LMFDB - Embedded newform 4025.2.a.x.1.5

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} + \cdots + 17 $ x^12 - 2x^11 - 14x^10 + 26x^9 + 71x^8 - 120x^7 - 162x^6 + 244x^5 + 170x^4 - 210x^3 - 81x^2 + 58*x + 17
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.23080$ 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)

$f(q)$	$=$	$q-1.23080 q^{2} +0.767488 q^{3} -0.485126 q^{4} -0.944626 q^{6} +1.00000 q^{7} +3.05870 q^{8} -2.41096 q^{9} +O(q^{10})$	\(q-1.23080 q^{2} +0.767488 q^{3} -0.485126 q^{4} -0.944626 q^{6} +1.00000 q^{7} +3.05870 q^{8} -2.41096 q^{9} +2.89133 q^{11} -0.372328 q^{12} -5.98987 q^{13} -1.23080 q^{14} -2.79440 q^{16} +3.74500 q^{17} +2.96742 q^{18} +3.96859 q^{19} +0.767488 q^{21} -3.55866 q^{22} -1.00000 q^{23} +2.34751 q^{24} +7.37234 q^{26} -4.15285 q^{27} -0.485126 q^{28} -5.11682 q^{29} -2.68931 q^{31} -2.67804 q^{32} +2.21906 q^{33} -4.60936 q^{34} +1.16962 q^{36} -0.781495 q^{37} -4.88455 q^{38} -4.59715 q^{39} -3.75841 q^{41} -0.944626 q^{42} +9.64575 q^{43} -1.40266 q^{44} +1.23080 q^{46} -6.15313 q^{47} -2.14467 q^{48} +1.00000 q^{49} +2.87424 q^{51} +2.90584 q^{52} +2.86672 q^{53} +5.11134 q^{54} +3.05870 q^{56} +3.04585 q^{57} +6.29779 q^{58} +5.12427 q^{59} -1.72146 q^{61} +3.31000 q^{62} -2.41096 q^{63} +8.88494 q^{64} -2.73123 q^{66} -6.58076 q^{67} -1.81680 q^{68} -0.767488 q^{69} -13.5418 q^{71} -7.37441 q^{72} +15.6308 q^{73} +0.961866 q^{74} -1.92527 q^{76} +2.89133 q^{77} +5.65819 q^{78} -3.72352 q^{79} +4.04562 q^{81} +4.62586 q^{82} -0.558554 q^{83} -0.372328 q^{84} -11.8720 q^{86} -3.92709 q^{87} +8.84372 q^{88} -8.00892 q^{89} -5.98987 q^{91} +0.485126 q^{92} -2.06401 q^{93} +7.57329 q^{94} -2.05536 q^{96} -12.4519 q^{97} -1.23080 q^{98} -6.97089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9	$ 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 12 q^{12} - 2 q^{13} - 2 q^{14} - 4 q^{16} + 8 q^{17} - 20 q^{18} - 26 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 22 q^{26} - 12 q^{27} + 8 q^{28} - 12 q^{29} - 50 q^{31} - 14 q^{32} - 4 q^{33} - 28 q^{34} - 18 q^{36} - 8 q^{37} + 4 q^{38} - 26 q^{39} - 4 q^{41} - 6 q^{42} - 26 q^{43} - 10 q^{44} + 2 q^{46} - 16 q^{47} + 40 q^{48} + 12 q^{49} - 32 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} - 6 q^{56} + 10 q^{57} + 18 q^{58} - 18 q^{59} + 8 q^{61} + 54 q^{62} + 8 q^{63} + 12 q^{64} - 2 q^{66} - 38 q^{67} + 36 q^{68} - 24 q^{71} - 18 q^{72} + 14 q^{73} + 36 q^{74} - 56 q^{76} - 8 q^{77} + 26 q^{78} - 44 q^{79} - 16 q^{81} + 44 q^{82} + 14 q^{83} + 12 q^{84} - 32 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} - 2 q^{91} - 8 q^{92} - 26 q^{93} + 18 q^{94} - 38 q^{96} + 4 q^{97} - 2 q^{98} - 56 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 12 * q^12 - 2 * q^13 - 2 * q^14 - 4 * q^16 + 8 * q^17 - 20 * q^18 - 26 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 22 * q^26 - 12 * q^27 + 8 * q^28 - 12 * q^29 - 50 * q^31 - 14 * q^32 - 4 * q^33 - 28 * q^34 - 18 * q^36 - 8 * q^37 + 4 * q^38 - 26 * q^39 - 4 * q^41 - 6 * q^42 - 26 * q^43 - 10 * q^44 + 2 * q^46 - 16 * q^47 + 40 * q^48 + 12 * q^49 - 32 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 - 6 * q^56 + 10 * q^57 + 18 * q^58 - 18 * q^59 + 8 * q^61 + 54 * q^62 + 8 * q^63 + 12 * q^64 - 2 * q^66 - 38 * q^67 + 36 * q^68 - 24 * q^71 - 18 * q^72 + 14 * q^73 + 36 * q^74 - 56 * q^76 - 8 * q^77 + 26 * q^78 - 44 * q^79 - 16 * q^81 + 44 * q^82 + 14 * q^83 + 12 * q^84 - 32 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 - 2 * q^91 - 8 * q^92 - 26 * q^93 + 18 * q^94 - 38 * q^96 + 4 * q^97 - 2 * q^98 - 56 * 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 $

$2$	−1.23080	−0.870309	−0.435154	−	0.900356i	$-0.643306\pi$
$2$	−1.23080	−0.870309	−0.435154	+	0.900356i	$0.643306\pi$
$3$	0.767488	0.443109	0.221555	−	0.975148i	$-0.428887\pi$
$3$	0.767488	0.443109	0.221555	+	0.975148i	$0.428887\pi$
$4$	−0.485126	−0.242563
$5$	0	0
$5$	0	0
$6$	−0.944626	−0.385642
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.05870	1.08141
$9$	−2.41096	−0.803654
$10$	0	0
$11$	2.89133	0.871770	0.435885	−	0.900002i	$-0.356435\pi$
$11$	2.89133	0.871770	0.435885	+	0.900002i	$0.356435\pi$
$12$	−0.372328	−0.107482
$13$	−5.98987	−1.66129	−0.830645	−	0.556802i	$-0.812028\pi$
$13$	−5.98987	−1.66129	−0.830645	+	0.556802i	$0.812028\pi$
$14$	−1.23080	−0.328946
$15$	0	0
$16$	−2.79440	−0.698600
$17$	3.74500	0.908296	0.454148	−	0.890926i	$-0.349944\pi$
$17$	3.74500	0.908296	0.454148	+	0.890926i	$0.349944\pi$
$18$	2.96742	0.699427
$19$	3.96859	0.910457	0.455229	−	0.890375i	$-0.349558\pi$
$19$	3.96859	0.910457	0.455229	+	0.890375i	$0.349558\pi$
$20$	0	0
$21$	0.767488	0.167480
$22$	−3.55866	−0.758709
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.34751	0.479184
$25$	0	0
$26$	7.37234	1.44584
$27$	−4.15285	−0.799216
$28$	−0.485126	−0.0916801
$29$	−5.11682	−0.950169	−0.475084	−	0.879940i	$-0.657582\pi$
$29$	−5.11682	−0.950169	−0.475084	+	0.879940i	$0.657582\pi$
$30$	0	0
$31$	−2.68931	−0.483013	−0.241507	−	0.970399i	$-0.577642\pi$
$31$	−2.68931	−0.483013	−0.241507	+	0.970399i	$0.577642\pi$
$32$	−2.67804	−0.473415
$33$	2.21906	0.386289
$34$	−4.60936	−0.790498
$35$	0	0
$36$	1.16962	0.194937
$37$	−0.781495	−0.128477	−0.0642385	−	0.997935i	$-0.520462\pi$
$37$	−0.781495	−0.128477	−0.0642385	+	0.997935i	$0.520462\pi$
$38$	−4.88455	−0.792379
$39$	−4.59715	−0.736134
$40$	0	0
$41$	−3.75841	−0.586965	−0.293483	−	0.955964i	$-0.594814\pi$
$41$	−3.75841	−0.586965	−0.293483	+	0.955964i	$0.594814\pi$
$42$	−0.944626	−0.145759
$43$	9.64575	1.47096	0.735481	−	0.677545i	$-0.236956\pi$
