LMFDB - Embedded newform 1850.2.b.k.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(149,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("1850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.k.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.44949i q^{3} -1.00000 q^{4} -1.44949 q^{6} -2.44949i q^{7} +1.00000i q^{8} +0.898979 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.44949i q^{3} -1.00000 q^{4} -1.44949 q^{6} -2.44949i q^{7} +1.00000i q^{8} +0.898979 q^{9} +3.44949 q^{11} +1.44949i q^{12} -0.449490i q^{13} -2.44949 q^{14} +1.00000 q^{16} -3.44949i q^{17} -0.898979i q^{18} +5.00000 q^{19} -3.55051 q^{21} -3.44949i q^{22} +2.00000i q^{23} +1.44949 q^{24} -0.449490 q^{26} -5.65153i q^{27} +2.44949i q^{28} +0.898979 q^{29} +4.44949 q^{31} -1.00000i q^{32} -5.00000i q^{33} -3.44949 q^{34} -0.898979 q^{36} +1.00000i q^{37} -5.00000i q^{38} -0.651531 q^{39} +1.00000 q^{41} +3.55051i q^{42} -1.10102i q^{43} -3.44949 q^{44} +2.00000 q^{46} -9.79796i q^{47} -1.44949i q^{48} +1.00000 q^{49} -5.00000 q^{51} +0.449490i q^{52} +6.00000i q^{53} -5.65153 q^{54} +2.44949 q^{56} -7.24745i q^{57} -0.898979i q^{58} +2.00000 q^{59} -6.44949 q^{61} -4.44949i q^{62} -2.20204i q^{63} -1.00000 q^{64} -5.00000 q^{66} -4.55051i q^{67} +3.44949i q^{68} +2.89898 q^{69} -7.55051 q^{71} +0.898979i q^{72} +12.7980i q^{73} +1.00000 q^{74} -5.00000 q^{76} -8.44949i q^{77} +0.651531i q^{78} -7.79796 q^{79} -5.49490 q^{81} -1.00000i q^{82} +3.44949i q^{83} +3.55051 q^{84} -1.10102 q^{86} -1.30306i q^{87} +3.44949i q^{88} -14.3485 q^{89} -1.10102 q^{91} -2.00000i q^{92} -6.44949i q^{93} -9.79796 q^{94} -1.44949 q^{96} -14.0000i q^{97} -1.00000i q^{98} +3.10102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 16 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 16 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 16 q^{9} + 4 q^{11} + 4 q^{16} + 20 q^{19} - 24 q^{21} - 4 q^{24} + 8 q^{26} - 16 q^{29} + 8 q^{31} - 4 q^{34} + 16 q^{36} - 32 q^{39} + 4 q^{41} - 4 q^{44} + 8 q^{46} + 4 q^{49} - 20 q^{51} - 52 q^{54} + 8 q^{59} - 16 q^{61} - 4 q^{64} - 20 q^{66} - 8 q^{69} - 40 q^{71} + 4 q^{74} - 20 q^{76} + 8 q^{79} + 76 q^{81} + 24 q^{84} - 24 q^{86} - 28 q^{89} - 24 q^{91} + 4 q^{96} + 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 16 * q^9 + 4 * q^11 + 4 * q^16 + 20 * q^19 - 24 * q^21 - 4 * q^24 + 8 * q^26 - 16 * q^29 + 8 * q^31 - 4 * q^34 + 16 * q^36 - 32 * q^39 + 4 * q^41 - 4 * q^44 + 8 * q^46 + 4 * q^49 - 20 * q^51 - 52 * q^54 + 8 * q^59 - 16 * q^61 - 4 * q^64 - 20 * q^66 - 8 * q^69 - 40 * q^71 + 4 * q^74 - 20 * q^76 + 8 * q^79 + 76 * q^81 + 24 * q^84 - 24 * q^86 - 28 * q^89 - 24 * q^91 + 4 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	− 1.44949i	− 0.836863i	−0.908248	−	0.418432i	$-0.862580\pi$
$3$	− 1.44949i	− 0.836863i	0.908248	−	0.418432i	$-0.137420\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.44949	−0.591752
$7$	− 2.44949i	− 0.925820i	−0.886405	−	0.462910i	$-0.846805\pi$
$7$	− 2.44949i	− 0.925820i	0.886405	−	0.462910i	$-0.153195\pi$
$8$	1.00000i	0.353553i
$9$	0.898979	0.299660
$10$	0	0
$11$	3.44949	1.04006	0.520030	−	0.854148i	$-0.325921\pi$
$11$	3.44949	1.04006	0.520030	+	0.854148i	$0.325921\pi$
$12$	1.44949i	0.418432i
$13$	− 0.449490i	− 0.124666i	−0.998055	−	0.0623330i	$-0.980146\pi$
$13$	− 0.449490i	− 0.124666i	0.998055	−	0.0623330i	$-0.0198541\pi$
$14$	−2.44949	−0.654654
$15$	0	0
$16$	1.00000	0.250000
$17$	− 3.44949i	− 0.836624i	−0.908303	−	0.418312i	$-0.862622\pi$
$17$	− 3.44949i	− 0.836624i	0.908303	−	0.418312i	$-0.137378\pi$
$18$	− 0.898979i	− 0.211891i
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	0	0
$21$	−3.55051	−0.774785
$22$	− 3.44949i	− 0.735434i
$23$	2.00000i	0.417029i	0.978019	+	0.208514i	$0.0668628\pi$
$23$	2.00000i	0.417029i	−0.978019	+	0.208514i	$0.933137\pi$
$24$	1.44949	0.295876
$25$	0	0
$26$	−0.449490	−0.0881522
$27$	− 5.65153i	− 1.08764i
$28$	2.44949i	0.462910i
$29$	0.898979	0.166936	0.0834681	−	0.996510i	$-0.473400\pi$
$29$	0.898979	0.166936	0.0834681	+	0.996510i	$0.473400\pi$
$30$	0	0
$31$	4.44949	0.799152	0.399576	−	0.916700i	$-0.369157\pi$
$31$	4.44949	0.799152	0.399576	+	0.916700i	$0.369157\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 5.00000i	− 0.870388i
$34$	−3.44949	−0.591583
$35$	0	0
$36$	−0.898979	−0.149830
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	− 5.00000i	− 0.811107i
$39$	−0.651531	−0.104328
$40$	0	0
$41$	1.00000	0.156174	0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000	0.156174	0.0780869	+	0.996947i	$0.475119\pi$
$42$	3.55051i	0.547856i
$43$	− 1.10102i	− 0.167904i	−0.996470	−	0.0839520i	$-0.973246\pi$
$43$	− 1.10102i	− 0.167904i	0.996470	−	0.0839520i	$-0.0267543\pi$
$44$	−3.44949	−0.520030
$45$	0	0
$46$	2.00000	0.294884
$47$	− 9.79796i	− 1.42918i	−0.699544	−	0.714590i	$-0.746613\pi$
$47$	− 9.79796i	− 1.42918i	0.699544	−	0.714590i	$-0.253387\pi$
$48$	− 1.44949i	− 0.209216i
$49$	1.00000	0.142857
$50$	0	0
$51$	−5.00000	−0.700140
$52$	0.449490i	0.0623330i
$53$	6.00000i	0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$	6.00000i	0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	−5.65153	−0.769076
$55$	0	0
$56$	2.44949	0.327327
$57$	− 7.24745i	− 0.959948i
$58$	− 0.898979i	− 0.118042i
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	0	0
$61$	−6.44949	−0.825773	−0.412886	−	0.910783i	$-0.635479\pi$
$61$	−6.44949	−0.825773	−0.412886	+	0.910783i	$0.635479\pi$
$62$	− 4.44949i	− 0.565086i
$63$	− 2.20204i	− 0.277431i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−5.00000	−0.615457
