LMFDB - Embedded newform 3549.2.a.y.1.2

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			1.2
Root			$3.07801$ 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)

$f(q)$	$=$	$q-1.80194 q^{2} -1.00000 q^{3} +1.24698 q^{4} +3.07801 q^{5} +1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.80194 q^{2} -1.00000 q^{3} +1.24698 q^{4} +3.07801 q^{5} +1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} -5.54638 q^{10} -6.47118 q^{11} -1.24698 q^{12} +1.80194 q^{14} -3.07801 q^{15} -4.93900 q^{16} -2.47976 q^{17} -1.80194 q^{18} +5.83821 q^{19} +3.83821 q^{20} +1.00000 q^{21} +11.6607 q^{22} +3.64015 q^{23} -1.35690 q^{24} +4.47413 q^{25} -1.00000 q^{27} -1.24698 q^{28} +4.48732 q^{29} +5.54638 q^{30} -2.78617 q^{31} +6.18598 q^{32} +6.47118 q^{33} +4.46837 q^{34} -3.07801 q^{35} +1.24698 q^{36} +1.16039 q^{37} -10.5201 q^{38} +4.17654 q^{40} +1.53218 q^{41} -1.80194 q^{42} -6.89765 q^{43} -8.06943 q^{44} +3.07801 q^{45} -6.55933 q^{46} +5.15603 q^{47} +4.93900 q^{48} +1.00000 q^{49} -8.06211 q^{50} +2.47976 q^{51} -9.65435 q^{53} +1.80194 q^{54} -19.9183 q^{55} -1.35690 q^{56} -5.83821 q^{57} -8.08588 q^{58} -11.5467 q^{59} -3.83821 q^{60} -7.28676 q^{61} +5.02051 q^{62} -1.00000 q^{63} -1.26875 q^{64} -11.6607 q^{66} -2.56252 q^{67} -3.09221 q^{68} -3.64015 q^{69} +5.54638 q^{70} +11.8167 q^{71} +1.35690 q^{72} +11.4677 q^{73} -2.09095 q^{74} -4.47413 q^{75} +7.28013 q^{76} +6.47118 q^{77} -11.8875 q^{79} -15.2023 q^{80} +1.00000 q^{81} -2.76089 q^{82} -7.58647 q^{83} +1.24698 q^{84} -7.63272 q^{85} +12.4291 q^{86} -4.48732 q^{87} -8.78072 q^{88} +18.6906 q^{89} -5.54638 q^{90} +4.53919 q^{92} +2.78617 q^{93} -9.29084 q^{94} +17.9701 q^{95} -6.18598 q^{96} +1.08433 q^{97} -1.80194 q^{98} -6.47118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.07801	1.37653	0.688263	−	0.725461i	$-0.258373\pi$
$5$	3.07801	1.37653	0.688263	+	0.725461i	$0.258373\pi$
$6$	1.80194	0.735638
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.35690	0.479735
$9$	1.00000	0.333333
$10$	−5.54638	−1.75392
$11$	−6.47118	−1.95113	−0.975567	−	0.219702i	$-0.929491\pi$
$11$	−6.47118	−1.95113	−0.975567	+	0.219702i	$0.929491\pi$
$12$	−1.24698	−0.359972
$13$	0	0
$13$	0	0
$14$	1.80194	0.481588
$15$	−3.07801	−0.794738
$16$	−4.93900	−1.23475
$17$	−2.47976	−0.601430	−0.300715	−	0.953714i	$-0.597225\pi$
$17$	−2.47976	−0.601430	−0.300715	+	0.953714i	$0.597225\pi$
$18$	−1.80194	−0.424721
$19$	5.83821	1.33938	0.669689	−	0.742642i	$-0.266427\pi$
$19$	5.83821	1.33938	0.669689	+	0.742642i	$0.266427\pi$
$20$	3.83821	0.858251
$21$	1.00000	0.218218
$22$	11.6607	2.48606
$23$	3.64015	0.759024	0.379512	−	0.925187i	$-0.376092\pi$
$23$	3.64015	0.759024	0.379512	+	0.925187i	$0.376092\pi$
$24$	−1.35690	−0.276975
$25$	4.47413	0.894826
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.24698	−0.235657
$29$	4.48732	0.833275	0.416637	−	0.909073i	$-0.363208\pi$
$29$	4.48732	0.833275	0.416637	+	0.909073i	$0.363208\pi$
$30$	5.54638	1.01263
$31$	−2.78617	−0.500412	−0.250206	−	0.968193i	$-0.580498\pi$
$31$	−2.78617	−0.500412	−0.250206	+	0.968193i	$0.580498\pi$
$32$	6.18598	1.09354
$33$	6.47118	1.12649
$34$	4.46837	0.766319
$35$	−3.07801	−0.520278
$36$	1.24698	0.207830
$37$	1.16039	0.190767	0.0953836	−	0.995441i	$-0.469592\pi$
$37$	1.16039	0.190767	0.0953836	+	0.995441i	$0.469592\pi$
$38$	−10.5201	−1.70658
$39$	0	0
$40$	4.17654	0.660368
$41$	1.53218	0.239286	0.119643	−	0.992817i	$-0.461825\pi$
$41$	1.53218	0.239286	0.119643	+	0.992817i	$0.461825\pi$
$42$	−1.80194	−0.278045
$43$	−6.89765	−1.05188	−0.525941	−	0.850521i	$-0.676287\pi$
$43$	−6.89765	−1.05188	−0.525941	+	0.850521i	$0.676287\pi$
$44$	−8.06943	−1.21651
$45$	3.07801	0.458842
$46$	−6.55933	−0.967120
$47$	5.15603	0.752084	0.376042	−	0.926603i	$-0.377285\pi$
$47$	5.15603	0.752084	0.376042	+	0.926603i	$0.377285\pi$
$48$	4.93900	0.712883
$49$	1.00000	0.142857
$50$	−8.06211	−1.14015
$51$	2.47976	0.347236
$52$	0	0
$53$	−9.65435	−1.32613	−0.663064	−	0.748563i	$-0.730744\pi$
$53$	−9.65435	−1.32613	−0.663064	+	0.748563i	$0.730744\pi$
$54$	1.80194	0.245213
$55$	−19.9183	−2.68579
$56$	−1.35690	−0.181323
$57$	−5.83821	−0.773290
$58$	−8.08588	−1.06173
$59$	−11.5467	−1.50325	−0.751625	−	0.659591i	$-0.770730\pi$
$59$	−11.5467	−1.50325	−0.751625	+	0.659591i	$0.770730\pi$
$60$	−3.83821	−0.495511
$61$	−7.28676	−0.932974	−0.466487	−	0.884528i	$-0.654480\pi$
$61$	−7.28676	−0.932974	−0.466487	+	0.884528i	$0.654480\pi$
$62$	5.02051	0.637606
$63$	−1.00000	−0.125988
$64$	−1.26875	−0.158594
$65$	0	0
$66$	−11.6607	−1.43533
$67$	−2.56252	−0.313062	−0.156531	−	0.987673i	$-0.550031\pi$
$67$	−2.56252	−0.313062	−0.156531	+	0.987673i	$0.550031\pi$
$68$	−3.09221	−0.374985
$69$	−3.64015	−0.438223
$70$	5.54638	0.662919
$71$	11.8167	1.40238	0.701191	−	0.712973i	$-0.252652\pi$
$71$	11.8167	1.40238	0.701191	+	0.712973i	$0.252652\pi$
$72$	1.35690	0.159912
$73$	11.4677	1.34219	0.671095	−	0.741371i	$-0.265824\pi$
$73$	11.4677	1.34219	0.671095	+	0.741371i	$0.265824\pi$
$74$	−2.09095	−0.243069
$75$	−4.47413	−0.516628
$76$	7.28013	0.835088
$77$	6.47118	0.737459
$78$	0	0
$79$	−11.8875	−1.33745	−0.668725	−	0.743510i	$-0.733160\pi$
$79$	−11.8875	−1.33745	−0.668725	+	0.743510i	$0.733160\pi$
$80$	−15.2023	−1.69967
$81$	1.00000	0.111111
$82$	−2.76089	−0.304889
$83$	−7.58647	−0.832723	−0.416362	−	0.909199i	$-0.636695\pi$
