LMFDB - Embedded newform 9025.2.a.bd.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:	$1$
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			$-1.53209$ 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)

$f(q)$	$=$	$q+2.53209 q^{2} +0.652704 q^{3} +4.41147 q^{4} +1.65270 q^{6} -1.53209 q^{7} +6.10607 q^{8} -2.57398 q^{9} +O(q^{10})$	\(q+2.53209 q^{2} +0.652704 q^{3} +4.41147 q^{4} +1.65270 q^{6} -1.53209 q^{7} +6.10607 q^{8} -2.57398 q^{9} -1.18479 q^{11} +2.87939 q^{12} -2.71688 q^{13} -3.87939 q^{14} +6.63816 q^{16} -3.87939 q^{17} -6.51754 q^{18} -1.00000 q^{21} -3.00000 q^{22} +5.06418 q^{23} +3.98545 q^{24} -6.87939 q^{26} -3.63816 q^{27} -6.75877 q^{28} -4.65270 q^{29} -3.83750 q^{31} +4.59627 q^{32} -0.773318 q^{33} -9.82295 q^{34} -11.3550 q^{36} +4.10607 q^{37} -1.77332 q^{39} -9.98545 q^{41} -2.53209 q^{42} +8.70233 q^{43} -5.22668 q^{44} +12.8229 q^{46} -0.573978 q^{47} +4.33275 q^{48} -4.65270 q^{49} -2.53209 q^{51} -11.9855 q^{52} -2.94356 q^{53} -9.21213 q^{54} -9.35504 q^{56} -11.7811 q^{58} -3.93582 q^{59} -4.51754 q^{61} -9.71688 q^{62} +3.94356 q^{63} -1.63816 q^{64} -1.95811 q^{66} +3.88713 q^{67} -17.1138 q^{68} +3.30541 q^{69} -6.93582 q^{71} -15.7169 q^{72} -6.12836 q^{73} +10.3969 q^{74} +1.81521 q^{77} -4.49020 q^{78} +9.80840 q^{79} +5.34730 q^{81} -25.2841 q^{82} -12.3182 q^{83} -4.41147 q^{84} +22.0351 q^{86} -3.03684 q^{87} -7.23442 q^{88} -2.42602 q^{89} +4.16250 q^{91} +22.3405 q^{92} -2.50475 q^{93} -1.45336 q^{94} +3.00000 q^{96} -7.36959 q^{97} -11.7811 q^{98} +3.04963 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.53209	1.79046	0.895229	−	0.445607i	$-0.147012\pi$
$2$	2.53209	1.79046	0.895229	+	0.445607i	$0.147012\pi$
$3$	0.652704	0.376839	0.188419	−	0.982089i	$-0.439664\pi$
$3$	0.652704	0.376839	0.188419	+	0.982089i	$0.439664\pi$
$4$	4.41147	2.20574
$5$	0	0
$5$	0	0
$6$	1.65270	0.674713
$7$	−1.53209	−0.579075	−0.289538	−	0.957167i	$-0.593502\pi$
$7$	−1.53209	−0.579075	−0.289538	+	0.957167i	$0.593502\pi$
$8$	6.10607	2.15882
$9$	−2.57398	−0.857993
$10$	0	0
$11$	−1.18479	−0.357228	−0.178614	−	0.983919i	$-0.557161\pi$
$11$	−1.18479	−0.357228	−0.178614	+	0.983919i	$0.557161\pi$
$12$	2.87939	0.831207
$13$	−2.71688	−0.753527	−0.376764	−	0.926309i	$-0.622963\pi$
$13$	−2.71688	−0.753527	−0.376764	+	0.926309i	$0.622963\pi$
$14$	−3.87939	−1.03681
$15$	0	0
$16$	6.63816	1.65954
$17$	−3.87939	−0.940889	−0.470445	−	0.882430i	$-0.655906\pi$
$17$	−3.87939	−0.940889	−0.470445	+	0.882430i	$0.655906\pi$
$18$	−6.51754	−1.53620
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−3.00000	−0.639602
$23$	5.06418	1.05595	0.527977	−	0.849259i	$-0.322951\pi$
$23$	5.06418	1.05595	0.527977	+	0.849259i	$0.322951\pi$
$24$	3.98545	0.813527
$25$	0	0
$26$	−6.87939	−1.34916
$27$	−3.63816	−0.700163
$28$	−6.75877	−1.27729
$29$	−4.65270	−0.863985	−0.431993	−	0.901877i	$-0.642189\pi$
$29$	−4.65270	−0.863985	−0.431993	+	0.901877i	$0.642189\pi$
$30$	0	0
$31$	−3.83750	−0.689235	−0.344617	−	0.938743i	$-0.611991\pi$
$31$	−3.83750	−0.689235	−0.344617	+	0.938743i	$0.611991\pi$
$32$	4.59627	0.812513
$33$	−0.773318	−0.134617
$34$	−9.82295	−1.68462
$35$	0	0
$36$	−11.3550	−1.89251
$37$	4.10607	0.675033	0.337517	−	0.941320i	$-0.390413\pi$
$37$	4.10607	0.675033	0.337517	+	0.941320i	$0.390413\pi$
$38$	0	0
$39$	−1.77332	−0.283958
$40$	0	0
$41$	−9.98545	−1.55947	−0.779733	−	0.626112i	$-0.784645\pi$
$41$	−9.98545	−1.55947	−0.779733	+	0.626112i	$0.784645\pi$
$42$	−2.53209	−0.390710
$43$	8.70233	1.32709	0.663547	−	0.748135i	$-0.269050\pi$
$43$	8.70233	1.32709	0.663547	+	0.748135i	$0.269050\pi$
$44$	−5.22668	−0.787952
$45$	0	0
$46$	12.8229	1.89064
$47$	−0.573978	−0.0837233	−0.0418616	−	0.999123i	$-0.513329\pi$
$47$	−0.573978	−0.0837233	−0.0418616	+	0.999123i	$0.513329\pi$
$48$	4.33275	0.625378
$49$	−4.65270	−0.664672
$50$	0	0
$51$	−2.53209	−0.354563
$52$	−11.9855	−1.66208
$53$	−2.94356	−0.404329	−0.202165	−	0.979352i	$-0.564798\pi$
$53$	−2.94356	−0.404329	−0.202165	+	0.979352i	$0.564798\pi$
$54$	−9.21213	−1.25361
$55$	0	0
$56$	−9.35504	−1.25012
$57$	0	0
$58$	−11.7811	−1.54693
$59$	−3.93582	−0.512400	−0.256200	−	0.966624i	$-0.582471\pi$
$59$	−3.93582	−0.512400	−0.256200	+	0.966624i	$0.582471\pi$
$60$	0	0
$61$	−4.51754	−0.578412	−0.289206	−	0.957267i	$-0.593391\pi$
$61$	−4.51754	−0.578412	−0.289206	+	0.957267i	$0.593391\pi$
$62$	−9.71688	−1.23405
$63$	3.94356	0.496842
$64$	−1.63816	−0.204769
$65$	0	0
$66$	−1.95811	−0.241027
$67$	3.88713	0.474888	0.237444	−	0.971401i	$-0.423690\pi$
$67$	3.88713	0.474888	0.237444	+	0.971401i	$0.423690\pi$
$68$	−17.1138	−2.07535
$69$	3.30541	0.397924
$70$	0	0
$71$	−6.93582	−0.823131	−0.411565	−	0.911380i	$-0.635018\pi$
$71$	−6.93582	−0.823131	−0.411565	+	0.911380i	$0.635018\pi$
$72$	−15.7169	−1.85225
$73$	−6.12836	−0.717270	−0.358635	−	0.933478i	$-0.616758\pi$
$73$	−6.12836	−0.717270	−0.358635	+	0.933478i	$0.616758\pi$
$74$	10.3969	1.20862
$75$	0	0
$76$	0	0
$77$	1.81521	0.206862
$78$	−4.49020	−0.508415
$79$	9.80840	1.10353	0.551766	−	0.833999i	$-0.313954\pi$
$79$	9.80840	1.10353	0.551766	+	0.833999i	$0.313954\pi$
$80$	0	0
$81$	5.34730	0.594144
$82$	−25.2841	−2.79216
$83$	−12.3182	−1.35210	−0.676049	−	0.736857i	$-0.736309\pi$
$83$	−12.3182	−1.35210	−0.676049	+	0.736857i	$0.736309\pi$
$84$	−4.41147	−0.481331
$85$	0	0
$86$	22.0351	2.37610
$87$	−3.03684	−0.325583
$88$	−7.23442	−0.771192
