LMFDB - Embedded newform 5929.2.a.bv.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$47.3433033584$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 26x^{8} + 245x^{6} - 1038x^{4} + 1884x^{2} - 968 $ x^10 - 26x^8 + 245x^6 - 1038x^4 + 1884x^2 - 968
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 539)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.32267$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.566092 q^{2} -2.32267 q^{3} -1.67954 q^{4} -3.58219 q^{5} +1.31484 q^{6} +2.08296 q^{8} +2.39479 q^{9} +O(q^{10})$	\(q-0.566092 q^{2} -2.32267 q^{3} -1.67954 q^{4} -3.58219 q^{5} +1.31484 q^{6} +2.08296 q^{8} +2.39479 q^{9} +2.02785 q^{10} +3.90101 q^{12} -2.11542 q^{13} +8.32025 q^{15} +2.17993 q^{16} +7.87739 q^{17} -1.35567 q^{18} -5.56323 q^{19} +6.01643 q^{20} -1.25426 q^{23} -4.83802 q^{24} +7.83210 q^{25} +1.19752 q^{26} +1.40570 q^{27} +0.991656 q^{29} -4.71003 q^{30} +6.06899 q^{31} -5.39996 q^{32} -4.45933 q^{34} -4.02214 q^{36} -1.67120 q^{37} +3.14930 q^{38} +4.91342 q^{39} -7.46156 q^{40} -5.35834 q^{41} +9.21855 q^{43} -8.57860 q^{45} +0.710028 q^{46} -9.40225 q^{47} -5.06326 q^{48} -4.43369 q^{50} -18.2966 q^{51} +3.55293 q^{52} +12.2102 q^{53} -0.795757 q^{54} +12.9216 q^{57} -0.561369 q^{58} -3.88070 q^{59} -13.9742 q^{60} -2.52992 q^{61} -3.43561 q^{62} -1.30299 q^{64} +7.57784 q^{65} -3.51863 q^{67} -13.2304 q^{68} +2.91323 q^{69} +0.481369 q^{71} +4.98825 q^{72} -14.9367 q^{73} +0.946051 q^{74} -18.1914 q^{75} +9.34367 q^{76} -2.78145 q^{78} +8.00813 q^{79} -7.80894 q^{80} -10.4494 q^{81} +3.03332 q^{82} -4.23084 q^{83} -28.2183 q^{85} -5.21855 q^{86} -2.30329 q^{87} -3.58219 q^{89} +4.85628 q^{90} +2.10658 q^{92} -14.0963 q^{93} +5.32254 q^{94} +19.9286 q^{95} +12.5423 q^{96} -0.164132 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 18 q^{4} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 18 * q^4 + 6 * q^8 + 22 * q^9	$ 10 q - 2 q^{2} + 18 q^{4} + 6 q^{8} + 22 q^{9} + 8 q^{15} + 42 q^{16} - 6 q^{18} + 4 q^{23} + 18 q^{25} - 12 q^{29} + 4 q^{30} + 30 q^{32} - 2 q^{36} + 40 q^{37} + 16 q^{39} + 8 q^{43} - 44 q^{46} + 62 q^{50} + 16 q^{53} + 8 q^{57} - 28 q^{58} + 36 q^{60} + 106 q^{64} + 32 q^{65} - 4 q^{67} + 36 q^{71} + 90 q^{72} + 28 q^{74} - 112 q^{78} - 8 q^{79} - 6 q^{81} - 88 q^{85} + 32 q^{86} - 52 q^{92} + 44 q^{93} + 64 q^{95}+O(q^{100}) $ 10 * q - 2 * q^2 + 18 * q^4 + 6 * q^8 + 22 * q^9 + 8 * q^15 + 42 * q^16 - 6 * q^18 + 4 * q^23 + 18 * q^25 - 12 * q^29 + 4 * q^30 + 30 * q^32 - 2 * q^36 + 40 * q^37 + 16 * q^39 + 8 * q^43 - 44 * q^46 + 62 * q^50 + 16 * q^53 + 8 * q^57 - 28 * q^58 + 36 * q^60 + 106 * q^64 + 32 * q^65 - 4 * q^67 + 36 * q^71 + 90 * q^72 + 28 * q^74 - 112 * q^78 - 8 * q^79 - 6 * q^81 - 88 * q^85 + 32 * q^86 - 52 * q^92 + 44 * q^93 + 64 * q^95

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.566092	−0.400288	−0.200144	−	0.979767i	$-0.564141\pi$
$2$	−0.566092	−0.400288	−0.200144	+	0.979767i	$0.564141\pi$
$3$	−2.32267	−1.34099	−0.670497	−	0.741913i	$-0.733919\pi$
$3$	−2.32267	−1.34099	−0.670497	+	0.741913i	$0.733919\pi$
$4$	−1.67954	−0.839770
$5$	−3.58219	−1.60201	−0.801003	−	0.598661i	$-0.795700\pi$
$5$	−3.58219	−1.60201	−0.801003	+	0.598661i	$0.795700\pi$
$6$	1.31484	0.536783
$7$	0	0
$7$	0	0
$8$	2.08296	0.736437
$9$	2.39479	0.798263
$10$	2.02785	0.641263
$11$	0	0
$11$	0	0
$12$	3.90101	1.12613
$13$	−2.11542	−0.586712	−0.293356	−	0.956003i	$-0.594772\pi$
$13$	−2.11542	−0.586712	−0.293356	+	0.956003i	$0.594772\pi$
$14$	0	0
$15$	8.32025	2.14828
$16$	2.17993	0.544983
$17$	7.87739	1.91055	0.955274	−	0.295722i	$-0.0955601\pi$
$17$	7.87739	1.91055	0.955274	+	0.295722i	$0.0955601\pi$
$18$	−1.35567	−0.319535
$19$	−5.56323	−1.27629	−0.638147	−	0.769915i	$-0.720299\pi$
$19$	−5.56323	−1.27629	−0.638147	+	0.769915i	$0.720299\pi$
$20$	6.01643	1.34532
$21$	0	0
$22$	0	0
$23$	−1.25426	−0.261532	−0.130766	−	0.991413i	$-0.541744\pi$
$23$	−1.25426	−0.261532	−0.130766	+	0.991413i	$0.541744\pi$
$24$	−4.83802	−0.987557
$25$	7.83210	1.56642
$26$	1.19752	0.234854
$27$	1.40570	0.270528
$28$	0	0
$29$	0.991656	0.184146	0.0920730	−	0.995752i	$-0.470651\pi$
$29$	0.991656	0.184146	0.0920730	+	0.995752i	$0.470651\pi$
$30$	−4.71003	−0.859929
$31$	6.06899	1.09002	0.545012	−	0.838428i	$-0.316525\pi$
$31$	6.06899	1.09002	0.545012	+	0.838428i	$0.316525\pi$
$32$	−5.39996	−0.954587
$33$	0	0
$34$	−4.45933	−0.764769
$35$	0	0
$36$	−4.02214	−0.670357
$37$	−1.67120	−0.274743	−0.137371	−	0.990520i	$-0.543865\pi$
$37$	−1.67120	−0.274743	−0.137371	+	0.990520i	$0.543865\pi$
$38$	3.14930	0.510885
$39$	4.91342	0.786777
$40$	−7.46156	−1.17978
$41$	−5.35834	−0.836833	−0.418416	−	0.908255i	$-0.637415\pi$
$41$	−5.35834	−0.836833	−0.418416	+	0.908255i	$0.637415\pi$
$42$	0	0
$43$	9.21855	1.40582	0.702908	−	0.711281i	$-0.251885\pi$
$43$	9.21855	1.40582	0.702908	+	0.711281i	$0.251885\pi$
$44$	0	0
$45$	−8.57860	−1.27882
$46$	0.710028	0.104688
$47$	−9.40225	−1.37146	−0.685729	−	0.727857i	$-0.740517\pi$
$47$	−9.40225	−1.37146	−0.685729	+	0.727857i	$0.740517\pi$
$48$	−5.06326	−0.730819
$49$	0	0
$50$	−4.43369	−0.627019
$51$	−18.2966	−2.56203
$52$	3.55293	0.492703
$53$	12.2102	1.67720	0.838600	−	0.544747i	$-0.183374\pi$
$53$	12.2102	1.67720	0.838600	+	0.544747i	$0.183374\pi$
$54$	−0.795757	−0.108289
$55$	0	0
$56$	0	0
$57$	12.9216	1.71150
$58$	−0.561369	−0.0737113
$59$	−3.88070	−0.505224	−0.252612	−	0.967568i	$-0.581290\pi$
