LMFDB - Embedded newform 3549.2.a.y.1.1

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			1.1
Root			$-2.07801$ 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)

$f(q)$	$=$	$q-1.80194 q^{2} -1.00000 q^{3} +1.24698 q^{4} -2.07801 q^{5} +1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.80194 q^{2} -1.00000 q^{3} +1.24698 q^{4} -2.07801 q^{5} +1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} +3.74444 q^{10} +5.11428 q^{11} -1.24698 q^{12} +1.80194 q^{14} +2.07801 q^{15} -4.93900 q^{16} -0.185116 q^{17} -1.80194 q^{18} -0.591233 q^{19} -2.59123 q^{20} +1.00000 q^{21} -9.21562 q^{22} -2.78930 q^{23} -1.35690 q^{24} -0.681883 q^{25} -1.00000 q^{27} -1.24698 q^{28} -9.95951 q^{29} -3.74444 q^{30} +5.23122 q^{31} +6.18598 q^{32} -5.11428 q^{33} +0.333567 q^{34} +2.07801 q^{35} +1.24698 q^{36} -2.97441 q^{37} +1.06537 q^{38} -2.81964 q^{40} -10.0533 q^{41} -1.80194 q^{42} +5.25454 q^{43} +6.37741 q^{44} -2.07801 q^{45} +5.02614 q^{46} +12.6067 q^{47} +4.93900 q^{48} +1.00000 q^{49} +1.22871 q^{50} +0.185116 q^{51} -5.51955 q^{53} +1.80194 q^{54} -10.6275 q^{55} -1.35690 q^{56} +0.591233 q^{57} +17.9464 q^{58} +6.46823 q^{59} +2.59123 q^{60} +8.43351 q^{61} -9.42632 q^{62} -1.00000 q^{63} -1.26875 q^{64} +9.21562 q^{66} +9.58967 q^{67} -0.230836 q^{68} +2.78930 q^{69} -3.74444 q^{70} -1.60894 q^{71} +1.35690 q^{72} +9.17303 q^{73} +5.35970 q^{74} +0.681883 q^{75} -0.737256 q^{76} -5.11428 q^{77} +5.42070 q^{79} +10.2633 q^{80} +1.00000 q^{81} +18.1154 q^{82} +3.99899 q^{83} +1.24698 q^{84} +0.384672 q^{85} -9.46836 q^{86} +9.95951 q^{87} +6.93955 q^{88} -9.63632 q^{89} +3.74444 q^{90} -3.47819 q^{92} -5.23122 q^{93} -22.7165 q^{94} +1.22859 q^{95} -6.18598 q^{96} -3.05048 q^{97} -1.80194 q^{98} +5.11428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.80194	−1.27416	−0.637081	−	0.770797i	$-0.719858\pi$
$2$	−1.80194	−1.27416	−0.637081	+	0.770797i	$0.719858\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.24698	0.623490
$5$	−2.07801	−0.929313	−0.464657	−	0.885491i	$-0.653822\pi$
$5$	−2.07801	−0.929313	−0.464657	+	0.885491i	$0.653822\pi$
$6$	1.80194	0.735638
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.35690	0.479735
$9$	1.00000	0.333333
$10$	3.74444	1.18410
$11$	5.11428	1.54201	0.771007	−	0.636826i	$-0.219753\pi$
$11$	5.11428	1.54201	0.771007	+	0.636826i	$0.219753\pi$
$12$	−1.24698	−0.359972
$13$	0	0
$13$	0	0
$14$	1.80194	0.481588
$15$	2.07801	0.536539
$16$	−4.93900	−1.23475
$17$	−0.185116	−0.0448972	−0.0224486	−	0.999748i	$-0.507146\pi$
$17$	−0.185116	−0.0448972	−0.0224486	+	0.999748i	$0.507146\pi$
$18$	−1.80194	−0.424721
$19$	−0.591233	−0.135638	−0.0678191	−	0.997698i	$-0.521604\pi$
$19$	−0.591233	−0.135638	−0.0678191	+	0.997698i	$0.521604\pi$
$20$	−2.59123	−0.579417
$21$	1.00000	0.218218
$22$	−9.21562	−1.96478
$23$	−2.78930	−0.581608	−0.290804	−	0.956783i	$-0.593923\pi$
$23$	−2.78930	−0.581608	−0.290804	+	0.956783i	$0.593923\pi$
$24$	−1.35690	−0.276975
$25$	−0.681883	−0.136377
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.24698	−0.235657
$29$	−9.95951	−1.84943	−0.924717	−	0.380654i	$-0.875699\pi$
$29$	−9.95951	−1.84943	−0.924717	+	0.380654i	$0.875699\pi$
$30$	−3.74444	−0.683638
$31$	5.23122	0.939554	0.469777	−	0.882785i	$-0.344334\pi$
$31$	5.23122	0.939554	0.469777	+	0.882785i	$0.344334\pi$
$32$	6.18598	1.09354
$33$	−5.11428	−0.890282
$34$	0.333567	0.0572063
$35$	2.07801	0.351247
$36$	1.24698	0.207830
$37$	−2.97441	−0.488990	−0.244495	−	0.969651i	$-0.578622\pi$
$37$	−2.97441	−0.488990	−0.244495	+	0.969651i	$0.578622\pi$
$38$	1.06537	0.172825
$39$	0	0
$40$	−2.81964	−0.445824
$41$	−10.0533	−1.57006	−0.785030	−	0.619458i	$-0.787352\pi$
$41$	−10.0533	−1.57006	−0.785030	+	0.619458i	$0.787352\pi$
$42$	−1.80194	−0.278045
$43$	5.25454	0.801310	0.400655	−	0.916229i	$-0.368783\pi$
$43$	5.25454	0.801310	0.400655	+	0.916229i	$0.368783\pi$
$44$	6.37741	0.961430
$45$	−2.07801	−0.309771
$46$	5.02614	0.741063
$47$	12.6067	1.83887	0.919437	−	0.393238i	$-0.128645\pi$
$47$	12.6067	1.83887	0.919437	+	0.393238i	$0.128645\pi$
$48$	4.93900	0.712883
$49$	1.00000	0.142857
$50$	1.22871	0.173766
$51$	0.185116	0.0259214
$52$	0	0
$53$	−5.51955	−0.758168	−0.379084	−	0.925362i	$-0.623761\pi$
$53$	−5.51955	−0.758168	−0.379084	+	0.925362i	$0.623761\pi$
$54$	1.80194	0.245213
$55$	−10.6275	−1.43301
$56$	−1.35690	−0.181323
$57$	0.591233	0.0783108
$58$	17.9464	2.35648
$59$	6.46823	0.842091	0.421046	−	0.907039i	$-0.361663\pi$
$59$	6.46823	0.842091	0.421046	+	0.907039i	$0.361663\pi$
$60$	2.59123	0.334527
$61$	8.43351	1.07980	0.539900	−	0.841729i	$-0.318462\pi$
$61$	8.43351	1.07980	0.539900	+	0.841729i	$0.318462\pi$
$62$	−9.42632	−1.19714
$63$	−1.00000	−0.125988
$64$	−1.26875	−0.158594
$65$	0	0
$66$	9.21562	1.13436
$67$	9.58967	1.17156	0.585782	−	0.810468i	$-0.300787\pi$
$67$	9.58967	1.17156	0.585782	+	0.810468i	$0.300787\pi$
$68$	−0.230836	−0.0279929
$69$	2.78930	0.335792
$70$	−3.74444	−0.447546
$71$	−1.60894	−0.190946	−0.0954728	−	0.995432i	$-0.530436\pi$
$71$	−1.60894	−0.190946	−0.0954728	+	0.995432i	$0.530436\pi$
$72$	1.35690	0.159912
$73$	9.17303	1.07362	0.536811	−	0.843702i	$-0.319629\pi$
$73$	9.17303	1.07362	0.536811	+	0.843702i	$0.319629\pi$
$74$	5.35970	0.623053
$75$	0.681883	0.0787371
$76$	−0.737256	−0.0845691
$77$	−5.11428	−0.582827
$78$	0	0
$79$	5.42070	0.609876	0.304938	−	0.952372i	$-0.401364\pi$
