.967589i	$-0.418737\pi$
$373$	9.75438	0.505063	0.252531	+	0.967589i	$0.418737\pi$
$374$	−5.00221	−0.258658
$375$	−5.42505	−0.280148
$376$	20.6263	1.06372
$377$	−22.2254	−1.14467
$378$	−9.64917	−0.496299
$379$	−23.0853	−1.18581	−0.592907	−	0.805271i	$-0.702020\pi$
$379$	−23.0853	−1.18581	−0.592907	+	0.805271i	$0.702020\pi$
$380$	−29.1559	−1.49567
$381$	3.03093	0.155279
$382$	7.73394	0.395703
$383$	4.64377	0.237285	0.118643	−	0.992937i	$-0.462146\pi$
$383$	4.64377	0.237285	0.118643	+	0.992937i	$0.462146\pi$
$384$	3.29992	0.168398
$385$	0.908565	0.0463048
$386$	35.7737	1.82084
$387$	−13.7776	−0.700354
$388$	60.9693	3.09525
$389$	−22.2361	−1.12742	−0.563708	−	0.825974i	$-0.690625\pi$
$389$	−22.2361	−1.12742	−0.563708	+	0.825974i	$0.690625\pi$
$390$	9.08785	0.460181
$391$	5.99213	0.303035
$392$	41.6854	2.10543
$393$	−12.1841	−0.614607
$394$	−25.9258	−1.30612
$395$	−13.3279	−0.670598
$396$	12.0535	0.605712
$397$	−28.2920	−1.41993	−0.709967	−	0.704235i	$-0.751290\pi$
$397$	−28.2920	−1.41993	−0.709967	+	0.704235i	$0.751290\pi$
$398$	18.1785	0.911208
$399$	4.64805	0.232694
$400$	−36.4629	−1.82314
$401$	−25.2630	−1.26157	−0.630786	−	0.775957i	$-0.717268\pi$
$401$	−25.2630	−1.26157	−0.630786	+	0.775957i	$0.717268\pi$
$402$	−23.7980	−1.18693
$403$	2.77622	0.138293
$404$	−71.7492	−3.56966
$405$	4.71836	0.234457
$406$	9.81452	0.487087
$407$	0.0454310	0.00225193
$408$	8.90143	0.440687
$409$	20.5606	1.01666	0.508329	−	0.861163i	$-0.330263\pi$
$409$	20.5606	1.01666	0.508329	+	0.861163i	$0.330263\pi$
$410$	9.34672	0.461602
$411$	6.43301	0.317317
$412$	71.7825	3.53647
$413$	−2.95352	−0.145333
$414$	−20.5847	−1.01168
$415$	−15.8694	−0.779000
$416$	50.6054	2.48113
$417$	−6.71328	−0.328751
$418$	−17.9582	−0.878362
$419$	7.68101	0.375242	0.187621	−	0.982242i	$-0.439922\pi$
$419$	7.68101	0.375242	0.187621	+	0.982242i	$0.439922\pi$
$420$	−2.81495	−0.137356
$421$	−6.66184	−0.324678	−0.162339	−	0.986735i	$-0.551904\pi$
$421$	−6.66184	−0.324678	−0.162339	+	0.986735i	$0.551904\pi$
$422$	−42.9066	−2.08866
$423$	7.57496	0.368307
$424$	44.2320	2.14809
$425$	8.11780	0.393771
$426$	−1.27575	−0.0618102
$427$	−7.53306	−0.364551
$428$	71.8937	3.47511
$429$	3.92633	0.189565
$430$	−12.4314	−0.599496
$431$	−28.0745	−1.35230	−0.676149	−	0.736765i	$-0.736353\pi$
$431$	−28.0745	−1.35230	−0.676149	+	0.736765i	$0.736353\pi$
$432$	−31.8557	−1.53266
$433$	−12.6237	−0.606655	−0.303327	−	0.952886i	$-0.598098\pi$
$433$	−12.6237	−0.606655	−0.303327	+	0.952886i	$0.598098\pi$
$434$	−1.22595	−0.0588476
$435$	2.20087	0.105524
$436$	3.91127	0.187316
$437$	21.5120	1.02906
$438$	3.45816	0.165237
$439$	16.2342	0.774814	0.387407	−	0.921909i	$-0.373371\pi$
$439$	16.2342	0.774814	0.387407	+	0.921909i	$0.373371\pi$
$440$	6.24662	0.297796
$441$	15.3088	0.728992
$442$	−29.7866	−1.41680
$443$	−3.04023	−0.144446	−0.0722228	−	0.997389i	$-0.523009\pi$
$443$	−3.04023	−0.144446	−0.0722228	+	0.997389i	$0.523009\pi$
$444$	−0.140756	−0.00667998
$445$	2.37416	0.112546
$446$	27.7510	1.31405
$447$	−2.05928	−0.0974006
$448$	−4.70737	−0.222402
$449$	−5.98417	−0.282410	−0.141205	−	0.989980i	$-0.545098\pi$
$449$	−5.98417	−0.282410	−0.141205	+	0.989980i	$0.545098\pi$
$450$	−27.8869	−1.31460
$451$	4.03817	0.190150
$452$	48.0339	2.25932
$453$	−3.06209	−0.143870
