LMFDB - Embedded newform 6025.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2x^{10} - 11x^{9} + 15x^{8} + 43x^{7} - 28x^{6} - 62x^{5} + 14x^{4} + 31x^{3} + x^{2} - 5x - 1 $ x^11 - 2x^10 - 11x^9 + 15x^8 + 43x^7 - 28x^6 - 62x^5 + 14x^4 + 31x^3 + x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.324121$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.76114 q^{2} +0.777505 q^{3} +1.10163 q^{4} -1.36930 q^{6} -0.840819 q^{7} +1.58216 q^{8} -2.39549 q^{9} +O(q^{10})$	\(q-1.76114 q^{2} +0.777505 q^{3} +1.10163 q^{4} -1.36930 q^{6} -0.840819 q^{7} +1.58216 q^{8} -2.39549 q^{9} -3.84997 q^{11} +0.856520 q^{12} +6.84790 q^{13} +1.48080 q^{14} -4.98967 q^{16} -4.50500 q^{17} +4.21879 q^{18} -4.75888 q^{19} -0.653741 q^{21} +6.78034 q^{22} +1.21663 q^{23} +1.23014 q^{24} -12.0601 q^{26} -4.19502 q^{27} -0.926269 q^{28} -1.98240 q^{29} +3.16644 q^{31} +5.62320 q^{32} -2.99337 q^{33} +7.93394 q^{34} -2.63893 q^{36} -4.75481 q^{37} +8.38107 q^{38} +5.32428 q^{39} -0.0513770 q^{41} +1.15133 q^{42} -4.71083 q^{43} -4.24123 q^{44} -2.14266 q^{46} +2.00615 q^{47} -3.87950 q^{48} -6.29302 q^{49} -3.50266 q^{51} +7.54383 q^{52} +8.94378 q^{53} +7.38803 q^{54} -1.33031 q^{56} -3.70005 q^{57} +3.49128 q^{58} +7.53782 q^{59} +2.30982 q^{61} -5.57655 q^{62} +2.01417 q^{63} +0.0760827 q^{64} +5.27175 q^{66} +3.71879 q^{67} -4.96282 q^{68} +0.945935 q^{69} -5.82583 q^{71} -3.79005 q^{72} -10.4167 q^{73} +8.37390 q^{74} -5.24251 q^{76} +3.23713 q^{77} -9.37682 q^{78} -5.99747 q^{79} +3.92481 q^{81} +0.0904822 q^{82} +12.7354 q^{83} -0.720179 q^{84} +8.29645 q^{86} -1.54132 q^{87} -6.09128 q^{88} -8.96588 q^{89} -5.75785 q^{91} +1.34027 q^{92} +2.46192 q^{93} -3.53312 q^{94} +4.37207 q^{96} +1.15002 q^{97} +11.0829 q^{98} +9.22254 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	$ 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) $ 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * 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 $

$2$	−1.76114	−1.24532	−0.622658	−	0.782494i	$-0.713947\pi$
$2$	−1.76114	−1.24532	−0.622658	+	0.782494i	$0.713947\pi$
$3$	0.777505	0.448893	0.224446	−	0.974486i	$-0.427943\pi$
$3$	0.777505	0.448893	0.224446	+	0.974486i	$0.427943\pi$
$4$	1.10163	0.550813
$5$	0	0
$5$	0	0
$6$	−1.36930	−0.559014
$7$	−0.840819	−0.317800	−0.158900	−	0.987295i	$-0.550795\pi$
$7$	−0.840819	−0.317800	−0.158900	+	0.987295i	$0.550795\pi$
$8$	1.58216	0.559380
$9$	−2.39549	−0.798495
$10$	0	0
$11$	−3.84997	−1.16081	−0.580404	−	0.814328i	$-0.697105\pi$
$11$	−3.84997	−1.16081	−0.580404	+	0.814328i	$0.697105\pi$
$12$	0.856520	0.247256
$13$	6.84790	1.89927	0.949633	−	0.313365i	$-0.101456\pi$
$13$	6.84790	1.89927	0.949633	+	0.313365i	$0.101456\pi$
$14$	1.48080	0.395761
$15$	0	0
$16$	−4.98967	−1.24742
$17$	−4.50500	−1.09262	−0.546311	−	0.837582i	$-0.683968\pi$
$17$	−4.50500	−1.09262	−0.546311	+	0.837582i	$0.683968\pi$
$18$	4.21879	0.994379
$19$	−4.75888	−1.09176	−0.545881	−	0.837863i	$-0.683805\pi$
$19$	−4.75888	−1.09176	−0.545881	+	0.837863i	$0.683805\pi$
$20$	0	0
$21$	−0.653741	−0.142658
$22$	6.78034	1.44557
$23$	1.21663	0.253685	0.126842	−	0.991923i	$-0.459516\pi$
$23$	1.21663	0.253685	0.126842	+	0.991923i	$0.459516\pi$
$24$	1.23014	0.251102
$25$	0	0
$26$	−12.0601	−2.36519
$27$	−4.19502	−0.807332
$28$	−0.926269	−0.175048
$29$	−1.98240	−0.368122	−0.184061	−	0.982915i	$-0.558924\pi$
$29$	−1.98240	−0.368122	−0.184061	+	0.982915i	$0.558924\pi$
$30$	0	0
$31$	3.16644	0.568709	0.284355	−	0.958719i	$-0.408221\pi$
$31$	3.16644	0.568709	0.284355	+	0.958719i	$0.408221\pi$
$32$	5.62320	0.994051
$33$	−2.99337	−0.521079
$34$	7.93394	1.36066
$35$	0	0
$36$	−2.63893	−0.439822
$37$	−4.75481	−0.781685	−0.390843	−	0.920457i	$-0.627816\pi$
$37$	−4.75481	−0.781685	−0.390843	+	0.920457i	$0.627816\pi$
$38$	8.38107	1.35959
$39$	5.32428	0.852567
$40$	0	0
$41$	−0.0513770	−0.00802373	−0.00401187	−	0.999992i	$-0.501277\pi$
$41$	−0.0513770	−0.00802373	−0.00401187	+	0.999992i	$0.501277\pi$
$42$	1.15133	0.177654
$43$	−4.71083	−0.718395	−0.359197	−	0.933262i	$-0.616950\pi$
$43$	−4.71083	−0.718395	−0.359197	+	0.933262i	$0.616950\pi$
$44$	−4.24123	−0.639389
$45$	0	0
$46$	−2.14266	−0.315918
$47$	2.00615	0.292628	0.146314	−	0.989238i	$-0.453259\pi$
$47$	2.00615	0.292628	0.146314	+	0.989238i	$0.453259\pi$
$48$	−3.87950	−0.559957
$49$	−6.29302	−0.899003
$50$	0	0
$51$	−3.50266	−0.490470
$52$	7.54383	1.04614
$53$	8.94378	1.22852	0.614261	−	0.789103i	$-0.289454\pi$
$53$	8.94378	1.22852	0.614261	+	0.789103i	$0.289454\pi$
$54$	7.38803	1.00538
$55$	0	0
$56$	−1.33031	−0.177771
$57$	−3.70005	−0.490084
$58$	3.49128	0.458428
$59$	7.53782	0.981340	0.490670	−	0.871346i	$-0.336752\pi$
$59$	7.53782	0.981340	0.490670	+	0.871346i	$0.336752\pi$
$60$	0	0
$61$	2.30982	0.295743	0.147871	−	0.989007i	$-0.452758\pi$
$61$	2.30982	0.295743	0.147871	+	0.989007i	$0.452758\pi$
$62$	−5.57655	−0.708223
$63$	2.01417	0.253762
$64$	0.0760827	0.00951034
$65$	0	0
$66$	5.27175	0.648908
$67$	3.71879	0.454323	0.227162	−	0.973857i	$-0.427055\pi$
$67$	3.71879	0.454323	0.227162	+	0.973857i	$0.427055\pi$
$68$	−4.96282	−0.601831
$69$	0.945935	0.113877
$70$	0	0
$71$	−5.82583	−0.691398	−0.345699	−	0.938345i	$-0.612358\pi$
$71$	−5.82583	−0.691398	−0.345699	+	0.938345i	$0.612358\pi$
$72$	−3.79005	−0.446662
$73$	−10.4167	−1.21918	−0.609590	−	0.792716i	$-0.708666\pi$
