LMFDB - Embedded newform 3549.2.a.bh.1.12

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:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 $ x^15 - 2x^14 - 27x^13 + 51x^12 + 290x^11 - 510x^10 - 1575x^9 + 2522x^8 + 4553x^7 - 6393x^6 - 6785x^5 + 7806x^4 + 4632x^3 - 3811x^2 - 1041x + 281
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			1.12
Root			$2.07185$ 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)

$f(q)$	$=$	$q+2.07185 q^{2} +1.00000 q^{3} +2.29258 q^{4} +3.98491 q^{5} +2.07185 q^{6} -1.00000 q^{7} +0.606176 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.07185 q^{2} +1.00000 q^{3} +2.29258 q^{4} +3.98491 q^{5} +2.07185 q^{6} -1.00000 q^{7} +0.606176 q^{8} +1.00000 q^{9} +8.25616 q^{10} +2.61487 q^{11} +2.29258 q^{12} -2.07185 q^{14} +3.98491 q^{15} -3.32925 q^{16} +2.46321 q^{17} +2.07185 q^{18} +5.30899 q^{19} +9.13572 q^{20} -1.00000 q^{21} +5.41763 q^{22} -8.91513 q^{23} +0.606176 q^{24} +10.8795 q^{25} +1.00000 q^{27} -2.29258 q^{28} -3.55037 q^{29} +8.25616 q^{30} +6.25363 q^{31} -8.11006 q^{32} +2.61487 q^{33} +5.10341 q^{34} -3.98491 q^{35} +2.29258 q^{36} -3.72795 q^{37} +10.9995 q^{38} +2.41556 q^{40} -6.88324 q^{41} -2.07185 q^{42} +7.59739 q^{43} +5.99479 q^{44} +3.98491 q^{45} -18.4709 q^{46} -2.43688 q^{47} -3.32925 q^{48} +1.00000 q^{49} +22.5408 q^{50} +2.46321 q^{51} -10.8574 q^{53} +2.07185 q^{54} +10.4200 q^{55} -0.606176 q^{56} +5.30899 q^{57} -7.35584 q^{58} -0.944885 q^{59} +9.13572 q^{60} +4.95925 q^{61} +12.9566 q^{62} -1.00000 q^{63} -10.1444 q^{64} +5.41763 q^{66} -16.0479 q^{67} +5.64710 q^{68} -8.91513 q^{69} -8.25616 q^{70} +15.8147 q^{71} +0.606176 q^{72} +3.16937 q^{73} -7.72376 q^{74} +10.8795 q^{75} +12.1713 q^{76} -2.61487 q^{77} -5.15670 q^{79} -13.2668 q^{80} +1.00000 q^{81} -14.2611 q^{82} +1.47510 q^{83} -2.29258 q^{84} +9.81567 q^{85} +15.7407 q^{86} -3.55037 q^{87} +1.58507 q^{88} +13.7404 q^{89} +8.25616 q^{90} -20.4386 q^{92} +6.25363 q^{93} -5.04886 q^{94} +21.1559 q^{95} -8.11006 q^{96} -4.52869 q^{97} +2.07185 q^{98} +2.61487 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.07185	1.46502	0.732511	−	0.680755i	$-0.238348\pi$
$2$	2.07185	1.46502	0.732511	+	0.680755i	$0.238348\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.29258	1.14629
$5$	3.98491	1.78211	0.891054	−	0.453898i	$-0.149967\pi$
$5$	3.98491	1.78211	0.891054	+	0.453898i	$0.149967\pi$
$6$	2.07185	0.845831
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.606176	0.214316
$9$	1.00000	0.333333
$10$	8.25616	2.61083
$11$	2.61487	0.788413	0.394207	−	0.919022i	$-0.371019\pi$
$11$	2.61487	0.788413	0.394207	+	0.919022i	$0.371019\pi$
$12$	2.29258	0.661810
$13$	0	0
$13$	0	0
$14$	−2.07185	−0.553726
$15$	3.98491	1.02890
$16$	−3.32925	−0.832311
$17$	2.46321	0.597416	0.298708	−	0.954345i	$-0.403444\pi$
$17$	2.46321	0.597416	0.298708	+	0.954345i	$0.403444\pi$
$18$	2.07185	0.488341
$19$	5.30899	1.21797	0.608983	−	0.793183i	$-0.291578\pi$
$19$	5.30899	1.21797	0.608983	+	0.793183i	$0.291578\pi$
$20$	9.13572	2.04281
$21$	−1.00000	−0.218218
$22$	5.41763	1.15504
$23$	−8.91513	−1.85893	−0.929467	−	0.368905i	$-0.879733\pi$
$23$	−8.91513	−1.85893	−0.929467	+	0.368905i	$0.879733\pi$
$24$	0.606176	0.123735
$25$	10.8795	2.17591
$26$	0	0
$27$	1.00000	0.192450
$28$	−2.29258	−0.433256
$29$	−3.55037	−0.659287	−0.329643	−	0.944105i	$-0.606929\pi$
$29$	−3.55037	−0.659287	−0.329643	+	0.944105i	$0.606929\pi$
$30$	8.25616	1.50736
$31$	6.25363	1.12319	0.561593	−	0.827414i	$-0.310189\pi$
$31$	6.25363	1.12319	0.561593	+	0.827414i	$0.310189\pi$
$32$	−8.11006	−1.43367
$33$	2.61487	0.455191
$34$	5.10341	0.875227
$35$	−3.98491	−0.673573
$36$	2.29258	0.382096
$37$	−3.72795	−0.612871	−0.306435	−	0.951891i	$-0.599136\pi$
$37$	−3.72795	−0.612871	−0.306435	+	0.951891i	$0.599136\pi$
$38$	10.9995	1.78435
$39$	0	0
$40$	2.41556	0.381934
$41$	−6.88324	−1.07498	−0.537490	−	0.843270i	$-0.680628\pi$
$41$	−6.88324	−1.07498	−0.537490	+	0.843270i	$0.680628\pi$
$42$	−2.07185	−0.319694
$43$	7.59739	1.15859	0.579296	−	0.815117i	$-0.303328\pi$
$43$	7.59739	1.15859	0.579296	+	0.815117i	$0.303328\pi$
$44$	5.99479	0.903749
$45$	3.98491	0.594036
$46$	−18.4709	−2.72338
$47$	−2.43688	−0.355455	−0.177728	−	0.984080i	$-0.556875\pi$
$47$	−2.43688	−0.355455	−0.177728	+	0.984080i	$0.556875\pi$
$48$	−3.32925	−0.480535
$49$	1.00000	0.142857
$50$	22.5408	3.18775
$51$	2.46321	0.344918
$52$	0	0
$53$	−10.8574	−1.49138	−0.745690	−	0.666293i	$-0.767880\pi$
$53$	−10.8574	−1.49138	−0.745690	+	0.666293i	$0.767880\pi$
$54$	2.07185	0.281944
$55$	10.4200	1.40504
$56$	−0.606176	−0.0810037
$57$	5.30899	0.703193
$58$	−7.35584	−0.965870
$59$	−0.944885	−0.123014	−0.0615068	−	0.998107i	$-0.519591\pi$
$59$	−0.944885	−0.123014	−0.0615068	+	0.998107i	$0.519591\pi$
$60$	9.13572	1.17942
$61$	4.95925	0.634967	0.317483	−	0.948264i	$-0.397162\pi$
$61$	4.95925	0.634967	0.317483	+	0.948264i	$0.397162\pi$
$62$	12.9566	1.64549
$63$	−1.00000	−0.125988
$64$	−10.1444	−1.26805
$65$	0	0
$66$	5.41763	0.666864
$67$	−16.0479	−1.96056	−0.980281	−	0.197609i	$-0.936682\pi$
$67$	−16.0479	−1.96056	−0.980281	+	0.197609i	$0.936682\pi$
$68$	5.64710	0.684811
$69$	−8.91513	−1.07326
$70$	−8.25616	−0.986799
$71$	15.8147	1.87686	0.938429	−	0.345471i	$-0.112281\pi$
$71$	15.8147	1.87686	0.938429	+	0.345471i	$0.112281\pi$
$72$	0.606176	0.0714386
$73$	3.16937	0.370947	0.185473	−	0.982649i	$-0.440618\pi$
$73$	3.16937	0.370947	0.185473	+	0.982649i	$0.440618\pi$
$74$	−7.72376	−0.897869
$75$	10.8795	1.25626
$76$	12.1713	1.39614
$77$	−2.61487	−0.297992
$78$	0	0
$79$	−5.15670	−0.580174	−0.290087	−	0.957000i	$-0.593684\pi$