$83$	−7.58647	−0.832723	−0.416362	+	0.909199i	$0.636695\pi$
$84$	1.24698	0.136057
$85$	−7.63272	−0.827884
$86$	12.4291	1.34027
$87$	−4.48732	−0.481092
$88$	−8.78072	−0.936027
$89$	18.6906	1.98120	0.990601	−	0.136785i	$-0.0436770\pi$
$89$	18.6906	1.98120	0.990601	+	0.136785i	$0.0436770\pi$
$90$	−5.54638	−0.584640
$91$	0	0
$92$	4.53919	0.473244
$93$	2.78617	0.288913
$94$	−9.29084	−0.958277
$95$	17.9701	1.84369
$96$	−6.18598	−0.631354
$97$	1.08433	0.110097	0.0550484	−	0.998484i	$-0.482469\pi$
$97$	1.08433	0.110097	0.0550484	+	0.998484i	$0.482469\pi$
$98$	−1.80194	−0.182023
$99$	−6.47118	−0.650378
$100$	5.57915	0.557915
$101$	−18.9676	−1.88735	−0.943675	−	0.330873i	$-0.892657\pi$
$101$	−18.9676	−1.88735	−0.943675	+	0.330873i	$0.892657\pi$
$102$	−4.46837	−0.442435
$103$	0.207896	0.0204846	0.0102423	−	0.999948i	$-0.496740\pi$
$103$	0.207896	0.0204846	0.0102423	+	0.999948i	$0.496740\pi$
$104$	0	0
$105$	3.07801	0.300383
$106$	17.3965	1.68970
$107$	−6.92160	−0.669136	−0.334568	−	0.942372i	$-0.608590\pi$
$107$	−6.92160	−0.669136	−0.334568	+	0.942372i	$0.608590\pi$
$108$	−1.24698	−0.119991
$109$	9.79742	0.938423	0.469211	−	0.883086i	$-0.344538\pi$
$109$	9.79742	0.938423	0.469211	+	0.883086i	$0.344538\pi$
$110$	35.8916	3.42213
$111$	−1.16039	−0.110140
$112$	4.93900	0.466692
$113$	−11.9913	−1.12805	−0.564023	−	0.825759i	$-0.690747\pi$
$113$	−11.9913	−1.12805	−0.564023	+	0.825759i	$0.690747\pi$
$114$	10.5201	0.985297
$115$	11.2044	1.04482
$116$	5.59560	0.519538
$117$	0	0
$118$	20.8064	1.91538
$119$	2.47976	0.227319
$120$	−4.17654	−0.381264
$121$	30.8762	2.80692
$122$	13.1303	1.18876
$123$	−1.53218	−0.138152
$124$	−3.47430	−0.312001
$125$	−1.61862	−0.144774
$126$	1.80194	0.160529
$127$	19.4114	1.72249	0.861243	−	0.508194i	$-0.169687\pi$
$127$	19.4114	1.72249	0.861243	+	0.508194i	$0.169687\pi$
$128$	−10.0858	−0.891463
$129$	6.89765	0.607304
$130$	0	0
$131$	−18.4298	−1.61022	−0.805111	−	0.593124i	$-0.797894\pi$
$131$	−18.4298	−1.61022	−0.805111	+	0.593124i	$0.797894\pi$
$132$	8.06943	0.702354
$133$	−5.83821	−0.506237
$134$	4.61751	0.398892
$135$	−3.07801	−0.264913
$136$	−3.36477	−0.288527
$137$	−8.25681	−0.705427	−0.352714	−	0.935731i	$-0.614741\pi$
$137$	−8.25681	−0.705427	−0.352714	+	0.935731i	$0.614741\pi$
$138$	6.55933	0.558367
$139$	12.8927	1.09355	0.546774	−	0.837280i	$-0.315856\pi$
$139$	12.8927	1.09355	0.546774	+	0.837280i	$0.315856\pi$
$140$	−3.83821	−0.324388
$141$	−5.15603	−0.434216
$142$	−21.2929	−1.78686
$143$	0	0
$144$	−4.93900	−0.411583
$145$	13.8120	1.14703
$146$	−20.6640	−1.71017
$147$	−1.00000	−0.0824786
$148$	1.44699	0.118941
$149$	0.731647	0.0599389	0.0299694	−	0.999551i	$-0.490459\pi$
$149$	0.731647	0.0599389	0.0299694	+	0.999551i	$0.490459\pi$
$150$	8.06211	0.658268
$151$	−1.03330	−0.0840886	−0.0420443	−	0.999116i	$-0.513387\pi$
$151$	−1.03330	−0.0840886	−0.0420443	+	0.999116i	$0.513387\pi$
$152$	7.92185	0.642547
$153$	−2.47976	−0.200477
$154$	−11.6607	−0.939643
$155$	−8.57586	−0.688830
$156$	0	0
$157$	6.14425	0.490364	0.245182	−	0.969477i	$-0.421152\pi$
$157$	6.14425	0.490364	0.245182	+	0.969477i	$0.421152\pi$
$158$	21.4206	1.70413
$159$	9.65435	0.765640
$160$	19.0405	1.50528
$161$	−3.64015	−0.286884
$162$	−1.80194	−0.141574
$163$	−7.70203	−0.603269	−0.301635	−	0.953424i	$-0.597532\pi$
$163$	−7.70203	−0.603269	−0.301635	+	0.953424i	$0.597532\pi$
$164$	1.91059	0.149192
$165$	19.9183	1.55064
$166$	13.6704	1.06102
$167$	−12.9563	−1.00259	−0.501293	−	0.865278i	$-0.667142\pi$
$167$	−12.9563	−1.00259	−0.501293	+	0.865278i	$0.667142\pi$
$168$	1.35690	0.104687
$169$	0	0
$170$	13.7537	1.05486
$171$	5.83821	0.446459
$172$	−8.60123	−0.655837
$173$	−10.0988	−0.767799	−0.383900	−	0.923375i	$-0.625419\pi$
$173$	−10.0988	−0.767799	−0.383900	+	0.923375i	$0.625419\pi$
$174$	8.08588	0.612989
$175$	−4.47413	−0.338213
$176$	31.9612	2.40916
$177$	11.5467	0.867902
$178$	−33.6793	−2.52437
$179$	−24.2768	−1.81453	−0.907267	−	0.420556i	$-0.861835\pi$
$179$	−24.2768	−1.81453	−0.907267	+	0.420556i	$0.861835\pi$
$180$	3.83821	0.286084
$181$	7.33317	0.545070	0.272535	−	0.962146i	$-0.412138\pi$
$181$	7.33317	0.545070	0.272535	+	0.962146i	$0.412138\pi$
$182$	0	0
$183$	7.28676	0.538653
$184$	4.93931	0.364130
$185$	3.57170	0.262596
$186$	−5.02051	−0.368122
$187$	16.0470	1.17347
$188$	6.42946	0.468916
$189$	1.00000	0.0727393
$190$	−32.3809	−2.34916
$191$	−0.103045	−0.00745611	−0.00372805	−	0.999993i	$-0.501187\pi$
$191$	−0.103045	−0.00745611	−0.00372805	+	0.999993i	$0.501187\pi$
$192$	1.26875	0.0915641
$193$	11.8062	0.849828	0.424914	−	0.905234i	$-0.360304\pi$
$193$	11.8062	0.849828	0.424914	+	0.905234i	$0.360304\pi$
$194$	−1.95389	−0.140281
$195$	0	0
$196$	1.24698	0.0890700
$197$	22.8672	1.62922	0.814609	−	0.580011i	$-0.196952\pi$
$197$	22.8672	1.62922	0.814609	+	0.580011i	$0.196952\pi$
$198$	11.6607	0.828687
$199$	0.821199	0.0582132	0.0291066	−	0.999576i	$-0.490734\pi$
$199$	0.821199	0.0582132	0.0291066	+	0.999576i	$0.490734\pi$
$200$	6.07093	0.429280
$201$	2.56252	0.180746
$202$	34.1785	2.40479
$203$	−4.48732	−0.314948
$204$	3.09221	0.216498
$205$	4.71606	0.329384
$206$	−0.374616	−0.0261007
$207$	3.64015	0.253008
$208$	0	0
$209$	−37.7801	−2.61331
$210$	−5.54638	−0.382736
$211$	−24.8233	−1.70891	−0.854453	−	0.519528i	$-0.826108\pi$
$211$	−24.8233	−1.70891	−0.854453	+	0.519528i	$0.826108\pi$
$212$	−12.0388	−0.826827