$59$	−3.88070	−0.505224	−0.252612	+	0.967568i	$0.581290\pi$
$60$	−13.9742	−1.80406
$61$	−2.52992	−0.323923	−0.161961	−	0.986797i	$-0.551782\pi$
$61$	−2.52992	−0.323923	−0.161961	+	0.986797i	$0.551782\pi$
$62$	−3.43561	−0.436323
$63$	0	0
$64$	−1.30299	−0.162873
$65$	7.57784	0.939916
$66$	0	0
$67$	−3.51863	−0.429869	−0.214935	−	0.976628i	$-0.568954\pi$
$67$	−3.51863	−0.429869	−0.214935	+	0.976628i	$0.568954\pi$
$68$	−13.2304	−1.60442
$69$	2.91323	0.350712
$70$	0	0
$71$	0.481369	0.0571280	0.0285640	−	0.999592i	$-0.490907\pi$
$71$	0.481369	0.0571280	0.0285640	+	0.999592i	$0.490907\pi$
$72$	4.98825	0.587871
$73$	−14.9367	−1.74820	−0.874102	−	0.485743i	$-0.838549\pi$
$73$	−14.9367	−1.74820	−0.874102	+	0.485743i	$0.838549\pi$
$74$	0.946051	0.109976
$75$	−18.1914	−2.10056
$76$	9.34367	1.07179
$77$	0	0
$78$	−2.78145	−0.314937
$79$	8.00813	0.900985	0.450493	−	0.892780i	$-0.351248\pi$
$79$	8.00813	0.900985	0.450493	+	0.892780i	$0.351248\pi$
$80$	−7.80894	−0.873066
$81$	−10.4494	−1.16104
$82$	3.03332	0.334974
$83$	−4.23084	−0.464395	−0.232198	−	0.972669i	$-0.574592\pi$
$83$	−4.23084	−0.464395	−0.232198	+	0.972669i	$0.574592\pi$
$84$	0	0
$85$	−28.2183	−3.06071
$86$	−5.21855	−0.562731
$87$	−2.30329	−0.246938
$88$	0	0
$89$	−3.58219	−0.379712	−0.189856	−	0.981812i	$-0.560802\pi$
$89$	−3.58219	−0.379712	−0.189856	+	0.981812i	$0.560802\pi$
$90$	4.85628	0.511897
$91$	0	0
$92$	2.10658	0.219626
$93$	−14.0963	−1.46171
$94$	5.32254	0.548978
$95$	19.9286	2.04463
$96$	12.5423	1.28010
$97$	−0.164132	−0.0166650	−0.00833252	−	0.999965i	$-0.502652\pi$
$97$	−0.164132	−0.0166650	−0.00833252	+	0.999965i	$0.502652\pi$
$98$	0	0
$99$	0	0
$100$	−13.1543	−1.31543
$101$	−12.1489	−1.20886	−0.604428	−	0.796660i	$-0.706598\pi$
$101$	−12.1489	−1.20886	−0.604428	+	0.796660i	$0.706598\pi$
$102$	10.3575	1.02555
$103$	6.46318	0.636836	0.318418	−	0.947950i	$-0.396848\pi$
$103$	6.46318	0.636836	0.318418	+	0.947950i	$0.396848\pi$
$104$	−4.40633	−0.432077
$105$	0	0
$106$	−6.91210	−0.671363
$107$	−15.4910	−1.49758	−0.748788	−	0.662809i	$-0.769364\pi$
$107$	−15.4910	−1.49758	−0.748788	+	0.662809i	$0.769364\pi$
$108$	−2.36093	−0.227181
$109$	−18.3507	−1.75768	−0.878841	−	0.477115i	$-0.841682\pi$
$109$	−18.3507	−1.75768	−0.878841	+	0.477115i	$0.841682\pi$
$110$	0	0
$111$	3.88163	0.368428
$112$	0	0
$113$	1.17993	0.110999	0.0554993	−	0.998459i	$-0.482325\pi$
$113$	1.17993	0.110999	0.0554993	+	0.998459i	$0.482325\pi$
$114$	−7.31479	−0.685093
$115$	4.49301	0.418975
$116$	−1.66553	−0.154640
$117$	−5.06599	−0.468351
$118$	2.19684	0.202235
$119$	0	0
$120$	17.3307	1.58207
$121$	0	0
$122$	1.43217	0.129662
$123$	12.4457	1.12219
$124$	−10.1931	−0.915369
$125$	−10.1451	−0.907409
$126$	0	0
$127$	6.50852	0.577538	0.288769	−	0.957399i	$-0.406754\pi$
$127$	6.50852	0.577538	0.288769	+	0.957399i	$0.406754\pi$
$128$	11.5375	1.01978
$129$	−21.4116	−1.88519
$130$	−4.28976	−0.376237
$131$	−7.36312	−0.643319	−0.321660	−	0.946855i	$-0.604241\pi$
$131$	−7.36312	−0.643319	−0.321660	+	0.946855i	$0.604241\pi$
$132$	0	0
$133$	0	0
$134$	1.99187	0.172071
$135$	−5.03550	−0.433387
$136$	16.4083	1.40700
$137$	8.76591	0.748922	0.374461	−	0.927243i	$-0.377828\pi$
$137$	8.76591	0.748922	0.374461	+	0.927243i	$0.377828\pi$
$138$	−1.64916	−0.140386
$139$	−3.64121	−0.308843	−0.154422	−	0.988005i	$-0.549351\pi$
$139$	−3.64121	−0.308843	−0.154422	+	0.988005i	$0.549351\pi$
$140$	0	0
$141$	21.8383	1.83912
$142$	−0.272500	−0.0228677
$143$	0	0
$144$	5.22048	0.435040
$145$	−3.55230	−0.295003
$146$	8.45553	0.699784
$147$	0	0
$148$	2.80684	0.230721
$149$	−0.728603	−0.0596895	−0.0298448	−	0.999555i	$-0.509501\pi$
$149$	−0.728603	−0.0596895	−0.0298448	+	0.999555i	$0.509501\pi$
$150$	10.2980	0.840828
$151$	6.42897	0.523182	0.261591	−	0.965179i	$-0.415753\pi$
$151$	6.42897	0.523182	0.261591	+	0.965179i	$0.415753\pi$
$152$	−11.5880	−0.939910
$153$	18.8647	1.52512
$154$	0	0
$155$	−21.7403	−1.74622
$156$	−8.25228	−0.660711
$157$	−3.55610	−0.283808	−0.141904	−	0.989880i	$-0.545322\pi$
$157$	−3.55610	−0.283808	−0.141904	+	0.989880i	$0.545322\pi$
$158$	−4.53334	−0.360653
$159$	−28.3603	−2.24912
$160$	19.3437	1.52925
$161$	0	0
$162$	5.91530	0.464750
$163$	13.8255	1.08290	0.541449	−	0.840733i	$-0.317876\pi$
$163$	13.8255	1.08290	0.541449	+	0.840733i	$0.317876\pi$
$164$	8.99955	0.702747
$165$	0	0
$166$	2.39505	0.185892
$167$	0.589634	0.0456272	0.0228136	−	0.999740i	$-0.492738\pi$
$167$	0.589634	0.0456272	0.0228136	+	0.999740i	$0.492738\pi$
$168$	0	0
$169$	−8.52500	−0.655769
$170$	15.9742	1.22516
$171$	−13.3228	−1.01882
$172$	−15.4829	−1.18056
$173$	4.28419	0.325721	0.162861	−	0.986649i	$-0.447928\pi$
$173$	4.28419	0.325721	0.162861	+	0.986649i	$0.447928\pi$
$174$	1.30387	0.0988464
$175$	0	0
$176$	0	0
$177$	9.01359	0.677503
$178$	2.02785	0.151994
$179$	−13.4606	−1.00609	−0.503045	−	0.864260i	$-0.667787\pi$
$179$	−13.4606	−1.00609	−0.503045	+	0.864260i	$0.667787\pi$
$180$	14.4081	1.07392
$181$	20.2099	1.50219	0.751095	−	0.660194i	$-0.229526\pi$
$181$	20.2099	1.50219	0.751095	+	0.660194i	$0.229526\pi$
$182$	0	0
$183$	5.87616	0.434378
$184$	−2.61258	−0.192602
$185$	5.98654	0.440140
$186$	7.97978	0.585106
$187$	0	0
$188$	15.7914	1.15171
$189$	0	0
$190$	−11.2814	−0.818440
$191$	20.1625	1.45890	0.729452	−	0.684032i	$-0.239775\pi$
$191$	20.1625	1.45890	0.729452	+	0.684032i	$0.239775\pi$
$192$	3.02641	0.218412
$193$	−1.85134	−0.133262	−0.0666312	−	0.997778i	$-0.521225\pi$
