LMFDB - Embedded newform 4025.2.a.ba.1.14

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:	$1$
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			1.14
Root			$-2.64833$ 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)

$f(q)$	$=$	$q+2.64833 q^{2} -0.547903 q^{3} +5.01366 q^{4} -1.45103 q^{6} -1.00000 q^{7} +7.98118 q^{8} -2.69980 q^{9} +O(q^{10})$	\(q+2.64833 q^{2} -0.547903 q^{3} +5.01366 q^{4} -1.45103 q^{6} -1.00000 q^{7} +7.98118 q^{8} -2.69980 q^{9} -6.33051 q^{11} -2.74700 q^{12} -4.94753 q^{13} -2.64833 q^{14} +11.1095 q^{16} +3.24481 q^{17} -7.14997 q^{18} -3.30506 q^{19} +0.547903 q^{21} -16.7653 q^{22} +1.00000 q^{23} -4.37291 q^{24} -13.1027 q^{26} +3.12294 q^{27} -5.01366 q^{28} +4.85327 q^{29} -0.831969 q^{31} +13.4593 q^{32} +3.46851 q^{33} +8.59334 q^{34} -13.5359 q^{36} -7.22045 q^{37} -8.75291 q^{38} +2.71077 q^{39} -12.2786 q^{41} +1.45103 q^{42} +3.64888 q^{43} -31.7391 q^{44} +2.64833 q^{46} -8.84448 q^{47} -6.08692 q^{48} +1.00000 q^{49} -1.77784 q^{51} -24.8053 q^{52} +5.17553 q^{53} +8.27058 q^{54} -7.98118 q^{56} +1.81085 q^{57} +12.8531 q^{58} -1.60258 q^{59} -3.84493 q^{61} -2.20333 q^{62} +2.69980 q^{63} +13.4256 q^{64} +9.18576 q^{66} -1.90402 q^{67} +16.2684 q^{68} -0.547903 q^{69} +2.75923 q^{71} -21.5476 q^{72} +9.45004 q^{73} -19.1221 q^{74} -16.5705 q^{76} +6.33051 q^{77} +7.17902 q^{78} -1.15751 q^{79} +6.38834 q^{81} -32.5177 q^{82} -15.8888 q^{83} +2.74700 q^{84} +9.66345 q^{86} -2.65912 q^{87} -50.5250 q^{88} +8.99645 q^{89} +4.94753 q^{91} +5.01366 q^{92} +0.455838 q^{93} -23.4231 q^{94} -7.37437 q^{96} -10.5928 q^{97} +2.64833 q^{98} +17.0911 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.64833	1.87265	0.936327	−	0.351130i	$-0.114202\pi$
$2$	2.64833	1.87265	0.936327	+	0.351130i	$0.114202\pi$
$3$	−0.547903	−0.316332	−0.158166	−	0.987413i	$-0.550558\pi$
$3$	−0.547903	−0.316332	−0.158166	+	0.987413i	$0.550558\pi$
$4$	5.01366	2.50683
$5$	0	0
$5$	0	0
$6$	−1.45103	−0.592380
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	7.98118	2.82177
$9$	−2.69980	−0.899934
$10$	0	0
$11$	−6.33051	−1.90872	−0.954361	−	0.298656i	$-0.903462\pi$
$11$	−6.33051	−1.90872	−0.954361	+	0.298656i	$0.903462\pi$
$12$	−2.74700	−0.792991
$13$	−4.94753	−1.37220	−0.686100	−	0.727508i	$-0.740679\pi$
$13$	−4.94753	−1.37220	−0.686100	+	0.727508i	$0.740679\pi$
$14$	−2.64833	−0.707797
$15$	0	0
$16$	11.1095	2.77737
$17$	3.24481	0.786982	0.393491	−	0.919328i	$-0.371267\pi$
$17$	3.24481	0.786982	0.393491	+	0.919328i	$0.371267\pi$
$18$	−7.14997	−1.68526
$19$	−3.30506	−0.758234	−0.379117	−	0.925349i	$-0.623772\pi$
$19$	−3.30506	−0.758234	−0.379117	+	0.925349i	$0.623772\pi$
$20$	0	0
$21$	0.547903	0.119562
$22$	−16.7653	−3.57437
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−4.37291	−0.892617
$25$	0	0
$26$	−13.1027	−2.56965
$27$	3.12294	0.601010
$28$	−5.01366	−0.947493
$29$	4.85327	0.901230	0.450615	−	0.892718i	$-0.351205\pi$
$29$	4.85327	0.901230	0.450615	+	0.892718i	$0.351205\pi$
$30$	0	0
$31$	−0.831969	−0.149426	−0.0747130	−	0.997205i	$-0.523804\pi$
$31$	−0.831969	−0.149426	−0.0747130	+	0.997205i	$0.523804\pi$
$32$	13.4593	2.37928
$33$	3.46851	0.603790
$34$	8.59334	1.47375
$35$	0	0
$36$	−13.5359	−2.25598
$37$	−7.22045	−1.18703	−0.593517	−	0.804821i	$-0.702261\pi$
$37$	−7.22045	−1.18703	−0.593517	+	0.804821i	$0.702261\pi$
$38$	−8.75291	−1.41991
$39$	2.71077	0.434070
$40$	0	0
$41$	−12.2786	−1.91759	−0.958794	−	0.284103i	$-0.908304\pi$
$41$	−12.2786	−1.91759	−0.958794	+	0.284103i	$0.908304\pi$
$42$	1.45103	0.223899
$43$	3.64888	0.556449	0.278225	−	0.960516i	$-0.410254\pi$
$43$	3.64888	0.556449	0.278225	+	0.960516i	$0.410254\pi$
$44$	−31.7391	−4.78484
$45$	0	0
$46$	2.64833	0.390475
$47$	−8.84448	−1.29010	−0.645050	−	0.764140i	$-0.723164\pi$
$47$	−8.84448	−1.29010	−0.645050	+	0.764140i	$0.723164\pi$
$48$	−6.08692	−0.878572
$49$	1.00000	0.142857
$50$	0	0
$51$	−1.77784	−0.248948
$52$	−24.8053	−3.43987
$53$	5.17553	0.710913	0.355457	−	0.934693i	$-0.384325\pi$
$53$	5.17553	0.710913	0.355457	+	0.934693i	$0.384325\pi$
$54$	8.27058	1.12548
$55$	0	0
$56$	−7.98118	−1.06653
$57$	1.81085	0.239854
$58$	12.8531	1.68769
$59$	−1.60258	−0.208638	−0.104319	−	0.994544i	$-0.533266\pi$
$59$	−1.60258	−0.208638	−0.104319	+	0.994544i	$0.533266\pi$
$60$	0	0
$61$	−3.84493	−0.492293	−0.246146	−	0.969233i	$-0.579164\pi$
$61$	−3.84493	−0.492293	−0.246146	+	0.969233i	$0.579164\pi$
$62$	−2.20333	−0.279823
$63$	2.69980	0.340143
$64$	13.4256	1.67820
$65$	0	0
$66$	9.18576	1.13069
$67$	−1.90402	−0.232613	−0.116306	−	0.993213i	$-0.537105\pi$
$67$	−1.90402	−0.232613	−0.116306	+	0.993213i	$0.537105\pi$
$68$	16.2684	1.97283
$69$	−0.547903	−0.0659598
$70$	0	0
$71$	2.75923	0.327461	0.163730	−	0.986505i	$-0.447647\pi$
$71$	2.75923	0.327461	0.163730	+	0.986505i	$0.447647\pi$
$72$	−21.5476	−2.53941
$73$	9.45004	1.10604	0.553022	−	0.833167i	$-0.313475\pi$
$73$	9.45004	1.10604	0.553022	+	0.833167i	$0.313475\pi$
$74$	−19.1221	−2.22290
$75$	0	0
$76$	−16.5705	−1.90076
$77$	6.33051	0.721429
$78$	7.17902	0.812863
$79$	−1.15751	−0.130230	−0.0651149	−	0.997878i	$-0.520741\pi$
