LMFDB - Embedded newform 4025.2.a.z.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 $ x^14 - 3x^13 - 18x^12 + 58x^11 + 111x^10 - 414x^9 - 244x^8 + 1330x^7 - 27x^6 - 1853x^5 + 539x^4 + 891x^3 - 218x^2 - 133*x - 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.80172$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80172 q^{2} +1.73197 q^{3} +5.84965 q^{4} -4.85249 q^{6} -1.00000 q^{7} -10.7857 q^{8} -0.000289796 q^{9} +O(q^{10})$	\(q-2.80172 q^{2} +1.73197 q^{3} +5.84965 q^{4} -4.85249 q^{6} -1.00000 q^{7} -10.7857 q^{8} -0.000289796 q^{9} +1.96838 q^{11} +10.1314 q^{12} -3.06234 q^{13} +2.80172 q^{14} +18.5191 q^{16} +5.01983 q^{17} +0.000811928 q^{18} -0.164590 q^{19} -1.73197 q^{21} -5.51485 q^{22} -1.00000 q^{23} -18.6804 q^{24} +8.57984 q^{26} -5.19640 q^{27} -5.84965 q^{28} -1.60357 q^{29} -1.84062 q^{31} -30.3142 q^{32} +3.40917 q^{33} -14.0642 q^{34} -0.00169521 q^{36} -7.42117 q^{37} +0.461136 q^{38} -5.30388 q^{39} +6.05737 q^{41} +4.85249 q^{42} -7.22063 q^{43} +11.5143 q^{44} +2.80172 q^{46} +4.25995 q^{47} +32.0746 q^{48} +1.00000 q^{49} +8.69418 q^{51} -17.9137 q^{52} +3.65970 q^{53} +14.5589 q^{54} +10.7857 q^{56} -0.285065 q^{57} +4.49276 q^{58} -7.76391 q^{59} +9.38754 q^{61} +5.15691 q^{62} +0.000289796 q^{63} +47.8937 q^{64} -9.55154 q^{66} -13.6408 q^{67} +29.3643 q^{68} -1.73197 q^{69} -16.4953 q^{71} +0.00312564 q^{72} +11.4879 q^{73} +20.7921 q^{74} -0.962796 q^{76} -1.96838 q^{77} +14.8600 q^{78} -6.11051 q^{79} -8.99913 q^{81} -16.9711 q^{82} +10.3687 q^{83} -10.1314 q^{84} +20.2302 q^{86} -2.77733 q^{87} -21.2303 q^{88} +8.46385 q^{89} +3.06234 q^{91} -5.84965 q^{92} -3.18789 q^{93} -11.9352 q^{94} -52.5032 q^{96} -4.55947 q^{97} -2.80172 q^{98} -0.000570428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	$ 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) $ 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.80172	−1.98112	−0.990559	−	0.137088i	$-0.956226\pi$
$2$	−2.80172	−1.98112	−0.990559	+	0.137088i	$0.956226\pi$
$3$	1.73197	0.999952	0.499976	−	0.866039i	$-0.333342\pi$
$3$	1.73197	0.999952	0.499976	+	0.866039i	$0.333342\pi$
$4$	5.84965	2.92483
$5$	0	0
$5$	0	0
$6$	−4.85249	−1.98102
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−10.7857	−3.81331
$9$	−0.000289796 0	−9.65986e−5 0
$10$	0	0
$11$	1.96838	0.593488	0.296744	−	0.954957i	$-0.404099\pi$
$11$	1.96838	0.593488	0.296744	+	0.954957i	$0.404099\pi$
$12$	10.1314	2.92469
$13$	−3.06234	−0.849342	−0.424671	−	0.905348i	$-0.639610\pi$
$13$	−3.06234	−0.849342	−0.424671	+	0.905348i	$0.639610\pi$
$14$	2.80172	0.748792
$15$	0	0
$16$	18.5191	4.62979
$17$	5.01983	1.21749	0.608744	−	0.793367i	$-0.291674\pi$
$17$	5.01983	1.21749	0.608744	+	0.793367i	$0.291674\pi$
$18$	0.000811928 0	0.000191373 0
$19$	−0.164590	−0.0377596	−0.0188798	−	0.999822i	$-0.506010\pi$
$19$	−0.164590	−0.0377596	−0.0188798	+	0.999822i	$0.506010\pi$
$20$	0	0
$21$	−1.73197	−0.377946
$22$	−5.51485	−1.17577
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−18.6804	−3.81312
$25$	0	0
$26$	8.57984	1.68265
$27$	−5.19640	−1.00005
$28$	−5.84965	−1.10548
$29$	−1.60357	−0.297776	−0.148888	−	0.988854i	$-0.547569\pi$
$29$	−1.60357	−0.297776	−0.148888	+	0.988854i	$0.547569\pi$
$30$	0	0
$31$	−1.84062	−0.330585	−0.165293	−	0.986245i	$-0.552857\pi$
$31$	−1.84062	−0.330585	−0.165293	+	0.986245i	$0.552857\pi$
$32$	−30.3142	−5.35884
$33$	3.40917	0.593460
$34$	−14.0642	−2.41199
$35$	0	0
$36$	−0.00169521	−0.000282534 0
$37$	−7.42117	−1.22003	−0.610016	−	0.792389i	$-0.708837\pi$
$37$	−7.42117	−1.22003	−0.610016	+	0.792389i	$0.708837\pi$
$38$	0.461136	0.0748062
$39$	−5.30388	−0.849301
$40$	0	0
$41$	6.05737	0.946002	0.473001	−	0.881062i	$-0.343171\pi$
$41$	6.05737	0.946002	0.473001	+	0.881062i	$0.343171\pi$
$42$	4.85249	0.748756
$43$	−7.22063	−1.10114	−0.550568	−	0.834790i	$-0.685589\pi$
$43$	−7.22063	−1.10114	−0.550568	+	0.834790i	$0.685589\pi$
$44$	11.5143	1.73585
$45$	0	0
$46$	2.80172	0.413092
$47$	4.25995	0.621377	0.310689	−	0.950512i	$-0.399440\pi$
$47$	4.25995	0.621377	0.310689	+	0.950512i	$0.399440\pi$
$48$	32.0746	4.62956
$49$	1.00000	0.142857
$50$	0	0
$51$	8.69418	1.21743
$52$	−17.9137	−2.48418
$53$	3.65970	0.502699	0.251349	−	0.967896i	$-0.419126\pi$
$53$	3.65970	0.502699	0.251349	+	0.967896i	$0.419126\pi$
$54$	14.5589	1.98121
$55$	0	0
$56$	10.7857	1.44130
$57$	−0.285065	−0.0377578
$58$	4.49276	0.589929
$59$	−7.76391	−1.01078	−0.505388	−	0.862892i	$-0.668650\pi$
$59$	−7.76391	−1.01078	−0.505388	+	0.862892i	$0.668650\pi$
$60$	0	0
$61$	9.38754	1.20195	0.600975	−	0.799268i	$-0.294779\pi$
$61$	9.38754	1.20195	0.600975	+	0.799268i	$0.294779\pi$
$62$	5.15691	0.654928
$63$	0.000289796 0	3.65109e−5 0
$64$	47.8937	5.98671
$65$	0	0
$66$	−9.55154	−1.17571
$67$	−13.6408	−1.66649	−0.833243	−	0.552906i	$-0.813519\pi$
$67$	−13.6408	−1.66649	−0.833243	+	0.552906i	$0.813519\pi$
$68$	29.3643	3.56094
$69$	−1.73197	−0.208504
$70$	0	0
$71$	−16.4953	−1.95764	−0.978818	−	0.204733i	$-0.934367\pi$
$71$	−16.4953	−1.95764	−0.978818	+	0.204733i	$0.934367\pi$
$72$	0.00312564	0.000368360 0
$73$	11.4879	1.34456	0.672280	−	0.740297i	$-0.265315\pi$
$73$	11.4879	1.34456	0.672280	+	0.740297i	$0.265315\pi$
$74$	20.7921	2.41703
$75$	0	0
$76$	−0.962796	−0.110440
$77$	−1.96838	−0.224318
