LMFDB - Embedded newform 4025.2.a.bb.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 22 x^{12} + 18 x^{11} + 187 x^{10} - 118 x^{9} - 772 x^{8} + 346 x^{7} + 1581 x^{6} + \cdots - 5 $ x^14 - x^13 - 22x^12 + 18x^11 + 187x^10 - 118x^9 - 772x^8 + 346x^7 + 1581x^6 - 443x^5 - 1429x^4 + 193x^3 + 386x^2 - 3x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.31493$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.31493 q^{2} +3.36299 q^{3} -0.270967 q^{4} +4.42209 q^{6} +1.00000 q^{7} -2.98616 q^{8} +8.30972 q^{9} +O(q^{10})$	\(q+1.31493 q^{2} +3.36299 q^{3} -0.270967 q^{4} +4.42209 q^{6} +1.00000 q^{7} -2.98616 q^{8} +8.30972 q^{9} +3.87792 q^{11} -0.911260 q^{12} +1.54065 q^{13} +1.31493 q^{14} -3.38464 q^{16} +0.695219 q^{17} +10.9267 q^{18} -2.86316 q^{19} +3.36299 q^{21} +5.09918 q^{22} -1.00000 q^{23} -10.0424 q^{24} +2.02584 q^{26} +17.8566 q^{27} -0.270967 q^{28} -1.71847 q^{29} +5.33847 q^{31} +1.52175 q^{32} +13.0414 q^{33} +0.914163 q^{34} -2.25166 q^{36} -6.64238 q^{37} -3.76485 q^{38} +5.18118 q^{39} -9.95327 q^{41} +4.42209 q^{42} +9.28230 q^{43} -1.05079 q^{44} -1.31493 q^{46} +2.61942 q^{47} -11.3825 q^{48} +1.00000 q^{49} +2.33802 q^{51} -0.417464 q^{52} -1.54511 q^{53} +23.4801 q^{54} -2.98616 q^{56} -9.62880 q^{57} -2.25967 q^{58} -12.4104 q^{59} +14.6629 q^{61} +7.01970 q^{62} +8.30972 q^{63} +8.77028 q^{64} +17.1485 q^{66} +3.55446 q^{67} -0.188381 q^{68} -3.36299 q^{69} +10.8286 q^{71} -24.8141 q^{72} +0.635034 q^{73} -8.73424 q^{74} +0.775822 q^{76} +3.87792 q^{77} +6.81288 q^{78} -8.47076 q^{79} +35.1223 q^{81} -13.0878 q^{82} -8.19151 q^{83} -0.911260 q^{84} +12.2056 q^{86} -5.77921 q^{87} -11.5801 q^{88} -8.11105 q^{89} +1.54065 q^{91} +0.270967 q^{92} +17.9532 q^{93} +3.44434 q^{94} +5.11764 q^{96} +0.0708678 q^{97} +1.31493 q^{98} +32.2244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + 6 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q + q^2 + 6 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 9 * q^8 + 18 * q^9	$ 14 q + q^{2} + 6 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 9 q^{8} + 18 q^{9} - 3 q^{11} + 11 q^{12} + 15 q^{13} + q^{14} + 23 q^{16} + 9 q^{17} + 17 q^{18} - 4 q^{19} + 6 q^{21} + 9 q^{22} - 14 q^{23} + 10 q^{24} - 5 q^{26} + 33 q^{27} + 17 q^{28} + 11 q^{29} - q^{31} + 24 q^{32} + 26 q^{33} - 6 q^{34} + 13 q^{36} + 18 q^{37} - 6 q^{38} + 6 q^{39} - 7 q^{41} - 4 q^{42} + 18 q^{43} - 16 q^{44} - q^{46} + 10 q^{47} + 40 q^{48} + 14 q^{49} + 28 q^{51} + 46 q^{52} + 5 q^{53} - 24 q^{54} + 9 q^{56} - 26 q^{57} + 2 q^{58} - 24 q^{59} - 6 q^{61} - 16 q^{62} + 18 q^{63} + 29 q^{64} + 27 q^{66} + 61 q^{67} + 35 q^{68} - 6 q^{69} + 11 q^{71} + 12 q^{72} + 28 q^{73} - 49 q^{74} - 27 q^{76} - 3 q^{77} + 38 q^{78} + 6 q^{79} + 26 q^{81} - 14 q^{82} + 16 q^{83} + 11 q^{84} + 46 q^{86} + 61 q^{87} + 58 q^{88} - 39 q^{89} + 15 q^{91} - 17 q^{92} + 21 q^{93} - 74 q^{94} + 41 q^{96} + 19 q^{97} + q^{98} - 9 q^{99}+O(q^{100}) $ 14 * q + q^2 + 6 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 9 * q^8 + 18 * q^9 - 3 * q^11 + 11 * q^12 + 15 * q^13 + q^14 + 23 * q^16 + 9 * q^17 + 17 * q^18 - 4 * q^19 + 6 * q^21 + 9 * q^22 - 14 * q^23 + 10 * q^24 - 5 * q^26 + 33 * q^27 + 17 * q^28 + 11 * q^29 - q^31 + 24 * q^32 + 26 * q^33 - 6 * q^34 + 13 * q^36 + 18 * q^37 - 6 * q^38 + 6 * q^39 - 7 * q^41 - 4 * q^42 + 18 * q^43 - 16 * q^44 - q^46 + 10 * q^47 + 40 * q^48 + 14 * q^49 + 28 * q^51 + 46 * q^52 + 5 * q^53 - 24 * q^54 + 9 * q^56 - 26 * q^57 + 2 * q^58 - 24 * q^59 - 6 * q^61 - 16 * q^62 + 18 * q^63 + 29 * q^64 + 27 * q^66 + 61 * q^67 + 35 * q^68 - 6 * q^69 + 11 * q^71 + 12 * q^72 + 28 * q^73 - 49 * q^74 - 27 * q^76 - 3 * q^77 + 38 * q^78 + 6 * q^79 + 26 * q^81 - 14 * q^82 + 16 * q^83 + 11 * q^84 + 46 * q^86 + 61 * q^87 + 58 * q^88 - 39 * q^89 + 15 * q^91 - 17 * q^92 + 21 * q^93 - 74 * q^94 + 41 * q^96 + 19 * q^97 + q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.31493	0.929794	0.464897	−	0.885365i	$-0.346091\pi$
$2$	1.31493	0.929794	0.464897	+	0.885365i	$0.346091\pi$
$3$	3.36299	1.94162	0.970812	−	0.239840i	$-0.0770949\pi$
$3$	3.36299	1.94162	0.970812	+	0.239840i	$0.0770949\pi$
$4$	−0.270967	−0.135483
$5$	0	0
$5$	0	0
$6$	4.42209	1.80531
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.98616	−1.05577
$9$	8.30972	2.76991
$10$	0	0
$11$	3.87792	1.16924	0.584618	−	0.811309i	$-0.301244\pi$
$11$	3.87792	1.16924	0.584618	+	0.811309i	$0.301244\pi$
$12$	−0.911260	−0.263058
$13$	1.54065	0.427298	0.213649	−	0.976910i	$-0.431465\pi$
$13$	1.54065	0.427298	0.213649	+	0.976910i	$0.431465\pi$
$14$	1.31493	0.351429
$15$	0	0
$16$	−3.38464	−0.846161
$17$	0.695219	0.168615	0.0843077	−	0.996440i	$-0.473132\pi$
$17$	0.695219	0.168615	0.0843077	+	0.996440i	$0.473132\pi$
$18$	10.9267	2.57544
$19$	−2.86316	−0.656855	−0.328427	−	0.944529i	$-0.606519\pi$
$19$	−2.86316	−0.656855	−0.328427	+	0.944529i	$0.606519\pi$
$20$	0	0
$21$	3.36299	0.733865
$22$	5.09918	1.08715
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−10.0424	−2.04990
$25$	0	0
$26$	2.02584	0.397299
$27$	17.8566	3.43650
$28$	−0.270967	−0.0512079
$29$	−1.71847	−0.319112	−0.159556	−	0.987189i	$-0.551006\pi$
$29$	−1.71847	−0.319112	−0.159556	+	0.987189i	$0.551006\pi$
$30$	0	0
$31$	5.33847	0.958818	0.479409	−	0.877592i	$-0.340851\pi$
$31$	5.33847	0.958818	0.479409	+	0.877592i	$0.340851\pi$
$32$	1.52175	0.269010
$33$	13.0414	2.27022
$34$	0.914163	0.156778
$35$	0	0
$36$	−2.25166	−0.375277
$37$	−6.64238	−1.09200	−0.546000	−	0.837785i	$-0.683850\pi$
$37$	−6.64238	−1.09200	−0.546000	+	0.837785i	$0.683850\pi$
$38$	−3.76485	−0.610739
$39$	5.18118	0.829653
$40$	0	0
