LMFDB - Embedded newform 725.2.b.e.349.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [725,2,Mod(349,725)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("725.349"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(725, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-2,0,-8,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.6
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	725.349
Dual form			725.2.b.e.349.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.17009i q^{2} +1.70928i q^{3} -2.70928 q^{4} -3.70928 q^{6} +3.70928i q^{7} -1.53919i q^{8} +0.0783777 q^{9} -0.630898 q^{11} -4.63090i q^{12} +4.34017i q^{13} -8.04945 q^{14} -2.07838 q^{16} -1.55252i q^{17} +0.170086i q^{18} +5.70928 q^{19} -6.34017 q^{21} -1.36910i q^{22} -6.63090i q^{23} +2.63090 q^{24} -9.41855 q^{26} +5.26180i q^{27} -10.0494i q^{28} +1.00000 q^{29} -2.29072 q^{31} -7.58864i q^{32} -1.07838i q^{33} +3.36910 q^{34} -0.212347 q^{36} -2.44748i q^{37} +12.3896i q^{38} -7.41855 q^{39} +5.60197 q^{41} -13.7587i q^{42} -12.5464i q^{43} +1.70928 q^{44} +14.3896 q^{46} +2.29072i q^{47} -3.55252i q^{48} -6.75872 q^{49} +2.65368 q^{51} -11.7587i q^{52} -0.921622i q^{53} -11.4186 q^{54} +5.70928 q^{56} +9.75872i q^{57} +2.17009i q^{58} +3.60197 q^{59} -13.0205 q^{61} -4.97107i q^{62} +0.290725i q^{63} +12.3112 q^{64} +2.34017 q^{66} +10.6309i q^{67} +4.20620i q^{68} +11.3340 q^{69} +15.6020 q^{71} -0.120638i q^{72} +10.9444i q^{73} +5.31124 q^{74} -15.4680 q^{76} -2.34017i q^{77} -16.0989i q^{78} +10.2062 q^{79} -8.75872 q^{81} +12.1568i q^{82} +3.12783i q^{83} +17.1773 q^{84} +27.2267 q^{86} +1.70928i q^{87} +0.971071i q^{88} -1.41855 q^{89} -16.0989 q^{91} +17.9649i q^{92} -3.91548i q^{93} -4.97107 q^{94} +12.9711 q^{96} +13.4680i q^{97} -14.6670i q^{98} -0.0494483 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} - 8 q^{6} - 6 q^{9} + 4 q^{11} - 12 q^{14} - 6 q^{16} + 20 q^{19} - 16 q^{21} + 8 q^{24} - 28 q^{26} + 6 q^{29} - 28 q^{31} + 28 q^{34} - 22 q^{36} - 16 q^{39} - 4 q^{41} - 4 q^{44} + 28 q^{46}+ \cdots + 36 q^{99}+O(q^{100}) $ 6 * q - 2 * q^4 - 8 * q^6 - 6 * q^9 + 4 * q^11 - 12 * q^14 - 6 * q^16 + 20 * q^19 - 16 * q^21 + 8 * q^24 - 28 * q^26 + 6 * q^29 - 28 * q^31 + 28 * q^34 - 22 * q^36 - 16 * q^39 - 4 * q^41 - 4 * q^44 + 28 * q^46 + 10 * q^49 - 32 * q^51 - 40 * q^54 + 20 * q^56 - 16 * q^59 - 12 * q^61 + 22 * q^64 - 8 * q^66 - 24 * q^69 + 56 * q^71 - 20 * q^74 - 28 * q^76 + 12 * q^79 - 2 * q^81 + 24 * q^84 + 48 * q^86 + 20 * q^89 - 24 * q^91 + 48 * q^96 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	2.17009i	1.53448i	0.641358	+	0.767241i	$0.278371\pi$
$2$	2.17009i	1.53448i	−0.641358	+	0.767241i	$0.721629\pi$
$3$	1.70928i	0.986851i	0.869788	+	0.493425i	$0.164255\pi$
$3$	1.70928i	0.986851i	−0.869788	+	0.493425i	$0.835745\pi$
$4$	−2.70928	−1.35464
$5$	0	0
$5$	0	0
$6$	−3.70928	−1.51431
$7$	3.70928i	1.40197i	0.713174	+	0.700987i	$0.247257\pi$
$7$	3.70928i	1.40197i	−0.713174	+	0.700987i	$0.752743\pi$
$8$	− 1.53919i	− 0.544185i
$9$	0.0783777	0.0261259
$10$	0	0
$11$	−0.630898	−0.190223	−0.0951114	−	0.995467i	$-0.530321\pi$
$11$	−0.630898	−0.190223	−0.0951114	+	0.995467i	$0.530321\pi$
$12$	− 4.63090i	− 1.33682i
$13$	4.34017i	1.20375i	0.798591	+	0.601874i	$0.205579\pi$
$13$	4.34017i	1.20375i	−0.798591	+	0.601874i	$0.794421\pi$
$14$	−8.04945	−2.15131
$15$	0	0
$16$	−2.07838	−0.519594
$17$	− 1.55252i	− 0.376541i	−0.982117	−	0.188271i	$-0.939712\pi$
$17$	− 1.55252i	− 0.376541i	0.982117	−	0.188271i	$-0.0602882\pi$
$18$	0.170086i	0.0400898i
$19$	5.70928	1.30980	0.654899	−	0.755717i	$-0.272711\pi$
$19$	5.70928	1.30980	0.654899	+	0.755717i	$0.272711\pi$
$20$	0	0
$21$	−6.34017	−1.38354
$22$	− 1.36910i	− 0.291894i
$23$	− 6.63090i	− 1.38264i	−0.722550	−	0.691319i	$-0.757030\pi$
$23$	− 6.63090i	− 1.38264i	0.722550	−	0.691319i	$-0.242970\pi$
$24$	2.63090	0.537030
$25$	0	0
$26$	−9.41855	−1.84713
$27$	5.26180i	1.01263i
$28$	− 10.0494i	− 1.89917i
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−2.29072	−0.411426	−0.205713	−	0.978612i	$-0.565951\pi$
$31$	−2.29072	−0.411426	−0.205713	+	0.978612i	$0.565951\pi$
$32$	− 7.58864i	− 1.34149i
$33$	− 1.07838i	− 0.187721i
$34$	3.36910	0.577796
$35$	0	0
$36$	−0.212347	−0.0353911
$37$	− 2.44748i	− 0.402363i	−0.979554	−	0.201182i	$-0.935522\pi$
$37$	− 2.44748i	− 0.402363i	0.979554	−	0.201182i	$-0.0644781\pi$
$38$	12.3896i	2.00986i
$39$	−7.41855	−1.18792
$40$	0	0
$41$	5.60197	0.874880	0.437440	−	0.899247i	$-0.355885\pi$
$41$	5.60197	0.874880	0.437440	+	0.899247i	$0.355885\pi$
$42$	− 13.7587i	− 2.12302i
$43$	− 12.5464i	− 1.91330i	−0.291233	−	0.956652i	$-0.594065\pi$
$43$	− 12.5464i	− 1.91330i	0.291233	−	0.956652i	$-0.405935\pi$
$44$	1.70928	0.257683
$45$	0	0
$46$	14.3896	2.12163
$47$	2.29072i	0.334137i	0.985945	+	0.167068i	$0.0534300\pi$
$47$	2.29072i	0.334137i	−0.985945	+	0.167068i	$0.946570\pi$
$48$	− 3.55252i	− 0.512762i
$49$	−6.75872	−0.965532
$50$	0	0
$51$	2.65368	0.371590
$52$	− 11.7587i	− 1.63064i
$53$	− 0.921622i	− 0.126595i	−0.997995	−	0.0632973i	$-0.979838\pi$
$53$	− 0.921622i	− 0.126595i	0.997995	−	0.0632973i	$-0.0201616\pi$
$54$	−11.4186	−1.55387
$55$	0	0
$56$	5.70928	0.762934
$57$	9.75872i	1.29257i
$58$	2.17009i	0.284946i
$59$	3.60197	0.468936	0.234468	−	0.972124i	$-0.424665\pi$
$59$	3.60197	0.468936	0.234468	+	0.972124i	$0.424665\pi$
$60$	0	0
$61$	−13.0205	−1.66711	−0.833553	−	0.552439i	$-0.813697\pi$
$61$	−13.0205	−1.66711	−0.833553	+	0.552439i	$0.813697\pi$
$62$	− 4.97107i	− 0.631327i
$63$	0.290725i	0.0366279i
$64$	12.3112	1.53891
$65$	0	0