$79$	5.42070	0.609876	0.304938	+	0.952372i	$0.401364\pi$
$80$	10.2633	1.14747
$81$	1.00000	0.111111
$82$	18.1154	2.00051
$83$	3.99899	0.438946	0.219473	−	0.975619i	$-0.429566\pi$
$83$	3.99899	0.438946	0.219473	+	0.975619i	$0.429566\pi$
$84$	1.24698	0.136057
$85$	0.384672	0.0417235
$86$	−9.46836	−1.02100
$87$	9.95951	1.06777
$88$	6.93955	0.739758
$89$	−9.63632	−1.02145	−0.510724	−	0.859745i	$-0.670623\pi$
$89$	−9.63632	−1.02145	−0.510724	+	0.859745i	$0.670623\pi$
$90$	3.74444	0.394699
$91$	0	0
$92$	−3.47819	−0.362627
$93$	−5.23122	−0.542452
$94$	−22.7165	−2.34302
$95$	1.22859	0.126050
$96$	−6.18598	−0.631354
$97$	−3.05048	−0.309729	−0.154864	−	0.987936i	$-0.549494\pi$
$97$	−3.05048	−0.309729	−0.154864	+	0.987936i	$0.549494\pi$
$98$	−1.80194	−0.182023
$99$	5.11428	0.514005
$100$	−0.850295	−0.0850295
$101$	−8.65561	−0.861265	−0.430633	−	0.902527i	$-0.641710\pi$
$101$	−8.65561	−0.861265	−0.430633	+	0.902527i	$0.641710\pi$
$102$	−0.333567	−0.0330281
$103$	14.0880	1.38813	0.694066	−	0.719911i	$-0.255818\pi$
$103$	14.0880	1.38813	0.694066	+	0.719911i	$0.255818\pi$
$104$	0	0
$105$	−2.07801	−0.202793
$106$	9.94588	0.966029
$107$	4.66386	0.450873	0.225436	−	0.974258i	$-0.427619\pi$
$107$	4.66386	0.450873	0.225436	+	0.974258i	$0.427619\pi$
$108$	−1.24698	−0.119991
$109$	−2.35477	−0.225546	−0.112773	−	0.993621i	$-0.535973\pi$
$109$	−2.35477	−0.225546	−0.112773	+	0.993621i	$0.535973\pi$
$110$	19.1501	1.82589
$111$	2.97441	0.282319
$112$	4.93900	0.466692
$113$	−6.58305	−0.619281	−0.309641	−	0.950854i	$-0.600209\pi$
$113$	−6.58305	−0.619281	−0.309641	+	0.950854i	$0.600209\pi$
$114$	−1.06537	−0.0997806
$115$	5.79618	0.540496
$116$	−12.4193	−1.15310
$117$	0	0
$118$	−11.6553	−1.07296
$119$	0.185116	0.0169695
$120$	2.81964	0.257397
$121$	15.1559	1.37781
$122$	−15.1967	−1.37584
$123$	10.0533	0.906474
$124$	6.52322	0.585802
$125$	11.8070	1.05605
$126$	1.80194	0.160529
$127$	−5.34744	−0.474509	−0.237254	−	0.971448i	$-0.576247\pi$
$127$	−5.34744	−0.474509	−0.237254	+	0.971448i	$0.576247\pi$
$128$	−10.0858	−0.891463
$129$	−5.25454	−0.462637
$130$	0	0
$131$	−16.8419	−1.47148	−0.735742	−	0.677262i	$-0.763166\pi$
$131$	−16.8419	−1.47148	−0.735742	+	0.677262i	$0.763166\pi$
$132$	−6.37741	−0.555082
$133$	0.591233	0.0512664
$134$	−17.2800	−1.49276
$135$	2.07801	0.178846
$136$	−0.251183	−0.0215387
$137$	−22.1369	−1.89128	−0.945642	−	0.325209i	$-0.894565\pi$
$137$	−22.1369	−1.89128	−0.945642	+	0.325209i	$0.894565\pi$
$138$	−5.02614	−0.427853
$139$	−18.2956	−1.55181	−0.775905	−	0.630850i	$-0.782706\pi$
$139$	−18.2956	−1.55181	−0.775905	+	0.630850i	$0.782706\pi$
$140$	2.59123	0.218999
$141$	−12.6067	−1.06167
$142$	2.89920	0.243296
$143$	0	0
$144$	−4.93900	−0.411583
$145$	20.6959	1.71870
$146$	−16.5292	−1.36797
$147$	−1.00000	−0.0824786
$148$	−3.70903	−0.304880
$149$	21.8601	1.79085	0.895427	−	0.445209i	$-0.146871\pi$
$149$	21.8601	1.79085	0.895427	+	0.445209i	$0.146871\pi$
$150$	−1.22871	−0.100324
$151$	−6.89601	−0.561190	−0.280595	−	0.959826i	$-0.590532\pi$
$151$	−6.89601	−0.561190	−0.280595	+	0.959826i	$0.590532\pi$
$152$	−0.802242	−0.0650704
$153$	−0.185116	−0.0149657
$154$	9.21562	0.742616
$155$	−10.8705	−0.873140
$156$	0	0
$157$	4.87082	0.388734	0.194367	−	0.980929i	$-0.437735\pi$
$157$	4.87082	0.388734	0.194367	+	0.980929i	$0.437735\pi$
$158$	−9.76776	−0.777081
$159$	5.51955	0.437729
$160$	−12.8545	−1.01624
$161$	2.78930	0.219827
$162$	−1.80194	−0.141574
$163$	−21.1276	−1.65485	−0.827423	−	0.561580i	$-0.810194\pi$
$163$	−21.1276	−1.65485	−0.827423	+	0.561580i	$0.810194\pi$
$164$	−12.5362	−0.978916
$165$	10.6275	0.827351
$166$	−7.20593	−0.559289
$167$	−0.804062	−0.0622202	−0.0311101	−	0.999516i	$-0.509904\pi$
$167$	−0.804062	−0.0622202	−0.0311101	+	0.999516i	$0.509904\pi$
$168$	1.35690	0.104687
$169$	0	0
$170$	−0.693155	−0.0531626
$171$	−0.591233	−0.0452127
$172$	6.55231	0.499609
$173$	18.2281	1.38586	0.692929	−	0.721006i	$-0.256320\pi$
$173$	18.2281	1.38586	0.692929	+	0.721006i	$0.256320\pi$
$174$	−17.9464	−1.36051
$175$	0.681883	0.0515455
$176$	−25.2594	−1.90400
$177$	−6.46823	−0.486182
$178$	17.3641	1.30149
$179$	−20.7087	−1.54784	−0.773921	−	0.633282i	$-0.781707\pi$
$179$	−20.7087	−1.54784	−0.773921	+	0.633282i	$0.781707\pi$
$180$	−2.59123	−0.193139
$181$	−9.66053	−0.718061	−0.359031	−	0.933326i	$-0.616893\pi$
$181$	−9.66053	−0.718061	−0.359031	+	0.933326i	$0.616893\pi$
$182$	0	0
$183$	−8.43351	−0.623423
$184$	−3.78478	−0.279018
$185$	6.18085	0.454425
$186$	9.42632	0.691172
$187$	−0.946734	−0.0692321
$188$	15.7203	1.14652
$189$	1.00000	0.0727393
$190$	−2.21384	−0.160609
$191$	−10.4151	−0.753609	−0.376804	−	0.926293i	$-0.622977\pi$
$191$	−10.4151	−0.753609	−0.376804	+	0.926293i	$0.622977\pi$
$192$	1.26875	0.0915641
$193$	26.2530	1.88973	0.944867	−	0.327455i	$-0.106191\pi$
$193$	26.2530	1.88973	0.944867	+	0.327455i	$0.106191\pi$
$194$	5.49677	0.394645
$195$	0	0
$196$	1.24698	0.0890700
$197$	−12.4560	−0.887451	−0.443725	−	0.896163i	$-0.646343\pi$
$197$	−12.4560	−0.887451	−0.443725	+	0.896163i	$0.646343\pi$
$198$	−9.21562	−0.654926
$199$	−10.3098	−0.730841	−0.365421	−	0.930843i	$-0.619075\pi$
$199$	−10.3098	−0.730841	−0.365421	+	0.930843i	$0.619075\pi$
$200$	−0.925245	−0.0654247
$201$	−9.58967	−0.676403
$202$	15.5969	1.09739
$203$	9.95951	0.699021
$204$	0.230836	0.0161617
$205$	20.8908	1.45908
