LMFDB - Embedded newform 3549.2.a.y.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.121819537.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 25x^{4} + 55x^{3} + 224x^{2} - 252x - 728 $ x^6 - 3x^5 - 25x^4 + 55x^3 + 224x^2 - 252*x - 728
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$4.06987$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24698 q^{2} -1.00000 q^{3} -0.445042 q^{4} +4.06987 q^{5} -1.24698 q^{6} -1.00000 q^{7} -3.04892 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.24698 q^{2} -1.00000 q^{3} -0.445042 q^{4} +4.06987 q^{5} -1.24698 q^{6} -1.00000 q^{7} -3.04892 q^{8} +1.00000 q^{9} +5.07504 q^{10} -0.456669 q^{11} +0.445042 q^{12} -1.24698 q^{14} -4.06987 q^{15} -2.91185 q^{16} -5.72977 q^{17} +1.24698 q^{18} +0.188738 q^{19} -1.81126 q^{20} +1.00000 q^{21} -0.569457 q^{22} -5.05824 q^{23} +3.04892 q^{24} +11.5638 q^{25} -1.00000 q^{27} +0.445042 q^{28} -6.16401 q^{29} -5.07504 q^{30} +1.19391 q^{31} +2.46681 q^{32} +0.456669 q^{33} -7.14491 q^{34} -4.06987 q^{35} -0.445042 q^{36} -10.7880 q^{37} +0.235353 q^{38} -12.4087 q^{40} -2.45519 q^{41} +1.24698 q^{42} +4.28991 q^{43} +0.203237 q^{44} +4.06987 q^{45} -6.30752 q^{46} -7.89748 q^{47} +2.91185 q^{48} +1.00000 q^{49} +14.4199 q^{50} +5.72977 q^{51} +5.67810 q^{53} -1.24698 q^{54} -1.85858 q^{55} +3.04892 q^{56} -0.188738 q^{57} -7.68639 q^{58} -13.4353 q^{59} +1.81126 q^{60} -0.497739 q^{61} +1.48878 q^{62} -1.00000 q^{63} +8.89977 q^{64} +0.569457 q^{66} +12.6957 q^{67} +2.54999 q^{68} +5.05824 q^{69} -5.07504 q^{70} -13.4669 q^{71} -3.04892 q^{72} +7.94961 q^{73} -13.4524 q^{74} -11.5638 q^{75} -0.0839964 q^{76} +0.456669 q^{77} +4.07089 q^{79} -11.8509 q^{80} +1.00000 q^{81} -3.06157 q^{82} -11.0702 q^{83} -0.445042 q^{84} -23.3194 q^{85} +5.34943 q^{86} +6.16401 q^{87} +1.39235 q^{88} +15.7948 q^{89} +5.07504 q^{90} +2.25113 q^{92} -1.19391 q^{93} -9.84799 q^{94} +0.768140 q^{95} -2.46681 q^{96} -9.85870 q^{97} +1.24698 q^{98} -0.456669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 6 * q^7 + 6 * q^9	$ 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9} - q^{10} + 2 q^{12} + 2 q^{14} - 3 q^{15} - 10 q^{16} - 9 q^{17} - 2 q^{18} + 11 q^{19} - q^{20} + 6 q^{21} + 7 q^{22} - 11 q^{23} + 29 q^{25} - 6 q^{27} + 2 q^{28} - 10 q^{29} + q^{30} + 7 q^{31} + 8 q^{32} + 10 q^{34} - 3 q^{35} - 2 q^{36} - 20 q^{37} - 6 q^{38} - 10 q^{41} - 2 q^{42} - 9 q^{43} + 3 q^{45} - 8 q^{46} + 36 q^{47} + 10 q^{48} + 6 q^{49} + 9 q^{50} + 9 q^{51} - 12 q^{53} + 2 q^{54} - 29 q^{55} - 11 q^{57} - 6 q^{58} - 41 q^{59} + q^{60} - 24 q^{61} - 6 q^{63} + 8 q^{64} - 7 q^{66} + 15 q^{67} + 10 q^{68} + 11 q^{69} + q^{70} + 13 q^{71} + 25 q^{73} + 2 q^{74} - 29 q^{75} + q^{76} - 16 q^{79} - 5 q^{80} + 6 q^{81} + q^{82} - 2 q^{83} - 2 q^{84} - 33 q^{85} - 4 q^{86} + 10 q^{87} - 14 q^{88} + 15 q^{89} - q^{90} + 13 q^{92} - 7 q^{93} - 33 q^{94} - 23 q^{95} - 8 q^{96} + 10 q^{97} - 2 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 6 * q^7 + 6 * q^9 - q^10 + 2 * q^12 + 2 * q^14 - 3 * q^15 - 10 * q^16 - 9 * q^17 - 2 * q^18 + 11 * q^19 - q^20 + 6 * q^21 + 7 * q^22 - 11 * q^23 + 29 * q^25 - 6 * q^27 + 2 * q^28 - 10 * q^29 + q^30 + 7 * q^31 + 8 * q^32 + 10 * q^34 - 3 * q^35 - 2 * q^36 - 20 * q^37 - 6 * q^38 - 10 * q^41 - 2 * q^42 - 9 * q^43 + 3 * q^45 - 8 * q^46 + 36 * q^47 + 10 * q^48 + 6 * q^49 + 9 * q^50 + 9 * q^51 - 12 * q^53 + 2 * q^54 - 29 * q^55 - 11 * q^57 - 6 * q^58 - 41 * q^59 + q^60 - 24 * q^61 - 6 * q^63 + 8 * q^64 - 7 * q^66 + 15 * q^67 + 10 * q^68 + 11 * q^69 + q^70 + 13 * q^71 + 25 * q^73 + 2 * q^74 - 29 * q^75 + q^76 - 16 * q^79 - 5 * q^80 + 6 * q^81 + q^82 - 2 * q^83 - 2 * q^84 - 33 * q^85 - 4 * q^86 + 10 * q^87 - 14 * q^88 + 15 * q^89 - q^90 + 13 * q^92 - 7 * q^93 - 33 * q^94 - 23 * q^95 - 8 * q^96 + 10 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.24698	0.881748	0.440874	−	0.897569i	$-0.354669\pi$
$2$	1.24698	0.881748	0.440874	+	0.897569i	$0.354669\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.445042	−0.222521
$5$	4.06987	1.82010	0.910050	−	0.414498i	$-0.136043\pi$
$5$	4.06987	1.82010	0.910050	+	0.414498i	$0.136043\pi$
$6$	−1.24698	−0.509077
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.04892	−1.07796
$9$	1.00000	0.333333
$10$	5.07504	1.60487
$11$	−0.456669	−0.137691	−0.0688454	−	0.997627i	$-0.521932\pi$
$11$	−0.456669	−0.137691	−0.0688454	+	0.997627i	$0.521932\pi$
$12$	0.445042	0.128473
$13$	0	0
$13$	0	0
$14$	−1.24698	−0.333269
$15$	−4.06987	−1.05084
$16$	−2.91185	−0.727963
$17$	−5.72977	−1.38967	−0.694837	−	0.719167i	$-0.744524\pi$
$17$	−5.72977	−1.38967	−0.694837	+	0.719167i	$0.744524\pi$
$18$	1.24698	0.293916
$19$	0.188738	0.0432995	0.0216498	−	0.999766i	$-0.493108\pi$
$19$	0.188738	0.0432995	0.0216498	+	0.999766i	$0.493108\pi$
$20$	−1.81126	−0.405010
$21$	1.00000	0.218218
$22$	−0.569457	−0.121409
$23$	−5.05824	−1.05472	−0.527358	−	0.849643i	$-0.676817\pi$
$23$	−5.05824	−1.05472	−0.527358	+	0.849643i	$0.676817\pi$
$24$	3.04892	0.622358
$25$	11.5638	2.31277
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0.445042	0.0841050
$29$	−6.16401	−1.14463	−0.572314	−	0.820035i	$-0.693954\pi$
$29$	−6.16401	−1.14463	−0.572314	+	0.820035i	$0.693954\pi$
$30$	−5.07504	−0.926572
$31$	1.19391	0.214433	0.107217	−	0.994236i	$-0.465806\pi$
$31$	1.19391	0.214433	0.107217	+	0.994236i	$0.465806\pi$
$32$	2.46681	0.436075
$33$	0.456669	0.0794958
$34$	−7.14491	−1.22534
$35$	−4.06987	−0.687933
$36$	−0.445042	−0.0741736
$37$	−10.7880	−1.77354	−0.886769	−	0.462212i	$-0.847056\pi$
$37$	−10.7880	−1.77354	−0.886769	+	0.462212i	$0.847056\pi$
$38$	0.235353	0.0381793
$39$	0	0
$40$	−12.4087	−1.96199
$41$	−2.45519	−0.383436	−0.191718	−	0.981450i	$-0.561406\pi$
$41$	−2.45519	−0.383436	−0.191718	+	0.981450i	$0.561406\pi$
$42$	1.24698	0.192413
$43$	4.28991	0.654205	0.327102	−	0.944989i	$-0.393928\pi$