$43$	9.64575	1.47096	0.735481	+	0.677545i	$0.236956\pi$
$44$	−1.40266	−0.211459
$45$	0	0
$46$	1.23080	0.181472
$47$	−6.15313	−0.897527	−0.448763	−	0.893651i	$-0.648135\pi$
$47$	−6.15313	−0.897527	−0.448763	+	0.893651i	$0.648135\pi$
$48$	−2.14467	−0.309556
$49$	1.00000	0.142857
$50$	0	0
$51$	2.87424	0.402475
$52$	2.90584	0.402967
$53$	2.86672	0.393774	0.196887	−	0.980426i	$-0.436917\pi$
$53$	2.86672	0.393774	0.196887	+	0.980426i	$0.436917\pi$
$54$	5.11134	0.695565
$55$	0	0
$56$	3.05870	0.408736
$57$	3.04585	0.403432
$58$	6.29779	0.826940
$59$	5.12427	0.667124	0.333562	−	0.942728i	$-0.391749\pi$
$59$	5.12427	0.667124	0.333562	+	0.942728i	$0.391749\pi$
$60$	0	0
$61$	−1.72146	−0.220410	−0.110205	−	0.993909i	$-0.535151\pi$
$61$	−1.72146	−0.220410	−0.110205	+	0.993909i	$0.535151\pi$
$62$	3.31000	0.420371
$63$	−2.41096	−0.303753
$64$	8.88494	1.11062
$65$	0	0
$66$	−2.73123	−0.336191
$67$	−6.58076	−0.803968	−0.401984	−	0.915647i	$-0.631679\pi$
$67$	−6.58076	−0.803968	−0.401984	+	0.915647i	$0.631679\pi$
$68$	−1.81680	−0.220319
$69$	−0.767488	−0.0923947
$70$	0	0
$71$	−13.5418	−1.60712	−0.803560	−	0.595224i	$-0.797064\pi$
$71$	−13.5418	−1.60712	−0.803560	+	0.595224i	$0.797064\pi$
$72$	−7.37441	−0.869082
$73$	15.6308	1.82944	0.914721	−	0.404086i	$-0.132410\pi$
$73$	15.6308	1.82944	0.914721	+	0.404086i	$0.132410\pi$
$74$	0.961866	0.111815
$75$	0	0
$76$	−1.92527	−0.220843
$77$	2.89133	0.329498
$78$	5.65819	0.640663
$79$	−3.72352	−0.418929	−0.209465	−	0.977816i	$-0.567172\pi$
$79$	−3.72352	−0.418929	−0.209465	+	0.977816i	$0.567172\pi$
$80$	0	0
$81$	4.04562	0.449514
$82$	4.62586	0.510841
$83$	−0.558554	−0.0613092	−0.0306546	−	0.999530i	$-0.509759\pi$
$83$	−0.558554	−0.0613092	−0.0306546	+	0.999530i	$0.509759\pi$
$84$	−0.372328	−0.0406243
$85$	0	0
$86$	−11.8720	−1.28019
$87$	−3.92709	−0.421029
$88$	8.84372	0.942743
$89$	−8.00892	−0.848944	−0.424472	−	0.905441i	$-0.639540\pi$
$89$	−8.00892	−0.848944	−0.424472	+	0.905441i	$0.639540\pi$
$90$	0	0
$91$	−5.98987	−0.627909
$92$	0.485126	0.0505779
$93$	−2.06401	−0.214028
$94$	7.57329	0.781125
$95$	0	0
$96$	−2.05536	−0.209775
$97$	−12.4519	−1.26430	−0.632150	−	0.774846i	$-0.717828\pi$
$97$	−12.4519	−1.26430	−0.632150	+	0.774846i	$0.717828\pi$
$98$	−1.23080	−0.124330
$99$	−6.97089	−0.700601
$100$	0	0
$101$	−19.4640	−1.93674	−0.968371	−	0.249513i	$-0.919729\pi$
$101$	−19.4640	−1.93674	−0.968371	+	0.249513i	$0.919729\pi$
$102$	−3.53763	−0.350277
$103$	10.2504	1.01000	0.504999	−	0.863120i	$-0.331493\pi$
$103$	10.2504	1.01000	0.504999	+	0.863120i	$0.331493\pi$
$104$	−18.3212	−1.79654
$105$	0	0
$106$	−3.52837	−0.342705
$107$	8.13181	0.786132	0.393066	−	0.919510i	$-0.371414\pi$
$107$	8.13181	0.786132	0.393066	+	0.919510i	$0.371414\pi$
$108$	2.01465	0.193860
$109$	−11.2492	−1.07748	−0.538741	−	0.842471i	$-0.681100\pi$
$109$	−11.2492	−1.07748	−0.538741	+	0.842471i	$0.681100\pi$
$110$	0	0
$111$	−0.599788	−0.0569294
$112$	−2.79440	−0.264046
$113$	−0.833318	−0.0783920	−0.0391960	−	0.999232i	$-0.512480\pi$
$113$	−0.833318	−0.0783920	−0.0391960	+	0.999232i	$0.512480\pi$
$114$	−3.74884	−0.351111
$115$	0	0
$116$	2.48230	0.230476
$117$	14.4413	1.33510
$118$	−6.30697	−0.580604
$119$	3.74500	0.343304
$120$	0	0
$121$	−2.64019	−0.240018
$122$	2.11877	0.191825
$123$	−2.88454	−0.260090
$124$	1.30465	0.117161
$125$	0	0
$126$	2.96742	0.264359
$127$	14.6167	1.29702	0.648510	−	0.761206i	$-0.275392\pi$
$127$	14.6167	1.29702	0.648510	+	0.761206i	$0.275392\pi$
$128$	−5.57953	−0.493165
$129$	7.40300	0.651798
$130$	0	0
$131$	17.3804	1.51853	0.759267	−	0.650780i	$-0.225558\pi$
$131$	17.3804	1.51853	0.759267	+	0.650780i	$0.225558\pi$
$132$	−1.07652	−0.0936994
$133$	3.96859	0.344121
$134$	8.09961	0.699700
$135$	0	0
$136$	11.4548	0.982243
$137$	−6.15314	−0.525698	−0.262849	−	0.964837i	$-0.584662\pi$
$137$	−6.15314	−0.525698	−0.262849	+	0.964837i	$0.584662\pi$
$138$	0.944626	0.0804119
$139$	−7.94813	−0.674152	−0.337076	−	0.941477i	$-0.609438\pi$
$139$	−7.94813	−0.674152	−0.337076	+	0.941477i	$0.609438\pi$
$140$	0	0
$141$	−4.72246	−0.397703
$142$	16.6673	1.39869
$143$	−17.3187	−1.44826
$144$	6.73720	0.561433
$145$	0	0
$146$	−19.2384	−1.59218
$147$	0.767488	0.0633013
$148$	0.379123	0.0311638
$149$	−18.3219	−1.50099	−0.750496	−	0.660876i	$-0.770185\pi$
$149$	−18.3219	−1.50099	−0.750496	+	0.660876i	$0.770185\pi$
$150$	0	0
$151$	−15.2382	−1.24007	−0.620033	−	0.784576i	$-0.712881\pi$
$151$	−15.2382	−1.24007	−0.620033	+	0.784576i	$0.712881\pi$
$152$	12.1387	0.984581
$153$	−9.02906	−0.729956
$154$	−3.55866	−0.286765
$155$	0	0
$156$	2.23020	0.178559
$157$	7.09858	0.566528	0.283264	−	0.959042i	$-0.408583\pi$
$157$	7.09858	0.566528	0.283264	+	0.959042i	$0.408583\pi$
$158$	4.58292	0.364598
$159$	2.20017	0.174485
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−4.97936	−0.391216
$163$	9.44101	0.739477	0.369739	−	0.929136i	$-0.379447\pi$
$163$	9.44101	0.739477	0.369739	+	0.929136i	$0.379447\pi$
$164$	1.82330	0.142376
$165$	0	0
$166$	0.687469	0.0533579
$167$	15.1442	1.17189	0.585945	−	0.810351i	$-0.300723\pi$
$167$	15.1442	1.17189	0.585945	+	0.810351i	$0.300723\pi$
$168$	2.34751	0.181115
$169$	22.8785	1.75989
$170$	0	0
$171$	−9.56812	−0.731693
$172$	−4.67940	−0.356801
$173$	−19.2225	−1.46146	−0.730730	−	0.682667i	$-0.760820\pi$
$173$	−19.2225	−1.46146	−0.730730	+	0.682667i	$0.760820\pi$
$174$	4.83348	0.366425
$175$	0	0
$176$	−8.07955	−0.609019
$177$	3.93282	0.295609
$178$	9.85740	0.738843
$179$	20.2975	1.51711	0.758554	−	0.651610i	$-0.225906\pi$
$179$	20.2975	1.51711	0.758554	+	0.651610i	$0.225906\pi$
$180$	0	0
$181$	−14.0681	−1.04568	−0.522838	−	0.852432i	$-0.675127\pi$