$41$	−9.95327	−1.55444	−0.777220	−	0.629229i	$-0.783371\pi$
$41$	−9.95327	−1.55444	−0.777220	+	0.629229i	$0.783371\pi$
$42$	4.42209	0.682343
$43$	9.28230	1.41554	0.707769	−	0.706444i	$-0.249702\pi$
$43$	9.28230	1.41554	0.707769	+	0.706444i	$0.249702\pi$
$44$	−1.05079	−0.158412
$45$	0	0
$46$	−1.31493	−0.193875
$47$	2.61942	0.382081	0.191040	−	0.981582i	$-0.438814\pi$
$47$	2.61942	0.382081	0.191040	+	0.981582i	$0.438814\pi$
$48$	−11.3825	−1.64293
$49$	1.00000	0.142857
$50$	0	0
$51$	2.33802	0.327388
$52$	−0.417464	−0.0578919
$53$	−1.54511	−0.212237	−0.106119	−	0.994353i	$-0.533842\pi$
$53$	−1.54511	−0.212237	−0.106119	+	0.994353i	$0.533842\pi$
$54$	23.4801	3.19523
$55$	0	0
$56$	−2.98616	−0.399042
$57$	−9.62880	−1.27537
$58$	−2.25967	−0.296709
$59$	−12.4104	−1.61570	−0.807851	−	0.589387i	$-0.799369\pi$
$59$	−12.4104	−1.61570	−0.807851	+	0.589387i	$0.799369\pi$
$60$	0	0
$61$	14.6629	1.87739	0.938693	−	0.344754i	$-0.112038\pi$
$61$	14.6629	1.87739	0.938693	+	0.344754i	$0.112038\pi$
$62$	7.01970	0.891503
$63$	8.30972	1.04693
$64$	8.77028	1.09629
$65$	0	0
$66$	17.1485	2.11083
$67$	3.55446	0.434247	0.217123	−	0.976144i	$-0.430333\pi$
$67$	3.55446	0.434247	0.217123	+	0.976144i	$0.430333\pi$
$68$	−0.188381	−0.0228446
$69$	−3.36299	−0.404857
$70$	0	0
$71$	10.8286	1.28512	0.642561	−	0.766234i	$-0.277872\pi$
$71$	10.8286	1.28512	0.642561	+	0.766234i	$0.277872\pi$
$72$	−24.8141	−2.92437
$73$	0.635034	0.0743251	0.0371626	−	0.999309i	$-0.488168\pi$
$73$	0.635034	0.0743251	0.0371626	+	0.999309i	$0.488168\pi$
$74$	−8.73424	−1.01533
$75$	0	0
$76$	0.775822	0.0889929
$77$	3.87792	0.441930
$78$	6.81288	0.771406
$79$	−8.47076	−0.953035	−0.476517	−	0.879165i	$-0.658101\pi$
$79$	−8.47076	−0.953035	−0.476517	+	0.879165i	$0.658101\pi$
$80$	0	0
$81$	35.1223	3.90248
$82$	−13.0878	−1.44531
$83$	−8.19151	−0.899135	−0.449568	−	0.893246i	$-0.648422\pi$
$83$	−8.19151	−0.899135	−0.449568	+	0.893246i	$0.648422\pi$
$84$	−0.911260	−0.0994266
$85$	0	0
$86$	12.2056	1.31616
$87$	−5.77921	−0.619597
$88$	−11.5801	−1.23444
$89$	−8.11105	−0.859769	−0.429885	−	0.902884i	$-0.641446\pi$
$89$	−8.11105	−0.859769	−0.429885	+	0.902884i	$0.641446\pi$
$90$	0	0
$91$	1.54065	0.161504
$92$	0.270967	0.0282503
$93$	17.9532	1.86166
$94$	3.44434	0.355257
$95$	0	0
$96$	5.11764	0.522317
$97$	0.0708678	0.00719554	0.00359777	−	0.999994i	$-0.498855\pi$
$97$	0.0708678	0.00719554	0.00359777	+	0.999994i	$0.498855\pi$
$98$	1.31493	0.132828
$99$	32.2244	3.23867
$100$	0	0
$101$	11.1471	1.10917	0.554587	−	0.832126i	$-0.312876\pi$
$101$	11.1471	1.10917	0.554587	+	0.832126i	$0.312876\pi$
$102$	3.07432	0.304403
$103$	−7.80632	−0.769180	−0.384590	−	0.923088i	$-0.625657\pi$
$103$	−7.80632	−0.769180	−0.384590	+	0.923088i	$0.625657\pi$
$104$	−4.60061	−0.451127
$105$	0	0
$106$	−2.03171	−0.197337
$107$	−18.5127	−1.78969	−0.894844	−	0.446379i	$-0.852713\pi$
$107$	−18.5127	−1.78969	−0.894844	+	0.446379i	$0.852713\pi$
$108$	−4.83854	−0.465588
$109$	5.64586	0.540775	0.270387	−	0.962752i	$-0.412848\pi$
$109$	5.64586	0.540775	0.270387	+	0.962752i	$0.412848\pi$
$110$	0	0
$111$	−22.3383	−2.12025
$112$	−3.38464	−0.319819
$113$	9.60160	0.903242	0.451621	−	0.892210i	$-0.350846\pi$
$113$	9.60160	0.903242	0.451621	+	0.892210i	$0.350846\pi$
$114$	−12.6612	−1.18583
$115$	0	0
$116$	0.465649	0.0432345
$117$	12.8023	1.18358
$118$	−16.3188	−1.50227
$119$	0.695219	0.0637307
$120$	0	0
$121$	4.03823	0.367112
$122$	19.2806	1.74558
$123$	−33.4728	−3.01814
$124$	−1.44655	−0.129904
$125$	0	0
$126$	10.9267	0.973426
$127$	−3.29566	−0.292442	−0.146221	−	0.989252i	$-0.546711\pi$
$127$	−3.29566	−0.292442	−0.146221	+	0.989252i	$0.546711\pi$
$128$	8.48877	0.750309
$129$	31.2163	2.74844
$130$	0	0
$131$	−14.6013	−1.27572	−0.637862	−	0.770151i	$-0.720181\pi$
$131$	−14.6013	−1.27572	−0.637862	+	0.770151i	$0.720181\pi$
$132$	−3.53379	−0.307577
$133$	−2.86316	−0.248268
$134$	4.67386	0.403760
$135$	0	0
$136$	−2.07603	−0.178018
$137$	−10.1918	−0.870745	−0.435372	−	0.900251i	$-0.643383\pi$
$137$	−10.1918	−0.870745	−0.435372	+	0.900251i	$0.643383\pi$
$138$	−4.42209	−0.376433
$139$	−11.5830	−0.982455	−0.491227	−	0.871031i	$-0.663452\pi$
$139$	−11.5830	−0.982455	−0.491227	+	0.871031i	$0.663452\pi$
$140$	0	0
$141$	8.80908	0.741858
$142$	14.2389	1.19490
$143$	5.97450	0.499612
$144$	−28.1254	−2.34379
$145$	0	0
$146$	0.835024	0.0691071
$147$	3.36299	0.277375
$148$	1.79986	0.147948
$149$	−4.30012	−0.352279	−0.176140	−	0.984365i	$-0.556361\pi$
$149$	−4.30012	−0.352279	−0.176140	+	0.984365i	$0.556361\pi$
$150$	0	0
$151$	2.88100	0.234452	0.117226	−	0.993105i	$-0.462600\pi$
$151$	2.88100	0.234452	0.117226	+	0.993105i	$0.462600\pi$
$152$	8.54985	0.693484
$153$	5.77708	0.467049
$154$	5.09918	0.410903
$155$	0	0
$156$	−1.40393	−0.112404
$157$	−24.2491	−1.93529	−0.967645	−	0.252317i	$-0.918808\pi$
$157$	−24.2491	−1.93529	−0.967645	+	0.252317i	$0.918808\pi$
$158$	−11.1384	−0.886126
$159$	−5.19620	−0.412086
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	46.1833	3.62850
$163$	0.875807	0.0685985	0.0342993	−	0.999412i	$-0.489080\pi$
$163$	0.875807	0.0685985	0.0342993	+	0.999412i	$0.489080\pi$
$164$	2.69701	0.210601
$165$	0	0
$166$	−10.7712	−0.836010
$167$	24.1852	1.87151	0.935753	−	0.352657i	$-0.114722\pi$
$167$	24.1852	1.87151	0.935753	+	0.352657i	$0.114722\pi$
$168$	−10.0424	−0.774790
$169$	−10.6264	−0.817416
$170$	0	0
$171$	−23.7921	−1.81943
$172$	−2.51520	−0.191782
$173$	1.09827	0.0835002	0.0417501	−	0.999128i	$-0.486707\pi$
$173$	1.09827	0.0835002	0.0417501	+	0.999128i	$0.486707\pi$
$174$	−7.59924	−0.576097
$175$	0	0
$176$	−13.1254	−0.989361
$177$	−41.7362	−3.13709
$178$	−10.6654	−0.799408