$43$	4.28991	0.654205	0.327102	+	0.944989i	$0.393928\pi$
$44$	0.203237	0.0306391
$45$	4.06987	0.606700
$46$	−6.30752	−0.929994
$47$	−7.89748	−1.15197	−0.575983	−	0.817462i	$-0.695380\pi$
$47$	−7.89748	−1.15197	−0.575983	+	0.817462i	$0.695380\pi$
$48$	2.91185	0.420290
$49$	1.00000	0.142857
$50$	14.4199	2.03928
$51$	5.72977	0.802329
$52$	0	0
$53$	5.67810	0.779947	0.389973	−	0.920826i	$-0.372484\pi$
$53$	5.67810	0.779947	0.389973	+	0.920826i	$0.372484\pi$
$54$	−1.24698	−0.169692
$55$	−1.85858	−0.250611
$56$	3.04892	0.407429
$57$	−0.188738	−0.0249990
$58$	−7.68639	−1.00927
$59$	−13.4353	−1.74912	−0.874561	−	0.484915i	$-0.838850\pi$
$59$	−13.4353	−1.74912	−0.874561	+	0.484915i	$0.838850\pi$
$60$	1.81126	0.233833
$61$	−0.497739	−0.0637289	−0.0318644	−	0.999492i	$-0.510144\pi$
$61$	−0.497739	−0.0637289	−0.0318644	+	0.999492i	$0.510144\pi$
$62$	1.48878	0.189076
$63$	−1.00000	−0.125988
$64$	8.89977	1.11247
$65$	0	0
$66$	0.569457	0.0700953
$67$	12.6957	1.55103	0.775514	−	0.631330i	$-0.217491\pi$
$67$	12.6957	1.55103	0.775514	+	0.631330i	$0.217491\pi$
$68$	2.54999	0.309232
$69$	5.05824	0.608941
$70$	−5.07504	−0.606584
$71$	−13.4669	−1.59823	−0.799115	−	0.601178i	$-0.794698\pi$
$71$	−13.4669	−1.59823	−0.799115	+	0.601178i	$0.794698\pi$
$72$	−3.04892	−0.359318
$73$	7.94961	0.930431	0.465216	−	0.885197i	$-0.345977\pi$
$73$	7.94961	0.930431	0.465216	+	0.885197i	$0.345977\pi$
$74$	−13.4524	−1.56381
$75$	−11.5638	−1.33528
$76$	−0.0839964	−0.00963505
$77$	0.456669	0.0520422
$78$	0	0
$79$	4.07089	0.458011	0.229006	−	0.973425i	$-0.426453\pi$
$79$	4.07089	0.458011	0.229006	+	0.973425i	$0.426453\pi$
$80$	−11.8509	−1.32497
$81$	1.00000	0.111111
$82$	−3.06157	−0.338093
$83$	−11.0702	−1.21512	−0.607558	−	0.794275i	$-0.707851\pi$
$83$	−11.0702	−1.21512	−0.607558	+	0.794275i	$0.707851\pi$
$84$	−0.445042	−0.0485580
$85$	−23.3194	−2.52935
$86$	5.34943	0.576843
$87$	6.16401	0.660851
$88$	1.39235	0.148425
$89$	15.7948	1.67425	0.837124	−	0.547013i	$-0.184235\pi$
$89$	15.7948	1.67425	0.837124	+	0.547013i	$0.184235\pi$
$90$	5.07504	0.534956
$91$	0	0
$92$	2.25113	0.234696
$93$	−1.19391	−0.123803
$94$	−9.84799	−1.01574
$95$	0.768140	0.0788095
$96$	−2.46681	−0.251768
$97$	−9.85870	−1.00100	−0.500500	−	0.865737i	$-0.666850\pi$
$97$	−9.85870	−1.00100	−0.500500	+	0.865737i	$0.666850\pi$
$98$	1.24698	0.125964
$99$	−0.456669	−0.0458969
$100$	−5.14639	−0.514639
$101$	−2.65786	−0.264467	−0.132233	−	0.991219i	$-0.542215\pi$
$101$	−2.65786	−0.264467	−0.132233	+	0.991219i	$0.542215\pi$
$102$	7.14491	0.707452
$103$	−4.48234	−0.441658	−0.220829	−	0.975313i	$-0.570876\pi$
$103$	−4.48234	−0.441658	−0.220829	+	0.975313i	$0.570876\pi$
$104$	0	0
$105$	4.06987	0.397178
$106$	7.08047	0.687716
$107$	−14.4760	−1.39945	−0.699726	−	0.714411i	$-0.746695\pi$
$107$	−14.4760	−1.39945	−0.699726	+	0.714411i	$0.746695\pi$
$108$	0.445042	0.0428242
$109$	−13.9209	−1.33338	−0.666692	−	0.745334i	$-0.732290\pi$
$109$	−13.9209	−1.33338	−0.666692	+	0.745334i	$0.732290\pi$
$110$	−2.31761	−0.220976
$111$	10.7880	1.02395
$112$	2.91185	0.275144
$113$	19.8159	1.86412	0.932061	−	0.362300i	$-0.118009\pi$
$113$	19.8159	1.86412	0.932061	+	0.362300i	$0.118009\pi$
$114$	−0.235353	−0.0220428
$115$	−20.5864	−1.91969
$116$	2.74324	0.254704
$117$	0	0
$118$	−16.7535	−1.54228
$119$	5.72977	0.525247
$120$	12.4087	1.13275
$121$	−10.7915	−0.981041
$122$	−0.620670	−0.0561928
$123$	2.45519	0.221377
$124$	−0.531341	−0.0477158
$125$	26.7139	2.38936
$126$	−1.24698	−0.111090
$127$	9.40331	0.834409	0.417205	−	0.908813i	$-0.363010\pi$
$127$	9.40331	0.834409	0.417205	+	0.908813i	$0.363010\pi$
$128$	6.16421	0.544844
$129$	−4.28991	−0.377705
$130$	0	0
$131$	−9.94710	−0.869082	−0.434541	−	0.900652i	$-0.643089\pi$
$131$	−9.94710	−0.869082	−0.434541	+	0.900652i	$0.643089\pi$
$132$	−0.203237	−0.0176895
$133$	−0.188738	−0.0163657
$134$	15.8313	1.36762
$135$	−4.06987	−0.350278
$136$	17.4696	1.49801
$137$	1.17436	0.100332	0.0501662	−	0.998741i	$-0.484025\pi$
$137$	1.17436	0.100332	0.0501662	+	0.998741i	$0.484025\pi$
$138$	6.30752	0.536932
$139$	1.64097	0.139185	0.0695925	−	0.997576i	$-0.477830\pi$
$139$	1.64097	0.139185	0.0695925	+	0.997576i	$0.477830\pi$
$140$	1.81126	0.153080
$141$	7.89748	0.665088
$142$	−16.7930	−1.40924
$143$	0	0
$144$	−2.91185	−0.242654
$145$	−25.0867	−2.08334
$146$	9.91300	0.820405
$147$	−1.00000	−0.0824786
$148$	4.80112	0.394649
$149$	24.0833	1.97298	0.986489	−	0.163829i	$-0.0523845\pi$
$149$	24.0833	1.97298	0.986489	+	0.163829i	$0.0523845\pi$
$150$	−14.4199	−1.17738
$151$	−2.86662	−0.233283	−0.116641	−	0.993174i	$-0.537213\pi$
$151$	−2.86662	−0.233283	−0.116641	+	0.993174i	$0.537213\pi$
$152$	−0.575447	−0.0466749
$153$	−5.72977	−0.463225
$154$	0.569457	0.0458881
$155$	4.85907	0.390290
$156$	0	0
$157$	−1.16734	−0.0931637	−0.0465819	−	0.998914i	$-0.514833\pi$
$157$	−1.16734	−0.0931637	−0.0465819	+	0.998914i	$0.514833\pi$
$158$	5.07632	0.403850
$159$	−5.67810	−0.450303
$160$	10.0396	0.793700
$161$	5.05824	0.398645
$162$	1.24698	0.0979720
$163$	−11.3245	−0.887003	−0.443501	−	0.896274i	$-0.646264\pi$
$163$	−11.3245	−0.887003	−0.443501	+	0.896274i	$0.646264\pi$
$164$	1.09266	0.0853224
$165$	1.85858	0.144690
$166$	−13.8044	−1.07143
$167$	18.2168	1.40966	0.704830	−	0.709376i	$-0.251023\pi$
$167$	18.2168	1.40966	0.704830	+	0.709376i	$0.251023\pi$
$168$	−3.04892	−0.235229
$169$	0	0
$170$	−29.0788	−2.23025
$171$	0.188738	0.0144332
$172$	−1.90919	−0.145574
$173$	−20.0690	−1.52581	−0.762907	−	0.646508i	$-0.776229\pi$
$173$	−20.0690	−1.52581	−0.762907	+	0.646508i	$0.776229\pi$
$174$	7.68639	0.582704
$175$	−11.5638	−0.874143
$176$	1.32975	0.100234
$177$	13.4353	1.00986
$178$	19.6958	1.47627
$179$	−9.37645	−0.700829	−0.350415	−	0.936595i	$-0.613959\pi$
$179$	−9.37645	−0.700829	−0.350415	+	0.936595i	$0.613959\pi$
$180$	−1.81126	−0.135003
$181$	2.71444	0.201763	0.100881	−	0.994898i	$-0.467834\pi$