$213$	−11.8167	−0.809666
$214$	12.4723	0.852588
$215$	−21.2310	−1.44794
$216$	−1.35690	−0.0923251
$217$	2.78617	0.189138
$218$	−17.6543	−1.19570
$219$	−11.4677	−0.774914
$220$	−24.8378	−1.67456
$221$	0	0
$222$	2.09095	0.140336
$223$	−21.2058	−1.42004	−0.710022	−	0.704179i	$-0.751315\pi$
$223$	−21.2058	−1.42004	−0.710022	+	0.704179i	$0.751315\pi$
$224$	−6.18598	−0.413318
$225$	4.47413	0.298275
$226$	21.6075	1.43731
$227$	−19.0786	−1.26629	−0.633144	−	0.774034i	$-0.718236\pi$
$227$	−19.0786	−1.26629	−0.633144	+	0.774034i	$0.718236\pi$
$228$	−7.28013	−0.482139
$229$	−13.5257	−0.893805	−0.446902	−	0.894583i	$-0.647473\pi$
$229$	−13.5257	−0.893805	−0.446902	+	0.894583i	$0.647473\pi$
$230$	−20.1897	−1.33127
$231$	−6.47118	−0.425772
$232$	6.08883	0.399751
$233$	−17.1313	−1.12231	−0.561154	−	0.827711i	$-0.689643\pi$
$233$	−17.1313	−1.12231	−0.561154	+	0.827711i	$0.689643\pi$
$234$	0	0
$235$	15.8703	1.03526
$236$	−14.3985	−0.937261
$237$	11.8875	0.772177
$238$	−4.46837	−0.289641
$239$	17.8428	1.15416	0.577078	−	0.816689i	$-0.304193\pi$
$239$	17.8428	1.15416	0.577078	+	0.816689i	$0.304193\pi$
$240$	15.2023	0.981303
$241$	−17.0689	−1.09950	−0.549752	−	0.835328i	$-0.685278\pi$
$241$	−17.0689	−1.09950	−0.549752	+	0.835328i	$0.685278\pi$
$242$	−55.6369	−3.57648
$243$	−1.00000	−0.0641500
$244$	−9.08644	−0.581700
$245$	3.07801	0.196647
$246$	2.76089	0.176028
$247$	0	0
$248$	−3.78055	−0.240065
$249$	7.58647	0.480773
$250$	2.91666	0.184466
$251$	−22.0735	−1.39327	−0.696633	−	0.717428i	$-0.745319\pi$
$251$	−22.0735	−1.39327	−0.696633	+	0.717428i	$0.745319\pi$
$252$	−1.24698	−0.0785523
$253$	−23.5561	−1.48096
$254$	−34.9782	−2.19473
$255$	7.63272	0.477979
$256$	20.7114	1.29446
$257$	−10.5585	−0.658619	−0.329309	−	0.944222i	$-0.606816\pi$
$257$	−10.5585	−0.658619	−0.329309	+	0.944222i	$0.606816\pi$
$258$	−12.4291	−0.773804
$259$	−1.16039	−0.0721033
$260$	0	0
$261$	4.48732	0.277758
$262$	33.2094	2.05168
$263$	24.6204	1.51816	0.759081	−	0.650997i	$-0.225649\pi$
$263$	24.6204	1.51816	0.759081	+	0.650997i	$0.225649\pi$
$264$	8.78072	0.540416
$265$	−29.7162	−1.82545
$266$	10.5201	0.645028
$267$	−18.6906	−1.14385
$268$	−3.19541	−0.195191
$269$	−12.5227	−0.763525	−0.381762	−	0.924260i	$-0.624683\pi$
$269$	−12.5227	−0.763525	−0.381762	+	0.924260i	$0.624683\pi$
$270$	5.54638	0.337542
$271$	−12.3506	−0.750243	−0.375122	−	0.926976i	$-0.622399\pi$
$271$	−12.3506	−0.750243	−0.375122	+	0.926976i	$0.622399\pi$
$272$	12.2475	0.742616
$273$	0	0
$274$	14.8783	0.898829
$275$	−28.9529	−1.74593
$276$	−4.53919	−0.273227
$277$	16.3139	0.980204	0.490102	−	0.871665i	$-0.336959\pi$
$277$	16.3139	0.980204	0.490102	+	0.871665i	$0.336959\pi$
$278$	−23.2319	−1.39336
$279$	−2.78617	−0.166804
$280$	−4.17654	−0.249596
$281$	10.5157	0.627315	0.313657	−	0.949536i	$-0.398446\pi$
$281$	10.5157	0.627315	0.313657	+	0.949536i	$0.398446\pi$
$282$	9.29084	0.553261
$283$	25.4773	1.51447	0.757233	−	0.653145i	$-0.226551\pi$
$283$	25.4773	1.51447	0.757233	+	0.653145i	$0.226551\pi$
$284$	14.7352	0.874371
$285$	−17.9701	−1.06445
$286$	0	0
$287$	−1.53218	−0.0904416
$288$	6.18598	0.364512
$289$	−10.8508	−0.638282
$290$	−24.8884	−1.46150
$291$	−1.08433	−0.0635644
$292$	14.3000	0.836842
$293$	4.73420	0.276575	0.138288	−	0.990392i	$-0.455840\pi$
$293$	4.73420	0.276575	0.138288	+	0.990392i	$0.455840\pi$
$294$	1.80194	0.105091
$295$	−35.5408	−2.06926
$296$	1.57453	0.0915178
$297$	6.47118	0.375496
$298$	−1.31838	−0.0763718
$299$	0	0
$300$	−5.57915	−0.322112
$301$	6.89765	0.397574
$302$	1.86194	0.107143
$303$	18.9676	1.08966
$304$	−28.8349	−1.65380
$305$	−22.4287	−1.28426
$306$	4.46837	0.255440
$307$	5.13876	0.293284	0.146642	−	0.989190i	$-0.453153\pi$
$307$	5.13876	0.293284	0.146642	+	0.989190i	$0.453153\pi$
$308$	8.06943	0.459798
$309$	−0.207896	−0.0118268
$310$	15.4532	0.877681
$311$	−14.4284	−0.818161	−0.409081	−	0.912498i	$-0.634150\pi$
$311$	−14.4284	−0.818161	−0.409081	+	0.912498i	$0.634150\pi$
$312$	0	0
$313$	−3.77751	−0.213518	−0.106759	−	0.994285i	$-0.534047\pi$
$313$	−3.77751	−0.213518	−0.106759	+	0.994285i	$0.534047\pi$
$314$	−11.0716	−0.624804
$315$	−3.07801	−0.173426
$316$	−14.8235	−0.833886
$317$	−17.6020	−0.988627	−0.494313	−	0.869284i	$-0.664580\pi$
$317$	−17.6020	−0.988627	−0.494313	+	0.869284i	$0.664580\pi$
$318$	−17.3965	−0.975550
$319$	−29.0383	−1.62583
$320$	−3.90522	−0.218309
$321$	6.92160	0.386326
$322$	6.55933	0.365537
$323$	−14.4774	−0.805542
$324$	1.24698	0.0692766
$325$	0	0
$326$	13.8786	0.768663
$327$	−9.79742	−0.541799
$328$	2.07901	0.114794
$329$	−5.15603	−0.284261
$330$	−35.8916	−1.97577
$331$	−8.93862	−0.491311	−0.245656	−	0.969357i	$-0.579003\pi$
$331$	−8.93862	−0.491311	−0.245656	+	0.969357i	$0.579003\pi$
$332$	−9.46018	−0.519195
$333$	1.16039	0.0635891
$334$	23.3464	1.27746
$335$	−7.88746	−0.430938
$336$	−4.93900	−0.269445
$337$	4.36539	0.237798	0.118899	−	0.992906i	$-0.462064\pi$
$337$	4.36539	0.237798	0.118899	+	0.992906i	$0.462064\pi$
$338$	0	0
$339$	11.9913	0.651277
$340$	−9.51784	−0.516177
$341$	18.0298	0.976370
$342$	−10.5201	−0.568862
$343$	−1.00000	−0.0539949
$344$	−9.35939	−0.504625
$345$	−11.2044	−0.603225
$346$	18.1975	0.978301
$347$	31.8740	1.71109	0.855544	−	0.517730i	$-0.173223\pi$
$347$	31.8740	1.71109	0.855544	+	0.517730i	$0.173223\pi$
$348$	−5.59560	−0.299956
$349$	6.86699	0.367582	0.183791	−	0.982965i	$-0.441163\pi$
