LMFDB - Embedded newform 725.2.b.d.349.5

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,-10,0,8,0,0,-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:	$\Z[a_1, a_2, a_3]$
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			349.5
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	725.349
Dual form			725.2.b.d.349.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.53919i q^{2} -1.70928i q^{3} -0.369102 q^{4} +2.63090 q^{6} +0.630898i q^{7} +2.51026i q^{8} +0.0783777 q^{9} +0.290725 q^{11} +0.630898i q^{12} +0.921622i q^{13} -0.971071 q^{14} -4.60197 q^{16} +4.97107i q^{17} +0.120638i q^{18} +6.04945 q^{19} +1.07838 q^{21} +0.447480i q^{22} -2.29072i q^{23} +4.29072 q^{24} -1.41855 q^{26} -5.26180i q^{27} -0.232866i q^{28} -1.00000 q^{29} +10.0494 q^{31} -2.06278i q^{32} -0.496928i q^{33} -7.65142 q^{34} -0.0289294 q^{36} +1.55252i q^{37} +9.31124i q^{38} +1.57531 q^{39} +0.340173 q^{41} +1.65983i q^{42} +5.70928i q^{43} -0.107307 q^{44} +3.52586 q^{46} -1.12783i q^{47} +7.86603i q^{48} +6.60197 q^{49} +8.49693 q^{51} -0.340173i q^{52} +0.340173i q^{53} +8.09890 q^{54} -1.58372 q^{56} -10.3402i q^{57} -1.53919i q^{58} -9.75872 q^{59} +3.07838 q^{61} +15.4680i q^{62} +0.0494483i q^{63} -6.02893 q^{64} +0.764867 q^{66} -5.70928i q^{67} -1.83483i q^{68} -3.91548 q^{69} +9.07838 q^{71} +0.196748i q^{72} +6.94441i q^{73} -2.38962 q^{74} -2.23287 q^{76} +0.183417i q^{77} +2.42469i q^{78} -12.3896 q^{79} -8.75872 q^{81} +0.523590i q^{82} -2.78765i q^{83} -0.398032 q^{84} -8.78765 q^{86} +1.70928i q^{87} +0.729794i q^{88} -4.73820 q^{89} -0.581449 q^{91} +0.845512i q^{92} -17.1773i q^{93} +1.73594 q^{94} -3.52586 q^{96} -15.8927i q^{97} +10.1617i q^{98} +0.0227863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 8 q^{6} - 6 q^{9} + 16 q^{11} + 24 q^{14} + 10 q^{16} + 40 q^{24} + 20 q^{26} - 6 q^{29} + 24 q^{31} + 28 q^{34} - 30 q^{36} - 32 q^{39} - 20 q^{41} - 24 q^{44} + 16 q^{46} + 2 q^{49} + 16 q^{51}+ \cdots - 40 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 8 * q^6 - 6 * q^9 + 16 * q^11 + 24 * q^14 + 10 * q^16 + 40 * q^24 + 20 * q^26 - 6 * q^29 + 24 * q^31 + 28 * q^34 - 30 * q^36 - 32 * q^39 - 20 * q^41 - 24 * q^44 + 16 * q^46 + 2 * q^49 + 16 * q^51 - 24 * q^54 - 64 * q^56 - 8 * q^59 + 12 * q^61 - 66 * q^64 + 24 * q^66 + 40 * q^69 + 48 * q^71 + 44 * q^74 + 32 * q^76 - 16 * q^79 - 2 * q^81 - 40 * q^84 - 32 * q^86 - 44 * q^89 - 32 * q^91 - 16 * q^96 - 40 * 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 $

$2$	1.53919i	1.08837i	0.838965	+	0.544185i	$0.183161\pi$
$2$	1.53919i	1.08837i	−0.838965	+	0.544185i	$0.816839\pi$
$3$	− 1.70928i	− 0.986851i	−0.869788	−	0.493425i	$-0.835745\pi$
$3$	− 1.70928i	− 0.986851i	0.869788	−	0.493425i	$-0.164255\pi$
$4$	−0.369102	−0.184551
$5$	0	0
$5$	0	0
$6$	2.63090	1.07406
$7$	0.630898i	0.238457i	0.992867	+	0.119228i	$0.0380421\pi$
$7$	0.630898i	0.238457i	−0.992867	+	0.119228i	$0.961958\pi$
$8$	2.51026i	0.887511i
$9$	0.0783777	0.0261259
$10$	0	0
$11$	0.290725	0.0876568	0.0438284	−	0.999039i	$-0.486045\pi$
$11$	0.290725	0.0876568	0.0438284	+	0.999039i	$0.486045\pi$
$12$	0.630898i	0.182124i
$13$	0.921622i	0.255612i	0.991799	+	0.127806i	$0.0407935\pi$
$13$	0.921622i	0.255612i	−0.991799	+	0.127806i	$0.959207\pi$
$14$	−0.971071	−0.259530
$15$	0	0
$16$	−4.60197	−1.15049
$17$	4.97107i	1.20566i	0.797869	+	0.602831i	$0.205961\pi$
$17$	4.97107i	1.20566i	−0.797869	+	0.602831i	$0.794039\pi$
$18$	0.120638i	0.0284347i
$19$	6.04945	1.38784	0.693919	−	0.720053i	$-0.255882\pi$
$19$	6.04945	1.38784	0.693919	+	0.720053i	$0.255882\pi$
$20$	0	0
$21$	1.07838	0.235321
$22$	0.447480i	0.0954031i
$23$	− 2.29072i	− 0.477649i	−0.971063	−	0.238825i	$-0.923238\pi$
$23$	− 2.29072i	− 0.477649i	0.971063	−	0.238825i	$-0.0767621\pi$
$24$	4.29072	0.875840
$25$	0	0
$26$	−1.41855	−0.278201
$27$	− 5.26180i	− 1.01263i
$28$	− 0.232866i	− 0.0440075i
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	10.0494	1.80493	0.902467	−	0.430759i	$-0.141754\pi$
$31$	10.0494	1.80493	0.902467	+	0.430759i	$0.141754\pi$
$32$	− 2.06278i	− 0.364651i
$33$	− 0.496928i	− 0.0865041i
$34$	−7.65142	−1.31221
$35$	0	0
$36$	−0.0289294	−0.00482157
$37$	1.55252i	0.255233i	0.991824	+	0.127616i	$0.0407326\pi$
$37$	1.55252i	0.255233i	−0.991824	+	0.127616i	$0.959267\pi$
$38$	9.31124i	1.51048i
$39$	1.57531	0.252251
$40$	0	0
$41$	0.340173	0.0531261	0.0265630	−	0.999647i	$-0.491544\pi$
$41$	0.340173	0.0531261	0.0265630	+	0.999647i	$0.491544\pi$
$42$	1.65983i	0.256117i
$43$	5.70928i	0.870656i	0.900272	+	0.435328i	$0.143368\pi$
$43$	5.70928i	0.870656i	−0.900272	+	0.435328i	$0.856632\pi$
$44$	−0.107307	−0.0161772
$45$	0	0
$46$	3.52586	0.519859
$47$	− 1.12783i	− 0.164510i	−0.996611	−	0.0822552i	$-0.973788\pi$
$47$	− 1.12783i	− 0.164510i	0.996611	−	0.0822552i	$-0.0262122\pi$
$48$	7.86603i	1.13536i
$49$	6.60197	0.943138
$50$	0	0
$51$	8.49693	1.18981
$52$	− 0.340173i	− 0.0471735i
$53$	0.340173i	0.0467264i	0.999727	+	0.0233632i	$0.00743741\pi$
$53$	0.340173i	0.0467264i	−0.999727	+	0.0233632i	$0.992563\pi$
$54$	8.09890	1.10212
$55$	0	0
$56$	−1.58372	−0.211633
$57$	− 10.3402i	− 1.36959i
$58$	− 1.53919i	− 0.202105i
$59$	−9.75872	−1.27048	−0.635239	−	0.772316i	$-0.719098\pi$
$59$	−9.75872	−1.27048	−0.635239	+	0.772316i	$0.719098\pi$
$60$	0	0
$61$	3.07838	0.394146	0.197073	−	0.980389i	$-0.436856\pi$
$61$	3.07838	0.394146	0.197073	+	0.980389i	$0.436856\pi$
$62$	15.4680i	1.96444i
$63$	0.0494483i	0.00622990i
$64$	−6.02893	−0.753616
$65$	0	0
$66$	0.764867	0.0941486
$67$	− 5.70928i	− 0.697499i	−0.937216	−	0.348749i	$-0.886606\pi$
