LMFDB - Embedded newform 2523.2.a.q.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2523,2,Mod(1,2523)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2523, 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("2523.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2523 = 3 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2523.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:	$20.1462564300$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 14x^{7} + 9x^{6} + 70x^{5} - 23x^{4} - 141x^{3} + 14x^{2} + 84x - 7 $ x^9 - x^8 - 14x^7 + 9x^6 + 70x^5 - 23x^4 - 141x^3 + 14x^2 + 84*x - 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.19659$ of defining polynomial
Character	$\chi$	$=$	2523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.19659 q^{2} +1.00000 q^{3} +2.82501 q^{4} -4.07769 q^{5} +2.19659 q^{6} +3.64733 q^{7} +1.81221 q^{8} +1.00000 q^{9} -8.95700 q^{10} +3.52776 q^{11} +2.82501 q^{12} +0.926540 q^{13} +8.01169 q^{14} -4.07769 q^{15} -1.66934 q^{16} -1.61861 q^{17} +2.19659 q^{18} +3.98608 q^{19} -11.5195 q^{20} +3.64733 q^{21} +7.74905 q^{22} +1.54577 q^{23} +1.81221 q^{24} +11.6275 q^{25} +2.03523 q^{26} +1.00000 q^{27} +10.3037 q^{28} -8.95700 q^{30} +1.60775 q^{31} -7.29128 q^{32} +3.52776 q^{33} -3.55543 q^{34} -14.8727 q^{35} +2.82501 q^{36} +5.30404 q^{37} +8.75579 q^{38} +0.926540 q^{39} -7.38960 q^{40} +6.71590 q^{41} +8.01169 q^{42} -4.42936 q^{43} +9.96596 q^{44} -4.07769 q^{45} +3.39542 q^{46} -3.33787 q^{47} -1.66934 q^{48} +6.30302 q^{49} +25.5409 q^{50} -1.61861 q^{51} +2.61748 q^{52} +2.03823 q^{53} +2.19659 q^{54} -14.3851 q^{55} +6.60971 q^{56} +3.98608 q^{57} +7.29049 q^{59} -11.5195 q^{60} +6.00554 q^{61} +3.53156 q^{62} +3.64733 q^{63} -12.6773 q^{64} -3.77814 q^{65} +7.74905 q^{66} +9.48235 q^{67} -4.57260 q^{68} +1.54577 q^{69} -32.6692 q^{70} +8.44759 q^{71} +1.81221 q^{72} -7.56757 q^{73} +11.6508 q^{74} +11.6275 q^{75} +11.2607 q^{76} +12.8669 q^{77} +2.03523 q^{78} -0.287887 q^{79} +6.80706 q^{80} +1.00000 q^{81} +14.7521 q^{82} -6.47754 q^{83} +10.3037 q^{84} +6.60020 q^{85} -9.72949 q^{86} +6.39303 q^{88} -16.5093 q^{89} -8.95700 q^{90} +3.37940 q^{91} +4.36681 q^{92} +1.60775 q^{93} -7.33194 q^{94} -16.2540 q^{95} -7.29128 q^{96} -10.0522 q^{97} +13.8451 q^{98} +3.52776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + q^{2} + 9 q^{3} + 11 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 9 q^{9} + 4 q^{10} + 3 q^{11} + 11 q^{12} + 5 q^{13} + 15 q^{14} - 5 q^{16} + 16 q^{17} + q^{18} - q^{19} + 8 q^{20} + 5 q^{21} + 24 q^{22}+ \cdots + 3 q^{99}+O(q^{100}) $ 9 * q + q^2 + 9 * q^3 + 11 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 9 * q^9 + 4 * q^10 + 3 * q^11 + 11 * q^12 + 5 * q^13 + 15 * q^14 - 5 * q^16 + 16 * q^17 + q^18 - q^19 + 8 * q^20 + 5 * q^21 + 24 * q^22 - 10 * q^23 + 12 * q^24 + 9 * q^25 + 12 * q^26 + 9 * q^27 - 24 * q^28 + 4 * q^30 - 4 * q^31 + 25 * q^32 + 3 * q^33 + 24 * q^34 - 44 * q^35 + 11 * q^36 + 25 * q^37 - 10 * q^38 + 5 * q^39 + 5 * q^40 + 34 * q^41 + 15 * q^42 + 12 * q^43 - 23 * q^44 + 6 * q^46 + 8 * q^47 - 5 * q^48 + 26 * q^49 + 27 * q^50 + 16 * q^51 - 23 * q^52 - 32 * q^53 + q^54 - 5 * q^55 - 14 * q^56 - q^57 + 10 * q^59 + 8 * q^60 + 51 * q^61 + 8 * q^62 + 5 * q^63 - 8 * q^64 - 11 * q^65 + 24 * q^66 + 7 * q^67 + 11 * q^68 - 10 * q^69 - 14 * q^70 + 7 * q^71 + 12 * q^72 + 17 * q^73 - 62 * q^74 + 9 * q^75 - 6 * q^76 + 64 * q^77 + 12 * q^78 + 13 * q^79 + 54 * q^80 + 9 * q^81 + 37 * q^82 - 31 * q^83 - 24 * q^84 + 42 * q^85 - 70 * q^86 - 29 * q^88 - 32 * q^89 + 4 * q^90 + 45 * q^91 + 9 * q^92 - 4 * q^93 + 38 * q^94 - 20 * q^95 + 25 * q^96 + 16 * q^97 - 12 * q^98 + 3 * q^99

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 $

$2$	2.19659	1.55322	0.776612	−	0.629979i	$-0.216937\pi$
$2$	2.19659	1.55322	0.776612	+	0.629979i	$0.216937\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.82501	1.41250
$5$	−4.07769	−1.82360	−0.911798	−	0.410638i	$-0.865306\pi$
$5$	−4.07769	−1.82360	−0.911798	+	0.410638i	$0.865306\pi$
$6$	2.19659	0.896754
$7$	3.64733	1.37856	0.689281	−	0.724495i	$-0.257927\pi$
$7$	3.64733	1.37856	0.689281	+	0.724495i	$0.257927\pi$
$8$	1.81221	0.640711
$9$	1.00000	0.333333
$10$	−8.95700	−2.83245
$11$	3.52776	1.06366	0.531830	−	0.846851i	$-0.321504\pi$
$11$	3.52776	1.06366	0.531830	+	0.846851i	$0.321504\pi$
$12$	2.82501	0.815510
$13$	0.926540	0.256976	0.128488	−	0.991711i	$-0.458988\pi$
$13$	0.926540	0.256976	0.128488	+	0.991711i	$0.458988\pi$
$14$	8.01169	2.14121
$15$	−4.07769	−1.05285
$16$	−1.66934	−0.417336
$17$	−1.61861	−0.392571	−0.196286	−	0.980547i	$-0.562888\pi$
$17$	−1.61861	−0.392571	−0.196286	+	0.980547i	$0.562888\pi$
$18$	2.19659	0.517741
$19$	3.98608	0.914470	0.457235	−	0.889346i	$-0.348840\pi$
$19$	3.98608	0.914470	0.457235	+	0.889346i	$0.348840\pi$
$20$	−11.5195	−2.57584
$21$	3.64733	0.795913
$22$	7.74905	1.65210
$23$	1.54577	0.322315	0.161158	−	0.986929i	$-0.448477\pi$
$23$	1.54577	0.322315	0.161158	+	0.986929i	$0.448477\pi$
$24$	1.81221	0.369915
$25$	11.6275	2.32550
$26$	2.03523	0.399141
$27$	1.00000	0.192450
$28$	10.3037	1.94722
$29$	0	0
$29$	0	0
$30$	−8.95700	−1.63532
$31$	1.60775	0.288760	0.144380	−	0.989522i	$-0.453881\pi$
$31$	1.60775	0.288760	0.144380	+	0.989522i	$0.453881\pi$
$32$	−7.29128	−1.28893
$33$	3.52776	0.614105
$34$	−3.55543	−0.609751
$35$	−14.8727	−2.51394
$36$	2.82501	0.470835
$37$	5.30404	0.871979	0.435990	−	0.899952i	$-0.356398\pi$
$37$	5.30404	0.871979	0.435990	+	0.899952i	$0.356398\pi$
$38$	8.75579	1.42038
$39$	0.926540	0.148365
$40$	−7.38960	−1.16840
$41$	6.71590	1.04885	0.524423	−	0.851458i	$-0.324281\pi$
$41$	6.71590	1.04885	0.524423	+	0.851458i	$0.324281\pi$
$42$	8.01169	1.23623
$43$	−4.42936	−0.675471	−0.337736	−	0.941241i	$-0.609661\pi$
$43$	−4.42936	−0.675471	−0.337736	+	0.941241i	$0.609661\pi$
$44$	9.96596	1.50242
$45$	−4.07769	−0.607866
