LMFDB - Embedded newform 9025.2.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, 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("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.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:	$72.0649878242$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.879385 q^{2} +0.532089 q^{3} -1.22668 q^{4} +0.467911 q^{6} +1.87939 q^{7} -2.83750 q^{8} -2.71688 q^{9} +O(q^{10})$	\(q+0.879385 q^{2} +0.532089 q^{3} -1.22668 q^{4} +0.467911 q^{6} +1.87939 q^{7} -2.83750 q^{8} -2.71688 q^{9} +3.41147 q^{11} -0.652704 q^{12} -5.29086 q^{13} +1.65270 q^{14} -0.0418891 q^{16} -1.65270 q^{17} -2.38919 q^{18} +1.00000 q^{21} +3.00000 q^{22} -1.75877 q^{23} -1.50980 q^{24} -4.65270 q^{26} -3.04189 q^{27} -2.30541 q^{28} +3.46791 q^{29} -1.94356 q^{31} +5.63816 q^{32} +1.81521 q^{33} -1.45336 q^{34} +3.33275 q^{36} -0.837496 q^{37} -2.81521 q^{39} +4.49020 q^{41} +0.879385 q^{42} -4.80066 q^{43} -4.18479 q^{44} -1.54664 q^{46} -0.716881 q^{47} -0.0222887 q^{48} -3.46791 q^{49} -0.879385 q^{51} +6.49020 q^{52} -6.10607 q^{53} -2.67499 q^{54} -5.33275 q^{56} +3.04963 q^{58} +10.7588 q^{59} +4.38919 q^{61} -1.70914 q^{62} -5.10607 q^{63} +5.04189 q^{64} +1.59627 q^{66} +14.2121 q^{67} +2.02734 q^{68} -0.935822 q^{69} +13.7588 q^{71} +7.70914 q^{72} +7.51754 q^{73} -0.736482 q^{74} +6.41147 q^{77} -2.47565 q^{78} +6.96316 q^{79} +6.53209 q^{81} +3.94862 q^{82} -2.51249 q^{83} -1.22668 q^{84} -4.22163 q^{86} +1.84524 q^{87} -9.68004 q^{88} +2.28312 q^{89} -9.94356 q^{91} +2.15745 q^{92} -1.03415 q^{93} -0.630415 q^{94} +3.00000 q^{96} -1.82295 q^{97} -3.04963 q^{98} -9.26857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - 6 q^{8}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 6 * q^6 - 6 * q^8	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - 6 q^{8} - 3 q^{12} + 6 q^{14} + 3 q^{16} - 6 q^{17} - 3 q^{18} + 3 q^{21} + 9 q^{22} + 6 q^{23} - 6 q^{24} - 15 q^{26} - 6 q^{27} - 9 q^{28} + 15 q^{29} + 9 q^{31} + 9 q^{33} + 9 q^{34} - 9 q^{36} - 12 q^{39} + 12 q^{41} - 3 q^{42} - 9 q^{44} - 18 q^{46} + 6 q^{47} + 6 q^{48} - 15 q^{49} + 3 q^{51} + 18 q^{52} - 6 q^{53} - 3 q^{54} + 3 q^{56} - 18 q^{58} + 21 q^{59} + 9 q^{61} - 21 q^{62} - 3 q^{63} + 12 q^{64} - 9 q^{66} + 18 q^{67} - 15 q^{68} - 12 q^{69} + 30 q^{71} + 39 q^{72} + 3 q^{74} + 9 q^{77} + 12 q^{78} + 9 q^{79} + 15 q^{81} - 18 q^{82} + 3 q^{84} - 21 q^{86} - 21 q^{87} - 9 q^{88} + 15 q^{89} - 15 q^{91} + 24 q^{92} - 24 q^{93} - 9 q^{94} + 9 q^{96} + 15 q^{97} + 18 q^{98} - 18 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 6 * q^6 - 6 * q^8 - 3 * q^12 + 6 * q^14 + 3 * q^16 - 6 * q^17 - 3 * q^18 + 3 * q^21 + 9 * q^22 + 6 * q^23 - 6 * q^24 - 15 * q^26 - 6 * q^27 - 9 * q^28 + 15 * q^29 + 9 * q^31 + 9 * q^33 + 9 * q^34 - 9 * q^36 - 12 * q^39 + 12 * q^41 - 3 * q^42 - 9 * q^44 - 18 * q^46 + 6 * q^47 + 6 * q^48 - 15 * q^49 + 3 * q^51 + 18 * q^52 - 6 * q^53 - 3 * q^54 + 3 * q^56 - 18 * q^58 + 21 * q^59 + 9 * q^61 - 21 * q^62 - 3 * q^63 + 12 * q^64 - 9 * q^66 + 18 * q^67 - 15 * q^68 - 12 * q^69 + 30 * q^71 + 39 * q^72 + 3 * q^74 + 9 * q^77 + 12 * q^78 + 9 * q^79 + 15 * q^81 - 18 * q^82 + 3 * q^84 - 21 * q^86 - 21 * q^87 - 9 * q^88 + 15 * q^89 - 15 * q^91 + 24 * q^92 - 24 * q^93 - 9 * q^94 + 9 * q^96 + 15 * q^97 + 18 * q^98 - 18 * 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 $

$2$	0.879385	0.621819	0.310910	−	0.950439i	$-0.399366\pi$
$2$	0.879385	0.621819	0.310910	+	0.950439i	$0.399366\pi$
$3$	0.532089	0.307202	0.153601	−	0.988133i	$-0.450913\pi$
$3$	0.532089	0.307202	0.153601	+	0.988133i	$0.450913\pi$
$4$	−1.22668	−0.613341
$5$	0	0
$5$	0	0
$6$	0.467911	0.191024
$7$	1.87939	0.710341	0.355170	−	0.934802i	$-0.384423\pi$
$7$	1.87939	0.710341	0.355170	+	0.934802i	$0.384423\pi$
$8$	−2.83750	−1.00321
$9$	−2.71688	−0.905627
$10$	0	0
$11$	3.41147	1.02860	0.514299	−	0.857611i	$-0.328052\pi$
$11$	3.41147	1.02860	0.514299	+	0.857611i	$0.328052\pi$
$12$	−0.652704	−0.188419
$13$	−5.29086	−1.46742	−0.733710	−	0.679463i	$-0.762213\pi$
$13$	−5.29086	−1.46742	−0.733710	+	0.679463i	$0.762213\pi$
$14$	1.65270	0.441704
$15$	0	0
$16$	−0.0418891	−0.0104723
$17$	−1.65270	−0.400840	−0.200420	−	0.979710i	$-0.564231\pi$
$17$	−1.65270	−0.400840	−0.200420	+	0.979710i	$0.564231\pi$
$18$	−2.38919	−0.563136
$19$	0	0
$19$	0	0
$20$	0	0
$21$	1.00000	0.218218
$22$	3.00000	0.639602
$23$	−1.75877	−0.366729	−0.183364	−	0.983045i	$-0.558699\pi$
$23$	−1.75877	−0.366729	−0.183364	+	0.983045i	$0.558699\pi$
$24$	−1.50980	−0.308187
$25$	0	0
$26$	−4.65270	−0.912470
$27$	−3.04189	−0.585412
$28$	−2.30541	−0.435681
$29$	3.46791	0.643975	0.321987	−	0.946744i	$-0.395649\pi$
$29$	3.46791	0.643975	0.321987	+	0.946744i	$0.395649\pi$
$30$	0	0
$31$	−1.94356	−0.349074	−0.174537	−	0.984651i	$-0.555843\pi$
$31$	−1.94356	−0.349074	−0.174537	+	0.984651i	$0.555843\pi$
$32$	5.63816	0.996695
$33$	1.81521	0.315987
$34$	−1.45336	−0.249250
$35$	0	0
$36$	3.33275	0.555458
$37$	−0.837496	−0.137684	−0.0688418	−	0.997628i	$-0.521930\pi$
$37$	−0.837496	−0.137684	−0.0688418	+	0.997628i	$0.521930\pi$
$38$	0	0
$39$	−2.81521	−0.450794
$40$	0	0
$41$	4.49020	0.701251	0.350626	−	0.936516i	$-0.385969\pi$
$41$	4.49020	0.701251	0.350626	+	0.936516i	$0.385969\pi$
$42$	0.879385	0.135692
$43$	−4.80066	−0.732094	−0.366047	−	0.930596i	$-0.619289\pi$
$43$	−4.80066	−0.732094	−0.366047	+	0.930596i	$0.619289\pi$
$44$	−4.18479	−0.630881
$45$	0	0
$46$	−1.54664	−0.228039
$47$	−0.716881	−0.104568	−0.0522840	−	0.998632i	$-0.516650\pi$
$47$	−0.716881	−0.104568	−0.0522840	+	0.998632i	$0.516650\pi$
$48$	−0.0222887	−0.00321710
$49$	−3.46791	−0.495416
$50$	0	0
$51$	−0.879385	−0.123139
$52$	6.49020	0.900029
$53$	−6.10607	−0.838733	−0.419366	−	0.907817i	$-0.637748\pi$
$53$	−6.10607	−0.838733	−0.419366	+	0.907817i	$0.637748\pi$