$193$	−1.85134	−0.133262	−0.0666312	+	0.997778i	$0.521225\pi$
$194$	0.0929136	0.00667081
$195$	−17.6008	−1.26042
$196$	0	0
$197$	−9.28141	−0.661273	−0.330637	−	0.943758i	$-0.607263\pi$
$197$	−9.28141	−0.661273	−0.330637	+	0.943758i	$0.607263\pi$
$198$	0	0
$199$	−0.993564	−0.0704319	−0.0352159	−	0.999380i	$-0.511212\pi$
$199$	−0.993564	−0.0704319	−0.0352159	+	0.999380i	$0.511212\pi$
$200$	16.3140	1.15357
$201$	8.17261	0.576452
$202$	6.87737	0.483890
$203$	0	0
$204$	30.7298	2.15152
$205$	19.1946	1.34061
$206$	−3.65876	−0.254918
$207$	−3.00369	−0.208771
$208$	−4.61147	−0.319748
$209$	0	0
$210$	0	0
$211$	−16.4840	−1.13481	−0.567403	−	0.823440i	$-0.692052\pi$
$211$	−16.4840	−1.13481	−0.567403	+	0.823440i	$0.692052\pi$
$212$	−20.5075	−1.40846
$213$	−1.11806	−0.0766083
$214$	8.76936	0.599461
$215$	−33.0226	−2.25212
$216$	2.92802	0.199227
$217$	0	0
$218$	10.3882	0.703578
$219$	34.6929	2.34433
$220$	0	0
$221$	−16.6640	−1.12094
$222$	−2.19736	−0.147477
$223$	−26.2084	−1.75504	−0.877521	−	0.479538i	$-0.840804\pi$
$223$	−26.2084	−1.75504	−0.877521	+	0.479538i	$0.840804\pi$
$224$	0	0
$225$	18.7562	1.25042
$226$	−0.667950	−0.0444314
$227$	18.3200	1.21594	0.607970	−	0.793960i	$-0.291984\pi$
$227$	18.3200	1.21594	0.607970	+	0.793960i	$0.291984\pi$
$228$	−21.7023	−1.43727
$229$	−13.4169	−0.886613	−0.443307	−	0.896370i	$-0.646195\pi$
$229$	−13.4169	−0.886613	−0.443307	+	0.896370i	$0.646195\pi$
$230$	−2.54346	−0.167711
$231$	0	0
$232$	2.06558	0.135612
$233$	4.43884	0.290798	0.145399	−	0.989373i	$-0.453553\pi$
$233$	4.43884	0.290798	0.145399	+	0.989373i	$0.453553\pi$
$234$	2.86782	0.187475
$235$	33.6807	2.19708
$236$	6.51779	0.424272
$237$	−18.6002	−1.20822
$238$	0	0
$239$	−9.13900	−0.591153	−0.295576	−	0.955319i	$-0.595512\pi$
$239$	−9.13900	−0.591153	−0.295576	+	0.955319i	$0.595512\pi$
$240$	18.1376	1.17078
$241$	17.1870	1.10711	0.553554	−	0.832813i	$-0.313271\pi$
$241$	17.1870	1.10711	0.553554	+	0.832813i	$0.313271\pi$
$242$	0	0
$243$	20.0533	1.28642
$244$	4.24910	0.272020
$245$	0	0
$246$	−7.04539	−0.449198
$247$	11.7686	0.748817
$248$	12.6415	0.802734
$249$	9.82684	0.622751
$250$	5.74309	0.363225
$251$	17.7972	1.12335	0.561675	−	0.827358i	$-0.310157\pi$
$251$	17.7972	1.12335	0.561675	+	0.827358i	$0.310157\pi$
$252$	0	0
$253$	0	0
$254$	−3.68442	−0.231181
$255$	65.5418	4.10439
$256$	−3.92533	−0.245333
$257$	−6.99447	−0.436303	−0.218152	−	0.975915i	$-0.570003\pi$
$257$	−6.99447	−0.436303	−0.218152	+	0.975915i	$0.570003\pi$
$258$	12.1210	0.754618
$259$	0	0
$260$	−12.7273	−0.789313
$261$	2.37481	0.146997
$262$	4.16821	0.257513
$263$	3.22711	0.198992	0.0994960	−	0.995038i	$-0.468277\pi$
$263$	3.22711	0.198992	0.0994960	+	0.995038i	$0.468277\pi$
$264$	0	0
$265$	−43.7393	−2.68688
$266$	0	0
$267$	8.32025	0.509191
$268$	5.90968	0.360991
$269$	−11.1383	−0.679112	−0.339556	−	0.940586i	$-0.610277\pi$
$269$	−11.1383	−0.679112	−0.339556	+	0.940586i	$0.610277\pi$
$270$	2.85056	0.173479
$271$	3.94320	0.239532	0.119766	−	0.992802i	$-0.461786\pi$
$271$	3.94320	0.239532	0.119766	+	0.992802i	$0.461786\pi$
$272$	17.1722	1.04122
$273$	0	0
$274$	−4.96231	−0.299784
$275$	0	0
$276$	−4.89289	−0.294517
$277$	−26.7624	−1.60800	−0.804000	−	0.594630i	$-0.797299\pi$
$277$	−26.7624	−1.60800	−0.804000	+	0.594630i	$0.797299\pi$
$278$	2.06126	0.123626
$279$	14.5340	0.870126
$280$	0	0
$281$	3.19505	0.190601	0.0953003	−	0.995449i	$-0.469619\pi$
$281$	3.19505	0.190601	0.0953003	+	0.995449i	$0.469619\pi$
$282$	−12.3625	−0.736176
$283$	4.65272	0.276576	0.138288	−	0.990392i	$-0.455840\pi$
$283$	4.65272	0.276576	0.138288	+	0.990392i	$0.455840\pi$
$284$	−0.808479	−0.0479744
$285$	−46.2875	−2.74183
$286$	0	0
$287$	0	0
$288$	−12.9318	−0.762012
$289$	45.0533	2.65019
$290$	2.01093	0.118086
$291$	0.381223	0.0223477
$292$	25.0867	1.46809
$293$	15.6199	0.912525	0.456263	−	0.889845i	$-0.349188\pi$
$293$	15.6199	0.912525	0.456263	+	0.889845i	$0.349188\pi$
$294$	0	0
$295$	13.9014	0.809372
$296$	−3.48103	−0.202331
$297$	0	0
$298$	0.412457	0.0238930
$299$	2.65329	0.153444
$300$	30.5531	1.76399
$301$	0	0
$302$	−3.63939	−0.209423
$303$	28.2178	1.62107
$304$	−12.1275	−0.695558
$305$	9.06265	0.518926
$306$	−10.6792	−0.610487
$307$	18.9815	1.08333	0.541666	−	0.840594i	$-0.317794\pi$
$307$	18.9815	1.08333	0.541666	+	0.840594i	$0.317794\pi$
$308$	0	0
$309$	−15.0118	−0.853993
$310$	12.3070	0.698992
$311$	17.5896	0.997417	0.498709	−	0.866770i	$-0.333808\pi$
$311$	17.5896	0.997417	0.498709	+	0.866770i	$0.333808\pi$
$312$	10.2345	0.579412
$313$	18.0021	1.01754	0.508769	−	0.860903i	$-0.330101\pi$
$313$	18.0021	1.01754	0.508769	+	0.860903i	$0.330101\pi$
$314$	2.01308	0.113605
$315$	0	0
$316$	−13.4500	−0.756620
$317$	6.97654	0.391841	0.195921	−	0.980620i	$-0.437230\pi$
$317$	6.97654	0.391841	0.195921	+	0.980620i	$0.437230\pi$
$318$	16.0545	0.900293
$319$	0	0
$320$	4.66755	0.260924
$321$	35.9806	2.00824
$322$	0	0
$323$	−43.8238	−2.43842
$324$	17.5501	0.975005
$325$	−16.5682	−0.919038
$326$	−7.82652	−0.433471
$327$	42.6227	2.35704
$328$	−11.1612	−0.616275
$329$	0	0
$330$	0	0
$331$	15.0208	0.825619	0.412810	−	0.910817i	$-0.364547\pi$
$331$	15.0208	0.825619	0.412810	+	0.910817i	$0.364547\pi$
$332$	7.10586	0.389985
$333$	−4.00216	−0.219317
$334$	−0.333787	−0.0182640
$335$	12.6044	0.688653
$336$	0	0
$337$	−11.4314	−0.622708	−0.311354	−	0.950294i	$-0.600782\pi$
$337$	−11.4314	−0.622708	−0.311354	+	0.950294i	$0.600782\pi$
$338$	4.82594	0.262496
