LMFDB - Embedded newform 5819.2.a.u.1.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [60,5,9,73,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.22583 q^{2} +1.22479 q^{3} -0.497336 q^{4} +2.74249 q^{5} -1.50139 q^{6} -4.85150 q^{7} +3.06131 q^{8} -1.49988 q^{9} -3.36183 q^{10} +1.00000 q^{11} -0.609133 q^{12} +5.50603 q^{13} +5.94713 q^{14} +3.35898 q^{15} -2.75798 q^{16} -2.68509 q^{17} +1.83861 q^{18} -6.28560 q^{19} -1.36394 q^{20} -5.94208 q^{21} -1.22583 q^{22} +3.74947 q^{24} +2.52126 q^{25} -6.74946 q^{26} -5.51142 q^{27} +2.41283 q^{28} -0.503263 q^{29} -4.11755 q^{30} +5.32627 q^{31} -2.74180 q^{32} +1.22479 q^{33} +3.29146 q^{34} -13.3052 q^{35} +0.745946 q^{36} -5.05352 q^{37} +7.70508 q^{38} +6.74374 q^{39} +8.39563 q^{40} +2.35569 q^{41} +7.28400 q^{42} -2.06045 q^{43} -0.497336 q^{44} -4.11342 q^{45} +9.96669 q^{47} -3.37796 q^{48} +16.5371 q^{49} -3.09064 q^{50} -3.28867 q^{51} -2.73835 q^{52} +10.3443 q^{53} +6.75608 q^{54} +2.74249 q^{55} -14.8520 q^{56} -7.69855 q^{57} +0.616915 q^{58} -0.292338 q^{59} -1.67054 q^{60} -4.55164 q^{61} -6.52912 q^{62} +7.27669 q^{63} +8.87696 q^{64} +15.1002 q^{65} -1.50139 q^{66} -0.220958 q^{67} +1.33539 q^{68} +16.3099 q^{70} -7.12567 q^{71} -4.59162 q^{72} +3.76611 q^{73} +6.19477 q^{74} +3.08802 q^{75} +3.12605 q^{76} -4.85150 q^{77} -8.26669 q^{78} +7.37456 q^{79} -7.56375 q^{80} -2.25070 q^{81} -2.88768 q^{82} +5.10176 q^{83} +2.95521 q^{84} -7.36383 q^{85} +2.52577 q^{86} -0.616392 q^{87} +3.06131 q^{88} +5.60679 q^{89} +5.04236 q^{90} -26.7125 q^{91} +6.52358 q^{93} -12.2175 q^{94} -17.2382 q^{95} -3.35814 q^{96} +3.89688 q^{97} -20.2717 q^{98} -1.49988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) $ 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * q^99

Coefficient data

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

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

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

$2$	−1.22583	−0.866794	−0.433397	−	0.901203i	$-0.642685\pi$
$2$	−1.22583	−0.866794	−0.433397	+	0.901203i	$0.642685\pi$
$3$	1.22479	0.707134	0.353567	−	0.935409i	$-0.384969\pi$
$3$	1.22479	0.707134	0.353567	+	0.935409i	$0.384969\pi$
$4$	−0.497336	−0.248668
$5$	2.74249	1.22648	0.613240	−	0.789897i	$-0.289866\pi$
$5$	2.74249	1.22648	0.613240	+	0.789897i	$0.289866\pi$
$6$	−1.50139	−0.612940
$7$	−4.85150	−1.83370	−0.916848	−	0.399237i	$-0.869275\pi$
$7$	−4.85150	−1.83370	−0.916848	+	0.399237i	$0.869275\pi$
$8$	3.06131	1.08234
$9$	−1.49988	−0.499961
$10$	−3.36183	−1.06311
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.609133	−0.175842
$13$	5.50603	1.52710	0.763548	−	0.645751i	$-0.223455\pi$
$13$	5.50603	1.52710	0.763548	+	0.645751i	$0.223455\pi$
$14$	5.94713	1.58944
$15$	3.35898	0.867285
$16$	−2.75798	−0.689496
$17$	−2.68509	−0.651229	−0.325615	−	0.945503i	$-0.605571\pi$
$17$	−2.68509	−0.651229	−0.325615	+	0.945503i	$0.605571\pi$
$18$	1.83861	0.433363
$19$	−6.28560	−1.44201	−0.721007	−	0.692927i	$-0.756321\pi$
$19$	−6.28560	−1.44201	−0.721007	+	0.692927i	$0.756321\pi$
$20$	−1.36394	−0.304986
$21$	−5.94208	−1.29667
$22$	−1.22583	−0.261348
$23$	0	0
$23$	0	0
$24$	3.74947	0.765358
$25$	2.52126	0.504252
$26$	−6.74946	−1.32368
$27$	−5.51142	−1.06067
$28$	2.41283	0.455982
$29$	−0.503263	−0.0934535	−0.0467268	−	0.998908i	$-0.514879\pi$
$29$	−0.503263	−0.0934535	−0.0467268	+	0.998908i	$0.514879\pi$
$30$	−4.11755	−0.751758
$31$	5.32627	0.956627	0.478313	−	0.878189i	$-0.341248\pi$
$31$	5.32627	0.956627	0.478313	+	0.878189i	$0.341248\pi$
$32$	−2.74180	−0.484687
$33$	1.22479	0.213209
$34$	3.29146	0.564482
$35$	−13.3052	−2.24899
$36$	0.745946	0.124324
$37$	−5.05352	−0.830794	−0.415397	−	0.909640i	$-0.636357\pi$
$37$	−5.05352	−0.830794	−0.415397	+	0.909640i	$0.636357\pi$
$38$	7.70508	1.24993
$39$	6.74374	1.07986
$40$	8.39563	1.32747
$41$	2.35569	0.367896	0.183948	−	0.982936i	$-0.441112\pi$
$41$	2.35569	0.367896	0.183948	+	0.982936i	$0.441112\pi$
$42$	7.28400	1.12394
$43$	−2.06045	−0.314216	−0.157108	−	0.987581i	$-0.550217\pi$
$43$	−2.06045	−0.314216	−0.157108	+	0.987581i	$0.550217\pi$
$44$	−0.497336	−0.0749762
$45$	−4.11342	−0.613192
$46$	0	0
$47$	9.96669	1.45379	0.726895	−	0.686748i	$-0.240963\pi$
$47$	9.96669	1.45379	0.726895	+	0.686748i	$0.240963\pi$
$48$	−3.37796	−0.487566
$49$	16.5371	2.36244
$50$	−3.09064	−0.437082
$51$	−3.28867	−0.460506
$52$	−2.73835	−0.379740
$53$	10.3443	1.42090	0.710450	−	0.703748i	$-0.248492\pi$
$53$	10.3443	1.42090	0.710450	+	0.703748i	$0.248492\pi$
$54$	6.75608	0.919386
$55$	2.74249	0.369797
$56$	−14.8520	−1.98468
$57$	−7.69855	−1.01970
$58$	0.616915	0.0810050
$59$	−0.292338	−0.0380591	−0.0190296	−	0.999819i	$-0.506058\pi$
$59$	−0.292338	−0.0380591	−0.0190296	+	0.999819i	$0.506058\pi$
$60$	−1.67054	−0.215666
$61$	−4.55164	−0.582777	−0.291389	−	0.956605i	$-0.594117\pi$
$61$	−4.55164	−0.582777	−0.291389	+	0.956605i	$0.594117\pi$
$62$	−6.52912	−0.829199
$63$	7.27669	0.916777
$64$	8.87696	1.10962
$65$	15.1002	1.87295
$66$	−1.50139	−0.184808
$67$	−0.220958	−0.0269944	−0.0134972	−	0.999909i	$-0.504296\pi$
$67$	−0.220958	−0.0269944	−0.0134972	+	0.999909i	$0.504296\pi$
$68$	1.33539	0.161940
$69$	0	0
$70$	16.3099	1.94941
$71$	−7.12567	−0.845662	−0.422831	−	0.906209i	$-0.638964\pi$
$71$	−7.12567	−0.845662	−0.422831	+	0.906209i	$0.638964\pi$
$72$	−4.59162	−0.541127
$73$	3.76611	0.440790	0.220395	−	0.975411i	$-0.429265\pi$
$73$	3.76611	0.440790	0.220395	+	0.975411i	$0.429265\pi$