$73$	−10.4167	−1.21918	−0.609590	+	0.792716i	$0.708666\pi$
$74$	8.37390	0.973446
$75$	0	0
$76$	−5.24251	−0.601357
$77$	3.23713	0.368905
$78$	−9.37682	−1.06172
$79$	−5.99747	−0.674768	−0.337384	−	0.941367i	$-0.609542\pi$
$79$	−5.99747	−0.674768	−0.337384	+	0.941367i	$0.609542\pi$
$80$	0	0
$81$	3.92481	0.436090
$82$	0.0904822	0.00999209
$83$	12.7354	1.39790	0.698948	−	0.715172i	$-0.253652\pi$
$83$	12.7354	1.39790	0.698948	+	0.715172i	$0.253652\pi$
$84$	−0.720179	−0.0785780
$85$	0	0
$86$	8.29645	0.894629
$87$	−1.54132	−0.165247
$88$	−6.09128	−0.649333
$89$	−8.96588	−0.950382	−0.475191	−	0.879883i	$-0.657621\pi$
$89$	−8.96588	−0.950382	−0.475191	+	0.879883i	$0.657621\pi$
$90$	0	0
$91$	−5.75785	−0.603586
$92$	1.34027	0.139733
$93$	2.46192	0.255290
$94$	−3.53312	−0.364414
$95$	0	0
$96$	4.37207	0.446222
$97$	1.15002	0.116766	0.0583832	−	0.998294i	$-0.481405\pi$
$97$	1.15002	0.116766	0.0583832	+	0.998294i	$0.481405\pi$
$98$	11.0829	1.11954
$99$	9.22254	0.926900
$100$	0	0
$101$	18.7877	1.86944	0.934722	−	0.355381i	$-0.115649\pi$
$101$	18.7877	1.86944	0.934722	+	0.355381i	$0.115649\pi$
$102$	6.16868	0.610791
$103$	−1.92531	−0.189707	−0.0948533	−	0.995491i	$-0.530238\pi$
$103$	−1.92531	−0.189707	−0.0948533	+	0.995491i	$0.530238\pi$
$104$	10.8345	1.06241
$105$	0	0
$106$	−15.7513	−1.52990
$107$	18.1543	1.75504	0.877521	−	0.479538i	$-0.159196\pi$
$107$	18.1543	1.75504	0.877521	+	0.479538i	$0.159196\pi$
$108$	−4.62134	−0.444689
$109$	−2.30000	−0.220300	−0.110150	−	0.993915i	$-0.535133\pi$
$109$	−2.30000	−0.220300	−0.110150	+	0.993915i	$0.535133\pi$
$110$	0	0
$111$	−3.69689	−0.350893
$112$	4.19541	0.396429
$113$	3.70457	0.348496	0.174248	−	0.984702i	$-0.444251\pi$
$113$	3.70457	0.348496	0.174248	+	0.984702i	$0.444251\pi$
$114$	6.51633	0.610310
$115$	0	0
$116$	−2.18386	−0.202766
$117$	−16.4040	−1.51655
$118$	−13.2752	−1.22208
$119$	3.78789	0.347235
$120$	0	0
$121$	3.82224	0.347477
$122$	−4.06793	−0.368293
$123$	−0.0399459	−0.00360180
$124$	3.48823	0.313253
$125$	0	0
$126$	−3.54724	−0.316014
$127$	−7.80431	−0.692520	−0.346260	−	0.938139i	$-0.612549\pi$
$127$	−7.80431	−0.692520	−0.346260	+	0.938139i	$0.612549\pi$
$128$	−11.3804	−1.00589
$129$	−3.66270	−0.322482
$130$	0	0
$131$	−9.17340	−0.801484	−0.400742	−	0.916191i	$-0.631248\pi$
$131$	−9.17340	−0.801484	−0.400742	+	0.916191i	$0.631248\pi$
$132$	−3.29758	−0.287017
$133$	4.00136	0.346962
$134$	−6.54933	−0.565776
$135$	0	0
$136$	−7.12764	−0.611190
$137$	−9.16541	−0.783054	−0.391527	−	0.920167i	$-0.628053\pi$
$137$	−9.16541	−0.783054	−0.391527	+	0.920167i	$0.628053\pi$
$138$	−1.66593	−0.141813
$139$	−17.5870	−1.49171	−0.745856	−	0.666107i	$-0.767960\pi$
$139$	−17.5870	−1.49171	−0.745856	+	0.666107i	$0.767960\pi$
$140$	0	0
$141$	1.55980	0.131358
$142$	10.2601	0.861010
$143$	−26.3642	−2.20468
$144$	11.9527	0.996057
$145$	0	0
$146$	18.3453	1.51827
$147$	−4.89286	−0.403556
$148$	−5.23802	−0.430563
$149$	13.6394	1.11738	0.558692	−	0.829375i	$-0.311304\pi$
$149$	13.6394	1.11738	0.558692	+	0.829375i	$0.311304\pi$
$150$	0	0
$151$	−0.664349	−0.0540640	−0.0270320	−	0.999635i	$-0.508606\pi$
$151$	−0.664349	−0.0540640	−0.0270320	+	0.999635i	$0.508606\pi$
$152$	−7.52933	−0.610709
$153$	10.7917	0.872453
$154$	−5.70104	−0.459403
$155$	0	0
$156$	5.86537	0.469605
$157$	15.9582	1.27360	0.636800	−	0.771029i	$-0.280258\pi$
$157$	15.9582	1.27360	0.636800	+	0.771029i	$0.280258\pi$
$158$	10.5624	0.840300
$159$	6.95384	0.551475
$160$	0	0
$161$	−1.02296	−0.0806209
$162$	−6.91215	−0.543070
$163$	11.5278	0.902926	0.451463	−	0.892290i	$-0.350902\pi$
$163$	11.5278	0.902926	0.451463	+	0.892290i	$0.350902\pi$
$164$	−0.0565982	−0.00441958
$165$	0	0
$166$	−22.4289	−1.74082
$167$	−3.33528	−0.258092	−0.129046	−	0.991639i	$-0.541191\pi$
$167$	−3.33528	−0.258092	−0.129046	+	0.991639i	$0.541191\pi$
$168$	−1.03433	−0.0798000
$169$	33.8937	2.60721
$170$	0	0
$171$	11.3998	0.871767
$172$	−5.18958	−0.395701
$173$	−7.50956	−0.570941	−0.285471	−	0.958387i	$-0.592150\pi$
$173$	−7.50956	−0.570941	−0.285471	+	0.958387i	$0.592150\pi$
$174$	2.71449	0.205785
$175$	0	0
$176$	19.2101	1.44801
$177$	5.86069	0.440517
$178$	15.7902	1.18353
$179$	19.2751	1.44069	0.720346	−	0.693615i	$-0.243983\pi$
$179$	19.2751	1.44069	0.720346	+	0.693615i	$0.243983\pi$
$180$	0	0
$181$	−12.9073	−0.959392	−0.479696	−	0.877435i	$-0.659253\pi$
$181$	−12.9073	−0.959392	−0.479696	+	0.877435i	$0.659253\pi$
$182$	10.1404	0.751656
$183$	1.79590	0.132757
$184$	1.92491	0.141906
$185$	0	0
$186$	−4.33580	−0.317916
$187$	17.3441	1.26832
$188$	2.21003	0.161183
$189$	3.52725	0.256570
$190$	0	0
$191$	−7.78070	−0.562992	−0.281496	−	0.959562i	$-0.590831\pi$
$191$	−7.78070	−0.562992	−0.281496	+	0.959562i	$0.590831\pi$
$192$	0.0591547	0.00426912
$193$	0.371852	0.0267665	0.0133832	−	0.999910i	$-0.495740\pi$
$193$	0.371852	0.0267665	0.0133832	+	0.999910i	$0.495740\pi$
$194$	−2.02534	−0.145411
$195$	0	0
$196$	−6.93256	−0.495183
$197$	17.0302	1.21335	0.606676	−	0.794949i	$-0.292503\pi$
$197$	17.0302	1.21335	0.606676	+	0.794949i	$0.292503\pi$
$198$	−16.2422	−1.15428
$199$	22.8071	1.61675	0.808377	−	0.588665i	$-0.200346\pi$
$199$	22.8071	1.61675	0.808377	+	0.588665i	$0.200346\pi$
$200$	0	0
$201$	2.89138	0.203942
$202$	−33.0878	−2.32805
$203$	1.66684	0.116989
$204$	−3.85862	−0.270157
$205$	0	0
$206$	3.39075	0.236245
$207$	−2.91442	−0.202566
$208$	−34.1688	−2.36918
$209$	18.3215	1.26733
$210$	0	0