$78$	14.8600	1.68256
$79$	−6.11051	−0.687486	−0.343743	−	0.939064i	$-0.611695\pi$
$79$	−6.11051	−0.687486	−0.343743	+	0.939064i	$0.611695\pi$
$80$	0	0
$81$	−8.99913	−0.999903
$82$	−16.9711	−1.87414
$83$	10.3687	1.13811	0.569056	−	0.822299i	$-0.307309\pi$
$83$	10.3687	1.13811	0.569056	+	0.822299i	$0.307309\pi$
$84$	−10.1314	−1.10543
$85$	0	0
$86$	20.2302	2.18148
$87$	−2.77733	−0.297761
$88$	−21.2303	−2.26315
$89$	8.46385	0.897166	0.448583	−	0.893741i	$-0.351929\pi$
$89$	8.46385	0.897166	0.448583	+	0.893741i	$0.351929\pi$
$90$	0	0
$91$	3.06234	0.321021
$92$	−5.84965	−0.609869
$93$	−3.18789	−0.330569
$94$	−11.9352	−1.23102
$95$	0	0
$96$	−52.5032	−5.35858
$97$	−4.55947	−0.462944	−0.231472	−	0.972842i	$-0.574354\pi$
$97$	−4.55947	−0.462944	−0.231472	+	0.972842i	$0.574354\pi$
$98$	−2.80172	−0.283017
$99$	−0.000570428 0	−5.73302e−5 0
$100$	0	0
$101$	−1.82561	−0.181655	−0.0908274	−	0.995867i	$-0.528951\pi$
$101$	−1.82561	−0.181655	−0.0908274	+	0.995867i	$0.528951\pi$
$102$	−24.3587	−2.41187
$103$	−11.5393	−1.13700	−0.568499	−	0.822684i	$-0.692476\pi$
$103$	−11.5393	−1.13700	−0.568499	+	0.822684i	$0.692476\pi$
$104$	33.0294	3.23880
$105$	0	0
$106$	−10.2535	−0.995905
$107$	0.820582	0.0793287	0.0396643	−	0.999213i	$-0.487371\pi$
$107$	0.820582	0.0793287	0.0396643	+	0.999213i	$0.487371\pi$
$108$	−30.3972	−2.92497
$109$	−5.41869	−0.519017	−0.259508	−	0.965741i	$-0.583560\pi$
$109$	−5.41869	−0.519017	−0.259508	+	0.965741i	$0.583560\pi$
$110$	0	0
$111$	−12.8532	−1.21997
$112$	−18.5191	−1.74989
$113$	0.845882	0.0795739	0.0397869	−	0.999208i	$-0.487332\pi$
$113$	0.845882	0.0795739	0.0397869	+	0.999208i	$0.487332\pi$
$114$	0.798673	0.0748026
$115$	0	0
$116$	−9.38034	−0.870943
$117$	0.000887455 0	8.20452e−5 0
$118$	21.7523	2.00246
$119$	−5.01983	−0.460167
$120$	0	0
$121$	−7.12549	−0.647772
$122$	−26.3013	−2.38121
$123$	10.4912	0.945956
$124$	−10.7670	−0.966904
$125$	0	0
$126$	−0.000811928 0	−7.23323e−5 0
$127$	1.90738	0.169252	0.0846261	−	0.996413i	$-0.473030\pi$
$127$	1.90738	0.169252	0.0846261	+	0.996413i	$0.473030\pi$
$128$	−73.5565	−6.50154
$129$	−12.5059	−1.10108
$130$	0	0
$131$	16.2089	1.41618	0.708091	−	0.706122i	$-0.249557\pi$
$131$	16.2089	1.41618	0.708091	+	0.706122i	$0.249557\pi$
$132$	19.9424	1.73577
$133$	0.164590	0.0142718
$134$	38.2177	3.30151
$135$	0	0
$136$	−54.1422	−4.64265
$137$	−8.74940	−0.747512	−0.373756	−	0.927527i	$-0.621930\pi$
$137$	−8.74940	−0.747512	−0.373756	+	0.927527i	$0.621930\pi$
$138$	4.85249	0.413072
$139$	−18.7390	−1.58942	−0.794711	−	0.606988i	$-0.792378\pi$
$139$	−18.7390	−1.58942	−0.794711	+	0.606988i	$0.792378\pi$
$140$	0	0
$141$	7.37809	0.621347
$142$	46.2154	3.87831
$143$	−6.02785	−0.504074
$144$	−0.00536677	−0.000447231 0
$145$	0	0
$146$	−32.1860	−2.66373
$147$	1.73197	0.142850
$148$	−43.4113	−3.56838
$149$	−16.8025	−1.37651	−0.688256	−	0.725468i	$-0.741624\pi$
$149$	−16.8025	−1.37651	−0.688256	+	0.725468i	$0.741624\pi$
$150$	0	0
$151$	22.8327	1.85810	0.929048	−	0.369960i	$-0.120629\pi$
$151$	22.8327	1.85810	0.929048	+	0.369960i	$0.120629\pi$
$152$	1.77521	0.143989
$153$	−0.00145473	−0.000117608 0
$154$	5.51485	0.444399
$155$	0	0
$156$	−31.0259	−2.48406
$157$	−23.0014	−1.83571	−0.917854	−	0.396918i	$-0.870080\pi$
$157$	−23.0014	−1.83571	−0.917854	+	0.396918i	$0.870080\pi$
$158$	17.1200	1.36199
$159$	6.33848	0.502674
$160$	0	0
$161$	1.00000	0.0788110
$162$	25.2131	1.98093
$163$	−21.8404	−1.71067	−0.855337	−	0.518073i	$-0.826650\pi$
$163$	−21.8404	−1.71067	−0.855337	+	0.518073i	$0.826650\pi$
$164$	35.4335	2.76689
$165$	0	0
$166$	−29.0502	−2.25473
$167$	−7.18029	−0.555628	−0.277814	−	0.960635i	$-0.589610\pi$
$167$	−7.18029	−0.555628	−0.277814	+	0.960635i	$0.589610\pi$
$168$	18.6804	1.44123
$169$	−3.62205	−0.278619
$170$	0	0
$171$	4.76976e−5 0	3.64752e−6 0
$172$	−42.2382	−3.22063
$173$	9.42006	0.716194	0.358097	−	0.933684i	$-0.383426\pi$
$173$	9.42006	0.716194	0.358097	+	0.933684i	$0.383426\pi$
$174$	7.78132	0.589900
$175$	0	0
$176$	36.4527	2.74772
$177$	−13.4468	−1.01073
$178$	−23.7134	−1.77739
$179$	−1.60900	−0.120262	−0.0601311	−	0.998190i	$-0.519152\pi$
$179$	−1.60900	−0.120262	−0.0601311	+	0.998190i	$0.519152\pi$
$180$	0	0
$181$	25.8702	1.92292	0.961459	−	0.274949i	$-0.0886610\pi$
$181$	25.8702	1.92292	0.961459	+	0.274949i	$0.0886610\pi$
$182$	−8.57984	−0.635980
$183$	16.2589	1.20189
$184$	10.7857	0.795130
$185$	0	0
$186$	8.93160	0.654896
$187$	9.88092	0.722565
$188$	24.9192	1.81742
$189$	5.19640	0.377983
$190$	0	0
$191$	6.52391	0.472053	0.236027	−	0.971747i	$-0.424155\pi$
$191$	6.52391	0.472053	0.236027	+	0.971747i	$0.424155\pi$
$192$	82.9503	5.98642
$193$	2.27932	0.164069	0.0820346	−	0.996629i	$-0.473858\pi$
$193$	2.27932	0.164069	0.0820346	+	0.996629i	$0.473858\pi$
$194$	12.7744	0.917147
$195$	0	0
$196$	5.84965	0.417832
$197$	2.02369	0.144182	0.0720911	−	0.997398i	$-0.477033\pi$
$197$	2.02369	0.144182	0.0720911	+	0.997398i	$0.477033\pi$
$198$	0.00159818	0.000113578 0
$199$	−23.2968	−1.65147	−0.825734	−	0.564060i	$-0.809239\pi$
$199$	−23.2968	−1.65147	−0.825734	+	0.564060i	$0.809239\pi$
$200$	0	0
$201$	−23.6254	−1.66641
$202$	5.11485	0.359880
$203$	1.60357	0.112549
$204$	50.8579	3.56077
$205$	0	0
$206$	32.3299	2.25253
$207$	0.000289796 0	2.01422e−5 0
$208$	−56.7120	−3.93227