$79$	−1.15751	−0.130230	−0.0651149	+	0.997878i	$0.520741\pi$
$80$	0	0
$81$	6.38834	0.709816
$82$	−32.5177	−3.59098
$83$	−15.8888	−1.74403	−0.872014	−	0.489481i	$-0.837186\pi$
$83$	−15.8888	−1.74403	−0.872014	+	0.489481i	$0.837186\pi$
$84$	2.74700	0.299722
$85$	0	0
$86$	9.66345	1.04204
$87$	−2.65912	−0.285088
$88$	−50.5250	−5.38598
$89$	8.99645	0.953621	0.476811	−	0.879006i	$-0.341793\pi$
$89$	8.99645	0.953621	0.476811	+	0.879006i	$0.341793\pi$
$90$	0	0
$91$	4.94753	0.518642
$92$	5.01366	0.522710
$93$	0.455838	0.0472682
$94$	−23.4231	−2.41591
$95$	0	0
$96$	−7.37437	−0.752643
$97$	−10.5928	−1.07554	−0.537770	−	0.843092i	$-0.680733\pi$
$97$	−10.5928	−1.07554	−0.537770	+	0.843092i	$0.680733\pi$
$98$	2.64833	0.267522
$99$	17.0911	1.71772
$100$	0	0
$101$	0.799268	0.0795302	0.0397651	−	0.999209i	$-0.487339\pi$
$101$	0.799268	0.0795302	0.0397651	+	0.999209i	$0.487339\pi$
$102$	−4.70832	−0.466193
$103$	−12.6035	−1.24186	−0.620930	−	0.783866i	$-0.713245\pi$
$103$	−12.6035	−1.24186	−0.620930	+	0.783866i	$0.713245\pi$
$104$	−39.4872	−3.87203
$105$	0	0
$106$	13.7065	1.33129
$107$	11.9938	1.15948	0.579742	−	0.814800i	$-0.303153\pi$
$107$	11.9938	1.15948	0.579742	+	0.814800i	$0.303153\pi$
$108$	15.6574	1.50663
$109$	1.77897	0.170394	0.0851972	−	0.996364i	$-0.472848\pi$
$109$	1.77897	0.170394	0.0851972	+	0.996364i	$0.472848\pi$
$110$	0	0
$111$	3.95610	0.375497
$112$	−11.1095	−1.04975
$113$	−2.38565	−0.224423	−0.112212	−	0.993684i	$-0.535793\pi$
$113$	−2.38565	−0.224423	−0.112212	+	0.993684i	$0.535793\pi$
$114$	4.79574	0.449163
$115$	0	0
$116$	24.3327	2.25923
$117$	13.3574	1.23489
$118$	−4.24417	−0.390707
$119$	−3.24481	−0.297451
$120$	0	0
$121$	29.0754	2.64322
$122$	−10.1826	−0.921893
$123$	6.72745	0.606594
$124$	−4.17121	−0.374586
$125$	0	0
$126$	7.14997	0.636970
$127$	−8.46927	−0.751526	−0.375763	−	0.926716i	$-0.622619\pi$
$127$	−8.46927	−0.751526	−0.375763	+	0.926716i	$0.622619\pi$
$128$	8.63695	0.763406
$129$	−1.99923	−0.176023
$130$	0	0
$131$	13.6464	1.19229	0.596145	−	0.802877i	$-0.296698\pi$
$131$	13.6464	1.19229	0.596145	+	0.802877i	$0.296698\pi$
$132$	17.3899	1.51360
$133$	3.30506	0.286585
$134$	−5.04247	−0.435603
$135$	0	0
$136$	25.8974	2.22069
$137$	−21.5543	−1.84150	−0.920752	−	0.390148i	$-0.872424\pi$
$137$	−21.5543	−1.84150	−0.920752	+	0.390148i	$0.872424\pi$
$138$	−1.45103	−0.123520
$139$	3.88467	0.329494	0.164747	−	0.986336i	$-0.447319\pi$
$139$	3.88467	0.329494	0.164747	+	0.986336i	$0.447319\pi$
$140$	0	0
$141$	4.84592	0.408100
$142$	7.30737	0.613220
$143$	31.3204	2.61915
$144$	−29.9934	−2.49945
$145$	0	0
$146$	25.0268	2.07124
$147$	−0.547903	−0.0451903
$148$	−36.2009	−2.97569
$149$	1.05534	0.0864565	0.0432282	−	0.999065i	$-0.486236\pi$
$149$	1.05534	0.0864565	0.0432282	+	0.999065i	$0.486236\pi$
$150$	0	0
$151$	10.6570	0.867257	0.433628	−	0.901092i	$-0.357233\pi$
$151$	10.6570	0.867257	0.433628	+	0.901092i	$0.357233\pi$
$152$	−26.3783	−2.13956
$153$	−8.76035	−0.708232
$154$	16.7653	1.35099
$155$	0	0
$156$	13.5909	1.08814
$157$	20.2886	1.61921	0.809605	−	0.586975i	$-0.199681\pi$
$157$	20.2886	1.61921	0.809605	+	0.586975i	$0.199681\pi$
$158$	−3.06546	−0.243875
$159$	−2.83569	−0.224885
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	16.9184	1.32924
$163$	22.5058	1.76279	0.881394	−	0.472382i	$-0.156606\pi$
$163$	22.5058	1.76279	0.881394	+	0.472382i	$0.156606\pi$
$164$	−61.5605	−4.80707
$165$	0	0
$166$	−42.0789	−3.26596
$167$	−20.0999	−1.55538	−0.777689	−	0.628649i	$-0.783608\pi$
$167$	−20.0999	−1.55538	−0.777689	+	0.628649i	$0.783608\pi$
$168$	4.37291	0.337378
$169$	11.4781	0.882930
$170$	0	0
$171$	8.92302	0.682361
$172$	18.2943	1.39492
$173$	8.00462	0.608580	0.304290	−	0.952579i	$-0.401581\pi$
$173$	8.00462	0.608580	0.304290	+	0.952579i	$0.401581\pi$
$174$	−7.04224	−0.533871
$175$	0	0
$176$	−70.3288	−5.30123
$177$	0.878059	0.0659989
$178$	23.8256	1.78580
$179$	−12.1231	−0.906121	−0.453060	−	0.891480i	$-0.649668\pi$
$179$	−12.1231	−0.906121	−0.453060	+	0.891480i	$0.649668\pi$
$180$	0	0
$181$	−16.5197	−1.22790	−0.613948	−	0.789346i	$-0.710420\pi$
$181$	−16.5197	−1.22790	−0.613948	+	0.789346i	$0.710420\pi$
$182$	13.1027	0.971238
$183$	2.10665	0.155728
$184$	7.98118	0.588380
$185$	0	0
$186$	1.20721	0.0885170
$187$	−20.5413	−1.50213
$188$	−44.3432	−3.23406
$189$	−3.12294	−0.227160
$190$	0	0
$191$	8.95661	0.648077	0.324039	−	0.946044i	$-0.394959\pi$
$191$	8.95661	0.648077	0.324039	+	0.946044i	$0.394959\pi$
$192$	−7.35593	−0.530869
$193$	17.3999	1.25247	0.626235	−	0.779634i	$-0.284595\pi$
$193$	17.3999	1.25247	0.626235	+	0.779634i	$0.284595\pi$
$194$	−28.0533	−2.01411
$195$	0	0
$196$	5.01366	0.358119
$197$	2.44198	0.173984	0.0869919	−	0.996209i	$-0.472275\pi$
$197$	2.44198	0.173984	0.0869919	+	0.996209i	$0.472275\pi$
$198$	45.2630	3.21670
$199$	1.86256	0.132034	0.0660168	−	0.997819i	$-0.478971\pi$
$199$	1.86256	0.132034	0.0660168	+	0.997819i	$0.478971\pi$
$200$	0	0
$201$	1.04322	0.0735829
$202$	2.11673	0.148932
$203$	−4.85327	−0.340633
$204$	−8.91350	−0.624070
$205$	0	0
$206$	−33.3783	−2.32557
$207$	−2.69980	−0.187649