$46$	3.39542	0.500628
$47$	−3.33787	−0.486879	−0.243439	−	0.969916i	$-0.578276\pi$
$47$	−3.33787	−0.486879	−0.243439	+	0.969916i	$0.578276\pi$
$48$	−1.66934	−0.240949
$49$	6.30302	0.900431
$50$	25.5409	3.61203
$51$	−1.61861	−0.226651
$52$	2.61748	0.362980
$53$	2.03823	0.279972	0.139986	−	0.990153i	$-0.455294\pi$
$53$	2.03823	0.279972	0.139986	+	0.990153i	$0.455294\pi$
$54$	2.19659	0.298918
$55$	−14.3851	−1.93969
$56$	6.60971	0.883260
$57$	3.98608	0.527970
$58$	0	0
$59$	7.29049	0.949141	0.474571	−	0.880217i	$-0.342603\pi$
$59$	7.29049	0.949141	0.474571	+	0.880217i	$0.342603\pi$
$60$	−11.5195	−1.48716
$61$	6.00554	0.768930	0.384465	−	0.923139i	$-0.374386\pi$
$61$	6.00554	0.768930	0.384465	+	0.923139i	$0.374386\pi$
$62$	3.53156	0.448509
$63$	3.64733	0.459520
$64$	−12.6773	−1.58466
$65$	−3.77814	−0.468620
$66$	7.74905	0.953842
$67$	9.48235	1.15845	0.579227	−	0.815167i	$-0.303355\pi$
$67$	9.48235	1.15845	0.579227	+	0.815167i	$0.303355\pi$
$68$	−4.57260	−0.554509
$69$	1.54577	0.186089
$70$	−32.6692	−3.90471
$71$	8.44759	1.00255	0.501273	−	0.865289i	$-0.332865\pi$
$71$	8.44759	1.00255	0.501273	+	0.865289i	$0.332865\pi$
$72$	1.81221	0.213570
$73$	−7.56757	−0.885718	−0.442859	−	0.896591i	$-0.646036\pi$
$73$	−7.56757	−0.885718	−0.442859	+	0.896591i	$0.646036\pi$
$74$	11.6508	1.35438
$75$	11.6275	1.34263
$76$	11.2607	1.29169
$77$	12.8669	1.46632
$78$	2.03523	0.230444
$79$	−0.287887	−0.0323898	−0.0161949	−	0.999869i	$-0.505155\pi$
$79$	−0.287887	−0.0323898	−0.0161949	+	0.999869i	$0.505155\pi$
$80$	6.80706	0.761053
$81$	1.00000	0.111111
$82$	14.7521	1.62909
$83$	−6.47754	−0.711003	−0.355501	−	0.934676i	$-0.615690\pi$
$83$	−6.47754	−0.711003	−0.355501	+	0.934676i	$0.615690\pi$
$84$	10.3037	1.12423
$85$	6.60020	0.715892
$86$	−9.72949	−1.04916
$87$	0	0
$88$	6.39303	0.681499
$89$	−16.5093	−1.74999	−0.874993	−	0.484136i	$-0.839134\pi$
$89$	−16.5093	−1.74999	−0.874993	+	0.484136i	$0.839134\pi$
$90$	−8.95700	−0.944151
$91$	3.37940	0.354257
$92$	4.36681	0.455272
$93$	1.60775	0.166716
$94$	−7.33194	−0.756232
$95$	−16.2540	−1.66762
$96$	−7.29128	−0.744163
$97$	−10.0522	−1.02064	−0.510322	−	0.859983i	$-0.670474\pi$
$97$	−10.0522	−1.02064	−0.510322	+	0.859983i	$0.670474\pi$
$98$	13.8451	1.39857
$99$	3.52776	0.354554
$100$	32.8478	3.28478
$101$	−8.23922	−0.819833	−0.409917	−	0.912123i	$-0.634442\pi$
$101$	−8.23922	−0.819833	−0.409917	+	0.912123i	$0.634442\pi$
$102$	−3.55543	−0.352040
$103$	7.62704	0.751515	0.375757	−	0.926718i	$-0.377383\pi$
$103$	7.62704	0.751515	0.375757	+	0.926718i	$0.377383\pi$
$104$	1.67908	0.164647
$105$	−14.8727	−1.45142
$106$	4.47715	0.434859
$107$	−16.7576	−1.62002	−0.810011	−	0.586414i	$-0.800539\pi$
$107$	−16.7576	−1.62002	−0.810011	+	0.586414i	$0.800539\pi$
$108$	2.82501	0.271837
$109$	−12.7116	−1.21755	−0.608775	−	0.793343i	$-0.708339\pi$
$109$	−12.7116	−1.21755	−0.608775	+	0.793343i	$0.708339\pi$
$110$	−31.5982	−3.01277
$111$	5.30404	0.503437
$112$	−6.08865	−0.575323
$113$	8.46482	0.796303	0.398152	−	0.917320i	$-0.369652\pi$
$113$	8.46482	0.796303	0.398152	+	0.917320i	$0.369652\pi$
$114$	8.75579	0.820055
$115$	−6.30316	−0.587773
$116$	0	0
$117$	0.926540	0.0856587
$118$	16.0142	1.47423
$119$	−5.90362	−0.541184
$120$	−7.38960	−0.674575
$121$	1.44511	0.131374
$122$	13.1917	1.19432
$123$	6.71590	0.605552
$124$	4.54190	0.407875
$125$	−27.0250	−2.41719
$126$	8.01169	0.713738
$127$	17.8052	1.57995	0.789977	−	0.613137i	$-0.210093\pi$
$127$	17.8052	1.57995	0.789977	+	0.613137i	$0.210093\pi$
$128$	−13.2642	−1.17240
$129$	−4.42936	−0.389983
$130$	−8.29902	−0.727872
$131$	−11.3299	−0.989897	−0.494949	−	0.868922i	$-0.664813\pi$
$131$	−11.3299	−0.989897	−0.494949	+	0.868922i	$0.664813\pi$
$132$	9.96596	0.867425
$133$	14.5386	1.26065
$134$	20.8288	1.79934
$135$	−4.07769	−0.350951
$136$	−2.93326	−0.251525
$137$	−8.31246	−0.710182	−0.355091	−	0.934832i	$-0.615550\pi$
$137$	−8.31246	−0.710182	−0.355091	+	0.934832i	$0.615550\pi$
$138$	3.39542	0.289038
$139$	−3.11275	−0.264020	−0.132010	−	0.991248i	$-0.542143\pi$
$139$	−3.11275	−0.264020	−0.132010	+	0.991248i	$0.542143\pi$
$140$	−42.0154	−3.55095
$141$	−3.33787	−0.281100
$142$	18.5559	1.55718
$143$	3.26861	0.273335
$144$	−1.66934	−0.139112
$145$	0	0
$146$	−16.6229	−1.37572
$147$	6.30302	0.519864
$148$	14.9840	1.23167
$149$	15.1558	1.24161	0.620807	−	0.783963i	$-0.286805\pi$
$149$	15.1558	1.24161	0.620807	+	0.783963i	$0.286805\pi$
$150$	25.5409	2.08541
$151$	0.678890	0.0552473	0.0276237	−	0.999618i	$-0.491206\pi$
$151$	0.678890	0.0552473	0.0276237	+	0.999618i	$0.491206\pi$
$152$	7.22360	0.585911
$153$	−1.61861	−0.130857
$154$	28.2633	2.27752
$155$	−6.55589	−0.526582
$156$	2.61748	0.209566
$157$	6.23584	0.497674	0.248837	−	0.968545i	$-0.419952\pi$
$157$	6.23584	0.497674	0.248837	+	0.968545i	$0.419952\pi$
$158$	−0.632370	−0.0503086
$159$	2.03823	0.161642
$160$	29.7315	2.35048
$161$	5.63793	0.444331
$162$	2.19659	0.172580
$163$	15.3163	1.19967	0.599834	−	0.800124i	$-0.295233\pi$
$163$	15.3163	1.19967	0.599834	+	0.800124i	$0.295233\pi$
$164$	18.9725	1.48150
$165$	−14.3851	−1.11988
$166$	−14.2285	−1.10435
$167$	−15.7861	−1.22156	−0.610781	−	0.791799i	$-0.709145\pi$
$167$	−15.7861	−1.22156	−0.610781	+	0.791799i	$0.709145\pi$
$168$	6.60971	0.509950
$169$	−12.1415	−0.933963
$170$	14.4979	1.11194
$171$	3.98608	0.304823
$172$	−12.5130	−0.954106
$173$	−3.44502	−0.261920	−0.130960	−	0.991388i	$-0.541806\pi$
$173$	−3.44502	−0.261920	−0.130960	+	0.991388i	$0.541806\pi$
$174$	0	0
$175$	42.4094	3.20585
$176$	−5.88905	−0.443904
$177$	7.29049	0.547987
$178$	−36.2642	−2.71812
$179$	−12.0378	−0.899744	−0.449872	−	0.893093i	$-0.648530\pi$
$179$	−12.0378	−0.899744	−0.449872	+	0.893093i	$0.648530\pi$
$180$	−11.5195	−0.858613
$181$	2.41926	0.179823	0.0899113	−	0.995950i	$-0.471342\pi$
$181$	2.41926	0.179823	0.0899113	+	0.995950i	$0.471342\pi$
$182$	7.42315	0.550241
