LMFDB - Embedded newform 3549.2.a.bg.1.13

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			1.13
Root			$-2.41695$ 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)

$f(q)$	$=$	$q+2.41695 q^{2} +1.00000 q^{3} +3.84166 q^{4} +1.98263 q^{5} +2.41695 q^{6} +1.00000 q^{7} +4.45120 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.41695 q^{2} +1.00000 q^{3} +3.84166 q^{4} +1.98263 q^{5} +2.41695 q^{6} +1.00000 q^{7} +4.45120 q^{8} +1.00000 q^{9} +4.79192 q^{10} +5.56184 q^{11} +3.84166 q^{12} +2.41695 q^{14} +1.98263 q^{15} +3.07502 q^{16} -5.66208 q^{17} +2.41695 q^{18} +2.77489 q^{19} +7.61658 q^{20} +1.00000 q^{21} +13.4427 q^{22} -2.20066 q^{23} +4.45120 q^{24} -1.06918 q^{25} +1.00000 q^{27} +3.84166 q^{28} -5.79053 q^{29} +4.79192 q^{30} +0.187633 q^{31} -1.47022 q^{32} +5.56184 q^{33} -13.6850 q^{34} +1.98263 q^{35} +3.84166 q^{36} -5.00098 q^{37} +6.70678 q^{38} +8.82508 q^{40} +8.39681 q^{41} +2.41695 q^{42} -6.93636 q^{43} +21.3667 q^{44} +1.98263 q^{45} -5.31889 q^{46} -11.6646 q^{47} +3.07502 q^{48} +1.00000 q^{49} -2.58417 q^{50} -5.66208 q^{51} -2.78207 q^{53} +2.41695 q^{54} +11.0271 q^{55} +4.45120 q^{56} +2.77489 q^{57} -13.9954 q^{58} -6.18664 q^{59} +7.61658 q^{60} +13.1933 q^{61} +0.453499 q^{62} +1.00000 q^{63} -9.70349 q^{64} +13.4427 q^{66} +10.0891 q^{67} -21.7518 q^{68} -2.20066 q^{69} +4.79192 q^{70} -13.0368 q^{71} +4.45120 q^{72} -3.12787 q^{73} -12.0871 q^{74} -1.06918 q^{75} +10.6602 q^{76} +5.56184 q^{77} -8.48573 q^{79} +6.09663 q^{80} +1.00000 q^{81} +20.2947 q^{82} +15.5582 q^{83} +3.84166 q^{84} -11.2258 q^{85} -16.7648 q^{86} -5.79053 q^{87} +24.7569 q^{88} +6.24519 q^{89} +4.79192 q^{90} -8.45418 q^{92} +0.187633 q^{93} -28.1929 q^{94} +5.50158 q^{95} -1.47022 q^{96} -0.650954 q^{97} +2.41695 q^{98} +5.56184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.41695	1.70904	0.854522	−	0.519416i	$-0.173850\pi$
$2$	2.41695	1.70904	0.854522	+	0.519416i	$0.173850\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.84166	1.92083
$5$	1.98263	0.886658	0.443329	−	0.896359i	$-0.353797\pi$
$5$	1.98263	0.886658	0.443329	+	0.896359i	$0.353797\pi$
$6$	2.41695	0.986717
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	4.45120	1.57374
$9$	1.00000	0.333333
$10$	4.79192	1.51534
$11$	5.56184	1.67696	0.838479	−	0.544934i	$-0.183445\pi$
$11$	5.56184	1.67696	0.838479	+	0.544934i	$0.183445\pi$
$12$	3.84166	1.10899
$13$	0	0
$13$	0	0
$14$	2.41695	0.645958
$15$	1.98263	0.511912
$16$	3.07502	0.768755
$17$	−5.66208	−1.37326	−0.686629	−	0.727008i	$-0.740910\pi$
$17$	−5.66208	−1.37326	−0.686629	+	0.727008i	$0.740910\pi$
$18$	2.41695	0.569681
$19$	2.77489	0.636603	0.318302	−	0.947989i	$-0.396888\pi$
$19$	2.77489	0.636603	0.318302	+	0.947989i	$0.396888\pi$
$20$	7.61658	1.70312
$21$	1.00000	0.218218
$22$	13.4427	2.86599
$23$	−2.20066	−0.458869	−0.229434	−	0.973324i	$-0.573688\pi$
$23$	−2.20066	−0.458869	−0.229434	+	0.973324i	$0.573688\pi$
$24$	4.45120	0.908597
$25$	−1.06918	−0.213837
$26$	0	0
$27$	1.00000	0.192450
$28$	3.84166	0.726005
$29$	−5.79053	−1.07527	−0.537637	−	0.843177i	$-0.680683\pi$
$29$	−5.79053	−1.07527	−0.537637	+	0.843177i	$0.680683\pi$
$30$	4.79192	0.874881
$31$	0.187633	0.0336998	0.0168499	−	0.999858i	$-0.494636\pi$
$31$	0.187633	0.0336998	0.0168499	+	0.999858i	$0.494636\pi$
$32$	−1.47022	−0.259901
$33$	5.56184	0.968192
$34$	−13.6850	−2.34696
$35$	1.98263	0.335125
$36$	3.84166	0.640276
$37$	−5.00098	−0.822157	−0.411078	−	0.911600i	$-0.634848\pi$
$37$	−5.00098	−0.822157	−0.411078	+	0.911600i	$0.634848\pi$
$38$	6.70678	1.08798
$39$	0	0
$40$	8.82508	1.39537
$41$	8.39681	1.31136	0.655681	−	0.755038i	$-0.272382\pi$
$41$	8.39681	1.31136	0.655681	+	0.755038i	$0.272382\pi$
$42$	2.41695	0.372944
$43$	−6.93636	−1.05778	−0.528892	−	0.848689i	$-0.677392\pi$
$43$	−6.93636	−1.05778	−0.528892	+	0.848689i	$0.677392\pi$
$44$	21.3667	3.22115
$45$	1.98263	0.295553
$46$	−5.31889	−0.784227
$47$	−11.6646	−1.70146	−0.850732	−	0.525601i	$-0.823841\pi$
$47$	−11.6646	−1.70146	−0.850732	+	0.525601i	$0.823841\pi$
$48$	3.07502	0.443841
$49$	1.00000	0.142857
$50$	−2.58417	−0.365456
$51$	−5.66208	−0.792850
$52$	0	0
$53$	−2.78207	−0.382147	−0.191073	−	0.981576i	$-0.561197\pi$
$53$	−2.78207	−0.382147	−0.191073	+	0.981576i	$0.561197\pi$
$54$	2.41695	0.328906
$55$	11.0271	1.48689
$56$	4.45120	0.594817
$57$	2.77489	0.367543
$58$	−13.9954	−1.83769
$59$	−6.18664	−0.805433	−0.402716	−	0.915325i	$-0.631934\pi$
$59$	−6.18664	−0.805433	−0.402716	+	0.915325i	$0.631934\pi$
$60$	7.61658	0.983296
$61$	13.1933	1.68922	0.844612	−	0.535380i	$-0.179831\pi$
$61$	13.1933	1.68922	0.844612	+	0.535380i	$0.179831\pi$
$62$	0.453499	0.0575944
$63$	1.00000	0.125988
$64$	−9.70349	−1.21294
$65$	0	0
$66$	13.4427	1.65468
$67$	10.0891	1.23258	0.616291	−	0.787519i	$-0.288635\pi$
$67$	10.0891	1.23258	0.616291	+	0.787519i	$0.288635\pi$
$68$	−21.7518	−2.63779
$69$	−2.20066	−0.264928
$70$	4.79192	0.572744
$71$	−13.0368	−1.54718	−0.773589	−	0.633688i	$-0.781540\pi$
$71$	−13.0368	−1.54718	−0.773589	+	0.633688i	$0.781540\pi$
$72$	4.45120	0.524579
$73$	−3.12787	−0.366090	−0.183045	−	0.983105i	$-0.558595\pi$
$73$	−3.12787	−0.366090	−0.183045	+	0.983105i	$0.558595\pi$
$74$	−12.0871	−1.40510
$75$	−1.06918	−0.123459
$76$	10.6602	1.22281
$77$	5.56184	0.633831
$78$	0	0
$79$	−8.48573	−0.954719	−0.477360	−	0.878708i	$-0.658406\pi$