$349$	6.86699	0.367582	0.183791	+	0.982965i	$0.441163\pi$
$350$	8.06211	0.430938
$351$	0	0
$352$	−40.0306	−2.13364
$353$	−4.18244	−0.222609	−0.111304	−	0.993786i	$-0.535503\pi$
$353$	−4.18244	−0.222609	−0.111304	+	0.993786i	$0.535503\pi$
$354$	−20.8064	−1.10585
$355$	36.3719	1.93042
$356$	23.3068	1.23526
$357$	−2.47976	−0.131243
$358$	43.7453	2.31201
$359$	−36.3813	−1.92013	−0.960067	−	0.279771i	$-0.909741\pi$
$359$	−36.3813	−1.92013	−0.960067	+	0.279771i	$0.909741\pi$
$360$	4.17654	0.220123
$361$	15.0847	0.793933
$362$	−13.2139	−0.694508
$363$	−30.8762	−1.62058
$364$	0	0
$365$	35.2976	1.84756
$366$	−13.1303	−0.686331
$367$	9.37858	0.489558	0.244779	−	0.969579i	$-0.421285\pi$
$367$	9.37858	0.489558	0.244779	+	0.969579i	$0.421285\pi$
$368$	−17.9787	−0.937205
$369$	1.53218	0.0797620
$370$	−6.43597	−0.334590
$371$	9.65435	0.501229
$372$	3.47430	0.180134
$373$	−25.2895	−1.30944	−0.654721	−	0.755871i	$-0.727214\pi$
$373$	−25.2895	−1.30944	−0.654721	+	0.755871i	$0.727214\pi$
$374$	−28.9156	−1.49519
$375$	1.61862	0.0835854
$376$	6.99619	0.360801
$377$	0	0
$378$	−1.80194	−0.0926817
$379$	12.7741	0.656163	0.328081	−	0.944649i	$-0.393598\pi$
$379$	12.7741	0.656163	0.328081	+	0.944649i	$0.393598\pi$
$380$	22.4083	1.14952
$381$	−19.4114	−0.994477
$382$	0.185682	0.00950029
$383$	−5.12177	−0.261710	−0.130855	−	0.991402i	$-0.541772\pi$
$383$	−5.12177	−0.261710	−0.130855	+	0.991402i	$0.541772\pi$
$384$	10.0858	0.514686
$385$	19.9183	1.01513
$386$	−21.2740	−1.08282
$387$	−6.89765	−0.350627
$388$	1.35213	0.0686442
$389$	−9.81899	−0.497843	−0.248921	−	0.968524i	$-0.580076\pi$
$389$	−9.81899	−0.497843	−0.248921	+	0.968524i	$0.580076\pi$
$390$	0	0
$391$	−9.02670	−0.456500
$392$	1.35690	0.0685336
$393$	18.4298	0.929662
$394$	−41.2052	−2.07589
$395$	−36.5898	−1.84104
$396$	−8.06943	−0.405504
$397$	3.04602	0.152876	0.0764378	−	0.997074i	$-0.475645\pi$
$397$	3.04602	0.152876	0.0764378	+	0.997074i	$0.475645\pi$
$398$	−1.47975	−0.0741731
$399$	5.83821	0.292276
$400$	−22.0977	−1.10489
$401$	−0.864643	−0.0431782	−0.0215891	−	0.999767i	$-0.506873\pi$
$401$	−0.864643	−0.0431782	−0.0215891	+	0.999767i	$0.506873\pi$
$402$	−4.61751	−0.230300
$403$	0	0
$404$	−23.6523	−1.17674
$405$	3.07801	0.152947
$406$	8.08588	0.401295
$407$	−7.50911	−0.372213
$408$	3.36477	0.166581
$409$	3.61305	0.178654	0.0893269	−	0.996002i	$-0.471528\pi$
$409$	3.61305	0.178654	0.0893269	+	0.996002i	$0.471528\pi$
$410$	−8.49804	−0.419688
$411$	8.25681	0.407279
$412$	0.259242	0.0127719
$413$	11.5467	0.568175
$414$	−6.55933	−0.322373
$415$	−23.3512	−1.14627
$416$	0	0
$417$	−12.8927	−0.631360
$418$	68.0774	3.32978
$419$	−24.8403	−1.21353	−0.606763	−	0.794883i	$-0.707532\pi$
$419$	−24.8403	−1.21353	−0.606763	+	0.794883i	$0.707532\pi$
$420$	3.83821	0.187286
$421$	−21.4647	−1.04612	−0.523062	−	0.852295i	$-0.675210\pi$
$421$	−21.4647	−1.04612	−0.523062	+	0.852295i	$0.675210\pi$
$422$	44.7300	2.17742
$423$	5.15603	0.250695
$424$	−13.0999	−0.636190
$425$	−11.0948	−0.538175
$426$	21.2929	1.03165
$427$	7.28676	0.352631
$428$	−8.63109	−0.417200
$429$	0	0
$430$	38.2570	1.84491
$431$	−15.8820	−0.765008	−0.382504	−	0.923954i	$-0.624938\pi$
$431$	−15.8820	−0.765008	−0.382504	+	0.923954i	$0.624938\pi$
$432$	4.93900	0.237628
$433$	−3.11055	−0.149483	−0.0747417	−	0.997203i	$-0.523813\pi$
$433$	−3.11055	−0.149483	−0.0747417	+	0.997203i	$0.523813\pi$
$434$	−5.02051	−0.240992
$435$	−13.8120	−0.662235
$436$	12.2172	0.585097
$437$	21.2520	1.01662
$438$	20.6640	0.987366
$439$	−6.37921	−0.304463	−0.152232	−	0.988345i	$-0.548646\pi$
$439$	−6.37921	−0.304463	−0.152232	+	0.988345i	$0.548646\pi$
$440$	−27.0271	−1.28847
$441$	1.00000	0.0476190
$442$	0	0
$443$	16.9667	0.806112	0.403056	−	0.915175i	$-0.367948\pi$
$443$	16.9667	0.806112	0.403056	+	0.915175i	$0.367948\pi$
$444$	−1.44699	−0.0686709
$445$	57.5299	2.72718
$446$	38.2115	1.80937
$447$	−0.731647	−0.0346057
$448$	1.26875	0.0599428
$449$	4.45098	0.210055	0.105027	−	0.994469i	$-0.466507\pi$
$449$	4.45098	0.210055	0.105027	+	0.994469i	$0.466507\pi$
$450$	−8.06211	−0.380051
$451$	−9.91500	−0.466879
$452$	−14.9529	−0.703325
$453$	1.03330	0.0485486
$454$	34.3784	1.61346
$455$	0	0
$456$	−7.92185	−0.370974
$457$	−5.95579	−0.278600	−0.139300	−	0.990250i	$-0.544485\pi$
$457$	−5.95579	−0.278600	−0.139300	+	0.990250i	$0.544485\pi$
$458$	24.3725	1.13885
$459$	2.47976	0.115745
$460$	13.9717	0.651433
$461$	2.58879	0.120572	0.0602860	−	0.998181i	$-0.480799\pi$
$461$	2.58879	0.120572	0.0602860	+	0.998181i	$0.480799\pi$
$462$	11.6607	0.542503
$463$	−36.0018	−1.67315	−0.836573	−	0.547855i	$-0.815445\pi$
$463$	−36.0018	−1.67315	−0.836573	+	0.547855i	$0.815445\pi$
$464$	−22.1629	−1.02889
$465$	8.57586	0.397696
$466$	30.8695	1.43000
$467$	35.6189	1.64825	0.824123	−	0.566411i	$-0.191669\pi$
$467$	35.6189	1.64825	0.824123	+	0.566411i	$0.191669\pi$
$468$	0	0
$469$	2.56252	0.118326
$470$	−28.5973	−1.31909
$471$	−6.14425	−0.283112
$472$	−15.6676	−0.721162
$473$	44.6359	2.05236
$474$	−21.4206	−0.983879
$475$	26.1209	1.19851
$476$	3.09221	0.141731
$477$	−9.65435	−0.442042
$478$	−32.1516	−1.47058
$479$	−35.6402	−1.62844	−0.814221	−	0.580556i	$-0.802835\pi$
$479$	−35.6402	−1.62844	−0.814221	+	0.580556i	$0.802835\pi$
$480$	−19.0405	−0.869076
$481$	0	0
$482$	30.7571	1.40095
$483$	3.64015	0.165633
$484$	38.5019	1.75009
$485$	3.33757	0.151551
$486$	1.80194	0.0817376
