LMFDB - Embedded newform 7865.2.a.u.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7865,2,Mod(1,7865)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7865, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("7865.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 7865 = 5 \cdot 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7865.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,1,-5,7,-8,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$62.8023411897$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 9x^{5} + 34x^{4} - 13x^{3} - 35x^{2} - 3x + 5 $ x^8 - x^7 - 11x^6 + 9x^5 + 34x^4 - 13x^3 - 35x^2 - 3x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.28679$ of defining polynomial
Character	$\chi$	$=$	7865.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.28679 q^{2} -0.0897034 q^{3} +3.22941 q^{4} -1.00000 q^{5} -0.205133 q^{6} -4.22248 q^{7} +2.81139 q^{8} -2.99195 q^{9} -2.28679 q^{10} -0.289689 q^{12} -1.00000 q^{13} -9.65593 q^{14} +0.0897034 q^{15} -0.0297495 q^{16} -0.295990 q^{17} -6.84197 q^{18} +5.10234 q^{19} -3.22941 q^{20} +0.378771 q^{21} +4.20345 q^{23} -0.252191 q^{24} +1.00000 q^{25} -2.28679 q^{26} +0.537498 q^{27} -13.6361 q^{28} +1.22057 q^{29} +0.205133 q^{30} -4.30728 q^{31} -5.69082 q^{32} -0.676868 q^{34} +4.22248 q^{35} -9.66223 q^{36} +0.0195553 q^{37} +11.6680 q^{38} +0.0897034 q^{39} -2.81139 q^{40} +4.83445 q^{41} +0.866170 q^{42} +2.39529 q^{43} +2.99195 q^{45} +9.61240 q^{46} +11.8632 q^{47} +0.00266863 q^{48} +10.8294 q^{49} +2.28679 q^{50} +0.0265513 q^{51} -3.22941 q^{52} +0.166482 q^{53} +1.22915 q^{54} -11.8711 q^{56} -0.457697 q^{57} +2.79118 q^{58} +5.42688 q^{59} +0.289689 q^{60} +3.36902 q^{61} -9.84984 q^{62} +12.6335 q^{63} -12.9542 q^{64} +1.00000 q^{65} -0.529973 q^{67} -0.955873 q^{68} -0.377064 q^{69} +9.65593 q^{70} +0.0282052 q^{71} -8.41155 q^{72} +16.3670 q^{73} +0.0447189 q^{74} -0.0897034 q^{75} +16.4775 q^{76} +0.205133 q^{78} +2.93331 q^{79} +0.0297495 q^{80} +8.92764 q^{81} +11.0554 q^{82} -15.4009 q^{83} +1.22321 q^{84} +0.295990 q^{85} +5.47751 q^{86} -0.109489 q^{87} -1.98790 q^{89} +6.84197 q^{90} +4.22248 q^{91} +13.5746 q^{92} +0.386378 q^{93} +27.1286 q^{94} -5.10234 q^{95} +0.510485 q^{96} -2.76500 q^{97} +24.7645 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 5 q^{3} + 7 q^{4} - 8 q^{5} - 7 q^{6} + 9 q^{7} + 3 q^{8} + 3 q^{9} - q^{10} - 15 q^{12} - 8 q^{13} - 7 q^{14} + 5 q^{15} + 9 q^{16} + 4 q^{17} + 8 q^{18} + 16 q^{19} - 7 q^{20} - 23 q^{21}+ \cdots + 41 q^{98}+O(q^{100}) $ 8 * q + q^2 - 5 * q^3 + 7 * q^4 - 8 * q^5 - 7 * q^6 + 9 * q^7 + 3 * q^8 + 3 * q^9 - q^10 - 15 * q^12 - 8 * q^13 - 7 * q^14 + 5 * q^15 + 9 * q^16 + 4 * q^17 + 8 * q^18 + 16 * q^19 - 7 * q^20 - 23 * q^21 - 9 * q^23 + 5 * q^24 + 8 * q^25 - q^26 - 11 * q^27 + 11 * q^28 - 13 * q^29 + 7 * q^30 - 28 * q^32 + 13 * q^34 - 9 * q^35 + 12 * q^36 - 5 * q^37 + 55 * q^38 + 5 * q^39 - 3 * q^40 + 13 * q^41 - 5 * q^42 + 5 * q^43 - 3 * q^45 + 27 * q^46 + 10 * q^47 - 36 * q^48 + 23 * q^49 + q^50 - 37 * q^51 - 7 * q^52 + 14 * q^53 - 45 * q^54 - 18 * q^56 - 21 * q^57 + 3 * q^58 - 20 * q^59 + 15 * q^60 + 6 * q^61 + 25 * q^62 + 26 * q^63 - 3 * q^64 + 8 * q^65 + 4 * q^67 - 9 * q^69 + 7 * q^70 - 9 * q^71 + 35 * q^72 + 10 * q^73 + 42 * q^74 - 5 * q^75 + 19 * q^76 + 7 * q^78 + 13 * q^79 - 9 * q^80 + 16 * q^82 + 26 * q^83 - 58 * q^84 - 4 * q^85 + 26 * q^86 + 11 * q^87 - 6 * q^89 - 8 * q^90 - 9 * q^91 - 16 * q^92 + 3 * q^93 + 23 * q^94 - 16 * q^95 + 21 * q^96 + 26 * q^97 + 41 * q^98

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 $

$2$	2.28679	1.61700	0.808502	−	0.588493i	$-0.200279\pi$
$2$	2.28679	1.61700	0.808502	+	0.588493i	$0.200279\pi$
$3$	−0.0897034	−0.0517903	−0.0258951	−	0.999665i	$-0.508244\pi$
$3$	−0.0897034	−0.0517903	−0.0258951	+	0.999665i	$0.508244\pi$
$4$	3.22941	1.61470
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.205133	−0.0837451
$7$	−4.22248	−1.59595	−0.797974	−	0.602691i	$-0.794095\pi$
$7$	−4.22248	−1.59595	−0.797974	+	0.602691i	$0.794095\pi$
$8$	2.81139	0.993977
$9$	−2.99195	−0.997318
$10$	−2.28679	−0.723146
$11$	0	0
$11$	0	0
$12$	−0.289689	−0.0836259
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−9.65593	−2.58066
$15$	0.0897034	0.0231613
$16$	−0.0297495	−0.00743737
$17$	−0.295990	−0.0717882	−0.0358941	−	0.999356i	$-0.511428\pi$
$17$	−0.295990	−0.0717882	−0.0358941	+	0.999356i	$0.511428\pi$
$18$	−6.84197	−1.61267
$19$	5.10234	1.17056	0.585278	−	0.810833i	$-0.300985\pi$
$19$	5.10234	1.17056	0.585278	+	0.810833i	$0.300985\pi$
$20$	−3.22941	−0.722117
$21$	0.378771	0.0826546
$22$	0	0
$23$	4.20345	0.876480	0.438240	−	0.898858i	$-0.355602\pi$
$23$	4.20345	0.876480	0.438240	+	0.898858i	$0.355602\pi$
$24$	−0.252191	−0.0514784
$25$	1.00000	0.200000
$26$	−2.28679	−0.448476
$27$	0.537498	0.103442
$28$	−13.6361	−2.57698
$29$	1.22057	0.226653	0.113327	−	0.993558i	$-0.463849\pi$
$29$	1.22057	0.226653	0.113327	+	0.993558i	$0.463849\pi$
$30$	0.205133	0.0374519
$31$	−4.30728	−0.773610	−0.386805	−	0.922161i	$-0.626421\pi$
$31$	−4.30728	−0.773610	−0.386805	+	0.922161i	$0.626421\pi$
$32$	−5.69082	−1.00600
$33$	0	0
$34$	−0.676868	−0.116082
$35$	4.22248	0.713730
$36$	−9.66223	−1.61037
$37$	0.0195553	0.00321487	0.00160744	−	0.999999i	$-0.499488\pi$
$37$	0.0195553	0.00321487	0.00160744	+	0.999999i	$0.499488\pi$
$38$	11.6680	1.89279
$39$	0.0897034	0.0143640
$40$	−2.81139	−0.444520
$41$	4.83445	0.755014	0.377507	−	0.926007i	$-0.376781\pi$
$41$	4.83445	0.755014	0.377507	+	0.926007i	$0.376781\pi$
$42$	0.866170	0.133653
$43$	2.39529	0.365278	0.182639	−	0.983180i	$-0.441536\pi$
$43$	2.39529	0.365278	0.182639	+	0.983180i	$0.441536\pi$
$44$	0	0
$45$	2.99195	0.446014
$46$	9.61240	1.41727
$47$	11.8632	1.73042	0.865211	−	0.501408i	$-0.167184\pi$