$54$	−2.67499	−0.364020
$55$	0	0
$56$	−5.33275	−0.712618
$57$	0	0
$58$	3.04963	0.400436
$59$	10.7588	1.40067	0.700336	−	0.713813i	$-0.253033\pi$
$59$	10.7588	1.40067	0.700336	+	0.713813i	$0.253033\pi$
$60$	0	0
$61$	4.38919	0.561978	0.280989	−	0.959711i	$-0.409338\pi$
$61$	4.38919	0.561978	0.280989	+	0.959711i	$0.409338\pi$
$62$	−1.70914	−0.217061
$63$	−5.10607	−0.643304
$64$	5.04189	0.630236
$65$	0	0
$66$	1.59627	0.196487
$67$	14.2121	1.73629	0.868144	−	0.496312i	$-0.165313\pi$
$67$	14.2121	1.73629	0.868144	+	0.496312i	$0.165313\pi$
$68$	2.02734	0.245851
$69$	−0.935822	−0.112660
$70$	0	0
$71$	13.7588	1.63287	0.816433	−	0.577440i	$-0.195948\pi$
$71$	13.7588	1.63287	0.816433	+	0.577440i	$0.195948\pi$
$72$	7.70914	0.908531
$73$	7.51754	0.879862	0.439931	−	0.898032i	$-0.355003\pi$
$73$	7.51754	0.879862	0.439931	+	0.898032i	$0.355003\pi$
$74$	−0.736482	−0.0856143
$75$	0	0
$76$	0	0
$77$	6.41147	0.730655
$78$	−2.47565	−0.280312
$79$	6.96316	0.783417	0.391709	−	0.920089i	$-0.371884\pi$
$79$	6.96316	0.783417	0.391709	+	0.920089i	$0.371884\pi$
$80$	0	0
$81$	6.53209	0.725788
$82$	3.94862	0.436052
$83$	−2.51249	−0.275781	−0.137891	−	0.990447i	$-0.544032\pi$
$83$	−2.51249	−0.275781	−0.137891	+	0.990447i	$0.544032\pi$
$84$	−1.22668	−0.133842
$85$	0	0
$86$	−4.22163	−0.455230
$87$	1.84524	0.197830
$88$	−9.68004	−1.03190
$89$	2.28312	0.242010	0.121005	−	0.992652i	$-0.461388\pi$
$89$	2.28312	0.242010	0.121005	+	0.992652i	$0.461388\pi$
$90$	0	0
$91$	−9.94356	−1.04237
$92$	2.15745	0.224930
$93$	−1.03415	−0.107236
$94$	−0.630415	−0.0650223
$95$	0	0
$96$	3.00000	0.306186
$97$	−1.82295	−0.185092	−0.0925462	−	0.995708i	$-0.529501\pi$
$97$	−1.82295	−0.185092	−0.0925462	+	0.995708i	$0.529501\pi$
$98$	−3.04963	−0.308059
$99$	−9.26857	−0.931526
$100$	0	0
$101$	−7.92127	−0.788196	−0.394098	−	0.919068i	$-0.628943\pi$
$101$	−7.92127	−0.788196	−0.394098	+	0.919068i	$0.628943\pi$
$102$	−0.773318	−0.0765699
$103$	−0.0145479	−0.00143345	−0.000716725	−	1.00000i	$-0.500228\pi$
$103$	−0.0145479	−0.00143345	−0.000716725		1.00000i	$0.500228\pi$
$104$	15.0128	1.47213
$105$	0	0
$106$	−5.36959	−0.521540
$107$	−3.55438	−0.343615	−0.171807	−	0.985131i	$-0.554961\pi$
$107$	−3.55438	−0.343615	−0.171807	+	0.985131i	$0.554961\pi$
$108$	3.73143	0.359057
$109$	−7.36959	−0.705878	−0.352939	−	0.935646i	$-0.614818\pi$
$109$	−7.36959	−0.705878	−0.352939	+	0.935646i	$0.614818\pi$
$110$	0	0
$111$	−0.445622	−0.0422966
$112$	−0.0787257	−0.00743888
$113$	7.37733	0.694000	0.347000	−	0.937865i	$-0.387200\pi$
$113$	7.37733	0.694000	0.347000	+	0.937865i	$0.387200\pi$
$114$	0	0
$115$	0	0
$116$	−4.25402	−0.394976
$117$	14.3746	1.32894
$118$	9.46110	0.870965
$119$	−3.10607	−0.284733
$120$	0	0
$121$	0.638156	0.0580142
$122$	3.85978	0.349449
$123$	2.38919	0.215426
$124$	2.38413	0.214101
$125$	0	0
$126$	−4.49020	−0.400019
$127$	−0.101014	−0.00896358	−0.00448179	−	0.999990i	$-0.501427\pi$
$127$	−0.101014	−0.00896358	−0.00448179	+	0.999990i	$0.501427\pi$
$128$	−6.84255	−0.604802
$129$	−2.55438	−0.224900
$130$	0	0
$131$	−3.03684	−0.265330	−0.132665	−	0.991161i	$-0.542353\pi$
$131$	−3.03684	−0.265330	−0.132665	+	0.991161i	$0.542353\pi$
$132$	−2.22668	−0.193808
$133$	0	0
$134$	12.4979	1.07966
$135$	0	0
$136$	4.68954	0.402125
$137$	−19.5398	−1.66940	−0.834700	−	0.550705i	$-0.814359\pi$
$137$	−19.5398	−1.66940	−0.834700	+	0.550705i	$0.814359\pi$
$138$	−0.822948	−0.0700540
$139$	15.3969	1.30595	0.652975	−	0.757379i	$-0.273521\pi$
$139$	15.3969	1.30595	0.652975	+	0.757379i	$0.273521\pi$
$140$	0	0
$141$	−0.381445	−0.0321234
$142$	12.0993	1.01535
$143$	−18.0496	−1.50939
$144$	0.113808	0.00948397
$145$	0	0
$146$	6.61081	0.547115
$147$	−1.84524	−0.152193
$148$	1.02734	0.0844469
$149$	−3.76651	−0.308565	−0.154282	−	0.988027i	$-0.549307\pi$
$149$	−3.76651	−0.308565	−0.154282	+	0.988027i	$0.549307\pi$
$150$	0	0
$151$	14.5963	1.18783	0.593914	−	0.804529i	$-0.297582\pi$
$151$	14.5963	1.18783	0.593914	+	0.804529i	$0.297582\pi$
$152$	0	0
$153$	4.49020	0.363011
$154$	5.63816	0.454336
$155$	0	0
$156$	3.45336	0.276490
$157$	10.3746	0.827986	0.413993	−	0.910280i	$-0.364134\pi$
$157$	10.3746	0.827986	0.413993	+	0.910280i	$0.364134\pi$
$158$	6.12330	0.487144
$159$	−3.24897	−0.257660
$160$	0	0
$161$	−3.30541	−0.260503
$162$	5.74422	0.451309
$163$	2.02229	0.158398	0.0791989	−	0.996859i	$-0.474764\pi$
$163$	2.02229	0.158398	0.0791989	+	0.996859i	$0.474764\pi$
$164$	−5.50805	−0.430106
$165$	0	0
$166$	−2.20945	−0.171486
$167$	−23.2567	−1.79966	−0.899829	−	0.436242i	$-0.856309\pi$
$167$	−23.2567	−1.79966	−0.899829	+	0.436242i	$0.856309\pi$
$168$	−2.83750	−0.218918
$169$	14.9932	1.15332
$170$	0	0
$171$	0	0
$172$	5.88888	0.449023
$173$	0.896622	0.0681689	0.0340844	−	0.999419i	$-0.489148\pi$
$173$	0.896622	0.0681689	0.0340844	+	0.999419i	$0.489148\pi$
$174$	1.62267	0.123015
$175$	0	0
$176$	−0.142903	−0.0107718
$177$	5.72462	0.430289
$178$	2.00774	0.150487
$179$	21.3182	1.59340	0.796699	−	0.604377i	$-0.206578\pi$
$179$	21.3182	1.59340	0.796699	+	0.604377i	$0.206578\pi$
$180$	0	0
$181$	16.0993	1.19665	0.598324	−	0.801254i	$-0.295833\pi$
$181$	16.0993	1.19665	0.598324	+	0.801254i	$0.295833\pi$
$182$	−8.74422	−0.648165
$183$	2.33544	0.172640
$184$	4.99050	0.367905
$185$	0	0
$186$	−0.909415	−0.0666815
$187$	−5.63816	−0.412303
$188$	0.879385	0.0641358
$189$	−5.71688	−0.415842
$190$	0	0
$191$	18.9486	1.37107	0.685537	−	0.728038i	$-0.259568\pi$
$191$	18.9486	1.37107	0.685537	+	0.728038i	$0.259568\pi$
$192$	2.68273	0.193610
$193$	12.9017	0.928683	0.464341	−	0.885656i	$-0.346291\pi$
$193$	12.9017	0.928683	0.464341	+	0.885656i	$0.346291\pi$
$194$	−1.60307	−0.115094
$195$	0	0
$196$	4.25402	0.303859
$197$	23.2003	1.65295	0.826476	−	0.562973i	$-0.190342\pi$
$197$	23.2003	1.65295	0.826476	+	0.562973i	$0.190342\pi$
$198$	−8.15064	−0.579241