$208$	−54.9646	−3.81111
$209$	20.9228	1.44726
$210$	0	0
$211$	18.9888	1.30724	0.653622	−	0.756821i	$-0.273249\pi$
$211$	18.9888	1.30724	0.653622	+	0.756821i	$0.273249\pi$
$212$	25.9484	1.78214
$213$	−1.51179	−0.103586
$214$	31.7635	2.17131
$215$	0	0
$216$	24.9247	1.69591
$217$	0.831969	0.0564777
$218$	4.71131	0.319090
$219$	−5.17770	−0.349877
$220$	0	0
$221$	−16.0538	−1.07990
$222$	10.4771	0.703175
$223$	3.08308	0.206458	0.103229	−	0.994658i	$-0.467083\pi$
$223$	3.08308	0.206458	0.103229	+	0.994658i	$0.467083\pi$
$224$	−13.4593	−0.899285
$225$	0	0
$226$	−6.31800	−0.420267
$227$	−21.2253	−1.40877	−0.704385	−	0.709818i	$-0.748777\pi$
$227$	−21.2253	−1.40877	−0.704385	+	0.709818i	$0.748777\pi$
$228$	9.07902	0.601272
$229$	−6.51587	−0.430581	−0.215290	−	0.976550i	$-0.569070\pi$
$229$	−6.51587	−0.430581	−0.215290	+	0.976550i	$0.569070\pi$
$230$	0	0
$231$	−3.46851	−0.228211
$232$	38.7348	2.54307
$233$	22.9320	1.50233	0.751163	−	0.660117i	$-0.229493\pi$
$233$	22.9320	1.50233	0.751163	+	0.660117i	$0.229493\pi$
$234$	35.3747	2.31252
$235$	0	0
$236$	−8.03480	−0.523021
$237$	0.634201	0.0411958
$238$	−8.59334	−0.557023
$239$	16.9464	1.09617	0.548086	−	0.836422i	$-0.315357\pi$
$239$	16.9464	1.09617	0.548086	+	0.836422i	$0.315357\pi$
$240$	0	0
$241$	−12.2746	−0.790678	−0.395339	−	0.918535i	$-0.629373\pi$
$241$	−12.2746	−0.790678	−0.395339	+	0.918535i	$0.629373\pi$
$242$	77.0014	4.94983
$243$	−12.8690	−0.825547
$244$	−19.2772	−1.23409
$245$	0	0
$246$	17.8165	1.13594
$247$	16.3519	1.04045
$248$	−6.64009	−0.421646
$249$	8.70555	0.551692
$250$	0	0
$251$	25.3597	1.60069	0.800346	−	0.599539i	$-0.204649\pi$
$251$	25.3597	1.60069	0.800346	+	0.599539i	$0.204649\pi$
$252$	13.5359	0.852681
$253$	−6.33051	−0.397996
$254$	−22.4294	−1.40735
$255$	0	0
$256$	−3.97770	−0.248607
$257$	9.04594	0.564271	0.282135	−	0.959375i	$-0.408957\pi$
$257$	9.04594	0.564271	0.282135	+	0.959375i	$0.408957\pi$
$258$	−5.29463	−0.329630
$259$	7.22045	0.448657
$260$	0	0
$261$	−13.1029	−0.811047
$262$	36.1401	2.23275
$263$	−21.0858	−1.30021	−0.650103	−	0.759846i	$-0.725274\pi$
$263$	−21.0858	−1.30021	−0.650103	+	0.759846i	$0.725274\pi$
$264$	27.6828	1.70376
$265$	0	0
$266$	8.75291	0.536675
$267$	−4.92918	−0.301661
$268$	−9.54611	−0.583121
$269$	4.96626	0.302798	0.151399	−	0.988473i	$-0.451622\pi$
$269$	4.96626	0.302798	0.151399	+	0.988473i	$0.451622\pi$
$270$	0	0
$271$	22.4423	1.36328	0.681638	−	0.731690i	$-0.261268\pi$
$271$	22.4423	1.36328	0.681638	+	0.731690i	$0.261268\pi$
$272$	36.0482	2.18574
$273$	−2.71077	−0.164063
$274$	−57.0828	−3.44850
$275$	0	0
$276$	−2.74700	−0.165350
$277$	9.00358	0.540973	0.270486	−	0.962724i	$-0.412815\pi$
$277$	9.00358	0.540973	0.270486	+	0.962724i	$0.412815\pi$
$278$	10.2879	0.617027
$279$	2.24615	0.134474
$280$	0	0
$281$	−21.0007	−1.25280	−0.626399	−	0.779503i	$-0.715472\pi$
$281$	−21.0007	−1.25280	−0.626399	+	0.779503i	$0.715472\pi$
$282$	12.8336	0.764230
$283$	−24.3379	−1.44674	−0.723370	−	0.690461i	$-0.757408\pi$
$283$	−24.3379	−1.44674	−0.723370	+	0.690461i	$0.757408\pi$
$284$	13.8339	0.820889
$285$	0	0
$286$	82.9469	4.90475
$287$	12.2786	0.724780
$288$	−36.3373	−2.14120
$289$	−6.47120	−0.380659
$290$	0	0
$291$	5.80385	0.340227
$292$	47.3793	2.77266
$293$	−9.57907	−0.559615	−0.279808	−	0.960056i	$-0.590271\pi$
$293$	−9.57907	−0.559615	−0.279808	+	0.960056i	$0.590271\pi$
$294$	−1.45103	−0.0846257
$295$	0	0
$296$	−57.6277	−3.34954
$297$	−19.7698	−1.14716
$298$	2.79488	0.161903
$299$	−4.94753	−0.286123
$300$	0	0
$301$	−3.64888	−0.210318
$302$	28.2233	1.62407
$303$	−0.437921	−0.0251579
$304$	−36.7176	−2.10590
$305$	0	0
$306$	−23.2003	−1.32627
$307$	−33.6946	−1.92305	−0.961527	−	0.274709i	$-0.911419\pi$
$307$	−33.6946	−1.92305	−0.961527	+	0.274709i	$0.911419\pi$
$308$	31.7391	1.80850
$309$	6.90550	0.392840
$310$	0	0
$311$	−27.1548	−1.53981	−0.769903	−	0.638161i	$-0.779695\pi$
$311$	−27.1548	−1.53981	−0.769903	+	0.638161i	$0.779695\pi$
$312$	21.6351	1.22485
$313$	10.5894	0.598548	0.299274	−	0.954167i	$-0.403255\pi$
$313$	10.5894	0.598548	0.299274	+	0.954167i	$0.403255\pi$
$314$	53.7311	3.03222
$315$	0	0
$316$	−5.80335	−0.326464
$317$	−23.1388	−1.29961	−0.649803	−	0.760103i	$-0.725149\pi$
$317$	−23.1388	−1.29961	−0.649803	+	0.760103i	$0.725149\pi$
$318$	−7.50984	−0.421131
$319$	−30.7237	−1.72020
$320$	0	0
$321$	−6.57143	−0.366782
$322$	−2.64833	−0.147586
$323$	−10.7243	−0.596717
$324$	32.0290	1.77939
$325$	0	0
$326$	59.6027	3.30109
$327$	−0.974703	−0.0539012
$328$	−97.9973	−5.41100
$329$	8.84448	0.487612
$330$	0	0
$331$	−21.1583	−1.16297	−0.581483	−	0.813559i	$-0.697527\pi$
$331$	−21.1583	−1.16297	−0.581483	+	0.813559i	$0.697527\pi$
$332$	−79.6613	−4.37198
$333$	19.4938	1.06825
$334$	−53.2312	−2.91268
$335$	0	0
$336$	6.08692	0.332069
$337$	−9.64653	−0.525480	−0.262740	−	0.964867i	$-0.584626\pi$
$337$	−9.64653	−0.525480	−0.262740	+	0.964867i	$0.584626\pi$
$338$	30.3978	1.65342
$339$	1.30711	0.0709923
$340$	0	0
$341$	5.26679	0.285213
$342$	23.6311	1.27782
$343$	−1.00000	−0.0539949
$344$	29.1224	1.57017
$345$	0	0
$346$	21.1989	1.13966
$347$	−14.9585	−0.803013	−0.401507	−	0.915856i	$-0.631513\pi$