$67$	− 4.55051i	− 0.555933i	−0.960591	−	0.277967i	$-0.910340\pi$
$67$	− 4.55051i	− 0.555933i	0.960591	−	0.277967i	$-0.0896605\pi$
$68$	3.44949i	0.418312i
$69$	2.89898	0.348996
$70$	0	0
$71$	−7.55051	−0.896081	−0.448040	−	0.894013i	$-0.647878\pi$
$71$	−7.55051	−0.896081	−0.448040	+	0.894013i	$0.647878\pi$
$72$	0.898979i	0.105946i
$73$	12.7980i	1.49789i	0.662633	+	0.748944i	$0.269439\pi$
$73$	12.7980i	1.49789i	−0.662633	+	0.748944i	$0.730561\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−5.00000	−0.573539
$77$	− 8.44949i	− 0.962909i
$78$	0.651531i	0.0737713i
$79$	−7.79796	−0.877339	−0.438669	−	0.898648i	$-0.644550\pi$
$79$	−7.79796	−0.877339	−0.438669	+	0.898648i	$0.644550\pi$
$80$	0	0
$81$	−5.49490	−0.610544
$82$	− 1.00000i	− 0.110432i
$83$	3.44949i	0.378631i	0.981916	+	0.189315i	$0.0606268\pi$
$83$	3.44949i	0.378631i	−0.981916	+	0.189315i	$0.939373\pi$
$84$	3.55051	0.387392
$85$	0	0
$86$	−1.10102	−0.118726
$87$	− 1.30306i	− 0.139703i
$88$	3.44949i	0.367717i
$89$	−14.3485	−1.52093	−0.760467	−	0.649376i	$-0.775030\pi$
$89$	−14.3485	−1.52093	−0.760467	+	0.649376i	$0.775030\pi$
$90$	0	0
$91$	−1.10102	−0.115418
$92$	− 2.00000i	− 0.208514i
$93$	− 6.44949i	− 0.668781i
$94$	−9.79796	−1.01058
$95$	0	0
$96$	−1.44949	−0.147938
$97$	− 14.0000i	− 1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$	− 14.0000i	− 1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$	− 1.00000i	− 0.101015i
$99$	3.10102	0.311664
$100$	0	0
$101$	1.10102	0.109556	0.0547778	−	0.998499i	$-0.482555\pi$
$101$	1.10102	0.109556	0.0547778	+	0.998499i	$0.482555\pi$
$102$	5.00000i	0.495074i
$103$	6.44949i	0.635487i	0.948177	+	0.317744i	$0.102925\pi$
$103$	6.44949i	0.635487i	−0.948177	+	0.317744i	$0.897075\pi$
$104$	0.449490	0.0440761
$105$	0	0
$106$	6.00000	0.582772
$107$	8.55051i	0.826609i	0.910593	+	0.413305i	$0.135625\pi$
$107$	8.55051i	0.826609i	−0.910593	+	0.413305i	$0.864375\pi$
$108$	5.65153i	0.543819i
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	0	0
$111$	1.44949	0.137579
$112$	− 2.44949i	− 0.231455i
$113$	− 4.55051i	− 0.428076i	−0.976825	−	0.214038i	$-0.931338\pi$
$113$	− 4.55051i	− 0.428076i	0.976825	−	0.214038i	$-0.0686616\pi$
$114$	−7.24745	−0.678786
$115$	0	0
$116$	−0.898979	−0.0834681
$117$	− 0.404082i	− 0.0373574i
$118$	− 2.00000i	− 0.184115i
$119$	−8.44949	−0.774563
$120$	0	0
$121$	0.898979	0.0817254
$122$	6.44949i	0.583909i
$123$	− 1.44949i	− 0.130696i
$124$	−4.44949	−0.399576
$125$	0	0
$126$	−2.20204	−0.196173
$127$	16.2474i	1.44173i	0.693077	+	0.720864i	$0.256255\pi$
$127$	16.2474i	1.44173i	−0.693077	+	0.720864i	$0.743745\pi$
$128$	1.00000i	0.0883883i
$129$	−1.59592	−0.140513
$130$	0	0
$131$	8.69694	0.759855	0.379928	−	0.925016i	$-0.375949\pi$
$131$	8.69694	0.759855	0.379928	+	0.925016i	$0.375949\pi$
$132$	5.00000i	0.435194i
$133$	− 12.2474i	− 1.06199i
$134$	−4.55051	−0.393104
$135$	0	0
$136$	3.44949	0.295791
$137$	− 9.69694i	− 0.828465i	−0.910171	−	0.414233i	$-0.864050\pi$
$137$	− 9.69694i	− 0.828465i	0.910171	−	0.414233i	$-0.135950\pi$
$138$	− 2.89898i	− 0.246778i
$139$	12.5505	1.06452	0.532260	−	0.846581i	$-0.321343\pi$
$139$	12.5505	1.06452	0.532260	+	0.846581i	$0.321343\pi$
$140$	0	0
$141$	−14.2020	−1.19603
$142$	7.55051i	0.633625i
$143$	− 1.55051i	− 0.129660i
$144$	0.898979	0.0749150
$145$	0	0
$146$	12.7980	1.05917
$147$	− 1.44949i	− 0.119552i
$148$	− 1.00000i	− 0.0821995i
$149$	4.65153	0.381068	0.190534	−	0.981681i	$-0.438978\pi$
$149$	4.65153	0.381068	0.190534	+	0.981681i	$0.438978\pi$
$150$	0	0
$151$	−14.0000	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$152$	5.00000i	0.405554i
$153$	− 3.10102i	− 0.250703i
$154$	−8.44949	−0.680879
$155$	0	0
$156$	0.651531	0.0521642
$157$	− 16.4495i	− 1.31281i	−0.754408	−	0.656406i	$-0.772076\pi$
$157$	− 16.4495i	− 1.31281i	0.754408	−	0.656406i	$-0.227924\pi$
$158$	7.79796i	0.620372i
$159$	8.69694	0.689712
$160$	0	0
$161$	4.89898	0.386094
$162$	5.49490i	0.431720i
$163$	10.1010i	0.791173i	0.918429	+	0.395586i	$0.129459\pi$
$163$	10.1010i	0.791173i	−0.918429	+	0.395586i	$0.870541\pi$
$164$	−1.00000	−0.0780869
$165$	0	0
$166$	3.44949	0.267732
$167$	10.4495i	0.808606i	0.914625	+	0.404303i	$0.132486\pi$
$167$	10.4495i	0.808606i	−0.914625	+	0.404303i	$0.867514\pi$
$168$	− 3.55051i	− 0.273928i
$169$	12.7980	0.984458
$170$	0	0
$171$	4.49490	0.343733
$172$	1.10102i	0.0839520i
$173$	− 6.69694i	− 0.509159i	−0.967052	−	0.254579i	$-0.918063\pi$
$173$	− 6.69694i	− 0.509159i	0.967052	−	0.254579i	$-0.0819370\pi$
$174$	−1.30306	−0.0987848
$175$	0	0
$176$	3.44949	0.260015
$177$	− 2.89898i	− 0.217901i
$178$	14.3485i	1.07546i
$179$	0.797959	0.0596423	0.0298211	−	0.999555i	$-0.490506\pi$
$179$	0.797959	0.0596423	0.0298211	+	0.999555i	$0.490506\pi$
$180$	0	0
$181$	6.89898	0.512797	0.256399	−	0.966571i	$-0.417464\pi$
$181$	6.89898	0.512797	0.256399	+	0.966571i	$0.417464\pi$
$182$	1.10102i	0.0816131i
$183$	9.34847i	0.691059i
$184$	−2.00000	−0.147442
$185$	0	0
$186$	−6.44949	−0.472900
$187$	− 11.8990i	− 0.870140i
$188$	9.79796i	0.714590i
$189$	−13.8434	−1.00696
$190$	0	0
$191$	−7.79796	−0.564241	−0.282120	−	0.959379i	$-0.591038\pi$
$191$	−7.79796	−0.564241	−0.282120	+	0.959379i	$0.591038\pi$
$192$	1.44949i	0.104608i
$193$	− 2.55051i	− 0.183590i	−0.995778	−	0.0917949i	$-0.970740\pi$
$193$	− 2.55051i	− 0.183590i	0.995778	−	0.0917949i	$-0.0292604\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	−1.00000	−0.0714286
$197$	17.3485i	1.23603i	0.786167	+	0.618014i	$0.212062\pi$
$197$	17.3485i	1.23603i	−0.786167	+	0.618014i	$0.787938\pi$