$179$	20.2791	1.51573	0.757865	−	0.652412i	$-0.226243\pi$
$179$	20.2791	1.51573	0.757865	+	0.652412i	$0.226243\pi$
$180$	0	0
$181$	8.36808	0.621994	0.310997	−	0.950411i	$-0.399337\pi$
$181$	8.36808	0.621994	0.310997	+	0.950411i	$0.399337\pi$
$182$	2.02584	0.150165
$183$	49.3111	3.64518
$184$	2.98616	0.220142
$185$	0	0
$186$	23.6072	1.73096
$187$	2.69600	0.197151
$188$	−0.709775	−0.0517657
$189$	17.8566	1.29887
$190$	0	0
$191$	−15.8629	−1.14780	−0.573899	−	0.818926i	$-0.694570\pi$
$191$	−15.8629	−1.14780	−0.573899	+	0.818926i	$0.694570\pi$
$192$	29.4944	2.12857
$193$	−1.45886	−0.105011	−0.0525054	−	0.998621i	$-0.516721\pi$
$193$	−1.45886	−0.105011	−0.0525054	+	0.998621i	$0.516721\pi$
$194$	0.0931860	0.00669037
$195$	0	0
$196$	−0.270967	−0.0193548
$197$	−0.354239	−0.0252385	−0.0126192	−	0.999920i	$-0.504017\pi$
$197$	−0.354239	−0.0252385	−0.0126192	+	0.999920i	$0.504017\pi$
$198$	42.3727	3.01130
$199$	−8.36751	−0.593157	−0.296579	−	0.955008i	$-0.595846\pi$
$199$	−8.36751	−0.593157	−0.296579	+	0.955008i	$0.595846\pi$
$200$	0	0
$201$	11.9536	0.843144
$202$	14.6576	1.03130
$203$	−1.71847	−0.120613
$204$	−0.633526	−0.0443557
$205$	0	0
$206$	−10.2647	−0.715179
$207$	−8.30972	−0.577566
$208$	−5.21454	−0.361563
$209$	−11.1031	−0.768018
$210$	0	0
$211$	−2.88073	−0.198318	−0.0991589	−	0.995072i	$-0.531615\pi$
$211$	−2.88073	−0.198318	−0.0991589	+	0.995072i	$0.531615\pi$
$212$	0.418674	0.0287547
$213$	36.4166	2.49523
$214$	−24.3428	−1.66404
$215$	0	0
$216$	−53.3225	−3.62813
$217$	5.33847	0.362399
$218$	7.42389	0.502809
$219$	2.13562	0.144312
$220$	0	0
$221$	1.07109	0.0720491
$222$	−29.3732	−1.97140
$223$	21.8489	1.46311	0.731554	−	0.681784i	$-0.238795\pi$
$223$	21.8489	1.46311	0.731554	+	0.681784i	$0.238795\pi$
$224$	1.52175	0.101676
$225$	0	0
$226$	12.6254	0.839829
$227$	17.7860	1.18050	0.590249	−	0.807221i	$-0.299029\pi$
$227$	17.7860	1.18050	0.590249	+	0.807221i	$0.299029\pi$
$228$	2.60909	0.172791
$229$	23.4802	1.55162	0.775808	−	0.630969i	$-0.217343\pi$
$229$	23.4802	1.55162	0.775808	+	0.630969i	$0.217343\pi$
$230$	0	0
$231$	13.0414	0.858061
$232$	5.13163	0.336908
$233$	25.5868	1.67625	0.838124	−	0.545480i	$-0.183653\pi$
$233$	25.5868	1.67625	0.838124	+	0.545480i	$0.183653\pi$
$234$	16.8341	1.10048
$235$	0	0
$236$	3.36282	0.218901
$237$	−28.4871	−1.85044
$238$	0.914163	0.0592564
$239$	−7.86929	−0.509022	−0.254511	−	0.967070i	$-0.581915\pi$
$239$	−7.86929	−0.509022	−0.254511	+	0.967070i	$0.581915\pi$
$240$	0	0
$241$	−19.5883	−1.26179	−0.630896	−	0.775868i	$-0.717312\pi$
$241$	−19.5883	−1.26179	−0.630896	+	0.775868i	$0.717312\pi$
$242$	5.30998	0.341339
$243$	64.5464	4.14066
$244$	−3.97315	−0.254355
$245$	0	0
$246$	−44.0142	−2.80625
$247$	−4.41112	−0.280673
$248$	−15.9415	−1.01229
$249$	−27.5480	−1.74578
$250$	0	0
$251$	3.87676	0.244699	0.122349	−	0.992487i	$-0.460957\pi$
$251$	3.87676	0.244699	0.122349	+	0.992487i	$0.460957\pi$
$252$	−2.25166	−0.141841
$253$	−3.87792	−0.243803
$254$	−4.33355	−0.271911
$255$	0	0
$256$	−6.37844	−0.398653
$257$	−20.9798	−1.30868	−0.654341	−	0.756200i	$-0.727054\pi$
$257$	−20.9798	−1.30868	−0.654341	+	0.756200i	$0.727054\pi$
$258$	41.0472	2.55549
$259$	−6.64238	−0.412737
$260$	0	0
$261$	−14.2800	−0.883912
$262$	−19.1997	−1.18616
$263$	−22.2801	−1.37385	−0.686926	−	0.726727i	$-0.741040\pi$
$263$	−22.2801	−1.37385	−0.686926	+	0.726727i	$0.741040\pi$
$264$	−38.9437	−2.39682
$265$	0	0
$266$	−3.76485	−0.230838
$267$	−27.2774	−1.66935
$268$	−0.963142	−0.0588333
$269$	1.28810	0.0785367	0.0392684	−	0.999229i	$-0.487497\pi$
$269$	1.28810	0.0785367	0.0392684	+	0.999229i	$0.487497\pi$
$270$	0	0
$271$	−0.323905	−0.0196758	−0.00983790	−	0.999952i	$-0.503132\pi$
$271$	−0.323905	−0.0196758	−0.00983790	+	0.999952i	$0.503132\pi$
$272$	−2.35307	−0.142676
$273$	5.18118	0.313579
$274$	−13.4015	−0.809613
$275$	0	0
$276$	0.911260	0.0548514
$277$	−16.1705	−0.971589	−0.485794	−	0.874073i	$-0.661470\pi$
$277$	−16.1705	−0.971589	−0.485794	+	0.874073i	$0.661470\pi$
$278$	−15.2308	−0.913480
$279$	44.3612	2.65584
$280$	0	0
$281$	5.70235	0.340174	0.170087	−	0.985429i	$-0.445595\pi$
$281$	5.70235	0.340174	0.170087	+	0.985429i	$0.445595\pi$
$282$	11.5833	0.689775
$283$	−13.7977	−0.820191	−0.410095	−	0.912043i	$-0.634505\pi$
$283$	−13.7977	−0.820191	−0.410095	+	0.912043i	$0.634505\pi$
$284$	−2.93420	−0.174113
$285$	0	0
$286$	7.85603	0.464537
$287$	−9.95327	−0.587523
$288$	12.6453	0.745134
$289$	−16.5167	−0.971569
$290$	0	0
$291$	0.238328	0.0139710
$292$	−0.172073	−0.0100698
$293$	−29.5491	−1.72628	−0.863140	−	0.504965i	$-0.831505\pi$
$293$	−29.5491	−1.72628	−0.863140	+	0.504965i	$0.831505\pi$
$294$	4.42209	0.257902
$295$	0	0
$296$	19.8352	1.15290
$297$	69.2462	4.01807
$298$	−5.65434	−0.327547
$299$	−1.54065	−0.0890979
$300$	0	0
$301$	9.28230	0.535023
$302$	3.78830	0.217992
$303$	37.4875	2.15360
$304$	9.69078	0.555805
$305$	0	0
$306$	7.59644	0.434260
$307$	25.8079	1.47294	0.736468	−	0.676473i	$-0.236492\pi$
$307$	25.8079	1.47294	0.736468	+	0.676473i	$0.236492\pi$
$308$	−1.05079	−0.0598741
$309$	−26.2526	−1.49346
$310$	0	0
$311$	8.96619	0.508426	0.254213	−	0.967148i	$-0.418184\pi$
$311$	8.96619	0.508426	0.254213	+	0.967148i	$0.418184\pi$
$312$	−15.4718	−0.875919
$313$	19.1320	1.08141	0.540703	−	0.841214i	$-0.318158\pi$
$313$	19.1320	1.08141	0.540703	+	0.841214i	$0.318158\pi$
$314$	−31.8858	−1.79942
$315$	0	0
$316$	2.29530	0.129120
$317$	19.8033	1.11227	0.556133	−	0.831093i	$-0.312284\pi$
$317$	19.8033	1.11227	0.556133	+	0.831093i	$0.312284\pi$
$318$	−6.83263	−0.383155
$319$	−6.66409	−0.373118
$320$	0	0
$321$	−62.2580	−3.47490
$322$	−1.31493	−0.0732780
$323$	−1.99053	−0.110756