$211$	7.35488	0.506331	0.253166	−	0.967423i	$-0.418528\pi$
$211$	7.35488	0.506331	0.253166	+	0.967423i	$0.418528\pi$
$212$	9.85270	0.676687
$213$	−4.52961	−0.310364
$214$	−31.9723	−2.18558
$215$	0	0
$216$	−6.63721	−0.451605
$217$	−2.66240	−0.180736
$218$	4.05062	0.274343
$219$	−8.09903	−0.547282
$220$	0	0
$221$	−30.8498	−2.07518
$222$	6.51075	0.436973
$223$	−2.99404	−0.200496	−0.100248	−	0.994962i	$-0.531964\pi$
$223$	−2.99404	−0.200496	−0.100248	+	0.994962i	$0.531964\pi$
$224$	−4.72809	−0.315909
$225$	0	0
$226$	−6.52427	−0.433988
$227$	20.7832	1.37943	0.689715	−	0.724081i	$-0.257736\pi$
$227$	20.7832	1.37943	0.689715	+	0.724081i	$0.257736\pi$
$228$	−4.07608	−0.269945
$229$	−4.49098	−0.296773	−0.148386	−	0.988929i	$-0.547408\pi$
$229$	−4.49098	−0.296773	−0.148386	+	0.988929i	$0.547408\pi$
$230$	0	0
$231$	2.51688	0.165599
$232$	−3.13648	−0.205920
$233$	−14.6860	−0.962112	−0.481056	−	0.876690i	$-0.659747\pi$
$233$	−14.6860	−0.962112	−0.481056	+	0.876690i	$0.659747\pi$
$234$	28.8899	1.88859
$235$	0	0
$236$	8.30386	0.540535
$237$	−4.66306	−0.302899
$238$	−6.67101	−0.432418
$239$	14.3188	0.926209	0.463104	−	0.886304i	$-0.346736\pi$
$239$	14.3188	0.926209	0.463104	+	0.886304i	$0.346736\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−6.73152	−0.432719
$243$	15.6366	1.00309
$244$	2.54456	0.162899
$245$	0	0
$246$	0.0703504	0.00448538
$247$	−32.5883	−2.07355
$248$	5.00983	0.318124
$249$	9.90188	0.627506
$250$	0	0
$251$	11.4995	0.725843	0.362921	−	0.931820i	$-0.381779\pi$
$251$	11.4995	0.725843	0.362921	+	0.931820i	$0.381779\pi$
$252$	2.21886	0.139775
$253$	−4.68398	−0.294479
$254$	13.7445	0.862407
$255$	0	0
$256$	19.8903	1.24315
$257$	−24.1897	−1.50891	−0.754456	−	0.656351i	$-0.772099\pi$
$257$	−24.1897	−1.50891	−0.754456	+	0.656351i	$0.772099\pi$
$258$	6.45053	0.401593
$259$	3.99793	0.248419
$260$	0	0
$261$	4.74880	0.293943
$262$	16.1557	0.998101
$263$	29.6335	1.82728	0.913640	−	0.406525i	$-0.133260\pi$
$263$	29.6335	1.82728	0.913640	+	0.406525i	$0.133260\pi$
$264$	−4.73600	−0.291481
$265$	0	0
$266$	−7.04697	−0.432077
$267$	−6.97102	−0.426620
$268$	4.09672	0.250247
$269$	−18.6448	−1.13679	−0.568397	−	0.822755i	$-0.692436\pi$
$269$	−18.6448	−1.13679	−0.568397	+	0.822755i	$0.692436\pi$
$270$	0	0
$271$	−20.4520	−1.24237	−0.621186	−	0.783663i	$-0.713349\pi$
$271$	−20.4520	−1.24237	−0.621186	+	0.783663i	$0.713349\pi$
$272$	22.4784	1.36296
$273$	−4.47676	−0.270946
$274$	16.1416	0.975150
$275$	0	0
$276$	1.04207	0.0627251
$277$	14.8573	0.892689	0.446345	−	0.894861i	$-0.352726\pi$
$277$	14.8573	0.892689	0.446345	+	0.894861i	$0.352726\pi$
$278$	30.9733	1.85765
$279$	−7.58516	−0.454112
$280$	0	0
$281$	7.87582	0.469832	0.234916	−	0.972016i	$-0.424518\pi$
$281$	7.87582	0.469832	0.234916	+	0.972016i	$0.424518\pi$
$282$	−2.74702	−0.163583
$283$	−11.8544	−0.704669	−0.352334	−	0.935874i	$-0.614612\pi$
$283$	−11.8544	−0.704669	−0.352334	+	0.935874i	$0.614612\pi$
$284$	−6.41788	−0.380831
$285$	0	0
$286$	46.4311	2.74553
$287$	0.0431987	0.00254994
$288$	−13.4703	−0.793745
$289$	3.29498	0.193823
$290$	0	0
$291$	0.894143	0.0524156
$292$	−11.4753	−0.671541
$293$	−25.8851	−1.51223	−0.756113	−	0.654441i	$-0.772904\pi$
$293$	−25.8851	−1.51223	−0.756113	+	0.654441i	$0.772904\pi$
$294$	8.61703	0.502555
$295$	0	0
$296$	−7.52289	−0.437259
$297$	16.1507	0.937158
$298$	−24.0209	−1.39150
$299$	8.33135	0.481814
$300$	0	0
$301$	3.96096	0.228306
$302$	1.17001	0.0673268
$303$	14.6075	0.839180
$304$	23.7452	1.36188
$305$	0	0
$306$	−19.0056	−1.08648
$307$	20.7981	1.18701	0.593507	−	0.804829i	$-0.297743\pi$
$307$	20.7981	1.18701	0.593507	+	0.804829i	$0.297743\pi$
$308$	3.56610	0.203198
$309$	−1.49694	−0.0851579
$310$	0	0
$311$	−13.1988	−0.748436	−0.374218	−	0.927341i	$-0.622089\pi$
$311$	−13.1988	−0.748436	−0.374218	+	0.927341i	$0.622089\pi$
$312$	8.42388	0.476908
$313$	1.39815	0.0790283	0.0395142	−	0.999219i	$-0.487419\pi$
$313$	1.39815	0.0790283	0.0395142	+	0.999219i	$0.487419\pi$
$314$	−28.1046	−1.58604
$315$	0	0
$316$	−6.60697	−0.371671
$317$	−6.94937	−0.390315	−0.195158	−	0.980772i	$-0.562522\pi$
$317$	−6.94937	−0.390315	−0.195158	+	0.980772i	$0.562522\pi$
$318$	−12.2467	−0.686761
$319$	7.63216	0.427319
$320$	0	0
$321$	14.1151	0.787826
$322$	1.80159	0.100399
$323$	21.4387	1.19288
$324$	4.32367	0.240204
$325$	0	0
$326$	−20.3021	−1.12443
$327$	−1.78826	−0.0988909
$328$	−0.0812868	−0.00448831
$329$	−1.68681	−0.0929970
$330$	0	0
$331$	21.4216	1.17744	0.588718	−	0.808339i	$-0.299633\pi$
$331$	21.4216	1.17744	0.588718	+	0.808339i	$0.299633\pi$
$332$	14.0297	0.769980
$333$	11.3901	0.624172
$334$	5.87391	0.321406
$335$	0	0
$336$	3.26196	0.177954
$337$	7.59079	0.413497	0.206748	−	0.978394i	$-0.433712\pi$
$337$	7.59079	0.413497	0.206748	+	0.978394i	$0.433712\pi$
$338$	−59.6917	−3.24680
$339$	2.88032	0.156437
$340$	0	0
$341$	−12.1907	−0.660163
$342$	−20.0767	−1.08563
$343$	11.1770	0.603503
$344$	−7.45331	−0.401855
$345$	0	0
$346$	13.2254	0.711002
$347$	23.1493	1.24272	0.621359	−	0.783526i	$-0.286581\pi$
$347$	23.1493	1.24272	0.621359	+	0.783526i	$0.286581\pi$
$348$	−1.69796	−0.0910203
$349$	−5.31226	−0.284359	−0.142179	−	0.989841i	$-0.545411\pi$
$349$	−5.31226	−0.284359	−0.142179	+	0.989841i	$0.545411\pi$
$350$	0	0
$351$	−28.7271	−1.53334
$352$	−21.6491	−1.15390
$353$	26.2325	1.39622	0.698108	−	0.715992i	$-0.254025\pi$
$353$	26.2325	1.39622	0.698108	+	0.715992i	$0.254025\pi$