$198$	− 3.10102i	− 0.220380i
$199$	15.5959	1.10557	0.552783	−	0.833325i	$-0.313566\pi$
$199$	15.5959	1.10557	0.552783	+	0.833325i	$0.313566\pi$
$200$	0	0
$201$	−6.59592	−0.465240
$202$	− 1.10102i	− 0.0774675i
$203$	− 2.20204i	− 0.154553i
$204$	5.00000	0.350070
$205$	0	0
$206$	6.44949	0.449357
$207$	1.79796i	0.124967i
$208$	− 0.449490i	− 0.0311665i
$209$	17.2474	1.19303
$210$	0	0
$211$	−4.55051	−0.313270	−0.156635	−	0.987657i	$-0.550065\pi$
$211$	−4.55051	−0.313270	−0.156635	+	0.987657i	$0.550065\pi$
$212$	− 6.00000i	− 0.412082i
$213$	10.9444i	0.749897i
$214$	8.55051	0.584501
$215$	0	0
$216$	5.65153	0.384538
$217$	− 10.8990i	− 0.739871i
$218$	14.0000i	0.948200i
$219$	18.5505	1.25353
$220$	0	0
$221$	−1.55051	−0.104299
$222$	− 1.44949i	− 0.0972834i
$223$	21.7980i	1.45970i	0.683608	+	0.729850i	$0.260410\pi$
$223$	21.7980i	1.45970i	−0.683608	+	0.729850i	$0.739590\pi$
$224$	−2.44949	−0.163663
$225$	0	0
$226$	−4.55051	−0.302695
$227$	16.6969i	1.10821i	0.832445	+	0.554107i	$0.186940\pi$
$227$	16.6969i	1.10821i	−0.832445	+	0.554107i	$0.813060\pi$
$228$	7.24745i	0.479974i
$229$	−5.79796	−0.383140	−0.191570	−	0.981479i	$-0.561358\pi$
$229$	−5.79796	−0.383140	−0.191570	+	0.981479i	$0.561358\pi$
$230$	0	0
$231$	−12.2474	−0.805823
$232$	0.898979i	0.0590209i
$233$	− 28.4949i	− 1.86676i	−0.358886	−	0.933381i	$-0.616843\pi$
$233$	− 28.4949i	− 1.86676i	0.358886	−	0.933381i	$-0.383157\pi$
$234$	−0.404082	−0.0264157
$235$	0	0
$236$	−2.00000	−0.130189
$237$	11.3031i	0.734213i
$238$	8.44949i	0.547699i
$239$	−0.898979	−0.0581501	−0.0290751	−	0.999577i	$-0.509256\pi$
$239$	−0.898979	−0.0581501	−0.0290751	+	0.999577i	$0.509256\pi$
$240$	0	0
$241$	−2.55051	−0.164293	−0.0821464	−	0.996620i	$-0.526178\pi$
$241$	−2.55051	−0.164293	−0.0821464	+	0.996620i	$0.526178\pi$
$242$	− 0.898979i	− 0.0577886i
$243$	− 8.98979i	− 0.576696i
$244$	6.44949	0.412886
$245$	0	0
$246$	−1.44949	−0.0924161
$247$	− 2.24745i	− 0.143002i
$248$	4.44949i	0.282543i
$249$	5.00000	0.316862
$250$	0	0
$251$	−30.7980	−1.94395	−0.971975	−	0.235084i	$-0.924463\pi$
$251$	−30.7980	−1.94395	−0.971975	+	0.235084i	$0.924463\pi$
$252$	2.20204i	0.138716i
$253$	6.89898i	0.433735i
$254$	16.2474	1.01946
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.89898i	0.430347i	0.976576	+	0.215173i	$0.0690316\pi$
$257$	6.89898i	0.430347i	−0.976576	+	0.215173i	$0.930968\pi$
$258$	1.59592i	0.0993575i
$259$	2.44949	0.152204
$260$	0	0
$261$	0.808164	0.0500241
$262$	− 8.69694i	− 0.537299i
$263$	0.202041i	0.0124584i	0.999981	+	0.00622919i	$0.00198283\pi$
$263$	0.202041i	0.0124584i	−0.999981	+	0.00622919i	$0.998017\pi$
$264$	5.00000	0.307729
$265$	0	0
$266$	−12.2474	−0.750939
$267$	20.7980i	1.27281i
$268$	4.55051i	0.277967i
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	0	0
$271$	30.0454	1.82513	0.912564	−	0.408933i	$-0.134099\pi$
$271$	30.0454	1.82513	0.912564	+	0.408933i	$0.134099\pi$
$272$	− 3.44949i	− 0.209156i
$273$	1.59592i	0.0965893i
$274$	−9.69694	−0.585813
$275$	0	0
$276$	−2.89898	−0.174498
$277$	− 5.79796i	− 0.348366i	−0.984713	−	0.174183i	$-0.944272\pi$
$277$	− 5.79796i	− 0.348366i	0.984713	−	0.174183i	$-0.0557284\pi$
$278$	− 12.5505i	− 0.752730i
$279$	4.00000	0.239474
$280$	0	0
$281$	8.89898	0.530869	0.265434	−	0.964129i	$-0.414485\pi$
$281$	8.89898	0.530869	0.265434	+	0.964129i	$0.414485\pi$
$282$	14.2020i	0.845719i
$283$	− 11.6969i	− 0.695311i	−0.937622	−	0.347655i	$-0.886978\pi$
$283$	− 11.6969i	− 0.695311i	0.937622	−	0.347655i	$-0.113022\pi$
$284$	7.55051	0.448040
$285$	0	0
$286$	−1.55051	−0.0916836
$287$	− 2.44949i	− 0.144589i
$288$	− 0.898979i	− 0.0529729i
$289$	5.10102	0.300060
$290$	0	0
$291$	−20.2929	−1.18959
$292$	− 12.7980i	− 0.748944i
$293$	− 28.0454i	− 1.63843i	−0.573486	−	0.819215i	$-0.694409\pi$
$293$	− 28.0454i	− 1.63843i	0.573486	−	0.819215i	$-0.305591\pi$
$294$	−1.44949	−0.0845360
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	− 19.4949i	− 1.13121i
$298$	− 4.65153i	− 0.269456i
$299$	0.898979	0.0519893
$300$	0	0
$301$	−2.69694	−0.155449
$302$	14.0000i	0.805609i
$303$	− 1.59592i	− 0.0916831i
$304$	5.00000	0.286770
$305$	0	0
$306$	−3.10102	−0.177274
$307$	− 7.65153i	− 0.436696i	−0.975871	−	0.218348i	$-0.929933\pi$
$307$	− 7.65153i	− 0.436696i	0.975871	−	0.218348i	$-0.0700668\pi$
$308$	8.44949i	0.481454i
$309$	9.34847	0.531816
$310$	0	0
$311$	−8.44949	−0.479127	−0.239563	−	0.970881i	$-0.577004\pi$
$311$	−8.44949	−0.479127	−0.239563	+	0.970881i	$0.577004\pi$
$312$	− 0.651531i	− 0.0368857i
$313$	8.89898i	0.503000i	0.967857	+	0.251500i	$0.0809239\pi$
$313$	8.89898i	0.503000i	−0.967857	+	0.251500i	$0.919076\pi$
$314$	−16.4495	−0.928298
$315$	0	0
$316$	7.79796	0.438669
$317$	9.55051i	0.536410i	0.963362	+	0.268205i	$0.0864305\pi$
$317$	9.55051i	0.536410i	−0.963362	+	0.268205i	$0.913570\pi$
$318$	− 8.69694i	− 0.487700i
$319$	3.10102	0.173624
$320$	0	0
$321$	12.3939	0.691759
$322$	− 4.89898i	− 0.273009i
$323$	− 17.2474i	− 0.959674i
$324$	5.49490	0.305272
$325$	0	0
$326$	10.1010	0.559444
$327$	20.2929i	1.12220i
$328$	1.00000i	0.0552158i
$329$	−24.0000	−1.32316
$330$	0	0
$331$	19.8990	1.09375	0.546873	−	0.837215i	$-0.315818\pi$
$331$	19.8990	1.09375	0.546873	+	0.837215i	$0.315818\pi$
$332$	− 3.44949i	− 0.189315i
$333$	0.898979i	0.0492638i
$334$	10.4495	0.571771
$335$	0	0
$336$	−3.55051	−0.193696
$337$	− 15.6969i	− 0.855067i	−0.904000	−	0.427533i	$-0.859383\pi$
$337$	− 15.6969i	− 0.855067i	0.904000	−	0.427533i	$-0.140617\pi$
$338$	− 12.7980i	− 0.696117i
$339$	−6.59592	−0.358241
$340$	0	0
$341$	15.3485	0.831166