$209$	−0.323976	−0.0224099
$210$	0	0
$211$	−13.9306	−0.959024	−0.479512	−	0.877535i	$-0.659186\pi$
$211$	−13.9306	−0.959024	−0.479512	+	0.877535i	$0.659186\pi$
$212$	21.4080	1.47031
$213$	−28.5694	−1.95754
$214$	−2.29904	−0.157159
$215$	0	0
$216$	56.0467	3.81349
$217$	1.84062	0.124949
$218$	15.1817	1.02823
$219$	19.8967	1.34449
$220$	0	0
$221$	−15.3724	−1.03406
$222$	36.0112	2.41691
$223$	3.14488	0.210597	0.105298	−	0.994441i	$-0.466420\pi$
$223$	3.14488	0.210597	0.105298	+	0.994441i	$0.466420\pi$
$224$	30.3142	2.02545
$225$	0	0
$226$	−2.36993	−0.157645
$227$	16.8929	1.12122	0.560611	−	0.828079i	$-0.310566\pi$
$227$	16.8929	1.12122	0.560611	+	0.828079i	$0.310566\pi$
$228$	−1.66753	−0.110435
$229$	−4.02594	−0.266041	−0.133021	−	0.991113i	$-0.542468\pi$
$229$	−4.02594	−0.266041	−0.133021	+	0.991113i	$0.542468\pi$
$230$	0	0
$231$	−3.40917	−0.224307
$232$	17.2956	1.13551
$233$	14.8042	0.969858	0.484929	−	0.874554i	$-0.338846\pi$
$233$	14.8042	0.969858	0.484929	+	0.874554i	$0.338846\pi$
$234$	−0.00248640	−0.000162541 0
$235$	0	0
$236$	−45.4162	−2.95634
$237$	−10.5832	−0.687453
$238$	14.0642	0.911645
$239$	−13.9903	−0.904960	−0.452480	−	0.891775i	$-0.649461\pi$
$239$	−13.9903	−0.904960	−0.452480	+	0.891775i	$0.649461\pi$
$240$	0	0
$241$	−28.7603	−1.85261	−0.926306	−	0.376771i	$-0.877034\pi$
$241$	−28.7603	−1.85261	−0.926306	+	0.376771i	$0.877034\pi$
$242$	19.9636	1.28331
$243$	0.00301165	0.000193197 0
$244$	54.9138	3.51550
$245$	0	0
$246$	−29.3933	−1.87405
$247$	0.504032	0.0320708
$248$	19.8523	1.26062
$249$	17.9582	1.13806
$250$	0	0
$251$	−0.0954598	−0.00602537	−0.00301268	−	0.999995i	$-0.500959\pi$
$251$	−0.0954598	−0.00602537	−0.00301268	+	0.999995i	$0.500959\pi$
$252$	0.00169521	0.000106788 0
$253$	−1.96838	−0.123751
$254$	−5.34394	−0.335309
$255$	0	0
$256$	110.298	6.89360
$257$	12.9724	0.809196	0.404598	−	0.914495i	$-0.367411\pi$
$257$	12.9724	0.809196	0.404598	+	0.914495i	$0.367411\pi$
$258$	35.0381	2.18137
$259$	7.42117	0.461129
$260$	0	0
$261$	0.000464709 0	2.87647e−5 0
$262$	−45.4130	−2.80562
$263$	−5.69130	−0.350940	−0.175470	−	0.984485i	$-0.556145\pi$
$263$	−5.69130	−0.350940	−0.175470	+	0.984485i	$0.556145\pi$
$264$	−36.7701	−2.26305
$265$	0	0
$266$	−0.461136	−0.0282741
$267$	14.6591	0.897123
$268$	−79.7939	−4.87419
$269$	−22.8837	−1.39524	−0.697622	−	0.716466i	$-0.745759\pi$
$269$	−22.8837	−1.39524	−0.697622	+	0.716466i	$0.745759\pi$
$270$	0	0
$271$	−19.4239	−1.17992	−0.589959	−	0.807433i	$-0.700856\pi$
$271$	−19.4239	−1.17992	−0.589959	+	0.807433i	$0.700856\pi$
$272$	92.9629	5.63671
$273$	5.30388	0.321005
$274$	24.5134	1.48091
$275$	0	0
$276$	−10.1314	−0.609839
$277$	15.9057	0.955680	0.477840	−	0.878447i	$-0.341420\pi$
$277$	15.9057	0.955680	0.477840	+	0.878447i	$0.341420\pi$
$278$	52.5015	3.14883
$279$	0.000533404 0	3.19341e−5 0
$280$	0	0
$281$	−10.3213	−0.615718	−0.307859	−	0.951432i	$-0.599612\pi$
$281$	−10.3213	−0.615718	−0.307859	+	0.951432i	$0.599612\pi$
$282$	−20.6714	−1.23096
$283$	−2.91321	−0.173173	−0.0865863	−	0.996244i	$-0.527596\pi$
$283$	−2.91321	−0.173173	−0.0865863	+	0.996244i	$0.527596\pi$
$284$	−96.4920	−5.72575
$285$	0	0
$286$	16.8884	0.998631
$287$	−6.05737	−0.357555
$288$	0.00878493	0.000517657 0
$289$	8.19868	0.482275
$290$	0	0
$291$	−7.89686	−0.462922
$292$	67.2004	3.93260
$293$	−18.3822	−1.07390	−0.536951	−	0.843613i	$-0.680424\pi$
$293$	−18.3822	−1.07390	−0.536951	+	0.843613i	$0.680424\pi$
$294$	−4.85249	−0.283003
$295$	0	0
$296$	80.0422	4.65236
$297$	−10.2285	−0.593517
$298$	47.0759	2.72703
$299$	3.06234	0.177100
$300$	0	0
$301$	7.22063	0.416190
$302$	−63.9708	−3.68111
$303$	−3.16189	−0.181646
$304$	−3.04807	−0.174819
$305$	0	0
$306$	0.00407574	0.000232994 0
$307$	7.87997	0.449733	0.224867	−	0.974390i	$-0.427805\pi$
$307$	7.87997	0.449733	0.224867	+	0.974390i	$0.427805\pi$
$308$	−11.5143	−0.656090
$309$	−19.9856	−1.13694
$310$	0	0
$311$	9.11384	0.516798	0.258399	−	0.966038i	$-0.416805\pi$
$311$	9.11384	0.516798	0.258399	+	0.966038i	$0.416805\pi$
$312$	57.2059	3.23865
$313$	2.44826	0.138384	0.0691919	−	0.997603i	$-0.477958\pi$
$313$	2.44826	0.138384	0.0691919	+	0.997603i	$0.477958\pi$
$314$	64.4434	3.63675
$315$	0	0
$316$	−35.7444	−2.01078
$317$	−31.4163	−1.76452	−0.882258	−	0.470767i	$-0.843977\pi$
$317$	−31.4163	−1.76452	−0.882258	+	0.470767i	$0.843977\pi$
$318$	−17.7587	−0.995857
$319$	−3.15644	−0.176726
$320$	0	0
$321$	1.42122	0.0793248
$322$	−2.80172	−0.156134
$323$	−0.826215	−0.0459718
$324$	−52.6418	−2.92454
$325$	0	0
$326$	61.1908	3.38904
$327$	−9.38500	−0.518992
$328$	−65.3327	−3.60740
$329$	−4.25995	−0.234859
$330$	0	0
$331$	13.1021	0.720156	0.360078	−	0.932922i	$-0.382750\pi$
$331$	13.1021	0.720156	0.360078	+	0.932922i	$0.382750\pi$
$332$	60.6532	3.32878
$333$	0.00215062	0.000117853 0
$334$	20.1172	1.10076
$335$	0	0
$336$	−32.0746	−1.74981
$337$	−3.40979	−0.185743	−0.0928716	−	0.995678i	$-0.529605\pi$
$337$	−3.40979	−0.185743	−0.0928716	+	0.995678i	$0.529605\pi$
$338$	10.1480	0.551977
$339$	1.46504	0.0795700
$340$	0	0
$341$	−3.62304	−0.196198
$342$	−0.000133635 0	−7.22617e−6 0
$343$	−1.00000	−0.0539949
$344$	77.8793	4.19897
$345$	0	0
$346$	−26.3924	−1.41886
$347$	28.2070	1.51423	0.757115	−	0.653282i	$-0.226608\pi$
$347$	28.2070	1.51423	0.757115	+	0.653282i	$0.226608\pi$