$454$	−11.5993	−0.544382
$455$	5.41022	0.253635
$456$	31.9566	1.49650
$457$	13.5627	0.634438	0.317219	−	0.948352i	$-0.397251\pi$
$457$	13.5627	0.634438	0.317219	+	0.948352i	$0.397251\pi$
$458$	−16.4662	−0.769413
$459$	7.09209	0.331030
$460$	−13.0281	−0.607438
$461$	−6.40848	−0.298473	−0.149236	−	0.988802i	$-0.547681\pi$
$461$	−6.40848	−0.298473	−0.149236	+	0.988802i	$0.547681\pi$
$462$	−1.73383	−0.0806650
$463$	−30.0049	−1.39444	−0.697222	−	0.716855i	$-0.745581\pi$
$463$	−30.0049	−1.39444	−0.697222	+	0.716855i	$0.745581\pi$
$464$	32.4016	1.50421
$465$	−0.274915	−0.0127489
$466$	42.7617	1.98090
$467$	−20.4342	−0.945581	−0.472790	−	0.881175i	$-0.656753\pi$
$467$	−20.4342	−0.945581	−0.472790	+	0.881175i	$0.656753\pi$
$468$	71.7749	3.31780
$469$	−14.1675	−0.654195
$470$	6.83483	0.315267
$471$	11.6080	0.534868
$472$	−20.3062	−0.934670
$473$	−5.37089	−0.246954
$474$	25.4338	1.16821
$475$	29.1433	1.33719
$476$	9.22635	0.422889
$477$	16.2440	0.743764
$478$	−0.948275	−0.0433731
$479$	−12.4367	−0.568247	−0.284123	−	0.958788i	$-0.591703\pi$
$479$	−12.4367	−0.568247	−0.284123	+	0.958788i	$0.591703\pi$
$480$	−5.01120	−0.228729
$481$	0.270527	0.0123350
$482$	−32.4627	−1.47864
$483$	2.07695	0.0945045
$484$	4.69880	0.213582
$485$	11.6038	0.526901
$486$	−37.4967	−1.70088
$487$	−26.1299	−1.18406	−0.592029	−	0.805916i	$-0.701673\pi$
$487$	−26.1299	−1.18406	−0.592029	+	0.805916i	$0.701673\pi$
$488$	−51.7918	−2.34450
$489$	10.8831	0.492152
$490$	13.8130	0.624010
$491$	−9.65346	−0.435654	−0.217827	−	0.975987i	$-0.569897\pi$
$491$	−9.65346	−0.435654	−0.217827	+	0.975987i	$0.569897\pi$
$492$	−12.5112	−0.564049
$493$	−7.21363	−0.324886
$494$	−106.935	−4.81124
$495$	2.29405	0.103110
$496$	−4.04735	−0.181731
$497$	−0.759484	−0.0340675
$498$	30.2839	1.35705
$499$	25.3667	1.13557	0.567784	−	0.823177i	$-0.307801\pi$
$499$	25.3667	1.13557	0.567784	+	0.823177i	$0.307801\pi$
$500$	−38.6601	−1.72893
$501$	3.87198	0.172987
$502$	19.8192	0.884575
$503$	2.02693	0.0903765	0.0451882	−	0.998978i	$-0.485611\pi$
$503$	2.02693	0.0903765	0.0451882	+	0.998978i	$0.485611\pi$
$504$	−18.2044	−0.810888
$505$	−13.6555	−0.607660
$506$	−8.02448	−0.356731
$507$	14.8083	0.657659
$508$	21.5991	0.958303
$509$	17.5470	0.777756	0.388878	−	0.921289i	$-0.372863\pi$
$509$	17.5470	0.777756	0.388878	+	0.921289i	$0.372863\pi$
$510$	2.94962	0.130611
$511$	2.05873	0.0910728
$512$	47.5002	2.09923
$513$	25.4609	1.12413
$514$	49.0539	2.16368
$515$	13.6618	0.602011
$516$	16.6403	0.732548
$517$	2.95293	0.129870
$518$	−0.119462	−0.00524887
$519$	13.8126	0.606306
$520$	37.1967	1.63118
$521$	8.78718	0.384973	0.192487	−	0.981300i	$-0.438345\pi$
$521$	8.78718	0.384973	0.192487	+	0.981300i	$0.438345\pi$
$522$	24.7809	1.08463
$523$	25.4997	1.11502	0.557512	−	0.830169i	$-0.311756\pi$
$523$	25.4997	1.11502	0.557512	+	0.830169i	$0.311756\pi$
$524$	−86.8266	−3.79304
$525$	2.81374	0.122802
$526$	65.7712	2.86776
$527$	0.901069	0.0392512
$528$	−5.72405	−0.249107
$529$	−13.3875	−0.582065
$530$	14.6569	0.636654
$531$	−7.45740	−0.323623
$532$	33.1230	1.43607
$533$	24.0461	1.04155
$534$	−4.53064	−0.196060
$535$	13.6830	0.591566
$536$	−97.4053	−4.20727
$537$	0.467504	0.0201743
$538$	3.14133	0.135433
$539$	5.96781	0.257052
$540$	−15.4196	−0.663556