$199$	9.22163	0.653704	0.326852	−	0.945076i	$-0.394012\pi$
$199$	9.22163	0.653704	0.326852	+	0.945076i	$0.394012\pi$
$200$	0	0
$201$	7.56212	0.533391
$202$	−6.96585	−0.490116
$203$	6.51754	0.457442
$204$	1.07873	0.0755259
$205$	0	0
$206$	−0.0127932	−0.000891346 0
$207$	4.77837	0.332120
$208$	0.221629	0.0153672
$209$	0	0
$210$	0	0
$211$	−14.6236	−1.00673	−0.503365	−	0.864074i	$-0.667905\pi$
$211$	−14.6236	−1.00673	−0.503365	+	0.864074i	$0.667905\pi$
$212$	7.49020	0.514429
$213$	7.32089	0.501619
$214$	−3.12567	−0.213666
$215$	0	0
$216$	8.63135	0.587289
$217$	−3.65270	−0.247962
$218$	−6.48070	−0.438929
$219$	4.00000	0.270295
$220$	0	0
$221$	8.74422	0.588200
$222$	−0.391874	−0.0263008
$223$	−3.01455	−0.201869	−0.100935	−	0.994893i	$-0.532183\pi$
$223$	−3.01455	−0.201869	−0.100935	+	0.994893i	$0.532183\pi$
$224$	10.5963	0.707993
$225$	0	0
$226$	6.48751	0.431543
$227$	−13.7219	−0.910757	−0.455378	−	0.890298i	$-0.650496\pi$
$227$	−13.7219	−0.910757	−0.455378	+	0.890298i	$0.650496\pi$
$228$	0	0
$229$	9.41416	0.622105	0.311053	−	0.950393i	$-0.399318\pi$
$229$	9.41416	0.622105	0.311053	+	0.950393i	$0.399318\pi$
$230$	0	0
$231$	3.41147	0.224459
$232$	−9.84018	−0.646040
$233$	24.1857	1.58446	0.792230	−	0.610223i	$-0.208920\pi$
$233$	24.1857	1.58446	0.792230	+	0.610223i	$0.208920\pi$
$234$	12.6408	0.826358
$235$	0	0
$236$	−13.1976	−0.859090
$237$	3.70502	0.240667
$238$	−2.73143	−0.177052
$239$	−23.3259	−1.50883	−0.754415	−	0.656398i	$-0.772079\pi$
$239$	−23.3259	−1.50883	−0.754415	+	0.656398i	$0.772079\pi$
$240$	0	0
$241$	−0.297667	−0.0191744	−0.00958719	−	0.999954i	$-0.503052\pi$
$241$	−0.297667	−0.0191744	−0.00958719	+	0.999954i	$0.503052\pi$
$242$	0.561185	0.0360743
$243$	12.6013	0.808375
$244$	−5.38413	−0.344684
$245$	0	0
$246$	2.10101	0.133956
$247$	0	0
$248$	5.51485	0.350193
$249$	−1.33687	−0.0847205
$250$	0	0
$251$	−16.1976	−1.02238	−0.511191	−	0.859467i	$-0.670796\pi$
$251$	−16.1976	−1.02238	−0.511191	+	0.859467i	$0.670796\pi$
$252$	6.26352	0.394565
$253$	−6.00000	−0.377217
$254$	−0.0888306	−0.00557373
$255$	0	0
$256$	−16.1010	−1.00631
$257$	15.3550	0.957821	0.478910	−	0.877864i	$-0.341032\pi$
$257$	15.3550	0.957821	0.478910	+	0.877864i	$0.341032\pi$
$258$	−2.24628	−0.139847
$259$	−1.57398	−0.0978022
$260$	0	0
$261$	−9.42190	−0.583201
$262$	−2.67055	−0.164987
$263$	−9.64321	−0.594626	−0.297313	−	0.954780i	$-0.596090\pi$
$263$	−9.64321	−0.594626	−0.297313	+	0.954780i	$0.596090\pi$
$264$	−5.15064	−0.317000
$265$	0	0
$266$	0	0
$267$	1.21482	0.0743459
$268$	−17.4338	−1.06494
$269$	18.2790	1.11449	0.557245	−	0.830348i	$-0.311858\pi$
$269$	18.2790	1.11449	0.557245	+	0.830348i	$0.311858\pi$
$270$	0	0
$271$	18.9641	1.15199	0.575993	−	0.817454i	$-0.304615\pi$
$271$	18.9641	1.15199	0.575993	+	0.817454i	$0.304615\pi$
$272$	0.0692302	0.00419770
$273$	−5.29086	−0.320217
$274$	−17.1830	−1.03807
$275$	0	0
$276$	1.14796	0.0690988
$277$	−13.7638	−0.826988	−0.413494	−	0.910507i	$-0.635692\pi$
$277$	−13.7638	−0.826988	−0.413494	+	0.910507i	$0.635692\pi$
$278$	13.5398	0.812065
$279$	5.28043	0.316131
$280$	0	0
$281$	−13.1111	−0.782144	−0.391072	−	0.920360i	$-0.627896\pi$
$281$	−13.1111	−0.782144	−0.391072	+	0.920360i	$0.627896\pi$
$282$	−0.335437	−0.0199750
$283$	17.3773	1.03297	0.516487	−	0.856295i	$-0.327239\pi$
$283$	17.3773	1.03297	0.516487	+	0.856295i	$0.327239\pi$
$284$	−16.8776	−1.00150
$285$	0	0
$286$	−15.8726	−0.938565
$287$	8.43882	0.498128
$288$	−15.3182	−0.902634
$289$	−14.2686	−0.839328
$290$	0	0
$291$	−0.969971	−0.0568607
$292$	−9.22163	−0.539655
$293$	15.6040	0.911596	0.455798	−	0.890083i	$-0.349354\pi$
$293$	15.6040	0.911596	0.455798	+	0.890083i	$0.349354\pi$
$294$	−1.62267	−0.0946363
$295$	0	0
$296$	2.37639	0.138125
$297$	−10.3773	−0.602154
$298$	−3.31221	−0.191871
$299$	9.30541	0.538146
$300$	0	0
$301$	−9.02229	−0.520036
$302$	12.8357	0.738614
$303$	−4.21482	−0.242135
$304$	0	0
$305$	0	0
$306$	3.94862	0.225727
$307$	21.5202	1.22822	0.614112	−	0.789219i	$-0.289514\pi$
$307$	21.5202	1.22822	0.614112	+	0.789219i	$0.289514\pi$
$308$	−7.86484	−0.448141
$309$	−0.00774079	−0.000440358 0
$310$	0	0
$311$	14.4953	0.821950	0.410975	−	0.911647i	$-0.365188\pi$
$311$	14.4953	0.821950	0.410975	+	0.911647i	$0.365188\pi$
$312$	7.98814	0.452239
$313$	−19.5185	−1.10325	−0.551625	−	0.834092i	$-0.685992\pi$
$313$	−19.5185	−1.10325	−0.551625	+	0.834092i	$0.685992\pi$
$314$	9.12330	0.514858
$315$	0	0
$316$	−8.54158	−0.480502
$317$	28.3473	1.59214	0.796071	−	0.605203i	$-0.206908\pi$
$317$	28.3473	1.59214	0.796071	+	0.605203i	$0.206908\pi$
$318$	−2.85710	−0.160218
$319$	11.8307	0.662391
$320$	0	0
$321$	−1.89124	−0.105559
$322$	−2.90673	−0.161986
$323$	0	0
$324$	−8.01279	−0.445155
$325$	0	0
$326$	1.77837	0.0984949
$327$	−3.92127	−0.216847
$328$	−12.7409	−0.703500
$329$	−1.34730	−0.0742789
$330$	0	0
$331$	1.71007	0.0939942	0.0469971	−	0.998895i	$-0.485035\pi$
$331$	1.71007	0.0939942	0.0469971	+	0.998895i	$0.485035\pi$
$332$	3.08202	0.169148
$333$	2.27538	0.124690
$334$	−20.4516	−1.11906
$335$	0	0
$336$	−0.0418891	−0.00228524
$337$	25.4388	1.38574	0.692870	−	0.721062i	$-0.256346\pi$
$337$	25.4388	1.38574	0.692870	+	0.721062i	$0.256346\pi$
$338$	13.1848	0.717158
$339$	3.92539	0.213198
$340$	0	0
$341$	−6.63041	−0.359057
$342$	0	0
$343$	−19.6732	−1.06225
$344$	13.6219	0.734441
$345$	0	0
$346$	0.788476	0.0423887
$347$	−7.70233	−0.413483	−0.206741	−	0.978396i	$-0.566286\pi$
$347$	−7.70233	−0.413483	−0.206741	+	0.978396i	$0.566286\pi$
$348$	−2.26352	−0.121337
$349$	22.7570	1.21816	0.609078	−	0.793111i	$-0.291540\pi$
$349$	22.7570	1.21816	0.609078	+	0.793111i	$0.291540\pi$
$350$	0	0
$351$	16.0942	0.859045
$352$	19.2344	1.02520
$353$	11.4456	0.609189	0.304595	−	0.952482i	$-0.401479\pi$
$353$	11.4456	0.609189	0.304595	+	0.952482i	$0.401479\pi$
$354$	5.03415	0.267562
$355$	0	0
$356$	−2.80066	−0.148435