$79$	−5.15670	−0.580174	−0.290087	+	0.957000i	$0.593684\pi$
$80$	−13.2668	−1.48327
$81$	1.00000	0.111111
$82$	−14.2611	−1.57487
$83$	1.47510	0.161913	0.0809567	−	0.996718i	$-0.474202\pi$
$83$	1.47510	0.161913	0.0809567	+	0.996718i	$0.474202\pi$
$84$	−2.29258	−0.250141
$85$	9.81567	1.06466
$86$	15.7407	1.69736
$87$	−3.55037	−0.380639
$88$	1.58507	0.168969
$89$	13.7404	1.45648	0.728241	−	0.685321i	$-0.240338\pi$
$89$	13.7404	1.45648	0.728241	+	0.685321i	$0.240338\pi$
$90$	8.25616	0.870275
$91$	0	0
$92$	−20.4386	−2.13087
$93$	6.25363	0.648472
$94$	−5.04886	−0.520750
$95$	21.1559	2.17055
$96$	−8.11006	−0.827730
$97$	−4.52869	−0.459819	−0.229910	−	0.973212i	$-0.573843\pi$
$97$	−4.52869	−0.459819	−0.229910	+	0.973212i	$0.573843\pi$
$98$	2.07185	0.209289
$99$	2.61487	0.262804
$100$	24.9422	2.49422
$101$	−2.65442	−0.264125	−0.132062	−	0.991241i	$-0.542160\pi$
$101$	−2.65442	−0.264125	−0.132062	+	0.991241i	$0.542160\pi$
$102$	5.10341	0.505313
$103$	−10.9414	−1.07809	−0.539044	−	0.842278i	$-0.681214\pi$
$103$	−10.9414	−1.07809	−0.539044	+	0.842278i	$0.681214\pi$
$104$	0	0
$105$	−3.98491	−0.388888
$106$	−22.4950	−2.18490
$107$	5.83503	0.564094	0.282047	−	0.959401i	$-0.408987\pi$
$107$	5.83503	0.564094	0.282047	+	0.959401i	$0.408987\pi$
$108$	2.29258	0.220603
$109$	14.4487	1.38393	0.691965	−	0.721931i	$-0.256745\pi$
$109$	14.4487	1.38393	0.691965	+	0.721931i	$0.256745\pi$
$110$	21.5888	2.05841
$111$	−3.72795	−0.353841
$112$	3.32925	0.314584
$113$	−9.37283	−0.881721	−0.440861	−	0.897576i	$-0.645327\pi$
$113$	−9.37283	−0.881721	−0.440861	+	0.897576i	$0.645327\pi$
$114$	10.9995	1.03019
$115$	−35.5260	−3.31282
$116$	−8.13949	−0.755733
$117$	0	0
$118$	−1.95766	−0.180218
$119$	−2.46321	−0.225802
$120$	2.41556	0.220509
$121$	−4.16245	−0.378405
$122$	10.2748	0.930240
$123$	−6.88324	−0.620640
$124$	14.3369	1.28749
$125$	23.4294	2.09559
$126$	−2.07185	−0.184575
$127$	−3.25452	−0.288792	−0.144396	−	0.989520i	$-0.546124\pi$
$127$	−3.25452	−0.288792	−0.144396	+	0.989520i	$0.546124\pi$
$128$	−4.79752	−0.424045
$129$	7.59739	0.668913
$130$	0	0
$131$	1.26410	0.110445	0.0552224	−	0.998474i	$-0.482413\pi$
$131$	1.26410	0.110445	0.0552224	+	0.998474i	$0.482413\pi$
$132$	5.99479	0.521780
$133$	−5.30899	−0.460348
$134$	−33.2489	−2.87227
$135$	3.98491	0.342967
$136$	1.49314	0.128036
$137$	−16.0982	−1.37536	−0.687682	−	0.726012i	$-0.741371\pi$
$137$	−16.0982	−1.37536	−0.687682	+	0.726012i	$0.741371\pi$
$138$	−18.4709	−1.57234
$139$	20.8156	1.76556	0.882778	−	0.469791i	$-0.155671\pi$
$139$	20.8156	1.76556	0.882778	+	0.469791i	$0.155671\pi$
$140$	−9.13572	−0.772109
$141$	−2.43688	−0.205222
$142$	32.7657	2.74964
$143$	0	0
$144$	−3.32925	−0.277437
$145$	−14.1479	−1.17492
$146$	6.56647	0.543445
$147$	1.00000	0.0824786
$148$	−8.54661	−0.702527
$149$	−14.5215	−1.18965	−0.594823	−	0.803856i	$-0.702778\pi$
$149$	−14.5215	−1.18965	−0.594823	+	0.803856i	$0.702778\pi$
$150$	22.5408	1.84045
$151$	−10.2052	−0.830489	−0.415245	−	0.909710i	$-0.636304\pi$
$151$	−10.2052	−0.830489	−0.415245	+	0.909710i	$0.636304\pi$
$152$	3.21819	0.261029
$153$	2.46321	0.199139
$154$	−5.41763	−0.436565
$155$	24.9202	2.00164
$156$	0	0
$157$	5.86827	0.468339	0.234170	−	0.972196i	$-0.424763\pi$
$157$	5.86827	0.468339	0.234170	+	0.972196i	$0.424763\pi$
$158$	−10.6839	−0.849968
$159$	−10.8574	−0.861048
$160$	−32.3179	−2.55495
$161$	8.91513	0.702611
$162$	2.07185	0.162780
$163$	−0.697676	−0.0546462	−0.0273231	−	0.999627i	$-0.508698\pi$
$163$	−0.697676	−0.0546462	−0.0273231	+	0.999627i	$0.508698\pi$
$164$	−15.7803	−1.23224
$165$	10.4200	0.811199
$166$	3.05620	0.237207
$167$	−25.1020	−1.94245	−0.971224	−	0.238169i	$-0.923453\pi$
$167$	−25.1020	−1.94245	−0.971224	+	0.238169i	$0.923453\pi$
$168$	−0.606176	−0.0467675
$169$	0	0
$170$	20.3366	1.55975
$171$	5.30899	0.405989
$172$	17.4176	1.32808
$173$	5.26644	0.400400	0.200200	−	0.979755i	$-0.435841\pi$
$173$	5.26644	0.400400	0.200200	+	0.979755i	$0.435841\pi$
$174$	−7.35584	−0.557645
$175$	−10.8795	−0.822415
$176$	−8.70555	−0.656205
$177$	−0.944885	−0.0710219
$178$	28.4681	2.13378
$179$	11.4454	0.855469	0.427734	−	0.903904i	$-0.359312\pi$
$179$	11.4454	0.855469	0.427734	+	0.903904i	$0.359312\pi$
$180$	9.13572	0.680936
$181$	−13.2259	−0.983072	−0.491536	−	0.870857i	$-0.663564\pi$
$181$	−13.2259	−0.983072	−0.491536	+	0.870857i	$0.663564\pi$
$182$	0	0
$183$	4.95925	0.366598
$184$	−5.40414	−0.398399
$185$	−14.8556	−1.09220
$186$	12.9566	0.950025
$187$	6.44097	0.471011
$188$	−5.58673	−0.407454
$189$	−1.00000	−0.0727393
$190$	43.8319	3.17990
$191$	2.77448	0.200754	0.100377	−	0.994949i	$-0.467995\pi$
$191$	2.77448	0.200754	0.100377	+	0.994949i	$0.467995\pi$
$192$	−10.1444	−0.732107
$193$	−16.6422	−1.19793	−0.598965	−	0.800776i	$-0.704421\pi$
$193$	−16.6422	−1.19793	−0.598965	+	0.800776i	$0.704421\pi$
$194$	−9.38279	−0.673645
$195$	0	0
$196$	2.29258	0.163755
$197$	−0.164331	−0.0117081	−0.00585404	−	0.999983i	$-0.501863\pi$
$197$	−0.164331	−0.0117081	−0.00585404	+	0.999983i	$0.501863\pi$
$198$	5.41763	0.385014
$199$	1.73169	0.122756	0.0613780	−	0.998115i	$-0.480450\pi$
$199$	1.73169	0.122756	0.0613780	+	0.998115i	$0.480450\pi$
$200$	6.59492	0.466331
$201$	−16.0479	−1.13193
$202$	−5.49957	−0.386948
$203$	3.55037	0.249187
$204$	5.64710	0.395376
$205$	−27.4291	−1.91573
$206$	−22.6690	−1.57942
$207$	−8.91513	−0.619645
$208$	0	0
$209$	13.8823	0.960261
$210$	−8.25616	−0.569729
$211$	14.7885	1.01808	0.509039	−	0.860743i	$-0.330001\pi$
$211$	14.7885	1.01808	0.509039	+	0.860743i	$0.330001\pi$
$212$	−24.8914	−1.70955
$213$	15.8147	1.08361
$214$	12.0893	0.826409
$215$	30.2749	2.06473
$216$	0.606176	0.0412451
$217$	−6.25363	−0.424524