$79$	−8.48573	−0.954719	−0.477360	+	0.878708i	$0.658406\pi$
$80$	6.09663	0.681623
$81$	1.00000	0.111111
$82$	20.2947	2.24117
$83$	15.5582	1.70773	0.853865	−	0.520494i	$-0.174252\pi$
$83$	15.5582	1.70773	0.853865	+	0.520494i	$0.174252\pi$
$84$	3.84166	0.419159
$85$	−11.2258	−1.21761
$86$	−16.7648	−1.80780
$87$	−5.79053	−0.620810
$88$	24.7569	2.63909
$89$	6.24519	0.661988	0.330994	−	0.943633i	$-0.392616\pi$
$89$	6.24519	0.661988	0.330994	+	0.943633i	$0.392616\pi$
$90$	4.79192	0.505113
$91$	0	0
$92$	−8.45418	−0.881409
$93$	0.187633	0.0194566
$94$	−28.1929	−2.90787
$95$	5.50158	0.564450
$96$	−1.47022	−0.150054
$97$	−0.650954	−0.0660944	−0.0330472	−	0.999454i	$-0.510521\pi$
$97$	−0.650954	−0.0660944	−0.0330472	+	0.999454i	$0.510521\pi$
$98$	2.41695	0.244149
$99$	5.56184	0.558986
$100$	−4.10744	−0.410744
$101$	1.72491	0.171635	0.0858174	−	0.996311i	$-0.472650\pi$
$101$	1.72491	0.171635	0.0858174	+	0.996311i	$0.472650\pi$
$102$	−13.6850	−1.35502
$103$	3.77565	0.372026	0.186013	−	0.982547i	$-0.440443\pi$
$103$	3.77565	0.372026	0.186013	+	0.982547i	$0.440443\pi$
$104$	0	0
$105$	1.98263	0.193485
$106$	−6.72413	−0.653105
$107$	15.7248	1.52017	0.760085	−	0.649824i	$-0.225157\pi$
$107$	15.7248	1.52017	0.760085	+	0.649824i	$0.225157\pi$
$108$	3.84166	0.369664
$109$	−17.5694	−1.68284	−0.841421	−	0.540380i	$-0.818280\pi$
$109$	−17.5694	−1.68284	−0.841421	+	0.540380i	$0.818280\pi$
$110$	26.6519	2.54116
$111$	−5.00098	−0.474672
$112$	3.07502	0.290562
$113$	14.2914	1.34442	0.672209	−	0.740362i	$-0.265346\pi$
$113$	14.2914	1.34442	0.672209	+	0.740362i	$0.265346\pi$
$114$	6.70678	0.628147
$115$	−4.36309	−0.406860
$116$	−22.2452	−2.06542
$117$	0	0
$118$	−14.9528	−1.37652
$119$	−5.66208	−0.519042
$120$	8.82508	0.805616
$121$	19.9341	1.81219
$122$	31.8875	2.88696
$123$	8.39681	0.757115
$124$	0.720820	0.0647316
$125$	−12.0329	−1.07626
$126$	2.41695	0.215319
$127$	−10.2530	−0.909807	−0.454903	−	0.890541i	$-0.650326\pi$
$127$	−10.2530	−0.909807	−0.454903	+	0.890541i	$0.650326\pi$
$128$	−20.5124	−1.81306
$129$	−6.93636	−0.610712
$130$	0	0
$131$	−11.7740	−1.02870	−0.514348	−	0.857582i	$-0.671966\pi$
$131$	−11.7740	−1.02870	−0.514348	+	0.857582i	$0.671966\pi$
$132$	21.3667	1.85973
$133$	2.77489	0.240613
$134$	24.3849	2.10654
$135$	1.98263	0.170637
$136$	−25.2031	−2.16115
$137$	19.6795	1.68133	0.840667	−	0.541552i	$-0.182163\pi$
$137$	19.6795	1.68133	0.840667	+	0.541552i	$0.182163\pi$
$138$	−5.31889	−0.452774
$139$	12.5276	1.06258	0.531288	−	0.847192i	$-0.321708\pi$
$139$	12.5276	1.06258	0.531288	+	0.847192i	$0.321708\pi$
$140$	7.61658	0.643719
$141$	−11.6646	−0.982340
$142$	−31.5092	−2.64419
$143$	0	0
$144$	3.07502	0.256252
$145$	−11.4805	−0.953400
$146$	−7.55991	−0.625663
$147$	1.00000	0.0824786
$148$	−19.2121	−1.57922
$149$	8.66190	0.709611	0.354805	−	0.934940i	$-0.384547\pi$
$149$	8.66190	0.709611	0.354805	+	0.934940i	$0.384547\pi$
$150$	−2.58417	−0.210996
$151$	13.5708	1.10438	0.552188	−	0.833720i	$-0.313793\pi$
$151$	13.5708	1.10438	0.552188	+	0.833720i	$0.313793\pi$
$152$	12.3516	1.00185
$153$	−5.66208	−0.457752
$154$	13.4427	1.08324
$155$	0.372006	0.0298802
$156$	0	0
$157$	5.12450	0.408979	0.204490	−	0.978869i	$-0.434447\pi$
$157$	5.12450	0.408979	0.204490	+	0.978869i	$0.434447\pi$
$158$	−20.5096	−1.63166
$159$	−2.78207	−0.220632
$160$	−2.91490	−0.230443
$161$	−2.20066	−0.173436
$162$	2.41695	0.189894
$163$	−17.6790	−1.38472	−0.692362	−	0.721550i	$-0.743430\pi$
$163$	−17.6790	−1.38472	−0.692362	+	0.721550i	$0.743430\pi$
$164$	32.2577	2.51890
$165$	11.0271	0.858456
$166$	37.6034	2.91859
$167$	−19.3998	−1.50120	−0.750600	−	0.660757i	$-0.770236\pi$
$167$	−19.3998	−1.50120	−0.750600	+	0.660757i	$0.770236\pi$
$168$	4.45120	0.343418
$169$	0	0
$170$	−27.1322	−2.08095
$171$	2.77489	0.212201
$172$	−26.6471	−2.03182
$173$	3.66425	0.278588	0.139294	−	0.990251i	$-0.455517\pi$
$173$	3.66425	0.278588	0.139294	+	0.990251i	$0.455517\pi$
$174$	−13.9954	−1.06099
$175$	−1.06918	−0.0808227
$176$	17.1028	1.28917
$177$	−6.18664	−0.465017
$178$	15.0943	1.13137
$179$	−5.59386	−0.418105	−0.209052	−	0.977904i	$-0.567038\pi$
$179$	−5.59386	−0.418105	−0.209052	+	0.977904i	$0.567038\pi$
$180$	7.61658	0.567706
$181$	−6.97271	−0.518277	−0.259139	−	0.965840i	$-0.583439\pi$
$181$	−6.97271	−0.518277	−0.259139	+	0.965840i	$0.583439\pi$
$182$	0	0
$183$	13.1933	0.975273
$184$	−9.79557	−0.722139
$185$	−9.91510	−0.728972
$186$	0.453499	0.0332522
$187$	−31.4916	−2.30289
$188$	−44.8116	−3.26822
$189$	1.00000	0.0727393
$190$	13.2970	0.964669
$191$	6.07010	0.439217	0.219609	−	0.975588i	$-0.429522\pi$
$191$	6.07010	0.439217	0.219609	+	0.975588i	$0.429522\pi$
$192$	−9.70349	−0.700289
$193$	10.9046	0.784929	0.392465	−	0.919767i	$-0.371623\pi$
$193$	10.9046	0.784929	0.392465	+	0.919767i	$0.371623\pi$
$194$	−1.57333	−0.112958
$195$	0	0
$196$	3.84166	0.274404
$197$	17.1724	1.22348	0.611742	−	0.791057i	$-0.290469\pi$
$197$	17.1724	1.22348	0.611742	+	0.791057i	$0.290469\pi$
$198$	13.4427	0.955331
$199$	1.10806	0.0785482	0.0392741	−	0.999228i	$-0.487495\pi$
$199$	1.10806	0.0785482	0.0392741	+	0.999228i	$0.487495\pi$
$200$	−4.75915	−0.336523
$201$	10.0891	0.711632
$202$	4.16902	0.293331
$203$	−5.79053	−0.406415
$204$	−21.7518	−1.52293
$205$	16.6478	1.16273
$206$	9.12558	0.635809
$207$	−2.20066	−0.152956
$208$	0	0
$209$	15.4335	1.06756