$47$	11.8632	1.73042	0.865211	+	0.501408i	$0.167184\pi$
$48$	0.00266863	0.000385183 0
$49$	10.8294	1.54705
$50$	2.28679	0.323401
$51$	0.0265513	0.00371793
$52$	−3.22941	−0.447838
$53$	0.166482	0.0228681	0.0114340	−	0.999935i	$-0.496360\pi$
$53$	0.166482	0.0228681	0.0114340	+	0.999935i	$0.496360\pi$
$54$	1.22915	0.167266
$55$	0	0
$56$	−11.8711	−1.58634
$57$	−0.457697	−0.0606234
$58$	2.79118	0.366500
$59$	5.42688	0.706520	0.353260	−	0.935525i	$-0.385073\pi$
$59$	5.42688	0.706520	0.353260	+	0.935525i	$0.385073\pi$
$60$	0.289689	0.0373986
$61$	3.36902	0.431358	0.215679	−	0.976464i	$-0.430803\pi$
$61$	3.36902	0.431358	0.215679	+	0.976464i	$0.430803\pi$
$62$	−9.84984	−1.25093
$63$	12.6335	1.59167
$64$	−12.9542	−1.61927
$65$	1.00000	0.124035
$66$	0	0
$67$	−0.529973	−0.0647465	−0.0323732	−	0.999476i	$-0.510307\pi$
$67$	−0.529973	−0.0647465	−0.0323732	+	0.999476i	$0.510307\pi$
$68$	−0.955873	−0.115917
$69$	−0.377064	−0.0453931
$70$	9.65593	1.15410
$71$	0.0282052	0.00334734	0.00167367	−	0.999999i	$-0.499467\pi$
$71$	0.0282052	0.00334734	0.00167367	+	0.999999i	$0.499467\pi$
$72$	−8.41155	−0.991311
$73$	16.3670	1.91561	0.957805	−	0.287420i	$-0.0927975\pi$
$73$	16.3670	1.91561	0.957805	+	0.287420i	$0.0927975\pi$
$74$	0.0447189	0.00519846
$75$	−0.0897034	−0.0103581
$76$	16.4775	1.89010
$77$	0	0
$78$	0.205133	0.0232267
$79$	2.93331	0.330024	0.165012	−	0.986292i	$-0.447234\pi$
$79$	2.93331	0.330024	0.165012	+	0.986292i	$0.447234\pi$
$80$	0.0297495	0.00332609
$81$	8.92764	0.991960
$82$	11.0554	1.22086
$83$	−15.4009	−1.69047	−0.845233	−	0.534398i	$-0.820538\pi$
$83$	−15.4009	−1.69047	−0.845233	+	0.534398i	$0.820538\pi$
$84$	1.22321	0.133463
$85$	0.295990	0.0321047
$86$	5.47751	0.590655
$87$	−0.109489	−0.0117384
$88$	0	0
$89$	−1.98790	−0.210717	−0.105358	−	0.994434i	$-0.533599\pi$
$89$	−1.98790	−0.210717	−0.105358	+	0.994434i	$0.533599\pi$
$90$	6.84197	0.721207
$91$	4.22248	0.442637
$92$	13.5746	1.41525
$93$	0.386378	0.0400655
$94$	27.1286	2.79810
$95$	−5.10234	−0.523489
$96$	0.510485	0.0521012
$97$	−2.76500	−0.280743	−0.140371	−	0.990099i	$-0.544830\pi$
$97$	−2.76500	−0.280743	−0.140371	+	0.990099i	$0.544830\pi$
$98$	24.7645	2.50159
$99$	0	0
$100$	3.22941	0.322941
$101$	−15.7480	−1.56698	−0.783491	−	0.621403i	$-0.786563\pi$
$101$	−15.7480	−1.56698	−0.783491	+	0.621403i	$0.786563\pi$
$102$	0.0607173	0.00601191
$103$	−7.53429	−0.742375	−0.371188	−	0.928558i	$-0.621049\pi$
$103$	−7.53429	−0.742375	−0.371188	+	0.928558i	$0.621049\pi$
$104$	−2.81139	−0.275680
$105$	−0.378771	−0.0369643
$106$	0.380709	0.0369778
$107$	16.9667	1.64023	0.820116	−	0.572197i	$-0.193909\pi$
$107$	16.9667	1.64023	0.820116	+	0.572197i	$0.193909\pi$
$108$	1.73580	0.167027
$109$	7.01141	0.671571	0.335786	−	0.941938i	$-0.390998\pi$
$109$	7.01141	0.671571	0.335786	+	0.941938i	$0.390998\pi$
$110$	0	0
$111$	−0.00175418	−0.000166499 0
$112$	0.125617	0.0118697
$113$	8.10174	0.762148	0.381074	−	0.924545i	$-0.375554\pi$
$113$	8.10174	0.762148	0.381074	+	0.924545i	$0.375554\pi$
$114$	−1.04666	−0.0980283
$115$	−4.20345	−0.391974
$116$	3.94170	0.365978
$117$	2.99195	0.276606
$118$	12.4101	1.14245
$119$	1.24981	0.114570
$120$	0.252191	0.0230218
$121$	0	0
$122$	7.70423	0.697508
$123$	−0.433667	−0.0391024
$124$	−13.9100	−1.24915
$125$	−1.00000	−0.0894427
$126$	28.8901	2.57373
$127$	18.5341	1.64463	0.822316	−	0.569031i	$-0.192681\pi$
$127$	18.5341	1.64463	0.822316	+	0.569031i	$0.192681\pi$
$128$	−18.2419	−1.61237
$129$	−0.214865	−0.0189178
$130$	2.28679	0.200565
$131$	−3.31782	−0.289880	−0.144940	−	0.989440i	$-0.546299\pi$
$131$	−3.31782	−0.289880	−0.144940	+	0.989440i	$0.546299\pi$
$132$	0	0
$133$	−21.5445	−1.86815
$134$	−1.21194	−0.104695
$135$	−0.537498	−0.0462605
$136$	−0.832145	−0.0713558
$137$	−4.22271	−0.360771	−0.180385	−	0.983596i	$-0.557734\pi$
$137$	−4.22271	−0.360771	−0.180385	+	0.983596i	$0.557734\pi$
$138$	−0.862265	−0.0734009
$139$	−2.33468	−0.198025	−0.0990126	−	0.995086i	$-0.531568\pi$
$139$	−2.33468	−0.198025	−0.0990126	+	0.995086i	$0.531568\pi$
$140$	13.6361	1.15246
$141$	−1.06417	−0.0896190
$142$	0.0644993	0.00541266
$143$	0	0
$144$	0.0890091	0.00741742
$145$	−1.22057	−0.101362
$146$	37.4278	3.09755
$147$	−0.971431	−0.0801222
$148$	0.0631520	0.00519107
$149$	21.2329	1.73947	0.869733	−	0.493523i	$-0.164291\pi$
$149$	21.2329	1.73947	0.869733	+	0.493523i	$0.164291\pi$
$150$	−0.205133	−0.0167490
$151$	5.78477	0.470758	0.235379	−	0.971904i	$-0.424367\pi$
$151$	5.78477	0.470758	0.235379	+	0.971904i	$0.424367\pi$
$152$	14.3447	1.16351
$153$	0.885589	0.0715956
$154$	0	0
$155$	4.30728	0.345969
$156$	0.289689	0.0231937
$157$	5.41751	0.432364	0.216182	−	0.976353i	$-0.430639\pi$
$157$	5.41751	0.432364	0.216182	+	0.976353i	$0.430639\pi$
$158$	6.70787	0.533650
$159$	−0.0149340	−0.00118434
$160$	5.69082	0.449898
$161$	−17.7490	−1.39882
$162$	20.4156	1.60400
$163$	−17.1618	−1.34422	−0.672108	−	0.740453i	$-0.734611\pi$
$163$	−17.1618	−1.34422	−0.672108	+	0.740453i	$0.734611\pi$
$164$	15.6124	1.21912
$165$	0	0
$166$	−35.2186	−2.73349
$167$	−1.15418	−0.0893131	−0.0446565	−	0.999002i	$-0.514219\pi$
$167$	−1.15418	−0.0893131	−0.0446565	+	0.999002i	$0.514219\pi$
$168$	1.06487	0.0821568
$169$	1.00000	0.0769231
$170$	0.676868	0.0519134
$171$	−15.2660	−1.16742
$172$	7.73535	0.589815
$173$	−3.47738	−0.264380	−0.132190	−	0.991224i	$-0.542201\pi$
$173$	−3.47738	−0.264380	−0.132190	+	0.991224i	$0.542201\pi$
$174$	−0.250378	−0.0189811
$175$	−4.22248	−0.319190
$176$	0	0
$177$	−0.486810	−0.0365909
$178$	−4.54590	−0.340730
$179$	−15.9242	−1.19023	−0.595115	−	0.803641i	$-0.702893\pi$
$179$	−15.9242	−1.19023	−0.595115	+	0.803641i	$0.702893\pi$
$180$	9.66223	0.720180
$181$	1.26334	0.0939031	0.0469516	−	0.998897i	$-0.485049\pi$
$181$	1.26334	0.0939031	0.0469516	+	0.998897i	$0.485049\pi$