$218$	29.9355	2.02749
$219$	3.16937	0.214166
$220$	23.8887	1.61058
$221$	0	0
$222$	−7.72376	−0.518385
$223$	16.6943	1.11793	0.558966	−	0.829191i	$-0.311198\pi$
$223$	16.6943	1.11793	0.558966	+	0.829191i	$0.311198\pi$
$224$	8.11006	0.541876
$225$	10.8795	0.725302
$226$	−19.4191	−1.29174
$227$	−15.2365	−1.01128	−0.505640	−	0.862745i	$-0.668743\pi$
$227$	−15.2365	−1.01128	−0.505640	+	0.862745i	$0.668743\pi$
$228$	12.1713	0.806062
$229$	−19.2701	−1.27341	−0.636703	−	0.771109i	$-0.719702\pi$
$229$	−19.2701	−1.27341	−0.636703	+	0.771109i	$0.719702\pi$
$230$	−73.6047	−4.85335
$231$	−2.61487	−0.172046
$232$	−2.15215	−0.141296
$233$	6.58317	0.431278	0.215639	−	0.976473i	$-0.430817\pi$
$233$	6.58317	0.431278	0.215639	+	0.976473i	$0.430817\pi$
$234$	0	0
$235$	−9.71075	−0.633460
$236$	−2.16622	−0.141009
$237$	−5.15670	−0.334964
$238$	−5.10341	−0.330805
$239$	−27.0508	−1.74977	−0.874885	−	0.484331i	$-0.839063\pi$
$239$	−27.0508	−1.74977	−0.874885	+	0.484331i	$0.839063\pi$
$240$	−13.2668	−0.856365
$241$	24.4670	1.57606	0.788029	−	0.615638i	$-0.211102\pi$
$241$	24.4670	1.57606	0.788029	+	0.615638i	$0.211102\pi$
$242$	−8.62399	−0.554371
$243$	1.00000	0.0641500
$244$	11.3695	0.727855
$245$	3.98491	0.254587
$246$	−14.2611	−0.909252
$247$	0	0
$248$	3.79080	0.240716
$249$	1.47510	0.0934808
$250$	48.5424	3.07009
$251$	2.93895	0.185505	0.0927524	−	0.995689i	$-0.470433\pi$
$251$	2.93895	0.185505	0.0927524	+	0.995689i	$0.470433\pi$
$252$	−2.29258	−0.144419
$253$	−23.3119	−1.46561
$254$	−6.74288	−0.423086
$255$	9.81567	0.614681
$256$	10.3490	0.646811
$257$	5.57830	0.347965	0.173982	−	0.984749i	$-0.444336\pi$
$257$	5.57830	0.347965	0.173982	+	0.984749i	$0.444336\pi$
$258$	15.7407	0.979972
$259$	3.72795	0.231643
$260$	0	0
$261$	−3.55037	−0.219762
$262$	2.61903	0.161804
$263$	21.2240	1.30873	0.654365	−	0.756179i	$-0.272936\pi$
$263$	21.2240	1.30873	0.654365	+	0.756179i	$0.272936\pi$
$264$	1.58507	0.0975545
$265$	−43.2658	−2.65780
$266$	−10.9995	−0.674420
$267$	13.7404	0.840900
$268$	−36.7910	−2.24737
$269$	−1.92240	−0.117211	−0.0586054	−	0.998281i	$-0.518665\pi$
$269$	−1.92240	−0.117211	−0.0586054	+	0.998281i	$0.518665\pi$
$270$	8.25616	0.502454
$271$	2.56202	0.155632	0.0778159	−	0.996968i	$-0.475205\pi$
$271$	2.56202	0.155632	0.0778159	+	0.996968i	$0.475205\pi$
$272$	−8.20063	−0.497236
$273$	0	0
$274$	−33.3531	−2.01494
$275$	28.4486	1.71551
$276$	−20.4386	−1.23026
$277$	−9.31382	−0.559613	−0.279807	−	0.960056i	$-0.590270\pi$
$277$	−9.31382	−0.559613	−0.279807	+	0.960056i	$0.590270\pi$
$278$	43.1269	2.58658
$279$	6.25363	0.374395
$280$	−2.41556	−0.144357
$281$	14.0421	0.837682	0.418841	−	0.908060i	$-0.362436\pi$
$281$	14.0421	0.837682	0.418841	+	0.908060i	$0.362436\pi$
$282$	−5.04886	−0.300655
$283$	12.6395	0.751342	0.375671	−	0.926753i	$-0.377412\pi$
$283$	12.6395	0.751342	0.375671	+	0.926753i	$0.377412\pi$
$284$	36.2564	2.15142
$285$	21.1559	1.25317
$286$	0	0
$287$	6.88324	0.406305
$288$	−8.11006	−0.477890
$289$	−10.9326	−0.643094
$290$	−29.3124	−1.72128
$291$	−4.52869	−0.265477
$292$	7.26603	0.425212
$293$	−22.0692	−1.28930	−0.644648	−	0.764480i	$-0.722996\pi$
$293$	−22.0692	−1.28930	−0.644648	+	0.764480i	$0.722996\pi$
$294$	2.07185	0.120833
$295$	−3.76529	−0.219223
$296$	−2.25979	−0.131348
$297$	2.61487	0.151730
$298$	−30.0864	−1.74286
$299$	0	0
$300$	24.9422	1.44004
$301$	−7.59739	−0.437906
$302$	−21.1437	−1.21668
$303$	−2.65442	−0.152492
$304$	−17.6749	−1.01373
$305$	19.7622	1.13158
$306$	5.10341	0.291742
$307$	3.30193	0.188451	0.0942255	−	0.995551i	$-0.469963\pi$
$307$	3.30193	0.188451	0.0942255	+	0.995551i	$0.469963\pi$
$308$	−5.99479	−0.341585
$309$	−10.9414	−0.622434
$310$	51.6310	2.93244
$311$	16.1831	0.917658	0.458829	−	0.888525i	$-0.348269\pi$
$311$	16.1831	0.917658	0.458829	+	0.888525i	$0.348269\pi$
$312$	0	0
$313$	2.50394	0.141531	0.0707656	−	0.997493i	$-0.477456\pi$
$313$	2.50394	0.141531	0.0707656	+	0.997493i	$0.477456\pi$
$314$	12.1582	0.686127
$315$	−3.98491	−0.224524
$316$	−11.8221	−0.665047
$317$	24.1074	1.35401	0.677005	−	0.735979i	$-0.263278\pi$
$317$	24.1074	1.35401	0.677005	+	0.735979i	$0.263278\pi$
$318$	−22.4950	−1.26145
$319$	−9.28376	−0.519791
$320$	−40.4244	−2.25979
$321$	5.83503	0.325680
$322$	18.4709	1.02934
$323$	13.0772	0.727632
$324$	2.29258	0.127365
$325$	0	0
$326$	−1.44548	−0.0800579
$327$	14.4487	0.799012
$328$	−4.17245	−0.230385
$329$	2.43688	0.134350
$330$	21.5888	1.18842
$331$	−5.36044	−0.294637	−0.147318	−	0.989089i	$-0.547064\pi$
$331$	−5.36044	−0.294637	−0.147318	+	0.989089i	$0.547064\pi$
$332$	3.38178	0.185600
$333$	−3.72795	−0.204290
$334$	−52.0076	−2.84573
$335$	−63.9495	−3.49393
$336$	3.32925	0.181625
$337$	−16.4659	−0.896952	−0.448476	−	0.893795i	$-0.648033\pi$
$337$	−16.4659	−0.896952	−0.448476	+	0.893795i	$0.648033\pi$
$338$	0	0
$339$	−9.37283	−0.509062
$340$	22.5032	1.22041
$341$	16.3524	0.885534
$342$	10.9995	0.594782
$343$	−1.00000	−0.0539949
$344$	4.60536	0.248304
$345$	−35.5260	−1.91266
$346$	10.9113	0.586595
$347$	−20.9577	−1.12507	−0.562534	−	0.826774i	$-0.690173\pi$
$347$	−20.9577	−1.12507	−0.562534	+	0.826774i	$0.690173\pi$
$348$	−8.13949	−0.436323
$349$	−22.9993	−1.23112	−0.615562	−	0.788088i	$-0.711071\pi$
$349$	−22.9993	−1.23112	−0.615562	+	0.788088i	$0.711071\pi$
$350$	−22.5408	−1.20486
$351$	0	0
$352$	−21.2068	−1.13032
$353$	−27.4204	−1.45944	−0.729722	−	0.683744i	$-0.760350\pi$
$353$	−27.4204	−1.45944	−0.729722	+	0.683744i	$0.760350\pi$
$354$	−1.95766	−0.104049
$355$	63.0202	3.34476
$356$	31.5010	1.66955
$357$	−2.46321	−0.130367
$358$	23.7132	1.25328
$359$	−21.3329	−1.12591	−0.562953	−	0.826489i	$-0.690335\pi$