$541$	38.8872	1.67189	0.835945	−	0.548813i	$-0.184920\pi$
$541$	38.8872	1.67189	0.835945	+	0.548813i	$0.184920\pi$
$542$	−34.7711	−1.49355
$543$	15.9662	0.685177
$544$	16.4248	0.704208
$545$	0.744401	0.0318866
$546$	−10.3244	−0.441844
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	45.8430	1.95832
$549$	−19.0204	−0.811769
$550$	−10.8711	−0.463546
$551$	−25.8973	−1.10326
$552$	14.2796	0.607779
$553$	15.1413	0.643876
$554$	−15.1288	−0.642760
$555$	−0.0267890	−0.00113713
$556$	−47.8403	−2.02888
$557$	3.60097	0.152578	0.0762890	−	0.997086i	$-0.475693\pi$
$557$	3.60097	0.152578	0.0762890	+	0.997086i	$0.475693\pi$
$558$	−3.09543	−0.131040
$559$	−31.9820	−1.35269
$560$	−7.88736	−0.333302
$561$	1.27436	0.0538034
$562$	44.0484	1.85807
$563$	10.5780	0.445811	0.222905	−	0.974840i	$-0.428446\pi$
$563$	10.5780	0.445811	0.222905	+	0.974840i	$0.428446\pi$
$564$	−9.14888	−0.385237
$565$	9.14190	0.384603
$566$	−27.6495	−1.16219
$567$	−5.36038	−0.225115
$568$	−5.22165	−0.219096
$569$	−8.52244	−0.357279	−0.178640	−	0.983915i	$-0.557170\pi$
$569$	−8.52244	−0.357279	−0.178640	+	0.983915i	$0.557170\pi$
$570$	10.5893	0.443535
$571$	−6.04697	−0.253058	−0.126529	−	0.991963i	$-0.540384\pi$
$571$	−6.04697	−0.253058	−0.126529	+	0.991963i	$0.540384\pi$
$572$	27.9799	1.16990
$573$	−1.97029	−0.0823101
$574$	−10.6185	−0.443208
$575$	13.0225	0.543075
$576$	−11.8857	−0.495238
$577$	21.5280	0.896222	0.448111	−	0.893978i	$-0.352097\pi$
$577$	21.5280	0.896222	0.448111	+	0.893978i	$0.352097\pi$
$578$	34.3317	1.42801
$579$	−9.11368	−0.378752
$580$	15.6839	0.651238
$581$	18.0287	0.747958
$582$	−22.1437	−0.917887
$583$	6.33238	0.262261
$584$	14.1543	0.585709
$585$	13.6604	0.564786
$586$	77.3759	3.19637
$587$	45.8006	1.89040	0.945198	−	0.326499i	$-0.105869\pi$
$587$	45.8006	1.89040	0.945198	+	0.326499i	$0.105869\pi$
$588$	−18.4897	−0.762502
$589$	3.23488	0.133291
$590$	−6.72876	−0.277019
$591$	6.60484	0.271687
$592$	−0.394392	−0.0162094
$593$	23.8140	0.977922	0.488961	−	0.872306i	$-0.337376\pi$
$593$	23.8140	0.977922	0.488961	+	0.872306i	$0.337376\pi$
$594$	−9.49751	−0.389688
$595$	1.75598	0.0719881
$596$	−14.6749	−0.601106
$597$	−4.63115	−0.189540
$598$	−47.7832	−1.95400
$599$	23.6871	0.967828	0.483914	−	0.875115i	$-0.339215\pi$
$599$	23.6871	0.967828	0.483914	+	0.875115i	$0.339215\pi$
$600$	19.3452	0.789763
$601$	3.70939	0.151309	0.0756546	−	0.997134i	$-0.475895\pi$
$601$	3.70939	0.151309	0.0756546	+	0.997134i	$0.475895\pi$
$602$	14.1229	0.575608
$603$	−35.7718	−1.45674
$604$	−21.8211	−0.887889
$605$	0.894285	0.0363579
$606$	26.0589	1.05857
$607$	−14.6968	−0.596524	−0.298262	−	0.954484i	$-0.596407\pi$
$607$	−14.6968	−0.596524	−0.298262	+	0.954484i	$0.596407\pi$
$608$	58.9659	2.39138
$609$	−2.50034	−0.101319
$610$	−17.1619	−0.694866
$611$	17.5838	0.711363
$612$	23.2958	0.941675
$613$	−35.7678	−1.44465	−0.722325	−	0.691554i	$-0.756926\pi$
$613$	−35.7678	−1.44465	−0.722325	+	0.691554i	$0.756926\pi$
$614$	23.9604	0.966964
$615$	−2.38116	−0.0960177
$616$	−7.09658	−0.285929
$617$	−14.6897	−0.591383	−0.295692	−	0.955283i	$-0.595550\pi$
$617$	−14.6897	−0.591383	−0.295692	+	0.955283i	$0.595550\pi$
$618$	−26.0710	−1.04873
$619$	44.5391	1.79018	0.895089	−	0.445888i	$-0.147112\pi$
$619$	44.5391	1.79018	0.895089	+	0.445888i	$0.147112\pi$