$182$	9.65593	0.715745
$183$	−0.302212	−0.0223402
$184$	11.8175	0.871201
$185$	−0.0195553	−0.00143774
$186$	0.883564	0.0647861
$187$	0	0
$188$	38.3110	2.79412
$189$	−2.26958	−0.165088
$190$	−11.6680	−0.846483
$191$	−1.14665	−0.0829689	−0.0414845	−	0.999139i	$-0.513209\pi$
$191$	−1.14665	−0.0829689	−0.0414845	+	0.999139i	$0.513209\pi$
$192$	1.16204	0.0838627
$193$	−11.7564	−0.846244	−0.423122	−	0.906073i	$-0.639066\pi$
$193$	−11.7564	−0.846244	−0.423122	+	0.906073i	$0.639066\pi$
$194$	−6.32296	−0.453962
$195$	−0.0897034	−0.00642379
$196$	34.9724	2.49803
$197$	17.3115	1.23339	0.616696	−	0.787201i	$-0.288471\pi$
$197$	17.3115	1.23339	0.616696	+	0.787201i	$0.288471\pi$
$198$	0	0
$199$	3.30924	0.234586	0.117293	−	0.993097i	$-0.462578\pi$
$199$	3.30924	0.234586	0.117293	+	0.993097i	$0.462578\pi$
$200$	2.81139	0.198795
$201$	0.0475403	0.00335324
$202$	−36.0123	−2.53382
$203$	−5.15382	−0.361727
$204$	0.0857450	0.00600335
$205$	−4.83445	−0.337653
$206$	−17.2293	−1.20042
$207$	−12.5765	−0.874129
$208$	0.0297495	0.00206276
$209$	0	0
$210$	−0.866170	−0.0597714
$211$	−20.5128	−1.41216	−0.706081	−	0.708131i	$-0.749539\pi$
$211$	−20.5128	−1.41216	−0.706081	+	0.708131i	$0.749539\pi$
$212$	0.537638	0.0369251
$213$	−0.00253010	−0.000173360 0
$214$	38.7993	2.65226
$215$	−2.39529	−0.163357
$216$	1.51112	0.102819
$217$	18.1874	1.23464
$218$	16.0336	1.08593
$219$	−1.46817	−0.0992099
$220$	0	0
$221$	0.295990	0.0199105
$222$	−0.00401144	−0.000269230 0
$223$	22.0748	1.47824	0.739119	−	0.673575i	$-0.235242\pi$
$223$	22.0748	1.47824	0.739119	+	0.673575i	$0.235242\pi$
$224$	24.0294	1.60553
$225$	−2.99195	−0.199464
$226$	18.5270	1.23240
$227$	−7.20806	−0.478416	−0.239208	−	0.970968i	$-0.576888\pi$
$227$	−7.20806	−0.478416	−0.239208	+	0.970968i	$0.576888\pi$
$228$	−1.47809	−0.0978888
$229$	−14.7498	−0.974694	−0.487347	−	0.873208i	$-0.662035\pi$
$229$	−14.7498	−0.974694	−0.487347	+	0.873208i	$0.662035\pi$
$230$	−9.61240	−0.633823
$231$	0	0
$232$	3.43149	0.225288
$233$	28.2147	1.84841	0.924204	−	0.381899i	$-0.124730\pi$
$233$	28.2147	1.84841	0.924204	+	0.381899i	$0.124730\pi$
$234$	6.84197	0.447273
$235$	−11.8632	−0.773868
$236$	17.5256	1.14082
$237$	−0.263128	−0.0170920
$238$	2.85806	0.185261
$239$	−11.8785	−0.768358	−0.384179	−	0.923259i	$-0.625515\pi$
$239$	−11.8785	−0.768358	−0.384179	+	0.923259i	$0.625515\pi$
$240$	−0.00266863	−0.000172259 0
$241$	14.8316	0.955386	0.477693	−	0.878527i	$-0.341473\pi$
$241$	14.8316	0.955386	0.477693	+	0.878527i	$0.341473\pi$
$242$	0	0
$243$	−2.41334	−0.154816
$244$	10.8799	0.696516
$245$	−10.8294	−0.691863
$246$	−0.991704	−0.0632287
$247$	−5.10234	−0.324654
$248$	−12.1095	−0.768951
$249$	1.38151	0.0875497
$250$	−2.28679	−0.144629
$251$	26.2337	1.65586	0.827929	−	0.560833i	$-0.189519\pi$
$251$	26.2337	1.65586	0.827929	+	0.560833i	$0.189519\pi$
$252$	40.7986	2.57007
$253$	0	0
$254$	42.3835	2.65938
$255$	−0.0265513	−0.00166271
$256$	−15.8070	−0.987936
$257$	19.2004	1.19769	0.598845	−	0.800865i	$-0.295627\pi$
$257$	19.2004	1.19769	0.598845	+	0.800865i	$0.295627\pi$
$258$	−0.491351	−0.0305902
$259$	−0.0825720	−0.00513077
$260$	3.22941	0.200279
$261$	−3.65188	−0.226045
$262$	−7.58717	−0.468737
$263$	23.7117	1.46213	0.731064	−	0.682309i	$-0.239024\pi$
$263$	23.7117	1.46213	0.731064	+	0.682309i	$0.239024\pi$
$264$	0	0
$265$	−0.166482	−0.0102269
$266$	−49.2678	−3.02080
$267$	0.178321	0.0109131
$268$	−1.71150	−0.104546
$269$	16.3216	0.995146	0.497573	−	0.867422i	$-0.334225\pi$
$269$	16.3216	0.995146	0.497573	+	0.867422i	$0.334225\pi$
$270$	−1.22915	−0.0748034
$271$	16.0782	0.976684	0.488342	−	0.872652i	$-0.337602\pi$
$271$	16.0782	0.976684	0.488342	+	0.872652i	$0.337602\pi$
$272$	0.00880556	0.000533916 0
$273$	−0.378771	−0.0229243
$274$	−9.65646	−0.583368
$275$	0	0
$276$	−1.21769	−0.0732964
$277$	−28.1527	−1.69153	−0.845766	−	0.533554i	$-0.820856\pi$
$277$	−28.1527	−1.69153	−0.845766	+	0.533554i	$0.820856\pi$
$278$	−5.33893	−0.320208
$279$	12.8872	0.771535
$280$	11.8711	0.709431
$281$	23.1804	1.38282	0.691412	−	0.722460i	$-0.256989\pi$
$281$	23.1804	1.38282	0.691412	+	0.722460i	$0.256989\pi$
$282$	−2.43353	−0.144914
$283$	13.2641	0.788466	0.394233	−	0.919011i	$-0.371010\pi$
$283$	13.2641	0.788466	0.394233	+	0.919011i	$0.371010\pi$
$284$	0.0910859	0.00540496
$285$	0.457697	0.0271116
$286$	0	0
$287$	−20.4134	−1.20496
$288$	17.0267	1.00331
$289$	−16.9124	−0.994846
$290$	−2.79118	−0.163904
$291$	0.248030	0.0145397
$292$	52.8556	3.09314
$293$	−7.32272	−0.427798	−0.213899	−	0.976856i	$-0.568616\pi$
$293$	−7.32272	−0.427798	−0.213899	+	0.976856i	$0.568616\pi$
$294$	−2.22146	−0.129558
$295$	−5.42688	−0.315965
$296$	0.0549777	0.00319551
$297$	0	0
$298$	48.5551	2.81272
$299$	−4.20345	−0.243092
$300$	−0.289689	−0.0167252
$301$	−10.1141	−0.582964
$302$	13.2286	0.761218
$303$	1.41265	0.0811544
$304$	−0.151792	−0.00870586
$305$	−3.36902	−0.192909
$306$	2.02516	0.115770
$307$	−30.8971	−1.76339	−0.881696	−	0.471817i	$-0.843598\pi$
$307$	−30.8971	−1.76339	−0.881696	+	0.471817i	$0.843598\pi$
$308$	0	0
$309$	0.675851	0.0384478
$310$	9.84984	0.559434
$311$	−21.7138	−1.23128	−0.615639	−	0.788028i	$-0.711102\pi$
$311$	−21.7138	−1.23128	−0.615639	+	0.788028i	$0.711102\pi$
$312$	0.252191	0.0142775
$313$	−32.6378	−1.84480	−0.922400	−	0.386237i	$-0.873775\pi$
$313$	−32.6378	−1.84480	−0.922400	+	0.386237i	$0.873775\pi$
$314$	12.3887	0.699135
$315$	−12.6335	−0.711816
$316$	9.47286	0.532890
$317$	14.7816	0.830215	0.415108	−	0.909772i	$-0.363744\pi$
$317$	14.7816	0.830215	0.415108	+	0.909772i	$0.363744\pi$
$318$	−0.0341509	−0.00191509
$319$	0	0
$320$	12.9542	0.724162
$321$	−1.52197	−0.0849481
$322$	−40.5882	−2.26189
$323$	−1.51024	−0.0840321
$324$	28.8310	1.60172
$325$	−1.00000	−0.0554700
$326$	−39.2454	−2.17360
$327$	−0.628947	−0.0347809
$328$	13.5915	0.750467