$206$	−25.3857	−1.76871
$207$	−2.78930	−0.193869
$208$	0	0
$209$	−3.02374	−0.209156
$210$	3.74444	0.258391
$211$	14.0679	0.968473	0.484237	−	0.874937i	$-0.339097\pi$
$211$	14.0679	0.968473	0.484237	+	0.874937i	$0.339097\pi$
$212$	−6.88276	−0.472710
$213$	1.60894	0.110242
$214$	−8.40399	−0.574485
$215$	−10.9190	−0.744669
$216$	−1.35690	−0.0923251
$217$	−5.23122	−0.355118
$218$	4.24315	0.287383
$219$	−9.17303	−0.619856
$220$	−13.2523	−0.893470
$221$	0	0
$222$	−5.35970	−0.359720
$223$	23.4082	1.56753	0.783763	−	0.621060i	$-0.213298\pi$
$223$	23.4082	1.56753	0.783763	+	0.621060i	$0.213298\pi$
$224$	−6.18598	−0.413318
$225$	−0.681883	−0.0454589
$226$	11.8622	0.789065
$227$	1.79773	0.119319	0.0596596	−	0.998219i	$-0.480998\pi$
$227$	1.79773	0.119319	0.0596596	+	0.998219i	$0.480998\pi$
$228$	0.737256	0.0488260
$229$	−4.80163	−0.317301	−0.158650	−	0.987335i	$-0.550714\pi$
$229$	−4.80163	−0.317301	−0.158650	+	0.987335i	$0.550714\pi$
$230$	−10.4444	−0.688680
$231$	5.11428	0.336495
$232$	−13.5140	−0.887239
$233$	−18.1525	−1.18921	−0.594605	−	0.804018i	$-0.702692\pi$
$233$	−18.1525	−1.18921	−0.594605	+	0.804018i	$0.702692\pi$
$234$	0	0
$235$	−26.1968	−1.70889
$236$	8.06575	0.525035
$237$	−5.42070	−0.352112
$238$	−0.333567	−0.0216219
$239$	−17.0258	−1.10131	−0.550654	−	0.834733i	$-0.685622\pi$
$239$	−17.0258	−1.10131	−0.550654	+	0.834733i	$0.685622\pi$
$240$	−10.2633	−0.662492
$241$	10.2368	0.659412	0.329706	−	0.944084i	$-0.393050\pi$
$241$	10.2368	0.659412	0.329706	+	0.944084i	$0.393050\pi$
$242$	−27.3100	−1.75555
$243$	−1.00000	−0.0641500
$244$	10.5164	0.673244
$245$	−2.07801	−0.132759
$246$	−18.1154	−1.15500
$247$	0	0
$248$	7.09821	0.450737
$249$	−3.99899	−0.253426
$250$	−21.2755	−1.34558
$251$	17.3844	1.09730	0.548648	−	0.836053i	$-0.315143\pi$
$251$	17.3844	1.09730	0.548648	+	0.836053i	$0.315143\pi$
$252$	−1.24698	−0.0785523
$253$	−14.2652	−0.896848
$254$	9.63576	0.604601
$255$	−0.384672	−0.0240891
$256$	20.7114	1.29446
$257$	−1.26764	−0.0790733	−0.0395366	−	0.999218i	$-0.512588\pi$
$257$	−1.26764	−0.0790733	−0.0395366	+	0.999218i	$0.512588\pi$
$258$	9.46836	0.589474
$259$	2.97441	0.184821
$260$	0	0
$261$	−9.95951	−0.616478
$262$	30.3480	1.87491
$263$	14.3084	0.882294	0.441147	−	0.897435i	$-0.354572\pi$
$263$	14.3084	0.882294	0.441147	+	0.897435i	$0.354572\pi$
$264$	−6.93955	−0.427100
$265$	11.4697	0.704576
$266$	−1.06537	−0.0653218
$267$	9.63632	0.589733
$268$	11.9581	0.730459
$269$	−6.23326	−0.380049	−0.190024	−	0.981779i	$-0.560857\pi$
$269$	−6.23326	−0.380049	−0.190024	+	0.981779i	$0.560857\pi$
$270$	−3.74444	−0.227879
$271$	10.8204	0.657290	0.328645	−	0.944454i	$-0.393408\pi$
$271$	10.8204	0.657290	0.328645	+	0.944454i	$0.393408\pi$
$272$	0.914287	0.0554368
$273$	0	0
$274$	39.8893	2.40980
$275$	−3.48734	−0.210295
$276$	3.47819	0.209363
$277$	16.5661	0.995359	0.497679	−	0.867361i	$-0.334186\pi$
$277$	16.5661	0.995359	0.497679	+	0.867361i	$0.334186\pi$
$278$	32.9675	1.97726
$279$	5.23122	0.313185
$280$	2.81964	0.168506
$281$	−21.4915	−1.28208	−0.641039	−	0.767508i	$-0.721496\pi$
$281$	−21.4915	−1.28208	−0.641039	+	0.767508i	$0.721496\pi$
$282$	22.7165	1.35275
$283$	−24.4327	−1.45237	−0.726185	−	0.687499i	$-0.758709\pi$
$283$	−24.4327	−1.45237	−0.726185	+	0.687499i	$0.758709\pi$
$284$	−2.00631	−0.119053
$285$	−1.22859	−0.0727753
$286$	0	0
$287$	10.0533	0.593427
$288$	6.18598	0.364512
$289$	−16.9657	−0.997984
$290$	−37.2928	−2.18991
$291$	3.05048	0.178822
$292$	11.4386	0.669393
$293$	11.1636	0.652187	0.326094	−	0.945337i	$-0.394268\pi$
$293$	11.1636	0.652187	0.326094	+	0.945337i	$0.394268\pi$
$294$	1.80194	0.105091
$295$	−13.4410	−0.782567
$296$	−4.03597	−0.234586
$297$	−5.11428	−0.296761
$298$	−39.3906	−2.28184
$299$	0	0
$300$	0.850295	0.0490918
$301$	−5.25454	−0.302867
$302$	12.4262	0.715047
$303$	8.65561	0.497252
$304$	2.92010	0.167479
$305$	−17.5249	−1.00347
$306$	0.333567	0.0190688
$307$	−2.87863	−0.164292	−0.0821461	−	0.996620i	$-0.526177\pi$
$307$	−2.87863	−0.164292	−0.0821461	+	0.996620i	$0.526177\pi$
$308$	−6.37741	−0.363386
$309$	−14.0880	−0.801438
$310$	19.5880	1.11252
$311$	27.7786	1.57518	0.787590	−	0.616199i	$-0.211328\pi$
$311$	27.7786	1.57518	0.787590	+	0.616199i	$0.211328\pi$
$312$	0	0
$313$	21.2336	1.20019	0.600096	−	0.799928i	$-0.295129\pi$
$313$	21.2336	1.20019	0.600096	+	0.799928i	$0.295129\pi$
$314$	−8.77691	−0.495310
$315$	2.07801	0.117082
$316$	6.75950	0.380252
$317$	1.54637	0.0868530	0.0434265	−	0.999057i	$-0.486173\pi$
$317$	1.54637	0.0868530	0.0434265	+	0.999057i	$0.486173\pi$
$318$	−9.94588	−0.557737
$319$	−50.9358	−2.85186
$320$	2.63647	0.147383
$321$	−4.66386	−0.260312
$322$	−5.02614	−0.280096
$323$	0.109447	0.00608977
$324$	1.24698	0.0692766
$325$	0	0
$326$	38.0707	2.10854
$327$	2.35477	0.130219
$328$	−13.6413	−0.753213
$329$	−12.6067	−0.695029
$330$	−19.1501	−1.05418
$331$	−24.2044	−1.33039	−0.665197	−	0.746668i	$-0.731653\pi$
$331$	−24.2044	−1.33039	−0.665197	+	0.746668i	$0.731653\pi$
$332$	4.98666	0.273678
$333$	−2.97441	−0.162997
$334$	1.44887	0.0792786
$335$	−19.9274	−1.08875
$336$	−4.93900	−0.269445
$337$	−11.8094	−0.643297	−0.321648	−	0.946859i	$-0.604237\pi$
$337$	−11.8094	−0.643297	−0.321648	+	0.946859i	$0.604237\pi$
$338$	0	0
$339$	6.58305	0.357542
$340$	0.479678	0.0260142
$341$	26.7539	1.44881
$342$	1.06537	0.0576084
$343$	−1.00000	−0.0539949
$344$	7.12987	0.384417