$347$	−14.9585	−0.803013	−0.401507	+	0.915856i	$0.631513\pi$
$348$	−13.3319	−0.714667
$349$	26.7335	1.43101	0.715507	−	0.698606i	$-0.246196\pi$
$349$	26.7335	1.43101	0.715507	+	0.698606i	$0.246196\pi$
$350$	0	0
$351$	−15.4508	−0.824705
$352$	−85.2040	−4.54139
$353$	−0.944708	−0.0502817	−0.0251409	−	0.999684i	$-0.508003\pi$
$353$	−0.944708	−0.0502817	−0.0251409	+	0.999684i	$0.508003\pi$
$354$	2.32539	0.123593
$355$	0	0
$356$	45.1052	2.39057
$357$	1.77784	0.0940934
$358$	−32.1059	−1.69685
$359$	−19.0217	−1.00392	−0.501962	−	0.864889i	$-0.667388\pi$
$359$	−19.0217	−1.00392	−0.501962	+	0.864889i	$0.667388\pi$
$360$	0	0
$361$	−8.07655	−0.425081
$362$	−43.7496	−2.29943
$363$	−15.9305	−0.836135
$364$	24.8053	1.30015
$365$	0	0
$366$	5.57910	0.291624
$367$	2.46175	0.128502	0.0642510	−	0.997934i	$-0.479534\pi$
$367$	2.46175	0.128502	0.0642510	+	0.997934i	$0.479534\pi$
$368$	11.1095	0.579122
$369$	33.1497	1.72570
$370$	0	0
$371$	−5.17553	−0.268700
$372$	2.28542	0.118493
$373$	16.7156	0.865499	0.432749	−	0.901514i	$-0.357543\pi$
$373$	16.7156	0.865499	0.432749	+	0.901514i	$0.357543\pi$
$374$	−54.4002	−2.81297
$375$	0	0
$376$	−70.5894	−3.64037
$377$	−24.0117	−1.23667
$378$	−8.27058	−0.425393
$379$	−5.50259	−0.282649	−0.141324	−	0.989963i	$-0.545136\pi$
$379$	−5.50259	−0.282649	−0.141324	+	0.989963i	$0.545136\pi$
$380$	0	0
$381$	4.64034	0.237732
$382$	23.7201	1.21362
$383$	−21.1260	−1.07949	−0.539745	−	0.841829i	$-0.681479\pi$
$383$	−21.1260	−1.07949	−0.539745	+	0.841829i	$0.681479\pi$
$384$	−4.73221	−0.241490
$385$	0	0
$386$	46.0806	2.34544
$387$	−9.85126	−0.500768
$388$	−53.1089	−2.69620
$389$	29.0240	1.47157	0.735786	−	0.677214i	$-0.236813\pi$
$389$	29.0240	1.47157	0.735786	+	0.677214i	$0.236813\pi$
$390$	0	0
$391$	3.24481	0.164097
$392$	7.98118	0.403110
$393$	−7.47689	−0.377159
$394$	6.46717	0.325812
$395$	0	0
$396$	85.6892	4.30604
$397$	−12.5032	−0.627519	−0.313759	−	0.949503i	$-0.601588\pi$
$397$	−12.5032	−0.627519	−0.313759	+	0.949503i	$0.601588\pi$
$398$	4.93269	0.247253
$399$	−1.81085	−0.0906561
$400$	0	0
$401$	−16.9297	−0.845429	−0.422714	−	0.906263i	$-0.638923\pi$
$401$	−16.9297	−0.845429	−0.422714	+	0.906263i	$0.638923\pi$
$402$	2.76279	0.137795
$403$	4.11619	0.205042
$404$	4.00726	0.199369
$405$	0	0
$406$	−12.8531	−0.637887
$407$	45.7091	2.26572
$408$	−14.1893	−0.702474
$409$	−28.9087	−1.42944	−0.714722	−	0.699409i	$-0.753447\pi$
$409$	−28.9087	−1.42944	−0.714722	+	0.699409i	$0.753447\pi$
$410$	0	0
$411$	11.8096	0.582527
$412$	−63.1897	−3.11313
$413$	1.60258	0.0788578
$414$	−7.14997	−0.351402
$415$	0	0
$416$	−66.5901	−3.26485
$417$	−2.12842	−0.104229
$418$	55.4104	2.71021
$419$	34.3434	1.67778	0.838892	−	0.544298i	$-0.183204\pi$
$419$	34.3434	1.67778	0.838892	+	0.544298i	$0.183204\pi$
$420$	0	0
$421$	5.68440	0.277041	0.138520	−	0.990360i	$-0.455765\pi$
$421$	5.68440	0.277041	0.138520	+	0.990360i	$0.455765\pi$
$422$	50.2887	2.44801
$423$	23.8784	1.16101
$424$	41.3068	2.00604
$425$	0	0
$426$	−4.00373	−0.193981
$427$	3.84493	0.186069
$428$	60.1328	2.90663
$429$	−17.1606	−0.828520
$430$	0	0
$431$	−38.4783	−1.85343	−0.926716	−	0.375762i	$-0.877381\pi$
$431$	−38.4783	−1.85343	−0.926716	+	0.375762i	$0.877381\pi$
$432$	34.6943	1.66923
$433$	−24.1743	−1.16174	−0.580871	−	0.813996i	$-0.697288\pi$
$433$	−24.1743	−1.16174	−0.580871	+	0.813996i	$0.697288\pi$
$434$	2.20333	0.105763
$435$	0	0
$436$	8.91916	0.427150
$437$	−3.30506	−0.158103
$438$	−13.7123	−0.655198
$439$	−23.6731	−1.12986	−0.564928	−	0.825141i	$-0.691096\pi$
$439$	−23.6731	−1.12986	−0.564928	+	0.825141i	$0.691096\pi$
$440$	0	0
$441$	−2.69980	−0.128562
$442$	−42.5158	−2.02227
$443$	−19.4495	−0.924074	−0.462037	−	0.886861i	$-0.652881\pi$
$443$	−19.4495	−0.924074	−0.462037	+	0.886861i	$0.652881\pi$
$444$	19.8346	0.941307
$445$	0	0
$446$	8.16501	0.386625
$447$	−0.578222	−0.0273489
$448$	−13.4256	−0.634300
$449$	40.6603	1.91888	0.959439	−	0.281916i	$-0.0909698\pi$
$449$	40.6603	1.91888	0.959439	+	0.281916i	$0.0909698\pi$
$450$	0	0
$451$	77.7295	3.66014
$452$	−11.9609	−0.562591
$453$	−5.83902	−0.274341
$454$	−56.2115	−2.63814
$455$	0	0
$456$	14.4528	0.676812
$457$	−13.8025	−0.645656	−0.322828	−	0.946458i	$-0.604634\pi$
$457$	−13.8025	−0.645656	−0.322828	+	0.946458i	$0.604634\pi$
$458$	−17.2562	−0.806329
$459$	10.1333	0.472984
$460$	0	0
$461$	16.0531	0.747668	0.373834	−	0.927496i	$-0.378043\pi$
$461$	16.0531	0.747668	0.373834	+	0.927496i	$0.378043\pi$
$462$	−9.18576	−0.427360
$463$	−2.60075	−0.120867	−0.0604335	−	0.998172i	$-0.519248\pi$
$463$	−2.60075	−0.120867	−0.0604335	+	0.998172i	$0.519248\pi$
$464$	53.9174	2.50305
$465$	0	0
$466$	60.7316	2.81334
$467$	−3.60743	−0.166932	−0.0834659	−	0.996511i	$-0.526599\pi$
$467$	−3.60743	−0.166932	−0.0834659	+	0.996511i	$0.526599\pi$
$468$	66.9693	3.09566
$469$	1.90402	0.0879194
$470$	0	0
$471$	−11.1162	−0.512208
$472$	−12.7905	−0.588730
$473$	−23.0993	−1.06211
$474$	1.67958	0.0771455
$475$	0	0
$476$	−16.2684	−0.745660
$477$	−13.9729	−0.639775
$478$	44.8797	2.05275
$479$	−38.2595	−1.74812	−0.874061	−	0.485815i	$-0.838523\pi$