$342$	− 4.49490i	− 0.243056i
$343$	− 19.5959i	− 1.05808i
$344$	1.10102	0.0593630
$345$	0	0
$346$	−6.69694	−0.360030
$347$	18.7980i	1.00913i	0.863374	+	0.504564i	$0.168347\pi$
$347$	18.7980i	1.00913i	−0.863374	+	0.504564i	$0.831653\pi$
$348$	1.30306i	0.0698514i
$349$	12.4495	0.666406	0.333203	−	0.942855i	$-0.391871\pi$
$349$	12.4495	0.666406	0.333203	+	0.942855i	$0.391871\pi$
$350$	0	0
$351$	−2.54031	−0.135591
$352$	− 3.44949i	− 0.183858i
$353$	14.8990i	0.792993i	0.918036	+	0.396496i	$0.129774\pi$
$353$	14.8990i	0.792993i	−0.918036	+	0.396496i	$0.870226\pi$
$354$	−2.89898	−0.154079
$355$	0	0
$356$	14.3485	0.760467
$357$	12.2474i	0.648204i
$358$	− 0.797959i	− 0.0421734i
$359$	31.3939	1.65691	0.828453	−	0.560059i	$-0.189222\pi$
$359$	31.3939	1.65691	0.828453	+	0.560059i	$0.189222\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	− 6.89898i	− 0.362602i
$363$	− 1.30306i	− 0.0683930i
$364$	1.10102	0.0577092
$365$	0	0
$366$	9.34847	0.488652
$367$	14.2474i	0.743711i	0.928291	+	0.371855i	$0.121278\pi$
$367$	14.2474i	0.743711i	−0.928291	+	0.371855i	$0.878722\pi$
$368$	2.00000i	0.104257i
$369$	0.898979	0.0467990
$370$	0	0
$371$	14.6969	0.763027
$372$	6.44949i	0.334390i
$373$	− 20.0454i	− 1.03791i	−0.854801	−	0.518956i	$-0.826321\pi$
$373$	− 20.0454i	− 1.03791i	0.854801	−	0.518956i	$-0.173679\pi$
$374$	−11.8990	−0.615282
$375$	0	0
$376$	9.79796	0.505291
$377$	− 0.404082i	− 0.0208113i
$378$	13.8434i	0.712026i
$379$	21.0454	1.08103	0.540515	−	0.841334i	$-0.318229\pi$
$379$	21.0454	1.08103	0.540515	+	0.841334i	$0.318229\pi$
$380$	0	0
$381$	23.5505	1.20653
$382$	7.79796i	0.398978i
$383$	− 5.34847i	− 0.273294i	−0.990620	−	0.136647i	$-0.956367\pi$
$383$	− 5.34847i	− 0.273294i	0.990620	−	0.136647i	$-0.0436326\pi$
$384$	1.44949	0.0739690
$385$	0	0
$386$	−2.55051	−0.129818
$387$	− 0.989795i	− 0.0503141i
$388$	14.0000i	0.710742i
$389$	−13.1464	−0.666550	−0.333275	−	0.942830i	$-0.608154\pi$
$389$	−13.1464	−0.666550	−0.333275	+	0.942830i	$0.608154\pi$
$390$	0	0
$391$	6.89898	0.348896
$392$	1.00000i	0.0505076i
$393$	− 12.6061i	− 0.635895i
$394$	17.3485	0.874003
$395$	0	0
$396$	−3.10102	−0.155832
$397$	15.3485i	0.770318i	0.922850	+	0.385159i	$0.125853\pi$
$397$	15.3485i	0.770318i	−0.922850	+	0.385159i	$0.874147\pi$
$398$	− 15.5959i	− 0.781753i
$399$	−17.7526	−0.888739
$400$	0	0
$401$	15.9444	0.796225	0.398112	−	0.917337i	$-0.369665\pi$
$401$	15.9444	0.796225	0.398112	+	0.917337i	$0.369665\pi$
$402$	6.59592i	0.328974i
$403$	− 2.00000i	− 0.0996271i
$404$	−1.10102	−0.0547778
$405$	0	0
$406$	−2.20204	−0.109285
$407$	3.44949i	0.170985i
$408$	− 5.00000i	− 0.247537i
$409$	34.1464	1.68843	0.844216	−	0.536003i	$-0.180066\pi$
$409$	34.1464	1.68843	0.844216	+	0.536003i	$0.180066\pi$
$410$	0	0
$411$	−14.0556	−0.693312
$412$	− 6.44949i	− 0.317744i
$413$	− 4.89898i	− 0.241063i
$414$	1.79796	0.0883649
$415$	0	0
$416$	−0.449490	−0.0220380
$417$	− 18.1918i	− 0.890858i
$418$	− 17.2474i	− 0.843600i
$419$	21.4495	1.04788	0.523938	−	0.851756i	$-0.324462\pi$
$419$	21.4495	1.04788	0.523938	+	0.851756i	$0.324462\pi$
$420$	0	0
$421$	32.8990	1.60340	0.801699	−	0.597728i	$-0.203930\pi$
$421$	32.8990	1.60340	0.801699	+	0.597728i	$0.203930\pi$
$422$	4.55051i	0.221515i
$423$	− 8.80816i	− 0.428268i
$424$	−6.00000	−0.291386
$425$	0	0
$426$	10.9444	0.530257
$427$	15.7980i	0.764517i
$428$	− 8.55051i	− 0.413305i
$429$	−2.24745	−0.108508
$430$	0	0
$431$	−20.6969	−0.996936	−0.498468	−	0.866908i	$-0.666104\pi$
$431$	−20.6969	−0.996936	−0.498468	+	0.866908i	$0.666104\pi$
$432$	− 5.65153i	− 0.271909i
$433$	19.0000i	0.913082i	0.889702	+	0.456541i	$0.150912\pi$
$433$	19.0000i	0.913082i	−0.889702	+	0.456541i	$0.849088\pi$
$434$	−10.8990	−0.523168
$435$	0	0
$436$	14.0000	0.670478
$437$	10.0000i	0.478365i
$438$	− 18.5505i	− 0.886378i
$439$	19.5959	0.935262	0.467631	−	0.883924i	$-0.345108\pi$
$439$	19.5959	0.935262	0.467631	+	0.883924i	$0.345108\pi$
$440$	0	0
$441$	0.898979	0.0428085
$442$	1.55051i	0.0737503i
$443$	− 17.4495i	− 0.829050i	−0.910038	−	0.414525i	$-0.863948\pi$
$443$	− 17.4495i	− 0.829050i	0.910038	−	0.414525i	$-0.136052\pi$
$444$	−1.44949	−0.0687897
$445$	0	0
$446$	21.7980	1.03216
$447$	− 6.74235i	− 0.318902i
$448$	2.44949i	0.115728i
$449$	−33.2474	−1.56904	−0.784522	−	0.620101i	$-0.787092\pi$
$449$	−33.2474	−1.56904	−0.784522	+	0.620101i	$0.787092\pi$
$450$	0	0
$451$	3.44949	0.162430
$452$	4.55051i	0.214038i
$453$	20.2929i	0.953442i
$454$	16.6969	0.783626
$455$	0	0
$456$	7.24745	0.339393
$457$	− 15.2474i	− 0.713246i	−0.934248	−	0.356623i	$-0.883928\pi$
$457$	− 15.2474i	− 0.713246i	0.934248	−	0.356623i	$-0.116072\pi$
$458$	5.79796i	0.270921i
$459$	−19.4949	−0.909944
$460$	0	0
$461$	9.30306	0.433287	0.216643	−	0.976251i	$-0.430489\pi$
$461$	9.30306	0.433287	0.216643	+	0.976251i	$0.430489\pi$
$462$	12.2474i	0.569803i
$463$	9.55051i	0.443850i	0.975064	+	0.221925i	$0.0712340\pi$
$463$	9.55051i	0.443850i	−0.975064	+	0.221925i	$0.928766\pi$
$464$	0.898979	0.0417341
$465$	0	0
$466$	−28.4949	−1.32000
$467$	12.0000i	0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$	12.0000i	0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$	0.404082i	0.0186787i
$469$	−11.1464	−0.514694
$470$	0	0
$471$	−23.8434	−1.09864
$472$	2.00000i	0.0920575i
$473$	− 3.79796i	− 0.174630i
$474$	11.3031	0.519167
$475$	0	0
$476$	8.44949	0.387282
$477$	5.39388i	0.246969i
$478$	0.898979i	0.0411184i
$479$	−6.24745	−0.285453	−0.142727	−	0.989762i	$-0.545587\pi$
$479$	−6.24745	−0.285453	−0.142727	+	0.989762i	$0.545587\pi$
$480$	0	0
$481$	0.449490	0.0204950