$181$	−14.0681	−1.04568	−0.522838	+	0.852432i	$0.675127\pi$
$182$	7.37234	0.546474
$183$	−1.32120	−0.0976658
$184$	−3.05870	−0.225490
$185$	0	0
$186$	2.54039	0.186270
$187$	10.8280	0.791825
$188$	2.98504	0.217707
$189$	−4.15285	−0.302075
$190$	0	0
$191$	25.5272	1.84708	0.923540	−	0.383501i	$-0.125282\pi$
$191$	25.5272	1.84708	0.923540	+	0.383501i	$0.125282\pi$
$192$	6.81909	0.492125
$193$	−20.2638	−1.45862	−0.729309	−	0.684184i	$-0.760158\pi$
$193$	−20.2638	−1.45862	−0.729309	+	0.684184i	$0.760158\pi$
$194$	15.3259	1.10033
$195$	0	0
$196$	−0.485126	−0.0346518
$197$	−18.5817	−1.32389	−0.661947	−	0.749551i	$-0.730270\pi$
$197$	−18.5817	−1.32389	−0.661947	+	0.749551i	$0.730270\pi$
$198$	8.57979	0.609739
$199$	−20.1872	−1.43103	−0.715517	−	0.698595i	$-0.753809\pi$
$199$	−20.1872	−1.43103	−0.715517	+	0.698595i	$0.753809\pi$
$200$	0	0
$201$	−5.05065	−0.356246
$202$	23.9564	1.68556
$203$	−5.11682	−0.359130
$204$	−1.39437	−0.0976254
$205$	0	0
$206$	−12.6162	−0.879010
$207$	2.41096	0.167573
$208$	16.7381	1.16058
$209$	11.4745	0.793709
$210$	0	0
$211$	−17.7695	−1.22330	−0.611651	−	0.791128i	$-0.709494\pi$
$211$	−17.7695	−1.22330	−0.611651	+	0.791128i	$0.709494\pi$
$212$	−1.39072	−0.0955151
$213$	−10.3932	−0.712130
$214$	−10.0087	−0.684177
$215$	0	0
$216$	−12.7023	−0.864283
$217$	−2.68931	−0.182562
$218$	13.8456	0.937742
$219$	11.9964	0.810643
$220$	0	0
$221$	−22.4321	−1.50894
$222$	0.738221	0.0495461
$223$	8.45760	0.566363	0.283181	−	0.959066i	$-0.408610\pi$
$223$	8.45760	0.566363	0.283181	+	0.959066i	$0.408610\pi$
$224$	−2.67804	−0.178934
$225$	0	0
$226$	1.02565	0.0682252
$227$	−2.09203	−0.138853	−0.0694263	−	0.997587i	$-0.522117\pi$
$227$	−2.09203	−0.138853	−0.0694263	+	0.997587i	$0.522117\pi$
$228$	−1.47762	−0.0978577
$229$	−17.0381	−1.12591	−0.562956	−	0.826487i	$-0.690336\pi$
$229$	−17.0381	−1.12591	−0.562956	+	0.826487i	$0.690336\pi$
$230$	0	0
$231$	2.21906	0.146004
$232$	−15.6508	−1.02753
$233$	−9.57962	−0.627582	−0.313791	−	0.949492i	$-0.601599\pi$
$233$	−9.57962	−0.627582	−0.313791	+	0.949492i	$0.601599\pi$
$234$	−17.7744	−1.16195
$235$	0	0
$236$	−2.48592	−0.161819
$237$	−2.85776	−0.185631
$238$	−4.60936	−0.298780
$239$	−12.6039	−0.815277	−0.407639	−	0.913143i	$-0.633648\pi$
$239$	−12.6039	−0.815277	−0.407639	+	0.913143i	$0.633648\pi$
$240$	0	0
$241$	−20.0405	−1.29092	−0.645460	−	0.763794i	$-0.723334\pi$
$241$	−20.0405	−1.29092	−0.645460	+	0.763794i	$0.723334\pi$
$242$	3.24956	0.208889
$243$	15.5635	0.998400
$244$	0.835123	0.0534633
$245$	0	0
$246$	3.55029	0.226358
$247$	−23.7713	−1.51253
$248$	−8.22577	−0.522337
$249$	−0.428683	−0.0271667
$250$	0	0
$251$	−1.21018	−0.0763860	−0.0381930	−	0.999270i	$-0.512160\pi$
$251$	−1.21018	−0.0763860	−0.0381930	+	0.999270i	$0.512160\pi$
$252$	1.16962	0.0736791
$253$	−2.89133	−0.181777
$254$	−17.9902	−1.12881
$255$	0	0
$256$	−10.9026	−0.681412
$257$	22.7652	1.42005	0.710027	−	0.704174i	$-0.248683\pi$
$257$	22.7652	1.42005	0.710027	+	0.704174i	$0.248683\pi$
$258$	−9.11163	−0.567265
$259$	−0.781495	−0.0485598
$260$	0	0
$261$	12.3364	0.763607
$262$	−21.3918	−1.32159
$263$	−18.7574	−1.15663	−0.578317	−	0.815812i	$-0.696290\pi$
$263$	−18.7574	−1.15663	−0.578317	+	0.815812i	$0.696290\pi$
$264$	6.78745	0.417738
$265$	0	0
$266$	−4.88455	−0.299491
$267$	−6.14675	−0.376175
$268$	3.19250	0.195013
$269$	5.50465	0.335624	0.167812	−	0.985819i	$-0.446330\pi$
$269$	5.50465	0.335624	0.167812	+	0.985819i	$0.446330\pi$
$270$	0	0
$271$	31.5759	1.91810	0.959051	−	0.283234i	$-0.0914072\pi$
$271$	31.5759	1.91810	0.959051	+	0.283234i	$0.0914072\pi$
$272$	−10.4650	−0.634536
$273$	−4.59715	−0.278232
$274$	7.57330	0.457520
$275$	0	0
$276$	0.372328	0.0224115
$277$	−10.4707	−0.629124	−0.314562	−	0.949237i	$-0.601858\pi$
$277$	−10.4707	−0.629124	−0.314562	+	0.949237i	$0.601858\pi$
$278$	9.78258	0.586720
$279$	6.48381	0.388176
$280$	0	0
$281$	−3.88701	−0.231880	−0.115940	−	0.993256i	$-0.536988\pi$
$281$	−3.88701	−0.231880	−0.115940	+	0.993256i	$0.536988\pi$
$282$	5.81241	0.346124
$283$	3.50559	0.208386	0.104193	−	0.994557i	$-0.466774\pi$
$283$	3.50559	0.208386	0.104193	+	0.994557i	$0.466774\pi$
$284$	6.56949	0.389828
$285$	0	0
$286$	21.3159	1.26044
$287$	−3.75841	−0.221852
$288$	6.45665	0.380462
$289$	−2.97497	−0.174998
$290$	0	0
$291$	−9.55670	−0.560224
$292$	−7.58288	−0.443755
$293$	−7.54753	−0.440931	−0.220466	−	0.975395i	$-0.570758\pi$
$293$	−7.54753	−0.440931	−0.220466	+	0.975395i	$0.570758\pi$
$294$	−0.944626	−0.0550917
$295$	0	0
$296$	−2.39036	−0.138937
$297$	−12.0073	−0.696732
$298$	22.5507	1.30633
$299$	5.98987	0.346403
$300$	0	0
$301$	9.64575	0.555972
$302$	18.7552	1.07924
$303$	−14.9384	−0.858189
$304$	−11.0898	−0.636046
$305$	0	0
$306$	11.1130	0.635287
$307$	3.40389	0.194270	0.0971351	−	0.995271i	$-0.469032\pi$
$307$	3.40389	0.194270	0.0971351	+	0.995271i	$0.469032\pi$
$308$	−1.40266	−0.0799240
$309$	7.86703	0.447540
$310$	0	0
$311$	−9.36739	−0.531176	−0.265588	−	0.964087i	$-0.585566\pi$
$311$	−9.36739	−0.531176	−0.265588	+	0.964087i	$0.585566\pi$
$312$	−14.0613	−0.796065
$313$	−14.8907	−0.841672	−0.420836	−	0.907137i	$-0.638263\pi$
$313$	−14.8907	−0.841672	−0.420836	+	0.907137i	$0.638263\pi$
$314$	−8.73694	−0.493054
$315$	0	0
$316$	1.80638	0.101617
$317$	−18.1816	−1.02118	−0.510591	−	0.859824i	$-0.670573\pi$
$317$	−18.1816	−1.02118	−0.510591	+	0.859824i	$0.670573\pi$
$318$	−2.70798	−0.151856
$319$	−14.7944	−0.828328
$320$	0	0
$321$	6.24107	0.348342
$322$	1.23080	0.0685899
$323$	14.8624	0.826965
$324$	−1.96264	−0.109035
$325$	0	0
$326$	−11.6200	−0.643573
$327$	−8.63366	−0.477442
$328$	−11.4958	−0.634752
$329$	−6.15313	−0.339233