$354$	−10.3215	−0.548582
$355$	0	0
$356$	−9.87706	−0.523483
$357$	2.94510	0.155871
$358$	−33.9463	−1.79412
$359$	−22.3500	−1.17959	−0.589795	−	0.807553i	$-0.700792\pi$
$359$	−22.3500	−1.17959	−0.589795	+	0.807553i	$0.700792\pi$
$360$	0	0
$361$	3.64694	0.191944
$362$	22.7316	1.19475
$363$	2.97182	0.155980
$364$	−6.34300	−0.332463
$365$	0	0
$366$	−3.16284	−0.165324
$367$	22.9966	1.20041	0.600205	−	0.799846i	$-0.295085\pi$
$367$	22.9966	1.20041	0.600205	+	0.799846i	$0.295085\pi$
$368$	−6.07058	−0.316451
$369$	0.123073	0.00640691
$370$	0	0
$371$	−7.52010	−0.390424
$372$	2.71212	0.140617
$373$	−4.66771	−0.241685	−0.120842	−	0.992672i	$-0.538560\pi$
$373$	−4.66771	−0.241685	−0.120842	+	0.992672i	$0.538560\pi$
$374$	−30.5454	−1.57947
$375$	0	0
$376$	3.17407	0.163690
$377$	−13.5752	−0.699161
$378$	−6.21200	−0.319511
$379$	−6.74925	−0.346686	−0.173343	−	0.984862i	$-0.555457\pi$
$379$	−6.74925	−0.346686	−0.173343	+	0.984862i	$0.555457\pi$
$380$	0	0
$381$	−6.06789	−0.310867
$382$	13.7029	0.701103
$383$	13.6277	0.696341	0.348170	−	0.937431i	$-0.386803\pi$
$383$	13.6277	0.696341	0.348170	+	0.937431i	$0.386803\pi$
$384$	−8.84831	−0.451539
$385$	0	0
$386$	−0.654885	−0.0333328
$387$	11.2847	0.573635
$388$	1.26689	0.0643165
$389$	−16.9600	−0.859905	−0.429953	−	0.902851i	$-0.641470\pi$
$389$	−16.9600	−0.859905	−0.429953	+	0.902851i	$0.641470\pi$
$390$	0	0
$391$	−5.48091	−0.277181
$392$	−9.95660	−0.502884
$393$	−7.13237	−0.359780
$394$	−29.9926	−1.51101
$395$	0	0
$396$	10.1598	0.510549
$397$	22.1463	1.11149	0.555746	−	0.831352i	$-0.312433\pi$
$397$	22.1463	1.11149	0.555746	+	0.831352i	$0.312433\pi$
$398$	−40.1666	−2.01337
$399$	3.11108	0.155749
$400$	0	0
$401$	10.7062	0.534643	0.267322	−	0.963607i	$-0.413861\pi$
$401$	10.7062	0.534643	0.267322	+	0.963607i	$0.413861\pi$
$402$	−5.09214	−0.253973
$403$	21.6835	1.08013
$404$	20.6970	1.02971
$405$	0	0
$406$	−2.93554	−0.145688
$407$	18.3058	0.907387
$408$	−5.54178	−0.274359
$409$	−14.6187	−0.722846	−0.361423	−	0.932402i	$-0.617709\pi$
$409$	−14.6187	−0.722846	−0.361423	+	0.932402i	$0.617709\pi$
$410$	0	0
$411$	−7.12615	−0.351507
$412$	−2.12097	−0.104493
$413$	−6.33794	−0.311870
$414$	5.13271	0.252259
$415$	0	0
$416$	38.5071	1.88797
$417$	−13.6740	−0.669619
$418$	−32.2668	−1.57822
$419$	16.4191	0.802123	0.401062	−	0.916051i	$-0.368641\pi$
$419$	16.4191	0.802123	0.401062	+	0.916051i	$0.368641\pi$
$420$	0	0
$421$	−14.1185	−0.688096	−0.344048	−	0.938952i	$-0.611798\pi$
$421$	−14.1185	−0.688096	−0.344048	+	0.938952i	$0.611798\pi$
$422$	−12.9530	−0.630542
$423$	−4.80571	−0.233662
$424$	14.1505	0.687210
$425$	0	0
$426$	7.97729	0.386501
$427$	−1.94214	−0.0939869
$428$	19.9993	0.966700
$429$	−20.4983	−0.989667
$430$	0	0
$431$	−10.6588	−0.513418	−0.256709	−	0.966489i	$-0.582638\pi$
$431$	−10.6588	−0.513418	−0.256709	+	0.966489i	$0.582638\pi$
$432$	20.9318	1.00708
$433$	−8.39923	−0.403641	−0.201821	−	0.979423i	$-0.564686\pi$
$433$	−8.39923	−0.403641	−0.201821	+	0.979423i	$0.564686\pi$
$434$	4.68887	0.225073
$435$	0	0
$436$	−2.53374	−0.121344
$437$	−5.78979	−0.276963
$438$	14.2636	0.681539
$439$	13.5726	0.647784	0.323892	−	0.946094i	$-0.395009\pi$
$439$	13.5726	0.647784	0.323892	+	0.946094i	$0.395009\pi$
$440$	0	0
$441$	15.0748	0.717850
$442$	54.3308	2.58425
$443$	−21.5690	−1.02477	−0.512387	−	0.858755i	$-0.671239\pi$
$443$	−21.5690	−1.02477	−0.512387	+	0.858755i	$0.671239\pi$
$444$	−4.07259	−0.193277
$445$	0	0
$446$	5.27294	0.249681
$447$	10.6047	0.501585
$448$	−0.0639718	−0.00302238
$449$	0.671701	0.0316995	0.0158498	−	0.999874i	$-0.494955\pi$
$449$	0.671701	0.0316995	0.0158498	+	0.999874i	$0.494955\pi$
$450$	0	0
$451$	0.197800	0.00931402
$452$	4.08105	0.191956
$453$	−0.516535	−0.0242689
$454$	−36.6022	−1.71783
$455$	0	0
$456$	−5.85409	−0.274143
$457$	−38.6974	−1.81019	−0.905095	−	0.425210i	$-0.860200\pi$
$457$	−38.6974	−1.81019	−0.905095	+	0.425210i	$0.860200\pi$
$458$	7.90927	0.369576
$459$	18.8985	0.882108
$460$	0	0
$461$	10.2750	0.478556	0.239278	−	0.970951i	$-0.423089\pi$
$461$	10.2750	0.478556	0.239278	+	0.970951i	$0.423089\pi$
$462$	−4.43259	−0.206223
$463$	28.1871	1.30997	0.654984	−	0.755643i	$-0.272675\pi$
$463$	28.1871	1.30997	0.654984	+	0.755643i	$0.272675\pi$
$464$	9.89150	0.459202
$465$	0	0
$466$	25.8642	1.19813
$467$	40.0157	1.85171	0.925854	−	0.377882i	$-0.123348\pi$
$467$	40.0157	1.85171	0.925854	+	0.377882i	$0.123348\pi$
$468$	−18.0711	−0.835338
$469$	−3.12683	−0.144384
$470$	0	0
$471$	12.4076	0.571710
$472$	11.9261	0.548942
$473$	18.1365	0.833919
$474$	8.21233	0.377205
$475$	0	0
$476$	4.17284	0.191262
$477$	−21.4247	−0.980969
$478$	−25.2175	−1.15342
$479$	−2.18596	−0.0998791	−0.0499395	−	0.998752i	$-0.515903\pi$
$479$	−2.18596	−0.0998791	−0.0499395	+	0.998752i	$0.515903\pi$
$480$	0	0
$481$	−32.5604	−1.48463
$482$	−1.76114	−0.0802179
$483$	−0.795361	−0.0361902
$484$	4.21069	0.191395
$485$	0	0
$486$	−27.5383	−1.24916
$487$	−2.45705	−0.111340	−0.0556699	−	0.998449i	$-0.517729\pi$
$487$	−2.45705	−0.111340	−0.0556699	+	0.998449i	$0.517729\pi$
$488$	3.65452	0.165432
$489$	8.96291	0.405317
$490$	0	0
$491$	6.36822	0.287394	0.143697	−	0.989622i	$-0.454101\pi$
$491$	6.36822	0.287394	0.143697	+	0.989622i	$0.454101\pi$
$492$	−0.0440054	−0.00198392
$493$	8.93068	0.402218
$494$	57.3927	2.58222
$495$	0	0
$496$	−15.7995	−0.709418
$497$	4.89847	0.219726
$498$	−17.4386	−0.781443