$66$	2.34017	0.288055
$67$	10.6309i	1.29877i	0.760459	+	0.649385i	$0.224974\pi$
$67$	10.6309i	1.29877i	−0.760459	+	0.649385i	$0.775026\pi$
$68$	4.20620i	0.510077i
$69$	11.3340	1.36446
$70$	0	0
$71$	15.6020	1.85161	0.925806	−	0.377998i	$-0.123387\pi$
$71$	15.6020	1.85161	0.925806	+	0.377998i	$0.123387\pi$
$72$	− 0.120638i	− 0.0142173i
$73$	10.9444i	1.28095i	0.767981	+	0.640473i	$0.221262\pi$
$73$	10.9444i	1.28095i	−0.767981	+	0.640473i	$0.778738\pi$
$74$	5.31124	0.617420
$75$	0	0
$76$	−15.4680	−1.77430
$77$	− 2.34017i	− 0.266687i
$78$	− 16.0989i	− 1.82284i
$79$	10.2062	1.14829	0.574144	−	0.818754i	$-0.305335\pi$
$79$	10.2062	1.14829	0.574144	+	0.818754i	$0.305335\pi$
$80$	0	0
$81$	−8.75872	−0.973192
$82$	12.1568i	1.34249i
$83$	3.12783i	0.343324i	0.985156	+	0.171662i	$0.0549136\pi$
$83$	3.12783i	0.343324i	−0.985156	+	0.171662i	$0.945086\pi$
$84$	17.1773	1.87419
$85$	0	0
$86$	27.2267	2.93593
$87$	1.70928i	0.183254i
$88$	0.971071i	0.103516i
$89$	−1.41855	−0.150366	−0.0751830	−	0.997170i	$-0.523954\pi$
$89$	−1.41855	−0.150366	−0.0751830	+	0.997170i	$0.523954\pi$
$90$	0	0
$91$	−16.0989	−1.68762
$92$	17.9649i	1.87297i
$93$	− 3.91548i	− 0.406016i
$94$	−4.97107	−0.512727
$95$	0	0
$96$	12.9711	1.32385
$97$	13.4680i	1.36747i	0.729731	+	0.683734i	$0.239645\pi$
$97$	13.4680i	1.36747i	−0.729731	+	0.683734i	$0.760355\pi$
$98$	− 14.6670i	− 1.48159i
$99$	−0.0494483	−0.00496974
$100$	0	0
$101$	1.10504	0.109956	0.0549778	−	0.998488i	$-0.482491\pi$
$101$	1.10504	0.109956	0.0549778	+	0.998488i	$0.482491\pi$
$102$	5.75872i	0.570199i
$103$	− 15.6248i	− 1.53955i	−0.638314	−	0.769776i	$-0.720368\pi$
$103$	− 15.6248i	− 1.53955i	0.638314	−	0.769776i	$-0.279632\pi$
$104$	6.68035	0.655062
$105$	0	0
$106$	2.00000	0.194257
$107$	2.81432i	0.272070i	0.990704	+	0.136035i	$0.0434360\pi$
$107$	2.81432i	0.272070i	−0.990704	+	0.136035i	$0.956564\pi$
$108$	− 14.2557i	− 1.37175i
$109$	−5.91548	−0.566600	−0.283300	−	0.959031i	$-0.591429\pi$
$109$	−5.91548	−0.566600	−0.283300	+	0.959031i	$0.591429\pi$
$110$	0	0
$111$	4.18342	0.397072
$112$	− 7.70928i	− 0.728458i
$113$	1.95055i	0.183492i	0.995782	+	0.0917462i	$0.0292449\pi$
$113$	1.95055i	0.183492i	−0.995782	+	0.0917462i	$0.970755\pi$
$114$	−21.1773	−1.98343
$115$	0	0
$116$	−2.70928	−0.251550
$117$	0.340173i	0.0314490i
$118$	7.81658i	0.719575i
$119$	5.75872	0.527901
$120$	0	0
$121$	−10.6020	−0.963815
$122$	− 28.2557i	− 2.55815i
$123$	9.57531i	0.863376i
$124$	6.20620	0.557334
$125$	0	0
$126$	−0.630898	−0.0562048
$127$	− 22.4885i	− 1.99553i	−0.0667962	−	0.997767i	$-0.521278\pi$
$127$	− 22.4885i	− 1.99553i	0.0667962	−	0.997767i	$-0.478722\pi$
$128$	11.5392i	1.01993i
$129$	21.4452	1.88815
$130$	0	0
$131$	3.86603	0.337777	0.168888	−	0.985635i	$-0.445982\pi$
$131$	3.86603	0.337777	0.168888	+	0.985635i	$0.445982\pi$
$132$	2.92162i	0.254295i
$133$	21.1773i	1.83630i
$134$	−23.0700	−1.99294
$135$	0	0
$136$	−2.38962	−0.204908
$137$	21.2846i	1.81846i	0.416289	+	0.909232i	$0.363330\pi$
$137$	21.2846i	1.81846i	−0.416289	+	0.909232i	$0.636670\pi$
$138$	24.5958i	2.09374i
$139$	−8.09890	−0.686939	−0.343470	−	0.939164i	$-0.611602\pi$
$139$	−8.09890	−0.686939	−0.343470	+	0.939164i	$0.611602\pi$
$140$	0	0
$141$	−3.91548	−0.329743
$142$	33.8576i	2.84127i
$143$	− 2.73820i	− 0.228980i
$144$	−0.162899	−0.0135749
$145$	0	0
$146$	−23.7503	−1.96559
$147$	− 11.5525i	− 0.952836i
$148$	6.63090i	0.545056i
$149$	−12.8371	−1.05166	−0.525828	−	0.850591i	$-0.676245\pi$
$149$	−12.8371	−1.05166	−0.525828	+	0.850591i	$0.676245\pi$
$150$	0	0
$151$	−20.5958	−1.67606	−0.838032	−	0.545621i	$-0.816294\pi$
$151$	−20.5958	−1.67606	−0.838032	+	0.545621i	$0.816294\pi$
$152$	− 8.78765i	− 0.712773i
$153$	− 0.121683i	− 0.00983749i
$154$	5.07838	0.409227
$155$	0	0
$156$	20.0989	1.60920
$157$	− 6.04945i	− 0.482799i	−0.970426	−	0.241399i	$-0.922394\pi$
$157$	− 6.04945i	− 0.482799i	0.970426	−	0.241399i	$-0.0776063\pi$
$158$	22.1483i	1.76203i
$159$	1.57531	0.124930
$160$	0	0
$161$	24.5958	1.93842
$162$	− 19.0072i	− 1.49335i
$163$	15.9649i	1.25047i	0.780437	+	0.625235i	$0.214997\pi$
$163$	15.9649i	1.25047i	−0.780437	+	0.625235i	$0.785003\pi$
$164$	−15.1773	−1.18515
$165$	0	0
$166$	−6.78765	−0.526824
$167$	− 11.3112i	− 0.875290i	−0.899148	−	0.437645i	$-0.855813\pi$
$167$	− 11.3112i	− 0.875290i	0.899148	−	0.437645i	$-0.144187\pi$
$168$	9.75872i	0.752902i
$169$	−5.83710	−0.449008
$170$	0	0
$171$	0.447480	0.0342197
$172$	33.9916i	2.59183i
$173$	10.4969i	0.798067i	0.916936	+	0.399033i	$0.130654\pi$
$173$	10.4969i	0.798067i	−0.916936	+	0.399033i	$0.869346\pi$
$174$	−3.70928	−0.281199
$175$	0	0
$176$	1.31124	0.0988387
$177$	6.15676i	0.462770i
$178$	− 3.07838i	− 0.230734i
$179$	12.3135	0.920355	0.460178	−	0.887827i	$-0.347786\pi$
$179$	12.3135	0.920355	0.460178	+	0.887827i	$0.347786\pi$
$180$	0	0
$181$	−1.60197	−0.119073	−0.0595367	−	0.998226i	$-0.518962\pi$
$181$	−1.60197	−0.119073	−0.0595367	+	0.998226i	$0.518962\pi$
$182$	− 34.9360i	− 2.58963i
$183$	− 22.2557i	− 1.64519i
$184$	−10.2062	−0.752411
$185$	0	0
$186$	8.49693	0.623025
$187$	0.979481i	0.0716268i
$188$	− 6.20620i	− 0.452634i
$189$	−19.5174	−1.41969
$190$	0	0
$191$	13.6248	0.985853	0.492926	−	0.870071i	$-0.335927\pi$
$191$	13.6248	0.985853	0.492926	+	0.870071i	$0.335927\pi$
$192$	21.0433i	1.51867i
$193$	16.9711i	1.22160i	0.791783	+	0.610802i	$0.209153\pi$
$193$	16.9711i	1.22160i	−0.791783	+	0.610802i	$0.790847\pi$
$194$	−29.2267	−2.09836
$195$	0	0
$196$	18.3112	1.30795
$197$	− 0.0578588i	− 0.00412227i	−0.999998	−	0.00206114i	$-0.999344\pi$
$197$	− 0.0578588i	− 0.00412227i	0.999998	−	0.00206114i	$-0.000656080\pi$