$324$	−9.51699	−0.528721
$325$	0	0
$326$	1.15162	0.0637825
$327$	18.9870	1.04998
$328$	29.7220	1.64112
$329$	2.61942	0.144413
$330$	0	0
$331$	−30.2292	−1.66154	−0.830772	−	0.556612i	$-0.812101\pi$
$331$	−30.2292	−1.66154	−0.830772	+	0.556612i	$0.812101\pi$
$332$	2.21963	0.121818
$333$	−55.1963	−3.02474
$334$	31.8017	1.74011
$335$	0	0
$336$	−11.3825	−0.620968
$337$	9.89620	0.539080	0.269540	−	0.962989i	$-0.413128\pi$
$337$	9.89620	0.539080	0.269540	+	0.962989i	$0.413128\pi$
$338$	−13.9730	−0.760028
$339$	32.2901	1.75376
$340$	0	0
$341$	20.7021	1.12108
$342$	−31.2849	−1.69169
$343$	1.00000	0.0539949
$344$	−27.7184	−1.49448
$345$	0	0
$346$	1.44415	0.0776380
$347$	−35.0253	−1.88026	−0.940128	−	0.340820i	$-0.889295\pi$
$347$	−35.0253	−1.88026	−0.940128	+	0.340820i	$0.889295\pi$
$348$	1.56598	0.0839451
$349$	15.1220	0.809464	0.404732	−	0.914435i	$-0.367365\pi$
$349$	15.1220	0.809464	0.404732	+	0.914435i	$0.367365\pi$
$350$	0	0
$351$	27.5106	1.46841
$352$	5.90123	0.314537
$353$	−18.5914	−0.989522	−0.494761	−	0.869029i	$-0.664744\pi$
$353$	−18.5914	−0.989522	−0.494761	+	0.869029i	$0.664744\pi$
$354$	−54.8801	−2.91684
$355$	0	0
$356$	2.19783	0.116484
$357$	2.33802	0.123741
$358$	26.6655	1.40932
$359$	3.45111	0.182142	0.0910712	−	0.995844i	$-0.470971\pi$
$359$	3.45111	0.182142	0.0910712	+	0.995844i	$0.470971\pi$
$360$	0	0
$361$	−10.8023	−0.568542
$362$	11.0034	0.578327
$363$	13.5806	0.712794
$364$	−0.417464	−0.0218811
$365$	0	0
$366$	64.8405	3.38927
$367$	−11.2579	−0.587659	−0.293829	−	0.955858i	$-0.594930\pi$
$367$	−11.2579	−0.587659	−0.293829	+	0.955858i	$0.594930\pi$
$368$	3.38464	0.176437
$369$	−82.7089	−4.30565
$370$	0	0
$371$	−1.54511	−0.0802182
$372$	−4.86473	−0.252225
$373$	−21.3444	−1.10517	−0.552586	−	0.833456i	$-0.686359\pi$
$373$	−21.3444	−1.10517	−0.552586	+	0.833456i	$0.686359\pi$
$374$	3.54505	0.183310
$375$	0	0
$376$	−7.82198	−0.403388
$377$	−2.64756	−0.136356
$378$	23.4801	1.20768
$379$	4.06597	0.208855	0.104428	−	0.994532i	$-0.466699\pi$
$379$	4.06597	0.208855	0.104428	+	0.994532i	$0.466699\pi$
$380$	0	0
$381$	−11.0833	−0.567813
$382$	−20.8585	−1.06721
$383$	−0.00674875	−0.000344845 0	−0.000172423	−	1.00000i	$-0.500055\pi$
$383$	−0.00674875	−0.000344845 0	−0.000172423		1.00000i	$0.500055\pi$
$384$	28.5477	1.45682
$385$	0	0
$386$	−1.91829	−0.0976385
$387$	77.1334	3.92091
$388$	−0.0192028	−0.000974876 0
$389$	14.9343	0.757198	0.378599	−	0.925561i	$-0.376406\pi$
$389$	14.9343	0.757198	0.378599	+	0.925561i	$0.376406\pi$
$390$	0	0
$391$	−0.695219	−0.0351588
$392$	−2.98616	−0.150824
$393$	−49.1042	−2.47698
$394$	−0.465798	−0.0234666
$395$	0	0
$396$	−8.73175	−0.438787
$397$	17.7245	0.889567	0.444784	−	0.895638i	$-0.353281\pi$
$397$	17.7245	0.889567	0.444784	+	0.895638i	$0.353281\pi$
$398$	−11.0027	−0.551514
$399$	−9.62880	−0.482043
$400$	0	0
$401$	−3.47084	−0.173325	−0.0866627	−	0.996238i	$-0.527620\pi$
$401$	−3.47084	−0.173325	−0.0866627	+	0.996238i	$0.527620\pi$
$402$	15.7182	0.783950
$403$	8.22469	0.409701
$404$	−3.02049	−0.150275
$405$	0	0
$406$	−2.25967	−0.112145
$407$	−25.7586	−1.27681
$408$	−6.98169	−0.345645
$409$	−23.0557	−1.14003	−0.570017	−	0.821633i	$-0.693063\pi$
$409$	−23.0557	−1.14003	−0.570017	+	0.821633i	$0.693063\pi$
$410$	0	0
$411$	−34.2750	−1.69066
$412$	2.11526	0.104211
$413$	−12.4104	−0.610678
$414$	−10.9267	−0.537017
$415$	0	0
$416$	2.34448	0.114948
$417$	−38.9535	−1.90756
$418$	−14.5998	−0.714098
$419$	−24.1025	−1.17748	−0.588742	−	0.808321i	$-0.700377\pi$
$419$	−24.1025	−1.17748	−0.588742	+	0.808321i	$0.700377\pi$
$420$	0	0
$421$	−15.5697	−0.758818	−0.379409	−	0.925229i	$-0.623873\pi$
$421$	−15.5697	−0.758818	−0.379409	+	0.925229i	$0.623873\pi$
$422$	−3.78795	−0.184395
$423$	21.7666	1.05833
$424$	4.61395	0.224073
$425$	0	0
$426$	47.8852	2.32005
$427$	14.6629	0.709585
$428$	5.01632	0.242473
$429$	20.0922	0.970060
$430$	0	0
$431$	32.1532	1.54877	0.774383	−	0.632717i	$-0.218060\pi$
$431$	32.1532	1.54877	0.774383	+	0.632717i	$0.218060\pi$
$432$	−60.4381	−2.90783
$433$	−5.40718	−0.259852	−0.129926	−	0.991524i	$-0.541474\pi$
$433$	−5.40718	−0.259852	−0.129926	+	0.991524i	$0.541474\pi$
$434$	7.01970	0.336956
$435$	0	0
$436$	−1.52984	−0.0732661
$437$	2.86316	0.136964
$438$	2.80818	0.134180
$439$	9.22702	0.440382	0.220191	−	0.975457i	$-0.429332\pi$
$439$	9.22702	0.440382	0.220191	+	0.975457i	$0.429332\pi$
$440$	0	0
$441$	8.30972	0.395701
$442$	1.40840	0.0669908
$443$	−19.4549	−0.924329	−0.462164	−	0.886794i	$-0.652927\pi$
$443$	−19.4549	−0.924329	−0.462164	+	0.886794i	$0.652927\pi$
$444$	6.05293	0.287259
$445$	0	0
$446$	28.7297	1.36039
$447$	−14.4613	−0.683994
$448$	8.77028	0.414357
$449$	25.0413	1.18177	0.590887	−	0.806755i	$-0.298778\pi$
$449$	25.0413	1.18177	0.590887	+	0.806755i	$0.298778\pi$
$450$	0	0
$451$	−38.5979	−1.81751
$452$	−2.60172	−0.122374
$453$	9.68877	0.455218
$454$	23.3873	1.09762
$455$	0	0
$456$	28.7531	1.34649
$457$	−33.7231	−1.57750	−0.788750	−	0.614715i	$-0.789271\pi$
$457$	−33.7231	−1.57750	−0.788750	+	0.614715i	$0.789271\pi$
$458$	30.8748	1.44268
$459$	12.4142	0.579446
$460$	0	0
$461$	−13.7841	−0.641988	−0.320994	−	0.947081i	$-0.604017\pi$
$461$	−13.7841	−0.641988	−0.320994	+	0.947081i	$0.604017\pi$
$462$	17.1485	0.797820
$463$	35.3898	1.64470	0.822352	−	0.568979i	$-0.192661\pi$
$463$	35.3898	1.64470	0.822352	+	0.568979i	$0.192661\pi$
$464$	5.81642	0.270020
$465$	0	0
$466$	33.6448	1.55856
$467$	−29.4419	−1.36241	−0.681205	−	0.732093i	$-0.738544\pi$
$467$	−29.4419	−1.36241	−0.681205	+	0.732093i	$0.738544\pi$
$468$	−3.46901	−0.160355
$469$	3.55446	0.164130
$470$	0	0
$471$	−81.5496	−3.75761
$472$	37.0595	1.70580
$473$	35.9960	1.65510