$348$	−16.2464	−0.870901
$349$	12.4114	0.664366	0.332183	−	0.943215i	$-0.392215\pi$
$349$	12.4114	0.664366	0.332183	+	0.943215i	$0.392215\pi$
$350$	0	0
$351$	15.9132	0.849383
$352$	−59.6698	−3.18041
$353$	31.8989	1.69781	0.848904	−	0.528546i	$-0.177263\pi$
$353$	31.8989	1.69781	0.848904	+	0.528546i	$0.177263\pi$
$354$	37.6743	2.00237
$355$	0	0
$356$	49.5106	2.62406
$357$	−8.69418	−0.460145
$358$	4.50797	0.238253
$359$	−14.0257	−0.740249	−0.370125	−	0.928982i	$-0.620685\pi$
$359$	−14.0257	−0.740249	−0.370125	+	0.928982i	$0.620685\pi$
$360$	0	0
$361$	−18.9729	−0.998574
$362$	−72.4812	−3.80953
$363$	−12.3411	−0.647740
$364$	17.9137	0.938931
$365$	0	0
$366$	−45.5530	−2.38109
$367$	26.3734	1.37668	0.688340	−	0.725389i	$-0.258340\pi$
$367$	26.3734	1.37668	0.688340	+	0.725389i	$0.258340\pi$
$368$	−18.5191	−0.965377
$369$	−0.00175540	−9.13825e−5 0
$370$	0	0
$371$	−3.65970	−0.190002
$372$	−18.6481	−0.966858
$373$	33.2683	1.72257	0.861284	−	0.508124i	$-0.169661\pi$
$373$	33.2683	1.72257	0.861284	+	0.508124i	$0.169661\pi$
$374$	−27.6836	−1.43149
$375$	0	0
$376$	−45.9464	−2.36950
$377$	4.91069	0.252913
$378$	−14.5589	−0.748828
$379$	−9.47885	−0.486896	−0.243448	−	0.969914i	$-0.578279\pi$
$379$	−9.47885	−0.486896	−0.243448	+	0.969914i	$0.578279\pi$
$380$	0	0
$381$	3.30351	0.169244
$382$	−18.2782	−0.935193
$383$	−11.6012	−0.592792	−0.296396	−	0.955065i	$-0.595785\pi$
$383$	−11.6012	−0.592792	−0.296396	+	0.955065i	$0.595785\pi$
$384$	−127.397	−6.50122
$385$	0	0
$386$	−6.38603	−0.325040
$387$	0.00209251	0.000106368 0
$388$	−26.6713	−1.35403
$389$	16.8170	0.852655	0.426327	−	0.904569i	$-0.359807\pi$
$389$	16.8170	0.852655	0.426327	+	0.904569i	$0.359807\pi$
$390$	0	0
$391$	−5.01983	−0.253864
$392$	−10.7857	−0.544758
$393$	28.0733	1.41611
$394$	−5.66983	−0.285642
$395$	0	0
$396$	−0.00333681	−0.000167681 0
$397$	−14.4914	−0.727301	−0.363650	−	0.931536i	$-0.618470\pi$
$397$	−14.4914	−0.727301	−0.363650	+	0.931536i	$0.618470\pi$
$398$	65.2713	3.27175
$399$	0.285065	0.0142711
$400$	0	0
$401$	−25.5629	−1.27655	−0.638274	−	0.769809i	$-0.720351\pi$
$401$	−25.5629	−1.27655	−0.638274	+	0.769809i	$0.720351\pi$
$402$	66.1918	3.30135
$403$	5.63661	0.280780
$404$	−10.6792	−0.531309
$405$	0	0
$406$	−4.49276	−0.222972
$407$	−14.6077	−0.724075
$408$	−93.7725	−4.64243
$409$	−13.5625	−0.670623	−0.335311	−	0.942107i	$-0.608842\pi$
$409$	−13.5625	−0.670623	−0.335311	+	0.942107i	$0.608842\pi$
$410$	0	0
$411$	−15.1537	−0.747476
$412$	−67.5008	−3.32552
$413$	7.76391	0.382037
$414$	−0.000811928 0	−3.99041e−5 0
$415$	0	0
$416$	92.8325	4.55149
$417$	−32.4554	−1.58935
$418$	0.907691	0.0443966
$419$	14.9218	0.728977	0.364489	−	0.931208i	$-0.381244\pi$
$419$	14.9218	0.728977	0.364489	+	0.931208i	$0.381244\pi$
$420$	0	0
$421$	−39.5654	−1.92830	−0.964150	−	0.265358i	$-0.914510\pi$
$421$	−39.5654	−1.92830	−0.964150	+	0.265358i	$0.914510\pi$
$422$	39.0298	1.89994
$423$	−0.00123452	−6.00242e−5 0
$424$	−39.4723	−1.91695
$425$	0	0
$426$	80.0435	3.87812
$427$	−9.38754	−0.454295
$428$	4.80012	0.232023
$429$	−10.4400	−0.504050
$430$	0	0
$431$	−25.2822	−1.21780	−0.608901	−	0.793246i	$-0.708389\pi$
$431$	−25.2822	−1.21780	−0.608901	+	0.793246i	$0.708389\pi$
$432$	−96.2329	−4.63001
$433$	4.49189	0.215866	0.107933	−	0.994158i	$-0.465577\pi$
$433$	4.49189	0.215866	0.107933	+	0.994158i	$0.465577\pi$
$434$	−5.15691	−0.247540
$435$	0	0
$436$	−31.6975	−1.51803
$437$	0.164590	0.00787342
$438$	−55.7451	−2.66360
$439$	−30.6305	−1.46191	−0.730956	−	0.682424i	$-0.760926\pi$
$439$	−30.6305	−1.46191	−0.730956	+	0.682424i	$0.760926\pi$
$440$	0	0
$441$	−0.000289796 0	−1.37998e−5 0
$442$	43.0693	2.04860
$443$	4.34787	0.206574	0.103287	−	0.994652i	$-0.467064\pi$
$443$	4.34787	0.206574	0.103287	+	0.994652i	$0.467064\pi$
$444$	−75.1869	−3.56821
$445$	0	0
$446$	−8.81107	−0.417216
$447$	−29.1013	−1.37645
$448$	−47.8937	−2.26276
$449$	−24.1293	−1.13873	−0.569367	−	0.822084i	$-0.692811\pi$
$449$	−24.1293	−1.13873	−0.569367	+	0.822084i	$0.692811\pi$
$450$	0	0
$451$	11.9232	0.561441
$452$	4.94812	0.232740
$453$	39.5454	1.85801
$454$	−47.3292	−2.22127
$455$	0	0
$456$	3.07461	0.143982
$457$	−4.02157	−0.188121	−0.0940607	−	0.995566i	$-0.529985\pi$
$457$	−4.02157	−0.188121	−0.0940607	+	0.995566i	$0.529985\pi$
$458$	11.2796	0.527059
$459$	−26.0851	−1.21755
$460$	0	0
$461$	−16.2045	−0.754717	−0.377358	−	0.926067i	$-0.623168\pi$
$461$	−16.2045	−0.754717	−0.377358	+	0.926067i	$0.623168\pi$
$462$	9.55154	0.444378
$463$	−5.27208	−0.245014	−0.122507	−	0.992468i	$-0.539093\pi$
$463$	−5.27208	−0.245014	−0.122507	+	0.992468i	$0.539093\pi$
$464$	−29.6968	−1.37864
$465$	0	0
$466$	−41.4774	−1.92140
$467$	−37.3929	−1.73034	−0.865169	−	0.501481i	$-0.832789\pi$
$467$	−37.3929	−1.73034	−0.865169	+	0.501481i	$0.832789\pi$
$468$	0.00519130	0.000239968 0
$469$	13.6408	0.629873
$470$	0	0
$471$	−39.8376	−1.83562
$472$	83.7390	3.85440
$473$	−14.2129	−0.653511
$474$	29.6512	1.36193
$475$	0	0
$476$	−29.3643	−1.34591
$477$	−0.00106057	−4.85600e−5 0
$478$	39.1971	1.79283
$479$	−35.0887	−1.60324	−0.801622	−	0.597832i	$-0.796029\pi$
$479$	−35.0887	−1.60324	−0.801622	+	0.597832i	$0.796029\pi$
$480$	0	0
$481$	22.7262	1.03622
$482$	80.5784	3.67024
$483$	1.73197	0.0788072
$484$	−41.6816	−1.89462
$485$	0	0
$486$	−0.00843780	−0.000382747 0