$357$	−1.65270	−0.0874704
$358$	18.7469	0.990805
$359$	10.3841	0.548054	0.274027	−	0.961722i	$-0.411644\pi$
$359$	10.3841	0.548054	0.274027	+	0.961722i	$0.411644\pi$
$360$	0	0
$361$	0	0
$362$	14.1575	0.744099
$363$	0.339556	0.0178220
$364$	12.1976	0.639327
$365$	0	0
$366$	2.05375	0.107351
$367$	32.5330	1.69821	0.849105	−	0.528224i	$-0.177142\pi$
$367$	32.5330	1.69821	0.849105	+	0.528224i	$0.177142\pi$
$368$	0.0736733	0.00384048
$369$	−12.1993	−0.635072
$370$	0	0
$371$	−11.4757	−0.595786
$372$	1.26857	0.0657723
$373$	30.4858	1.57849	0.789246	−	0.614077i	$-0.210471\pi$
$373$	30.4858	1.57849	0.789246	+	0.614077i	$0.210471\pi$
$374$	−4.95811	−0.256378
$375$	0	0
$376$	2.03415	0.104903
$377$	−18.3482	−0.944982
$378$	−5.02734	−0.258579
$379$	−17.8598	−0.917396	−0.458698	−	0.888592i	$-0.651684\pi$
$379$	−17.8598	−0.917396	−0.458698	+	0.888592i	$0.651684\pi$
$380$	0	0
$381$	−0.0537486	−0.00275363
$382$	16.6631	0.852560
$383$	−23.4561	−1.19855	−0.599274	−	0.800544i	$-0.704544\pi$
$383$	−23.4561	−1.19855	−0.599274	+	0.800544i	$0.704544\pi$
$384$	−3.64084	−0.185796
$385$	0	0
$386$	11.3455	0.577473
$387$	13.0428	0.663004
$388$	2.23618	0.113525
$389$	3.90941	0.198215	0.0991076	−	0.995077i	$-0.468401\pi$
$389$	3.90941	0.198215	0.0991076	+	0.995077i	$0.468401\pi$
$390$	0	0
$391$	2.90673	0.146999
$392$	9.84018	0.497004
$393$	−1.61587	−0.0815097
$394$	20.4020	1.02784
$395$	0	0
$396$	11.3696	0.571343
$397$	−8.95904	−0.449642	−0.224821	−	0.974400i	$-0.572180\pi$
$397$	−8.95904	−0.449642	−0.224821	+	0.974400i	$0.572180\pi$
$398$	8.10936	0.406486
$399$	0	0
$400$	0	0
$401$	2.02734	0.101241	0.0506203	−	0.998718i	$-0.483880\pi$
$401$	2.02734	0.101241	0.0506203	+	0.998718i	$0.483880\pi$
$402$	6.65002	0.331673
$403$	10.2831	0.512239
$404$	9.71688	0.483433
$405$	0	0
$406$	5.73143	0.284446
$407$	−2.85710	−0.141621
$408$	2.49525	0.123533
$409$	32.2080	1.59258	0.796292	−	0.604913i	$-0.206792\pi$
$409$	32.2080	1.59258	0.796292	+	0.604913i	$0.206792\pi$
$410$	0	0
$411$	−10.3969	−0.512843
$412$	0.0178457	0.000879193 0
$413$	20.2199	0.994955
$414$	4.20203	0.206518
$415$	0	0
$416$	−29.8307	−1.46257
$417$	8.19253	0.401190
$418$	0	0
$419$	−23.2499	−1.13583	−0.567916	−	0.823086i	$-0.692250\pi$
$419$	−23.2499	−1.13583	−0.567916	+	0.823086i	$0.692250\pi$
$420$	0	0
$421$	−6.45336	−0.314518	−0.157259	−	0.987557i	$-0.550266\pi$
$421$	−6.45336	−0.314518	−0.157259	+	0.987557i	$0.550266\pi$
$422$	−12.8598	−0.626005
$423$	1.94768	0.0946995
$424$	17.3259	0.841422
$425$	0	0
$426$	6.43788	0.311916
$427$	8.24897	0.399196
$428$	4.36009	0.210753
$429$	−9.60401	−0.463686
$430$	0	0
$431$	13.9973	0.674227	0.337113	−	0.941464i	$-0.390549\pi$
$431$	13.9973	0.674227	0.337113	+	0.941464i	$0.390549\pi$
$432$	0.127422	0.00613059
$433$	−28.6928	−1.37889	−0.689445	−	0.724338i	$-0.742145\pi$
$433$	−28.6928	−1.37889	−0.689445	+	0.724338i	$0.742145\pi$
$434$	−3.21213	−0.154187
$435$	0	0
$436$	9.04013	0.432944
$437$	0	0
$438$	3.51754	0.168075
$439$	13.3422	0.636791	0.318395	−	0.947958i	$-0.396856\pi$
$439$	13.3422	0.636791	0.318395	+	0.947958i	$0.396856\pi$
$440$	0	0
$441$	9.42190	0.448662
$442$	7.68954	0.365754
$443$	−33.8830	−1.60983	−0.804915	−	0.593390i	$-0.797789\pi$
$443$	−33.8830	−1.60983	−0.804915	+	0.593390i	$0.797789\pi$
$444$	0.546637	0.0259422
$445$	0	0
$446$	−2.65095	−0.125526
$447$	−2.00412	−0.0947916
$448$	9.47565	0.447682
$449$	−18.8402	−0.889123	−0.444562	−	0.895748i	$-0.646641\pi$
$449$	−18.8402	−0.889123	−0.444562	+	0.895748i	$0.646641\pi$
$450$	0	0
$451$	15.3182	0.721306
$452$	−9.04963	−0.425659
$453$	7.76651	0.364903
$454$	−12.0669	−0.566326
$455$	0	0
$456$	0	0
$457$	−14.2790	−0.667943	−0.333972	−	0.942583i	$-0.608389\pi$
$457$	−14.2790	−0.667943	−0.333972	+	0.942583i	$0.608389\pi$
$458$	8.27868	0.386837
$459$	5.02734	0.234656
$460$	0	0
$461$	−13.9281	−0.648695	−0.324348	−	0.945938i	$-0.605145\pi$
$461$	−13.9281	−0.648695	−0.324348	+	0.945938i	$0.605145\pi$
$462$	3.00000	0.139573
$463$	1.76289	0.0819284	0.0409642	−	0.999161i	$-0.486957\pi$
$463$	1.76289	0.0819284	0.0409642	+	0.999161i	$0.486957\pi$
$464$	−0.145268	−0.00674388
$465$	0	0
$466$	21.2686	0.985248
$467$	−22.0419	−1.01998	−0.509988	−	0.860181i	$-0.670350\pi$
$467$	−22.0419	−1.01998	−0.509988	+	0.860181i	$0.670350\pi$
$468$	−17.6331	−0.815090
$469$	26.7101	1.23336
$470$	0	0
$471$	5.52023	0.254359
$472$	−30.5280	−1.40516
$473$	−16.3773	−0.753030
$474$	3.25814	0.149651
$475$	0	0
$476$	3.81016	0.174638
$477$	16.5895	0.759579
$478$	−20.5125	−0.938219
$479$	−25.4570	−1.16316	−0.581580	−	0.813489i	$-0.697565\pi$
$479$	−25.4570	−1.16316	−0.581580	+	0.813489i	$0.697565\pi$
$480$	0	0
$481$	4.43107	0.202040
$482$	−0.261764	−0.0119230
$483$	−1.75877	−0.0800268
$484$	−0.782814	−0.0355824
$485$	0	0
$486$	11.0814	0.502663
$487$	−22.5107	−1.02006	−0.510029	−	0.860157i	$-0.670365\pi$
$487$	−22.5107	−1.02006	−0.510029	+	0.860157i	$0.670365\pi$
$488$	−12.4543	−0.563780
$489$	1.07604	0.0486601
$490$	0	0
$491$	15.6340	0.705554	0.352777	−	0.935707i	$-0.385237\pi$
$491$	15.6340	0.705554	0.352777	+	0.935707i	$0.385237\pi$
$492$	−2.93077	−0.132129
$493$	−5.73143	−0.258131
$494$	0	0
$495$	0	0
$496$	0.0814140	0.00365560
$497$	25.8580	1.15989
$498$	−1.17562	−0.0526809
$499$	−28.6168	−1.28106	−0.640532	−	0.767932i	$-0.721286\pi$
$499$	−28.6168	−1.28106	−0.640532	+	0.767932i	$0.721286\pi$
$500$	0	0
$501$	−12.3746	−0.552858
$502$	−14.2439	−0.635737
$503$	25.0455	1.11672	0.558362	−	0.829597i	$-0.311430\pi$
$503$	25.0455	1.11672	0.558362	+	0.829597i	$0.311430\pi$
$504$	14.4884	0.645367
$505$	0	0
$506$	−5.27631	−0.234561
$507$	7.97771	0.354303
$508$	0.123913	0.00549773
$509$	−33.5212	−1.48580	−0.742900	−	0.669403i	$-0.766550\pi$
$509$	−33.5212	−1.48580	−0.742900	+	0.669403i	$0.766550\pi$
$510$	0	0
$511$	14.1284	0.625002
$512$	−0.473897	−0.0209435
$513$	0	0
$514$	13.5030	0.595591