$329$	−50.0921	−2.76167
$330$	0	0
$331$	21.0299	1.15591	0.577954	−	0.816069i	$-0.303851\pi$
$331$	21.0299	1.15591	0.577954	+	0.816069i	$0.303851\pi$
$332$	−49.7357	−2.72960
$333$	−0.0585086	−0.00320625
$334$	−2.63936	−0.144420
$335$	0.529973	0.0289555
$336$	−0.0112682	−0.000614733 0
$337$	−7.00217	−0.381432	−0.190716	−	0.981645i	$-0.561081\pi$
$337$	−7.00217	−0.381432	−0.190716	+	0.981645i	$0.561081\pi$
$338$	2.28679	0.124385
$339$	−0.726754	−0.0394718
$340$	0.955873	0.0518395
$341$	0	0
$342$	−34.9100	−1.88772
$343$	−16.1694	−0.873067
$344$	6.73409	0.363078
$345$	0.377064	0.0203004
$346$	−7.95204	−0.427504
$347$	16.1037	0.864493	0.432246	−	0.901755i	$-0.357721\pi$
$347$	16.1037	0.864493	0.432246	+	0.901755i	$0.357721\pi$
$348$	−0.353584	−0.0189541
$349$	7.02005	0.375775	0.187887	−	0.982191i	$-0.439836\pi$
$349$	7.02005	0.375775	0.187887	+	0.982191i	$0.439836\pi$
$350$	−9.65593	−0.516131
$351$	−0.537498	−0.0286895
$352$	0	0
$353$	−7.72739	−0.411288	−0.205644	−	0.978627i	$-0.565929\pi$
$353$	−7.72739	−0.411288	−0.205644	+	0.978627i	$0.565929\pi$
$354$	−1.11323	−0.0591676
$355$	−0.0282052	−0.00149697
$356$	−6.41973	−0.340245
$357$	−0.112113	−0.00593363
$358$	−36.4153	−1.92461
$359$	−1.15902	−0.0611707	−0.0305854	−	0.999532i	$-0.509737\pi$
$359$	−1.15902	−0.0611707	−0.0305854	+	0.999532i	$0.509737\pi$
$360$	8.41155	0.443328
$361$	7.03383	0.370202
$362$	2.88899	0.151842
$363$	0	0
$364$	13.6361	0.714726
$365$	−16.3670	−0.856687
$366$	−0.691096	−0.0361241
$367$	32.8746	1.71604	0.858020	−	0.513616i	$-0.171694\pi$
$367$	32.8746	1.71604	0.858020	+	0.513616i	$0.171694\pi$
$368$	−0.125050	−0.00651871
$369$	−14.4644	−0.752989
$370$	−0.0447189	−0.00232482
$371$	−0.702968	−0.0364963
$372$	1.24777	0.0646939
$373$	4.17716	0.216285	0.108143	−	0.994135i	$-0.465510\pi$
$373$	4.17716	0.216285	0.108143	+	0.994135i	$0.465510\pi$
$374$	0	0
$375$	0.0897034	0.00463226
$376$	33.3520	1.72000
$377$	−1.22057	−0.0628623
$378$	−5.19005	−0.266947
$379$	−16.2306	−0.833709	−0.416854	−	0.908973i	$-0.636868\pi$
$379$	−16.2306	−0.833709	−0.416854	+	0.908973i	$0.636868\pi$
$380$	−16.4775	−0.845279
$381$	−1.66257	−0.0851760
$382$	−2.62215	−0.134161
$383$	32.3638	1.65371	0.826856	−	0.562414i	$-0.190127\pi$
$383$	32.3638	1.65371	0.826856	+	0.562414i	$0.190127\pi$
$384$	1.63636	0.0835051
$385$	0	0
$386$	−26.8844	−1.36838
$387$	−7.16658	−0.364298
$388$	−8.92930	−0.453316
$389$	−26.7941	−1.35852	−0.679258	−	0.733900i	$-0.737698\pi$
$389$	−26.7941	−1.35852	−0.679258	+	0.733900i	$0.737698\pi$
$390$	−0.205133	−0.0103873
$391$	−1.24418	−0.0629209
$392$	30.4456	1.53773
$393$	0.297620	0.0150129
$394$	39.5877	1.99440
$395$	−2.93331	−0.147591
$396$	0	0
$397$	4.70925	0.236350	0.118175	−	0.992993i	$-0.462296\pi$
$397$	4.70925	0.236350	0.118175	+	0.992993i	$0.462296\pi$
$398$	7.56753	0.379326
$399$	1.93262	0.0967519
$400$	−0.0297495	−0.00148747
$401$	−24.2196	−1.20947	−0.604735	−	0.796427i	$-0.706721\pi$
$401$	−24.2196	−1.20947	−0.604735	+	0.796427i	$0.706721\pi$
$402$	0.108715	0.00542220
$403$	4.30728	0.214561
$404$	−50.8566	−2.53021
$405$	−8.92764	−0.443618
$406$	−11.7857	−0.584914
$407$	0	0
$408$	0.0746462	0.00369554
$409$	−9.43737	−0.466648	−0.233324	−	0.972399i	$-0.574960\pi$
$409$	−9.43737	−0.466648	−0.233324	+	0.972399i	$0.574960\pi$
$410$	−11.0554	−0.545986
$411$	0.378792	0.0186844
$412$	−24.3313	−1.19872
$413$	−22.9149	−1.12757
$414$	−28.7599	−1.41347
$415$	15.4009	0.755999
$416$	5.69082	0.279015
$417$	0.209429	0.0102558
$418$	0	0
$419$	3.38273	0.165257	0.0826285	−	0.996580i	$-0.473668\pi$
$419$	3.38273	0.165257	0.0826285	+	0.996580i	$0.473668\pi$
$420$	−1.22321	−0.0596863
$421$	22.8421	1.11325	0.556627	−	0.830763i	$-0.312095\pi$
$421$	22.8421	1.11325	0.556627	+	0.830763i	$0.312095\pi$
$422$	−46.9086	−2.28347
$423$	−35.4941	−1.72578
$424$	0.468046	0.0227303
$425$	−0.295990	−0.0143576
$426$	−0.00578580	−0.000280323 0
$427$	−14.2256	−0.688426
$428$	54.7924	2.64849
$429$	0	0
$430$	−5.47751	−0.264149
$431$	−29.3771	−1.41505	−0.707523	−	0.706691i	$-0.750187\pi$
$431$	−29.3771	−1.41505	−0.707523	+	0.706691i	$0.750187\pi$
$432$	−0.0159903	−0.000769334 0
$433$	−27.3342	−1.31360	−0.656799	−	0.754066i	$-0.728090\pi$
$433$	−27.3342	−1.31360	−0.656799	+	0.754066i	$0.728090\pi$
$434$	41.5908	1.99642
$435$	0.109489	0.00524959
$436$	22.6427	1.08439
$437$	21.4474	1.02597
$438$	−3.35740	−0.160423
$439$	3.79116	0.180942	0.0904711	−	0.995899i	$-0.471163\pi$
$439$	3.79116	0.180942	0.0904711	+	0.995899i	$0.471163\pi$
$440$	0	0
$441$	−32.4010	−1.54290
$442$	0.676868	0.0321953
$443$	−23.3795	−1.11079	−0.555396	−	0.831586i	$-0.687433\pi$
$443$	−23.3795	−1.11079	−0.555396	+	0.831586i	$0.687433\pi$
$444$	−0.00566495	−0.000268847 0
$445$	1.98790	0.0942354
$446$	50.4804	2.39032
$447$	−1.90466	−0.0900874
$448$	54.6989	2.58428
$449$	15.2761	0.720922	0.360461	−	0.932774i	$-0.382619\pi$
$449$	15.2761	0.720922	0.360461	+	0.932774i	$0.382619\pi$
$450$	−6.84197	−0.322533
$451$	0	0
$452$	26.1638	1.23064
$453$	−0.518914	−0.0243807
$454$	−16.4833	−0.773601
$455$	−4.22248	−0.197953
$456$	−1.28677	−0.0602583
$457$	10.2756	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$457$	10.2756	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$458$	−33.7297	−1.57608
$459$	−0.159094	−0.00742589
$460$	−13.5746	−0.632921
$461$	38.4198	1.78939	0.894695	−	0.446677i	$-0.147393\pi$
$461$	38.4198	1.78939	0.894695	+	0.446677i	$0.147393\pi$
$462$	0	0
$463$	−17.7835	−0.826471	−0.413236	−	0.910624i	$-0.635601\pi$
$463$	−17.7835	−0.826471	−0.413236	+	0.910624i	$0.635601\pi$
$464$	−0.0363112	−0.00168571
$465$	−0.386378	−0.0179178
$466$	64.5211	2.98888
$467$	−27.5963	−1.27700	−0.638501	−	0.769621i	$-0.720445\pi$
$467$	−27.5963	−1.27700	−0.638501	+	0.769621i	$0.720445\pi$
$468$	9.66223	0.446637
$469$	2.23780	0.103332