$330$	0	0
$331$	−28.6377	−1.57407	−0.787036	−	0.616907i	$-0.788385\pi$
$331$	−28.6377	−1.57407	−0.787036	+	0.616907i	$0.788385\pi$
$332$	0.270969	0.0148713
$333$	1.88416	0.103251
$334$	−18.6395	−1.01991
$335$	0	0
$336$	−2.14467	−0.117001
$337$	−27.8674	−1.51803	−0.759016	−	0.651072i	$-0.774319\pi$
$337$	−27.8674	−1.51803	−0.759016	+	0.651072i	$0.774319\pi$
$338$	−28.1589	−1.53164
$339$	−0.639562	−0.0347362
$340$	0	0
$341$	−7.77568	−0.421076
$342$	11.7765	0.636798
$343$	1.00000	0.0539949
$344$	29.5034	1.59072
$345$	0	0
$346$	23.6591	1.27192
$347$	19.0625	1.02333	0.511665	−	0.859185i	$-0.329029\pi$
$347$	19.0625	1.02333	0.511665	+	0.859185i	$0.329029\pi$
$348$	1.90513	0.102126
$349$	−0.155087	−0.00830162	−0.00415081	−	0.999991i	$-0.501321\pi$
$349$	−0.155087	−0.00830162	−0.00415081	+	0.999991i	$0.501321\pi$
$350$	0	0
$351$	24.8750	1.32773
$352$	−7.74311	−0.412709
$353$	−12.9217	−0.687754	−0.343877	−	0.939015i	$-0.611740\pi$
$353$	−12.9217	−0.687754	−0.343877	+	0.939015i	$0.611740\pi$
$354$	−4.84052	−0.257271
$355$	0	0
$356$	3.88533	0.205922
$357$	2.87424	0.152121
$358$	−24.9822	−1.32035
$359$	18.7962	0.992024	0.496012	−	0.868316i	$-0.334797\pi$
$359$	18.7962	0.992024	0.496012	+	0.868316i	$0.334797\pi$
$360$	0	0
$361$	−3.25028	−0.171067
$362$	17.3151	0.910061
$363$	−2.02632	−0.106354
$364$	2.90584	0.152307
$365$	0	0
$366$	1.62613	0.0849994
$367$	−33.1027	−1.72795	−0.863973	−	0.503539i	$-0.832031\pi$
$367$	−33.1027	−1.72795	−0.863973	+	0.503539i	$0.832031\pi$
$368$	2.79440	0.145668
$369$	9.06139	0.471717
$370$	0	0
$371$	2.86672	0.148833
$372$	1.00130	0.0519152
$373$	−28.0685	−1.45333	−0.726665	−	0.686992i	$-0.758931\pi$
$373$	−28.0685	−1.45333	−0.726665	+	0.686992i	$0.758931\pi$
$374$	−13.3272	−0.689132
$375$	0	0
$376$	−18.8206	−0.970597
$377$	30.6491	1.57851
$378$	5.11134	0.262899
$379$	7.52475	0.386520	0.193260	−	0.981148i	$-0.438094\pi$
$379$	7.52475	0.386520	0.193260	+	0.981148i	$0.438094\pi$
$380$	0	0
$381$	11.2181	0.574722
$382$	−31.4189	−1.60753
$383$	−12.0417	−0.615304	−0.307652	−	0.951499i	$-0.599543\pi$
$383$	−12.0417	−0.615304	−0.307652	+	0.951499i	$0.599543\pi$
$384$	−4.28222	−0.218526
$385$	0	0
$386$	24.9407	1.26945
$387$	−23.2555	−1.18215
$388$	6.04075	0.306672
$389$	−7.41719	−0.376066	−0.188033	−	0.982163i	$-0.560211\pi$
$389$	−7.41719	−0.376066	−0.188033	+	0.982163i	$0.560211\pi$
$390$	0	0
$391$	−3.74500	−0.189393
$392$	3.05870	0.154488
$393$	13.3393	0.672876
$394$	22.8704	1.15220
$395$	0	0
$396$	3.38176	0.169940
$397$	10.9981	0.551978	0.275989	−	0.961161i	$-0.410995\pi$
$397$	10.9981	0.551978	0.275989	+	0.961161i	$0.410995\pi$
$398$	24.8465	1.24544
$399$	3.04585	0.152483
$400$	0	0
$401$	28.7534	1.43588	0.717938	−	0.696107i	$-0.245086\pi$
$401$	28.7534	1.43588	0.717938	+	0.696107i	$0.245086\pi$
$402$	6.21636	0.310044
$403$	16.1086	0.802426
$404$	9.44250	0.469782
$405$	0	0
$406$	6.29779	0.312554
$407$	−2.25956	−0.112002
$408$	8.79144	0.435241
$409$	−19.0125	−0.940108	−0.470054	−	0.882638i	$-0.655766\pi$
$409$	−19.0125	−0.940108	−0.470054	+	0.882638i	$0.655766\pi$
$410$	0	0
$411$	−4.72246	−0.232942
$412$	−4.97271	−0.244988
$413$	5.12427	0.252149
$414$	−2.96742	−0.145841
$415$	0	0
$416$	16.0411	0.786480
$417$	−6.10010	−0.298723
$418$	−14.1229	−0.690772
$419$	−27.0953	−1.32369	−0.661846	−	0.749640i	$-0.730227\pi$
$419$	−27.0953	−1.32369	−0.661846	+	0.749640i	$0.730227\pi$
$420$	0	0
$421$	−14.9265	−0.727472	−0.363736	−	0.931502i	$-0.618499\pi$
$421$	−14.9265	−0.727472	−0.363736	+	0.931502i	$0.618499\pi$
$422$	21.8707	1.06465
$423$	14.8350	0.721301
$424$	8.76844	0.425833
$425$	0	0
$426$	12.7920	0.619773
$427$	−1.72146	−0.0833072
$428$	−3.94495	−0.190686
$429$	−13.2919	−0.641739
$430$	0	0
$431$	−9.47468	−0.456379	−0.228190	−	0.973617i	$-0.573281\pi$
$431$	−9.47468	−0.456379	−0.228190	+	0.973617i	$0.573281\pi$
$432$	11.6047	0.558333
$433$	33.0972	1.59055	0.795275	−	0.606249i	$-0.207327\pi$
$433$	33.0972	1.59055	0.795275	+	0.606249i	$0.207327\pi$
$434$	3.31000	0.158885
$435$	0	0
$436$	5.45730	0.261357
$437$	−3.96859	−0.189843
$438$	−14.7652	−0.705510
$439$	3.47236	0.165727	0.0828633	−	0.996561i	$-0.473594\pi$
$439$	3.47236	0.165727	0.0828633	+	0.996561i	$0.473594\pi$
$440$	0	0
$441$	−2.41096	−0.114808
$442$	27.6094	1.31325
$443$	9.01324	0.428232	0.214116	−	0.976808i	$-0.431313\pi$
$443$	9.01324	0.428232	0.214116	+	0.976808i	$0.431313\pi$
$444$	0.290973	0.0138090
$445$	0	0
$446$	−10.4096	−0.492910
$447$	−14.0619	−0.665103
$448$	8.88494	0.419774
$449$	−2.25213	−0.106284	−0.0531422	−	0.998587i	$-0.516924\pi$
$449$	−2.25213	−0.106284	−0.0531422	+	0.998587i	$0.516924\pi$
$450$	0	0
$451$	−10.8668	−0.511698
$452$	0.404264	0.0190150
$453$	−11.6951	−0.549485
$454$	2.57487	0.120845
$455$	0	0
$456$	9.31633	0.436277
$457$	−20.5822	−0.962795	−0.481398	−	0.876502i	$-0.659871\pi$
$457$	−20.5822	−0.962795	−0.481398	+	0.876502i	$0.659871\pi$
$458$	20.9706	0.979891
$459$	−15.5524	−0.725925
$460$	0	0
$461$	−27.1061	−1.26246	−0.631229	−	0.775597i	$-0.717449\pi$
$461$	−27.1061	−1.26246	−0.631229	+	0.775597i	$0.717449\pi$
$462$	−2.73123	−0.127068
$463$	7.94045	0.369024	0.184512	−	0.982830i	$-0.440930\pi$
$463$	7.94045	0.369024	0.184512	+	0.982830i	$0.440930\pi$
$464$	14.2984	0.663788
$465$	0	0
$466$	11.7906	0.546190
$467$	23.9987	1.11053	0.555264	−	0.831674i	$-0.312617\pi$
$467$	23.9987	1.11053	0.555264	+	0.831674i	$0.312617\pi$
$468$	−7.00587	−0.323846
$469$	−6.58076	−0.303871
$470$	0	0
$471$	5.44807	0.251034
$472$	15.6736	0.721436
$473$	27.8891	1.28234
$474$	3.51734	0.161557
$475$	0	0
$476$	−1.81680	−0.0832727
$477$	−6.91156	−0.316458
