LMFDB - Embedded newform 4025.2.a.bb.1.11

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			1.11
Root			$1.82692$ 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)

$f(q)$	$=$	$q+1.82692 q^{2} -2.52976 q^{3} +1.33763 q^{4} -4.62167 q^{6} +1.00000 q^{7} -1.21009 q^{8} +3.39970 q^{9} +O(q^{10})$	\(q+1.82692 q^{2} -2.52976 q^{3} +1.33763 q^{4} -4.62167 q^{6} +1.00000 q^{7} -1.21009 q^{8} +3.39970 q^{9} -5.78402 q^{11} -3.38390 q^{12} -4.90825 q^{13} +1.82692 q^{14} -4.88600 q^{16} +2.45255 q^{17} +6.21098 q^{18} -2.78658 q^{19} -2.52976 q^{21} -10.5669 q^{22} -1.00000 q^{23} +3.06124 q^{24} -8.96698 q^{26} -1.01114 q^{27} +1.33763 q^{28} +3.77716 q^{29} +3.60581 q^{31} -6.50616 q^{32} +14.6322 q^{33} +4.48061 q^{34} +4.54756 q^{36} +3.72926 q^{37} -5.09085 q^{38} +12.4167 q^{39} +6.11199 q^{41} -4.62167 q^{42} +11.9057 q^{43} -7.73691 q^{44} -1.82692 q^{46} +0.288671 q^{47} +12.3604 q^{48} +1.00000 q^{49} -6.20437 q^{51} -6.56545 q^{52} -10.2509 q^{53} -1.84728 q^{54} -1.21009 q^{56} +7.04937 q^{57} +6.90057 q^{58} -11.2550 q^{59} -14.1458 q^{61} +6.58752 q^{62} +3.39970 q^{63} -2.11422 q^{64} +26.7319 q^{66} +13.2545 q^{67} +3.28062 q^{68} +2.52976 q^{69} +10.0117 q^{71} -4.11394 q^{72} +5.42017 q^{73} +6.81307 q^{74} -3.72742 q^{76} -5.78402 q^{77} +22.6843 q^{78} +15.9865 q^{79} -7.64114 q^{81} +11.1661 q^{82} -2.83383 q^{83} -3.38390 q^{84} +21.7507 q^{86} -9.55532 q^{87} +6.99918 q^{88} -13.4044 q^{89} -4.90825 q^{91} -1.33763 q^{92} -9.12183 q^{93} +0.527378 q^{94} +16.4590 q^{96} -9.98836 q^{97} +1.82692 q^{98} -19.6639 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.82692	1.29183	0.645914	−	0.763411i	$-0.276477\pi$
$2$	1.82692	1.29183	0.645914	+	0.763411i	$0.276477\pi$
$3$	−2.52976	−1.46056	−0.730280	−	0.683148i	$-0.760610\pi$
$3$	−2.52976	−1.46056	−0.730280	+	0.683148i	$0.760610\pi$
$4$	1.33763	0.668817
$5$	0	0
$5$	0	0
$6$	−4.62167	−1.88679
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.21009	−0.427831
$9$	3.39970	1.13323
$10$	0	0
$11$	−5.78402	−1.74395	−0.871974	−	0.489552i	$-0.837160\pi$
$11$	−5.78402	−1.74395	−0.871974	+	0.489552i	$0.837160\pi$
$12$	−3.38390	−0.976847
$13$	−4.90825	−1.36130	−0.680652	−	0.732607i	$-0.738304\pi$
$13$	−4.90825	−1.36130	−0.680652	+	0.732607i	$0.738304\pi$
$14$	1.82692	0.488265
$15$	0	0
$16$	−4.88600	−1.22150
$17$	2.45255	0.594831	0.297416	−	0.954748i	$-0.403875\pi$
$17$	2.45255	0.594831	0.297416	+	0.954748i	$0.403875\pi$
$18$	6.21098	1.46394
$19$	−2.78658	−0.639284	−0.319642	−	0.947538i	$-0.603563\pi$
$19$	−2.78658	−0.639284	−0.319642	+	0.947538i	$0.603563\pi$
$20$	0	0
$21$	−2.52976	−0.552039
$22$	−10.5669	−2.25288
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.06124	0.624872
$25$	0	0
$26$	−8.96698	−1.75857
$27$	−1.01114	−0.194595
$28$	1.33763	0.252789
$29$	3.77716	0.701401	0.350701	−	0.936488i	$-0.385943\pi$
$29$	3.77716	0.701401	0.350701	+	0.936488i	$0.385943\pi$
$30$	0	0
$31$	3.60581	0.647622	0.323811	−	0.946122i	$-0.395036\pi$
$31$	3.60581	0.647622	0.323811	+	0.946122i	$0.395036\pi$
$32$	−6.50616	−1.15014
$33$	14.6322	2.54714
$34$	4.48061	0.768419
$35$	0	0
$36$	4.54756	0.757926
$37$	3.72926	0.613087	0.306544	−	0.951857i	$-0.400827\pi$
$37$	3.72926	0.613087	0.306544	+	0.951857i	$0.400827\pi$
$38$	−5.09085	−0.825845
$39$	12.4167	1.98827
$40$	0	0
$41$	6.11199	0.954533	0.477266	−	0.878759i	$-0.341628\pi$
$41$	6.11199	0.954533	0.477266	+	0.878759i	$0.341628\pi$
$42$	−4.62167	−0.713140
$43$	11.9057	1.81560	0.907798	−	0.419408i	$-0.137762\pi$
$43$	11.9057	1.81560	0.907798	+	0.419408i	$0.137762\pi$
$44$	−7.73691	−1.16638
$45$	0	0
$46$	−1.82692	−0.269365
$47$	0.288671	0.0421070	0.0210535	−	0.999778i	$-0.493298\pi$
$47$	0.288671	0.0421070	0.0210535	+	0.999778i	$0.493298\pi$
$48$	12.3604	1.78407
$49$	1.00000	0.142857
$50$	0	0
$51$	−6.20437	−0.868786
$52$	−6.56545	−0.910464
$53$	−10.2509	−1.40807	−0.704037	−	0.710164i	$-0.748621\pi$
$53$	−10.2509	−1.40807	−0.704037	+	0.710164i	$0.748621\pi$
$54$	−1.84728	−0.251383
$55$	0	0
$56$	−1.21009	−0.161705
$57$	7.04937	0.933712
$58$	6.90057	0.906089
$59$	−11.2550	−1.46527	−0.732636	−	0.680621i	$-0.761710\pi$
$59$	−11.2550	−1.46527	−0.732636	+	0.680621i	$0.761710\pi$
$60$	0	0
$61$	−14.1458	−1.81119	−0.905595	−	0.424143i	$-0.860575\pi$
$61$	−14.1458	−1.81119	−0.905595	+	0.424143i	$0.860575\pi$
$62$	6.58752	0.836615
$63$	3.39970	0.428322
$64$	−2.11422	−0.264277
$65$	0	0
$66$	26.7319	3.29046
$67$	13.2545	1.61930	0.809648	−	0.586916i	$-0.199658\pi$
$67$	13.2545	1.61930	0.809648	+	0.586916i	$0.199658\pi$
$68$	3.28062	0.397833
$69$	2.52976	0.304548
$70$	0	0
$71$	10.0117	1.18817	0.594083	−	0.804404i	$-0.297515\pi$
$71$	10.0117	1.18817	0.594083	+	0.804404i	$0.297515\pi$
$72$	−4.11394	−0.484832
$73$	5.42017	0.634383	0.317192	−	0.948361i	$-0.397260\pi$
$73$	5.42017	0.634383	0.317192	+	0.948361i	$0.397260\pi$
$74$	6.81307	0.792003
$75$	0	0
$76$	−3.72742	−0.427564
$77$	−5.78402	−0.659150
$78$	22.6843	2.56850
$79$	15.9865	1.79862	0.899308	−	0.437315i	$-0.144071\pi$
$79$	15.9865	1.79862	0.899308	+	0.437315i	$0.144071\pi$
$80$	0	0
$81$	−7.64114	−0.849016