$482$	2.55051i	0.116173i
$483$	− 7.10102i	− 0.323108i
$484$	−0.898979	−0.0408627
$485$	0	0
$486$	−8.98979	−0.407785
$487$	30.7423i	1.39307i	0.717523	+	0.696534i	$0.245276\pi$
$487$	30.7423i	1.39307i	−0.717523	+	0.696534i	$0.754724\pi$
$488$	− 6.44949i	− 0.291955i
$489$	14.6413	0.662104
$490$	0	0
$491$	−41.7980	−1.88632	−0.943158	−	0.332345i	$-0.892160\pi$
$491$	−41.7980	−1.88632	−0.943158	+	0.332345i	$0.892160\pi$
$492$	1.44949i	0.0653480i
$493$	− 3.10102i	− 0.139663i
$494$	−2.24745	−0.101117
$495$	0	0
$496$	4.44949	0.199788
$497$	18.4949i	0.829610i
$498$	− 5.00000i	− 0.224055i
$499$	−22.0000	−0.984855	−0.492428	−	0.870353i	$-0.663890\pi$
$499$	−22.0000	−0.984855	−0.492428	+	0.870353i	$0.663890\pi$
$500$	0	0
$501$	15.1464	0.676693
$502$	30.7980i	1.37458i
$503$	9.79796i	0.436869i	0.975852	+	0.218435i	$0.0700951\pi$
$503$	9.79796i	0.436869i	−0.975852	+	0.218435i	$0.929905\pi$
$504$	2.20204	0.0980867
$505$	0	0
$506$	6.89898	0.306697
$507$	− 18.5505i	− 0.823857i
$508$	− 16.2474i	− 0.720864i
$509$	−29.3485	−1.30085	−0.650424	−	0.759571i	$-0.725409\pi$
$509$	−29.3485	−1.30085	−0.650424	+	0.759571i	$0.725409\pi$
$510$	0	0
$511$	31.3485	1.38677
$512$	− 1.00000i	− 0.0441942i
$513$	− 28.2577i	− 1.24761i
$514$	6.89898	0.304301
$515$	0	0
$516$	1.59592	0.0702564
$517$	− 33.7980i	− 1.48643i
$518$	− 2.44949i	− 0.107624i
$519$	−9.70714	−0.426096
$520$	0	0
$521$	10.1010	0.442534	0.221267	−	0.975213i	$-0.428981\pi$
$521$	10.1010	0.442534	0.221267	+	0.975213i	$0.428981\pi$
$522$	− 0.808164i	− 0.0353724i
$523$	− 18.3939i	− 0.804308i	−0.915572	−	0.402154i	$-0.868262\pi$
$523$	− 18.3939i	− 0.804308i	0.915572	−	0.402154i	$-0.131738\pi$
$524$	−8.69694	−0.379928
$525$	0	0
$526$	0.202041	0.00880941
$527$	− 15.3485i	− 0.668590i
$528$	− 5.00000i	− 0.217597i
$529$	19.0000	0.826087
$530$	0	0
$531$	1.79796	0.0780248
$532$	12.2474i	0.530994i
$533$	− 0.449490i	− 0.0194696i
$534$	20.7980	0.900016
$535$	0	0
$536$	4.55051	0.196552
$537$	− 1.15663i	− 0.0499124i
$538$	4.00000i	0.172452i
$539$	3.44949	0.148580
$540$	0	0
$541$	25.3485	1.08982	0.544908	−	0.838496i	$-0.316565\pi$
$541$	25.3485	1.08982	0.544908	+	0.838496i	$0.316565\pi$
$542$	− 30.0454i	− 1.29056i
$543$	− 10.0000i	− 0.429141i
$544$	−3.44949	−0.147896
$545$	0	0
$546$	1.59592	0.0682990
$547$	− 3.69694i	− 0.158070i	−0.996872	−	0.0790348i	$-0.974816\pi$
$547$	− 3.69694i	− 0.158070i	0.996872	−	0.0790348i	$-0.0251838\pi$
$548$	9.69694i	0.414233i
$549$	−5.79796	−0.247451
$550$	0	0
$551$	4.49490	0.191489
$552$	2.89898i	0.123389i
$553$	19.1010i	0.812258i
$554$	−5.79796	−0.246332
$555$	0	0
$556$	−12.5505	−0.532260
$557$	21.7980i	0.923609i	0.886982	+	0.461805i	$0.152798\pi$
$557$	21.7980i	0.923609i	−0.886982	+	0.461805i	$0.847202\pi$
$558$	− 4.00000i	− 0.169334i
$559$	−0.494897	−0.0209319
$560$	0	0
$561$	−17.2474	−0.728188
$562$	− 8.89898i	− 0.375381i
$563$	37.5959i	1.58448i	0.610210	+	0.792240i	$0.291085\pi$
$563$	37.5959i	1.58448i	−0.610210	+	0.792240i	$0.708915\pi$
$564$	14.2020	0.598014
$565$	0	0
$566$	−11.6969	−0.491659
$567$	13.4597i	0.565254i
$568$	− 7.55051i	− 0.316812i
$569$	−27.0454	−1.13380	−0.566901	−	0.823786i	$-0.691858\pi$
$569$	−27.0454	−1.13380	−0.566901	+	0.823786i	$0.691858\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	1.55051i	0.0648301i
$573$	11.3031i	0.472192i
$574$	−2.44949	−0.102240
$575$	0	0
$576$	−0.898979	−0.0374575
$577$	− 21.0454i	− 0.876132i	−0.898943	−	0.438066i	$-0.855664\pi$
$577$	− 21.0454i	− 0.876132i	0.898943	−	0.438066i	$-0.144336\pi$
$578$	− 5.10102i	− 0.212174i
$579$	−3.69694	−0.153640
$580$	0	0
$581$	8.44949	0.350544
$582$	20.2929i	0.841166i
$583$	20.6969i	0.857180i
$584$	−12.7980	−0.529583
$585$	0	0
$586$	−28.0454	−1.15855
$587$	6.30306i	0.260155i	0.991504	+	0.130078i	$0.0415226\pi$
$587$	6.30306i	0.260155i	−0.991504	+	0.130078i	$0.958477\pi$
$588$	1.44949i	0.0597759i
$589$	22.2474	0.916690
$590$	0	0
$591$	25.1464	1.03439
$592$	1.00000i	0.0410997i
$593$	46.3939i	1.90517i	0.304275	+	0.952584i	$0.401586\pi$
$593$	46.3939i	1.90517i	−0.304275	+	0.952584i	$0.598414\pi$
$594$	−19.4949	−0.799885
$595$	0	0
$596$	−4.65153	−0.190534
$597$	− 22.6061i	− 0.925207i
$598$	− 0.898979i	− 0.0367620i
$599$	−38.9444	−1.59122	−0.795612	−	0.605806i	$-0.792851\pi$
$599$	−38.9444	−1.59122	−0.795612	+	0.605806i	$0.792851\pi$
$600$	0	0
$601$	−7.00000	−0.285536	−0.142768	−	0.989756i	$-0.545600\pi$
$601$	−7.00000	−0.285536	−0.142768	+	0.989756i	$0.545600\pi$
$602$	2.69694i	0.109919i
$603$	− 4.09082i	− 0.166591i
$604$	14.0000	0.569652
$605$	0	0
$606$	−1.59592	−0.0648297
$607$	28.7423i	1.16662i	0.812251	+	0.583308i	$0.198242\pi$
$607$	28.7423i	1.16662i	−0.812251	+	0.583308i	$0.801758\pi$
$608$	− 5.00000i	− 0.202777i
$609$	−3.19184	−0.129340
$610$	0	0
$611$	−4.40408	−0.178170
$612$	3.10102i	0.125351i
$613$	− 34.4949i	− 1.39324i	−0.717442	−	0.696618i	$-0.754687\pi$
$613$	− 34.4949i	− 1.39324i	0.717442	−	0.696618i	$-0.245313\pi$
$614$	−7.65153	−0.308791
$615$	0	0
$616$	8.44949	0.340440
$617$	4.89898i	0.197225i	0.995126	+	0.0986127i	$0.0314405\pi$
$617$	4.89898i	0.197225i	−0.995126	+	0.0986127i	$0.968559\pi$
$618$	− 9.34847i	− 0.376051i
$619$	32.8990	1.32232	0.661161	−	0.750244i	$-0.270064\pi$
$619$	32.8990	1.32232	0.661161	+	0.750244i	$0.270064\pi$
$620$	0	0
$621$	11.3031	0.453576
$622$	8.44949i	0.338794i
$623$	35.1464i	1.40811i
$624$	−0.651531	−0.0260821
$625$	0	0
$626$	8.89898	0.355675
$627$	− 25.0000i	− 0.998404i
$628$	16.4495i	0.656406i
$629$	3.44949	0.137540
$630$	0	0
$631$	2.00000	0.0796187	0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000	0.0796187	0.0398094	+	0.999207i	$0.487325\pi$