$89$	−2.42602	−0.257158	−0.128579	−	0.991699i	$-0.541042\pi$
$89$	−2.42602	−0.257158	−0.128579	+	0.991699i	$0.541042\pi$
$90$	0	0
$91$	4.16250	0.436349
$92$	22.3405	2.32916
$93$	−2.50475	−0.259730
$94$	−1.45336	−0.149903
$95$	0	0
$96$	3.00000	0.306186
$97$	−7.36959	−0.748268	−0.374134	−	0.927375i	$-0.622060\pi$
$97$	−7.36959	−0.748268	−0.374134	+	0.927375i	$0.622060\pi$
$98$	−11.7811	−1.19007
$99$	3.04963	0.306499
$100$	0	0
$101$	2.17024	0.215947	0.107974	−	0.994154i	$-0.465564\pi$
$101$	2.17024	0.215947	0.107974	+	0.994154i	$0.465564\pi$
$102$	−6.41147	−0.634831
$103$	12.4757	1.22926	0.614631	−	0.788815i	$-0.289305\pi$
$103$	12.4757	1.22926	0.614631	+	0.788815i	$0.289305\pi$
$104$	−16.5895	−1.62673
$105$	0	0
$106$	−7.45336	−0.723935
$107$	6.68004	0.645784	0.322892	−	0.946436i	$-0.395345\pi$
$107$	6.68004	0.645784	0.322892	+	0.946436i	$0.395345\pi$
$108$	−16.0496	−1.54438
$109$	9.45336	0.905468	0.452734	−	0.891646i	$-0.350449\pi$
$109$	9.45336	0.905468	0.452734	+	0.891646i	$0.350449\pi$
$110$	0	0
$111$	2.68004	0.254379
$112$	−10.1702	−0.960998
$113$	−1.31046	−0.123278	−0.0616388	−	0.998099i	$-0.519633\pi$
$113$	−1.31046	−0.123278	−0.0616388	+	0.998099i	$0.519633\pi$
$114$	0	0
$115$	0	0
$116$	−20.5253	−1.90572
$117$	6.99319	0.646521
$118$	−9.96585	−0.917431
$119$	5.94356	0.544846
$120$	0	0
$121$	−9.59627	−0.872388
$122$	−11.4388	−1.03562
$123$	−6.51754	−0.587667
$124$	−16.9290	−1.52027
$125$	0	0
$126$	9.98545	0.889575
$127$	14.5030	1.28693	0.643466	−	0.765474i	$-0.277496\pi$
$127$	14.5030	1.28693	0.643466	+	0.765474i	$0.277496\pi$
$128$	−13.3405	−1.17914
$129$	5.68004	0.500100
$130$	0	0
$131$	−19.8084	−1.73067	−0.865334	−	0.501196i	$-0.832894\pi$
$131$	−19.8084	−1.73067	−0.865334	+	0.501196i	$0.832894\pi$
$132$	−3.41147	−0.296931
$133$	0	0
$134$	9.84255	0.850267
$135$	0	0
$136$	−23.6878	−2.03121
$137$	−10.2044	−0.871820	−0.435910	−	0.899990i	$-0.643573\pi$
$137$	−10.2044	−0.871820	−0.435910	+	0.899990i	$0.643573\pi$
$138$	8.36959	0.712466
$139$	−1.66044	−0.140837	−0.0704185	−	0.997518i	$-0.522433\pi$
$139$	−1.66044	−0.140837	−0.0704185	+	0.997518i	$0.522433\pi$
$140$	0	0
$141$	−0.374638	−0.0315502
$142$	−17.5621	−1.47378
$143$	3.21894	0.269181
$144$	−17.0865	−1.42387
$145$	0	0
$146$	−15.5175	−1.28424
$147$	−3.03684	−0.250474
$148$	18.1138	1.48895
$149$	11.2071	0.918120	0.459060	−	0.888405i	$-0.348186\pi$
$149$	11.2071	0.918120	0.459060	+	0.888405i	$0.348186\pi$
$150$	0	0
$151$	−11.0419	−0.898576	−0.449288	−	0.893387i	$-0.648322\pi$
$151$	−11.0419	−0.898576	−0.449288	+	0.893387i	$0.648322\pi$
$152$	0	0
$153$	9.98545	0.807276
$154$	4.59627	0.370378
$155$	0	0
$156$	−7.82295	−0.626337
$157$	−10.9932	−0.877352	−0.438676	−	0.898645i	$-0.644552\pi$
$157$	−10.9932	−0.877352	−0.438676	+	0.898645i	$0.644552\pi$
$158$	24.8357	1.97583
$159$	−1.92127	−0.152367
$160$	0	0
$161$	−7.75877	−0.611477
$162$	13.5398	1.06379
$163$	6.33275	0.496019	0.248010	−	0.968758i	$-0.420224\pi$
$163$	6.33275	0.496019	0.248010	+	0.968758i	$0.420224\pi$
$164$	−44.0506	−3.43977
$165$	0	0
$166$	−31.1908	−2.42087
$167$	13.7784	1.06620	0.533101	−	0.846051i	$-0.321027\pi$
$167$	13.7784	1.06620	0.533101	+	0.846051i	$0.321027\pi$
$168$	−6.10607	−0.471093
$169$	−5.61856	−0.432197
$170$	0	0
$171$	0	0
$172$	38.3901	2.92722
$173$	−25.2472	−1.91951	−0.959755	−	0.280838i	$-0.909388\pi$
$173$	−25.2472	−1.91951	−0.959755	+	0.280838i	$0.909388\pi$
$174$	−7.68954	−0.582943
$175$	0	0
$176$	−7.86484	−0.592834
$177$	−2.56893	−0.193092
$178$	−6.14290	−0.460430
$179$	5.83069	0.435806	0.217903	−	0.975970i	$-0.430078\pi$
$179$	5.83069	0.435806	0.217903	+	0.975970i	$0.430078\pi$
$180$	0	0
$181$	13.5621	1.00806	0.504032	−	0.863685i	$-0.331849\pi$
$181$	13.5621	1.00806	0.504032	+	0.863685i	$0.331849\pi$
$182$	10.5398	0.781264
$183$	−2.94862	−0.217968
$184$	30.9222	2.27962
$185$	0	0
$186$	−6.34224	−0.465036
$187$	4.59627	0.336112
$188$	−2.53209	−0.184672
$189$	5.57398	0.405447
$190$	0	0
$191$	−10.2841	−0.744128	−0.372064	−	0.928207i	$-0.621350\pi$
$191$	−10.2841	−0.744128	−0.372064	+	0.928207i	$0.621350\pi$
$192$	−1.06923	−0.0771650
$193$	−13.8007	−0.993393	−0.496697	−	0.867924i	$-0.665454\pi$
$193$	−13.8007	−0.993393	−0.496697	+	0.867924i	$0.665454\pi$
$194$	−18.6604	−1.33974
$195$	0	0
$196$	−20.5253	−1.46609
$197$	7.94087	0.565764	0.282882	−	0.959155i	$-0.408710\pi$
$197$	7.94087	0.565764	0.282882	+	0.959155i	$0.408710\pi$
$198$	7.72193	0.548774
$199$	27.0351	1.91647	0.958233	−	0.285988i	$-0.0923219\pi$
$199$	27.0351	1.91647	0.958233	+	0.285988i	$0.0923219\pi$
$200$	0	0
$201$	2.53714	0.178956
$202$	5.49525	0.386645
$203$	7.12836	0.500312
$204$	−11.1702	−0.782074
$205$	0	0
$206$	31.5895	2.20094
$207$	−13.0351	−0.906001
$208$	−18.0351	−1.25051
$209$	0	0
$210$	0	0
$211$	−8.07192	−0.555694	−0.277847	−	0.960625i	$-0.589621\pi$
$211$	−8.07192	−0.555694	−0.277847	+	0.960625i	$0.589621\pi$
$212$	−12.9855	−0.891845
$213$	−4.52704	−0.310187
$214$	16.9145	1.15625
$215$	0	0
$216$	−22.2148	−1.51153
$217$	5.87939	0.399119
$218$	23.9368	1.62120
$219$	−4.00000	−0.270295
$220$	0	0
$221$	10.5398	0.708986
$222$	6.78611	0.455454
$223$	15.4757	1.03633	0.518163	−	0.855282i	$-0.326616\pi$
$223$	15.4757	1.03633	0.518163	+	0.855282i	$0.326616\pi$
$224$	−7.04189	−0.470506
$225$	0	0
$226$	−3.31820	−0.220723
$227$	−9.87258	−0.655266	−0.327633	−	0.944805i	$-0.606251\pi$