$210$	4.79192	0.330674
$211$	3.56849	0.245665	0.122832	−	0.992427i	$-0.460802\pi$
$211$	3.56849	0.245665	0.122832	+	0.992427i	$0.460802\pi$
$212$	−10.6878	−0.734038
$213$	−13.0368	−0.893264
$214$	38.0060	2.59804
$215$	−13.7522	−0.937894
$216$	4.45120	0.302866
$217$	0.187633	0.0127373
$218$	−42.4644	−2.87605
$219$	−3.12787	−0.211362
$220$	42.3622	2.85606
$221$	0	0
$222$	−12.0871	−0.811236
$223$	12.2147	0.817954	0.408977	−	0.912545i	$-0.365886\pi$
$223$	12.2147	0.817954	0.408977	+	0.912545i	$0.365886\pi$
$224$	−1.47022	−0.0982332
$225$	−1.06918	−0.0712789
$226$	34.5415	2.29767
$227$	22.0874	1.46599	0.732995	−	0.680234i	$-0.238122\pi$
$227$	22.0874	1.46599	0.732995	+	0.680234i	$0.238122\pi$
$228$	10.6602	0.705987
$229$	21.2490	1.40418	0.702088	−	0.712090i	$-0.252251\pi$
$229$	21.2490	1.40418	0.702088	+	0.712090i	$0.252251\pi$
$230$	−10.5454	−0.695341
$231$	5.56184	0.365942
$232$	−25.7748	−1.69220
$233$	−2.11080	−0.138283	−0.0691414	−	0.997607i	$-0.522026\pi$
$233$	−2.11080	−0.138283	−0.0691414	+	0.997607i	$0.522026\pi$
$234$	0	0
$235$	−23.1267	−1.50862
$236$	−23.7670	−1.54710
$237$	−8.48573	−0.551208
$238$	−13.6850	−0.887066
$239$	−16.9892	−1.09894	−0.549469	−	0.835514i	$-0.685170\pi$
$239$	−16.9892	−1.09894	−0.549469	+	0.835514i	$0.685170\pi$
$240$	6.09663	0.393535
$241$	19.1884	1.23604	0.618018	−	0.786164i	$-0.287936\pi$
$241$	19.1884	1.23604	0.618018	+	0.786164i	$0.287936\pi$
$242$	48.1797	3.09711
$243$	1.00000	0.0641500
$244$	50.6840	3.24471
$245$	1.98263	0.126665
$246$	20.2947	1.29394
$247$	0	0
$248$	0.835190	0.0530346
$249$	15.5582	0.985959
$250$	−29.0830	−1.83937
$251$	12.1438	0.766509	0.383255	−	0.923643i	$-0.374803\pi$
$251$	12.1438	0.766509	0.383255	+	0.923643i	$0.374803\pi$
$252$	3.84166	0.242002
$253$	−12.2397	−0.769504
$254$	−24.7810	−1.55490
$255$	−11.2258	−0.702987
$256$	−30.1706	−1.88566
$257$	−16.8396	−1.05042	−0.525212	−	0.850972i	$-0.676014\pi$
$257$	−16.8396	−1.05042	−0.525212	+	0.850972i	$0.676014\pi$
$258$	−16.7648	−1.04373
$259$	−5.00098	−0.310746
$260$	0	0
$261$	−5.79053	−0.358425
$262$	−28.4571	−1.75808
$263$	−26.8348	−1.65471	−0.827353	−	0.561682i	$-0.810154\pi$
$263$	−26.8348	−1.65471	−0.827353	+	0.561682i	$0.810154\pi$
$264$	24.7569	1.52368
$265$	−5.51581	−0.338833
$266$	6.70678	0.411219
$267$	6.24519	0.382199
$268$	38.7589	2.36758
$269$	−6.86560	−0.418603	−0.209302	−	0.977851i	$-0.567119\pi$
$269$	−6.86560	−0.418603	−0.209302	+	0.977851i	$0.567119\pi$
$270$	4.79192	0.291627
$271$	7.27072	0.441665	0.220833	−	0.975312i	$-0.429123\pi$
$271$	7.27072	0.441665	0.220833	+	0.975312i	$0.429123\pi$
$272$	−17.4110	−1.05570
$273$	0	0
$274$	47.5644	2.87347
$275$	−5.94663	−0.358595
$276$	−8.45418	−0.508882
$277$	−8.01571	−0.481617	−0.240809	−	0.970573i	$-0.577413\pi$
$277$	−8.01571	−0.481617	−0.240809	+	0.970573i	$0.577413\pi$
$278$	30.2786	1.81599
$279$	0.187633	0.0112333
$280$	8.82508	0.527399
$281$	−7.76205	−0.463045	−0.231522	−	0.972830i	$-0.574371\pi$
$281$	−7.76205	−0.463045	−0.231522	+	0.972830i	$0.574371\pi$
$282$	−28.1929	−1.67886
$283$	9.99319	0.594033	0.297017	−	0.954872i	$-0.404008\pi$
$283$	9.99319	0.594033	0.297017	+	0.954872i	$0.404008\pi$
$284$	−50.0828	−2.97186
$285$	5.50158	0.325885
$286$	0	0
$287$	8.39681	0.495648
$288$	−1.47022	−0.0866335
$289$	15.0592	0.885835
$290$	−27.7477	−1.62940
$291$	−0.650954	−0.0381596
$292$	−12.0162	−0.703195
$293$	7.05939	0.412414	0.206207	−	0.978508i	$-0.433888\pi$
$293$	7.05939	0.412414	0.206207	+	0.978508i	$0.433888\pi$
$294$	2.41695	0.140960
$295$	−12.2658	−0.714144
$296$	−22.2604	−1.29386
$297$	5.56184	0.322731
$298$	20.9354	1.21276
$299$	0	0
$300$	−4.10744	−0.237143
$301$	−6.93636	−0.399805
$302$	32.8000	1.88743
$303$	1.72491	0.0990934
$304$	8.53285	0.489392
$305$	26.1573	1.49776
$306$	−13.6850	−0.782319
$307$	−25.6817	−1.46573	−0.732867	−	0.680372i	$-0.761818\pi$
$307$	−25.6817	−1.46573	−0.732867	+	0.680372i	$0.761818\pi$
$308$	21.3667	1.21748
$309$	3.77565	0.214789
$310$	0.899120	0.0510666
$311$	32.5563	1.84610	0.923050	−	0.384680i	$-0.125688\pi$
$311$	32.5563	1.84610	0.923050	+	0.384680i	$0.125688\pi$
$312$	0	0
$313$	−8.19460	−0.463186	−0.231593	−	0.972813i	$-0.574394\pi$
$313$	−8.19460	−0.463186	−0.231593	+	0.972813i	$0.574394\pi$
$314$	12.3857	0.698963
$315$	1.98263	0.111708
$316$	−32.5993	−1.83385
$317$	−29.1019	−1.63453	−0.817263	−	0.576264i	$-0.804510\pi$
$317$	−29.1019	−1.63453	−0.817263	+	0.576264i	$0.804510\pi$
$318$	−6.72413	−0.377070
$319$	−32.2060	−1.80319
$320$	−19.2384	−1.07546
$321$	15.7248	0.877670
$322$	−5.31889	−0.296410
$323$	−15.7117	−0.874220
$324$	3.84166	0.213425
$325$	0	0
$326$	−42.7293	−2.36655
$327$	−17.5694	−0.971589
$328$	37.3759	2.06374
$329$	−11.6646	−0.643093
$330$	26.6519	1.46714
$331$	−29.3311	−1.61218	−0.806091	−	0.591792i	$-0.798421\pi$
$331$	−29.3311	−1.61218	−0.806091	+	0.591792i	$0.798421\pi$
$332$	59.7692	3.28026
$333$	−5.00098	−0.274052
$334$	−46.8884	−2.56562
$335$	20.0030	1.09288
$336$	3.07502	0.167756
$337$	1.49519	0.0814479	0.0407240	−	0.999170i	$-0.487034\pi$
$337$	1.49519	0.0814479	0.0407240	+	0.999170i	$0.487034\pi$
$338$	0	0
$339$	14.2914	0.776200
$340$	−43.1257	−2.33882
$341$	1.04358	0.0565131
$342$	6.70678	0.362661
$343$	1.00000	0.0539949
$344$	−30.8751	−1.66467
$345$	−4.36309	−0.234901
$346$	8.85631	0.476118
$347$	−4.89127	−0.262577	−0.131289	−	0.991344i	$-0.541911\pi$