$620$	−1.95911	−0.0786796
$621$	11.3770	0.456545
$622$	13.4980	0.541219
$623$	−2.69720	−0.108061
$624$	−34.0849	−1.36449
$625$	13.6434	0.545736
$626$	75.2897	3.00918
$627$	4.57500	0.182708
$628$	82.7211	3.30093
$629$	0.0878042	0.00350098
$630$	−6.03228	−0.240332
$631$	−28.4378	−1.13209	−0.566046	−	0.824374i	$-0.691528\pi$
$631$	−28.4378	−1.13209	−0.566046	+	0.824374i	$0.691528\pi$
$632$	104.101	4.14090
$633$	10.9308	0.434462
$634$	20.6096	0.818511
$635$	4.11078	0.163131
$636$	−19.6192	−0.777953
$637$	35.5364	1.40800
$638$	9.66027	0.382454
$639$	−1.91763	−0.0758604
$640$	4.47560	0.176914
$641$	21.6617	0.855585	0.427792	−	0.903877i	$-0.359291\pi$
$641$	21.6617	0.855585	0.427792	+	0.903877i	$0.359291\pi$
$642$	−26.1114	−1.03054
$643$	−48.5265	−1.91370	−0.956850	−	0.290582i	$-0.906151\pi$
$643$	−48.5265	−1.91370	−0.956850	+	0.290582i	$0.906151\pi$
$644$	14.8008	0.583233
$645$	3.16702	0.124701
$646$	−34.7076	−1.36555
$647$	−21.4439	−0.843046	−0.421523	−	0.906818i	$-0.638504\pi$
$647$	−21.4439	−0.843046	−0.421523	+	0.906818i	$0.638504\pi$
$648$	−36.8540	−1.44776
$649$	−2.90710	−0.114114
$650$	−64.7341	−2.53908
$651$	0.312322	0.0122409
$652$	77.5556	3.03731
$653$	30.6556	1.19965	0.599823	−	0.800133i	$-0.295238\pi$
$653$	30.6556	1.19965	0.599823	+	0.800133i	$0.295238\pi$
$654$	−1.42055	−0.0555480
$655$	−16.5250	−0.645686
$656$	−35.0558	−1.36870
$657$	5.19812	0.202798
$658$	−7.76482	−0.302704
$659$	3.55868	0.138626	0.0693132	−	0.997595i	$-0.477919\pi$
$659$	3.55868	0.138626	0.0693132	+	0.997595i	$0.477919\pi$
$660$	−2.77071	−0.107850
$661$	−33.7294	−1.31192	−0.655961	−	0.754795i	$-0.727736\pi$
$661$	−33.7294	−1.31192	−0.655961	+	0.754795i	$0.727736\pi$
$662$	6.64047	0.258089
$663$	7.58839	0.294709
$664$	123.952	4.81028
$665$	6.30404	0.244460
$666$	−0.301632	−0.0116880
$667$	−11.5720	−0.448070
$668$	27.5925	1.06759
$669$	−7.06980	−0.273334
$670$	−32.2766	−1.24695
$671$	−7.41467	−0.286240
$672$	5.69306	0.219614
$673$	0.400126	0.0154237	0.00771186	−	0.999970i	$-0.497545\pi$
$673$	0.400126	0.0154237	0.00771186	+	0.999970i	$0.497545\pi$
$674$	27.9413	1.07626
$675$	15.4130	0.593246
$676$	105.527	4.05873
$677$	8.82186	0.339052	0.169526	−	0.985526i	$-0.445776\pi$
$677$	8.82186	0.339052	0.169526	+	0.985526i	$0.445776\pi$
$678$	−17.4456	−0.669996
$679$	−13.1827	−0.505905
$680$	12.0728	0.462971
$681$	2.95502	0.113237
$682$	−1.20668	−0.0462063
$683$	−10.0929	−0.386193	−0.193096	−	0.981180i	$-0.561853\pi$
$683$	−10.0929	−0.386193	−0.193096	+	0.981180i	$0.561853\pi$
$684$	83.6329	3.19778
$685$	8.72493	0.333363
$686$	−34.0993	−1.30192
$687$	4.19490	0.160045
$688$	46.6253	1.77757
$689$	37.7074	1.43654
$690$	4.73174	0.180134
$691$	−10.0224	−0.381270	−0.190635	−	0.981661i	$-0.561055\pi$
$691$	−10.0224	−0.381270	−0.190635	+	0.981661i	$0.561055\pi$
$692$	98.4316	3.74181
$693$	−2.60620	−0.0990012
$694$	28.6475	1.08744
$695$	−9.10506	−0.345375
$696$	−17.1905	−0.651603
$697$	7.80455	0.295618
$698$	−9.22416	−0.349140
$699$	−10.8939	−0.412046
$700$	20.0513	0.757868
$701$	−37.8140	−1.42822	−0.714108	−	0.700035i	$-0.753168\pi$
$701$	−37.8140	−1.42822	−0.714108	+	0.700035i	$0.753168\pi$
$702$	−56.5547	−2.13452
$703$	0.315221	0.0118888
$704$	−4.63339	−0.174627
$705$	−1.74123	−0.0655787
$706$	−44.9313	−1.69101