$67$	− 5.70928i	− 0.697499i	0.937216	−	0.348749i	$-0.113394\pi$
$68$	− 1.83483i	− 0.222506i
$69$	−3.91548	−0.471368
$70$	0	0
$71$	9.07838	1.07741	0.538703	−	0.842496i	$-0.318915\pi$
$71$	9.07838	1.07741	0.538703	+	0.842496i	$0.318915\pi$
$72$	0.196748i	0.0231870i
$73$	6.94441i	0.812782i	0.913699	+	0.406391i	$0.133213\pi$
$73$	6.94441i	0.812782i	−0.913699	+	0.406391i	$0.866787\pi$
$74$	−2.38962	−0.277788
$75$	0	0
$76$	−2.23287	−0.256127
$77$	0.183417i	0.0209024i
$78$	2.42469i	0.274543i
$79$	−12.3896	−1.39394	−0.696971	−	0.717100i	$-0.745469\pi$
$79$	−12.3896	−1.39394	−0.696971	+	0.717100i	$0.745469\pi$
$80$	0	0
$81$	−8.75872	−0.973192
$82$	0.523590i	0.0578209i
$83$	− 2.78765i	− 0.305985i	−0.988227	−	0.152992i	$-0.951109\pi$
$83$	− 2.78765i	− 0.305985i	0.988227	−	0.152992i	$-0.0488910\pi$
$84$	−0.398032	−0.0434288
$85$	0	0
$86$	−8.78765	−0.947597
$87$	1.70928i	0.183254i
$88$	0.729794i	0.0777963i
$89$	−4.73820	−0.502249	−0.251124	−	0.967955i	$-0.580800\pi$
$89$	−4.73820	−0.502249	−0.251124	+	0.967955i	$0.580800\pi$
$90$	0	0
$91$	−0.581449	−0.0609524
$92$	0.845512i	0.0881507i
$93$	− 17.1773i	− 1.78120i
$94$	1.73594	0.179048
$95$	0	0
$96$	−3.52586	−0.359856
$97$	− 15.8927i	− 1.61366i	−0.590785	−	0.806829i	$-0.701182\pi$
$97$	− 15.8927i	− 1.61366i	0.590785	−	0.806829i	$-0.298818\pi$
$98$	10.1617i	1.02648i
$99$	0.0227863	0.00229011
$100$	0	0
$101$	−12.2557	−1.21948	−0.609741	−	0.792600i	$-0.708727\pi$
$101$	−12.2557	−1.21948	−0.609741	+	0.792600i	$0.708727\pi$
$102$	13.0784i	1.29495i
$103$	7.86603i	0.775063i	0.921856	+	0.387532i	$0.126672\pi$
$103$	7.86603i	0.775063i	−0.921856	+	0.387532i	$0.873328\pi$
$104$	−2.31351	−0.226858
$105$	0	0
$106$	−0.523590	−0.0508556
$107$	12.7298i	1.23064i	0.788279	+	0.615318i	$0.210972\pi$
$107$	12.7298i	1.23064i	−0.788279	+	0.615318i	$0.789028\pi$
$108$	1.94214i	0.186883i
$109$	−12.4391	−1.19145	−0.595723	−	0.803190i	$-0.703135\pi$
$109$	−12.4391	−1.19145	−0.595723	+	0.803190i	$0.703135\pi$
$110$	0	0
$111$	2.65368	0.251877
$112$	− 2.90337i	− 0.274343i
$113$	− 12.5730i	− 1.18277i	−0.806389	−	0.591386i	$-0.798581\pi$
$113$	− 12.5730i	− 1.18277i	0.806389	−	0.591386i	$-0.201419\pi$
$114$	15.9155	1.49062
$115$	0	0
$116$	0.369102	0.0342703
$117$	0.0722347i	0.00667810i
$118$	− 15.0205i	− 1.38275i
$119$	−3.13624	−0.287498
$120$	0	0
$121$	−10.9155	−0.992316
$122$	4.73820i	0.428977i
$123$	− 0.581449i	− 0.0524275i
$124$	−3.70928	−0.333103
$125$	0	0
$126$	−0.0761103	−0.00678045
$127$	− 20.9132i	− 1.85575i	−0.372895	−	0.927874i	$-0.621635\pi$
$127$	− 20.9132i	− 1.85575i	0.372895	−	0.927874i	$-0.378365\pi$
$128$	− 13.4052i	− 1.18487i
$129$	9.75872	0.859208
$130$	0	0
$131$	−13.4680	−1.17670	−0.588352	−	0.808605i	$-0.700223\pi$
$131$	−13.4680	−1.17670	−0.588352	+	0.808605i	$0.700223\pi$
$132$	0.183417i	0.0159644i
$133$	3.81658i	0.330940i
$134$	8.78765	0.759138
$135$	0	0
$136$	−12.4787	−1.07004
$137$	− 13.5525i	− 1.15787i	−0.815374	−	0.578935i	$-0.803469\pi$
$137$	− 13.5525i	− 1.15787i	0.815374	−	0.578935i	$-0.196531\pi$
$138$	− 6.02666i	− 0.513024i
$139$	4.89496	0.415185	0.207593	−	0.978215i	$-0.433437\pi$
$139$	4.89496	0.415185	0.207593	+	0.978215i	$0.433437\pi$
$140$	0	0
$141$	−1.92777	−0.162347
$142$	13.9733i	1.17262i
$143$	0.267938i	0.0224061i
$144$	−0.360692	−0.0300577
$145$	0	0
$146$	−10.6888	−0.884608
$147$	− 11.2846i	− 0.930737i
$148$	− 0.573039i	− 0.0471035i
$149$	12.5236	1.02597	0.512986	−	0.858397i	$-0.328539\pi$
$149$	12.5236	1.02597	0.512986	+	0.858397i	$0.328539\pi$
$150$	0	0
$151$	7.60197	0.618639	0.309320	−	0.950958i	$-0.399899\pi$
$151$	7.60197	0.618639	0.309320	+	0.950958i	$0.399899\pi$
$152$	15.1857i	1.23172i
$153$	0.389621i	0.0314990i
$154$	−0.282314	−0.0227495
$155$	0	0
$156$	−0.581449	−0.0465532
$157$	− 24.8865i	− 1.98616i	−0.117428	−	0.993081i	$-0.537465\pi$
$157$	− 24.8865i	− 1.98616i	0.117428	−	0.993081i	$-0.462535\pi$
$158$	− 19.0700i	− 1.51713i
$159$	0.581449	0.0461119
$160$	0	0
$161$	1.44521	0.113899
$162$	− 13.4813i	− 1.05919i
$163$	− 0.447480i	− 0.0350493i	−0.999846	−	0.0175247i	$-0.994421\pi$
$163$	− 0.447480i	− 0.0350493i	0.999846	−	0.0175247i	$-0.00557856\pi$
$164$	−0.125559	−0.00980448
$165$	0	0
$166$	4.29072	0.333025
$167$	19.8660i	1.53728i	0.639682	+	0.768640i	$0.279066\pi$
$167$	19.8660i	1.53728i	−0.639682	+	0.768640i	$0.720934\pi$
$168$	2.70701i	0.208850i
$169$	12.1506	0.934662
$170$	0	0
$171$	0.474142	0.0362586
$172$	− 2.10731i	− 0.160681i
$173$	25.4329i	1.93363i	0.255478	+	0.966815i	$0.417767\pi$
$173$	25.4329i	1.93363i	−0.255478	+	0.966815i	$0.582233\pi$
$174$	−2.63090	−0.199448
$175$	0	0
$176$	−1.33791	−0.100848
$177$	16.6803i	1.25377i
$178$	− 7.29299i	− 0.546633i
$179$	−14.8371	−1.10898	−0.554489	−	0.832191i	$-0.687086\pi$
$179$	−14.8371	−1.10898	−0.554489	+	0.832191i	$0.687086\pi$
$180$	0	0
$181$	−5.91548	−0.439694	−0.219847	−	0.975534i	$-0.570556\pi$
$181$	−5.91548	−0.439694	−0.219847	+	0.975534i	$0.570556\pi$
$182$	− 0.894960i	− 0.0663389i
$183$	− 5.26180i	− 0.388963i
$184$	5.75031	0.423919
$185$	0	0
$186$	26.4391	1.93861
$187$	1.44521i	0.105684i
$188$	0.416283i	0.0303606i
$189$	3.31965	0.241469
$190$	0	0
$191$	7.02893	0.508595	0.254298	−	0.967126i	$-0.418156\pi$
$191$	7.02893	0.508595	0.254298	+	0.967126i	$0.418156\pi$
$192$	10.3051i	0.743707i
$193$	− 17.8660i	− 1.28603i	−0.765856	−	0.643013i	$-0.777684\pi$
$193$	− 17.8660i	− 1.28603i	0.765856	−	0.643013i	$-0.222316\pi$
$194$	24.4619	1.75626
$195$	0	0
$196$	−2.43680	−0.174057
$197$	6.09890i	0.434528i	0.976113	+	0.217264i	$0.0697133\pi$
$197$	6.09890i	0.434528i	−0.976113	+	0.217264i	$0.930287\pi$
$198$	0.0350725i	0.00249249i