$198$	− 0.107307i	− 0.00762599i
$199$	−5.39189	−0.382221	−0.191110	−	0.981569i	$-0.561209\pi$
$199$	−5.39189	−0.382221	−0.191110	+	0.981569i	$0.561209\pi$
$200$	0	0
$201$	−18.1711	−1.28169
$202$	2.39803i	0.168725i
$203$	3.70928i	0.260340i
$204$	−7.18956	−0.503370
$205$	0	0
$206$	33.9071	2.36242
$207$	− 0.519715i	− 0.0361227i
$208$	− 9.02052i	− 0.625460i
$209$	−3.60197	−0.249153
$210$	0	0
$211$	4.14834	0.285584	0.142792	−	0.989753i	$-0.454392\pi$
$211$	4.14834	0.285584	0.142792	+	0.989753i	$0.454392\pi$
$212$	2.49693i	0.171490i
$213$	26.6681i	1.82727i
$214$	−6.10731	−0.417487
$215$	0	0
$216$	8.09890	0.551060
$217$	− 8.49693i	− 0.576809i
$218$	− 12.8371i	− 0.869438i
$219$	−18.7070	−1.26410
$220$	0	0
$221$	6.73820	0.453261
$222$	9.07838i	0.609301i
$223$	6.72979i	0.450660i	0.974282	+	0.225330i	$0.0723461\pi$
$223$	6.72979i	0.450660i	−0.974282	+	0.225330i	$0.927654\pi$
$224$	28.1483	1.88074
$225$	0	0
$226$	−4.23287	−0.281566
$227$	− 22.2472i	− 1.47660i	−0.674472	−	0.738301i	$-0.735629\pi$
$227$	− 22.2472i	− 1.47660i	0.674472	−	0.738301i	$-0.264371\pi$
$228$	− 26.4391i	− 1.75097i
$229$	7.16290	0.473338	0.236669	−	0.971590i	$-0.423944\pi$
$229$	7.16290	0.473338	0.236669	+	0.971590i	$0.423944\pi$
$230$	0	0
$231$	4.00000	0.263181
$232$	− 1.53919i	− 0.101053i
$233$	− 30.1978i	− 1.97832i	−0.146831	−	0.989162i	$-0.546907\pi$
$233$	− 30.1978i	− 1.97832i	0.146831	−	0.989162i	$-0.453093\pi$
$234$	−0.738205	−0.0482580
$235$	0	0
$236$	−9.75872	−0.635239
$237$	17.4452i	1.13319i
$238$	12.4969i	0.810056i
$239$	6.43907	0.416509	0.208254	−	0.978075i	$-0.433222\pi$
$239$	6.43907	0.416509	0.208254	+	0.978075i	$0.433222\pi$
$240$	0	0
$241$	10.9939	0.708177	0.354088	−	0.935212i	$-0.384791\pi$
$241$	10.9939	0.708177	0.354088	+	0.935212i	$0.384791\pi$
$242$	− 23.0072i	− 1.47896i
$243$	0.814315i	0.0522383i
$244$	35.2762	2.25833
$245$	0	0
$246$	−20.7792	−1.32484
$247$	24.7792i	1.57667i
$248$	3.52586i	0.223892i
$249$	−5.34632	−0.338809
$250$	0	0
$251$	9.41014	0.593963	0.296981	−	0.954883i	$-0.404020\pi$
$251$	9.41014	0.593963	0.296981	+	0.954883i	$0.404020\pi$
$252$	− 0.787653i	− 0.0496175i
$253$	4.18342i	0.263009i
$254$	48.8020	3.06211
$255$	0	0
$256$	−0.418551	−0.0261594
$257$	5.81658i	0.362828i	0.983407	+	0.181414i	$0.0580675\pi$
$257$	5.81658i	0.362828i	−0.983407	+	0.181414i	$0.941933\pi$
$258$	46.5380i	2.89733i
$259$	9.07838	0.564103
$260$	0	0
$261$	0.0783777	0.00485146
$262$	8.38962i	0.518313i
$263$	8.91321i	0.549612i	0.961500	+	0.274806i	$0.0886137\pi$
$263$	8.91321i	0.549612i	−0.961500	+	0.274806i	$0.911386\pi$
$264$	−1.65983	−0.102155
$265$	0	0
$266$	−45.9565	−2.81777
$267$	− 2.42469i	− 0.148389i
$268$	− 28.8020i	− 1.75936i
$269$	16.4391	1.00231	0.501154	−	0.865358i	$-0.332909\pi$
$269$	16.4391	1.00231	0.501154	+	0.865358i	$0.332909\pi$
$270$	0	0
$271$	29.4101	1.78654	0.893269	−	0.449522i	$-0.148406\pi$
$271$	29.4101	1.78654	0.893269	+	0.449522i	$0.148406\pi$
$272$	3.22672i	0.195649i
$273$	− 27.5174i	− 1.66543i
$274$	−46.1894	−2.79040
$275$	0	0
$276$	−30.7070	−1.84834
$277$	11.0784i	0.665635i	0.942991	+	0.332818i	$0.107999\pi$
$277$	11.0784i	0.665635i	−0.942991	+	0.332818i	$0.892001\pi$
$278$	− 17.5753i	− 1.05410i
$279$	−0.179542	−0.0107489
$280$	0	0
$281$	−21.1194	−1.25988	−0.629939	−	0.776644i	$-0.716920\pi$
$281$	−21.1194	−1.25988	−0.629939	+	0.776644i	$0.716920\pi$
$282$	− 8.49693i	− 0.505985i
$283$	13.7815i	0.819226i	0.912259	+	0.409613i	$0.134336\pi$
$283$	13.7815i	0.819226i	−0.912259	+	0.409613i	$0.865664\pi$
$284$	−42.2700	−2.50826
$285$	0	0
$286$	5.94214	0.351366
$287$	20.7792i	1.22656i
$288$	− 0.594780i	− 0.0350478i
$289$	14.5897	0.858217
$290$	0	0
$291$	−23.0205	−1.34949
$292$	− 29.6514i	− 1.73522i
$293$	− 6.14834i	− 0.359190i	−0.983741	−	0.179595i	$-0.942521\pi$
$293$	− 6.14834i	− 0.359190i	0.983741	−	0.179595i	$-0.0574787\pi$
$294$	25.0700	1.46211
$295$	0	0
$296$	−3.76713	−0.218960
$297$	− 3.31965i	− 0.192626i
$298$	− 27.8576i	− 1.61375i
$299$	28.7792	1.66435
$300$	0	0
$301$	46.5380	2.68240
$302$	− 44.6947i	− 2.57189i
$303$	1.88882i	0.108510i
$304$	−11.8660	−0.680564
$305$	0	0
$306$	0.264063	0.0150955
$307$	10.3896i	0.592967i	0.955038	+	0.296484i	$0.0958140\pi$
$307$	10.3896i	0.592967i	−0.955038	+	0.296484i	$0.904186\pi$
$308$	6.34017i	0.361265i
$309$	26.7070	1.51931
$310$	0	0
$311$	18.7565	1.06358	0.531791	−	0.846876i	$-0.321519\pi$
$311$	18.7565	1.06358	0.531791	+	0.846876i	$0.321519\pi$
$312$	11.4186i	0.646448i
$313$	− 12.3402i	− 0.697508i	−0.937214	−	0.348754i	$-0.886605\pi$
$313$	− 12.3402i	− 0.697508i	0.937214	−	0.348754i	$-0.113395\pi$
$314$	13.1278	0.740846
$315$	0	0
$316$	−27.6514	−1.55551
$317$	− 30.6986i	− 1.72421i	−0.506734	−	0.862103i	$-0.669147\pi$
$317$	− 30.6986i	− 1.72421i	0.506734	−	0.862103i	$-0.330853\pi$
$318$	3.41855i	0.191703i
$319$	−0.630898	−0.0353235
$320$	0	0
$321$	−4.81044	−0.268493
$322$	53.3751i	2.97448i
$323$	− 8.86376i	− 0.493193i
$324$	23.7298	1.31832
$325$	0	0
$326$	−34.6453	−1.91882
$327$	− 10.1112i	− 0.559150i
$328$	− 8.62249i	− 0.476097i
$329$	−8.49693	−0.468451
$330$	0	0
$331$	−4.08065	−0.224293	−0.112146	−	0.993692i	$-0.535773\pi$
$331$	−4.08065	−0.224293	−0.112146	+	0.993692i	$0.535773\pi$
$332$	− 8.47414i	− 0.465079i
$333$	− 0.191828i	− 0.0105121i
$334$	24.5464	1.34312
$335$	0	0
$336$	13.1773	0.718879
$337$	− 18.3630i	− 1.00029i	−0.865940	−	0.500147i	$-0.833279\pi$
$337$	− 18.3630i	− 1.00029i	0.865940	−	0.500147i	$-0.166721\pi$
$338$	− 12.6670i	− 0.688995i
$339$	−3.33403	−0.181080
$340$	0	0
$341$	1.44521	0.0782627