$487$	−10.6754	−0.483750	−0.241875	−	0.970307i	$-0.577762\pi$
$487$	−10.6754	−0.483750	−0.241875	+	0.970307i	$0.577762\pi$
$488$	−9.88737	−0.447580
$489$	7.70203	0.348298
$490$	−5.54638	−0.250560
$491$	−36.8647	−1.66368	−0.831840	−	0.555016i	$-0.812712\pi$
$491$	−36.8647	−1.66368	−0.831840	+	0.555016i	$0.812712\pi$
$492$	−1.91059	−0.0861363
$493$	−11.1275	−0.501156
$494$	0	0
$495$	−19.9183	−0.895263
$496$	13.7609	0.617883
$497$	−11.8167	−0.530051
$498$	−13.6704	−0.612583
$499$	3.60337	0.161309	0.0806545	−	0.996742i	$-0.474299\pi$
$499$	3.60337	0.161309	0.0806545	+	0.996742i	$0.474299\pi$
$500$	−2.01839	−0.0902652
$501$	12.9563	0.578843
$502$	39.7750	1.77525
$503$	−34.9369	−1.55776	−0.778879	−	0.627174i	$-0.784212\pi$
$503$	−34.9369	−1.55776	−0.778879	+	0.627174i	$0.784212\pi$
$504$	−1.35690	−0.0604409
$505$	−58.3826	−2.59799
$506$	42.4466	1.88698
$507$	0	0
$508$	24.2057	1.07395
$509$	−12.8076	−0.567687	−0.283844	−	0.958871i	$-0.591610\pi$
$509$	−12.8076	−0.567687	−0.283844	+	0.958871i	$0.591610\pi$
$510$	−13.7537	−0.609023
$511$	−11.4677	−0.507300
$512$	−17.1491	−0.757892
$513$	−5.83821	−0.257763
$514$	19.0257	0.839187
$515$	0.639905	0.0281976
$516$	8.60123	0.378648
$517$	−33.3656	−1.46742
$518$	2.09095	0.0918713
$519$	10.0988	0.443289
$520$	0	0
$521$	8.90891	0.390307	0.195153	−	0.980773i	$-0.437480\pi$
$521$	8.90891	0.390307	0.195153	+	0.980773i	$0.437480\pi$
$522$	−8.08588	−0.353909
$523$	−4.62938	−0.202429	−0.101214	−	0.994865i	$-0.532273\pi$
$523$	−4.62938	−0.202429	−0.101214	+	0.994865i	$0.532273\pi$
$524$	−22.9816	−1.00396
$525$	4.47413	0.195267
$526$	−44.3645	−1.93438
$527$	6.90904	0.300962
$528$	−31.9612	−1.39093
$529$	−9.74930	−0.423883
$530$	53.5467	2.32592
$531$	−11.5467	−0.501083
$532$	−7.28013	−0.315634
$533$	0	0
$534$	33.6793	1.45745
$535$	−21.3047	−0.921084
$536$	−3.47708	−0.150187
$537$	24.2768	1.04762
$538$	22.5652	0.972855
$539$	−6.47118	−0.278733
$540$	−3.83821	−0.165170
$541$	−6.69318	−0.287762	−0.143881	−	0.989595i	$-0.545958\pi$
$541$	−6.69318	−0.287762	−0.143881	+	0.989595i	$0.545958\pi$
$542$	22.2549	0.955932
$543$	−7.33317	−0.314696
$544$	−15.3397	−0.657686
$545$	30.1565	1.29176
$546$	0	0
$547$	−11.3091	−0.483541	−0.241771	−	0.970333i	$-0.577728\pi$
$547$	−11.3091	−0.483541	−0.241771	+	0.970333i	$0.577728\pi$
$548$	−10.2961	−0.439827
$549$	−7.28676	−0.310991
$550$	52.1713	2.22459
$551$	26.1979	1.11607
$552$	−4.93931	−0.210231
$553$	11.8875	0.505508
$554$	−29.3965	−1.24894
$555$	−3.57170	−0.151610
$556$	16.0770	0.681816
$557$	−6.71339	−0.284456	−0.142228	−	0.989834i	$-0.545427\pi$
$557$	−6.71339	−0.284456	−0.142228	+	0.989834i	$0.545427\pi$
$558$	5.02051	0.212535
$559$	0	0
$560$	15.2023	0.642414
$561$	−16.0470	−0.677503
$562$	−18.9487	−0.799301
$563$	−12.5571	−0.529218	−0.264609	−	0.964356i	$-0.585243\pi$
$563$	−12.5571	−0.529218	−0.264609	+	0.964356i	$0.585243\pi$
$564$	−6.42946	−0.270729
$565$	−36.9093	−1.55278
$566$	−45.9084	−1.92968
$567$	−1.00000	−0.0419961
$568$	16.0340	0.672772
$569$	22.9022	0.960109	0.480055	−	0.877239i	$-0.340617\pi$
$569$	22.9022	0.960109	0.480055	+	0.877239i	$0.340617\pi$
$570$	32.3809	1.35629
$571$	−22.8646	−0.956854	−0.478427	−	0.878127i	$-0.658793\pi$
$571$	−22.8646	−0.956854	−0.478427	+	0.878127i	$0.658793\pi$
$572$	0	0
$573$	0.103045	0.00430479
$574$	2.76089	0.115237
$575$	16.2865	0.679195
$576$	−1.26875	−0.0528646
$577$	−14.3282	−0.596492	−0.298246	−	0.954489i	$-0.596402\pi$
$577$	−14.3282	−0.596492	−0.298246	+	0.954489i	$0.596402\pi$
$578$	19.5525	0.813275
$579$	−11.8062	−0.490648
$580$	17.2233	0.715159
$581$	7.58647	0.314740
$582$	1.95389	0.0809914
$583$	62.4750	2.58745
$584$	15.5604	0.643896
$585$	0	0
$586$	−8.53074	−0.352402
$587$	19.9113	0.821826	0.410913	−	0.911674i	$-0.365210\pi$
$587$	19.9113	0.821826	0.410913	+	0.911674i	$0.365210\pi$
$588$	−1.24698	−0.0514246
$589$	−16.2663	−0.670240
$590$	64.0423	2.63658
$591$	−22.8672	−0.940629
$592$	−5.73118	−0.235550
$593$	8.92435	0.366479	0.183239	−	0.983068i	$-0.441342\pi$
$593$	8.92435	0.366479	0.183239	+	0.983068i	$0.441342\pi$
$594$	−11.6607	−0.478443
$595$	7.63272	0.312911
$596$	0.912349	0.0373713
$597$	−0.821199	−0.0336094
$598$	0	0
$599$	9.43773	0.385615	0.192808	−	0.981237i	$-0.438241\pi$
$599$	9.43773	0.385615	0.192808	+	0.981237i	$0.438241\pi$
$600$	−6.07093	−0.247845
$601$	−9.25969	−0.377711	−0.188855	−	0.982005i	$-0.560478\pi$
$601$	−9.25969	−0.377711	−0.188855	+	0.982005i	$0.560478\pi$
$602$	−12.4291	−0.506574
$603$	−2.56252	−0.104354
$604$	−1.28850	−0.0524284
$605$	95.0371	3.86381
$606$	−34.1785	−1.38841
$607$	1.08268	0.0439447	0.0219724	−	0.999759i	$-0.493005\pi$
$607$	1.08268	0.0439447	0.0219724	+	0.999759i	$0.493005\pi$
$608$	36.1151	1.46466
$609$	4.48732	0.181836
$610$	40.4151	1.63636
$611$	0	0
$612$	−3.09221	−0.124995
$613$	35.5525	1.43595	0.717976	−	0.696067i	$-0.245069\pi$
$613$	35.5525	1.43595	0.717976	+	0.696067i	$0.245069\pi$
$614$	−9.25972	−0.373692
$615$	−4.71606	−0.190170
$616$	8.78072	0.353785
$617$	9.15107	0.368408	0.184204	−	0.982888i	$-0.441029\pi$
$617$	9.15107	0.368408	0.184204	+	0.982888i	$0.441029\pi$
$618$	0.374616	0.0150692
$619$	19.8832	0.799175	0.399587	−	0.916695i	$-0.369153\pi$
$619$	19.8832	0.799175	0.399587	+	0.916695i	$0.369153\pi$
$620$	−10.6939	−0.429478
$621$	−3.64015	−0.146074
$622$	25.9991	1.04247
$623$	−18.6906	−0.748824
$624$	0	0