$339$	−2.74059	−0.148848
$340$	47.3938	2.57029
$341$	0	0
$342$	7.54192	0.407820
$343$	0	0
$344$	19.2019	1.03530
$345$	−10.4358	−0.561843
$346$	−2.42525	−0.130382
$347$	−9.14713	−0.491044	−0.245522	−	0.969391i	$-0.578959\pi$
$347$	−9.14713	−0.491044	−0.245522	+	0.969391i	$0.578959\pi$
$348$	3.86846	0.207371
$349$	−28.2369	−1.51149	−0.755743	−	0.654868i	$-0.772724\pi$
$349$	−28.2369	−1.51149	−0.755743	+	0.654868i	$0.772724\pi$
$350$	0	0
$351$	−2.97365	−0.158722
$352$	0	0
$353$	−5.54734	−0.295255	−0.147627	−	0.989043i	$-0.547164\pi$
$353$	−5.54734	−0.295255	−0.147627	+	0.989043i	$0.547164\pi$
$354$	−5.10252	−0.271196
$355$	−1.72436	−0.0915194
$356$	6.01643	0.318870
$357$	0	0
$358$	7.61992	0.402725
$359$	0.333903	0.0176227	0.00881137	−	0.999961i	$-0.497195\pi$
$359$	0.333903	0.0176227	0.00881137	+	0.999961i	$0.497195\pi$
$360$	−17.8689	−0.941772
$361$	11.9496	0.628925
$362$	−11.4407	−0.601308
$363$	0	0
$364$	0	0
$365$	53.5060	2.80063
$366$	−3.32645	−0.173876
$367$	−8.11154	−0.423419	−0.211710	−	0.977333i	$-0.567903\pi$
$367$	−8.11154	−0.423419	−0.211710	+	0.977333i	$0.567903\pi$
$368$	−2.73420	−0.142530
$369$	−12.8321	−0.668013
$370$	−3.38894	−0.176182
$371$	0	0
$372$	23.6752	1.22750
$373$	−34.2270	−1.77221	−0.886104	−	0.463486i	$-0.846599\pi$
$373$	−34.2270	−1.77221	−0.886104	+	0.463486i	$0.846599\pi$
$374$	0	0
$375$	23.5638	1.21683
$376$	−19.5845	−1.00999
$377$	−2.09777	−0.108041
$378$	0	0
$379$	−21.9557	−1.12779	−0.563895	−	0.825846i	$-0.690698\pi$
$379$	−21.9557	−1.12779	−0.563895	+	0.825846i	$0.690698\pi$
$380$	−33.4708	−1.71702
$381$	−15.1171	−0.774475
$382$	−11.4138	−0.583981
$383$	−7.77526	−0.397297	−0.198649	−	0.980071i	$-0.563655\pi$
$383$	−7.77526	−0.397297	−0.198649	+	0.980071i	$0.563655\pi$
$384$	−26.7979	−1.36752
$385$	0	0
$386$	1.04803	0.0533433
$387$	22.0765	1.12221
$388$	0.275665	0.0139948
$389$	5.77816	0.292964	0.146482	−	0.989213i	$-0.453205\pi$
$389$	5.77816	0.292964	0.146482	+	0.989213i	$0.453205\pi$
$390$	9.96369	0.504531
$391$	−9.88031	−0.499669
$392$	0	0
$393$	17.1021	0.862687
$394$	5.25414	0.264700
$395$	−28.6867	−1.44338
$396$	0	0
$397$	20.0863	1.00810	0.504052	−	0.863673i	$-0.331842\pi$
$397$	20.0863	1.00810	0.504052	+	0.863673i	$0.331842\pi$
$398$	0.562449	0.0281930
$399$	0	0
$400$	17.0735	0.853673
$401$	−13.8268	−0.690479	−0.345240	−	0.938515i	$-0.612202\pi$
$401$	−13.8268	−0.690479	−0.345240	+	0.938515i	$0.612202\pi$
$402$	−4.62645	−0.230747
$403$	−12.8385	−0.639530
$404$	20.4045	1.01516
$405$	37.4316	1.85999
$406$	0	0
$407$	0	0
$408$	−38.1110	−1.88678
$409$	−5.33474	−0.263786	−0.131893	−	0.991264i	$-0.542106\pi$
$409$	−5.33474	−0.263786	−0.131893	+	0.991264i	$0.542106\pi$
$410$	−10.8659	−0.536630
$411$	−20.3603	−1.00430
$412$	−10.8552	−0.534796
$413$	0	0
$414$	1.70037	0.0835685
$415$	15.1557	0.743963
$416$	11.4232	0.560068
$417$	8.45732	0.414157
$418$	0	0
$419$	8.67099	0.423605	0.211803	−	0.977312i	$-0.432067\pi$
$419$	8.67099	0.423605	0.211803	+	0.977312i	$0.432067\pi$
$420$	0	0
$421$	29.7894	1.45184	0.725922	−	0.687777i	$-0.241413\pi$
$421$	29.7894	1.45184	0.725922	+	0.687777i	$0.241413\pi$
$422$	9.33148	0.454249
$423$	−22.5164	−1.09479
$424$	25.4334	1.23515
$425$	61.6966	2.99272
$426$	0.632926	0.0306654
$427$	0	0
$428$	26.0178	1.25762
$429$	0	0
$430$	18.6939	0.901498
$431$	−12.6486	−0.609263	−0.304631	−	0.952470i	$-0.598533\pi$
$431$	−12.6486	−0.609263	−0.304631	+	0.952470i	$0.598533\pi$
$432$	3.06434	0.147433
$433$	−6.32172	−0.303802	−0.151901	−	0.988396i	$-0.548540\pi$
$433$	−6.32172	−0.303802	−0.151901	+	0.988396i	$0.548540\pi$
$434$	0	0
$435$	8.25082	0.395597
$436$	30.8208	1.47605
$437$	6.97775	0.333791
$438$	−19.6394	−0.938406
$439$	−22.2462	−1.06175	−0.530876	−	0.847450i	$-0.678137\pi$
$439$	−22.2462	−1.06175	−0.530876	+	0.847450i	$0.678137\pi$
$440$	0	0
$441$	0	0
$442$	9.43336	0.448699
$443$	−14.3049	−0.679645	−0.339823	−	0.940490i	$-0.610367\pi$
$443$	−14.3049	−0.679645	−0.339823	+	0.940490i	$0.610367\pi$
$444$	−6.51936	−0.309395
$445$	12.8321	0.608300
$446$	14.8364	0.702522
$447$	1.69230	0.0800432
$448$	0	0
$449$	21.9196	1.03445	0.517224	−	0.855850i	$-0.326965\pi$
$449$	21.9196	1.03445	0.517224	+	0.855850i	$0.326965\pi$
$450$	−10.6178	−0.500526
$451$	0	0
$452$	−1.98174	−0.0932133
$453$	−14.9324	−0.701584
$454$	−10.3708	−0.486726
$455$	0	0
$456$	26.9151	1.26041
$457$	25.9527	1.21401	0.607007	−	0.794697i	$-0.292370\pi$
$457$	25.9527	1.21401	0.607007	+	0.794697i	$0.292370\pi$
$458$	7.59520	0.354900
$459$	11.0733	0.516856
$460$	−7.54618	−0.351843
$461$	18.5060	0.861910	0.430955	−	0.902374i	$-0.358177\pi$
$461$	18.5060	0.861910	0.430955	+	0.902374i	$0.358177\pi$
$462$	0	0
$463$	−8.76243	−0.407224	−0.203612	−	0.979052i	$-0.565268\pi$
$463$	−8.76243	−0.407224	−0.203612	+	0.979052i	$0.565268\pi$
$464$	2.16174	0.100356
$465$	50.4955	2.34167
$466$	−2.51280	−0.116403
$467$	−24.3313	−1.12592	−0.562960	−	0.826484i	$-0.690337\pi$
$467$	−24.3313	−1.12592	−0.562960	+	0.826484i	$0.690337\pi$
$468$	8.50853	0.393307
$469$	0	0
$470$	−19.0664	−0.879466
$471$	8.25964	0.380584
$472$	−8.08334	−0.372066
$473$	0	0
$474$	10.5294	0.483634
$475$	−43.5718	−1.99921
$476$	0	0
$477$	29.2409	1.33885
$478$	5.17352	0.236631
$479$	3.43695	0.157038	0.0785190	−	0.996913i	$-0.474981\pi$
$479$	3.43695	0.157038	0.0785190	+	0.996913i	$0.474981\pi$
$480$	−44.9290	−2.05072
$481$	3.53528	0.161195
$482$	−9.72940	−0.443162
$483$	0	0
$484$	0	0