$499$	−20.8311	−0.932529	−0.466264	−	0.884645i	$-0.654400\pi$
$499$	−20.8311	−0.932529	−0.466264	+	0.884645i	$0.654400\pi$
$500$	0	0
$501$	−2.59320	−0.115856
$502$	−20.2523	−0.903904
$503$	−7.86209	−0.350553	−0.175277	−	0.984519i	$-0.556082\pi$
$503$	−7.86209	−0.350553	−0.175277	+	0.984519i	$0.556082\pi$
$504$	3.18675	0.141949
$505$	0	0
$506$	8.24916	0.366720
$507$	26.3525	1.17036
$508$	−8.59743	−0.381449
$509$	34.9971	1.55122	0.775611	−	0.631212i	$-0.217442\pi$
$509$	34.9971	1.55122	0.775611	+	0.631212i	$0.217442\pi$
$510$	0	0
$511$	8.75855	0.387456
$512$	−12.2690	−0.542216
$513$	19.9636	0.881414
$514$	42.6015	1.87907
$515$	0	0
$516$	−4.03492	−0.177628
$517$	−7.72363	−0.339685
$518$	−7.04093	−0.309361
$519$	−5.83872	−0.256291
$520$	0	0
$521$	33.9931	1.48926	0.744632	−	0.667475i	$-0.232625\pi$
$521$	33.9931	1.48926	0.744632	+	0.667475i	$0.232625\pi$
$522$	−8.36332	−0.366053
$523$	23.7216	1.03727	0.518637	−	0.854994i	$-0.326440\pi$
$523$	23.7216	1.03727	0.518637	+	0.854994i	$0.326440\pi$
$524$	−10.1057	−0.441468
$525$	0	0
$526$	−52.1888	−2.27554
$527$	−14.2648	−0.621384
$528$	14.9359	0.650003
$529$	−21.5198	−0.935644
$530$	0	0
$531$	−18.0567	−0.783595
$532$	4.40800	0.191111
$533$	−0.351824	−0.0152392
$534$	12.2770	0.531276
$535$	0	0
$536$	5.88375	0.254139
$537$	14.9865	0.646716
$538$	32.8362	1.41567
$539$	24.2279	1.04357
$540$	0	0
$541$	35.8482	1.54123	0.770617	−	0.637299i	$-0.219948\pi$
$541$	35.8482	1.54123	0.770617	+	0.637299i	$0.219948\pi$
$542$	36.0189	1.54715
$543$	−10.0355	−0.430664
$544$	−25.3325	−1.08612
$545$	0	0
$546$	7.88421	0.337413
$547$	2.43476	0.104103	0.0520515	−	0.998644i	$-0.483424\pi$
$547$	2.43476	0.104103	0.0520515	+	0.998644i	$0.483424\pi$
$548$	−10.0969	−0.431316
$549$	−5.53315	−0.236149
$550$	0	0
$551$	9.43398	0.401901
$552$	1.49663	0.0637006
$553$	5.04279	0.214441
$554$	−26.1659	−1.11168
$555$	0	0
$556$	−19.3743	−0.821655
$557$	−36.9490	−1.56558	−0.782791	−	0.622285i	$-0.786204\pi$
$557$	−36.9490	−1.56558	−0.782791	+	0.622285i	$0.786204\pi$
$558$	13.3586	0.565513
$559$	−32.2593	−1.36442
$560$	0	0
$561$	13.4851	0.569342
$562$	−13.8704	−0.585090
$563$	24.9323	1.05077	0.525385	−	0.850865i	$-0.323921\pi$
$563$	24.9323	1.05077	0.525385	+	0.850865i	$0.323921\pi$
$564$	1.71831	0.0723540
$565$	0	0
$566$	20.8772	0.877536
$567$	−3.30005	−0.138589
$568$	−9.21742	−0.386754
$569$	38.7931	1.62629	0.813145	−	0.582061i	$-0.197754\pi$
$569$	38.7931	1.62629	0.813145	+	0.582061i	$0.197754\pi$
$570$	0	0
$571$	35.0598	1.46721	0.733604	−	0.679577i	$-0.237837\pi$
$571$	35.0598	1.46721	0.733604	+	0.679577i	$0.237837\pi$
$572$	−29.0435	−1.21437
$573$	−6.04953	−0.252723
$574$	−0.0760792	−0.00317548
$575$	0	0
$576$	−0.182255	−0.00759396
$577$	27.4454	1.14257	0.571283	−	0.820753i	$-0.306446\pi$
$577$	27.4454	1.14257	0.571283	+	0.820753i	$0.306446\pi$
$578$	−5.80294	−0.241370
$579$	0.289117	0.0120153
$580$	0	0
$581$	−10.7082	−0.444251
$582$	−1.57471	−0.0652740
$583$	−34.4333	−1.42608
$584$	−16.4809	−0.681985
$585$	0	0
$586$	45.5874	1.88320
$587$	35.1269	1.44984	0.724921	−	0.688832i	$-0.241876\pi$
$587$	35.1269	1.44984	0.724921	+	0.688832i	$0.241876\pi$
$588$	−5.39010	−0.222284
$589$	−15.0687	−0.620895
$590$	0	0
$591$	13.2411	0.544665
$592$	23.7249	0.975088
$593$	39.3866	1.61741	0.808707	−	0.588211i	$-0.200168\pi$
$593$	39.3866	1.61741	0.808707	+	0.588211i	$0.200168\pi$
$594$	−28.4437	−1.16706
$595$	0	0
$596$	15.0255	0.615470
$597$	17.7327	0.725750
$598$	−14.6727	−0.600011
$599$	21.0294	0.859238	0.429619	−	0.903010i	$-0.358648\pi$
$599$	21.0294	0.859238	0.429619	+	0.903010i	$0.358648\pi$
$600$	0	0
$601$	14.1052	0.575365	0.287682	−	0.957726i	$-0.407115\pi$
$601$	14.1052	0.575365	0.287682	+	0.957726i	$0.407115\pi$
$602$	−6.97581	−0.284313
$603$	−8.90832	−0.362775
$604$	−0.731865	−0.0297792
$605$	0	0
$606$	−25.7259	−1.04504
$607$	−29.6416	−1.20311	−0.601557	−	0.798830i	$-0.705453\pi$
$607$	−29.6416	−1.20311	−0.601557	+	0.798830i	$0.705453\pi$
$608$	−26.7601	−1.08527
$609$	1.29597	0.0525155
$610$	0	0
$611$	13.7379	0.555777
$612$	11.8884	0.480559
$613$	29.1045	1.17552	0.587759	−	0.809036i	$-0.300010\pi$
$613$	29.1045	1.17552	0.587759	+	0.809036i	$0.300010\pi$
$614$	−36.6285	−1.47821
$615$	0	0
$616$	5.12167	0.206358
$617$	−19.6823	−0.792379	−0.396190	−	0.918169i	$-0.629668\pi$
$617$	−19.6823	−0.792379	−0.396190	+	0.918169i	$0.629668\pi$
$618$	2.63633	0.106049
$619$	−45.6546	−1.83501	−0.917506	−	0.397722i	$-0.869801\pi$
$619$	−45.6546	−1.83501	−0.917506	+	0.397722i	$0.869801\pi$
$620$	0	0
$621$	−5.10378	−0.204808
$622$	23.2450	0.932040
$623$	7.53869	0.302031
$624$	−26.5664	−1.06351
$625$	0	0
$626$	−2.46235	−0.0984153
$627$	14.2451	0.568894
$628$	17.5799	0.701516
$629$	21.4204	0.854087
$630$	0	0
$631$	−28.5316	−1.13583	−0.567913	−	0.823088i	$-0.692249\pi$
$631$	−28.5316	−1.13583	−0.567913	+	0.823088i	$0.692249\pi$
$632$	−9.48899	−0.377452
$633$	5.71846	0.227288
$634$	12.2388	0.486066
$635$	0	0
$636$	7.66053	0.303760
$637$	−43.0940	−1.70745
$638$	−13.4413	−0.532147
$639$	13.9557	0.552078
$640$	0	0
$641$	43.5146	1.71872	0.859361	−	0.511370i	$-0.170862\pi$
$641$	43.5146	1.71872	0.859361	+	0.511370i	$0.170862\pi$
$642$	−24.8586	−0.981093
$643$	−4.99541	−0.197000	−0.0984998	−	0.995137i	$-0.531404\pi$
$643$	−4.99541	−0.197000	−0.0984998	+	0.995137i	$0.531404\pi$
$644$	−1.12693	−0.0444071
$645$	0	0
$646$	−37.7567	−1.48552