$74$	6.19477	0.720127
$75$	3.08802	0.356574
$76$	3.12605	0.358583
$77$	−4.85150	−0.552880
$78$	−8.26669	−0.936018
$79$	7.37456	0.829703	0.414852	−	0.909889i	$-0.363833\pi$
$79$	7.37456	0.829703	0.414852	+	0.909889i	$0.363833\pi$
$80$	−7.56375	−0.845653
$81$	−2.25070	−0.250077
$82$	−2.88768	−0.318890
$83$	5.10176	0.559990	0.279995	−	0.960001i	$-0.409667\pi$
$83$	5.10176	0.559990	0.279995	+	0.960001i	$0.409667\pi$
$84$	2.95521	0.322440
$85$	−7.36383	−0.798719
$86$	2.52577	0.272361
$87$	−0.616392	−0.0660842
$88$	3.06131	0.326337
$89$	5.60679	0.594319	0.297159	−	0.954828i	$-0.403961\pi$
$89$	5.60679	0.594319	0.297159	+	0.954828i	$0.403961\pi$
$90$	5.04236	0.531511
$91$	−26.7125	−2.80023
$92$	0	0
$93$	6.52358	0.676464
$94$	−12.2175	−1.26014
$95$	−17.2382	−1.76860
$96$	−3.35814	−0.342739
$97$	3.89688	0.395668	0.197834	−	0.980236i	$-0.436609\pi$
$97$	3.89688	0.395668	0.197834	+	0.980236i	$0.436609\pi$
$98$	−20.2717	−2.04775
$99$	−1.49988	−0.150744
$100$	−1.25391	−0.125391
$101$	12.5987	1.25362	0.626809	−	0.779173i	$-0.284361\pi$
$101$	12.5987	1.25362	0.626809	+	0.779173i	$0.284361\pi$
$102$	4.03136	0.399164
$103$	10.3957	1.02432	0.512160	−	0.858890i	$-0.328846\pi$
$103$	10.3957	1.02432	0.512160	+	0.858890i	$0.328846\pi$
$104$	16.8557	1.65283
$105$	−16.2961	−1.59034
$106$	−12.6804	−1.23163
$107$	2.79737	0.270432	0.135216	−	0.990816i	$-0.456827\pi$
$107$	2.79737	0.270432	0.135216	+	0.990816i	$0.456827\pi$
$108$	2.74103	0.263756
$109$	−8.59809	−0.823548	−0.411774	−	0.911286i	$-0.635091\pi$
$109$	−8.59809	−0.823548	−0.411774	+	0.911286i	$0.635091\pi$
$110$	−3.36183	−0.320538
$111$	−6.18951	−0.587483
$112$	13.3804	1.26433
$113$	1.25808	0.118350	0.0591750	−	0.998248i	$-0.481153\pi$
$113$	1.25808	0.118350	0.0591750	+	0.998248i	$0.481153\pi$
$114$	9.43713	0.883868
$115$	0	0
$116$	0.250291	0.0232389
$117$	−8.25840	−0.763489
$118$	0.358357	0.0329894
$119$	13.0267	1.19416
$120$	10.2829	0.938696
$121$	1.00000	0.0909091
$122$	5.57954	0.505148
$123$	2.88523	0.260152
$124$	−2.64895	−0.237883
$125$	−6.79793	−0.608025
$126$	−8.92000	−0.794657
$127$	−16.4988	−1.46403	−0.732016	−	0.681287i	$-0.761421\pi$
$127$	−16.4988	−1.46403	−0.732016	+	0.681287i	$0.761421\pi$
$128$	−5.39805	−0.477125
$129$	−2.52363	−0.222193
$130$	−18.5103	−1.62346
$131$	9.72892	0.850020	0.425010	−	0.905189i	$-0.360271\pi$
$131$	9.72892	0.850020	0.425010	+	0.905189i	$0.360271\pi$
$132$	−0.609133	−0.0530183
$133$	30.4946	2.64422
$134$	0.270858	0.0233986
$135$	−15.1150	−1.30089
$136$	−8.21989	−0.704850
$137$	6.06805	0.518429	0.259214	−	0.965820i	$-0.416536\pi$
$137$	6.06805	0.518429	0.259214	+	0.965820i	$0.416536\pi$
$138$	0	0
$139$	−16.5533	−1.40403	−0.702014	−	0.712163i	$-0.747716\pi$
$139$	−16.5533	−1.40403	−0.702014	+	0.712163i	$0.747716\pi$
$140$	6.61716	0.559252
$141$	12.2071	1.02802
$142$	8.73488	0.733014
$143$	5.50603	0.460437
$144$	4.13666	0.344721
$145$	−1.38019	−0.114619
$146$	−4.61662	−0.382074
$147$	20.2545	1.67056
$148$	2.51330	0.206592
$149$	11.8268	0.968889	0.484445	−	0.874822i	$-0.339022\pi$
$149$	11.8268	0.968889	0.484445	+	0.874822i	$0.339022\pi$
$150$	−3.78539	−0.309076
$151$	−18.0414	−1.46819	−0.734094	−	0.679047i	$-0.762393\pi$
$151$	−18.0414	−1.46819	−0.734094	+	0.679047i	$0.762393\pi$
$152$	−19.2422	−1.56075
$153$	4.02732	0.325589
$154$	5.94713	0.479233
$155$	14.6073	1.17328
$156$	−3.35390	−0.268527
$157$	−7.13305	−0.569279	−0.284639	−	0.958635i	$-0.591874\pi$
$157$	−7.13305	−0.569279	−0.284639	+	0.958635i	$0.591874\pi$
$158$	−9.03997	−0.719182
$159$	12.6696	1.00477
$160$	−7.51937	−0.594458
$161$	0	0
$162$	2.75898	0.216766
$163$	−7.26193	−0.568798	−0.284399	−	0.958706i	$-0.591794\pi$
$163$	−7.26193	−0.568798	−0.284399	+	0.958706i	$0.591794\pi$
$164$	−1.17157	−0.0914841
$165$	3.35898	0.261496
$166$	−6.25389	−0.485396
$167$	17.0812	1.32178	0.660890	−	0.750483i	$-0.270179\pi$
$167$	17.0812	1.32178	0.660890	+	0.750483i	$0.270179\pi$
$168$	−18.1906	−1.40343
$169$	17.3163	1.33202
$170$	9.02681	0.692325
$171$	9.42766	0.720952
$172$	1.02474	0.0781356
$173$	−16.4010	−1.24694	−0.623472	−	0.781846i	$-0.714278\pi$
$173$	−16.4010	−1.24694	−0.623472	+	0.781846i	$0.714278\pi$
$174$	0.755593	0.0572814
$175$	−12.2319	−0.924644
$176$	−2.75798	−0.207891
$177$	−0.358053	−0.0269129
$178$	−6.87298	−0.515152
$179$	23.5901	1.76321	0.881604	−	0.471990i	$-0.156464\pi$
$179$	23.5901	1.76321	0.881604	+	0.471990i	$0.156464\pi$
$180$	2.04575	0.152481
$181$	0.576953	0.0428845	0.0214423	−	0.999770i	$-0.493174\pi$
$181$	0.576953	0.0428845	0.0214423	+	0.999770i	$0.493174\pi$
$182$	32.7450	2.42722
$183$	−5.57481	−0.412102
$184$	0	0
$185$	−13.8592	−1.01895
$186$	−7.99681	−0.586355
$187$	−2.68509	−0.196353
$188$	−4.95679	−0.361511
$189$	26.7387	1.94495
$190$	21.1311	1.53301
$191$	15.7389	1.13882	0.569412	−	0.822052i	$-0.307171\pi$
$191$	15.7389	1.13882	0.569412	+	0.822052i	$0.307171\pi$
$192$	10.8724	0.784650
$193$	15.3177	1.10259	0.551295	−	0.834310i	$-0.314134\pi$
$193$	15.3177	1.10259	0.551295	+	0.834310i	$0.314134\pi$
$194$	−4.77692	−0.342963
$195$	18.4946	1.32443
$196$	−8.22449	−0.587463
$197$	11.3268	0.807004	0.403502	−	0.914979i	$-0.367793\pi$
$197$	11.3268	0.807004	0.403502	+	0.914979i	$0.367793\pi$
$198$	1.83861	0.130664
$199$	−22.8191	−1.61761	−0.808803	−	0.588080i	$-0.799884\pi$
$199$	−22.8191	−1.61761	−0.808803	+	0.588080i	$0.799884\pi$
$200$	7.71837	0.545771
$201$	−0.270628	−0.0190886
$202$	−15.4439	−1.08663
$203$	2.44158	0.171365