$470$	−27.1286	−1.25135
$471$	−0.485969	−0.0223923
$472$	15.2571	0.702265
$473$	0	0
$474$	−0.601719	−0.0276379
$475$	5.10234	0.234111
$476$	4.03616	0.184997
$477$	−0.498106	−0.0228067
$478$	−27.1637	−1.24244
$479$	−31.8303	−1.45436	−0.727181	−	0.686446i	$-0.759170\pi$
$479$	−31.8303	−1.45436	−0.727181	+	0.686446i	$0.759170\pi$
$480$	−0.510485	−0.0233004
$481$	−0.0195553	−0.000891646 0
$482$	33.9167	1.54486
$483$	1.59214	0.0724451
$484$	0	0
$485$	2.76500	0.125552
$486$	−5.51879	−0.250337
$487$	30.4831	1.38132	0.690660	−	0.723179i	$-0.257320\pi$
$487$	30.4831	1.38132	0.690660	+	0.723179i	$0.257320\pi$
$488$	9.47163	0.428760
$489$	1.53947	0.0696173
$490$	−24.7645	−1.11874
$491$	−25.5315	−1.15222	−0.576110	−	0.817372i	$-0.695430\pi$
$491$	−25.5315	−1.15222	−0.576110	+	0.817372i	$0.695430\pi$
$492$	−1.40049	−0.0631387
$493$	−0.361276	−0.0162710
$494$	−11.6680	−0.524967
$495$	0	0
$496$	0.128139	0.00575363
$497$	−0.119096	−0.00534218
$498$	3.15922	0.141568
$499$	−6.81417	−0.305044	−0.152522	−	0.988300i	$-0.548740\pi$
$499$	−6.81417	−0.305044	−0.152522	+	0.988300i	$0.548740\pi$
$500$	−3.22941	−0.144423
$501$	0.103534	0.00462555
$502$	59.9910	2.67753
$503$	3.26143	0.145420	0.0727101	−	0.997353i	$-0.476835\pi$
$503$	3.26143	0.145420	0.0727101	+	0.997353i	$0.476835\pi$
$504$	35.5176	1.58208
$505$	15.7480	0.700776
$506$	0	0
$507$	−0.0897034	−0.00398387
$508$	59.8540	2.65559
$509$	13.9854	0.619891	0.309945	−	0.950754i	$-0.399689\pi$
$509$	13.9854	0.619891	0.309945	+	0.950754i	$0.399689\pi$
$510$	−0.0607173	−0.00268861
$511$	−69.1093	−3.05721
$512$	0.336574	0.0148746
$513$	2.74250	0.121084
$514$	43.9073	1.93667
$515$	7.53429	0.332000
$516$	−0.693887	−0.0305467
$517$	0	0
$518$	−0.188825	−0.00829648
$519$	0.311933	0.0136923
$520$	2.81139	0.123288
$521$	−18.6309	−0.816235	−0.408118	−	0.912929i	$-0.633815\pi$
$521$	−18.6309	−0.816235	−0.408118	+	0.912929i	$0.633815\pi$
$522$	−8.35107	−0.365516
$523$	14.7000	0.642787	0.321393	−	0.946946i	$-0.395849\pi$
$523$	14.7000	0.642787	0.321393	+	0.946946i	$0.395849\pi$
$524$	−10.7146	−0.468070
$525$	0.378771	0.0165309
$526$	54.2237	2.36427
$527$	1.27491	0.0555361
$528$	0	0
$529$	−5.33102	−0.231783
$530$	−0.380709	−0.0165370
$531$	−16.2370	−0.704625
$532$	−69.5760	−3.01650
$533$	−4.83445	−0.209403
$534$	0.407783	0.0176465
$535$	−16.9667	−0.733534
$536$	−1.48996	−0.0643565
$537$	1.42845	0.0616423
$538$	37.3241	1.60916
$539$	0	0
$540$	−1.73580	−0.0746970
$541$	38.0499	1.63589	0.817945	−	0.575296i	$-0.195113\pi$
$541$	38.0499	1.63589	0.817945	+	0.575296i	$0.195113\pi$
$542$	36.7676	1.57930
$543$	−0.113326	−0.00486327
$544$	1.68443	0.0722192
$545$	−7.01141	−0.300336
$546$	−0.866170	−0.0370686
$547$	−16.5105	−0.705938	−0.352969	−	0.935635i	$-0.614828\pi$
$547$	−16.5105	−0.705938	−0.352969	+	0.935635i	$0.614828\pi$
$548$	−13.6369	−0.582538
$549$	−10.0799	−0.430201
$550$	0	0
$551$	6.22774	0.265311
$552$	−1.06007	−0.0451197
$553$	−12.3859	−0.526701
$554$	−64.3793	−2.73522
$555$	0.00175418	7.44607e−5 0
$556$	−7.53964	−0.319752
$557$	−18.3009	−0.775432	−0.387716	−	0.921779i	$-0.626736\pi$
$557$	−18.3009	−0.775432	−0.387716	+	0.921779i	$0.626736\pi$
$558$	29.4703	1.24758
$559$	−2.39529	−0.101310
$560$	−0.125617	−0.00530827
$561$	0	0
$562$	53.0086	2.23603
$563$	39.2124	1.65261	0.826304	−	0.563225i	$-0.190439\pi$
$563$	39.2124	1.65261	0.826304	+	0.563225i	$0.190439\pi$
$564$	−3.43663	−0.144708
$565$	−8.10174	−0.340843
$566$	30.3321	1.27495
$567$	−37.6968	−1.58312
$568$	0.0792958	0.00332718
$569$	30.2530	1.26827	0.634136	−	0.773221i	$-0.281356\pi$
$569$	30.2530	1.26827	0.634136	+	0.773221i	$0.281356\pi$
$570$	1.04666	0.0438396
$571$	17.5828	0.735817	0.367908	−	0.929862i	$-0.380074\pi$
$571$	17.5828	0.735817	0.367908	+	0.929862i	$0.380074\pi$
$572$	0	0
$573$	0.102859	0.00429698
$574$	−46.6811	−1.94843
$575$	4.20345	0.175296
$576$	38.7584	1.61493
$577$	35.2971	1.46944	0.734719	−	0.678372i	$-0.237314\pi$
$577$	35.2971	1.46944	0.734719	+	0.678372i	$0.237314\pi$
$578$	−38.6751	−1.60867
$579$	1.05459	0.0438272
$580$	−3.94170	−0.163670
$581$	65.0300	2.69790
$582$	0.567191	0.0235108
$583$	0	0
$584$	46.0140	1.90407
$585$	−2.99195	−0.123702
$586$	−16.7455	−0.691751
$587$	12.6387	0.521656	0.260828	−	0.965385i	$-0.416004\pi$
$587$	12.6387	0.521656	0.260828	+	0.965385i	$0.416004\pi$
$588$	−3.13714	−0.129374
$589$	−21.9772	−0.905555
$590$	−12.4101	−0.510917
$591$	−1.55290	−0.0638777
$592$	−0.000581761 0	−2.39102e−5 0
$593$	14.6517	0.601674	0.300837	−	0.953676i	$-0.402734\pi$
$593$	14.6517	0.601674	0.300837	+	0.953676i	$0.402734\pi$
$594$	0	0
$595$	−1.24981	−0.0512374
$596$	68.5696	2.80872
$597$	−0.296850	−0.0121492
$598$	−9.61240	−0.393080
$599$	1.28391	0.0524593	0.0262296	−	0.999656i	$-0.491650\pi$
$599$	1.28391	0.0524593	0.0262296	+	0.999656i	$0.491650\pi$
$600$	−0.252191	−0.0102957
$601$	7.46468	0.304491	0.152245	−	0.988343i	$-0.451350\pi$
$601$	7.46468	0.304491	0.152245	+	0.988343i	$0.451350\pi$
$602$	−23.1287	−0.942656
$603$	1.58565	0.0645728
$604$	18.6814	0.760134
$605$	0	0
$606$	3.23042	0.131227
$607$	41.6654	1.69115	0.845574	−	0.533858i	$-0.179258\pi$
$607$	41.6654	1.69115	0.845574	+	0.533858i	$0.179258\pi$
$608$	−29.0365	−1.17758
$609$	0.462315	0.0187339
$610$	−7.70423	−0.311935
$611$	−11.8632	−0.479933
$612$	2.85993	0.115606
$613$	−34.1977	−1.38123	−0.690617	−	0.723221i	$-0.742661\pi$
$613$	−34.1977	−1.38123	−0.690617	+	0.723221i	$0.742661\pi$
$614$	−70.6553	−2.85141
$615$	0.433667	0.0174871
$616$	0	0
$617$	−44.7288	−1.80071	−0.900357	−	0.435152i	$-0.856694\pi$
$617$	−44.7288	−1.80071	−0.900357	+	0.435152i	$0.856694\pi$
$618$	1.54553	0.0621703
$619$	−10.4063	−0.418264	−0.209132	−	0.977887i	$-0.567064\pi$
$619$	−10.4063	−0.418264	−0.209132	+	0.977887i	$0.567064\pi$
$620$	13.9100	0.558637