$707$	15.5135	0.583446
$708$	9.00689	0.338500
$709$	10.3162	0.387433	0.193717	−	0.981058i	$-0.437946\pi$
$709$	10.3162	0.387433	0.193717	+	0.981058i	$0.437946\pi$
$710$	−1.73027	−0.0649358
$711$	38.2306	1.43376
$712$	−18.5439	−0.694964
$713$	1.44548	0.0541338
$714$	−3.35096	−0.125407
$715$	5.32519	0.199151
$716$	3.33153	0.124505
$717$	0.241581	0.00902203
$718$	−36.7717	−1.37231
$719$	38.3772	1.43123	0.715615	−	0.698495i	$-0.246147\pi$
$719$	38.3772	1.43123	0.715615	+	0.698495i	$0.246147\pi$
$720$	−19.9149	−0.742185
$721$	−15.5207	−0.578022
$722$	−75.4261	−2.80707
$723$	8.27017	0.307571
$724$	113.779	4.22856
$725$	−15.6771	−0.582234
$726$	−1.70658	−0.0633371
$727$	−7.27755	−0.269909	−0.134955	−	0.990852i	$-0.543089\pi$
$727$	−7.27755	−0.269909	−0.134955	+	0.990852i	$0.543089\pi$
$728$	−42.2579	−1.56618
$729$	−6.27577	−0.232436
$730$	4.69023	0.173593
$731$	−10.3803	−0.383929
$732$	22.9724	0.849084
$733$	31.8582	1.17671	0.588355	−	0.808603i	$-0.299776\pi$
$733$	31.8582	1.17671	0.588355	+	0.808603i	$0.299776\pi$
$734$	−36.8215	−1.35911
$735$	−3.51900	−0.129800
$736$	26.3485	0.971218
$737$	−13.9448	−0.513665
$738$	−26.8108	−0.986921
$739$	26.8129	0.986330	0.493165	−	0.869936i	$-0.335840\pi$
$739$	26.8129	0.986330	0.493165	+	0.869936i	$0.335840\pi$
$740$	−0.190904	−0.00701777
$741$	27.2427	1.00079
$742$	−16.6512	−0.611285
$743$	42.7430	1.56809	0.784044	−	0.620705i	$-0.213154\pi$
$743$	42.7430	1.56809	0.784044	+	0.620705i	$0.213154\pi$
$744$	2.14730	0.0787237
$745$	−2.79295	−0.102326
$746$	−25.2463	−0.924334
$747$	45.5211	1.66553
$748$	9.08134	0.332047
$749$	−15.5448	−0.567993
$750$	14.0411	0.512710
$751$	21.9578	0.801252	0.400626	−	0.916242i	$-0.368793\pi$
$751$	21.9578	0.801252	0.400626	+	0.916242i	$0.368793\pi$
$752$	−25.6347	−0.934802
$753$	−5.04912	−0.184000
$754$	57.5239	2.09490
$755$	−4.15304	−0.151145
$756$	17.5177	0.637114
$757$	−12.0135	−0.436637	−0.218318	−	0.975878i	$-0.570057\pi$
$757$	−12.0135	−0.436637	−0.218318	+	0.975878i	$0.570057\pi$
$758$	59.7496	2.17020
$759$	2.04431	0.0742036
$760$	43.3419	1.57218
$761$	43.9361	1.59268	0.796342	−	0.604847i	$-0.206766\pi$
$761$	43.9361	1.59268	0.796342	+	0.604847i	$0.206766\pi$
$762$	−7.84466	−0.284182
$763$	−0.845689	−0.0306160
$764$	−14.0407	−0.507975
$765$	4.43370	0.160301
$766$	−12.0190	−0.434265
$767$	−17.3109	−0.625060
$768$	−14.6511	−0.528675
$769$	20.7834	0.749470	0.374735	−	0.927132i	$-0.377734\pi$
$769$	20.7834	0.749470	0.374735	+	0.927132i	$0.377734\pi$
$770$	−2.35155	−0.0847440
$771$	−12.4969	−0.450066
$772$	−64.9461	−2.33746
$773$	−35.8489	−1.28939	−0.644697	−	0.764438i	$-0.723016\pi$
$773$	−35.8489	−1.28939	−0.644697	+	0.764438i	$0.723016\pi$
$774$	35.6592	1.28174
$775$	1.95826	0.0703428
$776$	−90.6344	−3.25359
$777$	0.0304341	0.00109182
$778$	57.5516	2.06332
$779$	28.0187	1.00387
$780$	−16.4987	−0.590748
$781$	−0.747547	−0.0267493
$782$	−15.5089	−0.554595
$783$	−13.6963	−0.489465
$784$	−51.8072	−1.85026
$785$	15.7437	0.561915
$786$	31.5350	1.12482
$787$	26.3788	0.940303	0.470151	−	0.882586i	$-0.344199\pi$
$787$	26.3788	0.940303	0.470151	+	0.882586i	$0.344199\pi$
$788$	47.0675	1.67671
$789$	−16.7558	−0.596522
$790$	34.4952	1.22729
$791$	−10.3858	−0.369277
$792$	−17.9183	−0.636698
$793$	−44.1520	−1.56788
$794$	73.2254	2.59867