$204$	1.63558	0.114513
$205$	6.46045	0.451217
$206$	−12.7434	−0.887874
$207$	0	0
$208$	−15.1855	−1.05293
$209$	−6.28560	−0.434784
$210$	19.9763	1.37850
$211$	14.5989	1.00503	0.502515	−	0.864569i	$-0.332408\pi$
$211$	14.5989	1.00503	0.502515	+	0.864569i	$0.332408\pi$
$212$	−5.14460	−0.353332
$213$	−8.72747	−0.597996
$214$	−3.42910	−0.234409
$215$	−5.65078	−0.385380
$216$	−16.8722	−1.14801
$217$	−25.8404	−1.75416
$218$	10.5398	0.713846
$219$	4.61271	0.311698
$220$	−1.36394	−0.0919568
$221$	−14.7842	−0.994490
$222$	7.58730	0.509226
$223$	14.6609	0.981765	0.490883	−	0.871226i	$-0.336674\pi$
$223$	14.6609	0.981765	0.490883	+	0.871226i	$0.336674\pi$
$224$	13.3019	0.888768
$225$	−3.78160	−0.252106
$226$	−1.54219	−0.102585
$227$	24.7916	1.64548	0.822738	−	0.568420i	$-0.192445\pi$
$227$	24.7916	1.64548	0.822738	+	0.568420i	$0.192445\pi$
$228$	3.82877	0.253566
$229$	15.6701	1.03551	0.517756	−	0.855528i	$-0.326767\pi$
$229$	15.6701	1.03551	0.517756	+	0.855528i	$0.326767\pi$
$230$	0	0
$231$	−5.94208	−0.390960
$232$	−1.54064	−0.101148
$233$	19.2594	1.26173	0.630864	−	0.775893i	$-0.282701\pi$
$233$	19.2594	1.26173	0.630864	+	0.775893i	$0.282701\pi$
$234$	10.1234	0.661788
$235$	27.3336	1.78304
$236$	0.145390	0.00946409
$237$	9.03231	0.586711
$238$	−15.9686	−1.03509
$239$	3.57053	0.230958	0.115479	−	0.993310i	$-0.463160\pi$
$239$	3.57053	0.230958	0.115479	+	0.993310i	$0.463160\pi$
$240$	−9.26402	−0.597990
$241$	28.2414	1.81919	0.909595	−	0.415496i	$-0.136392\pi$
$241$	28.2414	1.81919	0.909595	+	0.415496i	$0.136392\pi$
$242$	−1.22583	−0.0787995
$243$	13.7776	0.883836
$244$	2.26369	0.144918
$245$	45.3528	2.89748
$246$	−3.53680	−0.225498
$247$	−34.6087	−2.20210
$248$	16.3054	1.03539
$249$	6.24859	0.395988
$250$	8.33311	0.527032
$251$	21.6182	1.36453	0.682265	−	0.731105i	$-0.260995\pi$
$251$	21.6182	1.36453	0.682265	+	0.731105i	$0.260995\pi$
$252$	−3.61896	−0.227973
$253$	0	0
$254$	20.2248	1.26901
$255$	−9.01916	−0.564802
$256$	−11.1368	−0.696051
$257$	17.0070	1.06087	0.530434	−	0.847726i	$-0.322029\pi$
$257$	17.0070	1.06087	0.530434	+	0.847726i	$0.322029\pi$
$258$	3.09355	0.192596
$259$	24.5172	1.52342
$260$	−7.50989	−0.465743
$261$	0.754835	0.0467231
$262$	−11.9260	−0.736792
$263$	−12.8899	−0.794828	−0.397414	−	0.917640i	$-0.630092\pi$
$263$	−12.8899	−0.794828	−0.397414	+	0.917640i	$0.630092\pi$
$264$	3.74947	0.230764
$265$	28.3692	1.74270
$266$	−37.3812	−2.29199
$267$	6.86716	0.420263
$268$	0.109891	0.00671264
$269$	10.4587	0.637678	0.318839	−	0.947809i	$-0.396707\pi$
$269$	10.4587	0.637678	0.318839	+	0.947809i	$0.396707\pi$
$270$	18.5285	1.12761
$271$	−29.2318	−1.77571	−0.887853	−	0.460127i	$-0.847804\pi$
$271$	−29.2318	−1.77571	−0.887853	+	0.460127i	$0.847804\pi$
$272$	7.40543	0.449020
$273$	−32.7173	−1.98014
$274$	−7.43841	−0.449371
$275$	2.52126	0.152038
$276$	0	0
$277$	15.6529	0.940491	0.470245	−	0.882536i	$-0.344165\pi$
$277$	15.6529	0.940491	0.470245	+	0.882536i	$0.344165\pi$
$278$	20.2915	1.21700
$279$	−7.98879	−0.478276
$280$	−40.7314	−2.43417
$281$	−27.3884	−1.63386	−0.816928	−	0.576739i	$-0.804325\pi$
$281$	−27.3884	−1.63386	−0.816928	+	0.576739i	$0.804325\pi$
$282$	−14.9639	−0.891086
$283$	−20.9439	−1.24499	−0.622493	−	0.782625i	$-0.713880\pi$
$283$	−20.9439	−1.24499	−0.622493	+	0.782625i	$0.713880\pi$
$284$	3.54385	0.210289
$285$	−21.1132	−1.25064
$286$	−6.74946	−0.399104
$287$	−11.4286	−0.674610
$288$	4.11239	0.242325
$289$	−9.79031	−0.575901
$290$	1.69189	0.0993509
$291$	4.77287	0.279791
$292$	−1.87302	−0.109610
$293$	−0.274026	−0.0160088	−0.00800438	−	0.999968i	$-0.502548\pi$
$293$	−0.274026	−0.0160088	−0.00800438	+	0.999968i	$0.502548\pi$
$294$	−24.8286	−1.44803
$295$	−0.801734	−0.0466787
$296$	−15.4704	−0.899200
$297$	−5.51142	−0.319805
$298$	−14.4977	−0.839827
$299$	0	0
$300$	−1.53578	−0.0886685
$301$	9.99630	0.576177
$302$	22.1157	1.27262
$303$	15.4308	0.886476
$304$	17.3356	0.994264
$305$	−12.4828	−0.714765
$306$	−4.93682	−0.282219
$307$	−13.2780	−0.757814	−0.378907	−	0.925435i	$-0.623700\pi$
$307$	−13.2780	−0.757814	−0.378907	+	0.925435i	$0.623700\pi$
$308$	2.41283	0.137484
$309$	12.7326	0.724331
$310$	−17.9060	−1.01700
$311$	5.26741	0.298688	0.149344	−	0.988785i	$-0.452284\pi$
$311$	5.26741	0.298688	0.149344	+	0.988785i	$0.452284\pi$
$312$	20.6447	1.16878
$313$	−26.1680	−1.47910	−0.739550	−	0.673101i	$-0.764962\pi$
$313$	−26.1680	−1.47910	−0.739550	+	0.673101i	$0.764962\pi$
$314$	8.74391	0.493448
$315$	19.9563	1.12441
$316$	−3.66764	−0.206321
$317$	−0.790561	−0.0444023	−0.0222012	−	0.999754i	$-0.507067\pi$
$317$	−0.790561	−0.0444023	−0.0222012	+	0.999754i	$0.507067\pi$
$318$	−15.5308	−0.870926
$319$	−0.503263	−0.0281773
$320$	24.3450	1.36093
$321$	3.42620	0.191232
$322$	0	0
$323$	16.8774	0.939082
$324$	1.11935	0.0621863
$325$	13.8821	0.770041
$326$	8.90190	0.493031
$327$	−10.5309	−0.582359
$328$	7.21150	0.398188
$329$	−48.3534	−2.66581
$330$	−4.11755	−0.226664
$331$	18.6500	1.02510	0.512548	−	0.858659i	$-0.328702\pi$
$331$	18.6500	1.02510	0.512548	+	0.858659i	$0.328702\pi$
$332$	−2.53729	−0.139252
$333$	7.57969	0.415365
$334$	−20.9386	−1.14571
$335$	−0.605977	−0.0331080
$336$	16.3882	0.894048
$337$	−9.14249	−0.498023	−0.249011	−	0.968501i	$-0.580106\pi$
$337$	−9.14249	−0.498023	−0.249011	+	0.968501i	$0.580106\pi$
$338$	−21.2269	−1.15459
$339$	1.54088	0.0836893
$340$	3.66230	0.198616
$341$	5.32627	0.288434
$342$	−11.5567	−0.624917
$343$	−46.2692	−2.49830
$344$	−6.30770	−0.340088
$345$	0	0