$181$	2.71444	0.201763	0.100881	+	0.994898i	$0.467834\pi$
$182$	0	0
$183$	0.497739	0.0367939
$184$	15.4222	1.13694
$185$	−43.9058	−3.22802
$186$	−1.48878	−0.109163
$187$	2.61661	0.191345
$188$	3.51471	0.256336
$189$	1.00000	0.0727393
$190$	0.957855	0.0694901
$191$	−3.19539	−0.231210	−0.115605	−	0.993295i	$-0.536881\pi$
$191$	−3.19539	−0.231210	−0.115605	+	0.993295i	$0.536881\pi$
$192$	−8.89977	−0.642286
$193$	−5.98812	−0.431034	−0.215517	−	0.976500i	$-0.569144\pi$
$193$	−5.98812	−0.431034	−0.215517	+	0.976500i	$0.569144\pi$
$194$	−12.2936	−0.882629
$195$	0	0
$196$	−0.445042	−0.0317887
$197$	3.38614	0.241253	0.120626	−	0.992698i	$-0.461510\pi$
$197$	3.38614	0.241253	0.120626	+	0.992698i	$0.461510\pi$
$198$	−0.569457	−0.0404695
$199$	−15.8519	−1.12371	−0.561855	−	0.827235i	$-0.689912\pi$
$199$	−15.8519	−1.12371	−0.561855	+	0.827235i	$0.689912\pi$
$200$	−35.2572	−2.49306
$201$	−12.6957	−0.895487
$202$	−3.31430	−0.233193
$203$	6.16401	0.432629
$204$	−2.54999	−0.178535
$205$	−9.99228	−0.697891
$206$	−5.58939	−0.389431
$207$	−5.05824	−0.351572
$208$	0	0
$209$	−0.0861909	−0.00596195
$210$	5.07504	0.350211
$211$	−15.1520	−1.04311	−0.521554	−	0.853218i	$-0.674647\pi$
$211$	−15.1520	−1.04311	−0.521554	+	0.853218i	$0.674647\pi$
$212$	−2.52699	−0.173555
$213$	13.4669	0.922739
$214$	−18.0513	−1.23396
$215$	17.4594	1.19072
$216$	3.04892	0.207453
$217$	−1.19391	−0.0810481
$218$	−17.3591	−1.17571
$219$	−7.94961	−0.537185
$220$	0.827147	0.0557662
$221$	0	0
$222$	13.4524	0.902868
$223$	−3.29902	−0.220918	−0.110459	−	0.993881i	$-0.535232\pi$
$223$	−3.29902	−0.220918	−0.110459	+	0.993881i	$0.535232\pi$
$224$	−2.46681	−0.164821
$225$	11.5638	0.770922
$226$	24.7100	1.64369
$227$	−4.46977	−0.296669	−0.148335	−	0.988937i	$-0.547391\pi$
$227$	−4.46977	−0.296669	−0.148335	+	0.988937i	$0.547391\pi$
$228$	0.0839964	0.00556280
$229$	1.06941	0.0706684	0.0353342	−	0.999376i	$-0.488750\pi$
$229$	1.06941	0.0706684	0.0353342	+	0.999376i	$0.488750\pi$
$230$	−25.6708	−1.69268
$231$	−0.456669	−0.0300466
$232$	18.7936	1.23386
$233$	0.549905	0.0360255	0.0180127	−	0.999838i	$-0.494266\pi$
$233$	0.549905	0.0360255	0.0180127	+	0.999838i	$0.494266\pi$
$234$	0	0
$235$	−32.1417	−2.09669
$236$	5.97925	0.389216
$237$	−4.07089	−0.264433
$238$	7.14491	0.463136
$239$	−26.8711	−1.73815	−0.869074	−	0.494682i	$-0.835284\pi$
$239$	−26.8711	−1.73815	−0.869074	+	0.494682i	$0.835284\pi$
$240$	11.8509	0.764970
$241$	5.20011	0.334969	0.167484	−	0.985875i	$-0.446436\pi$
$241$	5.20011	0.334969	0.167484	+	0.985875i	$0.446436\pi$
$242$	−13.4567	−0.865031
$243$	−1.00000	−0.0641500
$244$	0.221514	0.0141810
$245$	4.06987	0.260014
$246$	3.06157	0.195198
$247$	0	0
$248$	−3.64014	−0.231149
$249$	11.0702	0.701548
$250$	33.3117	2.10682
$251$	4.29627	0.271178	0.135589	−	0.990765i	$-0.456707\pi$
$251$	4.29627	0.271178	0.135589	+	0.990765i	$0.456707\pi$
$252$	0.445042	0.0280350
$253$	2.30994	0.145225
$254$	11.7257	0.735738
$255$	23.3194	1.46032
$256$	−10.1129	−0.632056
$257$	−6.70512	−0.418254	−0.209127	−	0.977888i	$-0.567062\pi$
$257$	−6.70512	−0.418254	−0.209127	+	0.977888i	$0.567062\pi$
$258$	−5.34943	−0.333041
$259$	10.7880	0.670335
$260$	0	0
$261$	−6.16401	−0.381543
$262$	−12.4038	−0.766311
$263$	−2.52812	−0.155891	−0.0779453	−	0.996958i	$-0.524836\pi$
$263$	−2.52812	−0.155891	−0.0779453	+	0.996958i	$0.524836\pi$
$264$	−1.39235	−0.0856929
$265$	23.1091	1.41958
$266$	−0.235353	−0.0144304
$267$	−15.7948	−0.966628
$268$	−5.65013	−0.345136
$269$	9.69741	0.591261	0.295631	−	0.955302i	$-0.404470\pi$
$269$	9.69741	0.591261	0.295631	+	0.955302i	$0.404470\pi$
$270$	−5.07504	−0.308857
$271$	−13.1875	−0.801081	−0.400541	−	0.916279i	$-0.631178\pi$
$271$	−13.1875	−0.801081	−0.400541	+	0.916279i	$0.631178\pi$
$272$	16.6843	1.01163
$273$	0	0
$274$	1.46440	0.0884679
$275$	−5.28084	−0.318447
$276$	−2.25113	−0.135502
$277$	6.42805	0.386224	0.193112	−	0.981177i	$-0.438142\pi$
$277$	6.42805	0.386224	0.193112	+	0.981177i	$0.438142\pi$
$278$	2.04625	0.122726
$279$	1.19391	0.0714777
$280$	12.4087	0.741561
$281$	−20.0959	−1.19882	−0.599411	−	0.800442i	$-0.704598\pi$
$281$	−20.0959	−1.19882	−0.599411	+	0.800442i	$0.704598\pi$
$282$	9.84799	0.586439
$283$	21.0787	1.25300	0.626500	−	0.779421i	$-0.284487\pi$
$283$	21.0787	1.25300	0.626500	+	0.779421i	$0.284487\pi$
$284$	5.99335	0.355640
$285$	−0.768140	−0.0455007
$286$	0	0
$287$	2.45519	0.144925
$288$	2.46681	0.145358
$289$	15.8303	0.931194
$290$	−31.2826	−1.83698
$291$	9.85870	0.577927
$292$	−3.53791	−0.207040
$293$	28.0069	1.63618	0.818091	−	0.575089i	$-0.195032\pi$
$293$	28.0069	1.63618	0.818091	+	0.575089i	$0.195032\pi$
$294$	−1.24698	−0.0727253
$295$	−54.6798	−3.18358
$296$	32.8918	1.91180
$297$	0.456669	0.0264986
$298$	30.0313	1.73967
$299$	0	0
$300$	5.14639	0.297127
$301$	−4.28991	−0.247266
$302$	−3.57462	−0.205696
$303$	2.65786	0.152690
$304$	−0.549578	−0.0315205
$305$	−2.02573	−0.115993
$306$	−7.14491	−0.408447
$307$	24.2095	1.38171	0.690855	−	0.722994i	$-0.257234\pi$
$307$	24.2095	1.38171	0.690855	+	0.722994i	$0.257234\pi$
$308$	−0.203237	−0.0115805
$309$	4.48234	0.254991
$310$	6.05916	0.344137
$311$	−8.75175	−0.496266	−0.248133	−	0.968726i	$-0.579817\pi$
$311$	−8.75175	−0.496266	−0.248133	+	0.968726i	$0.579817\pi$
$312$	0	0
$313$	3.44801	0.194893	0.0974465	−	0.995241i	$-0.468933\pi$
$313$	3.44801	0.194893	0.0974465	+	0.995241i	$0.468933\pi$
$314$	−1.45565	−0.0821469
$315$	−4.06987	−0.229311
$316$	−1.81172	−0.101917
$317$	15.2632	0.857269	0.428635	−	0.903478i	$-0.358995\pi$
$317$	15.2632	0.857269	0.428635	+	0.903478i	$0.358995\pi$
$318$	−7.08047	−0.397053
$319$	2.81491	0.157605
$320$	36.2209	2.02481
$321$	14.4760	0.807974
$322$	6.30752	0.351505
$323$	−1.08143	−0.0601722
$324$	−0.445042	−0.0247245
$325$	0	0
$326$	−14.1214	−0.782113
$327$	13.9209	0.769829
$328$	7.48566	0.413326
$329$	7.89748	0.435402
