LMFDB - Embedded newform 961.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(1,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("961.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$961 = 31^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	961.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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x - 1$ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	961.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} -2.61803 q^{5} -0.618034 q^{6} +3.00000 q^{7} +2.23607 q^{8} -2.00000 q^{9} +1.61803 q^{10} +0.763932 q^{11} -1.61803 q^{12} -4.85410 q^{13} -1.85410 q^{14} -2.61803 q^{15} +1.85410 q^{16} -0.236068 q^{17} +1.23607 q^{18} +5.00000 q^{19} +4.23607 q^{20} +3.00000 q^{21} -0.472136 q^{22} +5.47214 q^{23} +2.23607 q^{24} +1.85410 q^{25} +3.00000 q^{26} -5.00000 q^{27} -4.85410 q^{28} +8.61803 q^{29} +1.61803 q^{30} -5.61803 q^{32} +0.763932 q^{33} +0.145898 q^{34} -7.85410 q^{35} +3.23607 q^{36} -0.236068 q^{37} -3.09017 q^{38} -4.85410 q^{39} -5.85410 q^{40} +6.47214 q^{41} -1.85410 q^{42} +4.61803 q^{43} -1.23607 q^{44} +5.23607 q^{45} -3.38197 q^{46} -3.38197 q^{47} +1.85410 q^{48} +2.00000 q^{49} -1.14590 q^{50} -0.236068 q^{51} +7.85410 q^{52} +12.7082 q^{53} +3.09017 q^{54} -2.00000 q^{55} +6.70820 q^{56} +5.00000 q^{57} -5.32624 q^{58} +9.47214 q^{59} +4.23607 q^{60} +6.94427 q^{61} -6.00000 q^{63} -0.236068 q^{64} +12.7082 q^{65} -0.472136 q^{66} -4.23607 q^{67} +0.381966 q^{68} +5.47214 q^{69} +4.85410 q^{70} +0.0901699 q^{71} -4.47214 q^{72} +8.56231 q^{73} +0.145898 q^{74} +1.85410 q^{75} -8.09017 q^{76} +2.29180 q^{77} +3.00000 q^{78} -4.85410 q^{80} +1.00000 q^{81} -4.00000 q^{82} +4.09017 q^{83} -4.85410 q^{84} +0.618034 q^{85} -2.85410 q^{86} +8.61803 q^{87} +1.70820 q^{88} +6.38197 q^{89} -3.23607 q^{90} -14.5623 q^{91} -8.85410 q^{92} +2.09017 q^{94} -13.0902 q^{95} -5.61803 q^{96} -5.29180 q^{97} -1.23607 q^{98} -1.52786 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + q^{6} + 6 q^{7} - 4 q^{9} + q^{10} + 6 q^{11} - q^{12} - 3 q^{13} + 3 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 2 q^{18} + 10 q^{19} + 4 q^{20} + 6 q^{21}+ \cdots - 12 q^{99}+O(q^{100})$ 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + q^6 + 6 * q^7 - 4 * q^9 + q^10 + 6 * q^11 - q^12 - 3 * q^13 + 3 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 2 * q^18 + 10 * q^19 + 4 * q^20 + 6 * q^21 + 8 * q^22 + 2 * q^23 - 3 * q^25 + 6 * q^26 - 10 * q^27 - 3 * q^28 + 15 * q^29 + q^30 - 9 * q^32 + 6 * q^33 + 7 * q^34 - 9 * q^35 + 2 * q^36 + 4 * q^37 + 5 * q^38 - 3 * q^39 - 5 * q^40 + 4 * q^41 + 3 * q^42 + 7 * q^43 + 2 * q^44 + 6 * q^45 - 9 * q^46 - 9 * q^47 - 3 * q^48 + 4 * q^49 - 9 * q^50 + 4 * q^51 + 9 * q^52 + 12 * q^53 - 5 * q^54 - 4 * q^55 + 10 * q^57 + 5 * q^58 + 10 * q^59 + 4 * q^60 - 4 * q^61 - 12 * q^63 + 4 * q^64 + 12 * q^65 + 8 * q^66 - 4 * q^67 + 3 * q^68 + 2 * q^69 + 3 * q^70 - 11 * q^71 - 3 * q^73 + 7 * q^74 - 3 * q^75 - 5 * q^76 + 18 * q^77 + 6 * q^78 - 3 * q^80 + 2 * q^81 - 8 * q^82 - 3 * q^83 - 3 * q^84 - q^85 + q^86 + 15 * q^87 - 10 * q^88 + 15 * q^89 - 2 * q^90 - 9 * q^91 - 11 * q^92 - 7 * q^94 - 15 * q^95 - 9 * q^96 - 24 * q^97 + 2 * q^98 - 12 * q^99

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	−1.61803	−0.809017
$5$	−2.61803	−1.17082	−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803	−1.17082	−0.585410	+	0.810737i	$0.699067\pi$
$6$	−0.618034	−0.252311
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	2.23607	0.790569
$9$	−2.00000	−0.666667
$10$	1.61803	0.511667
$11$	0.763932	0.230334	0.115167	−	0.993346i	$-0.463260\pi$
$11$	0.763932	0.230334	0.115167	+	0.993346i	$0.463260\pi$
$12$	−1.61803	−0.467086
$13$	−4.85410	−1.34629	−0.673143	−	0.739512i	$-0.735056\pi$
$13$	−4.85410	−1.34629	−0.673143	+	0.739512i	$0.735056\pi$
$14$	−1.85410	−0.495530
$15$	−2.61803	−0.675973
$16$	1.85410	0.463525
$17$	−0.236068	−0.0572549	−0.0286274	−	0.999590i	$-0.509114\pi$
$17$	−0.236068	−0.0572549	−0.0286274	+	0.999590i	$0.509114\pi$
$18$	1.23607	0.291344
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	4.23607	0.947214
$21$	3.00000	0.654654
$22$	−0.472136	−0.100660
$23$	5.47214	1.14102	0.570510	−	0.821291i	$-0.306746\pi$
$23$	5.47214	1.14102	0.570510	+	0.821291i	$0.306746\pi$
$24$	2.23607	0.456435
$25$	1.85410	0.370820
$26$	3.00000	0.588348
$27$	−5.00000	−0.962250
$28$	−4.85410	−0.917339
$29$	8.61803	1.60033	0.800164	−	0.599781i	$-0.204746\pi$
$29$	8.61803	1.60033	0.800164	+	0.599781i	$0.204746\pi$
$30$	1.61803	0.295411
$31$	0	0
$31$	0	0
$32$	−5.61803	−0.993137
$33$	0.763932	0.132983
$34$	0.145898	0.0250213
$35$	−7.85410	−1.32759
$36$	3.23607	0.539345
$37$	−0.236068	−0.0388093	−0.0194047	−	0.999812i	$-0.506177\pi$
$37$	−0.236068	−0.0388093	−0.0194047	+	0.999812i	$0.506177\pi$
$38$	−3.09017	−0.501292
$39$	−4.85410	−0.777278
$40$	−5.85410	−0.925615
$41$	6.47214	1.01078	0.505389	−	0.862892i	$-0.331349\pi$
$41$	6.47214	1.01078	0.505389	+	0.862892i	$0.331349\pi$
$42$	−1.85410	−0.286094
$43$	4.61803	0.704244	0.352122	−	0.935954i	$-0.385460\pi$
$43$	4.61803	0.704244	0.352122	+	0.935954i	$0.385460\pi$
$44$	−1.23607	−0.186344
$45$	5.23607	0.780547
$46$	−3.38197	−0.498644
$47$	−3.38197	−0.493310	−0.246655	−	0.969103i	$-0.579332\pi$
$47$	−3.38197	−0.493310	−0.246655	+	0.969103i	$0.579332\pi$
$48$	1.85410	0.267617
$49$	2.00000	0.285714
$50$	−1.14590	−0.162054
$51$	−0.236068	−0.0330561
$52$	7.85410	1.08917
$53$	12.7082	1.74561	0.872803	−	0.488073i	$-0.162300\pi$
$53$	12.7082	1.74561	0.872803	+	0.488073i	$0.162300\pi$
$54$	3.09017	0.420519
$55$	−2.00000	−0.269680
$56$	6.70820	0.896421
$57$	5.00000	0.662266
$58$	−5.32624	−0.699369
$59$	9.47214	1.23317	0.616584	−	0.787289i	$-0.288516\pi$