$345$	−5.79618	−0.312056
$346$	−32.8459	−1.76581
$347$	−3.90357	−0.209555	−0.104777	−	0.994496i	$-0.533413\pi$
$347$	−3.90357	−0.209555	−0.104777	+	0.994496i	$0.533413\pi$
$348$	12.4193	0.665745
$349$	−3.89952	−0.208736	−0.104368	−	0.994539i	$-0.533282\pi$
$349$	−3.89952	−0.208736	−0.104368	+	0.994539i	$0.533282\pi$
$350$	−1.22871	−0.0656774
$351$	0	0
$352$	31.6369	1.68625
$353$	−10.0452	−0.534650	−0.267325	−	0.963606i	$-0.586140\pi$
$353$	−10.0452	−0.534650	−0.267325	+	0.963606i	$0.586140\pi$
$354$	11.6553	0.619474
$355$	3.34338	0.177448
$356$	−12.0163	−0.636863
$357$	−0.185116	−0.00979737
$358$	37.3158	1.97220
$359$	−27.3427	−1.44309	−0.721547	−	0.692365i	$-0.756569\pi$
$359$	−27.3427	−1.44309	−0.721547	+	0.692365i	$0.756569\pi$
$360$	−2.81964	−0.148608
$361$	−18.6504	−0.981602
$362$	17.4077	0.914927
$363$	−15.1559	−0.795478
$364$	0	0
$365$	−19.0616	−0.997732
$366$	15.1967	0.794342
$367$	−16.0870	−0.839734	−0.419867	−	0.907586i	$-0.637923\pi$
$367$	−16.0870	−0.839734	−0.419867	+	0.907586i	$0.637923\pi$
$368$	13.7763	0.718141
$369$	−10.0533	−0.523353
$370$	−11.1375	−0.579011
$371$	5.51955	0.286561
$372$	−6.52322	−0.338213
$373$	−8.23352	−0.426315	−0.213158	−	0.977018i	$-0.568375\pi$
$373$	−8.23352	−0.426315	−0.213158	+	0.977018i	$0.568375\pi$
$374$	1.70596	0.0882129
$375$	−11.8070	−0.609711
$376$	17.1060	0.882172
$377$	0	0
$378$	−1.80194	−0.0926817
$379$	8.18484	0.420427	0.210214	−	0.977655i	$-0.432584\pi$
$379$	8.18484	0.420427	0.210214	+	0.977655i	$0.432584\pi$
$380$	1.53202	0.0785912
$381$	5.34744	0.273958
$382$	18.7673	0.960220
$383$	26.3188	1.34483	0.672413	−	0.740176i	$-0.265258\pi$
$383$	26.3188	1.34483	0.672413	+	0.740176i	$0.265258\pi$
$384$	10.0858	0.514686
$385$	10.6275	0.541629
$386$	−47.3063	−2.40783
$387$	5.25454	0.267103
$388$	−3.80388	−0.193113
$389$	29.0722	1.47402	0.737010	−	0.675882i	$-0.236237\pi$
$389$	29.0722	1.47402	0.737010	+	0.675882i	$0.236237\pi$
$390$	0	0
$391$	0.516343	0.0261126
$392$	1.35690	0.0685336
$393$	16.8419	0.849561
$394$	22.4449	1.13076
$395$	−11.2643	−0.566766
$396$	6.37741	0.320477
$397$	−5.11134	−0.256531	−0.128265	−	0.991740i	$-0.540941\pi$
$397$	−5.11134	−0.256531	−0.128265	+	0.991740i	$0.540941\pi$
$398$	18.5776	0.931210
$399$	−0.591233	−0.0295987
$400$	3.36782	0.168391
$401$	−14.9970	−0.748913	−0.374456	−	0.927245i	$-0.622171\pi$
$401$	−14.9970	−0.748913	−0.374456	+	0.927245i	$0.622171\pi$
$402$	17.2800	0.861847
$403$	0	0
$404$	−10.7934	−0.536990
$405$	−2.07801	−0.103257
$406$	−17.9464	−0.890666
$407$	−15.2120	−0.754030
$408$	0.251183	0.0124354
$409$	−32.1645	−1.59043	−0.795217	−	0.606325i	$-0.792643\pi$
$409$	−32.1645	−1.59043	−0.795217	+	0.606325i	$0.792643\pi$
$410$	−37.6439	−1.85910
$411$	22.1369	1.09193
$412$	17.5674	0.865486
$413$	−6.46823	−0.318281
$414$	5.02614	0.247021
$415$	−8.30993	−0.407919
$416$	0	0
$417$	18.2956	0.895938
$418$	5.44858	0.266499
$419$	−22.8601	−1.11679	−0.558395	−	0.829575i	$-0.688583\pi$
$419$	−22.8601	−1.11679	−0.558395	+	0.829575i	$0.688583\pi$
$420$	−2.59123	−0.126439
$421$	−24.3260	−1.18558	−0.592789	−	0.805358i	$-0.701973\pi$
$421$	−24.3260	−1.18558	−0.592789	+	0.805358i	$0.701973\pi$
$422$	−25.3495	−1.23399
$423$	12.6067	0.612958
$424$	−7.48945	−0.363720
$425$	0.126227	0.00612293
$426$	−2.89920	−0.140467
$427$	−8.43351	−0.408126
$428$	5.81574	0.281115
$429$	0	0
$430$	19.6753	0.948829
$431$	25.1639	1.21210	0.606051	−	0.795426i	$-0.292753\pi$
$431$	25.1639	1.21210	0.606051	+	0.795426i	$0.292753\pi$
$432$	4.93900	0.237628
$433$	−29.9618	−1.43987	−0.719936	−	0.694040i	$-0.755829\pi$
$433$	−29.9618	−1.43987	−0.719936	+	0.694040i	$0.755829\pi$
$434$	9.42632	0.452478
$435$	−20.6959	−0.992295
$436$	−2.93635	−0.140626
$437$	1.64912	0.0788883
$438$	16.5292	0.789797
$439$	19.1986	0.916299	0.458150	−	0.888875i	$-0.348512\pi$
$439$	19.1986	0.916299	0.458150	+	0.888875i	$0.348512\pi$
$440$	−14.4204	−0.687467
$441$	1.00000	0.0476190
$442$	0	0
$443$	−8.61112	−0.409127	−0.204563	−	0.978853i	$-0.565577\pi$
$443$	−8.61112	−0.409127	−0.204563	+	0.978853i	$0.565577\pi$
$444$	3.70903	0.176023
$445$	20.0244	0.949245
$446$	−42.1800	−1.99728
$447$	−21.8601	−1.03395
$448$	1.26875	0.0599428
$449$	20.7380	0.978686	0.489343	−	0.872091i	$-0.337237\pi$
$449$	20.7380	0.978686	0.489343	+	0.872091i	$0.337237\pi$
$450$	1.22871	0.0579220
$451$	−51.4153	−2.42105
$452$	−8.20893	−0.386116
$453$	6.89601	0.324003
$454$	−3.23939	−0.152032
$455$	0	0
$456$	0.802242	0.0375684
$457$	−17.2267	−0.805833	−0.402916	−	0.915237i	$-0.632003\pi$
$457$	−17.2267	−0.805833	−0.402916	+	0.915237i	$0.632003\pi$
$458$	8.65224	0.404293
$459$	0.185116	0.00864046
$460$	7.22772	0.336994
$461$	−37.3236	−1.73833	−0.869167	−	0.494519i	$-0.835344\pi$
$461$	−37.3236	−1.73833	−0.869167	+	0.494519i	$0.835344\pi$
$462$	−9.21562	−0.428749
$463$	−0.678707	−0.0315422	−0.0157711	−	0.999876i	$-0.505020\pi$
$463$	−0.678707	−0.0315422	−0.0157711	+	0.999876i	$0.505020\pi$
$464$	49.1900	2.28359
$465$	10.8705	0.504108
$466$	32.7097	1.51525
$467$	−21.2872	−0.985055	−0.492527	−	0.870297i	$-0.663927\pi$
$467$	−21.2872	−0.985055	−0.492527	+	0.870297i	$0.663927\pi$
$468$	0	0
$469$	−9.58967	−0.442810
$470$	47.2050	2.17740
$471$	−4.87082	−0.224435
$472$	8.77671	0.403981
$473$	26.8732	1.23563
$474$	9.76776	0.448648
$475$	0.403152	0.0184979
$476$	0.230836	0.0105803
$477$	−5.51955	−0.252723