$199$	9.75872	0.691778	0.345889	−	0.938276i	$-0.387577\pi$
$199$	9.75872	0.691778	0.345889	+	0.938276i	$0.387577\pi$
$200$	0	0
$201$	−9.75872	−0.688327
$202$	− 18.8638i	− 1.32725i
$203$	− 0.630898i	− 0.0442803i
$204$	−3.13624	−0.219580
$205$	0	0
$206$	−12.1073	−0.843556
$207$	− 0.179542i	− 0.0124790i
$208$	− 4.24128i	− 0.294080i
$209$	1.75872	0.121653
$210$	0	0
$211$	9.86603	0.679206	0.339603	−	0.940569i	$-0.389707\pi$
$211$	9.86603	0.679206	0.339603	+	0.940569i	$0.389707\pi$
$212$	− 0.125559i	− 0.00862340i
$213$	− 15.5174i	− 1.06324i
$214$	−19.5936	−1.33939
$215$	0	0
$216$	13.2085	0.898723
$217$	6.34017i	0.430399i
$218$	− 19.1461i	− 1.29674i
$219$	11.8699	0.802094
$220$	0	0
$221$	−4.58145	−0.308182
$222$	4.08452i	0.274135i
$223$	− 10.9711i	− 0.734677i	−0.930087	−	0.367339i	$-0.880269\pi$
$223$	− 10.9711i	− 0.734677i	0.930087	−	0.367339i	$-0.119731\pi$
$224$	1.30140	0.0869536
$225$	0	0
$226$	19.3523	1.28729
$227$	− 12.5464i	− 0.832732i	−0.909197	−	0.416366i	$-0.863303\pi$
$227$	− 12.5464i	− 0.832732i	0.909197	−	0.416366i	$-0.136697\pi$
$228$	3.81658i	0.252759i
$229$	−23.3607	−1.54372	−0.771859	−	0.635794i	$-0.780673\pi$
$229$	−23.3607	−1.54372	−0.771859	+	0.635794i	$0.780673\pi$
$230$	0	0
$231$	0.313511	0.0206275
$232$	− 2.51026i	− 0.164807i
$233$	− 12.4703i	− 0.816954i	−0.912769	−	0.408477i	$-0.866060\pi$
$233$	− 12.4703i	− 0.816954i	0.912769	−	0.408477i	$-0.133940\pi$
$234$	−0.111183	−0.00726825
$235$	0	0
$236$	3.60197	0.234468
$237$	21.1773i	1.37561i
$238$	− 4.82726i	− 0.312905i
$239$	−13.7587	−0.889978	−0.444989	−	0.895536i	$-0.646792\pi$
$239$	−13.7587	−0.889978	−0.444989	+	0.895536i	$0.646792\pi$
$240$	0	0
$241$	−14.6803	−0.945644	−0.472822	−	0.881158i	$-0.656765\pi$
$241$	−14.6803	−0.945644	−0.472822	+	0.881158i	$0.656765\pi$
$242$	− 16.8010i	− 1.08001i
$243$	− 0.814315i	− 0.0522383i
$244$	−1.13624	−0.0727401
$245$	0	0
$246$	0.894960	0.0570606
$247$	5.57531i	0.354748i
$248$	25.2267i	1.60190i
$249$	−4.76487	−0.301961
$250$	0	0
$251$	15.4413	0.974649	0.487324	−	0.873221i	$-0.337973\pi$
$251$	15.4413	0.974649	0.487324	+	0.873221i	$0.337973\pi$
$252$	− 0.0182515i	− 0.00114974i
$253$	− 0.665970i	− 0.0418692i
$254$	32.1894	2.01974
$255$	0	0
$256$	8.57531	0.535957
$257$	− 6.28231i	− 0.391880i	−0.980616	−	0.195940i	$-0.937224\pi$
$257$	− 6.28231i	− 0.391880i	0.980616	−	0.195940i	$-0.0627758\pi$
$258$	15.0205i	0.935137i
$259$	−0.979481	−0.0608620
$260$	0	0
$261$	−0.0783777	−0.00485146
$262$	− 20.7298i	− 1.28069i
$263$	− 10.0761i	− 0.621320i	−0.950521	−	0.310660i	$-0.899450\pi$
$263$	− 10.0761i	− 0.621320i	0.950521	−	0.310660i	$-0.100550\pi$
$264$	1.24742	0.0767734
$265$	0	0
$266$	−5.87444	−0.360185
$267$	8.09890i	0.495644i
$268$	2.10731i	0.128724i
$269$	−28.1711	−1.71762	−0.858812	−	0.512291i	$-0.828797\pi$
$269$	−28.1711	−1.71762	−0.858812	+	0.512291i	$0.828797\pi$
$270$	0	0
$271$	28.8020	1.74960	0.874799	−	0.484485i	$-0.160993\pi$
$271$	28.8020	1.74960	0.874799	+	0.484485i	$0.160993\pi$
$272$	− 22.8767i	− 1.38710i
$273$	0.993857i	0.0601510i
$274$	20.8599	1.26019
$275$	0	0
$276$	1.44521	0.0869916
$277$	0.0266620i	0.00160196i	1.00000		0.000800982i	$0.000254960\pi$
$277$	0.0266620i	0.00160196i	−1.00000		0.000800982i	$0.999745\pi$
$278$	7.53427i	0.451875i
$279$	0.787653	0.0471556
$280$	0	0
$281$	−28.0722	−1.67465	−0.837325	−	0.546706i	$-0.815881\pi$
$281$	−28.0722	−1.67465	−0.837325	+	0.546706i	$0.815881\pi$
$282$	− 2.96719i	− 0.176694i
$283$	20.8143i	1.23728i	0.785674	+	0.618641i	$0.212317\pi$
$283$	20.8143i	1.23728i	−0.785674	+	0.618641i	$0.787683\pi$
$284$	−3.35085	−0.198836
$285$	0	0
$286$	−0.412408	−0.0243862
$287$	0.214614i	0.0126683i
$288$	− 0.161676i	− 0.00952685i
$289$	−7.71154	−0.453620
$290$	0	0
$291$	−27.1650	−1.59244
$292$	− 2.56320i	− 0.150000i
$293$	15.4101i	0.900270i	0.892961	+	0.450135i	$0.148624\pi$
$293$	15.4101i	0.900270i	−0.892961	+	0.450135i	$0.851376\pi$
$294$	17.3691	1.01299
$295$	0	0
$296$	−3.89723	−0.226522
$297$	− 1.52973i	− 0.0887641i
$298$	19.2762i	1.11664i
$299$	2.11118	0.122093
$300$	0	0
$301$	−3.60197	−0.207614
$302$	11.7009i	0.673309i
$303$	20.9483i	1.20345i
$304$	−27.8394	−1.59670
$305$	0	0
$306$	−0.599701	−0.0342826
$307$	− 28.4307i	− 1.62262i	−0.584614	−	0.811312i	$-0.698754\pi$
$307$	− 28.4307i	− 1.62262i	0.584614	−	0.811312i	$-0.301246\pi$
$308$	− 0.0676998i	− 0.00385756i
$309$	13.4452	0.764871
$310$	0	0
$311$	−19.6248	−1.11282	−0.556409	−	0.830909i	$-0.687821\pi$
$311$	−19.6248	−1.11282	−0.556409	+	0.830909i	$0.687821\pi$
$312$	3.95443i	0.223875i
$313$	− 22.9093i	− 1.29491i	−0.762103	−	0.647456i	$-0.775833\pi$
$313$	− 22.9093i	− 1.29491i	0.762103	−	0.647456i	$-0.224167\pi$
$314$	38.3051	2.16168
$315$	0	0
$316$	4.57304	0.257254
$317$	22.8599i	1.28394i	0.766730	+	0.641970i	$0.221882\pi$
$317$	22.8599i	1.28394i	−0.766730	+	0.641970i	$0.778118\pi$
$318$	0.894960i	0.0501869i
$319$	−0.290725	−0.0162775
$320$	0	0
$321$	21.7587	1.21445
$322$	2.22446i	0.123964i
$323$	30.0722i	1.67326i
$324$	3.23287	0.179604
$325$	0	0
$326$	0.688756	0.0381467
$327$	21.2618i	1.17578i
$328$	0.853922i	0.0471500i
$329$	0.711543	0.0392286
$330$	0	0
$331$	24.0905	1.32413	0.662066	−	0.749445i	$-0.269680\pi$
$331$	24.0905	1.32413	0.662066	+	0.749445i	$0.269680\pi$
$332$	1.02893i	0.0564698i
$333$	0.121683i	0.00666819i
$334$	−30.5776	−1.67313
$335$	0	0
$336$	−4.96266	−0.270735
$337$	12.7877i	0.696588i	0.937385	+	0.348294i	$0.113239\pi$
$337$	12.7877i	0.696588i	−0.937385	+	0.348294i	$0.886761\pi$
$338$	18.7021i	1.01726i
$339$	−21.4908	−1.16722
$340$	0	0
$341$	2.92162	0.158215
$342$	0.729794i	0.0394628i
$343$	8.58145i	0.463355i
$344$	−14.3318	−0.772717