$625$	−27.3528	−1.09411
$626$	6.80684	0.272056
$627$	37.7801	1.50879
$628$	7.66175	0.305737
$629$	−2.87749	−0.114733
$630$	5.54638	0.220973
$631$	5.93855	0.236410	0.118205	−	0.992989i	$-0.462286\pi$
$631$	5.93855	0.236410	0.118205	+	0.992989i	$0.462286\pi$
$632$	−16.1301	−0.641621
$633$	24.8233	0.986638
$634$	31.7177	1.25967
$635$	59.7485	2.37105
$636$	12.0388	0.477369
$637$	0	0
$638$	52.3252	2.07157
$639$	11.8167	0.467461
$640$	−31.0440	−1.22712
$641$	40.5393	1.60121	0.800604	−	0.599194i	$-0.204512\pi$
$641$	40.5393	1.60121	0.800604	+	0.599194i	$0.204512\pi$
$642$	−12.4723	−0.492242
$643$	48.4977	1.91256	0.956282	−	0.292446i	$-0.0944692\pi$
$643$	48.4977	1.91256	0.956282	+	0.292446i	$0.0944692\pi$
$644$	−4.53919	−0.178869
$645$	21.2310	0.835970
$646$	26.0873	1.02639
$647$	−22.0190	−0.865656	−0.432828	−	0.901476i	$-0.642484\pi$
$647$	−22.0190	−0.865656	−0.432828	+	0.901476i	$0.642484\pi$
$648$	1.35690	0.0533039
$649$	74.7207	2.93304
$650$	0	0
$651$	−2.78617	−0.109199
$652$	−9.60427	−0.376132
$653$	−3.53681	−0.138406	−0.0692031	−	0.997603i	$-0.522046\pi$
$653$	−3.53681	−0.138406	−0.0692031	+	0.997603i	$0.522046\pi$
$654$	17.6543	0.690339
$655$	−56.7272	−2.21651
$656$	−7.56743	−0.295458
$657$	11.4677	0.447397
$658$	9.29084	0.362195
$659$	−31.8032	−1.23888	−0.619438	−	0.785045i	$-0.712640\pi$
$659$	−31.8032	−1.23888	−0.619438	+	0.785045i	$0.712640\pi$
$660$	24.8378	0.966809
$661$	28.1365	1.09438	0.547191	−	0.837008i	$-0.315697\pi$
$661$	28.1365	1.09438	0.547191	+	0.837008i	$0.315697\pi$
$662$	16.1068	0.626010
$663$	0	0
$664$	−10.2941	−0.399487
$665$	−17.9701	−0.696849
$666$	−2.09095	−0.0810228
$667$	16.3345	0.632476
$668$	−16.1562	−0.625102
$669$	21.2058	0.819863
$670$	14.2127	0.549085
$671$	47.1539	1.82036
$672$	6.18598	0.238629
$673$	15.9373	0.614338	0.307169	−	0.951655i	$-0.400618\pi$
$673$	15.9373	0.614338	0.307169	+	0.951655i	$0.400618\pi$
$674$	−7.86615	−0.302993
$675$	−4.47413	−0.172209
$676$	0	0
$677$	−38.8890	−1.49463	−0.747314	−	0.664471i	$-0.768657\pi$
$677$	−38.8890	−1.49463	−0.747314	+	0.664471i	$0.768657\pi$
$678$	−21.6075	−0.829833
$679$	−1.08433	−0.0416127
$680$	−10.3568	−0.397165
$681$	19.0786	0.731092
$682$	−32.4886	−1.24405
$683$	−37.7568	−1.44472	−0.722362	−	0.691515i	$-0.756944\pi$
$683$	−37.7568	−1.44472	−0.722362	+	0.691515i	$0.756944\pi$
$684$	7.28013	0.278363
$685$	−25.4145	−0.971040
$686$	1.80194	0.0687983
$687$	13.5257	0.516039
$688$	34.0675	1.29881
$689$	0	0
$690$	20.1897	0.768607
$691$	−23.0633	−0.877370	−0.438685	−	0.898641i	$-0.644556\pi$
$691$	−23.0633	−0.877370	−0.438685	+	0.898641i	$0.644556\pi$
$692$	−12.5930	−0.478715
$693$	6.47118	0.245820
$694$	−57.4350	−2.18020
$695$	39.6840	1.50530
$696$	−6.08883	−0.230797
$697$	−3.79943	−0.143914
$698$	−12.3739	−0.468359
$699$	17.1313	0.647965
$700$	−5.57915	−0.210872
$701$	−42.7123	−1.61322	−0.806610	−	0.591084i	$-0.798700\pi$
$701$	−42.7123	−1.61322	−0.806610	+	0.591084i	$0.798700\pi$
$702$	0	0
$703$	6.77462	0.255509
$704$	8.21031	0.309438
$705$	−15.8703	−0.597710
$706$	7.53650	0.283640
$707$	18.9676	0.713352
$708$	14.3985	0.541128
$709$	−5.88615	−0.221059	−0.110529	−	0.993873i	$-0.535255\pi$
$709$	−5.88615	−0.221059	−0.110529	+	0.993873i	$0.535255\pi$
$710$	−65.5398	−2.45967
$711$	−11.8875	−0.445816
$712$	25.3612	0.950452
$713$	−10.1421	−0.379824
$714$	4.46837	0.167225
$715$	0	0
$716$	−30.2727	−1.13134
$717$	−17.8428	−0.666352
$718$	65.5569	2.44656
$719$	−22.3734	−0.834387	−0.417194	−	0.908818i	$-0.636986\pi$
$719$	−22.3734	−0.834387	−0.417194	+	0.908818i	$0.636986\pi$
$720$	−15.2023	−0.566556
$721$	−0.207896	−0.00774245
$722$	−27.1817	−1.01160
$723$	17.0689	0.634799
$724$	9.14431	0.339846
$725$	20.0769	0.745637
$726$	55.6369	2.06488
$727$	−27.1276	−1.00611	−0.503053	−	0.864256i	$-0.667790\pi$
$727$	−27.1276	−1.00611	−0.503053	+	0.864256i	$0.667790\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−63.6041	−2.35409
$731$	17.1045	0.632633
$732$	9.08644	0.335844
$733$	35.5147	1.31177	0.655884	−	0.754862i	$-0.272296\pi$
$733$	35.5147	1.31177	0.655884	+	0.754862i	$0.272296\pi$
$734$	−16.8996	−0.623776
$735$	−3.07801	−0.113534
$736$	22.5179	0.830021
$737$	16.5825	0.610826
$738$	−2.76089	−0.101630
$739$	35.1297	1.29227	0.646134	−	0.763224i	$-0.276385\pi$
$739$	35.1297	1.29227	0.646134	+	0.763224i	$0.276385\pi$
$740$	4.45383	0.163726
$741$	0	0
$742$	−17.3965	−0.638647
$743$	−9.33606	−0.342507	−0.171253	−	0.985227i	$-0.554782\pi$
$743$	−9.33606	−0.342507	−0.171253	+	0.985227i	$0.554782\pi$
$744$	3.78055	0.138602
$745$	2.25202	0.0825074
$746$	45.5701	1.66844
$747$	−7.58647	−0.277574
$748$	20.0102	0.731647
$749$	6.92160	0.252910
$750$	−2.91666	−0.106501
$751$	−14.9393	−0.545144	−0.272572	−	0.962135i	$-0.587874\pi$
$751$	−14.9393	−0.545144	−0.272572	+	0.962135i	$0.587874\pi$
$752$	−25.4656	−0.928635
$753$	22.0735	0.804402
$754$	0	0
$755$	−3.18050	−0.115750
$756$	1.24698	0.0453522
$757$	30.8483	1.12120	0.560601	−	0.828086i	$-0.310570\pi$
$757$	30.8483	1.12120	0.560601	+	0.828086i	$0.310570\pi$
$758$	−23.0182	−0.836058
$759$	23.5561	0.855031
$760$	24.3835	0.884483
$761$	−0.975789	−0.0353723	−0.0176862	−	0.999844i	$-0.505630\pi$
$761$	−0.975789	−0.0353723	−0.0176862	+	0.999844i	$0.505630\pi$
$762$	34.9782	1.26713
$763$	−9.79742	−0.354690
$764$	−0.128496	−0.00464881
$765$	−7.63272	−0.275961
$766$	9.22911	0.333461
$767$	0	0