$478$	30.6795	1.40325
$479$	−5.01859	−0.229305	−0.114653	−	0.993406i	$-0.536575\pi$
$479$	−5.01859	−0.229305	−0.114653	+	0.993406i	$0.536575\pi$
$480$	12.8545	0.586726
$481$	0	0
$482$	−18.4461	−0.840198
$483$	−2.78930	−0.126917
$484$	18.8991	0.859049
$485$	6.33891	0.287835
$486$	1.80194	0.0817376
$487$	−16.2859	−0.737986	−0.368993	−	0.929432i	$-0.620297\pi$
$487$	−16.2859	−0.737986	−0.368993	+	0.929432i	$0.620297\pi$
$488$	11.4434	0.518018
$489$	21.1276	0.955425
$490$	3.74444	0.169157
$491$	−3.69624	−0.166809	−0.0834045	−	0.996516i	$-0.526579\pi$
$491$	−3.69624	−0.166809	−0.0834045	+	0.996516i	$0.526579\pi$
$492$	12.5362	0.565177
$493$	1.84366	0.0830344
$494$	0	0
$495$	−10.6275	−0.477672
$496$	−25.8370	−1.16011
$497$	1.60894	0.0721706
$498$	7.20593	0.322905
$499$	−40.5061	−1.81330	−0.906652	−	0.421880i	$-0.861370\pi$
$499$	−40.5061	−1.81330	−0.906652	+	0.421880i	$0.861370\pi$
$500$	14.7231	0.658436
$501$	0.804062	0.0359228
$502$	−31.3257	−1.39813
$503$	−31.3688	−1.39867	−0.699333	−	0.714796i	$-0.746520\pi$
$503$	−31.3688	−1.39867	−0.699333	+	0.714796i	$0.746520\pi$
$504$	−1.35690	−0.0604409
$505$	17.9864	0.800385
$506$	25.7051	1.14273
$507$	0	0
$508$	−6.66815	−0.295851
$509$	−27.0022	−1.19685	−0.598426	−	0.801178i	$-0.704207\pi$
$509$	−27.0022	−1.19685	−0.598426	+	0.801178i	$0.704207\pi$
$510$	0.693155	0.0306934
$511$	−9.17303	−0.405791
$512$	−17.1491	−0.757892
$513$	0.591233	0.0261036
$514$	2.28421	0.100752
$515$	−29.2750	−1.29001
$516$	−6.55231	−0.288449
$517$	64.4742	2.83557
$518$	−5.35970	−0.235492
$519$	−18.2281	−0.800126
$520$	0	0
$521$	24.6292	1.07902	0.539512	−	0.841978i	$-0.318609\pi$
$521$	24.6292	1.07902	0.539512	+	0.841978i	$0.318609\pi$
$522$	17.9464	0.785493
$523$	6.84384	0.299260	0.149630	−	0.988742i	$-0.452192\pi$
$523$	6.84384	0.299260	0.149630	+	0.988742i	$0.452192\pi$
$524$	−21.0015	−0.917455
$525$	−0.681883	−0.0297598
$526$	−25.7829	−1.12419
$527$	−0.968380	−0.0421833
$528$	25.2594	1.09928
$529$	−15.2198	−0.661732
$530$	−20.6676	−0.897744
$531$	6.46823	0.280697
$532$	0.737256	0.0319641
$533$	0	0
$534$	−17.3641	−0.751416
$535$	−9.69155	−0.419002
$536$	13.0122	0.562041
$537$	20.7087	0.893647
$538$	11.2320	0.484244
$539$	5.11428	0.220288
$540$	2.59123	0.111509
$541$	26.4753	1.13826	0.569130	−	0.822247i	$-0.307280\pi$
$541$	26.4753	1.13826	0.569130	+	0.822247i	$0.307280\pi$
$542$	−19.4976	−0.837494
$543$	9.66053	0.414573
$544$	−1.14512	−0.0490967
$545$	4.89323	0.209603
$546$	0	0
$547$	15.7444	0.673183	0.336592	−	0.941651i	$-0.390726\pi$
$547$	15.7444	0.673183	0.336592	+	0.941651i	$0.390726\pi$
$548$	−27.6043	−1.17920
$549$	8.43351	0.359933
$550$	6.28398	0.267950
$551$	5.88840	0.250854
$552$	3.78478	0.161091
$553$	−5.42070	−0.230512
$554$	−29.8510	−1.26825
$555$	−6.18085	−0.262362
$556$	−22.8142	−0.967538
$557$	14.4151	0.610788	0.305394	−	0.952226i	$-0.401212\pi$
$557$	14.4151	0.610788	0.305394	+	0.952226i	$0.401212\pi$
$558$	−9.42632	−0.399048
$559$	0	0
$560$	−10.2633	−0.433703
$561$	0.946734	0.0399712
$562$	38.7264	1.63358
$563$	−22.7569	−0.959088	−0.479544	−	0.877518i	$-0.659198\pi$
$563$	−22.7569	−0.959088	−0.479544	+	0.877518i	$0.659198\pi$
$564$	−15.7203	−0.661943
$565$	13.6796	0.575506
$566$	44.0261	1.85056
$567$	−1.00000	−0.0419961
$568$	−2.18316	−0.0916033
$569$	−23.4397	−0.982642	−0.491321	−	0.870978i	$-0.663486\pi$
$569$	−23.4397	−0.982642	−0.491321	+	0.870978i	$0.663486\pi$
$570$	2.21384	0.0927275
$571$	−2.24053	−0.0937634	−0.0468817	−	0.998900i	$-0.514928\pi$
$571$	−2.24053	−0.0937634	−0.0468817	+	0.998900i	$0.514928\pi$
$572$	0	0
$573$	10.4151	0.435096
$574$	−18.1154	−0.756122
$575$	1.90197	0.0793178
$576$	−1.26875	−0.0528646
$577$	−39.6538	−1.65081	−0.825405	−	0.564541i	$-0.809053\pi$
$577$	−39.6538	−1.65081	−0.825405	+	0.564541i	$0.809053\pi$
$578$	30.5712	1.27159
$579$	−26.2530	−1.09104
$580$	25.8074	1.07159
$581$	−3.99899	−0.165906
$582$	−5.49677	−0.227848
$583$	−28.2285	−1.16911
$584$	12.4469	0.515054
$585$	0	0
$586$	−20.1162	−0.830993
$587$	−14.1384	−0.583555	−0.291777	−	0.956486i	$-0.594247\pi$
$587$	−14.1384	−0.583555	−0.291777	+	0.956486i	$0.594247\pi$
$588$	−1.24698	−0.0514246
$589$	−3.09287	−0.127439
$590$	24.2199	0.997117
$591$	12.4560	0.512370
$592$	14.6906	0.603781
$593$	−8.38386	−0.344284	−0.172142	−	0.985072i	$-0.555069\pi$
$593$	−8.38386	−0.344284	−0.172142	+	0.985072i	$0.555069\pi$
$594$	9.21562	0.378121
$595$	−0.384672	−0.0157700
$596$	27.2592	1.11658
$597$	10.3098	0.421951
$598$	0	0
$599$	−31.7481	−1.29719	−0.648596	−	0.761133i	$-0.724644\pi$
$599$	−31.7481	−1.29719	−0.648596	+	0.761133i	$0.724644\pi$
$600$	0.925245	0.0377730
$601$	4.22823	0.172473	0.0862365	−	0.996275i	$-0.472516\pi$
$601$	4.22823	0.172473	0.0862365	+	0.996275i	$0.472516\pi$
$602$	9.46836	0.385902
$603$	9.58967	0.390522
$604$	−8.59919	−0.349896
$605$	−31.4941	−1.28042
$606$	−15.5969	−0.633580
$607$	44.1087	1.79032	0.895158	−	0.445749i	$-0.147063\pi$
$607$	44.1087	1.79032	0.895158	+	0.445749i	$0.147063\pi$
$608$	−3.65736	−0.148325
$609$	−9.95951	−0.403580
$610$	31.5788	1.27859
$611$	0	0
$612$	−0.230836	−0.00933098
$613$	−46.2247	−1.86700	−0.933499	−	0.358580i	$-0.883261\pi$
$613$	−46.2247	−1.86700	−0.933499	+	0.358580i	$0.883261\pi$
$614$	5.18711	0.209335
$615$	−20.8908	−0.842399
$616$	−6.93955	−0.279602
$617$	−23.6252	−0.951114	−0.475557	−	0.879685i	$-0.657753\pi$