$227$	−9.87258	−0.655266	−0.327633	+	0.944805i	$0.606251\pi$
$228$	0	0
$229$	20.1189	1.32949	0.664746	−	0.747070i	$-0.268540\pi$
$229$	20.1189	1.32949	0.664746	+	0.747070i	$0.268540\pi$
$230$	0	0
$231$	1.18479	0.0779536
$232$	−28.4097	−1.86519
$233$	−3.53478	−0.231571	−0.115785	−	0.993274i	$-0.536939\pi$
$233$	−3.53478	−0.231571	−0.115785	+	0.993274i	$0.536939\pi$
$234$	17.7074	1.15757
$235$	0	0
$236$	−17.3628	−1.13022
$237$	6.40198	0.415853
$238$	15.0496	0.975523
$239$	11.9736	0.774507	0.387254	−	0.921973i	$-0.373424\pi$
$239$	11.9736	0.774507	0.387254	+	0.921973i	$0.373424\pi$
$240$	0	0
$241$	12.9017	0.831070	0.415535	−	0.909577i	$-0.363594\pi$
$241$	12.9017	0.831070	0.415535	+	0.909577i	$0.363594\pi$
$242$	−24.2986	−1.56197
$243$	14.4047	0.924060
$244$	−19.9290	−1.27582
$245$	0	0
$246$	−16.5030	−1.05219
$247$	0	0
$248$	−23.4320	−1.48793
$249$	−8.04013	−0.509523
$250$	0	0
$251$	14.3628	0.906571	0.453285	−	0.891366i	$-0.350252\pi$
$251$	14.3628	0.906571	0.453285	+	0.891366i	$0.350252\pi$
$252$	17.3969	1.09590
$253$	−6.00000	−0.377217
$254$	36.7229	2.30420
$255$	0	0
$256$	−30.5030	−1.90644
$257$	−4.97771	−0.310501	−0.155251	−	0.987875i	$-0.549618\pi$
$257$	−4.97771	−0.310501	−0.155251	+	0.987875i	$0.549618\pi$
$258$	14.3824	0.895408
$259$	−6.29086	−0.390895
$260$	0	0
$261$	11.9760	0.741293
$262$	−50.1566	−3.09869
$263$	24.0428	1.48254	0.741272	−	0.671205i	$-0.234223\pi$
$263$	24.0428	1.48254	0.741272	+	0.671205i	$0.234223\pi$
$264$	−4.72193	−0.290615
$265$	0	0
$266$	0	0
$267$	−1.58347	−0.0969070
$268$	17.1480	1.04748
$269$	−13.1111	−0.799399	−0.399700	−	0.916646i	$-0.630886\pi$
$269$	−13.1111	−0.799399	−0.399700	+	0.916646i	$0.630886\pi$
$270$	0	0
$271$	−26.5699	−1.61400	−0.807002	−	0.590549i	$-0.798911\pi$
$271$	−26.5699	−1.61400	−0.807002	+	0.590549i	$0.798911\pi$
$272$	−25.7520	−1.56144
$273$	2.71688	0.164433
$274$	−25.8384	−1.56096
$275$	0	0
$276$	14.5817	0.877716
$277$	16.5107	0.992034	0.496017	−	0.868313i	$-0.334795\pi$
$277$	16.5107	0.992034	0.496017	+	0.868313i	$0.334795\pi$
$278$	−4.20439	−0.252163
$279$	9.87763	0.591358
$280$	0	0
$281$	−19.3901	−1.15672	−0.578359	−	0.815783i	$-0.696307\pi$
$281$	−19.3901	−1.15672	−0.578359	+	0.815783i	$0.696307\pi$
$282$	−0.948615	−0.0564892
$283$	11.3105	0.672337	0.336169	−	0.941802i	$-0.390869\pi$
$283$	11.3105	0.672337	0.336169	+	0.941802i	$0.390869\pi$
$284$	−30.5972	−1.81561
$285$	0	0
$286$	8.15064	0.481958
$287$	15.2986	0.903048
$288$	−11.8307	−0.697130
$289$	−1.95037	−0.114728
$290$	0	0
$291$	−4.81016	−0.281976
$292$	−27.0351	−1.58211
$293$	−3.89899	−0.227781	−0.113891	−	0.993493i	$-0.536331\pi$
$293$	−3.89899	−0.227781	−0.113891	+	0.993493i	$0.536331\pi$
$294$	−7.68954	−0.448463
$295$	0	0
$296$	25.0719	1.45728
$297$	4.31046	0.250118
$298$	28.3773	1.64385
$299$	−13.7588	−0.795690
$300$	0	0
$301$	−13.3327	−0.768487
$302$	−27.9590	−1.60886
$303$	1.41653	0.0813773
$304$	0	0
$305$	0	0
$306$	25.2841	1.44539
$307$	−23.1753	−1.32268	−0.661342	−	0.750084i	$-0.730013\pi$
$307$	−23.1753	−1.32268	−0.661342	+	0.750084i	$0.730013\pi$
$308$	8.00774	0.456283
$309$	8.14290	0.463234
$310$	0	0
$311$	−3.46110	−0.196261	−0.0981306	−	0.995174i	$-0.531286\pi$
$311$	−3.46110	−0.196261	−0.0981306	+	0.995174i	$0.531286\pi$
$312$	−10.8280	−0.613015
$313$	22.8898	1.29381	0.646904	−	0.762571i	$-0.276063\pi$
$313$	22.8898	1.29381	0.646904	+	0.762571i	$0.276063\pi$
$314$	−27.8357	−1.57086
$315$	0	0
$316$	43.2695	2.43410
$317$	−26.1206	−1.46708	−0.733540	−	0.679646i	$-0.762133\pi$
$317$	−26.1206	−1.46708	−0.733540	+	0.679646i	$0.762133\pi$
$318$	−4.86484	−0.272807
$319$	5.51249	0.308640
$320$	0	0
$321$	4.36009	0.243356
$322$	−19.6459	−1.09482
$323$	0	0
$324$	23.5895	1.31053
$325$	0	0
$326$	16.0351	0.888101
$327$	6.17024	0.341215
$328$	−60.9718	−3.36661
$329$	0.879385	0.0484821
$330$	0	0
$331$	19.0446	1.04678	0.523392	−	0.852092i	$-0.324666\pi$
$331$	19.0446	1.04678	0.523392	+	0.852092i	$0.324666\pi$
$332$	−54.3414	−2.98237
$333$	−10.5689	−0.579174
$334$	34.8881	1.90899
$335$	0	0
$336$	−6.63816	−0.362141
$337$	−1.70140	−0.0926812	−0.0463406	−	0.998926i	$-0.514756\pi$
$337$	−1.70140	−0.0926812	−0.0463406	+	0.998926i	$0.514756\pi$
$338$	−14.2267	−0.773829
$339$	−0.855342	−0.0464558
$340$	0	0
$341$	4.54664	0.246214
$342$	0	0
$343$	17.8530	0.963970
$344$	53.1370	2.86496
$345$	0	0
$346$	−63.9282	−3.43680
$347$	4.90167	0.263136	0.131568	−	0.991307i	$-0.457999\pi$
$347$	4.90167	0.263136	0.131568	+	0.991307i	$0.457999\pi$
$348$	−13.3969	−0.718151
$349$	−28.1293	−1.50573	−0.752863	−	0.658177i	$-0.771328\pi$
$349$	−28.1293	−1.50573	−0.752863	+	0.658177i	$0.771328\pi$
$350$	0	0
$351$	9.88444	0.527592
$352$	−5.44562	−0.290253
$353$	8.31996	0.442827	0.221413	−	0.975180i	$-0.428933\pi$
$353$	8.31996	0.442827	0.221413	+	0.975180i	$0.428933\pi$
$354$	−6.50475	−0.345723
$355$	0	0
$356$	−10.7023	−0.567223
$357$	3.87939	0.205319
$358$	14.7638	0.780292
$359$	24.9290	1.31570	0.657852	−	0.753148i	$-0.271465\pi$
$359$	24.9290	1.31570	0.657852	+	0.753148i	$0.271465\pi$
$360$	0	0
$361$	0	0
$362$	34.3405	1.80490
$363$	−6.26352	−0.328749
$364$	18.3628	0.962471
$365$	0	0
$366$	−7.46616	−0.390262
$367$	2.58584	0.134980	0.0674898	−	0.997720i	$-0.478501\pi$
$367$	2.58584	0.134980	0.0674898	+	0.997720i	$0.478501\pi$
$368$	33.6168	1.75240
$369$	25.7023	1.33801
$370$	0	0
$371$	4.50980	0.234137
$372$	−11.0496	−0.572897
$373$	23.3833	1.21074	0.605371	−	0.795943i	$-0.293025\pi$