$474$	−37.4585	−1.72052
$475$	0	0
$476$	−0.188381	−0.00863445
$477$	−12.8395	−0.587878
$478$	−10.3475	−0.473286
$479$	−30.6266	−1.39936	−0.699682	−	0.714454i	$-0.746675\pi$
$479$	−30.6266	−1.39936	−0.699682	+	0.714454i	$0.746675\pi$
$480$	0	0
$481$	−10.2336	−0.466610
$482$	−25.7571	−1.17321
$483$	−3.36299	−0.153021
$484$	−1.09423	−0.0497376
$485$	0	0
$486$	84.8739	3.84996
$487$	3.91791	0.177537	0.0887686	−	0.996052i	$-0.471707\pi$
$487$	3.91791	0.177537	0.0887686	+	0.996052i	$0.471707\pi$
$488$	−43.7856	−1.98208
$489$	2.94533	0.133193
$490$	0	0
$491$	−0.978511	−0.0441596	−0.0220798	−	0.999756i	$-0.507029\pi$
$491$	−0.978511	−0.0441596	−0.0220798	+	0.999756i	$0.507029\pi$
$492$	9.07001	0.408908
$493$	−1.19472	−0.0538073
$494$	−5.80030	−0.260968
$495$	0	0
$496$	−18.0688	−0.811314
$497$	10.8286	0.485731
$498$	−36.2236	−1.62322
$499$	−34.3820	−1.53915	−0.769575	−	0.638556i	$-0.779532\pi$
$499$	−34.3820	−1.53915	−0.769575	+	0.638556i	$0.779532\pi$
$500$	0	0
$501$	81.3346	3.63376
$502$	5.09766	0.227520
$503$	−26.1193	−1.16460	−0.582302	−	0.812973i	$-0.697848\pi$
$503$	−26.1193	−1.16460	−0.582302	+	0.812973i	$0.697848\pi$
$504$	−24.8141	−1.10531
$505$	0	0
$506$	−5.09918	−0.226686
$507$	−35.7365	−1.58712
$508$	0.893014	0.0396211
$509$	−9.66500	−0.428393	−0.214197	−	0.976791i	$-0.568713\pi$
$509$	−9.66500	−0.428393	−0.214197	+	0.976791i	$0.568713\pi$
$510$	0	0
$511$	0.635034	0.0280923
$512$	−25.3647	−1.12097
$513$	−51.1262	−2.25728
$514$	−27.5869	−1.21680
$515$	0	0
$516$	−8.45859	−0.372369
$517$	10.1579	0.446743
$518$	−8.73424	−0.383760
$519$	3.69349	0.162126
$520$	0	0
$521$	−7.90004	−0.346107	−0.173054	−	0.984912i	$-0.555363\pi$
$521$	−7.90004	−0.346107	−0.173054	+	0.984912i	$0.555363\pi$
$522$	−18.7772	−0.821856
$523$	−2.07265	−0.0906305	−0.0453153	−	0.998973i	$-0.514429\pi$
$523$	−2.07265	−0.0906305	−0.0453153	+	0.998973i	$0.514429\pi$
$524$	3.95648	0.172839
$525$	0	0
$526$	−29.2968	−1.27740
$527$	3.71141	0.161671
$528$	−44.1405	−1.92097
$529$	1.00000	0.0434783
$530$	0	0
$531$	−103.127	−4.47534
$532$	0.775822	0.0336362
$533$	−15.3345	−0.664209
$534$	−35.8678	−1.55215
$535$	0	0
$536$	−10.6142	−0.458463
$537$	68.1984	2.94298
$538$	1.69375	0.0730230
$539$	3.87792	0.167034
$540$	0	0
$541$	16.9000	0.726586	0.363293	−	0.931675i	$-0.381652\pi$
$541$	16.9000	0.726586	0.363293	+	0.931675i	$0.381652\pi$
$542$	−0.425911	−0.0182944
$543$	28.1418	1.20768
$544$	1.05795	0.0453593
$545$	0	0
$546$	6.81288	0.291564
$547$	32.1844	1.37610	0.688052	−	0.725662i	$-0.258466\pi$
$547$	32.1844	1.37610	0.688052	+	0.725662i	$0.258466\pi$
$548$	2.76164	0.117971
$549$	121.844	5.20019
$550$	0	0
$551$	4.92027	0.209610
$552$	10.0424	0.427434
$553$	−8.47076	−0.360213
$554$	−21.2630	−0.903377
$555$	0	0
$556$	3.13860	0.133106
$557$	36.5940	1.55054	0.775269	−	0.631631i	$-0.217614\pi$
$557$	36.5940	1.55054	0.775269	+	0.631631i	$0.217614\pi$
$558$	58.3318	2.46938
$559$	14.3007	0.604857
$560$	0	0
$561$	9.06664	0.382794
$562$	7.49817	0.316291
$563$	27.8736	1.17473	0.587367	−	0.809321i	$-0.300164\pi$
$563$	27.8736	1.17473	0.587367	+	0.809321i	$0.300164\pi$
$564$	−2.38697	−0.100509
$565$	0	0
$566$	−18.1430	−0.762608
$567$	35.1223	1.47500
$568$	−32.3360	−1.35679
$569$	−31.4670	−1.31916	−0.659582	−	0.751633i	$-0.729267\pi$
$569$	−31.4670	−1.31916	−0.659582	+	0.751633i	$0.729267\pi$
$570$	0	0
$571$	−46.0417	−1.92678	−0.963392	−	0.268098i	$-0.913605\pi$
$571$	−46.0417	−1.92678	−0.963392	+	0.268098i	$0.913605\pi$
$572$	−1.61889	−0.0676892
$573$	−53.3467	−2.22859
$574$	−13.0878	−0.546275
$575$	0	0
$576$	72.8786	3.03661
$577$	35.8353	1.49184	0.745922	−	0.666033i	$-0.232009\pi$
$577$	35.8353	1.49184	0.745922	+	0.666033i	$0.232009\pi$
$578$	−21.7182	−0.903359
$579$	−4.90613	−0.203892
$580$	0	0
$581$	−8.19151	−0.339841
$582$	0.313384	0.0129902
$583$	−5.99182	−0.248156
$584$	−1.89631	−0.0784699
$585$	0	0
$586$	−38.8550	−1.60508
$587$	31.6912	1.30804	0.654019	−	0.756479i	$-0.273082\pi$
$587$	31.6912	1.30804	0.654019	+	0.756479i	$0.273082\pi$
$588$	−0.911260	−0.0375797
$589$	−15.2849	−0.629804
$590$	0	0
$591$	−1.19130	−0.0490037
$592$	22.4821	0.924008
$593$	−29.8135	−1.22430	−0.612148	−	0.790743i	$-0.709694\pi$
$593$	−29.8135	−1.22430	−0.612148	+	0.790743i	$0.709694\pi$
$594$	91.0538	3.73598
$595$	0	0
$596$	1.16519	0.0477280
$597$	−28.1399	−1.15169
$598$	−2.02584	−0.0828426
$599$	−39.1924	−1.60136	−0.800679	−	0.599094i	$-0.795528\pi$
$599$	−39.1924	−1.60136	−0.800679	+	0.599094i	$0.795528\pi$
$600$	0	0
$601$	36.4594	1.48721	0.743605	−	0.668619i	$-0.233114\pi$
$601$	36.4594	1.48721	0.743605	+	0.668619i	$0.233114\pi$
$602$	12.2056	0.497461
$603$	29.5366	1.20282
$604$	−0.780655	−0.0317644
$605$	0	0
$606$	49.2933	2.00240
$607$	−13.4064	−0.544149	−0.272075	−	0.962276i	$-0.587710\pi$
$607$	−13.4064	−0.544149	−0.272075	+	0.962276i	$0.587710\pi$
$608$	−4.35703	−0.176701
$609$	−5.77921	−0.234186
$610$	0	0
$611$	4.03559	0.163263
$612$	−1.56540	−0.0632774
$613$	6.66531	0.269209	0.134605	−	0.990899i	$-0.457024\pi$
$613$	6.66531	0.269209	0.134605	+	0.990899i	$0.457024\pi$
$614$	33.9355	1.36953
$615$	0	0
$616$	−11.5801	−0.466574
$617$	41.2472	1.66055	0.830275	−	0.557354i	$-0.188184\pi$
$617$	41.2472	1.66055	0.830275	+	0.557354i	$0.188184\pi$
$618$	−34.5203	−1.38861
$619$	−18.5403	−0.745196	−0.372598	−	0.927993i	$-0.621533\pi$
$619$	−18.5403	−0.745196	−0.372598	+	0.927993i	$0.621533\pi$
$620$	0	0
$621$	−17.8566	−0.716559
$622$	11.7899	0.472732
$623$	−8.11105	−0.324962
$624$	−17.5365	−0.702020
$625$	0	0
$626$	25.1572	1.00548
$627$	−37.3397	−1.49120
$628$	6.57071	0.262200
$629$	−4.61791	−0.184128
$630$	0	0