$359$	−21.3329	−1.12591	−0.562953	+	0.826489i	$0.690335\pi$
$360$	2.41556	0.127311
$361$	9.18541	0.483442
$362$	−27.4021	−1.44022
$363$	−4.16245	−0.218472
$364$	0	0
$365$	12.6297	0.661067
$366$	10.2748	0.537074
$367$	−16.9232	−0.883385	−0.441692	−	0.897167i	$-0.645622\pi$
$367$	−16.9232	−0.883385	−0.441692	+	0.897167i	$0.645622\pi$
$368$	29.6807	1.54721
$369$	−6.88324	−0.358327
$370$	−30.7785	−1.60010
$371$	10.8574	0.563689
$372$	14.3369	0.743335
$373$	17.0966	0.885228	0.442614	−	0.896712i	$-0.354051\pi$
$373$	17.0966	0.885228	0.442614	+	0.896712i	$0.354051\pi$
$374$	13.3448	0.690041
$375$	23.4294	1.20989
$376$	−1.47718	−0.0761797
$377$	0	0
$378$	−2.07185	−0.106565
$379$	9.18462	0.471782	0.235891	−	0.971779i	$-0.424199\pi$
$379$	9.18462	0.471782	0.235891	+	0.971779i	$0.424199\pi$
$380$	48.5015	2.48807
$381$	−3.25452	−0.166734
$382$	5.74831	0.294109
$383$	−38.9057	−1.98799	−0.993995	−	0.109427i	$-0.965098\pi$
$383$	−38.9057	−1.98799	−0.993995	+	0.109427i	$0.965098\pi$
$384$	−4.79752	−0.244822
$385$	−10.4200	−0.531054
$386$	−34.4801	−1.75499
$387$	7.59739	0.386197
$388$	−10.3824	−0.527086
$389$	24.3185	1.23299	0.616497	−	0.787357i	$-0.288551\pi$
$389$	24.3185	1.23299	0.616497	+	0.787357i	$0.288551\pi$
$390$	0	0
$391$	−21.9598	−1.11056
$392$	0.606176	0.0306165
$393$	1.26410	0.0637654
$394$	−0.340469	−0.0171526
$395$	−20.5490	−1.03393
$396$	5.99479	0.301250
$397$	−39.0819	−1.96146	−0.980732	−	0.195356i	$-0.937414\pi$
$397$	−39.0819	−1.96146	−0.980732	+	0.195356i	$0.937414\pi$
$398$	3.58780	0.179840
$399$	−5.30899	−0.265782
$400$	−36.2206	−1.81103
$401$	27.9732	1.39692	0.698458	−	0.715651i	$-0.253870\pi$
$401$	27.9732	1.39692	0.698458	+	0.715651i	$0.253870\pi$
$402$	−33.2489	−1.65830
$403$	0	0
$404$	−6.08546	−0.302763
$405$	3.98491	0.198012
$406$	7.35584	0.365064
$407$	−9.74810	−0.483196
$408$	1.49314	0.0739214
$409$	0.558520	0.0276171	0.0138085	−	0.999905i	$-0.495604\pi$
$409$	0.558520	0.0276171	0.0138085	+	0.999905i	$0.495604\pi$
$410$	−56.8291	−2.80659
$411$	−16.0982	−0.794066
$412$	−25.0840	−1.23580
$413$	0.944885	0.0464948
$414$	−18.4709	−0.907793
$415$	5.87815	0.288547
$416$	0	0
$417$	20.8156	1.01934
$418$	28.7622	1.40680
$419$	−8.74541	−0.427241	−0.213621	−	0.976917i	$-0.568526\pi$
$419$	−8.74541	−0.427241	−0.213621	+	0.976917i	$0.568526\pi$
$420$	−9.13572	−0.445777
$421$	25.1952	1.22794	0.613969	−	0.789330i	$-0.289572\pi$
$421$	25.1952	1.22794	0.613969	+	0.789330i	$0.289572\pi$
$422$	30.6395	1.49151
$423$	−2.43688	−0.118485
$424$	−6.58150	−0.319626
$425$	26.7986	1.29992
$426$	32.7657	1.58750
$427$	−4.95925	−0.239995
$428$	13.3773	0.646614
$429$	0	0
$430$	62.7253	3.02488
$431$	1.18445	0.0570532	0.0285266	−	0.999593i	$-0.490918\pi$
$431$	1.18445	0.0570532	0.0285266	+	0.999593i	$0.490918\pi$
$432$	−3.32925	−0.160178
$433$	−8.48096	−0.407569	−0.203785	−	0.979016i	$-0.565324\pi$
$433$	−8.48096	−0.407569	−0.203785	+	0.979016i	$0.565324\pi$
$434$	−12.9566	−0.621937
$435$	−14.1479	−0.678340
$436$	33.1246	1.58638
$437$	−47.3304	−2.26412
$438$	6.56647	0.313758
$439$	32.5677	1.55437	0.777186	−	0.629271i	$-0.216647\pi$
$439$	32.5677	1.55437	0.777186	+	0.629271i	$0.216647\pi$
$440$	6.31638	0.301121
$441$	1.00000	0.0476190
$442$	0	0
$443$	23.3749	1.11057	0.555287	−	0.831659i	$-0.312608\pi$
$443$	23.3749	1.11057	0.555287	+	0.831659i	$0.312608\pi$
$444$	−8.54661	−0.405604
$445$	54.7544	2.59561
$446$	34.5881	1.63779
$447$	−14.5215	−0.686843
$448$	10.1444	0.479276
$449$	−22.5296	−1.06324	−0.531618	−	0.846984i	$-0.678416\pi$
$449$	−22.5296	−1.06324	−0.531618	+	0.846984i	$0.678416\pi$
$450$	22.5408	1.06258
$451$	−17.9988	−0.847529
$452$	−21.4879	−1.01071
$453$	−10.2052	−0.479483
$454$	−31.5677	−1.48155
$455$	0	0
$456$	3.21819	0.150705
$457$	14.5781	0.681933	0.340966	−	0.940075i	$-0.389246\pi$
$457$	14.5781	0.681933	0.340966	+	0.940075i	$0.389246\pi$
$458$	−39.9249	−1.86557
$459$	2.46321	0.114973
$460$	−81.4462	−3.79745
$461$	−26.0945	−1.21534	−0.607670	−	0.794189i	$-0.707896\pi$
$461$	−26.0945	−1.21534	−0.607670	+	0.794189i	$0.707896\pi$
$462$	−5.41763	−0.252051
$463$	25.6187	1.19060	0.595301	−	0.803502i	$-0.297033\pi$
$463$	25.6187	1.19060	0.595301	+	0.803502i	$0.297033\pi$
$464$	11.8200	0.548732
$465$	24.9202	1.15565
$466$	13.6394	0.631831
$467$	33.3200	1.54187	0.770933	−	0.636917i	$-0.219790\pi$
$467$	33.3200	1.54187	0.770933	+	0.636917i	$0.219790\pi$
$468$	0	0
$469$	16.0479	0.741023
$470$	−20.1193	−0.928032
$471$	5.86827	0.270396
$472$	−0.572767	−0.0263637
$473$	19.8662	0.913449
$474$	−10.6839	−0.490729
$475$	57.7594	2.65018
$476$	−5.64710	−0.258834
$477$	−10.8574	−0.497127
$478$	−56.0453	−2.56345
$479$	6.09069	0.278291	0.139145	−	0.990272i	$-0.455564\pi$
$479$	6.09069	0.278291	0.139145	+	0.990272i	$0.455564\pi$
$480$	−32.3179	−1.47510
$481$	0	0
$482$	50.6920	2.30896
$483$	8.91513	0.405653
$484$	−9.54274	−0.433761
$485$	−18.0465	−0.819447
$486$	2.07185	0.0939812
$487$	29.1782	1.32219	0.661095	−	0.750302i	$-0.270092\pi$
$487$	29.1782	1.32219	0.661095	+	0.750302i	$0.270092\pi$
$488$	3.00618	0.136083
$489$	−0.697676	−0.0315500
$490$	8.25616	0.372975
$491$	31.2594	1.41072	0.705359	−	0.708850i	$-0.250786\pi$
$491$	31.2594	1.41072	0.705359	+	0.708850i	$0.250786\pi$
$492$	−15.7803	−0.711433
$493$	−8.74530	−0.393868
$494$	0	0
$495$	10.4200	0.468346
$496$	−20.8199	−0.934840
$497$	−15.8147	−0.709386
$498$	3.05620	0.136951
$499$	12.5804	0.563177	0.281588	−	0.959535i	$-0.409139\pi$
$499$	12.5804	0.563177	0.281588	+	0.959535i	$0.409139\pi$
$500$	53.7138	2.40215
$501$	−25.1020	−1.12147
$502$	6.08907	0.271769
$503$	39.2710	1.75101	0.875504	−	0.483211i	$-0.160530\pi$
$503$	39.2710	1.75101	0.875504	+	0.483211i	$0.160530\pi$