$59$	9.47214	1.23317	0.616584	+	0.787289i	$0.288516\pi$
$60$	4.23607	0.546874
$61$	6.94427	0.889123	0.444561	−	0.895748i	$-0.353360\pi$
$61$	6.94427	0.889123	0.444561	+	0.895748i	$0.353360\pi$
$62$	0	0
$63$	−6.00000	−0.755929
$64$	−0.236068	−0.0295085
$65$	12.7082	1.57626
$66$	−0.472136	−0.0581159
$67$	−4.23607	−0.517518	−0.258759	−	0.965942i	$-0.583314\pi$
$67$	−4.23607	−0.517518	−0.258759	+	0.965942i	$0.583314\pi$
$68$	0.381966	0.0463202
$69$	5.47214	0.658768
$70$	4.85410	0.580176
$71$	0.0901699	0.0107012	0.00535060	−	0.999986i	$-0.498297\pi$
$71$	0.0901699	0.0107012	0.00535060	+	0.999986i	$0.498297\pi$
$72$	−4.47214	−0.527046
$73$	8.56231	1.00214	0.501071	−	0.865406i	$-0.332940\pi$
$73$	8.56231	1.00214	0.501071	+	0.865406i	$0.332940\pi$
$74$	0.145898	0.0169603
$75$	1.85410	0.214093
$76$	−8.09017	−0.928006
$77$	2.29180	0.261174
$78$	3.00000	0.339683
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−4.85410	−0.542705
$81$	1.00000	0.111111
$82$	−4.00000	−0.441726
$83$	4.09017	0.448954	0.224477	−	0.974479i	$-0.427933\pi$
$83$	4.09017	0.448954	0.224477	+	0.974479i	$0.427933\pi$
$84$	−4.85410	−0.529626
$85$	0.618034	0.0670352
$86$	−2.85410	−0.307766
$87$	8.61803	0.923950
$88$	1.70820	0.182095
$89$	6.38197	0.676487	0.338244	−	0.941059i	$-0.390167\pi$
$89$	6.38197	0.676487	0.338244	+	0.941059i	$0.390167\pi$
$90$	−3.23607	−0.341112
$91$	−14.5623	−1.52654
$92$	−8.85410	−0.923104
$93$	0	0
$94$	2.09017	0.215585
$95$	−13.0902	−1.34302
$96$	−5.61803	−0.573388
$97$	−5.29180	−0.537300	−0.268650	−	0.963238i	$-0.586578\pi$
$97$	−5.29180	−0.537300	−0.268650	+	0.963238i	$0.586578\pi$
$98$	−1.23607	−0.124862
$99$	−1.52786	−0.153556
$100$	−3.00000	−0.300000
$101$	4.76393	0.474029	0.237014	−	0.971506i	$-0.423831\pi$
$101$	4.76393	0.474029	0.237014	+	0.971506i	$0.423831\pi$
$102$	0.145898	0.0144461
$103$	−0.145898	−0.0143758	−0.00718788	−	0.999974i	$-0.502288\pi$
$103$	−0.145898	−0.0143758	−0.00718788	+	0.999974i	$0.502288\pi$
$104$	−10.8541	−1.06433
$105$	−7.85410	−0.766482
$106$	−7.85410	−0.762858
$107$	1.09017	0.105391	0.0526954	−	0.998611i	$-0.483219\pi$
$107$	1.09017	0.105391	0.0526954	+	0.998611i	$0.483219\pi$
$108$	8.09017	0.778477
$109$	−8.41641	−0.806146	−0.403073	−	0.915168i	$-0.632058\pi$
$109$	−8.41641	−0.806146	−0.403073	+	0.915168i	$0.632058\pi$
$110$	1.23607	0.117854
$111$	−0.236068	−0.0224066
$112$	5.56231	0.525589
$113$	−1.85410	−0.174419	−0.0872096	−	0.996190i	$-0.527795\pi$
$113$	−1.85410	−0.174419	−0.0872096	+	0.996190i	$0.527795\pi$
$114$	−3.09017	−0.289421
$115$	−14.3262	−1.33593
$116$	−13.9443	−1.29469
$117$	9.70820	0.897524
$118$	−5.85410	−0.538914
$119$	−0.708204	−0.0649209
$120$	−5.85410	−0.534404
$121$	−10.4164	−0.946946
$122$	−4.29180	−0.388561
$123$	6.47214	0.583573
$124$	0	0
$125$	8.23607	0.736656
$126$	3.70820	0.330353
$127$	−10.2361	−0.908304	−0.454152	−	0.890924i	$-0.650058\pi$
$127$	−10.2361	−0.908304	−0.454152	+	0.890924i	$0.650058\pi$
$128$	11.3820	1.00603
$129$	4.61803	0.406595
$130$	−7.85410	−0.688850
$131$	0.0901699	0.00787818	0.00393909	−	0.999992i	$-0.498746\pi$
$131$	0.0901699	0.00787818	0.00393909	+	0.999992i	$0.498746\pi$
$132$	−1.23607	−0.107586
$133$	15.0000	1.30066
$134$	2.61803	0.226164
$135$	13.0902	1.12662
$136$	−0.527864	−0.0452640
$137$	6.47214	0.552952	0.276476	−	0.961021i	$-0.410833\pi$
$137$	6.47214	0.552952	0.276476	+	0.961021i	$0.410833\pi$
$138$	−3.38197	−0.287892
$139$	−5.85410	−0.496538	−0.248269	−	0.968691i	$-0.579862\pi$
$139$	−5.85410	−0.496538	−0.248269	+	0.968691i	$0.579862\pi$
$140$	12.7082	1.07404
$141$	−3.38197	−0.284813
$142$	−0.0557281	−0.00467660
$143$	−3.70820	−0.310096
$144$	−3.70820	−0.309017
$145$	−22.5623	−1.87370
$146$	−5.29180	−0.437952
$147$	2.00000	0.164957
$148$	0.381966	0.0313974
$149$	−17.0344	−1.39552	−0.697758	−	0.716334i	$-0.745819\pi$
$149$	−17.0344	−1.39552	−0.697758	+	0.716334i	$0.745819\pi$
$150$	−1.14590	−0.0935622
$151$	19.5066	1.58742	0.793711	−	0.608295i	$-0.208146\pi$
$151$	19.5066	1.58742	0.793711	+	0.608295i	$0.208146\pi$
$152$	11.1803	0.906845
$153$	0.472136	0.0381699
$154$	−1.41641	−0.114137
$155$	0	0
$156$	7.85410	0.628831
$157$	9.70820	0.774799	0.387400	−	0.921912i	$-0.373373\pi$
$157$	9.70820	0.774799	0.387400	+	0.921912i	$0.373373\pi$
$158$	0	0
$159$	12.7082	1.00783
$160$	14.7082	1.16279
$161$	16.4164	1.29379
$162$	−0.618034	−0.0485573
$163$	−12.7082	−0.995383	−0.497692	−	0.867354i	$-0.665819\pi$
$163$	−12.7082	−0.995383	−0.497692	+	0.867354i	$0.665819\pi$
$164$	−10.4721	−0.817736
$165$	−2.00000	−0.155700
$166$	−2.52786	−0.196200
$167$	9.23607	0.714708	0.357354	−	0.933969i	$-0.383679\pi$
$167$	9.23607	0.714708	0.357354	+	0.933969i	$0.383679\pi$
$168$	6.70820	0.517549
$169$	10.5623	0.812485
$170$	−0.381966	−0.0292955
$171$	−10.0000	−0.764719
$172$	−7.47214	−0.569745
$173$	0.909830	0.0691731	0.0345865	−	0.999402i	$-0.488989\pi$
$173$	0.909830	0.0691731	0.0345865	+	0.999402i	$0.488989\pi$
$174$	−5.32624	−0.403781
$175$	5.56231	0.420471
$176$	1.41641	0.106766
$177$	9.47214	0.711969
$178$	−3.94427	−0.295636
$179$	−19.7984	−1.47980	−0.739900	−	0.672717i	$-0.765127\pi$
$179$	−19.7984	−1.47980	−0.739900	+	0.672717i	$0.765127\pi$
$180$	−8.47214	−0.631476
$181$	−17.0000	−1.26360	−0.631800	−	0.775131i	$-0.717684\pi$
$181$	−17.0000	−1.26360	−0.631800	+	0.775131i	$0.717684\pi$
$182$	9.00000	0.667124
$183$	6.94427	0.513335
$184$	12.2361	0.902055
$185$	0.618034	0.0454388
$186$	0	0
$187$	−0.180340	−0.0131878
$188$	5.47214	0.399097
$189$	−15.0000	−1.09109
$190$	8.09017	0.586923
$191$	−16.0902	−1.16424	−0.582122	−	0.813102i	$-0.697777\pi$
$191$	−16.0902	−1.16424	−0.582122	+	0.813102i	$0.697777\pi$
$192$	−0.236068	−0.0170367
$193$	−2.38197	−0.171458	−0.0857288	−	0.996319i	$-0.527322\pi$