$647$	−11.1753	−0.439348	−0.219674	−	0.975573i	$-0.570499\pi$
$647$	−11.1753	−0.439348	−0.219674	+	0.975573i	$0.570499\pi$
$648$	6.20969	0.243940
$649$	−29.0203	−1.13915
$650$	0	0
$651$	−2.07003	−0.0811310
$652$	12.6993	0.497344
$653$	15.9098	0.622598	0.311299	−	0.950312i	$-0.399236\pi$
$653$	15.9098	0.622598	0.311299	+	0.950312i	$0.399236\pi$
$654$	3.14938	0.123151
$655$	0	0
$656$	0.256354	0.0100089
$657$	24.9530	0.973510
$658$	2.97072	0.115811
$659$	−5.90670	−0.230092	−0.115046	−	0.993360i	$-0.536702\pi$
$659$	−5.90670	−0.230092	−0.115046	+	0.993360i	$0.536702\pi$
$660$	0	0
$661$	2.06179	0.0801943	0.0400971	−	0.999196i	$-0.487233\pi$
$661$	2.06179	0.0801943	0.0400971	+	0.999196i	$0.487233\pi$
$662$	−37.7265	−1.46628
$663$	−23.9858	−0.931533
$664$	20.1496	0.781955
$665$	0	0
$666$	−20.0595	−0.777292
$667$	−2.41184	−0.0933868
$668$	−3.67423	−0.142160
$669$	−2.32788	−0.0900012
$670$	0	0
$671$	−8.89274	−0.343301
$672$	−3.67612	−0.141809
$673$	5.67527	0.218766	0.109383	−	0.994000i	$-0.465113\pi$
$673$	5.67527	0.218766	0.109383	+	0.994000i	$0.465113\pi$
$674$	−13.3685	−0.514934
$675$	0	0
$676$	37.3382	1.43609
$677$	−34.1859	−1.31387	−0.656936	−	0.753946i	$-0.728148\pi$
$677$	−34.1859	−1.31387	−0.656936	+	0.753946i	$0.728148\pi$
$678$	−5.07266	−0.194814
$679$	−0.966955	−0.0371083
$680$	0	0
$681$	16.1590	0.619216
$682$	21.4695	0.822111
$683$	−27.9631	−1.06998	−0.534988	−	0.844859i	$-0.679684\pi$
$683$	−27.9631	−1.06998	−0.534988	+	0.844859i	$0.679684\pi$
$684$	12.5584	0.480181
$685$	0	0
$686$	−19.6844	−0.751552
$687$	−3.49176	−0.133219
$688$	23.5055	0.896139
$689$	61.2461	2.33329
$690$	0	0
$691$	37.3251	1.41991	0.709956	−	0.704246i	$-0.248715\pi$
$691$	37.3251	1.41991	0.709956	+	0.704246i	$0.248715\pi$
$692$	−8.27273	−0.314482
$693$	−7.75449	−0.294569
$694$	−40.7692	−1.54758
$695$	0	0
$696$	−2.43863	−0.0924359
$697$	0.231453	0.00876691
$698$	9.35565	0.354117
$699$	−11.4184	−0.431885
$700$	0	0
$701$	13.9059	0.525220	0.262610	−	0.964902i	$-0.415417\pi$
$701$	13.9059	0.525220	0.262610	+	0.964902i	$0.415417\pi$
$702$	50.5925	1.90949
$703$	22.6276	0.853414
$704$	−0.292916	−0.0110397
$705$	0	0
$706$	−46.1993	−1.73873
$707$	−15.7970	−0.594109
$708$	6.45629	0.242642
$709$	10.7383	0.403287	0.201643	−	0.979459i	$-0.435372\pi$
$709$	10.7383	0.403287	0.201643	+	0.979459i	$0.435372\pi$
$710$	0	0
$711$	14.3669	0.538799
$712$	−14.1855	−0.531624
$713$	3.85238	0.144273
$714$	−5.18675	−0.194109
$715$	0	0
$716$	21.2340	0.793552
$717$	11.1330	0.415768
$718$	39.3616	1.46896
$719$	10.1192	0.377381	0.188691	−	0.982037i	$-0.439576\pi$
$719$	10.1192	0.377381	0.188691	+	0.982037i	$0.439576\pi$
$720$	0	0
$721$	1.61884	0.0602887
$722$	−6.42278	−0.239031
$723$	0.777505	0.0289157
$724$	−14.2190	−0.528446
$725$	0	0
$726$	−5.23379	−0.194244
$727$	43.3079	1.60620	0.803100	−	0.595845i	$-0.203183\pi$
$727$	43.3079	1.60620	0.803100	+	0.595845i	$0.203183\pi$
$728$	−9.10986	−0.337634
$729$	0.383126	0.0141899
$730$	0	0
$731$	21.2223	0.784934
$732$	1.97841	0.0731242
$733$	−5.46247	−0.201761	−0.100880	−	0.994899i	$-0.532166\pi$
$733$	−5.46247	−0.201761	−0.100880	+	0.994899i	$0.532166\pi$
$734$	−40.5002	−1.49489
$735$	0	0
$736$	6.84135	0.252175
$737$	−14.3172	−0.527382
$738$	−0.216749	−0.00797863
$739$	26.7081	0.982473	0.491237	−	0.871026i	$-0.336545\pi$
$739$	26.7081	0.982473	0.491237	+	0.871026i	$0.336545\pi$
$740$	0	0
$741$	−25.3376	−0.930800
$742$	13.2440	0.486202
$743$	26.4728	0.971194	0.485597	−	0.874183i	$-0.338602\pi$
$743$	26.4728	0.971194	0.485597	+	0.874183i	$0.338602\pi$
$744$	3.89517	0.142804
$745$	0	0
$746$	8.22051	0.300974
$747$	−30.5076	−1.11621
$748$	19.1067	0.698610
$749$	−15.2645	−0.557752
$750$	0	0
$751$	31.4414	1.14731	0.573657	−	0.819096i	$-0.305524\pi$
$751$	31.4414	1.14731	0.573657	+	0.819096i	$0.305524\pi$
$752$	−10.0100	−0.365029
$753$	8.94093	0.325826
$754$	23.9080	0.870676
$755$	0	0
$756$	3.88572	0.141322
$757$	−21.0137	−0.763756	−0.381878	−	0.924213i	$-0.624722\pi$
$757$	−21.0137	−0.763756	−0.381878	+	0.924213i	$0.624722\pi$
$758$	11.8864	0.431734
$759$	−3.64182	−0.132190
$760$	0	0
$761$	24.3895	0.884117	0.442059	−	0.896986i	$-0.354248\pi$
$761$	24.3895	0.884117	0.442059	+	0.896986i	$0.354248\pi$
$762$	10.6864	0.387128
$763$	1.93388	0.0700112
$764$	−8.57142	−0.310103
$765$	0	0
$766$	−24.0003	−0.867164
$767$	51.6182	1.86383
$768$	15.4648	0.558039
$769$	−24.9066	−0.898156	−0.449078	−	0.893493i	$-0.648247\pi$
$769$	−24.9066	−0.898156	−0.449078	+	0.893493i	$0.648247\pi$
$770$	0	0
$771$	−18.8076	−0.677340
$772$	0.409642	0.0147433
$773$	−18.8336	−0.677396	−0.338698	−	0.940895i	$-0.609987\pi$
$773$	−18.8336	−0.677396	−0.338698	+	0.940895i	$0.609987\pi$
$774$	−19.8740	−0.714357
$775$	0	0
$776$	1.81951	0.0653167
$777$	3.10841	0.111514
$778$	29.8690	1.07085
$779$	0.244497	0.00876001
$780$	0	0
$781$	22.4292	0.802581
$782$	9.65266	0.345179
$783$	8.31619	0.297196
$784$	31.4001	1.12143
$785$	0	0
$786$	12.5611	0.448041
$787$	2.77406	0.0988845	0.0494422	−	0.998777i	$-0.484256\pi$
$787$	2.77406	0.0988845	0.0494422	+	0.998777i	$0.484256\pi$
$788$	18.7609	0.668330
$789$	23.0402	0.820253
$790$	0	0
$791$	−3.11487	−0.110752
$792$	14.5916	0.518489
$793$	15.8174	0.561694
$794$	−39.0028	−1.38416
$795$	0	0
$796$	25.1249	0.890530
$797$	9.29411	0.329214	0.164607	−	0.986359i	$-0.447364\pi$
$797$	9.29411	0.329214	0.164607	+	0.986359i	$0.447364\pi$