$82$	11.1661	1.23309
$83$	−2.83383	−0.311053	−0.155526	−	0.987832i	$-0.549707\pi$
$83$	−2.83383	−0.311053	−0.155526	+	0.987832i	$0.549707\pi$
$84$	−3.38390	−0.369214
$85$	0	0
$86$	21.7507	2.34544
$87$	−9.55532	−1.02444
$88$	6.99918	0.746115
$89$	−13.4044	−1.42087	−0.710433	−	0.703764i	$-0.751501\pi$
$89$	−13.4044	−1.42087	−0.710433	+	0.703764i	$0.751501\pi$
$90$	0	0
$91$	−4.90825	−0.514525
$92$	−1.33763	−0.139458
$93$	−9.12183	−0.945890
$94$	0.527378	0.0543949
$95$	0	0
$96$	16.4590	1.67984
$97$	−9.98836	−1.01416	−0.507082	−	0.861898i	$-0.669276\pi$
$97$	−9.98836	−1.01416	−0.507082	+	0.861898i	$0.669276\pi$
$98$	1.82692	0.184547
$99$	−19.6639	−1.97630
$100$	0	0
$101$	−3.76665	−0.374796	−0.187398	−	0.982284i	$-0.560005\pi$
$101$	−3.76665	−0.374796	−0.187398	+	0.982284i	$0.560005\pi$
$102$	−11.3349	−1.12232
$103$	11.0443	1.08822	0.544111	−	0.839013i	$-0.316867\pi$
$103$	11.0443	1.08822	0.544111	+	0.839013i	$0.316867\pi$
$104$	5.93942	0.582408
$105$	0	0
$106$	−18.7276	−1.81899
$107$	5.49609	0.531327	0.265663	−	0.964066i	$-0.414409\pi$
$107$	5.49609	0.531327	0.265663	+	0.964066i	$0.414409\pi$
$108$	−1.35254	−0.130148
$109$	−12.4368	−1.19123	−0.595613	−	0.803271i	$-0.703091\pi$
$109$	−12.4368	−1.19123	−0.595613	+	0.803271i	$0.703091\pi$
$110$	0	0
$111$	−9.43415	−0.895450
$112$	−4.88600	−0.461684
$113$	17.0110	1.60026	0.800128	−	0.599829i	$-0.204765\pi$
$113$	17.0110	1.60026	0.800128	+	0.599829i	$0.204765\pi$
$114$	12.8786	1.20620
$115$	0	0
$116$	5.05246	0.469109
$117$	−16.6866	−1.54268
$118$	−20.5619	−1.89288
$119$	2.45255	0.224825
$120$	0	0
$121$	22.4549	2.04136
$122$	−25.8433	−2.33974
$123$	−15.4619	−1.39415
$124$	4.82325	0.433141
$125$	0	0
$126$	6.21098	0.553318
$127$	13.2974	1.17996	0.589978	−	0.807419i	$-0.299136\pi$
$127$	13.2974	1.17996	0.589978	+	0.807419i	$0.299136\pi$
$128$	9.14981	0.808736
$129$	−30.1185	−2.65178
$130$	0	0
$131$	18.7323	1.63665	0.818324	−	0.574757i	$-0.194903\pi$
$131$	18.7323	1.63665	0.818324	+	0.574757i	$0.194903\pi$
$132$	19.5725	1.70357
$133$	−2.78658	−0.241627
$134$	24.2149	2.09185
$135$	0	0
$136$	−2.96780	−0.254487
$137$	−2.41194	−0.206066	−0.103033	−	0.994678i	$-0.532855\pi$
$137$	−2.41194	−0.206066	−0.103033	+	0.994678i	$0.532855\pi$
$138$	4.62167	0.393423
$139$	−15.8928	−1.34801	−0.674006	−	0.738726i	$-0.735428\pi$
$139$	−15.8928	−1.34801	−0.674006	+	0.738726i	$0.735428\pi$
$140$	0	0
$141$	−0.730269	−0.0614997
$142$	18.2905	1.53490
$143$	28.3894	2.37404
$144$	−16.6109	−1.38424
$145$	0	0
$146$	9.90222	0.819514
$147$	−2.52976	−0.208651
$148$	4.98839	0.410043
$149$	4.47033	0.366224	0.183112	−	0.983092i	$-0.441383\pi$
$149$	4.47033	0.366224	0.183112	+	0.983092i	$0.441383\pi$
$150$	0	0
$151$	−10.5258	−0.856578	−0.428289	−	0.903642i	$-0.640883\pi$
$151$	−10.5258	−0.856578	−0.428289	+	0.903642i	$0.640883\pi$
$152$	3.37200	0.273505
$153$	8.33794	0.674082
$154$	−10.5669	−0.851508
$155$	0	0
$156$	16.6090	1.32979
$157$	4.34274	0.346589	0.173294	−	0.984870i	$-0.444559\pi$
$157$	4.34274	0.346589	0.173294	+	0.984870i	$0.444559\pi$
$158$	29.2060	2.32350
$159$	25.9324	2.05657
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−13.9598	−1.09678
$163$	18.0437	1.41329	0.706645	−	0.707568i	$-0.250208\pi$
$163$	18.0437	1.41329	0.706645	+	0.707568i	$0.250208\pi$
$164$	8.17561	0.638408
$165$	0	0
$166$	−5.17717	−0.401827
$167$	14.6893	1.13669	0.568345	−	0.822791i	$-0.307584\pi$
$167$	14.6893	1.13669	0.568345	+	0.822791i	$0.307584\pi$
$168$	3.06124	0.236179
$169$	11.0910	0.853150
$170$	0	0
$171$	−9.47352	−0.724458
$172$	15.9254	1.21430
$173$	−12.0926	−0.919382	−0.459691	−	0.888079i	$-0.652040\pi$
$173$	−12.0926	−0.919382	−0.459691	+	0.888079i	$0.652040\pi$
$174$	−17.4568	−1.32340
$175$	0	0
$176$	28.2607	2.13023
$177$	28.4724	2.14012
$178$	−24.4888	−1.83551
$179$	−3.56269	−0.266288	−0.133144	−	0.991097i	$-0.542507\pi$
$179$	−3.56269	−0.266288	−0.133144	+	0.991097i	$0.542507\pi$
$180$	0	0
$181$	8.30455	0.617273	0.308636	−	0.951180i	$-0.400127\pi$
$181$	8.30455	0.617273	0.308636	+	0.951180i	$0.400127\pi$
$182$	−8.96698	−0.664677
$183$	35.7856	2.64535
$184$	1.21009	0.0892089
$185$	0	0
$186$	−16.6649	−1.22193
$187$	−14.1856	−1.03735
$188$	0.386136	0.0281619
$189$	−1.01114	−0.0735499
$190$	0	0
$191$	5.08675	0.368064	0.184032	−	0.982920i	$-0.441085\pi$
$191$	5.08675	0.368064	0.184032	+	0.982920i	$0.441085\pi$
$192$	5.34847	0.385993
$193$	17.0696	1.22870	0.614350	−	0.789034i	$-0.289418\pi$
$193$	17.0696	1.22870	0.614350	+	0.789034i	$0.289418\pi$
$194$	−18.2479	−1.31012
$195$	0	0
$196$	1.33763	0.0955453
$197$	−1.45968	−0.103998	−0.0519990	−	0.998647i	$-0.516559\pi$
$197$	−1.45968	−0.103998	−0.0519990	+	0.998647i	$0.516559\pi$
$198$	−35.9244	−2.55304
$199$	10.6559	0.755377	0.377688	−	0.925933i	$-0.376719\pi$
$199$	10.6559	0.755377	0.377688	+	0.925933i	$0.376719\pi$
$200$	0	0
$201$	−33.5308	−2.36508
$202$	−6.88137	−0.484171
$203$	3.77716	0.265105
$204$	−8.29918	−0.581059
$205$	0	0
$206$	20.1770	1.40580
$207$	−3.39970	−0.236295
$208$	23.9817	1.66283
$209$	16.1176	1.11488
$210$	0	0
$211$	2.36405	0.162748	0.0813739	−	0.996684i	$-0.474069\pi$