$342$	0.971071i	0.0525095i
$343$	0.894960i	0.0483233i
$344$	−19.3112	−1.04119
$345$	0	0
$346$	−22.7792	−1.22462
$347$	8.97107i	0.481592i	0.970576	+	0.240796i	$0.0774085\pi$
$347$	8.97107i	0.481592i	−0.970576	+	0.240796i	$0.922591\pi$
$348$	− 4.63090i	− 0.248242i
$349$	−26.1978	−1.40234	−0.701168	−	0.712996i	$-0.747338\pi$
$349$	−26.1978	−1.40234	−0.701168	+	0.712996i	$0.747338\pi$
$350$	0	0
$351$	−22.8371	−1.21895
$352$	4.78765i	0.255183i
$353$	26.2823i	1.39887i	0.714698	+	0.699433i	$0.246564\pi$
$353$	26.2823i	1.39887i	−0.714698	+	0.699433i	$0.753436\pi$
$354$	−13.3607	−0.710113
$355$	0	0
$356$	3.84324	0.203692
$357$	9.84324i	0.520960i
$358$	26.7214i	1.41227i
$359$	−22.8722	−1.20715	−0.603574	−	0.797307i	$-0.706257\pi$
$359$	−22.8722	−1.20715	−0.603574	+	0.797307i	$0.706257\pi$
$360$	0	0
$361$	13.5958	0.715570
$362$	− 3.47641i	− 0.182716i
$363$	− 18.1217i	− 0.951142i
$364$	43.6163	2.28612
$365$	0	0
$366$	48.2967	2.52451
$367$	− 11.0700i	− 0.577848i	−0.957352	−	0.288924i	$-0.906703\pi$
$367$	− 11.0700i	− 0.577848i	0.957352	−	0.288924i	$-0.0932974\pi$
$368$	13.7815i	0.718411i
$369$	0.439070	0.0228571
$370$	0	0
$371$	3.41855	0.177482
$372$	10.6081i	0.550005i
$373$	− 11.5753i	− 0.599347i	−0.954042	−	0.299673i	$-0.903122\pi$
$373$	− 11.5753i	− 0.599347i	0.954042	−	0.299673i	$-0.0968777\pi$
$374$	−2.12556	−0.109910
$375$	0	0
$376$	3.52586	0.181832
$377$	4.34017i	0.223530i
$378$	− 42.3545i	− 2.17848i
$379$	9.31124	0.478286	0.239143	−	0.970984i	$-0.423133\pi$
$379$	9.31124	0.478286	0.239143	+	0.970984i	$0.423133\pi$
$380$	0	0
$381$	38.4391	1.96929
$382$	29.5669i	1.51277i
$383$	− 33.9649i	− 1.73553i	−0.496978	−	0.867763i	$-0.665557\pi$
$383$	− 33.9649i	− 1.73553i	0.496978	−	0.867763i	$-0.334443\pi$
$384$	−19.7237	−1.00652
$385$	0	0
$386$	−36.8287	−1.87453
$387$	− 0.983357i	− 0.0499868i
$388$	− 36.4885i	− 1.85242i
$389$	4.12556	0.209174	0.104587	−	0.994516i	$-0.466648\pi$
$389$	4.12556	0.209174	0.104587	+	0.994516i	$0.466648\pi$
$390$	0	0
$391$	−10.2946	−0.520620
$392$	10.4030i	0.525428i
$393$	6.60811i	0.333335i
$394$	0.125559	0.00632555
$395$	0	0
$396$	0.133969	0.00673220
$397$	17.1050i	0.858477i	0.903191	+	0.429239i	$0.141218\pi$
$397$	17.1050i	0.858477i	−0.903191	+	0.429239i	$0.858782\pi$
$398$	− 11.7009i	− 0.586511i
$399$	−36.1978	−1.81216
$400$	0	0
$401$	−0.554787	−0.0277048	−0.0138524	−	0.999904i	$-0.504409\pi$
$401$	−0.554787	−0.0277048	−0.0138524	+	0.999904i	$0.504409\pi$
$402$	− 39.4329i	− 1.96674i
$403$	− 9.94214i	− 0.495253i
$404$	−2.99386	−0.148950
$405$	0	0
$406$	−8.04945	−0.399487
$407$	1.54411i	0.0765387i
$408$	− 4.08452i	− 0.202214i
$409$	20.6537	1.02126	0.510629	−	0.859801i	$-0.329412\pi$
$409$	20.6537	1.02126	0.510629	+	0.859801i	$0.329412\pi$
$410$	0	0
$411$	−36.3812	−1.79455
$412$	42.3318i	2.08554i
$413$	13.3607i	0.657437i
$414$	1.12783	0.0554296
$415$	0	0
$416$	32.9360	1.61482
$417$	− 13.8432i	− 0.677907i
$418$	− 7.81658i	− 0.382322i
$419$	6.02666	0.294422	0.147211	−	0.989105i	$-0.452970\pi$
$419$	6.02666	0.294422	0.147211	+	0.989105i	$0.452970\pi$
$420$	0	0
$421$	−12.5380	−0.611063	−0.305532	−	0.952182i	$-0.598834\pi$
$421$	−12.5380	−0.611063	−0.305532	+	0.952182i	$0.598834\pi$
$422$	9.00227i	0.438224i
$423$	0.179542i	0.00872962i
$424$	−1.41855	−0.0688909
$425$	0	0
$426$	−57.8720	−2.80391
$427$	− 48.2967i	− 2.33724i
$428$	− 7.62475i	− 0.368556i
$429$	4.68035	0.225969
$430$	0	0
$431$	−18.0410	−0.869006	−0.434503	−	0.900670i	$-0.643076\pi$
$431$	−18.0410	−0.869006	−0.434503	+	0.900670i	$0.643076\pi$
$432$	− 10.9360i	− 0.526158i
$433$	− 18.8143i	− 0.904158i	−0.891978	−	0.452079i	$-0.850682\pi$
$433$	− 18.8143i	− 0.904158i	0.891978	−	0.452079i	$-0.149318\pi$
$434$	18.4391	0.885104
$435$	0	0
$436$	16.0267	0.767538
$437$	− 37.8576i	− 1.81098i
$438$	− 40.5958i	− 1.93974i
$439$	−5.54411	−0.264606	−0.132303	−	0.991209i	$-0.542237\pi$
$439$	−5.54411	−0.264606	−0.132303	+	0.991209i	$0.542237\pi$
$440$	0	0
$441$	−0.529734	−0.0252254
$442$	14.6225i	0.695521i
$443$	− 17.8082i	− 0.846092i	−0.906108	−	0.423046i	$-0.860961\pi$
$443$	− 17.8082i	− 0.846092i	0.906108	−	0.423046i	$-0.139039\pi$
$444$	−11.3340	−0.537889
$445$	0	0
$446$	−14.6042	−0.691531
$447$	− 21.9421i	− 1.03783i
$448$	45.6658i	2.15751i
$449$	10.6947	0.504715	0.252358	−	0.967634i	$-0.418794\pi$
$449$	10.6947	0.504715	0.252358	+	0.967634i	$0.418794\pi$
$450$	0	0
$451$	−3.53427	−0.166422
$452$	− 5.28458i	− 0.248566i
$453$	− 35.2039i	− 1.65403i
$454$	48.2784	2.26582
$455$	0	0
$456$	15.0205	0.703400
$457$	− 21.7998i	− 1.01975i	−0.860249	−	0.509875i	$-0.829692\pi$
$457$	− 21.7998i	− 1.01975i	0.860249	−	0.509875i	$-0.170308\pi$
$458$	15.5441i	0.726329i
$459$	8.16904	0.381298
$460$	0	0
$461$	22.4124	1.04385	0.521925	−	0.852991i	$-0.325214\pi$
$461$	22.4124	1.04385	0.521925	+	0.852991i	$0.325214\pi$
$462$	8.68035i	0.403846i
$463$	2.10277i	0.0977241i	0.998806	+	0.0488621i	$0.0155595\pi$
$463$	2.10277i	0.0977241i	−0.998806	+	0.0488621i	$0.984441\pi$
$464$	−2.07838	−0.0964863
$465$	0	0
$466$	65.5318	3.03570
$467$	− 18.6042i	− 0.860901i	−0.902614	−	0.430451i	$-0.858355\pi$
$467$	− 18.6042i	− 0.860901i	0.902614	−	0.430451i	$-0.141645\pi$
$468$	− 0.921622i	− 0.0426020i
$469$	−39.4329	−1.82084
$470$	0	0
$471$	10.3402	0.476450
$472$	− 5.54411i	− 0.255188i
$473$	7.91548i	0.363954i
$474$	−37.8576	−1.73886
$475$	0	0
$476$	−15.6020	−0.715115
$477$	− 0.0722347i	− 0.00330740i
$478$	13.9733i	0.639126i
$479$	−8.89884	−0.406598	−0.203299	−	0.979117i	$-0.565166\pi$
$479$	−8.89884	−0.406598	−0.203299	+	0.979117i	$0.565166\pi$
$480$	0	0
$481$	10.6225	0.484344