$479$	−38.2595	−1.74812	−0.874061	+	0.485815i	$0.838523\pi$
$480$	0	0
$481$	35.7234	1.62885
$482$	−32.5073	−1.48067
$483$	0.547903	0.0249304
$484$	145.774	6.62611
$485$	0	0
$486$	−34.0814	−1.54596
$487$	−25.7630	−1.16744	−0.583718	−	0.811957i	$-0.698402\pi$
$487$	−25.7630	−1.16744	−0.583718	+	0.811957i	$0.698402\pi$
$488$	−30.6871	−1.38914
$489$	−12.3310	−0.557626
$490$	0	0
$491$	−23.8104	−1.07455	−0.537273	−	0.843408i	$-0.680546\pi$
$491$	−23.8104	−1.07455	−0.537273	+	0.843408i	$0.680546\pi$
$492$	33.7292	1.52063
$493$	15.7479	0.709252
$494$	43.3053	1.94840
$495$	0	0
$496$	−9.24275	−0.415012
$497$	−2.75923	−0.123769
$498$	23.0552	1.03313
$499$	37.7168	1.68844	0.844219	−	0.535999i	$-0.180065\pi$
$499$	37.7168	1.68844	0.844219	+	0.535999i	$0.180065\pi$
$500$	0	0
$501$	11.0128	0.492016
$502$	67.1610	2.99754
$503$	30.8024	1.37341	0.686706	−	0.726935i	$-0.259056\pi$
$503$	30.8024	1.37341	0.686706	+	0.726935i	$0.259056\pi$
$504$	21.5476	0.959807
$505$	0	0
$506$	−16.7653	−0.745309
$507$	−6.28888	−0.279299
$508$	−42.4621	−1.88395
$509$	38.2677	1.69619	0.848093	−	0.529847i	$-0.177751\pi$
$509$	38.2677	1.69619	0.848093	+	0.529847i	$0.177751\pi$
$510$	0	0
$511$	−9.45004	−0.418045
$512$	−27.8082	−1.22896
$513$	−10.3215	−0.455706
$514$	23.9567	1.05668
$515$	0	0
$516$	−10.0235	−0.441259
$517$	55.9901	2.46244
$518$	19.1221	0.840179
$519$	−4.38575	−0.192513
$520$	0	0
$521$	8.49641	0.372234	0.186117	−	0.982528i	$-0.440410\pi$
$521$	8.49641	0.372234	0.186117	+	0.982528i	$0.440410\pi$
$522$	−34.7008	−1.51881
$523$	−6.63131	−0.289967	−0.144984	−	0.989434i	$-0.546313\pi$
$523$	−6.63131	−0.289967	−0.144984	+	0.989434i	$0.546313\pi$
$524$	68.4183	2.98887
$525$	0	0
$526$	−55.8422	−2.43484
$527$	−2.69958	−0.117596
$528$	38.5334	1.67695
$529$	1.00000	0.0434783
$530$	0	0
$531$	4.32665	0.187761
$532$	16.5705	0.718421
$533$	60.7486	2.63131
$534$	−13.0541	−0.564906
$535$	0	0
$536$	−15.1963	−0.656381
$537$	6.64226	0.286635
$538$	13.1523	0.567036
$539$	−6.33051	−0.272675
$540$	0	0
$541$	−0.983341	−0.0422771	−0.0211386	−	0.999777i	$-0.506729\pi$
$541$	−0.983341	−0.0422771	−0.0211386	+	0.999777i	$0.506729\pi$
$542$	59.4348	2.55294
$543$	9.05117	0.388423
$544$	43.6728	1.87245
$545$	0	0
$546$	−7.17902	−0.307233
$547$	−6.77630	−0.289734	−0.144867	−	0.989451i	$-0.546275\pi$
$547$	−6.77630	−0.289734	−0.144867	+	0.989451i	$0.546275\pi$
$548$	−108.066	−4.61634
$549$	10.3805	0.443031
$550$	0	0
$551$	−16.0404	−0.683343
$552$	−4.37291	−0.186124
$553$	1.15751	0.0492222
$554$	23.8445	1.01305
$555$	0	0
$556$	19.4764	0.825985
$557$	7.28989	0.308883	0.154441	−	0.988002i	$-0.450642\pi$
$557$	7.28989	0.308883	0.154441	+	0.988002i	$0.450642\pi$
$558$	5.94855	0.251822
$559$	−18.0530	−0.763559
$560$	0	0
$561$	11.2547	0.475172
$562$	−55.6169	−2.34606
$563$	7.20945	0.303842	0.151921	−	0.988393i	$-0.451454\pi$
$563$	7.20945	0.303842	0.151921	+	0.988393i	$0.451454\pi$
$564$	24.2958	1.02304
$565$	0	0
$566$	−64.4549	−2.70924
$567$	−6.38834	−0.268285
$568$	22.0219	0.924020
$569$	19.4046	0.813484	0.406742	−	0.913543i	$-0.366665\pi$
$569$	19.4046	0.813484	0.406742	+	0.913543i	$0.366665\pi$
$570$	0	0
$571$	4.99138	0.208883	0.104441	−	0.994531i	$-0.466695\pi$
$571$	4.99138	0.208883	0.104441	+	0.994531i	$0.466695\pi$
$572$	157.030	6.56576
$573$	−4.90735	−0.205008
$574$	32.5177	1.35726
$575$	0	0
$576$	−36.2465	−1.51027
$577$	−20.8901	−0.869666	−0.434833	−	0.900511i	$-0.643193\pi$
$577$	−20.8901	−0.869666	−0.434833	+	0.900511i	$0.643193\pi$
$578$	−17.1379	−0.712842
$579$	−9.53344	−0.396196
$580$	0	0
$581$	15.8888	0.659180
$582$	15.3705	0.637128
$583$	−32.7638	−1.35694
$584$	75.4224	3.12100
$585$	0	0
$586$	−25.3686	−1.04797
$587$	−7.60753	−0.313996	−0.156998	−	0.987599i	$-0.550182\pi$
$587$	−7.60753	−0.313996	−0.156998	+	0.987599i	$0.550182\pi$
$588$	−2.74700	−0.113284
$589$	2.74971	0.113300
$590$	0	0
$591$	−1.33797	−0.0550367
$592$	−80.2155	−3.29684
$593$	−15.0340	−0.617371	−0.308685	−	0.951164i	$-0.599889\pi$
$593$	−15.0340	−0.617371	−0.308685	+	0.951164i	$0.599889\pi$
$594$	−52.3570	−2.14823
$595$	0	0
$596$	5.29110	0.216732
$597$	−1.02050	−0.0417665
$598$	−13.1027	−0.535810
$599$	16.3849	0.669467	0.334734	−	0.942313i	$-0.391354\pi$
$599$	16.3849	0.669467	0.334734	+	0.942313i	$0.391354\pi$
$600$	0	0
$601$	−8.42633	−0.343717	−0.171859	−	0.985122i	$-0.554977\pi$
$601$	−8.42633	−0.343717	−0.171859	+	0.985122i	$0.554977\pi$
$602$	−9.66345	−0.393853
$603$	5.14047	0.209336
$604$	53.4307	2.17407
$605$	0	0
$606$	−1.15976	−0.0471121
$607$	−19.3727	−0.786313	−0.393156	−	0.919472i	$-0.628617\pi$
$607$	−19.3727	−0.786313	−0.393156	+	0.919472i	$0.628617\pi$
$608$	−44.4837	−1.80405
$609$	2.65912	0.107753
$610$	0	0
$611$	43.7584	1.77027
$612$	−43.9214	−1.77542
$613$	−26.5955	−1.07418	−0.537091	−	0.843524i	$-0.680477\pi$
$613$	−26.5955	−1.07418	−0.537091	+	0.843524i	$0.680477\pi$
$614$	−89.2346	−3.60122
$615$	0	0
$616$	50.5250	2.03571
$617$	11.3573	0.457226	0.228613	−	0.973517i	$-0.426581\pi$
$617$	11.3573	0.457226	0.228613	+	0.973517i	$0.426581\pi$
$618$	18.2880	0.735653
$619$	1.06487	0.0428006	0.0214003	−	0.999771i	$-0.493188\pi$