$478$	15.5129	0.709543
$479$	21.0540	0.961984	0.480992	−	0.876725i	$-0.340277\pi$
$479$	21.0540	0.961984	0.480992	+	0.876725i	$0.340277\pi$
$480$	0	0
$481$	4.68105	0.213438
$482$	24.6658	1.12350
$483$	−0.767488	−0.0349219
$484$	1.28083	0.0582194
$485$	0	0
$486$	−19.1556	−0.868916
$487$	10.7545	0.487333	0.243666	−	0.969859i	$-0.421650\pi$
$487$	10.7545	0.487333	0.243666	+	0.969859i	$0.421650\pi$
$488$	−5.26542	−0.238354
$489$	7.24587	0.327669
$490$	0	0
$491$	−21.1200	−0.953132	−0.476566	−	0.879139i	$-0.658119\pi$
$491$	−21.1200	−0.953132	−0.476566	+	0.879139i	$0.658119\pi$
$492$	1.39936	0.0630881
$493$	−19.1625	−0.863035
$494$	29.2578	1.31637
$495$	0	0
$496$	7.51500	0.337433
$497$	−13.5418	−0.607434
$498$	0.527624	0.0236434
$499$	−12.4894	−0.559104	−0.279552	−	0.960131i	$-0.590186\pi$
$499$	−12.4894	−0.559104	−0.279552	+	0.960131i	$0.590186\pi$
$500$	0	0
$501$	11.6230	0.519275
$502$	1.48950	0.0664794
$503$	−8.79383	−0.392097	−0.196049	−	0.980594i	$-0.562811\pi$
$503$	−8.79383	−0.392097	−0.196049	+	0.980594i	$0.562811\pi$
$504$	−7.37441	−0.328482
$505$	0	0
$506$	3.55866	0.158202
$507$	17.5590	0.779822
$508$	−7.09092	−0.314609
$509$	−25.5340	−1.13178	−0.565888	−	0.824482i	$-0.691467\pi$
$509$	−25.5340	−1.13178	−0.565888	+	0.824482i	$0.691467\pi$
$510$	0	0
$511$	15.6308	0.691464
$512$	24.5780	1.08620
$513$	−16.4810	−0.727652
$514$	−28.0195	−1.23589
$515$	0	0
$516$	−3.59138	−0.158102
$517$	−17.7908	−0.782436
$518$	0.961866	0.0422620
$519$	−14.7530	−0.647587
$520$	0	0
$521$	−7.62227	−0.333938	−0.166969	−	0.985962i	$-0.553398\pi$
$521$	−7.62227	−0.333938	−0.166969	+	0.985962i	$0.553398\pi$
$522$	−15.1837	−0.664574
$523$	5.49203	0.240150	0.120075	−	0.992765i	$-0.461687\pi$
$523$	5.49203	0.240150	0.120075	+	0.992765i	$0.461687\pi$
$524$	−8.43168	−0.368340
$525$	0	0
$526$	23.0867	1.00663
$527$	−10.0715	−0.438719
$528$	−6.20095	−0.269862
$529$	1.00000	0.0434783
$530$	0	0
$531$	−12.3544	−0.536137
$532$	−1.92527	−0.0834709
$533$	22.5124	0.975120
$534$	7.56543	0.327388
$535$	0	0
$536$	−20.1286	−0.869421
$537$	15.5781	0.672245
$538$	−6.77513	−0.292097
$539$	2.89133	0.124539
$540$	0	0
$541$	35.8577	1.54164	0.770821	−	0.637052i	$-0.219846\pi$
$541$	35.8577	1.54164	0.770821	+	0.637052i	$0.219846\pi$
$542$	−38.8637	−1.66934
$543$	−10.7971	−0.463349
$544$	−10.0293	−0.430001
$545$	0	0
$546$	5.65819	0.242148
$547$	−2.32908	−0.0995842	−0.0497921	−	0.998760i	$-0.515856\pi$
$547$	−2.32908	−0.0995842	−0.0497921	+	0.998760i	$0.515856\pi$
$548$	2.98505	0.127515
$549$	4.15037	0.177133
$550$	0	0
$551$	−20.3065	−0.865088
$552$	−2.34751	−0.0999169
$553$	−3.72352	−0.158340
$554$	12.8874	0.547532
$555$	0	0
$556$	3.85584	0.163524
$557$	34.7139	1.47087	0.735437	−	0.677593i	$-0.236977\pi$
$557$	34.7139	1.47087	0.735437	+	0.677593i	$0.236977\pi$
$558$	−7.98029	−0.337833
$559$	−57.7768	−2.44370
$560$	0	0
$561$	8.31040	0.350865
$562$	4.78415	0.201807
$563$	27.0364	1.13945	0.569723	−	0.821837i	$-0.307050\pi$
$563$	27.0364	1.13945	0.569723	+	0.821837i	$0.307050\pi$
$564$	2.29098	0.0964679
$565$	0	0
$566$	−4.31469	−0.181360
$567$	4.04562	0.169900
$568$	−41.4204	−1.73796
$569$	34.0755	1.42852	0.714260	−	0.699880i	$-0.246763\pi$
$569$	34.0755	1.42852	0.714260	+	0.699880i	$0.246763\pi$
$570$	0	0
$571$	−3.15405	−0.131993	−0.0659965	−	0.997820i	$-0.521023\pi$
$571$	−3.15405	−0.131993	−0.0659965	+	0.997820i	$0.521023\pi$
$572$	8.40175	0.351295
$573$	19.5918	0.818459
$574$	4.62586	0.193080
$575$	0	0
$576$	−21.4213	−0.892552
$577$	−25.6456	−1.06764	−0.533821	−	0.845598i	$-0.679244\pi$
$577$	−25.6456	−1.06764	−0.533821	+	0.845598i	$0.679244\pi$
$578$	3.66160	0.152302
$579$	−15.5522	−0.646328
$580$	0	0
$581$	−0.558554	−0.0231727
$582$	11.7624	0.487567
$583$	8.28865	0.343281
$584$	47.8098	1.97838
$585$	0	0
$586$	9.28951	0.383746
$587$	−4.89265	−0.201941	−0.100971	−	0.994889i	$-0.532195\pi$
$587$	−4.89265	−0.201941	−0.100971	+	0.994889i	$0.532195\pi$
$588$	−0.372328	−0.0153546
$589$	−10.6728	−0.439763
$590$	0	0
$591$	−14.2613	−0.586630
$592$	2.18381	0.0897541
$593$	7.29556	0.299593	0.149796	−	0.988717i	$-0.452138\pi$
$593$	7.29556	0.299593	0.149796	+	0.988717i	$0.452138\pi$
$594$	14.7786	0.606372
$595$	0	0
$596$	8.88844	0.364085
$597$	−15.4935	−0.634105
$598$	−7.37234	−0.301478
$599$	−13.8414	−0.565546	−0.282773	−	0.959187i	$-0.591254\pi$
$599$	−13.8414	−0.565546	−0.282773	+	0.959187i	$0.591254\pi$
$600$	0	0
$601$	−18.7356	−0.764242	−0.382121	−	0.924112i	$-0.624806\pi$
$601$	−18.7356	−0.764242	−0.382121	+	0.924112i	$0.624806\pi$
$602$	−11.8720	−0.483867
$603$	15.8660	0.646112
$604$	7.39243	0.300794
$605$	0	0
$606$	18.3862	0.746889
$607$	−5.10356	−0.207147	−0.103574	−	0.994622i	$-0.533028\pi$
$607$	−5.10356	−0.207147	−0.103574	+	0.994622i	$0.533028\pi$
$608$	−10.6281	−0.431024
$609$	−3.92709	−0.159134
$610$	0	0
$611$	36.8565	1.49105
$612$	4.38023	0.177060
$613$	−42.2725	−1.70737	−0.853684	−	0.520791i	$-0.825637\pi$
$613$	−42.2725	−1.70737	−0.853684	+	0.520791i	$0.825637\pi$
$614$	−4.18951	−0.169075
$615$	0	0
$616$	8.84372	0.356323
$617$	31.6837	1.27554	0.637769	−	0.770228i	$-0.279858\pi$
$617$	31.6837	1.27554	0.637769	+	0.770228i	$0.279858\pi$
$618$	−9.68276	−0.389498
$619$	−14.7816	−0.594123	−0.297062	−	0.954858i	$-0.596007\pi$
$619$	−14.7816	−0.594123	−0.297062	+	0.954858i	$0.596007\pi$
$620$	0	0
$621$	4.15285	0.166648
$622$	11.5294	0.462287
$623$	−8.00892	−0.320871
$624$	12.8463	0.514263
$625$	0	0
$626$	18.3275	0.732515
$627$	8.80656	0.351700
$628$	−3.44370	−0.137419
$629$	−2.92670	−0.116695
$630$	0	0
$631$	11.1856	0.445294	0.222647	−	0.974899i	$-0.428530\pi$
$631$	11.1856	0.445294	0.222647	+	0.974899i	$0.428530\pi$