$795$	−3.73397	−0.132430
$796$	−33.0026	−1.16974
$797$	−26.4022	−0.935214	−0.467607	−	0.883937i	$-0.654884\pi$
$797$	−26.4022	−0.935214	−0.467607	+	0.883937i	$0.654884\pi$
$798$	−12.0301	−0.425861
$799$	5.70711	0.201903
$800$	35.6955	1.26203
$801$	−6.81020	−0.240627
$802$	65.3857	2.30885
$803$	2.02637	0.0715091
$804$	43.2044	1.52370
$805$	2.81692	0.0992833
$806$	−7.18542	−0.253096
$807$	−0.800283	−0.0281713
$808$	106.659	3.75227
$809$	−38.1088	−1.33984	−0.669918	−	0.742435i	$-0.733671\pi$
$809$	−38.1088	−1.33984	−0.669918	+	0.742435i	$0.733671\pi$
$810$	−12.2121	−0.429089
$811$	−43.6044	−1.53116	−0.765579	−	0.643341i	$-0.777548\pi$
$811$	−43.6044	−1.53116	−0.765579	+	0.643341i	$0.777548\pi$
$812$	−17.8179	−0.625287
$813$	8.85825	0.310672
$814$	−0.117585	−0.00412134
$815$	14.7605	0.517039
$816$	−11.0628	−0.387277
$817$	−37.2657	−1.30376
$818$	−53.2151	−1.86062
$819$	−15.5191	−0.542280
$820$	−16.9687	−0.592572
$821$	−17.4786	−0.610008	−0.305004	−	0.952351i	$-0.598658\pi$
$821$	−17.4786	−0.610008	−0.305004	+	0.952351i	$0.598658\pi$
$822$	−16.6499	−0.580733
$823$	22.6363	0.789053	0.394527	−	0.918884i	$-0.370909\pi$
$823$	22.6363	0.789053	0.394527	+	0.918884i	$0.370909\pi$
$824$	−106.709	−3.71738
$825$	2.76951	0.0964221
$826$	7.64432	0.265980
$827$	−9.19823	−0.319854	−0.159927	−	0.987129i	$-0.551126\pi$
$827$	−9.19823	−0.319854	−0.159927	+	0.987129i	$0.551126\pi$
$828$	37.3708	1.29872
$829$	−48.9393	−1.69973	−0.849866	−	0.526999i	$-0.823317\pi$
$829$	−48.9393	−1.69973	−0.849866	+	0.526999i	$0.823317\pi$
$830$	41.0733	1.42568
$831$	3.85419	0.133700
$832$	−27.5904	−0.956524
$833$	11.5339	0.399628
$834$	17.3753	0.601658
$835$	5.25147	0.181735
$836$	32.6024	1.12758
$837$	1.71083	0.0591349
$838$	−19.8800	−0.686743
$839$	−27.9715	−0.965684	−0.482842	−	0.875708i	$-0.660395\pi$
$839$	−27.9715	−0.965684	−0.482842	+	0.875708i	$0.660395\pi$
$840$	4.18459	0.144382
$841$	−15.0690	−0.519621
$842$	17.2422	0.594205
$843$	−11.2217	−0.386496
$844$	77.8955	2.68127
$845$	20.0841	0.690915
$846$	−19.6055	−0.674052
$847$	−1.01597	−0.0349091
$848$	−54.9721	−1.88775
$849$	7.04395	0.241748
$850$	−21.0105	−0.720655
$851$	0.140854	0.00482843
$852$	2.31608	0.0793476
$853$	8.53179	0.292123	0.146061	−	0.989276i	$-0.453340\pi$
$853$	8.53179	0.292123	0.146061	+	0.989276i	$0.453340\pi$
$854$	19.4971	0.667177
$855$	15.9172	0.544356
$856$	−106.874	−3.65289
$857$	26.2004	0.894990	0.447495	−	0.894287i	$-0.352316\pi$
$857$	26.2004	0.894990	0.447495	+	0.894287i	$0.352316\pi$
$858$	−10.1621	−0.346930
$859$	9.42434	0.321554	0.160777	−	0.986991i	$-0.448600\pi$
$859$	9.42434	0.321554	0.160777	+	0.986991i	$0.448600\pi$
$860$	22.5688	0.769591
$861$	2.70516	0.0921916
$862$	72.6624	2.47489
$863$	11.6328	0.395985	0.197992	−	0.980204i	$-0.436558\pi$
$863$	11.6328	0.395985	0.197992	+	0.980204i	$0.436558\pi$
$864$	31.1852	1.06094
$865$	18.7337	0.636965
$866$	32.6726	1.11026
$867$	−8.74632	−0.297040
$868$	2.22568	0.0755443
$869$	14.9034	0.505562
$870$	−5.69630	−0.193123
$871$	−83.0371	−2.81361
$872$	−5.81433	−0.196898
$873$	−33.2852	−1.12653
$874$	−55.6775	−1.88332
$875$	8.35903	0.282587
$876$	−6.27818	−0.212120
$877$	9.16986	0.309644	0.154822	−	0.987942i	$-0.450520\pi$
$877$	9.16986	0.309644	0.154822	+	0.987942i	$0.450520\pi$