$183$	6.00554	0.443942
$184$	2.80125	0.206511
$185$	−21.6282	−1.59014
$186$	3.53156	0.258947
$187$	−5.71008	−0.417563
$188$	−9.42952	−0.687719
$189$	3.64733	0.265304
$190$	−35.7034	−2.59019
$191$	−5.83662	−0.422323	−0.211162	−	0.977451i	$-0.567725\pi$
$191$	−5.83662	−0.422323	−0.211162	+	0.977451i	$0.567725\pi$
$192$	−12.6773	−0.914902
$193$	−19.9903	−1.43894	−0.719468	−	0.694525i	$-0.755614\pi$
$193$	−19.9903	−1.43894	−0.719468	+	0.694525i	$0.755614\pi$
$194$	−22.0805	−1.58529
$195$	−3.77814	−0.270558
$196$	17.8061	1.27186
$197$	−11.7126	−0.834486	−0.417243	−	0.908795i	$-0.637004\pi$
$197$	−11.7126	−0.834486	−0.417243	+	0.908795i	$0.637004\pi$
$198$	7.74905	0.550701
$199$	−16.6484	−1.18017	−0.590086	−	0.807340i	$-0.700906\pi$
$199$	−16.6484	−1.18017	−0.590086	+	0.807340i	$0.700906\pi$
$200$	21.0715	1.48998
$201$	9.48235	0.668833
$202$	−18.0982	−1.27338
$203$	0	0
$204$	−4.57260	−0.320146
$205$	−27.3853	−1.91267
$206$	16.7535	1.16727
$207$	1.54577	0.107438
$208$	−1.54671	−0.107245
$209$	14.0620	0.972686
$210$	−32.6692	−2.25439
$211$	24.2435	1.66899	0.834496	−	0.551014i	$-0.185759\pi$
$211$	24.2435	1.66899	0.834496	+	0.551014i	$0.185759\pi$
$212$	5.75801	0.395462
$213$	8.44759	0.578820
$214$	−36.8097	−2.51626
$215$	18.0615	1.23179
$216$	1.81221	0.123305
$217$	5.86399	0.398073
$218$	−27.9222	−1.89113
$219$	−7.56757	−0.511369
$220$	−40.6381	−2.73982
$221$	−1.49971	−0.100881
$222$	11.6508	0.781951
$223$	28.3179	1.89631	0.948153	−	0.317814i	$-0.102949\pi$
$223$	28.3179	1.89631	0.948153	+	0.317814i	$0.102949\pi$
$224$	−26.5937	−1.77687
$225$	11.6275	0.775168
$226$	18.5937	1.23684
$227$	9.86418	0.654709	0.327354	−	0.944902i	$-0.393843\pi$
$227$	9.86418	0.654709	0.327354	+	0.944902i	$0.393843\pi$
$228$	11.2607	0.745759
$229$	−15.6570	−1.03464	−0.517322	−	0.855791i	$-0.673071\pi$
$229$	−15.6570	−1.03464	−0.517322	+	0.855791i	$0.673071\pi$
$230$	−13.8455	−0.912943
$231$	12.8669	0.846581
$232$	0	0
$233$	−19.7879	−1.29635	−0.648176	−	0.761491i	$-0.724468\pi$
$233$	−19.7879	−1.29635	−0.648176	+	0.761491i	$0.724468\pi$
$234$	2.03523	0.133047
$235$	13.6108	0.887871
$236$	20.5957	1.34067
$237$	−0.287887	−0.0187003
$238$	−12.9678	−0.840579
$239$	−9.33298	−0.603700	−0.301850	−	0.953355i	$-0.597604\pi$
$239$	−9.33298	−0.603700	−0.301850	+	0.953355i	$0.597604\pi$
$240$	6.80706	0.439394
$241$	−24.5737	−1.58293	−0.791464	−	0.611215i	$-0.790681\pi$
$241$	−24.5737	−1.58293	−0.791464	+	0.611215i	$0.790681\pi$
$242$	3.17432	0.204053
$243$	1.00000	0.0641500
$244$	16.9657	1.08612
$245$	−25.7017	−1.64202
$246$	14.7521	0.940558
$247$	3.69327	0.234997
$248$	2.91357	0.185012
$249$	−6.47754	−0.410498
$250$	−59.3627	−3.75443
$251$	−4.66182	−0.294252	−0.147126	−	0.989118i	$-0.547002\pi$
$251$	−4.66182	−0.294252	−0.147126	+	0.989118i	$0.547002\pi$
$252$	10.3037	0.649074
$253$	5.45311	0.342834
$254$	39.1107	2.45402
$255$	6.60020	0.413320
$256$	−3.78146	−0.236341
$257$	−28.3543	−1.76869	−0.884345	−	0.466834i	$-0.845395\pi$
$257$	−28.3543	−1.76869	−0.884345	+	0.466834i	$0.845395\pi$
$258$	−9.72949	−0.605732
$259$	19.3456	1.20208
$260$	−10.6733	−0.661928
$261$	0	0
$262$	−24.8871	−1.53753
$263$	26.7811	1.65139	0.825697	−	0.564114i	$-0.190782\pi$
$263$	26.7811	1.65139	0.825697	+	0.564114i	$0.190782\pi$
$264$	6.39303	0.393464
$265$	−8.31125	−0.510556
$266$	31.9353	1.95808
$267$	−16.5093	−1.01035
$268$	26.7877	1.63632
$269$	0.785551	0.0478959	0.0239479	−	0.999713i	$-0.492376\pi$
$269$	0.785551	0.0478959	0.0239479	+	0.999713i	$0.492376\pi$
$270$	−8.95700	−0.545106
$271$	12.1514	0.738148	0.369074	−	0.929400i	$-0.379675\pi$
$271$	12.1514	0.738148	0.369074	+	0.929400i	$0.379675\pi$
$272$	2.70202	0.163834
$273$	3.37940	0.204530
$274$	−18.2591	−1.10307
$275$	41.0191	2.47355
$276$	4.36681	0.262851
$277$	−15.7837	−0.948352	−0.474176	−	0.880430i	$-0.657254\pi$
$277$	−15.7837	−0.948352	−0.474176	+	0.880430i	$0.657254\pi$
$278$	−6.83744	−0.410083
$279$	1.60775	0.0962533
$280$	−26.9523	−1.61071
$281$	20.0723	1.19741	0.598705	−	0.800969i	$-0.295682\pi$
$281$	20.0723	1.19741	0.598705	+	0.800969i	$0.295682\pi$
$282$	−7.33194	−0.436611
$283$	−1.95557	−0.116246	−0.0581232	−	0.998309i	$-0.518512\pi$
$283$	−1.95557	−0.116246	−0.0581232	+	0.998309i	$0.518512\pi$
$284$	23.8645	1.41610
$285$	−16.2540	−0.962803
$286$	7.17980	0.424551
$287$	24.4951	1.44590
$288$	−7.29128	−0.429643
$289$	−14.3801	−0.845888
$290$	0	0
$291$	−10.0522	−0.589269
$292$	−21.3785	−1.25108
$293$	2.41420	0.141039	0.0705194	−	0.997510i	$-0.477534\pi$
$293$	2.41420	0.141039	0.0705194	+	0.997510i	$0.477534\pi$
$294$	13.8451	0.807465
$295$	−29.7283	−1.73085
$296$	9.61201	0.558687
$297$	3.52776	0.204702
$298$	33.2912	1.92851
$299$	1.43222	0.0828273
$300$	32.8478	1.89647
$301$	−16.1553	−0.931178
$302$	1.49124	0.0858114
$303$	−8.23922	−0.473331
$304$	−6.65415	−0.381641
$305$	−24.4887	−1.40222
$306$	−3.55543	−0.203250
$307$	1.11367	0.0635606	0.0317803	−	0.999495i	$-0.489882\pi$
$307$	1.11367	0.0635606	0.0317803	+	0.999495i	$0.489882\pi$
$308$	36.3491	2.07118
$309$	7.62704	0.433887
$310$	−14.4006	−0.817899
$311$	−4.42989	−0.251196	−0.125598	−	0.992081i	$-0.540085\pi$
$311$	−4.42989	−0.251196	−0.125598	+	0.992081i	$0.540085\pi$
$312$	1.67908	0.0950592
$313$	−30.1002	−1.70136	−0.850682	−	0.525680i	$-0.823811\pi$
$313$	−30.1002	−1.70136	−0.850682	+	0.525680i	$0.823811\pi$
$314$	13.6976	0.772999
$315$	−14.8727	−0.837980
$316$	−0.813283	−0.0457507
$317$	6.21069	0.348827	0.174414	−	0.984672i	$-0.444197\pi$
$317$	6.21069	0.348827	0.174414	+	0.984672i	$0.444197\pi$
$318$	4.47715	0.251066
$319$	0	0
$320$	51.6939	2.88978
$321$	−16.7576	−0.935321
$322$	12.3842	0.690146
$323$	−6.45193	−0.358995
$324$	2.82501	0.156945
$325$	10.7734	0.597599
$326$	33.6437	1.86335
$327$	−12.7116	−0.702953
$328$	12.1706	0.672008
$329$	−12.1743	−0.671192
$330$	−31.5982	−1.73942
$331$	−10.0058	−0.549967	−0.274984	−	0.961449i	$-0.588672\pi$