$632$	− 7.79796i	− 0.310186i
$633$	6.59592i	0.262164i
$634$	9.55051	0.379299
$635$	0	0
$636$	−8.69694	−0.344856
$637$	− 0.449490i	− 0.0178094i
$638$	− 3.10102i	− 0.122771i
$639$	−6.78775	−0.268519
$640$	0	0
$641$	21.5959	0.852987	0.426494	−	0.904491i	$-0.359749\pi$
$641$	21.5959	0.852987	0.426494	+	0.904491i	$0.359749\pi$
$642$	− 12.3939i	− 0.489147i
$643$	32.2929i	1.27351i	0.771068	+	0.636753i	$0.219723\pi$
$643$	32.2929i	1.27351i	−0.771068	+	0.636753i	$0.780277\pi$
$644$	−4.89898	−0.193047
$645$	0	0
$646$	−17.2474	−0.678592
$647$	40.2474i	1.58229i	0.611628	+	0.791145i	$0.290515\pi$
$647$	40.2474i	1.58229i	−0.611628	+	0.791145i	$0.709485\pi$
$648$	− 5.49490i	− 0.215860i
$649$	6.89898	0.270809
$650$	0	0
$651$	−15.7980	−0.619171
$652$	− 10.1010i	− 0.395586i
$653$	− 10.0454i	− 0.393107i	−0.980493	−	0.196554i	$-0.937025\pi$
$653$	− 10.0454i	− 0.393107i	0.980493	−	0.196554i	$-0.0629750\pi$
$654$	20.2929	0.793513
$655$	0	0
$656$	1.00000	0.0390434
$657$	11.5051i	0.448857i
$658$	24.0000i	0.935617i
$659$	−6.55051	−0.255172	−0.127586	−	0.991828i	$-0.540723\pi$
$659$	−6.55051	−0.255172	−0.127586	+	0.991828i	$0.540723\pi$
$660$	0	0
$661$	25.7980	1.00342	0.501712	−	0.865035i	$-0.332704\pi$
$661$	25.7980	1.00342	0.501712	+	0.865035i	$0.332704\pi$
$662$	− 19.8990i	− 0.773396i
$663$	2.24745i	0.0872837i
$664$	−3.44949	−0.133866
$665$	0	0
$666$	0.898979	0.0348347
$667$	1.79796i	0.0696172i
$668$	− 10.4495i	− 0.404303i
$669$	31.5959	1.22157
$670$	0	0
$671$	−22.2474	−0.858853
$672$	3.55051i	0.136964i
$673$	5.79796i	0.223495i	0.993737	+	0.111747i	$0.0356448\pi$
$673$	5.79796i	0.223495i	−0.993737	+	0.111747i	$0.964355\pi$
$674$	−15.6969	−0.604623
$675$	0	0
$676$	−12.7980	−0.492229
$677$	43.5959i	1.67553i	0.546033	+	0.837764i	$0.316137\pi$
$677$	43.5959i	1.67553i	−0.546033	+	0.837764i	$0.683863\pi$
$678$	6.59592i	0.253315i
$679$	−34.2929	−1.31604
$680$	0	0
$681$	24.2020	0.927424
$682$	− 15.3485i	− 0.587723i
$683$	− 7.00000i	− 0.267848i	−0.990992	−	0.133924i	$-0.957242\pi$
$683$	− 7.00000i	− 0.267848i	0.990992	−	0.133924i	$-0.0427577\pi$
$684$	−4.49490	−0.171867
$685$	0	0
$686$	−19.5959	−0.748176
$687$	8.40408i	0.320636i
$688$	− 1.10102i	− 0.0419760i
$689$	2.69694	0.102745
$690$	0	0
$691$	29.6515	1.12800	0.563999	−	0.825776i	$-0.309262\pi$
$691$	29.6515	1.12800	0.563999	+	0.825776i	$0.309262\pi$
$692$	6.69694i	0.254579i
$693$	− 7.59592i	− 0.288545i
$694$	18.7980	0.713561
$695$	0	0
$696$	1.30306	0.0493924
$697$	− 3.44949i	− 0.130659i
$698$	− 12.4495i	− 0.471220i
$699$	−41.3031	−1.56223
$700$	0	0
$701$	−34.2474	−1.29351	−0.646754	−	0.762699i	$-0.723874\pi$
$701$	−34.2474	−1.29351	−0.646754	+	0.762699i	$0.723874\pi$
$702$	2.54031i	0.0958776i
$703$	5.00000i	0.188579i
$704$	−3.44949	−0.130008
$705$	0	0
$706$	14.8990	0.560730
$707$	− 2.69694i	− 0.101429i
$708$	2.89898i	0.108950i
$709$	−16.8990	−0.634654	−0.317327	−	0.948316i	$-0.602785\pi$
$709$	−16.8990	−0.634654	−0.317327	+	0.948316i	$0.602785\pi$
$710$	0	0
$711$	−7.01021	−0.262903
$712$	− 14.3485i	− 0.537732i
$713$	8.89898i	0.333269i
$714$	12.2474	0.458349
$715$	0	0
$716$	−0.797959	−0.0298211
$717$	1.30306i	0.0486637i
$718$	− 31.3939i	− 1.17161i
$719$	0.651531	0.0242980	0.0121490	−	0.999926i	$-0.496133\pi$
$719$	0.651531	0.0242980	0.0121490	+	0.999926i	$0.496133\pi$
$720$	0	0
$721$	15.7980	0.588347
$722$	− 6.00000i	− 0.223297i
$723$	3.69694i	0.137491i
$724$	−6.89898	−0.256399
$725$	0	0
$726$	−1.30306	−0.0483611
$727$	− 36.0000i	− 1.33517i	−0.744535	−	0.667583i	$-0.767329\pi$
$727$	− 36.0000i	− 1.33517i	0.744535	−	0.667583i	$-0.232671\pi$
$728$	− 1.10102i	− 0.0408065i
$729$	−29.5153	−1.09316
$730$	0	0
$731$	−3.79796	−0.140473
$732$	− 9.34847i	− 0.345529i
$733$	− 15.5959i	− 0.576048i	−0.957623	−	0.288024i	$-0.907002\pi$
$733$	− 15.5959i	− 0.576048i	0.957623	−	0.288024i	$-0.0929984\pi$
$734$	14.2474	0.525883
$735$	0	0
$736$	2.00000	0.0737210
$737$	− 15.6969i	− 0.578204i
$738$	− 0.898979i	− 0.0330919i
$739$	31.5959	1.16227	0.581137	−	0.813806i	$-0.302608\pi$
$739$	31.5959	1.16227	0.581137	+	0.813806i	$0.302608\pi$
$740$	0	0
$741$	−3.25765	−0.119673
$742$	− 14.6969i	− 0.539542i
$743$	− 6.40408i	− 0.234943i	−0.993076	−	0.117471i	$-0.962521\pi$
$743$	− 6.40408i	− 0.234943i	0.993076	−	0.117471i	$-0.0374789\pi$
$744$	6.44949	0.236450
$745$	0	0
$746$	−20.0454	−0.733915
$747$	3.10102i	0.113460i
$748$	11.8990i	0.435070i
$749$	20.9444	0.765291
$750$	0	0
$751$	−30.6969	−1.12015	−0.560074	−	0.828443i	$-0.689227\pi$
$751$	−30.6969	−1.12015	−0.560074	+	0.828443i	$0.689227\pi$
$752$	− 9.79796i	− 0.357295i
$753$	44.6413i	1.62682i
$754$	−0.404082	−0.0147158
$755$	0	0
$756$	13.8434	0.503478
$757$	13.7980i	0.501495i	0.968052	+	0.250748i	$0.0806764\pi$
$757$	13.7980i	0.501495i	−0.968052	+	0.250748i	$0.919324\pi$
$758$	− 21.0454i	− 0.764404i
$759$	10.0000	0.362977
$760$	0	0
$761$	−14.3031	−0.518486	−0.259243	−	0.965812i	$-0.583473\pi$
$761$	−14.3031	−0.518486	−0.259243	+	0.965812i	$0.583473\pi$
$762$	− 23.5505i	− 0.853145i
$763$	34.2929i	1.24148i
$764$	7.79796	0.282120
$765$	0	0
$766$	−5.34847	−0.193248
$767$	− 0.898979i	− 0.0324603i
$768$	− 1.44949i	− 0.0523040i
$769$	−53.2474	−1.92015	−0.960076	−	0.279739i	$-0.909752\pi$
$769$	−53.2474	−1.92015	−0.960076	+	0.279739i	$0.909752\pi$
$770$	0	0
$771$	10.0000	0.360141
$772$	2.55051i	0.0917949i
$773$	22.0454i	0.792918i	0.918052	+	0.396459i	$0.129761\pi$
$773$	22.0454i	0.792918i	−0.918052	+	0.396459i	$0.870239\pi$
$774$	−0.989795	−0.0355774
$775$	0	0
$776$	14.0000	0.502571