$330$	2.31761	0.127580
$331$	−34.2089	−1.88029	−0.940145	−	0.340776i	$-0.889310\pi$
$331$	−34.2089	−1.88029	−0.940145	+	0.340776i	$0.889310\pi$
$332$	4.92672	0.270389
$333$	−10.7880	−0.591180
$334$	22.7160	1.24296
$335$	51.6699	2.82303
$336$	−2.91185	−0.158855
$337$	30.2804	1.64948	0.824739	−	0.565513i	$-0.191322\pi$
$337$	30.2804	1.64948	0.824739	+	0.565513i	$0.191322\pi$
$338$	0	0
$339$	−19.8159	−1.07625
$340$	10.3781	0.562833
$341$	−0.545223	−0.0295255
$342$	0.235353	0.0127264
$343$	−1.00000	−0.0539949
$344$	−13.0796	−0.705203
$345$	20.5864	1.10833
$346$	−25.0256	−1.34538
$347$	18.6458	1.00096	0.500479	−	0.865749i	$-0.333157\pi$
$347$	18.6458	1.00096	0.500479	+	0.865749i	$0.333157\pi$
$348$	−2.74324	−0.147053
$349$	21.5364	1.15282	0.576410	−	0.817161i	$-0.304453\pi$
$349$	21.5364	1.15282	0.576410	+	0.817161i	$0.304453\pi$
$350$	−14.4199	−0.770774
$351$	0	0
$352$	−1.12652	−0.0600435
$353$	−13.8056	−0.734799	−0.367400	−	0.930063i	$-0.619752\pi$
$353$	−13.8056	−0.734799	−0.367400	+	0.930063i	$0.619752\pi$
$354$	16.7535	0.890438
$355$	−54.8086	−2.90894
$356$	−7.02936	−0.372555
$357$	−5.72977	−0.303252
$358$	−11.6922	−0.617954
$359$	−16.2256	−0.856356	−0.428178	−	0.903694i	$-0.640844\pi$
$359$	−16.2256	−0.856356	−0.428178	+	0.903694i	$0.640844\pi$
$360$	−12.4087	−0.653995
$361$	−18.9644	−0.998125
$362$	3.38486	0.177904
$363$	10.7915	0.566404
$364$	0	0
$365$	32.3538	1.69348
$366$	0.620670	0.0324429
$367$	17.5526	0.916237	0.458118	−	0.888891i	$-0.348524\pi$
$367$	17.5526	0.916237	0.458118	+	0.888891i	$0.348524\pi$
$368$	14.7289	0.767795
$369$	−2.45519	−0.127812
$370$	−54.7496	−2.84630
$371$	−5.67810	−0.294792
$372$	0.531341	0.0275488
$373$	−5.20801	−0.269661	−0.134830	−	0.990869i	$-0.543049\pi$
$373$	−5.20801	−0.269661	−0.134830	+	0.990869i	$0.543049\pi$
$374$	3.26286	0.168718
$375$	−26.7139	−1.37950
$376$	24.0788	1.24177
$377$	0	0
$378$	1.24698	0.0641377
$379$	−8.81996	−0.453051	−0.226525	−	0.974005i	$-0.572737\pi$
$379$	−8.81996	−0.453051	−0.226525	+	0.974005i	$0.572737\pi$
$380$	−0.341854	−0.0175368
$381$	−9.40331	−0.481746
$382$	−3.98459	−0.203869
$383$	4.36919	0.223255	0.111628	−	0.993750i	$-0.464394\pi$
$383$	4.36919	0.223255	0.111628	+	0.993750i	$0.464394\pi$
$384$	−6.16421	−0.314566
$385$	1.85858	0.0947221
$386$	−7.46706	−0.380064
$387$	4.28991	0.218068
$388$	4.38754	0.222743
$389$	−27.6044	−1.39960	−0.699798	−	0.714341i	$-0.746727\pi$
$389$	−27.6044	−1.39960	−0.699798	+	0.714341i	$0.746727\pi$
$390$	0	0
$391$	28.9826	1.46571
$392$	−3.04892	−0.153994
$393$	9.94710	0.501765
$394$	4.22245	0.212724
$395$	16.5680	0.833626
$396$	0.203237	0.0102130
$397$	25.8215	1.29595	0.647973	−	0.761664i	$-0.275617\pi$
$397$	25.8215	1.29595	0.647973	+	0.761664i	$0.275617\pi$
$398$	−19.7670	−0.990830
$399$	0.188738	0.00944873
$400$	−33.6722	−1.68361
$401$	−24.5840	−1.22767	−0.613834	−	0.789435i	$-0.710374\pi$
$401$	−24.5840	−1.22767	−0.613834	+	0.789435i	$0.710374\pi$
$402$	−15.8313	−0.789594
$403$	0	0
$404$	1.18286	0.0588494
$405$	4.06987	0.202233
$406$	7.68639	0.381469
$407$	4.92655	0.244200
$408$	−17.4696	−0.864874
$409$	34.7781	1.71966	0.859832	−	0.510577i	$-0.170568\pi$
$409$	34.7781	1.71966	0.859832	+	0.510577i	$0.170568\pi$
$410$	−12.4602	−0.615364
$411$	−1.17436	−0.0579269
$412$	1.99483	0.0982782
$413$	13.4353	0.661106
$414$	−6.30752	−0.309998
$415$	−45.0544	−2.21163
$416$	0	0
$417$	−1.64097	−0.0803585
$418$	−0.107478	−0.00525693
$419$	−23.8666	−1.16596	−0.582981	−	0.812486i	$-0.698114\pi$
$419$	−23.8666	−1.16596	−0.582981	+	0.812486i	$0.698114\pi$
$420$	−1.81126	−0.0883805
$421$	23.7194	1.15601	0.578005	−	0.816033i	$-0.303831\pi$
$421$	23.7194	1.15601	0.578005	+	0.816033i	$0.303831\pi$
$422$	−18.8943	−0.919758
$423$	−7.89748	−0.383988
$424$	−17.3121	−0.840748
$425$	−66.2581	−3.21399
$426$	16.7930	0.813623
$427$	0.497739	0.0240873
$428$	6.44245	0.311407
$429$	0	0
$430$	21.7715	1.04991
$431$	31.8528	1.53430	0.767148	−	0.641470i	$-0.221675\pi$
$431$	31.8528	1.53430	0.767148	+	0.641470i	$0.221675\pi$
$432$	2.91185	0.140097
$433$	−38.8011	−1.86466	−0.932331	−	0.361605i	$-0.882229\pi$
$433$	−38.8011	−1.86466	−0.932331	+	0.361605i	$0.882229\pi$
$434$	−1.48878	−0.0714640
$435$	25.0867	1.20282
$436$	6.19540	0.296706
$437$	−0.954684	−0.0456687
$438$	−9.91300	−0.473661
$439$	34.1627	1.63049	0.815247	−	0.579113i	$-0.196601\pi$
$439$	34.1627	1.63049	0.815247	+	0.579113i	$0.196601\pi$
$440$	5.66666	0.270147
$441$	1.00000	0.0476190
$442$	0	0
$443$	−8.98444	−0.426864	−0.213432	−	0.976958i	$-0.568464\pi$
$443$	−8.98444	−0.426864	−0.213432	+	0.976958i	$0.568464\pi$
$444$	−4.80112	−0.227851
$445$	64.2829	3.04730
$446$	−4.11381	−0.194794
$447$	−24.0833	−1.13910
$448$	−8.89977	−0.420475
$449$	21.1704	0.999092	0.499546	−	0.866287i	$-0.333500\pi$
$449$	21.1704	0.999092	0.499546	+	0.866287i	$0.333500\pi$
$450$	14.4199	0.679759
$451$	1.12121	0.0527955
$452$	−8.81890	−0.414806
$453$	2.86662	0.134686
$454$	−5.57371	−0.261587
$455$	0	0
$456$	0.575447	0.0269478
$457$	15.6357	0.731409	0.365704	−	0.930731i	$-0.380828\pi$
$457$	15.6357	0.731409	0.365704	+	0.930731i	$0.380828\pi$
$458$	1.33353	0.0623117
$459$	5.72977	0.267443
$460$	9.16180	0.427171
$461$	7.86852	0.366474	0.183237	−	0.983069i	$-0.441342\pi$
$461$	7.86852	0.366474	0.183237	+	0.983069i	$0.441342\pi$
$462$	−0.569457	−0.0264935
$463$	4.47009	0.207743	0.103871	−	0.994591i	$-0.466877\pi$
$463$	4.47009	0.207743	0.103871	+	0.994591i	$0.466877\pi$
$464$	17.9487	0.833247
$465$	−4.85907	−0.225334
$466$	0.685720	0.0317654
$467$	−23.3252	−1.07936	−0.539680	−	0.841870i	$-0.681455\pi$
$467$	−23.3252	−1.07936	−0.539680	+	0.841870i	$0.681455\pi$
$468$	0	0
$469$	−12.6957	−0.586234
$470$	−40.0800	−1.84875
$471$	1.16734	0.0537881
$472$	40.9630	1.88548
$473$	−1.95907	−0.0900780
$474$	−5.07632	−0.233163
$475$	2.18254	0.100142
$476$	−2.54999	−0.116879
$477$	5.67810	0.259982
$478$	−33.5077	−1.53261