$504$	−0.606176	−0.0270012
$505$	−10.5776	−0.470698
$506$	−48.2989	−2.14715
$507$	0	0
$508$	−7.46123	−0.331039
$509$	32.2548	1.42967	0.714835	−	0.699293i	$-0.246502\pi$
$509$	32.2548	1.42967	0.714835	+	0.699293i	$0.246502\pi$
$510$	20.3366	0.900521
$511$	−3.16937	−0.140205
$512$	31.0366	1.37164
$513$	5.30899	0.234398
$514$	11.5574	0.509776
$515$	−43.6005	−1.92127
$516$	17.4176	0.766767
$517$	−6.37213	−0.280246
$518$	7.72376	0.339363
$519$	5.26644	0.231171
$520$	0	0
$521$	−14.2921	−0.626149	−0.313075	−	0.949728i	$-0.601359\pi$
$521$	−14.2921	−0.626149	−0.313075	+	0.949728i	$0.601359\pi$
$522$	−7.35584	−0.321957
$523$	15.6499	0.684322	0.342161	−	0.939641i	$-0.388841\pi$
$523$	15.6499	0.684322	0.342161	+	0.939641i	$0.388841\pi$
$524$	2.89804	0.126602
$525$	−10.8795	−0.474822
$526$	43.9731	1.91732
$527$	15.4040	0.671009
$528$	−8.70555	−0.378860
$529$	56.4796	2.45564
$530$	−89.6405	−3.89373
$531$	−0.944885	−0.0410045
$532$	−12.1713	−0.527692
$533$	0	0
$534$	28.4681	1.23194
$535$	23.2521	1.00528
$536$	−9.72785	−0.420179
$537$	11.4454	0.493905
$538$	−3.98293	−0.171716
$539$	2.61487	0.112630
$540$	9.13572	0.393139
$541$	−23.5020	−1.01043	−0.505216	−	0.862993i	$-0.668587\pi$
$541$	−23.5020	−1.01043	−0.505216	+	0.862993i	$0.668587\pi$
$542$	5.30814	0.228004
$543$	−13.2259	−0.567577
$544$	−19.9768	−0.856497
$545$	57.5766	2.46631
$546$	0	0
$547$	−12.5884	−0.538242	−0.269121	−	0.963106i	$-0.586733\pi$
$547$	−12.5884	−0.538242	−0.269121	+	0.963106i	$0.586733\pi$
$548$	−36.9064	−1.57656
$549$	4.95925	0.211656
$550$	58.9413	2.51326
$551$	−18.8489	−0.802989
$552$	−5.40414	−0.230016
$553$	5.15670	0.219285
$554$	−19.2969	−0.819845
$555$	−14.8556	−0.630583
$556$	47.7213	2.02384
$557$	7.12504	0.301898	0.150949	−	0.988542i	$-0.451767\pi$
$557$	7.12504	0.301898	0.150949	+	0.988542i	$0.451767\pi$
$558$	12.9566	0.548497
$559$	0	0
$560$	13.2668	0.560623
$561$	6.44097	0.271938
$562$	29.0932	1.22722
$563$	−37.5881	−1.58415	−0.792074	−	0.610425i	$-0.790999\pi$
$563$	−37.5881	−1.58415	−0.792074	+	0.610425i	$0.790999\pi$
$564$	−5.58673	−0.235244
$565$	−37.3499	−1.57132
$566$	26.1872	1.10073
$567$	−1.00000	−0.0419961
$568$	9.58649	0.402240
$569$	−15.9721	−0.669584	−0.334792	−	0.942292i	$-0.608666\pi$
$569$	−15.9721	−0.669584	−0.334792	+	0.942292i	$0.608666\pi$
$570$	43.8319	1.83592
$571$	1.19947	0.0501961	0.0250980	−	0.999685i	$-0.492010\pi$
$571$	1.19947	0.0501961	0.0250980	+	0.999685i	$0.492010\pi$
$572$	0	0
$573$	2.77448	0.115906
$574$	14.2611	0.595245
$575$	−96.9925	−4.04487
$576$	−10.1444	−0.422682
$577$	31.0326	1.29190	0.645952	−	0.763378i	$-0.276461\pi$
$577$	31.0326	1.29190	0.645952	+	0.763378i	$0.276461\pi$
$578$	−22.6508	−0.942147
$579$	−16.6422	−0.691625
$580$	−32.4352	−1.34680
$581$	−1.47510	−0.0611975
$582$	−9.38279	−0.388929
$583$	−28.3907	−1.17582
$584$	1.92120	0.0794997
$585$	0	0
$586$	−45.7241	−1.88885
$587$	9.60481	0.396433	0.198216	−	0.980158i	$-0.436485\pi$
$587$	9.60481	0.396433	0.198216	+	0.980158i	$0.436485\pi$
$588$	2.29258	0.0945443
$589$	33.2005	1.36800
$590$	−7.80112	−0.321167
$591$	−0.164331	−0.00675966
$592$	12.4113	0.510099
$593$	−30.7042	−1.26087	−0.630435	−	0.776242i	$-0.717123\pi$
$593$	−30.7042	−1.26087	−0.630435	+	0.776242i	$0.717123\pi$
$594$	5.41763	0.222288
$595$	−9.81567	−0.402403
$596$	−33.2916	−1.36368
$597$	1.73169	0.0708732
$598$	0	0
$599$	−25.9999	−1.06233	−0.531163	−	0.847269i	$-0.678245\pi$
$599$	−25.9999	−1.06233	−0.531163	+	0.847269i	$0.678245\pi$
$600$	6.59492	0.269236
$601$	9.31463	0.379952	0.189976	−	0.981789i	$-0.439159\pi$
$601$	9.31463	0.379952	0.189976	+	0.981789i	$0.439159\pi$
$602$	−15.7407	−0.641542
$603$	−16.0479	−0.653521
$604$	−23.3963	−0.951980
$605$	−16.5870	−0.674358
$606$	−5.49957	−0.223405
$607$	−15.3649	−0.623641	−0.311821	−	0.950141i	$-0.600939\pi$
$607$	−15.3649	−0.623641	−0.311821	+	0.950141i	$0.600939\pi$
$608$	−43.0563	−1.74616
$609$	3.55037	0.143868
$610$	40.9443	1.65779
$611$	0	0
$612$	5.64710	0.228270
$613$	−4.71856	−0.190581	−0.0952904	−	0.995450i	$-0.530378\pi$
$613$	−4.71856	−0.190581	−0.0952904	+	0.995450i	$0.530378\pi$
$614$	6.84111	0.276085
$615$	−27.4291	−1.10605
$616$	−1.58507	−0.0638644
$617$	16.7054	0.672533	0.336267	−	0.941767i	$-0.390836\pi$
$617$	16.7054	0.672533	0.336267	+	0.941767i	$0.390836\pi$
$618$	−22.6690	−0.911879
$619$	10.8625	0.436603	0.218301	−	0.975881i	$-0.429948\pi$
$619$	10.8625	0.436603	0.218301	+	0.975881i	$0.429948\pi$
$620$	57.1314	2.29445
$621$	−8.91513	−0.357752
$622$	33.5290	1.34439
$623$	−13.7404	−0.550498
$624$	0	0
$625$	38.9666	1.55866
$626$	5.18780	0.207346
$627$	13.8823	0.554407
$628$	13.4535	0.536852
$629$	−9.18271	−0.366139
$630$	−8.25616	−0.328933
$631$	−19.8405	−0.789837	−0.394918	−	0.918716i	$-0.629227\pi$
$631$	−19.8405	−0.789837	−0.394918	+	0.918716i	$0.629227\pi$
$632$	−3.12587	−0.124340
$633$	14.7885	0.587788
$634$	49.9471	1.98365
$635$	−12.9690	−0.514658
$636$	−24.8914	−0.987010
$637$	0	0
$638$	−19.2346	−0.761504
$639$	15.8147	0.625620
$640$	−19.1177	−0.755694
$641$	−25.7779	−1.01817	−0.509083	−	0.860717i	$-0.670015\pi$
$641$	−25.7779	−1.01817	−0.509083	+	0.860717i	$0.670015\pi$
$642$	12.0893	0.477128
$643$	25.4048	1.00187	0.500935	−	0.865485i	$-0.332990\pi$
$643$	25.4048	1.00187	0.500935	+	0.865485i	$0.332990\pi$
$644$	20.4386	0.805395
$645$	30.2749	1.19207
$646$	27.0940	1.06600
$647$	−19.5858	−0.769997	−0.384999	−	0.922917i	$-0.625798\pi$
$647$	−19.5858	−0.769997	−0.384999	+	0.922917i	$0.625798\pi$
$648$	0.606176	0.0238129
$649$	−2.47075	−0.0969855
$650$	0	0
$651$	−6.25363	−0.245099
$652$	−1.59948	−0.0626403
$653$	−13.7217	−0.536971	−0.268486	−	0.963284i	$-0.586523\pi$