$373$	23.3833	1.21074	0.605371	+	0.795943i	$0.293025\pi$
$374$	11.6382	0.601795
$375$	0	0
$376$	−3.50475	−0.180744
$377$	12.6408	0.651037
$378$	14.1138	0.725936
$379$	25.4388	1.30670	0.653352	−	0.757054i	$-0.273362\pi$
$379$	25.4388	1.30670	0.653352	+	0.757054i	$0.273362\pi$
$380$	0	0
$381$	9.46616	0.484966
$382$	−26.0401	−1.33233
$383$	27.4807	1.40420	0.702099	−	0.712079i	$-0.252246\pi$
$383$	27.4807	1.40420	0.702099	+	0.712079i	$0.252246\pi$
$384$	−8.70739	−0.444347
$385$	0	0
$386$	−34.9445	−1.77863
$387$	−22.3996	−1.13864
$388$	−32.5107	−1.65048
$389$	−3.34224	−0.169458	−0.0847292	−	0.996404i	$-0.527003\pi$
$389$	−3.34224	−0.169458	−0.0847292	+	0.996404i	$0.527003\pi$
$390$	0	0
$391$	−19.6459	−0.993536
$392$	−28.4097	−1.43491
$393$	−12.9290	−0.652183
$394$	20.1070	1.01298
$395$	0	0
$396$	13.4534	0.676057
$397$	13.1233	0.658640	0.329320	−	0.944218i	$-0.393181\pi$
$397$	13.1233	0.658640	0.329320	+	0.944218i	$0.393181\pi$
$398$	68.4552	3.43135
$399$	0	0
$400$	0	0
$401$	17.1138	0.854623	0.427311	−	0.904105i	$-0.359461\pi$
$401$	17.1138	0.854623	0.427311	+	0.904105i	$0.359461\pi$
$402$	6.42427	0.320413
$403$	10.4260	0.519357
$404$	9.57398	0.476323
$405$	0	0
$406$	18.0496	0.895788
$407$	−4.86484	−0.241141
$408$	−15.4611	−0.765439
$409$	−8.79797	−0.435032	−0.217516	−	0.976057i	$-0.569795\pi$
$409$	−8.79797	−0.435032	−0.217516	+	0.976057i	$0.569795\pi$
$410$	0	0
$411$	−6.66044	−0.328535
$412$	55.0360	2.71143
$413$	6.03003	0.296718
$414$	−33.0060	−1.62216
$415$	0	0
$416$	−12.4875	−0.612251
$417$	−1.08378	−0.0530728
$418$	0	0
$419$	6.84018	0.334165	0.167082	−	0.985943i	$-0.446565\pi$
$419$	6.84018	0.334165	0.167082	+	0.985943i	$0.446565\pi$
$420$	0	0
$421$	−4.82295	−0.235056	−0.117528	−	0.993070i	$-0.537497\pi$
$421$	−4.82295	−0.235056	−0.117528	+	0.993070i	$0.537497\pi$
$422$	−20.4388	−0.994946
$423$	1.47741	0.0718340
$424$	−17.9736	−0.872875
$425$	0	0
$426$	−11.4629	−0.555377
$427$	6.92127	0.334944
$428$	29.4688	1.42443
$429$	2.10101	0.101438
$430$	0	0
$431$	1.30365	0.0627947	0.0313974	−	0.999507i	$-0.490004\pi$
$431$	1.30365	0.0627947	0.0313974	+	0.999507i	$0.490004\pi$
$432$	−24.1506	−1.16195
$433$	−19.8239	−0.952675	−0.476337	−	0.879263i	$-0.658036\pi$
$433$	−19.8239	−0.952675	−0.476337	+	0.879263i	$0.658036\pi$
$434$	14.8871	0.714605
$435$	0	0
$436$	41.7033	1.99722
$437$	0	0
$438$	−10.1284	−0.483952
$439$	−34.5672	−1.64980	−0.824901	−	0.565278i	$-0.808769\pi$
$439$	−34.5672	−1.64980	−0.824901	+	0.565278i	$0.808769\pi$
$440$	0	0
$441$	11.9760	0.570284
$442$	26.6878	1.26941
$443$	−17.0101	−0.808174	−0.404087	−	0.914720i	$-0.632411\pi$
$443$	−17.0101	−0.808174	−0.404087	+	0.914720i	$0.632411\pi$
$444$	11.8229	0.561092
$445$	0	0
$446$	39.1857	1.85550
$447$	7.31490	0.345983
$448$	2.50980	0.118577
$449$	37.4097	1.76547	0.882737	−	0.469868i	$-0.155698\pi$
$449$	37.4097	1.76547	0.882737	+	0.469868i	$0.155698\pi$
$450$	0	0
$451$	11.8307	0.557085
$452$	−5.78106	−0.271918
$453$	−7.20708	−0.338618
$454$	−24.9982	−1.17323
$455$	0	0
$456$	0	0
$457$	−9.11112	−0.426200	−0.213100	−	0.977030i	$-0.568356\pi$
$457$	−9.11112	−0.426200	−0.213100	+	0.977030i	$0.568356\pi$
$458$	50.9427	2.38040
$459$	14.1138	0.658776
$460$	0	0
$461$	−24.4483	−1.13867	−0.569336	−	0.822105i	$-0.692800\pi$
$461$	−24.4483	−1.13867	−0.569336	+	0.822105i	$0.692800\pi$
$462$	3.00000	0.139573
$463$	0.250725	0.0116522	0.00582609	−	0.999983i	$-0.498145\pi$
$463$	0.250725	0.0116522	0.00582609	+	0.999983i	$0.498145\pi$
$464$	−30.8854	−1.43382
$465$	0	0
$466$	−8.95037	−0.414618
$467$	−15.3618	−0.710861	−0.355431	−	0.934703i	$-0.615666\pi$
$467$	−15.3618	−0.710861	−0.355431	+	0.934703i	$0.615666\pi$
$468$	30.8503	1.42606
$469$	−5.95542	−0.274996
$470$	0	0
$471$	−7.17530	−0.330620
$472$	−24.0324	−1.10618
$473$	−10.3105	−0.474075
$474$	16.2104	0.744567
$475$	0	0
$476$	26.2199	1.20179
$477$	7.57667	0.346912
$478$	30.3182	1.38672
$479$	−0.719246	−0.0328632	−0.0164316	−	0.999865i	$-0.505231\pi$
$479$	−0.719246	−0.0328632	−0.0164316	+	0.999865i	$0.505231\pi$
$480$	0	0
$481$	−11.1557	−0.508656
$482$	32.6682	1.48800
$483$	−5.06418	−0.230428
$484$	−42.3337	−1.92426
$485$	0	0
$486$	36.4739	1.65449
$487$	−11.7469	−0.532303	−0.266152	−	0.963931i	$-0.585752\pi$
$487$	−11.7469	−0.532303	−0.266152	+	0.963931i	$0.585752\pi$
$488$	−27.5844	−1.24869
$489$	4.13341	0.186919
$490$	0	0
$491$	0.0888306	0.00400887	0.00200443	−	0.999998i	$-0.499362\pi$
$491$	0.0888306	0.00400887	0.00200443	+	0.999998i	$0.499362\pi$
$492$	−28.7520	−1.29624
$493$	18.0496	0.812914
$494$	0	0
$495$	0	0
$496$	−25.4739	−1.14381
$497$	10.6263	0.476655
$498$	−20.3583	−0.912279
$499$	14.6905	0.657636	0.328818	−	0.944393i	$-0.393350\pi$
$499$	14.6905	0.657636	0.328818	+	0.944393i	$0.393350\pi$
$500$	0	0
$501$	8.99319	0.401786
$502$	36.3678	1.62318
$503$	4.90404	0.218660	0.109330	−	0.994005i	$-0.465129\pi$
$503$	4.90404	0.218660	0.109330	+	0.994005i	$0.465129\pi$
$504$	24.0797	1.07259
$505$	0	0
$506$	−15.1925	−0.675390
$507$	−3.66725	−0.162868
$508$	63.9796	2.83863
$509$	6.41384	0.284288	0.142144	−	0.989846i	$-0.454600\pi$
$509$	6.41384	0.284288	0.142144	+	0.989846i	$0.454600\pi$
$510$	0	0
$511$	9.38919	0.415353
$512$	−50.5553	−2.23425
$513$	0	0
$514$	−12.6040	−0.555939
$515$	0	0
$516$	25.0574	1.10309
$517$	0.680045	0.0299083
$518$	−15.9290	−0.699881
$519$	−16.4789	−0.723346
$520$	0	0