$617$	−23.6252	−0.951114	−0.475557	+	0.879685i	$0.657753\pi$
$618$	25.3857	1.02116
$619$	15.8607	0.637495	0.318747	−	0.947840i	$-0.396738\pi$
$619$	15.8607	0.637495	0.318747	+	0.947840i	$0.396738\pi$
$620$	−13.5553	−0.544394
$621$	2.78930	0.111931
$622$	−50.0553	−2.00704
$623$	9.63632	0.386071
$624$	0	0
$625$	−21.1256	−0.845025
$626$	−38.2616	−1.52924
$627$	3.02374	0.120756
$628$	6.07381	0.242371
$629$	0.550610	0.0219543
$630$	−3.74444	−0.149182
$631$	0.782536	0.0311523	0.0155761	−	0.999879i	$-0.495042\pi$
$631$	0.782536	0.0311523	0.0155761	+	0.999879i	$0.495042\pi$
$632$	7.35532	0.292579
$633$	−14.0679	−0.559148
$634$	−2.78647	−0.110665
$635$	11.1120	0.440967
$636$	6.88276	0.272919
$637$	0	0
$638$	91.7831	3.63373
$639$	−1.60894	−0.0636485
$640$	20.9583	0.828449
$641$	45.1286	1.78247	0.891237	−	0.453538i	$-0.149838\pi$
$641$	45.1286	1.78247	0.891237	+	0.453538i	$0.149838\pi$
$642$	8.40399	0.331679
$643$	30.1683	1.18972	0.594861	−	0.803828i	$-0.297207\pi$
$643$	30.1683	1.18972	0.594861	+	0.803828i	$0.297207\pi$
$644$	3.47819	0.137060
$645$	10.9190	0.429935
$646$	−0.197216	−0.00775936
$647$	−32.8978	−1.29334	−0.646672	−	0.762768i	$-0.723840\pi$
$647$	−32.8978	−1.29334	−0.646672	+	0.762768i	$0.723840\pi$
$648$	1.35690	0.0533039
$649$	33.0803	1.29852
$650$	0	0
$651$	5.23122	0.205027
$652$	−26.3457	−1.03178
$653$	−18.7526	−0.733848	−0.366924	−	0.930251i	$-0.619589\pi$
$653$	−18.7526	−0.733848	−0.366924	+	0.930251i	$0.619589\pi$
$654$	−4.24315	−0.165920
$655$	34.9976	1.36747
$656$	49.6532	1.93863
$657$	9.17303	0.357874
$658$	22.7165	0.885580
$659$	−30.9219	−1.20455	−0.602274	−	0.798289i	$-0.705739\pi$
$659$	−30.9219	−1.20455	−0.602274	+	0.798289i	$0.705739\pi$
$660$	13.2523	0.515845
$661$	31.2501	1.21549	0.607743	−	0.794133i	$-0.292075\pi$
$661$	31.2501	1.21549	0.607743	+	0.794133i	$0.292075\pi$
$662$	43.6148	1.69514
$663$	0	0
$664$	5.42621	0.210578
$665$	−1.22859	−0.0476426
$666$	5.35970	0.207684
$667$	27.7800	1.07565
$668$	−1.00265	−0.0387937
$669$	−23.4082	−0.905012
$670$	35.9079	1.38725
$671$	43.1314	1.66507
$672$	6.18598	0.238629
$673$	1.80497	0.0695765	0.0347883	−	0.999395i	$-0.488924\pi$
$673$	1.80497	0.0695765	0.0347883	+	0.999395i	$0.488924\pi$
$674$	21.2797	0.819665
$675$	0.681883	0.0262457
$676$	0	0
$677$	−32.4596	−1.24752	−0.623762	−	0.781614i	$-0.714397\pi$
$677$	−32.4596	−1.24752	−0.623762	+	0.781614i	$0.714397\pi$
$678$	−11.8622	−0.455567
$679$	3.05048	0.117067
$680$	0.521960	0.0200162
$681$	−1.79773	−0.0688890
$682$	−48.2089	−1.84601
$683$	21.4439	0.820529	0.410265	−	0.911967i	$-0.365436\pi$
$683$	21.4439	0.820529	0.410265	+	0.911967i	$0.365436\pi$
$684$	−0.737256	−0.0281897
$685$	46.0007	1.75760
$686$	1.80194	0.0687983
$687$	4.80163	0.183194
$688$	−25.9522	−0.989418
$689$	0	0
$690$	10.4444	0.397610
$691$	−9.69999	−0.369005	−0.184502	−	0.982832i	$-0.559067\pi$
$691$	−9.69999	−0.369005	−0.184502	+	0.982832i	$0.559067\pi$
$692$	22.7301	0.864068
$693$	−5.11428	−0.194276
$694$	7.03399	0.267007
$695$	38.0183	1.44212
$696$	13.5140	0.512248
$697$	1.86102	0.0704912
$698$	7.02669	0.265964
$699$	18.1525	0.686591
$700$	0.850295	0.0321381
$701$	−18.2679	−0.689969	−0.344984	−	0.938608i	$-0.612116\pi$
$701$	−18.2679	−0.689969	−0.344984	+	0.938608i	$0.612116\pi$
$702$	0	0
$703$	1.75857	0.0663258
$704$	−6.48875	−0.244554
$705$	26.1968	0.986628
$706$	18.1008	0.681231
$707$	8.65561	0.325528
$708$	−8.06575	−0.303129
$709$	−42.0282	−1.57840	−0.789201	−	0.614135i	$-0.789505\pi$
$709$	−42.0282	−1.57840	−0.789201	+	0.614135i	$0.789505\pi$
$710$	−6.02457	−0.226098
$711$	5.42070	0.203292
$712$	−13.0755	−0.490025
$713$	−14.5914	−0.546452
$714$	0.333567	0.0124834
$715$	0	0
$716$	−25.8234	−0.965064
$717$	17.0258	0.635841
$718$	49.2699	1.83874
$719$	18.9870	0.708094	0.354047	−	0.935228i	$-0.384805\pi$
$719$	18.9870	0.708094	0.354047	+	0.935228i	$0.384805\pi$
$720$	10.2633	0.382490
$721$	−14.0880	−0.524665
$722$	33.6069	1.25072
$723$	−10.2368	−0.380712
$724$	−12.0465	−0.447704
$725$	6.79123	0.252220
$726$	27.3100	1.01357
$727$	24.0558	0.892180	0.446090	−	0.894988i	$-0.352816\pi$
$727$	24.0558	0.892180	0.446090	+	0.894988i	$0.352816\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	34.3479	1.27127
$731$	−0.972699	−0.0359766
$732$	−10.5164	−0.388698
$733$	13.1128	0.484333	0.242166	−	0.970235i	$-0.422142\pi$
$733$	13.1128	0.484333	0.242166	+	0.970235i	$0.422142\pi$
$734$	28.9878	1.06996
$735$	2.07801	0.0766485
$736$	−17.2545	−0.636010
$737$	49.0443	1.80657
$738$	18.1154	0.666837
$739$	2.80795	0.103292	0.0516461	−	0.998665i	$-0.483553\pi$
$739$	2.80795	0.103292	0.0516461	+	0.998665i	$0.483553\pi$
$740$	7.70739	0.283329
$741$	0	0
$742$	−9.94588	−0.365125
$743$	−13.2186	−0.484945	−0.242472	−	0.970158i	$-0.577958\pi$
$743$	−13.2186	−0.484945	−0.242472	+	0.970158i	$0.577958\pi$
$744$	−7.09821	−0.260233
$745$	−45.4256	−1.66426
$746$	14.8363	0.543195
$747$	3.99899	0.146315
$748$	−1.18056	−0.0431655
$749$	−4.66386	−0.170414
$750$	21.2755	0.776871
$751$	−5.25633	−0.191806	−0.0959031	−	0.995391i	$-0.530574\pi$
$751$	−5.25633	−0.191806	−0.0959031	+	0.995391i	$0.530574\pi$
$752$	−62.2644	−2.27055
$753$	−17.3844	−0.633524
$754$	0	0
$755$	14.3300	0.521521
$756$	1.24698	0.0453522
$757$	−33.7607	−1.22705	−0.613526	−	0.789675i	$-0.710249\pi$
$757$	−33.7607	−1.22705	−0.613526	+	0.789675i	$0.710249\pi$
$758$	−14.7486	−0.535692
$759$	14.2652	0.517796