$878$	−42.0173	−1.41802
$879$	−19.7122	−0.664876
$880$	−7.76339	−0.261704
$881$	−52.8965	−1.78213	−0.891064	−	0.453879i	$-0.850040\pi$
$881$	−52.8965	−1.78213	−0.891064	+	0.453879i	$0.850040\pi$
$882$	−39.6224	−1.33415
$883$	40.0986	1.34943	0.674713	−	0.738080i	$-0.264267\pi$
$883$	40.0986	1.34943	0.674713	+	0.738080i	$0.264267\pi$
$884$	54.0765	1.81879
$885$	1.71421	0.0576226
$886$	7.86873	0.264355
$887$	−0.183828	−0.00617233	−0.00308616	−	0.999995i	$-0.500982\pi$
$887$	−0.183828	−0.00617233	−0.00308616	+	0.999995i	$0.500982\pi$
$888$	0.209242	0.00702171
$889$	−4.67012	−0.156631
$890$	−6.14480	−0.205974
$891$	−5.27613	−0.176757
$892$	−50.3809	−1.68688
$893$	20.4888	0.685631
$894$	5.32984	0.178256
$895$	0.634064	0.0211944
$896$	−5.08458	−0.169864
$897$	12.1732	0.406452
$898$	15.4882	0.516849
$899$	−1.74015	−0.0580371
$900$	50.6278	1.68759
$901$	12.2386	0.407725
$902$	−10.4516	−0.348001
$903$	−3.59794	−0.119732
$904$	−71.4052	−2.37490
$905$	21.6546	0.719824
$906$	7.92531	0.263301
$907$	−13.7113	−0.455276	−0.227638	−	0.973746i	$-0.573100\pi$
$907$	−13.7113	−0.455276	−0.227638	+	0.973746i	$0.573100\pi$
$908$	21.0581	0.698839
$909$	39.1703	1.29920
$910$	−14.0028	−0.464187
$911$	−19.7904	−0.655684	−0.327842	−	0.944733i	$-0.606321\pi$
$911$	−19.7904	−0.655684	−0.327842	+	0.944733i	$0.606321\pi$
$912$	−39.7161	−1.31513
$913$	17.7454	0.587287
$914$	−35.1031	−1.16111
$915$	4.37216	0.144539
$916$	29.8938	0.987718
$917$	18.7735	0.619957
$918$	−18.3558	−0.605831
$919$	−50.1760	−1.65515	−0.827576	−	0.561353i	$-0.810281\pi$
$919$	−50.1760	−1.65515	−0.827576	+	0.561353i	$0.810281\pi$
$920$	19.3670	0.638512
$921$	−6.10413	−0.201138
$922$	16.5864	0.546245
$923$	−4.45141	−0.146520
$924$	3.14771	0.103552
$925$	0.190822	0.00627418
$926$	77.6587	2.55202
$927$	−39.1885	−1.28712
$928$	−31.7197	−1.04125
$929$	29.3115	0.961680	0.480840	−	0.876808i	$-0.340332\pi$
$929$	29.3115	0.961680	0.480840	+	0.876808i	$0.340332\pi$
$930$	0.711537	0.0233322
$931$	41.4074	1.35707
$932$	−77.6325	−2.54294
$933$	−3.43873	−0.112579
$934$	52.8878	1.73054
$935$	1.72838	0.0565240
$936$	−106.698	−3.48752
$937$	47.5093	1.55206	0.776031	−	0.630695i	$-0.217230\pi$
$937$	47.5093	1.55206	0.776031	+	0.630695i	$0.217230\pi$
$938$	36.6684	1.19727
$939$	−19.1807	−0.625939
$940$	−12.4084	−0.404718
$941$	23.1448	0.754500	0.377250	−	0.926111i	$-0.376870\pi$
$941$	23.1448	0.754500	0.377250	+	0.926111i	$0.376870\pi$
$942$	−30.0439	−0.978882
$943$	12.5200	0.407706
$944$	25.2369	0.821391
$945$	3.33401	0.108455
$946$	13.9010	0.451959
$947$	51.0823	1.65995	0.829976	−	0.557799i	$-0.188354\pi$
$947$	51.0823	1.65995	0.829976	+	0.557799i	$0.188354\pi$
$948$	−46.1742	−1.49967
$949$	12.0664	0.391692
$950$	−75.4288	−2.44723
$951$	−5.25048	−0.170258
$952$	−13.7155	−0.444522
$953$	−11.7034	−0.379111	−0.189556	−	0.981870i	$-0.560705\pi$
$953$	−11.7034	−0.379111	−0.189556	+	0.981870i	$0.560705\pi$
$954$	−42.0429	−1.36119
$955$	−2.67226	−0.0864722
$956$	1.72156	0.0556793
$957$	−2.46104	−0.0795541
$958$	32.1887	1.03997
$959$	−9.91211	−0.320079
$960$	2.73214	0.0881793
$961$	−30.7826	−0.992988
$962$	−0.700180	−0.0225747
$963$	−39.2492	−1.26479
$964$	58.9351	1.89817
$965$	−12.3607	−0.397904
$966$	−5.37557	−0.172956
$967$	48.3533	1.55494	0.777469	−	0.628921i	$-0.216503\pi$