$193$	−2.38197	−0.171458	−0.0857288	+	0.996319i	$0.527322\pi$
$194$	3.27051	0.234809
$195$	12.7082	0.910053
$196$	−3.23607	−0.231148
$197$	−16.4164	−1.16962	−0.584810	−	0.811170i	$-0.698831\pi$
$197$	−16.4164	−1.16962	−0.584810	+	0.811170i	$0.698831\pi$
$198$	0.944272	0.0671065
$199$	26.7082	1.89329	0.946647	−	0.322272i	$-0.104446\pi$
$199$	26.7082	1.89329	0.946647	+	0.322272i	$0.104446\pi$
$200$	4.14590	0.293159
$201$	−4.23607	−0.298789
$202$	−2.94427	−0.207158
$203$	25.8541	1.81460
$204$	0.381966	0.0267430
$205$	−16.9443	−1.18344
$206$	0.0901699	0.00628244
$207$	−10.9443	−0.760679
$208$	−9.00000	−0.624038
$209$	3.81966	0.264211
$210$	4.85410	0.334965
$211$	−8.00000	−0.550743	−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000	−0.550743	−0.275371	+	0.961338i	$0.588801\pi$
$212$	−20.5623	−1.41222
$213$	0.0901699	0.00617834
$214$	−0.673762	−0.0460574
$215$	−12.0902	−0.824543
$216$	−11.1803	−0.760726
$217$	0	0
$218$	5.20163	0.352299
$219$	8.56231	0.578587
$220$	3.23607	0.218176
$221$	1.14590	0.0770814
$222$	0.145898	0.00979203
$223$	−0.708204	−0.0474248	−0.0237124	−	0.999719i	$-0.507549\pi$
$223$	−0.708204	−0.0474248	−0.0237124	+	0.999719i	$0.507549\pi$
$224$	−16.8541	−1.12611
$225$	−3.70820	−0.247214
$226$	1.14590	0.0762240
$227$	−20.7426	−1.37674	−0.688369	−	0.725361i	$-0.741673\pi$
$227$	−20.7426	−1.37674	−0.688369	+	0.725361i	$0.741673\pi$
$228$	−8.09017	−0.535785
$229$	7.23607	0.478173	0.239086	−	0.970998i	$-0.423152\pi$
$229$	7.23607	0.478173	0.239086	+	0.970998i	$0.423152\pi$
$230$	8.85410	0.583822
$231$	2.29180	0.150789
$232$	19.2705	1.26517
$233$	18.7984	1.23152	0.615761	−	0.787933i	$-0.288849\pi$
$233$	18.7984	1.23152	0.615761	+	0.787933i	$0.288849\pi$
$234$	−6.00000	−0.392232
$235$	8.85410	0.577578
$236$	−15.3262	−0.997653
$237$	0	0
$238$	0.437694	0.0283715
$239$	13.4164	0.867835	0.433918	−	0.900953i	$-0.357131\pi$
$239$	13.4164	0.867835	0.433918	+	0.900953i	$0.357131\pi$
$240$	−4.85410	−0.313331
$241$	8.52786	0.549328	0.274664	−	0.961540i	$-0.411433\pi$
$241$	8.52786	0.549328	0.274664	+	0.961540i	$0.411433\pi$
$242$	6.43769	0.413831
$243$	16.0000	1.02640
$244$	−11.2361	−0.719316
$245$	−5.23607	−0.334520
$246$	−4.00000	−0.255031
$247$	−24.2705	−1.54430
$248$	0	0
$249$	4.09017	0.259204
$250$	−5.09017	−0.321931
$251$	−0.944272	−0.0596019	−0.0298010	−	0.999556i	$-0.509487\pi$
$251$	−0.944272	−0.0596019	−0.0298010	+	0.999556i	$0.509487\pi$
$252$	9.70820	0.611559
$253$	4.18034	0.262816
$254$	6.32624	0.396943
$255$	0.618034	0.0387028
$256$	−6.56231	−0.410144
$257$	1.41641	0.0883531	0.0441765	−	0.999024i	$-0.485934\pi$
$257$	1.41641	0.0883531	0.0441765	+	0.999024i	$0.485934\pi$
$258$	−2.85410	−0.177689
$259$	−0.708204	−0.0440057
$260$	−20.5623	−1.27522
$261$	−17.2361	−1.06689
$262$	−0.0557281	−0.00344289
$263$	10.7984	0.665856	0.332928	−	0.942952i	$-0.391963\pi$
$263$	10.7984	0.665856	0.332928	+	0.942952i	$0.391963\pi$
$264$	1.70820	0.105133
$265$	−33.2705	−2.04379
$266$	−9.27051	−0.568411
$267$	6.38197	0.390570
$268$	6.85410	0.418681
$269$	1.38197	0.0842600	0.0421300	−	0.999112i	$-0.486586\pi$
$269$	1.38197	0.0842600	0.0421300	+	0.999112i	$0.486586\pi$
$270$	−8.09017	−0.492352
$271$	−9.56231	−0.580869	−0.290434	−	0.956895i	$-0.593800\pi$
$271$	−9.56231	−0.580869	−0.290434	+	0.956895i	$0.593800\pi$
$272$	−0.437694	−0.0265391
$273$	−14.5623	−0.881351
$274$	−4.00000	−0.241649
$275$	1.41641	0.0854126
$276$	−8.85410	−0.532954
$277$	−13.3262	−0.800696	−0.400348	−	0.916363i	$-0.631111\pi$
$277$	−13.3262	−0.800696	−0.400348	+	0.916363i	$0.631111\pi$
$278$	3.61803	0.216995
$279$	0	0
$280$	−17.5623	−1.04955
$281$	19.0344	1.13550	0.567750	−	0.823201i	$-0.307814\pi$
$281$	19.0344	1.13550	0.567750	+	0.823201i	$0.307814\pi$
$282$	2.09017	0.124468
$283$	6.56231	0.390089	0.195044	−	0.980794i	$-0.437515\pi$
$283$	6.56231	0.390089	0.195044	+	0.980794i	$0.437515\pi$
$284$	−0.145898	−0.00865746
$285$	−13.0902	−0.775395
$286$	2.29180	0.135517
$287$	19.4164	1.14611
$288$	11.2361	0.662092
$289$	−16.9443	−0.996722
$290$	13.9443	0.818836
$291$	−5.29180	−0.310211
$292$	−13.8541	−0.810750
$293$	−8.23607	−0.481156	−0.240578	−	0.970630i	$-0.577337\pi$
$293$	−8.23607	−0.481156	−0.240578	+	0.970630i	$0.577337\pi$
$294$	−1.23607	−0.0720889
$295$	−24.7984	−1.44382
$296$	−0.527864	−0.0306815
$297$	−3.81966	−0.221639
$298$	10.5279	0.609863
$299$	−26.5623	−1.53614
$300$	−3.00000	−0.173205
$301$	13.8541	0.798537
$302$	−12.0557	−0.693729
$303$	4.76393	0.273681
$304$	9.27051	0.531700
$305$	−18.1803	−1.04100
$306$	−0.291796	−0.0166809
$307$	6.09017	0.347584	0.173792	−	0.984782i	$-0.444398\pi$
$307$	6.09017	0.347584	0.173792	+	0.984782i	$0.444398\pi$
$308$	−3.70820	−0.211295
$309$	−0.145898	−0.00829985
$310$	0	0
$311$	16.4721	0.934049	0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721	0.934049	0.467025	+	0.884244i	$0.345326\pi$
$312$	−10.8541	−0.614493
$313$	−1.23607	−0.0698667	−0.0349333	−	0.999390i	$-0.511122\pi$
$313$	−1.23607	−0.0698667	−0.0349333	+	0.999390i	$0.511122\pi$
$314$	−6.00000	−0.338600
$315$	15.7082	0.885057
$316$	0	0
$317$	25.8885	1.45405	0.727023	−	0.686613i	$-0.240903\pi$
$317$	25.8885	1.45405	0.727023	+	0.686613i	$0.240903\pi$
$318$	−7.85410	−0.440436
$319$	6.58359	0.368610
$320$	0.618034	0.0345492
$321$	1.09017	0.0608474
$322$	−10.1459	−0.565409
$323$	−1.18034	−0.0656759
$324$	−1.61803	−0.0898908
$325$	−9.00000	−0.499230
$326$	7.85410	0.434998
$327$	−8.41641	−0.465428
$328$	14.4721	0.799090
$329$	−10.1459	−0.559361
$330$	1.23607	0.0680433
$331$	−11.2705	−0.619483	−0.309742	−	0.950821i	$-0.600243\pi$
$331$	−11.2705	−0.619483	−0.309742	+	0.950821i	$0.600243\pi$
$332$	−6.61803	−0.363212
$333$	0.472136	0.0258729
$334$	−5.70820	−0.312339
$335$	11.0902	0.605921