$619$	1.06487	0.0428006	0.0214003	+	0.999771i	$0.493188\pi$
$620$	0	0
$621$	3.12294	0.125319
$622$	−71.9149	−2.88352
$623$	−8.99645	−0.360435
$624$	30.1153	1.20558
$625$	0	0
$626$	28.0443	1.12087
$627$	−11.4636	−0.457814
$628$	101.720	4.05909
$629$	−23.4290	−0.934175
$630$	0	0
$631$	31.5369	1.25546	0.627732	−	0.778430i	$-0.283984\pi$
$631$	31.5369	1.25546	0.627732	+	0.778430i	$0.283984\pi$
$632$	−9.23827	−0.367479
$633$	−10.4040	−0.413523
$634$	−61.2793	−2.43371
$635$	0	0
$636$	−14.2172	−0.563748
$637$	−4.94753	−0.196028
$638$	−81.3666	−3.22133
$639$	−7.44938	−0.294693
$640$	0	0
$641$	−20.0029	−0.790069	−0.395034	−	0.918666i	$-0.629267\pi$
$641$	−20.0029	−0.790069	−0.395034	+	0.918666i	$0.629267\pi$
$642$	−17.4033	−0.686855
$643$	18.4707	0.728412	0.364206	−	0.931318i	$-0.381340\pi$
$643$	18.4707	0.728412	0.364206	+	0.931318i	$0.381340\pi$
$644$	−5.01366	−0.197566
$645$	0	0
$646$	−28.4015	−1.11744
$647$	−20.9175	−0.822353	−0.411177	−	0.911556i	$-0.634882\pi$
$647$	−20.9175	−0.822353	−0.411177	+	0.911556i	$0.634882\pi$
$648$	50.9865	2.00294
$649$	10.1452	0.398232
$650$	0	0
$651$	−0.455838	−0.0178657
$652$	112.836	4.41901
$653$	37.2317	1.45699	0.728494	−	0.685052i	$-0.240221\pi$
$653$	37.2317	1.45699	0.728494	+	0.685052i	$0.240221\pi$
$654$	−2.58134	−0.100938
$655$	0	0
$656$	−136.408	−5.32586
$657$	−25.5132	−0.995366
$658$	23.4231	0.913128
$659$	−49.8236	−1.94085	−0.970426	−	0.241400i	$-0.922393\pi$
$659$	−49.8236	−1.94085	−0.970426	+	0.241400i	$0.922393\pi$
$660$	0	0
$661$	−15.9554	−0.620594	−0.310297	−	0.950640i	$-0.600428\pi$
$661$	−15.9554	−0.620594	−0.310297	+	0.950640i	$0.600428\pi$
$662$	−56.0342	−2.17783
$663$	8.79593	0.341606
$664$	−126.812	−4.92125
$665$	0	0
$666$	51.6260	2.00047
$667$	4.85327	0.187919
$668$	−100.774	−3.89907
$669$	−1.68923	−0.0653093
$670$	0	0
$671$	24.3404	0.939650
$672$	7.37437	0.284472
$673$	−35.2002	−1.35687	−0.678433	−	0.734662i	$-0.737341\pi$
$673$	−35.2002	−1.35687	−0.678433	+	0.734662i	$0.737341\pi$
$674$	−25.5472	−0.984042
$675$	0	0
$676$	57.5473	2.21336
$677$	38.3772	1.47496	0.737478	−	0.675371i	$-0.236016\pi$
$677$	38.3772	1.47496	0.737478	+	0.675371i	$0.236016\pi$
$678$	3.46165	0.132944
$679$	10.5928	0.406516
$680$	0	0
$681$	11.6294	0.445639
$682$	13.9482	0.534104
$683$	4.69720	0.179733	0.0898666	−	0.995954i	$-0.471356\pi$
$683$	4.69720	0.179733	0.0898666	+	0.995954i	$0.471356\pi$
$684$	44.7370	1.71056
$685$	0	0
$686$	−2.64833	−0.101114
$687$	3.57006	0.136206
$688$	40.5372	1.54547
$689$	−25.6061	−0.975515
$690$	0	0
$691$	5.32364	0.202521	0.101260	−	0.994860i	$-0.467712\pi$
$691$	5.32364	0.202521	0.101260	+	0.994860i	$0.467712\pi$
$692$	40.1325	1.52561
$693$	−17.0911	−0.649239
$694$	−39.6150	−1.50377
$695$	0	0
$696$	−21.2229	−0.804453
$697$	−39.8416	−1.50911
$698$	70.7993	2.67979
$699$	−12.5645	−0.475234
$700$	0	0
$701$	−36.4808	−1.37786	−0.688930	−	0.724828i	$-0.741919\pi$
$701$	−36.4808	−1.37786	−0.688930	+	0.724828i	$0.741919\pi$
$702$	−40.9190	−1.54439
$703$	23.8640	0.900050
$704$	−84.9910	−3.20322
$705$	0	0
$706$	−2.50190	−0.0941603
$707$	−0.799268	−0.0300596
$708$	4.40229	0.165448
$709$	10.6405	0.399612	0.199806	−	0.979835i	$-0.435969\pi$
$709$	10.6405	0.399612	0.199806	+	0.979835i	$0.435969\pi$
$710$	0	0
$711$	3.12504	0.117198
$712$	71.8023	2.69090
$713$	−0.831969	−0.0311575
$714$	4.70832	0.176204
$715$	0	0
$716$	−60.7810	−2.27149
$717$	−9.28498	−0.346754
$718$	−50.3757	−1.88000
$719$	45.2312	1.68684	0.843419	−	0.537257i	$-0.180539\pi$
$719$	45.2312	1.68684	0.843419	+	0.537257i	$0.180539\pi$
$720$	0	0
$721$	12.6035	0.469379
$722$	−21.3894	−0.796030
$723$	6.72530	0.250117
$724$	−82.8240	−3.07813
$725$	0	0
$726$	−42.1893	−1.56579
$727$	48.9696	1.81618	0.908091	−	0.418773i	$-0.137540\pi$
$727$	48.9696	1.81618	0.908091	+	0.418773i	$0.137540\pi$
$728$	39.4872	1.46349
$729$	−12.1141	−0.448669
$730$	0	0
$731$	11.8399	0.437916
$732$	10.5620	0.390384
$733$	39.8053	1.47024	0.735121	−	0.677936i	$-0.237125\pi$
$733$	39.8053	1.47024	0.735121	+	0.677936i	$0.237125\pi$
$734$	6.51952	0.240640
$735$	0	0
$736$	13.4593	0.496115
$737$	12.0534	0.443993
$738$	87.7913	3.23164
$739$	23.7210	0.872591	0.436296	−	0.899803i	$-0.356290\pi$
$739$	23.7210	0.872591	0.436296	+	0.899803i	$0.356290\pi$
$740$	0	0
$741$	−8.95927	−0.329127
$742$	−13.7065	−0.503182
$743$	30.2940	1.11138	0.555690	−	0.831390i	$-0.312454\pi$
$743$	30.2940	1.11138	0.555690	+	0.831390i	$0.312454\pi$
$744$	3.63813	0.133380
$745$	0	0
$746$	44.2684	1.62078
$747$	42.8967	1.56951
$748$	−102.987	−3.76559
$749$	−11.9938	−0.438244
$750$	0	0
$751$	−19.4797	−0.710826	−0.355413	−	0.934709i	$-0.615660\pi$
$751$	−19.4797	−0.710826	−0.355413	+	0.934709i	$0.615660\pi$
$752$	−98.2577	−3.58309
$753$	−13.8947	−0.506350
$754$	−63.5910	−2.31585
$755$	0	0
$756$	−15.6574	−0.569453
$757$	−40.0576	−1.45592	−0.727959	−	0.685620i	$-0.759531\pi$
$757$	−40.0576	−1.45592	−0.727959	+	0.685620i	$0.759531\pi$
$758$	−14.5727	−0.529303
$759$	3.46851	0.125899
$760$	0	0
$761$	46.9528	1.70204	0.851018	−	0.525137i	$-0.175986\pi$
$761$	46.9528	1.70204	0.851018	+	0.525137i	$0.175986\pi$