$345$	0	0
$346$	−39.1461	−2.10451
$347$	8.41628i	0.451810i	0.974149	+	0.225905i	$0.0725339\pi$
$347$	8.41628i	0.451810i	−0.974149	+	0.225905i	$0.927466\pi$
$348$	− 0.630898i	− 0.0338197i
$349$	−22.1978	−1.18822	−0.594110	−	0.804384i	$-0.702496\pi$
$349$	−22.1978	−1.18822	−0.594110	+	0.804384i	$0.702496\pi$
$350$	0	0
$351$	4.84939	0.258841
$352$	− 0.599701i	− 0.0319642i
$353$	6.18342i	0.329110i	0.986368	+	0.164555i	$0.0526188\pi$
$353$	6.18342i	0.329110i	−0.986368	+	0.164555i	$0.947381\pi$
$354$	−25.6742	−1.36457
$355$	0	0
$356$	1.74888	0.0926906
$357$	5.36069i	0.283718i
$358$	− 22.8371i	− 1.20698i
$359$	−5.05559	−0.266824	−0.133412	−	0.991061i	$-0.542593\pi$
$359$	−5.05559	−0.266824	−0.133412	+	0.991061i	$0.542593\pi$
$360$	0	0
$361$	17.5958	0.926096
$362$	− 9.10504i	− 0.478550i
$363$	18.6576i	0.979268i
$364$	0.214614	0.0112488
$365$	0	0
$366$	8.09890	0.423336
$367$	29.5402i	1.54199i	0.636843	+	0.770994i	$0.280240\pi$
$367$	29.5402i	1.54199i	−0.636843	+	0.770994i	$0.719760\pi$
$368$	10.5418i	0.549531i
$369$	0.0266620	0.00138797
$370$	0	0
$371$	−0.214614	−0.0111422
$372$	6.34017i	0.328723i
$373$	− 14.4124i	− 0.746246i	−0.927782	−	0.373123i	$-0.878287\pi$
$373$	− 14.4124i	− 0.746246i	0.927782	−	0.373123i	$-0.121713\pi$
$374$	−2.22446	−0.115024
$375$	0	0
$376$	2.83114	0.146005
$377$	− 0.921622i	− 0.0474660i
$378$	5.10957i	0.262808i
$379$	−14.1340	−0.726013	−0.363007	−	0.931787i	$-0.618250\pi$
$379$	−14.1340	−0.726013	−0.363007	+	0.931787i	$0.618250\pi$
$380$	0	0
$381$	−35.7464	−1.83135
$382$	10.8188i	0.553541i
$383$	15.7815i	0.806397i	0.915112	+	0.403199i	$0.132102\pi$
$383$	15.7815i	0.806397i	−0.915112	+	0.403199i	$0.867898\pi$
$384$	−22.9132	−1.16928
$385$	0	0
$386$	27.4992	1.39967
$387$	0.447480i	0.0227467i
$388$	5.86603i	0.297803i
$389$	13.8166	0.700529	0.350264	−	0.936651i	$-0.386092\pi$
$389$	13.8166	0.700529	0.350264	+	0.936651i	$0.386092\pi$
$390$	0	0
$391$	11.3874	0.575883
$392$	16.5727i	0.837045i
$393$	23.0205i	1.16123i
$394$	−9.38735	−0.472928
$395$	0	0
$396$	−0.00841049	−0.000422643 0
$397$	9.05172i	0.454293i	0.973861	+	0.227146i	$0.0729396\pi$
$397$	9.05172i	0.454293i	−0.973861	+	0.227146i	$0.927060\pi$
$398$	15.0205i	0.752911i
$399$	6.52359	0.326588
$400$	0	0
$401$	19.7587	0.986704	0.493352	−	0.869830i	$-0.335772\pi$
$401$	19.7587	0.986704	0.493352	+	0.869830i	$0.335772\pi$
$402$	− 15.0205i	− 0.749155i
$403$	9.26180i	0.461363i
$404$	4.52359	0.225057
$405$	0	0
$406$	0.971071	0.0481934
$407$	0.451356i	0.0223729i
$408$	21.3295i	1.05597i
$409$	1.71769	0.0849341	0.0424670	−	0.999098i	$-0.486478\pi$
$409$	1.71769	0.0849341	0.0424670	+	0.999098i	$0.486478\pi$
$410$	0	0
$411$	−23.1650	−1.14264
$412$	− 2.90337i	− 0.143039i
$413$	− 6.15676i	− 0.302954i
$414$	0.276349	0.0135818
$415$	0	0
$416$	1.90110	0.0932093
$417$	− 8.36683i	− 0.409726i
$418$	2.70701i	0.132404i
$419$	35.5318	1.73584	0.867922	−	0.496701i	$-0.165456\pi$
$419$	35.5318	1.73584	0.867922	+	0.496701i	$0.165456\pi$
$420$	0	0
$421$	−12.0722	−0.588365	−0.294182	−	0.955749i	$-0.595047\pi$
$421$	−12.0722	−0.588365	−0.294182	+	0.955749i	$0.595047\pi$
$422$	15.1857i	0.739228i
$423$	− 0.0883965i	− 0.00429798i
$424$	−0.853922	−0.0414701
$425$	0	0
$426$	23.8843	1.15720
$427$	1.94214i	0.0939868i
$428$	− 4.69860i	− 0.227115i
$429$	0.457980	0.0221115
$430$	0	0
$431$	19.8310	0.955224	0.477612	−	0.878571i	$-0.341503\pi$
$431$	19.8310	0.955224	0.477612	+	0.878571i	$0.341503\pi$
$432$	24.2146i	1.16503i
$433$	− 14.8143i	− 0.711931i	−0.934499	−	0.355965i	$-0.884152\pi$
$433$	− 14.8143i	− 0.711931i	0.934499	−	0.355965i	$-0.115848\pi$
$434$	−9.75872	−0.468434
$435$	0	0
$436$	4.59129	0.219883
$437$	− 13.8576i	− 0.662900i
$438$	18.2700i	0.872976i
$439$	17.8576	0.852298	0.426149	−	0.904653i	$-0.359870\pi$
$439$	17.8576	0.852298	0.426149	+	0.904653i	$0.359870\pi$
$440$	0	0
$441$	0.517447	0.0246404
$442$	− 7.05172i	− 0.335416i
$443$	− 33.5936i	− 1.59608i	−0.602606	−	0.798039i	$-0.705871\pi$
$443$	− 33.5936i	− 1.59608i	0.602606	−	0.798039i	$-0.294129\pi$
$444$	−0.979481	−0.0464841
$445$	0	0
$446$	16.8865	0.799601
$447$	− 21.4063i	− 1.01248i
$448$	− 3.80364i	− 0.179705i
$449$	−7.07838	−0.334049	−0.167025	−	0.985953i	$-0.553416\pi$
$449$	−7.07838	−0.334049	−0.167025	+	0.985953i	$0.553416\pi$
$450$	0	0
$451$	0.0988967	0.00465686
$452$	4.64074i	0.218282i
$453$	− 12.9939i	− 0.610505i
$454$	19.3112	0.906322
$455$	0	0
$456$	25.9565	1.21553
$457$	− 5.81658i	− 0.272088i	−0.990703	−	0.136044i	$-0.956561\pi$
$457$	− 5.81658i	− 0.272088i	0.990703	−	0.136044i	$-0.0434389\pi$
$458$	− 35.9565i	− 1.68014i
$459$	26.1568	1.22089
$460$	0	0
$461$	−32.3090	−1.50478	−0.752390	−	0.658718i	$-0.771099\pi$
$461$	−32.3090	−1.50478	−0.752390	+	0.658718i	$0.771099\pi$
$462$	0.482553i	0.0224504i
$463$	− 1.44134i	− 0.0669846i	−0.999439	−	0.0334923i	$-0.989337\pi$
$463$	− 1.44134i	− 0.0669846i	0.999439	−	0.0334923i	$-0.0106629\pi$
$464$	4.60197	0.213641
$465$	0	0
$466$	19.1941	0.889149
$467$	− 11.7503i	− 0.543740i	−0.962334	−	0.271870i	$-0.912358\pi$
$467$	− 11.7503i	− 0.543740i	0.962334	−	0.271870i	$-0.0876420\pi$
$468$	− 0.0266620i	− 0.00123245i
$469$	3.60197	0.166323
$470$	0	0
$471$	−42.5380	−1.96005
$472$	− 24.4969i	− 1.12756i
$473$	1.65983i	0.0763189i
$474$	−32.5958	−1.49718
$475$	0	0
$476$	1.15759	0.0530582
$477$	0.0266620i	0.00122077i
$478$	− 21.1773i	− 0.968626i
$479$	−17.1689	−0.784465	−0.392233	−	0.919866i	$-0.628297\pi$
$479$	−17.1689	−0.784465	−0.392233	+	0.919866i	$0.628297\pi$
$480$	0	0
$481$	−1.43084	−0.0652405
$482$	− 22.5958i	− 1.02921i
$483$	− 2.47027i	− 0.112401i
$484$	4.02893	0.183133
$485$	0	0