$515$	0	0
$516$	3.13341	0.137941
$517$	−2.44562	−0.107558
$518$	−1.38413	−0.0608153
$519$	0.477082	0.0209416
$520$	0	0
$521$	27.4783	1.20385	0.601924	−	0.798553i	$-0.294401\pi$
$521$	27.4783	1.20385	0.601924	+	0.798553i	$0.294401\pi$
$522$	−8.28548	−0.362646
$523$	−10.3574	−0.452898	−0.226449	−	0.974023i	$-0.572712\pi$
$523$	−10.3574	−0.452898	−0.226449	+	0.974023i	$0.572712\pi$
$524$	3.72523	0.162737
$525$	0	0
$526$	−8.48009	−0.369750
$527$	3.21213	0.139923
$528$	−0.0760373	−0.00330910
$529$	−19.9067	−0.865510
$530$	0	0
$531$	−29.2303	−1.26849
$532$	0	0
$533$	−23.7570	−1.02903
$534$	1.06830	0.0462297
$535$	0	0
$536$	−40.3269	−1.74186
$537$	11.3432	0.489494
$538$	16.0743	0.693012
$539$	−11.8307	−0.509584
$540$	0	0
$541$	2.52435	0.108530	0.0542651	−	0.998527i	$-0.482718\pi$
$541$	2.52435	0.108530	0.0542651	+	0.998527i	$0.482718\pi$
$542$	16.6767	0.716328
$543$	8.56624	0.367612
$544$	−9.31820	−0.399515
$545$	0	0
$546$	−4.65270	−0.199117
$547$	7.67499	0.328159	0.164079	−	0.986447i	$-0.447535\pi$
$547$	7.67499	0.328159	0.164079	+	0.986447i	$0.447535\pi$
$548$	23.9691	1.02391
$549$	−11.9249	−0.508942
$550$	0	0
$551$	0	0
$552$	2.65539	0.113021
$553$	13.0865	0.556493
$554$	−12.1037	−0.514237
$555$	0	0
$556$	−18.8871	−0.800993
$557$	−3.25578	−0.137952	−0.0689759	−	0.997618i	$-0.521973\pi$
$557$	−3.25578	−0.137952	−0.0689759	+	0.997618i	$0.521973\pi$
$558$	4.64353	0.196576
$559$	25.3996	1.07429
$560$	0	0
$561$	−3.00000	−0.126660
$562$	−11.5297	−0.486352
$563$	5.25908	0.221644	0.110822	−	0.993840i	$-0.464652\pi$
$563$	5.25908	0.221644	0.110822	+	0.993840i	$0.464652\pi$
$564$	0.467911	0.0197026
$565$	0	0
$566$	15.2814	0.642324
$567$	12.2763	0.515557
$568$	−39.0405	−1.63810
$569$	29.9564	1.25584	0.627918	−	0.778280i	$-0.283907\pi$
$569$	29.9564	1.25584	0.627918	+	0.778280i	$0.283907\pi$
$570$	0	0
$571$	−16.7101	−0.699295	−0.349647	−	0.936881i	$-0.613699\pi$
$571$	−16.7101	−0.699295	−0.349647	+	0.936881i	$0.613699\pi$
$572$	22.1411	0.925768
$573$	10.0823	0.421196
$574$	7.42097	0.309745
$575$	0	0
$576$	−13.6982	−0.570759
$577$	13.6800	0.569508	0.284754	−	0.958601i	$-0.408088\pi$
$577$	13.6800	0.569508	0.284754	+	0.958601i	$0.408088\pi$
$578$	−12.5476	−0.521910
$579$	6.86484	0.285293
$580$	0	0
$581$	−4.72193	−0.195899
$582$	−0.852978	−0.0353571
$583$	−20.8307	−0.862719
$584$	−21.3310	−0.882683
$585$	0	0
$586$	13.7219	0.566848
$587$	24.0368	0.992106	0.496053	−	0.868292i	$-0.334782\pi$
$587$	24.0368	0.992106	0.496053	+	0.868292i	$0.334782\pi$
$588$	2.26352	0.0933459
$589$	0	0
$590$	0	0
$591$	12.3446	0.507789
$592$	0.0350819	0.00144186
$593$	4.24123	0.174166	0.0870832	−	0.996201i	$-0.472245\pi$
$593$	4.24123	0.174166	0.0870832	+	0.996201i	$0.472245\pi$
$594$	−9.12567	−0.374431
$595$	0	0
$596$	4.62031	0.189255
$597$	4.90673	0.200819
$598$	8.18304	0.334629
$599$	26.2739	1.07352	0.536762	−	0.843734i	$-0.319647\pi$
$599$	26.2739	1.07352	0.536762	+	0.843734i	$0.319647\pi$
$600$	0	0
$601$	42.2395	1.72298	0.861492	−	0.507771i	$-0.169530\pi$
$601$	42.2395	1.72298	0.861492	+	0.507771i	$0.169530\pi$
$602$	−7.93407	−0.323368
$603$	−38.6127	−1.57243
$604$	−17.9050	−0.728543
$605$	0	0
$606$	−3.70645	−0.150564
$607$	−22.0969	−0.896885	−0.448443	−	0.893812i	$-0.648021\pi$
$607$	−22.0969	−0.896885	−0.448443	+	0.893812i	$0.648021\pi$
$608$	0	0
$609$	3.46791	0.140527
$610$	0	0
$611$	3.79292	0.153445
$612$	−5.50805	−0.222650
$613$	−7.17705	−0.289878	−0.144939	−	0.989441i	$-0.546299\pi$
$613$	−7.17705	−0.289878	−0.144939	+	0.989441i	$0.546299\pi$
$614$	18.9246	0.763734
$615$	0	0
$616$	−18.1925	−0.732998
$617$	49.3729	1.98768	0.993839	−	0.110836i	$-0.0353528\pi$
$617$	49.3729	1.98768	0.993839	+	0.110836i	$0.0353528\pi$
$618$	−0.00680713	−0.000273823 0
$619$	26.4979	1.06504	0.532521	−	0.846417i	$-0.321245\pi$
$619$	26.4979	1.06504	0.532521	+	0.846417i	$0.321245\pi$
$620$	0	0
$621$	5.34998	0.214687
$622$	12.7469	0.511105
$623$	4.29086	0.171910
$624$	0.117926	0.00472083
$625$	0	0
$626$	−17.1643	−0.686022
$627$	0	0
$628$	−12.7264	−0.507838
$629$	1.38413	0.0551890
$630$	0	0
$631$	33.3209	1.32648	0.663242	−	0.748405i	$-0.269180\pi$
$631$	33.3209	1.32648	0.663242	+	0.748405i	$0.269180\pi$
$632$	−19.7579	−0.785929
$633$	−7.78106	−0.309269
$634$	24.9282	0.990025
$635$	0	0
$636$	3.98545	0.158033
$637$	18.3482	0.726983
$638$	10.4037	0.411888
$639$	−37.3809	−1.47877
$640$	0	0
$641$	0.136096	0.00537548	0.00268774	−	0.999996i	$-0.499144\pi$
$641$	0.136096	0.00537548	0.00268774	+	0.999996i	$0.499144\pi$
$642$	−1.66313	−0.0656386
$643$	−48.1780	−1.89995	−0.949977	−	0.312319i	$-0.898894\pi$
$643$	−48.1780	−1.89995	−0.949977	+	0.312319i	$0.898894\pi$
$644$	4.05468	0.159777
$645$	0	0
$646$	0	0
$647$	36.9718	1.45351	0.726756	−	0.686895i	$-0.241027\pi$
$647$	36.9718	1.45351	0.726756	+	0.686895i	$0.241027\pi$
$648$	−18.5348	−0.728115
$649$	36.7033	1.44073
$650$	0	0
$651$	−1.94356	−0.0761742
$652$	−2.48070	−0.0971519
$653$	−27.0000	−1.05659	−0.528296	−	0.849060i	$-0.677169\pi$
$653$	−27.0000	−1.05659	−0.528296	+	0.849060i	$0.677169\pi$
$654$	−3.44831	−0.134840
$655$	0	0
$656$	−0.188090	−0.00734369
$657$	−20.4243	−0.796827
$658$	−1.18479	−0.0461880
$659$	−18.8749	−0.735263	−0.367632	−	0.929971i	$-0.619831\pi$
$659$	−18.8749	−0.735263	−0.367632	+	0.929971i	$0.619831\pi$
$660$	0	0
$661$	30.6117	1.19066	0.595330	−	0.803482i	$-0.297022\pi$
$661$	30.6117	1.19066	0.595330	+	0.803482i	$0.297022\pi$
$662$	1.50381	0.0584474
$663$	4.65270	0.180696
$664$	7.12918	0.276666
$665$	0	0
$666$	2.00093	0.0775346
$667$	−6.09926	−0.236164
$668$	28.5286	1.10380
$669$	−1.60401	−0.0620145
$670$	0	0
$671$	14.9736	0.578049
$672$	5.63816	0.217497
$673$	11.9094	0.459074	0.229537	−	0.973300i	$-0.426279\pi$
$673$	11.9094	0.459074	0.229537	+	0.973300i	$0.426279\pi$
$674$	22.3705	0.861680
$675$	0	0
$676$	−18.3919	−0.707380