$485$	0.587951	0.0266975
$486$	−11.3520	−0.514937
$487$	−29.6366	−1.34296	−0.671482	−	0.741021i	$-0.734342\pi$
$487$	−29.6366	−1.34296	−0.671482	+	0.741021i	$0.734342\pi$
$488$	−5.26971	−0.238549
$489$	−32.1121	−1.45216
$490$	0	0
$491$	38.5364	1.73913	0.869563	−	0.493823i	$-0.164401\pi$
$491$	38.5364	1.73913	0.869563	+	0.493823i	$0.164401\pi$
$492$	−20.9030	−0.942379
$493$	7.81166	0.351820
$494$	−6.66210	−0.299742
$495$	0	0
$496$	13.2300	0.594044
$497$	0	0
$498$	−5.56290	−0.249279
$499$	−40.8755	−1.82984	−0.914920	−	0.403636i	$-0.867746\pi$
$499$	−40.8755	−1.82984	−0.914920	+	0.403636i	$0.867746\pi$
$500$	17.0392	0.762015
$501$	−1.36952	−0.0611858
$502$	−10.0749	−0.449663
$503$	26.9049	1.19963	0.599814	−	0.800139i	$-0.295241\pi$
$503$	26.9049	1.19963	0.599814	+	0.800139i	$0.295241\pi$
$504$	0	0
$505$	43.5195	1.93659
$506$	0	0
$507$	19.8007	0.879382
$508$	−10.9313	−0.484999
$509$	39.9683	1.77156	0.885781	−	0.464103i	$-0.153623\pi$
$509$	39.9683	1.77156	0.885781	+	0.464103i	$0.153623\pi$
$510$	−37.1027	−1.64294
$511$	0	0
$512$	−20.8530	−0.921580
$513$	−7.82025	−0.345273
$514$	3.95952	0.174647
$515$	−23.1524	−1.02021
$516$	35.9617	1.58313
$517$	0	0
$518$	0	0
$519$	−9.95076	−0.436790
$520$	15.7843	0.692189
$521$	−35.9052	−1.57303	−0.786517	−	0.617568i	$-0.788118\pi$
$521$	−35.9052	−1.57303	−0.786517	+	0.617568i	$0.788118\pi$
$522$	−1.34436	−0.0588411
$523$	−12.1191	−0.529931	−0.264966	−	0.964258i	$-0.585361\pi$
$523$	−12.1191	−0.529931	−0.264966	+	0.964258i	$0.585361\pi$
$524$	12.3667	0.540240
$525$	0	0
$526$	−1.82684	−0.0796541
$527$	47.8078	2.08254
$528$	0	0
$529$	−21.4268	−0.931601
$530$	24.7605	1.07553
$531$	−9.29347	−0.403302
$532$	0	0
$533$	11.3352	0.490980
$534$	−4.71003	−0.203823
$535$	55.4919	2.39913
$536$	−7.32916	−0.316572
$537$	31.2644	1.34916
$538$	6.30529	0.271840
$539$	0	0
$540$	8.45732	0.363945
$541$	−38.0198	−1.63460	−0.817299	−	0.576214i	$-0.804530\pi$
$541$	−38.0198	−1.63460	−0.817299	+	0.576214i	$0.804530\pi$
$542$	−2.23222	−0.0958818
$543$	−46.9409	−2.01443
$544$	−42.5376	−1.82378
$545$	65.7359	2.81582
$546$	0	0
$547$	21.8268	0.933248	0.466624	−	0.884456i	$-0.345470\pi$
$547$	21.8268	0.933248	0.466624	+	0.884456i	$0.345470\pi$
$548$	−14.7227	−0.628922
$549$	−6.05862	−0.258576
$550$	0	0
$551$	−5.51682	−0.235024
$552$	6.06815	0.258277
$553$	0	0
$554$	15.1500	0.643662
$555$	−13.9048	−0.590224
$556$	6.11555	0.259357
$557$	21.0982	0.893961	0.446981	−	0.894544i	$-0.352499\pi$
$557$	21.0982	0.893961	0.446981	+	0.894544i	$0.352499\pi$
$558$	−8.22756	−0.348301
$559$	−19.5011	−0.824809
$560$	0	0
$561$	0	0
$562$	−1.80869	−0.0762951
$563$	−36.7160	−1.54739	−0.773696	−	0.633557i	$-0.781594\pi$
$563$	−36.7160	−1.54739	−0.773696	+	0.633557i	$0.781594\pi$
$564$	−36.6783	−1.54443
$565$	−4.22674	−0.177820
$566$	−2.63387	−0.110710
$567$	0	0
$568$	1.00267	0.0420712
$569$	21.9167	0.918797	0.459399	−	0.888230i	$-0.348065\pi$
$569$	21.9167	0.918797	0.459399	+	0.888230i	$0.348065\pi$
$570$	26.2030	1.09752
$571$	11.8342	0.495247	0.247623	−	0.968856i	$-0.420350\pi$
$571$	11.8342	0.495247	0.247623	+	0.968856i	$0.420350\pi$
$572$	0	0
$573$	−46.8307	−1.95638
$574$	0	0
$575$	−9.82351	−0.409669
$576$	−3.12038	−0.130016
$577$	30.6197	1.27471	0.637357	−	0.770568i	$-0.280028\pi$
$577$	30.6197	1.27471	0.637357	+	0.770568i	$0.280028\pi$
$578$	−25.5043	−1.06084
$579$	4.30005	0.178704
$580$	5.96623	0.247734
$581$	0	0
$582$	−0.215808	−0.00894551
$583$	0	0
$584$	−31.1125	−1.28744
$585$	18.1473	0.750300
$586$	−8.84231	−0.365273
$587$	40.9866	1.69170	0.845848	−	0.533424i	$-0.179095\pi$
$587$	40.9866	1.69170	0.845848	+	0.533424i	$0.179095\pi$
$588$	0	0
$589$	−33.7632	−1.39119
$590$	−7.86949	−0.323982
$591$	21.5577	0.886763
$592$	−3.64309	−0.149730
$593$	−6.69626	−0.274983	−0.137491	−	0.990503i	$-0.543904\pi$
$593$	−6.69626	−0.274983	−0.137491	+	0.990503i	$0.543904\pi$
$594$	0	0
$595$	0	0
$596$	1.22372	0.0501255
$597$	2.30772	0.0944487
$598$	−1.50201	−0.0614216
$599$	17.9097	0.731770	0.365885	−	0.930660i	$-0.380766\pi$
$599$	17.9097	0.731770	0.365885	+	0.930660i	$0.380766\pi$
$600$	−37.8919	−1.54693
$601$	−21.3193	−0.869630	−0.434815	−	0.900520i	$-0.643186\pi$
$601$	−21.3193	−0.869630	−0.434815	+	0.900520i	$0.643186\pi$
$602$	0	0
$603$	−8.42638	−0.343149
$604$	−10.7977	−0.439353
$605$	0	0
$606$	−15.9739	−0.648894
$607$	−6.67801	−0.271052	−0.135526	−	0.990774i	$-0.543272\pi$
$607$	−6.67801	−0.271052	−0.135526	+	0.990774i	$0.543272\pi$
$608$	30.0412	1.21833
$609$	0	0
$610$	−5.13030	−0.207720
$611$	19.8897	0.804651
$612$	−31.6840	−1.28075
$613$	−24.7905	−1.00128	−0.500639	−	0.865656i	$-0.666902\pi$
$613$	−24.7905	−1.00128	−0.500639	+	0.865656i	$0.666902\pi$
$614$	−10.7453	−0.433644
$615$	−44.5827	−1.79775
$616$	0	0
$617$	23.0708	0.928795	0.464397	−	0.885627i	$-0.346271\pi$
$617$	23.0708	0.928795	0.464397	+	0.885627i	$0.346271\pi$
$618$	8.49808	0.341843
$619$	−27.1443	−1.09102	−0.545512	−	0.838103i	$-0.683665\pi$
$619$	−27.1443	−1.09102	−0.545512	+	0.838103i	$0.683665\pi$
$620$	36.5137	1.46643
$621$	−1.76312	−0.0707515
$622$	−9.95736	−0.399254
$623$	0	0
$624$	10.7109	0.428780
$625$	−2.81866	−0.112746
$626$	−10.1908	−0.407308
$627$	0	0
$628$	5.97261	0.238333
$629$	−13.1647	−0.524909
$630$	0	0
$631$	0.850302	0.0338500	0.0169250	−	0.999857i	$-0.494612\pi$
$631$	0.850302	0.0338500	0.0169250	+	0.999857i	$0.494612\pi$
$632$	16.6806	0.663519
$633$	38.2869	1.52177
$634$	−3.94937	−0.156849