$336$	5.56231	0.303449
$337$	−18.9787	−1.03384	−0.516918	−	0.856035i	$-0.672921\pi$
$337$	−18.9787	−1.03384	−0.516918	+	0.856035i	$0.672921\pi$
$338$	−6.52786	−0.355069
$339$	−1.85410	−0.100701
$340$	−1.00000	−0.0542326
$341$	0	0
$342$	6.18034	0.334195
$343$	−15.0000	−0.809924
$344$	10.3262	0.556753
$345$	−14.3262	−0.771299
$346$	−0.562306	−0.0302298
$347$	−8.12461	−0.436152	−0.218076	−	0.975932i	$-0.569978\pi$
$347$	−8.12461	−0.436152	−0.218076	+	0.975932i	$0.569978\pi$
$348$	−13.9443	−0.747491
$349$	−16.7082	−0.894370	−0.447185	−	0.894442i	$-0.647573\pi$
$349$	−16.7082	−0.894370	−0.447185	+	0.894442i	$0.647573\pi$
$350$	−3.43769	−0.183752
$351$	24.2705	1.29546
$352$	−4.29180	−0.228753
$353$	32.3820	1.72352	0.861759	−	0.507318i	$-0.169363\pi$
$353$	32.3820	1.72352	0.861759	+	0.507318i	$0.169363\pi$
$354$	−5.85410	−0.311142
$355$	−0.236068	−0.0125292
$356$	−10.3262	−0.547290
$357$	−0.708204	−0.0374821
$358$	12.2361	0.646696
$359$	−25.3262	−1.33667	−0.668334	−	0.743861i	$-0.732992\pi$
$359$	−25.3262	−1.33667	−0.668334	+	0.743861i	$0.732992\pi$
$360$	11.7082	0.617077
$361$	6.00000	0.315789
$362$	10.5066	0.552213
$363$	−10.4164	−0.546720
$364$	23.5623	1.23500
$365$	−22.4164	−1.17333
$366$	−4.29180	−0.224336
$367$	36.2705	1.89331	0.946653	−	0.322256i	$-0.104441\pi$
$367$	36.2705	1.89331	0.946653	+	0.322256i	$0.104441\pi$
$368$	10.1459	0.528891
$369$	−12.9443	−0.673852
$370$	−0.381966	−0.0198575
$371$	38.1246	1.97933
$372$	0	0
$373$	−0.347524	−0.0179941	−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524	−0.0179941	−0.00899706	+	0.999960i	$0.502864\pi$
$374$	0.111456	0.00576326
$375$	8.23607	0.425309
$376$	−7.56231	−0.389996
$377$	−41.8328	−2.15450
$378$	9.27051	0.476824
$379$	−18.4164	−0.945987	−0.472994	−	0.881066i	$-0.656827\pi$
$379$	−18.4164	−0.945987	−0.472994	+	0.881066i	$0.656827\pi$
$380$	21.1803	1.08653
$381$	−10.2361	−0.524410
$382$	9.94427	0.508793
$383$	16.8541	0.861204	0.430602	−	0.902542i	$-0.358301\pi$
$383$	16.8541	0.861204	0.430602	+	0.902542i	$0.358301\pi$
$384$	11.3820	0.580834
$385$	−6.00000	−0.305788
$386$	1.47214	0.0749297
$387$	−9.23607	−0.469496
$388$	8.56231	0.434685
$389$	29.0689	1.47385	0.736925	−	0.675974i	$-0.236277\pi$
$389$	29.0689	1.47385	0.736925	+	0.675974i	$0.236277\pi$
$390$	−7.85410	−0.397708
$391$	−1.29180	−0.0653289
$392$	4.47214	0.225877
$393$	0.0901699	0.00454847
$394$	10.1459	0.511143
$395$	0	0
$396$	2.47214	0.124230
$397$	16.2918	0.817662	0.408831	−	0.912610i	$-0.365937\pi$
$397$	16.2918	0.817662	0.408831	+	0.912610i	$0.365937\pi$
$398$	−16.5066	−0.827400
$399$	15.0000	0.750939
$400$	3.43769	0.171885
$401$	29.8328	1.48978	0.744890	−	0.667187i	$-0.232502\pi$
$401$	29.8328	1.48978	0.744890	+	0.667187i	$0.232502\pi$
$402$	2.61803	0.130576
$403$	0	0
$404$	−7.70820	−0.383497
$405$	−2.61803	−0.130091
$406$	−15.9787	−0.793010
$407$	−0.180340	−0.00893912
$408$	−0.527864	−0.0261332
$409$	6.18034	0.305598	0.152799	−	0.988257i	$-0.451171\pi$
$409$	6.18034	0.305598	0.152799	+	0.988257i	$0.451171\pi$
$410$	10.4721	0.517182
$411$	6.47214	0.319247
$412$	0.236068	0.0116302
$413$	28.4164	1.39828
$414$	6.76393	0.332429
$415$	−10.7082	−0.525645
$416$	27.2705	1.33705
$417$	−5.85410	−0.286677
$418$	−2.36068	−0.115465
$419$	4.47214	0.218478	0.109239	−	0.994016i	$-0.465159\pi$
$419$	4.47214	0.218478	0.109239	+	0.994016i	$0.465159\pi$
$420$	12.7082	0.620097
$421$	14.7639	0.719550	0.359775	−	0.933039i	$-0.382853\pi$
$421$	14.7639	0.719550	0.359775	+	0.933039i	$0.382853\pi$
$422$	4.94427	0.240683
$423$	6.76393	0.328874
$424$	28.4164	1.38002
$425$	−0.437694	−0.0212313
$426$	−0.0557281	−0.00270003
$427$	20.8328	1.00817
$428$	−1.76393	−0.0852629
$429$	−3.70820	−0.179034
$430$	7.47214	0.360338
$431$	29.2361	1.40825	0.704126	−	0.710075i	$-0.251339\pi$
$431$	29.2361	1.40825	0.704126	+	0.710075i	$0.251339\pi$
$432$	−9.27051	−0.446028
$433$	−0.583592	−0.0280456	−0.0140228	−	0.999902i	$-0.504464\pi$
$433$	−0.583592	−0.0280456	−0.0140228	+	0.999902i	$0.504464\pi$
$434$	0	0
$435$	−22.5623	−1.08178
$436$	13.6180	0.652186
$437$	27.3607	1.30884
$438$	−5.29180	−0.252852
$439$	41.8328	1.99657	0.998286	−	0.0585295i	$-0.0186412\pi$
$439$	41.8328	1.99657	0.998286	+	0.0585295i	$0.0186412\pi$
$440$	−4.47214	−0.213201
$441$	−4.00000	−0.190476
$442$	−0.708204	−0.0336858
$443$	−41.1246	−1.95389	−0.976945	−	0.213493i	$-0.931516\pi$
$443$	−41.1246	−1.95389	−0.976945	+	0.213493i	$0.931516\pi$
$444$	0.381966	0.0181273
$445$	−16.7082	−0.792045
$446$	0.437694	0.0207254
$447$	−17.0344	−0.805701
$448$	−0.708204	−0.0334595
$449$	−24.0689	−1.13588	−0.567940	−	0.823070i	$-0.692260\pi$
$449$	−24.0689	−1.13588	−0.567940	+	0.823070i	$0.692260\pi$
$450$	2.29180	0.108036
$451$	4.94427	0.232817
$452$	3.00000	0.141108
$453$	19.5066	0.916499
$454$	12.8197	0.601656
$455$	38.1246	1.78731
$456$	11.1803	0.523567
$457$	15.7426	0.736410	0.368205	−	0.929745i	$-0.379972\pi$
$457$	15.7426	0.736410	0.368205	+	0.929745i	$0.379972\pi$
$458$	−4.47214	−0.208969
$459$	1.18034	0.0550935
$460$	23.1803	1.08079
$461$	−10.7426	−0.500335	−0.250167	−	0.968203i	$-0.580486\pi$
$461$	−10.7426	−0.500335	−0.250167	+	0.968203i	$0.580486\pi$
$462$	−1.41641	−0.0658973
$463$	31.1246	1.44648	0.723242	−	0.690595i	$-0.242651\pi$
$463$	31.1246	1.44648	0.723242	+	0.690595i	$0.242651\pi$
$464$	15.9787	0.741793
$465$	0	0
$466$	−11.6180	−0.538195
$467$	−32.7771	−1.51674	−0.758371	−	0.651823i	$-0.774005\pi$
$467$	−32.7771	−1.51674	−0.758371	+	0.651823i	$0.774005\pi$
$468$	−15.7082	−0.726112
$469$	−12.7082	−0.586810
$470$	−5.47214	−0.252411
$471$	9.70820	0.447330
$472$	21.1803	0.974904
$473$	3.52786	0.162211
$474$	0	0
$475$	9.27051	0.425360
$476$	1.14590	0.0525222
$477$	−25.4164	−1.16374
$478$	−8.29180	−0.379258