$653$	−13.7217	−0.536971	−0.268486	+	0.963284i	$0.586523\pi$
$654$	29.9355	1.17057
$655$	5.03733	0.196825
$656$	22.9160	0.894719
$657$	3.16937	0.123649
$658$	5.04886	0.196825
$659$	26.6231	1.03709	0.518544	−	0.855051i	$-0.326474\pi$
$659$	26.6231	1.03709	0.518544	+	0.855051i	$0.326474\pi$
$660$	23.8887	0.929867
$661$	−35.1844	−1.36852	−0.684258	−	0.729240i	$-0.739874\pi$
$661$	−35.1844	−1.36852	−0.684258	+	0.729240i	$0.739874\pi$
$662$	−11.1061	−0.431649
$663$	0	0
$664$	0.894172	0.0347006
$665$	−21.1559	−0.820390
$666$	−7.72376	−0.299290
$667$	31.6520	1.22557
$668$	−57.5482	−2.22661
$669$	16.6943	0.645438
$670$	−132.494	−5.11869
$671$	12.9678	0.500616
$672$	8.11006	0.312852
$673$	−2.12183	−0.0817905	−0.0408953	−	0.999163i	$-0.513021\pi$
$673$	−2.12183	−0.0817905	−0.0408953	+	0.999163i	$0.513021\pi$
$674$	−34.1148	−1.31405
$675$	10.8795	0.418753
$676$	0	0
$677$	−14.8001	−0.568813	−0.284406	−	0.958704i	$-0.591797\pi$
$677$	−14.8001	−0.568813	−0.284406	+	0.958704i	$0.591797\pi$
$678$	−19.4191	−0.745787
$679$	4.52869	0.173795
$680$	5.95003	0.228173
$681$	−15.2365	−0.583862
$682$	33.8799	1.29733
$683$	17.8128	0.681590	0.340795	−	0.940138i	$-0.389304\pi$
$683$	17.8128	0.681590	0.340795	+	0.940138i	$0.389304\pi$
$684$	12.1713	0.465380
$685$	−64.1500	−2.45104
$686$	−2.07185	−0.0791037
$687$	−19.2701	−0.735202
$688$	−25.2936	−0.964309
$689$	0	0
$690$	−73.6047	−2.80208
$691$	−11.7835	−0.448264	−0.224132	−	0.974559i	$-0.571955\pi$
$691$	−11.7835	−0.448264	−0.224132	+	0.974559i	$0.571955\pi$
$692$	12.0737	0.458974
$693$	−2.61487	−0.0993307
$694$	−43.4212	−1.64825
$695$	82.9483	3.14641
$696$	−2.15215	−0.0815770
$697$	−16.9548	−0.642211
$698$	−47.6512	−1.80362
$699$	6.58317	0.248998
$700$	−24.9422	−0.942725
$701$	−10.5499	−0.398465	−0.199233	−	0.979952i	$-0.563845\pi$
$701$	−10.5499	−0.398465	−0.199233	+	0.979952i	$0.563845\pi$
$702$	0	0
$703$	−19.7917	−0.746456
$704$	−26.5262	−0.999744
$705$	−9.71075	−0.365728
$706$	−56.8112	−2.13812
$707$	2.65442	0.0998297
$708$	−2.16622	−0.0814116
$709$	−20.0085	−0.751435	−0.375717	−	0.926734i	$-0.622604\pi$
$709$	−20.0085	−0.751435	−0.375717	+	0.926734i	$0.622604\pi$
$710$	130.569	4.90015
$711$	−5.15670	−0.193391
$712$	8.32912	0.312147
$713$	−55.7520	−2.08793
$714$	−5.10341	−0.190990
$715$	0	0
$716$	26.2394	0.980614
$717$	−27.0508	−1.01023
$718$	−44.1986	−1.64948
$719$	2.64264	0.0985539	0.0492770	−	0.998785i	$-0.484308\pi$
$719$	2.64264	0.0985539	0.0492770	+	0.998785i	$0.484308\pi$
$720$	−13.2668	−0.494423
$721$	10.9414	0.407479
$722$	19.0308	0.708254
$723$	24.4670	0.909937
$724$	−30.3213	−1.12688
$725$	−38.6264	−1.43455
$726$	−8.62399	−0.320066
$727$	23.9042	0.886557	0.443279	−	0.896384i	$-0.353815\pi$
$727$	23.9042	0.886557	0.443279	+	0.896384i	$0.353815\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	26.1668	0.968478
$731$	18.7140	0.692161
$732$	11.3695	0.420227
$733$	−33.1800	−1.22553	−0.612766	−	0.790265i	$-0.709943\pi$
$733$	−33.1800	−1.22553	−0.612766	+	0.790265i	$0.709943\pi$
$734$	−35.0624	−1.29418
$735$	3.98491	0.146986
$736$	72.3023	2.66510
$737$	−41.9632	−1.54573
$738$	−14.2611	−0.524957
$739$	−1.27739	−0.0469894	−0.0234947	−	0.999724i	$-0.507479\pi$
$739$	−1.27739	−0.0469894	−0.0234947	+	0.999724i	$0.507479\pi$
$740$	−34.0575	−1.25198
$741$	0	0
$742$	22.4950	0.825816
$743$	39.2019	1.43818	0.719088	−	0.694919i	$-0.244560\pi$
$743$	39.2019	1.43818	0.719088	+	0.694919i	$0.244560\pi$
$744$	3.79080	0.138978
$745$	−57.8669	−2.12008
$746$	35.4216	1.29688
$747$	1.47510	0.0539712
$748$	14.7664	0.539914
$749$	−5.83503	−0.213207
$750$	48.5424	1.77252
$751$	−4.89411	−0.178589	−0.0892943	−	0.996005i	$-0.528461\pi$
$751$	−4.89411	−0.178589	−0.0892943	+	0.996005i	$0.528461\pi$
$752$	8.11297	0.295850
$753$	2.93895	0.107101
$754$	0	0
$755$	−40.6669	−1.48002
$756$	−2.29258	−0.0833802
$757$	−38.0701	−1.38368	−0.691841	−	0.722050i	$-0.743200\pi$
$757$	−38.0701	−1.38368	−0.691841	+	0.722050i	$0.743200\pi$
$758$	19.0292	0.691171
$759$	−23.3119	−0.846169
$760$	12.8242	0.465182
$761$	31.9088	1.15669	0.578346	−	0.815792i	$-0.303698\pi$
$761$	31.9088	1.15669	0.578346	+	0.815792i	$0.303698\pi$
$762$	−6.74288	−0.244269
$763$	−14.4487	−0.523076
$764$	6.36071	0.230122
$765$	9.81567	0.354886
$766$	−80.6070	−2.91245
$767$	0	0
$768$	10.3490	0.373436
$769$	−20.1643	−0.727143	−0.363571	−	0.931566i	$-0.618443\pi$
$769$	−20.1643	−0.727143	−0.363571	+	0.931566i	$0.618443\pi$
$770$	−21.5888	−0.778006
$771$	5.57830	0.200897
$772$	−38.1534	−1.37317
$773$	−27.6159	−0.993274	−0.496637	−	0.867958i	$-0.665432\pi$
$773$	−27.6159	−0.993274	−0.496637	+	0.867958i	$0.665432\pi$
$774$	15.7407	0.565787
$775$	68.0366	2.44395
$776$	−2.74519	−0.0985465
$777$	3.72795	0.133739
$778$	50.3843	1.80636
$779$	−36.5430	−1.30929
$780$	0	0
$781$	41.3534	1.47974
$782$	−45.4976	−1.62699
$783$	−3.55037	−0.126880
$784$	−3.32925	−0.118902
$785$	23.3846	0.834631
$786$	2.61903	0.0934176
$787$	−14.5494	−0.518631	−0.259315	−	0.965793i	$-0.583497\pi$
$787$	−14.5494	−0.518631	−0.259315	+	0.965793i	$0.583497\pi$
$788$	−0.376741	−0.0134208
$789$	21.2240	0.755596
$790$	−42.5745	−1.51473
$791$	9.37283	0.333259
$792$	1.58507	0.0563231
$793$	0	0
$794$	−80.9720	−2.87359
$795$	−43.2658	−1.53448
$796$	3.97003	0.140714
$797$	−12.9466	−0.458592	−0.229296	−	0.973357i	$-0.573642\pi$
$797$	−12.9466	−0.458592	−0.229296	+	0.973357i	$0.573642\pi$
$798$	−10.9995	−0.389377
$799$	−6.00254	−0.212355
$800$	−88.2337	−3.11953
$801$	13.7404	0.485494
$802$	57.9564	2.04651
$803$	8.28750	0.292459
$804$	−36.7910	−1.29752
$805$	35.5260	1.25213
$806$	0	0
$807$	−1.92240	−0.0676717
$808$	−1.60905	−0.0566060