$632$	−11.3891	−0.453035
$633$	−13.6379	−0.542056
$634$	22.3780	0.888744
$635$	0	0
$636$	−1.06736	−0.0423236
$637$	−5.98987	−0.237327
$638$	18.2090	0.720901
$639$	32.6489	1.29157
$640$	0	0
$641$	34.2835	1.35411	0.677057	−	0.735930i	$-0.263255\pi$
$641$	34.2835	1.35411	0.677057	+	0.735930i	$0.263255\pi$
$642$	−7.68152	−0.303165
$643$	−9.14558	−0.360666	−0.180333	−	0.983606i	$-0.557718\pi$
$643$	−9.14558	−0.360666	−0.180333	+	0.983606i	$0.557718\pi$
$644$	0.485126	0.0191166
$645$	0	0
$646$	−18.2927	−0.719715
$647$	−47.8465	−1.88104	−0.940521	−	0.339737i	$-0.889662\pi$
$647$	−47.8465	−1.88104	−0.940521	+	0.339737i	$0.889662\pi$
$648$	12.3743	0.486110
$649$	14.8160	0.581578
$650$	0	0
$651$	−2.06401	−0.0808949
$652$	−4.58008	−0.179370
$653$	−3.38063	−0.132294	−0.0661472	−	0.997810i	$-0.521071\pi$
$653$	−3.38063	−0.132294	−0.0661472	+	0.997810i	$0.521071\pi$
$654$	10.6263	0.415522
$655$	0	0
$656$	10.5025	0.410054
$657$	−37.6852	−1.47024
$658$	7.57329	0.295238
$659$	−21.8518	−0.851225	−0.425613	−	0.904905i	$-0.639941\pi$
$659$	−21.8518	−0.851225	−0.425613	+	0.904905i	$0.639941\pi$
$660$	0	0
$661$	−38.3381	−1.49118	−0.745589	−	0.666406i	$-0.767832\pi$
$661$	−38.3381	−1.49118	−0.745589	+	0.666406i	$0.767832\pi$
$662$	35.2474	1.36993
$663$	−17.2163	−0.668627
$664$	−1.70845	−0.0663006
$665$	0	0
$666$	−2.31902	−0.0898603
$667$	5.11682	0.198124
$668$	−7.34682	−0.284257
$669$	6.49111	0.250961
$670$	0	0
$671$	−4.97731	−0.192147
$672$	−2.05536	−0.0792874
$673$	−19.4719	−0.750588	−0.375294	−	0.926906i	$-0.622458\pi$
$673$	−19.4719	−0.750588	−0.375294	+	0.926906i	$0.622458\pi$
$674$	34.2992	1.32116
$675$	0	0
$676$	−11.0990	−0.426883
$677$	−22.2957	−0.856895	−0.428447	−	0.903567i	$-0.640939\pi$
$677$	−22.2957	−0.856895	−0.428447	+	0.903567i	$0.640939\pi$
$678$	0.787174	0.0302312
$679$	−12.4519	−0.477861
$680$	0	0
$681$	−1.60560	−0.0615269
$682$	9.57032	0.366467
$683$	−25.5929	−0.979284	−0.489642	−	0.871924i	$-0.662873\pi$
$683$	−25.5929	−0.979284	−0.489642	+	0.871924i	$0.662873\pi$
$684$	4.64174	0.177481
$685$	0	0
$686$	−1.23080	−0.0469923
$687$	−13.0766	−0.498902
$688$	−26.9541	−1.02762
$689$	−17.1713	−0.654174
$690$	0	0
$691$	−1.12405	−0.0427610	−0.0213805	−	0.999771i	$-0.506806\pi$
$691$	−1.12405	−0.0427610	−0.0213805	+	0.999771i	$0.506806\pi$
$692$	9.32533	0.354496
$693$	−6.97089	−0.264802
$694$	−23.4622	−0.890613
$695$	0	0
$696$	−12.0118	−0.455306
$697$	−14.0753	−0.533138
$698$	0.190881	0.00722497
$699$	−7.35224	−0.278087
$700$	0	0
$701$	20.7251	0.782776	0.391388	−	0.920226i	$-0.371995\pi$
$701$	20.7251	0.782776	0.391388	+	0.920226i	$0.371995\pi$
$702$	−30.6162	−1.15554
$703$	−3.10144	−0.116973
$704$	25.6893	0.968203
$705$	0	0
$706$	15.9041	0.598558
$707$	−19.4640	−0.732020
$708$	−1.90791	−0.0717037
$709$	41.3829	1.55417	0.777083	−	0.629398i	$-0.216699\pi$
$709$	41.3829	1.55417	0.777083	+	0.629398i	$0.216699\pi$
$710$	0	0
$711$	8.97727	0.336674
$712$	−24.4969	−0.918059
$713$	2.68931	0.100715
$714$	−3.53763	−0.132392
$715$	0	0
$716$	−9.84685	−0.367994
$717$	−9.67333	−0.361257
$718$	−23.1344	−0.863367
$719$	2.54848	0.0950423	0.0475212	−	0.998870i	$-0.484868\pi$
$719$	2.54848	0.0950423	0.0475212	+	0.998870i	$0.484868\pi$
$720$	0	0
$721$	10.2504	0.381743
$722$	4.00045	0.148881
$723$	−15.3808	−0.572019
$724$	6.82481	0.253642
$725$	0	0
$726$	2.49400	0.0925609
$727$	35.9776	1.33434	0.667168	−	0.744908i	$-0.267507\pi$
$727$	35.9776	1.33434	0.667168	+	0.744908i	$0.267507\pi$
$728$	−18.3212	−0.679029
$729$	−0.192061	−0.00711339
$730$	0	0
$731$	36.1233	1.33607
$732$	0.640947	0.0236901
$733$	−11.9046	−0.439707	−0.219853	−	0.975533i	$-0.570558\pi$
$733$	−11.9046	−0.439707	−0.219853	+	0.975533i	$0.570558\pi$
$734$	40.7428	1.50385
$735$	0	0
$736$	2.67804	0.0987139
$737$	−19.0272	−0.700875
$738$	−11.1528	−0.410539
$739$	33.3063	1.22519	0.612597	−	0.790396i	$-0.290125\pi$
$739$	33.3063	1.22519	0.612597	+	0.790396i	$0.290125\pi$
$740$	0	0
$741$	−18.2442	−0.670218
$742$	−3.52837	−0.129530
$743$	−7.37923	−0.270718	−0.135359	−	0.990797i	$-0.543219\pi$
$743$	−7.37923	−0.270718	−0.135359	+	0.990797i	$0.543219\pi$
$744$	−6.31318	−0.231453
$745$	0	0
$746$	34.5467	1.26485
$747$	1.34665	0.0492714
$748$	−5.25296	−0.192067
$749$	8.13181	0.297130
$750$	0	0
$751$	21.3270	0.778233	0.389116	−	0.921189i	$-0.372780\pi$
$751$	21.3270	0.778233	0.389116	+	0.921189i	$0.372780\pi$
$752$	17.1943	0.627012
$753$	−0.928801	−0.0338474
$754$	−37.7229	−1.37379
$755$	0	0
$756$	2.01465	0.0732722
$757$	50.3237	1.82904	0.914522	−	0.404535i	$-0.132567\pi$
$757$	50.3237	1.82904	0.914522	+	0.404535i	$0.132567\pi$
$758$	−9.26148	−0.336392
$759$	−2.21906	−0.0805469
$760$	0	0
$761$	30.6697	1.11178	0.555889	−	0.831257i	$-0.312378\pi$
$761$	30.6697	1.11178	0.555889	+	0.831257i	$0.312378\pi$
$762$	−13.8073	−0.500185
$763$	−11.2492	−0.407250
$764$	−12.3839	−0.448033
$765$	0	0
$766$	14.8210	0.535504
$767$	−30.6937	−1.10829
$768$	−8.36761	−0.301940
$769$	−7.06494	−0.254768	−0.127384	−	0.991853i	$-0.540658\pi$
$769$	−7.06494	−0.254768	−0.127384	+	0.991853i	$0.540658\pi$
$770$	0	0
$771$	17.4720	0.629240
$772$	9.83048	0.353807
$773$	25.8433	0.929519	0.464759	−	0.885437i	$-0.346141\pi$
$773$	25.8433	0.929519	0.464759	+	0.885437i	$0.346141\pi$
$774$	28.6230	1.02883
$775$	0	0
$776$	−38.0867	−1.36723
$777$	−0.599788	−0.0215173
$778$	9.12910	0.327294
$779$	−14.9156	−0.534407
$780$	0	0
$781$	−39.1540	−1.40104
$782$	4.60936	0.164830
$783$	21.2494	0.759390
$784$	−2.79440	−0.0998001
$785$	0	0
$786$	−16.4180	−0.585610
$787$	26.0828	0.929750	0.464875	−	0.885376i	$-0.346099\pi$