$798$	−5.47905	−0.193956
$799$	−9.03771	−0.319731
$800$	0	0
$801$	21.4776	0.758875
$802$	−18.8552	−0.665800
$803$	40.1039	1.41524
$804$	3.18522	0.112334
$805$	0	0
$806$	−38.1877	−1.34510
$807$	−14.4964	−0.510298
$808$	29.7252	1.04573
$809$	10.6918	0.375903	0.187951	−	0.982178i	$-0.439815\pi$
$809$	10.6918	0.375903	0.187951	+	0.982178i	$0.439815\pi$
$810$	0	0
$811$	−28.7280	−1.00878	−0.504388	−	0.863477i	$-0.668282\pi$
$811$	−28.7280	−1.00878	−0.504388	+	0.863477i	$0.668282\pi$
$812$	1.83623	0.0644391
$813$	−15.9016	−0.557692
$814$	−32.2392	−1.12998
$815$	0	0
$816$	17.4771	0.611821
$817$	22.4183	0.784316
$818$	25.7456	0.900172
$819$	13.7928	0.481961
$820$	0	0
$821$	4.95103	0.172792	0.0863961	−	0.996261i	$-0.472465\pi$
$821$	4.95103	0.172792	0.0863961	+	0.996261i	$0.472465\pi$
$822$	12.5502	0.437738
$823$	22.5033	0.784417	0.392208	−	0.919876i	$-0.371711\pi$
$823$	22.5033	0.784417	0.392208	+	0.919876i	$0.371711\pi$
$824$	−3.04616	−0.106118
$825$	0	0
$826$	11.1620	0.388376
$827$	12.1529	0.422599	0.211299	−	0.977421i	$-0.432231\pi$
$827$	12.1529	0.422599	0.211299	+	0.977421i	$0.432231\pi$
$828$	−3.21060	−0.111576
$829$	−41.3947	−1.43770	−0.718849	−	0.695166i	$-0.755331\pi$
$829$	−41.3947	−1.43770	−0.718849	+	0.695166i	$0.755331\pi$
$830$	0	0
$831$	11.5516	0.400722
$832$	0.521007	0.0180627
$833$	28.3500	0.982271
$834$	24.0819	0.833888
$835$	0	0
$836$	20.1835	0.698060
$837$	−13.2833	−0.459137
$838$	−28.9163	−0.998897
$839$	0.647490	0.0223538	0.0111769	−	0.999938i	$-0.496442\pi$
$839$	0.647490	0.0223538	0.0111769	+	0.999938i	$0.496442\pi$
$840$	0	0
$841$	−25.0701	−0.864486
$842$	24.8648	0.856897
$843$	6.12349	0.210904
$844$	8.10233	0.278894
$845$	0	0
$846$	8.46355	0.290983
$847$	−3.21382	−0.110428
$848$	−44.6265	−1.53248
$849$	−9.21683	−0.316321
$850$	0	0
$851$	−5.78483	−0.198302
$852$	−4.98994	−0.170952
$853$	57.8675	1.98134	0.990672	−	0.136268i	$-0.0435109\pi$
$853$	57.8675	1.98134	0.990672	+	0.136268i	$0.0435109\pi$
$854$	3.42039	0.117043
$855$	0	0
$856$	28.7231	0.981735
$857$	27.1840	0.928589	0.464294	−	0.885681i	$-0.346308\pi$
$857$	27.1840	0.928589	0.464294	+	0.885681i	$0.346308\pi$
$858$	36.1004	1.23245
$859$	−21.2042	−0.723479	−0.361740	−	0.932279i	$-0.617817\pi$
$859$	−21.2042	−0.723479	−0.361740	+	0.932279i	$0.617817\pi$
$860$	0	0
$861$	0.0335872	0.00114465
$862$	18.7717	0.639368
$863$	14.1529	0.481771	0.240885	−	0.970554i	$-0.422562\pi$
$863$	14.1529	0.481771	0.240885	+	0.970554i	$0.422562\pi$
$864$	−23.5894	−0.802529
$865$	0	0
$866$	14.7922	0.502661
$867$	2.56187	0.0870055
$868$	−2.93297	−0.0995516
$869$	23.0901	0.783277
$870$	0	0
$871$	25.4659	0.862880
$872$	−3.63897	−0.123231
$873$	−2.75485	−0.0932374
$874$	10.1967	0.344907
$875$	0	0
$876$	−8.92211	−0.301450
$877$	5.69110	0.192175	0.0960875	−	0.995373i	$-0.469367\pi$
$877$	5.69110	0.192175	0.0960875	+	0.995373i	$0.469367\pi$
$878$	−23.9033	−0.806696
$879$	−20.1258	−0.678827
$880$	0	0
$881$	−54.7404	−1.84425	−0.922125	−	0.386892i	$-0.873549\pi$
$881$	−54.7404	−1.84425	−0.922125	+	0.386892i	$0.873549\pi$
$882$	−26.5490	−0.893950
$883$	−6.54973	−0.220416	−0.110208	−	0.993909i	$-0.535152\pi$
$883$	−6.54973	−0.220416	−0.110208	+	0.993909i	$0.535152\pi$
$884$	−33.9849	−1.14304
$885$	0	0
$886$	37.9861	1.27617
$887$	40.3921	1.35623	0.678117	−	0.734954i	$-0.262796\pi$
$887$	40.3921	1.35623	0.678117	+	0.734954i	$0.262796\pi$
$888$	−5.84908	−0.196282
$889$	6.56201	0.220083
$890$	0	0
$891$	−15.1104	−0.506217
$892$	−3.29832	−0.110436
$893$	−9.54704	−0.319480
$894$	−18.6764	−0.624633
$895$	0	0
$896$	9.56885	0.319673
$897$	6.47767	0.216283
$898$	−1.18296	−0.0394760
$899$	−6.27713	−0.209354
$900$	0	0
$901$	−40.2917	−1.34231
$902$	−0.348353	−0.0115989
$903$	3.07967	0.102485
$904$	5.86123	0.194942
$905$	0	0
$906$	0.909692	0.0302225
$907$	58.3106	1.93617	0.968086	−	0.250617i	$-0.0806336\pi$
$907$	58.3106	1.93617	0.968086	+	0.250617i	$0.0806336\pi$
$908$	22.8953	0.759808
$909$	−45.0056	−1.49274
$910$	0	0
$911$	33.3298	1.10427	0.552133	−	0.833756i	$-0.313814\pi$
$911$	33.3298	1.10427	0.552133	+	0.833756i	$0.313814\pi$
$912$	18.4621	0.611340
$913$	−49.0310	−1.62269
$914$	68.1517	2.25426
$915$	0	0
$916$	−4.94739	−0.163466
$917$	7.71317	0.254711
$918$	−33.2830	−1.09850
$919$	−7.75814	−0.255917	−0.127959	−	0.991779i	$-0.540843\pi$
$919$	−7.75814	−0.255917	−0.127959	+	0.991779i	$0.540843\pi$
$920$	0	0
$921$	16.1707	0.532842
$922$	−18.0958	−0.595953
$923$	−39.8947	−1.31315
$924$	2.77267	0.0912140
$925$	0	0
$926$	−49.6416	−1.63132
$927$	4.61206	0.151480
$928$	−11.1474	−0.365932
$929$	45.7544	1.50115	0.750576	−	0.660784i	$-0.229776\pi$
$929$	45.7544	1.50115	0.750576	+	0.660784i	$0.229776\pi$
$930$	0	0
$931$	29.9477	0.981497
$932$	−16.1785	−0.529944
$933$	−10.2621	−0.335968
$934$	−70.4734	−2.30596
$935$	0	0
$936$	−25.9539	−0.848330
$937$	16.9588	0.554021	0.277011	−	0.960867i	$-0.410656\pi$
$937$	16.9588	0.554021	0.277011	+	0.960867i	$0.410656\pi$
$938$	5.50680	0.179804
$939$	1.08707	0.0354753
$940$	0	0
$941$	−5.17652	−0.168750	−0.0843748	−	0.996434i	$-0.526889\pi$
$941$	−5.17652	−0.168750	−0.0843748	+	0.996434i	$0.526889\pi$
$942$	−21.8515	−0.711960
$943$	−0.0625067	−0.00203550
$944$	−37.6112	−1.22414
$945$	0	0
$946$	−31.9411	−1.03849
$947$	−4.15194	−0.134920	−0.0674600	−	0.997722i	$-0.521489\pi$
$947$	−4.15194	−0.134920	−0.0674600	+	0.997722i	$0.521489\pi$
$948$	−5.13696	−0.166841