$346$	20.1048	1.08084
$347$	13.2995	0.713953	0.356976	−	0.934113i	$-0.383808\pi$
$347$	13.2995	0.713953	0.356976	+	0.934113i	$0.383808\pi$
$348$	0.306554	0.0164330
$349$	17.4492	0.934037	0.467018	−	0.884248i	$-0.345328\pi$
$349$	17.4492	0.934037	0.467018	+	0.884248i	$0.345328\pi$
$350$	14.9942	0.801476
$351$	−30.3460	−1.61975
$352$	−2.74180	−0.146139
$353$	−0.698808	−0.0371938	−0.0185969	−	0.999827i	$-0.505920\pi$
$353$	−0.698808	−0.0371938	−0.0185969	+	0.999827i	$0.505920\pi$
$354$	0.438913	0.0233279
$355$	−19.5421	−1.03719
$356$	−2.78846	−0.147788
$357$	15.9550	0.844429
$358$	−28.9175	−1.52834
$359$	−11.0123	−0.581209	−0.290604	−	0.956843i	$-0.593856\pi$
$359$	−11.0123	−0.581209	−0.290604	+	0.956843i	$0.593856\pi$
$360$	−12.5925	−0.663681
$361$	20.5087	1.07941
$362$	−0.707247	−0.0371721
$363$	1.22479	0.0642849
$364$	13.2851	0.696328
$365$	10.3285	0.540620
$366$	6.83378	0.357207
$367$	1.46121	0.0762744	0.0381372	−	0.999273i	$-0.487858\pi$
$367$	1.46121	0.0762744	0.0381372	+	0.999273i	$0.487858\pi$
$368$	0	0
$369$	−3.53326	−0.183934
$370$	16.9891	0.883221
$371$	−50.1854	−2.60550
$372$	−3.24441	−0.168215
$373$	10.9330	0.566090	0.283045	−	0.959107i	$-0.408655\pi$
$373$	10.9330	0.566090	0.283045	+	0.959107i	$0.408655\pi$
$374$	3.29146	0.170198
$375$	−8.32605	−0.429955
$376$	30.5112	1.57349
$377$	−2.77098	−0.142713
$378$	−32.7771	−1.68587
$379$	−22.4098	−1.15111	−0.575557	−	0.817762i	$-0.695215\pi$
$379$	−22.4098	−1.15111	−0.575557	+	0.817762i	$0.695215\pi$
$380$	8.57318	0.439795
$381$	−20.2076	−1.03527
$382$	−19.2932	−0.987126
$383$	0.797627	0.0407568	0.0203784	−	0.999792i	$-0.493513\pi$
$383$	0.797627	0.0407568	0.0203784	+	0.999792i	$0.493513\pi$
$384$	−6.61149	−0.337391
$385$	−13.3052	−0.678096
$386$	−18.7769	−0.955719
$387$	3.09044	0.157096
$388$	−1.93806	−0.0983900
$389$	8.54383	0.433189	0.216595	−	0.976262i	$-0.430505\pi$
$389$	8.54383	0.433189	0.216595	+	0.976262i	$0.430505\pi$
$390$	−22.6713	−1.14801
$391$	0	0
$392$	50.6252	2.55696
$393$	11.9159	0.601078
$394$	−13.8848	−0.699507
$395$	20.2247	1.01761
$396$	0.745946	0.0374852
$397$	−8.07631	−0.405338	−0.202669	−	0.979247i	$-0.564962\pi$
$397$	−8.07631	−0.405338	−0.202669	+	0.979247i	$0.564962\pi$
$398$	27.9724	1.40213
$399$	37.3495	1.86982
$400$	−6.95359	−0.347680
$401$	22.8958	1.14336	0.571681	−	0.820476i	$-0.306292\pi$
$401$	22.8958	1.14336	0.571681	+	0.820476i	$0.306292\pi$
$402$	0.331745	0.0165459
$403$	29.3266	1.46086
$404$	−6.26579	−0.311735
$405$	−6.17252	−0.306715
$406$	−2.99297	−0.148538
$407$	−5.05352	−0.250494
$408$	−10.0677	−0.498424
$409$	22.0923	1.09239	0.546196	−	0.837657i	$-0.316075\pi$
$409$	22.0923	1.09239	0.546196	+	0.837657i	$0.316075\pi$
$410$	−7.91943	−0.391113
$411$	7.43210	0.366599
$412$	−5.17016	−0.254715
$413$	1.41828	0.0697889
$414$	0	0
$415$	13.9915	0.686817
$416$	−15.0964	−0.740164
$417$	−20.2743	−0.992837
$418$	7.70508	0.376868
$419$	−24.8080	−1.21195	−0.605975	−	0.795483i	$-0.707217\pi$
$419$	−24.8080	−1.21195	−0.605975	+	0.795483i	$0.707217\pi$
$420$	8.10464	0.395466
$421$	−12.2191	−0.595523	−0.297761	−	0.954640i	$-0.596240\pi$
$421$	−12.2191	−0.595523	−0.297761	+	0.954640i	$0.596240\pi$
$422$	−17.8958	−0.871153
$423$	−14.9489	−0.726839
$424$	31.6672	1.53789
$425$	−6.76980	−0.328383
$426$	10.6984	0.518340
$427$	22.0823	1.06864
$428$	−1.39123	−0.0672478
$429$	6.74374	0.325591
$430$	6.92691	0.334045
$431$	−2.21514	−0.106700	−0.0533498	−	0.998576i	$-0.516990\pi$
$431$	−2.21514	−0.106700	−0.0533498	+	0.998576i	$0.516990\pi$
$432$	15.2004	0.731331
$433$	30.3761	1.45978	0.729891	−	0.683563i	$-0.239571\pi$
$433$	30.3761	1.45978	0.729891	+	0.683563i	$0.239571\pi$
$434$	31.6760	1.52050
$435$	−1.69045	−0.0810509
$436$	4.27614	0.204790
$437$	0	0
$438$	−5.65440	−0.270178
$439$	−27.7272	−1.32335	−0.661673	−	0.749793i	$-0.730153\pi$
$439$	−27.7272	−1.32335	−0.661673	+	0.749793i	$0.730153\pi$
$440$	8.39563	0.400246
$441$	−24.8037	−1.18113
$442$	18.1229	0.862018
$443$	14.1677	0.673128	0.336564	−	0.941661i	$-0.390735\pi$
$443$	14.1677	0.673128	0.336564	+	0.941661i	$0.390735\pi$
$444$	3.07827	0.146088
$445$	15.3766	0.728920
$446$	−17.9718	−0.850988
$447$	14.4854	0.685135
$448$	−43.0666	−2.03471
$449$	25.3779	1.19766	0.598828	−	0.800878i	$-0.295633\pi$
$449$	25.3779	1.19766	0.598828	+	0.800878i	$0.295633\pi$
$450$	4.63560	0.218524
$451$	2.35569	0.110925
$452$	−0.625687	−0.0294299
$453$	−22.0970	−1.03821
$454$	−30.3903	−1.42629
$455$	−73.2588	−3.43443
$456$	−23.5677	−1.10366
$457$	−2.25390	−0.105433	−0.0527166	−	0.998610i	$-0.516788\pi$
$457$	−2.25390	−0.105433	−0.0527166	+	0.998610i	$0.516788\pi$
$458$	−19.2090	−0.897576
$459$	14.7986	0.690742
$460$	0	0
$461$	13.1499	0.612452	0.306226	−	0.951959i	$-0.400934\pi$
$461$	13.1499	0.612452	0.306226	+	0.951959i	$0.400934\pi$
$462$	7.28400	0.338882
$463$	35.5605	1.65264	0.826319	−	0.563202i	$-0.190431\pi$
$463$	35.5605	1.65264	0.826319	+	0.563202i	$0.190431\pi$
$464$	1.38799	0.0644358
$465$	17.8909	0.829669
$466$	−23.6088	−1.09366
$467$	10.1296	0.468744	0.234372	−	0.972147i	$-0.424697\pi$
$467$	10.1296	0.468744	0.234372	+	0.972147i	$0.424697\pi$
$468$	4.10720	0.189855
$469$	1.07198	0.0494995
$470$	−33.5063	−1.54553
$471$	−8.73650	−0.402557
$472$	−0.894938	−0.0411928
$473$	−2.06045	−0.0947398
$474$	−11.0721	−0.508558
$475$	−15.8476	−0.727138
$476$	−6.47865	−0.296948
$477$	−15.5153	−0.710395
$478$	−4.37687	−0.200193
$479$	−18.5593	−0.847997	−0.423999	−	0.905663i	$-0.639374\pi$