$347$	−4.89127	−0.262577	−0.131289	+	0.991344i	$0.541911\pi$
$348$	−22.2452	−1.19247
$349$	−13.7842	−0.737850	−0.368925	−	0.929459i	$-0.620274\pi$
$349$	−13.7842	−0.737850	−0.368925	+	0.929459i	$0.620274\pi$
$350$	−2.58417	−0.138130
$351$	0	0
$352$	−8.17713	−0.435842
$353$	−1.70434	−0.0907128	−0.0453564	−	0.998971i	$-0.514442\pi$
$353$	−1.70434	−0.0907128	−0.0453564	+	0.998971i	$0.514442\pi$
$354$	−14.9528	−0.794734
$355$	−25.8470	−1.37182
$356$	23.9919	1.27157
$357$	−5.66208	−0.299669
$358$	−13.5201	−0.714559
$359$	−24.0112	−1.26726	−0.633630	−	0.773636i	$-0.718436\pi$
$359$	−24.0112	−1.26726	−0.633630	+	0.773636i	$0.718436\pi$
$360$	8.82508	0.465122
$361$	−11.3000	−0.594736
$362$	−16.8527	−0.885759
$363$	19.9341	1.04627
$364$	0	0
$365$	−6.20140	−0.324596
$366$	31.8875	1.66678
$367$	−5.26694	−0.274932	−0.137466	−	0.990506i	$-0.543896\pi$
$367$	−5.26694	−0.274932	−0.137466	+	0.990506i	$0.543896\pi$
$368$	−6.76707	−0.352758
$369$	8.39681	0.437120
$370$	−23.9643	−1.24585
$371$	−2.78207	−0.144438
$372$	0.720820	0.0373728
$373$	18.4633	0.955992	0.477996	−	0.878362i	$-0.341363\pi$
$373$	18.4633	0.955992	0.477996	+	0.878362i	$0.341363\pi$
$374$	−76.1137	−3.93575
$375$	−12.0329	−0.621378
$376$	−51.9217	−2.67766
$377$	0	0
$378$	2.41695	0.124315
$379$	5.24807	0.269575	0.134788	−	0.990875i	$-0.456965\pi$
$379$	5.24807	0.269575	0.134788	+	0.990875i	$0.456965\pi$
$380$	21.1352	1.08421
$381$	−10.2530	−0.525277
$382$	14.6711	0.750641
$383$	9.75424	0.498418	0.249209	−	0.968450i	$-0.419829\pi$
$383$	9.75424	0.498418	0.249209	+	0.968450i	$0.419829\pi$
$384$	−20.5124	−1.04677
$385$	11.0271	0.561991
$386$	26.3559	1.34148
$387$	−6.93636	−0.352595
$388$	−2.50074	−0.126956
$389$	12.0796	0.612458	0.306229	−	0.951958i	$-0.400933\pi$
$389$	12.0796	0.612458	0.306229	+	0.951958i	$0.400933\pi$
$390$	0	0
$391$	12.4603	0.630145
$392$	4.45120	0.224820
$393$	−11.7740	−0.593917
$394$	41.5049	2.09099
$395$	−16.8241	−0.846510
$396$	21.3667	1.07372
$397$	26.9213	1.35114	0.675571	−	0.737295i	$-0.263897\pi$
$397$	26.9213	1.35114	0.675571	+	0.737295i	$0.263897\pi$
$398$	2.67812	0.134242
$399$	2.77489	0.138918
$400$	−3.28776	−0.164388
$401$	−31.9449	−1.59525	−0.797626	−	0.603152i	$-0.793911\pi$
$401$	−31.9449	−1.59525	−0.797626	+	0.603152i	$0.793911\pi$
$402$	24.3849	1.21621
$403$	0	0
$404$	6.62651	0.329681
$405$	1.98263	0.0985176
$406$	−13.9954	−0.694581
$407$	−27.8147	−1.37872
$408$	−25.2031	−1.24774
$409$	−29.9248	−1.47969	−0.739843	−	0.672779i	$-0.765100\pi$
$409$	−29.9248	−1.47969	−0.739843	+	0.672779i	$0.765100\pi$
$410$	40.2368	1.98715
$411$	19.6795	0.970719
$412$	14.5048	0.714599
$413$	−6.18664	−0.304425
$414$	−5.31889	−0.261409
$415$	30.8461	1.51417
$416$	0	0
$417$	12.5276	0.613478
$418$	37.3020	1.82450
$419$	29.8715	1.45932	0.729660	−	0.683811i	$-0.239679\pi$
$419$	29.8715	1.45932	0.729660	+	0.683811i	$0.239679\pi$
$420$	7.61658	0.371651
$421$	−23.7308	−1.15657	−0.578283	−	0.815836i	$-0.696277\pi$
$421$	−23.7308	−1.15657	−0.578283	+	0.815836i	$0.696277\pi$
$422$	8.62486	0.419852
$423$	−11.6646	−0.567154
$424$	−12.3835	−0.601398
$425$	6.05381	0.293653
$426$	−31.5092	−1.52663
$427$	13.1933	0.638466
$428$	60.4091	2.91999
$429$	0	0
$430$	−33.2385	−1.60290
$431$	11.1024	0.534782	0.267391	−	0.963588i	$-0.413838\pi$
$431$	11.1024	0.534782	0.267391	+	0.963588i	$0.413838\pi$
$432$	3.07502	0.147947
$433$	10.4048	0.500025	0.250012	−	0.968243i	$-0.419565\pi$
$433$	10.4048	0.500025	0.250012	+	0.968243i	$0.419565\pi$
$434$	0.453499	0.0217686
$435$	−11.4805	−0.550446
$436$	−67.4956	−3.23245
$437$	−6.10658	−0.292118
$438$	−7.55991	−0.361227
$439$	5.20672	0.248503	0.124252	−	0.992251i	$-0.460347\pi$
$439$	5.20672	0.248503	0.124252	+	0.992251i	$0.460347\pi$
$440$	49.0837	2.33997
$441$	1.00000	0.0476190
$442$	0	0
$443$	15.1894	0.721669	0.360835	−	0.932630i	$-0.382492\pi$
$443$	15.1894	0.721669	0.360835	+	0.932630i	$0.382492\pi$
$444$	−19.2121	−0.911765
$445$	12.3819	0.586958
$446$	29.5223	1.39792
$447$	8.66190	0.409694
$448$	−9.70349	−0.458447
$449$	1.69273	0.0798847	0.0399423	−	0.999202i	$-0.487283\pi$
$449$	1.69273	0.0798847	0.0399423	+	0.999202i	$0.487283\pi$
$450$	−2.58417	−0.121819
$451$	46.7017	2.19910
$452$	54.9025	2.58240
$453$	13.5708	0.637612
$454$	53.3841	2.50544
$455$	0	0
$456$	12.3516	0.578416
$457$	3.72412	0.174207	0.0871036	−	0.996199i	$-0.472239\pi$
$457$	3.72412	0.174207	0.0871036	+	0.996199i	$0.472239\pi$
$458$	51.3579	2.39980
$459$	−5.66208	−0.264283
$460$	−16.7615	−0.781509
$461$	−26.3885	−1.22904	−0.614518	−	0.788903i	$-0.710650\pi$
$461$	−26.3885	−1.22904	−0.614518	+	0.788903i	$0.710650\pi$
$462$	13.4427	0.625411
$463$	−2.25761	−0.104920	−0.0524600	−	0.998623i	$-0.516706\pi$
$463$	−2.25761	−0.104920	−0.0524600	+	0.998623i	$0.516706\pi$
$464$	−17.8060	−0.826622
$465$	0.372006	0.0172513
$466$	−5.10169	−0.236331
$467$	−30.8908	−1.42945	−0.714727	−	0.699403i	$-0.753449\pi$
$467$	−30.8908	−1.42945	−0.714727	+	0.699403i	$0.753449\pi$
$468$	0	0
$469$	10.0891	0.465872
$470$	−55.8960	−2.57829
$471$	5.12450	0.236124
$472$	−27.5380	−1.26754
$473$	−38.5789	−1.77386
$474$	−20.5096	−0.942038
$475$	−2.96687	−0.136129
$476$	−21.7518	−0.996992
$477$	−2.78207	−0.127382
$478$	−41.0620	−1.87813
$479$	38.9723	1.78069	0.890346	−	0.455285i	$-0.150463\pi$
$479$	38.9723	1.78069	0.890346	+	0.455285i	$0.150463\pi$
$480$	−2.91490	−0.133046