$521$	−35.8135	−1.56902	−0.784508	−	0.620119i	$-0.787084\pi$
$521$	−35.8135	−1.56902	−0.784508	+	0.620119i	$0.787084\pi$
$522$	30.3242	1.32725
$523$	−38.7725	−1.69540	−0.847701	−	0.530474i	$-0.822014\pi$
$523$	−38.7725	−1.69540	−0.847701	+	0.530474i	$0.822014\pi$
$524$	−87.3842	−3.81740
$525$	0	0
$526$	60.8786	2.65443
$527$	14.8871	0.648493
$528$	−5.13341	−0.223403
$529$	2.64590	0.115039
$530$	0	0
$531$	10.1307	0.439636
$532$	0	0
$533$	27.1293	1.17510
$534$	−4.00950	−0.173508
$535$	0	0
$536$	23.7351	1.02520
$537$	3.80571	0.164229
$538$	−33.1985	−1.43129
$539$	5.51249	0.237440
$540$	0	0
$541$	9.49020	0.408016	0.204008	−	0.978969i	$-0.434603\pi$
$541$	9.49020	0.408016	0.204008	+	0.978969i	$0.434603\pi$
$542$	−67.2772	−2.88981
$543$	8.85204	0.379878
$544$	−17.8307	−0.764484
$545$	0	0
$546$	6.87939	0.294411
$547$	−14.2121	−0.607667	−0.303833	−	0.952725i	$-0.598267\pi$
$547$	−14.2121	−0.607667	−0.303833	+	0.952725i	$0.598267\pi$
$548$	−45.0164	−1.92301
$549$	11.6281	0.496273
$550$	0	0
$551$	0	0
$552$	20.1830	0.859047
$553$	−15.0273	−0.639028
$554$	41.8066	1.77619
$555$	0	0
$556$	−7.32501	−0.310650
$557$	−22.5398	−0.955043	−0.477522	−	0.878620i	$-0.658465\pi$
$557$	−22.5398	−0.955043	−0.477522	+	0.878620i	$0.658465\pi$
$558$	25.0110	1.05880
$559$	−23.6432	−1.00000
$560$	0	0
$561$	3.00000	0.126660
$562$	−49.0975	−2.07105
$563$	42.9718	1.81105	0.905524	−	0.424296i	$-0.139478\pi$
$563$	42.9718	1.81105	0.905524	+	0.424296i	$0.139478\pi$
$564$	−1.65270	−0.0695914
$565$	0	0
$566$	28.6391	1.20379
$567$	−8.19253	−0.344054
$568$	−42.3506	−1.77699
$569$	7.42696	0.311354	0.155677	−	0.987808i	$-0.450244\pi$
$569$	7.42696	0.311354	0.155677	+	0.987808i	$0.450244\pi$
$570$	0	0
$571$	4.04458	0.169260	0.0846301	−	0.996412i	$-0.473029\pi$
$571$	4.04458	0.169260	0.0846301	+	0.996412i	$0.473029\pi$
$572$	14.2003	0.593743
$573$	−6.71244	−0.280416
$574$	38.7374	1.61687
$575$	0	0
$576$	4.21658	0.175691
$577$	−3.23442	−0.134651	−0.0673254	−	0.997731i	$-0.521447\pi$
$577$	−3.23442	−0.134651	−0.0673254	+	0.997731i	$0.521447\pi$
$578$	−4.93851	−0.205415
$579$	−9.00774	−0.374349
$580$	0	0
$581$	18.8726	0.782966
$582$	−12.1797	−0.504866
$583$	3.48751	0.144438
$584$	−37.4201	−1.54846
$585$	0	0
$586$	−9.87258	−0.407832
$587$	40.8084	1.68434	0.842171	−	0.539210i	$-0.181277\pi$
$587$	40.8084	1.68434	0.842171	+	0.539210i	$0.181277\pi$
$588$	−13.3969	−0.552480
$589$	0	0
$590$	0	0
$591$	5.18304	0.213202
$592$	27.2567	1.12024
$593$	11.0642	0.454351	0.227176	−	0.973854i	$-0.427051\pi$
$593$	11.0642	0.454351	0.227176	+	0.973854i	$0.427051\pi$
$594$	10.9145	0.447826
$595$	0	0
$596$	49.4397	2.02513
$597$	17.6459	0.722198
$598$	−34.8384	−1.42465
$599$	−44.5577	−1.82058	−0.910289	−	0.413974i	$-0.864140\pi$
$599$	−44.5577	−1.82058	−0.910289	+	0.413974i	$0.864140\pi$
$600$	0	0
$601$	−4.99907	−0.203916	−0.101958	−	0.994789i	$-0.532511\pi$
$601$	−4.99907	−0.203916	−0.101958	+	0.994789i	$0.532511\pi$
$602$	−33.7597	−1.37594
$603$	−10.0054	−0.407450
$604$	−48.7110	−1.98202
$605$	0	0
$606$	3.58677	0.145703
$607$	31.1881	1.26589	0.632943	−	0.774199i	$-0.281847\pi$
$607$	31.1881	1.26589	0.632943	+	0.774199i	$0.281847\pi$
$608$	0	0
$609$	4.65270	0.188537
$610$	0	0
$611$	1.55943	0.0630878
$612$	44.0506	1.78064
$613$	−16.3696	−0.661161	−0.330581	−	0.943778i	$-0.607245\pi$
$613$	−16.3696	−0.661161	−0.330581	+	0.943778i	$0.607245\pi$
$614$	−58.6819	−2.36821
$615$	0	0
$616$	11.0838	0.446578
$617$	−16.0583	−0.646483	−0.323241	−	0.946317i	$-0.604773\pi$
$617$	−16.0583	−0.646483	−0.323241	+	0.946317i	$0.604773\pi$
$618$	20.6186	0.829400
$619$	23.8425	0.958313	0.479156	−	0.877730i	$-0.340943\pi$
$619$	23.8425	0.958313	0.479156	+	0.877730i	$0.340943\pi$
$620$	0	0
$621$	−18.4243	−0.739340
$622$	−8.76382	−0.351397
$623$	3.71688	0.148914
$624$	−11.7716	−0.471240
$625$	0	0
$626$	57.9590	2.31651
$627$	0	0
$628$	−48.4962	−1.93521
$629$	−15.9290	−0.635131
$630$	0	0
$631$	21.4730	0.854825	0.427413	−	0.904057i	$-0.359425\pi$
$631$	21.4730	0.854825	0.427413	+	0.904057i	$0.359425\pi$
$632$	59.8907	2.38233
$633$	−5.26857	−0.209407
$634$	−66.1397	−2.62674
$635$	0	0
$636$	−8.47565	−0.336081
$637$	12.6408	0.500848
$638$	13.9581	0.552607
$639$	17.8527	0.706240
$640$	0	0
$641$	12.7537	0.503742	0.251871	−	0.967761i	$-0.418954\pi$
$641$	12.7537	0.503742	0.251871	+	0.967761i	$0.418954\pi$
$642$	11.0401	0.435719
$643$	−28.6081	−1.12819	−0.564097	−	0.825708i	$-0.690776\pi$
$643$	−28.6081	−1.12819	−0.564097	+	0.825708i	$0.690776\pi$
$644$	−34.2276	−1.34876
$645$	0	0
$646$	0	0
$647$	−16.7128	−0.657046	−0.328523	−	0.944496i	$-0.606551\pi$
$647$	−16.7128	−0.657046	−0.328523	+	0.944496i	$0.606551\pi$
$648$	32.6509	1.28265
$649$	4.66313	0.183044
$650$	0	0
$651$	3.83750	0.150403
$652$	27.9368	1.09409
$653$	−27.0000	−1.05659	−0.528296	−	0.849060i	$-0.677169\pi$
$653$	−27.0000	−1.05659	−0.528296	+	0.849060i	$0.677169\pi$
$654$	15.6236	0.610931
$655$	0	0
$656$	−66.2850	−2.58799
$657$	15.7743	0.615412
$658$	2.22668	0.0868051
$659$	−43.9009	−1.71013	−0.855067	−	0.518517i	$-0.826484\pi$
$659$	−43.9009	−1.71013	−0.855067	+	0.518517i	$0.826484\pi$
$660$	0	0
$661$	−10.7561	−0.418363	−0.209182	−	0.977877i	$-0.567080\pi$
$661$	−10.7561	−0.418363	−0.209182	+	0.977877i	$0.567080\pi$
$662$	48.2226	1.87422
$663$	6.87939	0.267173
$664$	−75.2158	−2.91894
$665$	0	0
$666$	−26.7615	−1.03699
$667$	−23.5621	−0.912329