$787$	26.0828	0.929750	0.464875	+	0.885376i	$0.346099\pi$
$788$	9.01448	0.321127
$789$	−14.3961	−0.512515
$790$	0	0
$791$	−0.833318	−0.0296294
$792$	−21.3219	−0.757639
$793$	10.3113	0.366165
$794$	−13.5365	−0.480392
$795$	0	0
$796$	9.79334	0.347116
$797$	29.8617	1.05776	0.528879	−	0.848698i	$-0.322613\pi$
$797$	29.8617	1.05776	0.528879	+	0.848698i	$0.322613\pi$
$798$	−3.74884	−0.132707
$799$	−23.0435	−0.815220
$800$	0	0
$801$	19.3092	0.682257
$802$	−35.3897	−1.24965
$803$	45.1937	1.59485
$804$	2.45020	0.0864120
$805$	0	0
$806$	−19.8265	−0.698358
$807$	4.22475	0.148718
$808$	−59.5346	−2.09442
$809$	14.8724	0.522885	0.261442	−	0.965219i	$-0.415802\pi$
$809$	14.8724	0.522885	0.261442	+	0.965219i	$0.415802\pi$
$810$	0	0
$811$	27.1398	0.953006	0.476503	−	0.879173i	$-0.341904\pi$
$811$	27.1398	0.953006	0.476503	+	0.879173i	$0.341904\pi$
$812$	2.48230	0.0871116
$813$	24.2342	0.849929
$814$	2.78108	0.0974766
$815$	0	0
$816$	−8.03179	−0.281169
$817$	38.2800	1.33925
$818$	23.4006	0.818184
$819$	14.4413	0.504621
$820$	0	0
$821$	38.7104	1.35100	0.675501	−	0.737359i	$-0.263927\pi$
$821$	38.7104	1.35100	0.675501	+	0.737359i	$0.263927\pi$
$822$	5.81242	0.202731
$823$	1.74724	0.0609050	0.0304525	−	0.999536i	$-0.490305\pi$
$823$	1.74724	0.0609050	0.0304525	+	0.999536i	$0.490305\pi$
$824$	31.3528	1.09222
$825$	0	0
$826$	−6.30697	−0.219448
$827$	8.83233	0.307130	0.153565	−	0.988139i	$-0.450924\pi$
$827$	8.83233	0.307130	0.153565	+	0.988139i	$0.450924\pi$
$828$	−1.16962	−0.0406471
$829$	45.3881	1.57639	0.788197	−	0.615422i	$-0.211015\pi$
$829$	45.3881	1.57639	0.788197	+	0.615422i	$0.211015\pi$
$830$	0	0
$831$	−8.03614	−0.278771
$832$	−53.2196	−1.84506
$833$	3.74500	0.129757
$834$	7.50802	0.259981
$835$	0	0
$836$	−5.56658	−0.192524
$837$	11.1683	0.386032
$838$	33.3490	1.15202
$839$	−39.3294	−1.35780	−0.678901	−	0.734230i	$-0.737543\pi$
$839$	−39.3294	−1.35780	−0.678901	+	0.734230i	$0.737543\pi$
$840$	0	0
$841$	−2.81820	−0.0971793
$842$	18.3716	0.633126
$843$	−2.98324	−0.102748
$844$	8.62043	0.296728
$845$	0	0
$846$	−18.2589	−0.627754
$847$	−2.64019	−0.0907181
$848$	−8.01077	−0.275091
$849$	2.69050	0.0923378
$850$	0	0
$851$	0.781495	0.0267893
$852$	5.04201	0.172736
$853$	24.4401	0.836812	0.418406	−	0.908260i	$-0.362589\pi$
$853$	24.4401	0.836812	0.418406	+	0.908260i	$0.362589\pi$
$854$	2.11877	0.0725029
$855$	0	0
$856$	24.8728	0.850133
$857$	−4.64324	−0.158610	−0.0793050	−	0.996850i	$-0.525270\pi$
$857$	−4.64324	−0.158610	−0.0793050	+	0.996850i	$0.525270\pi$
$858$	16.3597	0.558511
$859$	25.9289	0.884683	0.442341	−	0.896847i	$-0.354148\pi$
$859$	25.9289	0.884683	0.442341	+	0.896847i	$0.354148\pi$
$860$	0	0
$861$	−2.88454	−0.0983047
$862$	11.6615	0.397191
$863$	22.4148	0.763008	0.381504	−	0.924367i	$-0.375406\pi$
$863$	22.4148	0.763008	0.381504	+	0.924367i	$0.375406\pi$
$864$	11.1215	0.378361
$865$	0	0
$866$	−40.7361	−1.38427
$867$	−2.28325	−0.0775433
$868$	1.30465	0.0442827
$869$	−10.7659	−0.365210
$870$	0	0
$871$	39.4179	1.33562
$872$	−34.4080	−1.16520
$873$	30.0211	1.01606
$874$	4.88455	0.165222
$875$	0	0
$876$	−5.81977	−0.196632
$877$	−11.3179	−0.382179	−0.191090	−	0.981573i	$-0.561202\pi$
$877$	−11.3179	−0.382179	−0.191090	+	0.981573i	$0.561202\pi$
$878$	−4.27379	−0.144233
$879$	−5.79264	−0.195381
$880$	0	0
$881$	−31.8348	−1.07254	−0.536270	−	0.844046i	$-0.680167\pi$
$881$	−31.8348	−1.07254	−0.536270	+	0.844046i	$0.680167\pi$
$882$	2.96742	0.0999182
$883$	9.22964	0.310602	0.155301	−	0.987867i	$-0.450365\pi$
$883$	9.22964	0.310602	0.155301	+	0.987867i	$0.450365\pi$
$884$	10.8824	0.366014
$885$	0	0
$886$	−11.0935	−0.372694
$887$	57.6424	1.93544	0.967722	−	0.252021i	$-0.0810951\pi$
$887$	57.6424	1.93544	0.967722	+	0.252021i	$0.0810951\pi$
$888$	−1.83457	−0.0615642
$889$	14.6167	0.490227
$890$	0	0
$891$	11.6972	0.391873
$892$	−4.10300	−0.137379
$893$	−24.4193	−0.817160
$894$	17.3074	0.578845
$895$	0	0
$896$	−5.57953	−0.186399
$897$	4.59715	0.153494
$898$	2.77192	0.0925002
$899$	13.7607	0.458944
$900$	0	0
$901$	10.7359	0.357664
$902$	13.3749	0.445336
$903$	7.40300	0.246356
$904$	−2.54887	−0.0847742
$905$	0	0
$906$	14.3944	0.478221
$907$	37.5533	1.24694	0.623468	−	0.781849i	$-0.285723\pi$
$907$	37.5533	1.24694	0.623468	+	0.781849i	$0.285723\pi$
$908$	1.01490	0.0336805
$909$	46.9270	1.55647
$910$	0	0
$911$	−8.75690	−0.290129	−0.145065	−	0.989422i	$-0.546339\pi$
$911$	−8.75690	−0.290129	−0.145065	+	0.989422i	$0.546339\pi$
$912$	−8.51132	−0.281838
$913$	−1.61496	−0.0534475
$914$	25.3326	0.837929
$915$	0	0
$916$	8.26564	0.273104
$917$	17.3804	0.573952
$918$	19.1420	0.631779
$919$	−35.0418	−1.15592	−0.577962	−	0.816064i	$-0.696152\pi$
$919$	−35.0418	−1.15592	−0.577962	+	0.816064i	$0.696152\pi$
$920$	0	0
$921$	2.61244	0.0860829
$922$	33.3623	1.09873
$923$	81.1138	2.66989
$924$	−1.07652	−0.0354151
$925$	0	0
$926$	−9.77312	−0.321165
$927$	−24.7132	−0.811689
$928$	13.7030	0.449824
$929$	22.7412	0.746114	0.373057	−	0.927808i	$-0.378310\pi$
$929$	22.7412	0.746114	0.373057	+	0.927808i	$0.378310\pi$
$930$	0	0
$931$	3.96859	0.130065
$932$	4.64732	0.152228
$933$	−7.18936	−0.235369
$934$	−29.5377	−0.966503
$935$	0	0
$936$	44.1717	1.44380
$937$	−16.7075	−0.545811	−0.272906	−	0.962041i	$-0.587985\pi$
$937$	−16.7075	−0.545811	−0.272906	+	0.962041i	$0.587985\pi$
$938$	8.09961	0.264462
$939$	−11.4284	−0.372953
$940$	0	0
$941$	27.7145	0.903466	0.451733	−	0.892153i	$-0.350806\pi$
$941$	27.7145	0.903466	0.451733	+	0.892153i	$0.350806\pi$
$942$	−6.70550	−0.218477
$943$	3.75841	0.122391
$944$	−14.3193	−0.466053
$945$	0	0
$946$	−34.3259	−1.11603
$947$	11.8870	0.386275	0.193137	−	0.981172i	$-0.438134\pi$