$481$	0	0
$482$	46.3776	2.11244
$483$	−2.20066	−0.100133
$484$	76.5799	3.48090
$485$	−1.29060	−0.0586032
$486$	2.41695	0.109635
$487$	26.8581	1.21706	0.608529	−	0.793532i	$-0.291760\pi$
$487$	26.8581	1.21706	0.608529	+	0.793532i	$0.291760\pi$
$488$	58.7258	2.65839
$489$	−17.6790	−0.799471
$490$	4.79192	0.216477
$491$	36.5076	1.64757	0.823783	−	0.566905i	$-0.191859\pi$
$491$	36.5076	1.64757	0.823783	+	0.566905i	$0.191859\pi$
$492$	32.2577	1.45429
$493$	32.7864	1.47663
$494$	0	0
$495$	11.0271	0.495630
$496$	0.576974	0.0259069
$497$	−13.0368	−0.584778
$498$	37.6034	1.68505
$499$	12.7129	0.569107	0.284553	−	0.958660i	$-0.408155\pi$
$499$	12.7129	0.569107	0.284553	+	0.958660i	$0.408155\pi$
$500$	−46.2264	−2.06731
$501$	−19.3998	−0.866718
$502$	29.3510	1.31000
$503$	−32.0950	−1.43105	−0.715523	−	0.698589i	$-0.753811\pi$
$503$	−32.0950	−1.43105	−0.715523	+	0.698589i	$0.753811\pi$
$504$	4.45120	0.198272
$505$	3.41985	0.152181
$506$	−29.5828	−1.31512
$507$	0	0
$508$	−39.3885	−1.74758
$509$	−21.8972	−0.970577	−0.485288	−	0.874354i	$-0.661285\pi$
$509$	−21.8972	−0.970577	−0.485288	+	0.874354i	$0.661285\pi$
$510$	−27.1322	−1.20144
$511$	−3.12787	−0.138369
$512$	−31.8960	−1.40962
$513$	2.77489	0.122514
$514$	−40.7004	−1.79522
$515$	7.48572	0.329860
$516$	−26.6471	−1.17307
$517$	−64.8769	−2.85328
$518$	−12.0871	−0.531079
$519$	3.66425	0.160843
$520$	0	0
$521$	17.7708	0.778554	0.389277	−	0.921121i	$-0.372725\pi$
$521$	17.7708	0.778554	0.389277	+	0.921121i	$0.372725\pi$
$522$	−13.9954	−0.612563
$523$	17.1501	0.749923	0.374961	−	0.927040i	$-0.377656\pi$
$523$	17.1501	0.749923	0.374961	+	0.927040i	$0.377656\pi$
$524$	−45.2315	−1.97595
$525$	−1.06918	−0.0466630
$526$	−64.8585	−2.82796
$527$	−1.06239	−0.0462785
$528$	17.1028	0.744303
$529$	−18.1571	−0.789439
$530$	−13.3314	−0.579081
$531$	−6.18664	−0.268478
$532$	10.6602	0.462177
$533$	0	0
$534$	15.0943	0.653195
$535$	31.1763	1.34787
$536$	44.9087	1.93976
$537$	−5.59386	−0.241393
$538$	−16.5938	−0.715411
$539$	5.56184	0.239565
$540$	7.61658	0.327765
$541$	36.1332	1.55349	0.776744	−	0.629817i	$-0.216870\pi$
$541$	36.1332	1.55349	0.776744	+	0.629817i	$0.216870\pi$
$542$	17.5730	0.754825
$543$	−6.97271	−0.299228
$544$	8.32451	0.356910
$545$	−34.8336	−1.49211
$546$	0	0
$547$	−9.66117	−0.413082	−0.206541	−	0.978438i	$-0.566221\pi$
$547$	−9.66117	−0.413082	−0.206541	+	0.978438i	$0.566221\pi$
$548$	75.6019	3.22956
$549$	13.1933	0.563074
$550$	−14.3727	−0.612855
$551$	−16.0681	−0.684523
$552$	−9.79557	−0.416927
$553$	−8.48573	−0.360850
$554$	−19.3736	−0.823105
$555$	−9.91510	−0.420872
$556$	48.1267	2.04103
$557$	−25.6174	−1.08544	−0.542722	−	0.839913i	$-0.682606\pi$
$557$	−25.6174	−1.08544	−0.542722	+	0.839913i	$0.682606\pi$
$558$	0.453499	0.0191981
$559$	0	0
$560$	6.09663	0.257629
$561$	−31.4916	−1.32958
$562$	−18.7605	−0.791364
$563$	−22.4791	−0.947380	−0.473690	−	0.880692i	$-0.657078\pi$
$563$	−22.4791	−0.947380	−0.473690	+	0.880692i	$0.657078\pi$
$564$	−44.8116	−1.88691
$565$	28.3345	1.19204
$566$	24.1531	1.01523
$567$	1.00000	0.0419961
$568$	−58.0292	−2.43485
$569$	35.4558	1.48638	0.743192	−	0.669078i	$-0.233311\pi$
$569$	35.4558	1.48638	0.743192	+	0.669078i	$0.233311\pi$
$570$	13.2970	0.556952
$571$	−25.4474	−1.06494	−0.532470	−	0.846449i	$-0.678736\pi$
$571$	−25.4474	−1.06494	−0.532470	+	0.846449i	$0.678736\pi$
$572$	0	0
$573$	6.07010	0.253582
$574$	20.2947	0.847084
$575$	2.35291	0.0981231
$576$	−9.70349	−0.404312
$577$	27.6703	1.15193	0.575965	−	0.817474i	$-0.304626\pi$
$577$	27.6703	1.15193	0.575965	+	0.817474i	$0.304626\pi$
$578$	36.3974	1.51393
$579$	10.9046	0.453179
$580$	−44.1040	−1.83132
$581$	15.5582	0.645462
$582$	−1.57333	−0.0652164
$583$	−15.4734	−0.640844
$584$	−13.9228	−0.576129
$585$	0	0
$586$	17.0622	0.704834
$587$	4.28089	0.176691	0.0883456	−	0.996090i	$-0.471842\pi$
$587$	4.28089	0.176691	0.0883456	+	0.996090i	$0.471842\pi$
$588$	3.84166	0.158427
$589$	0.520660	0.0214534
$590$	−29.6459	−1.22050
$591$	17.1724	0.706379
$592$	−15.3781	−0.632038
$593$	−22.7798	−0.935454	−0.467727	−	0.883873i	$-0.654927\pi$
$593$	−22.7798	−0.935454	−0.467727	+	0.883873i	$0.654927\pi$
$594$	13.4427	0.551561
$595$	−11.2258	−0.460213
$596$	33.2761	1.36304
$597$	1.10806	0.0453498
$598$	0	0
$599$	37.9205	1.54939	0.774694	−	0.632336i	$-0.217904\pi$
$599$	37.9205	1.54939	0.774694	+	0.632336i	$0.217904\pi$
$600$	−4.75915	−0.194292
$601$	−4.67311	−0.190620	−0.0953101	−	0.995448i	$-0.530384\pi$
$601$	−4.67311	−0.190620	−0.0953101	+	0.995448i	$0.530384\pi$
$602$	−16.7648	−0.683284
$603$	10.0891	0.410861
$604$	52.1344	2.12132
$605$	39.5218	1.60679
$606$	4.16902	0.169355
$607$	40.2861	1.63516	0.817580	−	0.575814i	$-0.195315\pi$
$607$	40.2861	1.63516	0.817580	+	0.575814i	$0.195315\pi$
$608$	−4.07970	−0.165454
$609$	−5.79053	−0.234644
$610$	63.2210	2.55974
$611$	0	0
$612$	−21.7518	−0.879264
$613$	−44.5102	−1.79775	−0.898874	−	0.438207i	$-0.855614\pi$
$613$	−44.5102	−1.79775	−0.898874	+	0.438207i	$0.855614\pi$
$614$	−62.0715	−2.50500
$615$	16.6478	0.671302
$616$	24.7569	0.997482
$617$	−2.06890	−0.0832907	−0.0416453	−	0.999132i	$-0.513260\pi$
$617$	−2.06890	−0.0832907	−0.0416453	+	0.999132i	$0.513260\pi$
$618$	9.12558	0.367085
$619$	−36.0887	−1.45053	−0.725264	−	0.688471i	$-0.758282\pi$
$619$	−36.0887	−1.45053	−0.725264	+	0.688471i	$0.758282\pi$
$620$	1.42912	0.0573948