$479$	−18.5593	−0.847997	−0.423999	+	0.905663i	$0.639374\pi$
$480$	−9.20967	−0.420362
$481$	−27.8248	−1.26870
$482$	−34.6192	−1.57686
$483$	0	0
$484$	−0.497336	−0.0226062
$485$	10.6872	0.485279
$486$	−16.8891	−0.766103
$487$	−18.5791	−0.841901	−0.420951	−	0.907084i	$-0.638303\pi$
$487$	−18.5791	−0.841901	−0.420951	+	0.907084i	$0.638303\pi$
$488$	−13.9340	−0.630762
$489$	−8.89435	−0.402216
$490$	−55.5949	−2.51152
$491$	−7.68850	−0.346977	−0.173489	−	0.984836i	$-0.555504\pi$
$491$	−7.68850	−0.346977	−0.173489	+	0.984836i	$0.555504\pi$
$492$	−1.43493	−0.0646915
$493$	1.35130	0.0608597
$494$	42.4244	1.90876
$495$	−4.11342	−0.184884
$496$	−14.6898	−0.659591
$497$	34.5702	1.55069
$498$	−7.65972	−0.343240
$499$	−18.1503	−0.812517	−0.406259	−	0.913758i	$-0.633167\pi$
$499$	−18.1503	−0.812517	−0.406259	+	0.913758i	$0.633167\pi$
$500$	3.38085	0.151196
$501$	20.9209	0.934676
$502$	−26.5003	−1.18277
$503$	17.3514	0.773661	0.386831	−	0.922151i	$-0.373570\pi$
$503$	17.3514	0.773661	0.386831	+	0.922151i	$0.373570\pi$
$504$	22.2762	0.992263
$505$	34.5518	1.53754
$506$	0	0
$507$	21.2089	0.941920
$508$	8.20545	0.364058
$509$	−3.41316	−0.151286	−0.0756428	−	0.997135i	$-0.524101\pi$
$509$	−3.41316	−0.151286	−0.0756428	+	0.997135i	$0.524101\pi$
$510$	11.0560	0.489567
$511$	−18.2713	−0.808275
$512$	24.4480	1.08046
$513$	34.6426	1.52951
$514$	−20.8477	−0.919554
$515$	28.5101	1.25631
$516$	1.25509	0.0552523
$517$	9.96669	0.438334
$518$	−30.0539	−1.32049
$519$	−20.0878	−0.881756
$520$	46.2265	2.02717
$521$	15.2088	0.666311	0.333156	−	0.942872i	$-0.391887\pi$
$521$	15.2088	0.666311	0.333156	+	0.942872i	$0.391887\pi$
$522$	−0.925301	−0.0404993
$523$	16.2411	0.710173	0.355086	−	0.934834i	$-0.384451\pi$
$523$	16.2411	0.710173	0.355086	+	0.934834i	$0.384451\pi$
$524$	−4.83854	−0.211373
$525$	−14.9815	−0.653848
$526$	15.8009	0.688952
$527$	−14.3015	−0.622983
$528$	−3.37796	−0.147007
$529$	0	0
$530$	−34.7758	−1.51057
$531$	0.438473	0.0190281
$532$	−15.1661	−0.657532
$533$	12.9705	0.561813
$534$	−8.41798	−0.364282
$535$	7.67176	0.331679
$536$	−0.676423	−0.0292170
$537$	28.8930	1.24682
$538$	−12.8206	−0.552736
$539$	16.5371	0.712302
$540$	7.51725	0.323491
$541$	−5.10124	−0.219320	−0.109660	−	0.993969i	$-0.534976\pi$
$541$	−5.10124	−0.219320	−0.109660	+	0.993969i	$0.534976\pi$
$542$	35.8333	1.53917
$543$	0.706647	0.0303251
$544$	7.36198	0.315642
$545$	−23.5802	−1.01006
$546$	40.1059	1.71637
$547$	23.2215	0.992878	0.496439	−	0.868072i	$-0.334641\pi$
$547$	23.2215	0.992878	0.496439	+	0.868072i	$0.334641\pi$
$548$	−3.01786	−0.128917
$549$	6.82693	0.291366
$550$	−3.09064	−0.131785
$551$	3.16331	0.134761
$552$	0	0
$553$	−35.7777	−1.52142
$554$	−19.1878	−0.815212
$555$	−16.9747	−0.720535
$556$	8.23253	0.349137
$557$	−10.7761	−0.456599	−0.228299	−	0.973591i	$-0.573317\pi$
$557$	−10.7761	−0.456599	−0.228299	+	0.973591i	$0.573317\pi$
$558$	9.79292	0.414567
$559$	−11.3449	−0.479839
$560$	36.6955	1.55067
$561$	−3.28867	−0.138848
$562$	33.5736	1.41622
$563$	−25.5390	−1.07634	−0.538171	−	0.842836i	$-0.680884\pi$
$563$	−25.5390	−1.07634	−0.538171	+	0.842836i	$0.680884\pi$
$564$	−6.07104	−0.255637
$565$	3.45027	0.145154
$566$	25.6737	1.07915
$567$	10.9193	0.458566
$568$	−21.8139	−0.915292
$569$	20.1579	0.845063	0.422531	−	0.906348i	$-0.361142\pi$
$569$	20.1579	0.845063	0.422531	+	0.906348i	$0.361142\pi$
$570$	25.8812	1.08405
$571$	32.9131	1.37737	0.688685	−	0.725060i	$-0.258188\pi$
$571$	32.9131	1.37737	0.688685	+	0.725060i	$0.258188\pi$
$572$	−2.73835	−0.114496
$573$	19.2768	0.805301
$574$	14.0096	0.584748
$575$	0	0
$576$	−13.3144	−0.554767
$577$	40.8072	1.69883	0.849413	−	0.527729i	$-0.176956\pi$
$577$	40.8072	1.69883	0.849413	+	0.527729i	$0.176956\pi$
$578$	12.0013	0.499187
$579$	18.7610	0.779679
$580$	0.686420	0.0285020
$581$	−24.7512	−1.02685
$582$	−5.85073	−0.242521
$583$	10.3443	0.428417
$584$	11.5293	0.477084
$585$	−22.6486	−0.936404
$586$	0.335909	0.0138763
$587$	−11.9665	−0.493912	−0.246956	−	0.969027i	$-0.579430\pi$
$587$	−11.9665	−0.493912	−0.246956	+	0.969027i	$0.579430\pi$
$588$	−10.0733	−0.415415
$589$	−33.4788	−1.37947
$590$	0.982791	0.0404608
$591$	13.8730	0.570660
$592$	13.9375	0.572829
$593$	−23.5359	−0.966506	−0.483253	−	0.875481i	$-0.660545\pi$
$593$	−23.5359	−0.966506	−0.483253	+	0.875481i	$0.660545\pi$
$594$	6.75608	0.277205
$595$	35.7256	1.46461
$596$	−5.88190	−0.240932
$597$	−27.9487	−1.14386
$598$	0	0
$599$	15.3469	0.627055	0.313528	−	0.949579i	$-0.398489\pi$
$599$	15.3469	0.627055	0.313528	+	0.949579i	$0.398489\pi$
$600$	9.45339	0.385933
$601$	2.71278	0.110656	0.0553282	−	0.998468i	$-0.482379\pi$
$601$	2.71278	0.110656	0.0553282	+	0.998468i	$0.482379\pi$
$602$	−12.2538	−0.499427
$603$	0.331412	0.0134961
$604$	8.97264	0.365092
$605$	2.74249	0.111498
$606$	−18.9156	−0.768392
$607$	16.2692	0.660348	0.330174	−	0.943920i	$-0.392893\pi$
$607$	16.2692	0.660348	0.330174	+	0.943920i	$0.392893\pi$
$608$	17.2339	0.698926
$609$	2.99043	0.121178
$610$	15.3018	0.619554
$611$	54.8768	2.22008
$612$	−2.00293	−0.0809637
$613$	18.2272	0.736188	0.368094	−	0.929789i	$-0.380011\pi$
$613$	18.2272	0.736188	0.368094	+	0.929789i	$0.380011\pi$
$614$	16.2766	0.656869
$615$	7.91271	0.319071
$616$	−14.8520	−0.598403
$617$	30.9061	1.24423	0.622116	−	0.782925i	$-0.286273\pi$
$617$	30.9061	1.24423	0.622116	+	0.782925i	$0.286273\pi$
$618$	−15.6080	−0.627846
$619$	13.1094	0.526912	0.263456	−	0.964671i	$-0.415138\pi$
$619$	13.1094	0.526912	0.263456	+	0.964671i	$0.415138\pi$