$482$	23.8576i	1.08668i
$483$	42.0410i	1.91293i
$484$	28.7237	1.30562
$485$	0	0
$486$	−1.76713	−0.0801588
$487$	− 12.9711i	− 0.587775i	−0.955840	−	0.293888i	$-0.905051\pi$
$487$	− 12.9711i	− 0.587775i	0.955840	−	0.293888i	$-0.0949492\pi$
$488$	20.0410i	0.907215i
$489$	−27.2885	−1.23403
$490$	0	0
$491$	−13.8615	−0.625561	−0.312780	−	0.949826i	$-0.601260\pi$
$491$	−13.8615	−0.625561	−0.312780	+	0.949826i	$0.601260\pi$
$492$	− 25.9421i	− 1.16956i
$493$	− 1.55252i	− 0.0699220i
$494$	−53.7731	−2.41937
$495$	0	0
$496$	4.76099	0.213775
$497$	57.8720i	2.59591i
$498$	− 11.6020i	− 0.519897i
$499$	22.3545	1.00073	0.500364	−	0.865815i	$-0.333200\pi$
$499$	22.3545	1.00073	0.500364	+	0.865815i	$0.333200\pi$
$500$	0	0
$501$	19.3340	0.863781
$502$	20.4208i	0.911426i
$503$	− 34.4885i	− 1.53777i	−0.639389	−	0.768884i	$-0.720813\pi$
$503$	− 34.4885i	− 1.53777i	0.639389	−	0.768884i	$-0.279187\pi$
$504$	0.447480	0.0199323
$505$	0	0
$506$	−9.07838	−0.403583
$507$	− 9.97721i	− 0.443104i
$508$	60.9276i	2.70322i
$509$	28.7526	1.27444	0.637218	−	0.770684i	$-0.280085\pi$
$509$	28.7526	1.27444	0.637218	+	0.770684i	$0.280085\pi$
$510$	0	0
$511$	−40.5958	−1.79585
$512$	22.1701i	0.979789i
$513$	30.0410i	1.32634i
$514$	−12.6225	−0.556754
$515$	0	0
$516$	−58.1010	−2.55775
$517$	− 1.44521i	− 0.0635604i
$518$	19.7009i	0.865606i
$519$	−17.9421	−0.787573
$520$	0	0
$521$	−21.6020	−0.946399	−0.473200	−	0.880955i	$-0.656901\pi$
$521$	−21.6020	−0.946399	−0.473200	+	0.880955i	$0.656901\pi$
$522$	0.170086i	0.00744448i
$523$	− 4.20620i	− 0.183924i	−0.995762	−	0.0919622i	$-0.970686\pi$
$523$	− 4.20620i	− 0.183924i	0.995762	−	0.0919622i	$-0.0293139\pi$
$524$	−10.4741	−0.457565
$525$	0	0
$526$	−19.3424	−0.843370
$527$	3.55640i	0.154919i
$528$	2.24128i	0.0975390i
$529$	−20.9688	−0.911687
$530$	0	0
$531$	0.282314	0.0122514
$532$	− 57.3751i	− 2.48752i
$533$	24.3135i	1.05314i
$534$	5.26180	0.227700
$535$	0	0
$536$	16.3630	0.706772
$537$	21.0472i	0.908253i
$538$	35.6742i	1.53802i
$539$	4.26406	0.183666
$540$	0	0
$541$	26.7792	1.15133	0.575665	−	0.817686i	$-0.304743\pi$
$541$	26.7792	1.15133	0.575665	+	0.817686i	$0.304743\pi$
$542$	63.8225i	2.74141i
$543$	− 2.73820i	− 0.117508i
$544$	−11.7815	−0.505128
$545$	0	0
$546$	59.7152	2.55558
$547$	2.33176i	0.0996990i	0.998757	+	0.0498495i	$0.0158742\pi$
$547$	2.33176i	0.0996990i	−0.998757	+	0.0498495i	$0.984126\pi$
$548$	− 57.6658i	− 2.46336i
$549$	−1.02052	−0.0435547
$550$	0	0
$551$	5.70928	0.243223
$552$	− 17.4452i	− 0.742518i
$553$	37.8576i	1.60987i
$554$	−24.0410	−1.02141
$555$	0	0
$556$	21.9421	0.930554
$557$	30.8781i	1.30835i	0.756344	+	0.654174i	$0.226984\pi$
$557$	30.8781i	1.30835i	−0.756344	+	0.654174i	$0.773016\pi$
$558$	− 0.389621i	− 0.0164940i
$559$	54.4534	2.30314
$560$	0	0
$561$	−1.67420	−0.0706849
$562$	− 45.8310i	− 1.93326i
$563$	34.1750i	1.44030i	0.693816	+	0.720152i	$0.255928\pi$
$563$	34.1750i	1.44030i	−0.693816	+	0.720152i	$0.744072\pi$
$564$	10.6081	0.446682
$565$	0	0
$566$	−29.9071	−1.25709
$567$	− 32.4885i	− 1.36439i
$568$	− 24.0144i	− 1.00762i
$569$	30.6947	1.28679	0.643395	−	0.765535i	$-0.277525\pi$
$569$	30.6947	1.28679	0.643395	+	0.765535i	$0.277525\pi$
$570$	0	0
$571$	−25.7275	−1.07666	−0.538332	−	0.842733i	$-0.680945\pi$
$571$	−25.7275	−1.07666	−0.538332	+	0.842733i	$0.680945\pi$
$572$	7.41855i	0.310185i
$573$	23.2885i	0.972889i
$574$	−45.0928	−1.88214
$575$	0	0
$576$	0.964928	0.0402053
$577$	16.0228i	0.667037i	0.942743	+	0.333519i	$0.108236\pi$
$577$	16.0228i	0.667037i	−0.942743	+	0.333519i	$0.891764\pi$
$578$	31.6609i	1.31692i
$579$	−29.0082	−1.20554
$580$	0	0
$581$	−11.6020	−0.481331
$582$	− 49.9565i	− 2.07076i
$583$	0.581449i	0.0240812i
$584$	16.8455	0.697072
$585$	0	0
$586$	13.3424	0.551171
$587$	19.6248i	0.810000i	0.914317	+	0.405000i	$0.132729\pi$
$587$	19.6248i	0.810000i	−0.914317	+	0.405000i	$0.867271\pi$
$588$	31.2990i	1.29075i
$589$	−13.0784	−0.538885
$590$	0	0
$591$	0.0988967	0.00406807
$592$	5.08679i	0.209066i
$593$	− 30.9627i	− 1.27148i	−0.771902	−	0.635742i	$-0.780694\pi$
$593$	− 30.9627i	− 1.27148i	0.771902	−	0.635742i	$-0.219306\pi$
$594$	7.20394	0.295581
$595$	0	0
$596$	34.7792	1.42461
$597$	− 9.21622i	− 0.377195i
$598$	62.4534i	2.55391i
$599$	−24.4619	−0.999484	−0.499742	−	0.866174i	$-0.666572\pi$
$599$	−24.4619	−0.999484	−0.499742	+	0.866174i	$0.666572\pi$
$600$	0	0
$601$	16.3857	0.668389	0.334194	−	0.942504i	$-0.391536\pi$
$601$	16.3857	0.668389	0.334194	+	0.942504i	$0.391536\pi$
$602$	100.991i	4.11610i
$603$	0.833226i	0.0339316i
$604$	55.7998	2.27046
$605$	0	0
$606$	−4.09890	−0.166506
$607$	16.6986i	0.677775i	0.940827	+	0.338888i	$0.110051\pi$
$607$	16.6986i	0.677775i	−0.940827	+	0.338888i	$0.889949\pi$
$608$	− 43.3256i	− 1.75709i
$609$	−6.34017	−0.256917
$610$	0	0
$611$	−9.94214	−0.402216
$612$	0.329673i	0.0133262i
$613$	− 5.83096i	− 0.235510i	−0.993043	−	0.117755i	$-0.962430\pi$
$613$	− 5.83096i	− 0.235510i	0.993043	−	0.117755i	$-0.0375698\pi$
$614$	−22.5464	−0.909898
$615$	0	0
$616$	−3.60197	−0.145127
$617$	− 11.7237i	− 0.471976i	−0.971756	−	0.235988i	$-0.924167\pi$
$617$	− 11.7237i	− 0.471976i	0.971756	−	0.235988i	$-0.0758327\pi$
$618$	57.9565i	2.33135i
$619$	8.41628	0.338279	0.169139	−	0.985592i	$-0.445901\pi$
$619$	8.41628	0.338279	0.169139	+	0.985592i	$0.445901\pi$
$620$	0	0
$621$	34.8904	1.40010
$622$	40.7031i	1.63205i
$623$	− 5.26180i	− 0.210809i
$624$	15.4186	0.617236
$625$	0	0
$626$	26.7792	1.07031
$627$	− 6.15676i	− 0.245877i
$628$	16.3896i	0.654017i
$629$	−3.79976	−0.151506
$630$	0	0
$631$	−12.7792	−0.508734	−0.254367	−	0.967108i	$-0.581867\pi$