$479$	−8.94427	−0.408674	−0.204337	−	0.978901i	$-0.565504\pi$
$479$	−8.94427	−0.408674	−0.204337	+	0.978901i	$0.565504\pi$
$480$	14.7082	0.671335
$481$	1.14590	0.0522485
$482$	−5.27051	−0.240065
$483$	16.4164	0.746972
$484$	16.8541	0.766096
$485$	13.8541	0.629082
$486$	−9.88854	−0.448553
$487$	−22.9230	−1.03874	−0.519370	−	0.854550i	$-0.673833\pi$
$487$	−22.9230	−1.03874	−0.519370	+	0.854550i	$0.673833\pi$
$488$	15.5279	0.702913
$489$	−12.7082	−0.574685
$490$	3.23607	0.146191
$491$	27.5967	1.24542	0.622712	−	0.782451i	$-0.286031\pi$
$491$	27.5967	1.24542	0.622712	+	0.782451i	$0.286031\pi$
$492$	−10.4721	−0.472120
$493$	−2.03444	−0.0916267
$494$	15.0000	0.674882
$495$	4.00000	0.179787
$496$	0	0
$497$	0.270510	0.0121340
$498$	−2.52786	−0.113276
$499$	−4.14590	−0.185596	−0.0927979	−	0.995685i	$-0.529581\pi$
$499$	−4.14590	−0.185596	−0.0927979	+	0.995685i	$0.529581\pi$
$500$	−13.3262	−0.595967
$501$	9.23607	0.412637
$502$	0.583592	0.0260470
$503$	13.1459	0.586147	0.293073	−	0.956090i	$-0.405322\pi$
$503$	13.1459	0.586147	0.293073	+	0.956090i	$0.405322\pi$
$504$	−13.4164	−0.597614
$505$	−12.4721	−0.555003
$506$	−2.58359	−0.114855
$507$	10.5623	0.469088
$508$	16.5623	0.734833
$509$	1.90983	0.0846517	0.0423259	−	0.999104i	$-0.486523\pi$
$509$	1.90983	0.0846517	0.0423259	+	0.999104i	$0.486523\pi$
$510$	−0.381966	−0.0169137
$511$	25.6869	1.13632
$512$	−18.7082	−0.826794
$513$	−25.0000	−1.10378
$514$	−0.875388	−0.0386117
$515$	0.381966	0.0168314
$516$	−7.47214	−0.328942
$517$	−2.58359	−0.113626
$518$	0.437694	0.0192312
$519$	0.909830	0.0399371
$520$	28.4164	1.24614
$521$	31.0689	1.36115	0.680576	−	0.732677i	$-0.261729\pi$
$521$	31.0689	1.36115	0.680576	+	0.732677i	$0.261729\pi$
$522$	10.6525	0.466246
$523$	−34.1246	−1.49217	−0.746083	−	0.665853i	$-0.768068\pi$
$523$	−34.1246	−1.49217	−0.746083	+	0.665853i	$0.768068\pi$
$524$	−0.145898	−0.00637359
$525$	5.56231	0.242759
$526$	−6.67376	−0.290990
$527$	0	0
$528$	1.41641	0.0616412
$529$	6.94427	0.301925
$530$	20.5623	0.893169
$531$	−18.9443	−0.822111
$532$	−24.2705	−1.05226
$533$	−31.4164	−1.36080
$534$	−3.94427	−0.170685
$535$	−2.85410	−0.123394
$536$	−9.47214	−0.409134
$537$	−19.7984	−0.854363
$538$	−0.854102	−0.0368230
$539$	1.52786	0.0658098
$540$	−21.1803	−0.911457
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	5.90983	0.253849
$543$	−17.0000	−0.729540
$544$	1.32624	0.0568620
$545$	22.0344	0.943852
$546$	9.00000	0.385164
$547$	−23.7082	−1.01369	−0.506845	−	0.862037i	$-0.669188\pi$
$547$	−23.7082	−1.01369	−0.506845	+	0.862037i	$0.669188\pi$
$548$	−10.4721	−0.447347
$549$	−13.8885	−0.592749
$550$	−0.875388	−0.0373267
$551$	43.0902	1.83570
$552$	12.2361	0.520802
$553$	0	0
$554$	8.23607	0.349917
$555$	0.618034	0.0262341
$556$	9.47214	0.401708
$557$	−35.8885	−1.52065	−0.760323	−	0.649545i	$-0.774959\pi$
$557$	−35.8885	−1.52065	−0.760323	+	0.649545i	$0.774959\pi$
$558$	0	0
$559$	−22.4164	−0.948113
$560$	−14.5623	−0.615370
$561$	−0.180340	−0.00761396
$562$	−11.7639	−0.496232
$563$	−8.56231	−0.360858	−0.180429	−	0.983588i	$-0.557749\pi$
$563$	−8.56231	−0.360858	−0.180429	+	0.983588i	$0.557749\pi$
$564$	5.47214	0.230418
$565$	4.85410	0.204214
$566$	−4.05573	−0.170475
$567$	3.00000	0.125988
$568$	0.201626	0.00846004
$569$	−15.5279	−0.650962	−0.325481	−	0.945549i	$-0.605526\pi$
$569$	−15.5279	−0.650962	−0.325481	+	0.945549i	$0.605526\pi$
$570$	8.09017	0.338860
$571$	−7.00000	−0.292941	−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000	−0.292941	−0.146470	+	0.989215i	$0.546791\pi$
$572$	6.00000	0.250873
$573$	−16.0902	−0.672176
$574$	−12.0000	−0.500870
$575$	10.1459	0.423113
$576$	0.472136	0.0196723
$577$	38.9787	1.62271	0.811353	−	0.584557i	$-0.198732\pi$
$577$	38.9787	1.62271	0.811353	+	0.584557i	$0.198732\pi$
$578$	10.4721	0.435583
$579$	−2.38197	−0.0989911
$580$	36.5066	1.51585
$581$	12.2705	0.509067
$582$	3.27051	0.135567
$583$	9.70820	0.402073
$584$	19.1459	0.792263
$585$	−25.4164	−1.05084
$586$	5.09017	0.210273
$587$	−36.0132	−1.48642	−0.743211	−	0.669057i	$-0.766698\pi$
$587$	−36.0132	−1.48642	−0.743211	+	0.669057i	$0.766698\pi$
$588$	−3.23607	−0.133453
$589$	0	0
$590$	15.3262	0.630971
$591$	−16.4164	−0.675281
$592$	−0.437694	−0.0179891
$593$	6.11146	0.250967	0.125484	−	0.992096i	$-0.459952\pi$
$593$	6.11146	0.250967	0.125484	+	0.992096i	$0.459952\pi$
$594$	2.36068	0.0968599
$595$	1.85410	0.0760108
$596$	27.5623	1.12900
$597$	26.7082	1.09309
$598$	16.4164	0.671317
$599$	29.7984	1.21753	0.608764	−	0.793351i	$-0.291666\pi$
$599$	29.7984	1.21753	0.608764	+	0.793351i	$0.291666\pi$
$600$	4.14590	0.169256
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	−8.56231	−0.348974
$603$	8.47214	0.345012
$604$	−31.5623	−1.28425
$605$	27.2705	1.10870
$606$	−2.94427	−0.119603
$607$	−25.4164	−1.03162	−0.515810	−	0.856703i	$-0.672509\pi$
$607$	−25.4164	−1.03162	−0.515810	+	0.856703i	$0.672509\pi$
$608$	−28.0902	−1.13921
$609$	25.8541	1.04766
$610$	11.2361	0.454935
$611$	16.4164	0.664137
$612$	−0.763932	−0.0308801
$613$	−25.0557	−1.01199	−0.505996	−	0.862536i	$-0.668875\pi$
$613$	−25.0557	−1.01199	−0.505996	+	0.862536i	$0.668875\pi$
$614$	−3.76393	−0.151900
$615$	−16.9443	−0.683259
$616$	5.12461	0.206476
$617$	−14.2361	−0.573123	−0.286561	−	0.958062i	$-0.592512\pi$
$617$	−14.2361	−0.573123	−0.286561	+	0.958062i	$0.592512\pi$
$618$	0.0901699	0.00362717
$619$	40.0000	1.60774	0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000	1.60774	0.803868	+	0.594808i	$0.202772\pi$
$620$	0	0
$621$	−27.3607	−1.09795
$622$	−10.1803	−0.408194
$623$	19.1459	0.767064
$624$	−9.00000	−0.360288
$625$	−30.8328	−1.23331
$626$	0.763932	0.0305329
$627$	3.81966	0.152543
$628$	−15.7082	−0.626826
$629$	0.0557281	0.00222202
$630$	−9.70820	−0.386784