$621$	2.25935	0.0906645
$622$	−49.6549	−1.99098
$623$	8.39386	0.336293
$624$	−0.00266863	−0.000106831 0
$625$	1.00000	0.0400000
$626$	−74.6358	−2.98305
$627$	0	0
$628$	17.4953	0.698140
$629$	−0.00578818	−0.000230790 0
$630$	−28.8901	−1.15101
$631$	10.8081	0.430265	0.215133	−	0.976585i	$-0.430982\pi$
$631$	10.8081	0.430265	0.215133	+	0.976585i	$0.430982\pi$
$632$	8.24670	0.328036
$633$	1.84007	0.0731363
$634$	33.8023	1.34246
$635$	−18.5341	−0.735502
$636$	−0.0482279	−0.00191236
$637$	−10.8294	−0.429075
$638$	0	0
$639$	−0.0843885	−0.00333836
$640$	18.2419	0.721074
$641$	−18.0688	−0.713676	−0.356838	−	0.934166i	$-0.616145\pi$
$641$	−18.0688	−0.713676	−0.356838	+	0.934166i	$0.616145\pi$
$642$	−3.48043	−0.137361
$643$	−39.7966	−1.56942	−0.784712	−	0.619861i	$-0.787189\pi$
$643$	−39.7966	−1.56942	−0.784712	+	0.619861i	$0.787189\pi$
$644$	−57.3187	−2.25867
$645$	0.214865	0.00846031
$646$	−3.45361	−0.135880
$647$	6.31669	0.248335	0.124167	−	0.992261i	$-0.460374\pi$
$647$	6.31669	0.248335	0.124167	+	0.992261i	$0.460374\pi$
$648$	25.0991	0.985986
$649$	0	0
$650$	−2.28679	−0.0896953
$651$	−1.63147	−0.0639425
$652$	−55.4224	−2.17051
$653$	34.7597	1.36025	0.680127	−	0.733094i	$-0.261925\pi$
$653$	34.7597	1.36025	0.680127	+	0.733094i	$0.261925\pi$
$654$	−1.43827	−0.0562408
$655$	3.31782	0.129638
$656$	−0.143822	−0.00561532
$657$	−48.9692	−1.91047
$658$	−114.550	−4.46562
$659$	−36.7071	−1.42991	−0.714953	−	0.699173i	$-0.753552\pi$
$659$	−36.7071	−1.42991	−0.714953	+	0.699173i	$0.753552\pi$
$660$	0	0
$661$	9.24285	0.359505	0.179753	−	0.983712i	$-0.442470\pi$
$661$	9.24285	0.359505	0.179753	+	0.983712i	$0.442470\pi$
$662$	48.0910	1.86911
$663$	−0.0265513	−0.00103117
$664$	−43.2979	−1.68028
$665$	21.5445	0.835461
$666$	−0.133797	−0.00518452
$667$	5.13059	0.198657
$668$	−3.72731	−0.144214
$669$	−1.98018	−0.0765584
$670$	1.21194	0.0468212
$671$	0	0
$672$	−2.15552	−0.0831508
$673$	22.7279	0.876097	0.438049	−	0.898951i	$-0.355670\pi$
$673$	22.7279	0.876097	0.438049	+	0.898951i	$0.355670\pi$
$674$	−16.0125	−0.616778
$675$	0.537498	0.0206883
$676$	3.22941	0.124208
$677$	49.3234	1.89565	0.947827	−	0.318786i	$-0.103275\pi$
$677$	49.3234	1.89565	0.947827	+	0.318786i	$0.103275\pi$
$678$	−1.66193	−0.0638261
$679$	11.6752	0.448051
$680$	0.832145	0.0319113
$681$	0.646587	0.0247773
$682$	0	0
$683$	35.0553	1.34136	0.670678	−	0.741749i	$-0.266003\pi$
$683$	35.0553	1.34136	0.670678	+	0.741749i	$0.266003\pi$
$684$	−49.3000	−1.88503
$685$	4.22271	0.161342
$686$	−36.9761	−1.41175
$687$	1.32311	0.0504797
$688$	−0.0712585	−0.00271670
$689$	−0.166482	−0.00634246
$690$	0.862265	0.0328259
$691$	13.0999	0.498343	0.249171	−	0.968459i	$-0.419842\pi$
$691$	13.0999	0.498343	0.249171	+	0.968459i	$0.419842\pi$
$692$	−11.2299	−0.426896
$693$	0	0
$694$	36.8258	1.39789
$695$	2.33468	0.0885596
$696$	−0.307816	−0.0116677
$697$	−1.43095	−0.0542011
$698$	16.0534	0.607629
$699$	−2.53096	−0.0957296
$700$	−13.6361	−0.515397
$701$	15.5593	0.587668	0.293834	−	0.955856i	$-0.405069\pi$
$701$	15.5593	0.587668	0.293834	+	0.955856i	$0.405069\pi$
$702$	−1.22915	−0.0463911
$703$	0.0997778	0.00376319
$704$	0	0
$705$	1.06417	0.0400789
$706$	−17.6709	−0.665054
$707$	66.4956	2.50082
$708$	−1.57211	−0.0590834
$709$	−19.1870	−0.720584	−0.360292	−	0.932840i	$-0.617323\pi$
$709$	−19.1870	−0.720584	−0.360292	+	0.932840i	$0.617323\pi$
$710$	−0.0644993	−0.00242061
$711$	−8.77634	−0.329138
$712$	−5.58876	−0.209448
$713$	−18.1054	−0.678054
$714$	−0.256378	−0.00959470
$715$	0	0
$716$	−51.4257	−1.92187
$717$	1.06554	0.0397935
$718$	−2.65043	−0.0989133
$719$	−22.5237	−0.839993	−0.419997	−	0.907526i	$-0.637969\pi$
$719$	−22.5237	−0.839993	−0.419997	+	0.907526i	$0.637969\pi$
$720$	−0.0890091	−0.00331717
$721$	31.8134	1.18479
$722$	16.0849	0.598618
$723$	−1.33044	−0.0494797
$724$	4.07983	0.151626
$725$	1.22057	0.0453307
$726$	0	0
$727$	42.8494	1.58920	0.794599	−	0.607135i	$-0.207681\pi$
$727$	42.8494	1.58920	0.794599	+	0.607135i	$0.207681\pi$
$728$	11.8711	0.439971
$729$	−26.5664	−0.983943
$730$	−37.4278	−1.38527
$731$	−0.708981	−0.0262226
$732$	−0.975966	−0.0360727
$733$	−31.6803	−1.17014	−0.585069	−	0.810983i	$-0.698933\pi$
$733$	−31.6803	−1.17014	−0.585069	+	0.810983i	$0.698933\pi$
$734$	75.1773	2.77484
$735$	0.971431	0.0358318
$736$	−23.9211	−0.881742
$737$	0	0
$738$	−33.0771	−1.21759
$739$	−25.7790	−0.948297	−0.474149	−	0.880445i	$-0.657244\pi$
$739$	−25.7790	−0.948297	−0.474149	+	0.880445i	$0.657244\pi$
$740$	−0.0631520	−0.00232152
$741$	0.457697	0.0168139
$742$	−1.60754	−0.0590146
$743$	23.0534	0.845747	0.422874	−	0.906189i	$-0.361021\pi$
$743$	23.0534	0.845747	0.422874	+	0.906189i	$0.361021\pi$
$744$	1.08626	0.0398242
$745$	−21.2329	−0.777913
$746$	9.55228	0.349734
$747$	46.0787	1.68593
$748$	0	0
$749$	−71.6416	−2.61773
$750$	0.205133	0.00749039
$751$	39.9892	1.45923	0.729613	−	0.683860i	$-0.239700\pi$
$751$	39.9892	1.45923	0.729613	+	0.683860i	$0.239700\pi$
$752$	−0.352923	−0.0128698
$753$	−2.35325	−0.0857574
$754$	−2.79118	−0.101649
$755$	−5.78477	−0.210529
$756$	−7.32939	−0.266567
$757$	−33.8193	−1.22918	−0.614592	−	0.788845i	$-0.710679\pi$
$757$	−33.8193	−1.22918	−0.614592	+	0.788845i	$0.710679\pi$
$758$	−37.1159	−1.34811
$759$	0	0
$760$	−14.3447	−0.520336
$761$	16.6131	0.602225	0.301113	−	0.953589i	$-0.402642\pi$
$761$	16.6131	0.602225	0.301113	+	0.953589i	$0.402642\pi$
$762$	−3.80194	−0.137730
$763$	−29.6056	−1.07179
$764$	−3.70301	−0.133970
$765$	−0.885589	−0.0320185
$766$	74.0091	2.67406
$767$	−5.42688	−0.195953
$768$	1.41794	0.0511654
$769$	−36.7810	−1.32636	−0.663178	−	0.748462i	$-0.730793\pi$
$769$	−36.7810	−1.32636	−0.663178	+	0.748462i	$0.730793\pi$
$770$	0	0
$771$	−1.72234	−0.0620287
$772$	−37.9662	−1.36643
$773$	9.00677	0.323951	0.161976	−	0.986795i	$-0.448213\pi$