$631$	−12.7792	−0.508734	−0.254367	+	0.967108i	$0.581867\pi$
$632$	− 15.7093i	− 0.624881i
$633$	7.09066i	0.281829i
$634$	66.6186	2.64576
$635$	0	0
$636$	−4.26794	−0.169235
$637$	− 29.3340i	− 1.16226i
$638$	− 1.36910i	− 0.0542033i
$639$	1.22285	0.0483751
$640$	0	0
$641$	−0.0722347	−0.00285310	−0.00142655	−	0.999999i	$-0.500454\pi$
$641$	−0.0722347	−0.00285310	−0.00142655	+	0.999999i	$0.500454\pi$
$642$	− 10.4391i	− 0.411997i
$643$	− 32.7175i	− 1.29025i	−0.764076	−	0.645126i	$-0.776805\pi$
$643$	− 32.7175i	− 1.29025i	0.764076	−	0.645126i	$-0.223195\pi$
$644$	−66.6369	−2.62586
$645$	0	0
$646$	19.2351	0.756796
$647$	− 15.8082i	− 0.621483i	−0.950494	−	0.310742i	$-0.899423\pi$
$647$	− 15.8082i	− 0.621483i	0.950494	−	0.310742i	$-0.100577\pi$
$648$	13.4813i	0.529597i
$649$	−2.27247	−0.0892024
$650$	0	0
$651$	14.5236	0.569224
$652$	− 43.2534i	− 1.69393i
$653$	15.3112i	0.599175i	0.954069	+	0.299588i	$0.0968491\pi$
$653$	15.3112i	0.599175i	−0.954069	+	0.299588i	$0.903151\pi$
$654$	21.9421	0.858006
$655$	0	0
$656$	−11.6430	−0.454583
$657$	0.857798i	0.0334659i
$658$	− 18.4391i	− 0.718830i
$659$	−17.1278	−0.667205	−0.333603	−	0.942714i	$-0.608264\pi$
$659$	−17.1278	−0.667205	−0.333603	+	0.942714i	$0.608264\pi$
$660$	0	0
$661$	−26.2290	−1.02019	−0.510095	−	0.860118i	$-0.670390\pi$
$661$	−26.2290	−1.02019	−0.510095	+	0.860118i	$0.670390\pi$
$662$	− 8.85535i	− 0.344173i
$663$	11.5174i	0.447301i
$664$	4.81432	0.186832
$665$	0	0
$666$	0.416283	0.0161307
$667$	− 6.63090i	− 0.256749i
$668$	30.6453i	1.18570i
$669$	−11.5031	−0.444734
$670$	0	0
$671$	8.21461	0.317122
$672$	48.1133i	1.85601i
$673$	− 46.4657i	− 1.79112i	−0.444938	−	0.895561i	$-0.646774\pi$
$673$	− 46.4657i	− 1.79112i	0.444938	−	0.895561i	$-0.353226\pi$
$674$	39.8492	1.53493
$675$	0	0
$676$	15.8143	0.608243
$677$	− 27.8394i	− 1.06995i	−0.844867	−	0.534977i	$-0.820320\pi$
$677$	− 27.8394i	− 1.06995i	0.844867	−	0.534977i	$-0.179680\pi$
$678$	− 7.23513i	− 0.277864i
$679$	−49.9565	−1.91716
$680$	0	0
$681$	38.0267	1.45718
$682$	3.13624i	0.120093i
$683$	− 39.0966i	− 1.49599i	−0.663704	−	0.747995i	$-0.731016\pi$
$683$	− 39.0966i	− 1.49599i	0.663704	−	0.747995i	$-0.268984\pi$
$684$	−1.21235	−0.0463552
$685$	0	0
$686$	−1.94214	−0.0741513
$687$	12.2434i	0.467114i
$688$	26.0761i	0.994142i
$689$	4.00000	0.152388
$690$	0	0
$691$	24.7480	0.941460	0.470730	−	0.882277i	$-0.343991\pi$
$691$	24.7480	0.941460	0.470730	+	0.882277i	$0.343991\pi$
$692$	− 28.4391i	− 1.08109i
$693$	− 0.183417i	− 0.00696745i
$694$	−19.4680	−0.738995
$695$	0	0
$696$	2.63090	0.0997239
$697$	− 8.69717i	− 0.329429i
$698$	− 56.8515i	− 2.15186i
$699$	51.6163	1.95231
$700$	0	0
$701$	0.187952	0.00709886	0.00354943	−	0.999994i	$-0.498870\pi$
$701$	0.187952	0.00709886	0.00354943	+	0.999994i	$0.498870\pi$
$702$	− 49.5585i	− 1.87046i
$703$	− 13.9733i	− 0.527014i
$704$	−7.76713	−0.292735
$705$	0	0
$706$	−57.0349	−2.14654
$707$	4.09890i	0.154155i
$708$	− 16.6803i	− 0.626886i
$709$	−13.6020	−0.510833	−0.255416	−	0.966831i	$-0.582213\pi$
$709$	−13.6020	−0.510833	−0.255416	+	0.966831i	$0.582213\pi$
$710$	0	0
$711$	0.799939	0.0300001
$712$	2.18342i	0.0818270i
$713$	15.1896i	0.568854i
$714$	−21.3607	−0.799404
$715$	0	0
$716$	−33.3607	−1.24675
$717$	11.0061i	0.411032i
$718$	− 49.6346i	− 1.85235i
$719$	9.27617	0.345943	0.172971	−	0.984927i	$-0.444663\pi$
$719$	9.27617	0.345943	0.172971	+	0.984927i	$0.444663\pi$
$720$	0	0
$721$	57.9565	2.15841
$722$	29.5041i	1.09803i
$723$	18.7915i	0.698864i
$724$	4.34017	0.161301
$725$	0	0
$726$	39.3256	1.45951
$727$	29.0121i	1.07600i	0.842945	+	0.538000i	$0.180820\pi$
$727$	29.0121i	1.07600i	−0.842945	+	0.538000i	$0.819180\pi$
$728$	24.7792i	0.918380i
$729$	−27.6681	−1.02474
$730$	0	0
$731$	−19.4785	−0.720438
$732$	60.2967i	2.22863i
$733$	34.0638i	1.25818i	0.777334	+	0.629088i	$0.216572\pi$
$733$	34.0638i	1.25818i	−0.777334	+	0.629088i	$0.783428\pi$
$734$	24.0228	0.886697
$735$	0	0
$736$	−50.3195	−1.85480
$737$	− 6.70701i	− 0.247056i
$738$	0.952819i	0.0350738i
$739$	−1.49466	−0.0549820	−0.0274910	−	0.999622i	$-0.508752\pi$
$739$	−1.49466	−0.0549820	−0.0274910	+	0.999622i	$0.508752\pi$
$740$	0	0
$741$	−42.3545	−1.55593
$742$	7.41855i	0.272344i
$743$	− 17.8082i	− 0.653318i	−0.945142	−	0.326659i	$-0.894077\pi$
$743$	− 17.8082i	− 0.653318i	0.945142	−	0.326659i	$-0.105923\pi$
$744$	−6.02666	−0.220948
$745$	0	0
$746$	25.1194	0.919687
$747$	0.245152i	0.00896964i
$748$	− 2.65368i	− 0.0970283i
$749$	−10.4391	−0.381435
$750$	0	0
$751$	−23.7503	−0.866661	−0.433331	−	0.901235i	$-0.642662\pi$
$751$	−23.7503	−0.866661	−0.433331	+	0.901235i	$0.642662\pi$
$752$	− 4.76099i	− 0.173615i
$753$	16.0845i	0.586153i
$754$	−9.41855	−0.343003
$755$	0	0
$756$	52.8781	1.92316
$757$	26.1939i	0.952034i	0.879436	+	0.476017i	$0.157920\pi$
$757$	26.1939i	0.952034i	−0.879436	+	0.476017i	$0.842080\pi$
$758$	20.2062i	0.733922i
$759$	−7.15061	−0.259551
$760$	0	0
$761$	−44.7214	−1.62115	−0.810574	−	0.585636i	$-0.800845\pi$
$761$	−44.7214	−1.62115	−0.810574	+	0.585636i	$0.800845\pi$
$762$	83.4161i	3.02185i
$763$	− 21.9421i	− 0.794359i
$764$	−36.9132	−1.33547
$765$	0	0
$766$	73.7068	2.66314
$767$	15.6332i	0.564481i
$768$	− 0.715418i	− 0.0258154i
$769$	−10.8950	−0.392882	−0.196441	−	0.980516i	$-0.562938\pi$
$769$	−10.8950	−0.392882	−0.196441	+	0.980516i	$0.562938\pi$
$770$	0	0
$771$	−9.94214	−0.358057
$772$	− 45.9793i	− 1.65483i
$773$	− 34.1171i	− 1.22711i	−0.789653	−	0.613554i	$-0.789739\pi$
$773$	− 34.1171i	− 1.22711i	0.789653	−	0.613554i	$-0.210261\pi$
$774$	2.13397	0.0767039
$775$	0	0