$768$	−20.7114	−0.747358
$769$	−51.9223	−1.87237	−0.936184	−	0.351511i	$-0.885668\pi$
$769$	−51.9223	−1.87237	−0.936184	+	0.351511i	$0.885668\pi$
$770$	−35.8916	−1.29344
$771$	10.5585	0.380254
$772$	14.7221	0.529859
$773$	9.10468	0.327473	0.163736	−	0.986504i	$-0.447645\pi$
$773$	9.10468	0.327473	0.163736	+	0.986504i	$0.447645\pi$
$774$	12.4291	0.446756
$775$	−12.4657	−0.447781
$776$	1.47132	0.0528173
$777$	1.16039	0.0416288
$778$	17.6932	0.634332
$779$	8.94518	0.320494
$780$	0	0
$781$	−76.4679	−2.73624
$782$	16.2655	0.581655
$783$	−4.48732	−0.160364
$784$	−4.93900	−0.176393
$785$	18.9120	0.675000
$786$	−33.2094	−1.18454
$787$	−41.4199	−1.47646	−0.738230	−	0.674550i	$-0.764338\pi$
$787$	−41.4199	−1.47646	−0.738230	+	0.674550i	$0.764338\pi$
$788$	28.5149	1.01580
$789$	−24.6204	−0.876511
$790$	65.9326	2.34578
$791$	11.9913	0.426361
$792$	−8.78072	−0.312009
$793$	0	0
$794$	−5.48875	−0.194788
$795$	29.7162	1.05392
$796$	1.02402	0.0362954
$797$	16.8411	0.596542	0.298271	−	0.954481i	$-0.403590\pi$
$797$	16.8411	0.596542	0.298271	+	0.954481i	$0.403590\pi$
$798$	−10.5201	−0.372407
$799$	−12.7857	−0.452325
$800$	27.6769	0.978526
$801$	18.6906	0.660400
$802$	1.55803	0.0550160
$803$	−74.2094	−2.61879
$804$	3.19541	0.112694
$805$	−11.2044	−0.394904
$806$	0	0
$807$	12.5227	0.440821
$808$	−25.7371	−0.905429
$809$	−21.4075	−0.752646	−0.376323	−	0.926488i	$-0.622812\pi$
$809$	−21.4075	−0.752646	−0.376323	+	0.926488i	$0.622812\pi$
$810$	−5.54638	−0.194880
$811$	27.5993	0.969141	0.484571	−	0.874752i	$-0.338976\pi$
$811$	27.5993	0.969141	0.484571	+	0.874752i	$0.338976\pi$
$812$	−5.59560	−0.196367
$813$	12.3506	0.433153
$814$	13.5309	0.474259
$815$	−23.7069	−0.830416
$816$	−12.2475	−0.428749
$817$	−40.2699	−1.40887
$818$	−6.51049	−0.227634
$819$	0	0
$820$	5.88083	0.205367
$821$	13.3942	0.467461	0.233731	−	0.972301i	$-0.424907\pi$
$821$	13.3942	0.467461	0.233731	+	0.972301i	$0.424907\pi$
$822$	−14.8783	−0.518939
$823$	−21.4686	−0.748349	−0.374175	−	0.927358i	$-0.622074\pi$
$823$	−21.4686	−0.748349	−0.374175	+	0.927358i	$0.622074\pi$
$824$	0.282093	0.00982718
$825$	28.9529	1.00801
$826$	−20.8064	−0.723947
$827$	−21.3923	−0.743882	−0.371941	−	0.928256i	$-0.621308\pi$
$827$	−21.3923	−0.743882	−0.371941	+	0.928256i	$0.621308\pi$
$828$	4.53919	0.157748
$829$	16.9639	0.589181	0.294591	−	0.955624i	$-0.404817\pi$
$829$	16.9639	0.589181	0.294591	+	0.955624i	$0.404817\pi$
$830$	42.0774	1.46053
$831$	−16.3139	−0.565921
$832$	0	0
$833$	−2.47976	−0.0859185
$834$	23.2319	0.804456
$835$	−39.8795	−1.38009
$836$	−47.1110	−1.62937
$837$	2.78617	0.0963042
$838$	44.7606	1.54623
$839$	−28.1419	−0.971565	−0.485782	−	0.874080i	$-0.661465\pi$
$839$	−28.1419	−0.971565	−0.485782	+	0.874080i	$0.661465\pi$
$840$	4.17654	0.144104
$841$	−8.86393	−0.305653
$842$	38.6780	1.33293
$843$	−10.5157	−0.362180
$844$	−30.9542	−1.06549
$845$	0	0
$846$	−9.29084	−0.319426
$847$	−30.8762	−1.06092
$848$	47.6829	1.63744
$849$	−25.4773	−0.874377
$850$	19.9921	0.685723
$851$	4.22400	0.144797
$852$	−14.7352	−0.504819
$853$	14.3944	0.492856	0.246428	−	0.969161i	$-0.420743\pi$
$853$	14.3944	0.492856	0.246428	+	0.969161i	$0.420743\pi$
$854$	−13.1303	−0.449309
$855$	17.9701	0.614563
$856$	−9.39189	−0.321008
$857$	31.7777	1.08550	0.542752	−	0.839893i	$-0.317382\pi$
$857$	31.7777	1.08550	0.542752	+	0.839893i	$0.317382\pi$
$858$	0	0
$859$	14.0645	0.479876	0.239938	−	0.970788i	$-0.422873\pi$
$859$	14.0645	0.479876	0.239938	+	0.970788i	$0.422873\pi$
$860$	−26.4746	−0.902778
$861$	1.53218	0.0522165
$862$	28.6183	0.974745
$863$	41.6977	1.41941	0.709704	−	0.704500i	$-0.248829\pi$
$863$	41.6977	1.41941	0.709704	+	0.704500i	$0.248829\pi$
$864$	−6.18598	−0.210451
$865$	−31.0843	−1.05690
$866$	5.60502	0.190466
$867$	10.8508	0.368512
$868$	3.47430	0.117925
$869$	76.9262	2.60954
$870$	24.8884	0.843796
$871$	0	0
$872$	13.2941	0.450194
$873$	1.08433	0.0366989
$874$	−38.2947	−1.29534
$875$	1.61862	0.0547195
$876$	−14.3000	−0.483151
$877$	−33.9320	−1.14580	−0.572901	−	0.819625i	$-0.694182\pi$
$877$	−33.9320	−1.14580	−0.572901	+	0.819625i	$0.694182\pi$
$878$	11.4949	0.387935
$879$	−4.73420	−0.159681
$880$	98.3767	3.31628
$881$	−33.4358	−1.12648	−0.563240	−	0.826294i	$-0.690445\pi$
$881$	−33.4358	−1.12648	−0.563240	+	0.826294i	$0.690445\pi$
$882$	−1.80194	−0.0606744
$883$	−14.8739	−0.500545	−0.250273	−	0.968175i	$-0.580520\pi$
$883$	−14.8739	−0.500545	−0.250273	+	0.968175i	$0.580520\pi$
$884$	0	0
$885$	35.5408	1.19469
$886$	−30.5729	−1.02712
$887$	−1.91185	−0.0641937	−0.0320968	−	0.999485i	$-0.510218\pi$
$887$	−1.91185	−0.0641937	−0.0320968	+	0.999485i	$0.510218\pi$
$888$	−1.57453	−0.0528378
$889$	−19.4114	−0.651038
$890$	−103.665	−3.47487
$891$	−6.47118	−0.216793
$892$	−26.4432	−0.885383
$893$	30.1020	1.00732
$894$	1.31838	0.0440933
$895$	−74.7242	−2.49775
$896$	10.0858	0.336941
$897$	0	0
$898$	−8.02040	−0.267644
$899$	−12.5025	−0.416980
$900$	5.57915	0.185972
$901$	23.9405	0.797572
$902$	17.8662	0.594880
$903$	−6.89765	−0.229539
$904$	−16.2709	−0.541163
$905$	22.5716	0.750304
$906$	−1.86194	−0.0618588
$907$	26.8212	0.890583	0.445292	−	0.895386i	$-0.353100\pi$
$907$	26.8212	0.890583	0.445292	+	0.895386i	$0.353100\pi$
$908$	−23.7906	−0.789518
$909$	−18.9676	−0.629117
$910$	0	0
$911$	−5.59749	−0.185453	−0.0927265	−	0.995692i	$-0.529558\pi$
$911$	−5.59749	−0.185453	−0.0927265	+	0.995692i	$0.529558\pi$