$635$	−23.3148	−0.925219
$636$	47.6322	1.88874
$637$	0	0
$638$	0	0
$639$	1.15278	0.0456032
$640$	−41.3297	−1.63370
$641$	40.6878	1.60707	0.803536	−	0.595256i	$-0.202949\pi$
$641$	40.6878	1.60707	0.803536	+	0.595256i	$0.202949\pi$
$642$	−20.3683	−0.803874
$643$	3.89995	0.153799	0.0768994	−	0.997039i	$-0.475498\pi$
$643$	3.89995	0.153799	0.0768994	+	0.997039i	$0.475498\pi$
$644$	0	0
$645$	76.7006	3.02008
$646$	24.8083	0.976070
$647$	21.3898	0.840918	0.420459	−	0.907311i	$-0.361869\pi$
$647$	21.3898	0.840918	0.420459	+	0.907311i	$0.361869\pi$
$648$	−21.7656	−0.855032
$649$	0	0
$650$	9.37913	0.367880
$651$	0	0
$652$	−23.2205	−0.909386
$653$	−9.70937	−0.379957	−0.189978	−	0.981788i	$-0.560842\pi$
$653$	−9.70937	−0.379957	−0.189978	+	0.981788i	$0.560842\pi$
$654$	−24.1284	−0.943494
$655$	26.3761	1.03060
$656$	−11.6808	−0.456060
$657$	−35.7702	−1.39553
$658$	0	0
$659$	−45.3120	−1.76511	−0.882553	−	0.470212i	$-0.844177\pi$
$659$	−45.3120	−1.76511	−0.882553	+	0.470212i	$0.844177\pi$
$660$	0	0
$661$	−25.1885	−0.979719	−0.489859	−	0.871802i	$-0.662952\pi$
$661$	−25.1885	−0.979719	−0.489859	+	0.871802i	$0.662952\pi$
$662$	−8.50317	−0.330485
$663$	38.7049	1.50318
$664$	−8.81267	−0.341998
$665$	0	0
$666$	2.26559	0.0877900
$667$	−1.24380	−0.0481600
$668$	−0.990314	−0.0383164
$669$	60.8734	2.35350
$670$	−7.13526	−0.275659
$671$	0	0
$672$	0	0
$673$	24.5134	0.944924	0.472462	−	0.881351i	$-0.343365\pi$
$673$	24.5134	0.944924	0.472462	+	0.881351i	$0.343365\pi$
$674$	6.47122	0.249262
$675$	11.0096	0.423760
$676$	14.3181	0.550695
$677$	9.46644	0.363825	0.181912	−	0.983315i	$-0.441771\pi$
$677$	9.46644	0.363825	0.181912	+	0.983315i	$0.441771\pi$
$678$	1.55143	0.0595822
$679$	0	0
$680$	−58.7776	−2.25402
$681$	−42.5512	−1.63057
$682$	0	0
$683$	−1.90836	−0.0730215	−0.0365107	−	0.999333i	$-0.511624\pi$
$683$	−1.90836	−0.0730215	−0.0365107	+	0.999333i	$0.511624\pi$
$684$	22.3761	0.855573
$685$	−31.4012	−1.19978
$686$	0	0
$687$	31.1630	1.18894
$688$	20.0958	0.766146
$689$	−25.8297	−0.984034
$690$	5.90761	0.224899
$691$	5.38145	0.204720	0.102360	−	0.994747i	$-0.467361\pi$
$691$	5.38145	0.204720	0.102360	+	0.994747i	$0.467361\pi$
$692$	−7.19547	−0.273531
$693$	0	0
$694$	5.17812	0.196559
$695$	13.0435	0.494768
$696$	−4.79766	−0.181855
$697$	−42.2098	−1.59881
$698$	15.9847	0.605029
$699$	−10.3100	−0.389959
$700$	0	0
$701$	−41.3569	−1.56203	−0.781014	−	0.624513i	$-0.785297\pi$
$701$	−41.3569	−1.56203	−0.781014	+	0.624513i	$0.785297\pi$
$702$	1.68336	0.0635344
$703$	9.29725	0.350653
$704$	0	0
$705$	−78.2290	−2.94628
$706$	3.14031	0.118187
$707$	0	0
$708$	−15.1387	−0.568946
$709$	−11.3771	−0.427276	−0.213638	−	0.976913i	$-0.568531\pi$
$709$	−11.3771	−0.427276	−0.213638	+	0.976913i	$0.568531\pi$
$710$	0.976146	0.0366341
$711$	19.1778	0.719223
$712$	−7.46156	−0.279634
$713$	−7.61210	−0.285076
$714$	0	0
$715$	0	0
$716$	22.6075	0.844884
$717$	21.2269	0.792732
$718$	−0.189020	−0.00705416
$719$	26.5668	0.990776	0.495388	−	0.868672i	$-0.335026\pi$
$719$	26.5668	0.990776	0.495388	+	0.868672i	$0.335026\pi$
$720$	−18.7008	−0.696936
$721$	0	0
$722$	−6.76456	−0.251751
$723$	−39.9196	−1.48463
$724$	−33.9433	−1.26149
$725$	7.76675	0.288450
$726$	0	0
$727$	20.1922	0.748889	0.374444	−	0.927249i	$-0.377833\pi$
$727$	20.1922	0.748889	0.374444	+	0.927249i	$0.377833\pi$
$728$	0	0
$729$	−15.2291	−0.564039
$730$	−30.2893	−1.12106
$731$	72.6181	2.68588
$732$	−9.86924	−0.364778
$733$	−33.9684	−1.25465	−0.627326	−	0.778757i	$-0.715851\pi$
$733$	−33.9684	−1.25465	−0.627326	+	0.778757i	$0.715851\pi$
$734$	4.59188	0.169489
$735$	0	0
$736$	6.77296	0.249655
$737$	0	0
$738$	7.26416	0.267397
$739$	3.64752	0.134176	0.0670881	−	0.997747i	$-0.478629\pi$
$739$	3.64752	0.134176	0.0670881	+	0.997747i	$0.478629\pi$
$740$	−10.0546	−0.369616
$741$	−27.3345	−1.00416
$742$	0	0
$743$	−13.0411	−0.478432	−0.239216	−	0.970966i	$-0.576890\pi$
$743$	−13.0411	−0.478432	−0.239216	+	0.970966i	$0.576890\pi$
$744$	−29.3619	−1.07646
$745$	2.61000	0.0956229
$746$	19.3757	0.709393
$747$	−10.1320	−0.370710
$748$	0	0
$749$	0	0
$750$	−13.3393	−0.487082
$751$	28.6269	1.04461	0.522305	−	0.852759i	$-0.325072\pi$
$751$	28.6269	1.04461	0.522305	+	0.852759i	$0.325072\pi$
$752$	−20.4963	−0.747422
$753$	−41.3370	−1.50640
$754$	1.18753	0.0432473
$755$	−23.0298	−0.838141
$756$	0	0
$757$	−41.8901	−1.52252	−0.761261	−	0.648446i	$-0.775419\pi$
$757$	−41.8901	−1.52252	−0.761261	+	0.648446i	$0.775419\pi$
$758$	12.4290	0.451441
$759$	0	0
$760$	41.5104	1.50574
$761$	22.7774	0.825682	0.412841	−	0.910803i	$-0.364537\pi$
$761$	22.7774	0.825682	0.412841	+	0.910803i	$0.364537\pi$
$762$	8.55770	0.310013
$763$	0	0
$764$	−33.8636	−1.22514
$765$	−67.5770	−2.44325
$766$	4.40152	0.159033
$767$	8.20932	0.296421
$768$	9.11725	0.328990
$769$	−13.3517	−0.481475	−0.240738	−	0.970590i	$-0.577389\pi$
$769$	−13.3517	−0.481475	−0.240738	+	0.970590i	$0.577389\pi$
$770$	0	0
$771$	16.2458	0.585080
$772$	3.10940	0.111910
$773$	−17.9214	−0.644588	−0.322294	−	0.946640i	$-0.604454\pi$
$773$	−17.9214	−0.644588	−0.322294	+	0.946640i	$0.604454\pi$
$774$	−12.4973	−0.449207
$775$	47.5330	1.70744
$776$	−0.341879	−0.0122728
$777$	0	0
$778$	−3.27097	−0.117270
$779$	29.8097	1.06804
$780$	29.5613	1.05846
$781$	0	0
$782$	5.59317	0.200011
$783$	1.39397	0.0498165
$784$	0	0
$785$	12.7386	0.454661
$786$	−9.68136	−0.345323
$787$	−8.61899	−0.307234	−0.153617	−	0.988130i	$-0.549092\pi$