$631$	−27.1990	−1.08277	−0.541387	−	0.840773i	$-0.682101\pi$
$631$	−27.1990	−1.08277	−0.541387	+	0.840773i	$0.682101\pi$
$632$	25.2950	1.00618
$633$	−9.68789	−0.385059
$634$	26.0400	1.03418
$635$	0	0
$636$	1.40800	0.0558308
$637$	1.54065	0.0610426
$638$	−8.76280	−0.346922
$639$	89.9829	3.55967
$640$	0	0
$641$	7.00261	0.276586	0.138293	−	0.990391i	$-0.455838\pi$
$641$	7.00261	0.276586	0.138293	+	0.990391i	$0.455838\pi$
$642$	−81.8647	−3.23094
$643$	−11.1010	−0.437783	−0.218891	−	0.975749i	$-0.570244\pi$
$643$	−11.1010	−0.437783	−0.218891	+	0.975749i	$0.570244\pi$
$644$	0.270967	0.0106776
$645$	0	0
$646$	−2.61740	−0.102980
$647$	44.2470	1.73953	0.869765	−	0.493465i	$-0.164270\pi$
$647$	44.2470	1.73953	0.869765	+	0.493465i	$0.164270\pi$
$648$	−104.881	−4.12010
$649$	−48.1266	−1.88914
$650$	0	0
$651$	17.9532	0.703643
$652$	−0.237315	−0.00929397
$653$	−9.01337	−0.352720	−0.176360	−	0.984326i	$-0.556432\pi$
$653$	−9.01337	−0.352720	−0.176360	+	0.984326i	$0.556432\pi$
$654$	24.9665	0.976267
$655$	0	0
$656$	33.6883	1.31531
$657$	5.27696	0.205874
$658$	3.44434	0.134274
$659$	−20.1300	−0.784154	−0.392077	−	0.919932i	$-0.628243\pi$
$659$	−20.1300	−0.784154	−0.392077	+	0.919932i	$0.628243\pi$
$660$	0	0
$661$	7.40048	0.287845	0.143923	−	0.989589i	$-0.454028\pi$
$661$	7.40048	0.287845	0.143923	+	0.989589i	$0.454028\pi$
$662$	−39.7491	−1.54489
$663$	3.60206	0.139892
$664$	24.4611	0.949276
$665$	0	0
$666$	−72.5791	−2.81238
$667$	1.71847	0.0665395
$668$	−6.55338	−0.253558
$669$	73.4776	2.84081
$670$	0	0
$671$	56.8613	2.19511
$672$	5.11764	0.197417
$673$	12.1863	0.469749	0.234874	−	0.972026i	$-0.424532\pi$
$673$	12.1863	0.469749	0.234874	+	0.972026i	$0.424532\pi$
$674$	13.0128	0.501234
$675$	0	0
$676$	2.87941	0.110746
$677$	−15.4824	−0.595038	−0.297519	−	0.954716i	$-0.596159\pi$
$677$	−15.4824	−0.595038	−0.297519	+	0.954716i	$0.596159\pi$
$678$	42.4591	1.63063
$679$	0.0708678	0.00271966
$680$	0	0
$681$	59.8142	2.29209
$682$	27.2218	1.04238
$683$	8.41814	0.322111	0.161055	−	0.986945i	$-0.448510\pi$
$683$	8.41814	0.322111	0.161055	+	0.986945i	$0.448510\pi$
$684$	6.44687	0.246502
$685$	0	0
$686$	1.31493	0.0502041
$687$	78.9638	3.01266
$688$	−31.4173	−1.19777
$689$	−2.38047	−0.0906887
$690$	0	0
$691$	−15.9030	−0.604977	−0.302489	−	0.953153i	$-0.597817\pi$
$691$	−15.9030	−0.604977	−0.302489	+	0.953153i	$0.597817\pi$
$692$	−0.297596	−0.0113129
$693$	32.2244	1.22410
$694$	−46.0557	−1.74825
$695$	0	0
$696$	17.2576	0.654149
$697$	−6.91970	−0.262103
$698$	19.8844	0.752634
$699$	86.0482	3.25464
$700$	0	0
$701$	−27.9164	−1.05439	−0.527193	−	0.849745i	$-0.676756\pi$
$701$	−27.9164	−1.05439	−0.527193	+	0.849745i	$0.676756\pi$
$702$	36.1745	1.36532
$703$	19.0182	0.717285
$704$	34.0104	1.28182
$705$	0	0
$706$	−24.4464	−0.920051
$707$	11.1471	0.419229
$708$	11.3091	0.425023
$709$	37.2328	1.39831	0.699153	−	0.714972i	$-0.253561\pi$
$709$	37.2328	1.39831	0.699153	+	0.714972i	$0.253561\pi$
$710$	0	0
$711$	−70.3897	−2.63982
$712$	24.2208	0.907715
$713$	−5.33847	−0.199927
$714$	3.07432	0.115054
$715$	0	0
$716$	−5.49496	−0.205356
$717$	−26.4644	−0.988330
$718$	4.53795	0.169355
$719$	−5.85441	−0.218333	−0.109166	−	0.994024i	$-0.534818\pi$
$719$	−5.85441	−0.218333	−0.109166	+	0.994024i	$0.534818\pi$
$720$	0	0
$721$	−7.80632	−0.290723
$722$	−14.2042	−0.528627
$723$	−65.8752	−2.44993
$724$	−2.26747	−0.0842700
$725$	0	0
$726$	17.8574	0.662752
$727$	−30.1848	−1.11949	−0.559747	−	0.828664i	$-0.689102\pi$
$727$	−30.1848	−1.11949	−0.559747	+	0.828664i	$0.689102\pi$
$728$	−4.60061	−0.170510
$729$	111.702	4.13712
$730$	0	0
$731$	6.45324	0.238682
$732$	−13.3617	−0.493861
$733$	−17.0925	−0.631327	−0.315664	−	0.948871i	$-0.602227\pi$
$733$	−17.0925	−0.631327	−0.315664	+	0.948871i	$0.602227\pi$
$734$	−14.8033	−0.546401
$735$	0	0
$736$	−1.52175	−0.0560926
$737$	13.7839	0.507737
$738$	−108.756	−4.00337
$739$	31.9358	1.17478	0.587388	−	0.809306i	$-0.300156\pi$
$739$	31.9358	1.17478	0.587388	+	0.809306i	$0.300156\pi$
$740$	0	0
$741$	−14.8346	−0.544961
$742$	−2.03171	−0.0745864
$743$	−32.4527	−1.19057	−0.595287	−	0.803513i	$-0.702962\pi$
$743$	−32.4527	−1.19057	−0.595287	+	0.803513i	$0.702962\pi$
$744$	−53.6112	−1.96548
$745$	0	0
$746$	−28.0664	−1.02758
$747$	−68.0692	−2.49052
$748$	−0.730528	−0.0267107
$749$	−18.5127	−0.676439
$750$	0	0
$751$	15.5840	0.568670	0.284335	−	0.958725i	$-0.408227\pi$
$751$	15.5840	0.568670	0.284335	+	0.958725i	$0.408227\pi$
$752$	−8.86579	−0.323302
$753$	13.0375	0.475114
$754$	−3.48135	−0.126783
$755$	0	0
$756$	−4.83854	−0.175976
$757$	45.9422	1.66980	0.834899	−	0.550404i	$-0.185526\pi$
$757$	45.9422	1.66980	0.834899	+	0.550404i	$0.185526\pi$
$758$	5.34646	0.194192
$759$	−13.0414	−0.473373
$760$	0	0
$761$	23.8379	0.864122	0.432061	−	0.901844i	$-0.357786\pi$
$761$	23.8379	0.864122	0.432061	+	0.901844i	$0.357786\pi$
$762$	−14.5737	−0.527949
$763$	5.64586	0.204394
$764$	4.29831	0.155508
$765$	0	0
$766$	−0.00887412	−0.000320635 0
$767$	−19.1201	−0.690386
$768$	−21.4507	−0.774034
$769$	23.9278	0.862859	0.431429	−	0.902147i	$-0.358009\pi$
$769$	23.9278	0.862859	0.431429	+	0.902147i	$0.358009\pi$
$770$	0	0
$771$	−70.5548	−2.54097
$772$	0.395302	0.0142272
$773$	9.48596	0.341186	0.170593	−	0.985342i	$-0.445432\pi$
$773$	9.48596	0.341186	0.170593	+	0.985342i	$0.445432\pi$
$774$	101.425	3.64564
$775$	0	0
$776$	−0.211622	−0.00759680
$777$	−22.3383	−0.801381
$778$	19.6375	0.704038
$779$	28.4978	1.02104
$780$	0	0
$781$	41.9925	1.50261
$782$	−0.914163	−0.0326904
$783$	−30.6860	−1.09663
$784$	−3.38464	−0.120880
$785$	0	0
$786$	−64.5684	−2.30308
$787$	24.4834	0.872740	0.436370	−	0.899767i	$-0.356264\pi$