$486$	1.25338	0.0568547
$487$	− 4.10277i	− 0.185914i	−0.995670	−	0.0929572i	$-0.970368\pi$
$487$	− 4.10277i	− 0.185914i	0.995670	−	0.0929572i	$-0.0296320\pi$
$488$	7.72753i	0.349809i
$489$	−0.764867	−0.0345885
$490$	0	0
$491$	40.7708	1.83996	0.919981	−	0.391963i	$-0.128204\pi$
$491$	40.7708	1.83996	0.919981	+	0.391963i	$0.128204\pi$
$492$	0.214614i	0.00967556i
$493$	− 4.97107i	− 0.223886i
$494$	−8.58145	−0.386098
$495$	0	0
$496$	−46.2472	−2.07656
$497$	5.72753i	0.256915i
$498$	− 7.33403i	− 0.328646i
$499$	18.4703	0.826843	0.413421	−	0.910540i	$-0.364334\pi$
$499$	18.4703	0.826843	0.413421	+	0.910540i	$0.364334\pi$
$500$	0	0
$501$	33.9565	1.51707
$502$	23.7671i	1.06078i
$503$	21.4947i	0.958400i	0.877706	+	0.479200i	$0.159073\pi$
$503$	21.4947i	0.958400i	−0.877706	+	0.479200i	$0.840927\pi$
$504$	−0.124128	−0.00552911
$505$	0	0
$506$	1.02505	0.0455692
$507$	− 20.7687i	− 0.922372i
$508$	7.71912i	0.342480i
$509$	−3.75872	−0.166602	−0.0833012	−	0.996524i	$-0.526546\pi$
$509$	−3.75872	−0.166602	−0.0833012	+	0.996524i	$0.526546\pi$
$510$	0	0
$511$	−4.38121	−0.193813
$512$	− 13.6114i	− 0.601546i
$513$	− 31.8310i	− 1.40537i
$514$	9.66967	0.426511
$515$	0	0
$516$	−3.60197	−0.158568
$517$	− 0.327887i	− 0.0144204i
$518$	− 1.50761i	− 0.0662404i
$519$	43.4719	1.90820
$520$	0	0
$521$	12.8059	0.561037	0.280518	−	0.959849i	$-0.409494\pi$
$521$	12.8059	0.561037	0.280518	+	0.959849i	$0.409494\pi$
$522$	− 0.120638i	− 0.00528019i
$523$	21.1278i	0.923855i	0.886918	+	0.461928i	$0.152842\pi$
$523$	21.1278i	0.923855i	−0.886918	+	0.461928i	$0.847158\pi$
$524$	4.97107	0.217162
$525$	0	0
$526$	15.5090	0.676226
$527$	49.9565i	2.17614i
$528$	2.28685i	0.0995223i
$529$	17.7526	0.771851
$530$	0	0
$531$	−0.764867	−0.0331924
$532$	− 1.40871i	− 0.0610753i
$533$	0.313511i	0.0135797i
$534$	−12.4657	−0.539445
$535$	0	0
$536$	14.3318	0.619038
$537$	25.3607i	1.09439i
$538$	− 43.3607i	− 1.86941i
$539$	1.91935	0.0826725
$540$	0	0
$541$	32.7382	1.40753	0.703763	−	0.710435i	$-0.251502\pi$
$541$	32.7382	1.40753	0.703763	+	0.710435i	$0.251502\pi$
$542$	44.3318i	1.90421i
$543$	10.1112i	0.433912i
$544$	10.2542	0.439646
$545$	0	0
$546$	−1.52973	−0.0654666
$547$	− 22.1073i	− 0.945240i	−0.881266	−	0.472620i	$-0.843308\pi$
$547$	− 22.1073i	− 0.945240i	0.881266	−	0.472620i	$-0.156692\pi$
$548$	5.00227i	0.213686i
$549$	0.241276	0.0102974
$550$	0	0
$551$	−6.04945	−0.257715
$552$	− 9.82887i	− 0.418344i
$553$	− 7.81658i	− 0.332395i
$554$	−0.0410378	−0.00174353
$555$	0	0
$556$	−1.80674	−0.0766229
$557$	− 39.8720i	− 1.68943i	−0.535216	−	0.844715i	$-0.679770\pi$
$557$	− 39.8720i	− 1.68943i	0.535216	−	0.844715i	$-0.320230\pi$
$558$	1.21235i	0.0513227i
$559$	−5.26180	−0.222550
$560$	0	0
$561$	2.47027	0.104295
$562$	− 43.2085i	− 1.82264i
$563$	− 10.1217i	− 0.426578i	−0.976989	−	0.213289i	$-0.931582\pi$
$563$	− 10.1217i	− 0.426578i	0.976989	−	0.213289i	$-0.0684176\pi$
$564$	0.711543	0.0299614
$565$	0	0
$566$	−32.0372	−1.34662
$567$	− 5.52586i	− 0.232064i
$568$	22.7891i	0.956209i
$569$	24.4391	1.02454	0.512270	−	0.858825i	$-0.328805\pi$
$569$	24.4391	1.02454	0.512270	+	0.858825i	$0.328805\pi$
$570$	0	0
$571$	−28.2511	−1.18227	−0.591136	−	0.806572i	$-0.701320\pi$
$571$	−28.2511	−1.18227	−0.591136	+	0.806572i	$0.701320\pi$
$572$	− 0.0988967i	− 0.00413508i
$573$	− 12.0144i	− 0.501908i
$574$	−0.330332	−0.0137878
$575$	0	0
$576$	−0.472534	−0.0196889
$577$	46.1171i	1.91988i	0.280202	+	0.959941i	$0.409598\pi$
$577$	46.1171i	1.91988i	−0.280202	+	0.959941i	$0.590402\pi$
$578$	− 11.8695i	− 0.493707i
$579$	−30.5380	−1.26911
$580$	0	0
$581$	1.75872	0.0729642
$582$	− 41.8120i	− 1.73317i
$583$	0.0988967i	0.00409588i
$584$	−17.4323	−0.721352
$585$	0	0
$586$	−23.7191	−0.979828
$587$	− 0.715418i	− 0.0295285i	−0.999891	−	0.0147642i	$-0.995300\pi$
$587$	− 0.715418i	− 0.0295285i	0.999891	−	0.0147642i	$-0.00469977\pi$
$588$	4.16517i	0.171769i
$589$	60.7936	2.50496
$590$	0	0
$591$	10.4247	0.428815
$592$	− 7.14465i	− 0.293643i
$593$	− 15.5441i	− 0.638320i	−0.947701	−	0.319160i	$-0.896599\pi$
$593$	− 15.5441i	− 0.638320i	0.947701	−	0.319160i	$-0.103401\pi$
$594$	2.35455	0.0966083
$595$	0	0
$596$	−4.62249	−0.189344
$597$	− 16.6803i	− 0.682681i
$598$	3.24951i	0.132882i
$599$	9.59809	0.392167	0.196084	−	0.980587i	$-0.437178\pi$
$599$	9.59809	0.392167	0.196084	+	0.980587i	$0.437178\pi$
$600$	0	0
$601$	6.81044	0.277804	0.138902	−	0.990306i	$-0.455643\pi$
$601$	6.81044	0.277804	0.138902	+	0.990306i	$0.455643\pi$
$602$	− 5.54411i	− 0.225961i
$603$	− 0.447480i	− 0.0182228i
$604$	−2.80590	−0.114171
$605$	0	0
$606$	−32.2434	−1.30980
$607$	31.6970i	1.28654i	0.765639	+	0.643271i	$0.222423\pi$
$607$	31.6970i	1.28654i	−0.765639	+	0.643271i	$0.777577\pi$
$608$	− 12.4787i	− 0.506077i
$609$	−1.07838	−0.0436981
$610$	0	0
$611$	1.03943	0.0420508
$612$	− 0.143810i	− 0.00581318i
$613$	− 1.20394i	− 0.0486265i	−0.999704	−	0.0243133i	$-0.992260\pi$
$613$	− 1.20394i	− 0.0486265i	0.999704	−	0.0243133i	$-0.00773992\pi$
$614$	43.7602	1.76602
$615$	0	0
$616$	−0.460425	−0.0185511
$617$	− 37.9337i	− 1.52715i	−0.645716	−	0.763577i	$-0.723441\pi$
$617$	− 37.9337i	− 1.52715i	0.645716	−	0.763577i	$-0.276559\pi$
$618$	20.6947i	0.832464i
$619$	4.60424	0.185060	0.0925299	−	0.995710i	$-0.470505\pi$
$619$	4.60424	0.185060	0.0925299	+	0.995710i	$0.470505\pi$
$620$	0	0
$621$	−12.0533	−0.483683
$622$	− 30.2062i	− 1.21116i
$623$	− 2.98932i	− 0.119765i
$624$	−7.24951	−0.290213
$625$	0	0
$626$	35.2618	1.40934
$627$	− 3.00614i	− 0.120054i
$628$	9.18568i	0.366549i
$629$	−7.71769	−0.307724
$630$	0	0
$631$	−8.41241	−0.334893	−0.167446	−	0.985881i	$-0.553552\pi$