$479$	−19.0742	−0.871522	−0.435761	−	0.900062i	$-0.643521\pi$
$479$	−19.0742	−0.871522	−0.435761	+	0.900062i	$0.643521\pi$
$480$	−10.0396	−0.458243
$481$	0	0
$482$	6.48444	0.295358
$483$	−5.05824	−0.230158
$484$	4.80265	0.218302
$485$	−40.1236	−1.82192
$486$	−1.24698	−0.0565641
$487$	32.1344	1.45615	0.728075	−	0.685497i	$-0.240415\pi$
$487$	32.1344	1.45615	0.728075	+	0.685497i	$0.240415\pi$
$488$	1.51756	0.0686969
$489$	11.3245	0.512111
$490$	5.07504	0.229267
$491$	−13.4490	−0.606944	−0.303472	−	0.952840i	$-0.598146\pi$
$491$	−13.4490	−0.606944	−0.303472	+	0.952840i	$0.598146\pi$
$492$	−1.09266	−0.0492609
$493$	35.3184	1.59066
$494$	0	0
$495$	−1.85858	−0.0835370
$496$	−3.47650	−0.156099
$497$	13.4669	0.604075
$498$	13.8044	0.618588
$499$	18.4105	0.824165	0.412083	−	0.911146i	$-0.364801\pi$
$499$	18.4105	0.824165	0.412083	+	0.911146i	$0.364801\pi$
$500$	−11.8888	−0.531684
$501$	−18.2168	−0.813868
$502$	5.35736	0.239111
$503$	28.0595	1.25111	0.625555	−	0.780180i	$-0.284872\pi$
$503$	28.0595	1.25111	0.625555	+	0.780180i	$0.284872\pi$
$504$	3.04892	0.135810
$505$	−10.8171	−0.481356
$506$	2.88045	0.128052
$507$	0	0
$508$	−4.18487	−0.185673
$509$	32.0230	1.41940	0.709698	−	0.704506i	$-0.248831\pi$
$509$	32.0230	1.41940	0.709698	+	0.704506i	$0.248831\pi$
$510$	29.0788	1.28763
$511$	−7.94961	−0.351670
$512$	−24.9390	−1.10216
$513$	−0.188738	−0.00833300
$514$	−8.36115	−0.368795
$515$	−18.2425	−0.803862
$516$	1.90919	0.0840473
$517$	3.60653	0.158615
$518$	13.4524	0.591066
$519$	20.0690	0.880930
$520$	0	0
$521$	−3.26582	−0.143078	−0.0715392	−	0.997438i	$-0.522791\pi$
$521$	−3.26582	−0.143078	−0.0715392	+	0.997438i	$0.522791\pi$
$522$	−7.68639	−0.336424
$523$	−39.8760	−1.74366	−0.871828	−	0.489813i	$-0.837065\pi$
$523$	−39.8760	−1.74366	−0.871828	+	0.489813i	$0.837065\pi$
$524$	4.42688	0.193389
$525$	11.5638	0.504687
$526$	−3.15252	−0.137456
$527$	−6.84085	−0.297992
$528$	−1.32975	−0.0578701
$529$	2.58581	0.112426
$530$	28.8166	1.25171
$531$	−13.4353	−0.583041
$532$	0.0839964	0.00364171
$533$	0	0
$534$	−19.6958	−0.852322
$535$	−58.9156	−2.54714
$536$	−38.7082	−1.67194
$537$	9.37645	0.404624
$538$	12.0925	0.521343
$539$	−0.456669	−0.0196701
$540$	1.81126	0.0779443
$541$	−15.7774	−0.678324	−0.339162	−	0.940728i	$-0.610143\pi$
$541$	−15.7774	−0.678324	−0.339162	+	0.940728i	$0.610143\pi$
$542$	−16.4445	−0.706352
$543$	−2.71444	−0.116488
$544$	−14.1343	−0.606002
$545$	−56.6563	−2.42689
$546$	0	0
$547$	−2.17231	−0.0928814	−0.0464407	−	0.998921i	$-0.514788\pi$
$547$	−2.17231	−0.0928814	−0.0464407	+	0.998921i	$0.514788\pi$
$548$	−0.522640	−0.0223261
$549$	−0.497739	−0.0212430
$550$	−6.58510	−0.280790
$551$	−1.16338	−0.0495618
$552$	−15.4222	−0.656411
$553$	−4.07089	−0.173112
$554$	8.01565	0.340552
$555$	43.9058	1.86370
$556$	−0.730299	−0.0309716
$557$	15.2813	0.647490	0.323745	−	0.946144i	$-0.395058\pi$
$557$	15.2813	0.647490	0.323745	+	0.946144i	$0.395058\pi$
$558$	1.48878	0.0630253
$559$	0	0
$560$	11.8509	0.500790
$561$	−2.61661	−0.110473
$562$	−25.0592	−1.05706
$563$	29.2981	1.23477	0.617384	−	0.786662i	$-0.288193\pi$
$563$	29.2981	1.23477	0.617384	+	0.786662i	$0.288193\pi$
$564$	−3.51471	−0.147996
$565$	80.6481	3.39289
$566$	26.2848	1.10483
$567$	−1.00000	−0.0419961
$568$	41.0596	1.72282
$569$	17.8243	0.747233	0.373616	−	0.927583i	$-0.378118\pi$
$569$	17.8243	0.747233	0.373616	+	0.927583i	$0.378118\pi$
$570$	−0.957855	−0.0401201
$571$	−3.46247	−0.144900	−0.0724499	−	0.997372i	$-0.523082\pi$
$571$	−3.46247	−0.144900	−0.0724499	+	0.997372i	$0.523082\pi$
$572$	0	0
$573$	3.19539	0.133489
$574$	3.06157	0.127787
$575$	−58.4926	−2.43931
$576$	8.89977	0.370824
$577$	15.2026	0.632892	0.316446	−	0.948610i	$-0.397510\pi$
$577$	15.2026	0.632892	0.316446	+	0.948610i	$0.397510\pi$
$578$	19.7401	0.821079
$579$	5.98812	0.248858
$580$	11.1646	0.463586
$581$	11.0702	0.459271
$582$	12.2936	0.509586
$583$	−2.59301	−0.107392
$584$	−24.2377	−1.00296
$585$	0	0
$586$	34.9241	1.44270
$587$	26.0354	1.07459	0.537297	−	0.843393i	$-0.319445\pi$
$587$	26.0354	1.07459	0.537297	+	0.843393i	$0.319445\pi$
$588$	0.445042	0.0183532
$589$	0.225337	0.00928485
$590$	−68.1845	−2.80711
$591$	−3.38614	−0.139287
$592$	31.4131	1.29107
$593$	−18.5431	−0.761473	−0.380737	−	0.924684i	$-0.624330\pi$
$593$	−18.5431	−0.761473	−0.380737	+	0.924684i	$0.624330\pi$
$594$	0.569457	0.0233651
$595$	23.3194	0.956003
$596$	−10.7181	−0.439029
$597$	15.8519	0.648775
$598$	0	0
$599$	−17.9744	−0.734416	−0.367208	−	0.930139i	$-0.619686\pi$
$599$	−17.9744	−0.734416	−0.367208	+	0.930139i	$0.619686\pi$
$600$	35.2572	1.43937
$601$	−2.38652	−0.0973480	−0.0486740	−	0.998815i	$-0.515500\pi$
$601$	−2.38652	−0.0973480	−0.0486740	+	0.998815i	$0.515500\pi$
$602$	−5.34943	−0.218026
$603$	12.6957	0.517010
$604$	1.27577	0.0519103
$605$	−43.9198	−1.78559
$606$	3.31430	0.134634
$607$	36.9416	1.49941	0.749706	−	0.661771i	$-0.230195\pi$
$607$	36.9416	1.49941	0.749706	+	0.661771i	$0.230195\pi$
$608$	0.465582	0.0188818
$609$	−6.16401	−0.249778
$610$	−2.52604	−0.102277
$611$	0	0
$612$	2.54999	0.103077
$613$	−10.2820	−0.415286	−0.207643	−	0.978205i	$-0.566579\pi$
$613$	−10.2820	−0.415286	−0.207643	+	0.978205i	$0.566579\pi$
$614$	30.1888	1.21832
$615$	9.99228	0.402928
$616$	−1.39235	−0.0560992
$617$	21.9165	0.882325	0.441162	−	0.897427i	$-0.354566\pi$
$617$	21.9165	0.882325	0.441162	+	0.897427i	$0.354566\pi$
$618$	5.58939	0.224838
$619$	32.5945	1.31008	0.655041	−	0.755593i	$-0.272651\pi$
$619$	32.5945	1.31008	0.655041	+	0.755593i	$0.272651\pi$
$620$	−2.16249	−0.0868476
$621$	5.05824	0.202980
$622$	−10.9133	−0.437582
$623$	−15.7948	−0.632807
$624$	0	0
$625$	50.9030	2.03612
$626$	4.29960	0.171847
$627$	0.0861909	0.00344213
$628$	0.519514	0.0207309
$629$	61.8129	2.46464
$630$	−5.07504	−0.202195
$631$	−16.1040	−0.641091	−0.320546	−	0.947233i	$-0.603866\pi$