$331$	−10.0058	−0.549967	−0.274984	+	0.961449i	$0.588672\pi$
$332$	−18.2991	−1.00429
$333$	5.30404	0.290660
$334$	−34.6755	−1.89736
$335$	−38.6660	−2.11255
$336$	−6.08865	−0.332163
$337$	27.2955	1.48688	0.743440	−	0.668803i	$-0.233193\pi$
$337$	27.2955	1.48688	0.743440	+	0.668803i	$0.233193\pi$
$338$	−26.6700	−1.45065
$339$	8.46482	0.459746
$340$	18.6456	1.01120
$341$	5.67175	0.307143
$342$	8.75579	0.473459
$343$	−2.54213	−0.137262
$344$	−8.02691	−0.432782
$345$	−6.30316	−0.339351
$346$	−7.56729	−0.406820
$347$	1.19493	0.0641473	0.0320736	−	0.999486i	$-0.489789\pi$
$347$	1.19493	0.0641473	0.0320736	+	0.999486i	$0.489789\pi$
$348$	0	0
$349$	7.25120	0.388148	0.194074	−	0.980987i	$-0.437830\pi$
$349$	7.25120	0.388148	0.194074	+	0.980987i	$0.437830\pi$
$350$	93.1561	4.97940
$351$	0.926540	0.0494550
$352$	−25.7219	−1.37098
$353$	−5.26353	−0.280150	−0.140075	−	0.990141i	$-0.544734\pi$
$353$	−5.26353	−0.280150	−0.140075	+	0.990141i	$0.544734\pi$
$354$	16.0142	0.851147
$355$	−34.4466	−1.82824
$356$	−46.6390	−2.47186
$357$	−5.90362	−0.312453
$358$	−26.4420	−1.39750
$359$	14.6286	0.772067	0.386034	−	0.922485i	$-0.373845\pi$
$359$	14.6286	0.772067	0.386034	+	0.922485i	$0.373845\pi$
$360$	−7.38960	−0.389466
$361$	−3.11114	−0.163744
$362$	5.31413	0.279305
$363$	1.44511	0.0758486
$364$	9.54682	0.500390
$365$	30.8582	1.61519
$366$	13.1917	0.689542
$367$	−5.55318	−0.289874	−0.144937	−	0.989441i	$-0.546298\pi$
$367$	−5.55318	−0.289874	−0.144937	+	0.989441i	$0.546298\pi$
$368$	−2.58042	−0.134514
$369$	6.71590	0.349616
$370$	−47.5083	−2.46984
$371$	7.43409	0.385959
$372$	4.54190	0.235487
$373$	29.7459	1.54019	0.770093	−	0.637931i	$-0.220210\pi$
$373$	29.7459	1.54019	0.770093	+	0.637931i	$0.220210\pi$
$374$	−12.5427	−0.648568
$375$	−27.0250	−1.39556
$376$	−6.04891	−0.311949
$377$	0	0
$378$	8.01169	0.412077
$379$	1.96231	0.100797	0.0503986	−	0.998729i	$-0.483951\pi$
$379$	1.96231	0.100797	0.0503986	+	0.998729i	$0.483951\pi$
$380$	−45.9177	−2.35553
$381$	17.8052	0.912187
$382$	−12.8207	−0.655962
$383$	−11.8165	−0.603796	−0.301898	−	0.953340i	$-0.597620\pi$
$383$	−11.8165	−0.603796	−0.301898	+	0.953340i	$0.597620\pi$
$384$	−13.2642	−0.676885
$385$	−52.4672	−2.67398
$386$	−43.9106	−2.23499
$387$	−4.42936	−0.225157
$388$	−28.3975	−1.44166
$389$	−11.9013	−0.603422	−0.301711	−	0.953399i	$-0.597558\pi$
$389$	−11.9013	−0.603422	−0.301711	+	0.953399i	$0.597558\pi$
$390$	−8.29902	−0.420237
$391$	−2.50200	−0.126532
$392$	11.4224	0.576916
$393$	−11.3299	−0.571517
$394$	−25.7277	−1.29614
$395$	1.17391	0.0590660
$396$	9.96596	0.500808
$397$	19.6778	0.987603	0.493801	−	0.869575i	$-0.335607\pi$
$397$	19.6778	0.987603	0.493801	+	0.869575i	$0.335607\pi$
$398$	−36.5697	−1.83307
$399$	14.5386	0.727838
$400$	−19.4103	−0.970517
$401$	−20.5264	−1.02504	−0.512520	−	0.858675i	$-0.671288\pi$
$401$	−20.5264	−1.02504	−0.512520	+	0.858675i	$0.671288\pi$
$402$	20.8288	1.03885
$403$	1.48964	0.0742044
$404$	−23.2759	−1.15802
$405$	−4.07769	−0.202622
$406$	0	0
$407$	18.7114	0.927490
$408$	−2.93326	−0.145218
$409$	−32.1820	−1.59130	−0.795648	−	0.605760i	$-0.792869\pi$
$409$	−32.1820	−1.59130	−0.795648	+	0.605760i	$0.792869\pi$
$410$	−60.1543	−2.97081
$411$	−8.31246	−0.410023
$412$	21.5464	1.06152
$413$	26.5908	1.30845
$414$	3.39542	0.166876
$415$	26.4134	1.29658
$416$	−6.75566	−0.331223
$417$	−3.11275	−0.152432
$418$	30.8884	1.51080
$419$	1.58695	0.0775275	0.0387638	−	0.999248i	$-0.487658\pi$
$419$	1.58695	0.0775275	0.0387638	+	0.999248i	$0.487658\pi$
$420$	−42.0154	−2.05014
$421$	−5.86317	−0.285753	−0.142877	−	0.989741i	$-0.545635\pi$
$421$	−5.86317	−0.285753	−0.142877	+	0.989741i	$0.545635\pi$
$422$	53.2530	2.59232
$423$	−3.33787	−0.162293
$424$	3.69369	0.179381
$425$	−18.8205	−0.912926
$426$	18.5559	0.899036
$427$	21.9042	1.06002
$428$	−47.3405	−2.28829
$429$	3.26861	0.157810
$430$	39.6738	1.91324
$431$	−8.46235	−0.407617	−0.203809	−	0.979011i	$-0.565332\pi$
$431$	−8.46235	−0.407617	−0.203809	+	0.979011i	$0.565332\pi$
$432$	−1.66934	−0.0803164
$433$	−12.7185	−0.611212	−0.305606	−	0.952158i	$-0.598859\pi$
$433$	−12.7185	−0.611212	−0.305606	+	0.952158i	$0.598859\pi$
$434$	12.8808	0.618297
$435$	0	0
$436$	−35.9104	−1.71980
$437$	6.16157	0.294748
$438$	−16.6229	−0.794271
$439$	−7.50539	−0.358213	−0.179106	−	0.983830i	$-0.557321\pi$
$439$	−7.50539	−0.358213	−0.179106	+	0.983830i	$0.557321\pi$
$440$	−26.0688	−1.24278
$441$	6.30302	0.300144
$442$	−3.29425	−0.156691
$443$	11.6583	0.553902	0.276951	−	0.960884i	$-0.410676\pi$
$443$	11.6583	0.553902	0.276951	+	0.960884i	$0.410676\pi$
$444$	14.9840	0.711107
$445$	67.3199	3.19127
$446$	62.2028	2.94539
$447$	15.1558	0.716847
$448$	−46.2381	−2.18455
$449$	19.4512	0.917957	0.458978	−	0.888447i	$-0.348216\pi$
$449$	19.4512	0.917957	0.458978	+	0.888447i	$0.348216\pi$
$450$	25.5409	1.20401
$451$	23.6921	1.11562
$452$	23.9132	1.12478
$453$	0.678890	0.0318971
$454$	21.6676	1.01691
$455$	−13.7801	−0.646022
$456$	7.22360	0.338276
$457$	17.1125	0.800489	0.400245	−	0.916408i	$-0.368925\pi$
$457$	17.1125	0.800489	0.400245	+	0.916408i	$0.368925\pi$
$458$	−34.3920	−1.60703
$459$	−1.61861	−0.0755504
$460$	−17.8065	−0.830232
$461$	−8.53020	−0.397291	−0.198646	−	0.980071i	$-0.563654\pi$
$461$	−8.53020	−0.397291	−0.198646	+	0.980071i	$0.563654\pi$
$462$	28.2633	1.31493
$463$	1.49772	0.0696050	0.0348025	−	0.999394i	$-0.488920\pi$
$463$	1.49772	0.0696050	0.0348025	+	0.999394i	$0.488920\pi$
$464$	0	0
$465$	−6.55589	−0.304022
$466$	−43.4660	−2.01352
$467$	21.4307	0.991695	0.495848	−	0.868410i	$-0.334857\pi$
$467$	21.4307	0.991695	0.495848	+	0.868410i	$0.334857\pi$
$468$	2.61748	0.120993
$469$	34.5853	1.59700
$470$	29.8974	1.37906
$471$	6.23584	0.287332
$472$	13.2119	0.608126
$473$	−15.6257	−0.718472
$474$	−0.632370	−0.0290457
$475$	46.3483	2.12660
$476$	−16.6778	−0.764424
$477$	2.03823	0.0933241