$631$	−8.41241	−0.334893	−0.167446	+	0.985881i	$0.553552\pi$
$632$	− 31.1012i	− 1.23714i
$633$	− 16.8638i	− 0.670274i
$634$	−35.1857	−1.39740
$635$	0	0
$636$	−0.214614	−0.00851001
$637$	6.08452i	0.241077i
$638$	− 0.447480i	− 0.0177159i
$639$	0.711543	0.0281482
$640$	0	0
$641$	32.5380	1.28517	0.642586	−	0.766213i	$-0.277861\pi$
$641$	32.5380	1.28517	0.642586	+	0.766213i	$0.277861\pi$
$642$	33.4908i	1.32178i
$643$	2.09293i	0.0825372i	0.999148	+	0.0412686i	$0.0131399\pi$
$643$	2.09293i	0.0825372i	−0.999148	+	0.0412686i	$0.986860\pi$
$644$	−0.533431	−0.0210201
$645$	0	0
$646$	−46.2868	−1.82113
$647$	45.1955i	1.77682i	0.459051	+	0.888410i	$0.348189\pi$
$647$	45.1955i	1.77682i	−0.459051	+	0.888410i	$0.651811\pi$
$648$	− 21.9867i	− 0.863718i
$649$	−2.83710	−0.111366
$650$	0	0
$651$	10.8371	0.424739
$652$	0.165166i	0.00646840i
$653$	2.14834i	0.0840712i	0.999116	+	0.0420356i	$0.0133843\pi$
$653$	2.14834i	0.0840712i	−0.999116	+	0.0420356i	$0.986616\pi$
$654$	−32.7259	−1.27968
$655$	0	0
$656$	−1.56547	−0.0611211
$657$	0.544287i	0.0212347i
$658$	1.09520i	0.0426953i
$659$	45.0843	1.75624	0.878118	−	0.478444i	$-0.158799\pi$
$659$	45.0843	1.75624	0.878118	+	0.478444i	$0.158799\pi$
$660$	0	0
$661$	−36.3234	−1.41281	−0.706407	−	0.707806i	$-0.749685\pi$
$661$	−36.3234	−1.41281	−0.706407	+	0.707806i	$0.749685\pi$
$662$	37.0798i	1.44115i
$663$	7.83096i	0.304129i
$664$	6.99773	0.271565
$665$	0	0
$666$	−0.187293	−0.00725746
$667$	2.29072i	0.0886972i
$668$	− 7.33260i	− 0.283707i
$669$	−18.7526	−0.725017
$670$	0	0
$671$	0.894960	0.0345496
$672$	− 2.22446i	− 0.0858102i
$673$	17.4719i	0.673491i	0.941596	+	0.336746i	$0.109326\pi$
$673$	17.4719i	0.673491i	−0.941596	+	0.336746i	$0.890674\pi$
$674$	−19.6826	−0.758146
$675$	0	0
$676$	−4.48482	−0.172493
$677$	− 40.0372i	− 1.53875i	−0.638796	−	0.769377i	$-0.720567\pi$
$677$	− 40.0372i	− 1.53875i	0.638796	−	0.769377i	$-0.279433\pi$
$678$	− 33.0784i	− 1.27037i
$679$	10.0267	0.384788
$680$	0	0
$681$	−21.4452	−0.821782
$682$	4.49693i	0.172196i
$683$	− 2.07611i	− 0.0794402i	−0.999211	−	0.0397201i	$-0.987353\pi$
$683$	− 2.07611i	− 0.0794402i	0.999211	−	0.0397201i	$-0.0126466\pi$
$684$	−0.175007	−0.00669156
$685$	0	0
$686$	−13.2085	−0.504302
$687$	39.9299i	1.52342i
$688$	− 26.2739i	− 1.00168i
$689$	−0.313511	−0.0119438
$690$	0	0
$691$	26.7070	1.01598	0.507991	−	0.861362i	$-0.330388\pi$
$691$	26.7070	1.01598	0.507991	+	0.861362i	$0.330388\pi$
$692$	− 9.38735i	− 0.356854i
$693$	0.0143758i	0 0.000546093i
$694$	−12.9542	−0.491737
$695$	0	0
$696$	−4.29072	−0.162639
$697$	1.69102i	0.0640521i
$698$	− 34.1666i	− 1.29322i
$699$	−21.3151	−0.806212
$700$	0	0
$701$	−21.9155	−0.827736	−0.413868	−	0.910337i	$-0.635823\pi$
$701$	−21.9155	−0.827736	−0.413868	+	0.910337i	$0.635823\pi$
$702$	7.46412i	0.281715i
$703$	9.39189i	0.354222i
$704$	−1.75276	−0.0660596
$705$	0	0
$706$	−9.51745	−0.358194
$707$	− 7.73206i	− 0.290794i
$708$	− 6.15676i	− 0.231385i
$709$	4.60811	0.173061	0.0865306	−	0.996249i	$-0.472422\pi$
$709$	4.60811	0.173061	0.0865306	+	0.996249i	$0.472422\pi$
$710$	0	0
$711$	−0.971071	−0.0364180
$712$	− 11.8941i	− 0.445751i
$713$	− 23.0205i	− 0.862125i
$714$	−8.25112	−0.308790
$715$	0	0
$716$	5.47641	0.204663
$717$	23.5174i	0.878275i
$718$	− 7.78151i	− 0.290403i
$719$	−6.80590	−0.253817	−0.126909	−	0.991914i	$-0.540506\pi$
$719$	−6.80590	−0.253817	−0.126909	+	0.991914i	$0.540506\pi$
$720$	0	0
$721$	−4.96266	−0.184819
$722$	27.0833i	1.00794i
$723$	25.0928i	0.933210i
$724$	2.18342	0.0811461
$725$	0	0
$726$	−28.7175	−1.06581
$727$	− 26.9711i	− 1.00030i	−0.865938	−	0.500151i	$-0.833278\pi$
$727$	− 26.9711i	− 1.00030i	0.865938	−	0.500151i	$-0.166722\pi$
$728$	− 1.45959i	− 0.0540960i
$729$	−27.6681	−1.02474
$730$	0	0
$731$	−28.3812	−1.04972
$732$	1.94214i	0.0717836i
$733$	30.0638i	1.11043i	0.831706	+	0.555216i	$0.187365\pi$
$733$	30.0638i	1.11043i	−0.831706	+	0.555216i	$0.812635\pi$
$734$	−45.4680	−1.67825
$735$	0	0
$736$	−4.72526	−0.174175
$737$	− 1.65983i	− 0.0611405i
$738$	0.0410378i	0.00151062i
$739$	−51.1422	−1.88130	−0.940648	−	0.339383i	$-0.889782\pi$
$739$	−51.1422	−1.88130	−0.940648	+	0.339383i	$0.889782\pi$
$740$	0	0
$741$	9.52973	0.350084
$742$	− 0.330332i	− 0.0121269i
$743$	− 11.1857i	− 0.410363i	−0.978724	−	0.205181i	$-0.934222\pi$
$743$	− 11.1857i	− 0.410363i	0.978724	−	0.205181i	$-0.0657785\pi$
$744$	43.1194	1.58083
$745$	0	0
$746$	22.1834	0.812193
$747$	− 0.218490i	− 0.00799413i
$748$	− 0.533431i	− 0.0195042i
$749$	−8.03120	−0.293454
$750$	0	0
$751$	−18.3630	−0.670074	−0.335037	−	0.942205i	$-0.608749\pi$
$751$	−18.3630	−0.670074	−0.335037	+	0.942205i	$0.608749\pi$
$752$	5.19022i	0.189268i
$753$	− 26.3935i	− 0.961832i
$754$	1.41855	0.0516606
$755$	0	0
$756$	−1.22529	−0.0445634
$757$	15.8927i	0.577630i	0.957385	+	0.288815i	$0.0932612\pi$
$757$	15.8927i	0.577630i	−0.957385	+	0.288815i	$0.906739\pi$
$758$	− 21.7548i	− 0.790172i
$759$	−1.13833	−0.0413186
$760$	0	0
$761$	13.8843	0.503305	0.251652	−	0.967818i	$-0.419026\pi$
$761$	13.8843	0.503305	0.251652	+	0.967818i	$0.419026\pi$
$762$	− 55.0205i	− 1.99318i
$763$	− 7.84778i	− 0.284109i
$764$	−2.59439	−0.0938619
$765$	0	0
$766$	−24.2907	−0.877660
$767$	− 8.99386i	− 0.324749i
$768$	− 14.6576i	− 0.528909i
$769$	35.4063	1.27678	0.638391	−	0.769712i	$-0.279600\pi$
$769$	35.4063	1.27678	0.638391	+	0.769712i	$0.279600\pi$
$770$	0	0
$771$	−10.7382	−0.386727
$772$	6.59439i	0.237337i
$773$	0.488518i	0.0175708i	0.999961	+	0.00878539i	$0.00279651\pi$
$773$	0.488518i	0.0175708i	−0.999961	+	0.00878539i	$0.997203\pi$
$774$	−0.688756	−0.0247568
$775$	0	0
$776$	39.8948	1.43214
$777$	1.67420i	0.0600617i