$777$	− 3.55051i	− 0.127374i
$778$	13.1464i	0.471322i
$779$	5.00000	0.179144
$780$	0	0
$781$	−26.0454	−0.931978
$782$	− 6.89898i	− 0.246707i
$783$	− 5.08061i	− 0.181566i
$784$	1.00000	0.0357143
$785$	0	0
$786$	−12.6061	−0.449646
$787$	− 30.6969i	− 1.09423i	−0.837058	−	0.547114i	$-0.815726\pi$
$787$	− 30.6969i	− 1.09423i	0.837058	−	0.547114i	$-0.184274\pi$
$788$	− 17.3485i	− 0.618014i
$789$	0.292856	0.0104260
$790$	0	0
$791$	−11.1464	−0.396321
$792$	3.10102i	0.110190i
$793$	2.89898i	0.102946i
$794$	15.3485	0.544697
$795$	0	0
$796$	−15.5959	−0.552783
$797$	− 4.24745i	− 0.150452i	−0.997166	−	0.0752262i	$-0.976032\pi$
$797$	− 4.24745i	− 0.150452i	0.997166	−	0.0752262i	$-0.0239679\pi$
$798$	17.7526i	0.628434i
$799$	−33.7980	−1.19569
$800$	0	0
$801$	−12.8990	−0.455763
$802$	− 15.9444i	− 0.563016i
$803$	44.1464i	1.55789i
$804$	6.59592	0.232620
$805$	0	0
$806$	−2.00000	−0.0704470
$807$	5.79796i	0.204098i
$808$	1.10102i	0.0387338i
$809$	39.3939	1.38501	0.692507	−	0.721411i	$-0.256506\pi$
$809$	39.3939	1.38501	0.692507	+	0.721411i	$0.256506\pi$
$810$	0	0
$811$	5.79796	0.203594	0.101797	−	0.994805i	$-0.467541\pi$
$811$	5.79796	0.203594	0.101797	+	0.994805i	$0.467541\pi$
$812$	2.20204i	0.0772765i
$813$	− 43.5505i	− 1.52738i
$814$	3.44949	0.120905
$815$	0	0
$816$	−5.00000	−0.175035
$817$	− 5.50510i	− 0.192599i
$818$	− 34.1464i	− 1.19390i
$819$	−0.989795	−0.0345862
$820$	0	0
$821$	4.04541	0.141186	0.0705929	−	0.997505i	$-0.477511\pi$
$821$	4.04541	0.141186	0.0705929	+	0.997505i	$0.477511\pi$
$822$	14.0556i	0.490246i
$823$	33.8434i	1.17971i	0.807511	+	0.589853i	$0.200814\pi$
$823$	33.8434i	1.17971i	−0.807511	+	0.589853i	$0.799186\pi$
$824$	−6.44949	−0.224679
$825$	0	0
$826$	−4.89898	−0.170457
$827$	− 27.0000i	− 0.938882i	−0.882964	−	0.469441i	$-0.844455\pi$
$827$	− 27.0000i	− 0.938882i	0.882964	−	0.469441i	$-0.155545\pi$
$828$	− 1.79796i	− 0.0624834i
$829$	−21.3485	−0.741463	−0.370731	−	0.928740i	$-0.620893\pi$
$829$	−21.3485	−0.741463	−0.370731	+	0.928740i	$0.620893\pi$
$830$	0	0
$831$	−8.40408	−0.291534
$832$	0.449490i	0.0155833i
$833$	− 3.44949i	− 0.119518i
$834$	−18.1918	−0.629932
$835$	0	0
$836$	−17.2474	−0.596515
$837$	− 25.1464i	− 0.869188i
$838$	− 21.4495i	− 0.740960i
$839$	1.34847	0.0465543	0.0232772	−	0.999729i	$-0.492590\pi$
$839$	1.34847	0.0465543	0.0232772	+	0.999729i	$0.492590\pi$
$840$	0	0
$841$	−28.1918	−0.972132
$842$	− 32.8990i	− 1.13377i
$843$	− 12.8990i	− 0.444264i
$844$	4.55051	0.156635
$845$	0	0
$846$	−8.80816	−0.302831
$847$	− 2.20204i	− 0.0756630i
$848$	6.00000i	0.206041i
$849$	−16.9546	−0.581880
$850$	0	0
$851$	−2.00000	−0.0685591
$852$	− 10.9444i	− 0.374949i
$853$	− 19.3485i	− 0.662479i	−0.943547	−	0.331239i	$-0.892533\pi$
$853$	− 19.3485i	− 0.662479i	0.943547	−	0.331239i	$-0.107467\pi$
$854$	15.7980	0.540595
$855$	0	0
$856$	−8.55051	−0.292250
$857$	32.1464i	1.09810i	0.835789	+	0.549051i	$0.185011\pi$
$857$	32.1464i	1.09810i	−0.835789	+	0.549051i	$0.814989\pi$
$858$	2.24745i	0.0767266i
$859$	9.49490	0.323962	0.161981	−	0.986794i	$-0.448212\pi$
$859$	9.49490	0.323962	0.161981	+	0.986794i	$0.448212\pi$
$860$	0	0
$861$	−3.55051	−0.121001
$862$	20.6969i	0.704941i
$863$	18.2474i	0.621150i	0.950549	+	0.310575i	$0.100522\pi$
$863$	18.2474i	0.621150i	−0.950549	+	0.310575i	$0.899478\pi$
$864$	−5.65153	−0.192269
$865$	0	0
$866$	19.0000	0.645646
$867$	− 7.39388i	− 0.251109i
$868$	10.8990i	0.369935i
$869$	−26.8990	−0.912485
$870$	0	0
$871$	−2.04541	−0.0693060
$872$	− 14.0000i	− 0.474100i
$873$	− 12.5857i	− 0.425962i
$874$	10.0000	0.338255
$875$	0	0
$876$	−18.5505	−0.626764
$877$	− 4.65153i	− 0.157071i	−0.996911	−	0.0785355i	$-0.974976\pi$
$877$	− 4.65153i	− 0.157071i	0.996911	−	0.0785355i	$-0.0250244\pi$
$878$	− 19.5959i	− 0.661330i
$879$	−40.6515	−1.37114
$880$	0	0
$881$	34.2929	1.15536	0.577678	−	0.816265i	$-0.303959\pi$
$881$	34.2929	1.15536	0.577678	+	0.816265i	$0.303959\pi$
$882$	− 0.898979i	− 0.0302702i
$883$	26.1010i	0.878369i	0.898397	+	0.439185i	$0.144733\pi$
$883$	26.1010i	0.878369i	−0.898397	+	0.439185i	$0.855267\pi$
$884$	1.55051	0.0521493
$885$	0	0
$886$	−17.4495	−0.586227
$887$	− 50.6969i	− 1.70224i	−0.524974	−	0.851118i	$-0.675925\pi$
$887$	− 50.6969i	− 1.70224i	0.524974	−	0.851118i	$-0.324075\pi$
$888$	1.44949i	0.0486417i
$889$	39.7980	1.33478
$890$	0	0
$891$	−18.9546	−0.635003
$892$	− 21.7980i	− 0.729850i
$893$	− 48.9898i	− 1.63938i
$894$	−6.74235	−0.225498
$895$	0	0
$896$	2.44949	0.0818317
$897$	− 1.30306i	− 0.0435080i
$898$	33.2474i	1.10948i
$899$	4.00000	0.133407
$900$	0	0
$901$	20.6969	0.689515
$902$	− 3.44949i	− 0.114855i
$903$	3.90918i	0.130090i
$904$	4.55051	0.151348
$905$	0	0
$906$	20.2929	0.674185
$907$	34.8990i	1.15880i	0.815043	+	0.579401i	$0.196713\pi$
$907$	34.8990i	1.15880i	−0.815043	+	0.579401i	$0.803287\pi$
$908$	− 16.6969i	− 0.554107i
$909$	0.989795	0.0328294
$910$	0	0
$911$	−16.2474	−0.538302	−0.269151	−	0.963098i	$-0.586743\pi$
$911$	−16.2474	−0.538302	−0.269151	+	0.963098i	$0.586743\pi$
$912$	− 7.24745i	− 0.239987i
$913$	11.8990i	0.393799i
$914$	−15.2474	−0.504341
$915$	0	0
$916$	5.79796	0.191570
$917$	− 21.3031i	− 0.703489i
$918$	19.4949i	0.643427i
$919$	51.7980	1.70866	0.854329	−	0.519733i	$-0.173969\pi$
$919$	51.7980	1.70866	0.854329	+	0.519733i	$0.173969\pi$
$920$	0	0
$921$	−11.0908	−0.365455
$922$	− 9.30306i	− 0.306380i
$923$	3.39388i	0.111711i
$924$	12.2474	0.402911
$925$	0	0
$926$	9.55051	0.313849
$927$	5.79796i	0.190430i
$928$	− 0.898979i	− 0.0295104i
$929$	5.79796	0.190225	0.0951124	−	0.995467i	$-0.469679\pi$