$631$	8.72949	0.347516	0.173758	−	0.984788i	$-0.444409\pi$
$631$	8.72949	0.347516	0.173758	+	0.984788i	$0.444409\pi$
$632$	0	0
$633$	−8.00000	−0.317971
$634$	−16.0000	−0.635441
$635$	26.7984	1.06346
$636$	−20.5623	−0.815348
$637$	−9.70820	−0.384653
$638$	−4.06888	−0.161089
$639$	−0.180340	−0.00713414
$640$	−29.7984	−1.17788
$641$	41.0902	1.62296	0.811482	−	0.584377i	$-0.198661\pi$
$641$	41.0902	1.62296	0.811482	+	0.584377i	$0.198661\pi$
$642$	−0.673762	−0.0265913
$643$	−8.14590	−0.321243	−0.160621	−	0.987016i	$-0.551350\pi$
$643$	−8.14590	−0.321243	−0.160621	+	0.987016i	$0.551350\pi$
$644$	−26.5623	−1.04670
$645$	−12.0902	−0.476050
$646$	0.729490	0.0287014
$647$	29.8885	1.17504	0.587520	−	0.809210i	$-0.300104\pi$
$647$	29.8885	1.17504	0.587520	+	0.809210i	$0.300104\pi$
$648$	2.23607	0.0878410
$649$	7.23607	0.284041
$650$	5.56231	0.218172
$651$	0	0
$652$	20.5623	0.805282
$653$	39.6525	1.55172	0.775861	−	0.630904i	$-0.217316\pi$
$653$	39.6525	1.55172	0.775861	+	0.630904i	$0.217316\pi$
$654$	5.20163	0.203400
$655$	−0.236068	−0.00922394
$656$	12.0000	0.468521
$657$	−17.1246	−0.668095
$658$	6.27051	0.244450
$659$	22.6869	0.883757	0.441878	−	0.897075i	$-0.354312\pi$
$659$	22.6869	0.883757	0.441878	+	0.897075i	$0.354312\pi$
$660$	3.23607	0.125964
$661$	−16.6180	−0.646367	−0.323183	−	0.946336i	$-0.604753\pi$
$661$	−16.6180	−0.646367	−0.323183	+	0.946336i	$0.604753\pi$
$662$	6.96556	0.270724
$663$	1.14590	0.0445030
$664$	9.14590	0.354930
$665$	−39.2705	−1.52285
$666$	−0.291796	−0.0113069
$667$	47.1591	1.82601
$668$	−14.9443	−0.578211
$669$	−0.708204	−0.0273807
$670$	−6.85410	−0.264797
$671$	5.30495	0.204795
$672$	−16.8541	−0.650161
$673$	4.41641	0.170240	0.0851200	−	0.996371i	$-0.472873\pi$
$673$	4.41641	0.170240	0.0851200	+	0.996371i	$0.472873\pi$
$674$	11.7295	0.451803
$675$	−9.27051	−0.356822
$676$	−17.0902	−0.657314
$677$	−28.6525	−1.10120	−0.550602	−	0.834768i	$-0.685602\pi$
$677$	−28.6525	−1.10120	−0.550602	+	0.834768i	$0.685602\pi$
$678$	1.14590	0.0440079
$679$	−15.8754	−0.609241
$680$	1.38197	0.0529960
$681$	−20.7426	−0.794860
$682$	0	0
$683$	10.0557	0.384772	0.192386	−	0.981319i	$-0.438377\pi$
$683$	10.0557	0.384772	0.192386	+	0.981319i	$0.438377\pi$
$684$	16.1803	0.618671
$685$	−16.9443	−0.647407
$686$	9.27051	0.353950
$687$	7.23607	0.276073
$688$	8.56231	0.326435
$689$	−61.6869	−2.35008
$690$	8.85410	0.337070
$691$	3.83282	0.145807	0.0729036	−	0.997339i	$-0.476773\pi$
$691$	3.83282	0.145807	0.0729036	+	0.997339i	$0.476773\pi$
$692$	−1.47214	−0.0559622
$693$	−4.58359	−0.174116
$694$	5.02129	0.190605
$695$	15.3262	0.581357
$696$	19.2705	0.730447
$697$	−1.52786	−0.0578720
$698$	10.3262	0.390854
$699$	18.7984	0.711020
$700$	−9.00000	−0.340168
$701$	−30.0344	−1.13439	−0.567193	−	0.823585i	$-0.691970\pi$
$701$	−30.0344	−1.13439	−0.567193	+	0.823585i	$0.691970\pi$
$702$	−15.0000	−0.566139
$703$	−1.18034	−0.0445174
$704$	−0.180340	−0.00679682
$705$	8.85410	0.333465
$706$	−20.0132	−0.753205
$707$	14.2918	0.537498
$708$	−15.3262	−0.575995
$709$	−4.14590	−0.155702	−0.0778512	−	0.996965i	$-0.524806\pi$
$709$	−4.14590	−0.155702	−0.0778512	+	0.996965i	$0.524806\pi$
$710$	0.145898	0.00547546
$711$	0	0
$712$	14.2705	0.534810
$713$	0	0
$714$	0.437694	0.0163803
$715$	9.70820	0.363066
$716$	32.0344	1.19718
$717$	13.4164	0.501045
$718$	15.6525	0.584145
$719$	41.3820	1.54329	0.771643	−	0.636055i	$-0.219435\pi$
$719$	41.3820	1.54329	0.771643	+	0.636055i	$0.219435\pi$
$720$	9.70820	0.361803
$721$	−0.437694	−0.0163006
$722$	−3.70820	−0.138005
$723$	8.52786	0.317155
$724$	27.5066	1.02227
$725$	15.9787	0.593435
$726$	6.43769	0.238925
$727$	−23.8328	−0.883910	−0.441955	−	0.897037i	$-0.645715\pi$
$727$	−23.8328	−0.883910	−0.441955	+	0.897037i	$0.645715\pi$
$728$	−32.5623	−1.20684
$729$	13.0000	0.481481
$730$	13.8541	0.512763
$731$	−1.09017	−0.0403214
$732$	−11.2361	−0.415297
$733$	27.9443	1.03215	0.516073	−	0.856545i	$-0.327393\pi$
$733$	27.9443	1.03215	0.516073	+	0.856545i	$0.327393\pi$
$734$	−22.4164	−0.827405
$735$	−5.23607	−0.193135
$736$	−30.7426	−1.13319
$737$	−3.23607	−0.119202
$738$	8.00000	0.294484
$739$	−21.7082	−0.798549	−0.399275	−	0.916831i	$-0.630738\pi$
$739$	−21.7082	−0.798549	−0.399275	+	0.916831i	$0.630738\pi$
$740$	−1.00000	−0.0367607
$741$	−24.2705	−0.891599
$742$	−23.5623	−0.864999
$743$	3.43769	0.126117	0.0630584	−	0.998010i	$-0.479915\pi$
$743$	3.43769	0.126117	0.0630584	+	0.998010i	$0.479915\pi$
$744$	0	0
$745$	44.5967	1.63390
$746$	0.214782	0.00786372
$747$	−8.18034	−0.299303
$748$	0.291796	0.0106691
$749$	3.27051	0.119502
$750$	−5.09017	−0.185867
$751$	−39.8328	−1.45352	−0.726760	−	0.686891i	$-0.758975\pi$
$751$	−39.8328	−1.45352	−0.726760	+	0.686891i	$0.758975\pi$
$752$	−6.27051	−0.228662
$753$	−0.944272	−0.0344112
$754$	25.8541	0.941551
$755$	−51.0689	−1.85859
$756$	24.2705	0.882710
$757$	−43.1246	−1.56739	−0.783695	−	0.621145i	$-0.786668\pi$
$757$	−43.1246	−1.56739	−0.783695	+	0.621145i	$0.786668\pi$
$758$	11.3820	0.413412
$759$	4.18034	0.151737
$760$	−29.2705	−1.06175
$761$	−3.50658	−0.127113	−0.0635567	−	0.997978i	$-0.520244\pi$
$761$	−3.50658	−0.127113	−0.0635567	+	0.997978i	$0.520244\pi$
$762$	6.32624	0.229175
$763$	−25.2492	−0.914083
$764$	26.0344	0.941893
$765$	−1.23607	−0.0446901
$766$	−10.4164	−0.376360
$767$	−45.9787	−1.66020
$768$	−6.56231	−0.236797
$769$	−53.7426	−1.93801	−0.969005	−	0.247042i	$-0.920541\pi$
$769$	−53.7426	−1.93801	−0.969005	+	0.247042i	$0.920541\pi$
$770$	3.70820	0.133634
$771$	1.41641	0.0510107
$772$	3.85410	0.138712
$773$	19.0902	0.686626	0.343313	−	0.939221i	$-0.388451\pi$
$773$	19.0902	0.686626	0.343313	+	0.939221i	$0.388451\pi$
$774$	5.70820	0.205177
$775$	0	0
$776$	−11.8328	−0.424773
$777$	−0.708204	−0.0254067