$778$	21.2663i	0.762435i
$779$	2.05786	0.0737304
$780$	0	0
$781$	2.63931	0.0944419
$782$	17.5273i	0.626775i
$783$	5.26180i	0.188041i
$784$	−30.3820	−1.08507
$785$	0	0
$786$	−35.4329	−1.26385
$787$	− 1.99159i	− 0.0709925i	−0.999370	−	0.0354962i	$-0.988699\pi$
$787$	− 1.99159i	− 0.0709925i	0.999370	−	0.0354962i	$-0.0113012\pi$
$788$	− 2.25112i	− 0.0801927i
$789$	−17.2228	−0.613150
$790$	0	0
$791$	7.93230	0.282040
$792$	0.0571996i	0.00203250i
$793$	2.83710i	0.100748i
$794$	−13.9323	−0.494439
$795$	0	0
$796$	−3.60197	−0.127668
$797$	− 17.2702i	− 0.611742i	−0.952073	−	0.305871i	$-0.901052\pi$
$797$	− 17.2702i	− 0.611742i	0.952073	−	0.305871i	$-0.0989476\pi$
$798$	10.0410i	0.355449i
$799$	5.60650	0.198344
$800$	0	0
$801$	−0.371370	−0.0131217
$802$	30.4124i	1.07390i
$803$	2.01891i	0.0712458i
$804$	3.60197	0.127032
$805$	0	0
$806$	−14.2557	−0.502134
$807$	48.1522i	1.69504i
$808$	− 30.7649i	− 1.08230i
$809$	56.5068	1.98667	0.993336	−	0.115254i	$-0.0367680\pi$
$809$	56.5068	1.98667	0.993336	+	0.115254i	$0.0367680\pi$
$810$	0	0
$811$	−8.77924	−0.308281	−0.154140	−	0.988049i	$-0.549261\pi$
$811$	−8.77924	−0.308281	−0.154140	+	0.988049i	$0.549261\pi$
$812$	0.232866i	0.00817199i
$813$	− 49.2306i	− 1.72659i
$814$	−0.694722	−0.0243500
$815$	0	0
$816$	−39.1026	−1.36886
$817$	34.5380i	1.20833i
$818$	2.64384i	0.0924398i
$819$	−0.0455727	−0.00159244
$820$	0	0
$821$	−28.1568	−0.982678	−0.491339	−	0.870969i	$-0.663492\pi$
$821$	−28.1568	−0.982678	−0.491339	+	0.870969i	$0.663492\pi$
$822$	− 35.6553i	− 1.24362i
$823$	− 20.7442i	− 0.723096i	−0.932353	−	0.361548i	$-0.882248\pi$
$823$	− 20.7442i	− 0.723096i	0.932353	−	0.361548i	$-0.117752\pi$
$824$	−19.7458	−0.687877
$825$	0	0
$826$	9.47641	0.329726
$827$	− 9.12783i	− 0.317406i	−0.987326	−	0.158703i	$-0.949269\pi$
$827$	− 9.12783i	− 0.317406i	0.987326	−	0.158703i	$-0.0507312\pi$
$828$	0.0662693i	0.00230302i
$829$	−31.8576	−1.10646	−0.553230	−	0.833028i	$-0.686605\pi$
$829$	−31.8576	−1.10646	−0.553230	+	0.833028i	$0.686605\pi$
$830$	0	0
$831$	0.0455727	0.00158090
$832$	− 5.55640i	− 0.192633i
$833$	32.8188i	1.13711i
$834$	12.8781	0.445933
$835$	0	0
$836$	−0.649149	−0.0224513
$837$	− 52.8781i	− 1.82774i
$838$	54.6902i	1.88924i
$839$	−27.4413	−0.947380	−0.473690	−	0.880692i	$-0.657078\pi$
$839$	−27.4413	−0.947380	−0.473690	+	0.880692i	$0.657078\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	− 18.5814i	− 0.640359i
$843$	47.9832i	1.65263i
$844$	−3.64158	−0.125348
$845$	0	0
$846$	0.136059	0.00467780
$847$	− 6.88655i	− 0.236625i
$848$	− 1.56547i	− 0.0537583i
$849$	35.5774	1.22101
$850$	0	0
$851$	3.55640	0.121912
$852$	5.72753i	0.196222i
$853$	56.0515i	1.91917i	0.281422	+	0.959584i	$0.409194\pi$
$853$	56.0515i	1.91917i	−0.281422	+	0.959584i	$0.590806\pi$
$854$	−2.98932	−0.102292
$855$	0	0
$856$	−31.9551	−1.09220
$857$	− 6.08452i	− 0.207843i	−0.994585	−	0.103922i	$-0.966861\pi$
$857$	− 6.08452i	− 0.207843i	0.994585	−	0.103922i	$-0.0331391\pi$
$858$	0.704918i	0.0240655i
$859$	−35.5936	−1.21444	−0.607218	−	0.794535i	$-0.707715\pi$
$859$	−35.5936	−1.21444	−0.607218	+	0.794535i	$0.707715\pi$
$860$	0	0
$861$	0.366835	0.0125017
$862$	30.5236i	1.03964i
$863$	12.8287i	0.436694i	0.975871	+	0.218347i	$0.0700664\pi$
$863$	12.8287i	0.436694i	−0.975871	+	0.218347i	$0.929934\pi$
$864$	−10.8539	−0.369258
$865$	0	0
$866$	22.8020	0.774844
$867$	13.1812i	0.447655i
$868$	− 2.34017i	− 0.0794306i
$869$	−3.60197	−0.122188
$870$	0	0
$871$	5.26180	0.178289
$872$	− 31.2253i	− 1.05742i
$873$	− 1.24563i	− 0.0421583i
$874$	21.3295	0.721481
$875$	0	0
$876$	−4.38121	−0.148027
$877$	− 1.50307i	− 0.0507551i	−0.999678	−	0.0253776i	$-0.991921\pi$
$877$	− 1.50307i	− 0.0507551i	0.999678	−	0.0253776i	$-0.00807880\pi$
$878$	27.4863i	0.927616i
$879$	26.3402	0.888432
$880$	0	0
$881$	23.4908	0.791425	0.395712	−	0.918375i	$-0.370498\pi$
$881$	23.4908	0.791425	0.395712	+	0.918375i	$0.370498\pi$
$882$	0.796449i	0.0268178i
$883$	29.0433i	0.977385i	0.872456	+	0.488693i	$0.162526\pi$
$883$	29.0433i	0.977385i	−0.872456	+	0.488693i	$0.837474\pi$
$884$	1.69102	0.0568753
$885$	0	0
$886$	51.7068	1.73712
$887$	− 19.0700i	− 0.640307i	−0.947366	−	0.320153i	$-0.896266\pi$
$887$	− 19.0700i	− 0.640307i	0.947366	−	0.320153i	$-0.103734\pi$
$888$	6.66144i	0.223543i
$889$	13.1941	0.442516
$890$	0	0
$891$	−2.54638	−0.0853068
$892$	4.04945i	0.135586i
$893$	− 6.82273i	− 0.228314i
$894$	32.9483	1.10196
$895$	0	0
$896$	8.45732	0.282539
$897$	− 3.60859i	− 0.120487i
$898$	− 10.8950i	− 0.363570i
$899$	−10.0494	−0.335168
$900$	0	0
$901$	−1.69102	−0.0563362
$902$	0.152221i	0.00506839i
$903$	6.15676i	0.204884i
$904$	31.5616	1.04972
$905$	0	0
$906$	20.0000	0.664455
$907$	5.54023i	0.183960i	0.995761	+	0.0919802i	$0.0293197\pi$
$907$	5.54023i	0.183960i	−0.995761	+	0.0919802i	$0.970680\pi$
$908$	4.63090i	0.153682i
$909$	−0.960570	−0.0318601
$910$	0	0
$911$	53.2990	1.76587	0.882937	−	0.469492i	$-0.155563\pi$
$911$	53.2990	1.76587	0.882937	+	0.469492i	$0.155563\pi$
$912$	47.5851i	1.57570i
$913$	− 0.810439i	− 0.0268216i
$914$	8.95282	0.296133
$915$	0	0
$916$	8.62249	0.284895
$917$	− 8.49693i	− 0.280593i
$918$	40.2602i	1.32878i
$919$	−37.5897	−1.23997	−0.619985	−	0.784614i	$-0.712861\pi$
$919$	−37.5897	−1.23997	−0.619985	+	0.784614i	$0.712861\pi$
$920$	0	0
$921$	−48.5958	−1.60129
$922$	− 49.7296i	− 1.63776i
$923$	8.36683i	0.275398i
$924$	−0.115718	−0.00380683
$925$	0	0
$926$	2.21849	0.0729041
$927$	0.616522i	0.0202492i
$928$	2.06278i	0.0677140i
$929$	−37.3197	−1.22442	−0.612209	−	0.790696i	$-0.709719\pi$
$929$	−37.3197	−1.22442	−0.612209	+	0.790696i	$0.709719\pi$
$930$	0	0
$931$	39.9383	1.30892