$677$	5.78106	0.222184	0.111092	−	0.993810i	$-0.464565\pi$
$677$	5.78106	0.222184	0.111092	+	0.993810i	$0.464565\pi$
$678$	3.45193	0.132571
$679$	−3.42602	−0.131479
$680$	0	0
$681$	−7.30129	−0.279786
$682$	−5.83069	−0.223269
$683$	21.0496	0.805442	0.402721	−	0.915323i	$-0.368065\pi$
$683$	21.0496	0.805442	0.402721	+	0.915323i	$0.368065\pi$
$684$	0	0
$685$	0	0
$686$	−17.3004	−0.660531
$687$	5.00917	0.191112
$688$	0.201095	0.00766668
$689$	32.3063	1.23077
$690$	0	0
$691$	−32.9377	−1.25301	−0.626504	−	0.779418i	$-0.715515\pi$
$691$	−32.9377	−1.25301	−0.626504	+	0.779418i	$0.715515\pi$
$692$	−1.09987	−0.0418107
$693$	−17.4192	−0.661701
$694$	−6.77332	−0.257112
$695$	0	0
$696$	−5.23585	−0.198464
$697$	−7.42097	−0.281089
$698$	20.0122	0.757472
$699$	12.8690	0.486749
$700$	0	0
$701$	21.3574	0.806658	0.403329	−	0.915055i	$-0.367853\pi$
$701$	21.3574	0.806658	0.403329	+	0.915055i	$0.367853\pi$
$702$	14.1530	0.534171
$703$	0	0
$704$	17.2003	0.648260
$705$	0	0
$706$	10.0651	0.378805
$707$	−14.8871	−0.559888
$708$	−7.02229	−0.263914
$709$	−15.7706	−0.592278	−0.296139	−	0.955145i	$-0.595699\pi$
$709$	−15.7706	−0.592278	−0.296139	+	0.955145i	$0.595699\pi$
$710$	0	0
$711$	−18.9181	−0.709484
$712$	−6.47834	−0.242786
$713$	3.41828	0.128016
$714$	−1.45336	−0.0543908
$715$	0	0
$716$	−26.1506	−0.977295
$717$	−12.4115	−0.463515
$718$	9.13165	0.340790
$719$	−35.3283	−1.31752	−0.658762	−	0.752352i	$-0.728919\pi$
$719$	−35.3283	−1.31752	−0.658762	+	0.752352i	$0.728919\pi$
$720$	0	0
$721$	−0.0273411	−0.00101824
$722$	0	0
$723$	−0.158385	−0.00589040
$724$	−19.7487	−0.733953
$725$	0	0
$726$	0.298600	0.0110821
$727$	−40.4216	−1.49915	−0.749577	−	0.661918i	$-0.769743\pi$
$727$	−40.4216	−1.49915	−0.749577	+	0.661918i	$0.769743\pi$
$728$	28.2148	1.04571
$729$	−12.8912	−0.477454
$730$	0	0
$731$	7.93407	0.293452
$732$	−2.86484	−0.105887
$733$	36.2763	1.33990	0.669948	−	0.742408i	$-0.266316\pi$
$733$	36.2763	1.33990	0.669948	+	0.742408i	$0.266316\pi$
$734$	28.6091	1.05598
$735$	0	0
$736$	−9.91622	−0.365517
$737$	48.4843	1.78594
$738$	−10.7279	−0.394900
$739$	−20.6759	−0.760576	−0.380288	−	0.924868i	$-0.624175\pi$
$739$	−20.6759	−0.760576	−0.380288	+	0.924868i	$0.624175\pi$
$740$	0	0
$741$	0	0
$742$	−10.0915	−0.370471
$743$	6.70409	0.245949	0.122975	−	0.992410i	$-0.460757\pi$
$743$	6.70409	0.245949	0.122975	+	0.992410i	$0.460757\pi$
$744$	2.93439	0.107580
$745$	0	0
$746$	26.8087	0.981537
$747$	6.82613	0.249755
$748$	6.91622	0.252882
$749$	−6.68004	−0.244084
$750$	0	0
$751$	−10.7074	−0.390718	−0.195359	−	0.980732i	$-0.562587\pi$
$751$	−10.7074	−0.390718	−0.195359	+	0.980732i	$0.562587\pi$
$752$	0.0300295	0.00109506
$753$	−8.61856	−0.314078
$754$	−16.1352	−0.587608
$755$	0	0
$756$	7.01279	0.255053
$757$	4.06242	0.147651	0.0738256	−	0.997271i	$-0.476479\pi$
$757$	4.06242	0.147651	0.0738256	+	0.997271i	$0.476479\pi$
$758$	−15.7056	−0.570454
$759$	−3.19253	−0.115882
$760$	0	0
$761$	−11.0077	−0.399030	−0.199515	−	0.979895i	$-0.563937\pi$
$761$	−11.0077	−0.399030	−0.199515	+	0.979895i	$0.563937\pi$
$762$	−0.0472658	−0.00171226
$763$	−13.8503	−0.501414
$764$	−23.2439	−0.840935
$765$	0	0
$766$	−20.6269	−0.745280
$767$	−56.9231	−2.05538
$768$	−8.56717	−0.309141
$769$	21.3473	0.769803	0.384902	−	0.922958i	$-0.374235\pi$
$769$	21.3473	0.769803	0.384902	+	0.922958i	$0.374235\pi$
$770$	0	0
$771$	8.17024	0.294244
$772$	−15.8262	−0.569599
$773$	17.9172	0.644435	0.322218	−	0.946666i	$-0.395572\pi$
$773$	17.9172	0.644435	0.322218	+	0.946666i	$0.395572\pi$
$774$	11.4697	0.412269
$775$	0	0
$776$	5.17261	0.185686
$777$	−0.837496	−0.0300450
$778$	3.43788	0.123254
$779$	0	0
$780$	0	0
$781$	46.9377	1.67956
$782$	2.55613	0.0914071
$783$	−10.5490	−0.376991
$784$	0.145268	0.00518813
$785$	0	0
$786$	−1.42097	−0.0506843
$787$	48.8316	1.74066	0.870330	−	0.492470i	$-0.163906\pi$
$787$	48.8316	1.74066	0.870330	+	0.492470i	$0.163906\pi$
$788$	−28.4593	−1.01382
$789$	−5.13104	−0.182670
$790$	0	0
$791$	13.8648	0.492977
$792$	26.2995	0.934513
$793$	−23.2226	−0.824657
$794$	−7.87845	−0.279596
$795$	0	0
$796$	−11.3120	−0.400943
$797$	−28.5262	−1.01045	−0.505225	−	0.862988i	$-0.668591\pi$
$797$	−28.5262	−1.01045	−0.505225	+	0.862988i	$0.668591\pi$
$798$	0	0
$799$	1.18479	0.0419149
$800$	0	0
$801$	−6.20296	−0.219171
$802$	1.78281	0.0629533
$803$	25.6459	0.905024
$804$	−9.27631	−0.327150
$805$	0	0
$806$	9.04282	0.318520
$807$	9.72605	0.342373
$808$	22.4766	0.790724
$809$	−14.8367	−0.521630	−0.260815	−	0.965389i	$-0.583991\pi$
$809$	−14.8367	−0.521630	−0.260815	+	0.965389i	$0.583991\pi$
$810$	0	0
$811$	8.37733	0.294168	0.147084	−	0.989124i	$-0.453011\pi$
$811$	8.37733	0.294168	0.147084	+	0.989124i	$0.453011\pi$
$812$	−7.99495	−0.280568
$813$	10.0906	0.353892
$814$	−2.51249	−0.0880627
$815$	0	0
$816$	0.0368366	0.00128954
$817$	0	0
$818$	28.3233	0.990299
$819$	27.0155	0.943997
$820$	0	0
$821$	6.27900	0.219139	0.109569	−	0.993979i	$-0.465053\pi$
$821$	6.27900	0.219139	0.109569	+	0.993979i	$0.465053\pi$
$822$	−9.14290	−0.318895
$823$	−11.0264	−0.384356	−0.192178	−	0.981360i	$-0.561555\pi$
$823$	−11.0264	−0.384356	−0.192178	+	0.981360i	$0.561555\pi$
$824$	0.0412797	0.00143805
$825$	0	0
$826$	17.7811	0.618682
$827$	33.9358	1.18006	0.590032	−	0.807380i	$-0.299115\pi$
$827$	33.9358	1.18006	0.590032	+	0.807380i	$0.299115\pi$
$828$	−5.86154	−0.203703
$829$	20.3669	0.707372	0.353686	−	0.935364i	$-0.384928\pi$
$829$	20.3669	0.707372	0.353686	+	0.935364i	$0.384928\pi$
$830$	0	0
$831$	−7.32358	−0.254052
$832$	−26.6759	−0.924821
$833$	5.73143	0.198582
$834$	7.20439	0.249468
$835$	0	0
$836$	0	0
$837$	5.91210	0.204352
$838$	−20.4456	−0.706282
$839$	−15.8093	−0.545799	−0.272899	−	0.962043i	$-0.587983\pi$
$839$	−15.8093	−0.545799	−0.272899	+	0.962043i	$0.587983\pi$
$840$	0	0
$841$	−16.9736	−0.585296
$842$	−5.67499	−0.195573
$843$	−6.97628	−0.240276