$912$	28.8349	0.954820
$913$	49.0934	1.62476
$914$	10.7320	0.354982
$915$	22.4287	0.741470
$916$	−16.8663	−0.557278
$917$	18.4298	0.608607
$918$	−4.46837	−0.147478
$919$	45.7248	1.50832	0.754160	−	0.656691i	$-0.228044\pi$
$919$	45.7248	1.50832	0.754160	+	0.656691i	$0.228044\pi$
$920$	15.2032	0.501235
$921$	−5.13876	−0.169328
$922$	−4.66484	−0.153628
$923$	0	0
$924$	−8.06943	−0.265465
$925$	5.19175	0.170704
$926$	64.8730	2.13186
$927$	0.207896	0.00682820
$928$	27.7585	0.911217
$929$	43.0428	1.41219	0.706094	−	0.708118i	$-0.250456\pi$
$929$	43.0428	1.41219	0.706094	+	0.708118i	$0.250456\pi$
$930$	−15.4532	−0.506729
$931$	5.83821	0.191340
$932$	−21.3624	−0.699748
$933$	14.4284	0.472365
$934$	−64.1830	−2.10013
$935$	49.3927	1.61531
$936$	0	0
$937$	34.5984	1.13028	0.565141	−	0.824994i	$-0.308822\pi$
$937$	34.5984	1.13028	0.565141	+	0.824994i	$0.308822\pi$
$938$	−4.61751	−0.150767
$939$	3.77751	0.123274
$940$	19.7899	0.645476
$941$	0.138429	0.00451266	0.00225633	−	0.999997i	$-0.499282\pi$
$941$	0.138429	0.00451266	0.00225633	+	0.999997i	$0.499282\pi$
$942$	11.0716	0.360731
$943$	5.57736	0.181624
$944$	57.0291	1.85614
$945$	3.07801	0.100128
$946$	−80.4311	−2.61504
$947$	−2.66158	−0.0864896	−0.0432448	−	0.999065i	$-0.513770\pi$
$947$	−2.66158	−0.0864896	−0.0432448	+	0.999065i	$0.513770\pi$
$948$	14.8235	0.481444
$949$	0	0
$950$	−47.0683	−1.52710
$951$	17.6020	0.570784
$952$	3.36477	0.109053
$953$	16.1600	0.523474	0.261737	−	0.965139i	$-0.415705\pi$
$953$	16.1600	0.523474	0.261737	+	0.965139i	$0.415705\pi$
$954$	17.3965	0.563234
$955$	−0.317175	−0.0102635
$956$	22.2496	0.719604
$957$	29.0383	0.938674
$958$	64.2214	2.07490
$959$	8.25681	0.266626
$960$	3.90522	0.126041
$961$	−23.2372	−0.749588
$962$	0	0
$963$	−6.92160	−0.223045
$964$	−21.2846	−0.685530
$965$	36.3395	1.16981
$966$	−6.55933	−0.211043
$967$	25.1632	0.809194	0.404597	−	0.914495i	$-0.367412\pi$
$967$	25.1632	0.809194	0.404597	+	0.914495i	$0.367412\pi$
$968$	41.8957	1.34658
$969$	14.4774	0.465080
$970$	−6.01409	−0.193101
$971$	−3.58992	−0.115206	−0.0576029	−	0.998340i	$-0.518346\pi$
$971$	−3.58992	−0.115206	−0.0576029	+	0.998340i	$0.518346\pi$
$972$	−1.24698	−0.0399969
$973$	−12.8927	−0.413322
$974$	19.2365	0.616376
$975$	0	0
$976$	35.9893	1.15199
$977$	−26.3689	−0.843615	−0.421807	−	0.906685i	$-0.638604\pi$
$977$	−26.3689	−0.843615	−0.421807	+	0.906685i	$0.638604\pi$
$978$	−13.8786	−0.443788
$979$	−120.950	−3.86559
$980$	3.83821	0.122607
$981$	9.79742	0.312808
$982$	66.4279	2.11980
$983$	17.9645	0.572978	0.286489	−	0.958084i	$-0.407512\pi$
$983$	17.9645	0.572978	0.286489	+	0.958084i	$0.407512\pi$
$984$	−2.07901	−0.0662763
$985$	70.3853	2.24266
$986$	20.0510	0.638555
$987$	5.15603	0.164118
$988$	0	0
$989$	−25.1085	−0.798403
$990$	35.8916	1.14071
$991$	10.3327	0.328230	0.164115	−	0.986441i	$-0.447523\pi$
$991$	10.3327	0.328230	0.164115	+	0.986441i	$0.447523\pi$
$992$	−17.2352	−0.547219
$993$	8.93862	0.283659
$994$	21.2929	0.675371
$995$	2.52766	0.0801321
$996$	9.46018	0.299757
$997$	12.8061	0.405574	0.202787	−	0.979223i	$-0.435000\pi$
$997$	12.8061	0.405574	0.202787	+	0.979223i	$0.435000\pi$
$998$	−6.49305	−0.205534
$999$	−1.16039	−0.0367132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.y.1.2	✓	6
13.12	even	2		3549.2.a.z.1.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.y.1.2	✓	6	1.1	even	1	trivial
3549.2.a.z.1.5	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)

\(f(q)\)	\(=\)	\(q-1.80194 q^{2} -1.00000 q^{3} +1.24698 q^{4} +3.07801 q^{5} +1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.80194 q^{2} -1.00000 q^{3} +1.24698 q^{4} +3.07801 q^{5} +1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} -5.54638 q^{10} -6.47118 q^{11} -1.24698 q^{12} +1.80194 q^{14} -3.07801 q^{15} -4.93900 q^{16} -2.47976 q^{17} -1.80194 q^{18} +5.83821 q^{19} +3.83821 q^{20} +1.00000 q^{21} +11.6607 q^{22} +3.64015 q^{23} -1.35690 q^{24} +4.47413 q^{25} -1.00000 q^{27} -1.24698 q^{28} +4.48732 q^{29} +5.54638 q^{30} -2.78617 q^{31} +6.18598 q^{32} +6.47118 q^{33} +4.46837 q^{34} -3.07801 q^{35} +1.24698 q^{36} +1.16039 q^{37} -10.5201 q^{38} +4.17654 q^{40} +1.53218 q^{41} -1.80194 q^{42} -6.89765 q^{43} -8.06943 q^{44} +3.07801 q^{45} -6.55933 q^{46} +5.15603 q^{47} +4.93900 q^{48} +1.00000 q^{49} -8.06211 q^{50} +2.47976 q^{51} -9.65435 q^{53} +1.80194 q^{54} -19.9183 q^{55} -1.35690 q^{56} -5.83821 q^{57} -8.08588 q^{58} -11.5467 q^{59} -3.83821 q^{60} -7.28676 q^{61} +5.02051 q^{62} -1.00000 q^{63} -1.26875 q^{64} -11.6607 q^{66} -2.56252 q^{67} -3.09221 q^{68} -3.64015 q^{69} +5.54638 q^{70} +11.8167 q^{71} +1.35690 q^{72} +11.4677 q^{73} -2.09095 q^{74} -4.47413 q^{75} +7.28013 q^{76} +6.47118 q^{77} -11.8875 q^{79} -15.2023 q^{80} +1.00000 q^{81} -2.76089 q^{82} -7.58647 q^{83} +1.24698 q^{84} -7.63272 q^{85} +12.4291 q^{86} -4.48732 q^{87} -8.78072 q^{88} +18.6906 q^{89} -5.54638 q^{90} +4.53919 q^{92} +2.78617 q^{93} -9.29084 q^{94} +17.9701 q^{95} -6.18598 q^{96} +1.08433 q^{97} -1.80194 q^{98} -6.47118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 3 q^{5} + 2 q^{6} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) 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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Representations

Groups

Database

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