$631$	−16.1040	−0.641091	−0.320546	+	0.947233i	$0.603866\pi$
$632$	−12.4118	−0.493716
$633$	15.1520	0.602239
$634$	19.0330	0.755895
$635$	38.2702	1.51871
$636$	2.52699	0.100202
$637$	0	0
$638$	3.51014	0.138968
$639$	−13.4669	−0.532744
$640$	25.0875	0.991671
$641$	−28.6147	−1.13021	−0.565106	−	0.825019i	$-0.691165\pi$
$641$	−28.6147	−1.13021	−0.565106	+	0.825019i	$0.691165\pi$
$642$	18.0513	0.712429
$643$	13.3312	0.525731	0.262865	−	0.964832i	$-0.415332\pi$
$643$	13.3312	0.525731	0.262865	+	0.964832i	$0.415332\pi$
$644$	−2.25113	−0.0887069
$645$	−17.4594	−0.687461
$646$	−1.34852	−0.0530567
$647$	2.90219	0.114097	0.0570484	−	0.998371i	$-0.481831\pi$
$647$	2.90219	0.114097	0.0570484	+	0.998371i	$0.481831\pi$
$648$	−3.04892	−0.119773
$649$	6.13546	0.240838
$650$	0	0
$651$	1.19391	0.0467931
$652$	5.03987	0.197377
$653$	45.4716	1.77944	0.889721	−	0.456504i	$-0.150899\pi$
$653$	45.4716	1.77944	0.889721	+	0.456504i	$0.150899\pi$
$654$	17.3591	0.678795
$655$	−40.4834	−1.58182
$656$	7.14914	0.279127
$657$	7.94961	0.310144
$658$	9.84799	0.383915
$659$	−21.4211	−0.834447	−0.417224	−	0.908804i	$-0.636997\pi$
$659$	−21.4211	−0.834447	−0.417224	+	0.908804i	$0.636997\pi$
$660$	−0.827147	−0.0321966
$661$	8.32956	0.323982	0.161991	−	0.986792i	$-0.448208\pi$
$661$	8.32956	0.323982	0.161991	+	0.986792i	$0.448208\pi$
$662$	−42.6578	−1.65794
$663$	0	0
$664$	33.7522	1.30984
$665$	−0.768140	−0.0297872
$666$	−13.4524	−0.521271
$667$	31.1790	1.20726
$668$	−8.10725	−0.313679
$669$	3.29902	0.127547
$670$	64.4313	2.48920
$671$	0.227302	0.00877488
$672$	2.46681	0.0951593
$673$	−10.8310	−0.417505	−0.208752	−	0.977969i	$-0.566940\pi$
$673$	−10.8310	−0.417505	−0.208752	+	0.977969i	$0.566940\pi$
$674$	37.7591	1.45442
$675$	−11.5638	−0.445092
$676$	0	0
$677$	20.9707	0.805969	0.402984	−	0.915207i	$-0.367973\pi$
$677$	20.9707	0.805969	0.402984	+	0.915207i	$0.367973\pi$
$678$	−24.7100	−0.948983
$679$	9.85870	0.378342
$680$	71.0990	2.72652
$681$	4.46977	0.171282
$682$	−0.679881	−0.0260340
$683$	16.5639	0.633801	0.316901	−	0.948459i	$-0.397358\pi$
$683$	16.5639	0.633801	0.316901	+	0.948459i	$0.397358\pi$
$684$	−0.0839964	−0.00321168
$685$	4.77949	0.182615
$686$	−1.24698	−0.0476099
$687$	−1.06941	−0.0408004
$688$	−12.4916	−0.476237
$689$	0	0
$690$	25.6708	0.977270
$691$	42.9786	1.63498	0.817491	−	0.575942i	$-0.195365\pi$
$691$	42.9786	1.63498	0.817491	+	0.575942i	$0.195365\pi$
$692$	8.93153	0.339526
$693$	0.456669	0.0173474
$694$	23.2509	0.882593
$695$	6.67852	0.253331
$696$	−18.7936	−0.712368
$697$	14.0677	0.532850
$698$	26.8555	1.01650
$699$	−0.549905	−0.0207993
$700$	5.14639	0.194515
$701$	−8.79731	−0.332270	−0.166135	−	0.986103i	$-0.553129\pi$
$701$	−8.79731	−0.332270	−0.166135	+	0.986103i	$0.553129\pi$
$702$	0	0
$703$	−2.03611	−0.0767934
$704$	−4.06425	−0.153177
$705$	32.1417	1.21053
$706$	−17.2153	−0.647908
$707$	2.65786	0.0999591
$708$	−5.97925	−0.224714
$709$	−9.83203	−0.369249	−0.184625	−	0.982809i	$-0.559107\pi$
$709$	−9.83203	−0.369249	−0.184625	+	0.982809i	$0.559107\pi$
$710$	−68.3453	−2.56495
$711$	4.07089	0.152670
$712$	−48.1571	−1.80477
$713$	−6.03910	−0.226166
$714$	−7.14491	−0.267392
$715$	0	0
$716$	4.17291	0.155949
$717$	26.8711	1.00352
$718$	−20.2330	−0.755090
$719$	−10.7411	−0.400575	−0.200288	−	0.979737i	$-0.564188\pi$
$719$	−10.7411	−0.400575	−0.200288	+	0.979737i	$0.564188\pi$
$720$	−11.8509	−0.441656
$721$	4.48234	0.166931
$722$	−23.6482	−0.880095
$723$	−5.20011	−0.193394
$724$	−1.20804	−0.0448965
$725$	−71.2795	−2.64726
$726$	13.4567	0.499426
$727$	−18.8015	−0.697308	−0.348654	−	0.937251i	$-0.613361\pi$
$727$	−18.8015	−0.697308	−0.348654	+	0.937251i	$0.613361\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	40.3446	1.49322
$731$	−24.5802	−0.909131
$732$	−0.221514	−0.00818741
$733$	−32.0870	−1.18516	−0.592580	−	0.805512i	$-0.701891\pi$
$733$	−32.0870	−1.18516	−0.592580	+	0.805512i	$0.701891\pi$
$734$	21.8877	0.807890
$735$	−4.06987	−0.150119
$736$	−12.4777	−0.459935
$737$	−5.79774	−0.213562
$738$	−3.06157	−0.112698
$739$	12.8616	0.473122	0.236561	−	0.971617i	$-0.423980\pi$
$739$	12.8616	0.473122	0.236561	+	0.971617i	$0.423980\pi$
$740$	19.5399	0.718302
$741$	0	0
$742$	−7.08047	−0.259932
$743$	−30.5328	−1.12014	−0.560070	−	0.828445i	$-0.689226\pi$
$743$	−30.5328	−1.12014	−0.560070	+	0.828445i	$0.689226\pi$
$744$	3.64014	0.133454
$745$	98.0157	3.59102
$746$	−6.49429	−0.237773
$747$	−11.0702	−0.405039
$748$	−1.16450	−0.0425783
$749$	14.4760	0.528943
$750$	−33.3117	−1.21637
$751$	7.15312	0.261021	0.130511	−	0.991447i	$-0.458338\pi$
$751$	7.15312	0.261021	0.130511	+	0.991447i	$0.458338\pi$
$752$	22.9963	0.838589
$753$	−4.29627	−0.156565
$754$	0	0
$755$	−11.6668	−0.424598
$756$	−0.445042	−0.0161860
$757$	−42.7488	−1.55373	−0.776866	−	0.629666i	$-0.783192\pi$
$757$	−42.7488	−1.55373	−0.776866	+	0.629666i	$0.783192\pi$
$758$	−10.9983	−0.399476
$759$	−2.30994	−0.0838455
$760$	−2.34199	−0.0849531
$761$	8.40665	0.304741	0.152370	−	0.988323i	$-0.451309\pi$
$761$	8.40665	0.304741	0.152370	+	0.988323i	$0.451309\pi$
$762$	−11.7257	−0.424779
$763$	13.9209	0.503971
$764$	1.42208	0.0514491
$765$	−23.3194	−0.843116
$766$	5.44829	0.196855
$767$	0	0
$768$	10.1129	0.364918
$769$	39.4149	1.42134	0.710669	−	0.703526i	$-0.248392\pi$
$769$	39.4149	1.42134	0.710669	+	0.703526i	$0.248392\pi$
$770$	2.31761	0.0835210
$771$	6.70512	0.241479
$772$	2.66496	0.0959142
$773$	−36.9933	−1.33056	−0.665279	−	0.746595i	$-0.731687\pi$
$773$	−36.9933	−1.33056	−0.665279	+	0.746595i	$0.731687\pi$
$774$	5.34943	0.192281
$775$	13.8062	0.495933
$776$	30.0584	1.07903
$777$	−10.7880	−0.387018
$778$	−34.4221	−1.23409
$779$	−0.463387	−0.0166026
$780$	0	0
$781$	6.14993	0.220062
$782$	36.1407	1.29239
$783$	6.16401	0.220284
$784$	−2.91185	−0.103995
$785$	−4.75091	−0.169567
$786$	12.4038	0.442430
$787$	18.1555	0.647175	0.323588	−	0.946198i	$-0.395111\pi$