$967$	48.3533	1.55494	0.777469	+	0.628921i	$0.216503\pi$
$968$	−6.98504	−0.224508
$969$	8.84207	0.284048
$970$	−30.0330	−0.964302
$971$	−34.8338	−1.11787	−0.558935	−	0.829211i	$-0.688790\pi$
$971$	−34.8338	−1.11787	−0.558935	+	0.829211i	$0.688790\pi$
$972$	68.0739	2.18347
$973$	10.3440	0.331612
$974$	67.6295	2.16699
$975$	16.4916	0.528153
$976$	64.3676	2.06036
$977$	9.76193	0.312312	0.156156	−	0.987732i	$-0.450090\pi$
$977$	9.76193	0.312312	0.156156	+	0.987732i	$0.450090\pi$
$978$	−28.1678	−0.900706
$979$	−2.65481	−0.0848480
$980$	−25.0771	−0.801060
$981$	−2.13529	−0.0681747
$982$	24.9851	0.797307
$983$	49.7542	1.58691	0.793456	−	0.608627i	$-0.208280\pi$
$983$	49.7542	1.58691	0.793456	+	0.608627i	$0.208280\pi$
$984$	18.5987	0.592904
$985$	8.95799	0.285425
$986$	18.6703	0.594585
$987$	1.97816	0.0629655
$988$	194.137	6.17633
$989$	−16.6519	−0.529501
$990$	−5.93747	−0.188705
$991$	−34.0305	−1.08101	−0.540507	−	0.841339i	$-0.681768\pi$
$991$	−34.0305	−1.08101	−0.540507	+	0.841339i	$0.681768\pi$
$992$	3.96217	0.125799
$993$	−1.69172	−0.0536851
$994$	1.96570	0.0623482
$995$	−6.28111	−0.199125
$996$	−54.9794	−1.74209
$997$	−6.11764	−0.193748	−0.0968738	−	0.995297i	$-0.530884\pi$
$997$	−6.11764	−0.193748	−0.0968738	+	0.995297i	$0.530884\pi$
$998$	−65.6542	−2.07825
$999$	0.166711	0.00527449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.8	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.8	✓	121	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58820 q^{2} +0.659368 q^{3} +4.69880 q^{4} +0.894285 q^{5} -1.70658 q^{6} -1.01597 q^{7} -6.98504 q^{8} -2.56523 q^{9} +O(q^{10})\)	\(q-2.58820 q^{2} +0.659368 q^{3} +4.69880 q^{4} +0.894285 q^{5} -1.70658 q^{6} -1.01597 q^{7} -6.98504 q^{8} -2.56523 q^{9} -2.31459 q^{10} -1.00000 q^{11} +3.09824 q^{12} -5.95469 q^{13} +2.62953 q^{14} +0.589663 q^{15} +8.68111 q^{16} -1.93269 q^{17} +6.63935 q^{18} -6.93846 q^{19} +4.20207 q^{20} -0.669897 q^{21} +2.58820 q^{22} -3.10040 q^{23} -4.60571 q^{24} -4.20025 q^{25} +15.4119 q^{26} -3.66954 q^{27} -4.77383 q^{28} +3.73242 q^{29} -1.52617 q^{30} -0.466224 q^{31} -8.49841 q^{32} -0.659368 q^{33} +5.00221 q^{34} -0.908565 q^{35} -12.0535 q^{36} -0.0454310 q^{37} +17.9582 q^{38} -3.92633 q^{39} -6.24662 q^{40} -4.03817 q^{41} +1.73383 q^{42} +5.37089 q^{43} -4.69880 q^{44} -2.29405 q^{45} +8.02448 q^{46} -2.95293 q^{47} +5.72405 q^{48} -5.96781 q^{49} +10.8711 q^{50} -1.27436 q^{51} -27.9799 q^{52} -6.33238 q^{53} +9.49751 q^{54} -0.894285 q^{55} +7.09658 q^{56} -4.57500 q^{57} -9.66027 q^{58} +2.90710 q^{59} +2.77071 q^{60} +7.41467 q^{61} +1.20668 q^{62} +2.60620 q^{63} +4.63339 q^{64} -5.32519 q^{65} +1.70658 q^{66} +13.9448 q^{67} -9.08134 q^{68} -2.04431 q^{69} +2.35155 q^{70} +0.747547 q^{71} +17.9183 q^{72} -2.02637 q^{73} +0.117585 q^{74} -2.76951 q^{75} -32.6024 q^{76} +1.01597 q^{77} +10.1621 q^{78} -14.9034 q^{79} +7.76339 q^{80} +5.27613 q^{81} +10.4516 q^{82} -17.7454 q^{83} -3.14771 q^{84} -1.72838 q^{85} -13.9010 q^{86} +2.46104 q^{87} +6.98504 q^{88} +2.65481 q^{89} +5.93747 q^{90} +6.04977 q^{91} -14.5682 q^{92} -0.307413 q^{93} +7.64279 q^{94} -6.20496 q^{95} -5.60358 q^{96} +12.9755 q^{97} +15.4459 q^{98} +2.56523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more