$620$	−7.26472	−0.291758
$621$	0	0
$622$	−6.45696	−0.258901
$623$	−27.2014	−1.08980
$624$	−18.5991	−0.744561
$625$	−31.2495	−1.24998
$626$	32.0775	1.28208
$627$	−7.69855	−0.307450
$628$	3.54752	0.141561
$629$	13.5691	0.541037
$630$	−24.4630	−0.974630
$631$	24.3573	0.969651	0.484825	−	0.874611i	$-0.338883\pi$
$631$	24.3573	0.969651	0.484825	+	0.874611i	$0.338883\pi$
$632$	22.5759	0.898019
$633$	17.8806	0.710691
$634$	0.969095	0.0384877
$635$	−45.2478	−1.79561
$636$	−6.30106	−0.249853
$637$	91.0536	3.60767
$638$	0.616915	0.0244239
$639$	10.6877	0.422798
$640$	−14.8041	−0.585184
$641$	8.66234	0.342142	0.171071	−	0.985259i	$-0.445277\pi$
$641$	8.66234	0.342142	0.171071	+	0.985259i	$0.445277\pi$
$642$	−4.19994	−0.165758
$643$	−10.5195	−0.414849	−0.207425	−	0.978251i	$-0.566508\pi$
$643$	−10.5195	−0.414849	−0.207425	+	0.978251i	$0.566508\pi$
$644$	0	0
$645$	−6.92103	−0.272515
$646$	−20.6888	−0.813991
$647$	42.6761	1.67777	0.838886	−	0.544307i	$-0.183207\pi$
$647$	42.6761	1.67777	0.838886	+	0.544307i	$0.183207\pi$
$648$	−6.89009	−0.270668
$649$	−0.292338	−0.0114753
$650$	−17.0171	−0.667467
$651$	−31.6492	−1.24043
$652$	3.61162	0.141442
$653$	−11.8041	−0.461931	−0.230966	−	0.972962i	$-0.574188\pi$
$653$	−11.8041	−0.461931	−0.230966	+	0.972962i	$0.574188\pi$
$654$	12.9091	0.504785
$655$	26.6815	1.04253
$656$	−6.49695	−0.253663
$657$	−5.64873	−0.220378
$658$	59.2731	2.31071
$659$	−33.6054	−1.30908	−0.654539	−	0.756028i	$-0.727137\pi$
$659$	−33.6054	−1.30908	−0.654539	+	0.756028i	$0.727137\pi$
$660$	−1.67054	−0.0650258
$661$	43.5782	1.69500	0.847498	−	0.530798i	$-0.178108\pi$
$661$	43.5782	1.69500	0.847498	+	0.530798i	$0.178108\pi$
$662$	−22.8617	−0.888546
$663$	−18.1075	−0.703238
$664$	15.6181	0.606099
$665$	83.6311	3.24308
$666$	−9.29143	−0.360036
$667$	0	0
$668$	−8.49508	−0.328684
$669$	17.9565	0.694240
$670$	0.742825	0.0286978
$671$	−4.55164	−0.175714
$672$	16.2920	0.628478
$673$	−34.8229	−1.34232	−0.671162	−	0.741310i	$-0.734205\pi$
$673$	−34.8229	−1.34232	−0.671162	+	0.741310i	$0.734205\pi$
$674$	11.2072	0.431683
$675$	−13.8957	−0.534847
$676$	−8.61203	−0.331232
$677$	29.8777	1.14829	0.574146	−	0.818753i	$-0.305334\pi$
$677$	29.8777	1.14829	0.574146	+	0.818753i	$0.305334\pi$
$678$	−1.88886	−0.0725414
$679$	−18.9057	−0.725535
$680$	−22.5430	−0.864484
$681$	30.3646	1.16357
$682$	−6.52912	−0.250013
$683$	41.7687	1.59823	0.799117	−	0.601176i	$-0.205301\pi$
$683$	41.7687	1.59823	0.799117	+	0.601176i	$0.205301\pi$
$684$	−4.68872	−0.179278
$685$	16.6416	0.635842
$686$	56.7182	2.16551
$687$	19.1927	0.732246
$688$	5.68270	0.216651
$689$	56.9560	2.16985
$690$	0	0
$691$	−1.56844	−0.0596662	−0.0298331	−	0.999555i	$-0.509498\pi$
$691$	−1.56844	−0.0596662	−0.0298331	+	0.999555i	$0.509498\pi$
$692$	8.15680	0.310075
$693$	7.27669	0.276419
$694$	−16.3029	−0.618850
$695$	−45.3972	−1.72201
$696$	−1.88697	−0.0715254
$697$	−6.32522	−0.239585
$698$	−21.3898	−0.809617
$699$	23.5888	0.892211
$700$	6.08336	0.229930
$701$	−15.0180	−0.567223	−0.283611	−	0.958939i	$-0.591533\pi$
$701$	−15.0180	−0.567223	−0.283611	+	0.958939i	$0.591533\pi$
$702$	37.1991	1.40399
$703$	31.7644	1.19802
$704$	8.87696	0.334563
$705$	33.4779	1.26085
$706$	0.856622	0.0322394
$707$	−61.1226	−2.29875
$708$	0.178073	0.00669238
$709$	36.4179	1.36770	0.683851	−	0.729622i	$-0.260304\pi$
$709$	36.4179	1.36770	0.683851	+	0.729622i	$0.260304\pi$
$710$	23.9553	0.899027
$711$	−11.0610	−0.414819
$712$	17.1642	0.643254
$713$	0	0
$714$	−19.5582	−0.731946
$715$	15.1002	0.564716
$716$	−11.7322	−0.438453
$717$	4.37316	0.163319
$718$	13.4993	0.503788
$719$	−10.1992	−0.380366	−0.190183	−	0.981749i	$-0.560908\pi$
$719$	−10.1992	−0.380366	−0.190183	+	0.981749i	$0.560908\pi$
$720$	11.3447	0.422794
$721$	−50.4348	−1.87829
$722$	−25.1402	−0.935623
$723$	34.5899	1.28641
$724$	−0.286939	−0.0106640
$725$	−1.26886	−0.0471241
$726$	−1.50139	−0.0557218
$727$	29.9989	1.11260	0.556299	−	0.830982i	$-0.312221\pi$
$727$	29.9989	1.11260	0.556299	+	0.830982i	$0.312221\pi$
$728$	−81.7753	−3.03080
$729$	23.6268	0.875068
$730$	−12.6611	−0.468606
$731$	5.53250	0.204627
$732$	2.77255	0.102477
$733$	−25.8879	−0.956193	−0.478097	−	0.878307i	$-0.658673\pi$
$733$	−25.8879	−0.956193	−0.478097	+	0.878307i	$0.658673\pi$
$734$	−1.79119	−0.0661142
$735$	55.5478	2.04891
$736$	0	0
$737$	−0.220958	−0.00813911
$738$	4.33118	0.159433
$739$	−13.3464	−0.490956	−0.245478	−	0.969402i	$-0.578945\pi$
$739$	−13.3464	−0.490956	−0.245478	+	0.969402i	$0.578945\pi$
$740$	6.89270	0.253381
$741$	−42.3884	−1.55718
$742$	61.5189	2.25843
$743$	32.1285	1.17868	0.589340	−	0.807885i	$-0.299388\pi$
$743$	32.1285	1.17868	0.589340	+	0.807885i	$0.299388\pi$
$744$	19.9707	0.732162
$745$	32.4349	1.18832
$746$	−13.4020	−0.490684
$747$	−7.65204	−0.279974
$748$	1.33539	0.0488267
$749$	−13.5714	−0.495890
$750$	10.2063	0.372683
$751$	−44.0901	−1.60887	−0.804436	−	0.594040i	$-0.797532\pi$
$751$	−44.0901	−1.60887	−0.804436	+	0.594040i	$0.797532\pi$
$752$	−27.4880	−1.00238
$753$	26.4778	0.964905
$754$	3.39675	0.123702
$755$	−49.4784	−1.80070
$756$	−13.2981	−0.483648
$757$	−24.8318	−0.902526	−0.451263	−	0.892391i	$-0.649026\pi$
$757$	−24.8318	−0.902526	−0.451263	+	0.892391i	$0.649026\pi$
$758$	27.4706	0.997779
$759$	0	0
$760$	−52.7715	−1.91422
$761$	5.41517	0.196300	0.0981498	−	0.995172i	$-0.468708\pi$
$761$	5.41517	0.196300	0.0981498	+	0.995172i	$0.468708\pi$
$762$	24.7711	0.897364
$763$	41.7137	1.51014