$773$	9.00677	0.323951	0.161976	+	0.986795i	$0.448213\pi$
$774$	−16.3885	−0.589071
$775$	−4.30728	−0.154722
$776$	−7.77349	−0.279052
$777$	0.00740699	0.000265724 0
$778$	−61.2725	−2.19673
$779$	24.6670	0.883787
$780$	−0.289689	−0.0103725
$781$	0	0
$782$	−2.84518	−0.101743
$783$	0.656052	0.0234454
$784$	−0.322168	−0.0115060
$785$	−5.41751	−0.193359
$786$	0.680594	0.0242760
$787$	54.2452	1.93363	0.966816	−	0.255475i	$-0.0822319\pi$
$787$	54.2452	1.93363	0.966816	+	0.255475i	$0.0822319\pi$
$788$	55.9058	1.99156
$789$	−2.12702	−0.0757240
$790$	−6.70787	−0.238655
$791$	−34.2095	−1.21635
$792$	0	0
$793$	−3.36902	−0.119637
$794$	10.7691	0.382179
$795$	0.0149340	0.000529654 0
$796$	10.6869	0.378786
$797$	45.4708	1.61066	0.805328	−	0.592829i	$-0.201989\pi$
$797$	45.4708	1.61066	0.805328	+	0.592829i	$0.201989\pi$
$798$	4.41949	0.156448
$799$	−3.51139	−0.124224
$800$	−5.69082	−0.201201
$801$	5.94770	0.210152
$802$	−55.3852	−1.95572
$803$	0	0
$804$	0.153527	0.00541448
$805$	17.7490	0.625570
$806$	9.84984	0.346946
$807$	−1.46410	−0.0515389
$808$	−44.2737	−1.55754
$809$	42.7872	1.50432	0.752158	−	0.658983i	$-0.229013\pi$
$809$	42.7872	1.50432	0.752158	+	0.658983i	$0.229013\pi$
$810$	−20.4156	−0.717333
$811$	46.8471	1.64502	0.822512	−	0.568748i	$-0.192572\pi$
$811$	46.8471	1.64502	0.822512	+	0.568748i	$0.192572\pi$
$812$	−16.6438	−0.584082
$813$	−1.44227	−0.0505827
$814$	0	0
$815$	17.1618	0.601152
$816$	−0.000789889 0	−2.76516e−5 0
$817$	12.2215	0.427578
$818$	−21.5813	−0.754572
$819$	−12.6335	−0.441449
$820$	−15.6124	−0.545209
$821$	−32.6402	−1.13915	−0.569576	−	0.821939i	$-0.692893\pi$
$821$	−32.6402	−1.13915	−0.569576	+	0.821939i	$0.692893\pi$
$822$	0.866217	0.0302128
$823$	−20.4742	−0.713687	−0.356844	−	0.934164i	$-0.616147\pi$
$823$	−20.4742	−0.713687	−0.356844	+	0.934164i	$0.616147\pi$
$824$	−21.1818	−0.737904
$825$	0	0
$826$	−52.4016	−1.82328
$827$	35.8528	1.24672	0.623362	−	0.781934i	$-0.285766\pi$
$827$	35.8528	1.24672	0.623362	+	0.781934i	$0.285766\pi$
$828$	−40.6147	−1.41146
$829$	−31.9326	−1.10906	−0.554532	−	0.832163i	$-0.687103\pi$
$829$	−31.9326	−1.10906	−0.554532	+	0.832163i	$0.687103\pi$
$830$	35.2186	1.22245
$831$	2.52539	0.0876049
$832$	12.9542	0.449106
$833$	−3.20539	−0.111060
$834$	0.478920	0.0165836
$835$	1.15418	0.0399420
$836$	0	0
$837$	−2.31516	−0.0800235
$838$	7.73559	0.267221
$839$	39.2793	1.35607	0.678036	−	0.735029i	$-0.262831\pi$
$839$	39.2793	1.35607	0.678036	+	0.735029i	$0.262831\pi$
$840$	−1.06487	−0.0367416
$841$	−27.5102	−0.948628
$842$	52.2350	1.80014
$843$	−2.07936	−0.0716169
$844$	−66.2443	−2.28022
$845$	−1.00000	−0.0344010
$846$	−81.1675	−2.79060
$847$	0	0
$848$	−0.00495275	−0.000170078 0
$849$	−1.18983	−0.0408349
$850$	−0.676868	−0.0232164
$851$	0.0821998	0.00281777
$852$	−0.00817072	−0.000279924 0
$853$	32.4254	1.11022	0.555112	−	0.831776i	$-0.312676\pi$
$853$	32.4254	1.11022	0.555112	+	0.831776i	$0.312676\pi$
$854$	−32.5310	−1.11319
$855$	15.2660	0.522085
$856$	47.7001	1.63035
$857$	37.2652	1.27295	0.636477	−	0.771295i	$-0.280391\pi$
$857$	37.2652	1.27295	0.636477	+	0.771295i	$0.280391\pi$
$858$	0	0
$859$	−24.5020	−0.835997	−0.417999	−	0.908448i	$-0.637268\pi$
$859$	−24.5020	−0.835997	−0.417999	+	0.908448i	$0.637268\pi$
$860$	−7.73535	−0.263773
$861$	1.83115	0.0624054
$862$	−67.1793	−2.28813
$863$	−0.986462	−0.0335796	−0.0167898	−	0.999859i	$-0.505345\pi$
$863$	−0.986462	−0.0335796	−0.0167898	+	0.999859i	$0.505345\pi$
$864$	−3.05880	−0.104063
$865$	3.47738	0.118235
$866$	−62.5075	−2.12409
$867$	1.51710	0.0515234
$868$	58.7346	1.99358
$869$	0	0
$870$	0.250378	0.00848861
$871$	0.529973	0.0179574
$872$	19.7118	0.667527
$873$	8.27274	0.279990
$874$	49.0457	1.65900
$875$	4.22248	0.142746
$876$	−4.74133	−0.160195
$877$	29.8557	1.00816	0.504078	−	0.863658i	$-0.331833\pi$
$877$	29.8557	1.00816	0.504078	+	0.863658i	$0.331833\pi$
$878$	8.66958	0.292584
$879$	0.656872	0.0221558
$880$	0	0
$881$	−58.5965	−1.97417	−0.987084	−	0.160205i	$-0.948785\pi$
$881$	−58.5965	−1.97417	−0.987084	+	0.160205i	$0.948785\pi$
$882$	−74.0942	−2.49488
$883$	−20.8430	−0.701423	−0.350711	−	0.936484i	$-0.614060\pi$
$883$	−20.8430	−0.701423	−0.350711	+	0.936484i	$0.614060\pi$
$884$	0.955873	0.0321495
$885$	0.486810	0.0163639
$886$	−53.4640	−1.79616
$887$	11.5614	0.388193	0.194097	−	0.980982i	$-0.437822\pi$
$887$	11.5614	0.388193	0.194097	+	0.980982i	$0.437822\pi$
$888$	−0.00493168	−0.000165496 0
$889$	−78.2598	−2.62475
$890$	4.54590	0.152379
$891$	0	0
$892$	71.2885	2.38692
$893$	60.5299	2.02556
$894$	−4.35556	−0.145672
$895$	15.9242	0.532287
$896$	77.0261	2.57326
$897$	0.377064	0.0125898
$898$	34.9331	1.16573
$899$	−5.25732	−0.175341
$900$	−9.66223	−0.322074
$901$	−0.0492771	−0.00164166
$902$	0	0
$903$	0.907265	0.0301919
$904$	22.7772	0.757558
$905$	−1.26334	−0.0419947
$906$	−1.18665	−0.0394237
$907$	24.6006	0.816850	0.408425	−	0.912792i	$-0.366078\pi$
$907$	24.6006	0.816850	0.408425	+	0.912792i	$0.366078\pi$
$908$	−23.2778	−0.772499
$909$	47.1172	1.56278
$910$	−9.65593	−0.320091
$911$	−21.2705	−0.704723	−0.352361	−	0.935864i	$-0.614621\pi$
$911$	−21.2705	−0.704723	−0.352361	+	0.935864i	$0.614621\pi$
$912$	0.0136162	0.000450879 0
$913$	0	0
$914$	23.4982	0.777251
$915$	0.302212	0.00999083
$916$	−47.6331	−1.57384
$917$	14.0095	0.462633
$918$	−0.363815	−0.0120077
$919$	56.4666	1.86266	0.931331	−	0.364175i	$-0.118649\pi$
$919$	56.4666	1.86266	0.931331	+	0.364175i	$0.118649\pi$
$920$	−11.8175	−0.389613
$921$	2.77158	0.0913266
$922$	87.8581	2.89345
$923$	−0.0282052	−0.000928384 0
$924$	0	0
$925$	0.0195553	0.000642975 0
$926$	−40.6672	−1.33641
$927$	22.5422	0.740384
$928$	−6.94602	−0.228014
$929$	−17.7758	−0.583205	−0.291602	−	0.956540i	$-0.594188\pi$
$929$	−17.7758	−0.583205	−0.291602	+	0.956540i	$0.594188\pi$
$930$	−0.883564	−0.0289732