$668$	60.7829	2.35176
$669$	10.1010	0.390528
$670$	0	0
$671$	5.35235	0.206625
$672$	−4.59627	−0.177305
$673$	−4.65776	−0.179543	−0.0897717	−	0.995962i	$-0.528614\pi$
$673$	−4.65776	−0.179543	−0.0897717	+	0.995962i	$0.528614\pi$
$674$	−4.30810	−0.165942
$675$	0	0
$676$	−24.7861	−0.953312
$677$	−3.26857	−0.125621	−0.0628107	−	0.998025i	$-0.520006\pi$
$677$	−3.26857	−0.125621	−0.0628107	+	0.998025i	$0.520006\pi$
$678$	−2.16580	−0.0831771
$679$	11.2909	0.433303
$680$	0	0
$681$	−6.44387	−0.246930
$682$	11.5125	0.440836
$683$	−6.21894	−0.237961	−0.118981	−	0.992897i	$-0.537963\pi$
$683$	−6.21894	−0.237961	−0.118981	+	0.992897i	$0.537963\pi$
$684$	0	0
$685$	0	0
$686$	45.2053	1.72595
$687$	13.1317	0.501004
$688$	57.7674	2.20236
$689$	7.99731	0.304673
$690$	0	0
$691$	22.2175	0.845194	0.422597	−	0.906318i	$-0.361119\pi$
$691$	22.2175	0.845194	0.422597	+	0.906318i	$0.361119\pi$
$692$	−111.377	−4.23393
$693$	−4.67230	−0.177486
$694$	12.4115	0.471133
$695$	0	0
$696$	−18.5431	−0.702875
$697$	38.7374	1.46728
$698$	−71.2259	−2.69594
$699$	−2.30716	−0.0872649
$700$	0	0
$701$	−27.7725	−1.04895	−0.524476	−	0.851425i	$-0.675739\pi$
$701$	−27.7725	−1.04895	−0.524476	+	0.851425i	$0.675739\pi$
$702$	25.0283	0.944631
$703$	0	0
$704$	1.94087	0.0731495
$705$	0	0
$706$	21.0669	0.792862
$707$	−3.32501	−0.125050
$708$	−11.3327	−0.425911
$709$	−6.10782	−0.229384	−0.114692	−	0.993401i	$-0.536588\pi$
$709$	−6.10782	−0.229384	−0.114692	+	0.993401i	$0.536588\pi$
$710$	0	0
$711$	−25.2466	−0.946822
$712$	−14.8135	−0.555158
$713$	−19.4338	−0.727800
$714$	9.82295	0.367615
$715$	0	0
$716$	25.7219	0.961274
$717$	7.81521	0.291864
$718$	63.1225	2.35571
$719$	38.7238	1.44415	0.722077	−	0.691813i	$-0.243188\pi$
$719$	38.7238	1.44415	0.722077	+	0.691813i	$0.243188\pi$
$720$	0	0
$721$	−19.1138	−0.711835
$722$	0	0
$723$	8.42097	0.313179
$724$	59.8289	2.22352
$725$	0	0
$726$	−15.8598	−0.588612
$727$	11.0779	0.410857	0.205428	−	0.978672i	$-0.434141\pi$
$727$	11.0779	0.410857	0.205428	+	0.978672i	$0.434141\pi$
$728$	25.4165	0.941999
$729$	−6.63991	−0.245923
$730$	0	0
$731$	−33.7597	−1.24865
$732$	−13.0077	−0.480780
$733$	15.8075	0.583862	0.291931	−	0.956439i	$-0.405702\pi$
$733$	15.8075	0.583862	0.291931	+	0.956439i	$0.405702\pi$
$734$	6.54757	0.241675
$735$	0	0
$736$	23.2763	0.857976
$737$	−4.60544	−0.169643
$738$	65.0806	2.39565
$739$	1.54933	0.0569928	0.0284964	−	0.999594i	$-0.490928\pi$
$739$	1.54933	0.0569928	0.0284964	+	0.999594i	$0.490928\pi$
$740$	0	0
$741$	0	0
$742$	11.4192	0.419213
$743$	−38.1634	−1.40008	−0.700040	−	0.714103i	$-0.746835\pi$
$743$	−38.1634	−1.40008	−0.700040	+	0.714103i	$0.746835\pi$
$744$	−15.2942	−0.560711
$745$	0	0
$746$	59.2086	2.16778
$747$	31.7068	1.16009
$748$	20.2763	0.741375
$749$	−10.2344	−0.373958
$750$	0	0
$751$	−25.3482	−0.924970	−0.462485	−	0.886627i	$-0.653042\pi$
$751$	−25.3482	−0.924970	−0.462485	+	0.886627i	$0.653042\pi$
$752$	−3.81016	−0.138942
$753$	9.37464	0.341631
$754$	32.0077	1.16565
$755$	0	0
$756$	24.5895	0.894310
$757$	−42.3705	−1.53998	−0.769991	−	0.638054i	$-0.779740\pi$
$757$	−42.3705	−1.53998	−0.769991	+	0.638054i	$0.779740\pi$
$758$	64.4133	2.33960
$759$	−3.91622	−0.142150
$760$	0	0
$761$	−2.85710	−0.103570	−0.0517848	−	0.998658i	$-0.516491\pi$
$761$	−2.85710	−0.103570	−0.0517848	+	0.998658i	$0.516491\pi$
$762$	23.9691	0.868311
$763$	−14.4834	−0.524334
$764$	−45.3678	−1.64135
$765$	0	0
$766$	69.5836	2.51416
$767$	10.6932	0.386108
$768$	−19.9094	−0.718419
$769$	19.1206	0.689507	0.344754	−	0.938693i	$-0.387963\pi$
$769$	19.1206	0.689507	0.344754	+	0.938693i	$0.387963\pi$
$770$	0	0
$771$	−3.24897	−0.117009
$772$	−60.8813	−2.19116
$773$	−2.51485	−0.0904530	−0.0452265	−	0.998977i	$-0.514401\pi$
$773$	−2.51485	−0.0904530	−0.0452265	+	0.998977i	$0.514401\pi$
$774$	−56.7178	−2.03868
$775$	0	0
$776$	−44.9992	−1.61538
$777$	−4.10607	−0.147304
$778$	−8.46286	−0.303408
$779$	0	0
$780$	0	0
$781$	8.21751	0.294046
$782$	−49.7452	−1.77888
$783$	16.9273	0.604931
$784$	−30.8854	−1.10305
$785$	0	0
$786$	−32.7374	−1.16770
$787$	−2.72605	−0.0971733	−0.0485866	−	0.998819i	$-0.515472\pi$
$787$	−2.72605	−0.0971733	−0.0485866	+	0.998819i	$0.515472\pi$
$788$	35.0310	1.24793
$789$	15.6928	0.558680
$790$	0	0
$791$	2.00774	0.0713870
$792$	18.6212	0.661677
$793$	12.2736	0.435849
$794$	33.2294	1.17927
$795$	0	0
$796$	119.265	4.22722
$797$	−22.0327	−0.780439	−0.390219	−	0.920722i	$-0.627601\pi$
$797$	−22.0327	−0.780439	−0.390219	+	0.920722i	$0.627601\pi$
$798$	0	0
$799$	2.22668	0.0787743
$800$	0	0
$801$	6.24453	0.220640
$802$	43.3337	1.53017
$803$	7.26083	0.256229
$804$	11.1925	0.394730
$805$	0	0
$806$	26.3996	0.929887
$807$	−8.55768	−0.301244
$808$	13.2517	0.466192
$809$	54.7205	1.92387	0.961935	−	0.273278i	$-0.0881077\pi$
$809$	54.7205	1.92387	0.961935	+	0.273278i	$0.0881077\pi$
$810$	0	0
$811$	−2.31046	−0.0811312	−0.0405656	−	0.999177i	$-0.512916\pi$
$811$	−2.31046	−0.0811312	−0.0405656	+	0.999177i	$0.512916\pi$
$812$	31.4466	1.10356
$813$	−17.3422	−0.608219
$814$	−12.3182	−0.431753
$815$	0	0
$816$	−16.8084	−0.588412
$817$	0	0
$818$	−22.2772	−0.778906
$819$	−10.7142	−0.374384
$820$	0	0
$821$	1.11112	0.0387783	0.0193892	−	0.999812i	$-0.493828\pi$
$821$	1.11112	0.0387783	0.0193892	+	0.999812i	$0.493828\pi$
$822$	−16.8648	−0.588229
$823$	−20.6477	−0.719732	−0.359866	−	0.933004i	$-0.617178\pi$
$823$	−20.6477	−0.719732	−0.359866	+	0.933004i	$0.617178\pi$