$787$	24.4834	0.872740	0.436370	+	0.899767i	$0.356264\pi$
$788$	0.0959870	0.00341940
$789$	−74.9279	−2.66751
$790$	0	0
$791$	9.60160	0.341394
$792$	−96.2271	−3.41928
$793$	22.5903	0.802204
$794$	23.3064	0.827114
$795$	0	0
$796$	2.26732	0.0803630
$797$	22.3153	0.790449	0.395224	−	0.918585i	$-0.370667\pi$
$797$	22.3153	0.790449	0.395224	+	0.918585i	$0.370667\pi$
$798$	−12.6612	−0.448200
$799$	1.82107	0.0644248
$800$	0	0
$801$	−67.4005	−2.38148
$802$	−4.56390	−0.161157
$803$	2.46261	0.0869036
$804$	−3.23904	−0.114232
$805$	0	0
$806$	10.8149	0.380938
$807$	4.33186	0.152489
$808$	−33.2869	−1.17103
$809$	48.3209	1.69887	0.849436	−	0.527691i	$-0.176942\pi$
$809$	48.3209	1.69887	0.849436	+	0.527691i	$0.176942\pi$
$810$	0	0
$811$	−10.4141	−0.365690	−0.182845	−	0.983142i	$-0.558531\pi$
$811$	−10.4141	−0.365690	−0.182845	+	0.983142i	$0.558531\pi$
$812$	0.465649	0.0163411
$813$	−1.08929	−0.0382030
$814$	−33.8707	−1.18717
$815$	0	0
$816$	−7.91336	−0.277023
$817$	−26.5767	−0.929802
$818$	−30.3166	−1.06000
$819$	12.8023	0.447350
$820$	0	0
$821$	33.9118	1.18353	0.591765	−	0.806111i	$-0.298431\pi$
$821$	33.9118	1.18353	0.591765	+	0.806111i	$0.298431\pi$
$822$	−45.0691	−1.57196
$823$	43.7469	1.52492	0.762461	−	0.647035i	$-0.223991\pi$
$823$	43.7469	1.52492	0.762461	+	0.647035i	$0.223991\pi$
$824$	23.3109	0.812073
$825$	0	0
$826$	−16.3188	−0.567804
$827$	17.3331	0.602730	0.301365	−	0.953509i	$-0.402558\pi$
$827$	17.3331	0.602730	0.301365	+	0.953509i	$0.402558\pi$
$828$	2.25166	0.0782506
$829$	8.24746	0.286446	0.143223	−	0.989690i	$-0.454253\pi$
$829$	8.24746	0.286446	0.143223	+	0.989690i	$0.454253\pi$
$830$	0	0
$831$	−54.3811	−1.88646
$832$	13.5119	0.468441
$833$	0.695219	0.0240879
$834$	−51.2209	−1.77364
$835$	0	0
$836$	3.00857	0.104054
$837$	95.3267	3.29497
$838$	−31.6930	−1.09482
$839$	−14.1386	−0.488118	−0.244059	−	0.969760i	$-0.578479\pi$
$839$	−14.1386	−0.488118	−0.244059	+	0.969760i	$0.578479\pi$
$840$	0	0
$841$	−26.0469	−0.898167
$842$	−20.4730	−0.705545
$843$	19.1770	0.660490
$844$	0.780583	0.0268688
$845$	0	0
$846$	28.6215	0.984028
$847$	4.03823	0.138755
$848$	5.22965	0.179587
$849$	−46.4017	−1.59250
$850$	0	0
$851$	6.64238	0.227698
$852$	−9.86770	−0.338062
$853$	−8.70234	−0.297962	−0.148981	−	0.988840i	$-0.547599\pi$
$853$	−8.70234	−0.297962	−0.148981	+	0.988840i	$0.547599\pi$
$854$	19.2806	0.659768
$855$	0	0
$856$	55.2817	1.88949
$857$	−46.6648	−1.59404	−0.797020	−	0.603953i	$-0.793592\pi$
$857$	−46.6648	−1.59404	−0.797020	+	0.603953i	$0.793592\pi$
$858$	26.4198	0.901956
$859$	16.0873	0.548891	0.274445	−	0.961603i	$-0.411506\pi$
$859$	16.0873	0.548891	0.274445	+	0.961603i	$0.411506\pi$
$860$	0	0
$861$	−33.4728	−1.14075
$862$	42.2791	1.44003
$863$	28.0284	0.954099	0.477050	−	0.878876i	$-0.341706\pi$
$863$	28.0284	0.954099	0.477050	+	0.878876i	$0.341706\pi$
$864$	27.1733	0.924453
$865$	0	0
$866$	−7.11004	−0.241609
$867$	−55.5454	−1.88642
$868$	−1.44655	−0.0490991
$869$	−32.8489	−1.11432
$870$	0	0
$871$	5.47617	0.185553
$872$	−16.8594	−0.570932
$873$	0.588892	0.0199310
$874$	3.76485	0.127348
$875$	0	0
$876$	−0.578681	−0.0195518
$877$	42.2483	1.42662	0.713312	−	0.700847i	$-0.247194\pi$
$877$	42.2483	1.42662	0.713312	+	0.700847i	$0.247194\pi$
$878$	12.1329	0.409464
$879$	−99.3736	−3.35179
$880$	0	0
$881$	−35.9657	−1.21171	−0.605857	−	0.795574i	$-0.707170\pi$
$881$	−35.9657	−1.21171	−0.605857	+	0.795574i	$0.707170\pi$
$882$	10.9267	0.367920
$883$	−1.09651	−0.0369004	−0.0184502	−	0.999830i	$-0.505873\pi$
$883$	−1.09651	−0.0369004	−0.0184502	+	0.999830i	$0.505873\pi$
$884$	−0.290229	−0.00976146
$885$	0	0
$886$	−25.5817	−0.859435
$887$	−31.4785	−1.05694	−0.528472	−	0.848950i	$-0.677235\pi$
$887$	−31.4785	−1.05694	−0.528472	+	0.848950i	$0.677235\pi$
$888$	66.7055	2.23849
$889$	−3.29566	−0.110533
$890$	0	0
$891$	136.201	4.56292
$892$	−5.92032	−0.198227
$893$	−7.49981	−0.250972
$894$	−19.0155	−0.635974
$895$	0	0
$896$	8.48877	0.283590
$897$	−5.18118	−0.172995
$898$	32.9275	1.09881
$899$	−9.17402	−0.305971
$900$	0	0
$901$	−1.07419	−0.0357865
$902$	−50.7535	−1.68991
$903$	31.2163	1.03881
$904$	−28.6719	−0.953612
$905$	0	0
$906$	12.7400	0.423259
$907$	52.2682	1.73554	0.867768	−	0.496969i	$-0.165554\pi$
$907$	52.2682	1.73554	0.867768	+	0.496969i	$0.165554\pi$
$908$	−4.81942	−0.159938
$909$	92.6290	3.07231
$910$	0	0
$911$	32.0056	1.06039	0.530196	−	0.847875i	$-0.322118\pi$
$911$	32.0056	1.06039	0.530196	+	0.847875i	$0.322118\pi$
$912$	32.5900	1.07916
$913$	−31.7660	−1.05130
$914$	−44.3434	−1.46675
$915$	0	0
$916$	−6.36236	−0.210218
$917$	−14.6013	−0.482178
$918$	16.3238	0.538766
$919$	26.7819	0.883454	0.441727	−	0.897149i	$-0.354366\pi$
$919$	26.7819	0.883454	0.441727	+	0.897149i	$0.354366\pi$
$920$	0	0
$921$	86.7918	2.85989
$922$	−18.1251	−0.596917
$923$	16.6831	0.549131
$924$	−3.53379	−0.116253
$925$	0	0
$926$	46.5350	1.52924
$927$	−64.8684	−2.13056
$928$	−2.61509	−0.0858446
$929$	−8.80344	−0.288831	−0.144416	−	0.989517i	$-0.546130\pi$
$929$	−8.80344	−0.288831	−0.144416	+	0.989517i	$0.546130\pi$
$930$	0	0
$931$	−2.86316	−0.0938364
$932$	−6.93318	−0.227104
$933$	30.1532	0.987173
$934$	−38.7140	−1.26676
$935$	0	0
$936$	−38.2298	−1.24958
$937$	−7.80026	−0.254823	−0.127412	−	0.991850i	$-0.540667\pi$
$937$	−7.80026	−0.254823	−0.127412	+	0.991850i	$0.540667\pi$
$938$	4.67386	0.152607
$939$	64.3409	2.09968
$940$	0	0
$941$	−16.2713	−0.530430	−0.265215	−	0.964189i	$-0.585443\pi$
$941$	−16.2713	−0.530430	−0.265215	+	0.964189i	$0.585443\pi$
$942$	−107.232	−3.49380
$943$	9.95327	0.324123
$944$	42.0049	1.36714
$945$	0	0
$946$	47.3321	1.53890
$947$	1.82257	0.0592255	0.0296127	−	0.999561i	$-0.490573\pi$