$844$	17.9385	0.617469
$845$	0	0
$846$	1.71276	0.0588860
$847$	1.19934	0.0412098
$848$	0.255777	0.00878343
$849$	9.24628	0.317332
$850$	0	0
$851$	1.47296	0.0504925
$852$	−8.98040	−0.307663
$853$	52.6492	1.80267	0.901337	−	0.433118i	$-0.142587\pi$
$853$	52.6492	1.80267	0.901337	+	0.433118i	$0.142587\pi$
$854$	7.25402	0.248228
$855$	0	0
$856$	10.0855	0.344716
$857$	−23.0273	−0.786599	−0.393299	−	0.919410i	$-0.628666\pi$
$857$	−23.0273	−0.786599	−0.393299	+	0.919410i	$0.628666\pi$
$858$	−8.44562	−0.288329
$859$	8.90941	0.303985	0.151993	−	0.988382i	$-0.451431\pi$
$859$	8.90941	0.303985	0.151993	+	0.988382i	$0.451431\pi$
$860$	0	0
$861$	4.49020	0.153026
$862$	12.3090	0.419247
$863$	29.7698	1.01338	0.506688	−	0.862129i	$-0.330870\pi$
$863$	29.7698	1.01338	0.506688	+	0.862129i	$0.330870\pi$
$864$	−17.1506	−0.583477
$865$	0	0
$866$	−25.2321	−0.857420
$867$	−7.59215	−0.257843
$868$	4.48070	0.152085
$869$	23.7547	0.805821
$870$	0	0
$871$	−75.1944	−2.54787
$872$	20.9112	0.708142
$873$	4.95273	0.167625
$874$	0	0
$875$	0	0
$876$	−4.90673	−0.165783
$877$	−25.0300	−0.845204	−0.422602	−	0.906315i	$-0.638883\pi$
$877$	−25.0300	−0.845204	−0.422602	+	0.906315i	$0.638883\pi$
$878$	11.7330	0.395969
$879$	8.30272	0.280044
$880$	0	0
$881$	20.3960	0.687158	0.343579	−	0.939124i	$-0.388361\pi$
$881$	20.3960	0.687158	0.343579	+	0.939124i	$0.388361\pi$
$882$	8.28548	0.278987
$883$	10.6281	0.357662	0.178831	−	0.983880i	$-0.442768\pi$
$883$	10.6281	0.357662	0.178831	+	0.983880i	$0.442768\pi$
$884$	−10.7264	−0.360767
$885$	0	0
$886$	−29.7962	−1.00102
$887$	−56.3387	−1.89167	−0.945835	−	0.324648i	$-0.894754\pi$
$887$	−56.3387	−1.89167	−0.945835	+	0.324648i	$0.894754\pi$
$888$	1.26445	0.0424322
$889$	−0.189845	−0.00636720
$890$	0	0
$891$	22.2841	0.746544
$892$	3.69789	0.123815
$893$	0	0
$894$	−1.76239	−0.0589432
$895$	0	0
$896$	−12.8598	−0.429615
$897$	4.95130	0.165319
$898$	−16.5678	−0.552874
$899$	−6.74010	−0.224795
$900$	0	0
$901$	10.0915	0.336197
$902$	13.4706	0.448522
$903$	−4.80066	−0.159756
$904$	−20.9331	−0.696226
$905$	0	0
$906$	6.82976	0.226903
$907$	−5.92364	−0.196691	−0.0983456	−	0.995152i	$-0.531355\pi$
$907$	−5.92364	−0.196691	−0.0983456	+	0.995152i	$0.531355\pi$
$908$	16.8324	0.558604
$909$	21.5212	0.713812
$910$	0	0
$911$	34.0591	1.12843	0.564215	−	0.825628i	$-0.309179\pi$
$911$	34.0591	1.12843	0.564215	+	0.825628i	$0.309179\pi$
$912$	0	0
$913$	−8.57129	−0.283668
$914$	−12.5567	−0.415340
$915$	0	0
$916$	−11.5482	−0.381563
$917$	−5.70739	−0.188474
$918$	4.42097	0.145914
$919$	−6.27395	−0.206958	−0.103479	−	0.994632i	$-0.532998\pi$
$919$	−6.27395	−0.206958	−0.103479	+	0.994632i	$0.532998\pi$
$920$	0	0
$921$	11.4507	0.377313
$922$	−12.2481	−0.403371
$923$	−72.7957	−2.39610
$924$	−4.18479	−0.137670
$925$	0	0
$926$	1.55026	0.0509447
$927$	0.0395250	0.00129817
$928$	19.5526	0.641846
$929$	28.3233	0.929256	0.464628	−	0.885506i	$-0.346188\pi$
$929$	28.3233	0.929256	0.464628	+	0.885506i	$0.346188\pi$
$930$	0	0
$931$	0	0
$932$	−29.6682	−0.971814
$933$	7.71276	0.252505
$934$	−19.3833	−0.634241
$935$	0	0
$936$	−40.7880	−1.33320
$937$	20.0719	0.655721	0.327860	−	0.944726i	$-0.393672\pi$
$937$	20.0719	0.655721	0.327860	+	0.944726i	$0.393672\pi$
$938$	23.4884	0.766925
$939$	−10.3856	−0.338920
$940$	0	0
$941$	−5.39517	−0.175878	−0.0879388	−	0.996126i	$-0.528028\pi$
$941$	−5.39517	−0.175878	−0.0879388	+	0.996126i	$0.528028\pi$
$942$	4.85441	0.158165
$943$	−7.89723	−0.257169
$944$	−0.450675	−0.0146682
$945$	0	0
$946$	−14.4020	−0.468249
$947$	−6.64321	−0.215875	−0.107938	−	0.994158i	$-0.534425\pi$
$947$	−6.64321	−0.215875	−0.107938	+	0.994158i	$0.534425\pi$
$948$	−4.54488	−0.147611
$949$	−39.7743	−1.29113
$950$	0	0
$951$	15.0833	0.489109
$952$	8.81345	0.285646
$953$	−14.8239	−0.480193	−0.240096	−	0.970749i	$-0.577179\pi$
$953$	−14.8239	−0.480193	−0.240096	+	0.970749i	$0.577179\pi$
$954$	14.5885	0.472321
$955$	0	0
$956$	28.6135	0.925427
$957$	6.29498	0.203488
$958$	−22.3865	−0.723275
$959$	−36.7229	−1.18584
$960$	0	0
$961$	−27.2226	−0.878147
$962$	3.89662	0.125632
$963$	9.65682	0.311187
$964$	0.365142	0.0117604
$965$	0	0
$966$	−1.54664	−0.0497622
$967$	−21.2216	−0.682442	−0.341221	−	0.939983i	$-0.610840\pi$
$967$	−21.2216	−0.682442	−0.341221	+	0.939983i	$0.610840\pi$
$968$	−1.81076	−0.0582002
$969$	0	0
$970$	0	0
$971$	37.6067	1.20686	0.603428	−	0.797417i	$-0.293801\pi$
$971$	37.6067	1.20686	0.603428	+	0.797417i	$0.293801\pi$
$972$	−15.4578	−0.495809
$973$	28.9368	0.927670
$974$	−19.7956	−0.634292
$975$	0	0
$976$	−0.183859	−0.00588518
$977$	−46.0215	−1.47236	−0.736179	−	0.676787i	$-0.763372\pi$
$977$	−46.0215	−1.47236	−0.736179	+	0.676787i	$0.763372\pi$
$978$	0.946251	0.0302578
$979$	7.78880	0.248931
$980$	0	0
$981$	20.0223	0.639262
$982$	13.7483	0.438727
$983$	60.5964	1.93272	0.966362	−	0.257185i	$-0.0827950\pi$
$983$	60.5964	1.93272	0.966362	+	0.257185i	$0.0827950\pi$
$984$	−6.77930	−0.216116
$985$	0	0
$986$	−5.04013	−0.160511
$987$	−0.716881	−0.0228186
$988$	0	0
$989$	8.44326	0.268480
$990$	0	0
$991$	−41.8982	−1.33094	−0.665470	−	0.746425i	$-0.731769\pi$
$991$	−41.8982	−1.33094	−0.665470	+	0.746425i	$0.731769\pi$
$992$	−10.9581	−0.347920
$993$	0.909912	0.0288752
$994$	22.7392	0.721243
$995$	0	0
$996$	1.63991	0.0519626
$997$	−33.7151	−1.06777	−0.533884	−	0.845557i	$-0.679268\pi$
$997$	−33.7151	−1.06777	−0.533884	+	0.845557i	$0.679268\pi$
$998$	−25.1652	−0.796590
$999$	2.54757	0.0806016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.x.1.3		3
5.4	even	2		361.2.a.h.1.1		3
15.14	odd	2		3249.2.a.s.1.3		3
19.2	odd	18		475.2.l.a.251.1		6
19.10	odd	18		475.2.l.a.176.1		6
19.18	odd	2		9025.2.a.bd.1.1		3
20.19	odd	2		5776.2.a.bi.1.3		3
95.2	even	36		475.2.u.a.99.1		12
95.4	even	18		361.2.e.b.54.1		6
95.9	even	18		361.2.e.h.62.1		6
95.14	odd	18		361.2.e.f.234.1		6