$947$	11.8870	0.386275	0.193137	+	0.981172i	$0.438134\pi$
$948$	1.38637	0.0450273
$949$	−93.6262	−3.03923
$950$	0	0
$951$	−13.9542	−0.452496
$952$	11.4548	0.371253
$953$	−35.9688	−1.16514	−0.582572	−	0.812779i	$-0.697953\pi$
$953$	−35.9688	−1.16514	−0.582572	+	0.812779i	$0.697953\pi$
$954$	8.50676	0.275417
$955$	0	0
$956$	6.11447	0.197756
$957$	−11.3545	−0.367040
$958$	−25.9134	−0.837223
$959$	−6.15314	−0.198695
$960$	0	0
$961$	−23.7676	−0.766698
$962$	−5.76145	−0.185757
$963$	−19.6055	−0.631778
$964$	9.72214	0.313129
$965$	0	0
$966$	0.944626	0.0303928
$967$	36.2305	1.16509	0.582547	−	0.812797i	$-0.302056\pi$
$967$	36.2305	1.16509	0.582547	+	0.812797i	$0.302056\pi$
$968$	−8.07556	−0.259558
$969$	11.4067	0.366436
$970$	0	0
$971$	2.89397	0.0928719	0.0464359	−	0.998921i	$-0.485214\pi$
$971$	2.89397	0.0928719	0.0464359	+	0.998921i	$0.485214\pi$
$972$	−7.55026	−0.242175
$973$	−7.94813	−0.254805
$974$	−13.2367	−0.424130
$975$	0	0
$976$	4.81044	0.153979
$977$	−35.1806	−1.12553	−0.562764	−	0.826618i	$-0.690262\pi$
$977$	−35.1806	−1.12553	−0.562764	+	0.826618i	$0.690262\pi$
$978$	−8.91823	−0.285173
$979$	−23.1564	−0.740083
$980$	0	0
$981$	27.1215	0.865923
$982$	25.9945	0.829519
$983$	14.6517	0.467317	0.233658	−	0.972319i	$-0.424930\pi$
$983$	14.6517	0.467317	0.233658	+	0.972319i	$0.424930\pi$
$984$	−8.82292	−0.281265
$985$	0	0
$986$	23.5852	0.751107
$987$	−4.72246	−0.150317
$988$	11.5321	0.366885
$989$	−9.64575	−0.306717
$990$	0	0
$991$	−12.5480	−0.398601	−0.199301	−	0.979938i	$-0.563867\pi$
$991$	−12.5480	−0.398601	−0.199301	+	0.979938i	$0.563867\pi$
$992$	7.20207	0.228666
$993$	−21.9791	−0.697486
$994$	16.6673	0.528655
$995$	0	0
$996$	0.207965	0.00658963
$997$	3.22687	0.102196	0.0510980	−	0.998694i	$-0.483728\pi$
$997$	3.22687	0.102196	0.0510980	+	0.998694i	$0.483728\pi$
$998$	15.3720	0.486593
$999$	3.24543	0.102681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.x.1.5		12
5.2	odd	4		805.2.c.b.484.8	✓	24
5.3	odd	4		805.2.c.b.484.17	yes	24
5.4	even	2		4025.2.a.y.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.b.484.8	✓	24	5.2	odd	4
805.2.c.b.484.17	yes	24	5.3	odd	4
4025.2.a.x.1.5		12	1.1	even	1	trivial
4025.2.a.y.1.8		12	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)

\(f(q)\)	\(=\)	\(q-1.23080 q^{2} +0.767488 q^{3} -0.485126 q^{4} -0.944626 q^{6} +1.00000 q^{7} +3.05870 q^{8} -2.41096 q^{9} +O(q^{10})\)	\(q-1.23080 q^{2} +0.767488 q^{3} -0.485126 q^{4} -0.944626 q^{6} +1.00000 q^{7} +3.05870 q^{8} -2.41096 q^{9} +2.89133 q^{11} -0.372328 q^{12} -5.98987 q^{13} -1.23080 q^{14} -2.79440 q^{16} +3.74500 q^{17} +2.96742 q^{18} +3.96859 q^{19} +0.767488 q^{21} -3.55866 q^{22} -1.00000 q^{23} +2.34751 q^{24} +7.37234 q^{26} -4.15285 q^{27} -0.485126 q^{28} -5.11682 q^{29} -2.68931 q^{31} -2.67804 q^{32} +2.21906 q^{33} -4.60936 q^{34} +1.16962 q^{36} -0.781495 q^{37} -4.88455 q^{38} -4.59715 q^{39} -3.75841 q^{41} -0.944626 q^{42} +9.64575 q^{43} -1.40266 q^{44} +1.23080 q^{46} -6.15313 q^{47} -2.14467 q^{48} +1.00000 q^{49} +2.87424 q^{51} +2.90584 q^{52} +2.86672 q^{53} +5.11134 q^{54} +3.05870 q^{56} +3.04585 q^{57} +6.29779 q^{58} +5.12427 q^{59} -1.72146 q^{61} +3.31000 q^{62} -2.41096 q^{63} +8.88494 q^{64} -2.73123 q^{66} -6.58076 q^{67} -1.81680 q^{68} -0.767488 q^{69} -13.5418 q^{71} -7.37441 q^{72} +15.6308 q^{73} +0.961866 q^{74} -1.92527 q^{76} +2.89133 q^{77} +5.65819 q^{78} -3.72352 q^{79} +4.04562 q^{81} +4.62586 q^{82} -0.558554 q^{83} -0.372328 q^{84} -11.8720 q^{86} -3.92709 q^{87} +8.84372 q^{88} -8.00892 q^{89} -5.98987 q^{91} +0.485126 q^{92} -2.06401 q^{93} +7.57329 q^{94} -2.05536 q^{96} -12.4519 q^{97} -1.23080 q^{98} -6.97089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9	\( 12 q - 2 q^{2} + 8 q^{4} - 6 q^{6} + 12 q^{7} - 6 q^{8} + 8 q^{9} - 8 q^{11} + 12 q^{12} - 2 q^{13} - 2 q^{14} - 4 q^{16} + 8 q^{17} - 20 q^{18} - 26 q^{19} - 4 q^{22} - 12 q^{23} - 12 q^{24} - 22 q^{26} - 12 q^{27} + 8 q^{28} - 12 q^{29} - 50 q^{31} - 14 q^{32} - 4 q^{33} - 28 q^{34} - 18 q^{36} - 8 q^{37} + 4 q^{38} - 26 q^{39} - 4 q^{41} - 6 q^{42} - 26 q^{43} - 10 q^{44} + 2 q^{46} - 16 q^{47} + 40 q^{48} + 12 q^{49} - 32 q^{51} - 10 q^{52} + 18 q^{53} - 10 q^{54} - 6 q^{56} + 10 q^{57} + 18 q^{58} - 18 q^{59} + 8 q^{61} + 54 q^{62} + 8 q^{63} + 12 q^{64} - 2 q^{66} - 38 q^{67} + 36 q^{68} - 24 q^{71} - 18 q^{72} + 14 q^{73} + 36 q^{74} - 56 q^{76} - 8 q^{77} + 26 q^{78} - 44 q^{79} - 16 q^{81} + 44 q^{82} + 14 q^{83} + 12 q^{84} - 32 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} - 2 q^{91} - 8 q^{92} - 26 q^{93} + 18 q^{94} - 38 q^{96} + 4 q^{97} - 2 q^{98} - 56 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + 8 * q^4 - 6 * q^6 + 12 * q^7 - 6 * q^8 + 8 * q^9 - 8 * q^11 + 12 * q^12 - 2 * q^13 - 2 * q^14 - 4 * q^16 + 8 * q^17 - 20 * q^18 - 26 * q^19 - 4 * q^22 - 12 * q^23 - 12 * q^24 - 22 * q^26 - 12 * q^27 + 8 * q^28 - 12 * q^29 - 50 * q^31 - 14 * q^32 - 4 * q^33 - 28 * q^34 - 18 * q^36 - 8 * q^37 + 4 * q^38 - 26 * q^39 - 4 * q^41 - 6 * q^42 - 26 * q^43 - 10 * q^44 + 2 * q^46 - 16 * q^47 + 40 * q^48 + 12 * q^49 - 32 * q^51 - 10 * q^52 + 18 * q^53 - 10 * q^54 - 6 * q^56 + 10 * q^57 + 18 * q^58 - 18 * q^59 + 8 * q^61 + 54 * q^62 + 8 * q^63 + 12 * q^64 - 2 * q^66 - 38 * q^67 + 36 * q^68 - 24 * q^71 - 18 * q^72 + 14 * q^73 + 36 * q^74 - 56 * q^76 - 8 * q^77 + 26 * q^78 - 44 * q^79 - 16 * q^81 + 44 * q^82 + 14 * q^83 + 12 * q^84 - 32 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 - 2 * q^91 - 8 * q^92 - 26 * q^93 + 18 * q^94 - 38 * q^96 + 4 * q^97 - 2 * q^98 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more