$621$	−2.20066	−0.0883094
$622$	78.6871	3.15506
$623$	6.24519	0.250208
$624$	0	0
$625$	−18.5109	−0.740437
$626$	−19.8060	−0.791605
$627$	15.4335	0.616354
$628$	19.6866	0.785579
$629$	28.3160	1.12903
$630$	4.79192	0.190915
$631$	24.1496	0.961380	0.480690	−	0.876891i	$-0.340386\pi$
$631$	24.1496	0.961380	0.480690	+	0.876891i	$0.340386\pi$
$632$	−37.7717	−1.50248
$633$	3.56849	0.141835
$634$	−70.3380	−2.79348
$635$	−20.3279	−0.806688
$636$	−10.6878	−0.423797
$637$	0	0
$638$	−77.8403	−3.08173
$639$	−13.0368	−0.515726
$640$	−40.6686	−1.60757
$641$	10.6004	0.418689	0.209344	−	0.977842i	$-0.432867\pi$
$641$	10.6004	0.418689	0.209344	+	0.977842i	$0.432867\pi$
$642$	38.0060	1.49998
$643$	22.0644	0.870137	0.435068	−	0.900397i	$-0.356724\pi$
$643$	22.0644	0.870137	0.435068	+	0.900397i	$0.356724\pi$
$644$	−8.45418	−0.333141
$645$	−13.7522	−0.541493
$646$	−37.9743	−1.49408
$647$	14.9272	0.586850	0.293425	−	0.955982i	$-0.405205\pi$
$647$	14.9272	0.586850	0.293425	+	0.955982i	$0.405205\pi$
$648$	4.45120	0.174860
$649$	−34.4091	−1.35068
$650$	0	0
$651$	0.187633	0.00735390
$652$	−67.9166	−2.65982
$653$	−43.8355	−1.71542	−0.857708	−	0.514137i	$-0.828112\pi$
$653$	−43.8355	−1.71542	−0.857708	+	0.514137i	$0.828112\pi$
$654$	−42.4644	−1.66049
$655$	−23.3434	−0.912101
$656$	25.8204	1.00812
$657$	−3.12787	−0.122030
$658$	−28.1929	−1.09907
$659$	8.12476	0.316496	0.158248	−	0.987399i	$-0.449416\pi$
$659$	8.12476	0.316496	0.158248	+	0.987399i	$0.449416\pi$
$660$	42.3622	1.64895
$661$	25.0158	0.973001	0.486501	−	0.873680i	$-0.338273\pi$
$661$	25.0158	0.973001	0.486501	+	0.873680i	$0.338273\pi$
$662$	−70.8918	−2.75529
$663$	0	0
$664$	69.2525	2.68752
$665$	5.50158	0.213342
$666$	−12.0871	−0.468367
$667$	12.7430	0.493410
$668$	−74.5273	−2.88355
$669$	12.2147	0.472246
$670$	48.3462	1.86778
$671$	73.3788	2.83276
$672$	−1.47022	−0.0567150
$673$	45.4238	1.75096	0.875480	−	0.483254i	$-0.160545\pi$
$673$	45.4238	1.75096	0.875480	+	0.483254i	$0.160545\pi$
$674$	3.61379	0.139198
$675$	−1.06918	−0.0411529
$676$	0	0
$677$	−18.3095	−0.703691	−0.351846	−	0.936058i	$-0.614446\pi$
$677$	−18.3095	−0.703691	−0.351846	+	0.936058i	$0.614446\pi$
$678$	34.5415	1.32656
$679$	−0.650954	−0.0249813
$680$	−49.9683	−1.91620
$681$	22.0874	0.846390
$682$	2.52229	0.0965834
$683$	−17.1187	−0.655029	−0.327515	−	0.944846i	$-0.606211\pi$
$683$	−17.1187	−0.655029	−0.327515	+	0.944846i	$0.606211\pi$
$684$	10.6602	0.407602
$685$	39.0172	1.49077
$686$	2.41695	0.0922797
$687$	21.2490	0.810701
$688$	−21.3295	−0.813178
$689$	0	0
$690$	−10.5454	−0.401456
$691$	17.1598	0.652791	0.326395	−	0.945233i	$-0.394166\pi$
$691$	17.1598	0.652791	0.326395	+	0.945233i	$0.394166\pi$
$692$	14.0768	0.535119
$693$	5.56184	0.211277
$694$	−11.8220	−0.448756
$695$	24.8375	0.942141
$696$	−25.7748	−0.976991
$697$	−47.5434	−1.80084
$698$	−33.3157	−1.26102
$699$	−2.11080	−0.0798377
$700$	−4.10744	−0.155247
$701$	1.44147	0.0544435	0.0272217	−	0.999629i	$-0.491334\pi$
$701$	1.44147	0.0544435	0.0272217	+	0.999629i	$0.491334\pi$
$702$	0	0
$703$	−13.8772	−0.523388
$704$	−53.9693	−2.03404
$705$	−23.1267	−0.871000
$706$	−4.11931	−0.155032
$707$	1.72491	0.0648719
$708$	−23.7670	−0.893218
$709$	−6.69692	−0.251508	−0.125754	−	0.992061i	$-0.540135\pi$
$709$	−6.69692	−0.251508	−0.125754	+	0.992061i	$0.540135\pi$
$710$	−62.4711	−2.34450
$711$	−8.48573	−0.318240
$712$	27.7986	1.04180
$713$	−0.412915	−0.0154638
$714$	−13.6850	−0.512148
$715$	0	0
$716$	−21.4897	−0.803108
$717$	−16.9892	−0.634472
$718$	−58.0338	−2.16580
$719$	−12.9791	−0.484039	−0.242020	−	0.970271i	$-0.577810\pi$
$719$	−12.9791	−0.484039	−0.242020	+	0.970271i	$0.577810\pi$
$720$	6.09663	0.227208
$721$	3.77565	0.140613
$722$	−27.3115	−1.01643
$723$	19.1884	0.713626
$724$	−26.7868	−0.995522
$725$	6.19114	0.229933
$726$	48.1797	1.78812
$727$	−19.0926	−0.708106	−0.354053	−	0.935225i	$-0.615197\pi$
$727$	−19.0926	−0.708106	−0.354053	+	0.935225i	$0.615197\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−14.9885	−0.554749
$731$	39.2742	1.45261
$732$	50.6840	1.87333
$733$	−3.15192	−0.116419	−0.0582094	−	0.998304i	$-0.518539\pi$
$733$	−3.15192	−0.116419	−0.0582094	+	0.998304i	$0.518539\pi$
$734$	−12.7299	−0.469871
$735$	1.98263	0.0731304
$736$	3.23545	0.119260
$737$	56.1141	2.06699
$738$	20.2947	0.747058
$739$	−7.52007	−0.276630	−0.138315	−	0.990388i	$-0.544169\pi$
$739$	−7.52007	−0.276630	−0.138315	+	0.990388i	$0.544169\pi$
$740$	−38.0904	−1.40023
$741$	0	0
$742$	−6.72413	−0.246850
$743$	21.2016	0.777812	0.388906	−	0.921277i	$-0.372853\pi$
$743$	21.2016	0.777812	0.388906	+	0.921277i	$0.372853\pi$
$744$	0.835190	0.0306195
$745$	17.1733	0.629182
$746$	44.6248	1.63383
$747$	15.5582	0.569244
$748$	−120.980	−4.42347
$749$	15.7248	0.574570
$750$	−29.0830	−1.06196
$751$	15.1412	0.552510	0.276255	−	0.961084i	$-0.410907\pi$
$751$	15.1412	0.552510	0.276255	+	0.961084i	$0.410907\pi$
$752$	−35.8690	−1.30801
$753$	12.1438	0.442544
$754$	0	0
$755$	26.9059	0.979204
$756$	3.84166	0.139720
$757$	−1.49444	−0.0543162	−0.0271581	−	0.999631i	$-0.508646\pi$
$757$	−1.49444	−0.0543162	−0.0271581	+	0.999631i	$0.508646\pi$
$758$	12.6843	0.460716
$759$	−12.2397	−0.444273
$760$	24.4886	0.888295
$761$	−19.6602	−0.712682	−0.356341	−	0.934356i	$-0.615976\pi$
$761$	−19.6602	−0.712682	−0.356341	+	0.934356i	$0.615976\pi$
$762$	−24.7810	−0.897722