$931$	55.2551	1.81091
$932$	91.1168	2.98463
$933$	1.94780	0.0637682
$934$	−63.1068	−2.06492
$935$	0	0
$936$	8.41155	0.274940
$937$	47.7343	1.55941	0.779706	−	0.626146i	$-0.215369\pi$
$937$	47.7343	1.55941	0.779706	+	0.626146i	$0.215369\pi$
$938$	5.11738	0.167088
$939$	2.92772	0.0955426
$940$	−38.3110	−1.24957
$941$	27.6323	0.900786	0.450393	−	0.892830i	$-0.351284\pi$
$941$	27.6323	0.900786	0.450393	+	0.892830i	$0.351284\pi$
$942$	−1.11131	−0.0362084
$943$	20.3214	0.661755
$944$	−0.161447	−0.00525465
$945$	2.26958	0.0738294
$946$	0	0
$947$	−15.9621	−0.518697	−0.259349	−	0.965784i	$-0.583508\pi$
$947$	−15.9621	−0.518697	−0.259349	+	0.965784i	$0.583508\pi$
$948$	−0.849748	−0.0275985
$949$	−16.3670	−0.531294
$950$	11.6680	0.378559
$951$	−1.32596	−0.0429971
$952$	3.51372	0.113880
$953$	25.4399	0.824079	0.412040	−	0.911166i	$-0.364816\pi$
$953$	25.4399	0.824079	0.412040	+	0.911166i	$0.364816\pi$
$954$	−1.13906	−0.0368786
$955$	1.14665	0.0371048
$956$	−38.3606	−1.24067
$957$	0	0
$958$	−72.7891	−2.35171
$959$	17.8303	0.575772
$960$	−1.16204	−0.0375045
$961$	−12.4473	−0.401527
$962$	−0.0447189	−0.00144179
$963$	−50.7636	−1.63583
$964$	47.8972	1.54266
$965$	11.7564	0.378452
$966$	3.64090	0.117144
$967$	−12.7377	−0.409615	−0.204808	−	0.978802i	$-0.565657\pi$
$967$	−12.7377	−0.409615	−0.204808	+	0.978802i	$0.565657\pi$
$968$	0	0
$969$	0.135474	0.00435205
$970$	6.32296	0.203018
$971$	40.0678	1.28584	0.642918	−	0.765935i	$-0.277724\pi$
$971$	40.0678	1.28584	0.642918	+	0.765935i	$0.277724\pi$
$972$	−7.79364	−0.249981
$973$	9.85816	0.316038
$974$	69.7084	2.23360
$975$	0.0897034	0.00287281
$976$	−0.100227	−0.00320817
$977$	−32.5175	−1.04033	−0.520164	−	0.854066i	$-0.674129\pi$
$977$	−32.5175	−1.04033	−0.520164	+	0.854066i	$0.674129\pi$
$978$	3.52045	0.112571
$979$	0	0
$980$	−34.9724	−1.11715
$981$	−20.9778	−0.669770
$982$	−58.3851	−1.86314
$983$	−44.0299	−1.40434	−0.702168	−	0.712011i	$-0.747784\pi$
$983$	−44.0299	−1.40434	−0.702168	+	0.712011i	$0.747784\pi$
$984$	−1.21921	−0.0388669
$985$	−17.3115	−0.551590
$986$	−0.826161	−0.0263103
$987$	4.49343	0.143027
$988$	−16.4775	−0.524220
$989$	10.0685	0.320158
$990$	0	0
$991$	3.72501	0.118329	0.0591644	−	0.998248i	$-0.481156\pi$
$991$	3.72501	0.118329	0.0591644	+	0.998248i	$0.481156\pi$
$992$	24.5119	0.778255
$993$	−1.88645	−0.0598648
$994$	−0.272347	−0.00863833
$995$	−3.30924	−0.104910
$996$	4.46146	0.141367
$997$	−35.5463	−1.12576	−0.562881	−	0.826538i	$-0.690307\pi$
$997$	−35.5463	−1.12576	−0.562881	+	0.826538i	$0.690307\pi$
$998$	−15.5826	−0.493258
$999$	0.0105110	0.000332552 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7865.2.a.u.1.7	yes	8
11.10	odd	2		7865.2.a.t.1.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7865.2.a.t.1.2	✓	8	11.10	odd	2
7865.2.a.u.1.7	yes	8	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:	\( N \)	\(=\)	\( 7865 = 5 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7865.a (trivial)

\(f(q)\)	\(=\)	\(q+2.28679 q^{2} -0.0897034 q^{3} +3.22941 q^{4} -1.00000 q^{5} -0.205133 q^{6} -4.22248 q^{7} +2.81139 q^{8} -2.99195 q^{9} -2.28679 q^{10} -0.289689 q^{12} -1.00000 q^{13} -9.65593 q^{14} +0.0897034 q^{15} -0.0297495 q^{16} -0.295990 q^{17} -6.84197 q^{18} +5.10234 q^{19} -3.22941 q^{20} +0.378771 q^{21} +4.20345 q^{23} -0.252191 q^{24} +1.00000 q^{25} -2.28679 q^{26} +0.537498 q^{27} -13.6361 q^{28} +1.22057 q^{29} +0.205133 q^{30} -4.30728 q^{31} -5.69082 q^{32} -0.676868 q^{34} +4.22248 q^{35} -9.66223 q^{36} +0.0195553 q^{37} +11.6680 q^{38} +0.0897034 q^{39} -2.81139 q^{40} +4.83445 q^{41} +0.866170 q^{42} +2.39529 q^{43} +2.99195 q^{45} +9.61240 q^{46} +11.8632 q^{47} +0.00266863 q^{48} +10.8294 q^{49} +2.28679 q^{50} +0.0265513 q^{51} -3.22941 q^{52} +0.166482 q^{53} +1.22915 q^{54} -11.8711 q^{56} -0.457697 q^{57} +2.79118 q^{58} +5.42688 q^{59} +0.289689 q^{60} +3.36902 q^{61} -9.84984 q^{62} +12.6335 q^{63} -12.9542 q^{64} +1.00000 q^{65} -0.529973 q^{67} -0.955873 q^{68} -0.377064 q^{69} +9.65593 q^{70} +0.0282052 q^{71} -8.41155 q^{72} +16.3670 q^{73} +0.0447189 q^{74} -0.0897034 q^{75} +16.4775 q^{76} +0.205133 q^{78} +2.93331 q^{79} +0.0297495 q^{80} +8.92764 q^{81} +11.0554 q^{82} -15.4009 q^{83} +1.22321 q^{84} +0.295990 q^{85} +5.47751 q^{86} -0.109489 q^{87} -1.98790 q^{89} +6.84197 q^{90} +4.22248 q^{91} +13.5746 q^{92} +0.386378 q^{93} +27.1286 q^{94} -5.10234 q^{95} +0.510485 q^{96} -2.76500 q^{97} +24.7645 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 5 q^{3} + 7 q^{4} - 8 q^{5} - 7 q^{6} + 9 q^{7} + 3 q^{8} + 3 q^{9} - q^{10} - 15 q^{12} - 8 q^{13} - 7 q^{14} + 5 q^{15} + 9 q^{16} + 4 q^{17} + 8 q^{18} + 16 q^{19} - 7 q^{20} - 23 q^{21}+ \cdots + 41 q^{98}+O(q^{100}) \) 8 * q + q^2 - 5 * q^3 + 7 * q^4 - 8 * q^5 - 7 * q^6 + 9 * q^7 + 3 * q^8 + 3 * q^9 - q^10 - 15 * q^12 - 8 * q^13 - 7 * q^14 + 5 * q^15 + 9 * q^16 + 4 * q^17 + 8 * q^18 + 16 * q^19 - 7 * q^20 - 23 * q^21 - 9 * q^23 + 5 * q^24 + 8 * q^25 - q^26 - 11 * q^27 + 11 * q^28 - 13 * q^29 + 7 * q^30 - 28 * q^32 + 13 * q^34 - 9 * q^35 + 12 * q^36 - 5 * q^37 + 55 * q^38 + 5 * q^39 - 3 * q^40 + 13 * q^41 - 5 * q^42 + 5 * q^43 - 3 * q^45 + 27 * q^46 + 10 * q^47 - 36 * q^48 + 23 * q^49 + q^50 - 37 * q^51 - 7 * q^52 + 14 * q^53 - 45 * q^54 - 18 * q^56 - 21 * q^57 + 3 * q^58 - 20 * q^59 + 15 * q^60 + 6 * q^61 + 25 * q^62 + 26 * q^63 - 3 * q^64 + 8 * q^65 + 4 * q^67 - 9 * q^69 + 7 * q^70 - 9 * q^71 + 35 * q^72 + 10 * q^73 + 42 * q^74 - 5 * q^75 + 19 * q^76 + 7 * q^78 + 13 * q^79 - 9 * q^80 + 16 * q^82 + 26 * q^83 - 58 * q^84 - 4 * q^85 + 26 * q^86 + 11 * q^87 - 6 * q^89 - 8 * q^90 - 9 * q^91 - 16 * q^92 + 3 * q^93 + 23 * q^94 - 16 * q^95 + 21 * q^96 + 26 * q^97 + 41 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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