$487$	−8.17541	−0.370463	−0.185232	−	0.982695i	$-0.559304\pi$
$487$	−8.17541	−0.370463	−0.185232	+	0.982695i	$0.559304\pi$
$488$	−101.251	−4.58341
$489$	−37.8269	−1.71059
$490$	0	0
$491$	33.6565	1.51889	0.759447	−	0.650569i	$-0.225469\pi$
$491$	33.6565	1.51889	0.759447	+	0.650569i	$0.225469\pi$
$492$	61.3697	2.76676
$493$	−8.04966	−0.362538
$494$	−1.41216	−0.0635360
$495$	0	0
$496$	−34.0867	−1.53054
$497$	16.4953	0.739917
$498$	−50.3140	−2.25462
$499$	34.0630	1.52487	0.762436	−	0.647064i	$-0.224003\pi$
$499$	34.0630	1.52487	0.762436	+	0.647064i	$0.224003\pi$
$500$	0	0
$501$	−12.4360	−0.555601
$502$	0.267452	0.0119370
$503$	−43.7840	−1.95223	−0.976116	−	0.217250i	$-0.930291\pi$
$503$	−43.7840	−1.95223	−0.976116	+	0.217250i	$0.930291\pi$
$504$	−0.00312564	−0.000139227 0
$505$	0	0
$506$	5.51485	0.245165
$507$	−6.27326	−0.278605
$508$	11.1575	0.495033
$509$	10.5402	0.467186	0.233593	−	0.972335i	$-0.424952\pi$
$509$	10.5402	0.467186	0.233593	+	0.972335i	$0.424952\pi$
$510$	0	0
$511$	−11.4879	−0.508196
$512$	−161.910	−7.15549
$513$	0.855277	0.0377614
$514$	−36.3451	−1.60311
$515$	0	0
$516$	−73.1552	−3.22048
$517$	8.38519	0.368780
$518$	−20.7921	−0.913550
$519$	16.3152	0.716160
$520$	0	0
$521$	26.9328	1.17995	0.589974	−	0.807423i	$-0.299138\pi$
$521$	26.9328	1.17995	0.589974	+	0.807423i	$0.299138\pi$
$522$	−0.00130198	−5.69863e−5 0
$523$	7.04134	0.307896	0.153948	−	0.988079i	$-0.450801\pi$
$523$	7.04134	0.307896	0.153948	+	0.988079i	$0.450801\pi$
$524$	94.8167	4.14209
$525$	0	0
$526$	15.9454	0.695254
$527$	−9.23960	−0.402483
$528$	63.1349	2.74759
$529$	1.00000	0.0434783
$530$	0	0
$531$	0.00224995	9.76395e−5 0
$532$	0.962796	0.0417425
$533$	−18.5497	−0.803479
$534$	−41.0708	−1.77731
$535$	0	0
$536$	147.125	6.35483
$537$	−2.78673	−0.120256
$538$	64.1138	2.76414
$539$	1.96838	0.0847841
$540$	0	0
$541$	−16.6283	−0.714908	−0.357454	−	0.933931i	$-0.616355\pi$
$541$	−16.6283	−0.714908	−0.357454	+	0.933931i	$0.616355\pi$
$542$	54.4204	2.33756
$543$	44.8064	1.92282
$544$	−152.172	−6.52432
$545$	0	0
$546$	−14.8600	−0.635950
$547$	14.4768	0.618982	0.309491	−	0.950902i	$-0.399841\pi$
$547$	14.4768	0.618982	0.309491	+	0.950902i	$0.399841\pi$
$548$	−51.1810	−2.18634
$549$	−0.00272047	−0.000116107 0
$550$	0	0
$551$	0.263932	0.0112439
$552$	18.6804	0.795091
$553$	6.11051	0.259845
$554$	−44.5633	−1.89331
$555$	0	0
$556$	−109.617	−4.64879
$557$	36.3690	1.54100	0.770502	−	0.637438i	$-0.220006\pi$
$557$	36.3690	1.54100	0.770502	+	0.637438i	$0.220006\pi$
$558$	−0.00149445	−6.32652e−5 0
$559$	22.1121	0.935240
$560$	0	0
$561$	17.1134	0.722530
$562$	28.9175	1.21981
$563$	14.1270	0.595383	0.297691	−	0.954662i	$-0.403783\pi$
$563$	14.1270	0.595383	0.297691	+	0.954662i	$0.403783\pi$
$564$	43.1593	1.81733
$565$	0	0
$566$	8.16202	0.343075
$567$	8.99913	0.377928
$568$	177.913	7.46507
$569$	−11.1036	−0.465489	−0.232745	−	0.972538i	$-0.574771\pi$
$569$	−11.1036	−0.465489	−0.232745	+	0.972538i	$0.574771\pi$
$570$	0	0
$571$	28.7756	1.20422	0.602111	−	0.798412i	$-0.294326\pi$
$571$	28.7756	1.20422	0.602111	+	0.798412i	$0.294326\pi$
$572$	−35.2609	−1.47433
$573$	11.2992	0.472031
$574$	16.9711	0.708359
$575$	0	0
$576$	−0.0138794	−0.000578308 0
$577$	−31.6960	−1.31952	−0.659761	−	0.751476i	$-0.729342\pi$
$577$	−31.6960	−1.31952	−0.659761	+	0.751476i	$0.729342\pi$
$578$	−22.9704	−0.955444
$579$	3.94771	0.164061
$580$	0	0
$581$	−10.3687	−0.430166
$582$	22.1248	0.917103
$583$	7.20368	0.298346
$584$	−123.905	−5.12722
$585$	0	0
$586$	51.5020	2.12753
$587$	−2.13491	−0.0881170	−0.0440585	−	0.999029i	$-0.514029\pi$
$587$	−2.13491	−0.0881170	−0.0440585	+	0.999029i	$0.514029\pi$
$588$	10.1314	0.417812
$589$	0.302948	0.0124828
$590$	0	0
$591$	3.50497	0.144175
$592$	−137.434	−5.64849
$593$	6.65285	0.273200	0.136600	−	0.990626i	$-0.456383\pi$
$593$	6.65285	0.273200	0.136600	+	0.990626i	$0.456383\pi$
$594$	28.6574	1.17583
$595$	0	0
$596$	−98.2887	−4.02606
$597$	−40.3493	−1.65139
$598$	−8.57984	−0.350856
$599$	2.08780	0.0853051	0.0426526	−	0.999090i	$-0.486419\pi$
$599$	2.08780	0.0853051	0.0426526	+	0.999090i	$0.486419\pi$
$600$	0	0
$601$	−27.7870	−1.13345	−0.566727	−	0.823906i	$-0.691791\pi$
$601$	−27.7870	−1.13345	−0.566727	+	0.823906i	$0.691791\pi$
$602$	−20.2302	−0.824522
$603$	0.00395304	0.000160980 0
$604$	133.563	5.43461
$605$	0	0
$606$	8.85875	0.359862
$607$	−14.1069	−0.572582	−0.286291	−	0.958143i	$-0.592422\pi$
$607$	−14.1069	−0.572582	−0.286291	+	0.958143i	$0.592422\pi$
$608$	4.98942	0.202348
$609$	2.77733	0.112543
$610$	0	0
$611$	−13.0454	−0.527762
$612$	−0.00850964	−0.000343982 0
$613$	46.0056	1.85815	0.929075	−	0.369892i	$-0.120605\pi$
$613$	46.0056	1.85815	0.929075	+	0.369892i	$0.120605\pi$
$614$	−22.0775	−0.890975
$615$	0	0
$616$	21.2303	0.855392
$617$	27.8600	1.12160	0.560801	−	0.827950i	$-0.310493\pi$
$617$	27.8600	1.12160	0.560801	+	0.827950i	$0.310493\pi$
$618$	55.9942	2.25242
$619$	34.2780	1.37775	0.688876	−	0.724880i	$-0.258105\pi$
$619$	34.2780	1.37775	0.688876	+	0.724880i	$0.258105\pi$
$620$	0	0
$621$	5.19640	0.208524
$622$	−25.5345	−1.02384
$623$	−8.46385	−0.339097
$624$	−98.2233	−3.93208
$625$	0	0
$626$	−6.85935	−0.274155
$627$	−0.561115	−0.0224088
$628$	−134.550	−5.36913
$629$	−37.2530	−1.48537
$630$	0	0