$947$	1.82257	0.0592255	0.0296127	+	0.999561i	$0.490573\pi$
$948$	7.71906	0.250703
$949$	0.978363	0.0317590
$950$	0	0
$951$	66.5985	2.15960
$952$	−2.07603	−0.0672846
$953$	17.5282	0.567795	0.283898	−	0.958855i	$-0.408372\pi$
$953$	17.5282	0.567795	0.283898	+	0.958855i	$0.408372\pi$
$954$	−16.8829	−0.546605
$955$	0	0
$956$	2.13232	0.0689641
$957$	−22.4113	−0.724455
$958$	−40.2717	−1.30112
$959$	−10.1918	−0.329111
$960$	0	0
$961$	−2.50073	−0.0806688
$962$	−13.4564	−0.433851
$963$	−153.835	−4.95727
$964$	5.30777	0.170952
$965$	0	0
$966$	−4.42209	−0.142278
$967$	4.12594	0.132681	0.0663407	−	0.997797i	$-0.478868\pi$
$967$	4.12594	0.132681	0.0663407	+	0.997797i	$0.478868\pi$
$968$	−12.0588	−0.387584
$969$	−6.69413	−0.215046
$970$	0	0
$971$	30.8552	0.990190	0.495095	−	0.868839i	$-0.335133\pi$
$971$	30.8552	0.990190	0.495095	+	0.868839i	$0.335133\pi$
$972$	−17.4899	−0.560990
$973$	−11.5830	−0.371333
$974$	5.15176	0.165073
$975$	0	0
$976$	−49.6285	−1.58857
$977$	45.4200	1.45312	0.726558	−	0.687106i	$-0.241119\pi$
$977$	45.4200	1.45312	0.726558	+	0.687106i	$0.241119\pi$
$978$	3.87290	0.123842
$979$	−31.4540	−1.00527
$980$	0	0
$981$	46.9155	1.49790
$982$	−1.28667	−0.0410593
$983$	55.0475	1.75574	0.877872	−	0.478896i	$-0.158963\pi$
$983$	55.0475	1.75574	0.877872	+	0.478896i	$0.158963\pi$
$984$	99.9549	3.18645
$985$	0	0
$986$	−1.57096	−0.0500297
$987$	8.80908	0.280396
$988$	1.19527	0.0380265
$989$	−9.28230	−0.295160
$990$	0	0
$991$	−8.00146	−0.254175	−0.127087	−	0.991892i	$-0.540563\pi$
$991$	−8.00146	−0.254175	−0.127087	+	0.991892i	$0.540563\pi$
$992$	8.12383	0.257932
$993$	−101.660	−3.22610
$994$	14.2389	0.451629
$995$	0	0
$996$	7.46460	0.236525
$997$	18.2815	0.578980	0.289490	−	0.957181i	$-0.406514\pi$
$997$	18.2815	0.578980	0.289490	+	0.957181i	$0.406514\pi$
$998$	−45.2098	−1.43109
$999$	−118.610	−3.75265

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bb.1.10	yes	14
5.4	even	2		4025.2.a.ba.1.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.ba.1.5	✓	14	5.4	even	2
4025.2.a.bb.1.10	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q+1.31493 q^{2} +3.36299 q^{3} -0.270967 q^{4} +4.42209 q^{6} +1.00000 q^{7} -2.98616 q^{8} +8.30972 q^{9} +O(q^{10})\)	\(q+1.31493 q^{2} +3.36299 q^{3} -0.270967 q^{4} +4.42209 q^{6} +1.00000 q^{7} -2.98616 q^{8} +8.30972 q^{9} +3.87792 q^{11} -0.911260 q^{12} +1.54065 q^{13} +1.31493 q^{14} -3.38464 q^{16} +0.695219 q^{17} +10.9267 q^{18} -2.86316 q^{19} +3.36299 q^{21} +5.09918 q^{22} -1.00000 q^{23} -10.0424 q^{24} +2.02584 q^{26} +17.8566 q^{27} -0.270967 q^{28} -1.71847 q^{29} +5.33847 q^{31} +1.52175 q^{32} +13.0414 q^{33} +0.914163 q^{34} -2.25166 q^{36} -6.64238 q^{37} -3.76485 q^{38} +5.18118 q^{39} -9.95327 q^{41} +4.42209 q^{42} +9.28230 q^{43} -1.05079 q^{44} -1.31493 q^{46} +2.61942 q^{47} -11.3825 q^{48} +1.00000 q^{49} +2.33802 q^{51} -0.417464 q^{52} -1.54511 q^{53} +23.4801 q^{54} -2.98616 q^{56} -9.62880 q^{57} -2.25967 q^{58} -12.4104 q^{59} +14.6629 q^{61} +7.01970 q^{62} +8.30972 q^{63} +8.77028 q^{64} +17.1485 q^{66} +3.55446 q^{67} -0.188381 q^{68} -3.36299 q^{69} +10.8286 q^{71} -24.8141 q^{72} +0.635034 q^{73} -8.73424 q^{74} +0.775822 q^{76} +3.87792 q^{77} +6.81288 q^{78} -8.47076 q^{79} +35.1223 q^{81} -13.0878 q^{82} -8.19151 q^{83} -0.911260 q^{84} +12.2056 q^{86} -5.77921 q^{87} -11.5801 q^{88} -8.11105 q^{89} +1.54065 q^{91} +0.270967 q^{92} +17.9532 q^{93} +3.44434 q^{94} +5.11764 q^{96} +0.0708678 q^{97} +1.31493 q^{98} +32.2244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + 6 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q + q^2 + 6 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 9 * q^8 + 18 * q^9	\( 14 q + q^{2} + 6 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 9 q^{8} + 18 q^{9} - 3 q^{11} + 11 q^{12} + 15 q^{13} + q^{14} + 23 q^{16} + 9 q^{17} + 17 q^{18} - 4 q^{19} + 6 q^{21} + 9 q^{22} - 14 q^{23} + 10 q^{24} - 5 q^{26} + 33 q^{27} + 17 q^{28} + 11 q^{29} - q^{31} + 24 q^{32} + 26 q^{33} - 6 q^{34} + 13 q^{36} + 18 q^{37} - 6 q^{38} + 6 q^{39} - 7 q^{41} - 4 q^{42} + 18 q^{43} - 16 q^{44} - q^{46} + 10 q^{47} + 40 q^{48} + 14 q^{49} + 28 q^{51} + 46 q^{52} + 5 q^{53} - 24 q^{54} + 9 q^{56} - 26 q^{57} + 2 q^{58} - 24 q^{59} - 6 q^{61} - 16 q^{62} + 18 q^{63} + 29 q^{64} + 27 q^{66} + 61 q^{67} + 35 q^{68} - 6 q^{69} + 11 q^{71} + 12 q^{72} + 28 q^{73} - 49 q^{74} - 27 q^{76} - 3 q^{77} + 38 q^{78} + 6 q^{79} + 26 q^{81} - 14 q^{82} + 16 q^{83} + 11 q^{84} + 46 q^{86} + 61 q^{87} + 58 q^{88} - 39 q^{89} + 15 q^{91} - 17 q^{92} + 21 q^{93} - 74 q^{94} + 41 q^{96} + 19 q^{97} + q^{98} - 9 q^{99}+O(q^{100}) \) 14 * q + q^2 + 6 * q^3 + 17 * q^4 - 4 * q^6 + 14 * q^7 + 9 * q^8 + 18 * q^9 - 3 * q^11 + 11 * q^12 + 15 * q^13 + q^14 + 23 * q^16 + 9 * q^17 + 17 * q^18 - 4 * q^19 + 6 * q^21 + 9 * q^22 - 14 * q^23 + 10 * q^24 - 5 * q^26 + 33 * q^27 + 17 * q^28 + 11 * q^29 - q^31 + 24 * q^32 + 26 * q^33 - 6 * q^34 + 13 * q^36 + 18 * q^37 - 6 * q^38 + 6 * q^39 - 7 * q^41 - 4 * q^42 + 18 * q^43 - 16 * q^44 - q^46 + 10 * q^47 + 40 * q^48 + 14 * q^49 + 28 * q^51 + 46 * q^52 + 5 * q^53 - 24 * q^54 + 9 * q^56 - 26 * q^57 + 2 * q^58 - 24 * q^59 - 6 * q^61 - 16 * q^62 + 18 * q^63 + 29 * q^64 + 27 * q^66 + 61 * q^67 + 35 * q^68 - 6 * q^69 + 11 * q^71 + 12 * q^72 + 28 * q^73 - 49 * q^74 - 27 * q^76 - 3 * q^77 + 38 * q^78 + 6 * q^79 + 26 * q^81 - 14 * q^82 + 16 * q^83 + 11 * q^84 + 46 * q^86 + 61 * q^87 + 58 * q^88 - 39 * q^89 + 15 * q^91 - 17 * q^92 + 21 * q^93 - 74 * q^94 + 41 * q^96 + 19 * q^97 + q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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