$762$	12.2892	0.445189
$763$	−1.77897	−0.0644031
$764$	44.9054	1.62462
$765$	0	0
$766$	−55.9488	−2.02151
$767$	7.92882	0.286293
$768$	2.17940	0.0786422
$769$	−8.64266	−0.311662	−0.155831	−	0.987784i	$-0.549806\pi$
$769$	−8.64266	−0.311662	−0.155831	+	0.987784i	$0.549806\pi$
$770$	0	0
$771$	−4.95630	−0.178497
$772$	87.2371	3.13973
$773$	−31.7595	−1.14231	−0.571154	−	0.820843i	$-0.693504\pi$
$773$	−31.7595	−1.14231	−0.571154	+	0.820843i	$0.693504\pi$
$774$	−26.0894	−0.937765
$775$	0	0
$776$	−84.5433	−3.03493
$777$	−3.95610	−0.141924
$778$	76.8651	2.75575
$779$	40.5814	1.45398
$780$	0	0
$781$	−17.4674	−0.625031
$782$	8.59334	0.307297
$783$	15.1565	0.541648
$784$	11.1095	0.396768
$785$	0	0
$786$	−19.8013	−0.706289
$787$	27.5714	0.982815	0.491407	−	0.870930i	$-0.336483\pi$
$787$	27.5714	0.982815	0.491407	+	0.870930i	$0.336483\pi$
$788$	12.2433	0.436148
$789$	11.5530	0.411297
$790$	0	0
$791$	2.38565	0.0848240
$792$	136.407	4.84703
$793$	19.0229	0.675523
$794$	−33.1127	−1.17512
$795$	0	0
$796$	9.33827	0.330986
$797$	−2.21479	−0.0784519	−0.0392260	−	0.999230i	$-0.512489\pi$
$797$	−2.21479	−0.0784519	−0.0392260	+	0.999230i	$0.512489\pi$
$798$	−4.79574	−0.169768
$799$	−28.6987	−1.01529
$800$	0	0
$801$	−24.2886	−0.858196
$802$	−44.8355	−1.58319
$803$	−59.8236	−2.11113
$804$	5.23034	0.184460
$805$	0	0
$806$	10.9010	0.383973
$807$	−2.72103	−0.0957848
$808$	6.37910	0.224416
$809$	17.8108	0.626195	0.313097	−	0.949721i	$-0.398633\pi$
$809$	17.8108	0.626195	0.313097	+	0.949721i	$0.398633\pi$
$810$	0	0
$811$	23.2471	0.816315	0.408157	−	0.912912i	$-0.366171\pi$
$811$	23.2471	0.816315	0.408157	+	0.912912i	$0.366171\pi$
$812$	−24.3327	−0.853909
$813$	−12.2962	−0.431248
$814$	121.053	4.24291
$815$	0	0
$816$	−19.7509	−0.691420
$817$	−12.0598	−0.421919
$818$	−76.5599	−2.67685
$819$	−13.3574	−0.466744
$820$	0	0
$821$	38.9554	1.35955	0.679777	−	0.733419i	$-0.262077\pi$
$821$	38.9554	1.35955	0.679777	+	0.733419i	$0.262077\pi$
$822$	31.2758	1.09087
$823$	−49.3818	−1.72134	−0.860671	−	0.509161i	$-0.829956\pi$
$823$	−49.3818	−1.72134	−0.860671	+	0.509161i	$0.829956\pi$
$824$	−100.591	−3.50425
$825$	0	0
$826$	4.24417	0.147673
$827$	19.9907	0.695144	0.347572	−	0.937653i	$-0.387006\pi$
$827$	19.9907	0.695144	0.347572	+	0.937653i	$0.387006\pi$
$828$	−13.5359	−0.470405
$829$	−26.4041	−0.917052	−0.458526	−	0.888681i	$-0.651622\pi$
$829$	−26.4041	−0.917052	−0.458526	+	0.888681i	$0.651622\pi$
$830$	0	0
$831$	−4.93309	−0.171127
$832$	−66.4237	−2.30283
$833$	3.24481	0.112426
$834$	−5.63677	−0.195185
$835$	0	0
$836$	104.900	3.62803
$837$	−2.59819	−0.0898065
$838$	90.9526	3.14191
$839$	−12.8515	−0.443684	−0.221842	−	0.975083i	$-0.571207\pi$
$839$	−12.8515	−0.443684	−0.221842	+	0.975083i	$0.571207\pi$
$840$	0	0
$841$	−5.44576	−0.187785
$842$	15.0542	0.518802
$843$	11.5064	0.396300
$844$	95.2035	3.27704
$845$	0	0
$846$	63.2378	2.17416
$847$	−29.0754	−0.999043
$848$	57.4975	1.97447
$849$	13.3348	0.457650
$850$	0	0
$851$	−7.22045	−0.247514
$852$	−7.57962	−0.259673
$853$	−49.4509	−1.69317	−0.846584	−	0.532255i	$-0.821345\pi$
$853$	−49.4509	−1.69317	−0.846584	+	0.532255i	$0.821345\pi$
$854$	10.1826	0.348443
$855$	0	0
$856$	95.7246	3.27180
$857$	6.26610	0.214046	0.107023	−	0.994257i	$-0.465868\pi$
$857$	6.26610	0.214046	0.107023	+	0.994257i	$0.465868\pi$
$858$	−45.4469	−1.55153
$859$	19.9363	0.680219	0.340109	−	0.940386i	$-0.389536\pi$
$859$	19.9363	0.680219	0.340109	+	0.940386i	$0.389536\pi$
$860$	0	0
$861$	−6.72745	−0.229271
$862$	−101.903	−3.47084
$863$	−23.1319	−0.787420	−0.393710	−	0.919235i	$-0.628809\pi$
$863$	−23.1319	−0.787420	−0.393710	+	0.919235i	$0.628809\pi$
$864$	42.0324	1.42997
$865$	0	0
$866$	−64.0215	−2.17554
$867$	3.54559	0.120415
$868$	4.17121	0.141580
$869$	7.32761	0.248572
$870$	0	0
$871$	9.42020	0.319191
$872$	14.1983	0.480815
$873$	28.5986	0.967915
$874$	−8.75291	−0.296072
$875$	0	0
$876$	−25.9593	−0.877082
$877$	10.6774	0.360552	0.180276	−	0.983616i	$-0.442301\pi$
$877$	10.6774	0.360552	0.180276	+	0.983616i	$0.442301\pi$
$878$	−62.6942	−2.11583
$879$	5.24840	0.177024
$880$	0	0
$881$	−7.69463	−0.259239	−0.129619	−	0.991564i	$-0.541376\pi$
$881$	−7.69463	−0.259239	−0.129619	+	0.991564i	$0.541376\pi$
$882$	−7.14997	−0.240752
$883$	−11.3000	−0.380276	−0.190138	−	0.981757i	$-0.560894\pi$
$883$	−11.3000	−0.380276	−0.190138	+	0.981757i	$0.560894\pi$
$884$	−80.4884	−2.70712
$885$	0	0
$886$	−51.5088	−1.73047
$887$	7.33548	0.246301	0.123151	−	0.992388i	$-0.460700\pi$
$887$	7.33548	0.246301	0.123151	+	0.992388i	$0.460700\pi$
$888$	31.5744	1.05957
$889$	8.46927	0.284050
$890$	0	0
$891$	−40.4415	−1.35484
$892$	15.4575	0.517556
$893$	29.2316	0.978198
$894$	−1.53132	−0.0512151
$895$	0	0
$896$	−8.63695	−0.288540
$897$	2.71077	0.0905099
$898$	107.682	3.59339
$899$	−4.03777	−0.134667
$900$	0	0
$901$	16.7936	0.559476
$902$	205.854	6.85418
$903$	1.99923	0.0665303
$904$	−19.0403	−0.633272
$905$	0	0
$906$	−15.4637	−0.513746
$907$	0.399911	0.0132788	0.00663942	−	0.999978i	$-0.497887\pi$
$907$	0.399911	0.0132788	0.00663942	+	0.999978i	$0.497887\pi$
$908$	−106.416	−3.53155