$631$	−24.9555	−0.993461	−0.496730	−	0.867905i	$-0.665466\pi$
$631$	−24.9555	−0.993461	−0.496730	+	0.867905i	$0.665466\pi$
$632$	65.9059	2.62160
$633$	−24.1274	−0.958977
$634$	88.0198	3.49571
$635$	0	0
$636$	37.0779	1.47024
$637$	−3.06234	−0.121335
$638$	8.84346	0.350116
$639$	0.00478028	0.000189105 0
$640$	0	0
$641$	−10.3721	−0.409673	−0.204836	−	0.978796i	$-0.565666\pi$
$641$	−10.3721	−0.409673	−0.204836	+	0.978796i	$0.565666\pi$
$642$	−3.98187	−0.157152
$643$	1.61996	0.0638849	0.0319424	−	0.999490i	$-0.489831\pi$
$643$	1.61996	0.0638849	0.0319424	+	0.999490i	$0.489831\pi$
$644$	5.84965	0.230509
$645$	0	0
$646$	2.31482	0.0910756
$647$	−31.5338	−1.23972	−0.619861	−	0.784711i	$-0.712811\pi$
$647$	−31.5338	−1.23972	−0.619861	+	0.784711i	$0.712811\pi$
$648$	97.0616	3.81294
$649$	−15.2823	−0.599883
$650$	0	0
$651$	3.18789	0.124943
$652$	−127.759	−5.00342
$653$	6.21910	0.243372	0.121686	−	0.992569i	$-0.461170\pi$
$653$	6.21910	0.243372	0.121686	+	0.992569i	$0.461170\pi$
$654$	26.2942	1.02818
$655$	0	0
$656$	112.177	4.37979
$657$	−0.00332915	−0.000129883 0
$658$	11.9352	0.465282
$659$	−15.2002	−0.592115	−0.296057	−	0.955170i	$-0.595672\pi$
$659$	−15.2002	−0.592115	−0.296057	+	0.955170i	$0.595672\pi$
$660$	0	0
$661$	35.0579	1.36359	0.681796	−	0.731542i	$-0.261199\pi$
$661$	35.0579	1.36359	0.681796	+	0.731542i	$0.261199\pi$
$662$	−36.7084	−1.42671
$663$	−26.6246	−1.03401
$664$	−111.833	−4.33997
$665$	0	0
$666$	−0.00602545	−0.000233482 0
$667$	1.60357	0.0620905
$668$	−42.0022	−1.62511
$669$	5.44682	0.210586
$670$	0	0
$671$	18.4782	0.713344
$672$	52.5032	2.02535
$673$	−17.4556	−0.672863	−0.336431	−	0.941708i	$-0.609220\pi$
$673$	−17.4556	−0.672863	−0.336431	+	0.941708i	$0.609220\pi$
$674$	9.55330	0.367979
$675$	0	0
$676$	−21.1877	−0.814912
$677$	14.2438	0.547432	0.273716	−	0.961811i	$-0.411747\pi$
$677$	14.2438	0.547432	0.273716	+	0.961811i	$0.411747\pi$
$678$	−4.10464	−0.157638
$679$	4.55947	0.174976
$680$	0	0
$681$	29.2580	1.12117
$682$	10.1507	0.388692
$683$	−29.5756	−1.13168	−0.565840	−	0.824515i	$-0.691448\pi$
$683$	−29.5756	−1.13168	−0.565840	+	0.824515i	$0.691448\pi$
$684$	0.000279014 0	1.06684e−5 0
$685$	0	0
$686$	2.80172	0.106970
$687$	−6.97279	−0.266029
$688$	−133.720	−5.09802
$689$	−11.2073	−0.426963
$690$	0	0
$691$	0.420090	0.0159810	0.00799049	−	0.999968i	$-0.497457\pi$
$691$	0.420090	0.0159810	0.00799049	+	0.999968i	$0.497457\pi$
$692$	55.1041	2.09474
$693$	0.000570428 0	2.16688e−5 0
$694$	−79.0281	−2.99987
$695$	0	0
$696$	29.9554	1.13546
$697$	30.4069	1.15174
$698$	−34.7732	−1.31619
$699$	25.6404	0.969811
$700$	0	0
$701$	17.8846	0.675491	0.337746	−	0.941237i	$-0.390336\pi$
$701$	17.8846	0.675491	0.337746	+	0.941237i	$0.390336\pi$
$702$	−44.5843	−1.68273
$703$	1.22145	0.0460679
$704$	94.2729	3.55304
$705$	0	0
$706$	−89.3720	−3.36356
$707$	1.82561	0.0686591
$708$	−78.6594	−2.95620
$709$	37.7351	1.41717	0.708585	−	0.705625i	$-0.249334\pi$
$709$	37.7351	1.41717	0.708585	+	0.705625i	$0.249334\pi$
$710$	0	0
$711$	0.00177080	6.64102e−5 0
$712$	−91.2883	−3.42117
$713$	1.84062	0.0689318
$714$	24.3587	0.911601
$715$	0	0
$716$	−9.41208	−0.351746
$717$	−24.2308	−0.904916
$718$	39.2962	1.46652
$719$	18.0899	0.674640	0.337320	−	0.941390i	$-0.390480\pi$
$719$	18.0899	0.674640	0.337320	+	0.941390i	$0.390480\pi$
$720$	0	0
$721$	11.5393	0.429745
$722$	53.1568	1.97829
$723$	−49.8119	−1.85252
$724$	151.332	5.62420
$725$	0	0
$726$	34.5764	1.28325
$727$	4.46598	0.165634	0.0828171	−	0.996565i	$-0.473608\pi$
$727$	4.46598	0.165634	0.0828171	+	0.996565i	$0.473608\pi$
$728$	−33.0294	−1.22415
$729$	27.0026	1.00010
$730$	0	0
$731$	−36.2463	−1.34062
$732$	95.1090	3.51533
$733$	−47.7138	−1.76235	−0.881174	−	0.472792i	$-0.843246\pi$
$733$	−47.7138	−1.76235	−0.881174	+	0.472792i	$0.843246\pi$
$734$	−73.8909	−2.72736
$735$	0	0
$736$	30.3142	1.11740
$737$	−26.8502	−0.989041
$738$	0.00491815	0.000181039 0
$739$	20.8292	0.766214	0.383107	−	0.923704i	$-0.374854\pi$
$739$	20.8292	0.766214	0.383107	+	0.923704i	$0.374854\pi$
$740$	0	0
$741$	0.872967	0.0320692
$742$	10.2535	0.376417
$743$	−5.83129	−0.213929	−0.106965	−	0.994263i	$-0.534113\pi$
$743$	−5.83129	−0.213929	−0.106965	+	0.994263i	$0.534113\pi$
$744$	34.3836	1.26056
$745$	0	0
$746$	−93.2086	−3.41261
$747$	−0.00300480	−0.000109940 0
$748$	57.8000	2.11338
$749$	−0.820582	−0.0299834
$750$	0	0
$751$	49.2146	1.79587	0.897933	−	0.440133i	$-0.145069\pi$
$751$	49.2146	1.79587	0.897933	+	0.440133i	$0.145069\pi$
$752$	78.8906	2.87684
$753$	−0.165333	−0.00602507
$754$	−13.7584	−0.501051
$755$	0	0
$756$	30.3972	1.10553
$757$	19.7407	0.717489	0.358744	−	0.933436i	$-0.383205\pi$
$757$	19.7407	0.717489	0.358744	+	0.933436i	$0.383205\pi$
$758$	26.5571	0.964598
$759$	−3.40917	−0.123745
$760$	0	0
$761$	43.8533	1.58968	0.794840	−	0.606819i	$-0.207555\pi$
$761$	43.8533	1.58968	0.794840	+	0.606819i	$0.207555\pi$
$762$	−9.25553	−0.335292
$763$	5.41869	0.196170
$764$	38.1626	1.38067
$765$	0	0
$766$	32.5033	1.17439
$767$	23.7758	0.858493
$768$	191.032	6.89326
$769$	16.5364	0.596316	0.298158	−	0.954516i	$-0.403628\pi$
$769$	16.5364	0.596316	0.298158	+	0.954516i	$0.403628\pi$
$770$	0	0
$771$	22.4678	0.809157
$772$	13.3332	0.479874
$773$	−24.3268	−0.874974	−0.437487	−	0.899225i	$-0.644131\pi$
$773$	−24.3268	−0.874974	−0.437487	+	0.899225i	$0.644131\pi$