$760$	1.66707	0.0604708
$761$	24.6020	0.891823	0.445911	−	0.895077i	$-0.352880\pi$
$761$	24.6020	0.891823	0.445911	+	0.895077i	$0.352880\pi$
$762$	−9.63576	−0.349067
$763$	2.35477	0.0852485
$764$	−12.9874	−0.469867
$765$	0.384672	0.0139078
$766$	−47.4248	−1.71353
$767$	0	0
$768$	−20.7114	−0.747358
$769$	26.9935	0.973411	0.486705	−	0.873566i	$-0.338199\pi$
$769$	26.9935	0.973411	0.486705	+	0.873566i	$0.338199\pi$
$770$	−19.1501	−0.690123
$771$	1.26764	0.0456530
$772$	32.7370	1.17823
$773$	−43.0722	−1.54920	−0.774599	−	0.632453i	$-0.782048\pi$
$773$	−43.0722	−1.54920	−0.774599	+	0.632453i	$0.782048\pi$
$774$	−9.46836	−0.340333
$775$	−3.56708	−0.128133
$776$	−4.13918	−0.148588
$777$	−2.97441	−0.106706
$778$	−52.3863	−1.87814
$779$	5.94384	0.212960
$780$	0	0
$781$	−8.22855	−0.294441
$782$	−0.930417	−0.0332717
$783$	9.95951	0.355924
$784$	−4.93900	−0.176393
$785$	−10.1216	−0.361255
$786$	−30.3480	−1.08248
$787$	20.8945	0.744807	0.372403	−	0.928071i	$-0.378534\pi$
$787$	20.8945	0.744807	0.372403	+	0.928071i	$0.378534\pi$
$788$	−15.5323	−0.553316
$789$	−14.3084	−0.509393
$790$	20.2975	0.722152
$791$	6.58305	0.234066
$792$	6.93955	0.246586
$793$	0	0
$794$	9.21031	0.326862
$795$	−11.4697	−0.406787
$796$	−12.8561	−0.455672
$797$	−8.62449	−0.305495	−0.152748	−	0.988265i	$-0.548812\pi$
$797$	−8.62449	−0.305495	−0.152748	+	0.988265i	$0.548812\pi$
$798$	1.06537	0.0377135
$799$	−2.33370	−0.0825602
$800$	−4.21812	−0.149133
$801$	−9.63632	−0.340483
$802$	27.0236	0.954236
$803$	46.9135	1.65554
$804$	−11.9581	−0.421730
$805$	−5.79618	−0.204288
$806$	0	0
$807$	6.23326	0.219421
$808$	−11.7448	−0.413179
$809$	25.7533	0.905439	0.452720	−	0.891653i	$-0.350454\pi$
$809$	25.7533	0.905439	0.452720	+	0.891653i	$0.350454\pi$
$810$	3.74444	0.131566
$811$	−22.3107	−0.783433	−0.391717	−	0.920086i	$-0.628119\pi$
$811$	−22.3107	−0.783433	−0.391717	+	0.920086i	$0.628119\pi$
$812$	12.4193	0.435832
$813$	−10.8204	−0.379487
$814$	27.4110	0.960757
$815$	43.9034	1.53787
$816$	−0.914287	−0.0320064
$817$	−3.10666	−0.108688
$818$	57.9585	2.02647
$819$	0	0
$820$	26.0504	0.909720
$821$	−18.3608	−0.640797	−0.320399	−	0.947283i	$-0.603817\pi$
$821$	−18.3608	−0.640797	−0.320399	+	0.947283i	$0.603817\pi$
$822$	−39.8893	−1.39130
$823$	31.6172	1.10211	0.551053	−	0.834470i	$-0.314226\pi$
$823$	31.6172	1.10211	0.551053	+	0.834470i	$0.314226\pi$
$824$	19.1160	0.665936
$825$	3.48734	0.121414
$826$	11.6553	0.405541
$827$	−25.2749	−0.878893	−0.439446	−	0.898269i	$-0.644825\pi$
$827$	−25.2749	−0.878893	−0.439446	+	0.898269i	$0.644825\pi$
$828$	−3.47819	−0.120876
$829$	32.3697	1.12425	0.562123	−	0.827054i	$-0.309985\pi$
$829$	32.3697	1.12425	0.562123	+	0.827054i	$0.309985\pi$
$830$	14.9740	0.519754
$831$	−16.5661	−0.574671
$832$	0	0
$833$	−0.185116	−0.00641388
$834$	−32.9675	−1.14157
$835$	1.67085	0.0578221
$836$	−3.77054	−0.130407
$837$	−5.23122	−0.180817
$838$	41.1925	1.42297
$839$	−39.1606	−1.35197	−0.675987	−	0.736914i	$-0.736282\pi$
$839$	−39.1606	−1.35197	−0.675987	+	0.736914i	$0.736282\pi$
$840$	−2.81964	−0.0972868
$841$	70.1919	2.42041
$842$	43.8340	1.51062
$843$	21.4915	0.740208
$844$	17.5424	0.603833
$845$	0	0
$846$	−22.7165	−0.781008
$847$	−15.1559	−0.520763
$848$	27.2611	0.936148
$849$	24.4327	0.838527
$850$	−0.227454	−0.00780160
$851$	8.29651	0.284401
$852$	2.00631	0.0687351
$853$	42.6091	1.45891	0.729454	−	0.684029i	$-0.239774\pi$
$853$	42.6091	1.45891	0.729454	+	0.684029i	$0.239774\pi$
$854$	15.1967	0.520019
$855$	1.22859	0.0420168
$856$	6.32838	0.216300
$857$	−33.6003	−1.14776	−0.573882	−	0.818938i	$-0.694563\pi$
$857$	−33.6003	−1.14776	−0.573882	+	0.818938i	$0.694563\pi$
$858$	0	0
$859$	−52.3846	−1.78734	−0.893670	−	0.448725i	$-0.851878\pi$
$859$	−52.3846	−1.78734	−0.893670	+	0.448725i	$0.851878\pi$
$860$	−13.6158	−0.464293
$861$	−10.0533	−0.342615
$862$	−45.3437	−1.54441
$863$	26.1175	0.889048	0.444524	−	0.895767i	$-0.353373\pi$
$863$	26.1175	0.889048	0.444524	+	0.895767i	$0.353373\pi$
$864$	−6.18598	−0.210451
$865$	−37.8782	−1.28790
$866$	53.9893	1.83463
$867$	16.9657	0.576186
$868$	−6.52322	−0.221412
$869$	27.7230	0.940438
$870$	37.2928	1.26434
$871$	0	0
$872$	−3.19518	−0.108202
$873$	−3.05048	−0.103243
$874$	−2.97162	−0.100517
$875$	−11.8070	−0.399149
$876$	−11.4386	−0.386474
$877$	46.4595	1.56883	0.784414	−	0.620238i	$-0.212964\pi$
$877$	46.4595	1.56883	0.784414	+	0.620238i	$0.212964\pi$
$878$	−34.5947	−1.16751
$879$	−11.1636	−0.376541
$880$	52.4893	1.76942
$881$	9.96703	0.335798	0.167899	−	0.985804i	$-0.446302\pi$
$881$	9.96703	0.335798	0.167899	+	0.985804i	$0.446302\pi$
$882$	−1.80194	−0.0606744
$883$	18.4968	0.622469	0.311234	−	0.950333i	$-0.399258\pi$
$883$	18.4968	0.622469	0.311234	+	0.950333i	$0.399258\pi$
$884$	0	0
$885$	13.4410	0.451815
$886$	15.5167	0.521294
$887$	3.55868	0.119489	0.0597443	−	0.998214i	$-0.480971\pi$
$887$	3.55868	0.119489	0.0597443	+	0.998214i	$0.480971\pi$
$888$	4.03597	0.135438
$889$	5.34744	0.179347
$890$	−36.0826	−1.20949
$891$	5.11428	0.171335
$892$	29.1895	0.977336
$893$	−7.45349	−0.249422
$894$	39.3906	1.31742
$895$	43.0329	1.43843
$896$	10.0858	0.336941
$897$	0	0
$898$	−37.3685	−1.24700
$899$	−52.1004	−1.73764
$900$	−0.850295	−0.0283432
$901$	1.02176	0.0340396
$902$	92.6472	3.08482
$903$	5.25454	0.174860
$904$	−8.93251	−0.297091
$905$	20.0746	0.667304
$906$	−12.4262	−0.412832