$809$	−9.93693	−0.349364	−0.174682	−	0.984625i	$-0.555890\pi$
$809$	−9.93693	−0.349364	−0.174682	+	0.984625i	$0.555890\pi$
$810$	8.25616	0.290092
$811$	−21.6049	−0.758650	−0.379325	−	0.925263i	$-0.623844\pi$
$811$	−21.6049	−0.758650	−0.379325	+	0.925263i	$0.623844\pi$
$812$	8.13949	0.285640
$813$	2.56202	0.0898541
$814$	−20.1966	−0.707892
$815$	−2.78018	−0.0973854
$816$	−8.20063	−0.287079
$817$	40.3345	1.41113
$818$	1.15717	0.0404596
$819$	0	0
$820$	−62.8833	−2.19598
$821$	−7.37066	−0.257238	−0.128619	−	0.991694i	$-0.541054\pi$
$821$	−7.37066	−0.257238	−0.128619	+	0.991694i	$0.541054\pi$
$822$	−33.3531	−1.16332
$823$	39.7759	1.38650	0.693250	−	0.720697i	$-0.256178\pi$
$823$	39.7759	1.38650	0.693250	+	0.720697i	$0.256178\pi$
$824$	−6.63241	−0.231051
$825$	28.4486	0.990452
$826$	1.95766	0.0681158
$827$	−2.35530	−0.0819019	−0.0409510	−	0.999161i	$-0.513039\pi$
$827$	−2.35530	−0.0819019	−0.0409510	+	0.999161i	$0.513039\pi$
$828$	−20.4386	−0.710292
$829$	−0.942767	−0.0327436	−0.0163718	−	0.999866i	$-0.505212\pi$
$829$	−0.942767	−0.0327436	−0.0163718	+	0.999866i	$0.505212\pi$
$830$	12.1787	0.422728
$831$	−9.31382	−0.323093
$832$	0	0
$833$	2.46321	0.0853451
$834$	43.1269	1.49336
$835$	−100.029	−3.46165
$836$	31.8263	1.10074
$837$	6.25363	0.216157
$838$	−18.1192	−0.625918
$839$	−22.0266	−0.760442	−0.380221	−	0.924896i	$-0.624152\pi$
$839$	−22.0266	−0.760442	−0.380221	+	0.924896i	$0.624152\pi$
$840$	−2.41556	−0.0833447
$841$	−16.3949	−0.565341
$842$	52.2007	1.79896
$843$	14.0421	0.483636
$844$	33.9037	1.16701
$845$	0	0
$846$	−5.04886	−0.173583
$847$	4.16245	0.143023
$848$	36.1470	1.24129
$849$	12.6395	0.433787
$850$	55.5227	1.90441
$851$	33.2352	1.13929
$852$	36.2564	1.24212
$853$	25.5160	0.873652	0.436826	−	0.899546i	$-0.356103\pi$
$853$	25.5160	0.873652	0.436826	+	0.899546i	$0.356103\pi$
$854$	−10.2748	−0.351598
$855$	21.1559	0.723516
$856$	3.53706	0.120894
$857$	11.1140	0.379646	0.189823	−	0.981818i	$-0.439209\pi$
$857$	11.1140	0.379646	0.189823	+	0.981818i	$0.439209\pi$
$858$	0	0
$859$	8.03548	0.274167	0.137083	−	0.990560i	$-0.456227\pi$
$859$	8.03548	0.274167	0.137083	+	0.990560i	$0.456227\pi$
$860$	69.4076	2.36678
$861$	6.88324	0.234580
$862$	2.45402	0.0835841
$863$	−3.40081	−0.115765	−0.0578825	−	0.998323i	$-0.518435\pi$
$863$	−3.40081	−0.115765	−0.0578825	+	0.998323i	$0.518435\pi$
$864$	−8.11006	−0.275910
$865$	20.9863	0.713556
$866$	−17.5713	−0.597098
$867$	−10.9326	−0.371291
$868$	−14.3369	−0.486627
$869$	−13.4841	−0.457417
$870$	−29.3124	−0.993783
$871$	0	0
$872$	8.75843	0.296598
$873$	−4.52869	−0.153273
$874$	−98.0616	−3.31698
$875$	−23.4294	−0.792059
$876$	7.26603	0.245496
$877$	22.1250	0.747110	0.373555	−	0.927608i	$-0.378139\pi$
$877$	22.1250	0.747110	0.373555	+	0.927608i	$0.378139\pi$
$878$	67.4755	2.27719
$879$	−22.0692	−0.744375
$880$	−34.6908	−1.16943
$881$	24.5254	0.826281	0.413141	−	0.910667i	$-0.364432\pi$
$881$	24.5254	0.826281	0.413141	+	0.910667i	$0.364432\pi$
$882$	2.07185	0.0697629
$883$	−3.60395	−0.121282	−0.0606412	−	0.998160i	$-0.519315\pi$
$883$	−3.60395	−0.121282	−0.0606412	+	0.998160i	$0.519315\pi$
$884$	0	0
$885$	−3.76529	−0.126569
$886$	48.4293	1.62701
$887$	28.8486	0.968642	0.484321	−	0.874890i	$-0.339067\pi$
$887$	28.8486	0.968642	0.484321	+	0.874890i	$0.339067\pi$
$888$	−2.25979	−0.0758337
$889$	3.25452	0.109153
$890$	113.443	3.80262
$891$	2.61487	0.0876015
$892$	38.2729	1.28147
$893$	−12.9374	−0.432933
$894$	−30.0864	−1.00624
$895$	45.6089	1.52454
$896$	4.79752	0.160274
$897$	0	0
$898$	−46.6779	−1.55766
$899$	−22.2027	−0.740502
$900$	24.9422	0.831406
$901$	−26.7441	−0.890974
$902$	−37.2908	−1.24165
$903$	−7.59739	−0.252825
$904$	−5.68159	−0.188967
$905$	−52.7040	−1.75194
$906$	−21.1437	−0.702453
$907$	−5.15964	−0.171323	−0.0856615	−	0.996324i	$-0.527300\pi$
$907$	−5.15964	−0.171323	−0.0856615	+	0.996324i	$0.527300\pi$
$908$	−34.9308	−1.15922
$909$	−2.65442	−0.0880415
$910$	0	0
$911$	38.1096	1.26263	0.631313	−	0.775528i	$-0.282516\pi$
$911$	38.1096	1.26263	0.631313	+	0.775528i	$0.282516\pi$
$912$	−17.6749	−0.585276
$913$	3.85720	0.127655
$914$	30.2036	0.999046
$915$	19.7622	0.653317
$916$	−44.1783	−1.45969
$917$	−1.26410	−0.0417442
$918$	5.10341	0.168438
$919$	2.13480	0.0704205	0.0352103	−	0.999380i	$-0.488790\pi$
$919$	2.13480	0.0704205	0.0352103	+	0.999380i	$0.488790\pi$
$920$	−21.5350	−0.709989
$921$	3.30193	0.108802
$922$	−54.0639	−1.78050
$923$	0	0
$924$	−5.99479	−0.197214
$925$	−40.5583	−1.33355
$926$	53.0782	1.74426
$927$	−10.9414	−0.359362
$928$	28.7937	0.945200
$929$	40.8343	1.33973	0.669865	−	0.742483i	$-0.266352\pi$
$929$	40.8343	1.33973	0.669865	+	0.742483i	$0.266352\pi$
$930$	51.6310	1.69305
$931$	5.30899	0.173995
$932$	15.0924	0.494369
$933$	16.1831	0.529810
$934$	69.0342	2.25887
$935$	25.6667	0.839391
$936$	0	0
$937$	45.9925	1.50251	0.751255	−	0.660012i	$-0.229449\pi$
$937$	45.9925	1.50251	0.751255	+	0.660012i	$0.229449\pi$
$938$	33.2489	1.08561
$939$	2.50394	0.0817130
$940$	−22.2626	−0.726128
$941$	9.55992	0.311645	0.155822	−	0.987785i	$-0.450197\pi$
$941$	9.55992	0.311645	0.155822	+	0.987785i	$0.450197\pi$
$942$	12.1582	0.396136
$943$	61.3650	1.99832
$944$	3.14575	0.102386
$945$	−3.98491	−0.129629
$946$	41.1599	1.33822
$947$	−30.1550	−0.979905	−0.489952	−	0.871749i	$-0.662986\pi$
$947$	−30.1550	−0.979905	−0.489952	+	0.871749i	$0.662986\pi$
$948$	−11.8221	−0.383965
$949$	0	0
$950$	119.669	3.88257
$951$	24.1074	0.781738
$952$	−1.49314	−0.0483929
$953$	8.11627	0.262912	0.131456	−	0.991322i	$-0.458035\pi$
$953$	8.11627	0.262912	0.131456	+	0.991322i	$0.458035\pi$
$954$	−22.4950	−0.728301
$955$	11.0561	0.357766
$956$	−62.0160	−2.00574