$776$	20.7298	0.744156
$777$	15.5174i	0.556685i
$778$	8.95282i	0.320974i
$779$	31.9832	1.14592
$780$	0	0
$781$	−9.84324	−0.352219
$782$	− 22.3402i	− 0.798883i
$783$	5.26180i	0.188041i
$784$	14.0472	0.501685
$785$	0	0
$786$	−14.3402	−0.511497
$787$	39.7548i	1.41711i	0.705657	+	0.708554i	$0.250652\pi$
$787$	39.7548i	1.41711i	−0.705657	+	0.708554i	$0.749348\pi$
$788$	0.156755i	0.00558418i
$789$	−15.2351	−0.542385
$790$	0	0
$791$	−7.23513	−0.257252
$792$	0.0761103i	0.00270446i
$793$	− 56.5113i	− 2.00678i
$794$	−37.1194	−1.31732
$795$	0	0
$796$	14.6081	0.517771
$797$	18.7298i	0.663443i	0.943377	+	0.331722i	$0.107629\pi$
$797$	18.7298i	0.663443i	−0.943377	+	0.331722i	$0.892371\pi$
$798$	− 78.5523i	− 2.78072i
$799$	3.55640	0.125816
$800$	0	0
$801$	−0.111183	−0.00392845
$802$	− 1.20394i	− 0.0425125i
$803$	− 6.90480i	− 0.243665i
$804$	49.2306	1.73623
$805$	0	0
$806$	21.5753	0.759958
$807$	28.0989i	0.989128i
$808$	− 1.70086i	− 0.0598362i
$809$	31.9421	1.12303	0.561513	−	0.827468i	$-0.310219\pi$
$809$	31.9421	1.12303	0.561513	+	0.827468i	$0.310219\pi$
$810$	0	0
$811$	−17.8888	−0.628161	−0.314081	−	0.949396i	$-0.601696\pi$
$811$	−17.8888	−0.628161	−0.314081	+	0.949396i	$0.601696\pi$
$812$	− 10.0494i	− 0.352666i
$813$	50.2700i	1.76305i
$814$	−3.35085	−0.117447
$815$	0	0
$816$	−5.51536	−0.193076
$817$	− 71.6307i	− 2.50604i
$818$	44.8203i	1.56710i
$819$	−1.26180	−0.0440907
$820$	0	0
$821$	30.9939	1.08169	0.540847	−	0.841121i	$-0.318104\pi$
$821$	30.9939	1.08169	0.540847	+	0.841121i	$0.318104\pi$
$822$	− 78.9504i	− 2.75371i
$823$	− 16.5008i	− 0.575182i	−0.957753	−	0.287591i	$-0.907146\pi$
$823$	− 16.5008i	− 0.575182i	0.957753	−	0.287591i	$-0.0928544\pi$
$824$	−24.0494	−0.837802
$825$	0	0
$826$	−28.9939	−1.00883
$827$	43.1155i	1.49927i	0.661849	+	0.749637i	$0.269772\pi$
$827$	43.1155i	1.49927i	−0.661849	+	0.749637i	$0.730228\pi$
$828$	1.40805i	0.0489331i
$829$	−22.5958	−0.784785	−0.392393	−	0.919798i	$-0.628353\pi$
$829$	−22.5958	−0.784785	−0.392393	+	0.919798i	$0.628353\pi$
$830$	0	0
$831$	−18.9360	−0.656882
$832$	53.4329i	1.85245i
$833$	10.4931i	0.363563i
$834$	30.0410	1.04024
$835$	0	0
$836$	9.75872	0.337513
$837$	− 12.0533i	− 0.416624i
$838$	13.0784i	0.451785i
$839$	−1.21235	−0.0418549	−0.0209274	−	0.999781i	$-0.506662\pi$
$839$	−1.21235	−0.0418549	−0.0209274	+	0.999781i	$0.506662\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	− 27.2085i	− 0.937666i
$843$	− 36.0989i	− 1.24331i
$844$	−11.2390	−0.386863
$845$	0	0
$846$	−0.389621	−0.0133955
$847$	− 39.3256i	− 1.35124i
$848$	1.91548i	0.0657778i
$849$	−23.5564	−0.808453
$850$	0	0
$851$	−16.2290	−0.556323
$852$	− 72.2511i	− 2.47528i
$853$	− 5.93618i	− 0.203251i	−0.994823	−	0.101625i	$-0.967596\pi$
$853$	− 5.93618i	− 0.203251i	0.994823	−	0.101625i	$-0.0324043\pi$
$854$	104.808	3.58646
$855$	0	0
$856$	4.33176	0.148057
$857$	14.5503i	0.497027i	0.968628	+	0.248514i	$0.0799421\pi$
$857$	14.5503i	0.497027i	−0.968628	+	0.248514i	$0.920058\pi$
$858$	10.1568i	0.346746i
$859$	6.32192	0.215701	0.107851	−	0.994167i	$-0.465603\pi$
$859$	6.32192	0.215701	0.107851	+	0.994167i	$0.465603\pi$
$860$	0	0
$861$	−35.5174	−1.21043
$862$	− 39.1506i	− 1.33348i
$863$	3.28005i	0.111654i	0.998440	+	0.0558270i	$0.0177795\pi$
$863$	3.28005i	0.111654i	−0.998440	+	0.0558270i	$0.982220\pi$
$864$	39.9299	1.35844
$865$	0	0
$866$	40.8287	1.38742
$867$	24.9378i	0.846932i
$868$	23.0205i	0.781367i
$869$	−6.43907	−0.218430
$870$	0	0
$871$	−46.1399	−1.56339
$872$	9.10504i	0.308336i
$873$	1.05559i	0.0357264i
$874$	82.1543	2.77891
$875$	0	0
$876$	50.6824	1.71240
$877$	18.2823i	0.617350i	0.951168	+	0.308675i	$0.0998855\pi$
$877$	18.2823i	0.617350i	−0.951168	+	0.308675i	$0.900114\pi$
$878$	− 12.0312i	− 0.406033i
$879$	10.5092	0.354467
$880$	0	0
$881$	29.7464	1.00218	0.501091	−	0.865394i	$-0.332932\pi$
$881$	29.7464	1.00218	0.501091	+	0.865394i	$0.332932\pi$
$882$	− 1.14957i	− 0.0387080i
$883$	− 13.8127i	− 0.464835i	−0.972616	−	0.232417i	$-0.925336\pi$
$883$	− 13.8127i	− 0.464835i	0.972616	−	0.232417i	$-0.0746635\pi$
$884$	−18.2557	−0.614004
$885$	0	0
$886$	38.6453	1.29831
$887$	− 56.3318i	− 1.89144i	−0.324989	−	0.945718i	$-0.605361\pi$
$887$	− 56.3318i	− 1.89144i	0.324989	−	0.945718i	$-0.394639\pi$
$888$	− 6.43907i	− 0.216081i
$889$	83.4161	2.79769
$890$	0	0
$891$	5.52586	0.185123
$892$	− 18.2329i	− 0.610482i
$893$	13.0784i	0.437651i
$894$	47.6163	1.59253
$895$	0	0
$896$	−42.8020	−1.42992
$897$	49.1917i	1.64246i
$898$	23.2085i	0.774477i
$899$	−2.29072	−0.0763999
$900$	0	0
$901$	−1.43084	−0.0476681
$902$	− 7.66967i	− 0.255372i
$903$	79.5462i	2.64713i
$904$	3.00227	0.0998539
$905$	0	0
$906$	76.3956	2.53807
$907$	21.8082i	0.724128i	0.932153	+	0.362064i	$0.117928\pi$
$907$	21.8082i	0.724128i	−0.932153	+	0.362064i	$0.882072\pi$
$908$	60.2739i	2.00026i
$909$	0.0866105	0.00287269
$910$	0	0
$911$	4.76099	0.157739	0.0788693	−	0.996885i	$-0.474869\pi$
$911$	4.76099	0.157739	0.0788693	+	0.996885i	$0.474869\pi$
$912$	− 20.2823i	− 0.671615i
$913$	− 1.97334i	− 0.0653080i
$914$	47.3074	1.56479
$915$	0	0
$916$	−19.4063	−0.641201
$917$	14.3402i	0.473554i
$918$	17.7275i	0.585096i
$919$	−34.1256	−1.12570	−0.562849	−	0.826560i	$-0.690295\pi$
$919$	−34.1256	−1.12570	−0.562849	+	0.826560i	$0.690295\pi$
$920$	0	0
$921$	−17.7587	−0.585170
$922$	48.6369i	1.60177i
$923$	67.7152i	2.22887i
$924$	−10.8371	−0.356514
$925$	0	0
$926$	−4.56320	−0.149956
$927$	− 1.22463i	− 0.0402222i
$928$	− 7.58864i	− 0.249109i
$929$	12.5769	0.412635	0.206318	−	0.978485i	$-0.433852\pi$
$929$	12.5769	0.412635	0.206318	+	0.978485i	$0.433852\pi$