$907$	11.9822	0.397862	0.198931	−	0.980014i	$-0.436253\pi$
$907$	11.9822	0.397862	0.198931	+	0.980014i	$0.436253\pi$
$908$	2.24173	0.0743943
$909$	−8.65561	−0.287088
$910$	0	0
$911$	5.98797	0.198390	0.0991952	−	0.995068i	$-0.468373\pi$
$911$	5.98797	0.198390	0.0991952	+	0.995068i	$0.468373\pi$
$912$	−2.92010	−0.0966943
$913$	20.4520	0.676861
$914$	31.0415	1.02676
$915$	17.5249	0.579355
$916$	−5.98754	−0.197834
$917$	16.8419	0.556168
$918$	−0.333567	−0.0110094
$919$	−46.7567	−1.54236	−0.771180	−	0.636617i	$-0.780333\pi$
$919$	−46.7567	−1.54236	−0.771180	+	0.636617i	$0.780333\pi$
$920$	7.86481	0.259295
$921$	2.87863	0.0948541
$922$	67.2548	2.21492
$923$	0	0
$924$	6.37741	0.209801
$925$	2.02820	0.0666869
$926$	1.22299	0.0401899
$927$	14.0880	0.462711
$928$	−61.6093	−2.02243
$929$	−53.8880	−1.76801	−0.884004	−	0.467480i	$-0.845162\pi$
$929$	−53.8880	−1.76801	−0.884004	+	0.467480i	$0.845162\pi$
$930$	−19.5880	−0.642315
$931$	−0.591233	−0.0193769
$932$	−22.6358	−0.741461
$933$	−27.7786	−0.909431
$934$	38.3582	1.25512
$935$	1.96732	0.0643383
$936$	0	0
$937$	−9.58874	−0.313251	−0.156625	−	0.987658i	$-0.550062\pi$
$937$	−9.58874	−0.313251	−0.156625	+	0.987658i	$0.550062\pi$
$938$	17.2800	0.564212
$939$	−21.2336	−0.692931
$940$	−32.6669	−1.06548
$941$	19.5667	0.637857	0.318929	−	0.947779i	$-0.396677\pi$
$941$	19.5667	0.637857	0.318929	+	0.947779i	$0.396677\pi$
$942$	8.77691	0.285967
$943$	28.0416	0.913160
$944$	−31.9466	−1.03977
$945$	−2.07801	−0.0675976
$946$	−48.4239	−1.57440
$947$	44.3870	1.44238	0.721191	−	0.692736i	$-0.243595\pi$
$947$	44.3870	1.44238	0.721191	+	0.692736i	$0.243595\pi$
$948$	−6.75950	−0.219538
$949$	0	0
$950$	−0.726455	−0.0235693
$951$	−1.54637	−0.0501446
$952$	0.251183	0.00814088
$953$	−60.0690	−1.94583	−0.972913	−	0.231172i	$-0.925744\pi$
$953$	−60.0690	−1.94583	−0.972913	+	0.231172i	$0.925744\pi$
$954$	9.94588	0.322010
$955$	21.6426	0.700338
$956$	−21.2308	−0.686655
$957$	50.9358	1.64652
$958$	9.04318	0.292172
$959$	22.1369	0.714838
$960$	−2.63647	−0.0850918
$961$	−3.63439	−0.117238
$962$	0	0
$963$	4.66386	0.150291
$964$	12.7651	0.411137
$965$	−54.5540	−1.75615
$966$	5.02614	0.161713
$967$	−50.5268	−1.62483	−0.812416	−	0.583078i	$-0.801848\pi$
$967$	−50.5268	−1.62483	−0.812416	+	0.583078i	$0.801848\pi$
$968$	20.5650	0.660983
$969$	−0.109447	−0.00351593
$970$	−11.4223	−0.366749
$971$	−50.4985	−1.62057	−0.810287	−	0.586033i	$-0.800689\pi$
$971$	−50.4985	−1.62057	−0.810287	+	0.586033i	$0.800689\pi$
$972$	−1.24698	−0.0399969
$973$	18.2956	0.586529
$974$	29.3462	0.940314
$975$	0	0
$976$	−41.6531	−1.33328
$977$	39.0091	1.24801	0.624006	−	0.781420i	$-0.285504\pi$
$977$	39.0091	1.24801	0.624006	+	0.781420i	$0.285504\pi$
$978$	−38.0707	−1.21737
$979$	−49.2829	−1.57509
$980$	−2.59123	−0.0827739
$981$	−2.35477	−0.0751821
$982$	6.66040	0.212542
$983$	35.4127	1.12949	0.564744	−	0.825266i	$-0.308975\pi$
$983$	35.4127	1.12949	0.564744	+	0.825266i	$0.308975\pi$
$984$	13.6413	0.434867
$985$	25.8836	0.824720
$986$	−3.32217	−0.105799
$987$	12.6067	0.401275
$988$	0	0
$989$	−14.6565	−0.466049
$990$	19.1501	0.608631
$991$	46.8170	1.48719	0.743596	−	0.668629i	$-0.233119\pi$
$991$	46.8170	1.48719	0.743596	+	0.668629i	$0.233119\pi$
$992$	32.3602	1.02744
$993$	24.2044	0.768104
$994$	−2.89920	−0.0919571
$995$	21.4238	0.679180
$996$	−4.98666	−0.158008
$997$	−20.4746	−0.648436	−0.324218	−	0.945982i	$-0.605101\pi$
$997$	−20.4746	−0.648436	−0.324218	+	0.945982i	$0.605101\pi$
$998$	72.9895	2.31044
$999$	2.97441	0.0941062

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.80194 q^{2} -1.00000 q^{3} +1.24698 q^{4} -2.07801 q^{5} +1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.80194 q^{2} -1.00000 q^{3} +1.24698 q^{4} -2.07801 q^{5} +1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} +3.74444 q^{10} +5.11428 q^{11} -1.24698 q^{12} +1.80194 q^{14} +2.07801 q^{15} -4.93900 q^{16} -0.185116 q^{17} -1.80194 q^{18} -0.591233 q^{19} -2.59123 q^{20} +1.00000 q^{21} -9.21562 q^{22} -2.78930 q^{23} -1.35690 q^{24} -0.681883 q^{25} -1.00000 q^{27} -1.24698 q^{28} -9.95951 q^{29} -3.74444 q^{30} +5.23122 q^{31} +6.18598 q^{32} -5.11428 q^{33} +0.333567 q^{34} +2.07801 q^{35} +1.24698 q^{36} -2.97441 q^{37} +1.06537 q^{38} -2.81964 q^{40} -10.0533 q^{41} -1.80194 q^{42} +5.25454 q^{43} +6.37741 q^{44} -2.07801 q^{45} +5.02614 q^{46} +12.6067 q^{47} +4.93900 q^{48} +1.00000 q^{49} +1.22871 q^{50} +0.185116 q^{51} -5.51955 q^{53} +1.80194 q^{54} -10.6275 q^{55} -1.35690 q^{56} +0.591233 q^{57} +17.9464 q^{58} +6.46823 q^{59} +2.59123 q^{60} +8.43351 q^{61} -9.42632 q^{62} -1.00000 q^{63} -1.26875 q^{64} +9.21562 q^{66} +9.58967 q^{67} -0.230836 q^{68} +2.78930 q^{69} -3.74444 q^{70} -1.60894 q^{71} +1.35690 q^{72} +9.17303 q^{73} +5.35970 q^{74} +0.681883 q^{75} -0.737256 q^{76} -5.11428 q^{77} +5.42070 q^{79} +10.2633 q^{80} +1.00000 q^{81} +18.1154 q^{82} +3.99899 q^{83} +1.24698 q^{84} +0.384672 q^{85} -9.46836 q^{86} +9.95951 q^{87} +6.93955 q^{88} -9.63632 q^{89} +3.74444 q^{90} -3.47819 q^{92} -5.23122 q^{93} -22.7165 q^{94} +1.22859 q^{95} -6.18598 q^{96} -3.05048 q^{97} -1.80194 q^{98} +5.11428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 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

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Database

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