$957$	−9.28376	−0.300101
$958$	12.6190	0.407702
$959$	16.0982	0.519838
$960$	−40.4244	−1.30469
$961$	8.10792	0.261546
$962$	0	0
$963$	5.83503	0.188031
$964$	56.0925	1.80662
$965$	−66.3176	−2.13484
$966$	18.4709	0.594290
$967$	32.9173	1.05855	0.529274	−	0.848451i	$-0.322464\pi$
$967$	32.9173	1.05855	0.529274	+	0.848451i	$0.322464\pi$
$968$	−2.52318	−0.0810980
$969$	13.0772	0.420099
$970$	−37.3896	−1.20051
$971$	21.6879	0.695997	0.347999	−	0.937495i	$-0.386861\pi$
$971$	21.6879	0.695997	0.347999	+	0.937495i	$0.386861\pi$
$972$	2.29258	0.0735344
$973$	−20.8156	−0.667317
$974$	60.4529	1.93704
$975$	0	0
$976$	−16.5106	−0.528490
$977$	13.2955	0.425360	0.212680	−	0.977122i	$-0.431781\pi$
$977$	13.2955	0.425360	0.212680	+	0.977122i	$0.431781\pi$
$978$	−1.44548	−0.0462214
$979$	35.9294	1.14831
$980$	9.13572	0.291830
$981$	14.4487	0.461310
$982$	64.7650	2.06673
$983$	53.4883	1.70601	0.853006	−	0.521902i	$-0.174777\pi$
$983$	53.4883	1.70601	0.853006	+	0.521902i	$0.174777\pi$
$984$	−4.17245	−0.133013
$985$	−0.654844	−0.0208651
$986$	−18.1190	−0.577026
$987$	2.43688	0.0775667
$988$	0	0
$989$	−67.7318	−2.15374
$990$	21.5888	0.686137
$991$	−23.0550	−0.732367	−0.366183	−	0.930543i	$-0.619336\pi$
$991$	−23.0550	−0.732367	−0.366183	+	0.930543i	$0.619336\pi$
$992$	−50.7173	−1.61028
$993$	−5.36044	−0.170109
$994$	−32.7657	−1.03927
$995$	6.90062	0.218764
$996$	3.38178	0.107156
$997$	−12.6450	−0.400470	−0.200235	−	0.979748i	$-0.564171\pi$
$997$	−12.6450	−0.400470	−0.200235	+	0.979748i	$0.564171\pi$
$998$	26.0648	0.825066
$999$	−3.72795	−0.117947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bh.1.12	yes	15
13.12	even	2		3549.2.a.bg.1.4	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.4	✓	15	13.12	even	2
3549.2.a.bh.1.12	yes	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.07185 q^{2} +1.00000 q^{3} +2.29258 q^{4} +3.98491 q^{5} +2.07185 q^{6} -1.00000 q^{7} +0.606176 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.07185 q^{2} +1.00000 q^{3} +2.29258 q^{4} +3.98491 q^{5} +2.07185 q^{6} -1.00000 q^{7} +0.606176 q^{8} +1.00000 q^{9} +8.25616 q^{10} +2.61487 q^{11} +2.29258 q^{12} -2.07185 q^{14} +3.98491 q^{15} -3.32925 q^{16} +2.46321 q^{17} +2.07185 q^{18} +5.30899 q^{19} +9.13572 q^{20} -1.00000 q^{21} +5.41763 q^{22} -8.91513 q^{23} +0.606176 q^{24} +10.8795 q^{25} +1.00000 q^{27} -2.29258 q^{28} -3.55037 q^{29} +8.25616 q^{30} +6.25363 q^{31} -8.11006 q^{32} +2.61487 q^{33} +5.10341 q^{34} -3.98491 q^{35} +2.29258 q^{36} -3.72795 q^{37} +10.9995 q^{38} +2.41556 q^{40} -6.88324 q^{41} -2.07185 q^{42} +7.59739 q^{43} +5.99479 q^{44} +3.98491 q^{45} -18.4709 q^{46} -2.43688 q^{47} -3.32925 q^{48} +1.00000 q^{49} +22.5408 q^{50} +2.46321 q^{51} -10.8574 q^{53} +2.07185 q^{54} +10.4200 q^{55} -0.606176 q^{56} +5.30899 q^{57} -7.35584 q^{58} -0.944885 q^{59} +9.13572 q^{60} +4.95925 q^{61} +12.9566 q^{62} -1.00000 q^{63} -10.1444 q^{64} +5.41763 q^{66} -16.0479 q^{67} +5.64710 q^{68} -8.91513 q^{69} -8.25616 q^{70} +15.8147 q^{71} +0.606176 q^{72} +3.16937 q^{73} -7.72376 q^{74} +10.8795 q^{75} +12.1713 q^{76} -2.61487 q^{77} -5.15670 q^{79} -13.2668 q^{80} +1.00000 q^{81} -14.2611 q^{82} +1.47510 q^{83} -2.29258 q^{84} +9.81567 q^{85} +15.7407 q^{86} -3.55037 q^{87} +1.58507 q^{88} +13.7404 q^{89} +8.25616 q^{90} -20.4386 q^{92} +6.25363 q^{93} -5.04886 q^{94} +21.1559 q^{95} -8.11006 q^{96} -4.52869 q^{97} +2.07185 q^{98} +2.61487 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9} + 21 q^{10} + 5 q^{11} + 28 q^{12} - 2 q^{14} - 9 q^{15} + 50 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} - 23 q^{20} - 15 q^{21} + 21 q^{22} + 4 q^{23} + 9 q^{24} + 50 q^{25} + 15 q^{27} - 28 q^{28} + 9 q^{29} + 21 q^{30} + 7 q^{31} + 35 q^{32} + 5 q^{33} - 2 q^{34} + 9 q^{35} + 28 q^{36} + 17 q^{37} - 12 q^{38} + 46 q^{40} - 22 q^{41} - 2 q^{42} + 36 q^{43} + 29 q^{44} - 9 q^{45} - q^{46} - 12 q^{47} + 50 q^{48} + 15 q^{49} + 53 q^{50} - q^{51} - 5 q^{53} + 2 q^{54} + 43 q^{55} - 9 q^{56} + 3 q^{57} + 29 q^{58} - 29 q^{59} - 23 q^{60} + 12 q^{61} + 14 q^{62} - 15 q^{63} + 95 q^{64} + 21 q^{66} - 12 q^{67} - 16 q^{68} + 4 q^{69} - 21 q^{70} + 36 q^{71} + 9 q^{72} - 29 q^{73} - 5 q^{74} + 50 q^{75} + 25 q^{76} - 5 q^{77} + 35 q^{79} - 89 q^{80} + 15 q^{81} + 51 q^{82} - 10 q^{83} - 28 q^{84} + 23 q^{85} + 19 q^{86} + 9 q^{87} + 73 q^{88} + 25 q^{89} + 21 q^{90} - 31 q^{92} + 7 q^{93} - 19 q^{94} - 7 q^{95} + 35 q^{96} - 26 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 15 * q + 2 * q^2 + 15 * q^3 + 28 * q^4 - 9 * q^5 + 2 * q^6 - 15 * q^7 + 9 * q^8 + 15 * q^9 + 21 * q^10 + 5 * q^11 + 28 * q^12 - 2 * q^14 - 9 * q^15 + 50 * q^16 - q^17 + 2 * q^18 + 3 * q^19 - 23 * q^20 - 15 * q^21 + 21 * q^22 + 4 * q^23 + 9 * q^24 + 50 * q^25 + 15 * q^27 - 28 * q^28 + 9 * q^29 + 21 * q^30 + 7 * q^31 + 35 * q^32 + 5 * q^33 - 2 * q^34 + 9 * q^35 + 28 * q^36 + 17 * q^37 - 12 * q^38 + 46 * q^40 - 22 * q^41 - 2 * q^42 + 36 * q^43 + 29 * q^44 - 9 * q^45 - q^46 - 12 * q^47 + 50 * q^48 + 15 * q^49 + 53 * q^50 - q^51 - 5 * q^53 + 2 * q^54 + 43 * q^55 - 9 * q^56 + 3 * q^57 + 29 * q^58 - 29 * q^59 - 23 * q^60 + 12 * q^61 + 14 * q^62 - 15 * q^63 + 95 * q^64 + 21 * q^66 - 12 * q^67 - 16 * q^68 + 4 * q^69 - 21 * q^70 + 36 * q^71 + 9 * q^72 - 29 * q^73 - 5 * q^74 + 50 * q^75 + 25 * q^76 - 5 * q^77 + 35 * q^79 - 89 * q^80 + 15 * q^81 + 51 * q^82 - 10 * q^83 - 28 * q^84 + 23 * q^85 + 19 * q^86 + 9 * q^87 + 73 * q^88 + 25 * q^89 + 21 * q^90 - 31 * q^92 + 7 * q^93 - 19 * q^94 - 7 * q^95 + 35 * q^96 - 26 * q^97 + 2 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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