$764$	−7.82750	−0.283189
$765$	11.0449	0.399329
$766$	−0.977757	−0.0353278
$767$	−1.60962	−0.0581200
$768$	−13.6403	−0.492201
$769$	−39.6677	−1.43045	−0.715227	−	0.698892i	$-0.753677\pi$
$769$	−39.6677	−1.43045	−0.715227	+	0.698892i	$0.753677\pi$
$770$	16.3099	0.587770
$771$	20.8300	0.750176
$772$	−7.61803	−0.274179
$773$	13.4717	0.484545	0.242272	−	0.970208i	$-0.422107\pi$
$773$	13.4717	0.484545	0.242272	+	0.970208i	$0.422107\pi$
$774$	−3.78836	−0.136170
$775$	13.4289	0.482381
$776$	11.9296	0.428247
$777$	30.0284	1.07726
$778$	−10.4733	−0.375486
$779$	−14.8069	−0.530512
$780$	−9.19805	−0.329343
$781$	−7.12567	−0.254977
$782$	0	0
$783$	2.77369	0.0991237
$784$	−45.6090	−1.62889
$785$	−19.5623	−0.698209
$786$	−14.6069	−0.521011
$787$	10.5427	0.375805	0.187903	−	0.982188i	$-0.439831\pi$
$787$	10.5427	0.375805	0.187903	+	0.982188i	$0.439831\pi$
$788$	−5.63325	−0.200676
$789$	−15.7875	−0.562050
$790$	−24.7921	−0.882062
$791$	−6.10357	−0.217018
$792$	−4.59162	−0.163156
$793$	−25.0614	−0.889957
$794$	9.90020	0.351345
$795$	34.7463	1.23233
$796$	11.3488	0.402247
$797$	−33.0552	−1.17088	−0.585438	−	0.810718i	$-0.699077\pi$
$797$	−33.0552	−1.17088	−0.585438	+	0.810718i	$0.699077\pi$
$798$	−45.7843	−1.62074
$799$	−26.7614	−0.946751
$800$	−6.91280	−0.244404
$801$	−8.40954	−0.297136
$802$	−28.0664	−0.991059
$803$	3.76611	0.132903
$804$	0.134593	0.00474673
$805$	0	0
$806$	−35.9495	−1.26627
$807$	12.8097	0.450924
$808$	38.5686	1.35684
$809$	23.8452	0.838354	0.419177	−	0.907905i	$-0.362319\pi$
$809$	23.8452	0.838354	0.419177	+	0.907905i	$0.362319\pi$
$810$	7.56647	0.265859
$811$	−13.7991	−0.484550	−0.242275	−	0.970208i	$-0.577894\pi$
$811$	−13.7991	−0.484550	−0.242275	+	0.970208i	$0.577894\pi$
$812$	−1.21429	−0.0426131
$813$	−35.8029	−1.25566
$814$	6.19477	0.217126
$815$	−19.9158	−0.697619
$816$	9.07011	0.317517
$817$	12.9512	0.453105
$818$	−27.0814	−0.946879
$819$	40.0656	1.40001
$820$	−3.21302	−0.112203
$821$	2.89848	0.101158	0.0505788	−	0.998720i	$-0.483893\pi$
$821$	2.89848	0.101158	0.0505788	+	0.998720i	$0.483893\pi$
$822$	−9.11051	−0.317766
$823$	−11.6184	−0.404992	−0.202496	−	0.979283i	$-0.564905\pi$
$823$	−11.6184	−0.404992	−0.202496	+	0.979283i	$0.564905\pi$
$824$	31.8245	1.10866
$825$	3.08802	0.107511
$826$	−1.73857	−0.0604926
$827$	−48.3541	−1.68144	−0.840718	−	0.541473i	$-0.817867\pi$
$827$	−48.3541	−1.68144	−0.840718	+	0.541473i	$0.817867\pi$
$828$	0	0
$829$	35.0072	1.21585	0.607925	−	0.793994i	$-0.292002\pi$
$829$	35.0072	1.21585	0.607925	+	0.793994i	$0.292002\pi$
$830$	−17.1513	−0.595329
$831$	19.1715	0.665053
$832$	48.8768	1.69450
$833$	−44.4035	−1.53849
$834$	24.8529	0.860585
$835$	46.8449	1.62114
$836$	3.12605	0.108117
$837$	−29.3553	−1.01467
$838$	30.4105	1.05051
$839$	−2.76971	−0.0956212	−0.0478106	−	0.998856i	$-0.515224\pi$
$839$	−2.76971	−0.0956212	−0.0478106	+	0.998856i	$0.515224\pi$
$840$	−49.8875	−1.72128
$841$	−28.7467	−0.991266
$842$	14.9786	0.516196
$843$	−33.5451	−1.15536
$844$	−7.26056	−0.249919
$845$	47.4898	1.63370
$846$	18.3248	0.630020
$847$	−4.85150	−0.166700
$848$	−28.5294	−0.979705
$849$	−25.6519	−0.880372
$850$	8.29864	0.284641
$851$	0	0
$852$	4.34048	0.148703
$853$	−49.3637	−1.69018	−0.845090	−	0.534625i	$-0.820453\pi$
$853$	−49.3637	−1.69018	−0.845090	+	0.534625i	$0.820453\pi$
$854$	−27.0692	−0.926288
$855$	25.8553	0.884232
$856$	8.56363	0.292699
$857$	30.8614	1.05420	0.527102	−	0.849802i	$-0.323278\pi$
$857$	30.8614	1.05420	0.527102	+	0.849802i	$0.323278\pi$
$858$	−8.26669	−0.282220
$859$	5.67360	0.193581	0.0967903	−	0.995305i	$-0.469142\pi$
$859$	5.67360	0.193581	0.0967903	+	0.995305i	$0.469142\pi$
$860$	2.81034	0.0958317
$861$	−13.9977	−0.477040
$862$	2.71539	0.0924866
$863$	−27.9405	−0.951104	−0.475552	−	0.879688i	$-0.657752\pi$
$863$	−27.9405	−0.951104	−0.475552	+	0.879688i	$0.657752\pi$
$864$	15.1112	0.514095
$865$	−44.9796	−1.52935
$866$	−37.2360	−1.26533
$867$	−11.9911	−0.407239
$868$	12.8514	0.436204
$869$	7.37456	0.250165
$870$	2.07221	0.0702544
$871$	−1.21660	−0.0412230
$872$	−26.3215	−0.891357
$873$	−5.84487	−0.197819
$874$	0	0
$875$	32.9802	1.11493
$876$	−2.29407	−0.0775093
$877$	32.4640	1.09623	0.548116	−	0.836402i	$-0.315345\pi$
$877$	32.4640	1.09623	0.548116	+	0.836402i	$0.315345\pi$
$878$	33.9888	1.14707
$879$	−0.335625	−0.0113203
$880$	−7.56375	−0.254974
$881$	23.7814	0.801217	0.400609	−	0.916249i	$-0.368799\pi$
$881$	23.7814	0.801217	0.400609	+	0.916249i	$0.368799\pi$
$882$	30.4052	1.02380
$883$	25.9477	0.873210	0.436605	−	0.899653i	$-0.356181\pi$
$883$	25.9477	0.873210	0.436605	+	0.899653i	$0.356181\pi$
$884$	7.35269	0.247298
$885$	−0.981957	−0.0330081
$886$	−17.3672	−0.583463
$887$	−35.6756	−1.19787	−0.598934	−	0.800798i	$-0.704409\pi$
$887$	−35.6756	−1.19787	−0.598934	+	0.800798i	$0.704409\pi$
$888$	−18.9480	−0.635855
$889$	80.0440	2.68459
$890$	−18.8491	−0.631823
$891$	−2.25070	−0.0754012
$892$	−7.29138	−0.244134
$893$	−62.6466	−2.09639
$894$	−17.7566	−0.593871
$895$	64.6957	2.16254
$896$	26.1887	0.874902
$897$	0	0
$898$	−31.1090	−1.03812
$899$	−2.68051	−0.0894002
$900$	1.88072	0.0626908
$901$	−27.7754	−0.925331
$902$	−2.88768	−0.0961491
$903$	12.2434	0.407435
$904$	3.85137	0.128095
$905$	1.58229	0.0525970
$906$	27.0872	0.899911
$907$	−35.5540	−1.18055	−0.590276	−	0.807201i	$-0.700981\pi$
$907$	−35.5540	−1.18055	−0.590276	+	0.807201i	$0.700981\pi$
$908$	−12.3298	−0.409178
$909$	−18.8966	−0.626760
$910$	89.8030	2.97694