$211$	2.36405	0.162748	0.0813739	+	0.996684i	$0.474069\pi$
$212$	−13.7120	−0.941744
$213$	−25.3271	−1.73539
$214$	10.0409	0.686382
$215$	0	0
$216$	1.22357	0.0832536
$217$	3.60581	0.244778
$218$	−22.7210	−1.53886
$219$	−13.7118	−0.926554
$220$	0	0
$221$	−12.0377	−0.809746
$222$	−17.2354	−1.15677
$223$	−8.94028	−0.598685	−0.299343	−	0.954146i	$-0.596767\pi$
$223$	−8.94028	−0.598685	−0.299343	+	0.954146i	$0.596767\pi$
$224$	−6.50616	−0.434711
$225$	0	0
$226$	31.0776	2.06725
$227$	16.1576	1.07242	0.536208	−	0.844086i	$-0.319856\pi$
$227$	16.1576	1.07242	0.536208	+	0.844086i	$0.319856\pi$
$228$	9.42949	0.624483
$229$	8.18378	0.540799	0.270400	−	0.962748i	$-0.412844\pi$
$229$	8.18378	0.540799	0.270400	+	0.962748i	$0.412844\pi$
$230$	0	0
$231$	14.6322	0.962728
$232$	−4.57070	−0.300081
$233$	−10.8381	−0.710028	−0.355014	−	0.934861i	$-0.615524\pi$
$233$	−10.8381	−0.710028	−0.355014	+	0.934861i	$0.615524\pi$
$234$	−30.4850	−1.99287
$235$	0	0
$236$	−15.0550	−0.979999
$237$	−40.4419	−2.62699
$238$	4.48061	0.290435
$239$	−5.68127	−0.367491	−0.183746	−	0.982974i	$-0.558822\pi$
$239$	−5.68127	−0.367491	−0.183746	+	0.982974i	$0.558822\pi$
$240$	0	0
$241$	−22.0611	−1.42108	−0.710542	−	0.703655i	$-0.751550\pi$
$241$	−22.0611	−1.42108	−0.710542	+	0.703655i	$0.751550\pi$
$242$	41.0233	2.63708
$243$	22.3637	1.43463
$244$	−18.9220	−1.21136
$245$	0	0
$246$	−28.2476	−1.80100
$247$	13.6772	0.870261
$248$	−4.36334	−0.277073
$249$	7.16891	0.454311
$250$	0	0
$251$	−2.35500	−0.148646	−0.0743231	−	0.997234i	$-0.523680\pi$
$251$	−2.35500	−0.148646	−0.0743231	+	0.997234i	$0.523680\pi$
$252$	4.54756	0.286469
$253$	5.78402	0.363638
$254$	24.2934	1.52430
$255$	0	0
$256$	20.9444	1.30902
$257$	16.5850	1.03454	0.517272	−	0.855821i	$-0.326947\pi$
$257$	16.5850	1.03454	0.517272	+	0.855821i	$0.326947\pi$
$258$	−55.0240	−3.42565
$259$	3.72926	0.231725
$260$	0	0
$261$	12.8412	0.794851
$262$	34.2224	2.11427
$263$	−8.03090	−0.495207	−0.247603	−	0.968862i	$-0.579643\pi$
$263$	−8.03090	−0.495207	−0.247603	+	0.968862i	$0.579643\pi$
$264$	−17.7063	−1.08974
$265$	0	0
$266$	−5.09085	−0.312140
$267$	33.9100	2.07526
$268$	17.7297	1.08301
$269$	14.2867	0.871074	0.435537	−	0.900171i	$-0.356558\pi$
$269$	14.2867	0.871074	0.435537	+	0.900171i	$0.356558\pi$
$270$	0	0
$271$	−15.4525	−0.938671	−0.469335	−	0.883020i	$-0.655506\pi$
$271$	−15.4525	−0.938671	−0.469335	+	0.883020i	$0.655506\pi$
$272$	−11.9832	−0.726587
$273$	12.4167	0.751494
$274$	−4.40642	−0.266201
$275$	0	0
$276$	3.38390	0.203687
$277$	−15.5942	−0.936966	−0.468483	−	0.883472i	$-0.655199\pi$
$277$	−15.5942	−0.936966	−0.468483	+	0.883472i	$0.655199\pi$
$278$	−29.0349	−1.74140
$279$	12.2587	0.733906
$280$	0	0
$281$	5.56077	0.331727	0.165864	−	0.986149i	$-0.446959\pi$
$281$	5.56077	0.331727	0.165864	+	0.986149i	$0.446959\pi$
$282$	−1.33414	−0.0794470
$283$	−11.1449	−0.662494	−0.331247	−	0.943544i	$-0.607469\pi$
$283$	−11.1449	−0.662494	−0.331247	+	0.943544i	$0.607469\pi$
$284$	13.3919	0.794666
$285$	0	0
$286$	51.8652	3.06686
$287$	6.11199	0.360779
$288$	−22.1190	−1.30337
$289$	−10.9850	−0.646176
$290$	0	0
$291$	25.2682	1.48125
$292$	7.25021	0.424287
$293$	−4.14817	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$293$	−4.14817	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$294$	−4.62167	−0.269541
$295$	0	0
$296$	−4.51274	−0.262298
$297$	5.84848	0.339363
$298$	8.16693	0.473098
$299$	4.90825	0.283852
$300$	0	0
$301$	11.9057	0.686231
$302$	−19.2298	−1.10655
$303$	9.52873	0.547411
$304$	13.6152	0.780886
$305$	0	0
$306$	15.2327	0.870798
$307$	−23.6284	−1.34854	−0.674271	−	0.738484i	$-0.735542\pi$
$307$	−23.6284	−1.34854	−0.674271	+	0.738484i	$0.735542\pi$
$308$	−7.73691	−0.440851
$309$	−27.9393	−1.58941
$310$	0	0
$311$	−4.94956	−0.280664	−0.140332	−	0.990105i	$-0.544817\pi$
$311$	−4.94956	−0.280664	−0.140332	+	0.990105i	$0.544817\pi$
$312$	−15.0253	−0.850641
$313$	21.3265	1.20545	0.602723	−	0.797951i	$-0.294083\pi$
$313$	21.3265	1.20545	0.602723	+	0.797951i	$0.294083\pi$
$314$	7.93384	0.447733
$315$	0	0
$316$	21.3840	1.20295
$317$	10.2285	0.574492	0.287246	−	0.957857i	$-0.407260\pi$
$317$	10.2285	0.574492	0.287246	+	0.957857i	$0.407260\pi$
$318$	47.3764	2.65674
$319$	−21.8472	−1.22321
$320$	0	0
$321$	−13.9038	−0.776034
$322$	−1.82692	−0.101810
$323$	−6.83422	−0.380266
$324$	−10.2211	−0.567837
$325$	0	0
$326$	32.9643	1.82573
$327$	31.4621	1.73986
$328$	−7.39605	−0.408378
$329$	0.288671	0.0159149
$330$	0	0
$331$	−0.723513	−0.0397678	−0.0198839	−	0.999802i	$-0.506330\pi$
$331$	−0.723513	−0.0397678	−0.0198839	+	0.999802i	$0.506330\pi$
$332$	−3.79062	−0.208038
$333$	12.6784	0.694771
$334$	26.8361	1.46841
$335$	0	0
$336$	12.3604	0.674317
$337$	−29.6792	−1.61673	−0.808364	−	0.588683i	$-0.799647\pi$
$337$	−29.6792	−1.61673	−0.808364	+	0.588683i	$0.799647\pi$
$338$	20.2623	1.10212
$339$	−43.0337	−2.33727
$340$	0	0
$341$	−20.8561	−1.12942
$342$	−17.3074	−0.935875
$343$	1.00000	0.0539949
$344$	−14.4069	−0.776768
$345$	0	0
$346$	−22.0922	−1.18768
$347$	15.5289	0.833636	0.416818	−	0.908990i	$-0.363145\pi$
$347$	15.5289	0.833636	0.416818	+	0.908990i	$0.363145\pi$