$909$	−2.15787	−0.0715719
$910$	0	0
$911$	−45.4059	−1.50436	−0.752182	−	0.658955i	$-0.770999\pi$
$911$	−45.4059	−1.50436	−0.752182	+	0.658955i	$0.770999\pi$
$912$	20.1177	0.666163
$913$	100.585	3.32886
$914$	−36.5537	−1.20909
$915$	0	0
$916$	−32.6684	−1.07939
$917$	−13.6464	−0.450643
$918$	26.8365	0.885735
$919$	26.9365	0.888554	0.444277	−	0.895889i	$-0.353461\pi$
$919$	26.9365	0.888554	0.444277	+	0.895889i	$0.353461\pi$
$920$	0	0
$921$	18.4614	0.608324
$922$	42.5140	1.40012
$923$	−13.6514	−0.449341
$924$	−17.3899	−0.572087
$925$	0	0
$926$	−6.88764	−0.226342
$927$	34.0270	1.11759
$928$	65.3214	2.14428
$929$	8.55142	0.280563	0.140281	−	0.990112i	$-0.455199\pi$
$929$	8.55142	0.280563	0.140281	+	0.990112i	$0.455199\pi$
$930$	0	0
$931$	−3.30506	−0.108319
$932$	114.973	3.76608
$933$	14.8782	0.487090
$934$	−9.55366	−0.312605
$935$	0	0
$936$	106.608	3.48458
$937$	−51.7864	−1.69179	−0.845895	−	0.533350i	$-0.820933\pi$
$937$	−51.7864	−1.69179	−0.845895	+	0.533350i	$0.820933\pi$
$938$	5.04247	0.164643
$939$	−5.80196	−0.189340
$940$	0	0
$941$	34.0316	1.10940	0.554699	−	0.832051i	$-0.312834\pi$
$941$	34.0316	1.10940	0.554699	+	0.832051i	$0.312834\pi$
$942$	−29.4394	−0.959188
$943$	−12.2786	−0.399845
$944$	−17.8039	−0.579466
$945$	0	0
$946$	−61.1746	−1.98896
$947$	8.00544	0.260142	0.130071	−	0.991505i	$-0.458479\pi$
$947$	8.00544	0.260142	0.130071	+	0.991505i	$0.458479\pi$
$948$	3.17967	0.103271
$949$	−46.7544	−1.51771
$950$	0	0
$951$	12.6778	0.411107
$952$	−25.8974	−0.839340
$953$	2.48170	0.0803902	0.0401951	−	0.999192i	$-0.487202\pi$
$953$	2.48170	0.0803902	0.0401951	+	0.999192i	$0.487202\pi$
$954$	−37.0049	−1.19808
$955$	0	0
$956$	84.9635	2.74792
$957$	16.8336	0.544153
$958$	−101.324	−3.27363
$959$	21.5543	0.696023
$960$	0	0
$961$	−30.3078	−0.977672
$962$	94.6075	3.05027
$963$	−32.3809	−1.04346
$964$	−61.5408	−1.98210
$965$	0	0
$966$	1.45103	0.0466861
$967$	−26.5215	−0.852873	−0.426437	−	0.904517i	$-0.640231\pi$
$967$	−26.5215	−0.852873	−0.426437	+	0.904517i	$0.640231\pi$
$968$	232.056	7.45857
$969$	5.87588	0.188761
$970$	0	0
$971$	−38.2561	−1.22770	−0.613848	−	0.789424i	$-0.710379\pi$
$971$	−38.2561	−1.22770	−0.613848	+	0.789424i	$0.710379\pi$
$972$	−64.5209	−2.06951
$973$	−3.88467	−0.124537
$974$	−68.2291	−2.18620
$975$	0	0
$976$	−42.7152	−1.36728
$977$	16.5433	0.529266	0.264633	−	0.964349i	$-0.414749\pi$
$977$	16.5433	0.529266	0.264633	+	0.964349i	$0.414749\pi$
$978$	−32.6565	−1.04424
$979$	−56.9521	−1.82020
$980$	0	0
$981$	−4.80287	−0.153344
$982$	−63.0577	−2.01225
$983$	−1.61279	−0.0514399	−0.0257200	−	0.999669i	$-0.508188\pi$
$983$	−1.61279	−0.0514399	−0.0257200	+	0.999669i	$0.508188\pi$
$984$	53.6930	1.71167
$985$	0	0
$986$	41.7058	1.32818
$987$	−4.84592	−0.154247
$988$	81.9830	2.60823
$989$	3.64888	0.116028
$990$	0	0
$991$	−53.6963	−1.70572	−0.852860	−	0.522140i	$-0.825134\pi$
$991$	−53.6963	−1.70572	−0.852860	+	0.522140i	$0.825134\pi$
$992$	−11.1977	−0.355527
$993$	11.5927	0.367883
$994$	−7.30737	−0.231776
$995$	0	0
$996$	43.6467	1.38300
$997$	11.8957	0.376739	0.188370	−	0.982098i	$-0.439680\pi$
$997$	11.8957	0.376739	0.188370	+	0.982098i	$0.439680\pi$
$998$	99.8867	3.16186
$999$	−22.5490	−0.713419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.ba.1.14	✓	14
5.4	even	2		4025.2.a.bb.1.1	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4025.2.a.ba.1.14	✓	14	1.1	even	1	trivial
4025.2.a.bb.1.1	yes	14	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+2.64833 q^{2} -0.547903 q^{3} +5.01366 q^{4} -1.45103 q^{6} -1.00000 q^{7} +7.98118 q^{8} -2.69980 q^{9} +O(q^{10})\)	\(q+2.64833 q^{2} -0.547903 q^{3} +5.01366 q^{4} -1.45103 q^{6} -1.00000 q^{7} +7.98118 q^{8} -2.69980 q^{9} -6.33051 q^{11} -2.74700 q^{12} -4.94753 q^{13} -2.64833 q^{14} +11.1095 q^{16} +3.24481 q^{17} -7.14997 q^{18} -3.30506 q^{19} +0.547903 q^{21} -16.7653 q^{22} +1.00000 q^{23} -4.37291 q^{24} -13.1027 q^{26} +3.12294 q^{27} -5.01366 q^{28} +4.85327 q^{29} -0.831969 q^{31} +13.4593 q^{32} +3.46851 q^{33} +8.59334 q^{34} -13.5359 q^{36} -7.22045 q^{37} -8.75291 q^{38} +2.71077 q^{39} -12.2786 q^{41} +1.45103 q^{42} +3.64888 q^{43} -31.7391 q^{44} +2.64833 q^{46} -8.84448 q^{47} -6.08692 q^{48} +1.00000 q^{49} -1.77784 q^{51} -24.8053 q^{52} +5.17553 q^{53} +8.27058 q^{54} -7.98118 q^{56} +1.81085 q^{57} +12.8531 q^{58} -1.60258 q^{59} -3.84493 q^{61} -2.20333 q^{62} +2.69980 q^{63} +13.4256 q^{64} +9.18576 q^{66} -1.90402 q^{67} +16.2684 q^{68} -0.547903 q^{69} +2.75923 q^{71} -21.5476 q^{72} +9.45004 q^{73} -19.1221 q^{74} -16.5705 q^{76} +6.33051 q^{77} +7.17902 q^{78} -1.15751 q^{79} +6.38834 q^{81} -32.5177 q^{82} -15.8888 q^{83} +2.74700 q^{84} +9.66345 q^{86} -2.65912 q^{87} -50.5250 q^{88} +8.99645 q^{89} +4.94753 q^{91} +5.01366 q^{92} +0.455838 q^{93} -23.4231 q^{94} -7.37437 q^{96} -10.5928 q^{97} +2.64833 q^{98} +17.0911 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 6 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 9 q^{8} + 18 q^{9}+O(q^{10}) \) 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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