$787$	−8.61899	−0.307234	−0.153617	+	0.988130i	$0.549092\pi$
$788$	15.5885	0.555317
$789$	−7.49550	−0.266847
$790$	16.2393	0.577768
$791$	0	0
$792$	0	0
$793$	5.35184	0.190049
$794$	−11.3707	−0.403532
$795$	101.592	3.60309
$796$	1.66873	0.0591466
$797$	−8.15199	−0.288758	−0.144379	−	0.989522i	$-0.546118\pi$
$797$	−8.15199	−0.288758	−0.144379	+	0.989522i	$0.546118\pi$
$798$	0	0
$799$	−74.0652	−2.62024
$800$	−42.2931	−1.49529
$801$	−8.57860	−0.303110
$802$	7.82727	0.276390
$803$	0	0
$804$	−13.7262	−0.484087
$805$	0	0
$806$	7.26776	0.255996
$807$	25.8705	0.910685
$808$	−25.3056	−0.890247
$809$	−17.8331	−0.626978	−0.313489	−	0.949592i	$-0.601498\pi$
$809$	−17.8331	−0.626978	−0.313489	+	0.949592i	$0.601498\pi$
$810$	−21.1897	−0.744531
$811$	−33.8231	−1.18769	−0.593845	−	0.804580i	$-0.702391\pi$
$811$	−33.8231	−1.18769	−0.593845	+	0.804580i	$0.702391\pi$
$812$	0	0
$813$	−9.15875	−0.321211
$814$	0	0
$815$	−49.5257	−1.73481
$816$	−39.8853	−1.39626
$817$	−51.2850	−1.79423
$818$	3.01996	0.105590
$819$	0	0
$820$	−32.2381	−1.12580
$821$	−18.0163	−0.628772	−0.314386	−	0.949295i	$-0.601799\pi$
$821$	−18.0163	−0.628772	−0.314386	+	0.949295i	$0.601799\pi$
$822$	11.5258	0.402009
$823$	−6.20675	−0.216354	−0.108177	−	0.994132i	$-0.534501\pi$
$823$	−6.20675	−0.216354	−0.108177	+	0.994132i	$0.534501\pi$
$824$	13.4625	0.468990
$825$	0	0
$826$	0	0
$827$	−14.4737	−0.503299	−0.251650	−	0.967818i	$-0.580973\pi$
$827$	−14.4737	−0.503299	−0.251650	+	0.967818i	$0.580973\pi$
$828$	5.04482	0.175320
$829$	−17.3725	−0.603371	−0.301685	−	0.953408i	$-0.597549\pi$
$829$	−17.3725	−0.603371	−0.301685	+	0.953408i	$0.597549\pi$
$830$	−8.57952	−0.297799
$831$	62.1603	2.15632
$832$	2.75637	0.0955598
$833$	0	0
$834$	−4.78762	−0.165782
$835$	−2.11218	−0.0730951
$836$	0	0
$837$	8.53120	0.294881
$838$	−4.90858	−0.169564
$839$	1.93117	0.0666713	0.0333357	−	0.999444i	$-0.489387\pi$
$839$	1.93117	0.0666713	0.0333357	+	0.999444i	$0.489387\pi$
$840$	0	0
$841$	−28.0166	−0.966090
$842$	−16.8635	−0.581156
$843$	−7.42104	−0.255594
$844$	27.6856	0.952977
$845$	30.5382	1.05055
$846$	12.7464	0.438229
$847$	0	0
$848$	26.6174	0.914046
$849$	−10.8067	−0.370886
$850$	−34.9259	−1.19795
$851$	2.09612	0.0718539
$852$	1.87783	0.0643334
$853$	1.10204	0.0377332	0.0188666	−	0.999822i	$-0.493994\pi$
$853$	1.10204	0.0377332	0.0188666	+	0.999822i	$0.493994\pi$
$854$	0	0
$855$	47.7248	1.63215
$856$	−32.2672	−1.10287
$857$	−21.7149	−0.741766	−0.370883	−	0.928680i	$-0.620945\pi$
$857$	−21.7149	−0.741766	−0.370883	+	0.928680i	$0.620945\pi$
$858$	0	0
$859$	39.6186	1.35177	0.675885	−	0.737007i	$-0.263762\pi$
$859$	39.6186	1.35177	0.675885	+	0.737007i	$0.263762\pi$
$860$	55.4628	1.89127
$861$	0	0
$862$	7.16029	0.243880
$863$	2.29774	0.0782161	0.0391081	−	0.999235i	$-0.487548\pi$
$863$	2.29774	0.0782161	0.0391081	+	0.999235i	$0.487548\pi$
$864$	−7.59074	−0.258242
$865$	−15.3468	−0.521807
$866$	3.57867	0.121608
$867$	−104.644	−3.55389
$868$	0	0
$869$	0	0
$870$	−4.67073	−0.158352
$871$	7.44338	0.252209
$872$	−38.2238	−1.29442
$873$	−0.393061	−0.0133031
$874$	−3.95005	−0.133612
$875$	0	0
$876$	−58.2681	−1.96870
$877$	−16.2876	−0.549992	−0.274996	−	0.961445i	$-0.588676\pi$
$877$	−16.2876	−0.549992	−0.274996	+	0.961445i	$0.588676\pi$
$878$	12.5934	0.425006
$879$	−36.2799	−1.22369
$880$	0	0
$881$	23.8815	0.804588	0.402294	−	0.915511i	$-0.368213\pi$
$881$	23.8815	0.804588	0.402294	+	0.915511i	$0.368213\pi$
$882$	0	0
$883$	34.7760	1.17031	0.585153	−	0.810923i	$-0.301035\pi$
$883$	34.7760	1.17031	0.585153	+	0.810923i	$0.301035\pi$
$884$	27.9878	0.941333
$885$	−32.2884	−1.08536
$886$	8.09788	0.272054
$887$	−20.9659	−0.703965	−0.351983	−	0.936006i	$-0.614492\pi$
$887$	−20.9659	−0.703965	−0.351983	+	0.936006i	$0.614492\pi$
$888$	8.08528	0.271324
$889$	0	0
$890$	−7.26416	−0.243495
$891$	0	0
$892$	44.0180	1.47383
$893$	52.3069	1.75038
$894$	−0.958000	−0.0320403
$895$	48.2183	1.61176
$896$	0	0
$897$	−6.16271	−0.205767
$898$	−12.4085	−0.414077
$899$	6.01835	0.200723
$900$	−31.5019	−1.05006
$901$	96.1846	3.20437
$902$	0	0
$903$	0	0
$904$	2.45775	0.0817435
$905$	−72.3957	−2.40652
$906$	8.45310	0.280835
$907$	−32.4206	−1.07651	−0.538254	−	0.842783i	$-0.680916\pi$
$907$	−32.4206	−1.07651	−0.538254	+	0.842783i	$0.680916\pi$
$908$	−30.7691	−1.02111
$909$	−29.0940	−0.964986
$910$	0	0
$911$	31.2801	1.03636	0.518178	−	0.855273i	$-0.326610\pi$
$911$	31.2801	1.03636	0.518178	+	0.855273i	$0.326610\pi$
$912$	28.1681	0.932739
$913$	0	0
$914$	−14.6916	−0.485955
$915$	−21.0495	−0.695876
$916$	22.5342	0.744551
$917$	0	0
$918$	−6.26849	−0.206891
$919$	12.0241	0.396638	0.198319	−	0.980138i	$-0.436452\pi$
$919$	12.0241	0.396638	0.198319	+	0.980138i	$0.436452\pi$
$920$	9.35875	0.308549
$921$	−44.0877	−1.45274
$922$	−10.4761	−0.345012
$923$	−1.01830	−0.0335177
$924$	0	0
$925$	−13.0890	−0.430363
$926$	4.96034	0.163007
$927$	15.4780	0.508363
$928$	−5.35490	−0.175783
$929$	46.3451	1.52053	0.760267	−	0.649611i	$-0.225068\pi$
$929$	46.3451	1.52053	0.760267	+	0.649611i	$0.225068\pi$
$930$	−28.5851	−0.937343
$931$	0	0
$932$	−7.45522	−0.244204
$933$	−40.8549	−1.33753
$934$	13.7738	0.450692
$935$	0	0
$936$	−10.5522	−0.344911
$937$	−47.5786	−1.55433	−0.777163	−	0.629299i	$-0.783342\pi$
$937$	−47.5786	−1.55433	−0.777163	+	0.629299i	$0.783342\pi$
$938$	0	0
$939$	−41.8129	−1.36451
$940$	−56.5680	−1.84504
$941$	51.5693	1.68111	0.840556	−	0.541725i	$-0.182229\pi$
$941$	51.5693	1.68111	0.840556	+	0.541725i	$0.182229\pi$