$348$	−12.7815	−0.685162
$349$	31.3704	1.67922	0.839608	−	0.543192i	$-0.182785\pi$
$349$	31.3704	1.67922	0.839608	+	0.543192i	$0.182785\pi$
$350$	0	0
$351$	4.96295	0.264903
$352$	37.6318	2.00578
$353$	−23.1766	−1.23357	−0.616783	−	0.787133i	$-0.711564\pi$
$353$	−23.1766	−1.23357	−0.616783	+	0.787133i	$0.711564\pi$
$354$	52.0168	2.76466
$355$	0	0
$356$	−17.9302	−0.950300
$357$	−6.20437	−0.328370
$358$	−6.50874	−0.343998
$359$	−1.92443	−0.101567	−0.0507836	−	0.998710i	$-0.516172\pi$
$359$	−1.92443	−0.101567	−0.0507836	+	0.998710i	$0.516172\pi$
$360$	0	0
$361$	−11.2350	−0.591316
$362$	15.1717	0.797409
$363$	−56.8056	−2.98152
$364$	−6.56545	−0.344123
$365$	0	0
$366$	65.3775	3.41734
$367$	17.9788	0.938487	0.469244	−	0.883069i	$-0.344527\pi$
$367$	17.9788	0.938487	0.469244	+	0.883069i	$0.344527\pi$
$368$	4.88600	0.254701
$369$	20.7789	1.08171
$370$	0	0
$371$	−10.2509	−0.532202
$372$	−12.2017	−0.632628
$373$	−24.0391	−1.24470	−0.622348	−	0.782741i	$-0.713821\pi$
$373$	−24.0391	−1.24470	−0.622348	+	0.782741i	$0.713821\pi$
$374$	−25.9160	−1.34008
$375$	0	0
$376$	−0.349317	−0.0180147
$377$	−18.5393	−0.954821
$378$	−1.84728	−0.0950138
$379$	4.09993	0.210599	0.105300	−	0.994441i	$-0.466420\pi$
$379$	4.09993	0.210599	0.105300	+	0.994441i	$0.466420\pi$
$380$	0	0
$381$	−33.6394	−1.72340
$382$	9.29308	0.475475
$383$	−8.78480	−0.448882	−0.224441	−	0.974488i	$-0.572056\pi$
$383$	−8.78480	−0.448882	−0.224441	+	0.974488i	$0.572056\pi$
$384$	−23.1468	−1.18121
$385$	0	0
$386$	31.1849	1.58727
$387$	40.4756	2.05749
$388$	−13.3608	−0.678290
$389$	31.0872	1.57618	0.788091	−	0.615559i	$-0.211070\pi$
$389$	31.0872	1.57618	0.788091	+	0.615559i	$0.211070\pi$
$390$	0	0
$391$	−2.45255	−0.124031
$392$	−1.21009	−0.0611187
$393$	−47.3883	−2.39042
$394$	−2.66672	−0.134347
$395$	0	0
$396$	−26.3032	−1.32178
$397$	10.6026	0.532127	0.266063	−	0.963956i	$-0.414277\pi$
$397$	10.6026	0.532127	0.266063	+	0.963956i	$0.414277\pi$
$398$	19.4675	0.975816
$399$	7.04937	0.352910
$400$	0	0
$401$	−7.73552	−0.386294	−0.193147	−	0.981170i	$-0.561869\pi$
$401$	−7.73552	−0.386294	−0.193147	+	0.981170i	$0.561869\pi$
$402$	−61.2580	−3.05527
$403$	−17.6982	−0.881611
$404$	−5.03840	−0.250670
$405$	0	0
$406$	6.90057	0.342469
$407$	−21.5701	−1.06919
$408$	7.50784	0.371693
$409$	22.1747	1.09647	0.548234	−	0.836325i	$-0.315300\pi$
$409$	22.1747	1.09647	0.548234	+	0.836325i	$0.315300\pi$
$410$	0	0
$411$	6.10163	0.300971
$412$	14.7732	0.727822
$413$	−11.2550	−0.553821
$414$	−6.21098	−0.305253
$415$	0	0
$416$	31.9339	1.56569
$417$	40.2051	1.96885
$418$	29.4456	1.44023
$419$	24.7961	1.21137	0.605684	−	0.795705i	$-0.292900\pi$
$419$	24.7961	1.21137	0.605684	+	0.795705i	$0.292900\pi$
$420$	0	0
$421$	36.0726	1.75807	0.879036	−	0.476756i	$-0.158188\pi$
$421$	36.0726	1.75807	0.879036	+	0.476756i	$0.158188\pi$
$422$	4.31892	0.210242
$423$	0.981394	0.0477170
$424$	12.4045	0.602417
$425$	0	0
$426$	−46.2706	−2.24182
$427$	−14.1458	−0.684566
$428$	7.35176	0.355361
$429$	−71.8186	−3.46743
$430$	0	0
$431$	−27.1397	−1.30728	−0.653638	−	0.756808i	$-0.726758\pi$
$431$	−27.1397	−1.30728	−0.653638	+	0.756808i	$0.726758\pi$
$432$	4.94045	0.237698
$433$	27.5973	1.32624	0.663122	−	0.748512i	$-0.269231\pi$
$433$	27.5973	1.32624	0.663122	+	0.748512i	$0.269231\pi$
$434$	6.58752	0.316211
$435$	0	0
$436$	−16.6359	−0.796713
$437$	2.78658	0.133300
$438$	−25.0503	−1.19695
$439$	−18.3362	−0.875139	−0.437569	−	0.899185i	$-0.644161\pi$
$439$	−18.3362	−0.875139	−0.437569	+	0.899185i	$0.644161\pi$
$440$	0	0
$441$	3.39970	0.161890
$442$	−21.9920	−1.04605
$443$	−6.35111	−0.301750	−0.150875	−	0.988553i	$-0.548209\pi$
$443$	−6.35111	−0.301750	−0.150875	+	0.988553i	$0.548209\pi$
$444$	−12.6195	−0.598893
$445$	0	0
$446$	−16.3332	−0.773398
$447$	−11.3089	−0.534891
$448$	−2.11422	−0.0998875
$449$	−35.8464	−1.69170	−0.845848	−	0.533424i	$-0.820905\pi$
$449$	−35.8464	−1.69170	−0.845848	+	0.533424i	$0.820905\pi$
$450$	0	0
$451$	−35.3519	−1.66466
$452$	22.7544	1.07028
$453$	26.6278	1.25108
$454$	29.5186	1.38538
$455$	0	0
$456$	−8.53036	−0.399471
$457$	15.4249	0.721547	0.360773	−	0.932653i	$-0.382513\pi$
$457$	15.4249	0.721547	0.360773	+	0.932653i	$0.382513\pi$
$458$	14.9511	0.698619
$459$	−2.47988	−0.115751
$460$	0	0
$461$	28.1866	1.31278	0.656391	−	0.754421i	$-0.272082\pi$
$461$	28.1866	1.31278	0.656391	+	0.754421i	$0.272082\pi$
$462$	26.7319	1.24368
$463$	15.8308	0.735718	0.367859	−	0.929882i	$-0.380091\pi$
$463$	15.8308	0.735718	0.367859	+	0.929882i	$0.380091\pi$
$464$	−18.4552	−0.856762
$465$	0	0
$466$	−19.8003	−0.917233
$467$	−3.01021	−0.139296	−0.0696480	−	0.997572i	$-0.522188\pi$
$467$	−3.01021	−0.139296	−0.0696480	+	0.997572i	$0.522188\pi$
$468$	−22.3206	−1.03177
$469$	13.2545	0.612036
$470$	0	0
$471$	−10.9861	−0.506213
$472$	13.6195	0.626888
$473$	−68.8626	−3.16630
$474$	−73.8841	−3.39361
$475$	0	0
$476$	3.28062	0.150367
$477$	−34.8501	−1.59568
$478$	−10.3792	−0.474735
$479$	−2.22604	−0.101710	−0.0508552	−	0.998706i	$-0.516195\pi$
$479$	−2.22604	−0.101710	−0.0508552	+	0.998706i	$0.516195\pi$
$480$	0	0