$478$	−20.5007	−0.937682
$479$	28.5538	1.30465	0.652327	−	0.757937i	$-0.273793\pi$
$479$	28.5538	1.30465	0.652327	+	0.757937i	$0.273793\pi$
$480$	29.7315	1.35705
$481$	4.91441	0.224078
$482$	−53.9783	−2.45864
$483$	5.63793	0.256535
$484$	4.08245	0.185566
$485$	40.9896	1.86124
$486$	2.19659	0.0996394
$487$	25.1555	1.13991	0.569953	−	0.821677i	$-0.306961\pi$
$487$	25.1555	1.13991	0.569953	+	0.821677i	$0.306961\pi$
$488$	10.8833	0.492662
$489$	15.3163	0.692629
$490$	−56.4561	−2.55043
$491$	21.6846	0.978614	0.489307	−	0.872112i	$-0.337250\pi$
$491$	21.6846	0.978614	0.489307	+	0.872112i	$0.337250\pi$
$492$	18.9725	0.855345
$493$	0	0
$494$	8.11259	0.365003
$495$	−14.3851	−0.646563
$496$	−2.68388	−0.120510
$497$	30.8112	1.38207
$498$	−14.2285	−0.637595
$499$	5.68927	0.254687	0.127343	−	0.991859i	$-0.459355\pi$
$499$	5.68927	0.254687	0.127343	+	0.991859i	$0.459355\pi$
$500$	−76.3457	−3.41428
$501$	−15.7861	−0.705269
$502$	−10.2401	−0.457039
$503$	9.46973	0.422234	0.211117	−	0.977461i	$-0.432290\pi$
$503$	9.46973	0.422234	0.211117	+	0.977461i	$0.432290\pi$
$504$	6.60971	0.294420
$505$	33.5970	1.49505
$506$	11.9782	0.532498
$507$	−12.1415	−0.539224
$508$	50.2998	2.23169
$509$	−30.5939	−1.35605	−0.678024	−	0.735039i	$-0.737164\pi$
$509$	−30.5939	−1.35605	−0.678024	+	0.735039i	$0.737164\pi$
$510$	14.4979	0.641979
$511$	−27.6014	−1.22102
$512$	18.2220	0.805308
$513$	3.98608	0.175990
$514$	−62.2827	−2.74717
$515$	−31.1007	−1.37046
$516$	−12.5130	−0.550853
$517$	−11.7752	−0.517874
$518$	42.4943	1.86709
$519$	−3.44502	−0.151220
$520$	−6.84676	−0.300250
$521$	8.99098	0.393902	0.196951	−	0.980413i	$-0.436896\pi$
$521$	8.99098	0.393902	0.196951	+	0.980413i	$0.436896\pi$
$522$	0	0
$523$	−1.43930	−0.0629362	−0.0314681	−	0.999505i	$-0.510018\pi$
$523$	−1.43930	−0.0629362	−0.0314681	+	0.999505i	$0.510018\pi$
$524$	−32.0070	−1.39823
$525$	42.4094	1.85090
$526$	58.8271	2.56498
$527$	−2.60232	−0.113359
$528$	−5.88905	−0.256288
$529$	−20.6106	−0.896113
$530$	−18.2564	−0.793008
$531$	7.29049	0.316380
$532$	41.0715	1.78068
$533$	6.22255	0.269528
$534$	−36.2642	−1.56931
$535$	68.3324	2.95427
$536$	17.1840	0.742234
$537$	−12.0378	−0.519468
$538$	1.72553	0.0743930
$539$	22.2355	0.957753
$540$	−11.5195	−0.495720
$541$	27.0344	1.16230	0.581150	−	0.813796i	$-0.302603\pi$
$541$	27.0344	1.16230	0.581150	+	0.813796i	$0.302603\pi$
$542$	26.6917	1.14651
$543$	2.41926	0.103821
$544$	11.8018	0.505996
$545$	51.8339	2.22032
$546$	7.42315	0.317682
$547$	−37.2739	−1.59372	−0.796858	−	0.604166i	$-0.793506\pi$
$547$	−37.2739	−1.59372	−0.796858	+	0.604166i	$0.793506\pi$
$548$	−23.4828	−1.00313
$549$	6.00554	0.256310
$550$	90.1022	3.84197
$551$	0	0
$552$	2.80125	0.119229
$553$	−1.05002	−0.0446513
$554$	−34.6704	−1.47300
$555$	−21.6282	−0.918067
$556$	−8.79356	−0.372930
$557$	31.7679	1.34605	0.673026	−	0.739619i	$-0.264994\pi$
$557$	31.7679	1.34605	0.673026	+	0.739619i	$0.264994\pi$
$558$	3.53156	0.149503
$559$	−4.10398	−0.173580
$560$	24.8276	1.04916
$561$	−5.71008	−0.241080
$562$	44.0905	1.85985
$563$	−13.4735	−0.567842	−0.283921	−	0.958848i	$-0.591635\pi$
$563$	−13.4735	−0.567842	−0.283921	+	0.958848i	$0.591635\pi$
$564$	−9.42952	−0.397054
$565$	−34.5169	−1.45214
$566$	−4.29558	−0.180557
$567$	3.64733	0.153173
$568$	15.3088	0.642342
$569$	5.53839	0.232181	0.116091	−	0.993239i	$-0.462964\pi$
$569$	5.53839	0.232181	0.116091	+	0.993239i	$0.462964\pi$
$570$	−35.7034	−1.49545
$571$	41.3036	1.72850	0.864250	−	0.503062i	$-0.167793\pi$
$571$	41.3036	1.72850	0.864250	+	0.503062i	$0.167793\pi$
$572$	9.23386	0.386087
$573$	−5.83662	−0.243828
$574$	53.8057	2.24581
$575$	17.9735	0.749546
$576$	−12.6773	−0.528219
$577$	39.7871	1.65636	0.828180	−	0.560463i	$-0.189377\pi$
$577$	39.7871	1.65636	0.828180	+	0.560463i	$0.189377\pi$
$578$	−31.5872	−1.31385
$579$	−19.9903	−0.830770
$580$	0	0
$581$	−23.6257	−0.980161
$582$	−22.0805	−0.915267
$583$	7.19039	0.297795
$584$	−13.7140	−0.567489
$585$	−3.77814	−0.156207
$586$	5.30300	0.219065
$587$	38.7105	1.59775	0.798877	−	0.601495i	$-0.205428\pi$
$587$	38.7105	1.59775	0.798877	+	0.601495i	$0.205428\pi$
$588$	17.8061	0.734310
$589$	6.40861	0.264062
$590$	−65.3010	−2.68840
$591$	−11.7126	−0.481791
$592$	−8.85427	−0.363908
$593$	−1.40712	−0.0577833	−0.0288916	−	0.999583i	$-0.509198\pi$
$593$	−1.40712	−0.0577833	−0.0288916	+	0.999583i	$0.509198\pi$
$594$	7.74905	0.317947
$595$	24.0731	0.986901
$596$	42.8154	1.75379
$597$	−16.6484	−0.681373
$598$	3.14599	0.128649
$599$	−30.7455	−1.25623	−0.628113	−	0.778122i	$-0.716173\pi$
$599$	−30.7455	−1.25623	−0.628113	+	0.778122i	$0.716173\pi$
$600$	21.0715	0.860239
$601$	13.2534	0.540616	0.270308	−	0.962774i	$-0.412875\pi$
$601$	13.2534	0.540616	0.270308	+	0.962774i	$0.412875\pi$
$602$	−35.4867	−1.44633
$603$	9.48235	0.386151
$604$	1.91787	0.0780371
$605$	−5.89271	−0.239573
$606$	−18.0982	−0.735189
$607$	−9.85282	−0.399914	−0.199957	−	0.979805i	$-0.564080\pi$
$607$	−9.85282	−0.399914	−0.199957	+	0.979805i	$0.564080\pi$
$608$	−29.0636	−1.17869
$609$	0	0
$610$	−53.7916	−2.17796
$611$	−3.09267	−0.125116
$612$	−4.57260	−0.184836
$613$	−23.0646	−0.931571	−0.465785	−	0.884898i	$-0.654228\pi$
$613$	−23.0646	−0.931571	−0.465785	+	0.884898i	$0.654228\pi$
$614$	2.44628	0.0987238
$615$	−27.3853	−1.10428
$616$	23.3175	0.939488
$617$	2.14430	0.0863262	0.0431631	−	0.999068i	$-0.486256\pi$
$617$	2.14430	0.0863262	0.0431631	+	0.999068i	$0.486256\pi$
$618$	16.7535	0.673924
$619$	−29.7463	−1.19560	−0.597802	−	0.801644i	$-0.703959\pi$
$619$	−29.7463	−1.19560	−0.597802	+	0.801644i	$0.703959\pi$
$620$	−18.5204	−0.743799
$621$	1.54577	0.0620296
$622$	−9.73065	−0.390163
$623$	−60.2150	−2.41246
$624$	−1.54671	−0.0619181
$625$	52.0617	2.08247
$626$	−66.1178	−2.64260
$627$	14.0620	0.561580
$628$	17.6163	0.702966
$629$	−8.58519	−0.342314
$630$	−32.6692	−1.30157
$631$	−4.52395	−0.180096	−0.0900478	−	0.995937i	$-0.528702\pi$