95.24	even	18		361.2.e.b.234.1		6
95.29	odd	18		19.2.e.a.5.1	yes	6
95.34	odd	18		361.2.e.f.54.1		6
95.44	even	18		361.2.e.a.245.1		6
95.48	even	36		475.2.u.a.24.1		12
95.49	even	6		361.2.c.h.292.3		6
95.54	even	18		361.2.e.a.28.1		6
95.59	odd	18		19.2.e.a.4.1	✓	6
95.64	even	6		361.2.c.h.68.3		6
95.67	even	36		475.2.u.a.24.2		12
95.69	odd	6		361.2.c.i.68.1		6
95.74	even	18		361.2.e.h.99.1		6
95.78	even	36		475.2.u.a.99.2		12
95.79	odd	18		361.2.e.g.28.1		6
95.84	odd	6		361.2.c.i.292.1		6
95.89	odd	18		361.2.e.g.245.1		6
95.94	odd	2		361.2.a.g.1.3		3
285.29	even	18		171.2.u.c.100.1		6
285.59	even	18		171.2.u.c.118.1		6
285.284	even	2		3249.2.a.z.1.1		3
380.59	even	18		304.2.u.b.289.1		6
380.219	even	18		304.2.u.b.81.1		6
380.379	even	2		5776.2.a.br.1.1		3
665.59	even	18		931.2.v.a.422.1		6
665.124	even	18		931.2.v.a.214.1		6
665.219	odd	18		931.2.v.b.214.1		6
665.249	odd	18		931.2.v.b.422.1		6
665.314	even	18		931.2.w.a.442.1		6
665.409	even	18		931.2.x.b.765.1		6
665.439	even	18		931.2.x.b.802.1		6
665.534	odd	18		931.2.x.a.802.1		6
665.599	odd	18		931.2.x.a.765.1		6
665.629	even	18		931.2.w.a.99.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	95.59	odd	18
19.2.e.a.5.1	yes	6	95.29	odd	18
171.2.u.c.100.1		6	285.29	even	18
171.2.u.c.118.1		6	285.59	even	18
304.2.u.b.81.1		6	380.219	even	18
304.2.u.b.289.1		6	380.59	even	18
361.2.a.g.1.3		3	95.94	odd	2
361.2.a.h.1.1		3	5.4	even	2
361.2.c.h.68.3		6	95.64	even	6
361.2.c.h.292.3		6	95.49	even	6
361.2.c.i.68.1		6	95.69	odd	6
361.2.c.i.292.1		6	95.84	odd	6
361.2.e.a.28.1		6	95.54	even	18
361.2.e.a.245.1		6	95.44	even	18
361.2.e.b.54.1		6	95.4	even	18
361.2.e.b.234.1		6	95.24	even	18
361.2.e.f.54.1		6	95.34	odd	18
361.2.e.f.234.1		6	95.14	odd	18
361.2.e.g.28.1		6	95.79	odd	18
361.2.e.g.245.1		6	95.89	odd	18
361.2.e.h.62.1		6	95.9	even	18
361.2.e.h.99.1		6	95.74	even	18
475.2.l.a.176.1		6	19.10	odd	18
475.2.l.a.251.1		6	19.2	odd	18
475.2.u.a.24.1		12	95.48	even	36
475.2.u.a.24.2		12	95.67	even	36
475.2.u.a.99.1		12	95.2	even	36
475.2.u.a.99.2		12	95.78	even	36
931.2.v.a.214.1		6	665.124	even	18
931.2.v.a.422.1		6	665.59	even	18
931.2.v.b.214.1		6	665.219	odd	18
931.2.v.b.422.1		6	665.249	odd	18
931.2.w.a.99.1		6	665.629	even	18
931.2.w.a.442.1		6	665.314	even	18
931.2.x.a.765.1		6	665.599	odd	18
931.2.x.a.802.1		6	665.534	odd	18
931.2.x.b.765.1		6	665.409	even	18
931.2.x.b.802.1		6	665.439	even	18
3249.2.a.s.1.3		3	15.14	odd	2
3249.2.a.z.1.1		3	285.284	even	2
5776.2.a.bi.1.3		3	20.19	odd	2
5776.2.a.br.1.1		3	380.379	even	2
9025.2.a.x.1.3		3	1.1	even	1	trivial
9025.2.a.bd.1.1		3	19.18	odd	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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.879385 q^{2} +0.532089 q^{3} -1.22668 q^{4} +0.467911 q^{6} +1.87939 q^{7} -2.83750 q^{8} -2.71688 q^{9} +O(q^{10})\)	\(q+0.879385 q^{2} +0.532089 q^{3} -1.22668 q^{4} +0.467911 q^{6} +1.87939 q^{7} -2.83750 q^{8} -2.71688 q^{9} +3.41147 q^{11} -0.652704 q^{12} -5.29086 q^{13} +1.65270 q^{14} -0.0418891 q^{16} -1.65270 q^{17} -2.38919 q^{18} +1.00000 q^{21} +3.00000 q^{22} -1.75877 q^{23} -1.50980 q^{24} -4.65270 q^{26} -3.04189 q^{27} -2.30541 q^{28} +3.46791 q^{29} -1.94356 q^{31} +5.63816 q^{32} +1.81521 q^{33} -1.45336 q^{34} +3.33275 q^{36} -0.837496 q^{37} -2.81521 q^{39} +4.49020 q^{41} +0.879385 q^{42} -4.80066 q^{43} -4.18479 q^{44} -1.54664 q^{46} -0.716881 q^{47} -0.0222887 q^{48} -3.46791 q^{49} -0.879385 q^{51} +6.49020 q^{52} -6.10607 q^{53} -2.67499 q^{54} -5.33275 q^{56} +3.04963 q^{58} +10.7588 q^{59} +4.38919 q^{61} -1.70914 q^{62} -5.10607 q^{63} +5.04189 q^{64} +1.59627 q^{66} +14.2121 q^{67} +2.02734 q^{68} -0.935822 q^{69} +13.7588 q^{71} +7.70914 q^{72} +7.51754 q^{73} -0.736482 q^{74} +6.41147 q^{77} -2.47565 q^{78} +6.96316 q^{79} +6.53209 q^{81} +3.94862 q^{82} -2.51249 q^{83} -1.22668 q^{84} -4.22163 q^{86} +1.84524 q^{87} -9.68004 q^{88} +2.28312 q^{89} -9.94356 q^{91} +2.15745 q^{92} -1.03415 q^{93} -0.630415 q^{94} +3.00000 q^{96} -1.82295 q^{97} -3.04963 q^{98} -9.26857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - 6 q^{8}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 6 * q^6 - 6 * q^8	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{6} - 6 q^{8} - 3 q^{12} + 6 q^{14} + 3 q^{16} - 6 q^{17} - 3 q^{18} + 3 q^{21} + 9 q^{22} + 6 q^{23} - 6 q^{24} - 15 q^{26} - 6 q^{27} - 9 q^{28} + 15 q^{29} + 9 q^{31} + 9 q^{33} + 9 q^{34} - 9 q^{36} - 12 q^{39} + 12 q^{41} - 3 q^{42} - 9 q^{44} - 18 q^{46} + 6 q^{47} + 6 q^{48} - 15 q^{49} + 3 q^{51} + 18 q^{52} - 6 q^{53} - 3 q^{54} + 3 q^{56} - 18 q^{58} + 21 q^{59} + 9 q^{61} - 21 q^{62} - 3 q^{63} + 12 q^{64} - 9 q^{66} + 18 q^{67} - 15 q^{68} - 12 q^{69} + 30 q^{71} + 39 q^{72} + 3 q^{74} + 9 q^{77} + 12 q^{78} + 9 q^{79} + 15 q^{81} - 18 q^{82} + 3 q^{84} - 21 q^{86} - 21 q^{87} - 9 q^{88} + 15 q^{89} - 15 q^{91} + 24 q^{92} - 24 q^{93} - 9 q^{94} + 9 q^{96} + 15 q^{97} + 18 q^{98} - 18 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 6 * q^6 - 6 * q^8 - 3 * q^12 + 6 * q^14 + 3 * q^16 - 6 * q^17 - 3 * q^18 + 3 * q^21 + 9 * q^22 + 6 * q^23 - 6 * q^24 - 15 * q^26 - 6 * q^27 - 9 * q^28 + 15 * q^29 + 9 * q^31 + 9 * q^33 + 9 * q^34 - 9 * q^36 - 12 * q^39 + 12 * q^41 - 3 * q^42 - 9 * q^44 - 18 * q^46 + 6 * q^47 + 6 * q^48 - 15 * q^49 + 3 * q^51 + 18 * q^52 - 6 * q^53 - 3 * q^54 + 3 * q^56 - 18 * q^58 + 21 * q^59 + 9 * q^61 - 21 * q^62 - 3 * q^63 + 12 * q^64 - 9 * q^66 + 18 * q^67 - 15 * q^68 - 12 * q^69 + 30 * q^71 + 39 * q^72 + 3 * q^74 + 9 * q^77 + 12 * q^78 + 9 * q^79 + 15 * q^81 - 18 * q^82 + 3 * q^84 - 21 * q^86 - 21 * q^87 - 9 * q^88 + 15 * q^89 - 15 * q^91 + 24 * q^92 - 24 * q^93 - 9 * q^94 + 9 * q^96 + 15 * q^97 + 18 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

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