$481$	−18.3042	−0.834599
$482$	−40.3039	−1.83579
$483$	2.52976	0.115108
$484$	30.0365	1.36529
$485$	0	0
$486$	40.8567	1.85330
$487$	26.5169	1.20159	0.600797	−	0.799402i	$-0.294850\pi$
$487$	26.5169	1.20159	0.600797	+	0.799402i	$0.294850\pi$
$488$	17.1177	0.774883
$489$	−45.6462	−2.06419
$490$	0	0
$491$	−39.3262	−1.77477	−0.887383	−	0.461032i	$-0.847479\pi$
$491$	−39.3262	−1.77477	−0.887383	+	0.461032i	$0.847479\pi$
$492$	−20.6824	−0.932433
$493$	9.26368	0.417215
$494$	24.9872	1.12423
$495$	0	0
$496$	−17.6180	−0.791071
$497$	10.0117	0.449084
$498$	13.0970	0.586891
$499$	−28.8627	−1.29207	−0.646036	−	0.763307i	$-0.723574\pi$
$499$	−28.8627	−1.29207	−0.646036	+	0.763307i	$0.723574\pi$
$500$	0	0
$501$	−37.1604	−1.66020
$502$	−4.30240	−0.192025
$503$	2.99114	0.133368	0.0666841	−	0.997774i	$-0.478758\pi$
$503$	2.99114	0.133368	0.0666841	+	0.997774i	$0.478758\pi$
$504$	−4.11394	−0.183249
$505$	0	0
$506$	10.5669	0.469758
$507$	−28.0575	−1.24608
$508$	17.7871	0.789176
$509$	−1.59180	−0.0705551	−0.0352775	−	0.999378i	$-0.511232\pi$
$509$	−1.59180	−0.0705551	−0.0352775	+	0.999378i	$0.511232\pi$
$510$	0	0
$511$	5.42017	0.239774
$512$	19.9641	0.882298
$513$	2.81763	0.124401
$514$	30.2995	1.33645
$515$	0	0
$516$	−40.2875	−1.77356
$517$	−1.66968	−0.0734324
$518$	6.81307	0.299349
$519$	30.5914	1.34281
$520$	0	0
$521$	−42.2767	−1.85218	−0.926088	−	0.377308i	$-0.876850\pi$
$521$	−42.2767	−1.85218	−0.926088	+	0.377308i	$0.876850\pi$
$522$	23.4599	1.02681
$523$	9.22101	0.403207	0.201603	−	0.979467i	$-0.435385\pi$
$523$	9.22101	0.403207	0.201603	+	0.979467i	$0.435385\pi$
$524$	25.0570	1.09462
$525$	0	0
$526$	−14.6718	−0.639721
$527$	8.84342	0.385226
$528$	−71.4930	−3.11133
$529$	1.00000	0.0434783
$530$	0	0
$531$	−38.2635	−1.66049
$532$	−3.72742	−0.161604
$533$	−29.9992	−1.29941
$534$	61.9509	2.68088
$535$	0	0
$536$	−16.0391	−0.692785
$537$	9.01275	0.388929
$538$	26.1006	1.12528
$539$	−5.78402	−0.249135
$540$	0	0
$541$	1.62636	0.0699227	0.0349614	−	0.999389i	$-0.488869\pi$
$541$	1.62636	0.0699227	0.0349614	+	0.999389i	$0.488869\pi$
$542$	−28.2304	−1.21260
$543$	−21.0085	−0.901563
$544$	−15.9567	−0.684137
$545$	0	0
$546$	22.6843	0.970800
$547$	41.1130	1.75786	0.878932	−	0.476947i	$-0.158257\pi$
$547$	41.1130	1.75786	0.878932	+	0.476947i	$0.158257\pi$
$548$	−3.22629	−0.137820
$549$	−48.0916	−2.05250
$550$	0	0
$551$	−10.5253	−0.448395
$552$	−3.06124	−0.130295
$553$	15.9865	0.679813
$554$	−28.4894	−1.21040
$555$	0	0
$556$	−21.2588	−0.901574
$557$	−13.7492	−0.582571	−0.291285	−	0.956636i	$-0.594083\pi$
$557$	−13.7492	−0.582571	−0.291285	+	0.956636i	$0.594083\pi$
$558$	22.3956	0.948080
$559$	−58.4360	−2.47158
$560$	0	0
$561$	35.8862	1.51512
$562$	10.1591	0.428535
$563$	−29.9348	−1.26160	−0.630800	−	0.775946i	$-0.717273\pi$
$563$	−29.9348	−1.26160	−0.630800	+	0.775946i	$0.717273\pi$
$564$	−0.976832	−0.0411321
$565$	0	0
$566$	−20.3608	−0.855827
$567$	−7.64114	−0.320898
$568$	−12.1150	−0.508334
$569$	1.98604	0.0832590	0.0416295	−	0.999133i	$-0.486745\pi$
$569$	1.98604	0.0832590	0.0416295	+	0.999133i	$0.486745\pi$
$570$	0	0
$571$	13.0838	0.547539	0.273770	−	0.961795i	$-0.411729\pi$
$571$	13.0838	0.547539	0.273770	+	0.961795i	$0.411729\pi$
$572$	37.9747	1.58780
$573$	−12.8683	−0.537580
$574$	11.1661	0.466065
$575$	0	0
$576$	−7.18771	−0.299488
$577$	17.2380	0.717629	0.358814	−	0.933409i	$-0.383181\pi$
$577$	17.2380	0.717629	0.358814	+	0.933409i	$0.383181\pi$
$578$	−20.0687	−0.834748
$579$	−43.1821	−1.79459
$580$	0	0
$581$	−2.83383	−0.117567
$582$	46.1629	1.91351
$583$	59.2916	2.45561
$584$	−6.55889	−0.271409
$585$	0	0
$586$	−7.57837	−0.313059
$587$	40.6184	1.67650	0.838251	−	0.545284i	$-0.183578\pi$
$587$	40.6184	1.67650	0.838251	+	0.545284i	$0.183578\pi$
$588$	−3.38390	−0.139550
$589$	−10.0478	−0.414014
$590$	0	0
$591$	3.69264	0.151895
$592$	−18.2212	−0.748887
$593$	23.0606	0.946984	0.473492	−	0.880798i	$-0.342993\pi$
$593$	23.0606	0.946984	0.473492	+	0.880798i	$0.342993\pi$
$594$	10.6847	0.438399
$595$	0	0
$596$	5.97967	0.244937
$597$	−26.9569	−1.10327
$598$	8.96698	0.366687
$599$	4.43175	0.181076	0.0905381	−	0.995893i	$-0.471141\pi$
$599$	4.43175	0.181076	0.0905381	+	0.995893i	$0.471141\pi$
$600$	0	0
$601$	−25.6591	−1.04666	−0.523328	−	0.852131i	$-0.675310\pi$
$601$	−25.6591	−1.04666	−0.523328	+	0.852131i	$0.675310\pi$
$602$	21.7507	0.886491
$603$	45.0613	1.83504
$604$	−14.0797	−0.572894
$605$	0	0
$606$	17.4082	0.707161
$607$	−17.2311	−0.699390	−0.349695	−	0.936864i	$-0.613715\pi$
$607$	−17.2311	−0.699390	−0.349695	+	0.936864i	$0.613715\pi$
$608$	18.1299	0.735264
$609$	−9.55532	−0.387201
$610$	0	0
$611$	−1.41687	−0.0573204
$612$	11.1531	0.450838
$613$	31.4917	1.27194	0.635969	−	0.771714i	$-0.280600\pi$
$613$	31.4917	1.27194	0.635969	+	0.771714i	$0.280600\pi$
$614$	−43.1671	−1.74208
$615$	0	0
$616$	6.99918	0.282005
$617$	17.0986	0.688365	0.344182	−	0.938903i	$-0.388156\pi$
$617$	17.0986	0.688365	0.344182	+	0.938903i	$0.388156\pi$
$618$	−51.0429	−2.05325
$619$	−4.44201	−0.178539	−0.0892697	−	0.996007i	$-0.528453\pi$
$619$	−4.44201	−0.178539	−0.0892697	+	0.996007i	$0.528453\pi$