$824$	76.1772	2.65376
$825$	0	0
$826$	15.2686	0.531262
$827$	−36.3054	−1.26246	−0.631231	−	0.775595i	$-0.717450\pi$
$827$	−36.3054	−1.26246	−0.631231	+	0.775595i	$0.717450\pi$
$828$	−57.5039	−1.99840
$829$	−7.14971	−0.248320	−0.124160	−	0.992262i	$-0.539624\pi$
$829$	−7.14971	−0.248320	−0.124160	+	0.992262i	$0.539624\pi$
$830$	0	0
$831$	10.7766	0.373837
$832$	4.45067	0.154299
$833$	18.0496	0.625383
$834$	−2.74422	−0.0950247
$835$	0	0
$836$	0	0
$837$	13.9614	0.482577
$838$	17.3200	0.598308
$839$	−34.6067	−1.19476	−0.597378	−	0.801960i	$-0.703791\pi$
$839$	−34.6067	−1.19476	−0.597378	+	0.801960i	$0.703791\pi$
$840$	0	0
$841$	−7.35235	−0.253529
$842$	−12.2121	−0.420858
$843$	−12.6560	−0.435896
$844$	−35.6091	−1.22571
$845$	0	0
$846$	3.74092	0.128616
$847$	14.7023	0.505178
$848$	−19.5398	−0.671001
$849$	7.38238	0.253363
$850$	0	0
$851$	20.7939	0.712804
$852$	−19.9709	−0.684192
$853$	−33.2508	−1.13849	−0.569243	−	0.822169i	$-0.692764\pi$
$853$	−33.2508	−1.13849	−0.569243	+	0.822169i	$0.692764\pi$
$854$	17.5253	0.599703
$855$	0	0
$856$	40.7888	1.39413
$857$	3.88619	0.132750	0.0663749	−	0.997795i	$-0.478857\pi$
$857$	3.88619	0.132750	0.0663749	+	0.997795i	$0.478857\pi$
$858$	5.31996	0.181620
$859$	1.65776	0.0565619	0.0282810	−	0.999600i	$-0.490997\pi$
$859$	1.65776	0.0565619	0.0282810	+	0.999600i	$0.490997\pi$
$860$	0	0
$861$	9.98545	0.340303
$862$	3.30096	0.112431
$863$	52.7187	1.79457	0.897284	−	0.441455i	$-0.145537\pi$
$863$	52.7187	1.79457	0.897284	+	0.441455i	$0.145537\pi$
$864$	−16.7219	−0.568892
$865$	0	0
$866$	−50.1958	−1.70572
$867$	−1.27301	−0.0432338
$868$	25.9368	0.880351
$869$	−11.6209	−0.394213
$870$	0	0
$871$	−10.5609	−0.357841
$872$	57.7229	1.95474
$873$	18.9691	0.642008
$874$	0	0
$875$	0	0
$876$	−17.6459	−0.596200
$877$	21.1898	0.715530	0.357765	−	0.933812i	$-0.383539\pi$
$877$	21.1898	0.715530	0.357765	+	0.933812i	$0.383539\pi$
$878$	−87.5271	−2.95390
$879$	−2.54488	−0.0858367
$880$	0	0
$881$	32.1010	1.08151	0.540755	−	0.841180i	$-0.318138\pi$
$881$	32.1010	1.08151	0.540755	+	0.841180i	$0.318138\pi$
$882$	30.3242	1.02107
$883$	47.2968	1.59167	0.795833	−	0.605516i	$-0.207033\pi$
$883$	47.2968	1.59167	0.795833	+	0.605516i	$0.207033\pi$
$884$	46.4962	1.56384
$885$	0	0
$886$	−43.0711	−1.44700
$887$	−10.5631	−0.354673	−0.177336	−	0.984150i	$-0.556748\pi$
$887$	−10.5631	−0.354673	−0.177336	+	0.984150i	$0.556748\pi$
$888$	16.3645	0.549158
$889$	−22.2199	−0.745231
$890$	0	0
$891$	−6.33544	−0.212245
$892$	68.2704	2.28586
$893$	0	0
$894$	18.5220	0.619468
$895$	0	0
$896$	20.4388	0.682813
$897$	−8.98040	−0.299847
$898$	94.7247	3.16101
$899$	17.8547	0.595489
$900$	0	0
$901$	11.4192	0.380429
$902$	29.9564	0.997438
$903$	−8.70233	−0.289596
$904$	−8.00175	−0.266134
$905$	0	0
$906$	−18.2490	−0.606281
$907$	−42.9205	−1.42515	−0.712575	−	0.701596i	$-0.752471\pi$
$907$	−42.9205	−1.42515	−0.712575	+	0.701596i	$0.752471\pi$
$908$	−43.5526	−1.44534
$909$	−5.58616	−0.185281
$910$	0	0
$911$	−55.1411	−1.82691	−0.913454	−	0.406942i	$-0.866595\pi$
$911$	−55.1411	−1.82691	−0.913454	+	0.406942i	$0.866595\pi$
$912$	0	0
$913$	14.5945	0.483008
$914$	−23.0702	−0.763093
$915$	0	0
$916$	88.7538	2.93251
$917$	30.3482	1.00219
$918$	35.7374	1.17951
$919$	−24.5577	−0.810083	−0.405041	−	0.914298i	$-0.632743\pi$
$919$	−24.5577	−0.810083	−0.405041	+	0.914298i	$0.632743\pi$
$920$	0	0
$921$	−15.1266	−0.498438
$922$	−61.9053	−2.03874
$923$	18.8438	0.620251
$924$	5.22668	0.171945
$925$	0	0
$926$	0.634858	0.0208627
$927$	−32.1121	−1.05470
$928$	−21.3851	−0.701999
$929$	−22.2772	−0.730893	−0.365446	−	0.930832i	$-0.619084\pi$
$929$	−22.2772	−0.730893	−0.365446	+	0.930832i	$0.619084\pi$
$930$	0	0
$931$	0	0
$932$	−15.5936	−0.510785
$933$	−2.25908	−0.0739588
$934$	−38.8976	−1.27277
$935$	0	0
$936$	42.7009	1.39572
$937$	9.55169	0.312040	0.156020	−	0.987754i	$-0.450134\pi$
$937$	9.55169	0.312040	0.156020	+	0.987754i	$0.450134\pi$
$938$	−15.0797	−0.492368
$939$	14.9403	0.487557
$940$	0	0
$941$	−55.7256	−1.81660	−0.908301	−	0.418318i	$-0.862620\pi$
$941$	−55.7256	−1.81660	−0.908301	+	0.418318i	$0.862620\pi$
$942$	−18.1685	−0.591961
$943$	−50.5681	−1.64672
$944$	−26.1266	−0.850348
$945$	0	0
$946$	−26.1070	−0.848812
$947$	27.0428	0.878774	0.439387	−	0.898298i	$-0.355196\pi$
$947$	27.0428	0.878774	0.439387	+	0.898298i	$0.355196\pi$
$948$	28.2422	0.917263
$949$	16.6500	0.540482
$950$	0	0
$951$	−17.0490	−0.552852
$952$	36.2918	1.17622
$953$	−23.1310	−0.749288	−0.374644	−	0.927169i	$-0.622235\pi$
$953$	−23.1310	−0.749288	−0.374644	+	0.927169i	$0.622235\pi$
$954$	19.1848	0.621131
$955$	0	0
$956$	52.8212	1.70836
$957$	3.59802	0.116308
$958$	−1.82119	−0.0588401
$959$	15.6340	0.504849
$960$	0	0
$961$	−16.2736	−0.524956
$962$	−28.2472	−0.910727
$963$	−17.1943	−0.554078
$964$	56.9154	1.83312
$965$	0	0
$966$	−12.8229	−0.412572
$967$	−39.0351	−1.25528	−0.627642	−	0.778502i	$-0.715980\pi$
$967$	−39.0351	−1.25528	−0.627642	+	0.778502i	$0.715980\pi$
$968$	−58.5954	−1.88333
$969$	0	0
$970$	0	0
$971$	−41.2026	−1.32226	−0.661128	−	0.750273i	$-0.729922\pi$
$971$	−41.2026	−1.32226	−0.661128	+	0.750273i	$0.729922\pi$
$972$	63.5458	2.03823
$973$	2.54395	0.0815552
$974$	−29.7442	−0.953066
$975$	0	0
$976$	−29.9881	−0.959897
$977$	−22.4938	−0.719641	−0.359821	−	0.933022i	$-0.617162\pi$
$977$	−22.4938	−0.719641	−0.359821	+	0.933022i	$0.617162\pi$
$978$	10.4662	0.334671