$911$	−6.64958	−0.220310	−0.110155	−	0.993914i	$-0.535135\pi$
$911$	−6.64958	−0.220310	−0.110155	+	0.993914i	$0.535135\pi$
$912$	21.2325	0.703078
$913$	5.10176	0.168843
$914$	2.76291	0.0913888
$915$	−15.2889	−0.505434
$916$	−7.79333	−0.257499
$917$	−47.1999	−1.55868
$918$	−18.1407	−0.598731
$919$	−17.7463	−0.585397	−0.292698	−	0.956205i	$-0.594553\pi$
$919$	−17.7463	−0.585397	−0.292698	+	0.956205i	$0.594553\pi$
$920$	0	0
$921$	−16.2628	−0.535876
$922$	−16.1196	−0.530870
$923$	−39.2341	−1.29141
$924$	2.95521	0.0972194
$925$	−12.7412	−0.418929
$926$	−43.5912	−1.43250
$927$	−15.5923	−0.512120
$928$	1.37985	0.0452957
$929$	5.07120	0.166381	0.0831904	−	0.996534i	$-0.473489\pi$
$929$	5.07120	0.166381	0.0831904	+	0.996534i	$0.473489\pi$
$930$	−21.9312	−0.719152
$931$	−103.945	−3.40667
$932$	−9.57842	−0.313751
$933$	6.45149	0.211212
$934$	−12.4172	−0.406304
$935$	−7.36383	−0.240823
$936$	−25.2816	−0.826353
$937$	−39.7236	−1.29771	−0.648857	−	0.760910i	$-0.724753\pi$
$937$	−39.7236	−1.29771	−0.648857	+	0.760910i	$0.724753\pi$
$938$	−1.31407	−0.0429058
$939$	−32.0503	−1.04592
$940$	−13.5940	−0.443386
$941$	−21.3636	−0.696433	−0.348217	−	0.937414i	$-0.613213\pi$
$941$	−21.3636	−0.696433	−0.348217	+	0.937414i	$0.613213\pi$
$942$	10.7095	0.348934
$943$	0	0
$944$	0.806263	0.0262416
$945$	73.3306	2.38544
$946$	2.52577	0.0821199
$947$	−0.336647	−0.0109396	−0.00546978	−	0.999985i	$-0.501741\pi$
$947$	−0.336647	−0.0109396	−0.00546978	+	0.999985i	$0.501741\pi$
$948$	−4.49209	−0.145896
$949$	20.7363	0.673130
$950$	19.4265	0.630279
$951$	−0.968273	−0.0313984
$952$	39.8788	1.29248
$953$	−17.2068	−0.557383	−0.278691	−	0.960381i	$-0.589901\pi$
$953$	−17.2068	−0.557383	−0.278691	+	0.960381i	$0.589901\pi$
$954$	19.0191	0.615766
$955$	43.1637	1.39674
$956$	−1.77575	−0.0574320
$957$	−0.616392	−0.0199251
$958$	22.7506	0.735039
$959$	−29.4392	−0.950640
$960$	29.8175	0.962357
$961$	−2.63081	−0.0848648
$962$	34.1085	1.09970
$963$	−4.19573	−0.135205
$964$	−14.0455	−0.452375
$965$	42.0086	1.35230
$966$	0	0
$967$	−42.3647	−1.36236	−0.681179	−	0.732117i	$-0.738532\pi$
$967$	−42.3647	−1.36236	−0.681179	+	0.732117i	$0.738532\pi$
$968$	3.06131	0.0983944
$969$	20.6713	0.664057
$970$	−13.1007	−0.420637
$971$	−46.9548	−1.50685	−0.753426	−	0.657533i	$-0.771600\pi$
$971$	−46.9548	−1.50685	−0.753426	+	0.657533i	$0.771600\pi$
$972$	−6.85211	−0.219782
$973$	80.3081	2.57456
$974$	22.7749	0.729755
$975$	17.0027	0.544522
$976$	12.5533	0.401823
$977$	−8.46398	−0.270787	−0.135393	−	0.990792i	$-0.543230\pi$
$977$	−8.46398	−0.270787	−0.135393	+	0.990792i	$0.543230\pi$
$978$	10.9030	0.348639
$979$	5.60679	0.179194
$980$	−22.5556	−0.720512
$981$	12.8961	0.411742
$982$	9.42481	0.300758
$983$	37.3488	1.19124	0.595622	−	0.803265i	$-0.296906\pi$
$983$	37.3488	1.19124	0.595622	+	0.803265i	$0.296906\pi$
$984$	8.83259	0.281573
$985$	31.0638	0.989774
$986$	−1.65647	−0.0527528
$987$	−59.2229	−1.88508
$988$	17.2121	0.547591
$989$	0	0
$990$	5.04236	0.160257
$991$	52.7757	1.67648	0.838238	−	0.545305i	$-0.183586\pi$
$991$	52.7757	1.67648	0.838238	+	0.545305i	$0.183586\pi$
$992$	−14.6036	−0.463665
$993$	22.8423	0.724880
$994$	−42.3773	−1.34413
$995$	−62.5813	−1.98396
$996$	−3.10765	−0.0984696
$997$	−0.605331	−0.0191710	−0.00958551	−	0.999954i	$-0.503051\pi$
$997$	−0.605331	−0.0191710	−0.00958551	+	0.999954i	$0.503051\pi$
$998$	22.2492	0.704285
$999$	27.8521	0.881201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.u.1.19		60
23.2	even	11		253.2.i.b.188.4	yes	120
23.12	even	11		253.2.i.b.144.4	✓	120
23.22	odd	2		5819.2.a.t.1.19		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.144.4	✓	120	23.12	even	11
253.2.i.b.188.4	yes	120	23.2	even	11
5819.2.a.t.1.19		60	23.22	odd	2
5819.2.a.u.1.19		60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q-1.22583 q^{2} +1.22479 q^{3} -0.497336 q^{4} +2.74249 q^{5} -1.50139 q^{6} -4.85150 q^{7} +3.06131 q^{8} -1.49988 q^{9} -3.36183 q^{10} +1.00000 q^{11} -0.609133 q^{12} +5.50603 q^{13} +5.94713 q^{14} +3.35898 q^{15} -2.75798 q^{16} -2.68509 q^{17} +1.83861 q^{18} -6.28560 q^{19} -1.36394 q^{20} -5.94208 q^{21} -1.22583 q^{22} +3.74947 q^{24} +2.52126 q^{25} -6.74946 q^{26} -5.51142 q^{27} +2.41283 q^{28} -0.503263 q^{29} -4.11755 q^{30} +5.32627 q^{31} -2.74180 q^{32} +1.22479 q^{33} +3.29146 q^{34} -13.3052 q^{35} +0.745946 q^{36} -5.05352 q^{37} +7.70508 q^{38} +6.74374 q^{39} +8.39563 q^{40} +2.35569 q^{41} +7.28400 q^{42} -2.06045 q^{43} -0.497336 q^{44} -4.11342 q^{45} +9.96669 q^{47} -3.37796 q^{48} +16.5371 q^{49} -3.09064 q^{50} -3.28867 q^{51} -2.73835 q^{52} +10.3443 q^{53} +6.75608 q^{54} +2.74249 q^{55} -14.8520 q^{56} -7.69855 q^{57} +0.616915 q^{58} -0.292338 q^{59} -1.67054 q^{60} -4.55164 q^{61} -6.52912 q^{62} +7.27669 q^{63} +8.87696 q^{64} +15.1002 q^{65} -1.50139 q^{66} -0.220958 q^{67} +1.33539 q^{68} +16.3099 q^{70} -7.12567 q^{71} -4.59162 q^{72} +3.76611 q^{73} +6.19477 q^{74} +3.08802 q^{75} +3.12605 q^{76} -4.85150 q^{77} -8.26669 q^{78} +7.37456 q^{79} -7.56375 q^{80} -2.25070 q^{81} -2.88768 q^{82} +5.10176 q^{83} +2.95521 q^{84} -7.36383 q^{85} +2.52577 q^{86} -0.616392 q^{87} +3.06131 q^{88} +5.60679 q^{89} +5.04236 q^{90} -26.7125 q^{91} +6.52358 q^{93} -12.2175 q^{94} -17.2382 q^{95} -3.35814 q^{96} +3.89688 q^{97} -20.2717 q^{98} -1.49988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) \) 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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