$620$	0	0
$621$	1.01114	0.0405758
$622$	−9.04245	−0.362569
$623$	−13.4044	−0.537037
$624$	−60.6681	−2.42867
$625$	0	0
$626$	38.9618	1.55723
$627$	−40.7737	−1.62835
$628$	5.80900	0.231804
$629$	9.14621	0.364683
$630$	0	0
$631$	27.8069	1.10697	0.553487	−	0.832858i	$-0.313297\pi$
$631$	27.8069	1.10697	0.553487	+	0.832858i	$0.313297\pi$
$632$	−19.3450	−0.769503
$633$	−5.98048	−0.237703
$634$	18.6867	0.742145
$635$	0	0
$636$	34.6881	1.37547
$637$	−4.90825	−0.194472
$638$	−39.9130	−1.58017
$639$	34.0366	1.34647
$640$	0	0
$641$	22.2198	0.877628	0.438814	−	0.898578i	$-0.355399\pi$
$641$	22.2198	0.877628	0.438814	+	0.898578i	$0.355399\pi$
$642$	−25.4011	−1.00250
$643$	11.2057	0.441909	0.220954	−	0.975284i	$-0.429083\pi$
$643$	11.2057	0.441909	0.220954	+	0.975284i	$0.429083\pi$
$644$	−1.33763	−0.0527102
$645$	0	0
$646$	−12.4856	−0.491238
$647$	12.9846	0.510477	0.255238	−	0.966878i	$-0.417846\pi$
$647$	12.9846	0.510477	0.255238	+	0.966878i	$0.417846\pi$
$648$	9.24646	0.363235
$649$	65.0990	2.55536
$650$	0	0
$651$	−9.12183	−0.357513
$652$	24.1359	0.945233
$653$	31.2697	1.22368	0.611838	−	0.790983i	$-0.290430\pi$
$653$	31.2697	1.22368	0.611838	+	0.790983i	$0.290430\pi$
$654$	57.4787	2.24759
$655$	0	0
$656$	−29.8632	−1.16596
$657$	18.4270	0.718904
$658$	0.527378	0.0205593
$659$	43.0584	1.67732	0.838658	−	0.544658i	$-0.183341\pi$
$659$	43.0584	1.67732	0.838658	+	0.544658i	$0.183341\pi$
$660$	0	0
$661$	5.42315	0.210936	0.105468	−	0.994423i	$-0.466366\pi$
$661$	5.42315	0.210936	0.105468	+	0.994423i	$0.466366\pi$
$662$	−1.32180	−0.0513732
$663$	30.4526	1.18268
$664$	3.42918	0.133078
$665$	0	0
$666$	23.1624	0.897524
$667$	−3.77716	−0.146252
$668$	19.6489	0.760238
$669$	22.6168	0.874416
$670$	0	0
$671$	81.8199	3.15862
$672$	16.4590	0.634921
$673$	−29.0155	−1.11847	−0.559233	−	0.829011i	$-0.688904\pi$
$673$	−29.0155	−1.11847	−0.559233	+	0.829011i	$0.688904\pi$
$674$	−54.2215	−2.08853
$675$	0	0
$676$	14.8356	0.570602
$677$	−32.9430	−1.26610	−0.633051	−	0.774110i	$-0.718197\pi$
$677$	−32.9430	−1.26610	−0.633051	+	0.774110i	$0.718197\pi$
$678$	−78.6191	−3.01935
$679$	−9.98836	−0.383318
$680$	0	0
$681$	−40.8748	−1.56633
$682$	−38.1023	−1.45901
$683$	−15.0532	−0.575996	−0.287998	−	0.957631i	$-0.592990\pi$
$683$	−15.0532	−0.575996	−0.287998	+	0.957631i	$0.592990\pi$
$684$	−12.6721	−0.484530
$685$	0	0
$686$	1.82692	0.0697521
$687$	−20.7030	−0.789869
$688$	−58.1711	−2.21775
$689$	50.3142	1.91682
$690$	0	0
$691$	13.8460	0.526727	0.263364	−	0.964697i	$-0.415168\pi$
$691$	13.8460	0.526727	0.263364	+	0.964697i	$0.415168\pi$
$692$	−16.1755	−0.614899
$693$	−19.6639	−0.746971
$694$	28.3701	1.07691
$695$	0	0
$696$	11.5628	0.438286
$697$	14.9900	0.567786
$698$	57.3111	2.16926
$699$	27.4178	1.03704
$700$	0	0
$701$	−23.2278	−0.877301	−0.438651	−	0.898658i	$-0.644543\pi$
$701$	−23.2278	−0.877301	−0.438651	+	0.898658i	$0.644543\pi$
$702$	9.06691	0.342209
$703$	−10.3919	−0.391937
$704$	12.2287	0.460886
$705$	0	0
$706$	−42.3418	−1.59355
$707$	−3.76665	−0.141659
$708$	38.0857	1.43135
$709$	28.4044	1.06675	0.533375	−	0.845879i	$-0.320924\pi$
$709$	28.4044	1.06675	0.533375	+	0.845879i	$0.320924\pi$
$710$	0	0
$711$	54.3491	2.03825
$712$	16.2205	0.607891
$713$	−3.60581	−0.135038
$714$	−11.3349	−0.424198
$715$	0	0
$716$	−4.76557	−0.178098
$717$	14.3723	0.536742
$718$	−3.51577	−0.131207
$719$	3.43315	0.128035	0.0640174	−	0.997949i	$-0.479609\pi$
$719$	3.43315	0.128035	0.0640174	+	0.997949i	$0.479609\pi$
$720$	0	0
$721$	11.0443	0.411309
$722$	−20.5254	−0.763878
$723$	55.8095	2.07558
$724$	11.1085	0.412843
$725$	0	0
$726$	−103.779	−3.85161
$727$	−29.0596	−1.07776	−0.538880	−	0.842382i	$-0.681152\pi$
$727$	−29.0596	−1.07776	−0.538880	+	0.842382i	$0.681152\pi$
$728$	5.93942	0.220130
$729$	−33.6515	−1.24635
$730$	0	0
$731$	29.1992	1.07997
$732$	47.8681	1.76926
$733$	15.6345	0.577473	0.288736	−	0.957409i	$-0.406765\pi$
$733$	15.6345	0.577473	0.288736	+	0.957409i	$0.406765\pi$
$734$	32.8459	1.21236
$735$	0	0
$736$	6.50616	0.239820
$737$	−76.6644	−2.82397
$738$	37.9614	1.39738
$739$	−44.1640	−1.62460	−0.812299	−	0.583241i	$-0.801784\pi$
$739$	−44.1640	−1.62460	−0.812299	+	0.583241i	$0.801784\pi$
$740$	0	0
$741$	−34.6001	−1.27107
$742$	−18.7276	−0.687512
$743$	26.4939	0.971966	0.485983	−	0.873968i	$-0.338462\pi$
$743$	26.4939	0.971966	0.485983	+	0.873968i	$0.338462\pi$
$744$	11.0382	0.404681
$745$	0	0
$746$	−43.9175	−1.60793
$747$	−9.63416	−0.352495
$748$	−18.9752	−0.693801
$749$	5.49609	0.200823
$750$	0	0
$751$	−10.6393	−0.388233	−0.194117	−	0.980978i	$-0.562184\pi$
$751$	−10.6393	−0.388233	−0.194117	+	0.980978i	$0.562184\pi$
$752$	−1.41045	−0.0514337
$753$	5.95759	0.217107
$754$	−33.8697	−1.23346
$755$	0	0
$756$	−1.35254	−0.0491914
$757$	13.1719	0.478741	0.239371	−	0.970928i	$-0.423059\pi$
$757$	13.1719	0.478741	0.239371	+	0.970928i	$0.423059\pi$
$758$	7.49024	0.272058
$759$	−14.6322	−0.531115
$760$	0	0
$761$	39.2590	1.42314	0.711569	−	0.702616i	$-0.247985\pi$
$761$	39.2590	1.42314	0.711569	+	0.702616i	$0.247985\pi$
$762$	−61.4564	−2.22633
$763$	−12.4368	−0.450241
$764$	6.80421	0.246168
$765$	0	0