$942$	−4.67572	−0.152343
$943$	6.72076	0.218858
$944$	−8.45967	−0.275339
$945$	0	0
$946$	0	0
$947$	17.2878	0.561779	0.280889	−	0.959740i	$-0.409371\pi$
$947$	17.2878	0.561779	0.280889	+	0.959740i	$0.409371\pi$
$948$	31.2398	1.01462
$949$	31.5973	1.02569
$950$	24.6657	0.800260
$951$	−16.2042	−0.525457
$952$	0	0
$953$	−4.25417	−0.137806	−0.0689031	−	0.997623i	$-0.521950\pi$
$953$	−4.25417	−0.137806	−0.0689031	+	0.997623i	$0.521950\pi$
$954$	−16.5530	−0.535924
$955$	−72.2258	−2.33717
$956$	15.3493	0.496432
$957$	0	0
$958$	−1.94563	−0.0628604
$959$	0	0
$960$	−10.8412	−0.349898
$961$	5.83268	0.188151
$962$	−2.00130	−0.0645244
$963$	−37.0978	−1.19546
$964$	−28.8662	−0.929717
$965$	6.63186	0.213487
$966$	0	0
$967$	−5.87353	−0.188880	−0.0944399	−	0.995531i	$-0.530106\pi$
$967$	−5.87353	−0.188880	−0.0944399	+	0.995531i	$0.530106\pi$
$968$	0	0
$969$	101.788	3.26991
$970$	−0.332835	−0.0106867
$971$	−25.2611	−0.810667	−0.405333	−	0.914169i	$-0.632845\pi$
$971$	−25.2611	−0.810667	−0.405333	+	0.914169i	$0.632845\pi$
$972$	−33.6803	−1.08029
$973$	0	0
$974$	16.7771	0.537572
$975$	38.4824	1.23242
$976$	−5.51505	−0.176532
$977$	−25.4971	−0.815724	−0.407862	−	0.913043i	$-0.633726\pi$
$977$	−25.4971	−0.815724	−0.407862	+	0.913043i	$0.633726\pi$
$978$	18.1784	0.581282
$979$	0	0
$980$	0	0
$981$	−43.9462	−1.40309
$982$	−21.8152	−0.696150
$983$	37.0719	1.18241	0.591205	−	0.806521i	$-0.298653\pi$
$983$	37.0719	1.18241	0.591205	+	0.806521i	$0.298653\pi$
$984$	25.9238	0.826420
$985$	33.2478	1.05936
$986$	−4.42212	−0.140829
$987$	0	0
$988$	−19.7658	−0.628834
$989$	−11.5625	−0.367665
$990$	0	0
$991$	18.7006	0.594044	0.297022	−	0.954871i	$-0.404007\pi$
$991$	18.7006	0.594044	0.297022	+	0.954871i	$0.404007\pi$
$992$	−32.7723	−1.04052
$993$	−34.8884	−1.10715
$994$	0	0
$995$	3.55914	0.112832
$996$	−16.5046	−0.522967
$997$	32.8555	1.04054	0.520272	−	0.854001i	$-0.325831\pi$
$997$	32.8555	1.04054	0.520272	+	0.854001i	$0.325831\pi$
$998$	23.1393	0.732462
$999$	−2.34920	−0.0743255

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bv.1.5		10
7.6	odd	2	inner	5929.2.a.bv.1.6		10
11.10	odd	2		539.2.a.l.1.5	✓	10
33.32	even	2		4851.2.a.cg.1.6		10
44.43	even	2		8624.2.a.df.1.9		10
77.10	even	6		539.2.e.o.177.5		20
77.32	odd	6		539.2.e.o.177.6		20
77.54	even	6		539.2.e.o.67.5		20
77.65	odd	6		539.2.e.o.67.6		20
77.76	even	2		539.2.a.l.1.6	yes	10
231.230	odd	2		4851.2.a.cg.1.5		10
308.307	odd	2		8624.2.a.df.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.a.l.1.5	✓	10	11.10	odd	2
539.2.a.l.1.6	yes	10	77.76	even	2
539.2.e.o.67.5		20	77.54	even	6
539.2.e.o.67.6		20	77.65	odd	6
539.2.e.o.177.5		20	77.10	even	6
539.2.e.o.177.6		20	77.32	odd	6
4851.2.a.cg.1.5		10	231.230	odd	2
4851.2.a.cg.1.6		10	33.32	even	2
5929.2.a.bv.1.5		10	1.1	even	1	trivial
5929.2.a.bv.1.6		10	7.6	odd	2	inner
8624.2.a.df.1.2		10	308.307	odd	2
8624.2.a.df.1.9		10	44.43	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q-0.566092 q^{2} -2.32267 q^{3} -1.67954 q^{4} -3.58219 q^{5} +1.31484 q^{6} +2.08296 q^{8} +2.39479 q^{9} +O(q^{10})\)	\(q-0.566092 q^{2} -2.32267 q^{3} -1.67954 q^{4} -3.58219 q^{5} +1.31484 q^{6} +2.08296 q^{8} +2.39479 q^{9} +2.02785 q^{10} +3.90101 q^{12} -2.11542 q^{13} +8.32025 q^{15} +2.17993 q^{16} +7.87739 q^{17} -1.35567 q^{18} -5.56323 q^{19} +6.01643 q^{20} -1.25426 q^{23} -4.83802 q^{24} +7.83210 q^{25} +1.19752 q^{26} +1.40570 q^{27} +0.991656 q^{29} -4.71003 q^{30} +6.06899 q^{31} -5.39996 q^{32} -4.45933 q^{34} -4.02214 q^{36} -1.67120 q^{37} +3.14930 q^{38} +4.91342 q^{39} -7.46156 q^{40} -5.35834 q^{41} +9.21855 q^{43} -8.57860 q^{45} +0.710028 q^{46} -9.40225 q^{47} -5.06326 q^{48} -4.43369 q^{50} -18.2966 q^{51} +3.55293 q^{52} +12.2102 q^{53} -0.795757 q^{54} +12.9216 q^{57} -0.561369 q^{58} -3.88070 q^{59} -13.9742 q^{60} -2.52992 q^{61} -3.43561 q^{62} -1.30299 q^{64} +7.57784 q^{65} -3.51863 q^{67} -13.2304 q^{68} +2.91323 q^{69} +0.481369 q^{71} +4.98825 q^{72} -14.9367 q^{73} +0.946051 q^{74} -18.1914 q^{75} +9.34367 q^{76} -2.78145 q^{78} +8.00813 q^{79} -7.80894 q^{80} -10.4494 q^{81} +3.03332 q^{82} -4.23084 q^{83} -28.2183 q^{85} -5.21855 q^{86} -2.30329 q^{87} -3.58219 q^{89} +4.85628 q^{90} +2.10658 q^{92} -14.0963 q^{93} +5.32254 q^{94} +19.9286 q^{95} +12.5423 q^{96} -0.164132 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 18 q^{4} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 18 * q^4 + 6 * q^8 + 22 * q^9	\( 10 q - 2 q^{2} + 18 q^{4} + 6 q^{8} + 22 q^{9} + 8 q^{15} + 42 q^{16} - 6 q^{18} + 4 q^{23} + 18 q^{25} - 12 q^{29} + 4 q^{30} + 30 q^{32} - 2 q^{36} + 40 q^{37} + 16 q^{39} + 8 q^{43} - 44 q^{46} + 62 q^{50} + 16 q^{53} + 8 q^{57} - 28 q^{58} + 36 q^{60} + 106 q^{64} + 32 q^{65} - 4 q^{67} + 36 q^{71} + 90 q^{72} + 28 q^{74} - 112 q^{78} - 8 q^{79} - 6 q^{81} - 88 q^{85} + 32 q^{86} - 52 q^{92} + 44 q^{93} + 64 q^{95}+O(q^{100}) \) 10 * q - 2 * q^2 + 18 * q^4 + 6 * q^8 + 22 * q^9 + 8 * q^15 + 42 * q^16 - 6 * q^18 + 4 * q^23 + 18 * q^25 - 12 * q^29 + 4 * q^30 + 30 * q^32 - 2 * q^36 + 40 * q^37 + 16 * q^39 + 8 * q^43 - 44 * q^46 + 62 * q^50 + 16 * q^53 + 8 * q^57 - 28 * q^58 + 36 * q^60 + 106 * q^64 + 32 * q^65 - 4 * q^67 + 36 * q^71 + 90 * q^72 + 28 * q^74 - 112 * q^78 - 8 * q^79 - 6 * q^81 - 88 * q^85 + 32 * q^86 - 52 * q^92 + 44 * q^93 + 64 * q^95

Introduction

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