$774$	−0.00586263	−0.000210728 0
$775$	0	0
$776$	49.1769	1.76535
$777$	12.8532	0.461107
$778$	−47.1165	−1.68921
$779$	−0.996983	−0.0357206
$780$	0	0
$781$	−32.4691	−1.16183
$782$	14.0642	0.502934
$783$	8.33281	0.297790
$784$	18.5191	0.661398
$785$	0	0
$786$	−78.6538	−2.80549
$787$	−27.8243	−0.991830	−0.495915	−	0.868371i	$-0.665167\pi$
$787$	−27.8243	−0.991830	−0.495915	+	0.868371i	$0.665167\pi$
$788$	11.8379	0.421708
$789$	−9.85714	−0.350923
$790$	0	0
$791$	−0.845882	−0.0300761
$792$	0.00615245	0.000218618 0
$793$	−28.7479	−1.02087
$794$	40.6008	1.44087
$795$	0	0
$796$	−136.278	−4.83026
$797$	−10.5441	−0.373491	−0.186746	−	0.982408i	$-0.559794\pi$
$797$	−10.5441	−0.373491	−0.186746	+	0.982408i	$0.559794\pi$
$798$	−0.798673	−0.0282727
$799$	21.3842	0.756519
$800$	0	0
$801$	−0.00245279	−8.66650e−5 0
$802$	71.6201	2.52899
$803$	22.6126	0.797980
$804$	−138.200	−4.87395
$805$	0	0
$806$	−15.7922	−0.556258
$807$	−39.6338	−1.39518
$808$	19.6904	0.692706
$809$	−10.8405	−0.381132	−0.190566	−	0.981674i	$-0.561032\pi$
$809$	−10.8405	−0.381132	−0.190566	+	0.981674i	$0.561032\pi$
$810$	0	0
$811$	−30.1903	−1.06013	−0.530063	−	0.847959i	$-0.677832\pi$
$811$	−30.1903	−1.06013	−0.530063	+	0.847959i	$0.677832\pi$
$812$	9.38034	0.329185
$813$	−33.6416	−1.17986
$814$	40.9266	1.43448
$815$	0	0
$816$	161.009	5.63643
$817$	1.18844	0.0415784
$818$	37.9984	1.32858
$819$	−0.000887455 0	−3.10102e−5 0
$820$	0	0
$821$	−21.3428	−0.744870	−0.372435	−	0.928058i	$-0.621477\pi$
$821$	−21.3428	−0.744870	−0.372435	+	0.928058i	$0.621477\pi$
$822$	42.4564	1.48084
$823$	29.6059	1.03200	0.515998	−	0.856590i	$-0.327421\pi$
$823$	29.6059	1.03200	0.515998	+	0.856590i	$0.327421\pi$
$824$	124.459	4.33573
$825$	0	0
$826$	−21.7523	−0.756860
$827$	31.4922	1.09509	0.547545	−	0.836776i	$-0.315563\pi$
$827$	31.4922	1.09509	0.547545	+	0.836776i	$0.315563\pi$
$828$	0.00169521	5.89125e−5 0
$829$	−27.4940	−0.954905	−0.477452	−	0.878658i	$-0.658440\pi$
$829$	−27.4940	−0.954905	−0.477452	+	0.878658i	$0.658440\pi$
$830$	0	0
$831$	27.5481	0.955634
$832$	−146.667	−5.08476
$833$	5.01983	0.173927
$834$	90.9309	3.14868
$835$	0	0
$836$	−1.89515	−0.0655450
$837$	9.56460	0.330601
$838$	−41.8067	−1.44419
$839$	35.9545	1.24129	0.620643	−	0.784093i	$-0.286871\pi$
$839$	35.9545	1.24129	0.620643	+	0.784093i	$0.286871\pi$
$840$	0	0
$841$	−26.4286	−0.911330
$842$	110.851	3.82019
$843$	−17.8762	−0.615688
$844$	−81.4893	−2.80498
$845$	0	0
$846$	0.00345877	0.000118915 0
$847$	7.12549	0.244835
$848$	67.7745	2.32739
$849$	−5.04559	−0.173164
$850$	0	0
$851$	7.42117	0.254394
$852$	−167.121	−5.72547
$853$	30.4795	1.04360	0.521799	−	0.853068i	$-0.325261\pi$
$853$	30.4795	1.04360	0.521799	+	0.853068i	$0.325261\pi$
$854$	26.3013	0.900011
$855$	0	0
$856$	−8.85053	−0.302505
$857$	−3.98363	−0.136078	−0.0680391	−	0.997683i	$-0.521674\pi$
$857$	−3.98363	−0.136078	−0.0680391	+	0.997683i	$0.521674\pi$
$858$	29.2501	0.998582
$859$	49.8467	1.70075	0.850374	−	0.526179i	$-0.176376\pi$
$859$	49.8467	1.70075	0.850374	+	0.526179i	$0.176376\pi$
$860$	0	0
$861$	−10.4912	−0.357538
$862$	70.8338	2.41261
$863$	−12.1535	−0.413711	−0.206855	−	0.978372i	$-0.566323\pi$
$863$	−12.1535	−0.413711	−0.206855	+	0.978372i	$0.566323\pi$
$864$	157.525	5.35910
$865$	0	0
$866$	−12.5850	−0.427657
$867$	14.1998	0.482252
$868$	10.7670	0.365455
$869$	−12.0278	−0.408015
$870$	0	0
$871$	41.7728	1.41542
$872$	58.4442	1.97917
$873$	0.00132132	4.47198e−5 0
$874$	−0.461136	−0.0155982
$875$	0	0
$876$	116.389	3.93241
$877$	56.5162	1.90842	0.954209	−	0.299141i	$-0.0967000\pi$
$877$	56.5162	1.90842	0.954209	+	0.299141i	$0.0967000\pi$
$878$	85.8181	2.89622
$879$	−31.8374	−1.07385
$880$	0	0
$881$	0.619072	0.0208571	0.0104285	−	0.999946i	$-0.496680\pi$
$881$	0.619072	0.0208571	0.0104285	+	0.999946i	$0.496680\pi$
$882$	0.000811928 0	2.73390e−5 0
$883$	−50.2806	−1.69208	−0.846039	−	0.533121i	$-0.821019\pi$
$883$	−50.2806	−1.69208	−0.846039	+	0.533121i	$0.821019\pi$
$884$	−89.9235	−3.02445
$885$	0	0
$886$	−12.1815	−0.409246
$887$	−23.9620	−0.804567	−0.402283	−	0.915515i	$-0.631783\pi$
$887$	−23.9620	−0.804567	−0.402283	+	0.915515i	$0.631783\pi$
$888$	138.630	4.65213
$889$	−1.90738	−0.0639713
$890$	0	0
$891$	−17.7137	−0.593431
$892$	18.3964	0.615958
$893$	−0.701146	−0.0234629
$894$	81.5339	2.72690
$895$	0	0
$896$	73.5565	2.45735
$897$	5.30388	0.177091
$898$	67.6037	2.25596
$899$	2.95157	0.0984402
$900$	0	0
$901$	18.3711	0.612029
$902$	−33.4055	−1.11228
$903$	12.5059	0.416170
$904$	−9.12340	−0.303440
$905$	0	0
$906$	−110.795	−3.68093
$907$	−27.7804	−0.922432	−0.461216	−	0.887288i	$-0.652587\pi$
$907$	−27.7804	−0.922432	−0.461216	+	0.887288i	$0.652587\pi$
$908$	98.8176	3.27938
$909$	0.000529054 0	1.75476e−5 0
$910$	0	0
$911$	27.6697	0.916738	0.458369	−	0.888762i	$-0.348434\pi$
$911$	27.6697	0.916738	0.458369	+	0.888762i	$0.348434\pi$
$912$	−5.27916	−0.174810
$913$	20.4095	0.675456
$914$	11.2673	0.372690
$915$	0	0
$916$	−23.5503	−0.778125
$917$	−16.2089	−0.535266
$918$	73.0831	2.41210
$919$	−40.1657	−1.32495	−0.662473	−	0.749086i	$-0.730493\pi$
$919$	−40.1657	−1.32495	−0.662473	+	0.749086i	$0.730493\pi$
$920$	0	0
$921$	13.6478	0.449712
$922$	45.4004	1.49518
$923$	50.5144	1.66270
$924$	−19.9424	−0.656058
$925$	0	0
$926$	14.7709	0.485402