$979$	2.87433	0.0918641
$980$	0	0
$981$	−24.3327	−0.776885
$982$	0.224927	0.00717771
$983$	44.5461	1.42080	0.710401	−	0.703798i	$-0.248514\pi$
$983$	44.5461	1.42080	0.710401	+	0.703798i	$0.248514\pi$
$984$	−39.7965	−1.26867
$985$	0	0
$986$	45.7033	1.45549
$987$	0.573978	0.0182699
$988$	0	0
$989$	44.0702	1.40135
$990$	0	0
$991$	−45.3296	−1.43994	−0.719971	−	0.694005i	$-0.755845\pi$
$991$	−45.3296	−1.43994	−0.719971	+	0.694005i	$0.755845\pi$
$992$	−17.6382	−0.560012
$993$	12.4305	0.394469
$994$	26.9067	0.853430
$995$	0	0
$996$	−35.4688	−1.12387
$997$	10.4911	0.332258	0.166129	−	0.986104i	$-0.446873\pi$
$997$	10.4911	0.332258	0.166129	+	0.986104i	$0.446873\pi$
$998$	37.1976	1.17747
$999$	−14.9385	−0.472634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.bd.1.3		3
5.4	even	2		361.2.a.g.1.1		3
15.14	odd	2		3249.2.a.z.1.3		3
19.4	even	9		475.2.l.a.301.1		6
19.5	even	9		475.2.l.a.101.1		6
19.18	odd	2		9025.2.a.x.1.1		3
20.19	odd	2		5776.2.a.br.1.2		3
95.4	even	18		19.2.e.a.16.1	yes	6
95.9	even	18		361.2.e.g.62.1		6
95.14	odd	18		361.2.e.h.234.1		6
95.23	odd	36		475.2.u.a.149.2		12
95.24	even	18		19.2.e.a.6.1	✓	6
95.29	odd	18		361.2.e.a.62.1		6
95.34	odd	18		361.2.e.h.54.1		6
95.42	odd	36		475.2.u.a.149.1		12
95.43	odd	36		475.2.u.a.424.1		12
95.44	even	18		361.2.e.f.245.1		6
95.49	even	6		361.2.c.i.292.3		6
95.54	even	18		361.2.e.f.28.1		6
95.59	odd	18		361.2.e.a.99.1		6
95.62	odd	36		475.2.u.a.424.2		12
95.64	even	6		361.2.c.i.68.3		6
95.69	odd	6		361.2.c.h.68.1		6
95.74	even	18		361.2.e.g.99.1		6
95.79	odd	18		361.2.e.b.28.1		6
95.84	odd	6		361.2.c.h.292.1		6
95.89	odd	18		361.2.e.b.245.1		6
95.94	odd	2		361.2.a.h.1.3		3
285.119	odd	18		171.2.u.c.82.1		6
285.194	odd	18		171.2.u.c.73.1		6
285.284	even	2		3249.2.a.s.1.1		3
380.99	odd	18		304.2.u.b.225.1		6
380.119	odd	18		304.2.u.b.177.1		6
380.379	even	2		5776.2.a.bi.1.2		3
665.4	even	18		931.2.x.a.814.1		6
665.24	odd	18		931.2.v.a.177.1		6
665.194	odd	18		931.2.v.a.263.1		6
665.214	even	18		931.2.v.b.177.1		6
665.289	even	18		931.2.v.b.263.1		6
665.384	odd	18		931.2.w.a.491.1		6
665.404	odd	18		931.2.x.b.557.1		6
665.479	odd	18		931.2.x.b.814.1		6
665.499	even	18		931.2.x.a.557.1		6
665.594	odd	18		931.2.w.a.785.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	95.24	even	18
19.2.e.a.16.1	yes	6	95.4	even	18
171.2.u.c.73.1		6	285.194	odd	18
171.2.u.c.82.1		6	285.119	odd	18
304.2.u.b.177.1		6	380.119	odd	18
304.2.u.b.225.1		6	380.99	odd	18
361.2.a.g.1.1		3	5.4	even	2
361.2.a.h.1.3		3	95.94	odd	2
361.2.c.h.68.1		6	95.69	odd	6
361.2.c.h.292.1		6	95.84	odd	6
361.2.c.i.68.3		6	95.64	even	6
361.2.c.i.292.3		6	95.49	even	6
361.2.e.a.62.1		6	95.29	odd	18
361.2.e.a.99.1		6	95.59	odd	18
361.2.e.b.28.1		6	95.79	odd	18
361.2.e.b.245.1		6	95.89	odd	18
361.2.e.f.28.1		6	95.54	even	18
361.2.e.f.245.1		6	95.44	even	18
361.2.e.g.62.1		6	95.9	even	18
361.2.e.g.99.1		6	95.74	even	18
361.2.e.h.54.1		6	95.34	odd	18
361.2.e.h.234.1		6	95.14	odd	18
475.2.l.a.101.1		6	19.5	even	9
475.2.l.a.301.1		6	19.4	even	9
475.2.u.a.149.1		12	95.42	odd	36
475.2.u.a.149.2		12	95.23	odd	36
475.2.u.a.424.1		12	95.43	odd	36
475.2.u.a.424.2		12	95.62	odd	36
931.2.v.a.177.1		6	665.24	odd	18
931.2.v.a.263.1		6	665.194	odd	18
931.2.v.b.177.1		6	665.214	even	18
931.2.v.b.263.1		6	665.289	even	18
931.2.w.a.491.1		6	665.384	odd	18
931.2.w.a.785.1		6	665.594	odd	18
931.2.x.a.557.1		6	665.499	even	18
931.2.x.a.814.1		6	665.4	even	18
931.2.x.b.557.1		6	665.404	odd	18
931.2.x.b.814.1		6	665.479	odd	18
3249.2.a.s.1.1		3	285.284	even	2
3249.2.a.z.1.3		3	15.14	odd	2
5776.2.a.bi.1.2		3	380.379	even	2
5776.2.a.br.1.2		3	20.19	odd	2
9025.2.a.x.1.1		3	19.18	odd	2
9025.2.a.bd.1.3		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.53209 q^{2} +0.652704 q^{3} +4.41147 q^{4} +1.65270 q^{6} -1.53209 q^{7} +6.10607 q^{8} -2.57398 q^{9} +O(q^{10})\)	\(q+2.53209 q^{2} +0.652704 q^{3} +4.41147 q^{4} +1.65270 q^{6} -1.53209 q^{7} +6.10607 q^{8} -2.57398 q^{9} -1.18479 q^{11} +2.87939 q^{12} -2.71688 q^{13} -3.87939 q^{14} +6.63816 q^{16} -3.87939 q^{17} -6.51754 q^{18} -1.00000 q^{21} -3.00000 q^{22} +5.06418 q^{23} +3.98545 q^{24} -6.87939 q^{26} -3.63816 q^{27} -6.75877 q^{28} -4.65270 q^{29} -3.83750 q^{31} +4.59627 q^{32} -0.773318 q^{33} -9.82295 q^{34} -11.3550 q^{36} +4.10607 q^{37} -1.77332 q^{39} -9.98545 q^{41} -2.53209 q^{42} +8.70233 q^{43} -5.22668 q^{44} +12.8229 q^{46} -0.573978 q^{47} +4.33275 q^{48} -4.65270 q^{49} -2.53209 q^{51} -11.9855 q^{52} -2.94356 q^{53} -9.21213 q^{54} -9.35504 q^{56} -11.7811 q^{58} -3.93582 q^{59} -4.51754 q^{61} -9.71688 q^{62} +3.94356 q^{63} -1.63816 q^{64} -1.95811 q^{66} +3.88713 q^{67} -17.1138 q^{68} +3.30541 q^{69} -6.93582 q^{71} -15.7169 q^{72} -6.12836 q^{73} +10.3969 q^{74} +1.81521 q^{77} -4.49020 q^{78} +9.80840 q^{79} +5.34730 q^{81} -25.2841 q^{82} -12.3182 q^{83} -4.41147 q^{84} +22.0351 q^{86} -3.03684 q^{87} -7.23442 q^{88} -2.42602 q^{89} +4.16250 q^{91} +22.3405 q^{92} -2.50475 q^{93} -1.45336 q^{94} +3.00000 q^{96} -7.36959 q^{97} -11.7811 q^{98} +3.04963 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{6} + 6 q^{8}+O(q^{10}) \) 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

Varieties

Fields

Representations

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Database

Properties

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