$787$	18.1555	0.647175	0.323588	+	0.946198i	$0.395111\pi$
$788$	−1.50697	−0.0536837
$789$	2.52812	0.0900035
$790$	20.6600	0.735048
$791$	−19.8159	−0.704572
$792$	1.39235	0.0494748
$793$	0	0
$794$	32.1989	1.14270
$795$	−23.1091	−0.819596
$796$	7.05476	0.250049
$797$	45.3521	1.60645	0.803227	−	0.595673i	$-0.203114\pi$
$797$	45.3521	1.60645	0.803227	+	0.595673i	$0.203114\pi$
$798$	0.235353	0.00833140
$799$	45.2508	1.60086
$800$	28.5258	1.00854
$801$	15.7948	0.558083
$802$	−30.6558	−1.08249
$803$	−3.63034	−0.128112
$804$	5.65013	0.199265
$805$	20.5864	0.725574
$806$	0	0
$807$	−9.69741	−0.341365
$808$	8.10359	0.285083
$809$	34.5412	1.21440	0.607202	−	0.794547i	$-0.292292\pi$
$809$	34.5412	1.21440	0.607202	+	0.794547i	$0.292292\pi$
$810$	5.07504	0.178319
$811$	27.2550	0.957054	0.478527	−	0.878073i	$-0.341171\pi$
$811$	27.2550	0.957054	0.478527	+	0.878073i	$0.341171\pi$
$812$	−2.74324	−0.0962689
$813$	13.1875	0.462505
$814$	6.14331	0.215323
$815$	−46.0892	−1.61443
$816$	−16.6843	−0.584066
$817$	0.809669	0.0283267
$818$	43.3675	1.51631
$819$	0	0
$820$	4.44698	0.155295
$821$	−43.7047	−1.52530	−0.762652	−	0.646809i	$-0.776103\pi$
$821$	−43.7047	−1.52530	−0.762652	+	0.646809i	$0.776103\pi$
$822$	−1.46440	−0.0510770
$823$	11.0857	0.386422	0.193211	−	0.981157i	$-0.438110\pi$
$823$	11.0857	0.386422	0.193211	+	0.981157i	$0.438110\pi$
$824$	13.6663	0.476087
$825$	5.28084	0.183855
$826$	16.7535	0.582929
$827$	−0.590813	−0.0205446	−0.0102723	−	0.999947i	$-0.503270\pi$
$827$	−0.590813	−0.0205446	−0.0102723	+	0.999947i	$0.503270\pi$
$828$	2.25113	0.0782321
$829$	−15.3785	−0.534118	−0.267059	−	0.963680i	$-0.586052\pi$
$829$	−15.3785	−0.534118	−0.267059	+	0.963680i	$0.586052\pi$
$830$	−56.1819	−1.95010
$831$	−6.42805	−0.222987
$832$	0	0
$833$	−5.72977	−0.198525
$834$	−2.04625	−0.0708559
$835$	74.1401	2.56572
$836$	0.0383585	0.00132666
$837$	−1.19391	−0.0412677
$838$	−29.7612	−1.02808
$839$	6.54912	0.226101	0.113050	−	0.993589i	$-0.463938\pi$
$839$	6.54912	0.226101	0.113050	+	0.993589i	$0.463938\pi$
$840$	−12.4087	−0.428141
$841$	8.99500	0.310172
$842$	29.5775	1.01931
$843$	20.0959	0.692140
$844$	6.74328	0.232113
$845$	0	0
$846$	−9.84799	−0.338581
$847$	10.7915	0.370799
$848$	−16.5338	−0.567773
$849$	−21.0787	−0.723420
$850$	−82.6225	−2.83393
$851$	54.5684	1.87058
$852$	−5.99335	−0.205329
$853$	−30.0196	−1.02785	−0.513925	−	0.857835i	$-0.671809\pi$
$853$	−30.0196	−1.02785	−0.513925	+	0.857835i	$0.671809\pi$
$854$	0.620670	0.0212389
$855$	0.768140	0.0262698
$856$	44.1363	1.50855
$857$	44.5939	1.52330	0.761650	−	0.647989i	$-0.224390\pi$
$857$	44.5939	1.52330	0.761650	+	0.647989i	$0.224390\pi$
$858$	0	0
$859$	−45.5987	−1.55581	−0.777904	−	0.628383i	$-0.783717\pi$
$859$	−45.5987	−1.55581	−0.777904	+	0.628383i	$0.783717\pi$
$860$	−7.77014	−0.264960
$861$	−2.45519	−0.0836725
$862$	39.7198	1.35286
$863$	−15.5188	−0.528265	−0.264132	−	0.964486i	$-0.585086\pi$
$863$	−15.5188	−0.528265	−0.264132	+	0.964486i	$0.585086\pi$
$864$	−2.46681	−0.0839227
$865$	−81.6780	−2.77714
$866$	−48.3842	−1.64416
$867$	−15.8303	−0.537625
$868$	0.531341	0.0180349
$869$	−1.85905	−0.0630639
$870$	31.2826	1.06058
$871$	0	0
$872$	42.4438	1.43733
$873$	−9.85870	−0.333667
$874$	−1.19047	−0.0402683
$875$	−26.7139	−0.903095
$876$	3.53791	0.119535
$877$	22.6489	0.764799	0.382400	−	0.923997i	$-0.375098\pi$
$877$	22.6489	0.764799	0.382400	+	0.923997i	$0.375098\pi$
$878$	42.6001	1.43768
$879$	−28.0069	−0.944650
$880$	5.41192	0.182436
$881$	−4.99915	−0.168426	−0.0842129	−	0.996448i	$-0.526838\pi$
$881$	−4.99915	−0.168426	−0.0842129	+	0.996448i	$0.526838\pi$
$882$	1.24698	0.0419880
$883$	−29.1039	−0.979424	−0.489712	−	0.871884i	$-0.662898\pi$
$883$	−29.1039	−0.979424	−0.489712	+	0.871884i	$0.662898\pi$
$884$	0	0
$885$	54.6798	1.83804
$886$	−11.2034	−0.376386
$887$	−5.81964	−0.195404	−0.0977022	−	0.995216i	$-0.531149\pi$
$887$	−5.81964	−0.195404	−0.0977022	+	0.995216i	$0.531149\pi$
$888$	−32.8918	−1.10378
$889$	−9.40331	−0.315377
$890$	80.1594	2.68695
$891$	−0.456669	−0.0152990
$892$	1.46820	0.0491590
$893$	−1.49056	−0.0498795
$894$	−30.0313	−1.00440
$895$	−38.1609	−1.27558
$896$	−6.16421	−0.205932
$897$	0	0
$898$	26.3990	0.880947
$899$	−7.35929	−0.245446
$900$	−5.14639	−0.171546
$901$	−32.5342	−1.08387
$902$	1.39812	0.0465524
$903$	4.28991	0.142759
$904$	−60.4170	−2.00944
$905$	11.0474	0.367229
$906$	3.57462	0.118759
$907$	−46.7976	−1.55389	−0.776945	−	0.629569i	$-0.783232\pi$
$907$	−46.7976	−1.55389	−0.776945	+	0.629569i	$0.783232\pi$
$908$	1.98924	0.0660151
$909$	−2.65786	−0.0881556
$910$	0	0
$911$	23.8194	0.789171	0.394586	−	0.918859i	$-0.370888\pi$
$911$	23.8194	0.789171	0.394586	+	0.918859i	$0.370888\pi$
$912$	0.549578	0.0181984
$913$	5.05543	0.167310
$914$	19.4974	0.644918
$915$	2.02573	0.0669686
$916$	−0.475931	−0.0157252
$917$	9.94710	0.328482
$918$	7.14491	0.235817
$919$	−46.1841	−1.52347	−0.761736	−	0.647887i	$-0.775653\pi$
$919$	−46.1841	−1.52347	−0.761736	+	0.647887i	$0.775653\pi$
$920$	62.7662	2.06934
$921$	−24.2095	−0.797730
$922$	9.81189	0.323137
$923$	0	0
$924$	0.203237	0.00668600
$925$	−124.751	−4.10178
$926$	5.57411	0.183177
$927$	−4.48234	−0.147219
$928$	−15.2054	−0.499143
$929$	−46.4387	−1.52360	−0.761802	−	0.647810i	$-0.775685\pi$
$929$	−46.4387	−1.52360	−0.761802	+	0.647810i	$0.775685\pi$
$930$	−6.05916	−0.198688
$931$	0.188738	0.00618565
$932$	−0.244731	−0.00801642
$933$	8.75175	0.286520
$934$	−29.0860	−0.951723
$935$	10.6493	0.348268
$936$	0	0
$937$	19.8068	0.647059	0.323529	−	0.946218i	$-0.395131\pi$
$937$	19.8068	0.647059	0.323529	+	0.946218i	$0.395131\pi$
$938$	−15.8313	−0.516910
$939$	−3.44801	−0.112522
$940$	14.3044	0.466558
$941$	24.2373	0.790112	0.395056	−	0.918657i	$-0.370725\pi$
$941$	24.2373	0.790112	0.395056	+	0.918657i	$0.370725\pi$
$942$	1.45565	0.0474275
$943$	12.4189	0.404416
$944$	39.1215	1.27330
$945$	4.06987	0.132393
$946$	−2.44292	−0.0794260