$631$	−4.52395	−0.180096	−0.0900478	+	0.995937i	$0.528702\pi$
$632$	−0.521710	−0.0207525
$633$	24.2435	0.963593
$634$	13.6423	0.541807
$635$	−72.6039	−2.88120
$636$	5.75801	0.228320
$637$	5.84000	0.231389
$638$	0	0
$639$	8.44759	0.334182
$640$	54.0872	2.13798
$641$	30.7540	1.21471	0.607354	−	0.794431i	$-0.292231\pi$
$641$	30.7540	1.21471	0.607354	+	0.794431i	$0.292231\pi$
$642$	−36.8097	−1.45276
$643$	16.8712	0.665337	0.332668	−	0.943044i	$-0.392051\pi$
$643$	16.8712	0.665337	0.332668	+	0.943044i	$0.392051\pi$
$644$	15.9272	0.627620
$645$	18.0615	0.711172
$646$	−14.1722	−0.557599
$647$	14.1310	0.555548	0.277774	−	0.960646i	$-0.410403\pi$
$647$	14.1310	0.555548	0.277774	+	0.960646i	$0.410403\pi$
$648$	1.81221	0.0711901
$649$	25.7191	1.00956
$650$	23.6647	0.928205
$651$	5.86399	0.229828
$652$	43.2688	1.69454
$653$	38.7238	1.51538	0.757689	−	0.652615i	$-0.226328\pi$
$653$	38.7238	1.51538	0.757689	+	0.652615i	$0.226328\pi$
$654$	−27.9222	−1.09184
$655$	46.1997	1.80517
$656$	−11.2111	−0.437722
$657$	−7.56757	−0.295239
$658$	−26.7420	−1.04251
$659$	−17.3822	−0.677116	−0.338558	−	0.940945i	$-0.609939\pi$
$659$	−17.3822	−0.677116	−0.338558	+	0.940945i	$0.609939\pi$
$660$	−40.6381	−1.58183
$661$	0.959081	0.0373039	0.0186520	−	0.999826i	$-0.494063\pi$
$661$	0.959081	0.0373039	0.0186520	+	0.999826i	$0.494063\pi$
$662$	−21.9786	−0.854222
$663$	−1.49971	−0.0582439
$664$	−11.7386	−0.455547
$665$	−59.2837	−2.29892
$666$	11.6508	0.451460
$667$	0	0
$668$	−44.5958	−1.72546
$669$	28.3179	1.09483
$670$	−84.9334	−3.28127
$671$	21.1861	0.817881
$672$	−26.5937	−1.02587
$673$	−30.1107	−1.16068	−0.580341	−	0.814374i	$-0.697081\pi$
$673$	−30.1107	−1.16068	−0.580341	+	0.814374i	$0.697081\pi$
$674$	59.9570	2.30946
$675$	11.6275	0.447544
$676$	−34.2999	−1.31923
$677$	−41.7661	−1.60520	−0.802602	−	0.596515i	$-0.796552\pi$
$677$	−41.7661	−1.60520	−0.802602	+	0.596515i	$0.796552\pi$
$678$	18.5937	0.714088
$679$	−36.6636	−1.40702
$680$	11.9609	0.458680
$681$	9.86418	0.377996
$682$	12.4585	0.477061
$683$	40.2674	1.54079	0.770396	−	0.637566i	$-0.220059\pi$
$683$	40.2674	1.54079	0.770396	+	0.637566i	$0.220059\pi$
$684$	11.2607	0.430564
$685$	33.8956	1.29508
$686$	−5.58402	−0.213199
$687$	−15.6570	−0.597352
$688$	7.39413	0.281899
$689$	1.88850	0.0719461
$690$	−13.8455	−0.527088
$691$	41.3791	1.57414	0.787069	−	0.616866i	$-0.211598\pi$
$691$	41.3791	1.57414	0.787069	+	0.616866i	$0.211598\pi$
$692$	−9.73221	−0.369963
$693$	12.8669	0.488774
$694$	2.62477	0.0996351
$695$	12.6928	0.481467
$696$	0	0
$697$	−10.8704	−0.411747
$698$	15.9279	0.602881
$699$	−19.7879	−0.748449
$700$	119.807	4.52828
$701$	2.28878	0.0864459	0.0432230	−	0.999065i	$-0.486237\pi$
$701$	2.28878	0.0864459	0.0432230	+	0.999065i	$0.486237\pi$
$702$	2.03523	0.0768148
$703$	21.1423	0.797399
$704$	−44.7224	−1.68554
$705$	13.6108	0.512612
$706$	−11.5618	−0.435135
$707$	−30.0512	−1.13019
$708$	20.5957	0.774034
$709$	−27.3080	−1.02557	−0.512786	−	0.858516i	$-0.671387\pi$
$709$	−27.3080	−1.02557	−0.512786	+	0.858516i	$0.671387\pi$
$710$	−75.6651	−2.83966
$711$	−0.287887	−0.0107966
$712$	−29.9183	−1.12124
$713$	2.48521	0.0930717
$714$	−12.9678	−0.485309
$715$	−13.3284	−0.498453
$716$	−34.0068	−1.27089
$717$	−9.33298	−0.348547
$718$	32.1330	1.19919
$719$	−19.0751	−0.711383	−0.355691	−	0.934604i	$-0.615755\pi$
$719$	−19.0751	−0.711383	−0.355691	+	0.934604i	$0.615755\pi$
$720$	6.80706	0.253684
$721$	27.8183	1.03601
$722$	−6.83391	−0.254332
$723$	−24.5737	−0.913904
$724$	6.83444	0.254000
$725$	0	0
$726$	3.17432	0.117810
$727$	29.2574	1.08510	0.542548	−	0.840024i	$-0.317459\pi$
$727$	29.2574	1.08510	0.542548	+	0.840024i	$0.317459\pi$
$728$	6.12416	0.226976
$729$	1.00000	0.0370370
$730$	67.7828	2.50875
$731$	7.16942	0.265171
$732$	16.9657	0.627070
$733$	−20.9488	−0.773760	−0.386880	−	0.922130i	$-0.626447\pi$
$733$	−20.9488	−0.773760	−0.386880	+	0.922130i	$0.626447\pi$
$734$	−12.1981	−0.450239
$735$	−25.7017	−0.948022
$736$	−11.2706	−0.415441
$737$	33.4515	1.23220
$738$	14.7521	0.543031
$739$	33.7623	1.24197	0.620983	−	0.783824i	$-0.286734\pi$
$739$	33.7623	1.24197	0.620983	+	0.783824i	$0.286734\pi$
$740$	−61.0999	−2.24608
$741$	3.69327	0.135675
$742$	16.3297	0.599480
$743$	44.2943	1.62500	0.812500	−	0.582962i	$-0.198106\pi$
$743$	44.2943	1.62500	0.812500	+	0.582962i	$0.198106\pi$
$744$	2.91357	0.106817
$745$	−61.8007	−2.26420
$746$	65.3396	2.39225
$747$	−6.47754	−0.237001
$748$	−16.1310	−0.589809
$749$	−61.1207	−2.23330
$750$	−59.3627	−2.16762
$751$	7.65239	0.279240	0.139620	−	0.990205i	$-0.455412\pi$
$751$	7.65239	0.279240	0.139620	+	0.990205i	$0.455412\pi$
$752$	5.57206	0.203192
$753$	−4.66182	−0.169886
$754$	0	0
$755$	−2.76830	−0.100749
$756$	10.3037	0.374743
$757$	−16.2856	−0.591911	−0.295955	−	0.955202i	$-0.595638\pi$
$757$	−16.2856	−0.591911	−0.295955	+	0.955202i	$0.595638\pi$
$758$	4.31040	0.156561
$759$	5.45311	0.197935
$760$	−29.4556	−1.06847
$761$	−28.5492	−1.03491	−0.517453	−	0.855711i	$-0.673120\pi$
$761$	−28.5492	−1.03491	−0.517453	+	0.855711i	$0.673120\pi$
$762$	39.1107	1.41683
$763$	−46.3634	−1.67847
$764$	−16.4885	−0.596533
$765$	6.60020	0.238631
$766$	−25.9560	−0.937830
$767$	6.75493	0.243907
$768$	−3.78146	−0.136452
$769$	−49.8716	−1.79842	−0.899208	−	0.437521i	$-0.855857\pi$
$769$	−49.8716	−1.79842	−0.899208	+	0.437521i	$0.855857\pi$
$770$	−115.249	−4.15329
$771$	−28.3543	−1.02115
$772$	−56.4729	−2.03250
$773$	−4.99992	−0.179835	−0.0899173	−	0.995949i	$-0.528660\pi$
$773$	−4.99992	−0.179835	−0.0899173	+	0.995949i	$0.528660\pi$
$774$	−9.72949	−0.349719
$775$	18.6941	0.671513
$776$	−18.2166	−0.653938
$777$	19.3456	0.694019
$778$	−26.1424	−0.937249
$779$	26.7701	0.959139
$780$	−10.6733	−0.382165
$781$	29.8011	1.06637
$782$	−5.49588	−0.196532
$783$	0	0
$784$	−10.5219	−0.375782
$785$	−25.4278	−0.907556
$786$	−24.8871	−0.887694