$932$	4.60281i	0.150770i
$933$	33.5441i	1.09818i
$934$	18.0860	0.591790
$935$	0	0
$936$	−0.181328	−0.00592688
$937$	− 22.8638i	− 0.746927i	−0.927645	−	0.373463i	$-0.878170\pi$
$937$	− 22.8638i	− 0.746927i	0.927645	−	0.373463i	$-0.121830\pi$
$938$	5.54411i	0.181022i
$939$	−39.1584	−1.27788
$940$	0	0
$941$	0.523590	0.0170686	0.00853428	−	0.999964i	$-0.497283\pi$
$941$	0.523590	0.0170686	0.00853428	+	0.999964i	$0.497283\pi$
$942$	− 65.4740i	− 2.13326i
$943$	− 0.779243i	− 0.0253756i
$944$	44.9093	1.46167
$945$	0	0
$946$	−2.55479	−0.0830633
$947$	− 10.0228i	− 0.325697i	−0.986651	−	0.162848i	$-0.947932\pi$
$947$	− 10.0228i	− 0.325697i	0.986651	−	0.162848i	$-0.0520681\pi$
$948$	− 7.81658i	− 0.253871i
$949$	−6.40012	−0.207757
$950$	0	0
$951$	39.0738	1.26706
$952$	− 7.87277i	− 0.255158i
$953$	8.15676i	0.264223i	0.991235	+	0.132112i	$0.0421757\pi$
$953$	8.15676i	0.264223i	−0.991235	+	0.132112i	$0.957824\pi$
$954$	−0.0410378	−0.00132865
$955$	0	0
$956$	5.07838	0.164246
$957$	0.496928i	0.0160634i
$958$	− 26.4261i	− 0.853789i
$959$	8.55025	0.276102
$960$	0	0
$961$	69.9914	2.25779
$962$	− 2.20233i	− 0.0710059i
$963$	0.997733i	0.0321515i
$964$	5.41855	0.174520
$965$	0	0
$966$	3.80221	0.122334
$967$	15.7671i	0.507037i	0.967331	+	0.253518i	$0.0815878\pi$
$967$	15.7671i	0.507037i	−0.967331	+	0.253518i	$0.918412\pi$
$968$	− 27.4007i	− 0.880691i
$969$	51.4017	1.65126
$970$	0	0
$971$	−17.8804	−0.573810	−0.286905	−	0.957959i	$-0.592626\pi$
$971$	−17.8804	−0.573810	−0.286905	+	0.957959i	$0.592626\pi$
$972$	0.300566i	0.00964065i
$973$	3.08822i	0.0990037i
$974$	6.31494	0.202344
$975$	0	0
$976$	−14.1666	−0.453462
$977$	− 55.1071i	− 1.76303i	−0.472153	−	0.881517i	$-0.656523\pi$
$977$	− 55.1071i	− 1.76303i	0.472153	−	0.881517i	$-0.343477\pi$
$978$	− 1.17727i	− 0.0376451i
$979$	−1.37751	−0.0440255
$980$	0	0
$981$	−0.974946	−0.0311276
$982$	62.7540i	2.00256i
$983$	1.29687i	0.0413637i	0.999786	+	0.0206818i	$0.00658370\pi$
$983$	1.29687i	0.0413637i	−0.999786	+	0.0206818i	$0.993416\pi$
$984$	1.45959	0.0465300
$985$	0	0
$986$	7.65142	0.243671
$987$	− 1.21622i	− 0.0387128i
$988$	− 2.05786i	− 0.0654692i
$989$	13.0784	0.415868
$990$	0	0
$991$	−3.11942	−0.0990915	−0.0495458	−	0.998772i	$-0.515777\pi$
$991$	−3.11942	−0.0990915	−0.0495458	+	0.998772i	$0.515777\pi$
$992$	− 20.7298i	− 0.658172i
$993$	− 41.1773i	− 1.30672i
$994$	−8.81575	−0.279618
$995$	0	0
$996$	1.75872	0.0557273
$997$	30.2472i	0.957940i	0.877831	+	0.478970i	$0.158990\pi$
$997$	30.2472i	0.957940i	−0.877831	+	0.478970i	$0.841010\pi$
$998$	28.4292i	0.899912i
$999$	8.16904	0.258457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.b.d.349.5		6
5.2	odd	4		725.2.a.d.1.2		3
5.3	odd	4		145.2.a.d.1.2	✓	3
5.4	even	2	inner	725.2.b.d.349.2		6
15.2	even	4		6525.2.a.bh.1.2		3
15.8	even	4		1305.2.a.o.1.2		3
20.3	even	4		2320.2.a.s.1.1		3
35.13	even	4		7105.2.a.p.1.2		3
40.3	even	4		9280.2.a.bm.1.3		3
40.13	odd	4		9280.2.a.bu.1.1		3
145.28	odd	4		4205.2.a.e.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.a.d.1.2	✓	3	5.3	odd	4
725.2.a.d.1.2		3	5.2	odd	4
725.2.b.d.349.2		6	5.4	even	2	inner
725.2.b.d.349.5		6	1.1	even	1	trivial
1305.2.a.o.1.2		3	15.8	even	4
2320.2.a.s.1.1		3	20.3	even	4
4205.2.a.e.1.2		3	145.28	odd	4
6525.2.a.bh.1.2		3	15.2	even	4
7105.2.a.p.1.2		3	35.13	even	4
9280.2.a.bm.1.3		3	40.3	even	4
9280.2.a.bu.1.1		3	40.13	odd	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)

\(f(q)\)	\(=\)	\(q+1.53919i q^{2} -1.70928i q^{3} -0.369102 q^{4} +2.63090 q^{6} +0.630898i q^{7} +2.51026i q^{8} +0.0783777 q^{9} +0.290725 q^{11} +0.630898i q^{12} +0.921622i q^{13} -0.971071 q^{14} -4.60197 q^{16} +4.97107i q^{17} +0.120638i q^{18} +6.04945 q^{19} +1.07838 q^{21} +0.447480i q^{22} -2.29072i q^{23} +4.29072 q^{24} -1.41855 q^{26} -5.26180i q^{27} -0.232866i q^{28} -1.00000 q^{29} +10.0494 q^{31} -2.06278i q^{32} -0.496928i q^{33} -7.65142 q^{34} -0.0289294 q^{36} +1.55252i q^{37} +9.31124i q^{38} +1.57531 q^{39} +0.340173 q^{41} +1.65983i q^{42} +5.70928i q^{43} -0.107307 q^{44} +3.52586 q^{46} -1.12783i q^{47} +7.86603i q^{48} +6.60197 q^{49} +8.49693 q^{51} -0.340173i q^{52} +0.340173i q^{53} +8.09890 q^{54} -1.58372 q^{56} -10.3402i q^{57} -1.53919i q^{58} -9.75872 q^{59} +3.07838 q^{61} +15.4680i q^{62} +0.0494483i q^{63} -6.02893 q^{64} +0.764867 q^{66} -5.70928i q^{67} -1.83483i q^{68} -3.91548 q^{69} +9.07838 q^{71} +0.196748i q^{72} +6.94441i q^{73} -2.38962 q^{74} -2.23287 q^{76} +0.183417i q^{77} +2.42469i q^{78} -12.3896 q^{79} -8.75872 q^{81} +0.523590i q^{82} -2.78765i q^{83} -0.398032 q^{84} -8.78765 q^{86} +1.70928i q^{87} +0.729794i q^{88} -4.73820 q^{89} -0.581449 q^{91} +0.845512i q^{92} -17.1773i q^{93} +1.73594 q^{94} -3.52586 q^{96} -15.8927i q^{97} +10.1617i q^{98} +0.0227863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 8 q^{6} - 6 q^{9} + 16 q^{11} + 24 q^{14} + 10 q^{16} + 40 q^{24} + 20 q^{26} - 6 q^{29} + 24 q^{31} + 28 q^{34} - 30 q^{36} - 32 q^{39} - 20 q^{41} - 24 q^{44} + 16 q^{46} + 2 q^{49} + 16 q^{51}+ \cdots - 40 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 8 * q^6 - 6 * q^9 + 16 * q^11 + 24 * q^14 + 10 * q^16 + 40 * q^24 + 20 * q^26 - 6 * q^29 + 24 * q^31 + 28 * q^34 - 30 * q^36 - 32 * q^39 - 20 * q^41 - 24 * q^44 + 16 * q^46 + 2 * q^49 + 16 * q^51 - 24 * q^54 - 64 * q^56 - 8 * q^59 + 12 * q^61 - 66 * q^64 + 24 * q^66 + 40 * q^69 + 48 * q^71 + 44 * q^74 + 32 * q^76 - 16 * q^79 - 2 * q^81 - 40 * q^84 - 32 * q^86 - 44 * q^89 - 32 * q^91 - 16 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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