$766$	−16.0491	−0.579878
$767$	55.2422	1.99468
$768$	−52.9844	−1.91191
$769$	22.8291	0.823237	0.411619	−	0.911356i	$-0.364964\pi$
$769$	22.8291	0.823237	0.411619	+	0.911356i	$0.364964\pi$
$770$	0	0
$771$	−41.9562	−1.51101
$772$	22.8329	0.821776
$773$	−12.2539	−0.440743	−0.220371	−	0.975416i	$-0.570727\pi$
$773$	−12.2539	−0.440743	−0.220371	+	0.975416i	$0.570727\pi$
$774$	73.9457	2.65792
$775$	0	0
$776$	12.0868	0.433891
$777$	−9.43415	−0.338448
$778$	56.7937	2.03615
$779$	−17.0315	−0.610218
$780$	0	0
$781$	−57.9077	−2.07210
$782$	−4.48061	−0.160226
$783$	−3.81925	−0.136489
$784$	−4.88600	−0.174500
$785$	0	0
$786$	−86.5746	−3.08801
$787$	−37.4131	−1.33363	−0.666816	−	0.745222i	$-0.732343\pi$
$787$	−37.4131	−1.33363	−0.666816	+	0.745222i	$0.732343\pi$
$788$	−1.95252	−0.0695556
$789$	20.3163	0.723278
$790$	0	0
$791$	17.0110	0.604840
$792$	23.7951	0.845522
$793$	69.4314	2.46558
$794$	19.3700	0.687416
$795$	0	0
$796$	14.2537	0.505209
$797$	−50.7287	−1.79690	−0.898451	−	0.439073i	$-0.855307\pi$
$797$	−50.7287	−1.79690	−0.898451	+	0.439073i	$0.855307\pi$
$798$	12.8786	0.455899
$799$	0.707980	0.0250465
$800$	0	0
$801$	−45.5710	−1.61017
$802$	−14.1322	−0.499025
$803$	−31.3504	−1.10633
$804$	−44.8519	−1.58180
$805$	0	0
$806$	−32.3332	−1.13889
$807$	−36.1419	−1.27226
$808$	4.55798	0.160349
$809$	43.5861	1.53241	0.766203	−	0.642599i	$-0.222144\pi$
$809$	43.5861	1.53241	0.766203	+	0.642599i	$0.222144\pi$
$810$	0	0
$811$	−2.46794	−0.0866612	−0.0433306	−	0.999061i	$-0.513797\pi$
$811$	−2.46794	−0.0866612	−0.0433306	+	0.999061i	$0.513797\pi$
$812$	5.05246	0.177307
$813$	39.0911	1.37098
$814$	−39.4069	−1.38121
$815$	0	0
$816$	30.3146	1.06122
$817$	−33.1760	−1.16068
$818$	40.5114	1.41645
$819$	−16.6866	−0.583077
$820$	0	0
$821$	14.3476	0.500734	0.250367	−	0.968151i	$-0.419449\pi$
$821$	14.3476	0.500734	0.250367	+	0.968151i	$0.419449\pi$
$822$	11.1472	0.388803
$823$	3.32547	0.115919	0.0579593	−	0.998319i	$-0.481541\pi$
$823$	3.32547	0.115919	0.0579593	+	0.998319i	$0.481541\pi$
$824$	−13.3645	−0.465575
$825$	0	0
$826$	−20.5619	−0.715440
$827$	9.96072	0.346368	0.173184	−	0.984889i	$-0.444594\pi$
$827$	9.96072	0.346368	0.173184	+	0.984889i	$0.444594\pi$
$828$	−4.54756	−0.158038
$829$	−0.467697	−0.0162438	−0.00812189	−	0.999967i	$-0.502585\pi$
$829$	−0.467697	−0.0162438	−0.00812189	+	0.999967i	$0.502585\pi$
$830$	0	0
$831$	39.4497	1.36849
$832$	10.3771	0.359762
$833$	2.45255	0.0849759
$834$	73.4515	2.54342
$835$	0	0
$836$	21.5595	0.745650
$837$	−3.64599	−0.126024
$838$	45.3005	1.56488
$839$	26.2706	0.906961	0.453481	−	0.891266i	$-0.350182\pi$
$839$	26.2706	0.906961	0.453481	+	0.891266i	$0.350182\pi$
$840$	0	0
$841$	−14.7331	−0.508036
$842$	65.9017	2.27112
$843$	−14.0674	−0.484508
$844$	3.16223	0.108848
$845$	0	0
$846$	1.79293	0.0616421
$847$	22.4549	0.771560
$848$	50.0861	1.71996
$849$	28.1939	0.967611
$850$	0	0
$851$	−3.72926	−0.127838
$852$	−33.8784	−1.16066
$853$	14.4508	0.494785	0.247393	−	0.968915i	$-0.420426\pi$
$853$	14.4508	0.494785	0.247393	+	0.968915i	$0.420426\pi$
$854$	−25.8433	−0.884340
$855$	0	0
$856$	−6.65075	−0.227318
$857$	−55.8194	−1.90675	−0.953376	−	0.301784i	$-0.902418\pi$
$857$	−55.8194	−1.90675	−0.953376	+	0.301784i	$0.902418\pi$
$858$	−131.207	−4.47932
$859$	49.6284	1.69330	0.846650	−	0.532150i	$-0.178616\pi$
$859$	49.6284	1.69330	0.846650	+	0.532150i	$0.178616\pi$
$860$	0	0
$861$	−15.4619	−0.526940
$862$	−49.5821	−1.68877
$863$	5.18738	0.176580	0.0882902	−	0.996095i	$-0.471860\pi$
$863$	5.18738	0.176580	0.0882902	+	0.996095i	$0.471860\pi$
$864$	6.57866	0.223811
$865$	0	0
$866$	50.4181	1.71328
$867$	27.7894	0.943778
$868$	4.82325	0.163712
$869$	−92.4660	−3.13669
$870$	0	0
$871$	−65.0565	−2.20436
$872$	15.0496	0.509643
$873$	−33.9574	−1.14928
$874$	5.09085	0.172201
$875$	0	0
$876$	−18.3413	−0.619696
$877$	−38.9911	−1.31664	−0.658318	−	0.752740i	$-0.728732\pi$
$877$	−38.9911	−1.31664	−0.658318	+	0.752740i	$0.728732\pi$
$878$	−33.4987	−1.13053
$879$	10.4939	0.353950
$880$	0	0
$881$	−14.2027	−0.478500	−0.239250	−	0.970958i	$-0.576902\pi$
$881$	−14.2027	−0.478500	−0.239250	+	0.970958i	$0.576902\pi$
$882$	6.21098	0.209134
$883$	−9.02128	−0.303590	−0.151795	−	0.988412i	$-0.548505\pi$
$883$	−9.02128	−0.303590	−0.151795	+	0.988412i	$0.548505\pi$
$884$	−16.1021	−0.541572
$885$	0	0
$886$	−11.6030	−0.389809
$887$	−15.4038	−0.517208	−0.258604	−	0.965983i	$-0.583262\pi$
$887$	−15.4038	−0.517208	−0.258604	+	0.965983i	$0.583262\pi$
$888$	11.4162	0.383101
$889$	13.2974	0.445982
$890$	0	0
$891$	44.1965	1.48064
$892$	−11.9588	−0.400411
$893$	−0.804403	−0.0269183
$894$	−20.6604	−0.690987
$895$	0	0
$896$	9.14981	0.305674
$897$	−12.4167	−0.414582
$898$	−65.4885	−2.18538
$899$	13.6197	0.454243
$900$	0	0
$901$	−25.1409	−0.837566
$902$	−64.5851	−2.15045
$903$	−30.1185	−1.00228
$904$	−20.5848	−0.684639
$905$	0	0
$906$	48.6468	1.61618
$907$	13.4259	0.445801	0.222900	−	0.974841i	$-0.428448\pi$
$907$	13.4259	0.445801	0.222900	+	0.974841i	$0.428448\pi$
$908$	21.6129	0.717251
$909$	−12.8055	−0.424731
$910$	0	0
$911$	−0.622499	−0.0206243	−0.0103122	−	0.999947i	$-0.503283\pi$