$930$	0	0
$931$	−38.5874	−1.26465
$932$	81.8141i	2.67991i
$933$	32.0599i	1.04960i
$934$	40.3728	1.32104
$935$	0	0
$936$	0.523590	0.0171141
$937$	− 29.7464i	− 0.971774i	−0.874022	−	0.485887i	$-0.838497\pi$
$937$	− 29.7464i	− 0.971774i	0.874022	−	0.485887i	$-0.161503\pi$
$938$	− 85.5729i	− 2.79405i
$939$	21.0928	0.688336
$940$	0	0
$941$	−7.47641	−0.243724	−0.121862	−	0.992547i	$-0.538887\pi$
$941$	−7.47641	−0.243724	−0.121862	+	0.992547i	$0.538887\pi$
$942$	22.4391i	0.731104i
$943$	− 37.1461i	− 1.20964i
$944$	−7.48625	−0.243657
$945$	0	0
$946$	−17.1773	−0.558481
$947$	− 15.2846i	− 0.496682i	−0.968673	−	0.248341i	$-0.920115\pi$
$947$	− 15.2846i	− 0.496682i	0.968673	−	0.248341i	$-0.0798854\pi$
$948$	− 47.2639i	− 1.53506i
$949$	−47.5006	−1.54194
$950$	0	0
$951$	52.4724	1.70153
$952$	− 8.86376i	− 0.287276i
$953$	54.0288i	1.75016i	0.483976	+	0.875081i	$0.339192\pi$
$953$	54.0288i	1.75016i	−0.483976	+	0.875081i	$0.660808\pi$
$954$	0.156755	0.00507515
$955$	0	0
$956$	−17.4452	−0.564219
$957$	− 1.07838i	− 0.0348590i
$958$	− 19.3112i	− 0.623918i
$959$	−78.9504	−2.54944
$960$	0	0
$961$	−25.7526	−0.830728
$962$	23.0517i	0.743217i
$963$	0.220580i	0.00710808i
$964$	−29.7854	−0.959323
$965$	0	0
$966$	−91.2327	−2.93536
$967$	− 15.7671i	− 0.507037i	−0.967331	−	0.253518i	$-0.918412\pi$
$967$	− 15.7671i	− 0.507037i	0.967331	−	0.253518i	$-0.0815878\pi$
$968$	16.3184i	0.524494i
$969$	15.1506	0.486708
$970$	0	0
$971$	48.1627	1.54562	0.772808	−	0.634640i	$-0.218852\pi$
$971$	48.1627	1.54562	0.772808	+	0.634640i	$0.218852\pi$
$972$	− 2.20620i	− 0.0707640i
$973$	− 30.0410i	− 0.963071i
$974$	28.1483	0.901931
$975$	0	0
$976$	27.0616	0.866219
$977$	− 8.28685i	− 0.265120i	−0.991175	−	0.132560i	$-0.957680\pi$
$977$	− 8.28685i	− 0.265120i	0.991175	−	0.132560i	$-0.0423197\pi$
$978$	− 59.2183i	− 1.89359i
$979$	0.894960	0.0286031
$980$	0	0
$981$	−0.463642	−0.0148029
$982$	− 30.0806i	− 0.959912i
$983$	− 22.9177i	− 0.730963i	−0.930819	−	0.365481i	$-0.880904\pi$
$983$	− 22.9177i	− 0.730963i	0.930819	−	0.365481i	$-0.119096\pi$
$984$	14.7382	0.469837
$985$	0	0
$986$	3.36910	0.107294
$987$	− 14.5236i	− 0.462291i
$988$	− 67.1338i	− 2.13581i
$989$	−83.1937	−2.64541
$990$	0	0
$991$	22.3234	0.709125	0.354562	−	0.935032i	$-0.384630\pi$
$991$	22.3234	0.709125	0.354562	+	0.935032i	$0.384630\pi$
$992$	17.3835i	0.551926i
$993$	− 6.97495i	− 0.221343i
$994$	−125.587	−3.98339
$995$	0	0
$996$	14.4846	0.458963
$997$	14.3630i	0.454879i	0.973792	+	0.227440i	$0.0730355\pi$
$997$	14.3630i	0.454879i	−0.973792	+	0.227440i	$0.926965\pi$
$998$	48.5113i	1.53560i
$999$	12.8781	0.407446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.b.e.349.6		6
5.2	odd	4		725.2.a.e.1.1		3
5.3	odd	4		145.2.a.c.1.3	✓	3
5.4	even	2	inner	725.2.b.e.349.1		6
15.2	even	4		6525.2.a.be.1.3		3
15.8	even	4		1305.2.a.p.1.1		3
20.3	even	4		2320.2.a.n.1.3		3
35.13	even	4		7105.2.a.o.1.3		3
40.3	even	4		9280.2.a.br.1.1		3
40.13	odd	4		9280.2.a.bj.1.3		3
145.28	odd	4		4205.2.a.f.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.a.c.1.3	✓	3	5.3	odd	4
725.2.a.e.1.1		3	5.2	odd	4
725.2.b.e.349.1		6	5.4	even	2	inner
725.2.b.e.349.6		6	1.1	even	1	trivial
1305.2.a.p.1.1		3	15.8	even	4
2320.2.a.n.1.3		3	20.3	even	4
4205.2.a.f.1.1		3	145.28	odd	4
6525.2.a.be.1.3		3	15.2	even	4
7105.2.a.o.1.3		3	35.13	even	4
9280.2.a.bj.1.3		3	40.13	odd	4
9280.2.a.br.1.1		3	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.17009i q^{2} +1.70928i q^{3} -2.70928 q^{4} -3.70928 q^{6} +3.70928i q^{7} -1.53919i q^{8} +0.0783777 q^{9} -0.630898 q^{11} -4.63090i q^{12} +4.34017i q^{13} -8.04945 q^{14} -2.07838 q^{16} -1.55252i q^{17} +0.170086i q^{18} +5.70928 q^{19} -6.34017 q^{21} -1.36910i q^{22} -6.63090i q^{23} +2.63090 q^{24} -9.41855 q^{26} +5.26180i q^{27} -10.0494i q^{28} +1.00000 q^{29} -2.29072 q^{31} -7.58864i q^{32} -1.07838i q^{33} +3.36910 q^{34} -0.212347 q^{36} -2.44748i q^{37} +12.3896i q^{38} -7.41855 q^{39} +5.60197 q^{41} -13.7587i q^{42} -12.5464i q^{43} +1.70928 q^{44} +14.3896 q^{46} +2.29072i q^{47} -3.55252i q^{48} -6.75872 q^{49} +2.65368 q^{51} -11.7587i q^{52} -0.921622i q^{53} -11.4186 q^{54} +5.70928 q^{56} +9.75872i q^{57} +2.17009i q^{58} +3.60197 q^{59} -13.0205 q^{61} -4.97107i q^{62} +0.290725i q^{63} +12.3112 q^{64} +2.34017 q^{66} +10.6309i q^{67} +4.20620i q^{68} +11.3340 q^{69} +15.6020 q^{71} -0.120638i q^{72} +10.9444i q^{73} +5.31124 q^{74} -15.4680 q^{76} -2.34017i q^{77} -16.0989i q^{78} +10.2062 q^{79} -8.75872 q^{81} +12.1568i q^{82} +3.12783i q^{83} +17.1773 q^{84} +27.2267 q^{86} +1.70928i q^{87} +0.971071i q^{88} -1.41855 q^{89} -16.0989 q^{91} +17.9649i q^{92} -3.91548i q^{93} -4.97107 q^{94} +12.9711 q^{96} +13.4680i q^{97} -14.6670i q^{98} -0.0494483 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} - 8 q^{6} - 6 q^{9} + 4 q^{11} - 12 q^{14} - 6 q^{16} + 20 q^{19} - 16 q^{21} + 8 q^{24} - 28 q^{26} + 6 q^{29} - 28 q^{31} + 28 q^{34} - 22 q^{36} - 16 q^{39} - 4 q^{41} - 4 q^{44} + 28 q^{46}+ \cdots + 36 q^{99}+O(q^{100}) \) 6 * q - 2 * q^4 - 8 * q^6 - 6 * q^9 + 4 * q^11 - 12 * q^14 - 6 * q^16 + 20 * q^19 - 16 * q^21 + 8 * q^24 - 28 * q^26 + 6 * q^29 - 28 * q^31 + 28 * q^34 - 22 * q^36 - 16 * q^39 - 4 * q^41 - 4 * q^44 + 28 * q^46 + 10 * q^49 - 32 * q^51 - 40 * q^54 + 20 * q^56 - 16 * q^59 - 12 * q^61 + 22 * q^64 - 8 * q^66 - 24 * q^69 + 56 * q^71 - 20 * q^74 - 28 * q^76 + 12 * q^79 - 2 * q^81 + 24 * q^84 + 48 * q^86 + 20 * q^89 - 24 * q^91 + 48 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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