$778$	−17.9656	−0.644096
$779$	32.3607	1.15944
$780$	−20.5623	−0.736249
$781$	0.0688837	0.00246485
$782$	0.798374	0.0285498
$783$	−43.0902	−1.53992
$784$	3.70820	0.132436
$785$	−25.4164	−0.907150
$786$	−0.0557281	−0.00198776
$787$	−31.2918	−1.11543	−0.557716	−	0.830032i	$-0.688322\pi$
$787$	−31.2918	−1.11543	−0.557716	+	0.830032i	$0.688322\pi$
$788$	26.5623	0.946243
$789$	10.7984	0.384432
$790$	0	0
$791$	−5.56231	−0.197773
$792$	−3.41641	−0.121397
$793$	−33.7082	−1.19701
$794$	−10.0689	−0.357331
$795$	−33.2705	−1.17998
$796$	−43.2148	−1.53171
$797$	−9.05573	−0.320770	−0.160385	−	0.987055i	$-0.551274\pi$
$797$	−9.05573	−0.320770	−0.160385	+	0.987055i	$0.551274\pi$
$798$	−9.27051	−0.328172
$799$	0.798374	0.0282444
$800$	−10.4164	−0.368276
$801$	−12.7639	−0.450991
$802$	−18.4377	−0.651058
$803$	6.54102	0.230828
$804$	6.85410	0.241726
$805$	−42.9787	−1.51480
$806$	0	0
$807$	1.38197	0.0486475
$808$	10.6525	0.374753
$809$	−54.7984	−1.92661	−0.963304	−	0.268412i	$-0.913501\pi$
$809$	−54.7984	−1.92661	−0.963304	+	0.268412i	$0.913501\pi$
$810$	1.61803	0.0568519
$811$	42.7771	1.50211	0.751053	−	0.660242i	$-0.229546\pi$
$811$	42.7771	1.50211	0.751053	+	0.660242i	$0.229546\pi$
$812$	−41.8328	−1.46804
$813$	−9.56231	−0.335365
$814$	0.111456	0.00390654
$815$	33.2705	1.16542
$816$	−0.437694	−0.0153224
$817$	23.0902	0.807823
$818$	−3.81966	−0.133551
$819$	29.1246	1.01770
$820$	27.4164	0.957422
$821$	32.4721	1.13329	0.566643	−	0.823964i	$-0.308242\pi$
$821$	32.4721	1.13329	0.566643	+	0.823964i	$0.308242\pi$
$822$	−4.00000	−0.139516
$823$	6.12461	0.213491	0.106745	−	0.994286i	$-0.465957\pi$
$823$	6.12461	0.213491	0.106745	+	0.994286i	$0.465957\pi$
$824$	−0.326238	−0.0113650
$825$	1.41641	0.0493130
$826$	−17.5623	−0.611071
$827$	−2.67376	−0.0929758	−0.0464879	−	0.998919i	$-0.514803\pi$
$827$	−2.67376	−0.0929758	−0.0464879	+	0.998919i	$0.514803\pi$
$828$	17.7082	0.615403
$829$	21.7082	0.753957	0.376979	−	0.926222i	$-0.376963\pi$
$829$	21.7082	0.753957	0.376979	+	0.926222i	$0.376963\pi$
$830$	6.61803	0.229715
$831$	−13.3262	−0.462282
$832$	1.14590	0.0397269
$833$	−0.472136	−0.0163585
$834$	3.61803	0.125282
$835$	−24.1803	−0.836795
$836$	−6.18034	−0.213752
$837$	0	0
$838$	−2.76393	−0.0954784
$839$	11.1803	0.385988	0.192994	−	0.981200i	$-0.438180\pi$
$839$	11.1803	0.385988	0.192994	+	0.981200i	$0.438180\pi$
$840$	−17.5623	−0.605957
$841$	45.2705	1.56105
$842$	−9.12461	−0.314455
$843$	19.0344	0.655581
$844$	12.9443	0.445560
$845$	−27.6525	−0.951274
$846$	−4.18034	−0.143723
$847$	−31.2492	−1.07374
$848$	23.5623	0.809133
$849$	6.56231	0.225218
$850$	0.270510	0.00927841
$851$	−1.29180	−0.0442822
$852$	−0.145898	−0.00499838
$853$	4.00000	0.136957	0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000	0.136957	0.0684787	+	0.997653i	$0.478185\pi$
$854$	−12.8754	−0.440587
$855$	26.1803	0.895349
$856$	2.43769	0.0833187
$857$	−8.18034	−0.279435	−0.139718	−	0.990191i	$-0.544619\pi$
$857$	−8.18034	−0.279435	−0.139718	+	0.990191i	$0.544619\pi$
$858$	2.29180	0.0782406
$859$	−43.2918	−1.47710	−0.738549	−	0.674200i	$-0.764488\pi$
$859$	−43.2918	−1.47710	−0.738549	+	0.674200i	$0.764488\pi$
$860$	19.5623	0.667069
$861$	19.4164	0.661709
$862$	−18.0689	−0.615429
$863$	−2.49342	−0.0848771	−0.0424385	−	0.999099i	$-0.513513\pi$
$863$	−2.49342	−0.0848771	−0.0424385	+	0.999099i	$0.513513\pi$
$864$	28.0902	0.955647
$865$	−2.38197	−0.0809893
$866$	0.360680	0.0122564
$867$	−16.9443	−0.575458
$868$	0	0
$869$	0	0
$870$	13.9443	0.472755
$871$	20.5623	0.696727
$872$	−18.8197	−0.637314
$873$	10.5836	0.358200
$874$	−16.9098	−0.571984
$875$	24.7082	0.835290
$876$	−13.8541	−0.468087
$877$	16.2918	0.550135	0.275067	−	0.961425i	$-0.411300\pi$
$877$	16.2918	0.550135	0.275067	+	0.961425i	$0.411300\pi$
$878$	−25.8541	−0.872534
$879$	−8.23607	−0.277796
$880$	−3.70820	−0.125004
$881$	15.3607	0.517514	0.258757	−	0.965942i	$-0.416687\pi$
$881$	15.3607	0.517514	0.258757	+	0.965942i	$0.416687\pi$
$882$	2.47214	0.0832411
$883$	1.00000	0.0336527	0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000	0.0336527	0.0168263	+	0.999858i	$0.494644\pi$
$884$	−1.85410	−0.0623602
$885$	−24.7984	−0.833588
$886$	25.4164	0.853881
$887$	39.1033	1.31296	0.656481	−	0.754343i	$-0.272044\pi$
$887$	39.1033	1.31296	0.656481	+	0.754343i	$0.272044\pi$
$888$	−0.527864	−0.0177140
$889$	−30.7082	−1.02992
$890$	10.3262	0.346136
$891$	0.763932	0.0255927
$892$	1.14590	0.0383675
$893$	−16.9098	−0.565866
$894$	10.5279	0.352104
$895$	51.8328	1.73258
$896$	34.1459	1.14073
$897$	−26.5623	−0.886890
$898$	14.8754	0.496398
$899$	0	0
$900$	6.00000	0.200000
$901$	−3.00000	−0.0999445
$902$	−3.05573	−0.101745
$903$	13.8541	0.461036
$904$	−4.14590	−0.137891
$905$	44.5066	1.47945
$906$	−12.0557	−0.400525
$907$	52.9230	1.75728	0.878639	−	0.477486i	$-0.158452\pi$
$907$	52.9230	1.75728	0.878639	+	0.477486i	$0.158452\pi$
$908$	33.5623	1.11380
$909$	−9.52786	−0.316019
$910$	−23.5623	−0.781083
$911$	−8.18034	−0.271027	−0.135513	−	0.990776i	$-0.543268\pi$
$911$	−8.18034	−0.271027	−0.135513	+	0.990776i	$0.543268\pi$
$912$	9.27051	0.306977
$913$	3.12461	0.103410
$914$	−9.72949	−0.321823
$915$	−18.1803	−0.601023
$916$	−11.7082	−0.386850
$917$	0.270510	0.00893302
$918$	−0.729490	−0.0240768
$919$	9.87539	0.325759	0.162879	−	0.986646i	$-0.447922\pi$
$919$	9.87539	0.325759	0.162879	+	0.986646i	$0.447922\pi$
$920$	−32.0344	−1.05614
$921$	6.09017	0.200678
$922$	6.63932	0.218654
$923$	−0.437694	−0.0144069
$924$	−3.70820	−0.121991
$925$	−0.437694	−0.0143913
$926$	−19.2361	−0.632136
$927$	0.291796	0.00958384
$928$	−48.4164	−1.58935
$929$	−33.5410	−1.10045	−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410	−1.10045	−0.550223	+	0.835018i	$0.685457\pi$
$930$	0	0
$931$	10.0000	0.327737