$949$	−71.3324	−2.31555
$950$	0	0
$951$	−5.40317	−0.175210
$952$	5.99306	0.194236
$953$	−57.2662	−1.85503	−0.927517	−	0.373780i	$-0.878061\pi$
$953$	−57.2662	−1.85503	−0.927517	+	0.373780i	$0.878061\pi$
$954$	37.7320	1.22162
$955$	0	0
$956$	15.7740	0.510168
$957$	5.93404	0.191820
$958$	3.84979	0.124381
$959$	7.70645	0.248854
$960$	0	0
$961$	−20.9737	−0.676570
$962$	57.3436	1.84883
$963$	−43.4884	−1.40139
$964$	1.10163	0.0354810
$965$	0	0
$966$	1.40074	0.0450682
$967$	4.49860	0.144665	0.0723327	−	0.997381i	$-0.476956\pi$
$967$	4.49860	0.144665	0.0723327	+	0.997381i	$0.476956\pi$
$968$	6.04742	0.194371
$969$	16.6687	0.535477
$970$	0	0
$971$	−36.9890	−1.18703	−0.593517	−	0.804822i	$-0.702261\pi$
$971$	−36.9890	−1.18703	−0.593517	+	0.804822i	$0.702261\pi$
$972$	17.2257	0.552515
$973$	14.7875	0.474066
$974$	4.32723	0.138653
$975$	0	0
$976$	−11.5253	−0.368915
$977$	−50.3628	−1.61125	−0.805624	−	0.592427i	$-0.798170\pi$
$977$	−50.3628	−1.61125	−0.805624	+	0.592427i	$0.798170\pi$
$978$	−15.7850	−0.504748
$979$	34.5184	1.10321
$980$	0	0
$981$	5.50961	0.175908
$982$	−11.2153	−0.357896
$983$	−4.86130	−0.155051	−0.0775257	−	0.996990i	$-0.524702\pi$
$983$	−4.86130	−0.155051	−0.0775257	+	0.996990i	$0.524702\pi$
$984$	−0.0632009	−0.00201477
$985$	0	0
$986$	−15.7282	−0.500888
$987$	−1.31151	−0.0417457
$988$	−35.9002	−1.14214
$989$	−5.73133	−0.182246
$990$	0	0
$991$	8.76042	0.278284	0.139142	−	0.990272i	$-0.455566\pi$
$991$	8.76042	0.278284	0.139142	+	0.990272i	$0.455566\pi$
$992$	17.8055	0.565326
$993$	16.6554	0.528543
$994$	−8.62690	−0.273629
$995$	0	0
$996$	10.9082	0.345639
$997$	−37.5824	−1.19025	−0.595123	−	0.803635i	$-0.702897\pi$
$997$	−37.5824	−1.19025	−0.595123	+	0.803635i	$0.702897\pi$
$998$	36.6866	1.16129
$999$	19.9465	0.631079

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.g.1.1		11
5.4	even	2		1205.2.a.b.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.b.1.11	✓	11	5.4	even	2
6025.2.a.g.1.1		11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.76114 q^{2} +0.777505 q^{3} +1.10163 q^{4} -1.36930 q^{6} -0.840819 q^{7} +1.58216 q^{8} -2.39549 q^{9} +O(q^{10})\)	\(q-1.76114 q^{2} +0.777505 q^{3} +1.10163 q^{4} -1.36930 q^{6} -0.840819 q^{7} +1.58216 q^{8} -2.39549 q^{9} -3.84997 q^{11} +0.856520 q^{12} +6.84790 q^{13} +1.48080 q^{14} -4.98967 q^{16} -4.50500 q^{17} +4.21879 q^{18} -4.75888 q^{19} -0.653741 q^{21} +6.78034 q^{22} +1.21663 q^{23} +1.23014 q^{24} -12.0601 q^{26} -4.19502 q^{27} -0.926269 q^{28} -1.98240 q^{29} +3.16644 q^{31} +5.62320 q^{32} -2.99337 q^{33} +7.93394 q^{34} -2.63893 q^{36} -4.75481 q^{37} +8.38107 q^{38} +5.32428 q^{39} -0.0513770 q^{41} +1.15133 q^{42} -4.71083 q^{43} -4.24123 q^{44} -2.14266 q^{46} +2.00615 q^{47} -3.87950 q^{48} -6.29302 q^{49} -3.50266 q^{51} +7.54383 q^{52} +8.94378 q^{53} +7.38803 q^{54} -1.33031 q^{56} -3.70005 q^{57} +3.49128 q^{58} +7.53782 q^{59} +2.30982 q^{61} -5.57655 q^{62} +2.01417 q^{63} +0.0760827 q^{64} +5.27175 q^{66} +3.71879 q^{67} -4.96282 q^{68} +0.945935 q^{69} -5.82583 q^{71} -3.79005 q^{72} -10.4167 q^{73} +8.37390 q^{74} -5.24251 q^{76} +3.23713 q^{77} -9.37682 q^{78} -5.99747 q^{79} +3.92481 q^{81} +0.0904822 q^{82} +12.7354 q^{83} -0.720179 q^{84} +8.29645 q^{86} -1.54132 q^{87} -6.09128 q^{88} -8.96588 q^{89} -5.75785 q^{91} +1.34027 q^{92} +2.46192 q^{93} -3.53312 q^{94} +4.37207 q^{96} +1.15002 q^{97} +11.0829 q^{98} +9.22254 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9	\( 11 q + 4 q^{2} + 8 q^{3} + 6 q^{4} + 7 q^{6} + 9 q^{7} + 12 q^{8} + 9 q^{9} - 3 q^{11} + 28 q^{12} + 9 q^{13} + 2 q^{14} - 16 q^{16} + 4 q^{17} + 6 q^{18} - 33 q^{19} + 2 q^{21} - 6 q^{22} + 31 q^{23} + 32 q^{24} - 20 q^{26} + 32 q^{27} + q^{28} + q^{29} + 6 q^{31} - 7 q^{32} + 35 q^{33} + 9 q^{34} + 33 q^{36} + 23 q^{37} - 20 q^{38} + 14 q^{39} + 8 q^{41} + 26 q^{42} + 19 q^{43} + 6 q^{46} + 35 q^{47} - 16 q^{48} + 4 q^{49} - 3 q^{51} + 3 q^{52} - 14 q^{53} + 9 q^{54} + 33 q^{56} - q^{57} + 11 q^{58} - 6 q^{59} + 9 q^{61} + 23 q^{62} + 31 q^{63} + 18 q^{64} - 36 q^{66} + 54 q^{67} - q^{68} + 17 q^{69} - 5 q^{71} + 64 q^{72} - 17 q^{73} + 8 q^{74} - 31 q^{76} + 18 q^{77} - 15 q^{78} - 16 q^{79} + 43 q^{81} + 61 q^{82} + 29 q^{83} + 69 q^{84} + 5 q^{86} - 5 q^{87} + 14 q^{88} - 5 q^{89} - 54 q^{91} + 6 q^{92} + 25 q^{93} - 19 q^{94} + 9 q^{96} - 6 q^{97} + 29 q^{98} + 60 q^{99}+O(q^{100}) \) 11 * q + 4 * q^2 + 8 * q^3 + 6 * q^4 + 7 * q^6 + 9 * q^7 + 12 * q^8 + 9 * q^9 - 3 * q^11 + 28 * q^12 + 9 * q^13 + 2 * q^14 - 16 * q^16 + 4 * q^17 + 6 * q^18 - 33 * q^19 + 2 * q^21 - 6 * q^22 + 31 * q^23 + 32 * q^24 - 20 * q^26 + 32 * q^27 + q^28 + q^29 + 6 * q^31 - 7 * q^32 + 35 * q^33 + 9 * q^34 + 33 * q^36 + 23 * q^37 - 20 * q^38 + 14 * q^39 + 8 * q^41 + 26 * q^42 + 19 * q^43 + 6 * q^46 + 35 * q^47 - 16 * q^48 + 4 * q^49 - 3 * q^51 + 3 * q^52 - 14 * q^53 + 9 * q^54 + 33 * q^56 - q^57 + 11 * q^58 - 6 * q^59 + 9 * q^61 + 23 * q^62 + 31 * q^63 + 18 * q^64 - 36 * q^66 + 54 * q^67 - q^68 + 17 * q^69 - 5 * q^71 + 64 * q^72 - 17 * q^73 + 8 * q^74 - 31 * q^76 + 18 * q^77 - 15 * q^78 - 16 * q^79 + 43 * q^81 + 61 * q^82 + 29 * q^83 + 69 * q^84 + 5 * q^86 - 5 * q^87 + 14 * q^88 - 5 * q^89 - 54 * q^91 + 6 * q^92 + 25 * q^93 - 19 * q^94 + 9 * q^96 - 6 * q^97 + 29 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

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