$929$	5.79796	0.190225	0.0951124	+	0.995467i	$0.469679\pi$
$930$	0	0
$931$	5.00000	0.163868
$932$	28.4949i	0.933381i
$933$	12.2474i	0.400963i
$934$	12.0000	0.392652
$935$	0	0
$936$	0.404082	0.0132078
$937$	− 14.5959i	− 0.476828i	−0.971164	−	0.238414i	$-0.923373\pi$
$937$	− 14.5959i	− 0.476828i	0.971164	−	0.238414i	$-0.0766275\pi$
$938$	11.1464i	0.363944i
$939$	12.8990	0.420942
$940$	0	0
$941$	−41.3939	−1.34940	−0.674701	−	0.738091i	$-0.735727\pi$
$941$	−41.3939	−1.34940	−0.674701	+	0.738091i	$0.735727\pi$
$942$	23.8434i	0.776859i
$943$	2.00000i	0.0651290i
$944$	2.00000	0.0650945
$945$	0	0
$946$	−3.79796	−0.123482
$947$	− 32.0000i	− 1.03986i	−0.854209	−	0.519930i	$-0.825958\pi$
$947$	− 32.0000i	− 1.03986i	0.854209	−	0.519930i	$-0.174042\pi$
$948$	− 11.3031i	− 0.367106i
$949$	5.75255	0.186736
$950$	0	0
$951$	13.8434	0.448902
$952$	− 8.44949i	− 0.273850i
$953$	25.4949i	0.825861i	0.910763	+	0.412930i	$0.135495\pi$
$953$	25.4949i	0.825861i	−0.910763	+	0.412930i	$0.864505\pi$
$954$	5.39388	0.174633
$955$	0	0
$956$	0.898979	0.0290751
$957$	− 4.49490i	− 0.145299i
$958$	6.24745i	0.201846i
$959$	−23.7526	−0.767010
$960$	0	0
$961$	−11.2020	−0.361356
$962$	− 0.449490i	− 0.0144921i
$963$	7.68673i	0.247702i
$964$	2.55051	0.0821464
$965$	0	0
$966$	−7.10102	−0.228472
$967$	44.0000i	1.41494i	0.706741	+	0.707472i	$0.250165\pi$
$967$	44.0000i	1.41494i	−0.706741	+	0.707472i	$0.749835\pi$
$968$	0.898979i	0.0288943i
$969$	−25.0000	−0.803116
$970$	0	0
$971$	−53.5403	−1.71819	−0.859095	−	0.511816i	$-0.828973\pi$
$971$	−53.5403	−1.71819	−0.859095	+	0.511816i	$0.828973\pi$
$972$	8.98979i	0.288348i
$973$	− 30.7423i	− 0.985554i
$974$	30.7423	0.985048
$975$	0	0
$976$	−6.44949	−0.206443
$977$	23.7423i	0.759585i	0.925072	+	0.379792i	$0.124005\pi$
$977$	23.7423i	0.759585i	−0.925072	+	0.379792i	$0.875995\pi$
$978$	− 14.6413i	− 0.468178i
$979$	−49.4949	−1.58186
$980$	0	0
$981$	−12.5857	−0.401831
$982$	41.7980i	1.33383i
$983$	18.4949i	0.589896i	0.955513	+	0.294948i	$0.0953023\pi$
$983$	18.4949i	0.589896i	−0.955513	+	0.294948i	$0.904698\pi$
$984$	1.44949	0.0462080
$985$	0	0
$986$	−3.10102	−0.0987566
$987$	34.7878i	1.10731i
$988$	2.24745i	0.0715009i
$989$	2.20204	0.0700208
$990$	0	0
$991$	−16.4495	−0.522535	−0.261268	−	0.965266i	$-0.584141\pi$
$991$	−16.4495	−0.522535	−0.261268	+	0.965266i	$0.584141\pi$
$992$	− 4.44949i	− 0.141271i
$993$	− 28.8434i	− 0.915317i
$994$	18.4949	0.586623
$995$	0	0
$996$	−5.00000	−0.158431
$997$	− 39.5505i	− 1.25258i	−0.779591	−	0.626289i	$-0.784573\pi$
$997$	− 39.5505i	− 1.25258i	0.779591	−	0.626289i	$-0.215427\pi$
$998$	22.0000i	0.696398i
$999$	5.65153	0.178807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.k.149.1		4
5.2	odd	4		1850.2.a.w.1.1	yes	2
5.3	odd	4		1850.2.a.r.1.2	✓	2
5.4	even	2	inner	1850.2.b.k.149.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.r.1.2	✓	2	5.3	odd	4
1850.2.a.w.1.1	yes	2	5.2	odd	4
1850.2.b.k.149.1		4	1.1	even	1	trivial
1850.2.b.k.149.4		4	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.44949i q^{3} -1.00000 q^{4} -1.44949 q^{6} -2.44949i q^{7} +1.00000i q^{8} +0.898979 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.44949i q^{3} -1.00000 q^{4} -1.44949 q^{6} -2.44949i q^{7} +1.00000i q^{8} +0.898979 q^{9} +3.44949 q^{11} +1.44949i q^{12} -0.449490i q^{13} -2.44949 q^{14} +1.00000 q^{16} -3.44949i q^{17} -0.898979i q^{18} +5.00000 q^{19} -3.55051 q^{21} -3.44949i q^{22} +2.00000i q^{23} +1.44949 q^{24} -0.449490 q^{26} -5.65153i q^{27} +2.44949i q^{28} +0.898979 q^{29} +4.44949 q^{31} -1.00000i q^{32} -5.00000i q^{33} -3.44949 q^{34} -0.898979 q^{36} +1.00000i q^{37} -5.00000i q^{38} -0.651531 q^{39} +1.00000 q^{41} +3.55051i q^{42} -1.10102i q^{43} -3.44949 q^{44} +2.00000 q^{46} -9.79796i q^{47} -1.44949i q^{48} +1.00000 q^{49} -5.00000 q^{51} +0.449490i q^{52} +6.00000i q^{53} -5.65153 q^{54} +2.44949 q^{56} -7.24745i q^{57} -0.898979i q^{58} +2.00000 q^{59} -6.44949 q^{61} -4.44949i q^{62} -2.20204i q^{63} -1.00000 q^{64} -5.00000 q^{66} -4.55051i q^{67} +3.44949i q^{68} +2.89898 q^{69} -7.55051 q^{71} +0.898979i q^{72} +12.7980i q^{73} +1.00000 q^{74} -5.00000 q^{76} -8.44949i q^{77} +0.651531i q^{78} -7.79796 q^{79} -5.49490 q^{81} -1.00000i q^{82} +3.44949i q^{83} +3.55051 q^{84} -1.10102 q^{86} -1.30306i q^{87} +3.44949i q^{88} -14.3485 q^{89} -1.10102 q^{91} -2.00000i q^{92} -6.44949i q^{93} -9.79796 q^{94} -1.44949 q^{96} -14.0000i q^{97} -1.00000i q^{98} +3.10102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 16 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 16 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 16 q^{9} + 4 q^{11} + 4 q^{16} + 20 q^{19} - 24 q^{21} - 4 q^{24} + 8 q^{26} - 16 q^{29} + 8 q^{31} - 4 q^{34} + 16 q^{36} - 32 q^{39} + 4 q^{41} - 4 q^{44} + 8 q^{46} + 4 q^{49} - 20 q^{51} - 52 q^{54} + 8 q^{59} - 16 q^{61} - 4 q^{64} - 20 q^{66} - 8 q^{69} - 40 q^{71} + 4 q^{74} - 20 q^{76} + 8 q^{79} + 76 q^{81} + 24 q^{84} - 24 q^{86} - 28 q^{89} - 24 q^{91} + 4 q^{96} + 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 16 * q^9 + 4 * q^11 + 4 * q^16 + 20 * q^19 - 24 * q^21 - 4 * q^24 + 8 * q^26 - 16 * q^29 + 8 * q^31 - 4 * q^34 + 16 * q^36 - 32 * q^39 + 4 * q^41 - 4 * q^44 + 8 * q^46 + 4 * q^49 - 20 * q^51 - 52 * q^54 + 8 * q^59 - 16 * q^61 - 4 * q^64 - 20 * q^66 - 8 * q^69 - 40 * q^71 + 4 * q^74 - 20 * q^76 + 8 * q^79 + 76 * q^81 + 24 * q^84 - 24 * q^86 - 28 * q^89 - 24 * q^91 + 4 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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