$927$	0.00334403	0.000109832 0
$928$	48.6110	1.59573
$929$	−21.6852	−0.711469	−0.355734	−	0.934587i	$-0.615769\pi$
$929$	−21.6852	−0.711469	−0.355734	+	0.934587i	$0.615769\pi$
$930$	0	0
$931$	−0.164590	−0.00539423
$932$	86.5996	2.83667
$933$	15.7849	0.516773
$934$	104.765	3.42800
$935$	0	0
$936$	−0.00957179	−0.000312864 0
$937$	−8.63117	−0.281968	−0.140984	−	0.990012i	$-0.545027\pi$
$937$	−8.63117	−0.281968	−0.140984	+	0.990012i	$0.545027\pi$
$938$	−38.2177	−1.24785
$939$	4.24031	0.138377
$940$	0	0
$941$	−25.0813	−0.817626	−0.408813	−	0.912618i	$-0.634057\pi$
$941$	−25.0813	−0.817626	−0.408813	+	0.912618i	$0.634057\pi$
$942$	111.614	3.63658
$943$	−6.05737	−0.197255
$944$	−143.781	−4.67967
$945$	0	0
$946$	39.8207	1.29468
$947$	4.94123	0.160568	0.0802842	−	0.996772i	$-0.474417\pi$
$947$	4.94123	0.160568	0.0802842	+	0.996772i	$0.474417\pi$
$948$	−61.9081	−2.01068
$949$	−35.1800	−1.14199
$950$	0	0
$951$	−54.4120	−1.76443
$952$	54.1422	1.75476
$953$	7.21931	0.233856	0.116928	−	0.993140i	$-0.462695\pi$
$953$	7.21931	0.233856	0.116928	+	0.993140i	$0.462695\pi$
$954$	0.00297141	9.62031e−5 0
$955$	0	0
$956$	−81.8387	−2.64685
$957$	−5.46684	−0.176718
$958$	98.3088	3.17621
$959$	8.74940	0.282533
$960$	0	0
$961$	−27.6121	−0.890713
$962$	−63.6724	−2.05288
$963$	−0.000237801 0	−7.66304e−6 0
$964$	−168.238	−5.41857
$965$	0	0
$966$	−4.85249	−0.156126
$967$	−26.2278	−0.843430	−0.421715	−	0.906728i	$-0.638572\pi$
$967$	−26.2278	−0.843430	−0.421715	+	0.906728i	$0.638572\pi$
$968$	76.8531	2.47015
$969$	−1.43098	−0.0459696
$970$	0	0
$971$	25.5539	0.820063	0.410032	−	0.912071i	$-0.365518\pi$
$971$	25.5539	0.820063	0.410032	+	0.912071i	$0.365518\pi$
$972$	0.0176171	0.000565069 0
$973$	18.7390	0.600745
$974$	22.9052	0.733931
$975$	0	0
$976$	173.849	5.56478
$977$	−2.92251	−0.0934993	−0.0467497	−	0.998907i	$-0.514886\pi$
$977$	−2.92251	−0.0934993	−0.0467497	+	0.998907i	$0.514886\pi$
$978$	105.980	3.38888
$979$	16.6601	0.532458
$980$	0	0
$981$	0.00157031	5.01363e−5 0
$982$	−94.2961	−3.00911
$983$	−17.6138	−0.561792	−0.280896	−	0.959738i	$-0.590632\pi$
$983$	−17.6138	−0.561792	−0.280896	+	0.959738i	$0.590632\pi$
$984$	−113.154	−3.60722
$985$	0	0
$986$	22.5529	0.718231
$987$	−7.37809	−0.234847
$988$	2.94841	0.0938015
$989$	7.22063	0.229603
$990$	0	0
$991$	−33.1062	−1.05165	−0.525827	−	0.850592i	$-0.676244\pi$
$991$	−33.1062	−1.05165	−0.525827	+	0.850592i	$0.676244\pi$
$992$	55.7969	1.77155
$993$	22.6924	0.720121
$994$	−46.2154	−1.46586
$995$	0	0
$996$	105.049	3.32862
$997$	16.6806	0.528280	0.264140	−	0.964484i	$-0.414912\pi$
$997$	16.6806	0.528280	0.264140	+	0.964484i	$0.414912\pi$
$998$	−95.4352	−3.02095
$999$	38.5634	1.22009

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.80172 q^{2} +1.73197 q^{3} +5.84965 q^{4} -4.85249 q^{6} -1.00000 q^{7} -10.7857 q^{8} -0.000289796 q^{9} +O(q^{10})\)	\(q-2.80172 q^{2} +1.73197 q^{3} +5.84965 q^{4} -4.85249 q^{6} -1.00000 q^{7} -10.7857 q^{8} -0.000289796 q^{9} +1.96838 q^{11} +10.1314 q^{12} -3.06234 q^{13} +2.80172 q^{14} +18.5191 q^{16} +5.01983 q^{17} +0.000811928 q^{18} -0.164590 q^{19} -1.73197 q^{21} -5.51485 q^{22} -1.00000 q^{23} -18.6804 q^{24} +8.57984 q^{26} -5.19640 q^{27} -5.84965 q^{28} -1.60357 q^{29} -1.84062 q^{31} -30.3142 q^{32} +3.40917 q^{33} -14.0642 q^{34} -0.00169521 q^{36} -7.42117 q^{37} +0.461136 q^{38} -5.30388 q^{39} +6.05737 q^{41} +4.85249 q^{42} -7.22063 q^{43} +11.5143 q^{44} +2.80172 q^{46} +4.25995 q^{47} +32.0746 q^{48} +1.00000 q^{49} +8.69418 q^{51} -17.9137 q^{52} +3.65970 q^{53} +14.5589 q^{54} +10.7857 q^{56} -0.285065 q^{57} +4.49276 q^{58} -7.76391 q^{59} +9.38754 q^{61} +5.15691 q^{62} +0.000289796 q^{63} +47.8937 q^{64} -9.55154 q^{66} -13.6408 q^{67} +29.3643 q^{68} -1.73197 q^{69} -16.4953 q^{71} +0.00312564 q^{72} +11.4879 q^{73} +20.7921 q^{74} -0.962796 q^{76} -1.96838 q^{77} +14.8600 q^{78} -6.11051 q^{79} -8.99913 q^{81} -16.9711 q^{82} +10.3687 q^{83} -10.1314 q^{84} +20.2302 q^{86} -2.77733 q^{87} -21.2303 q^{88} +8.46385 q^{89} +3.06234 q^{91} -5.84965 q^{92} -3.18789 q^{93} -11.9352 q^{94} -52.5032 q^{96} -4.55947 q^{97} -2.80172 q^{98} -0.000570428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9	\( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 4 * q^3 + 17 * q^4 - 4 * q^6 - 14 * q^7 - 3 * q^8 + 18 * q^9 + 5 * q^11 - 17 * q^12 - 11 * q^13 + 3 * q^14 + 23 * q^16 - 3 * q^17 - 15 * q^18 - 2 * q^19 + 4 * q^21 - 23 * q^22 - 14 * q^23 - 12 * q^24 - 9 * q^26 - 25 * q^27 - 17 * q^28 + 7 * q^29 - 3 * q^31 - 24 * q^32 - 6 * q^33 - 14 * q^34 + 13 * q^36 - 22 * q^37 - 20 * q^38 - 10 * q^39 - 17 * q^41 + 4 * q^42 - 18 * q^43 + 28 * q^44 + 3 * q^46 - 30 * q^47 - 8 * q^48 + 14 * q^49 + 4 * q^51 - 8 * q^52 - 11 * q^53 + 20 * q^54 + 3 * q^56 - 18 * q^57 - 38 * q^58 - 22 * q^59 - 8 * q^61 + 22 * q^62 - 18 * q^63 + 29 * q^64 - 9 * q^66 - 39 * q^67 - q^68 + 4 * q^69 - 5 * q^71 + 24 * q^72 - 18 * q^73 + 35 * q^74 - 41 * q^76 - 5 * q^77 + 22 * q^78 + 10 * q^79 + 2 * q^81 + 8 * q^82 - 24 * q^83 + 17 * q^84 - 26 * q^86 - 5 * q^87 - 58 * q^88 + 25 * q^89 + 11 * q^91 - 17 * q^92 - 47 * q^93 - 2 * q^94 - 117 * q^96 - 43 * q^97 - 3 * q^98 + 55 * q^99

Introduction

L-functions

Modular forms

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