$787$	19.1052	0.681027	0.340513	−	0.940240i	$-0.389399\pi$
$787$	19.1052	0.681027	0.340513	+	0.940240i	$0.389399\pi$
$788$	−33.0881	−1.17872
$789$	26.7811	0.953433
$790$	2.57860	0.0917426
$791$	30.8740	1.09775
$792$	6.39303	0.227166
$793$	5.56437	0.197597
$794$	43.2242	1.53397
$795$	−8.31125	−0.294770
$796$	−47.0318	−1.66700
$797$	23.2432	0.823318	0.411659	−	0.911338i	$-0.364950\pi$
$797$	23.2432	0.823318	0.411659	+	0.911338i	$0.364950\pi$
$798$	31.9353	1.13050
$799$	5.40273	0.191135
$800$	−84.7795	−2.99741
$801$	−16.5093	−0.583328
$802$	−45.0881	−1.59212
$803$	−26.6966	−0.942103
$804$	26.7877	0.944730
$805$	−22.9897	−0.810281
$806$	3.27213	0.115256
$807$	0.785551	0.0276527
$808$	−14.9312	−0.525276
$809$	7.53860	0.265043	0.132521	−	0.991180i	$-0.457693\pi$
$809$	7.53860	0.265043	0.132521	+	0.991180i	$0.457693\pi$
$810$	−8.95700	−0.314717
$811$	−48.2745	−1.69515	−0.847573	−	0.530679i	$-0.821937\pi$
$811$	−48.2745	−1.69515	−0.847573	+	0.530679i	$0.821937\pi$
$812$	0	0
$813$	12.1514	0.426170
$814$	41.1013	1.44060
$815$	−62.4552	−2.18771
$816$	2.70202	0.0945897
$817$	−17.6558	−0.617698
$818$	−70.6906	−2.47164
$819$	3.37940	0.118086
$820$	−77.3637	−2.70166
$821$	6.07390	0.211980	0.105990	−	0.994367i	$-0.466199\pi$
$821$	6.07390	0.211980	0.105990	+	0.994367i	$0.466199\pi$
$822$	−18.2591	−0.636858
$823$	−40.0147	−1.39483	−0.697413	−	0.716670i	$-0.745666\pi$
$823$	−40.0147	−1.39483	−0.697413	+	0.716670i	$0.745666\pi$
$824$	13.8218	0.481504
$825$	41.0191	1.42810
$826$	58.4092	2.03231
$827$	28.8632	1.00367	0.501837	−	0.864962i	$-0.332658\pi$
$827$	28.8632	1.00367	0.501837	+	0.864962i	$0.332658\pi$
$828$	4.36681	0.151757
$829$	41.9301	1.45629	0.728147	−	0.685421i	$-0.240382\pi$
$829$	41.9301	1.45629	0.728147	+	0.685421i	$0.240382\pi$
$830$	58.0194	2.01388
$831$	−15.7837	−0.547531
$832$	−11.7460	−0.407219
$833$	−10.2021	−0.353483
$834$	−6.83744	−0.236761
$835$	64.3706	2.22764
$836$	39.7251	1.37392
$837$	1.60775	0.0555719
$838$	3.48588	0.120418
$839$	30.7540	1.06175	0.530873	−	0.847451i	$-0.321864\pi$
$839$	30.7540	1.06175	0.530873	+	0.847451i	$0.321864\pi$
$840$	−26.9523	−0.929943
$841$	0	0
$842$	−12.8790	−0.443839
$843$	20.0723	0.691325
$844$	68.4881	2.35746
$845$	49.5093	1.70317
$846$	−7.33194	−0.252077
$847$	5.27079	0.181107
$848$	−3.40251	−0.116843
$849$	−1.95557	−0.0671148
$850$	−41.3408	−1.41798
$851$	8.19883	0.281052
$852$	23.8645	0.817585
$853$	14.3499	0.491330	0.245665	−	0.969355i	$-0.420994\pi$
$853$	14.3499	0.491330	0.245665	+	0.969355i	$0.420994\pi$
$854$	48.1145	1.64644
$855$	−16.2540	−0.555875
$856$	−30.3683	−1.03797
$857$	12.0892	0.412959	0.206479	−	0.978451i	$-0.433799\pi$
$857$	12.0892	0.412959	0.206479	+	0.978451i	$0.433799\pi$
$858$	7.17980	0.245114
$859$	−22.5722	−0.770154	−0.385077	−	0.922885i	$-0.625825\pi$
$859$	−22.5722	−0.770154	−0.385077	+	0.922885i	$0.625825\pi$
$860$	51.0240	1.73990
$861$	24.4951	0.834790
$862$	−18.5883	−0.633121
$863$	−20.0243	−0.681637	−0.340818	−	0.940129i	$-0.610704\pi$
$863$	−20.0243	−0.681637	−0.340818	+	0.940129i	$0.610704\pi$
$864$	−7.29128	−0.248054
$865$	14.0477	0.477636
$866$	−27.9373	−0.949348
$867$	−14.3801	−0.488374
$868$	16.5658	0.562280
$869$	−1.01560	−0.0344518
$870$	0	0
$871$	8.78578	0.297695
$872$	−23.0360	−0.780098
$873$	−10.0522	−0.340215
$874$	13.5344	0.457809
$875$	−98.5689	−3.33224
$876$	−21.3785	−0.722311
$877$	−42.0059	−1.41844	−0.709219	−	0.704988i	$-0.750952\pi$
$877$	−42.0059	−1.41844	−0.709219	+	0.704988i	$0.750952\pi$
$878$	−16.4863	−0.556384
$879$	2.41420	0.0814288
$880$	24.0137	0.809502
$881$	−56.1769	−1.89265	−0.946323	−	0.323221i	$-0.895234\pi$
$881$	−56.1769	−1.89265	−0.946323	+	0.323221i	$0.895234\pi$
$882$	13.8451	0.466190
$883$	−54.5727	−1.83652	−0.918259	−	0.395980i	$-0.870405\pi$
$883$	−54.5727	−1.83652	−0.918259	+	0.395980i	$0.870405\pi$
$884$	−4.23669	−0.142495
$885$	−29.7283	−0.999307
$886$	25.6085	0.860334
$887$	−39.2007	−1.31623	−0.658115	−	0.752917i	$-0.728646\pi$
$887$	−39.2007	−1.31623	−0.658115	+	0.752917i	$0.728646\pi$
$888$	9.61201	0.322558
$889$	64.9413	2.17806
$890$	147.874	4.95675
$891$	3.52776	0.118185
$892$	79.9983	2.67854
$893$	−13.3050	−0.445236
$894$	33.2912	1.11342
$895$	49.0862	1.64077
$896$	−48.3789	−1.61622
$897$	1.43222	0.0478203
$898$	42.7262	1.42579
$899$	0	0
$900$	32.8478	1.09493
$901$	−3.29910	−0.109909
$902$	52.0418	1.73280
$903$	−16.1553	−0.537616
$904$	15.3400	0.510200
$905$	−9.86500	−0.327924
$906$	1.49124	0.0495433
$907$	−3.36661	−0.111786	−0.0558932	−	0.998437i	$-0.517801\pi$
$907$	−3.36661	−0.111786	−0.0558932	+	0.998437i	$0.517801\pi$
$908$	27.8664	0.924779
$909$	−8.23922	−0.273278
$910$	−30.2693	−1.00342
$911$	−54.9714	−1.82128	−0.910641	−	0.413198i	$-0.864412\pi$
$911$	−54.9714	−1.82128	−0.910641	+	0.413198i	$0.864412\pi$
$912$	−6.65415	−0.220341
$913$	−22.8512	−0.756265
$914$	37.5892	1.24334
$915$	−24.4887	−0.809571
$916$	−44.2312	−1.46144
$917$	−41.3238	−1.36463
$918$	−3.55543	−0.117347
$919$	26.6983	0.880696	0.440348	−	0.897827i	$-0.354855\pi$
$919$	26.6983	0.880696	0.440348	+	0.897827i	$0.354855\pi$
$920$	−11.4226	−0.376593
$921$	1.11367	0.0366967
$922$	−18.7374	−0.617082
$923$	7.82703	0.257630
$924$	36.3491	1.19580
$925$	61.6729	2.02779
$926$	3.28988	0.108112
$927$	7.62704	0.250505
$928$	0	0
$929$	34.4983	1.13185	0.565926	−	0.824456i	$-0.308519\pi$
$929$	34.4983	1.13185	0.565926	+	0.824456i	$0.308519\pi$
$930$	−14.4006	−0.472214
$931$	25.1243	0.823417
$932$	−55.9011	−1.83110
$933$	−4.42989	−0.145028
$934$	47.0745	1.54032
$935$	23.2839	0.761466
$936$	1.67908	0.0548825
$937$	−36.3860	−1.18868	−0.594340	−	0.804214i	$-0.702587\pi$
$937$	−36.3860	−1.18868	−0.594340	+	0.804214i	$0.702587\pi$
$938$	75.9696	2.48050
$939$	−30.1002	−0.982284
$940$	38.4506	1.25412
$941$	10.4980	0.342226	0.171113	−	0.985251i	$-0.445264\pi$
$941$	10.4980	0.342226	0.171113	+	0.985251i	$0.445264\pi$
$942$	13.6976	0.446291