$932$	−30.4164	−0.996323
$933$	16.4721	0.539274
$934$	20.2574	0.662841
$935$	0.472136	0.0154405
$936$	21.7082	0.709555
$937$	40.4853	1.32260	0.661298	−	0.750123i	$-0.270006\pi$
$937$	40.4853	1.32260	0.661298	+	0.750123i	$0.270006\pi$
$938$	7.85410	0.256446
$939$	−1.23607	−0.0403376
$940$	−14.3262	−0.467270
$941$	−28.5836	−0.931798	−0.465899	−	0.884838i	$-0.654269\pi$
$941$	−28.5836	−0.931798	−0.465899	+	0.884838i	$0.654269\pi$
$942$	−6.00000	−0.195491
$943$	35.4164	1.15332
$944$	17.5623	0.571604
$945$	39.2705	1.27747
$946$	−2.18034	−0.0708890
$947$	−22.0689	−0.717142	−0.358571	−	0.933502i	$-0.616736\pi$
$947$	−22.0689	−0.717142	−0.358571	+	0.933502i	$0.616736\pi$
$948$	0	0
$949$	−41.5623	−1.34917
$950$	−5.72949	−0.185889
$951$	25.8885	0.839494
$952$	−1.58359	−0.0513245
$953$	−42.2148	−1.36747	−0.683735	−	0.729730i	$-0.739646\pi$
$953$	−42.2148	−1.36747	−0.683735	+	0.729730i	$0.739646\pi$
$954$	15.7082	0.508572
$955$	42.1246	1.36312
$956$	−21.7082	−0.702093
$957$	6.58359	0.212817
$958$	5.52786	0.178597
$959$	19.4164	0.626989
$960$	0.618034	0.0199470
$961$	0	0
$962$	−0.708204	−0.0228334
$963$	−2.18034	−0.0702605
$964$	−13.7984	−0.444416
$965$	6.23607	0.200746
$966$	−10.1459	−0.326439
$967$	−43.6525	−1.40377	−0.701884	−	0.712291i	$-0.747658\pi$
$967$	−43.6525	−1.40377	−0.701884	+	0.712291i	$0.747658\pi$
$968$	−23.2918	−0.748627
$969$	−1.18034	−0.0379180
$970$	−8.56231	−0.274919
$971$	−20.5623	−0.659876	−0.329938	−	0.944003i	$-0.607028\pi$
$971$	−20.5623	−0.659876	−0.329938	+	0.944003i	$0.607028\pi$
$972$	−25.8885	−0.830375
$973$	−17.5623	−0.563022
$974$	14.1672	0.453946
$975$	−9.00000	−0.288231
$976$	12.8754	0.412131
$977$	−6.06888	−0.194161	−0.0970804	−	0.995277i	$-0.530950\pi$
$977$	−6.06888	−0.194161	−0.0970804	+	0.995277i	$0.530950\pi$
$978$	7.85410	0.251146
$979$	4.87539	0.155818
$980$	8.47214	0.270632
$981$	16.8328	0.537430
$982$	−17.0557	−0.544270
$983$	−21.0344	−0.670895	−0.335447	−	0.942059i	$-0.608887\pi$
$983$	−21.0344	−0.670895	−0.335447	+	0.942059i	$0.608887\pi$
$984$	14.4721	0.461355
$985$	42.9787	1.36942
$986$	1.25735	0.0400423
$987$	−10.1459	−0.322947
$988$	39.2705	1.24936
$989$	25.2705	0.803555
$990$	−2.47214	−0.0785696
$991$	17.2705	0.548616	0.274308	−	0.961642i	$-0.411551\pi$
$991$	17.2705	0.548616	0.274308	+	0.961642i	$0.411551\pi$
$992$	0	0
$993$	−11.2705	−0.357659
$994$	−0.167184	−0.00530276
$995$	−69.9230	−2.21671
$996$	−6.61803	−0.209700
$997$	−27.2492	−0.862992	−0.431496	−	0.902115i	$-0.642014\pi$
$997$	−27.2492	−0.862992	−0.431496	+	0.902115i	$0.642014\pi$
$998$	2.56231	0.0811084
$999$	1.18034	0.0373443

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.a.e.1.1		2
3.2	odd	2		8649.2.a.f.1.2		2
31.2	even	5		961.2.d.b.531.1		4
31.3	odd	30		961.2.g.b.846.1		8
31.4	even	5		961.2.d.e.388.1		4
31.5	even	3		961.2.c.d.521.1		4
31.6	odd	6		961.2.c.f.439.1		4
31.7	even	15		961.2.g.g.235.1		8
31.8	even	5		961.2.d.e.374.1		4
31.9	even	15		961.2.g.g.732.1		8
31.10	even	15		961.2.g.c.844.1		8
31.11	odd	30		961.2.g.f.338.1		8
31.12	odd	30		961.2.g.b.547.1		8
31.13	odd	30		961.2.g.b.448.1		8
31.14	even	15		961.2.g.g.816.1		8
31.15	odd	10		31.2.d.a.8.1	yes	4
31.16	even	5		961.2.d.b.628.1		4
31.17	odd	30		961.2.g.f.816.1		8
31.18	even	15		961.2.g.c.448.1		8
31.19	even	15		961.2.g.c.547.1		8
31.20	even	15		961.2.g.g.338.1		8
31.21	odd	30		961.2.g.b.844.1		8
31.22	odd	30		961.2.g.f.732.1		8
31.23	odd	10		961.2.d.f.374.1		4
31.24	odd	30		961.2.g.f.235.1		8
31.25	even	3		961.2.c.d.439.1		4
31.26	odd	6		961.2.c.f.521.1		4
31.27	odd	10		961.2.d.f.388.1		4
31.28	even	15		961.2.g.c.846.1		8
31.29	odd	10		31.2.d.a.4.1	✓	4
31.30	odd	2		961.2.a.d.1.1		2
93.29	even	10		279.2.i.a.190.1		4
93.77	even	10		279.2.i.a.163.1		4
93.92	even	2		8649.2.a.g.1.2		2
124.15	even	10		496.2.n.b.225.1		4
124.91	even	10		496.2.n.b.97.1		4
155.29	odd	10		775.2.k.c.376.1		4
155.77	even	20		775.2.bf.a.349.1		8
155.108	even	20		775.2.bf.a.349.2		8
155.122	even	20		775.2.bf.a.624.2		8
155.139	odd	10		775.2.k.c.101.1		4
155.153	even	20		775.2.bf.a.624.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	31.29	odd	10
31.2.d.a.8.1	yes	4	31.15	odd	10
279.2.i.a.163.1		4	93.77	even	10
279.2.i.a.190.1		4	93.29	even	10
496.2.n.b.97.1		4	124.91	even	10
496.2.n.b.225.1		4	124.15	even	10
775.2.k.c.101.1		4	155.139	odd	10
775.2.k.c.376.1		4	155.29	odd	10
775.2.bf.a.349.1		8	155.77	even	20
775.2.bf.a.349.2		8	155.108	even	20
775.2.bf.a.624.1		8	155.153	even	20
775.2.bf.a.624.2		8	155.122	even	20
961.2.a.d.1.1		2	31.30	odd	2
961.2.a.e.1.1		2	1.1	even	1	trivial
961.2.c.d.439.1		4	31.25	even	3
961.2.c.d.521.1		4	31.5	even	3
961.2.c.f.439.1		4	31.6	odd	6
961.2.c.f.521.1		4	31.26	odd	6
961.2.d.b.531.1		4	31.2	even	5
961.2.d.b.628.1		4	31.16	even	5
961.2.d.e.374.1		4	31.8	even	5
961.2.d.e.388.1		4	31.4	even	5
961.2.d.f.374.1		4	31.23	odd	10
961.2.d.f.388.1		4	31.27	odd	10
961.2.g.b.448.1		8	31.13	odd	30
961.2.g.b.547.1		8	31.12	odd	30
961.2.g.b.844.1		8	31.21	odd	30
961.2.g.b.846.1		8	31.3	odd	30
961.2.g.c.448.1		8	31.18	even	15
961.2.g.c.547.1		8	31.19	even	15
961.2.g.c.844.1		8	31.10	even	15
961.2.g.c.846.1		8	31.28	even	15
961.2.g.f.235.1		8	31.24	odd	30
961.2.g.f.338.1		8	31.11	odd	30
961.2.g.f.732.1		8	31.22	odd	30
961.2.g.f.816.1		8	31.17	odd	30
961.2.g.g.235.1		8	31.7	even	15
961.2.g.g.338.1		8	31.20	even	15
961.2.g.g.732.1		8	31.9	even	15
961.2.g.g.816.1		8	31.14	even	15
8649.2.a.f.1.2		2	3.2	odd	2
8649.2.a.g.1.2		2	93.92	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 $\F_{q}$

Introduction

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	961.2.a.e.1.1

Level	$961$
Weight	$2$
Character	961.1
Self dual	yes
Analytic conductor	$7.674$
Analytic rank	$0$
Dimension	$2$
CM	no
Inner twists	$1$