$763$	−17.5694	−0.636055
$764$	23.3193	0.843661
$765$	−11.2258	−0.405870
$766$	23.5755	0.851819
$767$	0	0
$768$	−30.1706	−1.08869
$769$	30.8663	1.11307	0.556534	−	0.830825i	$-0.312131\pi$
$769$	30.8663	1.11307	0.556534	+	0.830825i	$0.312131\pi$
$770$	26.6519	0.960467
$771$	−16.8396	−0.606462
$772$	41.8917	1.50772
$773$	−5.18435	−0.186468	−0.0932341	−	0.995644i	$-0.529721\pi$
$773$	−5.18435	−0.186468	−0.0932341	+	0.995644i	$0.529721\pi$
$774$	−16.7648	−0.602600
$775$	−0.200614	−0.00720626
$776$	−2.89753	−0.104015
$777$	−5.00098	−0.179409
$778$	29.1957	1.04672
$779$	23.3002	0.834817
$780$	0	0
$781$	−72.5083	−2.59455
$782$	30.1160	1.07695
$783$	−5.79053	−0.206937
$784$	3.07502	0.109822
$785$	10.1600	0.362625
$786$	−28.4571	−1.01503
$787$	2.19799	0.0783499	0.0391749	−	0.999232i	$-0.487527\pi$
$787$	2.19799	0.0783499	0.0391749	+	0.999232i	$0.487527\pi$
$788$	65.9706	2.35011
$789$	−26.8348	−0.955345
$790$	−40.6629	−1.44672
$791$	14.2914	0.508142
$792$	24.7569	0.879697
$793$	0	0
$794$	65.0676	2.30916
$795$	−5.51581	−0.195626
$796$	4.25678	0.150878
$797$	−43.7794	−1.55074	−0.775372	−	0.631505i	$-0.782438\pi$
$797$	−43.7794	−1.55074	−0.775372	+	0.631505i	$0.782438\pi$
$798$	6.70678	0.237417
$799$	66.0462	2.33655
$800$	1.57194	0.0555763
$801$	6.24519	0.220663
$802$	−77.2093	−2.72635
$803$	−17.3967	−0.613917
$804$	38.7589	1.36692
$805$	−4.36309	−0.153779
$806$	0	0
$807$	−6.86560	−0.241681
$808$	7.67791	0.270108
$809$	−17.6845	−0.621755	−0.310877	−	0.950450i	$-0.600623\pi$
$809$	−17.6845	−0.621755	−0.310877	+	0.950450i	$0.600623\pi$
$810$	4.79192	0.168371
$811$	−11.9195	−0.418549	−0.209275	−	0.977857i	$-0.567110\pi$
$811$	−11.9195	−0.418549	−0.209275	+	0.977857i	$0.567110\pi$
$812$	−22.2452	−0.780654
$813$	7.27072	0.254995
$814$	−67.2267	−2.35630
$815$	−35.0509	−1.22778
$816$	−17.4110	−0.609508
$817$	−19.2476	−0.673389
$818$	−72.3268	−2.52885
$819$	0	0
$820$	63.9550	2.23340
$821$	−3.20092	−0.111713	−0.0558564	−	0.998439i	$-0.517789\pi$
$821$	−3.20092	−0.111713	−0.0558564	+	0.998439i	$0.517789\pi$
$822$	47.5644	1.65900
$823$	8.84236	0.308225	0.154113	−	0.988053i	$-0.450748\pi$
$823$	8.84236	0.308225	0.154113	+	0.988053i	$0.450748\pi$
$824$	16.8062	0.585471
$825$	−5.94663	−0.207035
$826$	−14.9528	−0.520275
$827$	−0.901661	−0.0313538	−0.0156769	−	0.999877i	$-0.504990\pi$
$827$	−0.901661	−0.0313538	−0.0156769	+	0.999877i	$0.504990\pi$
$828$	−8.45418	−0.293803
$829$	−12.5125	−0.434578	−0.217289	−	0.976107i	$-0.569721\pi$
$829$	−12.5125	−0.434578	−0.217289	+	0.976107i	$0.569721\pi$
$830$	74.5535	2.58779
$831$	−8.01571	−0.278062
$832$	0	0
$833$	−5.66208	−0.196180
$834$	30.2786	1.04846
$835$	−38.4626	−1.33105
$836$	59.2902	2.05059
$837$	0.187633	0.00648553
$838$	72.1980	2.49404
$839$	24.4528	0.844205	0.422103	−	0.906548i	$-0.361292\pi$
$839$	24.4528	0.844205	0.422103	+	0.906548i	$0.361292\pi$
$840$	8.82508	0.304494
$841$	4.53019	0.156213
$842$	−57.3561	−1.97662
$843$	−7.76205	−0.267339
$844$	13.7089	0.471880
$845$	0	0
$846$	−28.1929	−0.969291
$847$	19.9341	0.684943
$848$	−8.55492	−0.293777
$849$	9.99319	0.342965
$850$	14.6318	0.501866
$851$	11.0055	0.377262
$852$	−50.0828	−1.71581
$853$	45.3747	1.55360	0.776800	−	0.629747i	$-0.216842\pi$
$853$	45.3747	1.55360	0.776800	+	0.629747i	$0.216842\pi$
$854$	31.8875	1.09117
$855$	5.50158	0.188150
$856$	69.9940	2.39235
$857$	−52.7495	−1.80189	−0.900944	−	0.433935i	$-0.857125\pi$
$857$	−52.7495	−1.80189	−0.900944	+	0.433935i	$0.857125\pi$
$858$	0	0
$859$	39.1342	1.33524	0.667621	−	0.744501i	$-0.267313\pi$
$859$	39.1342	1.33524	0.667621	+	0.744501i	$0.267313\pi$
$860$	−52.8313	−1.80153
$861$	8.39681	0.286162
$862$	26.8339	0.913966
$863$	−30.7592	−1.04706	−0.523528	−	0.852008i	$-0.675385\pi$
$863$	−30.7592	−1.04706	−0.523528	+	0.852008i	$0.675385\pi$
$864$	−1.47022	−0.0500179
$865$	7.26484	0.247012
$866$	25.1480	0.854564
$867$	15.0592	0.511437
$868$	0.720820	0.0244662
$869$	−47.1963	−1.60102
$870$	−27.7477	−0.940736
$871$	0	0
$872$	−78.2049	−2.64835
$873$	−0.650954	−0.0220315
$874$	−14.7593	−0.499241
$875$	−12.0329	−0.406788
$876$	−12.0162	−0.405990
$877$	−20.5689	−0.694562	−0.347281	−	0.937761i	$-0.612895\pi$
$877$	−20.5689	−0.694562	−0.347281	+	0.937761i	$0.612895\pi$
$878$	12.5844	0.424703
$879$	7.05939	0.238107
$880$	33.9085	1.14305
$881$	36.8744	1.24233	0.621166	−	0.783679i	$-0.286659\pi$
$881$	36.8744	1.24233	0.621166	+	0.783679i	$0.286659\pi$
$882$	2.41695	0.0813830
$883$	−19.6942	−0.662761	−0.331381	−	0.943497i	$-0.607514\pi$
$883$	−19.6942	−0.662761	−0.331381	+	0.943497i	$0.607514\pi$
$884$	0	0
$885$	−12.2658	−0.412311
$886$	36.7120	1.23336
$887$	10.1145	0.339612	0.169806	−	0.985478i	$-0.445686\pi$
$887$	10.1145	0.339612	0.169806	+	0.985478i	$0.445686\pi$
$888$	−22.2604	−0.747010
$889$	−10.2530	−0.343875
$890$	29.9264	1.00314
$891$	5.56184	0.186329
$892$	46.9246	1.57115
$893$	−32.3681	−1.08316
$894$	20.9354	0.700185
$895$	−11.0905	−0.370716
$896$	−20.5124	−0.685273
$897$	0	0
$898$	4.09124	0.136526
$899$	−1.08649	−0.0362365
$900$	−4.10744	−0.136915
$901$	15.7523	0.524785
$902$	112.876	3.75835
$903$	−6.93636	−0.230828
$904$	63.6137	2.11576
$905$	−13.8243	−0.459535
$906$	32.8000	1.08971
$907$	−21.9042	−0.727316	−0.363658	−	0.931533i	$-0.618472\pi$
$907$	−21.9042	−0.727316	−0.363658	+	0.931533i	$0.618472\pi$
$908$	84.8521	2.81592
$909$	1.72491	0.0572116
$910$	0	0