$943$	10.3812	0.338059
$944$	−12.1703	−0.396111
$945$	−14.8727	−0.483808
$946$	−34.3233	−1.11595
$947$	8.01774	0.260542	0.130271	−	0.991478i	$-0.458415\pi$
$947$	8.01774	0.260542	0.130271	+	0.991478i	$0.458415\pi$
$948$	−0.813283	−0.0264142
$949$	−7.01166	−0.227608
$950$	101.808	3.30309
$951$	6.21069	0.201395
$952$	−10.6986	−0.346742
$953$	−23.8505	−0.772594	−0.386297	−	0.922374i	$-0.626246\pi$
$953$	−23.8505	−0.772594	−0.386297	+	0.922374i	$0.626246\pi$
$954$	4.47715	0.144953
$955$	23.7999	0.770147
$956$	−26.3658	−0.852729
$957$	0	0
$958$	62.7209	2.02642
$959$	−30.3183	−0.979029
$960$	51.6939	1.66841
$961$	−28.4151	−0.916618
$962$	10.7949	0.348043
$963$	−16.7576	−0.540008
$964$	−69.4208	−2.23589
$965$	81.5143	2.62404
$966$	12.3842	0.398456
$967$	1.65641	0.0532667	0.0266333	−	0.999645i	$-0.491521\pi$
$967$	1.65641	0.0532667	0.0266333	+	0.999645i	$0.491521\pi$
$968$	2.61884	0.0841726
$969$	−6.45193	−0.207266
$970$	90.0374	2.89093
$971$	30.7444	0.986635	0.493317	−	0.869849i	$-0.335784\pi$
$971$	30.7444	0.986635	0.493317	+	0.869849i	$0.335784\pi$
$972$	2.82501	0.0906122
$973$	−11.3532	−0.363968
$974$	55.2564	1.77053
$975$	10.7734	0.345024
$976$	−10.0253	−0.320902
$977$	−45.2764	−1.44852	−0.724260	−	0.689527i	$-0.757819\pi$
$977$	−45.2764	−1.44852	−0.724260	+	0.689527i	$0.757819\pi$
$978$	33.6437	1.07581
$979$	−58.2410	−1.86139
$980$	−72.6076	−2.31936
$981$	−12.7116	−0.405850
$982$	47.6323	1.52001
$983$	54.0341	1.72342	0.861711	−	0.507400i	$-0.169393\pi$
$983$	54.0341	1.72342	0.861711	+	0.507400i	$0.169393\pi$
$984$	12.1706	0.387984
$985$	47.7602	1.52177
$986$	0	0
$987$	−12.1743	−0.387513
$988$	10.4335	0.331934
$989$	−6.84677	−0.217715
$990$	−31.5982	−1.00426
$991$	2.45456	0.0779718	0.0389859	−	0.999240i	$-0.487587\pi$
$991$	2.45456	0.0779718	0.0389859	+	0.999240i	$0.487587\pi$
$992$	−11.7225	−0.372191
$993$	−10.0058	−0.317524
$994$	67.6795	2.14666
$995$	67.8868	2.15216
$996$	−18.2991	−0.579829
$997$	18.5499	0.587480	0.293740	−	0.955885i	$-0.405100\pi$
$997$	18.5499	0.587480	0.293740	+	0.955885i	$0.405100\pi$
$998$	12.4970	0.395586
$999$	5.30404	0.167812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2523.2.a.q.1.8		9
3.2	odd	2		7569.2.a.bk.1.2		9
29.9	even	14		87.2.g.b.52.1	✓	18
29.13	even	14		87.2.g.b.82.1	yes	18
29.28	even	2		2523.2.a.p.1.2		9
87.38	odd	14		261.2.k.b.226.3		18
87.71	odd	14		261.2.k.b.82.3		18
87.86	odd	2		7569.2.a.bl.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.b.52.1	✓	18	29.9	even	14
87.2.g.b.82.1	yes	18	29.13	even	14
261.2.k.b.82.3		18	87.71	odd	14
261.2.k.b.226.3		18	87.38	odd	14
2523.2.a.p.1.2		9	29.28	even	2
2523.2.a.q.1.8		9	1.1	even	1	trivial
7569.2.a.bk.1.2		9	3.2	odd	2
7569.2.a.bl.1.8		9	87.86	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2523.a (trivial)

\(f(q)\)	\(=\)	\(q+2.19659 q^{2} +1.00000 q^{3} +2.82501 q^{4} -4.07769 q^{5} +2.19659 q^{6} +3.64733 q^{7} +1.81221 q^{8} +1.00000 q^{9} -8.95700 q^{10} +3.52776 q^{11} +2.82501 q^{12} +0.926540 q^{13} +8.01169 q^{14} -4.07769 q^{15} -1.66934 q^{16} -1.61861 q^{17} +2.19659 q^{18} +3.98608 q^{19} -11.5195 q^{20} +3.64733 q^{21} +7.74905 q^{22} +1.54577 q^{23} +1.81221 q^{24} +11.6275 q^{25} +2.03523 q^{26} +1.00000 q^{27} +10.3037 q^{28} -8.95700 q^{30} +1.60775 q^{31} -7.29128 q^{32} +3.52776 q^{33} -3.55543 q^{34} -14.8727 q^{35} +2.82501 q^{36} +5.30404 q^{37} +8.75579 q^{38} +0.926540 q^{39} -7.38960 q^{40} +6.71590 q^{41} +8.01169 q^{42} -4.42936 q^{43} +9.96596 q^{44} -4.07769 q^{45} +3.39542 q^{46} -3.33787 q^{47} -1.66934 q^{48} +6.30302 q^{49} +25.5409 q^{50} -1.61861 q^{51} +2.61748 q^{52} +2.03823 q^{53} +2.19659 q^{54} -14.3851 q^{55} +6.60971 q^{56} +3.98608 q^{57} +7.29049 q^{59} -11.5195 q^{60} +6.00554 q^{61} +3.53156 q^{62} +3.64733 q^{63} -12.6773 q^{64} -3.77814 q^{65} +7.74905 q^{66} +9.48235 q^{67} -4.57260 q^{68} +1.54577 q^{69} -32.6692 q^{70} +8.44759 q^{71} +1.81221 q^{72} -7.56757 q^{73} +11.6508 q^{74} +11.6275 q^{75} +11.2607 q^{76} +12.8669 q^{77} +2.03523 q^{78} -0.287887 q^{79} +6.80706 q^{80} +1.00000 q^{81} +14.7521 q^{82} -6.47754 q^{83} +10.3037 q^{84} +6.60020 q^{85} -9.72949 q^{86} +6.39303 q^{88} -16.5093 q^{89} -8.95700 q^{90} +3.37940 q^{91} +4.36681 q^{92} +1.60775 q^{93} -7.33194 q^{94} -16.2540 q^{95} -7.29128 q^{96} -10.0522 q^{97} +13.8451 q^{98} +3.52776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} + 9 q^{3} + 11 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 9 q^{9} + 4 q^{10} + 3 q^{11} + 11 q^{12} + 5 q^{13} + 15 q^{14} - 5 q^{16} + 16 q^{17} + q^{18} - q^{19} + 8 q^{20} + 5 q^{21} + 24 q^{22}+ \cdots + 3 q^{99}+O(q^{100}) \) 9 * q + q^2 + 9 * q^3 + 11 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 9 * q^9 + 4 * q^10 + 3 * q^11 + 11 * q^12 + 5 * q^13 + 15 * q^14 - 5 * q^16 + 16 * q^17 + q^18 - q^19 + 8 * q^20 + 5 * q^21 + 24 * q^22 - 10 * q^23 + 12 * q^24 + 9 * q^25 + 12 * q^26 + 9 * q^27 - 24 * q^28 + 4 * q^30 - 4 * q^31 + 25 * q^32 + 3 * q^33 + 24 * q^34 - 44 * q^35 + 11 * q^36 + 25 * q^37 - 10 * q^38 + 5 * q^39 + 5 * q^40 + 34 * q^41 + 15 * q^42 + 12 * q^43 - 23 * q^44 + 6 * q^46 + 8 * q^47 - 5 * q^48 + 26 * q^49 + 27 * q^50 + 16 * q^51 - 23 * q^52 - 32 * q^53 + q^54 - 5 * q^55 - 14 * q^56 - q^57 + 10 * q^59 + 8 * q^60 + 51 * q^61 + 8 * q^62 + 5 * q^63 - 8 * q^64 - 11 * q^65 + 24 * q^66 + 7 * q^67 + 11 * q^68 - 10 * q^69 - 14 * q^70 + 7 * q^71 + 12 * q^72 + 17 * q^73 - 62 * q^74 + 9 * q^75 - 6 * q^76 + 64 * q^77 + 12 * q^78 + 13 * q^79 + 54 * q^80 + 9 * q^81 + 37 * q^82 - 31 * q^83 - 24 * q^84 + 42 * q^85 - 70 * q^86 - 29 * q^88 - 32 * q^89 + 4 * q^90 + 45 * q^91 + 9 * q^92 - 4 * q^93 + 38 * q^94 - 20 * q^95 + 25 * q^96 + 16 * q^97 - 12 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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Database

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