$947$	−27.9615	−0.908625	−0.454313	−	0.890842i	$-0.650115\pi$
$947$	−27.9615	−0.908625	−0.454313	+	0.890842i	$0.650115\pi$
$948$	1.81172	0.0588419
$949$	0	0
$950$	2.72158	0.0882997
$951$	−15.2632	−0.494945
$952$	−17.4696	−0.566193
$953$	1.81197	0.0586956	0.0293478	−	0.999569i	$-0.490657\pi$
$953$	1.81197	0.0586956	0.0293478	+	0.999569i	$0.490657\pi$
$954$	7.08047	0.229239
$955$	−13.0048	−0.420826
$956$	11.9588	0.386774
$957$	−2.81491	−0.0909931
$958$	−23.7851	−0.768462
$959$	−1.17436	−0.0379221
$960$	−36.2209	−1.16902
$961$	−29.5746	−0.954018
$962$	0	0
$963$	−14.4760	−0.466484
$964$	−2.31427	−0.0745376
$965$	−24.3709	−0.784526
$966$	−6.30752	−0.202941
$967$	19.2910	0.620357	0.310179	−	0.950678i	$-0.399611\pi$
$967$	19.2910	0.620357	0.310179	+	0.950678i	$0.399611\pi$
$968$	32.9023	1.05752
$969$	1.08143	0.0347405
$970$	−50.0333	−1.60647
$971$	−2.63417	−0.0845344	−0.0422672	−	0.999106i	$-0.513458\pi$
$971$	−2.63417	−0.0845344	−0.0422672	+	0.999106i	$0.513458\pi$
$972$	0.445042	0.0142747
$973$	−1.64097	−0.0526070
$974$	40.0710	1.28396
$975$	0	0
$976$	1.44934	0.0463923
$977$	−58.1325	−1.85982	−0.929912	−	0.367783i	$-0.880117\pi$
$977$	−58.1325	−1.85982	−0.929912	+	0.367783i	$0.880117\pi$
$978$	14.1214	0.451553
$979$	−7.21301	−0.230529
$980$	−1.81126	−0.0578586
$981$	−13.9209	−0.444461
$982$	−16.7706	−0.535172
$983$	−45.0158	−1.43578	−0.717891	−	0.696156i	$-0.754892\pi$
$983$	−45.0158	−1.43578	−0.717891	+	0.696156i	$0.754892\pi$
$984$	−7.48566	−0.238634
$985$	13.7811	0.439104
$986$	44.0413	1.40256
$987$	−7.89748	−0.251379
$988$	0	0
$989$	−21.6994	−0.690000
$990$	−2.31761	−0.0736586
$991$	−5.10840	−0.162274	−0.0811368	−	0.996703i	$-0.525855\pi$
$991$	−5.10840	−0.162274	−0.0811368	+	0.996703i	$0.525855\pi$
$992$	2.94516	0.0935089
$993$	34.2089	1.08559
$994$	16.7930	0.532641
$995$	−64.5151	−2.04527
$996$	−4.92672	−0.156109
$997$	−7.52662	−0.238371	−0.119185	−	0.992872i	$-0.538028\pi$
$997$	−7.52662	−0.238371	−0.119185	+	0.992872i	$0.538028\pi$
$998$	22.9575	0.726706
$999$	10.7880	0.341318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.y.1.6	✓	6
13.12	even	2		3549.2.a.z.1.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.y.1.6	✓	6	1.1	even	1	trivial
3549.2.a.z.1.1	yes	6	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+1.24698 q^{2} -1.00000 q^{3} -0.445042 q^{4} +4.06987 q^{5} -1.24698 q^{6} -1.00000 q^{7} -3.04892 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.24698 q^{2} -1.00000 q^{3} -0.445042 q^{4} +4.06987 q^{5} -1.24698 q^{6} -1.00000 q^{7} -3.04892 q^{8} +1.00000 q^{9} +5.07504 q^{10} -0.456669 q^{11} +0.445042 q^{12} -1.24698 q^{14} -4.06987 q^{15} -2.91185 q^{16} -5.72977 q^{17} +1.24698 q^{18} +0.188738 q^{19} -1.81126 q^{20} +1.00000 q^{21} -0.569457 q^{22} -5.05824 q^{23} +3.04892 q^{24} +11.5638 q^{25} -1.00000 q^{27} +0.445042 q^{28} -6.16401 q^{29} -5.07504 q^{30} +1.19391 q^{31} +2.46681 q^{32} +0.456669 q^{33} -7.14491 q^{34} -4.06987 q^{35} -0.445042 q^{36} -10.7880 q^{37} +0.235353 q^{38} -12.4087 q^{40} -2.45519 q^{41} +1.24698 q^{42} +4.28991 q^{43} +0.203237 q^{44} +4.06987 q^{45} -6.30752 q^{46} -7.89748 q^{47} +2.91185 q^{48} +1.00000 q^{49} +14.4199 q^{50} +5.72977 q^{51} +5.67810 q^{53} -1.24698 q^{54} -1.85858 q^{55} +3.04892 q^{56} -0.188738 q^{57} -7.68639 q^{58} -13.4353 q^{59} +1.81126 q^{60} -0.497739 q^{61} +1.48878 q^{62} -1.00000 q^{63} +8.89977 q^{64} +0.569457 q^{66} +12.6957 q^{67} +2.54999 q^{68} +5.05824 q^{69} -5.07504 q^{70} -13.4669 q^{71} -3.04892 q^{72} +7.94961 q^{73} -13.4524 q^{74} -11.5638 q^{75} -0.0839964 q^{76} +0.456669 q^{77} +4.07089 q^{79} -11.8509 q^{80} +1.00000 q^{81} -3.06157 q^{82} -11.0702 q^{83} -0.445042 q^{84} -23.3194 q^{85} +5.34943 q^{86} +6.16401 q^{87} +1.39235 q^{88} +15.7948 q^{89} +5.07504 q^{90} +2.25113 q^{92} -1.19391 q^{93} -9.84799 q^{94} +0.768140 q^{95} -2.46681 q^{96} -9.85870 q^{97} +1.24698 q^{98} -0.456669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 6 * q^7 + 6 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9} - q^{10} + 2 q^{12} + 2 q^{14} - 3 q^{15} - 10 q^{16} - 9 q^{17} - 2 q^{18} + 11 q^{19} - q^{20} + 6 q^{21} + 7 q^{22} - 11 q^{23} + 29 q^{25} - 6 q^{27} + 2 q^{28} - 10 q^{29} + q^{30} + 7 q^{31} + 8 q^{32} + 10 q^{34} - 3 q^{35} - 2 q^{36} - 20 q^{37} - 6 q^{38} - 10 q^{41} - 2 q^{42} - 9 q^{43} + 3 q^{45} - 8 q^{46} + 36 q^{47} + 10 q^{48} + 6 q^{49} + 9 q^{50} + 9 q^{51} - 12 q^{53} + 2 q^{54} - 29 q^{55} - 11 q^{57} - 6 q^{58} - 41 q^{59} + q^{60} - 24 q^{61} - 6 q^{63} + 8 q^{64} - 7 q^{66} + 15 q^{67} + 10 q^{68} + 11 q^{69} + q^{70} + 13 q^{71} + 25 q^{73} + 2 q^{74} - 29 q^{75} + q^{76} - 16 q^{79} - 5 q^{80} + 6 q^{81} + q^{82} - 2 q^{83} - 2 q^{84} - 33 q^{85} - 4 q^{86} + 10 q^{87} - 14 q^{88} + 15 q^{89} - q^{90} + 13 q^{92} - 7 q^{93} - 33 q^{94} - 23 q^{95} - 8 q^{96} + 10 q^{97} - 2 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 3 * q^5 + 2 * q^6 - 6 * q^7 + 6 * q^9 - q^10 + 2 * q^12 + 2 * q^14 - 3 * q^15 - 10 * q^16 - 9 * q^17 - 2 * q^18 + 11 * q^19 - q^20 + 6 * q^21 + 7 * q^22 - 11 * q^23 + 29 * q^25 - 6 * q^27 + 2 * q^28 - 10 * q^29 + q^30 + 7 * q^31 + 8 * q^32 + 10 * q^34 - 3 * q^35 - 2 * q^36 - 20 * q^37 - 6 * q^38 - 10 * q^41 - 2 * q^42 - 9 * q^43 + 3 * q^45 - 8 * q^46 + 36 * q^47 + 10 * q^48 + 6 * q^49 + 9 * q^50 + 9 * q^51 - 12 * q^53 + 2 * q^54 - 29 * q^55 - 11 * q^57 - 6 * q^58 - 41 * q^59 + q^60 - 24 * q^61 - 6 * q^63 + 8 * q^64 - 7 * q^66 + 15 * q^67 + 10 * q^68 + 11 * q^69 + q^70 + 13 * q^71 + 25 * q^73 + 2 * q^74 - 29 * q^75 + q^76 - 16 * q^79 - 5 * q^80 + 6 * q^81 + q^82 - 2 * q^83 - 2 * q^84 - 33 * q^85 - 4 * q^86 + 10 * q^87 - 14 * q^88 + 15 * q^89 - q^90 + 13 * q^92 - 7 * q^93 - 33 * q^94 - 23 * q^95 - 8 * q^96 + 10 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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