$911$	−15.5338	−0.514656	−0.257328	−	0.966324i	$-0.582842\pi$
$911$	−15.5338	−0.514656	−0.257328	+	0.966324i	$0.582842\pi$
$912$	8.53285	0.282551
$913$	86.5321	2.86379
$914$	9.00103	0.297728
$915$	26.1573	0.864734
$916$	81.6316	2.69718
$917$	−11.7740	−0.388810
$918$	−13.6850	−0.451672
$919$	−8.81313	−0.290718	−0.145359	−	0.989379i	$-0.546434\pi$
$919$	−8.81313	−0.290718	−0.145359	+	0.989379i	$0.546434\pi$
$920$	−19.4210	−0.640291
$921$	−25.6817	−0.846242
$922$	−63.7798	−2.10048
$923$	0	0
$924$	21.3667	0.702912
$925$	5.34697	0.175807
$926$	−5.45653	−0.179313
$927$	3.77565	0.124009
$928$	8.51334	0.279464
$929$	−30.1854	−0.990352	−0.495176	−	0.868793i	$-0.664896\pi$
$929$	−30.1854	−0.990352	−0.495176	+	0.868793i	$0.664896\pi$
$930$	0.899120	0.0294833
$931$	2.77489	0.0909433
$932$	−8.10896	−0.265618
$933$	32.5563	1.06585
$934$	−74.6615	−2.44300
$935$	−62.4362	−2.04188
$936$	0	0
$937$	−21.7393	−0.710192	−0.355096	−	0.934830i	$-0.615552\pi$
$937$	−21.7393	−0.710192	−0.355096	+	0.934830i	$0.615552\pi$
$938$	24.3849	0.796196
$939$	−8.19460	−0.267421
$940$	−88.8447	−2.89779
$941$	23.8691	0.778109	0.389055	−	0.921215i	$-0.372802\pi$
$941$	23.8691	0.778109	0.389055	+	0.921215i	$0.372802\pi$
$942$	12.3857	0.403547
$943$	−18.4785	−0.601743
$944$	−19.0241	−0.619181
$945$	1.98263	0.0644949
$946$	−93.2434	−3.03160
$947$	−33.0288	−1.07329	−0.536645	−	0.843808i	$-0.680309\pi$
$947$	−33.0288	−1.07329	−0.536645	+	0.843808i	$0.680309\pi$
$948$	−32.5993	−1.05878
$949$	0	0
$950$	−7.17078	−0.232651
$951$	−29.1019	−0.943694
$952$	−25.2031	−0.816836
$953$	−6.54439	−0.211994	−0.105997	−	0.994366i	$-0.533803\pi$
$953$	−6.54439	−0.211994	−0.105997	+	0.994366i	$0.533803\pi$
$954$	−6.72413	−0.217702
$955$	12.0348	0.389436
$956$	−65.2666	−2.11087
$957$	−32.2060	−1.04107
$958$	94.1943	3.04328
$959$	19.6795	0.635485
$960$	−19.2384	−0.620917
$961$	−30.9648	−0.998864
$962$	0	0
$963$	15.7248	0.506723
$964$	73.7154	2.37421
$965$	21.6197	0.695964
$966$	−5.31889	−0.171132
$967$	−6.58745	−0.211838	−0.105919	−	0.994375i	$-0.533778\pi$
$967$	−6.58745	−0.211838	−0.105919	+	0.994375i	$0.533778\pi$
$968$	88.7305	2.85191
$969$	−15.7117	−0.504731
$970$	−3.11932	−0.100155
$971$	−32.8858	−1.05535	−0.527677	−	0.849445i	$-0.676937\pi$
$971$	−32.8858	−1.05535	−0.527677	+	0.849445i	$0.676937\pi$
$972$	3.84166	0.123221
$973$	12.5276	0.401616
$974$	64.9148	2.08000
$975$	0	0
$976$	40.5695	1.29860
$977$	7.48594	0.239496	0.119748	−	0.992804i	$-0.461791\pi$
$977$	7.48594	0.239496	0.119748	+	0.992804i	$0.461791\pi$
$978$	−42.7293	−1.36633
$979$	34.7347	1.11013
$980$	7.61658	0.243303
$981$	−17.5694	−0.560947
$982$	88.2372	2.81576
$983$	−7.84023	−0.250065	−0.125032	−	0.992153i	$-0.539903\pi$
$983$	−7.84023	−0.250065	−0.125032	+	0.992153i	$0.539903\pi$
$984$	37.3759	1.19150
$985$	34.0465	1.08481
$986$	79.2433	2.52362
$987$	−11.6646	−0.371290
$988$	0	0
$989$	15.2646	0.485385
$990$	26.6519	0.847053
$991$	−17.0937	−0.542999	−0.271500	−	0.962439i	$-0.587520\pi$
$991$	−17.0937	−0.542999	−0.271500	+	0.962439i	$0.587520\pi$
$992$	−0.275861	−0.00875860
$993$	−29.3311	−0.930794
$994$	−31.5092	−0.999412
$995$	2.19687	0.0696454
$996$	59.7692	1.89386
$997$	−58.6850	−1.85857	−0.929287	−	0.369358i	$-0.879577\pi$
$997$	−58.6850	−1.85857	−0.929287	+	0.369358i	$0.879577\pi$
$998$	30.7264	0.972628
$999$	−5.00098	−0.158224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bg.1.13	✓	15
13.12	even	2		3549.2.a.bh.1.3	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.13	✓	15	1.1	even	1	trivial
3549.2.a.bh.1.3	yes	15	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)

\(f(q)\)	\(=\)	\(q+2.41695 q^{2} +1.00000 q^{3} +3.84166 q^{4} +1.98263 q^{5} +2.41695 q^{6} +1.00000 q^{7} +4.45120 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.41695 q^{2} +1.00000 q^{3} +3.84166 q^{4} +1.98263 q^{5} +2.41695 q^{6} +1.00000 q^{7} +4.45120 q^{8} +1.00000 q^{9} +4.79192 q^{10} +5.56184 q^{11} +3.84166 q^{12} +2.41695 q^{14} +1.98263 q^{15} +3.07502 q^{16} -5.66208 q^{17} +2.41695 q^{18} +2.77489 q^{19} +7.61658 q^{20} +1.00000 q^{21} +13.4427 q^{22} -2.20066 q^{23} +4.45120 q^{24} -1.06918 q^{25} +1.00000 q^{27} +3.84166 q^{28} -5.79053 q^{29} +4.79192 q^{30} +0.187633 q^{31} -1.47022 q^{32} +5.56184 q^{33} -13.6850 q^{34} +1.98263 q^{35} +3.84166 q^{36} -5.00098 q^{37} +6.70678 q^{38} +8.82508 q^{40} +8.39681 q^{41} +2.41695 q^{42} -6.93636 q^{43} +21.3667 q^{44} +1.98263 q^{45} -5.31889 q^{46} -11.6646 q^{47} +3.07502 q^{48} +1.00000 q^{49} -2.58417 q^{50} -5.66208 q^{51} -2.78207 q^{53} +2.41695 q^{54} +11.0271 q^{55} +4.45120 q^{56} +2.77489 q^{57} -13.9954 q^{58} -6.18664 q^{59} +7.61658 q^{60} +13.1933 q^{61} +0.453499 q^{62} +1.00000 q^{63} -9.70349 q^{64} +13.4427 q^{66} +10.0891 q^{67} -21.7518 q^{68} -2.20066 q^{69} +4.79192 q^{70} -13.0368 q^{71} +4.45120 q^{72} -3.12787 q^{73} -12.0871 q^{74} -1.06918 q^{75} +10.6602 q^{76} +5.56184 q^{77} -8.48573 q^{79} +6.09663 q^{80} +1.00000 q^{81} +20.2947 q^{82} +15.5582 q^{83} +3.84166 q^{84} -11.2258 q^{85} -16.7648 q^{86} -5.79053 q^{87} +24.7569 q^{88} +6.24519 q^{89} +4.79192 q^{90} -8.45418 q^{92} +0.187633 q^{93} -28.1929 q^{94} +5.50158 q^{95} -1.47022 q^{96} -0.650954 q^{97} +2.41695 q^{98} +5.56184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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