$911$	−0.622499	−0.0206243	−0.0103122	+	0.999947i	$0.503283\pi$
$912$	−34.4433	−1.14053
$913$	16.3909	0.542460
$914$	28.1801	0.932114
$915$	0	0
$916$	10.9469	0.361696
$917$	18.7323	0.618595
$918$	−4.53054	−0.149530
$919$	−19.9545	−0.658237	−0.329118	−	0.944289i	$-0.606751\pi$
$919$	−19.9545	−0.658237	−0.329118	+	0.944289i	$0.606751\pi$
$920$	0	0
$921$	59.7741	1.96962
$922$	51.4947	1.69589
$923$	−49.1398	−1.61746
$924$	19.5725	0.643889
$925$	0	0
$926$	28.9215	0.950420
$927$	37.5471	1.23321
$928$	−24.5748	−0.806707
$929$	18.7796	0.616140	0.308070	−	0.951364i	$-0.400317\pi$
$929$	18.7796	0.616140	0.308070	+	0.951364i	$0.400317\pi$
$930$	0	0
$931$	−2.78658	−0.0913263
$932$	−14.4974	−0.474879
$933$	12.5212	0.409926
$934$	−5.49942	−0.179946
$935$	0	0
$936$	20.1922	0.660004
$937$	−25.3031	−0.826615	−0.413308	−	0.910591i	$-0.635627\pi$
$937$	−25.3031	−0.826615	−0.413308	+	0.910591i	$0.635627\pi$
$938$	24.2149	0.790645
$939$	−53.9510	−1.76062
$940$	0	0
$941$	−14.1370	−0.460854	−0.230427	−	0.973090i	$-0.574012\pi$
$941$	−14.1370	−0.460854	−0.230427	+	0.973090i	$0.574012\pi$
$942$	−20.0707	−0.653940
$943$	−6.11199	−0.199034
$944$	54.9918	1.78983
$945$	0	0
$946$	−125.806	−4.09032
$947$	−3.72765	−0.121132	−0.0605661	−	0.998164i	$-0.519291\pi$
$947$	−3.72765	−0.121132	−0.0605661	+	0.998164i	$0.519291\pi$
$948$	−54.0965	−1.75697
$949$	−26.6036	−0.863589
$950$	0	0
$951$	−25.8758	−0.839080
$952$	−2.96780	−0.0961871
$953$	−18.3821	−0.595455	−0.297727	−	0.954651i	$-0.596229\pi$
$953$	−18.3821	−0.595455	−0.297727	+	0.954651i	$0.596229\pi$
$954$	−63.6683	−2.06134
$955$	0	0
$956$	−7.59947	−0.245784
$957$	55.2682	1.78657
$958$	−4.06680	−0.131392
$959$	−2.41194	−0.0778855
$960$	0	0
$961$	−17.9982	−0.580586
$962$	−33.4403	−1.07816
$963$	18.6850	0.602117
$964$	−29.5098	−0.950445
$965$	0	0
$966$	4.62167	0.148700
$967$	−13.4257	−0.431742	−0.215871	−	0.976422i	$-0.569259\pi$
$967$	−13.4257	−0.431742	−0.215871	+	0.976422i	$0.569259\pi$
$968$	−27.1724	−0.873355
$969$	17.2890	0.555401
$970$	0	0
$971$	32.0039	1.02705	0.513527	−	0.858073i	$-0.328338\pi$
$971$	32.0039	1.02705	0.513527	+	0.858073i	$0.328338\pi$
$972$	29.9145	0.959507
$973$	−15.8928	−0.509501
$974$	48.4442	1.55225
$975$	0	0
$976$	69.1167	2.21237
$977$	35.4730	1.13488	0.567440	−	0.823415i	$-0.307934\pi$
$977$	35.4730	1.13488	0.567440	+	0.823415i	$0.307934\pi$
$978$	−83.3920	−2.66658
$979$	77.5315	2.47792
$980$	0	0
$981$	−42.2813	−1.34994
$982$	−71.8458	−2.29269
$983$	−43.4412	−1.38556	−0.692780	−	0.721149i	$-0.743614\pi$
$983$	−43.4412	−1.38556	−0.692780	+	0.721149i	$0.743614\pi$
$984$	18.7102	0.596461
$985$	0	0
$986$	16.9240	0.538970
$987$	−0.730269	−0.0232447
$988$	18.2951	0.582045
$989$	−11.9057	−0.378578
$990$	0	0
$991$	11.9894	0.380857	0.190428	−	0.981701i	$-0.439012\pi$
$991$	11.9894	0.380857	0.190428	+	0.981701i	$0.439012\pi$
$992$	−23.4599	−0.744854
$993$	1.83032	0.0580833
$994$	18.2905	0.580139
$995$	0	0
$996$	9.58938	0.303851
$997$	20.4804	0.648621	0.324311	−	0.945951i	$-0.394868\pi$
$997$	20.4804	0.648621	0.324311	+	0.945951i	$0.394868\pi$
$998$	−52.7298	−1.66913
$999$	−3.77082	−0.119304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bb.1.11	yes	14
5.4	even	2		4025.2.a.ba.1.4	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.ba.1.4	✓	14	5.4	even	2
4025.2.a.bb.1.11	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)

\(f(q)\)	\(=\)	\(q+1.82692 q^{2} -2.52976 q^{3} +1.33763 q^{4} -4.62167 q^{6} +1.00000 q^{7} -1.21009 q^{8} +3.39970 q^{9} +O(q^{10})\)	\(q+1.82692 q^{2} -2.52976 q^{3} +1.33763 q^{4} -4.62167 q^{6} +1.00000 q^{7} -1.21009 q^{8} +3.39970 q^{9} -5.78402 q^{11} -3.38390 q^{12} -4.90825 q^{13} +1.82692 q^{14} -4.88600 q^{16} +2.45255 q^{17} +6.21098 q^{18} -2.78658 q^{19} -2.52976 q^{21} -10.5669 q^{22} -1.00000 q^{23} +3.06124 q^{24} -8.96698 q^{26} -1.01114 q^{27} +1.33763 q^{28} +3.77716 q^{29} +3.60581 q^{31} -6.50616 q^{32} +14.6322 q^{33} +4.48061 q^{34} +4.54756 q^{36} +3.72926 q^{37} -5.09085 q^{38} +12.4167 q^{39} +6.11199 q^{41} -4.62167 q^{42} +11.9057 q^{43} -7.73691 q^{44} -1.82692 q^{46} +0.288671 q^{47} +12.3604 q^{48} +1.00000 q^{49} -6.20437 q^{51} -6.56545 q^{52} -10.2509 q^{53} -1.84728 q^{54} -1.21009 q^{56} +7.04937 q^{57} +6.90057 q^{58} -11.2550 q^{59} -14.1458 q^{61} +6.58752 q^{62} +3.39970 q^{63} -2.11422 q^{64} +26.7319 q^{66} +13.2545 q^{67} +3.28062 q^{68} +2.52976 q^{69} +10.0117 q^{71} -4.11394 q^{72} +5.42017 q^{73} +6.81307 q^{74} -3.72742 q^{76} -5.78402 q^{77} +22.6843 q^{78} +15.9865 q^{79} -7.64114 q^{81} +11.1661 q^{82} -2.83383 q^{83} -3.38390 q^{84} +21.7507 q^{86} -9.55532 q^{87} +6.99918 q^{88} -13.4044 q^{89} -4.90825 q^{91} -1.33763 q^{92} -9.12183 q^{93} +0.527378 q^{94} +16.4590 q^{96} -9.98836 q^{97} +1.82692 q^{98} -19.6639 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + 6 q^{3} + 17 q^{4} - 4 q^{6} + 14 q^{7} + 9 q^{8} + 18 q^{9}+O(q^{10}) \) 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

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Database

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